Properties

Label 6013.2.a.e.1.9
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 1.9
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.40830 q^{2}\) \(-1.24102 q^{3}\) \(+3.79989 q^{4}\) \(+3.14441 q^{5}\) \(+2.98874 q^{6}\) \(+1.00000 q^{7}\) \(-4.33466 q^{8}\) \(-1.45987 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.40830 q^{2}\) \(-1.24102 q^{3}\) \(+3.79989 q^{4}\) \(+3.14441 q^{5}\) \(+2.98874 q^{6}\) \(+1.00000 q^{7}\) \(-4.33466 q^{8}\) \(-1.45987 q^{9}\) \(-7.57267 q^{10}\) \(-3.50851 q^{11}\) \(-4.71573 q^{12}\) \(+2.92121 q^{13}\) \(-2.40830 q^{14}\) \(-3.90228 q^{15}\) \(+2.83936 q^{16}\) \(+0.641897 q^{17}\) \(+3.51580 q^{18}\) \(+5.64090 q^{19}\) \(+11.9484 q^{20}\) \(-1.24102 q^{21}\) \(+8.44953 q^{22}\) \(-3.37263 q^{23}\) \(+5.37939 q^{24}\) \(+4.88733 q^{25}\) \(-7.03515 q^{26}\) \(+5.53479 q^{27}\) \(+3.79989 q^{28}\) \(+6.63940 q^{29}\) \(+9.39783 q^{30}\) \(-5.79156 q^{31}\) \(+1.83129 q^{32}\) \(+4.35413 q^{33}\) \(-1.54588 q^{34}\) \(+3.14441 q^{35}\) \(-5.54735 q^{36}\) \(-6.37868 q^{37}\) \(-13.5850 q^{38}\) \(-3.62528 q^{39}\) \(-13.6299 q^{40}\) \(-4.06048 q^{41}\) \(+2.98874 q^{42}\) \(+2.46362 q^{43}\) \(-13.3319 q^{44}\) \(-4.59044 q^{45}\) \(+8.12229 q^{46}\) \(+12.7009 q^{47}\) \(-3.52370 q^{48}\) \(+1.00000 q^{49}\) \(-11.7701 q^{50}\) \(-0.796607 q^{51}\) \(+11.1003 q^{52}\) \(-6.16844 q^{53}\) \(-13.3294 q^{54}\) \(-11.0322 q^{55}\) \(-4.33466 q^{56}\) \(-7.00047 q^{57}\) \(-15.9896 q^{58}\) \(+8.67673 q^{59}\) \(-14.8282 q^{60}\) \(-1.52967 q^{61}\) \(+13.9478 q^{62}\) \(-1.45987 q^{63}\) \(-10.0890 q^{64}\) \(+9.18550 q^{65}\) \(-10.4860 q^{66}\) \(-12.8166 q^{67}\) \(+2.43914 q^{68}\) \(+4.18550 q^{69}\) \(-7.57267 q^{70}\) \(+15.0394 q^{71}\) \(+6.32804 q^{72}\) \(-12.7326 q^{73}\) \(+15.3617 q^{74}\) \(-6.06526 q^{75}\) \(+21.4348 q^{76}\) \(-3.50851 q^{77}\) \(+8.73075 q^{78}\) \(-0.395850 q^{79}\) \(+8.92813 q^{80}\) \(-2.48916 q^{81}\) \(+9.77883 q^{82}\) \(-0.703021 q^{83}\) \(-4.71573 q^{84}\) \(+2.01839 q^{85}\) \(-5.93313 q^{86}\) \(-8.23962 q^{87}\) \(+15.2082 q^{88}\) \(+1.81800 q^{89}\) \(+11.0551 q^{90}\) \(+2.92121 q^{91}\) \(-12.8156 q^{92}\) \(+7.18744 q^{93}\) \(-30.5876 q^{94}\) \(+17.7373 q^{95}\) \(-2.27267 q^{96}\) \(-0.0756201 q^{97}\) \(-2.40830 q^{98}\) \(+5.12198 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40830 −1.70292 −0.851461 0.524418i \(-0.824283\pi\)
−0.851461 + 0.524418i \(0.824283\pi\)
\(3\) −1.24102 −0.716503 −0.358251 0.933625i \(-0.616627\pi\)
−0.358251 + 0.933625i \(0.616627\pi\)
\(4\) 3.79989 1.89994
\(5\) 3.14441 1.40622 0.703112 0.711079i \(-0.251793\pi\)
0.703112 + 0.711079i \(0.251793\pi\)
\(6\) 2.98874 1.22015
\(7\) 1.00000 0.377964
\(8\) −4.33466 −1.53253
\(9\) −1.45987 −0.486624
\(10\) −7.57267 −2.39469
\(11\) −3.50851 −1.05786 −0.528928 0.848667i \(-0.677406\pi\)
−0.528928 + 0.848667i \(0.677406\pi\)
\(12\) −4.71573 −1.36131
\(13\) 2.92121 0.810199 0.405100 0.914273i \(-0.367237\pi\)
0.405100 + 0.914273i \(0.367237\pi\)
\(14\) −2.40830 −0.643644
\(15\) −3.90228 −1.00756
\(16\) 2.83936 0.709841
\(17\) 0.641897 0.155683 0.0778415 0.996966i \(-0.475197\pi\)
0.0778415 + 0.996966i \(0.475197\pi\)
\(18\) 3.51580 0.828682
\(19\) 5.64090 1.29411 0.647056 0.762443i \(-0.276000\pi\)
0.647056 + 0.762443i \(0.276000\pi\)
\(20\) 11.9484 2.67174
\(21\) −1.24102 −0.270813
\(22\) 8.44953 1.80145
\(23\) −3.37263 −0.703242 −0.351621 0.936142i \(-0.614369\pi\)
−0.351621 + 0.936142i \(0.614369\pi\)
\(24\) 5.37939 1.09806
\(25\) 4.88733 0.977465
\(26\) −7.03515 −1.37971
\(27\) 5.53479 1.06517
\(28\) 3.79989 0.718111
\(29\) 6.63940 1.23291 0.616453 0.787392i \(-0.288569\pi\)
0.616453 + 0.787392i \(0.288569\pi\)
\(30\) 9.39783 1.71580
\(31\) −5.79156 −1.04019 −0.520097 0.854107i \(-0.674104\pi\)
−0.520097 + 0.854107i \(0.674104\pi\)
\(32\) 1.83129 0.323730
\(33\) 4.35413 0.757957
\(34\) −1.54588 −0.265116
\(35\) 3.14441 0.531503
\(36\) −5.54735 −0.924558
\(37\) −6.37868 −1.04865 −0.524324 0.851519i \(-0.675682\pi\)
−0.524324 + 0.851519i \(0.675682\pi\)
\(38\) −13.5850 −2.20377
\(39\) −3.62528 −0.580510
\(40\) −13.6299 −2.15508
\(41\) −4.06048 −0.634140 −0.317070 0.948402i \(-0.602699\pi\)
−0.317070 + 0.948402i \(0.602699\pi\)
\(42\) 2.98874 0.461173
\(43\) 2.46362 0.375699 0.187850 0.982198i \(-0.439848\pi\)
0.187850 + 0.982198i \(0.439848\pi\)
\(44\) −13.3319 −2.00987
\(45\) −4.59044 −0.684302
\(46\) 8.12229 1.19757
\(47\) 12.7009 1.85262 0.926311 0.376759i \(-0.122962\pi\)
0.926311 + 0.376759i \(0.122962\pi\)
\(48\) −3.52370 −0.508603
\(49\) 1.00000 0.142857
\(50\) −11.7701 −1.66455
\(51\) −0.796607 −0.111547
\(52\) 11.1003 1.53933
\(53\) −6.16844 −0.847301 −0.423650 0.905826i \(-0.639252\pi\)
−0.423650 + 0.905826i \(0.639252\pi\)
\(54\) −13.3294 −1.81390
\(55\) −11.0322 −1.48758
\(56\) −4.33466 −0.579243
\(57\) −7.00047 −0.927235
\(58\) −15.9896 −2.09954
\(59\) 8.67673 1.12961 0.564807 0.825223i \(-0.308951\pi\)
0.564807 + 0.825223i \(0.308951\pi\)
\(60\) −14.8282 −1.91431
\(61\) −1.52967 −0.195854 −0.0979271 0.995194i \(-0.531221\pi\)
−0.0979271 + 0.995194i \(0.531221\pi\)
\(62\) 13.9478 1.77137
\(63\) −1.45987 −0.183927
\(64\) −10.0890 −1.26113
\(65\) 9.18550 1.13932
\(66\) −10.4860 −1.29074
\(67\) −12.8166 −1.56580 −0.782898 0.622151i \(-0.786259\pi\)
−0.782898 + 0.622151i \(0.786259\pi\)
\(68\) 2.43914 0.295789
\(69\) 4.18550 0.503875
\(70\) −7.57267 −0.905107
\(71\) 15.0394 1.78484 0.892421 0.451203i \(-0.149005\pi\)
0.892421 + 0.451203i \(0.149005\pi\)
\(72\) 6.32804 0.745767
\(73\) −12.7326 −1.49024 −0.745118 0.666932i \(-0.767607\pi\)
−0.745118 + 0.666932i \(0.767607\pi\)
\(74\) 15.3617 1.78577
\(75\) −6.06526 −0.700356
\(76\) 21.4348 2.45874
\(77\) −3.50851 −0.399832
\(78\) 8.73075 0.988563
\(79\) −0.395850 −0.0445367 −0.0222683 0.999752i \(-0.507089\pi\)
−0.0222683 + 0.999752i \(0.507089\pi\)
\(80\) 8.92813 0.998195
\(81\) −2.48916 −0.276573
\(82\) 9.77883 1.07989
\(83\) −0.703021 −0.0771666 −0.0385833 0.999255i \(-0.512284\pi\)
−0.0385833 + 0.999255i \(0.512284\pi\)
\(84\) −4.71573 −0.514528
\(85\) 2.01839 0.218925
\(86\) −5.93313 −0.639786
\(87\) −8.23962 −0.883380
\(88\) 15.2082 1.62120
\(89\) 1.81800 0.192708 0.0963540 0.995347i \(-0.469282\pi\)
0.0963540 + 0.995347i \(0.469282\pi\)
\(90\) 11.0551 1.16531
\(91\) 2.92121 0.306226
\(92\) −12.8156 −1.33612
\(93\) 7.18744 0.745302
\(94\) −30.5876 −3.15487
\(95\) 17.7373 1.81981
\(96\) −2.27267 −0.231953
\(97\) −0.0756201 −0.00767806 −0.00383903 0.999993i \(-0.501222\pi\)
−0.00383903 + 0.999993i \(0.501222\pi\)
\(98\) −2.40830 −0.243275
\(99\) 5.12198 0.514778
\(100\) 18.5713 1.85713
\(101\) −0.691745 −0.0688312 −0.0344156 0.999408i \(-0.510957\pi\)
−0.0344156 + 0.999408i \(0.510957\pi\)
\(102\) 1.91846 0.189956
\(103\) −5.98162 −0.589386 −0.294693 0.955592i \(-0.595217\pi\)
−0.294693 + 0.955592i \(0.595217\pi\)
\(104\) −12.6625 −1.24166
\(105\) −3.90228 −0.380823
\(106\) 14.8554 1.44289
\(107\) 4.40987 0.426318 0.213159 0.977018i \(-0.431625\pi\)
0.213159 + 0.977018i \(0.431625\pi\)
\(108\) 21.0316 2.02376
\(109\) 16.8904 1.61781 0.808905 0.587940i \(-0.200061\pi\)
0.808905 + 0.587940i \(0.200061\pi\)
\(110\) 26.5688 2.53324
\(111\) 7.91606 0.751359
\(112\) 2.83936 0.268295
\(113\) 3.78265 0.355842 0.177921 0.984045i \(-0.443063\pi\)
0.177921 + 0.984045i \(0.443063\pi\)
\(114\) 16.8592 1.57901
\(115\) −10.6049 −0.988916
\(116\) 25.2290 2.34245
\(117\) −4.26460 −0.394262
\(118\) −20.8961 −1.92364
\(119\) 0.641897 0.0588426
\(120\) 16.9150 1.54412
\(121\) 1.30965 0.119059
\(122\) 3.68390 0.333525
\(123\) 5.03913 0.454363
\(124\) −22.0073 −1.97631
\(125\) −0.354296 −0.0316892
\(126\) 3.51580 0.313213
\(127\) 10.8852 0.965902 0.482951 0.875647i \(-0.339565\pi\)
0.482951 + 0.875647i \(0.339565\pi\)
\(128\) 20.6347 1.82387
\(129\) −3.05740 −0.269189
\(130\) −22.1214 −1.94017
\(131\) 13.2945 1.16155 0.580774 0.814065i \(-0.302750\pi\)
0.580774 + 0.814065i \(0.302750\pi\)
\(132\) 16.5452 1.44007
\(133\) 5.64090 0.489128
\(134\) 30.8661 2.66643
\(135\) 17.4036 1.49787
\(136\) −2.78240 −0.238589
\(137\) 19.2893 1.64799 0.823996 0.566595i \(-0.191740\pi\)
0.823996 + 0.566595i \(0.191740\pi\)
\(138\) −10.0799 −0.858060
\(139\) 21.1228 1.79161 0.895804 0.444449i \(-0.146600\pi\)
0.895804 + 0.444449i \(0.146600\pi\)
\(140\) 11.9484 1.00982
\(141\) −15.7621 −1.32741
\(142\) −36.2192 −3.03945
\(143\) −10.2491 −0.857074
\(144\) −4.14511 −0.345425
\(145\) 20.8770 1.73374
\(146\) 30.6638 2.53776
\(147\) −1.24102 −0.102358
\(148\) −24.2383 −1.99237
\(149\) −20.4229 −1.67311 −0.836557 0.547881i \(-0.815435\pi\)
−0.836557 + 0.547881i \(0.815435\pi\)
\(150\) 14.6069 1.19265
\(151\) 13.3098 1.08313 0.541567 0.840657i \(-0.317831\pi\)
0.541567 + 0.840657i \(0.317831\pi\)
\(152\) −24.4514 −1.98327
\(153\) −0.937087 −0.0757590
\(154\) 8.44953 0.680883
\(155\) −18.2110 −1.46275
\(156\) −13.7757 −1.10294
\(157\) 21.4641 1.71302 0.856511 0.516129i \(-0.172627\pi\)
0.856511 + 0.516129i \(0.172627\pi\)
\(158\) 0.953325 0.0758424
\(159\) 7.65516 0.607093
\(160\) 5.75833 0.455236
\(161\) −3.37263 −0.265801
\(162\) 5.99463 0.470983
\(163\) 8.57324 0.671508 0.335754 0.941950i \(-0.391009\pi\)
0.335754 + 0.941950i \(0.391009\pi\)
\(164\) −15.4294 −1.20483
\(165\) 13.6912 1.06586
\(166\) 1.69308 0.131409
\(167\) 7.54532 0.583874 0.291937 0.956438i \(-0.405700\pi\)
0.291937 + 0.956438i \(0.405700\pi\)
\(168\) 5.37939 0.415029
\(169\) −4.46651 −0.343578
\(170\) −4.86088 −0.372812
\(171\) −8.23499 −0.629746
\(172\) 9.36149 0.713807
\(173\) −4.75466 −0.361490 −0.180745 0.983530i \(-0.557851\pi\)
−0.180745 + 0.983530i \(0.557851\pi\)
\(174\) 19.8434 1.50433
\(175\) 4.88733 0.369447
\(176\) −9.96194 −0.750909
\(177\) −10.7680 −0.809371
\(178\) −4.37829 −0.328167
\(179\) −23.6130 −1.76492 −0.882459 0.470390i \(-0.844113\pi\)
−0.882459 + 0.470390i \(0.844113\pi\)
\(180\) −17.4431 −1.30013
\(181\) −12.2622 −0.911446 −0.455723 0.890122i \(-0.650619\pi\)
−0.455723 + 0.890122i \(0.650619\pi\)
\(182\) −7.03515 −0.521480
\(183\) 1.89835 0.140330
\(184\) 14.6192 1.07774
\(185\) −20.0572 −1.47463
\(186\) −17.3095 −1.26919
\(187\) −2.25210 −0.164690
\(188\) 48.2621 3.51988
\(189\) 5.53479 0.402596
\(190\) −42.7167 −3.09900
\(191\) −2.86748 −0.207484 −0.103742 0.994604i \(-0.533082\pi\)
−0.103742 + 0.994604i \(0.533082\pi\)
\(192\) 12.5207 0.903601
\(193\) −7.41051 −0.533420 −0.266710 0.963777i \(-0.585937\pi\)
−0.266710 + 0.963777i \(0.585937\pi\)
\(194\) 0.182116 0.0130751
\(195\) −11.3994 −0.816327
\(196\) 3.79989 0.271420
\(197\) 17.9053 1.27570 0.637848 0.770162i \(-0.279825\pi\)
0.637848 + 0.770162i \(0.279825\pi\)
\(198\) −12.3352 −0.876627
\(199\) −11.1803 −0.792551 −0.396276 0.918132i \(-0.629698\pi\)
−0.396276 + 0.918132i \(0.629698\pi\)
\(200\) −21.1849 −1.49800
\(201\) 15.9056 1.12190
\(202\) 1.66593 0.117214
\(203\) 6.63940 0.465995
\(204\) −3.02701 −0.211933
\(205\) −12.7678 −0.891743
\(206\) 14.4055 1.00368
\(207\) 4.92361 0.342214
\(208\) 8.29439 0.575112
\(209\) −19.7912 −1.36898
\(210\) 9.39783 0.648512
\(211\) −7.88892 −0.543096 −0.271548 0.962425i \(-0.587535\pi\)
−0.271548 + 0.962425i \(0.587535\pi\)
\(212\) −23.4394 −1.60982
\(213\) −18.6641 −1.27884
\(214\) −10.6203 −0.725987
\(215\) 7.74665 0.528317
\(216\) −23.9914 −1.63241
\(217\) −5.79156 −0.393157
\(218\) −40.6771 −2.75500
\(219\) 15.8014 1.06776
\(220\) −41.9211 −2.82632
\(221\) 1.87512 0.126134
\(222\) −19.0642 −1.27951
\(223\) −28.1454 −1.88475 −0.942377 0.334553i \(-0.891415\pi\)
−0.942377 + 0.334553i \(0.891415\pi\)
\(224\) 1.83129 0.122358
\(225\) −7.13487 −0.475658
\(226\) −9.10973 −0.605970
\(227\) 14.4722 0.960555 0.480277 0.877117i \(-0.340536\pi\)
0.480277 + 0.877117i \(0.340536\pi\)
\(228\) −26.6010 −1.76169
\(229\) −17.8283 −1.17813 −0.589063 0.808087i \(-0.700503\pi\)
−0.589063 + 0.808087i \(0.700503\pi\)
\(230\) 25.5398 1.68405
\(231\) 4.35413 0.286481
\(232\) −28.7795 −1.88947
\(233\) 22.8441 1.49657 0.748283 0.663379i \(-0.230878\pi\)
0.748283 + 0.663379i \(0.230878\pi\)
\(234\) 10.2704 0.671398
\(235\) 39.9370 2.60520
\(236\) 32.9706 2.14620
\(237\) 0.491258 0.0319106
\(238\) −1.54588 −0.100204
\(239\) −5.62397 −0.363785 −0.181892 0.983318i \(-0.558222\pi\)
−0.181892 + 0.983318i \(0.558222\pi\)
\(240\) −11.0800 −0.715209
\(241\) −3.00778 −0.193748 −0.0968742 0.995297i \(-0.530884\pi\)
−0.0968742 + 0.995297i \(0.530884\pi\)
\(242\) −3.15402 −0.202748
\(243\) −13.5153 −0.867004
\(244\) −5.81258 −0.372112
\(245\) 3.14441 0.200889
\(246\) −12.1357 −0.773745
\(247\) 16.4783 1.04849
\(248\) 25.1044 1.59413
\(249\) 0.872462 0.0552900
\(250\) 0.853250 0.0539643
\(251\) 14.6369 0.923873 0.461936 0.886913i \(-0.347155\pi\)
0.461936 + 0.886913i \(0.347155\pi\)
\(252\) −5.54735 −0.349450
\(253\) 11.8329 0.743929
\(254\) −26.2147 −1.64486
\(255\) −2.50486 −0.156860
\(256\) −29.5165 −1.84478
\(257\) 18.0883 1.12832 0.564158 0.825667i \(-0.309201\pi\)
0.564158 + 0.825667i \(0.309201\pi\)
\(258\) 7.36313 0.458409
\(259\) −6.37868 −0.396352
\(260\) 34.9039 2.16465
\(261\) −9.69267 −0.599961
\(262\) −32.0172 −1.97803
\(263\) 10.8821 0.671022 0.335511 0.942036i \(-0.391091\pi\)
0.335511 + 0.942036i \(0.391091\pi\)
\(264\) −18.8737 −1.16159
\(265\) −19.3961 −1.19149
\(266\) −13.5850 −0.832947
\(267\) −2.25618 −0.138076
\(268\) −48.7016 −2.97492
\(269\) −19.3444 −1.17945 −0.589725 0.807604i \(-0.700764\pi\)
−0.589725 + 0.807604i \(0.700764\pi\)
\(270\) −41.9131 −2.55075
\(271\) 0.418926 0.0254479 0.0127240 0.999919i \(-0.495950\pi\)
0.0127240 + 0.999919i \(0.495950\pi\)
\(272\) 1.82258 0.110510
\(273\) −3.62528 −0.219412
\(274\) −46.4542 −2.80640
\(275\) −17.1472 −1.03402
\(276\) 15.9044 0.957334
\(277\) 20.8779 1.25443 0.627215 0.778846i \(-0.284195\pi\)
0.627215 + 0.778846i \(0.284195\pi\)
\(278\) −50.8698 −3.05097
\(279\) 8.45493 0.506184
\(280\) −13.6299 −0.814545
\(281\) −7.15228 −0.426669 −0.213335 0.976979i \(-0.568432\pi\)
−0.213335 + 0.976979i \(0.568432\pi\)
\(282\) 37.9598 2.26047
\(283\) 1.83135 0.108862 0.0544311 0.998518i \(-0.482665\pi\)
0.0544311 + 0.998518i \(0.482665\pi\)
\(284\) 57.1478 3.39110
\(285\) −22.0124 −1.30390
\(286\) 24.6829 1.45953
\(287\) −4.06048 −0.239682
\(288\) −2.67345 −0.157535
\(289\) −16.5880 −0.975763
\(290\) −50.2780 −2.95243
\(291\) 0.0938460 0.00550135
\(292\) −48.3824 −2.83136
\(293\) −5.54156 −0.323742 −0.161871 0.986812i \(-0.551753\pi\)
−0.161871 + 0.986812i \(0.551753\pi\)
\(294\) 2.98874 0.174307
\(295\) 27.2832 1.58849
\(296\) 27.6494 1.60709
\(297\) −19.4189 −1.12680
\(298\) 49.1845 2.84918
\(299\) −9.85218 −0.569766
\(300\) −23.0473 −1.33064
\(301\) 2.46362 0.142001
\(302\) −32.0539 −1.84449
\(303\) 0.858468 0.0493177
\(304\) 16.0166 0.918613
\(305\) −4.80991 −0.275415
\(306\) 2.25678 0.129012
\(307\) 1.34605 0.0768232 0.0384116 0.999262i \(-0.487770\pi\)
0.0384116 + 0.999262i \(0.487770\pi\)
\(308\) −13.3319 −0.759658
\(309\) 7.42330 0.422297
\(310\) 43.8576 2.49094
\(311\) 6.35151 0.360161 0.180081 0.983652i \(-0.442364\pi\)
0.180081 + 0.983652i \(0.442364\pi\)
\(312\) 15.7144 0.889650
\(313\) −14.2425 −0.805033 −0.402517 0.915413i \(-0.631864\pi\)
−0.402517 + 0.915413i \(0.631864\pi\)
\(314\) −51.6919 −2.91714
\(315\) −4.59044 −0.258642
\(316\) −1.50419 −0.0846171
\(317\) −25.4749 −1.43081 −0.715407 0.698708i \(-0.753759\pi\)
−0.715407 + 0.698708i \(0.753759\pi\)
\(318\) −18.4359 −1.03383
\(319\) −23.2944 −1.30424
\(320\) −31.7240 −1.77343
\(321\) −5.47273 −0.305458
\(322\) 8.12229 0.452638
\(323\) 3.62088 0.201471
\(324\) −9.45853 −0.525474
\(325\) 14.2769 0.791941
\(326\) −20.6469 −1.14353
\(327\) −20.9613 −1.15916
\(328\) 17.6008 0.971841
\(329\) 12.7009 0.700225
\(330\) −32.9724 −1.81507
\(331\) 25.8934 1.42323 0.711614 0.702571i \(-0.247964\pi\)
0.711614 + 0.702571i \(0.247964\pi\)
\(332\) −2.67140 −0.146612
\(333\) 9.31205 0.510297
\(334\) −18.1714 −0.994292
\(335\) −40.3006 −2.20186
\(336\) −3.52370 −0.192234
\(337\) 16.2948 0.887633 0.443817 0.896118i \(-0.353624\pi\)
0.443817 + 0.896118i \(0.353624\pi\)
\(338\) 10.7567 0.585086
\(339\) −4.69434 −0.254961
\(340\) 7.66965 0.415945
\(341\) 20.3198 1.10038
\(342\) 19.8323 1.07241
\(343\) 1.00000 0.0539949
\(344\) −10.6790 −0.575771
\(345\) 13.1609 0.708561
\(346\) 11.4506 0.615589
\(347\) 9.72335 0.521977 0.260988 0.965342i \(-0.415952\pi\)
0.260988 + 0.965342i \(0.415952\pi\)
\(348\) −31.3096 −1.67837
\(349\) −17.0947 −0.915061 −0.457530 0.889194i \(-0.651266\pi\)
−0.457530 + 0.889194i \(0.651266\pi\)
\(350\) −11.7701 −0.629139
\(351\) 16.1683 0.863000
\(352\) −6.42510 −0.342459
\(353\) −13.2400 −0.704694 −0.352347 0.935869i \(-0.614616\pi\)
−0.352347 + 0.935869i \(0.614616\pi\)
\(354\) 25.9325 1.37830
\(355\) 47.2899 2.50989
\(356\) 6.90821 0.366134
\(357\) −0.796607 −0.0421609
\(358\) 56.8670 3.00552
\(359\) 22.3458 1.17937 0.589684 0.807634i \(-0.299252\pi\)
0.589684 + 0.807634i \(0.299252\pi\)
\(360\) 19.8980 1.04872
\(361\) 12.8198 0.674726
\(362\) 29.5311 1.55212
\(363\) −1.62530 −0.0853062
\(364\) 11.1003 0.581813
\(365\) −40.0365 −2.09561
\(366\) −4.57179 −0.238971
\(367\) −26.5224 −1.38446 −0.692228 0.721679i \(-0.743371\pi\)
−0.692228 + 0.721679i \(0.743371\pi\)
\(368\) −9.57612 −0.499190
\(369\) 5.92778 0.308588
\(370\) 48.3036 2.51119
\(371\) −6.16844 −0.320250
\(372\) 27.3114 1.41603
\(373\) 29.6427 1.53484 0.767420 0.641145i \(-0.221540\pi\)
0.767420 + 0.641145i \(0.221540\pi\)
\(374\) 5.42373 0.280454
\(375\) 0.439689 0.0227054
\(376\) −55.0542 −2.83920
\(377\) 19.3951 0.998899
\(378\) −13.3294 −0.685590
\(379\) 29.9541 1.53864 0.769319 0.638865i \(-0.220596\pi\)
0.769319 + 0.638865i \(0.220596\pi\)
\(380\) 67.3998 3.45754
\(381\) −13.5087 −0.692072
\(382\) 6.90575 0.353329
\(383\) 36.9983 1.89052 0.945262 0.326313i \(-0.105806\pi\)
0.945262 + 0.326313i \(0.105806\pi\)
\(384\) −25.6081 −1.30681
\(385\) −11.0322 −0.562253
\(386\) 17.8467 0.908373
\(387\) −3.59658 −0.182824
\(388\) −0.287348 −0.0145879
\(389\) −29.2477 −1.48292 −0.741460 0.670997i \(-0.765866\pi\)
−0.741460 + 0.670997i \(0.765866\pi\)
\(390\) 27.4531 1.39014
\(391\) −2.16488 −0.109483
\(392\) −4.33466 −0.218933
\(393\) −16.4988 −0.832253
\(394\) −43.1211 −2.17241
\(395\) −1.24472 −0.0626285
\(396\) 19.4629 0.978049
\(397\) 23.2999 1.16939 0.584694 0.811254i \(-0.301214\pi\)
0.584694 + 0.811254i \(0.301214\pi\)
\(398\) 26.9255 1.34965
\(399\) −7.00047 −0.350462
\(400\) 13.8769 0.693844
\(401\) −22.0448 −1.10086 −0.550431 0.834881i \(-0.685537\pi\)
−0.550431 + 0.834881i \(0.685537\pi\)
\(402\) −38.3054 −1.91050
\(403\) −16.9184 −0.842765
\(404\) −2.62855 −0.130775
\(405\) −7.82694 −0.388924
\(406\) −15.9896 −0.793552
\(407\) 22.3797 1.10932
\(408\) 3.45302 0.170950
\(409\) 4.26103 0.210695 0.105347 0.994435i \(-0.466405\pi\)
0.105347 + 0.994435i \(0.466405\pi\)
\(410\) 30.7487 1.51857
\(411\) −23.9383 −1.18079
\(412\) −22.7295 −1.11980
\(413\) 8.67673 0.426954
\(414\) −11.8575 −0.582764
\(415\) −2.21059 −0.108513
\(416\) 5.34959 0.262285
\(417\) −26.2137 −1.28369
\(418\) 47.6630 2.33127
\(419\) 28.2856 1.38184 0.690920 0.722931i \(-0.257206\pi\)
0.690920 + 0.722931i \(0.257206\pi\)
\(420\) −14.8282 −0.723542
\(421\) −10.5650 −0.514908 −0.257454 0.966290i \(-0.582884\pi\)
−0.257454 + 0.966290i \(0.582884\pi\)
\(422\) 18.9988 0.924849
\(423\) −18.5417 −0.901530
\(424\) 26.7381 1.29852
\(425\) 3.13716 0.152175
\(426\) 44.9487 2.17777
\(427\) −1.52967 −0.0740260
\(428\) 16.7570 0.809980
\(429\) 12.7193 0.614096
\(430\) −18.6562 −0.899683
\(431\) 8.92627 0.429963 0.214982 0.976618i \(-0.431031\pi\)
0.214982 + 0.976618i \(0.431031\pi\)
\(432\) 15.7153 0.756101
\(433\) 11.9748 0.575470 0.287735 0.957710i \(-0.407098\pi\)
0.287735 + 0.957710i \(0.407098\pi\)
\(434\) 13.9478 0.669515
\(435\) −25.9088 −1.24223
\(436\) 64.1817 3.07375
\(437\) −19.0247 −0.910074
\(438\) −38.0544 −1.81831
\(439\) −10.4685 −0.499634 −0.249817 0.968293i \(-0.580371\pi\)
−0.249817 + 0.968293i \(0.580371\pi\)
\(440\) 47.8208 2.27977
\(441\) −1.45987 −0.0695177
\(442\) −4.51584 −0.214797
\(443\) 31.5564 1.49929 0.749645 0.661841i \(-0.230224\pi\)
0.749645 + 0.661841i \(0.230224\pi\)
\(444\) 30.0801 1.42754
\(445\) 5.71655 0.270991
\(446\) 67.7824 3.20959
\(447\) 25.3453 1.19879
\(448\) −10.0890 −0.476661
\(449\) 7.42773 0.350536 0.175268 0.984521i \(-0.443921\pi\)
0.175268 + 0.984521i \(0.443921\pi\)
\(450\) 17.1829 0.810008
\(451\) 14.2462 0.670829
\(452\) 14.3736 0.676079
\(453\) −16.5177 −0.776069
\(454\) −34.8534 −1.63575
\(455\) 9.18550 0.430623
\(456\) 30.3446 1.42102
\(457\) 29.4311 1.37673 0.688364 0.725365i \(-0.258329\pi\)
0.688364 + 0.725365i \(0.258329\pi\)
\(458\) 42.9358 2.00626
\(459\) 3.55276 0.165829
\(460\) −40.2976 −1.87888
\(461\) −24.3599 −1.13455 −0.567277 0.823527i \(-0.692003\pi\)
−0.567277 + 0.823527i \(0.692003\pi\)
\(462\) −10.4860 −0.487854
\(463\) 17.4460 0.810784 0.405392 0.914143i \(-0.367135\pi\)
0.405392 + 0.914143i \(0.367135\pi\)
\(464\) 18.8517 0.875167
\(465\) 22.6003 1.04806
\(466\) −55.0153 −2.54854
\(467\) −12.7661 −0.590744 −0.295372 0.955382i \(-0.595444\pi\)
−0.295372 + 0.955382i \(0.595444\pi\)
\(468\) −16.2050 −0.749076
\(469\) −12.8166 −0.591815
\(470\) −96.1800 −4.43645
\(471\) −26.6374 −1.22739
\(472\) −37.6106 −1.73117
\(473\) −8.64365 −0.397436
\(474\) −1.18309 −0.0543413
\(475\) 27.5689 1.26495
\(476\) 2.43914 0.111798
\(477\) 9.00514 0.412317
\(478\) 13.5442 0.619497
\(479\) 24.8401 1.13497 0.567487 0.823382i \(-0.307916\pi\)
0.567487 + 0.823382i \(0.307916\pi\)
\(480\) −7.14620 −0.326178
\(481\) −18.6335 −0.849614
\(482\) 7.24363 0.329938
\(483\) 4.18550 0.190447
\(484\) 4.97652 0.226205
\(485\) −0.237781 −0.0107971
\(486\) 32.5487 1.47644
\(487\) −0.252386 −0.0114367 −0.00571836 0.999984i \(-0.501820\pi\)
−0.00571836 + 0.999984i \(0.501820\pi\)
\(488\) 6.63060 0.300153
\(489\) −10.6396 −0.481137
\(490\) −7.57267 −0.342098
\(491\) −1.26049 −0.0568853 −0.0284427 0.999595i \(-0.509055\pi\)
−0.0284427 + 0.999595i \(0.509055\pi\)
\(492\) 19.1481 0.863264
\(493\) 4.26181 0.191942
\(494\) −39.6846 −1.78549
\(495\) 16.1056 0.723893
\(496\) −16.4443 −0.738373
\(497\) 15.0394 0.674607
\(498\) −2.10115 −0.0941546
\(499\) 30.5208 1.36630 0.683149 0.730279i \(-0.260610\pi\)
0.683149 + 0.730279i \(0.260610\pi\)
\(500\) −1.34629 −0.0602077
\(501\) −9.36388 −0.418347
\(502\) −35.2500 −1.57328
\(503\) 4.80935 0.214438 0.107219 0.994235i \(-0.465805\pi\)
0.107219 + 0.994235i \(0.465805\pi\)
\(504\) 6.32804 0.281873
\(505\) −2.17513 −0.0967920
\(506\) −28.4971 −1.26685
\(507\) 5.54302 0.246174
\(508\) 41.3624 1.83516
\(509\) −31.1781 −1.38195 −0.690973 0.722881i \(-0.742818\pi\)
−0.690973 + 0.722881i \(0.742818\pi\)
\(510\) 6.03244 0.267121
\(511\) −12.7326 −0.563256
\(512\) 29.8150 1.31765
\(513\) 31.2212 1.37845
\(514\) −43.5619 −1.92143
\(515\) −18.8087 −0.828809
\(516\) −11.6178 −0.511445
\(517\) −44.5614 −1.95981
\(518\) 15.3617 0.674956
\(519\) 5.90062 0.259009
\(520\) −39.8160 −1.74605
\(521\) 21.9529 0.961775 0.480887 0.876782i \(-0.340315\pi\)
0.480887 + 0.876782i \(0.340315\pi\)
\(522\) 23.3428 1.02169
\(523\) −22.6338 −0.989707 −0.494854 0.868976i \(-0.664778\pi\)
−0.494854 + 0.868976i \(0.664778\pi\)
\(524\) 50.5177 2.20688
\(525\) −6.06526 −0.264710
\(526\) −26.2074 −1.14270
\(527\) −3.71759 −0.161941
\(528\) 12.3630 0.538028
\(529\) −11.6254 −0.505451
\(530\) 46.7116 2.02902
\(531\) −12.6669 −0.549697
\(532\) 21.4348 0.929316
\(533\) −11.8615 −0.513780
\(534\) 5.43354 0.235132
\(535\) 13.8664 0.599499
\(536\) 55.5555 2.39963
\(537\) 29.3042 1.26457
\(538\) 46.5871 2.00851
\(539\) −3.50851 −0.151122
\(540\) 66.1319 2.84586
\(541\) 35.6859 1.53426 0.767128 0.641494i \(-0.221685\pi\)
0.767128 + 0.641494i \(0.221685\pi\)
\(542\) −1.00890 −0.0433358
\(543\) 15.2177 0.653053
\(544\) 1.17550 0.0503992
\(545\) 53.1105 2.27500
\(546\) 8.73075 0.373642
\(547\) 26.1133 1.11652 0.558262 0.829665i \(-0.311468\pi\)
0.558262 + 0.829665i \(0.311468\pi\)
\(548\) 73.2970 3.13109
\(549\) 2.23312 0.0953074
\(550\) 41.2956 1.76085
\(551\) 37.4522 1.59552
\(552\) −18.1427 −0.772205
\(553\) −0.395850 −0.0168333
\(554\) −50.2801 −2.13619
\(555\) 24.8914 1.05658
\(556\) 80.2641 3.40395
\(557\) 1.45276 0.0615556 0.0307778 0.999526i \(-0.490202\pi\)
0.0307778 + 0.999526i \(0.490202\pi\)
\(558\) −20.3620 −0.861991
\(559\) 7.19677 0.304391
\(560\) 8.92813 0.377282
\(561\) 2.79490 0.118001
\(562\) 17.2248 0.726584
\(563\) −3.80149 −0.160214 −0.0801068 0.996786i \(-0.525526\pi\)
−0.0801068 + 0.996786i \(0.525526\pi\)
\(564\) −59.8942 −2.52200
\(565\) 11.8942 0.500393
\(566\) −4.41042 −0.185384
\(567\) −2.48916 −0.104535
\(568\) −65.1904 −2.73533
\(569\) 34.3658 1.44069 0.720345 0.693616i \(-0.243984\pi\)
0.720345 + 0.693616i \(0.243984\pi\)
\(570\) 53.0123 2.22044
\(571\) −28.0427 −1.17355 −0.586775 0.809750i \(-0.699603\pi\)
−0.586775 + 0.809750i \(0.699603\pi\)
\(572\) −38.9455 −1.62839
\(573\) 3.55860 0.148663
\(574\) 9.77883 0.408161
\(575\) −16.4831 −0.687395
\(576\) 14.7287 0.613694
\(577\) 38.0673 1.58476 0.792381 0.610027i \(-0.208841\pi\)
0.792381 + 0.610027i \(0.208841\pi\)
\(578\) 39.9487 1.66165
\(579\) 9.19659 0.382197
\(580\) 79.3303 3.29401
\(581\) −0.703021 −0.0291662
\(582\) −0.226009 −0.00936837
\(583\) 21.6421 0.896322
\(584\) 55.1914 2.28384
\(585\) −13.4096 −0.554421
\(586\) 13.3457 0.551307
\(587\) 24.0554 0.992873 0.496436 0.868073i \(-0.334642\pi\)
0.496436 + 0.868073i \(0.334642\pi\)
\(588\) −4.71573 −0.194473
\(589\) −32.6696 −1.34613
\(590\) −65.7060 −2.70507
\(591\) −22.2208 −0.914040
\(592\) −18.1114 −0.744373
\(593\) 13.6054 0.558707 0.279353 0.960188i \(-0.409880\pi\)
0.279353 + 0.960188i \(0.409880\pi\)
\(594\) 46.7663 1.91885
\(595\) 2.01839 0.0827459
\(596\) −77.6049 −3.17882
\(597\) 13.8750 0.567865
\(598\) 23.7269 0.970267
\(599\) 19.6152 0.801453 0.400727 0.916198i \(-0.368758\pi\)
0.400727 + 0.916198i \(0.368758\pi\)
\(600\) 26.2908 1.07332
\(601\) 1.17591 0.0479663 0.0239832 0.999712i \(-0.492365\pi\)
0.0239832 + 0.999712i \(0.492365\pi\)
\(602\) −5.93313 −0.241817
\(603\) 18.7106 0.761953
\(604\) 50.5757 2.05789
\(605\) 4.11808 0.167424
\(606\) −2.06745 −0.0839842
\(607\) −13.2980 −0.539749 −0.269875 0.962895i \(-0.586982\pi\)
−0.269875 + 0.962895i \(0.586982\pi\)
\(608\) 10.3301 0.418942
\(609\) −8.23962 −0.333886
\(610\) 11.5837 0.469010
\(611\) 37.1022 1.50099
\(612\) −3.56083 −0.143938
\(613\) −38.2145 −1.54347 −0.771734 0.635946i \(-0.780610\pi\)
−0.771734 + 0.635946i \(0.780610\pi\)
\(614\) −3.24169 −0.130824
\(615\) 15.8451 0.638936
\(616\) 15.2082 0.612756
\(617\) 25.8884 1.04223 0.521113 0.853487i \(-0.325517\pi\)
0.521113 + 0.853487i \(0.325517\pi\)
\(618\) −17.8775 −0.719139
\(619\) −16.5780 −0.666325 −0.333162 0.942869i \(-0.608116\pi\)
−0.333162 + 0.942869i \(0.608116\pi\)
\(620\) −69.1999 −2.77914
\(621\) −18.6668 −0.749072
\(622\) −15.2963 −0.613327
\(623\) 1.81800 0.0728368
\(624\) −10.2935 −0.412069
\(625\) −25.5507 −1.02203
\(626\) 34.3001 1.37091
\(627\) 24.5612 0.980881
\(628\) 81.5612 3.25464
\(629\) −4.09445 −0.163257
\(630\) 11.0551 0.440447
\(631\) −23.1328 −0.920904 −0.460452 0.887685i \(-0.652313\pi\)
−0.460452 + 0.887685i \(0.652313\pi\)
\(632\) 1.71588 0.0682539
\(633\) 9.79030 0.389129
\(634\) 61.3511 2.43656
\(635\) 34.2275 1.35827
\(636\) 29.0887 1.15344
\(637\) 2.92121 0.115743
\(638\) 56.0998 2.22101
\(639\) −21.9555 −0.868547
\(640\) 64.8841 2.56477
\(641\) −41.1789 −1.62647 −0.813234 0.581937i \(-0.802295\pi\)
−0.813234 + 0.581937i \(0.802295\pi\)
\(642\) 13.1800 0.520171
\(643\) −6.28777 −0.247966 −0.123983 0.992284i \(-0.539567\pi\)
−0.123983 + 0.992284i \(0.539567\pi\)
\(644\) −12.8156 −0.505006
\(645\) −9.61374 −0.378541
\(646\) −8.72015 −0.343090
\(647\) −5.64701 −0.222007 −0.111003 0.993820i \(-0.535406\pi\)
−0.111003 + 0.993820i \(0.535406\pi\)
\(648\) 10.7897 0.423858
\(649\) −30.4424 −1.19497
\(650\) −34.3830 −1.34861
\(651\) 7.18744 0.281698
\(652\) 32.5773 1.27583
\(653\) 10.2416 0.400786 0.200393 0.979716i \(-0.435778\pi\)
0.200393 + 0.979716i \(0.435778\pi\)
\(654\) 50.4811 1.97397
\(655\) 41.8035 1.63340
\(656\) −11.5292 −0.450139
\(657\) 18.5879 0.725185
\(658\) −30.5876 −1.19243
\(659\) −20.8401 −0.811814 −0.405907 0.913914i \(-0.633044\pi\)
−0.405907 + 0.913914i \(0.633044\pi\)
\(660\) 52.0249 2.02507
\(661\) −5.77834 −0.224752 −0.112376 0.993666i \(-0.535846\pi\)
−0.112376 + 0.993666i \(0.535846\pi\)
\(662\) −62.3589 −2.42365
\(663\) −2.32706 −0.0903755
\(664\) 3.04735 0.118260
\(665\) 17.7373 0.687824
\(666\) −22.4262 −0.868996
\(667\) −22.3923 −0.867031
\(668\) 28.6713 1.10933
\(669\) 34.9289 1.35043
\(670\) 97.0558 3.74959
\(671\) 5.36687 0.207186
\(672\) −2.27267 −0.0876700
\(673\) 38.4623 1.48261 0.741307 0.671166i \(-0.234206\pi\)
0.741307 + 0.671166i \(0.234206\pi\)
\(674\) −39.2426 −1.51157
\(675\) 27.0503 1.04117
\(676\) −16.9722 −0.652778
\(677\) 9.88274 0.379825 0.189912 0.981801i \(-0.439180\pi\)
0.189912 + 0.981801i \(0.439180\pi\)
\(678\) 11.3054 0.434179
\(679\) −0.0756201 −0.00290203
\(680\) −8.74902 −0.335510
\(681\) −17.9603 −0.688240
\(682\) −48.9360 −1.87385
\(683\) −12.7107 −0.486361 −0.243180 0.969981i \(-0.578191\pi\)
−0.243180 + 0.969981i \(0.578191\pi\)
\(684\) −31.2920 −1.19648
\(685\) 60.6534 2.31745
\(686\) −2.40830 −0.0919491
\(687\) 22.1252 0.844131
\(688\) 6.99512 0.266687
\(689\) −18.0193 −0.686482
\(690\) −31.6954 −1.20662
\(691\) −49.8279 −1.89554 −0.947772 0.318950i \(-0.896670\pi\)
−0.947772 + 0.318950i \(0.896670\pi\)
\(692\) −18.0672 −0.686810
\(693\) 5.12198 0.194568
\(694\) −23.4167 −0.888886
\(695\) 66.4186 2.51940
\(696\) 35.7159 1.35381
\(697\) −2.60641 −0.0987248
\(698\) 41.1692 1.55828
\(699\) −28.3500 −1.07229
\(700\) 18.5713 0.701928
\(701\) −29.3009 −1.10668 −0.553340 0.832955i \(-0.686647\pi\)
−0.553340 + 0.832955i \(0.686647\pi\)
\(702\) −38.9380 −1.46962
\(703\) −35.9815 −1.35707
\(704\) 35.3974 1.33409
\(705\) −49.5626 −1.86663
\(706\) 31.8858 1.20004
\(707\) −0.691745 −0.0260157
\(708\) −40.9171 −1.53776
\(709\) 23.8011 0.893870 0.446935 0.894566i \(-0.352516\pi\)
0.446935 + 0.894566i \(0.352516\pi\)
\(710\) −113.888 −4.27414
\(711\) 0.577891 0.0216726
\(712\) −7.88042 −0.295331
\(713\) 19.5328 0.731509
\(714\) 1.91846 0.0717967
\(715\) −32.2274 −1.20524
\(716\) −89.7267 −3.35324
\(717\) 6.97946 0.260653
\(718\) −53.8154 −2.00837
\(719\) 7.60718 0.283700 0.141850 0.989888i \(-0.454695\pi\)
0.141850 + 0.989888i \(0.454695\pi\)
\(720\) −13.0339 −0.485745
\(721\) −5.98162 −0.222767
\(722\) −30.8738 −1.14901
\(723\) 3.73272 0.138821
\(724\) −46.5951 −1.73170
\(725\) 32.4489 1.20512
\(726\) 3.91420 0.145270
\(727\) 29.5495 1.09593 0.547965 0.836501i \(-0.315403\pi\)
0.547965 + 0.836501i \(0.315403\pi\)
\(728\) −12.6625 −0.469302
\(729\) 24.2402 0.897784
\(730\) 96.4197 3.56865
\(731\) 1.58139 0.0584899
\(732\) 7.21352 0.266619
\(733\) −8.05358 −0.297466 −0.148733 0.988877i \(-0.547519\pi\)
−0.148733 + 0.988877i \(0.547519\pi\)
\(734\) 63.8737 2.35762
\(735\) −3.90228 −0.143938
\(736\) −6.17627 −0.227660
\(737\) 44.9671 1.65639
\(738\) −14.2758 −0.525501
\(739\) 23.3554 0.859141 0.429571 0.903033i \(-0.358665\pi\)
0.429571 + 0.903033i \(0.358665\pi\)
\(740\) −76.2150 −2.80172
\(741\) −20.4499 −0.751245
\(742\) 14.8554 0.545360
\(743\) 18.1284 0.665067 0.332533 0.943091i \(-0.392097\pi\)
0.332533 + 0.943091i \(0.392097\pi\)
\(744\) −31.1551 −1.14220
\(745\) −64.2182 −2.35277
\(746\) −71.3883 −2.61371
\(747\) 1.02632 0.0375511
\(748\) −8.55774 −0.312902
\(749\) 4.40987 0.161133
\(750\) −1.05890 −0.0386656
\(751\) −5.91102 −0.215696 −0.107848 0.994167i \(-0.534396\pi\)
−0.107848 + 0.994167i \(0.534396\pi\)
\(752\) 36.0626 1.31507
\(753\) −18.1647 −0.661957
\(754\) −46.7092 −1.70105
\(755\) 41.8514 1.52313
\(756\) 21.0316 0.764910
\(757\) −16.7691 −0.609482 −0.304741 0.952435i \(-0.598570\pi\)
−0.304741 + 0.952435i \(0.598570\pi\)
\(758\) −72.1383 −2.62018
\(759\) −14.6849 −0.533027
\(760\) −76.8852 −2.78892
\(761\) −14.5888 −0.528845 −0.264422 0.964407i \(-0.585181\pi\)
−0.264422 + 0.964407i \(0.585181\pi\)
\(762\) 32.5329 1.17854
\(763\) 16.8904 0.611475
\(764\) −10.8961 −0.394207
\(765\) −2.94659 −0.106534
\(766\) −89.1028 −3.21941
\(767\) 25.3466 0.915212
\(768\) 36.6306 1.32179
\(769\) −4.22945 −0.152518 −0.0762590 0.997088i \(-0.524298\pi\)
−0.0762590 + 0.997088i \(0.524298\pi\)
\(770\) 26.5688 0.957473
\(771\) −22.4479 −0.808442
\(772\) −28.1591 −1.01347
\(773\) 13.5165 0.486155 0.243077 0.970007i \(-0.421843\pi\)
0.243077 + 0.970007i \(0.421843\pi\)
\(774\) 8.66161 0.311335
\(775\) −28.3052 −1.01675
\(776\) 0.327787 0.0117669
\(777\) 7.91606 0.283987
\(778\) 70.4372 2.52530
\(779\) −22.9048 −0.820648
\(780\) −43.3163 −1.55097
\(781\) −52.7657 −1.88811
\(782\) 5.21367 0.186441
\(783\) 36.7477 1.31325
\(784\) 2.83936 0.101406
\(785\) 67.4920 2.40889
\(786\) 39.7339 1.41726
\(787\) −6.06251 −0.216105 −0.108053 0.994145i \(-0.534461\pi\)
−0.108053 + 0.994145i \(0.534461\pi\)
\(788\) 68.0379 2.42375
\(789\) −13.5049 −0.480789
\(790\) 2.99765 0.106651
\(791\) 3.78265 0.134495
\(792\) −22.2020 −0.788914
\(793\) −4.46850 −0.158681
\(794\) −56.1130 −1.99138
\(795\) 24.0710 0.853709
\(796\) −42.4839 −1.50580
\(797\) 17.8726 0.633078 0.316539 0.948579i \(-0.397479\pi\)
0.316539 + 0.948579i \(0.397479\pi\)
\(798\) 16.8592 0.596809
\(799\) 8.15270 0.288422
\(800\) 8.95011 0.316434
\(801\) −2.65405 −0.0937763
\(802\) 53.0903 1.87468
\(803\) 44.6724 1.57646
\(804\) 60.4396 2.13154
\(805\) −10.6049 −0.373775
\(806\) 40.7445 1.43516
\(807\) 24.0068 0.845079
\(808\) 2.99848 0.105486
\(809\) 6.71726 0.236166 0.118083 0.993004i \(-0.462325\pi\)
0.118083 + 0.993004i \(0.462325\pi\)
\(810\) 18.8496 0.662307
\(811\) −45.2239 −1.58803 −0.794013 0.607901i \(-0.792012\pi\)
−0.794013 + 0.607901i \(0.792012\pi\)
\(812\) 25.2290 0.885363
\(813\) −0.519895 −0.0182335
\(814\) −53.8968 −1.88908
\(815\) 26.9578 0.944290
\(816\) −2.26186 −0.0791808
\(817\) 13.8971 0.486197
\(818\) −10.2618 −0.358796
\(819\) −4.26460 −0.149017
\(820\) −48.5162 −1.69426
\(821\) −53.0091 −1.85003 −0.925015 0.379931i \(-0.875948\pi\)
−0.925015 + 0.379931i \(0.875948\pi\)
\(822\) 57.6506 2.01080
\(823\) −39.7600 −1.38595 −0.692973 0.720963i \(-0.743700\pi\)
−0.692973 + 0.720963i \(0.743700\pi\)
\(824\) 25.9283 0.903254
\(825\) 21.2800 0.740876
\(826\) −20.8961 −0.727069
\(827\) 14.0302 0.487877 0.243938 0.969791i \(-0.421561\pi\)
0.243938 + 0.969791i \(0.421561\pi\)
\(828\) 18.7091 0.650188
\(829\) 49.5301 1.72025 0.860126 0.510082i \(-0.170385\pi\)
0.860126 + 0.510082i \(0.170385\pi\)
\(830\) 5.32375 0.184790
\(831\) −25.9098 −0.898802
\(832\) −29.4722 −1.02176
\(833\) 0.641897 0.0222404
\(834\) 63.1304 2.18603
\(835\) 23.7256 0.821058
\(836\) −75.2042 −2.60099
\(837\) −32.0550 −1.10798
\(838\) −68.1200 −2.35317
\(839\) 20.9319 0.722650 0.361325 0.932440i \(-0.382325\pi\)
0.361325 + 0.932440i \(0.382325\pi\)
\(840\) 16.9150 0.583624
\(841\) 15.0817 0.520057
\(842\) 25.4437 0.876849
\(843\) 8.87612 0.305710
\(844\) −29.9770 −1.03185
\(845\) −14.0445 −0.483147
\(846\) 44.6540 1.53524
\(847\) 1.30965 0.0450001
\(848\) −17.5144 −0.601449
\(849\) −2.27274 −0.0780001
\(850\) −7.55521 −0.259141
\(851\) 21.5129 0.737454
\(852\) −70.9215 −2.42973
\(853\) −36.4904 −1.24941 −0.624704 0.780862i \(-0.714780\pi\)
−0.624704 + 0.780862i \(0.714780\pi\)
\(854\) 3.68390 0.126060
\(855\) −25.8942 −0.885563
\(856\) −19.1153 −0.653347
\(857\) 15.3649 0.524855 0.262428 0.964952i \(-0.415477\pi\)
0.262428 + 0.964952i \(0.415477\pi\)
\(858\) −30.6319 −1.04576
\(859\) −1.00000 −0.0341196
\(860\) 29.4364 1.00377
\(861\) 5.03913 0.171733
\(862\) −21.4971 −0.732194
\(863\) 54.0284 1.83915 0.919574 0.392918i \(-0.128534\pi\)
0.919574 + 0.392918i \(0.128534\pi\)
\(864\) 10.1358 0.344827
\(865\) −14.9506 −0.508336
\(866\) −28.8387 −0.979980
\(867\) 20.5860 0.699137
\(868\) −22.0073 −0.746975
\(869\) 1.38885 0.0471134
\(870\) 62.3960 2.11542
\(871\) −37.4400 −1.26861
\(872\) −73.2142 −2.47935
\(873\) 0.110396 0.00373633
\(874\) 45.8171 1.54978
\(875\) −0.354296 −0.0119774
\(876\) 60.0435 2.02868
\(877\) −18.7554 −0.633326 −0.316663 0.948538i \(-0.602562\pi\)
−0.316663 + 0.948538i \(0.602562\pi\)
\(878\) 25.2112 0.850838
\(879\) 6.87719 0.231962
\(880\) −31.3244 −1.05595
\(881\) 4.75397 0.160165 0.0800827 0.996788i \(-0.474482\pi\)
0.0800827 + 0.996788i \(0.474482\pi\)
\(882\) 3.51580 0.118383
\(883\) −30.6492 −1.03143 −0.515714 0.856761i \(-0.672473\pi\)
−0.515714 + 0.856761i \(0.672473\pi\)
\(884\) 7.12524 0.239648
\(885\) −33.8590 −1.13816
\(886\) −75.9971 −2.55317
\(887\) 2.92476 0.0982039 0.0491020 0.998794i \(-0.484364\pi\)
0.0491020 + 0.998794i \(0.484364\pi\)
\(888\) −34.3134 −1.15148
\(889\) 10.8852 0.365077
\(890\) −13.7671 −0.461476
\(891\) 8.73325 0.292575
\(892\) −106.949 −3.58092
\(893\) 71.6448 2.39750
\(894\) −61.0389 −2.04145
\(895\) −74.2490 −2.48187
\(896\) 20.6347 0.689358
\(897\) 12.2267 0.408239
\(898\) −17.8882 −0.596936
\(899\) −38.4525 −1.28246
\(900\) −27.1117 −0.903723
\(901\) −3.95951 −0.131910
\(902\) −34.3091 −1.14237
\(903\) −3.05740 −0.101744
\(904\) −16.3965 −0.545339
\(905\) −38.5576 −1.28170
\(906\) 39.7795 1.32158
\(907\) −46.1094 −1.53104 −0.765520 0.643413i \(-0.777518\pi\)
−0.765520 + 0.643413i \(0.777518\pi\)
\(908\) 54.9928 1.82500
\(909\) 1.00986 0.0334949
\(910\) −22.1214 −0.733317
\(911\) 58.8205 1.94881 0.974406 0.224796i \(-0.0721716\pi\)
0.974406 + 0.224796i \(0.0721716\pi\)
\(912\) −19.8769 −0.658189
\(913\) 2.46656 0.0816311
\(914\) −70.8788 −2.34446
\(915\) 5.96920 0.197336
\(916\) −67.7455 −2.23837
\(917\) 13.2945 0.439024
\(918\) −8.55610 −0.282393
\(919\) 33.7453 1.11316 0.556578 0.830795i \(-0.312114\pi\)
0.556578 + 0.830795i \(0.312114\pi\)
\(920\) 45.9688 1.51555
\(921\) −1.67048 −0.0550440
\(922\) 58.6659 1.93206
\(923\) 43.9332 1.44608
\(924\) 16.5452 0.544297
\(925\) −31.1747 −1.02502
\(926\) −42.0151 −1.38070
\(927\) 8.73239 0.286809
\(928\) 12.1587 0.399128
\(929\) −17.5778 −0.576710 −0.288355 0.957524i \(-0.593108\pi\)
−0.288355 + 0.957524i \(0.593108\pi\)
\(930\) −54.4281 −1.78477
\(931\) 5.64090 0.184873
\(932\) 86.8050 2.84339
\(933\) −7.88235 −0.258057
\(934\) 30.7445 1.00599
\(935\) −7.08154 −0.231591
\(936\) 18.4856 0.604220
\(937\) 32.6995 1.06825 0.534123 0.845407i \(-0.320642\pi\)
0.534123 + 0.845407i \(0.320642\pi\)
\(938\) 30.8661 1.00781
\(939\) 17.6752 0.576808
\(940\) 151.756 4.94973
\(941\) 42.6495 1.39033 0.695167 0.718848i \(-0.255330\pi\)
0.695167 + 0.718848i \(0.255330\pi\)
\(942\) 64.1506 2.09014
\(943\) 13.6945 0.445954
\(944\) 24.6364 0.801846
\(945\) 17.4036 0.566141
\(946\) 20.8165 0.676802
\(947\) −5.27919 −0.171551 −0.0857753 0.996315i \(-0.527337\pi\)
−0.0857753 + 0.996315i \(0.527337\pi\)
\(948\) 1.86672 0.0606284
\(949\) −37.1946 −1.20739
\(950\) −66.3941 −2.15411
\(951\) 31.6149 1.02518
\(952\) −2.78240 −0.0901782
\(953\) 29.5957 0.958698 0.479349 0.877624i \(-0.340873\pi\)
0.479349 + 0.877624i \(0.340873\pi\)
\(954\) −21.6870 −0.702143
\(955\) −9.01655 −0.291769
\(956\) −21.3705 −0.691170
\(957\) 28.9088 0.934489
\(958\) −59.8223 −1.93277
\(959\) 19.2893 0.622883
\(960\) 39.3701 1.27066
\(961\) 2.54216 0.0820053
\(962\) 44.8749 1.44683
\(963\) −6.43784 −0.207457
\(964\) −11.4292 −0.368111
\(965\) −23.3017 −0.750108
\(966\) −10.0799 −0.324316
\(967\) 46.1791 1.48502 0.742510 0.669835i \(-0.233635\pi\)
0.742510 + 0.669835i \(0.233635\pi\)
\(968\) −5.67688 −0.182462
\(969\) −4.49358 −0.144355
\(970\) 0.572647 0.0183866
\(971\) 12.8291 0.411704 0.205852 0.978583i \(-0.434003\pi\)
0.205852 + 0.978583i \(0.434003\pi\)
\(972\) −51.3565 −1.64726
\(973\) 21.1228 0.677164
\(974\) 0.607821 0.0194758
\(975\) −17.7179 −0.567428
\(976\) −4.34329 −0.139025
\(977\) 47.1682 1.50905 0.754523 0.656274i \(-0.227869\pi\)
0.754523 + 0.656274i \(0.227869\pi\)
\(978\) 25.6232 0.819339
\(979\) −6.37849 −0.203857
\(980\) 11.9484 0.381678
\(981\) −24.6579 −0.787265
\(982\) 3.03564 0.0968712
\(983\) 10.8091 0.344755 0.172378 0.985031i \(-0.444855\pi\)
0.172378 + 0.985031i \(0.444855\pi\)
\(984\) −21.8429 −0.696326
\(985\) 56.3015 1.79391
\(986\) −10.2637 −0.326863
\(987\) −15.7621 −0.501713
\(988\) 62.6156 1.99207
\(989\) −8.30889 −0.264207
\(990\) −38.7870 −1.23273
\(991\) −10.5663 −0.335649 −0.167825 0.985817i \(-0.553674\pi\)
−0.167825 + 0.985817i \(0.553674\pi\)
\(992\) −10.6060 −0.336742
\(993\) −32.1342 −1.01975
\(994\) −36.2192 −1.14880
\(995\) −35.1555 −1.11450
\(996\) 3.31526 0.105048
\(997\) 18.0974 0.573150 0.286575 0.958058i \(-0.407483\pi\)
0.286575 + 0.958058i \(0.407483\pi\)
\(998\) −73.5030 −2.32670
\(999\) −35.3046 −1.11699
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 \(a_p\))