LMFDB - Embedded newform 45.5.h.a.14.8

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			14.8
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59606 - 2.76446i) q^{2} +(-0.340063 - 8.99357i) q^{3} +(2.90517 - 5.03190i) q^{4} +(24.0861 - 6.69764i) 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} +(-68.4265 - 214.343i) q^{15} +(64.6373 + 111.955i) q^{16} -318.348 q^{17} +(145.821 + 213.519i) q^{18} +572.803 q^{19} +(36.2724 - 140.657i) 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} +(535.283 - 322.640i) q^{25} -288.196i q^{26} +(82.4780 + 724.319i) q^{27} -141.492i q^{28} +(1202.32 - 694.158i) q^{29} +(-483.329 + 531.267i) 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} +(-1676.91 + 466.298i) q^{40} +(-1888.80 - 1090.50i) q^{41} +(-326.661 + 618.662i) q^{42} +(1193.76 - 689.217i) q^{43} +240.292i q^{44} +(-1904.44 + 688.289i) q^{45} +597.751 q^{46} +(-342.127 - 592.582i) q^{47} +(984.895 - 619.392i) q^{48} +(-903.994 + 1565.76i) q^{49} +(-1746.27 - 964.816i) 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} +(-1277.34 - 278.387i) q^{60} +(-3222.16 - 5580.94i) q^{61} -584.698 q^{62} +(-1628.88 + 1112.43i) q^{63} +4306.97 q^{64} +(2185.58 + 563.616i) 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} +(-1881.79 - 485.274i) q^{70} +6781.69i q^{71} +(5623.22 - 425.857i) q^{72} +9049.69i q^{73} +(-963.412 + 556.226i) q^{74} +(-3083.72 - 4704.39i) 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} +(-7667.76 + 2132.18i) q^{85} +(-3810.63 - 2200.07i) q^{86} +(-6651.82 - 10577.1i) q^{87} +(2493.51 - 1439.63i) q^{88} -1469.15i q^{89} +(4942.35 + 4166.19i) q^{90} +2198.57 q^{91} +(544.016 + 942.263i) q^{92} +(-1457.79 - 769.728i) q^{93} +(-1092.11 + 1891.59i) q^{94} +(13796.6 - 3836.43i) 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	0.594589	−	0.804030i	$-0.297315\pi$
$2$	−1.59606	−	2.76446i	−0.399016	−	0.691115i	−0.993605	+	0.112914i	$0.963981\pi$
$3$	−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
$5$	24.0861	−	6.69764i	0.963445	−	0.267906i
$5$	24.0861	−	6.69764i	0.963445	−	0.267906i
$6$	−24.3196	+	15.2944i	−0.675545	+	0.424844i
$7$	21.0893	−	12.1759i	0.430394	−	0.248488i	−0.269120	−	0.963107i	$-0.586733\pi$
$7$	21.0893	−	12.1759i	0.430394	−	0.248488i	0.699515	+	0.714618i	$0.253400\pi$
$8$	−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	0.713158	−	0.701004i	$-0.247264\pi$
$13$	78.1878	+	45.1417i	0.462650	+	0.267111i	−0.250508	+	0.968115i	$0.580598\pi$
$14$	−67.3197	−	38.8671i	−0.343468	−	0.198301i
$15$	−68.4265	−	214.343i	−0.304118	−	0.952634i
$16$	64.6373	+	111.955i	0.252489	+	0.437325i
$17$	−318.348			−1.10155			−0.550774	−	0.834654i	$-0.685667\pi$
$17$	−318.348			−1.10155			−0.550774	+	0.834654i	$0.685667\pi$
$18$	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	$0.208332\pi$
$20$	36.2724	−	140.657i	0.0906811	−	0.351642i
$21$	−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	−0.940849	−	0.338826i	$-0.889970\pi$
$23$	−93.6290	+	162.170i	−0.176992	+	0.306560i	0.763857	+	0.645386i	$0.223303\pi$
$24$	23.6756	+	626.144i	0.0411035	+	1.08706i
$25$	535.283	−	322.640i	0.856453	−	0.516225i
$26$		−	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	$0.0242852\pi$
$30$	−483.329	+	531.267i	−0.537033	+	0.590297i
$31$	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	$-0.959375\pi$
$37$		−	348.499i		−	0.254565i	0.991867	−	0.127282i	$-0.0406254\pi$
$38$	−914.230	−	1583.49i	−0.633123	−	1.09660i
$39$	379.397	−	718.539i	0.249439	−	0.472412i
$40$	−1676.91	+	466.298i	−1.04807	+	0.291437i
$41$	−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	−0.141154	−	0.989988i	$-0.545081\pi$
$43$	1193.76	−	689.217i	0.645624	−	0.372751i	0.786778	+	0.617236i	$0.211748\pi$
$44$			240.292i			0.124118i
$45$	−1904.44	+	688.289i	−0.940463	+	0.339896i
$46$	597.751			0.282491
$47$	−342.127	−	592.582i	−0.154879	−	0.268258i	0.778136	−	0.628096i	$-0.216165\pi$
$47$	−342.127	−	592.582i	−0.154879	−	0.268258i	−0.933015	+	0.359838i	$0.882832\pi$
$48$	984.895	−	619.392i	0.427472	−	0.268833i
$49$	−903.994	+	1565.76i	−0.376507	+	0.652130i
$50$	−1746.27	−	964.816i	−0.698509	−	0.385926i
$51$	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	$-0.378454\pi$
$53$	2093.47			0.745271			0.372636	+	0.927978i	$0.378454\pi$
$54$	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	$0.376425\pi$
$60$	−1277.34	−	278.387i	−0.354817	−	0.0773296i
$61$	−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
$65$	2185.58	+	563.616i	0.517298	+	0.133400i
$66$	554.757	−	1050.65i	0.127355	−	0.241197i
$67$	4148.13	+	2394.92i	0.924065	+	0.533509i	0.884930	−	0.465725i	$-0.154206\pi$
$67$	4148.13	+	2394.92i	0.924065	+	0.533509i	0.0391353	+	0.999234i	$0.487540\pi$
$68$	−924.853	+	1601.89i	−0.200012	+	0.346430i
$69$	1490.33	+	786.911i	0.313029	+	0.165283i
$70$	−1881.79	−	485.274i	−0.384039	−	0.0990355i
$71$			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	$0.322854\pi$
$73$			9049.69i			1.69820i	−0.528235	+	0.849098i	$0.677146\pi$
$74$	−963.412	+	556.226i	−0.175934	+	0.101575i
$75$	−3083.72	−	4704.39i	−0.548217	−	0.836336i
$76$	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	0.998476	−	0.0551944i	$-0.0175779\pi$
$83$	3109.96	+	5386.60i	0.451438	+	0.781914i	−0.547038	+	0.837108i	$0.684245\pi$
$84$	−1272.52	+	48.1163i	−0.180346	+	0.00681921i
$85$	−7667.76	+	2132.18i	−1.06128	+	0.295111i
$86$	−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	$-0.0295617\pi$
$90$	4942.35	+	4166.19i	0.610167	+	0.514345i
$91$	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
$95$	13796.6	−	3836.43i	1.52871	−	0.425089i
$96$	5581.28	+	2946.98i	0.605607	+	0.319768i
$97$	1918.24	−	1107.50i	0.203873	−	0.117706i	−0.394588	−	0.918858i	$-0.629113\pi$
$97$	1918.24	−	1107.50i	0.203873	−	0.117706i	0.598461	+	0.801152i	$0.295779\pi$
$98$	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	−0.153299	−	0.988180i	$-0.548990\pi$
$103$	−11518.6	−	6650.26i	−1.08574	−	0.626851i	−0.932438	+	0.361329i	$0.882323\pi$
$104$	−5443.54	−	3142.83i	−0.503286	−	0.290572i
$105$	−4052.89	−	3687.19i	−0.367609	−	0.334439i
$106$	−3341.30	−	5787.31i	−0.297375	−	0.515069i
$107$	−15948.2			−1.39298			−0.696490	−	0.717566i	$-0.745256\pi$
$107$	−15948.2			−1.39298			−0.696490	+	0.717566i	$0.745256\pi$
$108$	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	$0.623659\pi$
$110$	3195.78	+	824.124i	0.264114	+	0.0681095i
$111$	−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	$-0.598090\pi$
$113$	8600.91	−	14897.2i	0.673578	−	1.16667i	0.976882	−	0.213777i	$-0.0685766\pi$
$114$	−13930.4	+	8760.68i	−1.07190	+	0.674106i
$115$	−1169.00	+	4533.14i	−0.0883934	+	0.342771i
$116$		−	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
$120$	4763.94	+	14922.8i	0.330829	+	1.03631i
$121$	−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	$0.285786\pi$
$127$			25224.9i			1.56395i	−0.623313	+	0.781973i	$0.714214\pi$
$128$	−1263.95	−	2189.22i	−0.0771452	−	0.133619i
$129$	−6604.48	−	10501.8i	−0.396880	−	0.631079i
$130$	−1930.23	−	6941.53i	−0.114215	−	0.410741i
$131$	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
$135$	6837.80	+	16893.6i	0.375188	+	0.926949i
$136$	22163.8			1.19830
$137$	−4670.29	−	8089.17i	−0.248830	−	0.430986i	0.714372	−	0.699767i	$-0.246713\pi$
$137$	−4670.29	−	8089.17i	−0.248830	−	0.430986i	−0.963201	+	0.268781i	$0.913379\pi$
$138$	−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	$0.273361\pi$
$140$	−947.665	−	3408.01i	−0.0483503	−	0.173878i
$141$	−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	$0.638902\pi$
$150$	−8083.30	+	16033.3i	−0.359258	+	0.712592i
$151$	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
$155$	1143.48	−	4434.16i	0.0475953	−	0.184564i
$156$	−2513.40	−	3996.56i	−0.103279	−	0.164224i
$157$	32083.5	+	18523.4i	1.30161	+	0.751488i	0.980681	−	0.195614i	$-0.0626699\pi$
$157$	32083.5	+	18523.4i	1.30161	+	0.751488i	0.320934	+	0.947102i	$0.396003\pi$
$158$	−6725.12	+	11648.3i	−0.269393	+	0.466602i
$159$	−711.911	−	18827.8i	−0.0281599	−	0.744739i
$160$	−4377.91	+	16976.6i	−0.171012	+	0.663149i
$161$			4560.08i			0.175922i
$162$	−13083.9	−	16353.7i	−0.498547	−	0.623141i
$163$			24903.7i			0.937323i	0.883378	+	0.468662i	$0.155264\pi$
$163$			24903.7i			0.937323i	−0.883378	+	0.468662i	$0.844736\pi$
$164$	−10974.6	+	6336.17i	−0.408037	+	0.235580i
$165$	6882.88	+	6261.82i	0.252815	+	0.230003i
$166$	9927.37	−	17194.7i	0.360262	−	0.623992i
$167$	−7604.05	+	13170.6i	−0.272654	+	0.472251i	−0.969541	−	0.244931i	$-0.921235\pi$
$167$	−7604.05	+	13170.6i	−0.272654	+	0.472251i	0.696886	+	0.717181i	$0.254568\pi$
$168$	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	0.838069	−	0.545564i	$-0.183685\pi$
$173$	−1599.34	−	2770.14i	−0.0534379	−	0.0925572i	−0.891507	+	0.453007i	$0.850351\pi$
$174$	−18623.2	+	35270.4i	−0.615113	+	1.16496i
$175$	7360.32	−	13321.8i	0.240337	−	0.434999i
$176$	−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	$-0.0193261\pi$
$180$	−2069.31	+	11582.5i	−0.0638677	+	0.357486i
$181$	−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
$185$	−2334.12	−	8393.99i	−0.0681993	−	0.245259i
$186$	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	−0.162934	−	0.986637i	$-0.552096\pi$
$193$	−40931.2	−	23631.6i	−1.09885	−	0.634424i	−0.935920	+	0.352213i	$0.885429\pi$
$194$	−6123.28	−	3535.28i	−0.162697	−	0.0939334i
$195$	4325.69	−	19847.9i	0.113759	−	0.521969i
$196$	5252.51	+	9097.61i	0.136727	+	0.236818i
$197$	7655.76			0.197268			0.0986338	−	0.995124i	$-0.468553\pi$
$197$	7655.76			0.197268			0.0986338	+	0.995124i	$0.468553\pi$
$198$	−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	$0.457040\pi$
$200$	−37267.1	+	22462.7i	−0.931678	+	0.561566i
$201$	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
$205$	−52797.6	−	13615.4i	−1.25634	−	0.323983i
$206$			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
$210$	−3724.42	+	17089.0i	−0.0844540	+	0.387507i
$211$	−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
$220$	1609.39	+	5787.70i	0.0332518	+	0.119581i
$221$	−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	−0.592330	−	0.805695i	$-0.701792\pi$
$223$	−9485.42	+	5476.41i	−0.190742	+	0.110125i	0.401588	+	0.915821i	$0.368458\pi$
$224$			17077.5i			0.340352i
$225$	−41260.6	+	29333.4i	−0.815025	+	0.579426i
$226$	−54910.4			−1.07507
$227$	6989.91	+	12106.9i	0.135650	+	0.234953i	0.925846	−	0.377902i	$-0.123354\pi$
$227$	6989.91	+	12106.9i	0.135650	+	0.234953i	−0.790196	+	0.612855i	$0.790021\pi$
$228$	−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	$-0.119043\pi$
$230$	14397.5	−	4003.52i	0.272165	−	0.0756809i
$231$	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	$-0.344821\pi$
$233$	50860.9			0.936854			0.468427	+	0.883502i	$0.344821\pi$
$234$	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	$0.570985\pi$
$240$	19573.9	−	21515.2i	0.339824	−	0.373528i
$241$	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
$245$	−11286.8	+	43767.8i	−0.188035	+	0.729159i
$246$	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
$250$	−48522.9	−	11542.8i	−0.776367	−	0.184684i
$251$			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
$255$	21783.4	+	68235.5i	0.335001	+	1.04937i
$256$	30421.1	−	52690.8i	0.464189	−	0.803998i
$257$	−42251.7	+	73182.1i	−0.639702	+	1.10800i	0.345796	+	0.938310i	$0.387609\pi$
$257$	−42251.7	+	73182.1i	−0.639702	+	1.10800i	−0.985498	+	0.169687i	$0.945724\pi$
$258$	−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	0.658679	−	0.752424i	$-0.271115\pi$
$263$	−22291.7	−	38610.3i	−0.322278	−	0.558202i	−0.980958	+	0.194221i	$0.937782\pi$
$264$	−13795.3	−	21936.0i	−0.197936	−	0.314738i
$265$	50423.5	−	14021.3i	0.718028	−	0.199662i
$266$	−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	$0.806322\pi$
$270$	35788.3	−	45866.2i	0.490923	−	0.629165i
$271$	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
$275$	−12499.8	+	22624.0i	−0.165286	+	0.299161i
$276$	8289.31	−	5213.08i	0.108818	−	0.0684346i
$277$	−46521.1	+	26859.0i	−0.606304	+	0.350050i	−0.771517	−	0.636208i	$-0.780502\pi$
$277$	−46521.1	+	26859.0i	−0.606304	+	0.350050i	0.165214	+	0.986258i	$0.447169\pi$
$278$	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	0.102943	−	0.994687i	$-0.467174\pi$
$283$	−56623.7	−	32691.7i	−0.707010	−	0.408192i	−0.809953	+	0.586495i	$0.800507\pi$
$284$	34124.8	+	19701.9i	0.423090	+	0.244271i
$285$	−39194.9	−	122776.i	−0.482547	−	1.51156i
$286$	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
$290$	−107282.	−	27665.8i	−1.27565	−	0.328963i
$291$	−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	−0.950374	−	0.311111i	$-0.899299\pi$
$293$	−17664.0	+	30595.0i	−0.205757	+	0.356382i	0.744617	+	0.667492i	$0.232632\pi$
$294$	−1962.61	−	51904.8i	−0.0227060	−	0.600500i
$295$	133248.	+	34361.9i	1.53115	+	0.394851i
$296$			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
$300$	−32630.8	+	1849.92i	−0.362564	+	0.0205547i
$301$	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	$-0.771973\pi$
$307$		−	123777.i		−	1.31330i	0.754196	−	0.656650i	$-0.228027\pi$
$308$	2925.77	+	5067.59i	0.0308418	+	0.0534195i
$309$	−55892.6	+	105855.i	−0.585379	+	1.10865i
$310$	−14083.1	+	3916.10i	−0.146547	+	0.0407502i
$311$	−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	−0.0640324	−	0.997948i	$-0.520396\pi$
$313$	75259.7	−	43451.2i	0.768199	−	0.443520i	0.832232	+	0.554428i	$0.187063\pi$
$314$		−	118258.i		−	1.19942i
$315$	−31782.7	+	37703.8i	−0.320310	+	0.379983i
$316$	−24482.3			−0.245176
$317$	15188.6	+	26307.4i	0.151147	+	0.261794i	0.931649	−	0.363359i	$-0.118370\pi$
$317$	15188.6	+	26307.4i	0.151147	+	0.261794i	−0.780503	+	0.625153i	$0.785037\pi$
$318$	−50912.3	+	32018.3i	−0.503464	+	0.316624i
$319$	−28707.5	+	49722.9i	−0.282107	+	0.488624i
$320$	103738.	−	28846.5i	1.01307	−	0.281704i
$321$	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
$330$	6325.06	−	29021.7i	0.0580813	−	0.266499i
$331$	−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
$335$	115953.	+	29901.8i	1.03322	+	0.266445i
$336$	13229.1	−	25054.6i	0.117180	−	0.221926i
$337$	−181315.	−	104682.i	−1.59652	−	0.921752i	−0.992151	−	0.125049i	$-0.960091\pi$
$337$	−181315.	−	104682.i	−1.59652	−	0.921752i	−0.604371	−	0.796703i	$-0.706576\pi$
$338$	−32575.5	+	56422.4i	−0.285139	+	0.493876i
$339$	−136904.	−	72287.0i	−1.19129	−	0.629014i
$340$	−11547.2	+	44777.7i	−0.0998896	+	0.387351i
$341$			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
$345$	41166.7	+	8971.96i	0.345866	+	0.0753788i
$346$	−5105.30	+	8842.64i	−0.0426451	+	0.0738635i
$347$	92398.9	−	160040.i	0.767376	−	1.32913i	−0.171606	−	0.985166i	$-0.554895\pi$
$347$	92398.9	−	160040.i	0.767376	−	1.32913i	0.938981	−	0.343968i	$-0.111771\pi$
$348$	−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	0.923939	−	0.382539i	$-0.124950\pi$
$353$	16284.0	+	28204.8i	0.130681	+	0.226346i	−0.793258	+	0.608885i	$0.791617\pi$
$354$	−158021.	+	5975.05i	−1.26098	+	0.0476799i
$355$	45421.3	+	163345.i	0.360415	+	1.29613i
$356$	−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	$-0.340766\pi$
$360$	132589.	−	47919.6i	1.02307	−	0.369750i
$361$	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
$365$	60611.5	+	217972.i	0.454956	+	1.63612i
$366$	163719.	+	86445.5i	1.22218	+	0.645327i
$367$	117772.	−	67995.5i	0.874397	−	0.504834i	0.00559037	−	0.999984i	$-0.498221\pi$
$367$	117772.	−	67995.5i	0.874397	−	0.504834i	0.868807	+	0.495151i	$0.164887\pi$
$368$	−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	−0.140027	−	0.990148i	$-0.544719\pi$
$373$	−148525.	−	85750.9i	−1.06753	−	0.616341i	−0.927507	+	0.373807i	$0.878052\pi$
$374$	−36395.7	−	21013.0i	−0.260199	−	0.150226i
$375$	−105783.	−	92656.9i	−0.752236	−	0.658894i
$376$	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	$0.570771\pi$
$380$	20777.0	−	80568.6i	0.143885	−	0.557955i
$381$	226862.	−	8578.04i	1.56283	−	0.0590933i
$382$	−100619.	−	58092.4i	−0.689530	−	0.398100i
$383$	46631.9	−	80768.8i	0.317896	−	0.550612i	−0.662153	−	0.749369i	$-0.730357\pi$
$383$	46631.9	−	80768.8i	0.317896	−	0.550612i	0.980049	+	0.198757i	$0.0636903\pi$
$384$	−19259.1	+	12111.9i	−0.130609	+	0.0821389i
$385$	−6287.02	+	24379.7i	−0.0424154	+	0.164478i
$386$			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	$0.421861\pi$
$390$	−61772.8	+	19720.3i	−0.406133	+	0.129653i
$391$	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	$-0.964374\pi$
$397$		−	35206.6i		−	0.223379i	0.993743	−	0.111690i	$-0.0356263\pi$
$398$	−17009.1	−	29460.7i	−0.107378	−	0.185985i
$399$	−66832.8	−	106271.i	−0.419802	−	0.667527i
$400$	70720.5	+	39073.1i	0.442003	+	0.244207i
$401$	−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
$405$	149609.	−	67241.2i	0.912110	−	0.409945i
$406$	−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	$0.331141\pi$
$410$	46629.1	+	167688.i	0.277389	+	0.997549i
$411$	−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	$0.628005\pi$
$420$	−30327.9	+	9681.83i	−0.171927	+	0.0548857i
$421$	−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
$425$	−170406.	+	102712.i	−0.943425	+	0.568646i
$426$	−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
$430$	−106519.	−	27468.9i	−0.576087	−	0.148561i
$431$			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	$0.229103\pi$
$433$			247184.i			1.31839i	−0.751971	+	0.659196i	$0.770897\pi$
$434$	−12330.9	+	7119.24i	−0.0654659	+	0.0377967i
$435$	−231058.	−	210209.i	−1.22108	−	1.11090i
$436$	−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	$-0.975810\pi$
$443$	−110745.	−	191816.i	−0.564308	−	0.977410i	0.432805	−	0.901487i	$-0.357524\pi$
$444$	−8509.19	+	16115.5i	−0.0431641	+	0.0817483i
$445$	−9839.82	−	35386.1i	−0.0496898	−	0.178695i
$446$	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	$0.722961\pi$
$450$	146946.	+	67245.4i	0.725658	+	0.332076i
$451$	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
$455$	52955.0	−	14725.2i	0.255791	−	0.0711278i
$456$	13561.5	+	358658.i	0.0652195	+	1.72485i
$457$	−24586.7	+	14195.2i	−0.117725	+	0.0679685i	−0.557706	−	0.830038i	$-0.688318\pi$
$457$	−24586.7	+	14195.2i	−0.117725	+	0.0679685i	0.439981	+	0.898007i	$0.354985\pi$
$458$	−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	0.774885	−	0.632102i	$-0.217808\pi$
$463$	131818.	+	76105.1i	0.614912	+	0.355019i	−0.159974	+	0.987121i	$0.551141\pi$
$464$	155429.	+	89737.0i	0.721932	+	0.416808i
$465$	−40267.8	−	8776.05i	−0.186231	−	0.0405876i
$466$	−81177.2	−	140603.i	−0.373820	−	0.647474i
$467$	284030.			1.30236			0.651180	−	0.758923i	$-0.274274\pi$
$467$	284030.			1.30236			0.651180	+	0.758923i	$0.274274\pi$
$468$	−35088.7	+	23963.6i	−0.160205	+	0.109411i
$469$	116642.			0.530283
$470$	−13635.6	+	52875.8i	−0.0617273	+	0.239365i
$471$	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
$475$	306612.	−	184809.i	1.35895	−	0.819100i
$476$			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	$0.328753\pi$
$480$	154169.	+	33600.0i	0.669137	+	0.145833i
$481$	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	$0.182239\pi$
$487$			256973.i			1.08350i	−0.840538	+	0.541752i	$0.817761\pi$
$488$	224331.	+	388553.i	0.941997	+	1.63159i
$489$	223974.	−	8468.84i	0.936654	−	0.0354165i
$490$	139009.	−	38654.2i	0.578962	−	0.160992i
$491$	−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
$495$	53975.6	−	64031.1i	0.220286	−	0.261325i
$496$	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	$0.214360\pi$
$500$	−25965.5	−	86994.2i	−0.103862	−	0.347977i
$501$	121037.	+	63908.7i	0.482216	+	0.254616i
$502$	63355.3	−	36578.2i	0.251406	−	0.145149i
$503$	253194.			1.00073			0.500366	−	0.865814i	$-0.333199\pi$
$503$	253194.			1.00073			0.500366	+	0.865814i	$0.333199\pi$
$504$	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	$0.713882\pi$
$510$	153867.	−	169127.i	0.591567	−	0.650240i
$511$	110188.	+	190852.i	0.421982	+	0.730894i
$512$	−234662.			−0.895165
$513$	47243.7	+	414892.i	0.179518	+	1.57652i
$514$	269745.			1.02100
$515$	−321979.	−	83031.7i	−1.21399	−	0.313061i
$516$	−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
$520$	−152163.	−	39239.7i	−0.562734	−	0.145117i
$521$		−	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	$-0.930536\pi$
$523$		−	118438.i		−	0.432999i	0.976283	−	0.216499i	$-0.0694639\pi$
$524$	35086.6	−	20257.3i	0.127785	−	0.0737765i
$525$	−122314.	−	61665.3i	−0.443769	−	0.223729i
$526$	−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
$535$	−384131.	+	106815.i	−1.34206	+	0.373187i
$536$	−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
$540$	104872.	+	14671.7i	0.359644	+	0.0503146i
$541$	−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
$545$	−216794.	+	60283.9i	−0.729884	+	0.202959i
$546$	−53468.4	+	33625.8i	−0.179354	+	0.112794i
$547$	122480.	−	70713.6i	0.409344	−	0.236335i	−0.281164	−	0.959660i	$-0.590720\pi$
$547$	122480.	−	70713.6i	0.409344	−	0.236335i	0.690508	+	0.723325i	$0.257387\pi$
$548$	−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
$555$	−74698.2	+	23846.6i	−0.242507	+	0.0774176i
$556$	36928.4	+	63961.9i	0.119457	+	0.206905i
$557$	27193.3			0.0876499			0.0438249	−	0.999039i	$-0.486046\pi$
$557$	27193.3			0.0876499			0.0438249	+	0.999039i	$0.486046\pi$
$558$	47225.3	−	3576.46i	0.151672	−	0.0114864i
$559$	124450.			0.398264
$560$	76208.7	+	19652.6i	0.243012	+	0.0626678i
$561$	−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	$-0.658683\pi$
$563$	165319.	−	286341.i	0.521562	−	0.903372i	0.999685	−	0.0250792i	$-0.00798379\pi$
$564$	1352.00	+	35756.2i	0.00425030	+	0.112407i
$565$	107387.	−	416422.i	0.336398	−	1.30448i
$566$			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	$0.362779\pi$
$570$	−276853.	+	304311.i	−0.852116	+	0.936631i
$571$	−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	$-0.775199\pi$
$577$		−	432123.i		−	1.29794i	0.760812	−	0.648972i	$-0.224801\pi$
$578$	−28448.5	−	49274.2i	−0.0851536	−	0.147490i
$579$	−198614.	+	376154.i	−0.592451	+	1.12204i
$580$	−54027.1	−	194293.i	−0.160604	−	0.577565i
$581$	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
$585$	−179974.	−	32153.9i	−0.525895	−	0.0939553i
$586$	112772.			0.328401
$587$	−265683.	−	460176.i	−0.771059	−	1.33551i	−0.936983	−	0.349374i	$-0.886394\pi$
$587$	−265683.	−	460176.i	−0.771059	−	1.33551i	0.165925	−	0.986138i	$-0.446939\pi$
$588$	80033.9	−	50332.6i	0.231483	−	0.145578i
$589$	52459.9	−	90863.2i	0.151216	−	0.261913i
$590$	−117680.	−	423203.i	−0.338065	−	1.21575i
$591$	−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	$-0.664099\pi$
$593$	−346725.			−0.985998			−0.492999	+	0.870030i	$0.664099\pi$
$594$	−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	$0.556608\pi$
$600$	214693.	+	327526.i	0.596368	+	0.909794i
$601$	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
$605$	−80722.9	+	313026.i	−0.220539	+	0.855205i
$606$	112432.	−	212934.i	0.306157	−	0.579830i
$607$	614804.	+	354957.i	1.66863	+	0.963382i	0.968379	+	0.249482i	$0.0802605\pi$
$607$	614804.	+	354957.i	1.66863	+	0.963382i	0.700248	+	0.713900i	$0.253073\pi$
$608$	−200848.	+	347879.i	−0.543325	+	0.941067i
$609$	−269068.	−	142071.i	−0.725483	−	0.383064i
$610$	−128420.	+	497985.i	−0.345122	+	1.33831i
$611$		−	61776.9i		−	0.165479i
$612$	64900.8	−	135040.i	0.173280	−	0.360545i
$613$		−	74706.8i		−	0.198810i	−0.995047	−	0.0994052i	$-0.968306\pi$
$613$		−	74706.8i		−	0.198810i	0.995047	−	0.0994052i	$-0.0316940\pi$
$614$	−342177.	+	197556.i	−0.907642	+	0.524027i
$615$	−104497.	+	479470.i	−0.276282	+	1.26768i
$616$	35057.6	−	60721.5i	0.0923890	−	0.160022i
$617$	−4028.70	+	6977.91i	−0.0105826	+	0.0183297i	−0.871268	−	0.490807i	$-0.836702\pi$
$617$	−4028.70	+	6977.91i	−0.0105826	+	0.0183297i	0.860686	+	0.509137i	$0.170035\pi$
$618$	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
$625$	182431.	−	345408.i	0.467024	−	0.884244i
$626$	−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
$630$	154958.	+	27684.5i	0.390421	+	0.0697518i
$631$	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
$635$	168947.	+	607569.i	0.418990	+	1.50678i
$636$	−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	0.636588	−	0.771204i	$-0.280345\pi$
$643$	118660.	+	68508.2i	0.287000	+	0.165699i	−0.349588	+	0.936903i	$0.613679\pi$
$644$	22945.9	+	13247.8i	0.0553264	+	0.0319427i
$645$	−229413.	−	208713.i	−0.551442	−	0.501684i
$646$	291043.	+	504101.i	0.697416	+	1.20796i
$647$	−745072.			−1.77988			−0.889938	−	0.456081i	$-0.849253\pi$
$647$	−745072.			−1.77988			−0.889938	+	0.456081i	$0.849253\pi$
$648$	−451576.	+	68791.9i	−1.07543	+	0.163828i
$649$	−227635.			−0.540444
$650$	−92983.7	−	154267.i	−0.220080	−	0.365128i
$651$	−40115.9	+	1516.85i	−0.0946573	+	0.00357916i
$652$	125313.	+	72349.6i	0.294782	+	0.170193i
$653$	165697.	−	286996.i	0.388588	−	0.673054i	−0.603672	−	0.797233i	$-0.706296\pi$
$653$	165697.	−	286996.i	0.388588	−	0.673054i	0.992260	+	0.124179i	$0.0396297\pi$
$654$	218895.	−	137661.i	0.511777	−	0.321852i
$655$	168799.	+	43529.6i	0.393447	+	0.101462i
$656$		−	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	$0.244842\pi$
$660$	51504.8	−	16442.3i	0.118239	−	0.0377464i
$661$	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
$670$	−102405.	−	368272.i	−0.228125	−	0.820387i
$671$	230805.	+	133255.i	0.512625	+	0.295964i
$672$	153588.	−	5807.42i	0.340108	−	0.0128601i
$673$	−618772.	+	357248.i	−1.36616	+	0.788751i	−0.990435	−	0.137981i	$-0.955939\pi$
$673$	−618772.	+	357248.i	−1.36616	+	0.788751i	−0.375722	+	0.926732i	$0.622605\pi$
$674$			668319.i			1.47117i
$675$	277844.	+	361105.i	0.609808	+	0.792549i
$676$	−118588.			−0.259507
$677$	314445.	+	544634.i	0.686068	+	1.18830i	0.973100	+	0.230383i	$0.0739979\pi$
$677$	314445.	+	544634.i	0.686068	+	1.18830i	−0.287033	+	0.957921i	$0.592669\pi$
$678$	18673.0	+	493841.i	0.0406214	+	1.07430i
$679$	26969.6	−	46712.8i	0.0584973	−	0.101320i
$680$	533840.	−	148445.i	1.15450	−	0.321031i
$681$	106507.	−	66981.3i	0.229659	−	0.144431i
$682$	20941.1	−	12090.4i	0.0450227	−	0.0259939i
$683$	619254.			1.32748			0.663740	−	0.747964i	$-0.268968\pi$
$683$	619254.			1.32748			0.663740	+	0.747964i	$0.268968\pi$
$684$	−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
$690$	−40902.0	−	128124.i	−0.0859105	−	0.269111i
$691$	−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
$695$	−79353.2	+	307715.i	−0.164284	+	0.637058i
$696$	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
$700$	−45651.2	−	75738.5i	−0.0931657	−	0.154568i
$701$			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
$705$	−103605.	+	113881.i	−0.208450	+	0.229125i
$706$	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
$715$	−89931.7	+	25007.3i	−0.175914	+	0.0489165i
$716$	−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	$-0.0798034\pi$
$720$	−200155.	−	168722.i	−0.386102	−	0.325468i
$721$	−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
$725$	419617.	−	759487.i	0.798320	−	1.44492i
$726$	−14036.6	−	371222.i	−0.0266310	−	0.704305i
$727$	−232904.	+	134467.i	−0.440664	+	0.254418i	−0.703879	−	0.710320i	$-0.748550\pi$
$727$	−232904.	+	134467.i	−0.440664	+	0.254418i	0.263215	+	0.964737i	$0.415217\pi$
$728$	−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	0.385489	−	0.922712i	$-0.374033\pi$
$733$	−118665.	−	68511.0i	−0.220858	−	0.127512i	−0.606347	+	0.795200i	$0.707366\pi$
$734$	−375942.	−	217050.i	−0.697796	−	0.402873i
$735$	397467.	+	86624.8i	0.735744	+	0.160350i
$736$	−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	$0.704597\pi$
$740$	−49018.7	−	12640.9i	−0.0895156	−	0.0230842i
$741$	217320.	−	411581.i	0.395788	−	0.749582i
$742$	−140932.	−	81367.0i	−0.255977	−	0.147788i
$743$	202784.	−	351232.i	0.367329	−	0.636233i	−0.621818	−	0.783162i	$-0.713606\pi$
$743$	202784.	−	351232.i	0.367329	−	0.636233i	0.989147	+	0.146929i	$0.0469389\pi$
$744$	101493.	+	53589.5i	0.183354	+	0.0968130i
$745$	93637.7	+	24147.2i	0.168709	+	0.0435065i
$746$			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
$750$	−87310.0	+	440320.i	−0.155218	+	0.782791i
$751$	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	$0.0220246\pi$
$757$			79237.9i			0.138274i	−0.997607	+	0.0691371i	$0.977975\pi$
$758$	101107.	+	175122.i	0.175971	+	0.304791i
$759$	−69648.2	+	2633.52i	−0.120900	+	0.00457145i
$760$	−960538.	+	267097.i	−1.66298	+	0.462426i
$761$	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
$765$	606273.	−	219115.i	1.03597	−	0.374412i
$766$	−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	$0.172798\pi$
$770$	77431.3	−	21531.3i	0.130598	−	0.0363153i
$771$	672537.	+	355107.i	1.13138	+	0.597380i
$772$	−237824.	+	137308.i	−0.399045	+	0.230388i
$773$	265643.			0.444569			0.222284	−	0.974982i	$-0.428649\pi$
$773$	265643.			0.444569			0.222284	+	0.974982i	$0.428649\pi$
$774$	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
$780$	−87305.7	−	79427.9i	−0.143500	−	0.130552i
$781$	−140231.	−	242888.i	−0.229902	−	0.398202i
$782$	−190293.			−0.311177
$783$	601957.	+	813609.i	0.981842	+	1.32706i
$784$	−233727.			−0.380256
$785$	896831.	+	231274.i	1.45536	+	0.375307i
$786$	−200180.	+	7569.18i	−0.324024	+	0.0122519i
$787$	−87831.8	−	50709.7i	−0.141809	−	0.0818732i	0.427417	−	0.904055i	$-0.359424\pi$
$787$	−87831.8	−	50709.7i	−0.141809	−	0.0818732i	−0.569226	+	0.822181i	$0.692757\pi$
$788$	22241.3	−	38523.0i	0.0358185	−	0.0620394i
$789$	−339664.	+	213612.i	−0.545627	+	0.343140i
$790$	−83966.4	+	325604.i	−0.134540	+	0.521717i
$791$		−	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
$795$	−143249.	−	448720.i	−0.226650	−	0.709971i
$796$	30960.2	−	53624.7i	0.0488627	−	0.0846327i
$797$	−259138.	+	448841.i	−0.407958	+	0.706603i	−0.994661	−	0.103199i	$-0.967092\pi$
$797$	−259138.	+	448841.i	−0.407958	+	0.706603i	0.586703	+	0.809802i	$0.300426\pi$
$798$	−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
$805$	30541.7	+	109835.i	0.0471305	+	0.169491i
$806$	−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	$-0.0375077\pi$
$810$	−424671.	−	306267.i	−0.647265	−	0.466799i
$811$	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
$815$	166796.	+	599835.i	0.251114	+	0.903060i
$816$	−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	0.249753	−	0.968310i	$-0.419651\pi$
$823$	−314247.	−	181431.i	−0.463951	−	0.267862i	−0.713704	+	0.700447i	$0.752984\pi$
$824$	801940.	+	463000.i	1.18110	+	0.681909i
$825$	207721.	+	104724.i	0.305192	+	0.153865i
$826$	−213936.	−	370548.i	−0.313562	−	0.543106i
$827$	−711891.			−1.04088			−0.520442	−	0.853897i	$-0.674233\pi$
$827$	−711891.			−1.04088			−0.520442	+	0.853897i	$0.674233\pi$
$828$	−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	$0.311005\pi$
$830$	123948.	−	480644.i	0.179922	−	0.697698i
$831$	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
$835$	−94940.2	+	368158.i	−0.136169	+	0.528033i
$836$			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	$0.0556608\pi$
$840$	282168.	+	256707.i	0.399897	+	0.363814i
$841$	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
$850$	555922.	+	307147.i	0.769442	+	0.425117i
$851$	56516.1	+	32629.6i	0.0780393	+	0.0450560i
$852$	165586.	−	313603.i	0.228110	−	0.432018i
$853$	−140070.	+	80869.4i	−0.192507	+	0.111144i	−0.593156	−	0.805088i	$-0.702118\pi$
$853$	−140070.	+	80869.4i	−0.192507	+	0.111144i	0.400649	+	0.916232i	$0.368785\pi$
$854$			500944.i			0.686868i
$855$	−1.09087e6	+	394254.i	−1.49224	+	0.539317i
$856$	1.11034e6			1.51533
$857$	−353645.	−	612531.i	−0.481510	−	0.834001i	0.518264	−	0.855220i	$-0.326578\pi$
$857$	−353645.	−	612531.i	−0.481510	−	0.834001i	−0.999775	+	0.0212199i	$0.993245\pi$
$858$	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	$0.0389832\pi$
$860$	−53642.5	−	192910.i	−0.0725291	−	0.260830i
$861$	18061.2	+	477661.i	0.0243635	+	0.644337i
$862$	837706.	−	483650.i	1.12740	−	0.650904i
$863$	−867975.			−1.16543			−0.582714	−	0.812677i	$-0.698009\pi$
$863$	−867975.			−1.16543			−0.582714	+	0.812677i	$0.698009\pi$
$864$	−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
$870$	−212332.	+	974258.i	−0.280528	+	1.28717i
$871$	216222.	+	374507.i	0.285012	+	0.493656i
$872$	626646.			0.824117
$873$	−148160.	+	101185.i	−0.194403	+	0.132766i
$874$	342394.			0.448232
$875$	88056.7	−	370168.i	0.115013	−	0.483485i
$876$	220963.	−	418482.i	0.287947	−	0.545342i
$877$	267200.	+	154268.i	0.347406	+	0.200575i	0.663542	−	0.748139i	$-0.269052\pi$
$877$	267200.	+	154268.i	0.347406	+	0.200575i	−0.316136	+	0.948714i	$0.602386\pi$
$878$	−490692.	+	849904.i	−0.636532	+	1.10251i
$879$	281165.	+	148459.i	0.363902	+	0.192144i
$880$	−129423.	−	33375.4i	−0.167126	−	0.0430984i
$881$		−	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	$0.0171686\pi$
$883$			84067.1i			0.107821i	−0.998546	+	0.0539106i	$0.982831\pi$
$884$	−144624.	+	83499.0i	−0.185071	+	0.106851i
$885$	263724.	−	1.21006e6i	0.336715	−	1.54498i
$886$	−353512.	+	612300.i	−0.450336	+	0.780004i
$887$	−195121.	+	337960.i	−0.248003	+	0.429554i	−0.962972	−	0.269603i	$-0.913108\pi$
$887$	−195121.	+	337960.i	−0.248003	+	0.429554i	0.714969	+	0.699157i	$0.246441\pi$
$888$	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
$895$	−26042.6	−	93654.8i	−0.0325116	−	0.116919i
$896$	−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
$900$	27733.9	+	292838.i	0.0342394	+	0.361528i
$901$	−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
$905$	−802380.	+	223118.i	−0.979677	+	0.272419i
$906$	−616635.	−	325591.i	−0.751228	−	0.396657i
$907$	73779.7	−	42596.7i	0.0896855	−	0.0517800i	−0.454487	−	0.890754i	$-0.650177\pi$
$907$	73779.7	−	42596.7i	0.0896855	−	0.0517800i	0.544172	+	0.838974i	$0.316844\pi$
$908$	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
$915$	−975754.	+	1.07253e6i	−1.16546	+	1.28105i
$916$	−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	$0.307787\pi$
$920$	81387.5	−	315604.i	0.0961573	−	0.372878i
$921$	−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
$925$	−112440.	−	186546.i	−0.131413	−	0.218023i
$926$		−	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	$0.100364\pi$
$930$	40008.9	+	125326.i	0.0462584	+	0.144902i
$931$	−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	$-0.650759\pi$
$937$		−	1.56265e6i		−	1.77984i	0.456114	−	0.889922i	$-0.349241\pi$
$938$	−186167.	−	322451.i	−0.211591	−	0.366487i
$939$	−416375.	−	662078.i	−0.472230	−	0.750893i
$940$	−95760.4	+	26628.1i	−0.108375	+	0.0301360i
$941$	−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
$945$	349900.	+	273019.i	0.391815	+	0.305724i
$946$	181972.			0.203339
$947$	−259582.	−	449609.i	−0.289451	−	0.501343i	0.684228	−	0.729268i	$-0.260139\pi$
$947$	−259582.	−	449609.i	−0.289451	−	0.501343i	−0.973679	+	0.227925i	$0.926806\pi$
$948$	8325.51	+	220183.i	0.00926391	+	0.245001i
$949$	−408519.	+	707575.i	−0.453607	+	0.785670i
$950$	−1.00027e6	−	552650.i	−1.10833	−	0.612354i
$951$	231432.	−	145546.i	0.255896	−	0.160931i
$952$	467419.	−	269864.i	0.515742	−	0.297764i
$953$	−270328.			−0.297650			−0.148825	−	0.988864i	$-0.547549\pi$
$953$	−270328.			−0.297650			−0.148825	+	0.988864i	$0.547549\pi$
$954$	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
$960$	−294711.	−	923167.i	−0.319782	−	1.00170i
$961$	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
$965$	−1.14415e6	−	295052.i	−1.22865	−	0.316843i
$966$	−69743.6	−	110899.i	−0.0747395	−	0.118843i
$967$	−352654.	−	203605.i	−0.377135	−	0.217739i	0.299436	−	0.954116i	$-0.403201\pi$
$967$	−352654.	−	203605.i	−0.377135	−	0.217739i	−0.676571	+	0.736378i	$0.736535\pi$
$968$	450126.	−	779641.i	0.480378	−	0.832039i
$969$	62010.6	+	1.63998e6i	0.0660418	+	1.74659i
$970$	−171164.	−	44139.6i	−0.181915	−	0.0469121i
$971$			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
$975$	−28744.8	−	507030.i	−0.0302378	−	0.533365i
$976$	416543.	−	721474.i	0.437281	−	0.757393i
$977$	535395.	−	927331.i	0.560900	−	0.971507i	−0.436518	−	0.899695i	$-0.643789\pi$
$977$	535395.	−	927331.i	0.560900	−	0.971507i	0.997418	−	0.0718115i	$-0.0228780\pi$
$978$	−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	$0.0218268\pi$
$983$	539346.	+	934175.i	0.558163	+	0.966766i	−0.439487	+	0.898249i	$0.644840\pi$
$984$	638091.	−	1.20848e6i	0.659011	−	1.24810i
$985$	184398.	−	51275.5i	0.190056	−	0.0528491i
$986$	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
$990$	−263160.	−	47015.6i	−0.268503	−	0.0479703i
$991$	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
$995$	256684.	−	71376.3i	0.259271	−	0.0720955i
$996$	−12289.8	−	325026.i	−0.0123887	−	0.327642i
$997$	−1.64875e6	+	951904.i	−1.65868	+	0.957641i	−0.685359	+	0.728205i	$0.740355\pi$
$997$	−1.64875e6	+	951904.i	−1.65868	+	0.957641i	−0.973324	+	0.229435i	$0.926312\pi$
$998$	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.14.8	✓	44
3.2	odd	2		135.5.h.a.44.15		44
5.4	even	2	inner	45.5.h.a.14.15	yes	44
9.2	odd	6	inner	45.5.h.a.29.15	yes	44
9.4	even	3		405.5.d.a.404.29		44
9.5	odd	6		405.5.d.a.404.15		44
9.7	even	3		135.5.h.a.89.8		44
15.14	odd	2		135.5.h.a.44.8		44
45.4	even	6		405.5.d.a.404.16		44
45.14	odd	6		405.5.d.a.404.30		44
45.29	odd	6	inner	45.5.h.a.29.8	yes	44
45.34	even	6		135.5.h.a.89.15		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.8	✓	44	1.1	even	1	trivial
45.5.h.a.14.15	yes	44	5.4	even	2	inner
45.5.h.a.29.8	yes	44	45.29	odd	6	inner
45.5.h.a.29.15	yes	44	9.2	odd	6	inner
135.5.h.a.44.8		44	15.14	odd	2
135.5.h.a.44.15		44	3.2	odd	2
135.5.h.a.89.8		44	9.7	even	3
135.5.h.a.89.15		44	45.34	even	6
405.5.d.a.404.15		44	9.5	odd	6
405.5.d.a.404.16		44	45.4	even	6
405.5.d.a.404.29		44	9.4	even	3
405.5.d.a.404.30		44	45.14	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} +(24.0861 - 6.69764i) 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} +(-68.4265 - 214.343i) q^{15} +(64.6373 + 111.955i) q^{16} -318.348 q^{17} +(145.821 + 213.519i) q^{18} +572.803 q^{19} +(36.2724 - 140.657i) 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} +(535.283 - 322.640i) q^{25} -288.196i q^{26} +(82.4780 + 724.319i) q^{27} -141.492i q^{28} +(1202.32 - 694.158i) q^{29} +(-483.329 + 531.267i) 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} +(-1676.91 + 466.298i) q^{40} +(-1888.80 - 1090.50i) q^{41} +(-326.661 + 618.662i) q^{42} +(1193.76 - 689.217i) q^{43} +240.292i q^{44} +(-1904.44 + 688.289i) q^{45} +597.751 q^{46} +(-342.127 - 592.582i) q^{47} +(984.895 - 619.392i) q^{48} +(-903.994 + 1565.76i) q^{49} +(-1746.27 - 964.816i) 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} +(-1277.34 - 278.387i) q^{60} +(-3222.16 - 5580.94i) q^{61} -584.698 q^{62} +(-1628.88 + 1112.43i) q^{63} +4306.97 q^{64} +(2185.58 + 563.616i) 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} +(-1881.79 - 485.274i) q^{70} +6781.69i q^{71} +(5623.22 - 425.857i) q^{72} +9049.69i q^{73} +(-963.412 + 556.226i) q^{74} +(-3083.72 - 4704.39i) 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} +(-7667.76 + 2132.18i) q^{85} +(-3810.63 - 2200.07i) q^{86} +(-6651.82 - 10577.1i) q^{87} +(2493.51 - 1439.63i) q^{88} -1469.15i q^{89} +(4942.35 + 4166.19i) q^{90} +2198.57 q^{91} +(544.016 + 942.263i) q^{92} +(-1457.79 - 769.728i) q^{93} +(-1092.11 + 1891.59i) q^{94} +(13796.6 - 3836.43i) 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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