Properties

Label 8001.2.a.o.1.4
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.45503\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.45503 q^{2}\) \(+0.117115 q^{4}\) \(+0.420019 q^{5}\) \(+1.00000 q^{7}\) \(+2.73966 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.45503 q^{2}\) \(+0.117115 q^{4}\) \(+0.420019 q^{5}\) \(+1.00000 q^{7}\) \(+2.73966 q^{8}\) \(-0.611141 q^{10}\) \(-4.09314 q^{11}\) \(+5.95755 q^{13}\) \(-1.45503 q^{14}\) \(-4.22051 q^{16}\) \(+7.99832 q^{17}\) \(+1.20264 q^{19}\) \(+0.0491906 q^{20}\) \(+5.95565 q^{22}\) \(+0.806334 q^{23}\) \(-4.82358 q^{25}\) \(-8.66843 q^{26}\) \(+0.117115 q^{28}\) \(-5.46630 q^{29}\) \(+3.58774 q^{31}\) \(+0.661667 q^{32}\) \(-11.6378 q^{34}\) \(+0.420019 q^{35}\) \(-3.79745 q^{37}\) \(-1.74988 q^{38}\) \(+1.15071 q^{40}\) \(-9.24830 q^{41}\) \(-4.78854 q^{43}\) \(-0.479369 q^{44}\) \(-1.17324 q^{46}\) \(-10.3421 q^{47}\) \(+1.00000 q^{49}\) \(+7.01846 q^{50}\) \(+0.697719 q^{52}\) \(-3.29407 q^{53}\) \(-1.71920 q^{55}\) \(+2.73966 q^{56}\) \(+7.95363 q^{58}\) \(-5.19779 q^{59}\) \(-4.46437 q^{61}\) \(-5.22027 q^{62}\) \(+7.47828 q^{64}\) \(+2.50229 q^{65}\) \(+10.1874 q^{67}\) \(+0.936724 q^{68}\) \(-0.611141 q^{70}\) \(-8.24577 q^{71}\) \(+8.96444 q^{73}\) \(+5.52541 q^{74}\) \(+0.140847 q^{76}\) \(-4.09314 q^{77}\) \(-11.1975 q^{79}\) \(-1.77270 q^{80}\) \(+13.4566 q^{82}\) \(-14.0246 q^{83}\) \(+3.35945 q^{85}\) \(+6.96747 q^{86}\) \(-11.2138 q^{88}\) \(-12.7389 q^{89}\) \(+5.95755 q^{91}\) \(+0.0944338 q^{92}\) \(+15.0480 q^{94}\) \(+0.505131 q^{95}\) \(-8.63018 q^{97}\) \(-1.45503 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45503 −1.02886 −0.514431 0.857532i \(-0.671997\pi\)
−0.514431 + 0.857532i \(0.671997\pi\)
\(3\) 0 0
\(4\) 0.117115 0.0585575
\(5\) 0.420019 0.187838 0.0939191 0.995580i \(-0.470060\pi\)
0.0939191 + 0.995580i \(0.470060\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.73966 0.968615
\(9\) 0 0
\(10\) −0.611141 −0.193260
\(11\) −4.09314 −1.23413 −0.617065 0.786912i \(-0.711678\pi\)
−0.617065 + 0.786912i \(0.711678\pi\)
\(12\) 0 0
\(13\) 5.95755 1.65233 0.826164 0.563430i \(-0.190518\pi\)
0.826164 + 0.563430i \(0.190518\pi\)
\(14\) −1.45503 −0.388873
\(15\) 0 0
\(16\) −4.22051 −1.05513
\(17\) 7.99832 1.93988 0.969939 0.243348i \(-0.0782457\pi\)
0.969939 + 0.243348i \(0.0782457\pi\)
\(18\) 0 0
\(19\) 1.20264 0.275904 0.137952 0.990439i \(-0.455948\pi\)
0.137952 + 0.990439i \(0.455948\pi\)
\(20\) 0.0491906 0.0109993
\(21\) 0 0
\(22\) 5.95565 1.26975
\(23\) 0.806334 0.168132 0.0840661 0.996460i \(-0.473209\pi\)
0.0840661 + 0.996460i \(0.473209\pi\)
\(24\) 0 0
\(25\) −4.82358 −0.964717
\(26\) −8.66843 −1.70002
\(27\) 0 0
\(28\) 0.117115 0.0221327
\(29\) −5.46630 −1.01507 −0.507533 0.861632i \(-0.669442\pi\)
−0.507533 + 0.861632i \(0.669442\pi\)
\(30\) 0 0
\(31\) 3.58774 0.644376 0.322188 0.946676i \(-0.395582\pi\)
0.322188 + 0.946676i \(0.395582\pi\)
\(32\) 0.661667 0.116967
\(33\) 0 0
\(34\) −11.6378 −1.99587
\(35\) 0.420019 0.0709962
\(36\) 0 0
\(37\) −3.79745 −0.624297 −0.312149 0.950033i \(-0.601049\pi\)
−0.312149 + 0.950033i \(0.601049\pi\)
\(38\) −1.74988 −0.283867
\(39\) 0 0
\(40\) 1.15071 0.181943
\(41\) −9.24830 −1.44434 −0.722171 0.691715i \(-0.756855\pi\)
−0.722171 + 0.691715i \(0.756855\pi\)
\(42\) 0 0
\(43\) −4.78854 −0.730245 −0.365123 0.930959i \(-0.618973\pi\)
−0.365123 + 0.930959i \(0.618973\pi\)
\(44\) −0.479369 −0.0722676
\(45\) 0 0
\(46\) −1.17324 −0.172985
\(47\) −10.3421 −1.50855 −0.754273 0.656561i \(-0.772010\pi\)
−0.754273 + 0.656561i \(0.772010\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 7.01846 0.992561
\(51\) 0 0
\(52\) 0.697719 0.0967563
\(53\) −3.29407 −0.452475 −0.226238 0.974072i \(-0.572643\pi\)
−0.226238 + 0.974072i \(0.572643\pi\)
\(54\) 0 0
\(55\) −1.71920 −0.231817
\(56\) 2.73966 0.366102
\(57\) 0 0
\(58\) 7.95363 1.04436
\(59\) −5.19779 −0.676695 −0.338347 0.941021i \(-0.609868\pi\)
−0.338347 + 0.941021i \(0.609868\pi\)
\(60\) 0 0
\(61\) −4.46437 −0.571605 −0.285802 0.958289i \(-0.592260\pi\)
−0.285802 + 0.958289i \(0.592260\pi\)
\(62\) −5.22027 −0.662974
\(63\) 0 0
\(64\) 7.47828 0.934785
\(65\) 2.50229 0.310371
\(66\) 0 0
\(67\) 10.1874 1.24459 0.622297 0.782781i \(-0.286200\pi\)
0.622297 + 0.782781i \(0.286200\pi\)
\(68\) 0.936724 0.113594
\(69\) 0 0
\(70\) −0.611141 −0.0730453
\(71\) −8.24577 −0.978592 −0.489296 0.872118i \(-0.662746\pi\)
−0.489296 + 0.872118i \(0.662746\pi\)
\(72\) 0 0
\(73\) 8.96444 1.04921 0.524604 0.851346i \(-0.324213\pi\)
0.524604 + 0.851346i \(0.324213\pi\)
\(74\) 5.52541 0.642316
\(75\) 0 0
\(76\) 0.140847 0.0161563
\(77\) −4.09314 −0.466457
\(78\) 0 0
\(79\) −11.1975 −1.25982 −0.629911 0.776667i \(-0.716909\pi\)
−0.629911 + 0.776667i \(0.716909\pi\)
\(80\) −1.77270 −0.198194
\(81\) 0 0
\(82\) 13.4566 1.48603
\(83\) −14.0246 −1.53940 −0.769699 0.638407i \(-0.779594\pi\)
−0.769699 + 0.638407i \(0.779594\pi\)
\(84\) 0 0
\(85\) 3.35945 0.364383
\(86\) 6.96747 0.751322
\(87\) 0 0
\(88\) −11.2138 −1.19540
\(89\) −12.7389 −1.35032 −0.675162 0.737669i \(-0.735926\pi\)
−0.675162 + 0.737669i \(0.735926\pi\)
\(90\) 0 0
\(91\) 5.95755 0.624521
\(92\) 0.0944338 0.00984540
\(93\) 0 0
\(94\) 15.0480 1.55209
\(95\) 0.505131 0.0518254
\(96\) 0 0
\(97\) −8.63018 −0.876262 −0.438131 0.898911i \(-0.644359\pi\)
−0.438131 + 0.898911i \(0.644359\pi\)
\(98\) −1.45503 −0.146980
\(99\) 0 0
\(100\) −0.564914 −0.0564914
\(101\) 13.9999 1.39305 0.696523 0.717535i \(-0.254730\pi\)
0.696523 + 0.717535i \(0.254730\pi\)
\(102\) 0 0
\(103\) 18.1046 1.78390 0.891950 0.452133i \(-0.149337\pi\)
0.891950 + 0.452133i \(0.149337\pi\)
\(104\) 16.3216 1.60047
\(105\) 0 0
\(106\) 4.79297 0.465534
\(107\) 8.11725 0.784725 0.392362 0.919811i \(-0.371658\pi\)
0.392362 + 0.919811i \(0.371658\pi\)
\(108\) 0 0
\(109\) 5.74750 0.550511 0.275256 0.961371i \(-0.411238\pi\)
0.275256 + 0.961371i \(0.411238\pi\)
\(110\) 2.50149 0.238507
\(111\) 0 0
\(112\) −4.22051 −0.398801
\(113\) −14.6228 −1.37559 −0.687797 0.725903i \(-0.741422\pi\)
−0.687797 + 0.725903i \(0.741422\pi\)
\(114\) 0 0
\(115\) 0.338676 0.0315817
\(116\) −0.640186 −0.0594398
\(117\) 0 0
\(118\) 7.56294 0.696225
\(119\) 7.99832 0.733205
\(120\) 0 0
\(121\) 5.75383 0.523075
\(122\) 6.49580 0.588102
\(123\) 0 0
\(124\) 0.420178 0.0377331
\(125\) −4.12609 −0.369049
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −12.2045 −1.07873
\(129\) 0 0
\(130\) −3.64091 −0.319329
\(131\) 8.56457 0.748290 0.374145 0.927370i \(-0.377936\pi\)
0.374145 + 0.927370i \(0.377936\pi\)
\(132\) 0 0
\(133\) 1.20264 0.104282
\(134\) −14.8230 −1.28052
\(135\) 0 0
\(136\) 21.9127 1.87899
\(137\) −11.6339 −0.993952 −0.496976 0.867764i \(-0.665556\pi\)
−0.496976 + 0.867764i \(0.665556\pi\)
\(138\) 0 0
\(139\) −5.36556 −0.455101 −0.227550 0.973766i \(-0.573072\pi\)
−0.227550 + 0.973766i \(0.573072\pi\)
\(140\) 0.0491906 0.00415736
\(141\) 0 0
\(142\) 11.9978 1.00684
\(143\) −24.3851 −2.03919
\(144\) 0 0
\(145\) −2.29595 −0.190668
\(146\) −13.0435 −1.07949
\(147\) 0 0
\(148\) −0.444739 −0.0365573
\(149\) 2.26030 0.185171 0.0925856 0.995705i \(-0.470487\pi\)
0.0925856 + 0.995705i \(0.470487\pi\)
\(150\) 0 0
\(151\) 5.84583 0.475727 0.237863 0.971299i \(-0.423553\pi\)
0.237863 + 0.971299i \(0.423553\pi\)
\(152\) 3.29482 0.267245
\(153\) 0 0
\(154\) 5.95565 0.479920
\(155\) 1.50692 0.121039
\(156\) 0 0
\(157\) −2.77780 −0.221692 −0.110846 0.993838i \(-0.535356\pi\)
−0.110846 + 0.993838i \(0.535356\pi\)
\(158\) 16.2928 1.29618
\(159\) 0 0
\(160\) 0.277913 0.0219709
\(161\) 0.806334 0.0635480
\(162\) 0 0
\(163\) −7.22816 −0.566153 −0.283076 0.959097i \(-0.591355\pi\)
−0.283076 + 0.959097i \(0.591355\pi\)
\(164\) −1.08311 −0.0845770
\(165\) 0 0
\(166\) 20.4062 1.58383
\(167\) −19.3352 −1.49620 −0.748102 0.663584i \(-0.769035\pi\)
−0.748102 + 0.663584i \(0.769035\pi\)
\(168\) 0 0
\(169\) 22.4925 1.73019
\(170\) −4.88810 −0.374900
\(171\) 0 0
\(172\) −0.560810 −0.0427614
\(173\) −10.9047 −0.829067 −0.414533 0.910034i \(-0.636055\pi\)
−0.414533 + 0.910034i \(0.636055\pi\)
\(174\) 0 0
\(175\) −4.82358 −0.364629
\(176\) 17.2752 1.30216
\(177\) 0 0
\(178\) 18.5355 1.38930
\(179\) 24.2428 1.81199 0.905995 0.423289i \(-0.139124\pi\)
0.905995 + 0.423289i \(0.139124\pi\)
\(180\) 0 0
\(181\) −2.20670 −0.164023 −0.0820114 0.996631i \(-0.526134\pi\)
−0.0820114 + 0.996631i \(0.526134\pi\)
\(182\) −8.66843 −0.642546
\(183\) 0 0
\(184\) 2.20908 0.162855
\(185\) −1.59500 −0.117267
\(186\) 0 0
\(187\) −32.7383 −2.39406
\(188\) −1.21121 −0.0883367
\(189\) 0 0
\(190\) −0.734982 −0.0533212
\(191\) 21.7204 1.57164 0.785818 0.618458i \(-0.212242\pi\)
0.785818 + 0.618458i \(0.212242\pi\)
\(192\) 0 0
\(193\) −6.27244 −0.451500 −0.225750 0.974185i \(-0.572483\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(194\) 12.5572 0.901553
\(195\) 0 0
\(196\) 0.117115 0.00836536
\(197\) −20.0593 −1.42917 −0.714584 0.699550i \(-0.753384\pi\)
−0.714584 + 0.699550i \(0.753384\pi\)
\(198\) 0 0
\(199\) −0.345721 −0.0245075 −0.0122538 0.999925i \(-0.503901\pi\)
−0.0122538 + 0.999925i \(0.503901\pi\)
\(200\) −13.2150 −0.934439
\(201\) 0 0
\(202\) −20.3703 −1.43325
\(203\) −5.46630 −0.383659
\(204\) 0 0
\(205\) −3.88446 −0.271303
\(206\) −26.3428 −1.83539
\(207\) 0 0
\(208\) −25.1439 −1.74342
\(209\) −4.92257 −0.340501
\(210\) 0 0
\(211\) −17.4577 −1.20184 −0.600919 0.799310i \(-0.705199\pi\)
−0.600919 + 0.799310i \(0.705199\pi\)
\(212\) −0.385785 −0.0264958
\(213\) 0 0
\(214\) −11.8109 −0.807374
\(215\) −2.01128 −0.137168
\(216\) 0 0
\(217\) 3.58774 0.243551
\(218\) −8.36280 −0.566400
\(219\) 0 0
\(220\) −0.201344 −0.0135746
\(221\) 47.6504 3.20532
\(222\) 0 0
\(223\) −8.39861 −0.562412 −0.281206 0.959647i \(-0.590734\pi\)
−0.281206 + 0.959647i \(0.590734\pi\)
\(224\) 0.661667 0.0442095
\(225\) 0 0
\(226\) 21.2766 1.41530
\(227\) −7.77384 −0.515968 −0.257984 0.966149i \(-0.583058\pi\)
−0.257984 + 0.966149i \(0.583058\pi\)
\(228\) 0 0
\(229\) −25.0564 −1.65577 −0.827885 0.560897i \(-0.810456\pi\)
−0.827885 + 0.560897i \(0.810456\pi\)
\(230\) −0.492783 −0.0324932
\(231\) 0 0
\(232\) −14.9758 −0.983208
\(233\) 30.1760 1.97689 0.988446 0.151571i \(-0.0484332\pi\)
0.988446 + 0.151571i \(0.0484332\pi\)
\(234\) 0 0
\(235\) −4.34387 −0.283363
\(236\) −0.608739 −0.0396256
\(237\) 0 0
\(238\) −11.6378 −0.754367
\(239\) 5.76988 0.373222 0.186611 0.982434i \(-0.440250\pi\)
0.186611 + 0.982434i \(0.440250\pi\)
\(240\) 0 0
\(241\) −11.9312 −0.768559 −0.384279 0.923217i \(-0.625550\pi\)
−0.384279 + 0.923217i \(0.625550\pi\)
\(242\) −8.37199 −0.538172
\(243\) 0 0
\(244\) −0.522845 −0.0334717
\(245\) 0.420019 0.0268340
\(246\) 0 0
\(247\) 7.16478 0.455884
\(248\) 9.82916 0.624152
\(249\) 0 0
\(250\) 6.00359 0.379701
\(251\) −27.8947 −1.76070 −0.880350 0.474325i \(-0.842692\pi\)
−0.880350 + 0.474325i \(0.842692\pi\)
\(252\) 0 0
\(253\) −3.30044 −0.207497
\(254\) 1.45503 0.0912968
\(255\) 0 0
\(256\) 2.80131 0.175082
\(257\) 1.37008 0.0854634 0.0427317 0.999087i \(-0.486394\pi\)
0.0427317 + 0.999087i \(0.486394\pi\)
\(258\) 0 0
\(259\) −3.79745 −0.235962
\(260\) 0.293055 0.0181745
\(261\) 0 0
\(262\) −12.4617 −0.769888
\(263\) −6.11351 −0.376975 −0.188488 0.982076i \(-0.560358\pi\)
−0.188488 + 0.982076i \(0.560358\pi\)
\(264\) 0 0
\(265\) −1.38357 −0.0849921
\(266\) −1.74988 −0.107292
\(267\) 0 0
\(268\) 1.19310 0.0728803
\(269\) 14.3108 0.872547 0.436274 0.899814i \(-0.356298\pi\)
0.436274 + 0.899814i \(0.356298\pi\)
\(270\) 0 0
\(271\) −19.0355 −1.15632 −0.578162 0.815922i \(-0.696230\pi\)
−0.578162 + 0.815922i \(0.696230\pi\)
\(272\) −33.7570 −2.04682
\(273\) 0 0
\(274\) 16.9277 1.02264
\(275\) 19.7436 1.19059
\(276\) 0 0
\(277\) 17.7110 1.06415 0.532076 0.846697i \(-0.321412\pi\)
0.532076 + 0.846697i \(0.321412\pi\)
\(278\) 7.80705 0.468236
\(279\) 0 0
\(280\) 1.15071 0.0687680
\(281\) 27.6078 1.64694 0.823472 0.567357i \(-0.192034\pi\)
0.823472 + 0.567357i \(0.192034\pi\)
\(282\) 0 0
\(283\) 11.8324 0.703360 0.351680 0.936120i \(-0.385610\pi\)
0.351680 + 0.936120i \(0.385610\pi\)
\(284\) −0.965703 −0.0573039
\(285\) 0 0
\(286\) 35.4811 2.09804
\(287\) −9.24830 −0.545910
\(288\) 0 0
\(289\) 46.9732 2.76313
\(290\) 3.34068 0.196171
\(291\) 0 0
\(292\) 1.04987 0.0614390
\(293\) −17.9876 −1.05085 −0.525423 0.850841i \(-0.676093\pi\)
−0.525423 + 0.850841i \(0.676093\pi\)
\(294\) 0 0
\(295\) −2.18317 −0.127109
\(296\) −10.4037 −0.604703
\(297\) 0 0
\(298\) −3.28881 −0.190516
\(299\) 4.80378 0.277810
\(300\) 0 0
\(301\) −4.78854 −0.276007
\(302\) −8.50586 −0.489457
\(303\) 0 0
\(304\) −5.07575 −0.291114
\(305\) −1.87512 −0.107369
\(306\) 0 0
\(307\) 13.1148 0.748500 0.374250 0.927328i \(-0.377900\pi\)
0.374250 + 0.927328i \(0.377900\pi\)
\(308\) −0.479369 −0.0273146
\(309\) 0 0
\(310\) −2.19261 −0.124532
\(311\) 9.74688 0.552695 0.276347 0.961058i \(-0.410876\pi\)
0.276347 + 0.961058i \(0.410876\pi\)
\(312\) 0 0
\(313\) 20.0884 1.13547 0.567733 0.823213i \(-0.307821\pi\)
0.567733 + 0.823213i \(0.307821\pi\)
\(314\) 4.04178 0.228091
\(315\) 0 0
\(316\) −1.31140 −0.0737721
\(317\) 23.1449 1.29995 0.649974 0.759956i \(-0.274780\pi\)
0.649974 + 0.759956i \(0.274780\pi\)
\(318\) 0 0
\(319\) 22.3743 1.25272
\(320\) 3.14102 0.175588
\(321\) 0 0
\(322\) −1.17324 −0.0653821
\(323\) 9.61909 0.535220
\(324\) 0 0
\(325\) −28.7368 −1.59403
\(326\) 10.5172 0.582493
\(327\) 0 0
\(328\) −25.3371 −1.39901
\(329\) −10.3421 −0.570177
\(330\) 0 0
\(331\) −12.8235 −0.704842 −0.352421 0.935841i \(-0.614642\pi\)
−0.352421 + 0.935841i \(0.614642\pi\)
\(332\) −1.64249 −0.0901434
\(333\) 0 0
\(334\) 28.1333 1.53939
\(335\) 4.27892 0.233782
\(336\) 0 0
\(337\) 10.3028 0.561228 0.280614 0.959821i \(-0.409462\pi\)
0.280614 + 0.959821i \(0.409462\pi\)
\(338\) −32.7272 −1.78013
\(339\) 0 0
\(340\) 0.393442 0.0213374
\(341\) −14.6851 −0.795244
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −13.1189 −0.707326
\(345\) 0 0
\(346\) 15.8666 0.852996
\(347\) −19.3807 −1.04041 −0.520206 0.854041i \(-0.674145\pi\)
−0.520206 + 0.854041i \(0.674145\pi\)
\(348\) 0 0
\(349\) 26.2455 1.40489 0.702446 0.711737i \(-0.252091\pi\)
0.702446 + 0.711737i \(0.252091\pi\)
\(350\) 7.01846 0.375153
\(351\) 0 0
\(352\) −2.70830 −0.144353
\(353\) −22.3694 −1.19060 −0.595300 0.803503i \(-0.702967\pi\)
−0.595300 + 0.803503i \(0.702967\pi\)
\(354\) 0 0
\(355\) −3.46338 −0.183817
\(356\) −1.49192 −0.0790716
\(357\) 0 0
\(358\) −35.2740 −1.86429
\(359\) −26.1003 −1.37752 −0.688759 0.724990i \(-0.741844\pi\)
−0.688759 + 0.724990i \(0.741844\pi\)
\(360\) 0 0
\(361\) −17.5537 −0.923877
\(362\) 3.21082 0.168757
\(363\) 0 0
\(364\) 0.697719 0.0365704
\(365\) 3.76524 0.197081
\(366\) 0 0
\(367\) −34.4353 −1.79751 −0.898754 0.438454i \(-0.855526\pi\)
−0.898754 + 0.438454i \(0.855526\pi\)
\(368\) −3.40314 −0.177401
\(369\) 0 0
\(370\) 2.32078 0.120652
\(371\) −3.29407 −0.171019
\(372\) 0 0
\(373\) 1.95485 0.101218 0.0506091 0.998719i \(-0.483884\pi\)
0.0506091 + 0.998719i \(0.483884\pi\)
\(374\) 47.6352 2.46316
\(375\) 0 0
\(376\) −28.3337 −1.46120
\(377\) −32.5658 −1.67722
\(378\) 0 0
\(379\) −29.7272 −1.52698 −0.763492 0.645817i \(-0.776517\pi\)
−0.763492 + 0.645817i \(0.776517\pi\)
\(380\) 0.0591585 0.00303477
\(381\) 0 0
\(382\) −31.6039 −1.61700
\(383\) 35.6298 1.82060 0.910300 0.413949i \(-0.135851\pi\)
0.910300 + 0.413949i \(0.135851\pi\)
\(384\) 0 0
\(385\) −1.71920 −0.0876185
\(386\) 9.12660 0.464532
\(387\) 0 0
\(388\) −1.01072 −0.0513118
\(389\) 28.9904 1.46987 0.734935 0.678138i \(-0.237213\pi\)
0.734935 + 0.678138i \(0.237213\pi\)
\(390\) 0 0
\(391\) 6.44932 0.326156
\(392\) 2.73966 0.138374
\(393\) 0 0
\(394\) 29.1869 1.47042
\(395\) −4.70318 −0.236643
\(396\) 0 0
\(397\) −3.59161 −0.180258 −0.0901289 0.995930i \(-0.528728\pi\)
−0.0901289 + 0.995930i \(0.528728\pi\)
\(398\) 0.503035 0.0252149
\(399\) 0 0
\(400\) 20.3580 1.01790
\(401\) −9.61960 −0.480380 −0.240190 0.970726i \(-0.577210\pi\)
−0.240190 + 0.970726i \(0.577210\pi\)
\(402\) 0 0
\(403\) 21.3741 1.06472
\(404\) 1.63960 0.0815733
\(405\) 0 0
\(406\) 7.95363 0.394732
\(407\) 15.5435 0.770464
\(408\) 0 0
\(409\) 31.7875 1.57179 0.785894 0.618361i \(-0.212203\pi\)
0.785894 + 0.618361i \(0.212203\pi\)
\(410\) 5.65201 0.279133
\(411\) 0 0
\(412\) 2.12032 0.104461
\(413\) −5.19779 −0.255766
\(414\) 0 0
\(415\) −5.89060 −0.289158
\(416\) 3.94192 0.193268
\(417\) 0 0
\(418\) 7.16249 0.350329
\(419\) −21.3043 −1.04078 −0.520392 0.853928i \(-0.674214\pi\)
−0.520392 + 0.853928i \(0.674214\pi\)
\(420\) 0 0
\(421\) −25.4806 −1.24185 −0.620924 0.783871i \(-0.713242\pi\)
−0.620924 + 0.783871i \(0.713242\pi\)
\(422\) 25.4015 1.23653
\(423\) 0 0
\(424\) −9.02461 −0.438274
\(425\) −38.5806 −1.87143
\(426\) 0 0
\(427\) −4.46437 −0.216046
\(428\) 0.950653 0.0459515
\(429\) 0 0
\(430\) 2.92647 0.141127
\(431\) 27.6736 1.33299 0.666495 0.745510i \(-0.267794\pi\)
0.666495 + 0.745510i \(0.267794\pi\)
\(432\) 0 0
\(433\) 28.1288 1.35178 0.675892 0.737000i \(-0.263758\pi\)
0.675892 + 0.737000i \(0.263758\pi\)
\(434\) −5.22027 −0.250581
\(435\) 0 0
\(436\) 0.673119 0.0322366
\(437\) 0.969728 0.0463884
\(438\) 0 0
\(439\) 22.3769 1.06799 0.533995 0.845488i \(-0.320690\pi\)
0.533995 + 0.845488i \(0.320690\pi\)
\(440\) −4.71001 −0.224541
\(441\) 0 0
\(442\) −69.3329 −3.29783
\(443\) −27.7545 −1.31866 −0.659328 0.751856i \(-0.729159\pi\)
−0.659328 + 0.751856i \(0.729159\pi\)
\(444\) 0 0
\(445\) −5.35060 −0.253643
\(446\) 12.2202 0.578645
\(447\) 0 0
\(448\) 7.47828 0.353316
\(449\) −0.741298 −0.0349840 −0.0174920 0.999847i \(-0.505568\pi\)
−0.0174920 + 0.999847i \(0.505568\pi\)
\(450\) 0 0
\(451\) 37.8546 1.78250
\(452\) −1.71255 −0.0805514
\(453\) 0 0
\(454\) 11.3112 0.530860
\(455\) 2.50229 0.117309
\(456\) 0 0
\(457\) 18.5086 0.865798 0.432899 0.901442i \(-0.357491\pi\)
0.432899 + 0.901442i \(0.357491\pi\)
\(458\) 36.4578 1.70356
\(459\) 0 0
\(460\) 0.0396640 0.00184934
\(461\) 40.2184 1.87316 0.936579 0.350456i \(-0.113973\pi\)
0.936579 + 0.350456i \(0.113973\pi\)
\(462\) 0 0
\(463\) −33.6466 −1.56369 −0.781844 0.623474i \(-0.785721\pi\)
−0.781844 + 0.623474i \(0.785721\pi\)
\(464\) 23.0706 1.07103
\(465\) 0 0
\(466\) −43.9070 −2.03395
\(467\) −14.6853 −0.679554 −0.339777 0.940506i \(-0.610352\pi\)
−0.339777 + 0.940506i \(0.610352\pi\)
\(468\) 0 0
\(469\) 10.1874 0.470412
\(470\) 6.32046 0.291541
\(471\) 0 0
\(472\) −14.2402 −0.655456
\(473\) 19.6002 0.901217
\(474\) 0 0
\(475\) −5.80103 −0.266169
\(476\) 0.936724 0.0429347
\(477\) 0 0
\(478\) −8.39535 −0.383994
\(479\) −10.4227 −0.476227 −0.238113 0.971237i \(-0.576529\pi\)
−0.238113 + 0.971237i \(0.576529\pi\)
\(480\) 0 0
\(481\) −22.6235 −1.03154
\(482\) 17.3603 0.790741
\(483\) 0 0
\(484\) 0.673859 0.0306300
\(485\) −3.62484 −0.164596
\(486\) 0 0
\(487\) −33.8424 −1.53355 −0.766773 0.641918i \(-0.778139\pi\)
−0.766773 + 0.641918i \(0.778139\pi\)
\(488\) −12.2308 −0.553665
\(489\) 0 0
\(490\) −0.611141 −0.0276085
\(491\) −23.3096 −1.05195 −0.525975 0.850500i \(-0.676299\pi\)
−0.525975 + 0.850500i \(0.676299\pi\)
\(492\) 0 0
\(493\) −43.7212 −1.96910
\(494\) −10.4250 −0.469042
\(495\) 0 0
\(496\) −15.1421 −0.679900
\(497\) −8.24577 −0.369873
\(498\) 0 0
\(499\) −0.990923 −0.0443598 −0.0221799 0.999754i \(-0.507061\pi\)
−0.0221799 + 0.999754i \(0.507061\pi\)
\(500\) −0.483228 −0.0216106
\(501\) 0 0
\(502\) 40.5877 1.81152
\(503\) −12.6071 −0.562124 −0.281062 0.959690i \(-0.590687\pi\)
−0.281062 + 0.959690i \(0.590687\pi\)
\(504\) 0 0
\(505\) 5.88024 0.261667
\(506\) 4.80224 0.213486
\(507\) 0 0
\(508\) −0.117115 −0.00519614
\(509\) −32.4113 −1.43661 −0.718303 0.695730i \(-0.755081\pi\)
−0.718303 + 0.695730i \(0.755081\pi\)
\(510\) 0 0
\(511\) 8.96444 0.396563
\(512\) 20.3329 0.898597
\(513\) 0 0
\(514\) −1.99351 −0.0879300
\(515\) 7.60429 0.335085
\(516\) 0 0
\(517\) 42.3316 1.86174
\(518\) 5.52541 0.242773
\(519\) 0 0
\(520\) 6.85541 0.300629
\(521\) −7.88673 −0.345524 −0.172762 0.984964i \(-0.555269\pi\)
−0.172762 + 0.984964i \(0.555269\pi\)
\(522\) 0 0
\(523\) −5.81467 −0.254258 −0.127129 0.991886i \(-0.540576\pi\)
−0.127129 + 0.991886i \(0.540576\pi\)
\(524\) 1.00304 0.0438180
\(525\) 0 0
\(526\) 8.89534 0.387855
\(527\) 28.6959 1.25001
\(528\) 0 0
\(529\) −22.3498 −0.971732
\(530\) 2.01314 0.0874452
\(531\) 0 0
\(532\) 0.140847 0.00610649
\(533\) −55.0972 −2.38653
\(534\) 0 0
\(535\) 3.40940 0.147401
\(536\) 27.9101 1.20553
\(537\) 0 0
\(538\) −20.8227 −0.897731
\(539\) −4.09314 −0.176304
\(540\) 0 0
\(541\) 11.4384 0.491777 0.245889 0.969298i \(-0.420920\pi\)
0.245889 + 0.969298i \(0.420920\pi\)
\(542\) 27.6972 1.18970
\(543\) 0 0
\(544\) 5.29223 0.226902
\(545\) 2.41406 0.103407
\(546\) 0 0
\(547\) −11.5776 −0.495021 −0.247510 0.968885i \(-0.579612\pi\)
−0.247510 + 0.968885i \(0.579612\pi\)
\(548\) −1.36251 −0.0582034
\(549\) 0 0
\(550\) −28.7276 −1.22495
\(551\) −6.57398 −0.280061
\(552\) 0 0
\(553\) −11.1975 −0.476168
\(554\) −25.7701 −1.09486
\(555\) 0 0
\(556\) −0.628388 −0.0266496
\(557\) 4.77210 0.202201 0.101100 0.994876i \(-0.467764\pi\)
0.101100 + 0.994876i \(0.467764\pi\)
\(558\) 0 0
\(559\) −28.5280 −1.20660
\(560\) −1.77270 −0.0749101
\(561\) 0 0
\(562\) −40.1702 −1.69448
\(563\) 24.0710 1.01447 0.507236 0.861807i \(-0.330667\pi\)
0.507236 + 0.861807i \(0.330667\pi\)
\(564\) 0 0
\(565\) −6.14184 −0.258389
\(566\) −17.2164 −0.723661
\(567\) 0 0
\(568\) −22.5906 −0.947879
\(569\) 29.5305 1.23798 0.618991 0.785398i \(-0.287542\pi\)
0.618991 + 0.785398i \(0.287542\pi\)
\(570\) 0 0
\(571\) −10.5476 −0.441402 −0.220701 0.975342i \(-0.570834\pi\)
−0.220701 + 0.975342i \(0.570834\pi\)
\(572\) −2.85587 −0.119410
\(573\) 0 0
\(574\) 13.4566 0.561666
\(575\) −3.88942 −0.162200
\(576\) 0 0
\(577\) −23.4100 −0.974573 −0.487286 0.873242i \(-0.662013\pi\)
−0.487286 + 0.873242i \(0.662013\pi\)
\(578\) −68.3474 −2.84288
\(579\) 0 0
\(580\) −0.268890 −0.0111651
\(581\) −14.0246 −0.581838
\(582\) 0 0
\(583\) 13.4831 0.558413
\(584\) 24.5595 1.01628
\(585\) 0 0
\(586\) 26.1725 1.08118
\(587\) 37.0926 1.53098 0.765488 0.643451i \(-0.222498\pi\)
0.765488 + 0.643451i \(0.222498\pi\)
\(588\) 0 0
\(589\) 4.31475 0.177786
\(590\) 3.17658 0.130778
\(591\) 0 0
\(592\) 16.0272 0.658714
\(593\) 13.9145 0.571400 0.285700 0.958319i \(-0.407774\pi\)
0.285700 + 0.958319i \(0.407774\pi\)
\(594\) 0 0
\(595\) 3.35945 0.137724
\(596\) 0.264715 0.0108432
\(597\) 0 0
\(598\) −6.98964 −0.285828
\(599\) −21.8080 −0.891051 −0.445526 0.895269i \(-0.646983\pi\)
−0.445526 + 0.895269i \(0.646983\pi\)
\(600\) 0 0
\(601\) 17.0329 0.694785 0.347393 0.937720i \(-0.387067\pi\)
0.347393 + 0.937720i \(0.387067\pi\)
\(602\) 6.96747 0.283973
\(603\) 0 0
\(604\) 0.684635 0.0278574
\(605\) 2.41672 0.0982535
\(606\) 0 0
\(607\) −38.0454 −1.54422 −0.772108 0.635491i \(-0.780798\pi\)
−0.772108 + 0.635491i \(0.780798\pi\)
\(608\) 0.795746 0.0322718
\(609\) 0 0
\(610\) 2.72836 0.110468
\(611\) −61.6134 −2.49261
\(612\) 0 0
\(613\) 16.0498 0.648245 0.324123 0.946015i \(-0.394931\pi\)
0.324123 + 0.946015i \(0.394931\pi\)
\(614\) −19.0824 −0.770103
\(615\) 0 0
\(616\) −11.2138 −0.451817
\(617\) −28.5918 −1.15106 −0.575532 0.817779i \(-0.695205\pi\)
−0.575532 + 0.817779i \(0.695205\pi\)
\(618\) 0 0
\(619\) −0.179381 −0.00720994 −0.00360497 0.999994i \(-0.501148\pi\)
−0.00360497 + 0.999994i \(0.501148\pi\)
\(620\) 0.176483 0.00708772
\(621\) 0 0
\(622\) −14.1820 −0.568647
\(623\) −12.7389 −0.510375
\(624\) 0 0
\(625\) 22.3849 0.895395
\(626\) −29.2293 −1.16824
\(627\) 0 0
\(628\) −0.325322 −0.0129818
\(629\) −30.3732 −1.21106
\(630\) 0 0
\(631\) −29.5538 −1.17652 −0.588258 0.808673i \(-0.700186\pi\)
−0.588258 + 0.808673i \(0.700186\pi\)
\(632\) −30.6774 −1.22028
\(633\) 0 0
\(634\) −33.6766 −1.33747
\(635\) −0.420019 −0.0166680
\(636\) 0 0
\(637\) 5.95755 0.236047
\(638\) −32.5554 −1.28888
\(639\) 0 0
\(640\) −5.12611 −0.202627
\(641\) 4.17299 0.164823 0.0824116 0.996598i \(-0.473738\pi\)
0.0824116 + 0.996598i \(0.473738\pi\)
\(642\) 0 0
\(643\) −0.715991 −0.0282359 −0.0141180 0.999900i \(-0.504494\pi\)
−0.0141180 + 0.999900i \(0.504494\pi\)
\(644\) 0.0944338 0.00372121
\(645\) 0 0
\(646\) −13.9961 −0.550668
\(647\) −18.4983 −0.727245 −0.363622 0.931546i \(-0.618460\pi\)
−0.363622 + 0.931546i \(0.618460\pi\)
\(648\) 0 0
\(649\) 21.2753 0.835129
\(650\) 41.8129 1.64004
\(651\) 0 0
\(652\) −0.846526 −0.0331525
\(653\) −24.6148 −0.963251 −0.481626 0.876377i \(-0.659954\pi\)
−0.481626 + 0.876377i \(0.659954\pi\)
\(654\) 0 0
\(655\) 3.59728 0.140558
\(656\) 39.0326 1.52397
\(657\) 0 0
\(658\) 15.0480 0.586633
\(659\) 29.6799 1.15616 0.578082 0.815979i \(-0.303801\pi\)
0.578082 + 0.815979i \(0.303801\pi\)
\(660\) 0 0
\(661\) 0.127223 0.00494841 0.00247420 0.999997i \(-0.499212\pi\)
0.00247420 + 0.999997i \(0.499212\pi\)
\(662\) 18.6586 0.725186
\(663\) 0 0
\(664\) −38.4225 −1.49108
\(665\) 0.505131 0.0195881
\(666\) 0 0
\(667\) −4.40766 −0.170665
\(668\) −2.26445 −0.0876140
\(669\) 0 0
\(670\) −6.22596 −0.240530
\(671\) 18.2733 0.705434
\(672\) 0 0
\(673\) 18.7015 0.720891 0.360445 0.932780i \(-0.382625\pi\)
0.360445 + 0.932780i \(0.382625\pi\)
\(674\) −14.9908 −0.577426
\(675\) 0 0
\(676\) 2.63420 0.101316
\(677\) −37.6012 −1.44513 −0.722567 0.691301i \(-0.757038\pi\)
−0.722567 + 0.691301i \(0.757038\pi\)
\(678\) 0 0
\(679\) −8.63018 −0.331196
\(680\) 9.20373 0.352947
\(681\) 0 0
\(682\) 21.3673 0.818196
\(683\) −1.76839 −0.0676657 −0.0338328 0.999428i \(-0.510771\pi\)
−0.0338328 + 0.999428i \(0.510771\pi\)
\(684\) 0 0
\(685\) −4.88647 −0.186702
\(686\) −1.45503 −0.0555533
\(687\) 0 0
\(688\) 20.2101 0.770503
\(689\) −19.6246 −0.747637
\(690\) 0 0
\(691\) −6.84776 −0.260501 −0.130250 0.991481i \(-0.541578\pi\)
−0.130250 + 0.991481i \(0.541578\pi\)
\(692\) −1.27710 −0.0485481
\(693\) 0 0
\(694\) 28.1996 1.07044
\(695\) −2.25364 −0.0854854
\(696\) 0 0
\(697\) −73.9708 −2.80185
\(698\) −38.1881 −1.44544
\(699\) 0 0
\(700\) −0.564914 −0.0213518
\(701\) 27.6613 1.04475 0.522376 0.852715i \(-0.325046\pi\)
0.522376 + 0.852715i \(0.325046\pi\)
\(702\) 0 0
\(703\) −4.56696 −0.172246
\(704\) −30.6097 −1.15365
\(705\) 0 0
\(706\) 32.5481 1.22496
\(707\) 13.9999 0.526522
\(708\) 0 0
\(709\) 45.0037 1.69015 0.845075 0.534648i \(-0.179556\pi\)
0.845075 + 0.534648i \(0.179556\pi\)
\(710\) 5.03932 0.189122
\(711\) 0 0
\(712\) −34.9003 −1.30794
\(713\) 2.89291 0.108340
\(714\) 0 0
\(715\) −10.2422 −0.383037
\(716\) 2.83919 0.106106
\(717\) 0 0
\(718\) 37.9767 1.41728
\(719\) −0.0406017 −0.00151419 −0.000757094 1.00000i \(-0.500241\pi\)
−0.000757094 1.00000i \(0.500241\pi\)
\(720\) 0 0
\(721\) 18.1046 0.674251
\(722\) 25.5411 0.950542
\(723\) 0 0
\(724\) −0.258438 −0.00960477
\(725\) 26.3671 0.979251
\(726\) 0 0
\(727\) −29.7498 −1.10336 −0.551679 0.834056i \(-0.686013\pi\)
−0.551679 + 0.834056i \(0.686013\pi\)
\(728\) 16.3216 0.604921
\(729\) 0 0
\(730\) −5.47853 −0.202770
\(731\) −38.3003 −1.41659
\(732\) 0 0
\(733\) −3.84361 −0.141967 −0.0709835 0.997477i \(-0.522614\pi\)
−0.0709835 + 0.997477i \(0.522614\pi\)
\(734\) 50.1044 1.84939
\(735\) 0 0
\(736\) 0.533524 0.0196660
\(737\) −41.6987 −1.53599
\(738\) 0 0
\(739\) −13.5757 −0.499391 −0.249695 0.968324i \(-0.580331\pi\)
−0.249695 + 0.968324i \(0.580331\pi\)
\(740\) −0.186799 −0.00686686
\(741\) 0 0
\(742\) 4.79297 0.175955
\(743\) −7.62422 −0.279706 −0.139853 0.990172i \(-0.544663\pi\)
−0.139853 + 0.990172i \(0.544663\pi\)
\(744\) 0 0
\(745\) 0.949370 0.0347822
\(746\) −2.84437 −0.104140
\(747\) 0 0
\(748\) −3.83415 −0.140190
\(749\) 8.11725 0.296598
\(750\) 0 0
\(751\) −38.7369 −1.41353 −0.706765 0.707449i \(-0.749846\pi\)
−0.706765 + 0.707449i \(0.749846\pi\)
\(752\) 43.6488 1.59171
\(753\) 0 0
\(754\) 47.3842 1.72563
\(755\) 2.45536 0.0893597
\(756\) 0 0
\(757\) 13.7525 0.499841 0.249921 0.968266i \(-0.419595\pi\)
0.249921 + 0.968266i \(0.419595\pi\)
\(758\) 43.2540 1.57106
\(759\) 0 0
\(760\) 1.38389 0.0501988
\(761\) −29.3366 −1.06345 −0.531725 0.846917i \(-0.678456\pi\)
−0.531725 + 0.846917i \(0.678456\pi\)
\(762\) 0 0
\(763\) 5.74750 0.208074
\(764\) 2.54379 0.0920311
\(765\) 0 0
\(766\) −51.8425 −1.87315
\(767\) −30.9661 −1.11812
\(768\) 0 0
\(769\) −29.4417 −1.06170 −0.530848 0.847467i \(-0.678127\pi\)
−0.530848 + 0.847467i \(0.678127\pi\)
\(770\) 2.50149 0.0901474
\(771\) 0 0
\(772\) −0.734598 −0.0264387
\(773\) 14.9074 0.536180 0.268090 0.963394i \(-0.413608\pi\)
0.268090 + 0.963394i \(0.413608\pi\)
\(774\) 0 0
\(775\) −17.3057 −0.621641
\(776\) −23.6437 −0.848760
\(777\) 0 0
\(778\) −42.1819 −1.51229
\(779\) −11.1224 −0.398500
\(780\) 0 0
\(781\) 33.7511 1.20771
\(782\) −9.38395 −0.335570
\(783\) 0 0
\(784\) −4.22051 −0.150733
\(785\) −1.16673 −0.0416423
\(786\) 0 0
\(787\) −52.7973 −1.88202 −0.941010 0.338379i \(-0.890121\pi\)
−0.941010 + 0.338379i \(0.890121\pi\)
\(788\) −2.34925 −0.0836885
\(789\) 0 0
\(790\) 6.84328 0.243473
\(791\) −14.6228 −0.519926
\(792\) 0 0
\(793\) −26.5968 −0.944478
\(794\) 5.22590 0.185460
\(795\) 0 0
\(796\) −0.0404891 −0.00143510
\(797\) 19.3955 0.687023 0.343511 0.939148i \(-0.388384\pi\)
0.343511 + 0.939148i \(0.388384\pi\)
\(798\) 0 0
\(799\) −82.7192 −2.92639
\(800\) −3.19161 −0.112840
\(801\) 0 0
\(802\) 13.9968 0.494245
\(803\) −36.6927 −1.29486
\(804\) 0 0
\(805\) 0.338676 0.0119367
\(806\) −31.1000 −1.09545
\(807\) 0 0
\(808\) 38.3550 1.34932
\(809\) −16.1411 −0.567490 −0.283745 0.958900i \(-0.591577\pi\)
−0.283745 + 0.958900i \(0.591577\pi\)
\(810\) 0 0
\(811\) −29.7370 −1.04421 −0.522104 0.852882i \(-0.674853\pi\)
−0.522104 + 0.852882i \(0.674853\pi\)
\(812\) −0.640186 −0.0224661
\(813\) 0 0
\(814\) −22.6163 −0.792701
\(815\) −3.03596 −0.106345
\(816\) 0 0
\(817\) −5.75888 −0.201478
\(818\) −46.2517 −1.61715
\(819\) 0 0
\(820\) −0.454929 −0.0158868
\(821\) −13.5406 −0.472570 −0.236285 0.971684i \(-0.575930\pi\)
−0.236285 + 0.971684i \(0.575930\pi\)
\(822\) 0 0
\(823\) −20.0304 −0.698216 −0.349108 0.937083i \(-0.613515\pi\)
−0.349108 + 0.937083i \(0.613515\pi\)
\(824\) 49.6004 1.72791
\(825\) 0 0
\(826\) 7.56294 0.263148
\(827\) 40.3235 1.40219 0.701094 0.713069i \(-0.252696\pi\)
0.701094 + 0.713069i \(0.252696\pi\)
\(828\) 0 0
\(829\) −49.5541 −1.72108 −0.860542 0.509379i \(-0.829875\pi\)
−0.860542 + 0.509379i \(0.829875\pi\)
\(830\) 8.57100 0.297504
\(831\) 0 0
\(832\) 44.5523 1.54457
\(833\) 7.99832 0.277125
\(834\) 0 0
\(835\) −8.12116 −0.281044
\(836\) −0.576507 −0.0199389
\(837\) 0 0
\(838\) 30.9984 1.07082
\(839\) 34.0265 1.17473 0.587363 0.809324i \(-0.300166\pi\)
0.587363 + 0.809324i \(0.300166\pi\)
\(840\) 0 0
\(841\) 0.880417 0.0303592
\(842\) 37.0750 1.27769
\(843\) 0 0
\(844\) −2.04456 −0.0703767
\(845\) 9.44726 0.324996
\(846\) 0 0
\(847\) 5.75383 0.197704
\(848\) 13.9027 0.477419
\(849\) 0 0
\(850\) 56.1359 1.92545
\(851\) −3.06201 −0.104964
\(852\) 0 0
\(853\) 27.8105 0.952213 0.476107 0.879388i \(-0.342048\pi\)
0.476107 + 0.879388i \(0.342048\pi\)
\(854\) 6.49580 0.222282
\(855\) 0 0
\(856\) 22.2385 0.760096
\(857\) 55.1687 1.88453 0.942263 0.334874i \(-0.108694\pi\)
0.942263 + 0.334874i \(0.108694\pi\)
\(858\) 0 0
\(859\) 14.0090 0.477980 0.238990 0.971022i \(-0.423184\pi\)
0.238990 + 0.971022i \(0.423184\pi\)
\(860\) −0.235551 −0.00803222
\(861\) 0 0
\(862\) −40.2659 −1.37146
\(863\) 7.64204 0.260138 0.130069 0.991505i \(-0.458480\pi\)
0.130069 + 0.991505i \(0.458480\pi\)
\(864\) 0 0
\(865\) −4.58017 −0.155731
\(866\) −40.9283 −1.39080
\(867\) 0 0
\(868\) 0.420178 0.0142618
\(869\) 45.8332 1.55478
\(870\) 0 0
\(871\) 60.6922 2.05648
\(872\) 15.7462 0.533233
\(873\) 0 0
\(874\) −1.41098 −0.0477272
\(875\) −4.12609 −0.139487
\(876\) 0 0
\(877\) 0.769283 0.0259768 0.0129884 0.999916i \(-0.495866\pi\)
0.0129884 + 0.999916i \(0.495866\pi\)
\(878\) −32.5590 −1.09881
\(879\) 0 0
\(880\) 7.25590 0.244596
\(881\) 3.94890 0.133042 0.0665209 0.997785i \(-0.478810\pi\)
0.0665209 + 0.997785i \(0.478810\pi\)
\(882\) 0 0
\(883\) 37.5238 1.26278 0.631388 0.775467i \(-0.282486\pi\)
0.631388 + 0.775467i \(0.282486\pi\)
\(884\) 5.58058 0.187695
\(885\) 0 0
\(886\) 40.3836 1.35671
\(887\) −23.7485 −0.797397 −0.398698 0.917082i \(-0.630538\pi\)
−0.398698 + 0.917082i \(0.630538\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 7.78528 0.260963
\(891\) 0 0
\(892\) −0.983604 −0.0329335
\(893\) −12.4378 −0.416214
\(894\) 0 0
\(895\) 10.1824 0.340361
\(896\) −12.2045 −0.407723
\(897\) 0 0
\(898\) 1.07861 0.0359937
\(899\) −19.6116 −0.654085
\(900\) 0 0
\(901\) −26.3470 −0.877746
\(902\) −55.0796 −1.83395
\(903\) 0 0
\(904\) −40.0614 −1.33242
\(905\) −0.926857 −0.0308098
\(906\) 0 0
\(907\) −25.2818 −0.839468 −0.419734 0.907647i \(-0.637877\pi\)
−0.419734 + 0.907647i \(0.637877\pi\)
\(908\) −0.910434 −0.0302138
\(909\) 0 0
\(910\) −3.64091 −0.120695
\(911\) −3.77037 −0.124918 −0.0624589 0.998048i \(-0.519894\pi\)
−0.0624589 + 0.998048i \(0.519894\pi\)
\(912\) 0 0
\(913\) 57.4047 1.89982
\(914\) −26.9306 −0.890787
\(915\) 0 0
\(916\) −2.93448 −0.0969578
\(917\) 8.56457 0.282827
\(918\) 0 0
\(919\) 31.0902 1.02557 0.512785 0.858517i \(-0.328614\pi\)
0.512785 + 0.858517i \(0.328614\pi\)
\(920\) 0.927855 0.0305905
\(921\) 0 0
\(922\) −58.5190 −1.92722
\(923\) −49.1246 −1.61696
\(924\) 0 0
\(925\) 18.3173 0.602270
\(926\) 48.9568 1.60882
\(927\) 0 0
\(928\) −3.61687 −0.118730
\(929\) −29.7655 −0.976574 −0.488287 0.872683i \(-0.662378\pi\)
−0.488287 + 0.872683i \(0.662378\pi\)
\(930\) 0 0
\(931\) 1.20264 0.0394149
\(932\) 3.53406 0.115762
\(933\) 0 0
\(934\) 21.3676 0.699168
\(935\) −13.7507 −0.449696
\(936\) 0 0
\(937\) 31.5815 1.03172 0.515862 0.856672i \(-0.327472\pi\)
0.515862 + 0.856672i \(0.327472\pi\)
\(938\) −14.8230 −0.483989
\(939\) 0 0
\(940\) −0.508732 −0.0165930
\(941\) 7.00125 0.228234 0.114117 0.993467i \(-0.463596\pi\)
0.114117 + 0.993467i \(0.463596\pi\)
\(942\) 0 0
\(943\) −7.45721 −0.242840
\(944\) 21.9373 0.714000
\(945\) 0 0
\(946\) −28.5189 −0.927228
\(947\) −34.3629 −1.11664 −0.558322 0.829624i \(-0.688555\pi\)
−0.558322 + 0.829624i \(0.688555\pi\)
\(948\) 0 0
\(949\) 53.4061 1.73364
\(950\) 8.44067 0.273852
\(951\) 0 0
\(952\) 21.9127 0.710193
\(953\) −1.56016 −0.0505386 −0.0252693 0.999681i \(-0.508044\pi\)
−0.0252693 + 0.999681i \(0.508044\pi\)
\(954\) 0 0
\(955\) 9.12300 0.295213
\(956\) 0.675739 0.0218550
\(957\) 0 0
\(958\) 15.1654 0.489972
\(959\) −11.6339 −0.375679
\(960\) 0 0
\(961\) −18.1282 −0.584779
\(962\) 32.9179 1.06132
\(963\) 0 0
\(964\) −1.39733 −0.0450049
\(965\) −2.63455 −0.0848091
\(966\) 0 0
\(967\) 30.5017 0.980868 0.490434 0.871478i \(-0.336838\pi\)
0.490434 + 0.871478i \(0.336838\pi\)
\(968\) 15.7635 0.506658
\(969\) 0 0
\(970\) 5.27426 0.169346
\(971\) 25.2755 0.811131 0.405565 0.914066i \(-0.367075\pi\)
0.405565 + 0.914066i \(0.367075\pi\)
\(972\) 0 0
\(973\) −5.36556 −0.172012
\(974\) 49.2418 1.57781
\(975\) 0 0
\(976\) 18.8420 0.603116
\(977\) −32.0198 −1.02440 −0.512202 0.858865i \(-0.671170\pi\)
−0.512202 + 0.858865i \(0.671170\pi\)
\(978\) 0 0
\(979\) 52.1423 1.66647
\(980\) 0.0491906 0.00157134
\(981\) 0 0
\(982\) 33.9162 1.08231
\(983\) −44.6458 −1.42398 −0.711989 0.702190i \(-0.752206\pi\)
−0.711989 + 0.702190i \(0.752206\pi\)
\(984\) 0 0
\(985\) −8.42530 −0.268452
\(986\) 63.6157 2.02594
\(987\) 0 0
\(988\) 0.839104 0.0266955
\(989\) −3.86116 −0.122778
\(990\) 0 0
\(991\) 23.0161 0.731129 0.365565 0.930786i \(-0.380876\pi\)
0.365565 + 0.930786i \(0.380876\pi\)
\(992\) 2.37389 0.0753710
\(993\) 0 0
\(994\) 11.9978 0.380548
\(995\) −0.145209 −0.00460345
\(996\) 0 0
\(997\) 31.6803 1.00333 0.501663 0.865063i \(-0.332722\pi\)
0.501663 + 0.865063i \(0.332722\pi\)
\(998\) 1.44182 0.0456401
\(999\) 0 0
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 \(a_p\))