LMFDB - Embedded newform 135.5.h.a.89.6

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			89.6
Character	$\chi$	$=$	135.89
Dual form			135.5.h.a.44.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.30921 + 3.99967i) q^{2} +(-2.66491 - 4.61577i) q^{4} +(-1.07184 - 24.9770i) q^{5} +(45.6166 + 26.3368i) q^{7} -49.2794 q^{8} +(102.375 + 53.3902i) q^{10} +(1.90271 + 1.09853i) q^{11} +(-226.996 + 131.056i) q^{13} +(-210.677 + 121.634i) q^{14} +(156.435 - 270.954i) q^{16} -487.118 q^{17} +8.08421 q^{19} +(-112.432 + 71.5090i) q^{20} +(-8.78750 + 5.07347i) q^{22} +(178.836 + 309.753i) q^{23} +(-622.702 + 53.5429i) q^{25} -1210.54i q^{26} -280.741i q^{28} +(-25.7123 - 14.8450i) q^{29} +(-534.206 - 925.271i) q^{31} +(328.248 + 568.543i) q^{32} +(1124.86 - 1948.31i) q^{34} +(608.920 - 1167.60i) q^{35} -1722.01i q^{37} +(-18.6682 + 32.3342i) q^{38} +(52.8198 + 1230.85i) q^{40} +(-2234.51 + 1290.10i) q^{41} +(597.707 + 345.086i) q^{43} -11.7099i q^{44} -1651.88 q^{46} +(817.918 - 1416.68i) q^{47} +(186.752 + 323.464i) q^{49} +(1223.80 - 2614.25i) q^{50} +(1209.85 + 698.506i) q^{52} -3354.40 q^{53} +(25.3986 - 48.7014i) q^{55} +(-2247.96 - 1297.86i) q^{56} +(118.750 - 68.5606i) q^{58} +(-1245.61 + 719.153i) q^{59} +(-256.779 + 444.755i) q^{61} +4934.37 q^{62} +1973.94 q^{64} +(3516.69 + 5529.20i) q^{65} +(-3800.99 + 2194.50i) q^{67} +(1298.13 + 2248.42i) q^{68} +(3263.88 + 5131.71i) q^{70} +4437.85i q^{71} +4046.87i q^{73} +(6887.47 + 3976.48i) q^{74} +(-21.5437 - 37.3148i) q^{76} +(57.8634 + 100.222i) q^{77} +(-2005.14 + 3473.00i) q^{79} +(-6935.28 - 3616.86i) q^{80} -11916.4i q^{82} +(3259.68 - 5645.94i) q^{83} +(522.115 + 12166.8i) q^{85} +(-2760.46 + 1593.75i) q^{86} +(-93.7642 - 54.1348i) q^{88} +7631.84i q^{89} -13806.4 q^{91} +(953.164 - 1650.93i) q^{92} +(3777.49 + 6542.81i) q^{94} +(-8.66501 - 201.919i) q^{95} +(11001.1 + 6351.50i) q^{97} -1725.00 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.30921	+	3.99967i	−0.577303	+	0.999918i	0.418484	+	0.908224i	$0.362561\pi$
$2$	−2.30921	+	3.99967i	−0.577303	+	0.999918i	−0.995787	+	0.0916939i	$0.970772\pi$
$3$		0			0
$3$		0			0
$4$	−2.66491	−	4.61577i	−0.166557	−	0.288485i
$5$	−1.07184	−	24.9770i	−0.0428738	−	0.999080i
$5$	−1.07184	−	24.9770i	−0.0428738	−	0.999080i
$6$		0			0
$7$	45.6166	+	26.3368i	0.930952	+	0.537485i	0.887112	−	0.461553i	$-0.152708\pi$
$7$	45.6166	+	26.3368i	0.930952	+	0.537485i	0.0438393	+	0.999039i	$0.486041\pi$
$8$	−49.2794			−0.769990
$9$		0			0
$10$	102.375	+	53.3902i	1.02375	+	0.533902i
$11$	1.90271	+	1.09853i	0.0157249	+	0.00907875i	0.507842	−	0.861450i	$-0.330443\pi$
$11$	1.90271	+	1.09853i	0.0157249	+	0.00907875i	−0.492117	+	0.870529i	$0.663777\pi$
$12$		0			0
$13$	−226.996	+	131.056i	−1.34317	+	0.775479i	−0.987271	−	0.159045i	$-0.949158\pi$
$13$	−226.996	+	131.056i	−1.34317	+	0.775479i	−0.355898	+	0.934525i	$0.615825\pi$
$14$	−210.677	+	121.634i	−1.07488	+	0.620584i
$15$		0			0
$16$	156.435	−	270.954i	0.611075	−	1.05841i
$17$	−487.118			−1.68553			−0.842765	−	0.538281i	$-0.819074\pi$
$17$	−487.118			−1.68553			−0.842765	+	0.538281i	$0.819074\pi$
$18$		0			0
$19$	8.08421			0.0223939			0.0111970	−	0.999937i	$-0.496436\pi$
$19$	8.08421			0.0223939			0.0111970	+	0.999937i	$0.496436\pi$
$20$	−112.432	+	71.5090i	−0.281079	+	0.178772i
$21$		0			0
$22$	−8.78750	+	5.07347i	−0.0181560	+	0.0104824i
$23$	178.836	+	309.753i	0.338064	+	0.585544i	0.984069	−	0.177789i	$-0.0568946\pi$
$23$	178.836	+	309.753i	0.338064	+	0.585544i	−0.646004	+	0.763334i	$0.723561\pi$
$24$		0			0
$25$	−622.702	+	53.5429i	−0.996324	+	0.0856687i
$26$		−	1210.54i		−	1.79075i
$27$		0			0
$28$		−	280.741i		−	0.358088i
$29$	−25.7123	−	14.8450i	−0.0305735	−	0.0176516i	0.484635	−	0.874716i	$-0.338952\pi$
$29$	−25.7123	−	14.8450i	−0.0305735	−	0.0176516i	−0.515209	+	0.857065i	$0.672286\pi$
$30$		0			0
$31$	−534.206	−	925.271i	−0.555885	−	0.962821i	−0.997834	−	0.0657811i	$-0.979046\pi$
$31$	−534.206	−	925.271i	−0.555885	−	0.962821i	0.441949	−	0.897040i	$-0.354287\pi$
$32$	328.248	+	568.543i	0.320555	+	0.555218i
$33$		0			0
$34$	1124.86	−	1948.31i	0.973062	−	1.68539i
$35$	608.920	−	1167.60i	0.497078	−	0.953140i
$36$		0			0
$37$		−	1722.01i		−	1.25786i	−0.777463	−	0.628929i	$-0.783494\pi$
$37$		−	1722.01i		−	1.25786i	0.777463	−	0.628929i	$-0.216506\pi$
$38$	−18.6682	+	32.3342i	−0.0129281	+	0.0223921i
$39$		0			0
$40$	52.8198	+	1230.85i	0.0330124	+	0.769282i
$41$	−2234.51	+	1290.10i	−1.32928	+	0.767458i	−0.985188	−	0.171479i	$-0.945145\pi$
$41$	−2234.51	+	1290.10i	−1.32928	+	0.767458i	−0.344088	+	0.938937i	$0.611812\pi$
$42$		0			0
$43$	597.707	+	345.086i	0.323260	+	0.186634i	0.652845	−	0.757492i	$-0.273575\pi$
$43$	597.707	+	345.086i	0.323260	+	0.186634i	−0.329585	+	0.944126i	$0.606909\pi$
$44$		−	11.7099i		−	0.00604852i
$45$		0			0
$46$	−1651.88			−0.780661
$47$	817.918	−	1416.68i	0.370266	−	0.641320i	−0.619340	−	0.785123i	$-0.712600\pi$
$47$	817.918	−	1416.68i	0.370266	−	0.641320i	0.989606	+	0.143803i	$0.0459331\pi$
$48$		0			0
$49$	186.752	+	323.464i	0.0777809	+	0.134720i
$50$	1223.80	−	2614.25i	0.489519	−	1.04570i
$51$		0			0
$52$	1209.85	+	698.506i	0.447429	+	0.258323i
$53$	−3354.40			−1.19416			−0.597081	−	0.802181i	$-0.703673\pi$
$53$	−3354.40			−1.19416			−0.597081	+	0.802181i	$0.703673\pi$
$54$		0			0
$55$	25.3986	−	48.7014i	0.00839622	−	0.0160996i
$56$	−2247.96	−	1297.86i	−0.716824	−	0.413858i
$57$		0			0
$58$	118.750	−	68.5606i	0.0353003	−	0.0203807i
$59$	−1245.61	+	719.153i	−0.357831	+	0.206594i	−0.668129	−	0.744046i	$-0.732905\pi$
$59$	−1245.61	+	719.153i	−0.357831	+	0.206594i	0.310298	+	0.950639i	$0.399571\pi$
$60$		0			0
$61$	−256.779	+	444.755i	−0.0690081	+	0.119526i	−0.898465	−	0.439045i	$-0.855317\pi$
$61$	−256.779	+	444.755i	−0.0690081	+	0.119526i	0.829457	+	0.558571i	$0.188650\pi$
$62$	4934.37			1.28366
$63$		0			0
$64$	1973.94			0.481920
$65$	3516.69	+	5529.20i	0.832353	+	1.30869i
$66$		0			0
$67$	−3800.99	+	2194.50i	−0.846735	+	0.488863i	−0.859548	−	0.511055i	$-0.829255\pi$
$67$	−3800.99	+	2194.50i	−0.846735	+	0.488863i	0.0128128	+	0.999918i	$0.495921\pi$
$68$	1298.13	+	2248.42i	0.280737	+	0.486251i
$69$		0			0
$70$	3263.88	+	5131.71i	0.666097	+	1.04729i
$71$			4437.85i			0.880351i	0.897912	+	0.440176i	$0.145084\pi$
$71$			4437.85i			0.880351i	−0.897912	+	0.440176i	$0.854916\pi$
$72$		0			0
$73$			4046.87i			0.759406i	0.925108	+	0.379703i	$0.123974\pi$
$73$			4046.87i			0.759406i	−0.925108	+	0.379703i	$0.876026\pi$
$74$	6887.47	+	3976.48i	1.25775	+	0.726165i
$75$		0			0
$76$	−21.5437	−	37.3148i	−0.00372987	−	0.00646032i
$77$	57.8634	+	100.222i	0.00975939	+	0.0169038i
$78$		0			0
$79$	−2005.14	+	3473.00i	−0.321285	+	0.556482i	−0.980753	−	0.195250i	$-0.937448\pi$
$79$	−2005.14	+	3473.00i	−0.321285	+	0.556482i	0.659469	+	0.751732i	$0.270781\pi$
$80$	−6935.28	−	3616.86i	−1.08364	−	0.565135i
$81$		0			0
$82$		−	11916.4i		−	1.77222i
$83$	3259.68	−	5645.94i	0.473172	−	0.819559i	−0.526356	−	0.850264i	$-0.676442\pi$
$83$	3259.68	−	5645.94i	0.473172	−	0.819559i	0.999528	+	0.0307056i	$0.00977544\pi$
$84$		0			0
$85$	522.115	+	12166.8i	0.0722650	+	1.68398i
$86$	−2760.46	+	1593.75i	−0.373237	+	0.215489i
$87$		0			0
$88$	−93.7642	−	54.1348i	−0.0121080	−	0.00699054i
$89$			7631.84i			0.963495i	0.876310	+	0.481747i	$0.159998\pi$
$89$			7631.84i			0.963495i	−0.876310	+	0.481747i	$0.840002\pi$
$90$		0			0
$91$	−13806.4			−1.66724
$92$	953.164	−	1650.93i	0.112614	−	0.195053i
$93$		0			0
$94$	3777.49	+	6542.81i	0.427512	+	0.740472i
$95$	−8.66501	−	201.919i	−0.000960112	−	0.0223733i
$96$		0			0
$97$	11001.1	+	6351.50i	1.16921	+	0.675045i	0.953494	−	0.301411i	$-0.0974575\pi$
$97$	11001.1	+	6351.50i	1.16921	+	0.675045i	0.215718	+	0.976456i	$0.430791\pi$
$98$	−1725.00			−0.179612
$99$		0			0
$100$	1906.59	+	2731.56i	0.190659	+	0.273156i
$101$	−4041.66	−	2333.45i	−0.396202	−	0.228748i	0.288642	−	0.957437i	$-0.406796\pi$
$101$	−4041.66	−	2333.45i	−0.396202	−	0.228748i	−0.684844	+	0.728690i	$0.740130\pi$
$102$		0			0
$103$	−4561.55	+	2633.61i	−0.429970	+	0.248243i	−0.699334	−	0.714795i	$-0.746520\pi$
$103$	−4561.55	+	2633.61i	−0.429970	+	0.248243i	0.269364	+	0.963038i	$0.413187\pi$
$104$	11186.2	−	6458.36i	1.03423	−	0.597111i
$105$		0			0
$106$	7746.02	−	13416.5i	0.689393	−	1.19406i
$107$	19673.1			1.71833			0.859164	−	0.511700i	$-0.170984\pi$
$107$	19673.1			1.71833			0.859164	+	0.511700i	$0.170984\pi$
$108$		0			0
$109$	−7535.14			−0.634218			−0.317109	−	0.948389i	$-0.602712\pi$
$109$	−7535.14			−0.634218			−0.317109	+	0.948389i	$0.602712\pi$
$110$	136.139	+	214.048i	0.0112511	+	0.0176899i
$111$		0			0
$112$	14272.1	−	8239.99i	1.13776	−	0.656887i
$113$	−3244.24	−	5619.19i	−0.254072	−	0.440065i	0.710571	−	0.703625i	$-0.248437\pi$
$113$	−3244.24	−	5619.19i	−0.254072	−	0.440065i	−0.964643	+	0.263560i	$0.915103\pi$
$114$		0			0
$115$	7545.02	−	4798.79i	0.570512	−	0.362858i
$116$			158.243i			0.0117600i
$117$		0			0
$118$		−	6642.70i		−	0.477069i
$119$	−22220.7	−	12829.1i	−1.56915	−	0.905948i
$120$		0			0
$121$	−7318.09	−	12675.3i	−0.499835	−	0.865740i
$122$	−1185.92	−	2054.07i	−0.0796772	−	0.138005i
$123$		0			0
$124$	−2847.22	+	4931.54i	−0.185173	+	0.320729i
$125$	2004.78	+	15495.9i	0.128306	+	0.991735i
$126$		0			0
$127$		−	24919.2i		−	1.54500i	−0.635017	−	0.772498i	$-0.719007\pi$
$127$		−	24919.2i		−	1.54500i	0.635017	−	0.772498i	$-0.280993\pi$
$128$	−9810.23	+	16991.8i	−0.598769	+	1.03710i
$129$		0			0
$130$	−30235.8	+	1297.51i	−1.78910	+	0.0767760i
$131$	7372.56	−	4256.55i	0.429611	−	0.248036i	−0.269570	−	0.962981i	$-0.586881\pi$
$131$	7372.56	−	4256.55i	0.429611	−	0.248036i	0.699181	+	0.714945i	$0.253548\pi$
$132$		0			0
$133$	368.775	+	212.912i	0.0208477	+	0.0120364i
$134$		−	20270.3i		−	1.12889i
$135$		0			0
$136$	24004.9			1.29784
$137$	930.725	−	1612.06i	0.0495884	−	0.0858897i	−0.840166	−	0.542330i	$-0.817542\pi$
$137$	930.725	−	1612.06i	0.0495884	−	0.0858897i	0.889754	+	0.456440i	$0.150876\pi$
$138$		0			0
$139$	2469.13	+	4276.67i	0.127795	+	0.221348i	0.922822	−	0.385226i	$-0.125877\pi$
$139$	2469.13	+	4276.67i	0.127795	+	0.221348i	−0.795027	+	0.606574i	$0.792543\pi$
$140$	−7012.07	+	300.910i	−0.357759	+	0.0153526i
$141$		0			0
$142$	−17749.9	−	10247.9i	−0.880279	−	0.508229i
$143$	−575.875			−0.0281615
$144$		0			0
$145$	−343.225	+	658.129i	−0.0163246	+	0.0313022i
$146$	−16186.2	−	9345.09i	−0.759344	−	0.438407i
$147$		0			0
$148$	−7948.39	+	4589.00i	−0.362874	+	0.209505i
$149$	13670.0	−	7892.39i	0.615739	−	0.355497i	−0.159469	−	0.987203i	$-0.550978\pi$
$149$	13670.0	−	7892.39i	0.615739	−	0.355497i	0.775208	+	0.631706i	$0.217645\pi$
$150$		0			0
$151$	−7763.12	+	13446.1i	−0.340473	+	0.589716i	−0.984521	−	0.175269i	$-0.943920\pi$
$151$	−7763.12	+	13446.1i	−0.340473	+	0.589716i	0.644048	+	0.764985i	$0.277254\pi$
$152$	−398.385			−0.0172431
$153$		0			0
$154$	−534.475			−0.0225365
$155$	−22537.9	+	14334.6i	−0.938103	+	0.596654i
$156$		0			0
$157$	7659.23	−	4422.06i	0.310732	−	0.179401i	−0.336522	−	0.941676i	$-0.609251\pi$
$157$	7659.23	−	4422.06i	0.310732	−	0.179401i	0.647254	+	0.762274i	$0.275917\pi$
$158$	−9260.58	−	16039.8i	−0.370957	−	0.642517i
$159$		0			0
$160$	13848.7	−	8808.05i	0.540964	−	0.344065i
$161$			18839.8i			0.726818i
$162$		0			0
$163$			45394.1i			1.70854i	0.519833	+	0.854268i	$0.325994\pi$
$163$			45394.1i			1.70854i	−0.519833	+	0.854268i	$0.674006\pi$
$164$	11909.6	+	6875.99i	0.442801	+	0.255651i
$165$		0			0
$166$	15054.6	+	26075.3i	0.546328	+	0.946267i
$167$	19920.0	+	34502.5i	0.714261	+	1.23714i	0.963244	+	0.268629i	$0.0865704\pi$
$167$	19920.0	+	34502.5i	0.714261	+	1.23714i	−0.248983	+	0.968508i	$0.580096\pi$
$168$		0			0
$169$	20070.9	−	34763.8i	0.702737	−	1.21718i
$170$	−49868.7	−	26007.3i	−1.72556	−	0.899908i
$171$		0			0
$172$		−	3678.50i		−	0.124341i
$173$	−16397.7	+	28401.6i	−0.547886	+	0.948966i	0.450533	+	0.892760i	$0.351234\pi$
$173$	−16397.7	+	28401.6i	−0.547886	+	0.948966i	−0.998419	+	0.0562065i	$0.982099\pi$
$174$		0			0
$175$	−29815.7	−	13957.5i	−0.973575	−	0.455756i
$176$	595.300	−	343.697i	0.0192181	−	0.0110956i
$177$		0			0
$178$	−30524.9	−	17623.5i	−0.963415	−	0.556228i
$179$		−	3241.64i		−	0.101172i	−0.998720	−	0.0505858i	$-0.983891\pi$
$179$		−	3241.64i		−	0.101172i	0.998720	−	0.0505858i	$-0.0161088\pi$
$180$		0			0
$181$	2975.07			0.0908113			0.0454057	−	0.998969i	$-0.485542\pi$
$181$	2975.07			0.0908113			0.0454057	+	0.998969i	$0.485542\pi$
$182$	31881.8	−	55221.0i	0.962500	−	1.66710i
$183$		0			0
$184$	−8812.92	−	15264.4i	−0.260306	−	0.450863i
$185$	−43010.6	+	1845.72i	−1.25670	+	0.0539291i
$186$		0			0
$187$	−926.844	−	535.113i	−0.0265047	−	0.0153025i
$188$	−8718.73			−0.246682
$189$		0			0
$190$	827.621	+	431.618i	0.0229258	+	0.0119562i
$191$	41545.5	+	23986.3i	1.13882	+	0.657501i	0.946139	−	0.323760i	$-0.104947\pi$
$191$	41545.5	+	23986.3i	1.13882	+	0.657501i	0.192685	+	0.981261i	$0.438280\pi$
$192$		0			0
$193$	47565.0	−	27461.7i	1.27695	−	0.737246i	0.300662	−	0.953731i	$-0.402792\pi$
$193$	47565.0	−	27461.7i	1.27695	−	0.737246i	0.976286	+	0.216484i	$0.0694590\pi$
$194$	−50807.8	+	29333.9i	−1.34998	+	0.779411i
$195$		0			0
$196$	995.355	−	1724.01i	0.0259099	−	0.0448773i
$197$	27187.3			0.700540			0.350270	−	0.936649i	$-0.386090\pi$
$197$	27187.3			0.700540			0.350270	+	0.936649i	$0.386090\pi$
$198$		0			0
$199$	−5662.22			−0.142982			−0.0714909	−	0.997441i	$-0.522776\pi$
$199$	−5662.22			−0.142982			−0.0714909	+	0.997441i	$0.522776\pi$
$200$	30686.4	−	2638.56i	0.767159	−	0.0659640i
$201$		0			0
$202$	18666.1	−	10776.9i	0.457458	−	0.264113i
$203$	−781.940	−	1354.36i	−0.0189750	−	0.0328656i
$204$		0			0
$205$	34617.8	+	54428.7i	0.823743	+	1.29515i
$206$		−	24326.3i		−	0.573246i
$207$		0			0
$208$			82007.0i			1.89550i
$209$	15.3819	+	8.88074i	0.000352141	+	0.000203309i
$210$		0			0
$211$	25552.1	+	44257.5i	0.573933	+	0.994081i	0.996157	+	0.0875895i	$0.0279164\pi$
$211$	25552.1	+	44257.5i	0.573933	+	0.994081i	−0.422224	+	0.906492i	$0.638750\pi$
$212$	8939.19	+	15483.1i	0.198896	+	0.344498i
$213$		0			0
$214$	−45429.4	+	78686.1i	−0.991996	+	1.71819i
$215$	7978.58	−	15298.8i	0.172603	−	0.330964i
$216$		0			0
$217$		−	56277.0i		−	1.19512i
$218$	17400.2	−	30138.1i	0.366136	−	0.634166i
$219$		0			0
$220$	−292.479	+	12.5512i	−0.00604296	+	0.000259323i
$221$	110574.	−	63839.8i	2.26395	−	1.30709i
$222$		0			0
$223$	−59559.4	−	34386.7i	−1.19768	−	0.691481i	−0.237643	−	0.971353i	$-0.576375\pi$
$223$	−59559.4	−	34386.7i	−1.19768	−	0.691481i	−0.960037	+	0.279872i	$0.909708\pi$
$224$			34580.0i			0.689175i
$225$		0			0
$226$	29966.6			0.586706
$227$	13649.9	−	23642.3i	0.264897	−	0.458816i	−0.702639	−	0.711546i	$-0.747995\pi$
$227$	13649.9	−	23642.3i	0.264897	−	0.458816i	0.967537	+	0.252731i	$0.0813286\pi$
$228$		0			0
$229$	−26698.6	−	46243.3i	−0.509117	−	0.881816i	−0.999944	−	0.0105593i	$-0.996639\pi$
$229$	−26698.6	−	46243.3i	−0.509117	−	0.881816i	0.490827	−	0.871257i	$-0.336695\pi$
$230$	1770.56	+	41259.0i	0.0334699	+	0.779944i
$231$		0			0
$232$	1267.09	+	731.553i	0.0235413	+	0.0135916i
$233$	−741.777			−0.0136635			−0.00683174	−	0.999977i	$-0.502175\pi$
$233$	−741.777			−0.0136635			−0.00683174	+	0.999977i	$0.502175\pi$
$234$		0			0
$235$	−36261.0	−	18910.7i	−0.656605	−	0.342430i
$236$	6638.88	+	3832.96i	0.119199	+	0.0688193i
$237$		0			0
$238$	102625.	−	59250.3i	1.81175	−	1.04601i
$239$	−69798.3	+	40298.1i	−1.22194	+	0.705486i	−0.965331	−	0.261029i	$-0.915938\pi$
$239$	−69798.3	+	40298.1i	−1.22194	+	0.705486i	−0.256607	+	0.966516i	$0.582605\pi$
$240$		0			0
$241$	−44199.7	+	76556.1i	−0.761001	+	1.31809i	0.181334	+	0.983422i	$0.441958\pi$
$241$	−44199.7	+	76556.1i	−0.761001	+	1.31809i	−0.942335	+	0.334671i	$0.891375\pi$
$242$	67596.0			1.15422
$243$		0			0
$244$	2737.18			0.0459752
$245$	7878.99	−	5011.21i	0.131262	−	0.0834853i
$246$		0			0
$247$	−1835.08	+	1059.48i	−0.0300789	+	0.0173660i
$248$	26325.3	+	45596.8i	0.428026	+	0.741363i
$249$		0			0
$250$	−66607.8	−	27764.7i	−1.06572	−	0.444236i
$251$			48276.4i			0.766280i	0.923690	+	0.383140i	$0.125157\pi$
$251$			48276.4i			0.766280i	−0.923690	+	0.383140i	$0.874843\pi$
$252$		0			0
$253$			785.825i			0.0122768i
$254$	99668.8	+	57543.8i	1.54487	+	0.891930i
$255$		0			0
$256$	−29516.2	−	51123.6i	−0.450382	−	0.780084i
$257$	−28514.6	−	49388.7i	−0.431719	−	0.747759i	0.565302	−	0.824884i	$-0.308759\pi$
$257$	−28514.6	−	49388.7i	−0.431719	−	0.747759i	−0.997021	+	0.0771245i	$0.975426\pi$
$258$		0			0
$259$	45352.1	−	78552.2i	0.676080	−	1.17101i
$260$	16149.8	−	30967.1i	0.238903	−	0.458093i
$261$		0			0
$262$			39317.1i			0.572768i
$263$	18313.7	−	31720.3i	0.264768	−	0.458591i	−0.702735	−	0.711452i	$-0.748038\pi$
$263$	18313.7	−	31720.3i	0.264768	−	0.458591i	0.967503	+	0.252861i	$0.0813714\pi$
$264$		0			0
$265$	3595.40	+	83783.0i	0.0511982	+	1.19306i
$266$	−1703.16	+	983.318i	−0.0240708	+	0.0138973i
$267$		0			0
$268$	20258.6	+	11696.3i	0.282059	+	0.162847i
$269$		−	51318.1i		−	0.709196i	−0.935019	−	0.354598i	$-0.884618\pi$
$269$		−	51318.1i		−	0.709196i	0.935019	−	0.354598i	$-0.115382\pi$
$270$		0			0
$271$	−17528.9			−0.238679			−0.119340	−	0.992853i	$-0.538078\pi$
$271$	−17528.9			−0.238679			−0.119340	+	0.992853i	$0.538078\pi$
$272$	−76202.4	+	131986.i	−1.02999	+	1.78399i
$273$		0			0
$274$	4298.48	+	7445.19i	0.0572551	+	0.0991687i
$275$	−1243.64	−	582.180i	−0.0164448	−	0.00769824i
$276$		0			0
$277$	65710.4	+	37937.9i	0.856396	+	0.494440i	0.862804	−	0.505539i	$-0.168706\pi$
$277$	65710.4	+	37937.9i	0.856396	+	0.494440i	−0.00640796	+	0.999979i	$0.502040\pi$
$278$	−22807.0			−0.295106
$279$		0			0
$280$	−30007.2	+	57538.4i	−0.382745	+	0.733908i
$281$	−67750.7	−	39115.9i	−0.858027	−	0.495382i	0.00532421	−	0.999986i	$-0.498305\pi$
$281$	−67750.7	−	39115.9i	−0.858027	−	0.495382i	−0.863351	+	0.504604i	$0.831639\pi$
$282$		0			0
$283$	−94524.2	+	54573.6i	−1.18024	+	0.681412i	−0.956070	−	0.293138i	$-0.905300\pi$
$283$	−94524.2	+	54573.6i	−1.18024	+	0.681412i	−0.224170	+	0.974550i	$0.571967\pi$
$284$	20484.1	−	11826.5i	0.253968	−	0.146629i
$285$		0			0
$286$	1329.82	−	2303.31i	0.0162577	−	0.0281592i
$287$	−135908.			−1.64999
$288$		0			0
$289$	153763.			1.84101
$290$	−1839.72	−	2892.54i	−0.0218754	−	0.0343941i
$291$		0			0
$292$	18679.4	−	10784.6i	0.219078	−	0.126484i
$293$	−40696.9	−	70489.1i	−0.474052	−	0.821082i	0.525507	−	0.850790i	$-0.323876\pi$
$293$	−40696.9	−	70489.1i	−0.474052	−	0.821082i	−0.999559	+	0.0297072i	$0.990543\pi$
$294$		0			0
$295$	19297.4	+	30340.8i	0.221745	+	0.348644i
$296$			84859.5i			0.968538i
$297$		0			0
$298$			72900.8i			0.820918i
$299$	−81189.9	−	46875.0i	−0.908155	−	0.524323i
$300$		0			0
$301$	18176.9	+	31483.4i	0.200626	+	0.347495i
$302$	−35853.4	−	62099.9i	−0.393112	−	0.680890i
$303$		0			0
$304$	1264.65	−	2190.45i	0.0136844	−	0.0237020i
$305$	11383.9	+	5936.87i	0.122374	+	0.0638202i
$306$		0			0
$307$			89841.0i			0.953230i	0.879112	+	0.476615i	$0.158136\pi$
$307$			89841.0i			0.953230i	−0.879112	+	0.476615i	$0.841864\pi$
$308$	308.402	−	534.168i	0.00325099	−	0.00563088i
$309$		0			0
$310$	−5288.88	−	123246.i	−0.0550352	−	1.28248i
$311$	−41303.4	+	23846.5i	−0.427036	+	0.246550i	−0.698083	−	0.716017i	$-0.745964\pi$
$311$	−41303.4	+	23846.5i	−0.427036	+	0.246550i	0.271047	+	0.962566i	$0.412630\pi$
$312$		0			0
$313$	−155948.	−	90036.4i	−1.59181	−	0.919029i	−0.992997	−	0.118136i	$-0.962308\pi$
$313$	−155948.	−	90036.4i	−1.59181	−	0.919029i	−0.598808	−	0.800893i	$-0.704359\pi$
$314$			40845.9i			0.414275i
$315$		0			0
$316$	21374.1			0.214049
$317$	−5275.71	+	9137.79i	−0.0525004	+	0.0909333i	−0.891081	−	0.453844i	$-0.850052\pi$
$317$	−5275.71	+	9137.79i	−0.0525004	+	0.0909333i	0.838581	+	0.544777i	$0.183386\pi$
$318$		0			0
$319$	−32.6153	−	56.4914i	−0.000320509	−	0.000555138i
$320$	−2115.76	−	49303.2i	−0.0206617	−	0.481477i
$321$		0			0
$322$	−75353.2	−	43505.2i	−0.726758	−	0.419594i
$323$	−3937.97			−0.0377457
$324$		0			0
$325$	134334.	−	93762.9i	1.27180	−	0.887696i
$326$	−181561.	−	104825.i	−1.70840	−	0.986343i
$327$		0			0
$328$	110115.	−	63575.2i	1.02353	−	0.590935i
$329$	74621.4	−	43082.7i	0.689400	−	0.398025i
$330$		0			0
$331$	102147.	−	176924.i	0.932329	−	1.61484i	0.153001	−	0.988226i	$-0.451106\pi$
$331$	102147.	−	176924.i	0.932329	−	1.61484i	0.779329	−	0.626615i	$-0.215560\pi$
$332$	−34747.1			−0.315241
$333$		0			0
$334$	−183998.			−1.64938
$335$	58886.2	+	92585.3i	0.524716	+	0.824997i
$336$		0			0
$337$	−139338.	+	80447.0i	−1.22690	+	0.708353i	−0.966381	−	0.257114i	$-0.917228\pi$
$337$	−139338.	+	80447.0i	−1.22690	+	0.708353i	−0.260523	+	0.965468i	$0.583895\pi$
$338$	92695.7	+	160554.i	0.811384	+	1.40536i
$339$		0			0
$340$	54767.5	−	34833.3i	0.473768	−	0.301326i
$341$		−	2347.36i		−	0.0201870i
$342$		0			0
$343$		−	106795.i		−	0.907746i
$344$	−29454.6	−	17005.6i	−0.248907	−	0.143706i
$345$		0			0
$346$	−75731.4	−	131171.i	−0.632592	−	1.09568i
$347$	30149.8	+	52221.1i	0.250395	+	0.433697i	0.963635	−	0.267223i	$-0.0861061\pi$
$347$	30149.8	+	52221.1i	0.250395	+	0.433697i	−0.713239	+	0.700921i	$0.752773\pi$
$348$		0			0
$349$	−11957.3	+	20710.7i	−0.0981711	+	0.170037i	−0.910928	−	0.412566i	$-0.864633\pi$
$349$	−11957.3	+	20710.7i	−0.0981711	+	0.170037i	0.812757	+	0.582603i	$0.197966\pi$
$350$	124676.	−	87022.3i	1.01777	−	0.710386i
$351$		0			0
$352$			1442.36i			0.0116410i
$353$	11439.7	−	19814.2i	0.0918050	−	0.159011i	−0.816466	−	0.577394i	$-0.804070\pi$
$353$	11439.7	−	19814.2i	0.0918050	−	0.159011i	0.908271	+	0.418383i	$0.137403\pi$
$354$		0			0
$355$	110844.	−	4756.68i	0.879542	−	0.0377440i
$356$	35226.8	−	20338.2i	0.277954	−	0.160477i
$357$		0			0
$358$	12965.5	+	7485.63i	0.101163	+	0.0584067i
$359$		−	232933.i		−	1.80735i	−0.428216	−	0.903677i	$-0.640858\pi$
$359$		−	232933.i		−	1.80735i	0.428216	−	0.903677i	$-0.359142\pi$
$360$		0			0
$361$	−130256.			−0.999499
$362$	−6870.06	+	11899.3i	−0.0524256	+	0.0908038i
$363$		0			0
$364$	36792.8	+	63727.0i	0.277690	+	0.480973i
$365$	101079.	−	4337.62i	0.758708	−	0.0325586i
$366$		0			0
$367$	43801.9	+	25289.1i	0.325208	+	0.187759i	0.653712	−	0.756744i	$-0.273211\pi$
$367$	43801.9	+	25289.1i	0.325208	+	0.187759i	−0.328504	+	0.944503i	$0.606544\pi$
$368$	111905.			0.826329
$369$		0			0
$370$	91938.3	−	176290.i	0.671573	−	1.28773i
$371$	−153017.	−	88344.2i	−1.11171	−	0.641845i
$372$		0			0
$373$	56423.6	−	32576.2i	0.405549	−	0.234144i	−0.283326	−	0.959024i	$-0.591438\pi$
$373$	56423.6	−	32576.2i	0.405549	−	0.234144i	0.688876	+	0.724880i	$0.258105\pi$
$374$	4280.56	−	2471.38i	0.0306025	−	0.0176684i
$375$		0			0
$376$	−40306.5	+	69812.9i	−0.285101	+	0.493810i
$377$	7782.12			0.0547539
$378$		0			0
$379$	−57876.1			−0.402922			−0.201461	−	0.979497i	$-0.564569\pi$
$379$	−57876.1			−0.402922			−0.201461	+	0.979497i	$0.564569\pi$
$380$	−908.922	+	578.094i	−0.00629447	+	0.00400342i
$381$		0			0
$382$	−191875.	+	110779.i	−1.31489	+	0.759154i
$383$	−47179.9	−	81718.0i	−0.321632	−	0.557084i	0.659193	−	0.751974i	$-0.270898\pi$
$383$	−47179.9	−	81718.0i	−0.321632	−	0.557084i	−0.980825	+	0.194891i	$0.937565\pi$
$384$		0			0
$385$	2441.23	−	1552.68i	0.0164698	−	0.0104751i
$386$			253659.i			1.70246i
$387$		0			0
$388$		−	67704.8i		−	0.449734i
$389$	118204.	+	68245.3i	0.781150	+	0.450997i	0.836838	−	0.547451i	$-0.184402\pi$
$389$	118204.	+	68245.3i	0.781150	+	0.450997i	−0.0556879	+	0.998448i	$0.517735\pi$
$390$		0			0
$391$	−87114.3	−	150886.i	−0.569817	−	0.986953i
$392$	−9203.01	−	15940.1i	−0.0598905	−	0.103733i
$393$		0			0
$394$	−62781.2	+	108740.i	−0.404424	+	0.700483i
$395$	88894.4	+	46359.9i	0.569745	+	0.297131i
$396$		0			0
$397$		−	98285.2i		−	0.623602i	−0.950148	−	0.311801i	$-0.899068\pi$
$397$		−	98285.2i		−	0.623602i	0.950148	−	0.311801i	$-0.100932\pi$
$398$	13075.3	−	22647.0i	0.0825437	−	0.142970i
$399$		0			0
$400$	−82904.9	+	177099.i	−0.518155	+	1.10687i
$401$	39459.3	−	22781.9i	0.245392	−	0.141677i	−0.372260	−	0.928128i	$-0.621417\pi$
$401$	39459.3	−	22781.9i	0.245392	−	0.141677i	0.617653	+	0.786451i	$0.288084\pi$
$402$		0			0
$403$	242525.	+	140022.i	1.49330	+	0.862155i
$404$			24873.8i			0.152398i
$405$		0			0
$406$	7222.66			0.0438172
$407$	1891.67	−	3276.48i	0.0114198	−	0.0197796i
$408$		0			0
$409$	108165.	+	187348.i	0.646609	+	1.11996i	0.983927	+	0.178569i	$0.0571467\pi$
$409$	108165.	+	187348.i	0.646609	+	1.11996i	−0.337319	+	0.941391i	$0.609520\pi$
$410$	−297637.	+	12772.5i	−1.77059	+	0.0759818i
$411$		0			0
$412$	24312.3	+	14036.7i	0.143229	+	0.0826934i
$413$	−75760.7			−0.444164
$414$		0			0
$415$	−144513.	−	75365.6i	−0.839092	−	0.437600i
$416$	−149022.	−	86037.9i	−0.861120	−	0.497168i
$417$		0			0
$418$	−71.0401	+	41.0150i	−0.000406584	+	0.000234742i
$419$	−15411.4	+	8897.78i	−0.0877838	+	0.0506820i	−0.543249	−	0.839571i	$-0.682806\pi$
$419$	−15411.4	+	8897.78i	−0.0877838	+	0.0506820i	0.455466	+	0.890253i	$0.349473\pi$
$420$		0			0
$421$	50184.0	−	86921.3i	0.283140	−	0.490413i	−0.689016	−	0.724746i	$-0.741957\pi$
$421$	50184.0	−	86921.3i	0.283140	−	0.490413i	0.972156	+	0.234333i	$0.0752905\pi$
$422$	−236021.			−1.32533
$423$		0			0
$424$	165303.			0.919493
$425$	303330.	−	26081.7i	1.67933	−	0.144397i
$426$		0			0
$427$	−23426.8	+	13525.5i	−0.128487	+	0.0741817i
$428$	−52427.2	−	90806.6i	−0.286200	−	0.495713i
$429$		0			0
$430$	42766.0	+	67239.9i	0.231293	+	0.363655i
$431$			164947.i			0.887952i	0.896039	+	0.443976i	$0.146432\pi$
$431$			164947.i			0.887952i	−0.896039	+	0.443976i	$0.853568\pi$
$432$		0			0
$433$			9861.68i			0.0525987i	0.999654	+	0.0262994i	$0.00837231\pi$
$433$			9861.68i			0.0525987i	−0.999654	+	0.0262994i	$0.991628\pi$
$434$	225090.	+	129956.i	1.19502	+	0.689946i
$435$		0			0
$436$	20080.5	+	34780.4i	0.105633	+	0.182963i
$437$	1445.75	+	2504.11i	0.00757059	+	0.0131126i
$438$		0			0
$439$	19146.6	−	33162.9i	0.0993487	−	0.172077i	−0.812067	−	0.583565i	$-0.801657\pi$
$439$	19146.6	−	33162.9i	0.0993487	−	0.172077i	0.911415	+	0.411488i	$0.134991\pi$
$440$	−1251.62	+	2399.97i	−0.00646500	+	0.0123966i
$441$		0			0
$442$			589678.i			3.01836i
$443$	−79637.0	+	137935.i	−0.405796	+	0.702859i	−0.994414	−	0.105553i	$-0.966339\pi$
$443$	−79637.0	+	137935.i	−0.405796	+	0.702859i	0.588618	+	0.808411i	$0.299672\pi$
$444$		0			0
$445$	190621.	−	8180.14i	0.962609	−	0.0413086i
$446$	275071.	−	158812.i	1.38285	−	0.798388i
$447$		0			0
$448$	90044.6	+	51987.3i	0.448644	+	0.259025i
$449$			9321.06i			0.0462352i	0.999733	+	0.0231176i	$0.00735922\pi$
$449$			9321.06i			0.0462352i	−0.999733	+	0.0231176i	$0.992641\pi$
$450$		0			0
$451$	−5668.83			−0.0278702
$452$	−17291.3	+	29949.3i	−0.0846349	+	0.146592i
$453$		0			0
$454$	63041.0	+	109190.i	0.305852	+	0.529751i
$455$	14798.3	+	344842.i	0.0714806	+	1.66570i
$456$		0			0
$457$	208802.	+	120552.i	0.999775	+	0.577220i	0.908182	−	0.418576i	$-0.137471\pi$
$457$	208802.	+	120552.i	0.999775	+	0.577220i	0.0915931	+	0.995797i	$0.470804\pi$
$458$	246611.			1.17566
$459$		0			0
$460$	−42256.9	−	22037.7i	−0.199702	−	0.104148i
$461$	183415.	+	105895.i	0.863043	+	0.498278i	0.865030	−	0.501720i	$-0.167299\pi$
$461$	183415.	+	105895.i	0.863043	+	0.498278i	−0.00198694	+	0.999998i	$0.500632\pi$
$462$		0			0
$463$	−314347.	+	181488.i	−1.46638	+	0.846616i	−0.999293	−	0.0375951i	$-0.988030\pi$
$463$	−314347.	+	181488.i	−1.46638	+	0.846616i	−0.467088	+	0.884211i	$0.654697\pi$
$464$	−8044.62	+	4644.56i	−0.0373654	+	0.0215729i
$465$		0			0
$466$	1712.92	−	2966.86i	0.00788797	−	0.0136624i
$467$	−225929.			−1.03595			−0.517974	−	0.855396i	$-0.673314\pi$
$467$	−225929.			−1.03595			−0.517974	+	0.855396i	$0.673314\pi$
$468$		0			0
$469$	−231185.			−1.05103
$470$	159371.	−	101363.i	0.721462	−	0.458865i
$471$		0			0
$472$	61382.8	−	35439.4i	0.275526	−	0.159075i
$473$	758.174	+	1313.20i	0.00338881	+	0.00586959i
$474$		0			0
$475$	−5034.06	+	432.852i	−0.0223116	+	0.00191846i
$476$			136754.i			0.603568i
$477$		0			0
$478$		−	372227.i		−	1.62912i
$479$	−101218.	−	58438.2i	−0.441150	−	0.254698i	0.262935	−	0.964813i	$-0.415309\pi$
$479$	−101218.	−	58438.2i	−0.441150	−	0.254698i	−0.704085	+	0.710115i	$0.748643\pi$
$480$		0			0
$481$	225680.	+	390888.i	0.975443	+	1.68952i
$482$	−204133.	−	353568.i	−0.878656	−	1.52188i
$483$		0			0
$484$	−39004.1	+	67557.2i	−0.166502	+	0.288390i
$485$	146850.	−	281583.i	0.624296	−	1.19708i
$486$		0			0
$487$		−	297474.i		−	1.25427i	−0.778911	−	0.627134i	$-0.784228\pi$
$487$		−	297474.i		−	1.25427i	0.778911	−	0.627134i	$-0.215772\pi$
$488$	12653.9	−	21917.2i	0.0531356	−	0.0920335i
$489$		0			0
$490$	1848.93	+	43085.3i	0.00770066	+	0.179447i
$491$	−176709.	+	102023.i	−0.732984	+	0.423189i	−0.819513	−	0.573061i	$-0.805756\pi$
$491$	−176709.	+	102023.i	−0.732984	+	0.423189i	0.0865286	+	0.996249i	$0.472423\pi$
$492$		0			0
$493$	12524.9	+	7231.28i	0.0515326	+	0.0297524i
$494$		−	9786.30i		−	0.0401019i
$495$		0			0
$496$	−334274.			−1.35875
$497$	−116879.	+	202440.i	−0.473176	+	0.819564i
$498$		0			0
$499$	−191606.	−	331872.i	−0.769501	−	1.33281i	−0.937834	−	0.347084i	$-0.887172\pi$
$499$	−191606.	−	331872.i	−0.769501	−	1.33281i	0.168333	−	0.985730i	$-0.446162\pi$
$500$	66182.7	−	50548.7i	0.264731	−	0.202195i
$501$		0			0
$502$	−193090.	−	111480.i	−0.766217	−	0.442376i
$503$	76671.8			0.303040			0.151520	−	0.988454i	$-0.451583\pi$
$503$	76671.8			0.303040			0.151520	+	0.988454i	$0.451583\pi$
$504$		0			0
$505$	−53950.7	+	103450.i	−0.211551	+	0.405645i
$506$	−3143.04	−	1814.64i	−0.0122758	−	0.00708743i
$507$		0			0
$508$	−115021.	+	66407.6i	−0.445709	+	0.257330i
$509$	−213621.	+	123334.i	−0.824534	+	0.476045i	−0.851977	−	0.523579i	$-0.824597\pi$
$509$	−213621.	+	123334.i	−0.824534	+	0.476045i	0.0274438	+	0.999623i	$0.491263\pi$
$510$		0			0
$511$	−106582.	+	184605.i	−0.408170	+	0.706970i
$512$	−41290.4			−0.157510
$513$		0			0
$514$	263385.			0.996930
$515$	70669.1	+	111111.i	0.266450	+	0.418932i
$516$		0			0
$517$	3112.52	−	1797.01i	0.0116448	−	0.00672311i
$518$	209455.	+	362787.i	0.780606	+	1.35205i
$519$		0			0
$520$	−173300.	−	272476.i	−0.640904	−	1.00768i
$521$		−	170783.i		−	0.629171i	−0.949229	−	0.314586i	$-0.898134\pi$
$521$		−	170783.i		−	0.629171i	0.949229	−	0.314586i	$-0.101866\pi$
$522$		0			0
$523$		−	213600.i		−	0.780905i	−0.920623	−	0.390452i	$-0.872319\pi$
$523$		−	213600.i		−	0.780905i	0.920623	−	0.390452i	$-0.127681\pi$
$524$	−39294.5	−	22686.7i	−0.143110	−	0.0826244i
$525$		0			0
$526$	84580.5	+	146498.i	0.305702	+	0.529492i
$527$	260221.	+	450717.i	0.936962	+	1.62287i
$528$		0			0
$529$	75956.0	−	131560.i	0.271425	−	0.470123i
$530$	−343407.	−	179092.i	−1.22252	−	0.637565i
$531$		0			0
$532$		−	2269.57i		−	0.00801900i
$533$	338150.	−	585693.i	1.19030	−	2.06165i
$534$		0			0
$535$	−21086.5	−	491376.i	−0.0736712	−	1.71675i
$536$	187311.	−	108144.i	0.651978	−	0.376419i
$537$		0			0
$538$	205256.	+	118504.i	0.709137	+	0.409421i
$539$			820.609i			0.00282461i
$540$		0			0
$541$	445341.			1.52159			0.760795	−	0.648992i	$-0.224809\pi$
$541$	445341.			1.52159			0.760795	+	0.648992i	$0.224809\pi$
$542$	40477.8	−	70109.7i	0.137790	−	0.238660i
$543$		0			0
$544$	−159896.	−	276948.i	−0.540306	−	0.935837i
$545$	8076.49	+	188205.i	0.0271913	+	0.633634i
$546$		0			0
$547$	150902.	+	87123.4i	0.504337	+	0.291179i	0.730503	−	0.682910i	$-0.239286\pi$
$547$	150902.	+	87123.4i	0.504337	+	0.291179i	−0.226166	+	0.974089i	$0.572619\pi$
$548$	−9921.21			−0.0330372
$549$		0			0
$550$	5200.35	−	3629.77i	0.0171912	−	0.0119992i
$551$	−207.864	−	120.010i	−0.000684661	−	0.000395289i
$552$		0			0
$553$	−182935.	+	105618.i	−0.598201	+	0.345372i
$554$	−303478.	+	175213.i	−0.988799	+	0.570884i
$555$		0			0
$556$	13160.1	−	22793.9i	0.0425704	−	0.0737342i
$557$	376126.			1.21234			0.606168	−	0.795337i	$-0.292706\pi$
$557$	376126.			1.21234			0.606168	+	0.795337i	$0.292706\pi$
$558$		0			0
$559$	−180903.			−0.578924
$560$	−221108.	−	347642.i	−0.705063	−	1.10855i
$561$		0			0
$562$	312901.	−	180654.i	0.990683	−	0.571971i
$563$	−255128.	−	441894.i	−0.804897	−	1.39412i	−0.916360	−	0.400355i	$-0.868887\pi$
$563$	−255128.	−	441894.i	−0.804897	−	1.39412i	0.111463	−	0.993769i	$-0.464446\pi$
$564$		0			0
$565$	−136873.	+	87054.4i	−0.428768	+	0.272705i
$566$		−	504088.i		−	1.57352i
$567$		0			0
$568$		−	218694.i		−	0.677862i
$569$	134061.	+	77400.4i	0.414075	+	0.239067i	0.692539	−	0.721380i	$-0.256492\pi$
$569$	134061.	+	77400.4i	0.414075	+	0.239067i	−0.278464	+	0.960447i	$0.589825\pi$
$570$		0			0
$571$	−45551.8	−	78898.0i	−0.139712	−	0.241988i	0.787676	−	0.616090i	$-0.211284\pi$
$571$	−45551.8	−	78898.0i	−0.139712	−	0.241988i	−0.927388	+	0.374102i	$0.877951\pi$
$572$	1534.66	+	2658.10i	0.00469050	+	0.00812419i
$573$		0			0
$574$	313840.	−	543587.i	0.952544	−	1.64985i
$575$	−127947.	−	183308.i	−0.386984	−	0.554430i
$576$		0			0
$577$			117325.i			0.352403i	0.984354	+	0.176201i	$0.0563810\pi$
$577$			117325.i			0.352403i	−0.984354	+	0.176201i	$0.943619\pi$
$578$	−355072.	+	615003.i	−1.06282	+	1.84086i
$579$		0			0
$580$	3952.43	−	169.612i	0.0117492	−	0.000504196i
$581$	297392.	−	171699.i	0.881001	−	0.508646i
$582$		0			0
$583$	−6382.44	−	3684.91i	−0.0187780	−	0.0108415i
$584$		−	199427.i		−	0.584735i
$585$		0			0
$586$	375911.			1.09469
$587$	92049.2	−	159434.i	0.267143	−	0.462705i	−0.700980	−	0.713181i	$-0.747254\pi$
$587$	92049.2	−	159434.i	0.267143	−	0.462705i	0.968123	+	0.250476i	$0.0805870\pi$
$588$		0			0
$589$	−4318.63	−	7480.09i	−0.0124485	−	0.0215614i
$590$	−165915.	+	7119.94i	−0.476630	+	0.0204537i
$591$		0			0
$592$	−466584.	−	269382.i	−1.33133	−	0.768645i
$593$	−459312.			−1.30617			−0.653083	−	0.757286i	$-0.726525\pi$
$593$	−459312.			−1.30617			−0.653083	+	0.757286i	$0.726525\pi$
$594$		0			0
$595$	−296616.	+	568758.i	−0.837840	+	1.60655i
$596$	−72858.9	−	42065.1i	−0.205111	−	0.118421i
$597$		0			0
$598$	374970.	−	216489.i	1.04856	−	0.605387i
$599$	−98904.0	+	57102.3i	−0.275652	+	0.159147i	−0.631453	−	0.775414i	$-0.717541\pi$
$599$	−98904.0	+	57102.3i	−0.275652	+	0.159147i	0.355802	+	0.934561i	$0.384208\pi$
$600$		0			0
$601$	−45927.0	+	79547.9i	−0.127151	+	0.220232i	−0.922572	−	0.385826i	$-0.873917\pi$
$601$	−45927.0	+	79547.9i	−0.127151	+	0.220232i	0.795421	+	0.606058i	$0.207250\pi$
$602$	−167897.			−0.463288
$603$		0			0
$604$	82752.2			0.226833
$605$	−308747.	+	196370.i	−0.843514	+	0.536493i
$606$		0			0
$607$	−516300.	+	298086.i	−1.40128	+	0.809029i	−0.994524	−	0.104509i	$-0.966673\pi$
$607$	−516300.	+	298086.i	−1.40128	+	0.809029i	−0.406755	+	0.913537i	$0.633340\pi$
$608$	2653.63	+	4596.22i	0.00717849	+	0.0124335i
$609$		0			0
$610$	−50033.3	+	31822.3i	−0.134462	+	0.0855207i
$611$			428773.i			1.14854i
$612$		0			0
$613$			338475.i			0.900753i	0.892839	+	0.450377i	$0.148710\pi$
$613$			338475.i			0.900753i	−0.892839	+	0.450377i	$0.851290\pi$
$614$	−359334.	−	207462.i	−0.953152	−	0.550302i
$615$		0			0
$616$	−2851.47	−	4938.89i	−0.00751463	−	0.0130157i
$617$	−252706.	−	437700.i	−0.663813	−	1.14976i	−0.979606	−	0.200930i	$-0.935604\pi$
$617$	−252706.	−	437700.i	−0.663813	−	1.14976i	0.315792	−	0.948828i	$-0.397730\pi$
$618$		0			0
$619$	−1186.23	+	2054.61i	−0.00309590	+	0.00536226i	−0.867569	−	0.497316i	$-0.834319\pi$
$619$	−1186.23	+	2054.61i	−0.00309590	+	0.00536226i	0.864473	+	0.502679i	$0.167652\pi$
$620$	126227.	+	65829.3i	0.328374	+	0.171252i
$621$		0			0
$622$		−	220267.i		−	0.569335i
$623$	−200998.	+	348139.i	−0.517864	+	0.896967i
$624$		0			0
$625$	384891.	−	66682.6i	0.985322	−	0.170707i
$626$	720232.	−	415826.i	1.83791	−	1.06112i
$627$		0			0
$628$	−40822.4	−	23568.8i	−0.103509	−	0.0597611i
$629$			838822.i			2.12016i
$630$		0			0
$631$	92165.6			0.231478			0.115739	−	0.993280i	$-0.463076\pi$
$631$	92165.6			0.231478			0.115739	+	0.993280i	$0.463076\pi$
$632$	98812.0	−	171147.i	0.247386	−	0.428485i
$633$		0			0
$634$	−24365.4	−	42202.2i	−0.0606172	−	0.104992i
$635$	−622408.	+	26709.5i	−1.54358	+	0.0662398i
$636$		0			0
$637$	−84783.7	−	48949.9i	−0.208946	−	0.120635i
$638$	301.263			0.000740124
$639$		0			0
$640$	434920.	+	226818.i	1.06182	+	0.553754i
$641$	−449455.	−	259493.i	−1.09388	−	0.631552i	−0.159274	−	0.987234i	$-0.550915\pi$
$641$	−449455.	−	259493.i	−1.09388	−	0.631552i	−0.934607	+	0.355682i	$0.884249\pi$
$642$		0			0
$643$	−468605.	+	270549.i	−1.13340	+	0.654372i	−0.944789	−	0.327679i	$-0.893733\pi$
$643$	−468605.	+	270549.i	−1.13340	+	0.654372i	−0.188616	+	0.982051i	$0.560400\pi$
$644$	86960.3	−	50206.6i	0.209676	−	0.121057i
$645$		0			0
$646$	9093.60	−	15750.6i	0.0217907	−	0.0377426i
$647$	692153.			1.65346			0.826730	−	0.562599i	$-0.190198\pi$
$647$	692153.			1.65346			0.826730	+	0.562599i	$0.190198\pi$
$648$		0			0
$649$	−3160.04			−0.00750245
$650$	64816.1	+	753809.i	0.153411	+	1.78416i
$651$		0			0
$652$	209529.	−	120971.i	0.492888	−	0.284569i
$653$	3155.89	+	5466.17i	0.00740109	+	0.0128191i	0.869702	−	0.493577i	$-0.164311\pi$
$653$	3155.89	+	5466.17i	0.00740109	+	0.0128191i	−0.862301	+	0.506396i	$0.830977\pi$
$654$		0			0
$655$	−114218.	−	179582.i	−0.266227	−	0.418582i
$656$			807266.i			1.87590i
$657$		0			0
$658$			397948.i			0.919125i
$659$	−209705.	−	121073.i	−0.482879	−	0.278790i	0.238737	−	0.971084i	$-0.423267\pi$
$659$	−209705.	−	121073.i	−0.482879	−	0.278790i	−0.721615	+	0.692294i	$0.756600\pi$
$660$		0			0
$661$	−95483.2	−	165382.i	−0.218536	−	0.378516i	0.735824	−	0.677172i	$-0.236795\pi$
$661$	−95483.2	−	165382.i	−0.218536	−	0.378516i	−0.954361	+	0.298656i	$0.903462\pi$
$662$	471758.	+	817108.i	1.07647	+	1.86451i
$663$		0			0
$664$	−160635.	+	278228.i	−0.364338	+	0.631052i
$665$	4922.64	−	9439.10i	0.0111315	−	0.0213446i
$666$		0			0
$667$		−	10619.3i		−	0.0238695i
$668$	106170.	−	183892.i	0.237931	−	0.412108i
$669$		0			0
$670$	−506292.	+	21726.6i	−1.12785	+	0.0483996i
$671$	−977.151	+	564.159i	−0.00217029	+	0.00125301i
$672$		0			0
$673$	−413218.	−	238572.i	−0.912324	−	0.526731i	−0.0311462	−	0.999515i	$-0.509916\pi$
$673$	−413218.	−	238572.i	−0.912324	−	0.526731i	−0.881178	+	0.472784i	$0.843249\pi$
$674$		−	743076.i		−	1.63574i
$675$		0			0
$676$	−213948.			−0.468183
$677$	−104291.	+	180637.i	−0.227546	+	0.394122i	−0.957080	−	0.289823i	$-0.906404\pi$
$677$	−104291.	+	180637.i	−0.227546	+	0.394122i	0.729534	+	0.683944i	$0.239737\pi$
$678$		0			0
$679$	334556.	+	579468.i	0.725654	+	1.25687i
$680$	−25729.5	−	599570.i	−0.0556434	−	1.29665i
$681$		0			0
$682$	9388.67	+	5420.55i	0.0201853	+	0.0116540i
$683$	−166389.			−0.356683			−0.178342	−	0.983969i	$-0.557073\pi$
$683$	−166389.			−0.356683			−0.178342	+	0.983969i	$0.557073\pi$
$684$		0			0
$685$	−41262.1	−	21518.9i	−0.0879367	−	0.0458604i
$686$	427147.	+	246613.i	0.907672	+	0.524045i
$687$		0			0
$688$	187005.	−	107967.i	0.395072	−	0.228095i
$689$	761435.	−	439615.i	1.60396	−	0.926048i
$690$		0			0
$691$	−25681.9	+	44482.3i	−0.0537862	+	0.0931604i	−0.891665	−	0.452696i	$-0.850462\pi$
$691$	−25681.9	+	44482.3i	−0.0537862	+	0.0931604i	0.837879	+	0.545856i	$0.183796\pi$
$692$	174794.			0.365017
$693$		0			0
$694$	−278489.			−0.578216
$695$	104172.	−	66255.5i	0.215665	−	0.137168i
$696$		0			0
$697$	1.08847e6	−	628430.i	2.24054	−	1.29357i
$698$	−55224.1	−	95650.9i	−0.113349	−	0.196326i
$699$		0			0
$700$	15031.7	+	174818.i	0.0306769	+	0.356772i
$701$		−	30751.1i		−	0.0625783i	−0.999510	−	0.0312892i	$-0.990039\pi$
$701$		−	30751.1i		−	0.0625783i	0.999510	−	0.0312892i	$-0.00996128\pi$
$702$		0			0
$703$		−	13921.1i		−	0.0281684i
$704$	3755.83	+	2168.43i	0.00757811	+	0.00437523i
$705$		0			0
$706$	52833.5	+	91510.3i	0.105999	+	0.183595i
$707$	−122911.	−	212889.i	−0.245897	−	0.425906i
$708$		0			0
$709$	−452291.	+	783391.i	−0.899758	+	1.55843i	−0.0719549	+	0.997408i	$0.522924\pi$
$709$	−452291.	+	783391.i	−0.899758	+	1.55843i	−0.827803	+	0.561019i	$0.810410\pi$
$710$	−236938.	+	454325.i	−0.470021	+	0.901259i
$711$		0			0
$712$		−	376092.i		−	0.741881i
$713$	191070.	−	330943.i	0.375850	−	0.650991i
$714$		0			0
$715$	617.248	+	14383.6i	0.00120739	+	0.0281356i
$716$	−14962.7	+	8638.69i	−0.0291865	+	0.0168509i
$717$		0			0
$718$	931657.	+	537893.i	1.80720	+	1.04339i
$719$			98242.0i			0.190038i	0.995475	+	0.0950188i	$0.0302911\pi$
$719$			98242.0i			0.190038i	−0.995475	+	0.0950188i	$0.969709\pi$
$720$		0			0
$721$	−277444.			−0.533709
$722$	300788.	−	520980.i	0.577013	−	0.999416i
$723$		0			0
$724$	−7928.30	−	13732.2i	−0.0151253	−	0.0261977i
$725$	16806.0	+	7867.31i	0.0319733	+	0.0149675i
$726$		0			0
$727$	40935.0	+	23633.8i	0.0774508	+	0.0447163i	0.538225	−	0.842801i	$-0.319095\pi$
$727$	40935.0	+	23633.8i	0.0774508	+	0.0447163i	−0.460774	+	0.887517i	$0.652428\pi$
$728$	680369.			1.28375
$729$		0			0
$730$	−216063.	+	414299.i	−0.405448	+	0.777442i
$731$	−291154.	−	168098.i	−0.544864	−	0.314578i
$732$		0			0
$733$	−83352.7	+	48123.7i	−0.155136	+	0.0895676i	−0.575558	−	0.817761i	$-0.695215\pi$
$733$	−83352.7	+	48123.7i	−0.155136	+	0.0895676i	0.420423	+	0.907328i	$0.361882\pi$
$734$	−202296.	+	116796.i	−0.375487	+	0.216788i
$735$		0			0
$736$	−117405.	+	203352.i	−0.216736	+	0.375398i
$737$	−9642.90			−0.0177530
$738$		0			0
$739$	466099.			0.853473			0.426736	−	0.904376i	$-0.359663\pi$
$739$	466099.			0.853473			0.426736	+	0.904376i	$0.359663\pi$
$740$	123139.	+	193608.i	0.224870	+	0.353558i
$741$		0			0
$742$	706695.	−	408011.i	1.28358	−	0.741078i
$743$	329802.	+	571234.i	0.597415	+	1.03475i	0.993201	+	0.116410i	$0.0371388\pi$
$743$	329802.	+	571234.i	0.597415	+	1.03475i	−0.395786	+	0.918343i	$0.629528\pi$
$744$		0			0
$745$	−211780.	−	332977.i	−0.381569	−	0.599931i
$746$			300901.i			0.540688i
$747$		0			0
$748$			5704.12i			0.0101950i
$749$	897423.	+	518127.i	1.59968	+	0.923576i
$750$		0			0
$751$	−141713.	−	245454.i	−0.251263	−	0.435201i	0.712611	−	0.701560i	$-0.247513\pi$
$751$	−141713.	−	245454.i	−0.251263	−	0.435201i	−0.963874	+	0.266359i	$0.914179\pi$
$752$	−255902.	−	443236.i	−0.452521	−	0.783789i
$753$		0			0
$754$	−17970.5	+	31125.9i	−0.0316096	+	0.0547494i
$755$	344165.	+	179487.i	0.603771	+	0.314876i
$756$		0			0
$757$			4073.41i			0.00710831i	0.999994	+	0.00355415i	$0.00113132\pi$
$757$			4073.41i			0.00710831i	−0.999994	+	0.00355415i	$0.998869\pi$
$758$	133648.	−	231485.i	0.232608	−	0.402889i
$759$		0			0
$760$	427.006	+	9950.46i	0.000739277	+	0.0172273i
$761$	−782690.	+	451886.i	−1.35151	+	0.780297i	−0.988462	−	0.151471i	$-0.951599\pi$
$761$	−782690.	+	451886.i	−1.35151	+	0.780297i	−0.363053	+	0.931769i	$0.618265\pi$
$762$		0			0
$763$	−343728.	−	198451.i	−0.590426	−	0.340883i
$764$		−	255686.i		−	0.438046i
$765$		0			0
$766$	435794.			0.742717
$767$	188499.	−	326489.i	0.320418	−	0.554981i
$768$		0			0
$769$	−332180.	−	575352.i	−0.561721	−	0.972929i	−0.997346	−	0.0728012i	$-0.976806\pi$
$769$	−332180.	−	575352.i	−0.561721	−	0.972929i	0.435626	−	0.900128i	$-0.356527\pi$
$770$	572.874	+	13349.6i	0.000966224	+	0.0225158i
$771$		0			0
$772$	−253513.	−	146366.i	−0.425370	−	0.245587i
$773$	−617606.			−1.03360			−0.516800	−	0.856106i	$-0.672877\pi$
$773$	−617606.			−1.03360			−0.516800	+	0.856106i	$0.672877\pi$
$774$		0			0
$775$	382193.	+	547566.i	0.636325	+	0.911660i
$776$	−542128.	−	312998.i	−0.900282	−	0.519778i
$777$		0			0
$778$	−545918.	+	315186.i	−0.901920	+	0.520724i
$779$	−18064.3	+	10429.4i	−0.0297677	+	0.0171864i
$780$		0			0
$781$	−4875.10	+	8443.93i	−0.00799248	+	0.0138434i
$782$	804661.			1.31583
$783$		0			0
$784$	116858.			0.190120
$785$	−118659.	−	186565.i	−0.192559	−	0.302755i
$786$		0			0
$787$	359252.	−	207414.i	0.580029	−	0.334880i	−0.181116	−	0.983462i	$-0.557971\pi$
$787$	359252.	−	207414.i	0.580029	−	0.334880i	0.761145	+	0.648582i	$0.224638\pi$
$788$	−72451.7	−	125490.i	−0.116680	−	0.202096i
$789$		0			0
$790$	−390700.	+	248494.i	−0.626022	+	0.398163i
$791$		−	341772.i		−	0.546240i
$792$		0			0
$793$		−	134610.i		−	0.214058i
$794$	393109.	+	226961.i	0.623550	+	0.360007i
$795$		0			0
$796$	15089.3	+	26135.5i	0.0238146	+	0.0412481i
$797$	235403.	+	407730.i	0.370592	+	0.641884i	0.989657	−	0.143456i	$-0.0458216\pi$
$797$	235403.	+	407730.i	0.370592	+	0.641884i	−0.619065	+	0.785340i	$0.712488\pi$
$798$		0			0
$799$	−398423.	+	690089.i	−0.624095	+	1.08097i
$800$	−234843.	−	336458.i	−0.366941	−	0.525715i
$801$		0			0
$802$			210433.i			0.327163i
$803$	−4445.61	+	7700.02i	−0.00689446	+	0.0119415i
$804$		0			0
$805$	470563.	−	20193.4i	0.726150	−	0.0311614i
$806$	−1.12008e6	+	646679.i	−1.72417	+	0.995449i
$807$		0			0
$808$	199170.	+	114991.i	0.305072	+	0.176133i
$809$		−	292131.i		−	0.446355i	−0.974778	−	0.223178i	$-0.928357\pi$
$809$		−	292131.i		−	0.446355i	0.974778	−	0.223178i	$-0.0716430\pi$
$810$		0			0
$811$	−730678.			−1.11092			−0.555462	−	0.831542i	$-0.687459\pi$
$811$	−730678.			−1.11092			−0.555462	+	0.831542i	$0.687459\pi$
$812$	−4167.60	+	7218.50i	−0.00632084	+	0.0109480i
$813$		0			0
$814$	8736.55	+	15132.2i	0.0131853	+	0.0228377i
$815$	1.13381e6	−	48655.4i	1.70697	−	0.0732514i
$816$		0			0
$817$	4831.99	+	2789.75i	0.00723906	+	0.00417947i
$818$	−999107.			−1.49316
$819$		0			0
$820$	158977.	−	304835.i	0.236432	−	0.453354i
$821$	490256.	+	283049.i	0.727338	+	0.419929i	0.817448	−	0.576003i	$-0.195388\pi$
$821$	490256.	+	283049.i	0.727338	+	0.419929i	−0.0901094	+	0.995932i	$0.528722\pi$
$822$		0			0
$823$	314264.	−	181440.i	0.463975	−	0.267876i	−0.249739	−	0.968313i	$-0.580345\pi$
$823$	314264.	−	181440.i	0.463975	−	0.267876i	0.713714	+	0.700437i	$0.247012\pi$
$824$	224790.	−	129783.i	0.331073	−	0.191145i
$825$		0			0
$826$	174947.	−	303018.i	0.256417	−	0.444128i
$827$	−109531.			−0.160149			−0.0800747	−	0.996789i	$-0.525516\pi$
$827$	−109531.			−0.160149			−0.0800747	+	0.996789i	$0.525516\pi$
$828$		0			0
$829$	−194710.			−0.283321			−0.141661	−	0.989915i	$-0.545244\pi$
$829$	−194710.			−0.283321			−0.141661	+	0.989915i	$0.545244\pi$
$830$	635148.	−	403968.i	0.921974	−	0.586395i
$831$		0			0
$832$	−448077.	+	258697.i	−0.647300	+	0.373719i
$833$	−90970.3	−	157565.i	−0.131102	−	0.227075i
$834$		0			0
$835$	840418.	−	534524.i	1.20538	−	0.766645i
$836$		−	94.6656i		−	0.000135450i
$837$		0			0
$838$		−	82187.4i		−	0.117035i
$839$	−441445.	−	254868.i	−0.627122	−	0.362069i	0.152514	−	0.988301i	$-0.451263\pi$
$839$	−441445.	−	254868.i	−0.627122	−	0.362069i	−0.779637	+	0.626232i	$0.784596\pi$
$840$		0			0
$841$	−353200.	−	611760.i	−0.499377	−	0.864946i
$842$	231771.	+	401439.i	0.326915	+	0.566234i
$843$		0			0
$844$	136188.	−	235885.i	0.191185	−	0.331143i
$845$	−889807.	−	464049.i	−1.24619	−	0.649906i
$846$		0			0
$847$		−	770939.i		−	1.07462i
$848$	−524746.	+	908887.i	−0.729722	+	1.26392i
$849$		0			0
$850$	−596134.	+	1.27345e6i	−0.825099	+	1.76256i
$851$	533397.	−	307957.i	0.736532	−	0.425237i
$852$		0			0
$853$	−31939.1	−	18440.1i	−0.0438960	−	0.0253434i	0.477891	−	0.878419i	$-0.341401\pi$
$853$	−31939.1	−	18440.1i	−0.0438960	−	0.0253434i	−0.521787	+	0.853076i	$0.674735\pi$
$854$		−	124933.i		−	0.171301i
$855$		0			0
$856$	−969480.			−1.32310
$857$	−340133.	+	589127.i	−0.463113	+	0.802135i	−0.999114	−	0.0420823i	$-0.986601\pi$
$857$	−340133.	+	589127.i	−0.463113	+	0.802135i	0.536001	+	0.844217i	$0.319934\pi$
$858$		0			0
$859$	548928.	+	950771.i	0.743925	+	1.28852i	0.950695	+	0.310126i	$0.100371\pi$
$859$	548928.	+	950771.i	0.743925	+	1.28852i	−0.206770	+	0.978390i	$0.566295\pi$
$860$	−91878.0	+	3942.78i	−0.124227	+	0.00533096i
$861$		0			0
$862$	−659733.	−	380897.i	−0.887879	−	0.512617i
$863$	296486.			0.398092			0.199046	−	0.979990i	$-0.436216\pi$
$863$	296486.			0.398092			0.199046	+	0.979990i	$0.436216\pi$
$864$		0			0
$865$	726963.	+	379123.i	0.971583	+	0.506696i
$866$	−39443.5	−	22772.7i	−0.0525944	−	0.0303654i
$867$		0			0
$868$	−259762.	+	149973.i	−0.344775	+	0.199056i
$869$	−7630.38	+	4405.40i	−0.0101043	+	0.00583373i
$870$		0			0
$871$	575206.	−	996286.i	0.758206	−	1.31325i
$872$	371327.			0.488341
$873$		0			0
$874$	−13354.1			−0.0174821
$875$	−316659.	+	759668.i	−0.413596	+	0.992220i
$876$		0			0
$877$	−270519.	+	156184.i	−0.351722	+	0.203067i	−0.665443	−	0.746448i	$-0.731757\pi$
$877$	−270519.	+	156184.i	−0.351722	+	0.203067i	0.313722	+	0.949515i	$0.398424\pi$
$878$	88427.0	+	153160.i	0.114709	+	0.198681i
$879$		0			0
$880$	−9222.59	−	14500.4i	−0.0119093	−	0.0187247i
$881$		−	468939.i		−	0.604178i	−0.953280	−	0.302089i	$-0.902316\pi$
$881$		−	468939.i		−	0.604178i	0.953280	−	0.302089i	$-0.0976840\pi$
$882$		0			0
$883$			331976.i			0.425780i	0.977076	+	0.212890i	$0.0682876\pi$
$883$			331976.i			0.425780i	−0.977076	+	0.212890i	$0.931712\pi$
$884$	−589339.	−	340255.i	−0.754155	−	0.435412i
$885$		0			0
$886$	−367797.	−	637044.i	−0.468534	−	0.811525i
$887$	−306317.	−	530557.i	−0.389335	−	0.674349i	0.603025	−	0.797722i	$-0.293962\pi$
$887$	−306317.	−	530557.i	−0.389335	−	0.674349i	−0.992360	+	0.123374i	$0.960629\pi$
$888$		0			0
$889$	656292.	−	1.13673e6i	0.830412	−	1.43832i
$890$	−407465.	+	781309.i	−0.514411	+	0.986377i
$891$		0			0
$892$			366550.i			0.460684i
$893$	6612.23	−	11452.7i	0.00829172	−	0.0143617i
$894$		0			0
$895$	−80966.5	+	3474.53i	−0.101079	+	0.00433761i
$896$	−895019.	+	516740.i	−1.11485	+	0.643659i
$897$		0			0
$898$	−37281.2	−	21524.3i	−0.0462314	−	0.0266917i
$899$			31721.2i			0.0392491i
$900$		0			0
$901$	1.63399e6			2.01280
$902$	13090.5	−	22673.5i	0.0160896	−	0.0278679i
$903$		0			0
$904$	159874.	+	276910.i	0.195633	+	0.338846i
$905$	−3188.81	−	74308.3i	−0.00389342	−	0.0907278i
$906$		0			0
$907$	96590.6	+	55766.6i	0.117414	+	0.0677891i	0.557557	−	0.830139i	$-0.311739\pi$
$907$	96590.6	+	55766.6i	0.117414	+	0.0677891i	−0.440143	+	0.897928i	$0.645072\pi$
$908$	−145503.			−0.176482
$909$		0			0
$910$	−1.41343e6	−	737125.i	−1.70683	−	0.890140i
$911$	−106056.	−	61231.6i	−0.127791	−	0.0737801i	0.434742	−	0.900555i	$-0.356840\pi$
$911$	−106056.	−	61231.6i	−0.127791	−	0.0737801i	−0.562533	+	0.826775i	$0.690173\pi$
$912$		0			0
$913$	12404.4	−	7161.71i	0.0148811	−	0.00859162i
$914$	−964336.	+	556759.i	−1.15435	+	0.666462i
$915$		0			0
$916$	−142299.	+	246469.i	−0.169594	+	0.293746i
$917$	448415.			0.533263
$918$		0			0
$919$	166880.			0.197594			0.0987971	−	0.995108i	$-0.468501\pi$
$919$	166880.			0.197594			0.0987971	+	0.995108i	$0.468501\pi$
$920$	−371814.	+	236481.i	−0.439288	+	0.279397i
$921$		0			0
$922$	−847087.	+	489066.i	−0.996475	+	0.575315i
$923$	−581607.	−	1.00737e6i	−0.682694	−	1.18246i
$924$		0			0
$925$	92201.3	+	1.07230e6i	0.107759	+	1.25323i
$926$		−	1.67638e6i		−	1.95501i
$927$		0			0
$928$		−	19491.4i		−	0.0226333i
$929$	−103179.	−	59570.5i	−0.119553	−	0.0690239i	0.439031	−	0.898472i	$-0.355322\pi$
$929$	−103179.	−	59570.5i	−0.119553	−	0.0690239i	−0.558584	+	0.829448i	$0.688655\pi$
$930$		0			0
$931$	1509.74	+	2614.95i	0.00174182	+	0.00301692i
$932$	1976.77	+	3423.87i	0.00227575	+	0.00394171i
$933$		0			0
$934$	521718.	−	903641.i	0.598056	−	1.03586i
$935$	−12372.1	+	23723.3i	−0.0141521	+	0.0271364i
$936$		0			0
$937$			75209.2i			0.0856627i	0.999082	+	0.0428314i	$0.0136378\pi$
$937$			75209.2i			0.0856627i	−0.999082	+	0.0428314i	$0.986362\pi$
$938$	533854.	−	924663.i	0.606760	−	1.05094i
$939$		0			0
$940$	9345.12	+	217768.i	0.0105762	+	0.246455i
$941$	117440.	−	67804.2i	0.132629	−	0.0765733i	−0.432218	−	0.901769i	$-0.642269\pi$
$941$	117440.	−	67804.2i	0.132629	−	0.0765733i	0.564846	+	0.825196i	$0.308935\pi$
$942$		0			0
$943$	−799222.	−	461431.i	−0.898761	−	0.518900i
$944$			450003.i			0.504977i
$945$		0			0
$946$	−7003.14			−0.00782547
$947$	105097.	−	182033.i	0.117190	−	0.202978i	−0.801463	−	0.598044i	$-0.795945\pi$
$947$	105097.	−	182033.i	0.117190	−	0.202978i	0.918653	+	0.395066i	$0.129278\pi$
$948$		0			0
$949$	−530367.	−	918623.i	−0.588904	−	1.02001i
$950$	9893.44	−	21134.1i	0.0109623	−	0.0234173i
$951$		0			0
$952$	1.09502e6	+	632211.i	1.20823	+	0.697571i
$953$	364743.			0.401607			0.200803	−	0.979632i	$-0.435645\pi$
$953$	364743.			0.401607			0.200803	+	0.979632i	$0.435645\pi$
$954$		0			0
$955$	554576.	−	1.06339e6i	0.608071	−	1.16597i
$956$	372013.	+	214782.i	0.407045	+	0.235008i
$957$		0			0
$958$	467467.	−	269892.i	0.509355	−	0.294076i
$959$	84913.1	−	49024.6i	0.0923289	−	0.0533061i
$960$		0			0
$961$	−108991.	+	188778.i	−0.118017	+	0.204411i
$962$	−2.08457e6			−2.25250
$963$		0			0
$964$	471154.			0.507000
$965$	−736893.	−	1.15860e6i	−0.791316	−	1.24417i
$966$		0			0
$967$	−702148.	+	405385.i	−0.750889	+	0.433526i	−0.826015	−	0.563648i	$-0.809397\pi$
$967$	−702148.	+	405385.i	−0.750889	+	0.433526i	0.0751260	+	0.997174i	$0.476064\pi$
$968$	360631.	+	624631.i	0.384868	+	0.666611i
$969$		0			0
$970$	787131.	+	1.23759e6i	0.836573	+	1.31532i
$971$		−	822586.i		−	0.872454i	−0.899837	−	0.436227i	$-0.856314\pi$
$971$		−	822586.i		−	0.872454i	0.899837	−	0.436227i	$-0.143686\pi$
$972$		0			0
$973$			260116.i			0.274752i
$974$	1.18980e6	+	686929.i	1.25417	+	0.724093i
$975$		0			0
$976$	80338.6	+	139151.i	0.0843382	+	0.146078i
$977$	659593.	+	1.14245e6i	0.691014	+	1.19687i	0.971506	+	0.237015i	$0.0761689\pi$
$977$	659593.	+	1.14245e6i	0.691014	+	1.19687i	−0.280492	+	0.959856i	$0.590498\pi$
$978$		0			0
$979$	−8383.79	+	14521.2i	−0.00874732	+	0.0151508i
$980$	−44127.4	−	23013.1i	−0.0459469	−	0.0239620i
$981$		0			0
$982$		−	942368.i		−	0.977232i
$983$	−382478.	+	662471.i	−0.395821	+	0.685582i	−0.993206	−	0.116373i	$-0.962873\pi$
$983$	−382478.	+	662471.i	−0.395821	+	0.685582i	0.597384	+	0.801955i	$0.296207\pi$
$984$		0			0
$985$	−29140.5	−	679057.i	−0.0300348	−	0.699896i
$986$	−57845.5	+	33397.1i	−0.0594998	+	0.0343522i
$987$		0			0
$988$	9780.67	+	5646.87i	0.0100197	+	0.00578487i
$989$			246855.i			0.252377i
$990$		0			0
$991$	−1.52049e6			−1.54823			−0.774116	−	0.633043i	$-0.781806\pi$
$991$	−1.52049e6			−1.54823			−0.774116	+	0.633043i	$0.781806\pi$
$992$	350704.	−	607438.i	0.356384	−	0.617275i
$993$		0			0
$994$	−539795.	−	934952.i	−0.546331	−	0.946274i
$995$	6069.01	+	141425.i	0.00613016	+	0.142850i
$996$		0			0
$997$	550617.	+	317899.i	0.553936	+	0.319815i	0.750708	−	0.660634i	$-0.229713\pi$
$997$	550617.	+	317899.i	0.553936	+	0.319815i	−0.196772	+	0.980449i	$0.563046\pi$
$998$	1.76984e6			1.77694
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.5.h.a.89.6		44
3.2	odd	2		45.5.h.a.29.17	yes	44
5.4	even	2	inner	135.5.h.a.89.17		44
9.2	odd	6		405.5.d.a.404.12		44
9.4	even	3		45.5.h.a.14.6	✓	44
9.5	odd	6	inner	135.5.h.a.44.17		44
9.7	even	3		405.5.d.a.404.34		44
15.14	odd	2		45.5.h.a.29.6	yes	44
45.4	even	6		45.5.h.a.14.17	yes	44
45.14	odd	6	inner	135.5.h.a.44.6		44
45.29	odd	6		405.5.d.a.404.33		44
45.34	even	6		405.5.d.a.404.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.6	✓	44	9.4	even	3
45.5.h.a.14.17	yes	44	45.4	even	6
45.5.h.a.29.6	yes	44	15.14	odd	2
45.5.h.a.29.17	yes	44	3.2	odd	2
135.5.h.a.44.6		44	45.14	odd	6	inner
135.5.h.a.44.17		44	9.5	odd	6	inner
135.5.h.a.89.6		44	1.1	even	1	trivial
135.5.h.a.89.17		44	5.4	even	2	inner
405.5.d.a.404.11		44	45.34	even	6
405.5.d.a.404.12		44	9.2	odd	6
405.5.d.a.404.33		44	45.29	odd	6
405.5.d.a.404.34		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)

\(f(q)\)	\(=\)	\(q+(-2.30921 + 3.99967i) q^{2} +(-2.66491 - 4.61577i) q^{4} +(-1.07184 - 24.9770i) q^{5} +(45.6166 + 26.3368i) q^{7} -49.2794 q^{8} +(102.375 + 53.3902i) q^{10} +(1.90271 + 1.09853i) q^{11} +(-226.996 + 131.056i) q^{13} +(-210.677 + 121.634i) q^{14} +(156.435 - 270.954i) q^{16} -487.118 q^{17} +8.08421 q^{19} +(-112.432 + 71.5090i) q^{20} +(-8.78750 + 5.07347i) q^{22} +(178.836 + 309.753i) q^{23} +(-622.702 + 53.5429i) q^{25} -1210.54i q^{26} -280.741i q^{28} +(-25.7123 - 14.8450i) q^{29} +(-534.206 - 925.271i) q^{31} +(328.248 + 568.543i) q^{32} +(1124.86 - 1948.31i) q^{34} +(608.920 - 1167.60i) q^{35} -1722.01i q^{37} +(-18.6682 + 32.3342i) q^{38} +(52.8198 + 1230.85i) q^{40} +(-2234.51 + 1290.10i) q^{41} +(597.707 + 345.086i) q^{43} -11.7099i q^{44} -1651.88 q^{46} +(817.918 - 1416.68i) q^{47} +(186.752 + 323.464i) q^{49} +(1223.80 - 2614.25i) q^{50} +(1209.85 + 698.506i) q^{52} -3354.40 q^{53} +(25.3986 - 48.7014i) q^{55} +(-2247.96 - 1297.86i) q^{56} +(118.750 - 68.5606i) q^{58} +(-1245.61 + 719.153i) q^{59} +(-256.779 + 444.755i) q^{61} +4934.37 q^{62} +1973.94 q^{64} +(3516.69 + 5529.20i) q^{65} +(-3800.99 + 2194.50i) q^{67} +(1298.13 + 2248.42i) q^{68} +(3263.88 + 5131.71i) q^{70} +4437.85i q^{71} +4046.87i q^{73} +(6887.47 + 3976.48i) q^{74} +(-21.5437 - 37.3148i) q^{76} +(57.8634 + 100.222i) q^{77} +(-2005.14 + 3473.00i) q^{79} +(-6935.28 - 3616.86i) q^{80} -11916.4i q^{82} +(3259.68 - 5645.94i) q^{83} +(522.115 + 12166.8i) q^{85} +(-2760.46 + 1593.75i) q^{86} +(-93.7642 - 54.1348i) q^{88} +7631.84i q^{89} -13806.4 q^{91} +(953.164 - 1650.93i) q^{92} +(3777.49 + 6542.81i) q^{94} +(-8.66501 - 201.919i) q^{95} +(11001.1 + 6351.50i) q^{97} -1725.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) \) 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

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