Properties

Label 8001.2.a.o.1.3
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 1.3
Root \(2.28328\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.28328 q^{2}\) \(+3.21337 q^{4}\) \(-2.58645 q^{5}\) \(+1.00000 q^{7}\) \(-2.77047 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.28328 q^{2}\) \(+3.21337 q^{4}\) \(-2.58645 q^{5}\) \(+1.00000 q^{7}\) \(-2.77047 q^{8}\) \(+5.90560 q^{10}\) \(-3.21396 q^{11}\) \(-1.17753 q^{13}\) \(-2.28328 q^{14}\) \(-0.100977 q^{16}\) \(-1.07054 q^{17}\) \(+5.70698 q^{19}\) \(-8.31124 q^{20}\) \(+7.33837 q^{22}\) \(+0.390812 q^{23}\) \(+1.68974 q^{25}\) \(+2.68862 q^{26}\) \(+3.21337 q^{28}\) \(+1.39899 q^{29}\) \(-0.821549 q^{31}\) \(+5.77151 q^{32}\) \(+2.44435 q^{34}\) \(-2.58645 q^{35}\) \(+2.05441 q^{37}\) \(-13.0306 q^{38}\) \(+7.16570 q^{40}\) \(+0.263558 q^{41}\) \(-8.34093 q^{43}\) \(-10.3276 q^{44}\) \(-0.892333 q^{46}\) \(-8.74495 q^{47}\) \(+1.00000 q^{49}\) \(-3.85814 q^{50}\) \(-3.78383 q^{52}\) \(-0.256854 q^{53}\) \(+8.31275 q^{55}\) \(-2.77047 q^{56}\) \(-3.19429 q^{58}\) \(+5.69629 q^{59}\) \(-2.53528 q^{61}\) \(+1.87583 q^{62}\) \(-12.9760 q^{64}\) \(+3.04561 q^{65}\) \(+14.2247 q^{67}\) \(-3.44005 q^{68}\) \(+5.90560 q^{70}\) \(+7.31522 q^{71}\) \(+9.20546 q^{73}\) \(-4.69081 q^{74}\) \(+18.3386 q^{76}\) \(-3.21396 q^{77}\) \(+0.721272 q^{79}\) \(+0.261173 q^{80}\) \(-0.601776 q^{82}\) \(+5.52329 q^{83}\) \(+2.76890 q^{85}\) \(+19.0447 q^{86}\) \(+8.90418 q^{88}\) \(-5.73214 q^{89}\) \(-1.17753 q^{91}\) \(+1.25582 q^{92}\) \(+19.9672 q^{94}\) \(-14.7608 q^{95}\) \(+12.1101 q^{97}\) \(-2.28328 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28328 −1.61452 −0.807262 0.590193i \(-0.799051\pi\)
−0.807262 + 0.590193i \(0.799051\pi\)
\(3\) 0 0
\(4\) 3.21337 1.60669
\(5\) −2.58645 −1.15670 −0.578348 0.815790i \(-0.696303\pi\)
−0.578348 + 0.815790i \(0.696303\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.77047 −0.979510
\(9\) 0 0
\(10\) 5.90560 1.86751
\(11\) −3.21396 −0.969045 −0.484522 0.874779i \(-0.661007\pi\)
−0.484522 + 0.874779i \(0.661007\pi\)
\(12\) 0 0
\(13\) −1.17753 −0.326587 −0.163293 0.986578i \(-0.552212\pi\)
−0.163293 + 0.986578i \(0.552212\pi\)
\(14\) −2.28328 −0.610233
\(15\) 0 0
\(16\) −0.100977 −0.0252444
\(17\) −1.07054 −0.259644 −0.129822 0.991537i \(-0.541441\pi\)
−0.129822 + 0.991537i \(0.541441\pi\)
\(18\) 0 0
\(19\) 5.70698 1.30927 0.654635 0.755945i \(-0.272822\pi\)
0.654635 + 0.755945i \(0.272822\pi\)
\(20\) −8.31124 −1.85845
\(21\) 0 0
\(22\) 7.33837 1.56455
\(23\) 0.390812 0.0814899 0.0407449 0.999170i \(-0.487027\pi\)
0.0407449 + 0.999170i \(0.487027\pi\)
\(24\) 0 0
\(25\) 1.68974 0.337947
\(26\) 2.68862 0.527282
\(27\) 0 0
\(28\) 3.21337 0.607271
\(29\) 1.39899 0.259786 0.129893 0.991528i \(-0.458537\pi\)
0.129893 + 0.991528i \(0.458537\pi\)
\(30\) 0 0
\(31\) −0.821549 −0.147555 −0.0737773 0.997275i \(-0.523505\pi\)
−0.0737773 + 0.997275i \(0.523505\pi\)
\(32\) 5.77151 1.02027
\(33\) 0 0
\(34\) 2.44435 0.419202
\(35\) −2.58645 −0.437190
\(36\) 0 0
\(37\) 2.05441 0.337744 0.168872 0.985638i \(-0.445988\pi\)
0.168872 + 0.985638i \(0.445988\pi\)
\(38\) −13.0306 −2.11385
\(39\) 0 0
\(40\) 7.16570 1.13300
\(41\) 0.263558 0.0411608 0.0205804 0.999788i \(-0.493449\pi\)
0.0205804 + 0.999788i \(0.493449\pi\)
\(42\) 0 0
\(43\) −8.34093 −1.27198 −0.635990 0.771697i \(-0.719408\pi\)
−0.635990 + 0.771697i \(0.719408\pi\)
\(44\) −10.3276 −1.55695
\(45\) 0 0
\(46\) −0.892333 −0.131567
\(47\) −8.74495 −1.27558 −0.637791 0.770209i \(-0.720152\pi\)
−0.637791 + 0.770209i \(0.720152\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −3.85814 −0.545624
\(51\) 0 0
\(52\) −3.78383 −0.524723
\(53\) −0.256854 −0.0352815 −0.0176408 0.999844i \(-0.505616\pi\)
−0.0176408 + 0.999844i \(0.505616\pi\)
\(54\) 0 0
\(55\) 8.31275 1.12089
\(56\) −2.77047 −0.370220
\(57\) 0 0
\(58\) −3.19429 −0.419430
\(59\) 5.69629 0.741593 0.370797 0.928714i \(-0.379085\pi\)
0.370797 + 0.928714i \(0.379085\pi\)
\(60\) 0 0
\(61\) −2.53528 −0.324609 −0.162304 0.986741i \(-0.551893\pi\)
−0.162304 + 0.986741i \(0.551893\pi\)
\(62\) 1.87583 0.238230
\(63\) 0 0
\(64\) −12.9760 −1.62200
\(65\) 3.04561 0.377762
\(66\) 0 0
\(67\) 14.2247 1.73782 0.868912 0.494967i \(-0.164820\pi\)
0.868912 + 0.494967i \(0.164820\pi\)
\(68\) −3.44005 −0.417167
\(69\) 0 0
\(70\) 5.90560 0.705854
\(71\) 7.31522 0.868157 0.434079 0.900875i \(-0.357074\pi\)
0.434079 + 0.900875i \(0.357074\pi\)
\(72\) 0 0
\(73\) 9.20546 1.07742 0.538709 0.842492i \(-0.318912\pi\)
0.538709 + 0.842492i \(0.318912\pi\)
\(74\) −4.69081 −0.545295
\(75\) 0 0
\(76\) 18.3386 2.10359
\(77\) −3.21396 −0.366265
\(78\) 0 0
\(79\) 0.721272 0.0811495 0.0405747 0.999177i \(-0.487081\pi\)
0.0405747 + 0.999177i \(0.487081\pi\)
\(80\) 0.261173 0.0292001
\(81\) 0 0
\(82\) −0.601776 −0.0664551
\(83\) 5.52329 0.606260 0.303130 0.952949i \(-0.401968\pi\)
0.303130 + 0.952949i \(0.401968\pi\)
\(84\) 0 0
\(85\) 2.76890 0.300330
\(86\) 19.0447 2.05364
\(87\) 0 0
\(88\) 8.90418 0.949189
\(89\) −5.73214 −0.607606 −0.303803 0.952735i \(-0.598256\pi\)
−0.303803 + 0.952735i \(0.598256\pi\)
\(90\) 0 0
\(91\) −1.17753 −0.123438
\(92\) 1.25582 0.130929
\(93\) 0 0
\(94\) 19.9672 2.05946
\(95\) −14.7608 −1.51443
\(96\) 0 0
\(97\) 12.1101 1.22959 0.614797 0.788686i \(-0.289238\pi\)
0.614797 + 0.788686i \(0.289238\pi\)
\(98\) −2.28328 −0.230646
\(99\) 0 0
\(100\) 5.42975 0.542975
\(101\) −15.0055 −1.49311 −0.746553 0.665326i \(-0.768293\pi\)
−0.746553 + 0.665326i \(0.768293\pi\)
\(102\) 0 0
\(103\) −15.8235 −1.55913 −0.779566 0.626320i \(-0.784560\pi\)
−0.779566 + 0.626320i \(0.784560\pi\)
\(104\) 3.26230 0.319895
\(105\) 0 0
\(106\) 0.586469 0.0569629
\(107\) 3.24337 0.313549 0.156774 0.987634i \(-0.449890\pi\)
0.156774 + 0.987634i \(0.449890\pi\)
\(108\) 0 0
\(109\) −12.2937 −1.17752 −0.588760 0.808308i \(-0.700384\pi\)
−0.588760 + 0.808308i \(0.700384\pi\)
\(110\) −18.9803 −1.80971
\(111\) 0 0
\(112\) −0.100977 −0.00954147
\(113\) 18.7120 1.76028 0.880138 0.474717i \(-0.157450\pi\)
0.880138 + 0.474717i \(0.157450\pi\)
\(114\) 0 0
\(115\) −1.01082 −0.0942591
\(116\) 4.49547 0.417394
\(117\) 0 0
\(118\) −13.0062 −1.19732
\(119\) −1.07054 −0.0981364
\(120\) 0 0
\(121\) −0.670473 −0.0609521
\(122\) 5.78875 0.524089
\(123\) 0 0
\(124\) −2.63994 −0.237074
\(125\) 8.56184 0.765794
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 18.0849 1.59849
\(129\) 0 0
\(130\) −6.95400 −0.609906
\(131\) 5.84698 0.510853 0.255426 0.966829i \(-0.417784\pi\)
0.255426 + 0.966829i \(0.417784\pi\)
\(132\) 0 0
\(133\) 5.70698 0.494858
\(134\) −32.4790 −2.80576
\(135\) 0 0
\(136\) 2.96591 0.254324
\(137\) −1.43625 −0.122707 −0.0613537 0.998116i \(-0.519542\pi\)
−0.0613537 + 0.998116i \(0.519542\pi\)
\(138\) 0 0
\(139\) 9.24219 0.783912 0.391956 0.919984i \(-0.371799\pi\)
0.391956 + 0.919984i \(0.371799\pi\)
\(140\) −8.31124 −0.702428
\(141\) 0 0
\(142\) −16.7027 −1.40166
\(143\) 3.78452 0.316477
\(144\) 0 0
\(145\) −3.61842 −0.300493
\(146\) −21.0187 −1.73952
\(147\) 0 0
\(148\) 6.60160 0.542648
\(149\) 4.33821 0.355400 0.177700 0.984085i \(-0.443134\pi\)
0.177700 + 0.984085i \(0.443134\pi\)
\(150\) 0 0
\(151\) −1.12546 −0.0915883 −0.0457942 0.998951i \(-0.514582\pi\)
−0.0457942 + 0.998951i \(0.514582\pi\)
\(152\) −15.8110 −1.28244
\(153\) 0 0
\(154\) 7.33837 0.591343
\(155\) 2.12490 0.170676
\(156\) 0 0
\(157\) 4.14724 0.330985 0.165493 0.986211i \(-0.447079\pi\)
0.165493 + 0.986211i \(0.447079\pi\)
\(158\) −1.64687 −0.131018
\(159\) 0 0
\(160\) −14.9277 −1.18014
\(161\) 0.390812 0.0308003
\(162\) 0 0
\(163\) −9.28635 −0.727363 −0.363682 0.931523i \(-0.618480\pi\)
−0.363682 + 0.931523i \(0.618480\pi\)
\(164\) 0.846909 0.0661325
\(165\) 0 0
\(166\) −12.6112 −0.978821
\(167\) −7.82020 −0.605145 −0.302573 0.953126i \(-0.597845\pi\)
−0.302573 + 0.953126i \(0.597845\pi\)
\(168\) 0 0
\(169\) −11.6134 −0.893341
\(170\) −6.32219 −0.484890
\(171\) 0 0
\(172\) −26.8025 −2.04367
\(173\) 1.32777 0.100948 0.0504741 0.998725i \(-0.483927\pi\)
0.0504741 + 0.998725i \(0.483927\pi\)
\(174\) 0 0
\(175\) 1.68974 0.127732
\(176\) 0.324537 0.0244629
\(177\) 0 0
\(178\) 13.0881 0.980994
\(179\) −12.6185 −0.943148 −0.471574 0.881826i \(-0.656314\pi\)
−0.471574 + 0.881826i \(0.656314\pi\)
\(180\) 0 0
\(181\) 16.1667 1.20166 0.600832 0.799375i \(-0.294836\pi\)
0.600832 + 0.799375i \(0.294836\pi\)
\(182\) 2.68862 0.199294
\(183\) 0 0
\(184\) −1.08273 −0.0798202
\(185\) −5.31365 −0.390667
\(186\) 0 0
\(187\) 3.44068 0.251607
\(188\) −28.1008 −2.04946
\(189\) 0 0
\(190\) 33.7031 2.44508
\(191\) 3.33542 0.241343 0.120671 0.992693i \(-0.461495\pi\)
0.120671 + 0.992693i \(0.461495\pi\)
\(192\) 0 0
\(193\) 3.32925 0.239645 0.119822 0.992795i \(-0.461767\pi\)
0.119822 + 0.992795i \(0.461767\pi\)
\(194\) −27.6507 −1.98521
\(195\) 0 0
\(196\) 3.21337 0.229527
\(197\) −15.9172 −1.13405 −0.567026 0.823700i \(-0.691906\pi\)
−0.567026 + 0.823700i \(0.691906\pi\)
\(198\) 0 0
\(199\) −20.6832 −1.46620 −0.733098 0.680123i \(-0.761926\pi\)
−0.733098 + 0.680123i \(0.761926\pi\)
\(200\) −4.68137 −0.331023
\(201\) 0 0
\(202\) 34.2619 2.41066
\(203\) 1.39899 0.0981898
\(204\) 0 0
\(205\) −0.681679 −0.0476106
\(206\) 36.1294 2.51726
\(207\) 0 0
\(208\) 0.118904 0.00824448
\(209\) −18.3420 −1.26874
\(210\) 0 0
\(211\) 2.72646 0.187697 0.0938487 0.995586i \(-0.470083\pi\)
0.0938487 + 0.995586i \(0.470083\pi\)
\(212\) −0.825366 −0.0566864
\(213\) 0 0
\(214\) −7.40554 −0.506232
\(215\) 21.5734 1.47130
\(216\) 0 0
\(217\) −0.821549 −0.0557704
\(218\) 28.0699 1.90113
\(219\) 0 0
\(220\) 26.7120 1.80092
\(221\) 1.26059 0.0847965
\(222\) 0 0
\(223\) 10.6503 0.713197 0.356598 0.934258i \(-0.383936\pi\)
0.356598 + 0.934258i \(0.383936\pi\)
\(224\) 5.77151 0.385625
\(225\) 0 0
\(226\) −42.7248 −2.84201
\(227\) 3.10452 0.206054 0.103027 0.994679i \(-0.467147\pi\)
0.103027 + 0.994679i \(0.467147\pi\)
\(228\) 0 0
\(229\) −0.123627 −0.00816948 −0.00408474 0.999992i \(-0.501300\pi\)
−0.00408474 + 0.999992i \(0.501300\pi\)
\(230\) 2.30798 0.152184
\(231\) 0 0
\(232\) −3.87586 −0.254463
\(233\) 7.62240 0.499360 0.249680 0.968328i \(-0.419675\pi\)
0.249680 + 0.968328i \(0.419675\pi\)
\(234\) 0 0
\(235\) 22.6184 1.47546
\(236\) 18.3043 1.19151
\(237\) 0 0
\(238\) 2.44435 0.158443
\(239\) 22.7517 1.47168 0.735841 0.677154i \(-0.236787\pi\)
0.735841 + 0.677154i \(0.236787\pi\)
\(240\) 0 0
\(241\) 12.7612 0.822020 0.411010 0.911631i \(-0.365176\pi\)
0.411010 + 0.911631i \(0.365176\pi\)
\(242\) 1.53088 0.0984086
\(243\) 0 0
\(244\) −8.14679 −0.521545
\(245\) −2.58645 −0.165242
\(246\) 0 0
\(247\) −6.72011 −0.427590
\(248\) 2.27608 0.144531
\(249\) 0 0
\(250\) −19.5491 −1.23639
\(251\) 21.1413 1.33443 0.667213 0.744867i \(-0.267487\pi\)
0.667213 + 0.744867i \(0.267487\pi\)
\(252\) 0 0
\(253\) −1.25605 −0.0789674
\(254\) 2.28328 0.143266
\(255\) 0 0
\(256\) −15.3408 −0.958803
\(257\) −2.75313 −0.171736 −0.0858678 0.996307i \(-0.527366\pi\)
−0.0858678 + 0.996307i \(0.527366\pi\)
\(258\) 0 0
\(259\) 2.05441 0.127655
\(260\) 9.78670 0.606945
\(261\) 0 0
\(262\) −13.3503 −0.824784
\(263\) 10.0766 0.621352 0.310676 0.950516i \(-0.399445\pi\)
0.310676 + 0.950516i \(0.399445\pi\)
\(264\) 0 0
\(265\) 0.664340 0.0408101
\(266\) −13.0306 −0.798959
\(267\) 0 0
\(268\) 45.7093 2.79214
\(269\) 14.2329 0.867798 0.433899 0.900962i \(-0.357137\pi\)
0.433899 + 0.900962i \(0.357137\pi\)
\(270\) 0 0
\(271\) 0.448422 0.0272397 0.0136199 0.999907i \(-0.495665\pi\)
0.0136199 + 0.999907i \(0.495665\pi\)
\(272\) 0.108101 0.00655456
\(273\) 0 0
\(274\) 3.27937 0.198114
\(275\) −5.43074 −0.327486
\(276\) 0 0
\(277\) −0.932903 −0.0560527 −0.0280264 0.999607i \(-0.508922\pi\)
−0.0280264 + 0.999607i \(0.508922\pi\)
\(278\) −21.1025 −1.26564
\(279\) 0 0
\(280\) 7.16570 0.428232
\(281\) −3.75909 −0.224249 −0.112124 0.993694i \(-0.535766\pi\)
−0.112124 + 0.993694i \(0.535766\pi\)
\(282\) 0 0
\(283\) −14.5739 −0.866330 −0.433165 0.901315i \(-0.642603\pi\)
−0.433165 + 0.901315i \(0.642603\pi\)
\(284\) 23.5065 1.39486
\(285\) 0 0
\(286\) −8.64112 −0.510960
\(287\) 0.263558 0.0155573
\(288\) 0 0
\(289\) −15.8539 −0.932585
\(290\) 8.26187 0.485154
\(291\) 0 0
\(292\) 29.5806 1.73107
\(293\) 0.169691 0.00991343 0.00495672 0.999988i \(-0.498422\pi\)
0.00495672 + 0.999988i \(0.498422\pi\)
\(294\) 0 0
\(295\) −14.7332 −0.857799
\(296\) −5.69170 −0.330823
\(297\) 0 0
\(298\) −9.90536 −0.573802
\(299\) −0.460191 −0.0266135
\(300\) 0 0
\(301\) −8.34093 −0.480763
\(302\) 2.56973 0.147871
\(303\) 0 0
\(304\) −0.576276 −0.0330517
\(305\) 6.55737 0.375474
\(306\) 0 0
\(307\) −18.2671 −1.04256 −0.521279 0.853386i \(-0.674545\pi\)
−0.521279 + 0.853386i \(0.674545\pi\)
\(308\) −10.3276 −0.588472
\(309\) 0 0
\(310\) −4.85174 −0.275560
\(311\) 14.0534 0.796894 0.398447 0.917191i \(-0.369549\pi\)
0.398447 + 0.917191i \(0.369549\pi\)
\(312\) 0 0
\(313\) 2.27563 0.128626 0.0643130 0.997930i \(-0.479514\pi\)
0.0643130 + 0.997930i \(0.479514\pi\)
\(314\) −9.46931 −0.534384
\(315\) 0 0
\(316\) 2.31772 0.130382
\(317\) −33.0480 −1.85616 −0.928080 0.372382i \(-0.878541\pi\)
−0.928080 + 0.372382i \(0.878541\pi\)
\(318\) 0 0
\(319\) −4.49629 −0.251744
\(320\) 33.5619 1.87616
\(321\) 0 0
\(322\) −0.892333 −0.0497278
\(323\) −6.10955 −0.339945
\(324\) 0 0
\(325\) −1.98971 −0.110369
\(326\) 21.2034 1.17435
\(327\) 0 0
\(328\) −0.730179 −0.0403174
\(329\) −8.74495 −0.482125
\(330\) 0 0
\(331\) −24.6358 −1.35411 −0.677054 0.735933i \(-0.736744\pi\)
−0.677054 + 0.735933i \(0.736744\pi\)
\(332\) 17.7484 0.974070
\(333\) 0 0
\(334\) 17.8557 0.977021
\(335\) −36.7915 −2.01013
\(336\) 0 0
\(337\) −7.74642 −0.421974 −0.210987 0.977489i \(-0.567668\pi\)
−0.210987 + 0.977489i \(0.567668\pi\)
\(338\) 26.5167 1.44232
\(339\) 0 0
\(340\) 8.89752 0.482536
\(341\) 2.64043 0.142987
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 23.1083 1.24592
\(345\) 0 0
\(346\) −3.03166 −0.162983
\(347\) 33.8629 1.81786 0.908928 0.416953i \(-0.136902\pi\)
0.908928 + 0.416953i \(0.136902\pi\)
\(348\) 0 0
\(349\) −20.8238 −1.11467 −0.557337 0.830286i \(-0.688177\pi\)
−0.557337 + 0.830286i \(0.688177\pi\)
\(350\) −3.85814 −0.206226
\(351\) 0 0
\(352\) −18.5494 −0.988685
\(353\) 8.51240 0.453069 0.226535 0.974003i \(-0.427260\pi\)
0.226535 + 0.974003i \(0.427260\pi\)
\(354\) 0 0
\(355\) −18.9205 −1.00419
\(356\) −18.4195 −0.976232
\(357\) 0 0
\(358\) 28.8115 1.52274
\(359\) −3.33523 −0.176027 −0.0880135 0.996119i \(-0.528052\pi\)
−0.0880135 + 0.996119i \(0.528052\pi\)
\(360\) 0 0
\(361\) 13.5696 0.714188
\(362\) −36.9132 −1.94012
\(363\) 0 0
\(364\) −3.78383 −0.198327
\(365\) −23.8095 −1.24625
\(366\) 0 0
\(367\) 24.0171 1.25368 0.626842 0.779147i \(-0.284347\pi\)
0.626842 + 0.779147i \(0.284347\pi\)
\(368\) −0.0394632 −0.00205716
\(369\) 0 0
\(370\) 12.1326 0.630741
\(371\) −0.256854 −0.0133352
\(372\) 0 0
\(373\) −3.43047 −0.177623 −0.0888115 0.996048i \(-0.528307\pi\)
−0.0888115 + 0.996048i \(0.528307\pi\)
\(374\) −7.85603 −0.406226
\(375\) 0 0
\(376\) 24.2277 1.24945
\(377\) −1.64735 −0.0848426
\(378\) 0 0
\(379\) −7.05174 −0.362223 −0.181112 0.983463i \(-0.557970\pi\)
−0.181112 + 0.983463i \(0.557970\pi\)
\(380\) −47.4320 −2.43321
\(381\) 0 0
\(382\) −7.61571 −0.389654
\(383\) −37.6211 −1.92235 −0.961174 0.275943i \(-0.911010\pi\)
−0.961174 + 0.275943i \(0.911010\pi\)
\(384\) 0 0
\(385\) 8.31275 0.423657
\(386\) −7.60162 −0.386912
\(387\) 0 0
\(388\) 38.9142 1.97557
\(389\) 14.5892 0.739704 0.369852 0.929091i \(-0.379408\pi\)
0.369852 + 0.929091i \(0.379408\pi\)
\(390\) 0 0
\(391\) −0.418380 −0.0211584
\(392\) −2.77047 −0.139930
\(393\) 0 0
\(394\) 36.3434 1.83095
\(395\) −1.86554 −0.0938653
\(396\) 0 0
\(397\) −1.75296 −0.0879787 −0.0439894 0.999032i \(-0.514007\pi\)
−0.0439894 + 0.999032i \(0.514007\pi\)
\(398\) 47.2257 2.36721
\(399\) 0 0
\(400\) −0.170625 −0.00853126
\(401\) 7.49775 0.374420 0.187210 0.982320i \(-0.440056\pi\)
0.187210 + 0.982320i \(0.440056\pi\)
\(402\) 0 0
\(403\) 0.967396 0.0481894
\(404\) −48.2184 −2.39895
\(405\) 0 0
\(406\) −3.19429 −0.158530
\(407\) −6.60280 −0.327289
\(408\) 0 0
\(409\) −17.8323 −0.881750 −0.440875 0.897568i \(-0.645332\pi\)
−0.440875 + 0.897568i \(0.645332\pi\)
\(410\) 1.55647 0.0768684
\(411\) 0 0
\(412\) −50.8467 −2.50504
\(413\) 5.69629 0.280296
\(414\) 0 0
\(415\) −14.2857 −0.701259
\(416\) −6.79610 −0.333206
\(417\) 0 0
\(418\) 41.8799 2.04841
\(419\) 7.83938 0.382979 0.191490 0.981495i \(-0.438668\pi\)
0.191490 + 0.981495i \(0.438668\pi\)
\(420\) 0 0
\(421\) −14.0995 −0.687167 −0.343584 0.939122i \(-0.611641\pi\)
−0.343584 + 0.939122i \(0.611641\pi\)
\(422\) −6.22528 −0.303042
\(423\) 0 0
\(424\) 0.711606 0.0345586
\(425\) −1.80893 −0.0877461
\(426\) 0 0
\(427\) −2.53528 −0.122691
\(428\) 10.4222 0.503775
\(429\) 0 0
\(430\) −49.2582 −2.37544
\(431\) 14.5822 0.702400 0.351200 0.936301i \(-0.385774\pi\)
0.351200 + 0.936301i \(0.385774\pi\)
\(432\) 0 0
\(433\) −4.78704 −0.230051 −0.115025 0.993363i \(-0.536695\pi\)
−0.115025 + 0.993363i \(0.536695\pi\)
\(434\) 1.87583 0.0900426
\(435\) 0 0
\(436\) −39.5041 −1.89190
\(437\) 2.23035 0.106692
\(438\) 0 0
\(439\) −5.34817 −0.255254 −0.127627 0.991822i \(-0.540736\pi\)
−0.127627 + 0.991822i \(0.540736\pi\)
\(440\) −23.0303 −1.09792
\(441\) 0 0
\(442\) −2.87828 −0.136906
\(443\) 26.3283 1.25089 0.625447 0.780267i \(-0.284917\pi\)
0.625447 + 0.780267i \(0.284917\pi\)
\(444\) 0 0
\(445\) 14.8259 0.702816
\(446\) −24.3176 −1.15147
\(447\) 0 0
\(448\) −12.9760 −0.613059
\(449\) −20.1615 −0.951482 −0.475741 0.879585i \(-0.657820\pi\)
−0.475741 + 0.879585i \(0.657820\pi\)
\(450\) 0 0
\(451\) −0.847063 −0.0398867
\(452\) 60.1286 2.82821
\(453\) 0 0
\(454\) −7.08850 −0.332680
\(455\) 3.04561 0.142781
\(456\) 0 0
\(457\) 20.4546 0.956826 0.478413 0.878135i \(-0.341212\pi\)
0.478413 + 0.878135i \(0.341212\pi\)
\(458\) 0.282275 0.0131898
\(459\) 0 0
\(460\) −3.24813 −0.151445
\(461\) −2.10294 −0.0979436 −0.0489718 0.998800i \(-0.515594\pi\)
−0.0489718 + 0.998800i \(0.515594\pi\)
\(462\) 0 0
\(463\) 7.38019 0.342986 0.171493 0.985185i \(-0.445141\pi\)
0.171493 + 0.985185i \(0.445141\pi\)
\(464\) −0.141266 −0.00655813
\(465\) 0 0
\(466\) −17.4041 −0.806229
\(467\) 5.28658 0.244634 0.122317 0.992491i \(-0.460968\pi\)
0.122317 + 0.992491i \(0.460968\pi\)
\(468\) 0 0
\(469\) 14.2247 0.656835
\(470\) −51.6442 −2.38217
\(471\) 0 0
\(472\) −15.7814 −0.726398
\(473\) 26.8074 1.23261
\(474\) 0 0
\(475\) 9.64328 0.442464
\(476\) −3.44005 −0.157674
\(477\) 0 0
\(478\) −51.9484 −2.37607
\(479\) 9.01045 0.411698 0.205849 0.978584i \(-0.434004\pi\)
0.205849 + 0.978584i \(0.434004\pi\)
\(480\) 0 0
\(481\) −2.41913 −0.110303
\(482\) −29.1374 −1.32717
\(483\) 0 0
\(484\) −2.15448 −0.0979309
\(485\) −31.3222 −1.42227
\(486\) 0 0
\(487\) −2.84576 −0.128954 −0.0644768 0.997919i \(-0.520538\pi\)
−0.0644768 + 0.997919i \(0.520538\pi\)
\(488\) 7.02391 0.317958
\(489\) 0 0
\(490\) 5.90560 0.266788
\(491\) 13.1851 0.595034 0.297517 0.954716i \(-0.403841\pi\)
0.297517 + 0.954716i \(0.403841\pi\)
\(492\) 0 0
\(493\) −1.49768 −0.0674519
\(494\) 15.3439 0.690355
\(495\) 0 0
\(496\) 0.0829580 0.00372492
\(497\) 7.31522 0.328133
\(498\) 0 0
\(499\) 2.96311 0.132647 0.0663234 0.997798i \(-0.478873\pi\)
0.0663234 + 0.997798i \(0.478873\pi\)
\(500\) 27.5124 1.23039
\(501\) 0 0
\(502\) −48.2715 −2.15446
\(503\) −38.2091 −1.70366 −0.851830 0.523819i \(-0.824507\pi\)
−0.851830 + 0.523819i \(0.824507\pi\)
\(504\) 0 0
\(505\) 38.8111 1.72707
\(506\) 2.86792 0.127495
\(507\) 0 0
\(508\) −3.21337 −0.142570
\(509\) −23.2050 −1.02854 −0.514272 0.857627i \(-0.671938\pi\)
−0.514272 + 0.857627i \(0.671938\pi\)
\(510\) 0 0
\(511\) 9.20546 0.407226
\(512\) −1.14230 −0.0504831
\(513\) 0 0
\(514\) 6.28617 0.277271
\(515\) 40.9266 1.80344
\(516\) 0 0
\(517\) 28.1059 1.23610
\(518\) −4.69081 −0.206102
\(519\) 0 0
\(520\) −8.43779 −0.370022
\(521\) 17.4609 0.764977 0.382488 0.923960i \(-0.375067\pi\)
0.382488 + 0.923960i \(0.375067\pi\)
\(522\) 0 0
\(523\) −22.5165 −0.984576 −0.492288 0.870432i \(-0.663839\pi\)
−0.492288 + 0.870432i \(0.663839\pi\)
\(524\) 18.7885 0.820780
\(525\) 0 0
\(526\) −23.0078 −1.00319
\(527\) 0.879503 0.0383117
\(528\) 0 0
\(529\) −22.8473 −0.993359
\(530\) −1.51687 −0.0658888
\(531\) 0 0
\(532\) 18.3386 0.795081
\(533\) −0.310346 −0.0134426
\(534\) 0 0
\(535\) −8.38883 −0.362681
\(536\) −39.4091 −1.70222
\(537\) 0 0
\(538\) −32.4978 −1.40108
\(539\) −3.21396 −0.138435
\(540\) 0 0
\(541\) 5.43712 0.233760 0.116880 0.993146i \(-0.462711\pi\)
0.116880 + 0.993146i \(0.462711\pi\)
\(542\) −1.02387 −0.0439791
\(543\) 0 0
\(544\) −6.17864 −0.264907
\(545\) 31.7970 1.36203
\(546\) 0 0
\(547\) 14.1214 0.603788 0.301894 0.953342i \(-0.402381\pi\)
0.301894 + 0.953342i \(0.402381\pi\)
\(548\) −4.61521 −0.197152
\(549\) 0 0
\(550\) 12.3999 0.528734
\(551\) 7.98400 0.340130
\(552\) 0 0
\(553\) 0.721272 0.0306716
\(554\) 2.13008 0.0904984
\(555\) 0 0
\(556\) 29.6986 1.25950
\(557\) 33.5497 1.42155 0.710773 0.703421i \(-0.248345\pi\)
0.710773 + 0.703421i \(0.248345\pi\)
\(558\) 0 0
\(559\) 9.82166 0.415412
\(560\) 0.261173 0.0110366
\(561\) 0 0
\(562\) 8.58307 0.362055
\(563\) −11.7812 −0.496518 −0.248259 0.968694i \(-0.579858\pi\)
−0.248259 + 0.968694i \(0.579858\pi\)
\(564\) 0 0
\(565\) −48.3977 −2.03611
\(566\) 33.2764 1.39871
\(567\) 0 0
\(568\) −20.2666 −0.850369
\(569\) −35.0339 −1.46870 −0.734349 0.678772i \(-0.762513\pi\)
−0.734349 + 0.678772i \(0.762513\pi\)
\(570\) 0 0
\(571\) 2.79170 0.116829 0.0584145 0.998292i \(-0.481395\pi\)
0.0584145 + 0.998292i \(0.481395\pi\)
\(572\) 12.1611 0.508480
\(573\) 0 0
\(574\) −0.601776 −0.0251177
\(575\) 0.660369 0.0275393
\(576\) 0 0
\(577\) 25.1595 1.04741 0.523703 0.851901i \(-0.324550\pi\)
0.523703 + 0.851901i \(0.324550\pi\)
\(578\) 36.1990 1.50568
\(579\) 0 0
\(580\) −11.6273 −0.482799
\(581\) 5.52329 0.229145
\(582\) 0 0
\(583\) 0.825517 0.0341894
\(584\) −25.5035 −1.05534
\(585\) 0 0
\(586\) −0.387451 −0.0160055
\(587\) 13.4468 0.555010 0.277505 0.960724i \(-0.410493\pi\)
0.277505 + 0.960724i \(0.410493\pi\)
\(588\) 0 0
\(589\) −4.68856 −0.193189
\(590\) 33.6400 1.38494
\(591\) 0 0
\(592\) −0.207450 −0.00852613
\(593\) −20.6997 −0.850034 −0.425017 0.905185i \(-0.639732\pi\)
−0.425017 + 0.905185i \(0.639732\pi\)
\(594\) 0 0
\(595\) 2.76890 0.113514
\(596\) 13.9403 0.571017
\(597\) 0 0
\(598\) 1.05075 0.0429682
\(599\) −25.5749 −1.04496 −0.522481 0.852651i \(-0.674993\pi\)
−0.522481 + 0.852651i \(0.674993\pi\)
\(600\) 0 0
\(601\) 48.4029 1.97440 0.987198 0.159497i \(-0.0509873\pi\)
0.987198 + 0.159497i \(0.0509873\pi\)
\(602\) 19.0447 0.776204
\(603\) 0 0
\(604\) −3.61651 −0.147154
\(605\) 1.73415 0.0705031
\(606\) 0 0
\(607\) −40.8197 −1.65682 −0.828410 0.560122i \(-0.810754\pi\)
−0.828410 + 0.560122i \(0.810754\pi\)
\(608\) 32.9378 1.33581
\(609\) 0 0
\(610\) −14.9723 −0.606211
\(611\) 10.2974 0.416589
\(612\) 0 0
\(613\) 24.4892 0.989110 0.494555 0.869146i \(-0.335331\pi\)
0.494555 + 0.869146i \(0.335331\pi\)
\(614\) 41.7089 1.68324
\(615\) 0 0
\(616\) 8.90418 0.358760
\(617\) −42.3749 −1.70595 −0.852974 0.521953i \(-0.825204\pi\)
−0.852974 + 0.521953i \(0.825204\pi\)
\(618\) 0 0
\(619\) −33.9298 −1.36375 −0.681877 0.731467i \(-0.738836\pi\)
−0.681877 + 0.731467i \(0.738836\pi\)
\(620\) 6.82809 0.274223
\(621\) 0 0
\(622\) −32.0878 −1.28660
\(623\) −5.73214 −0.229653
\(624\) 0 0
\(625\) −30.5935 −1.22374
\(626\) −5.19590 −0.207670
\(627\) 0 0
\(628\) 13.3266 0.531790
\(629\) −2.19934 −0.0876933
\(630\) 0 0
\(631\) −40.1689 −1.59910 −0.799549 0.600601i \(-0.794928\pi\)
−0.799549 + 0.600601i \(0.794928\pi\)
\(632\) −1.99827 −0.0794867
\(633\) 0 0
\(634\) 75.4578 2.99681
\(635\) 2.58645 0.102640
\(636\) 0 0
\(637\) −1.17753 −0.0466553
\(638\) 10.2663 0.406447
\(639\) 0 0
\(640\) −46.7757 −1.84897
\(641\) −37.9472 −1.49882 −0.749411 0.662105i \(-0.769663\pi\)
−0.749411 + 0.662105i \(0.769663\pi\)
\(642\) 0 0
\(643\) 26.0146 1.02591 0.512957 0.858414i \(-0.328550\pi\)
0.512957 + 0.858414i \(0.328550\pi\)
\(644\) 1.25582 0.0494864
\(645\) 0 0
\(646\) 13.9498 0.548849
\(647\) −30.8493 −1.21281 −0.606405 0.795156i \(-0.707389\pi\)
−0.606405 + 0.795156i \(0.707389\pi\)
\(648\) 0 0
\(649\) −18.3076 −0.718637
\(650\) 4.54306 0.178194
\(651\) 0 0
\(652\) −29.8405 −1.16864
\(653\) −30.2629 −1.18428 −0.592140 0.805835i \(-0.701717\pi\)
−0.592140 + 0.805835i \(0.701717\pi\)
\(654\) 0 0
\(655\) −15.1229 −0.590902
\(656\) −0.0266134 −0.00103908
\(657\) 0 0
\(658\) 19.9672 0.778402
\(659\) −4.03804 −0.157300 −0.0786498 0.996902i \(-0.525061\pi\)
−0.0786498 + 0.996902i \(0.525061\pi\)
\(660\) 0 0
\(661\) −7.92170 −0.308118 −0.154059 0.988062i \(-0.549235\pi\)
−0.154059 + 0.988062i \(0.549235\pi\)
\(662\) 56.2505 2.18624
\(663\) 0 0
\(664\) −15.3021 −0.593838
\(665\) −14.7608 −0.572400
\(666\) 0 0
\(667\) 0.546741 0.0211699
\(668\) −25.1292 −0.972279
\(669\) 0 0
\(670\) 84.0053 3.24541
\(671\) 8.14827 0.314560
\(672\) 0 0
\(673\) −17.1617 −0.661535 −0.330768 0.943712i \(-0.607308\pi\)
−0.330768 + 0.943712i \(0.607308\pi\)
\(674\) 17.6873 0.681287
\(675\) 0 0
\(676\) −37.3183 −1.43532
\(677\) −34.0415 −1.30832 −0.654160 0.756356i \(-0.726978\pi\)
−0.654160 + 0.756356i \(0.726978\pi\)
\(678\) 0 0
\(679\) 12.1101 0.464743
\(680\) −7.67118 −0.294176
\(681\) 0 0
\(682\) −6.02883 −0.230856
\(683\) −2.51831 −0.0963604 −0.0481802 0.998839i \(-0.515342\pi\)
−0.0481802 + 0.998839i \(0.515342\pi\)
\(684\) 0 0
\(685\) 3.71480 0.141935
\(686\) −2.28328 −0.0871761
\(687\) 0 0
\(688\) 0.842246 0.0321103
\(689\) 0.302452 0.0115225
\(690\) 0 0
\(691\) −45.6601 −1.73699 −0.868497 0.495695i \(-0.834914\pi\)
−0.868497 + 0.495695i \(0.834914\pi\)
\(692\) 4.26661 0.162192
\(693\) 0 0
\(694\) −77.3185 −2.93497
\(695\) −23.9045 −0.906749
\(696\) 0 0
\(697\) −0.282149 −0.0106872
\(698\) 47.5467 1.79967
\(699\) 0 0
\(700\) 5.42975 0.205225
\(701\) −16.7859 −0.633996 −0.316998 0.948426i \(-0.602675\pi\)
−0.316998 + 0.948426i \(0.602675\pi\)
\(702\) 0 0
\(703\) 11.7245 0.442198
\(704\) 41.7044 1.57179
\(705\) 0 0
\(706\) −19.4362 −0.731491
\(707\) −15.0055 −0.564341
\(708\) 0 0
\(709\) 17.0746 0.641250 0.320625 0.947206i \(-0.396107\pi\)
0.320625 + 0.947206i \(0.396107\pi\)
\(710\) 43.2008 1.62130
\(711\) 0 0
\(712\) 15.8807 0.595156
\(713\) −0.321071 −0.0120242
\(714\) 0 0
\(715\) −9.78848 −0.366068
\(716\) −40.5478 −1.51534
\(717\) 0 0
\(718\) 7.61528 0.284200
\(719\) 28.6856 1.06979 0.534897 0.844918i \(-0.320351\pi\)
0.534897 + 0.844918i \(0.320351\pi\)
\(720\) 0 0
\(721\) −15.8235 −0.589297
\(722\) −30.9831 −1.15307
\(723\) 0 0
\(724\) 51.9498 1.93070
\(725\) 2.36392 0.0877939
\(726\) 0 0
\(727\) −26.2955 −0.975245 −0.487623 0.873055i \(-0.662136\pi\)
−0.487623 + 0.873055i \(0.662136\pi\)
\(728\) 3.26230 0.120909
\(729\) 0 0
\(730\) 54.3638 2.01209
\(731\) 8.92931 0.330263
\(732\) 0 0
\(733\) −16.2742 −0.601101 −0.300550 0.953766i \(-0.597170\pi\)
−0.300550 + 0.953766i \(0.597170\pi\)
\(734\) −54.8379 −2.02410
\(735\) 0 0
\(736\) 2.25557 0.0831415
\(737\) −45.7176 −1.68403
\(738\) 0 0
\(739\) 17.4545 0.642074 0.321037 0.947067i \(-0.395969\pi\)
0.321037 + 0.947067i \(0.395969\pi\)
\(740\) −17.0747 −0.627680
\(741\) 0 0
\(742\) 0.586469 0.0215300
\(743\) 6.62388 0.243007 0.121503 0.992591i \(-0.461228\pi\)
0.121503 + 0.992591i \(0.461228\pi\)
\(744\) 0 0
\(745\) −11.2206 −0.411090
\(746\) 7.83273 0.286777
\(747\) 0 0
\(748\) 11.0562 0.404254
\(749\) 3.24337 0.118510
\(750\) 0 0
\(751\) −11.6724 −0.425930 −0.212965 0.977060i \(-0.568312\pi\)
−0.212965 + 0.977060i \(0.568312\pi\)
\(752\) 0.883043 0.0322013
\(753\) 0 0
\(754\) 3.76135 0.136980
\(755\) 2.91094 0.105940
\(756\) 0 0
\(757\) 3.63056 0.131955 0.0659775 0.997821i \(-0.478983\pi\)
0.0659775 + 0.997821i \(0.478983\pi\)
\(758\) 16.1011 0.584818
\(759\) 0 0
\(760\) 40.8945 1.48340
\(761\) 1.51369 0.0548711 0.0274355 0.999624i \(-0.491266\pi\)
0.0274355 + 0.999624i \(0.491266\pi\)
\(762\) 0 0
\(763\) −12.2937 −0.445060
\(764\) 10.7180 0.387762
\(765\) 0 0
\(766\) 85.8995 3.10368
\(767\) −6.70753 −0.242195
\(768\) 0 0
\(769\) 4.01256 0.144697 0.0723484 0.997379i \(-0.476951\pi\)
0.0723484 + 0.997379i \(0.476951\pi\)
\(770\) −18.9803 −0.684004
\(771\) 0 0
\(772\) 10.6981 0.385034
\(773\) −13.1068 −0.471418 −0.235709 0.971824i \(-0.575741\pi\)
−0.235709 + 0.971824i \(0.575741\pi\)
\(774\) 0 0
\(775\) −1.38820 −0.0498657
\(776\) −33.5507 −1.20440
\(777\) 0 0
\(778\) −33.3113 −1.19427
\(779\) 1.50412 0.0538906
\(780\) 0 0
\(781\) −23.5108 −0.841283
\(782\) 0.955280 0.0341607
\(783\) 0 0
\(784\) −0.100977 −0.00360634
\(785\) −10.7266 −0.382850
\(786\) 0 0
\(787\) 29.6322 1.05627 0.528136 0.849160i \(-0.322891\pi\)
0.528136 + 0.849160i \(0.322891\pi\)
\(788\) −51.1478 −1.82207
\(789\) 0 0
\(790\) 4.25954 0.151548
\(791\) 18.7120 0.665322
\(792\) 0 0
\(793\) 2.98535 0.106013
\(794\) 4.00251 0.142044
\(795\) 0 0
\(796\) −66.4630 −2.35572
\(797\) −45.0974 −1.59743 −0.798715 0.601709i \(-0.794487\pi\)
−0.798715 + 0.601709i \(0.794487\pi\)
\(798\) 0 0
\(799\) 9.36183 0.331198
\(800\) 9.75232 0.344797
\(801\) 0 0
\(802\) −17.1195 −0.604510
\(803\) −29.5860 −1.04407
\(804\) 0 0
\(805\) −1.01082 −0.0356266
\(806\) −2.20884 −0.0778029
\(807\) 0 0
\(808\) 41.5724 1.46251
\(809\) −19.5504 −0.687356 −0.343678 0.939088i \(-0.611673\pi\)
−0.343678 + 0.939088i \(0.611673\pi\)
\(810\) 0 0
\(811\) −1.85130 −0.0650078 −0.0325039 0.999472i \(-0.510348\pi\)
−0.0325039 + 0.999472i \(0.510348\pi\)
\(812\) 4.49547 0.157760
\(813\) 0 0
\(814\) 15.0761 0.528416
\(815\) 24.0187 0.841339
\(816\) 0 0
\(817\) −47.6015 −1.66537
\(818\) 40.7161 1.42361
\(819\) 0 0
\(820\) −2.19049 −0.0764952
\(821\) −6.10030 −0.212902 −0.106451 0.994318i \(-0.533949\pi\)
−0.106451 + 0.994318i \(0.533949\pi\)
\(822\) 0 0
\(823\) 27.7252 0.966440 0.483220 0.875499i \(-0.339467\pi\)
0.483220 + 0.875499i \(0.339467\pi\)
\(824\) 43.8385 1.52719
\(825\) 0 0
\(826\) −13.0062 −0.452545
\(827\) −21.2307 −0.738266 −0.369133 0.929377i \(-0.620345\pi\)
−0.369133 + 0.929377i \(0.620345\pi\)
\(828\) 0 0
\(829\) 17.4420 0.605787 0.302894 0.953024i \(-0.402047\pi\)
0.302894 + 0.953024i \(0.402047\pi\)
\(830\) 32.6183 1.13220
\(831\) 0 0
\(832\) 15.2796 0.529725
\(833\) −1.07054 −0.0370921
\(834\) 0 0
\(835\) 20.2266 0.699970
\(836\) −58.9396 −2.03847
\(837\) 0 0
\(838\) −17.8995 −0.618329
\(839\) −32.6569 −1.12744 −0.563721 0.825965i \(-0.690631\pi\)
−0.563721 + 0.825965i \(0.690631\pi\)
\(840\) 0 0
\(841\) −27.0428 −0.932511
\(842\) 32.1931 1.10945
\(843\) 0 0
\(844\) 8.76115 0.301571
\(845\) 30.0376 1.03332
\(846\) 0 0
\(847\) −0.670473 −0.0230377
\(848\) 0.0259364 0.000890660 0
\(849\) 0 0
\(850\) 4.13030 0.141668
\(851\) 0.802889 0.0275227
\(852\) 0 0
\(853\) 37.2064 1.27392 0.636961 0.770896i \(-0.280191\pi\)
0.636961 + 0.770896i \(0.280191\pi\)
\(854\) 5.78875 0.198087
\(855\) 0 0
\(856\) −8.98568 −0.307124
\(857\) −14.5500 −0.497020 −0.248510 0.968629i \(-0.579941\pi\)
−0.248510 + 0.968629i \(0.579941\pi\)
\(858\) 0 0
\(859\) 8.66396 0.295611 0.147805 0.989016i \(-0.452779\pi\)
0.147805 + 0.989016i \(0.452779\pi\)
\(860\) 69.3235 2.36391
\(861\) 0 0
\(862\) −33.2953 −1.13404
\(863\) −40.2943 −1.37163 −0.685816 0.727775i \(-0.740555\pi\)
−0.685816 + 0.727775i \(0.740555\pi\)
\(864\) 0 0
\(865\) −3.43420 −0.116766
\(866\) 10.9302 0.371422
\(867\) 0 0
\(868\) −2.63994 −0.0896056
\(869\) −2.31814 −0.0786375
\(870\) 0 0
\(871\) −16.7499 −0.567550
\(872\) 34.0593 1.15339
\(873\) 0 0
\(874\) −5.09252 −0.172257
\(875\) 8.56184 0.289443
\(876\) 0 0
\(877\) 14.7099 0.496718 0.248359 0.968668i \(-0.420109\pi\)
0.248359 + 0.968668i \(0.420109\pi\)
\(878\) 12.2114 0.412114
\(879\) 0 0
\(880\) −0.839400 −0.0282962
\(881\) 4.99439 0.168265 0.0841327 0.996455i \(-0.473188\pi\)
0.0841327 + 0.996455i \(0.473188\pi\)
\(882\) 0 0
\(883\) −19.8711 −0.668716 −0.334358 0.942446i \(-0.608520\pi\)
−0.334358 + 0.942446i \(0.608520\pi\)
\(884\) 4.05075 0.136241
\(885\) 0 0
\(886\) −60.1148 −2.01960
\(887\) 20.6755 0.694214 0.347107 0.937825i \(-0.387164\pi\)
0.347107 + 0.937825i \(0.387164\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) −33.8517 −1.13471
\(891\) 0 0
\(892\) 34.2234 1.14588
\(893\) −49.9072 −1.67008
\(894\) 0 0
\(895\) 32.6371 1.09094
\(896\) 18.0849 0.604174
\(897\) 0 0
\(898\) 46.0345 1.53619
\(899\) −1.14934 −0.0383326
\(900\) 0 0
\(901\) 0.274972 0.00916066
\(902\) 1.93408 0.0643979
\(903\) 0 0
\(904\) −51.8411 −1.72421
\(905\) −41.8145 −1.38996
\(906\) 0 0
\(907\) −21.2937 −0.707044 −0.353522 0.935426i \(-0.615016\pi\)
−0.353522 + 0.935426i \(0.615016\pi\)
\(908\) 9.97600 0.331065
\(909\) 0 0
\(910\) −6.95400 −0.230523
\(911\) −48.1047 −1.59378 −0.796891 0.604124i \(-0.793523\pi\)
−0.796891 + 0.604124i \(0.793523\pi\)
\(912\) 0 0
\(913\) −17.7516 −0.587493
\(914\) −46.7036 −1.54482
\(915\) 0 0
\(916\) −0.397259 −0.0131258
\(917\) 5.84698 0.193084
\(918\) 0 0
\(919\) 47.6807 1.57284 0.786421 0.617691i \(-0.211932\pi\)
0.786421 + 0.617691i \(0.211932\pi\)
\(920\) 2.80044 0.0923277
\(921\) 0 0
\(922\) 4.80160 0.158132
\(923\) −8.61386 −0.283529
\(924\) 0 0
\(925\) 3.47142 0.114140
\(926\) −16.8510 −0.553760
\(927\) 0 0
\(928\) 8.07427 0.265051
\(929\) −42.9353 −1.40866 −0.704332 0.709871i \(-0.748753\pi\)
−0.704332 + 0.709871i \(0.748753\pi\)
\(930\) 0 0
\(931\) 5.70698 0.187039
\(932\) 24.4936 0.802316
\(933\) 0 0
\(934\) −12.0707 −0.394967
\(935\) −8.89914 −0.291033
\(936\) 0 0
\(937\) −10.3116 −0.336865 −0.168432 0.985713i \(-0.553870\pi\)
−0.168432 + 0.985713i \(0.553870\pi\)
\(938\) −32.4790 −1.06048
\(939\) 0 0
\(940\) 72.6814 2.37061
\(941\) −48.1796 −1.57061 −0.785305 0.619109i \(-0.787494\pi\)
−0.785305 + 0.619109i \(0.787494\pi\)
\(942\) 0 0
\(943\) 0.103001 0.00335419
\(944\) −0.575197 −0.0187211
\(945\) 0 0
\(946\) −61.2088 −1.99007
\(947\) 18.3826 0.597354 0.298677 0.954354i \(-0.403455\pi\)
0.298677 + 0.954354i \(0.403455\pi\)
\(948\) 0 0
\(949\) −10.8397 −0.351871
\(950\) −22.0183 −0.714369
\(951\) 0 0
\(952\) 2.96591 0.0961256
\(953\) −48.2826 −1.56403 −0.782014 0.623261i \(-0.785807\pi\)
−0.782014 + 0.623261i \(0.785807\pi\)
\(954\) 0 0
\(955\) −8.62691 −0.279160
\(956\) 73.1096 2.36453
\(957\) 0 0
\(958\) −20.5734 −0.664696
\(959\) −1.43625 −0.0463790
\(960\) 0 0
\(961\) −30.3251 −0.978228
\(962\) 5.52355 0.178086
\(963\) 0 0
\(964\) 41.0065 1.32073
\(965\) −8.61095 −0.277196
\(966\) 0 0
\(967\) 4.90647 0.157781 0.0788907 0.996883i \(-0.474862\pi\)
0.0788907 + 0.996883i \(0.474862\pi\)
\(968\) 1.85753 0.0597032
\(969\) 0 0
\(970\) 71.5173 2.29628
\(971\) −38.4381 −1.23354 −0.616768 0.787145i \(-0.711558\pi\)
−0.616768 + 0.787145i \(0.711558\pi\)
\(972\) 0 0
\(973\) 9.24219 0.296291
\(974\) 6.49767 0.208199
\(975\) 0 0
\(976\) 0.256006 0.00819454
\(977\) 8.48769 0.271545 0.135773 0.990740i \(-0.456648\pi\)
0.135773 + 0.990740i \(0.456648\pi\)
\(978\) 0 0
\(979\) 18.4229 0.588797
\(980\) −8.31124 −0.265493
\(981\) 0 0
\(982\) −30.1052 −0.960697
\(983\) 11.7097 0.373480 0.186740 0.982409i \(-0.440208\pi\)
0.186740 + 0.982409i \(0.440208\pi\)
\(984\) 0 0
\(985\) 41.1690 1.31175
\(986\) 3.41961 0.108903
\(987\) 0 0
\(988\) −21.5942 −0.687004
\(989\) −3.25973 −0.103654
\(990\) 0 0
\(991\) −51.1937 −1.62622 −0.813110 0.582110i \(-0.802227\pi\)
−0.813110 + 0.582110i \(0.802227\pi\)
\(992\) −4.74158 −0.150545
\(993\) 0 0
\(994\) −16.7027 −0.529778
\(995\) 53.4962 1.69594
\(996\) 0 0
\(997\) −12.6330 −0.400090 −0.200045 0.979787i \(-0.564109\pi\)
−0.200045 + 0.979787i \(0.564109\pi\)
\(998\) −6.76561 −0.214162
\(999\) 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 \(a_p\))