LMFDB - Embedded newform 45.5.h.a.14.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, 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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.15
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59606 + 2.76446i) q^{2} +(0.340063 + 8.99357i) q^{3} +(2.90517 - 5.03190i) q^{4} +(6.24274 + 24.2080i) q^{5} +(-24.3196 + 15.2944i) q^{6} +(-21.0893 + 12.1759i) q^{7} +69.6213 q^{8} +(-80.7687 + 6.11676i) q^{9} +(-56.9583 + 55.8953i) q^{10} +(-35.8153 + 20.6780i) q^{11} +(46.2427 + 24.4167i) q^{12} +(-78.1878 - 45.1417i) q^{13} +(-67.3197 - 38.8671i) q^{14} +(-215.594 + 64.3768i) q^{15} +(64.6373 + 111.955i) q^{16} +318.348 q^{17} +(-145.821 - 213.519i) q^{18} +572.803 q^{19} +(139.949 + 38.9155i) q^{20} +(-116.677 - 185.528i) q^{21} +(-114.327 - 66.0066i) q^{22} +(93.6290 - 162.170i) q^{23} +(23.6756 + 626.144i) q^{24} +(-547.056 + 302.249i) q^{25} -288.196i q^{26} +(-82.4780 - 724.319i) q^{27} +141.492i q^{28} +(1202.32 - 694.158i) q^{29} +(-522.068 - 493.251i) q^{30} +(91.5845 - 158.629i) q^{31} +(350.640 - 607.327i) q^{32} +(-198.148 - 315.075i) q^{33} +(508.103 + 880.059i) q^{34} +(-426.410 - 434.520i) q^{35} +(-203.868 + 424.190i) q^{36} +348.499i q^{37} +(914.230 + 1583.49i) q^{38} +(379.397 - 718.539i) q^{39} +(434.628 + 1685.39i) q^{40} +(-1888.80 - 1090.50i) q^{41} +(326.661 - 618.662i) q^{42} +(-1193.76 + 689.217i) q^{43} +240.292i q^{44} +(-652.293 - 1917.07i) q^{45} +597.751 q^{46} +(342.127 + 592.582i) q^{47} +(-984.895 + 619.392i) q^{48} +(-903.994 + 1565.76i) q^{49} +(-1708.69 - 1029.91i) q^{50} +(108.258 + 2863.08i) q^{51} +(-454.297 + 262.289i) q^{52} -2093.47 q^{53} +(1870.71 - 1384.07i) q^{54} +(-724.158 - 737.930i) q^{55} +(-1468.27 + 847.704i) q^{56} +(194.789 + 5151.55i) q^{57} +(3837.95 + 2215.84i) q^{58} +(4766.87 + 2752.15i) q^{59} +(-302.398 + 1271.87i) q^{60} +(-3222.16 - 5580.94i) q^{61} +584.698 q^{62} +(1628.88 - 1112.43i) q^{63} +4306.97 q^{64} +(604.686 - 2174.58i) q^{65} +(554.757 - 1050.65i) q^{66} +(-4148.13 - 2394.92i) q^{67} +(924.853 - 1601.89i) q^{68} +(1490.33 + 786.911i) q^{69} +(520.635 - 1872.31i) q^{70} +6781.69i q^{71} +(-5623.22 + 425.857i) q^{72} -9049.69i q^{73} +(-963.412 + 556.226i) q^{74} +(-2904.33 - 4817.21i) q^{75} +(1664.09 - 2882.29i) q^{76} +(503.546 - 872.168i) q^{77} +(2591.91 - 98.0048i) q^{78} +(-2106.79 - 3649.06i) q^{79} +(-2306.70 + 2263.65i) q^{80} +(6486.17 - 988.086i) q^{81} -6962.02i q^{82} +(-3109.96 - 5386.60i) q^{83} +(-1272.52 + 48.1163i) q^{84} +(1987.36 + 7706.56i) q^{85} +(-3810.63 - 2200.07i) q^{86} +(6651.82 + 10577.1i) q^{87} +(-2493.51 + 1439.63i) q^{88} -1469.15i q^{89} +(4258.55 - 4862.99i) q^{90} +2198.57 q^{91} +(-544.016 - 942.263i) q^{92} +(1457.79 + 769.728i) q^{93} +(-1092.11 + 1891.59i) q^{94} +(3575.86 + 13866.4i) q^{95} +(5581.28 + 2946.98i) q^{96} +(-1918.24 + 1107.50i) q^{97} -5771.32 q^{98} +(2766.27 - 1889.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.59606	+	2.76446i	0.399016	+	0.691115i	0.993605	−	0.112914i	$-0.0360186\pi$
$2$	1.59606	+	2.76446i	0.399016	+	0.691115i	−0.594589	+	0.804030i	$0.702685\pi$
$3$	0.340063	+	8.99357i	0.0377848	+	0.999286i
$3$	0.340063	+	8.99357i	0.0377848	+	0.999286i
$4$	2.90517	−	5.03190i	0.181573	−	0.314494i
$5$	6.24274	+	24.2080i	0.249710	+	0.968321i
$5$	6.24274	+	24.2080i	0.249710	+	0.968321i
$6$	−24.3196	+	15.2944i	−0.675545	+	0.424844i
$7$	−21.0893	+	12.1759i	−0.430394	+	0.248488i	−0.699515	−	0.714618i	$-0.746600\pi$
$7$	−21.0893	+	12.1759i	−0.430394	+	0.248488i	0.269120	+	0.963107i	$0.413267\pi$
$8$	69.6213			1.08783
$9$	−80.7687	+	6.11676i	−0.997145	+	0.0755156i
$10$	−56.9583	+	55.8953i	−0.569583	+	0.558953i
$11$	−35.8153	+	20.6780i	−0.295994	+	0.170892i	−0.640642	−	0.767840i	$-0.721332\pi$
$11$	−35.8153	+	20.6780i	−0.295994	+	0.170892i	0.344648	+	0.938732i	$0.387998\pi$
$12$	46.2427	+	24.4167i	0.321130	+	0.169560i
$13$	−78.1878	−	45.1417i	−0.462650	−	0.267111i	0.250508	−	0.968115i	$-0.419402\pi$
$13$	−78.1878	−	45.1417i	−0.462650	−	0.267111i	−0.713158	+	0.701004i	$0.752736\pi$
$14$	−67.3197	−	38.8671i	−0.343468	−	0.198301i
$15$	−215.594	+	64.3768i	−0.958194	+	0.286119i
$16$	64.6373	+	111.955i	0.252489	+	0.437325i
$17$	318.348			1.10155			0.550774	−	0.834654i	$-0.314333\pi$
$17$	318.348			1.10155			0.550774	+	0.834654i	$0.314333\pi$
$18$	−145.821	−	213.519i	−0.450066	−	0.659010i
$19$	572.803			1.58671			0.793356	−	0.608758i	$-0.208332\pi$
$19$	572.803			1.58671			0.793356	+	0.608758i	$0.208332\pi$
$20$	139.949	+	38.9155i	0.349871	+	0.0972888i
$21$	−116.677	−	185.528i	−0.264573	−	0.420698i
$22$	−114.327	−	66.0066i	−0.236212	−	0.136377i
$23$	93.6290	−	162.170i	0.176992	−	0.306560i	−0.763857	−	0.645386i	$-0.776697\pi$
$23$	93.6290	−	162.170i	0.176992	−	0.306560i	0.940849	+	0.338826i	$0.110030\pi$
$24$	23.6756	+	626.144i	0.0411035	+	1.08706i
$25$	−547.056	+	302.249i	−0.875290	+	0.483598i
$26$		−	288.196i		−	0.426326i
$27$	−82.4780	−	724.319i	−0.113139	−	0.993579i
$28$			141.492i			0.180475i
$29$	1202.32	−	694.158i	1.42963	−	0.825396i	0.432537	−	0.901616i	$-0.357619\pi$
$29$	1202.32	−	694.158i	1.42963	−	0.825396i	0.997091	+	0.0762203i	$0.0242852\pi$
$30$	−522.068	−	493.251i	−0.580076	−	0.548057i
$31$	91.5845	−	158.629i	0.0953012	−	0.165067i	−0.814433	−	0.580258i	$-0.802952\pi$
$31$	91.5845	−	158.629i	0.0953012	−	0.165067i	0.909734	+	0.415191i	$0.136285\pi$
$32$	350.640	−	607.327i	0.342422	−	0.593093i
$33$	−198.148	−	315.075i	−0.181954	−	0.289325i
$34$	508.103	+	880.059i	0.439535	+	0.761297i
$35$	−426.410	−	434.520i	−0.348090	−	0.354710i
$36$	−203.868	+	424.190i	−0.157305	+	0.327307i
$37$			348.499i			0.254565i	0.991867	+	0.127282i	$0.0406254\pi$
$37$			348.499i			0.254565i	−0.991867	+	0.127282i	$0.959375\pi$
$38$	914.230	+	1583.49i	0.633123	+	1.09660i
$39$	379.397	−	718.539i	0.249439	−	0.472412i
$40$	434.628	+	1685.39i	0.271642	+	1.05337i
$41$	−1888.80	−	1090.50i	−1.12362	−	0.648720i	−0.181295	−	0.983429i	$-0.558029\pi$
$41$	−1888.80	−	1090.50i	−1.12362	−	0.648720i	−0.942322	+	0.334708i	$0.891362\pi$
$42$	326.661	−	618.662i	0.185182	−	0.350716i
$43$	−1193.76	+	689.217i	−0.645624	+	0.372751i	−0.786778	−	0.617236i	$-0.788252\pi$
$43$	−1193.76	+	689.217i	−0.645624	+	0.372751i	0.141154	+	0.989988i	$0.454919\pi$
$44$			240.292i			0.124118i
$45$	−652.293	−	1917.07i	−0.322120	−	0.946699i
$46$	597.751			0.282491
$47$	342.127	+	592.582i	0.154879	+	0.268258i	0.933015	−	0.359838i	$-0.117168\pi$
$47$	342.127	+	592.582i	0.154879	+	0.268258i	−0.778136	+	0.628096i	$0.783835\pi$
$48$	−984.895	+	619.392i	−0.427472	+	0.268833i
$49$	−903.994	+	1565.76i	−0.376507	+	0.652130i
$50$	−1708.69	−	1029.91i	−0.683476	−	0.411963i
$51$	108.258	+	2863.08i	0.0416218	+	1.10076i
$52$	−454.297	+	262.289i	−0.168009	+	0.0970003i
$53$	−2093.47			−0.745271			−0.372636	−	0.927978i	$-0.621546\pi$
$53$	−2093.47			−0.745271			−0.372636	+	0.927978i	$0.621546\pi$
$54$	1870.71	−	1384.07i	0.641534	−	0.474645i
$55$	−724.158	−	737.930i	−0.239391	−	0.243944i
$56$	−1468.27	+	847.704i	−0.468197	+	0.270314i
$57$	194.789	+	5151.55i	0.0599536	+	1.58558i
$58$	3837.95	+	2215.84i	1.14089	+	0.658692i
$59$	4766.87	+	2752.15i	1.36940	+	0.790621i	0.990851	−	0.134962i	$-0.0430913\pi$
$59$	4766.87	+	2752.15i	1.36940	+	0.790621i	0.378545	+	0.925583i	$0.376425\pi$
$60$	−302.398	+	1271.87i	−0.0839996	+	0.353298i
$61$	−3222.16	−	5580.94i	−0.865939	−	1.49985i	−0.866112	−	0.499850i	$-0.833388\pi$
$61$	−3222.16	−	5580.94i	−0.865939	−	1.49985i	0.000172838	−	1.00000i	$-0.499945\pi$
$62$	584.698			0.152107
$63$	1628.88	−	1112.43i	0.410401	−	0.280280i
$64$	4306.97			1.05151
$65$	604.686	−	2174.58i	0.143121	−	0.514693i
$66$	554.757	−	1050.65i	0.127355	−	0.241197i
$67$	−4148.13	−	2394.92i	−0.924065	−	0.533509i	−0.0391353	−	0.999234i	$-0.512460\pi$
$67$	−4148.13	−	2394.92i	−0.924065	−	0.533509i	−0.884930	+	0.465725i	$0.845794\pi$
$68$	924.853	−	1601.89i	0.200012	−	0.346430i
$69$	1490.33	+	786.911i	0.313029	+	0.165283i
$70$	520.635	−	1872.31i	0.106252	−	0.382105i
$71$			6781.69i			1.34531i	0.739958	+	0.672653i	$0.234845\pi$
$71$			6781.69i			1.34531i	−0.739958	+	0.672653i	$0.765155\pi$
$72$	−5623.22	+	425.857i	−1.08473	+	0.0821484i
$73$		−	9049.69i		−	1.69820i	−0.528235	−	0.849098i	$-0.677146\pi$
$73$		−	9049.69i		−	1.69820i	0.528235	−	0.849098i	$-0.322854\pi$
$74$	−963.412	+	556.226i	−0.175934	+	0.101575i
$75$	−2904.33	−	4817.21i	−0.516325	−	0.856393i
$76$	1664.09	−	2882.29i	0.288104	−	0.499011i
$77$	503.546	−	872.168i	0.0849294	−	0.147102i
$78$	2591.91	−	98.0048i	0.426021	−	0.0161086i
$79$	−2106.79	−	3649.06i	−0.337572	−	0.584691i	0.646404	−	0.762996i	$-0.276272\pi$
$79$	−2106.79	−	3649.06i	−0.337572	−	0.584691i	−0.983975	+	0.178304i	$0.942939\pi$
$80$	−2306.70	+	2263.65i	−0.360421	+	0.353695i
$81$	6486.17	−	988.086i	0.988595	−	0.150600i
$82$		−	6962.02i		−	1.03540i
$83$	−3109.96	−	5386.60i	−0.451438	−	0.781914i	0.547038	−	0.837108i	$-0.315755\pi$
$83$	−3109.96	−	5386.60i	−0.451438	−	0.781914i	−0.998476	+	0.0551944i	$0.982422\pi$
$84$	−1272.52	+	48.1163i	−0.180346	+	0.00681921i
$85$	1987.36	+	7706.56i	0.275067	+	1.06665i
$86$	−3810.63	−	2200.07i	−0.515228	−	0.297467i
$87$	6651.82	+	10577.1i	0.878825	+	1.39742i
$88$	−2493.51	+	1439.63i	−0.321992	+	0.185902i
$89$		−	1469.15i		−	0.185475i	−0.995691	−	0.0927375i	$-0.970438\pi$
$89$		−	1469.15i		−	0.185475i	0.995691	−	0.0927375i	$-0.0295617\pi$
$90$	4258.55	−	4862.99i	0.525747	−	0.600370i
$91$	2198.57			0.265496
$92$	−544.016	−	942.263i	−0.0642741	−	0.111326i
$93$	1457.79	+	769.728i	0.168550	+	0.0889962i
$94$	−1092.11	+	1891.59i	−0.123598	+	0.214078i
$95$	3575.86	+	13866.4i	0.396217	+	1.53645i
$96$	5581.28	+	2946.98i	0.605607	+	0.319768i
$97$	−1918.24	+	1107.50i	−0.203873	+	0.117706i	−0.598461	−	0.801152i	$-0.704221\pi$
$97$	−1918.24	+	1107.50i	−0.203873	+	0.117706i	0.394588	+	0.918858i	$0.370887\pi$
$98$	−5771.32			−0.600929
$99$	2766.27	−	1889.21i	0.282244	−	0.192756i
$100$	−68.4058	+	3630.82i	−0.00684058	+	0.363082i
$101$	−7258.63	+	4190.77i	−0.711560	+	0.410820i	−0.811639	−	0.584160i	$-0.801424\pi$
$101$	−7258.63	+	4190.77i	−0.711560	+	0.410820i	0.100078	+	0.994980i	$0.468091\pi$
$102$	−7742.09	+	4868.93i	−0.744146	+	0.467987i
$103$	11518.6	+	6650.26i	1.08574	+	0.626851i	0.932438	−	0.361329i	$-0.117677\pi$
$103$	11518.6	+	6650.26i	1.08574	+	0.626851i	0.153299	+	0.988180i	$0.451010\pi$
$104$	−5443.54	−	3142.83i	−0.503286	−	0.290572i
$105$	3762.88	−	3982.71i	0.341304	−	0.361244i
$106$	−3341.30	−	5787.31i	−0.297375	−	0.515069i
$107$	15948.2			1.39298			0.696490	−	0.717566i	$-0.254744\pi$
$107$	15948.2			1.39298			0.696490	+	0.717566i	$0.254744\pi$
$108$	−3884.31	−	1689.25i	−0.333017	−	0.144826i
$109$	−9000.77			−0.757577			−0.378788	−	0.925483i	$-0.623659\pi$
$109$	−9000.77			−0.757577			−0.378788	+	0.925483i	$0.623659\pi$
$110$	884.177	−	3179.69i	0.0730725	−	0.262784i
$111$	−3134.25	+	118.512i	−0.254383	+	0.00961867i
$112$	−2726.31	−	1574.04i	−0.217340	−	0.125481i
$113$	−8600.91	+	14897.2i	−0.673578	+	1.16667i	0.303305	+	0.952894i	$0.401910\pi$
$113$	−8600.91	+	14897.2i	−0.673578	+	1.16667i	−0.976882	+	0.213777i	$0.931423\pi$
$114$	−13930.4	+	8760.68i	−1.07190	+	0.674106i
$115$	4510.32	+	1254.19i	0.341045	+	0.0948345i
$116$		−	8066.58i		−	0.599479i
$117$	6591.25	+	3167.78i	0.481500	+	0.231411i
$118$			17570.4i			1.26188i
$119$	−6713.73	+	3876.18i	−0.474100	+	0.273722i
$120$	−15009.9	+	4482.00i	−1.04236	+	0.311250i
$121$	−6465.34	+	11198.3i	−0.441592	+	0.764859i
$122$	10285.5	−	17815.1i	0.691046	−	1.19693i
$123$	9165.17	−	17357.9i	0.605802	−	1.14733i
$124$	−532.137	−	921.688i	−0.0346083	−	0.0599433i
$125$	−10732.0	−	11356.3i	−0.686846	−	0.726803i
$126$	5675.07	+	2727.46i	0.357462	+	0.171798i
$127$		−	25224.9i		−	1.56395i	−0.623313	−	0.781973i	$-0.714214\pi$
$127$		−	25224.9i		−	1.56395i	0.623313	−	0.781973i	$-0.285786\pi$
$128$	1263.95	+	2189.22i	0.0771452	+	0.133619i
$129$	−6604.48	−	10501.8i	−0.396880	−	0.631079i
$130$	6976.66	−	1799.13i	0.412820	−	0.106458i
$131$	6038.65	+	3486.42i	0.351882	+	0.203159i	0.665514	−	0.746385i	$-0.268212\pi$
$131$	6038.65	+	3486.42i	0.351882	+	0.203159i	−0.313632	+	0.949545i	$0.601546\pi$
$132$	−2161.08	+	81.7143i	−0.124029	+	0.00468976i
$133$	−12080.0	+	6974.41i	−0.682912	+	0.394279i
$134$		−	15289.8i		−	0.851514i
$135$	17019.4	−	6518.37i	0.933852	−	0.357661i
$136$	22163.8			1.19830
$137$	4670.29	+	8089.17i	0.248830	+	0.430986i	0.963201	−	0.268781i	$-0.0866207\pi$
$137$	4670.29	+	8089.17i	0.248830	+	0.430986i	−0.714372	+	0.699767i	$0.753287\pi$
$138$	203.273	+	5375.92i	0.0106739	+	0.282289i
$139$	−6355.64	+	11008.3i	−0.328950	+	0.569758i	−0.982304	−	0.187295i	$-0.940028\pi$
$139$	−6355.64	+	11008.3i	−0.328950	+	0.569758i	0.653354	+	0.757053i	$0.273361\pi$
$140$	−3425.25	+	883.301i	−0.174758	+	0.0450664i
$141$	−5213.08	+	3278.46i	−0.262214	+	0.164904i
$142$	−18747.7	+	10824.0i	−0.929762	+	0.536798i
$143$	3733.76			0.182589
$144$	−5905.47	−	8647.10i	−0.284793	−	0.417009i
$145$	24309.9	+	24772.3i	1.15624	+	1.17823i
$146$	25017.5	−	14443.9i	1.17365	−	0.677607i
$147$	−14389.2	−	7597.68i	−0.665890	−	0.351598i
$148$	1753.61	+	1012.45i	0.0800590	+	0.0462221i
$149$	3349.82	+	1934.02i	0.150886	+	0.0871142i	0.573542	−	0.819176i	$-0.305569\pi$
$149$	3349.82	+	1934.02i	0.150886	+	0.0871142i	−0.422656	+	0.906290i	$0.638902\pi$
$150$	8681.49	−	15717.5i	0.385844	−	0.698554i
$151$	12136.0	+	21020.2i	0.532259	+	0.921899i	0.999291	+	0.0376587i	$0.0119900\pi$
$151$	12136.0	+	21020.2i	0.532259	+	0.921899i	−0.467032	+	0.884240i	$0.654677\pi$
$152$	39879.3			1.72608
$153$	−25712.5	+	1947.26i	−1.09840	+	0.0831841i
$154$	3214.77			0.135553
$155$	4411.83	+	1226.80i	0.183635	+	0.0510635i
$156$	−2513.40	−	3996.56i	−0.103279	−	0.164224i
$157$	−32083.5	−	18523.4i	−1.30161	−	0.751488i	−0.320934	−	0.947102i	$-0.603997\pi$
$157$	−32083.5	−	18523.4i	−1.30161	−	0.751488i	−0.980681	+	0.195614i	$0.937330\pi$
$158$	6725.12	−	11648.3i	0.269393	−	0.466602i
$159$	−711.911	−	18827.8i	−0.0281599	−	0.744739i
$160$	16891.1	+	4696.92i	0.659810	+	0.183474i
$161$			4560.08i			0.175922i
$162$	13083.9	+	16353.7i	0.498547	+	0.623141i
$163$		−	24903.7i		−	0.937323i	−0.883378	−	0.468662i	$-0.844736\pi$
$163$		−	24903.7i		−	0.937323i	0.883378	−	0.468662i	$-0.155264\pi$
$164$	−10974.6	+	6336.17i	−0.408037	+	0.235580i
$165$	6390.37	−	6763.71i	0.234724	−	0.248437i
$166$	9927.37	−	17194.7i	0.360262	−	0.623992i
$167$	7604.05	−	13170.6i	0.272654	−	0.472251i	−0.696886	−	0.717181i	$-0.745432\pi$
$167$	7604.05	−	13170.6i	0.272654	−	0.472251i	0.969541	+	0.244931i	$0.0787652\pi$
$168$	−8123.19	−	12916.7i	−0.287811	−	0.457649i
$169$	−10204.9	−	17675.5i	−0.357304	−	0.618868i
$170$	−18132.5	+	17794.1i	−0.627424	+	0.615714i
$171$	−46264.6	+	3503.70i	−1.58218	+	0.119822i
$172$			8009.17i			0.270726i
$173$	1599.34	+	2770.14i	0.0534379	+	0.0925572i	0.891507	−	0.453007i	$-0.149649\pi$
$173$	1599.34	+	2770.14i	0.0534379	+	0.0925572i	−0.838069	+	0.545564i	$0.816315\pi$
$174$	−18623.2	+	35270.4i	−0.615113	+	1.16496i
$175$	7856.89	−	13035.1i	0.256551	−	0.425637i
$176$	−4630.00	−	2673.13i	−0.149471	−	0.0862970i
$177$	−23130.6	+	43807.1i	−0.738314	+	1.39829i
$178$	4061.40	−	2344.85i	0.128185	−	0.0740074i
$179$		−	3888.33i		−	0.121355i	−0.998157	−	0.0606774i	$-0.980674\pi$
$179$		−	3888.33i		−	0.121355i	0.998157	−	0.0606774i	$-0.0193261\pi$
$180$	−11541.5	−	2287.13i	−0.356219	−	0.0705903i
$181$	−33312.9			−1.01685			−0.508424	−	0.861107i	$-0.669772\pi$
$181$	−33312.9			−1.01685			−0.508424	+	0.861107i	$0.669772\pi$
$182$	3509.05	+	6077.86i	0.105937	+	0.183488i
$183$	49096.9	−	30876.6i	1.46606	−	0.921992i
$184$	6518.57	−	11290.5i	0.192538	−	0.333486i
$185$	−8436.47	+	2175.59i	−0.246500	+	0.0635672i
$186$	198.834	+	5258.53i	0.00574732	+	0.151998i
$187$	−11401.7	+	6582.78i	−0.326052	+	0.188246i
$188$	3975.75			0.112487
$189$	10558.7	+	14271.2i	0.295587	+	0.399517i
$190$	−32625.9	+	32017.0i	−0.903765	+	0.886898i
$191$	31521.0	−	18198.7i	0.864038	−	0.498853i	−0.00132412	−	0.999999i	$-0.500421\pi$
$191$	31521.0	−	18198.7i	0.864038	−	0.498853i	0.865363	+	0.501146i	$0.167088\pi$
$192$	1464.64	+	38735.0i	0.0397309	+	1.05076i
$193$	40931.2	+	23631.6i	1.09885	+	0.634424i	0.935920	−	0.352213i	$-0.114571\pi$
$193$	40931.2	+	23631.6i	1.09885	+	0.634424i	0.162934	+	0.986637i	$0.447904\pi$
$194$	−6123.28	−	3535.28i	−0.162697	−	0.0939334i
$195$	19762.9	+	4698.79i	0.519734	+	0.123571i
$196$	5252.51	+	9097.61i	0.136727	+	0.236818i
$197$	−7655.76			−0.197268			−0.0986338	−	0.995124i	$-0.531447\pi$
$197$	−7655.76			−0.197268			−0.0986338	+	0.995124i	$0.531447\pi$
$198$	9637.78	+	4631.96i	0.245837	+	0.118150i
$199$	10656.9			0.269108			0.134554	−	0.990906i	$-0.457040\pi$
$199$	10656.9			0.269108			0.134554	+	0.990906i	$0.457040\pi$
$200$	−38086.8	+	21043.0i	−0.952170	+	0.526074i
$201$	20128.3	−	38120.9i	0.498213	−	0.943564i
$202$	−23170.5	−	13377.5i	−0.567848	−	0.327847i
$203$	−16904.0	+	29278.6i	−0.410202	+	0.710491i
$204$	14721.2	+	7772.99i	0.353740	+	0.186779i
$205$	14607.5	−	52531.8i	0.347592	−	1.25001i
$206$			42456.9i			1.00049i
$207$	−6570.34	+	13671.0i	−0.153337	+	0.319050i
$208$		−	11671.4i		−	0.269771i
$209$	−20515.1	+	11844.4i	−0.469657	+	0.271157i
$210$	17015.8	+	4045.67i	0.385847	+	0.0917385i
$211$	−29816.2	+	51643.1i	−0.669710	+	1.15997i	0.308275	+	0.951297i	$0.400248\pi$
$211$	−29816.2	+	51643.1i	−0.669710	+	1.15997i	−0.977985	+	0.208675i	$0.933085\pi$
$212$	−6081.88	+	10534.1i	−0.135321	+	0.234383i
$213$	−60991.6	+	2306.20i	−1.34435	+	0.0508321i
$214$	25454.4	+	44088.3i	0.555821	+	0.962710i
$215$	−24136.9	−	24595.9i	−0.522161	−	0.532092i
$216$	−5742.23	−	50428.1i	−0.123076	−	1.08085i
$217$			4460.50i			0.0947250i
$218$	−14365.8	−	24882.3i	−0.302285	−	0.523573i
$219$	81389.0	−	3077.46i	1.69698	−	0.0641660i
$220$	−5816.99	+	1500.08i	−0.120186	+	0.0309934i
$221$	−24890.9	−	14370.8i	−0.509631	−	0.294236i
$222$	−5330.08	−	8475.36i	−0.108150	−	0.171970i
$223$	9485.42	−	5476.41i	0.190742	−	0.110125i	−0.401588	−	0.915821i	$-0.631542\pi$
$223$	9485.42	−	5476.41i	0.190742	−	0.110125i	0.592330	+	0.805695i	$0.298208\pi$
$224$			17077.5i			0.340352i
$225$	42336.3	−	27758.5i	0.836272	−	0.548315i
$226$	−54910.4			−1.07507
$227$	−6989.91	−	12106.9i	−0.135650	−	0.234953i	0.790196	−	0.612855i	$-0.209979\pi$
$227$	−6989.91	−	12106.9i	−0.135650	−	0.234953i	−0.925846	+	0.377902i	$0.876646\pi$
$228$	26488.0	+	13986.0i	0.509541	+	0.269043i
$229$	40999.5	−	71013.3i	0.781822	−	1.35416i	−0.149057	−	0.988829i	$-0.547624\pi$
$229$	40999.5	−	71013.3i	0.781822	−	1.35416i	0.930879	−	0.365327i	$-0.119043\pi$
$230$	3731.60	+	14470.4i	0.0705407	+	0.273542i
$231$	8015.14	+	4232.09i	0.150206	+	0.0793105i
$232$	83706.9	−	48328.2i	1.55520	−	0.897893i
$233$	−50860.9			−0.936854			−0.468427	−	0.883502i	$-0.655179\pi$
$233$	−50860.9			−0.936854			−0.468427	+	0.883502i	$0.655179\pi$
$234$	1762.83	+	23277.2i	0.0321942	+	0.425108i
$235$	−12209.4	+	11981.6i	−0.221085	+	0.216959i
$236$	27697.1	−	15990.9i	0.497291	−	0.287111i
$237$	32101.6	−	20188.4i	0.571519	−	0.359423i
$238$	−21431.1	−	12373.2i	−0.378347	−	0.218439i
$239$	29293.9	+	16912.8i	0.512839	+	0.296088i	0.734000	−	0.679149i	$-0.237651\pi$
$239$	29293.9	+	16912.8i	0.512839	+	0.296088i	−0.221161	+	0.975237i	$0.570985\pi$
$240$	−21142.7	−	19975.7i	−0.367061	−	0.346800i
$241$	7129.20	+	12348.1i	0.122746	+	0.212602i	0.920850	−	0.389918i	$-0.127497\pi$
$241$	7129.20	+	12348.1i	0.122746	+	0.212602i	−0.798104	+	0.602520i	$0.794163\pi$
$242$	−41276.4			−0.704808
$243$	11092.1	+	57997.8i	0.187846	+	0.982198i
$244$	−37443.7			−0.628925
$245$	−43547.4	−	12109.2i	−0.725488	−	0.201737i
$246$	62613.4	−	2367.52i	1.03466	−	0.0391223i
$247$	−44786.2	−	25857.3i	−0.734092	−	0.423828i
$248$	6376.23	−	11044.0i	0.103672	−	0.179565i
$249$	47387.2	−	29801.4i	0.764298	−	0.480660i
$250$	14265.1	−	47793.5i	0.228242	−	0.764696i
$251$			22917.8i			0.363768i	0.983320	+	0.181884i	$0.0582196\pi$
$251$			22917.8i			0.363768i	−0.983320	+	0.181884i	$0.941780\pi$
$252$	−865.476	−	11428.2i	−0.0136287	−	0.179960i
$253$			7744.22i			0.120986i
$254$	69733.2	−	40260.5i	1.08087	−	0.624039i
$255$	−68633.7	+	20494.2i	−1.05550	+	0.315174i
$256$	30421.1	−	52690.8i	0.464189	−	0.803998i
$257$	42251.7	−	73182.1i	0.639702	−	1.10800i	−0.345796	−	0.938310i	$-0.612391\pi$
$257$	42251.7	−	73182.1i	0.639702	−	1.10800i	0.985498	−	0.169687i	$-0.0542756\pi$
$258$	18490.6	−	35019.3i	0.277787	−	0.526100i
$259$	−4243.30	−	7349.61i	−0.0632563	−	0.109563i
$260$	−9185.55	−	9360.24i	−0.135881	−	0.138465i
$261$	−92863.6	+	63420.5i	−1.36322	+	0.930998i
$262$			22258.2i			0.324255i
$263$	22291.7	+	38610.3i	0.322278	+	0.558202i	0.980958	−	0.194221i	$-0.0622180\pi$
$263$	22291.7	+	38610.3i	0.322278	+	0.558202i	−0.658679	+	0.752424i	$0.728885\pi$
$264$	−13795.3	−	21936.0i	−0.197936	−	0.314738i
$265$	−13069.0	−	50678.7i	−0.186101	−	0.721662i
$266$	−38561.0	−	22263.2i	−0.544985	−	0.314647i
$267$	13212.9	−	499.602i	0.185342	−	0.00700813i
$268$	−24102.0	+	13915.3i	−0.335571	+	0.193742i
$269$			82723.6i			1.14321i	0.820530	+	0.571603i	$0.193678\pi$
$269$			82723.6i			1.14321i	−0.820530	+	0.571603i	$0.806322\pi$
$270$	45183.9	+	36645.9i	0.619806	+	0.502687i
$271$	27000.0			0.367643			0.183821	−	0.982960i	$-0.441153\pi$
$271$	27000.0			0.367643			0.183821	+	0.982960i	$0.441153\pi$
$272$	20577.1	+	35640.6i	0.278129	+	0.481734i
$273$	747.652	+	19773.0i	0.0100317	+	0.265306i
$274$	−14908.1	+	25821.7i	−0.198574	+	0.343940i
$275$	13343.1	−	22137.1i	0.176438	−	0.292722i
$276$	8289.31	−	5213.08i	0.108818	−	0.0684346i
$277$	46521.1	−	26859.0i	0.606304	−	0.350050i	−0.165214	−	0.986258i	$-0.552831\pi$
$277$	46521.1	−	26859.0i	0.606304	−	0.350050i	0.771517	+	0.636208i	$0.219498\pi$
$278$	−40576.0			−0.525024
$279$	−6426.87	+	13372.5i	−0.0825640	+	0.171792i
$280$	−29687.2	−	30251.8i	−0.378664	−	0.385865i
$281$	−20136.1	+	11625.6i	−0.255013	+	0.147232i	−0.622057	−	0.782972i	$-0.713703\pi$
$281$	−20136.1	+	11625.6i	−0.255013	+	0.147232i	0.367045	+	0.930203i	$0.380370\pi$
$282$	−17383.6	−	9178.73i	−0.218595	−	0.115421i
$283$	56623.7	+	32691.7i	0.707010	+	0.408192i	0.809953	−	0.586495i	$-0.199493\pi$
$283$	56623.7	+	32691.7i	0.707010	+	0.408192i	−0.102943	+	0.994687i	$0.532826\pi$
$284$	34124.8	+	19701.9i	0.423090	+	0.244271i
$285$	−123493.	+	36875.2i	−1.52038	+	0.453989i
$286$	5959.31	+	10321.8i	0.0728557	+	0.126190i
$287$	53111.3			0.644798
$288$	−24605.9	+	51197.8i	−0.296657	+	0.617257i
$289$	17824.2			0.213409
$290$	−29681.8	+	106742.i	−0.352934	+	1.26923i
$291$	−10612.7	−	16875.3i	−0.125326	−	0.199280i
$292$	−45537.1	−	26290.9i	−0.534072	−	0.308347i
$293$	17664.0	−	30595.0i	0.205757	−	0.356382i	−0.744617	−	0.667492i	$-0.767368\pi$
$293$	17664.0	−	30595.0i	0.205757	−	0.356382i	0.950374	+	0.311111i	$0.100701\pi$
$294$	−1962.61	−	51904.8i	−0.0227060	−	0.600500i
$295$	−36865.8	+	132577.i	−0.423623	+	1.52344i
$296$			24263.0i			0.276924i
$297$	17931.4	+	24236.2i	0.203283	+	0.274759i
$298$			12347.3i			0.139040i
$299$	−14641.3	+	8453.15i	−0.163771	+	0.0945532i
$300$	−32677.3	+	619.494i	−0.363081	+	0.00688326i
$301$	16783.7	−	29070.2i	0.185249	−	0.320860i
$302$	−38739.7	+	67099.2i	−0.424759	+	0.735704i
$303$	−40158.4	−	63855.9i	−0.437412	−	0.695530i
$304$	37024.4	+	64128.2i	0.400628	+	0.693908i
$305$	114988.	−	112842.i	1.23610	−	1.21303i
$306$	−46421.9	−	67973.3i	−0.495770	−	0.725932i
$307$			123777.i			1.31330i	0.754196	+	0.656650i	$0.228027\pi$
$307$			123777.i			1.31330i	−0.754196	+	0.656650i	$0.771973\pi$
$308$	−2925.77	−	5067.59i	−0.0308418	−	0.0534195i
$309$	−55892.6	+	105855.i	−0.585379	+	1.10865i
$310$	3650.12	+	14154.4i	0.0379825	+	0.147288i
$311$	−47408.6	−	27371.4i	−0.490158	−	0.282993i	0.234482	−	0.972121i	$-0.424661\pi$
$311$	−47408.6	−	27371.4i	−0.490158	−	0.282993i	−0.724640	+	0.689127i	$0.757994\pi$
$312$	26414.1	−	50025.6i	0.271348	−	0.513905i
$313$	−75259.7	+	43451.2i	−0.768199	+	0.443520i	−0.832232	−	0.554428i	$-0.812937\pi$
$313$	−75259.7	+	43451.2i	−0.768199	+	0.443520i	0.0640324	+	0.997948i	$0.479604\pi$
$314$		−	118258.i		−	1.19942i
$315$	37098.5	+	32487.3i	0.373882	+	0.327411i
$316$	−24482.3			−0.245176
$317$	−15188.6	−	26307.4i	−0.151147	−	0.261794i	0.780503	−	0.625153i	$-0.214963\pi$
$317$	−15188.6	−	26307.4i	−0.151147	−	0.261794i	−0.931649	+	0.363359i	$0.881630\pi$
$318$	50912.3	−	32018.3i	0.503464	−	0.316624i
$319$	−28707.5	+	49722.9i	−0.282107	+	0.488624i
$320$	26887.3	+	104263.i	0.262571	+	1.01820i
$321$	5423.40	+	143432.i	0.0526335	+	1.39199i
$322$	−12606.2	+	7278.17i	−0.121582	+	0.0701957i
$323$	182350.			1.74784
$324$	13871.5	−	35508.3i	0.132139	−	0.338252i
$325$	56417.2	+	1062.92i	0.534127	+	0.0100631i
$326$	68845.4	−	39747.9i	0.647799	−	0.374007i
$327$	−3060.83	−	80949.1i	−0.0286249	−	0.757036i
$328$	−131501.	−	75922.0i	−1.22231	−	0.705700i
$329$	−14430.5	−	8331.43i	−0.133318	−	0.0769711i
$330$	28897.4	+	6870.62i	0.265358	+	0.0630911i
$331$	−37209.9	−	64449.4i	−0.339627	−	0.588252i	0.644735	−	0.764406i	$-0.276968\pi$
$331$	−37209.9	−	64449.4i	−0.339627	−	0.588252i	−0.984363	+	0.176154i	$0.943634\pi$
$332$	−36139.8			−0.327876
$333$	−2131.69	−	28147.8i	−0.0192236	−	0.253838i
$334$	48546.2			0.435173
$335$	32080.7	−	115369.i	0.285860	−	1.02801i
$336$	13229.1	−	25054.6i	0.117180	−	0.221926i
$337$	181315.	+	104682.i	1.59652	+	0.921752i	0.992151	+	0.125049i	$0.0399088\pi$
$337$	181315.	+	104682.i	1.59652	+	0.921752i	0.604371	+	0.796703i	$0.293424\pi$
$338$	32575.5	−	56422.4i	0.285139	−	0.493876i
$339$	−136904.	−	72287.0i	−1.19129	−	0.629014i
$340$	44552.3	+	12388.7i	0.385400	+	0.107168i
$341$			7575.12i			0.0651450i
$342$	−83527.0	−	122305.i	−0.714126	−	1.04566i
$343$		−	102497.i		−	0.871207i
$344$	−83111.1	+	47984.2i	−0.702331	+	0.405491i
$345$	−9745.82	+	40990.4i	−0.0818805	+	0.344385i
$346$	−5105.30	+	8842.64i	−0.0426451	+	0.0738635i
$347$	−92398.9	+	160040.i	−0.767376	+	1.32913i	0.171606	+	0.985166i	$0.445105\pi$
$347$	−92398.9	+	160040.i	−0.767376	+	1.32913i	−0.938981	+	0.343968i	$0.888229\pi$
$348$	72547.4	−	2743.15i	0.599051	−	0.0226512i
$349$	−27063.1	−	46874.7i	−0.222191	−	0.384846i	0.733282	−	0.679925i	$-0.237988\pi$
$349$	−27063.1	−	46874.7i	−0.222191	−	0.384846i	−0.955473	+	0.295078i	$0.904654\pi$
$350$	48575.2	+	915.173i	0.396532	+	0.00747080i
$351$	−26248.3	+	60356.1i	−0.213052	+	0.489900i
$352$			29002.1i			0.234069i
$353$	−16284.0	−	28204.8i	−0.130681	−	0.226346i	0.793258	−	0.608885i	$-0.208383\pi$
$353$	−16284.0	−	28204.8i	−0.130681	−	0.226346i	−0.923939	+	0.382539i	$0.875050\pi$
$354$	−158021.	+	5975.05i	−1.26098	+	0.0476799i
$355$	−164171.	+	42336.3i	−1.30269	+	0.335936i
$356$	−7392.60	−	4268.12i	−0.0583307	−	0.0336772i
$357$	−37143.8	−	59062.3i	−0.291440	−	0.463419i
$358$	10749.1	−	6206.01i	0.0838701	−	0.0484224i
$359$		−	226177.i		−	1.75493i	−0.479645	−	0.877463i	$-0.659234\pi$
$359$		−	226177.i		−	1.75493i	0.479645	−	0.877463i	$-0.340766\pi$
$360$	−45413.5	−	133469.i	−0.350413	−	1.02985i
$361$	197782.			1.51766
$362$	−53169.5	−	92092.3i	−0.405738	−	0.702759i
$363$	−102911.	−	54338.4i	−0.780999	−	0.412376i
$364$	6387.22	−	11063.0i	0.0482069	−	0.0834967i
$365$	219075.	−	56494.9i	1.64440	−	0.424056i
$366$	163719.	+	86445.5i	1.22218	+	0.645327i
$367$	−117772.	+	67995.5i	−0.874397	+	0.504834i	−0.868807	−	0.495151i	$-0.835113\pi$
$367$	−117772.	+	67995.5i	−0.874397	+	0.504834i	−0.00559037	+	0.999984i	$0.501779\pi$
$368$	24207.7			0.178755
$369$	159226.	+	76524.9i	1.16940	+	0.562017i
$370$	−19479.5	−	19849.9i	−0.142290	−	0.144996i
$371$	44149.8	−	25489.9i	0.320761	−	0.185191i
$372$	8108.31	−	5099.24i	0.0585928	−	0.0368485i
$373$	148525.	+	85750.9i	1.06753	+	0.616341i	0.927507	−	0.373807i	$-0.121948\pi$
$373$	148525.	+	85750.9i	1.06753	+	0.616341i	0.140027	+	0.990148i	$0.455281\pi$
$374$	−36395.7	−	21013.0i	−0.260199	−	0.150226i
$375$	98484.1	−	100381.i	0.700331	−	0.713818i
$376$	23819.3	+	41256.3i	0.168482	+	0.291820i
$377$	−125342.			−0.881889
$378$	−22599.8	+	51966.7i	−0.158169	+	0.363698i
$379$	−63347.6			−0.441013			−0.220507	−	0.975385i	$-0.570771\pi$
$379$	−63347.6			−0.441013			−0.220507	+	0.975385i	$0.570771\pi$
$380$	80163.0	+	22290.9i	0.555145	+	0.154369i
$381$	226862.	−	8578.04i	1.56283	−	0.0590933i
$382$	100619.	+	58092.4i	0.689530	+	0.398100i
$383$	−46631.9	+	80768.8i	−0.317896	+	0.550612i	−0.980049	−	0.198757i	$-0.936310\pi$
$383$	−46631.9	+	80768.8i	−0.317896	+	0.550612i	0.662153	+	0.749369i	$0.269643\pi$
$384$	−19259.1	+	12111.9i	−0.130609	+	0.0821389i
$385$	24257.0	+	6745.14i	0.163650	+	0.0455061i
$386$			150870.i			1.01258i
$387$	92202.6	−	62969.1i	0.615632	−	0.420442i
$388$			12869.9i			0.0854892i
$389$	−71957.2	+	41544.5i	−0.475527	+	0.274546i	−0.718551	−	0.695475i	$-0.755194\pi$
$389$	−71957.2	+	41544.5i	−0.475527	+	0.274546i	0.243023	+	0.970020i	$0.421861\pi$
$390$	18553.1	+	62133.3i	0.121980	+	0.408503i
$391$	29806.6	−	51626.5i	0.194966	−	0.337691i
$392$	−62937.2	+	109011.i	−0.409577	+	0.709408i
$393$	−29301.8	+	55494.7i	−0.189718	+	0.359307i
$394$	−12219.1	−	21164.0i	−0.0787128	−	0.136335i
$395$	75184.4	−	73781.2i	0.481874	−	0.472881i
$396$	−1469.81	−	19408.1i	−0.00937282	−	0.123763i
$397$			35206.6i			0.223379i	0.993743	+	0.111690i	$0.0356263\pi$
$397$			35206.6i			0.223379i	−0.993743	+	0.111690i	$0.964374\pi$
$398$	17009.1	+	29460.7i	0.107378	+	0.185985i
$399$	−66832.8	−	106271.i	−0.419802	−	0.667527i
$400$	−69198.5	−	41709.2i	−0.432491	−	0.260683i
$401$	−271339.	−	156657.i	−1.68742	−	0.974232i	−0.956484	−	0.291786i	$-0.905751\pi$
$401$	−271339.	−	156657.i	−1.68742	−	0.974232i	−0.730936	−	0.682446i	$-0.760916\pi$
$402$	137510.	−	5199.49i	0.850906	−	0.0321743i
$403$	−14321.6	+	8268.57i	−0.0881822	+	0.0509120i
$404$			48699.6i			0.298375i
$405$	64411.1	+	150849.i	0.392691	+	0.919671i
$406$	−107920.			−0.654709
$407$	−7206.25	−	12481.6i	−0.0435031	−	0.0753496i
$408$	7537.08	+	199332.i	0.0452775	+	1.19745i
$409$	−82640.8	+	143138.i	−0.494024	+	0.855675i	−0.999976	−	0.00688668i	$-0.997808\pi$
$409$	−82640.8	+	143138.i	−0.494024	+	0.855675i	0.505952	+	0.862562i	$0.331141\pi$
$410$	168537.	−	43462.1i	1.00260	−	0.258549i
$411$	−71162.4	+	44753.4i	−0.421276	+	0.264937i
$412$	66926.9	−	38640.3i	0.394281	−	0.227638i
$413$	−134040.			−0.785840
$414$	−48279.6	+	3656.30i	−0.281684	+	0.0213325i
$415$	110984.	−	108913.i	0.644415	−	0.632388i
$416$	−54831.6	+	31657.0i	−0.316843	+	0.182929i
$417$	−101165.	−	53416.4i	−0.581780	−	0.307187i
$418$	−65486.8	−	37808.8i	−0.374801	−	0.216392i
$419$	36842.3	+	21270.9i	0.209855	+	0.121160i	0.601244	−	0.799066i	$-0.294672\pi$
$419$	36842.3	+	21270.9i	0.209855	+	0.121160i	−0.391389	+	0.920225i	$0.628005\pi$
$420$	−9108.83	−	30504.9i	−0.0516374	−	0.172930i
$421$	−77284.9	−	133861.i	−0.436044	−	0.755251i	0.561336	−	0.827588i	$-0.310288\pi$
$421$	−77284.9	−	133861.i	−0.436044	−	0.755251i	−0.997380	+	0.0723373i	$0.976954\pi$
$422$	−190354.			−1.06890
$423$	−31257.9	−	45769.3i	−0.174694	−	0.255796i
$424$	−145750.			−0.810731
$425$	−174154.	+	96220.1i	−0.964175	+	0.532707i
$426$	−103722.	−	164928.i	−0.571546	−	0.908815i
$427$	135906.	+	78465.5i	0.745390	+	0.430351i
$428$	46332.3	−	80249.9i	0.252928	−	0.438084i
$429$	1269.71	+	33579.8i	0.00689907	+	0.182458i
$430$	29470.5	−	105982.i	0.159386	−	0.573187i
$431$			303027.i			1.63127i	0.578564	+	0.815637i	$0.303613\pi$
$431$			303027.i			1.63127i	−0.578564	+	0.815637i	$0.696387\pi$
$432$	75760.1	−	56051.9i	0.405950	−	0.300347i
$433$		−	247184.i		−	1.31839i	−0.751971	−	0.659196i	$-0.770897\pi$
$433$		−	247184.i		−	1.31839i	0.751971	−	0.659196i	$-0.229103\pi$
$434$	−12330.9	+	7119.24i	−0.0654659	+	0.0377967i
$435$	−214524.	+	227057.i	−1.13370	+	1.19993i
$436$	−26148.8	+	45291.0i	−0.137556	+	0.238253i
$437$	53631.0	−	92891.6i	0.280836	−	0.486422i
$438$	138410.	+	220085.i	0.721469	+	1.14721i
$439$	−153720.	−	266250.i	−0.797628	−	1.38153i	−0.921157	−	0.389191i	$-0.872755\pi$
$439$	−153720.	−	266250.i	−0.797628	−	1.38153i	0.123529	−	0.992341i	$-0.460579\pi$
$440$	−50416.8	−	51375.6i	−0.260417	−	0.265370i
$441$	63437.0	−	131994.i	0.326186	−	0.678700i
$442$		−	91746.5i		−	0.469618i
$443$	110745.	+	191816.i	0.564308	+	0.977410i	0.997114	+	0.0759231i	$0.0241904\pi$
$443$	110745.	+	191816.i	0.564308	+	0.977410i	−0.432805	+	0.901487i	$0.642476\pi$
$444$	−8509.19	+	16115.5i	−0.0431641	+	0.0817483i
$445$	35565.1	−	9171.50i	0.179599	−	0.0463149i
$446$	30278.6	+	17481.4i	0.152218	+	0.0878832i
$447$	−16254.6	+	30784.6i	−0.0813508	+	0.154070i
$448$	−90831.0	+	52441.3i	−0.452562	+	0.261287i
$449$			308268.i			1.52910i	0.644565	+	0.764550i	$0.277039\pi$
$449$			308268.i			1.52910i	−0.644565	+	0.764550i	$0.722961\pi$
$450$	144308.	+	72732.7i	0.712635	+	0.359174i
$451$	90197.2			0.443445
$452$	49974.2	+	86557.9i	0.244607	+	0.423672i
$453$	−184920.	+	116294.i	−0.901130	+	0.566712i
$454$	22312.7	−	38646.7i	0.108253	−	0.187500i
$455$	13725.1	+	53223.0i	0.0662968	+	0.257085i
$456$	13561.5	+	358658.i	0.0652195	+	1.72485i
$457$	24586.7	−	14195.2i	0.117725	−	0.0679685i	−0.439981	−	0.898007i	$-0.645015\pi$
$457$	24586.7	−	14195.2i	0.117725	−	0.0679685i	0.557706	+	0.830038i	$0.311682\pi$
$458$	261751.			1.24784
$459$	−26256.7	−	230585.i	−0.124628	−	1.09448i
$460$	19414.2	−	19051.9i	0.0917494	−	0.0900371i
$461$	243466.	−	140565.i	1.14561	−	0.661417i	0.197794	−	0.980244i	$-0.436622\pi$
$461$	243466.	−	140565.i	1.14561	−	0.661417i	0.947813	+	0.318827i	$0.103289\pi$
$462$	1093.22	+	28912.2i	0.00512183	+	0.135456i
$463$	−131818.	−	76105.1i	−0.614912	−	0.355019i	0.159974	−	0.987121i	$-0.448859\pi$
$463$	−131818.	−	76105.1i	−0.614912	−	0.355019i	−0.774885	+	0.632102i	$0.782192\pi$
$464$	155429.	+	89737.0i	0.721932	+	0.416808i
$465$	−9533.01	+	40095.3i	−0.0440884	+	0.185433i
$466$	−81177.2	−	140603.i	−0.373820	−	0.647474i
$467$	−284030.			−1.30236			−0.651180	−	0.758923i	$-0.725726\pi$
$467$	−284030.			−1.30236			−0.651180	+	0.758923i	$0.725726\pi$
$468$	35088.7	−	23963.6i	0.160205	−	0.109411i
$469$	116642.			0.530283
$470$	−52609.5	−	14629.2i	−0.238160	−	0.0662252i
$471$	155681.	−	294844.i	0.701770	−	1.32908i
$472$	331876.	+	191608.i	1.48967	+	0.860064i
$473$	28503.2	−	49369.0i	0.127401	−	0.220664i
$474$	107046.	+	56521.7i	0.476448	+	0.251570i
$475$	−313356.	+	173129.i	−1.38883	+	0.767331i
$476$			45043.8i			0.198802i
$477$	169087.	−	12805.2i	0.743143	−	0.0562796i
$478$			107976.i			0.472575i
$479$	5718.15	−	3301.37i	0.0249221	−	0.0143888i	−0.487487	−	0.873130i	$-0.662086\pi$
$479$	5718.15	−	3301.37i	0.0249221	−	0.0143888i	0.512409	+	0.858741i	$0.328753\pi$
$480$	−36498.1	+	153509.i	−0.158412	+	0.666271i
$481$	15731.8	−	27248.4i	0.0679970	−	0.117774i
$482$	−22757.3	+	39416.8i	−0.0979550	+	0.169663i
$483$	−41011.4	+	1550.71i	−0.175797	+	0.00664718i
$484$	37565.8	+	65065.9i	0.160362	+	0.277756i
$485$	−38785.5	−	39523.1i	−0.164887	−	0.168022i
$486$	−142629.	+	123232.i	−0.603859	+	0.521736i
$487$		−	256973.i		−	1.08350i	−0.840538	−	0.541752i	$-0.817761\pi$
$487$		−	256973.i		−	1.08350i	0.840538	−	0.541752i	$-0.182239\pi$
$488$	−224331.	−	388553.i	−0.941997	−	1.63159i
$489$	223974.	−	8468.84i	0.936654	−	0.0354165i
$490$	−36028.9	−	139712.i	−0.150058	−	0.581892i
$491$	−60010.2	−	34646.9i	−0.248921	−	0.143715i	0.370349	−	0.928893i	$-0.379238\pi$
$491$	−60010.2	−	34646.9i	−0.248921	−	0.143715i	−0.619270	+	0.785178i	$0.712571\pi$
$492$	−60716.8	−	96545.8i	−0.250830	−	0.398844i
$493$	382755.	−	220983.i	1.57480	−	0.909214i
$494$		−	165080.i		−	0.676456i
$495$	63003.0	+	55172.1i	0.257129	+	0.225169i
$496$	23679.1			0.0962502
$497$	−82573.3	−	143021.i	−0.334293	−	0.579012i
$498$	158018.	+	83435.3i	0.637158	+	0.336427i
$499$	−37169.4	+	64379.3i	−0.149274	+	0.258550i	−0.930959	−	0.365123i	$-0.881027\pi$
$499$	−37169.4	+	64379.3i	−0.149274	+	0.258550i	0.781685	+	0.623673i	$0.214360\pi$
$500$	−88321.9	+	21010.3i	−0.353288	+	0.0840411i
$501$	121037.	+	63908.7i	0.482216	+	0.254616i
$502$	−63355.3	+	36578.2i	−0.251406	+	0.145149i
$503$	−253194.			−1.00073			−0.500366	−	0.865814i	$-0.666801\pi$
$503$	−253194.			−1.00073			−0.500366	+	0.865814i	$0.666801\pi$
$504$	113405.	−	77449.0i	0.446447	−	0.304898i
$505$	−146764.	−	149555.i	−0.575489	−	0.586433i
$506$	−21408.6	+	12360.3i	−0.0836156	+	0.0482755i
$507$	155495.	−	97789.7i	0.604925	−	0.380432i
$508$	−126929.	−	73282.5i	−0.491851	−	0.283970i
$509$	−66318.5	−	38289.0i	−0.255976	−	0.147788i	0.366522	−	0.930410i	$-0.380549\pi$
$509$	−66318.5	−	38289.0i	−0.255976	−	0.147788i	−0.622497	+	0.782622i	$0.713882\pi$
$510$	−166199.	−	157025.i	−0.638982	−	0.603711i
$511$	110188.	+	190852.i	0.421982	+	0.730894i
$512$	234662.			0.895165
$513$	−47243.7	−	414892.i	−0.179518	−	1.57652i
$514$	269745.			1.02100
$515$	−89082.1	+	320358.i	−0.335874	+	1.20787i
$516$	−72031.0	+	2723.62i	−0.270533	+	0.0102293i
$517$	−24506.8	−	14149.0i	−0.0916864	−	0.0529351i
$518$	13545.1	−	23460.9i	0.0504805	−	0.0874348i
$519$	−24369.6	+	15325.8i	−0.0904719	+	0.0568970i
$520$	42099.0	−	151397.i	0.155692	−	0.559901i
$521$		−	24843.4i		−	0.0915241i	−0.998952	−	0.0457621i	$-0.985428\pi$
$521$		−	24843.4i		−	0.0915241i	0.998952	−	0.0457621i	$-0.0145716\pi$
$522$	−323540.	−	155495.i	−1.18737	−	0.570656i
$523$			118438.i			0.432999i	0.976283	+	0.216499i	$0.0694639\pi$
$523$			118438.i			0.432999i	−0.976283	+	0.216499i	$0.930536\pi$
$524$	35086.6	−	20257.3i	0.127785	−	0.0737765i
$525$	119904.	+	66228.7i	0.435027	+	0.240286i
$526$	−71157.8	+	123249.i	−0.257188	+	0.445463i
$527$	29155.7	−	50499.2i	0.104979	−	0.181829i
$528$	22466.5	−	42549.3i	0.0805876	−	0.152625i
$529$	122388.	+	211982.i	0.437347	+	0.757508i
$530$	119240.	−	117015.i	0.424494	−	0.416572i
$531$	−401848.	−	193130.i	−1.42519	−	0.684953i
$532$			81047.3i			0.286362i
$533$	98454.0	+	170527.i	0.346561	+	0.600260i
$534$	22469.7	+	35729.1i	0.0787980	+	0.125297i
$535$	99560.7	+	386075.i	0.347841	+	1.34885i
$536$	−288798.	−	166738.i	−1.00523	−	0.580369i
$537$	34970.0	−	1322.28i	0.121268	−	0.00458536i
$538$	−228686.	+	132032.i	−0.790088	+	0.456157i
$539$		−	74771.0i		−	0.257369i
$540$	16644.6	−	104577.i	0.0570802	−	0.358632i
$541$	−262210.			−0.895891			−0.447946	−	0.894061i	$-0.647844\pi$
$541$	−262210.			−0.895891			−0.447946	+	0.894061i	$0.647844\pi$
$542$	43093.8	+	74640.6i	0.146695	+	0.254083i
$543$	−11328.5	−	299602.i	−0.0384213	−	1.01612i
$544$	111625.	−	193341.i	0.377195	−	0.653320i
$545$	−56189.5	−	217891.i	−0.189174	−	0.733577i
$546$	−53468.4	+	33625.8i	−0.179354	+	0.112794i
$547$	−122480.	+	70713.6i	−0.409344	+	0.236335i	−0.690508	−	0.723325i	$-0.742613\pi$
$547$	−122480.	+	70713.6i	−0.409344	+	0.236335i	0.281164	+	0.959660i	$0.409280\pi$
$548$	54271.9			0.180723
$549$	294387.	+	431056.i	0.976728	+	1.43018i
$550$	82493.6	+	1554.21i	0.272706	+	0.00513788i
$551$	688691.	−	397616.i	2.26841	−	1.30967i
$552$	103759.	+	54785.8i	0.340523	+	0.179800i
$553$	88861.3	+	51304.1i	0.290578	+	0.167765i
$554$	148501.	+	85737.2i	0.483849	+	0.279351i
$555$	−22435.2	−	75134.2i	−0.0728358	−	0.243922i
$556$	36928.4	+	63961.9i	0.119457	+	0.206905i
$557$	−27193.3			−0.0876499			−0.0438249	−	0.999039i	$-0.513954\pi$
$557$	−27193.3			−0.0876499			−0.0438249	+	0.999039i	$0.513954\pi$
$558$	−47225.3	+	3576.46i	−0.151672	+	0.0114864i
$559$	124450.			0.398264
$560$	21084.7	−	75824.9i	0.0672343	−	0.241789i
$561$	−63080.0	−	100303.i	−0.200431	−	0.318706i
$562$	−64276.8	−	37110.3i	−0.203508	−	0.117496i
$563$	−165319.	+	286341.i	−0.521562	+	0.903372i	0.478124	+	0.878293i	$0.341317\pi$
$563$	−165319.	+	286341.i	−0.521562	+	0.903372i	−0.999685	+	0.0250792i	$0.992016\pi$
$564$	1352.00	+	35756.2i	0.00425030	+	0.112407i
$565$	−414325.	−	115212.i	−1.29791	−	0.360910i
$566$			208712.i			0.651500i
$567$	−124758.	+	99813.2i	−0.388063	+	0.310472i
$568$			472150.i			1.46347i
$569$	−51800.1	+	29906.8i	−0.159995	+	0.0923731i	−0.577860	−	0.816136i	$-0.696112\pi$
$569$	−51800.1	+	29906.8i	−0.159995	+	0.0923731i	0.417865	+	0.908509i	$0.362779\pi$
$570$	−299042.	−	282536.i	−0.920413	−	0.869608i
$571$	−261212.	+	452433.i	−0.801163	+	1.38766i	0.117688	+	0.993051i	$0.462452\pi$
$571$	−261212.	+	452433.i	−0.801163	+	1.38766i	−0.918851	+	0.394605i	$0.870881\pi$
$572$	10847.2	−	18787.9i	0.0331532	−	0.0574230i
$573$	174390.	+	277298.i	0.531144	+	0.844572i
$574$	84769.0	+	146824.i	0.257284	+	0.445629i
$575$	−2204.61	+	117015.i	−0.00666801	+	0.353922i
$576$	−347868.	+	26344.7i	−1.04850	+	0.0794051i
$577$			432123.i			1.29794i	0.760812	+	0.648972i	$0.224801\pi$
$577$			432123.i			1.29794i	−0.760812	+	0.648972i	$0.775199\pi$
$578$	28448.5	+	49274.2i	0.0851536	+	0.147490i
$579$	−198614.	+	376154.i	−0.592451	+	1.12204i
$580$	195276.	−	50357.6i	0.580488	−	0.149696i
$581$	131174.	+	75733.2i	0.388593	+	0.224354i
$582$	29712.5	−	56272.4i	0.0877188	−	0.166130i
$583$	74978.1	−	43288.6i	0.220596	−	0.127361i
$584$		−	630051.i		−	1.84735i
$585$	−35538.3	+	179337.i	−0.103845	+	0.524032i
$586$	112772.			0.328401
$587$	265683.	+	460176.i	0.771059	+	1.33551i	0.936983	+	0.349374i	$0.113606\pi$
$587$	265683.	+	460176.i	0.771059	+	1.33551i	−0.165925	+	0.986138i	$0.553061\pi$
$588$	−80033.9	+	50332.6i	−0.231483	+	0.145578i
$589$	52459.9	−	90863.2i	0.151216	−	0.261913i
$590$	−425345.	+	109688.i	−1.22190	+	0.315104i
$591$	−2603.44	−	68852.6i	−0.00745371	−	0.197127i
$592$	−39016.2	+	22526.0i	−0.111327	+	0.0642749i
$593$	346725.			0.985998			0.492999	−	0.870030i	$-0.335901\pi$
$593$	346725.			0.985998			0.492999	+	0.870030i	$0.335901\pi$
$594$	−38380.4	+	88253.2i	−0.108777	+	0.250125i
$595$	−135747.	−	138328.i	−0.383438	−	0.390730i
$596$	19463.6	−	11237.3i	0.0547937	−	0.0316352i
$597$	3624.03	+	95844.0i	0.0101682	+	0.268916i
$598$	−46736.8	−	26983.5i	−0.130694	−	0.0754564i
$599$	210621.	+	121602.i	0.587013	+	0.338912i	0.763915	−	0.645316i	$-0.223274\pi$
$599$	210621.	+	121602.i	0.587013	+	0.338912i	−0.176903	+	0.984228i	$0.556608\pi$
$600$	−202203.	−	335380.i	−0.561676	−	0.931612i
$601$	15921.8	+	27577.3i	0.0440801	+	0.0763490i	0.887224	−	0.461339i	$-0.152631\pi$
$601$	15921.8	+	27577.3i	0.0440801	+	0.0763490i	−0.843144	+	0.537689i	$0.819298\pi$
$602$	107151.			0.295668
$603$	349688.	+	168062.i	0.961715	+	0.462204i
$604$	141029.			0.386575
$605$	−311450.	−	86605.1i	−0.850899	−	0.236610i
$606$	112432.	−	212934.i	0.306157	−	0.579830i
$607$	−614804.	−	354957.i	−1.66863	−	0.963382i	−0.968379	−	0.249482i	$-0.919740\pi$
$607$	−614804.	−	354957.i	−1.66863	−	0.963382i	−0.700248	−	0.713900i	$-0.746927\pi$
$608$	200848.	−	347879.i	0.543325	−	0.941067i
$609$	−269068.	−	142071.i	−0.725483	−	0.383064i
$610$	495477.	+	137778.i	1.33157	+	0.370270i
$611$		−	61776.9i		−	0.165479i
$612$	−64900.8	+	135040.i	−0.173280	+	0.360545i
$613$			74706.8i			0.198810i	0.995047	+	0.0994052i	$0.0316940\pi$
$613$			74706.8i			0.198810i	−0.995047	+	0.0994052i	$0.968306\pi$
$614$	−342177.	+	197556.i	−0.907642	+	0.524027i
$615$	477416.	+	113510.i	1.26225	+	0.300112i
$616$	35057.6	−	60721.5i	0.0923890	−	0.160022i
$617$	4028.70	−	6977.91i	0.0105826	−	0.0183297i	−0.860686	−	0.509137i	$-0.829965\pi$
$617$	4028.70	−	6977.91i	0.0105826	−	0.0183297i	0.871268	+	0.490807i	$0.163298\pi$
$618$	−381840.	+	14438.0i	−0.999779	+	0.0378034i
$619$	57322.1	+	99284.8i	0.149603	+	0.259120i	0.931081	−	0.364813i	$-0.118867\pi$
$619$	57322.1	+	99284.8i	0.149603	+	0.259120i	−0.781478	+	0.623933i	$0.785534\pi$
$620$	18990.2	−	18635.8i	0.0494023	−	0.0484803i
$621$	−125185.	−	54441.8i	−0.324616	−	0.141172i
$622$		−	174746.i		−	0.451675i
$623$	17888.2	+	30983.3i	0.0460883	+	0.0798274i
$624$	104967.	−	3969.00i	0.269578	−	0.0101932i
$625$	207916.	−	330694.i	0.532266	−	0.846577i
$626$	−240238.	−	138702.i	−0.613047	−	0.353943i
$627$	−113500.	−	180476.i	−0.288709	−	0.459076i
$628$	−186416.	+	107627.i	−0.472676	+	0.272900i
$629$			110944.i			0.280415i
$630$	−30598.5	+	154409.i	−0.0770938	+	0.389038i
$631$	65346.0			0.164120			0.0820598	−	0.996627i	$-0.473850\pi$
$631$	65346.0			0.164120			0.0820598	+	0.996627i	$0.473850\pi$
$632$	−146677.	−	254052.i	−0.367222	−	0.636047i
$633$	−474596.	−	250592.i	−1.18445	−	0.625403i
$634$	48483.8	−	83976.5i	0.120620	−	0.208920i
$635$	610644.	−	157472.i	1.51440	−	0.390532i
$636$	−96807.6	−	51115.5i	−0.239329	−	0.126368i
$637$	141363.	−	81615.7i	0.348382	−	0.201138i
$638$	−183276.			−0.450261
$639$	−41482.0	−	547748.i	−0.101592	−	1.34146i
$640$	−45106.2	+	44264.4i	−0.110123	+	0.108067i
$641$	−208522.	+	120390.i	−0.507499	+	0.293005i	−0.731805	−	0.681514i	$-0.761322\pi$
$641$	−208522.	+	120390.i	−0.507499	+	0.293005i	0.224306	+	0.974519i	$0.427989\pi$
$642$	−387855.	+	243919.i	−0.941021	+	0.591800i
$643$	−118660.	−	68508.2i	−0.287000	−	0.165699i	0.349588	−	0.936903i	$-0.386321\pi$
$643$	−118660.	−	68508.2i	−0.287000	−	0.165699i	−0.636588	+	0.771204i	$0.719655\pi$
$644$	22945.9	+	13247.8i	0.0553264	+	0.0319427i
$645$	212997.	−	225441.i	0.511982	−	0.541893i
$646$	291043.	+	504101.i	0.697416	+	1.20796i
$647$	745072.			1.77988			0.889938	−	0.456081i	$-0.150747\pi$
$647$	745072.			1.77988			0.889938	+	0.456081i	$0.150747\pi$
$648$	451576.	−	68791.9i	1.07543	−	0.163828i
$649$	−227635.			−0.540444
$650$	87106.9	+	157660.i	0.206170	+	0.373159i
$651$	−40115.9	+	1516.85i	−0.0946573	+	0.00357916i
$652$	−125313.	−	72349.6i	−0.294782	−	0.170193i
$653$	−165697.	+	286996.i	−0.388588	+	0.673054i	−0.992260	−	0.124179i	$-0.960370\pi$
$653$	−165697.	+	286996.i	−0.388588	+	0.673054i	0.603672	+	0.797233i	$0.293704\pi$
$654$	218895.	−	137661.i	0.511777	−	0.321852i
$655$	−46701.5	+	167949.i	−0.108855	+	0.391466i
$656$		−	281948.i		−	0.655180i
$657$	55354.8	+	730932.i	0.128240	+	1.69335i
$658$		−	53189.9i		−	0.122851i
$659$	206431.	−	119183.i	0.475339	−	0.274437i	−0.243133	−	0.969993i	$-0.578175\pi$
$659$	206431.	−	119183.i	0.475339	−	0.274437i	0.718472	+	0.695556i	$0.244842\pi$
$660$	−15469.2	−	51805.4i	−0.0355124	−	0.118929i
$661$	308885.	−	535004.i	0.706958	−	1.22449i	−0.259023	−	0.965871i	$-0.583401\pi$
$661$	308885.	−	535004.i	0.706958	−	1.22449i	0.965980	−	0.258615i	$-0.0832661\pi$
$662$	118779.	−	205731.i	0.271033	−	0.469443i
$663$	120780.	−	228745.i	0.274769	−	0.520385i
$664$	−216519.	−	375022.i	−0.491089	−	0.850592i
$665$	−244249.	−	248894.i	−0.552319	−	0.562822i
$666$	74411.2	−	50818.6i	0.167761	−	0.114571i
$667$		−	259973.i		−	0.584355i
$668$	−44182.1	−	76525.6i	−0.0990133	−	0.171496i
$669$	52478.1	+	83445.5i	0.117254	+	0.186445i
$670$	370135.	−	95450.2i	0.824539	−	0.212631i
$671$	230805.	+	133255.i	0.512625	+	0.295964i
$672$	−153588.	+	5807.42i	−0.340108	+	0.0128601i
$673$	618772.	−	357248.i	1.36616	−	0.788751i	0.375722	−	0.926732i	$-0.377395\pi$
$673$	618772.	−	357248.i	1.36616	−	0.788751i	0.990435	+	0.137981i	$0.0440614\pi$
$674$			668319.i			1.47117i
$675$	264045.	+	371315.i	0.579522	+	0.814957i
$676$	−118588.			−0.259507
$677$	−314445.	−	544634.i	−0.686068	−	1.18830i	−0.973100	−	0.230383i	$-0.926002\pi$
$677$	−314445.	−	544634.i	−0.686068	−	1.18830i	0.287033	−	0.957921i	$-0.407331\pi$
$678$	−18673.0	−	493841.i	−0.0406214	−	1.07430i
$679$	26969.6	−	46712.8i	0.0584973	−	0.101320i
$680$	138363.	+	536541.i	0.299227	+	1.16034i
$681$	106507.	−	66981.3i	0.229659	−	0.144431i
$682$	−20941.1	+	12090.4i	−0.0450227	+	0.0259939i
$683$	−619254.			−1.32748			−0.663740	−	0.747964i	$-0.731032\pi$
$683$	−619254.			−1.32748			−0.663740	+	0.747964i	$0.731032\pi$
$684$	−116776.	+	242978.i	−0.249598	+	0.519343i
$685$	−166668.	+	163557.i	−0.355197	+	0.348568i
$686$	283348.	−	163591.i	0.602104	−	0.347625i
$687$	652606.	+	344583.i	1.38273	+	0.730097i
$688$	−154323.	−	89098.3i	−0.326027	−	0.188232i
$689$	163684.	+	94502.8i	0.344800	+	0.199070i
$690$	−128871.	+	38481.3i	−0.270681	+	0.0808260i
$691$	−98482.9	−	170577.i	−0.206255	−	0.357244i	0.744277	−	0.667871i	$-0.232794\pi$
$691$	−98482.9	−	170577.i	−0.206255	−	0.357244i	−0.950532	+	0.310627i	$0.899461\pi$
$692$	18585.4			0.0388115
$693$	−35336.0	+	73524.0i	−0.0735784	+	0.153096i
$694$	−589898.			−1.22478
$695$	−306165.	−	85135.5i	−0.633850	−	0.176255i
$696$	463109.	+	736389.i	0.956015	+	1.52016i
$697$	−601295.	−	347158.i	−1.23772	−	0.714597i
$698$	86388.8	−	149630.i	0.177315	−	0.307119i
$699$	−17295.9	−	457421.i	−0.0353988	−	0.936185i
$700$	−42765.9	−	77404.3i	−0.0872774	−	0.157968i
$701$			430439.i			0.875942i	0.898989	+	0.437971i	$0.144303\pi$
$701$			430439.i			0.875942i	−0.898989	+	0.437971i	$0.855697\pi$
$702$	−208746.	+	23769.8i	−0.423588	+	0.0482339i
$703$			199621.i			0.403921i
$704$	−154255.	+	89059.3i	−0.311239	+	0.179694i
$705$	−111909.	−	105732.i	−0.225158	−	0.212729i
$706$	51980.7	−	90033.1i	0.104288	−	0.180631i
$707$	102053.	−	176761.i	0.204168	−	0.353629i
$708$	153234.	+	243658.i	0.305696	+	0.486087i
$709$	112160.	+	194266.i	0.223123	+	0.386461i	0.955755	−	0.294165i	$-0.0950414\pi$
$709$	112160.	+	194266.i	0.223123	+	0.386461i	−0.732632	+	0.680625i	$0.761708\pi$
$710$	−379065.	−	386274.i	−0.751963	−	0.766264i
$711$	192483.	+	281843.i	0.380761	+	0.557530i
$712$		−	102284.i		−	0.201766i
$713$	−17149.9	−	29704.5i	−0.0337352	−	0.0584311i
$714$	103992.	−	196950.i	0.203987	−	0.386330i
$715$	23308.9	+	90386.8i	0.0455941	+	0.176804i
$716$	−19565.7	−	11296.2i	−0.0381653	−	0.0220347i
$717$	−142145.	+	269208.i	−0.276499	+	0.523661i
$718$	625256.	−	360992.i	1.21286	−	0.700243i
$719$		−	256508.i		−	0.496183i	−0.968737	−	0.248092i	$-0.920197\pi$
$719$		−	256508.i		−	0.496183i	0.968737	−	0.248092i	$-0.0798034\pi$
$720$	172463.	−	196941.i	0.332683	−	0.379902i
$721$	−323892.			−0.623060
$722$	315673.	+	546762.i	0.605569	+	1.04888i
$723$	−108629.	+	68316.1i	−0.207812	+	0.130691i
$724$	−96779.7	+	167627.i	−0.184632	+	0.319792i
$725$	−447927.	+	743142.i	−0.852179	+	1.41383i
$726$	−14036.6	−	371222.i	−0.0266310	−	0.704305i
$727$	232904.	−	134467.i	0.440664	−	0.254418i	−0.263215	−	0.964737i	$-0.584783\pi$
$727$	232904.	−	134467.i	0.440664	−	0.254418i	0.703879	+	0.710320i	$0.251450\pi$
$728$	153067.			0.288815
$729$	−517836.	+	119481.i	−0.974399	+	0.224824i
$730$	505835.	+	515455.i	0.949213	+	0.967264i
$731$	−380030.	+	219411.i	−0.711186	+	0.410604i
$732$	−12733.2	−	336752.i	−0.0237638	−	0.628476i
$733$	118665.	+	68511.0i	0.220858	+	0.127512i	0.606347	−	0.795200i	$-0.292634\pi$
$733$	118665.	+	68511.0i	0.220858	+	0.127512i	−0.385489	+	0.922712i	$0.625967\pi$
$734$	−375942.	−	217050.i	−0.697796	−	0.402873i
$735$	94096.5	−	395765.i	0.174180	−	0.732593i
$736$	−65660.2	−	113727.i	−0.121212	−	0.209946i
$737$	198088.			0.364690
$738$	42585.0	+	562313.i	0.0781887	+	1.03244i
$739$	−654699.			−1.19882			−0.599408	−	0.800443i	$-0.704597\pi$
$739$	−654699.			−1.19882			−0.599408	+	0.800443i	$0.704597\pi$
$740$	−13562.0	+	48771.9i	−0.0247663	+	0.0890649i
$741$	217320.	−	411581.i	0.395788	−	0.749582i
$742$	140932.	+	81367.0i	0.255977	+	0.147788i
$743$	−202784.	+	351232.i	−0.367329	+	0.636233i	−0.989147	−	0.146929i	$-0.953061\pi$
$743$	−202784.	+	351232.i	−0.367329	+	0.636233i	0.621818	+	0.783162i	$0.286394\pi$
$744$	101493.	+	53589.5i	0.183354	+	0.0968130i
$745$	−25906.8	+	93166.2i	−0.0466767	+	0.167859i
$746$			547455.i			0.983718i
$747$	284136.	+	416046.i	0.509196	+	0.745590i
$748$			76496.3i			0.136722i
$749$	−336337.	+	194184.i	−0.599531	+	0.346139i
$750$	434685.	+	112042.i	0.772774	+	0.199185i
$751$	7832.01	−	13565.4i	0.0138865	−	0.0240522i	−0.858999	−	0.511978i	$-0.828913\pi$
$751$	7832.01	−	13565.4i	0.0138865	−	0.0240522i	0.872885	+	0.487926i	$0.162246\pi$
$752$	−44228.3	+	76605.7i	−0.0782105	+	0.135465i
$753$	−206113.	+	7793.48i	−0.363508	+	0.0137449i
$754$	−200054.	−	346503.i	−0.351887	−	0.609487i
$755$	−433096.	+	425013.i	−0.759784	+	0.745604i
$756$	102486.	−	11670.0i	0.179316	−	0.0204187i
$757$		−	79237.9i		−	0.138274i	−0.997607	−	0.0691371i	$-0.977975\pi$
$757$		−	79237.9i		−	0.138274i	0.997607	−	0.0691371i	$-0.0220246\pi$
$758$	−101107.	−	175122.i	−0.175971	−	0.304791i
$759$	−69648.2	+	2633.52i	−0.120900	+	0.00457145i
$760$	248956.	+	965399.i	0.431018	+	1.67140i
$761$	1521.35	+	878.351i	0.00262700	+	0.00151670i	0.501313	−	0.865266i	$-0.332851\pi$
$761$	1521.35	+	878.351i	0.00262700	+	0.00151670i	−0.498686	+	0.866783i	$0.666184\pi$
$762$	385799.	+	613459.i	0.664433	+	1.05652i
$763$	189820.	−	109593.i	0.326057	−	0.188249i
$764$		−	211481.i		−	0.362313i
$765$	−207656.	−	610293.i	−0.354831	−	1.04283i
$766$	−297710.			−0.507382
$767$	−248474.	−	430369.i	−0.422367	−	0.731561i
$768$	484224.	+	255676.i	0.820964	+	0.433478i
$769$	−11390.7	+	19729.3i	−0.0192619	+	0.0333626i	−0.875496	−	0.483226i	$-0.839465\pi$
$769$	−11390.7	+	19729.3i	−0.0192619	+	0.0333626i	0.856234	+	0.516589i	$0.172798\pi$
$770$	20069.0	+	77823.1i	0.0338488	+	0.131258i
$771$	672537.	+	355107.i	1.13138	+	0.597380i
$772$	237824.	−	137308.i	0.399045	−	0.230388i
$773$	−265643.			−0.444569			−0.222284	−	0.974982i	$-0.571351\pi$
$773$	−265643.			−0.444569			−0.222284	+	0.974982i	$0.571351\pi$
$774$	321237.	+	154388.i	0.536221	+	0.257710i
$775$	−2156.47	+	114460.i	−0.00359038	+	0.190569i
$776$	−133551.	+	77105.6i	−0.221780	+	0.128045i
$777$	64656.2	−	40661.7i	0.107095	−	0.0673510i
$778$	−229696.	−	132615.i	−0.379485	−	0.219096i
$779$	−1.08191e6	−	624641.i	−1.78286	−	1.02933i
$780$	81058.3	−	85794.0i	0.133232	−	0.141016i
$781$	−140231.	−	242888.i	−0.229902	−	0.398202i
$782$	190293.			0.311177
$783$	−601957.	−	813609.i	−0.981842	−	1.32706i
$784$	−233727.			−0.380256
$785$	248126.	−	892315.i	0.402655	−	1.44803i
$786$	−200180.	+	7569.18i	−0.324024	+	0.0122519i
$787$	87831.8	+	50709.7i	0.141809	+	0.0818732i	0.569226	−	0.822181i	$-0.307243\pi$
$787$	87831.8	+	50709.7i	0.141809	+	0.0818732i	−0.427417	+	0.904055i	$0.640576\pi$
$788$	−22241.3	+	38523.0i	−0.0358185	+	0.0620394i
$789$	−339664.	+	213612.i	−0.545627	+	0.343140i
$790$	323964.	+	90084.9i	0.519090	+	0.144344i
$791$		−	418896.i		−	0.669505i
$792$	192591.	−	131529.i	0.307034	−	0.209687i
$793$			581815.i			0.925207i
$794$	−97327.3	+	56191.9i	−0.154381	+	0.0891319i
$795$	451338.	−	134771.i	0.714115	−	0.213236i
$796$	30960.2	−	53624.7i	0.0488627	−	0.0846327i
$797$	259138.	−	448841.i	0.407958	−	0.706603i	−0.586703	−	0.809802i	$-0.699574\pi$
$797$	259138.	−	448841.i	0.407958	−	0.706603i	0.994661	+	0.103199i	$0.0329078\pi$
$798$	187112.	−	354372.i	0.293830	−	0.556485i
$799$	108915.	+	188647.i	0.170606	+	0.295499i
$800$	−8256.26	+	438223.i	−0.0129004	+	0.684723i
$801$	8986.42	+	118661.i	0.0140062	+	0.184945i
$802$		−	1.00014e6i		−	1.55494i
$803$	187129.	+	324117.i	0.290209	+	0.502656i
$804$	−133345.	−	212031.i	−0.206283	−	0.328010i
$805$	−110390.	+	28467.4i	−0.170349	+	0.0439294i
$806$	−45716.3	−	26394.3i	−0.0703721	−	0.0406294i
$807$	−743981.	+	28131.2i	−1.14239	+	0.0431958i
$808$	−505355.	+	291767.i	−0.774059	+	0.446903i
$809$		−	153884.i		−	0.235123i	−0.993066	−	0.117562i	$-0.962492\pi$
$809$		−	153884.i		−	0.235123i	0.993066	−	0.117562i	$-0.0375077\pi$
$810$	−314212.	+	418826.i	−0.478909	+	0.638357i
$811$	349404.			0.531235			0.265617	−	0.964079i	$-0.414424\pi$
$811$	349404.			0.531235			0.265617	+	0.964079i	$0.414424\pi$
$812$	98218.1	+	170119.i	0.148963	+	0.258012i
$813$	9181.71	+	242827.i	0.0138913	+	0.367380i
$814$	23003.2	−	39842.8i	0.0347168	−	0.0601313i
$815$	602870.	−	155468.i	0.907630	−	0.234059i
$816$	−313539.	+	197182.i	−0.470881	+	0.296133i
$817$	−683789.	+	394786.i	−1.02442	+	0.591449i
$818$	−527600.			−0.788493
$819$	−177576.	+	13448.1i	−0.264738	+	0.0200491i
$820$	−221897.	−	226117.i	−0.330008	−	0.336284i
$821$	−452698.	+	261365.i	−0.671618	+	0.387759i	−0.796689	−	0.604389i	$-0.793417\pi$
$821$	−452698.	+	261365.i	−0.671618	+	0.387759i	0.125072	+	0.992148i	$0.460084\pi$
$822$	−237299.	−	125296.i	−0.351198	−	0.185436i
$823$	314247.	+	181431.i	0.463951	+	0.267862i	0.713704	−	0.700447i	$-0.247016\pi$
$823$	314247.	+	181431.i	0.463951	+	0.267862i	−0.249753	+	0.968310i	$0.580349\pi$
$824$	801940.	+	463000.i	1.18110	+	0.681909i
$825$	203629.	+	112474.i	0.299180	+	0.165251i
$826$	−213936.	−	370548.i	−0.313562	−	0.543106i
$827$	711891.			1.04088			0.520442	−	0.853897i	$-0.325767\pi$
$827$	711891.			1.04088			0.520442	+	0.853897i	$0.325767\pi$
$828$	49703.1	+	72777.8i	0.0724974	+	0.106154i
$829$	768979.			1.11894			0.559468	−	0.828852i	$-0.311005\pi$
$829$	768979.			1.11894			0.559468	+	0.828852i	$0.311005\pi$
$830$	478224.	+	132980.i	0.694185	+	0.193032i
$831$	257378.	+	409257.i	0.372709	+	0.592644i
$832$	−336752.	−	194424.i	−0.486479	−	0.280869i
$833$	−287784.	+	498457.i	−0.414741	+	0.718352i
$834$	−13798.4	−	364923.i	−0.0198379	−	0.524650i
$835$	366304.	+	101858.i	0.525375	+	0.146091i
$836$			137640.i			0.196939i
$837$	−122452.	−	53253.0i	−0.174789	−	0.0760139i
$838$			135799.i			0.193378i
$839$	933723.	−	539085.i	1.32646	−	0.765832i	0.341709	−	0.939806i	$-0.388994\pi$
$839$	933723.	−	539085.i	1.32646	−	0.765832i	0.984750	+	0.173974i	$0.0556608\pi$
$840$	261976.	−	277282.i	0.371282	−	0.392973i
$841$	610070.	−	1.05667e6i	0.862557	−	1.49399i
$842$	246703.	−	427302.i	0.347977	−	0.602714i
$843$	−111403.	−	177142.i	−0.156762	−	0.249268i
$844$	173242.	+	300064.i	0.243203	+	0.421239i
$845$	364182.	−	357385.i	0.510041	−	0.500522i
$846$	76638.1	−	159462.i	0.107079	−	0.222800i
$847$		−	314886.i		−	0.438921i
$848$	−135316.	−	234374.i	−0.188173	−	0.325925i
$849$	−274760.	+	520366.i	−0.381186	+	0.721928i
$850$	−543958.	−	327869.i	−0.752883	−	0.453798i
$851$	56516.1	+	32629.6i	0.0780393	+	0.0450560i
$852$	−165586.	+	313603.i	−0.228110	+	0.432018i
$853$	140070.	−	80869.4i	0.192507	−	0.111144i	−0.400649	−	0.916232i	$-0.631215\pi$
$853$	140070.	−	80869.4i	0.192507	−	0.111144i	0.593156	+	0.805088i	$0.297882\pi$
$854$			500944.i			0.686868i
$855$	−373635.	−	1.09810e6i	−0.511112	−	1.50214i
$856$	1.11034e6			1.51533
$857$	353645.	+	612531.i	0.481510	+	0.834001i	0.999775	−	0.0212199i	$-0.00675500\pi$
$857$	353645.	+	612531.i	0.481510	+	0.834001i	−0.518264	+	0.855220i	$0.673422\pi$
$858$	−90803.5	+	57105.5i	−0.123347	+	0.0775718i
$859$	288112.	−	499024.i	0.390458	−	0.676294i	−0.602052	−	0.798457i	$-0.705650\pi$
$859$	288112.	−	499024.i	0.390458	−	0.676294i	0.992510	+	0.122163i	$0.0389832\pi$
$860$	−193886.	+	49999.2i	−0.262150	+	0.0676030i
$861$	18061.2	+	477661.i	0.0243635	+	0.644337i
$862$	−837706.	+	483650.i	−1.12740	+	0.650904i
$863$	867975.			1.16543			0.582714	−	0.812677i	$-0.301991\pi$
$863$	867975.			1.16543			0.582714	+	0.812677i	$0.301991\pi$
$864$	−468819.	−	203884.i	−0.628026	−	0.273122i
$865$	−57075.4	+	56010.2i	−0.0762811	+	0.0748574i
$866$	683330.	−	394521.i	0.911161	−	0.526059i
$867$	6061.33	+	160303.i	0.00806362	+	0.213257i
$868$	22444.8	+	12958.5i	0.0297904	+	0.0171995i
$869$	150910.	+	87128.0i	0.199838	+	0.115377i
$870$	−970085.	−	230646.i	−1.28166	−	0.304725i
$871$	216222.	+	374507.i	0.285012	+	0.493656i
$872$	−626646.			−0.824117
$873$	148160.	−	101185.i	0.194403	−	0.132766i
$874$	342394.			0.448232
$875$	364603.	+	108825.i	0.476217	+	0.142138i
$876$	220963.	−	418482.i	0.287947	−	0.545342i
$877$	−267200.	−	154268.i	−0.347406	−	0.200575i	0.316136	−	0.948714i	$-0.397614\pi$
$877$	−267200.	−	154268.i	−0.347406	−	0.200575i	−0.663542	+	0.748139i	$0.730948\pi$
$878$	490692.	−	849904.i	0.636532	−	1.10251i
$879$	281165.	+	148459.i	0.363902	+	0.192144i
$880$	35807.4	−	128771.i	0.0462389	−	0.166285i
$881$		−	612661.i		−	0.789347i	−0.918821	−	0.394674i	$-0.870858\pi$
$881$		−	612661.i		−	0.789347i	0.918821	−	0.394674i	$-0.129142\pi$
$882$	466142.	−	35301.8i	0.599213	−	0.0453795i
$883$		−	84067.1i		−	0.107821i	−0.998546	−	0.0539106i	$-0.982831\pi$
$883$		−	84067.1i		−	0.107821i	0.998546	−	0.0539106i	$-0.0171686\pi$
$884$	−144624.	+	83499.0i	−0.185071	+	0.106851i
$885$	−1.20488e6	−	286471.i	−1.53836	−	0.365758i
$886$	−353512.	+	612300.i	−0.450336	+	0.780004i
$887$	195121.	−	337960.i	0.248003	−	0.429554i	−0.714969	−	0.699157i	$-0.753559\pi$
$887$	195121.	−	337960.i	0.248003	−	0.429554i	0.962972	+	0.269603i	$0.0868924\pi$
$888$	−218211.	+	8250.93i	−0.276726	+	0.0104635i
$889$	307136.	+	531975.i	0.388622	+	0.673113i
$890$	82118.5	+	83680.2i	0.103672	+	0.105643i
$891$	−211872.	+	169509.i	−0.266882	+	0.213520i
$892$		−	63639.6i		−	0.0799830i
$893$	195972.	+	339433.i	0.245748	+	0.425648i
$894$	−111046.	+	4198.85i	−0.138940	+	0.00525358i
$895$	94128.7	−	24273.8i	0.117510	−	0.0303034i
$896$	−53311.6	−	30779.4i	−0.0664057	−	0.0383394i
$897$	−81003.0	−	128803.i	−0.100674	−	0.160081i
$898$	−852195.	+	492015.i	−1.05678	+	0.610134i
$899$		−	254296.i		−	0.314645i
$900$	−16683.8	−	293675.i	−0.0205973	−	0.362561i
$901$	−666450.			−0.820953
$902$	143960.	+	249347.i	0.176941	+	0.306472i
$903$	267153.	+	141060.i	0.327631	+	0.172993i
$904$	−598807.	+	1.03716e6i	−0.732740	+	1.26914i
$905$	−207964.	−	806440.i	−0.253917	−	0.984634i
$906$	−616635.	−	325591.i	−0.751228	−	0.396657i
$907$	−73779.7	+	42596.7i	−0.0896855	+	0.0517800i	−0.544172	−	0.838974i	$-0.683156\pi$
$907$	−73779.7	+	42596.7i	−0.0896855	+	0.0517800i	0.454487	+	0.890754i	$0.349823\pi$
$908$	−81227.4			−0.0985215
$909$	560636.	−	382883.i	0.678505	−	0.463381i
$910$	−125227.	+	122890.i	−0.151222	+	0.148400i
$911$	−1.40320e6	+	810136.i	−1.69076	+	0.976160i	−0.736853	+	0.676053i	$0.763689\pi$
$911$	−1.40320e6	+	810136.i	−1.69076	+	0.976160i	−0.953905	+	0.300107i	$0.902978\pi$
$912$	−564151.	+	354790.i	−0.678275	+	0.426561i
$913$	222768.	+	128615.i	0.267246	+	0.154294i
$914$	78484.0	+	45312.7i	0.0939482	+	0.0542410i
$915$	1.05396e6	+	995784.i	1.25887	+	1.18939i
$916$	−238221.	−	412611.i	−0.283916	−	0.491756i
$917$	−169801.			−0.201931
$918$	595537.	−	440614.i	0.706681	−	0.522845i
$919$	959118.			1.13564			0.567821	−	0.823152i	$-0.307787\pi$
$919$	959118.			1.13564			0.567821	+	0.823152i	$0.307787\pi$
$920$	314014.	+	87318.1i	0.371000	+	0.103164i
$921$	−1.11320e6	+	42092.0i	−1.31236	+	0.0496227i
$922$	777173.	+	448701.i	0.914231	+	0.527831i
$923$	306137.	−	530245.i	0.359346	−	0.622405i
$924$	44580.8	−	28036.5i	0.0522160	−	0.0328382i
$925$	−105333.	−	190649.i	−0.123107	−	0.222818i
$926$		−	485874.i		−	0.566633i
$927$	−971020.	−	466677.i	−1.12997	−	0.543071i
$928$		−	973599.i		−	1.13054i
$929$	998967.	−	576754.i	1.15750	−	0.668281i	0.206794	−	0.978385i	$-0.433697\pi$
$929$	998967.	−	576754.i	1.15750	−	0.668281i	0.950703	+	0.310104i	$0.100364\pi$
$930$	−126057.	+	37641.0i	−0.145748	+	0.0435206i
$931$	−517810.	+	896874.i	−0.597409	+	1.03474i
$932$	−147759.	+	255927.i	−0.170108	+	0.294635i
$933$	230045.	−	435681.i	0.264271	−	0.500501i
$934$	−453330.	−	785191.i	−0.519662	−	0.900081i
$935$	−230534.	−	234918.i	−0.263701	−	0.268716i
$936$	458891.	+	220545.i	0.523791	+	0.251736i
$937$			1.56265e6i			1.77984i	0.456114	+	0.889922i	$0.349241\pi$
$937$			1.56265e6i			1.77984i	−0.456114	+	0.889922i	$0.650759\pi$
$938$	186167.	+	322451.i	0.211591	+	0.366487i
$939$	−416375.	−	662078.i	−0.472230	−	0.750893i
$940$	24819.6	+	96245.0i	0.0280891	+	0.108924i
$941$	−1.07979e6	−	623416.i	−1.21944	−	0.704042i	−0.254640	−	0.967036i	$-0.581957\pi$
$941$	−1.07979e6	−	623416.i	−1.21944	−	0.704042i	−0.964798	+	0.262994i	$0.915290\pi$
$942$	1.06356e6	−	40215.2i	1.19856	−	0.0453199i
$943$	−353693.	+	204205.i	−0.397743	+	0.229637i
$944$			711566.i			0.798494i
$945$	−279561.	+	344695.i	−0.313050	+	0.385986i
$946$	181972.			0.203339
$947$	259582.	+	449609.i	0.289451	+	0.501343i	0.973679	−	0.227925i	$-0.0731941\pi$
$947$	259582.	+	449609.i	0.289451	+	0.501343i	−0.684228	+	0.729268i	$0.739861\pi$
$948$	−8325.51	−	220183.i	−0.00926391	−	0.245001i
$949$	−408519.	+	707575.i	−0.453607	+	0.785670i
$950$	−978744.	−	589935.i	−1.08448	−	0.653667i
$951$	231432.	−	145546.i	0.255896	−	0.160931i
$952$	−467419.	+	269864.i	−0.515742	+	0.297764i
$953$	270328.			0.297650			0.148825	−	0.988864i	$-0.452451\pi$
$953$	270328.			0.297650			0.148825	+	0.988864i	$0.452451\pi$
$954$	305273.	+	446996.i	0.335422	+	0.491141i
$955$	637331.	+	649451.i	0.698808	+	0.712098i
$956$	170207.	−	98269.3i	0.186236	−	0.107523i
$957$	−456949.	−	241274.i	−0.498935	−	0.263443i
$958$	18253.0	+	10538.4i	0.0198886	+	0.0114827i
$959$	−196986.	−	113730.i	−0.214190	−	0.123663i
$960$	−928555.	+	277269.i	−1.00755	+	0.300856i
$961$	444985.	+	770737.i	0.481835	+	0.834563i
$962$	100436.			0.108527
$963$	−1.28812e6	+	97551.5i	−1.38900	+	0.105192i
$964$	82846.1			0.0891493
$965$	−316552.	+	1.13839e6i	−0.339931	+	1.22246i
$966$	−69743.6	−	110899.i	−0.0747395	−	0.118843i
$967$	352654.	+	203605.i	0.377135	+	0.217739i	0.676571	−	0.736378i	$-0.263465\pi$
$967$	352654.	+	203605.i	0.377135	+	0.217739i	−0.299436	+	0.954116i	$0.596799\pi$
$968$	−450126.	+	779641.i	−0.480378	+	0.832039i
$969$	62010.6	+	1.63998e6i	0.0660418	+	1.74659i
$970$	47356.0	−	170302.i	0.0503305	−	0.180999i
$971$			526829.i			0.558768i	0.960179	+	0.279384i	$0.0901302\pi$
$971$			526829.i			0.558768i	−0.960179	+	0.279384i	$0.909870\pi$
$972$	324064.	+	112679.i	0.343003	+	0.119264i
$973$		−	309543.i		−	0.326961i
$974$	710393.	−	410146.i	0.748826	−	0.432335i
$975$	9625.96	+	507753.i	0.0101259	+	0.534126i
$976$	416543.	−	721474.i	0.437281	−	0.757393i
$977$	−535395.	+	927331.i	−0.560900	+	0.971507i	0.436518	+	0.899695i	$0.356211\pi$
$977$	−535395.	+	927331.i	−0.560900	+	0.971507i	−0.997418	+	0.0718115i	$0.977122\pi$
$978$	380888.	+	605650.i	0.398217	+	0.633204i
$979$	30379.0	+	52617.9i	0.0316962	+	0.0548995i
$980$	−187445.	+	183947.i	−0.195174	+	0.191531i
$981$	726981.	−	55055.6i	0.755414	−	0.0572089i
$982$		−	221195.i		−	0.229378i
$983$	−539346.	−	934175.i	−0.558163	−	0.966766i	−0.997650	−	0.0685171i	$-0.978173\pi$
$983$	−539346.	−	934175.i	−0.558163	−	0.966766i	0.439487	−	0.898249i	$-0.355160\pi$
$984$	638091.	−	1.20848e6i	0.659011	−	1.24810i
$985$	−47792.9	−	185331.i	−0.0492596	−	0.191018i
$986$	1.22180e6	+	705407.i	1.25674	+	0.725581i
$987$	70022.1	−	132615.i	0.0718788	−	0.136131i
$988$	−260223.	+	150240.i	−0.266583	+	0.153912i
$989$			258123.i			0.263897i
$990$	−51964.4	+	262228.i	−0.0530195	+	0.267552i
$991$	151851.			0.154621			0.0773107	−	0.997007i	$-0.475367\pi$
$991$	151851.			0.154621			0.0773107	+	0.997007i	$0.475367\pi$
$992$	−64226.4	−	111243.i	−0.0652665	−	0.113045i
$993$	566977.	−	356567.i	0.574999	−	0.361612i
$994$	263584.	−	456541.i	0.266776	−	0.462070i
$995$	66528.5	+	257983.i	0.0671988	+	0.260583i
$996$	−12289.8	−	325026.i	−0.0123887	−	0.327642i
$997$	1.64875e6	−	951904.i	1.65868	−	0.957641i	0.685359	−	0.728205i	$-0.259645\pi$
$997$	1.64875e6	−	951904.i	1.65868	−	0.957641i	0.973324	−	0.229435i	$-0.0736880\pi$
$998$	−237299.			−0.238251
$999$	252425.	−	28743.5i	0.252930	−	0.0288011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.15	yes	44
3.2	odd	2		135.5.h.a.44.8		44
5.4	even	2	inner	45.5.h.a.14.8	✓	44
9.2	odd	6	inner	45.5.h.a.29.8	yes	44
9.4	even	3		405.5.d.a.404.16		44
9.5	odd	6		405.5.d.a.404.30		44
9.7	even	3		135.5.h.a.89.15		44
15.14	odd	2		135.5.h.a.44.15		44
45.4	even	6		405.5.d.a.404.29		44
45.14	odd	6		405.5.d.a.404.15		44
45.29	odd	6	inner	45.5.h.a.29.15	yes	44
45.34	even	6		135.5.h.a.89.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.8	✓	44	5.4	even	2	inner
45.5.h.a.14.15	yes	44	1.1	even	1	trivial
45.5.h.a.29.8	yes	44	9.2	odd	6	inner
45.5.h.a.29.15	yes	44	45.29	odd	6	inner
135.5.h.a.44.8		44	3.2	odd	2
135.5.h.a.44.15		44	15.14	odd	2
135.5.h.a.89.8		44	45.34	even	6
135.5.h.a.89.15		44	9.7	even	3
405.5.d.a.404.15		44	45.14	odd	6
405.5.d.a.404.16		44	9.4	even	3
405.5.d.a.404.29		44	45.4	even	6
405.5.d.a.404.30		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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59606 + 2.76446i) q^{2} +(0.340063 + 8.99357i) q^{3} +(2.90517 - 5.03190i) q^{4} +(6.24274 + 24.2080i) q^{5} +(-24.3196 + 15.2944i) q^{6} +(-21.0893 + 12.1759i) q^{7} +69.6213 q^{8} +(-80.7687 + 6.11676i) q^{9} +(-56.9583 + 55.8953i) q^{10} +(-35.8153 + 20.6780i) q^{11} +(46.2427 + 24.4167i) q^{12} +(-78.1878 - 45.1417i) q^{13} +(-67.3197 - 38.8671i) q^{14} +(-215.594 + 64.3768i) q^{15} +(64.6373 + 111.955i) q^{16} +318.348 q^{17} +(-145.821 - 213.519i) q^{18} +572.803 q^{19} +(139.949 + 38.9155i) q^{20} +(-116.677 - 185.528i) q^{21} +(-114.327 - 66.0066i) q^{22} +(93.6290 - 162.170i) q^{23} +(23.6756 + 626.144i) q^{24} +(-547.056 + 302.249i) q^{25} -288.196i q^{26} +(-82.4780 - 724.319i) q^{27} +141.492i q^{28} +(1202.32 - 694.158i) q^{29} +(-522.068 - 493.251i) q^{30} +(91.5845 - 158.629i) q^{31} +(350.640 - 607.327i) q^{32} +(-198.148 - 315.075i) q^{33} +(508.103 + 880.059i) q^{34} +(-426.410 - 434.520i) q^{35} +(-203.868 + 424.190i) q^{36} +348.499i q^{37} +(914.230 + 1583.49i) q^{38} +(379.397 - 718.539i) q^{39} +(434.628 + 1685.39i) q^{40} +(-1888.80 - 1090.50i) q^{41} +(326.661 - 618.662i) q^{42} +(-1193.76 + 689.217i) q^{43} +240.292i q^{44} +(-652.293 - 1917.07i) q^{45} +597.751 q^{46} +(342.127 + 592.582i) q^{47} +(-984.895 + 619.392i) q^{48} +(-903.994 + 1565.76i) q^{49} +(-1708.69 - 1029.91i) q^{50} +(108.258 + 2863.08i) q^{51} +(-454.297 + 262.289i) q^{52} -2093.47 q^{53} +(1870.71 - 1384.07i) q^{54} +(-724.158 - 737.930i) q^{55} +(-1468.27 + 847.704i) q^{56} +(194.789 + 5151.55i) q^{57} +(3837.95 + 2215.84i) q^{58} +(4766.87 + 2752.15i) q^{59} +(-302.398 + 1271.87i) q^{60} +(-3222.16 - 5580.94i) q^{61} +584.698 q^{62} +(1628.88 - 1112.43i) q^{63} +4306.97 q^{64} +(604.686 - 2174.58i) q^{65} +(554.757 - 1050.65i) q^{66} +(-4148.13 - 2394.92i) q^{67} +(924.853 - 1601.89i) q^{68} +(1490.33 + 786.911i) q^{69} +(520.635 - 1872.31i) q^{70} +6781.69i q^{71} +(-5623.22 + 425.857i) q^{72} -9049.69i q^{73} +(-963.412 + 556.226i) q^{74} +(-2904.33 - 4817.21i) q^{75} +(1664.09 - 2882.29i) q^{76} +(503.546 - 872.168i) q^{77} +(2591.91 - 98.0048i) q^{78} +(-2106.79 - 3649.06i) q^{79} +(-2306.70 + 2263.65i) q^{80} +(6486.17 - 988.086i) q^{81} -6962.02i q^{82} +(-3109.96 - 5386.60i) q^{83} +(-1272.52 + 48.1163i) q^{84} +(1987.36 + 7706.56i) q^{85} +(-3810.63 - 2200.07i) q^{86} +(6651.82 + 10577.1i) q^{87} +(-2493.51 + 1439.63i) q^{88} -1469.15i q^{89} +(4258.55 - 4862.99i) q^{90} +2198.57 q^{91} +(-544.016 - 942.263i) q^{92} +(1457.79 + 769.728i) q^{93} +(-1092.11 + 1891.59i) q^{94} +(3575.86 + 13866.4i) q^{95} +(5581.28 + 2946.98i) q^{96} +(-1918.24 + 1107.50i) q^{97} -5771.32 q^{98} +(2766.27 - 1889.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

L-functions

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