Properties

Label 6013.2.a.e.1.19
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 1.19
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.82060 q^{2}\) \(+2.13458 q^{3}\) \(+1.31457 q^{4}\) \(-4.26535 q^{5}\) \(-3.88622 q^{6}\) \(+1.00000 q^{7}\) \(+1.24789 q^{8}\) \(+1.55645 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.82060 q^{2}\) \(+2.13458 q^{3}\) \(+1.31457 q^{4}\) \(-4.26535 q^{5}\) \(-3.88622 q^{6}\) \(+1.00000 q^{7}\) \(+1.24789 q^{8}\) \(+1.55645 q^{9}\) \(+7.76548 q^{10}\) \(+5.61533 q^{11}\) \(+2.80606 q^{12}\) \(+3.58656 q^{13}\) \(-1.82060 q^{14}\) \(-9.10475 q^{15}\) \(-4.90105 q^{16}\) \(+6.50418 q^{17}\) \(-2.83366 q^{18}\) \(+1.68108 q^{19}\) \(-5.60710 q^{20}\) \(+2.13458 q^{21}\) \(-10.2232 q^{22}\) \(+3.27680 q^{23}\) \(+2.66373 q^{24}\) \(+13.1932 q^{25}\) \(-6.52967 q^{26}\) \(-3.08138 q^{27}\) \(+1.31457 q^{28}\) \(+2.92030 q^{29}\) \(+16.5761 q^{30}\) \(-0.235003 q^{31}\) \(+6.42704 q^{32}\) \(+11.9864 q^{33}\) \(-11.8415 q^{34}\) \(-4.26535 q^{35}\) \(+2.04606 q^{36}\) \(+9.23601 q^{37}\) \(-3.06056 q^{38}\) \(+7.65581 q^{39}\) \(-5.32269 q^{40}\) \(-7.75357 q^{41}\) \(-3.88622 q^{42}\) \(-0.257386 q^{43}\) \(+7.38174 q^{44}\) \(-6.63880 q^{45}\) \(-5.96572 q^{46}\) \(+4.49731 q^{47}\) \(-10.4617 q^{48}\) \(+1.00000 q^{49}\) \(-24.0195 q^{50}\) \(+13.8837 q^{51}\) \(+4.71478 q^{52}\) \(-1.70941 q^{53}\) \(+5.60995 q^{54}\) \(-23.9514 q^{55}\) \(+1.24789 q^{56}\) \(+3.58840 q^{57}\) \(-5.31668 q^{58}\) \(+0.207733 q^{59}\) \(-11.9688 q^{60}\) \(+2.18300 q^{61}\) \(+0.427845 q^{62}\) \(+1.55645 q^{63}\) \(-1.89896 q^{64}\) \(-15.2979 q^{65}\) \(-21.8224 q^{66}\) \(+0.0456908 q^{67}\) \(+8.55020 q^{68}\) \(+6.99460 q^{69}\) \(+7.76548 q^{70}\) \(+7.95734 q^{71}\) \(+1.94228 q^{72}\) \(+3.04428 q^{73}\) \(-16.8150 q^{74}\) \(+28.1620 q^{75}\) \(+2.20990 q^{76}\) \(+5.61533 q^{77}\) \(-13.9381 q^{78}\) \(-10.9791 q^{79}\) \(+20.9047 q^{80}\) \(-11.2468 q^{81}\) \(+14.1161 q^{82}\) \(+7.07037 q^{83}\) \(+2.80606 q^{84}\) \(-27.7426 q^{85}\) \(+0.468596 q^{86}\) \(+6.23362 q^{87}\) \(+7.00732 q^{88}\) \(+18.3857 q^{89}\) \(+12.0866 q^{90}\) \(+3.58656 q^{91}\) \(+4.30758 q^{92}\) \(-0.501633 q^{93}\) \(-8.18779 q^{94}\) \(-7.17039 q^{95}\) \(+13.7191 q^{96}\) \(-11.9692 q^{97}\) \(-1.82060 q^{98}\) \(+8.73997 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82060 −1.28736 −0.643678 0.765297i \(-0.722592\pi\)
−0.643678 + 0.765297i \(0.722592\pi\)
\(3\) 2.13458 1.23240 0.616201 0.787589i \(-0.288671\pi\)
0.616201 + 0.787589i \(0.288671\pi\)
\(4\) 1.31457 0.657285
\(5\) −4.26535 −1.90752 −0.953762 0.300564i \(-0.902825\pi\)
−0.953762 + 0.300564i \(0.902825\pi\)
\(6\) −3.88622 −1.58654
\(7\) 1.00000 0.377964
\(8\) 1.24789 0.441196
\(9\) 1.55645 0.518816
\(10\) 7.76548 2.45566
\(11\) 5.61533 1.69309 0.846543 0.532321i \(-0.178680\pi\)
0.846543 + 0.532321i \(0.178680\pi\)
\(12\) 2.80606 0.810040
\(13\) 3.58656 0.994732 0.497366 0.867541i \(-0.334301\pi\)
0.497366 + 0.867541i \(0.334301\pi\)
\(14\) −1.82060 −0.486575
\(15\) −9.10475 −2.35084
\(16\) −4.90105 −1.22526
\(17\) 6.50418 1.57750 0.788748 0.614717i \(-0.210730\pi\)
0.788748 + 0.614717i \(0.210730\pi\)
\(18\) −2.83366 −0.667901
\(19\) 1.68108 0.385666 0.192833 0.981232i \(-0.438232\pi\)
0.192833 + 0.981232i \(0.438232\pi\)
\(20\) −5.60710 −1.25379
\(21\) 2.13458 0.465804
\(22\) −10.2232 −2.17960
\(23\) 3.27680 0.683259 0.341630 0.939835i \(-0.389021\pi\)
0.341630 + 0.939835i \(0.389021\pi\)
\(24\) 2.66373 0.543731
\(25\) 13.1932 2.63864
\(26\) −6.52967 −1.28057
\(27\) −3.08138 −0.593012
\(28\) 1.31457 0.248430
\(29\) 2.92030 0.542286 0.271143 0.962539i \(-0.412598\pi\)
0.271143 + 0.962539i \(0.412598\pi\)
\(30\) 16.5761 3.02636
\(31\) −0.235003 −0.0422077 −0.0211039 0.999777i \(-0.506718\pi\)
−0.0211039 + 0.999777i \(0.506718\pi\)
\(32\) 6.42704 1.13615
\(33\) 11.9864 2.08656
\(34\) −11.8415 −2.03080
\(35\) −4.26535 −0.720976
\(36\) 2.04606 0.341010
\(37\) 9.23601 1.51839 0.759196 0.650863i \(-0.225593\pi\)
0.759196 + 0.650863i \(0.225593\pi\)
\(38\) −3.06056 −0.496489
\(39\) 7.65581 1.22591
\(40\) −5.32269 −0.841592
\(41\) −7.75357 −1.21090 −0.605452 0.795882i \(-0.707008\pi\)
−0.605452 + 0.795882i \(0.707008\pi\)
\(42\) −3.88622 −0.599656
\(43\) −0.257386 −0.0392510 −0.0196255 0.999807i \(-0.506247\pi\)
−0.0196255 + 0.999807i \(0.506247\pi\)
\(44\) 7.38174 1.11284
\(45\) −6.63880 −0.989654
\(46\) −5.96572 −0.879598
\(47\) 4.49731 0.656000 0.328000 0.944678i \(-0.393625\pi\)
0.328000 + 0.944678i \(0.393625\pi\)
\(48\) −10.4617 −1.51002
\(49\) 1.00000 0.142857
\(50\) −24.0195 −3.39687
\(51\) 13.8837 1.94411
\(52\) 4.71478 0.653822
\(53\) −1.70941 −0.234805 −0.117403 0.993084i \(-0.537457\pi\)
−0.117403 + 0.993084i \(0.537457\pi\)
\(54\) 5.60995 0.763418
\(55\) −23.9514 −3.22960
\(56\) 1.24789 0.166756
\(57\) 3.58840 0.475296
\(58\) −5.31668 −0.698115
\(59\) 0.207733 0.0270446 0.0135223 0.999909i \(-0.495696\pi\)
0.0135223 + 0.999909i \(0.495696\pi\)
\(60\) −11.9688 −1.54517
\(61\) 2.18300 0.279505 0.139753 0.990186i \(-0.455369\pi\)
0.139753 + 0.990186i \(0.455369\pi\)
\(62\) 0.427845 0.0543364
\(63\) 1.55645 0.196094
\(64\) −1.89896 −0.237370
\(65\) −15.2979 −1.89747
\(66\) −21.8224 −2.68615
\(67\) 0.0456908 0.00558203 0.00279101 0.999996i \(-0.499112\pi\)
0.00279101 + 0.999996i \(0.499112\pi\)
\(68\) 8.55020 1.03686
\(69\) 6.99460 0.842050
\(70\) 7.76548 0.928153
\(71\) 7.95734 0.944363 0.472181 0.881501i \(-0.343467\pi\)
0.472181 + 0.881501i \(0.343467\pi\)
\(72\) 1.94228 0.228900
\(73\) 3.04428 0.356306 0.178153 0.984003i \(-0.442988\pi\)
0.178153 + 0.984003i \(0.442988\pi\)
\(74\) −16.8150 −1.95471
\(75\) 28.1620 3.25187
\(76\) 2.20990 0.253492
\(77\) 5.61533 0.639926
\(78\) −13.9381 −1.57818
\(79\) −10.9791 −1.23525 −0.617625 0.786473i \(-0.711905\pi\)
−0.617625 + 0.786473i \(0.711905\pi\)
\(80\) 20.9047 2.33721
\(81\) −11.2468 −1.24965
\(82\) 14.1161 1.55886
\(83\) 7.07037 0.776074 0.388037 0.921644i \(-0.373153\pi\)
0.388037 + 0.921644i \(0.373153\pi\)
\(84\) 2.80606 0.306166
\(85\) −27.7426 −3.00911
\(86\) 0.468596 0.0505300
\(87\) 6.23362 0.668314
\(88\) 7.00732 0.746983
\(89\) 18.3857 1.94888 0.974442 0.224638i \(-0.0721198\pi\)
0.974442 + 0.224638i \(0.0721198\pi\)
\(90\) 12.0866 1.27404
\(91\) 3.58656 0.375973
\(92\) 4.30758 0.449096
\(93\) −0.501633 −0.0520169
\(94\) −8.18779 −0.844506
\(95\) −7.17039 −0.735667
\(96\) 13.7191 1.40020
\(97\) −11.9692 −1.21528 −0.607642 0.794211i \(-0.707884\pi\)
−0.607642 + 0.794211i \(0.707884\pi\)
\(98\) −1.82060 −0.183908
\(99\) 8.73997 0.878400
\(100\) 17.3434 1.73434
\(101\) 8.20118 0.816048 0.408024 0.912971i \(-0.366218\pi\)
0.408024 + 0.912971i \(0.366218\pi\)
\(102\) −25.2766 −2.50276
\(103\) −11.8039 −1.16307 −0.581535 0.813521i \(-0.697548\pi\)
−0.581535 + 0.813521i \(0.697548\pi\)
\(104\) 4.47563 0.438872
\(105\) −9.10475 −0.888533
\(106\) 3.11214 0.302278
\(107\) −3.24876 −0.314069 −0.157035 0.987593i \(-0.550193\pi\)
−0.157035 + 0.987593i \(0.550193\pi\)
\(108\) −4.05069 −0.389778
\(109\) −15.8052 −1.51386 −0.756931 0.653495i \(-0.773302\pi\)
−0.756931 + 0.653495i \(0.773302\pi\)
\(110\) 43.6057 4.15764
\(111\) 19.7150 1.87127
\(112\) −4.90105 −0.463105
\(113\) −1.58337 −0.148951 −0.0744754 0.997223i \(-0.523728\pi\)
−0.0744754 + 0.997223i \(0.523728\pi\)
\(114\) −6.53303 −0.611874
\(115\) −13.9767 −1.30333
\(116\) 3.83894 0.356436
\(117\) 5.58229 0.516083
\(118\) −0.378199 −0.0348160
\(119\) 6.50418 0.596237
\(120\) −11.3617 −1.03718
\(121\) 20.5319 1.86654
\(122\) −3.97437 −0.359823
\(123\) −16.5506 −1.49232
\(124\) −0.308928 −0.0277425
\(125\) −34.9470 −3.12575
\(126\) −2.83366 −0.252443
\(127\) −10.0100 −0.888241 −0.444121 0.895967i \(-0.646484\pi\)
−0.444121 + 0.895967i \(0.646484\pi\)
\(128\) −9.39685 −0.830572
\(129\) −0.549412 −0.0483731
\(130\) 27.8513 2.44272
\(131\) 7.46642 0.652344 0.326172 0.945310i \(-0.394241\pi\)
0.326172 + 0.945310i \(0.394241\pi\)
\(132\) 15.7569 1.37147
\(133\) 1.68108 0.145768
\(134\) −0.0831846 −0.00718605
\(135\) 13.1432 1.13118
\(136\) 8.11651 0.695985
\(137\) 0.580775 0.0496190 0.0248095 0.999692i \(-0.492102\pi\)
0.0248095 + 0.999692i \(0.492102\pi\)
\(138\) −12.7343 −1.08402
\(139\) 9.51874 0.807369 0.403684 0.914898i \(-0.367729\pi\)
0.403684 + 0.914898i \(0.367729\pi\)
\(140\) −5.60710 −0.473887
\(141\) 9.59989 0.808457
\(142\) −14.4871 −1.21573
\(143\) 20.1397 1.68417
\(144\) −7.62823 −0.635685
\(145\) −12.4561 −1.03442
\(146\) −5.54240 −0.458693
\(147\) 2.13458 0.176058
\(148\) 12.1414 0.998016
\(149\) −9.72554 −0.796748 −0.398374 0.917223i \(-0.630425\pi\)
−0.398374 + 0.917223i \(0.630425\pi\)
\(150\) −51.2717 −4.18632
\(151\) −10.9342 −0.889810 −0.444905 0.895578i \(-0.646763\pi\)
−0.444905 + 0.895578i \(0.646763\pi\)
\(152\) 2.09780 0.170154
\(153\) 10.1234 0.818430
\(154\) −10.2232 −0.823813
\(155\) 1.00237 0.0805122
\(156\) 10.0641 0.805772
\(157\) −14.1466 −1.12902 −0.564510 0.825426i \(-0.690935\pi\)
−0.564510 + 0.825426i \(0.690935\pi\)
\(158\) 19.9886 1.59021
\(159\) −3.64887 −0.289374
\(160\) −27.4136 −2.16723
\(161\) 3.27680 0.258248
\(162\) 20.4759 1.60874
\(163\) −16.9021 −1.32388 −0.661938 0.749559i \(-0.730266\pi\)
−0.661938 + 0.749559i \(0.730266\pi\)
\(164\) −10.1926 −0.795909
\(165\) −51.1262 −3.98017
\(166\) −12.8723 −0.999083
\(167\) −11.0074 −0.851777 −0.425888 0.904776i \(-0.640038\pi\)
−0.425888 + 0.904776i \(0.640038\pi\)
\(168\) 2.66373 0.205511
\(169\) −0.136615 −0.0105088
\(170\) 50.5081 3.87379
\(171\) 2.61651 0.200090
\(172\) −0.338352 −0.0257991
\(173\) −9.84735 −0.748680 −0.374340 0.927291i \(-0.622131\pi\)
−0.374340 + 0.927291i \(0.622131\pi\)
\(174\) −11.3489 −0.860358
\(175\) 13.1932 0.997314
\(176\) −27.5210 −2.07447
\(177\) 0.443424 0.0333298
\(178\) −33.4730 −2.50891
\(179\) −10.6460 −0.795719 −0.397859 0.917446i \(-0.630247\pi\)
−0.397859 + 0.917446i \(0.630247\pi\)
\(180\) −8.72717 −0.650485
\(181\) 16.5515 1.23026 0.615131 0.788425i \(-0.289103\pi\)
0.615131 + 0.788425i \(0.289103\pi\)
\(182\) −6.52967 −0.484011
\(183\) 4.65981 0.344463
\(184\) 4.08909 0.301451
\(185\) −39.3948 −2.89637
\(186\) 0.913271 0.0669643
\(187\) 36.5231 2.67083
\(188\) 5.91203 0.431179
\(189\) −3.08138 −0.224138
\(190\) 13.0544 0.947065
\(191\) −3.89190 −0.281608 −0.140804 0.990037i \(-0.544969\pi\)
−0.140804 + 0.990037i \(0.544969\pi\)
\(192\) −4.05348 −0.292535
\(193\) −12.9598 −0.932868 −0.466434 0.884556i \(-0.654462\pi\)
−0.466434 + 0.884556i \(0.654462\pi\)
\(194\) 21.7910 1.56450
\(195\) −32.6547 −2.33845
\(196\) 1.31457 0.0938979
\(197\) 0.703936 0.0501534 0.0250767 0.999686i \(-0.492017\pi\)
0.0250767 + 0.999686i \(0.492017\pi\)
\(198\) −15.9120 −1.13081
\(199\) 2.09958 0.148835 0.0744176 0.997227i \(-0.476290\pi\)
0.0744176 + 0.997227i \(0.476290\pi\)
\(200\) 16.4637 1.16416
\(201\) 0.0975309 0.00687930
\(202\) −14.9310 −1.05054
\(203\) 2.92030 0.204965
\(204\) 18.2511 1.27783
\(205\) 33.0717 2.30983
\(206\) 21.4901 1.49729
\(207\) 5.10016 0.354486
\(208\) −17.5779 −1.21881
\(209\) 9.43981 0.652965
\(210\) 16.5761 1.14386
\(211\) 12.4870 0.859643 0.429822 0.902914i \(-0.358576\pi\)
0.429822 + 0.902914i \(0.358576\pi\)
\(212\) −2.24714 −0.154334
\(213\) 16.9856 1.16384
\(214\) 5.91467 0.404319
\(215\) 1.09784 0.0748722
\(216\) −3.84523 −0.261635
\(217\) −0.235003 −0.0159530
\(218\) 28.7749 1.94888
\(219\) 6.49827 0.439113
\(220\) −31.4857 −2.12277
\(221\) 23.3276 1.56918
\(222\) −35.8931 −2.40899
\(223\) 17.5345 1.17419 0.587097 0.809516i \(-0.300271\pi\)
0.587097 + 0.809516i \(0.300271\pi\)
\(224\) 6.42704 0.429425
\(225\) 20.5346 1.36897
\(226\) 2.88267 0.191753
\(227\) 13.7706 0.913990 0.456995 0.889469i \(-0.348926\pi\)
0.456995 + 0.889469i \(0.348926\pi\)
\(228\) 4.71721 0.312405
\(229\) −27.8043 −1.83736 −0.918681 0.395000i \(-0.870745\pi\)
−0.918681 + 0.395000i \(0.870745\pi\)
\(230\) 25.4459 1.67785
\(231\) 11.9864 0.788647
\(232\) 3.64421 0.239254
\(233\) −1.10960 −0.0726926 −0.0363463 0.999339i \(-0.511572\pi\)
−0.0363463 + 0.999339i \(0.511572\pi\)
\(234\) −10.1631 −0.664382
\(235\) −19.1826 −1.25134
\(236\) 0.273080 0.0177760
\(237\) −23.4359 −1.52233
\(238\) −11.8415 −0.767569
\(239\) 5.19532 0.336057 0.168028 0.985782i \(-0.446260\pi\)
0.168028 + 0.985782i \(0.446260\pi\)
\(240\) 44.6228 2.88039
\(241\) 20.2803 1.30637 0.653184 0.757199i \(-0.273433\pi\)
0.653184 + 0.757199i \(0.273433\pi\)
\(242\) −37.3803 −2.40290
\(243\) −14.7631 −0.947055
\(244\) 2.86971 0.183715
\(245\) −4.26535 −0.272503
\(246\) 30.1320 1.92115
\(247\) 6.02928 0.383634
\(248\) −0.293258 −0.0186219
\(249\) 15.0923 0.956436
\(250\) 63.6243 4.02396
\(251\) 20.2166 1.27606 0.638030 0.770012i \(-0.279750\pi\)
0.638030 + 0.770012i \(0.279750\pi\)
\(252\) 2.04606 0.128890
\(253\) 18.4003 1.15682
\(254\) 18.2241 1.14348
\(255\) −59.2189 −3.70843
\(256\) 20.9058 1.30661
\(257\) −9.89146 −0.617012 −0.308506 0.951222i \(-0.599829\pi\)
−0.308506 + 0.951222i \(0.599829\pi\)
\(258\) 1.00026 0.0622733
\(259\) 9.23601 0.573898
\(260\) −20.1102 −1.24718
\(261\) 4.54529 0.281347
\(262\) −13.5933 −0.839799
\(263\) 29.3137 1.80756 0.903779 0.428000i \(-0.140782\pi\)
0.903779 + 0.428000i \(0.140782\pi\)
\(264\) 14.9577 0.920583
\(265\) 7.29122 0.447896
\(266\) −3.06056 −0.187655
\(267\) 39.2459 2.40181
\(268\) 0.0600638 0.00366898
\(269\) 13.6832 0.834279 0.417139 0.908842i \(-0.363033\pi\)
0.417139 + 0.908842i \(0.363033\pi\)
\(270\) −23.9284 −1.45624
\(271\) −2.04532 −0.124244 −0.0621221 0.998069i \(-0.519787\pi\)
−0.0621221 + 0.998069i \(0.519787\pi\)
\(272\) −31.8773 −1.93284
\(273\) 7.65581 0.463350
\(274\) −1.05736 −0.0638773
\(275\) 74.0843 4.46745
\(276\) 9.19489 0.553467
\(277\) −1.46575 −0.0880687 −0.0440343 0.999030i \(-0.514021\pi\)
−0.0440343 + 0.999030i \(0.514021\pi\)
\(278\) −17.3298 −1.03937
\(279\) −0.365770 −0.0218981
\(280\) −5.32269 −0.318092
\(281\) −0.981284 −0.0585385 −0.0292693 0.999572i \(-0.509318\pi\)
−0.0292693 + 0.999572i \(0.509318\pi\)
\(282\) −17.4775 −1.04077
\(283\) 17.4400 1.03670 0.518349 0.855169i \(-0.326547\pi\)
0.518349 + 0.855169i \(0.326547\pi\)
\(284\) 10.4605 0.620715
\(285\) −15.3058 −0.906637
\(286\) −36.6662 −2.16812
\(287\) −7.75357 −0.457679
\(288\) 10.0034 0.589454
\(289\) 25.3044 1.48849
\(290\) 22.6775 1.33167
\(291\) −25.5492 −1.49772
\(292\) 4.00192 0.234195
\(293\) 15.3193 0.894960 0.447480 0.894294i \(-0.352321\pi\)
0.447480 + 0.894294i \(0.352321\pi\)
\(294\) −3.88622 −0.226649
\(295\) −0.886056 −0.0515882
\(296\) 11.5255 0.669908
\(297\) −17.3030 −1.00402
\(298\) 17.7063 1.02570
\(299\) 11.7524 0.679660
\(300\) 37.0210 2.13741
\(301\) −0.257386 −0.0148355
\(302\) 19.9067 1.14550
\(303\) 17.5061 1.00570
\(304\) −8.23904 −0.472541
\(305\) −9.31128 −0.533162
\(306\) −18.4307 −1.05361
\(307\) 18.3167 1.04539 0.522695 0.852520i \(-0.324927\pi\)
0.522695 + 0.852520i \(0.324927\pi\)
\(308\) 7.38174 0.420614
\(309\) −25.1964 −1.43337
\(310\) −1.82491 −0.103648
\(311\) 29.6733 1.68262 0.841310 0.540553i \(-0.181785\pi\)
0.841310 + 0.540553i \(0.181785\pi\)
\(312\) 9.55361 0.540867
\(313\) 15.8373 0.895179 0.447589 0.894239i \(-0.352283\pi\)
0.447589 + 0.894239i \(0.352283\pi\)
\(314\) 25.7552 1.45345
\(315\) −6.63880 −0.374054
\(316\) −14.4329 −0.811911
\(317\) −24.4618 −1.37391 −0.686954 0.726701i \(-0.741053\pi\)
−0.686954 + 0.726701i \(0.741053\pi\)
\(318\) 6.64312 0.372528
\(319\) 16.3984 0.918136
\(320\) 8.09972 0.452788
\(321\) −6.93474 −0.387060
\(322\) −5.96572 −0.332457
\(323\) 10.9340 0.608386
\(324\) −14.7847 −0.821374
\(325\) 47.3182 2.62474
\(326\) 30.7719 1.70430
\(327\) −33.7375 −1.86569
\(328\) −9.67561 −0.534246
\(329\) 4.49731 0.247945
\(330\) 93.0801 5.12389
\(331\) 10.2857 0.565354 0.282677 0.959215i \(-0.408778\pi\)
0.282677 + 0.959215i \(0.408778\pi\)
\(332\) 9.29450 0.510102
\(333\) 14.3754 0.787766
\(334\) 20.0400 1.09654
\(335\) −0.194888 −0.0106478
\(336\) −10.4617 −0.570732
\(337\) 24.8172 1.35188 0.675939 0.736958i \(-0.263738\pi\)
0.675939 + 0.736958i \(0.263738\pi\)
\(338\) 0.248721 0.0135286
\(339\) −3.37983 −0.183567
\(340\) −36.4696 −1.97784
\(341\) −1.31962 −0.0714613
\(342\) −4.76361 −0.257587
\(343\) 1.00000 0.0539949
\(344\) −0.321190 −0.0173174
\(345\) −29.8344 −1.60623
\(346\) 17.9281 0.963818
\(347\) −7.04715 −0.378311 −0.189156 0.981947i \(-0.560575\pi\)
−0.189156 + 0.981947i \(0.560575\pi\)
\(348\) 8.19453 0.439273
\(349\) −30.3701 −1.62567 −0.812837 0.582491i \(-0.802078\pi\)
−0.812837 + 0.582491i \(0.802078\pi\)
\(350\) −24.0195 −1.28390
\(351\) −11.0515 −0.589888
\(352\) 36.0900 1.92360
\(353\) 23.5215 1.25192 0.625960 0.779855i \(-0.284707\pi\)
0.625960 + 0.779855i \(0.284707\pi\)
\(354\) −0.807297 −0.0429073
\(355\) −33.9409 −1.80139
\(356\) 24.1693 1.28097
\(357\) 13.8837 0.734804
\(358\) 19.3820 1.02437
\(359\) 29.7328 1.56924 0.784619 0.619978i \(-0.212858\pi\)
0.784619 + 0.619978i \(0.212858\pi\)
\(360\) −8.28450 −0.436631
\(361\) −16.1740 −0.851262
\(362\) −30.1335 −1.58378
\(363\) 43.8271 2.30033
\(364\) 4.71478 0.247122
\(365\) −12.9849 −0.679662
\(366\) −8.48363 −0.443446
\(367\) −16.1997 −0.845619 −0.422809 0.906219i \(-0.638956\pi\)
−0.422809 + 0.906219i \(0.638956\pi\)
\(368\) −16.0597 −0.837171
\(369\) −12.0680 −0.628237
\(370\) 71.7221 3.72865
\(371\) −1.70941 −0.0887480
\(372\) −0.659432 −0.0341899
\(373\) −4.44785 −0.230301 −0.115150 0.993348i \(-0.536735\pi\)
−0.115150 + 0.993348i \(0.536735\pi\)
\(374\) −66.4938 −3.43831
\(375\) −74.5973 −3.85219
\(376\) 5.61216 0.289425
\(377\) 10.4738 0.539429
\(378\) 5.60995 0.288545
\(379\) −18.9489 −0.973338 −0.486669 0.873587i \(-0.661788\pi\)
−0.486669 + 0.873587i \(0.661788\pi\)
\(380\) −9.42598 −0.483543
\(381\) −21.3671 −1.09467
\(382\) 7.08558 0.362530
\(383\) −24.4184 −1.24772 −0.623862 0.781535i \(-0.714437\pi\)
−0.623862 + 0.781535i \(0.714437\pi\)
\(384\) −20.0584 −1.02360
\(385\) −23.9514 −1.22067
\(386\) 23.5946 1.20093
\(387\) −0.400608 −0.0203641
\(388\) −15.7343 −0.798788
\(389\) −21.9115 −1.11096 −0.555479 0.831531i \(-0.687465\pi\)
−0.555479 + 0.831531i \(0.687465\pi\)
\(390\) 59.4510 3.01042
\(391\) 21.3129 1.07784
\(392\) 1.24789 0.0630280
\(393\) 15.9377 0.803950
\(394\) −1.28158 −0.0645653
\(395\) 46.8299 2.35627
\(396\) 11.4893 0.577359
\(397\) 26.7193 1.34100 0.670501 0.741908i \(-0.266079\pi\)
0.670501 + 0.741908i \(0.266079\pi\)
\(398\) −3.82248 −0.191604
\(399\) 3.58840 0.179645
\(400\) −64.6606 −3.23303
\(401\) −1.20324 −0.0600872 −0.0300436 0.999549i \(-0.509565\pi\)
−0.0300436 + 0.999549i \(0.509565\pi\)
\(402\) −0.177564 −0.00885611
\(403\) −0.842851 −0.0419854
\(404\) 10.7810 0.536376
\(405\) 47.9716 2.38373
\(406\) −5.31668 −0.263863
\(407\) 51.8632 2.57077
\(408\) 17.3254 0.857734
\(409\) 6.40723 0.316817 0.158409 0.987374i \(-0.449364\pi\)
0.158409 + 0.987374i \(0.449364\pi\)
\(410\) −60.2102 −2.97357
\(411\) 1.23971 0.0611505
\(412\) −15.5170 −0.764469
\(413\) 0.207733 0.0102219
\(414\) −9.28534 −0.456350
\(415\) −30.1576 −1.48038
\(416\) 23.0509 1.13017
\(417\) 20.3185 0.995004
\(418\) −17.1861 −0.840598
\(419\) −22.8724 −1.11739 −0.558694 0.829374i \(-0.688697\pi\)
−0.558694 + 0.829374i \(0.688697\pi\)
\(420\) −11.9688 −0.584019
\(421\) −19.1397 −0.932814 −0.466407 0.884570i \(-0.654452\pi\)
−0.466407 + 0.884570i \(0.654452\pi\)
\(422\) −22.7339 −1.10667
\(423\) 6.99984 0.340344
\(424\) −2.13315 −0.103595
\(425\) 85.8111 4.16245
\(426\) −30.9239 −1.49827
\(427\) 2.18300 0.105643
\(428\) −4.27072 −0.206433
\(429\) 42.9899 2.07557
\(430\) −1.99873 −0.0963872
\(431\) 21.7704 1.04864 0.524321 0.851521i \(-0.324319\pi\)
0.524321 + 0.851521i \(0.324319\pi\)
\(432\) 15.1020 0.726595
\(433\) −9.98779 −0.479983 −0.239991 0.970775i \(-0.577145\pi\)
−0.239991 + 0.970775i \(0.577145\pi\)
\(434\) 0.427845 0.0205372
\(435\) −26.5886 −1.27483
\(436\) −20.7770 −0.995039
\(437\) 5.50855 0.263510
\(438\) −11.8307 −0.565294
\(439\) 15.7465 0.751541 0.375770 0.926713i \(-0.377378\pi\)
0.375770 + 0.926713i \(0.377378\pi\)
\(440\) −29.8887 −1.42489
\(441\) 1.55645 0.0741166
\(442\) −42.4701 −2.02010
\(443\) −19.8878 −0.944899 −0.472449 0.881358i \(-0.656630\pi\)
−0.472449 + 0.881358i \(0.656630\pi\)
\(444\) 25.9168 1.22996
\(445\) −78.4217 −3.71754
\(446\) −31.9232 −1.51161
\(447\) −20.7600 −0.981914
\(448\) −1.89896 −0.0897172
\(449\) −10.7474 −0.507200 −0.253600 0.967309i \(-0.581615\pi\)
−0.253600 + 0.967309i \(0.581615\pi\)
\(450\) −37.3852 −1.76235
\(451\) −43.5388 −2.05016
\(452\) −2.08145 −0.0979031
\(453\) −23.3399 −1.09660
\(454\) −25.0708 −1.17663
\(455\) −15.2979 −0.717178
\(456\) 4.47794 0.209699
\(457\) 25.2525 1.18126 0.590630 0.806942i \(-0.298879\pi\)
0.590630 + 0.806942i \(0.298879\pi\)
\(458\) 50.6205 2.36534
\(459\) −20.0419 −0.935474
\(460\) −18.3733 −0.856661
\(461\) 17.5848 0.819007 0.409504 0.912309i \(-0.365702\pi\)
0.409504 + 0.912309i \(0.365702\pi\)
\(462\) −21.8224 −1.01527
\(463\) −36.5263 −1.69752 −0.848761 0.528776i \(-0.822651\pi\)
−0.848761 + 0.528776i \(0.822651\pi\)
\(464\) −14.3125 −0.664442
\(465\) 2.13964 0.0992235
\(466\) 2.02014 0.0935813
\(467\) −7.55266 −0.349495 −0.174748 0.984613i \(-0.555911\pi\)
−0.174748 + 0.984613i \(0.555911\pi\)
\(468\) 7.33831 0.339214
\(469\) 0.0456908 0.00210981
\(470\) 34.9238 1.61091
\(471\) −30.1971 −1.39141
\(472\) 0.259229 0.0119320
\(473\) −1.44531 −0.0664553
\(474\) 42.6673 1.95977
\(475\) 22.1788 1.01764
\(476\) 8.55020 0.391898
\(477\) −2.66060 −0.121821
\(478\) −9.45857 −0.432625
\(479\) 39.2183 1.79193 0.895966 0.444123i \(-0.146485\pi\)
0.895966 + 0.444123i \(0.146485\pi\)
\(480\) −58.5166 −2.67091
\(481\) 33.1255 1.51039
\(482\) −36.9222 −1.68176
\(483\) 6.99460 0.318265
\(484\) 26.9906 1.22685
\(485\) 51.0527 2.31818
\(486\) 26.8777 1.21920
\(487\) 10.6747 0.483717 0.241859 0.970311i \(-0.422243\pi\)
0.241859 + 0.970311i \(0.422243\pi\)
\(488\) 2.72415 0.123317
\(489\) −36.0790 −1.63155
\(490\) 7.76548 0.350809
\(491\) −12.5081 −0.564483 −0.282242 0.959343i \(-0.591078\pi\)
−0.282242 + 0.959343i \(0.591078\pi\)
\(492\) −21.7570 −0.980880
\(493\) 18.9941 0.855453
\(494\) −10.9769 −0.493873
\(495\) −37.2790 −1.67557
\(496\) 1.15176 0.0517155
\(497\) 7.95734 0.356936
\(498\) −27.4770 −1.23127
\(499\) 11.1949 0.501154 0.250577 0.968097i \(-0.419380\pi\)
0.250577 + 0.968097i \(0.419380\pi\)
\(500\) −45.9403 −2.05451
\(501\) −23.4962 −1.04973
\(502\) −36.8062 −1.64274
\(503\) −39.3965 −1.75660 −0.878301 0.478109i \(-0.841322\pi\)
−0.878301 + 0.478109i \(0.841322\pi\)
\(504\) 1.94228 0.0865160
\(505\) −34.9809 −1.55663
\(506\) −33.4995 −1.48923
\(507\) −0.291616 −0.0129511
\(508\) −13.1588 −0.583828
\(509\) −27.1255 −1.20232 −0.601159 0.799130i \(-0.705294\pi\)
−0.601159 + 0.799130i \(0.705294\pi\)
\(510\) 107.814 4.77407
\(511\) 3.04428 0.134671
\(512\) −19.2673 −0.851502
\(513\) −5.18004 −0.228705
\(514\) 18.0083 0.794314
\(515\) 50.3477 2.21858
\(516\) −0.722241 −0.0317949
\(517\) 25.2539 1.11066
\(518\) −16.8150 −0.738811
\(519\) −21.0200 −0.922676
\(520\) −19.0901 −0.837158
\(521\) 21.0533 0.922362 0.461181 0.887306i \(-0.347426\pi\)
0.461181 + 0.887306i \(0.347426\pi\)
\(522\) −8.27514 −0.362193
\(523\) 37.9110 1.65773 0.828867 0.559446i \(-0.188986\pi\)
0.828867 + 0.559446i \(0.188986\pi\)
\(524\) 9.81513 0.428776
\(525\) 28.1620 1.22909
\(526\) −53.3683 −2.32697
\(527\) −1.52850 −0.0665825
\(528\) −58.7458 −2.55658
\(529\) −12.2626 −0.533157
\(530\) −13.2744 −0.576602
\(531\) 0.323326 0.0140312
\(532\) 2.20990 0.0958111
\(533\) −27.8086 −1.20452
\(534\) −71.4509 −3.09198
\(535\) 13.8571 0.599094
\(536\) 0.0570172 0.00246277
\(537\) −22.7248 −0.980646
\(538\) −24.9116 −1.07401
\(539\) 5.61533 0.241869
\(540\) 17.2776 0.743511
\(541\) −18.8947 −0.812348 −0.406174 0.913796i \(-0.633137\pi\)
−0.406174 + 0.913796i \(0.633137\pi\)
\(542\) 3.72370 0.159946
\(543\) 35.3305 1.51618
\(544\) 41.8026 1.79227
\(545\) 67.4147 2.88773
\(546\) −13.9381 −0.596497
\(547\) −33.9922 −1.45340 −0.726701 0.686954i \(-0.758947\pi\)
−0.726701 + 0.686954i \(0.758947\pi\)
\(548\) 0.763469 0.0326138
\(549\) 3.39773 0.145012
\(550\) −134.878 −5.75120
\(551\) 4.90925 0.209141
\(552\) 8.72850 0.371509
\(553\) −10.9791 −0.466881
\(554\) 2.66855 0.113376
\(555\) −84.0916 −3.56949
\(556\) 12.5130 0.530672
\(557\) 45.1875 1.91466 0.957329 0.289001i \(-0.0933231\pi\)
0.957329 + 0.289001i \(0.0933231\pi\)
\(558\) 0.665919 0.0281906
\(559\) −0.923130 −0.0390442
\(560\) 20.9047 0.883384
\(561\) 77.9616 3.29154
\(562\) 1.78652 0.0753599
\(563\) 7.47593 0.315073 0.157536 0.987513i \(-0.449645\pi\)
0.157536 + 0.987513i \(0.449645\pi\)
\(564\) 12.6197 0.531386
\(565\) 6.75362 0.284127
\(566\) −31.7511 −1.33460
\(567\) −11.2468 −0.472322
\(568\) 9.92990 0.416649
\(569\) 7.29330 0.305751 0.152875 0.988245i \(-0.451147\pi\)
0.152875 + 0.988245i \(0.451147\pi\)
\(570\) 27.8657 1.16716
\(571\) −10.6713 −0.446581 −0.223290 0.974752i \(-0.571680\pi\)
−0.223290 + 0.974752i \(0.571680\pi\)
\(572\) 26.4750 1.10698
\(573\) −8.30758 −0.347054
\(574\) 14.1161 0.589195
\(575\) 43.2315 1.80288
\(576\) −2.95563 −0.123151
\(577\) 20.0993 0.836743 0.418372 0.908276i \(-0.362601\pi\)
0.418372 + 0.908276i \(0.362601\pi\)
\(578\) −46.0690 −1.91622
\(579\) −27.6638 −1.14967
\(580\) −16.3744 −0.679911
\(581\) 7.07037 0.293328
\(582\) 46.5147 1.92810
\(583\) −9.59888 −0.397545
\(584\) 3.79893 0.157201
\(585\) −23.8104 −0.984440
\(586\) −27.8902 −1.15213
\(587\) −3.49847 −0.144397 −0.0721986 0.997390i \(-0.523002\pi\)
−0.0721986 + 0.997390i \(0.523002\pi\)
\(588\) 2.80606 0.115720
\(589\) −0.395058 −0.0162781
\(590\) 1.61315 0.0664124
\(591\) 1.50261 0.0618092
\(592\) −45.2661 −1.86043
\(593\) 33.0720 1.35810 0.679052 0.734090i \(-0.262391\pi\)
0.679052 + 0.734090i \(0.262391\pi\)
\(594\) 31.5017 1.29253
\(595\) −27.7426 −1.13734
\(596\) −12.7849 −0.523690
\(597\) 4.48172 0.183425
\(598\) −21.3964 −0.874964
\(599\) −0.987390 −0.0403437 −0.0201718 0.999797i \(-0.506421\pi\)
−0.0201718 + 0.999797i \(0.506421\pi\)
\(600\) 35.1432 1.43471
\(601\) −26.0016 −1.06063 −0.530313 0.847802i \(-0.677926\pi\)
−0.530313 + 0.847802i \(0.677926\pi\)
\(602\) 0.468596 0.0190986
\(603\) 0.0711154 0.00289604
\(604\) −14.3737 −0.584859
\(605\) −87.5759 −3.56046
\(606\) −31.8716 −1.29469
\(607\) −45.5582 −1.84915 −0.924576 0.380999i \(-0.875580\pi\)
−0.924576 + 0.380999i \(0.875580\pi\)
\(608\) 10.8044 0.438175
\(609\) 6.23362 0.252599
\(610\) 16.9521 0.686370
\(611\) 16.1299 0.652544
\(612\) 13.3079 0.537942
\(613\) −37.6967 −1.52255 −0.761277 0.648427i \(-0.775427\pi\)
−0.761277 + 0.648427i \(0.775427\pi\)
\(614\) −33.3473 −1.34579
\(615\) 70.5943 2.84664
\(616\) 7.00732 0.282333
\(617\) 2.09344 0.0842788 0.0421394 0.999112i \(-0.486583\pi\)
0.0421394 + 0.999112i \(0.486583\pi\)
\(618\) 45.8724 1.84526
\(619\) 3.89000 0.156352 0.0781762 0.996940i \(-0.475090\pi\)
0.0781762 + 0.996940i \(0.475090\pi\)
\(620\) 1.31768 0.0529195
\(621\) −10.0971 −0.405181
\(622\) −54.0231 −2.16613
\(623\) 18.3857 0.736609
\(624\) −37.5215 −1.50206
\(625\) 83.0950 3.32380
\(626\) −28.8334 −1.15241
\(627\) 20.1501 0.804716
\(628\) −18.5967 −0.742088
\(629\) 60.0727 2.39525
\(630\) 12.0866 0.481541
\(631\) 11.0173 0.438591 0.219296 0.975658i \(-0.429624\pi\)
0.219296 + 0.975658i \(0.429624\pi\)
\(632\) −13.7008 −0.544988
\(633\) 26.6546 1.05943
\(634\) 44.5350 1.76871
\(635\) 42.6961 1.69434
\(636\) −4.79670 −0.190201
\(637\) 3.58656 0.142105
\(638\) −29.8549 −1.18197
\(639\) 12.3852 0.489951
\(640\) 40.0809 1.58434
\(641\) 20.8626 0.824021 0.412011 0.911179i \(-0.364827\pi\)
0.412011 + 0.911179i \(0.364827\pi\)
\(642\) 12.6254 0.498283
\(643\) −22.9451 −0.904867 −0.452433 0.891798i \(-0.649444\pi\)
−0.452433 + 0.891798i \(0.649444\pi\)
\(644\) 4.30758 0.169742
\(645\) 2.34344 0.0922727
\(646\) −19.9065 −0.783209
\(647\) −21.9113 −0.861421 −0.430710 0.902490i \(-0.641737\pi\)
−0.430710 + 0.902490i \(0.641737\pi\)
\(648\) −14.0348 −0.551339
\(649\) 1.16649 0.0457888
\(650\) −86.1474 −3.37898
\(651\) −0.501633 −0.0196606
\(652\) −22.2190 −0.870164
\(653\) 23.8261 0.932388 0.466194 0.884683i \(-0.345625\pi\)
0.466194 + 0.884683i \(0.345625\pi\)
\(654\) 61.4223 2.40180
\(655\) −31.8469 −1.24436
\(656\) 38.0006 1.48367
\(657\) 4.73827 0.184857
\(658\) −8.18779 −0.319193
\(659\) 36.5573 1.42407 0.712034 0.702145i \(-0.247774\pi\)
0.712034 + 0.702145i \(0.247774\pi\)
\(660\) −67.2089 −2.61610
\(661\) 0.293241 0.0114058 0.00570288 0.999984i \(-0.498185\pi\)
0.00570288 + 0.999984i \(0.498185\pi\)
\(662\) −18.7261 −0.727812
\(663\) 49.7947 1.93387
\(664\) 8.82305 0.342401
\(665\) −7.17039 −0.278056
\(666\) −26.1718 −1.01413
\(667\) 9.56922 0.370522
\(668\) −14.4700 −0.559860
\(669\) 37.4288 1.44708
\(670\) 0.354811 0.0137076
\(671\) 12.2583 0.473226
\(672\) 13.7191 0.529224
\(673\) −2.80263 −0.108033 −0.0540166 0.998540i \(-0.517202\pi\)
−0.0540166 + 0.998540i \(0.517202\pi\)
\(674\) −45.1820 −1.74035
\(675\) −40.6534 −1.56475
\(676\) −0.179590 −0.00690731
\(677\) −31.9674 −1.22861 −0.614304 0.789069i \(-0.710563\pi\)
−0.614304 + 0.789069i \(0.710563\pi\)
\(678\) 6.15331 0.236316
\(679\) −11.9692 −0.459334
\(680\) −34.6198 −1.32761
\(681\) 29.3946 1.12640
\(682\) 2.40249 0.0919961
\(683\) 38.9838 1.49167 0.745837 0.666128i \(-0.232050\pi\)
0.745837 + 0.666128i \(0.232050\pi\)
\(684\) 3.43959 0.131516
\(685\) −2.47721 −0.0946493
\(686\) −1.82060 −0.0695107
\(687\) −59.3507 −2.26437
\(688\) 1.26146 0.0480928
\(689\) −6.13088 −0.233568
\(690\) 54.3164 2.06779
\(691\) 27.9256 1.06234 0.531170 0.847266i \(-0.321753\pi\)
0.531170 + 0.847266i \(0.321753\pi\)
\(692\) −12.9450 −0.492096
\(693\) 8.73997 0.332004
\(694\) 12.8300 0.487021
\(695\) −40.6008 −1.54008
\(696\) 7.77888 0.294858
\(697\) −50.4306 −1.91020
\(698\) 55.2917 2.09282
\(699\) −2.36854 −0.0895866
\(700\) 17.3434 0.655520
\(701\) −41.0731 −1.55131 −0.775655 0.631157i \(-0.782580\pi\)
−0.775655 + 0.631157i \(0.782580\pi\)
\(702\) 20.1204 0.759396
\(703\) 15.5265 0.585592
\(704\) −10.6633 −0.401887
\(705\) −40.9469 −1.54215
\(706\) −42.8231 −1.61167
\(707\) 8.20118 0.308437
\(708\) 0.582913 0.0219072
\(709\) 14.9751 0.562400 0.281200 0.959649i \(-0.409268\pi\)
0.281200 + 0.959649i \(0.409268\pi\)
\(710\) 61.7926 2.31903
\(711\) −17.0885 −0.640868
\(712\) 22.9434 0.859840
\(713\) −0.770056 −0.0288388
\(714\) −25.2766 −0.945955
\(715\) −85.9029 −3.21259
\(716\) −13.9949 −0.523014
\(717\) 11.0898 0.414158
\(718\) −54.1315 −2.02017
\(719\) −49.8307 −1.85837 −0.929186 0.369614i \(-0.879490\pi\)
−0.929186 + 0.369614i \(0.879490\pi\)
\(720\) 32.5371 1.21258
\(721\) −11.8039 −0.439599
\(722\) 29.4463 1.09588
\(723\) 43.2900 1.60997
\(724\) 21.7581 0.808632
\(725\) 38.5282 1.43090
\(726\) −79.7914 −2.96134
\(727\) −44.1039 −1.63572 −0.817862 0.575414i \(-0.804841\pi\)
−0.817862 + 0.575414i \(0.804841\pi\)
\(728\) 4.47563 0.165878
\(729\) 2.22732 0.0824933
\(730\) 23.6403 0.874967
\(731\) −1.67409 −0.0619183
\(732\) 6.12564 0.226410
\(733\) −43.1951 −1.59545 −0.797723 0.603024i \(-0.793962\pi\)
−0.797723 + 0.603024i \(0.793962\pi\)
\(734\) 29.4932 1.08861
\(735\) −9.10475 −0.335834
\(736\) 21.0601 0.776286
\(737\) 0.256569 0.00945085
\(738\) 21.9710 0.808764
\(739\) −35.3058 −1.29874 −0.649372 0.760471i \(-0.724968\pi\)
−0.649372 + 0.760471i \(0.724968\pi\)
\(740\) −51.7873 −1.90374
\(741\) 12.8700 0.472792
\(742\) 3.11214 0.114250
\(743\) −21.6573 −0.794531 −0.397265 0.917704i \(-0.630041\pi\)
−0.397265 + 0.917704i \(0.630041\pi\)
\(744\) −0.625983 −0.0229497
\(745\) 41.4829 1.51981
\(746\) 8.09773 0.296479
\(747\) 11.0047 0.402640
\(748\) 48.0122 1.75550
\(749\) −3.24876 −0.118707
\(750\) 135.811 4.95913
\(751\) −41.3517 −1.50894 −0.754472 0.656332i \(-0.772107\pi\)
−0.754472 + 0.656332i \(0.772107\pi\)
\(752\) −22.0415 −0.803772
\(753\) 43.1540 1.57262
\(754\) −19.0686 −0.694437
\(755\) 46.6381 1.69733
\(756\) −4.05069 −0.147322
\(757\) 36.7061 1.33410 0.667052 0.745011i \(-0.267556\pi\)
0.667052 + 0.745011i \(0.267556\pi\)
\(758\) 34.4982 1.25303
\(759\) 39.2770 1.42566
\(760\) −8.94787 −0.324573
\(761\) 41.9058 1.51908 0.759542 0.650458i \(-0.225423\pi\)
0.759542 + 0.650458i \(0.225423\pi\)
\(762\) 38.9009 1.40923
\(763\) −15.8052 −0.572186
\(764\) −5.11617 −0.185097
\(765\) −43.1799 −1.56117
\(766\) 44.4561 1.60626
\(767\) 0.745048 0.0269021
\(768\) 44.6252 1.61027
\(769\) 23.8829 0.861239 0.430619 0.902534i \(-0.358295\pi\)
0.430619 + 0.902534i \(0.358295\pi\)
\(770\) 43.6057 1.57144
\(771\) −21.1141 −0.760407
\(772\) −17.0366 −0.613160
\(773\) −38.7478 −1.39366 −0.696831 0.717235i \(-0.745407\pi\)
−0.696831 + 0.717235i \(0.745407\pi\)
\(774\) 0.729346 0.0262158
\(775\) −3.10044 −0.111371
\(776\) −14.9362 −0.536179
\(777\) 19.7150 0.707273
\(778\) 39.8920 1.43020
\(779\) −13.0344 −0.467004
\(780\) −42.9269 −1.53703
\(781\) 44.6831 1.59889
\(782\) −38.8021 −1.38756
\(783\) −8.99855 −0.321582
\(784\) −4.90105 −0.175037
\(785\) 60.3401 2.15363
\(786\) −29.0161 −1.03497
\(787\) −44.7902 −1.59660 −0.798298 0.602262i \(-0.794266\pi\)
−0.798298 + 0.602262i \(0.794266\pi\)
\(788\) 0.925374 0.0329651
\(789\) 62.5725 2.22764
\(790\) −85.2583 −3.03336
\(791\) −1.58337 −0.0562981
\(792\) 10.9065 0.387547
\(793\) 7.82947 0.278033
\(794\) −48.6450 −1.72635
\(795\) 15.5637 0.551988
\(796\) 2.76004 0.0978271
\(797\) 26.0812 0.923842 0.461921 0.886921i \(-0.347160\pi\)
0.461921 + 0.886921i \(0.347160\pi\)
\(798\) −6.53303 −0.231267
\(799\) 29.2513 1.03484
\(800\) 84.7934 2.99790
\(801\) 28.6165 1.01111
\(802\) 2.19062 0.0773536
\(803\) 17.0946 0.603257
\(804\) 0.128211 0.00452166
\(805\) −13.9767 −0.492614
\(806\) 1.53449 0.0540501
\(807\) 29.2079 1.02817
\(808\) 10.2342 0.360037
\(809\) −4.53939 −0.159596 −0.0797982 0.996811i \(-0.525428\pi\)
−0.0797982 + 0.996811i \(0.525428\pi\)
\(810\) −87.3369 −3.06871
\(811\) 37.3724 1.31232 0.656161 0.754621i \(-0.272179\pi\)
0.656161 + 0.754621i \(0.272179\pi\)
\(812\) 3.83894 0.134720
\(813\) −4.36590 −0.153119
\(814\) −94.4220 −3.30949
\(815\) 72.0935 2.52532
\(816\) −68.0447 −2.38204
\(817\) −0.432686 −0.0151378
\(818\) −11.6650 −0.407856
\(819\) 5.58229 0.195061
\(820\) 43.4751 1.51821
\(821\) 11.0612 0.386039 0.193019 0.981195i \(-0.438172\pi\)
0.193019 + 0.981195i \(0.438172\pi\)
\(822\) −2.25702 −0.0787225
\(823\) 4.79314 0.167078 0.0835392 0.996504i \(-0.473378\pi\)
0.0835392 + 0.996504i \(0.473378\pi\)
\(824\) −14.7300 −0.513142
\(825\) 158.139 5.50570
\(826\) −0.378199 −0.0131592
\(827\) −3.83408 −0.133324 −0.0666620 0.997776i \(-0.521235\pi\)
−0.0666620 + 0.997776i \(0.521235\pi\)
\(828\) 6.70452 0.232998
\(829\) 6.48471 0.225223 0.112612 0.993639i \(-0.464078\pi\)
0.112612 + 0.993639i \(0.464078\pi\)
\(830\) 54.9048 1.90577
\(831\) −3.12878 −0.108536
\(832\) −6.81071 −0.236119
\(833\) 6.50418 0.225356
\(834\) −36.9919 −1.28092
\(835\) 46.9504 1.62478
\(836\) 12.4093 0.429184
\(837\) 0.724133 0.0250297
\(838\) 41.6413 1.43848
\(839\) 3.63196 0.125389 0.0626946 0.998033i \(-0.480031\pi\)
0.0626946 + 0.998033i \(0.480031\pi\)
\(840\) −11.3617 −0.392017
\(841\) −20.4719 −0.705926
\(842\) 34.8457 1.20086
\(843\) −2.09463 −0.0721430
\(844\) 16.4151 0.565031
\(845\) 0.582711 0.0200459
\(846\) −12.7439 −0.438143
\(847\) 20.5319 0.705485
\(848\) 8.37788 0.287698
\(849\) 37.2270 1.27763
\(850\) −156.227 −5.35855
\(851\) 30.2645 1.03745
\(852\) 22.3288 0.764971
\(853\) 52.4757 1.79673 0.898367 0.439245i \(-0.144754\pi\)
0.898367 + 0.439245i \(0.144754\pi\)
\(854\) −3.97437 −0.136000
\(855\) −11.1603 −0.381676
\(856\) −4.05409 −0.138566
\(857\) −49.3632 −1.68622 −0.843108 0.537744i \(-0.819277\pi\)
−0.843108 + 0.537744i \(0.819277\pi\)
\(858\) −78.2672 −2.67200
\(859\) −1.00000 −0.0341196
\(860\) 1.44319 0.0492124
\(861\) −16.5506 −0.564044
\(862\) −39.6350 −1.34998
\(863\) −2.40054 −0.0817154 −0.0408577 0.999165i \(-0.513009\pi\)
−0.0408577 + 0.999165i \(0.513009\pi\)
\(864\) −19.8042 −0.673752
\(865\) 42.0024 1.42813
\(866\) 18.1837 0.617908
\(867\) 54.0143 1.83442
\(868\) −0.308928 −0.0104857
\(869\) −61.6515 −2.09138
\(870\) 48.4071 1.64115
\(871\) 0.163873 0.00555262
\(872\) −19.7231 −0.667910
\(873\) −18.6294 −0.630509
\(874\) −10.0288 −0.339231
\(875\) −34.9470 −1.18142
\(876\) 8.54243 0.288622
\(877\) 46.4409 1.56820 0.784099 0.620636i \(-0.213126\pi\)
0.784099 + 0.620636i \(0.213126\pi\)
\(878\) −28.6681 −0.967500
\(879\) 32.7002 1.10295
\(880\) 117.387 3.95710
\(881\) −58.2585 −1.96278 −0.981389 0.192029i \(-0.938493\pi\)
−0.981389 + 0.192029i \(0.938493\pi\)
\(882\) −2.83366 −0.0954144
\(883\) −29.7742 −1.00198 −0.500991 0.865453i \(-0.667031\pi\)
−0.500991 + 0.865453i \(0.667031\pi\)
\(884\) 30.6658 1.03140
\(885\) −1.89136 −0.0635774
\(886\) 36.2077 1.21642
\(887\) −43.8807 −1.47337 −0.736684 0.676237i \(-0.763610\pi\)
−0.736684 + 0.676237i \(0.763610\pi\)
\(888\) 24.6022 0.825597
\(889\) −10.0100 −0.335724
\(890\) 142.774 4.78580
\(891\) −63.1546 −2.11576
\(892\) 23.0503 0.771780
\(893\) 7.56033 0.252997
\(894\) 37.7956 1.26407
\(895\) 45.4089 1.51785
\(896\) −9.39685 −0.313927
\(897\) 25.0865 0.837614
\(898\) 19.5666 0.652946
\(899\) −0.686278 −0.0228887
\(900\) 26.9941 0.899804
\(901\) −11.1183 −0.370404
\(902\) 79.2666 2.63929
\(903\) −0.549412 −0.0182833
\(904\) −1.97587 −0.0657165
\(905\) −70.5978 −2.34675
\(906\) 42.4925 1.41172
\(907\) −54.9548 −1.82474 −0.912372 0.409363i \(-0.865751\pi\)
−0.912372 + 0.409363i \(0.865751\pi\)
\(908\) 18.1025 0.600752
\(909\) 12.7647 0.423379
\(910\) 27.8513 0.923263
\(911\) −23.1905 −0.768337 −0.384168 0.923263i \(-0.625512\pi\)
−0.384168 + 0.923263i \(0.625512\pi\)
\(912\) −17.5869 −0.582361
\(913\) 39.7025 1.31396
\(914\) −45.9745 −1.52070
\(915\) −19.8757 −0.657071
\(916\) −36.5508 −1.20767
\(917\) 7.46642 0.246563
\(918\) 36.4881 1.20429
\(919\) −49.7989 −1.64271 −0.821356 0.570416i \(-0.806782\pi\)
−0.821356 + 0.570416i \(0.806782\pi\)
\(920\) −17.4414 −0.575025
\(921\) 39.0986 1.28834
\(922\) −32.0149 −1.05435
\(923\) 28.5395 0.939388
\(924\) 15.7569 0.518366
\(925\) 121.853 4.00649
\(926\) 66.4997 2.18532
\(927\) −18.3721 −0.603420
\(928\) 18.7689 0.616119
\(929\) 18.0642 0.592668 0.296334 0.955084i \(-0.404236\pi\)
0.296334 + 0.955084i \(0.404236\pi\)
\(930\) −3.89542 −0.127736
\(931\) 1.68108 0.0550951
\(932\) −1.45865 −0.0477798
\(933\) 63.3402 2.07366
\(934\) 13.7503 0.449925
\(935\) −155.784 −5.09468
\(936\) 6.96609 0.227694
\(937\) 28.9035 0.944235 0.472118 0.881536i \(-0.343490\pi\)
0.472118 + 0.881536i \(0.343490\pi\)
\(938\) −0.0831846 −0.00271607
\(939\) 33.8061 1.10322
\(940\) −25.2169 −0.822484
\(941\) 19.0503 0.621023 0.310512 0.950570i \(-0.399500\pi\)
0.310512 + 0.950570i \(0.399500\pi\)
\(942\) 54.9766 1.79124
\(943\) −25.4069 −0.827361
\(944\) −1.01811 −0.0331367
\(945\) 13.1432 0.427548
\(946\) 2.63132 0.0855517
\(947\) 48.9196 1.58967 0.794837 0.606822i \(-0.207556\pi\)
0.794837 + 0.606822i \(0.207556\pi\)
\(948\) −30.8081 −1.00060
\(949\) 10.9185 0.354429
\(950\) −40.3787 −1.31006
\(951\) −52.2157 −1.69321
\(952\) 8.11651 0.263058
\(953\) 2.60148 0.0842702 0.0421351 0.999112i \(-0.486584\pi\)
0.0421351 + 0.999112i \(0.486584\pi\)
\(954\) 4.84389 0.156827
\(955\) 16.6003 0.537174
\(956\) 6.82961 0.220885
\(957\) 35.0038 1.13151
\(958\) −71.4008 −2.30685
\(959\) 0.580775 0.0187542
\(960\) 17.2895 0.558017
\(961\) −30.9448 −0.998219
\(962\) −60.3081 −1.94441
\(963\) −5.05652 −0.162944
\(964\) 26.6599 0.858656
\(965\) 55.2782 1.77947
\(966\) −12.7343 −0.409721
\(967\) 25.6453 0.824698 0.412349 0.911026i \(-0.364709\pi\)
0.412349 + 0.911026i \(0.364709\pi\)
\(968\) 25.6216 0.823509
\(969\) 23.3396 0.749777
\(970\) −92.9463 −2.98433
\(971\) 1.26687 0.0406558 0.0203279 0.999793i \(-0.493529\pi\)
0.0203279 + 0.999793i \(0.493529\pi\)
\(972\) −19.4072 −0.622485
\(973\) 9.51874 0.305157
\(974\) −19.4343 −0.622716
\(975\) 101.005 3.23474
\(976\) −10.6990 −0.342467
\(977\) 37.9536 1.21424 0.607121 0.794609i \(-0.292324\pi\)
0.607121 + 0.794609i \(0.292324\pi\)
\(978\) 65.6852 2.10038
\(979\) 103.242 3.29963
\(980\) −5.60710 −0.179112
\(981\) −24.6000 −0.785416
\(982\) 22.7722 0.726691
\(983\) 0.385613 0.0122992 0.00614958 0.999981i \(-0.498043\pi\)
0.00614958 + 0.999981i \(0.498043\pi\)
\(984\) −20.6534 −0.658406
\(985\) −3.00254 −0.0956688
\(986\) −34.5807 −1.10127
\(987\) 9.59989 0.305568
\(988\) 7.92591 0.252157
\(989\) −0.843402 −0.0268186
\(990\) 67.8701 2.15705
\(991\) −47.3175 −1.50309 −0.751544 0.659682i \(-0.770691\pi\)
−0.751544 + 0.659682i \(0.770691\pi\)
\(992\) −1.51037 −0.0479544
\(993\) 21.9557 0.696744
\(994\) −14.4871 −0.459503
\(995\) −8.95544 −0.283906
\(996\) 19.8399 0.628651
\(997\) −38.9599 −1.23387 −0.616936 0.787013i \(-0.711626\pi\)
−0.616936 + 0.787013i \(0.711626\pi\)
\(998\) −20.3814 −0.645163
\(999\) −28.4597 −0.900424
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 \(a_p\))