LMFDB - Embedded newform 81.5.f.a.8.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,5,Mod(8,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.8"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.98494 - 1.05531i) q^{2} +(19.6707 + 7.15955i) q^{4} +(-10.5942 - 12.6257i) q^{5} +(7.09675 - 2.58301i) q^{7} +(-25.9633 - 14.9899i) q^{8} +(50.0816 + 86.7438i) q^{10} +(120.209 - 143.260i) q^{11} +(-9.75217 - 55.3073i) q^{13} +(-45.1995 + 7.96989i) q^{14} +(-117.001 - 98.1758i) q^{16} +(-396.435 + 228.882i) q^{17} +(-233.647 + 404.688i) q^{19} +(-118.001 - 324.205i) q^{20} +(-870.626 + 730.542i) q^{22} +(-177.454 + 487.552i) q^{23} +(61.3597 - 347.988i) q^{25} +341.302i q^{26} +158.091 q^{28} +(-1518.15 - 267.691i) q^{29} +(-719.064 - 261.718i) q^{31} +(904.971 + 1078.50i) q^{32} +(2614.18 - 951.483i) q^{34} +(-107.796 - 62.2363i) q^{35} +(-254.299 - 440.459i) q^{37} +(1825.43 - 2175.46i) q^{38} +(85.8024 + 486.610i) q^{40} +(562.688 - 99.2171i) q^{41} +(850.976 + 714.053i) q^{43} +(3390.27 - 1957.37i) q^{44} +(1576.57 - 2730.70i) q^{46} +(-54.5162 - 149.782i) q^{47} +(-1795.58 + 1506.67i) q^{49} +(-734.467 + 2017.93i) q^{50} +(204.143 - 1157.75i) q^{52} +1535.13i q^{53} -3082.26 q^{55} +(-222.974 - 39.3164i) q^{56} +(8803.55 + 3204.23i) q^{58} +(-1352.46 - 1611.80i) q^{59} +(-1362.35 + 495.855i) q^{61} +(4027.36 + 2325.20i) q^{62} +(-3056.17 - 5293.44i) q^{64} +(-594.974 + 709.063i) q^{65} +(-1241.97 - 7043.56i) q^{67} +(-9436.84 + 1663.97i) q^{68} +(579.476 + 486.238i) q^{70} +(2436.79 - 1406.88i) q^{71} +(-2132.26 + 3693.19i) q^{73} +(1057.14 + 2904.48i) q^{74} +(-7493.38 + 6287.69i) q^{76} +(483.054 - 1327.18i) q^{77} +(-992.133 + 5626.67i) q^{79} +2517.31i q^{80} -3472.36 q^{82} +(-4026.67 - 710.011i) q^{83} +(7089.69 + 2580.44i) q^{85} +(-4339.49 - 5171.60i) q^{86} +(-5268.48 + 1917.57i) q^{88} +(-5385.27 - 3109.19i) q^{89} +(-212.068 - 367.312i) q^{91} +(-6981.30 + 8319.99i) q^{92} +(168.210 + 953.968i) q^{94} +(7584.75 - 1337.40i) q^{95} +(7112.63 + 5968.20i) q^{97} +(12336.4 - 7122.44i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−5.98494	−	1.05531i	−1.49623	−	0.263826i	−0.635189	−	0.772356i	$-0.719078\pi$
$2$	−5.98494	−	1.05531i	−1.49623	−	0.263826i	−0.861044	+	0.508530i	$0.830189\pi$
$3$		0			0
$3$		0			0
$4$	19.6707	+	7.15955i	1.22942	+	0.447472i
$5$	−10.5942	−	12.6257i	−0.423767	−	0.505026i	0.511346	−	0.859375i	$-0.329147\pi$
$5$	−10.5942	−	12.6257i	−0.423767	−	0.505026i	−0.935113	+	0.354349i	$0.884703\pi$
$6$		0			0
$7$	7.09675	−	2.58301i	0.144832	−	0.0527144i	−0.268587	−	0.963255i	$-0.586557\pi$
$7$	7.09675	−	2.58301i	0.144832	−	0.0527144i	0.413419	+	0.910541i	$0.364335\pi$
$8$	−25.9633	−	14.9899i	−0.405677	−	0.234218i
$9$		0			0
$10$	50.0816	+	86.7438i	0.500816	+	0.867438i
$11$	120.209	−	143.260i	0.993463	−	1.18396i	0.0105406	−	0.999944i	$-0.496645\pi$
$11$	120.209	−	143.260i	0.993463	−	1.18396i	0.982923	−	0.184019i	$-0.0589108\pi$
$12$		0			0
$13$	−9.75217	−	55.3073i	−0.0577051	−	0.327262i	0.942266	−	0.334865i	$-0.108691\pi$
$13$	−9.75217	−	55.3073i	−0.0577051	−	0.327262i	−0.999971	+	0.00760334i	$0.997580\pi$
$14$	−45.1995	+	7.96989i	−0.230610	+	0.0406627i
$15$		0			0
$16$	−117.001	−	98.1758i	−0.457037	−	0.383499i
$17$	−396.435	+	228.882i	−1.37175	+	0.791979i	−0.991148	−	0.132761i	$-0.957616\pi$
$17$	−396.435	+	228.882i	−1.37175	+	0.791979i	−0.380599	+	0.924740i	$0.624282\pi$
$18$		0			0
$19$	−233.647	+	404.688i	−0.647221	+	1.12102i	0.336562	+	0.941661i	$0.390736\pi$
$19$	−233.647	+	404.688i	−0.647221	+	1.12102i	−0.983784	+	0.179359i	$0.942598\pi$
$20$	−118.001	−	324.205i	−0.295002	−	0.810512i
$21$		0			0
$22$	−870.626	+	730.542i	−1.79881	+	1.50938i
$23$	−177.454	+	487.552i	−0.335452	+	0.921648i	0.651214	+	0.758894i	$0.274260\pi$
$23$	−177.454	+	487.552i	−0.335452	+	0.921648i	−0.986667	+	0.162754i	$0.947962\pi$
$24$		0			0
$25$	61.3597	−	347.988i	0.0981755	−	0.556781i
$26$			341.302i			0.504885i
$27$		0			0
$28$	158.091			0.201647
$29$	−1518.15	−	267.691i	−1.80518	−	0.318301i	−0.833127	−	0.553082i	$-0.813452\pi$
$29$	−1518.15	−	267.691i	−1.80518	−	0.318301i	−0.972048	+	0.234781i	$0.924563\pi$
$30$		0			0
$31$	−719.064	−	261.718i	−0.748246	−	0.272339i	−0.0603785	−	0.998176i	$-0.519231\pi$
$31$	−719.064	−	261.718i	−0.748246	−	0.272339i	−0.687867	+	0.725836i	$0.741453\pi$
$32$	904.971	+	1078.50i	0.883761	+	1.05323i
$33$		0			0
$34$	2614.18	−	951.483i	2.26140	−	0.823082i
$35$	−107.796	−	62.2363i	−0.0879971	−	0.0508051i
$36$		0			0
$37$	−254.299	−	440.459i	−0.185755	−	0.321738i	0.758075	−	0.652167i	$-0.226140\pi$
$37$	−254.299	−	440.459i	−0.185755	−	0.321738i	−0.943831	+	0.330429i	$0.892807\pi$
$38$	1825.43	−	2175.46i	1.26415	−	1.50655i
$39$		0			0
$40$	85.8024	+	486.610i	0.0536265	+	0.304131i
$41$	562.688	−	99.2171i	0.334734	−	0.0590227i	−0.00375496	−	0.999993i	$-0.501195\pi$
$41$	562.688	−	99.2171i	0.334734	−	0.0590227i	0.338489	+	0.940970i	$0.390084\pi$
$42$		0			0
$43$	850.976	+	714.053i	0.460236	+	0.386183i	0.843218	−	0.537572i	$-0.180658\pi$
$43$	850.976	+	714.053i	0.460236	+	0.386183i	−0.382982	+	0.923756i	$0.625103\pi$
$44$	3390.27	−	1957.37i	1.75117	−	1.01104i
$45$		0			0
$46$	1576.57	−	2730.70i	0.745070	−	1.29050i
$47$	−54.5162	−	149.782i	−0.0246792	−	0.0678054i	0.926741	−	0.375700i	$-0.122598\pi$
$47$	−54.5162	−	149.782i	−0.0246792	−	0.0678054i	−0.951420	+	0.307895i	$0.900376\pi$
$48$		0			0
$49$	−1795.58	+	1506.67i	−0.747847	+	0.627518i
$50$	−734.467	+	2017.93i	−0.293787	+	0.807173i
$51$		0			0
$52$	204.143	−	1157.75i	0.0754968	−	0.428164i
$53$			1535.13i			0.546503i	0.961943	+	0.273251i	$0.0880991\pi$
$53$			1535.13i			0.546503i	−0.961943	+	0.273251i	$0.911901\pi$
$54$		0			0
$55$	−3082.26			−1.01893
$56$	−222.974	−	39.3164i	−0.0711015	−	0.0125371i
$57$		0			0
$58$	8803.55	+	3204.23i	2.61699	+	0.952506i
$59$	−1352.46	−	1611.80i	−0.388527	−	0.463028i	0.535959	−	0.844244i	$-0.319950\pi$
$59$	−1352.46	−	1611.80i	−0.388527	−	0.463028i	−0.924486	+	0.381215i	$0.875506\pi$
$60$		0			0
$61$	−1362.35	+	495.855i	−0.366124	+	0.133258i	−0.518530	−	0.855060i	$-0.673520\pi$
$61$	−1362.35	+	495.855i	−0.366124	+	0.133258i	0.152405	+	0.988318i	$0.451298\pi$
$62$	4027.36	+	2325.20i	1.04770	+	0.604890i
$63$		0			0
$64$	−3056.17	−	5293.44i	−0.746135	−	1.29234i
$65$	−594.974	+	709.063i	−0.140822	+	0.167826i
$66$		0			0
$67$	−1241.97	−	7043.56i	−0.276669	−	1.56907i	−0.733609	−	0.679572i	$-0.762165\pi$
$67$	−1241.97	−	7043.56i	−0.276669	−	1.56907i	0.456939	−	0.889498i	$-0.348946\pi$
$68$	−9436.84	+	1663.97i	−2.04084	+	0.359855i
$69$		0			0
$70$	579.476	+	486.238i	0.118260	+	0.0992323i
$71$	2436.79	−	1406.88i	0.483395	−	0.279088i	−0.238435	−	0.971158i	$-0.576635\pi$
$71$	2436.79	−	1406.88i	0.483395	−	0.279088i	0.721830	+	0.692070i	$0.243301\pi$
$72$		0			0
$73$	−2132.26	+	3693.19i	−0.400125	+	0.693036i	−0.993741	−	0.111712i	$-0.964367\pi$
$73$	−2132.26	+	3693.19i	−0.400125	+	0.693036i	0.593616	+	0.804749i	$0.297700\pi$
$74$	1057.14	+	2904.48i	0.193051	+	0.530402i
$75$		0			0
$76$	−7493.38	+	6287.69i	−1.29733	+	1.08859i
$77$	483.054	−	1327.18i	0.0814730	−	0.223845i
$78$		0			0
$79$	−992.133	+	5626.67i	−0.158970	+	0.901565i	0.796096	+	0.605171i	$0.206895\pi$
$79$	−992.133	+	5626.67i	−0.158970	+	0.901565i	−0.955066	+	0.296394i	$0.904216\pi$
$80$			2517.31i			0.393330i
$81$		0			0
$82$	−3472.36			−0.516412
$83$	−4026.67	−	710.011i	−0.584508	−	0.103064i	−0.126428	−	0.991976i	$-0.540351\pi$
$83$	−4026.67	−	710.011i	−0.584508	−	0.103064i	−0.458079	+	0.888911i	$0.651462\pi$
$84$		0			0
$85$	7089.69	+	2580.44i	0.981272	+	0.357154i
$86$	−4339.49	−	5171.60i	−0.586735	−	0.699243i
$87$		0			0
$88$	−5268.48	+	1917.57i	−0.680330	+	0.247620i
$89$	−5385.27	−	3109.19i	−0.679873	−	0.392525i	0.119934	−	0.992782i	$-0.461732\pi$
$89$	−5385.27	−	3109.19i	−0.679873	−	0.392525i	−0.799807	+	0.600257i	$0.795065\pi$
$90$		0			0
$91$	−212.068	−	367.312i	−0.0256090	−	0.0443560i
$92$	−6981.30	+	8319.99i	−0.824823	+	0.982986i
$93$		0			0
$94$	168.210	+	953.968i	0.0190369	+	0.107964i
$95$	7584.75	−	1337.40i	0.840416	−	0.148188i
$96$		0			0
$97$	7112.63	+	5968.20i	0.755939	+	0.634308i	0.937066	−	0.349152i	$-0.113530\pi$
$97$	7112.63	+	5968.20i	0.755939	+	0.634308i	−0.181127	+	0.983460i	$0.557975\pi$
$98$	12336.4	−	7122.44i	1.28451	−	0.741612i
$99$		0			0
$100$	3698.42	−	6405.86i	0.369842	−	0.640586i
$101$	−6539.12	−	17966.1i	−0.641027	−	1.76121i	−0.648476	−	0.761235i	$-0.724593\pi$
$101$	−6539.12	−	17966.1i	−0.641027	−	1.76121i	0.00744872	−	0.999972i	$-0.497629\pi$
$102$		0			0
$103$	−4736.32	+	3974.24i	−0.446443	+	0.374611i	−0.838114	−	0.545495i	$-0.816342\pi$
$103$	−4736.32	+	3974.24i	−0.446443	+	0.374611i	0.391671	+	0.920105i	$0.371897\pi$
$104$	−575.854	+	1582.15i	−0.0532409	+	0.146278i
$105$		0			0
$106$	1620.03	−	9187.63i	0.144182	−	0.817696i
$107$			1546.43i			0.135072i	0.997717	+	0.0675358i	$0.0215137\pi$
$107$			1546.43i			0.135072i	−0.997717	+	0.0675358i	$0.978486\pi$
$108$		0			0
$109$	8909.57			0.749901			0.374951	−	0.927045i	$-0.377660\pi$
$109$	8909.57			0.749901			0.374951	+	0.927045i	$0.377660\pi$
$110$	18447.1	+	3252.73i	1.52456	+	0.268821i
$111$		0			0
$112$	−1083.92	−	394.514i	−0.0864093	−	0.0314504i
$113$	10815.5	+	12889.4i	0.847012	+	1.00943i	0.999776	+	0.0211670i	$0.00673816\pi$
$113$	10815.5	+	12889.4i	0.847012	+	1.00943i	−0.152764	+	0.988263i	$0.548817\pi$
$114$		0			0
$115$	8035.64	−	2924.73i	0.607610	−	0.221152i
$116$	−27946.6	−	16135.0i	−2.07689	−	1.19909i
$117$		0			0
$118$	6393.46	+	11073.8i	0.459168	+	0.795302i
$119$	−2222.20	+	2648.31i	−0.156924	+	0.187015i
$120$		0			0
$121$	−3530.71	−	20023.6i	−0.241152	−	1.36764i
$122$	8676.85	−	1529.96i	0.582965	−	0.102792i
$123$		0			0
$124$	−12270.7	−	10296.4i	−0.798043	−	0.669638i
$125$	−13964.6	+	8062.45i	−0.893732	+	0.515997i
$126$		0			0
$127$	−7193.47	+	12459.5i	−0.445996	+	0.772488i	−0.998121	−	0.0612733i	$-0.980484\pi$
$127$	−7193.47	+	12459.5i	−0.445996	+	0.772488i	0.552125	+	0.833762i	$0.313817\pi$
$128$	5000.37	+	13738.4i	0.305198	+	0.838526i
$129$		0			0
$130$	4309.16	−	3615.82i	0.254980	−	0.213954i
$131$	1057.26	−	2904.79i	0.0616082	−	0.169267i	−0.905069	−	0.425264i	$-0.860181\pi$
$131$	1057.26	−	2904.79i	0.0616082	−	0.169267i	0.966678	+	0.255997i	$0.0824036\pi$
$132$		0			0
$133$	−612.822	+	3475.48i	−0.0346442	+	0.196477i
$134$			43465.9i			2.42069i
$135$		0			0
$136$	13723.7			0.741982
$137$	5162.83	+	910.346i	0.275072	+	0.0485026i	0.309482	−	0.950905i	$-0.399844\pi$
$137$	5162.83	+	910.346i	0.275072	+	0.0485026i	−0.0344104	+	0.999408i	$0.510955\pi$
$138$		0			0
$139$	−19913.9	−	7248.08i	−1.03069	−	0.375140i	−0.229345	−	0.973345i	$-0.573659\pi$
$139$	−19913.9	−	7248.08i	−1.03069	−	0.375140i	−0.801343	+	0.598205i	$0.795881\pi$
$140$	−1674.85	−	1996.01i	−0.0854514	−	0.101837i
$141$		0			0
$142$	−16068.7	+	5848.54i	−0.796902	+	0.290049i
$143$	−9095.60	−	5251.35i	−0.444794	−	0.256802i
$144$		0			0
$145$	12703.8	+	22003.6i	0.604224	+	1.04655i
$146$	16658.9	−	19853.3i	0.781521	−	0.931381i
$147$		0			0
$148$	−1848.75	−	10484.8i	−0.0844025	−	0.478671i
$149$	28666.8	−	5054.73i	1.29124	−	0.227680i	0.514493	−	0.857495i	$-0.327980\pi$
$149$	28666.8	−	5054.73i	1.29124	−	0.227680i	0.776745	+	0.629815i	$0.216869\pi$
$150$		0			0
$151$	−27382.8	−	22976.9i	−1.20095	−	1.00771i	−0.999603	−	0.0281918i	$-0.991025\pi$
$151$	−27382.8	−	22976.9i	−1.20095	−	1.00771i	−0.201343	−	0.979521i	$-0.564530\pi$
$152$	12132.5	−	7004.70i	0.525125	−	0.303181i
$153$		0			0
$154$	−4291.62	+	7433.31i	−0.180959	+	0.313430i
$155$	4313.54	+	11851.3i	0.179544	+	0.493292i
$156$		0			0
$157$	18847.0	−	15814.5i	0.764616	−	0.641589i	−0.174708	−	0.984620i	$-0.555898\pi$
$157$	18847.0	−	15814.5i	0.764616	−	0.641589i	0.939324	+	0.343031i	$0.111454\pi$
$158$	11875.7	−	32628.2i	0.475713	−	1.30701i
$159$		0			0
$160$	4029.37	−	22851.7i	0.157397	−	0.892644i
$161$			3918.40i			0.151167i
$162$		0			0
$163$	17266.5			0.649875			0.324938	−	0.945735i	$-0.394657\pi$
$163$	17266.5			0.649875			0.324938	+	0.945735i	$0.394657\pi$
$164$	11778.8	+	2076.92i	0.437940	+	0.0772206i
$165$		0			0
$166$	23350.1	+	8498.74i	0.847369	+	0.308417i
$167$	3705.73	+	4416.31i	0.132874	+	0.158353i	0.828379	−	0.560168i	$-0.189264\pi$
$167$	3705.73	+	4416.31i	0.132874	+	0.158353i	−0.695505	+	0.718522i	$0.744819\pi$
$168$		0			0
$169$	23874.8	−	8689.71i	0.835922	−	0.304251i
$170$	−39708.2	−	22925.5i	−1.37399	−	0.793271i
$171$		0			0
$172$	11627.0	+	20138.5i	0.393016	+	0.680724i
$173$	−12635.0	+	15057.8i	−0.422166	+	0.503118i	−0.934645	−	0.355582i	$-0.884283\pi$
$173$	−12635.0	+	15057.8i	−0.422166	+	0.503118i	0.512479	+	0.858700i	$0.328727\pi$
$174$		0			0
$175$	−463.401	−	2628.08i	−0.0151315	−	0.0858148i
$176$	−28129.2	+	4959.95i	−0.908098	+	0.160122i
$177$		0			0
$178$	28949.4	+	24291.4i	0.913690	+	0.766677i
$179$	19435.1	−	11220.9i	0.606570	−	0.350203i	−0.165052	−	0.986285i	$-0.552779\pi$
$179$	19435.1	−	11220.9i	0.606570	−	0.350203i	0.771622	+	0.636082i	$0.219446\pi$
$180$		0			0
$181$	13955.7	−	24172.0i	0.425985	−	0.737828i	−0.570527	−	0.821279i	$-0.693261\pi$
$181$	13955.7	−	24172.0i	0.425985	−	0.737828i	0.996512	+	0.0834510i	$0.0265942\pi$
$182$	881.586	+	2422.14i	0.0266147	+	0.0731233i
$183$		0			0
$184$	11915.7	−	9998.43i	0.351951	−	0.295322i
$185$	−2866.99	+	7876.99i	−0.0837689	+	0.230153i
$186$		0			0
$187$	−14865.6	+	84306.8i	−0.425107	+	2.41090i
$188$		−	3336.63i		−	0.0944045i
$189$		0			0
$190$	−46805.6			−1.29655
$191$	−52758.3	−	9302.72i	−1.44619	−	0.255002i	−0.605207	−	0.796068i	$-0.706910\pi$
$191$	−52758.3	−	9302.72i	−1.44619	−	0.255002i	−0.840980	+	0.541067i	$0.818021\pi$
$192$		0			0
$193$	−40023.4	−	14567.3i	−1.07448	−	0.391080i	−0.256631	−	0.966509i	$-0.582613\pi$
$193$	−40023.4	−	14567.3i	−1.07448	−	0.391080i	−0.817851	+	0.575430i	$0.804835\pi$
$194$	−36270.3	−	43225.3i	−0.963714	−	1.14851i
$195$		0			0
$196$	−46107.4	+	16781.7i	−1.20021	+	0.436842i
$197$	7509.39	+	4335.55i	0.193496	+	0.111715i	0.593618	−	0.804747i	$-0.297699\pi$
$197$	7509.39	+	4335.55i	0.193496	+	0.111715i	−0.400122	+	0.916462i	$0.631032\pi$
$198$		0			0
$199$	−31430.7	−	54439.5i	−0.793684	−	1.37470i	−0.923671	−	0.383185i	$-0.874827\pi$
$199$	−31430.7	−	54439.5i	−0.793684	−	1.37470i	0.129987	−	0.991516i	$-0.458506\pi$
$200$	−6809.42	+	8115.15i	−0.170235	+	0.202879i
$201$		0			0
$202$	20176.5	+	114427.i	0.494473	+	2.80430i
$203$	−11465.4	+	2021.66i	−0.278226	+	0.0490587i
$204$		0			0
$205$	−7213.90	−	6053.18i	−0.171657	−	0.144038i
$206$	32540.6	−	18787.3i	0.766816	−	0.442721i
$207$		0			0
$208$	−4288.82	+	7428.46i	−0.0991314	+	0.171701i
$209$	29889.0	+	82119.3i	0.684256	+	1.87998i
$210$		0			0
$211$	43363.7	−	36386.5i	0.974006	−	0.817288i	−0.00916815	−	0.999958i	$-0.502918\pi$
$211$	43363.7	−	36386.5i	0.974006	−	0.817288i	0.983174	+	0.182670i	$0.0584739\pi$
$212$	−10990.8	+	30197.0i	−0.244545	+	0.671881i
$213$		0			0
$214$	1631.96	−	9255.31i	0.0356354	−	0.202099i
$215$		−	18308.9i		−	0.396083i
$216$		0			0
$217$	−5779.04			−0.122726
$218$	−53323.2	−	9402.32i	−1.12203	−	0.197844i
$219$		0			0
$220$	−60630.2	−	22067.6i	−1.25269	−	0.455942i
$221$	16524.9	+	19693.7i	0.338342	+	0.403220i
$222$		0			0
$223$	−32580.8	+	11858.5i	−0.655168	+	0.238462i	−0.648149	−	0.761514i	$-0.724456\pi$
$223$	−32580.8	+	11858.5i	−0.655168	+	0.238462i	−0.00701901	+	0.999975i	$0.502234\pi$
$224$	9208.14	+	5316.32i	0.183517	+	0.105953i
$225$		0			0
$226$	−51127.8	−	88555.9i	−1.00101	−	1.73381i
$227$	3339.70	−	3980.10i	0.0648120	−	0.0772400i	−0.732664	−	0.680590i	$-0.761723\pi$
$227$	3339.70	−	3980.10i	0.0648120	−	0.0772400i	0.797476	+	0.603350i	$0.206168\pi$
$228$		0			0
$229$	7561.02	+	42880.7i	0.144182	+	0.817694i	0.968021	+	0.250870i	$0.0807168\pi$
$229$	7561.02	+	42880.7i	0.144182	+	0.817694i	−0.823839	+	0.566824i	$0.808172\pi$
$230$	−51179.3	+	9024.29i	−0.967472	+	0.170591i
$231$		0			0
$232$	35403.6	+	29707.1i	0.657766	+	0.551931i
$233$	81822.2	−	47240.1i	1.50716	−	0.870159i	0.507194	−	0.861832i	$-0.330683\pi$
$233$	81822.2	−	47240.1i	1.50716	−	0.870159i	0.999965	−	0.00832740i	$-0.00265072\pi$
$234$		0			0
$235$	−1313.54	+	2275.12i	−0.0237853	+	0.0411973i
$236$	−15064.1	−	41388.3i	−0.270470	−	0.743110i
$237$		0			0
$238$	16094.5	−	13504.9i	0.284134	−	0.238417i
$239$	−6808.48	+	18706.1i	−0.119194	+	0.327483i	−0.984914	−	0.173046i	$-0.944639\pi$
$239$	−6808.48	+	18706.1i	−0.119194	+	0.327483i	0.865720	+	0.500529i	$0.166861\pi$
$240$		0			0
$241$	5724.19	−	32463.5i	0.0985554	−	0.558935i	−0.895044	−	0.445977i	$-0.852856\pi$
$241$	5724.19	−	32463.5i	0.0985554	−	0.558935i	0.993600	−	0.112958i	$-0.0360326\pi$
$242$			123566.i			2.10993i
$243$		0			0
$244$	−30348.5			−0.509750
$245$	38045.4	+	6708.43i	0.633826	+	0.111761i
$246$		0			0
$247$	24660.8	+	8975.79i	0.404215	+	0.147122i
$248$	14746.2	+	17573.8i	0.239759	+	0.285734i
$249$		0			0
$250$	92085.4	−	33516.3i	1.47337	−	0.536261i
$251$	−36889.4	−	21298.1i	−0.585537	−	0.338060i	0.177794	−	0.984068i	$-0.443104\pi$
$251$	−36889.4	−	21298.1i	−0.585537	−	0.338060i	−0.763331	+	0.646008i	$0.776437\pi$
$252$		0			0
$253$	48514.8	+	84030.2i	0.757938	+	1.31279i
$254$	56201.0	−	66977.8i	0.871118	−	1.03816i
$255$		0			0
$256$	1553.65	+	8811.21i	0.0237069	+	0.134448i
$257$	14099.5	−	2486.12i	0.213470	−	0.0376406i	−0.0658901	−	0.997827i	$-0.520989\pi$
$257$	14099.5	−	2486.12i	0.213470	−	0.0376406i	0.279360	+	0.960186i	$0.409878\pi$
$258$		0			0
$259$	−2942.41	−	2468.97i	−0.0438635	−	0.0368058i
$260$	−16780.1	+	9688.01i	−0.248227	+	0.143314i
$261$		0			0
$262$	−9393.07	+	16269.3i	−0.136837	+	0.237009i
$263$	−32691.1	−	89818.0i	−0.472626	−	1.29853i	−0.915634	−	0.402012i	$-0.868311\pi$
$263$	−32691.1	−	89818.0i	−0.472626	−	1.29853i	0.443008	−	0.896518i	$-0.353911\pi$
$264$		0			0
$265$	19382.0	−	16263.4i	0.275998	−	0.231590i
$266$	7335.40	−	20153.8i	0.103672	−	0.284836i
$267$		0			0
$268$	25998.3	−	147444.i	0.361972	−	2.05285i
$269$		−	18139.2i		−	0.250677i	−0.992114	−	0.125338i	$-0.959998\pi$
$269$		−	18139.2i		−	0.250677i	0.992114	−	0.125338i	$-0.0400017\pi$
$270$		0			0
$271$	128010.			1.74303			0.871513	−	0.490373i	$-0.163140\pi$
$271$	128010.			1.74303			0.871513	+	0.490373i	$0.163140\pi$
$272$	68854.1	+	12140.8i	0.930662	+	0.164101i
$273$		0			0
$274$	−29938.5	−	10896.7i	−0.398776	−	0.145143i
$275$	−42476.6	−	50621.7i	−0.561674	−	0.669377i
$276$		0			0
$277$	50103.9	−	18236.3i	0.652998	−	0.237672i	0.00578738	−	0.999983i	$-0.498158\pi$
$277$	50103.9	−	18236.3i	0.652998	−	0.237672i	0.647210	+	0.762312i	$0.275936\pi$
$278$	111535.	+	64394.6i	1.44318	+	0.833220i
$279$		0			0
$280$	1865.84	+	3231.72i	0.0237989	+	0.0412209i
$281$	−19299.9	+	23000.8i	−0.244424	+	0.291293i	−0.874283	−	0.485416i	$-0.838668\pi$
$281$	−19299.9	+	23000.8i	−0.244424	+	0.291293i	0.629859	+	0.776709i	$0.283113\pi$
$282$		0			0
$283$	449.898	+	2551.50i	0.00561747	+	0.0318583i	0.987488	−	0.157696i	$-0.0504067\pi$
$283$	449.898	+	2551.50i	0.00561747	+	0.0318583i	−0.981870	+	0.189555i	$0.939296\pi$
$284$	58006.1	−	10228.0i	0.719178	−	0.126811i
$285$		0			0
$286$	48894.8	+	41027.6i	0.597765	+	0.501584i
$287$	3736.98	−	2157.55i	0.0453688	−	0.0261937i
$288$		0			0
$289$	63013.3	−	109142.i	0.754461	−	1.30676i
$290$	−52810.9	−	145097.i	−0.627953	−	1.72529i
$291$		0			0
$292$	−68384.7	+	57381.6i	−0.802035	+	0.672987i
$293$	−16296.1	+	44773.2i	−0.189823	+	0.521535i	−0.997698	−	0.0678198i	$-0.978396\pi$
$293$	−16296.1	+	44773.2i	−0.189823	+	0.521535i	0.807874	+	0.589355i	$0.200618\pi$
$294$		0			0
$295$	−6021.82	+	34151.4i	−0.0691964	+	0.392432i
$296$			15247.7i			0.174029i
$297$		0			0
$298$	−176903.			−1.99206
$299$	28695.7	+	5059.83i	0.320978	+	0.0565970i
$300$		0			0
$301$	7883.57	+	2869.38i	0.0870141	+	0.0316706i
$302$	139636.	+	166412.i	1.53103	+	1.82461i
$303$		0			0
$304$	67067.6	−	24410.6i	0.725714	−	0.264138i
$305$	20693.5	+	11947.4i	0.222451	+	0.128432i
$306$		0			0
$307$	11346.8	+	19653.3i	0.120392	+	0.208525i	0.919922	−	0.392101i	$-0.128252\pi$
$307$	11346.8	+	19653.3i	0.120392	+	0.208525i	−0.799530	+	0.600626i	$0.794918\pi$
$308$	19004.0	−	22648.1i	0.200329	−	0.238743i
$309$		0			0
$310$	−13309.4	−	75481.6i	−0.138496	−	0.785449i
$311$	33510.1	−	5908.73i	0.346461	−	0.0610905i	0.00229010	−	0.999997i	$-0.499271\pi$
$311$	33510.1	−	5908.73i	0.346461	−	0.0610905i	0.344171	+	0.938907i	$0.388160\pi$
$312$		0			0
$313$	−110952.	−	93099.5i	−1.13252	−	0.950295i	−0.133349	−	0.991069i	$-0.542573\pi$
$313$	−110952.	−	93099.5i	−1.13252	−	0.950295i	−0.999168	+	0.0407737i	$0.987018\pi$
$314$	−129487.	+	74759.6i	−1.31331	+	0.758242i
$315$		0			0
$316$	−59800.3	+	103577.i	−0.598866	+	1.03727i
$317$	10091.2	+	27725.3i	0.100421	+	0.275904i	0.979722	−	0.200363i	$-0.0642120\pi$
$317$	10091.2	+	27725.3i	0.100421	+	0.275904i	−0.879301	+	0.476266i	$0.841990\pi$
$318$		0			0
$319$	−220845.	+	185311.i	−2.17023	+	1.82104i
$320$	−34455.5	+	94665.7i	−0.336480	+	0.924470i
$321$		0			0
$322$	4135.11	−	23451.4i	0.0398819	−	0.226181i
$323$		−	213910.i		−	2.05034i
$324$		0			0
$325$	−19844.7			−0.187878
$326$	−103339.	−	18221.5i	−0.972366	−	0.171454i
$327$		0			0
$328$	−16096.5	−	5858.65i	−0.149618	−	0.0544565i
$329$	−773.777	−	922.151i	−0.00714865	−	0.00851943i
$330$		0			0
$331$	−22731.9	+	8273.74i	−0.207482	+	0.0755172i	−0.443670	−	0.896190i	$-0.646324\pi$
$331$	−22731.9	+	8273.74i	−0.207482	+	0.0755172i	0.236189	+	0.971707i	$0.424102\pi$
$332$	−74124.1	−	42795.6i	−0.672486	−	0.388260i
$333$		0			0
$334$	−17518.0	−	30342.0i	−0.157033	−	0.271989i
$335$	−75771.8	+	90301.4i	−0.675178	+	0.804646i
$336$		0			0
$337$	7201.64	+	40842.5i	0.0634120	+	0.359627i	0.999959	+	0.00908453i	$0.00289173\pi$
$337$	7201.64	+	40842.5i	0.0634120	+	0.359627i	−0.936547	+	0.350543i	$0.885997\pi$
$338$	−152059.	+	26812.1i	−1.33100	+	0.234692i
$339$		0			0
$340$	120984.	+	101518.i	1.04658	+	0.878183i
$341$	−123932.	+	71552.0i	−1.06579	+	0.615337i
$342$		0			0
$343$	−17917.5	+	31034.0i	−0.152296	+	0.263784i
$344$	−11390.5	−	31295.3i	−0.0962559	−	0.264461i
$345$		0			0
$346$	91510.3	−	76786.2i	0.764395	−	0.641403i
$347$	−36634.2	+	100652.i	−0.304248	+	0.835916i	0.689501	+	0.724284i	$0.257830\pi$
$347$	−36634.2	+	100652.i	−0.304248	+	0.835916i	−0.993750	+	0.111631i	$0.964392\pi$
$348$		0			0
$349$	−35243.1	+	199874.i	−0.289350	+	1.64098i	0.399970	+	0.916528i	$0.369020\pi$
$349$	−35243.1	+	199874.i	−0.289350	+	1.64098i	−0.689320	+	0.724457i	$0.742091\pi$
$350$			16217.9i			0.132391i
$351$		0			0
$352$	263292.			2.12496
$353$	24057.6	+	4242.00i	0.193064	+	0.0340425i	0.269344	−	0.963044i	$-0.413193\pi$
$353$	24057.6	+	4242.00i	0.193064	+	0.0340425i	−0.0762797	+	0.997086i	$0.524304\pi$
$354$		0			0
$355$	−43578.6	−	15861.3i	−0.345794	−	0.125859i
$356$	−83671.7	−	99716.0i	−0.660204	−	0.786801i
$357$		0			0
$358$	−128159.	+	46646.2i	−0.999963	+	0.363957i
$359$	−33774.1	−	19499.5i	−0.262056	−	0.151298i	0.363216	−	0.931705i	$-0.381679\pi$
$359$	−33774.1	−	19499.5i	−0.262056	−	0.151298i	−0.625272	+	0.780407i	$0.715012\pi$
$360$		0			0
$361$	−44021.2	−	76247.0i	−0.337791	−	0.585071i
$362$	−109033.	+	129940.i	−0.832032	+	0.991577i
$363$		0			0
$364$	−1541.73	−	8743.60i	−0.0116361	−	0.0659914i
$365$	69218.5	−	12205.1i	0.519561	−	0.0916127i
$366$		0			0
$367$	−107689.	−	90361.5i	−0.799536	−	0.670890i	0.148550	−	0.988905i	$-0.452539\pi$
$367$	−107689.	−	90361.5i	−0.799536	−	0.670890i	−0.948086	+	0.318015i	$0.896984\pi$
$368$	68628.2	−	39622.5i	0.506765	−	0.292581i
$369$		0			0
$370$	25471.4	−	44117.7i	0.186058	−	0.322262i
$371$	3965.24	+	10894.4i	0.0288086	+	0.0791509i
$372$		0			0
$373$	106543.	−	89399.9i	0.765783	−	0.642568i	−0.173842	−	0.984774i	$-0.555618\pi$
$373$	106543.	−	89399.9i	0.765783	−	0.642568i	0.939625	+	0.342205i	$0.111174\pi$
$374$	177939.	−	488883.i	1.27212	−	3.49512i
$375$		0			0
$376$	−829.801	+	4706.04i	−0.00586946	+	0.0332874i
$377$			86575.5i			0.609133i
$378$		0			0
$379$	−205238.			−1.42883			−0.714414	−	0.699723i	$-0.753307\pi$
$379$	−205238.			−1.42883			−0.714414	+	0.699723i	$0.753307\pi$
$380$	158772.	+	27995.9i	1.09953	+	0.193877i
$381$		0			0
$382$	305938.	+	111352.i	2.09656	+	0.763084i
$383$	−118294.	−	140977.i	−0.806428	−	0.961064i	0.193371	−	0.981126i	$-0.438058\pi$
$383$	−118294.	−	140977.i	−0.806428	−	0.961064i	−0.999799	+	0.0200622i	$0.993614\pi$
$384$		0			0
$385$	−21874.1	+	7961.50i	−0.147573	+	0.0537123i
$386$	224165.	+	129421.i	1.50450	+	0.868624i
$387$		0			0
$388$	97180.7	+	168322.i	0.645530	+	1.11809i
$389$	82339.4	−	98128.2i	0.544137	−	0.648477i	−0.421973	−	0.906608i	$-0.638662\pi$
$389$	82339.4	−	98128.2i	0.544137	−	0.648477i	0.966110	+	0.258131i	$0.0831067\pi$
$390$		0			0
$391$	−41242.6	−	233899.i	−0.269770	−	1.52994i
$392$	69204.1	−	12202.6i	0.450360	−	0.0794106i
$393$		0			0
$394$	−40367.9	−	33872.7i	−0.260042	−	0.218201i
$395$	81551.2	−	47083.6i	0.522680	−	0.301769i
$396$		0			0
$397$	−40759.2	+	70596.9i	−0.258609	+	0.447925i	−0.965870	−	0.259029i	$-0.916598\pi$
$397$	−40759.2	+	70596.9i	−0.258609	+	0.447925i	0.707260	+	0.706953i	$0.249931\pi$
$398$	130660.	+	358986.i	0.824854	+	2.26627i
$399$		0			0
$400$	−41343.2	+	34691.0i	−0.258395	+	0.216819i
$401$	−20232.1	+	55587.3i	−0.125821	+	0.345690i	−0.986570	−	0.163339i	$-0.947773\pi$
$401$	−20232.1	+	55587.3i	−0.125821	+	0.345690i	0.860749	+	0.509030i	$0.169996\pi$
$402$		0			0
$403$	−7462.48	+	42321.8i	−0.0459487	+	0.260588i
$404$		−	400222.i		−	2.45210i
$405$		0			0
$406$	70753.2			0.429234
$407$	−93669.0	−	16516.4i	−0.565467	−	0.0997070i
$408$		0			0
$409$	273913.	+	99696.1i	1.63744	+	0.595980i	0.986589	−	0.163225i	$-0.0521897\pi$
$409$	273913.	+	99696.1i	1.63744	+	0.595980i	0.650852	+	0.759205i	$0.274412\pi$
$410$	36786.8	+	43840.8i	0.218839	+	0.260802i
$411$		0			0
$412$	−121620.	+	44266.2i	−0.716494	+	0.260782i
$413$	−13761.4	−	7945.14i	−0.0806793	−	0.0465802i
$414$		0			0
$415$	33695.0	+	58361.4i	0.195645	+	0.338867i
$416$	50823.6	−	60569.2i	0.293683	−	0.349998i
$417$		0			0
$418$	−92222.7	−	523021.i	−0.527819	−	2.99341i
$419$	−121024.	+	21339.9i	−0.689358	+	0.121552i	−0.507344	−	0.861744i	$-0.669373\pi$
$419$	−121024.	+	21339.9i	−0.689358	+	0.121552i	−0.182014	+	0.983296i	$0.558262\pi$
$420$		0			0
$421$	−58336.5	−	48950.2i	−0.329137	−	0.276179i	0.463211	−	0.886248i	$-0.346697\pi$
$421$	−58336.5	−	48950.2i	−0.329137	−	0.276179i	−0.792348	+	0.610069i	$0.791142\pi$
$422$	−297928.	+	172009.i	−1.67296	+	0.965886i
$423$		0			0
$424$	23011.4	−	39857.0i	0.128001	−	0.221704i
$425$	55323.0	+	151999.i	0.306287	+	0.841516i
$426$		0			0
$427$	−8387.46	+	7037.92i	−0.0460018	+	0.0386001i
$428$	−11071.8	+	30419.4i	−0.0604407	+	0.166059i
$429$		0			0
$430$	−19321.5	+	109578.i	−0.104497	+	0.592633i
$431$			188543.i			1.01497i	0.861659	+	0.507487i	$0.169425\pi$
$431$			188543.i			1.01497i	−0.861659	+	0.507487i	$0.830575\pi$
$432$		0			0
$433$	4635.55			0.0247244			0.0123622	−	0.999924i	$-0.496065\pi$
$433$	4635.55			0.0247244			0.0123622	+	0.999924i	$0.496065\pi$
$434$	34587.2	+	6098.66i	0.183627	+	0.0323783i
$435$		0			0
$436$	175258.	+	63788.5i	0.921942	+	0.335560i
$437$	−155845.	−	185729.i	−0.816074	−	0.972559i
$438$		0			0
$439$	45262.1	−	16474.0i	0.234858	−	0.0854813i	−0.221910	−	0.975067i	$-0.571229\pi$
$439$	45262.1	−	16474.0i	0.234858	−	0.0854813i	0.456768	+	0.889586i	$0.349007\pi$
$440$	80025.7	+	46202.9i	0.413356	+	0.238651i
$441$		0			0
$442$	−78117.9	−	135304.i	−0.399858	−	0.692574i
$443$	−8365.55	+	9969.67i	−0.0426272	+	0.0508011i	−0.786937	−	0.617034i	$-0.788334\pi$
$443$	−8365.55	+	9969.67i	−0.0426272	+	0.0508011i	0.744310	+	0.667835i	$0.232779\pi$
$444$		0			0
$445$	17797.0	+	100932.i	0.0898725	+	0.509692i
$446$	207508.	−	36589.3i	1.04320	−	0.183944i
$447$		0			0
$448$	−35361.9	−	29672.1i	−0.176189	−	0.147840i
$449$	−128969.	+	74460.5i	−0.639726	+	0.369346i	−0.784509	−	0.620118i	$-0.787085\pi$
$449$	−128969.	+	74460.5i	−0.639726	+	0.369346i	0.144783	+	0.989463i	$0.453752\pi$
$450$		0			0
$451$	53426.4	−	92537.3i	0.262666	−	0.454950i
$452$	120466.	+	330978.i	0.589641	+	1.62003i
$453$		0			0
$454$	−24188.1	+	20296.2i	−0.117352	+	0.0984699i
$455$	−2390.87	+	6568.87i	−0.0115487	+	0.0317298i
$456$		0			0
$457$	3815.40	−	21638.2i	0.0182687	−	0.103607i	−0.974310	−	0.225211i	$-0.927693\pi$
$457$	3815.40	−	21638.2i	0.0182687	−	0.103607i	0.992579	+	0.121604i	$0.0388039\pi$
$458$		−	264617.i		−	1.26150i
$459$		0			0
$460$	179006.			0.845966
$461$	−136057.	−	23990.6i	−0.640206	−	0.112886i	−0.155884	−	0.987775i	$-0.549823\pi$
$461$	−136057.	−	23990.6i	−0.640206	−	0.112886i	−0.484322	+	0.874890i	$0.660934\pi$
$462$		0			0
$463$	−192898.	−	70209.0i	−0.899840	−	0.327515i	−0.149651	−	0.988739i	$-0.547815\pi$
$463$	−192898.	−	70209.0i	−0.899840	−	0.327515i	−0.750189	+	0.661224i	$0.770037\pi$
$464$	151345.	+	180366.i	0.702963	+	0.837759i
$465$		0			0
$466$	−539553.	+	196381.i	−2.48463	+	0.904333i
$467$	186474.	+	107661.i	0.855035	+	0.493655i	0.862346	−	0.506319i	$-0.168994\pi$
$467$	186474.	+	107661.i	0.855035	+	0.493655i	−0.00731154	+	0.999973i	$0.502327\pi$
$468$		0			0
$469$	−27007.5	−	46778.4i	−0.122783	−	0.212667i
$470$	10262.4	−	12230.3i	0.0464573	−	0.0553656i
$471$		0			0
$472$	10953.6	+	62121.0i	0.0491670	+	0.278840i
$473$	204590.	−	36074.7i	0.914454	−	0.161243i
$474$		0			0
$475$	126490.	+	106138.i	0.560621	+	0.470417i
$476$	−62672.9	+	36184.2i	−0.276609	+	0.159700i
$477$		0			0
$478$	60489.0	−	104770.i	0.264741	−	0.458544i
$479$	−72574.2	−	199396.i	−0.316309	−	0.869051i	−0.991347	−	0.131268i	$-0.958095\pi$
$479$	−72574.2	−	199396.i	−0.316309	−	0.869051i	0.675038	−	0.737783i	$-0.264127\pi$
$480$		0			0
$481$	−21880.6	+	18360.0i	−0.0945735	+	0.0793566i
$482$	−68517.9	+	188251.i	−0.294924	+	0.810296i
$483$		0			0
$484$	73908.7	−	419157.i	0.315504	−	1.78931i
$485$		−	153030.i		−	0.650568i
$486$		0			0
$487$	−5941.97			−0.0250537			−0.0125269	−	0.999922i	$-0.503988\pi$
$487$	−5941.97			−0.0250537			−0.0125269	+	0.999922i	$0.503988\pi$
$488$	42803.9	+	7547.49i	0.179740	+	0.0316930i
$489$		0			0
$490$	−220620.	−	80299.1i	−0.918867	−	0.334440i
$491$	240755.	+	286921.i	0.998649	+	1.19014i	0.981729	+	0.190287i	$0.0609418\pi$
$491$	240755.	+	286921.i	0.998649	+	1.19014i	0.0169206	+	0.999857i	$0.494614\pi$
$492$		0			0
$493$	663118.	−	241355.i	2.72833	−	0.993032i
$494$	−138121.	−	79744.2i	−0.565986	−	0.326772i
$495$		0			0
$496$	58437.1	+	101216.i	0.237534	+	0.411421i
$497$	13659.3	−	16278.6i	0.0552989	−	0.0659027i
$498$		0			0
$499$	−13156.0	−	74611.3i	−0.0528351	−	0.299642i	0.946927	−	0.321448i	$-0.104170\pi$
$499$	−13156.0	−	74611.3i	−0.0528351	−	0.299642i	−0.999762	+	0.0218057i	$0.993058\pi$
$500$	−332416.	+	58614.0i	−1.32967	+	0.234456i
$501$		0			0
$502$	198305.	+	166397.i	0.786911	+	0.660296i
$503$	−88820.2	+	51280.3i	−0.351055	+	0.202682i	−0.665150	−	0.746710i	$-0.731632\pi$
$503$	−88820.2	+	51280.3i	−0.351055	+	0.202682i	0.314095	+	0.949392i	$0.398299\pi$
$504$		0			0
$505$	−157557.	+	272896.i	−0.617809	+	1.07008i
$506$	−201681.	−	554113.i	−0.787704	−	2.16420i
$507$		0			0
$508$	−230705.	+	193584.i	−0.893983	+	0.750141i
$509$	117615.	−	323146.i	0.453972	−	1.24728i	−0.475934	−	0.879481i	$-0.657890\pi$
$509$	117615.	−	323146.i	0.453972	−	1.24728i	0.929906	−	0.367797i	$-0.119888\pi$
$510$		0			0
$511$	−5592.62	+	31717.3i	−0.0214177	+	0.121466i
$512$		−	288296.i		−	1.09976i
$513$		0			0
$514$	−87008.2			−0.329332
$515$	100355.	+	17695.3i	0.378376	+	0.0667179i
$516$		0			0
$517$	−28011.1	−	10195.2i	−0.104797	−	0.0381430i
$518$	15004.6	+	17881.8i	0.0559197	+	0.0666425i
$519$		0			0
$520$	26076.3	−	9491.00i	0.0964361	−	0.0350999i
$521$	−2025.59	−	1169.47i	−0.00746235	−	0.00430839i	0.496264	−	0.868172i	$-0.334705\pi$
$521$	−2025.59	−	1169.47i	−0.00746235	−	0.00430839i	−0.503727	+	0.863863i	$0.668038\pi$
$522$		0			0
$523$	96052.9	+	166369.i	0.351162	+	0.608230i	0.986453	−	0.164042i	$-0.0524534\pi$
$523$	96052.9	+	166369.i	0.351162	+	0.608230i	−0.635291	+	0.772272i	$0.719120\pi$
$524$	41594.0	−	49569.8i	0.151485	−	0.180532i
$525$		0			0
$526$	100869.	+	572054.i	0.364573	+	2.06760i
$527$	344965.	−	60826.6i	1.24209	−	0.219014i
$528$		0			0
$529$	8153.95	+	6841.97i	0.0291378	+	0.0244495i
$530$	−133163.	+	76881.5i	−0.474057	+	0.273697i
$531$		0			0
$532$	−36937.5	+	63977.7i	−0.130510	+	0.226050i
$533$	−10974.9	−	30153.2i	−0.0386318	−	0.106140i
$534$		0			0
$535$	19524.7	−	16383.2i	0.0682146	−	0.0572389i
$536$	−73336.8	+	201491.i	−0.255266	+	0.701336i
$537$		0			0
$538$	−19142.4	+	108562.i	−0.0661352	+	0.375071i
$539$			438350.i			1.50884i
$540$		0			0
$541$	−97098.5			−0.331755			−0.165878	−	0.986146i	$-0.553046\pi$
$541$	−97098.5			−0.331755			−0.165878	+	0.986146i	$0.553046\pi$
$542$	−766129.	−	135089.i	−2.60797	−	0.459856i
$543$		0			0
$544$	−605612.	−	220425.i	−2.04643	−	0.744839i
$545$	−94389.6	−	112489.i	−0.317783	−	0.378720i
$546$		0			0
$547$	187642.	−	68296.1i	0.627127	−	0.228256i	−0.00885339	−	0.999961i	$-0.502818\pi$
$547$	187642.	−	68296.1i	0.627127	−	0.228256i	0.635980	+	0.771705i	$0.280596\pi$
$548$	95038.7	+	54870.6i	0.316475	+	0.182717i
$549$		0			0
$550$	200799.	+	347793.i	0.663797	+	1.14973i
$551$	463043.	−	551833.i	1.52517	−	1.81763i
$552$		0			0
$553$	7492.79	+	42493.7i	0.0245015	+	0.138955i
$554$	−319113.	+	56268.3i	−1.03974	+	0.183334i
$555$		0			0
$556$	−339828.	−	285149.i	−1.09928	−	0.922408i
$557$	−136110.	+	78583.1i	−0.438712	+	0.253290i	−0.703051	−	0.711139i	$-0.748179\pi$
$557$	−136110.	+	78583.1i	−0.438712	+	0.253290i	0.264339	+	0.964430i	$0.414846\pi$
$558$		0			0
$559$	31193.5	−	54028.7i	0.0998253	−	0.172902i
$560$	6502.23	+	17864.7i	0.0207342	+	0.0569666i
$561$		0			0
$562$	139782.	−	117291.i	0.442566	−	0.371357i
$563$	−164752.	+	452653.i	−0.519773	+	1.42807i	0.350997	+	0.936376i	$0.385843\pi$
$563$	−164752.	+	452653.i	−0.519773	+	1.42807i	−0.870771	+	0.491689i	$0.836380\pi$
$564$		0			0
$565$	48155.9	−	273105.i	0.150852	−	0.855526i
$566$		−	15745.3i		−	0.0491495i
$567$		0			0
$568$	−84356.3			−0.261469
$569$	431178.	+	76028.3i	1.33178	+	0.234828i	0.793825	−	0.608146i	$-0.208087\pi$
$569$	431178.	+	76028.3i	1.33178	+	0.234828i	0.537953	+	0.842975i	$0.319198\pi$
$570$		0			0
$571$	86789.3	+	31588.7i	0.266191	+	0.0968857i	0.471668	−	0.881776i	$-0.343652\pi$
$571$	86789.3	+	31588.7i	0.266191	+	0.0968857i	−0.205476	+	0.978662i	$0.565874\pi$
$572$	−141320.	−	168418.i	−0.431927	−	0.514750i
$573$		0			0
$574$	−24642.5	+	8969.12i	−0.0747929	+	0.0272224i
$575$	158774.	+	91668.0i	0.480223	+	0.277257i
$576$		0			0
$577$	−121423.	−	210311.i	−0.364711	−	0.631699i	0.624018	−	0.781410i	$-0.285499\pi$
$577$	−121423.	−	210311.i	−0.364711	−	0.631699i	−0.988730	+	0.149711i	$0.952166\pi$
$578$	−492309.	+	586711.i	−1.47361	+	1.75618i
$579$		0			0
$580$	92356.6	+	523780.i	0.274544	+	1.55702i
$581$	−30410.3	+	5362.15i	−0.0900882	+	0.0158850i
$582$		0			0
$583$	219922.	+	184536.i	0.647039	+	0.542930i
$584$	110721.	−	63925.0i	0.324643	−	0.187433i
$585$		0			0
$586$	144781.	−	250768.i	0.421614	−	0.730258i
$587$	−188159.	−	516964.i	−0.546072	−	1.50032i	−0.838971	−	0.544177i	$-0.816842\pi$
$587$	−188159.	−	516964.i	−0.546072	−	1.50032i	0.292899	−	0.956144i	$-0.405380\pi$
$588$		0			0
$589$	273921.	−	229847.i	0.789579	−	0.662535i
$590$	72080.4	−	198039.i	0.207068	−	0.568915i
$591$		0			0
$592$	−13489.1	+	76500.3i	−0.0384892	+	0.218283i
$593$			265204.i			0.754172i	0.926178	+	0.377086i	$0.123074\pi$
$593$			265204.i			0.754172i	−0.926178	+	0.377086i	$0.876926\pi$
$594$		0			0
$595$	56979.0			0.160946
$596$	600085.	+	105811.i	1.68935	+	0.297878i
$597$		0			0
$598$	−166402.	−	60565.5i	−0.465326	−	0.169365i
$599$	−96884.8	−	115463.i	−0.270024	−	0.321802i	0.613944	−	0.789350i	$-0.289582\pi$
$599$	−96884.8	−	115463.i	−0.270024	−	0.321802i	−0.883968	+	0.467548i	$0.845138\pi$
$600$		0			0
$601$	−292365.	+	106412.i	−0.809424	+	0.294606i	−0.713386	−	0.700772i	$-0.752839\pi$
$601$	−292365.	+	106412.i	−0.809424	+	0.294606i	−0.0960378	+	0.995378i	$0.530617\pi$
$602$	−44154.6	−	25492.7i	−0.121838	−	0.0703432i
$603$		0			0
$604$	−374134.	−	648019.i	−1.02554	−	1.77629i
$605$	−215406.	+	256711.i	−0.588502	+	0.701349i
$606$		0			0
$607$	34423.9	+	195228.i	0.0934293	+	0.529864i	0.995217	+	0.0976852i	$0.0311438\pi$
$607$	34423.9	+	195228.i	0.0934293	+	0.529864i	−0.901788	+	0.432178i	$0.857745\pi$
$608$	−647901.	+	114242.i	−1.75268	+	0.309044i
$609$		0			0
$610$	−111241.	−	93342.2i	−0.298954	−	0.250852i
$611$	−7752.39	+	4475.85i	−0.0207660	+	0.0119893i
$612$		0			0
$613$	−312175.	+	540703.i	−0.830763	+	1.43892i	0.0666714	+	0.997775i	$0.478762\pi$
$613$	−312175.	+	540703.i	−0.830763	+	1.43892i	−0.897434	+	0.441148i	$0.854571\pi$
$614$	−47169.8	−	129598.i	−0.125120	−	0.343765i
$615$		0			0
$616$	−32436.0	+	27217.0i	−0.0854802	+	0.0717264i
$617$	−57927.0	+	159153.i	−0.152164	+	0.418066i	−0.992230	−	0.124418i	$-0.960294\pi$
$617$	−57927.0	+	159153.i	−0.152164	+	0.418066i	0.840066	+	0.542484i	$0.182516\pi$
$618$		0			0
$619$	25857.6	−	146646.i	0.0674850	−	0.382726i	−0.932294	−	0.361701i	$-0.882196\pi$
$619$	25857.6	−	146646.i	0.0674850	−	0.382726i	0.999779	−	0.0210249i	$-0.00669292\pi$
$620$			264007.i			0.686803i
$621$		0			0
$622$	−206791.			−0.534504
$623$	−46249.0	−	8154.95i	−0.119159	−	0.0210109i
$624$		0			0
$625$	42207.9	+	15362.4i	0.108052	+	0.0393278i
$626$	565790.	+	674282.i	1.44380	+	1.72065i
$627$		0			0
$628$	483959.	−	176147.i	1.22713	−	0.446638i
$629$	201626.	+	116409.i	0.509619	+	0.294229i
$630$		0			0
$631$	−298176.	−	516456.i	−0.748883	−	1.29710i	−0.948359	−	0.317200i	$-0.897257\pi$
$631$	−298176.	−	516456.i	−0.748883	−	1.29710i	0.199476	−	0.979903i	$-0.436076\pi$
$632$	110102.	−	131215.i	0.275653	−	0.328510i
$633$		0			0
$634$	−31136.4	−	176583.i	−0.0774622	−	0.439310i
$635$	233518.	−	41175.5i	0.579125	−	0.102115i
$636$		0			0
$637$	100841.	+	84615.4i	0.248518	+	0.208531i
$638$	1.51730e6	−	876015.i	3.72761	−	2.15214i
$639$		0			0
$640$	120482.	−	208680.i	0.294144	−	0.509473i
$641$	50133.6	+	137741.i	0.122015	+	0.335233i	0.985630	−	0.168918i	$-0.0540275\pi$
$641$	50133.6	+	137741.i	0.122015	+	0.335233i	−0.863615	+	0.504152i	$0.831805\pi$
$642$		0			0
$643$	121340.	−	101816.i	0.293482	−	0.246261i	−0.484143	−	0.874989i	$-0.660869\pi$
$643$	121340.	−	101816.i	0.293482	−	0.246261i	0.777625	+	0.628728i	$0.216424\pi$
$644$	−28054.0	+	77077.7i	−0.0676430	+	0.185848i
$645$		0			0
$646$	−225741.	+	1.28024e6i	−0.540934	+	3.06779i
$647$		−	428602.i		−	1.02387i	−0.859023	−	0.511936i	$-0.828928\pi$
$647$		−	428602.i		−	1.02387i	0.859023	−	0.511936i	$-0.171072\pi$
$648$		0			0
$649$	−393484.			−0.934196
$650$	118769.	+	20942.2i	0.281110	+	0.0495673i
$651$		0			0
$652$	339645.	+	123621.i	0.798969	+	0.290801i
$653$	−472730.	−	563377.i	−1.10863	−	1.32121i	−0.942159	−	0.335167i	$-0.891207\pi$
$653$	−472730.	−	563377.i	−1.10863	−	1.32121i	−0.166470	−	0.986046i	$-0.553237\pi$
$654$		0			0
$655$	−47875.7	+	17425.3i	−0.111592	+	0.0406161i
$656$	−75576.0	−	43633.8i	−0.175621	−	0.101395i
$657$		0			0
$658$	3657.85	+	6335.59i	0.00844840	+	0.0146331i
$659$	−318200.	+	379216.i	−0.732706	+	0.873205i	−0.995799	−	0.0915652i	$-0.970813\pi$
$659$	−318200.	+	379216.i	−0.732706	+	0.873205i	0.263093	+	0.964771i	$0.415257\pi$
$660$		0			0
$661$	102468.	+	581125.i	0.234523	+	1.33005i	0.843616	+	0.536947i	$0.180423\pi$
$661$	102468.	+	581125.i	0.234523	+	1.33005i	−0.609093	+	0.793099i	$0.708466\pi$
$662$	144780.	−	25528.7i	0.330365	−	0.0582522i
$663$		0			0
$664$	93902.8	+	78793.8i	0.212982	+	0.178713i
$665$	50372.6	−	29082.6i	0.113907	−	0.0657643i
$666$		0			0
$667$	399916.	−	692675.i	0.898912	−	1.55696i
$668$	41275.4	+	113403.i	0.0924993	+	0.254140i
$669$		0			0
$670$	548785.	−	460485.i	1.22251	−	1.02581i
$671$	−92730.8	+	254776.i	−0.205958	+	0.565865i
$672$		0			0
$673$	148961.	−	844798.i	0.328883	−	1.86519i	−0.151968	−	0.988385i	$-0.548561\pi$
$673$	148961.	−	844798.i	0.328883	−	1.86519i	0.480851	−	0.876802i	$-0.340328\pi$
$674$		−	252040.i		−	0.554816i
$675$		0			0
$676$	531848.			1.16384
$677$	264276.	+	46598.9i	0.576607	+	0.101671i	0.454344	−	0.890826i	$-0.349874\pi$
$677$	264276.	+	46598.9i	0.576607	+	0.101671i	0.122263	+	0.992498i	$0.460985\pi$
$678$		0			0
$679$	65892.5	+	23982.9i	0.142921	+	0.0520190i
$680$	−145391.	−	173271.i	−0.314427	−	0.374720i
$681$		0			0
$682$	817232.	−	297448.i	1.75702	−	0.639503i
$683$	165671.	+	95650.1i	0.355144	+	0.205043i	0.666949	−	0.745104i	$-0.267600\pi$
$683$	165671.	+	95650.1i	0.355144	+	0.205043i	−0.311804	+	0.950146i	$0.600933\pi$
$684$		0			0
$685$	−43202.2	−	74828.4i	−0.0920714	−	0.159472i
$686$	139985.	−	166828.i	0.297464	−	0.354504i
$687$		0			0
$688$	−29462.5	−	167090.i	−0.0622434	−	0.353000i
$689$	84903.7	−	14970.8i	0.178850	−	0.0315360i
$690$		0			0
$691$	201952.	+	169458.i	0.422953	+	0.354900i	0.829285	−	0.558826i	$-0.188748\pi$
$691$	201952.	+	169458.i	0.422953	+	0.354900i	−0.406332	+	0.913725i	$0.633192\pi$
$692$	−356346.	+	205737.i	−0.744150	+	0.429635i
$693$		0			0
$694$	325472.	−	563734.i	0.675763	−	1.17046i
$695$	119460.	+	328214.i	0.247316	+	0.679496i
$696$		0			0
$697$	−200360.	+	168122.i	−0.412426	+	0.346067i
$698$	421855.	−	1.15904e6i	0.865870	−	2.37896i
$699$		0			0
$700$	9700.43	−	55013.9i	0.0197968	−	0.112273i
$701$			330892.i			0.673364i	0.941618	+	0.336682i	$0.109305\pi$
$701$			330892.i			0.673364i	−0.941618	+	0.336682i	$0.890695\pi$
$702$		0			0
$703$	237665.			0.480899
$704$	−1.12571e6	−	198494.i	−2.27134	−	0.400499i
$705$		0			0
$706$	−139506.	−	50776.2i	−0.279888	−	0.101871i
$707$	−92813.0	−	110610.i	−0.185682	−	0.221287i
$708$		0			0
$709$	−854464.	+	311000.i	−1.69981	+	0.618682i	−0.995804	−	0.0915085i	$-0.970831\pi$
$709$	−854464.	+	311000.i	−1.69981	+	0.618682i	−0.704010	+	0.710190i	$0.748609\pi$
$710$	244077.	+	140918.i	0.484183	+	0.279543i
$711$		0			0
$712$	93213.0	+	161450.i	0.183872	+	0.318476i
$713$	255202.	−	304138.i	0.502002	−	0.598263i
$714$		0			0
$715$	30058.7	+	170472.i	0.0587975	+	0.333457i
$716$	462638.	−	81575.6i	0.902434	−	0.159123i
$717$		0			0
$718$	181558.	+	152345.i	0.352181	+	0.295515i
$719$	534889.	−	308818.i	1.03468	−	0.597372i	0.116358	−	0.993207i	$-0.462878\pi$
$719$	534889.	−	308818.i	1.03468	−	0.597372i	0.918322	+	0.395835i	$0.129545\pi$
$720$		0			0
$721$	−23347.0	+	40438.2i	−0.0449118	+	0.0777895i
$722$	183000.	+	502789.i	0.351057	+	0.964520i
$723$		0			0
$724$	447579.	−	375563.i	0.853871	−	0.716483i
$725$	−186307.	+	511873.i	−0.354448	+	0.973837i
$726$		0			0
$727$	−113322.	+	642684.i	−0.214411	+	1.21599i	0.667514	+	0.744597i	$0.267358\pi$
$727$	−113322.	+	642684.i	−0.214411	+	1.21599i	−0.881926	+	0.471389i	$0.843753\pi$
$728$			12715.5i			0.0239923i
$729$		0			0
$730$	−427149.			−0.801555
$731$	−500790.	−	88302.9i	−0.937176	−	0.165249i
$732$		0			0
$733$	−853703.	−	310723.i	−1.58891	−	0.578316i	−0.611792	−	0.791019i	$-0.709551\pi$
$733$	−853703.	−	310723.i	−1.58891	−	0.578316i	−0.977117	+	0.212703i	$0.931773\pi$
$734$	549151.	+	654452.i	1.01929	+	1.21475i
$735$		0			0
$736$	−686417.	+	249835.i	−1.26716	+	0.461209i
$737$	−1.15835e6	−	668775.i	−2.13258	−	1.23125i
$738$		0			0
$739$	346054.	+	599383.i	0.633658	+	1.09753i	0.986798	+	0.161958i	$0.0517808\pi$
$739$	346054.	+	599383.i	0.633658	+	1.09753i	−0.353139	+	0.935571i	$0.614886\pi$
$740$	−112791.	+	134420.i	−0.205974	+	0.245470i
$741$		0			0
$742$	−12234.8	−	69386.9i	−0.0222223	−	0.126029i
$743$	−868910.	+	153212.i	−1.57397	+	0.277534i	−0.891377	−	0.453263i	$-0.850260\pi$
$743$	−868910.	+	153212.i	−1.57397	+	0.277534i	−0.682595	+	0.730797i	$0.739149\pi$
$744$		0			0
$745$	−367520.	−	308386.i	−0.662169	−	0.555625i
$746$	−731995.	+	422618.i	−1.31532	+	0.759399i
$747$		0			0
$748$	−896014.	+	1.55194e6i	−1.60144	+	2.77378i
$749$	3994.45	+	10974.7i	0.00712022	+	0.0195626i
$750$		0			0
$751$	−116154.	+	97464.8i	−0.205946	+	0.172810i	−0.739927	−	0.672687i	$-0.765140\pi$
$751$	−116154.	+	97464.8i	−0.205946	+	0.172810i	0.533981	+	0.845497i	$0.320696\pi$
$752$	−8326.51	+	22876.9i	−0.0147240	+	0.0404540i
$753$		0			0
$754$	91363.6	−	518149.i	0.160705	−	0.911405i
$755$			589146.i			1.03354i
$756$		0			0
$757$	−593090.			−1.03497			−0.517486	−	0.855692i	$-0.673132\pi$
$757$	−593090.			−1.03497			−0.517486	+	0.855692i	$0.673132\pi$
$758$	1.22834e6	+	216589.i	2.13786	+	0.376963i
$759$		0			0
$760$	−216973.	−	78971.6i	−0.375645	−	0.136724i
$761$	−503625.	−	600197.i	−0.869638	−	1.03639i	−0.998996	−	0.0447960i	$-0.985736\pi$
$761$	−503625.	−	600197.i	−0.869638	−	1.03639i	0.129358	−	0.991598i	$-0.458708\pi$
$762$		0			0
$763$	63229.1	−	23013.5i	0.108609	−	0.0395306i
$764$	−971190.	−	560717.i	−1.66386	−	0.960631i
$765$		0			0
$766$	559208.	+	968577.i	0.953051	+	1.65073i
$767$	−75955.0	+	90519.6i	−0.129112	+	0.153869i
$768$		0			0
$769$	26752.7	+	151722.i	0.0452392	+	0.256564i	0.999037	−	0.0438864i	$-0.0139740\pi$
$769$	26752.7	+	151722.i	0.0452392	+	0.256564i	−0.953797	+	0.300451i	$0.902863\pi$
$770$	139317.	−	24565.3i	0.234975	−	0.0414324i
$771$		0			0
$772$	−682993.	−	573099.i	−1.14599	−	0.961601i
$773$	−617858.	+	356720.i	−1.03402	+	0.596992i	−0.918134	−	0.396270i	$-0.870304\pi$
$773$	−617858.	+	356720.i	−1.03402	+	0.596992i	−0.115887	+	0.993262i	$0.536971\pi$
$774$		0			0
$775$	−135196.	+	234167.i	−0.225093	+	0.389872i
$776$	−95204.5	−	261572.i	−0.158101	−	0.434378i
$777$		0			0
$778$	−596351.	+	500398.i	−0.985242	+	0.826716i
$779$	−91318.4	+	250895.i	−0.150482	+	0.413445i
$780$		0			0
$781$	91375.1	−	518214.i	0.149805	−	0.849585i
$782$			1.44339e6i			2.36032i
$783$		0			0
$784$	358004.			0.582446
$785$	−399338.	−	70414.0i	−0.648039	−	0.114267i
$786$		0			0
$787$	118383.	+	43087.8i	0.191134	+	0.0695672i	0.435814	−	0.900037i	$-0.356461\pi$
$787$	118383.	+	43087.8i	0.191134	+	0.0695672i	−0.244680	+	0.969604i	$0.578683\pi$
$788$	116674.	+	139047.i	0.187898	+	0.223928i
$789$		0			0
$790$	−537766.	+	195731.i	−0.861666	+	0.313621i
$791$	110048.	+	63536.4i	0.175886	+	0.101548i
$792$		0			0
$793$	40710.2	+	70512.2i	0.0647377	+	0.112129i
$794$	318442.	−	379505.i	0.505114	−	0.601972i
$795$		0			0
$796$	−228501.	−	1.29589e6i	−0.360630	−	2.04523i
$797$	989241.	−	174430.i	1.55735	−	0.274602i	0.672362	−	0.740222i	$-0.265280\pi$
$797$	989241.	−	174430.i	1.55735	−	0.274602i	0.884985	+	0.465620i	$0.154169\pi$
$798$		0			0
$799$	55894.6	+	46901.1i	0.0875540	+	0.0734665i
$800$	430835.	−	248742.i	0.673179	−	0.388660i
$801$		0			0
$802$	179750.	−	311335.i	0.279460	−	0.484038i
$803$	272767.	+	749422.i	0.423020	+	1.16224i
$804$		0			0
$805$	49472.4	−	41512.2i	0.0763433	−	0.0640596i
$806$	89324.9	−	245418.i	0.137500	−	0.377778i
$807$		0			0
$808$	−99533.0	+	564480.i	−0.152456	+	0.864621i
$809$		−	583220.i		−	0.891118i	−0.895253	−	0.445559i	$-0.853005\pi$
$809$		−	583220.i		−	0.891118i	0.895253	−	0.445559i	$-0.146995\pi$
$810$		0			0
$811$	1.19604e6			1.81846			0.909228	−	0.416298i	$-0.136673\pi$
$811$	1.19604e6			1.81846			0.909228	+	0.416298i	$0.136673\pi$
$812$	−240007.	−	42319.6i	−0.364008	−	0.0641845i
$813$		0			0
$814$	543173.	+	197699.i	0.819765	+	0.298370i
$815$	−182925.	−	218001.i	−0.275396	−	0.328204i
$816$		0			0
$817$	−487797.	+	177543.i	−0.730794	+	0.265987i
$818$	−1.53414e6	−	885736.i	−2.29276	−	1.32372i
$819$		0			0
$820$	−98564.4	−	170719.i	−0.146586	−	0.253894i
$821$	590669.	−	703931.i	0.876310	−	1.04435i	−0.122345	−	0.992488i	$-0.539041\pi$
$821$	590669.	−	703931.i	0.876310	−	1.04435i	0.998654	−	0.0518575i	$-0.0165142\pi$
$822$		0			0
$823$	−141705.	−	803651.i	−0.209212	−	1.18650i	−0.890672	−	0.454646i	$-0.849766\pi$
$823$	−141705.	−	803651.i	−0.209212	−	1.18650i	0.681460	−	0.731855i	$-0.261345\pi$
$824$	182544.	−	32187.5i	0.268852	−	0.0474059i
$825$		0			0
$826$	73976.5	+	62073.6i	0.108426	+	0.0909802i
$827$	308224.	−	177953.i	0.450666	−	0.260192i	−0.257445	−	0.966293i	$-0.582881\pi$
$827$	308224.	−	177953.i	0.450666	−	0.260192i	0.708112	+	0.706101i	$0.249547\pi$
$828$		0			0
$829$	−224839.	+	389432.i	−0.327161	+	0.566660i	−0.981947	−	0.189154i	$-0.939425\pi$
$829$	−224839.	+	389432.i	−0.327161	+	0.566660i	0.654786	+	0.755814i	$0.272759\pi$
$830$	−140073.	−	384848.i	−0.203329	−	0.558641i
$831$		0			0
$832$	−262961.	+	220651.i	−0.379879	+	0.318756i
$833$	366981.	−	1.00827e6i	0.528876	−	1.45308i
$834$		0			0
$835$	16499.7	−	93574.4i	0.0236648	−	0.134210i
$836$			1.82934e6i			2.61747i
$837$		0			0
$838$	746843.			1.06351
$839$	167593.	+	29551.1i	0.238085	+	0.0419807i	0.291417	−	0.956596i	$-0.405873\pi$
$839$	167593.	+	29551.1i	0.238085	+	0.0419807i	−0.0533326	+	0.998577i	$0.516984\pi$
$840$		0			0
$841$	1.56850e6	+	570888.i	2.21765	+	0.807158i
$842$	297483.	+	354526.i	0.419602	+	0.500063i
$843$		0			0
$844$	1.11351e6	−	405283.i	1.56317	−	0.568949i
$845$	−362647.	−	209374.i	−0.507891	−	0.293231i
$846$		0			0
$847$	−76777.7	−	132983.i	−0.107021	−	0.185366i
$848$	150712.	−	179612.i	0.209583	−	0.249772i
$849$		0			0
$850$	−170700.	−	968085.i	−0.236262	−	1.33991i
$851$	259873.	−	45822.6i	0.358841	−	0.0632733i
$852$		0			0
$853$	81021.3	+	67984.9i	0.111353	+	0.0934360i	0.696764	−	0.717300i	$-0.254622\pi$
$853$	81021.3	+	67984.9i	0.111353	+	0.0934360i	−0.585411	+	0.810736i	$0.699067\pi$
$854$	57625.6	−	33270.1i	0.0790132	−	0.0456183i
$855$		0			0
$856$	23180.9	−	40150.6i	0.0316361	−	0.0547954i
$857$	143295.	+	393699.i	0.195105	+	0.536047i	0.998211	−	0.0597895i	$-0.0190430\pi$
$857$	143295.	+	393699.i	0.195105	+	0.536047i	−0.803106	+	0.595836i	$0.796821\pi$
$858$		0			0
$859$	−770583.	+	646596.i	−1.04432	+	0.876288i	−0.992485	−	0.122368i	$-0.960951\pi$
$859$	−770583.	+	646596.i	−1.04432	+	0.876288i	−0.0518343	+	0.998656i	$0.516507\pi$
$860$	131084.	−	360149.i	0.177236	−	0.486952i
$861$		0			0
$862$	198970.	−	1.12842e6i	0.267777	−	1.51864i
$863$		−	1.38007e6i		−	1.85302i	−0.376271	−	0.926510i	$-0.622794\pi$
$863$		−	1.38007e6i		−	1.85302i	0.376271	−	0.926510i	$-0.377206\pi$
$864$		0			0
$865$	323972.			0.432988
$866$	−27743.5	−	4891.92i	−0.0369935	−	0.00652295i
$867$		0			0
$868$	−113678.	−	41375.3i	−0.150882	−	0.0549164i
$869$	686810.	+	818509.i	0.909489	+	1.08389i
$870$		0			0
$871$	−377448.	+	137380.i	−0.497532	+	0.181087i
$872$	−231322.	−	133554.i	−0.304218	−	0.175640i
$873$		0			0
$874$	736721.	+	1.27604e6i	0.964451	+	1.67048i
$875$	−78277.7	+	93287.8i	−0.102240	+	0.121845i
$876$		0			0
$877$	38998.8	+	221173.i	0.0507051	+	0.287563i	0.999608	−	0.0280060i	$-0.00891576\pi$
$877$	38998.8	+	221173.i	0.0507051	+	0.287563i	−0.948903	+	0.315569i	$0.897805\pi$
$878$	−288276.	+	50830.8i	−0.373955	+	0.0659383i
$879$		0			0
$880$	360629.	+	302604.i	0.465688	+	0.390759i
$881$	216321.	−	124893.i	0.278707	−	0.160912i	−0.354131	−	0.935196i	$-0.615223\pi$
$881$	216321.	−	124893.i	0.278707	−	0.160912i	0.632838	+	0.774284i	$0.281890\pi$
$882$		0			0
$883$	564079.	−	977013.i	0.723466	−	1.25308i	−0.236136	−	0.971720i	$-0.575881\pi$
$883$	564079.	−	977013.i	0.723466	−	1.25308i	0.959602	−	0.281361i	$-0.0907857\pi$
$884$	184059.	+	505699.i	0.235534	+	0.647124i
$885$		0			0
$886$	60588.3	−	50839.6i	0.0771829	−	0.0647642i
$887$	−385201.	+	1.05833e6i	−0.489598	+	1.34516i	0.411447	+	0.911434i	$0.365024\pi$
$887$	−385201.	+	1.05833e6i	−0.489598	+	1.34516i	−0.901045	+	0.433726i	$0.857199\pi$
$888$		0			0
$889$	−18867.4	+	107003.i	−0.0238731	+	0.135391i
$890$		−	622852.i		−	0.786330i
$891$		0			0
$892$	−725789.			−0.912180
$893$	73352.6	+	12934.0i	0.0919841	+	0.0162193i
$894$		0			0
$895$	−347570.	−	126505.i	−0.433906	−	0.157929i
$896$	70972.8	+	84582.1i	0.0884048	+	0.105357i
$897$		0			0
$898$	850452.	−	309539.i	1.05462	−	0.383851i
$899$	1.02159e6	+	589815.i	1.26403	+	0.729788i
$900$		0			0
$901$	−351363.	−	608578.i	−0.432819	−	0.749664i
$902$	−417409.	+	497448.i	−0.513037	+	0.611413i
$903$		0			0
$904$	−87594.9	−	496775.i	−0.107187	−	0.607887i
$905$	−453036.	+	79882.5i	−0.553141	+	0.0975337i
$906$		0			0
$907$	560559.	+	470365.i	0.681407	+	0.571769i	0.916417	−	0.400224i	$-0.131068\pi$
$907$	560559.	+	470365.i	0.681407	+	0.571769i	−0.235010	+	0.971993i	$0.575512\pi$
$908$	94189.9	−	54380.6i	0.114244	−	0.0659587i
$909$		0			0
$910$	21241.4	−	36791.2i	0.0256507	−	0.0444284i
$911$	−439260.	−	1.20686e6i	−0.529279	−	1.45418i	−0.859922	−	0.510426i	$-0.829488\pi$
$911$	−439260.	−	1.20686e6i	−0.529279	−	1.45418i	0.330642	−	0.943756i	$-0.392735\pi$
$912$		0			0
$913$	−585759.	+	491510.i	−0.702712	+	0.589645i
$914$	−45669.9	+	125477.i	−0.0546685	+	0.150200i
$915$		0			0
$916$	−158276.	+	897627.i	−0.188636	+	1.06981i
$917$		−	23345.5i		−	0.0277629i
$918$		0			0
$919$	−321358.			−0.380503			−0.190252	−	0.981735i	$-0.560930\pi$
$919$	−321358.			−0.380503			−0.190252	+	0.981735i	$0.560930\pi$
$920$	−252474.	−	44517.9i	−0.298291	−	0.0525968i
$921$		0			0
$922$	788976.	+	287164.i	0.928116	+	0.337807i
$923$	−101575.	−	121052.i	−0.119229	−	0.142092i
$924$		0			0
$925$	−168878.	+	61466.6i	−0.197374	+	0.0718382i
$926$	1.08039e6	+	623763.i	1.25996	+	0.727440i
$927$		0			0
$928$	−1.08518e6	−	1.87958e6i	−1.26010	−	2.18256i
$929$	−845059.	+	1.00710e6i	−0.979164	+	1.16692i	0.00680175	+	0.999977i	$0.497835\pi$
$929$	−845059.	+	1.00710e6i	−0.979164	+	1.16692i	−0.985966	+	0.166946i	$0.946610\pi$
$930$		0			0
$931$	−190200.	−	1.07868e6i	−0.219438	−	1.24449i
$932$	1.94772e6	−	343435.i	2.24230	−	0.395378i
$933$		0			0
$934$	−1.00242e6	−	841129.i	−1.14909	−	0.964204i
$935$	1.22192e6	−	705474.i	1.39771	−	0.806971i
$936$		0			0
$937$	−91197.1	+	157958.i	−0.103873	+	0.179913i	−0.913277	−	0.407339i	$-0.866457\pi$
$937$	−91197.1	+	157958.i	−0.103873	+	0.179913i	0.809404	+	0.587252i	$0.199790\pi$
$938$	112273.	+	308467.i	0.127605	+	0.350592i
$939$		0			0
$940$	−42127.1	+	35348.9i	−0.0476767	+	0.0400055i
$941$	314314.	−	863570.i	0.354964	−	0.975255i	−0.625788	−	0.779994i	$-0.715222\pi$
$941$	314314.	−	863570.i	0.354964	−	0.975255i	0.980751	−	0.195261i	$-0.0625555\pi$
$942$		0			0
$943$	−51478.0	+	291946.i	−0.0578893	+	0.328306i
$944$			321362.i			0.360621i
$945$		0			0
$946$	−1.26253e6			−1.41078
$947$	1.27507e6	+	224828.i	1.42178	+	0.250698i	0.831062	−	0.556180i	$-0.187733\pi$
$947$	1.27507e6	+	224828.i	1.42178	+	0.250698i	0.590718	+	0.806878i	$0.298845\pi$
$948$		0			0
$949$	225055.	+	81913.2i	0.249894	+	0.0909539i
$950$	−645028.	−	768714.i	−0.714712	−	0.851760i
$951$		0			0
$952$	97393.7	−	35448.4i	0.107462	−	0.0391131i
$953$	26148.8	+	15097.0i	0.0287917	+	0.0166229i	0.514327	−	0.857594i	$-0.328042\pi$
$953$	26148.8	+	15097.0i	0.0287917	+	0.0166229i	−0.485535	+	0.874217i	$0.661375\pi$
$954$		0			0
$955$	441478.	+	764663.i	0.484064	+	0.838423i
$956$	−267855.	+	319217.i	−0.293079	+	0.349278i
$957$		0			0
$958$	223928.	+	1.26996e6i	0.243993	+	1.38375i
$959$	38990.7	−	6875.12i	0.0423959	−	0.00747555i
$960$		0			0
$961$	−258901.	−	217244.i	−0.280341	−	0.235234i
$962$	150330.	−	86792.8i	0.162440	−	0.0937850i
$963$		0			0
$964$	345023.	−	597597.i	0.371274	−	0.643065i
$965$	240093.	+	659651.i	0.257825	+	0.708369i
$966$		0			0
$967$	671929.	−	563815.i	0.718572	−	0.602954i	−0.208418	−	0.978040i	$-0.566831\pi$
$967$	671929.	−	563815.i	0.718572	−	0.602954i	0.926990	+	0.375086i	$0.122387\pi$
$968$	−208484.	+	572805.i	−0.222496	+	0.611302i
$969$		0			0
$970$	−161493.	+	915874.i	−0.171637	+	0.973402i
$971$			552699.i			0.586206i	0.956081	+	0.293103i	$0.0946879\pi$
$971$			552699.i			0.586206i	−0.956081	+	0.293103i	$0.905312\pi$
$972$		0			0
$973$	−160046.			−0.169052
$974$	35562.3	+	6270.59i	0.0374862	+	0.00660984i
$975$		0			0
$976$	208078.	+	75734.1i	0.218437	+	0.0795045i
$977$	−661005.	−	787755.i	−0.692494	−	0.825282i	0.299161	−	0.954203i	$-0.403293\pi$
$977$	−661005.	−	787755.i	−0.692494	−	0.825282i	−0.991655	+	0.128921i	$0.958849\pi$
$978$		0			0
$979$	−1.09278e6	+	397739.i	−1.14016	+	0.414986i
$980$	700350.	+	404348.i	0.729228	+	0.421020i
$981$		0			0
$982$	−1.13812e6	−	1.97127e6i	−1.18022	−	2.04420i
$983$	−1.15088e6	+	1.37157e6i	−1.19103	+	1.41942i	−0.307180	+	0.951652i	$0.599385\pi$
$983$	−1.15088e6	+	1.37157e6i	−1.19103	+	1.41942i	−0.883853	+	0.467765i	$0.845059\pi$
$984$		0			0
$985$	−24816.7	−	140742.i	−0.0255783	−	0.145062i
$986$	−4.22342e6	+	744704.i	−4.34421	+	0.766002i
$987$		0			0
$988$	420832.	+	353120.i	0.431117	+	0.361750i
$989$	−499147.	+	288183.i	−0.510312	+	0.294629i
$990$		0			0
$991$	219634.	−	380417.i	0.223641	−	0.387358i	−0.732270	−	0.681015i	$-0.761539\pi$
$991$	219634.	−	380417.i	0.223641	−	0.387358i	0.955911	+	0.293657i	$0.0948723\pi$
$992$	−368469.	−	1.01236e6i	−0.374436	−	1.02875i
$993$		0			0
$994$	−98929.1	+	83011.3i	−0.100127	+	0.0840165i
$995$	−354352.	+	973575.i	−0.357923	+	0.983384i
$996$		0			0
$997$	120978.	−	686100.i	0.121707	−	0.690235i	−0.861502	−	0.507754i	$-0.830476\pi$
$997$	120978.	−	686100.i	0.121707	−	0.690235i	0.983209	−	0.182481i	$-0.0584128\pi$
$998$			460427.i			0.462274i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.2		66
3.2	odd	2		27.5.f.a.2.10	✓	66
27.13	even	9		27.5.f.a.14.10	yes	66
27.14	odd	18	inner	81.5.f.a.71.2		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.10	✓	66	3.2	odd	2
27.5.f.a.14.10	yes	66	27.13	even	9
81.5.f.a.8.2		66	1.1	even	1	trivial
81.5.f.a.71.2		66	27.14	odd	18	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.98494 - 1.05531i) q^{2} +(19.6707 + 7.15955i) q^{4} +(-10.5942 - 12.6257i) q^{5} +(7.09675 - 2.58301i) q^{7} +(-25.9633 - 14.9899i) q^{8} +(50.0816 + 86.7438i) q^{10} +(120.209 - 143.260i) q^{11} +(-9.75217 - 55.3073i) q^{13} +(-45.1995 + 7.96989i) q^{14} +(-117.001 - 98.1758i) q^{16} +(-396.435 + 228.882i) q^{17} +(-233.647 + 404.688i) q^{19} +(-118.001 - 324.205i) q^{20} +(-870.626 + 730.542i) q^{22} +(-177.454 + 487.552i) q^{23} +(61.3597 - 347.988i) q^{25} +341.302i q^{26} +158.091 q^{28} +(-1518.15 - 267.691i) q^{29} +(-719.064 - 261.718i) q^{31} +(904.971 + 1078.50i) q^{32} +(2614.18 - 951.483i) q^{34} +(-107.796 - 62.2363i) q^{35} +(-254.299 - 440.459i) q^{37} +(1825.43 - 2175.46i) q^{38} +(85.8024 + 486.610i) q^{40} +(562.688 - 99.2171i) q^{41} +(850.976 + 714.053i) q^{43} +(3390.27 - 1957.37i) q^{44} +(1576.57 - 2730.70i) q^{46} +(-54.5162 - 149.782i) q^{47} +(-1795.58 + 1506.67i) q^{49} +(-734.467 + 2017.93i) q^{50} +(204.143 - 1157.75i) q^{52} +1535.13i q^{53} -3082.26 q^{55} +(-222.974 - 39.3164i) q^{56} +(8803.55 + 3204.23i) q^{58} +(-1352.46 - 1611.80i) q^{59} +(-1362.35 + 495.855i) q^{61} +(4027.36 + 2325.20i) q^{62} +(-3056.17 - 5293.44i) q^{64} +(-594.974 + 709.063i) q^{65} +(-1241.97 - 7043.56i) q^{67} +(-9436.84 + 1663.97i) q^{68} +(579.476 + 486.238i) q^{70} +(2436.79 - 1406.88i) q^{71} +(-2132.26 + 3693.19i) q^{73} +(1057.14 + 2904.48i) q^{74} +(-7493.38 + 6287.69i) q^{76} +(483.054 - 1327.18i) q^{77} +(-992.133 + 5626.67i) q^{79} +2517.31i q^{80} -3472.36 q^{82} +(-4026.67 - 710.011i) q^{83} +(7089.69 + 2580.44i) q^{85} +(-4339.49 - 5171.60i) q^{86} +(-5268.48 + 1917.57i) q^{88} +(-5385.27 - 3109.19i) q^{89} +(-212.068 - 367.312i) q^{91} +(-6981.30 + 8319.99i) q^{92} +(168.210 + 953.968i) q^{94} +(7584.75 - 1337.40i) q^{95} +(7112.63 + 5968.20i) q^{97} +(12336.4 - 7122.44i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

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