LMFDB - Embedded newform 45.5.h.a.14.18

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			14.18
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.61690 + 4.53261i) q^{2} +(-8.42379 + 3.16855i) q^{3} +(-5.69638 + 9.86641i) q^{4} +(-23.1420 - 9.45767i) q^{5} +(-36.4061 - 29.8900i) q^{6} +(-50.0684 + 28.9070i) q^{7} +24.1135 q^{8} +(60.9206 - 53.3825i) q^{9} +(-17.6925 - 129.644i) q^{10} +(-146.496 + 84.5798i) q^{11} +(16.7228 - 101.162i) q^{12} +(99.1268 + 57.2309i) q^{13} +(-262.048 - 151.294i) q^{14} +(224.911 + 6.34275i) q^{15} +(154.245 + 267.160i) q^{16} -209.860 q^{17} +(401.385 + 136.432i) q^{18} +26.9887 q^{19} +(225.139 - 174.454i) q^{20} +(330.173 - 402.151i) q^{21} +(-766.735 - 442.674i) q^{22} +(-458.642 + 794.390i) q^{23} +(-203.127 + 76.4047i) q^{24} +(446.105 + 437.739i) q^{25} +599.071i q^{26} +(-344.037 + 642.713i) q^{27} -658.661i q^{28} +(308.888 - 178.337i) q^{29} +(559.820 + 1036.03i) q^{30} +(629.269 - 1089.93i) q^{31} +(-614.379 + 1064.14i) q^{32} +(966.061 - 1176.66i) q^{33} +(-549.182 - 951.212i) q^{34} +(1432.08 - 195.436i) q^{35} +(179.667 + 905.154i) q^{36} -368.530i q^{37} +(70.6268 + 122.329i) q^{38} +(-1016.36 - 168.013i) q^{39} +(-558.034 - 228.057i) q^{40} +(1591.16 + 918.657i) q^{41} +(2686.82 + 444.153i) q^{42} +(277.639 - 160.295i) q^{43} -1927.19i q^{44} +(-1914.70 + 659.211i) q^{45} -4800.88 q^{46} +(-1224.29 - 2120.54i) q^{47} +(-2145.83 - 1761.76i) q^{48} +(470.730 - 815.329i) q^{49} +(-816.685 + 3167.54i) q^{50} +(1767.81 - 664.951i) q^{51} +(-1129.33 + 652.018i) q^{52} -1898.83 q^{53} +(-3813.48 + 122.531i) q^{54} +(4190.15 - 571.831i) q^{55} +(-1207.32 + 697.048i) q^{56} +(-227.347 + 85.5151i) q^{57} +(1616.66 + 933.380i) q^{58} +(-4208.65 - 2429.87i) q^{59} +(-1343.76 + 2182.93i) q^{60} +(-473.839 - 820.714i) q^{61} +6586.95 q^{62} +(-1507.07 + 4433.81i) q^{63} -1495.26 q^{64} +(-1752.72 - 2261.95i) q^{65} +(7861.45 + 1299.56i) q^{66} +(1877.97 + 1084.25i) q^{67} +(1195.44 - 2070.56i) q^{68} +(1346.43 - 8145.01i) q^{69} +(4633.44 + 5979.61i) q^{70} +9078.87i q^{71} +(1469.00 - 1287.24i) q^{72} +984.836i q^{73} +(1670.40 - 964.407i) q^{74} +(-5144.89 - 2273.91i) q^{75} +(-153.738 + 266.282i) q^{76} +(4889.90 - 8469.55i) q^{77} +(-1898.19 - 5046.45i) q^{78} +(5125.48 + 8877.60i) q^{79} +(-1042.82 - 7641.40i) q^{80} +(861.628 - 6504.18i) q^{81} +9616.15i q^{82} +(2390.39 + 4140.27i) q^{83} +(2087.00 + 5548.42i) q^{84} +(4856.57 + 1984.78i) q^{85} +(1453.11 + 838.954i) q^{86} +(-2036.94 + 2481.00i) q^{87} +(-3532.54 + 2039.51i) q^{88} +858.461i q^{89} +(-7998.53 - 6953.49i) q^{90} -6617.50 q^{91} +(-5225.19 - 9050.29i) q^{92} +(-1847.35 + 11175.2i) q^{93} +(6407.71 - 11098.5i) q^{94} +(-624.572 - 255.250i) q^{95} +(1803.63 - 10910.8i) q^{96} +(-3694.13 + 2132.80i) q^{97} +4927.43 q^{98} +(-4409.57 + 12973.0i) 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 $

$2$	2.61690	+	4.53261i	0.654226	+	1.13315i	0.982087	+	0.188427i	$0.0603388\pi$
$2$	2.61690	+	4.53261i	0.654226	+	1.13315i	−0.327861	+	0.944726i	$0.606328\pi$
$3$	−8.42379	+	3.16855i	−0.935977	+	0.352061i
$3$	−8.42379	+	3.16855i	−0.935977	+	0.352061i
$4$	−5.69638	+	9.86641i	−0.356024	+	0.616651i
$5$	−23.1420	−	9.45767i	−0.925680	−	0.378307i
$5$	−23.1420	−	9.45767i	−0.925680	−	0.378307i
$6$	−36.4061	−	29.8900i	−1.01128	−	0.830277i
$7$	−50.0684	+	28.9070i	−1.02180	+	0.589939i	−0.914626	−	0.404301i	$-0.867515\pi$
$7$	−50.0684	+	28.9070i	−1.02180	+	0.589939i	−0.107178	+	0.994240i	$0.534182\pi$
$8$	24.1135			0.376773
$9$	60.9206	−	53.3825i	0.752106	−	0.659043i
$10$	−17.6925	−	129.644i	−0.176925	−	1.29644i
$11$	−146.496	+	84.5798i	−1.21071	+	0.699007i	−0.962915	−	0.269805i	$-0.913041\pi$
$11$	−146.496	+	84.5798i	−1.21071	+	0.699007i	−0.247800	+	0.968811i	$0.579708\pi$
$12$	16.7228	−	101.162i	0.116131	−	0.702513i
$13$	99.1268	+	57.2309i	0.586549	+	0.338644i	0.763732	−	0.645534i	$-0.223365\pi$
$13$	99.1268	+	57.2309i	0.586549	+	0.338644i	−0.177183	+	0.984178i	$0.556698\pi$
$14$	−262.048	−	151.294i	−1.33698	−	0.771907i
$15$	224.911	+	6.34275i	0.999603	+	0.0281900i
$16$	154.245	+	267.160i	0.602518	+	1.04359i
$17$	−209.860			−0.726158			−0.363079	−	0.931758i	$-0.618274\pi$
$17$	−209.860			−0.726158			−0.363079	+	0.931758i	$0.618274\pi$
$18$	401.385	+	136.432i	1.23884	+	0.421088i
$19$	26.9887			0.0747609			0.0373805	−	0.999301i	$-0.488099\pi$
$19$	26.9887			0.0747609			0.0373805	+	0.999301i	$0.488099\pi$
$20$	225.139	−	174.454i	0.562847	−	0.436135i
$21$	330.173	−	402.151i	0.748690	−	0.911907i
$22$	−766.735	−	442.674i	−1.58416	−	0.914617i
$23$	−458.642	+	794.390i	−0.866997	+	1.50168i	−0.00194692	+	0.999998i	$0.500620\pi$
$23$	−458.642	+	794.390i	−0.866997	+	1.50168i	−0.865050	+	0.501685i	$0.832714\pi$
$24$	−203.127	+	76.4047i	−0.352651	+	0.132647i
$25$	446.105	+	437.739i	0.713768	+	0.700382i
$26$			599.071i			0.886200i
$27$	−344.037	+	642.713i	−0.471930	+	0.881636i
$28$		−	658.661i		−	0.840129i
$29$	308.888	−	178.337i	0.367287	−	0.212053i	−0.304986	−	0.952357i	$-0.598652\pi$
$29$	308.888	−	178.337i	0.367287	−	0.212053i	0.672272	+	0.740304i	$0.265318\pi$
$30$	559.820	+	1036.03i	0.622022	+	1.15115i
$31$	629.269	−	1089.93i	0.654807	−	1.13416i	−0.327135	−	0.944977i	$-0.606083\pi$
$31$	629.269	−	1089.93i	0.654807	−	1.13416i	0.981942	−	0.189181i	$-0.0605833\pi$
$32$	−614.379	+	1064.14i	−0.599980	+	1.03920i
$33$	966.061	−	1176.66i	0.887108	−	1.08050i
$34$	−549.182	−	951.212i	−0.475071	−	0.822848i
$35$	1432.08	−	195.436i	1.16904	−	0.159540i
$36$	179.667	+	905.154i	0.138632	+	0.698421i
$37$		−	368.530i		−	0.269196i	−0.990900	−	0.134598i	$-0.957026\pi$
$37$		−	368.530i		−	0.269196i	0.990900	−	0.134598i	$-0.0429744\pi$
$38$	70.6268	+	122.329i	0.0489105	+	0.0847155i
$39$	−1016.36	−	168.013i	−0.668220	−	0.110462i
$40$	−558.034	−	228.057i	−0.348771	−	0.142536i
$41$	1591.16	+	918.657i	0.946556	+	0.546494i	0.892009	−	0.452017i	$-0.149295\pi$
$41$	1591.16	+	918.657i	0.946556	+	0.546494i	0.0545466	+	0.998511i	$0.482629\pi$
$42$	2686.82	+	444.153i	1.52314	+	0.251787i
$43$	277.639	−	160.295i	0.150156	−	0.0866929i	−0.423039	−	0.906111i	$-0.639037\pi$
$43$	277.639	−	160.295i	0.150156	−	0.0866929i	0.573196	+	0.819418i	$0.305703\pi$
$44$		−	1927.19i		−	0.995451i
$45$	−1914.70	+	659.211i	−0.945530	+	0.325536i
$46$	−4800.88			−2.26885
$47$	−1224.29	−	2120.54i	−0.554229	−	0.959953i	−0.997963	−	0.0637941i	$-0.979680\pi$
$47$	−1224.29	−	2120.54i	−0.554229	−	0.959953i	0.443734	−	0.896158i	$-0.353653\pi$
$48$	−2145.83	−	1761.76i	−0.931351	−	0.764655i
$49$	470.730	−	815.329i	0.196056	−	0.339579i
$50$	−816.685	+	3167.54i	−0.326674	+	1.26702i
$51$	1767.81	−	664.951i	0.679667	−	0.255652i
$52$	−1129.33	+	652.018i	−0.417651	+	0.241131i
$53$	−1898.83			−0.675981			−0.337991	−	0.941149i	$-0.609747\pi$
$53$	−1898.83			−0.675981			−0.337991	+	0.941149i	$0.609747\pi$
$54$	−3813.48	+	122.531i	−1.30778	+	0.0420204i
$55$	4190.15	−	571.831i	1.38517	−	0.189035i
$56$	−1207.32	+	697.048i	−0.384988	+	0.222273i
$57$	−227.347	+	85.5151i	−0.0699745	+	0.0263204i
$58$	1616.66	+	933.380i	0.480577	+	0.277461i
$59$	−4208.65	−	2429.87i	−1.20904	−	0.698037i	−0.246487	−	0.969146i	$-0.579276\pi$
$59$	−4208.65	−	2429.87i	−1.20904	−	0.698037i	−0.962549	+	0.271109i	$0.912609\pi$
$60$	−1343.76	+	2182.93i	−0.373265	+	0.606369i
$61$	−473.839	−	820.714i	−0.127342	−	0.220563i	0.795304	−	0.606211i	$-0.207311\pi$
$61$	−473.839	−	820.714i	−0.127342	−	0.220563i	−0.922646	+	0.385648i	$0.873978\pi$
$62$	6586.95			1.71357
$63$	−1507.07	+	4433.81i	−0.379710	+	1.11711i
$64$	−1495.26			−0.365053
$65$	−1752.72	−	2261.95i	−0.414846	−	0.535372i
$66$	7861.45	+	1299.56i	1.80474	+	0.298338i
$67$	1877.97	+	1084.25i	0.418349	+	0.241534i	0.694371	−	0.719617i	$-0.255683\pi$
$67$	1877.97	+	1084.25i	0.418349	+	0.241534i	−0.276022	+	0.961151i	$0.589016\pi$
$68$	1195.44	−	2070.56i	0.258529	−	0.447786i
$69$	1346.43	−	8145.01i	0.282805	−	1.71078i
$70$	4633.44	+	5979.61i	0.945600	+	1.22033i
$71$			9078.87i			1.80101i	0.434850	+	0.900503i	$0.356801\pi$
$71$			9078.87i			1.80101i	−0.434850	+	0.900503i	$0.643199\pi$
$72$	1469.00	−	1287.24i	0.283373	−	0.248309i
$73$			984.836i			0.184807i	0.995722	+	0.0924035i	$0.0294550\pi$
$73$			984.836i			0.184807i	−0.995722	+	0.0924035i	$0.970545\pi$
$74$	1670.40	−	964.407i	0.305041	−	0.176115i
$75$	−5144.89	−	2273.91i	−0.914648	−	0.404251i
$76$	−153.738	+	266.282i	−0.0266166	+	0.0461014i
$77$	4889.90	−	8469.55i	0.824742	−	1.42850i
$78$	−1898.19	−	5046.45i	−0.311997	−	0.829463i
$79$	5125.48	+	8877.60i	0.821260	+	1.42246i	0.904745	+	0.425955i	$0.140062\pi$
$79$	5125.48	+	8877.60i	0.821260	+	1.42246i	−0.0834848	+	0.996509i	$0.526605\pi$
$80$	−1042.82	−	7641.40i	−0.162941	−	1.19397i
$81$	861.628	−	6504.18i	0.131326	−	0.991339i
$82$			9616.15i			1.43012i
$83$	2390.39	+	4140.27i	0.346986	+	0.600997i	0.985713	−	0.168436i	$-0.0538718\pi$
$83$	2390.39	+	4140.27i	0.346986	+	0.600997i	−0.638726	+	0.769434i	$0.720538\pi$
$84$	2087.00	+	5548.42i	0.295777	+	0.786341i
$85$	4856.57	+	1984.78i	0.672190	+	0.274710i
$86$	1453.11	+	838.954i	0.196473	+	0.113433i
$87$	−2036.94	+	2481.00i	−0.269116	+	0.327784i
$88$	−3532.54	+	2039.51i	−0.456164	+	0.263367i
$89$			858.461i			0.108378i	0.998531	+	0.0541889i	$0.0172573\pi$
$89$			858.461i			0.108378i	−0.998531	+	0.0541889i	$0.982743\pi$
$90$	−7998.53	−	6953.49i	−0.987472	−	0.858455i
$91$	−6617.50			−0.799118
$92$	−5225.19	−	9050.29i	−0.617343	−	1.06927i
$93$	−1847.35	+	11175.2i	−0.213591	+	1.29208i
$94$	6407.71	−	11098.5i	0.725182	−	1.25605i
$95$	−624.572	−	255.250i	−0.0692047	−	0.0282825i
$96$	1803.63	−	10910.8i	0.195707	−	1.18389i
$97$	−3694.13	+	2132.80i	−0.392616	+	0.226677i	−0.683293	−	0.730144i	$-0.739453\pi$
$97$	−3694.13	+	2132.80i	−0.392616	+	0.226677i	0.290677	+	0.956821i	$0.406120\pi$
$98$	4927.43			0.513060
$99$	−4409.57	+	12973.0i	−0.449910	+	1.32364i
$100$	−6860.09	+	1907.93i	−0.686009	+	0.190793i
$101$	−3710.95	+	2142.52i	−0.363783	+	0.210030i	−0.670739	−	0.741693i	$-0.734023\pi$
$101$	−3710.95	+	2142.52i	−0.363783	+	0.210030i	0.306956	+	0.951724i	$0.400690\pi$
$102$	7640.16	+	6272.70i	0.734349	+	0.602912i
$103$	9070.03	+	5236.58i	0.854937	+	0.493598i	0.862314	−	0.506375i	$-0.169015\pi$
$103$	9070.03	+	5236.58i	0.854937	+	0.493598i	−0.00737655	+	0.999973i	$0.502348\pi$
$104$	2390.29	+	1380.03i	0.220996	+	0.127592i
$105$	−11444.3	+	6183.92i	−1.03803	+	0.560900i
$106$	−4969.06	−	8606.67i	−0.442245	−	0.765990i
$107$	−17871.6			−1.56097			−0.780487	−	0.625171i	$-0.785029\pi$
$107$	−17871.6			−1.56097			−0.780487	+	0.625171i	$0.785029\pi$
$108$	−4381.50	−	7055.54i	−0.375643	−	0.604899i
$109$	−14838.6			−1.24894			−0.624469	−	0.781049i	$-0.714685\pi$
$109$	−14838.6			−1.24894			−0.624469	+	0.781049i	$0.714685\pi$
$110$	13557.1	+	17495.9i	1.12042	+	1.44594i
$111$	1167.71	+	3104.42i	0.0947736	+	0.251962i
$112$	−15445.6	−	8917.50i	−1.23131	−	0.710898i
$113$	4689.23	−	8121.99i	0.367236	−	0.636071i	−0.621896	−	0.783099i	$-0.713638\pi$
$113$	4689.23	−	8121.99i	0.367236	−	0.636071i	0.989132	+	0.147028i	$0.0469709\pi$
$114$	−982.552	−	806.691i	−0.0756042	−	0.0620723i
$115$	18127.0	−	14046.1i	1.37066	−	1.06209i
$116$			4063.49i			0.301984i
$117$	9093.99	−	1805.10i	0.664328	−	0.131865i
$118$		−	25434.9i		−	1.82670i
$119$	10507.3	−	6066.41i	0.741991	−	0.428389i
$120$	5423.37	+	152.946i	0.376623	+	0.0106212i
$121$	6986.98	−	12101.8i	0.477220	−	0.826570i
$122$	2479.98	−	4295.46i	0.166621	−	0.288596i
$123$	−16314.4	−	2696.90i	−1.07835	−	0.178260i
$124$	7169.11	+	12417.3i	0.466253	+	0.807574i
$125$	−6183.78	−	14349.3i	−0.395762	−	0.918353i
$126$	−24040.6	+	4771.89i	−1.51427	+	0.300573i
$127$			3644.02i			0.225929i	0.993599	+	0.112965i	$0.0360347\pi$
$127$			3644.02i			0.225929i	−0.993599	+	0.112965i	$0.963965\pi$
$128$	5917.12	+	10248.8i	0.361152	+	0.625534i
$129$	−1830.87	+	2230.01i	−0.110022	+	0.134007i
$130$	5665.82	−	13863.7i	0.335255	−	0.820338i
$131$	4646.98	+	2682.93i	0.270787	+	0.156339i	0.629245	−	0.777207i	$-0.283364\pi$
$131$	4646.98	+	2682.93i	0.270787	+	0.156339i	−0.358458	+	0.933546i	$0.616697\pi$
$132$	6106.41	+	16234.3i	0.350460	+	0.931719i
$133$	−1351.28	+	780.162i	−0.0763910	+	0.0441044i
$134$			11349.5i			0.632071i
$135$	14040.3	−	11619.9i	0.770385	−	0.637579i
$136$	−5060.44			−0.273596
$137$	1222.29	+	2117.07i	0.0651230	+	0.112796i	0.896749	−	0.442540i	$-0.145923\pi$
$137$	1222.29	+	2117.07i	0.0651230	+	0.112796i	−0.831626	+	0.555337i	$0.812589\pi$
$138$	40441.6	−	15211.9i	2.12359	−	0.798774i
$139$	−7504.01	+	12997.3i	−0.388386	+	0.672704i	−0.992233	−	0.124396i	$-0.960301\pi$
$139$	−7504.01	+	12997.3i	−0.388386	+	0.672704i	0.603847	+	0.797101i	$0.293634\pi$
$140$	−6229.39	+	15242.7i	−0.317826	+	0.777690i
$141$	17032.2	+	13983.7i	0.856708	+	0.703371i
$142$	−41151.0	+	23758.5i	−2.04081	+	1.17826i
$143$	−19362.3			−0.946859
$144$	23658.3	+	8041.55i	1.14093	+	0.387806i
$145$	−8834.94	+	1205.71i	−0.420211	+	0.0573464i
$146$	−4463.88	+	2577.22i	−0.209415	+	0.120906i
$147$	−1381.92	+	8359.70i	−0.0639513	+	0.386862i
$148$	3636.07	+	2099.28i	0.166000	+	0.0958402i
$149$	10932.2	+	6311.73i	0.492421	+	0.284299i	0.725578	−	0.688140i	$-0.241572\pi$
$149$	10932.2	+	6311.73i	0.492421	+	0.284299i	−0.233157	+	0.972439i	$0.574906\pi$
$150$	−3156.93	−	29270.4i	−0.140308	−	1.30091i
$151$	11641.2	+	20163.1i	0.510556	+	0.884309i	0.999925	+	0.0122322i	$0.00389373\pi$
$151$	11641.2	+	20163.1i	0.510556	+	0.884309i	−0.489369	+	0.872077i	$0.662773\pi$
$152$	650.790			0.0281679
$153$	−12784.8	+	11202.8i	−0.546147	+	0.478569i
$154$	51185.6			2.15827
$155$	−24870.7	+	19271.7i	−1.03520	+	0.802151i
$156$	7447.27	−	9070.79i	0.306019	−	0.372732i
$157$	−14800.5	−	8545.07i	−0.600450	−	0.346670i	0.168768	−	0.985656i	$-0.446021\pi$
$157$	−14800.5	−	8545.07i	−0.600450	−	0.346670i	−0.769219	+	0.638986i	$0.779354\pi$
$158$	−26825.8	+	46463.6i	−1.07458	+	1.86123i
$159$	15995.4	−	6016.55i	0.632703	−	0.237987i
$160$	24282.2	−	18815.6i	0.948524	−	0.734986i
$161$		−	53031.8i		−	2.04590i
$162$	31735.7	−	13115.4i	1.20926	−	0.499748i
$163$		−	26012.6i		−	0.979059i	−0.871987	−	0.489530i	$-0.837169\pi$
$163$		−	26012.6i		−	0.979059i	0.871987	−	0.489530i	$-0.162831\pi$
$164$	−18127.7	+	10466.0i	−0.673992	+	0.389130i
$165$	−33485.1	+	18093.7i	−1.22994	+	0.664599i
$166$	−12510.8	+	21669.4i	−0.454015	+	0.786376i
$167$	22677.9	−	39279.2i	0.813148	−	1.40841i	−0.0975023	−	0.995235i	$-0.531085\pi$
$167$	22677.9	−	39279.2i	0.813148	−	1.40841i	0.910650	−	0.413178i	$-0.135581\pi$
$168$	7961.60	−	9697.25i	0.282086	−	0.343582i
$169$	−7729.75	−	13388.3i	−0.270640	−	0.468762i
$170$	3712.94	+	27206.9i	0.128475	+	0.941417i
$171$	1644.17	−	1440.72i	0.0562281	−	0.0492706i
$172$			3652.41i			0.123459i
$173$	2848.13	+	4933.11i	0.0951630	+	0.164827i	0.909677	−	0.415317i	$-0.136329\pi$
$173$	2848.13	+	4933.11i	0.0951630	+	0.164827i	−0.814514	+	0.580144i	$0.802996\pi$
$174$	−16575.9	−	2740.12i	−0.547492	−	0.0905048i
$175$	−34989.5	−	9021.32i	−1.14251	−	0.294574i
$176$	−45192.6	−	26092.0i	−1.45896	−	0.842328i
$177$	43152.0	+	7133.36i	1.37738	+	0.227692i
$178$	−3891.07	+	2246.51i	−0.122809	+	0.0709036i
$179$			28582.7i			0.892066i	0.895017	+	0.446033i	$0.147164\pi$
$179$			28582.7i			0.892066i	−0.895017	+	0.446033i	$0.852836\pi$
$180$	4402.79	−	22646.3i	0.135889	−	0.698960i
$181$	34257.3			1.04567			0.522837	−	0.852433i	$-0.324874\pi$
$181$	34257.3			1.04567			0.522837	+	0.852433i	$0.324874\pi$
$182$	−17317.4	−	29994.5i	−0.522804	−	0.905523i
$183$	6592.00	+	5412.14i	0.196841	+	0.161609i
$184$	−11059.4	+	19155.5i	−0.326661	+	0.565793i
$185$	−3485.43	+	8528.52i	−0.101839	+	0.249190i
$186$	−55487.1	+	20871.1i	−1.60386	+	0.603281i
$187$	30743.7	−	17749.9i	0.879170	−	0.507589i
$188$	27896.1			0.789274
$189$	−1353.51	−	42124.7i	−0.0378913	−	1.17927i
$190$	−477.497	−	3498.91i	−0.0132271	−	0.0969227i
$191$	61661.0	−	35600.0i	1.69022	−	0.975850i	0.735889	−	0.677102i	$-0.236764\pi$
$191$	61661.0	−	35600.0i	1.69022	−	0.975850i	0.954332	−	0.298748i	$-0.0965690\pi$
$192$	12595.7	−	4737.80i	0.341681	−	0.128521i
$193$	53250.9	+	30744.4i	1.42959	+	0.825375i	0.997088	−	0.0762568i	$-0.0242969\pi$
$193$	53250.9	+	30744.4i	1.42959	+	0.825375i	0.432504	+	0.901632i	$0.357630\pi$
$194$	−19334.3	−	11162.7i	−0.513720	−	0.296596i
$195$	21931.7	+	13500.6i	0.576770	+	0.355045i
$196$	5362.91	+	9288.84i	0.139601	+	0.241796i
$197$	14233.7			0.366763			0.183382	−	0.983042i	$-0.441296\pi$
$197$	14233.7			0.366763			0.183382	+	0.983042i	$0.441296\pi$
$198$	−70340.9	+	13962.2i	−1.79423	+	0.356142i
$199$	−58493.1			−1.47706			−0.738531	−	0.674220i	$-0.764480\pi$
$199$	−58493.1			−1.47706			−0.738531	+	0.674220i	$0.764480\pi$
$200$	10757.1	+	10555.4i	0.268928	+	0.263885i
$201$	−19255.1	−	3183.02i	−0.476600	−	0.0787857i
$202$	−19422.4	−	11213.5i	−0.475993	−	0.274815i
$203$	−10310.4	+	17858.1i	−0.250197	+	0.433353i
$204$	−3509.45	+	21229.8i	−0.0843293	+	0.510135i
$205$	−28134.3	−	36308.2i	−0.669466	−	0.863968i
$206$			54814.5i			1.29170i
$207$	14465.8	+	72878.1i	0.337600	+	1.70081i
$208$			35310.2i			0.816158i
$209$	−3953.75	+	2282.70i	−0.0905141	+	0.0522584i
$210$	−57977.9	−	35689.7i	−1.31469	−	0.809290i
$211$	16666.2	−	28866.8i	0.374346	−	0.648386i	−0.615883	−	0.787838i	$-0.711201\pi$
$211$	16666.2	−	28866.8i	0.374346	−	0.648386i	0.990229	+	0.139452i	$0.0445340\pi$
$212$	10816.5	−	18734.7i	0.240665	−	0.416844i
$213$	−28766.9	−	76478.5i	−0.634065	−	1.68570i
$214$	−46768.3	−	81005.0i	−1.02123	−	1.76882i
$215$	−7941.15	+	1083.73i	−0.171793	+	0.0234447i
$216$	−8295.92	+	15498.0i	−0.177810	+	0.332176i
$217$			72761.2i			1.54518i
$218$	−38831.3	−	67257.8i	−0.817088	−	1.41524i
$219$	−3120.51	−	8296.06i	−0.0650634	−	0.172975i
$220$	−18226.8	+	44599.1i	−0.376586	+	0.921469i
$221$	−20802.7	−	12010.5i	−0.425927	−	0.245909i
$222$	−11015.3	+	13416.7i	−0.223508	+	0.272233i
$223$	−40241.9	+	23233.7i	−0.809223	+	0.467205i	−0.846686	−	0.532093i	$-0.821406\pi$
$223$	−40241.9	+	23233.7i	−0.809223	+	0.467205i	0.0374627	+	0.999298i	$0.488072\pi$
$224$		−	71039.5i		−	1.41581i
$225$	50544.5	+	2853.10i	0.998411	+	0.0563576i
$226$	49085.1			0.961021
$227$	−12971.6	−	22467.6i	−0.251735	−	0.436018i	0.712269	−	0.701907i	$-0.247668\pi$
$227$	−12971.6	−	22467.6i	−0.251735	−	0.436018i	−0.964004	+	0.265889i	$0.914334\pi$
$228$	451.328	−	2730.23i	0.00868205	−	0.0525205i
$229$	12098.4	−	20955.0i	0.230705	−	0.399593i	−0.727311	−	0.686308i	$-0.759230\pi$
$229$	12098.4	−	20955.0i	0.230705	−	0.399593i	0.958016	+	0.286716i	$0.0925635\pi$
$230$	111102.	+	45405.2i	2.10023	+	0.858321i
$231$	−14355.3	+	86839.6i	−0.269022	+	1.62740i
$232$	7448.36	−	4300.31i	0.138384	−	0.0798958i
$233$	59802.9			1.10157			0.550783	−	0.834648i	$-0.314329\pi$
$233$	59802.9			1.10157			0.550783	+	0.834648i	$0.314329\pi$
$234$	31979.9	+	36495.8i	0.584044	+	0.666516i
$235$	8277.25	+	60652.4i	0.149882	+	1.09828i
$236$	47948.1	−	27682.9i	0.860890	−	0.497035i
$237$	−71305.1	−	58542.7i	−1.26947	−	1.04226i
$238$	54993.4	+	31750.4i	0.970860	+	0.560526i
$239$	64376.8	+	37168.0i	1.12703	+	0.650689i	0.943185	−	0.332267i	$-0.107814\pi$
$239$	64376.8	+	37168.0i	1.12703	+	0.650689i	0.183841	+	0.982956i	$0.441147\pi$
$240$	32996.7	+	61065.3i	0.572860	+	1.06016i
$241$	27807.6	+	48164.2i	0.478773	+	0.829259i	0.999704	−	0.0243398i	$-0.00774835\pi$
$241$	27807.6	+	48164.2i	0.478773	+	0.829259i	−0.520931	+	0.853599i	$0.674415\pi$
$242$	73137.1			1.24884
$243$	13350.7	+	57519.9i	0.226094	+	0.974105i
$244$	10796.7			0.181347
$245$	−18604.8	+	14416.3i	−0.309950	+	0.240172i
$246$	−30469.3	−	81004.5i	−0.503491	−	1.33856i
$247$	2675.30	+	1544.59i	0.0438510	+	0.0253174i
$248$	15173.9	−	26281.9i	0.246713	−	0.427320i
$249$	−33254.8	−	27302.7i	−0.536359	−	0.440359i
$250$	48857.3	−	65579.3i	0.781717	−	1.04927i
$251$			31731.5i			0.503666i	0.967771	+	0.251833i	$0.0810334\pi$
$251$			31731.5i			0.503666i	−0.967771	+	0.251833i	$0.918967\pi$
$252$	−35160.9	−	40126.0i	−0.553681	−	0.631865i
$253$		−	155167.i		−	2.42415i
$254$	−16516.9	+	9536.04i	−0.256013	+	0.147809i
$255$	−47199.6	−	1331.09i	−0.725869	−	0.0204704i
$256$	−42931.1	+	74358.9i	−0.655077	+	1.13463i
$257$	−21760.7	+	37690.7i	−0.329463	+	0.570647i	−0.982405	−	0.186761i	$-0.940201\pi$
$257$	−21760.7	+	37690.7i	−0.329463	+	0.570647i	0.652942	+	0.757408i	$0.273534\pi$
$258$	−14899.0	−	2462.92i	−0.223829	−	0.0370007i
$259$	10653.1	+	18451.7i	0.158809	+	0.275066i
$260$	32301.5	−	4408.19i	0.477832	−	0.0652100i
$261$	9297.59	−	27353.6i	0.136486	−	0.401544i
$262$			28083.9i			0.409124i
$263$	20223.6	+	35028.3i	0.292380	+	0.506417i	0.974372	−	0.224943i	$-0.0722195\pi$
$263$	20223.6	+	35028.3i	0.292380	+	0.506417i	−0.681992	+	0.731360i	$0.738886\pi$
$264$	23295.1	−	28373.4i	0.334238	−	0.407103i
$265$	43942.8	+	17958.5i	0.625743	+	0.255728i
$266$	−7072.34	−	4083.22i	−0.0999540	−	0.0577085i
$267$	−2720.08	−	7231.50i	−0.0381557	−	0.101439i
$268$	−21395.2	+	12352.5i	−0.297884	+	0.171984i
$269$		−	16975.9i		−	0.234600i	−0.993097	−	0.117300i	$-0.962576\pi$
$269$		−	16975.9i		−	0.234600i	0.993097	−	0.117300i	$-0.0374239\pi$
$270$	89410.4	+	33231.0i	1.22648	+	0.455843i
$271$	79819.5			1.08685			0.543426	−	0.839457i	$-0.317127\pi$
$271$	79819.5			1.08685			0.543426	+	0.839457i	$0.317127\pi$
$272$	−32369.7	−	56066.0i	−0.437523	−	0.757812i
$273$	55744.4	−	20967.9i	0.747956	−	0.281339i
$274$	−6397.25	+	11080.4i	−0.0852103	+	0.147589i
$275$	−102377.	−	26395.7i	−1.35374	−	0.349034i
$276$	72692.2	+	59681.5i	0.954267	+	0.783469i
$277$	−76743.8	+	44308.0i	−1.00019	+	0.577461i	−0.908305	−	0.418308i	$-0.862623\pi$
$277$	−76743.8	+	44308.0i	−1.00019	+	0.577461i	−0.0918873	+	0.995769i	$0.529290\pi$
$278$	−78549.1			−1.01637
$279$	−19847.5	−	99990.9i	−0.254975	−	1.28455i
$280$	34532.3	−	4712.64i	0.440463	−	0.0601101i
$281$	−63506.1	+	36665.3i	−0.804272	+	0.464346i	−0.844963	−	0.534825i	$-0.820377\pi$
$281$	−63506.1	+	36665.3i	−0.804272	+	0.464346i	0.0406910	+	0.999172i	$0.487044\pi$
$282$	−18811.1	+	113794.i	−0.236546	+	1.43094i
$283$	−50958.4	−	29420.9i	−0.636272	−	0.367352i	0.146905	−	0.989151i	$-0.453069\pi$
$283$	−50958.4	−	29420.9i	−0.636272	−	0.367352i	−0.783177	+	0.621799i	$0.786402\pi$
$284$	−89575.9	−	51716.7i	−1.11059	−	0.641200i
$285$	6070.04	+	171.183i	0.0747312	+	0.00210751i
$286$	−50669.3	−	87761.8i	−0.619460	−	1.07294i
$287$	−106223.			−1.28959
$288$	19377.9	+	97624.8i	0.233626	+	1.17700i
$289$	−39479.9			−0.472695
$290$	−28585.2	−	36890.1i	−0.339895	−	0.438646i
$291$	24360.6	−	29671.3i	0.287675	−	0.350390i
$292$	−9716.80	−	5610.00i	−0.113961	−	0.0657956i
$293$	50633.1	−	87699.2i	0.589793	−	1.02155i	−0.404466	−	0.914553i	$-0.632543\pi$
$293$	50633.1	−	87699.2i	0.589793	−	1.02155i	0.994259	−	0.106998i	$-0.0341240\pi$
$294$	−41507.6	+	15612.8i	−0.480212	+	0.180628i
$295$	74415.8	+	96036.0i	0.855108	+	1.10354i
$296$		−	8886.52i		−	0.101426i
$297$	−3960.29	−	123254.i	−0.0448966	−	1.39729i
$298$			66068.8i			0.743984i
$299$	−90927.4	+	52496.9i	−1.01707	+	0.587208i
$300$	51742.6	−	37808.6i	0.574918	−	0.420095i
$301$	−9267.31	+	16051.4i	−0.102287	+	0.177166i
$302$	−60927.7	+	105530.i	−0.668038	+	1.15708i
$303$	24471.6	−	29806.5i	0.266549	−	0.324658i
$304$	4162.86	+	7210.28i	0.0450448	+	0.0780199i
$305$	3203.56	+	23474.4i	0.0344376	+	0.252345i
$306$	−84234.5	−	28631.7i	−0.899596	−	0.305776i
$307$		−	43494.6i		−	0.461487i	−0.973015	−	0.230743i	$-0.925884\pi$
$307$		−	43494.6i		−	0.461487i	0.973015	−	0.230743i	$-0.0741158\pi$
$308$	55709.4	+	96491.5i	0.587255	+	1.01716i
$309$	−92996.4	−	15373.0i	−0.973978	−	0.161006i
$310$	−152435.	−	62297.2i	−1.58622	−	0.648254i
$311$	−65710.8	−	37938.2i	−0.679385	−	0.392243i	0.120238	−	0.992745i	$-0.461634\pi$
$311$	−65710.8	−	37938.2i	−0.679385	−	0.392243i	−0.799623	+	0.600502i	$0.794967\pi$
$312$	−24508.0	−	4051.37i	−0.251767	−	0.0416191i
$313$	−58416.4	+	33726.7i	−0.596274	+	0.344259i	−0.767574	−	0.640960i	$-0.778537\pi$
$313$	−58416.4	+	33726.7i	−0.596274	+	0.344259i	0.171300	+	0.985219i	$0.445203\pi$
$314$		−	89446.5i		−	0.907202i
$315$	76810.0	−	88353.8i	0.774100	−	0.890439i
$316$	−116787.			−1.16955
$317$	90575.3	+	156881.i	0.901345	+	1.56118i	0.825749	+	0.564037i	$0.190752\pi$
$317$	90575.3	+	156881.i	0.901345	+	1.56118i	0.0755957	+	0.997139i	$0.475914\pi$
$318$	69129.0	+	56756.0i	0.683606	+	0.561252i
$319$	−30167.3	+	52251.4i	−0.296453	+	0.513472i
$320$	34603.3	+	14141.7i	0.337923	+	0.138102i
$321$	150547.	−	56627.1i	1.46104	−	0.549559i
$322$	240373.	−	138779.i	2.31832	−	1.33848i
$323$	−5663.83			−0.0542882
$324$	59264.7	+	45551.4i	0.564555	+	0.433922i
$325$	19168.8	+	68922.7i	0.181480	+	0.652522i
$326$	117905.	−	68072.5i	1.10942	−	0.640526i
$327$	124998.	−	47017.0i	1.16898	−	0.439703i
$328$	38368.4	+	22152.0i	0.356636	+	0.205904i
$329$	122597.	+	70781.2i	1.13263	+	0.653922i
$330$	−169639.	−	104425.i	−1.55775	−	0.958911i
$331$	−78059.4	−	135203.i	−0.712475	−	1.23404i	−0.963926	−	0.266172i	$-0.914241\pi$
$331$	−78059.4	−	135203.i	−0.712475	−	1.23404i	0.251451	−	0.967870i	$-0.419092\pi$
$332$	−54466.2			−0.494141
$333$	−19673.0	−	22451.0i	−0.177412	−	0.202464i
$334$	237383.			2.12793
$335$	−33205.5	−	42852.8i	−0.295884	−	0.381847i
$336$	158366.	+	26179.1i	1.40276	+	0.231887i
$337$	−120915.	−	69810.3i	−1.06468	−	0.614695i	−0.137959	−	0.990438i	$-0.544054\pi$
$337$	−120915.	−	69810.3i	−1.06468	−	0.614695i	−0.926724	+	0.375743i	$0.877388\pi$
$338$	40456.0	−	70071.9i	0.354119	−	0.613353i
$339$	−13766.2	+	83276.0i	−0.119788	+	0.724637i
$340$	−47247.5	+	36610.9i	−0.408716	+	0.316703i
$341$			212894.i			1.83086i
$342$	10832.9	+	3682.13i	0.0926170	+	0.0314809i
$343$		−	84381.8i		−	0.717234i
$344$	6694.84	−	3865.27i	0.0565749	−	0.0326635i
$345$	−108192.	+	175758.i	−0.908985	+	1.47665i
$346$	−14906.6	+	25819.0i	−0.124516	+	0.215668i
$347$	−304.265	+	527.002i	−0.00252693	+	0.00437677i	−0.867286	−	0.497810i	$-0.834138\pi$
$347$	−304.265	+	527.002i	−0.00252693	+	0.00437677i	0.864759	+	0.502187i	$0.167471\pi$
$348$	−12875.4	−	34230.0i	−0.106317	−	0.282650i
$349$	31381.4	+	54354.2i	0.257645	+	0.446254i	0.965611	−	0.259993i	$-0.0837202\pi$
$349$	31381.4	+	54354.2i	0.257645	+	0.446254i	−0.707966	+	0.706247i	$0.750387\pi$
$350$	−50674.0	−	182202.i	−0.413665	−	1.48736i
$351$	−70886.3	+	44020.5i	−0.575371	+	0.357307i
$352$		−	207856.i		−	1.67756i
$353$	54482.8	+	94367.0i	0.437230	+	0.757305i	0.997475	−	0.0710225i	$-0.0226262\pi$
$353$	54482.8	+	94367.0i	0.437230	+	0.757305i	−0.560245	+	0.828327i	$0.689293\pi$
$354$	80591.8	+	214258.i	0.643109	+	1.70974i
$355$	85864.9	−	210103.i	0.681332	−	1.66716i
$356$	−8469.93	−	4890.12i	−0.0668313	−	0.0385851i
$357$	−69289.9	+	84395.3i	−0.543667	+	0.662188i
$358$	−129554.	+	74798.1i	−1.01085	+	0.583613i
$359$			11414.0i			0.0885621i	0.999019	+	0.0442811i	$0.0140997\pi$
$359$			11414.0i			0.0885621i	−0.999019	+	0.0442811i	$0.985900\pi$
$360$	−46170.0	+	15895.8i	−0.356250	+	0.122653i
$361$	−129593.			−0.994411
$362$	89648.1	+	155275.i	0.684107	+	1.18491i
$363$	−20511.7	+	124082.i	−0.155664	+	0.941661i
$364$	37695.8	−	65291.0i	0.284505	−	0.492777i
$365$	9314.25	−	22791.1i	0.0699137	−	0.171072i
$366$	−7280.49	+	44042.0i	−0.0543499	+	0.328780i
$367$	112351.	−	64865.6i	0.834148	−	0.481595i	−0.0211230	−	0.999777i	$-0.506724\pi$
$367$	112351.	−	64865.6i	0.834148	−	0.481595i	0.855271	+	0.518182i	$0.173391\pi$
$368$	−282972.			−2.08953
$369$	145975.	−	28975.0i	1.07207	−	0.212799i
$370$	−47777.5	+	6520.21i	−0.348996	+	0.0476275i
$371$	95071.5	−	54889.5i	0.690721	−	0.398788i
$372$	−99735.8	−	81884.7i	−0.720718	−	0.591721i
$373$	−49139.4	−	28370.6i	−0.353193	−	0.203916i	0.312898	−	0.949787i	$-0.398700\pi$
$373$	−49139.4	−	28370.6i	−0.353193	−	0.203916i	−0.666091	+	0.745871i	$0.732034\pi$
$374$	160907.	+	92899.5i	1.15035	+	0.664156i
$375$	97557.3	+	101282.i	0.693741	+	0.720225i
$376$	−29521.9	−	51133.4i	−0.208818	−	0.361684i
$377$	40825.5			0.287242
$378$	187393.	−	116371.i	1.31150	−	0.814445i
$379$	−98981.2			−0.689087			−0.344544	−	0.938770i	$-0.611966\pi$
$379$	−98981.2			−0.689087			−0.344544	+	0.938770i	$0.611966\pi$
$380$	6076.20	−	4708.29i	0.0420790	−	0.0326059i
$381$	−11546.3	−	30696.4i	−0.0795410	−	0.211465i
$382$	322722.	+	186323.i	2.21157	+	1.27685i
$383$	−90868.5	+	157389.i	−0.619464	+	1.07294i	0.370120	+	0.928984i	$0.379317\pi$
$383$	−90868.5	+	157389.i	−0.619464	+	1.07294i	−0.989584	+	0.143959i	$0.954017\pi$
$384$	−82318.3	−	67584.6i	−0.558257	−	0.458338i
$385$	−193264.	+	149755.i	−1.30386	+	1.01032i
$386$			321821.i			2.15993i
$387$	8356.99	−	24586.3i	0.0557992	−	0.164162i
$388$		−	48597.0i		−	0.322810i
$389$	141766.	−	81848.8i	0.936858	−	0.540895i	0.0478838	−	0.998853i	$-0.484752\pi$
$389$	141766.	−	81848.8i	0.936858	−	0.540895i	0.888974	+	0.457958i	$0.151419\pi$
$390$	−3799.76	+	134737.i	−0.0249820	+	0.885848i
$391$	96250.3	−	166710.i	0.629577	−	1.09046i
$392$	11350.9	−	19660.4i	0.0738685	−	0.127944i
$393$	−47646.2	−	7876.28i	−0.308491	−	0.0509960i
$394$	37248.3	+	64515.9i	0.239946	+	0.415599i
$395$	−34652.6	−	253920.i	−0.222097	−	1.62743i
$396$	−102878.	−	117406.i	−0.656045	−	0.748684i
$397$			170885.i			1.08424i	0.840302	+	0.542118i	$0.182378\pi$
$397$			170885.i			1.08424i	−0.840302	+	0.542118i	$0.817622\pi$
$398$	−153071.	−	265127.i	−0.966332	−	1.67374i
$399$	8910.92	−	10853.5i	0.0559728	−	0.0681750i
$400$	−48136.8	+	186700.i	−0.300855	+	1.16688i
$401$	−55371.9	−	31969.0i	−0.344350	−	0.198811i	0.317844	−	0.948143i	$-0.397041\pi$
$401$	−55371.9	−	31969.0i	−0.344350	−	0.198811i	−0.662194	+	0.749332i	$0.730375\pi$
$402$	−35961.4	−	95605.6i	−0.222528	−	0.591604i
$403$	124755.	−	72027.3i	0.768153	−	0.443493i
$404$		−	48818.4i		−	0.299103i
$405$	−81454.1	+	142371.i	−0.496596	+	0.867982i
$406$	−107925.			−0.654741
$407$	31170.2	+	53988.3i	0.188170	+	0.325920i
$408$	42628.1	−	16034.3i	0.256080	−	0.0963227i
$409$	−22555.8	+	39067.7i	−0.134838	+	0.233546i	−0.925535	−	0.378661i	$-0.876385\pi$
$409$	−22555.8	+	39067.7i	−0.134838	+	0.233546i	0.790698	+	0.612207i	$0.209718\pi$
$410$	90946.3	−	222537.i	0.541025	−	1.32384i
$411$	−17004.4	−	13960.9i	−0.100665	−	0.0826474i
$412$	−103333.	+	59659.1i	−0.608755	+	0.351465i
$413$	280961.			1.64720
$414$	−292473.	+	256283.i	−1.70641	+	1.49527i
$415$	−16161.0	−	118422.i	−0.0938368	−	0.687599i
$416$	−121803.	+	70323.0i	−0.703835	+	0.406360i
$417$	22029.5	−	133264.i	0.126687	−	0.766372i
$418$	−20693.2	−	11947.2i	−0.118433	−	0.0683776i
$419$	−107823.	−	62251.4i	−0.614160	−	0.354585i	0.160432	−	0.987047i	$-0.448711\pi$
$419$	−107823.	−	62251.4i	−0.614160	−	0.354585i	−0.774592	+	0.632461i	$0.782045\pi$
$420$	4177.72	−	148140.i	0.0236832	−	0.839795i
$421$	91249.6	+	158049.i	0.514834	+	0.891718i	0.999852	+	0.0172140i	$0.00547966\pi$
$421$	91249.6	+	158049.i	0.514834	+	0.891718i	−0.485018	+	0.874504i	$0.661187\pi$
$422$	174456.			0.979627
$423$	−187784.	−	63828.5i	−1.04949	−	0.356725i
$424$	−45787.4			−0.254691
$425$	−93619.4	−	91863.7i	−0.518308	−	0.508588i
$426$	271367.	−	330526.i	1.49533	−	1.82132i
$427$	47448.8	+	27394.6i	0.260237	+	0.150248i
$428$	101803.	−	176329.i	0.555744	−	0.962577i
$429$	163104.	−	61350.5i	0.886238	−	0.333352i
$430$	−25693.4	−	33158.1i	−0.138958	−	0.179330i
$431$		−	52320.0i		−	0.281652i	−0.990034	−	0.140826i	$-0.955024\pi$
$431$		−	52320.0i		−	0.281652i	0.990034	−	0.140826i	$-0.0449758\pi$
$432$	−224773.	+	7222.21i	−1.20441	+	0.0386992i
$433$			342116.i			1.82473i	0.409383	+	0.912363i	$0.365744\pi$
$433$			342116.i			1.82473i	−0.409383	+	0.912363i	$0.634256\pi$
$434$	−329798.	+	190409.i	−1.75093	+	1.01090i
$435$	70603.3	−	38150.6i	0.373118	−	0.201615i
$436$	84526.5	−	146404.i	0.444652	−	0.770159i
$437$	−12378.1	+	21439.6i	−0.0648175	+	0.112267i
$438$	29436.7	−	35854.0i	0.153441	−	0.186892i
$439$	130466.	+	225974.i	0.676970	+	1.17255i	0.975889	+	0.218268i	$0.0700406\pi$
$439$	130466.	+	225974.i	0.676970	+	1.17255i	−0.298919	+	0.954278i	$0.596626\pi$
$440$	101039.	−	13788.8i	0.521896	−	0.0712233i
$441$	−14847.1	−	74799.0i	−0.0763422	−	0.384608i
$442$		−	125721.i		−	0.643521i
$443$	−93230.8	−	161480.i	−0.475064	−	0.822835i	0.524528	−	0.851393i	$-0.324242\pi$
$443$	−93230.8	−	161480.i	−0.475064	−	0.822835i	−0.999592	+	0.0285583i	$0.990908\pi$
$444$	−37281.2	−	6162.87i	−0.189114	−	0.0312620i
$445$	8119.04	−	19866.5i	0.0410001	−	0.100323i
$446$	−210618.	−	121600.i	−1.05883	−	0.611316i
$447$	−112090.	−	18529.3i	−0.560986	−	0.0927353i
$448$	74865.2	−	43223.4i	0.373013	−	0.215359i
$449$		−	65910.0i		−	0.326933i	−0.986549	−	0.163466i	$-0.947732\pi$
$449$		−	65910.0i		−	0.326933i	0.986549	−	0.163466i	$-0.0522675\pi$
$450$	119338.	+	236565.i	0.589324	+	1.16822i
$451$	−310799.			−1.52801
$452$	53423.3	+	92531.8i	0.261489	+	0.452912i
$453$	−161951.	−	132964.i	−0.789200	−	0.647946i
$454$	67891.1	−	117591.i	0.329383	−	0.570508i
$455$	153142.	+	62586.1i	0.739728	+	0.302312i
$456$	−5482.12	+	2062.06i	−0.0263645	+	0.00991682i
$457$	143662.	−	82943.1i	0.687874	−	0.397144i	−0.114941	−	0.993372i	$-0.536668\pi$
$457$	143662.	−	82943.1i	0.687874	−	0.397144i	0.802815	+	0.596228i	$0.203335\pi$
$458$	126641.			0.603733
$459$	72199.5	−	134879.i	0.342696	−	0.640207i
$460$	35326.7	+	258860.i	0.166950	+	1.22335i
$461$	−21859.7	+	12620.7i	−0.102859	+	0.0593857i	−0.550547	−	0.834804i	$-0.685581\pi$
$461$	−21859.7	+	12620.7i	−0.102859	+	0.0593857i	0.447688	+	0.894190i	$0.352248\pi$
$462$	−431177.	+	162184.i	−2.02009	+	0.759844i
$463$	88939.9	+	51349.5i	0.414892	+	0.239538i	0.692889	−	0.721044i	$-0.256337\pi$
$463$	88939.9	+	51349.5i	0.414892	+	0.239538i	−0.277998	+	0.960582i	$0.589671\pi$
$464$	95288.7	+	55014.9i	0.442594	+	0.255532i
$465$	148442.	−	241145.i	0.686519	−	1.11525i
$466$	156499.	+	271063.i	0.720673	+	1.24824i
$467$	−88039.3			−0.403685			−0.201843	−	0.979418i	$-0.564693\pi$
$467$	−88039.3			−0.403685			−0.201843	+	0.979418i	$0.564693\pi$
$468$	−33993.0	+	100008.i	−0.155202	+	0.456605i
$469$	−125369.			−0.569961
$470$	−253253.	+	196239.i	−1.14646	+	0.888361i
$471$	151752.	+	25085.8i	0.684057	+	0.113080i
$472$	−101485.	−	58592.5i	−0.455531	−	0.263001i
$473$	−27115.5	+	46965.4i	−0.121198	+	0.209921i
$474$	78752.4	−	476399.i	0.350516	−	2.12038i
$475$	12039.8	+	11814.0i	0.0533620	+	0.0523612i
$476$			138226.i			0.610066i
$477$	−115678.	+	101364.i	−0.508409	+	0.445501i
$478$			389060.i			1.70279i
$479$	241773.	−	139588.i	1.05375	−	0.608383i	0.130053	−	0.991507i	$-0.458485\pi$
$479$	241773.	−	139588.i	1.05375	−	0.608383i	0.923697	+	0.383124i	$0.125152\pi$
$480$	−144930.	+	235439.i	−0.629036	+	1.02187i
$481$	21091.3	−	36531.2i	0.0911618	−	0.157897i
$482$	−145540.	+	252082.i	−0.626452	+	1.08505i
$483$	168034.	+	446729.i	0.720283	+	1.91492i
$484$	79601.0	+	137873.i	0.339803	+	0.588557i
$485$	105661.	−	14419.6i	0.449191	−	0.0613012i
$486$	−225778.	+	211038.i	−0.955893	+	0.893485i
$487$		−	250438.i		−	1.05595i	−0.849261	−	0.527974i	$-0.822952\pi$
$487$		−	250438.i		−	1.05595i	0.849261	−	0.527974i	$-0.177048\pi$
$488$	−11425.9	−	19790.2i	−0.0479790	−	0.0831020i
$489$	82422.3	+	219125.i	0.344689	+	0.916377i
$490$	−114031.	−	46601.9i	−0.474929	−	0.194094i
$491$	−69322.6	−	40023.4i	−0.287549	−	0.166016i	0.349287	−	0.937016i	$-0.386424\pi$
$491$	−69322.6	−	40023.4i	−0.287549	−	0.166016i	−0.636836	+	0.770999i	$0.719757\pi$
$492$	119542.	−	145602.i	0.493844	−	0.601503i
$493$	−64823.1	+	37425.7i	−0.266708	+	0.153984i
$494$			16168.1i			0.0662531i
$495$	224741.	−	258517.i	0.917215	−	1.05506i
$496$	388246.			1.57813
$497$	−262443.	−	454565.i	−1.06248	−	1.84028i
$498$	36728.0	−	222180.i	0.148094	−	0.895871i
$499$	21430.3	−	37118.4i	0.0860652	−	0.149069i	−0.819779	−	0.572679i	$-0.805904\pi$
$499$	21430.3	−	37118.4i	0.0860652	−	0.149069i	0.905845	+	0.423610i	$0.139237\pi$
$500$	176801.	+	20727.1i	0.707204	+	0.0829084i
$501$	−66575.4	+	402736.i	−0.265240	+	1.60452i
$502$	−143826.	+	83038.2i	−0.570731	+	0.329512i
$503$	189896.			0.750549			0.375274	−	0.926914i	$-0.377548\pi$
$503$	189896.			0.750549			0.375274	+	0.926914i	$0.377548\pi$
$504$	−36340.6	+	106914.i	−0.143064	+	0.420896i
$505$	106142.	−	14485.3i	0.416203	−	0.0567993i
$506$	703313.	−	406058.i	2.74693	−	1.58594i
$507$	107535.	+	88288.3i	0.418346	+	0.343469i
$508$	−35953.4	−	20757.7i	−0.139320	−	0.0804362i
$509$	−18105.6	−	10453.2i	−0.0698838	−	0.0403474i	0.464651	−	0.885494i	$-0.346180\pi$
$509$	−18105.6	−	10453.2i	−0.0698838	−	0.0403474i	−0.534535	+	0.845147i	$0.679513\pi$
$510$	−117484.	−	217421.i	−0.451686	−	0.835913i
$511$	−28468.7	−	49309.2i	−0.109025	−	0.188837i
$512$	−260039.			−0.991970
$513$	−9285.11	+	17346.0i	−0.0352819	+	0.0659119i
$514$	−227783.			−0.862174
$515$	−160373.	−	206966.i	−0.604667	−	0.780342i
$516$	−11572.8	−	30767.1i	−0.0434651	−	0.115555i
$517$	358709.	+	207101.i	1.34203	+	0.774819i
$518$	−55756.2	+	96572.7i	−0.207794	+	0.359911i
$519$	−39622.9	−	32531.0i	−0.147100	−	0.120771i
$520$	−42264.2	−	54543.3i	−0.156303	−	0.201714i
$521$		−	54650.3i		−	0.201334i	−0.994920	−	0.100667i	$-0.967902\pi$
$521$		−	54650.3i		−	0.201334i	0.994920	−	0.100667i	$-0.0320977\pi$
$522$	148314.	−	29439.3i	0.544304	−	0.108041i
$523$		−	543509.i		−	1.98703i	−0.113723	−	0.993513i	$-0.536278\pi$
$523$		−	543509.i		−	1.98703i	0.113723	−	0.993513i	$-0.463722\pi$
$524$	−52941.8	+	30566.0i	−0.192813	+	0.111321i
$525$	323329.	−	34872.3i	1.17307	−	0.126521i
$526$	−105847.	+	183332.i	−0.382565	+	0.662622i
$527$	−132058.	+	228732.i	−0.475493	+	0.823578i
$528$	463367.	+	76598.1i	1.66210	+	0.274758i
$529$	−280784.	−	486331.i	−1.00337	−	1.73788i
$530$	33595.1	+	246171.i	0.119598	+	0.876366i
$531$	−386106.	+	76639.3i	−1.36936	+	0.271808i
$532$		−	17776.4i		−	0.0628088i
$533$	105151.	+	182127.i	0.370135	+	0.641092i
$534$	25659.4	−	31253.2i	0.0899837	−	0.109600i
$535$	413585.	+	169024.i	1.44496	+	0.590527i
$536$	45284.3	+	26144.9i	0.157623	+	0.0910034i
$537$	−90565.7	−	240775.i	−0.314062	−	0.834953i
$538$	76945.1	−	44424.3i	0.265838	−	0.153481i
$539$			159257.i			0.548178i
$540$	34667.8	+	204718.i	0.118888	+	0.702052i
$541$	−17290.1			−0.0590748			−0.0295374	−	0.999564i	$-0.509403\pi$
$541$	−17290.1			−0.0590748			−0.0295374	+	0.999564i	$0.509403\pi$
$542$	208880.	+	361791.i	0.711047	+	1.23157i
$543$	−288576.	+	108546.i	−0.978726	+	0.368141i
$544$	128933.	−	223319.i	0.435680	−	0.754620i
$545$	343396.	+	140339.i	1.15612	+	0.472482i
$546$	240917.	+	197797.i	0.808132	+	0.663490i
$547$	−70540.3	+	40726.4i	−0.235756	+	0.136114i	−0.613225	−	0.789909i	$-0.710128\pi$
$547$	−70540.3	+	40726.4i	−0.235756	+	0.136114i	0.377469	+	0.926022i	$0.376795\pi$
$548$	−27850.6			−0.0927412
$549$	−72678.3	−	24703.6i	−0.241135	−	0.0819627i
$550$	−148268.	−	533109.i	−0.490144	−	1.76234i
$551$	8336.48	−	4813.07i	0.0274587	−	0.0158533i
$552$	32467.2	−	196404.i	0.106553	−	0.644574i
$553$	−513249.	−	296325.i	−1.67833	−	0.968986i
$554$	−401662.	−	231900.i	−1.30870	−	0.755581i
$555$	2337.49	−	82886.2i	0.00758865	−	0.269089i
$556$	−85491.3	−	148075.i	−0.276549	−	0.478997i
$557$	449197.			1.44786			0.723930	−	0.689873i	$-0.242334\pi$
$557$	449197.			1.44786			0.723930	+	0.689873i	$0.242334\pi$
$558$	401281.	−	351628.i	1.28878	−	1.12931i
$559$	36695.4			0.117432
$560$	273103.	+	352448.i	0.870863	+	1.12388i
$561$	−202737.	+	246934.i	−0.644180	+	0.784613i
$562$	−332379.	−	191899.i	−1.05235	−	0.607575i
$563$	−122509.	+	212192.i	−0.386501	+	0.669440i	−0.991976	−	0.126424i	$-0.959650\pi$
$563$	−122509.	+	212192.i	−0.386501	+	0.669440i	0.605475	+	0.795864i	$0.292983\pi$
$564$	−234991.	+	88390.3i	−0.738742	+	0.277873i
$565$	−185333.	+	143610.i	−0.580573	+	0.449871i
$566$		−	307966.i		−	0.961325i
$567$	144876.	+	350561.i	0.450641	+	1.09043i
$568$			218923.i			0.678570i
$569$	−92989.2	+	53687.3i	−0.287216	+	0.165824i	−0.636685	−	0.771124i	$-0.719695\pi$
$569$	−92989.2	+	53687.3i	−0.287216	+	0.165824i	0.349470	+	0.936948i	$0.386362\pi$
$570$	15108.8	+	27961.1i	0.0465030	+	0.0860606i
$571$	−153839.	+	266458.i	−0.471841	+	0.817252i	−0.999481	−	0.0322159i	$-0.989744\pi$
$571$	−153839.	+	266458.i	−0.471841	+	0.817252i	0.527640	+	0.849468i	$0.323077\pi$
$572$	110295.	−	191037.i	0.337104	−	0.583881i
$573$	−406619.	+	495263.i	−1.23845	+	1.50843i
$574$	−277974.	−	481465.i	−0.843686	−	1.46131i
$575$	−552338.	+	153616.i	−1.67059	+	0.464624i
$576$	−91092.0	+	79820.6i	−0.274559	+	0.240586i
$577$			310091.i			0.931404i	0.884942	+	0.465702i	$0.154198\pi$
$577$			310091.i			0.931404i	−0.884942	+	0.465702i	$0.845802\pi$
$578$	−103315.	−	178947.i	−0.309249	−	0.535636i
$579$	−545990.	−	90256.3i	−1.62865	−	0.269228i
$580$	38431.1	−	94037.3i	0.114242	−	0.279540i
$581$	−239366.	−	138198.i	−0.709104	−	0.409401i
$582$	198238.	+	32770.3i	0.585250	+	0.0967463i
$583$	278172.	−	160603.i	0.818421	−	0.472515i
$584$			23747.8i			0.0696302i
$585$	−227525.	−	44234.4i	−0.664841	−	0.129255i
$586$	530008.			1.54343
$587$	−33542.3	−	58097.0i	−0.0973456	−	0.168608i	0.813240	−	0.581929i	$-0.197702\pi$
$587$	−33542.3	−	58097.0i	−0.0973456	−	0.168608i	−0.910585	+	0.413322i	$0.864369\pi$
$588$	−74608.3	−	61254.6i	−0.215790	−	0.177167i
$589$	16983.2	−	29415.7i	0.0489539	−	0.0847907i
$590$	−240555.	+	588615.i	−0.691051	+	1.69094i
$591$	−119902.	+	45100.2i	−0.343282	+	0.129123i
$592$	98456.2	−	56843.7i	0.280931	−	0.162196i
$593$	−82855.9			−0.235621			−0.117810	−	0.993036i	$-0.537588\pi$
$593$	−82855.9			−0.235621			−0.117810	+	0.993036i	$0.537588\pi$
$594$	548298.	−	340494.i	1.55397	−	0.965020i
$595$	−300535.	+	41014.1i	−0.848909	+	0.115851i
$596$	−124548.	+	71908.0i	−0.350627	+	0.202435i
$597$	492734.	−	185338.i	1.38250	−	0.520016i
$598$	−475896.	−	274759.i	−1.33079	−	0.768333i
$599$	−11075.7	−	6394.54i	−0.0308685	−	0.0178220i	0.484486	−	0.874799i	$-0.339007\pi$
$599$	−11075.7	−	6394.54i	−0.0308685	−	0.0178220i	−0.515355	+	0.856977i	$0.672340\pi$
$600$	−124061.	−	54831.9i	−0.344614	−	0.152311i
$601$	260678.	+	451507.i	0.721698	+	1.25002i	0.960319	+	0.278904i	$0.0899712\pi$
$601$	260678.	+	451507.i	0.721698	+	1.25002i	−0.238621	+	0.971113i	$0.576695\pi$
$602$	−97006.6			−0.267675
$603$	172287.	−	34197.7i	0.473824	−	0.0940508i
$604$	−265250.			−0.727080
$605$	−276148.	+	213980.i	−0.754450	+	0.584604i
$606$	199141.	+	32919.6i	0.542270	+	0.0896415i
$607$	−125226.	−	72299.3i	−0.339874	−	0.196226i	0.320343	−	0.947302i	$-0.396202\pi$
$607$	−125226.	−	72299.3i	−0.339874	−	0.196226i	−0.660216	+	0.751076i	$0.729535\pi$
$608$	−16581.3	+	28719.6i	−0.0448550	+	0.0776912i
$609$	30268.1	−	183102.i	0.0816114	−	0.493693i
$610$	−98016.9	+	75950.7i	−0.263415	+	0.204114i
$611$		−	280269.i		−	0.750746i
$612$	−37704.8	−	189955.i	−0.100669	−	0.507164i
$613$		−	39623.7i		−	0.105447i	−0.998609	−	0.0527235i	$-0.983210\pi$
$613$		−	39623.7i		−	0.105447i	0.998609	−	0.0527235i	$-0.0167902\pi$
$614$	197144.	−	113821.i	0.522935	−	0.301917i
$615$	352042.	+	216708.i	0.930774	+	0.572961i
$616$	117912.	−	204230.i	0.310740	−	0.538218i
$617$	81457.2	−	141088.i	0.213973	−	0.370612i	−0.738981	−	0.673726i	$-0.764693\pi$
$617$	81457.2	−	141088.i	0.213973	−	0.370612i	0.952954	+	0.303114i	$0.0980262\pi$
$618$	−173683.	−	461746.i	−0.454757	−	1.20900i
$619$	139987.	+	242465.i	0.365348	+	0.632801i	0.988832	−	0.149035i	$-0.0476168\pi$
$619$	139987.	+	242465.i	0.365348	+	0.632801i	−0.623484	+	0.781836i	$0.714283\pi$
$620$	−48469.3	−	355163.i	−0.126091	−	0.923942i
$621$	−352775.	−	568074.i	−0.914776	−	1.47307i
$622$		−	397122.i		−	1.02646i
$623$	−24815.5	−	42981.8i	−0.0639363	−	0.110741i
$624$	−111882.	−	297446.i	−0.287338	−	0.763905i
$625$	7394.52	+	390555.i	0.0189300	+	0.999821i
$626$	−305740.	−	176519.i	−0.780196	−	0.450447i
$627$	26072.7	−	31756.6i	0.0663210	−	0.0807791i
$628$	168618.	−	97351.9i	0.427549	−	0.246845i
$629$			77339.5i			0.195479i
$630$	601478.	+	116937.i	1.51544	+	0.294625i
$631$	521595.			1.31001			0.655005	−	0.755624i	$-0.272666\pi$
$631$	521595.			1.31001			0.655005	+	0.755624i	$0.272666\pi$
$632$	123593.	+	214069.i	0.309428	+	0.535945i
$633$	−48927.1	+	295976.i	−0.122107	+	0.738667i
$634$	−474054.	+	821085.i	−1.17937	+	2.04272i
$635$	34463.9	−	84329.8i	0.0854706	−	0.209138i
$636$	−31753.9	+	192089.i	−0.0785023	+	0.474886i
$637$	93324.0	−	53880.7i	0.229993	−	0.132787i
$638$	−315780.			−0.775789
$639$	484652.	+	553090.i	1.18694	+	1.35455i
$640$	−40004.8	−	293139.i	−0.0976679	−	0.715671i
$641$	−69970.9	+	40397.7i	−0.170295	+	0.0983197i	−0.582725	−	0.812670i	$-0.698013\pi$
$641$	−69970.9	+	40397.7i	−0.170295	+	0.0983197i	0.412430	+	0.910989i	$0.364680\pi$
$642$	650635.	+	534182.i	1.57858	+	1.29604i
$643$	163613.	+	94462.0i	0.395727	+	0.228473i	0.684639	−	0.728883i	$-0.259960\pi$
$643$	163613.	+	94462.0i	0.395727	+	0.228473i	−0.288911	+	0.957356i	$0.593293\pi$
$644$	523234.	+	302089.i	1.26161	+	0.728389i
$645$	63460.7	−	34291.1i	0.152541	−	0.0824255i
$646$	−14821.7	−	25672.0i	−0.0355168	−	0.0615168i
$647$	−315560.			−0.753829			−0.376915	−	0.926248i	$-0.623015\pi$
$647$	−315560.			−0.753829			−0.376915	+	0.926248i	$0.623015\pi$
$648$	20776.8	−	156838.i	0.0494799	−	0.373510i
$649$	822070.			1.95173
$650$	−262237.	+	267249.i	−0.620679	+	0.632541i
$651$	−230548.	−	612925.i	−0.544000	−	1.44626i
$652$	256651.	+	148178.i	0.603738	+	0.348568i
$653$	252626.	−	437561.i	0.592450	−	1.02615i	−0.401452	−	0.915880i	$-0.631494\pi$
$653$	252626.	−	437561.i	0.592450	−	1.02615i	0.993901	−	0.110273i	$-0.0351724\pi$
$654$	540217.	+	443527.i	1.26303	+	1.03697i
$655$	−82166.1	−	106038.i	−0.191518	−	0.247160i
$656$			566792.i			1.31709i
$657$	52573.0	+	59996.8i	0.121796	+	0.138994i
$658$			740911.i			1.71125i
$659$	−667937.	+	385634.i	−1.53803	+	0.887982i	−0.539076	+	0.842257i	$0.681226\pi$
$659$	−667937.	+	385634.i	−1.53803	+	0.887982i	−0.998954	+	0.0457248i	$0.985440\pi$
$660$	12223.7	−	433446.i	0.0280618	−	0.995055i
$661$	28063.6	−	48607.6i	0.0642304	−	0.111250i	−0.832122	−	0.554593i	$-0.812874\pi$
$661$	28063.6	−	48607.6i	0.0642304	−	0.111250i	0.896352	+	0.443342i	$0.146207\pi$
$662$	408548.	−	707626.i	0.932239	−	1.61469i
$663$	213294.	+	35259.1i	0.485233	+	0.0802129i
$664$	57640.5	+	99836.2i	0.130735	+	0.226439i
$665$	38649.9	−	5274.56i	0.0873986	−	0.0119273i
$666$	50279.4	−	147922.i	0.113355	−	0.333492i
$667$			327170.i			0.735398i
$668$	258363.	+	447499.i	0.579000	+	1.00286i
$669$	265372.	−	323224.i	0.592929	−	0.722190i
$670$	107340.	−	262650.i	0.239117	−	0.585096i
$671$	138832.	+	80154.5i	0.308350	+	0.178026i
$672$	225092.	+	598422.i	0.498450	+	1.32516i
$673$	457732.	−	264271.i	1.01060	−	0.583472i	0.0992350	−	0.995064i	$-0.468360\pi$
$673$	457732.	−	264271.i	1.01060	−	0.583472i	0.911368	+	0.411592i	$0.135027\pi$
$674$		−	730747.i		−	1.60860i
$675$	−434817.	+	136119.i	−0.954331	+	0.298752i
$676$	176126.			0.385417
$677$	−226733.	−	392712.i	−0.494694	−	0.856835i	0.505287	−	0.862951i	$-0.331386\pi$
$677$	−226733.	−	392712.i	−0.494694	−	0.856835i	−0.999981	+	0.00611624i	$0.998053\pi$
$678$	−413483.	+	155529.i	−0.899493	+	0.338338i
$679$	123306.	−	213572.i	0.267451	−	0.463239i
$680$	117109.	+	47859.9i	0.253263	+	0.103503i
$681$	180460.	+	148161.i	0.389123	+	0.319476i
$682$	−964965.	+	557123.i	−2.07464	+	1.19779i
$683$	−210879.			−0.452055			−0.226027	−	0.974121i	$-0.572574\pi$
$683$	−210879.			−0.452055			−0.226027	+	0.974121i	$0.572574\pi$
$684$	4848.97	+	24428.9i	0.0103642	+	0.0522146i
$685$	−8263.74	−	60553.4i	−0.0176115	−	0.129050i
$686$	382470.	−	220819.i	0.812735	−	0.469233i
$687$	−35517.3	+	214855.i	−0.0752534	+	0.455232i
$688$	85648.8	+	49449.3i	0.180944	+	0.104468i
$689$	−188225.	−	108672.i	−0.396496	−	0.228917i
$690$	−1.07977e6	−	30450.8i	−2.26795	−	0.0639589i
$691$	12289.0	+	21285.1i	0.0257371	+	0.0445780i	0.878607	−	0.477545i	$-0.158473\pi$
$691$	12289.0	+	21285.1i	0.0257371	+	0.0445780i	−0.852870	+	0.522123i	$0.825140\pi$
$692$	−64896.2			−0.135521
$693$	−154230.	−	777004.i	−0.321146	−	1.61792i
$694$	−3184.93			−0.00661273
$695$	296582.	−	229814.i	0.614010	−	0.475780i
$696$	−49117.7	+	59825.4i	−0.101396	+	0.123500i
$697$	−333920.	−	192789.i	−0.687349	−	0.396841i
$698$	−164244.	+	284479.i	−0.337116	+	0.583902i
$699$	−503767.	+	189489.i	−1.03104	+	0.387819i
$700$	288321.	−	293832.i	0.588411	−	0.599657i
$701$			349841.i			0.711925i	0.934500	+	0.355963i	$0.115847\pi$
$701$			349841.i			0.711925i	−0.934500	+	0.355963i	$0.884153\pi$
$702$	−385031.	−	206103.i	−0.781306	−	0.418224i
$703$		−	9946.13i		−	0.0201254i
$704$	219050.	−	126469.i	0.441975	−	0.255175i
$705$	−261906.	−	484696.i	−0.526948	−	0.975195i
$706$	−285153.	+	493899.i	−0.572095	+	0.990897i
$707$	123868.	−	214545.i	0.247810	−	0.429220i
$708$	−316190.	+	385121.i	−0.630786	+	0.768299i
$709$	−94271.7	−	163283.i	−0.187538	−	0.324825i	0.756891	−	0.653541i	$-0.226717\pi$
$709$	−94271.7	−	163283.i	−0.187538	−	0.324825i	−0.944429	+	0.328716i	$0.893384\pi$
$710$	1.17702e6	−	160628.i	2.33489	−	0.318643i
$711$	786155.	+	267217.i	1.55514	+	0.528598i
$712$			20700.5i			0.0408338i
$713$	577218.	+	999771.i	1.13543	+	1.96662i
$714$	−563856.	−	93209.8i	−1.10604	−	0.182837i
$715$	448083.	+	183122.i	0.876489	+	0.358203i
$716$	−282008.	−	162818.i	−0.550093	−	0.317596i
$717$	−660066.	−	109114.i	−1.28395	−	0.212247i
$718$	−51735.1	+	29869.3i	−0.100354	+	0.0579396i
$719$			570498.i			1.10356i	0.833989	+	0.551781i	$0.186051\pi$
$719$			570498.i			1.10356i	−0.833989	+	0.551781i	$0.813949\pi$
$720$	−471446.	−	409850.i	−0.909426	−	0.790605i
$721$	−605496.			−1.16477
$722$	−339131.	−	587393.i	−0.650569	−	1.12682i
$723$	−386856.	−	317615.i	−0.740071	−	0.607610i
$724$	−195143.	+	337997.i	−0.372284	+	0.644815i
$725$	215861.	+	55655.4i	0.410676	+	0.105884i
$726$	−616091.	+	231739.i	−1.16889	+	0.439668i
$727$	−309462.	+	178668.i	−0.585515	+	0.338047i	−0.763322	−	0.646018i	$-0.776433\pi$
$727$	−309462.	+	178668.i	−0.585515	+	0.338047i	0.177807	+	0.984065i	$0.443100\pi$
$728$	−159571.			−0.301086
$729$	−294718.	−	442234.i	−0.554564	−	0.832141i
$730$	127678.	−	17424.2i	0.239590	−	0.0326970i
$731$	−58265.3	+	33639.5i	−0.109037	+	0.0629527i
$732$	−90948.9	+	34209.8i	−0.169737	+	0.0638452i
$733$	310569.	+	179307.i	0.578029	+	0.333725i	0.760350	−	0.649514i	$-0.225028\pi$
$733$	310569.	+	179307.i	0.578029	+	0.333725i	−0.182321	+	0.983239i	$0.558361\pi$
$734$	588021.	+	339494.i	1.09144	+	0.630144i
$735$	111044.	−	180390.i	0.205551	−	0.333917i
$736$	−563560.	−	976114.i	−1.04036	−	1.80196i
$737$	−366821.			−0.675335
$738$	513334.	+	585821.i	0.942512	+	1.07560i
$739$	−121677.			−0.222802			−0.111401	−	0.993776i	$-0.535534\pi$
$739$	−121677.			−0.222802			−0.111401	+	0.993776i	$0.535534\pi$
$740$	−64291.6	−	82970.4i	−0.117406	−	0.151516i
$741$	−27430.3	−	4534.44i	−0.0499568	−	0.00825824i
$742$	497586.	+	287281.i	0.903775	+	0.521795i
$743$	336425.	−	582705.i	0.609411	−	1.05553i	−0.381927	−	0.924193i	$-0.624739\pi$
$743$	336425.	−	582705.i	0.609411	−	1.05553i	0.991338	−	0.131338i	$-0.0419274\pi$
$744$	−44545.9	+	269472.i	−0.0804751	+	0.486820i
$745$	−193300.	−	249460.i	−0.348272	−	0.449456i
$746$		−	296973.i		−	0.533628i
$747$	366642.	+	124623.i	0.657053	+	0.223335i
$748$			404440.i			0.722855i
$749$	894803.	−	516615.i	1.59501	−	0.920880i
$750$	−203772.	+	707234.i	−0.362262	+	1.25730i
$751$	−75730.1	+	131168.i	−0.134273	+	0.232568i	−0.925319	−	0.379188i	$-0.876203\pi$
$751$	−75730.1	+	131168.i	−0.134273	+	0.232568i	0.791047	+	0.611756i	$0.209537\pi$
$752$	377681.	−	654162.i	0.667866	−	1.15678i
$753$	−100543.	−	267299.i	−0.177321	−	0.471420i
$754$	106836.	+	185046.i	0.187921	+	0.325489i
$755$	−78704.3	−	576714.i	−0.138072	−	1.01173i
$756$	423330.	+	226604.i	0.740688	+	0.396482i
$757$			667098.i			1.16412i	0.813146	+	0.582060i	$0.197753\pi$
$757$			667098.i			1.16412i	−0.813146	+	0.582060i	$0.802247\pi$
$758$	−259024.	−	448643.i	−0.450819	−	0.780841i
$759$	491655.	+	1.30710e6i	0.853448	+	2.26895i
$760$	−15060.6	−	6154.96i	−0.0260744	−	0.0106561i
$761$	93560.3	+	54017.1i	0.161556	+	0.0932742i	0.578598	−	0.815613i	$-0.303600\pi$
$761$	93560.3	+	54017.1i	0.161556	+	0.0932742i	−0.417042	+	0.908887i	$0.636933\pi$
$762$	108920.	−	132664.i	0.187584	−	0.228478i
$763$	742947.	−	428941.i	1.27617	−	0.736798i
$764$			811163.i			1.38970i
$765$	401818.	−	138342.i	0.686604	−	0.236391i
$766$	−951177.			−1.62108
$767$	−278127.	−	481730.i	−0.472773	−	0.818866i
$768$	126033.	−	762414.i	0.213679	−	1.29261i
$769$	341156.	−	590900.i	0.576900	−	0.999220i	−0.418932	−	0.908017i	$-0.637596\pi$
$769$	341156.	−	590900.i	0.576900	−	0.999220i	0.995832	−	0.0912025i	$-0.0290711\pi$
$770$	−1.18454e6	−	484096.i	−1.99787	−	0.816489i
$771$	63882.9	−	386448.i	0.107467	−	0.650104i
$772$	−606674.	+	350263.i	−1.01794	+	0.587706i
$773$	−70204.3			−0.117491			−0.0587455	−	0.998273i	$-0.518710\pi$
$773$	−70204.3			−0.117491			−0.0587455	+	0.998273i	$0.518710\pi$
$774$	133310.	−	26461.1i	0.222526	−	0.0441698i
$775$	757823.	−	210766.i	1.26172	−	0.350911i
$776$	−89078.1	+	51429.3i	−0.147927	+	0.0854057i
$777$	−148205.	−	121678.i	−0.245482	−	0.201545i
$778$	741977.	+	428381.i	1.22583	+	0.707735i
$779$	42943.3	+	24793.3i	0.0707654	+	0.0408564i
$780$	−258133.	+	139483.i	−0.424282	+	0.229261i
$781$	−767889.	−	1.33002e6i	−1.25891	−	2.18050i
$782$	1.00751e6			1.64754
$783$	8350.27	+	259881.i	0.0136200	+	0.423887i
$784$	290431.			0.472509
$785$	261697.	+	337728.i	0.424677	+	0.548060i
$786$	−88985.3	−	236573.i	−0.144037	−	0.382931i
$787$	−1.02067e6	−	589282.i	−1.64791	−	0.951423i	−0.977900	−	0.209072i	$-0.932956\pi$
$787$	−1.02067e6	−	589282.i	−1.64791	−	0.951423i	−0.670012	−	0.742350i	$-0.733711\pi$
$788$	−81080.6	+	140436.i	−0.130576	+	0.226165i
$789$	−281349.	−	230992.i	−0.451951	−	0.371059i
$790$	1.06024e6	−	821552.i	1.69883	−	1.31638i
$791$			542207.i			0.866587i
$792$	−106330.	+	312824.i	−0.169514	+	0.498711i
$793$		−	108473.i		−	0.172495i
$794$	−774557.	+	447191.i	−1.22861	+	0.709336i
$795$	−427067.	−	12043.8i	−0.675713	−	0.0190559i
$796$	333199.	−	577117.i	0.525869	−	0.910831i
$797$	−259145.	+	448852.i	−0.407968	+	0.706622i	−0.994662	−	0.103187i	$-0.967096\pi$
$797$	−259145.	+	448852.i	−0.407968	+	0.706622i	0.586694	+	0.809809i	$0.300429\pi$
$798$	72513.8	+	11987.1i	0.113872	+	0.0188239i
$799$	256929.	+	445015.i	0.402458	+	0.697077i
$800$	−739891.	+	205779.i	−1.15608	+	0.321530i
$801$	45826.8	+	52297.9i	0.0714257	+	0.0815116i
$802$		−	334639.i		−	0.520269i
$803$	−83297.2	−	144275.i	−0.129181	−	0.223749i
$804$	141089.	−	171847.i	0.218264	−	0.265846i
$805$	−501557.	+	1.22726e6i	−0.773978	+	1.89385i
$806$	652944.	+	376977.i	1.00509	+	0.580290i
$807$	53789.0	+	143001.i	0.0825936	+	0.219580i
$808$	−89483.9	+	51663.5i	−0.137064	+	0.0791337i
$809$		−	1.25627e6i		−	1.91948i	−0.280881	−	0.959742i	$-0.590627\pi$
$809$		−	1.25627e6i		−	1.91948i	0.280881	−	0.959742i	$-0.409373\pi$
$810$	−858469.	+	3370.68i	−1.30844	+	0.00513744i
$811$	−28967.0			−0.0440415			−0.0220207	−	0.999758i	$-0.507010\pi$
$811$	−28967.0			−0.0440415			−0.0220207	+	0.999758i	$0.507010\pi$
$812$	−117463.	−	203452.i	−0.178152	−	0.308568i
$813$	−672383.	+	252912.i	−1.01727	+	0.382638i
$814$	−163139.	+	282565.i	−0.246211	+	0.426451i
$815$	−246019.	+	601984.i	−0.370385	+	0.906296i
$816$	450324.	+	369723.i	0.676308	+	0.555260i
$817$	7493.12	−	4326.16i	0.0112258	−	0.00648124i
$818$	−236105.			−0.352857
$819$	−403142.	+	353258.i	−0.601021	+	0.526653i
$820$	518496.	−	70759.3i	0.771112	−	0.105234i
$821$	318927.	−	184132.i	0.473156	−	0.273177i	−0.244404	−	0.969674i	$-0.578592\pi$
$821$	318927.	−	184132.i	0.473156	−	0.273177i	0.717560	+	0.696497i	$0.245259\pi$
$822$	18780.4	−	113609.i	0.0277946	−	0.168139i
$823$	−547754.	−	316246.i	−0.808697	−	0.466902i	0.0378059	−	0.999285i	$-0.487963\pi$
$823$	−547754.	−	316246.i	−0.808697	−	0.466902i	−0.846503	+	0.532383i	$0.821296\pi$
$824$	218710.	+	126272.i	0.322117	+	0.185974i
$825$	946036.	−	102034.i	1.38995	−	0.149912i
$826$	735247.	+	1.27349e6i	1.07764	+	1.86653i
$827$	290970.			0.425439			0.212719	−	0.977113i	$-0.431768\pi$
$827$	290970.			0.425439			0.212719	+	0.977113i	$0.431768\pi$
$828$	−801448.	−	272415.i	−1.16900	−	0.397348i
$829$	893630.			1.30032			0.650158	−	0.759799i	$-0.274703\pi$
$829$	893630.			1.30032			0.650158	+	0.759799i	$0.274703\pi$
$830$	494467.	−	383150.i	0.717764	−	0.556176i
$831$	506081.	−	616408.i	0.732855	−	0.892620i
$832$	−148220.	−	85575.0i	−0.214122	−	0.123623i
$833$	−98787.3	+	171105.i	−0.142368	+	0.246588i
$834$	661681.	−	248887.i	0.951298	−	0.357824i
$835$	−896302.	+	694521.i	−1.28553	+	0.996121i
$836$		−	52012.4i		−	0.0744208i
$837$	484018.	+	779414.i	0.690892	+	1.11254i
$838$		−	651624.i		−	0.927916i
$839$	−120902.	+	69802.6i	−0.171755	+	0.0991625i	−0.583413	−	0.812176i	$-0.698283\pi$
$839$	−120902.	+	69802.6i	−0.171755	+	0.0991625i	0.411658	+	0.911338i	$0.364950\pi$
$840$	−275961.	+	149116.i	−0.391101	+	0.211332i
$841$	−290033.	+	502351.i	−0.410067	+	0.710257i
$842$	−477583.	+	827198.i	−0.673635	+	1.16677i
$843$	418786.	−	510083.i	0.589301	−	0.717771i
$844$	189874.	+	328872.i	0.266552	+	0.461681i
$845$	52259.6	+	382938.i	0.0731902	+	0.536309i
$846$	−202103.	−	1.01818e6i	−0.282378	−	1.42261i
$847$			807891.i			1.12612i
$848$	−292885.	−	507291.i	−0.407291	−	0.705449i
$849$	522485.	+	86370.8i	0.724867	+	0.119826i
$850$	171389.	−	664739.i	0.237217	−	0.920054i
$851$	292757.	+	169023.i	0.404248	+	0.233392i
$852$	918436.	+	151825.i	1.26523	+	0.209152i
$853$	−702105.	+	405361.i	−0.964948	+	0.557113i	−0.897692	−	0.440623i	$-0.854758\pi$
$853$	−702105.	+	405361.i	−0.964948	+	0.557113i	−0.0672558	+	0.997736i	$0.521424\pi$
$854$			286756.i			0.393185i
$855$	−51675.2	+	17791.2i	−0.0706886	+	0.0243374i
$856$	−430946.			−0.588133
$857$	415009.	+	718817.i	0.565062	+	0.978716i	0.997044	+	0.0768340i	$0.0244812\pi$
$857$	415009.	+	718817.i	0.565062	+	0.978716i	−0.431982	+	0.901882i	$0.642186\pi$
$858$	704906.	+	578739.i	0.957539	+	0.786155i
$859$	−152784.	+	264629.i	−0.207057	+	0.358634i	−0.950786	−	0.309847i	$-0.899722\pi$
$859$	−152784.	+	264629.i	−0.207057	+	0.358634i	0.743729	+	0.668481i	$0.233055\pi$
$860$	34543.2	−	84524.0i	0.0467053	−	0.114283i
$861$	894796.	−	336572.i	1.20703	−	0.454016i
$862$	237146.	−	136916.i	0.319155	−	0.184264i
$863$	1.37893e6			1.85149			0.925746	−	0.378147i	$-0.123439\pi$
$863$	1.37893e6			1.85149			0.925746	+	0.378147i	$0.123439\pi$
$864$	−472564.	−	760971.i	−0.633044	−	1.01939i
$865$	−19255.8	−	141099.i	−0.0257353	−	0.188578i
$866$	−1.55068e6	+	895285.i	−2.06769	+	1.19378i
$867$	332571.	−	125094.i	0.442431	−	0.166418i
$868$	−717892.	−	414475.i	−0.952839	−	0.550122i
$869$	−1.50173e6	−	867024.i	−1.98862	−	1.14813i
$870$	357684.	+	220181.i	0.472564	+	0.290898i
$871$	124105.	+	214956.i	0.163588	+	0.283343i
$872$	−357811.			−0.470566
$873$	−111194.	+	327133.i	−0.145899	+	0.429236i
$874$	−129570.			−0.169621
$875$	724406.	+	539690.i	0.946164	+	0.704902i
$876$	99627.9	+	16469.3i	0.129829	+	0.0214618i
$877$	618881.	+	357311.i	0.804652	+	0.464566i	0.845095	−	0.534616i	$-0.179544\pi$
$877$	618881.	+	357311.i	0.804652	+	0.464566i	−0.0404430	+	0.999182i	$0.512877\pi$
$878$	−682836.	+	1.18271e6i	−0.885783	+	1.53422i
$879$	−148644.	+	899193.i	−0.192384	+	1.16379i
$880$	799078.	+	1.03124e6i	1.03187	+	1.33166i
$881$			390992.i			0.503751i	0.967760	+	0.251875i	$0.0810473\pi$
$881$			390992.i			0.503751i	−0.967760	+	0.251875i	$0.918953\pi$
$882$	300181.	−	263038.i	0.385875	−	0.338128i
$883$		−	1.05235e6i		−	1.34971i	−0.737950	−	0.674855i	$-0.764206\pi$
$883$		−	1.05235e6i		−	1.34971i	0.737950	−	0.674855i	$-0.235794\pi$
$884$	237000.	−	136832.i	0.303280	−	0.175099i
$885$	−931158.	−	573197.i	−1.18888	−	0.731842i
$886$	487952.	−	845158.i	0.621598	−	1.07664i
$887$	432865.	−	749744.i	0.550181	−	0.952941i	−0.448080	−	0.893993i	$-0.647892\pi$
$887$	432865.	−	749744.i	0.550181	−	0.952941i	0.998261	−	0.0589476i	$-0.0187745\pi$
$888$	28157.4	+	74858.2i	0.0357081	+	0.0949322i
$889$	−105338.	−	182450.i	−0.133285	−	0.230856i
$890$	111294.	−	15188.3i	0.140505	−	0.0191748i
$891$	423896.	+	1.02572e6i	0.533955	+	1.29203i
$892$		−	529391.i		−	0.665344i
$893$	−33042.0	−	57230.5i	−0.0414347	−	0.0717669i
$894$	−209342.	−	556550.i	−0.261928	−	0.696352i
$895$	270325.	−	661461.i	0.337474	−	0.825768i
$896$	−592521.	−	342092.i	−0.738054	−	0.426116i
$897$	599614.	−	730332.i	0.745224	−	0.907685i
$898$	298744.	−	172480.i	0.370465	−	0.213888i
$899$		−	448887.i		−	0.555415i
$900$	−316071.	+	482441.i	−0.390211	+	0.595606i
$901$	398488.			0.490869
$902$	−813332.	−	1.40873e6i	−0.999666	−	1.73147i
$903$	27206.0	−	164578.i	0.0333649	−	0.201835i
$904$	113074.	−	195849.i	0.138364	−	0.239654i
$905$	−792783.	−	323994.i	−0.967959	−	0.395585i
$906$	178866.	−	1.08202e6i	0.217907	−	1.31819i
$907$	936179.	−	540503.i	1.13800	−	0.657027i	0.192069	−	0.981381i	$-0.438480\pi$
$907$	936179.	−	540503.i	1.13800	−	0.657027i	0.945936	+	0.324354i	$0.105147\pi$
$908$	295566.			0.358494
$909$	−111700.	+	328623.i	−0.135184	+	0.397714i
$910$	117080.	+	857916.i	0.141384	+	1.03601i
$911$	−218106.	+	125923.i	−0.262803	+	0.151729i	−0.625613	−	0.780134i	$-0.715151\pi$
$911$	−218106.	+	125923.i	−0.262803	+	0.151729i	0.362809	+	0.931863i	$0.381818\pi$
$912$	−57913.2	−	47547.7i	−0.0696287	−	0.0571663i
$913$	−700367.	−	404357.i	−0.840202	−	0.485091i
$914$	751898.	+	434108.i	0.900050	+	0.519644i
$915$	−101366.	−	187593.i	−0.121074	−	0.224065i
$916$	137834.	+	238736.i	0.164273	+	0.284529i
$917$	−310222.			−0.368922
$918$	800295.	−	25714.4i	0.949653	−	0.0305134i
$919$	−1.32687e6			−1.57108			−0.785541	−	0.618809i	$-0.787615\pi$
$919$	−1.32687e6			−1.57108			−0.785541	+	0.618809i	$0.787615\pi$
$920$	437104.	−	338700.i	0.516427	−	0.400166i
$921$	137815.	+	366390.i	0.162472	+	0.431941i
$922$	−114409.	−	66054.3i	−0.134586	−	0.0777033i
$923$	−519592.	+	899960.i	−0.609901	+	1.05638i
$924$	−775023.	−	636306.i	−0.907759	−	0.745285i
$925$	161320.	−	164403.i	0.188540	−	0.192144i
$926$			537507.i			0.626847i
$927$	832093.	−	165165.i	0.968305	−	0.192202i
$928$			438265.i			0.508910i
$929$	−611138.	+	352841.i	−0.708122	+	0.408834i	−0.810365	−	0.585925i	$-0.800731\pi$
$929$	−611138.	+	352841.i	−0.708122	+	0.408834i	0.102243	+	0.994759i	$0.467398\pi$
$930$	1.48147e6	+	41779.4i	1.71289	+	0.0483055i
$931$	12704.4	−	22004.7i	0.0146573	−	0.0253872i
$932$	−340660.	+	590040.i	−0.392183	+	0.679282i
$933$	673743.	+	111375.i	0.773982	+	0.127945i
$934$	−230390.	−	399048.i	−0.264101	−	0.457437i
$935$	−879343.	+	120004.i	−1.00585	+	0.137269i
$936$	219287.	−	43527.1i	0.250301	−	0.0496830i
$937$		−	1.20291e6i		−	1.37011i	−0.728493	−	0.685053i	$-0.759779\pi$
$937$		−	1.20291e6i		−	1.37011i	0.728493	−	0.685053i	$-0.240221\pi$
$938$	−328079.	−	568250.i	−0.372883	−	0.645853i
$939$	385223.	−	469202.i	0.436899	−	0.532144i
$940$	−645572.	−	263832.i	−0.730615	−	0.298588i
$941$	1.39400e6	+	804825.i	1.57428	+	0.908912i	0.995635	+	0.0933347i	$0.0297527\pi$
$941$	1.39400e6	+	804825.i	1.57428	+	0.908912i	0.578648	+	0.815578i	$0.303581\pi$
$942$	283416.	+	753479.i	0.319391	+	0.849120i
$943$	−1.45954e6	+	842669.i	−1.64132	+	0.947618i
$944$		−	1.49918e6i		−	1.68232i
$945$	−367078.	+	987651.i	−0.411050	+	1.10596i
$946$	−283834.			−0.317163
$947$	584691.	+	1.01271e6i	0.651968	+	1.12924i	0.982645	+	0.185498i	$0.0593898\pi$
$947$	584691.	+	1.01271e6i	0.651968	+	1.12924i	−0.330676	+	0.943744i	$0.607277\pi$
$948$	983787.	−	370045.i	1.09467	−	0.411754i
$949$	−56363.1	+	97623.7i	−0.0625839	+	0.108398i
$950$	−22041.3	+	85487.8i	−0.0244225	+	0.0947233i
$951$	−1.26007e6	−	1.03454e6i	−1.39327	−	1.14390i
$952$	253368.	−	146282.i	0.279562	−	0.161405i
$953$	−92982.8			−0.102380			−0.0511902	−	0.998689i	$-0.516301\pi$
$953$	−92982.8			−0.102380			−0.0511902	+	0.998689i	$0.516301\pi$
$954$	−762163.	−	259062.i	−0.837435	−	0.284647i
$955$	−1.76365e6	+	240686.i	−1.93378	+	0.263903i
$956$	−733429.	+	423446.i	−0.802495	+	0.463321i
$957$	88562.3	−	535742.i	0.0966996	−	0.584967i
$958$	1.26540e6	+	730577.i	1.37878	+	0.796040i
$959$	−122397.	−	70665.7i	−0.133086	−	0.0768371i
$960$	−336299.	−	9484.06i	−0.364908	−	0.0102909i
$961$	−330199.	−	571922.i	−0.357544	−	0.619284i
$962$	220776.			0.238562
$963$	−1.08875e6	+	954030.i	−1.17402	+	1.02875i
$964$	−633611.			−0.681818
$965$	−941562.	−	1.21512e6i	−1.01110	−	1.30486i
$966$	−1.58512e6	+	1.93068e6i	−1.69867	+	2.06898i
$967$	−370274.	−	213778.i	−0.395977	−	0.228618i	0.288769	−	0.957399i	$-0.406754\pi$
$967$	−370274.	−	213778.i	−0.395977	−	0.228618i	−0.684747	+	0.728781i	$0.740087\pi$
$968$	168480.	−	291816.i	0.179804	−	0.311429i
$969$	47711.0	−	17946.2i	0.0508125	−	0.0191128i
$970$	341863.	+	441185.i	0.363336	+	0.468897i
$971$		−	967416.i		−	1.02606i	−0.858369	−	0.513032i	$-0.828522\pi$
$971$		−	967416.i		−	1.02606i	0.858369	−	0.513032i	$-0.171478\pi$
$972$	−643566.	−	195932.i	−0.681178	−	0.207383i
$973$		−	867674.i		−	0.916496i
$974$	1.13514e6	−	655372.i	1.19655	−	0.690828i
$975$	−379859.	−	519853.i	−0.399589	−	0.546854i
$976$	146174.	−	253181.i	0.153452	−	0.265786i
$977$	−267215.	+	462829.i	−0.279944	+	0.484877i	−0.971370	−	0.237570i	$-0.923649\pi$
$977$	−267215.	+	462829.i	−0.279944	+	0.484877i	0.691427	+	0.722447i	$0.256983\pi$
$978$	−777517.	+	947017.i	−0.812890	+	0.990103i
$979$	−72608.5	−	125762.i	−0.0757569	−	0.131215i
$980$	−36257.9	−	265683.i	−0.0377529	−	0.276638i
$981$	−903978.	+	792123.i	−0.939334	+	0.823104i
$982$		−	418950.i		−	0.434449i
$983$	405897.	+	703034.i	0.420057	+	0.727561i	0.995945	−	0.0899684i	$-0.0286766\pi$
$983$	405897.	+	703034.i	0.420057	+	0.727561i	−0.575887	+	0.817529i	$0.695343\pi$
$984$	−393397.	−	65031.6i	−0.406294	−	0.0671636i
$985$	−329397.	−	134618.i	−0.339505	−	0.138749i
$986$	−339272.	−	195879.i	−0.348975	−	0.201481i
$987$	−1.25700e6	−	207792.i	−1.29033	−	0.213302i
$988$	−30479.1	+	17597.1i	−0.0312239	+	0.0180272i
$989$			294072.i			0.300650i
$990$	1.75988e6	+	342148.i	1.79561	+	0.349095i
$991$	−25780.3			−0.0262507			−0.0131254	−	0.999914i	$-0.504178\pi$
$991$	−25780.3			−0.0262507			−0.0131254	+	0.999914i	$0.504178\pi$
$992$	773220.	+	1.33926e6i	0.785742	+	1.36094i
$993$	1.08595e6	+	891586.i	1.10132	+	0.904200i
$994$	1.37358e6	−	2.37910e6i	1.39021	−	2.40791i
$995$	1.35365e6	+	553208.i	1.36729	+	0.558782i
$996$	458812.	−	172579.i	0.462504	−	0.173968i
$997$	−696124.	+	401907.i	−0.700319	+	0.404329i	−0.807466	−	0.589914i	$-0.799162\pi$
$997$	−696124.	+	401907.i	−0.700319	+	0.404329i	0.107147	+	0.994243i	$0.465828\pi$
$998$	224324.			0.225224
$999$	236859.	+	126788.i	0.237333	+	0.127042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.18	yes	44
3.2	odd	2		135.5.h.a.44.5		44
5.4	even	2	inner	45.5.h.a.14.5	✓	44
9.2	odd	6	inner	45.5.h.a.29.5	yes	44
9.4	even	3		405.5.d.a.404.9		44
9.5	odd	6		405.5.d.a.404.35		44
9.7	even	3		135.5.h.a.89.18		44
15.14	odd	2		135.5.h.a.44.18		44
45.4	even	6		405.5.d.a.404.36		44
45.14	odd	6		405.5.d.a.404.10		44
45.29	odd	6	inner	45.5.h.a.29.18	yes	44
45.34	even	6		135.5.h.a.89.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.5	✓	44	5.4	even	2	inner
45.5.h.a.14.18	yes	44	1.1	even	1	trivial
45.5.h.a.29.5	yes	44	9.2	odd	6	inner
45.5.h.a.29.18	yes	44	45.29	odd	6	inner
135.5.h.a.44.5		44	3.2	odd	2
135.5.h.a.44.18		44	15.14	odd	2
135.5.h.a.89.5		44	45.34	even	6
135.5.h.a.89.18		44	9.7	even	3
405.5.d.a.404.9		44	9.4	even	3
405.5.d.a.404.10		44	45.14	odd	6
405.5.d.a.404.35		44	9.5	odd	6
405.5.d.a.404.36		44	45.4	even	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+(2.61690 + 4.53261i) q^{2} +(-8.42379 + 3.16855i) q^{3} +(-5.69638 + 9.86641i) q^{4} +(-23.1420 - 9.45767i) q^{5} +(-36.4061 - 29.8900i) q^{6} +(-50.0684 + 28.9070i) q^{7} +24.1135 q^{8} +(60.9206 - 53.3825i) q^{9} +(-17.6925 - 129.644i) q^{10} +(-146.496 + 84.5798i) q^{11} +(16.7228 - 101.162i) q^{12} +(99.1268 + 57.2309i) q^{13} +(-262.048 - 151.294i) q^{14} +(224.911 + 6.34275i) q^{15} +(154.245 + 267.160i) q^{16} -209.860 q^{17} +(401.385 + 136.432i) q^{18} +26.9887 q^{19} +(225.139 - 174.454i) q^{20} +(330.173 - 402.151i) q^{21} +(-766.735 - 442.674i) q^{22} +(-458.642 + 794.390i) q^{23} +(-203.127 + 76.4047i) q^{24} +(446.105 + 437.739i) q^{25} +599.071i q^{26} +(-344.037 + 642.713i) q^{27} -658.661i q^{28} +(308.888 - 178.337i) q^{29} +(559.820 + 1036.03i) q^{30} +(629.269 - 1089.93i) q^{31} +(-614.379 + 1064.14i) q^{32} +(966.061 - 1176.66i) q^{33} +(-549.182 - 951.212i) q^{34} +(1432.08 - 195.436i) q^{35} +(179.667 + 905.154i) q^{36} -368.530i q^{37} +(70.6268 + 122.329i) q^{38} +(-1016.36 - 168.013i) q^{39} +(-558.034 - 228.057i) q^{40} +(1591.16 + 918.657i) q^{41} +(2686.82 + 444.153i) q^{42} +(277.639 - 160.295i) q^{43} -1927.19i q^{44} +(-1914.70 + 659.211i) q^{45} -4800.88 q^{46} +(-1224.29 - 2120.54i) q^{47} +(-2145.83 - 1761.76i) q^{48} +(470.730 - 815.329i) q^{49} +(-816.685 + 3167.54i) q^{50} +(1767.81 - 664.951i) q^{51} +(-1129.33 + 652.018i) q^{52} -1898.83 q^{53} +(-3813.48 + 122.531i) q^{54} +(4190.15 - 571.831i) q^{55} +(-1207.32 + 697.048i) q^{56} +(-227.347 + 85.5151i) q^{57} +(1616.66 + 933.380i) q^{58} +(-4208.65 - 2429.87i) q^{59} +(-1343.76 + 2182.93i) q^{60} +(-473.839 - 820.714i) q^{61} +6586.95 q^{62} +(-1507.07 + 4433.81i) q^{63} -1495.26 q^{64} +(-1752.72 - 2261.95i) q^{65} +(7861.45 + 1299.56i) q^{66} +(1877.97 + 1084.25i) q^{67} +(1195.44 - 2070.56i) q^{68} +(1346.43 - 8145.01i) q^{69} +(4633.44 + 5979.61i) q^{70} +9078.87i q^{71} +(1469.00 - 1287.24i) q^{72} +984.836i q^{73} +(1670.40 - 964.407i) q^{74} +(-5144.89 - 2273.91i) q^{75} +(-153.738 + 266.282i) q^{76} +(4889.90 - 8469.55i) q^{77} +(-1898.19 - 5046.45i) q^{78} +(5125.48 + 8877.60i) q^{79} +(-1042.82 - 7641.40i) q^{80} +(861.628 - 6504.18i) q^{81} +9616.15i q^{82} +(2390.39 + 4140.27i) q^{83} +(2087.00 + 5548.42i) q^{84} +(4856.57 + 1984.78i) q^{85} +(1453.11 + 838.954i) q^{86} +(-2036.94 + 2481.00i) q^{87} +(-3532.54 + 2039.51i) q^{88} +858.461i q^{89} +(-7998.53 - 6953.49i) q^{90} -6617.50 q^{91} +(-5225.19 - 9050.29i) q^{92} +(-1847.35 + 11175.2i) q^{93} +(6407.71 - 11098.5i) q^{94} +(-624.572 - 255.250i) q^{95} +(1803.63 - 10910.8i) q^{96} +(-3694.13 + 2132.80i) q^{97} +4927.43 q^{98} +(-4409.57 + 12973.0i) 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

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