Properties

Label 8001.2.a.u.1.6
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
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: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.665348\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.665348 q^{2}\) \(-1.55731 q^{4}\) \(+3.70415 q^{5}\) \(+1.00000 q^{7}\) \(+2.36685 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.665348 q^{2}\) \(-1.55731 q^{4}\) \(+3.70415 q^{5}\) \(+1.00000 q^{7}\) \(+2.36685 q^{8}\) \(-2.46455 q^{10}\) \(-1.00383 q^{11}\) \(+3.77620 q^{13}\) \(-0.665348 q^{14}\) \(+1.53985 q^{16}\) \(-4.06728 q^{17}\) \(-8.44025 q^{19}\) \(-5.76853 q^{20}\) \(+0.667895 q^{22}\) \(-0.442232 q^{23}\) \(+8.72076 q^{25}\) \(-2.51249 q^{26}\) \(-1.55731 q^{28}\) \(-5.65212 q^{29}\) \(+8.26348 q^{31}\) \(-5.75823 q^{32}\) \(+2.70616 q^{34}\) \(+3.70415 q^{35}\) \(-10.2212 q^{37}\) \(+5.61570 q^{38}\) \(+8.76718 q^{40}\) \(+5.95725 q^{41}\) \(+2.00895 q^{43}\) \(+1.56327 q^{44}\) \(+0.294238 q^{46}\) \(-3.17856 q^{47}\) \(+1.00000 q^{49}\) \(-5.80234 q^{50}\) \(-5.88073 q^{52}\) \(+0.363462 q^{53}\) \(-3.71833 q^{55}\) \(+2.36685 q^{56}\) \(+3.76063 q^{58}\) \(+10.0577 q^{59}\) \(+3.57488 q^{61}\) \(-5.49809 q^{62}\) \(+0.751538 q^{64}\) \(+13.9876 q^{65}\) \(+3.95922 q^{67}\) \(+6.33403 q^{68}\) \(-2.46455 q^{70}\) \(+10.6852 q^{71}\) \(-13.5615 q^{73}\) \(+6.80067 q^{74}\) \(+13.1441 q^{76}\) \(-1.00383 q^{77}\) \(+14.7485 q^{79}\) \(+5.70383 q^{80}\) \(-3.96364 q^{82}\) \(+3.52844 q^{83}\) \(-15.0658 q^{85}\) \(-1.33665 q^{86}\) \(-2.37591 q^{88}\) \(+5.89993 q^{89}\) \(+3.77620 q^{91}\) \(+0.688694 q^{92}\) \(+2.11485 q^{94}\) \(-31.2640 q^{95}\) \(-6.24359 q^{97}\) \(-0.665348 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.665348 −0.470472 −0.235236 0.971938i \(-0.575586\pi\)
−0.235236 + 0.971938i \(0.575586\pi\)
\(3\) 0 0
\(4\) −1.55731 −0.778656
\(5\) 3.70415 1.65655 0.828274 0.560323i \(-0.189323\pi\)
0.828274 + 0.560323i \(0.189323\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.36685 0.836808
\(9\) 0 0
\(10\) −2.46455 −0.779360
\(11\) −1.00383 −0.302665 −0.151333 0.988483i \(-0.548356\pi\)
−0.151333 + 0.988483i \(0.548356\pi\)
\(12\) 0 0
\(13\) 3.77620 1.04733 0.523665 0.851924i \(-0.324564\pi\)
0.523665 + 0.851924i \(0.324564\pi\)
\(14\) −0.665348 −0.177822
\(15\) 0 0
\(16\) 1.53985 0.384961
\(17\) −4.06728 −0.986461 −0.493231 0.869899i \(-0.664184\pi\)
−0.493231 + 0.869899i \(0.664184\pi\)
\(18\) 0 0
\(19\) −8.44025 −1.93633 −0.968163 0.250321i \(-0.919464\pi\)
−0.968163 + 0.250321i \(0.919464\pi\)
\(20\) −5.76853 −1.28988
\(21\) 0 0
\(22\) 0.667895 0.142396
\(23\) −0.442232 −0.0922118 −0.0461059 0.998937i \(-0.514681\pi\)
−0.0461059 + 0.998937i \(0.514681\pi\)
\(24\) 0 0
\(25\) 8.72076 1.74415
\(26\) −2.51249 −0.492740
\(27\) 0 0
\(28\) −1.55731 −0.294304
\(29\) −5.65212 −1.04957 −0.524786 0.851234i \(-0.675855\pi\)
−0.524786 + 0.851234i \(0.675855\pi\)
\(30\) 0 0
\(31\) 8.26348 1.48417 0.742083 0.670308i \(-0.233838\pi\)
0.742083 + 0.670308i \(0.233838\pi\)
\(32\) −5.75823 −1.01792
\(33\) 0 0
\(34\) 2.70616 0.464102
\(35\) 3.70415 0.626116
\(36\) 0 0
\(37\) −10.2212 −1.68036 −0.840179 0.542309i \(-0.817550\pi\)
−0.840179 + 0.542309i \(0.817550\pi\)
\(38\) 5.61570 0.910987
\(39\) 0 0
\(40\) 8.76718 1.38621
\(41\) 5.95725 0.930366 0.465183 0.885215i \(-0.345989\pi\)
0.465183 + 0.885215i \(0.345989\pi\)
\(42\) 0 0
\(43\) 2.00895 0.306362 0.153181 0.988198i \(-0.451048\pi\)
0.153181 + 0.988198i \(0.451048\pi\)
\(44\) 1.56327 0.235672
\(45\) 0 0
\(46\) 0.294238 0.0433831
\(47\) −3.17856 −0.463640 −0.231820 0.972759i \(-0.574468\pi\)
−0.231820 + 0.972759i \(0.574468\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −5.80234 −0.820575
\(51\) 0 0
\(52\) −5.88073 −0.815510
\(53\) 0.363462 0.0499253 0.0249627 0.999688i \(-0.492053\pi\)
0.0249627 + 0.999688i \(0.492053\pi\)
\(54\) 0 0
\(55\) −3.71833 −0.501380
\(56\) 2.36685 0.316284
\(57\) 0 0
\(58\) 3.76063 0.493795
\(59\) 10.0577 1.30940 0.654700 0.755889i \(-0.272795\pi\)
0.654700 + 0.755889i \(0.272795\pi\)
\(60\) 0 0
\(61\) 3.57488 0.457717 0.228858 0.973460i \(-0.426501\pi\)
0.228858 + 0.973460i \(0.426501\pi\)
\(62\) −5.49809 −0.698258
\(63\) 0 0
\(64\) 0.751538 0.0939423
\(65\) 13.9876 1.73495
\(66\) 0 0
\(67\) 3.95922 0.483695 0.241848 0.970314i \(-0.422247\pi\)
0.241848 + 0.970314i \(0.422247\pi\)
\(68\) 6.33403 0.768114
\(69\) 0 0
\(70\) −2.46455 −0.294570
\(71\) 10.6852 1.26810 0.634052 0.773291i \(-0.281391\pi\)
0.634052 + 0.773291i \(0.281391\pi\)
\(72\) 0 0
\(73\) −13.5615 −1.58725 −0.793625 0.608407i \(-0.791809\pi\)
−0.793625 + 0.608407i \(0.791809\pi\)
\(74\) 6.80067 0.790562
\(75\) 0 0
\(76\) 13.1441 1.50773
\(77\) −1.00383 −0.114397
\(78\) 0 0
\(79\) 14.7485 1.65934 0.829669 0.558255i \(-0.188529\pi\)
0.829669 + 0.558255i \(0.188529\pi\)
\(80\) 5.70383 0.637707
\(81\) 0 0
\(82\) −3.96364 −0.437711
\(83\) 3.52844 0.387297 0.193648 0.981071i \(-0.437968\pi\)
0.193648 + 0.981071i \(0.437968\pi\)
\(84\) 0 0
\(85\) −15.0658 −1.63412
\(86\) −1.33665 −0.144135
\(87\) 0 0
\(88\) −2.37591 −0.253273
\(89\) 5.89993 0.625392 0.312696 0.949853i \(-0.398768\pi\)
0.312696 + 0.949853i \(0.398768\pi\)
\(90\) 0 0
\(91\) 3.77620 0.395854
\(92\) 0.688694 0.0718013
\(93\) 0 0
\(94\) 2.11485 0.218130
\(95\) −31.2640 −3.20762
\(96\) 0 0
\(97\) −6.24359 −0.633941 −0.316970 0.948435i \(-0.602666\pi\)
−0.316970 + 0.948435i \(0.602666\pi\)
\(98\) −0.665348 −0.0672103
\(99\) 0 0
\(100\) −13.5810 −1.35810
\(101\) 18.8071 1.87138 0.935688 0.352828i \(-0.114780\pi\)
0.935688 + 0.352828i \(0.114780\pi\)
\(102\) 0 0
\(103\) 11.1061 1.09431 0.547157 0.837030i \(-0.315710\pi\)
0.547157 + 0.837030i \(0.315710\pi\)
\(104\) 8.93771 0.876415
\(105\) 0 0
\(106\) −0.241829 −0.0234885
\(107\) 0.580119 0.0560822 0.0280411 0.999607i \(-0.491073\pi\)
0.0280411 + 0.999607i \(0.491073\pi\)
\(108\) 0 0
\(109\) 17.5353 1.67958 0.839788 0.542914i \(-0.182679\pi\)
0.839788 + 0.542914i \(0.182679\pi\)
\(110\) 2.47399 0.235885
\(111\) 0 0
\(112\) 1.53985 0.145502
\(113\) 19.4000 1.82499 0.912497 0.409083i \(-0.134151\pi\)
0.912497 + 0.409083i \(0.134151\pi\)
\(114\) 0 0
\(115\) −1.63810 −0.152753
\(116\) 8.80212 0.817256
\(117\) 0 0
\(118\) −6.69186 −0.616036
\(119\) −4.06728 −0.372847
\(120\) 0 0
\(121\) −9.99233 −0.908394
\(122\) −2.37854 −0.215343
\(123\) 0 0
\(124\) −12.8688 −1.15565
\(125\) 13.7823 1.23272
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 11.0164 0.973724
\(129\) 0 0
\(130\) −9.30665 −0.816247
\(131\) 19.5438 1.70755 0.853775 0.520642i \(-0.174307\pi\)
0.853775 + 0.520642i \(0.174307\pi\)
\(132\) 0 0
\(133\) −8.44025 −0.731862
\(134\) −2.63426 −0.227565
\(135\) 0 0
\(136\) −9.62665 −0.825478
\(137\) 6.60487 0.564292 0.282146 0.959371i \(-0.408954\pi\)
0.282146 + 0.959371i \(0.408954\pi\)
\(138\) 0 0
\(139\) −5.63615 −0.478052 −0.239026 0.971013i \(-0.576828\pi\)
−0.239026 + 0.971013i \(0.576828\pi\)
\(140\) −5.76853 −0.487529
\(141\) 0 0
\(142\) −7.10939 −0.596607
\(143\) −3.79066 −0.316991
\(144\) 0 0
\(145\) −20.9363 −1.73867
\(146\) 9.02310 0.746757
\(147\) 0 0
\(148\) 15.9176 1.30842
\(149\) −3.12232 −0.255790 −0.127895 0.991788i \(-0.540822\pi\)
−0.127895 + 0.991788i \(0.540822\pi\)
\(150\) 0 0
\(151\) 13.7417 1.11828 0.559140 0.829073i \(-0.311131\pi\)
0.559140 + 0.829073i \(0.311131\pi\)
\(152\) −19.9768 −1.62033
\(153\) 0 0
\(154\) 0.667895 0.0538205
\(155\) 30.6092 2.45859
\(156\) 0 0
\(157\) 18.9828 1.51499 0.757497 0.652838i \(-0.226422\pi\)
0.757497 + 0.652838i \(0.226422\pi\)
\(158\) −9.81290 −0.780672
\(159\) 0 0
\(160\) −21.3294 −1.68624
\(161\) −0.442232 −0.0348528
\(162\) 0 0
\(163\) −22.2933 −1.74615 −0.873075 0.487586i \(-0.837877\pi\)
−0.873075 + 0.487586i \(0.837877\pi\)
\(164\) −9.27729 −0.724435
\(165\) 0 0
\(166\) −2.34764 −0.182212
\(167\) 1.57767 0.122084 0.0610421 0.998135i \(-0.480558\pi\)
0.0610421 + 0.998135i \(0.480558\pi\)
\(168\) 0 0
\(169\) 1.25972 0.0969017
\(170\) 10.0240 0.768808
\(171\) 0 0
\(172\) −3.12856 −0.238551
\(173\) 4.11390 0.312774 0.156387 0.987696i \(-0.450015\pi\)
0.156387 + 0.987696i \(0.450015\pi\)
\(174\) 0 0
\(175\) 8.72076 0.659228
\(176\) −1.54574 −0.116514
\(177\) 0 0
\(178\) −3.92551 −0.294229
\(179\) −5.78579 −0.432450 −0.216225 0.976344i \(-0.569374\pi\)
−0.216225 + 0.976344i \(0.569374\pi\)
\(180\) 0 0
\(181\) −6.54333 −0.486362 −0.243181 0.969981i \(-0.578191\pi\)
−0.243181 + 0.969981i \(0.578191\pi\)
\(182\) −2.51249 −0.186238
\(183\) 0 0
\(184\) −1.04670 −0.0771636
\(185\) −37.8610 −2.78360
\(186\) 0 0
\(187\) 4.08285 0.298568
\(188\) 4.95000 0.361016
\(189\) 0 0
\(190\) 20.8014 1.50909
\(191\) 7.70840 0.557760 0.278880 0.960326i \(-0.410037\pi\)
0.278880 + 0.960326i \(0.410037\pi\)
\(192\) 0 0
\(193\) 26.8743 1.93445 0.967227 0.253914i \(-0.0817179\pi\)
0.967227 + 0.253914i \(0.0817179\pi\)
\(194\) 4.15416 0.298251
\(195\) 0 0
\(196\) −1.55731 −0.111237
\(197\) −9.18051 −0.654084 −0.327042 0.945010i \(-0.606052\pi\)
−0.327042 + 0.945010i \(0.606052\pi\)
\(198\) 0 0
\(199\) −15.6252 −1.10764 −0.553821 0.832636i \(-0.686831\pi\)
−0.553821 + 0.832636i \(0.686831\pi\)
\(200\) 20.6407 1.45952
\(201\) 0 0
\(202\) −12.5133 −0.880430
\(203\) −5.65212 −0.396701
\(204\) 0 0
\(205\) 22.0666 1.54120
\(206\) −7.38941 −0.514845
\(207\) 0 0
\(208\) 5.81477 0.403182
\(209\) 8.47256 0.586059
\(210\) 0 0
\(211\) 0.566441 0.0389954 0.0194977 0.999810i \(-0.493793\pi\)
0.0194977 + 0.999810i \(0.493793\pi\)
\(212\) −0.566023 −0.0388746
\(213\) 0 0
\(214\) −0.385981 −0.0263851
\(215\) 7.44147 0.507504
\(216\) 0 0
\(217\) 8.26348 0.560962
\(218\) −11.6671 −0.790194
\(219\) 0 0
\(220\) 5.79061 0.390403
\(221\) −15.3589 −1.03315
\(222\) 0 0
\(223\) −5.32002 −0.356255 −0.178128 0.984007i \(-0.557004\pi\)
−0.178128 + 0.984007i \(0.557004\pi\)
\(224\) −5.75823 −0.384738
\(225\) 0 0
\(226\) −12.9077 −0.858609
\(227\) −25.5949 −1.69879 −0.849397 0.527754i \(-0.823034\pi\)
−0.849397 + 0.527754i \(0.823034\pi\)
\(228\) 0 0
\(229\) −16.0579 −1.06114 −0.530568 0.847642i \(-0.678021\pi\)
−0.530568 + 0.847642i \(0.678021\pi\)
\(230\) 1.08990 0.0718661
\(231\) 0 0
\(232\) −13.3777 −0.878291
\(233\) −23.0614 −1.51080 −0.755401 0.655262i \(-0.772558\pi\)
−0.755401 + 0.655262i \(0.772558\pi\)
\(234\) 0 0
\(235\) −11.7739 −0.768042
\(236\) −15.6630 −1.01957
\(237\) 0 0
\(238\) 2.70616 0.175414
\(239\) 21.7293 1.40555 0.702777 0.711410i \(-0.251943\pi\)
0.702777 + 0.711410i \(0.251943\pi\)
\(240\) 0 0
\(241\) 13.4723 0.867830 0.433915 0.900954i \(-0.357132\pi\)
0.433915 + 0.900954i \(0.357132\pi\)
\(242\) 6.64838 0.427374
\(243\) 0 0
\(244\) −5.56721 −0.356404
\(245\) 3.70415 0.236650
\(246\) 0 0
\(247\) −31.8721 −2.02797
\(248\) 19.5584 1.24196
\(249\) 0 0
\(250\) −9.17001 −0.579963
\(251\) 21.8629 1.37997 0.689987 0.723822i \(-0.257616\pi\)
0.689987 + 0.723822i \(0.257616\pi\)
\(252\) 0 0
\(253\) 0.443925 0.0279093
\(254\) −0.665348 −0.0417476
\(255\) 0 0
\(256\) −8.83284 −0.552052
\(257\) −18.8653 −1.17679 −0.588393 0.808575i \(-0.700239\pi\)
−0.588393 + 0.808575i \(0.700239\pi\)
\(258\) 0 0
\(259\) −10.2212 −0.635116
\(260\) −21.7831 −1.35093
\(261\) 0 0
\(262\) −13.0034 −0.803354
\(263\) 5.02576 0.309901 0.154951 0.987922i \(-0.450478\pi\)
0.154951 + 0.987922i \(0.450478\pi\)
\(264\) 0 0
\(265\) 1.34632 0.0827037
\(266\) 5.61570 0.344321
\(267\) 0 0
\(268\) −6.16574 −0.376632
\(269\) 14.3454 0.874652 0.437326 0.899303i \(-0.355926\pi\)
0.437326 + 0.899303i \(0.355926\pi\)
\(270\) 0 0
\(271\) 11.0365 0.670418 0.335209 0.942144i \(-0.391193\pi\)
0.335209 + 0.942144i \(0.391193\pi\)
\(272\) −6.26299 −0.379749
\(273\) 0 0
\(274\) −4.39454 −0.265484
\(275\) −8.75414 −0.527895
\(276\) 0 0
\(277\) −17.6419 −1.06000 −0.530000 0.847998i \(-0.677808\pi\)
−0.530000 + 0.847998i \(0.677808\pi\)
\(278\) 3.75000 0.224910
\(279\) 0 0
\(280\) 8.76718 0.523939
\(281\) −7.54428 −0.450054 −0.225027 0.974353i \(-0.572247\pi\)
−0.225027 + 0.974353i \(0.572247\pi\)
\(282\) 0 0
\(283\) −10.6025 −0.630253 −0.315127 0.949050i \(-0.602047\pi\)
−0.315127 + 0.949050i \(0.602047\pi\)
\(284\) −16.6402 −0.987416
\(285\) 0 0
\(286\) 2.52211 0.149135
\(287\) 5.95725 0.351645
\(288\) 0 0
\(289\) −0.457208 −0.0268946
\(290\) 13.9299 0.817995
\(291\) 0 0
\(292\) 21.1194 1.23592
\(293\) 31.2181 1.82378 0.911890 0.410435i \(-0.134623\pi\)
0.911890 + 0.410435i \(0.134623\pi\)
\(294\) 0 0
\(295\) 37.2552 2.16908
\(296\) −24.1921 −1.40614
\(297\) 0 0
\(298\) 2.07743 0.120342
\(299\) −1.66996 −0.0965762
\(300\) 0 0
\(301\) 2.00895 0.115794
\(302\) −9.14299 −0.526120
\(303\) 0 0
\(304\) −12.9967 −0.745411
\(305\) 13.2419 0.758230
\(306\) 0 0
\(307\) 26.3560 1.50422 0.752109 0.659038i \(-0.229036\pi\)
0.752109 + 0.659038i \(0.229036\pi\)
\(308\) 1.56327 0.0890757
\(309\) 0 0
\(310\) −20.3658 −1.15670
\(311\) 19.7761 1.12140 0.560699 0.828020i \(-0.310533\pi\)
0.560699 + 0.828020i \(0.310533\pi\)
\(312\) 0 0
\(313\) −11.3455 −0.641288 −0.320644 0.947200i \(-0.603899\pi\)
−0.320644 + 0.947200i \(0.603899\pi\)
\(314\) −12.6302 −0.712763
\(315\) 0 0
\(316\) −22.9681 −1.29205
\(317\) −15.5335 −0.872448 −0.436224 0.899838i \(-0.643684\pi\)
−0.436224 + 0.899838i \(0.643684\pi\)
\(318\) 0 0
\(319\) 5.67376 0.317669
\(320\) 2.78381 0.155620
\(321\) 0 0
\(322\) 0.294238 0.0163973
\(323\) 34.3289 1.91011
\(324\) 0 0
\(325\) 32.9314 1.82670
\(326\) 14.8328 0.821515
\(327\) 0 0
\(328\) 14.0999 0.778537
\(329\) −3.17856 −0.175239
\(330\) 0 0
\(331\) 2.58933 0.142322 0.0711612 0.997465i \(-0.477330\pi\)
0.0711612 + 0.997465i \(0.477330\pi\)
\(332\) −5.49488 −0.301571
\(333\) 0 0
\(334\) −1.04970 −0.0574372
\(335\) 14.6656 0.801265
\(336\) 0 0
\(337\) 29.4115 1.60214 0.801072 0.598568i \(-0.204263\pi\)
0.801072 + 0.598568i \(0.204263\pi\)
\(338\) −0.838154 −0.0455896
\(339\) 0 0
\(340\) 23.4622 1.27242
\(341\) −8.29511 −0.449205
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 4.75489 0.256366
\(345\) 0 0
\(346\) −2.73717 −0.147151
\(347\) 4.05583 0.217728 0.108864 0.994057i \(-0.465279\pi\)
0.108864 + 0.994057i \(0.465279\pi\)
\(348\) 0 0
\(349\) −23.9595 −1.28252 −0.641261 0.767323i \(-0.721588\pi\)
−0.641261 + 0.767323i \(0.721588\pi\)
\(350\) −5.80234 −0.310148
\(351\) 0 0
\(352\) 5.78027 0.308090
\(353\) 20.2726 1.07900 0.539501 0.841985i \(-0.318613\pi\)
0.539501 + 0.841985i \(0.318613\pi\)
\(354\) 0 0
\(355\) 39.5797 2.10067
\(356\) −9.18804 −0.486965
\(357\) 0 0
\(358\) 3.84956 0.203456
\(359\) −29.0431 −1.53284 −0.766418 0.642342i \(-0.777963\pi\)
−0.766418 + 0.642342i \(0.777963\pi\)
\(360\) 0 0
\(361\) 52.2378 2.74936
\(362\) 4.35359 0.228820
\(363\) 0 0
\(364\) −5.88073 −0.308234
\(365\) −50.2338 −2.62936
\(366\) 0 0
\(367\) 6.09658 0.318239 0.159120 0.987259i \(-0.449134\pi\)
0.159120 + 0.987259i \(0.449134\pi\)
\(368\) −0.680969 −0.0354980
\(369\) 0 0
\(370\) 25.1907 1.30960
\(371\) 0.363462 0.0188700
\(372\) 0 0
\(373\) −27.3423 −1.41573 −0.707865 0.706348i \(-0.750342\pi\)
−0.707865 + 0.706348i \(0.750342\pi\)
\(374\) −2.71652 −0.140468
\(375\) 0 0
\(376\) −7.52316 −0.387978
\(377\) −21.3436 −1.09925
\(378\) 0 0
\(379\) 10.1244 0.520054 0.260027 0.965601i \(-0.416268\pi\)
0.260027 + 0.965601i \(0.416268\pi\)
\(380\) 48.6878 2.49763
\(381\) 0 0
\(382\) −5.12877 −0.262410
\(383\) −3.42254 −0.174883 −0.0874417 0.996170i \(-0.527869\pi\)
−0.0874417 + 0.996170i \(0.527869\pi\)
\(384\) 0 0
\(385\) −3.71833 −0.189504
\(386\) −17.8808 −0.910106
\(387\) 0 0
\(388\) 9.72322 0.493622
\(389\) 17.2100 0.872582 0.436291 0.899806i \(-0.356292\pi\)
0.436291 + 0.899806i \(0.356292\pi\)
\(390\) 0 0
\(391\) 1.79868 0.0909633
\(392\) 2.36685 0.119544
\(393\) 0 0
\(394\) 6.10823 0.307728
\(395\) 54.6308 2.74877
\(396\) 0 0
\(397\) −21.9471 −1.10149 −0.550747 0.834672i \(-0.685657\pi\)
−0.550747 + 0.834672i \(0.685657\pi\)
\(398\) 10.3962 0.521114
\(399\) 0 0
\(400\) 13.4286 0.671431
\(401\) 18.4565 0.921673 0.460837 0.887485i \(-0.347549\pi\)
0.460837 + 0.887485i \(0.347549\pi\)
\(402\) 0 0
\(403\) 31.2046 1.55441
\(404\) −29.2885 −1.45716
\(405\) 0 0
\(406\) 3.76063 0.186637
\(407\) 10.2603 0.508586
\(408\) 0 0
\(409\) −11.7867 −0.582817 −0.291408 0.956599i \(-0.594124\pi\)
−0.291408 + 0.956599i \(0.594124\pi\)
\(410\) −14.6819 −0.725090
\(411\) 0 0
\(412\) −17.2956 −0.852095
\(413\) 10.0577 0.494907
\(414\) 0 0
\(415\) 13.0699 0.641576
\(416\) −21.7443 −1.06610
\(417\) 0 0
\(418\) −5.63720 −0.275724
\(419\) −14.7894 −0.722511 −0.361255 0.932467i \(-0.617652\pi\)
−0.361255 + 0.932467i \(0.617652\pi\)
\(420\) 0 0
\(421\) −14.4728 −0.705360 −0.352680 0.935744i \(-0.614730\pi\)
−0.352680 + 0.935744i \(0.614730\pi\)
\(422\) −0.376880 −0.0183462
\(423\) 0 0
\(424\) 0.860260 0.0417779
\(425\) −35.4698 −1.72054
\(426\) 0 0
\(427\) 3.57488 0.173001
\(428\) −0.903427 −0.0436688
\(429\) 0 0
\(430\) −4.95117 −0.238766
\(431\) 17.0346 0.820529 0.410264 0.911967i \(-0.365436\pi\)
0.410264 + 0.911967i \(0.365436\pi\)
\(432\) 0 0
\(433\) −6.44778 −0.309860 −0.154930 0.987925i \(-0.549515\pi\)
−0.154930 + 0.987925i \(0.549515\pi\)
\(434\) −5.49809 −0.263917
\(435\) 0 0
\(436\) −27.3079 −1.30781
\(437\) 3.73255 0.178552
\(438\) 0 0
\(439\) −2.94169 −0.140399 −0.0701995 0.997533i \(-0.522364\pi\)
−0.0701995 + 0.997533i \(0.522364\pi\)
\(440\) −8.80074 −0.419559
\(441\) 0 0
\(442\) 10.2190 0.486069
\(443\) 4.26199 0.202493 0.101247 0.994861i \(-0.467717\pi\)
0.101247 + 0.994861i \(0.467717\pi\)
\(444\) 0 0
\(445\) 21.8543 1.03599
\(446\) 3.53967 0.167608
\(447\) 0 0
\(448\) 0.751538 0.0355068
\(449\) 13.2152 0.623666 0.311833 0.950137i \(-0.399057\pi\)
0.311833 + 0.950137i \(0.399057\pi\)
\(450\) 0 0
\(451\) −5.98005 −0.281590
\(452\) −30.2118 −1.42104
\(453\) 0 0
\(454\) 17.0295 0.799235
\(455\) 13.9876 0.655751
\(456\) 0 0
\(457\) −35.9385 −1.68113 −0.840566 0.541709i \(-0.817778\pi\)
−0.840566 + 0.541709i \(0.817778\pi\)
\(458\) 10.6841 0.499235
\(459\) 0 0
\(460\) 2.55103 0.118942
\(461\) 0.433465 0.0201885 0.0100942 0.999949i \(-0.496787\pi\)
0.0100942 + 0.999949i \(0.496787\pi\)
\(462\) 0 0
\(463\) −3.27537 −0.152219 −0.0761096 0.997099i \(-0.524250\pi\)
−0.0761096 + 0.997099i \(0.524250\pi\)
\(464\) −8.70339 −0.404045
\(465\) 0 0
\(466\) 15.3439 0.710790
\(467\) 22.0551 1.02059 0.510293 0.860000i \(-0.329537\pi\)
0.510293 + 0.860000i \(0.329537\pi\)
\(468\) 0 0
\(469\) 3.95922 0.182820
\(470\) 7.83371 0.361342
\(471\) 0 0
\(472\) 23.8050 1.09572
\(473\) −2.01664 −0.0927253
\(474\) 0 0
\(475\) −73.6054 −3.37725
\(476\) 6.33403 0.290320
\(477\) 0 0
\(478\) −14.4576 −0.661274
\(479\) 2.91609 0.133240 0.0666198 0.997778i \(-0.478779\pi\)
0.0666198 + 0.997778i \(0.478779\pi\)
\(480\) 0 0
\(481\) −38.5974 −1.75989
\(482\) −8.96379 −0.408290
\(483\) 0 0
\(484\) 15.5612 0.707326
\(485\) −23.1272 −1.05015
\(486\) 0 0
\(487\) 23.2024 1.05140 0.525702 0.850669i \(-0.323803\pi\)
0.525702 + 0.850669i \(0.323803\pi\)
\(488\) 8.46121 0.383021
\(489\) 0 0
\(490\) −2.46455 −0.111337
\(491\) −34.2673 −1.54646 −0.773231 0.634125i \(-0.781361\pi\)
−0.773231 + 0.634125i \(0.781361\pi\)
\(492\) 0 0
\(493\) 22.9888 1.03536
\(494\) 21.2060 0.954105
\(495\) 0 0
\(496\) 12.7245 0.571346
\(497\) 10.6852 0.479298
\(498\) 0 0
\(499\) −28.5434 −1.27778 −0.638890 0.769298i \(-0.720606\pi\)
−0.638890 + 0.769298i \(0.720606\pi\)
\(500\) −21.4633 −0.959869
\(501\) 0 0
\(502\) −14.5464 −0.649239
\(503\) 34.3100 1.52981 0.764904 0.644145i \(-0.222787\pi\)
0.764904 + 0.644145i \(0.222787\pi\)
\(504\) 0 0
\(505\) 69.6644 3.10003
\(506\) −0.295365 −0.0131306
\(507\) 0 0
\(508\) −1.55731 −0.0690946
\(509\) 23.2579 1.03089 0.515444 0.856923i \(-0.327627\pi\)
0.515444 + 0.856923i \(0.327627\pi\)
\(510\) 0 0
\(511\) −13.5615 −0.599924
\(512\) −16.1560 −0.713999
\(513\) 0 0
\(514\) 12.5520 0.553645
\(515\) 41.1387 1.81279
\(516\) 0 0
\(517\) 3.19072 0.140328
\(518\) 6.80067 0.298804
\(519\) 0 0
\(520\) 33.1067 1.45182
\(521\) −24.7606 −1.08478 −0.542391 0.840126i \(-0.682481\pi\)
−0.542391 + 0.840126i \(0.682481\pi\)
\(522\) 0 0
\(523\) 2.59245 0.113360 0.0566799 0.998392i \(-0.481949\pi\)
0.0566799 + 0.998392i \(0.481949\pi\)
\(524\) −30.4358 −1.32959
\(525\) 0 0
\(526\) −3.34388 −0.145800
\(527\) −33.6099 −1.46407
\(528\) 0 0
\(529\) −22.8044 −0.991497
\(530\) −0.895770 −0.0389098
\(531\) 0 0
\(532\) 13.1441 0.569869
\(533\) 22.4958 0.974401
\(534\) 0 0
\(535\) 2.14885 0.0929030
\(536\) 9.37087 0.404760
\(537\) 0 0
\(538\) −9.54465 −0.411499
\(539\) −1.00383 −0.0432379
\(540\) 0 0
\(541\) −17.7457 −0.762946 −0.381473 0.924380i \(-0.624583\pi\)
−0.381473 + 0.924380i \(0.624583\pi\)
\(542\) −7.34310 −0.315413
\(543\) 0 0
\(544\) 23.4204 1.00414
\(545\) 64.9535 2.78230
\(546\) 0 0
\(547\) 17.1810 0.734609 0.367304 0.930101i \(-0.380281\pi\)
0.367304 + 0.930101i \(0.380281\pi\)
\(548\) −10.2858 −0.439389
\(549\) 0 0
\(550\) 5.82455 0.248360
\(551\) 47.7053 2.03232
\(552\) 0 0
\(553\) 14.7485 0.627171
\(554\) 11.7380 0.498700
\(555\) 0 0
\(556\) 8.77725 0.372238
\(557\) 24.3474 1.03163 0.515815 0.856700i \(-0.327489\pi\)
0.515815 + 0.856700i \(0.327489\pi\)
\(558\) 0 0
\(559\) 7.58621 0.320863
\(560\) 5.70383 0.241031
\(561\) 0 0
\(562\) 5.01957 0.211738
\(563\) 15.3841 0.648363 0.324181 0.945995i \(-0.394911\pi\)
0.324181 + 0.945995i \(0.394911\pi\)
\(564\) 0 0
\(565\) 71.8605 3.02319
\(566\) 7.05435 0.296517
\(567\) 0 0
\(568\) 25.2903 1.06116
\(569\) −15.5356 −0.651288 −0.325644 0.945492i \(-0.605581\pi\)
−0.325644 + 0.945492i \(0.605581\pi\)
\(570\) 0 0
\(571\) 1.68607 0.0705597 0.0352799 0.999377i \(-0.488768\pi\)
0.0352799 + 0.999377i \(0.488768\pi\)
\(572\) 5.90324 0.246827
\(573\) 0 0
\(574\) −3.96364 −0.165439
\(575\) −3.85660 −0.160831
\(576\) 0 0
\(577\) −19.6600 −0.818458 −0.409229 0.912432i \(-0.634202\pi\)
−0.409229 + 0.912432i \(0.634202\pi\)
\(578\) 0.304203 0.0126532
\(579\) 0 0
\(580\) 32.6044 1.35382
\(581\) 3.52844 0.146384
\(582\) 0 0
\(583\) −0.364853 −0.0151107
\(584\) −32.0980 −1.32822
\(585\) 0 0
\(586\) −20.7709 −0.858038
\(587\) 1.52868 0.0630953 0.0315476 0.999502i \(-0.489956\pi\)
0.0315476 + 0.999502i \(0.489956\pi\)
\(588\) 0 0
\(589\) −69.7459 −2.87383
\(590\) −24.7877 −1.02049
\(591\) 0 0
\(592\) −15.7391 −0.646873
\(593\) 22.5830 0.927373 0.463686 0.885999i \(-0.346526\pi\)
0.463686 + 0.885999i \(0.346526\pi\)
\(594\) 0 0
\(595\) −15.0658 −0.617639
\(596\) 4.86242 0.199173
\(597\) 0 0
\(598\) 1.11110 0.0454364
\(599\) 39.1873 1.60115 0.800575 0.599232i \(-0.204527\pi\)
0.800575 + 0.599232i \(0.204527\pi\)
\(600\) 0 0
\(601\) 33.3105 1.35877 0.679383 0.733784i \(-0.262248\pi\)
0.679383 + 0.733784i \(0.262248\pi\)
\(602\) −1.33665 −0.0544779
\(603\) 0 0
\(604\) −21.4001 −0.870756
\(605\) −37.0131 −1.50480
\(606\) 0 0
\(607\) 25.4329 1.03229 0.516145 0.856501i \(-0.327367\pi\)
0.516145 + 0.856501i \(0.327367\pi\)
\(608\) 48.6009 1.97103
\(609\) 0 0
\(610\) −8.81048 −0.356726
\(611\) −12.0029 −0.485584
\(612\) 0 0
\(613\) −47.2216 −1.90726 −0.953631 0.300978i \(-0.902687\pi\)
−0.953631 + 0.300978i \(0.902687\pi\)
\(614\) −17.5359 −0.707693
\(615\) 0 0
\(616\) −2.37591 −0.0957281
\(617\) −6.12983 −0.246778 −0.123389 0.992358i \(-0.539376\pi\)
−0.123389 + 0.992358i \(0.539376\pi\)
\(618\) 0 0
\(619\) −24.5315 −0.986003 −0.493002 0.870028i \(-0.664100\pi\)
−0.493002 + 0.870028i \(0.664100\pi\)
\(620\) −47.6681 −1.91440
\(621\) 0 0
\(622\) −13.1580 −0.527586
\(623\) 5.89993 0.236376
\(624\) 0 0
\(625\) 7.44790 0.297916
\(626\) 7.54873 0.301708
\(627\) 0 0
\(628\) −29.5622 −1.17966
\(629\) 41.5726 1.65761
\(630\) 0 0
\(631\) −3.62627 −0.144360 −0.0721798 0.997392i \(-0.522996\pi\)
−0.0721798 + 0.997392i \(0.522996\pi\)
\(632\) 34.9075 1.38855
\(633\) 0 0
\(634\) 10.3352 0.410462
\(635\) 3.70415 0.146995
\(636\) 0 0
\(637\) 3.77620 0.149619
\(638\) −3.77502 −0.149455
\(639\) 0 0
\(640\) 40.8066 1.61302
\(641\) −39.9869 −1.57939 −0.789693 0.613502i \(-0.789760\pi\)
−0.789693 + 0.613502i \(0.789760\pi\)
\(642\) 0 0
\(643\) −28.0038 −1.10436 −0.552181 0.833724i \(-0.686204\pi\)
−0.552181 + 0.833724i \(0.686204\pi\)
\(644\) 0.688694 0.0271383
\(645\) 0 0
\(646\) −22.8407 −0.898653
\(647\) −7.74784 −0.304599 −0.152299 0.988334i \(-0.548668\pi\)
−0.152299 + 0.988334i \(0.548668\pi\)
\(648\) 0 0
\(649\) −10.0962 −0.396310
\(650\) −21.9108 −0.859414
\(651\) 0 0
\(652\) 34.7177 1.35965
\(653\) −4.00319 −0.156657 −0.0783284 0.996928i \(-0.524958\pi\)
−0.0783284 + 0.996928i \(0.524958\pi\)
\(654\) 0 0
\(655\) 72.3933 2.82864
\(656\) 9.17324 0.358155
\(657\) 0 0
\(658\) 2.11485 0.0824453
\(659\) 25.1729 0.980598 0.490299 0.871554i \(-0.336887\pi\)
0.490299 + 0.871554i \(0.336887\pi\)
\(660\) 0 0
\(661\) −16.8774 −0.656453 −0.328227 0.944599i \(-0.606451\pi\)
−0.328227 + 0.944599i \(0.606451\pi\)
\(662\) −1.72281 −0.0669587
\(663\) 0 0
\(664\) 8.35129 0.324093
\(665\) −31.2640 −1.21237
\(666\) 0 0
\(667\) 2.49955 0.0967830
\(668\) −2.45693 −0.0950615
\(669\) 0 0
\(670\) −9.75770 −0.376973
\(671\) −3.58857 −0.138535
\(672\) 0 0
\(673\) −13.8992 −0.535776 −0.267888 0.963450i \(-0.586326\pi\)
−0.267888 + 0.963450i \(0.586326\pi\)
\(674\) −19.5689 −0.753764
\(675\) 0 0
\(676\) −1.96178 −0.0754531
\(677\) 17.9526 0.689973 0.344986 0.938608i \(-0.387884\pi\)
0.344986 + 0.938608i \(0.387884\pi\)
\(678\) 0 0
\(679\) −6.24359 −0.239607
\(680\) −35.6586 −1.36745
\(681\) 0 0
\(682\) 5.51914 0.211339
\(683\) 5.72385 0.219017 0.109508 0.993986i \(-0.465072\pi\)
0.109508 + 0.993986i \(0.465072\pi\)
\(684\) 0 0
\(685\) 24.4655 0.934777
\(686\) −0.665348 −0.0254031
\(687\) 0 0
\(688\) 3.09347 0.117938
\(689\) 1.37251 0.0522883
\(690\) 0 0
\(691\) 12.8512 0.488884 0.244442 0.969664i \(-0.421395\pi\)
0.244442 + 0.969664i \(0.421395\pi\)
\(692\) −6.40662 −0.243543
\(693\) 0 0
\(694\) −2.69854 −0.102435
\(695\) −20.8772 −0.791917
\(696\) 0 0
\(697\) −24.2298 −0.917770
\(698\) 15.9414 0.603390
\(699\) 0 0
\(700\) −13.5810 −0.513312
\(701\) −44.1253 −1.66659 −0.833295 0.552829i \(-0.813548\pi\)
−0.833295 + 0.552829i \(0.813548\pi\)
\(702\) 0 0
\(703\) 86.2697 3.25372
\(704\) −0.754415 −0.0284331
\(705\) 0 0
\(706\) −13.4883 −0.507640
\(707\) 18.8071 0.707314
\(708\) 0 0
\(709\) −5.03792 −0.189203 −0.0946016 0.995515i \(-0.530158\pi\)
−0.0946016 + 0.995515i \(0.530158\pi\)
\(710\) −26.3343 −0.988309
\(711\) 0 0
\(712\) 13.9643 0.523333
\(713\) −3.65438 −0.136858
\(714\) 0 0
\(715\) −14.0412 −0.525111
\(716\) 9.01028 0.336730
\(717\) 0 0
\(718\) 19.3238 0.721156
\(719\) 23.6695 0.882724 0.441362 0.897329i \(-0.354495\pi\)
0.441362 + 0.897329i \(0.354495\pi\)
\(720\) 0 0
\(721\) 11.1061 0.413612
\(722\) −34.7563 −1.29350
\(723\) 0 0
\(724\) 10.1900 0.378708
\(725\) −49.2908 −1.83062
\(726\) 0 0
\(727\) 43.0170 1.59541 0.797707 0.603045i \(-0.206046\pi\)
0.797707 + 0.603045i \(0.206046\pi\)
\(728\) 8.93771 0.331254
\(729\) 0 0
\(730\) 33.4229 1.23704
\(731\) −8.17097 −0.302214
\(732\) 0 0
\(733\) 19.0267 0.702768 0.351384 0.936231i \(-0.385711\pi\)
0.351384 + 0.936231i \(0.385711\pi\)
\(734\) −4.05635 −0.149723
\(735\) 0 0
\(736\) 2.54648 0.0938644
\(737\) −3.97437 −0.146398
\(738\) 0 0
\(739\) 24.5099 0.901609 0.450805 0.892623i \(-0.351137\pi\)
0.450805 + 0.892623i \(0.351137\pi\)
\(740\) 58.9614 2.16746
\(741\) 0 0
\(742\) −0.241829 −0.00887781
\(743\) 46.4668 1.70470 0.852350 0.522971i \(-0.175177\pi\)
0.852350 + 0.522971i \(0.175177\pi\)
\(744\) 0 0
\(745\) −11.5655 −0.423729
\(746\) 18.1921 0.666062
\(747\) 0 0
\(748\) −6.35827 −0.232482
\(749\) 0.580119 0.0211971
\(750\) 0 0
\(751\) −52.6553 −1.92142 −0.960709 0.277556i \(-0.910476\pi\)
−0.960709 + 0.277556i \(0.910476\pi\)
\(752\) −4.89448 −0.178483
\(753\) 0 0
\(754\) 14.2009 0.517166
\(755\) 50.9012 1.85249
\(756\) 0 0
\(757\) −22.1215 −0.804019 −0.402009 0.915636i \(-0.631688\pi\)
−0.402009 + 0.915636i \(0.631688\pi\)
\(758\) −6.73623 −0.244671
\(759\) 0 0
\(760\) −73.9972 −2.68416
\(761\) −31.7423 −1.15066 −0.575329 0.817922i \(-0.695126\pi\)
−0.575329 + 0.817922i \(0.695126\pi\)
\(762\) 0 0
\(763\) 17.5353 0.634820
\(764\) −12.0044 −0.434303
\(765\) 0 0
\(766\) 2.27718 0.0822778
\(767\) 37.9799 1.37137
\(768\) 0 0
\(769\) 22.2299 0.801630 0.400815 0.916159i \(-0.368727\pi\)
0.400815 + 0.916159i \(0.368727\pi\)
\(770\) 2.47399 0.0891562
\(771\) 0 0
\(772\) −41.8517 −1.50627
\(773\) 5.30786 0.190910 0.0954552 0.995434i \(-0.469569\pi\)
0.0954552 + 0.995434i \(0.469569\pi\)
\(774\) 0 0
\(775\) 72.0639 2.58861
\(776\) −14.7776 −0.530487
\(777\) 0 0
\(778\) −11.4506 −0.410525
\(779\) −50.2807 −1.80149
\(780\) 0 0
\(781\) −10.7261 −0.383811
\(782\) −1.19675 −0.0427957
\(783\) 0 0
\(784\) 1.53985 0.0549945
\(785\) 70.3154 2.50966
\(786\) 0 0
\(787\) 25.0906 0.894383 0.447191 0.894438i \(-0.352424\pi\)
0.447191 + 0.894438i \(0.352424\pi\)
\(788\) 14.2969 0.509306
\(789\) 0 0
\(790\) −36.3485 −1.29322
\(791\) 19.4000 0.689783
\(792\) 0 0
\(793\) 13.4995 0.479381
\(794\) 14.6025 0.518222
\(795\) 0 0
\(796\) 24.3333 0.862471
\(797\) −19.1556 −0.678528 −0.339264 0.940691i \(-0.610178\pi\)
−0.339264 + 0.940691i \(0.610178\pi\)
\(798\) 0 0
\(799\) 12.9281 0.457363
\(800\) −50.2162 −1.77541
\(801\) 0 0
\(802\) −12.2800 −0.433621
\(803\) 13.6134 0.480406
\(804\) 0 0
\(805\) −1.63810 −0.0577353
\(806\) −20.7619 −0.731307
\(807\) 0 0
\(808\) 44.5136 1.56598
\(809\) −3.57506 −0.125692 −0.0628462 0.998023i \(-0.520018\pi\)
−0.0628462 + 0.998023i \(0.520018\pi\)
\(810\) 0 0
\(811\) 7.26875 0.255240 0.127620 0.991823i \(-0.459266\pi\)
0.127620 + 0.991823i \(0.459266\pi\)
\(812\) 8.80212 0.308894
\(813\) 0 0
\(814\) −6.82670 −0.239276
\(815\) −82.5780 −2.89258
\(816\) 0 0
\(817\) −16.9561 −0.593217
\(818\) 7.84228 0.274199
\(819\) 0 0
\(820\) −34.3645 −1.20006
\(821\) 50.6189 1.76661 0.883306 0.468797i \(-0.155312\pi\)
0.883306 + 0.468797i \(0.155312\pi\)
\(822\) 0 0
\(823\) −23.9420 −0.834565 −0.417282 0.908777i \(-0.637017\pi\)
−0.417282 + 0.908777i \(0.637017\pi\)
\(824\) 26.2864 0.915731
\(825\) 0 0
\(826\) −6.69186 −0.232840
\(827\) −6.33527 −0.220299 −0.110150 0.993915i \(-0.535133\pi\)
−0.110150 + 0.993915i \(0.535133\pi\)
\(828\) 0 0
\(829\) −15.8957 −0.552080 −0.276040 0.961146i \(-0.589022\pi\)
−0.276040 + 0.961146i \(0.589022\pi\)
\(830\) −8.69602 −0.301843
\(831\) 0 0
\(832\) 2.83796 0.0983887
\(833\) −4.06728 −0.140923
\(834\) 0 0
\(835\) 5.84395 0.202238
\(836\) −13.1944 −0.456338
\(837\) 0 0
\(838\) 9.84012 0.339921
\(839\) −10.1898 −0.351790 −0.175895 0.984409i \(-0.556282\pi\)
−0.175895 + 0.984409i \(0.556282\pi\)
\(840\) 0 0
\(841\) 2.94649 0.101603
\(842\) 9.62944 0.331852
\(843\) 0 0
\(844\) −0.882125 −0.0303640
\(845\) 4.66621 0.160522
\(846\) 0 0
\(847\) −9.99233 −0.343341
\(848\) 0.559675 0.0192193
\(849\) 0 0
\(850\) 23.5998 0.809465
\(851\) 4.52015 0.154949
\(852\) 0 0
\(853\) 33.6392 1.15178 0.575892 0.817526i \(-0.304655\pi\)
0.575892 + 0.817526i \(0.304655\pi\)
\(854\) −2.37854 −0.0813920
\(855\) 0 0
\(856\) 1.37306 0.0469301
\(857\) 37.5136 1.28144 0.640721 0.767774i \(-0.278636\pi\)
0.640721 + 0.767774i \(0.278636\pi\)
\(858\) 0 0
\(859\) 17.2642 0.589048 0.294524 0.955644i \(-0.404839\pi\)
0.294524 + 0.955644i \(0.404839\pi\)
\(860\) −11.5887 −0.395171
\(861\) 0 0
\(862\) −11.3339 −0.386036
\(863\) −46.7804 −1.59242 −0.796212 0.605017i \(-0.793166\pi\)
−0.796212 + 0.605017i \(0.793166\pi\)
\(864\) 0 0
\(865\) 15.2385 0.518125
\(866\) 4.29002 0.145781
\(867\) 0 0
\(868\) −12.8688 −0.436796
\(869\) −14.8050 −0.502224
\(870\) 0 0
\(871\) 14.9508 0.506589
\(872\) 41.5034 1.40548
\(873\) 0 0
\(874\) −2.48344 −0.0840038
\(875\) 13.7823 0.465926
\(876\) 0 0
\(877\) 7.19645 0.243007 0.121503 0.992591i \(-0.461228\pi\)
0.121503 + 0.992591i \(0.461228\pi\)
\(878\) 1.95725 0.0660539
\(879\) 0 0
\(880\) −5.72566 −0.193012
\(881\) −20.8602 −0.702797 −0.351399 0.936226i \(-0.614294\pi\)
−0.351399 + 0.936226i \(0.614294\pi\)
\(882\) 0 0
\(883\) 26.7712 0.900922 0.450461 0.892796i \(-0.351260\pi\)
0.450461 + 0.892796i \(0.351260\pi\)
\(884\) 23.9186 0.804469
\(885\) 0 0
\(886\) −2.83571 −0.0952675
\(887\) 25.5549 0.858050 0.429025 0.903292i \(-0.358857\pi\)
0.429025 + 0.903292i \(0.358857\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −14.5407 −0.487405
\(891\) 0 0
\(892\) 8.28494 0.277400
\(893\) 26.8278 0.897758
\(894\) 0 0
\(895\) −21.4315 −0.716374
\(896\) 11.0164 0.368033
\(897\) 0 0
\(898\) −8.79274 −0.293417
\(899\) −46.7062 −1.55774
\(900\) 0 0
\(901\) −1.47830 −0.0492494
\(902\) 3.97881 0.132480
\(903\) 0 0
\(904\) 45.9168 1.52717
\(905\) −24.2375 −0.805682
\(906\) 0 0
\(907\) −6.56205 −0.217889 −0.108945 0.994048i \(-0.534747\pi\)
−0.108945 + 0.994048i \(0.534747\pi\)
\(908\) 39.8593 1.32278
\(909\) 0 0
\(910\) −9.30665 −0.308513
\(911\) −34.3146 −1.13689 −0.568447 0.822720i \(-0.692456\pi\)
−0.568447 + 0.822720i \(0.692456\pi\)
\(912\) 0 0
\(913\) −3.54195 −0.117221
\(914\) 23.9116 0.790926
\(915\) 0 0
\(916\) 25.0072 0.826260
\(917\) 19.5438 0.645393
\(918\) 0 0
\(919\) 33.0506 1.09024 0.545119 0.838359i \(-0.316485\pi\)
0.545119 + 0.838359i \(0.316485\pi\)
\(920\) −3.87713 −0.127825
\(921\) 0 0
\(922\) −0.288405 −0.00949811
\(923\) 40.3496 1.32812
\(924\) 0 0
\(925\) −89.1369 −2.93080
\(926\) 2.17926 0.0716149
\(927\) 0 0
\(928\) 32.5462 1.06838
\(929\) 53.9455 1.76989 0.884947 0.465691i \(-0.154194\pi\)
0.884947 + 0.465691i \(0.154194\pi\)
\(930\) 0 0
\(931\) −8.44025 −0.276618
\(932\) 35.9138 1.17640
\(933\) 0 0
\(934\) −14.6743 −0.480157
\(935\) 15.1235 0.494592
\(936\) 0 0
\(937\) 13.0572 0.426559 0.213279 0.976991i \(-0.431586\pi\)
0.213279 + 0.976991i \(0.431586\pi\)
\(938\) −2.63426 −0.0860115
\(939\) 0 0
\(940\) 18.3356 0.598041
\(941\) 3.15078 0.102713 0.0513563 0.998680i \(-0.483646\pi\)
0.0513563 + 0.998680i \(0.483646\pi\)
\(942\) 0 0
\(943\) −2.63449 −0.0857907
\(944\) 15.4873 0.504068
\(945\) 0 0
\(946\) 1.34177 0.0436246
\(947\) −46.2541 −1.50306 −0.751528 0.659702i \(-0.770683\pi\)
−0.751528 + 0.659702i \(0.770683\pi\)
\(948\) 0 0
\(949\) −51.2109 −1.66238
\(950\) 48.9732 1.58890
\(951\) 0 0
\(952\) −9.62665 −0.312002
\(953\) 13.1147 0.424826 0.212413 0.977180i \(-0.431868\pi\)
0.212413 + 0.977180i \(0.431868\pi\)
\(954\) 0 0
\(955\) 28.5531 0.923956
\(956\) −33.8393 −1.09444
\(957\) 0 0
\(958\) −1.94022 −0.0626855
\(959\) 6.60487 0.213282
\(960\) 0 0
\(961\) 37.2851 1.20275
\(962\) 25.6807 0.827980
\(963\) 0 0
\(964\) −20.9806 −0.675741
\(965\) 99.5465 3.20452
\(966\) 0 0
\(967\) 31.4093 1.01005 0.505027 0.863103i \(-0.331482\pi\)
0.505027 + 0.863103i \(0.331482\pi\)
\(968\) −23.6503 −0.760151
\(969\) 0 0
\(970\) 15.3877 0.494068
\(971\) −37.6772 −1.20912 −0.604560 0.796560i \(-0.706651\pi\)
−0.604560 + 0.796560i \(0.706651\pi\)
\(972\) 0 0
\(973\) −5.63615 −0.180687
\(974\) −15.4377 −0.494656
\(975\) 0 0
\(976\) 5.50477 0.176203
\(977\) −27.2703 −0.872454 −0.436227 0.899837i \(-0.643686\pi\)
−0.436227 + 0.899837i \(0.643686\pi\)
\(978\) 0 0
\(979\) −5.92251 −0.189284
\(980\) −5.76853 −0.184269
\(981\) 0 0
\(982\) 22.7997 0.727567
\(983\) −39.9820 −1.27523 −0.637614 0.770356i \(-0.720079\pi\)
−0.637614 + 0.770356i \(0.720079\pi\)
\(984\) 0 0
\(985\) −34.0060 −1.08352
\(986\) −15.2955 −0.487109
\(987\) 0 0
\(988\) 49.6348 1.57909
\(989\) −0.888423 −0.0282502
\(990\) 0 0
\(991\) 34.6355 1.10023 0.550116 0.835088i \(-0.314584\pi\)
0.550116 + 0.835088i \(0.314584\pi\)
\(992\) −47.5831 −1.51076
\(993\) 0 0
\(994\) −7.10939 −0.225496
\(995\) −57.8782 −1.83486
\(996\) 0 0
\(997\) −15.7082 −0.497483 −0.248742 0.968570i \(-0.580017\pi\)
−0.248742 + 0.968570i \(0.580017\pi\)
\(998\) 18.9913 0.601160
\(999\) 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 \(a_p\))