Properties

Label 8023.2.a.c.1.17
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.44908 q^{2}\) \(-0.864554 q^{3}\) \(+3.99799 q^{4}\) \(+2.08542 q^{5}\) \(+2.11736 q^{6}\) \(-1.35512 q^{7}\) \(-4.89325 q^{8}\) \(-2.25255 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.44908 q^{2}\) \(-0.864554 q^{3}\) \(+3.99799 q^{4}\) \(+2.08542 q^{5}\) \(+2.11736 q^{6}\) \(-1.35512 q^{7}\) \(-4.89325 q^{8}\) \(-2.25255 q^{9}\) \(-5.10735 q^{10}\) \(+1.47121 q^{11}\) \(-3.45648 q^{12}\) \(+5.96106 q^{13}\) \(+3.31881 q^{14}\) \(-1.80295 q^{15}\) \(+3.98797 q^{16}\) \(-1.61074 q^{17}\) \(+5.51667 q^{18}\) \(-6.49286 q^{19}\) \(+8.33748 q^{20}\) \(+1.17158 q^{21}\) \(-3.60312 q^{22}\) \(+5.72671 q^{23}\) \(+4.23048 q^{24}\) \(-0.651039 q^{25}\) \(-14.5991 q^{26}\) \(+4.54111 q^{27}\) \(-5.41778 q^{28}\) \(+7.46702 q^{29}\) \(+4.41558 q^{30}\) \(-9.92398 q^{31}\) \(+0.0196355 q^{32}\) \(-1.27194 q^{33}\) \(+3.94483 q^{34}\) \(-2.82600 q^{35}\) \(-9.00567 q^{36}\) \(-6.38891 q^{37}\) \(+15.9015 q^{38}\) \(-5.15366 q^{39}\) \(-10.2045 q^{40}\) \(+10.6962 q^{41}\) \(-2.86929 q^{42}\) \(+6.09363 q^{43}\) \(+5.88190 q^{44}\) \(-4.69750 q^{45}\) \(-14.0252 q^{46}\) \(-5.75546 q^{47}\) \(-3.44782 q^{48}\) \(-5.16364 q^{49}\) \(+1.59445 q^{50}\) \(+1.39257 q^{51}\) \(+23.8323 q^{52}\) \(-11.1072 q^{53}\) \(-11.1215 q^{54}\) \(+3.06809 q^{55}\) \(+6.63096 q^{56}\) \(+5.61343 q^{57}\) \(-18.2873 q^{58}\) \(-0.156976 q^{59}\) \(-7.20820 q^{60}\) \(-5.80708 q^{61}\) \(+24.3046 q^{62}\) \(+3.05248 q^{63}\) \(-8.02403 q^{64}\) \(+12.4313 q^{65}\) \(+3.11509 q^{66}\) \(+10.2973 q^{67}\) \(-6.43973 q^{68}\) \(-4.95105 q^{69}\) \(+6.92110 q^{70}\) \(-1.00000 q^{71}\) \(+11.0223 q^{72}\) \(-9.98717 q^{73}\) \(+15.6470 q^{74}\) \(+0.562858 q^{75}\) \(-25.9584 q^{76}\) \(-1.99368 q^{77}\) \(+12.6217 q^{78}\) \(+15.2568 q^{79}\) \(+8.31658 q^{80}\) \(+2.83161 q^{81}\) \(-26.1959 q^{82}\) \(-4.92825 q^{83}\) \(+4.68396 q^{84}\) \(-3.35907 q^{85}\) \(-14.9238 q^{86}\) \(-6.45564 q^{87}\) \(-7.19901 q^{88}\) \(-7.42802 q^{89}\) \(+11.5046 q^{90}\) \(-8.07798 q^{91}\) \(+22.8954 q^{92}\) \(+8.57981 q^{93}\) \(+14.0956 q^{94}\) \(-13.5403 q^{95}\) \(-0.0169760 q^{96}\) \(-1.44322 q^{97}\) \(+12.6462 q^{98}\) \(-3.31397 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44908 −1.73176 −0.865881 0.500251i \(-0.833241\pi\)
−0.865881 + 0.500251i \(0.833241\pi\)
\(3\) −0.864554 −0.499150 −0.249575 0.968355i \(-0.580291\pi\)
−0.249575 + 0.968355i \(0.580291\pi\)
\(4\) 3.99799 1.99900
\(5\) 2.08542 0.932627 0.466313 0.884620i \(-0.345582\pi\)
0.466313 + 0.884620i \(0.345582\pi\)
\(6\) 2.11736 0.864409
\(7\) −1.35512 −0.512189 −0.256094 0.966652i \(-0.582436\pi\)
−0.256094 + 0.966652i \(0.582436\pi\)
\(8\) −4.89325 −1.73002
\(9\) −2.25255 −0.750849
\(10\) −5.10735 −1.61509
\(11\) 1.47121 0.443587 0.221794 0.975094i \(-0.428809\pi\)
0.221794 + 0.975094i \(0.428809\pi\)
\(12\) −3.45648 −0.997800
\(13\) 5.96106 1.65330 0.826651 0.562715i \(-0.190243\pi\)
0.826651 + 0.562715i \(0.190243\pi\)
\(14\) 3.31881 0.886989
\(15\) −1.80295 −0.465521
\(16\) 3.98797 0.996993
\(17\) −1.61074 −0.390662 −0.195331 0.980737i \(-0.562578\pi\)
−0.195331 + 0.980737i \(0.562578\pi\)
\(18\) 5.51667 1.30029
\(19\) −6.49286 −1.48957 −0.744783 0.667307i \(-0.767447\pi\)
−0.744783 + 0.667307i \(0.767447\pi\)
\(20\) 8.33748 1.86432
\(21\) 1.17158 0.255659
\(22\) −3.60312 −0.768187
\(23\) 5.72671 1.19410 0.597051 0.802203i \(-0.296339\pi\)
0.597051 + 0.802203i \(0.296339\pi\)
\(24\) 4.23048 0.863542
\(25\) −0.651039 −0.130208
\(26\) −14.5991 −2.86312
\(27\) 4.54111 0.873937
\(28\) −5.41778 −1.02386
\(29\) 7.46702 1.38659 0.693296 0.720653i \(-0.256158\pi\)
0.693296 + 0.720653i \(0.256158\pi\)
\(30\) 4.41558 0.806171
\(31\) −9.92398 −1.78240 −0.891200 0.453611i \(-0.850135\pi\)
−0.891200 + 0.453611i \(0.850135\pi\)
\(32\) 0.0196355 0.00347110
\(33\) −1.27194 −0.221417
\(34\) 3.94483 0.676534
\(35\) −2.82600 −0.477681
\(36\) −9.00567 −1.50095
\(37\) −6.38891 −1.05033 −0.525165 0.851000i \(-0.675996\pi\)
−0.525165 + 0.851000i \(0.675996\pi\)
\(38\) 15.9015 2.57957
\(39\) −5.15366 −0.825246
\(40\) −10.2045 −1.61347
\(41\) 10.6962 1.67047 0.835234 0.549895i \(-0.185332\pi\)
0.835234 + 0.549895i \(0.185332\pi\)
\(42\) −2.86929 −0.442741
\(43\) 6.09363 0.929270 0.464635 0.885502i \(-0.346186\pi\)
0.464635 + 0.885502i \(0.346186\pi\)
\(44\) 5.88190 0.886730
\(45\) −4.69750 −0.700262
\(46\) −14.0252 −2.06790
\(47\) −5.75546 −0.839521 −0.419760 0.907635i \(-0.637886\pi\)
−0.419760 + 0.907635i \(0.637886\pi\)
\(48\) −3.44782 −0.497649
\(49\) −5.16364 −0.737663
\(50\) 1.59445 0.225489
\(51\) 1.39257 0.194999
\(52\) 23.8323 3.30494
\(53\) −11.1072 −1.52569 −0.762844 0.646583i \(-0.776197\pi\)
−0.762844 + 0.646583i \(0.776197\pi\)
\(54\) −11.1215 −1.51345
\(55\) 3.06809 0.413701
\(56\) 6.63096 0.886099
\(57\) 5.61343 0.743517
\(58\) −18.2873 −2.40124
\(59\) −0.156976 −0.0204365 −0.0102182 0.999948i \(-0.503253\pi\)
−0.0102182 + 0.999948i \(0.503253\pi\)
\(60\) −7.20820 −0.930575
\(61\) −5.80708 −0.743521 −0.371760 0.928329i \(-0.621246\pi\)
−0.371760 + 0.928329i \(0.621246\pi\)
\(62\) 24.3046 3.08669
\(63\) 3.05248 0.384576
\(64\) −8.02403 −1.00300
\(65\) 12.4313 1.54191
\(66\) 3.11509 0.383441
\(67\) 10.2973 1.25801 0.629007 0.777400i \(-0.283462\pi\)
0.629007 + 0.777400i \(0.283462\pi\)
\(68\) −6.43973 −0.780933
\(69\) −4.95105 −0.596036
\(70\) 6.92110 0.827229
\(71\) −1.00000 −0.118678
\(72\) 11.0223 1.29899
\(73\) −9.98717 −1.16891 −0.584455 0.811426i \(-0.698692\pi\)
−0.584455 + 0.811426i \(0.698692\pi\)
\(74\) 15.6470 1.81892
\(75\) 0.562858 0.0649933
\(76\) −25.9584 −2.97764
\(77\) −1.99368 −0.227200
\(78\) 12.6217 1.42913
\(79\) 15.2568 1.71652 0.858259 0.513216i \(-0.171546\pi\)
0.858259 + 0.513216i \(0.171546\pi\)
\(80\) 8.31658 0.929822
\(81\) 2.83161 0.314623
\(82\) −26.1959 −2.89285
\(83\) −4.92825 −0.540945 −0.270473 0.962728i \(-0.587180\pi\)
−0.270473 + 0.962728i \(0.587180\pi\)
\(84\) 4.68396 0.511062
\(85\) −3.35907 −0.364342
\(86\) −14.9238 −1.60927
\(87\) −6.45564 −0.692117
\(88\) −7.19901 −0.767417
\(89\) −7.42802 −0.787369 −0.393684 0.919246i \(-0.628800\pi\)
−0.393684 + 0.919246i \(0.628800\pi\)
\(90\) 11.5046 1.21269
\(91\) −8.07798 −0.846802
\(92\) 22.8954 2.38701
\(93\) 8.57981 0.889685
\(94\) 14.0956 1.45385
\(95\) −13.5403 −1.38921
\(96\) −0.0169760 −0.00173260
\(97\) −1.44322 −0.146537 −0.0732686 0.997312i \(-0.523343\pi\)
−0.0732686 + 0.997312i \(0.523343\pi\)
\(98\) 12.6462 1.27746
\(99\) −3.31397 −0.333067
\(100\) −2.60285 −0.260285
\(101\) 7.52388 0.748654 0.374327 0.927297i \(-0.377874\pi\)
0.374327 + 0.927297i \(0.377874\pi\)
\(102\) −3.41052 −0.337692
\(103\) 15.4335 1.52071 0.760356 0.649507i \(-0.225024\pi\)
0.760356 + 0.649507i \(0.225024\pi\)
\(104\) −29.1690 −2.86025
\(105\) 2.44323 0.238435
\(106\) 27.2024 2.64213
\(107\) 11.1130 1.07434 0.537168 0.843475i \(-0.319494\pi\)
0.537168 + 0.843475i \(0.319494\pi\)
\(108\) 18.1553 1.74700
\(109\) 7.19380 0.689041 0.344520 0.938779i \(-0.388042\pi\)
0.344520 + 0.938779i \(0.388042\pi\)
\(110\) −7.51400 −0.716432
\(111\) 5.52356 0.524273
\(112\) −5.40420 −0.510649
\(113\) −1.00000 −0.0940721
\(114\) −13.7477 −1.28759
\(115\) 11.9426 1.11365
\(116\) 29.8531 2.77179
\(117\) −13.4276 −1.24138
\(118\) 0.384446 0.0353911
\(119\) 2.18275 0.200093
\(120\) 8.82230 0.805363
\(121\) −8.83553 −0.803230
\(122\) 14.2220 1.28760
\(123\) −9.24745 −0.833814
\(124\) −39.6760 −3.56301
\(125\) −11.7848 −1.05406
\(126\) −7.47577 −0.665995
\(127\) 11.9197 1.05771 0.528853 0.848714i \(-0.322622\pi\)
0.528853 + 0.848714i \(0.322622\pi\)
\(128\) 19.6122 1.73349
\(129\) −5.26827 −0.463845
\(130\) −30.4452 −2.67022
\(131\) −13.8354 −1.20881 −0.604403 0.796678i \(-0.706588\pi\)
−0.604403 + 0.796678i \(0.706588\pi\)
\(132\) −5.08522 −0.442611
\(133\) 8.79864 0.762939
\(134\) −25.2189 −2.17858
\(135\) 9.47010 0.815057
\(136\) 7.88176 0.675855
\(137\) −21.1300 −1.80526 −0.902628 0.430421i \(-0.858365\pi\)
−0.902628 + 0.430421i \(0.858365\pi\)
\(138\) 12.1255 1.03219
\(139\) −3.59876 −0.305243 −0.152621 0.988285i \(-0.548772\pi\)
−0.152621 + 0.988285i \(0.548772\pi\)
\(140\) −11.2983 −0.954883
\(141\) 4.97591 0.419047
\(142\) 2.44908 0.205522
\(143\) 8.76999 0.733383
\(144\) −8.98309 −0.748591
\(145\) 15.5718 1.29317
\(146\) 24.4594 2.02427
\(147\) 4.46424 0.368205
\(148\) −25.5428 −2.09961
\(149\) −18.6704 −1.52954 −0.764768 0.644305i \(-0.777147\pi\)
−0.764768 + 0.644305i \(0.777147\pi\)
\(150\) −1.37848 −0.112553
\(151\) −14.6861 −1.19514 −0.597569 0.801818i \(-0.703866\pi\)
−0.597569 + 0.801818i \(0.703866\pi\)
\(152\) 31.7712 2.57698
\(153\) 3.62827 0.293328
\(154\) 4.88267 0.393457
\(155\) −20.6956 −1.66231
\(156\) −20.6043 −1.64966
\(157\) 1.05125 0.0838988 0.0419494 0.999120i \(-0.486643\pi\)
0.0419494 + 0.999120i \(0.486643\pi\)
\(158\) −37.3650 −2.97260
\(159\) 9.60275 0.761547
\(160\) 0.0409483 0.00323724
\(161\) −7.76041 −0.611606
\(162\) −6.93484 −0.544852
\(163\) −15.1265 −1.18480 −0.592401 0.805643i \(-0.701820\pi\)
−0.592401 + 0.805643i \(0.701820\pi\)
\(164\) 42.7634 3.33926
\(165\) −2.65253 −0.206499
\(166\) 12.0697 0.936788
\(167\) −22.4133 −1.73439 −0.867197 0.497965i \(-0.834081\pi\)
−0.867197 + 0.497965i \(0.834081\pi\)
\(168\) −5.73282 −0.442297
\(169\) 22.5343 1.73341
\(170\) 8.22662 0.630953
\(171\) 14.6255 1.11844
\(172\) 24.3623 1.85761
\(173\) −4.22624 −0.321315 −0.160658 0.987010i \(-0.551362\pi\)
−0.160658 + 0.987010i \(0.551362\pi\)
\(174\) 15.8104 1.19858
\(175\) 0.882239 0.0666910
\(176\) 5.86715 0.442253
\(177\) 0.135714 0.0102009
\(178\) 18.1918 1.36353
\(179\) 22.5991 1.68914 0.844569 0.535447i \(-0.179857\pi\)
0.844569 + 0.535447i \(0.179857\pi\)
\(180\) −18.7806 −1.39982
\(181\) 14.3464 1.06636 0.533181 0.846001i \(-0.320996\pi\)
0.533181 + 0.846001i \(0.320996\pi\)
\(182\) 19.7836 1.46646
\(183\) 5.02053 0.371128
\(184\) −28.0222 −2.06583
\(185\) −13.3235 −0.979566
\(186\) −21.0126 −1.54072
\(187\) −2.36974 −0.173293
\(188\) −23.0103 −1.67820
\(189\) −6.15377 −0.447621
\(190\) 33.1613 2.40578
\(191\) −16.4509 −1.19034 −0.595171 0.803599i \(-0.702916\pi\)
−0.595171 + 0.803599i \(0.702916\pi\)
\(192\) 6.93721 0.500650
\(193\) −7.37814 −0.531090 −0.265545 0.964098i \(-0.585552\pi\)
−0.265545 + 0.964098i \(0.585552\pi\)
\(194\) 3.53457 0.253767
\(195\) −10.7475 −0.769646
\(196\) −20.6442 −1.47459
\(197\) −4.04485 −0.288183 −0.144092 0.989564i \(-0.546026\pi\)
−0.144092 + 0.989564i \(0.546026\pi\)
\(198\) 8.11619 0.576793
\(199\) 10.9601 0.776939 0.388470 0.921462i \(-0.373004\pi\)
0.388470 + 0.921462i \(0.373004\pi\)
\(200\) 3.18570 0.225263
\(201\) −8.90256 −0.627938
\(202\) −18.4266 −1.29649
\(203\) −10.1187 −0.710196
\(204\) 5.56750 0.389803
\(205\) 22.3061 1.55792
\(206\) −37.7980 −2.63351
\(207\) −12.8997 −0.896590
\(208\) 23.7725 1.64833
\(209\) −9.55238 −0.660752
\(210\) −5.98366 −0.412912
\(211\) 2.63498 0.181399 0.0906997 0.995878i \(-0.471090\pi\)
0.0906997 + 0.995878i \(0.471090\pi\)
\(212\) −44.4064 −3.04984
\(213\) 0.864554 0.0592382
\(214\) −27.2167 −1.86049
\(215\) 12.7078 0.866662
\(216\) −22.2208 −1.51193
\(217\) 13.4482 0.912925
\(218\) −17.6182 −1.19325
\(219\) 8.63444 0.583461
\(220\) 12.2662 0.826988
\(221\) −9.60173 −0.645882
\(222\) −13.5276 −0.907915
\(223\) 4.58869 0.307281 0.153641 0.988127i \(-0.450900\pi\)
0.153641 + 0.988127i \(0.450900\pi\)
\(224\) −0.0266086 −0.00177786
\(225\) 1.46650 0.0977664
\(226\) 2.44908 0.162910
\(227\) 4.40742 0.292531 0.146265 0.989245i \(-0.453275\pi\)
0.146265 + 0.989245i \(0.453275\pi\)
\(228\) 22.4425 1.48629
\(229\) 2.84757 0.188173 0.0940863 0.995564i \(-0.470007\pi\)
0.0940863 + 0.995564i \(0.470007\pi\)
\(230\) −29.2483 −1.92858
\(231\) 1.72364 0.113407
\(232\) −36.5380 −2.39884
\(233\) −23.9930 −1.57183 −0.785916 0.618333i \(-0.787808\pi\)
−0.785916 + 0.618333i \(0.787808\pi\)
\(234\) 32.8852 2.14977
\(235\) −12.0025 −0.782959
\(236\) −0.627588 −0.0408525
\(237\) −13.1903 −0.856801
\(238\) −5.34574 −0.346513
\(239\) 0.535564 0.0346428 0.0173214 0.999850i \(-0.494486\pi\)
0.0173214 + 0.999850i \(0.494486\pi\)
\(240\) −7.19013 −0.464121
\(241\) −6.95189 −0.447810 −0.223905 0.974611i \(-0.571881\pi\)
−0.223905 + 0.974611i \(0.571881\pi\)
\(242\) 21.6389 1.39100
\(243\) −16.0714 −1.03098
\(244\) −23.2167 −1.48630
\(245\) −10.7683 −0.687964
\(246\) 22.6477 1.44397
\(247\) −38.7044 −2.46270
\(248\) 48.5605 3.08360
\(249\) 4.26073 0.270013
\(250\) 28.8618 1.82538
\(251\) −2.24810 −0.141899 −0.0709494 0.997480i \(-0.522603\pi\)
−0.0709494 + 0.997480i \(0.522603\pi\)
\(252\) 12.2038 0.768767
\(253\) 8.42521 0.529688
\(254\) −29.1924 −1.83169
\(255\) 2.90409 0.181861
\(256\) −31.9839 −1.99899
\(257\) −6.58419 −0.410710 −0.205355 0.978688i \(-0.565835\pi\)
−0.205355 + 0.978688i \(0.565835\pi\)
\(258\) 12.9024 0.803270
\(259\) 8.65777 0.537967
\(260\) 49.7003 3.08228
\(261\) −16.8198 −1.04112
\(262\) 33.8841 2.09336
\(263\) −19.7920 −1.22043 −0.610214 0.792237i \(-0.708916\pi\)
−0.610214 + 0.792237i \(0.708916\pi\)
\(264\) 6.22393 0.383056
\(265\) −23.1631 −1.42290
\(266\) −21.5486 −1.32123
\(267\) 6.42192 0.393015
\(268\) 41.1685 2.51477
\(269\) 25.6567 1.56432 0.782158 0.623080i \(-0.214119\pi\)
0.782158 + 0.623080i \(0.214119\pi\)
\(270\) −23.1930 −1.41148
\(271\) 23.5312 1.42942 0.714710 0.699421i \(-0.246559\pi\)
0.714710 + 0.699421i \(0.246559\pi\)
\(272\) −6.42359 −0.389487
\(273\) 6.98385 0.422682
\(274\) 51.7490 3.12627
\(275\) −0.957817 −0.0577585
\(276\) −19.7943 −1.19147
\(277\) 19.1637 1.15143 0.575717 0.817649i \(-0.304723\pi\)
0.575717 + 0.817649i \(0.304723\pi\)
\(278\) 8.81365 0.528608
\(279\) 22.3542 1.33831
\(280\) 13.8283 0.826400
\(281\) 9.91591 0.591533 0.295767 0.955260i \(-0.404425\pi\)
0.295767 + 0.955260i \(0.404425\pi\)
\(282\) −12.1864 −0.725689
\(283\) 21.3353 1.26825 0.634127 0.773229i \(-0.281359\pi\)
0.634127 + 0.773229i \(0.281359\pi\)
\(284\) −3.99799 −0.237237
\(285\) 11.7063 0.693424
\(286\) −21.4784 −1.27004
\(287\) −14.4947 −0.855595
\(288\) −0.0442300 −0.00260627
\(289\) −14.4055 −0.847383
\(290\) −38.1367 −2.23946
\(291\) 1.24774 0.0731441
\(292\) −39.9286 −2.33665
\(293\) −23.0255 −1.34516 −0.672581 0.740024i \(-0.734814\pi\)
−0.672581 + 0.740024i \(0.734814\pi\)
\(294\) −10.9333 −0.637642
\(295\) −0.327360 −0.0190596
\(296\) 31.2625 1.81710
\(297\) 6.68093 0.387667
\(298\) 45.7252 2.64879
\(299\) 34.1373 1.97421
\(300\) 2.25030 0.129921
\(301\) −8.25763 −0.475962
\(302\) 35.9674 2.06969
\(303\) −6.50480 −0.373691
\(304\) −25.8934 −1.48509
\(305\) −12.1102 −0.693427
\(306\) −8.88593 −0.507975
\(307\) 21.0297 1.20023 0.600114 0.799914i \(-0.295122\pi\)
0.600114 + 0.799914i \(0.295122\pi\)
\(308\) −7.97070 −0.454173
\(309\) −13.3431 −0.759064
\(310\) 50.6853 2.87873
\(311\) 10.4687 0.593624 0.296812 0.954936i \(-0.404077\pi\)
0.296812 + 0.954936i \(0.404077\pi\)
\(312\) 25.2181 1.42770
\(313\) −33.5417 −1.89589 −0.947944 0.318438i \(-0.896842\pi\)
−0.947944 + 0.318438i \(0.896842\pi\)
\(314\) −2.57459 −0.145293
\(315\) 6.36569 0.358666
\(316\) 60.9964 3.43132
\(317\) −9.89314 −0.555654 −0.277827 0.960631i \(-0.589614\pi\)
−0.277827 + 0.960631i \(0.589614\pi\)
\(318\) −23.5179 −1.31882
\(319\) 10.9856 0.615074
\(320\) −16.7334 −0.935428
\(321\) −9.60780 −0.536255
\(322\) 19.0059 1.05915
\(323\) 10.4583 0.581917
\(324\) 11.3208 0.628931
\(325\) −3.88088 −0.215273
\(326\) 37.0461 2.05179
\(327\) −6.21942 −0.343935
\(328\) −52.3392 −2.88995
\(329\) 7.79937 0.429993
\(330\) 6.49626 0.357607
\(331\) −23.7035 −1.30286 −0.651430 0.758709i \(-0.725831\pi\)
−0.651430 + 0.758709i \(0.725831\pi\)
\(332\) −19.7031 −1.08135
\(333\) 14.3913 0.788640
\(334\) 54.8920 3.00356
\(335\) 21.4741 1.17326
\(336\) 4.67222 0.254890
\(337\) 12.0155 0.654523 0.327262 0.944934i \(-0.393874\pi\)
0.327262 + 0.944934i \(0.393874\pi\)
\(338\) −55.1882 −3.00184
\(339\) 0.864554 0.0469561
\(340\) −13.4295 −0.728318
\(341\) −14.6003 −0.790649
\(342\) −35.8190 −1.93687
\(343\) 16.4832 0.890011
\(344\) −29.8177 −1.60766
\(345\) −10.3250 −0.555879
\(346\) 10.3504 0.556441
\(347\) 35.1027 1.88441 0.942206 0.335033i \(-0.108747\pi\)
0.942206 + 0.335033i \(0.108747\pi\)
\(348\) −25.8096 −1.38354
\(349\) −30.2834 −1.62103 −0.810517 0.585715i \(-0.800814\pi\)
−0.810517 + 0.585715i \(0.800814\pi\)
\(350\) −2.16067 −0.115493
\(351\) 27.0698 1.44488
\(352\) 0.0288880 0.00153974
\(353\) −15.9204 −0.847357 −0.423678 0.905813i \(-0.639261\pi\)
−0.423678 + 0.905813i \(0.639261\pi\)
\(354\) −0.332374 −0.0176655
\(355\) −2.08542 −0.110682
\(356\) −29.6972 −1.57395
\(357\) −1.88711 −0.0998764
\(358\) −55.3471 −2.92518
\(359\) 29.7326 1.56923 0.784614 0.619985i \(-0.212861\pi\)
0.784614 + 0.619985i \(0.212861\pi\)
\(360\) 22.9860 1.21147
\(361\) 23.1573 1.21880
\(362\) −35.1356 −1.84668
\(363\) 7.63879 0.400933
\(364\) −32.2957 −1.69276
\(365\) −20.8274 −1.09016
\(366\) −12.2957 −0.642706
\(367\) 8.54500 0.446046 0.223023 0.974813i \(-0.428408\pi\)
0.223023 + 0.974813i \(0.428408\pi\)
\(368\) 22.8380 1.19051
\(369\) −24.0937 −1.25427
\(370\) 32.6304 1.69637
\(371\) 15.0516 0.781440
\(372\) 34.3020 1.77848
\(373\) −15.3775 −0.796214 −0.398107 0.917339i \(-0.630333\pi\)
−0.398107 + 0.917339i \(0.630333\pi\)
\(374\) 5.80369 0.300102
\(375\) 10.1886 0.526135
\(376\) 28.1629 1.45239
\(377\) 44.5114 2.29245
\(378\) 15.0711 0.775172
\(379\) −24.3022 −1.24832 −0.624160 0.781296i \(-0.714559\pi\)
−0.624160 + 0.781296i \(0.714559\pi\)
\(380\) −54.1341 −2.77702
\(381\) −10.3053 −0.527954
\(382\) 40.2895 2.06139
\(383\) −23.2475 −1.18789 −0.593947 0.804504i \(-0.702431\pi\)
−0.593947 + 0.804504i \(0.702431\pi\)
\(384\) −16.9558 −0.865273
\(385\) −4.15764 −0.211893
\(386\) 18.0696 0.919721
\(387\) −13.7262 −0.697742
\(388\) −5.77000 −0.292927
\(389\) 29.0483 1.47281 0.736404 0.676542i \(-0.236522\pi\)
0.736404 + 0.676542i \(0.236522\pi\)
\(390\) 26.3215 1.33284
\(391\) −9.22425 −0.466490
\(392\) 25.2670 1.27617
\(393\) 11.9615 0.603376
\(394\) 9.90615 0.499065
\(395\) 31.8167 1.60087
\(396\) −13.2493 −0.665800
\(397\) 3.58867 0.180110 0.0900551 0.995937i \(-0.471296\pi\)
0.0900551 + 0.995937i \(0.471296\pi\)
\(398\) −26.8421 −1.34547
\(399\) −7.60689 −0.380821
\(400\) −2.59633 −0.129816
\(401\) 23.4606 1.17157 0.585784 0.810467i \(-0.300787\pi\)
0.585784 + 0.810467i \(0.300787\pi\)
\(402\) 21.8031 1.08744
\(403\) −59.1575 −2.94684
\(404\) 30.0804 1.49656
\(405\) 5.90508 0.293426
\(406\) 24.7816 1.22989
\(407\) −9.39944 −0.465913
\(408\) −6.81420 −0.337353
\(409\) 4.08861 0.202169 0.101084 0.994878i \(-0.467769\pi\)
0.101084 + 0.994878i \(0.467769\pi\)
\(410\) −54.6293 −2.69795
\(411\) 18.2680 0.901094
\(412\) 61.7032 3.03990
\(413\) 0.212722 0.0104673
\(414\) 31.5924 1.55268
\(415\) −10.2774 −0.504500
\(416\) 0.117049 0.00573878
\(417\) 3.11132 0.152362
\(418\) 23.3945 1.14426
\(419\) 0.792388 0.0387107 0.0193553 0.999813i \(-0.493839\pi\)
0.0193553 + 0.999813i \(0.493839\pi\)
\(420\) 9.76801 0.476630
\(421\) 27.9728 1.36331 0.681656 0.731673i \(-0.261260\pi\)
0.681656 + 0.731673i \(0.261260\pi\)
\(422\) −6.45327 −0.314140
\(423\) 12.9645 0.630353
\(424\) 54.3502 2.63948
\(425\) 1.04866 0.0508673
\(426\) −2.11736 −0.102586
\(427\) 7.86932 0.380823
\(428\) 44.4298 2.14759
\(429\) −7.58213 −0.366068
\(430\) −31.1223 −1.50085
\(431\) −1.39614 −0.0672495 −0.0336248 0.999435i \(-0.510705\pi\)
−0.0336248 + 0.999435i \(0.510705\pi\)
\(432\) 18.1098 0.871309
\(433\) −5.56443 −0.267410 −0.133705 0.991021i \(-0.542687\pi\)
−0.133705 + 0.991021i \(0.542687\pi\)
\(434\) −32.9358 −1.58097
\(435\) −13.4627 −0.645487
\(436\) 28.7608 1.37739
\(437\) −37.1828 −1.77869
\(438\) −21.1464 −1.01042
\(439\) 23.1446 1.10463 0.552316 0.833635i \(-0.313744\pi\)
0.552316 + 0.833635i \(0.313744\pi\)
\(440\) −15.0129 −0.715713
\(441\) 11.6313 0.553873
\(442\) 23.5154 1.11851
\(443\) 21.8189 1.03665 0.518324 0.855184i \(-0.326556\pi\)
0.518324 + 0.855184i \(0.326556\pi\)
\(444\) 22.0831 1.04802
\(445\) −15.4905 −0.734321
\(446\) −11.2381 −0.532138
\(447\) 16.1415 0.763469
\(448\) 10.8736 0.513727
\(449\) −30.2810 −1.42905 −0.714525 0.699610i \(-0.753357\pi\)
−0.714525 + 0.699610i \(0.753357\pi\)
\(450\) −3.59157 −0.169308
\(451\) 15.7364 0.740998
\(452\) −3.99799 −0.188050
\(453\) 12.6969 0.596553
\(454\) −10.7941 −0.506594
\(455\) −16.8460 −0.789750
\(456\) −27.4679 −1.28630
\(457\) 1.56632 0.0732693 0.0366347 0.999329i \(-0.488336\pi\)
0.0366347 + 0.999329i \(0.488336\pi\)
\(458\) −6.97392 −0.325870
\(459\) −7.31455 −0.341414
\(460\) 47.7464 2.22619
\(461\) −24.4301 −1.13782 −0.568911 0.822399i \(-0.692635\pi\)
−0.568911 + 0.822399i \(0.692635\pi\)
\(462\) −4.22133 −0.196394
\(463\) −23.4823 −1.09132 −0.545658 0.838008i \(-0.683720\pi\)
−0.545658 + 0.838008i \(0.683720\pi\)
\(464\) 29.7783 1.38242
\(465\) 17.8925 0.829744
\(466\) 58.7607 2.72204
\(467\) −12.9173 −0.597740 −0.298870 0.954294i \(-0.596610\pi\)
−0.298870 + 0.954294i \(0.596610\pi\)
\(468\) −53.6834 −2.48151
\(469\) −13.9541 −0.644341
\(470\) 29.3952 1.35590
\(471\) −0.908861 −0.0418781
\(472\) 0.768121 0.0353556
\(473\) 8.96503 0.412212
\(474\) 32.3041 1.48377
\(475\) 4.22711 0.193953
\(476\) 8.72664 0.399985
\(477\) 25.0194 1.14556
\(478\) −1.31164 −0.0599930
\(479\) 22.7754 1.04064 0.520318 0.853972i \(-0.325813\pi\)
0.520318 + 0.853972i \(0.325813\pi\)
\(480\) −0.0354020 −0.00161587
\(481\) −38.0847 −1.73651
\(482\) 17.0257 0.775501
\(483\) 6.70929 0.305283
\(484\) −35.3244 −1.60566
\(485\) −3.00972 −0.136664
\(486\) 39.3602 1.78541
\(487\) 41.9663 1.90167 0.950837 0.309692i \(-0.100226\pi\)
0.950837 + 0.309692i \(0.100226\pi\)
\(488\) 28.4155 1.28631
\(489\) 13.0777 0.591394
\(490\) 26.3725 1.19139
\(491\) 24.4468 1.10327 0.551635 0.834086i \(-0.314004\pi\)
0.551635 + 0.834086i \(0.314004\pi\)
\(492\) −36.9713 −1.66679
\(493\) −12.0274 −0.541689
\(494\) 94.7901 4.26481
\(495\) −6.91102 −0.310627
\(496\) −39.5765 −1.77704
\(497\) 1.35512 0.0607856
\(498\) −10.4349 −0.467598
\(499\) 30.8452 1.38082 0.690410 0.723418i \(-0.257430\pi\)
0.690410 + 0.723418i \(0.257430\pi\)
\(500\) −47.1154 −2.10707
\(501\) 19.3775 0.865723
\(502\) 5.50578 0.245735
\(503\) −7.91484 −0.352905 −0.176453 0.984309i \(-0.556462\pi\)
−0.176453 + 0.984309i \(0.556462\pi\)
\(504\) −14.9365 −0.665327
\(505\) 15.6904 0.698215
\(506\) −20.6340 −0.917294
\(507\) −19.4821 −0.865230
\(508\) 47.6550 2.11435
\(509\) −21.6493 −0.959588 −0.479794 0.877381i \(-0.659289\pi\)
−0.479794 + 0.877381i \(0.659289\pi\)
\(510\) −7.11236 −0.314940
\(511\) 13.5338 0.598702
\(512\) 39.1066 1.72828
\(513\) −29.4848 −1.30179
\(514\) 16.1252 0.711252
\(515\) 32.1854 1.41826
\(516\) −21.0625 −0.927226
\(517\) −8.46751 −0.372401
\(518\) −21.2036 −0.931631
\(519\) 3.65381 0.160385
\(520\) −60.8294 −2.66755
\(521\) −30.5129 −1.33679 −0.668397 0.743804i \(-0.733019\pi\)
−0.668397 + 0.743804i \(0.733019\pi\)
\(522\) 41.1931 1.80297
\(523\) −35.2936 −1.54328 −0.771640 0.636060i \(-0.780563\pi\)
−0.771640 + 0.636060i \(0.780563\pi\)
\(524\) −55.3140 −2.41640
\(525\) −0.762743 −0.0332888
\(526\) 48.4722 2.11349
\(527\) 15.9850 0.696316
\(528\) −5.07247 −0.220751
\(529\) 9.79523 0.425879
\(530\) 56.7282 2.46412
\(531\) 0.353595 0.0153447
\(532\) 35.1769 1.52511
\(533\) 63.7608 2.76179
\(534\) −15.7278 −0.680609
\(535\) 23.1753 1.00195
\(536\) −50.3872 −2.17640
\(537\) −19.5382 −0.843133
\(538\) −62.8353 −2.70902
\(539\) −7.59681 −0.327218
\(540\) 37.8614 1.62930
\(541\) −1.28420 −0.0552123 −0.0276061 0.999619i \(-0.508788\pi\)
−0.0276061 + 0.999619i \(0.508788\pi\)
\(542\) −57.6299 −2.47541
\(543\) −12.4033 −0.532275
\(544\) −0.0316278 −0.00135603
\(545\) 15.0021 0.642618
\(546\) −17.1040 −0.731984
\(547\) 15.8614 0.678185 0.339093 0.940753i \(-0.389880\pi\)
0.339093 + 0.940753i \(0.389880\pi\)
\(548\) −84.4776 −3.60870
\(549\) 13.0807 0.558272
\(550\) 2.34577 0.100024
\(551\) −48.4824 −2.06542
\(552\) 24.2267 1.03116
\(553\) −20.6748 −0.879182
\(554\) −46.9334 −1.99401
\(555\) 11.5189 0.488951
\(556\) −14.3878 −0.610179
\(557\) −11.5059 −0.487521 −0.243760 0.969836i \(-0.578381\pi\)
−0.243760 + 0.969836i \(0.578381\pi\)
\(558\) −54.7473 −2.31764
\(559\) 36.3245 1.53636
\(560\) −11.2700 −0.476244
\(561\) 2.04877 0.0864991
\(562\) −24.2849 −1.02439
\(563\) −17.2585 −0.727361 −0.363680 0.931524i \(-0.618480\pi\)
−0.363680 + 0.931524i \(0.618480\pi\)
\(564\) 19.8936 0.837674
\(565\) −2.08542 −0.0877341
\(566\) −52.2520 −2.19631
\(567\) −3.83718 −0.161146
\(568\) 4.89325 0.205316
\(569\) 21.0424 0.882144 0.441072 0.897472i \(-0.354598\pi\)
0.441072 + 0.897472i \(0.354598\pi\)
\(570\) −28.6698 −1.20084
\(571\) −15.9225 −0.666334 −0.333167 0.942868i \(-0.608117\pi\)
−0.333167 + 0.942868i \(0.608117\pi\)
\(572\) 35.0624 1.46603
\(573\) 14.2226 0.594160
\(574\) 35.4987 1.48169
\(575\) −3.72831 −0.155481
\(576\) 18.0745 0.753105
\(577\) −26.1480 −1.08855 −0.544277 0.838905i \(-0.683196\pi\)
−0.544277 + 0.838905i \(0.683196\pi\)
\(578\) 35.2803 1.46747
\(579\) 6.37879 0.265094
\(580\) 62.2562 2.58505
\(581\) 6.67838 0.277066
\(582\) −3.05583 −0.126668
\(583\) −16.3410 −0.676775
\(584\) 48.8697 2.02224
\(585\) −28.0021 −1.15774
\(586\) 56.3912 2.32950
\(587\) −22.8786 −0.944301 −0.472151 0.881518i \(-0.656522\pi\)
−0.472151 + 0.881518i \(0.656522\pi\)
\(588\) 17.8480 0.736040
\(589\) 64.4350 2.65500
\(590\) 0.801730 0.0330067
\(591\) 3.49699 0.143847
\(592\) −25.4788 −1.04717
\(593\) 28.6707 1.17737 0.588683 0.808364i \(-0.299647\pi\)
0.588683 + 0.808364i \(0.299647\pi\)
\(594\) −16.3621 −0.671347
\(595\) 4.55195 0.186612
\(596\) −74.6441 −3.05754
\(597\) −9.47558 −0.387810
\(598\) −83.6050 −3.41886
\(599\) −17.5970 −0.718995 −0.359498 0.933146i \(-0.617052\pi\)
−0.359498 + 0.933146i \(0.617052\pi\)
\(600\) −2.75421 −0.112440
\(601\) −39.3729 −1.60605 −0.803027 0.595942i \(-0.796779\pi\)
−0.803027 + 0.595942i \(0.796779\pi\)
\(602\) 20.2236 0.824252
\(603\) −23.1951 −0.944579
\(604\) −58.7149 −2.38908
\(605\) −18.4258 −0.749114
\(606\) 15.9308 0.647144
\(607\) −19.8124 −0.804161 −0.402081 0.915604i \(-0.631713\pi\)
−0.402081 + 0.915604i \(0.631713\pi\)
\(608\) −0.127491 −0.00517044
\(609\) 8.74819 0.354495
\(610\) 29.6588 1.20085
\(611\) −34.3087 −1.38798
\(612\) 14.5058 0.586362
\(613\) 4.87598 0.196939 0.0984694 0.995140i \(-0.468605\pi\)
0.0984694 + 0.995140i \(0.468605\pi\)
\(614\) −51.5034 −2.07851
\(615\) −19.2848 −0.777637
\(616\) 9.75555 0.393062
\(617\) 42.6838 1.71839 0.859193 0.511652i \(-0.170966\pi\)
0.859193 + 0.511652i \(0.170966\pi\)
\(618\) 32.6784 1.31452
\(619\) −39.1413 −1.57322 −0.786611 0.617448i \(-0.788166\pi\)
−0.786611 + 0.617448i \(0.788166\pi\)
\(620\) −82.7410 −3.32296
\(621\) 26.0056 1.04357
\(622\) −25.6386 −1.02801
\(623\) 10.0659 0.403281
\(624\) −20.5526 −0.822764
\(625\) −21.3210 −0.852838
\(626\) 82.1462 3.28322
\(627\) 8.25855 0.329815
\(628\) 4.20289 0.167714
\(629\) 10.2909 0.410324
\(630\) −15.5901 −0.621124
\(631\) 31.1728 1.24097 0.620484 0.784219i \(-0.286936\pi\)
0.620484 + 0.784219i \(0.286936\pi\)
\(632\) −74.6551 −2.96962
\(633\) −2.27808 −0.0905456
\(634\) 24.2291 0.962261
\(635\) 24.8576 0.986444
\(636\) 38.3917 1.52233
\(637\) −30.7808 −1.21958
\(638\) −26.9046 −1.06516
\(639\) 2.25255 0.0891094
\(640\) 40.8997 1.61670
\(641\) 5.27277 0.208262 0.104131 0.994564i \(-0.466794\pi\)
0.104131 + 0.994564i \(0.466794\pi\)
\(642\) 23.5303 0.928666
\(643\) −35.4983 −1.39992 −0.699958 0.714184i \(-0.746798\pi\)
−0.699958 + 0.714184i \(0.746798\pi\)
\(644\) −31.0261 −1.22260
\(645\) −10.9865 −0.432595
\(646\) −25.6133 −1.00774
\(647\) 8.74239 0.343699 0.171849 0.985123i \(-0.445026\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(648\) −13.8558 −0.544306
\(649\) −0.230945 −0.00906537
\(650\) 9.50460 0.372801
\(651\) −11.6267 −0.455687
\(652\) −60.4758 −2.36841
\(653\) −12.1886 −0.476977 −0.238488 0.971145i \(-0.576652\pi\)
−0.238488 + 0.971145i \(0.576652\pi\)
\(654\) 15.2319 0.595613
\(655\) −28.8526 −1.12737
\(656\) 42.6562 1.66544
\(657\) 22.4966 0.877674
\(658\) −19.1013 −0.744645
\(659\) −20.9704 −0.816891 −0.408446 0.912783i \(-0.633929\pi\)
−0.408446 + 0.912783i \(0.633929\pi\)
\(660\) −10.6048 −0.412791
\(661\) 10.7768 0.419169 0.209585 0.977791i \(-0.432789\pi\)
0.209585 + 0.977791i \(0.432789\pi\)
\(662\) 58.0517 2.25624
\(663\) 8.30121 0.322392
\(664\) 24.1151 0.935849
\(665\) 18.3488 0.711537
\(666\) −35.2455 −1.36574
\(667\) 42.7615 1.65573
\(668\) −89.6083 −3.46705
\(669\) −3.96717 −0.153380
\(670\) −52.5919 −2.03180
\(671\) −8.54345 −0.329816
\(672\) 0.0230045 0.000887420 0
\(673\) 17.9406 0.691558 0.345779 0.938316i \(-0.387615\pi\)
0.345779 + 0.938316i \(0.387615\pi\)
\(674\) −29.4268 −1.13348
\(675\) −2.95644 −0.113793
\(676\) 90.0919 3.46507
\(677\) −47.2978 −1.81780 −0.908901 0.417012i \(-0.863077\pi\)
−0.908901 + 0.417012i \(0.863077\pi\)
\(678\) −2.11736 −0.0813168
\(679\) 1.95575 0.0750547
\(680\) 16.4367 0.630320
\(681\) −3.81045 −0.146017
\(682\) 35.7573 1.36922
\(683\) 0.639679 0.0244766 0.0122383 0.999925i \(-0.496104\pi\)
0.0122383 + 0.999925i \(0.496104\pi\)
\(684\) 58.4726 2.23576
\(685\) −44.0648 −1.68363
\(686\) −40.3688 −1.54129
\(687\) −2.46187 −0.0939264
\(688\) 24.3012 0.926476
\(689\) −66.2105 −2.52242
\(690\) 25.2868 0.962650
\(691\) −44.3739 −1.68806 −0.844031 0.536294i \(-0.819824\pi\)
−0.844031 + 0.536294i \(0.819824\pi\)
\(692\) −16.8965 −0.642308
\(693\) 4.49085 0.170593
\(694\) −85.9694 −3.26335
\(695\) −7.50491 −0.284678
\(696\) 31.5891 1.19738
\(697\) −17.2288 −0.652588
\(698\) 74.1665 2.80724
\(699\) 20.7432 0.784580
\(700\) 3.52719 0.133315
\(701\) 16.8460 0.636265 0.318133 0.948046i \(-0.396944\pi\)
0.318133 + 0.948046i \(0.396944\pi\)
\(702\) −66.2962 −2.50219
\(703\) 41.4823 1.56454
\(704\) −11.8051 −0.444920
\(705\) 10.3768 0.390814
\(706\) 38.9903 1.46742
\(707\) −10.1958 −0.383452
\(708\) 0.542584 0.0203915
\(709\) 1.10791 0.0416083 0.0208042 0.999784i \(-0.493377\pi\)
0.0208042 + 0.999784i \(0.493377\pi\)
\(710\) 5.10735 0.191676
\(711\) −34.3666 −1.28885
\(712\) 36.3472 1.36217
\(713\) −56.8318 −2.12837
\(714\) 4.62168 0.172962
\(715\) 18.2891 0.683973
\(716\) 90.3512 3.37658
\(717\) −0.463024 −0.0172920
\(718\) −72.8175 −2.71753
\(719\) −22.4076 −0.835664 −0.417832 0.908524i \(-0.637210\pi\)
−0.417832 + 0.908524i \(0.637210\pi\)
\(720\) −18.7335 −0.698156
\(721\) −20.9144 −0.778892
\(722\) −56.7140 −2.11068
\(723\) 6.01028 0.223525
\(724\) 57.3570 2.13165
\(725\) −4.86132 −0.180545
\(726\) −18.7080 −0.694320
\(727\) −20.8038 −0.771570 −0.385785 0.922589i \(-0.626069\pi\)
−0.385785 + 0.922589i \(0.626069\pi\)
\(728\) 39.5276 1.46499
\(729\) 5.39976 0.199991
\(730\) 51.0080 1.88789
\(731\) −9.81526 −0.363031
\(732\) 20.0721 0.741885
\(733\) −42.0747 −1.55407 −0.777033 0.629460i \(-0.783276\pi\)
−0.777033 + 0.629460i \(0.783276\pi\)
\(734\) −20.9274 −0.772444
\(735\) 9.30980 0.343397
\(736\) 0.112447 0.00414485
\(737\) 15.1495 0.558039
\(738\) 59.0075 2.17209
\(739\) 11.9650 0.440141 0.220070 0.975484i \(-0.429371\pi\)
0.220070 + 0.975484i \(0.429371\pi\)
\(740\) −53.2674 −1.95815
\(741\) 33.4620 1.22926
\(742\) −36.8626 −1.35327
\(743\) −34.1527 −1.25294 −0.626470 0.779445i \(-0.715501\pi\)
−0.626470 + 0.779445i \(0.715501\pi\)
\(744\) −41.9832 −1.53918
\(745\) −38.9355 −1.42649
\(746\) 37.6606 1.37885
\(747\) 11.1011 0.406168
\(748\) −9.47422 −0.346412
\(749\) −15.0595 −0.550263
\(750\) −24.9526 −0.911141
\(751\) 43.8020 1.59836 0.799179 0.601093i \(-0.205268\pi\)
0.799179 + 0.601093i \(0.205268\pi\)
\(752\) −22.9526 −0.836996
\(753\) 1.94360 0.0708289
\(754\) −109.012 −3.96998
\(755\) −30.6266 −1.11462
\(756\) −24.6027 −0.894792
\(757\) 5.81934 0.211507 0.105754 0.994392i \(-0.466274\pi\)
0.105754 + 0.994392i \(0.466274\pi\)
\(758\) 59.5181 2.16179
\(759\) −7.28404 −0.264394
\(760\) 66.2562 2.40336
\(761\) 1.24970 0.0453016 0.0226508 0.999743i \(-0.492789\pi\)
0.0226508 + 0.999743i \(0.492789\pi\)
\(762\) 25.2384 0.914290
\(763\) −9.74849 −0.352919
\(764\) −65.7704 −2.37949
\(765\) 7.56645 0.273566
\(766\) 56.9351 2.05715
\(767\) −0.935742 −0.0337877
\(768\) 27.6518 0.997797
\(769\) −1.02219 −0.0368611 −0.0184306 0.999830i \(-0.505867\pi\)
−0.0184306 + 0.999830i \(0.505867\pi\)
\(770\) 10.1824 0.366948
\(771\) 5.69238 0.205006
\(772\) −29.4977 −1.06165
\(773\) −7.62955 −0.274416 −0.137208 0.990542i \(-0.543813\pi\)
−0.137208 + 0.990542i \(0.543813\pi\)
\(774\) 33.6165 1.20832
\(775\) 6.46090 0.232082
\(776\) 7.06205 0.253513
\(777\) −7.48510 −0.268527
\(778\) −71.1417 −2.55055
\(779\) −69.4490 −2.48827
\(780\) −42.9685 −1.53852
\(781\) −1.47121 −0.0526441
\(782\) 22.5909 0.807850
\(783\) 33.9086 1.21179
\(784\) −20.5924 −0.735444
\(785\) 2.19229 0.0782463
\(786\) −29.2946 −1.04490
\(787\) −20.8999 −0.745002 −0.372501 0.928032i \(-0.621500\pi\)
−0.372501 + 0.928032i \(0.621500\pi\)
\(788\) −16.1713 −0.576078
\(789\) 17.1113 0.609177
\(790\) −77.9216 −2.77233
\(791\) 1.35512 0.0481827
\(792\) 16.2161 0.576214
\(793\) −34.6164 −1.22926
\(794\) −8.78894 −0.311908
\(795\) 20.0257 0.710239
\(796\) 43.8183 1.55310
\(797\) −9.73088 −0.344686 −0.172343 0.985037i \(-0.555134\pi\)
−0.172343 + 0.985037i \(0.555134\pi\)
\(798\) 18.6299 0.659491
\(799\) 9.27056 0.327969
\(800\) −0.0127835 −0.000451965 0
\(801\) 16.7320 0.591195
\(802\) −57.4570 −2.02888
\(803\) −14.6932 −0.518513
\(804\) −35.5924 −1.25525
\(805\) −16.1837 −0.570400
\(806\) 144.881 5.10323
\(807\) −22.1816 −0.780829
\(808\) −36.8162 −1.29519
\(809\) −28.5975 −1.00543 −0.502717 0.864451i \(-0.667666\pi\)
−0.502717 + 0.864451i \(0.667666\pi\)
\(810\) −14.4620 −0.508144
\(811\) −18.0658 −0.634375 −0.317187 0.948363i \(-0.602738\pi\)
−0.317187 + 0.948363i \(0.602738\pi\)
\(812\) −40.4547 −1.41968
\(813\) −20.3440 −0.713495
\(814\) 23.0200 0.806850
\(815\) −31.5451 −1.10498
\(816\) 5.55354 0.194413
\(817\) −39.5651 −1.38421
\(818\) −10.0133 −0.350108
\(819\) 18.1960 0.635821
\(820\) 89.1795 3.11428
\(821\) −37.5775 −1.31147 −0.655733 0.754993i \(-0.727640\pi\)
−0.655733 + 0.754993i \(0.727640\pi\)
\(822\) −44.7398 −1.56048
\(823\) −33.8817 −1.18104 −0.590521 0.807022i \(-0.701078\pi\)
−0.590521 + 0.807022i \(0.701078\pi\)
\(824\) −75.5202 −2.63087
\(825\) 0.828084 0.0288302
\(826\) −0.520972 −0.0181269
\(827\) −19.9806 −0.694793 −0.347397 0.937718i \(-0.612934\pi\)
−0.347397 + 0.937718i \(0.612934\pi\)
\(828\) −51.5729 −1.79228
\(829\) −20.0184 −0.695268 −0.347634 0.937630i \(-0.613015\pi\)
−0.347634 + 0.937630i \(0.613015\pi\)
\(830\) 25.1703 0.873673
\(831\) −16.5680 −0.574739
\(832\) −47.8318 −1.65827
\(833\) 8.31729 0.288177
\(834\) −7.61987 −0.263855
\(835\) −46.7411 −1.61754
\(836\) −38.1904 −1.32084
\(837\) −45.0659 −1.55770
\(838\) −1.94062 −0.0670377
\(839\) 26.9539 0.930551 0.465275 0.885166i \(-0.345955\pi\)
0.465275 + 0.885166i \(0.345955\pi\)
\(840\) −11.9553 −0.412498
\(841\) 26.7564 0.922635
\(842\) −68.5077 −2.36093
\(843\) −8.57283 −0.295264
\(844\) 10.5346 0.362617
\(845\) 46.9933 1.61662
\(846\) −31.7510 −1.09162
\(847\) 11.9732 0.411406
\(848\) −44.2951 −1.52110
\(849\) −18.4456 −0.633050
\(850\) −2.56824 −0.0880899
\(851\) −36.5874 −1.25420
\(852\) 3.45648 0.118417
\(853\) −53.3140 −1.82544 −0.912719 0.408588i \(-0.866021\pi\)
−0.912719 + 0.408588i \(0.866021\pi\)
\(854\) −19.2726 −0.659494
\(855\) 30.5002 1.04309
\(856\) −54.3788 −1.85863
\(857\) 39.7102 1.35647 0.678237 0.734843i \(-0.262744\pi\)
0.678237 + 0.734843i \(0.262744\pi\)
\(858\) 18.5692 0.633943
\(859\) 2.16148 0.0737486 0.0368743 0.999320i \(-0.488260\pi\)
0.0368743 + 0.999320i \(0.488260\pi\)
\(860\) 50.8056 1.73246
\(861\) 12.5314 0.427070
\(862\) 3.41925 0.116460
\(863\) −37.8709 −1.28914 −0.644570 0.764545i \(-0.722964\pi\)
−0.644570 + 0.764545i \(0.722964\pi\)
\(864\) 0.0891671 0.00303353
\(865\) −8.81348 −0.299667
\(866\) 13.6277 0.463089
\(867\) 12.4543 0.422972
\(868\) 53.7659 1.82493
\(869\) 22.4459 0.761426
\(870\) 32.9712 1.11783
\(871\) 61.3828 2.07988
\(872\) −35.2010 −1.19206
\(873\) 3.25093 0.110027
\(874\) 91.0636 3.08027
\(875\) 15.9698 0.539879
\(876\) 34.5204 1.16634
\(877\) −17.9900 −0.607477 −0.303739 0.952755i \(-0.598235\pi\)
−0.303739 + 0.952755i \(0.598235\pi\)
\(878\) −56.6830 −1.91296
\(879\) 19.9067 0.671438
\(880\) 12.2355 0.412457
\(881\) 15.5504 0.523906 0.261953 0.965081i \(-0.415633\pi\)
0.261953 + 0.965081i \(0.415633\pi\)
\(882\) −28.4861 −0.959176
\(883\) 25.6121 0.861916 0.430958 0.902372i \(-0.358176\pi\)
0.430958 + 0.902372i \(0.358176\pi\)
\(884\) −38.3877 −1.29112
\(885\) 0.283020 0.00951361
\(886\) −53.4363 −1.79523
\(887\) −52.0324 −1.74708 −0.873538 0.486756i \(-0.838180\pi\)
−0.873538 + 0.486756i \(0.838180\pi\)
\(888\) −27.0281 −0.907005
\(889\) −16.1527 −0.541745
\(890\) 37.9375 1.27167
\(891\) 4.16590 0.139563
\(892\) 18.3456 0.614255
\(893\) 37.3694 1.25052
\(894\) −39.5319 −1.32215
\(895\) 47.1286 1.57533
\(896\) −26.5770 −0.887875
\(897\) −29.5135 −0.985428
\(898\) 74.1607 2.47477
\(899\) −74.1026 −2.47146
\(900\) 5.86304 0.195435
\(901\) 17.8908 0.596028
\(902\) −38.5397 −1.28323
\(903\) 7.13916 0.237576
\(904\) 4.89325 0.162747
\(905\) 29.9183 0.994517
\(906\) −31.0958 −1.03309
\(907\) −14.7406 −0.489454 −0.244727 0.969592i \(-0.578698\pi\)
−0.244727 + 0.969592i \(0.578698\pi\)
\(908\) 17.6208 0.584768
\(909\) −16.9479 −0.562126
\(910\) 41.2571 1.36766
\(911\) 6.98453 0.231408 0.115704 0.993284i \(-0.463088\pi\)
0.115704 + 0.993284i \(0.463088\pi\)
\(912\) 22.3862 0.741281
\(913\) −7.25050 −0.239956
\(914\) −3.83604 −0.126885
\(915\) 10.4699 0.346124
\(916\) 11.3846 0.376156
\(917\) 18.7487 0.619137
\(918\) 17.9139 0.591248
\(919\) −11.0893 −0.365803 −0.182901 0.983131i \(-0.558549\pi\)
−0.182901 + 0.983131i \(0.558549\pi\)
\(920\) −58.4380 −1.92664
\(921\) −18.1813 −0.599094
\(922\) 59.8312 1.97044
\(923\) −5.96106 −0.196211
\(924\) 6.89110 0.226701
\(925\) 4.15943 0.136761
\(926\) 57.5100 1.88990
\(927\) −34.7648 −1.14183
\(928\) 0.146619 0.00481300
\(929\) 6.56344 0.215339 0.107670 0.994187i \(-0.465661\pi\)
0.107670 + 0.994187i \(0.465661\pi\)
\(930\) −43.8201 −1.43692
\(931\) 33.5268 1.09880
\(932\) −95.9238 −3.14209
\(933\) −9.05073 −0.296308
\(934\) 31.6354 1.03514
\(935\) −4.94190 −0.161617
\(936\) 65.7045 2.14762
\(937\) 15.8966 0.519318 0.259659 0.965700i \(-0.416390\pi\)
0.259659 + 0.965700i \(0.416390\pi\)
\(938\) 34.1747 1.11584
\(939\) 28.9986 0.946333
\(940\) −47.9861 −1.56513
\(941\) −8.57197 −0.279438 −0.139719 0.990191i \(-0.544620\pi\)
−0.139719 + 0.990191i \(0.544620\pi\)
\(942\) 2.22587 0.0725229
\(943\) 61.2541 1.99471
\(944\) −0.626015 −0.0203750
\(945\) −12.8332 −0.417463
\(946\) −21.9561 −0.713853
\(947\) 35.4116 1.15072 0.575361 0.817899i \(-0.304861\pi\)
0.575361 + 0.817899i \(0.304861\pi\)
\(948\) −52.7347 −1.71274
\(949\) −59.5341 −1.93256
\(950\) −10.3525 −0.335880
\(951\) 8.55315 0.277355
\(952\) −10.6808 −0.346165
\(953\) 21.9178 0.709987 0.354994 0.934869i \(-0.384483\pi\)
0.354994 + 0.934869i \(0.384483\pi\)
\(954\) −61.2746 −1.98384
\(955\) −34.3069 −1.11014
\(956\) 2.14118 0.0692508
\(957\) −9.49762 −0.307014
\(958\) −55.7789 −1.80213
\(959\) 28.6338 0.924632
\(960\) 14.4670 0.466919
\(961\) 67.4854 2.17695
\(962\) 93.2725 3.00723
\(963\) −25.0326 −0.806664
\(964\) −27.7936 −0.895172
\(965\) −15.3865 −0.495309
\(966\) −16.4316 −0.528677
\(967\) −51.9498 −1.67059 −0.835297 0.549800i \(-0.814704\pi\)
−0.835297 + 0.549800i \(0.814704\pi\)
\(968\) 43.2345 1.38961
\(969\) −9.04178 −0.290464
\(970\) 7.37105 0.236670
\(971\) −22.7215 −0.729169 −0.364584 0.931170i \(-0.618789\pi\)
−0.364584 + 0.931170i \(0.618789\pi\)
\(972\) −64.2534 −2.06093
\(973\) 4.87677 0.156342
\(974\) −102.779 −3.29325
\(975\) 3.35523 0.107453
\(976\) −23.1585 −0.741285
\(977\) −1.10046 −0.0352070 −0.0176035 0.999845i \(-0.505604\pi\)
−0.0176035 + 0.999845i \(0.505604\pi\)
\(978\) −32.0283 −1.02415
\(979\) −10.9282 −0.349267
\(980\) −43.0517 −1.37524
\(981\) −16.2044 −0.517365
\(982\) −59.8723 −1.91060
\(983\) 2.10873 0.0672581 0.0336291 0.999434i \(-0.489294\pi\)
0.0336291 + 0.999434i \(0.489294\pi\)
\(984\) 45.2501 1.44252
\(985\) −8.43519 −0.268767
\(986\) 29.4562 0.938075
\(987\) −6.74297 −0.214631
\(988\) −154.740 −4.92293
\(989\) 34.8965 1.10964
\(990\) 16.9256 0.537932
\(991\) −7.37805 −0.234371 −0.117186 0.993110i \(-0.537387\pi\)
−0.117186 + 0.993110i \(0.537387\pi\)
\(992\) −0.194863 −0.00618689
\(993\) 20.4929 0.650323
\(994\) −3.31881 −0.105266
\(995\) 22.8563 0.724594
\(996\) 17.0344 0.539755
\(997\) −15.6697 −0.496263 −0.248131 0.968726i \(-0.579817\pi\)
−0.248131 + 0.968726i \(0.579817\pi\)
\(998\) −75.5423 −2.39125
\(999\) −29.0127 −0.917922
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 \(a_p\))