LMFDB - Embedded newform 81.5.f.a.17.8

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			17.8
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40615 - 3.86336i) q^{2} +(-0.691617 - 0.580335i) q^{4} +(11.8424 + 2.08814i) q^{5} +(13.5416 - 11.3628i) q^{7} +(53.7534 - 31.0345i) q^{8} +(24.7194 - 42.8153i) q^{10} +(-10.9334 + 1.92785i) q^{11} +(272.944 - 99.3436i) q^{13} +(-24.8570 - 68.2939i) q^{14} +(-46.8208 - 265.534i) q^{16} +(-329.418 - 190.190i) q^{17} +(72.9105 + 126.285i) q^{19} +(-6.97859 - 8.31676i) q^{20} +(-7.92598 + 44.9505i) q^{22} +(57.0807 - 68.0262i) q^{23} +(-451.426 - 164.305i) q^{25} -1194.17i q^{26} -15.9598 q^{28} +(-310.157 + 852.151i) q^{29} +(663.014 + 556.335i) q^{31} +(-113.675 - 20.0439i) q^{32} +(-1197.98 + 1005.23i) q^{34} +(184.092 - 106.286i) q^{35} +(398.049 - 689.441i) q^{37} +(590.407 - 104.105i) q^{38} +(701.374 - 255.279i) q^{40} +(612.946 + 1684.06i) q^{41} +(-253.959 - 1440.27i) q^{43} +(8.68051 + 5.01170i) q^{44} +(-182.546 - 316.179i) q^{46} +(2547.10 + 3035.52i) q^{47} +(-362.666 + 2056.78i) q^{49} +(-1269.54 + 1512.98i) q^{50} +(-246.425 - 89.6915i) q^{52} +526.213i q^{53} -133.503 q^{55} +(375.270 - 1031.04i) q^{56} +(2856.04 + 2396.50i) q^{58} +(-6213.52 - 1095.61i) q^{59} +(-5105.31 + 4283.86i) q^{61} +(3081.62 - 1779.17i) q^{62} +(1919.76 - 3325.13i) q^{64} +(3439.76 - 606.522i) q^{65} +(-5993.11 + 2181.31i) q^{67} +(117.457 + 322.711i) q^{68} +(-151.759 - 860.669i) q^{70} +(-1965.51 - 1134.79i) q^{71} +(-3190.17 - 5525.54i) q^{73} +(-2103.84 - 2507.26i) q^{74} +(22.8613 - 129.653i) q^{76} +(-126.150 + 150.340i) q^{77} +(8933.61 + 3251.57i) q^{79} -3242.33i q^{80} +7368.01 q^{82} +(905.297 - 2487.28i) q^{83} +(-3503.96 - 2940.17i) q^{85} +(-5921.41 - 1044.10i) q^{86} +(-527.876 + 442.941i) q^{88} +(-4547.60 + 2625.56i) q^{89} +(2567.29 - 4446.67i) q^{91} +(-78.9560 + 13.9221i) q^{92} +(15308.9 - 5571.99i) q^{94} +(599.736 + 1647.76i) q^{95} +(-1949.57 - 11056.5i) q^{97} +(7436.14 + 4293.26i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	1.40615	−	3.86336i	0.351537	−	0.965841i	−0.630339	−	0.776320i	$-0.717084\pi$
$2$	1.40615	−	3.86336i	0.351537	−	0.965841i	0.981877	−	0.189521i	$-0.0606936\pi$
$3$		0			0
$3$		0			0
$4$	−0.691617	−	0.580335i	−0.0432260	−	0.0362710i
$5$	11.8424	+	2.08814i	0.473696	+	0.0835254i	0.405399	−	0.914140i	$-0.367132\pi$
$5$	11.8424	+	2.08814i	0.473696	+	0.0835254i	0.0682967	+	0.997665i	$0.478244\pi$
$6$		0			0
$7$	13.5416	−	11.3628i	0.276360	−	0.231893i	−0.494064	−	0.869425i	$-0.664489\pi$
$7$	13.5416	−	11.3628i	0.276360	−	0.231893i	0.770424	+	0.637532i	$0.220045\pi$
$8$	53.7534	−	31.0345i	0.839896	−	0.484914i
$9$		0			0
$10$	24.7194	−	42.8153i	0.247194	−	0.428153i
$11$	−10.9334	+	1.92785i	−0.0903585	+	0.0159326i	−0.218645	−	0.975805i	$-0.570164\pi$
$11$	−10.9334	+	1.92785i	−0.0903585	+	0.0159326i	0.128286	+	0.991737i	$0.459052\pi$
$12$		0			0
$13$	272.944	−	99.3436i	1.61505	−	0.587832i	0.632624	−	0.774459i	$-0.281978\pi$
$13$	272.944	−	99.3436i	1.61505	−	0.587832i	0.982431	+	0.186628i	$0.0597558\pi$
$14$	−24.8570	−	68.2939i	−0.126821	−	0.348438i
$15$		0			0
$16$	−46.8208	−	265.534i	−0.182894	−	1.03724i
$17$	−329.418	−	190.190i	−1.13986	−	0.658096i	−0.193460	−	0.981108i	$-0.561971\pi$
$17$	−329.418	−	190.190i	−1.13986	−	0.658096i	−0.946395	+	0.323012i	$0.895304\pi$
$18$		0			0
$19$	72.9105	+	126.285i	0.201968	+	0.349819i	0.949163	−	0.314787i	$-0.101933\pi$
$19$	72.9105	+	126.285i	0.201968	+	0.349819i	−0.747194	+	0.664606i	$0.768600\pi$
$20$	−6.97859	−	8.31676i	−0.0174465	−	0.0207919i
$21$		0			0
$22$	−7.92598	+	44.9505i	−0.0163760	+	0.0928729i
$23$	57.0807	−	68.0262i	0.107903	−	0.128594i	−0.709390	−	0.704816i	$-0.751029\pi$
$23$	57.0807	−	68.0262i	0.107903	−	0.128594i	0.817293	+	0.576222i	$0.195474\pi$
$24$		0			0
$25$	−451.426	−	164.305i	−0.722281	−	0.262889i
$26$		−	1194.17i		−	1.76653i
$27$		0			0
$28$	−15.9598			−0.0203569
$29$	−310.157	+	852.151i	−0.368796	+	1.01326i	0.607024	+	0.794683i	$0.292363\pi$
$29$	−310.157	+	852.151i	−0.368796	+	1.01326i	−0.975820	+	0.218575i	$0.929859\pi$
$30$		0			0
$31$	663.014	+	556.335i	0.689921	+	0.578912i	0.918886	−	0.394522i	$-0.129090\pi$
$31$	663.014	+	556.335i	0.689921	+	0.578912i	−0.228966	+	0.973434i	$0.573534\pi$
$32$	−113.675	−	20.0439i	−0.111010	−	0.0195741i
$33$		0			0
$34$	−1197.98	+	1005.23i	−1.03632	+	0.869574i
$35$	184.092	−	106.286i	0.150279	−	0.0867639i
$36$		0			0
$37$	398.049	−	689.441i	0.290759	−	0.503609i	−0.683231	−	0.730203i	$-0.739426\pi$
$37$	398.049	−	689.441i	0.290759	−	0.503609i	0.973989	+	0.226594i	$0.0727589\pi$
$38$	590.407	−	104.105i	0.408869	−	0.0720946i
$39$		0			0
$40$	701.374	−	255.279i	0.438358	−	0.159549i
$41$	612.946	+	1684.06i	0.364632	+	1.00182i	0.977371	+	0.211532i	$0.0678454\pi$
$41$	612.946	+	1684.06i	0.364632	+	1.00182i	−0.612739	+	0.790285i	$0.709932\pi$
$42$		0			0
$43$	−253.959	−	1440.27i	−0.137350	−	0.778948i	−0.973195	−	0.229983i	$-0.926133\pi$
$43$	−253.959	−	1440.27i	−0.137350	−	0.778948i	0.835845	−	0.548965i	$-0.184978\pi$
$44$	8.68051	+	5.01170i	0.00448373	+	0.00258869i
$45$		0			0
$46$	−182.546	−	316.179i	−0.0862693	−	0.149423i
$47$	2547.10	+	3035.52i	1.15306	+	1.37416i	0.915270	+	0.402842i	$0.131978\pi$
$47$	2547.10	+	3035.52i	1.15306	+	1.37416i	0.237787	+	0.971317i	$0.423578\pi$
$48$		0			0
$49$	−362.666	+	2056.78i	−0.151048	+	0.856636i
$50$	−1269.54	+	1512.98i	−0.507818	+	0.605193i
$51$		0			0
$52$	−246.425	−	89.6915i	−0.0911336	−	0.0331699i
$53$			526.213i			0.187331i	0.995604	+	0.0936655i	$0.0298584\pi$
$53$			526.213i			0.187331i	−0.995604	+	0.0936655i	$0.970142\pi$
$54$		0			0
$55$	−133.503			−0.0441333
$56$	375.270	−	1031.04i	0.119665	−	0.328777i
$57$		0			0
$58$	2856.04	+	2396.50i	0.849001	+	0.712397i
$59$	−6213.52	−	1095.61i	−1.78498	−	0.314740i	−0.819085	−	0.573672i	$-0.805518\pi$
$59$	−6213.52	−	1095.61i	−1.78498	−	0.314740i	−0.965895	+	0.258932i	$0.916629\pi$
$60$		0			0
$61$	−5105.31	+	4283.86i	−1.37203	+	1.15127i	−0.399966	+	0.916530i	$0.630978\pi$
$61$	−5105.31	+	4283.86i	−1.37203	+	1.15127i	−0.972059	+	0.234736i	$0.924577\pi$
$62$	3081.62	−	1779.17i	0.801670	−	0.462844i
$63$		0			0
$64$	1919.76	−	3325.13i	0.468692	−	0.811798i
$65$	3439.76	−	606.522i	0.814144	−	0.143556i
$66$		0			0
$67$	−5993.11	+	2181.31i	−1.33507	+	0.485924i	−0.908255	−	0.418417i	$-0.862585\pi$
$67$	−5993.11	+	2181.31i	−1.33507	+	0.485924i	−0.426811	+	0.904341i	$0.640363\pi$
$68$	117.457	+	322.711i	0.0254017	+	0.0697905i
$69$		0			0
$70$	−151.759	−	860.669i	−0.0309713	−	0.175647i
$71$	−1965.51	−	1134.79i	−0.389904	−	0.225111i	0.292214	−	0.956353i	$-0.405608\pi$
$71$	−1965.51	−	1134.79i	−0.389904	−	0.225111i	−0.682119	+	0.731242i	$0.738941\pi$
$72$		0			0
$73$	−3190.17	−	5525.54i	−0.598643	−	1.03688i	−0.993022	−	0.117933i	$-0.962373\pi$
$73$	−3190.17	−	5525.54i	−0.598643	−	1.03688i	0.394378	−	0.918948i	$-0.370960\pi$
$74$	−2103.84	−	2507.26i	−0.384194	−	0.457864i
$75$		0			0
$76$	22.8613	−	129.653i	0.00395799	−	0.0224469i
$77$	−126.150	+	150.340i	−0.0212768	+	0.0253567i
$78$		0			0
$79$	8933.61	+	3251.57i	1.43144	+	0.521001i	0.937344	−	0.348406i	$-0.113277\pi$
$79$	8933.61	+	3251.57i	1.43144	+	0.521001i	0.494096	+	0.869408i	$0.335499\pi$
$80$		−	3242.33i		−	0.506614i
$81$		0			0
$82$	7368.01			1.09578
$83$	905.297	−	2487.28i	0.131412	−	0.361051i	−0.856483	−	0.516175i	$-0.827355\pi$
$83$	905.297	−	2487.28i	0.131412	−	0.361051i	0.987895	+	0.155124i	$0.0495776\pi$
$84$		0			0
$85$	−3503.96	−	2940.17i	−0.484977	−	0.406944i
$86$	−5921.41	−	1044.10i	−0.800623	−	0.141171i
$87$		0			0
$88$	−527.876	+	442.941i	−0.0681658	+	0.0571979i
$89$	−4547.60	+	2625.56i	−0.574119	+	0.331468i	−0.758793	−	0.651332i	$-0.774210\pi$
$89$	−4547.60	+	2625.56i	−0.574119	+	0.331468i	0.184674	+	0.982800i	$0.440877\pi$
$90$		0			0
$91$	2567.29	−	4446.67i	0.310021	−	0.536973i
$92$	−78.9560	+	13.9221i	−0.00932845	+	0.00164486i
$93$		0			0
$94$	15308.9	−	5571.99i	1.73256	−	0.630601i
$95$	599.736	+	1647.76i	0.0664528	+	0.182577i
$96$		0			0
$97$	−1949.57	−	11056.5i	−0.207202	−	1.17510i	−0.893936	−	0.448194i	$-0.852067\pi$
$97$	−1949.57	−	11056.5i	−0.207202	−	1.17510i	0.686734	−	0.726909i	$-0.259044\pi$
$98$	7436.14	+	4293.26i	0.774275	+	0.447028i
$99$		0			0
$100$	216.861	+	375.615i	0.0216861	+	0.0375615i
$101$	1860.39	+	2217.12i	0.182373	+	0.217344i	0.849484	−	0.527615i	$-0.176914\pi$
$101$	1860.39	+	2217.12i	0.182373	+	0.217344i	−0.667111	+	0.744959i	$0.732469\pi$
$102$		0			0
$103$	−588.301	+	3336.42i	−0.0554530	+	0.314489i	−0.999900	−	0.0141756i	$-0.995488\pi$
$103$	−588.301	+	3336.42i	−0.0554530	+	0.314489i	0.944447	+	0.328665i	$0.106599\pi$
$104$	11588.6	−	13810.7i	1.07143	−	1.27688i
$105$		0			0
$106$	2032.95	+	739.934i	0.180932	+	0.0658539i
$107$		−	2849.06i		−	0.248848i	−0.992229	−	0.124424i	$-0.960292\pi$
$107$		−	2849.06i		−	0.248848i	0.992229	−	0.124424i	$-0.0397082\pi$
$108$		0			0
$109$	−4098.48			−0.344961			−0.172480	−	0.985013i	$-0.555178\pi$
$109$	−4098.48			−0.344961			−0.172480	+	0.985013i	$0.555178\pi$
$110$	−187.725	+	515.771i	−0.0155145	+	0.0426257i
$111$		0			0
$112$	−3651.23	−	3063.75i	−0.291074	−	0.244240i
$113$	−1765.41	−	311.289i	−0.138257	−	0.0243785i	0.104091	−	0.994568i	$-0.466807\pi$
$113$	−1765.41	−	311.289i	−0.138257	−	0.0243785i	−0.242348	+	0.970189i	$0.577918\pi$
$114$		0			0
$115$	818.021	−	686.401i	0.0618541	−	0.0519018i
$116$	709.043	−	409.366i	0.0526935	−	0.0304226i
$117$		0			0
$118$	−12969.9	+	22464.5i	−0.931476	+	1.61336i
$119$	−6621.93	+	1167.63i	−0.467618	+	0.0824536i
$120$		0			0
$121$	−13642.2	+	4965.36i	−0.931782	+	0.339141i
$122$	9371.29	+	25747.4i	0.629622	+	1.72987i
$123$		0			0
$124$	−135.691	−	769.541i	−0.00882484	−	0.0500482i
$125$	−11511.6	−	6646.25i	−0.736745	−	0.425360i
$126$		0			0
$127$	11399.5	+	19744.5i	0.706771	+	1.22416i	0.966048	+	0.258361i	$0.0831824\pi$
$127$	11399.5	+	19744.5i	0.706771	+	1.22416i	−0.259277	+	0.965803i	$0.583484\pi$
$128$	−11333.8	−	13507.1i	−0.691762	−	0.824410i
$129$		0			0
$130$	2493.60	−	14141.9i	0.147550	−	0.836799i
$131$	13483.3	−	16068.8i	0.785694	−	0.936354i	−0.213482	−	0.976947i	$-0.568480\pi$
$131$	13483.3	−	16068.8i	0.785694	−	0.936354i	0.999176	+	0.0405934i	$0.0129248\pi$
$132$		0			0
$133$	2422.27	+	881.634i	0.136936	+	0.0498408i
$134$			26220.8i			1.46028i
$135$		0			0
$136$	−23609.8			−1.27648
$137$	−6162.67	+	16931.8i	−0.328343	+	0.902116i	0.660188	+	0.751100i	$0.270477\pi$
$137$	−6162.67	+	16931.8i	−0.328343	+	0.902116i	−0.988531	+	0.151015i	$0.951746\pi$
$138$		0			0
$139$	1597.12	+	1340.15i	0.0826626	+	0.0693622i	0.683183	−	0.730248i	$-0.260595\pi$
$139$	1597.12	+	1340.15i	0.0826626	+	0.0693622i	−0.600520	+	0.799610i	$0.705040\pi$
$140$	−189.003	−	33.3263i	−0.00964299	−	0.00170032i
$141$		0			0
$142$	−7147.89	+	5997.79i	−0.354488	+	0.297450i
$143$	−2792.68	+	1612.36i	−0.136568	+	0.0788477i
$144$		0			0
$145$	−5452.42	+	9443.86i	−0.259330	+	0.449173i
$146$	−25833.0	+	4555.06i	−1.21191	+	0.213692i
$147$		0			0
$148$	−675.404	+	245.827i	−0.0308347	+	0.0112229i
$149$	5741.36	+	15774.3i	0.258608	+	0.710521i	0.999254	+	0.0386245i	$0.0122976\pi$
$149$	5741.36	+	15774.3i	0.258608	+	0.710521i	−0.740645	+	0.671896i	$0.765480\pi$
$150$		0			0
$151$	736.148	+	4174.90i	0.0322858	+	0.183102i	0.996686	−	0.0813454i	$-0.0259217\pi$
$151$	736.148	+	4174.90i	0.0322858	+	0.183102i	−0.964400	+	0.264447i	$0.914811\pi$
$152$	7838.37	+	4525.49i	0.339265	+	0.195875i
$153$		0			0
$154$	403.431	+	698.763i	0.0170109	+	0.0294638i
$155$	6689.98	+	7972.80i	0.278459	+	0.331854i
$156$		0			0
$157$	2487.47	−	14107.1i	0.100916	−	0.572321i	−0.891858	−	0.452316i	$-0.850598\pi$
$157$	2487.47	−	14107.1i	0.100916	−	0.572321i	0.992773	−	0.120005i	$-0.0382910\pi$
$158$	25124.0	−	29941.6i	1.00641	−	1.19939i
$159$		0			0
$160$	−1304.33	−	474.736i	−0.0509503	−	0.0185444i
$161$		−	1569.78i		−	0.0605601i
$162$		0			0
$163$	7997.10			0.300994			0.150497	−	0.988611i	$-0.451913\pi$
$163$	7997.10			0.300994			0.150497	+	0.988611i	$0.451913\pi$
$164$	553.393	−	1520.43i	0.0205753	−	0.0565301i
$165$		0			0
$166$	−8336.29	−	6994.98i	−0.302522	−	0.253846i
$167$	−1555.28	−	274.238i	−0.0557668	−	0.00983318i	0.145695	−	0.989330i	$-0.453458\pi$
$167$	−1555.28	−	274.238i	−0.0557668	−	0.00983318i	−0.201462	+	0.979496i	$0.564569\pi$
$168$		0			0
$169$	42750.4	−	35871.8i	1.49681	−	1.25597i
$170$	−16286.1	+	9402.76i	−0.563531	+	0.325355i
$171$		0			0
$172$	−660.200	+	1143.50i	−0.0223161	+	0.0386526i
$173$	27390.5	−	4829.68i	0.915183	−	0.161371i	0.303827	−	0.952727i	$-0.401736\pi$
$173$	27390.5	−	4829.68i	0.915183	−	0.161371i	0.611356	+	0.791356i	$0.290624\pi$
$174$		0			0
$175$	−7980.00	+	2904.48i	−0.260571	+	0.0948402i
$176$	1023.82	+	2812.92i	0.0330520	+	0.0908097i
$177$		0			0
$178$	3748.88	+	21260.9i	0.118321	+	0.671031i
$179$	14349.2	+	8284.51i	0.447839	+	0.258560i	0.706917	−	0.707297i	$-0.250085\pi$
$179$	14349.2	+	8284.51i	0.447839	+	0.258560i	−0.259078	+	0.965856i	$0.583419\pi$
$180$		0			0
$181$	9509.33	+	16470.6i	0.290264	+	0.502752i	0.973872	−	0.227097i	$-0.0729236\pi$
$181$	9509.33	+	16470.6i	0.290264	+	0.502752i	−0.683608	+	0.729849i	$0.739590\pi$
$182$	−13569.1	−	16171.1i	−0.409646	−	0.488198i
$183$		0			0
$184$	957.122	−	5428.11i	0.0282704	−	0.160329i
$185$	6153.50	−	7333.46i	0.179796	−	0.214272i
$186$		0			0
$187$	3968.31	+	1444.35i	0.113481	+	0.0413037i
$188$		−	3577.59i		−	0.101222i
$189$		0			0
$190$	7209.22			0.199701
$191$	22067.8	−	60630.8i	0.604912	−	1.66198i	−0.136265	−	0.990672i	$-0.543510\pi$
$191$	22067.8	−	60630.8i	0.604912	−	1.66198i	0.741177	−	0.671310i	$-0.234268\pi$
$192$		0			0
$193$	−12350.6	−	10363.4i	−0.331568	−	0.278219i	0.461770	−	0.886999i	$-0.347214\pi$
$193$	−12350.6	−	10363.4i	−0.331568	−	0.278219i	−0.793338	+	0.608781i	$0.791659\pi$
$194$	−45456.8	−	8015.26i	−1.20780	−	0.212968i
$195$		0			0
$196$	1444.45	−	1212.04i	0.0376002	−	0.0315503i
$197$	12811.1	−	7396.48i	0.330106	−	0.190587i	−0.325782	−	0.945445i	$-0.605628\pi$
$197$	12811.1	−	7396.48i	0.330106	−	0.190587i	0.655888	+	0.754858i	$0.272294\pi$
$198$		0			0
$199$	29055.3	−	50325.3i	0.733702	−	1.27081i	−0.221588	−	0.975140i	$-0.571124\pi$
$199$	29055.3	−	50325.3i	0.733702	−	1.27081i	0.955290	−	0.295669i	$-0.0955425\pi$
$200$	−29364.8	+	5177.81i	−0.734120	+	0.129445i
$201$		0			0
$202$	11181.5	−	4069.74i	0.274030	−	0.0997388i
$203$	5482.75	+	15063.7i	0.133047	+	0.365545i
$204$		0			0
$205$	3742.22	+	21223.2i	0.0890474	+	0.505013i
$206$	12062.6	+	6964.32i	0.284253	+	0.164114i
$207$		0			0
$208$	−39158.6	−	67824.6i	−0.905107	−	1.56769i
$209$	−1040.62	−	1240.16i	−0.0238231	−	0.0283913i
$210$		0			0
$211$	−6871.82	+	38972.0i	−0.154350	+	0.875363i	0.805028	+	0.593237i	$0.202150\pi$
$211$	−6871.82	+	38972.0i	−0.154350	+	0.875363i	−0.959378	+	0.282125i	$0.908961\pi$
$212$	305.380	−	363.938i	0.00679468	−	0.00809758i
$213$		0			0
$214$	−11006.9	−	4006.20i	−0.240347	−	0.0874793i
$215$		−	17586.6i		−	0.380457i
$216$		0			0
$217$	15299.8			0.324912
$218$	−5763.07	+	15833.9i	−0.121267	+	0.333177i
$219$		0			0
$220$	92.3330	+	77.4766i	0.00190771	+	0.00160076i
$221$	−108807.	−	19185.6i	−2.22778	−	0.392817i
$222$		0			0
$223$	31137.8	−	26127.7i	0.626149	−	0.525401i	−0.273581	−	0.961849i	$-0.588208\pi$
$223$	31137.8	−	26127.7i	0.626149	−	0.525401i	0.899730	+	0.436448i	$0.143764\pi$
$224$	−1767.09	+	1020.23i	−0.0352179	+	0.0203331i
$225$		0			0
$226$	−3685.04	+	6382.68i	−0.0721483	+	0.124964i
$227$	38926.8	−	6863.84i	0.755434	−	0.133203i	0.217349	−	0.976094i	$-0.430259\pi$
$227$	38926.8	−	6863.84i	0.755434	−	0.133203i	0.538085	+	0.842891i	$0.319148\pi$
$228$		0			0
$229$	−188.164	+	68.4859i	−0.00358810	+	0.00130596i	−0.343814	−	0.939038i	$-0.611719\pi$
$229$	−188.164	+	68.4859i	−0.00358810	+	0.00130596i	0.340225	+	0.940344i	$0.389497\pi$
$230$	−1501.56	−	4125.50i	−0.0283848	−	0.0779867i
$231$		0			0
$232$	9774.08	+	55431.6i	0.181593	+	1.02987i
$233$	−49625.0	−	28651.0i	−0.914090	−	0.527750i	−0.0323454	−	0.999477i	$-0.510298\pi$
$233$	−49625.0	−	28651.0i	−0.914090	−	0.527750i	−0.881745	+	0.471726i	$0.843631\pi$
$234$		0			0
$235$	23825.2	+	41266.5i	0.431421	+	0.747244i
$236$	3661.55	+	4363.67i	0.0657417	+	0.0783479i
$237$		0			0
$238$	−4800.47	+	27224.8i	−0.0847480	+	0.480630i
$239$	−10020.5	+	11941.9i	−0.175426	+	0.209064i	−0.846592	−	0.532243i	$-0.821349\pi$
$239$	−10020.5	+	11941.9i	−0.175426	+	0.209064i	0.671166	+	0.741307i	$0.265794\pi$
$240$		0			0
$241$	−105374.	−	38353.0i	−1.81426	−	0.660336i	−0.996387	−	0.0849336i	$-0.972932\pi$
$241$	−105374.	−	38353.0i	−1.81426	−	0.660336i	−0.817871	−	0.575402i	$-0.804846\pi$
$242$			59686.9i			1.01917i
$243$		0			0
$244$	6016.99			0.101065
$245$	−8589.68	+	23600.0i	−0.143102	+	0.393169i
$246$		0			0
$247$	32446.1	+	27225.5i	0.531824	+	0.446254i
$248$	52904.8	+	9328.54i	0.860185	+	0.151674i
$249$		0			0
$250$	−41864.0	+	35128.1i	−0.669824	+	0.562049i
$251$	53491.8	−	30883.5i	0.849063	−	0.490207i	−0.0112713	−	0.999936i	$-0.503588\pi$
$251$	53491.8	−	30883.5i	0.849063	−	0.490207i	0.860335	+	0.509730i	$0.170255\pi$
$252$		0			0
$253$	−492.941	+	853.799i	−0.00770112	+	0.0133387i
$254$	92309.8	−	16276.7i	1.43080	−	0.252289i
$255$		0			0
$256$	−10392.5	+	3782.56i	−0.158577	+	0.0577172i
$257$	26987.4	+	74147.4i	0.408597	+	1.12261i	0.957929	+	0.287007i	$0.0926603\pi$
$257$	26987.4	+	74147.4i	0.408597	+	1.12261i	−0.549331	+	0.835605i	$0.685118\pi$
$258$		0			0
$259$	−2443.73	−	13859.1i	−0.0364295	−	0.206602i
$260$	−2730.98	−	1576.73i	−0.0403991	−	0.0233244i
$261$		0			0
$262$	−43120.0	−	74686.0i	−0.628168	−	1.08802i
$263$	63507.9	+	75685.7i	0.918155	+	1.09421i	0.995266	+	0.0971921i	$0.0309861\pi$
$263$	63507.9	+	75685.7i	0.918155	+	1.09421i	−0.0771106	+	0.997023i	$0.524569\pi$
$264$		0			0
$265$	−1098.80	+	6231.63i	−0.0156469	+	0.0887380i
$266$	6812.15	−	8118.40i	0.0962766	−	0.114738i
$267$		0			0
$268$	5410.83	+	1969.38i	0.0753346	+	0.0274195i
$269$		−	119957.i		−	1.65775i	−0.559431	−	0.828877i	$-0.688980\pi$
$269$		−	119957.i		−	1.65775i	0.559431	−	0.828877i	$-0.311020\pi$
$270$		0			0
$271$	5304.88			0.0722333			0.0361166	−	0.999348i	$-0.488501\pi$
$271$	5304.88			0.0722333			0.0361166	+	0.999348i	$0.488501\pi$
$272$	−35078.2	+	96376.6i	−0.474132	+	1.30267i
$273$		0			0
$274$	56748.1	+	47617.3i	0.755875	+	0.634255i
$275$	5252.37	+	926.134i	0.0694528	+	0.0122464i
$276$		0			0
$277$	−44362.4	+	37224.5i	−0.578170	+	0.485142i	−0.884346	−	0.466833i	$-0.845395\pi$
$277$	−44362.4	+	37224.5i	−0.578170	+	0.485142i	0.306176	+	0.951975i	$0.400951\pi$
$278$	7423.27	−	4285.83i	0.0960518	−	0.0554555i
$279$		0			0
$280$	6597.05	−	11426.4i	0.0841461	−	0.145745i
$281$	−77732.3	+	13706.3i	−0.984439	+	0.173583i	−0.642622	−	0.766183i	$-0.722153\pi$
$281$	−77732.3	+	13706.3i	−0.984439	+	0.173583i	−0.341817	+	0.939767i	$0.611042\pi$
$282$		0			0
$283$	30816.1	−	11216.2i	0.384774	−	0.140046i	−0.142389	−	0.989811i	$-0.545478\pi$
$283$	30816.1	−	11216.2i	0.384774	−	0.140046i	0.527162	+	0.849765i	$0.323256\pi$
$284$	700.821	+	1925.49i	0.00868901	+	0.0238729i
$285$		0			0
$286$	2302.19	+	13056.4i	0.0281455	+	0.159621i
$287$	27435.8	+	15840.1i	0.333084	+	0.192306i
$288$		0			0
$289$	30583.7	+	52972.5i	0.366180	+	0.634242i
$290$	28818.2	+	34344.2i	0.342665	+	0.408373i
$291$		0			0
$292$	−1000.29	+	5672.92i	−0.0117317	+	0.0665336i
$293$	−73359.6	+	87426.6i	−0.854519	+	1.01838i	0.145061	+	0.989423i	$0.453662\pi$
$293$	−73359.6	+	87426.6i	−0.854519	+	1.01838i	−0.999581	+	0.0289539i	$0.990782\pi$
$294$		0			0
$295$	−71295.2	−	25949.3i	−0.819250	−	0.298182i
$296$		−	49413.0i		−	0.563973i
$297$		0			0
$298$	69015.0			0.777161
$299$	8821.89	−	24237.9i	0.0986778	−	0.271115i
$300$		0			0
$301$	−19804.5	−	16618.0i	−0.218590	−	0.183419i
$302$	17164.3	+	3026.53i	0.188197	+	0.0331842i
$303$		0			0
$304$	30119.2	−	25273.0i	0.325908	−	0.273470i
$305$	−69404.4	+	40070.6i	−0.746083	+	0.430751i
$306$		0			0
$307$	−17813.7	+	30854.2i	−0.189006	+	0.327369i	−0.944919	−	0.327304i	$-0.893860\pi$
$307$	−17813.7	+	30854.2i	−0.189006	+	0.327369i	0.755913	+	0.654672i	$0.227193\pi$
$308$	174.495	−	30.7681i	0.00183942	−	0.000324340i
$309$		0			0
$310$	40208.9	−	14634.9i	0.418407	−	0.152288i
$311$	−695.964	−	1912.14i	−0.00719558	−	0.0197697i	0.936043	−	0.351886i	$-0.114460\pi$
$311$	−695.964	−	1912.14i	−0.00719558	−	0.0197697i	−0.943238	+	0.332116i	$0.892237\pi$
$312$		0			0
$313$	−22695.2	−	128711.i	−0.231657	−	1.31379i	−0.849541	−	0.527523i	$-0.823121\pi$
$313$	−22695.2	−	128711.i	−0.231657	−	1.31379i	0.617884	−	0.786269i	$-0.287990\pi$
$314$	−51003.3	−	29446.7i	−0.517295	−	0.298661i
$315$		0			0
$316$	−4291.64	−	7433.33i	−0.0429782	−	0.0744405i
$317$	−19846.0	−	23651.5i	−0.197494	−	0.235364i	0.658204	−	0.752840i	$-0.271316\pi$
$317$	−19846.0	−	23651.5i	−0.197494	−	0.235364i	−0.855698	+	0.517475i	$0.826872\pi$
$318$		0			0
$319$	1748.25	−	9914.83i	0.0171800	−	0.0974325i
$320$	29677.9	−	35368.8i	0.289823	−	0.345398i
$321$		0			0
$322$	−6064.63	−	2207.34i	−0.0584915	−	0.0212891i
$323$		−	55467.3i		−	0.531657i
$324$		0			0
$325$	−139537.			−1.32106
$326$	11245.1	−	30895.7i	0.105810	−	0.290712i
$327$		0			0
$328$	85211.8	+	71501.2i	0.792049	+	0.664608i
$329$	68983.8	+	12163.7i	0.637316	+	0.112376i
$330$		0			0
$331$	−66829.8	+	56076.9i	−0.609978	+	0.511832i	−0.894635	−	0.446797i	$-0.852565\pi$
$331$	−66829.8	+	56076.9i	−0.609978	+	0.511832i	0.284657	+	0.958629i	$0.408120\pi$
$332$	−2069.58	+	1194.87i	−0.0187761	+	0.0108404i
$333$		0			0
$334$	−3246.43	+	5622.99i	−0.0291014	+	0.0504051i
$335$	−75527.7	+	13317.6i	−0.673003	+	0.118669i
$336$		0			0
$337$	−29849.5	+	10864.3i	−0.262832	+	0.0956629i	−0.470075	−	0.882627i	$-0.655773\pi$
$337$	−29849.5	+	10864.3i	−0.262832	+	0.0956629i	0.207243	+	0.978289i	$0.433551\pi$
$338$	−78472.5	−	215602.i	−0.686885	−	1.88720i
$339$		0			0
$340$	717.112	+	4066.95i	0.00620339	+	0.0351812i
$341$	−8321.51	−	4804.43i	−0.0715638	−	0.0413174i
$342$		0			0
$343$	39681.3	+	68730.0i	0.337285	+	0.584195i
$344$	−58349.4	−	69538.1i	−0.493082	−	0.587633i
$345$		0			0
$346$	19856.3	−	112611.i	0.165862	−	0.940649i
$347$	−22788.4	+	27158.1i	−0.189258	+	0.225549i	−0.852327	−	0.523010i	$-0.824809\pi$
$347$	−22788.4	+	27158.1i	−0.189258	+	0.225549i	0.663069	+	0.748558i	$0.269254\pi$
$348$		0			0
$349$	116640.	+	42453.6i	0.957630	+	0.348549i	0.773104	−	0.634279i	$-0.218703\pi$
$349$	116640.	+	42453.6i	0.957630	+	0.348549i	0.184526	+	0.982828i	$0.440925\pi$
$350$			34913.8i			0.285010i
$351$		0			0
$352$	1281.49			0.0103426
$353$	28678.2	−	78792.8i	0.230146	−	0.632320i	−0.769837	−	0.638241i	$-0.779662\pi$
$353$	28678.2	−	78792.8i	0.230146	−	0.632320i	0.999982	+	0.00592061i	$0.00188460\pi$
$354$		0			0
$355$	−20906.7	−	17542.8i	−0.165894	−	0.139201i
$356$	4668.90	+	823.252i	0.0368395	+	0.00649580i
$357$		0			0
$358$	52183.2	−	43786.9i	0.407160	−	0.341648i
$359$	105317.	−	60804.8i	0.817165	−	0.471790i	−0.0322729	−	0.999479i	$-0.510275\pi$
$359$	105317.	−	60804.8i	0.817165	−	0.471790i	0.849438	+	0.527689i	$0.176941\pi$
$360$		0			0
$361$	54528.6	−	94446.3i	0.418418	−	0.724721i
$362$	77003.7	−	13577.8i	0.587617	−	0.103613i
$363$		0			0
$364$	−4356.14	+	1585.51i	−0.0328775	+	0.0119664i
$365$	−26241.2	−	72097.2i	−0.196969	−	0.541169i
$366$		0			0
$367$	−9551.45	−	54169.0i	−0.0709149	−	0.402178i	−0.999516	−	0.0310995i	$-0.990099\pi$
$367$	−9551.45	−	54169.0i	−0.0709149	−	0.402178i	0.928601	−	0.371079i	$-0.121012\pi$
$368$	−20735.8	−	11971.8i	−0.153118	−	0.0884026i
$369$		0			0
$370$	−19679.1	−	34085.2i	−0.143748	−	0.248978i
$371$	5979.23	+	7125.77i	0.0434408	+	0.0517707i
$372$		0			0
$373$	4192.29	−	23775.7i	0.0301324	−	0.170889i	−0.966028	−	0.258438i	$-0.916792\pi$
$373$	4192.29	−	23775.7i	0.0301324	−	0.170889i	0.996160	+	0.0875486i	$0.0279033\pi$
$374$	11160.1	−	13300.1i	0.0797855	−	0.0950847i
$375$		0			0
$376$	231121.	+	84121.2i	1.63480	+	0.595018i
$377$			263402.i			1.85326i
$378$		0			0
$379$	75720.5			0.527151			0.263575	−	0.964639i	$-0.415098\pi$
$379$	75720.5			0.527151			0.263575	+	0.964639i	$0.415098\pi$
$380$	541.467	−	1487.67i	0.00374977	−	0.0103024i
$381$		0			0
$382$	−203208.	−	170512.i	−1.39256	−	1.16850i
$383$	180897.	+	31897.0i	1.23320	+	0.217446i	0.751999	−	0.659165i	$-0.229090\pi$
$383$	180897.	+	31897.0i	1.23320	+	0.217446i	0.481200	+	0.876611i	$0.340201\pi$
$384$		0			0
$385$	−1807.85	+	1516.97i	−0.0121967	+	0.0102342i
$386$	−57404.2	+	33142.3i	−0.385273	+	0.222438i
$387$		0			0
$388$	−5068.15	+	8778.29i	−0.0336656	+	0.0583104i
$389$	−4172.15	+	735.663i	−0.0275715	+	0.00486161i	−0.187417	−	0.982280i	$-0.560012\pi$
$389$	−4172.15	+	735.663i	−0.0275715	+	0.00486161i	0.159845	+	0.987142i	$0.448900\pi$
$390$		0			0
$391$	−31741.3	+	11552.9i	−0.207621	+	0.0755678i
$392$	44336.7	+	121814.i	0.288530	+	0.792731i
$393$		0			0
$394$	−10561.0	−	59894.4i	−0.0680319	−	0.385828i
$395$	99005.7	+	57161.0i	0.634551	+	0.366358i
$396$		0			0
$397$	3127.34	+	5416.72i	0.0198424	+	0.0343681i	0.875776	−	0.482718i	$-0.160350\pi$
$397$	3127.34	+	5416.72i	0.0198424	+	0.0343681i	−0.855934	+	0.517086i	$0.827017\pi$
$398$	−153569.	−	183016.i	−0.969476	−	1.15538i
$399$		0			0
$400$	−22492.6	+	127562.i	−0.140579	+	0.797261i
$401$	−114476.	+	136427.i	−0.711910	+	0.848422i	−0.993818	−	0.111020i	$-0.964588\pi$
$401$	−114476.	+	136427.i	−0.711910	+	0.848422i	0.281908	+	0.959441i	$0.409033\pi$
$402$		0			0
$403$	236234.	+	85982.1i	1.45456	+	0.529417i
$404$		−	2613.05i		−	0.0160097i
$405$		0			0
$406$	65906.3			0.399830
$407$	−3022.88	+	8305.30i	−0.0182487	+	0.0501379i
$408$		0			0
$409$	−180496.	−	151454.i	−1.07900	−	0.905389i	−0.0831628	−	0.996536i	$-0.526502\pi$
$409$	−180496.	−	151454.i	−1.07900	−	0.905389i	−0.995837	+	0.0911473i	$0.970947\pi$
$410$	87255.0	+	15385.4i	0.519066	+	0.0915253i
$411$		0			0
$412$	2343.12	−	1966.11i	0.0138038	−	0.0115828i
$413$	−96590.2	+	55766.4i	−0.566282	+	0.326943i
$414$		0			0
$415$	15914.7	−	27565.0i	0.0924063	−	0.160052i
$416$	−33018.1	+	5821.98i	−0.190794	+	0.0336421i
$417$		0			0
$418$	−6254.45	+	2276.43i	−0.0357961	+	0.0130287i
$419$	−81688.7	−	224438.i	−0.465301	−	1.27840i	−0.921449	−	0.388500i	$-0.872993\pi$
$419$	−81688.7	−	224438.i	−0.465301	−	1.27840i	0.456148	−	0.889904i	$-0.349229\pi$
$420$		0			0
$421$	22489.4	+	127544.i	0.126886	+	0.719606i	0.980170	+	0.198159i	$0.0634964\pi$
$421$	22489.4	+	127544.i	0.126886	+	0.719606i	−0.853284	+	0.521447i	$0.825393\pi$
$422$	140900.	+	81348.8i	0.791201	+	0.456800i
$423$		0			0
$424$	16330.8	+	28285.7i	0.0908395	+	0.157339i
$425$	117459.	+	139982.i	0.650290	+	0.774985i
$426$		0			0
$427$	−20457.6	+	116021.i	−0.112202	+	0.636327i
$428$	−1653.41	+	1970.46i	−0.00902594	+	0.0107567i
$429$		0			0
$430$	−67943.5	−	24729.4i	−0.367461	−	0.133745i
$431$			200264.i			1.07807i	0.842283	+	0.539036i	$0.181211\pi$
$431$			200264.i			1.07807i	−0.842283	+	0.539036i	$0.818789\pi$
$432$		0			0
$433$	−280494.			−1.49606			−0.748028	−	0.663667i	$-0.768999\pi$
$433$	−280494.			−1.49606			−0.748028	+	0.663667i	$0.768999\pi$
$434$	21513.8	−	59108.6i	0.114219	−	0.313813i
$435$		0			0
$436$	2834.57	+	2378.49i	0.0149113	+	0.0125120i
$437$	12752.4	+	2248.60i	0.0667776	+	0.0117747i
$438$		0			0
$439$	−98639.1	+	82768.1i	−0.511823	+	0.429471i	−0.861770	−	0.507299i	$-0.830644\pi$
$439$	−98639.1	+	82768.1i	−0.511823	+	0.429471i	0.349947	+	0.936770i	$0.386200\pi$
$440$	−7176.25	+	4143.21i	−0.0370674	+	0.0214009i
$441$		0			0
$442$	−227120.	+	393383.i	−1.16255	+	2.01359i
$443$	−197872.	+	34890.1i	−1.00827	+	0.177785i	−0.653305	−	0.757095i	$-0.726618\pi$
$443$	−197872.	+	34890.1i	−1.00827	+	0.177785i	−0.354964	+	0.934880i	$0.615507\pi$
$444$		0			0
$445$	−59337.0	+	21596.9i	−0.299644	+	0.109061i
$446$	−57156.4	−	157036.i	−0.287339	−	0.789459i
$447$		0			0
$448$	−11785.9	−	66841.4i	−0.0587230	−	0.333035i
$449$	73795.8	+	42606.0i	0.366049	+	0.211338i	0.671731	−	0.740795i	$-0.265551\pi$
$449$	73795.8	+	42606.0i	0.366049	+	0.211338i	−0.305682	+	0.952134i	$0.598884\pi$
$450$		0			0
$451$	−9948.18	−	17230.8i	−0.0489092	−	0.0847132i
$452$	1040.33	+	1239.82i	0.00509208	+	0.00606850i
$453$		0			0
$454$	28219.3	−	160040.i	0.136910	−	0.776455i
$455$	39688.1	−	47298.5i	0.191707	−	0.228467i
$456$		0			0
$457$	48536.5	+	17665.8i	0.232400	+	0.0845866i	0.455595	−	0.890187i	$-0.349427\pi$
$457$	48536.5	+	17665.8i	0.232400	+	0.0845866i	−0.223195	+	0.974774i	$0.571649\pi$
$458$			823.246i			0.00392463i
$459$		0			0
$460$	−964.100			−0.00455624
$461$	50708.6	−	139321.i	0.238605	−	0.655563i	−0.761369	−	0.648319i	$-0.775472\pi$
$461$	50708.6	−	139321.i	0.238605	−	0.655563i	0.999974	−	0.00724317i	$-0.00230559\pi$
$462$		0			0
$463$	211282.	+	177287.i	0.985602	+	0.827018i	0.984925	−	0.172982i	$-0.0553402\pi$
$463$	211282.	+	177287.i	0.985602	+	0.827018i	0.000676500		1.00000i	$0.499785\pi$
$464$	240797.	+	42459.0i	1.11845	+	0.197212i
$465$		0			0
$466$	−180470.	+	151432.i	−0.831060	+	0.697342i
$467$	−240247.	+	138707.i	−1.10160	+	0.636010i	−0.936641	−	0.350290i	$-0.886083\pi$
$467$	−240247.	+	138707.i	−1.10160	+	0.636010i	−0.164961	+	0.986300i	$0.552750\pi$
$468$		0			0
$469$	−56370.6	+	97636.8i	−0.256276	+	0.443882i
$470$	192929.	−	34018.7i	0.873379	−	0.154000i
$471$		0			0
$472$	−367999.	+	133941.i	−1.65182	+	0.601214i
$473$	5553.27	+	15257.5i	0.0248214	+	0.0681962i
$474$		0			0
$475$	−12164.4	−	68987.7i	−0.0539142	−	0.305763i
$476$	5257.45	+	3035.39i	0.0232039	+	0.0133968i
$477$		0			0
$478$	32045.8	+	55504.9i	0.140254	+	0.242927i
$479$	−191385.	−	228084.i	−0.834136	−	0.994085i	−0.999969	−	0.00793071i	$-0.997476\pi$
$479$	−191385.	−	228084.i	−0.834136	−	0.994085i	0.165832	−	0.986154i	$-0.446969\pi$
$480$		0			0
$481$	40153.6	−	227722.i	0.173554	−	0.984273i
$482$	−296343.	+	353168.i	−1.27556	+	1.52015i
$483$		0			0
$484$	12316.8	+	4482.93i	0.0525782	+	0.0191369i
$485$		−	135007.i		−	0.573948i
$486$		0			0
$487$	37822.8			0.159476			0.0797381	−	0.996816i	$-0.474592\pi$
$487$	37822.8			0.159476			0.0797381	+	0.996816i	$0.474592\pi$
$488$	−141480.	+	388713.i	−0.594094	+	1.63226i
$489$		0			0
$490$	79096.9	+	66370.2i	0.329433	+	0.276427i
$491$	309745.	+	54616.3i	1.28482	+	0.226548i	0.774024	−	0.633157i	$-0.218241\pi$
$491$	309745.	+	54616.3i	1.28482	+	0.226548i	0.510792	+	0.859704i	$0.329352\pi$
$492$		0			0
$493$	264242.	−	221725.i	1.08720	−	0.912265i
$494$	150806.	−	87067.9i	0.617966	−	0.356783i
$495$		0			0
$496$	116683.	−	202101.i	0.474290	−	0.821494i
$497$	−39510.4	+	6966.76i	−0.159955	+	0.0282045i
$498$		0			0
$499$	280957.	−	102260.i	1.12834	−	0.410681i	0.290648	−	0.956830i	$-0.406129\pi$
$499$	280957.	−	102260.i	1.12834	−	0.410681i	0.837688	+	0.546150i	$0.183907\pi$
$500$	4104.59	+	11277.3i	0.0164184	+	0.0451091i
$501$		0			0
$502$	−44096.8	−	250085.i	−0.174984	−	0.992386i
$503$	−300466.	−	173474.i	−1.18757	−	0.685644i	−0.229817	−	0.973234i	$-0.573813\pi$
$503$	−300466.	−	173474.i	−1.18757	−	0.685644i	−0.957754	+	0.287590i	$0.907146\pi$
$504$		0			0
$505$	17401.8	+	30140.8i	0.0682356	+	0.118188i
$506$	2605.39	+	3104.98i	0.0101759	+	0.0121271i
$507$		0			0
$508$	3574.36	−	20271.2i	0.0138507	−	0.0785510i
$509$	189996.	−	226428.i	0.733344	−	0.873965i	−0.262510	−	0.964929i	$-0.584550\pi$
$509$	189996.	−	226428.i	0.733344	−	0.873965i	0.995854	+	0.0909638i	$0.0289948\pi$
$510$		0			0
$511$	−105985.	−	38575.6i	−0.405886	−	0.147731i
$512$		−	236648.i		−	0.902741i
$513$		0			0
$514$	324407.			1.22790
$515$	−13933.8	+	38282.8i	−0.0525357	+	0.144341i
$516$		0			0
$517$	−33700.5	−	28278.0i	−0.126083	−	0.105796i
$518$	−56978.9	−	10046.9i	−0.212351	−	0.0374432i
$519$		0			0
$520$	166075.	−	139354.i	0.614185	−	0.515362i
$521$	351292.	−	202819.i	1.29417	−	0.747192i	0.314783	−	0.949164i	$-0.398068\pi$
$521$	351292.	−	202819.i	1.29417	−	0.747192i	0.979391	+	0.201971i	$0.0647348\pi$
$522$		0			0
$523$	90472.8	−	156703.i	0.330761	−	0.572895i	−0.651900	−	0.758305i	$-0.726028\pi$
$523$	90472.8	−	156703.i	0.330761	−	0.572895i	0.982661	+	0.185410i	$0.0593612\pi$
$524$	−18650.5	+	3288.59i	−0.0679249	+	0.0119770i
$525$		0			0
$526$	381703.	−	138929.i	1.37960	−	0.502135i
$527$	−112600.	−	309365.i	−0.405430	−	1.11391i
$528$		0			0
$529$	47224.5	+	267824.i	0.168755	+	0.957056i
$530$	22530.0	+	13007.7i	0.0802063	+	0.0463072i
$531$		0			0
$532$	−1163.64	−	2015.48i	−0.00411145	−	0.00712124i
$533$	334600.	+	398761.i	1.17780	+	1.40365i
$534$		0			0
$535$	5949.22	−	33739.7i	0.0207851	−	0.117878i
$536$	−254454.	+	303246.i	−0.885685	+	1.05552i
$537$		0			0
$538$	−463437.	−	168677.i	−1.60113	−	0.582763i
$539$		−	23186.8i		−	0.0798110i
$540$		0			0
$541$	49286.0			0.168395			0.0841975	−	0.996449i	$-0.473167\pi$
$541$	49286.0			0.168395			0.0841975	+	0.996449i	$0.473167\pi$
$542$	7459.46	−	20494.7i	0.0253927	−	0.0697658i
$543$		0			0
$544$	33634.3	+	28222.6i	0.113654	+	0.0953671i
$545$	−48535.8	−	8558.17i	−0.163407	−	0.0288130i
$546$		0			0
$547$	−201260.	+	168877.i	−0.672641	+	0.564413i	−0.913846	−	0.406061i	$-0.866902\pi$
$547$	−201260.	+	168877.i	−0.672641	+	0.564413i	0.241205	+	0.970474i	$0.422457\pi$
$548$	14088.3	−	8133.90i	0.0469136	−	0.0270856i
$549$		0			0
$550$	10963.6	−	18989.5i	0.0362433	−	0.0627753i
$551$	−130227.	+	22962.6i	−0.428942	+	0.0756341i
$552$		0			0
$553$	157922.	−	57479.0i	0.516408	−	0.187957i
$554$	81431.5	+	223731.i	0.265322	+	0.728966i
$555$		0			0
$556$	−326.863	−	1853.73i	−0.00105735	−	0.00599650i
$557$	−361469.	−	208694.i	−1.16509	−	0.672667i	−0.212575	−	0.977145i	$-0.568185\pi$
$557$	−361469.	−	208694.i	−1.16509	−	0.672667i	−0.952520	+	0.304477i	$0.901518\pi$
$558$		0			0
$559$	−212399.	−	367885.i	−0.679717	−	1.17730i
$560$	−36841.8	−	43906.4i	−0.117480	−	0.140008i
$561$		0			0
$562$	−56350.8	+	319581.i	−0.178413	+	1.01183i
$563$	354009.	−	421892.i	1.11686	−	1.33102i	0.179059	−	0.983838i	$-0.442695\pi$
$563$	354009.	−	421892.i	1.11686	−	1.33102i	0.937798	−	0.347181i	$-0.112861\pi$
$564$		0			0
$565$	−20256.6	−	7372.81i	−0.0634557	−	0.0230960i
$566$		−	134826.i		−	0.420862i
$567$		0			0
$568$	−140870.			−0.436639
$569$	97084.8	−	266738.i	0.299866	−	0.823874i	−0.694656	−	0.719342i	$-0.744443\pi$
$569$	97084.8	−	266738.i	0.299866	−	0.823874i	0.994522	−	0.104532i	$-0.0333344\pi$
$570$		0			0
$571$	214704.	+	180158.i	0.658517	+	0.552561i	0.909642	−	0.415393i	$-0.136356\pi$
$571$	214704.	+	180158.i	0.658517	+	0.552561i	−0.251125	+	0.967955i	$0.580800\pi$
$572$	2867.17	+	505.560i	0.00876319	+	0.00154519i
$573$		0			0
$574$	99774.8	−	83721.0i	0.302829	−	0.254103i
$575$	−36944.8	+	21330.1i	−0.111742	+	0.0645144i
$576$		0			0
$577$	14979.1	−	25944.6i	0.0449919	−	0.0779283i	−0.842652	−	0.538458i	$-0.819007\pi$
$577$	14979.1	−	25944.6i	0.0449919	−	0.0779283i	0.887644	+	0.460530i	$0.152340\pi$
$578$	247658.	−	43668.7i	0.741303	−	0.130712i
$579$		0			0
$580$	9251.59	−	3367.30i	0.0275018	−	0.0100098i
$581$	−16003.2	−	43968.5i	−0.0474084	−	0.130253i
$582$		0			0
$583$	−1014.46	−	5753.29i	−0.00298468	−	0.0169270i
$584$	−342965.	−	198011.i	−1.00560	−	0.580582i
$585$		0			0
$586$	234606.	+	406350.i	0.683194	+	1.18333i
$587$	51892.9	+	61843.6i	0.150602	+	0.179481i	0.836071	−	0.548621i	$-0.184847\pi$
$587$	51892.9	+	61843.6i	0.150602	+	0.179481i	−0.685469	+	0.728102i	$0.740403\pi$
$588$		0			0
$589$	−21915.9	+	124291.i	−0.0631725	+	0.358269i
$590$	−200503.	+	238951.i	−0.575994	+	0.686443i
$591$		0			0
$592$	−201707.	−	73415.3i	−0.575543	−	0.209480i
$593$		−	381690.i		−	1.08543i	−0.839917	−	0.542715i	$-0.817396\pi$
$593$		−	381690.i		−	1.08543i	0.839917	−	0.542715i	$-0.182604\pi$
$594$		0			0
$595$	−80857.8			−0.228396
$596$	5183.54	−	14241.7i	0.0145926	−	0.0400930i
$597$		0			0
$598$	−81235.1	−	68164.4i	−0.227165	−	0.190614i
$599$	−526210.	−	92785.0i	−1.46658	−	0.258598i	−0.617378	−	0.786667i	$-0.711805\pi$
$599$	−526210.	−	92785.0i	−1.46658	−	0.258598i	−0.849201	+	0.528069i	$0.822916\pi$
$600$		0			0
$601$	−90810.2	+	76198.8i	−0.251412	+	0.210960i	−0.759780	−	0.650180i	$-0.774693\pi$
$601$	−90810.2	+	76198.8i	−0.251412	+	0.210960i	0.508368	+	0.861140i	$0.330249\pi$
$602$	−92049.4	+	53144.7i	−0.253997	+	0.146645i
$603$		0			0
$604$	1913.71	−	3314.64i	0.00524569	−	0.00908580i
$605$	−171925.	+	30315.0i	−0.469708	+	0.0828223i
$606$		0			0
$607$	−312790.	+	113846.i	−0.848936	+	0.308988i	−0.729607	−	0.683867i	$-0.760297\pi$
$607$	−312790.	+	113846.i	−0.848936	+	0.308988i	−0.119330	+	0.992855i	$0.538075\pi$
$608$	−5756.84	−	15816.8i	−0.0155732	−	0.0427869i
$609$		0			0
$610$	57214.5	+	324480.i	0.153761	+	0.872023i
$611$	996776.	+	575489.i	2.67002	+	1.54154i
$612$		0			0
$613$	−157547.	−	272880.i	−0.419266	−	0.726189i	0.576600	−	0.817027i	$-0.304379\pi$
$613$	−157547.	−	272880.i	−0.419266	−	0.726189i	−0.995866	+	0.0908370i	$0.971046\pi$
$614$	94152.2	+	112206.i	0.249743	+	0.297632i
$615$		0			0
$616$	−2115.27	+	11996.3i	−0.00557447	+	0.0316144i
$617$	−362195.	+	431647.i	−0.951419	+	1.13386i	0.0394766	+	0.999220i	$0.487431\pi$
$617$	−362195.	+	431647.i	−0.951419	+	1.13386i	−0.990895	+	0.134636i	$0.957013\pi$
$618$		0			0
$619$	−391662.	−	142553.i	−1.02219	−	0.372045i	−0.224085	−	0.974570i	$-0.571939\pi$
$619$	−391662.	−	142553.i	−1.02219	−	0.372045i	−0.798100	+	0.602524i	$0.794162\pi$
$620$		−	9396.55i		−	0.0244447i
$621$		0			0
$622$	−8365.94			−0.0216239
$623$	−31748.2	+	87227.5i	−0.0817981	+	0.224738i
$624$		0			0
$625$	107556.	+	90250.3i	0.275344	+	0.231041i
$626$	−529170.	−	93307.0i	−1.35035	−	0.238103i
$627$		0			0
$628$	−9907.25	+	8313.17i	−0.0251208	+	0.0210789i
$629$	−262249.	+	151410.i	−0.662846	+	0.382694i
$630$		0			0
$631$	284792.	−	493273.i	0.715267	−	1.23888i	−0.247589	−	0.968865i	$-0.579638\pi$
$631$	284792.	−	493273.i	0.715267	−	1.23888i	0.962856	−	0.270014i	$-0.0870284\pi$
$632$	581123.	−	102468.i	1.45490	−	0.256538i
$633$		0			0
$634$	−119281.	+	43414.7i	−0.296751	+	0.108009i
$635$	93768.4	+	257627.i	0.232546	+	0.638915i
$636$		0			0
$637$	105340.	+	597416.i	0.259607	+	1.47230i
$638$	−35846.3	−	20695.9i	−0.0880649	−	0.0508443i
$639$		0			0
$640$	−106015.	−	183624.i	−0.258826	−	0.448300i
$641$	62890.6	+	74950.1i	0.153063	+	0.182413i	0.837127	−	0.547009i	$-0.184234\pi$
$641$	62890.6	+	74950.1i	0.153063	+	0.182413i	−0.684064	+	0.729422i	$0.739789\pi$
$642$		0			0
$643$	−81087.7	+	459871.i	−0.196125	+	1.11228i	0.714683	+	0.699449i	$0.246571\pi$
$643$	−81087.7	+	459871.i	−0.196125	+	1.11228i	−0.910808	+	0.412831i	$0.864540\pi$
$644$	−910.998	+	1085.69i	−0.00219657	+	0.00261777i
$645$		0			0
$646$	−214290.	−	77995.3i	−0.513497	−	0.186897i
$647$			308321.i			0.736537i	0.929719	+	0.368269i	$0.120049\pi$
$647$			308321.i			0.736537i	−0.929719	+	0.368269i	$0.879951\pi$
$648$		0			0
$649$	70046.9			0.166303
$650$	−196209.	+	539081.i	−0.464401	+	1.27593i
$651$		0			0
$652$	−5530.93	−	4641.00i	−0.0130108	−	0.0109173i
$653$	286044.	+	50437.3i	0.670821	+	0.118284i	0.498677	−	0.866788i	$-0.333819\pi$
$653$	286044.	+	50437.3i	0.670821	+	0.118284i	0.172144	+	0.985072i	$0.444930\pi$
$654$		0			0
$655$	193228.	−	162138.i	0.450390	−	0.377922i
$656$	418475.	−	241607.i	0.972439	−	0.561438i
$657$		0			0
$658$	143994.	−	249405.i	0.332578	−	0.576042i
$659$	−85168.9	+	15017.6i	−0.196115	+	0.0345803i	−0.270843	−	0.962624i	$-0.587302\pi$
$659$	−85168.9	+	15017.6i	−0.196115	+	0.0345803i	0.0747279	+	0.997204i	$0.476191\pi$
$660$		0			0
$661$	94722.6	−	34476.2i	0.216796	−	0.0789072i	−0.231339	−	0.972873i	$-0.574311\pi$
$661$	94722.6	−	34476.2i	0.216796	−	0.0789072i	0.448135	+	0.893966i	$0.352088\pi$
$662$	122673.	+	337040.i	0.279919	+	0.769070i
$663$		0			0
$664$	−28528.9	−	161795.i	−0.0647066	−	0.366969i
$665$	26844.5	+	15498.7i	0.0607033	+	0.0350471i
$666$		0			0
$667$	40264.5	+	69740.2i	0.0905046	+	0.156759i
$668$	916.507	+	1092.25i	0.00205392	+	0.00244776i
$669$		0			0
$670$	−54752.6	+	310518.i	−0.121971	+	0.691730i
$671$	47559.6	−	56679.4i	0.105631	−	0.125887i
$672$		0			0
$673$	574259.	+	209013.i	1.26788	+	0.461470i	0.886405	−	0.462910i	$-0.153195\pi$
$673$	574259.	+	209013.i	1.26788	+	0.461470i	0.381473	+	0.924380i	$0.375417\pi$
$674$			130596.i			0.287483i
$675$		0			0
$676$	−50384.6			−0.110257
$677$	288194.	−	791806.i	0.628792	−	1.72759i	−0.0555745	−	0.998455i	$-0.517699\pi$
$677$	288194.	−	791806.i	0.628792	−	1.72759i	0.684367	−	0.729138i	$-0.260079\pi$
$678$		0			0
$679$	−152033.	−	127571.i	−0.329760	−	0.276702i
$680$	−279597.	−	49300.4i	−0.604664	−	0.106619i
$681$		0			0
$682$	−30262.5	+	25393.3i	−0.0650634	+	0.0545947i
$683$	−26369.8	+	15224.6i	−0.0565283	+	0.0326366i	−0.527998	−	0.849246i	$-0.677057\pi$
$683$	−26369.8	+	15224.6i	−0.0565283	+	0.0326366i	0.471469	+	0.881882i	$0.343724\pi$
$684$		0			0
$685$	−108337.	+	187645.i	−0.230885	+	0.399904i
$686$	321327.	−	56658.6i	0.682808	−	0.120398i
$687$		0			0
$688$	−370551.	+	134870.i	−0.782837	+	0.284929i
$689$	52275.9	+	143627.i	0.110119	+	0.302550i
$690$		0			0
$691$	80071.0	+	454105.i	0.167695	+	0.951044i	0.946242	+	0.323459i	$0.104846\pi$
$691$	80071.0	+	454105.i	0.167695	+	0.951044i	−0.778548	+	0.627586i	$0.784043\pi$
$692$	−21746.6	−	12555.4i	−0.0454128	−	0.0262191i
$693$		0			0
$694$	72877.8	+	126228.i	0.151313	+	0.262082i
$695$	16115.4	+	19205.6i	0.0333635	+	0.0397610i
$696$		0			0
$697$	118374.	−	671334.i	0.243664	−	1.38189i
$698$	328027.	−	390928.i	0.673285	−	0.802390i
$699$		0			0
$700$	7204.67	+	2622.29i	0.0147034	+	0.00535160i
$701$			614818.i			1.25115i	0.780163	+	0.625576i	$0.215136\pi$
$701$			614818.i			1.25115i	−0.780163	+	0.625576i	$0.784864\pi$
$702$		0			0
$703$	116088.			0.234896
$704$	−14579.2	+	40055.9i	−0.0294162	+	0.0808204i
$705$		0			0
$706$	−264079.	−	221589.i	−0.529816	−	0.444568i
$707$	50385.3	+	8884.28i	0.100801	+	0.0177739i
$708$		0			0
$709$	241186.	−	202379.i	0.479800	−	0.402600i	−0.370554	−	0.928811i	$-0.620832\pi$
$709$	241186.	−	202379.i	0.479800	−	0.402600i	0.850354	+	0.526211i	$0.176388\pi$
$710$	−97172.4	+	56102.5i	−0.192764	+	0.111292i
$711$		0			0
$712$	−162966.	+	282265.i	−0.321467	+	0.556797i
$713$	75690.6	−	13346.3i	0.148889	−	0.0262532i
$714$		0			0
$715$	−36438.9	+	13262.7i	−0.0712776	+	0.0259429i
$716$	−5116.35	−	14057.1i	−0.00998008	−	0.0274201i
$717$		0			0
$718$	−86819.7	−	492379.i	−0.168411	−	0.955104i
$719$	−235409.	−	135914.i	−0.455371	−	0.262909i	0.254725	−	0.967014i	$-0.418015\pi$
$719$	−235409.	−	135914.i	−0.455371	−	0.262909i	−0.710096	+	0.704105i	$0.751348\pi$
$720$		0			0
$721$	29944.4	+	51865.2i	0.0576030	+	0.0997713i
$722$	−288205.	−	343470.i	−0.552876	−	0.658892i
$723$		0			0
$724$	2981.69	−	16910.0i	0.00568833	−	0.0322601i
$725$	280026.	−	333722.i	0.532749	−	0.634905i
$726$		0			0
$727$	−635226.	−	231203.i	−1.20187	−	0.437447i	−0.337997	−	0.941147i	$-0.609749\pi$
$727$	−635226.	−	231203.i	−1.20187	−	0.437447i	−0.863878	+	0.503701i	$0.831971\pi$
$728$		−	318698.i		−	0.601336i
$729$		0			0
$730$	−315437.			−0.591925
$731$	−190267.	+	522753.i	−0.356064	+	0.978277i
$732$		0			0
$733$	385837.	+	323756.i	0.718118	+	0.602573i	0.926864	−	0.375397i	$-0.122494\pi$
$733$	385837.	+	323756.i	0.718118	+	0.602573i	−0.208746	+	0.977970i	$0.566938\pi$
$734$	−222705.	−	39268.9i	−0.413369	−	0.0728882i
$735$		0			0
$736$	−7852.14	+	6588.73i	−0.0144955	+	0.0121631i
$737$	61319.7	−	35403.0i	0.112893	−	0.0651785i
$738$		0			0
$739$	−158873.	+	275175.i	−0.290911	+	0.503873i	−0.974025	−	0.226439i	$-0.927292\pi$
$739$	−158873.	+	275175.i	−0.290911	+	0.503873i	0.683114	+	0.730311i	$0.260625\pi$
$740$	−8511.73	+	1500.85i	−0.0155437	+	0.00274077i
$741$		0			0
$742$	35937.2	−	13080.1i	0.0652733	−	0.0237576i
$743$	−25391.3	−	69762.1i	−0.0459947	−	0.126369i	0.914569	−	0.404431i	$-0.132530\pi$
$743$	−25391.3	−	69762.1i	−0.0459947	−	0.126369i	−0.960563	+	0.278061i	$0.910308\pi$
$744$		0			0
$745$	35052.8	+	198794.i	0.0631553	+	0.358171i
$746$	−85959.1	−	49628.5i	−0.154459	−	0.0891772i
$747$		0			0
$748$	−1906.35	−	3301.89i	−0.00340721	−	0.00590145i
$749$	−32373.2	−	38580.8i	−0.0577061	−	0.0687714i
$750$		0			0
$751$	124048.	−	703510.i	0.219943	−	1.24736i	−0.652178	−	0.758066i	$-0.726145\pi$
$751$	124048.	−	703510.i	0.219943	−	1.24736i	0.872121	−	0.489291i	$-0.162744\pi$
$752$	686776.	−	818468.i	1.21445	−	1.44732i
$753$		0			0
$754$	1.01762e6	+	370382.i	1.78995	+	0.651489i
$755$			50978.0i			0.0894312i
$756$		0			0
$757$	128518.			0.224271			0.112136	−	0.993693i	$-0.464231\pi$
$757$	128518.			0.224271			0.112136	+	0.993693i	$0.464231\pi$
$758$	106474.	−	292536.i	0.185313	−	0.509144i
$759$		0			0
$760$	83375.3	+	69960.2i	0.144348	+	0.121122i
$761$	−351980.	−	62063.5i	−0.607783	−	0.107169i	−0.138718	−	0.990332i	$-0.544298\pi$
$761$	−351980.	−	62063.5i	−0.607783	−	0.107169i	−0.469065	+	0.883163i	$0.655409\pi$
$762$		0			0
$763$	−55500.0	+	46570.0i	−0.0953331	+	0.0799940i
$764$	−50448.6	+	29126.5i	−0.0864296	+	0.0499002i
$765$		0			0
$766$	377597.	−	654018.i	0.643534	−	1.11463i
$767$	−1.80479e6	+	318232.i	−3.06785	+	0.540946i
$768$		0			0
$769$	376537.	−	137048.i	0.636730	−	0.231751i	−0.00342793	−	0.999994i	$-0.501091\pi$
$769$	376537.	−	137048.i	0.636730	−	0.231751i	0.640158	+	0.768243i	$0.278869\pi$
$770$	3318.48	+	9117.46i	0.00559704	+	0.0153777i
$771$		0			0
$772$	2527.64	+	14334.9i	0.00424112	+	0.0240526i
$773$	−380708.	−	219802.i	−0.637137	−	0.367851i	0.146374	−	0.989229i	$-0.453240\pi$
$773$	−380708.	−	219802.i	−0.637137	−	0.367851i	−0.783511	+	0.621378i	$0.786573\pi$
$774$		0			0
$775$	−207893.	−	360080.i	−0.346127	−	0.599510i
$776$	−447930.	−	533822.i	−0.743852	−	0.886489i
$777$		0			0
$778$	−3024.54	+	17153.0i	−0.00499689	+	0.0283388i
$779$	−167980.	+	200191.i	−0.276811	+	0.329890i
$780$		0			0
$781$	23677.3	+	8617.85i	0.0388178	+	0.0141285i
$782$			138873.i			0.227094i
$783$		0			0
$784$	563126.			0.916165
$785$	58915.2	−	161868.i	0.0956067	−	0.262677i
$786$		0			0
$787$	−611134.	−	512802.i	−0.986704	−	0.827943i	−0.00161698	−	0.999999i	$-0.500515\pi$
$787$	−611134.	−	512802.i	−0.986704	−	0.827943i	−0.985087	+	0.172056i	$0.944959\pi$
$788$	−13152.8	−	2319.19i	−0.0211819	−	0.00373495i
$789$		0			0
$790$	360051.	−	302118.i	0.576912	−	0.484086i
$791$	−27443.5	+	15844.5i	−0.0438619	+	0.0253237i
$792$		0			0
$793$	−967890.	+	1.67643e6i	−1.53914	+	2.66588i
$794$	25324.3	−	4465.35i	0.0401694	−	0.00708296i
$795$		0			0
$796$	−49300.7	+	17944.0i	−0.0778085	+	0.0283200i
$797$	389198.	+	1.06931e6i	0.612709	+	1.68341i	0.724157	+	0.689635i	$0.242229\pi$
$797$	389198.	+	1.06931e6i	0.612709	+	1.68341i	−0.111448	+	0.993770i	$0.535549\pi$
$798$		0			0
$799$	−261738.	−	1.48439e6i	−0.409989	−	2.32516i
$800$	48022.3	+	27725.7i	0.0750349	+	0.0433214i
$801$		0			0
$802$	366097.	+	634099.i	0.569177	+	0.985844i
$803$	45531.8	+	54262.7i	0.0706128	+	0.0841531i
$804$		0			0
$805$	3277.91	−	18590.0i	0.00505831	−	0.0286871i
$806$	664361.	−	791754.i	1.02267	−	1.21877i
$807$		0			0
$808$	168809.	+	61441.6i	0.258567	+	0.0941108i
$809$		−	752497.i		−	1.14976i	−0.818237	−	0.574881i	$-0.805048\pi$
$809$		−	752497.i		−	1.14976i	0.818237	−	0.574881i	$-0.194952\pi$
$810$		0			0
$811$	−145940.			−0.221888			−0.110944	−	0.993827i	$-0.535387\pi$
$811$	−145940.			−0.221888			−0.110944	+	0.993827i	$0.535387\pi$
$812$	4950.06	−	13600.2i	0.00750755	−	0.0206268i
$813$		0			0
$814$	27835.8	+	23357.0i	0.0420102	+	0.0352507i
$815$	94704.9	+	16699.0i	0.142579	+	0.0251406i
$816$		0			0
$817$	163368.	−	137082.i	0.244751	−	0.205370i
$818$	−838928.	+	484355.i	−1.25377	+	0.723865i
$819$		0			0
$820$	9728.38	−	16850.0i	0.0144681	−	0.0250596i
$821$	437205.	−	77091.0i	0.648633	−	0.114371i	0.160355	−	0.987059i	$-0.448736\pi$
$821$	437205.	−	77091.0i	0.648633	−	0.114371i	0.488278	+	0.872688i	$0.337625\pi$
$822$		0			0
$823$	10177.4	−	3704.25i	0.0150257	−	0.00546892i	−0.334496	−	0.942397i	$-0.608566\pi$
$823$	10177.4	−	3704.25i	0.0150257	−	0.00546892i	0.349522	+	0.936928i	$0.386344\pi$
$824$	71921.0	+	197601.i	0.105926	+	0.291028i
$825$		0			0
$826$	79625.6	+	451579.i	0.116706	+	0.661872i
$827$	602735.	+	347989.i	0.881283	+	0.508809i	0.871081	−	0.491139i	$-0.163419\pi$
$827$	602735.	+	347989.i	0.881283	+	0.508809i	0.0102019	+	0.999948i	$0.496753\pi$
$828$		0			0
$829$	294129.	+	509447.i	0.427986	+	0.741293i	0.996694	−	0.0812460i	$-0.0258899\pi$
$829$	294129.	+	509447.i	0.427986	+	0.741293i	−0.568708	+	0.822539i	$0.692557\pi$
$830$	−84115.3	−	100245.i	−0.122101	−	0.145514i
$831$		0			0
$832$	193658.	−	1.09829e6i	0.279762	−	1.58661i
$833$	510648.	−	608566.i	0.735921	−	0.877037i
$834$		0			0
$835$	−17845.6	−	6495.27i	−0.0255952	−	0.00931588i
$836$			1461.62i			0.00209133i
$837$		0			0
$838$	−981952.			−1.39831
$839$	199851.	−	549086.i	0.283911	−	0.780039i	−0.712975	−	0.701189i	$-0.752653\pi$
$839$	199851.	−	549086.i	0.283911	−	0.780039i	0.996886	−	0.0788501i	$-0.0251249\pi$
$840$		0			0
$841$	−88154.3	−	73970.2i	−0.124638	−	0.104584i
$842$	524371.	+	92460.8i	0.739630	+	0.130417i
$843$		0			0
$844$	27369.5	−	22965.7i	0.0384222	−	0.0322400i
$845$	581173.	−	335540.i	0.813939	−	0.469928i
$846$		0			0
$847$	−128317.	+	222252.i	−0.178862	+	0.309799i
$848$	139727.	−	24637.7i	0.194308	−	0.0342617i
$849$		0			0
$850$	705965.	−	256950.i	0.977114	−	0.355640i
$851$	−24179.1	−	66431.5i	−0.0333873	−	0.0917308i
$852$		0			0
$853$	−131822.	−	747602.i	−0.181172	−	1.02748i	−0.930776	−	0.365591i	$-0.880867\pi$
$853$	−131822.	−	747602.i	−0.181172	−	1.02748i	0.749604	−	0.661887i	$-0.230244\pi$
$854$	419464.	+	242178.i	0.575147	+	0.332061i
$855$		0			0
$856$	−88419.1	−	153146.i	−0.120670	−	0.209006i
$857$	257103.	+	306404.i	0.350063	+	0.417188i	0.912129	−	0.409904i	$-0.134438\pi$
$857$	257103.	+	306404.i	0.350063	+	0.417188i	−0.562066	+	0.827092i	$0.689993\pi$
$858$		0			0
$859$	−141991.	+	805270.i	−0.192430	+	1.09133i	0.723600	+	0.690219i	$0.242486\pi$
$859$	−141991.	+	805270.i	−0.192430	+	1.09133i	−0.916031	+	0.401108i	$0.868625\pi$
$860$	−10206.1	+	12163.2i	−0.0137995	+	0.0164456i
$861$		0			0
$862$	773692.	+	281601.i	1.04125	+	0.378983i
$863$			959981.i			1.28896i	0.764619	+	0.644482i	$0.222927\pi$
$863$			959981.i			1.28896i	−0.764619	+	0.644482i	$0.777073\pi$
$864$		0			0
$865$	334454.			0.446997
$866$	−394416.	+	1.08365e6i	−0.525920	+	1.44495i
$867$		0			0
$868$	−10581.6	−	8879.00i	−0.0140447	−	0.0117849i
$869$	−103943.	−	18328.0i	−0.137644	−	0.0242703i
$870$		0			0
$871$	−1.41909e6	+	1.19075e6i	−1.87056	+	1.56959i
$872$	−220307.	+	127194.i	−0.289731	+	0.167276i
$873$		0			0
$874$	26619.0	−	46105.5i	0.0348473	−	0.0603573i
$875$	−231406.	+	40803.1i	−0.302245	+	0.0532939i
$876$		0			0
$877$	−256957.	+	93524.7i	−0.334088	+	0.121598i	−0.503617	−	0.863927i	$-0.667998\pi$
$877$	−256957.	+	93524.7i	−0.334088	+	0.121598i	0.169529	+	0.985525i	$0.445776\pi$
$878$	181062.	+	497463.i	0.234876	+	0.645315i
$879$		0			0
$880$	6250.73	+	35449.6i	0.00807170	+	0.0457769i
$881$	−231604.	−	133716.i	−0.298396	−	0.172279i	0.343326	−	0.939216i	$-0.388446\pi$
$881$	−231604.	−	133716.i	−0.298396	−	0.172279i	−0.641722	+	0.766937i	$0.721780\pi$
$882$		0			0
$883$	−3266.91	−	5658.46i	−0.00419002	−	0.00725733i	0.863923	−	0.503624i	$-0.168000\pi$
$883$	−3266.91	−	5658.46i	−0.00419002	−	0.00725733i	−0.868113	+	0.496367i	$0.834667\pi$
$884$	64118.6	+	76413.6i	0.0820502	+	0.0977836i
$885$		0			0
$886$	−143444.	+	813512.i	−0.182732	+	1.03633i
$887$	239740.	−	285711.i	0.304715	−	0.363145i	−0.591857	−	0.806043i	$-0.701605\pi$
$887$	239740.	−	285711.i	0.304715	−	0.363145i	0.896572	+	0.442898i	$0.146050\pi$
$888$		0			0
$889$	378720.	+	137843.i	0.479198	+	0.174414i
$890$			259609.i			0.327748i
$891$		0			0
$892$	−36698.2			−0.0461228
$893$	−197629.	+	542981.i	−0.247826	+	0.680898i
$894$		0			0
$895$	152630.	+	128072.i	0.190543	+	0.159885i
$896$	−306957.	−	54124.8i	−0.382350	−	0.0674186i
$897$		0			0
$898$	268371.	−	225190.i	0.332799	−	0.279252i
$899$	−679719.	+	392436.i	−0.841028	+	0.485568i
$900$		0			0
$901$	100080.	−	173344.i	0.123282	−	0.213530i
$902$	−80557.3	+	14204.4i	−0.0990129	+	0.0174586i
$903$		0			0
$904$	−104557.	+	38055.7i	−0.127943	+	0.0465675i
$905$	78220.4	+	214909.i	0.0955043	+	0.262396i
$906$		0			0
$907$	−72227.6	−	409623.i	−0.0877988	−	0.497932i	−0.996717	−	0.0809584i	$-0.974202\pi$
$907$	−72227.6	−	409623.i	−0.0877988	−	0.497932i	0.908919	−	0.416973i	$-0.136909\pi$
$908$	−30905.7	−	17843.4i	−0.0374858	−	0.0216425i
$909$		0			0
$910$	−126924.	−	219838.i	−0.153271	−	0.265473i
$911$	−136751.	−	162974.i	−0.164776	−	0.196373i	0.677338	−	0.735672i	$-0.263134\pi$
$911$	−136751.	−	162974.i	−0.164776	−	0.196373i	−0.842114	+	0.539299i	$0.818689\pi$
$912$		0			0
$913$	−5102.85	+	28939.7i	−0.00612168	+	0.0347178i
$914$	136499.	−	162673.i	0.163395	−	0.194726i
$915$		0			0
$916$	169.882	+	61.8319i	0.000202468	+	7.36923e-5i
$917$		−	370805.i		−	0.440967i
$918$		0			0
$919$	−112790.			−0.133548			−0.0667741	−	0.997768i	$-0.521271\pi$
$919$	−112790.			−0.133548			−0.0667741	+	0.997768i	$0.521271\pi$
$920$	22669.3	−	62283.3i	0.0267831	−	0.0735861i
$921$		0			0
$922$	−466943.	−	391812.i	−0.549291	−	0.460910i
$923$	−649207.	−	114473.i	−0.762044	−	0.134369i
$924$		0			0
$925$	−292968.	+	245830.i	−0.342403	+	0.287310i
$926$	982019.	−	566969.i	1.14524	−	0.661207i
$927$		0			0
$928$	52337.5	−	90651.1i	0.0607738	−	0.105263i
$929$	316551.	−	55816.5i	0.366786	−	0.0646742i	0.0127823	−	0.999918i	$-0.495931\pi$
$929$	316551.	−	55816.5i	0.366786	−	0.0646742i	0.354004	+	0.935244i	$0.384820\pi$
$930$		0			0
$931$	−286182.	+	104162.i	−0.330175	+	0.120174i
$932$	17694.3	+	48614.7i	0.0203705	+	0.0559675i
$933$		0			0
$934$	198051.	+	1.12321e6i	0.227030	+	1.28755i
$935$	43978.4	+	25390.9i	0.0503056	+	0.0290439i
$936$		0			0
$937$	68899.7	+	119338.i	0.0784763	+	0.135925i	0.902593	−	0.430496i	$-0.141661\pi$
$937$	68899.7	+	119338.i	0.0784763	+	0.135925i	−0.824116	+	0.566420i	$0.808328\pi$
$938$	297941.	+	355072.i	0.338629	+	0.403563i
$939$		0			0
$940$	7470.49	−	42367.3i	0.00845461	−	0.0479485i
$941$	−1.07706e6	+	1.28358e6i	−1.21635	+	1.44959i	−0.360191	+	0.932879i	$0.617288\pi$
$941$	−1.07706e6	+	1.28358e6i	−1.21635	+	1.44959i	−0.856160	+	0.516711i	$0.827156\pi$
$942$		0			0
$943$	149547.	+	54430.7i	0.168172	+	0.0612098i
$944$			1.70120e6i			1.90902i
$945$		0			0
$946$	66753.9			0.0745924
$947$	492103.	−	1.35204e6i	0.548727	−	1.50761i	−0.286704	−	0.958019i	$-0.592560\pi$
$947$	492103.	−	1.35204e6i	0.548727	−	1.50761i	0.835431	−	0.549595i	$-0.185218\pi$
$948$		0			0
$949$	−1.41967e6	−	1.19124e6i	−1.57635	−	1.32272i
$950$	−283630.	−	50011.6i	−0.314271	−	0.0554145i
$951$		0			0
$952$	−319715.	+	268272.i	−0.352767	+	0.296007i
$953$	338219.	−	195271.i	0.372403	−	0.215007i	−0.302105	−	0.953275i	$-0.597689\pi$
$953$	338219.	−	195271.i	0.372403	−	0.215007i	0.674508	+	0.738268i	$0.264356\pi$
$954$		0			0
$955$	387941.	−	671934.i	0.425362	−	0.736749i
$956$	13860.7	−	2444.01i	0.0151659	−	0.00267416i
$957$		0			0
$958$	−1.15029e6	+	418670.i	−1.25336	+	0.456185i
$959$	108940.	+	299309.i	0.118454	+	0.325449i
$960$		0			0
$961$	−30288.7	−	171776.i	−0.0327970	−	0.186001i
$962$	−823313.	−	475340.i	−0.889641	−	0.513634i
$963$		0			0
$964$	50620.8	+	87677.7i	0.0544722	+	0.0943486i
$965$	−124620.	−	148517.i	−0.133824	−	0.159485i
$966$		0			0
$967$	−150326.	+	852540.i	−0.160761	+	0.911721i	0.792567	+	0.609785i	$0.208744\pi$
$967$	−150326.	+	852540.i	−0.160761	+	0.911721i	−0.953328	+	0.301936i	$0.902367\pi$
$968$	−579218.	+	690285.i	−0.618146	+	0.736678i
$969$		0			0
$970$	−521581.	−	189840.i	−0.554343	−	0.201764i
$971$		−	805538.i		−	0.854373i	−0.904164	−	0.427186i	$-0.859505\pi$
$971$		−	805538.i		−	0.854373i	0.904164	−	0.427186i	$-0.140495\pi$
$972$		0			0
$973$	36855.4			0.0389292
$974$	53184.5	−	146123.i	0.0560618	−	0.154029i
$975$		0			0
$976$	1.37655e6	+	1.15506e6i	1.44508	+	1.21256i
$977$	−342796.	−	60444.2i	−0.359126	−	0.0633236i	−0.00882579	−	0.999961i	$-0.502809\pi$
$977$	−342796.	−	60444.2i	−0.359126	−	0.0633236i	−0.350300	+	0.936637i	$0.613920\pi$
$978$		0			0
$979$	44658.9	−	37473.3i	0.0465954	−	0.0390982i
$980$	19636.7	−	11337.2i	0.0204463	−	0.0118047i
$981$		0			0
$982$	646550.	−	1.11986e6i	0.670470	−	1.16129i
$983$	262107.	−	46216.5i	0.271251	−	0.0478289i	−0.0363680	−	0.999338i	$-0.511579\pi$
$983$	262107.	−	46216.5i	0.271251	−	0.0478289i	0.307619	+	0.951510i	$0.400468\pi$
$984$		0			0
$985$	167159.	−	60840.8i	0.172289	−	0.0627080i
$986$	−485042.	−	1.33264e6i	−0.498913	−	1.37075i
$987$		0			0
$988$	−6640.33	−	37659.2i	−0.00680262	−	0.0385796i
$989$	−112473.	−	64936.0i	−0.114988	−	0.0663885i
$990$		0			0
$991$	−415065.	−	718913.i	−0.422638	−	0.732031i	0.573559	−	0.819165i	$-0.305563\pi$
$991$	−415065.	−	718913.i	−0.422638	−	0.732031i	−0.996197	+	0.0871339i	$0.972229\pi$
$992$	−64216.7	−	76530.5i	−0.0652567	−	0.0777698i
$993$		0			0
$994$	−28642.5	+	162440.i	−0.0289893	+	0.164406i
$995$	449171.	−	535301.i	0.453697	−	0.540695i
$996$		0			0
$997$	1.49897e6	+	545579.i	1.50800	+	0.548867i	0.958118	−	0.286375i	$-0.0924502\pi$
$997$	1.49897e6	+	545579.i	1.50800	+	0.548867i	0.549883	+	0.835242i	$0.314672\pi$
$998$		−	1.22923e6i		−	1.23416i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.8		66
3.2	odd	2		27.5.f.a.23.4	yes	66
27.7	even	9		27.5.f.a.20.4	✓	66
27.20	odd	18	inner	81.5.f.a.62.8		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.4	✓	66	27.7	even	9
27.5.f.a.23.4	yes	66	3.2	odd	2
81.5.f.a.17.8		66	1.1	even	1	trivial
81.5.f.a.62.8		66	27.20	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)

\(f(q)\)	\(=\)	\(q+(1.40615 - 3.86336i) q^{2} +(-0.691617 - 0.580335i) q^{4} +(11.8424 + 2.08814i) q^{5} +(13.5416 - 11.3628i) q^{7} +(53.7534 - 31.0345i) q^{8} +(24.7194 - 42.8153i) q^{10} +(-10.9334 + 1.92785i) q^{11} +(272.944 - 99.3436i) q^{13} +(-24.8570 - 68.2939i) q^{14} +(-46.8208 - 265.534i) q^{16} +(-329.418 - 190.190i) q^{17} +(72.9105 + 126.285i) q^{19} +(-6.97859 - 8.31676i) q^{20} +(-7.92598 + 44.9505i) q^{22} +(57.0807 - 68.0262i) q^{23} +(-451.426 - 164.305i) q^{25} -1194.17i q^{26} -15.9598 q^{28} +(-310.157 + 852.151i) q^{29} +(663.014 + 556.335i) q^{31} +(-113.675 - 20.0439i) q^{32} +(-1197.98 + 1005.23i) q^{34} +(184.092 - 106.286i) q^{35} +(398.049 - 689.441i) q^{37} +(590.407 - 104.105i) q^{38} +(701.374 - 255.279i) q^{40} +(612.946 + 1684.06i) q^{41} +(-253.959 - 1440.27i) q^{43} +(8.68051 + 5.01170i) q^{44} +(-182.546 - 316.179i) q^{46} +(2547.10 + 3035.52i) q^{47} +(-362.666 + 2056.78i) q^{49} +(-1269.54 + 1512.98i) q^{50} +(-246.425 - 89.6915i) q^{52} +526.213i q^{53} -133.503 q^{55} +(375.270 - 1031.04i) q^{56} +(2856.04 + 2396.50i) q^{58} +(-6213.52 - 1095.61i) q^{59} +(-5105.31 + 4283.86i) q^{61} +(3081.62 - 1779.17i) q^{62} +(1919.76 - 3325.13i) q^{64} +(3439.76 - 606.522i) q^{65} +(-5993.11 + 2181.31i) q^{67} +(117.457 + 322.711i) q^{68} +(-151.759 - 860.669i) q^{70} +(-1965.51 - 1134.79i) q^{71} +(-3190.17 - 5525.54i) q^{73} +(-2103.84 - 2507.26i) q^{74} +(22.8613 - 129.653i) q^{76} +(-126.150 + 150.340i) q^{77} +(8933.61 + 3251.57i) q^{79} -3242.33i q^{80} +7368.01 q^{82} +(905.297 - 2487.28i) q^{83} +(-3503.96 - 2940.17i) q^{85} +(-5921.41 - 1044.10i) q^{86} +(-527.876 + 442.941i) q^{88} +(-4547.60 + 2625.56i) q^{89} +(2567.29 - 4446.67i) q^{91} +(-78.9560 + 13.9221i) q^{92} +(15308.9 - 5571.99i) q^{94} +(599.736 + 1647.76i) q^{95} +(-1949.57 - 11056.5i) q^{97} +(7436.14 + 4293.26i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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