Properties

Label 6013.2.a.e.1.17
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.02275 q^{2}\) \(+2.43668 q^{3}\) \(+2.09152 q^{4}\) \(+0.154664 q^{5}\) \(-4.92881 q^{6}\) \(+1.00000 q^{7}\) \(-0.185129 q^{8}\) \(+2.93743 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.02275 q^{2}\) \(+2.43668 q^{3}\) \(+2.09152 q^{4}\) \(+0.154664 q^{5}\) \(-4.92881 q^{6}\) \(+1.00000 q^{7}\) \(-0.185129 q^{8}\) \(+2.93743 q^{9}\) \(-0.312846 q^{10}\) \(-6.02597 q^{11}\) \(+5.09638 q^{12}\) \(+2.43832 q^{13}\) \(-2.02275 q^{14}\) \(+0.376867 q^{15}\) \(-3.80858 q^{16}\) \(+4.14887 q^{17}\) \(-5.94168 q^{18}\) \(+0.405818 q^{19}\) \(+0.323483 q^{20}\) \(+2.43668 q^{21}\) \(+12.1890 q^{22}\) \(+9.04004 q^{23}\) \(-0.451100 q^{24}\) \(-4.97608 q^{25}\) \(-4.93212 q^{26}\) \(-0.152471 q^{27}\) \(+2.09152 q^{28}\) \(+2.00739 q^{29}\) \(-0.762308 q^{30}\) \(+2.00947 q^{31}\) \(+8.07406 q^{32}\) \(-14.6834 q^{33}\) \(-8.39214 q^{34}\) \(+0.154664 q^{35}\) \(+6.14370 q^{36}\) \(+5.46293 q^{37}\) \(-0.820869 q^{38}\) \(+5.94141 q^{39}\) \(-0.0286327 q^{40}\) \(-2.37026 q^{41}\) \(-4.92881 q^{42}\) \(+7.65144 q^{43}\) \(-12.6035 q^{44}\) \(+0.454314 q^{45}\) \(-18.2858 q^{46}\) \(+5.36048 q^{47}\) \(-9.28030 q^{48}\) \(+1.00000 q^{49}\) \(+10.0654 q^{50}\) \(+10.1095 q^{51}\) \(+5.09980 q^{52}\) \(-2.84233 q^{53}\) \(+0.308411 q^{54}\) \(-0.932000 q^{55}\) \(-0.185129 q^{56}\) \(+0.988850 q^{57}\) \(-4.06045 q^{58}\) \(+0.593797 q^{59}\) \(+0.788226 q^{60}\) \(-12.9042 q^{61}\) \(-4.06467 q^{62}\) \(+2.93743 q^{63}\) \(-8.71467 q^{64}\) \(+0.377120 q^{65}\) \(+29.7009 q^{66}\) \(-3.94386 q^{67}\) \(+8.67746 q^{68}\) \(+22.0277 q^{69}\) \(-0.312846 q^{70}\) \(+1.58408 q^{71}\) \(-0.543802 q^{72}\) \(-5.90454 q^{73}\) \(-11.0502 q^{74}\) \(-12.1251 q^{75}\) \(+0.848778 q^{76}\) \(-6.02597 q^{77}\) \(-12.0180 q^{78}\) \(-4.92092 q^{79}\) \(-0.589049 q^{80}\) \(-9.18380 q^{81}\) \(+4.79445 q^{82}\) \(-4.58111 q^{83}\) \(+5.09638 q^{84}\) \(+0.641681 q^{85}\) \(-15.4770 q^{86}\) \(+4.89138 q^{87}\) \(+1.11558 q^{88}\) \(+10.9094 q^{89}\) \(-0.918964 q^{90}\) \(+2.43832 q^{91}\) \(+18.9075 q^{92}\) \(+4.89645 q^{93}\) \(-10.8429 q^{94}\) \(+0.0627653 q^{95}\) \(+19.6739 q^{96}\) \(+17.7928 q^{97}\) \(-2.02275 q^{98}\) \(-17.7009 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.02275 −1.43030 −0.715151 0.698970i \(-0.753642\pi\)
−0.715151 + 0.698970i \(0.753642\pi\)
\(3\) 2.43668 1.40682 0.703410 0.710784i \(-0.251660\pi\)
0.703410 + 0.710784i \(0.251660\pi\)
\(4\) 2.09152 1.04576
\(5\) 0.154664 0.0691678 0.0345839 0.999402i \(-0.488989\pi\)
0.0345839 + 0.999402i \(0.488989\pi\)
\(6\) −4.92881 −2.01218
\(7\) 1.00000 0.377964
\(8\) −0.185129 −0.0654529
\(9\) 2.93743 0.979142
\(10\) −0.312846 −0.0989307
\(11\) −6.02597 −1.81690 −0.908450 0.417994i \(-0.862733\pi\)
−0.908450 + 0.417994i \(0.862733\pi\)
\(12\) 5.09638 1.47120
\(13\) 2.43832 0.676268 0.338134 0.941098i \(-0.390204\pi\)
0.338134 + 0.941098i \(0.390204\pi\)
\(14\) −2.02275 −0.540603
\(15\) 0.376867 0.0973066
\(16\) −3.80858 −0.952144
\(17\) 4.14887 1.00625 0.503125 0.864214i \(-0.332184\pi\)
0.503125 + 0.864214i \(0.332184\pi\)
\(18\) −5.94168 −1.40047
\(19\) 0.405818 0.0931010 0.0465505 0.998916i \(-0.485177\pi\)
0.0465505 + 0.998916i \(0.485177\pi\)
\(20\) 0.323483 0.0723330
\(21\) 2.43668 0.531728
\(22\) 12.1890 2.59871
\(23\) 9.04004 1.88498 0.942489 0.334236i \(-0.108478\pi\)
0.942489 + 0.334236i \(0.108478\pi\)
\(24\) −0.451100 −0.0920805
\(25\) −4.97608 −0.995216
\(26\) −4.93212 −0.967267
\(27\) −0.152471 −0.0293431
\(28\) 2.09152 0.395261
\(29\) 2.00739 0.372763 0.186382 0.982477i \(-0.440324\pi\)
0.186382 + 0.982477i \(0.440324\pi\)
\(30\) −0.762308 −0.139178
\(31\) 2.00947 0.360912 0.180456 0.983583i \(-0.442243\pi\)
0.180456 + 0.983583i \(0.442243\pi\)
\(32\) 8.07406 1.42731
\(33\) −14.6834 −2.55605
\(34\) −8.39214 −1.43924
\(35\) 0.154664 0.0261430
\(36\) 6.14370 1.02395
\(37\) 5.46293 0.898101 0.449050 0.893506i \(-0.351762\pi\)
0.449050 + 0.893506i \(0.351762\pi\)
\(38\) −0.820869 −0.133162
\(39\) 5.94141 0.951388
\(40\) −0.0286327 −0.00452723
\(41\) −2.37026 −0.370173 −0.185086 0.982722i \(-0.559257\pi\)
−0.185086 + 0.982722i \(0.559257\pi\)
\(42\) −4.92881 −0.760531
\(43\) 7.65144 1.16683 0.583417 0.812173i \(-0.301715\pi\)
0.583417 + 0.812173i \(0.301715\pi\)
\(44\) −12.6035 −1.90004
\(45\) 0.454314 0.0677251
\(46\) −18.2858 −2.69609
\(47\) 5.36048 0.781907 0.390953 0.920410i \(-0.372145\pi\)
0.390953 + 0.920410i \(0.372145\pi\)
\(48\) −9.28030 −1.33950
\(49\) 1.00000 0.142857
\(50\) 10.0654 1.42346
\(51\) 10.1095 1.41561
\(52\) 5.09980 0.707215
\(53\) −2.84233 −0.390424 −0.195212 0.980761i \(-0.562540\pi\)
−0.195212 + 0.980761i \(0.562540\pi\)
\(54\) 0.308411 0.0419694
\(55\) −0.932000 −0.125671
\(56\) −0.185129 −0.0247389
\(57\) 0.988850 0.130976
\(58\) −4.06045 −0.533164
\(59\) 0.593797 0.0773058 0.0386529 0.999253i \(-0.487693\pi\)
0.0386529 + 0.999253i \(0.487693\pi\)
\(60\) 0.788226 0.101759
\(61\) −12.9042 −1.65221 −0.826106 0.563514i \(-0.809449\pi\)
−0.826106 + 0.563514i \(0.809449\pi\)
\(62\) −4.06467 −0.516213
\(63\) 2.93743 0.370081
\(64\) −8.71467 −1.08933
\(65\) 0.377120 0.0467760
\(66\) 29.7009 3.65592
\(67\) −3.94386 −0.481819 −0.240909 0.970548i \(-0.577446\pi\)
−0.240909 + 0.970548i \(0.577446\pi\)
\(68\) 8.67746 1.05230
\(69\) 22.0277 2.65183
\(70\) −0.312846 −0.0373923
\(71\) 1.58408 0.187996 0.0939978 0.995572i \(-0.470035\pi\)
0.0939978 + 0.995572i \(0.470035\pi\)
\(72\) −0.543802 −0.0640877
\(73\) −5.90454 −0.691075 −0.345537 0.938405i \(-0.612303\pi\)
−0.345537 + 0.938405i \(0.612303\pi\)
\(74\) −11.0502 −1.28455
\(75\) −12.1251 −1.40009
\(76\) 0.848778 0.0973615
\(77\) −6.02597 −0.686723
\(78\) −12.0180 −1.36077
\(79\) −4.92092 −0.553647 −0.276823 0.960921i \(-0.589282\pi\)
−0.276823 + 0.960921i \(0.589282\pi\)
\(80\) −0.589049 −0.0658577
\(81\) −9.18380 −1.02042
\(82\) 4.79445 0.529459
\(83\) −4.58111 −0.502842 −0.251421 0.967878i \(-0.580898\pi\)
−0.251421 + 0.967878i \(0.580898\pi\)
\(84\) 5.09638 0.556061
\(85\) 0.641681 0.0696000
\(86\) −15.4770 −1.66892
\(87\) 4.89138 0.524411
\(88\) 1.11558 0.118921
\(89\) 10.9094 1.15640 0.578198 0.815897i \(-0.303756\pi\)
0.578198 + 0.815897i \(0.303756\pi\)
\(90\) −0.918964 −0.0968673
\(91\) 2.43832 0.255605
\(92\) 18.9075 1.97124
\(93\) 4.89645 0.507738
\(94\) −10.8429 −1.11836
\(95\) 0.0627653 0.00643959
\(96\) 19.6739 2.00796
\(97\) 17.7928 1.80659 0.903295 0.429020i \(-0.141141\pi\)
0.903295 + 0.429020i \(0.141141\pi\)
\(98\) −2.02275 −0.204329
\(99\) −17.7009 −1.77900
\(100\) −10.4076 −1.04076
\(101\) 12.1296 1.20694 0.603469 0.797386i \(-0.293785\pi\)
0.603469 + 0.797386i \(0.293785\pi\)
\(102\) −20.4490 −2.02475
\(103\) 11.1810 1.10169 0.550847 0.834606i \(-0.314305\pi\)
0.550847 + 0.834606i \(0.314305\pi\)
\(104\) −0.451403 −0.0442637
\(105\) 0.376867 0.0367784
\(106\) 5.74933 0.558424
\(107\) −7.66156 −0.740671 −0.370335 0.928898i \(-0.620757\pi\)
−0.370335 + 0.928898i \(0.620757\pi\)
\(108\) −0.318897 −0.0306858
\(109\) 12.4052 1.18820 0.594099 0.804392i \(-0.297509\pi\)
0.594099 + 0.804392i \(0.297509\pi\)
\(110\) 1.88520 0.179747
\(111\) 13.3114 1.26347
\(112\) −3.80858 −0.359877
\(113\) −20.2860 −1.90835 −0.954174 0.299252i \(-0.903263\pi\)
−0.954174 + 0.299252i \(0.903263\pi\)
\(114\) −2.00020 −0.187336
\(115\) 1.39817 0.130380
\(116\) 4.19850 0.389821
\(117\) 7.16239 0.662163
\(118\) −1.20110 −0.110571
\(119\) 4.14887 0.380327
\(120\) −0.0697689 −0.00636900
\(121\) 25.3124 2.30112
\(122\) 26.1020 2.36316
\(123\) −5.77558 −0.520766
\(124\) 4.20286 0.377428
\(125\) −1.54294 −0.138005
\(126\) −5.94168 −0.529327
\(127\) −8.89457 −0.789265 −0.394633 0.918839i \(-0.629128\pi\)
−0.394633 + 0.918839i \(0.629128\pi\)
\(128\) 1.47948 0.130769
\(129\) 18.6441 1.64153
\(130\) −0.762820 −0.0669037
\(131\) 14.0327 1.22605 0.613023 0.790065i \(-0.289953\pi\)
0.613023 + 0.790065i \(0.289953\pi\)
\(132\) −30.7107 −2.67302
\(133\) 0.405818 0.0351889
\(134\) 7.97745 0.689146
\(135\) −0.0235817 −0.00202959
\(136\) −0.768076 −0.0658620
\(137\) −9.36185 −0.799837 −0.399918 0.916551i \(-0.630962\pi\)
−0.399918 + 0.916551i \(0.630962\pi\)
\(138\) −44.5566 −3.79291
\(139\) −16.2985 −1.38242 −0.691209 0.722655i \(-0.742922\pi\)
−0.691209 + 0.722655i \(0.742922\pi\)
\(140\) 0.323483 0.0273393
\(141\) 13.0618 1.10000
\(142\) −3.20420 −0.268890
\(143\) −14.6933 −1.22871
\(144\) −11.1874 −0.932285
\(145\) 0.310471 0.0257832
\(146\) 11.9434 0.988445
\(147\) 2.43668 0.200974
\(148\) 11.4259 0.939199
\(149\) 20.4003 1.67126 0.835628 0.549296i \(-0.185104\pi\)
0.835628 + 0.549296i \(0.185104\pi\)
\(150\) 24.5261 2.00255
\(151\) 5.60047 0.455760 0.227880 0.973689i \(-0.426821\pi\)
0.227880 + 0.973689i \(0.426821\pi\)
\(152\) −0.0751286 −0.00609373
\(153\) 12.1870 0.985261
\(154\) 12.1890 0.982221
\(155\) 0.310793 0.0249635
\(156\) 12.4266 0.994925
\(157\) 4.94963 0.395024 0.197512 0.980301i \(-0.436714\pi\)
0.197512 + 0.980301i \(0.436714\pi\)
\(158\) 9.95379 0.791881
\(159\) −6.92586 −0.549257
\(160\) 1.24877 0.0987236
\(161\) 9.04004 0.712455
\(162\) 18.5766 1.45951
\(163\) −16.9609 −1.32848 −0.664239 0.747521i \(-0.731244\pi\)
−0.664239 + 0.747521i \(0.731244\pi\)
\(164\) −4.95746 −0.387113
\(165\) −2.27099 −0.176796
\(166\) 9.26644 0.719216
\(167\) 9.25774 0.716386 0.358193 0.933648i \(-0.383393\pi\)
0.358193 + 0.933648i \(0.383393\pi\)
\(168\) −0.451100 −0.0348031
\(169\) −7.05460 −0.542661
\(170\) −1.29796 −0.0995490
\(171\) 1.19206 0.0911591
\(172\) 16.0032 1.22023
\(173\) 21.1837 1.61057 0.805284 0.592890i \(-0.202013\pi\)
0.805284 + 0.592890i \(0.202013\pi\)
\(174\) −9.89404 −0.750065
\(175\) −4.97608 −0.376156
\(176\) 22.9504 1.72995
\(177\) 1.44690 0.108755
\(178\) −22.0670 −1.65399
\(179\) 23.3684 1.74664 0.873320 0.487147i \(-0.161963\pi\)
0.873320 + 0.487147i \(0.161963\pi\)
\(180\) 0.950208 0.0708243
\(181\) −9.27292 −0.689251 −0.344625 0.938740i \(-0.611994\pi\)
−0.344625 + 0.938740i \(0.611994\pi\)
\(182\) −4.93212 −0.365593
\(183\) −31.4434 −2.32437
\(184\) −1.67357 −0.123377
\(185\) 0.844918 0.0621196
\(186\) −9.90430 −0.726219
\(187\) −25.0010 −1.82825
\(188\) 11.2116 0.817688
\(189\) −0.152471 −0.0110906
\(190\) −0.126959 −0.00921055
\(191\) 7.38023 0.534015 0.267007 0.963695i \(-0.413965\pi\)
0.267007 + 0.963695i \(0.413965\pi\)
\(192\) −21.2349 −1.53250
\(193\) 7.34765 0.528895 0.264448 0.964400i \(-0.414810\pi\)
0.264448 + 0.964400i \(0.414810\pi\)
\(194\) −35.9905 −2.58397
\(195\) 0.918922 0.0658054
\(196\) 2.09152 0.149395
\(197\) 16.6346 1.18517 0.592583 0.805509i \(-0.298108\pi\)
0.592583 + 0.805509i \(0.298108\pi\)
\(198\) 35.8044 2.54451
\(199\) 13.2399 0.938548 0.469274 0.883053i \(-0.344516\pi\)
0.469274 + 0.883053i \(0.344516\pi\)
\(200\) 0.921216 0.0651398
\(201\) −9.60994 −0.677833
\(202\) −24.5351 −1.72629
\(203\) 2.00739 0.140891
\(204\) 21.1442 1.48039
\(205\) −0.366594 −0.0256040
\(206\) −22.6163 −1.57575
\(207\) 26.5545 1.84566
\(208\) −9.28653 −0.643905
\(209\) −2.44545 −0.169155
\(210\) −0.762308 −0.0526042
\(211\) −20.6429 −1.42112 −0.710560 0.703637i \(-0.751558\pi\)
−0.710560 + 0.703637i \(0.751558\pi\)
\(212\) −5.94480 −0.408291
\(213\) 3.85990 0.264476
\(214\) 15.4974 1.05938
\(215\) 1.18340 0.0807073
\(216\) 0.0282268 0.00192059
\(217\) 2.00947 0.136412
\(218\) −25.0925 −1.69948
\(219\) −14.3875 −0.972218
\(220\) −1.94930 −0.131422
\(221\) 10.1163 0.680495
\(222\) −26.9257 −1.80714
\(223\) −10.4998 −0.703119 −0.351560 0.936166i \(-0.614349\pi\)
−0.351560 + 0.936166i \(0.614349\pi\)
\(224\) 8.07406 0.539471
\(225\) −14.6169 −0.974458
\(226\) 41.0336 2.72951
\(227\) 15.9423 1.05813 0.529065 0.848581i \(-0.322543\pi\)
0.529065 + 0.848581i \(0.322543\pi\)
\(228\) 2.06820 0.136970
\(229\) 16.2562 1.07424 0.537121 0.843505i \(-0.319512\pi\)
0.537121 + 0.843505i \(0.319512\pi\)
\(230\) −2.82814 −0.186482
\(231\) −14.6834 −0.966096
\(232\) −0.371626 −0.0243984
\(233\) 22.6309 1.48260 0.741300 0.671174i \(-0.234209\pi\)
0.741300 + 0.671174i \(0.234209\pi\)
\(234\) −14.4877 −0.947092
\(235\) 0.829073 0.0540827
\(236\) 1.24194 0.0808435
\(237\) −11.9907 −0.778881
\(238\) −8.39214 −0.543982
\(239\) 14.6513 0.947714 0.473857 0.880602i \(-0.342861\pi\)
0.473857 + 0.880602i \(0.342861\pi\)
\(240\) −1.43533 −0.0926499
\(241\) 2.96559 0.191030 0.0955152 0.995428i \(-0.469550\pi\)
0.0955152 + 0.995428i \(0.469550\pi\)
\(242\) −51.2006 −3.29130
\(243\) −21.9206 −1.40621
\(244\) −26.9894 −1.72782
\(245\) 0.154664 0.00988111
\(246\) 11.6826 0.744853
\(247\) 0.989514 0.0629613
\(248\) −0.372012 −0.0236228
\(249\) −11.1627 −0.707408
\(250\) 3.12098 0.197388
\(251\) 26.5345 1.67484 0.837420 0.546559i \(-0.184063\pi\)
0.837420 + 0.546559i \(0.184063\pi\)
\(252\) 6.14370 0.387017
\(253\) −54.4751 −3.42482
\(254\) 17.9915 1.12889
\(255\) 1.56357 0.0979147
\(256\) 14.4367 0.902295
\(257\) −28.4472 −1.77449 −0.887244 0.461300i \(-0.847383\pi\)
−0.887244 + 0.461300i \(0.847383\pi\)
\(258\) −37.7125 −2.34788
\(259\) 5.46293 0.339450
\(260\) 0.788755 0.0489165
\(261\) 5.89656 0.364988
\(262\) −28.3848 −1.75362
\(263\) 14.7196 0.907646 0.453823 0.891092i \(-0.350060\pi\)
0.453823 + 0.891092i \(0.350060\pi\)
\(264\) 2.71832 0.167301
\(265\) −0.439606 −0.0270048
\(266\) −0.820869 −0.0503307
\(267\) 26.5828 1.62684
\(268\) −8.24867 −0.503868
\(269\) 7.64083 0.465869 0.232935 0.972492i \(-0.425167\pi\)
0.232935 + 0.972492i \(0.425167\pi\)
\(270\) 0.0477000 0.00290293
\(271\) 21.5785 1.31080 0.655401 0.755281i \(-0.272500\pi\)
0.655401 + 0.755281i \(0.272500\pi\)
\(272\) −15.8013 −0.958095
\(273\) 5.94141 0.359591
\(274\) 18.9367 1.14401
\(275\) 29.9857 1.80821
\(276\) 46.0715 2.77318
\(277\) 18.2872 1.09877 0.549387 0.835568i \(-0.314861\pi\)
0.549387 + 0.835568i \(0.314861\pi\)
\(278\) 32.9678 1.97727
\(279\) 5.90268 0.353384
\(280\) −0.0286327 −0.00171113
\(281\) −13.6766 −0.815877 −0.407939 0.913009i \(-0.633752\pi\)
−0.407939 + 0.913009i \(0.633752\pi\)
\(282\) −26.4208 −1.57333
\(283\) −16.8499 −1.00162 −0.500812 0.865556i \(-0.666965\pi\)
−0.500812 + 0.865556i \(0.666965\pi\)
\(284\) 3.31314 0.196598
\(285\) 0.152939 0.00905934
\(286\) 29.7208 1.75743
\(287\) −2.37026 −0.139912
\(288\) 23.7170 1.39754
\(289\) 0.213148 0.0125381
\(290\) −0.628005 −0.0368777
\(291\) 43.3555 2.54155
\(292\) −12.3495 −0.722699
\(293\) 16.8405 0.983833 0.491917 0.870642i \(-0.336296\pi\)
0.491917 + 0.870642i \(0.336296\pi\)
\(294\) −4.92881 −0.287454
\(295\) 0.0918390 0.00534707
\(296\) −1.01135 −0.0587833
\(297\) 0.918786 0.0533134
\(298\) −41.2647 −2.39040
\(299\) 22.0425 1.27475
\(300\) −25.3600 −1.46416
\(301\) 7.65144 0.441022
\(302\) −11.3284 −0.651874
\(303\) 29.5560 1.69795
\(304\) −1.54559 −0.0886456
\(305\) −1.99581 −0.114280
\(306\) −24.6513 −1.40922
\(307\) 0.887521 0.0506535 0.0253267 0.999679i \(-0.491937\pi\)
0.0253267 + 0.999679i \(0.491937\pi\)
\(308\) −12.6035 −0.718149
\(309\) 27.2445 1.54988
\(310\) −0.628657 −0.0357053
\(311\) −15.6147 −0.885431 −0.442715 0.896662i \(-0.645985\pi\)
−0.442715 + 0.896662i \(0.645985\pi\)
\(312\) −1.09993 −0.0622711
\(313\) −18.0098 −1.01797 −0.508987 0.860774i \(-0.669980\pi\)
−0.508987 + 0.860774i \(0.669980\pi\)
\(314\) −10.0119 −0.565003
\(315\) 0.454314 0.0255977
\(316\) −10.2922 −0.578982
\(317\) 6.03074 0.338720 0.169360 0.985554i \(-0.445830\pi\)
0.169360 + 0.985554i \(0.445830\pi\)
\(318\) 14.0093 0.785603
\(319\) −12.0965 −0.677273
\(320\) −1.34784 −0.0753467
\(321\) −18.6688 −1.04199
\(322\) −18.2858 −1.01903
\(323\) 1.68369 0.0936828
\(324\) −19.2081 −1.06712
\(325\) −12.1333 −0.673033
\(326\) 34.3076 1.90012
\(327\) 30.2274 1.67158
\(328\) 0.438804 0.0242289
\(329\) 5.36048 0.295533
\(330\) 4.59365 0.252872
\(331\) 12.5649 0.690628 0.345314 0.938487i \(-0.387772\pi\)
0.345314 + 0.938487i \(0.387772\pi\)
\(332\) −9.58150 −0.525853
\(333\) 16.0470 0.879368
\(334\) −18.7261 −1.02465
\(335\) −0.609972 −0.0333263
\(336\) −9.28030 −0.506282
\(337\) −3.57605 −0.194800 −0.0974000 0.995245i \(-0.531053\pi\)
−0.0974000 + 0.995245i \(0.531053\pi\)
\(338\) 14.2697 0.776169
\(339\) −49.4306 −2.68470
\(340\) 1.34209 0.0727850
\(341\) −12.1090 −0.655741
\(342\) −2.41124 −0.130385
\(343\) 1.00000 0.0539949
\(344\) −1.41650 −0.0763727
\(345\) 3.40689 0.183421
\(346\) −42.8494 −2.30360
\(347\) 8.78586 0.471650 0.235825 0.971796i \(-0.424221\pi\)
0.235825 + 0.971796i \(0.424221\pi\)
\(348\) 10.2304 0.548408
\(349\) −22.3650 −1.19717 −0.598587 0.801058i \(-0.704271\pi\)
−0.598587 + 0.801058i \(0.704271\pi\)
\(350\) 10.0654 0.538017
\(351\) −0.371773 −0.0198438
\(352\) −48.6541 −2.59327
\(353\) −24.4439 −1.30102 −0.650509 0.759498i \(-0.725444\pi\)
−0.650509 + 0.759498i \(0.725444\pi\)
\(354\) −2.92671 −0.155553
\(355\) 0.245000 0.0130032
\(356\) 22.8173 1.20931
\(357\) 10.1095 0.535051
\(358\) −47.2686 −2.49822
\(359\) −11.3843 −0.600839 −0.300419 0.953807i \(-0.597127\pi\)
−0.300419 + 0.953807i \(0.597127\pi\)
\(360\) −0.0841066 −0.00443280
\(361\) −18.8353 −0.991332
\(362\) 18.7568 0.985836
\(363\) 61.6782 3.23727
\(364\) 5.09980 0.267302
\(365\) −0.913219 −0.0478001
\(366\) 63.6022 3.32454
\(367\) 29.5178 1.54082 0.770409 0.637550i \(-0.220052\pi\)
0.770409 + 0.637550i \(0.220052\pi\)
\(368\) −34.4297 −1.79477
\(369\) −6.96247 −0.362452
\(370\) −1.70906 −0.0888498
\(371\) −2.84233 −0.147567
\(372\) 10.2410 0.530973
\(373\) 13.4156 0.694635 0.347317 0.937748i \(-0.387093\pi\)
0.347317 + 0.937748i \(0.387093\pi\)
\(374\) 50.5708 2.61495
\(375\) −3.75965 −0.194148
\(376\) −0.992380 −0.0511781
\(377\) 4.89466 0.252088
\(378\) 0.308411 0.0158629
\(379\) −0.774457 −0.0397812 −0.0198906 0.999802i \(-0.506332\pi\)
−0.0198906 + 0.999802i \(0.506332\pi\)
\(380\) 0.131275 0.00673427
\(381\) −21.6732 −1.11035
\(382\) −14.9284 −0.763802
\(383\) 26.6853 1.36356 0.681778 0.731559i \(-0.261207\pi\)
0.681778 + 0.731559i \(0.261207\pi\)
\(384\) 3.60502 0.183968
\(385\) −0.932000 −0.0474991
\(386\) −14.8625 −0.756479
\(387\) 22.4756 1.14250
\(388\) 37.2142 1.88926
\(389\) −28.9357 −1.46710 −0.733549 0.679636i \(-0.762138\pi\)
−0.733549 + 0.679636i \(0.762138\pi\)
\(390\) −1.85875 −0.0941215
\(391\) 37.5060 1.89676
\(392\) −0.185129 −0.00935042
\(393\) 34.1934 1.72483
\(394\) −33.6477 −1.69514
\(395\) −0.761088 −0.0382945
\(396\) −37.0218 −1.86041
\(397\) 12.8159 0.643213 0.321606 0.946873i \(-0.395777\pi\)
0.321606 + 0.946873i \(0.395777\pi\)
\(398\) −26.7809 −1.34241
\(399\) 0.988850 0.0495044
\(400\) 18.9518 0.947589
\(401\) 37.0403 1.84970 0.924852 0.380327i \(-0.124189\pi\)
0.924852 + 0.380327i \(0.124189\pi\)
\(402\) 19.4385 0.969505
\(403\) 4.89974 0.244073
\(404\) 25.3693 1.26217
\(405\) −1.42040 −0.0705804
\(406\) −4.06045 −0.201517
\(407\) −32.9195 −1.63176
\(408\) −1.87156 −0.0926559
\(409\) −15.3728 −0.760135 −0.380067 0.924959i \(-0.624099\pi\)
−0.380067 + 0.924959i \(0.624099\pi\)
\(410\) 0.741528 0.0366215
\(411\) −22.8119 −1.12523
\(412\) 23.3853 1.15211
\(413\) 0.593797 0.0292189
\(414\) −53.7131 −2.63985
\(415\) −0.708532 −0.0347805
\(416\) 19.6871 0.965242
\(417\) −39.7142 −1.94481
\(418\) 4.94653 0.241943
\(419\) −26.2244 −1.28115 −0.640573 0.767897i \(-0.721303\pi\)
−0.640573 + 0.767897i \(0.721303\pi\)
\(420\) 0.788226 0.0384615
\(421\) 22.2189 1.08288 0.541441 0.840739i \(-0.317879\pi\)
0.541441 + 0.840739i \(0.317879\pi\)
\(422\) 41.7556 2.03263
\(423\) 15.7460 0.765598
\(424\) 0.526198 0.0255544
\(425\) −20.6451 −1.00144
\(426\) −7.80761 −0.378280
\(427\) −12.9042 −0.624478
\(428\) −16.0243 −0.774565
\(429\) −35.8028 −1.72858
\(430\) −2.39373 −0.115436
\(431\) −3.31222 −0.159544 −0.0797719 0.996813i \(-0.525419\pi\)
−0.0797719 + 0.996813i \(0.525419\pi\)
\(432\) 0.580698 0.0279388
\(433\) −16.9985 −0.816898 −0.408449 0.912781i \(-0.633930\pi\)
−0.408449 + 0.912781i \(0.633930\pi\)
\(434\) −4.06467 −0.195110
\(435\) 0.756519 0.0362723
\(436\) 25.9457 1.24257
\(437\) 3.66861 0.175493
\(438\) 29.1023 1.39056
\(439\) −27.3353 −1.30464 −0.652322 0.757942i \(-0.726205\pi\)
−0.652322 + 0.757942i \(0.726205\pi\)
\(440\) 0.172540 0.00822553
\(441\) 2.93743 0.139877
\(442\) −20.4627 −0.973312
\(443\) −5.23181 −0.248571 −0.124285 0.992247i \(-0.539664\pi\)
−0.124285 + 0.992247i \(0.539664\pi\)
\(444\) 27.8412 1.32128
\(445\) 1.68729 0.0799853
\(446\) 21.2385 1.00567
\(447\) 49.7090 2.35116
\(448\) −8.71467 −0.411729
\(449\) −13.5090 −0.637528 −0.318764 0.947834i \(-0.603268\pi\)
−0.318764 + 0.947834i \(0.603268\pi\)
\(450\) 29.5663 1.39377
\(451\) 14.2831 0.672567
\(452\) −42.4287 −1.99568
\(453\) 13.6466 0.641172
\(454\) −32.2474 −1.51345
\(455\) 0.377120 0.0176797
\(456\) −0.183065 −0.00857279
\(457\) 19.5468 0.914359 0.457179 0.889374i \(-0.348860\pi\)
0.457179 + 0.889374i \(0.348860\pi\)
\(458\) −32.8823 −1.53649
\(459\) −0.632583 −0.0295264
\(460\) 2.92430 0.136346
\(461\) −28.5166 −1.32815 −0.664076 0.747665i \(-0.731175\pi\)
−0.664076 + 0.747665i \(0.731175\pi\)
\(462\) 29.7009 1.38181
\(463\) 34.2827 1.59325 0.796626 0.604473i \(-0.206616\pi\)
0.796626 + 0.604473i \(0.206616\pi\)
\(464\) −7.64530 −0.354924
\(465\) 0.757304 0.0351191
\(466\) −45.7767 −2.12057
\(467\) 6.87513 0.318143 0.159072 0.987267i \(-0.449150\pi\)
0.159072 + 0.987267i \(0.449150\pi\)
\(468\) 14.9803 0.692465
\(469\) −3.94386 −0.182110
\(470\) −1.67701 −0.0773546
\(471\) 12.0607 0.555727
\(472\) −0.109929 −0.00505989
\(473\) −46.1074 −2.12002
\(474\) 24.2542 1.11403
\(475\) −2.01938 −0.0926556
\(476\) 8.67746 0.397731
\(477\) −8.34914 −0.382281
\(478\) −29.6359 −1.35552
\(479\) −20.6377 −0.942962 −0.471481 0.881876i \(-0.656280\pi\)
−0.471481 + 0.881876i \(0.656280\pi\)
\(480\) 3.04285 0.138886
\(481\) 13.3204 0.607357
\(482\) −5.99865 −0.273231
\(483\) 22.0277 1.00230
\(484\) 52.9414 2.40643
\(485\) 2.75191 0.124958
\(486\) 44.3399 2.01130
\(487\) −13.8911 −0.629467 −0.314733 0.949180i \(-0.601915\pi\)
−0.314733 + 0.949180i \(0.601915\pi\)
\(488\) 2.38894 0.108142
\(489\) −41.3283 −1.86893
\(490\) −0.312846 −0.0141330
\(491\) 6.35905 0.286980 0.143490 0.989652i \(-0.454167\pi\)
0.143490 + 0.989652i \(0.454167\pi\)
\(492\) −12.0798 −0.544598
\(493\) 8.32841 0.375093
\(494\) −2.00154 −0.0900536
\(495\) −2.73768 −0.123050
\(496\) −7.65324 −0.343640
\(497\) 1.58408 0.0710556
\(498\) 22.5794 1.01181
\(499\) −0.828797 −0.0371020 −0.0185510 0.999828i \(-0.505905\pi\)
−0.0185510 + 0.999828i \(0.505905\pi\)
\(500\) −3.22709 −0.144320
\(501\) 22.5582 1.00783
\(502\) −53.6726 −2.39553
\(503\) −31.9044 −1.42255 −0.711273 0.702916i \(-0.751881\pi\)
−0.711273 + 0.702916i \(0.751881\pi\)
\(504\) −0.543802 −0.0242229
\(505\) 1.87601 0.0834813
\(506\) 110.189 4.89852
\(507\) −17.1898 −0.763427
\(508\) −18.6032 −0.825383
\(509\) 34.8356 1.54406 0.772030 0.635586i \(-0.219241\pi\)
0.772030 + 0.635586i \(0.219241\pi\)
\(510\) −3.16272 −0.140048
\(511\) −5.90454 −0.261202
\(512\) −32.1608 −1.42132
\(513\) −0.0618755 −0.00273187
\(514\) 57.5416 2.53805
\(515\) 1.72929 0.0762017
\(516\) 38.9947 1.71664
\(517\) −32.3021 −1.42065
\(518\) −11.0502 −0.485516
\(519\) 51.6180 2.26578
\(520\) −0.0698158 −0.00306162
\(521\) −29.6274 −1.29800 −0.648999 0.760789i \(-0.724812\pi\)
−0.648999 + 0.760789i \(0.724812\pi\)
\(522\) −11.9273 −0.522043
\(523\) 8.55677 0.374161 0.187081 0.982345i \(-0.440097\pi\)
0.187081 + 0.982345i \(0.440097\pi\)
\(524\) 29.3498 1.28215
\(525\) −12.1251 −0.529184
\(526\) −29.7740 −1.29821
\(527\) 8.33705 0.363168
\(528\) 55.9228 2.43373
\(529\) 58.7223 2.55315
\(530\) 0.889213 0.0386250
\(531\) 1.74424 0.0756934
\(532\) 0.848778 0.0367992
\(533\) −5.77946 −0.250336
\(534\) −53.7704 −2.32687
\(535\) −1.18497 −0.0512305
\(536\) 0.730122 0.0315365
\(537\) 56.9415 2.45721
\(538\) −15.4555 −0.666334
\(539\) −6.02597 −0.259557
\(540\) −0.0493218 −0.00212247
\(541\) −40.2943 −1.73239 −0.866194 0.499708i \(-0.833441\pi\)
−0.866194 + 0.499708i \(0.833441\pi\)
\(542\) −43.6480 −1.87484
\(543\) −22.5952 −0.969652
\(544\) 33.4983 1.43623
\(545\) 1.91863 0.0821850
\(546\) −12.0180 −0.514323
\(547\) −33.3517 −1.42601 −0.713007 0.701157i \(-0.752667\pi\)
−0.713007 + 0.701157i \(0.752667\pi\)
\(548\) −19.5805 −0.836439
\(549\) −37.9051 −1.61775
\(550\) −60.6537 −2.58628
\(551\) 0.814635 0.0347046
\(552\) −4.07797 −0.173570
\(553\) −4.92092 −0.209259
\(554\) −36.9905 −1.57158
\(555\) 2.05880 0.0873911
\(556\) −34.0886 −1.44568
\(557\) −6.58646 −0.279077 −0.139539 0.990217i \(-0.544562\pi\)
−0.139539 + 0.990217i \(0.544562\pi\)
\(558\) −11.9397 −0.505446
\(559\) 18.6567 0.789093
\(560\) −0.589049 −0.0248919
\(561\) −60.9195 −2.57202
\(562\) 27.6644 1.16695
\(563\) −3.75212 −0.158133 −0.0790666 0.996869i \(-0.525194\pi\)
−0.0790666 + 0.996869i \(0.525194\pi\)
\(564\) 27.3191 1.15034
\(565\) −3.13751 −0.131996
\(566\) 34.0832 1.43262
\(567\) −9.18380 −0.385684
\(568\) −0.293259 −0.0123049
\(569\) 46.5289 1.95060 0.975298 0.220895i \(-0.0708979\pi\)
0.975298 + 0.220895i \(0.0708979\pi\)
\(570\) −0.309358 −0.0129576
\(571\) 24.2171 1.01346 0.506728 0.862106i \(-0.330855\pi\)
0.506728 + 0.862106i \(0.330855\pi\)
\(572\) −30.7313 −1.28494
\(573\) 17.9833 0.751262
\(574\) 4.79445 0.200117
\(575\) −44.9840 −1.87596
\(576\) −25.5987 −1.06661
\(577\) −2.26146 −0.0941456 −0.0470728 0.998891i \(-0.514989\pi\)
−0.0470728 + 0.998891i \(0.514989\pi\)
\(578\) −0.431146 −0.0179333
\(579\) 17.9039 0.744060
\(580\) 0.649357 0.0269631
\(581\) −4.58111 −0.190056
\(582\) −87.6975 −3.63518
\(583\) 17.1278 0.709362
\(584\) 1.09310 0.0452329
\(585\) 1.10776 0.0458003
\(586\) −34.0642 −1.40718
\(587\) −16.9579 −0.699927 −0.349963 0.936763i \(-0.613806\pi\)
−0.349963 + 0.936763i \(0.613806\pi\)
\(588\) 5.09638 0.210171
\(589\) 0.815480 0.0336013
\(590\) −0.185767 −0.00764792
\(591\) 40.5333 1.66732
\(592\) −20.8060 −0.855121
\(593\) −41.4356 −1.70155 −0.850777 0.525526i \(-0.823868\pi\)
−0.850777 + 0.525526i \(0.823868\pi\)
\(594\) −1.85848 −0.0762542
\(595\) 0.641681 0.0263063
\(596\) 42.6677 1.74774
\(597\) 32.2613 1.32037
\(598\) −44.5865 −1.82328
\(599\) 18.8829 0.771534 0.385767 0.922596i \(-0.373937\pi\)
0.385767 + 0.922596i \(0.373937\pi\)
\(600\) 2.24471 0.0916399
\(601\) 43.3056 1.76647 0.883235 0.468930i \(-0.155360\pi\)
0.883235 + 0.468930i \(0.155360\pi\)
\(602\) −15.4770 −0.630794
\(603\) −11.5848 −0.471769
\(604\) 11.7135 0.476616
\(605\) 3.91491 0.159164
\(606\) −59.7844 −2.42857
\(607\) −19.9864 −0.811222 −0.405611 0.914046i \(-0.632941\pi\)
−0.405611 + 0.914046i \(0.632941\pi\)
\(608\) 3.27660 0.132884
\(609\) 4.89138 0.198209
\(610\) 4.03703 0.163455
\(611\) 13.0706 0.528779
\(612\) 25.4894 1.03035
\(613\) −25.8536 −1.04422 −0.522108 0.852880i \(-0.674854\pi\)
−0.522108 + 0.852880i \(0.674854\pi\)
\(614\) −1.79523 −0.0724497
\(615\) −0.893273 −0.0360203
\(616\) 1.11558 0.0449481
\(617\) 35.8417 1.44293 0.721467 0.692449i \(-0.243468\pi\)
0.721467 + 0.692449i \(0.243468\pi\)
\(618\) −55.1088 −2.21680
\(619\) −22.1690 −0.891047 −0.445523 0.895270i \(-0.646982\pi\)
−0.445523 + 0.895270i \(0.646982\pi\)
\(620\) 0.650031 0.0261059
\(621\) −1.37834 −0.0553110
\(622\) 31.5847 1.26643
\(623\) 10.9094 0.437076
\(624\) −22.6283 −0.905858
\(625\) 24.6418 0.985670
\(626\) 36.4294 1.45601
\(627\) −5.95878 −0.237971
\(628\) 10.3523 0.413101
\(629\) 22.6650 0.903713
\(630\) −0.918964 −0.0366124
\(631\) 9.78444 0.389513 0.194756 0.980852i \(-0.437608\pi\)
0.194756 + 0.980852i \(0.437608\pi\)
\(632\) 0.911004 0.0362378
\(633\) −50.3003 −1.99926
\(634\) −12.1987 −0.484472
\(635\) −1.37567 −0.0545917
\(636\) −14.4856 −0.574392
\(637\) 2.43832 0.0966098
\(638\) 24.4682 0.968705
\(639\) 4.65311 0.184074
\(640\) 0.228822 0.00904498
\(641\) −22.7471 −0.898458 −0.449229 0.893417i \(-0.648301\pi\)
−0.449229 + 0.893417i \(0.648301\pi\)
\(642\) 37.7623 1.49036
\(643\) −18.3657 −0.724272 −0.362136 0.932125i \(-0.617952\pi\)
−0.362136 + 0.932125i \(0.617952\pi\)
\(644\) 18.9075 0.745058
\(645\) 2.88358 0.113541
\(646\) −3.40568 −0.133995
\(647\) 4.05191 0.159297 0.0796486 0.996823i \(-0.474620\pi\)
0.0796486 + 0.996823i \(0.474620\pi\)
\(648\) 1.70019 0.0667896
\(649\) −3.57821 −0.140457
\(650\) 24.5426 0.962640
\(651\) 4.89645 0.191907
\(652\) −35.4740 −1.38927
\(653\) −12.8958 −0.504652 −0.252326 0.967642i \(-0.581195\pi\)
−0.252326 + 0.967642i \(0.581195\pi\)
\(654\) −61.1426 −2.39086
\(655\) 2.17036 0.0848029
\(656\) 9.02733 0.352458
\(657\) −17.3442 −0.676660
\(658\) −10.8429 −0.422701
\(659\) −6.63878 −0.258610 −0.129305 0.991605i \(-0.541275\pi\)
−0.129305 + 0.991605i \(0.541275\pi\)
\(660\) −4.74983 −0.184887
\(661\) 19.2318 0.748028 0.374014 0.927423i \(-0.377981\pi\)
0.374014 + 0.927423i \(0.377981\pi\)
\(662\) −25.4156 −0.987806
\(663\) 24.6502 0.957333
\(664\) 0.848095 0.0329125
\(665\) 0.0627653 0.00243394
\(666\) −32.4590 −1.25776
\(667\) 18.1469 0.702651
\(668\) 19.3628 0.749169
\(669\) −25.5847 −0.989162
\(670\) 1.23382 0.0476667
\(671\) 77.7603 3.00190
\(672\) 19.6739 0.758938
\(673\) −36.9412 −1.42398 −0.711989 0.702191i \(-0.752205\pi\)
−0.711989 + 0.702191i \(0.752205\pi\)
\(674\) 7.23347 0.278623
\(675\) 0.758708 0.0292027
\(676\) −14.7549 −0.567494
\(677\) 36.1584 1.38968 0.694840 0.719164i \(-0.255475\pi\)
0.694840 + 0.719164i \(0.255475\pi\)
\(678\) 99.9859 3.83993
\(679\) 17.7928 0.682827
\(680\) −0.118794 −0.00455553
\(681\) 38.8464 1.48860
\(682\) 24.4936 0.937907
\(683\) 14.8851 0.569562 0.284781 0.958593i \(-0.408079\pi\)
0.284781 + 0.958593i \(0.408079\pi\)
\(684\) 2.49322 0.0953307
\(685\) −1.44794 −0.0553229
\(686\) −2.02275 −0.0772290
\(687\) 39.6113 1.51127
\(688\) −29.1411 −1.11099
\(689\) −6.93051 −0.264032
\(690\) −6.89129 −0.262347
\(691\) 18.7366 0.712775 0.356388 0.934338i \(-0.384008\pi\)
0.356388 + 0.934338i \(0.384008\pi\)
\(692\) 44.3062 1.68427
\(693\) −17.7009 −0.672400
\(694\) −17.7716 −0.674601
\(695\) −2.52078 −0.0956188
\(696\) −0.905535 −0.0343242
\(697\) −9.83392 −0.372486
\(698\) 45.2389 1.71232
\(699\) 55.1444 2.08575
\(700\) −10.4076 −0.393370
\(701\) 7.47892 0.282475 0.141238 0.989976i \(-0.454892\pi\)
0.141238 + 0.989976i \(0.454892\pi\)
\(702\) 0.752005 0.0283826
\(703\) 2.21696 0.0836141
\(704\) 52.5144 1.97921
\(705\) 2.02019 0.0760847
\(706\) 49.4440 1.86085
\(707\) 12.1296 0.456180
\(708\) 3.02622 0.113732
\(709\) 35.7612 1.34304 0.671519 0.740987i \(-0.265642\pi\)
0.671519 + 0.740987i \(0.265642\pi\)
\(710\) −0.495573 −0.0185985
\(711\) −14.4548 −0.542099
\(712\) −2.01965 −0.0756894
\(713\) 18.1657 0.680312
\(714\) −20.4490 −0.765284
\(715\) −2.27251 −0.0849872
\(716\) 48.8756 1.82657
\(717\) 35.7006 1.33326
\(718\) 23.0276 0.859381
\(719\) −12.3968 −0.462321 −0.231160 0.972916i \(-0.574252\pi\)
−0.231160 + 0.972916i \(0.574252\pi\)
\(720\) −1.73029 −0.0644840
\(721\) 11.1810 0.416401
\(722\) 38.0992 1.41790
\(723\) 7.22620 0.268745
\(724\) −19.3945 −0.720792
\(725\) −9.98894 −0.370980
\(726\) −124.760 −4.63027
\(727\) 7.65166 0.283784 0.141892 0.989882i \(-0.454681\pi\)
0.141892 + 0.989882i \(0.454681\pi\)
\(728\) −0.451403 −0.0167301
\(729\) −25.8622 −0.957859
\(730\) 1.84722 0.0683685
\(731\) 31.7449 1.17413
\(732\) −65.7647 −2.43073
\(733\) 14.5095 0.535921 0.267961 0.963430i \(-0.413650\pi\)
0.267961 + 0.963430i \(0.413650\pi\)
\(734\) −59.7072 −2.20383
\(735\) 0.376867 0.0139009
\(736\) 72.9898 2.69044
\(737\) 23.7656 0.875417
\(738\) 14.0834 0.518415
\(739\) 11.0266 0.405621 0.202811 0.979218i \(-0.434992\pi\)
0.202811 + 0.979218i \(0.434992\pi\)
\(740\) 1.76717 0.0649623
\(741\) 2.41113 0.0885752
\(742\) 5.74933 0.211065
\(743\) 33.6029 1.23277 0.616386 0.787444i \(-0.288596\pi\)
0.616386 + 0.787444i \(0.288596\pi\)
\(744\) −0.906474 −0.0332330
\(745\) 3.15519 0.115597
\(746\) −27.1365 −0.993537
\(747\) −13.4567 −0.492354
\(748\) −52.2902 −1.91192
\(749\) −7.66156 −0.279947
\(750\) 7.60484 0.277690
\(751\) 23.8259 0.869418 0.434709 0.900571i \(-0.356851\pi\)
0.434709 + 0.900571i \(0.356851\pi\)
\(752\) −20.4158 −0.744488
\(753\) 64.6561 2.35620
\(754\) −9.90068 −0.360562
\(755\) 0.866190 0.0315239
\(756\) −0.318897 −0.0115982
\(757\) −40.3615 −1.46696 −0.733482 0.679709i \(-0.762106\pi\)
−0.733482 + 0.679709i \(0.762106\pi\)
\(758\) 1.56653 0.0568991
\(759\) −132.738 −4.81810
\(760\) −0.0116197 −0.000421490 0
\(761\) 41.7849 1.51470 0.757350 0.653009i \(-0.226494\pi\)
0.757350 + 0.653009i \(0.226494\pi\)
\(762\) 43.8396 1.58814
\(763\) 12.4052 0.449097
\(764\) 15.4359 0.558452
\(765\) 1.88489 0.0681483
\(766\) −53.9778 −1.95030
\(767\) 1.44787 0.0522795
\(768\) 35.1777 1.26937
\(769\) −35.3192 −1.27364 −0.636822 0.771011i \(-0.719751\pi\)
−0.636822 + 0.771011i \(0.719751\pi\)
\(770\) 1.88520 0.0679381
\(771\) −69.3168 −2.49639
\(772\) 15.3678 0.553098
\(773\) −13.2622 −0.477008 −0.238504 0.971141i \(-0.576657\pi\)
−0.238504 + 0.971141i \(0.576657\pi\)
\(774\) −45.4625 −1.63411
\(775\) −9.99930 −0.359185
\(776\) −3.29397 −0.118247
\(777\) 13.3114 0.477545
\(778\) 58.5298 2.09839
\(779\) −0.961895 −0.0344635
\(780\) 1.92195 0.0688167
\(781\) −9.54562 −0.341569
\(782\) −75.8653 −2.71294
\(783\) −0.306069 −0.0109380
\(784\) −3.80858 −0.136021
\(785\) 0.765529 0.0273229
\(786\) −69.1647 −2.46702
\(787\) 21.2952 0.759093 0.379547 0.925173i \(-0.376080\pi\)
0.379547 + 0.925173i \(0.376080\pi\)
\(788\) 34.7917 1.23940
\(789\) 35.8669 1.27690
\(790\) 1.53949 0.0547727
\(791\) −20.2860 −0.721288
\(792\) 3.27694 0.116441
\(793\) −31.4645 −1.11734
\(794\) −25.9234 −0.919988
\(795\) −1.07118 −0.0379909
\(796\) 27.6915 0.981498
\(797\) 17.5116 0.620291 0.310145 0.950689i \(-0.399622\pi\)
0.310145 + 0.950689i \(0.399622\pi\)
\(798\) −2.00020 −0.0708062
\(799\) 22.2400 0.786793
\(800\) −40.1772 −1.42048
\(801\) 32.0456 1.13228
\(802\) −74.9233 −2.64563
\(803\) 35.5806 1.25561
\(804\) −20.0994 −0.708851
\(805\) 1.39817 0.0492789
\(806\) −9.91096 −0.349099
\(807\) 18.6183 0.655394
\(808\) −2.24554 −0.0789977
\(809\) −14.1499 −0.497483 −0.248741 0.968570i \(-0.580017\pi\)
−0.248741 + 0.968570i \(0.580017\pi\)
\(810\) 2.87312 0.100951
\(811\) −3.56196 −0.125077 −0.0625387 0.998043i \(-0.519920\pi\)
−0.0625387 + 0.998043i \(0.519920\pi\)
\(812\) 4.19850 0.147339
\(813\) 52.5800 1.84406
\(814\) 66.5879 2.33391
\(815\) −2.62323 −0.0918878
\(816\) −38.5028 −1.34787
\(817\) 3.10509 0.108633
\(818\) 31.0953 1.08722
\(819\) 7.16239 0.250274
\(820\) −0.766740 −0.0267757
\(821\) −13.9282 −0.486099 −0.243050 0.970014i \(-0.578148\pi\)
−0.243050 + 0.970014i \(0.578148\pi\)
\(822\) 46.1427 1.60941
\(823\) −1.17949 −0.0411146 −0.0205573 0.999789i \(-0.506544\pi\)
−0.0205573 + 0.999789i \(0.506544\pi\)
\(824\) −2.06992 −0.0721091
\(825\) 73.0657 2.54382
\(826\) −1.20110 −0.0417918
\(827\) 27.9784 0.972905 0.486453 0.873707i \(-0.338291\pi\)
0.486453 + 0.873707i \(0.338291\pi\)
\(828\) 55.5393 1.93012
\(829\) 39.5668 1.37421 0.687106 0.726557i \(-0.258881\pi\)
0.687106 + 0.726557i \(0.258881\pi\)
\(830\) 1.43318 0.0497465
\(831\) 44.5602 1.54578
\(832\) −21.2491 −0.736682
\(833\) 4.14887 0.143750
\(834\) 80.3320 2.78167
\(835\) 1.43184 0.0495508
\(836\) −5.11471 −0.176896
\(837\) −0.306386 −0.0105903
\(838\) 53.0455 1.83243
\(839\) 34.1221 1.17803 0.589013 0.808123i \(-0.299517\pi\)
0.589013 + 0.808123i \(0.299517\pi\)
\(840\) −0.0697689 −0.00240726
\(841\) −24.9704 −0.861048
\(842\) −44.9433 −1.54885
\(843\) −33.3255 −1.14779
\(844\) −43.1752 −1.48615
\(845\) −1.09109 −0.0375347
\(846\) −31.8503 −1.09504
\(847\) 25.3124 0.869743
\(848\) 10.8252 0.371740
\(849\) −41.0580 −1.40911
\(850\) 41.7599 1.43235
\(851\) 49.3851 1.69290
\(852\) 8.07307 0.276579
\(853\) −37.0724 −1.26934 −0.634668 0.772785i \(-0.718863\pi\)
−0.634668 + 0.772785i \(0.718863\pi\)
\(854\) 26.1020 0.893191
\(855\) 0.184369 0.00630527
\(856\) 1.41838 0.0484791
\(857\) −16.7742 −0.572997 −0.286498 0.958081i \(-0.592491\pi\)
−0.286498 + 0.958081i \(0.592491\pi\)
\(858\) 72.4202 2.47238
\(859\) −1.00000 −0.0341196
\(860\) 2.47511 0.0844006
\(861\) −5.77558 −0.196831
\(862\) 6.69979 0.228196
\(863\) 18.8428 0.641416 0.320708 0.947178i \(-0.396079\pi\)
0.320708 + 0.947178i \(0.396079\pi\)
\(864\) −1.23106 −0.0418815
\(865\) 3.27635 0.111399
\(866\) 34.3838 1.16841
\(867\) 0.519375 0.0176389
\(868\) 4.20286 0.142654
\(869\) 29.6533 1.00592
\(870\) −1.53025 −0.0518803
\(871\) −9.61639 −0.325839
\(872\) −2.29655 −0.0777710
\(873\) 52.2652 1.76891
\(874\) −7.42069 −0.251008
\(875\) −1.54294 −0.0521608
\(876\) −30.0918 −1.01671
\(877\) 33.7402 1.13933 0.569664 0.821878i \(-0.307074\pi\)
0.569664 + 0.821878i \(0.307074\pi\)
\(878\) 55.2926 1.86603
\(879\) 41.0350 1.38408
\(880\) 3.54959 0.119657
\(881\) 41.3175 1.39202 0.696012 0.718030i \(-0.254956\pi\)
0.696012 + 0.718030i \(0.254956\pi\)
\(882\) −5.94168 −0.200067
\(883\) 38.2527 1.28730 0.643652 0.765318i \(-0.277418\pi\)
0.643652 + 0.765318i \(0.277418\pi\)
\(884\) 21.1584 0.711635
\(885\) 0.223783 0.00752237
\(886\) 10.5827 0.355531
\(887\) −5.41313 −0.181755 −0.0908776 0.995862i \(-0.528967\pi\)
−0.0908776 + 0.995862i \(0.528967\pi\)
\(888\) −2.46433 −0.0826975
\(889\) −8.89457 −0.298314
\(890\) −3.41297 −0.114403
\(891\) 55.3414 1.85401
\(892\) −21.9606 −0.735295
\(893\) 2.17538 0.0727963
\(894\) −100.549 −3.36286
\(895\) 3.61425 0.120811
\(896\) 1.47948 0.0494260
\(897\) 53.7106 1.79335
\(898\) 27.3253 0.911858
\(899\) 4.03380 0.134535
\(900\) −30.5715 −1.01905
\(901\) −11.7925 −0.392864
\(902\) −28.8912 −0.961973
\(903\) 18.6441 0.620438
\(904\) 3.75553 0.124907
\(905\) −1.43419 −0.0476739
\(906\) −27.6036 −0.917069
\(907\) −40.2489 −1.33644 −0.668221 0.743963i \(-0.732944\pi\)
−0.668221 + 0.743963i \(0.732944\pi\)
\(908\) 33.3438 1.10655
\(909\) 35.6298 1.18176
\(910\) −0.762820 −0.0252872
\(911\) 35.5958 1.17934 0.589670 0.807644i \(-0.299258\pi\)
0.589670 + 0.807644i \(0.299258\pi\)
\(912\) −3.76611 −0.124708
\(913\) 27.6056 0.913613
\(914\) −39.5382 −1.30781
\(915\) −4.86316 −0.160771
\(916\) 34.0003 1.12340
\(917\) 14.0327 0.463402
\(918\) 1.27956 0.0422317
\(919\) 22.1713 0.731365 0.365682 0.930740i \(-0.380836\pi\)
0.365682 + 0.930740i \(0.380836\pi\)
\(920\) −0.258841 −0.00853374
\(921\) 2.16261 0.0712603
\(922\) 57.6821 1.89966
\(923\) 3.86249 0.127135
\(924\) −30.7107 −1.01031
\(925\) −27.1840 −0.893804
\(926\) −69.3453 −2.27883
\(927\) 32.8433 1.07871
\(928\) 16.2078 0.532047
\(929\) 28.5714 0.937399 0.468699 0.883358i \(-0.344723\pi\)
0.468699 + 0.883358i \(0.344723\pi\)
\(930\) −1.53184 −0.0502309
\(931\) 0.405818 0.0133001
\(932\) 47.3331 1.55045
\(933\) −38.0482 −1.24564
\(934\) −13.9067 −0.455040
\(935\) −3.86675 −0.126456
\(936\) −1.32596 −0.0433405
\(937\) −58.9923 −1.92719 −0.963596 0.267361i \(-0.913848\pi\)
−0.963596 + 0.267361i \(0.913848\pi\)
\(938\) 7.97745 0.260473
\(939\) −43.8842 −1.43211
\(940\) 1.73402 0.0565577
\(941\) 7.14219 0.232829 0.116414 0.993201i \(-0.462860\pi\)
0.116414 + 0.993201i \(0.462860\pi\)
\(942\) −24.3958 −0.794857
\(943\) −21.4273 −0.697768
\(944\) −2.26152 −0.0736063
\(945\) −0.0235817 −0.000767114 0
\(946\) 93.2638 3.03227
\(947\) 33.4537 1.08710 0.543550 0.839377i \(-0.317080\pi\)
0.543550 + 0.839377i \(0.317080\pi\)
\(948\) −25.0789 −0.814524
\(949\) −14.3972 −0.467352
\(950\) 4.08471 0.132525
\(951\) 14.6950 0.476518
\(952\) −0.768076 −0.0248935
\(953\) −44.6055 −1.44491 −0.722456 0.691417i \(-0.756987\pi\)
−0.722456 + 0.691417i \(0.756987\pi\)
\(954\) 16.8882 0.546777
\(955\) 1.14145 0.0369366
\(956\) 30.6435 0.991083
\(957\) −29.4753 −0.952801
\(958\) 41.7450 1.34872
\(959\) −9.36185 −0.302310
\(960\) −3.28427 −0.105999
\(961\) −26.9620 −0.869742
\(962\) −26.9438 −0.868703
\(963\) −22.5053 −0.725222
\(964\) 6.20260 0.199772
\(965\) 1.13642 0.0365825
\(966\) −44.5566 −1.43359
\(967\) 29.6459 0.953347 0.476674 0.879080i \(-0.341842\pi\)
0.476674 + 0.879080i \(0.341842\pi\)
\(968\) −4.68605 −0.150615
\(969\) 4.10261 0.131795
\(970\) −5.56643 −0.178727
\(971\) −43.3189 −1.39017 −0.695085 0.718928i \(-0.744633\pi\)
−0.695085 + 0.718928i \(0.744633\pi\)
\(972\) −45.8475 −1.47056
\(973\) −16.2985 −0.522505
\(974\) 28.0983 0.900327
\(975\) −29.5649 −0.946836
\(976\) 49.1466 1.57314
\(977\) −38.8361 −1.24248 −0.621239 0.783621i \(-0.713370\pi\)
−0.621239 + 0.783621i \(0.713370\pi\)
\(978\) 83.5968 2.67313
\(979\) −65.7398 −2.10105
\(980\) 0.323483 0.0103333
\(981\) 36.4392 1.16341
\(982\) −12.8628 −0.410468
\(983\) −12.9551 −0.413204 −0.206602 0.978425i \(-0.566241\pi\)
−0.206602 + 0.978425i \(0.566241\pi\)
\(984\) 1.06923 0.0340857
\(985\) 2.57277 0.0819753
\(986\) −16.8463 −0.536496
\(987\) 13.0618 0.415762
\(988\) 2.06959 0.0658425
\(989\) 69.1694 2.19946
\(990\) 5.53765 0.175998
\(991\) −46.2652 −1.46966 −0.734832 0.678249i \(-0.762739\pi\)
−0.734832 + 0.678249i \(0.762739\pi\)
\(992\) 16.2246 0.515132
\(993\) 30.6166 0.971589
\(994\) −3.20420 −0.101631
\(995\) 2.04773 0.0649173
\(996\) −23.3471 −0.739780
\(997\) −55.1516 −1.74667 −0.873335 0.487121i \(-0.838047\pi\)
−0.873335 + 0.487121i \(0.838047\pi\)
\(998\) 1.67645 0.0530671
\(999\) −0.832939 −0.0263530
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 \(a_p\))