Properties

Label 4009.2.a.c.1.16
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.93894 q^{2}\) \(-1.61421 q^{3}\) \(+1.75950 q^{4}\) \(-0.710068 q^{5}\) \(+3.12986 q^{6}\) \(-1.51648 q^{7}\) \(+0.466323 q^{8}\) \(-0.394323 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.93894 q^{2}\) \(-1.61421 q^{3}\) \(+1.75950 q^{4}\) \(-0.710068 q^{5}\) \(+3.12986 q^{6}\) \(-1.51648 q^{7}\) \(+0.466323 q^{8}\) \(-0.394323 q^{9}\) \(+1.37678 q^{10}\) \(+4.83786 q^{11}\) \(-2.84020 q^{12}\) \(-3.42790 q^{13}\) \(+2.94037 q^{14}\) \(+1.14620 q^{15}\) \(-4.42317 q^{16}\) \(+2.25296 q^{17}\) \(+0.764570 q^{18}\) \(+1.00000 q^{19}\) \(-1.24936 q^{20}\) \(+2.44792 q^{21}\) \(-9.38033 q^{22}\) \(+5.02944 q^{23}\) \(-0.752744 q^{24}\) \(-4.49580 q^{25}\) \(+6.64650 q^{26}\) \(+5.47915 q^{27}\) \(-2.66824 q^{28}\) \(-9.09232 q^{29}\) \(-2.22241 q^{30}\) \(-7.95846 q^{31}\) \(+7.64362 q^{32}\) \(-7.80933 q^{33}\) \(-4.36836 q^{34}\) \(+1.07680 q^{35}\) \(-0.693810 q^{36}\) \(+0.118446 q^{37}\) \(-1.93894 q^{38}\) \(+5.53335 q^{39}\) \(-0.331121 q^{40}\) \(+4.81219 q^{41}\) \(-4.74637 q^{42}\) \(+7.87596 q^{43}\) \(+8.51220 q^{44}\) \(+0.279996 q^{45}\) \(-9.75180 q^{46}\) \(-4.37650 q^{47}\) \(+7.13992 q^{48}\) \(-4.70029 q^{49}\) \(+8.71710 q^{50}\) \(-3.63675 q^{51}\) \(-6.03137 q^{52}\) \(-2.80310 q^{53}\) \(-10.6238 q^{54}\) \(-3.43521 q^{55}\) \(-0.707169 q^{56}\) \(-1.61421 q^{57}\) \(+17.6295 q^{58}\) \(+13.7278 q^{59}\) \(+2.01673 q^{60}\) \(+5.59544 q^{61}\) \(+15.4310 q^{62}\) \(+0.597983 q^{63}\) \(-5.97420 q^{64}\) \(+2.43404 q^{65}\) \(+15.1418 q^{66}\) \(-4.65901 q^{67}\) \(+3.96408 q^{68}\) \(-8.11858 q^{69}\) \(-2.08786 q^{70}\) \(+4.73205 q^{71}\) \(-0.183882 q^{72}\) \(+8.30981 q^{73}\) \(-0.229659 q^{74}\) \(+7.25717 q^{75}\) \(+1.75950 q^{76}\) \(-7.33651 q^{77}\) \(-10.7288 q^{78}\) \(-1.73416 q^{79}\) \(+3.14075 q^{80}\) \(-7.66154 q^{81}\) \(-9.33056 q^{82}\) \(-10.6561 q^{83}\) \(+4.30710 q^{84}\) \(-1.59976 q^{85}\) \(-15.2710 q^{86}\) \(+14.6769 q^{87}\) \(+2.25601 q^{88}\) \(-0.175995 q^{89}\) \(-0.542897 q^{90}\) \(+5.19834 q^{91}\) \(+8.84929 q^{92}\) \(+12.8466 q^{93}\) \(+8.48579 q^{94}\) \(-0.710068 q^{95}\) \(-12.3384 q^{96}\) \(-6.23723 q^{97}\) \(+9.11359 q^{98}\) \(-1.90768 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93894 −1.37104 −0.685520 0.728054i \(-0.740425\pi\)
−0.685520 + 0.728054i \(0.740425\pi\)
\(3\) −1.61421 −0.931965 −0.465983 0.884794i \(-0.654299\pi\)
−0.465983 + 0.884794i \(0.654299\pi\)
\(4\) 1.75950 0.879748
\(5\) −0.710068 −0.317552 −0.158776 0.987315i \(-0.550755\pi\)
−0.158776 + 0.987315i \(0.550755\pi\)
\(6\) 3.12986 1.27776
\(7\) −1.51648 −0.573175 −0.286588 0.958054i \(-0.592521\pi\)
−0.286588 + 0.958054i \(0.592521\pi\)
\(8\) 0.466323 0.164870
\(9\) −0.394323 −0.131441
\(10\) 1.37678 0.435376
\(11\) 4.83786 1.45867 0.729335 0.684157i \(-0.239830\pi\)
0.729335 + 0.684157i \(0.239830\pi\)
\(12\) −2.84020 −0.819894
\(13\) −3.42790 −0.950728 −0.475364 0.879789i \(-0.657684\pi\)
−0.475364 + 0.879789i \(0.657684\pi\)
\(14\) 2.94037 0.785846
\(15\) 1.14620 0.295948
\(16\) −4.42317 −1.10579
\(17\) 2.25296 0.546423 0.273212 0.961954i \(-0.411914\pi\)
0.273212 + 0.961954i \(0.411914\pi\)
\(18\) 0.764570 0.180211
\(19\) 1.00000 0.229416
\(20\) −1.24936 −0.279366
\(21\) 2.44792 0.534179
\(22\) −9.38033 −1.99989
\(23\) 5.02944 1.04871 0.524356 0.851499i \(-0.324306\pi\)
0.524356 + 0.851499i \(0.324306\pi\)
\(24\) −0.752744 −0.153653
\(25\) −4.49580 −0.899161
\(26\) 6.64650 1.30349
\(27\) 5.47915 1.05446
\(28\) −2.66824 −0.504250
\(29\) −9.09232 −1.68840 −0.844200 0.536028i \(-0.819924\pi\)
−0.844200 + 0.536028i \(0.819924\pi\)
\(30\) −2.22241 −0.405756
\(31\) −7.95846 −1.42938 −0.714691 0.699440i \(-0.753433\pi\)
−0.714691 + 0.699440i \(0.753433\pi\)
\(32\) 7.64362 1.35121
\(33\) −7.80933 −1.35943
\(34\) −4.36836 −0.749168
\(35\) 1.07680 0.182013
\(36\) −0.693810 −0.115635
\(37\) 0.118446 0.0194724 0.00973618 0.999953i \(-0.496901\pi\)
0.00973618 + 0.999953i \(0.496901\pi\)
\(38\) −1.93894 −0.314538
\(39\) 5.53335 0.886045
\(40\) −0.331121 −0.0523549
\(41\) 4.81219 0.751538 0.375769 0.926713i \(-0.377379\pi\)
0.375769 + 0.926713i \(0.377379\pi\)
\(42\) −4.74637 −0.732381
\(43\) 7.87596 1.20107 0.600537 0.799597i \(-0.294954\pi\)
0.600537 + 0.799597i \(0.294954\pi\)
\(44\) 8.51220 1.28326
\(45\) 0.279996 0.0417394
\(46\) −9.75180 −1.43782
\(47\) −4.37650 −0.638379 −0.319189 0.947691i \(-0.603411\pi\)
−0.319189 + 0.947691i \(0.603411\pi\)
\(48\) 7.13992 1.03056
\(49\) −4.70029 −0.671470
\(50\) 8.71710 1.23278
\(51\) −3.63675 −0.509248
\(52\) −6.03137 −0.836401
\(53\) −2.80310 −0.385036 −0.192518 0.981293i \(-0.561665\pi\)
−0.192518 + 0.981293i \(0.561665\pi\)
\(54\) −10.6238 −1.44571
\(55\) −3.43521 −0.463204
\(56\) −0.707169 −0.0944995
\(57\) −1.61421 −0.213807
\(58\) 17.6295 2.31486
\(59\) 13.7278 1.78721 0.893607 0.448851i \(-0.148167\pi\)
0.893607 + 0.448851i \(0.148167\pi\)
\(60\) 2.01673 0.260359
\(61\) 5.59544 0.716423 0.358211 0.933640i \(-0.383387\pi\)
0.358211 + 0.933640i \(0.383387\pi\)
\(62\) 15.4310 1.95974
\(63\) 0.597983 0.0753388
\(64\) −5.97420 −0.746774
\(65\) 2.43404 0.301906
\(66\) 15.1418 1.86383
\(67\) −4.65901 −0.569189 −0.284594 0.958648i \(-0.591859\pi\)
−0.284594 + 0.958648i \(0.591859\pi\)
\(68\) 3.96408 0.480715
\(69\) −8.11858 −0.977362
\(70\) −2.08786 −0.249547
\(71\) 4.73205 0.561591 0.280795 0.959768i \(-0.409402\pi\)
0.280795 + 0.959768i \(0.409402\pi\)
\(72\) −0.183882 −0.0216707
\(73\) 8.30981 0.972589 0.486295 0.873795i \(-0.338348\pi\)
0.486295 + 0.873795i \(0.338348\pi\)
\(74\) −0.229659 −0.0266974
\(75\) 7.25717 0.837986
\(76\) 1.75950 0.201828
\(77\) −7.33651 −0.836073
\(78\) −10.7288 −1.21480
\(79\) −1.73416 −0.195108 −0.0975539 0.995230i \(-0.531102\pi\)
−0.0975539 + 0.995230i \(0.531102\pi\)
\(80\) 3.14075 0.351146
\(81\) −7.66154 −0.851282
\(82\) −9.33056 −1.03039
\(83\) −10.6561 −1.16966 −0.584831 0.811155i \(-0.698839\pi\)
−0.584831 + 0.811155i \(0.698839\pi\)
\(84\) 4.30710 0.469943
\(85\) −1.59976 −0.173518
\(86\) −15.2710 −1.64672
\(87\) 14.6769 1.57353
\(88\) 2.25601 0.240491
\(89\) −0.175995 −0.0186555 −0.00932773 0.999956i \(-0.502969\pi\)
−0.00932773 + 0.999956i \(0.502969\pi\)
\(90\) −0.542897 −0.0572263
\(91\) 5.19834 0.544934
\(92\) 8.84929 0.922602
\(93\) 12.8466 1.33213
\(94\) 8.48579 0.875242
\(95\) −0.710068 −0.0728515
\(96\) −12.3384 −1.25928
\(97\) −6.23723 −0.633295 −0.316648 0.948543i \(-0.602557\pi\)
−0.316648 + 0.948543i \(0.602557\pi\)
\(98\) 9.11359 0.920612
\(99\) −1.90768 −0.191729
\(100\) −7.91035 −0.791035
\(101\) 10.6438 1.05910 0.529551 0.848278i \(-0.322360\pi\)
0.529551 + 0.848278i \(0.322360\pi\)
\(102\) 7.05146 0.698198
\(103\) 10.3097 1.01585 0.507923 0.861402i \(-0.330413\pi\)
0.507923 + 0.861402i \(0.330413\pi\)
\(104\) −1.59851 −0.156747
\(105\) −1.73819 −0.169630
\(106\) 5.43505 0.527899
\(107\) −11.2971 −1.09213 −0.546065 0.837743i \(-0.683875\pi\)
−0.546065 + 0.837743i \(0.683875\pi\)
\(108\) 9.64055 0.927662
\(109\) −8.43282 −0.807717 −0.403859 0.914821i \(-0.632331\pi\)
−0.403859 + 0.914821i \(0.632331\pi\)
\(110\) 6.66067 0.635070
\(111\) −0.191196 −0.0181476
\(112\) 6.70764 0.633812
\(113\) 1.82578 0.171755 0.0858774 0.996306i \(-0.472631\pi\)
0.0858774 + 0.996306i \(0.472631\pi\)
\(114\) 3.12986 0.293138
\(115\) −3.57125 −0.333021
\(116\) −15.9979 −1.48537
\(117\) 1.35170 0.124965
\(118\) −26.6175 −2.45034
\(119\) −3.41657 −0.313196
\(120\) 0.534499 0.0487929
\(121\) 12.4049 1.12772
\(122\) −10.8492 −0.982244
\(123\) −7.76789 −0.700407
\(124\) −14.0029 −1.25750
\(125\) 6.74267 0.603083
\(126\) −1.15945 −0.103292
\(127\) 18.6381 1.65387 0.826933 0.562300i \(-0.190083\pi\)
0.826933 + 0.562300i \(0.190083\pi\)
\(128\) −3.70361 −0.327356
\(129\) −12.7135 −1.11936
\(130\) −4.71947 −0.413925
\(131\) 13.0963 1.14423 0.572113 0.820174i \(-0.306124\pi\)
0.572113 + 0.820174i \(0.306124\pi\)
\(132\) −13.7405 −1.19596
\(133\) −1.51648 −0.131495
\(134\) 9.03356 0.780380
\(135\) −3.89057 −0.334847
\(136\) 1.05061 0.0900889
\(137\) 12.1805 1.04065 0.520325 0.853968i \(-0.325811\pi\)
0.520325 + 0.853968i \(0.325811\pi\)
\(138\) 15.7415 1.34000
\(139\) 6.69201 0.567609 0.283804 0.958882i \(-0.408403\pi\)
0.283804 + 0.958882i \(0.408403\pi\)
\(140\) 1.89463 0.160126
\(141\) 7.06460 0.594947
\(142\) −9.17517 −0.769963
\(143\) −16.5837 −1.38680
\(144\) 1.74416 0.145346
\(145\) 6.45616 0.536155
\(146\) −16.1122 −1.33346
\(147\) 7.58726 0.625787
\(148\) 0.208405 0.0171308
\(149\) 15.0153 1.23010 0.615050 0.788488i \(-0.289136\pi\)
0.615050 + 0.788488i \(0.289136\pi\)
\(150\) −14.0712 −1.14891
\(151\) −1.59359 −0.129685 −0.0648423 0.997896i \(-0.520654\pi\)
−0.0648423 + 0.997896i \(0.520654\pi\)
\(152\) 0.466323 0.0378238
\(153\) −0.888395 −0.0718225
\(154\) 14.2251 1.14629
\(155\) 5.65105 0.453903
\(156\) 9.73591 0.779497
\(157\) −18.4721 −1.47423 −0.737115 0.675767i \(-0.763812\pi\)
−0.737115 + 0.675767i \(0.763812\pi\)
\(158\) 3.36243 0.267500
\(159\) 4.52480 0.358840
\(160\) −5.42749 −0.429081
\(161\) −7.62705 −0.601095
\(162\) 14.8553 1.16714
\(163\) 19.3453 1.51524 0.757621 0.652695i \(-0.226362\pi\)
0.757621 + 0.652695i \(0.226362\pi\)
\(164\) 8.46703 0.661164
\(165\) 5.54515 0.431690
\(166\) 20.6616 1.60365
\(167\) 22.4293 1.73563 0.867817 0.496884i \(-0.165523\pi\)
0.867817 + 0.496884i \(0.165523\pi\)
\(168\) 1.14152 0.0880702
\(169\) −1.24951 −0.0961161
\(170\) 3.10183 0.237900
\(171\) −0.394323 −0.0301546
\(172\) 13.8577 1.05664
\(173\) −6.57092 −0.499578 −0.249789 0.968300i \(-0.580361\pi\)
−0.249789 + 0.968300i \(0.580361\pi\)
\(174\) −28.4577 −2.15737
\(175\) 6.81779 0.515377
\(176\) −21.3987 −1.61298
\(177\) −22.1596 −1.66562
\(178\) 0.341245 0.0255774
\(179\) −19.4022 −1.45019 −0.725096 0.688648i \(-0.758205\pi\)
−0.725096 + 0.688648i \(0.758205\pi\)
\(180\) 0.492652 0.0367201
\(181\) −22.0532 −1.63920 −0.819600 0.572936i \(-0.805804\pi\)
−0.819600 + 0.572936i \(0.805804\pi\)
\(182\) −10.0793 −0.747126
\(183\) −9.03222 −0.667681
\(184\) 2.34535 0.172901
\(185\) −0.0841046 −0.00618349
\(186\) −24.9089 −1.82641
\(187\) 10.8995 0.797051
\(188\) −7.70044 −0.561613
\(189\) −8.30902 −0.604392
\(190\) 1.37678 0.0998822
\(191\) 5.74002 0.415334 0.207667 0.978200i \(-0.433413\pi\)
0.207667 + 0.978200i \(0.433413\pi\)
\(192\) 9.64361 0.695968
\(193\) 12.5726 0.904995 0.452497 0.891766i \(-0.350533\pi\)
0.452497 + 0.891766i \(0.350533\pi\)
\(194\) 12.0936 0.868272
\(195\) −3.92906 −0.281366
\(196\) −8.27014 −0.590724
\(197\) −22.4687 −1.60083 −0.800414 0.599448i \(-0.795387\pi\)
−0.800414 + 0.599448i \(0.795387\pi\)
\(198\) 3.69888 0.262868
\(199\) −14.4119 −1.02163 −0.510816 0.859690i \(-0.670657\pi\)
−0.510816 + 0.859690i \(0.670657\pi\)
\(200\) −2.09650 −0.148245
\(201\) 7.52063 0.530464
\(202\) −20.6378 −1.45207
\(203\) 13.7883 0.967750
\(204\) −6.39886 −0.448010
\(205\) −3.41699 −0.238653
\(206\) −19.9899 −1.39277
\(207\) −1.98323 −0.137844
\(208\) 15.1622 1.05131
\(209\) 4.83786 0.334642
\(210\) 3.37025 0.232569
\(211\) 1.00000 0.0688428
\(212\) −4.93205 −0.338734
\(213\) −7.63852 −0.523383
\(214\) 21.9044 1.49735
\(215\) −5.59247 −0.381403
\(216\) 2.55506 0.173850
\(217\) 12.0688 0.819287
\(218\) 16.3507 1.10741
\(219\) −13.4138 −0.906419
\(220\) −6.04424 −0.407503
\(221\) −7.72292 −0.519500
\(222\) 0.370719 0.0248810
\(223\) 22.4017 1.50013 0.750065 0.661364i \(-0.230022\pi\)
0.750065 + 0.661364i \(0.230022\pi\)
\(224\) −11.5914 −0.774482
\(225\) 1.77280 0.118187
\(226\) −3.54008 −0.235482
\(227\) 4.24493 0.281746 0.140873 0.990028i \(-0.455009\pi\)
0.140873 + 0.990028i \(0.455009\pi\)
\(228\) −2.84020 −0.188097
\(229\) 24.9751 1.65040 0.825199 0.564842i \(-0.191063\pi\)
0.825199 + 0.564842i \(0.191063\pi\)
\(230\) 6.92444 0.456584
\(231\) 11.8427 0.779191
\(232\) −4.23996 −0.278367
\(233\) −9.42191 −0.617250 −0.308625 0.951184i \(-0.599869\pi\)
−0.308625 + 0.951184i \(0.599869\pi\)
\(234\) −2.62087 −0.171332
\(235\) 3.10762 0.202719
\(236\) 24.1541 1.57230
\(237\) 2.79929 0.181834
\(238\) 6.62453 0.429405
\(239\) −16.2998 −1.05435 −0.527173 0.849758i \(-0.676748\pi\)
−0.527173 + 0.849758i \(0.676748\pi\)
\(240\) −5.06983 −0.327256
\(241\) −12.7871 −0.823690 −0.411845 0.911254i \(-0.635115\pi\)
−0.411845 + 0.911254i \(0.635115\pi\)
\(242\) −24.0524 −1.54614
\(243\) −4.07012 −0.261098
\(244\) 9.84516 0.630272
\(245\) 3.33753 0.213227
\(246\) 15.0615 0.960286
\(247\) −3.42790 −0.218112
\(248\) −3.71122 −0.235662
\(249\) 17.2012 1.09008
\(250\) −13.0736 −0.826850
\(251\) −23.6809 −1.49472 −0.747362 0.664417i \(-0.768680\pi\)
−0.747362 + 0.664417i \(0.768680\pi\)
\(252\) 1.05215 0.0662791
\(253\) 24.3317 1.52972
\(254\) −36.1383 −2.26752
\(255\) 2.58234 0.161713
\(256\) 19.1295 1.19559
\(257\) −3.38495 −0.211147 −0.105574 0.994411i \(-0.533668\pi\)
−0.105574 + 0.994411i \(0.533668\pi\)
\(258\) 24.6507 1.53468
\(259\) −0.179621 −0.0111611
\(260\) 4.28269 0.265601
\(261\) 3.58531 0.221925
\(262\) −25.3929 −1.56878
\(263\) 27.4938 1.69534 0.847670 0.530524i \(-0.178005\pi\)
0.847670 + 0.530524i \(0.178005\pi\)
\(264\) −3.64167 −0.224129
\(265\) 1.99039 0.122269
\(266\) 2.94037 0.180285
\(267\) 0.284093 0.0173862
\(268\) −8.19751 −0.500743
\(269\) −26.1034 −1.59155 −0.795775 0.605592i \(-0.792936\pi\)
−0.795775 + 0.605592i \(0.792936\pi\)
\(270\) 7.54359 0.459089
\(271\) −19.7467 −1.19953 −0.599763 0.800177i \(-0.704739\pi\)
−0.599763 + 0.800177i \(0.704739\pi\)
\(272\) −9.96522 −0.604230
\(273\) −8.39121 −0.507859
\(274\) −23.6173 −1.42677
\(275\) −21.7501 −1.31158
\(276\) −14.2846 −0.859833
\(277\) 22.9531 1.37912 0.689558 0.724230i \(-0.257805\pi\)
0.689558 + 0.724230i \(0.257805\pi\)
\(278\) −12.9754 −0.778214
\(279\) 3.13821 0.187880
\(280\) 0.502138 0.0300085
\(281\) −14.0236 −0.836576 −0.418288 0.908314i \(-0.637370\pi\)
−0.418288 + 0.908314i \(0.637370\pi\)
\(282\) −13.6979 −0.815695
\(283\) −14.4795 −0.860716 −0.430358 0.902658i \(-0.641613\pi\)
−0.430358 + 0.902658i \(0.641613\pi\)
\(284\) 8.32602 0.494058
\(285\) 1.14620 0.0678950
\(286\) 32.1548 1.90135
\(287\) −7.29759 −0.430763
\(288\) −3.01405 −0.177605
\(289\) −11.9242 −0.701421
\(290\) −12.5181 −0.735090
\(291\) 10.0682 0.590209
\(292\) 14.6211 0.855634
\(293\) −26.4389 −1.54458 −0.772288 0.635273i \(-0.780888\pi\)
−0.772288 + 0.635273i \(0.780888\pi\)
\(294\) −14.7113 −0.857978
\(295\) −9.74771 −0.567533
\(296\) 0.0552340 0.00321041
\(297\) 26.5074 1.53811
\(298\) −29.1137 −1.68651
\(299\) −17.2404 −0.997039
\(300\) 12.7690 0.737217
\(301\) −11.9437 −0.688426
\(302\) 3.08988 0.177803
\(303\) −17.1814 −0.987046
\(304\) −4.42317 −0.253686
\(305\) −3.97315 −0.227502
\(306\) 1.72255 0.0984714
\(307\) −2.14032 −0.122155 −0.0610773 0.998133i \(-0.519454\pi\)
−0.0610773 + 0.998133i \(0.519454\pi\)
\(308\) −12.9086 −0.735534
\(309\) −16.6421 −0.946734
\(310\) −10.9571 −0.622319
\(311\) −16.8102 −0.953217 −0.476609 0.879116i \(-0.658134\pi\)
−0.476609 + 0.879116i \(0.658134\pi\)
\(312\) 2.58033 0.146082
\(313\) 19.2019 1.08536 0.542678 0.839941i \(-0.317410\pi\)
0.542678 + 0.839941i \(0.317410\pi\)
\(314\) 35.8162 2.02123
\(315\) −0.424609 −0.0239240
\(316\) −3.05124 −0.171646
\(317\) −7.18411 −0.403500 −0.201750 0.979437i \(-0.564663\pi\)
−0.201750 + 0.979437i \(0.564663\pi\)
\(318\) −8.77332 −0.491983
\(319\) −43.9874 −2.46282
\(320\) 4.24209 0.237140
\(321\) 18.2359 1.01783
\(322\) 14.7884 0.824125
\(323\) 2.25296 0.125358
\(324\) −13.4804 −0.748914
\(325\) 15.4112 0.854857
\(326\) −37.5094 −2.07746
\(327\) 13.6123 0.752764
\(328\) 2.24404 0.123906
\(329\) 6.63688 0.365903
\(330\) −10.7517 −0.591863
\(331\) −22.1654 −1.21832 −0.609162 0.793046i \(-0.708494\pi\)
−0.609162 + 0.793046i \(0.708494\pi\)
\(332\) −18.7494 −1.02901
\(333\) −0.0467059 −0.00255947
\(334\) −43.4892 −2.37962
\(335\) 3.30822 0.180747
\(336\) −10.8275 −0.590691
\(337\) 21.0069 1.14432 0.572159 0.820143i \(-0.306106\pi\)
0.572159 + 0.820143i \(0.306106\pi\)
\(338\) 2.42273 0.131779
\(339\) −2.94719 −0.160069
\(340\) −2.81476 −0.152652
\(341\) −38.5019 −2.08500
\(342\) 0.764570 0.0413432
\(343\) 17.7432 0.958045
\(344\) 3.67274 0.198021
\(345\) 5.76475 0.310364
\(346\) 12.7406 0.684941
\(347\) 9.85372 0.528975 0.264488 0.964389i \(-0.414797\pi\)
0.264488 + 0.964389i \(0.414797\pi\)
\(348\) 25.8240 1.38431
\(349\) −14.4455 −0.773250 −0.386625 0.922237i \(-0.626359\pi\)
−0.386625 + 0.922237i \(0.626359\pi\)
\(350\) −13.2193 −0.706602
\(351\) −18.7820 −1.00251
\(352\) 36.9787 1.97097
\(353\) 3.85238 0.205041 0.102521 0.994731i \(-0.467309\pi\)
0.102521 + 0.994731i \(0.467309\pi\)
\(354\) 42.9663 2.28363
\(355\) −3.36008 −0.178334
\(356\) −0.309663 −0.0164121
\(357\) 5.51506 0.291888
\(358\) 37.6198 1.98827
\(359\) −15.9317 −0.840840 −0.420420 0.907329i \(-0.638117\pi\)
−0.420420 + 0.907329i \(0.638117\pi\)
\(360\) 0.130569 0.00688158
\(361\) 1.00000 0.0526316
\(362\) 42.7598 2.24741
\(363\) −20.0241 −1.05099
\(364\) 9.14646 0.479405
\(365\) −5.90053 −0.308848
\(366\) 17.5130 0.915417
\(367\) −25.5007 −1.33112 −0.665562 0.746343i \(-0.731808\pi\)
−0.665562 + 0.746343i \(0.731808\pi\)
\(368\) −22.2461 −1.15966
\(369\) −1.89756 −0.0987830
\(370\) 0.163074 0.00847781
\(371\) 4.25085 0.220693
\(372\) 22.6036 1.17194
\(373\) 28.4844 1.47486 0.737432 0.675421i \(-0.236038\pi\)
0.737432 + 0.675421i \(0.236038\pi\)
\(374\) −21.1335 −1.09279
\(375\) −10.8841 −0.562052
\(376\) −2.04087 −0.105250
\(377\) 31.1675 1.60521
\(378\) 16.1107 0.828646
\(379\) 16.3569 0.840200 0.420100 0.907478i \(-0.361995\pi\)
0.420100 + 0.907478i \(0.361995\pi\)
\(380\) −1.24936 −0.0640909
\(381\) −30.0859 −1.54135
\(382\) −11.1296 −0.569439
\(383\) −3.96299 −0.202499 −0.101250 0.994861i \(-0.532284\pi\)
−0.101250 + 0.994861i \(0.532284\pi\)
\(384\) 5.97841 0.305084
\(385\) 5.20943 0.265497
\(386\) −24.3775 −1.24078
\(387\) −3.10568 −0.157870
\(388\) −10.9744 −0.557140
\(389\) 2.67002 0.135375 0.0676877 0.997707i \(-0.478438\pi\)
0.0676877 + 0.997707i \(0.478438\pi\)
\(390\) 7.61821 0.385763
\(391\) 11.3311 0.573040
\(392\) −2.19185 −0.110705
\(393\) −21.1402 −1.06638
\(394\) 43.5655 2.19480
\(395\) 1.23137 0.0619569
\(396\) −3.35656 −0.168673
\(397\) −1.51398 −0.0759846 −0.0379923 0.999278i \(-0.512096\pi\)
−0.0379923 + 0.999278i \(0.512096\pi\)
\(398\) 27.9438 1.40070
\(399\) 2.44792 0.122549
\(400\) 19.8857 0.994284
\(401\) 34.0918 1.70246 0.851232 0.524790i \(-0.175856\pi\)
0.851232 + 0.524790i \(0.175856\pi\)
\(402\) −14.5821 −0.727287
\(403\) 27.2808 1.35895
\(404\) 18.7278 0.931743
\(405\) 5.44022 0.270326
\(406\) −26.7347 −1.32682
\(407\) 0.573024 0.0284037
\(408\) −1.69590 −0.0839597
\(409\) −30.4921 −1.50774 −0.753869 0.657024i \(-0.771815\pi\)
−0.753869 + 0.657024i \(0.771815\pi\)
\(410\) 6.62534 0.327202
\(411\) −19.6619 −0.969849
\(412\) 18.1399 0.893689
\(413\) −20.8180 −1.02439
\(414\) 3.84536 0.188989
\(415\) 7.56658 0.371429
\(416\) −26.2015 −1.28464
\(417\) −10.8023 −0.528991
\(418\) −9.38033 −0.458807
\(419\) 24.0107 1.17300 0.586499 0.809950i \(-0.300506\pi\)
0.586499 + 0.809950i \(0.300506\pi\)
\(420\) −3.05834 −0.149231
\(421\) −23.6431 −1.15230 −0.576148 0.817346i \(-0.695445\pi\)
−0.576148 + 0.817346i \(0.695445\pi\)
\(422\) −1.93894 −0.0943862
\(423\) 1.72576 0.0839092
\(424\) −1.30715 −0.0634809
\(425\) −10.1289 −0.491322
\(426\) 14.8107 0.717579
\(427\) −8.48537 −0.410636
\(428\) −19.8772 −0.960799
\(429\) 26.7696 1.29245
\(430\) 10.8435 0.522919
\(431\) −35.5519 −1.71247 −0.856237 0.516583i \(-0.827204\pi\)
−0.856237 + 0.516583i \(0.827204\pi\)
\(432\) −24.2352 −1.16602
\(433\) −22.7300 −1.09233 −0.546166 0.837677i \(-0.683913\pi\)
−0.546166 + 0.837677i \(0.683913\pi\)
\(434\) −23.4008 −1.12327
\(435\) −10.4216 −0.499678
\(436\) −14.8375 −0.710588
\(437\) 5.02944 0.240591
\(438\) 26.0085 1.24274
\(439\) −34.1119 −1.62807 −0.814036 0.580814i \(-0.802734\pi\)
−0.814036 + 0.580814i \(0.802734\pi\)
\(440\) −1.60192 −0.0763684
\(441\) 1.85343 0.0882587
\(442\) 14.9743 0.712255
\(443\) −27.3154 −1.29779 −0.648897 0.760876i \(-0.724769\pi\)
−0.648897 + 0.760876i \(0.724769\pi\)
\(444\) −0.336409 −0.0159653
\(445\) 0.124969 0.00592408
\(446\) −43.4356 −2.05674
\(447\) −24.2378 −1.14641
\(448\) 9.05974 0.428033
\(449\) −26.5782 −1.25430 −0.627151 0.778897i \(-0.715779\pi\)
−0.627151 + 0.778897i \(0.715779\pi\)
\(450\) −3.43736 −0.162038
\(451\) 23.2807 1.09625
\(452\) 3.21245 0.151101
\(453\) 2.57239 0.120862
\(454\) −8.23067 −0.386284
\(455\) −3.69117 −0.173045
\(456\) −0.752744 −0.0352505
\(457\) −11.0655 −0.517624 −0.258812 0.965928i \(-0.583331\pi\)
−0.258812 + 0.965928i \(0.583331\pi\)
\(458\) −48.4252 −2.26276
\(459\) 12.3443 0.576184
\(460\) −6.28360 −0.292974
\(461\) 20.9443 0.975473 0.487737 0.872991i \(-0.337823\pi\)
0.487737 + 0.872991i \(0.337823\pi\)
\(462\) −22.9623 −1.06830
\(463\) −30.7131 −1.42736 −0.713680 0.700472i \(-0.752973\pi\)
−0.713680 + 0.700472i \(0.752973\pi\)
\(464\) 40.2168 1.86702
\(465\) −9.12199 −0.423022
\(466\) 18.2685 0.846273
\(467\) −15.3672 −0.711111 −0.355555 0.934655i \(-0.615708\pi\)
−0.355555 + 0.934655i \(0.615708\pi\)
\(468\) 2.37831 0.109937
\(469\) 7.06530 0.326245
\(470\) −6.02549 −0.277935
\(471\) 29.8178 1.37393
\(472\) 6.40161 0.294658
\(473\) 38.1028 1.75197
\(474\) −5.42767 −0.249301
\(475\) −4.49580 −0.206282
\(476\) −6.01144 −0.275534
\(477\) 1.10533 0.0506095
\(478\) 31.6043 1.44555
\(479\) −21.2338 −0.970196 −0.485098 0.874460i \(-0.661216\pi\)
−0.485098 + 0.874460i \(0.661216\pi\)
\(480\) 8.76111 0.399888
\(481\) −0.406020 −0.0185129
\(482\) 24.7935 1.12931
\(483\) 12.3117 0.560200
\(484\) 21.8264 0.992107
\(485\) 4.42886 0.201104
\(486\) 7.89173 0.357976
\(487\) −16.8974 −0.765696 −0.382848 0.923811i \(-0.625057\pi\)
−0.382848 + 0.923811i \(0.625057\pi\)
\(488\) 2.60928 0.118117
\(489\) −31.2274 −1.41215
\(490\) −6.47127 −0.292342
\(491\) −22.5677 −1.01847 −0.509234 0.860628i \(-0.670071\pi\)
−0.509234 + 0.860628i \(0.670071\pi\)
\(492\) −13.6676 −0.616182
\(493\) −20.4846 −0.922582
\(494\) 6.64650 0.299040
\(495\) 1.35458 0.0608840
\(496\) 35.2016 1.58060
\(497\) −7.17605 −0.321890
\(498\) −33.3522 −1.49455
\(499\) −13.4511 −0.602156 −0.301078 0.953600i \(-0.597346\pi\)
−0.301078 + 0.953600i \(0.597346\pi\)
\(500\) 11.8637 0.530561
\(501\) −36.2057 −1.61755
\(502\) 45.9159 2.04933
\(503\) −4.75979 −0.212228 −0.106114 0.994354i \(-0.533841\pi\)
−0.106114 + 0.994354i \(0.533841\pi\)
\(504\) 0.278853 0.0124211
\(505\) −7.55786 −0.336320
\(506\) −47.1778 −2.09731
\(507\) 2.01697 0.0895768
\(508\) 32.7937 1.45499
\(509\) −1.27382 −0.0564612 −0.0282306 0.999601i \(-0.508987\pi\)
−0.0282306 + 0.999601i \(0.508987\pi\)
\(510\) −5.00702 −0.221714
\(511\) −12.6017 −0.557464
\(512\) −29.6837 −1.31185
\(513\) 5.47915 0.241911
\(514\) 6.56322 0.289491
\(515\) −7.32060 −0.322584
\(516\) −22.3693 −0.984753
\(517\) −21.1729 −0.931184
\(518\) 0.348274 0.0153023
\(519\) 10.6068 0.465589
\(520\) 1.13505 0.0497752
\(521\) −12.1115 −0.530616 −0.265308 0.964164i \(-0.585474\pi\)
−0.265308 + 0.964164i \(0.585474\pi\)
\(522\) −6.95171 −0.304268
\(523\) 35.7349 1.56258 0.781288 0.624170i \(-0.214563\pi\)
0.781288 + 0.624170i \(0.214563\pi\)
\(524\) 23.0428 1.00663
\(525\) −11.0054 −0.480313
\(526\) −53.3089 −2.32438
\(527\) −17.9301 −0.781048
\(528\) 34.5419 1.50325
\(529\) 2.29530 0.0997956
\(530\) −3.85926 −0.167635
\(531\) −5.41321 −0.234913
\(532\) −2.66824 −0.115683
\(533\) −16.4957 −0.714509
\(534\) −0.550841 −0.0238372
\(535\) 8.02170 0.346808
\(536\) −2.17261 −0.0938423
\(537\) 31.3193 1.35153
\(538\) 50.6129 2.18208
\(539\) −22.7393 −0.979453
\(540\) −6.84545 −0.294581
\(541\) 1.29855 0.0558291 0.0279145 0.999610i \(-0.491113\pi\)
0.0279145 + 0.999610i \(0.491113\pi\)
\(542\) 38.2877 1.64460
\(543\) 35.5985 1.52768
\(544\) 17.2208 0.738334
\(545\) 5.98788 0.256492
\(546\) 16.2701 0.696295
\(547\) −25.5778 −1.09363 −0.546814 0.837254i \(-0.684160\pi\)
−0.546814 + 0.837254i \(0.684160\pi\)
\(548\) 21.4315 0.915509
\(549\) −2.20641 −0.0941674
\(550\) 42.1721 1.79823
\(551\) −9.09232 −0.387346
\(552\) −3.78588 −0.161138
\(553\) 2.62981 0.111831
\(554\) −44.5047 −1.89082
\(555\) 0.135762 0.00576280
\(556\) 11.7746 0.499353
\(557\) −39.8206 −1.68725 −0.843626 0.536931i \(-0.819583\pi\)
−0.843626 + 0.536931i \(0.819583\pi\)
\(558\) −6.08480 −0.257590
\(559\) −26.9980 −1.14189
\(560\) −4.76288 −0.201268
\(561\) −17.5941 −0.742824
\(562\) 27.1909 1.14698
\(563\) 11.4528 0.482680 0.241340 0.970441i \(-0.422413\pi\)
0.241340 + 0.970441i \(0.422413\pi\)
\(564\) 12.4301 0.523403
\(565\) −1.29643 −0.0545411
\(566\) 28.0749 1.18008
\(567\) 11.6186 0.487934
\(568\) 2.20666 0.0925895
\(569\) −2.46885 −0.103500 −0.0517498 0.998660i \(-0.516480\pi\)
−0.0517498 + 0.998660i \(0.516480\pi\)
\(570\) −2.22241 −0.0930867
\(571\) −28.1346 −1.17739 −0.588697 0.808354i \(-0.700359\pi\)
−0.588697 + 0.808354i \(0.700359\pi\)
\(572\) −29.1789 −1.22003
\(573\) −9.26561 −0.387076
\(574\) 14.1496 0.590593
\(575\) −22.6114 −0.942960
\(576\) 2.35576 0.0981568
\(577\) 20.2880 0.844603 0.422301 0.906456i \(-0.361222\pi\)
0.422301 + 0.906456i \(0.361222\pi\)
\(578\) 23.1203 0.961676
\(579\) −20.2948 −0.843423
\(580\) 11.3596 0.471682
\(581\) 16.1598 0.670422
\(582\) −19.5217 −0.809199
\(583\) −13.5610 −0.561640
\(584\) 3.87506 0.160351
\(585\) −0.959799 −0.0396828
\(586\) 51.2634 2.11767
\(587\) 15.9598 0.658730 0.329365 0.944203i \(-0.393165\pi\)
0.329365 + 0.944203i \(0.393165\pi\)
\(588\) 13.3498 0.550535
\(589\) −7.95846 −0.327923
\(590\) 18.9002 0.778111
\(591\) 36.2692 1.49192
\(592\) −0.523905 −0.0215324
\(593\) 15.8008 0.648860 0.324430 0.945910i \(-0.394827\pi\)
0.324430 + 0.945910i \(0.394827\pi\)
\(594\) −51.3963 −2.10881
\(595\) 2.42600 0.0994562
\(596\) 26.4193 1.08218
\(597\) 23.2638 0.952125
\(598\) 33.4282 1.36698
\(599\) −4.63147 −0.189237 −0.0946184 0.995514i \(-0.530163\pi\)
−0.0946184 + 0.995514i \(0.530163\pi\)
\(600\) 3.38419 0.138159
\(601\) −12.3540 −0.503929 −0.251964 0.967737i \(-0.581077\pi\)
−0.251964 + 0.967737i \(0.581077\pi\)
\(602\) 23.1582 0.943858
\(603\) 1.83716 0.0748148
\(604\) −2.80392 −0.114090
\(605\) −8.80832 −0.358109
\(606\) 33.3138 1.35328
\(607\) −11.3892 −0.462274 −0.231137 0.972921i \(-0.574245\pi\)
−0.231137 + 0.972921i \(0.574245\pi\)
\(608\) 7.64362 0.309990
\(609\) −22.2572 −0.901909
\(610\) 7.70370 0.311914
\(611\) 15.0022 0.606925
\(612\) −1.56313 −0.0631857
\(613\) 10.3331 0.417350 0.208675 0.977985i \(-0.433085\pi\)
0.208675 + 0.977985i \(0.433085\pi\)
\(614\) 4.14996 0.167479
\(615\) 5.51573 0.222416
\(616\) −3.42119 −0.137844
\(617\) −5.53466 −0.222817 −0.111408 0.993775i \(-0.535536\pi\)
−0.111408 + 0.993775i \(0.535536\pi\)
\(618\) 32.2680 1.29801
\(619\) 14.9342 0.600256 0.300128 0.953899i \(-0.402971\pi\)
0.300128 + 0.953899i \(0.402971\pi\)
\(620\) 9.94300 0.399321
\(621\) 27.5571 1.10583
\(622\) 32.5939 1.30690
\(623\) 0.266893 0.0106928
\(624\) −24.4749 −0.979781
\(625\) 17.6913 0.707650
\(626\) −37.2314 −1.48807
\(627\) −7.80933 −0.311874
\(628\) −32.5015 −1.29695
\(629\) 0.266854 0.0106402
\(630\) 0.823292 0.0328007
\(631\) −22.5759 −0.898732 −0.449366 0.893348i \(-0.648350\pi\)
−0.449366 + 0.893348i \(0.648350\pi\)
\(632\) −0.808677 −0.0321674
\(633\) −1.61421 −0.0641591
\(634\) 13.9296 0.553214
\(635\) −13.2343 −0.525189
\(636\) 7.96136 0.315689
\(637\) 16.1121 0.638385
\(638\) 85.2889 3.37662
\(639\) −1.86596 −0.0738161
\(640\) 2.62982 0.103953
\(641\) 7.33130 0.289569 0.144784 0.989463i \(-0.453751\pi\)
0.144784 + 0.989463i \(0.453751\pi\)
\(642\) −35.3583 −1.39548
\(643\) 31.4635 1.24080 0.620399 0.784286i \(-0.286971\pi\)
0.620399 + 0.784286i \(0.286971\pi\)
\(644\) −13.4198 −0.528813
\(645\) 9.02743 0.355455
\(646\) −4.36836 −0.171871
\(647\) −32.1732 −1.26486 −0.632429 0.774618i \(-0.717942\pi\)
−0.632429 + 0.774618i \(0.717942\pi\)
\(648\) −3.57275 −0.140351
\(649\) 66.4134 2.60695
\(650\) −29.8813 −1.17204
\(651\) −19.4817 −0.763546
\(652\) 34.0380 1.33303
\(653\) −40.2209 −1.57396 −0.786982 0.616976i \(-0.788358\pi\)
−0.786982 + 0.616976i \(0.788358\pi\)
\(654\) −26.3936 −1.03207
\(655\) −9.29925 −0.363352
\(656\) −21.2851 −0.831045
\(657\) −3.27675 −0.127838
\(658\) −12.8685 −0.501667
\(659\) −41.6504 −1.62247 −0.811235 0.584720i \(-0.801204\pi\)
−0.811235 + 0.584720i \(0.801204\pi\)
\(660\) 9.75668 0.379778
\(661\) −15.5677 −0.605513 −0.302757 0.953068i \(-0.597907\pi\)
−0.302757 + 0.953068i \(0.597907\pi\)
\(662\) 42.9775 1.67037
\(663\) 12.4664 0.484156
\(664\) −4.96920 −0.192842
\(665\) 1.07680 0.0417567
\(666\) 0.0905600 0.00350913
\(667\) −45.7293 −1.77064
\(668\) 39.4643 1.52692
\(669\) −36.1611 −1.39807
\(670\) −6.41444 −0.247811
\(671\) 27.0700 1.04502
\(672\) 18.7109 0.721790
\(673\) −21.7671 −0.839059 −0.419530 0.907742i \(-0.637805\pi\)
−0.419530 + 0.907742i \(0.637805\pi\)
\(674\) −40.7311 −1.56890
\(675\) −24.6332 −0.948132
\(676\) −2.19851 −0.0845579
\(677\) 14.2408 0.547319 0.273659 0.961827i \(-0.411766\pi\)
0.273659 + 0.961827i \(0.411766\pi\)
\(678\) 5.71443 0.219461
\(679\) 9.45863 0.362989
\(680\) −0.746003 −0.0286079
\(681\) −6.85221 −0.262577
\(682\) 74.6530 2.85861
\(683\) −27.6097 −1.05646 −0.528228 0.849102i \(-0.677144\pi\)
−0.528228 + 0.849102i \(0.677144\pi\)
\(684\) −0.693810 −0.0265285
\(685\) −8.64898 −0.330460
\(686\) −34.4031 −1.31352
\(687\) −40.3150 −1.53811
\(688\) −34.8367 −1.32814
\(689\) 9.60875 0.366064
\(690\) −11.1775 −0.425521
\(691\) 30.2222 1.14971 0.574854 0.818256i \(-0.305059\pi\)
0.574854 + 0.818256i \(0.305059\pi\)
\(692\) −11.5615 −0.439503
\(693\) 2.89296 0.109894
\(694\) −19.1058 −0.725246
\(695\) −4.75178 −0.180245
\(696\) 6.84418 0.259428
\(697\) 10.8417 0.410658
\(698\) 28.0090 1.06016
\(699\) 15.2089 0.575255
\(700\) 11.9959 0.453402
\(701\) 49.8089 1.88126 0.940628 0.339438i \(-0.110237\pi\)
0.940628 + 0.339438i \(0.110237\pi\)
\(702\) 36.4172 1.37448
\(703\) 0.118446 0.00446727
\(704\) −28.9023 −1.08930
\(705\) −5.01635 −0.188927
\(706\) −7.46954 −0.281120
\(707\) −16.1412 −0.607051
\(708\) −38.9898 −1.46533
\(709\) 33.8181 1.27007 0.635033 0.772485i \(-0.280987\pi\)
0.635033 + 0.772485i \(0.280987\pi\)
\(710\) 6.51499 0.244503
\(711\) 0.683818 0.0256452
\(712\) −0.0820706 −0.00307573
\(713\) −40.0266 −1.49901
\(714\) −10.6934 −0.400190
\(715\) 11.7756 0.440381
\(716\) −34.1382 −1.27580
\(717\) 26.3113 0.982613
\(718\) 30.8906 1.15283
\(719\) −18.0136 −0.671794 −0.335897 0.941899i \(-0.609039\pi\)
−0.335897 + 0.941899i \(0.609039\pi\)
\(720\) −1.23847 −0.0461551
\(721\) −15.6345 −0.582258
\(722\) −1.93894 −0.0721599
\(723\) 20.6411 0.767650
\(724\) −38.8025 −1.44208
\(725\) 40.8773 1.51814
\(726\) 38.8256 1.44095
\(727\) 27.6422 1.02519 0.512595 0.858630i \(-0.328684\pi\)
0.512595 + 0.858630i \(0.328684\pi\)
\(728\) 2.42411 0.0898433
\(729\) 29.5547 1.09462
\(730\) 11.4408 0.423442
\(731\) 17.7442 0.656295
\(732\) −15.8922 −0.587391
\(733\) 32.4675 1.19922 0.599608 0.800294i \(-0.295323\pi\)
0.599608 + 0.800294i \(0.295323\pi\)
\(734\) 49.4443 1.82502
\(735\) −5.38747 −0.198720
\(736\) 38.4431 1.41703
\(737\) −22.5397 −0.830259
\(738\) 3.67926 0.135435
\(739\) 8.02656 0.295262 0.147631 0.989043i \(-0.452835\pi\)
0.147631 + 0.989043i \(0.452835\pi\)
\(740\) −0.147982 −0.00543991
\(741\) 5.53335 0.203273
\(742\) −8.24214 −0.302579
\(743\) 45.1744 1.65729 0.828644 0.559776i \(-0.189113\pi\)
0.828644 + 0.559776i \(0.189113\pi\)
\(744\) 5.99068 0.219629
\(745\) −10.6619 −0.390621
\(746\) −55.2295 −2.02210
\(747\) 4.20196 0.153742
\(748\) 19.1776 0.701204
\(749\) 17.1318 0.625982
\(750\) 21.1036 0.770595
\(751\) 29.4782 1.07568 0.537838 0.843048i \(-0.319241\pi\)
0.537838 + 0.843048i \(0.319241\pi\)
\(752\) 19.3580 0.705914
\(753\) 38.2260 1.39303
\(754\) −60.4321 −2.20081
\(755\) 1.13156 0.0411816
\(756\) −14.6197 −0.531713
\(757\) −22.6655 −0.823793 −0.411896 0.911231i \(-0.635133\pi\)
−0.411896 + 0.911231i \(0.635133\pi\)
\(758\) −31.7152 −1.15195
\(759\) −39.2766 −1.42565
\(760\) −0.331121 −0.0120110
\(761\) 23.1047 0.837543 0.418772 0.908092i \(-0.362461\pi\)
0.418772 + 0.908092i \(0.362461\pi\)
\(762\) 58.3348 2.11325
\(763\) 12.7882 0.462964
\(764\) 10.0996 0.365389
\(765\) 0.630821 0.0228074
\(766\) 7.68401 0.277635
\(767\) −47.0577 −1.69915
\(768\) −30.8790 −1.11425
\(769\) 20.8502 0.751877 0.375939 0.926645i \(-0.377320\pi\)
0.375939 + 0.926645i \(0.377320\pi\)
\(770\) −10.1008 −0.364007
\(771\) 5.46402 0.196782
\(772\) 22.1214 0.796167
\(773\) 34.7891 1.25128 0.625639 0.780113i \(-0.284838\pi\)
0.625639 + 0.780113i \(0.284838\pi\)
\(774\) 6.02172 0.216446
\(775\) 35.7797 1.28524
\(776\) −2.90857 −0.104411
\(777\) 0.289945 0.0104017
\(778\) −5.17701 −0.185605
\(779\) 4.81219 0.172415
\(780\) −6.91316 −0.247531
\(781\) 22.8930 0.819175
\(782\) −21.9704 −0.785661
\(783\) −49.8182 −1.78036
\(784\) 20.7902 0.742506
\(785\) 13.1164 0.468145
\(786\) 40.9895 1.46205
\(787\) −9.81657 −0.349923 −0.174961 0.984575i \(-0.555980\pi\)
−0.174961 + 0.984575i \(0.555980\pi\)
\(788\) −39.5336 −1.40832
\(789\) −44.3808 −1.58000
\(790\) −2.38755 −0.0849453
\(791\) −2.76875 −0.0984456
\(792\) −0.889596 −0.0316104
\(793\) −19.1806 −0.681123
\(794\) 2.93552 0.104178
\(795\) −3.21291 −0.113950
\(796\) −25.3577 −0.898778
\(797\) 29.2697 1.03679 0.518393 0.855143i \(-0.326531\pi\)
0.518393 + 0.855143i \(0.326531\pi\)
\(798\) −4.74637 −0.168020
\(799\) −9.86010 −0.348825
\(800\) −34.3642 −1.21496
\(801\) 0.0693990 0.00245209
\(802\) −66.1020 −2.33414
\(803\) 40.2017 1.41869
\(804\) 13.2325 0.466675
\(805\) 5.41572 0.190879
\(806\) −52.8959 −1.86318
\(807\) 42.1364 1.48327
\(808\) 4.96347 0.174614
\(809\) 44.9580 1.58064 0.790320 0.612695i \(-0.209915\pi\)
0.790320 + 0.612695i \(0.209915\pi\)
\(810\) −10.5483 −0.370628
\(811\) 12.0436 0.422908 0.211454 0.977388i \(-0.432180\pi\)
0.211454 + 0.977388i \(0.432180\pi\)
\(812\) 24.2605 0.851376
\(813\) 31.8753 1.11792
\(814\) −1.11106 −0.0389426
\(815\) −13.7365 −0.481168
\(816\) 16.0860 0.563122
\(817\) 7.87596 0.275545
\(818\) 59.1225 2.06717
\(819\) −2.04983 −0.0716267
\(820\) −6.01217 −0.209954
\(821\) 9.76338 0.340744 0.170372 0.985380i \(-0.445503\pi\)
0.170372 + 0.985380i \(0.445503\pi\)
\(822\) 38.1232 1.32970
\(823\) 6.09808 0.212566 0.106283 0.994336i \(-0.466105\pi\)
0.106283 + 0.994336i \(0.466105\pi\)
\(824\) 4.80766 0.167483
\(825\) 35.1092 1.22235
\(826\) 40.3649 1.40447
\(827\) 7.68780 0.267331 0.133666 0.991026i \(-0.457325\pi\)
0.133666 + 0.991026i \(0.457325\pi\)
\(828\) −3.48948 −0.121268
\(829\) −41.3837 −1.43731 −0.718657 0.695365i \(-0.755243\pi\)
−0.718657 + 0.695365i \(0.755243\pi\)
\(830\) −14.6712 −0.509243
\(831\) −37.0511 −1.28529
\(832\) 20.4789 0.709979
\(833\) −10.5896 −0.366907
\(834\) 20.9451 0.725268
\(835\) −15.9264 −0.551154
\(836\) 8.51220 0.294400
\(837\) −43.6056 −1.50723
\(838\) −46.5553 −1.60823
\(839\) −26.4281 −0.912399 −0.456199 0.889878i \(-0.650790\pi\)
−0.456199 + 0.889878i \(0.650790\pi\)
\(840\) −0.810557 −0.0279669
\(841\) 53.6702 1.85070
\(842\) 45.8426 1.57984
\(843\) 22.6370 0.779660
\(844\) 1.75950 0.0605644
\(845\) 0.887237 0.0305219
\(846\) −3.34614 −0.115043
\(847\) −18.8118 −0.646380
\(848\) 12.3986 0.425769
\(849\) 23.3729 0.802157
\(850\) 19.6393 0.673622
\(851\) 0.595716 0.0204209
\(852\) −13.4400 −0.460445
\(853\) 44.8321 1.53502 0.767510 0.641037i \(-0.221495\pi\)
0.767510 + 0.641037i \(0.221495\pi\)
\(854\) 16.4526 0.562998
\(855\) 0.279996 0.00957567
\(856\) −5.26809 −0.180060
\(857\) 36.7482 1.25529 0.627647 0.778498i \(-0.284018\pi\)
0.627647 + 0.778498i \(0.284018\pi\)
\(858\) −51.9047 −1.77200
\(859\) −43.4808 −1.48355 −0.741774 0.670650i \(-0.766015\pi\)
−0.741774 + 0.670650i \(0.766015\pi\)
\(860\) −9.83993 −0.335539
\(861\) 11.7799 0.401456
\(862\) 68.9330 2.34787
\(863\) 9.85100 0.335332 0.167666 0.985844i \(-0.446377\pi\)
0.167666 + 0.985844i \(0.446377\pi\)
\(864\) 41.8805 1.42480
\(865\) 4.66580 0.158642
\(866\) 44.0721 1.49763
\(867\) 19.2481 0.653700
\(868\) 21.2351 0.720766
\(869\) −8.38960 −0.284598
\(870\) 20.2069 0.685078
\(871\) 15.9706 0.541144
\(872\) −3.93242 −0.133168
\(873\) 2.45949 0.0832410
\(874\) −9.75180 −0.329860
\(875\) −10.2251 −0.345672
\(876\) −23.6015 −0.797421
\(877\) −46.1145 −1.55718 −0.778589 0.627534i \(-0.784064\pi\)
−0.778589 + 0.627534i \(0.784064\pi\)
\(878\) 66.1410 2.23215
\(879\) 42.6779 1.43949
\(880\) 15.1945 0.512207
\(881\) 18.8370 0.634634 0.317317 0.948319i \(-0.397218\pi\)
0.317317 + 0.948319i \(0.397218\pi\)
\(882\) −3.59370 −0.121006
\(883\) 15.8320 0.532789 0.266394 0.963864i \(-0.414168\pi\)
0.266394 + 0.963864i \(0.414168\pi\)
\(884\) −13.5885 −0.457029
\(885\) 15.7349 0.528921
\(886\) 52.9630 1.77933
\(887\) −38.9792 −1.30879 −0.654397 0.756151i \(-0.727077\pi\)
−0.654397 + 0.756151i \(0.727077\pi\)
\(888\) −0.0891593 −0.00299199
\(889\) −28.2643 −0.947956
\(890\) −0.242307 −0.00812215
\(891\) −37.0655 −1.24174
\(892\) 39.4157 1.31974
\(893\) −4.37650 −0.146454
\(894\) 46.9957 1.57177
\(895\) 13.7769 0.460512
\(896\) 5.61645 0.187632
\(897\) 27.8297 0.929206
\(898\) 51.5336 1.71970
\(899\) 72.3609 2.41337
\(900\) 3.11923 0.103974
\(901\) −6.31528 −0.210392
\(902\) −45.1400 −1.50300
\(903\) 19.2797 0.641589
\(904\) 0.851402 0.0283172
\(905\) 15.6593 0.520532
\(906\) −4.98772 −0.165706
\(907\) 16.2101 0.538246 0.269123 0.963106i \(-0.413266\pi\)
0.269123 + 0.963106i \(0.413266\pi\)
\(908\) 7.46893 0.247865
\(909\) −4.19712 −0.139210
\(910\) 7.15697 0.237251
\(911\) −1.93959 −0.0642616 −0.0321308 0.999484i \(-0.510229\pi\)
−0.0321308 + 0.999484i \(0.510229\pi\)
\(912\) 7.13992 0.236426
\(913\) −51.5529 −1.70615
\(914\) 21.4554 0.709683
\(915\) 6.41349 0.212024
\(916\) 43.9435 1.45193
\(917\) −19.8602 −0.655843
\(918\) −23.9349 −0.789970
\(919\) −14.6607 −0.483613 −0.241807 0.970324i \(-0.577740\pi\)
−0.241807 + 0.970324i \(0.577740\pi\)
\(920\) −1.66536 −0.0549051
\(921\) 3.45493 0.113844
\(922\) −40.6098 −1.33741
\(923\) −16.2210 −0.533920
\(924\) 20.8372 0.685492
\(925\) −0.532509 −0.0175088
\(926\) 59.5509 1.95696
\(927\) −4.06536 −0.133524
\(928\) −69.4982 −2.28139
\(929\) 25.6528 0.841642 0.420821 0.907144i \(-0.361742\pi\)
0.420821 + 0.907144i \(0.361742\pi\)
\(930\) 17.6870 0.579980
\(931\) −4.70029 −0.154046
\(932\) −16.5778 −0.543024
\(933\) 27.1352 0.888365
\(934\) 29.7962 0.974961
\(935\) −7.73940 −0.253105
\(936\) 0.630329 0.0206029
\(937\) −24.2289 −0.791525 −0.395763 0.918353i \(-0.629520\pi\)
−0.395763 + 0.918353i \(0.629520\pi\)
\(938\) −13.6992 −0.447295
\(939\) −30.9959 −1.01151
\(940\) 5.46784 0.178341
\(941\) −54.4971 −1.77655 −0.888277 0.459308i \(-0.848097\pi\)
−0.888277 + 0.459308i \(0.848097\pi\)
\(942\) −57.8150 −1.88371
\(943\) 24.2027 0.788147
\(944\) −60.7205 −1.97629
\(945\) 5.89997 0.191926
\(946\) −73.8791 −2.40202
\(947\) 6.51946 0.211854 0.105927 0.994374i \(-0.466219\pi\)
0.105927 + 0.994374i \(0.466219\pi\)
\(948\) 4.92535 0.159968
\(949\) −28.4852 −0.924668
\(950\) 8.71710 0.282820
\(951\) 11.5967 0.376048
\(952\) −1.59323 −0.0516367
\(953\) −36.3798 −1.17846 −0.589229 0.807966i \(-0.700569\pi\)
−0.589229 + 0.807966i \(0.700569\pi\)
\(954\) −2.14317 −0.0693876
\(955\) −4.07581 −0.131890
\(956\) −28.6794 −0.927558
\(957\) 71.0049 2.29526
\(958\) 41.1711 1.33018
\(959\) −18.4715 −0.596475
\(960\) −6.84762 −0.221006
\(961\) 32.3371 1.04313
\(962\) 0.787249 0.0253819
\(963\) 4.45470 0.143551
\(964\) −22.4989 −0.724640
\(965\) −8.92739 −0.287383
\(966\) −23.8716 −0.768056
\(967\) 18.2294 0.586219 0.293110 0.956079i \(-0.405310\pi\)
0.293110 + 0.956079i \(0.405310\pi\)
\(968\) 5.78469 0.185927
\(969\) −3.63675 −0.116829
\(970\) −8.58730 −0.275722
\(971\) −41.7816 −1.34084 −0.670418 0.741984i \(-0.733885\pi\)
−0.670418 + 0.741984i \(0.733885\pi\)
\(972\) −7.16136 −0.229701
\(973\) −10.1483 −0.325339
\(974\) 32.7631 1.04980
\(975\) −24.8769 −0.796697
\(976\) −24.7496 −0.792214
\(977\) 19.6861 0.629813 0.314906 0.949123i \(-0.398027\pi\)
0.314906 + 0.949123i \(0.398027\pi\)
\(978\) 60.5481 1.93612
\(979\) −0.851440 −0.0272122
\(980\) 5.87237 0.187586
\(981\) 3.32526 0.106167
\(982\) 43.7576 1.39636
\(983\) −49.8680 −1.59054 −0.795271 0.606254i \(-0.792671\pi\)
−0.795271 + 0.606254i \(0.792671\pi\)
\(984\) −3.62235 −0.115476
\(985\) 15.9543 0.508346
\(986\) 39.7185 1.26490
\(987\) −10.7133 −0.341009
\(988\) −6.03137 −0.191884
\(989\) 39.6117 1.25958
\(990\) −2.62646 −0.0834743
\(991\) −4.85857 −0.154337 −0.0771687 0.997018i \(-0.524588\pi\)
−0.0771687 + 0.997018i \(0.524588\pi\)
\(992\) −60.8314 −1.93140
\(993\) 35.7797 1.13543
\(994\) 13.9140 0.441324
\(995\) 10.2334 0.324421
\(996\) 30.2655 0.959000
\(997\) −7.93651 −0.251352 −0.125676 0.992071i \(-0.540110\pi\)
−0.125676 + 0.992071i \(0.540110\pi\)
\(998\) 26.0810 0.825579
\(999\) 0.648982 0.0205329
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 \(a_p\))