LMFDB - Embedded newform 1014.3.f.e.577.2

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			577.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.577
Dual form			1014.3.f.e.775.2

$q$-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 $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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	−0.822441	−	0.568851i	$-0.807388\pi$
$5$	−1.26795	+	1.26795i	−0.253590	+	0.253590i	0.568851	+	0.822441i	$0.307388\pi$
$6$	1.73205	−	1.73205i	0.288675	−	0.288675i
$7$	−6.83013	−	6.83013i	−0.975732	−	0.975732i	0.0239800	−	0.999712i	$-0.492366\pi$
$7$	−6.83013	−	6.83013i	−0.975732	−	0.975732i	−0.999712	+	0.0239800i	$0.992366\pi$
$8$	−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	0.294828	−	0.955550i	$-0.404738\pi$
$11$	−7.26795	−	7.26795i	−0.660723	−	0.660723i	−0.955550	+	0.294828i	$0.904738\pi$
$12$		−	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	$0.187937\pi$
$17$			18.9282i			1.11342i	−0.830706	+	0.556712i	$0.812063\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$	−23.3923	+	23.3923i	−1.23117	+	1.23117i	−0.267661	+	0.963513i	$0.586251\pi$
$19$	−23.3923	+	23.3923i	−1.23117	+	1.23117i	−0.963513	+	0.267661i	$0.913749\pi$
$20$	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	$0.0287117\pi$
$23$			4.14359i			0.180156i	−0.995935	+	0.0900781i	$0.971288\pi$
$24$	−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	−0.252452	−	0.967609i	$-0.581237\pi$
$31$	22.1699	−	22.1699i	0.715157	−	0.715157i	0.967609	+	0.252452i	$0.0812370\pi$
$32$	−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	0.966006	−	0.258521i	$-0.0832352\pi$
$37$	26.1769	+	26.1769i	0.707484	+	0.707484i	−0.258521	+	0.966006i	$0.583235\pi$
$38$			46.7846i			1.23117i
$39$		0			0
$40$	5.07180			0.126795
$41$	−18.2487	+	18.2487i	−0.445091	+	0.445091i	−0.893719	−	0.448628i	$-0.851913\pi$
$41$	−18.2487	+	18.2487i	−0.445091	+	0.445091i	0.448628	+	0.893719i	$0.351913\pi$
$42$	−23.6603			−0.563339
$43$		−	15.3397i		−	0.356738i	−0.983964	−	0.178369i	$-0.942918\pi$
$43$		−	15.3397i		−	0.356738i	0.983964	−	0.178369i	$-0.0570821\pi$
$44$	−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	0.777826	−	0.628480i	$-0.216323\pi$
$47$	7.01924	+	7.01924i	0.149345	+	0.149345i	−0.628480	+	0.777826i	$0.716323\pi$
$48$	−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	0.189762	−	0.981830i	$-0.439229\pi$
$59$	−46.7321	−	46.7321i	−0.792069	−	0.792069i	−0.981830	+	0.189762i	$0.939229\pi$
$60$	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	−0.883135	−	0.469119i	$-0.844572\pi$
$67$	−27.7391	+	27.7391i	−0.414016	+	0.414016i	0.469119	+	0.883135i	$0.344572\pi$
$68$	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	−0.0738969	+	0.997266i	$0.523544\pi$
$71$	−76.0526	+	76.0526i	−1.07116	+	1.07116i	−0.997266	+	0.0738969i	$0.976456\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−67.4186	−	67.4186i	−0.923542	−	0.923542i	0.0737356	−	0.997278i	$-0.476508\pi$
$73$	−67.4186	−	67.4186i	−0.923542	−	0.923542i	−0.997278	+	0.0737356i	$0.976508\pi$
$74$	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	0.439516	−	0.898235i	$-0.355150\pi$
$83$	111.033	−	111.033i	1.33775	−	1.33775i	0.898235	−	0.439516i	$-0.144850\pi$
$84$	−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	−0.902632	−	0.430413i	$-0.858368\pi$
$89$	−118.641	−	118.641i	−1.33305	−	1.33305i	−0.430413	−	0.902632i	$-0.641632\pi$
$90$			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	−0.144371	+	0.989524i	$0.546116\pi$
$97$	−109.988	+	109.988i	−1.13389	+	1.13389i	−0.989524	+	0.144371i	$0.953884\pi$
$98$	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	$0.375781\pi$
$101$			186.813i			1.84963i	−0.380415	+	0.924816i	$0.624219\pi$
$102$	32.7846	+	32.7846i	0.321418	+	0.321418i
$103$		−	83.2628i		−	0.808377i	−0.914676	−	0.404188i	$-0.867554\pi$
$103$		−	83.2628i		−	0.808377i	0.914676	−	0.404188i	$-0.132446\pi$
$104$		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	−0.450616	−	0.892718i	$-0.648796\pi$
$109$	48.1891	−	48.1891i	0.442102	−	0.442102i	0.892718	+	0.450616i	$0.148796\pi$
$110$	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	$-0.617653\pi$
$127$		−	236.846i		−	1.86493i	0.361260	−	0.932465i	$-0.382347\pi$
$128$	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	0.937050	−	0.349196i	$-0.113545\pi$
$137$	80.5359	+	80.5359i	0.587853	+	0.587853i	−0.349196	+	0.937050i	$0.613545\pi$
$138$	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	−0.559179	−	0.829047i	$-0.688884\pi$
$149$	40.2102	−	40.2102i	0.269867	−	0.269867i	0.829047	+	0.559179i	$0.188884\pi$
$150$	37.7321	+	37.7321i	0.251547	+	0.251547i
$151$	−55.0385	−	55.0385i	−0.364493	−	0.364493i	0.500971	−	0.865464i	$-0.332976\pi$
$151$	−55.0385	−	55.0385i	−0.364493	−	0.364493i	−0.865464	+	0.500971i	$0.832976\pi$
$152$	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	0.106834	−	0.994277i	$-0.465929\pi$
$163$	−144.653	−	144.653i	−0.887443	−	0.887443i	−0.994277	+	0.106834i	$0.965929\pi$
$164$	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	0.961170	−	0.275956i	$-0.0889944\pi$
$167$	114.431	+	114.431i	0.685214	+	0.685214i	−0.275956	+	0.961170i	$0.588994\pi$
$168$			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	$0.282700\pi$
$173$			268.459i			1.55179i	−0.630865	+	0.775893i	$0.717300\pi$
$174$	−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	$0.294249\pi$
$179$			285.779i			1.59653i	−0.602304	+	0.798267i	$0.705751\pi$
$180$	7.60770	+	7.60770i	0.0422650	+	0.0422650i
$181$		−	177.646i		−	0.981471i	−0.871309	−	0.490735i	$-0.836728\pi$
$181$		−	177.646i		−	0.981471i	0.871309	−	0.490735i	$-0.163272\pi$
$182$		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	0.744529	−	0.667590i	$-0.232674\pi$
$193$	14.8494	+	14.8494i	0.0769397	+	0.0769397i	−0.667590	+	0.744529i	$0.732674\pi$
$194$			219.976i			1.13389i
$195$		0			0
$196$	88.6025			0.452054
$197$	106.956	−	106.956i	0.542926	−	0.542926i	−0.381460	−	0.924385i	$-0.624579\pi$
$197$	106.956	−	106.956i	0.542926	−	0.542926i	0.924385	+	0.381460i	$0.124579\pi$
$198$	−43.6077			−0.220241
$199$			22.2154i			0.111635i	0.998441	+	0.0558176i	$0.0177765\pi$
$199$			22.2154i			0.111635i	−0.998441	+	0.0558176i	$0.982223\pi$
$200$	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	−0.962883	−	0.269920i	$-0.913003\pi$
$223$	−154.531	+	154.531i	−0.692963	+	0.692963i	0.269920	+	0.962883i	$0.413003\pi$
$224$	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	−0.800590	−	0.599212i	$-0.795481\pi$
$227$	−45.7128	+	45.7128i	−0.201378	+	0.201378i	0.599212	+	0.800590i	$0.295481\pi$
$228$	81.0333	+	81.0333i	0.355409	+	0.355409i
$229$	58.6846	+	58.6846i	0.256265	+	0.256265i	0.823533	−	0.567268i	$-0.192000\pi$
$229$	58.6846	+	58.6846i	0.256265	+	0.256265i	−0.567268	+	0.823533i	$0.692000\pi$
$230$	−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	$-0.695698\pi$
$233$		−	380.669i		−	1.63377i	0.576798	−	0.816887i	$-0.304302\pi$
$234$		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	−0.964265	−	0.264941i	$-0.914648\pi$
$239$	−167.138	+	167.138i	−0.699324	+	0.699324i	0.264941	+	0.964265i	$0.414648\pi$
$240$	8.78461	−	8.78461i	0.0366025	−	0.0366025i
$241$	2.17691	+	2.17691i	0.00903284	+	0.00903284i	0.711609	−	0.702576i	$-0.247967\pi$
$241$	2.17691	+	2.17691i	0.00903284	+	0.00903284i	−0.702576	+	0.711609i	$0.747967\pi$
$242$	−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	$-0.863518\pi$
$251$		−	208.708i		−	0.831505i	0.909478	−	0.415752i	$-0.136482\pi$
$252$	−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	$-0.953875\pi$
$257$		−	74.2205i		−	0.288796i	0.989520	−	0.144398i	$-0.0461245\pi$
$258$	−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	0.242937	−	0.970042i	$-0.421889\pi$
$271$	−197.046	−	197.046i	−0.727105	−	0.727105i	−0.970042	+	0.242937i	$0.921889\pi$
$272$		−	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	$-0.701181\pi$
$277$		−	446.985i		−	1.61366i	0.590782	−	0.806831i	$-0.298819\pi$
$278$	−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	0.697172	−	0.716904i	$-0.254442\pi$
$281$	−5.54483	−	5.54483i	−0.0197325	−	0.0197325i	−0.716904	+	0.697172i	$0.754442\pi$
$282$	24.3154			0.0862247
$283$		−	16.6462i		−	0.0588204i	−0.999567	−	0.0294102i	$-0.990637\pi$
$283$		−	16.6462i		−	0.0588204i	0.999567	−	0.0294102i	$-0.00936291\pi$
$284$	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	0.896060	−	0.443933i	$-0.146417\pi$
$293$	132.473	+	132.473i	0.452126	+	0.452126i	−0.443933	+	0.896060i	$0.646417\pi$
$294$	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	0.967020	+	0.254702i	$0.0819774\pi$
$307$	375.069	+	375.069i	1.22172	+	1.22172i	0.254702	+	0.967020i	$0.418023\pi$
$308$	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	$0.158011\pi$
$311$			296.238i			0.952535i	−0.879300	+	0.476268i	$0.841989\pi$
$312$		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	−0.994088	−	0.108575i	$-0.965371\pi$
$317$	−280.708	+	280.708i	−0.885513	+	0.885513i	0.108575	+	0.994088i	$0.465371\pi$
$318$	−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	−0.538577	−	0.842576i	$-0.681038\pi$
$331$	100.624	−	100.624i	0.303999	−	0.303999i	0.842576	+	0.538577i	$0.181038\pi$
$332$	−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	$-0.827573\pi$
$337$		−	347.508i		−	1.03118i	0.856835	−	0.515590i	$-0.172427\pi$
$338$		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	0.996112	−	0.0880981i	$-0.0280789\pi$
$349$	316.897	+	316.897i	0.908014	+	0.908014i	−0.0880981	+	0.996112i	$0.528079\pi$
$350$		−	297.583i		−	0.850238i
$351$		0			0
$352$	58.1436			0.165181
$353$	−415.037	+	415.037i	−1.17574	+	1.17574i	−0.194924	+	0.980818i	$0.562446\pi$
$353$	−415.037	+	415.037i	−1.17574	+	1.17574i	−0.980818	+	0.194924i	$0.937554\pi$
$354$	−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	0.790939	−	0.611895i	$-0.209592\pi$
$359$	64.2769	+	64.2769i	0.179044	+	0.179044i	−0.611895	+	0.790939i	$0.709592\pi$
$360$	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	−0.502701	−	0.864461i	$-0.667660\pi$
$379$	137.107	−	137.107i	0.361760	−	0.361760i	0.864461	+	0.502701i	$0.167660\pi$
$380$	−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	−0.863689	−	0.504025i	$-0.831852\pi$
$383$	−137.751	+	137.751i	−0.359664	+	0.359664i	0.504025	+	0.863689i	$0.331852\pi$
$384$	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	$0.00726337\pi$
$389$			17.7513i			0.0456331i	−0.999740	+	0.0228166i	$0.992737\pi$
$390$		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	0.339493	−	0.940609i	$-0.389745\pi$
$397$	−238.643	−	238.643i	−0.601116	−	0.601116i	−0.940609	+	0.339493i	$0.889745\pi$
$398$	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	0.995969	−	0.0896965i	$-0.0285897\pi$
$401$	363.415	+	363.415i	0.906273	+	0.906273i	−0.0896965	+	0.995969i	$0.528590\pi$
$402$			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	0.00742680	−	0.999972i	$-0.497636\pi$
$409$	412.026	−	412.026i	1.00740	−	1.00740i	0.999972	−	0.00742680i	$-0.00236404\pi$
$410$	−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	−0.738486	−	0.674269i	$-0.764459\pi$
$421$	−27.0352	+	27.0352i	−0.0642166	+	0.0642166i	0.674269	+	0.738486i	$0.264459\pi$
$422$	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	0.0337728	−	0.999430i	$-0.489248\pi$
$431$	445.310	−	445.310i	1.03320	−	1.03320i	0.999430	−	0.0337728i	$-0.0107523\pi$
$432$	−20.7846			−0.0481125
$433$		−	237.785i		−	0.549156i	−0.961565	−	0.274578i	$-0.911462\pi$
$433$		−	237.785i		−	0.549156i	0.961565	−	0.274578i	$-0.0885382\pi$
$434$	−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	$-0.712527\pi$
$439$		−	689.463i		−	1.57053i	0.619160	−	0.785265i	$-0.287473\pi$
$440$	−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	0.447370	−	0.894349i	$-0.352361\pi$
$449$	−200.694	−	200.694i	−0.446979	−	0.446979i	−0.894349	+	0.447370i	$0.852361\pi$
$450$	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	−0.809400	−	0.587258i	$-0.800207\pi$
$457$	−101.519	+	101.519i	−0.222141	+	0.222141i	0.587258	+	0.809400i	$0.300207\pi$
$458$	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	−0.995665	−	0.0930121i	$-0.970350\pi$
$461$	−416.123	+	416.123i	−0.902653	+	0.902653i	0.0930121	+	0.995665i	$0.470350\pi$
$462$	171.962	+	171.962i	0.372211	+	0.372211i
$463$	−169.599	−	169.599i	−0.366305	−	0.366305i	0.499823	−	0.866128i	$-0.333399\pi$
$463$	−169.599	−	169.599i	−0.366305	−	0.366305i	−0.866128	+	0.499823i	$0.833399\pi$
$464$	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	$-0.712961\pi$
$467$		−	732.649i		−	1.56884i	0.620230	−	0.784420i	$-0.287039\pi$
$468$		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	0.925239	−	0.379385i	$-0.123864\pi$
$479$	261.464	+	261.464i	0.545854	+	0.545854i	−0.379385	+	0.925239i	$0.623864\pi$
$480$		−	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	−0.833633	−	0.552319i	$-0.813743\pi$
$487$	−137.000	+	137.000i	−0.281314	+	0.281314i	0.552319	+	0.833633i	$0.313743\pi$
$488$	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	$0.0119729\pi$
$491$			36.9282i			0.0752102i	−0.999293	+	0.0376051i	$0.988027\pi$
$492$	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	−0.0701438	−	0.997537i	$-0.522346\pi$
$499$	462.769	−	462.769i	0.927393	−	0.927393i	0.997537	+	0.0701438i	$0.0223458\pi$
$500$	−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	−0.0253604	+	0.999678i	$0.508073\pi$
$509$	−521.745	+	521.745i	−1.02504	+	1.02504i	−0.999678	+	0.0253604i	$0.991927\pi$
$510$	−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	0.702989	−	0.711201i	$-0.251848\pi$
$541$	−4.44298	−	4.44298i	−0.00821253	−	0.00821253i	−0.711201	+	0.702989i	$0.751848\pi$
$542$	−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	0.988376	−	0.152028i	$-0.0485803\pi$
$557$	465.846	+	465.846i	0.836348	+	0.836348i	−0.152028	+	0.988376i	$0.548580\pi$
$558$		−	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	$0.0251079\pi$
$563$			88.7255i			0.157594i	−0.996891	+	0.0787971i	$0.974892\pi$
$564$	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	$0.123813\pi$
$569$			431.569i			0.758470i	−0.925300	+	0.379235i	$0.876187\pi$
$570$	−102.746	−	102.746i	−0.180256	−	0.180256i
$571$			959.892i			1.68107i	0.541756	+	0.840536i	$0.317760\pi$
$571$			959.892i			1.68107i	−0.541756	+	0.840536i	$0.682240\pi$
$572$		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	−0.924588	−	0.380968i	$-0.875591\pi$
$577$	−313.669	+	313.669i	−0.543621	+	0.543621i	0.380968	+	0.924588i	$0.375591\pi$
$578$	−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	−0.830138	−	0.557559i	$-0.811738\pi$
$587$	−160.004	+	160.004i	−0.272579	+	0.272579i	0.557559	+	0.830138i	$0.311738\pi$
$588$	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	0.930811	−	0.365500i	$-0.119102\pi$
$593$	335.229	+	335.229i	0.565311	+	0.565311i	−0.365500	+	0.930811i	$0.619102\pi$
$594$	−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	−0.970056	−	0.242883i	$-0.921907\pi$
$613$	−445.757	+	445.757i	−0.727173	+	0.727173i	0.242883	+	0.970056i	$0.421907\pi$
$614$	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	−0.767736	−	0.640767i	$-0.778617\pi$
$617$	−78.3397	+	78.3397i	−0.126969	+	0.126969i	0.640767	+	0.767736i	$0.278617\pi$
$618$	−144.215	−	144.215i	−0.233358	−	0.233358i
$619$	−111.970	−	111.970i	−0.180888	−	0.180888i	0.610854	−	0.791743i	$-0.290826\pi$
$619$	−111.970	−	111.970i	−0.180888	−	0.180888i	−0.791743	+	0.610854i	$0.790826\pi$
$620$	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	0.965558	+	0.260187i	$0.0837843\pi$
$631$	773.445	+	773.445i	1.22575	+	1.22575i	0.260187	+	0.965558i	$0.416216\pi$
$632$	−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	$-0.896743\pi$
$641$		−	408.613i		−	0.637462i	0.947845	−	0.318731i	$-0.103257\pi$
$642$	177.531	−	177.531i	0.276528	−	0.276528i
$643$	316.730	−	316.730i	0.492582	−	0.492582i	−0.416537	−	0.909119i	$-0.636756\pi$
$643$	316.730	−	316.730i	0.492582	−	0.492582i	0.909119	+	0.416537i	$0.136756\pi$
$644$	−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	$0.0802632\pi$
$647$			322.841i			0.498981i	−0.968377	+	0.249491i	$0.919737\pi$
$648$	−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	0.621511	−	0.783405i	$-0.286519\pi$
$661$	−107.012	−	107.012i	−0.161894	−	0.161894i	−0.783405	+	0.621511i	$0.786519\pi$
$662$		−	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	$0.176307\pi$
$673$			707.991i			1.05199i	−0.850487	+	0.525996i	$0.823693\pi$
$674$	−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	0.628743	−	0.777613i	$-0.283570\pi$
$683$	−101.678	−	101.678i	−0.148870	−	0.148870i	−0.777613	+	0.628743i	$0.783570\pi$
$684$	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	−0.371304	−	0.928511i	$-0.621089\pi$
$691$	385.030	−	385.030i	0.557207	−	0.557207i	0.928511	+	0.371304i	$0.121089\pi$
$692$	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	$0.132861\pi$
$701$			568.344i			0.810761i	−0.914148	+	0.405381i	$0.867139\pi$
$702$		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	0.865977	−	0.500084i	$-0.166697\pi$
$709$	259.419	+	259.419i	0.365894	+	0.365894i	−0.500084	+	0.865977i	$0.666697\pi$
$710$	−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	$0.0586633\pi$
$719$			263.520i			0.366510i	−0.983065	+	0.183255i	$0.941337\pi$
$720$	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	$0.206482\pi$
$727$			878.415i			1.20827i	−0.796880	+	0.604137i	$0.793518\pi$
$728$		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	−0.800016	−	0.599979i	$-0.795176\pi$
$733$	−146.627	+	146.627i	−0.200037	+	0.200037i	0.599979	+	0.800016i	$0.295176\pi$
$734$	−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	0.328566	−	0.944481i	$-0.393435\pi$
$739$	−455.161	−	455.161i	−0.615915	−	0.615915i	−0.944481	+	0.328566i	$0.893435\pi$
$740$			132.764i			0.179411i
$741$		0			0
$742$	842.487			1.13543
$743$	−9.63963	+	9.63963i	−0.0129739	+	0.0129739i	−0.713564	−	0.700590i	$-0.752920\pi$
$743$	−9.63963	+	9.63963i	−0.0129739	+	0.0129739i	0.700590	+	0.713564i	$0.252920\pi$
$744$	−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	$0.0339887\pi$
$751$			160.077i			0.213152i	−0.994305	+	0.106576i	$0.966011\pi$
$752$	−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	0.786977	−	0.616982i	$-0.211645\pi$
$761$	129.367	+	129.367i	0.169995	+	0.169995i	−0.616982	+	0.786977i	$0.711645\pi$
$762$	−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	0.294404	−	0.955681i	$-0.404879\pi$
$769$	961.315	−	961.315i	1.25008	−	1.25008i	0.955681	−	0.294404i	$-0.0951211\pi$
$770$	−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	−0.995035	−	0.0995220i	$-0.968269\pi$
$773$	−692.232	+	692.232i	−0.895513	+	0.895513i	0.0995220	+	0.995035i	$0.468269\pi$
$774$	−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	0.758136	−	0.652096i	$-0.226110\pi$
$787$	83.4533	+	83.4533i	0.106040	+	0.106040i	−0.652096	+	0.758136i	$0.726110\pi$
$788$	−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	$0.115786\pi$
$797$			567.118i			0.711566i	−0.934569	+	0.355783i	$0.884214\pi$
$798$	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	−0.950602	−	0.310413i	$-0.899533\pi$
$811$	−519.193	+	519.193i	−0.640189	+	0.640189i	0.310413	+	0.950602i	$0.399533\pi$
$812$	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	−0.414580	−	0.910013i	$-0.636072\pi$
$821$	406.750	−	406.750i	0.495432	−	0.495432i	0.910013	+	0.414580i	$0.136072\pi$
$822$	278.985			0.339397
$823$		−	329.169i		−	0.399963i	−0.979800	−	0.199981i	$-0.935912\pi$
$823$		−	329.169i		−	0.399963i	0.979800	−	0.199981i	$-0.0640882\pi$
$824$	−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	0.946048	−	0.324028i	$-0.105037\pi$
$827$	514.410	+	514.410i	0.622020	+	0.622020i	−0.324028	+	0.946048i	$0.605037\pi$
$828$	24.8616			0.0300260
$829$			943.092i			1.13763i	0.822467	+	0.568813i	$0.192597\pi$
$829$			943.092i			1.13763i	−0.822467	+	0.568813i	$0.807403\pi$
$830$	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	0.293256	−	0.956034i	$-0.405261\pi$
$839$	−556.070	−	556.070i	−0.662778	−	0.662778i	−0.956034	+	0.293256i	$0.905261\pi$
$840$	−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	0.927581	−	0.373622i	$-0.121884\pi$
$853$	472.527	+	472.527i	0.553960	+	0.553960i	−0.373622	+	0.927581i	$0.621884\pi$
$854$	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	$0.0819743\pi$
$857$			436.543i			0.509386i	−0.967022	+	0.254693i	$0.918026\pi$
$858$		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	−0.144365	−	0.989525i	$-0.546114\pi$
$863$	729.373	−	729.373i	0.845160	−	0.845160i	0.989525	+	0.144365i	$0.0461138\pi$
$864$	−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	−0.102240	+	0.994760i	$0.532601\pi$
$877$	−962.069	+	962.069i	−1.09700	+	1.09700i	−0.994760	+	0.102240i	$0.967399\pi$
$878$	−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	$-0.652484\pi$
$881$		−	1563.66i		−	1.77487i	0.460929	−	0.887437i	$-0.347516\pi$
$882$	132.904	+	132.904i	0.150685	+	0.150685i
$883$			452.723i			0.512710i	0.966583	+	0.256355i	$0.0825216\pi$
$883$			452.723i			0.512710i	−0.966583	+	0.256355i	$0.917478\pi$
$884$		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	$-0.921084\pi$
$907$		−	445.138i		−	0.490781i	0.969424	−	0.245391i	$-0.0789162\pi$
$908$	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	−0.130814	+	0.991407i	$0.541759\pi$
$929$	−1042.54	+	1042.54i	−1.12222	+	1.12222i	−0.991407	+	0.130814i	$0.958241\pi$
$930$	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	−0.625819	−	0.779969i	$-0.715235\pi$
$941$	145.055	−	145.055i	0.154150	−	0.154150i	0.779969	+	0.625819i	$0.215235\pi$
$942$	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	0.915980	−	0.401224i	$-0.131415\pi$
$947$	487.474	+	487.474i	0.514757	+	0.514757i	−0.401224	+	0.915980i	$0.631415\pi$
$948$		−	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	$-0.781797\pi$
$953$		−	1206.62i		−	1.26613i	0.774100	−	0.633063i	$-0.218203\pi$
$954$	−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	−0.789446	−	0.613820i	$-0.789632\pi$
$967$	−169.831	+	169.831i	−0.175626	+	0.175626i	0.613820	+	0.789446i	$0.289632\pi$
$968$	−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	−0.781044	−	0.624476i	$-0.785313\pi$
$977$	−152.967	+	152.967i	−0.156568	+	0.156568i	0.624476	+	0.781044i	$0.285313\pi$
$978$	−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	0.821783	+	0.569801i	$0.192980\pi$
$983$	1367.93	+	1367.93i	1.39158	+	1.39158i	0.569801	+	0.821783i	$0.307020\pi$
$984$	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.577.2		4
13.3	even	3		78.3.l.a.19.1	✓	4
13.5	odd	4		1014.3.f.d.775.2		4
13.7	odd	12		78.3.l.a.37.1	yes	4
13.8	odd	4	inner	1014.3.f.e.775.2		4
13.12	even	2		1014.3.f.d.577.2		4
39.20	even	12		234.3.bb.c.37.1		4
39.29	odd	6		234.3.bb.c.19.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.19.1	✓	4	13.3	even	3
78.3.l.a.37.1	yes	4	13.7	odd	12
234.3.bb.c.19.1		4	39.29	odd	6
234.3.bb.c.37.1		4	39.20	even	12
1014.3.f.d.577.2		4	13.12	even	2
1014.3.f.d.775.2		4	13.5	odd	4
1014.3.f.e.577.2		4	1.1	even	1	trivial
1014.3.f.e.775.2		4	13.8	odd	4	inner

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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