LMFDB - Embedded newform 135.5.h.a.44.19

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			44.19
Character	$\chi$	$=$	135.44
Dual form			135.5.h.a.89.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.87361 + 4.97724i) q^{2} +(-8.51525 + 14.7488i) q^{4} +(-7.19048 - 23.9436i) q^{5} +(41.4151 - 23.9110i) q^{7} -5.92246 q^{8} +(98.5104 - 104.593i) q^{10} +(73.2455 - 42.2883i) q^{11} +(193.485 + 111.709i) q^{13} +(238.021 + 137.422i) q^{14} +(119.225 + 206.504i) q^{16} -434.998 q^{17} +378.461 q^{19} +(414.369 + 97.8346i) q^{20} +(420.958 + 243.040i) q^{22} +(326.825 - 566.078i) q^{23} +(-521.594 + 344.332i) q^{25} +1284.03i q^{26} +814.433i q^{28} +(430.201 - 248.377i) q^{29} +(151.498 - 262.402i) q^{31} +(-732.592 + 1268.89i) q^{32} +(-1250.01 - 2165.09i) q^{34} +(-870.311 - 819.695i) q^{35} -55.6914i q^{37} +(1087.55 + 1883.69i) q^{38} +(42.5853 + 141.805i) q^{40} +(-411.405 - 237.525i) q^{41} +(707.073 - 408.229i) q^{43} +1440.38i q^{44} +3756.67 q^{46} +(435.232 + 753.844i) q^{47} +(-57.0270 + 98.7737i) q^{49} +(-3212.68 - 1606.62i) q^{50} +(-3295.14 + 1902.45i) q^{52} -2339.28 q^{53} +(-1539.21 - 1449.69i) q^{55} +(-245.279 + 141.612i) q^{56} +(2472.46 + 1427.47i) q^{58} +(1019.68 + 588.710i) q^{59} +(3456.52 + 5986.86i) q^{61} +1741.38 q^{62} -4605.53 q^{64} +(1283.46 - 5435.97i) q^{65} +(-3356.29 - 1937.75i) q^{67} +(3704.11 - 6415.71i) q^{68} +(1578.89 - 6687.22i) q^{70} +5822.30i q^{71} -6443.82i q^{73} +(277.189 - 160.035i) q^{74} +(-3222.69 + 5581.85i) q^{76} +(2022.31 - 3502.75i) q^{77} +(-2446.72 - 4237.84i) q^{79} +(4087.17 - 4339.54i) q^{80} -2730.21i q^{82} +(-3257.36 - 5641.91i) q^{83} +(3127.84 + 10415.4i) q^{85} +(4063.70 + 2346.18i) q^{86} +(-433.793 + 250.451i) q^{88} -13898.7i q^{89} +10684.3 q^{91} +(5566.00 + 9640.59i) q^{92} +(-2501.37 + 4332.50i) q^{94} +(-2721.31 - 9061.72i) q^{95} +(-11681.7 + 6744.42i) q^{97} -655.493 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.961633	+	0.274340i	$0.0884595\pi$
$2$	2.87361	+	4.97724i	0.718402	+	1.24431i	−0.243231	+	0.969968i	$0.578207\pi$
$3$		0			0
$3$		0			0
$4$	−8.51525	+	14.7488i	−0.532203	+	0.921802i
$5$	−7.19048	−	23.9436i	−0.287619	−	0.957745i
$5$	−7.19048	−	23.9436i	−0.287619	−	0.957745i
$6$		0			0
$7$	41.4151	−	23.9110i	0.845206	−	0.487980i	−0.0138245	−	0.999904i	$-0.504401\pi$
$7$	41.4151	−	23.9110i	0.845206	−	0.487980i	0.859030	+	0.511925i	$0.171067\pi$
$8$	−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	−0.165803	−	0.986159i	$-0.553021\pi$
$11$	73.2455	−	42.2883i	0.605335	−	0.349490i	0.771137	+	0.636669i	$0.219688\pi$
$12$		0			0
$13$	193.485	+	111.709i	1.14488	+	0.660998i	0.947635	−	0.319356i	$-0.103467\pi$
$13$	193.485	+	111.709i	1.14488	+	0.660998i	0.197247	+	0.980354i	$0.436800\pi$
$14$	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	$-0.771196\pi$
$17$	−434.998			−1.50518			−0.752591	+	0.658488i	$0.771196\pi$
$18$		0			0
$19$	378.461			1.04837			0.524184	−	0.851605i	$-0.324371\pi$
$19$	378.461			1.04837			0.524184	+	0.851605i	$0.324371\pi$
$20$	414.369	+	97.8346i	1.03592	+	0.244586i
$21$		0			0
$22$	420.958	+	243.040i	0.869747	+	0.502149i
$23$	326.825	−	566.078i	0.617818	−	1.07009i	−0.372066	−	0.928206i	$-0.621350\pi$
$23$	326.825	−	566.078i	0.617818	−	1.07009i	0.989883	−	0.141885i	$-0.0453163\pi$
$24$		0			0
$25$	−521.594	+	344.332i	−0.834550	+	0.550932i
$26$			1284.03i			1.89945i
$27$		0			0
$28$			814.433i			1.03882i
$29$	430.201	−	248.377i	0.511535	−	0.295335i	−0.221929	−	0.975063i	$-0.571235\pi$
$29$	430.201	−	248.377i	0.511535	−	0.295335i	0.733464	+	0.679728i	$0.237902\pi$
$30$		0			0
$31$	151.498	−	262.402i	0.157646	−	0.273051i	−0.776373	−	0.630273i	$-0.782943\pi$
$31$	151.498	−	262.402i	0.157646	−	0.273051i	0.934019	+	0.357222i	$0.116276\pi$
$32$	−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
$40$	42.5853	+	141.805i	0.0266158	+	0.0886282i
$41$	−411.405	−	237.525i	−0.244738	−	0.141300i	0.372614	−	0.927986i	$-0.378461\pi$
$41$	−411.405	−	237.525i	−0.244738	−	0.141300i	−0.617353	+	0.786687i	$0.711795\pi$
$42$		0			0
$43$	707.073	−	408.229i	0.382409	−	0.220784i	−0.296457	−	0.955046i	$-0.595805\pi$
$43$	707.073	−	408.229i	0.382409	−	0.220784i	0.678866	+	0.734262i	$0.262472\pi$
$44$			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	$-0.103538\pi$
$47$	435.232	+	753.844i	0.197027	+	0.341260i	−0.750536	+	0.660829i	$0.770205\pi$
$48$		0			0
$49$	−57.0270	+	98.7737i	−0.0237514	+	0.0411386i
$50$	−3212.68	−	1606.62i	−1.28507	−	0.642648i
$51$		0			0
$52$	−3295.14	+	1902.45i	−1.21862	+	0.703570i
$53$	−2339.28			−0.832780			−0.416390	−	0.909186i	$-0.636705\pi$
$53$	−2339.28			−0.832780			−0.416390	+	0.909186i	$0.636705\pi$
$54$		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	0.639261	−	0.768990i	$-0.279240\pi$
$59$	1019.68	+	588.710i	0.292926	+	0.169121i	−0.346335	+	0.938111i	$0.612574\pi$
$60$		0			0
$61$	3456.52	+	5986.86i	0.928921	+	1.60894i	0.785130	+	0.619331i	$0.212596\pi$
$61$	3456.52	+	5986.86i	0.928921	+	1.60894i	0.143792	+	0.989608i	$0.454070\pi$
$62$	1741.38			0.453013
$63$		0			0
$64$	−4605.53			−1.12440
$65$	1283.46	−	5435.97i	0.303777	−	1.28662i
$66$		0			0
$67$	−3356.29	−	1937.75i	−0.747669	−	0.431667i	0.0771820	−	0.997017i	$-0.475408\pi$
$67$	−3356.29	−	1937.75i	−0.747669	−	0.431667i	−0.824851	+	0.565350i	$0.808741\pi$
$68$	3704.11	−	6415.71i	0.801063	−	1.38748i
$69$		0			0
$70$	1578.89	−	6687.22i	0.322222	−	1.36474i
$71$			5822.30i			1.15499i	0.816394	+	0.577495i	$0.195970\pi$
$71$			5822.30i			1.15499i	−0.816394	+	0.577495i	$0.804030\pi$
$72$		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	0.600679	−	0.799490i	$-0.294897\pi$
$79$	−2446.72	−	4237.84i	−0.392039	−	0.679032i	−0.992718	+	0.120459i	$0.961564\pi$
$80$	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	$-0.323436\pi$
$83$	−3257.36	−	5641.91i	−0.472835	−	0.818974i	−0.999517	+	0.0310882i	$0.990103\pi$
$84$		0			0
$85$	3127.84	+	10415.4i	0.432920	+	1.44158i
$86$	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	$-0.659320\pi$
$89$		−	13898.7i		−	1.75467i	0.479881	−	0.877333i	$-0.340680\pi$
$90$		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
$95$	−2721.31	−	9061.72i	−0.301531	−	1.00407i
$96$		0			0
$97$	−11681.7	+	6744.42i	−1.24154	+	0.716805i	−0.969408	−	0.245454i	$-0.921063\pi$
$97$	−11681.7	+	6744.42i	−1.24154	+	0.716805i	−0.272134	+	0.962259i	$0.587729\pi$
$98$	−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	−0.547886	+	0.836553i	$0.684567\pi$
$101$	−15773.9	+	9107.04i	−1.54631	+	0.892760i	−0.998419	+	0.0562073i	$0.982099\pi$
$102$		0			0
$103$	−11205.3	−	6469.37i	−1.05620	−	0.609800i	−0.131825	−	0.991273i	$-0.542084\pi$
$103$	−11205.3	−	6469.37i	−1.05620	−	0.609800i	−0.924380	+	0.381473i	$0.875417\pi$
$104$	−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	$-0.519089\pi$
$107$	−1372.35			−0.119867			−0.0599333	+	0.998202i	$0.519089\pi$
$108$		0			0
$109$	8324.99			0.700698			0.350349	−	0.936619i	$-0.386063\pi$
$109$	8324.99			0.700698			0.350349	+	0.936619i	$0.386063\pi$
$110$	2792.37	−	11826.8i	0.230774	−	0.977424i
$111$		0			0
$112$	9875.44	+	5701.59i	0.787264	+	0.454527i
$113$	−10406.4	+	18024.4i	−0.814972	+	1.41157i	0.0943766	+	0.995537i	$0.469914\pi$
$113$	−10406.4	+	18024.4i	−0.814972	+	1.41157i	−0.909348	+	0.416036i	$0.863419\pi$
$114$		0			0
$115$	−15904.0	−	3755.01i	−1.20257	−	0.283933i
$116$			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
$130$	30744.2	−	9232.77i	1.81919	−	0.546318i
$131$	4773.97	+	2756.25i	0.278187	+	0.160611i	0.632602	−	0.774477i	$-0.281987\pi$
$131$	4773.97	+	2756.25i	0.278187	+	0.160611i	−0.354415	+	0.935088i	$0.615320\pi$
$132$		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	$-0.203501\pi$
$137$	−2167.08	−	3753.49i	−0.115460	−	0.199983i	−0.917964	+	0.396664i	$0.870168\pi$
$138$		0			0
$139$	−1687.03	+	2922.01i	−0.0873157	+	0.151235i	−0.906376	−	0.422473i	$-0.861162\pi$
$139$	−1687.03	+	2922.01i	−0.0873157	+	0.151235i	0.819060	+	0.573708i	$0.194496\pi$
$140$	19500.5	−	5856.16i	0.994922	−	0.298784i
$141$		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	0.981793	−	0.189956i	$-0.0608347\pi$
$149$	29042.9	+	16768.0i	1.30818	+	0.755279i	0.326389	+	0.945235i	$0.394168\pi$
$150$		0			0
$151$	−517.293	−	895.978i	−0.0226873	−	0.0392955i	0.854459	−	0.519519i	$-0.173889\pi$
$151$	−517.293	−	895.978i	−0.0226873	−	0.0392955i	−0.877146	+	0.480224i	$0.840556\pi$
$152$	−2241.42			−0.0970143
$153$		0			0
$154$	23245.3			0.980154
$155$	−7372.19	−	1740.61i	−0.306855	−	0.0724499i
$156$		0			0
$157$	3936.83	+	2272.93i	0.159716	+	0.0922119i	0.577728	−	0.816230i	$-0.303940\pi$
$157$	3936.83	+	2272.93i	0.159716	+	0.0922119i	−0.418012	+	0.908442i	$0.637273\pi$
$158$	14061.8	−	24355.8i	0.563283	−	0.975635i
$159$		0			0
$160$	35649.4	+	8417.00i	1.39256	+	0.328789i
$161$		−	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	$-0.963741\pi$
$167$	−11108.8	+	19241.0i	−0.398322	+	0.689914i	0.595197	+	0.803580i	$0.297074\pi$
$168$		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	−0.994503	−	0.104704i	$-0.966610\pi$
$173$	−17596.1	−	30477.3i	−0.587928	−	1.01832i	0.406575	−	0.913617i	$-0.366723\pi$
$174$		0			0
$175$	−13368.5	+	26732.4i	−0.436523	+	0.872894i
$176$	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	$0.242203\pi$
$179$			44189.5i			1.37915i	−0.724213	+	0.689577i	$0.757797\pi$
$180$		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
$185$	−1333.45	+	400.448i	−0.0389614	+	0.0117005i
$186$		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	−0.756315	−	0.654208i	$-0.773002\pi$
$191$	−20718.0	+	11961.5i	−0.567912	+	0.327884i	0.188403	+	0.982092i	$0.439669\pi$
$192$		0			0
$193$	2034.57	+	1174.66i	0.0546209	+	0.0315354i	0.527062	−	0.849827i	$-0.323294\pi$
$193$	2034.57	+	1174.66i	0.0546209	+	0.0315354i	−0.472441	+	0.881362i	$0.656627\pi$
$194$	−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	$-0.461710\pi$
$197$	9314.30			0.240004			0.120002	+	0.992774i	$0.461710\pi$
$198$		0			0
$199$	−6189.82			−0.156305			−0.0781524	−	0.996941i	$-0.524902\pi$
$199$	−6189.82			−0.156305			−0.0781524	+	0.996941i	$0.524902\pi$
$200$	3089.12	−	2039.29i	0.0772280	−	0.0509823i
$201$		0			0
$202$	−90655.8	−	52340.2i	−2.22174	−	1.28272i
$203$	11877.9	−	20573.1i	0.288235	−	0.499238i
$204$		0			0
$205$	−2729.00	+	11558.4i	−0.0649377	+	0.275037i
$206$		−	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	−0.873963	−	0.485992i	$-0.838459\pi$
$211$	−716.811	+	1241.55i	−0.0161005	+	0.0278869i	0.857863	+	0.513879i	$0.171792\pi$
$212$	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
$220$	34487.9	−	10357.0i	0.712561	−	0.213988i
$221$	−84165.5	−	48593.0i	−1.72326	−	0.994922i
$222$		0			0
$223$	322.537	−	186.217i	0.00648589	−	0.00374463i	−0.496754	−	0.867892i	$-0.665475\pi$
$223$	322.537	−	186.217i	0.00648589	−	0.00374463i	0.503239	+	0.864147i	$0.332141\pi$
$224$			70068.1i			1.39645i
$225$		0			0
$226$	−119615.			−2.34191
$227$	15116.7	+	26182.9i	0.293363	+	0.508119i	0.974603	−	0.223941i	$-0.0718922\pi$
$227$	15116.7	+	26182.9i	0.293363	+	0.508119i	−0.681240	+	0.732060i	$0.738559\pi$
$228$		0			0
$229$	22086.6	−	38255.1i	0.421171	−	0.729489i	−0.574884	−	0.818235i	$-0.694953\pi$
$229$	22086.6	−	38255.1i	0.421171	−	0.729489i	0.996054	+	0.0887464i	$0.0282861\pi$
$230$	−27012.3	−	89948.4i	−0.510629	−	1.70035i
$231$		0			0
$232$	−2547.85	+	1471.00i	−0.0473367	+	0.0273298i
$233$	22978.1			0.423255			0.211628	−	0.977350i	$-0.432124\pi$
$233$	22978.1			0.423255			0.211628	+	0.977350i	$0.432124\pi$
$234$		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	0.917273	−	0.398258i	$-0.130385\pi$
$239$	58892.2	+	34001.4i	1.03101	+	0.595253i	0.113735	+	0.993511i	$0.463719\pi$
$240$		0			0
$241$	−34731.9	−	60157.4i	−0.597991	−	1.03575i	−0.993117	−	0.117124i	$-0.962633\pi$
$241$	−34731.9	−	60157.4i	−0.597991	−	1.03575i	0.395126	−	0.918627i	$-0.370701\pi$
$242$	−43034.0			−0.734820
$243$		0			0
$244$	−117732.			−1.97750
$245$	2775.05	+	655.203i	0.0462316	+	0.0109155i
$246$		0			0
$247$	73226.4	+	42277.3i	1.20026	+	0.692968i
$248$	−897.239	+	1554.06i	−0.0145883	+	0.0252677i
$249$		0			0
$250$	−15367.6	+	88475.5i	−0.245881	+	1.41561i
$251$		−	44839.6i		−	0.711728i	−0.934538	−	0.355864i	$-0.884187\pi$
$251$		−	44839.6i		−	0.711728i	0.934538	−	0.355864i	$-0.115813\pi$
$252$		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	$-0.834568\pi$
$257$	−256.172	+	443.703i	−0.00387852	+	0.00671779i	0.864080	+	0.503355i	$0.167901\pi$
$258$		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	$-0.276801\pi$
$263$	−23457.5	−	40629.7i	−0.339134	−	0.587397i	−0.984270	+	0.176671i	$0.943467\pi$
$264$		0			0
$265$	16820.5	+	56010.8i	0.239524	+	0.797591i
$266$	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	$0.0410661\pi$
$269$			18619.3i			0.257311i	−0.991689	+	0.128655i	$0.958934\pi$
$270$		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
$275$	−23643.2	+	47278.1i	−0.312637	+	0.625165i
$276$		0			0
$277$	24078.5	−	13901.7i	0.313812	−	0.181179i	−0.334819	−	0.942282i	$-0.608675\pi$
$277$	24078.5	−	13901.7i	0.313812	−	0.181179i	0.648631	+	0.761103i	$0.275342\pi$
$278$	−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	−0.529754	−	0.848151i	$-0.677716\pi$
$281$	−4746.39	+	2740.33i	−0.0601106	+	0.0347049i	0.469644	+	0.882856i	$0.344382\pi$
$282$		0			0
$283$	−104022.	−	60056.9i	−1.29883	−	0.749877i	−0.318624	−	0.947881i	$-0.603221\pi$
$283$	−104022.	−	60056.9i	−1.29883	−	0.749877i	−0.980201	+	0.198004i	$0.936554\pi$
$284$	−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
$290$	16400.7	−	69463.8i	0.195015	−	0.825967i
$291$		0			0
$292$	95038.8	+	54870.7i	1.11464	+	0.643539i
$293$	−10131.5	+	17548.3i	−0.118016	+	0.204409i	−0.918981	−	0.394301i	$-0.870987\pi$
$293$	−10131.5	+	17548.3i	−0.118016	+	0.204409i	0.800966	+	0.598710i	$0.204320\pi$
$294$		0			0
$295$	6763.89	−	28647.8i	0.0777235	−	0.329191i
$296$			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
$310$	−12521.4	−	41694.9i	−0.130295	−	0.433870i
$311$	118174.	+	68227.6i	1.22180	+	0.705406i	0.965301	−	0.261139i	$-0.0840981\pi$
$311$	118174.	+	68227.6i	1.22180	+	0.705406i	0.256498	+	0.966545i	$0.417431\pi$
$312$		0			0
$313$	94500.3	−	54559.8i	0.964594	−	0.556909i	0.0670101	−	0.997752i	$-0.478654\pi$
$313$	94500.3	−	54559.8i	0.964594	−	0.556909i	0.897584	+	0.440844i	$0.145321\pi$
$314$			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	$-0.0982935\pi$
$317$	21419.5	+	37099.7i	0.213153	+	0.369191i	−0.739547	+	0.673105i	$0.764960\pi$
$318$		0			0
$319$	21006.9	−	36384.9i	0.206433	−	0.357553i
$320$	33116.0	+	110273.i	0.323398	+	1.07688i
$321$		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	1.00000		4.48028e-5i	$1.42612e-5\pi$
$331$	54784.8	+	94890.0i	0.500039	+	0.866093i	−0.499961	+	0.866048i	$0.666652\pi$
$332$	110949.			1.00658
$333$		0			0
$334$	−127689.			−1.14462
$335$	−22263.5	+	94295.0i	−0.198383	+	0.840232i
$336$		0			0
$337$	7974.17	+	4603.89i	0.0702143	+	0.0405383i	0.534696	−	0.845044i	$-0.320426\pi$
$337$	7974.17	+	4603.89i	0.0702143	+	0.0405383i	−0.464482	+	0.885583i	$0.653759\pi$
$338$	−61363.7	+	106285.i	−0.537128	+	0.930334i
$339$		0			0
$340$	−180250.	−	42557.8i	−1.55925	−	0.368147i
$341$		−	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	$-0.803476\pi$
$347$	11277.8	−	19533.8i	0.0936628	−	0.162229i	0.909050	+	0.416688i	$0.136809\pi$
$348$		0			0
$349$	−101902.	−	176500.i	−0.836629	−	1.44908i	−0.892697	−	0.450657i	$-0.851190\pi$
$349$	−101902.	−	176500.i	−0.836629	−	1.44908i	0.0560687	−	0.998427i	$-0.482143\pi$
$350$	−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	$-0.0831906\pi$
$353$	32305.1	+	55954.1i	0.259252	+	0.449038i	−0.706790	+	0.707424i	$0.749857\pi$
$354$		0			0
$355$	139407.	−	41865.1i	1.10619	−	0.332197i
$356$	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	$0.0490587\pi$
$359$			39569.8i			0.307026i	−0.988147	+	0.153513i	$0.950941\pi$
$360$		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
$365$	−154288.	+	46334.2i	−1.15810	+	0.347789i
$366$		0			0
$367$	−168361.	+	97203.5i	−1.25000	+	0.721688i	−0.971109	−	0.238634i	$-0.923300\pi$
$367$	−168361.	+	97203.5i	−1.25000	+	0.721688i	−0.278891	+	0.960323i	$0.589967\pi$
$368$	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	$-0.207240\pi$
$373$	92982.6	+	53683.5i	0.668319	+	0.385854i	−0.127120	+	0.991887i	$0.540573\pi$
$374$	−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	$0.201627\pi$
$380$	156822.	+	37026.5i	1.08603	+	0.256416i
$381$		0			0
$382$	−119071.	−	68745.5i	−0.815978	−	0.471105i
$383$	23281.5	−	40324.7i	0.158713	−	0.274899i	−0.775692	−	0.631112i	$-0.782599\pi$
$383$	23281.5	−	40324.7i	0.158713	−	0.274899i	0.934405	+	0.356213i	$0.115932\pi$
$384$		0			0
$385$	−98409.9	−	23235.0i	−0.663922	−	0.156755i
$386$			13502.1i			0.0906204i
$387$		0			0
$388$		−	229721.i		−	1.52594i
$389$	13106.7	−	7567.17i	0.0866154	−	0.0500074i	−0.456067	−	0.889946i	$-0.650742\pi$
$389$	13106.7	−	7567.17i	0.0866154	−	0.0500074i	0.542682	+	0.839938i	$0.317409\pi$
$390$		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
$400$	−133293.	−	66658.2i	−0.833082	−	0.416613i
$401$	116070.	+	67013.0i	0.721823	+	0.416745i	0.815423	−	0.578865i	$-0.196504\pi$
$401$	116070.	+	67013.0i	0.721823	+	0.416745i	−0.0936000	+	0.995610i	$0.529837\pi$
$402$		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	−0.773546	−	0.633740i	$-0.781519\pi$
$409$	27109.9	−	46955.6i	0.162062	−	0.280699i	0.935608	+	0.353041i	$0.114852\pi$
$410$	−65371.2	+	19631.5i	−0.388883	+	0.116785i
$411$		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	−0.00360107	−	0.999994i	$-0.501146\pi$
$419$	−152988.	−	88327.4i	−0.871421	−	0.503115i	−0.867820	+	0.496878i	$0.834480\pi$
$420$		0			0
$421$	−71752.2	−	124278.i	−0.404829	−	0.701184i	0.589473	−	0.807788i	$-0.299335\pi$
$421$	−71752.2	−	124278.i	−0.404829	−	0.701184i	−0.994302	+	0.106605i	$0.966002\pi$
$422$	−8239.33			−0.0462665
$423$		0			0
$424$	13854.3			0.0770642
$425$	226892.	−	149784.i	1.25615	−	0.829253i
$426$		0			0
$427$	286304.	+	165298.i	1.57026	+	0.906590i
$428$	11685.9	−	20240.6i	0.0637933	−	0.110493i
$429$		0			0
$430$	26956.1	−	114170.i	0.145787	−	0.617469i
$431$			96119.3i			0.517435i	0.965953	+	0.258718i	$0.0832999\pi$
$431$			96119.3i			0.517435i	−0.965953	+	0.258718i	$0.916700\pi$
$432$		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	0.969036	−	0.246921i	$-0.0794188\pi$
$439$	52165.3	+	90353.0i	0.270678	+	0.468828i	−0.698358	+	0.715749i	$0.746085\pi$
$440$	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	$-0.141722\pi$
$443$	15363.5	+	26610.4i	0.0782860	+	0.135595i	−0.824225	+	0.566263i	$0.808389\pi$
$444$		0			0
$445$	−332786.	+	99938.5i	−1.68052	+	0.504676i
$446$	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	$0.0374529\pi$
$449$			47332.1i			0.234781i	−0.993086	+	0.117391i	$0.962547\pi$
$450$		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
$455$	−76825.0	−	255820.i	−0.371090	−	1.23570i
$456$		0			0
$457$	101954.	−	58863.4i	0.488173	−	0.281847i	−0.235643	−	0.971840i	$-0.575720\pi$
$457$	101954.	−	58863.4i	0.488173	−	0.281847i	0.723816	+	0.689993i	$0.242386\pi$
$458$	253873.			1.21028
$459$		0			0
$460$	190808.	−	202591.i	0.901741	−	0.957423i
$461$	38057.7	−	21972.6i	0.179077	−	0.103390i	−0.407782	−	0.913079i	$-0.633698\pi$
$461$	38057.7	−	21972.6i	0.179077	−	0.103390i	0.586859	+	0.809689i	$0.300364\pi$
$462$		0			0
$463$	32818.2	+	18947.6i	0.153092	+	0.0883878i	0.574589	−	0.818442i	$-0.305162\pi$
$463$	32818.2	+	18947.6i	0.153092	+	0.0883878i	−0.421497	+	0.906830i	$0.638495\pi$
$464$	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	$-0.676560\pi$
$467$	−229722.			−1.05334			−0.526671	+	0.850069i	$0.676560\pi$
$468$		0			0
$469$	−185335.			−0.842579
$470$	121722.	+	28739.1i	0.551027	+	0.130100i
$471$		0			0
$472$	−6038.99	−	3486.61i	−0.0271069	−	0.0156502i
$473$	34526.6	−	59801.9i	0.154323	−	0.267296i
$474$		0			0
$475$	−197403.	+	130316.i	−0.874915	+	0.577579i
$476$		−	354276.i		−	1.56361i
$477$		0			0
$478$			390827.i			1.71052i
$479$	42607.9	−	24599.7i	0.185703	−	0.107216i	−0.404266	−	0.914641i	$-0.632473\pi$
$479$	42607.9	−	24599.7i	0.185703	−	0.107216i	0.589969	+	0.807426i	$0.299140\pi$
$480$		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
$490$	4713.31	+	15694.9i	0.0196306	+	0.0653681i
$491$	−146133.	−	84370.0i	−0.606158	−	0.349965i	0.165302	−	0.986243i	$-0.447140\pi$
$491$	−146133.	−	84370.0i	−0.606158	−	0.349965i	−0.771460	+	0.636278i	$0.780473\pi$
$492$		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	−0.986323	−	0.164825i	$-0.947294\pi$
$499$	−87254.6	+	151129.i	−0.350419	+	0.606943i	0.635904	+	0.771768i	$0.280627\pi$
$500$	−249820.	+	91650.8i	−0.999281	+	0.366603i
$501$		0			0
$502$	223177.	−	128851.i	0.885610	−	0.511307i
$503$	−384923.			−1.52138			−0.760691	−	0.649115i	$-0.775140\pi$
$503$	−384923.			−1.52138			−0.760691	+	0.649115i	$0.775140\pi$
$504$		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	0.706731	−	0.707482i	$-0.250169\pi$
$509$	115913.	+	66922.3i	0.447400	+	0.258306i	−0.259332	+	0.965788i	$0.583502\pi$
$510$		0			0
$511$	−154078.	−	266871.i	−0.590065	−	1.02202i
$512$	−371969.			−1.41895
$513$		0			0
$514$	−2944.55			−0.0111453
$515$	−74328.8	+	314813.i	−0.280248	+	1.18696i
$516$		0			0
$517$	63757.6	+	36810.5i	0.238534	+	0.137718i
$518$	7653.21	−	13255.8i	0.0285223	−	0.0494020i
$519$		0			0
$520$	−7601.23	+	32194.3i	−0.0281111	+	0.119062i
$521$		−	128028.i		−	0.471662i	−0.971794	−	0.235831i	$-0.924219\pi$
$521$		−	128028.i		−	0.471662i	0.971794	−	0.235831i	$-0.0757812\pi$
$522$		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
$535$	9867.87	+	32859.1i	0.0344759	+	0.114802i
$536$	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
$545$	−59860.7	−	199330.i	−0.201534	−	0.671090i
$546$		0			0
$547$	−224830.	+	129806.i	−0.751414	+	0.433829i	−0.826205	−	0.563370i	$-0.809505\pi$
$547$	−224830.	+	129806.i	−0.751414	+	0.433829i	0.0747906	+	0.997199i	$0.476171\pi$
$548$	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	$-0.361558\pi$
$557$	261444.			0.842691			0.421345	+	0.906900i	$0.361558\pi$
$558$		0			0
$559$	182411.			0.583750
$560$	65507.5	−	277451.i	0.208889	−	0.884728i
$561$		0			0
$562$	−27278.5	−	15749.3i	−0.0863671	−	0.0498641i
$563$	−185109.	+	320619.i	−0.583999	+	1.01152i	0.411001	+	0.911635i	$0.365179\pi$
$563$	−185109.	+	320619.i	−0.583999	+	1.01152i	−0.994999	+	0.0998803i	$0.968154\pi$
$564$		0			0
$565$	506395.	+	119562.i	1.58633	+	0.374540i
$566$		−	690320.i		−	2.15485i
$567$		0			0
$568$		−	34482.3i		−	0.106881i
$569$	−442601.	+	255536.i	−1.36706	+	0.789273i	−0.990552	−	0.137140i	$-0.956209\pi$
$569$	−442601.	+	255536.i	−1.36706	+	0.789273i	−0.376509	+	0.926413i	$0.622876\pi$
$570$		0			0
$571$	−9362.89	+	16217.0i	−0.0287169	+	0.0497391i	−0.880027	−	0.474924i	$-0.842475\pi$
$571$	−9362.89	+	16217.0i	−0.0287169	+	0.0497391i	0.851310	+	0.524663i	$0.175809\pi$
$572$	−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
$580$	202562.	−	60831.1i	0.602146	−	0.180830i
$581$	−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	−0.911770	−	0.410701i	$-0.865284\pi$
$587$	−279639.	−	484350.i	−0.811563	−	1.40567i	0.100207	−	0.994967i	$-0.468049\pi$
$588$		0			0
$589$	57335.9	−	99308.7i	0.165271	−	0.286257i
$590$	162024.	−	48657.2i	0.465452	−	0.139779i
$591$		0			0
$592$	11500.5	−	6639.82i	0.0328151	−	0.0189458i
$593$	−398735.			−1.13390			−0.566950	−	0.823752i	$-0.691877\pi$
$593$	−398735.			−1.13390			−0.566950	+	0.823752i	$0.691877\pi$
$594$		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	0.755749	−	0.654861i	$-0.227273\pi$
$599$	203260.	+	117352.i	0.566497	+	0.327067i	−0.189252	+	0.981929i	$0.560606\pi$
$600$		0			0
$601$	115910.	+	200763.i	0.320903	+	0.555820i	0.980675	−	0.195646i	$-0.0626805\pi$
$601$	115910.	+	200763.i	0.320903	+	0.555820i	−0.659772	+	0.751466i	$0.729347\pi$
$602$	224398.			0.619193
$603$		0			0
$604$	17619.5			0.0482970
$605$	182186.	+	43014.9i	0.497741	+	0.117519i
$606$		0			0
$607$	−459653.	−	265381.i	−1.24753	−	0.720264i	−0.276917	−	0.960894i	$-0.589313\pi$
$607$	−459653.	−	265381.i	−1.24753	−	0.720264i	−0.970617	+	0.240630i	$0.922646\pi$
$608$	−277257.	+	480224.i	−0.750025	+	1.29908i
$609$		0			0
$610$	966689.	+	228240.i	2.59793	+	0.613383i
$611$			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	$-0.773729\pi$
$617$	70869.2	−	122749.i	0.186160	−	0.322439i	0.943967	+	0.330040i	$0.107062\pi$
$618$		0			0
$619$	276156.	+	478316.i	0.720731	+	1.24834i	0.960707	+	0.277563i	$0.0895268\pi$
$619$	276156.	+	478316.i	0.720731	+	1.24834i	−0.239977	+	0.970779i	$0.577140\pi$
$620$	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
$625$	153496.	−	359203.i	0.392949	−	0.919560i
$626$	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
$635$	82435.4	−	24756.1i	0.204440	−	0.0613952i
$636$		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	0.0566340	−	0.998395i	$-0.481963\pi$
$641$	390167.	−	225263.i	0.949587	−	0.548244i	0.892952	+	0.450151i	$0.148630\pi$
$642$		0			0
$643$	265023.	+	153011.i	0.641006	+	0.370085i	0.785002	−	0.619493i	$-0.212662\pi$
$643$	265023.	+	153011.i	0.641006	+	0.370085i	−0.143996	+	0.989578i	$0.545995\pi$
$644$	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	$-0.423216\pi$
$647$	200004.			0.477782			0.238891	+	0.971046i	$0.423216\pi$
$648$		0			0
$649$	99582.2			0.236424
$650$	−442132.	−	669741.i	−1.04647	−	1.58518i
$651$		0			0
$652$	−528859.	−	305337.i	−1.24407	−	0.718263i
$653$	257809.	−	446538.i	0.604604	−	1.04721i	−0.387509	−	0.921866i	$-0.626665\pi$
$653$	257809.	−	446538.i	0.604604	−	1.04721i	0.992114	−	0.125340i	$-0.0400021\pi$
$654$		0			0
$655$	31667.5	−	134125.i	0.0738128	−	0.312627i
$656$		−	113276.i		−	0.263226i
$657$		0			0
$658$			239241.i			0.552567i
$659$	−301526.	+	174086.i	−0.694312	+	0.400861i	−0.805225	−	0.592969i	$-0.797956\pi$
$659$	−301526.	+	174086.i	−0.694312	+	0.400861i	0.110913	+	0.993830i	$0.464622\pi$
$660$		0			0
$661$	12324.1	−	21346.0i	0.0282068	−	0.0488556i	−0.851577	−	0.524229i	$-0.824354\pi$
$661$	12324.1	−	21346.0i	0.0282068	−	0.0488556i	0.879784	+	0.475373i	$0.157687\pi$
$662$	−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
$670$	−533305.	+	160156.i	−1.18803	+	0.356775i
$671$	506349.	+	292340.i	1.12462	+	0.649298i
$672$		0			0
$673$	275390.	−	158997.i	0.608020	−	0.351041i	−0.164170	−	0.986432i	$-0.552495\pi$
$673$	275390.	−	158997.i	0.608020	−	0.351041i	0.772190	+	0.635391i	$0.219161\pi$
$674$			52919.1i			0.116491i
$675$		0			0
$676$	−363673.			−0.795825
$677$	65955.5	+	114238.i	0.143904	+	0.249250i	0.928964	−	0.370171i	$-0.120701\pi$
$677$	65955.5	+	114238.i	0.143904	+	0.249250i	−0.785059	+	0.619421i	$0.787368\pi$
$678$		0			0
$679$	−322532.	+	558641.i	−0.699573	+	1.21170i
$680$	−18524.5	−	61684.9i	−0.0400617	−	0.133402i
$681$		0			0
$682$	127548.	−	73640.0i	0.274224	−	0.158323i
$683$	539667.			1.15687			0.578435	−	0.815729i	$-0.303664\pi$
$683$	539667.			1.15687			0.578435	+	0.815729i	$0.303664\pi$
$684$		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	0.994676	−	0.103054i	$-0.0328614\pi$
$691$	194856.	+	337500.i	0.408091	+	0.706834i	−0.586585	+	0.809888i	$0.699528\pi$
$692$	599341.			1.25159
$693$		0			0
$694$	129632.			0.269150
$695$	82094.1	+	19382.8i	0.169958	+	0.0401280i
$696$		0			0
$697$	178960.	+	103323.i	0.368376	+	0.212682i
$698$	585654.	−	1.01438e6i	1.20207	−	2.08205i
$699$		0			0
$700$	−280435.	−	424803.i	−0.572317	−	0.866945i
$701$		−	831525.i		−	1.69215i	−0.533063	−	0.846076i	$-0.678959\pi$
$701$		−	831525.i		−	1.69215i	0.533063	−	0.846076i	$-0.321041\pi$
$702$		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	0.844574	−	0.535439i	$-0.179854\pi$
$709$	−20819.3	−	36060.0i	−0.0414164	−	0.0717354i	−0.885991	+	0.463703i	$0.846520\pi$
$710$	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
$715$	−135870.	−	452435.i	−0.265774	−	0.885003i
$716$	−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	$-0.717915\pi$
$719$		−	800950.i		−	1.54934i	0.632364	−	0.774671i	$-0.282085\pi$
$720$		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
$725$	−138866.	+	277684.i	−0.264192	+	0.528293i
$726$		0			0
$727$	−722549.	+	417164.i	−1.36709	+	0.789292i	−0.990556	−	0.137109i	$-0.956219\pi$
$727$	−722549.	+	417164.i	−1.36709	+	0.789292i	−0.376538	+	0.926401i	$0.622886\pi$
$728$	−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	$-0.459644\pi$
$733$	−359667.	−	207654.i	−0.669411	−	0.386485i	−0.795854	+	0.605489i	$0.792978\pi$
$734$	−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	$0.789513\pi$
$740$	5448.55	−	23076.8i	0.00994987	−	0.0421417i
$741$		0			0
$742$	−556799.	−	321468.i	−1.01132	−	0.583888i
$743$	152108.	−	263459.i	0.275534	−	0.477239i	−0.694736	−	0.719265i	$-0.744479\pi$
$743$	152108.	−	263459.i	0.275534	−	0.477239i	0.970270	+	0.242026i	$0.0778120\pi$
$744$		0			0
$745$	192653.	−	815963.i	0.347106	−	1.47014i
$746$			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	−0.0371095	−	0.999311i	$-0.511815\pi$
$751$	477638.	−	827293.i	0.846874	−	1.46683i	0.883984	−	0.467518i	$-0.154852\pi$
$752$	−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
$760$	16116.9	+	53667.7i	0.0279032	+	0.0929149i
$761$	309676.	+	178791.i	0.534734	+	0.308729i	0.742942	−	0.669356i	$-0.233430\pi$
$761$	309676.	+	178791.i	0.534734	+	0.308729i	−0.208208	+	0.978085i	$0.566763\pi$
$762$		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	−0.764443	−	0.644692i	$-0.776986\pi$
$769$	104137.	−	180371.i	0.176098	−	0.305010i	0.940541	+	0.339681i	$0.110319\pi$
$770$	−167145.	−	556577.i	−0.281911	−	0.938737i
$771$		0			0
$772$	−34649.8	+	20005.1i	−0.0581388	+	0.0335665i
$773$	−328500.			−0.549764			−0.274882	−	0.961478i	$-0.588639\pi$
$773$	−328500.			−0.549764			−0.274882	+	0.961478i	$0.588639\pi$
$774$		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
$785$	26114.5	−	110605.i	0.0423781	−	0.179489i
$786$		0			0
$787$	184283.	+	106396.i	0.297533	+	0.171781i	0.641334	−	0.767262i	$-0.278381\pi$
$787$	184283.	+	106396.i	0.297533	+	0.171781i	−0.343801	+	0.939042i	$0.611715\pi$
$788$	−79313.6	+	137375.i	−0.127731	+	0.221236i
$789$		0			0
$790$	−684276.	−	161561.i	−1.09642	−	0.258870i
$791$			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	$-0.871417\pi$
$797$	−75817.1	+	131319.i	−0.119358	+	0.206734i	0.800156	+	0.599792i	$0.204750\pi$
$798$		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
$805$	−748452.	+	224767.i	−1.15497	+	0.346849i
$806$	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	$-0.983823\pi$
$809$		−	66493.9i		−	0.101598i	0.998709	−	0.0507989i	$-0.0161768\pi$
$810$		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
$815$	858562.	−	257834.i	1.29258	−	0.388172i
$816$		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	−0.775300	−	0.631593i	$-0.782402\pi$
$821$	−415193.	+	239712.i	−0.615975	+	0.355634i	0.159325	+	0.987226i	$0.449068\pi$
$822$		0			0
$823$	−125938.	−	72710.6i	−0.185934	−	0.107349i	0.404144	−	0.914695i	$-0.367570\pi$
$823$	−125938.	−	72710.6i	−0.185934	−	0.107349i	−0.590078	+	0.807346i	$0.700903\pi$
$824$	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	$-0.273390\pi$
$827$	893602.			1.30657			0.653286	+	0.757111i	$0.273390\pi$
$828$		0			0
$829$	−659734.			−0.959975			−0.479988	−	0.877275i	$-0.659359\pi$
$829$	−659734.			−0.959975			−0.479988	+	0.877275i	$0.659359\pi$
$830$	−910990.	−	215089.i	−1.32238	−	0.312221i
$831$		0			0
$832$	−891100.	−	514477.i	−1.28730	−	0.743223i
$833$	24806.6	−	42966.4i	0.0357501	−	0.0619211i
$834$		0			0
$835$	540577.	+	127633.i	0.775327	+	0.183058i
$836$			545128.i			0.779984i
$837$		0			0
$838$		−	1.01527e6i		−	1.44576i
$839$	797201.	−	460264.i	1.13251	−	0.653857i	0.187948	−	0.982179i	$-0.439816\pi$
$839$	797201.	−	460264.i	1.13251	−	0.653857i	0.944566	+	0.328322i	$0.106483\pi$
$840$		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
$850$	1.39751e6	+	698876.i	1.93427	+	0.967303i
$851$	−31525.7	−	18201.4i	−0.0435317	−	0.0251330i
$852$		0			0
$853$	627776.	−	362447.i	0.862793	−	0.498134i	−0.00215352	−	0.999998i	$-0.500685\pi$
$853$	627776.	−	362447.i	0.862793	−	0.498134i	0.864947	+	0.501864i	$0.167352\pi$
$854$			1.90000e6i			2.60518i
$855$		0			0
$856$	8127.70			0.0110923
$857$	492013.	+	852192.i	0.669908	+	1.16032i	0.977929	+	0.208936i	$0.0669999\pi$
$857$	492013.	+	852192.i	0.669908	+	1.16032i	−0.308021	+	0.951380i	$0.599667\pi$
$858$		0			0
$859$	−365776.	+	633542.i	−0.495711	+	0.858597i	−0.999988	−	0.00494530i	$-0.998426\pi$
$859$	−365776.	+	633542.i	−0.495711	+	0.858597i	0.504277	+	0.863542i	$0.331759\pi$
$860$	332928.	−	99981.3i	0.450147	−	0.135183i
$861$		0			0
$862$	−478408.	+	276209.i	−0.643849	+	0.371727i
$863$	−498062.			−0.668747			−0.334374	−	0.942441i	$-0.608525\pi$
$863$	−498062.			−0.668747			−0.334374	+	0.942441i	$0.608525\pi$
$864$		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
$875$	736196.	+	127872.i	0.961563	+	0.167017i
$876$		0			0
$877$	1.18504e6	+	684183.i	1.54076	+	0.889556i	0.998791	+	0.0491545i	$0.0156527\pi$
$877$	1.18504e6	+	684183.i	1.54076	+	0.889556i	0.541965	+	0.840401i	$0.317681\pi$
$878$	−299805.	+	519278.i	−0.388911	+	0.673614i
$879$		0			0
$880$	115855.	−	490691.i	0.149606	−	0.633641i
$881$			1.19744e6i			1.54277i	0.636368	+	0.771386i	$0.280436\pi$
$881$			1.19744e6i			1.54277i	−0.636368	+	0.771386i	$0.719564\pi$
$882$		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	−0.455695	−	0.890136i	$-0.650609\pi$
$887$	427242.	−	740004.i	0.543033	−	0.940561i	0.998728	−	0.0504250i	$-0.0160576\pi$
$888$		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
$895$	1.05806e6	−	317743.i	1.32088	−	0.396671i
$896$	−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
$905$	297163.	+	989526.i	0.362826	+	1.20818i
$906$		0			0
$907$	−403158.	+	232764.i	−0.490073	+	0.282944i	−0.724605	−	0.689164i	$-0.757978\pi$
$907$	−403158.	+	232764.i	−0.490073	+	0.282944i	0.234531	+	0.972109i	$0.424644\pi$
$908$	−514890.			−0.624514
$909$		0			0
$910$	1.05251e6	−	1.11750e6i	1.27099	−	1.34948i
$911$	−596214.	+	344224.i	−0.718398	+	0.414767i	−0.814163	−	0.580637i	$-0.802804\pi$
$911$	−596214.	+	344224.i	−0.718398	+	0.414767i	0.0957646	+	0.995404i	$0.469470\pi$
$912$		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	$0.634441\pi$
$920$	94190.8	+	22238.9i	0.111284	+	0.0262747i
$921$		0			0
$922$	218726.	+	126281.i	0.257299	+	0.148552i
$923$	−650401.	+	1.12653e6i	−0.763445	+	1.32233i
$924$		0			0
$925$	19176.4	+	29048.3i	0.0224121	+	0.0339498i
$926$			217792.i			0.253992i
$927$		0			0
$928$			727835.i			0.845157i
$929$	−430458.	+	248525.i	−0.498768	+	0.287964i	−0.728205	−	0.685360i	$-0.759645\pi$
$929$	−430458.	+	248525.i	−0.498768	+	0.287964i	0.229436	+	0.973324i	$0.426312\pi$
$930$		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
$940$	106595.	+	354951.i	0.120637	+	0.401710i
$941$	222911.	+	128697.i	0.251740	+	0.145342i	0.620561	−	0.784159i	$-0.286905\pi$
$941$	222911.	+	128697.i	0.251740	+	0.145342i	−0.368821	+	0.929500i	$0.620238\pi$
$942$		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	$-0.0835537\pi$
$947$	231511.	+	400990.i	0.258150	+	0.447129i	−0.707596	+	0.706617i	$0.750220\pi$
$948$		0			0
$949$	719830.	−	1.24678e6i	0.799277	−	1.38439i
$950$	−1.21587e6	−	608042.i	−1.34723	−	0.673731i
$951$		0			0
$952$	106696.	−	61600.9i	0.117726	−	0.0679694i
$953$	323955.			0.356696			0.178348	−	0.983967i	$-0.442925\pi$
$953$	323955.			0.356696			0.178348	+	0.983967i	$0.442925\pi$
$954$		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
$965$	13496.1	−	57161.5i	0.0144928	−	0.0613831i
$966$		0			0
$967$	511790.	+	295482.i	0.547317	+	0.315994i	0.748039	−	0.663654i	$-0.230995\pi$
$967$	511790.	+	295482.i	0.547317	+	0.315994i	−0.200722	+	0.979648i	$0.564329\pi$
$968$	22173.1	−	38404.9i	0.0236633	−	0.0409861i
$969$		0			0
$970$	−445346.	+	1.88622e6i	−0.473319	+	2.00470i
$971$		−	1.14727e6i		−	1.21682i	−0.793622	−	0.608412i	$-0.791807\pi$
$971$		−	1.14727e6i		−	1.21682i	0.793622	−	0.608412i	$-0.208193\pi$
$972$		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	$-0.981815\pi$
$977$	−429287.	+	743546.i	−0.449737	+	0.778967i	0.548632	+	0.836064i	$0.315149\pi$
$978$		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	0.992735	+	0.120318i	$0.0383913\pi$
$983$	580320.	+	1.00514e6i	0.600566	+	1.04021i	−0.392170	+	0.919893i	$0.628275\pi$
$984$		0			0
$985$	−66974.3	−	223018.i	−0.0690297	−	0.229862i
$986$	−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
$995$	44507.8	+	148207.i	0.0449562	+	0.149700i
$996$		0			0
$997$	−1.12879e6	+	651705.i	−1.13559	+	0.655633i	−0.945334	−	0.326102i	$-0.894265\pi$
$997$	−1.12879e6	+	651705.i	−1.13559	+	0.655633i	−0.190254	+	0.981735i	$0.560931\pi$
$998$	−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.44.19		44
3.2	odd	2		45.5.h.a.14.4	✓	44
5.4	even	2	inner	135.5.h.a.44.4		44
9.2	odd	6	inner	135.5.h.a.89.4		44
9.4	even	3		405.5.d.a.404.8		44
9.5	odd	6		405.5.d.a.404.38		44
9.7	even	3		45.5.h.a.29.19	yes	44
15.14	odd	2		45.5.h.a.14.19	yes	44
45.4	even	6		405.5.d.a.404.37		44
45.14	odd	6		405.5.d.a.404.7		44
45.29	odd	6	inner	135.5.h.a.89.19		44
45.34	even	6		45.5.h.a.29.4	yes	44

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

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)

\(f(q)\)	\(=\)	\(q+(2.87361 + 4.97724i) q^{2} +(-8.51525 + 14.7488i) q^{4} +(-7.19048 - 23.9436i) q^{5} +(41.4151 - 23.9110i) q^{7} -5.92246 q^{8} +(98.5104 - 104.593i) q^{10} +(73.2455 - 42.2883i) q^{11} +(193.485 + 111.709i) q^{13} +(238.021 + 137.422i) q^{14} +(119.225 + 206.504i) q^{16} -434.998 q^{17} +378.461 q^{19} +(414.369 + 97.8346i) q^{20} +(420.958 + 243.040i) q^{22} +(326.825 - 566.078i) q^{23} +(-521.594 + 344.332i) q^{25} +1284.03i q^{26} +814.433i q^{28} +(430.201 - 248.377i) q^{29} +(151.498 - 262.402i) q^{31} +(-732.592 + 1268.89i) q^{32} +(-1250.01 - 2165.09i) q^{34} +(-870.311 - 819.695i) q^{35} -55.6914i q^{37} +(1087.55 + 1883.69i) q^{38} +(42.5853 + 141.805i) q^{40} +(-411.405 - 237.525i) q^{41} +(707.073 - 408.229i) q^{43} +1440.38i q^{44} +3756.67 q^{46} +(435.232 + 753.844i) q^{47} +(-57.0270 + 98.7737i) q^{49} +(-3212.68 - 1606.62i) q^{50} +(-3295.14 + 1902.45i) q^{52} -2339.28 q^{53} +(-1539.21 - 1449.69i) q^{55} +(-245.279 + 141.612i) q^{56} +(2472.46 + 1427.47i) q^{58} +(1019.68 + 588.710i) q^{59} +(3456.52 + 5986.86i) q^{61} +1741.38 q^{62} -4605.53 q^{64} +(1283.46 - 5435.97i) q^{65} +(-3356.29 - 1937.75i) q^{67} +(3704.11 - 6415.71i) q^{68} +(1578.89 - 6687.22i) q^{70} +5822.30i q^{71} -6443.82i q^{73} +(277.189 - 160.035i) q^{74} +(-3222.69 + 5581.85i) q^{76} +(2022.31 - 3502.75i) q^{77} +(-2446.72 - 4237.84i) q^{79} +(4087.17 - 4339.54i) q^{80} -2730.21i q^{82} +(-3257.36 - 5641.91i) q^{83} +(3127.84 + 10415.4i) q^{85} +(4063.70 + 2346.18i) q^{86} +(-433.793 + 250.451i) q^{88} -13898.7i q^{89} +10684.3 q^{91} +(5566.00 + 9640.59i) q^{92} +(-2501.37 + 4332.50i) q^{94} +(-2721.31 - 9061.72i) q^{95} +(-11681.7 + 6744.42i) q^{97} -655.493 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) \) 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

Groups

Database

Properties

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