LMFDB - Embedded newform 135.5.h.a.89.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,5,Mod(44,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.44"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	135.h (of order $6$, degree $2$, 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:	$13.9549450163$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.4
Character	$\chi$	$=$	135.89
Dual form			135.5.h.a.44.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.87361 + 4.97724i) q^{2} +(-8.51525 - 14.7488i) q^{4} +(-24.3310 - 5.74467i) q^{5} +(-41.4151 - 23.9110i) q^{7} +5.92246 q^{8} +(98.5104 - 104.593i) q^{10} +(73.2455 + 42.2883i) q^{11} +(-193.485 + 111.709i) q^{13} +(238.021 - 137.422i) q^{14} +(119.225 - 206.504i) q^{16} +434.998 q^{17} +378.461 q^{19} +(122.457 + 407.772i) q^{20} +(-420.958 + 243.040i) q^{22} +(-326.825 - 566.078i) q^{23} +(558.998 + 279.547i) q^{25} -1284.03i q^{26} +814.433i q^{28} +(430.201 + 248.377i) q^{29} +(151.498 + 262.402i) q^{31} +(732.592 + 1268.89i) q^{32} +(-1250.01 + 2165.09i) q^{34} +(870.311 + 819.695i) q^{35} -55.6914i q^{37} +(-1087.55 + 1883.69i) q^{38} +(-144.099 - 34.0226i) q^{40} +(-411.405 + 237.525i) q^{41} +(-707.073 - 408.229i) q^{43} -1440.38i q^{44} +3756.67 q^{46} +(-435.232 + 753.844i) q^{47} +(-57.0270 - 98.7737i) q^{49} +(-2997.71 + 1978.95i) q^{50} +(3295.14 + 1902.45i) q^{52} +2339.28 q^{53} +(-1539.21 - 1449.69i) q^{55} +(-245.279 - 141.612i) q^{56} +(-2472.46 + 1427.47i) q^{58} +(1019.68 - 588.710i) q^{59} +(3456.52 - 5986.86i) q^{61} -1741.38 q^{62} -4605.53 q^{64} +(5349.42 - 1606.48i) q^{65} +(3356.29 - 1937.75i) q^{67} +(-3704.11 - 6415.71i) q^{68} +(-6580.75 + 1976.26i) q^{70} -5822.30i q^{71} -6443.82i q^{73} +(277.189 + 160.035i) q^{74} +(-3222.69 - 5581.85i) q^{76} +(-2022.31 - 3502.75i) q^{77} +(-2446.72 + 4237.84i) q^{79} +(-4087.17 + 4339.54i) q^{80} -2730.21i q^{82} +(3257.36 - 5641.91i) q^{83} +(-10583.9 - 2498.92i) q^{85} +(4063.70 - 2346.18i) q^{86} +(433.793 + 250.451i) q^{88} +13898.7i q^{89} +10684.3 q^{91} +(-5566.00 + 9640.59i) q^{92} +(-2501.37 - 4332.50i) q^{94} +(-9208.33 - 2174.13i) q^{95} +(11681.7 + 6744.42i) q^{97} +655.493 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) $ 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−2.87361	+	4.97724i	−0.718402	+	1.24431i	0.243231	+	0.969968i	$0.421793\pi$
$2$	−2.87361	+	4.97724i	−0.718402	+	1.24431i	−0.961633	+	0.274340i	$0.911541\pi$
$3$		0			0
$3$		0			0
$4$	−8.51525	−	14.7488i	−0.532203	−	0.921802i
$5$	−24.3310	−	5.74467i	−0.973241	−	0.229787i
$5$	−24.3310	−	5.74467i	−0.973241	−	0.229787i
$6$		0			0
$7$	−41.4151	−	23.9110i	−0.845206	−	0.487980i	0.0138245	−	0.999904i	$-0.495599\pi$
$7$	−41.4151	−	23.9110i	−0.845206	−	0.487980i	−0.859030	+	0.511925i	$0.828933\pi$
$8$	5.92246			0.0925384
$9$		0			0
$10$	98.5104	−	104.593i	0.985104	−	1.04593i
$11$	73.2455	+	42.2883i	0.605335	+	0.349490i	0.771137	−	0.636669i	$-0.219688\pi$
$11$	73.2455	+	42.2883i	0.605335	+	0.349490i	−0.165803	+	0.986159i	$0.553021\pi$
$12$		0			0
$13$	−193.485	+	111.709i	−1.14488	+	0.660998i	−0.947635	−	0.319356i	$-0.896533\pi$
$13$	−193.485	+	111.709i	−1.14488	+	0.660998i	−0.197247	+	0.980354i	$0.563200\pi$
$14$	238.021	−	137.422i	1.21440	−	0.701131i
$15$		0			0
$16$	119.225	−	206.504i	0.465723	−	0.806656i
$17$	434.998			1.50518			0.752591	−	0.658488i	$-0.228804\pi$
$17$	434.998			1.50518			0.752591	+	0.658488i	$0.228804\pi$
$18$		0			0
$19$	378.461			1.04837			0.524184	−	0.851605i	$-0.324371\pi$
$19$	378.461			1.04837			0.524184	+	0.851605i	$0.324371\pi$
$20$	122.457	+	407.772i	0.306144	+	1.01943i
$21$		0			0
$22$	−420.958	+	243.040i	−0.869747	+	0.502149i
$23$	−326.825	−	566.078i	−0.617818	−	1.07009i	−0.989883	−	0.141885i	$-0.954684\pi$
$23$	−326.825	−	566.078i	−0.617818	−	1.07009i	0.372066	−	0.928206i	$-0.378650\pi$
$24$		0			0
$25$	558.998	+	279.547i	0.894396	+	0.447276i
$26$		−	1284.03i		−	1.89945i
$27$		0			0
$28$			814.433i			1.03882i
$29$	430.201	+	248.377i	0.511535	+	0.295335i	0.733464	−	0.679728i	$-0.237902\pi$
$29$	430.201	+	248.377i	0.511535	+	0.295335i	−0.221929	+	0.975063i	$0.571235\pi$
$30$		0			0
$31$	151.498	+	262.402i	0.157646	+	0.273051i	0.934019	−	0.357222i	$-0.116276\pi$
$31$	151.498	+	262.402i	0.157646	+	0.273051i	−0.776373	+	0.630273i	$0.782943\pi$
$32$	732.592	+	1268.89i	0.715422	+	1.23915i
$33$		0			0
$34$	−1250.01	+	2165.09i	−1.08133	+	1.87291i
$35$	870.311	+	819.695i	0.710458	+	0.669139i
$36$		0			0
$37$		−	55.6914i		−	0.0406804i	−0.999793	−	0.0203402i	$-0.993525\pi$
$37$		−	55.6914i		−	0.0406804i	0.999793	−	0.0203402i	$-0.00647493\pi$
$38$	−1087.55	+	1883.69i	−0.753149	+	1.30449i
$39$		0			0
$40$	−144.099	−	34.0226i	−0.0900622	−	0.0212641i
$41$	−411.405	+	237.525i	−0.244738	+	0.141300i	−0.617353	−	0.786687i	$-0.711795\pi$
$41$	−411.405	+	237.525i	−0.244738	+	0.141300i	0.372614	+	0.927986i	$0.378461\pi$
$42$		0			0
$43$	−707.073	−	408.229i	−0.382409	−	0.220784i	0.296457	−	0.955046i	$-0.404195\pi$
$43$	−707.073	−	408.229i	−0.382409	−	0.220784i	−0.678866	+	0.734262i	$0.737528\pi$
$44$		−	1440.38i		−	0.743999i
$45$		0			0
$46$	3756.67			1.77537
$47$	−435.232	+	753.844i	−0.197027	+	0.341260i	−0.947563	−	0.319569i	$-0.896462\pi$
$47$	−435.232	+	753.844i	−0.197027	+	0.341260i	0.750536	+	0.660829i	$0.229795\pi$
$48$		0			0
$49$	−57.0270	−	98.7737i	−0.0237514	−	0.0411386i
$50$	−2997.71	+	1978.95i	−1.19909	+	0.791581i
$51$		0			0
$52$	3295.14	+	1902.45i	1.21862	+	0.703570i
$53$	2339.28			0.832780			0.416390	−	0.909186i	$-0.363295\pi$
$53$	2339.28			0.832780			0.416390	+	0.909186i	$0.363295\pi$
$54$		0			0
$55$	−1539.21	−	1449.69i	−0.508828	−	0.479236i
$56$	−245.279	−	141.612i	−0.0782140	−	0.0451569i
$57$		0			0
$58$	−2472.46	+	1427.47i	−0.734976	+	0.424338i
$59$	1019.68	−	588.710i	0.292926	−	0.169121i	−0.346335	−	0.938111i	$-0.612574\pi$
$59$	1019.68	−	588.710i	0.292926	−	0.169121i	0.639261	+	0.768990i	$0.279240\pi$
$60$		0			0
$61$	3456.52	−	5986.86i	0.928921	−	1.60894i	0.143792	−	0.989608i	$-0.454070\pi$
$61$	3456.52	−	5986.86i	0.928921	−	1.60894i	0.785130	−	0.619331i	$-0.212596\pi$
$62$	−1741.38			−0.453013
$63$		0			0
$64$	−4605.53			−1.12440
$65$	5349.42	−	1606.48i	1.26613	−	0.380231i
$66$		0			0
$67$	3356.29	−	1937.75i	0.747669	−	0.431667i	−0.0771820	−	0.997017i	$-0.524592\pi$
$67$	3356.29	−	1937.75i	0.747669	−	0.431667i	0.824851	+	0.565350i	$0.191259\pi$
$68$	−3704.11	−	6415.71i	−0.801063	−	1.38748i
$69$		0			0
$70$	−6580.75	+	1976.26i	−1.34301	+	0.403318i
$71$		−	5822.30i		−	1.15499i	−0.816394	−	0.577495i	$-0.804030\pi$
$71$		−	5822.30i		−	1.15499i	0.816394	−	0.577495i	$-0.195970\pi$
$72$		0			0
$73$		−	6443.82i		−	1.20920i	−0.796530	−	0.604599i	$-0.793333\pi$
$73$		−	6443.82i		−	1.20920i	0.796530	−	0.604599i	$-0.206667\pi$
$74$	277.189	+	160.035i	0.0506189	+	0.0292249i
$75$		0			0
$76$	−3222.69	−	5581.85i	−0.557944	−	0.966388i
$77$	−2022.31	−	3502.75i	−0.341088	−	0.590782i
$78$		0			0
$79$	−2446.72	+	4237.84i	−0.392039	+	0.679032i	−0.992718	−	0.120459i	$-0.961564\pi$
$79$	−2446.72	+	4237.84i	−0.392039	+	0.679032i	0.600679	+	0.799490i	$0.294897\pi$
$80$	−4087.17	+	4339.54i	−0.638620	+	0.678054i
$81$		0			0
$82$		−	2730.21i		−	0.406040i
$83$	3257.36	−	5641.91i	0.472835	−	0.818974i	−0.526682	−	0.850063i	$-0.676564\pi$
$83$	3257.36	−	5641.91i	0.472835	−	0.818974i	0.999517	+	0.0310882i	$0.00989729\pi$
$84$		0			0
$85$	−10583.9	−	2498.92i	−1.46491	−	0.345871i
$86$	4063.70	−	2346.18i	0.549446	−	0.317223i
$87$		0			0
$88$	433.793	+	250.451i	0.0560167	+	0.0323413i
$89$			13898.7i			1.75467i	0.479881	+	0.877333i	$0.340680\pi$
$89$			13898.7i			1.75467i	−0.479881	+	0.877333i	$0.659320\pi$
$90$		0			0
$91$	10684.3			1.29021
$92$	−5566.00	+	9640.59i	−0.657609	+	1.13901i
$93$		0			0
$94$	−2501.37	−	4332.50i	−0.283089	−	0.490324i
$95$	−9208.33	−	2174.13i	−1.02031	−	0.240901i
$96$		0			0
$97$	11681.7	+	6744.42i	1.24154	+	0.716805i	0.969408	−	0.245454i	$-0.0789372\pi$
$97$	11681.7	+	6744.42i	1.24154	+	0.716805i	0.272134	+	0.962259i	$0.412271\pi$
$98$	655.493			0.0682521
$99$		0			0
$100$	−637.001	−	10625.0i	−0.0637001	−	1.06250i
$101$	−15773.9	−	9107.04i	−1.54631	−	0.892760i	−0.998419	−	0.0562073i	$-0.982099\pi$
$101$	−15773.9	−	9107.04i	−1.54631	−	0.892760i	−0.547886	−	0.836553i	$-0.684567\pi$
$102$		0			0
$103$	11205.3	−	6469.37i	1.05620	−	0.609800i	0.131825	−	0.991273i	$-0.457916\pi$
$103$	11205.3	−	6469.37i	1.05620	−	0.609800i	0.924380	+	0.381473i	$0.124583\pi$
$104$	−1145.91	+	661.590i	−0.105946	+	0.0611677i
$105$		0			0
$106$	−6722.17	+	11643.1i	−0.598271	+	1.03624i
$107$	1372.35			0.119867			0.0599333	−	0.998202i	$-0.480911\pi$
$107$	1372.35			0.119867			0.0599333	+	0.998202i	$0.480911\pi$
$108$		0			0
$109$	8324.99			0.700698			0.350349	−	0.936619i	$-0.386063\pi$
$109$	8324.99			0.700698			0.350349	+	0.936619i	$0.386063\pi$
$110$	11638.5	−	3495.15i	0.961861	−	0.288855i
$111$		0			0
$112$	−9875.44	+	5701.59i	−0.787264	+	0.454527i
$113$	10406.4	+	18024.4i	0.814972	+	1.41157i	0.909348	+	0.416036i	$0.136581\pi$
$113$	10406.4	+	18024.4i	0.814972	+	1.41157i	−0.0943766	+	0.995537i	$0.530086\pi$
$114$		0			0
$115$	4700.06	+	15650.8i	0.355392	+	1.18342i
$116$		−	8459.96i		−	0.628712i
$117$		0			0
$118$			6766.89i			0.485987i
$119$	−18015.5	−	10401.2i	−1.27219	−	0.734499i
$120$		0			0
$121$	−3743.90	−	6484.62i	−0.255713	−	0.442908i
$122$	19865.3	+	34407.8i	1.33468	+	2.31173i
$123$		0			0
$124$	2580.08	−	4468.83i	0.167799	−	0.290637i
$125$	−11995.1	−	10012.9i	−0.767685	−	0.640828i
$126$		0			0
$127$			3442.90i			0.213460i	0.994288	+	0.106730i	$0.0340380\pi$
$127$			3442.90i			0.213460i	−0.994288	+	0.106730i	$0.965962\pi$
$128$	1513.00	−	2620.60i	0.0923465	−	0.159949i
$129$		0			0
$130$	−7376.31	+	31241.7i	−0.436468	+	1.84862i
$131$	4773.97	−	2756.25i	0.278187	−	0.160611i	−0.354415	−	0.935088i	$-0.615320\pi$
$131$	4773.97	−	2756.25i	0.278187	−	0.160611i	0.632602	+	0.774477i	$0.281987\pi$
$132$		0			0
$133$	−15674.0	−	9049.38i	−0.886086	−	0.511582i
$134$			22273.4i			1.24044i
$135$		0			0
$136$	2576.26			0.139287
$137$	2167.08	−	3753.49i	0.115460	−	0.199983i	−0.802503	−	0.596648i	$-0.796499\pi$
$137$	2167.08	−	3753.49i	0.115460	−	0.199983i	0.917964	+	0.396664i	$0.129832\pi$
$138$		0			0
$139$	−1687.03	−	2922.01i	−0.0873157	−	0.151235i	0.819060	−	0.573708i	$-0.194496\pi$
$139$	−1687.03	−	2922.01i	−0.0873157	−	0.151235i	−0.906376	+	0.422473i	$0.861162\pi$
$140$	4678.65	−	19816.0i	0.238707	−	1.01102i
$141$		0			0
$142$	28979.0	+	16731.0i	1.43716	+	0.829747i
$143$	−18895.9			−0.924048
$144$		0			0
$145$	−9040.39	−	8514.62i	−0.429983	−	0.404976i
$146$	32072.4	+	18517.0i	1.50462	+	0.868691i
$147$		0			0
$148$	−821.384	+	474.226i	−0.0374993	+	0.0216502i
$149$	29042.9	−	16768.0i	1.30818	−	0.755279i	0.326389	−	0.945235i	$-0.394168\pi$
$149$	29042.9	−	16768.0i	1.30818	−	0.755279i	0.981793	+	0.189956i	$0.0608347\pi$
$150$		0			0
$151$	−517.293	+	895.978i	−0.0226873	+	0.0392955i	−0.877146	−	0.480224i	$-0.840556\pi$
$151$	−517.293	+	895.978i	−0.0226873	+	0.0392955i	0.854459	+	0.519519i	$0.173889\pi$
$152$	2241.42			0.0970143
$153$		0			0
$154$	23245.3			0.980154
$155$	−2178.68	−	7254.81i	−0.0906840	−	0.301969i
$156$		0			0
$157$	−3936.83	+	2272.93i	−0.159716	+	0.0922119i	−0.577728	−	0.816230i	$-0.696060\pi$
$157$	−3936.83	+	2272.93i	−0.159716	+	0.0922119i	0.418012	+	0.908442i	$0.362727\pi$
$158$	−14061.8	−	24355.8i	−0.563283	−	0.975635i
$159$		0			0
$160$	−10535.4	−	35081.8i	−0.411538	−	1.37038i
$161$			31258.9i			1.20593i
$162$		0			0
$163$			35857.6i			1.34960i	0.737999	+	0.674802i	$0.235771\pi$
$163$			35857.6i			1.34960i	−0.737999	+	0.674802i	$0.764229\pi$
$164$	7006.43	+	4045.17i	0.260501	+	0.150400i
$165$		0			0
$166$	18720.8	+	32425.3i	0.679371	+	1.17671i
$167$	11108.8	+	19241.0i	0.398322	+	0.689914i	0.993519	−	0.113666i	$-0.0362593\pi$
$167$	11108.8	+	19241.0i	0.398322	+	0.689914i	−0.595197	+	0.803580i	$0.702926\pi$
$168$		0			0
$169$	10677.1	−	18493.3i	0.373836	−	0.647502i
$170$	42851.8	−	45497.9i	1.48276	−	1.57432i
$171$		0			0
$172$			13904.7i			0.470007i
$173$	17596.1	−	30477.3i	0.587928	−	1.01832i	−0.406575	−	0.913617i	$-0.633277\pi$
$173$	17596.1	−	30477.3i	0.587928	−	1.01832i	0.994503	−	0.104704i	$-0.0333896\pi$
$174$		0			0
$175$	−16466.7	−	24943.7i	−0.537687	−	0.814487i
$176$	17465.4	−	10083.7i	0.563837	−	0.325531i
$177$		0			0
$178$	−69177.2	−	39939.5i	−2.18335	−	1.26056i
$179$		−	44189.5i		−	1.37915i	−0.724213	−	0.689577i	$-0.757797\pi$
$179$		−	44189.5i		−	1.37915i	0.724213	−	0.689577i	$-0.242203\pi$
$180$		0			0
$181$	−41327.3			−1.26148			−0.630740	−	0.775994i	$-0.717249\pi$
$181$	−41327.3			−1.26148			−0.630740	+	0.775994i	$0.717249\pi$
$182$	−30702.4	+	53178.1i	−0.926892	+	1.60542i
$183$		0			0
$184$	−1935.61	−	3352.58i	−0.0571719	−	0.0990246i
$185$	−319.929	+	1355.03i	−0.00934781	+	0.0395918i
$186$		0			0
$187$	31861.6	+	18395.3i	0.911139	+	0.526046i
$188$	14824.4			0.419433
$189$		0			0
$190$	37282.3	−	39584.4i	1.03275	−	1.09652i
$191$	−20718.0	−	11961.5i	−0.567912	−	0.327884i	0.188403	−	0.982092i	$-0.439669\pi$
$191$	−20718.0	−	11961.5i	−0.567912	−	0.327884i	−0.756315	+	0.654208i	$0.773002\pi$
$192$		0			0
$193$	−2034.57	+	1174.66i	−0.0546209	+	0.0315354i	−0.527062	−	0.849827i	$-0.676706\pi$
$193$	−2034.57	+	1174.66i	−0.0546209	+	0.0315354i	0.472441	+	0.881362i	$0.343373\pi$
$194$	−67137.1	+	38761.6i	−1.78385	+	1.02991i
$195$		0			0
$196$	−971.198	+	1682.16i	−0.0252811	+	0.0437881i
$197$	−9314.30			−0.240004			−0.120002	−	0.992774i	$-0.538290\pi$
$197$	−9314.30			−0.240004			−0.120002	+	0.992774i	$0.538290\pi$
$198$		0			0
$199$	−6189.82			−0.156305			−0.0781524	−	0.996941i	$-0.524902\pi$
$199$	−6189.82			−0.156305			−0.0781524	+	0.996941i	$0.524902\pi$
$200$	3310.64	+	1655.61i	0.0827660	+	0.0413902i
$201$		0			0
$202$	90655.8	−	52340.2i	2.22174	−	1.28272i
$203$	−11877.9	−	20573.1i	−0.288235	−	0.499238i
$204$		0			0
$205$	11374.4	−	3415.84i	0.270658	−	0.0812811i
$206$			74361.7i			1.75233i
$207$		0			0
$208$			53273.9i			1.23137i
$209$	27720.5	+	16004.5i	0.634613	+	0.366394i
$210$		0			0
$211$	−716.811	−	1241.55i	−0.0161005	−	0.0278869i	0.857863	−	0.513879i	$-0.171792\pi$
$211$	−716.811	−	1241.55i	−0.0161005	−	0.0278869i	−0.873963	+	0.485992i	$0.838459\pi$
$212$	−19919.5	−	34501.7i	−0.443208	−	0.767659i
$213$		0			0
$214$	−3943.60	+	6830.52i	−0.0861124	+	0.149151i
$215$	14858.7	+	13994.5i	0.321442	+	0.302748i
$216$		0			0
$217$		−	14489.9i		−	0.307712i
$218$	−23922.8	+	41435.4i	−0.503383	+	0.871884i
$219$		0			0
$220$	−8274.52	+	35045.9i	−0.170961	+	0.724090i
$221$	−84165.5	+	48593.0i	−1.72326	+	0.994922i
$222$		0			0
$223$	−322.537	−	186.217i	−0.00648589	−	0.00374463i	0.496754	−	0.867892i	$-0.334525\pi$
$223$	−322.537	−	186.217i	−0.00648589	−	0.00374463i	−0.503239	+	0.864147i	$0.667859\pi$
$224$		−	70068.1i		−	1.39645i
$225$		0			0
$226$	−119615.			−2.34191
$227$	−15116.7	+	26182.9i	−0.293363	+	0.508119i	−0.974603	−	0.223941i	$-0.928108\pi$
$227$	−15116.7	+	26182.9i	−0.293363	+	0.508119i	0.681240	+	0.732060i	$0.261441\pi$
$228$		0			0
$229$	22086.6	+	38255.1i	0.421171	+	0.729489i	0.996054	−	0.0887464i	$-0.0282861\pi$
$229$	22086.6	+	38255.1i	0.421171	+	0.729489i	−0.574884	+	0.818235i	$0.694953\pi$
$230$	−91403.7	−	21580.9i	−1.72786	−	0.407956i
$231$		0			0
$232$	2547.85	+	1471.00i	0.0473367	+	0.0273298i
$233$	−22978.1			−0.423255			−0.211628	−	0.977350i	$-0.567876\pi$
$233$	−22978.1			−0.423255			−0.211628	+	0.977350i	$0.567876\pi$
$234$		0			0
$235$	14920.2	−	15841.5i	0.270172	−	0.286854i
$236$	−17365.6	−	10026.0i	−0.311792	−	0.180013i
$237$		0			0
$238$	103539.	−	59778.2i	1.82789	−	1.05533i
$239$	58892.2	−	34001.4i	1.03101	−	0.595253i	0.113735	−	0.993511i	$-0.463719\pi$
$239$	58892.2	−	34001.4i	1.03101	−	0.595253i	0.917273	+	0.398258i	$0.130385\pi$
$240$		0			0
$241$	−34731.9	+	60157.4i	−0.597991	+	1.03575i	0.395126	+	0.918627i	$0.370701\pi$
$241$	−34731.9	+	60157.4i	−0.597991	+	1.03575i	−0.993117	+	0.117124i	$0.962633\pi$
$242$	43034.0			0.734820
$243$		0			0
$244$	−117732.			−1.97750
$245$	820.104	+	2730.87i	0.0136627	+	0.0454955i
$246$		0			0
$247$	−73226.4	+	42277.3i	−1.20026	+	0.692968i
$248$	897.239	+	1554.06i	0.0145883	+	0.0252677i
$249$		0			0
$250$	84305.9	−	30929.1i	1.34889	−	0.494865i
$251$			44839.6i			0.711728i	0.934538	+	0.355864i	$0.115813\pi$
$251$			44839.6i			0.711728i	−0.934538	+	0.355864i	$0.884187\pi$
$252$		0			0
$253$		−	55283.6i		−	0.863684i
$254$	−17136.1	−	9893.53i	−0.265610	−	0.153350i
$255$		0			0
$256$	−28148.6	−	48754.9i	−0.429514	−	0.743941i
$257$	256.172	+	443.703i	0.00387852	+	0.00671779i	0.867958	−	0.496637i	$-0.165432\pi$
$257$	256.172	+	443.703i	0.00387852	+	0.00671779i	−0.864080	+	0.503355i	$0.832099\pi$
$258$		0			0
$259$	−1331.64	+	2306.47i	−0.0198512	+	0.0343833i
$260$	−69245.3	−	65218.1i	−1.02434	−	0.964765i
$261$		0			0
$262$			31681.6i			0.461534i
$263$	23457.5	−	40629.7i	0.339134	−	0.587397i	−0.645136	−	0.764068i	$-0.723199\pi$
$263$	23457.5	−	40629.7i	0.339134	−	0.587397i	0.984270	+	0.176671i	$0.0565327\pi$
$264$		0			0
$265$	−56917.1	−	13438.4i	−0.810496	−	0.191362i
$266$	90081.7	−	52008.7i	1.27313	−	0.735043i
$267$		0			0
$268$	−57159.2	−	33000.9i	−0.795823	−	0.459469i
$269$		−	18619.3i		−	0.257311i	−0.991689	−	0.128655i	$-0.958934\pi$
$269$		−	18619.3i		−	0.257311i	0.991689	−	0.128655i	$-0.0410661\pi$
$270$		0			0
$271$	119151.			1.62240			0.811201	−	0.584767i	$-0.198814\pi$
$271$	119151.			1.62240			0.811201	+	0.584767i	$0.198814\pi$
$272$	51862.7	−	89828.8i	0.700998	−	1.21416i
$273$		0			0
$274$	12454.7	+	21572.1i	0.165894	+	0.287337i
$275$	29122.5	+	44114.6i	0.385090	+	0.583334i
$276$		0			0
$277$	−24078.5	−	13901.7i	−0.313812	−	0.181179i	0.334819	−	0.942282i	$-0.391325\pi$
$277$	−24078.5	−	13901.7i	−0.313812	−	0.181179i	−0.648631	+	0.761103i	$0.724658\pi$
$278$	19391.4			0.250911
$279$		0			0
$280$	5154.38	+	4854.61i	0.0657446	+	0.0619211i
$281$	−4746.39	−	2740.33i	−0.0601106	−	0.0347049i	0.469644	−	0.882856i	$-0.344382\pi$
$281$	−4746.39	−	2740.33i	−0.0601106	−	0.0347049i	−0.529754	+	0.848151i	$0.677716\pi$
$282$		0			0
$283$	104022.	−	60056.9i	1.29883	−	0.749877i	0.318624	−	0.947881i	$-0.396779\pi$
$283$	104022.	−	60056.9i	1.29883	−	0.749877i	0.980201	+	0.198004i	$0.0634460\pi$
$284$	−85872.2	+	49578.3i	−1.06467	+	0.614689i
$285$		0			0
$286$	54299.3	−	94049.2i	0.663838	−	1.14980i
$287$	22717.8			0.275806
$288$		0			0
$289$	105702.			1.26558
$290$	68357.8	−	20528.5i	0.812816	−	0.244096i
$291$		0			0
$292$	−95038.8	+	54870.7i	−1.11464	+	0.643539i
$293$	10131.5	+	17548.3i	0.118016	+	0.204409i	0.918981	−	0.394301i	$-0.129013\pi$
$293$	10131.5	+	17548.3i	0.118016	+	0.204409i	−0.800966	+	0.598710i	$0.795680\pi$
$294$		0			0
$295$	−28191.7	+	8466.22i	−0.323949	+	0.0972849i
$296$		−	329.830i		−	0.00376450i
$297$		0			0
$298$			192738.i			2.17038i
$299$	126472.	+	73018.4i	1.41466	+	0.816752i
$300$		0			0
$301$	19522.3	+	33813.7i	0.215476	+	0.373215i
$302$	−2972.99	−	5149.38i	−0.0325972	−	0.0564600i
$303$		0			0
$304$	45122.0	−	78153.6i	0.488249	−	0.845672i
$305$	−118493.	+	125810.i	−1.27378	+	1.35243i
$306$		0			0
$307$		−	132432.i		−	1.40512i	−0.711623	−	0.702562i	$-0.752039\pi$
$307$		−	132432.i		−	1.40512i	0.711623	−	0.702562i	$-0.247961\pi$
$308$	−34441.0	+	59653.5i	−0.363056	+	0.628832i
$309$		0			0
$310$	42369.6	+	10003.7i	0.440890	+	0.104096i
$311$	118174.	−	68227.6i	1.22180	−	0.705406i	0.256498	−	0.966545i	$-0.417431\pi$
$311$	118174.	−	68227.6i	1.22180	−	0.705406i	0.965301	+	0.261139i	$0.0840981\pi$
$312$		0			0
$313$	−94500.3	−	54559.8i	−0.964594	−	0.556909i	−0.0670101	−	0.997752i	$-0.521346\pi$
$313$	−94500.3	−	54559.8i	−0.964594	−	0.556909i	−0.897584	+	0.440844i	$0.854679\pi$
$314$		−	26126.0i		−	0.264981i
$315$		0			0
$316$	83337.5			0.834577
$317$	−21419.5	+	37099.7i	−0.213153	+	0.369191i	−0.952700	−	0.303914i	$-0.901707\pi$
$317$	−21419.5	+	37099.7i	−0.213153	+	0.369191i	0.739547	+	0.673105i	$0.235040\pi$
$318$		0			0
$319$	21006.9	+	36384.9i	0.206433	+	0.357553i
$320$	112057.	+	26457.2i	1.09431	+	0.258371i
$321$		0			0
$322$	−155583.	−	89825.9i	−1.50055	−	0.866343i
$323$	164630.			1.57798
$324$		0			0
$325$	−139385.	+	8356.59i	−1.31963	+	0.0791157i
$326$	−178472.	−	103041.i	−1.67932	−	0.969559i
$327$		0			0
$328$	−2436.53	+	1406.73i	−0.0226477	+	0.0130757i
$329$	36050.3	−	20813.7i	0.333056	−	0.192290i
$330$		0			0
$331$	54784.8	−	94890.0i	0.500039	−	0.866093i	−0.499961	−	0.866048i	$-0.666652\pi$
$331$	54784.8	−	94890.0i	0.500039	−	0.866093i	1.00000		4.48028e-5i	$-1.42612e-5\pi$
$332$	−110949.			−1.00658
$333$		0			0
$334$	−127689.			−1.14462
$335$	−92793.6	+	27866.7i	−0.826854	+	0.248311i
$336$		0			0
$337$	−7974.17	+	4603.89i	−0.0702143	+	0.0405383i	−0.534696	−	0.845044i	$-0.679574\pi$
$337$	−7974.17	+	4603.89i	−0.0702143	+	0.0405383i	0.464482	+	0.885583i	$0.346241\pi$
$338$	61363.7	+	106285.i	0.537128	+	0.930334i
$339$		0			0
$340$	53268.7	+	177380.i	0.460802	+	1.53443i
$341$			25626.3i			0.220383i
$342$		0			0
$343$			120275.i			1.02232i
$344$	−4187.61	−	2417.72i	−0.0353875	−	0.0204310i
$345$		0			0
$346$	101129.	+	175160.i	0.844737	+	1.46313i
$347$	−11277.8	−	19533.8i	−0.0936628	−	0.162229i	0.815387	−	0.578916i	$-0.196524\pi$
$347$	−11277.8	−	19533.8i	−0.0936628	−	0.162229i	−0.909050	+	0.416688i	$0.863191\pi$
$348$		0			0
$349$	−101902.	+	176500.i	−0.836629	+	1.44908i	0.0560687	+	0.998427i	$0.482143\pi$
$349$	−101902.	+	176500.i	−0.836629	+	1.44908i	−0.892697	+	0.450657i	$0.851190\pi$
$350$	171469.	−	10280.1i	1.39975	−	0.0839193i
$351$		0			0
$352$			123920.i			1.00013i
$353$	−32305.1	+	55954.1i	−0.259252	+	0.449038i	−0.966042	−	0.258386i	$-0.916809\pi$
$353$	−32305.1	+	55954.1i	−0.259252	+	0.449038i	0.706790	+	0.707424i	$0.250143\pi$
$354$		0			0
$355$	−33447.2	+	141663.i	−0.265401	+	1.12408i
$356$	204990.	−	118351.i	1.61746	−	0.933839i
$357$		0			0
$358$	219941.	+	126983.i	1.71609	+	0.990787i
$359$		−	39569.8i		−	0.307026i	−0.988147	−	0.153513i	$-0.950941\pi$
$359$		−	39569.8i		−	0.307026i	0.988147	−	0.153513i	$-0.0490587\pi$
$360$		0			0
$361$	12911.4			0.0990741
$362$	118759.	−	205696.i	0.906250	−	1.56967i
$363$		0			0
$364$	−90979.1	−	157580.i	−0.686656	−	1.18932i
$365$	−37017.6	+	156785.i	−0.277858	+	1.17684i
$366$		0			0
$367$	168361.	+	97203.5i	1.25000	+	0.721688i	0.971109	−	0.238634i	$-0.0766998\pi$
$367$	168361.	+	97203.5i	1.25000	+	0.721688i	0.278891	+	0.960323i	$0.410033\pi$
$368$	−155863.			−1.15093
$369$		0			0
$370$	−5824.95	−	5486.18i	−0.0425489	−	0.0400744i
$371$	−96881.5	−	55934.5i	−0.703871	−	0.406380i
$372$		0			0
$373$	−92982.6	+	53683.5i	−0.668319	+	0.385854i	−0.795439	−	0.606033i	$-0.792760\pi$
$373$	−92982.6	+	53683.5i	−0.668319	+	0.385854i	0.127120	+	0.991887i	$0.459427\pi$
$374$	−183116.	+	105722.i	−1.30913	+	0.755826i
$375$		0			0
$376$	−2577.64	+	4464.61i	−0.0182325	+	0.0315797i
$377$	−110983.			−0.780863
$378$		0			0
$379$	231550.			1.61200			0.806002	−	0.591913i	$-0.201627\pi$
$379$	231550.			1.61200			0.806002	+	0.591913i	$0.201627\pi$
$380$	46345.3	+	154326.i	0.320951	+	1.06874i
$381$		0			0
$382$	119071.	−	68745.5i	0.815978	−	0.471105i
$383$	−23281.5	−	40324.7i	−0.158713	−	0.274899i	0.775692	−	0.631112i	$-0.217401\pi$
$383$	−23281.5	−	40324.7i	−0.158713	−	0.274899i	−0.934405	+	0.356213i	$0.884068\pi$
$384$		0			0
$385$	29082.8	+	96843.0i	0.196207	+	0.653351i
$386$		−	13502.1i		−	0.0906204i
$387$		0			0
$388$		−	229721.i		−	1.52594i
$389$	13106.7	+	7567.17i	0.0866154	+	0.0500074i	0.542682	−	0.839938i	$-0.317409\pi$
$389$	13106.7	+	7567.17i	0.0866154	+	0.0500074i	−0.456067	+	0.889946i	$0.650742\pi$
$390$		0			0
$391$	−142168.	−	246243.i	−0.929928	−	1.61068i
$392$	−337.740	−	584.983i	−0.00219791	−	0.00380690i
$393$		0			0
$394$	26765.7	−	46359.5i	0.172419	−	0.298639i
$395$	83876.1	−	89055.3i	0.537581	−	0.570776i
$396$		0			0
$397$		−	49119.2i		−	0.311652i	−0.987784	−	0.155826i	$-0.950196\pi$
$397$		−	49119.2i		−	0.311652i	0.987784	−	0.155826i	$-0.0498040\pi$
$398$	17787.1	−	30808.2i	0.112290	−	0.194491i
$399$		0			0
$400$	124374.	−	82106.1i	0.777339	−	0.513163i
$401$	116070.	−	67013.0i	0.721823	−	0.416745i	−0.0936000	−	0.995610i	$-0.529837\pi$
$401$	116070.	−	67013.0i	0.721823	−	0.416745i	0.815423	+	0.578865i	$0.196504\pi$
$402$		0			0
$403$	−58625.1	−	33847.2i	−0.360972	−	0.208407i
$404$			310195.i			1.90052i
$405$		0			0
$406$	136529.			0.828274
$407$	2355.10	−	4079.15i	0.0142174	−	0.0246252i
$408$		0			0
$409$	27109.9	+	46955.6i	0.162062	+	0.280699i	0.935608	−	0.353041i	$-0.114852\pi$
$409$	27109.9	+	46955.6i	0.162062	+	0.280699i	−0.773546	+	0.633740i	$0.781519\pi$
$410$	−15684.2	+	66428.9i	−0.0933027	+	0.395175i
$411$		0			0
$412$	−190831.	−	110177.i	−1.12423	−	0.649075i
$413$	−56306.6			−0.330110
$414$		0			0
$415$	−111666.	+	118561.i	−0.648372	+	0.688408i
$416$	−283491.	−	163674.i	−1.63815	−	0.945784i
$417$		0			0
$418$	−159316.	+	91981.1i	−0.911815	+	0.526436i
$419$	−152988.	+	88327.4i	−0.871421	+	0.503115i	−0.867820	−	0.496878i	$-0.834480\pi$
$419$	−152988.	+	88327.4i	−0.871421	+	0.503115i	−0.00360107	+	0.999994i	$0.501146\pi$
$420$		0			0
$421$	−71752.2	+	124278.i	−0.404829	+	0.701184i	−0.994302	−	0.106605i	$-0.966002\pi$
$421$	−71752.2	+	124278.i	−0.404829	+	0.701184i	0.589473	+	0.807788i	$0.299335\pi$
$422$	8239.33			0.0462665
$423$		0			0
$424$	13854.3			0.0770642
$425$	243163.	+	121603.i	1.34623	+	0.673232i
$426$		0			0
$427$	−286304.	+	165298.i	−1.57026	+	0.906590i
$428$	−11685.9	−	20240.6i	−0.0637933	−	0.110493i
$429$		0			0
$430$	−112352.	+	33740.3i	−0.607637	+	0.182479i
$431$		−	96119.3i		−	0.517435i	−0.965953	−	0.258718i	$-0.916700\pi$
$431$		−	96119.3i		−	0.517435i	0.965953	−	0.258718i	$-0.0832999\pi$
$432$		0			0
$433$		−	313068.i		−	1.66979i	−0.550406	−	0.834897i	$-0.685527\pi$
$433$		−	313068.i		−	1.66979i	0.550406	−	0.834897i	$-0.314473\pi$
$434$	72119.4	+	41638.2i	0.382889	+	0.221061i
$435$		0			0
$436$	−70889.3	−	122784.i	−0.372913	−	0.645905i
$437$	−123691.	−	214238.i	−0.647700	−	1.12185i
$438$		0			0
$439$	52165.3	−	90353.0i	0.270678	−	0.468828i	−0.698358	−	0.715749i	$-0.746085\pi$
$439$	52165.3	−	90353.0i	0.270678	−	0.468828i	0.969036	+	0.246921i	$0.0794188\pi$
$440$	−9115.88	−	8585.72i	−0.0470862	−	0.0443477i
$441$		0			0
$442$		−	558549.i		−	2.85902i
$443$	−15363.5	+	26610.4i	−0.0782860	+	0.135595i	−0.902511	−	0.430668i	$-0.858278\pi$
$443$	−15363.5	+	26610.4i	−0.0782860	+	0.135595i	0.824225	+	0.566263i	$0.191611\pi$
$444$		0			0
$445$	79843.6	−	338170.i	0.403199	−	1.70771i
$446$	1853.69	−	1070.23i	0.00931896	−	0.00538030i
$447$		0			0
$448$	190738.	+	110123.i	0.950346	+	0.548683i
$449$		−	47332.1i		−	0.234781i	−0.993086	−	0.117391i	$-0.962547\pi$
$449$		−	47332.1i		−	0.234781i	0.993086	−	0.117391i	$-0.0374529\pi$
$450$		0			0
$451$	−40178.1			−0.197531
$452$	177226.	−	306964.i	0.867461	−	1.50249i
$453$		0			0
$454$	−86878.9	−	150479.i	−0.421505	−	0.730068i
$455$	−259959.	−	61377.6i	−1.25569	−	0.296474i
$456$		0			0
$457$	−101954.	−	58863.4i	−0.488173	−	0.281847i	0.235643	−	0.971840i	$-0.424280\pi$
$457$	−101954.	−	58863.4i	−0.488173	−	0.281847i	−0.723816	+	0.689993i	$0.757614\pi$
$458$	−253873.			−1.21028
$459$		0			0
$460$	190808.	−	202591.i	0.901741	−	0.957423i
$461$	38057.7	+	21972.6i	0.179077	+	0.103390i	0.586859	−	0.809689i	$-0.300364\pi$
$461$	38057.7	+	21972.6i	0.179077	+	0.103390i	−0.407782	+	0.913079i	$0.633698\pi$
$462$		0			0
$463$	−32818.2	+	18947.6i	−0.153092	+	0.0883878i	−0.574589	−	0.818442i	$-0.694838\pi$
$463$	−32818.2	+	18947.6i	−0.153092	+	0.0883878i	0.421497	+	0.906830i	$0.361505\pi$
$464$	102582.	−	59225.5i	0.476467	−	0.275089i
$465$		0			0
$466$	66030.0	−	114367.i	0.304067	−	0.526660i
$467$	229722.			1.05334			0.526671	−	0.850069i	$-0.323440\pi$
$467$	229722.			1.05334			0.526671	+	0.850069i	$0.323440\pi$
$468$		0			0
$469$	−185335.			−0.842579
$470$	35972.1	+	119784.i	0.162844	+	0.542254i
$471$		0			0
$472$	6038.99	−	3486.61i	0.0271069	−	0.0156502i
$473$	−34526.6	−	59801.9i	−0.154323	−	0.267296i
$474$		0			0
$475$	211559.	+	105798.i	0.937656	+	0.468910i
$476$			354276.i			1.56361i
$477$		0			0
$478$			390827.i			1.71052i
$479$	42607.9	+	24599.7i	0.185703	+	0.107216i	0.589969	−	0.807426i	$-0.299140\pi$
$479$	42607.9	+	24599.7i	0.185703	+	0.107216i	−0.404266	+	0.914641i	$0.632473\pi$
$480$		0			0
$481$	6221.21	+	10775.5i	0.0268896	+	0.0465742i
$482$	−199612.	−	345738.i	−0.859196	−	1.48817i
$483$		0			0
$484$	−63760.4	+	110436.i	−0.272183	+	0.471434i
$485$	−245483.	−	231206.i	−1.04361	−	0.982914i
$486$		0			0
$487$			154002.i			0.649335i	0.945828	+	0.324668i	$0.105252\pi$
$487$			154002.i			0.649335i	−0.945828	+	0.324668i	$0.894748\pi$
$488$	20471.1	−	35456.9i	0.0859609	−	0.148889i
$489$		0			0
$490$	−15948.8	−	3765.59i	−0.0664258	−	0.0156834i
$491$	−146133.	+	84370.0i	−0.606158	+	0.349965i	−0.771460	−	0.636278i	$-0.780473\pi$
$491$	−146133.	+	84370.0i	−0.606158	+	0.349965i	0.165302	+	0.986243i	$0.447140\pi$
$492$		0			0
$493$	187137.	+	108043.i	0.769954	+	0.444533i
$494$		−	485954.i		−	1.99132i
$495$		0			0
$496$	72249.3			0.293677
$497$	−139217.	+	241131.i	−0.563612	+	0.976204i
$498$		0			0
$499$	−87254.6	−	151129.i	−0.350419	−	0.606943i	0.635904	−	0.771768i	$-0.280627\pi$
$499$	−87254.6	−	151129.i	−0.350419	−	0.606943i	−0.986323	+	0.164825i	$0.947294\pi$
$500$	−45538.1	+	262176.i	−0.182153	+	1.04870i
$501$		0			0
$502$	−223177.	−	128851.i	−0.885610	−	0.511307i
$503$	384923.			1.52138			0.760691	−	0.649115i	$-0.224860\pi$
$503$	384923.			1.52138			0.760691	+	0.649115i	$0.224860\pi$
$504$		0			0
$505$	331477.	+	312199.i	1.29978	+	1.22419i
$506$	275159.	+	158863.i	1.07469	+	0.620473i
$507$		0			0
$508$	50778.7	−	29317.1i	0.196768	−	0.113604i
$509$	115913.	−	66922.3i	0.447400	−	0.258306i	−0.259332	−	0.965788i	$-0.583502\pi$
$509$	115913.	−	66922.3i	0.447400	−	0.258306i	0.706731	+	0.707482i	$0.250169\pi$
$510$		0			0
$511$	−154078.	+	266871.i	−0.590065	+	1.02202i
$512$	371969.			1.41895
$513$		0			0
$514$	−2944.55			−0.0111453
$515$	−309800.	+	93035.7i	−1.16807	+	0.350780i
$516$		0			0
$517$	−63757.6	+	36810.5i	−0.238534	+	0.137718i
$518$	−7653.21	−	13255.8i	−0.0285223	−	0.0494020i
$519$		0			0
$520$	31681.7	−	9514.29i	0.117166	−	0.0351860i
$521$			128028.i			0.471662i	0.971794	+	0.235831i	$0.0757812\pi$
$521$			128028.i			0.471662i	−0.971794	+	0.235831i	$0.924219\pi$
$522$		0			0
$523$		−	396160.i		−	1.44833i	−0.689627	−	0.724165i	$-0.742225\pi$
$523$		−	396160.i		−	1.44833i	0.689627	−	0.724165i	$-0.257775\pi$
$524$	−81303.1	−	46940.3i	−0.296104	−	0.170956i
$525$		0			0
$526$	134816.	+	233507.i	0.487269	+	0.843974i
$527$	65901.2	+	114144.i	0.237286	+	0.410991i
$528$		0			0
$529$	−73709.3	+	127668.i	−0.263397	+	0.456217i
$530$	230443.	−	244673.i	0.820375	−	0.871032i
$531$		0			0
$532$			308231.i			1.08906i
$533$	53067.1	−	91915.0i	0.186798	−	0.323543i
$534$		0			0
$535$	−33390.7	−	7883.71i	−0.116659	−	0.0275438i
$536$	19877.5	−	11476.3i	0.0691881	−	0.0399458i
$537$		0			0
$538$	92672.5	+	53504.5i	0.320174	+	0.184853i
$539$		−	9646.31i		−	0.0332035i
$540$		0			0
$541$	−411433.			−1.40574			−0.702870	−	0.711318i	$-0.748098\pi$
$541$	−411433.			−1.40574			−0.702870	+	0.711318i	$0.748098\pi$
$542$	−342393.	+	593042.i	−1.16554	+	2.01877i
$543$		0			0
$544$	318676.	+	551963.i	1.07684	+	1.86514i
$545$	−202556.	−	47824.3i	−0.681948	−	0.161011i
$546$		0			0
$547$	224830.	+	129806.i	0.751414	+	0.433829i	0.826205	−	0.563370i	$-0.190495\pi$
$547$	224830.	+	129806.i	0.751414	+	0.433829i	−0.0747906	+	0.997199i	$0.523829\pi$
$548$	−73812.8			−0.245794
$549$		0			0
$550$	−303255.	+	18181.1i	−1.00250	+	0.0601028i
$551$	162814.	+	94000.8i	0.536277	+	0.309620i
$552$		0			0
$553$	202662.	−	117007.i	0.662707	−	0.382614i
$554$	138384.	−	79896.1i	0.450886	−	0.260319i
$555$		0			0
$556$	−28730.9	+	49763.3i	−0.0929393	+	0.160976i
$557$	−261444.			−0.842691			−0.421345	−	0.906900i	$-0.638442\pi$
$557$	−261444.			−0.842691			−0.421345	+	0.906900i	$0.638442\pi$
$558$		0			0
$559$	182411.			0.583750
$560$	273033.	−	81994.3i	0.870642	−	0.261461i
$561$		0			0
$562$	27278.5	−	15749.3i	0.0863671	−	0.0498641i
$563$	185109.	+	320619.i	0.583999	+	1.01152i	0.994999	+	0.0998803i	$0.0318460\pi$
$563$	185109.	+	320619.i	0.583999	+	1.01152i	−0.411001	+	0.911635i	$0.634821\pi$
$564$		0			0
$565$	−149654.	−	498333.i	−0.468803	−	1.56107i
$566$			690320.i			2.15485i
$567$		0			0
$568$		−	34482.3i		−	0.106881i
$569$	−442601.	−	255536.i	−1.36706	−	0.789273i	−0.376509	−	0.926413i	$-0.622876\pi$
$569$	−442601.	−	255536.i	−1.36706	−	0.789273i	−0.990552	+	0.137140i	$0.956209\pi$
$570$		0			0
$571$	−9362.89	−	16217.0i	−0.0287169	−	0.0497391i	0.851310	−	0.524663i	$-0.175809\pi$
$571$	−9362.89	−	16217.0i	−0.0287169	−	0.0497391i	−0.880027	+	0.474924i	$0.842475\pi$
$572$	160903.	+	278692.i	0.491781	+	0.851790i
$573$		0			0
$574$	−65282.2	+	113072.i	−0.198139	+	0.343187i
$575$	−24448.9	−	407800.i	−0.0739474	−	1.23342i
$576$		0			0
$577$			165587.i			0.497364i	0.968585	+	0.248682i	$0.0799975\pi$
$577$			165587.i			0.497364i	−0.968585	+	0.248682i	$0.920003\pi$
$578$	−303746.	+	526104.i	−0.909192	+	1.57477i
$579$		0			0
$580$	−48599.7	+	205839.i	−0.144470	+	0.611889i
$581$	−269808.	+	155774.i	−0.799286	+	0.461468i
$582$		0			0
$583$	171342.	+	98924.2i	0.504111	+	0.291048i
$584$		−	38163.3i		−	0.111897i
$585$		0			0
$586$	−116456.			−0.339131
$587$	279639.	−	484350.i	0.811563	−	1.40567i	−0.100207	−	0.994967i	$-0.531951\pi$
$587$	279639.	−	484350.i	0.811563	−	1.40567i	0.911770	−	0.410701i	$-0.134716\pi$
$588$		0			0
$589$	57335.9	+	99308.7i	0.165271	+	0.286257i
$590$	38873.5	−	164645.i	0.111673	−	0.472983i
$591$		0			0
$592$	−11500.5	−	6639.82i	−0.0328151	−	0.0189458i
$593$	398735.			1.13390			0.566950	−	0.823752i	$-0.308123\pi$
$593$	398735.			1.13390			0.566950	+	0.823752i	$0.308123\pi$
$594$		0			0
$595$	378583.	+	356566.i	1.06937	+	1.00718i
$596$	−494616.	−	285566.i	−1.39244	−	0.803923i
$597$		0			0
$598$	−726860.	+	419653.i	−2.03258	+	1.17351i
$599$	203260.	−	117352.i	0.566497	−	0.327067i	−0.189252	−	0.981929i	$-0.560606\pi$
$599$	203260.	−	117352.i	0.566497	−	0.327067i	0.755749	+	0.654861i	$0.227273\pi$
$600$		0			0
$601$	115910.	−	200763.i	0.320903	−	0.555820i	−0.659772	−	0.751466i	$-0.729347\pi$
$601$	115910.	−	200763.i	0.320903	−	0.555820i	0.980675	+	0.195646i	$0.0626805\pi$
$602$	−224398.			−0.619193
$603$		0			0
$604$	17619.5			0.0482970
$605$	53840.9	+	179285.i	0.147096	+	0.489816i
$606$		0			0
$607$	459653.	−	265381.i	1.24753	−	0.720264i	0.276917	−	0.960894i	$-0.410687\pi$
$607$	459653.	−	265381.i	1.24753	−	0.720264i	0.970617	+	0.240630i	$0.0773539\pi$
$608$	277257.	+	480224.i	0.750025	+	1.29908i
$609$		0			0
$610$	−285683.	−	951297.i	−0.767758	−	2.55656i
$611$		−	194477.i		−	0.520937i
$612$		0			0
$613$		−	688057.i		−	1.83106i	−0.402247	−	0.915531i	$-0.631771\pi$
$613$		−	688057.i		−	1.83106i	0.402247	−	0.915531i	$-0.368229\pi$
$614$	659143.	+	380556.i	1.74841	+	1.00944i
$615$		0			0
$616$	−11977.1	−	20744.9i	−0.0315638	−	0.0546701i
$617$	−70869.2	−	122749.i	−0.186160	−	0.322439i	0.757807	−	0.652479i	$-0.226271\pi$
$617$	−70869.2	−	122749.i	−0.186160	−	0.322439i	−0.943967	+	0.330040i	$0.892938\pi$
$618$		0			0
$619$	276156.	−	478316.i	0.720731	−	1.24834i	−0.239977	−	0.970779i	$-0.577140\pi$
$619$	276156.	−	478316.i	0.720731	−	1.24834i	0.960707	−	0.277563i	$-0.0895268\pi$
$620$	−88448.0	+	93909.5i	−0.230094	+	0.244302i
$621$		0			0
$622$			784237.i			2.02706i
$623$	332332.	−	575617.i	0.856242	−	1.48305i
$624$		0			0
$625$	234331.	+	312533.i	0.599888	+	0.800084i
$626$	543114.	−	313567.i	1.38593	−	0.800168i
$627$		0			0
$628$	67046.2	+	38709.1i	0.170002	+	0.0981508i
$629$		−	24225.6i		−	0.0612314i
$630$		0			0
$631$	231361.			0.581073			0.290537	−	0.956864i	$-0.406166\pi$
$631$	231361.			0.581073			0.290537	+	0.956864i	$0.406166\pi$
$632$	−14490.6	+	25098.4i	−0.0362787	+	0.0628365i
$633$		0			0
$634$	−123103.	−	213220.i	−0.306259	−	0.530456i
$635$	19778.3	−	83769.2i	0.0490503	−	0.207748i
$636$		0			0
$637$	22067.7	+	12740.8i	0.0543850	+	0.0313992i
$638$	−241462.			−0.593208
$639$		0			0
$640$	−51867.5	+	55070.2i	−0.126630	+	0.134449i
$641$	390167.	+	225263.i	0.949587	+	0.548244i	0.892952	−	0.450151i	$-0.148630\pi$
$641$	390167.	+	225263.i	0.949587	+	0.548244i	0.0566340	+	0.998395i	$0.481963\pi$
$642$		0			0
$643$	−265023.	+	153011.i	−0.641006	+	0.370085i	−0.785002	−	0.619493i	$-0.787338\pi$
$643$	−265023.	+	153011.i	−0.641006	+	0.370085i	0.143996	+	0.989578i	$0.454005\pi$
$644$	461033.	−	266177.i	1.11163	−	0.641799i
$645$		0			0
$646$	−473081.	+	819400.i	−1.13363	+	1.96350i
$647$	−200004.			−0.477782			−0.238891	−	0.971046i	$-0.576784\pi$
$647$	−200004.			−0.477782			−0.238891	+	0.971046i	$0.576784\pi$
$648$		0			0
$649$	99582.2			0.236424
$650$	358946.	−	717768.i	0.849577	−	1.69886i
$651$		0			0
$652$	528859.	−	305337.i	1.24407	−	0.718263i
$653$	−257809.	−	446538.i	−0.604604	−	1.04721i	−0.992114	−	0.125340i	$-0.959998\pi$
$653$	−257809.	−	446538.i	−0.604604	−	1.04721i	0.387509	−	0.921866i	$-0.373335\pi$
$654$		0			0
$655$	−131989.	+	39637.6i	−0.307650	+	0.0923899i
$656$			113276.i			0.263226i
$657$		0			0
$658$			239241.i			0.552567i
$659$	−301526.	−	174086.i	−0.694312	−	0.400861i	0.110913	−	0.993830i	$-0.464622\pi$
$659$	−301526.	−	174086.i	−0.694312	−	0.400861i	−0.805225	+	0.592969i	$0.797956\pi$
$660$		0			0
$661$	12324.1	+	21346.0i	0.0282068	+	0.0488556i	0.879784	−	0.475373i	$-0.157687\pi$
$661$	12324.1	+	21346.0i	0.0282068	+	0.0488556i	−0.851577	+	0.524229i	$0.824354\pi$
$662$	314860.	+	545353.i	0.718458	+	1.24441i
$663$		0			0
$664$	19291.6	−	33414.0i	0.0437554	−	0.0757866i
$665$	329378.	+	310222.i	0.744821	+	0.701504i
$666$		0			0
$667$		−	324703.i		−	0.729852i
$668$	189188.	−	327684.i	0.423976	−	0.734348i
$669$		0			0
$670$	127953.	−	541934.i	0.285037	−	1.20725i
$671$	506349.	−	292340.i	1.12462	−	0.649298i
$672$		0			0
$673$	−275390.	−	158997.i	−0.608020	−	0.351041i	0.164170	−	0.986432i	$-0.447505\pi$
$673$	−275390.	−	158997.i	−0.608020	−	0.351041i	−0.772190	+	0.635391i	$0.780839\pi$
$674$		−	52919.1i		−	0.116491i
$675$		0			0
$676$	−363673.			−0.795825
$677$	−65955.5	+	114238.i	−0.143904	+	0.249250i	−0.928964	−	0.370171i	$-0.879299\pi$
$677$	−65955.5	+	114238.i	−0.143904	+	0.249250i	0.785059	+	0.619421i	$0.212632\pi$
$678$		0			0
$679$	−322532.	−	558641.i	−0.699573	−	1.21170i
$680$	−62683.0	−	14799.7i	−0.135560	−	0.0320064i
$681$		0			0
$682$	−127548.	−	73640.0i	−0.274224	−	0.158323i
$683$	−539667.			−1.15687			−0.578435	−	0.815729i	$-0.696336\pi$
$683$	−539667.			−1.15687			−0.578435	+	0.815729i	$0.696336\pi$
$684$		0			0
$685$	−74289.8	+	78877.1i	−0.158324	+	0.168101i
$686$	−598637.	−	345623.i	−1.27208	−	0.734437i
$687$		0			0
$688$	−168602.	+	97342.3i	−0.356193	+	0.205648i
$689$	−452615.	+	261318.i	−0.953435	+	0.550466i
$690$		0			0
$691$	194856.	−	337500.i	0.408091	−	0.706834i	−0.586585	−	0.809888i	$-0.699528\pi$
$691$	194856.	−	337500.i	0.408091	−	0.706834i	0.994676	+	0.103054i	$0.0328614\pi$
$692$	−599341.			−1.25159
$693$		0			0
$694$	129632.			0.269150
$695$	24261.1	+	80787.0i	0.0502273	+	0.167252i
$696$		0			0
$697$	−178960.	+	103323.i	−0.368376	+	0.212682i
$698$	−585654.	−	1.01438e6i	−1.20207	−	2.08205i
$699$		0			0
$700$	−227673.	+	455266.i	−0.464638	+	0.929114i
$701$			831525.i			1.69215i	0.533063	+	0.846076i	$0.321041\pi$
$701$			831525.i			1.69215i	−0.533063	+	0.846076i	$0.678959\pi$
$702$		0			0
$703$		−	21077.0i		−	0.0426480i
$704$	−337334.	−	194760.i	−0.680636	−	0.392965i
$705$		0			0
$706$	−185665.	−	321580.i	−0.372494	−	0.645179i
$707$	435517.	+	754338.i	0.871298	+	1.50913i
$708$		0			0
$709$	−20819.3	+	36060.0i	−0.0414164	+	0.0717354i	−0.885991	−	0.463703i	$-0.846520\pi$
$709$	−20819.3	+	36060.0i	−0.0414164	+	0.0717354i	0.844574	+	0.535439i	$0.179854\pi$
$710$	−608974.	−	573557.i	−1.20804	−	1.13778i
$711$		0			0
$712$			82314.6i			0.162374i
$713$	99026.6	−	171519.i	0.194793	−	0.337391i
$714$		0			0
$715$	459756.	+	108551.i	0.899322	+	0.212334i
$716$	−651743.	+	376284.i	−1.27131	+	0.733989i
$717$		0			0
$718$	196948.	+	113708.i	0.382035	+	0.220568i
$719$			800950.i			1.54934i	0.632364	+	0.774671i	$0.282085\pi$
$719$			800950.i			1.54934i	−0.632364	+	0.774671i	$0.717915\pi$
$720$		0			0
$721$	−618757.			−1.19028
$722$	−37102.4	+	64263.3i	−0.0711750	+	0.123279i
$723$		0			0
$724$	351912.	+	609530.i	0.671363	+	1.16284i
$725$	171048.	+	259104.i	0.325419	+	0.492944i
$726$		0			0
$727$	722549.	+	417164.i	1.36709	+	0.789292i	0.990556	−	0.137109i	$-0.0437810\pi$
$727$	722549.	+	417164.i	1.36709	+	0.789292i	0.376538	+	0.926401i	$0.377114\pi$
$728$	63277.1			0.119394
$729$		0			0
$730$	−673980.	−	634783.i	−1.26474	−	1.19119i
$731$	−307575.	−	177579.i	−0.575595	−	0.332320i
$732$		0			0
$733$	359667.	−	207654.i	0.669411	−	0.386485i	−0.126442	−	0.991974i	$-0.540356\pi$
$733$	359667.	−	207654.i	0.669411	−	0.386485i	0.795854	+	0.605489i	$0.207022\pi$
$734$	−967609.	+	558649.i	−1.79601	+	1.03692i
$735$		0			0
$736$	478860.	−	829409.i	0.884000	−	1.53113i
$737$	327777.			0.603453
$738$		0			0
$739$	−862015.			−1.57843			−0.789216	−	0.614115i	$-0.789513\pi$
$739$	−862015.			−1.57843			−0.789216	+	0.614115i	$0.789513\pi$
$740$	22709.4	−	6819.83i	0.0414708	−	0.0124540i
$741$		0			0
$742$	556799.	−	321468.i	1.01132	−	0.583888i
$743$	−152108.	−	263459.i	−0.275534	−	0.477239i	0.694736	−	0.719265i	$-0.255521\pi$
$743$	−152108.	−	263459.i	−0.275534	−	0.477239i	−0.970270	+	0.242026i	$0.922188\pi$
$744$		0			0
$745$	−802971.	+	241139.i	−1.44673	+	0.434466i
$746$		−	617062.i		−	1.10879i
$747$		0			0
$748$		−	626563.i		−	1.11985i
$749$	−56836.1	−	32814.3i	−0.101312	−	0.0584925i
$750$		0			0
$751$	477638.	+	827293.i	0.846874	+	1.46683i	0.883984	+	0.467518i	$0.154852\pi$
$751$	477638.	+	827293.i	0.846874	+	1.46683i	−0.0371095	+	0.999311i	$0.511815\pi$
$752$	103781.	+	179754.i	0.183520	+	0.317866i
$753$		0			0
$754$	318922.	−	552390.i	0.560973	−	0.971634i
$755$	17733.4	−	18828.4i	0.0311098	−	0.0330308i
$756$		0			0
$757$		−	233252.i		−	0.407037i	−0.979071	−	0.203518i	$-0.934762\pi$
$757$		−	233252.i		−	0.407037i	0.979071	−	0.203518i	$-0.0652377\pi$
$758$	−665383.	+	1.15248e6i	−1.15807	+	2.00583i
$759$		0			0
$760$	−54536.0	−	12876.2i	−0.0944183	−	0.0222926i
$761$	309676.	−	178791.i	0.534734	−	0.308729i	−0.208208	−	0.978085i	$-0.566763\pi$
$761$	309676.	−	178791.i	0.534734	−	0.308729i	0.742942	+	0.669356i	$0.233430\pi$
$762$		0			0
$763$	−344780.	−	199059.i	−0.592234	−	0.341926i
$764$			407422.i			0.698003i
$765$		0			0
$766$	267607.			0.456079
$767$	−131528.	+	227813.i	−0.223577	+	0.387247i
$768$		0			0
$769$	104137.	+	180371.i	0.176098	+	0.305010i	0.940541	−	0.339681i	$-0.110319\pi$
$769$	104137.	+	180371.i	0.176098	+	0.305010i	−0.764443	+	0.644692i	$0.776986\pi$
$770$	−565583.	−	133537.i	−0.953926	−	0.225226i
$771$		0			0
$772$	34649.8	+	20005.1i	0.0581388	+	0.0335665i
$773$	328500.			0.549764			0.274882	−	0.961478i	$-0.411361\pi$
$773$	328500.			0.549764			0.274882	+	0.961478i	$0.411361\pi$
$774$		0			0
$775$	11333.1	+	189033.i	0.0188688	+	0.314727i
$776$	69184.2	+	39943.5i	0.114890	+	0.0663320i
$777$		0			0
$778$	−75327.2	+	43490.2i	−0.124449	+	0.0718509i
$779$	−155701.	+	89893.8i	−0.256576	+	0.148134i
$780$		0			0
$781$	246215.	−	426457.i	0.403657	−	0.699155i
$782$	1.63414e6			2.67225
$783$		0			0
$784$	−27196.2			−0.0442462
$785$	108844.	−	32686.9i	0.176631	−	0.0530438i
$786$		0			0
$787$	−184283.	+	106396.i	−0.297533	+	0.171781i	−0.641334	−	0.767262i	$-0.721619\pi$
$787$	−184283.	+	106396.i	−0.297533	+	0.171781i	0.343801	+	0.939042i	$0.388285\pi$
$788$	79313.6	+	137375.i	0.127731	+	0.221236i
$789$		0			0
$790$	202222.	+	673381.i	0.324022	+	1.07896i
$791$		−	995308.i		−	1.59076i
$792$		0			0
$793$			1.54449e6i			2.45606i
$794$	244478.	+	141149.i	0.387792	+	0.223892i
$795$		0			0
$796$	52707.9	+	91292.7i	0.0831858	+	0.144082i
$797$	75817.1	+	131319.i	0.119358	+	0.206734i	0.919513	−	0.393059i	$-0.128583\pi$
$797$	75817.1	+	131319.i	0.119358	+	0.206734i	−0.800156	+	0.599792i	$0.795250\pi$
$798$		0			0
$799$	−189325.	+	327921.i	−0.296561	+	0.513659i
$800$	54803.1	+	914099.i	0.0856298	+	1.42828i
$801$		0			0
$802$			770276.i			1.19756i
$803$	272498.	−	471981.i	0.422603	−	0.731970i
$804$		0			0
$805$	179572.	−	760561.i	0.277107	−	1.17366i
$806$	336931.	−	194527.i	0.518646	−	0.299440i
$807$		0			0
$808$	−93420.1	−	53936.1i	−0.143093	−	0.0826146i
$809$			66493.9i			0.101598i	0.998709	+	0.0507989i	$0.0161768\pi$
$809$			66493.9i			0.101598i	−0.998709	+	0.0507989i	$0.983823\pi$
$810$		0			0
$811$	1.27019e6			1.93120			0.965602	−	0.260025i	$-0.0837307\pi$
$811$	1.27019e6			1.93120			0.965602	+	0.260025i	$0.0837307\pi$
$812$	−202286.	+	350370.i	−0.306799	+	0.531391i
$813$		0			0
$814$	13535.2	+	23443.7i	0.0204276	+	0.0353816i
$815$	205990.	−	872453.i	0.310121	−	1.31349i
$816$		0			0
$817$	−267599.	−	154499.i	−0.400905	−	0.231462i
$818$	−311612.			−0.465702
$819$		0			0
$820$	−147236.	−	138673.i	−0.218970	−	0.206235i
$821$	−415193.	−	239712.i	−0.615975	−	0.355634i	0.159325	−	0.987226i	$-0.449068\pi$
$821$	−415193.	−	239712.i	−0.615975	−	0.355634i	−0.775300	+	0.631593i	$0.782402\pi$
$822$		0			0
$823$	125938.	−	72710.6i	0.185934	−	0.107349i	−0.404144	−	0.914695i	$-0.632430\pi$
$823$	125938.	−	72710.6i	0.185934	−	0.107349i	0.590078	+	0.807346i	$0.299097\pi$
$824$	66362.8	−	38314.6i	0.0977395	−	0.0564299i
$825$		0			0
$826$	161803.	−	280251.i	0.237152	−	0.410759i
$827$	−893602.			−1.30657			−0.653286	−	0.757111i	$-0.726610\pi$
$827$	−893602.			−1.30657			−0.653286	+	0.757111i	$0.726610\pi$
$828$		0			0
$829$	−659734.			−0.959975			−0.479988	−	0.877275i	$-0.659359\pi$
$829$	−659734.			−0.959975			−0.479988	+	0.877275i	$0.659359\pi$
$830$	−269223.	−	896485.i	−0.390801	−	1.30133i
$831$		0			0
$832$	891100.	−	514477.i	1.28730	−	0.743223i
$833$	−24806.6	−	42966.4i	−0.0357501	−	0.0619211i
$834$		0			0
$835$	−159755.	−	531970.i	−0.229130	−	0.762982i
$836$		−	545128.i		−	0.779984i
$837$		0			0
$838$		−	1.01527e6i		−	1.44576i
$839$	797201.	+	460264.i	1.13251	+	0.653857i	0.944566	−	0.328322i	$-0.106483\pi$
$839$	797201.	+	460264.i	1.13251	+	0.653857i	0.187948	+	0.982179i	$0.439816\pi$
$840$		0			0
$841$	−230259.	−	398819.i	−0.325555	−	0.563877i
$842$	−412375.	−	714255.i	−0.581659	−	1.00746i
$843$		0			0
$844$	−12207.6	+	21144.2i	−0.0171375	+	0.0296830i
$845$	−366023.	+	388625.i	−0.512620	+	0.544273i
$846$		0			0
$847$			358082.i			0.499132i
$848$	278901.	−	483070.i	0.387845	−	0.671767i
$849$		0			0
$850$	−1.30400e6	+	860840.i	−1.80484	+	1.19147i
$851$	−31525.7	+	18201.4i	−0.0435317	+	0.0251330i
$852$		0			0
$853$	−627776.	−	362447.i	−0.862793	−	0.498134i	0.00215352	−	0.999998i	$-0.499315\pi$
$853$	−627776.	−	362447.i	−0.862793	−	0.498134i	−0.864947	+	0.501864i	$0.832648\pi$
$854$		−	1.90000e6i		−	2.60518i
$855$		0			0
$856$	8127.70			0.0110923
$857$	−492013.	+	852192.i	−0.669908	+	1.16032i	0.308021	+	0.951380i	$0.400333\pi$
$857$	−492013.	+	852192.i	−0.669908	+	1.16032i	−0.977929	+	0.208936i	$0.933000\pi$
$858$		0			0
$859$	−365776.	−	633542.i	−0.495711	−	0.858597i	0.504277	−	0.863542i	$-0.331759\pi$
$859$	−365776.	−	633542.i	−0.495711	−	0.858597i	−0.999988	+	0.00494530i	$0.998426\pi$
$860$	79877.8	−	338315.i	0.108001	−	0.457430i
$861$		0			0
$862$	478408.	+	276209.i	0.643849	+	0.371727i
$863$	498062.			0.668747			0.334374	−	0.942441i	$-0.391475\pi$
$863$	498062.			0.668747			0.334374	+	0.942441i	$0.391475\pi$
$864$		0			0
$865$	−603213.	+	640461.i	−0.806193	+	0.855974i
$866$	1.55821e6	+	899635.i	2.07774	+	1.19958i
$867$		0			0
$868$	−213709.	+	123385.i	−0.283650	+	0.163765i
$869$	−358422.	+	206935.i	−0.474630	+	0.274028i
$870$		0			0
$871$	−432927.	+	749852.i	−0.570662	+	0.988415i
$872$	49304.4			0.0648415
$873$		0			0
$874$	1.42175e6			1.86124
$875$	257358.	+	701501.i	0.336141	+	0.916246i
$876$		0			0
$877$	−1.18504e6	+	684183.i	−1.54076	+	0.889556i	−0.541965	+	0.840401i	$0.682319\pi$
$877$	−1.18504e6	+	684183.i	−1.54076	+	0.889556i	−0.998791	+	0.0491545i	$0.984347\pi$
$878$	299805.	+	519278.i	0.388911	+	0.673614i
$879$		0			0
$880$	−482878.	+	145013.i	−0.623552	+	0.187258i
$881$		−	1.19744e6i		−	1.54277i	−0.636368	−	0.771386i	$-0.719564\pi$
$881$		−	1.19744e6i		−	1.54277i	0.636368	−	0.771386i	$-0.280436\pi$
$882$		0			0
$883$		−	461117.i		−	0.591412i	−0.955279	−	0.295706i	$-0.904445\pi$
$883$		−	461117.i		−	0.591412i	0.955279	−	0.295706i	$-0.0955548\pi$
$884$	1.43338e6	+	827563.i	1.83424	+	1.05900i
$885$		0			0
$886$	−88297.6	−	152936.i	−0.112482	−	0.194824i
$887$	−427242.	−	740004.i	−0.543033	−	0.940561i	−0.998728	−	0.0504250i	$-0.983942\pi$
$887$	−427242.	−	740004.i	−0.543033	−	0.940561i	0.455695	−	0.890136i	$-0.349391\pi$
$888$		0			0
$889$	82323.1	−	142588.i	0.104164	−	0.180418i
$890$	1.45371e6	+	1.36917e6i	1.83526	+	1.72853i
$891$		0			0
$892$			6342.73i			0.00797162i
$893$	−164718.	+	285300.i	−0.206556	+	0.357766i
$894$		0			0
$895$	−253854.	+	1.07517e6i	−0.316911	+	1.34225i
$896$	−125322.	+	72355.0i	−0.156104	+	0.0901265i
$897$		0			0
$898$	235583.	+	136014.i	0.292140	+	0.168667i
$899$			150514.i			0.186233i
$900$		0			0
$901$	1.01758e6			1.25349
$902$	115456.	−	199976.i	0.141907	−	0.245790i
$903$		0			0
$904$	61631.3	+	106749.i	0.0754162	+	0.130625i
$905$	1.00554e6	+	237412.i	1.22772	+	0.289871i
$906$		0			0
$907$	403158.	+	232764.i	0.490073	+	0.282944i	0.724605	−	0.689164i	$-0.242022\pi$
$907$	403158.	+	232764.i	0.490073	+	0.282944i	−0.234531	+	0.972109i	$0.575356\pi$
$908$	514890.			0.624514
$909$		0			0
$910$	1.05251e6	−	1.11750e6i	1.27099	−	1.34948i
$911$	−596214.	−	344224.i	−0.718398	−	0.414767i	0.0957646	−	0.995404i	$-0.469470\pi$
$911$	−596214.	−	344224.i	−0.718398	−	0.414767i	−0.814163	+	0.580637i	$0.802804\pi$
$912$		0			0
$913$	477174.	−	275497.i	0.572447	−	0.330502i
$914$	585954.	−	338301.i	0.701409	−	0.404959i
$915$		0			0
$916$	376146.	−	651504.i	0.448296	−	0.776472i
$917$	−263619.			−0.313501
$918$		0			0
$919$	−692392.			−0.819825			−0.409912	−	0.912125i	$-0.634441\pi$
$919$	−692392.			−0.819825			−0.409912	+	0.912125i	$0.634441\pi$
$920$	27835.9	+	92691.0i	0.0328875	+	0.109512i
$921$		0			0
$922$	−218726.	+	126281.i	−0.257299	+	0.148552i
$923$	650401.	+	1.12653e6i	0.763445	+	1.32233i
$924$		0			0
$925$	15568.4	−	31131.4i	0.0181954	−	0.0363844i
$926$		−	217792.i		−	0.253992i
$927$		0			0
$928$			727835.i			0.845157i
$929$	−430458.	−	248525.i	−0.498768	−	0.287964i	0.229436	−	0.973324i	$-0.426312\pi$
$929$	−430458.	−	248525.i	−0.498768	−	0.287964i	−0.728205	+	0.685360i	$0.759645\pi$
$930$		0			0
$931$	−21582.5	−	37382.0i	−0.0249002	−	0.0431283i
$932$	195664.	+	338900.i	0.225258	+	0.390158i
$933$		0			0
$934$	−660132.	+	1.14338e6i	−0.756723	+	1.31068i
$935$	−669551.	−	630612.i	−0.765879	−	0.721338i
$936$		0			0
$937$		−	761906.i		−	0.867805i	−0.900960	−	0.433903i	$-0.857136\pi$
$937$		−	761906.i		−	0.867805i	0.900960	−	0.433903i	$-0.142864\pi$
$938$	532579.	−	922453.i	0.605310	−	1.04843i
$939$		0			0
$940$	−360694.	−	85161.5i	−0.408209	−	0.0963801i
$941$	222911.	−	128697.i	0.251740	−	0.145342i	−0.368821	−	0.929500i	$-0.620238\pi$
$941$	222911.	−	128697.i	0.251740	−	0.145342i	0.620561	+	0.784159i	$0.286905\pi$
$942$		0			0
$943$	268915.	+	155258.i	0.302407	+	0.174595i
$944$		−	280756.i		−	0.315054i
$945$		0			0
$946$	396864.			0.443465
$947$	−231511.	+	400990.i	−0.258150	+	0.447129i	−0.965746	−	0.259488i	$-0.916446\pi$
$947$	−231511.	+	400990.i	−0.258150	+	0.447129i	0.707596	+	0.706617i	$0.249780\pi$
$948$		0			0
$949$	719830.	+	1.24678e6i	0.799277	+	1.38439i
$950$	−1.13452e6	+	748955.i	−1.25708	+	0.829868i
$951$		0			0
$952$	−106696.	−	61600.9i	−0.117726	−	0.0679694i
$953$	−323955.			−0.356696			−0.178348	−	0.983967i	$-0.557075\pi$
$953$	−323955.			−0.356696			−0.178348	+	0.983967i	$0.557075\pi$
$954$		0			0
$955$	435375.	+	410054.i	0.477371	+	0.449609i
$956$	−1.00296e6	−	579061.i	−1.09741	−	0.633591i
$957$		0			0
$958$	−244877.	+	141380.i	−0.266819	+	0.154048i
$959$	−179499.	+	103634.i	−0.195176	+	0.112685i
$960$		0			0
$961$	415857.	−	720286.i	0.450296	−	0.779935i
$962$	−71509.3			−0.0772702
$963$		0			0
$964$	1.18300e6			1.27301
$965$	56251.3	−	16892.8i	0.0604057	−	0.0181404i
$966$		0			0
$967$	−511790.	+	295482.i	−0.547317	+	0.315994i	−0.748039	−	0.663654i	$-0.769005\pi$
$967$	−511790.	+	295482.i	−0.547317	+	0.315994i	0.200722	+	0.979648i	$0.435671\pi$
$968$	−22173.1	−	38404.9i	−0.0236633	−	0.0409861i
$969$		0			0
$970$	1.85619e6	−	557429.i	1.97278	−	0.592443i
$971$			1.14727e6i			1.21682i	0.793622	+	0.608412i	$0.208193\pi$
$971$			1.14727e6i			1.21682i	−0.793622	+	0.608412i	$0.791807\pi$
$972$		0			0
$973$			161354.i			0.170433i
$974$	−766505.	−	442542.i	−0.807973	−	0.466484i
$975$		0			0
$976$	−824207.	−	1.42757e6i	−0.865240	−	1.49864i
$977$	429287.	+	743546.i	0.449737	+	0.778967i	0.998369	−	0.0570972i	$-0.0181845\pi$
$977$	429287.	+	743546.i	0.449737	+	0.778967i	−0.548632	+	0.836064i	$0.684851\pi$
$978$		0			0
$979$	−587753.	+	1.01802e6i	−0.613239	+	1.06216i
$980$	33293.7	−	35349.6i	0.0346665	−	0.0368071i
$981$		0			0
$982$		−	969785.i		−	1.00566i
$983$	−580320.	+	1.00514e6i	−0.600566	+	1.04021i	0.392170	+	0.919893i	$0.371725\pi$
$983$	−580320.	+	1.00514e6i	−0.600566	+	1.04021i	−0.992735	+	0.120318i	$0.961609\pi$
$984$		0			0
$985$	226627.	+	53507.6i	0.233581	+	0.0551497i
$986$	−1.07551e6	+	620948.i	−1.10627	+	0.638707i
$987$		0			0
$988$	1.24708e6	+	720003.i	1.27756	+	0.737599i
$989$			533679.i			0.545616i
$990$		0			0
$991$	−1.59778e6			−1.62693			−0.813467	−	0.581611i	$-0.802422\pi$
$991$	−1.59778e6			−1.62693			−0.813467	+	0.581611i	$0.802422\pi$
$992$	−221972.	+	384467.i	−0.225567	+	0.390693i
$993$		0			0
$994$	−800111.	−	1.38583e6i	−0.809799	−	1.40261i
$995$	150605.	+	35558.5i	0.152122	+	0.0359168i
$996$		0			0
$997$	1.12879e6	+	651705.i	1.13559	+	0.655633i	0.945334	−	0.326102i	$-0.105735\pi$
$997$	1.12879e6	+	651705.i	1.13559	+	0.655633i	0.190254	+	0.981735i	$0.439069\pi$
$998$	1.00294e6			1.00697
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.5.h.a.89.4		44
3.2	odd	2		45.5.h.a.29.19	yes	44
5.4	even	2	inner	135.5.h.a.89.19		44
9.2	odd	6		405.5.d.a.404.8		44
9.4	even	3		45.5.h.a.14.4	✓	44
9.5	odd	6	inner	135.5.h.a.44.19		44
9.7	even	3		405.5.d.a.404.38		44
15.14	odd	2		45.5.h.a.29.4	yes	44
45.4	even	6		45.5.h.a.14.19	yes	44
45.14	odd	6	inner	135.5.h.a.44.4		44
45.29	odd	6		405.5.d.a.404.37		44
45.34	even	6		405.5.d.a.404.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.4	✓	44	9.4	even	3
45.5.h.a.14.19	yes	44	45.4	even	6
45.5.h.a.29.4	yes	44	15.14	odd	2
45.5.h.a.29.19	yes	44	3.2	odd	2
135.5.h.a.44.4		44	45.14	odd	6	inner
135.5.h.a.44.19		44	9.5	odd	6	inner
135.5.h.a.89.4		44	1.1	even	1	trivial
135.5.h.a.89.19		44	5.4	even	2	inner
405.5.d.a.404.7		44	45.34	even	6
405.5.d.a.404.8		44	9.2	odd	6
405.5.d.a.404.37		44	45.29	odd	6
405.5.d.a.404.38		44	9.7	even	3

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.87361 + 4.97724i) q^{2} +(-8.51525 - 14.7488i) q^{4} +(-24.3310 - 5.74467i) q^{5} +(-41.4151 - 23.9110i) q^{7} +5.92246 q^{8} +(98.5104 - 104.593i) q^{10} +(73.2455 + 42.2883i) q^{11} +(-193.485 + 111.709i) q^{13} +(238.021 - 137.422i) q^{14} +(119.225 - 206.504i) q^{16} +434.998 q^{17} +378.461 q^{19} +(122.457 + 407.772i) q^{20} +(-420.958 + 243.040i) q^{22} +(-326.825 - 566.078i) q^{23} +(558.998 + 279.547i) q^{25} -1284.03i q^{26} +814.433i q^{28} +(430.201 + 248.377i) q^{29} +(151.498 + 262.402i) q^{31} +(732.592 + 1268.89i) q^{32} +(-1250.01 + 2165.09i) q^{34} +(870.311 + 819.695i) q^{35} -55.6914i q^{37} +(-1087.55 + 1883.69i) q^{38} +(-144.099 - 34.0226i) q^{40} +(-411.405 + 237.525i) q^{41} +(-707.073 - 408.229i) q^{43} -1440.38i q^{44} +3756.67 q^{46} +(-435.232 + 753.844i) q^{47} +(-57.0270 - 98.7737i) q^{49} +(-2997.71 + 1978.95i) q^{50} +(3295.14 + 1902.45i) q^{52} +2339.28 q^{53} +(-1539.21 - 1449.69i) q^{55} +(-245.279 - 141.612i) q^{56} +(-2472.46 + 1427.47i) q^{58} +(1019.68 - 588.710i) q^{59} +(3456.52 - 5986.86i) q^{61} -1741.38 q^{62} -4605.53 q^{64} +(5349.42 - 1606.48i) q^{65} +(3356.29 - 1937.75i) q^{67} +(-3704.11 - 6415.71i) q^{68} +(-6580.75 + 1976.26i) q^{70} -5822.30i q^{71} -6443.82i q^{73} +(277.189 + 160.035i) q^{74} +(-3222.69 - 5581.85i) q^{76} +(-2022.31 - 3502.75i) q^{77} +(-2446.72 + 4237.84i) q^{79} +(-4087.17 + 4339.54i) q^{80} -2730.21i q^{82} +(3257.36 - 5641.91i) q^{83} +(-10583.9 - 2498.92i) q^{85} +(4063.70 - 2346.18i) q^{86} +(433.793 + 250.451i) q^{88} +13898.7i q^{89} +10684.3 q^{91} +(-5566.00 + 9640.59i) q^{92} +(-2501.37 - 4332.50i) q^{94} +(-9208.33 - 2174.13i) q^{95} +(11681.7 + 6744.42i) q^{97} +655.493 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) \) 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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