LMFDB - Embedded newform 702.2.e.d.469.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(235,702)] 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("702.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,0,-3,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			469.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	702.469
Dual form			702.2.e.d.235.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.64400 - 2.84748i) q^{5} +(1.40545 + 2.43430i) q^{7} +1.00000 q^{8} -3.28799 q^{10} +(2.58836 + 4.48318i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.40545 - 2.43430i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.699628 q^{17} +7.17673 q^{19} +(1.64400 + 2.84748i) q^{20} +(2.58836 - 4.48318i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-2.90545 - 5.03238i) q^{25} +1.00000 q^{26} -2.81089 q^{28} +(-1.11126 - 1.92477i) q^{29} +(-1.38874 + 2.40536i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.349814 - 0.605896i) q^{34} +9.24219 q^{35} -0.712008 q^{37} +(-3.58836 - 6.21523i) q^{38} +(1.64400 - 2.84748i) q^{40} +(-0.411636 + 0.712974i) q^{41} +(-5.74907 - 9.95768i) q^{43} -5.17673 q^{44} +6.00000 q^{46} +(0.761450 + 1.31887i) q^{47} +(-0.450558 + 0.780389i) q^{49} +(-2.90545 + 5.03238i) q^{50} +(-0.500000 - 0.866025i) q^{52} +11.0210 q^{53} +17.0210 q^{55} +(1.40545 + 2.43430i) q^{56} +(-1.11126 + 1.92477i) q^{58} +(7.39926 - 12.8159i) q^{59} +(-4.69963 - 8.13999i) q^{61} +2.77747 q^{62} +1.00000 q^{64} +(1.64400 + 2.84748i) q^{65} +(-0.222528 + 0.385430i) q^{67} +(-0.349814 + 0.605896i) q^{68} +(-4.62110 - 8.00397i) q^{70} +1.18911 q^{71} -0.222528 q^{73} +(0.356004 + 0.616617i) q^{74} +(-3.58836 + 6.21523i) q^{76} +(-7.27561 + 12.6017i) q^{77} +(7.87636 + 13.6422i) q^{79} -3.28799 q^{80} +0.823272 q^{82} +(-3.98762 - 6.90676i) q^{83} +(1.15019 - 1.99218i) q^{85} +(-5.74907 + 9.95768i) q^{86} +(2.58836 + 4.48318i) q^{88} -7.39926 q^{89} -2.81089 q^{91} +(-3.00000 - 5.19615i) q^{92} +(0.761450 - 1.31887i) q^{94} +(11.7985 - 20.4356i) q^{95} +(-2.47710 - 4.29046i) q^{97} +0.901116 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 2 q^{7} + 6 q^{8} + 4 q^{10} + 4 q^{11} - 3 q^{13} + 2 q^{14} - 3 q^{16} - 8 q^{17} + 20 q^{19} - 2 q^{20} + 4 q^{22} - 18 q^{23} - 11 q^{25} + 6 q^{26} - 4 q^{28} - 6 q^{29}+ \cdots + 42 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 2 * q^7 + 6 * q^8 + 4 * q^10 + 4 * q^11 - 3 * q^13 + 2 * q^14 - 3 * q^16 - 8 * q^17 + 20 * q^19 - 2 * q^20 + 4 * q^22 - 18 * q^23 - 11 * q^25 + 6 * q^26 - 4 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 + 4 * q^34 + 10 * q^35 - 28 * q^37 - 10 * q^38 - 2 * q^40 - 14 * q^41 - 4 * q^43 - 8 * q^44 + 36 * q^46 + 10 * q^47 - 21 * q^49 - 11 * q^50 - 3 * q^52 + 16 * q^53 + 52 * q^55 + 2 * q^56 - 6 * q^58 + 20 * q^59 - 16 * q^61 + 18 * q^62 + 6 * q^64 - 2 * q^65 + 4 * q^68 - 5 * q^70 + 20 * q^71 + 14 * q^74 - 10 * q^76 + 16 * q^77 + 12 * q^79 + 4 * q^80 + 28 * q^82 + 12 * q^83 + 13 * q^85 - 4 * q^86 + 4 * q^88 - 20 * q^89 - 4 * q^91 - 18 * q^92 + 10 * q^94 + 22 * q^95 - 4 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.64400	−	2.84748i	0.735217	−	1.27343i	−0.219411	−	0.975633i	$-0.570413\pi$
$5$	1.64400	−	2.84748i	0.735217	−	1.27343i	0.954628	−	0.297801i	$-0.0962533\pi$
$6$		0			0
$7$	1.40545	+	2.43430i	0.531209	+	0.920080i	0.999337	+	0.0364197i	$0.0115953\pi$
$7$	1.40545	+	2.43430i	0.531209	+	0.920080i	−0.468128	+	0.883661i	$0.655071\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.28799			−1.03975
$11$	2.58836	+	4.48318i	0.780421	+	1.35173i	0.931697	+	0.363237i	$0.118329\pi$
$11$	2.58836	+	4.48318i	0.780421	+	1.35173i	−0.151276	+	0.988492i	$0.548338\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	1.40545	−	2.43430i	0.375621	−	0.650595i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.699628			0.169685			0.0848424	−	0.996394i	$-0.472961\pi$
$17$	0.699628			0.169685			0.0848424	+	0.996394i	$0.472961\pi$
$18$		0			0
$19$	7.17673			1.64645			0.823227	−	0.567712i	$-0.192171\pi$
$19$	7.17673			1.64645			0.823227	+	0.567712i	$0.192171\pi$
$20$	1.64400	+	2.84748i	0.367609	+	0.636717i
$21$		0			0
$22$	2.58836	−	4.48318i	0.551841	−	0.955817i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−2.90545	−	5.03238i	−0.581089	−	1.00648i
$26$	1.00000			0.196116
$27$		0			0
$28$	−2.81089			−0.531209
$29$	−1.11126	−	1.92477i	−0.206357	−	0.357420i	0.744208	−	0.667948i	$-0.232827\pi$
$29$	−1.11126	−	1.92477i	−0.206357	−	0.357420i	−0.950564	+	0.310528i	$0.899494\pi$
$30$		0			0
$31$	−1.38874	+	2.40536i	−0.249424	+	0.432016i	−0.963366	−	0.268189i	$-0.913575\pi$
$31$	−1.38874	+	2.40536i	−0.249424	+	0.432016i	0.713942	+	0.700205i	$0.246908\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−0.349814	−	0.605896i	−0.0599926	−	0.103910i
$35$	9.24219			1.56222
$36$		0			0
$37$	−0.712008			−0.117053			−0.0585267	−	0.998286i	$-0.518640\pi$
$37$	−0.712008			−0.117053			−0.0585267	+	0.998286i	$0.518640\pi$
$38$	−3.58836	−	6.21523i	−0.582110	−	1.00824i
$39$		0			0
$40$	1.64400	−	2.84748i	0.259939	−	0.450227i
$41$	−0.411636	+	0.712974i	−0.0642867	+	0.111348i	−0.896377	−	0.443292i	$-0.853811\pi$
$41$	−0.411636	+	0.712974i	−0.0642867	+	0.111348i	0.832091	+	0.554640i	$0.187144\pi$
$42$		0			0
$43$	−5.74907	−	9.95768i	−0.876725	−	1.51853i	−0.854914	−	0.518770i	$-0.826390\pi$
$43$	−5.74907	−	9.95768i	−0.876725	−	1.51853i	−0.0218113	−	0.999762i	$-0.506943\pi$
$44$	−5.17673			−0.780421
$45$		0			0
$46$	6.00000			0.884652
$47$	0.761450	+	1.31887i	0.111069	+	0.192377i	0.916202	−	0.400718i	$-0.131239\pi$
$47$	0.761450	+	1.31887i	0.111069	+	0.192377i	−0.805133	+	0.593095i	$0.797906\pi$
$48$		0			0
$49$	−0.450558	+	0.780389i	−0.0643654	+	0.111484i
$50$	−2.90545	+	5.03238i	−0.410892	+	0.711686i
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	11.0210			1.51386			0.756928	−	0.653498i	$-0.226699\pi$
$53$	11.0210			1.51386			0.756928	+	0.653498i	$0.226699\pi$
$54$		0			0
$55$	17.0210			2.29512
$56$	1.40545	+	2.43430i	0.187811	+	0.325298i
$57$		0			0
$58$	−1.11126	+	1.92477i	−0.145916	+	0.252734i
$59$	7.39926	−	12.8159i	0.963301	−	1.66849i	0.249189	−	0.968455i	$-0.419836\pi$
$59$	7.39926	−	12.8159i	0.963301	−	1.66849i	0.714112	−	0.700032i	$-0.246831\pi$
$60$		0			0
$61$	−4.69963	−	8.13999i	−0.601726	−	1.04222i	−0.992560	−	0.121758i	$-0.961147\pi$
$61$	−4.69963	−	8.13999i	−0.601726	−	1.04222i	0.390834	−	0.920461i	$-0.372187\pi$
$62$	2.77747			0.352739
$63$		0			0
$64$	1.00000			0.125000
$65$	1.64400	+	2.84748i	0.203913	+	0.353187i
$66$		0			0
$67$	−0.222528	+	0.385430i	−0.0271862	+	0.0470878i	−0.879298	−	0.476271i	$-0.841988\pi$
$67$	−0.222528	+	0.385430i	−0.0271862	+	0.0470878i	0.852112	+	0.523359i	$0.175321\pi$
$68$	−0.349814	+	0.605896i	−0.0424212	+	0.0734757i
$69$		0			0
$70$	−4.62110	−	8.00397i	−0.552327	−	0.956658i
$71$	1.18911			0.141121			0.0705606	−	0.997507i	$-0.477521\pi$
$71$	1.18911			0.141121			0.0705606	+	0.997507i	$0.477521\pi$
$72$		0			0
$73$	−0.222528			−0.0260450			−0.0130225	−	0.999915i	$-0.504145\pi$
$73$	−0.222528			−0.0260450			−0.0130225	+	0.999915i	$0.504145\pi$
$74$	0.356004	+	0.616617i	0.0413846	+	0.0716803i
$75$		0			0
$76$	−3.58836	+	6.21523i	−0.411614	+	0.712936i
$77$	−7.27561	+	12.6017i	−0.829133	+	1.43610i
$78$		0			0
$79$	7.87636	+	13.6422i	0.886159	+	1.53487i	0.844379	+	0.535746i	$0.179970\pi$
$79$	7.87636	+	13.6422i	0.886159	+	1.53487i	0.0417802	+	0.999127i	$0.486697\pi$
$80$	−3.28799			−0.367609
$81$		0			0
$82$	0.823272			0.0909152
$83$	−3.98762	−	6.90676i	−0.437698	−	0.758116i	0.559813	−	0.828619i	$-0.310873\pi$
$83$	−3.98762	−	6.90676i	−0.437698	−	0.758116i	−0.997512	+	0.0705032i	$0.977539\pi$
$84$		0			0
$85$	1.15019	−	1.99218i	0.124755	−	0.216082i
$86$	−5.74907	+	9.95768i	−0.619938	+	1.07376i
$87$		0			0
$88$	2.58836	+	4.48318i	0.275921	+	0.477908i
$89$	−7.39926			−0.784320			−0.392160	−	0.919897i	$-0.628272\pi$
$89$	−7.39926			−0.784320			−0.392160	+	0.919897i	$0.628272\pi$
$90$		0			0
$91$	−2.81089			−0.294662
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$	0.761450	−	1.31887i	0.0785376	−	0.136031i
$95$	11.7985	−	20.4356i	1.21050	−	2.09665i
$96$		0			0
$97$	−2.47710	−	4.29046i	−0.251511	−	0.435630i	0.712431	−	0.701742i	$-0.247594\pi$
$97$	−2.47710	−	4.29046i	−0.251511	−	0.435630i	−0.963942	+	0.266112i	$0.914261\pi$
$98$	0.901116			0.0910264
$99$		0			0
$100$	5.81089			0.581089
$101$	−1.47710	−	2.55841i	−0.146977	−	0.254572i	0.783132	−	0.621856i	$-0.213621\pi$
$101$	−1.47710	−	2.55841i	−0.146977	−	0.254572i	−0.930109	+	0.367284i	$0.880288\pi$
$102$		0			0
$103$	−4.69963	+	8.13999i	−0.463068	+	0.802058i	−0.999112	−	0.0421326i	$-0.986585\pi$
$103$	−4.69963	+	8.13999i	−0.463068	+	0.802058i	0.536044	+	0.844190i	$0.319918\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$		0			0
$106$	−5.51052	−	9.54450i	−0.535229	−	0.927044i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−6.67487			−0.639336			−0.319668	−	0.947530i	$-0.603571\pi$
$109$	−6.67487			−0.639336			−0.319668	+	0.947530i	$0.603571\pi$
$110$	−8.51052	−	14.7407i	−0.811446	−	1.40547i
$111$		0			0
$112$	1.40545	−	2.43430i	0.132802	−	0.230020i
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$		0			0
$115$	9.86398	+	17.0849i	0.919821	+	1.59318i
$116$	2.22253			0.206357
$117$		0			0
$118$	−14.7985			−1.36231
$119$	0.983290	+	1.70311i	0.0901380	+	0.156124i
$120$		0			0
$121$	−7.89926	+	13.6819i	−0.718114	+	1.24381i
$122$	−4.69963	+	8.13999i	−0.425484	+	0.736960i
$123$		0			0
$124$	−1.38874	−	2.40536i	−0.124712	−	0.216008i
$125$	−2.66621			−0.238473
$126$		0			0
$127$	−3.42402			−0.303832			−0.151916	−	0.988393i	$-0.548544\pi$
$127$	−3.42402			−0.303832			−0.151916	+	0.988393i	$0.548544\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.64400	−	2.84748i	0.144188	−	0.249741i
$131$	4.12729	−	7.14867i	0.360603	−	0.624582i	−0.627458	−	0.778651i	$-0.715904\pi$
$131$	4.12729	−	7.14867i	0.360603	−	0.624582i	0.988060	+	0.154069i	$0.0492377\pi$
$132$		0			0
$133$	10.0865	+	17.4703i	0.874611	+	1.51487i
$134$	0.445057			0.0384470
$135$		0			0
$136$	0.699628			0.0599926
$137$	−2.30037	−	3.98436i	−0.196534	−	0.340407i	0.750868	−	0.660452i	$-0.229635\pi$
$137$	−2.30037	−	3.98436i	−0.196534	−	0.340407i	−0.947402	+	0.320045i	$0.896302\pi$
$138$		0			0
$139$	−5.29418	+	9.16979i	−0.449047	+	0.777772i	−0.998324	−	0.0578683i	$-0.981570\pi$
$139$	−5.29418	+	9.16979i	−0.449047	+	0.777772i	0.549278	+	0.835640i	$0.314903\pi$
$140$	−4.62110	+	8.00397i	−0.390554	+	0.676459i
$141$		0			0
$142$	−0.594554	−	1.02980i	−0.0498939	−	0.0864187i
$143$	−5.17673			−0.432900
$144$		0			0
$145$	−7.30766			−0.606868
$146$	0.111264	+	0.192715i	0.00920829	+	0.0159492i
$147$		0			0
$148$	0.356004	−	0.616617i	0.0292633	−	0.0506856i
$149$	−8.48762	+	14.7010i	−0.695333	+	1.20435i	0.274735	+	0.961520i	$0.411410\pi$
$149$	−8.48762	+	14.7010i	−0.695333	+	1.20435i	−0.970068	+	0.242832i	$0.921924\pi$
$150$		0			0
$151$	−11.1087	−	19.2409i	−0.904015	−	1.56580i	−0.822235	−	0.569149i	$-0.807273\pi$
$151$	−11.1087	−	19.2409i	−0.904015	−	1.56580i	−0.0817798	−	0.996650i	$-0.526060\pi$
$152$	7.17673			0.582110
$153$		0			0
$154$	14.5512			1.17257
$155$	4.56615	+	7.90881i	0.366762	+	0.635251i
$156$		0			0
$157$	2.33379	−	4.04225i	0.186257	−	0.322606i	−0.757742	−	0.652554i	$-0.773698\pi$
$157$	2.33379	−	4.04225i	0.186257	−	0.322606i	0.943999	+	0.329947i	$0.107031\pi$
$158$	7.87636	−	13.6422i	0.626609	−	1.08532i
$159$		0			0
$160$	1.64400	+	2.84748i	0.129969	+	0.225113i
$161$	−16.8654			−1.32918
$162$		0			0
$163$	−11.9752			−0.937973			−0.468987	−	0.883205i	$-0.655381\pi$
$163$	−11.9752			−0.937973			−0.468987	+	0.883205i	$0.655381\pi$
$164$	−0.411636	−	0.712974i	−0.0321434	−	0.0556740i
$165$		0			0
$166$	−3.98762	+	6.90676i	−0.309499	+	0.536069i
$167$	−3.38874	+	5.86946i	−0.262228	+	0.454193i	−0.966834	−	0.255407i	$-0.917791\pi$
$167$	−3.38874	+	5.86946i	−0.262228	+	0.454193i	0.704605	+	0.709599i	$0.251124\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−2.30037			−0.176430
$171$		0			0
$172$	11.4981			0.876725
$173$	9.57598	+	16.5861i	0.728049	+	1.26102i	0.957707	+	0.287746i	$0.0929058\pi$
$173$	9.57598	+	16.5861i	0.728049	+	1.26102i	−0.229658	+	0.973271i	$0.573761\pi$
$174$		0			0
$175$	8.16690	−	14.1455i	0.617359	−	1.06930i
$176$	2.58836	−	4.48318i	0.195105	−	0.337932i
$177$		0			0
$178$	3.69963	+	6.40794i	0.277299	+	0.480296i
$179$	0.210149			0.0157072			0.00785362	−	0.999969i	$-0.497500\pi$
$179$	0.210149			0.0157072			0.00785362	+	0.999969i	$0.497500\pi$
$180$		0			0
$181$	6.44506			0.479057			0.239529	−	0.970889i	$-0.423007\pi$
$181$	6.44506			0.479057			0.239529	+	0.970889i	$0.423007\pi$
$182$	1.40545	+	2.43430i	0.104179	+	0.180443i
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−1.17054	+	2.02743i	−0.0860597	+	0.149060i
$186$		0			0
$187$	1.81089	+	3.13656i	0.132426	+	0.229368i
$188$	−1.52290			−0.111069
$189$		0			0
$190$	−23.5970			−1.71191
$191$	−11.6749	−	20.2215i	−0.844764	−	1.46317i	−0.885826	−	0.464017i	$-0.846408\pi$
$191$	−11.6749	−	20.2215i	−0.844764	−	1.46317i	0.0410623	−	0.999157i	$-0.486926\pi$
$192$		0			0
$193$	−12.4647	+	21.5895i	−0.897230	+	1.55405i	−0.0662102	+	0.997806i	$0.521091\pi$
$193$	−12.4647	+	21.5895i	−0.897230	+	1.55405i	−0.831020	+	0.556243i	$0.812243\pi$
$194$	−2.47710	+	4.29046i	−0.177845	+	0.308037i
$195$		0			0
$196$	−0.450558	−	0.780389i	−0.0321827	−	0.0557421i
$197$	10.2349			0.729207			0.364604	−	0.931163i	$-0.381205\pi$
$197$	10.2349			0.729207			0.364604	+	0.931163i	$0.381205\pi$
$198$		0			0
$199$	26.9047			1.90722			0.953611	−	0.301041i	$-0.0973342\pi$
$199$	26.9047			1.90722			0.953611	+	0.301041i	$0.0973342\pi$
$200$	−2.90545	−	5.03238i	−0.205446	−	0.355843i
$201$		0			0
$202$	−1.47710	+	2.55841i	−0.103928	+	0.180009i
$203$	3.12364	−	5.41031i	0.219237	−	0.379729i
$204$		0			0
$205$	1.35346	+	2.34425i	0.0945295	+	0.163730i
$206$	9.39926			0.654877
$207$		0			0
$208$	1.00000			0.0693375
$209$	18.5760	+	32.1745i	1.28493	+	2.22556i
$210$		0			0
$211$	−2.35600	+	4.08072i	−0.162194	+	0.280928i	−0.935655	−	0.352915i	$-0.885190\pi$
$211$	−2.35600	+	4.08072i	−0.162194	+	0.280928i	0.773461	+	0.633844i	$0.218524\pi$
$212$	−5.51052	+	9.54450i	−0.378464	+	0.655519i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−37.8058			−2.57833
$216$		0			0
$217$	−7.80717			−0.529985
$218$	3.33743	+	5.78061i	0.226040	+	0.391512i
$219$		0			0
$220$	−8.51052	+	14.7407i	−0.573779	+	0.993815i
$221$	−0.349814	+	0.605896i	−0.0235310	+	0.0407570i
$222$		0			0
$223$	−3.81453	−	6.60697i	−0.255440	−	0.442435i	0.709575	−	0.704630i	$-0.248887\pi$
$223$	−3.81453	−	6.60697i	−0.255440	−	0.442435i	−0.965015	+	0.262195i	$0.915554\pi$
$224$	−2.81089			−0.187811
$225$		0			0
$226$	3.00000			0.199557
$227$	11.0210	+	19.0890i	0.731492	+	1.26698i	0.956245	+	0.292566i	$0.0945091\pi$
$227$	11.0210	+	19.0890i	0.731492	+	1.26698i	−0.224753	+	0.974416i	$0.572158\pi$
$228$		0			0
$229$	2.24474	−	3.88800i	0.148337	−	0.256926i	−0.782276	−	0.622932i	$-0.785941\pi$
$229$	2.24474	−	3.88800i	0.148337	−	0.256926i	0.930613	+	0.366005i	$0.119275\pi$
$230$	9.86398	−	17.0849i	0.650411	−	1.12655i
$231$		0			0
$232$	−1.11126	−	1.92477i	−0.0729581	−	0.126367i
$233$	−5.54256			−0.363105			−0.181553	−	0.983381i	$-0.558112\pi$
$233$	−5.54256			−0.363105			−0.181553	+	0.983381i	$0.558112\pi$
$234$		0			0
$235$	5.00728			0.326639
$236$	7.39926	+	12.8159i	0.481651	+	0.834243i
$237$		0			0
$238$	0.983290	−	1.70311i	0.0637372	−	0.110396i
$239$	3.71565	−	6.43569i	0.240345	−	0.416290i	−0.720467	−	0.693489i	$-0.756073\pi$
$239$	3.71565	−	6.43569i	0.240345	−	0.416290i	0.960813	+	0.277198i	$0.0894060\pi$
$240$		0			0
$241$	−4.69963	−	8.13999i	−0.302730	−	0.524343i	0.674024	−	0.738710i	$-0.264565\pi$
$241$	−4.69963	−	8.13999i	−0.302730	−	0.524343i	−0.976753	+	0.214367i	$0.931231\pi$
$242$	15.7985			1.01557
$243$		0			0
$244$	9.39926			0.601726
$245$	1.48143	+	2.56591i	0.0946451	+	0.163930i
$246$		0			0
$247$	−3.58836	+	6.21523i	−0.228322	+	0.395466i
$248$	−1.38874	+	2.40536i	−0.0881848	+	0.152741i
$249$		0			0
$250$	1.33310	+	2.30900i	0.0843129	+	0.146034i
$251$	−15.9963			−1.00968			−0.504838	−	0.863214i	$-0.668448\pi$
$251$	−15.9963			−1.00968			−0.504838	+	0.863214i	$0.668448\pi$
$252$		0			0
$253$	−31.0604			−1.95275
$254$	1.71201	+	2.96528i	0.107421	+	0.186059i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.0432524	+	0.0749153i	−0.00269801	+	0.00467309i	−0.867371	−	0.497662i	$-0.834192\pi$
$257$	−0.0432524	+	0.0749153i	−0.00269801	+	0.00467309i	0.864673	+	0.502335i	$0.167525\pi$
$258$		0			0
$259$	−1.00069	−	1.73324i	−0.0621798	−	0.107699i
$260$	−3.28799			−0.203913
$261$		0			0
$262$	−8.25457			−0.509969
$263$	0.489480	+	0.847803i	0.0301826	+	0.0522778i	0.880722	−	0.473633i	$-0.157058\pi$
$263$	0.489480	+	0.847803i	0.0301826	+	0.0522778i	−0.850540	+	0.525911i	$0.823724\pi$
$264$		0			0
$265$	18.1185	−	31.3822i	1.11301	−	1.92780i
$266$	10.0865	−	17.4703i	0.618443	−	1.07118i
$267$		0			0
$268$	−0.222528	−	0.385430i	−0.0135931	−	0.0235439i
$269$	25.5723			1.55917			0.779584	−	0.626297i	$-0.215430\pi$
$269$	25.5723			1.55917			0.779584	+	0.626297i	$0.215430\pi$
$270$		0			0
$271$	16.9766			1.03126			0.515628	−	0.856813i	$-0.327559\pi$
$271$	16.9766			1.03126			0.515628	+	0.856813i	$0.327559\pi$
$272$	−0.349814	−	0.605896i	−0.0212106	−	0.0367378i
$273$		0			0
$274$	−2.30037	+	3.98436i	−0.138971	+	0.240704i
$275$	15.0407	−	26.0513i	0.906989	−	1.57095i
$276$		0			0
$277$	−1.69963	−	2.94384i	−0.102121	−	0.176878i	0.810437	−	0.585825i	$-0.199229\pi$
$277$	−1.69963	−	2.94384i	−0.102121	−	0.176878i	−0.912558	+	0.408947i	$0.865896\pi$
$278$	10.5884			0.635048
$279$		0			0
$280$	9.24219			0.552327
$281$	−14.3411	−	24.8395i	−0.855517	−	1.48180i	−0.876165	−	0.482012i	$-0.839906\pi$
$281$	−14.3411	−	24.8395i	−0.855517	−	1.48180i	0.0206478	−	0.999787i	$-0.493427\pi$
$282$		0			0
$283$	5.59888	−	9.69755i	0.332819	−	0.576460i	−0.650244	−	0.759725i	$-0.725333\pi$
$283$	5.59888	−	9.69755i	0.332819	−	0.576460i	0.983063	+	0.183266i	$0.0586668\pi$
$284$	−0.594554	+	1.02980i	−0.0352803	+	0.0611072i
$285$		0			0
$286$	2.58836	+	4.48318i	0.153053	+	0.265096i
$287$	−2.31413			−0.136599
$288$		0			0
$289$	−16.5105			−0.971207
$290$	3.65383	+	6.32862i	0.214560	+	0.371629i
$291$		0			0
$292$	0.111264	−	0.192715i	0.00651124	−	0.0112778i
$293$	3.47091	−	6.01179i	0.202773	−	0.351213i	−0.746648	−	0.665219i	$-0.768338\pi$
$293$	3.47091	−	6.01179i	0.202773	−	0.351213i	0.949421	+	0.314007i	$0.101671\pi$
$294$		0			0
$295$	−24.3287	−	42.1385i	−1.41647	−	2.45340i
$296$	−0.712008			−0.0413846
$297$		0			0
$298$	16.9752			0.983349
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$	16.1600	−	27.9900i	0.931448	−	1.61332i
$302$	−11.1087	+	19.2409i	−0.639235	+	1.10719i
$303$		0			0
$304$	−3.58836	−	6.21523i	−0.205807	−	0.356468i
$305$	−30.9047			−1.76960
$306$		0			0
$307$	−15.0210			−0.857296			−0.428648	−	0.903472i	$-0.641010\pi$
$307$	−15.0210			−0.857296			−0.428648	+	0.903472i	$0.641010\pi$
$308$	−7.27561	−	12.6017i	−0.414566	−	0.718050i
$309$		0			0
$310$	4.56615	−	7.90881i	0.259340	−	0.449190i
$311$	−3.98762	+	6.90676i	−0.226117	+	0.391646i	−0.956654	−	0.291227i	$-0.905937\pi$
$311$	−3.98762	+	6.90676i	−0.226117	+	0.391646i	0.730537	+	0.682873i	$0.239270\pi$
$312$		0			0
$313$	−6.99745	−	12.1199i	−0.395519	−	0.685060i	0.597648	−	0.801759i	$-0.296102\pi$
$313$	−6.99745	−	12.1199i	−0.395519	−	0.685060i	−0.993167	+	0.116699i	$0.962769\pi$
$314$	−4.66758			−0.263407
$315$		0			0
$316$	−15.7527			−0.886159
$317$	−4.71015	−	8.15822i	−0.264548	−	0.458211i	0.702897	−	0.711292i	$-0.251890\pi$
$317$	−4.71015	−	8.15822i	−0.264548	−	0.458211i	−0.967445	+	0.253081i	$0.918556\pi$
$318$		0			0
$319$	5.75271	−	9.96399i	0.322090	−	0.557876i
$320$	1.64400	−	2.84748i	0.0919022	−	0.159179i
$321$		0			0
$322$	8.43268	+	14.6058i	0.469935	+	0.813951i
$323$	5.02104			0.279378
$324$		0			0
$325$	5.81089			0.322330
$326$	5.98762	+	10.3709i	0.331624	+	0.574389i
$327$		0			0
$328$	−0.411636	+	0.712974i	−0.0227288	+	0.0393674i
$329$	−2.14035	+	3.70720i	−0.118002	+	0.204385i
$330$		0			0
$331$	5.77747	+	10.0069i	0.317559	+	0.550028i	0.979978	−	0.199106i	$-0.0638037\pi$
$331$	5.77747	+	10.0069i	0.317559	+	0.550028i	−0.662419	+	0.749133i	$0.730470\pi$
$332$	7.97524			0.437698
$333$		0			0
$334$	6.77747			0.370847
$335$	0.731671	+	1.26729i	0.0399755	+	0.0692396i
$336$		0			0
$337$	−0.405446	+	0.702253i	−0.0220861	+	0.0382542i	−0.876857	−	0.480751i	$-0.840364\pi$
$337$	−0.405446	+	0.702253i	−0.0220861	+	0.0382542i	0.854771	+	0.519005i	$0.173697\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$	1.15019	+	1.99218i	0.0623776	+	0.108041i
$341$	−14.3782			−0.778624
$342$		0			0
$343$	17.1433			0.925652
$344$	−5.74907	−	9.95768i	−0.309969	−	0.536882i
$345$		0			0
$346$	9.57598	−	16.5861i	0.514808	−	0.891674i
$347$	7.15452	−	12.3920i	0.384075	−	0.665237i	−0.607566	−	0.794269i	$-0.707854\pi$
$347$	7.15452	−	12.3920i	0.384075	−	0.665237i	0.991640	+	0.129033i	$0.0411872\pi$
$348$		0			0
$349$	7.75526	+	13.4325i	0.415130	+	0.719025i	0.995442	−	0.0953684i	$-0.0304029\pi$
$349$	7.75526	+	13.4325i	0.415130	+	0.719025i	−0.580312	+	0.814394i	$0.697070\pi$
$350$	−16.3338			−0.873078
$351$		0			0
$352$	−5.17673			−0.275921
$353$	−17.3869	−	30.1150i	−0.925410	−	1.60286i	−0.790900	−	0.611945i	$-0.790387\pi$
$353$	−17.3869	−	30.1150i	−0.925410	−	1.60286i	−0.134510	−	0.990912i	$-0.542946\pi$
$354$		0			0
$355$	1.95489	−	3.38597i	0.103755	−	0.179708i
$356$	3.69963	−	6.40794i	0.196080	−	0.339620i
$357$		0			0
$358$	−0.105074	−	0.181994i	−0.00555335	−	0.00961868i
$359$	24.2829			1.28160			0.640801	−	0.767707i	$-0.278602\pi$
$359$	24.2829			1.28160			0.640801	+	0.767707i	$0.278602\pi$
$360$		0			0
$361$	32.5054			1.71081
$362$	−3.22253	−	5.58158i	−0.169372	−	0.293361i
$363$		0			0
$364$	1.40545	−	2.43430i	0.0736654	−	0.127592i
$365$	−0.365836	+	0.633646i	−0.0191487	+	0.0331665i
$366$		0			0
$367$	7.95420	+	13.7771i	0.415206	+	0.719158i	0.995450	−	0.0952849i	$-0.0303762\pi$
$367$	7.95420	+	13.7771i	0.415206	+	0.719158i	−0.580244	+	0.814443i	$0.697043\pi$
$368$	6.00000			0.312772
$369$		0			0
$370$	2.34108			0.121707
$371$	15.4895	+	26.8286i	0.804174	+	1.39287i
$372$		0			0
$373$	−5.73305	+	9.92993i	−0.296846	+	0.514152i	−0.975413	−	0.220386i	$-0.929268\pi$
$373$	−5.73305	+	9.92993i	−0.296846	+	0.514152i	0.678567	+	0.734539i	$0.262601\pi$
$374$	1.81089	−	3.13656i	0.0936390	−	0.162188i
$375$		0			0
$376$	0.761450	+	1.31887i	0.0392688	+	0.0680155i
$377$	2.22253			0.114466
$378$		0			0
$379$	3.71063			0.190602			0.0953011	−	0.995448i	$-0.469619\pi$
$379$	3.71063			0.190602			0.0953011	+	0.995448i	$0.469619\pi$
$380$	11.7985	+	20.4356i	0.605251	+	1.04833i
$381$		0			0
$382$	−11.6749	+	20.2215i	−0.597338	+	1.03462i
$383$	1.78366	−	3.08939i	0.0911408	−	0.157861i	−0.816851	−	0.576849i	$-0.804282\pi$
$383$	1.78366	−	3.08939i	0.0911408	−	0.157861i	0.907991	+	0.418989i	$0.137615\pi$
$384$		0			0
$385$	23.9222	+	41.4344i	1.21919	+	2.11169i
$386$	24.9294			1.26888
$387$		0			0
$388$	4.95420			0.251511
$389$	−2.71201	−	4.69734i	−0.137504	−	0.238164i	0.789047	−	0.614333i	$-0.210575\pi$
$389$	−2.71201	−	4.69734i	−0.137504	−	0.238164i	−0.926551	+	0.376168i	$0.877241\pi$
$390$		0			0
$391$	−2.09888	+	3.63537i	−0.106145	+	0.183849i
$392$	−0.450558	+	0.780389i	−0.0227566	+	0.0394156i
$393$		0			0
$394$	−5.11745	−	8.86369i	−0.257814	−	0.446546i
$395$	51.7948			2.60608
$396$		0			0
$397$	−28.1272			−1.41166			−0.705832	−	0.708379i	$-0.749427\pi$
$397$	−28.1272			−1.41166			−0.705832	+	0.708379i	$0.749427\pi$
$398$	−13.4523	−	23.3001i	−0.674305	−	1.16793i
$399$		0			0
$400$	−2.90545	+	5.03238i	−0.145272	+	0.251619i
$401$	−7.43130	+	12.8714i	−0.371101	+	0.642766i	−0.989735	−	0.142913i	$-0.954353\pi$
$401$	−7.43130	+	12.8714i	−0.371101	+	0.642766i	0.618634	+	0.785679i	$0.287686\pi$
$402$		0			0
$403$	−1.38874	−	2.40536i	−0.0691779	−	0.119820i
$404$	2.95420			0.146977
$405$		0			0
$406$	−6.24729			−0.310048
$407$	−1.84294	−	3.19206i	−0.0913509	−	0.158224i
$408$		0			0
$409$	8.98762	−	15.5670i	0.444409	−	0.769739i	−0.553602	−	0.832782i	$-0.686747\pi$
$409$	8.98762	−	15.5670i	0.444409	−	0.769739i	0.998011	+	0.0630423i	$0.0200803\pi$
$410$	1.35346	−	2.34425i	0.0668424	−	0.115774i
$411$		0			0
$412$	−4.69963	−	8.13999i	−0.231534	−	0.401029i
$413$	41.5970			2.04686
$414$		0			0
$415$	−26.2225			−1.28721
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	18.5760	−	32.1745i	0.908581	−	1.57371i
$419$	−13.7305	+	23.7819i	−0.670779	+	1.16182i	0.306905	+	0.951740i	$0.400707\pi$
$419$	−13.7305	+	23.7819i	−0.670779	+	1.16182i	−0.977684	+	0.210083i	$0.932627\pi$
$420$		0			0
$421$	−1.47091	−	2.54769i	−0.0716878	−	0.124167i	0.827953	−	0.560797i	$-0.189505\pi$
$421$	−1.47091	−	2.54769i	−0.0716878	−	0.124167i	−0.899641	+	0.436630i	$0.856172\pi$
$422$	4.71201			0.229377
$423$		0			0
$424$	11.0210			0.535229
$425$	−2.03273	−	3.52079i	−0.0986020	−	0.170784i
$426$		0			0
$427$	13.2101	−	22.8806i	0.639284	−	1.10727i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$		0			0
$430$	18.9029	+	32.7408i	0.911579	+	1.57890i
$431$	−3.37959			−0.162789			−0.0813946	−	0.996682i	$-0.525937\pi$
$431$	−3.37959			−0.162789			−0.0813946	+	0.996682i	$0.525937\pi$
$432$		0			0
$433$	8.36584			0.402036			0.201018	−	0.979588i	$-0.435575\pi$
$433$	8.36584			0.402036			0.201018	+	0.979588i	$0.435575\pi$
$434$	3.90359	+	6.76121i	0.187378	+	0.324549i
$435$		0			0
$436$	3.33743	−	5.78061i	0.159834	−	0.276841i
$437$	−21.5302	+	37.2914i	−1.02993	+	1.78389i
$438$		0			0
$439$	14.2880	+	24.7475i	0.681929	+	1.18114i	0.974391	+	0.224858i	$0.0721919\pi$
$439$	14.2880	+	24.7475i	0.681929	+	1.18114i	−0.292463	+	0.956277i	$0.594475\pi$
$440$	17.0210			0.811446
$441$		0			0
$442$	0.699628			0.0332779
$443$	−9.26942	−	16.0551i	−0.440404	−	0.762801i	0.557316	−	0.830301i	$-0.311831\pi$
$443$	−9.26942	−	16.0551i	−0.440404	−	0.762801i	−0.997719	+	0.0674993i	$0.978498\pi$
$444$		0			0
$445$	−12.1643	+	21.0693i	−0.576645	+	0.998779i
$446$	−3.81453	+	6.60697i	−0.180623	+	0.312849i
$447$		0			0
$448$	1.40545	+	2.43430i	0.0664011	+	0.115010i
$449$	14.8626			0.701409			0.350705	−	0.936486i	$-0.385942\pi$
$449$	14.8626			0.701409			0.350705	+	0.936486i	$0.385942\pi$
$450$		0			0
$451$	−4.26186			−0.200683
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$		0			0
$454$	11.0210	−	19.0890i	0.517243	−	0.895891i
$455$	−4.62110	+	8.00397i	−0.216640	+	0.375232i
$456$		0			0
$457$	−11.1520	−	19.3158i	−0.521667	−	0.903554i	−0.999682	−	0.0252024i	$-0.991977\pi$
$457$	−11.1520	−	19.3158i	−0.521667	−	0.903554i	0.478015	−	0.878352i	$-0.341356\pi$
$458$	−4.48948			−0.209780
$459$		0			0
$460$	−19.7280			−0.919821
$461$	4.87017	+	8.43538i	0.226826	+	0.392875i	0.956866	−	0.290530i	$-0.0938317\pi$
$461$	4.87017	+	8.43538i	0.226826	+	0.392875i	−0.730040	+	0.683405i	$0.760498\pi$
$462$		0			0
$463$	1.81275	−	3.13978i	0.0842457	−	0.145918i	−0.820824	−	0.571181i	$-0.806485\pi$
$463$	1.81275	−	3.13978i	0.0842457	−	0.145918i	0.905070	+	0.425264i	$0.139819\pi$
$464$	−1.11126	+	1.92477i	−0.0515891	+	0.0893550i
$465$		0			0
$466$	2.77128	+	4.80000i	0.128377	+	0.222356i
$467$	0.0458003			0.00211939			0.00105969	−	0.999999i	$-0.499663\pi$
$467$	0.0458003			0.00211939			0.00105969	+	0.999999i	$0.499663\pi$
$468$		0			0
$469$	−1.25101			−0.0577661
$470$	−2.50364	−	4.33643i	−0.115484	−	0.200025i
$471$		0			0
$472$	7.39926	−	12.8159i	0.340578	−	0.589899i
$473$	29.7614	−	51.5482i	1.36843	−	2.37019i
$474$		0			0
$475$	−20.8516	−	36.1160i	−0.956737	−	1.65712i
$476$	−1.96658			−0.0901380
$477$		0			0
$478$	−7.43130			−0.339900
$479$	8.84176	+	15.3144i	0.403991	+	0.699732i	0.994203	−	0.107515i	$-0.0342895\pi$
$479$	8.84176	+	15.3144i	0.403991	+	0.699732i	−0.590213	+	0.807248i	$0.700956\pi$
$480$		0			0
$481$	0.356004	−	0.616617i	0.0162324	−	0.0281153i
$482$	−4.69963	+	8.13999i	−0.214062	+	0.370767i
$483$		0			0
$484$	−7.89926	−	13.6819i	−0.359057	−	0.621905i
$485$	−16.2894			−0.739662
$486$		0			0
$487$	−23.2436			−1.05327			−0.526633	−	0.850093i	$-0.676546\pi$
$487$	−23.2436			−1.05327			−0.526633	+	0.850093i	$0.676546\pi$
$488$	−4.69963	−	8.13999i	−0.212742	−	0.368480i
$489$		0			0
$490$	1.48143	−	2.56591i	0.0669242	−	0.115916i
$491$	−9.27197	+	16.0595i	−0.418438	+	0.724756i	−0.995783	−	0.0917446i	$-0.970756\pi$
$491$	−9.27197	+	16.0595i	−0.418438	+	0.724756i	0.577344	+	0.816501i	$0.304089\pi$
$492$		0			0
$493$	−0.777472	−	1.34662i	−0.0350156	−	0.0606487i
$494$	7.17673			0.322896
$495$		0			0
$496$	2.77747			0.124712
$497$	1.67123	+	2.89465i	0.0749648	+	0.129843i
$498$		0			0
$499$	15.7738	−	27.3209i	0.706130	−	1.22305i	−0.260152	−	0.965568i	$-0.583773\pi$
$499$	15.7738	−	27.3209i	0.706130	−	1.22305i	0.966282	−	0.257486i	$-0.0828940\pi$
$500$	1.33310	−	2.30900i	0.0596182	−	0.103262i
$501$		0			0
$502$	7.99814	+	13.8532i	0.356974	+	0.618298i
$503$	−21.2188			−0.946100			−0.473050	−	0.881036i	$-0.656847\pi$
$503$	−21.2188			−0.946100			−0.473050	+	0.881036i	$0.656847\pi$
$504$		0			0
$505$	−9.71339			−0.432240
$506$	15.5302	+	26.8991i	0.690401	+	1.19581i
$507$		0			0
$508$	1.71201	−	2.96528i	0.0759581	−	0.131563i
$509$	1.71015	−	2.96206i	0.0758010	−	0.131291i	−0.825633	−	0.564207i	$-0.809182\pi$
$509$	1.71015	−	2.96206i	0.0758010	−	0.131291i	0.901434	+	0.432916i	$0.142515\pi$
$510$		0			0
$511$	−0.312752	−	0.541702i	−0.0138353	−	0.0239635i
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.0865047			0.00381556
$515$	15.4523	+	26.7642i	0.680911	+	1.17937i
$516$		0			0
$517$	−3.94182	+	6.82743i	−0.173361	+	0.300270i
$518$	−1.00069	+	1.73324i	−0.0439677	+	0.0761544i
$519$		0			0
$520$	1.64400	+	2.84748i	0.0720940	+	0.124870i
$521$	−25.5498			−1.11936			−0.559680	−	0.828709i	$-0.689076\pi$
$521$	−25.5498			−1.11936			−0.559680	+	0.828709i	$0.689076\pi$
$522$		0			0
$523$	−16.0458			−0.701634			−0.350817	−	0.936444i	$-0.614096\pi$
$523$	−16.0458			−0.701634			−0.350817	+	0.936444i	$0.614096\pi$
$524$	4.12729	+	7.14867i	0.180301	+	0.312291i
$525$		0			0
$526$	0.489480	−	0.847803i	0.0213423	−	0.0369660i
$527$	−0.971599	+	1.68286i	−0.0423235	+	0.0733065i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−36.2371			−1.57404
$531$		0			0
$532$	−20.1730			−0.874611
$533$	−0.411636	−	0.712974i	−0.0178299	−	0.0308824i
$534$		0			0
$535$	−19.7280	+	34.1698i	−0.852914	+	1.47729i
$536$	−0.222528	+	0.385430i	−0.00961176	+	0.0166481i
$537$		0			0
$538$	−12.7861	−	22.1462i	−0.551249	−	0.954792i
$539$	−4.66483			−0.200928
$540$		0			0
$541$	−0.899738			−0.0386828			−0.0193414	−	0.999813i	$-0.506157\pi$
$541$	−0.899738			−0.0386828			−0.0193414	+	0.999813i	$0.506157\pi$
$542$	−8.48831	−	14.7022i	−0.364604	−	0.631513i
$543$		0			0
$544$	−0.349814	+	0.605896i	−0.0149982	+	0.0259776i
$545$	−10.9735	+	19.0066i	−0.470051	+	0.814153i
$546$		0			0
$547$	16.7095	+	28.9416i	0.714445	+	1.23745i	0.963173	+	0.268882i	$0.0866540\pi$
$547$	16.7095	+	28.9416i	0.714445	+	1.23745i	−0.248728	+	0.968573i	$0.580013\pi$
$548$	4.60074			0.196534
$549$		0			0
$550$	−30.0814			−1.28268
$551$	−7.97524	−	13.8135i	−0.339757	−	0.588476i
$552$		0			0
$553$	−22.1396	+	38.3469i	−0.941471	+	1.63068i
$554$	−1.69963	+	2.94384i	−0.0722103	+	0.125072i
$555$		0			0
$556$	−5.29418	−	9.16979i	−0.224523	−	0.388886i
$557$	0.123644			0.00523896			0.00261948	−	0.999997i	$-0.499166\pi$
$557$	0.123644			0.00523896			0.00261948	+	0.999997i	$0.499166\pi$
$558$		0			0
$559$	11.4981			0.486320
$560$	−4.62110	−	8.00397i	−0.195277	−	0.338230i
$561$		0			0
$562$	−14.3411	+	24.8395i	−0.604942	+	1.04779i
$563$	1.29418	−	2.24159i	0.0545433	−	0.0944717i	−0.837465	−	0.546492i	$-0.815963\pi$
$563$	1.29418	−	2.24159i	0.0545433	−	0.0944717i	0.892008	+	0.452020i	$0.149296\pi$
$564$		0			0
$565$	4.93199	+	8.54245i	0.207490	+	0.359384i
$566$	−11.1978			−0.470677
$567$		0			0
$568$	1.18911			0.0498939
$569$	−3.73422	−	6.46786i	−0.156547	−	0.271147i	0.777074	−	0.629409i	$-0.216703\pi$
$569$	−3.73422	−	6.46786i	−0.156547	−	0.271147i	−0.933621	+	0.358262i	$0.883369\pi$
$570$		0			0
$571$	16.3251	−	28.2758i	0.683182	−	1.18331i	−0.290822	−	0.956777i	$-0.593929\pi$
$571$	16.3251	−	28.2758i	0.683182	−	1.18331i	0.974004	−	0.226529i	$-0.0727379\pi$
$572$	2.58836	−	4.48318i	0.108225	−	0.187451i
$573$		0			0
$574$	1.15706	+	2.00409i	0.0482949	+	0.0836493i
$575$	34.8654			1.45399
$576$		0			0
$577$	−18.9542			−0.789074			−0.394537	−	0.918880i	$-0.629095\pi$
$577$	−18.9542			−0.789074			−0.394537	+	0.918880i	$0.629095\pi$
$578$	8.25526	+	14.2985i	0.343374	+	0.594740i
$579$		0			0
$580$	3.65383	−	6.32862i	0.151717	−	0.262781i
$581$	11.2088	−	19.4142i	0.465018	−	0.805435i
$582$		0			0
$583$	28.5265	+	49.4093i	1.18145	+	2.04632i
$584$	−0.222528			−0.00920829
$585$		0			0
$586$	−6.94182			−0.286764
$587$	−15.5760	−	26.9784i	−0.642890	−	1.11352i	−0.984785	−	0.173779i	$-0.944402\pi$
$587$	−15.5760	−	26.9784i	−0.642890	−	1.11352i	0.341895	−	0.939738i	$-0.388931\pi$
$588$		0			0
$589$	−9.96658	+	17.2626i	−0.410666	+	0.711294i
$590$	−24.3287	+	42.1385i	−1.00160	+	1.73482i
$591$		0			0
$592$	0.356004	+	0.616617i	0.0146317	+	0.0253428i
$593$	−39.0631			−1.60413			−0.802065	−	0.597237i	$-0.796265\pi$
$593$	−39.0631			−1.60413			−0.802065	+	0.597237i	$0.796265\pi$
$594$		0			0
$595$	6.46610			0.265084
$596$	−8.48762	−	14.7010i	−0.347666	−	0.602176i
$597$		0			0
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	9.86398	−	17.0849i	0.403031	−	0.698070i	−0.591059	−	0.806628i	$-0.701290\pi$
$599$	9.86398	−	17.0849i	0.403031	−	0.698070i	0.994090	+	0.108558i	$0.0346233\pi$
$600$		0			0
$601$	0.703270	+	1.21810i	0.0286870	+	0.0496873i	0.880012	−	0.474951i	$-0.157534\pi$
$601$	0.703270	+	1.21810i	0.0286870	+	0.0496873i	−0.851325	+	0.524638i	$0.824201\pi$
$602$	−32.3200			−1.31727
$603$		0			0
$604$	22.2174			0.904015
$605$	25.9727	+	44.9860i	1.05594	+	1.82894i
$606$		0			0
$607$	5.12364	−	8.87441i	0.207962	−	0.360201i	−0.743110	−	0.669169i	$-0.766650\pi$
$607$	5.12364	−	8.87441i	0.207962	−	0.360201i	0.951073	+	0.308968i	$0.0999835\pi$
$608$	−3.58836	+	6.21523i	−0.145527	+	0.252061i
$609$		0			0
$610$	15.4523	+	26.7642i	0.625647	+	1.08365i
$611$	−1.52290			−0.0616099
$612$		0			0
$613$	−43.3287			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$613$	−43.3287			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$614$	7.51052	+	13.0086i	0.303100	+	0.524984i
$615$		0			0
$616$	−7.27561	+	12.6017i	−0.293143	+	0.507738i
$617$	1.44506	−	2.50291i	0.0581758	−	0.100763i	−0.835471	−	0.549535i	$-0.814805\pi$
$617$	1.44506	−	2.50291i	0.0581758	−	0.100763i	0.893647	+	0.448771i	$0.148138\pi$
$618$		0			0
$619$	−0.346172	−	0.599588i	−0.0139138	−	0.0240995i	0.858985	−	0.512001i	$-0.171096\pi$
$619$	−0.346172	−	0.599588i	−0.0139138	−	0.0240995i	−0.872898	+	0.487902i	$0.837762\pi$
$620$	−9.13231			−0.366762
$621$		0			0
$622$	7.97524			0.319778
$623$	−10.3993	−	18.0120i	−0.416637	−	0.721637i
$624$		0			0
$625$	10.1440	−	17.5699i	0.405760	−	0.702797i
$626$	−6.99745	+	12.1199i	−0.279674	+	0.484410i
$627$		0			0
$628$	2.33379	+	4.04225i	0.0931285	+	0.161303i
$629$	−0.498141			−0.0198622
$630$		0			0
$631$	30.4771			1.21327			0.606637	−	0.794979i	$-0.292518\pi$
$631$	30.4771			1.21327			0.606637	+	0.794979i	$0.292518\pi$
$632$	7.87636	+	13.6422i	0.313305	+	0.542660i
$633$		0			0
$634$	−4.71015	+	8.15822i	−0.187064	+	0.324004i
$635$	−5.62907	+	9.74983i	−0.223383	+	0.386910i
$636$		0			0
$637$	−0.450558	−	0.780389i	−0.0178517	−	0.0309201i
$638$	−11.5054			−0.455504
$639$		0			0
$640$	−3.28799			−0.129969
$641$	−19.0970	−	33.0770i	−0.754287	−	1.30646i	−0.945728	−	0.324959i	$-0.894649\pi$
$641$	−19.0970	−	33.0770i	−0.754287	−	1.30646i	0.191441	−	0.981504i	$-0.438684\pi$
$642$		0			0
$643$	−6.30903	+	10.9276i	−0.248804	+	0.430941i	−0.963194	−	0.268806i	$-0.913371\pi$
$643$	−6.30903	+	10.9276i	−0.248804	+	0.430941i	0.714390	+	0.699747i	$0.246704\pi$
$644$	8.43268	−	14.6058i	0.332294	−	0.575550i
$645$		0			0
$646$	−2.51052	−	4.34835i	−0.0987751	−	0.171084i
$647$	−35.9257			−1.41239			−0.706193	−	0.708019i	$-0.749589\pi$
$647$	−35.9257			−1.41239			−0.706193	+	0.708019i	$0.749589\pi$
$648$		0			0
$649$	76.6079			3.00712
$650$	−2.90545	−	5.03238i	−0.113961	−	0.197386i
$651$		0			0
$652$	5.98762	−	10.3709i	0.234493	−	0.406154i
$653$	−10.7193	+	18.5664i	−0.419478	+	0.726558i	−0.995887	−	0.0906038i	$-0.971120\pi$
$653$	−10.7193	+	18.5664i	−0.419478	+	0.726558i	0.576409	+	0.817162i	$0.304454\pi$
$654$		0			0
$655$	−13.5705	−	23.5048i	−0.530243	−	0.918407i
$656$	0.823272			0.0321434
$657$		0			0
$658$	4.28071			0.166879
$659$	16.3764	+	28.3647i	0.637932	+	1.10493i	0.985886	+	0.167419i	$0.0535434\pi$
$659$	16.3764	+	28.3647i	0.637932	+	1.10493i	−0.347954	+	0.937512i	$0.613123\pi$
$660$		0			0
$661$	−0.268329	+	0.464759i	−0.0104368	+	0.0180770i	−0.871197	−	0.490934i	$-0.836656\pi$
$661$	−0.268329	+	0.464759i	−0.0104368	+	0.0180770i	0.860760	+	0.509011i	$0.169989\pi$
$662$	5.77747	−	10.0069i	0.224548	−	0.388928i
$663$		0			0
$664$	−3.98762	−	6.90676i	−0.154750	−	0.268034i
$665$	66.3287			2.57212
$666$		0			0
$667$	13.3352			0.516340
$668$	−3.38874	−	5.86946i	−0.131114	−	0.227096i
$669$		0			0
$670$	0.731671	−	1.26729i	0.0282669	−	0.0489598i
$671$	24.3287	−	42.1385i	0.939199	−	1.62674i
$672$		0			0
$673$	−16.9530	−	29.3635i	−0.653491	−	1.13188i	−0.982270	−	0.187473i	$-0.939970\pi$
$673$	−16.9530	−	29.3635i	−0.653491	−	1.13188i	0.328779	−	0.944407i	$-0.393363\pi$
$674$	0.810892			0.0312344
$675$		0			0
$676$	1.00000			0.0384615
$677$	−13.3993	−	23.2082i	−0.514975	−	0.891963i	−0.999849	−	0.0173791i	$-0.994468\pi$
$677$	−13.3993	−	23.2082i	−0.514975	−	0.891963i	0.484874	−	0.874584i	$-0.338866\pi$
$678$		0			0
$679$	6.96286	−	12.0600i	0.267210	−	0.462821i
$680$	1.15019	−	1.99218i	0.0441076	−	0.0763966i
$681$		0			0
$682$	7.18911	+	12.4519i	0.275285	+	0.476808i
$683$	−0.978959			−0.0374588			−0.0187294	−	0.999825i	$-0.505962\pi$
$683$	−0.978959			−0.0374588			−0.0187294	+	0.999825i	$0.505962\pi$
$684$		0			0
$685$	−15.1272			−0.577981
$686$	−8.57165	−	14.8465i	−0.327267	−	0.566844i
$687$		0			0
$688$	−5.74907	+	9.95768i	−0.219181	+	0.379633i
$689$	−5.51052	+	9.54450i	−0.209934	+	0.363617i
$690$		0			0
$691$	25.2632	+	43.7572i	0.961059	+	1.66460i	0.719851	+	0.694129i	$0.244210\pi$
$691$	25.2632	+	43.7572i	0.961059	+	1.66460i	0.241208	+	0.970473i	$0.422456\pi$
$692$	−19.1520			−0.728049
$693$		0			0
$694$	−14.3090			−0.543163
$695$	17.4072	+	30.1502i	0.660294	+	1.14366i
$696$		0			0
$697$	−0.287992	+	0.498817i	−0.0109085	+	0.0188940i
$698$	7.75526	−	13.4325i	0.293541	−	0.508428i
$699$		0			0
$700$	8.16690	+	14.1455i	0.308680	+	0.534649i
$701$	9.37450			0.354070			0.177035	−	0.984205i	$-0.443349\pi$
$701$	9.37450			0.354070			0.177035	+	0.984205i	$0.443349\pi$
$702$		0			0
$703$	−5.10989			−0.192723
$704$	2.58836	+	4.48318i	0.0975526	+	0.168966i
$705$		0			0
$706$	−17.3869	+	30.1150i	−0.654364	+	1.13339i
$707$	4.15197	−	7.19142i	0.156151	−	0.270461i
$708$		0			0
$709$	7.28613	+	12.6200i	0.273636	+	0.473952i	0.969790	−	0.243940i	$-0.0784402\pi$
$709$	7.28613	+	12.6200i	0.273636	+	0.473952i	−0.696154	+	0.717893i	$0.745107\pi$
$710$	−3.90978			−0.146731
$711$		0			0
$712$	−7.39926			−0.277299
$713$	−8.33242	−	14.4322i	−0.312051	−	0.540489i
$714$		0			0
$715$	−8.51052	+	14.7407i	−0.318275	+	0.551269i
$716$	−0.105074	+	0.181994i	−0.00392681	+	0.00680144i
$717$		0			0
$718$	−12.1414	−	21.0296i	−0.453115	−	0.784818i
$719$	33.3104			1.24227			0.621134	−	0.783704i	$-0.286672\pi$
$719$	33.3104			1.24227			0.621134	+	0.783704i	$0.286672\pi$
$720$		0			0
$721$	−26.4203			−0.983943
$722$	−16.2527	−	28.1505i	−0.604863	−	1.04765i
$723$		0			0
$724$	−3.22253	+	5.58158i	−0.119764	+	0.207438i
$725$	−6.45744	+	11.1846i	−0.239823	+	0.415386i
$726$		0			0
$727$	16.6428	+	28.8262i	0.617248	+	1.06911i	0.989986	+	0.141168i	$0.0450859\pi$
$727$	16.6428	+	28.8262i	0.617248	+	1.06911i	−0.372737	+	0.927937i	$0.621581\pi$
$728$	−2.81089			−0.104179
$729$		0			0
$730$	0.731671			0.0270804
$731$	−4.02221	−	6.96667i	−0.148767	−	0.257672i
$732$		0			0
$733$	−23.4585	+	40.6314i	−0.866461	+	1.50075i	−0.000871020		1.00000i	$0.500277\pi$
$733$	−23.4585	+	40.6314i	−0.866461	+	1.50075i	−0.865590	+	0.500754i	$0.833056\pi$
$734$	7.95420	−	13.7771i	0.293595	−	0.508521i
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	−2.30394			−0.0848666
$738$		0			0
$739$	−43.6116			−1.60428			−0.802139	−	0.597137i	$-0.796305\pi$
$739$	−43.6116			−1.60428			−0.802139	+	0.597137i	$0.796305\pi$
$740$	−1.17054	−	2.02743i	−0.0430298	−	0.0745299i
$741$		0			0
$742$	15.4895	−	26.8286i	0.568637	−	0.984908i
$743$	−20.0371	+	34.7052i	−0.735089	+	1.27321i	0.219596	+	0.975591i	$0.429526\pi$
$743$	−20.0371	+	34.7052i	−0.735089	+	1.27321i	−0.954684	+	0.297620i	$0.903807\pi$
$744$		0			0
$745$	27.9072	+	48.3367i	1.02244	+	1.77092i
$746$	11.4661			0.419804
$747$		0			0
$748$	−3.62178			−0.132426
$749$	−16.8654	−	29.2116i	−0.616247	−	1.06737i
$750$		0			0
$751$	−22.6538	+	39.2376i	−0.826650	+	1.43180i	0.0740019	+	0.997258i	$0.476423\pi$
$751$	−22.6538	+	39.2376i	−0.826650	+	1.43180i	−0.900652	+	0.434542i	$0.856910\pi$
$752$	0.761450	−	1.31887i	0.0277672	−	0.0480942i
$753$		0			0
$754$	−1.11126	−	1.92477i	−0.0404699	−	0.0700958i
$755$	−73.0507			−2.65859
$756$		0			0
$757$	38.3287			1.39308			0.696540	−	0.717518i	$-0.254722\pi$
$757$	38.3287			1.39308			0.696540	+	0.717518i	$0.254722\pi$
$758$	−1.85532	−	3.21350i	−0.0673881	−	0.116720i
$759$		0			0
$760$	11.7985	−	20.4356i	0.427977	−	0.741278i
$761$	−5.34108	+	9.25102i	−0.193614	+	0.335349i	−0.946445	−	0.322864i	$-0.895354\pi$
$761$	−5.34108	+	9.25102i	−0.193614	+	0.335349i	0.752831	+	0.658213i	$0.228688\pi$
$762$		0			0
$763$	−9.38117	−	16.2487i	−0.339621	−	0.588241i
$764$	23.3497			0.844764
$765$		0			0
$766$	−3.56732			−0.128893
$767$	7.39926	+	12.8159i	0.267172	+	0.462755i
$768$		0			0
$769$	24.2843	−	42.0616i	0.875713	−	1.51678i	0.0197124	−	0.999806i	$-0.493725\pi$
$769$	24.2843	−	42.0616i	0.875713	−	1.51678i	0.856001	−	0.516974i	$-0.172942\pi$
$770$	23.9222	−	41.4344i	0.862095	−	1.49319i
$771$		0			0
$772$	−12.4647	−	21.5895i	−0.448615	−	0.777024i
$773$	−1.45881			−0.0524699			−0.0262349	−	0.999656i	$-0.508352\pi$
$773$	−1.45881			−0.0524699			−0.0262349	+	0.999656i	$0.508352\pi$
$774$		0			0
$775$	16.1396			0.579751
$776$	−2.47710	−	4.29046i	−0.0889227	−	0.154019i
$777$		0			0
$778$	−2.71201	+	4.69734i	−0.0972302	+	0.168408i
$779$	−2.95420	+	5.11682i	−0.105845	+	0.183329i
$780$		0			0
$781$	3.07784	+	5.33098i	0.110134	+	0.190758i
$782$	4.19777			0.150112
$783$		0			0
$784$	0.901116			0.0321827
$785$	−7.67349	−	13.2909i	−0.273879	−	0.474372i
$786$		0			0
$787$	7.05308	−	12.2163i	0.251415	−	0.435464i	−0.712500	−	0.701672i	$-0.752437\pi$
$787$	7.05308	−	12.2163i	0.251415	−	0.435464i	0.963916	+	0.266208i	$0.0857707\pi$
$788$	−5.11745	+	8.86369i	−0.182302	+	0.315756i
$789$		0			0
$790$	−25.8974	−	44.8556i	−0.921388	−	1.59589i
$791$	−8.43268			−0.299831
$792$		0			0
$793$	9.39926			0.333777
$794$	14.0636	+	24.3589i	0.499099	+	0.864464i
$795$		0			0
$796$	−13.4523	+	23.3001i	−0.476806	+	0.825851i
$797$	14.5970	−	25.2828i	0.517053	−	0.895562i	−0.482751	−	0.875758i	$-0.660362\pi$
$797$	14.5970	−	25.2828i	0.517053	−	0.895562i	0.999804	−	0.0198045i	$-0.00630439\pi$
$798$		0			0
$799$	0.532732	+	0.922719i	0.0188467	+	0.0326434i
$800$	5.81089			0.205446
$801$		0			0
$802$	14.8626			0.524817
$803$	−0.575984	−	0.997634i	−0.0203260	−	0.0352057i
$804$		0			0
$805$	−27.7266	+	48.0238i	−0.977233	+	1.69262i
$806$	−1.38874	+	2.40536i	−0.0489161	+	0.0847252i
$807$		0			0
$808$	−1.47710	−	2.55841i	−0.0519642	−	0.0900046i
$809$	24.4523			0.859699			0.429849	−	0.902901i	$-0.358567\pi$
$809$	24.4523			0.859699			0.429849	+	0.902901i	$0.358567\pi$
$810$		0			0
$811$	−21.5970			−0.758374			−0.379187	−	0.925320i	$-0.623796\pi$
$811$	−21.5970			−0.758374			−0.379187	+	0.925320i	$0.623796\pi$
$812$	3.12364	+	5.41031i	0.109618	+	0.189865i
$813$		0			0
$814$	−1.84294	+	3.19206i	−0.0645949	+	0.111882i
$815$	−19.6872	+	34.0993i	−0.689614	+	1.19445i
$816$		0			0
$817$	−41.2595	−	71.4636i	−1.44349	−	2.50019i
$818$	−17.9752			−0.628490
$819$		0			0
$820$	−2.70691			−0.0945295
$821$	−2.16071	−	3.74245i	−0.0754092	−	0.130613i	0.825855	−	0.563883i	$-0.190693\pi$
$821$	−2.16071	−	3.74245i	−0.0754092	−	0.130613i	−0.901264	+	0.433270i	$0.857360\pi$
$822$		0			0
$823$	13.8764	−	24.0346i	0.483699	−	0.837792i	−0.516125	−	0.856513i	$-0.672626\pi$
$823$	13.8764	−	24.0346i	0.483699	−	0.837792i	0.999825	+	0.0187212i	$0.00595948\pi$
$824$	−4.69963	+	8.13999i	−0.163719	+	0.283570i
$825$		0			0
$826$	−20.7985	−	36.0241i	−0.723673	−	1.25344i
$827$	−8.55122			−0.297355			−0.148678	−	0.988886i	$-0.547502\pi$
$827$	−8.55122			−0.297355			−0.148678	+	0.988886i	$0.547502\pi$
$828$		0			0
$829$	38.2371			1.32803			0.664015	−	0.747720i	$-0.268851\pi$
$829$	38.2371			1.32803			0.664015	+	0.747720i	$0.268851\pi$
$830$	13.1113	+	22.7094i	0.455099	+	0.788254i
$831$		0			0
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	−0.315223	+	0.545982i	−0.0109218	+	0.0189172i
$834$		0			0
$835$	11.1421	+	19.2987i	0.385590	+	0.667861i
$836$	−37.1520			−1.28493
$837$		0			0
$838$	27.4610			0.948625
$839$	−22.5407	−	39.0416i	−0.778192	−	1.34787i	−0.932983	−	0.359920i	$-0.882804\pi$
$839$	−22.5407	−	39.0416i	−0.778192	−	1.34787i	0.154792	−	0.987947i	$-0.450529\pi$
$840$		0			0
$841$	12.0302	−	20.8369i	0.414834	−	0.718513i
$842$	−1.47091	+	2.54769i	−0.0506909	+	0.0877992i
$843$		0			0
$844$	−2.35600	−	4.08072i	−0.0810970	−	0.140464i
$845$	−3.28799			−0.113110
$846$		0			0
$847$	−44.4079			−1.52587
$848$	−5.51052	−	9.54450i	−0.189232	−	0.327760i
$849$		0			0
$850$	−2.03273	+	3.52079i	−0.0697221	+	0.120762i
$851$	2.13602	−	3.69970i	0.0732219	−	0.126824i
$852$		0			0
$853$	−12.9840	−	22.4889i	−0.444563	−	0.770006i	0.553459	−	0.832877i	$-0.313308\pi$
$853$	−12.9840	−	22.4889i	−0.444563	−	0.770006i	−0.998022	+	0.0628710i	$0.979974\pi$
$854$	−26.4203			−0.904084
$855$		0			0
$856$	−12.0000			−0.410152
$857$	9.05494	+	15.6836i	0.309311	+	0.535742i	0.978212	−	0.207609i	$-0.0665683\pi$
$857$	9.05494	+	15.6836i	0.309311	+	0.535742i	−0.668901	+	0.743352i	$0.733235\pi$
$858$		0			0
$859$	16.1080	−	27.8999i	0.549599	−	0.951933i	−0.448703	−	0.893681i	$-0.648114\pi$
$859$	16.1080	−	27.8999i	0.549599	−	0.951933i	0.998302	−	0.0582522i	$-0.0185527\pi$
$860$	18.9029	−	32.7408i	0.644583	−	1.11645i
$861$		0			0
$862$	1.68980	+	2.92681i	0.0575547	+	0.0996877i
$863$	5.01594			0.170745			0.0853724	−	0.996349i	$-0.472792\pi$
$863$	5.01594			0.170745			0.0853724	+	0.996349i	$0.472792\pi$
$864$		0			0
$865$	62.9715			2.14110
$866$	−4.18292	−	7.24503i	−0.142141	−	0.246196i
$867$		0			0
$868$	3.90359	−	6.76121i	0.132496	−	0.229490i
$869$	−40.7738	+	70.6222i	−1.38315	+	2.39569i
$870$		0			0
$871$	−0.222528	−	0.385430i	−0.00754008	−	0.0130598i
$872$	−6.67487			−0.226040
$873$		0			0
$874$	43.0604			1.45654
$875$	−3.74721	−	6.49036i	−0.126679	−	0.219414i
$876$		0			0
$877$	−9.75526	+	16.8966i	−0.329412	+	0.570558i	−0.982395	−	0.186814i	$-0.940184\pi$
$877$	−9.75526	+	16.8966i	−0.329412	+	0.570558i	0.652984	+	0.757372i	$0.273517\pi$
$878$	14.2880	−	24.7475i	0.482196	−	0.835189i
$879$		0			0
$880$	−8.51052	−	14.7407i	−0.286890	−	0.496907i
$881$	30.4895			1.02722			0.513608	−	0.858025i	$-0.328308\pi$
$881$	30.4895			1.02722			0.513608	+	0.858025i	$0.328308\pi$
$882$		0			0
$883$	−0.217432			−0.00731718			−0.00365859	−	0.999993i	$-0.501165\pi$
$883$	−0.217432			−0.00731718			−0.00365859	+	0.999993i	$0.501165\pi$
$884$	−0.349814	−	0.605896i	−0.0117655	−	0.0203785i
$885$		0			0
$886$	−9.26942	+	16.0551i	−0.311412	+	0.539382i
$887$	−2.22253	+	3.84953i	−0.0746252	+	0.129255i	−0.900923	−	0.433979i	$-0.857109\pi$
$887$	−2.22253	+	3.84953i	−0.0746252	+	0.129255i	0.826298	+	0.563233i	$0.190443\pi$
$888$		0			0
$889$	−4.81227	−	8.33510i	−0.161398	−	0.279550i
$890$	24.3287			0.815500
$891$		0			0
$892$	7.62907			0.255440
$893$	5.46472	+	9.46517i	0.182870	+	0.316740i
$894$		0			0
$895$	0.345483	−	0.598395i	0.0115482	−	0.0200021i
$896$	1.40545	−	2.43430i	0.0469527	−	0.0813244i
$897$		0			0
$898$	−7.43130	−	12.8714i	−0.247986	−	0.429524i
$899$	6.17301			0.205881
$900$		0			0
$901$	7.71063			0.256878
$902$	2.13093	+	3.69087i	0.0709521	+	0.122893i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$	10.5956	−	18.3522i	0.352211	−	0.610048i
$906$		0			0
$907$	9.25704	+	16.0337i	0.307375	+	0.532389i	0.977787	−	0.209600i	$-0.0672161\pi$
$907$	9.25704	+	16.0337i	0.307375	+	0.532389i	−0.670412	+	0.741989i	$0.733883\pi$
$908$	−22.0421			−0.731492
$909$		0			0
$910$	9.24219			0.306376
$911$	−2.14468	−	3.71470i	−0.0710566	−	0.123074i	0.828308	−	0.560273i	$-0.189304\pi$
$911$	−2.14468	−	3.71470i	−0.0710566	−	0.123074i	−0.899365	+	0.437199i	$0.855970\pi$
$912$		0			0
$913$	20.6428	−	35.7544i	0.683178	−	1.18330i
$914$	−11.1520	+	19.3158i	−0.368874	+	0.638909i
$915$		0			0
$916$	2.24474	+	3.88800i	0.0741683	+	0.128463i
$917$	23.2027			0.766221
$918$		0			0
$919$	53.5302			1.76580			0.882899	−	0.469563i	$-0.155589\pi$
$919$	53.5302			1.76580			0.882899	+	0.469563i	$0.155589\pi$
$920$	9.86398	+	17.0849i	0.325206	+	0.563273i
$921$		0			0
$922$	4.87017	−	8.43538i	0.160390	−	0.277804i
$923$	−0.594554	+	1.02980i	−0.0195700	+	0.0338962i
$924$		0			0
$925$	2.06870	+	3.58309i	0.0680185	+	0.117811i
$926$	−3.62550			−0.119141
$927$		0			0
$928$	2.22253			0.0729581
$929$	−22.8974	−	39.6595i	−0.751239	−	1.30118i	−0.947222	−	0.320577i	$-0.896123\pi$
$929$	−22.8974	−	39.6595i	−0.751239	−	1.30118i	0.195983	−	0.980607i	$-0.437210\pi$
$930$		0			0
$931$	−3.23353	+	5.60064i	−0.105975	+	0.183554i
$932$	2.77128	−	4.80000i	0.0907764	−	0.157229i
$933$		0			0
$934$	−0.0229002	−	0.0396643i	−0.000749316	−	0.00129785i
$935$	11.9084			0.389446
$936$		0			0
$937$	−32.0604			−1.04737			−0.523683	−	0.851913i	$-0.675442\pi$
$937$	−32.0604			−1.04737			−0.523683	+	0.851913i	$0.675442\pi$
$938$	0.625503	+	1.08340i	0.0204234	+	0.0353744i
$939$		0			0
$940$	−2.50364	+	4.33643i	−0.0816598	+	0.141439i
$941$	−7.18430	+	12.4436i	−0.234201	+	0.405649i	−0.959040	−	0.283270i	$-0.908581\pi$
$941$	−7.18430	+	12.4436i	−0.234201	+	0.405649i	0.724839	+	0.688918i	$0.241914\pi$
$942$		0			0
$943$	−2.46982	−	4.27785i	−0.0804283	−	0.139306i
$944$	−14.7985			−0.481651
$945$		0			0
$946$	−59.5227			−1.93525
$947$	−1.07922	−	1.86927i	−0.0350700	−	0.0607430i	0.847958	−	0.530064i	$-0.177832\pi$
$947$	−1.07922	−	1.86927i	−0.0350700	−	0.0607430i	−0.883028	+	0.469321i	$0.844499\pi$
$948$		0			0
$949$	0.111264	−	0.192715i	0.00361179	−	0.00625580i
$950$	−20.8516	+	36.1160i	−0.676515	+	1.17176i
$951$		0			0
$952$	0.983290	+	1.70311i	0.0318686	+	0.0551980i
$953$	53.0480			1.71839			0.859196	−	0.511646i	$-0.170964\pi$
$953$	53.0480			1.71839			0.859196	+	0.511646i	$0.170964\pi$
$954$		0			0
$955$	−76.7738			−2.48434
$956$	3.71565	+	6.43569i	0.120173	+	0.208145i
$957$		0			0
$958$	8.84176	−	15.3144i	0.285664	−	0.494785i
$959$	6.46610	−	11.1996i	0.208801	−	0.361654i
$960$		0			0
$961$	11.6428	+	20.1660i	0.375575	+	0.650515i
$962$	−0.712008			−0.0229561
$963$		0			0
$964$	9.39926			0.302730
$965$	40.9839	+	70.9862i	1.31932	+	2.28513i
$966$		0			0
$967$	−13.5279	+	23.4310i	−0.435029	+	0.753492i	−0.997298	−	0.0734625i	$-0.976595\pi$
$967$	−13.5279	+	23.4310i	−0.435029	+	0.753492i	0.562269	+	0.826954i	$0.309928\pi$
$968$	−7.89926	+	13.6819i	−0.253892	+	0.439753i
$969$		0			0
$970$	8.14468	+	14.1070i	0.261510	+	0.452949i
$971$	−30.3979			−0.975514			−0.487757	−	0.872979i	$-0.662185\pi$
$971$	−30.3979			−0.975514			−0.487757	+	0.872979i	$0.662185\pi$
$972$		0			0
$973$	−29.7628			−0.954150
$974$	11.6218	+	20.1295i	0.372386	+	0.644991i
$975$		0			0
$976$	−4.69963	+	8.13999i	−0.150431	+	0.260555i
$977$	−8.55632	+	14.8200i	−0.273741	+	0.474133i	−0.969817	−	0.243835i	$-0.921594\pi$
$977$	−8.55632	+	14.8200i	−0.273741	+	0.474133i	0.696076	+	0.717968i	$0.254928\pi$
$978$		0			0
$979$	−19.1520	−	33.1722i	−0.612100	−	1.06019i
$980$	−2.96286			−0.0946451
$981$		0			0
$982$	18.5439			0.591761
$983$	20.6861	+	35.8293i	0.659783	+	1.14278i	0.980672	+	0.195661i	$0.0626853\pi$
$983$	20.6861	+	35.8293i	0.659783	+	1.14278i	−0.320888	+	0.947117i	$0.603981\pi$
$984$		0			0
$985$	16.8261	−	29.1437i	0.536126	−	0.928597i
$986$	−0.777472	+	1.34662i	−0.0247597	+	0.0428851i
$987$		0			0
$988$	−3.58836	−	6.21523i	−0.114161	−	0.197733i
$989$	68.9888			2.19372
$990$		0			0
$991$	−38.8552			−1.23427			−0.617137	−	0.786855i	$-0.711708\pi$
$991$	−38.8552			−1.23427			−0.617137	+	0.786855i	$0.711708\pi$
$992$	−1.38874	−	2.40536i	−0.0440924	−	0.0763703i
$993$		0			0
$994$	1.67123	−	2.89465i	0.0530081	−	0.0918127i
$995$	44.2312	−	76.6107i	1.40222	−	2.42872i
$996$		0			0
$997$	2.73167	+	4.73139i	0.0865129	+	0.149845i	0.906035	−	0.423203i	$-0.139094\pi$
$997$	2.73167	+	4.73139i	0.0865129	+	0.149845i	−0.819522	+	0.573048i	$0.805761\pi$
$998$	−31.5475			−0.998619
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.e.d.469.3		6
3.2	odd	2		234.2.e.d.157.3	yes	6
9.2	odd	6		234.2.e.d.79.3	✓	6
9.4	even	3		2106.2.a.r.1.1		3
9.5	odd	6		2106.2.a.q.1.3		3
9.7	even	3	inner	702.2.e.d.235.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.e.d.79.3	✓	6	9.2	odd	6
234.2.e.d.157.3	yes	6	3.2	odd	2
702.2.e.d.235.3		6	9.7	even	3	inner
702.2.e.d.469.3		6	1.1	even	1	trivial
2106.2.a.q.1.3		3	9.5	odd	6
2106.2.a.r.1.1		3	9.4	even	3

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.64400 - 2.84748i) q^{5} +(1.40545 + 2.43430i) q^{7} +1.00000 q^{8} -3.28799 q^{10} +(2.58836 + 4.48318i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.40545 - 2.43430i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.699628 q^{17} +7.17673 q^{19} +(1.64400 + 2.84748i) q^{20} +(2.58836 - 4.48318i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-2.90545 - 5.03238i) q^{25} +1.00000 q^{26} -2.81089 q^{28} +(-1.11126 - 1.92477i) q^{29} +(-1.38874 + 2.40536i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.349814 - 0.605896i) q^{34} +9.24219 q^{35} -0.712008 q^{37} +(-3.58836 - 6.21523i) q^{38} +(1.64400 - 2.84748i) q^{40} +(-0.411636 + 0.712974i) q^{41} +(-5.74907 - 9.95768i) q^{43} -5.17673 q^{44} +6.00000 q^{46} +(0.761450 + 1.31887i) q^{47} +(-0.450558 + 0.780389i) q^{49} +(-2.90545 + 5.03238i) q^{50} +(-0.500000 - 0.866025i) q^{52} +11.0210 q^{53} +17.0210 q^{55} +(1.40545 + 2.43430i) q^{56} +(-1.11126 + 1.92477i) q^{58} +(7.39926 - 12.8159i) q^{59} +(-4.69963 - 8.13999i) q^{61} +2.77747 q^{62} +1.00000 q^{64} +(1.64400 + 2.84748i) q^{65} +(-0.222528 + 0.385430i) q^{67} +(-0.349814 + 0.605896i) q^{68} +(-4.62110 - 8.00397i) q^{70} +1.18911 q^{71} -0.222528 q^{73} +(0.356004 + 0.616617i) q^{74} +(-3.58836 + 6.21523i) q^{76} +(-7.27561 + 12.6017i) q^{77} +(7.87636 + 13.6422i) q^{79} -3.28799 q^{80} +0.823272 q^{82} +(-3.98762 - 6.90676i) q^{83} +(1.15019 - 1.99218i) q^{85} +(-5.74907 + 9.95768i) q^{86} +(2.58836 + 4.48318i) q^{88} -7.39926 q^{89} -2.81089 q^{91} +(-3.00000 - 5.19615i) q^{92} +(0.761450 - 1.31887i) q^{94} +(11.7985 - 20.4356i) q^{95} +(-2.47710 - 4.29046i) q^{97} +0.901116 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 2 q^{7} + 6 q^{8} + 4 q^{10} + 4 q^{11} - 3 q^{13} + 2 q^{14} - 3 q^{16} - 8 q^{17} + 20 q^{19} - 2 q^{20} + 4 q^{22} - 18 q^{23} - 11 q^{25} + 6 q^{26} - 4 q^{28} - 6 q^{29}+ \cdots + 42 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 2 * q^7 + 6 * q^8 + 4 * q^10 + 4 * q^11 - 3 * q^13 + 2 * q^14 - 3 * q^16 - 8 * q^17 + 20 * q^19 - 2 * q^20 + 4 * q^22 - 18 * q^23 - 11 * q^25 + 6 * q^26 - 4 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 + 4 * q^34 + 10 * q^35 - 28 * q^37 - 10 * q^38 - 2 * q^40 - 14 * q^41 - 4 * q^43 - 8 * q^44 + 36 * q^46 + 10 * q^47 - 21 * q^49 - 11 * q^50 - 3 * q^52 + 16 * q^53 + 52 * q^55 + 2 * q^56 - 6 * q^58 + 20 * q^59 - 16 * q^61 + 18 * q^62 + 6 * q^64 - 2 * q^65 + 4 * q^68 - 5 * q^70 + 20 * q^71 + 14 * q^74 - 10 * q^76 + 16 * q^77 + 12 * q^79 + 4 * q^80 + 28 * q^82 + 12 * q^83 + 13 * q^85 - 4 * q^86 + 4 * q^88 - 20 * q^89 - 4 * q^91 - 18 * q^92 + 10 * q^94 + 22 * q^95 - 4 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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