LMFDB - Embedded newform 1014.3.f.d.775.1

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			775.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.d.577.1

$q$-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} +(4.73205 + 4.73205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-1.83013 + 1.83013i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -9.46410i q^{10} +(10.7321 - 10.7321i) q^{11} -3.46410i q^{12} +3.66025 q^{14} +(-8.19615 - 8.19615i) q^{15} -4.00000 q^{16} -5.07180i q^{17} +(-3.00000 - 3.00000i) q^{18} +(2.60770 + 2.60770i) q^{19} +(-9.46410 + 9.46410i) q^{20} +(3.16987 - 3.16987i) q^{21} -21.4641 q^{22} -31.8564i q^{23} +(-3.46410 + 3.46410i) q^{24} +19.7846i q^{25} -5.19615 q^{27} +(-3.66025 - 3.66025i) q^{28} +17.3205 q^{29} +16.3923i q^{30} +(-30.8301 - 30.8301i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-18.5885 + 18.5885i) q^{33} +(-5.07180 + 5.07180i) q^{34} -17.3205 q^{35} +6.00000i q^{36} +(36.1769 - 36.1769i) q^{37} -5.21539i q^{38} +18.9282 q^{40} +(-30.2487 - 30.2487i) q^{41} -6.33975 q^{42} +32.6603i q^{43} +(21.4641 + 21.4641i) q^{44} +(14.1962 + 14.1962i) q^{45} +(-31.8564 + 31.8564i) q^{46} +(-58.9808 + 58.9808i) q^{47} +6.92820 q^{48} +42.3013i q^{49} +(19.7846 - 19.7846i) q^{50} +8.78461i q^{51} +97.6743 q^{53} +(5.19615 + 5.19615i) q^{54} +101.569 q^{55} +7.32051i q^{56} +(-4.51666 - 4.51666i) q^{57} +(-17.3205 - 17.3205i) q^{58} +(43.2679 - 43.2679i) q^{59} +(16.3923 - 16.3923i) q^{60} +79.3013 q^{61} +61.6603i q^{62} +(-5.49038 + 5.49038i) q^{63} -8.00000i q^{64} +37.1769 q^{66} +(-46.7391 - 46.7391i) q^{67} +10.1436 q^{68} +55.1769i q^{69} +(17.3205 + 17.3205i) q^{70} +(37.9474 + 37.9474i) q^{71} +(6.00000 - 6.00000i) q^{72} +(27.5814 - 27.5814i) q^{73} -72.3538 q^{74} -34.2679i q^{75} +(-5.21539 + 5.21539i) q^{76} +39.2820i q^{77} +36.1244 q^{79} +(-18.9282 - 18.9282i) q^{80} +9.00000 q^{81} +60.4974i q^{82} +(-20.9667 - 20.9667i) q^{83} +(6.33975 + 6.33975i) q^{84} +(24.0000 - 24.0000i) q^{85} +(32.6603 - 32.6603i) q^{86} -30.0000 q^{87} -42.9282i q^{88} +(49.3590 - 49.3590i) q^{89} -28.3923i q^{90} +63.7128 q^{92} +(53.3993 + 53.3993i) q^{93} +117.962 q^{94} +24.6795i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-12.9878 - 12.9878i) q^{97} +(42.3013 - 42.3013i) q^{98} +(32.1962 - 32.1962i) 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
$5$	4.73205	+	4.73205i	0.946410	+	0.946410i	0.998635	−	0.0522252i	$-0.0166314\pi$
$5$	4.73205	+	4.73205i	0.946410	+	0.946410i	−0.0522252	+	0.998635i	$0.516631\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	−1.83013	+	1.83013i	−0.261447	+	0.261447i	−0.825642	−	0.564195i	$-0.809187\pi$
$7$	−1.83013	+	1.83013i	−0.261447	+	0.261447i	0.564195	+	0.825642i	$0.309187\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	3.00000			0.333333
$10$		−	9.46410i		−	0.946410i
$11$	10.7321	−	10.7321i	0.975641	−	0.975641i	−0.0240693	−	0.999710i	$-0.507662\pi$
$11$	10.7321	−	10.7321i	0.975641	−	0.975641i	0.999710	+	0.0240693i	$0.00766224\pi$
$12$		−	3.46410i		−	0.288675i
$13$		0			0
$13$		0			0
$14$	3.66025			0.261447
$15$	−8.19615	−	8.19615i	−0.546410	−	0.546410i
$16$	−4.00000			−0.250000
$17$		−	5.07180i		−	0.298341i	−0.988811	−	0.149170i	$-0.952340\pi$
$17$		−	5.07180i		−	0.298341i	0.988811	−	0.149170i	$-0.0476603\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	2.60770	+	2.60770i	0.137247	+	0.137247i	0.772393	−	0.635145i	$-0.219060\pi$
$19$	2.60770	+	2.60770i	0.137247	+	0.137247i	−0.635145	+	0.772393i	$0.719060\pi$
$20$	−9.46410	+	9.46410i	−0.473205	+	0.473205i
$21$	3.16987	−	3.16987i	0.150946	−	0.150946i
$22$	−21.4641			−0.975641
$23$		−	31.8564i		−	1.38506i	−0.721389	−	0.692531i	$-0.756496\pi$
$23$		−	31.8564i		−	1.38506i	0.721389	−	0.692531i	$-0.243504\pi$
$24$	−3.46410	+	3.46410i	−0.144338	+	0.144338i
$25$			19.7846i			0.791384i
$26$		0			0
$27$	−5.19615			−0.192450
$28$	−3.66025	−	3.66025i	−0.130723	−	0.130723i
$29$	17.3205			0.597259			0.298629	−	0.954369i	$-0.403471\pi$
$29$	17.3205			0.597259			0.298629	+	0.954369i	$0.403471\pi$
$30$			16.3923i			0.546410i
$31$	−30.8301	−	30.8301i	−0.994520	−	0.994520i	0.00546484	−	0.999985i	$-0.498260\pi$
$31$	−30.8301	−	30.8301i	−0.994520	−	0.994520i	−0.999985	+	0.00546484i	$0.998260\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−18.5885	+	18.5885i	−0.563287	+	0.563287i
$34$	−5.07180	+	5.07180i	−0.149170	+	0.149170i
$35$	−17.3205			−0.494872
$36$			6.00000i			0.166667i
$37$	36.1769	−	36.1769i	0.977754	−	0.977754i	−0.0220034	−	0.999758i	$-0.507004\pi$
$37$	36.1769	−	36.1769i	0.977754	−	0.977754i	0.999758	+	0.0220034i	$0.00700448\pi$
$38$		−	5.21539i		−	0.137247i
$39$		0			0
$40$	18.9282			0.473205
$41$	−30.2487	−	30.2487i	−0.737773	−	0.737773i	0.234373	−	0.972147i	$-0.424696\pi$
$41$	−30.2487	−	30.2487i	−0.737773	−	0.737773i	−0.972147	+	0.234373i	$0.924696\pi$
$42$	−6.33975			−0.150946
$43$			32.6603i			0.759541i	0.925081	+	0.379770i	$0.123997\pi$
$43$			32.6603i			0.759541i	−0.925081	+	0.379770i	$0.876003\pi$
$44$	21.4641	+	21.4641i	0.487820	+	0.487820i
$45$	14.1962	+	14.1962i	0.315470	+	0.315470i
$46$	−31.8564	+	31.8564i	−0.692531	+	0.692531i
$47$	−58.9808	+	58.9808i	−1.25491	+	1.25491i	−0.301418	+	0.953492i	$0.597460\pi$
$47$	−58.9808	+	58.9808i	−1.25491	+	1.25491i	−0.953492	+	0.301418i	$0.902540\pi$
$48$	6.92820			0.144338
$49$			42.3013i			0.863291i
$50$	19.7846	−	19.7846i	0.395692	−	0.395692i
$51$			8.78461i			0.172247i
$52$		0			0
$53$	97.6743			1.84291			0.921456	−	0.388483i	$-0.127001\pi$
$53$	97.6743			1.84291			0.921456	+	0.388483i	$0.127001\pi$
$54$	5.19615	+	5.19615i	0.0962250	+	0.0962250i
$55$	101.569			1.84671
$56$			7.32051i			0.130723i
$57$	−4.51666	−	4.51666i	−0.0792397	−	0.0792397i
$58$	−17.3205	−	17.3205i	−0.298629	−	0.298629i
$59$	43.2679	−	43.2679i	0.733355	−	0.733355i	−0.237928	−	0.971283i	$-0.576468\pi$
$59$	43.2679	−	43.2679i	0.733355	−	0.733355i	0.971283	+	0.237928i	$0.0764682\pi$
$60$	16.3923	−	16.3923i	0.273205	−	0.273205i
$61$	79.3013			1.30002			0.650010	−	0.759925i	$-0.274765\pi$
$61$	79.3013			1.30002			0.650010	+	0.759925i	$0.274765\pi$
$62$			61.6603i			0.994520i
$63$	−5.49038	+	5.49038i	−0.0871489	+	0.0871489i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	37.1769			0.563287
$67$	−46.7391	−	46.7391i	−0.697598	−	0.697598i	0.266294	−	0.963892i	$-0.414201\pi$
$67$	−46.7391	−	46.7391i	−0.697598	−	0.697598i	−0.963892	+	0.266294i	$0.914201\pi$
$68$	10.1436			0.149170
$69$			55.1769i			0.799665i
$70$	17.3205	+	17.3205i	0.247436	+	0.247436i
$71$	37.9474	+	37.9474i	0.534471	+	0.534471i	0.921900	−	0.387429i	$-0.126637\pi$
$71$	37.9474	+	37.9474i	0.534471	+	0.534471i	−0.387429	+	0.921900i	$0.626637\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	27.5814	−	27.5814i	0.377828	−	0.377828i	−0.492490	−	0.870318i	$-0.663913\pi$
$73$	27.5814	−	27.5814i	0.377828	−	0.377828i	0.870318	+	0.492490i	$0.163913\pi$
$74$	−72.3538			−0.977754
$75$		−	34.2679i		−	0.456906i
$76$	−5.21539	+	5.21539i	−0.0686236	+	0.0686236i
$77$			39.2820i			0.510156i
$78$		0			0
$79$	36.1244			0.457270			0.228635	−	0.973512i	$-0.426574\pi$
$79$	36.1244			0.457270			0.228635	+	0.973512i	$0.426574\pi$
$80$	−18.9282	−	18.9282i	−0.236603	−	0.236603i
$81$	9.00000			0.111111
$82$			60.4974i			0.737773i
$83$	−20.9667	−	20.9667i	−0.252611	−	0.252611i	0.569430	−	0.822040i	$-0.307164\pi$
$83$	−20.9667	−	20.9667i	−0.252611	−	0.252611i	−0.822040	+	0.569430i	$0.807164\pi$
$84$	6.33975	+	6.33975i	0.0754732	+	0.0754732i
$85$	24.0000	−	24.0000i	0.282353	−	0.282353i
$86$	32.6603	−	32.6603i	0.379770	−	0.379770i
$87$	−30.0000			−0.344828
$88$		−	42.9282i		−	0.487820i
$89$	49.3590	−	49.3590i	0.554595	−	0.554595i	−0.373168	−	0.927764i	$-0.621729\pi$
$89$	49.3590	−	49.3590i	0.554595	−	0.554595i	0.927764	+	0.373168i	$0.121729\pi$
$90$		−	28.3923i		−	0.315470i
$91$		0			0
$92$	63.7128			0.692531
$93$	53.3993	+	53.3993i	0.574187	+	0.574187i
$94$	117.962			1.25491
$95$			24.6795i			0.259784i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	−12.9878	−	12.9878i	−0.133895	−	0.133895i	0.636983	−	0.770878i	$-0.280182\pi$
$97$	−12.9878	−	12.9878i	−0.133895	−	0.133895i	−0.770878	+	0.636983i	$0.780182\pi$
$98$	42.3013	−	42.3013i	0.431646	−	0.431646i
$99$	32.1962	−	32.1962i	0.325214	−	0.325214i
$100$	−39.5692			−0.395692
$101$			138.813i			1.37438i	0.726476	+	0.687192i	$0.241157\pi$
$101$			138.813i			1.37438i	−0.726476	+	0.687192i	$0.758843\pi$
$102$	8.78461	−	8.78461i	0.0861236	−	0.0861236i
$103$		−	107.263i		−	1.04139i	−0.853744	−	0.520693i	$-0.825674\pi$
$103$		−	107.263i		−	1.04139i	0.853744	−	0.520693i	$-0.174326\pi$
$104$		0			0
$105$	30.0000			0.285714
$106$	−97.6743	−	97.6743i	−0.921456	−	0.921456i
$107$	5.50258			0.0514260			0.0257130	−	0.999669i	$-0.491814\pi$
$107$	5.50258			0.0514260			0.0257130	+	0.999669i	$0.491814\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−108.811	−	108.811i	−0.998265	−	0.998265i	0.00173346	−	0.999998i	$-0.499448\pi$
$109$	−108.811	−	108.811i	−0.998265	−	0.998265i	−0.999998	+	0.00173346i	$0.999448\pi$
$110$	−101.569	−	101.569i	−0.923357	−	0.923357i
$111$	−62.6603	+	62.6603i	−0.564507	+	0.564507i
$112$	7.32051	−	7.32051i	0.0653617	−	0.0653617i
$113$	−86.7846			−0.768005			−0.384003	−	0.923332i	$-0.625455\pi$
$113$	−86.7846			−0.768005			−0.384003	+	0.923332i	$0.625455\pi$
$114$			9.03332i			0.0792397i
$115$	150.746	−	150.746i	1.31084	−	1.31084i
$116$			34.6410i			0.298629i
$117$		0			0
$118$	−86.5359			−0.733355
$119$	9.28203	+	9.28203i	0.0780003	+	0.0780003i
$120$	−32.7846			−0.273205
$121$		−	109.354i		−	0.903751i
$122$	−79.3013	−	79.3013i	−0.650010	−	0.650010i
$123$	52.3923	+	52.3923i	0.425954	+	0.425954i
$124$	61.6603	−	61.6603i	0.497260	−	0.497260i
$125$	24.6795	−	24.6795i	0.197436	−	0.197436i
$126$	10.9808			0.0871489
$127$		−	178.846i		−	1.40824i	−0.710082	−	0.704118i	$-0.751342\pi$
$127$		−	178.846i		−	1.40824i	0.710082	−	0.704118i	$-0.248658\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	56.5692i		−	0.438521i
$130$		0			0
$131$	53.6359			0.409434			0.204717	−	0.978821i	$-0.434373\pi$
$131$	53.6359			0.409434			0.204717	+	0.978821i	$0.434373\pi$
$132$	−37.1769	−	37.1769i	−0.281643	−	0.281643i
$133$	−9.54483			−0.0717656
$134$			93.4782i			0.697598i
$135$	−24.5885	−	24.5885i	−0.182137	−	0.182137i
$136$	−10.1436	−	10.1436i	−0.0745852	−	0.0745852i
$137$	−87.4641	+	87.4641i	−0.638424	+	0.638424i	−0.950167	−	0.311743i	$-0.899087\pi$
$137$	−87.4641	+	87.4641i	−0.638424	+	0.638424i	0.311743	+	0.950167i	$0.399087\pi$
$138$	55.1769	−	55.1769i	0.399833	−	0.399833i
$139$	153.708			1.10581			0.552905	−	0.833244i	$-0.313519\pi$
$139$	153.708			1.10581			0.552905	+	0.833244i	$0.313519\pi$
$140$		−	34.6410i		−	0.247436i
$141$	102.158	−	102.158i	0.724523	−	0.724523i
$142$		−	75.8949i		−	0.534471i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	81.9615	+	81.9615i	0.565252	+	0.565252i
$146$	−55.1628			−0.377828
$147$		−	73.2679i		−	0.498421i
$148$	72.3538	+	72.3538i	0.488877	+	0.488877i
$149$	112.210	+	112.210i	0.753089	+	0.753089i	0.975054	−	0.221966i	$-0.0712473\pi$
$149$	112.210	+	112.210i	0.753089	+	0.753089i	−0.221966	+	0.975054i	$0.571247\pi$
$150$	−34.2679	+	34.2679i	−0.228453	+	0.228453i
$151$	158.962	−	158.962i	1.05273	−	1.05273i	0.0541950	−	0.998530i	$-0.482741\pi$
$151$	158.962	−	158.962i	1.05273	−	1.05273i	0.998530	−	0.0541950i	$-0.0172592\pi$
$152$	10.4308			0.0686236
$153$		−	15.2154i		−	0.0994470i
$154$	39.2820	−	39.2820i	0.255078	−	0.255078i
$155$		−	291.779i		−	1.88245i
$156$		0			0
$157$	138.569			0.882606			0.441303	−	0.897358i	$-0.354516\pi$
$157$	138.569			0.882606			0.441303	+	0.897358i	$0.354516\pi$
$158$	−36.1244	−	36.1244i	−0.228635	−	0.228635i
$159$	−169.177			−1.06401
$160$			37.8564i			0.236603i
$161$	58.3013	+	58.3013i	0.362120	+	0.362120i
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	198.347	−	198.347i	1.21685	−	1.21685i	0.248123	−	0.968729i	$-0.420186\pi$
$163$	198.347	−	198.347i	1.21685	−	1.21685i	0.968729	−	0.248123i	$-0.0798137\pi$
$164$	60.4974	−	60.4974i	0.368887	−	0.368887i
$165$	−175.923			−1.06620
$166$			41.9334i			0.252611i
$167$	−197.569	+	197.569i	−1.18305	+	1.18305i	−0.204099	+	0.978950i	$0.565426\pi$
$167$	−197.569	+	197.569i	−1.18305	+	1.18305i	−0.978950	+	0.204099i	$0.934574\pi$
$168$		−	12.6795i		−	0.0754732i
$169$		0			0
$170$	−48.0000			−0.282353
$171$	7.82309	+	7.82309i	0.0457490	+	0.0457490i
$172$	−65.3205			−0.379770
$173$		−	67.5411i		−	0.390411i	−0.980762	−	0.195205i	$-0.937463\pi$
$173$		−	67.5411i		−	0.390411i	0.980762	−	0.195205i	$-0.0625373\pi$
$174$	30.0000	+	30.0000i	0.172414	+	0.172414i
$175$	−36.2083	−	36.2083i	−0.206905	−	0.206905i
$176$	−42.9282	+	42.9282i	−0.243910	+	0.243910i
$177$	−74.9423	+	74.9423i	−0.423403	+	0.423403i
$178$	−98.7180			−0.554595
$179$		−	50.2205i		−	0.280562i	−0.990112	−	0.140281i	$-0.955199\pi$
$179$		−	50.2205i		−	0.280562i	0.990112	−	0.140281i	$-0.0448005\pi$
$180$	−28.3923	+	28.3923i	−0.157735	+	0.157735i
$181$			302.354i			1.67046i	0.549898	+	0.835232i	$0.314666\pi$
$181$			302.354i			1.67046i	−0.549898	+	0.835232i	$0.685334\pi$
$182$		0			0
$183$	−137.354			−0.750567
$184$	−63.7128	−	63.7128i	−0.346265	−	0.346265i
$185$	342.382			1.85071
$186$		−	106.799i		−	0.574187i
$187$	−54.4308	−	54.4308i	−0.291074	−	0.291074i
$188$	−117.962	−	117.962i	−0.627455	−	0.627455i
$189$	9.50962	−	9.50962i	0.0503154	−	0.0503154i
$190$	24.6795	−	24.6795i	0.129892	−	0.129892i
$191$	162.679			0.851725			0.425863	−	0.904788i	$-0.359971\pi$
$191$	162.679			0.851725			0.425863	+	0.904788i	$0.359971\pi$
$192$			13.8564i			0.0721688i
$193$	−58.1506	+	58.1506i	−0.301299	+	0.301299i	−0.841522	−	0.540223i	$-0.818340\pi$
$193$	−58.1506	+	58.1506i	−0.301299	+	0.301299i	0.540223	+	0.841522i	$0.318340\pi$
$194$			25.9756i			0.133895i
$195$		0			0
$196$	−84.6025			−0.431646
$197$	190.956	+	190.956i	0.969322	+	0.969322i	0.999543	−	0.0302216i	$-0.00962128\pi$
$197$	190.956	+	190.956i	0.969322	+	0.969322i	−0.0302216	+	0.999543i	$0.509621\pi$
$198$	−64.3923			−0.325214
$199$		−	63.7846i		−	0.320526i	−0.987074	−	0.160263i	$-0.948766\pi$
$199$		−	63.7846i		−	0.320526i	0.987074	−	0.160263i	$-0.0512342\pi$
$200$	39.5692	+	39.5692i	0.197846	+	0.197846i
$201$	80.9545	+	80.9545i	0.402759	+	0.402759i
$202$	138.813	−	138.813i	0.687192	−	0.687192i
$203$	−31.6987	+	31.6987i	−0.156151	+	0.156151i
$204$	−17.5692			−0.0861236
$205$		−	286.277i		−	1.39647i
$206$	−107.263	+	107.263i	−0.520693	+	0.520693i
$207$		−	95.5692i		−	0.461687i
$208$		0			0
$209$	55.9718			0.267808
$210$	−30.0000	−	30.0000i	−0.142857	−	0.142857i
$211$	247.799			1.17440			0.587201	−	0.809441i	$-0.300230\pi$
$211$	247.799			1.17440			0.587201	+	0.809441i	$0.300230\pi$
$212$			195.349i			0.921456i
$213$	−65.7269	−	65.7269i	−0.308577	−	0.308577i
$214$	−5.50258	−	5.50258i	−0.0257130	−	0.0257130i
$215$	−154.550	+	154.550i	−0.718837	+	0.718837i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	112.846			0.520028
$218$			217.622i			0.998265i
$219$	−47.7724	+	47.7724i	−0.218139	+	0.218139i
$220$			203.138i			0.923357i
$221$		0			0
$222$	125.321			0.564507
$223$	−32.5307	−	32.5307i	−0.145878	−	0.145878i	0.630396	−	0.776274i	$-0.282893\pi$
$223$	−32.5307	−	32.5307i	−0.145878	−	0.145878i	−0.776274	+	0.630396i	$0.782893\pi$
$224$	−14.6410			−0.0653617
$225$			59.3538i			0.263795i
$226$	86.7846	+	86.7846i	0.384003	+	0.384003i
$227$	−9.71281	−	9.71281i	−0.0427877	−	0.0427877i	0.685389	−	0.728177i	$-0.259632\pi$
$227$	−9.71281	−	9.71281i	−0.0427877	−	0.0427877i	−0.728177	+	0.685389i	$0.759632\pi$
$228$	9.03332	−	9.03332i	0.0396198	−	0.0396198i
$229$	−287.315	+	287.315i	−1.25465	+	1.25465i	−0.301041	+	0.953611i	$0.597334\pi$
$229$	−287.315	+	287.315i	−1.25465	+	1.25465i	−0.953611	+	0.301041i	$0.902666\pi$
$230$	−301.492			−1.31084
$231$		−	68.0385i		−	0.294539i
$232$	34.6410	−	34.6410i	0.149315	−	0.149315i
$233$			27.3308i			0.117300i	0.998279	+	0.0586498i	$0.0186795\pi$
$233$			27.3308i			0.117300i	−0.998279	+	0.0586498i	$0.981320\pi$
$234$		0			0
$235$	−558.200			−2.37532
$236$	86.5359	+	86.5359i	0.366678	+	0.366678i
$237$	−62.5692			−0.264005
$238$		−	18.5641i		−	0.0780003i
$239$	0.861561	+	0.861561i	0.00360486	+	0.00360486i	0.708907	−	0.705302i	$-0.249189\pi$
$239$	0.861561	+	0.861561i	0.00360486	+	0.00360486i	−0.705302	+	0.708907i	$0.749189\pi$
$240$	32.7846	+	32.7846i	0.136603	+	0.136603i
$241$	60.1769	−	60.1769i	0.249697	−	0.249697i	−0.571149	−	0.820846i	$-0.693502\pi$
$241$	60.1769	−	60.1769i	0.249697	−	0.249697i	0.820846	+	0.571149i	$0.193502\pi$
$242$	−109.354	+	109.354i	−0.451875	+	0.451875i
$243$	−15.5885			−0.0641500
$244$			158.603i			0.650010i
$245$	−200.172	+	200.172i	−0.817028	+	0.817028i
$246$		−	104.785i		−	0.425954i
$247$		0			0
$248$	−123.321			−0.497260
$249$	36.3154	+	36.3154i	0.145845	+	0.145845i
$250$	−49.3590			−0.197436
$251$		−	40.7077i		−	0.162182i	−0.996707	−	0.0810910i	$-0.974160\pi$
$251$		−	40.7077i		−	0.162182i	0.996707	−	0.0810910i	$-0.0258404\pi$
$252$	−10.9808	−	10.9808i	−0.0435745	−	0.0435745i
$253$	−341.885	−	341.885i	−1.35132	−	1.35132i
$254$	−178.846	+	178.846i	−0.704118	+	0.704118i
$255$	−41.5692	+	41.5692i	−0.163017	+	0.163017i
$256$	16.0000			0.0625000
$257$			309.779i			1.20537i	0.797980	+	0.602684i	$0.205902\pi$
$257$			309.779i			1.20537i	−0.797980	+	0.602684i	$0.794098\pi$
$258$	−56.5692	+	56.5692i	−0.219261	+	0.219261i
$259$			132.417i			0.511261i
$260$		0			0
$261$	51.9615			0.199086
$262$	−53.6359	−	53.6359i	−0.204717	−	0.204717i
$263$	−287.636			−1.09367			−0.546836	−	0.837240i	$-0.684168\pi$
$263$	−287.636			−1.09367			−0.546836	+	0.837240i	$0.684168\pi$
$264$			74.3538i			0.281643i
$265$	462.200	+	462.200i	1.74415	+	1.74415i
$266$	9.54483	+	9.54483i	0.0358828	+	0.0358828i
$267$	−85.4923	+	85.4923i	−0.320196	+	0.320196i
$268$	93.4782	−	93.4782i	0.348799	−	0.348799i
$269$	163.741			0.608703			0.304351	−	0.952560i	$-0.401560\pi$
$269$	163.741			0.608703			0.304351	+	0.952560i	$0.401560\pi$
$270$			49.1769i			0.182137i
$271$	229.954	−	229.954i	0.848541	−	0.848541i	−0.141411	−	0.989951i	$-0.545164\pi$
$271$	229.954	−	229.954i	0.848541	−	0.848541i	0.989951	+	0.141411i	$0.0451637\pi$
$272$			20.2872i			0.0745852i
$273$		0			0
$274$	174.928			0.638424
$275$	212.329	+	212.329i	0.772107	+	0.772107i
$276$	−110.354			−0.399833
$277$		−	134.985i		−	0.487309i	−0.969862	−	0.243654i	$-0.921654\pi$
$277$		−	134.985i		−	0.487309i	0.969862	−	0.243654i	$-0.0783463\pi$
$278$	−153.708	−	153.708i	−0.552905	−	0.552905i
$279$	−92.4904	−	92.4904i	−0.331507	−	0.331507i
$280$	−34.6410	+	34.6410i	−0.123718	+	0.123718i
$281$	−323.545	+	323.545i	−1.15141	+	1.15141i	−0.165134	+	0.986271i	$0.552806\pi$
$281$	−323.545	+	323.545i	−1.15141	+	1.15141i	−0.986271	+	0.165134i	$0.947194\pi$
$282$	−204.315			−0.724523
$283$			141.354i			0.499483i	0.968312	+	0.249742i	$0.0803457\pi$
$283$			141.354i			0.499483i	−0.968312	+	0.249742i	$0.919654\pi$
$284$	−75.8949	+	75.8949i	−0.267236	+	0.267236i
$285$		−	42.7461i		−	0.149986i
$286$		0			0
$287$	110.718			0.385777
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	263.277			0.910993
$290$		−	163.923i		−	0.565252i
$291$	22.4955	+	22.4955i	0.0773042	+	0.0773042i
$292$	55.1628	+	55.1628i	0.188914	+	0.188914i
$293$	210.473	−	210.473i	0.718338	−	0.718338i	−0.249927	−	0.968265i	$-0.580407\pi$
$293$	210.473	−	210.473i	0.718338	−	0.718338i	0.968265	+	0.249927i	$0.0804065\pi$
$294$	−73.2679	+	73.2679i	−0.249211	+	0.249211i
$295$	409.492			1.38811
$296$		−	144.708i		−	0.488877i
$297$	−55.7654	+	55.7654i	−0.187762	+	0.187762i
$298$		−	224.420i		−	0.753089i
$299$		0			0
$300$	68.5359			0.228453
$301$	−59.7724	−	59.7724i	−0.198579	−	0.198579i
$302$	−317.923			−1.05273
$303$		−	240.431i		−	0.793501i
$304$	−10.4308	−	10.4308i	−0.0343118	−	0.0343118i
$305$	375.258	+	375.258i	1.23035	+	1.23035i
$306$	−15.2154	+	15.2154i	−0.0497235	+	0.0497235i
$307$	70.0685	−	70.0685i	0.228236	−	0.228236i	−0.583719	−	0.811956i	$-0.698403\pi$
$307$	70.0685	−	70.0685i	0.228236	−	0.228236i	0.811956	+	0.583719i	$0.198403\pi$
$308$	−78.5641			−0.255078
$309$			185.785i			0.601245i
$310$	−291.779	+	291.779i	−0.941224	+	0.941224i
$311$			140.238i			0.450927i	0.974252	+	0.225464i	$0.0723897\pi$
$311$			140.238i			0.450927i	−0.974252	+	0.225464i	$0.927610\pi$
$312$		0			0
$313$	−550.286			−1.75810			−0.879051	−	0.476728i	$-0.841823\pi$
$313$	−550.286			−1.75810			−0.879051	+	0.476728i	$0.841823\pi$
$314$	−138.569	−	138.569i	−0.441303	−	0.441303i
$315$	−51.9615			−0.164957
$316$			72.2487i			0.228635i
$317$	31.2923	+	31.2923i	0.0987140	+	0.0987140i	0.754739	−	0.656025i	$-0.227763\pi$
$317$	31.2923	+	31.2923i	0.0987140	+	0.0987140i	−0.656025	+	0.754739i	$0.727763\pi$
$318$	169.177	+	169.177i	0.532003	+	0.532003i
$319$	185.885	−	185.885i	0.582710	−	0.582710i
$320$	37.8564	−	37.8564i	0.118301	−	0.118301i
$321$	−9.53074			−0.0296908
$322$		−	116.603i		−	0.362120i
$323$	13.2257	−	13.2257i	0.0409464	−	0.0409464i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−396.694			−1.21685
$327$	188.466	+	188.466i	0.576349	+	0.576349i
$328$	−120.995			−0.368887
$329$		−	215.885i		−	0.656184i
$330$	175.923	+	175.923i	0.533100	+	0.533100i
$331$	285.624	+	285.624i	0.862911	+	0.862911i	0.991675	−	0.128764i	$-0.0411009\pi$
$331$	285.624	+	285.624i	0.862911	+	0.862911i	−0.128764	+	0.991675i	$0.541101\pi$
$332$	41.9334	−	41.9334i	0.126305	−	0.126305i
$333$	108.531	−	108.531i	0.325918	−	0.325918i
$334$	395.138			1.18305
$335$		−	442.344i		−	1.32043i
$336$	−12.6795	+	12.6795i	−0.0377366	+	0.0377366i
$337$			638.492i			1.89464i	0.320295	+	0.947318i	$0.396218\pi$
$337$			638.492i			1.89464i	−0.320295	+	0.947318i	$0.603782\pi$
$338$		0			0
$339$	150.315			0.443408
$340$	48.0000	+	48.0000i	0.141176	+	0.141176i
$341$	−661.741			−1.94059
$342$		−	15.6462i		−	0.0457490i
$343$	−167.093	−	167.093i	−0.487151	−	0.487151i
$344$	65.3205	+	65.3205i	0.189885	+	0.189885i
$345$	−261.100	+	261.100i	−0.756811	+	0.756811i
$346$	−67.5411	+	67.5411i	−0.195205	+	0.195205i
$347$	−5.70250			−0.0164337			−0.00821686	−	0.999966i	$-0.502616\pi$
$347$	−5.70250			−0.0164337			−0.00821686	+	0.999966i	$0.502616\pi$
$348$		−	60.0000i		−	0.172414i
$349$	−128.103	+	128.103i	−0.367058	+	0.367058i	−0.866403	−	0.499345i	$-0.833574\pi$
$349$	−128.103	+	128.103i	−0.367058	+	0.367058i	0.499345	+	0.866403i	$0.333574\pi$
$350$			72.4167i			0.206905i
$351$		0			0
$352$	85.8564			0.243910
$353$	−205.037	−	205.037i	−0.580842	−	0.580842i	0.354293	−	0.935135i	$-0.384722\pi$
$353$	−205.037	−	205.037i	−0.580842	−	0.580842i	−0.935135	+	0.354293i	$0.884722\pi$
$354$	149.885			0.423403
$355$			359.138i			1.01166i
$356$	98.7180	+	98.7180i	0.277298	+	0.277298i
$357$	−16.0770	−	16.0770i	−0.0450335	−	0.0450335i
$358$	−50.2205	+	50.2205i	−0.140281	+	0.140281i
$359$	268.277	−	268.277i	0.747289	−	0.747289i	−0.226680	−	0.973969i	$-0.572787\pi$
$359$	268.277	−	268.277i	0.747289	−	0.747289i	0.973969	+	0.226680i	$0.0727871\pi$
$360$	56.7846			0.157735
$361$		−	347.400i		−	0.962326i
$362$	302.354	−	302.354i	0.835232	−	0.835232i
$363$			189.406i			0.521781i
$364$		0			0
$365$	261.033			0.715160
$366$	137.354	+	137.354i	0.375284	+	0.375284i
$367$	−176.215			−0.480151			−0.240075	−	0.970754i	$-0.577172\pi$
$367$	−176.215			−0.480151			−0.240075	+	0.970754i	$0.577172\pi$
$368$			127.426i			0.346265i
$369$	−90.7461	−	90.7461i	−0.245924	−	0.245924i
$370$	−342.382	−	342.382i	−0.925357	−	0.925357i
$371$	−178.756	+	178.756i	−0.481823	+	0.481823i
$372$	−106.799	+	106.799i	−0.287093	+	0.287093i
$373$	483.606			1.29653			0.648266	−	0.761414i	$-0.275495\pi$
$373$	483.606			1.29653			0.648266	+	0.761414i	$0.275495\pi$
$374$			108.862i			0.291074i
$375$	−42.7461	+	42.7461i	−0.113990	+	0.113990i
$376$			235.923i			0.627455i
$377$		0			0
$378$	−19.0192			−0.0503154
$379$	204.107	+	204.107i	0.538541	+	0.538541i	0.923100	−	0.384559i	$-0.125647\pi$
$379$	204.107	+	204.107i	0.538541	+	0.538541i	−0.384559	+	0.923100i	$0.625647\pi$
$380$	−49.3590			−0.129892
$381$			309.771i			0.813046i
$382$	−162.679	−	162.679i	−0.425863	−	0.425863i
$383$	186.249	+	186.249i	0.486289	+	0.486289i	0.907133	−	0.420844i	$-0.138266\pi$
$383$	186.249	+	186.249i	0.486289	+	0.486289i	−0.420844	+	0.907133i	$0.638266\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	−185.885	+	185.885i	−0.482817	+	0.482817i
$386$	116.301			0.301299
$387$			97.9808i			0.253180i
$388$	25.9756	−	25.9756i	0.0669474	−	0.0669474i
$389$		−	66.2487i		−	0.170305i	−0.996368	−	0.0851526i	$-0.972862\pi$
$389$		−	66.2487i		−	0.170305i	0.996368	−	0.0851526i	$-0.0271378\pi$
$390$		0			0
$391$	−161.569			−0.413221
$392$	84.6025	+	84.6025i	0.215823	+	0.215823i
$393$	−92.9000			−0.236387
$394$		−	381.913i		−	0.969322i
$395$	170.942	+	170.942i	0.432765	+	0.432765i
$396$	64.3923	+	64.3923i	0.162607	+	0.162607i
$397$	−95.6429	+	95.6429i	−0.240914	+	0.240914i	−0.817228	−	0.576314i	$-0.804490\pi$
$397$	−95.6429	+	95.6429i	−0.240914	+	0.240914i	0.576314	+	0.817228i	$0.304490\pi$
$398$	−63.7846	+	63.7846i	−0.160263	+	0.160263i
$399$	16.5321			0.0414339
$400$		−	79.1384i		−	0.197846i
$401$	135.415	−	135.415i	0.337694	−	0.337694i	−0.517805	−	0.855499i	$-0.673251\pi$
$401$	135.415	−	135.415i	0.337694	−	0.337694i	0.855499	+	0.517805i	$0.173251\pi$
$402$		−	161.909i		−	0.402759i
$403$		0			0
$404$	−277.626			−0.687192
$405$	42.5885	+	42.5885i	0.105157	+	0.105157i
$406$	63.3975			0.156151
$407$		−	776.505i		−	1.90787i
$408$	17.5692	+	17.5692i	0.0430618	+	0.0430618i
$409$	−392.974	−	392.974i	−0.960816	−	0.960816i	0.0384448	−	0.999261i	$-0.487760\pi$
$409$	−392.974	−	392.974i	−0.960816	−	0.960816i	−0.999261	+	0.0384448i	$0.987760\pi$
$410$	−286.277	+	286.277i	−0.698236	+	0.698236i
$411$	151.492	−	151.492i	0.368594	−	0.368594i
$412$	214.526			0.520693
$413$			158.372i			0.383467i
$414$	−95.5692	+	95.5692i	−0.230844	+	0.230844i
$415$		−	198.431i		−	0.478146i
$416$		0			0
$417$	−266.229			−0.638440
$418$	−55.9718	−	55.9718i	−0.133904	−	0.133904i
$419$	−657.646			−1.56956			−0.784781	−	0.619774i	$-0.787224\pi$
$419$	−657.646			−1.56956			−0.784781	+	0.619774i	$0.787224\pi$
$420$			60.0000i			0.142857i
$421$	−328.035	−	328.035i	−0.779181	−	0.779181i	0.200511	−	0.979692i	$-0.435740\pi$
$421$	−328.035	−	328.035i	−0.779181	−	0.779181i	−0.979692	+	0.200511i	$0.935740\pi$
$422$	−247.799	−	247.799i	−0.587201	−	0.587201i
$423$	−176.942	+	176.942i	−0.418303	+	0.418303i
$424$	195.349	−	195.349i	0.460728	−	0.460728i
$425$	100.344			0.236102
$426$			131.454i			0.308577i
$427$	−145.131	+	145.131i	−0.339886	+	0.339886i
$428$			11.0052i			0.0257130i
$429$		0			0
$430$	309.100			0.718837
$431$	−22.6898	−	22.6898i	−0.0526446	−	0.0526446i	0.680294	−	0.732939i	$-0.261852\pi$
$431$	−22.6898	−	22.6898i	−0.0526446	−	0.0526446i	−0.732939	+	0.680294i	$0.761852\pi$
$432$	20.7846			0.0481125
$433$			196.215i			0.453153i	0.973993	+	0.226577i	$0.0727534\pi$
$433$			196.215i			0.453153i	−0.973993	+	0.226577i	$0.927247\pi$
$434$	−112.846	−	112.846i	−0.260014	−	0.260014i
$435$	−141.962	−	141.962i	−0.326348	−	0.326348i
$436$	217.622	−	217.622i	0.499133	−	0.499133i
$437$	83.0718	−	83.0718i	0.190096	−	0.190096i
$438$	95.5448			0.218139
$439$		−	41.4627i		−	0.0944481i	−0.998884	−	0.0472241i	$-0.984963\pi$
$439$		−	41.4627i		−	0.0944481i	0.998884	−	0.0472241i	$-0.0150375\pi$
$440$	203.138	−	203.138i	0.461678	−	0.461678i
$441$			126.904i			0.287764i
$442$		0			0
$443$	−19.9718			−0.0450831			−0.0225416	−	0.999746i	$-0.507176\pi$
$443$	−19.9718			−0.0450831			−0.0225416	+	0.999746i	$0.507176\pi$
$444$	−125.321	−	125.321i	−0.282253	−	0.282253i
$445$	467.138			1.04975
$446$			65.0615i			0.145878i
$447$	−194.354	−	194.354i	−0.434796	−	0.434796i
$448$	14.6410	+	14.6410i	0.0326808	+	0.0326808i
$449$	93.3064	−	93.3064i	0.207809	−	0.207809i	−0.595526	−	0.803336i	$-0.703056\pi$
$449$	93.3064	−	93.3064i	0.207809	−	0.207809i	0.803336	+	0.595526i	$0.203056\pi$
$450$	59.3538	−	59.3538i	0.131897	−	0.131897i
$451$	−649.261			−1.43960
$452$		−	173.569i		−	0.384003i
$453$	−275.329	+	275.329i	−0.607791	+	0.607791i
$454$			19.4256i			0.0427877i
$455$		0			0
$456$	−18.0666			−0.0396198
$457$	−208.519	−	208.519i	−0.456277	−	0.456277i	0.441154	−	0.897431i	$-0.354569\pi$
$457$	−208.519	−	208.519i	−0.456277	−	0.456277i	−0.897431	+	0.441154i	$0.854569\pi$
$458$	574.631			1.25465
$459$			26.3538i			0.0574157i
$460$	301.492	+	301.492i	0.655418	+	0.655418i
$461$	−332.123	−	332.123i	−0.720440	−	0.720440i	0.248255	−	0.968695i	$-0.420143\pi$
$461$	−332.123	−	332.123i	−0.720440	−	0.720440i	−0.968695	+	0.248255i	$0.920143\pi$
$462$	−68.0385	+	68.0385i	−0.147269	+	0.147269i
$463$	−462.599	+	462.599i	−0.999134	+	0.999134i	−1.00000		0.000865128i	$-0.999725\pi$
$463$	−462.599	+	462.599i	−0.999134	+	0.999134i	0.000865128		1.00000i	$0.499725\pi$
$464$	−69.2820			−0.149315
$465$			505.377i			1.08683i
$466$	27.3308	−	27.3308i	0.0586498	−	0.0586498i
$467$		−	396.649i		−	0.849355i	−0.905345	−	0.424677i	$-0.860388\pi$
$467$		−	396.649i		−	0.849355i	0.905345	−	0.424677i	$-0.139612\pi$
$468$		0			0
$469$	171.077			0.364770
$470$	558.200	+	558.200i	1.18766	+	1.18766i
$471$	−240.009			−0.509573
$472$		−	173.072i		−	0.366678i
$473$	350.512	+	350.512i	0.741039	+	0.741039i
$474$	62.5692	+	62.5692i	0.132003	+	0.132003i
$475$	−51.5922	+	51.5922i	−0.108615	+	0.108615i
$476$	−18.5641	+	18.5641i	−0.0390001	+	0.0390001i
$477$	293.023			0.614304
$478$		−	1.72312i		−	0.00360486i
$479$	−254.536	+	254.536i	−0.531390	+	0.531390i	−0.920986	−	0.389596i	$-0.872615\pi$
$479$	−254.536	+	254.536i	−0.531390	+	0.531390i	0.389596	+	0.920986i	$0.372615\pi$
$480$		−	65.5692i		−	0.136603i
$481$		0			0
$482$	−120.354			−0.249697
$483$	−100.981	−	100.981i	−0.209070	−	0.209070i
$484$	218.708			0.451875
$485$		−	122.918i		−	0.253439i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	137.000	+	137.000i	0.281314	+	0.281314i	0.833633	−	0.552319i	$-0.186257\pi$
$487$	137.000	+	137.000i	0.281314	+	0.281314i	−0.552319	+	0.833633i	$0.686257\pi$
$488$	158.603	−	158.603i	0.325005	−	0.325005i
$489$	−343.547	+	343.547i	−0.702550	+	0.702550i
$490$	400.344			0.817028
$491$		−	23.0718i		−	0.0469894i	−0.999724	−	0.0234947i	$-0.992521\pi$
$491$		−	23.0718i		−	0.0469894i	0.999724	−	0.0234947i	$-0.00747928\pi$
$492$	−104.785	+	104.785i	−0.212977	+	0.212977i
$493$		−	87.8461i		−	0.178187i
$494$		0			0
$495$	304.708			0.615571
$496$	123.321	+	123.321i	0.248630	+	0.248630i
$497$	−138.897			−0.279471
$498$		−	72.6307i		−	0.145845i
$499$	160.769	+	160.769i	0.322183	+	0.322183i	0.849604	−	0.527421i	$-0.176841\pi$
$499$	160.769	+	160.769i	0.322183	+	0.322183i	−0.527421	+	0.849604i	$0.676841\pi$
$500$	49.3590	+	49.3590i	0.0987180	+	0.0987180i
$501$	342.200	−	342.200i	0.683034	−	0.683034i
$502$	−40.7077	+	40.7077i	−0.0810910	+	0.0810910i
$503$	−601.244			−1.19532			−0.597658	−	0.801751i	$-0.703902\pi$
$503$	−601.244			−1.19532			−0.597658	+	0.801751i	$0.703902\pi$
$504$			21.9615i			0.0435745i
$505$	−656.869	+	656.869i	−1.30073	+	1.30073i
$506$			683.769i			1.35132i
$507$		0			0
$508$	357.692			0.704118
$509$	−347.745	−	347.745i	−0.683192	−	0.683192i	0.277526	−	0.960718i	$-0.410486\pi$
$509$	−347.745	−	347.745i	−0.683192	−	0.683192i	−0.960718	+	0.277526i	$0.910486\pi$
$510$	83.1384			0.163017
$511$			100.955i			0.197564i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−13.5500	−	13.5500i	−0.0264132	−	0.0264132i
$514$	309.779	−	309.779i	0.602684	−	0.602684i
$515$	507.573	−	507.573i	0.985579	−	0.985579i
$516$	113.138			0.219261
$517$			1265.97i			2.44868i
$518$	132.417	−	132.417i	0.255631	−	0.255631i
$519$			116.985i			0.225404i
$520$		0			0
$521$	647.951			1.24367			0.621834	−	0.783149i	$-0.286388\pi$
$521$	647.951			1.24367			0.621834	+	0.783149i	$0.286388\pi$
$522$	−51.9615	−	51.9615i	−0.0995431	−	0.0995431i
$523$	−165.923			−0.317252			−0.158626	−	0.987339i	$-0.550706\pi$
$523$	−165.923			−0.317252			−0.158626	+	0.987339i	$0.550706\pi$
$524$			107.272i			0.204717i
$525$	62.7147	+	62.7147i	0.119457	+	0.119457i
$526$	287.636	+	287.636i	0.546836	+	0.546836i
$527$	−156.364	+	156.364i	−0.296706	+	0.296706i
$528$	74.3538	−	74.3538i	0.140822	−	0.140822i
$529$	−485.831			−0.918394
$530$		−	924.400i		−	1.74415i
$531$	129.804	−	129.804i	0.244452	−	0.244452i
$532$		−	19.0897i		−	0.0358828i
$533$		0			0
$534$	170.985			0.320196
$535$	26.0385	+	26.0385i	0.0486700	+	0.0486700i
$536$	−186.956			−0.348799
$537$			86.9845i			0.161982i
$538$	−163.741	−	163.741i	−0.304351	−	0.304351i
$539$	453.979	+	453.979i	0.842262	+	0.842262i
$540$	49.1769	−	49.1769i	0.0910684	−	0.0910684i
$541$	210.557	−	210.557i	0.389200	−	0.389200i	−0.485202	−	0.874402i	$-0.661254\pi$
$541$	210.557	−	210.557i	0.389200	−	0.389200i	0.874402	+	0.485202i	$0.161254\pi$
$542$	−459.909			−0.848541
$543$		−	523.692i		−	0.964442i
$544$	20.2872	−	20.2872i	0.0372926	−	0.0372926i
$545$		−	1029.80i		−	1.88954i
$546$		0			0
$547$	−392.492			−0.717536			−0.358768	−	0.933427i	$-0.616803\pi$
$547$	−392.492			−0.717536			−0.358768	+	0.933427i	$0.616803\pi$
$548$	−174.928	−	174.928i	−0.319212	−	0.319212i
$549$	237.904			0.433340
$550$		−	424.659i		−	0.772107i
$551$	45.1666	+	45.1666i	0.0819721	+	0.0819721i
$552$	110.354	+	110.354i	0.199916	+	0.199916i
$553$	−66.1122	+	66.1122i	−0.119552	+	0.119552i
$554$	−134.985	+	134.985i	−0.243654	+	0.243654i
$555$	−593.023			−1.06851
$556$			307.415i			0.552905i
$557$	−50.1539	+	50.1539i	−0.0900429	+	0.0900429i	−0.750694	−	0.660651i	$-0.770280\pi$
$557$	−50.1539	+	50.1539i	−0.0900429	+	0.0900429i	0.660651	+	0.750694i	$0.270280\pi$
$558$			184.981i			0.331507i
$559$		0			0
$560$	69.2820			0.123718
$561$	94.2769	+	94.2769i	0.168051	+	0.168051i
$562$	647.090			1.15141
$563$			832.726i			1.47909i	0.673109	+	0.739543i	$0.264958\pi$
$563$			832.726i			1.47909i	−0.673109	+	0.739543i	$0.735042\pi$
$564$	204.315	+	204.315i	0.362261	+	0.362261i
$565$	−410.669	−	410.669i	−0.726848	−	0.726848i
$566$	141.354	−	141.354i	0.249742	−	0.249742i
$567$	−16.4711	+	16.4711i	−0.0290496	+	0.0290496i
$568$	151.790			0.267236
$569$		−	348.431i		−	0.612356i	−0.951974	−	0.306178i	$-0.900950\pi$
$569$		−	348.431i		−	0.612356i	0.951974	−	0.306178i	$-0.0990503\pi$
$570$	−42.7461	+	42.7461i	−0.0749932	+	0.0749932i
$571$			411.892i			0.721352i	0.932691	+	0.360676i	$0.117454\pi$
$571$			411.892i			0.721352i	−0.932691	+	0.360676i	$0.882546\pi$
$572$		0			0
$573$	−281.769			−0.491744
$574$	−110.718	−	110.718i	−0.192888	−	0.192888i
$575$	630.267			1.09612
$576$		−	24.0000i		−	0.0416667i
$577$	−39.6692	−	39.6692i	−0.0687507	−	0.0687507i	0.671895	−	0.740646i	$-0.265480\pi$
$577$	−39.6692	−	39.6692i	−0.0687507	−	0.0687507i	−0.740646	+	0.671895i	$0.765480\pi$
$578$	−263.277	−	263.277i	−0.455496	−	0.455496i
$579$	100.720	−	100.720i	0.173955	−	0.173955i
$580$	−163.923	+	163.923i	−0.282626	+	0.282626i
$581$	76.7434			0.132088
$582$		−	44.9911i		−	0.0773042i
$583$	1048.25	−	1048.25i	1.79802	−	1.79802i
$584$		−	110.326i		−	0.188914i
$585$		0			0
$586$	−420.946			−0.718338
$587$	−370.004	−	370.004i	−0.630330	−	0.630330i	0.317821	−	0.948151i	$-0.397049\pi$
$587$	−370.004	−	370.004i	−0.630330	−	0.630330i	−0.948151	+	0.317821i	$0.897049\pi$
$588$	146.536			0.249211
$589$		−	160.791i		−	0.272990i
$590$	−409.492	−	409.492i	−0.694055	−	0.694055i
$591$	−330.746	−	330.746i	−0.559638	−	0.559638i
$592$	−144.708	+	144.708i	−0.244439	+	0.244439i
$593$	−234.771	+	234.771i	−0.395903	+	0.395903i	−0.876785	−	0.480882i	$-0.840316\pi$
$593$	−234.771	+	234.771i	−0.395903	+	0.395903i	0.480882	+	0.876785i	$0.340316\pi$
$594$	111.531			0.187762
$595$			87.8461i			0.147640i
$596$	−224.420	+	224.420i	−0.376544	+	0.376544i
$597$			110.478i			0.185056i
$598$		0			0
$599$	−652.908			−1.09000			−0.544998	−	0.838437i	$-0.683470\pi$
$599$	−652.908			−1.09000			−0.544998	+	0.838437i	$0.683470\pi$
$600$	−68.5359	−	68.5359i	−0.114226	−	0.114226i
$601$	65.5692			0.109100			0.0545501	−	0.998511i	$-0.482628\pi$
$601$	65.5692			0.109100			0.0545501	+	0.998511i	$0.482628\pi$
$602$			119.545i			0.198579i
$603$	−140.217	−	140.217i	−0.232533	−	0.232533i
$604$	317.923	+	317.923i	0.526363	+	0.526363i
$605$	517.468	−	517.468i	0.855319	−	0.855319i
$606$	−240.431	+	240.431i	−0.396750	+	0.396750i
$607$	−776.600			−1.27941			−0.639703	−	0.768622i	$-0.720943\pi$
$607$	−776.600			−1.27941			−0.639703	+	0.768622i	$0.720943\pi$
$608$			20.8616i			0.0343118i
$609$	54.9038	−	54.9038i	0.0901540	−	0.0901540i
$610$		−	750.515i		−	1.23035i
$611$		0			0
$612$	30.4308			0.0497235
$613$	−300.757	−	300.757i	−0.490631	−	0.490631i	0.417874	−	0.908505i	$-0.362775\pi$
$613$	−300.757	−	300.757i	−0.490631	−	0.490631i	−0.908505	+	0.417874i	$0.862775\pi$
$614$	−140.137			−0.228236
$615$			495.846i			0.806254i
$616$	78.5641	+	78.5641i	0.127539	+	0.127539i
$617$	95.6603	+	95.6603i	0.155041	+	0.155041i	0.780365	−	0.625324i	$-0.215033\pi$
$617$	95.6603	+	95.6603i	0.155041	+	0.155041i	−0.625324	+	0.780365i	$0.715033\pi$
$618$	185.785	−	185.785i	0.300622	−	0.300622i
$619$	661.030	−	661.030i	1.06790	−	1.06790i	0.0703796	−	0.997520i	$-0.477579\pi$
$619$	661.030	−	661.030i	1.06790	−	1.06790i	0.997520	−	0.0703796i	$-0.0224211\pi$
$620$	583.559			0.941224
$621$			165.531i			0.266555i
$622$	140.238	−	140.238i	0.225464	−	0.225464i
$623$			180.666i			0.289994i
$624$		0			0
$625$	728.184			1.16510
$626$	550.286	+	550.286i	0.879051	+	0.879051i
$627$	−96.9461			−0.154619
$628$			277.138i			0.441303i
$629$	−183.482	−	183.482i	−0.291704	−	0.291704i
$630$	51.9615	+	51.9615i	0.0824786	+	0.0824786i
$631$	274.445	−	274.445i	0.434937	−	0.434937i	−0.455367	−	0.890304i	$-0.650492\pi$
$631$	274.445	−	274.445i	0.434937	−	0.434937i	0.890304	+	0.455367i	$0.150492\pi$
$632$	72.2487	−	72.2487i	0.114318	−	0.114318i
$633$	−429.200			−0.678041
$634$		−	62.5847i		−	0.0987140i
$635$	846.309	−	846.309i	1.33277	−	1.33277i
$636$		−	338.354i		−	0.532003i
$637$		0			0
$638$	−371.769			−0.582710
$639$	113.842	+	113.842i	0.178157	+	0.178157i
$640$	−75.7128			−0.118301
$641$			623.387i			0.972523i	0.873813	+	0.486261i	$0.161640\pi$
$641$			623.387i			0.972523i	−0.873813	+	0.486261i	$0.838360\pi$
$642$	9.53074	+	9.53074i	0.0148454	+	0.0148454i
$643$	−578.270	−	578.270i	−0.899331	−	0.899331i	0.0960459	−	0.995377i	$-0.469380\pi$
$643$	−578.270	−	578.270i	−0.899331	−	0.899331i	−0.995377	+	0.0960459i	$0.969380\pi$
$644$	−116.603	+	116.603i	−0.181060	+	0.181060i
$645$	267.688	−	267.688i	0.415021	−	0.415021i
$646$	−26.4514			−0.0409464
$647$			286.841i			0.443340i	0.975122	+	0.221670i	$0.0711508\pi$
$647$			286.841i			0.443340i	−0.975122	+	0.221670i	$0.928849\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	928.708i		−	1.43098i
$650$		0			0
$651$	−195.455			−0.300238
$652$	396.694	+	396.694i	0.608426	+	0.608426i
$653$	648.848			0.993642			0.496821	−	0.867853i	$-0.334500\pi$
$653$	648.848			0.993642			0.496821	+	0.867853i	$0.334500\pi$
$654$		−	376.932i		−	0.576349i
$655$	253.808	+	253.808i	0.387493	+	0.387493i
$656$	120.995	+	120.995i	0.184443	+	0.184443i
$657$	82.7442	−	82.7442i	0.125943	−	0.125943i
$658$	−215.885	+	215.885i	−0.328092	+	0.328092i
$659$	456.315			0.692436			0.346218	−	0.938154i	$-0.387466\pi$
$659$	456.315			0.692436			0.346218	+	0.938154i	$0.387466\pi$
$660$		−	351.846i		−	0.533100i
$661$	229.988	−	229.988i	0.347939	−	0.347939i	−0.511402	−	0.859341i	$-0.670874\pi$
$661$	229.988	−	229.988i	0.347939	−	0.347939i	0.859341	+	0.511402i	$0.170874\pi$
$662$		−	571.247i		−	0.862911i
$663$		0			0
$664$	−83.8667			−0.126305
$665$	−45.1666	−	45.1666i	−0.0679197	−	0.0679197i
$666$	−217.061			−0.325918
$667$		−	551.769i		−	0.827240i
$668$	−395.138	−	395.138i	−0.591525	−	0.591525i
$669$	56.3449	+	56.3449i	0.0842226	+	0.0842226i
$670$	−442.344	+	442.344i	−0.660214	+	0.660214i
$671$	851.065	−	851.065i	1.26835	−	1.26835i
$672$	25.3590			0.0377366
$673$		−	1044.01i		−	1.55128i	−0.631178	−	0.775638i	$-0.717428\pi$
$673$		−	1044.01i		−	1.55128i	0.631178	−	0.775638i	$-0.282572\pi$
$674$	638.492	−	638.492i	0.947318	−	0.947318i
$675$		−	102.804i		−	0.152302i
$676$		0			0
$677$	−193.408			−0.285684			−0.142842	−	0.989746i	$-0.545624\pi$
$677$	−193.408			−0.285684			−0.142842	+	0.989746i	$0.545624\pi$
$678$	−150.315	−	150.315i	−0.221704	−	0.221704i
$679$	47.5387			0.0700128
$680$		−	96.0000i		−	0.141176i
$681$	16.8231	+	16.8231i	0.0247035	+	0.0247035i
$682$	661.741	+	661.741i	0.970295	+	0.970295i
$683$	−587.678	+	587.678i	−0.860436	+	0.860436i	−0.991389	−	0.130952i	$-0.958197\pi$
$683$	−587.678	+	587.678i	−0.860436	+	0.860436i	0.130952	+	0.991389i	$0.458197\pi$
$684$	−15.6462	+	15.6462i	−0.0228745	+	0.0228745i
$685$	−827.769			−1.20842
$686$			334.186i			0.487151i
$687$	497.645	−	497.645i	0.724374	−	0.724374i
$688$		−	130.641i		−	0.189885i
$689$		0			0
$690$	522.200			0.756811
$691$	164.030	+	164.030i	0.237381	+	0.237381i	0.815765	−	0.578384i	$-0.196316\pi$
$691$	164.030	+	164.030i	0.237381	+	0.237381i	−0.578384	+	0.815765i	$0.696316\pi$
$692$	135.082			0.195205
$693$			117.846i			0.170052i
$694$	5.70250	+	5.70250i	0.00821686	+	0.00821686i
$695$	727.352	+	727.352i	1.04655	+	1.04655i
$696$	−60.0000	+	60.0000i	−0.0862069	+	0.0862069i
$697$	−153.415	+	153.415i	−0.220108	+	0.220108i
$698$	256.206			0.367058
$699$		−	47.3384i		−	0.0677230i
$700$	72.4167	−	72.4167i	0.103452	−	0.103452i
$701$		−	55.6565i		−	0.0793958i	−0.999212	−	0.0396979i	$-0.987360\pi$
$701$		−	55.6565i		−	0.0793958i	0.999212	−	0.0396979i	$-0.0126396\pi$
$702$		0			0
$703$	188.677			0.268388
$704$	−85.8564	−	85.8564i	−0.121955	−	0.121955i
$705$	966.831			1.37139
$706$			410.074i			0.580842i
$707$	−254.045	−	254.045i	−0.359328	−	0.359328i
$708$	−149.885	−	149.885i	−0.211701	−	0.211701i
$709$	−219.581	+	219.581i	−0.309706	+	0.309706i	−0.844795	−	0.535090i	$-0.820278\pi$
$709$	−219.581	+	219.581i	−0.309706	+	0.309706i	0.535090	+	0.844795i	$0.320278\pi$
$710$	359.138	−	359.138i	0.505829	−	0.505829i
$711$	108.373			0.152423
$712$		−	197.436i		−	0.277298i
$713$	−982.137	+	982.137i	−1.37747	+	1.37747i
$714$			32.1539i			0.0450335i
$715$		0			0
$716$	100.441			0.140281
$717$	−1.49227	−	1.49227i	−0.00208127	−	0.00208127i
$718$	−536.554			−0.747289
$719$			311.520i			0.433269i	0.976253	+	0.216635i	$0.0695080\pi$
$719$			311.520i			0.433269i	−0.976253	+	0.216635i	$0.930492\pi$
$720$	−56.7846	−	56.7846i	−0.0788675	−	0.0788675i
$721$	196.305	+	196.305i	0.272267	+	0.272267i
$722$	−347.400	+	347.400i	−0.481163	+	0.481163i
$723$	−104.229	+	104.229i	−0.144162	+	0.144162i
$724$	−604.708			−0.835232
$725$			342.679i			0.472661i
$726$	189.406	−	189.406i	0.260890	−	0.260890i
$727$		−	379.585i		−	0.522125i	−0.965322	−	0.261062i	$-0.915927\pi$
$727$		−	379.585i		−	0.522125i	0.965322	−	0.261062i	$-0.0840728\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−261.033	−	261.033i	−0.357580	−	0.357580i
$731$	165.646			0.226602
$732$		−	274.708i		−	0.375284i
$733$	−769.627	−	769.627i	−1.04997	−	1.04997i	−0.998684	−	0.0512852i	$-0.983668\pi$
$733$	−769.627	−	769.627i	−1.04997	−	1.04997i	−0.0512852	−	0.998684i	$-0.516332\pi$
$734$	176.215	+	176.215i	0.240075	+	0.240075i
$735$	346.708	−	346.708i	0.471711	−	0.471711i
$736$	127.426	−	127.426i	0.173133	−	0.173133i
$737$	−1003.21			−1.36121
$738$			181.492i			0.245924i
$739$	−189.161	+	189.161i	−0.255969	+	0.255969i	−0.823413	−	0.567443i	$-0.807933\pi$
$739$	−189.161	+	189.161i	−0.255969	+	0.255969i	0.567443	+	0.823413i	$0.307933\pi$
$740$			684.764i			0.925357i
$741$		0			0
$742$	357.513			0.481823
$743$	−783.640	−	783.640i	−1.05470	−	1.05470i	−0.998415	−	0.0562818i	$-0.982075\pi$
$743$	−783.640	−	783.640i	−1.05470	−	1.05470i	−0.0562818	−	0.998415i	$-0.517925\pi$
$744$	213.597			0.287093
$745$			1061.97i			1.42546i
$746$	−483.606	−	483.606i	−0.648266	−	0.648266i
$747$	−62.9000	−	62.9000i	−0.0842035	−	0.0842035i
$748$	108.862	−	108.862i	0.145537	−	0.145537i
$749$	−10.0704	+	10.0704i	−0.0134451	+	0.0134451i
$750$	85.4923			0.113990
$751$		−	367.923i		−	0.489911i	−0.969534	−	0.244955i	$-0.921227\pi$
$751$		−	367.923i		−	0.489911i	0.969534	−	0.244955i	$-0.0787733\pi$
$752$	235.923	−	235.923i	0.313727	−	0.313727i
$753$			70.5077i			0.0936358i
$754$		0			0
$755$	1504.43			1.99262
$756$	19.0192	+	19.0192i	0.0251577	+	0.0251577i
$757$	195.384			0.258104			0.129052	−	0.991638i	$-0.458807\pi$
$757$	195.384			0.258104			0.129052	+	0.991638i	$0.458807\pi$
$758$		−	408.214i		−	0.538541i
$759$	592.161	+	592.161i	0.780186	+	0.780186i
$760$	49.3590	+	49.3590i	0.0649460	+	0.0649460i
$761$	861.367	−	861.367i	1.13189	−	1.13189i	0.142025	−	0.989863i	$-0.454639\pi$
$761$	861.367	−	861.367i	1.13189	−	1.13189i	0.989863	−	0.142025i	$-0.0453612\pi$
$762$	309.771	−	309.771i	0.406523	−	0.406523i
$763$	398.275			0.521986
$764$			325.359i			0.425863i
$765$	72.0000	−	72.0000i	0.0941176	−	0.0941176i
$766$		−	372.497i		−	0.486289i
$767$		0			0
$768$	−27.7128			−0.0360844
$769$	−732.685	−	732.685i	−0.952776	−	0.952776i	0.0461583	−	0.998934i	$-0.485302\pi$
$769$	−732.685	−	732.685i	−0.952776	−	0.952776i	−0.998934	+	0.0461583i	$0.985302\pi$
$770$	371.769			0.482817
$771$		−	536.554i		−	0.695919i
$772$	−116.301	−	116.301i	−0.150649	−	0.150649i
$773$	−662.232	−	662.232i	−0.856704	−	0.856704i	0.134245	−	0.990948i	$-0.457139\pi$
$773$	−662.232	−	662.232i	−0.856704	−	0.856704i	−0.990948	+	0.134245i	$0.957139\pi$
$774$	97.9808	−	97.9808i	0.126590	−	0.126590i
$775$	609.962	−	609.962i	0.787048	−	0.787048i
$776$	−51.9512			−0.0669474
$777$		−	229.352i		−	0.295177i
$778$	−66.2487	+	66.2487i	−0.0851526	+	0.0851526i
$779$		−	157.759i		−	0.202515i
$780$		0			0
$781$	814.508			1.04290
$782$	161.569	+	161.569i	0.206610	+	0.206610i
$783$	−90.0000			−0.114943
$784$		−	169.205i		−	0.215823i
$785$	655.717	+	655.717i	0.835308	+	0.835308i
$786$	92.9000	+	92.9000i	0.118193	+	0.118193i
$787$	−677.547	+	677.547i	−0.860923	+	0.860923i	−0.991445	−	0.130522i	$-0.958335\pi$
$787$	−677.547	+	677.547i	−0.860923	+	0.860923i	0.130522	+	0.991445i	$0.458335\pi$
$788$	−381.913	+	381.913i	−0.484661	+	0.484661i
$789$	498.200			0.631432
$790$		−	341.885i		−	0.432765i
$791$	158.827	−	158.827i	0.200792	−	0.200792i
$792$		−	128.785i		−	0.162607i
$793$		0			0
$794$	191.286			0.240914
$795$	−800.554	−	800.554i	−1.00699	−	1.00699i
$796$	127.569			0.160263
$797$			375.118i			0.470662i	0.971915	+	0.235331i	$0.0756175\pi$
$797$			375.118i			0.470662i	−0.971915	+	0.235331i	$0.924383\pi$
$798$	−16.5321	−	16.5321i	−0.0207169	−	0.0207169i
$799$	299.138	+	299.138i	0.374391	+	0.374391i
$800$	−79.1384	+	79.1384i	−0.0989230	+	0.0989230i
$801$	148.077	−	148.077i	0.184865	−	0.184865i
$802$	−270.831			−0.337694
$803$		−	592.010i		−	0.737248i
$804$	−161.909	+	161.909i	−0.201379	+	0.201379i
$805$			551.769i			0.685428i
$806$		0			0
$807$	−283.608			−0.351435
$808$	277.626	+	277.626i	0.343596	+	0.343596i
$809$	752.554			0.930227			0.465114	−	0.885251i	$-0.346013\pi$
$809$	752.554			0.930227			0.465114	+	0.885251i	$0.346013\pi$
$810$		−	85.1769i		−	0.105157i
$811$	49.8071	+	49.8071i	0.0614144	+	0.0614144i	0.737147	−	0.675732i	$-0.236173\pi$
$811$	49.8071	+	49.8071i	0.0614144	+	0.0614144i	−0.675732	+	0.737147i	$0.736173\pi$
$812$	−63.3975	−	63.3975i	−0.0780757	−	0.0780757i
$813$	−398.293	+	398.293i	−0.489905	+	0.489905i
$814$	−776.505	+	776.505i	−0.953937	+	0.953937i
$815$	1877.17			2.30328
$816$		−	35.1384i		−	0.0430618i
$817$	−85.1680	+	85.1680i	−0.104245	+	0.104245i
$818$			785.947i			0.960816i
$819$		0			0
$820$	572.554			0.698236
$821$	268.750	+	268.750i	0.327345	+	0.327345i	0.851576	−	0.524231i	$-0.175647\pi$
$821$	268.750	+	268.750i	0.327345	+	0.327345i	−0.524231	+	0.851576i	$0.675647\pi$
$822$	−302.985			−0.368594
$823$			1326.83i			1.61219i	0.591788	+	0.806094i	$0.298422\pi$
$823$			1326.83i			1.61219i	−0.591788	+	0.806094i	$0.701578\pi$
$824$	−214.526	−	214.526i	−0.260347	−	0.260347i
$825$	−367.765	−	367.765i	−0.445776	−	0.445776i
$826$	158.372	−	158.372i	0.191733	−	0.191733i
$827$	178.410	−	178.410i	0.215732	−	0.215732i	−0.590965	−	0.806697i	$-0.701253\pi$
$827$	178.410	−	178.410i	0.215732	−	0.215732i	0.806697	+	0.590965i	$0.201253\pi$
$828$	191.138			0.230844
$829$			969.092i			1.16899i	0.811398	+	0.584495i	$0.198707\pi$
$829$			969.092i			1.16899i	−0.811398	+	0.584495i	$0.801293\pi$
$830$	−198.431	+	198.431i	−0.239073	+	0.239073i
$831$			233.800i			0.281348i
$832$		0			0
$833$	214.543			0.257555
$834$	266.229	+	266.229i	0.319220	+	0.319220i
$835$	−1869.82			−2.23930
$836$			111.944i			0.133904i
$837$	160.198	+	160.198i	0.191396	+	0.191396i
$838$	657.646	+	657.646i	0.784781	+	0.784781i
$839$	−154.070	+	154.070i	−0.183636	+	0.183636i	−0.792938	−	0.609302i	$-0.791450\pi$
$839$	−154.070	+	154.070i	−0.183636	+	0.183636i	0.609302	+	0.792938i	$0.291450\pi$
$840$	60.0000	−	60.0000i	0.0714286	−	0.0714286i
$841$	−541.000			−0.643282
$842$			656.070i			0.779181i
$843$	560.396	−	560.396i	0.664764	−	0.664764i
$844$			495.597i			0.587201i
$845$		0			0
$846$	353.885			0.418303
$847$	200.131	+	200.131i	0.236283	+	0.236283i
$848$	−390.697			−0.460728
$849$		−	244.832i		−	0.288377i
$850$	−100.344	−	100.344i	−0.118051	−	0.118051i
$851$	−1152.47	−	1152.47i	−1.35425	−	1.35425i
$852$	131.454	−	131.454i	0.154288	−	0.154288i
$853$	173.527	−	173.527i	0.203432	−	0.203432i	−0.598037	−	0.801469i	$-0.704052\pi$
$853$	173.527	−	173.527i	0.203432	−	0.203432i	0.801469	+	0.598037i	$0.204052\pi$
$854$	290.263			0.339886
$855$			74.0385i			0.0865947i
$856$	11.0052	−	11.0052i	0.0128565	−	0.0128565i
$857$			616.543i			0.719421i	0.933064	+	0.359710i	$0.117124\pi$
$857$			616.543i			0.719421i	−0.933064	+	0.359710i	$0.882876\pi$
$858$		0			0
$859$	566.398			0.659370			0.329685	−	0.944091i	$-0.393058\pi$
$859$	566.398			0.659370			0.329685	+	0.944091i	$0.393058\pi$
$860$	−309.100	−	309.100i	−0.359419	−	0.359419i
$861$	−191.769			−0.222728
$862$			45.3796i			0.0526446i
$863$	−656.627	−	656.627i	−0.760866	−	0.760866i	0.215613	−	0.976479i	$-0.430825\pi$
$863$	−656.627	−	656.627i	−0.760866	−	0.760866i	−0.976479	+	0.215613i	$0.930825\pi$
$864$	−20.7846	−	20.7846i	−0.0240563	−	0.0240563i
$865$	319.608	−	319.608i	0.369489	−	0.369489i
$866$	196.215	−	196.215i	0.226577	−	0.226577i
$867$	−456.009			−0.525962
$868$			225.692i			0.260014i
$869$	387.688	−	387.688i	0.446132	−	0.446132i
$870$			283.923i			0.326348i
$871$		0			0
$872$	−435.244			−0.499133
$873$	−38.9634	−	38.9634i	−0.0446316	−	0.0446316i
$874$	−166.144			−0.190096
$875$			90.3332i			0.103238i
$876$	−95.5448	−	95.5448i	−0.109069	−	0.109069i
$877$	−472.069	−	472.069i	−0.538277	−	0.538277i	0.384746	−	0.923023i	$-0.374289\pi$
$877$	−472.069	−	472.069i	−0.538277	−	0.538277i	−0.923023	+	0.384746i	$0.874289\pi$
$878$	−41.4627	+	41.4627i	−0.0472241	+	0.0472241i
$879$	−364.550	+	364.550i	−0.414733	+	0.414733i
$880$	−406.277			−0.461678
$881$			1016.34i			1.15362i	0.816880	+	0.576808i	$0.195702\pi$
$881$			1016.34i			1.15362i	−0.816880	+	0.576808i	$0.804298\pi$
$882$	126.904	−	126.904i	0.143882	−	0.143882i
$883$		−	785.277i		−	0.889328i	−0.895697	−	0.444664i	$-0.853323\pi$
$883$		−	785.277i		−	0.889328i	0.895697	−	0.444664i	$-0.146677\pi$
$884$		0			0
$885$	−709.261			−0.801425
$886$	19.9718	+	19.9718i	0.0225416	+	0.0225416i
$887$	1285.06			1.44877			0.724386	−	0.689394i	$-0.242123\pi$
$887$	1285.06			1.44877			0.724386	+	0.689394i	$0.242123\pi$
$888$			250.641i			0.282253i
$889$	327.311	+	327.311i	0.368179	+	0.368179i
$890$	−467.138	−	467.138i	−0.524875	−	0.524875i
$891$	96.5885	−	96.5885i	0.108405	−	0.108405i
$892$	65.0615	−	65.0615i	0.0729389	−	0.0729389i
$893$	−307.608			−0.344466
$894$			388.708i			0.434796i
$895$	237.646	−	237.646i	0.265526	−	0.265526i
$896$		−	29.2820i		−	0.0326808i
$897$		0			0
$898$	−186.613			−0.207809
$899$	−533.993	−	533.993i	−0.593986	−	0.593986i
$900$	−118.708			−0.131897
$901$		−	495.384i		−	0.549816i
$902$	649.261	+	649.261i	0.719802	+	0.719802i
$903$	103.529	+	103.529i	0.114650	+	0.114650i
$904$	−173.569	+	173.569i	−0.192001	+	0.192001i
$905$	−1430.75	+	1430.75i	−1.58094	+	1.58094i
$906$	550.659			0.607791
$907$			278.862i			0.307455i	0.988113	+	0.153727i	$0.0491278\pi$
$907$			278.862i			0.307455i	−0.988113	+	0.153727i	$0.950872\pi$
$908$	19.4256	−	19.4256i	0.0213939	−	0.0213939i
$909$			416.438i			0.458128i
$910$		0			0
$911$	86.7668			0.0952434			0.0476217	−	0.998865i	$-0.484836\pi$
$911$	86.7668			0.0952434			0.0476217	+	0.998865i	$0.484836\pi$
$912$	18.0666	+	18.0666i	0.0198099	+	0.0198099i
$913$	−450.031			−0.492914
$914$			417.037i			0.456277i
$915$	−649.965	−	649.965i	−0.710345	−	0.710345i
$916$	−574.631	−	574.631i	−0.627326	−	0.627326i
$917$	−98.1604	+	98.1604i	−0.107045	+	0.107045i
$918$	26.3538	−	26.3538i	0.0287079	−	0.0287079i
$919$	576.862			0.627706			0.313853	−	0.949472i	$-0.398380\pi$
$919$	576.862			0.627706			0.313853	+	0.949472i	$0.398380\pi$
$920$		−	602.985i		−	0.655418i
$921$	−121.362	+	121.362i	−0.131772	+	0.131772i
$922$			664.246i			0.720440i
$923$		0			0
$924$	136.077			0.147269
$925$	715.746	+	715.746i	0.773780	+	0.773780i
$926$	925.199			0.999134
$927$		−	321.788i		−	0.347129i
$928$	69.2820	+	69.2820i	0.0746574	+	0.0746574i
$929$	−10.5434	−	10.5434i	−0.0113492	−	0.0113492i	0.701409	−	0.712759i	$-0.252555\pi$
$929$	−10.5434	−	10.5434i	−0.0113492	−	0.0113492i	−0.712759	+	0.701409i	$0.752555\pi$
$930$	505.377	−	505.377i	0.543416	−	0.543416i
$931$	−110.309	+	110.309i	−0.118484	+	0.118484i
$932$	−54.6616			−0.0586498
$933$		−	242.900i		−	0.260343i
$934$	−396.649	+	396.649i	−0.424677	+	0.424677i
$935$		−	515.138i		−	0.550950i
$936$		0			0
$937$	700.477			0.747574			0.373787	−	0.927515i	$-0.378059\pi$
$937$	700.477			0.747574			0.373787	+	0.927515i	$0.378059\pi$
$938$	−171.077	−	171.077i	−0.182385	−	0.182385i
$939$	953.123			1.01504
$940$		−	1116.40i		−	1.18766i
$941$	1147.05	+	1147.05i	1.21897	+	1.21897i	0.967992	+	0.250983i	$0.0807538\pi$
$941$	1147.05	+	1147.05i	1.21897	+	1.21897i	0.250983	+	0.967992i	$0.419246\pi$
$942$	240.009	+	240.009i	0.254787	+	0.254787i
$943$	−963.615	+	963.615i	−1.02186	+	1.02186i
$944$	−173.072	+	173.072i	−0.183339	+	0.183339i
$945$	90.0000			0.0952381
$946$		−	701.023i		−	0.741039i
$947$	−868.526	+	868.526i	−0.917134	+	0.917134i	−0.996820	−	0.0796863i	$-0.974608\pi$
$947$	−868.526	+	868.526i	−0.917134	+	0.917134i	0.0796863	+	0.996820i	$0.474608\pi$
$948$		−	125.138i		−	0.132003i
$949$		0			0
$950$	103.184			0.108615
$951$	−54.1999	−	54.1999i	−0.0569926	−	0.0569926i
$952$	37.1281			0.0390001
$953$		−	1086.62i		−	1.14021i	−0.821573	−	0.570104i	$-0.806903\pi$
$953$		−	1086.62i		−	1.14021i	0.821573	−	0.570104i	$-0.193097\pi$
$954$	−293.023	−	293.023i	−0.307152	−	0.307152i
$955$	769.808	+	769.808i	0.806081	+	0.806081i
$956$	−1.72312	+	1.72312i	−0.00180243	+	0.00180243i
$957$	−321.962	+	321.962i	−0.336428	+	0.336428i
$958$	509.072			0.531390
$959$		−	320.141i		−	0.333828i
$960$	−65.5692	+	65.5692i	−0.0683013	+	0.0683013i
$961$			939.993i			0.978141i
$962$		0			0
$963$	16.5077			0.0171420
$964$	120.354	+	120.354i	0.124848	+	0.124848i
$965$	−550.344			−0.570304
$966$			201.962i			0.209070i
$967$	−827.831	−	827.831i	−0.856081	−	0.856081i	0.134793	−	0.990874i	$-0.456963\pi$
$967$	−827.831	−	827.831i	−0.856081	−	0.856081i	−0.990874	+	0.134793i	$0.956963\pi$
$968$	−218.708	−	218.708i	−0.225938	−	0.225938i
$969$	−22.9076	+	22.9076i	−0.0236404	+	0.0236404i
$970$	−122.918	+	122.918i	−0.126719	+	0.126719i
$971$	−1143.70			−1.17786			−0.588929	−	0.808185i	$-0.700450\pi$
$971$	−1143.70			−1.17786			−0.588929	+	0.808185i	$0.700450\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−281.305	+	281.305i	−0.289111	+	0.289111i
$974$		−	274.000i		−	0.281314i
$975$		0			0
$976$	−317.205			−0.325005
$977$	243.033	+	243.033i	0.248755	+	0.248755i	0.820459	−	0.571705i	$-0.193718\pi$
$977$	243.033	+	243.033i	0.248755	+	0.248755i	−0.571705	+	0.820459i	$0.693718\pi$
$978$	687.093			0.702550
$979$		−	1059.45i		−	1.08217i
$980$	−400.344	−	400.344i	−0.408514	−	0.408514i
$981$	−326.433	−	326.433i	−0.332755	−	0.332755i
$982$	−23.0718	+	23.0718i	−0.0234947	+	0.0234947i
$983$	−630.073	+	630.073i	−0.640970	+	0.640970i	−0.950794	−	0.309824i	$-0.899730\pi$
$983$	−630.073	+	630.073i	−0.640970	+	0.640970i	0.309824	+	0.950794i	$0.399730\pi$
$984$	209.569			0.212977
$985$			1807.23i			1.83475i
$986$	−87.8461	+	87.8461i	−0.0890934	+	0.0890934i
$987$			373.923i			0.378848i
$988$		0			0
$989$	1040.44			1.05201
$990$	−304.708	−	304.708i	−0.307786	−	0.307786i
$991$	−956.739			−0.965427			−0.482714	−	0.875778i	$-0.660349\pi$
$991$	−956.739			−0.965427			−0.482714	+	0.875778i	$0.660349\pi$
$992$		−	246.641i		−	0.248630i
$993$	−494.715	−	494.715i	−0.498202	−	0.498202i
$994$	138.897	+	138.897i	0.139736	+	0.139736i
$995$	301.832	−	301.832i	0.303349	−	0.303349i
$996$	−72.6307	+	72.6307i	−0.0729224	+	0.0729224i
$997$	−167.169			−0.167672			−0.0838360	−	0.996480i	$-0.526717\pi$
$997$	−167.169			−0.167672			−0.0838360	+	0.996480i	$0.526717\pi$
$998$		−	321.538i		−	0.322183i
$999$	−187.981	+	187.981i	−0.188169	+	0.188169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.d.775.1		4
13.5	odd	4	inner	1014.3.f.d.577.1		4
13.7	odd	12		78.3.l.a.67.1	yes	4
13.8	odd	4		1014.3.f.e.577.1		4
13.10	even	6		78.3.l.a.7.1	✓	4
13.12	even	2		1014.3.f.e.775.1		4
39.20	even	12		234.3.bb.c.145.1		4
39.23	odd	6		234.3.bb.c.163.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.7.1	✓	4	13.10	even	6
78.3.l.a.67.1	yes	4	13.7	odd	12
234.3.bb.c.145.1		4	39.20	even	12
234.3.bb.c.163.1		4	39.23	odd	6
1014.3.f.d.577.1		4	13.5	odd	4	inner
1014.3.f.d.775.1		4	1.1	even	1	trivial
1014.3.f.e.577.1		4	13.8	odd	4
1014.3.f.e.775.1		4	13.12	even	2

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} +(4.73205 + 4.73205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-1.83013 + 1.83013i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -9.46410i q^{10} +(10.7321 - 10.7321i) q^{11} -3.46410i q^{12} +3.66025 q^{14} +(-8.19615 - 8.19615i) q^{15} -4.00000 q^{16} -5.07180i q^{17} +(-3.00000 - 3.00000i) q^{18} +(2.60770 + 2.60770i) q^{19} +(-9.46410 + 9.46410i) q^{20} +(3.16987 - 3.16987i) q^{21} -21.4641 q^{22} -31.8564i q^{23} +(-3.46410 + 3.46410i) q^{24} +19.7846i q^{25} -5.19615 q^{27} +(-3.66025 - 3.66025i) q^{28} +17.3205 q^{29} +16.3923i q^{30} +(-30.8301 - 30.8301i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-18.5885 + 18.5885i) q^{33} +(-5.07180 + 5.07180i) q^{34} -17.3205 q^{35} +6.00000i q^{36} +(36.1769 - 36.1769i) q^{37} -5.21539i q^{38} +18.9282 q^{40} +(-30.2487 - 30.2487i) q^{41} -6.33975 q^{42} +32.6603i q^{43} +(21.4641 + 21.4641i) q^{44} +(14.1962 + 14.1962i) q^{45} +(-31.8564 + 31.8564i) q^{46} +(-58.9808 + 58.9808i) q^{47} +6.92820 q^{48} +42.3013i q^{49} +(19.7846 - 19.7846i) q^{50} +8.78461i q^{51} +97.6743 q^{53} +(5.19615 + 5.19615i) q^{54} +101.569 q^{55} +7.32051i q^{56} +(-4.51666 - 4.51666i) q^{57} +(-17.3205 - 17.3205i) q^{58} +(43.2679 - 43.2679i) q^{59} +(16.3923 - 16.3923i) q^{60} +79.3013 q^{61} +61.6603i q^{62} +(-5.49038 + 5.49038i) q^{63} -8.00000i q^{64} +37.1769 q^{66} +(-46.7391 - 46.7391i) q^{67} +10.1436 q^{68} +55.1769i q^{69} +(17.3205 + 17.3205i) q^{70} +(37.9474 + 37.9474i) q^{71} +(6.00000 - 6.00000i) q^{72} +(27.5814 - 27.5814i) q^{73} -72.3538 q^{74} -34.2679i q^{75} +(-5.21539 + 5.21539i) q^{76} +39.2820i q^{77} +36.1244 q^{79} +(-18.9282 - 18.9282i) q^{80} +9.00000 q^{81} +60.4974i q^{82} +(-20.9667 - 20.9667i) q^{83} +(6.33975 + 6.33975i) q^{84} +(24.0000 - 24.0000i) q^{85} +(32.6603 - 32.6603i) q^{86} -30.0000 q^{87} -42.9282i q^{88} +(49.3590 - 49.3590i) q^{89} -28.3923i q^{90} +63.7128 q^{92} +(53.3993 + 53.3993i) q^{93} +117.962 q^{94} +24.6795i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-12.9878 - 12.9878i) q^{97} +(42.3013 - 42.3013i) q^{98} +(32.1962 - 32.1962i) 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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