Properties

Label 6010.2.a.c.1.6
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.624714\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.62471 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.62471 q^{6}\) \(-0.333284 q^{7}\) \(+1.00000 q^{8}\) \(-0.360304 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.62471 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.62471 q^{6}\) \(-0.333284 q^{7}\) \(+1.00000 q^{8}\) \(-0.360304 q^{9}\) \(+1.00000 q^{10}\) \(-2.68771 q^{11}\) \(-1.62471 q^{12}\) \(+1.45394 q^{13}\) \(-0.333284 q^{14}\) \(-1.62471 q^{15}\) \(+1.00000 q^{16}\) \(-4.11004 q^{17}\) \(-0.360304 q^{18}\) \(+8.34271 q^{19}\) \(+1.00000 q^{20}\) \(+0.541491 q^{21}\) \(-2.68771 q^{22}\) \(-4.74671 q^{23}\) \(-1.62471 q^{24}\) \(+1.00000 q^{25}\) \(+1.45394 q^{26}\) \(+5.45953 q^{27}\) \(-0.333284 q^{28}\) \(-1.44606 q^{29}\) \(-1.62471 q^{30}\) \(-3.92911 q^{31}\) \(+1.00000 q^{32}\) \(+4.36676 q^{33}\) \(-4.11004 q^{34}\) \(-0.333284 q^{35}\) \(-0.360304 q^{36}\) \(+3.53964 q^{37}\) \(+8.34271 q^{38}\) \(-2.36224 q^{39}\) \(+1.00000 q^{40}\) \(+2.16999 q^{41}\) \(+0.541491 q^{42}\) \(-5.62222 q^{43}\) \(-2.68771 q^{44}\) \(-0.360304 q^{45}\) \(-4.74671 q^{46}\) \(+6.48708 q^{47}\) \(-1.62471 q^{48}\) \(-6.88892 q^{49}\) \(+1.00000 q^{50}\) \(+6.67763 q^{51}\) \(+1.45394 q^{52}\) \(-5.31846 q^{53}\) \(+5.45953 q^{54}\) \(-2.68771 q^{55}\) \(-0.333284 q^{56}\) \(-13.5545 q^{57}\) \(-1.44606 q^{58}\) \(-3.43978 q^{59}\) \(-1.62471 q^{60}\) \(-8.19878 q^{61}\) \(-3.92911 q^{62}\) \(+0.120083 q^{63}\) \(+1.00000 q^{64}\) \(+1.45394 q^{65}\) \(+4.36676 q^{66}\) \(+3.23813 q^{67}\) \(-4.11004 q^{68}\) \(+7.71204 q^{69}\) \(-0.333284 q^{70}\) \(+0.556242 q^{71}\) \(-0.360304 q^{72}\) \(+12.1155 q^{73}\) \(+3.53964 q^{74}\) \(-1.62471 q^{75}\) \(+8.34271 q^{76}\) \(+0.895770 q^{77}\) \(-2.36224 q^{78}\) \(+2.81119 q^{79}\) \(+1.00000 q^{80}\) \(-7.78927 q^{81}\) \(+2.16999 q^{82}\) \(-5.47476 q^{83}\) \(+0.541491 q^{84}\) \(-4.11004 q^{85}\) \(-5.62222 q^{86}\) \(+2.34944 q^{87}\) \(-2.68771 q^{88}\) \(-11.3071 q^{89}\) \(-0.360304 q^{90}\) \(-0.484576 q^{91}\) \(-4.74671 q^{92}\) \(+6.38368 q^{93}\) \(+6.48708 q^{94}\) \(+8.34271 q^{95}\) \(-1.62471 q^{96}\) \(+13.6146 q^{97}\) \(-6.88892 q^{98}\) \(+0.968392 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.62471 −0.938029 −0.469015 0.883190i \(-0.655391\pi\)
−0.469015 + 0.883190i \(0.655391\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.62471 −0.663287
\(7\) −0.333284 −0.125969 −0.0629847 0.998014i \(-0.520062\pi\)
−0.0629847 + 0.998014i \(0.520062\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.360304 −0.120101
\(10\) 1.00000 0.316228
\(11\) −2.68771 −0.810375 −0.405187 0.914234i \(-0.632794\pi\)
−0.405187 + 0.914234i \(0.632794\pi\)
\(12\) −1.62471 −0.469015
\(13\) 1.45394 0.403251 0.201625 0.979463i \(-0.435378\pi\)
0.201625 + 0.979463i \(0.435378\pi\)
\(14\) −0.333284 −0.0890739
\(15\) −1.62471 −0.419499
\(16\) 1.00000 0.250000
\(17\) −4.11004 −0.996830 −0.498415 0.866939i \(-0.666084\pi\)
−0.498415 + 0.866939i \(0.666084\pi\)
\(18\) −0.360304 −0.0849244
\(19\) 8.34271 1.91395 0.956975 0.290172i \(-0.0937124\pi\)
0.956975 + 0.290172i \(0.0937124\pi\)
\(20\) 1.00000 0.223607
\(21\) 0.541491 0.118163
\(22\) −2.68771 −0.573022
\(23\) −4.74671 −0.989757 −0.494878 0.868962i \(-0.664787\pi\)
−0.494878 + 0.868962i \(0.664787\pi\)
\(24\) −1.62471 −0.331643
\(25\) 1.00000 0.200000
\(26\) 1.45394 0.285141
\(27\) 5.45953 1.05069
\(28\) −0.333284 −0.0629847
\(29\) −1.44606 −0.268527 −0.134264 0.990946i \(-0.542867\pi\)
−0.134264 + 0.990946i \(0.542867\pi\)
\(30\) −1.62471 −0.296631
\(31\) −3.92911 −0.705689 −0.352844 0.935682i \(-0.614785\pi\)
−0.352844 + 0.935682i \(0.614785\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.36676 0.760155
\(34\) −4.11004 −0.704865
\(35\) −0.333284 −0.0563353
\(36\) −0.360304 −0.0600506
\(37\) 3.53964 0.581913 0.290956 0.956736i \(-0.406027\pi\)
0.290956 + 0.956736i \(0.406027\pi\)
\(38\) 8.34271 1.35337
\(39\) −2.36224 −0.378261
\(40\) 1.00000 0.158114
\(41\) 2.16999 0.338896 0.169448 0.985539i \(-0.445801\pi\)
0.169448 + 0.985539i \(0.445801\pi\)
\(42\) 0.541491 0.0835539
\(43\) −5.62222 −0.857381 −0.428690 0.903451i \(-0.641025\pi\)
−0.428690 + 0.903451i \(0.641025\pi\)
\(44\) −2.68771 −0.405187
\(45\) −0.360304 −0.0537109
\(46\) −4.74671 −0.699864
\(47\) 6.48708 0.946238 0.473119 0.880999i \(-0.343128\pi\)
0.473119 + 0.880999i \(0.343128\pi\)
\(48\) −1.62471 −0.234507
\(49\) −6.88892 −0.984132
\(50\) 1.00000 0.141421
\(51\) 6.67763 0.935056
\(52\) 1.45394 0.201625
\(53\) −5.31846 −0.730547 −0.365273 0.930900i \(-0.619025\pi\)
−0.365273 + 0.930900i \(0.619025\pi\)
\(54\) 5.45953 0.742948
\(55\) −2.68771 −0.362411
\(56\) −0.333284 −0.0445369
\(57\) −13.5545 −1.79534
\(58\) −1.44606 −0.189877
\(59\) −3.43978 −0.447822 −0.223911 0.974610i \(-0.571882\pi\)
−0.223911 + 0.974610i \(0.571882\pi\)
\(60\) −1.62471 −0.209750
\(61\) −8.19878 −1.04975 −0.524873 0.851181i \(-0.675887\pi\)
−0.524873 + 0.851181i \(0.675887\pi\)
\(62\) −3.92911 −0.498997
\(63\) 0.120083 0.0151291
\(64\) 1.00000 0.125000
\(65\) 1.45394 0.180339
\(66\) 4.36676 0.537511
\(67\) 3.23813 0.395600 0.197800 0.980242i \(-0.436620\pi\)
0.197800 + 0.980242i \(0.436620\pi\)
\(68\) −4.11004 −0.498415
\(69\) 7.71204 0.928421
\(70\) −0.333284 −0.0398350
\(71\) 0.556242 0.0660137 0.0330069 0.999455i \(-0.489492\pi\)
0.0330069 + 0.999455i \(0.489492\pi\)
\(72\) −0.360304 −0.0424622
\(73\) 12.1155 1.41801 0.709007 0.705201i \(-0.249143\pi\)
0.709007 + 0.705201i \(0.249143\pi\)
\(74\) 3.53964 0.411475
\(75\) −1.62471 −0.187606
\(76\) 8.34271 0.956975
\(77\) 0.895770 0.102083
\(78\) −2.36224 −0.267471
\(79\) 2.81119 0.316283 0.158142 0.987416i \(-0.449450\pi\)
0.158142 + 0.987416i \(0.449450\pi\)
\(80\) 1.00000 0.111803
\(81\) −7.78927 −0.865474
\(82\) 2.16999 0.239636
\(83\) −5.47476 −0.600933 −0.300466 0.953792i \(-0.597142\pi\)
−0.300466 + 0.953792i \(0.597142\pi\)
\(84\) 0.541491 0.0590815
\(85\) −4.11004 −0.445796
\(86\) −5.62222 −0.606260
\(87\) 2.34944 0.251886
\(88\) −2.68771 −0.286511
\(89\) −11.3071 −1.19855 −0.599276 0.800542i \(-0.704545\pi\)
−0.599276 + 0.800542i \(0.704545\pi\)
\(90\) −0.360304 −0.0379793
\(91\) −0.484576 −0.0507973
\(92\) −4.74671 −0.494878
\(93\) 6.38368 0.661956
\(94\) 6.48708 0.669091
\(95\) 8.34271 0.855944
\(96\) −1.62471 −0.165822
\(97\) 13.6146 1.38235 0.691174 0.722688i \(-0.257094\pi\)
0.691174 + 0.722688i \(0.257094\pi\)
\(98\) −6.88892 −0.695886
\(99\) 0.968392 0.0973270
\(100\) 1.00000 0.100000
\(101\) −11.3537 −1.12973 −0.564865 0.825183i \(-0.691072\pi\)
−0.564865 + 0.825183i \(0.691072\pi\)
\(102\) 6.67763 0.661184
\(103\) −12.9895 −1.27990 −0.639948 0.768418i \(-0.721044\pi\)
−0.639948 + 0.768418i \(0.721044\pi\)
\(104\) 1.45394 0.142571
\(105\) 0.541491 0.0528441
\(106\) −5.31846 −0.516575
\(107\) −11.8474 −1.14533 −0.572664 0.819790i \(-0.694090\pi\)
−0.572664 + 0.819790i \(0.694090\pi\)
\(108\) 5.45953 0.525344
\(109\) −15.6620 −1.50015 −0.750073 0.661355i \(-0.769982\pi\)
−0.750073 + 0.661355i \(0.769982\pi\)
\(110\) −2.68771 −0.256263
\(111\) −5.75090 −0.545851
\(112\) −0.333284 −0.0314924
\(113\) −3.77807 −0.355411 −0.177705 0.984084i \(-0.556867\pi\)
−0.177705 + 0.984084i \(0.556867\pi\)
\(114\) −13.5545 −1.26950
\(115\) −4.74671 −0.442633
\(116\) −1.44606 −0.134264
\(117\) −0.523861 −0.0484309
\(118\) −3.43978 −0.316658
\(119\) 1.36981 0.125570
\(120\) −1.62471 −0.148315
\(121\) −3.77622 −0.343292
\(122\) −8.19878 −0.742282
\(123\) −3.52562 −0.317894
\(124\) −3.92911 −0.352844
\(125\) 1.00000 0.0894427
\(126\) 0.120083 0.0106979
\(127\) −18.1828 −1.61346 −0.806729 0.590921i \(-0.798764\pi\)
−0.806729 + 0.590921i \(0.798764\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.13450 0.804248
\(130\) 1.45394 0.127519
\(131\) −16.2325 −1.41824 −0.709119 0.705088i \(-0.750907\pi\)
−0.709119 + 0.705088i \(0.750907\pi\)
\(132\) 4.36676 0.380078
\(133\) −2.78049 −0.241099
\(134\) 3.23813 0.279732
\(135\) 5.45953 0.469882
\(136\) −4.11004 −0.352433
\(137\) 13.9834 1.19468 0.597341 0.801988i \(-0.296224\pi\)
0.597341 + 0.801988i \(0.296224\pi\)
\(138\) 7.71204 0.656493
\(139\) 13.7715 1.16808 0.584040 0.811725i \(-0.301471\pi\)
0.584040 + 0.811725i \(0.301471\pi\)
\(140\) −0.333284 −0.0281676
\(141\) −10.5396 −0.887599
\(142\) 0.556242 0.0466788
\(143\) −3.90777 −0.326784
\(144\) −0.360304 −0.0300253
\(145\) −1.44606 −0.120089
\(146\) 12.1155 1.00269
\(147\) 11.1925 0.923144
\(148\) 3.53964 0.290956
\(149\) −7.71007 −0.631634 −0.315817 0.948820i \(-0.602279\pi\)
−0.315817 + 0.948820i \(0.602279\pi\)
\(150\) −1.62471 −0.132657
\(151\) 16.0886 1.30927 0.654635 0.755945i \(-0.272822\pi\)
0.654635 + 0.755945i \(0.272822\pi\)
\(152\) 8.34271 0.676683
\(153\) 1.48086 0.119721
\(154\) 0.895770 0.0721832
\(155\) −3.92911 −0.315593
\(156\) −2.36224 −0.189131
\(157\) −1.65930 −0.132426 −0.0662132 0.997805i \(-0.521092\pi\)
−0.0662132 + 0.997805i \(0.521092\pi\)
\(158\) 2.81119 0.223646
\(159\) 8.64098 0.685274
\(160\) 1.00000 0.0790569
\(161\) 1.58200 0.124679
\(162\) −7.78927 −0.611983
\(163\) 2.60909 0.204360 0.102180 0.994766i \(-0.467418\pi\)
0.102180 + 0.994766i \(0.467418\pi\)
\(164\) 2.16999 0.169448
\(165\) 4.36676 0.339952
\(166\) −5.47476 −0.424924
\(167\) −0.268612 −0.0207858 −0.0103929 0.999946i \(-0.503308\pi\)
−0.0103929 + 0.999946i \(0.503308\pi\)
\(168\) 0.541491 0.0417769
\(169\) −10.8861 −0.837389
\(170\) −4.11004 −0.315225
\(171\) −3.00591 −0.229868
\(172\) −5.62222 −0.428690
\(173\) −11.6388 −0.884882 −0.442441 0.896798i \(-0.645887\pi\)
−0.442441 + 0.896798i \(0.645887\pi\)
\(174\) 2.34944 0.178110
\(175\) −0.333284 −0.0251939
\(176\) −2.68771 −0.202594
\(177\) 5.58867 0.420070
\(178\) −11.3071 −0.847504
\(179\) 6.79330 0.507755 0.253878 0.967236i \(-0.418294\pi\)
0.253878 + 0.967236i \(0.418294\pi\)
\(180\) −0.360304 −0.0268555
\(181\) 0.611592 0.0454593 0.0227296 0.999742i \(-0.492764\pi\)
0.0227296 + 0.999742i \(0.492764\pi\)
\(182\) −0.484576 −0.0359191
\(183\) 13.3207 0.984692
\(184\) −4.74671 −0.349932
\(185\) 3.53964 0.260239
\(186\) 6.38368 0.468074
\(187\) 11.0466 0.807806
\(188\) 6.48708 0.473119
\(189\) −1.81957 −0.132355
\(190\) 8.34271 0.605244
\(191\) −23.5883 −1.70679 −0.853396 0.521263i \(-0.825461\pi\)
−0.853396 + 0.521263i \(0.825461\pi\)
\(192\) −1.62471 −0.117254
\(193\) −8.93664 −0.643274 −0.321637 0.946863i \(-0.604233\pi\)
−0.321637 + 0.946863i \(0.604233\pi\)
\(194\) 13.6146 0.977468
\(195\) −2.36224 −0.169164
\(196\) −6.88892 −0.492066
\(197\) −16.9345 −1.20653 −0.603266 0.797540i \(-0.706134\pi\)
−0.603266 + 0.797540i \(0.706134\pi\)
\(198\) 0.968392 0.0688206
\(199\) 10.3990 0.737169 0.368584 0.929594i \(-0.379843\pi\)
0.368584 + 0.929594i \(0.379843\pi\)
\(200\) 1.00000 0.0707107
\(201\) −5.26103 −0.371085
\(202\) −11.3537 −0.798840
\(203\) 0.481949 0.0338262
\(204\) 6.67763 0.467528
\(205\) 2.16999 0.151559
\(206\) −12.9895 −0.905024
\(207\) 1.71026 0.118871
\(208\) 1.45394 0.100813
\(209\) −22.4228 −1.55102
\(210\) 0.541491 0.0373664
\(211\) 4.69539 0.323244 0.161622 0.986853i \(-0.448328\pi\)
0.161622 + 0.986853i \(0.448328\pi\)
\(212\) −5.31846 −0.365273
\(213\) −0.903734 −0.0619228
\(214\) −11.8474 −0.809869
\(215\) −5.62222 −0.383432
\(216\) 5.45953 0.371474
\(217\) 1.30951 0.0888952
\(218\) −15.6620 −1.06076
\(219\) −19.6843 −1.33014
\(220\) −2.68771 −0.181205
\(221\) −5.97575 −0.401973
\(222\) −5.75090 −0.385975
\(223\) 15.9530 1.06829 0.534145 0.845393i \(-0.320634\pi\)
0.534145 + 0.845393i \(0.320634\pi\)
\(224\) −0.333284 −0.0222685
\(225\) −0.360304 −0.0240202
\(226\) −3.77807 −0.251313
\(227\) 19.0713 1.26581 0.632904 0.774230i \(-0.281863\pi\)
0.632904 + 0.774230i \(0.281863\pi\)
\(228\) −13.5545 −0.897670
\(229\) −17.3615 −1.14728 −0.573639 0.819109i \(-0.694469\pi\)
−0.573639 + 0.819109i \(0.694469\pi\)
\(230\) −4.74671 −0.312989
\(231\) −1.45537 −0.0957564
\(232\) −1.44606 −0.0949386
\(233\) 12.4461 0.815369 0.407684 0.913123i \(-0.366336\pi\)
0.407684 + 0.913123i \(0.366336\pi\)
\(234\) −0.523861 −0.0342458
\(235\) 6.48708 0.423170
\(236\) −3.43978 −0.223911
\(237\) −4.56737 −0.296683
\(238\) 1.36981 0.0887915
\(239\) 19.8560 1.28438 0.642189 0.766546i \(-0.278026\pi\)
0.642189 + 0.766546i \(0.278026\pi\)
\(240\) −1.62471 −0.104875
\(241\) 13.1376 0.846270 0.423135 0.906067i \(-0.360930\pi\)
0.423135 + 0.906067i \(0.360930\pi\)
\(242\) −3.77622 −0.242744
\(243\) −3.72326 −0.238847
\(244\) −8.19878 −0.524873
\(245\) −6.88892 −0.440117
\(246\) −3.52562 −0.224785
\(247\) 12.1298 0.771802
\(248\) −3.92911 −0.249499
\(249\) 8.89492 0.563693
\(250\) 1.00000 0.0632456
\(251\) 9.77582 0.617044 0.308522 0.951217i \(-0.400166\pi\)
0.308522 + 0.951217i \(0.400166\pi\)
\(252\) 0.120083 0.00756454
\(253\) 12.7578 0.802074
\(254\) −18.1828 −1.14089
\(255\) 6.67763 0.418170
\(256\) 1.00000 0.0625000
\(257\) −9.08949 −0.566987 −0.283493 0.958974i \(-0.591493\pi\)
−0.283493 + 0.958974i \(0.591493\pi\)
\(258\) 9.13450 0.568689
\(259\) −1.17970 −0.0733033
\(260\) 1.45394 0.0901697
\(261\) 0.521022 0.0322504
\(262\) −16.2325 −1.00285
\(263\) −22.2251 −1.37046 −0.685230 0.728327i \(-0.740298\pi\)
−0.685230 + 0.728327i \(0.740298\pi\)
\(264\) 4.36676 0.268756
\(265\) −5.31846 −0.326711
\(266\) −2.78049 −0.170483
\(267\) 18.3708 1.12428
\(268\) 3.23813 0.197800
\(269\) −20.4234 −1.24523 −0.622617 0.782526i \(-0.713931\pi\)
−0.622617 + 0.782526i \(0.713931\pi\)
\(270\) 5.45953 0.332257
\(271\) 2.62739 0.159603 0.0798014 0.996811i \(-0.474571\pi\)
0.0798014 + 0.996811i \(0.474571\pi\)
\(272\) −4.11004 −0.249208
\(273\) 0.787297 0.0476494
\(274\) 13.9834 0.844767
\(275\) −2.68771 −0.162075
\(276\) 7.71204 0.464210
\(277\) 10.6123 0.637631 0.318816 0.947817i \(-0.396715\pi\)
0.318816 + 0.947817i \(0.396715\pi\)
\(278\) 13.7715 0.825957
\(279\) 1.41567 0.0847541
\(280\) −0.333284 −0.0199175
\(281\) −26.4013 −1.57497 −0.787483 0.616336i \(-0.788616\pi\)
−0.787483 + 0.616336i \(0.788616\pi\)
\(282\) −10.5396 −0.627627
\(283\) −0.0558568 −0.00332034 −0.00166017 0.999999i \(-0.500528\pi\)
−0.00166017 + 0.999999i \(0.500528\pi\)
\(284\) 0.556242 0.0330069
\(285\) −13.5545 −0.802901
\(286\) −3.90777 −0.231072
\(287\) −0.723224 −0.0426906
\(288\) −0.360304 −0.0212311
\(289\) −0.107604 −0.00632965
\(290\) −1.44606 −0.0849157
\(291\) −22.1198 −1.29668
\(292\) 12.1155 0.709007
\(293\) 30.4694 1.78004 0.890020 0.455921i \(-0.150690\pi\)
0.890020 + 0.455921i \(0.150690\pi\)
\(294\) 11.1925 0.652762
\(295\) −3.43978 −0.200272
\(296\) 3.53964 0.205737
\(297\) −14.6736 −0.851451
\(298\) −7.71007 −0.446633
\(299\) −6.90144 −0.399120
\(300\) −1.62471 −0.0938029
\(301\) 1.87380 0.108004
\(302\) 16.0886 0.925794
\(303\) 18.4464 1.05972
\(304\) 8.34271 0.478487
\(305\) −8.19878 −0.469461
\(306\) 1.48086 0.0846552
\(307\) −8.88609 −0.507156 −0.253578 0.967315i \(-0.581607\pi\)
−0.253578 + 0.967315i \(0.581607\pi\)
\(308\) 0.895770 0.0510413
\(309\) 21.1043 1.20058
\(310\) −3.92911 −0.223158
\(311\) −3.17282 −0.179914 −0.0899570 0.995946i \(-0.528673\pi\)
−0.0899570 + 0.995946i \(0.528673\pi\)
\(312\) −2.36224 −0.133736
\(313\) 13.4188 0.758476 0.379238 0.925299i \(-0.376186\pi\)
0.379238 + 0.925299i \(0.376186\pi\)
\(314\) −1.65930 −0.0936397
\(315\) 0.120083 0.00676593
\(316\) 2.81119 0.158142
\(317\) −33.6522 −1.89009 −0.945047 0.326935i \(-0.893984\pi\)
−0.945047 + 0.326935i \(0.893984\pi\)
\(318\) 8.64098 0.484562
\(319\) 3.88660 0.217608
\(320\) 1.00000 0.0559017
\(321\) 19.2486 1.07435
\(322\) 1.58200 0.0881615
\(323\) −34.2888 −1.90788
\(324\) −7.78927 −0.432737
\(325\) 1.45394 0.0806502
\(326\) 2.60909 0.144504
\(327\) 25.4463 1.40718
\(328\) 2.16999 0.119818
\(329\) −2.16204 −0.119197
\(330\) 4.36676 0.240382
\(331\) −8.64239 −0.475029 −0.237514 0.971384i \(-0.576333\pi\)
−0.237514 + 0.971384i \(0.576333\pi\)
\(332\) −5.47476 −0.300466
\(333\) −1.27534 −0.0698885
\(334\) −0.268612 −0.0146978
\(335\) 3.23813 0.176918
\(336\) 0.541491 0.0295408
\(337\) −14.0322 −0.764383 −0.382192 0.924083i \(-0.624831\pi\)
−0.382192 + 0.924083i \(0.624831\pi\)
\(338\) −10.8861 −0.592123
\(339\) 6.13828 0.333386
\(340\) −4.11004 −0.222898
\(341\) 10.5603 0.571872
\(342\) −3.00591 −0.162541
\(343\) 4.62895 0.249940
\(344\) −5.62222 −0.303130
\(345\) 7.71204 0.415202
\(346\) −11.6388 −0.625706
\(347\) −27.7738 −1.49098 −0.745489 0.666518i \(-0.767784\pi\)
−0.745489 + 0.666518i \(0.767784\pi\)
\(348\) 2.34944 0.125943
\(349\) −0.464225 −0.0248494 −0.0124247 0.999923i \(-0.503955\pi\)
−0.0124247 + 0.999923i \(0.503955\pi\)
\(350\) −0.333284 −0.0178148
\(351\) 7.93784 0.423691
\(352\) −2.68771 −0.143255
\(353\) −30.2986 −1.61263 −0.806316 0.591485i \(-0.798542\pi\)
−0.806316 + 0.591485i \(0.798542\pi\)
\(354\) 5.58867 0.297034
\(355\) 0.556242 0.0295222
\(356\) −11.3071 −0.599276
\(357\) −2.22555 −0.117788
\(358\) 6.79330 0.359037
\(359\) −8.38256 −0.442414 −0.221207 0.975227i \(-0.571000\pi\)
−0.221207 + 0.975227i \(0.571000\pi\)
\(360\) −0.360304 −0.0189897
\(361\) 50.6008 2.66320
\(362\) 0.611592 0.0321446
\(363\) 6.13527 0.322018
\(364\) −0.484576 −0.0253987
\(365\) 12.1155 0.634155
\(366\) 13.3207 0.696283
\(367\) −15.7099 −0.820051 −0.410025 0.912074i \(-0.634480\pi\)
−0.410025 + 0.912074i \(0.634480\pi\)
\(368\) −4.74671 −0.247439
\(369\) −0.781857 −0.0407018
\(370\) 3.53964 0.184017
\(371\) 1.77256 0.0920266
\(372\) 6.38368 0.330978
\(373\) −19.8047 −1.02545 −0.512723 0.858554i \(-0.671363\pi\)
−0.512723 + 0.858554i \(0.671363\pi\)
\(374\) 11.0466 0.571205
\(375\) −1.62471 −0.0838999
\(376\) 6.48708 0.334546
\(377\) −2.10249 −0.108284
\(378\) −1.81957 −0.0935888
\(379\) −0.485721 −0.0249498 −0.0124749 0.999922i \(-0.503971\pi\)
−0.0124749 + 0.999922i \(0.503971\pi\)
\(380\) 8.34271 0.427972
\(381\) 29.5418 1.51347
\(382\) −23.5883 −1.20688
\(383\) 34.4148 1.75851 0.879256 0.476349i \(-0.158040\pi\)
0.879256 + 0.476349i \(0.158040\pi\)
\(384\) −1.62471 −0.0829109
\(385\) 0.895770 0.0456527
\(386\) −8.93664 −0.454863
\(387\) 2.02571 0.102972
\(388\) 13.6146 0.691174
\(389\) −12.7219 −0.645025 −0.322512 0.946565i \(-0.604527\pi\)
−0.322512 + 0.946565i \(0.604527\pi\)
\(390\) −2.36224 −0.119617
\(391\) 19.5091 0.986619
\(392\) −6.88892 −0.347943
\(393\) 26.3732 1.33035
\(394\) −16.9345 −0.853148
\(395\) 2.81119 0.141446
\(396\) 0.968392 0.0486635
\(397\) −15.6156 −0.783726 −0.391863 0.920024i \(-0.628169\pi\)
−0.391863 + 0.920024i \(0.628169\pi\)
\(398\) 10.3990 0.521257
\(399\) 4.51750 0.226158
\(400\) 1.00000 0.0500000
\(401\) −12.8988 −0.644133 −0.322067 0.946717i \(-0.604377\pi\)
−0.322067 + 0.946717i \(0.604377\pi\)
\(402\) −5.26103 −0.262396
\(403\) −5.71269 −0.284570
\(404\) −11.3537 −0.564865
\(405\) −7.78927 −0.387052
\(406\) 0.481949 0.0239187
\(407\) −9.51352 −0.471568
\(408\) 6.67763 0.330592
\(409\) −8.25106 −0.407988 −0.203994 0.978972i \(-0.565392\pi\)
−0.203994 + 0.978972i \(0.565392\pi\)
\(410\) 2.16999 0.107168
\(411\) −22.7190 −1.12065
\(412\) −12.9895 −0.639948
\(413\) 1.14642 0.0564119
\(414\) 1.71026 0.0840545
\(415\) −5.47476 −0.268745
\(416\) 1.45394 0.0712854
\(417\) −22.3747 −1.09569
\(418\) −22.4228 −1.09673
\(419\) 23.2358 1.13514 0.567571 0.823324i \(-0.307883\pi\)
0.567571 + 0.823324i \(0.307883\pi\)
\(420\) 0.541491 0.0264221
\(421\) −18.8075 −0.916620 −0.458310 0.888792i \(-0.651545\pi\)
−0.458310 + 0.888792i \(0.651545\pi\)
\(422\) 4.69539 0.228568
\(423\) −2.33732 −0.113644
\(424\) −5.31846 −0.258287
\(425\) −4.11004 −0.199366
\(426\) −0.903734 −0.0437860
\(427\) 2.73252 0.132236
\(428\) −11.8474 −0.572664
\(429\) 6.34902 0.306533
\(430\) −5.62222 −0.271128
\(431\) −30.4849 −1.46841 −0.734203 0.678930i \(-0.762444\pi\)
−0.734203 + 0.678930i \(0.762444\pi\)
\(432\) 5.45953 0.262672
\(433\) 27.9441 1.34291 0.671455 0.741046i \(-0.265670\pi\)
0.671455 + 0.741046i \(0.265670\pi\)
\(434\) 1.30951 0.0628584
\(435\) 2.34944 0.112647
\(436\) −15.6620 −0.750073
\(437\) −39.6004 −1.89434
\(438\) −19.6843 −0.940550
\(439\) −28.9237 −1.38045 −0.690227 0.723593i \(-0.742489\pi\)
−0.690227 + 0.723593i \(0.742489\pi\)
\(440\) −2.68771 −0.128132
\(441\) 2.48210 0.118195
\(442\) −5.97575 −0.284238
\(443\) 24.7452 1.17568 0.587839 0.808978i \(-0.299979\pi\)
0.587839 + 0.808978i \(0.299979\pi\)
\(444\) −5.75090 −0.272926
\(445\) −11.3071 −0.536009
\(446\) 15.9530 0.755395
\(447\) 12.5267 0.592491
\(448\) −0.333284 −0.0157462
\(449\) 9.52218 0.449380 0.224690 0.974430i \(-0.427863\pi\)
0.224690 + 0.974430i \(0.427863\pi\)
\(450\) −0.360304 −0.0169849
\(451\) −5.83231 −0.274633
\(452\) −3.77807 −0.177705
\(453\) −26.1394 −1.22813
\(454\) 19.0713 0.895062
\(455\) −0.484576 −0.0227173
\(456\) −13.5545 −0.634749
\(457\) −37.8541 −1.77074 −0.885371 0.464885i \(-0.846096\pi\)
−0.885371 + 0.464885i \(0.846096\pi\)
\(458\) −17.3615 −0.811247
\(459\) −22.4389 −1.04736
\(460\) −4.74671 −0.221316
\(461\) −3.49481 −0.162769 −0.0813847 0.996683i \(-0.525934\pi\)
−0.0813847 + 0.996683i \(0.525934\pi\)
\(462\) −1.45537 −0.0677100
\(463\) 28.8258 1.33965 0.669825 0.742519i \(-0.266369\pi\)
0.669825 + 0.742519i \(0.266369\pi\)
\(464\) −1.44606 −0.0671318
\(465\) 6.38368 0.296036
\(466\) 12.4461 0.576553
\(467\) −40.6843 −1.88264 −0.941322 0.337510i \(-0.890415\pi\)
−0.941322 + 0.337510i \(0.890415\pi\)
\(468\) −0.523861 −0.0242155
\(469\) −1.07922 −0.0498336
\(470\) 6.48708 0.299227
\(471\) 2.69589 0.124220
\(472\) −3.43978 −0.158329
\(473\) 15.1109 0.694800
\(474\) −4.56737 −0.209786
\(475\) 8.34271 0.382790
\(476\) 1.36981 0.0627851
\(477\) 1.91626 0.0877396
\(478\) 19.8560 0.908193
\(479\) 35.4903 1.62159 0.810797 0.585327i \(-0.199034\pi\)
0.810797 + 0.585327i \(0.199034\pi\)
\(480\) −1.62471 −0.0741577
\(481\) 5.14643 0.234657
\(482\) 13.1376 0.598403
\(483\) −2.57030 −0.116953
\(484\) −3.77622 −0.171646
\(485\) 13.6146 0.618205
\(486\) −3.72326 −0.168891
\(487\) 8.70620 0.394515 0.197258 0.980352i \(-0.436796\pi\)
0.197258 + 0.980352i \(0.436796\pi\)
\(488\) −8.19878 −0.371141
\(489\) −4.23902 −0.191695
\(490\) −6.88892 −0.311210
\(491\) 23.0004 1.03800 0.518998 0.854776i \(-0.326305\pi\)
0.518998 + 0.854776i \(0.326305\pi\)
\(492\) −3.52562 −0.158947
\(493\) 5.94337 0.267676
\(494\) 12.1298 0.545746
\(495\) 0.968392 0.0435260
\(496\) −3.92911 −0.176422
\(497\) −0.185386 −0.00831572
\(498\) 8.89492 0.398591
\(499\) 21.6725 0.970196 0.485098 0.874460i \(-0.338784\pi\)
0.485098 + 0.874460i \(0.338784\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0.436418 0.0194977
\(502\) 9.77582 0.436316
\(503\) −40.7529 −1.81708 −0.908541 0.417796i \(-0.862803\pi\)
−0.908541 + 0.417796i \(0.862803\pi\)
\(504\) 0.120083 0.00534894
\(505\) −11.3537 −0.505231
\(506\) 12.7578 0.567152
\(507\) 17.6867 0.785495
\(508\) −18.1828 −0.806729
\(509\) 8.50319 0.376897 0.188449 0.982083i \(-0.439654\pi\)
0.188449 + 0.982083i \(0.439654\pi\)
\(510\) 6.67763 0.295691
\(511\) −4.03791 −0.178627
\(512\) 1.00000 0.0441942
\(513\) 45.5473 2.01096
\(514\) −9.08949 −0.400920
\(515\) −12.9895 −0.572387
\(516\) 9.13450 0.402124
\(517\) −17.4354 −0.766807
\(518\) −1.17970 −0.0518332
\(519\) 18.9097 0.830046
\(520\) 1.45394 0.0637596
\(521\) 34.9279 1.53022 0.765110 0.643899i \(-0.222684\pi\)
0.765110 + 0.643899i \(0.222684\pi\)
\(522\) 0.521022 0.0228045
\(523\) 6.43054 0.281188 0.140594 0.990067i \(-0.455099\pi\)
0.140594 + 0.990067i \(0.455099\pi\)
\(524\) −16.2325 −0.709119
\(525\) 0.541491 0.0236326
\(526\) −22.2251 −0.969062
\(527\) 16.1488 0.703452
\(528\) 4.36676 0.190039
\(529\) −0.468773 −0.0203815
\(530\) −5.31846 −0.231019
\(531\) 1.23937 0.0537840
\(532\) −2.78049 −0.120550
\(533\) 3.15505 0.136660
\(534\) 18.3708 0.794984
\(535\) −11.8474 −0.512206
\(536\) 3.23813 0.139866
\(537\) −11.0372 −0.476289
\(538\) −20.4234 −0.880514
\(539\) 18.5154 0.797516
\(540\) 5.45953 0.234941
\(541\) −34.8380 −1.49780 −0.748901 0.662682i \(-0.769418\pi\)
−0.748901 + 0.662682i \(0.769418\pi\)
\(542\) 2.62739 0.112856
\(543\) −0.993662 −0.0426421
\(544\) −4.11004 −0.176216
\(545\) −15.6620 −0.670886
\(546\) 0.787297 0.0336932
\(547\) 42.9689 1.83722 0.918608 0.395169i \(-0.129314\pi\)
0.918608 + 0.395169i \(0.129314\pi\)
\(548\) 13.9834 0.597341
\(549\) 2.95405 0.126076
\(550\) −2.68771 −0.114604
\(551\) −12.0641 −0.513947
\(552\) 7.71204 0.328246
\(553\) −0.936923 −0.0398420
\(554\) 10.6123 0.450873
\(555\) −5.75090 −0.244112
\(556\) 13.7715 0.584040
\(557\) −11.6767 −0.494759 −0.247380 0.968919i \(-0.579569\pi\)
−0.247380 + 0.968919i \(0.579569\pi\)
\(558\) 1.41567 0.0599302
\(559\) −8.17438 −0.345740
\(560\) −0.333284 −0.0140838
\(561\) −17.9475 −0.757746
\(562\) −26.4013 −1.11367
\(563\) 42.0773 1.77335 0.886674 0.462395i \(-0.153010\pi\)
0.886674 + 0.462395i \(0.153010\pi\)
\(564\) −10.5396 −0.443799
\(565\) −3.77807 −0.158945
\(566\) −0.0558568 −0.00234784
\(567\) 2.59604 0.109023
\(568\) 0.556242 0.0233394
\(569\) −13.3817 −0.560990 −0.280495 0.959855i \(-0.590499\pi\)
−0.280495 + 0.959855i \(0.590499\pi\)
\(570\) −13.5545 −0.567736
\(571\) −38.9405 −1.62961 −0.814804 0.579737i \(-0.803155\pi\)
−0.814804 + 0.579737i \(0.803155\pi\)
\(572\) −3.90777 −0.163392
\(573\) 38.3243 1.60102
\(574\) −0.723224 −0.0301868
\(575\) −4.74671 −0.197951
\(576\) −0.360304 −0.0150127
\(577\) −17.2284 −0.717226 −0.358613 0.933486i \(-0.616750\pi\)
−0.358613 + 0.933486i \(0.616750\pi\)
\(578\) −0.107604 −0.00447574
\(579\) 14.5195 0.603410
\(580\) −1.44606 −0.0600445
\(581\) 1.82465 0.0756992
\(582\) −22.1198 −0.916894
\(583\) 14.2945 0.592017
\(584\) 12.1155 0.501344
\(585\) −0.523861 −0.0216590
\(586\) 30.4694 1.25868
\(587\) 6.29000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(588\) 11.1925 0.461572
\(589\) −32.7794 −1.35065
\(590\) −3.43978 −0.141614
\(591\) 27.5137 1.13176
\(592\) 3.53964 0.145478
\(593\) 15.8226 0.649756 0.324878 0.945756i \(-0.394677\pi\)
0.324878 + 0.945756i \(0.394677\pi\)
\(594\) −14.6736 −0.602067
\(595\) 1.36981 0.0561567
\(596\) −7.71007 −0.315817
\(597\) −16.8955 −0.691486
\(598\) −6.90144 −0.282221
\(599\) −17.7875 −0.726776 −0.363388 0.931638i \(-0.618380\pi\)
−0.363388 + 0.931638i \(0.618380\pi\)
\(600\) −1.62471 −0.0663287
\(601\) −1.00000 −0.0407909
\(602\) 1.87380 0.0763702
\(603\) −1.16671 −0.0475121
\(604\) 16.0886 0.654635
\(605\) −3.77622 −0.153525
\(606\) 18.4464 0.749336
\(607\) −26.1579 −1.06172 −0.530858 0.847461i \(-0.678130\pi\)
−0.530858 + 0.847461i \(0.678130\pi\)
\(608\) 8.34271 0.338342
\(609\) −0.783030 −0.0317300
\(610\) −8.19878 −0.331959
\(611\) 9.43184 0.381571
\(612\) 1.48086 0.0598603
\(613\) −20.1097 −0.812224 −0.406112 0.913823i \(-0.633116\pi\)
−0.406112 + 0.913823i \(0.633116\pi\)
\(614\) −8.88609 −0.358614
\(615\) −3.52562 −0.142167
\(616\) 0.895770 0.0360916
\(617\) 35.7908 1.44088 0.720442 0.693516i \(-0.243939\pi\)
0.720442 + 0.693516i \(0.243939\pi\)
\(618\) 21.1043 0.848938
\(619\) −43.9013 −1.76454 −0.882271 0.470742i \(-0.843986\pi\)
−0.882271 + 0.470742i \(0.843986\pi\)
\(620\) −3.92911 −0.157797
\(621\) −25.9148 −1.03993
\(622\) −3.17282 −0.127218
\(623\) 3.76848 0.150981
\(624\) −2.36224 −0.0945653
\(625\) 1.00000 0.0400000
\(626\) 13.4188 0.536324
\(627\) 36.4306 1.45490
\(628\) −1.65930 −0.0662132
\(629\) −14.5480 −0.580068
\(630\) 0.120083 0.00478424
\(631\) −2.74625 −0.109326 −0.0546631 0.998505i \(-0.517408\pi\)
−0.0546631 + 0.998505i \(0.517408\pi\)
\(632\) 2.81119 0.111823
\(633\) −7.62866 −0.303212
\(634\) −33.6522 −1.33650
\(635\) −18.1828 −0.721561
\(636\) 8.64098 0.342637
\(637\) −10.0161 −0.396852
\(638\) 3.88660 0.153872
\(639\) −0.200416 −0.00792833
\(640\) 1.00000 0.0395285
\(641\) −24.5608 −0.970093 −0.485046 0.874488i \(-0.661197\pi\)
−0.485046 + 0.874488i \(0.661197\pi\)
\(642\) 19.2486 0.759681
\(643\) 33.6868 1.32848 0.664240 0.747520i \(-0.268755\pi\)
0.664240 + 0.747520i \(0.268755\pi\)
\(644\) 1.58200 0.0623396
\(645\) 9.13450 0.359671
\(646\) −34.2888 −1.34908
\(647\) 1.86914 0.0734834 0.0367417 0.999325i \(-0.488302\pi\)
0.0367417 + 0.999325i \(0.488302\pi\)
\(648\) −7.78927 −0.305991
\(649\) 9.24514 0.362904
\(650\) 1.45394 0.0570283
\(651\) −2.12758 −0.0833863
\(652\) 2.60909 0.102180
\(653\) 41.9660 1.64226 0.821128 0.570743i \(-0.193345\pi\)
0.821128 + 0.570743i \(0.193345\pi\)
\(654\) 25.4463 0.995027
\(655\) −16.2325 −0.634256
\(656\) 2.16999 0.0847240
\(657\) −4.36527 −0.170305
\(658\) −2.16204 −0.0842851
\(659\) 48.4170 1.88606 0.943030 0.332707i \(-0.107962\pi\)
0.943030 + 0.332707i \(0.107962\pi\)
\(660\) 4.36676 0.169976
\(661\) −41.8331 −1.62712 −0.813559 0.581483i \(-0.802473\pi\)
−0.813559 + 0.581483i \(0.802473\pi\)
\(662\) −8.64239 −0.335896
\(663\) 9.70889 0.377062
\(664\) −5.47476 −0.212462
\(665\) −2.78049 −0.107823
\(666\) −1.27534 −0.0494186
\(667\) 6.86403 0.265776
\(668\) −0.268612 −0.0103929
\(669\) −25.9190 −1.00209
\(670\) 3.23813 0.125100
\(671\) 22.0359 0.850688
\(672\) 0.541491 0.0208885
\(673\) 47.3383 1.82476 0.912378 0.409349i \(-0.134244\pi\)
0.912378 + 0.409349i \(0.134244\pi\)
\(674\) −14.0322 −0.540500
\(675\) 5.45953 0.210138
\(676\) −10.8861 −0.418694
\(677\) 33.6319 1.29258 0.646289 0.763093i \(-0.276320\pi\)
0.646289 + 0.763093i \(0.276320\pi\)
\(678\) 6.13828 0.235739
\(679\) −4.53751 −0.174134
\(680\) −4.11004 −0.157613
\(681\) −30.9855 −1.18737
\(682\) 10.5603 0.404375
\(683\) −21.0748 −0.806405 −0.403203 0.915111i \(-0.632103\pi\)
−0.403203 + 0.915111i \(0.632103\pi\)
\(684\) −3.00591 −0.114934
\(685\) 13.9834 0.534278
\(686\) 4.62895 0.176734
\(687\) 28.2074 1.07618
\(688\) −5.62222 −0.214345
\(689\) −7.73274 −0.294594
\(690\) 7.71204 0.293592
\(691\) 19.7067 0.749679 0.374839 0.927090i \(-0.377698\pi\)
0.374839 + 0.927090i \(0.377698\pi\)
\(692\) −11.6388 −0.442441
\(693\) −0.322749 −0.0122602
\(694\) −27.7738 −1.05428
\(695\) 13.7715 0.522381
\(696\) 2.34944 0.0890552
\(697\) −8.91875 −0.337822
\(698\) −0.464225 −0.0175712
\(699\) −20.2213 −0.764840
\(700\) −0.333284 −0.0125969
\(701\) 22.4682 0.848611 0.424305 0.905519i \(-0.360518\pi\)
0.424305 + 0.905519i \(0.360518\pi\)
\(702\) 7.93784 0.299595
\(703\) 29.5302 1.11375
\(704\) −2.68771 −0.101297
\(705\) −10.5396 −0.396946
\(706\) −30.2986 −1.14030
\(707\) 3.78399 0.142312
\(708\) 5.58867 0.210035
\(709\) 1.04779 0.0393504 0.0196752 0.999806i \(-0.493737\pi\)
0.0196752 + 0.999806i \(0.493737\pi\)
\(710\) 0.556242 0.0208754
\(711\) −1.01288 −0.0379860
\(712\) −11.3071 −0.423752
\(713\) 18.6503 0.698460
\(714\) −2.22555 −0.0832890
\(715\) −3.90777 −0.146142
\(716\) 6.79330 0.253878
\(717\) −32.2603 −1.20478
\(718\) −8.38256 −0.312834
\(719\) 27.4040 1.02200 0.510998 0.859582i \(-0.329276\pi\)
0.510998 + 0.859582i \(0.329276\pi\)
\(720\) −0.360304 −0.0134277
\(721\) 4.32920 0.161228
\(722\) 50.6008 1.88317
\(723\) −21.3449 −0.793826
\(724\) 0.611592 0.0227296
\(725\) −1.44606 −0.0537054
\(726\) 6.13527 0.227701
\(727\) 26.9437 0.999287 0.499644 0.866231i \(-0.333464\pi\)
0.499644 + 0.866231i \(0.333464\pi\)
\(728\) −0.484576 −0.0179596
\(729\) 29.4170 1.08952
\(730\) 12.1155 0.448415
\(731\) 23.1075 0.854663
\(732\) 13.3207 0.492346
\(733\) −7.56912 −0.279572 −0.139786 0.990182i \(-0.544641\pi\)
−0.139786 + 0.990182i \(0.544641\pi\)
\(734\) −15.7099 −0.579864
\(735\) 11.1925 0.412843
\(736\) −4.74671 −0.174966
\(737\) −8.70315 −0.320585
\(738\) −0.781857 −0.0287805
\(739\) 33.0602 1.21614 0.608069 0.793884i \(-0.291944\pi\)
0.608069 + 0.793884i \(0.291944\pi\)
\(740\) 3.53964 0.130120
\(741\) −19.7075 −0.723973
\(742\) 1.77256 0.0650727
\(743\) 49.0273 1.79864 0.899318 0.437294i \(-0.144063\pi\)
0.899318 + 0.437294i \(0.144063\pi\)
\(744\) 6.38368 0.234037
\(745\) −7.71007 −0.282475
\(746\) −19.8047 −0.725100
\(747\) 1.97258 0.0721728
\(748\) 11.0466 0.403903
\(749\) 3.94854 0.144276
\(750\) −1.62471 −0.0593262
\(751\) −17.1169 −0.624604 −0.312302 0.949983i \(-0.601100\pi\)
−0.312302 + 0.949983i \(0.601100\pi\)
\(752\) 6.48708 0.236559
\(753\) −15.8829 −0.578806
\(754\) −2.10249 −0.0765682
\(755\) 16.0886 0.585524
\(756\) −1.81957 −0.0661773
\(757\) 29.7065 1.07970 0.539850 0.841761i \(-0.318481\pi\)
0.539850 + 0.841761i \(0.318481\pi\)
\(758\) −0.485721 −0.0176422
\(759\) −20.7277 −0.752369
\(760\) 8.34271 0.302622
\(761\) −49.7109 −1.80202 −0.901009 0.433801i \(-0.857172\pi\)
−0.901009 + 0.433801i \(0.857172\pi\)
\(762\) 29.5418 1.07019
\(763\) 5.21989 0.188973
\(764\) −23.5883 −0.853396
\(765\) 1.48086 0.0535406
\(766\) 34.4148 1.24346
\(767\) −5.00125 −0.180585
\(768\) −1.62471 −0.0586268
\(769\) 10.4087 0.375346 0.187673 0.982232i \(-0.439906\pi\)
0.187673 + 0.982232i \(0.439906\pi\)
\(770\) 0.895770 0.0322813
\(771\) 14.7678 0.531850
\(772\) −8.93664 −0.321637
\(773\) 34.6792 1.24733 0.623663 0.781694i \(-0.285644\pi\)
0.623663 + 0.781694i \(0.285644\pi\)
\(774\) 2.02571 0.0728125
\(775\) −3.92911 −0.141138
\(776\) 13.6146 0.488734
\(777\) 1.91668 0.0687606
\(778\) −12.7219 −0.456101
\(779\) 18.1036 0.648630
\(780\) −2.36224 −0.0845818
\(781\) −1.49502 −0.0534959
\(782\) 19.5091 0.697645
\(783\) −7.89482 −0.282138
\(784\) −6.88892 −0.246033
\(785\) −1.65930 −0.0592229
\(786\) 26.3732 0.940699
\(787\) 42.9333 1.53041 0.765203 0.643789i \(-0.222639\pi\)
0.765203 + 0.643789i \(0.222639\pi\)
\(788\) −16.9345 −0.603266
\(789\) 36.1095 1.28553
\(790\) 2.81119 0.100018
\(791\) 1.25917 0.0447709
\(792\) 0.968392 0.0344103
\(793\) −11.9205 −0.423311
\(794\) −15.6156 −0.554178
\(795\) 8.64098 0.306464
\(796\) 10.3990 0.368584
\(797\) 27.0481 0.958092 0.479046 0.877790i \(-0.340983\pi\)
0.479046 + 0.877790i \(0.340983\pi\)
\(798\) 4.51750 0.159918
\(799\) −26.6621 −0.943238
\(800\) 1.00000 0.0353553
\(801\) 4.07400 0.143948
\(802\) −12.8988 −0.455471
\(803\) −32.5630 −1.14912
\(804\) −5.26103 −0.185542
\(805\) 1.58200 0.0557582
\(806\) −5.71269 −0.201221
\(807\) 33.1821 1.16807
\(808\) −11.3537 −0.399420
\(809\) 26.6791 0.937987 0.468993 0.883202i \(-0.344617\pi\)
0.468993 + 0.883202i \(0.344617\pi\)
\(810\) −7.78927 −0.273687
\(811\) −24.3470 −0.854938 −0.427469 0.904030i \(-0.640595\pi\)
−0.427469 + 0.904030i \(0.640595\pi\)
\(812\) 0.481949 0.0169131
\(813\) −4.26876 −0.149712
\(814\) −9.51352 −0.333449
\(815\) 2.60909 0.0913924
\(816\) 6.67763 0.233764
\(817\) −46.9046 −1.64098
\(818\) −8.25106 −0.288491
\(819\) 0.174594 0.00610082
\(820\) 2.16999 0.0757795
\(821\) −14.8525 −0.518355 −0.259178 0.965830i \(-0.583452\pi\)
−0.259178 + 0.965830i \(0.583452\pi\)
\(822\) −22.7190 −0.792416
\(823\) 52.8539 1.84237 0.921186 0.389122i \(-0.127222\pi\)
0.921186 + 0.389122i \(0.127222\pi\)
\(824\) −12.9895 −0.452512
\(825\) 4.36676 0.152031
\(826\) 1.14642 0.0398892
\(827\) 21.1336 0.734889 0.367444 0.930045i \(-0.380233\pi\)
0.367444 + 0.930045i \(0.380233\pi\)
\(828\) 1.71026 0.0594355
\(829\) −8.20142 −0.284847 −0.142424 0.989806i \(-0.545490\pi\)
−0.142424 + 0.989806i \(0.545490\pi\)
\(830\) −5.47476 −0.190032
\(831\) −17.2420 −0.598117
\(832\) 1.45394 0.0504064
\(833\) 28.3137 0.981012
\(834\) −22.3747 −0.774772
\(835\) −0.268612 −0.00929571
\(836\) −22.4228 −0.775508
\(837\) −21.4511 −0.741458
\(838\) 23.2358 0.802667
\(839\) −25.2567 −0.871957 −0.435978 0.899957i \(-0.643598\pi\)
−0.435978 + 0.899957i \(0.643598\pi\)
\(840\) 0.541491 0.0186832
\(841\) −26.9089 −0.927893
\(842\) −18.8075 −0.648148
\(843\) 42.8945 1.47736
\(844\) 4.69539 0.161622
\(845\) −10.8861 −0.374492
\(846\) −2.33732 −0.0803587
\(847\) 1.25855 0.0432444
\(848\) −5.31846 −0.182637
\(849\) 0.0907514 0.00311458
\(850\) −4.11004 −0.140973
\(851\) −16.8016 −0.575952
\(852\) −0.903734 −0.0309614
\(853\) 43.7081 1.49654 0.748269 0.663396i \(-0.230885\pi\)
0.748269 + 0.663396i \(0.230885\pi\)
\(854\) 2.73252 0.0935049
\(855\) −3.00591 −0.102800
\(856\) −11.8474 −0.404935
\(857\) −39.6884 −1.35573 −0.677866 0.735186i \(-0.737095\pi\)
−0.677866 + 0.735186i \(0.737095\pi\)
\(858\) 6.34902 0.216752
\(859\) −54.3917 −1.85582 −0.927911 0.372801i \(-0.878397\pi\)
−0.927911 + 0.372801i \(0.878397\pi\)
\(860\) −5.62222 −0.191716
\(861\) 1.17503 0.0400450
\(862\) −30.4849 −1.03832
\(863\) 44.3274 1.50892 0.754461 0.656345i \(-0.227898\pi\)
0.754461 + 0.656345i \(0.227898\pi\)
\(864\) 5.45953 0.185737
\(865\) −11.6388 −0.395731
\(866\) 27.9441 0.949580
\(867\) 0.174826 0.00593740
\(868\) 1.30951 0.0444476
\(869\) −7.55565 −0.256308
\(870\) 2.34944 0.0796534
\(871\) 4.70805 0.159526
\(872\) −15.6620 −0.530382
\(873\) −4.90537 −0.166022
\(874\) −39.6004 −1.33950
\(875\) −0.333284 −0.0112671
\(876\) −19.6843 −0.665069
\(877\) 16.6593 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(878\) −28.9237 −0.976128
\(879\) −49.5040 −1.66973
\(880\) −2.68771 −0.0906027
\(881\) −18.5108 −0.623645 −0.311823 0.950140i \(-0.600939\pi\)
−0.311823 + 0.950140i \(0.600939\pi\)
\(882\) 2.48210 0.0835768
\(883\) 15.4100 0.518586 0.259293 0.965799i \(-0.416510\pi\)
0.259293 + 0.965799i \(0.416510\pi\)
\(884\) −5.97575 −0.200986
\(885\) 5.58867 0.187861
\(886\) 24.7452 0.831330
\(887\) −56.8466 −1.90872 −0.954361 0.298654i \(-0.903462\pi\)
−0.954361 + 0.298654i \(0.903462\pi\)
\(888\) −5.75090 −0.192988
\(889\) 6.06002 0.203247
\(890\) −11.3071 −0.379015
\(891\) 20.9353 0.701359
\(892\) 15.9530 0.534145
\(893\) 54.1198 1.81105
\(894\) 12.5267 0.418954
\(895\) 6.79330 0.227075
\(896\) −0.333284 −0.0111342
\(897\) 11.2129 0.374387
\(898\) 9.52218 0.317759
\(899\) 5.68173 0.189496
\(900\) −0.360304 −0.0120101
\(901\) 21.8591 0.728231
\(902\) −5.83231 −0.194195
\(903\) −3.04438 −0.101311
\(904\) −3.77807 −0.125657
\(905\) 0.611592 0.0203300
\(906\) −26.1394 −0.868422
\(907\) 48.0315 1.59486 0.797430 0.603412i \(-0.206193\pi\)
0.797430 + 0.603412i \(0.206193\pi\)
\(908\) 19.0713 0.632904
\(909\) 4.09076 0.135682
\(910\) −0.484576 −0.0160635
\(911\) 21.8425 0.723675 0.361838 0.932241i \(-0.382149\pi\)
0.361838 + 0.932241i \(0.382149\pi\)
\(912\) −13.5545 −0.448835
\(913\) 14.7146 0.486981
\(914\) −37.8541 −1.25210
\(915\) 13.3207 0.440368
\(916\) −17.3615 −0.573639
\(917\) 5.41003 0.178655
\(918\) −22.4389 −0.740593
\(919\) 38.0442 1.25496 0.627482 0.778631i \(-0.284086\pi\)
0.627482 + 0.778631i \(0.284086\pi\)
\(920\) −4.74671 −0.156494
\(921\) 14.4374 0.475727
\(922\) −3.49481 −0.115095
\(923\) 0.808743 0.0266201
\(924\) −1.45537 −0.0478782
\(925\) 3.53964 0.116383
\(926\) 28.8258 0.947275
\(927\) 4.68018 0.153717
\(928\) −1.44606 −0.0474693
\(929\) −34.7468 −1.14001 −0.570003 0.821643i \(-0.693058\pi\)
−0.570003 + 0.821643i \(0.693058\pi\)
\(930\) 6.38368 0.209329
\(931\) −57.4723 −1.88358
\(932\) 12.4461 0.407684
\(933\) 5.15492 0.168765
\(934\) −40.6843 −1.33123
\(935\) 11.0466 0.361262
\(936\) −0.523861 −0.0171229
\(937\) 12.6504 0.413270 0.206635 0.978418i \(-0.433749\pi\)
0.206635 + 0.978418i \(0.433749\pi\)
\(938\) −1.07922 −0.0352377
\(939\) −21.8017 −0.711473
\(940\) 6.48708 0.211585
\(941\) −8.09526 −0.263898 −0.131949 0.991257i \(-0.542124\pi\)
−0.131949 + 0.991257i \(0.542124\pi\)
\(942\) 2.69589 0.0878367
\(943\) −10.3003 −0.335425
\(944\) −3.43978 −0.111955
\(945\) −1.81957 −0.0591908
\(946\) 15.1109 0.491298
\(947\) 12.9704 0.421480 0.210740 0.977542i \(-0.432413\pi\)
0.210740 + 0.977542i \(0.432413\pi\)
\(948\) −4.56737 −0.148341
\(949\) 17.6153 0.571816
\(950\) 8.34271 0.270673
\(951\) 54.6751 1.77296
\(952\) 1.36981 0.0443958
\(953\) −19.2288 −0.622881 −0.311441 0.950266i \(-0.600811\pi\)
−0.311441 + 0.950266i \(0.600811\pi\)
\(954\) 1.91626 0.0620413
\(955\) −23.5883 −0.763301
\(956\) 19.8560 0.642189
\(957\) −6.31461 −0.204122
\(958\) 35.4903 1.14664
\(959\) −4.66044 −0.150493
\(960\) −1.62471 −0.0524374
\(961\) −15.5621 −0.502004
\(962\) 5.14643 0.165928
\(963\) 4.26865 0.137555
\(964\) 13.1376 0.423135
\(965\) −8.93664 −0.287681
\(966\) −2.57030 −0.0826980
\(967\) −36.0112 −1.15804 −0.579021 0.815313i \(-0.696565\pi\)
−0.579021 + 0.815313i \(0.696565\pi\)
\(968\) −3.77622 −0.121372
\(969\) 55.7096 1.78965
\(970\) 13.6146 0.437137
\(971\) 34.8909 1.11970 0.559852 0.828593i \(-0.310858\pi\)
0.559852 + 0.828593i \(0.310858\pi\)
\(972\) −3.72326 −0.119424
\(973\) −4.58981 −0.147142
\(974\) 8.70620 0.278965
\(975\) −2.36224 −0.0756522
\(976\) −8.19878 −0.262436
\(977\) 0.795280 0.0254433 0.0127216 0.999919i \(-0.495950\pi\)
0.0127216 + 0.999919i \(0.495950\pi\)
\(978\) −4.23902 −0.135549
\(979\) 30.3902 0.971277
\(980\) −6.88892 −0.220059
\(981\) 5.64307 0.180169
\(982\) 23.0004 0.733973
\(983\) 31.1377 0.993140 0.496570 0.867997i \(-0.334593\pi\)
0.496570 + 0.867997i \(0.334593\pi\)
\(984\) −3.52562 −0.112393
\(985\) −16.9345 −0.539578
\(986\) 5.94337 0.189275
\(987\) 3.51270 0.111810
\(988\) 12.1298 0.385901
\(989\) 26.6870 0.848598
\(990\) 0.968392 0.0307775
\(991\) 24.0845 0.765070 0.382535 0.923941i \(-0.375051\pi\)
0.382535 + 0.923941i \(0.375051\pi\)
\(992\) −3.92911 −0.124749
\(993\) 14.0414 0.445591
\(994\) −0.185386 −0.00588010
\(995\) 10.3990 0.329672
\(996\) 8.89492 0.281846
\(997\) 1.06741 0.0338052 0.0169026 0.999857i \(-0.494619\pi\)
0.0169026 + 0.999857i \(0.494619\pi\)
\(998\) 21.6725 0.686032
\(999\) 19.3248 0.611409
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 \(a_p\))