LMFDB - Embedded newform 1014.3.f.e.577.1

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			577.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.577
Dual form			1014.3.f.e.775.1

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

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

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
$5$	−4.73205	+	4.73205i	−0.946410	+	0.946410i	−0.998635	−	0.0522252i	$-0.983369\pi$
$5$	−4.73205	+	4.73205i	−0.946410	+	0.946410i	0.0522252	+	0.998635i	$0.483369\pi$
$6$	−1.73205	+	1.73205i	−0.288675	+	0.288675i
$7$	1.83013	+	1.83013i	0.261447	+	0.261447i	0.825642	−	0.564195i	$-0.190813\pi$
$7$	1.83013	+	1.83013i	0.261447	+	0.261447i	−0.564195	+	0.825642i	$0.690813\pi$
$8$	−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	$-0.492338\pi$
$11$	−10.7321	−	10.7321i	−0.975641	−	0.975641i	−0.999710	+	0.0240693i	$0.992338\pi$
$12$			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	$0.0476603\pi$
$17$			5.07180i			0.298341i	−0.988811	+	0.149170i	$0.952340\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$	−2.60770	+	2.60770i	−0.137247	+	0.137247i	−0.772393	−	0.635145i	$-0.780940\pi$
$19$	−2.60770	+	2.60770i	−0.137247	+	0.137247i	0.635145	+	0.772393i	$0.280940\pi$
$20$	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	$0.243504\pi$
$23$			31.8564i			1.38506i	−0.721389	+	0.692531i	$0.756496\pi$
$24$	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	$-0.501740\pi$
$31$	30.8301	−	30.8301i	0.994520	−	0.994520i	0.999985	+	0.00546484i	$0.00173952\pi$
$32$	−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	$-0.492996\pi$
$37$	−36.1769	−	36.1769i	−0.977754	−	0.977754i	−0.999758	+	0.0220034i	$0.992996\pi$
$38$			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	$-0.575304\pi$
$41$	30.2487	−	30.2487i	0.737773	−	0.737773i	0.972147	+	0.234373i	$0.0753038\pi$
$42$	−6.33975			−0.150946
$43$		−	32.6603i		−	0.759541i	−0.925081	−	0.379770i	$-0.876003\pi$
$43$		−	32.6603i		−	0.759541i	0.925081	−	0.379770i	$-0.123997\pi$
$44$	−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	0.953492	+	0.301418i	$0.0974598\pi$
$47$	58.9808	+	58.9808i	1.25491	+	1.25491i	0.301418	+	0.953492i	$0.402540\pi$
$48$	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	$-0.423532\pi$
$59$	−43.2679	−	43.2679i	−0.733355	−	0.733355i	−0.971283	+	0.237928i	$0.923532\pi$
$60$	−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	$-0.585799\pi$
$67$	46.7391	−	46.7391i	0.697598	−	0.697598i	0.963892	+	0.266294i	$0.0857991\pi$
$68$	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	$-0.873363\pi$
$71$	−37.9474	+	37.9474i	−0.534471	+	0.534471i	0.387429	+	0.921900i	$0.373363\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−27.5814	−	27.5814i	−0.377828	−	0.377828i	0.492490	−	0.870318i	$-0.336087\pi$
$73$	−27.5814	−	27.5814i	−0.377828	−	0.377828i	−0.870318	+	0.492490i	$0.836087\pi$
$74$	−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	$-0.692836\pi$
$83$	20.9667	−	20.9667i	0.252611	−	0.252611i	0.822040	+	0.569430i	$0.192836\pi$
$84$	−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	$-0.378271\pi$
$89$	−49.3590	−	49.3590i	−0.554595	−	0.554595i	−0.927764	+	0.373168i	$0.878271\pi$
$90$			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	$-0.719818\pi$
$97$	12.9878	−	12.9878i	0.133895	−	0.133895i	0.770878	+	0.636983i	$0.219818\pi$
$98$	−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	$-0.758843\pi$
$101$		−	138.813i		−	1.37438i	0.726476	−	0.687192i	$-0.241157\pi$
$102$	−8.78461	−	8.78461i	−0.0861236	−	0.0861236i
$103$			107.263i			1.04139i	0.853744	+	0.520693i	$0.174326\pi$
$103$			107.263i			1.04139i	−0.853744	+	0.520693i	$0.825674\pi$
$104$		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	$-0.500552\pi$
$109$	108.811	−	108.811i	0.998265	−	0.998265i	0.999998	+	0.00173346i	$0.000551778\pi$
$110$	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	$0.248658\pi$
$127$			178.846i			1.40824i	−0.710082	+	0.704118i	$0.751342\pi$
$128$	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	$-0.100913\pi$
$137$	87.4641	+	87.4641i	0.638424	+	0.638424i	−0.311743	+	0.950167i	$0.600913\pi$
$138$	−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	$-0.928753\pi$
$149$	−112.210	+	112.210i	−0.753089	+	0.753089i	0.221966	+	0.975054i	$0.428753\pi$
$150$	34.2679	+	34.2679i	0.228453	+	0.228453i
$151$	−158.962	−	158.962i	−1.05273	−	1.05273i	−0.998530	−	0.0541950i	$-0.982741\pi$
$151$	−158.962	−	158.962i	−1.05273	−	1.05273i	−0.0541950	−	0.998530i	$-0.517259\pi$
$152$	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	−0.968729	−	0.248123i	$-0.920186\pi$
$163$	−198.347	−	198.347i	−1.21685	−	1.21685i	−0.248123	−	0.968729i	$-0.579814\pi$
$164$	−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	0.978950	+	0.204099i	$0.0654264\pi$
$167$	197.569	+	197.569i	1.18305	+	1.18305i	0.204099	+	0.978950i	$0.434574\pi$
$168$			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	$0.0625373\pi$
$173$			67.5411i			0.390411i	−0.980762	+	0.195205i	$0.937463\pi$
$174$	−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	$0.0448005\pi$
$179$			50.2205i			0.280562i	−0.990112	+	0.140281i	$0.955199\pi$
$180$	28.3923	+	28.3923i	0.157735	+	0.157735i
$181$		−	302.354i		−	1.67046i	−0.549898	−	0.835232i	$-0.685334\pi$
$181$		−	302.354i		−	1.67046i	0.549898	−	0.835232i	$-0.314666\pi$
$182$		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	$-0.181660\pi$
$193$	58.1506	+	58.1506i	0.301299	+	0.301299i	−0.540223	+	0.841522i	$0.681660\pi$
$194$		−	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	$-0.990379\pi$
$197$	−190.956	+	190.956i	−0.969322	+	0.969322i	0.0302216	+	0.999543i	$0.490379\pi$
$198$	−64.3923			−0.325214
$199$			63.7846i			0.320526i	0.987074	+	0.160263i	$0.0512342\pi$
$199$			63.7846i			0.320526i	−0.987074	+	0.160263i	$0.948766\pi$
$200$	−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	$-0.717107\pi$
$223$	32.5307	−	32.5307i	0.145878	−	0.145878i	0.776274	+	0.630396i	$0.217107\pi$
$224$	−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	$-0.740368\pi$
$227$	9.71281	−	9.71281i	0.0427877	−	0.0427877i	0.728177	+	0.685389i	$0.240368\pi$
$228$	−9.03332	−	9.03332i	−0.0396198	−	0.0396198i
$229$	287.315	+	287.315i	1.25465	+	1.25465i	0.953611	+	0.301041i	$0.0973341\pi$
$229$	287.315	+	287.315i	1.25465	+	1.25465i	0.301041	+	0.953611i	$0.402666\pi$
$230$	−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	$-0.981320\pi$
$233$		−	27.3308i		−	0.117300i	0.998279	−	0.0586498i	$-0.0186795\pi$
$234$		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	$-0.750811\pi$
$239$	−0.861561	+	0.861561i	−0.00360486	+	0.00360486i	0.705302	+	0.708907i	$0.250811\pi$
$240$	−32.7846	+	32.7846i	−0.136603	+	0.136603i
$241$	−60.1769	−	60.1769i	−0.249697	−	0.249697i	0.571149	−	0.820846i	$-0.306498\pi$
$241$	−60.1769	−	60.1769i	−0.249697	−	0.249697i	−0.820846	+	0.571149i	$0.806498\pi$
$242$	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	$0.0258404\pi$
$251$			40.7077i			0.162182i	−0.996707	+	0.0810910i	$0.974160\pi$
$252$	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	$-0.794098\pi$
$257$		−	309.779i		−	1.20537i	0.797980	−	0.602684i	$-0.205902\pi$
$258$	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	$-0.454836\pi$
$271$	−229.954	−	229.954i	−0.848541	−	0.848541i	−0.989951	+	0.141411i	$0.954836\pi$
$272$		−	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	$0.0783463\pi$
$277$			134.985i			0.487309i	−0.969862	+	0.243654i	$0.921654\pi$
$278$	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	0.986271	+	0.165134i	$0.0528056\pi$
$281$	323.545	+	323.545i	1.15141	+	1.15141i	0.165134	+	0.986271i	$0.447194\pi$
$282$	−204.315			−0.724523
$283$		−	141.354i		−	0.499483i	−0.968312	−	0.249742i	$-0.919654\pi$
$283$		−	141.354i		−	0.499483i	0.968312	−	0.249742i	$-0.0803457\pi$
$284$	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	$-0.419593\pi$
$293$	−210.473	−	210.473i	−0.718338	−	0.718338i	−0.968265	+	0.249927i	$0.919593\pi$
$294$	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	$-0.301597\pi$
$307$	−70.0685	−	70.0685i	−0.228236	−	0.228236i	−0.811956	+	0.583719i	$0.801597\pi$
$308$	−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	$-0.927610\pi$
$311$		−	140.238i		−	0.450927i	0.974252	−	0.225464i	$-0.0723897\pi$
$312$		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	$-0.772237\pi$
$317$	−31.2923	+	31.2923i	−0.0987140	+	0.0987140i	0.656025	+	0.754739i	$0.272237\pi$
$318$	−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	$-0.958899\pi$
$331$	−285.624	+	285.624i	−0.862911	+	0.862911i	0.128764	+	0.991675i	$0.458899\pi$
$332$	−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	$-0.603782\pi$
$337$		−	638.492i		−	1.89464i	0.320295	−	0.947318i	$-0.396218\pi$
$338$		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	$-0.166426\pi$
$349$	128.103	+	128.103i	0.367058	+	0.367058i	−0.499345	+	0.866403i	$0.666426\pi$
$350$		−	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	$-0.615278\pi$
$353$	205.037	−	205.037i	0.580842	−	0.580842i	0.935135	+	0.354293i	$0.115278\pi$
$354$	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	$-0.427213\pi$
$359$	−268.277	−	268.277i	−0.747289	−	0.747289i	−0.973969	+	0.226680i	$0.927213\pi$
$360$	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	$-0.874353\pi$
$379$	−204.107	+	204.107i	−0.538541	+	0.538541i	0.384559	+	0.923100i	$0.374353\pi$
$380$	−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	$-0.861734\pi$
$383$	−186.249	+	186.249i	−0.486289	+	0.486289i	0.420844	+	0.907133i	$0.361734\pi$
$384$	−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	$0.0271378\pi$
$389$			66.2487i			0.170305i	−0.996368	+	0.0851526i	$0.972862\pi$
$390$		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	$-0.195510\pi$
$397$	95.6429	+	95.6429i	0.240914	+	0.240914i	−0.576314	+	0.817228i	$0.695510\pi$
$398$	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	$-0.326749\pi$
$401$	−135.415	−	135.415i	−0.337694	−	0.337694i	−0.855499	+	0.517805i	$0.826749\pi$
$402$			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	$-0.512240\pi$
$409$	392.974	−	392.974i	0.960816	−	0.960816i	0.999261	+	0.0384448i	$0.0122404\pi$
$410$	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	$-0.564260\pi$
$421$	328.035	−	328.035i	0.779181	−	0.779181i	0.979692	+	0.200511i	$0.0642601\pi$
$422$	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	$-0.738148\pi$
$431$	22.6898	−	22.6898i	0.0526446	−	0.0526446i	0.732939	+	0.680294i	$0.238148\pi$
$432$	20.7846			0.0481125
$433$		−	196.215i		−	0.453153i	−0.973993	−	0.226577i	$-0.927247\pi$
$433$		−	196.215i		−	0.453153i	0.973993	−	0.226577i	$-0.0727534\pi$
$434$	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	$0.0150375\pi$
$439$			41.4627i			0.0944481i	−0.998884	+	0.0472241i	$0.984963\pi$
$440$	−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	$-0.296944\pi$
$449$	−93.3064	−	93.3064i	−0.207809	−	0.207809i	−0.803336	+	0.595526i	$0.796944\pi$
$450$	−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	$-0.645431\pi$
$457$	208.519	−	208.519i	0.456277	−	0.456277i	0.897431	+	0.441154i	$0.145431\pi$
$458$	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	$-0.579857\pi$
$461$	332.123	−	332.123i	0.720440	−	0.720440i	0.968695	+	0.248255i	$0.0798569\pi$
$462$	68.0385	+	68.0385i	0.147269	+	0.147269i
$463$	462.599	+	462.599i	0.999134	+	0.999134i	1.00000		0.000865128i	$-0.000275379\pi$
$463$	462.599	+	462.599i	0.999134	+	0.999134i	−0.000865128		1.00000i	$0.500275\pi$
$464$	−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	$0.139612\pi$
$467$			396.649i			0.849355i	−0.905345	+	0.424677i	$0.860388\pi$
$468$		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	$-0.127385\pi$
$479$	254.536	+	254.536i	0.531390	+	0.531390i	−0.389596	+	0.920986i	$0.627385\pi$
$480$			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	$-0.813743\pi$
$487$	−137.000	+	137.000i	−0.281314	+	0.281314i	0.552319	+	0.833633i	$0.313743\pi$
$488$	−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	$0.00747928\pi$
$491$			23.0718i			0.0469894i	−0.999724	+	0.0234947i	$0.992521\pi$
$492$	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	$-0.823159\pi$
$499$	−160.769	+	160.769i	−0.322183	+	0.322183i	0.527421	+	0.849604i	$0.323159\pi$
$500$	−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	$-0.589514\pi$
$509$	347.745	−	347.745i	0.683192	−	0.683192i	0.960718	+	0.277526i	$0.0895145\pi$
$510$	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	$-0.338746\pi$
$541$	−210.557	−	210.557i	−0.389200	−	0.389200i	−0.874402	+	0.485202i	$0.838746\pi$
$542$	−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	$-0.229720\pi$
$557$	50.1539	+	50.1539i	0.0900429	+	0.0900429i	−0.660651	+	0.750694i	$0.729720\pi$
$558$		−	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	$-0.735042\pi$
$563$		−	832.726i		−	1.47909i	0.673109	−	0.739543i	$-0.264958\pi$
$564$	−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	$0.0990503\pi$
$569$			348.431i			0.612356i	−0.951974	+	0.306178i	$0.900950\pi$
$570$	42.7461	+	42.7461i	0.0749932	+	0.0749932i
$571$		−	411.892i		−	0.721352i	−0.932691	−	0.360676i	$-0.882546\pi$
$571$		−	411.892i		−	0.721352i	0.932691	−	0.360676i	$-0.117454\pi$
$572$		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	$-0.734520\pi$
$577$	39.6692	−	39.6692i	0.0687507	−	0.0687507i	0.740646	+	0.671895i	$0.234520\pi$
$578$	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	$-0.602951\pi$
$587$	370.004	−	370.004i	0.630330	−	0.630330i	0.948151	+	0.317821i	$0.102951\pi$
$588$	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	$-0.159684\pi$
$593$	234.771	+	234.771i	0.395903	+	0.395903i	−0.480882	+	0.876785i	$0.659684\pi$
$594$	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	$-0.637225\pi$
$613$	300.757	−	300.757i	0.490631	−	0.490631i	0.908505	+	0.417874i	$0.137225\pi$
$614$	−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	$-0.784967\pi$
$617$	−95.6603	+	95.6603i	−0.155041	+	0.155041i	0.625324	+	0.780365i	$0.284967\pi$
$618$	−185.785	−	185.785i	−0.300622	−	0.300622i
$619$	−661.030	−	661.030i	−1.06790	−	1.06790i	−0.997520	−	0.0703796i	$-0.977579\pi$
$619$	−661.030	−	661.030i	−1.06790	−	1.06790i	−0.0703796	−	0.997520i	$-0.522421\pi$
$620$	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	$-0.349508\pi$
$631$	−274.445	−	274.445i	−0.434937	−	0.434937i	−0.890304	+	0.455367i	$0.849508\pi$
$632$	−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	$-0.838360\pi$
$641$		−	623.387i		−	0.972523i	0.873813	−	0.486261i	$-0.161640\pi$
$642$	−9.53074	+	9.53074i	−0.0148454	+	0.0148454i
$643$	578.270	−	578.270i	0.899331	−	0.899331i	−0.0960459	−	0.995377i	$-0.530620\pi$
$643$	578.270	−	578.270i	0.899331	−	0.899331i	0.995377	+	0.0960459i	$0.0306196\pi$
$644$	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	$-0.928849\pi$
$647$		−	286.841i		−	0.443340i	0.975122	−	0.221670i	$-0.0711508\pi$
$648$	−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	$-0.329126\pi$
$661$	−229.988	−	229.988i	−0.347939	−	0.347939i	−0.859341	+	0.511402i	$0.829126\pi$
$662$			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	$0.282572\pi$
$673$			1044.01i			1.55128i	−0.631178	+	0.775638i	$0.717428\pi$
$674$	−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	$-0.0418034\pi$
$683$	587.678	+	587.678i	0.860436	+	0.860436i	−0.130952	+	0.991389i	$0.541803\pi$
$684$	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	$-0.803684\pi$
$691$	−164.030	+	164.030i	−0.237381	+	0.237381i	0.578384	+	0.815765i	$0.303684\pi$
$692$	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	$0.0126396\pi$
$701$			55.6565i			0.0793958i	−0.999212	+	0.0396979i	$0.987360\pi$
$702$		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	$-0.179722\pi$
$709$	219.581	+	219.581i	0.309706	+	0.309706i	−0.535090	+	0.844795i	$0.679722\pi$
$710$	−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	$-0.930492\pi$
$719$		−	311.520i		−	0.433269i	0.976253	−	0.216635i	$-0.0695080\pi$
$720$	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	$0.0840728\pi$
$727$			379.585i			0.522125i	−0.965322	+	0.261062i	$0.915927\pi$
$728$		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	0.0512852	−	0.998684i	$-0.483668\pi$
$733$	769.627	−	769.627i	1.04997	−	1.04997i	0.998684	−	0.0512852i	$-0.0163317\pi$
$734$	−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	$-0.192067\pi$
$739$	189.161	+	189.161i	0.255969	+	0.255969i	−0.567443	+	0.823413i	$0.692067\pi$
$740$		−	684.764i		−	0.925357i
$741$		0			0
$742$	357.513			0.481823
$743$	783.640	−	783.640i	1.05470	−	1.05470i	0.0562818	−	0.998415i	$-0.482075\pi$
$743$	783.640	−	783.640i	1.05470	−	1.05470i	0.998415	−	0.0562818i	$-0.0179245\pi$
$744$	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	$0.0787733\pi$
$751$			367.923i			0.489911i	−0.969534	+	0.244955i	$0.921227\pi$
$752$	−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	−0.989863	−	0.142025i	$-0.954639\pi$
$761$	−861.367	−	861.367i	−1.13189	−	1.13189i	−0.142025	−	0.989863i	$-0.545361\pi$
$762$	−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	$-0.514698\pi$
$769$	732.685	−	732.685i	0.952776	−	0.952776i	0.998934	+	0.0461583i	$0.0146979\pi$
$770$	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	$-0.542861\pi$
$773$	662.232	−	662.232i	0.856704	−	0.856704i	0.990948	+	0.134245i	$0.0428608\pi$
$774$	−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	$-0.0416653\pi$
$787$	677.547	+	677.547i	0.860923	+	0.860923i	−0.130522	+	0.991445i	$0.541665\pi$
$788$	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	$-0.924383\pi$
$797$		−	375.118i		−	0.470662i	0.971915	−	0.235331i	$-0.0756175\pi$
$798$	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	$-0.763827\pi$
$811$	−49.8071	+	49.8071i	−0.0614144	+	0.0614144i	0.675732	+	0.737147i	$0.263827\pi$
$812$	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	$-0.824353\pi$
$821$	−268.750	+	268.750i	−0.327345	+	0.327345i	0.524231	+	0.851576i	$0.324353\pi$
$822$	−302.985			−0.368594
$823$		−	1326.83i		−	1.61219i	−0.591788	−	0.806094i	$-0.701578\pi$
$823$		−	1326.83i		−	1.61219i	0.591788	−	0.806094i	$-0.298422\pi$
$824$	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	$-0.298747\pi$
$827$	−178.410	−	178.410i	−0.215732	−	0.215732i	−0.806697	+	0.590965i	$0.798747\pi$
$828$	191.138			0.230844
$829$		−	969.092i		−	1.16899i	−0.811398	−	0.584495i	$-0.801293\pi$
$829$		−	969.092i		−	1.16899i	0.811398	−	0.584495i	$-0.198707\pi$
$830$	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	$-0.208550\pi$
$839$	154.070	+	154.070i	0.183636	+	0.183636i	−0.609302	+	0.792938i	$0.708550\pi$
$840$	−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	$-0.295948\pi$
$853$	−173.527	−	173.527i	−0.203432	−	0.203432i	−0.801469	+	0.598037i	$0.795948\pi$
$854$	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	$-0.882876\pi$
$857$		−	616.543i		−	0.719421i	0.933064	−	0.359710i	$-0.117124\pi$
$858$		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	$-0.569175\pi$
$863$	656.627	−	656.627i	0.760866	−	0.760866i	0.976479	+	0.215613i	$0.0691751\pi$
$864$	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	$-0.625711\pi$
$877$	472.069	−	472.069i	0.538277	−	0.538277i	0.923023	+	0.384746i	$0.125711\pi$
$878$	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	$-0.804298\pi$
$881$		−	1016.34i		−	1.15362i	0.816880	−	0.576808i	$-0.195702\pi$
$882$	−126.904	−	126.904i	−0.143882	−	0.143882i
$883$			785.277i			0.889328i	0.895697	+	0.444664i	$0.146677\pi$
$883$			785.277i			0.889328i	−0.895697	+	0.444664i	$0.853323\pi$
$884$		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	$-0.950872\pi$
$907$		−	278.862i		−	0.307455i	0.988113	−	0.153727i	$-0.0491278\pi$
$908$	−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	$-0.747445\pi$
$929$	10.5434	−	10.5434i	0.0113492	−	0.0113492i	0.712759	+	0.701409i	$0.247445\pi$
$930$	−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	−0.250983	+	0.967992i	$0.580754\pi$
$941$	−1147.05	+	1147.05i	−1.21897	+	1.21897i	−0.967992	+	0.250983i	$0.919246\pi$
$942$	−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	$-0.0253919\pi$
$947$	868.526	+	868.526i	0.917134	+	0.917134i	−0.0796863	+	0.996820i	$0.525392\pi$
$948$			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	$0.193097\pi$
$953$			1086.62i			1.14021i	−0.821573	+	0.570104i	$0.806903\pi$
$954$	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	$-0.543037\pi$
$967$	827.831	−	827.831i	0.856081	−	0.856081i	0.990874	+	0.134793i	$0.0430368\pi$
$968$	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	$-0.806282\pi$
$977$	−243.033	+	243.033i	−0.248755	+	0.248755i	0.571705	+	0.820459i	$0.306282\pi$
$978$	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	$-0.100270\pi$
$983$	630.073	+	630.073i	0.640970	+	0.640970i	−0.309824	+	0.950794i	$0.600270\pi$
$984$	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.e.577.1		4
13.5	odd	4		1014.3.f.d.775.1		4
13.8	odd	4	inner	1014.3.f.e.775.1		4
13.9	even	3		78.3.l.a.67.1	yes	4
13.11	odd	12		78.3.l.a.7.1	✓	4
13.12	even	2		1014.3.f.d.577.1		4
39.11	even	12		234.3.bb.c.163.1		4
39.35	odd	6		234.3.bb.c.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.7.1	✓	4	13.11	odd	12
78.3.l.a.67.1	yes	4	13.9	even	3
234.3.bb.c.145.1		4	39.35	odd	6
234.3.bb.c.163.1		4	39.11	even	12
1014.3.f.d.577.1		4	13.12	even	2
1014.3.f.d.775.1		4	13.5	odd	4
1014.3.f.e.577.1		4	1.1	even	1	trivial
1014.3.f.e.775.1		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} +(-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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