LMFDB - Embedded newform 1014.3.f.e.775.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,3,Mod(577,1014)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1014.577");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			775.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.e.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-1.26795 - 1.26795i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-6.83013 + 6.83013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} -2.53590i q^{10} +(-7.26795 + 7.26795i) q^{11} +3.46410i q^{12} -13.6603 q^{14} +(-2.19615 - 2.19615i) q^{15} -4.00000 q^{16} -18.9282i q^{17} +(3.00000 + 3.00000i) q^{18} +(-23.3923 - 23.3923i) q^{19} +(2.53590 - 2.53590i) q^{20} +(-11.8301 + 11.8301i) q^{21} -14.5359 q^{22} -4.14359i q^{23} +(-3.46410 + 3.46410i) q^{24} -21.7846i q^{25} +5.19615 q^{27} +(-13.6603 - 13.6603i) q^{28} -17.3205 q^{29} -4.39230i q^{30} +(22.1699 + 22.1699i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-12.5885 + 12.5885i) q^{33} +(18.9282 - 18.9282i) q^{34} +17.3205 q^{35} +6.00000i q^{36} +(26.1769 - 26.1769i) q^{37} -46.7846i q^{38} +5.07180 q^{40} +(-18.2487 - 18.2487i) q^{41} -23.6603 q^{42} +15.3397i q^{43} +(-14.5359 - 14.5359i) q^{44} +(-3.80385 - 3.80385i) q^{45} +(4.14359 - 4.14359i) q^{46} +(7.01924 - 7.01924i) q^{47} -6.92820 q^{48} -44.3013i q^{49} +(21.7846 - 21.7846i) q^{50} -32.7846i q^{51} -61.6743 q^{53} +(5.19615 + 5.19615i) q^{54} +18.4308 q^{55} -27.3205i q^{56} +(-40.5167 - 40.5167i) q^{57} +(-17.3205 - 17.3205i) q^{58} +(-46.7321 + 46.7321i) q^{59} +(4.39230 - 4.39230i) q^{60} -7.30127 q^{61} +44.3397i q^{62} +(-20.4904 + 20.4904i) q^{63} -8.00000i q^{64} -25.1769 q^{66} +(-27.7391 - 27.7391i) q^{67} +37.8564 q^{68} -7.17691i q^{69} +(17.3205 + 17.3205i) q^{70} +(-76.0526 - 76.0526i) q^{71} +(-6.00000 + 6.00000i) q^{72} +(-67.4186 + 67.4186i) q^{73} +52.3538 q^{74} -37.7321i q^{75} +(46.7846 - 46.7846i) q^{76} -99.2820i q^{77} +11.8756 q^{79} +(5.07180 + 5.07180i) q^{80} +9.00000 q^{81} -36.4974i q^{82} +(111.033 + 111.033i) q^{83} +(-23.6603 - 23.6603i) q^{84} +(-24.0000 + 24.0000i) q^{85} +(-15.3397 + 15.3397i) q^{86} -30.0000 q^{87} -29.0718i q^{88} +(-118.641 + 118.641i) q^{89} -7.60770i q^{90} +8.28719 q^{92} +(38.3993 + 38.3993i) q^{93} +14.0385 q^{94} +59.3205i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-109.988 - 109.988i) q^{97} +(44.3013 - 44.3013i) q^{98} +(-21.8038 + 21.8038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 12 q^{5} - 10 q^{7} - 8 q^{8} + 12 q^{9} - 36 q^{11} - 20 q^{14} + 12 q^{15} - 16 q^{16} + 12 q^{18} - 52 q^{19} + 24 q^{20} - 30 q^{21} - 72 q^{22} - 20 q^{28} + 106 q^{31} - 16 q^{32}+ \cdots - 108 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 12 * q^5 - 10 * q^7 - 8 * q^8 + 12 * q^9 - 36 * q^11 - 20 * q^14 + 12 * q^15 - 16 * q^16 + 12 * q^18 - 52 * q^19 + 24 * q^20 - 30 * q^21 - 72 * q^22 - 20 * q^28 + 106 * q^31 - 16 * q^32 + 12 * q^33 + 48 * q^34 - 20 * q^37 + 48 * q^40 + 24 * q^41 - 60 * q^42 - 72 * q^44 - 36 * q^45 + 72 * q^46 + 132 * q^47 + 4 * q^50 + 72 * q^53 + 240 * q^55 - 72 * q^57 - 180 * q^59 - 24 * q^60 + 144 * q^61 - 30 * q^63 + 24 * q^66 + 38 * q^67 + 96 * q^68 - 228 * q^71 - 24 * q^72 - 190 * q^73 - 40 * q^74 + 104 * q^76 + 96 * q^79 + 48 * q^80 + 36 * q^81 + 264 * q^83 - 60 * q^84 - 96 * q^85 - 96 * q^86 - 120 * q^87 - 336 * q^89 + 144 * q^92 - 30 * q^93 + 264 * q^94 - 194 * q^97 + 4 * q^98 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$			2.00000i			0.500000i
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	0.568851	−	0.822441i	$-0.307388\pi$
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	−0.822441	+	0.568851i	$0.807388\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	−6.83013	+	6.83013i	−0.975732	+	0.975732i	−0.999712	−	0.0239800i	$-0.992366\pi$
$7$	−6.83013	+	6.83013i	−0.975732	+	0.975732i	0.0239800	+	0.999712i	$0.492366\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	3.00000			0.333333
$10$		−	2.53590i		−	0.253590i
$11$	−7.26795	+	7.26795i	−0.660723	+	0.660723i	−0.955550	−	0.294828i	$-0.904738\pi$
$11$	−7.26795	+	7.26795i	−0.660723	+	0.660723i	0.294828	+	0.955550i	$0.404738\pi$
$12$			3.46410i			0.288675i
$13$		0			0
$13$		0			0
$14$	−13.6603			−0.975732
$15$	−2.19615	−	2.19615i	−0.146410	−	0.146410i
$16$	−4.00000			−0.250000
$17$		−	18.9282i		−	1.11342i	−0.830706	−	0.556712i	$-0.812063\pi$
$17$		−	18.9282i		−	1.11342i	0.830706	−	0.556712i	$-0.187937\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$	−23.3923	−	23.3923i	−1.23117	−	1.23117i	−0.963513	−	0.267661i	$-0.913749\pi$
$19$	−23.3923	−	23.3923i	−1.23117	−	1.23117i	−0.267661	−	0.963513i	$-0.586251\pi$
$20$	2.53590	−	2.53590i	0.126795	−	0.126795i
$21$	−11.8301	+	11.8301i	−0.563339	+	0.563339i
$22$	−14.5359			−0.660723
$23$		−	4.14359i		−	0.180156i	−0.995935	−	0.0900781i	$-0.971288\pi$
$23$		−	4.14359i		−	0.180156i	0.995935	−	0.0900781i	$-0.0287117\pi$
$24$	−3.46410	+	3.46410i	−0.144338	+	0.144338i
$25$		−	21.7846i		−	0.871384i
$26$		0			0
$27$	5.19615			0.192450
$28$	−13.6603	−	13.6603i	−0.487866	−	0.487866i
$29$	−17.3205			−0.597259			−0.298629	−	0.954369i	$-0.596529\pi$
$29$	−17.3205			−0.597259			−0.298629	+	0.954369i	$0.596529\pi$
$30$		−	4.39230i		−	0.146410i
$31$	22.1699	+	22.1699i	0.715157	+	0.715157i	0.967609	−	0.252452i	$-0.0812370\pi$
$31$	22.1699	+	22.1699i	0.715157	+	0.715157i	−0.252452	+	0.967609i	$0.581237\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−12.5885	+	12.5885i	−0.381468	+	0.381468i
$34$	18.9282	−	18.9282i	0.556712	−	0.556712i
$35$	17.3205			0.494872
$36$			6.00000i			0.166667i
$37$	26.1769	−	26.1769i	0.707484	−	0.707484i	−0.258521	−	0.966006i	$-0.583235\pi$
$37$	26.1769	−	26.1769i	0.707484	−	0.707484i	0.966006	+	0.258521i	$0.0832352\pi$
$38$		−	46.7846i		−	1.23117i
$39$		0			0
$40$	5.07180			0.126795
$41$	−18.2487	−	18.2487i	−0.445091	−	0.445091i	0.448628	−	0.893719i	$-0.351913\pi$
$41$	−18.2487	−	18.2487i	−0.445091	−	0.445091i	−0.893719	+	0.448628i	$0.851913\pi$
$42$	−23.6603			−0.563339
$43$			15.3397i			0.356738i	0.983964	+	0.178369i	$0.0570821\pi$
$43$			15.3397i			0.356738i	−0.983964	+	0.178369i	$0.942918\pi$
$44$	−14.5359	−	14.5359i	−0.330361	−	0.330361i
$45$	−3.80385	−	3.80385i	−0.0845299	−	0.0845299i
$46$	4.14359	−	4.14359i	0.0900781	−	0.0900781i
$47$	7.01924	−	7.01924i	0.149345	−	0.149345i	−0.628480	−	0.777826i	$-0.716323\pi$
$47$	7.01924	−	7.01924i	0.149345	−	0.149345i	0.777826	+	0.628480i	$0.216323\pi$
$48$	−6.92820			−0.144338
$49$		−	44.3013i		−	0.904108i
$50$	21.7846	−	21.7846i	0.435692	−	0.435692i
$51$		−	32.7846i		−	0.642835i
$52$		0			0
$53$	−61.6743			−1.16367			−0.581833	−	0.813308i	$-0.697664\pi$
$53$	−61.6743			−1.16367			−0.581833	+	0.813308i	$0.697664\pi$
$54$	5.19615	+	5.19615i	0.0962250	+	0.0962250i
$55$	18.4308			0.335105
$56$		−	27.3205i		−	0.487866i
$57$	−40.5167	−	40.5167i	−0.710819	−	0.710819i
$58$	−17.3205	−	17.3205i	−0.298629	−	0.298629i
$59$	−46.7321	+	46.7321i	−0.792069	+	0.792069i	−0.981830	−	0.189762i	$-0.939229\pi$
$59$	−46.7321	+	46.7321i	−0.792069	+	0.792069i	0.189762	+	0.981830i	$0.439229\pi$
$60$	4.39230	−	4.39230i	0.0732051	−	0.0732051i
$61$	−7.30127			−0.119693			−0.0598465	−	0.998208i	$-0.519061\pi$
$61$	−7.30127			−0.119693			−0.0598465	+	0.998208i	$0.519061\pi$
$62$			44.3397i			0.715157i
$63$	−20.4904	+	20.4904i	−0.325244	+	0.325244i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−25.1769			−0.381468
$67$	−27.7391	−	27.7391i	−0.414016	−	0.414016i	0.469119	−	0.883135i	$-0.344572\pi$
$67$	−27.7391	−	27.7391i	−0.414016	−	0.414016i	−0.883135	+	0.469119i	$0.844572\pi$
$68$	37.8564			0.556712
$69$		−	7.17691i		−	0.104013i
$70$	17.3205	+	17.3205i	0.247436	+	0.247436i
$71$	−76.0526	−	76.0526i	−1.07116	−	1.07116i	−0.997266	−	0.0738969i	$-0.976456\pi$
$71$	−76.0526	−	76.0526i	−1.07116	−	1.07116i	−0.0738969	−	0.997266i	$-0.523544\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−67.4186	+	67.4186i	−0.923542	+	0.923542i	−0.997278	−	0.0737356i	$-0.976508\pi$
$73$	−67.4186	+	67.4186i	−0.923542	+	0.923542i	0.0737356	+	0.997278i	$0.476508\pi$
$74$	52.3538			0.707484
$75$		−	37.7321i		−	0.503094i
$76$	46.7846	−	46.7846i	0.615587	−	0.615587i
$77$		−	99.2820i		−	1.28938i
$78$		0			0
$79$	11.8756			0.150325			0.0751623	−	0.997171i	$-0.476053\pi$
$79$	11.8756			0.150325			0.0751623	+	0.997171i	$0.476053\pi$
$80$	5.07180	+	5.07180i	0.0633975	+	0.0633975i
$81$	9.00000			0.111111
$82$		−	36.4974i		−	0.445091i
$83$	111.033	+	111.033i	1.33775	+	1.33775i	0.898235	+	0.439516i	$0.144850\pi$
$83$	111.033	+	111.033i	1.33775	+	1.33775i	0.439516	+	0.898235i	$0.355150\pi$
$84$	−23.6603	−	23.6603i	−0.281670	−	0.281670i
$85$	−24.0000	+	24.0000i	−0.282353	+	0.282353i
$86$	−15.3397	+	15.3397i	−0.178369	+	0.178369i
$87$	−30.0000			−0.344828
$88$		−	29.0718i		−	0.330361i
$89$	−118.641	+	118.641i	−1.33305	+	1.33305i	−0.430413	+	0.902632i	$0.641632\pi$
$89$	−118.641	+	118.641i	−1.33305	+	1.33305i	−0.902632	+	0.430413i	$0.858368\pi$
$90$		−	7.60770i		−	0.0845299i
$91$		0			0
$92$	8.28719			0.0900781
$93$	38.3993	+	38.3993i	0.412896	+	0.412896i
$94$	14.0385			0.149345
$95$			59.3205i			0.624426i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	−109.988	−	109.988i	−1.13389	−	1.13389i	−0.989524	−	0.144371i	$-0.953884\pi$
$97$	−109.988	−	109.988i	−1.13389	−	1.13389i	−0.144371	−	0.989524i	$-0.546116\pi$
$98$	44.3013	−	44.3013i	0.452054	−	0.452054i
$99$	−21.8038	+	21.8038i	−0.220241	+	0.220241i
$100$	43.5692			0.435692
$101$		−	186.813i		−	1.84963i	−0.380415	−	0.924816i	$-0.624219\pi$
$101$		−	186.813i		−	1.84963i	0.380415	−	0.924816i	$-0.375781\pi$
$102$	32.7846	−	32.7846i	0.321418	−	0.321418i
$103$			83.2628i			0.808377i	0.914676	+	0.404188i	$0.132446\pi$
$103$			83.2628i			0.808377i	−0.914676	+	0.404188i	$0.867554\pi$
$104$		0			0
$105$	30.0000			0.285714
$106$	−61.6743	−	61.6743i	−0.581833	−	0.581833i
$107$	102.497			0.957920			0.478960	−	0.877837i	$-0.341014\pi$
$107$	102.497			0.957920			0.478960	+	0.877837i	$0.341014\pi$
$108$			10.3923i			0.0962250i
$109$	48.1891	+	48.1891i	0.442102	+	0.442102i	0.892718	−	0.450616i	$-0.148796\pi$
$109$	48.1891	+	48.1891i	0.442102	+	0.442102i	−0.450616	+	0.892718i	$0.648796\pi$
$110$	18.4308	+	18.4308i	0.167553	+	0.167553i
$111$	45.3397	−	45.3397i	0.408466	−	0.408466i
$112$	27.3205	−	27.3205i	0.243933	−	0.243933i
$113$	−45.2154			−0.400136			−0.200068	−	0.979782i	$-0.564116\pi$
$113$	−45.2154			−0.400136			−0.200068	+	0.979782i	$0.564116\pi$
$114$		−	81.0333i		−	0.710819i
$115$	−5.25387	+	5.25387i	−0.0456858	+	0.0456858i
$116$		−	34.6410i		−	0.298629i
$117$		0			0
$118$	−93.4641			−0.792069
$119$	129.282	+	129.282i	1.08640	+	1.08640i
$120$	8.78461			0.0732051
$121$			15.3538i			0.126891i
$122$	−7.30127	−	7.30127i	−0.0598465	−	0.0598465i
$123$	−31.6077	−	31.6077i	−0.256973	−	0.256973i
$124$	−44.3397	+	44.3397i	−0.357579	+	0.357579i
$125$	−59.3205	+	59.3205i	−0.474564	+	0.474564i
$126$	−40.9808			−0.325244
$127$			236.846i			1.86493i	0.361260	+	0.932465i	$0.382347\pi$
$127$			236.846i			1.86493i	−0.361260	+	0.932465i	$0.617653\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			26.5692i			0.205963i
$130$		0			0
$131$	−209.636			−1.60027			−0.800137	−	0.599817i	$-0.795240\pi$
$131$	−209.636			−1.60027			−0.800137	+	0.599817i	$0.795240\pi$
$132$	−25.1769	−	25.1769i	−0.190734	−	0.190734i
$133$	319.545			2.40259
$134$		−	55.4782i		−	0.414016i
$135$	−6.58846	−	6.58846i	−0.0488034	−	0.0488034i
$136$	37.8564	+	37.8564i	0.278356	+	0.278356i
$137$	80.5359	−	80.5359i	0.587853	−	0.587853i	−0.349196	−	0.937050i	$-0.613545\pi$
$137$	80.5359	−	80.5359i	0.587853	−	0.587853i	0.937050	+	0.349196i	$0.113545\pi$
$138$	7.17691	−	7.17691i	0.0520066	−	0.0520066i
$139$	−95.7077			−0.688544			−0.344272	−	0.938870i	$-0.611874\pi$
$139$	−95.7077			−0.688544			−0.344272	+	0.938870i	$0.611874\pi$
$140$			34.6410i			0.247436i
$141$	12.1577	−	12.1577i	0.0862247	−	0.0862247i
$142$		−	152.105i		−	1.07116i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	21.9615	+	21.9615i	0.151459	+	0.151459i
$146$	−134.837			−0.923542
$147$		−	76.7321i		−	0.521987i
$148$	52.3538	+	52.3538i	0.353742	+	0.353742i
$149$	40.2102	+	40.2102i	0.269867	+	0.269867i	0.829047	−	0.559179i	$-0.188884\pi$
$149$	40.2102	+	40.2102i	0.269867	+	0.269867i	−0.559179	+	0.829047i	$0.688884\pi$
$150$	37.7321	−	37.7321i	0.251547	−	0.251547i
$151$	−55.0385	+	55.0385i	−0.364493	+	0.364493i	−0.865464	−	0.500971i	$-0.832976\pi$
$151$	−55.0385	+	55.0385i	−0.364493	+	0.364493i	0.500971	+	0.865464i	$0.332976\pi$
$152$	93.5692			0.615587
$153$		−	56.7846i		−	0.371141i
$154$	99.2820	−	99.2820i	0.644689	−	0.644689i
$155$		−	56.2205i		−	0.362713i
$156$		0			0
$157$	55.4308			0.353062			0.176531	−	0.984295i	$-0.443512\pi$
$157$	55.4308			0.353062			0.176531	+	0.984295i	$0.443512\pi$
$158$	11.8756	+	11.8756i	0.0751623	+	0.0751623i
$159$	−106.823			−0.671843
$160$			10.1436i			0.0633975i
$161$	28.3013	+	28.3013i	0.175784	+	0.175784i
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−144.653	+	144.653i	−0.887443	+	0.887443i	−0.994277	−	0.106834i	$-0.965929\pi$
$163$	−144.653	+	144.653i	−0.887443	+	0.887443i	0.106834	+	0.994277i	$0.465929\pi$
$164$	36.4974	−	36.4974i	0.222545	−	0.222545i
$165$	31.9230			0.193473
$166$			222.067i			1.33775i
$167$	114.431	−	114.431i	0.685214	−	0.685214i	−0.275956	−	0.961170i	$-0.588994\pi$
$167$	114.431	−	114.431i	0.685214	−	0.685214i	0.961170	+	0.275956i	$0.0889944\pi$
$168$		−	47.3205i		−	0.281670i
$169$		0			0
$170$	−48.0000			−0.282353
$171$	−70.1769	−	70.1769i	−0.410391	−	0.410391i
$172$	−30.6795			−0.178369
$173$		−	268.459i		−	1.55179i	−0.630865	−	0.775893i	$-0.717300\pi$
$173$		−	268.459i		−	1.55179i	0.630865	−	0.775893i	$-0.282700\pi$
$174$	−30.0000	−	30.0000i	−0.172414	−	0.172414i
$175$	148.792	+	148.792i	0.850238	+	0.850238i
$176$	29.0718	−	29.0718i	0.165181	−	0.165181i
$177$	−80.9423	+	80.9423i	−0.457301	+	0.457301i
$178$	−237.282			−1.33305
$179$		−	285.779i		−	1.59653i	−0.602304	−	0.798267i	$-0.705751\pi$
$179$		−	285.779i		−	1.59653i	0.602304	−	0.798267i	$-0.294249\pi$
$180$	7.60770	−	7.60770i	0.0422650	−	0.0422650i
$181$			177.646i			0.981471i	0.871309	+	0.490735i	$0.163272\pi$
$181$			177.646i			0.981471i	−0.871309	+	0.490735i	$0.836728\pi$
$182$		0			0
$183$	−12.6462			−0.0691048
$184$	8.28719	+	8.28719i	0.0450391	+	0.0450391i
$185$	−66.3820			−0.358822
$186$			76.7987i			0.412896i
$187$	137.569	+	137.569i	0.735664	+	0.735664i
$188$	14.0385	+	14.0385i	0.0746727	+	0.0746727i
$189$	−35.4904	+	35.4904i	−0.187780	+	0.187780i
$190$	−59.3205	+	59.3205i	−0.312213	+	0.312213i
$191$	197.321			1.03309			0.516546	−	0.856260i	$-0.327218\pi$
$191$	197.321			1.03309			0.516546	+	0.856260i	$0.327218\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	14.8494	−	14.8494i	0.0769397	−	0.0769397i	−0.667590	−	0.744529i	$-0.732674\pi$
$193$	14.8494	−	14.8494i	0.0769397	−	0.0769397i	0.744529	+	0.667590i	$0.232674\pi$
$194$		−	219.976i		−	1.13389i
$195$		0			0
$196$	88.6025			0.452054
$197$	106.956	+	106.956i	0.542926	+	0.542926i	0.924385	−	0.381460i	$-0.124579\pi$
$197$	106.956	+	106.956i	0.542926	+	0.542926i	−0.381460	+	0.924385i	$0.624579\pi$
$198$	−43.6077			−0.220241
$199$		−	22.2154i		−	0.111635i	−0.998441	−	0.0558176i	$-0.982223\pi$
$199$		−	22.2154i		−	0.111635i	0.998441	−	0.0558176i	$-0.0177765\pi$
$200$	43.5692	+	43.5692i	0.217846	+	0.217846i
$201$	−48.0455	−	48.0455i	−0.239032	−	0.239032i
$202$	186.813	−	186.813i	0.924816	−	0.924816i
$203$	118.301	−	118.301i	0.582765	−	0.582765i
$204$	65.5692			0.321418
$205$			46.2769i			0.225741i
$206$	−83.2628	+	83.2628i	−0.404188	+	0.404188i
$207$		−	12.4308i		−	0.0600521i
$208$		0			0
$209$	340.028			1.62693
$210$	30.0000	+	30.0000i	0.142857	+	0.142857i
$211$	64.2013			0.304272			0.152136	−	0.988360i	$-0.451385\pi$
$211$	64.2013			0.304272			0.152136	+	0.988360i	$0.451385\pi$
$212$		−	123.349i		−	0.581833i
$213$	−131.727	−	131.727i	−0.618436	−	0.618436i
$214$	102.497	+	102.497i	0.478960	+	0.478960i
$215$	19.4500	−	19.4500i	0.0904652	−	0.0904652i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	−302.846			−1.39560
$218$			96.3782i			0.442102i
$219$	−116.772	+	116.772i	−0.533207	+	0.533207i
$220$			36.8616i			0.167553i
$221$		0			0
$222$	90.6795			0.408466
$223$	−154.531	−	154.531i	−0.692963	−	0.692963i	0.269920	−	0.962883i	$-0.413003\pi$
$223$	−154.531	−	154.531i	−0.692963	−	0.692963i	−0.962883	+	0.269920i	$0.913003\pi$
$224$	54.6410			0.243933
$225$		−	65.3538i		−	0.290461i
$226$	−45.2154	−	45.2154i	−0.200068	−	0.200068i
$227$	−45.7128	−	45.7128i	−0.201378	−	0.201378i	0.599212	−	0.800590i	$-0.295481\pi$
$227$	−45.7128	−	45.7128i	−0.201378	−	0.201378i	−0.800590	+	0.599212i	$0.795481\pi$
$228$	81.0333	−	81.0333i	0.355409	−	0.355409i
$229$	58.6846	−	58.6846i	0.256265	−	0.256265i	−0.567268	−	0.823533i	$-0.692000\pi$
$229$	58.6846	−	58.6846i	0.256265	−	0.256265i	0.823533	+	0.567268i	$0.192000\pi$
$230$	−10.5077			−0.0456858
$231$		−	171.962i		−	0.744422i
$232$	34.6410	−	34.6410i	0.149315	−	0.149315i
$233$			380.669i			1.63377i	0.576798	+	0.816887i	$0.304302\pi$
$233$			380.669i			1.63377i	−0.576798	+	0.816887i	$0.695698\pi$
$234$		0			0
$235$	−17.8001			−0.0757450
$236$	−93.4641	−	93.4641i	−0.396034	−	0.396034i
$237$	20.5692			0.0867900
$238$			258.564i			1.08640i
$239$	−167.138	−	167.138i	−0.699324	−	0.699324i	0.264941	−	0.964265i	$-0.414648\pi$
$239$	−167.138	−	167.138i	−0.699324	−	0.699324i	−0.964265	+	0.264941i	$0.914648\pi$
$240$	8.78461	+	8.78461i	0.0366025	+	0.0366025i
$241$	2.17691	−	2.17691i	0.00903284	−	0.00903284i	−0.702576	−	0.711609i	$-0.747967\pi$
$241$	2.17691	−	2.17691i	0.00903284	−	0.00903284i	0.711609	+	0.702576i	$0.247967\pi$
$242$	−15.3538	+	15.3538i	−0.0634456	+	0.0634456i
$243$	15.5885			0.0641500
$244$		−	14.6025i		−	0.0598465i
$245$	−56.1718	+	56.1718i	−0.229272	+	0.229272i
$246$		−	63.2154i		−	0.256973i
$247$		0			0
$248$	−88.6795			−0.357579
$249$	192.315	+	192.315i	0.772351	+	0.772351i
$250$	−118.641			−0.474564
$251$			208.708i			0.831505i	0.909478	+	0.415752i	$0.136482\pi$
$251$			208.708i			0.831505i	−0.909478	+	0.415752i	$0.863518\pi$
$252$	−40.9808	−	40.9808i	−0.162622	−	0.162622i
$253$	30.1154	+	30.1154i	0.119033	+	0.119033i
$254$	−236.846	+	236.846i	−0.932465	+	0.932465i
$255$	−41.5692	+	41.5692i	−0.163017	+	0.163017i
$256$	16.0000			0.0625000
$257$			74.2205i			0.288796i	0.989520	+	0.144398i	$0.0461245\pi$
$257$			74.2205i			0.288796i	−0.989520	+	0.144398i	$0.953875\pi$
$258$	−26.5692	+	26.5692i	−0.102981	+	0.102981i
$259$			357.583i			1.38063i
$260$		0			0
$261$	−51.9615			−0.199086
$262$	−209.636	−	209.636i	−0.800137	−	0.800137i
$263$	−24.3641			−0.0926393			−0.0463197	−	0.998927i	$-0.514749\pi$
$263$	−24.3641			−0.0926393			−0.0463197	+	0.998927i	$0.514749\pi$
$264$		−	50.3538i		−	0.190734i
$265$	78.1999	+	78.1999i	0.295094	+	0.295094i
$266$	319.545	+	319.545i	1.20130	+	1.20130i
$267$	−205.492	+	205.492i	−0.769634	+	0.769634i
$268$	55.4782	−	55.4782i	0.207008	−	0.207008i
$269$	−175.741			−0.653312			−0.326656	−	0.945143i	$-0.605922\pi$
$269$	−175.741			−0.653312			−0.326656	+	0.945143i	$0.605922\pi$
$270$		−	13.1769i		−	0.0488034i
$271$	−197.046	+	197.046i	−0.727105	+	0.727105i	−0.970042	−	0.242937i	$-0.921889\pi$
$271$	−197.046	+	197.046i	−0.727105	+	0.727105i	0.242937	+	0.970042i	$0.421889\pi$
$272$			75.7128i			0.278356i
$273$		0			0
$274$	161.072			0.587853
$275$	158.329	+	158.329i	0.575743	+	0.575743i
$276$	14.3538			0.0520066
$277$			446.985i			1.61366i	0.590782	+	0.806831i	$0.298819\pi$
$277$			446.985i			1.61366i	−0.590782	+	0.806831i	$0.701181\pi$
$278$	−95.7077	−	95.7077i	−0.344272	−	0.344272i
$279$	66.5096	+	66.5096i	0.238386	+	0.238386i
$280$	−34.6410	+	34.6410i	−0.123718	+	0.123718i
$281$	−5.54483	+	5.54483i	−0.0197325	+	0.0197325i	−0.716904	−	0.697172i	$-0.754442\pi$
$281$	−5.54483	+	5.54483i	−0.0197325	+	0.0197325i	0.697172	+	0.716904i	$0.254442\pi$
$282$	24.3154			0.0862247
$283$			16.6462i			0.0588204i	0.999567	+	0.0294102i	$0.00936291\pi$
$283$			16.6462i			0.0588204i	−0.999567	+	0.0294102i	$0.990637\pi$
$284$	152.105	−	152.105i	0.535581	−	0.535581i
$285$			102.746i			0.360513i
$286$		0			0
$287$	249.282			0.868579
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$	−69.2769			−0.239712
$290$			43.9230i			0.151459i
$291$	−190.504	−	190.504i	−0.654655	−	0.654655i
$292$	−134.837	−	134.837i	−0.461771	−	0.461771i
$293$	132.473	−	132.473i	0.452126	−	0.452126i	−0.443933	−	0.896060i	$-0.646417\pi$
$293$	132.473	−	132.473i	0.452126	−	0.452126i	0.896060	+	0.443933i	$0.146417\pi$
$294$	76.7321	−	76.7321i	0.260993	−	0.260993i
$295$	118.508			0.401721
$296$			104.708i			0.353742i
$297$	−37.7654	+	37.7654i	−0.127156	+	0.127156i
$298$			80.4205i			0.269867i
$299$		0			0
$300$	75.4641			0.251547
$301$	−104.772	−	104.772i	−0.348081	−	0.348081i
$302$	−110.077			−0.364493
$303$		−	323.569i		−	1.06789i
$304$	93.5692	+	93.5692i	0.307793	+	0.307793i
$305$	9.25764	+	9.25764i	0.0303529	+	0.0303529i
$306$	56.7846	−	56.7846i	0.185571	−	0.185571i
$307$	375.069	−	375.069i	1.22172	−	1.22172i	0.254702	−	0.967020i	$-0.418023\pi$
$307$	375.069	−	375.069i	1.22172	−	1.22172i	0.967020	−	0.254702i	$-0.0819774\pi$
$308$	198.564			0.644689
$309$			144.215i			0.466716i
$310$	56.2205	−	56.2205i	0.181357	−	0.181357i
$311$		−	296.238i		−	0.952535i	−0.879300	−	0.476268i	$-0.841989\pi$
$311$		−	296.238i		−	0.952535i	0.879300	−	0.476268i	$-0.158011\pi$
$312$		0			0
$313$	118.286			0.377910			0.188955	−	0.981986i	$-0.439490\pi$
$313$	118.286			0.377910			0.188955	+	0.981986i	$0.439490\pi$
$314$	55.4308	+	55.4308i	0.176531	+	0.176531i
$315$	51.9615			0.164957
$316$			23.7513i			0.0751623i
$317$	−280.708	−	280.708i	−0.885513	−	0.885513i	0.108575	−	0.994088i	$-0.465371\pi$
$317$	−280.708	−	280.708i	−0.885513	−	0.885513i	−0.994088	+	0.108575i	$0.965371\pi$
$318$	−106.823	−	106.823i	−0.335922	−	0.335922i
$319$	125.885	−	125.885i	0.394622	−	0.394622i
$320$	−10.1436	+	10.1436i	−0.0316987	+	0.0316987i
$321$	177.531			0.553055
$322$			56.6025i			0.175784i
$323$	−442.774	+	442.774i	−1.37082	+	1.37082i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−289.306			−0.887443
$327$	83.4660	+	83.4660i	0.255248	+	0.255248i
$328$	72.9948			0.222545
$329$			95.8846i			0.291442i
$330$	31.9230	+	31.9230i	0.0967365	+	0.0967365i
$331$	100.624	+	100.624i	0.303999	+	0.303999i	0.842576	−	0.538577i	$-0.181038\pi$
$331$	100.624	+	100.624i	0.303999	+	0.303999i	−0.538577	+	0.842576i	$0.681038\pi$
$332$	−222.067	+	222.067i	−0.668875	+	0.668875i
$333$	78.5307	−	78.5307i	0.235828	−	0.235828i
$334$	228.862			0.685214
$335$			70.3435i			0.209981i
$336$	47.3205	−	47.3205i	0.140835	−	0.140835i
$337$			347.508i			1.03118i	0.856835	+	0.515590i	$0.172427\pi$
$337$			347.508i			1.03118i	−0.856835	+	0.515590i	$0.827573\pi$
$338$		0			0
$339$	−78.3154			−0.231019
$340$	−48.0000	−	48.0000i	−0.141176	−	0.141176i
$341$	−322.259			−0.945041
$342$		−	140.354i		−	0.410391i
$343$	−32.0929	−	32.0929i	−0.0935654	−	0.0935654i
$344$	−30.6795	−	30.6795i	−0.0891846	−	0.0891846i
$345$	−9.09996	+	9.09996i	−0.0263767	+	0.0263767i
$346$	268.459	−	268.459i	0.775893	−	0.775893i
$347$	437.703			1.26139			0.630695	−	0.776031i	$-0.282770\pi$
$347$	437.703			1.26139			0.630695	+	0.776031i	$0.282770\pi$
$348$		−	60.0000i		−	0.172414i
$349$	316.897	−	316.897i	0.908014	−	0.908014i	−0.0880981	−	0.996112i	$-0.528079\pi$
$349$	316.897	−	316.897i	0.908014	−	0.908014i	0.996112	+	0.0880981i	$0.0280789\pi$
$350$			297.583i			0.850238i
$351$		0			0
$352$	58.1436			0.165181
$353$	−415.037	−	415.037i	−1.17574	−	1.17574i	−0.980818	−	0.194924i	$-0.937554\pi$
$353$	−415.037	−	415.037i	−1.17574	−	1.17574i	−0.194924	−	0.980818i	$-0.562446\pi$
$354$	−161.885			−0.457301
$355$			192.862i			0.543272i
$356$	−237.282	−	237.282i	−0.666523	−	0.666523i
$357$	223.923	+	223.923i	0.627235	+	0.627235i
$358$	285.779	−	285.779i	0.798267	−	0.798267i
$359$	64.2769	−	64.2769i	0.179044	−	0.179044i	−0.611895	−	0.790939i	$-0.709592\pi$
$359$	64.2769	−	64.2769i	0.179044	−	0.179044i	0.790939	+	0.611895i	$0.209592\pi$
$360$	15.2154			0.0422650
$361$			733.400i			2.03158i
$362$	−177.646	+	177.646i	−0.490735	+	0.490735i
$363$			26.5936i			0.0732606i
$364$		0			0
$365$	170.967			0.468402
$366$	−12.6462	−	12.6462i	−0.0345524	−	0.0345524i
$367$	−217.785			−0.593419			−0.296709	−	0.954968i	$-0.595889\pi$
$367$	−217.785			−0.593419			−0.296709	+	0.954968i	$0.595889\pi$
$368$			16.5744i			0.0450391i
$369$	−54.7461	−	54.7461i	−0.148364	−	0.148364i
$370$	−66.3820	−	66.3820i	−0.179411	−	0.179411i
$371$	421.244	−	421.244i	1.13543	−	1.13543i
$372$	−76.7987	+	76.7987i	−0.206448	+	0.206448i
$373$	−219.606			−0.588757			−0.294378	−	0.955689i	$-0.595113\pi$
$373$	−219.606			−0.588757			−0.294378	+	0.955689i	$0.595113\pi$
$374$			275.138i			0.735664i
$375$	−102.746	+	102.746i	−0.273990	+	0.273990i
$376$			28.0770i			0.0746727i
$377$		0			0
$378$	−70.9808			−0.187780
$379$	137.107	+	137.107i	0.361760	+	0.361760i	0.864461	−	0.502701i	$-0.167660\pi$
$379$	137.107	+	137.107i	0.361760	+	0.361760i	−0.502701	+	0.864461i	$0.667660\pi$
$380$	−118.641			−0.312213
$381$			410.229i			1.07672i
$382$	197.321	+	197.321i	0.516546	+	0.516546i
$383$	−137.751	−	137.751i	−0.359664	−	0.359664i	0.504025	−	0.863689i	$-0.331852\pi$
$383$	−137.751	−	137.751i	−0.359664	−	0.359664i	−0.863689	+	0.504025i	$0.831852\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	−125.885	+	125.885i	−0.326973	+	0.326973i
$386$	29.6987			0.0769397
$387$			46.0192i			0.118913i
$388$	219.976	−	219.976i	0.566947	−	0.566947i
$389$		−	17.7513i		−	0.0456331i	−0.999740	−	0.0228166i	$-0.992737\pi$
$389$		−	17.7513i		−	0.0456331i	0.999740	−	0.0228166i	$-0.00726337\pi$
$390$		0			0
$391$	−78.4308			−0.200590
$392$	88.6025	+	88.6025i	0.226027	+	0.226027i
$393$	−363.100			−0.923918
$394$			213.913i			0.542926i
$395$	−15.0577	−	15.0577i	−0.0381208	−	0.0381208i
$396$	−43.6077	−	43.6077i	−0.110120	−	0.110120i
$397$	−238.643	+	238.643i	−0.601116	+	0.601116i	−0.940609	−	0.339493i	$-0.889745\pi$
$397$	−238.643	+	238.643i	−0.601116	+	0.601116i	0.339493	+	0.940609i	$0.389745\pi$
$398$	22.2154	−	22.2154i	0.0558176	−	0.0558176i
$399$	553.468			1.38714
$400$			87.1384i			0.217846i
$401$	363.415	−	363.415i	0.906273	−	0.906273i	−0.0896965	−	0.995969i	$-0.528590\pi$
$401$	363.415	−	363.415i	0.906273	−	0.906273i	0.995969	+	0.0896965i	$0.0285897\pi$
$402$		−	96.0910i		−	0.239032i
$403$		0			0
$404$	373.626			0.924816
$405$	−11.4115	−	11.4115i	−0.0281766	−	0.0281766i
$406$	236.603			0.582765
$407$			380.505i			0.934902i
$408$	65.5692	+	65.5692i	0.160709	+	0.160709i
$409$	412.026	+	412.026i	1.00740	+	1.00740i	0.999972	+	0.00742680i	$0.00236404\pi$
$409$	412.026	+	412.026i	1.00740	+	1.00740i	0.00742680	+	0.999972i	$0.497636\pi$
$410$	−46.2769	+	46.2769i	−0.112870	+	0.112870i
$411$	139.492	−	139.492i	0.339397	−	0.339397i
$412$	−166.526			−0.404188
$413$		−	638.372i		−	1.54569i
$414$	12.4308	−	12.4308i	0.0300260	−	0.0300260i
$415$		−	281.569i		−	0.678480i
$416$		0			0
$417$	−165.771			−0.397531
$418$	340.028	+	340.028i	0.813465	+	0.813465i
$419$	−782.354			−1.86719			−0.933596	−	0.358326i	$-0.883348\pi$
$419$	−782.354			−1.86719			−0.933596	+	0.358326i	$0.883348\pi$
$420$			60.0000i			0.142857i
$421$	−27.0352	−	27.0352i	−0.0642166	−	0.0642166i	0.674269	−	0.738486i	$-0.264459\pi$
$421$	−27.0352	−	27.0352i	−0.0642166	−	0.0642166i	−0.738486	+	0.674269i	$0.764459\pi$
$422$	64.2013	+	64.2013i	0.152136	+	0.152136i
$423$	21.0577	−	21.0577i	0.0497818	−	0.0497818i
$424$	123.349	−	123.349i	0.290917	−	0.290917i
$425$	−412.344			−0.970220
$426$		−	263.454i		−	0.618436i
$427$	49.8686	−	49.8686i	0.116788	−	0.116788i
$428$			204.995i			0.478960i
$429$		0			0
$430$	38.9000			0.0904652
$431$	445.310	+	445.310i	1.03320	+	1.03320i	0.999430	+	0.0337728i	$0.0107523\pi$
$431$	445.310	+	445.310i	1.03320	+	1.03320i	0.0337728	+	0.999430i	$0.489248\pi$
$432$	−20.7846			−0.0481125
$433$			237.785i			0.549156i	0.961565	+	0.274578i	$0.0885382\pi$
$433$			237.785i			0.549156i	−0.961565	+	0.274578i	$0.911462\pi$
$434$	−302.846	−	302.846i	−0.697802	−	0.697802i
$435$	38.0385	+	38.0385i	0.0874448	+	0.0874448i
$436$	−96.3782	+	96.3782i	−0.221051	+	0.221051i
$437$	−96.9282	+	96.9282i	−0.221804	+	0.221804i
$438$	−233.545			−0.533207
$439$			689.463i			1.57053i	0.619160	+	0.785265i	$0.287473\pi$
$439$			689.463i			1.57053i	−0.619160	+	0.785265i	$0.712527\pi$
$440$	−36.8616	+	36.8616i	−0.0837763	+	0.0837763i
$441$		−	132.904i		−	0.301369i
$442$		0			0
$443$	−304.028			−0.686294			−0.343147	−	0.939282i	$-0.611493\pi$
$443$	−304.028			−0.686294			−0.343147	+	0.939282i	$0.611493\pi$
$444$	90.6795	+	90.6795i	0.204233	+	0.204233i
$445$	300.862			0.676093
$446$		−	309.061i		−	0.692963i
$447$	69.6462	+	69.6462i	0.155808	+	0.155808i
$448$	54.6410	+	54.6410i	0.121967	+	0.121967i
$449$	−200.694	+	200.694i	−0.446979	+	0.446979i	−0.894349	−	0.447370i	$-0.852361\pi$
$449$	−200.694	+	200.694i	−0.446979	+	0.446979i	0.447370	+	0.894349i	$0.352361\pi$
$450$	65.3538	−	65.3538i	0.145231	−	0.145231i
$451$	265.261			0.588163
$452$		−	90.4308i		−	0.200068i
$453$	−95.3294	+	95.3294i	−0.210440	+	0.210440i
$454$		−	91.4256i		−	0.201378i
$455$		0			0
$456$	162.067			0.355409
$457$	−101.519	−	101.519i	−0.222141	−	0.222141i	0.587258	−	0.809400i	$-0.300207\pi$
$457$	−101.519	−	101.519i	−0.222141	−	0.222141i	−0.809400	+	0.587258i	$0.800207\pi$
$458$	117.369			0.256265
$459$		−	98.3538i		−	0.214278i
$460$	−10.5077	−	10.5077i	−0.0228429	−	0.0228429i
$461$	−416.123	−	416.123i	−0.902653	−	0.902653i	0.0930121	−	0.995665i	$-0.470350\pi$
$461$	−416.123	−	416.123i	−0.902653	−	0.902653i	−0.995665	+	0.0930121i	$0.970350\pi$
$462$	171.962	−	171.962i	0.372211	−	0.372211i
$463$	−169.599	+	169.599i	−0.366305	+	0.366305i	−0.866128	−	0.499823i	$-0.833399\pi$
$463$	−169.599	+	169.599i	−0.366305	+	0.366305i	0.499823	+	0.866128i	$0.333399\pi$
$464$	69.2820			0.149315
$465$		−	97.3768i		−	0.209413i
$466$	−380.669	+	380.669i	−0.816887	+	0.816887i
$467$			732.649i			1.56884i	0.620230	+	0.784420i	$0.287039\pi$
$467$			732.649i			1.56884i	−0.620230	+	0.784420i	$0.712961\pi$
$468$		0			0
$469$	378.923			0.807938
$470$	−17.8001	−	17.8001i	−0.0378725	−	0.0378725i
$471$	96.0089			0.203841
$472$		−	186.928i		−	0.396034i
$473$	−111.488	−	111.488i	−0.235705	−	0.235705i
$474$	20.5692	+	20.5692i	0.0433950	+	0.0433950i
$475$	−509.592	+	509.592i	−1.07283	+	1.07283i
$476$	−258.564	+	258.564i	−0.543202	+	0.543202i
$477$	−185.023			−0.387889
$478$		−	334.277i		−	0.699324i
$479$	261.464	−	261.464i	0.545854	−	0.545854i	−0.379385	−	0.925239i	$-0.623864\pi$
$479$	261.464	−	261.464i	0.545854	−	0.545854i	0.925239	+	0.379385i	$0.123864\pi$
$480$			17.5692i			0.0366025i
$481$		0			0
$482$	4.35383			0.00903284
$483$	49.0192	+	49.0192i	0.101489	+	0.101489i
$484$	−30.7077			−0.0634456
$485$			278.918i			0.575088i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	−137.000	−	137.000i	−0.281314	−	0.281314i	0.552319	−	0.833633i	$-0.313743\pi$
$487$	−137.000	−	137.000i	−0.281314	−	0.281314i	−0.833633	+	0.552319i	$0.813743\pi$
$488$	14.6025	−	14.6025i	0.0299232	−	0.0299232i
$489$	−250.547	+	250.547i	−0.512365	+	0.512365i
$490$	−112.344			−0.229272
$491$		−	36.9282i		−	0.0752102i	−0.999293	−	0.0376051i	$-0.988027\pi$
$491$		−	36.9282i		−	0.0752102i	0.999293	−	0.0376051i	$-0.0119729\pi$
$492$	63.2154	−	63.2154i	0.128487	−	0.128487i
$493$			327.846i			0.665002i
$494$		0			0
$495$	55.2923			0.111702
$496$	−88.6795	−	88.6795i	−0.178789	−	0.178789i
$497$	1038.90			2.09034
$498$			384.631i			0.772351i
$499$	462.769	+	462.769i	0.927393	+	0.927393i	0.997537	−	0.0701438i	$-0.0223458\pi$
$499$	462.769	+	462.769i	0.927393	+	0.927393i	−0.0701438	+	0.997537i	$0.522346\pi$
$500$	−118.641	−	118.641i	−0.237282	−	0.237282i
$501$	198.200	−	198.200i	0.395609	−	0.395609i
$502$	−208.708	+	208.708i	−0.415752	+	0.415752i
$503$	−358.756			−0.713233			−0.356617	−	0.934251i	$-0.616070\pi$
$503$	−358.756			−0.713233			−0.356617	+	0.934251i	$0.616070\pi$
$504$		−	81.9615i		−	0.162622i
$505$	−236.869	+	236.869i	−0.469048	+	0.469048i
$506$			60.2309i			0.119033i
$507$		0			0
$508$	−473.692			−0.932465
$509$	−521.745	−	521.745i	−1.02504	−	1.02504i	−0.999678	−	0.0253604i	$-0.991927\pi$
$509$	−521.745	−	521.745i	−1.02504	−	1.02504i	−0.0253604	−	0.999678i	$-0.508073\pi$
$510$	−83.1384			−0.163017
$511$		−	920.955i		−	1.80226i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−121.550	−	121.550i	−0.236940	−	0.236940i
$514$	−74.2205	+	74.2205i	−0.144398	+	0.144398i
$515$	105.573	−	105.573i	0.204996	−	0.204996i
$516$	−53.1384			−0.102981
$517$			102.031i			0.197352i
$518$	−357.583	+	357.583i	−0.690315	+	0.690315i
$519$		−	464.985i		−	0.895924i
$520$		0			0
$521$	156.049			0.299518			0.149759	−	0.988723i	$-0.452150\pi$
$521$	156.049			0.299518			0.149759	+	0.988723i	$0.452150\pi$
$522$	−51.9615	−	51.9615i	−0.0995431	−	0.0995431i
$523$	41.9230			0.0801588			0.0400794	−	0.999196i	$-0.487239\pi$
$523$	41.9230			0.0801588			0.0400794	+	0.999196i	$0.487239\pi$
$524$		−	419.272i		−	0.800137i
$525$	257.715	+	257.715i	0.490885	+	0.490885i
$526$	−24.3641	−	24.3641i	−0.0463197	−	0.0463197i
$527$	419.636	−	419.636i	0.796273	−	0.796273i
$528$	50.3538	−	50.3538i	0.0953671	−	0.0953671i
$529$	511.831			0.967544
$530$			156.400i			0.295094i
$531$	−140.196	+	140.196i	−0.264023	+	0.264023i
$532$			639.090i			1.20130i
$533$		0			0
$534$	−410.985			−0.769634
$535$	−129.962	−	129.962i	−0.242919	−	0.242919i
$536$	110.956			0.207008
$537$		−	494.985i		−	0.921759i
$538$	−175.741	−	175.741i	−0.326656	−	0.326656i
$539$	321.979	+	321.979i	0.597364	+	0.597364i
$540$	13.1769	−	13.1769i	0.0244017	−	0.0244017i
$541$	−4.44298	+	4.44298i	−0.00821253	+	0.00821253i	−0.711201	−	0.702989i	$-0.751848\pi$
$541$	−4.44298	+	4.44298i	−0.00821253	+	0.00821253i	0.702989	+	0.711201i	$0.251848\pi$
$542$	−394.091			−0.727105
$543$			307.692i			0.566652i
$544$	−75.7128	+	75.7128i	−0.139178	+	0.139178i
$545$		−	122.203i		−	0.224225i
$546$		0			0
$547$	−101.508			−0.185572			−0.0927859	−	0.995686i	$-0.529577\pi$
$547$	−101.508			−0.185572			−0.0927859	+	0.995686i	$0.529577\pi$
$548$	161.072	+	161.072i	0.293927	+	0.293927i
$549$	−21.9038			−0.0398977
$550$			316.659i			0.575743i
$551$	405.167	+	405.167i	0.735330	+	0.735330i
$552$	14.3538	+	14.3538i	0.0260033	+	0.0260033i
$553$	−81.1122	+	81.1122i	−0.146677	+	0.146677i
$554$	−446.985	+	446.985i	−0.806831	+	0.806831i
$555$	−114.977			−0.207166
$556$		−	191.415i		−	0.344272i
$557$	465.846	−	465.846i	0.836348	−	0.836348i	−0.152028	−	0.988376i	$-0.548580\pi$
$557$	465.846	−	465.846i	0.836348	−	0.836348i	0.988376	+	0.152028i	$0.0485803\pi$
$558$			133.019i			0.238386i
$559$		0			0
$560$	−69.2820			−0.123718
$561$	238.277	+	238.277i	0.424736	+	0.424736i
$562$	−11.0897			−0.0197325
$563$		−	88.7255i		−	0.157594i	−0.996891	−	0.0787971i	$-0.974892\pi$
$563$		−	88.7255i		−	0.157594i	0.996891	−	0.0787971i	$-0.0251079\pi$
$564$	24.3154	+	24.3154i	0.0431123	+	0.0431123i
$565$	57.3308	+	57.3308i	0.101470	+	0.101470i
$566$	−16.6462	+	16.6462i	−0.0294102	+	0.0294102i
$567$	−61.4711	+	61.4711i	−0.108415	+	0.108415i
$568$	304.210			0.535581
$569$		−	431.569i		−	0.758470i	−0.925300	−	0.379235i	$-0.876187\pi$
$569$		−	431.569i		−	0.758470i	0.925300	−	0.379235i	$-0.123813\pi$
$570$	−102.746	+	102.746i	−0.180256	+	0.180256i
$571$		−	959.892i		−	1.68107i	−0.541756	−	0.840536i	$-0.682240\pi$
$571$		−	959.892i		−	1.68107i	0.541756	−	0.840536i	$-0.317760\pi$
$572$		0			0
$573$	341.769			0.596456
$574$	249.282	+	249.282i	0.434289	+	0.434289i
$575$	−90.2666			−0.156985
$576$		−	24.0000i		−	0.0416667i
$577$	−313.669	−	313.669i	−0.543621	−	0.543621i	0.380968	−	0.924588i	$-0.375591\pi$
$577$	−313.669	−	313.669i	−0.543621	−	0.543621i	−0.924588	+	0.380968i	$0.875591\pi$
$578$	−69.2769	−	69.2769i	−0.119856	−	0.119856i
$579$	25.7199	−	25.7199i	0.0444212	−	0.0444212i
$580$	−43.9230	+	43.9230i	−0.0757294	+	0.0757294i
$581$	−1516.74			−2.61057
$582$		−	381.009i		−	0.654655i
$583$	448.246	−	448.246i	0.768861	−	0.768861i
$584$		−	269.674i		−	0.461771i
$585$		0			0
$586$	264.946			0.452126
$587$	−160.004	−	160.004i	−0.272579	−	0.272579i	0.557559	−	0.830138i	$-0.311738\pi$
$587$	−160.004	−	160.004i	−0.272579	−	0.272579i	−0.830138	+	0.557559i	$0.811738\pi$
$588$	153.464			0.260993
$589$		−	1037.21i		−	1.76097i
$590$	118.508	+	118.508i	0.200861	+	0.200861i
$591$	185.254	+	185.254i	0.313458	+	0.313458i
$592$	−104.708	+	104.708i	−0.176871	+	0.176871i
$593$	335.229	−	335.229i	0.565311	−	0.565311i	−0.365500	−	0.930811i	$-0.619102\pi$
$593$	335.229	−	335.229i	0.565311	−	0.565311i	0.930811	+	0.365500i	$0.119102\pi$
$594$	−75.5307			−0.127156
$595$		−	327.846i		−	0.551002i
$596$	−80.4205	+	80.4205i	−0.134934	+	0.134934i
$597$		−	38.4782i		−	0.0644526i
$598$		0			0
$599$	136.908			0.228560			0.114280	−	0.993449i	$-0.463544\pi$
$599$	136.908			0.228560			0.114280	+	0.993449i	$0.463544\pi$
$600$	75.4641	+	75.4641i	0.125774	+	0.125774i
$601$	−17.5692			−0.0292333			−0.0146167	−	0.999893i	$-0.504653\pi$
$601$	−17.5692			−0.0292333			−0.0146167	+	0.999893i	$0.504653\pi$
$602$		−	209.545i		−	0.348081i
$603$	−83.2173	−	83.2173i	−0.138005	−	0.138005i
$604$	−110.077	−	110.077i	−0.182247	−	0.182247i
$605$	19.4679	−	19.4679i	0.0321783	−	0.0321783i
$606$	323.569	−	323.569i	0.533943	−	0.533943i
$607$	844.600			1.39143			0.695716	−	0.718317i	$-0.255087\pi$
$607$	844.600			1.39143			0.695716	+	0.718317i	$0.255087\pi$
$608$			187.138i			0.307793i
$609$	204.904	−	204.904i	0.336459	−	0.336459i
$610$			18.5153i			0.0303529i
$611$		0			0
$612$	113.569			0.185571
$613$	−445.757	−	445.757i	−0.727173	−	0.727173i	0.242883	−	0.970056i	$-0.421907\pi$
$613$	−445.757	−	445.757i	−0.727173	−	0.727173i	−0.970056	+	0.242883i	$0.921907\pi$
$614$	750.137			1.22172
$615$			80.1539i			0.130332i
$616$	198.564	+	198.564i	0.322344	+	0.322344i
$617$	−78.3397	−	78.3397i	−0.126969	−	0.126969i	0.640767	−	0.767736i	$-0.278617\pi$
$617$	−78.3397	−	78.3397i	−0.126969	−	0.126969i	−0.767736	+	0.640767i	$0.778617\pi$
$618$	−144.215	+	144.215i	−0.233358	+	0.233358i
$619$	−111.970	+	111.970i	−0.180888	+	0.180888i	−0.791743	−	0.610854i	$-0.790826\pi$
$619$	−111.970	+	111.970i	−0.180888	+	0.180888i	0.610854	+	0.791743i	$0.290826\pi$
$620$	112.441			0.181357
$621$		−	21.5307i		−	0.0346711i
$622$	296.238	−	296.238i	0.476268	−	0.476268i
$623$		−	1620.67i		−	2.60139i
$624$		0			0
$625$	−394.184			−0.630695
$626$	118.286	+	118.286i	0.188955	+	0.188955i
$627$	588.946			0.939308
$628$			110.862i			0.176531i
$629$	−495.482	−	495.482i	−0.787730	−	0.787730i
$630$	51.9615	+	51.9615i	0.0824786	+	0.0824786i
$631$	773.445	−	773.445i	1.22575	−	1.22575i	0.260187	−	0.965558i	$-0.416216\pi$
$631$	773.445	−	773.445i	1.22575	−	1.22575i	0.965558	−	0.260187i	$-0.0837843\pi$
$632$	−23.7513	+	23.7513i	−0.0375812	+	0.0375812i
$633$	111.200			0.175671
$634$		−	561.415i		−	0.885513i
$635$	300.309	−	300.309i	0.472927	−	0.472927i
$636$		−	213.646i		−	0.335922i
$637$		0			0
$638$	251.769			0.394622
$639$	−228.158	−	228.158i	−0.357054	−	0.357054i
$640$	−20.2872			−0.0316987
$641$			408.613i			0.637462i	0.947845	+	0.318731i	$0.103257\pi$
$641$			408.613i			0.637462i	−0.947845	+	0.318731i	$0.896743\pi$
$642$	177.531	+	177.531i	0.276528	+	0.276528i
$643$	316.730	+	316.730i	0.492582	+	0.492582i	0.909119	−	0.416537i	$-0.136756\pi$
$643$	316.730	+	316.730i	0.492582	+	0.492582i	−0.416537	+	0.909119i	$0.636756\pi$
$644$	−56.6025	+	56.6025i	−0.0878921	+	0.0878921i
$645$	33.6884	−	33.6884i	0.0522301	−	0.0522301i
$646$	−885.549			−1.37082
$647$		−	322.841i		−	0.498981i	−0.968377	−	0.249491i	$-0.919737\pi$
$647$		−	322.841i		−	0.498981i	0.968377	−	0.249491i	$-0.0802632\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	679.292i		−	1.04668i
$650$		0			0
$651$	−524.545			−0.805752
$652$	−289.306	−	289.306i	−0.443722	−	0.443722i
$653$	−1020.85			−1.56332			−0.781660	−	0.623704i	$-0.785627\pi$
$653$	−1020.85			−1.56332			−0.781660	+	0.623704i	$0.785627\pi$
$654$			166.932i			0.255248i
$655$	265.808	+	265.808i	0.405813	+	0.405813i
$656$	72.9948	+	72.9948i	0.111273	+	0.111273i
$657$	−202.256	+	202.256i	−0.307847	+	0.307847i
$658$	−95.8846	+	95.8846i	−0.145721	+	0.145721i
$659$	227.685			0.345500			0.172750	−	0.984966i	$-0.444735\pi$
$659$	227.685			0.345500			0.172750	+	0.984966i	$0.444735\pi$
$660$			63.8461i			0.0967365i
$661$	−107.012	+	107.012i	−0.161894	+	0.161894i	−0.783405	−	0.621511i	$-0.786519\pi$
$661$	−107.012	+	107.012i	−0.161894	+	0.161894i	0.621511	+	0.783405i	$0.286519\pi$
$662$			201.247i			0.303999i
$663$		0			0
$664$	−444.133			−0.668875
$665$	−405.167	−	405.167i	−0.609273	−	0.609273i
$666$	157.061			0.235828
$667$			71.7691i			0.107600i
$668$	228.862	+	228.862i	0.342607	+	0.342607i
$669$	−267.655	−	267.655i	−0.400082	−	0.400082i
$670$	−70.3435	+	70.3435i	−0.104990	+	0.104990i
$671$	53.0653	−	53.0653i	0.0790838	−	0.0790838i
$672$	94.6410			0.140835
$673$		−	707.991i		−	1.05199i	−0.850487	−	0.525996i	$-0.823693\pi$
$673$		−	707.991i		−	1.05199i	0.850487	−	0.525996i	$-0.176307\pi$
$674$	−347.508	+	347.508i	−0.515590	+	0.515590i
$675$		−	113.196i		−	0.167698i
$676$		0			0
$677$	−754.592			−1.11461			−0.557306	−	0.830307i	$-0.688165\pi$
$677$	−754.592			−1.11461			−0.557306	+	0.830307i	$0.688165\pi$
$678$	−78.3154	−	78.3154i	−0.115509	−	0.115509i
$679$	1502.46			2.21276
$680$		−	96.0000i		−	0.141176i
$681$	−79.1769	−	79.1769i	−0.116266	−	0.116266i
$682$	−322.259	−	322.259i	−0.472521	−	0.472521i
$683$	−101.678	+	101.678i	−0.148870	+	0.148870i	−0.777613	−	0.628743i	$-0.783570\pi$
$683$	−101.678	+	101.678i	−0.148870	+	0.148870i	0.628743	+	0.777613i	$0.283570\pi$
$684$	140.354	−	140.354i	0.205196	−	0.205196i
$685$	−204.231			−0.298147
$686$		−	64.1858i		−	0.0935654i
$687$	101.645	−	101.645i	0.147955	−	0.147955i
$688$		−	61.3590i		−	0.0891846i
$689$		0			0
$690$	−18.1999			−0.0263767
$691$	385.030	+	385.030i	0.557207	+	0.557207i	0.928511	−	0.371304i	$-0.121089\pi$
$691$	385.030	+	385.030i	0.557207	+	0.557207i	−0.371304	+	0.928511i	$0.621089\pi$
$692$	536.918			0.775893
$693$		−	297.846i		−	0.429792i
$694$	437.703	+	437.703i	0.630695	+	0.630695i
$695$	121.352	+	121.352i	0.174608	+	0.174608i
$696$	60.0000	−	60.0000i	0.0862069	−	0.0862069i
$697$	−345.415	+	345.415i	−0.495574	+	0.495574i
$698$	633.794			0.908014
$699$			659.338i			0.943259i
$700$	−297.583	+	297.583i	−0.425119	+	0.425119i
$701$		−	568.344i		−	0.810761i	−0.914148	−	0.405381i	$-0.867139\pi$
$701$		−	568.344i		−	0.810761i	0.914148	−	0.405381i	$-0.132861\pi$
$702$		0			0
$703$	−1224.68			−1.74207
$704$	58.1436	+	58.1436i	0.0825903	+	0.0825903i
$705$	−30.8306			−0.0437314
$706$		−	830.074i		−	1.17574i
$707$	1275.95	+	1275.95i	1.80475	+	1.80475i
$708$	−161.885	−	161.885i	−0.228651	−	0.228651i
$709$	259.419	−	259.419i	0.365894	−	0.365894i	−0.500084	−	0.865977i	$-0.666697\pi$
$709$	259.419	−	259.419i	0.365894	−	0.365894i	0.865977	+	0.500084i	$0.166697\pi$
$710$	−192.862	+	192.862i	−0.271636	+	0.271636i
$711$	35.6269			0.0501082
$712$		−	474.564i		−	0.666523i
$713$	91.8629	−	91.8629i	0.128840	−	0.128840i
$714$			447.846i			0.627235i
$715$		0			0
$716$	571.559			0.798267
$717$	−289.492	−	289.492i	−0.403755	−	0.403755i
$718$	128.554			0.179044
$719$		−	263.520i		−	0.366510i	−0.983065	−	0.183255i	$-0.941337\pi$
$719$		−	263.520i		−	0.366510i	0.983065	−	0.183255i	$-0.0586633\pi$
$720$	15.2154	+	15.2154i	0.0211325	+	0.0211325i
$721$	−568.695	−	568.695i	−0.788759	−	0.788759i
$722$	−733.400	+	733.400i	−1.01579	+	1.01579i
$723$	3.77053	−	3.77053i	0.00521511	−	0.00521511i
$724$	−355.292			−0.490735
$725$			377.321i			0.520442i
$726$	−26.5936	+	26.5936i	−0.0366303	+	0.0366303i
$727$		−	878.415i		−	1.20827i	−0.796880	−	0.604137i	$-0.793518\pi$
$727$		−	878.415i		−	1.20827i	0.796880	−	0.604137i	$-0.206482\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	170.967	+	170.967i	0.234201	+	0.234201i
$731$	290.354			0.397201
$732$		−	25.2923i		−	0.0345524i
$733$	−146.627	−	146.627i	−0.200037	−	0.200037i	0.599979	−	0.800016i	$-0.295176\pi$
$733$	−146.627	−	146.627i	−0.200037	−	0.200037i	−0.800016	+	0.599979i	$0.795176\pi$
$734$	−217.785	−	217.785i	−0.296709	−	0.296709i
$735$	−97.2923	+	97.2923i	−0.132371	+	0.132371i
$736$	−16.5744	+	16.5744i	−0.0225195	+	0.0225195i
$737$	403.213			0.547100
$738$		−	109.492i		−	0.148364i
$739$	−455.161	+	455.161i	−0.615915	+	0.615915i	−0.944481	−	0.328566i	$-0.893435\pi$
$739$	−455.161	+	455.161i	−0.615915	+	0.615915i	0.328566	+	0.944481i	$0.393435\pi$
$740$		−	132.764i		−	0.179411i
$741$		0			0
$742$	842.487			1.13543
$743$	−9.63963	−	9.63963i	−0.0129739	−	0.0129739i	0.700590	−	0.713564i	$-0.252920\pi$
$743$	−9.63963	−	9.63963i	−0.0129739	−	0.0129739i	−0.713564	+	0.700590i	$0.752920\pi$
$744$	−153.597			−0.206448
$745$		−	101.969i		−	0.136871i
$746$	−219.606	−	219.606i	−0.294378	−	0.294378i
$747$	333.100	+	333.100i	0.445917	+	0.445917i
$748$	−275.138	+	275.138i	−0.367832	+	0.367832i
$749$	−700.070	+	700.070i	−0.934673	+	0.934673i
$750$	−205.492			−0.273990
$751$		−	160.077i		−	0.213152i	−0.994305	−	0.106576i	$-0.966011\pi$
$751$		−	160.077i		−	0.213152i	0.994305	−	0.106576i	$-0.0339887\pi$
$752$	−28.0770	+	28.0770i	−0.0373364	+	0.0373364i
$753$			361.492i			0.480069i
$754$		0			0
$755$	139.572			0.184864
$756$	−70.9808	−	70.9808i	−0.0938899	−	0.0938899i
$757$	−1467.38			−1.93842			−0.969210	−	0.246234i	$-0.920807\pi$
$757$	−1467.38			−1.93842			−0.969210	+	0.246234i	$0.920807\pi$
$758$			274.214i			0.361760i
$759$	52.1615	+	52.1615i	0.0687239	+	0.0687239i
$760$	−118.641	−	118.641i	−0.156107	−	0.156107i
$761$	129.367	−	129.367i	0.169995	−	0.169995i	−0.616982	−	0.786977i	$-0.711645\pi$
$761$	129.367	−	129.367i	0.169995	−	0.169995i	0.786977	+	0.616982i	$0.211645\pi$
$762$	−410.229	+	410.229i	−0.538359	+	0.538359i
$763$	−658.275			−0.862746
$764$			394.641i			0.516546i
$765$	−72.0000	+	72.0000i	−0.0941176	+	0.0941176i
$766$		−	275.503i		−	0.359664i
$767$		0			0
$768$	27.7128			0.0360844
$769$	961.315	+	961.315i	1.25008	+	1.25008i	0.955681	+	0.294404i	$0.0951211\pi$
$769$	961.315	+	961.315i	1.25008	+	1.25008i	0.294404	+	0.955681i	$0.404879\pi$
$770$	−251.769			−0.326973
$771$			128.554i			0.166736i
$772$	29.6987	+	29.6987i	0.0384699	+	0.0384699i
$773$	−692.232	−	692.232i	−0.895513	−	0.895513i	0.0995220	−	0.995035i	$-0.468269\pi$
$773$	−692.232	−	692.232i	−0.895513	−	0.895513i	−0.995035	+	0.0995220i	$0.968269\pi$
$774$	−46.0192	+	46.0192i	−0.0594564	+	0.0594564i
$775$	482.962	−	482.962i	0.623177	−	0.623177i
$776$	439.951			0.566947
$777$			619.352i			0.797107i
$778$	17.7513	−	17.7513i	0.0228166	−	0.0228166i
$779$			853.759i			1.09597i
$780$		0			0
$781$	1105.49			1.41548
$782$	−78.4308	−	78.4308i	−0.100295	−	0.100295i
$783$	−90.0000			−0.114943
$784$			177.205i			0.226027i
$785$	−70.2834	−	70.2834i	−0.0895330	−	0.0895330i
$786$	−363.100	−	363.100i	−0.461959	−	0.461959i
$787$	83.4533	−	83.4533i	0.106040	−	0.106040i	−0.652096	−	0.758136i	$-0.726110\pi$
$787$	83.4533	−	83.4533i	0.106040	−	0.106040i	0.758136	+	0.652096i	$0.226110\pi$
$788$	−213.913	+	213.913i	−0.271463	+	0.271463i
$789$	−42.1999			−0.0534853
$790$		−	30.1154i		−	0.0381208i
$791$	308.827	−	308.827i	0.390426	−	0.390426i
$792$		−	87.2154i		−	0.110120i
$793$		0			0
$794$	−477.286			−0.601116
$795$	135.446	+	135.446i	0.170373	+	0.170373i
$796$	44.4308			0.0558176
$797$		−	567.118i		−	0.711566i	−0.934569	−	0.355783i	$-0.884214\pi$
$797$		−	567.118i		−	0.711566i	0.934569	−	0.355783i	$-0.115786\pi$
$798$	553.468	+	553.468i	0.693569	+	0.693569i
$799$	−132.862	−	132.862i	−0.166285	−	0.166285i
$800$	−87.1384	+	87.1384i	−0.108923	+	0.108923i
$801$	−355.923	+	355.923i	−0.444348	+	0.444348i
$802$	726.831			0.906273
$803$		−	979.990i		−	1.22041i
$804$	96.0910	−	96.0910i	0.119516	−	0.119516i
$805$		−	71.7691i		−	0.0891542i
$806$		0			0
$807$	−304.392			−0.377190
$808$	373.626	+	373.626i	0.462408	+	0.462408i
$809$	87.4462			0.108092			0.0540459	−	0.998538i	$-0.482788\pi$
$809$	87.4462			0.108092			0.0540459	+	0.998538i	$0.482788\pi$
$810$		−	22.8231i		−	0.0281766i
$811$	−519.193	−	519.193i	−0.640189	−	0.640189i	0.310413	−	0.950602i	$-0.399533\pi$
$811$	−519.193	−	519.193i	−0.640189	−	0.640189i	−0.950602	+	0.310413i	$0.899533\pi$
$812$	236.603	+	236.603i	0.291382	+	0.291382i
$813$	−341.293	+	341.293i	−0.419794	+	0.419794i
$814$	−380.505	+	380.505i	−0.467451	+	0.467451i
$815$	366.826			0.450093
$816$			131.138i			0.160709i
$817$	358.832	−	358.832i	0.439207	−	0.439207i
$818$			824.053i			1.00740i
$819$		0			0
$820$	−92.5538			−0.112870
$821$	406.750	+	406.750i	0.495432	+	0.495432i	0.910013	−	0.414580i	$-0.136072\pi$
$821$	406.750	+	406.750i	0.495432	+	0.495432i	−0.414580	+	0.910013i	$0.636072\pi$
$822$	278.985			0.339397
$823$			329.169i			0.399963i	0.979800	+	0.199981i	$0.0640882\pi$
$823$			329.169i			0.399963i	−0.979800	+	0.199981i	$0.935912\pi$
$824$	−166.526	−	166.526i	−0.202094	−	0.202094i
$825$	274.235	+	274.235i	0.332406	+	0.332406i
$826$	638.372	−	638.372i	0.772847	−	0.772847i
$827$	514.410	−	514.410i	0.622020	−	0.622020i	−0.324028	−	0.946048i	$-0.605037\pi$
$827$	514.410	−	514.410i	0.622020	−	0.622020i	0.946048	+	0.324028i	$0.105037\pi$
$828$	24.8616			0.0300260
$829$		−	943.092i		−	1.13763i	−0.822467	−	0.568813i	$-0.807403\pi$
$829$		−	943.092i		−	1.13763i	0.822467	−	0.568813i	$-0.192597\pi$
$830$	281.569	−	281.569i	0.339240	−	0.339240i
$831$			774.200i			0.931649i
$832$		0			0
$833$	−838.543			−1.00665
$834$	−165.771	−	165.771i	−0.198766	−	0.198766i
$835$	−290.185			−0.347527
$836$			680.056i			0.813465i
$837$	115.198	+	115.198i	0.137632	+	0.137632i
$838$	−782.354	−	782.354i	−0.933596	−	0.933596i
$839$	−556.070	+	556.070i	−0.662778	+	0.662778i	−0.956034	−	0.293256i	$-0.905261\pi$
$839$	−556.070	+	556.070i	−0.662778	+	0.662778i	0.293256	+	0.956034i	$0.405261\pi$
$840$	−60.0000	+	60.0000i	−0.0714286	+	0.0714286i
$841$	−541.000			−0.643282
$842$		−	54.0704i		−	0.0642166i
$843$	−9.60392	+	9.60392i	−0.0113926	+	0.0113926i
$844$			128.403i			0.152136i
$845$		0			0
$846$	42.1154			0.0497818
$847$	−104.869	−	104.869i	−0.123812	−	0.123812i
$848$	246.697			0.290917
$849$			28.8320i			0.0339600i
$850$	−412.344	−	412.344i	−0.485110	−	0.485110i
$851$	−108.466	−	108.466i	−0.127458	−	0.127458i
$852$	263.454	−	263.454i	0.309218	−	0.309218i
$853$	472.527	−	472.527i	0.553960	−	0.553960i	−0.373622	−	0.927581i	$-0.621884\pi$
$853$	472.527	−	472.527i	0.553960	−	0.553960i	0.927581	+	0.373622i	$0.121884\pi$
$854$	99.7372			0.116788
$855$			177.962i			0.208142i
$856$	−204.995	+	204.995i	−0.239480	+	0.239480i
$857$		−	436.543i		−	0.509386i	−0.967022	−	0.254693i	$-0.918026\pi$
$857$		−	436.543i		−	0.509386i	0.967022	−	0.254693i	$-0.0819743\pi$
$858$		0			0
$859$	−1238.40			−1.44167			−0.720837	−	0.693104i	$-0.756243\pi$
$859$	−1238.40			−1.44167			−0.720837	+	0.693104i	$0.756243\pi$
$860$	38.9000	+	38.9000i	0.0452326	+	0.0452326i
$861$	431.769			0.501474
$862$			890.620i			1.03320i
$863$	729.373	+	729.373i	0.845160	+	0.845160i	0.989525	−	0.144365i	$-0.0461138\pi$
$863$	729.373	+	729.373i	0.845160	+	0.845160i	−0.144365	+	0.989525i	$0.546114\pi$
$864$	−20.7846	−	20.7846i	−0.0240563	−	0.0240563i
$865$	−340.392	+	340.392i	−0.393517	+	0.393517i
$866$	−237.785	+	237.785i	−0.274578	+	0.274578i
$867$	−119.991			−0.138398
$868$		−	605.692i		−	0.697802i
$869$	−86.3116	+	86.3116i	−0.0993229	+	0.0993229i
$870$			76.0770i			0.0874448i
$871$		0			0
$872$	−192.756			−0.221051
$873$	−329.963	−	329.963i	−0.377965	−	0.377965i
$874$	−193.856			−0.221804
$875$		−	810.333i		−	0.926095i
$876$	−233.545	−	233.545i	−0.266604	−	0.266604i
$877$	−962.069	−	962.069i	−1.09700	−	1.09700i	−0.994760	−	0.102240i	$-0.967399\pi$
$877$	−962.069	−	962.069i	−1.09700	−	1.09700i	−0.102240	−	0.994760i	$-0.532601\pi$
$878$	−689.463	+	689.463i	−0.785265	+	0.785265i
$879$	229.450	−	229.450i	0.261035	−	0.261035i
$880$	−73.7231			−0.0837763
$881$			1563.66i			1.77487i	0.460929	+	0.887437i	$0.347516\pi$
$881$			1563.66i			1.77487i	−0.460929	+	0.887437i	$0.652484\pi$
$882$	132.904	−	132.904i	0.150685	−	0.150685i
$883$		−	452.723i		−	0.512710i	−0.966583	−	0.256355i	$-0.917478\pi$
$883$		−	452.723i		−	0.512710i	0.966583	−	0.256355i	$-0.0825216\pi$
$884$		0			0
$885$	205.261			0.231934
$886$	−304.028	−	304.028i	−0.343147	−	0.343147i
$887$	910.939			1.02699			0.513494	−	0.858093i	$-0.328351\pi$
$887$	910.939			1.02699			0.513494	+	0.858093i	$0.328351\pi$
$888$			181.359i			0.204233i
$889$	−1617.69	−	1617.69i	−1.81967	−	1.81967i
$890$	300.862	+	300.862i	0.338047	+	0.338047i
$891$	−65.4115	+	65.4115i	−0.0734136	+	0.0734136i
$892$	309.061	−	309.061i	0.346481	−	0.346481i
$893$	−328.392			−0.367741
$894$			139.292i			0.155808i
$895$	−362.354	+	362.354i	−0.404865	+	0.404865i
$896$			109.282i			0.121967i
$897$		0			0
$898$	−401.387			−0.446979
$899$	−383.993	−	383.993i	−0.427134	−	0.427134i
$900$	130.708			0.145231
$901$			1167.38i			1.29565i
$902$	265.261	+	265.261i	0.294081	+	0.294081i
$903$	−181.471	−	181.471i	−0.200965	−	0.200965i
$904$	90.4308	−	90.4308i	0.100034	−	0.100034i
$905$	225.246	−	225.246i	0.248891	−	0.248891i
$906$	−190.659			−0.210440
$907$			445.138i			0.490781i	0.969424	+	0.245391i	$0.0789162\pi$
$907$			445.138i			0.490781i	−0.969424	+	0.245391i	$0.921084\pi$
$908$	91.4256	−	91.4256i	0.100689	−	0.100689i
$909$		−	560.438i		−	0.616544i
$910$		0			0
$911$	717.233			0.787303			0.393652	−	0.919260i	$-0.371212\pi$
$911$	717.233			0.787303			0.393652	+	0.919260i	$0.371212\pi$
$912$	162.067	+	162.067i	0.177705	+	0.177705i
$913$	−1613.97			−1.76776
$914$		−	203.037i		−	0.222141i
$915$	16.0347	+	16.0347i	0.0175243	+	0.0175243i
$916$	117.369	+	117.369i	0.128132	+	0.128132i
$917$	1431.84	−	1431.84i	1.56144	−	1.56144i
$918$	98.3538	−	98.3538i	0.107139	−	0.107139i
$919$	743.138			0.808638			0.404319	−	0.914618i	$-0.367509\pi$
$919$	743.138			0.808638			0.404319	+	0.914618i	$0.367509\pi$
$920$		−	21.0155i		−	0.0228429i
$921$	649.638	−	649.638i	0.705361	−	0.705361i
$922$		−	832.246i		−	0.902653i
$923$		0			0
$924$	343.923			0.372211
$925$	−570.254	−	570.254i	−0.616491	−	0.616491i
$926$	−339.199			−0.366305
$927$			249.788i			0.269459i
$928$	69.2820	+	69.2820i	0.0746574	+	0.0746574i
$929$	−1042.54	−	1042.54i	−1.12222	−	1.12222i	−0.991407	−	0.130814i	$-0.958241\pi$
$929$	−1042.54	−	1042.54i	−1.12222	−	1.12222i	−0.130814	−	0.991407i	$-0.541759\pi$
$930$	97.3768	−	97.3768i	0.104706	−	0.104706i
$931$	−1036.31	+	1036.31i	−1.11311	+	1.11311i
$932$	−761.338			−0.816887
$933$		−	513.100i		−	0.549946i
$934$	−732.649	+	732.649i	−0.784420	+	0.784420i
$935$		−	348.862i		−	0.373114i
$936$		0			0
$937$	−172.477			−0.184073			−0.0920367	−	0.995756i	$-0.529338\pi$
$937$	−172.477			−0.184073			−0.0920367	+	0.995756i	$0.529338\pi$
$938$	378.923	+	378.923i	0.403969	+	0.403969i
$939$	204.877			0.218186
$940$		−	35.6001i		−	0.0378725i
$941$	145.055	+	145.055i	0.154150	+	0.154150i	0.779969	−	0.625819i	$-0.215235\pi$
$941$	145.055	+	145.055i	0.154150	+	0.154150i	−0.625819	+	0.779969i	$0.715235\pi$
$942$	96.0089	+	96.0089i	0.101920	+	0.101920i
$943$	−75.6152	+	75.6152i	−0.0801858	+	0.0801858i
$944$	186.928	−	186.928i	0.198017	−	0.198017i
$945$	90.0000			0.0952381
$946$		−	222.977i		−	0.235705i
$947$	487.474	−	487.474i	0.514757	−	0.514757i	−0.401224	−	0.915980i	$-0.631415\pi$
$947$	487.474	−	487.474i	0.514757	−	0.514757i	0.915980	+	0.401224i	$0.131415\pi$
$948$			41.1384i			0.0433950i
$949$		0			0
$950$	−1019.18			−1.07283
$951$	−486.200	−	486.200i	−0.511251	−	0.511251i
$952$	−517.128			−0.543202
$953$			1206.62i			1.26613i	0.774100	+	0.633063i	$0.218203\pi$
$953$			1206.62i			1.26613i	−0.774100	+	0.633063i	$0.781797\pi$
$954$	−185.023	−	185.023i	−0.193944	−	0.193944i
$955$	−250.192	−	250.192i	−0.261982	−	0.261982i
$956$	334.277	−	334.277i	0.349662	−	0.349662i
$957$	218.038	−	218.038i	0.227835	−	0.227835i
$958$	522.928			0.545854
$959$			1100.14i			1.14718i
$960$	−17.5692	+	17.5692i	−0.0183013	+	0.0183013i
$961$			22.0065i			0.0228996i
$962$		0			0
$963$	307.492			0.319307
$964$	4.35383	+	4.35383i	0.00451642	+	0.00451642i
$965$	−37.6565			−0.0390223
$966$			98.0385i			0.101489i
$967$	−169.831	−	169.831i	−0.175626	−	0.175626i	0.613820	−	0.789446i	$-0.289632\pi$
$967$	−169.831	−	169.831i	−0.175626	−	0.175626i	−0.789446	+	0.613820i	$0.789632\pi$
$968$	−30.7077	−	30.7077i	−0.0317228	−	0.0317228i
$969$	−766.908	+	766.908i	−0.791442	+	0.791442i
$970$	−278.918	+	278.918i	−0.287544	+	0.287544i
$971$	747.700			0.770031			0.385015	−	0.922910i	$-0.374196\pi$
$971$	747.700			0.770031			0.385015	+	0.922910i	$0.374196\pi$
$972$			31.1769i			0.0320750i
$973$	653.695	−	653.695i	0.671835	−	0.671835i
$974$		−	274.000i		−	0.281314i
$975$		0			0
$976$	29.2051			0.0299232
$977$	−152.967	−	152.967i	−0.156568	−	0.156568i	0.624476	−	0.781044i	$-0.285313\pi$
$977$	−152.967	−	152.967i	−0.156568	−	0.156568i	−0.781044	+	0.624476i	$0.785313\pi$
$978$	−501.093			−0.512365
$979$		−	1724.55i		−	1.76155i
$980$	−112.344	−	112.344i	−0.114636	−	0.114636i
$981$	144.567	+	144.567i	0.147367	+	0.147367i
$982$	36.9282	−	36.9282i	0.0376051	−	0.0376051i
$983$	1367.93	−	1367.93i	1.39158	−	1.39158i	0.569801	−	0.821783i	$-0.307020\pi$
$983$	1367.93	−	1367.93i	1.39158	−	1.39158i	0.821783	−	0.569801i	$-0.192980\pi$
$984$	126.431			0.128487
$985$		−	271.230i		−	0.275361i
$986$	−327.846	+	327.846i	−0.332501	+	0.332501i
$987$			166.077i			0.168264i
$988$		0			0
$989$	63.5617			0.0642686
$990$	55.2923	+	55.2923i	0.0558509	+	0.0558509i
$991$	−1871.26			−1.88826			−0.944128	−	0.329579i	$-0.893093\pi$
$991$	−1871.26			−1.88826			−0.944128	+	0.329579i	$0.893093\pi$
$992$		−	177.359i		−	0.178789i
$993$	174.285	+	174.285i	0.175514	+	0.175514i
$994$	1038.90	+	1038.90i	1.04517	+	1.04517i
$995$	−28.1680	+	28.1680i	−0.0283095	+	0.0283095i
$996$	−384.631	+	384.631i	−0.386175	+	0.386175i
$997$	1537.17			1.54179			0.770897	−	0.636960i	$-0.219808\pi$
$997$	1537.17			1.54179			0.770897	+	0.636960i	$0.219808\pi$
$998$			925.538i			0.927393i
$999$	136.019	−	136.019i	0.136155	−	0.136155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.e.775.2		4
13.2	odd	12		78.3.l.a.19.1	✓	4
13.5	odd	4	inner	1014.3.f.e.577.2		4
13.8	odd	4		1014.3.f.d.577.2		4
13.9	even	3		78.3.l.a.37.1	yes	4
13.12	even	2		1014.3.f.d.775.2		4
39.2	even	12		234.3.bb.c.19.1		4
39.35	odd	6		234.3.bb.c.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.19.1	✓	4	13.2	odd	12
78.3.l.a.37.1	yes	4	13.9	even	3
234.3.bb.c.19.1		4	39.2	even	12
234.3.bb.c.37.1		4	39.35	odd	6
1014.3.f.d.577.2		4	13.8	odd	4
1014.3.f.d.775.2		4	13.12	even	2
1014.3.f.e.577.2		4	13.5	odd	4	inner
1014.3.f.e.775.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-1.26795 - 1.26795i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-6.83013 + 6.83013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} -2.53590i q^{10} +(-7.26795 + 7.26795i) q^{11} +3.46410i q^{12} -13.6603 q^{14} +(-2.19615 - 2.19615i) q^{15} -4.00000 q^{16} -18.9282i q^{17} +(3.00000 + 3.00000i) q^{18} +(-23.3923 - 23.3923i) q^{19} +(2.53590 - 2.53590i) q^{20} +(-11.8301 + 11.8301i) q^{21} -14.5359 q^{22} -4.14359i q^{23} +(-3.46410 + 3.46410i) q^{24} -21.7846i q^{25} +5.19615 q^{27} +(-13.6603 - 13.6603i) q^{28} -17.3205 q^{29} -4.39230i q^{30} +(22.1699 + 22.1699i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-12.5885 + 12.5885i) q^{33} +(18.9282 - 18.9282i) q^{34} +17.3205 q^{35} +6.00000i q^{36} +(26.1769 - 26.1769i) q^{37} -46.7846i q^{38} +5.07180 q^{40} +(-18.2487 - 18.2487i) q^{41} -23.6603 q^{42} +15.3397i q^{43} +(-14.5359 - 14.5359i) q^{44} +(-3.80385 - 3.80385i) q^{45} +(4.14359 - 4.14359i) q^{46} +(7.01924 - 7.01924i) q^{47} -6.92820 q^{48} -44.3013i q^{49} +(21.7846 - 21.7846i) q^{50} -32.7846i q^{51} -61.6743 q^{53} +(5.19615 + 5.19615i) q^{54} +18.4308 q^{55} -27.3205i q^{56} +(-40.5167 - 40.5167i) q^{57} +(-17.3205 - 17.3205i) q^{58} +(-46.7321 + 46.7321i) q^{59} +(4.39230 - 4.39230i) q^{60} -7.30127 q^{61} +44.3397i q^{62} +(-20.4904 + 20.4904i) q^{63} -8.00000i q^{64} -25.1769 q^{66} +(-27.7391 - 27.7391i) q^{67} +37.8564 q^{68} -7.17691i q^{69} +(17.3205 + 17.3205i) q^{70} +(-76.0526 - 76.0526i) q^{71} +(-6.00000 + 6.00000i) q^{72} +(-67.4186 + 67.4186i) q^{73} +52.3538 q^{74} -37.7321i q^{75} +(46.7846 - 46.7846i) q^{76} -99.2820i q^{77} +11.8756 q^{79} +(5.07180 + 5.07180i) q^{80} +9.00000 q^{81} -36.4974i q^{82} +(111.033 + 111.033i) q^{83} +(-23.6603 - 23.6603i) q^{84} +(-24.0000 + 24.0000i) q^{85} +(-15.3397 + 15.3397i) q^{86} -30.0000 q^{87} -29.0718i q^{88} +(-118.641 + 118.641i) q^{89} -7.60770i q^{90} +8.28719 q^{92} +(38.3993 + 38.3993i) q^{93} +14.0385 q^{94} +59.3205i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-109.988 - 109.988i) q^{97} +(44.3013 - 44.3013i) q^{98} +(-21.8038 + 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 12 q^{5} - 10 q^{7} - 8 q^{8} + 12 q^{9} - 36 q^{11} - 20 q^{14} + 12 q^{15} - 16 q^{16} + 12 q^{18} - 52 q^{19} + 24 q^{20} - 30 q^{21} - 72 q^{22} - 20 q^{28} + 106 q^{31} - 16 q^{32}+ \cdots - 108 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 12 * q^5 - 10 * q^7 - 8 * q^8 + 12 * q^9 - 36 * q^11 - 20 * q^14 + 12 * q^15 - 16 * q^16 + 12 * q^18 - 52 * q^19 + 24 * q^20 - 30 * q^21 - 72 * q^22 - 20 * q^28 + 106 * q^31 - 16 * q^32 + 12 * q^33 + 48 * q^34 - 20 * q^37 + 48 * q^40 + 24 * q^41 - 60 * q^42 - 72 * q^44 - 36 * q^45 + 72 * q^46 + 132 * q^47 + 4 * q^50 + 72 * q^53 + 240 * q^55 - 72 * q^57 - 180 * q^59 - 24 * q^60 + 144 * q^61 - 30 * q^63 + 24 * q^66 + 38 * q^67 + 96 * q^68 - 228 * q^71 - 24 * q^72 - 190 * q^73 - 40 * q^74 + 104 * q^76 + 96 * q^79 + 48 * q^80 + 36 * q^81 + 264 * q^83 - 60 * q^84 - 96 * q^85 - 96 * q^86 - 120 * q^87 - 336 * q^89 + 144 * q^92 - 30 * q^93 + 264 * q^94 - 194 * q^97 + 4 * q^98 - 108 * q^99

Introduction

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