Properties

Label 4031.2.a.c.1.11
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.87723 q^{2}\) \(+1.73503 q^{3}\) \(+1.52398 q^{4}\) \(-2.87174 q^{5}\) \(-3.25705 q^{6}\) \(-0.555991 q^{7}\) \(+0.893598 q^{8}\) \(+0.0103383 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.87723 q^{2}\) \(+1.73503 q^{3}\) \(+1.52398 q^{4}\) \(-2.87174 q^{5}\) \(-3.25705 q^{6}\) \(-0.555991 q^{7}\) \(+0.893598 q^{8}\) \(+0.0103383 q^{9}\) \(+5.39090 q^{10}\) \(+4.53489 q^{11}\) \(+2.64415 q^{12}\) \(+0.0502541 q^{13}\) \(+1.04372 q^{14}\) \(-4.98256 q^{15}\) \(-4.72545 q^{16}\) \(-5.51691 q^{17}\) \(-0.0194073 q^{18}\) \(+2.23583 q^{19}\) \(-4.37647 q^{20}\) \(-0.964663 q^{21}\) \(-8.51301 q^{22}\) \(+4.63926 q^{23}\) \(+1.55042 q^{24}\) \(+3.24688 q^{25}\) \(-0.0943384 q^{26}\) \(-5.18716 q^{27}\) \(-0.847320 q^{28}\) \(-1.00000 q^{29}\) \(+9.35339 q^{30}\) \(+3.13694 q^{31}\) \(+7.08354 q^{32}\) \(+7.86818 q^{33}\) \(+10.3565 q^{34}\) \(+1.59666 q^{35}\) \(+0.0157553 q^{36}\) \(-7.81281 q^{37}\) \(-4.19716 q^{38}\) \(+0.0871926 q^{39}\) \(-2.56618 q^{40}\) \(+2.79553 q^{41}\) \(+1.81089 q^{42}\) \(+3.53482 q^{43}\) \(+6.91108 q^{44}\) \(-0.0296888 q^{45}\) \(-8.70894 q^{46}\) \(+5.92942 q^{47}\) \(-8.19880 q^{48}\) \(-6.69087 q^{49}\) \(-6.09513 q^{50}\) \(-9.57202 q^{51}\) \(+0.0765863 q^{52}\) \(-3.16623 q^{53}\) \(+9.73748 q^{54}\) \(-13.0230 q^{55}\) \(-0.496833 q^{56}\) \(+3.87924 q^{57}\) \(+1.87723 q^{58}\) \(-3.96686 q^{59}\) \(-7.59332 q^{60}\) \(+8.34344 q^{61}\) \(-5.88875 q^{62}\) \(-0.00574798 q^{63}\) \(-3.84651 q^{64}\) \(-0.144317 q^{65}\) \(-14.7704 q^{66}\) \(-5.12166 q^{67}\) \(-8.40766 q^{68}\) \(+8.04926 q^{69}\) \(-2.99730 q^{70}\) \(-9.84323 q^{71}\) \(+0.00923824 q^{72}\) \(+5.05914 q^{73}\) \(+14.6664 q^{74}\) \(+5.63344 q^{75}\) \(+3.40736 q^{76}\) \(-2.52136 q^{77}\) \(-0.163680 q^{78}\) \(+11.1417 q^{79}\) \(+13.5702 q^{80}\) \(-9.03091 q^{81}\) \(-5.24784 q^{82}\) \(+1.12211 q^{83}\) \(-1.47013 q^{84}\) \(+15.8431 q^{85}\) \(-6.63566 q^{86}\) \(-1.73503 q^{87}\) \(+4.05237 q^{88}\) \(-18.2657 q^{89}\) \(+0.0557325 q^{90}\) \(-0.0279409 q^{91}\) \(+7.07013 q^{92}\) \(+5.44269 q^{93}\) \(-11.1309 q^{94}\) \(-6.42072 q^{95}\) \(+12.2902 q^{96}\) \(-0.708636 q^{97}\) \(+12.5603 q^{98}\) \(+0.0468828 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87723 −1.32740 −0.663700 0.747999i \(-0.731015\pi\)
−0.663700 + 0.747999i \(0.731015\pi\)
\(3\) 1.73503 1.00172 0.500861 0.865528i \(-0.333017\pi\)
0.500861 + 0.865528i \(0.333017\pi\)
\(4\) 1.52398 0.761990
\(5\) −2.87174 −1.28428 −0.642140 0.766587i \(-0.721953\pi\)
−0.642140 + 0.766587i \(0.721953\pi\)
\(6\) −3.25705 −1.32968
\(7\) −0.555991 −0.210145 −0.105073 0.994465i \(-0.533507\pi\)
−0.105073 + 0.994465i \(0.533507\pi\)
\(8\) 0.893598 0.315935
\(9\) 0.0103383 0.00344609
\(10\) 5.39090 1.70475
\(11\) 4.53489 1.36732 0.683660 0.729801i \(-0.260387\pi\)
0.683660 + 0.729801i \(0.260387\pi\)
\(12\) 2.64415 0.763302
\(13\) 0.0502541 0.0139380 0.00696900 0.999976i \(-0.497782\pi\)
0.00696900 + 0.999976i \(0.497782\pi\)
\(14\) 1.04372 0.278946
\(15\) −4.98256 −1.28649
\(16\) −4.72545 −1.18136
\(17\) −5.51691 −1.33805 −0.669024 0.743241i \(-0.733288\pi\)
−0.669024 + 0.743241i \(0.733288\pi\)
\(18\) −0.0194073 −0.00457433
\(19\) 2.23583 0.512935 0.256467 0.966553i \(-0.417441\pi\)
0.256467 + 0.966553i \(0.417441\pi\)
\(20\) −4.37647 −0.978609
\(21\) −0.964663 −0.210507
\(22\) −8.51301 −1.81498
\(23\) 4.63926 0.967352 0.483676 0.875247i \(-0.339301\pi\)
0.483676 + 0.875247i \(0.339301\pi\)
\(24\) 1.55042 0.316478
\(25\) 3.24688 0.649376
\(26\) −0.0943384 −0.0185013
\(27\) −5.18716 −0.998270
\(28\) −0.847320 −0.160128
\(29\) −1.00000 −0.185695
\(30\) 9.35339 1.70769
\(31\) 3.13694 0.563411 0.281706 0.959501i \(-0.409100\pi\)
0.281706 + 0.959501i \(0.409100\pi\)
\(32\) 7.08354 1.25220
\(33\) 7.86818 1.36967
\(34\) 10.3565 1.77612
\(35\) 1.59666 0.269885
\(36\) 0.0157553 0.00262588
\(37\) −7.81281 −1.28442 −0.642209 0.766529i \(-0.721982\pi\)
−0.642209 + 0.766529i \(0.721982\pi\)
\(38\) −4.19716 −0.680869
\(39\) 0.0871926 0.0139620
\(40\) −2.56618 −0.405748
\(41\) 2.79553 0.436589 0.218294 0.975883i \(-0.429951\pi\)
0.218294 + 0.975883i \(0.429951\pi\)
\(42\) 1.81089 0.279427
\(43\) 3.53482 0.539055 0.269528 0.962993i \(-0.413132\pi\)
0.269528 + 0.962993i \(0.413132\pi\)
\(44\) 6.91108 1.04188
\(45\) −0.0296888 −0.00442574
\(46\) −8.70894 −1.28406
\(47\) 5.92942 0.864895 0.432448 0.901659i \(-0.357650\pi\)
0.432448 + 0.901659i \(0.357650\pi\)
\(48\) −8.19880 −1.18340
\(49\) −6.69087 −0.955839
\(50\) −6.09513 −0.861981
\(51\) −9.57202 −1.34035
\(52\) 0.0765863 0.0106206
\(53\) −3.16623 −0.434915 −0.217457 0.976070i \(-0.569776\pi\)
−0.217457 + 0.976070i \(0.569776\pi\)
\(54\) 9.73748 1.32510
\(55\) −13.0230 −1.75602
\(56\) −0.496833 −0.0663921
\(57\) 3.87924 0.513818
\(58\) 1.87723 0.246492
\(59\) −3.96686 −0.516441 −0.258221 0.966086i \(-0.583136\pi\)
−0.258221 + 0.966086i \(0.583136\pi\)
\(60\) −7.59332 −0.980293
\(61\) 8.34344 1.06827 0.534134 0.845400i \(-0.320638\pi\)
0.534134 + 0.845400i \(0.320638\pi\)
\(62\) −5.88875 −0.747872
\(63\) −0.00574798 −0.000724178 0
\(64\) −3.84651 −0.480814
\(65\) −0.144317 −0.0179003
\(66\) −14.7704 −1.81810
\(67\) −5.12166 −0.625710 −0.312855 0.949801i \(-0.601285\pi\)
−0.312855 + 0.949801i \(0.601285\pi\)
\(68\) −8.40766 −1.01958
\(69\) 8.04926 0.969017
\(70\) −2.99730 −0.358245
\(71\) −9.84323 −1.16818 −0.584088 0.811690i \(-0.698548\pi\)
−0.584088 + 0.811690i \(0.698548\pi\)
\(72\) 0.00923824 0.00108874
\(73\) 5.05914 0.592128 0.296064 0.955168i \(-0.404326\pi\)
0.296064 + 0.955168i \(0.404326\pi\)
\(74\) 14.6664 1.70494
\(75\) 5.63344 0.650494
\(76\) 3.40736 0.390851
\(77\) −2.52136 −0.287335
\(78\) −0.163680 −0.0185331
\(79\) 11.1417 1.25354 0.626768 0.779206i \(-0.284377\pi\)
0.626768 + 0.779206i \(0.284377\pi\)
\(80\) 13.5702 1.51720
\(81\) −9.03091 −1.00343
\(82\) −5.24784 −0.579528
\(83\) 1.12211 0.123168 0.0615840 0.998102i \(-0.480385\pi\)
0.0615840 + 0.998102i \(0.480385\pi\)
\(84\) −1.47013 −0.160404
\(85\) 15.8431 1.71843
\(86\) −6.63566 −0.715542
\(87\) −1.73503 −0.186015
\(88\) 4.05237 0.431984
\(89\) −18.2657 −1.93616 −0.968079 0.250645i \(-0.919357\pi\)
−0.968079 + 0.250645i \(0.919357\pi\)
\(90\) 0.0557325 0.00587473
\(91\) −0.0279409 −0.00292900
\(92\) 7.07013 0.737112
\(93\) 5.44269 0.564381
\(94\) −11.1309 −1.14806
\(95\) −6.42072 −0.658752
\(96\) 12.2902 1.25436
\(97\) −0.708636 −0.0719511 −0.0359755 0.999353i \(-0.511454\pi\)
−0.0359755 + 0.999353i \(0.511454\pi\)
\(98\) 12.5603 1.26878
\(99\) 0.0468828 0.00471190
\(100\) 4.94818 0.494818
\(101\) 8.88952 0.884541 0.442270 0.896882i \(-0.354173\pi\)
0.442270 + 0.896882i \(0.354173\pi\)
\(102\) 17.9688 1.77918
\(103\) 10.9052 1.07453 0.537263 0.843415i \(-0.319458\pi\)
0.537263 + 0.843415i \(0.319458\pi\)
\(104\) 0.0449070 0.00440349
\(105\) 2.77026 0.270350
\(106\) 5.94372 0.577306
\(107\) 19.2551 1.86146 0.930728 0.365712i \(-0.119174\pi\)
0.930728 + 0.365712i \(0.119174\pi\)
\(108\) −7.90513 −0.760671
\(109\) −18.9877 −1.81869 −0.909345 0.416043i \(-0.863416\pi\)
−0.909345 + 0.416043i \(0.863416\pi\)
\(110\) 24.4471 2.33094
\(111\) −13.5555 −1.28663
\(112\) 2.62731 0.248257
\(113\) 12.4107 1.16750 0.583751 0.811933i \(-0.301584\pi\)
0.583751 + 0.811933i \(0.301584\pi\)
\(114\) −7.28221 −0.682042
\(115\) −13.3227 −1.24235
\(116\) −1.52398 −0.141498
\(117\) 0.000519540 0 4.80315e−5 0
\(118\) 7.44670 0.685524
\(119\) 3.06735 0.281184
\(120\) −4.45240 −0.406447
\(121\) 9.56520 0.869564
\(122\) −15.6625 −1.41802
\(123\) 4.85034 0.437340
\(124\) 4.78063 0.429314
\(125\) 5.03451 0.450300
\(126\) 0.0107903 0.000961273 0
\(127\) −16.4531 −1.45997 −0.729987 0.683461i \(-0.760474\pi\)
−0.729987 + 0.683461i \(0.760474\pi\)
\(128\) −6.94630 −0.613972
\(129\) 6.13303 0.539983
\(130\) 0.270915 0.0237608
\(131\) −1.76276 −0.154013 −0.0770063 0.997031i \(-0.524536\pi\)
−0.0770063 + 0.997031i \(0.524536\pi\)
\(132\) 11.9909 1.04368
\(133\) −1.24310 −0.107791
\(134\) 9.61451 0.830567
\(135\) 14.8962 1.28206
\(136\) −4.92990 −0.422735
\(137\) −6.06793 −0.518418 −0.259209 0.965821i \(-0.583462\pi\)
−0.259209 + 0.965821i \(0.583462\pi\)
\(138\) −15.1103 −1.28627
\(139\) −1.00000 −0.0848189
\(140\) 2.43328 0.205650
\(141\) 10.2877 0.866384
\(142\) 18.4780 1.55064
\(143\) 0.227897 0.0190577
\(144\) −0.0488529 −0.00407107
\(145\) 2.87174 0.238485
\(146\) −9.49716 −0.785990
\(147\) −11.6089 −0.957485
\(148\) −11.9066 −0.978714
\(149\) 13.4094 1.09854 0.549270 0.835645i \(-0.314906\pi\)
0.549270 + 0.835645i \(0.314906\pi\)
\(150\) −10.5752 −0.863465
\(151\) −21.1918 −1.72456 −0.862281 0.506429i \(-0.830965\pi\)
−0.862281 + 0.506429i \(0.830965\pi\)
\(152\) 1.99793 0.162054
\(153\) −0.0570352 −0.00461103
\(154\) 4.73316 0.381409
\(155\) −9.00847 −0.723578
\(156\) 0.132880 0.0106389
\(157\) −12.2330 −0.976296 −0.488148 0.872761i \(-0.662327\pi\)
−0.488148 + 0.872761i \(0.662327\pi\)
\(158\) −20.9155 −1.66394
\(159\) −5.49351 −0.435663
\(160\) −20.3421 −1.60818
\(161\) −2.57939 −0.203284
\(162\) 16.9531 1.33196
\(163\) −18.9697 −1.48582 −0.742911 0.669390i \(-0.766556\pi\)
−0.742911 + 0.669390i \(0.766556\pi\)
\(164\) 4.26033 0.332676
\(165\) −22.5953 −1.75905
\(166\) −2.10646 −0.163493
\(167\) −0.954794 −0.0738841 −0.0369421 0.999317i \(-0.511762\pi\)
−0.0369421 + 0.999317i \(0.511762\pi\)
\(168\) −0.862021 −0.0665064
\(169\) −12.9975 −0.999806
\(170\) −29.7411 −2.28104
\(171\) 0.0231146 0.00176762
\(172\) 5.38700 0.410755
\(173\) −6.05437 −0.460305 −0.230153 0.973155i \(-0.573923\pi\)
−0.230153 + 0.973155i \(0.573923\pi\)
\(174\) 3.25705 0.246916
\(175\) −1.80524 −0.136463
\(176\) −21.4294 −1.61530
\(177\) −6.88263 −0.517330
\(178\) 34.2888 2.57006
\(179\) −0.809763 −0.0605245 −0.0302623 0.999542i \(-0.509634\pi\)
−0.0302623 + 0.999542i \(0.509634\pi\)
\(180\) −0.0452451 −0.00337237
\(181\) −23.3538 −1.73588 −0.867938 0.496673i \(-0.834555\pi\)
−0.867938 + 0.496673i \(0.834555\pi\)
\(182\) 0.0524513 0.00388795
\(183\) 14.4761 1.07011
\(184\) 4.14563 0.305620
\(185\) 22.4363 1.64955
\(186\) −10.2172 −0.749159
\(187\) −25.0186 −1.82954
\(188\) 9.03632 0.659042
\(189\) 2.88402 0.209781
\(190\) 12.0531 0.874427
\(191\) −20.7297 −1.49995 −0.749976 0.661465i \(-0.769935\pi\)
−0.749976 + 0.661465i \(0.769935\pi\)
\(192\) −6.67382 −0.481642
\(193\) −18.4922 −1.33110 −0.665549 0.746354i \(-0.731803\pi\)
−0.665549 + 0.746354i \(0.731803\pi\)
\(194\) 1.33027 0.0955078
\(195\) −0.250394 −0.0179311
\(196\) −10.1968 −0.728340
\(197\) 24.4204 1.73988 0.869939 0.493159i \(-0.164158\pi\)
0.869939 + 0.493159i \(0.164158\pi\)
\(198\) −0.0880097 −0.00625458
\(199\) 8.95807 0.635020 0.317510 0.948255i \(-0.397153\pi\)
0.317510 + 0.948255i \(0.397153\pi\)
\(200\) 2.90140 0.205160
\(201\) −8.88624 −0.626787
\(202\) −16.6877 −1.17414
\(203\) 0.555991 0.0390229
\(204\) −14.5876 −1.02133
\(205\) −8.02803 −0.560702
\(206\) −20.4716 −1.42632
\(207\) 0.0479618 0.00333358
\(208\) −0.237473 −0.0164658
\(209\) 10.1392 0.701346
\(210\) −5.20041 −0.358862
\(211\) −12.6860 −0.873343 −0.436672 0.899621i \(-0.643843\pi\)
−0.436672 + 0.899621i \(0.643843\pi\)
\(212\) −4.82526 −0.331401
\(213\) −17.0783 −1.17019
\(214\) −36.1461 −2.47090
\(215\) −10.1511 −0.692298
\(216\) −4.63524 −0.315388
\(217\) −1.74411 −0.118398
\(218\) 35.6442 2.41413
\(219\) 8.77778 0.593147
\(220\) −19.8468 −1.33807
\(221\) −0.277248 −0.0186497
\(222\) 25.4467 1.70787
\(223\) 10.9470 0.733065 0.366533 0.930405i \(-0.380545\pi\)
0.366533 + 0.930405i \(0.380545\pi\)
\(224\) −3.93839 −0.263144
\(225\) 0.0335671 0.00223780
\(226\) −23.2977 −1.54974
\(227\) −17.7156 −1.17582 −0.587912 0.808925i \(-0.700050\pi\)
−0.587912 + 0.808925i \(0.700050\pi\)
\(228\) 5.91188 0.391524
\(229\) −7.38899 −0.488278 −0.244139 0.969740i \(-0.578505\pi\)
−0.244139 + 0.969740i \(0.578505\pi\)
\(230\) 25.0098 1.64910
\(231\) −4.37464 −0.287830
\(232\) −0.893598 −0.0586676
\(233\) −14.1646 −0.927951 −0.463975 0.885848i \(-0.653577\pi\)
−0.463975 + 0.885848i \(0.653577\pi\)
\(234\) −0.000975295 0 −6.37570e−5 0
\(235\) −17.0278 −1.11077
\(236\) −6.04541 −0.393523
\(237\) 19.3312 1.25569
\(238\) −5.75812 −0.373243
\(239\) −15.1599 −0.980613 −0.490306 0.871550i \(-0.663115\pi\)
−0.490306 + 0.871550i \(0.663115\pi\)
\(240\) 23.5448 1.51981
\(241\) 1.15403 0.0743376 0.0371688 0.999309i \(-0.488166\pi\)
0.0371688 + 0.999309i \(0.488166\pi\)
\(242\) −17.9561 −1.15426
\(243\) −0.107438 −0.00689214
\(244\) 12.7152 0.814010
\(245\) 19.2144 1.22757
\(246\) −9.10518 −0.580525
\(247\) 0.112360 0.00714928
\(248\) 2.80316 0.178001
\(249\) 1.94691 0.123380
\(250\) −9.45091 −0.597728
\(251\) −2.34647 −0.148108 −0.0740541 0.997254i \(-0.523594\pi\)
−0.0740541 + 0.997254i \(0.523594\pi\)
\(252\) −0.00875981 −0.000551816 0
\(253\) 21.0385 1.32268
\(254\) 30.8862 1.93797
\(255\) 27.4883 1.72139
\(256\) 20.7328 1.29580
\(257\) 6.69918 0.417883 0.208942 0.977928i \(-0.432998\pi\)
0.208942 + 0.977928i \(0.432998\pi\)
\(258\) −11.5131 −0.716774
\(259\) 4.34386 0.269914
\(260\) −0.219936 −0.0136398
\(261\) −0.0103383 −0.000639922 0
\(262\) 3.30909 0.204436
\(263\) 10.9858 0.677414 0.338707 0.940892i \(-0.390010\pi\)
0.338707 + 0.940892i \(0.390010\pi\)
\(264\) 7.03099 0.432727
\(265\) 9.09257 0.558552
\(266\) 2.33359 0.143081
\(267\) −31.6915 −1.93949
\(268\) −7.80530 −0.476785
\(269\) −5.03654 −0.307083 −0.153542 0.988142i \(-0.549068\pi\)
−0.153542 + 0.988142i \(0.549068\pi\)
\(270\) −27.9635 −1.70180
\(271\) −11.9016 −0.722972 −0.361486 0.932377i \(-0.617731\pi\)
−0.361486 + 0.932377i \(0.617731\pi\)
\(272\) 26.0699 1.58072
\(273\) −0.0484783 −0.00293404
\(274\) 11.3909 0.688148
\(275\) 14.7242 0.887904
\(276\) 12.2669 0.738381
\(277\) 1.67104 0.100403 0.0502016 0.998739i \(-0.484014\pi\)
0.0502016 + 0.998739i \(0.484014\pi\)
\(278\) 1.87723 0.112589
\(279\) 0.0324305 0.00194156
\(280\) 1.42677 0.0852660
\(281\) 26.1846 1.56204 0.781020 0.624506i \(-0.214700\pi\)
0.781020 + 0.624506i \(0.214700\pi\)
\(282\) −19.3124 −1.15004
\(283\) −7.60325 −0.451966 −0.225983 0.974131i \(-0.572559\pi\)
−0.225983 + 0.974131i \(0.572559\pi\)
\(284\) −15.0009 −0.890139
\(285\) −11.1402 −0.659886
\(286\) −0.427814 −0.0252972
\(287\) −1.55429 −0.0917469
\(288\) 0.0732314 0.00431520
\(289\) 13.4363 0.790371
\(290\) −5.39090 −0.316565
\(291\) −1.22951 −0.0720749
\(292\) 7.71003 0.451195
\(293\) −1.98952 −0.116229 −0.0581146 0.998310i \(-0.518509\pi\)
−0.0581146 + 0.998310i \(0.518509\pi\)
\(294\) 21.7925 1.27096
\(295\) 11.3918 0.663255
\(296\) −6.98151 −0.405792
\(297\) −23.5232 −1.36495
\(298\) −25.1725 −1.45820
\(299\) 0.233142 0.0134829
\(300\) 8.58525 0.495669
\(301\) −1.96533 −0.113280
\(302\) 39.7818 2.28918
\(303\) 15.4236 0.886063
\(304\) −10.5653 −0.605961
\(305\) −23.9602 −1.37196
\(306\) 0.107068 0.00612067
\(307\) −12.7789 −0.729333 −0.364666 0.931138i \(-0.618817\pi\)
−0.364666 + 0.931138i \(0.618817\pi\)
\(308\) −3.84250 −0.218947
\(309\) 18.9210 1.07638
\(310\) 16.9109 0.960477
\(311\) −17.2271 −0.976857 −0.488429 0.872604i \(-0.662430\pi\)
−0.488429 + 0.872604i \(0.662430\pi\)
\(312\) 0.0779151 0.00441107
\(313\) −11.7200 −0.662451 −0.331226 0.943552i \(-0.607462\pi\)
−0.331226 + 0.943552i \(0.607462\pi\)
\(314\) 22.9640 1.29594
\(315\) 0.0165067 0.000930047 0
\(316\) 16.9797 0.955182
\(317\) 18.8120 1.05658 0.528292 0.849063i \(-0.322833\pi\)
0.528292 + 0.849063i \(0.322833\pi\)
\(318\) 10.3126 0.578299
\(319\) −4.53489 −0.253905
\(320\) 11.0462 0.617500
\(321\) 33.4081 1.86466
\(322\) 4.84209 0.269839
\(323\) −12.3349 −0.686331
\(324\) −13.7629 −0.764607
\(325\) 0.163169 0.00905099
\(326\) 35.6105 1.97228
\(327\) −32.9442 −1.82182
\(328\) 2.49808 0.137933
\(329\) −3.29671 −0.181753
\(330\) 42.4166 2.33496
\(331\) −9.17684 −0.504405 −0.252202 0.967674i \(-0.581155\pi\)
−0.252202 + 0.967674i \(0.581155\pi\)
\(332\) 1.71008 0.0938528
\(333\) −0.0807709 −0.00442622
\(334\) 1.79236 0.0980738
\(335\) 14.7081 0.803587
\(336\) 4.55846 0.248685
\(337\) −18.1106 −0.986546 −0.493273 0.869875i \(-0.664200\pi\)
−0.493273 + 0.869875i \(0.664200\pi\)
\(338\) 24.3992 1.32714
\(339\) 21.5330 1.16951
\(340\) 24.1446 1.30942
\(341\) 14.2257 0.770363
\(342\) −0.0433913 −0.00234633
\(343\) 7.61201 0.411010
\(344\) 3.15871 0.170306
\(345\) −23.1154 −1.24449
\(346\) 11.3654 0.611009
\(347\) −19.6054 −1.05247 −0.526235 0.850339i \(-0.676397\pi\)
−0.526235 + 0.850339i \(0.676397\pi\)
\(348\) −2.64415 −0.141742
\(349\) −21.1608 −1.13271 −0.566355 0.824161i \(-0.691647\pi\)
−0.566355 + 0.824161i \(0.691647\pi\)
\(350\) 3.38884 0.181141
\(351\) −0.260676 −0.0139139
\(352\) 32.1230 1.71216
\(353\) 16.9254 0.900848 0.450424 0.892815i \(-0.351273\pi\)
0.450424 + 0.892815i \(0.351273\pi\)
\(354\) 12.9203 0.686704
\(355\) 28.2672 1.50027
\(356\) −27.8365 −1.47533
\(357\) 5.32196 0.281668
\(358\) 1.52011 0.0803402
\(359\) 32.9921 1.74126 0.870629 0.491941i \(-0.163712\pi\)
0.870629 + 0.491941i \(0.163712\pi\)
\(360\) −0.0265298 −0.00139824
\(361\) −14.0011 −0.736898
\(362\) 43.8404 2.30420
\(363\) 16.5959 0.871061
\(364\) −0.0425813 −0.00223187
\(365\) −14.5285 −0.760458
\(366\) −27.1750 −1.42046
\(367\) −25.8411 −1.34890 −0.674448 0.738323i \(-0.735618\pi\)
−0.674448 + 0.738323i \(0.735618\pi\)
\(368\) −21.9226 −1.14279
\(369\) 0.0289009 0.00150452
\(370\) −42.1181 −2.18962
\(371\) 1.76039 0.0913951
\(372\) 8.29455 0.430053
\(373\) −4.12079 −0.213366 −0.106683 0.994293i \(-0.534023\pi\)
−0.106683 + 0.994293i \(0.534023\pi\)
\(374\) 46.9655 2.42853
\(375\) 8.73503 0.451075
\(376\) 5.29852 0.273250
\(377\) −0.0502541 −0.00258822
\(378\) −5.41395 −0.278464
\(379\) 7.22882 0.371319 0.185660 0.982614i \(-0.440558\pi\)
0.185660 + 0.982614i \(0.440558\pi\)
\(380\) −9.78505 −0.501962
\(381\) −28.5466 −1.46249
\(382\) 38.9144 1.99104
\(383\) −16.9406 −0.865622 −0.432811 0.901485i \(-0.642478\pi\)
−0.432811 + 0.901485i \(0.642478\pi\)
\(384\) −12.0521 −0.615029
\(385\) 7.24068 0.369019
\(386\) 34.7141 1.76690
\(387\) 0.0365439 0.00185763
\(388\) −1.07995 −0.0548260
\(389\) −8.63213 −0.437666 −0.218833 0.975762i \(-0.570225\pi\)
−0.218833 + 0.975762i \(0.570225\pi\)
\(390\) 0.470047 0.0238017
\(391\) −25.5944 −1.29436
\(392\) −5.97895 −0.301983
\(393\) −3.05844 −0.154278
\(394\) −45.8425 −2.30951
\(395\) −31.9960 −1.60989
\(396\) 0.0714485 0.00359042
\(397\) −4.05509 −0.203519 −0.101760 0.994809i \(-0.532447\pi\)
−0.101760 + 0.994809i \(0.532447\pi\)
\(398\) −16.8163 −0.842926
\(399\) −2.15682 −0.107976
\(400\) −15.3429 −0.767147
\(401\) 23.3972 1.16840 0.584200 0.811610i \(-0.301409\pi\)
0.584200 + 0.811610i \(0.301409\pi\)
\(402\) 16.6815 0.831997
\(403\) 0.157644 0.00785282
\(404\) 13.5475 0.674011
\(405\) 25.9344 1.28869
\(406\) −1.04372 −0.0517990
\(407\) −35.4302 −1.75621
\(408\) −8.55354 −0.423463
\(409\) −24.6601 −1.21936 −0.609682 0.792646i \(-0.708703\pi\)
−0.609682 + 0.792646i \(0.708703\pi\)
\(410\) 15.0704 0.744276
\(411\) −10.5281 −0.519311
\(412\) 16.6194 0.818778
\(413\) 2.20554 0.108528
\(414\) −0.0900352 −0.00442499
\(415\) −3.22242 −0.158182
\(416\) 0.355977 0.0174532
\(417\) −1.73503 −0.0849649
\(418\) −19.0337 −0.930966
\(419\) −21.9411 −1.07189 −0.535947 0.844251i \(-0.680045\pi\)
−0.535947 + 0.844251i \(0.680045\pi\)
\(420\) 4.22182 0.206004
\(421\) −0.244138 −0.0118986 −0.00594928 0.999982i \(-0.501894\pi\)
−0.00594928 + 0.999982i \(0.501894\pi\)
\(422\) 23.8146 1.15928
\(423\) 0.0612999 0.00298050
\(424\) −2.82933 −0.137405
\(425\) −17.9127 −0.868895
\(426\) 32.0599 1.55331
\(427\) −4.63888 −0.224491
\(428\) 29.3443 1.41841
\(429\) 0.395408 0.0190905
\(430\) 19.0559 0.918956
\(431\) 7.71546 0.371641 0.185820 0.982584i \(-0.440506\pi\)
0.185820 + 0.982584i \(0.440506\pi\)
\(432\) 24.5116 1.17932
\(433\) 17.2662 0.829760 0.414880 0.909876i \(-0.363824\pi\)
0.414880 + 0.909876i \(0.363824\pi\)
\(434\) 3.27409 0.157161
\(435\) 4.98256 0.238895
\(436\) −28.9368 −1.38582
\(437\) 10.3726 0.496188
\(438\) −16.4779 −0.787343
\(439\) −12.0832 −0.576698 −0.288349 0.957525i \(-0.593106\pi\)
−0.288349 + 0.957525i \(0.593106\pi\)
\(440\) −11.6373 −0.554788
\(441\) −0.0691720 −0.00329390
\(442\) 0.520457 0.0247556
\(443\) −38.6299 −1.83536 −0.917680 0.397320i \(-0.869940\pi\)
−0.917680 + 0.397320i \(0.869940\pi\)
\(444\) −20.6583 −0.980399
\(445\) 52.4542 2.48657
\(446\) −20.5500 −0.973071
\(447\) 23.2657 1.10043
\(448\) 2.13863 0.101041
\(449\) −14.4885 −0.683754 −0.341877 0.939745i \(-0.611063\pi\)
−0.341877 + 0.939745i \(0.611063\pi\)
\(450\) −0.0630130 −0.00297046
\(451\) 12.6774 0.596956
\(452\) 18.9137 0.889625
\(453\) −36.7684 −1.72753
\(454\) 33.2561 1.56079
\(455\) 0.0802389 0.00376166
\(456\) 3.46648 0.162333
\(457\) −14.9329 −0.698532 −0.349266 0.937024i \(-0.613569\pi\)
−0.349266 + 0.937024i \(0.613569\pi\)
\(458\) 13.8708 0.648141
\(459\) 28.6171 1.33573
\(460\) −20.3036 −0.946659
\(461\) −14.3483 −0.668266 −0.334133 0.942526i \(-0.608443\pi\)
−0.334133 + 0.942526i \(0.608443\pi\)
\(462\) 8.21219 0.382066
\(463\) 31.9347 1.48413 0.742067 0.670326i \(-0.233846\pi\)
0.742067 + 0.670326i \(0.233846\pi\)
\(464\) 4.72545 0.219373
\(465\) −15.6300 −0.724823
\(466\) 26.5901 1.23176
\(467\) 13.1388 0.607989 0.303995 0.952674i \(-0.401680\pi\)
0.303995 + 0.952674i \(0.401680\pi\)
\(468\) 0.000791769 0 3.65995e−5 0
\(469\) 2.84760 0.131490
\(470\) 31.9649 1.47443
\(471\) −21.2246 −0.977977
\(472\) −3.54478 −0.163162
\(473\) 16.0300 0.737061
\(474\) −36.2890 −1.66681
\(475\) 7.25947 0.333087
\(476\) 4.67459 0.214259
\(477\) −0.0327333 −0.00149875
\(478\) 28.4586 1.30167
\(479\) 10.4910 0.479344 0.239672 0.970854i \(-0.422960\pi\)
0.239672 + 0.970854i \(0.422960\pi\)
\(480\) −35.2941 −1.61095
\(481\) −0.392626 −0.0179022
\(482\) −2.16637 −0.0986757
\(483\) −4.47532 −0.203634
\(484\) 14.5772 0.662599
\(485\) 2.03502 0.0924053
\(486\) 0.201685 0.00914863
\(487\) 21.1668 0.959158 0.479579 0.877499i \(-0.340789\pi\)
0.479579 + 0.877499i \(0.340789\pi\)
\(488\) 7.45568 0.337503
\(489\) −32.9131 −1.48838
\(490\) −36.0698 −1.62947
\(491\) −17.8744 −0.806659 −0.403330 0.915055i \(-0.632147\pi\)
−0.403330 + 0.915055i \(0.632147\pi\)
\(492\) 7.39182 0.333249
\(493\) 5.51691 0.248469
\(494\) −0.210925 −0.00948995
\(495\) −0.134635 −0.00605140
\(496\) −14.8234 −0.665592
\(497\) 5.47275 0.245486
\(498\) −3.65478 −0.163775
\(499\) 17.7387 0.794091 0.397046 0.917799i \(-0.370035\pi\)
0.397046 + 0.917799i \(0.370035\pi\)
\(500\) 7.67249 0.343124
\(501\) −1.65660 −0.0740113
\(502\) 4.40486 0.196599
\(503\) −15.2157 −0.678437 −0.339218 0.940708i \(-0.610163\pi\)
−0.339218 + 0.940708i \(0.610163\pi\)
\(504\) −0.00513638 −0.000228793 0
\(505\) −25.5284 −1.13600
\(506\) −39.4940 −1.75572
\(507\) −22.5510 −1.00153
\(508\) −25.0742 −1.11249
\(509\) −20.2993 −0.899749 −0.449875 0.893092i \(-0.648531\pi\)
−0.449875 + 0.893092i \(0.648531\pi\)
\(510\) −51.6018 −2.28497
\(511\) −2.81284 −0.124433
\(512\) −25.0276 −1.10607
\(513\) −11.5976 −0.512047
\(514\) −12.5759 −0.554698
\(515\) −31.3170 −1.37999
\(516\) 9.34662 0.411462
\(517\) 26.8893 1.18259
\(518\) −8.15440 −0.358284
\(519\) −10.5045 −0.461098
\(520\) −0.128961 −0.00565532
\(521\) 18.8313 0.825016 0.412508 0.910954i \(-0.364653\pi\)
0.412508 + 0.910954i \(0.364653\pi\)
\(522\) 0.0194073 0.000849432 0
\(523\) 42.2221 1.84624 0.923121 0.384509i \(-0.125629\pi\)
0.923121 + 0.384509i \(0.125629\pi\)
\(524\) −2.68640 −0.117356
\(525\) −3.13214 −0.136698
\(526\) −20.6229 −0.899200
\(527\) −17.3062 −0.753871
\(528\) −37.1806 −1.61808
\(529\) −1.47730 −0.0642305
\(530\) −17.0688 −0.741422
\(531\) −0.0410104 −0.00177970
\(532\) −1.89446 −0.0821354
\(533\) 0.140487 0.00608517
\(534\) 59.4922 2.57448
\(535\) −55.2955 −2.39063
\(536\) −4.57670 −0.197683
\(537\) −1.40497 −0.0606287
\(538\) 9.45473 0.407622
\(539\) −30.3424 −1.30694
\(540\) 22.7015 0.976915
\(541\) 9.39905 0.404097 0.202048 0.979376i \(-0.435240\pi\)
0.202048 + 0.979376i \(0.435240\pi\)
\(542\) 22.3421 0.959673
\(543\) −40.5196 −1.73886
\(544\) −39.0792 −1.67551
\(545\) 54.5276 2.33571
\(546\) 0.0910048 0.00389465
\(547\) −9.33972 −0.399337 −0.199669 0.979863i \(-0.563987\pi\)
−0.199669 + 0.979863i \(0.563987\pi\)
\(548\) −9.24740 −0.395029
\(549\) 0.0862567 0.00368134
\(550\) −27.6407 −1.17860
\(551\) −2.23583 −0.0952496
\(552\) 7.19280 0.306146
\(553\) −6.19468 −0.263424
\(554\) −3.13693 −0.133275
\(555\) 38.9278 1.65239
\(556\) −1.52398 −0.0646311
\(557\) 16.7378 0.709202 0.354601 0.935018i \(-0.384617\pi\)
0.354601 + 0.935018i \(0.384617\pi\)
\(558\) −0.0608794 −0.00257723
\(559\) 0.177639 0.00751335
\(560\) −7.54494 −0.318832
\(561\) −43.4080 −1.83269
\(562\) −49.1544 −2.07345
\(563\) −32.5590 −1.37220 −0.686100 0.727508i \(-0.740679\pi\)
−0.686100 + 0.727508i \(0.740679\pi\)
\(564\) 15.6783 0.660176
\(565\) −35.6403 −1.49940
\(566\) 14.2730 0.599940
\(567\) 5.02111 0.210867
\(568\) −8.79589 −0.369067
\(569\) −25.7628 −1.08003 −0.540016 0.841655i \(-0.681582\pi\)
−0.540016 + 0.841655i \(0.681582\pi\)
\(570\) 20.9126 0.875932
\(571\) −35.8263 −1.49928 −0.749642 0.661843i \(-0.769774\pi\)
−0.749642 + 0.661843i \(0.769774\pi\)
\(572\) 0.347310 0.0145218
\(573\) −35.9668 −1.50253
\(574\) 2.91776 0.121785
\(575\) 15.0631 0.628175
\(576\) −0.0397662 −0.00165693
\(577\) −34.9677 −1.45573 −0.727863 0.685723i \(-0.759486\pi\)
−0.727863 + 0.685723i \(0.759486\pi\)
\(578\) −25.2230 −1.04914
\(579\) −32.0846 −1.33339
\(580\) 4.37647 0.181723
\(581\) −0.623886 −0.0258832
\(582\) 2.30806 0.0956722
\(583\) −14.3585 −0.594667
\(584\) 4.52084 0.187074
\(585\) −0.00149198 −6.16859e−5 0
\(586\) 3.73479 0.154283
\(587\) −0.0633451 −0.00261453 −0.00130727 0.999999i \(-0.500416\pi\)
−0.00130727 + 0.999999i \(0.500416\pi\)
\(588\) −17.6917 −0.729594
\(589\) 7.01367 0.288993
\(590\) −21.3850 −0.880405
\(591\) 42.3701 1.74287
\(592\) 36.9190 1.51736
\(593\) 23.6098 0.969536 0.484768 0.874643i \(-0.338904\pi\)
0.484768 + 0.874643i \(0.338904\pi\)
\(594\) 44.1584 1.81184
\(595\) −8.80864 −0.361119
\(596\) 20.4356 0.837077
\(597\) 15.5425 0.636114
\(598\) −0.437660 −0.0178972
\(599\) 15.7719 0.644422 0.322211 0.946668i \(-0.395574\pi\)
0.322211 + 0.946668i \(0.395574\pi\)
\(600\) 5.03403 0.205513
\(601\) 0.148506 0.00605770 0.00302885 0.999995i \(-0.499036\pi\)
0.00302885 + 0.999995i \(0.499036\pi\)
\(602\) 3.68937 0.150368
\(603\) −0.0529490 −0.00215625
\(604\) −32.2958 −1.31410
\(605\) −27.4688 −1.11676
\(606\) −28.9536 −1.17616
\(607\) −22.0786 −0.896143 −0.448072 0.893998i \(-0.647889\pi\)
−0.448072 + 0.893998i \(0.647889\pi\)
\(608\) 15.8376 0.642299
\(609\) 0.964663 0.0390901
\(610\) 44.9787 1.82113
\(611\) 0.297978 0.0120549
\(612\) −0.0869205 −0.00351355
\(613\) −34.9845 −1.41301 −0.706506 0.707707i \(-0.749730\pi\)
−0.706506 + 0.707707i \(0.749730\pi\)
\(614\) 23.9890 0.968116
\(615\) −13.9289 −0.561667
\(616\) −2.25308 −0.0907792
\(617\) −11.5785 −0.466132 −0.233066 0.972461i \(-0.574876\pi\)
−0.233066 + 0.972461i \(0.574876\pi\)
\(618\) −35.5189 −1.42878
\(619\) −18.5995 −0.747577 −0.373788 0.927514i \(-0.621941\pi\)
−0.373788 + 0.927514i \(0.621941\pi\)
\(620\) −13.7287 −0.551359
\(621\) −24.0646 −0.965678
\(622\) 32.3391 1.29668
\(623\) 10.1556 0.406874
\(624\) −0.412024 −0.0164941
\(625\) −30.6922 −1.22769
\(626\) 22.0010 0.879338
\(627\) 17.5919 0.702553
\(628\) −18.6428 −0.743928
\(629\) 43.1026 1.71861
\(630\) −0.0309868 −0.00123454
\(631\) 38.3653 1.52730 0.763649 0.645631i \(-0.223406\pi\)
0.763649 + 0.645631i \(0.223406\pi\)
\(632\) 9.95618 0.396035
\(633\) −22.0107 −0.874847
\(634\) −35.3143 −1.40251
\(635\) 47.2489 1.87502
\(636\) −8.37199 −0.331971
\(637\) −0.336244 −0.0133225
\(638\) 8.51301 0.337033
\(639\) −0.101762 −0.00402564
\(640\) 19.9479 0.788512
\(641\) −15.2952 −0.604123 −0.302061 0.953288i \(-0.597675\pi\)
−0.302061 + 0.953288i \(0.597675\pi\)
\(642\) −62.7147 −2.47515
\(643\) 4.91363 0.193774 0.0968872 0.995295i \(-0.469111\pi\)
0.0968872 + 0.995295i \(0.469111\pi\)
\(644\) −3.93093 −0.154900
\(645\) −17.6125 −0.693490
\(646\) 23.1554 0.911035
\(647\) −36.7115 −1.44328 −0.721639 0.692270i \(-0.756611\pi\)
−0.721639 + 0.692270i \(0.756611\pi\)
\(648\) −8.07000 −0.317020
\(649\) −17.9893 −0.706140
\(650\) −0.306305 −0.0120143
\(651\) −3.02609 −0.118602
\(652\) −28.9095 −1.13218
\(653\) 6.45160 0.252471 0.126235 0.992000i \(-0.459711\pi\)
0.126235 + 0.992000i \(0.459711\pi\)
\(654\) 61.8438 2.41828
\(655\) 5.06217 0.197795
\(656\) −13.2101 −0.515769
\(657\) 0.0523027 0.00204052
\(658\) 6.18867 0.241259
\(659\) 25.7894 1.00461 0.502307 0.864690i \(-0.332485\pi\)
0.502307 + 0.864690i \(0.332485\pi\)
\(660\) −34.4348 −1.34037
\(661\) 10.7697 0.418894 0.209447 0.977820i \(-0.432834\pi\)
0.209447 + 0.977820i \(0.432834\pi\)
\(662\) 17.2270 0.669547
\(663\) −0.481034 −0.0186818
\(664\) 1.00272 0.0389130
\(665\) 3.56986 0.138433
\(666\) 0.151625 0.00587536
\(667\) −4.63926 −0.179633
\(668\) −1.45509 −0.0562990
\(669\) 18.9934 0.734327
\(670\) −27.6103 −1.06668
\(671\) 37.8366 1.46066
\(672\) −6.83323 −0.263597
\(673\) 49.1765 1.89562 0.947808 0.318841i \(-0.103293\pi\)
0.947808 + 0.318841i \(0.103293\pi\)
\(674\) 33.9977 1.30954
\(675\) −16.8421 −0.648252
\(676\) −19.8079 −0.761842
\(677\) −13.6283 −0.523777 −0.261889 0.965098i \(-0.584345\pi\)
−0.261889 + 0.965098i \(0.584345\pi\)
\(678\) −40.4223 −1.55241
\(679\) 0.393995 0.0151202
\(680\) 14.1574 0.542911
\(681\) −30.7371 −1.17785
\(682\) −26.7048 −1.02258
\(683\) −11.8483 −0.453361 −0.226680 0.973969i \(-0.572787\pi\)
−0.226680 + 0.973969i \(0.572787\pi\)
\(684\) 0.0352262 0.00134691
\(685\) 17.4255 0.665794
\(686\) −14.2895 −0.545574
\(687\) −12.8201 −0.489119
\(688\) −16.7036 −0.636819
\(689\) −0.159116 −0.00606184
\(690\) 43.3928 1.65193
\(691\) −5.19618 −0.197672 −0.0988361 0.995104i \(-0.531512\pi\)
−0.0988361 + 0.995104i \(0.531512\pi\)
\(692\) −9.22673 −0.350748
\(693\) −0.0260665 −0.000990183 0
\(694\) 36.8037 1.39705
\(695\) 2.87174 0.108931
\(696\) −1.55042 −0.0587686
\(697\) −15.4227 −0.584176
\(698\) 39.7236 1.50356
\(699\) −24.5760 −0.929548
\(700\) −2.75114 −0.103983
\(701\) 48.1565 1.81885 0.909423 0.415873i \(-0.136524\pi\)
0.909423 + 0.415873i \(0.136524\pi\)
\(702\) 0.489348 0.0184693
\(703\) −17.4681 −0.658823
\(704\) −17.4435 −0.657427
\(705\) −29.5437 −1.11268
\(706\) −31.7728 −1.19579
\(707\) −4.94250 −0.185882
\(708\) −10.4890 −0.394200
\(709\) 17.7774 0.667644 0.333822 0.942636i \(-0.391662\pi\)
0.333822 + 0.942636i \(0.391662\pi\)
\(710\) −53.0639 −1.99145
\(711\) 0.115186 0.00431979
\(712\) −16.3222 −0.611699
\(713\) 14.5531 0.545017
\(714\) −9.99053 −0.373886
\(715\) −0.654460 −0.0244754
\(716\) −1.23406 −0.0461191
\(717\) −26.3029 −0.982301
\(718\) −61.9337 −2.31134
\(719\) −0.0699317 −0.00260801 −0.00130401 0.999999i \(-0.500415\pi\)
−0.00130401 + 0.999999i \(0.500415\pi\)
\(720\) 0.140293 0.00522840
\(721\) −6.06322 −0.225806
\(722\) 26.2832 0.978158
\(723\) 2.00228 0.0744655
\(724\) −35.5907 −1.32272
\(725\) −3.24688 −0.120586
\(726\) −31.1543 −1.15625
\(727\) −31.4674 −1.16706 −0.583531 0.812091i \(-0.698329\pi\)
−0.583531 + 0.812091i \(0.698329\pi\)
\(728\) −0.0249679 −0.000925372 0
\(729\) 26.9063 0.996530
\(730\) 27.2733 1.00943
\(731\) −19.5013 −0.721282
\(732\) 22.0614 0.815411
\(733\) 46.0133 1.69954 0.849769 0.527155i \(-0.176741\pi\)
0.849769 + 0.527155i \(0.176741\pi\)
\(734\) 48.5096 1.79052
\(735\) 33.3377 1.22968
\(736\) 32.8623 1.21132
\(737\) −23.2261 −0.855545
\(738\) −0.0542536 −0.00199710
\(739\) 37.4764 1.37859 0.689296 0.724480i \(-0.257920\pi\)
0.689296 + 0.724480i \(0.257920\pi\)
\(740\) 34.1925 1.25694
\(741\) 0.194948 0.00716159
\(742\) −3.30466 −0.121318
\(743\) 41.1979 1.51141 0.755703 0.654914i \(-0.227295\pi\)
0.755703 + 0.654914i \(0.227295\pi\)
\(744\) 4.86358 0.178307
\(745\) −38.5083 −1.41083
\(746\) 7.73566 0.283223
\(747\) 0.0116007 0.000424448 0
\(748\) −38.1278 −1.39409
\(749\) −10.7056 −0.391176
\(750\) −16.3976 −0.598757
\(751\) −18.1934 −0.663887 −0.331944 0.943299i \(-0.607704\pi\)
−0.331944 + 0.943299i \(0.607704\pi\)
\(752\) −28.0192 −1.02175
\(753\) −4.07121 −0.148363
\(754\) 0.0943384 0.00343560
\(755\) 60.8572 2.21482
\(756\) 4.39518 0.159851
\(757\) 37.5292 1.36402 0.682011 0.731342i \(-0.261106\pi\)
0.682011 + 0.731342i \(0.261106\pi\)
\(758\) −13.5701 −0.492889
\(759\) 36.5025 1.32496
\(760\) −5.73754 −0.208122
\(761\) 47.1347 1.70863 0.854315 0.519755i \(-0.173977\pi\)
0.854315 + 0.519755i \(0.173977\pi\)
\(762\) 53.5885 1.94131
\(763\) 10.5570 0.382189
\(764\) −31.5917 −1.14295
\(765\) 0.163790 0.00592185
\(766\) 31.8013 1.14903
\(767\) −0.199351 −0.00719815
\(768\) 35.9721 1.29803
\(769\) −39.5419 −1.42592 −0.712959 0.701206i \(-0.752645\pi\)
−0.712959 + 0.701206i \(0.752645\pi\)
\(770\) −13.5924 −0.489836
\(771\) 11.6233 0.418603
\(772\) −28.1818 −1.01428
\(773\) 32.1256 1.15548 0.577740 0.816221i \(-0.303935\pi\)
0.577740 + 0.816221i \(0.303935\pi\)
\(774\) −0.0686012 −0.00246582
\(775\) 10.1853 0.365865
\(776\) −0.633235 −0.0227318
\(777\) 7.53673 0.270379
\(778\) 16.2045 0.580958
\(779\) 6.25033 0.223941
\(780\) −0.381596 −0.0136633
\(781\) −44.6379 −1.59727
\(782\) 48.0464 1.71814
\(783\) 5.18716 0.185374
\(784\) 31.6174 1.12919
\(785\) 35.1298 1.25384
\(786\) 5.74138 0.204788
\(787\) 39.0458 1.39183 0.695917 0.718122i \(-0.254998\pi\)
0.695917 + 0.718122i \(0.254998\pi\)
\(788\) 37.2161 1.32577
\(789\) 19.0608 0.678581
\(790\) 60.0637 2.13697
\(791\) −6.90025 −0.245345
\(792\) 0.0418944 0.00148865
\(793\) 0.419293 0.0148895
\(794\) 7.61232 0.270151
\(795\) 15.7759 0.559514
\(796\) 13.6519 0.483879
\(797\) 11.3681 0.402680 0.201340 0.979521i \(-0.435470\pi\)
0.201340 + 0.979521i \(0.435470\pi\)
\(798\) 4.04885 0.143328
\(799\) −32.7121 −1.15727
\(800\) 22.9994 0.813151
\(801\) −0.188835 −0.00667217
\(802\) −43.9218 −1.55093
\(803\) 22.9426 0.809628
\(804\) −13.5424 −0.477605
\(805\) 7.40732 0.261074
\(806\) −0.295934 −0.0104238
\(807\) −8.73857 −0.307612
\(808\) 7.94366 0.279457
\(809\) −41.2031 −1.44862 −0.724312 0.689472i \(-0.757843\pi\)
−0.724312 + 0.689472i \(0.757843\pi\)
\(810\) −48.6847 −1.71061
\(811\) −18.0016 −0.632123 −0.316062 0.948739i \(-0.602361\pi\)
−0.316062 + 0.948739i \(0.602361\pi\)
\(812\) 0.847320 0.0297351
\(813\) −20.6497 −0.724217
\(814\) 66.5106 2.33119
\(815\) 54.4760 1.90821
\(816\) 45.2321 1.58344
\(817\) 7.90326 0.276500
\(818\) 46.2926 1.61858
\(819\) −0.000288860 0 −1.00936e−5 0
\(820\) −12.2346 −0.427249
\(821\) −8.73756 −0.304943 −0.152471 0.988308i \(-0.548723\pi\)
−0.152471 + 0.988308i \(0.548723\pi\)
\(822\) 19.7635 0.689333
\(823\) 7.33282 0.255606 0.127803 0.991800i \(-0.459207\pi\)
0.127803 + 0.991800i \(0.459207\pi\)
\(824\) 9.74490 0.339480
\(825\) 25.5470 0.889433
\(826\) −4.14030 −0.144059
\(827\) −29.4782 −1.02506 −0.512529 0.858670i \(-0.671291\pi\)
−0.512529 + 0.858670i \(0.671291\pi\)
\(828\) 0.0730928 0.00254015
\(829\) 29.6707 1.03051 0.515254 0.857038i \(-0.327698\pi\)
0.515254 + 0.857038i \(0.327698\pi\)
\(830\) 6.04921 0.209971
\(831\) 2.89931 0.100576
\(832\) −0.193303 −0.00670158
\(833\) 36.9129 1.27896
\(834\) 3.25705 0.112782
\(835\) 2.74192 0.0948879
\(836\) 15.4520 0.534418
\(837\) −16.2718 −0.562436
\(838\) 41.1885 1.42283
\(839\) 29.8847 1.03174 0.515868 0.856668i \(-0.327470\pi\)
0.515868 + 0.856668i \(0.327470\pi\)
\(840\) 2.47550 0.0854128
\(841\) 1.00000 0.0344828
\(842\) 0.458302 0.0157941
\(843\) 45.4311 1.56473
\(844\) −19.3333 −0.665479
\(845\) 37.3253 1.28403
\(846\) −0.115074 −0.00395632
\(847\) −5.31817 −0.182735
\(848\) 14.9618 0.513791
\(849\) −13.1919 −0.452744
\(850\) 33.6263 1.15337
\(851\) −36.2456 −1.24248
\(852\) −26.0270 −0.891671
\(853\) 11.2910 0.386596 0.193298 0.981140i \(-0.438082\pi\)
0.193298 + 0.981140i \(0.438082\pi\)
\(854\) 8.70823 0.297990
\(855\) −0.0663790 −0.00227012
\(856\) 17.2063 0.588098
\(857\) −25.9231 −0.885518 −0.442759 0.896641i \(-0.646000\pi\)
−0.442759 + 0.896641i \(0.646000\pi\)
\(858\) −0.742271 −0.0253407
\(859\) 3.96198 0.135181 0.0675905 0.997713i \(-0.478469\pi\)
0.0675905 + 0.997713i \(0.478469\pi\)
\(860\) −15.4700 −0.527524
\(861\) −2.69675 −0.0919049
\(862\) −14.4837 −0.493316
\(863\) −55.4334 −1.88697 −0.943487 0.331409i \(-0.892476\pi\)
−0.943487 + 0.331409i \(0.892476\pi\)
\(864\) −36.7434 −1.25004
\(865\) 17.3866 0.591161
\(866\) −32.4126 −1.10142
\(867\) 23.3124 0.791731
\(868\) −2.65799 −0.0902181
\(869\) 50.5262 1.71399
\(870\) −9.35339 −0.317110
\(871\) −0.257384 −0.00872114
\(872\) −16.9673 −0.574587
\(873\) −0.00732606 −0.000247950 0
\(874\) −19.4717 −0.658640
\(875\) −2.79914 −0.0946283
\(876\) 13.3772 0.451972
\(877\) 6.19149 0.209072 0.104536 0.994521i \(-0.466664\pi\)
0.104536 + 0.994521i \(0.466664\pi\)
\(878\) 22.6828 0.765509
\(879\) −3.45189 −0.116429
\(880\) 61.5395 2.07450
\(881\) −7.09173 −0.238926 −0.119463 0.992839i \(-0.538117\pi\)
−0.119463 + 0.992839i \(0.538117\pi\)
\(882\) 0.129851 0.00437233
\(883\) 20.7671 0.698870 0.349435 0.936961i \(-0.386374\pi\)
0.349435 + 0.936961i \(0.386374\pi\)
\(884\) −0.422520 −0.0142109
\(885\) 19.7651 0.664397
\(886\) 72.5170 2.43626
\(887\) 53.6912 1.80277 0.901387 0.433013i \(-0.142550\pi\)
0.901387 + 0.433013i \(0.142550\pi\)
\(888\) −12.1132 −0.406491
\(889\) 9.14777 0.306806
\(890\) −98.4685 −3.30067
\(891\) −40.9542 −1.37202
\(892\) 16.6830 0.558588
\(893\) 13.2572 0.443635
\(894\) −43.6751 −1.46071
\(895\) 2.32543 0.0777304
\(896\) 3.86208 0.129023
\(897\) 0.404509 0.0135062
\(898\) 27.1982 0.907614
\(899\) −3.13694 −0.104623
\(900\) 0.0511555 0.00170518
\(901\) 17.4678 0.581936
\(902\) −23.7984 −0.792400
\(903\) −3.40991 −0.113475
\(904\) 11.0902 0.368854
\(905\) 67.0660 2.22935
\(906\) 69.0227 2.29312
\(907\) −41.0193 −1.36202 −0.681012 0.732272i \(-0.738460\pi\)
−0.681012 + 0.732272i \(0.738460\pi\)
\(908\) −26.9982 −0.895966
\(909\) 0.0919022 0.00304820
\(910\) −0.150627 −0.00499322
\(911\) 10.3907 0.344260 0.172130 0.985074i \(-0.444935\pi\)
0.172130 + 0.985074i \(0.444935\pi\)
\(912\) −18.3311 −0.607004
\(913\) 5.08866 0.168410
\(914\) 28.0324 0.927231
\(915\) −41.5717 −1.37432
\(916\) −11.2607 −0.372063
\(917\) 0.980077 0.0323650
\(918\) −53.7208 −1.77305
\(919\) −59.3865 −1.95898 −0.979489 0.201495i \(-0.935420\pi\)
−0.979489 + 0.201495i \(0.935420\pi\)
\(920\) −11.9052 −0.392502
\(921\) −22.1719 −0.730588
\(922\) 26.9350 0.887056
\(923\) −0.494663 −0.0162820
\(924\) −6.66686 −0.219324
\(925\) −25.3672 −0.834070
\(926\) −59.9488 −1.97004
\(927\) 0.112741 0.00370291
\(928\) −7.08354 −0.232528
\(929\) 5.84210 0.191673 0.0958366 0.995397i \(-0.469447\pi\)
0.0958366 + 0.995397i \(0.469447\pi\)
\(930\) 29.3410 0.962130
\(931\) −14.9597 −0.490283
\(932\) −21.5865 −0.707089
\(933\) −29.8895 −0.978539
\(934\) −24.6644 −0.807045
\(935\) 71.8468 2.34964
\(936\) 0.000464260 0 1.51748e−5 0
\(937\) −15.2965 −0.499714 −0.249857 0.968283i \(-0.580384\pi\)
−0.249857 + 0.968283i \(0.580384\pi\)
\(938\) −5.34558 −0.174540
\(939\) −20.3345 −0.663592
\(940\) −25.9499 −0.846394
\(941\) −21.5741 −0.703295 −0.351648 0.936132i \(-0.614379\pi\)
−0.351648 + 0.936132i \(0.614379\pi\)
\(942\) 39.8433 1.29817
\(943\) 12.9692 0.422335
\(944\) 18.7452 0.610104
\(945\) −8.28214 −0.269418
\(946\) −30.0920 −0.978375
\(947\) −26.1596 −0.850072 −0.425036 0.905176i \(-0.639739\pi\)
−0.425036 + 0.905176i \(0.639739\pi\)
\(948\) 29.4603 0.956827
\(949\) 0.254243 0.00825307
\(950\) −13.6277 −0.442140
\(951\) 32.6394 1.05840
\(952\) 2.74098 0.0888357
\(953\) 56.0352 1.81516 0.907580 0.419880i \(-0.137928\pi\)
0.907580 + 0.419880i \(0.137928\pi\)
\(954\) 0.0614478 0.00198944
\(955\) 59.5304 1.92636
\(956\) −23.1034 −0.747217
\(957\) −7.86818 −0.254342
\(958\) −19.6939 −0.636281
\(959\) 3.37372 0.108943
\(960\) 19.1655 0.618563
\(961\) −21.1596 −0.682568
\(962\) 0.737048 0.0237634
\(963\) 0.199064 0.00641474
\(964\) 1.75872 0.0566445
\(965\) 53.1048 1.70950
\(966\) 8.40119 0.270304
\(967\) −37.9486 −1.22034 −0.610172 0.792269i \(-0.708900\pi\)
−0.610172 + 0.792269i \(0.708900\pi\)
\(968\) 8.54745 0.274725
\(969\) −21.4014 −0.687512
\(970\) −3.82019 −0.122659
\(971\) −42.8778 −1.37601 −0.688006 0.725705i \(-0.741514\pi\)
−0.688006 + 0.725705i \(0.741514\pi\)
\(972\) −0.163733 −0.00525174
\(973\) 0.555991 0.0178243
\(974\) −39.7348 −1.27319
\(975\) 0.283104 0.00906657
\(976\) −39.4265 −1.26201
\(977\) 6.07486 0.194352 0.0971760 0.995267i \(-0.469019\pi\)
0.0971760 + 0.995267i \(0.469019\pi\)
\(978\) 61.7853 1.97568
\(979\) −82.8328 −2.64735
\(980\) 29.2824 0.935392
\(981\) −0.196299 −0.00626736
\(982\) 33.5543 1.07076
\(983\) −13.1994 −0.420996 −0.210498 0.977594i \(-0.567508\pi\)
−0.210498 + 0.977594i \(0.567508\pi\)
\(984\) 4.33425 0.138171
\(985\) −70.1288 −2.23449
\(986\) −10.3565 −0.329818
\(987\) −5.71990 −0.182066
\(988\) 0.171234 0.00544768
\(989\) 16.3989 0.521456
\(990\) 0.252741 0.00803263
\(991\) 45.3527 1.44068 0.720338 0.693623i \(-0.243987\pi\)
0.720338 + 0.693623i \(0.243987\pi\)
\(992\) 22.2206 0.705506
\(993\) −15.9221 −0.505273
\(994\) −10.2736 −0.325859
\(995\) −25.7252 −0.815544
\(996\) 2.96704 0.0940144
\(997\) 53.5534 1.69605 0.848027 0.529954i \(-0.177791\pi\)
0.848027 + 0.529954i \(0.177791\pi\)
\(998\) −33.2995 −1.05408
\(999\) 40.5263 1.28220
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 \(a_p\))