Properties

Label 8046.2.a.l.1.12
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(4.25305\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+4.25305 q^{5}\) \(+2.10378 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+4.25305 q^{5}\) \(+2.10378 q^{7}\) \(-1.00000 q^{8}\) \(-4.25305 q^{10}\) \(-4.67709 q^{11}\) \(+0.547094 q^{13}\) \(-2.10378 q^{14}\) \(+1.00000 q^{16}\) \(-0.524967 q^{17}\) \(-8.11080 q^{19}\) \(+4.25305 q^{20}\) \(+4.67709 q^{22}\) \(+6.00153 q^{23}\) \(+13.0884 q^{25}\) \(-0.547094 q^{26}\) \(+2.10378 q^{28}\) \(+8.07750 q^{29}\) \(+4.87410 q^{31}\) \(-1.00000 q^{32}\) \(+0.524967 q^{34}\) \(+8.94750 q^{35}\) \(-10.1411 q^{37}\) \(+8.11080 q^{38}\) \(-4.25305 q^{40}\) \(-2.58901 q^{41}\) \(+7.72324 q^{43}\) \(-4.67709 q^{44}\) \(-6.00153 q^{46}\) \(-5.67930 q^{47}\) \(-2.57409 q^{49}\) \(-13.0884 q^{50}\) \(+0.547094 q^{52}\) \(-0.544241 q^{53}\) \(-19.8919 q^{55}\) \(-2.10378 q^{56}\) \(-8.07750 q^{58}\) \(+7.68172 q^{59}\) \(+3.68590 q^{61}\) \(-4.87410 q^{62}\) \(+1.00000 q^{64}\) \(+2.32682 q^{65}\) \(+0.0374969 q^{67}\) \(-0.524967 q^{68}\) \(-8.94750 q^{70}\) \(+13.0756 q^{71}\) \(+14.3053 q^{73}\) \(+10.1411 q^{74}\) \(-8.11080 q^{76}\) \(-9.83959 q^{77}\) \(-4.75832 q^{79}\) \(+4.25305 q^{80}\) \(+2.58901 q^{82}\) \(-7.02674 q^{83}\) \(-2.23271 q^{85}\) \(-7.72324 q^{86}\) \(+4.67709 q^{88}\) \(-15.5764 q^{89}\) \(+1.15097 q^{91}\) \(+6.00153 q^{92}\) \(+5.67930 q^{94}\) \(-34.4956 q^{95}\) \(+8.91148 q^{97}\) \(+2.57409 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 4.25305 1.90202 0.951011 0.309158i \(-0.100047\pi\)
0.951011 + 0.309158i \(0.100047\pi\)
\(6\) 0 0
\(7\) 2.10378 0.795156 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −4.25305 −1.34493
\(11\) −4.67709 −1.41020 −0.705098 0.709110i \(-0.749097\pi\)
−0.705098 + 0.709110i \(0.749097\pi\)
\(12\) 0 0
\(13\) 0.547094 0.151736 0.0758682 0.997118i \(-0.475827\pi\)
0.0758682 + 0.997118i \(0.475827\pi\)
\(14\) −2.10378 −0.562260
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.524967 −0.127323 −0.0636616 0.997972i \(-0.520278\pi\)
−0.0636616 + 0.997972i \(0.520278\pi\)
\(18\) 0 0
\(19\) −8.11080 −1.86074 −0.930372 0.366617i \(-0.880516\pi\)
−0.930372 + 0.366617i \(0.880516\pi\)
\(20\) 4.25305 0.951011
\(21\) 0 0
\(22\) 4.67709 0.997159
\(23\) 6.00153 1.25141 0.625703 0.780061i \(-0.284812\pi\)
0.625703 + 0.780061i \(0.284812\pi\)
\(24\) 0 0
\(25\) 13.0884 2.61768
\(26\) −0.547094 −0.107294
\(27\) 0 0
\(28\) 2.10378 0.397578
\(29\) 8.07750 1.49995 0.749977 0.661464i \(-0.230065\pi\)
0.749977 + 0.661464i \(0.230065\pi\)
\(30\) 0 0
\(31\) 4.87410 0.875414 0.437707 0.899118i \(-0.355791\pi\)
0.437707 + 0.899118i \(0.355791\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0.524967 0.0900311
\(35\) 8.94750 1.51240
\(36\) 0 0
\(37\) −10.1411 −1.66718 −0.833591 0.552382i \(-0.813719\pi\)
−0.833591 + 0.552382i \(0.813719\pi\)
\(38\) 8.11080 1.31574
\(39\) 0 0
\(40\) −4.25305 −0.672466
\(41\) −2.58901 −0.404336 −0.202168 0.979351i \(-0.564799\pi\)
−0.202168 + 0.979351i \(0.564799\pi\)
\(42\) 0 0
\(43\) 7.72324 1.17778 0.588892 0.808212i \(-0.299564\pi\)
0.588892 + 0.808212i \(0.299564\pi\)
\(44\) −4.67709 −0.705098
\(45\) 0 0
\(46\) −6.00153 −0.884878
\(47\) −5.67930 −0.828412 −0.414206 0.910183i \(-0.635941\pi\)
−0.414206 + 0.910183i \(0.635941\pi\)
\(48\) 0 0
\(49\) −2.57409 −0.367727
\(50\) −13.0884 −1.85098
\(51\) 0 0
\(52\) 0.547094 0.0758682
\(53\) −0.544241 −0.0747573 −0.0373786 0.999301i \(-0.511901\pi\)
−0.0373786 + 0.999301i \(0.511901\pi\)
\(54\) 0 0
\(55\) −19.8919 −2.68222
\(56\) −2.10378 −0.281130
\(57\) 0 0
\(58\) −8.07750 −1.06063
\(59\) 7.68172 1.00007 0.500037 0.866004i \(-0.333320\pi\)
0.500037 + 0.866004i \(0.333320\pi\)
\(60\) 0 0
\(61\) 3.68590 0.471931 0.235966 0.971761i \(-0.424175\pi\)
0.235966 + 0.971761i \(0.424175\pi\)
\(62\) −4.87410 −0.619011
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.32682 0.288606
\(66\) 0 0
\(67\) 0.0374969 0.00458098 0.00229049 0.999997i \(-0.499271\pi\)
0.00229049 + 0.999997i \(0.499271\pi\)
\(68\) −0.524967 −0.0636616
\(69\) 0 0
\(70\) −8.94750 −1.06943
\(71\) 13.0756 1.55179 0.775894 0.630863i \(-0.217299\pi\)
0.775894 + 0.630863i \(0.217299\pi\)
\(72\) 0 0
\(73\) 14.3053 1.67431 0.837155 0.546965i \(-0.184217\pi\)
0.837155 + 0.546965i \(0.184217\pi\)
\(74\) 10.1411 1.17888
\(75\) 0 0
\(76\) −8.11080 −0.930372
\(77\) −9.83959 −1.12133
\(78\) 0 0
\(79\) −4.75832 −0.535353 −0.267676 0.963509i \(-0.586256\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(80\) 4.25305 0.475505
\(81\) 0 0
\(82\) 2.58901 0.285909
\(83\) −7.02674 −0.771284 −0.385642 0.922648i \(-0.626020\pi\)
−0.385642 + 0.922648i \(0.626020\pi\)
\(84\) 0 0
\(85\) −2.23271 −0.242172
\(86\) −7.72324 −0.832818
\(87\) 0 0
\(88\) 4.67709 0.498579
\(89\) −15.5764 −1.65110 −0.825548 0.564332i \(-0.809134\pi\)
−0.825548 + 0.564332i \(0.809134\pi\)
\(90\) 0 0
\(91\) 1.15097 0.120654
\(92\) 6.00153 0.625703
\(93\) 0 0
\(94\) 5.67930 0.585776
\(95\) −34.4956 −3.53917
\(96\) 0 0
\(97\) 8.91148 0.904823 0.452412 0.891809i \(-0.350564\pi\)
0.452412 + 0.891809i \(0.350564\pi\)
\(98\) 2.57409 0.260022
\(99\) 0 0
\(100\) 13.0884 1.30884
\(101\) 10.7801 1.07266 0.536329 0.844009i \(-0.319810\pi\)
0.536329 + 0.844009i \(0.319810\pi\)
\(102\) 0 0
\(103\) 1.83807 0.181110 0.0905552 0.995891i \(-0.471136\pi\)
0.0905552 + 0.995891i \(0.471136\pi\)
\(104\) −0.547094 −0.0536469
\(105\) 0 0
\(106\) 0.544241 0.0528614
\(107\) 17.1840 1.66124 0.830619 0.556841i \(-0.187987\pi\)
0.830619 + 0.556841i \(0.187987\pi\)
\(108\) 0 0
\(109\) −3.72734 −0.357015 −0.178507 0.983939i \(-0.557127\pi\)
−0.178507 + 0.983939i \(0.557127\pi\)
\(110\) 19.8919 1.89662
\(111\) 0 0
\(112\) 2.10378 0.198789
\(113\) 20.5365 1.93191 0.965955 0.258712i \(-0.0832979\pi\)
0.965955 + 0.258712i \(0.0832979\pi\)
\(114\) 0 0
\(115\) 25.5248 2.38020
\(116\) 8.07750 0.749977
\(117\) 0 0
\(118\) −7.68172 −0.707160
\(119\) −1.10442 −0.101242
\(120\) 0 0
\(121\) 10.8752 0.988652
\(122\) −3.68590 −0.333706
\(123\) 0 0
\(124\) 4.87410 0.437707
\(125\) 34.4005 3.07687
\(126\) 0 0
\(127\) −17.7968 −1.57921 −0.789606 0.613614i \(-0.789715\pi\)
−0.789606 + 0.613614i \(0.789715\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −2.32682 −0.204075
\(131\) 19.4735 1.70141 0.850704 0.525645i \(-0.176176\pi\)
0.850704 + 0.525645i \(0.176176\pi\)
\(132\) 0 0
\(133\) −17.0634 −1.47958
\(134\) −0.0374969 −0.00323924
\(135\) 0 0
\(136\) 0.524967 0.0450156
\(137\) 8.78583 0.750624 0.375312 0.926899i \(-0.377536\pi\)
0.375312 + 0.926899i \(0.377536\pi\)
\(138\) 0 0
\(139\) 2.73608 0.232071 0.116036 0.993245i \(-0.462981\pi\)
0.116036 + 0.993245i \(0.462981\pi\)
\(140\) 8.94750 0.756202
\(141\) 0 0
\(142\) −13.0756 −1.09728
\(143\) −2.55881 −0.213978
\(144\) 0 0
\(145\) 34.3540 2.85294
\(146\) −14.3053 −1.18392
\(147\) 0 0
\(148\) −10.1411 −0.833591
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) 2.34994 0.191235 0.0956175 0.995418i \(-0.469517\pi\)
0.0956175 + 0.995418i \(0.469517\pi\)
\(152\) 8.11080 0.657872
\(153\) 0 0
\(154\) 9.83959 0.792897
\(155\) 20.7298 1.66506
\(156\) 0 0
\(157\) 5.88317 0.469528 0.234764 0.972052i \(-0.424568\pi\)
0.234764 + 0.972052i \(0.424568\pi\)
\(158\) 4.75832 0.378552
\(159\) 0 0
\(160\) −4.25305 −0.336233
\(161\) 12.6259 0.995063
\(162\) 0 0
\(163\) 0.559443 0.0438190 0.0219095 0.999760i \(-0.493025\pi\)
0.0219095 + 0.999760i \(0.493025\pi\)
\(164\) −2.58901 −0.202168
\(165\) 0 0
\(166\) 7.02674 0.545380
\(167\) 12.8886 0.997349 0.498674 0.866789i \(-0.333820\pi\)
0.498674 + 0.866789i \(0.333820\pi\)
\(168\) 0 0
\(169\) −12.7007 −0.976976
\(170\) 2.23271 0.171241
\(171\) 0 0
\(172\) 7.72324 0.588892
\(173\) 15.4812 1.17701 0.588506 0.808493i \(-0.299716\pi\)
0.588506 + 0.808493i \(0.299716\pi\)
\(174\) 0 0
\(175\) 27.5352 2.08147
\(176\) −4.67709 −0.352549
\(177\) 0 0
\(178\) 15.5764 1.16750
\(179\) −18.5958 −1.38991 −0.694957 0.719051i \(-0.744577\pi\)
−0.694957 + 0.719051i \(0.744577\pi\)
\(180\) 0 0
\(181\) 12.7960 0.951123 0.475561 0.879683i \(-0.342245\pi\)
0.475561 + 0.879683i \(0.342245\pi\)
\(182\) −1.15097 −0.0853154
\(183\) 0 0
\(184\) −6.00153 −0.442439
\(185\) −43.1305 −3.17102
\(186\) 0 0
\(187\) 2.45532 0.179551
\(188\) −5.67930 −0.414206
\(189\) 0 0
\(190\) 34.4956 2.50257
\(191\) −5.71191 −0.413300 −0.206650 0.978415i \(-0.566256\pi\)
−0.206650 + 0.978415i \(0.566256\pi\)
\(192\) 0 0
\(193\) 5.85587 0.421515 0.210758 0.977538i \(-0.432407\pi\)
0.210758 + 0.977538i \(0.432407\pi\)
\(194\) −8.91148 −0.639807
\(195\) 0 0
\(196\) −2.57409 −0.183864
\(197\) 20.7385 1.47756 0.738778 0.673949i \(-0.235403\pi\)
0.738778 + 0.673949i \(0.235403\pi\)
\(198\) 0 0
\(199\) −1.14505 −0.0811706 −0.0405853 0.999176i \(-0.512922\pi\)
−0.0405853 + 0.999176i \(0.512922\pi\)
\(200\) −13.0884 −0.925491
\(201\) 0 0
\(202\) −10.7801 −0.758484
\(203\) 16.9933 1.19270
\(204\) 0 0
\(205\) −11.0112 −0.769055
\(206\) −1.83807 −0.128064
\(207\) 0 0
\(208\) 0.547094 0.0379341
\(209\) 37.9349 2.62401
\(210\) 0 0
\(211\) 3.55721 0.244888 0.122444 0.992475i \(-0.460927\pi\)
0.122444 + 0.992475i \(0.460927\pi\)
\(212\) −0.544241 −0.0373786
\(213\) 0 0
\(214\) −17.1840 −1.17467
\(215\) 32.8473 2.24017
\(216\) 0 0
\(217\) 10.2540 0.696090
\(218\) 3.72734 0.252447
\(219\) 0 0
\(220\) −19.8919 −1.34111
\(221\) −0.287206 −0.0193196
\(222\) 0 0
\(223\) −5.36433 −0.359222 −0.179611 0.983738i \(-0.557484\pi\)
−0.179611 + 0.983738i \(0.557484\pi\)
\(224\) −2.10378 −0.140565
\(225\) 0 0
\(226\) −20.5365 −1.36607
\(227\) 11.7698 0.781188 0.390594 0.920563i \(-0.372270\pi\)
0.390594 + 0.920563i \(0.372270\pi\)
\(228\) 0 0
\(229\) −23.6187 −1.56077 −0.780384 0.625301i \(-0.784976\pi\)
−0.780384 + 0.625301i \(0.784976\pi\)
\(230\) −25.5248 −1.68306
\(231\) 0 0
\(232\) −8.07750 −0.530314
\(233\) 27.4243 1.79662 0.898312 0.439358i \(-0.144794\pi\)
0.898312 + 0.439358i \(0.144794\pi\)
\(234\) 0 0
\(235\) −24.1544 −1.57566
\(236\) 7.68172 0.500037
\(237\) 0 0
\(238\) 1.10442 0.0715888
\(239\) −19.9867 −1.29283 −0.646416 0.762985i \(-0.723733\pi\)
−0.646416 + 0.762985i \(0.723733\pi\)
\(240\) 0 0
\(241\) 1.69539 0.109209 0.0546047 0.998508i \(-0.482610\pi\)
0.0546047 + 0.998508i \(0.482610\pi\)
\(242\) −10.8752 −0.699082
\(243\) 0 0
\(244\) 3.68590 0.235966
\(245\) −10.9477 −0.699425
\(246\) 0 0
\(247\) −4.43736 −0.282343
\(248\) −4.87410 −0.309505
\(249\) 0 0
\(250\) −34.4005 −2.17568
\(251\) −25.2458 −1.59350 −0.796752 0.604307i \(-0.793450\pi\)
−0.796752 + 0.604307i \(0.793450\pi\)
\(252\) 0 0
\(253\) −28.0697 −1.76473
\(254\) 17.7968 1.11667
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −22.0313 −1.37428 −0.687138 0.726527i \(-0.741133\pi\)
−0.687138 + 0.726527i \(0.741133\pi\)
\(258\) 0 0
\(259\) −21.3346 −1.32567
\(260\) 2.32682 0.144303
\(261\) 0 0
\(262\) −19.4735 −1.20308
\(263\) −28.4131 −1.75203 −0.876013 0.482287i \(-0.839806\pi\)
−0.876013 + 0.482287i \(0.839806\pi\)
\(264\) 0 0
\(265\) −2.31468 −0.142190
\(266\) 17.0634 1.04622
\(267\) 0 0
\(268\) 0.0374969 0.00229049
\(269\) 16.6698 1.01638 0.508189 0.861245i \(-0.330315\pi\)
0.508189 + 0.861245i \(0.330315\pi\)
\(270\) 0 0
\(271\) 8.61463 0.523302 0.261651 0.965163i \(-0.415733\pi\)
0.261651 + 0.965163i \(0.415733\pi\)
\(272\) −0.524967 −0.0318308
\(273\) 0 0
\(274\) −8.78583 −0.530771
\(275\) −61.2157 −3.69145
\(276\) 0 0
\(277\) 4.78762 0.287660 0.143830 0.989602i \(-0.454058\pi\)
0.143830 + 0.989602i \(0.454058\pi\)
\(278\) −2.73608 −0.164099
\(279\) 0 0
\(280\) −8.94750 −0.534715
\(281\) 1.93881 0.115660 0.0578298 0.998326i \(-0.481582\pi\)
0.0578298 + 0.998326i \(0.481582\pi\)
\(282\) 0 0
\(283\) −28.3283 −1.68394 −0.841972 0.539521i \(-0.818606\pi\)
−0.841972 + 0.539521i \(0.818606\pi\)
\(284\) 13.0756 0.775894
\(285\) 0 0
\(286\) 2.55881 0.151305
\(287\) −5.44672 −0.321510
\(288\) 0 0
\(289\) −16.7244 −0.983789
\(290\) −34.3540 −2.01734
\(291\) 0 0
\(292\) 14.3053 0.837155
\(293\) 24.7952 1.44855 0.724275 0.689511i \(-0.242174\pi\)
0.724275 + 0.689511i \(0.242174\pi\)
\(294\) 0 0
\(295\) 32.6707 1.90216
\(296\) 10.1411 0.589438
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 3.28340 0.189884
\(300\) 0 0
\(301\) 16.2480 0.936521
\(302\) −2.34994 −0.135224
\(303\) 0 0
\(304\) −8.11080 −0.465186
\(305\) 15.6763 0.897623
\(306\) 0 0
\(307\) −15.6307 −0.892093 −0.446046 0.895010i \(-0.647168\pi\)
−0.446046 + 0.895010i \(0.647168\pi\)
\(308\) −9.83959 −0.560663
\(309\) 0 0
\(310\) −20.7298 −1.17737
\(311\) −0.803622 −0.0455692 −0.0227846 0.999740i \(-0.507253\pi\)
−0.0227846 + 0.999740i \(0.507253\pi\)
\(312\) 0 0
\(313\) −20.3580 −1.15070 −0.575350 0.817907i \(-0.695134\pi\)
−0.575350 + 0.817907i \(0.695134\pi\)
\(314\) −5.88317 −0.332006
\(315\) 0 0
\(316\) −4.75832 −0.267676
\(317\) 23.4979 1.31977 0.659886 0.751365i \(-0.270604\pi\)
0.659886 + 0.751365i \(0.270604\pi\)
\(318\) 0 0
\(319\) −37.7792 −2.11523
\(320\) 4.25305 0.237753
\(321\) 0 0
\(322\) −12.6259 −0.703616
\(323\) 4.25790 0.236916
\(324\) 0 0
\(325\) 7.16059 0.397198
\(326\) −0.559443 −0.0309847
\(327\) 0 0
\(328\) 2.58901 0.142954
\(329\) −11.9480 −0.658716
\(330\) 0 0
\(331\) 3.55426 0.195360 0.0976799 0.995218i \(-0.468858\pi\)
0.0976799 + 0.995218i \(0.468858\pi\)
\(332\) −7.02674 −0.385642
\(333\) 0 0
\(334\) −12.8886 −0.705232
\(335\) 0.159476 0.00871312
\(336\) 0 0
\(337\) 23.3744 1.27328 0.636642 0.771159i \(-0.280323\pi\)
0.636642 + 0.771159i \(0.280323\pi\)
\(338\) 12.7007 0.690826
\(339\) 0 0
\(340\) −2.23271 −0.121086
\(341\) −22.7966 −1.23450
\(342\) 0 0
\(343\) −20.1418 −1.08756
\(344\) −7.72324 −0.416409
\(345\) 0 0
\(346\) −15.4812 −0.832274
\(347\) −14.6186 −0.784768 −0.392384 0.919801i \(-0.628350\pi\)
−0.392384 + 0.919801i \(0.628350\pi\)
\(348\) 0 0
\(349\) 19.9685 1.06889 0.534443 0.845204i \(-0.320521\pi\)
0.534443 + 0.845204i \(0.320521\pi\)
\(350\) −27.5352 −1.47182
\(351\) 0 0
\(352\) 4.67709 0.249290
\(353\) 32.4912 1.72933 0.864667 0.502346i \(-0.167530\pi\)
0.864667 + 0.502346i \(0.167530\pi\)
\(354\) 0 0
\(355\) 55.6112 2.95153
\(356\) −15.5764 −0.825548
\(357\) 0 0
\(358\) 18.5958 0.982818
\(359\) 11.0126 0.581222 0.290611 0.956841i \(-0.406141\pi\)
0.290611 + 0.956841i \(0.406141\pi\)
\(360\) 0 0
\(361\) 46.7850 2.46237
\(362\) −12.7960 −0.672545
\(363\) 0 0
\(364\) 1.15097 0.0603271
\(365\) 60.8412 3.18457
\(366\) 0 0
\(367\) −32.4535 −1.69406 −0.847031 0.531544i \(-0.821612\pi\)
−0.847031 + 0.531544i \(0.821612\pi\)
\(368\) 6.00153 0.312852
\(369\) 0 0
\(370\) 43.1305 2.24225
\(371\) −1.14497 −0.0594437
\(372\) 0 0
\(373\) 8.06417 0.417547 0.208773 0.977964i \(-0.433053\pi\)
0.208773 + 0.977964i \(0.433053\pi\)
\(374\) −2.45532 −0.126962
\(375\) 0 0
\(376\) 5.67930 0.292888
\(377\) 4.41915 0.227598
\(378\) 0 0
\(379\) 2.31863 0.119100 0.0595499 0.998225i \(-0.481033\pi\)
0.0595499 + 0.998225i \(0.481033\pi\)
\(380\) −34.4956 −1.76959
\(381\) 0 0
\(382\) 5.71191 0.292247
\(383\) 32.0190 1.63610 0.818048 0.575150i \(-0.195056\pi\)
0.818048 + 0.575150i \(0.195056\pi\)
\(384\) 0 0
\(385\) −41.8483 −2.13278
\(386\) −5.85587 −0.298056
\(387\) 0 0
\(388\) 8.91148 0.452412
\(389\) 5.77502 0.292805 0.146403 0.989225i \(-0.453231\pi\)
0.146403 + 0.989225i \(0.453231\pi\)
\(390\) 0 0
\(391\) −3.15061 −0.159333
\(392\) 2.57409 0.130011
\(393\) 0 0
\(394\) −20.7385 −1.04479
\(395\) −20.2374 −1.01825
\(396\) 0 0
\(397\) 1.60163 0.0803833 0.0401917 0.999192i \(-0.487203\pi\)
0.0401917 + 0.999192i \(0.487203\pi\)
\(398\) 1.14505 0.0573963
\(399\) 0 0
\(400\) 13.0884 0.654421
\(401\) 32.9876 1.64732 0.823662 0.567081i \(-0.191928\pi\)
0.823662 + 0.567081i \(0.191928\pi\)
\(402\) 0 0
\(403\) 2.66659 0.132832
\(404\) 10.7801 0.536329
\(405\) 0 0
\(406\) −16.9933 −0.843364
\(407\) 47.4307 2.35105
\(408\) 0 0
\(409\) −20.9325 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(410\) 11.0112 0.543804
\(411\) 0 0
\(412\) 1.83807 0.0905552
\(413\) 16.1607 0.795215
\(414\) 0 0
\(415\) −29.8850 −1.46700
\(416\) −0.547094 −0.0268235
\(417\) 0 0
\(418\) −37.9349 −1.85546
\(419\) −18.6183 −0.909562 −0.454781 0.890603i \(-0.650282\pi\)
−0.454781 + 0.890603i \(0.650282\pi\)
\(420\) 0 0
\(421\) −29.0112 −1.41392 −0.706960 0.707254i \(-0.749934\pi\)
−0.706960 + 0.707254i \(0.749934\pi\)
\(422\) −3.55721 −0.173162
\(423\) 0 0
\(424\) 0.544241 0.0264307
\(425\) −6.87099 −0.333292
\(426\) 0 0
\(427\) 7.75434 0.375259
\(428\) 17.1840 0.830619
\(429\) 0 0
\(430\) −32.8473 −1.58404
\(431\) −20.0767 −0.967059 −0.483530 0.875328i \(-0.660645\pi\)
−0.483530 + 0.875328i \(0.660645\pi\)
\(432\) 0 0
\(433\) −26.1410 −1.25626 −0.628129 0.778109i \(-0.716179\pi\)
−0.628129 + 0.778109i \(0.716179\pi\)
\(434\) −10.2540 −0.492210
\(435\) 0 0
\(436\) −3.72734 −0.178507
\(437\) −48.6772 −2.32855
\(438\) 0 0
\(439\) 1.54942 0.0739497 0.0369749 0.999316i \(-0.488228\pi\)
0.0369749 + 0.999316i \(0.488228\pi\)
\(440\) 19.8919 0.948309
\(441\) 0 0
\(442\) 0.287206 0.0136610
\(443\) −7.35831 −0.349604 −0.174802 0.984604i \(-0.555929\pi\)
−0.174802 + 0.984604i \(0.555929\pi\)
\(444\) 0 0
\(445\) −66.2472 −3.14042
\(446\) 5.36433 0.254008
\(447\) 0 0
\(448\) 2.10378 0.0993945
\(449\) 5.07130 0.239330 0.119665 0.992814i \(-0.461818\pi\)
0.119665 + 0.992814i \(0.461818\pi\)
\(450\) 0 0
\(451\) 12.1090 0.570193
\(452\) 20.5365 0.965955
\(453\) 0 0
\(454\) −11.7698 −0.552383
\(455\) 4.89512 0.229487
\(456\) 0 0
\(457\) 6.68190 0.312566 0.156283 0.987712i \(-0.450049\pi\)
0.156283 + 0.987712i \(0.450049\pi\)
\(458\) 23.6187 1.10363
\(459\) 0 0
\(460\) 25.5248 1.19010
\(461\) −17.6016 −0.819788 −0.409894 0.912133i \(-0.634434\pi\)
−0.409894 + 0.912133i \(0.634434\pi\)
\(462\) 0 0
\(463\) 12.1244 0.563467 0.281734 0.959493i \(-0.409091\pi\)
0.281734 + 0.959493i \(0.409091\pi\)
\(464\) 8.07750 0.374988
\(465\) 0 0
\(466\) −27.4243 −1.27041
\(467\) −32.6155 −1.50927 −0.754633 0.656147i \(-0.772185\pi\)
−0.754633 + 0.656147i \(0.772185\pi\)
\(468\) 0 0
\(469\) 0.0788855 0.00364259
\(470\) 24.1544 1.11416
\(471\) 0 0
\(472\) −7.68172 −0.353580
\(473\) −36.1223 −1.66090
\(474\) 0 0
\(475\) −106.158 −4.87084
\(476\) −1.10442 −0.0506209
\(477\) 0 0
\(478\) 19.9867 0.914171
\(479\) 26.8635 1.22742 0.613712 0.789530i \(-0.289675\pi\)
0.613712 + 0.789530i \(0.289675\pi\)
\(480\) 0 0
\(481\) −5.54812 −0.252972
\(482\) −1.69539 −0.0772227
\(483\) 0 0
\(484\) 10.8752 0.494326
\(485\) 37.9009 1.72099
\(486\) 0 0
\(487\) 35.2025 1.59518 0.797590 0.603201i \(-0.206108\pi\)
0.797590 + 0.603201i \(0.206108\pi\)
\(488\) −3.68590 −0.166853
\(489\) 0 0
\(490\) 10.9477 0.494568
\(491\) 13.8169 0.623548 0.311774 0.950156i \(-0.399077\pi\)
0.311774 + 0.950156i \(0.399077\pi\)
\(492\) 0 0
\(493\) −4.24042 −0.190979
\(494\) 4.43736 0.199646
\(495\) 0 0
\(496\) 4.87410 0.218853
\(497\) 27.5082 1.23391
\(498\) 0 0
\(499\) −29.5985 −1.32501 −0.662505 0.749057i \(-0.730507\pi\)
−0.662505 + 0.749057i \(0.730507\pi\)
\(500\) 34.4005 1.53844
\(501\) 0 0
\(502\) 25.2458 1.12678
\(503\) −11.1481 −0.497070 −0.248535 0.968623i \(-0.579949\pi\)
−0.248535 + 0.968623i \(0.579949\pi\)
\(504\) 0 0
\(505\) 45.8482 2.04022
\(506\) 28.0697 1.24785
\(507\) 0 0
\(508\) −17.7968 −0.789606
\(509\) −22.5150 −0.997962 −0.498981 0.866613i \(-0.666292\pi\)
−0.498981 + 0.866613i \(0.666292\pi\)
\(510\) 0 0
\(511\) 30.0953 1.33134
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 22.0313 0.971759
\(515\) 7.81740 0.344476
\(516\) 0 0
\(517\) 26.5626 1.16822
\(518\) 21.3346 0.937390
\(519\) 0 0
\(520\) −2.32682 −0.102038
\(521\) −41.1084 −1.80099 −0.900496 0.434864i \(-0.856797\pi\)
−0.900496 + 0.434864i \(0.856797\pi\)
\(522\) 0 0
\(523\) 8.70738 0.380747 0.190374 0.981712i \(-0.439030\pi\)
0.190374 + 0.981712i \(0.439030\pi\)
\(524\) 19.4735 0.850704
\(525\) 0 0
\(526\) 28.4131 1.23887
\(527\) −2.55874 −0.111460
\(528\) 0 0
\(529\) 13.0184 0.566018
\(530\) 2.31468 0.100543
\(531\) 0 0
\(532\) −17.0634 −0.739791
\(533\) −1.41643 −0.0613525
\(534\) 0 0
\(535\) 73.0843 3.15971
\(536\) −0.0374969 −0.00161962
\(537\) 0 0
\(538\) −16.6698 −0.718688
\(539\) 12.0393 0.518567
\(540\) 0 0
\(541\) −13.3238 −0.572836 −0.286418 0.958105i \(-0.592465\pi\)
−0.286418 + 0.958105i \(0.592465\pi\)
\(542\) −8.61463 −0.370030
\(543\) 0 0
\(544\) 0.524967 0.0225078
\(545\) −15.8526 −0.679049
\(546\) 0 0
\(547\) −25.3966 −1.08588 −0.542940 0.839771i \(-0.682689\pi\)
−0.542940 + 0.839771i \(0.682689\pi\)
\(548\) 8.78583 0.375312
\(549\) 0 0
\(550\) 61.2157 2.61025
\(551\) −65.5149 −2.79103
\(552\) 0 0
\(553\) −10.0105 −0.425689
\(554\) −4.78762 −0.203407
\(555\) 0 0
\(556\) 2.73608 0.116036
\(557\) 24.2298 1.02665 0.513325 0.858194i \(-0.328413\pi\)
0.513325 + 0.858194i \(0.328413\pi\)
\(558\) 0 0
\(559\) 4.22534 0.178713
\(560\) 8.94750 0.378101
\(561\) 0 0
\(562\) −1.93881 −0.0817837
\(563\) −2.60064 −0.109604 −0.0548019 0.998497i \(-0.517453\pi\)
−0.0548019 + 0.998497i \(0.517453\pi\)
\(564\) 0 0
\(565\) 87.3426 3.67453
\(566\) 28.3283 1.19073
\(567\) 0 0
\(568\) −13.0756 −0.548640
\(569\) 0.0803760 0.00336954 0.00168477 0.999999i \(-0.499464\pi\)
0.00168477 + 0.999999i \(0.499464\pi\)
\(570\) 0 0
\(571\) −26.9549 −1.12803 −0.564013 0.825766i \(-0.690743\pi\)
−0.564013 + 0.825766i \(0.690743\pi\)
\(572\) −2.55881 −0.106989
\(573\) 0 0
\(574\) 5.44672 0.227342
\(575\) 78.5506 3.27579
\(576\) 0 0
\(577\) −18.8989 −0.786772 −0.393386 0.919373i \(-0.628696\pi\)
−0.393386 + 0.919373i \(0.628696\pi\)
\(578\) 16.7244 0.695644
\(579\) 0 0
\(580\) 34.3540 1.42647
\(581\) −14.7827 −0.613291
\(582\) 0 0
\(583\) 2.54546 0.105422
\(584\) −14.3053 −0.591958
\(585\) 0 0
\(586\) −24.7952 −1.02428
\(587\) −6.24700 −0.257841 −0.128921 0.991655i \(-0.541151\pi\)
−0.128921 + 0.991655i \(0.541151\pi\)
\(588\) 0 0
\(589\) −39.5328 −1.62892
\(590\) −32.6707 −1.34503
\(591\) 0 0
\(592\) −10.1411 −0.416796
\(593\) −30.7455 −1.26257 −0.631283 0.775553i \(-0.717471\pi\)
−0.631283 + 0.775553i \(0.717471\pi\)
\(594\) 0 0
\(595\) −4.69714 −0.192564
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −3.28340 −0.134268
\(599\) 34.6147 1.41432 0.707158 0.707055i \(-0.249977\pi\)
0.707158 + 0.707055i \(0.249977\pi\)
\(600\) 0 0
\(601\) 10.2891 0.419702 0.209851 0.977733i \(-0.432702\pi\)
0.209851 + 0.977733i \(0.432702\pi\)
\(602\) −16.2480 −0.662220
\(603\) 0 0
\(604\) 2.34994 0.0956175
\(605\) 46.2526 1.88044
\(606\) 0 0
\(607\) 38.5414 1.56435 0.782173 0.623062i \(-0.214111\pi\)
0.782173 + 0.623062i \(0.214111\pi\)
\(608\) 8.11080 0.328936
\(609\) 0 0
\(610\) −15.6763 −0.634715
\(611\) −3.10711 −0.125700
\(612\) 0 0
\(613\) 11.4761 0.463517 0.231759 0.972773i \(-0.425552\pi\)
0.231759 + 0.972773i \(0.425552\pi\)
\(614\) 15.6307 0.630805
\(615\) 0 0
\(616\) 9.83959 0.396448
\(617\) 8.32005 0.334952 0.167476 0.985876i \(-0.446438\pi\)
0.167476 + 0.985876i \(0.446438\pi\)
\(618\) 0 0
\(619\) −20.0989 −0.807841 −0.403921 0.914794i \(-0.632353\pi\)
−0.403921 + 0.914794i \(0.632353\pi\)
\(620\) 20.7298 0.832528
\(621\) 0 0
\(622\) 0.803622 0.0322223
\(623\) −32.7694 −1.31288
\(624\) 0 0
\(625\) 80.8647 3.23459
\(626\) 20.3580 0.813668
\(627\) 0 0
\(628\) 5.88317 0.234764
\(629\) 5.32373 0.212271
\(630\) 0 0
\(631\) −19.8280 −0.789339 −0.394670 0.918823i \(-0.629141\pi\)
−0.394670 + 0.918823i \(0.629141\pi\)
\(632\) 4.75832 0.189276
\(633\) 0 0
\(634\) −23.4979 −0.933220
\(635\) −75.6907 −3.00370
\(636\) 0 0
\(637\) −1.40827 −0.0557976
\(638\) 37.7792 1.49569
\(639\) 0 0
\(640\) −4.25305 −0.168117
\(641\) −14.5984 −0.576600 −0.288300 0.957540i \(-0.593090\pi\)
−0.288300 + 0.957540i \(0.593090\pi\)
\(642\) 0 0
\(643\) 6.63135 0.261515 0.130757 0.991414i \(-0.458259\pi\)
0.130757 + 0.991414i \(0.458259\pi\)
\(644\) 12.6259 0.497532
\(645\) 0 0
\(646\) −4.25790 −0.167525
\(647\) −10.4522 −0.410917 −0.205458 0.978666i \(-0.565869\pi\)
−0.205458 + 0.978666i \(0.565869\pi\)
\(648\) 0 0
\(649\) −35.9281 −1.41030
\(650\) −7.16059 −0.280862
\(651\) 0 0
\(652\) 0.559443 0.0219095
\(653\) −9.33999 −0.365502 −0.182751 0.983159i \(-0.558500\pi\)
−0.182751 + 0.983159i \(0.558500\pi\)
\(654\) 0 0
\(655\) 82.8217 3.23611
\(656\) −2.58901 −0.101084
\(657\) 0 0
\(658\) 11.9480 0.465783
\(659\) −29.1535 −1.13566 −0.567830 0.823146i \(-0.692217\pi\)
−0.567830 + 0.823146i \(0.692217\pi\)
\(660\) 0 0
\(661\) −24.9644 −0.971004 −0.485502 0.874236i \(-0.661363\pi\)
−0.485502 + 0.874236i \(0.661363\pi\)
\(662\) −3.55426 −0.138140
\(663\) 0 0
\(664\) 7.02674 0.272690
\(665\) −72.5713 −2.81420
\(666\) 0 0
\(667\) 48.4774 1.87705
\(668\) 12.8886 0.498674
\(669\) 0 0
\(670\) −0.159476 −0.00616111
\(671\) −17.2393 −0.665515
\(672\) 0 0
\(673\) 20.0978 0.774712 0.387356 0.921930i \(-0.373389\pi\)
0.387356 + 0.921930i \(0.373389\pi\)
\(674\) −23.3744 −0.900348
\(675\) 0 0
\(676\) −12.7007 −0.488488
\(677\) −45.6993 −1.75637 −0.878184 0.478323i \(-0.841245\pi\)
−0.878184 + 0.478323i \(0.841245\pi\)
\(678\) 0 0
\(679\) 18.7478 0.719475
\(680\) 2.23271 0.0856206
\(681\) 0 0
\(682\) 22.7966 0.872927
\(683\) −35.2201 −1.34766 −0.673830 0.738886i \(-0.735352\pi\)
−0.673830 + 0.738886i \(0.735352\pi\)
\(684\) 0 0
\(685\) 37.3666 1.42770
\(686\) 20.1418 0.769018
\(687\) 0 0
\(688\) 7.72324 0.294446
\(689\) −0.297751 −0.0113434
\(690\) 0 0
\(691\) −18.6521 −0.709558 −0.354779 0.934950i \(-0.615444\pi\)
−0.354779 + 0.934950i \(0.615444\pi\)
\(692\) 15.4812 0.588506
\(693\) 0 0
\(694\) 14.6186 0.554915
\(695\) 11.6367 0.441404
\(696\) 0 0
\(697\) 1.35915 0.0514813
\(698\) −19.9685 −0.755817
\(699\) 0 0
\(700\) 27.5352 1.04073
\(701\) 46.3334 1.74999 0.874995 0.484133i \(-0.160865\pi\)
0.874995 + 0.484133i \(0.160865\pi\)
\(702\) 0 0
\(703\) 82.2522 3.10220
\(704\) −4.67709 −0.176274
\(705\) 0 0
\(706\) −32.4912 −1.22282
\(707\) 22.6790 0.852931
\(708\) 0 0
\(709\) −5.62028 −0.211074 −0.105537 0.994415i \(-0.533656\pi\)
−0.105537 + 0.994415i \(0.533656\pi\)
\(710\) −55.6112 −2.08705
\(711\) 0 0
\(712\) 15.5764 0.583750
\(713\) 29.2521 1.09550
\(714\) 0 0
\(715\) −10.8827 −0.406991
\(716\) −18.5958 −0.694957
\(717\) 0 0
\(718\) −11.0126 −0.410986
\(719\) −1.38058 −0.0514870 −0.0257435 0.999669i \(-0.508195\pi\)
−0.0257435 + 0.999669i \(0.508195\pi\)
\(720\) 0 0
\(721\) 3.86690 0.144011
\(722\) −46.7850 −1.74116
\(723\) 0 0
\(724\) 12.7960 0.475561
\(725\) 105.722 3.92641
\(726\) 0 0
\(727\) 33.6994 1.24984 0.624920 0.780689i \(-0.285131\pi\)
0.624920 + 0.780689i \(0.285131\pi\)
\(728\) −1.15097 −0.0426577
\(729\) 0 0
\(730\) −60.8412 −2.25183
\(731\) −4.05445 −0.149959
\(732\) 0 0
\(733\) 6.43137 0.237548 0.118774 0.992921i \(-0.462104\pi\)
0.118774 + 0.992921i \(0.462104\pi\)
\(734\) 32.4535 1.19788
\(735\) 0 0
\(736\) −6.00153 −0.221220
\(737\) −0.175377 −0.00646008
\(738\) 0 0
\(739\) −4.37703 −0.161012 −0.0805058 0.996754i \(-0.525654\pi\)
−0.0805058 + 0.996754i \(0.525654\pi\)
\(740\) −43.1305 −1.58551
\(741\) 0 0
\(742\) 1.14497 0.0420330
\(743\) −29.5010 −1.08229 −0.541144 0.840930i \(-0.682009\pi\)
−0.541144 + 0.840930i \(0.682009\pi\)
\(744\) 0 0
\(745\) 4.25305 0.155820
\(746\) −8.06417 −0.295250
\(747\) 0 0
\(748\) 2.45532 0.0897753
\(749\) 36.1514 1.32094
\(750\) 0 0
\(751\) 34.4108 1.25567 0.627834 0.778347i \(-0.283942\pi\)
0.627834 + 0.778347i \(0.283942\pi\)
\(752\) −5.67930 −0.207103
\(753\) 0 0
\(754\) −4.41915 −0.160936
\(755\) 9.99439 0.363733
\(756\) 0 0
\(757\) −20.1601 −0.732733 −0.366366 0.930471i \(-0.619398\pi\)
−0.366366 + 0.930471i \(0.619398\pi\)
\(758\) −2.31863 −0.0842163
\(759\) 0 0
\(760\) 34.4956 1.25129
\(761\) 9.96886 0.361371 0.180686 0.983541i \(-0.442168\pi\)
0.180686 + 0.983541i \(0.442168\pi\)
\(762\) 0 0
\(763\) −7.84152 −0.283882
\(764\) −5.71191 −0.206650
\(765\) 0 0
\(766\) −32.0190 −1.15689
\(767\) 4.20262 0.151748
\(768\) 0 0
\(769\) 23.3004 0.840233 0.420117 0.907470i \(-0.361989\pi\)
0.420117 + 0.907470i \(0.361989\pi\)
\(770\) 41.8483 1.50811
\(771\) 0 0
\(772\) 5.85587 0.210758
\(773\) −24.2668 −0.872816 −0.436408 0.899749i \(-0.643750\pi\)
−0.436408 + 0.899749i \(0.643750\pi\)
\(774\) 0 0
\(775\) 63.7942 2.29156
\(776\) −8.91148 −0.319903
\(777\) 0 0
\(778\) −5.77502 −0.207044
\(779\) 20.9990 0.752366
\(780\) 0 0
\(781\) −61.1558 −2.18833
\(782\) 3.15061 0.112666
\(783\) 0 0
\(784\) −2.57409 −0.0919318
\(785\) 25.0214 0.893052
\(786\) 0 0
\(787\) −29.1694 −1.03978 −0.519889 0.854234i \(-0.674027\pi\)
−0.519889 + 0.854234i \(0.674027\pi\)
\(788\) 20.7385 0.738778
\(789\) 0 0
\(790\) 20.2374 0.720013
\(791\) 43.2043 1.53617
\(792\) 0 0
\(793\) 2.01653 0.0716092
\(794\) −1.60163 −0.0568396
\(795\) 0 0
\(796\) −1.14505 −0.0405853
\(797\) 13.1392 0.465414 0.232707 0.972547i \(-0.425242\pi\)
0.232707 + 0.972547i \(0.425242\pi\)
\(798\) 0 0
\(799\) 2.98145 0.105476
\(800\) −13.0884 −0.462746
\(801\) 0 0
\(802\) −32.9876 −1.16483
\(803\) −66.9072 −2.36111
\(804\) 0 0
\(805\) 53.6987 1.89263
\(806\) −2.66659 −0.0939265
\(807\) 0 0
\(808\) −10.7801 −0.379242
\(809\) 42.6320 1.49886 0.749432 0.662082i \(-0.230327\pi\)
0.749432 + 0.662082i \(0.230327\pi\)
\(810\) 0 0
\(811\) 45.8586 1.61031 0.805156 0.593063i \(-0.202081\pi\)
0.805156 + 0.593063i \(0.202081\pi\)
\(812\) 16.9933 0.596348
\(813\) 0 0
\(814\) −47.4307 −1.66245
\(815\) 2.37934 0.0833446
\(816\) 0 0
\(817\) −62.6416 −2.19155
\(818\) 20.9325 0.731886
\(819\) 0 0
\(820\) −11.0112 −0.384528
\(821\) −42.4539 −1.48165 −0.740825 0.671698i \(-0.765565\pi\)
−0.740825 + 0.671698i \(0.765565\pi\)
\(822\) 0 0
\(823\) −8.96445 −0.312481 −0.156241 0.987719i \(-0.549937\pi\)
−0.156241 + 0.987719i \(0.549937\pi\)
\(824\) −1.83807 −0.0640322
\(825\) 0 0
\(826\) −16.1607 −0.562302
\(827\) 16.7639 0.582936 0.291468 0.956581i \(-0.405856\pi\)
0.291468 + 0.956581i \(0.405856\pi\)
\(828\) 0 0
\(829\) 33.0424 1.14761 0.573805 0.818992i \(-0.305467\pi\)
0.573805 + 0.818992i \(0.305467\pi\)
\(830\) 29.8850 1.03733
\(831\) 0 0
\(832\) 0.547094 0.0189671
\(833\) 1.35131 0.0468202
\(834\) 0 0
\(835\) 54.8158 1.89698
\(836\) 37.9349 1.31201
\(837\) 0 0
\(838\) 18.6183 0.643157
\(839\) −16.0385 −0.553712 −0.276856 0.960911i \(-0.589292\pi\)
−0.276856 + 0.960911i \(0.589292\pi\)
\(840\) 0 0
\(841\) 36.2460 1.24986
\(842\) 29.0112 0.999792
\(843\) 0 0
\(844\) 3.55721 0.122444
\(845\) −54.0166 −1.85823
\(846\) 0 0
\(847\) 22.8790 0.786132
\(848\) −0.544241 −0.0186893
\(849\) 0 0
\(850\) 6.87099 0.235673
\(851\) −60.8620 −2.08632
\(852\) 0 0
\(853\) −4.31797 −0.147845 −0.0739223 0.997264i \(-0.523552\pi\)
−0.0739223 + 0.997264i \(0.523552\pi\)
\(854\) −7.75434 −0.265348
\(855\) 0 0
\(856\) −17.1840 −0.587336
\(857\) −32.3939 −1.10656 −0.553278 0.832997i \(-0.686623\pi\)
−0.553278 + 0.832997i \(0.686623\pi\)
\(858\) 0 0
\(859\) 7.15934 0.244274 0.122137 0.992513i \(-0.461025\pi\)
0.122137 + 0.992513i \(0.461025\pi\)
\(860\) 32.8473 1.12008
\(861\) 0 0
\(862\) 20.0767 0.683814
\(863\) 18.8898 0.643016 0.321508 0.946907i \(-0.395810\pi\)
0.321508 + 0.946907i \(0.395810\pi\)
\(864\) 0 0
\(865\) 65.8422 2.23870
\(866\) 26.1410 0.888308
\(867\) 0 0
\(868\) 10.2540 0.348045
\(869\) 22.2551 0.754952
\(870\) 0 0
\(871\) 0.0205143 0.000695102 0
\(872\) 3.72734 0.126224
\(873\) 0 0
\(874\) 48.6772 1.64653
\(875\) 72.3712 2.44659
\(876\) 0 0
\(877\) −16.1749 −0.546189 −0.273094 0.961987i \(-0.588047\pi\)
−0.273094 + 0.961987i \(0.588047\pi\)
\(878\) −1.54942 −0.0522904
\(879\) 0 0
\(880\) −19.8919 −0.670556
\(881\) 18.4187 0.620540 0.310270 0.950648i \(-0.399581\pi\)
0.310270 + 0.950648i \(0.399581\pi\)
\(882\) 0 0
\(883\) 19.7770 0.665547 0.332774 0.943007i \(-0.392015\pi\)
0.332774 + 0.943007i \(0.392015\pi\)
\(884\) −0.287206 −0.00965979
\(885\) 0 0
\(886\) 7.35831 0.247207
\(887\) −29.2805 −0.983143 −0.491571 0.870837i \(-0.663577\pi\)
−0.491571 + 0.870837i \(0.663577\pi\)
\(888\) 0 0
\(889\) −37.4407 −1.25572
\(890\) 66.2472 2.22061
\(891\) 0 0
\(892\) −5.36433 −0.179611
\(893\) 46.0637 1.54146
\(894\) 0 0
\(895\) −79.0888 −2.64365
\(896\) −2.10378 −0.0702825
\(897\) 0 0
\(898\) −5.07130 −0.169232
\(899\) 39.3705 1.31308
\(900\) 0 0
\(901\) 0.285709 0.00951834
\(902\) −12.1090 −0.403187
\(903\) 0 0
\(904\) −20.5365 −0.683033
\(905\) 54.4222 1.80906
\(906\) 0 0
\(907\) 11.0299 0.366241 0.183120 0.983090i \(-0.441380\pi\)
0.183120 + 0.983090i \(0.441380\pi\)
\(908\) 11.7698 0.390594
\(909\) 0 0
\(910\) −4.89512 −0.162272
\(911\) −46.2825 −1.53341 −0.766704 0.642001i \(-0.778105\pi\)
−0.766704 + 0.642001i \(0.778105\pi\)
\(912\) 0 0
\(913\) 32.8647 1.08766
\(914\) −6.68190 −0.221018
\(915\) 0 0
\(916\) −23.6187 −0.780384
\(917\) 40.9680 1.35288
\(918\) 0 0
\(919\) 2.95357 0.0974293 0.0487146 0.998813i \(-0.484488\pi\)
0.0487146 + 0.998813i \(0.484488\pi\)
\(920\) −25.5248 −0.841528
\(921\) 0 0
\(922\) 17.6016 0.579678
\(923\) 7.15358 0.235463
\(924\) 0 0
\(925\) −132.731 −4.36416
\(926\) −12.1244 −0.398432
\(927\) 0 0
\(928\) −8.07750 −0.265157
\(929\) −48.6223 −1.59525 −0.797623 0.603156i \(-0.793910\pi\)
−0.797623 + 0.603156i \(0.793910\pi\)
\(930\) 0 0
\(931\) 20.8779 0.684246
\(932\) 27.4243 0.898312
\(933\) 0 0
\(934\) 32.6155 1.06721
\(935\) 10.4426 0.341509
\(936\) 0 0
\(937\) 12.4395 0.406380 0.203190 0.979139i \(-0.434869\pi\)
0.203190 + 0.979139i \(0.434869\pi\)
\(938\) −0.0788855 −0.00257570
\(939\) 0 0
\(940\) −24.1544 −0.787828
\(941\) −14.0582 −0.458283 −0.229142 0.973393i \(-0.573592\pi\)
−0.229142 + 0.973393i \(0.573592\pi\)
\(942\) 0 0
\(943\) −15.5380 −0.505988
\(944\) 7.68172 0.250019
\(945\) 0 0
\(946\) 36.1223 1.17444
\(947\) −9.24375 −0.300382 −0.150191 0.988657i \(-0.547989\pi\)
−0.150191 + 0.988657i \(0.547989\pi\)
\(948\) 0 0
\(949\) 7.82635 0.254054
\(950\) 106.158 3.44421
\(951\) 0 0
\(952\) 1.10442 0.0357944
\(953\) 8.96912 0.290538 0.145269 0.989392i \(-0.453595\pi\)
0.145269 + 0.989392i \(0.453595\pi\)
\(954\) 0 0
\(955\) −24.2931 −0.786105
\(956\) −19.9867 −0.646416
\(957\) 0 0
\(958\) −26.8635 −0.867920
\(959\) 18.4835 0.596863
\(960\) 0 0
\(961\) −7.24318 −0.233651
\(962\) 5.54812 0.178879
\(963\) 0 0
\(964\) 1.69539 0.0546047
\(965\) 24.9053 0.801731
\(966\) 0 0
\(967\) −20.7749 −0.668074 −0.334037 0.942560i \(-0.608411\pi\)
−0.334037 + 0.942560i \(0.608411\pi\)
\(968\) −10.8752 −0.349541
\(969\) 0 0
\(970\) −37.9009 −1.21693
\(971\) −30.2800 −0.971731 −0.485865 0.874034i \(-0.661495\pi\)
−0.485865 + 0.874034i \(0.661495\pi\)
\(972\) 0 0
\(973\) 5.75612 0.184533
\(974\) −35.2025 −1.12796
\(975\) 0 0
\(976\) 3.68590 0.117983
\(977\) 3.60470 0.115325 0.0576623 0.998336i \(-0.481635\pi\)
0.0576623 + 0.998336i \(0.481635\pi\)
\(978\) 0 0
\(979\) 72.8522 2.32837
\(980\) −10.9477 −0.349713
\(981\) 0 0
\(982\) −13.8169 −0.440915
\(983\) 5.97607 0.190607 0.0953036 0.995448i \(-0.469618\pi\)
0.0953036 + 0.995448i \(0.469618\pi\)
\(984\) 0 0
\(985\) 88.2018 2.81034
\(986\) 4.24042 0.135043
\(987\) 0 0
\(988\) −4.43736 −0.141171
\(989\) 46.3513 1.47389
\(990\) 0 0
\(991\) 28.9520 0.919691 0.459845 0.887999i \(-0.347905\pi\)
0.459845 + 0.887999i \(0.347905\pi\)
\(992\) −4.87410 −0.154753
\(993\) 0 0
\(994\) −27.5082 −0.872509
\(995\) −4.86996 −0.154388
\(996\) 0 0
\(997\) 7.17728 0.227307 0.113653 0.993520i \(-0.463745\pi\)
0.113653 + 0.993520i \(0.463745\pi\)
\(998\) 29.5985 0.936924
\(999\) 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 \(a_p\))