Properties

Label 8046.2.a.l.1.4
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 1.4
Root \(-1.17050\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.17050 q^{5}\) \(+0.506529 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.17050 q^{5}\) \(+0.506529 q^{7}\) \(-1.00000 q^{8}\) \(+1.17050 q^{10}\) \(-3.88070 q^{11}\) \(-3.61369 q^{13}\) \(-0.506529 q^{14}\) \(+1.00000 q^{16}\) \(+6.95227 q^{17}\) \(-2.33695 q^{19}\) \(-1.17050 q^{20}\) \(+3.88070 q^{22}\) \(-1.72649 q^{23}\) \(-3.62993 q^{25}\) \(+3.61369 q^{26}\) \(+0.506529 q^{28}\) \(+4.21919 q^{29}\) \(-3.29279 q^{31}\) \(-1.00000 q^{32}\) \(-6.95227 q^{34}\) \(-0.592892 q^{35}\) \(-7.04259 q^{37}\) \(+2.33695 q^{38}\) \(+1.17050 q^{40}\) \(+10.5485 q^{41}\) \(-6.84084 q^{43}\) \(-3.88070 q^{44}\) \(+1.72649 q^{46}\) \(-4.17683 q^{47}\) \(-6.74343 q^{49}\) \(+3.62993 q^{50}\) \(-3.61369 q^{52}\) \(+12.8841 q^{53}\) \(+4.54236 q^{55}\) \(-0.506529 q^{56}\) \(-4.21919 q^{58}\) \(-7.05273 q^{59}\) \(+11.2400 q^{61}\) \(+3.29279 q^{62}\) \(+1.00000 q^{64}\) \(+4.22983 q^{65}\) \(-5.00991 q^{67}\) \(+6.95227 q^{68}\) \(+0.592892 q^{70}\) \(-0.923816 q^{71}\) \(+2.46929 q^{73}\) \(+7.04259 q^{74}\) \(-2.33695 q^{76}\) \(-1.96569 q^{77}\) \(-7.80783 q^{79}\) \(-1.17050 q^{80}\) \(-10.5485 q^{82}\) \(-8.00835 q^{83}\) \(-8.13763 q^{85}\) \(+6.84084 q^{86}\) \(+3.88070 q^{88}\) \(+15.6581 q^{89}\) \(-1.83044 q^{91}\) \(-1.72649 q^{92}\) \(+4.17683 q^{94}\) \(+2.73540 q^{95}\) \(+1.02168 q^{97}\) \(+6.74343 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.17050 −0.523463 −0.261732 0.965141i \(-0.584294\pi\)
−0.261732 + 0.965141i \(0.584294\pi\)
\(6\) 0 0
\(7\) 0.506529 0.191450 0.0957249 0.995408i \(-0.469483\pi\)
0.0957249 + 0.995408i \(0.469483\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.17050 0.370144
\(11\) −3.88070 −1.17008 −0.585038 0.811006i \(-0.698920\pi\)
−0.585038 + 0.811006i \(0.698920\pi\)
\(12\) 0 0
\(13\) −3.61369 −1.00226 −0.501129 0.865372i \(-0.667082\pi\)
−0.501129 + 0.865372i \(0.667082\pi\)
\(14\) −0.506529 −0.135375
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.95227 1.68617 0.843087 0.537777i \(-0.180736\pi\)
0.843087 + 0.537777i \(0.180736\pi\)
\(18\) 0 0
\(19\) −2.33695 −0.536133 −0.268066 0.963400i \(-0.586385\pi\)
−0.268066 + 0.963400i \(0.586385\pi\)
\(20\) −1.17050 −0.261732
\(21\) 0 0
\(22\) 3.88070 0.827369
\(23\) −1.72649 −0.359997 −0.179999 0.983667i \(-0.557609\pi\)
−0.179999 + 0.983667i \(0.557609\pi\)
\(24\) 0 0
\(25\) −3.62993 −0.725986
\(26\) 3.61369 0.708704
\(27\) 0 0
\(28\) 0.506529 0.0957249
\(29\) 4.21919 0.783483 0.391742 0.920075i \(-0.371873\pi\)
0.391742 + 0.920075i \(0.371873\pi\)
\(30\) 0 0
\(31\) −3.29279 −0.591403 −0.295702 0.955280i \(-0.595553\pi\)
−0.295702 + 0.955280i \(0.595553\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −6.95227 −1.19231
\(35\) −0.592892 −0.100217
\(36\) 0 0
\(37\) −7.04259 −1.15779 −0.578897 0.815400i \(-0.696517\pi\)
−0.578897 + 0.815400i \(0.696517\pi\)
\(38\) 2.33695 0.379103
\(39\) 0 0
\(40\) 1.17050 0.185072
\(41\) 10.5485 1.64740 0.823700 0.567026i \(-0.191906\pi\)
0.823700 + 0.567026i \(0.191906\pi\)
\(42\) 0 0
\(43\) −6.84084 −1.04322 −0.521609 0.853184i \(-0.674668\pi\)
−0.521609 + 0.853184i \(0.674668\pi\)
\(44\) −3.88070 −0.585038
\(45\) 0 0
\(46\) 1.72649 0.254557
\(47\) −4.17683 −0.609253 −0.304627 0.952472i \(-0.598532\pi\)
−0.304627 + 0.952472i \(0.598532\pi\)
\(48\) 0 0
\(49\) −6.74343 −0.963347
\(50\) 3.62993 0.513350
\(51\) 0 0
\(52\) −3.61369 −0.501129
\(53\) 12.8841 1.76976 0.884880 0.465819i \(-0.154240\pi\)
0.884880 + 0.465819i \(0.154240\pi\)
\(54\) 0 0
\(55\) 4.54236 0.612492
\(56\) −0.506529 −0.0676877
\(57\) 0 0
\(58\) −4.21919 −0.554006
\(59\) −7.05273 −0.918188 −0.459094 0.888388i \(-0.651826\pi\)
−0.459094 + 0.888388i \(0.651826\pi\)
\(60\) 0 0
\(61\) 11.2400 1.43913 0.719566 0.694424i \(-0.244341\pi\)
0.719566 + 0.694424i \(0.244341\pi\)
\(62\) 3.29279 0.418185
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.22983 0.524646
\(66\) 0 0
\(67\) −5.00991 −0.612058 −0.306029 0.952022i \(-0.599000\pi\)
−0.306029 + 0.952022i \(0.599000\pi\)
\(68\) 6.95227 0.843087
\(69\) 0 0
\(70\) 0.592892 0.0708641
\(71\) −0.923816 −0.109637 −0.0548184 0.998496i \(-0.517458\pi\)
−0.0548184 + 0.998496i \(0.517458\pi\)
\(72\) 0 0
\(73\) 2.46929 0.289009 0.144505 0.989504i \(-0.453841\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(74\) 7.04259 0.818685
\(75\) 0 0
\(76\) −2.33695 −0.268066
\(77\) −1.96569 −0.224011
\(78\) 0 0
\(79\) −7.80783 −0.878450 −0.439225 0.898377i \(-0.644747\pi\)
−0.439225 + 0.898377i \(0.644747\pi\)
\(80\) −1.17050 −0.130866
\(81\) 0 0
\(82\) −10.5485 −1.16489
\(83\) −8.00835 −0.879030 −0.439515 0.898235i \(-0.644850\pi\)
−0.439515 + 0.898235i \(0.644850\pi\)
\(84\) 0 0
\(85\) −8.13763 −0.882650
\(86\) 6.84084 0.737667
\(87\) 0 0
\(88\) 3.88070 0.413684
\(89\) 15.6581 1.65975 0.829877 0.557946i \(-0.188410\pi\)
0.829877 + 0.557946i \(0.188410\pi\)
\(90\) 0 0
\(91\) −1.83044 −0.191882
\(92\) −1.72649 −0.179999
\(93\) 0 0
\(94\) 4.17683 0.430807
\(95\) 2.73540 0.280646
\(96\) 0 0
\(97\) 1.02168 0.103736 0.0518681 0.998654i \(-0.483482\pi\)
0.0518681 + 0.998654i \(0.483482\pi\)
\(98\) 6.74343 0.681189
\(99\) 0 0
\(100\) −3.62993 −0.362993
\(101\) −4.32214 −0.430069 −0.215035 0.976606i \(-0.568986\pi\)
−0.215035 + 0.976606i \(0.568986\pi\)
\(102\) 0 0
\(103\) 6.94103 0.683920 0.341960 0.939715i \(-0.388909\pi\)
0.341960 + 0.939715i \(0.388909\pi\)
\(104\) 3.61369 0.354352
\(105\) 0 0
\(106\) −12.8841 −1.25141
\(107\) −14.3087 −1.38327 −0.691636 0.722246i \(-0.743110\pi\)
−0.691636 + 0.722246i \(0.743110\pi\)
\(108\) 0 0
\(109\) −7.75669 −0.742957 −0.371478 0.928442i \(-0.621149\pi\)
−0.371478 + 0.928442i \(0.621149\pi\)
\(110\) −4.54236 −0.433097
\(111\) 0 0
\(112\) 0.506529 0.0478625
\(113\) −1.71654 −0.161479 −0.0807393 0.996735i \(-0.525728\pi\)
−0.0807393 + 0.996735i \(0.525728\pi\)
\(114\) 0 0
\(115\) 2.02085 0.188445
\(116\) 4.21919 0.391742
\(117\) 0 0
\(118\) 7.05273 0.649257
\(119\) 3.52153 0.322818
\(120\) 0 0
\(121\) 4.05985 0.369077
\(122\) −11.2400 −1.01762
\(123\) 0 0
\(124\) −3.29279 −0.295702
\(125\) 10.1013 0.903490
\(126\) 0 0
\(127\) 3.86129 0.342634 0.171317 0.985216i \(-0.445198\pi\)
0.171317 + 0.985216i \(0.445198\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −4.22983 −0.370980
\(131\) −7.45036 −0.650941 −0.325470 0.945552i \(-0.605523\pi\)
−0.325470 + 0.945552i \(0.605523\pi\)
\(132\) 0 0
\(133\) −1.18373 −0.102642
\(134\) 5.00991 0.432790
\(135\) 0 0
\(136\) −6.95227 −0.596153
\(137\) −11.7309 −1.00223 −0.501117 0.865379i \(-0.667077\pi\)
−0.501117 + 0.865379i \(0.667077\pi\)
\(138\) 0 0
\(139\) −0.614537 −0.0521244 −0.0260622 0.999660i \(-0.508297\pi\)
−0.0260622 + 0.999660i \(0.508297\pi\)
\(140\) −0.592892 −0.0501085
\(141\) 0 0
\(142\) 0.923816 0.0775249
\(143\) 14.0237 1.17272
\(144\) 0 0
\(145\) −4.93855 −0.410125
\(146\) −2.46929 −0.204360
\(147\) 0 0
\(148\) −7.04259 −0.578897
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) 17.5323 1.42676 0.713378 0.700779i \(-0.247164\pi\)
0.713378 + 0.700779i \(0.247164\pi\)
\(152\) 2.33695 0.189551
\(153\) 0 0
\(154\) 1.96569 0.158400
\(155\) 3.85422 0.309578
\(156\) 0 0
\(157\) 22.2770 1.77790 0.888950 0.458005i \(-0.151436\pi\)
0.888950 + 0.458005i \(0.151436\pi\)
\(158\) 7.80783 0.621158
\(159\) 0 0
\(160\) 1.17050 0.0925361
\(161\) −0.874515 −0.0689214
\(162\) 0 0
\(163\) 13.4831 1.05608 0.528038 0.849221i \(-0.322928\pi\)
0.528038 + 0.849221i \(0.322928\pi\)
\(164\) 10.5485 0.823700
\(165\) 0 0
\(166\) 8.00835 0.621568
\(167\) 12.6208 0.976625 0.488313 0.872669i \(-0.337613\pi\)
0.488313 + 0.872669i \(0.337613\pi\)
\(168\) 0 0
\(169\) 0.0587896 0.00452227
\(170\) 8.13763 0.624128
\(171\) 0 0
\(172\) −6.84084 −0.521609
\(173\) 13.5303 1.02869 0.514346 0.857583i \(-0.328035\pi\)
0.514346 + 0.857583i \(0.328035\pi\)
\(174\) 0 0
\(175\) −1.83866 −0.138990
\(176\) −3.88070 −0.292519
\(177\) 0 0
\(178\) −15.6581 −1.17362
\(179\) −7.23353 −0.540659 −0.270330 0.962768i \(-0.587133\pi\)
−0.270330 + 0.962768i \(0.587133\pi\)
\(180\) 0 0
\(181\) 3.30723 0.245824 0.122912 0.992418i \(-0.460777\pi\)
0.122912 + 0.992418i \(0.460777\pi\)
\(182\) 1.83044 0.135681
\(183\) 0 0
\(184\) 1.72649 0.127278
\(185\) 8.24335 0.606063
\(186\) 0 0
\(187\) −26.9797 −1.97295
\(188\) −4.17683 −0.304627
\(189\) 0 0
\(190\) −2.73540 −0.198446
\(191\) 12.7158 0.920083 0.460042 0.887897i \(-0.347835\pi\)
0.460042 + 0.887897i \(0.347835\pi\)
\(192\) 0 0
\(193\) −3.36901 −0.242507 −0.121253 0.992622i \(-0.538691\pi\)
−0.121253 + 0.992622i \(0.538691\pi\)
\(194\) −1.02168 −0.0733526
\(195\) 0 0
\(196\) −6.74343 −0.481673
\(197\) −0.815685 −0.0581151 −0.0290576 0.999578i \(-0.509251\pi\)
−0.0290576 + 0.999578i \(0.509251\pi\)
\(198\) 0 0
\(199\) 5.35685 0.379737 0.189868 0.981810i \(-0.439194\pi\)
0.189868 + 0.981810i \(0.439194\pi\)
\(200\) 3.62993 0.256675
\(201\) 0 0
\(202\) 4.32214 0.304105
\(203\) 2.13714 0.149998
\(204\) 0 0
\(205\) −12.3470 −0.862353
\(206\) −6.94103 −0.483604
\(207\) 0 0
\(208\) −3.61369 −0.250565
\(209\) 9.06900 0.627316
\(210\) 0 0
\(211\) 13.3550 0.919398 0.459699 0.888075i \(-0.347957\pi\)
0.459699 + 0.888075i \(0.347957\pi\)
\(212\) 12.8841 0.884880
\(213\) 0 0
\(214\) 14.3087 0.978122
\(215\) 8.00720 0.546087
\(216\) 0 0
\(217\) −1.66790 −0.113224
\(218\) 7.75669 0.525350
\(219\) 0 0
\(220\) 4.54236 0.306246
\(221\) −25.1234 −1.68998
\(222\) 0 0
\(223\) 18.7279 1.25411 0.627057 0.778974i \(-0.284259\pi\)
0.627057 + 0.778974i \(0.284259\pi\)
\(224\) −0.506529 −0.0338439
\(225\) 0 0
\(226\) 1.71654 0.114183
\(227\) 8.54460 0.567125 0.283562 0.958954i \(-0.408484\pi\)
0.283562 + 0.958954i \(0.408484\pi\)
\(228\) 0 0
\(229\) −5.34208 −0.353015 −0.176507 0.984299i \(-0.556480\pi\)
−0.176507 + 0.984299i \(0.556480\pi\)
\(230\) −2.02085 −0.133251
\(231\) 0 0
\(232\) −4.21919 −0.277003
\(233\) 14.8123 0.970387 0.485194 0.874407i \(-0.338749\pi\)
0.485194 + 0.874407i \(0.338749\pi\)
\(234\) 0 0
\(235\) 4.88898 0.318922
\(236\) −7.05273 −0.459094
\(237\) 0 0
\(238\) −3.52153 −0.228267
\(239\) 6.91374 0.447212 0.223606 0.974680i \(-0.428217\pi\)
0.223606 + 0.974680i \(0.428217\pi\)
\(240\) 0 0
\(241\) 8.56369 0.551636 0.275818 0.961210i \(-0.411051\pi\)
0.275818 + 0.961210i \(0.411051\pi\)
\(242\) −4.05985 −0.260977
\(243\) 0 0
\(244\) 11.2400 0.719566
\(245\) 7.89318 0.504277
\(246\) 0 0
\(247\) 8.44501 0.537343
\(248\) 3.29279 0.209093
\(249\) 0 0
\(250\) −10.1013 −0.638864
\(251\) 16.1199 1.01748 0.508741 0.860920i \(-0.330111\pi\)
0.508741 + 0.860920i \(0.330111\pi\)
\(252\) 0 0
\(253\) 6.69998 0.421224
\(254\) −3.86129 −0.242279
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.39190 0.149203 0.0746013 0.997213i \(-0.476232\pi\)
0.0746013 + 0.997213i \(0.476232\pi\)
\(258\) 0 0
\(259\) −3.56727 −0.221660
\(260\) 4.22983 0.262323
\(261\) 0 0
\(262\) 7.45036 0.460285
\(263\) −28.7218 −1.77106 −0.885532 0.464579i \(-0.846206\pi\)
−0.885532 + 0.464579i \(0.846206\pi\)
\(264\) 0 0
\(265\) −15.0808 −0.926405
\(266\) 1.18373 0.0725792
\(267\) 0 0
\(268\) −5.00991 −0.306029
\(269\) −10.6420 −0.648853 −0.324427 0.945911i \(-0.605171\pi\)
−0.324427 + 0.945911i \(0.605171\pi\)
\(270\) 0 0
\(271\) −16.2311 −0.985969 −0.492984 0.870038i \(-0.664094\pi\)
−0.492984 + 0.870038i \(0.664094\pi\)
\(272\) 6.95227 0.421544
\(273\) 0 0
\(274\) 11.7309 0.708687
\(275\) 14.0867 0.849459
\(276\) 0 0
\(277\) −17.4271 −1.04709 −0.523545 0.851998i \(-0.675391\pi\)
−0.523545 + 0.851998i \(0.675391\pi\)
\(278\) 0.614537 0.0368575
\(279\) 0 0
\(280\) 0.592892 0.0354321
\(281\) 10.0480 0.599414 0.299707 0.954031i \(-0.403111\pi\)
0.299707 + 0.954031i \(0.403111\pi\)
\(282\) 0 0
\(283\) −2.11210 −0.125551 −0.0627756 0.998028i \(-0.519995\pi\)
−0.0627756 + 0.998028i \(0.519995\pi\)
\(284\) −0.923816 −0.0548184
\(285\) 0 0
\(286\) −14.0237 −0.829237
\(287\) 5.34312 0.315394
\(288\) 0 0
\(289\) 31.3341 1.84318
\(290\) 4.93855 0.290002
\(291\) 0 0
\(292\) 2.46929 0.144505
\(293\) −17.4877 −1.02164 −0.510820 0.859687i \(-0.670658\pi\)
−0.510820 + 0.859687i \(0.670658\pi\)
\(294\) 0 0
\(295\) 8.25522 0.480638
\(296\) 7.04259 0.409342
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 6.23900 0.360810
\(300\) 0 0
\(301\) −3.46508 −0.199724
\(302\) −17.5323 −1.00887
\(303\) 0 0
\(304\) −2.33695 −0.134033
\(305\) −13.1564 −0.753333
\(306\) 0 0
\(307\) 14.4985 0.827474 0.413737 0.910396i \(-0.364223\pi\)
0.413737 + 0.910396i \(0.364223\pi\)
\(308\) −1.96569 −0.112005
\(309\) 0 0
\(310\) −3.85422 −0.218905
\(311\) −27.0815 −1.53565 −0.767826 0.640659i \(-0.778661\pi\)
−0.767826 + 0.640659i \(0.778661\pi\)
\(312\) 0 0
\(313\) 20.4400 1.15534 0.577668 0.816272i \(-0.303963\pi\)
0.577668 + 0.816272i \(0.303963\pi\)
\(314\) −22.2770 −1.25716
\(315\) 0 0
\(316\) −7.80783 −0.439225
\(317\) −10.5261 −0.591206 −0.295603 0.955311i \(-0.595521\pi\)
−0.295603 + 0.955311i \(0.595521\pi\)
\(318\) 0 0
\(319\) −16.3734 −0.916735
\(320\) −1.17050 −0.0654329
\(321\) 0 0
\(322\) 0.874515 0.0487348
\(323\) −16.2471 −0.904013
\(324\) 0 0
\(325\) 13.1175 0.727626
\(326\) −13.4831 −0.746758
\(327\) 0 0
\(328\) −10.5485 −0.582444
\(329\) −2.11568 −0.116641
\(330\) 0 0
\(331\) −10.1909 −0.560140 −0.280070 0.959980i \(-0.590358\pi\)
−0.280070 + 0.959980i \(0.590358\pi\)
\(332\) −8.00835 −0.439515
\(333\) 0 0
\(334\) −12.6208 −0.690578
\(335\) 5.86410 0.320390
\(336\) 0 0
\(337\) −14.6134 −0.796042 −0.398021 0.917376i \(-0.630303\pi\)
−0.398021 + 0.917376i \(0.630303\pi\)
\(338\) −0.0587896 −0.00319773
\(339\) 0 0
\(340\) −8.13763 −0.441325
\(341\) 12.7784 0.691987
\(342\) 0 0
\(343\) −6.96144 −0.375882
\(344\) 6.84084 0.368833
\(345\) 0 0
\(346\) −13.5303 −0.727395
\(347\) 18.1962 0.976822 0.488411 0.872614i \(-0.337577\pi\)
0.488411 + 0.872614i \(0.337577\pi\)
\(348\) 0 0
\(349\) 18.9456 1.01413 0.507067 0.861907i \(-0.330730\pi\)
0.507067 + 0.861907i \(0.330730\pi\)
\(350\) 1.83866 0.0982807
\(351\) 0 0
\(352\) 3.88070 0.206842
\(353\) 36.1335 1.92319 0.961596 0.274468i \(-0.0885018\pi\)
0.961596 + 0.274468i \(0.0885018\pi\)
\(354\) 0 0
\(355\) 1.08133 0.0573908
\(356\) 15.6581 0.829877
\(357\) 0 0
\(358\) 7.23353 0.382304
\(359\) 13.2222 0.697842 0.348921 0.937152i \(-0.386548\pi\)
0.348921 + 0.937152i \(0.386548\pi\)
\(360\) 0 0
\(361\) −13.5387 −0.712562
\(362\) −3.30723 −0.173824
\(363\) 0 0
\(364\) −1.83044 −0.0959411
\(365\) −2.89031 −0.151286
\(366\) 0 0
\(367\) −2.09001 −0.109098 −0.0545488 0.998511i \(-0.517372\pi\)
−0.0545488 + 0.998511i \(0.517372\pi\)
\(368\) −1.72649 −0.0899993
\(369\) 0 0
\(370\) −8.24335 −0.428551
\(371\) 6.52614 0.338820
\(372\) 0 0
\(373\) −15.6737 −0.811552 −0.405776 0.913973i \(-0.632999\pi\)
−0.405776 + 0.913973i \(0.632999\pi\)
\(374\) 26.9797 1.39509
\(375\) 0 0
\(376\) 4.17683 0.215404
\(377\) −15.2468 −0.785253
\(378\) 0 0
\(379\) 29.1521 1.49744 0.748722 0.662884i \(-0.230668\pi\)
0.748722 + 0.662884i \(0.230668\pi\)
\(380\) 2.73540 0.140323
\(381\) 0 0
\(382\) −12.7158 −0.650597
\(383\) −13.1248 −0.670648 −0.335324 0.942103i \(-0.608846\pi\)
−0.335324 + 0.942103i \(0.608846\pi\)
\(384\) 0 0
\(385\) 2.30084 0.117261
\(386\) 3.36901 0.171478
\(387\) 0 0
\(388\) 1.02168 0.0518681
\(389\) 32.1642 1.63079 0.815394 0.578907i \(-0.196521\pi\)
0.815394 + 0.578907i \(0.196521\pi\)
\(390\) 0 0
\(391\) −12.0030 −0.607018
\(392\) 6.74343 0.340595
\(393\) 0 0
\(394\) 0.815685 0.0410936
\(395\) 9.13906 0.459836
\(396\) 0 0
\(397\) 33.8252 1.69764 0.848818 0.528685i \(-0.177315\pi\)
0.848818 + 0.528685i \(0.177315\pi\)
\(398\) −5.35685 −0.268514
\(399\) 0 0
\(400\) −3.62993 −0.181497
\(401\) −9.59093 −0.478948 −0.239474 0.970903i \(-0.576975\pi\)
−0.239474 + 0.970903i \(0.576975\pi\)
\(402\) 0 0
\(403\) 11.8992 0.592739
\(404\) −4.32214 −0.215035
\(405\) 0 0
\(406\) −2.13714 −0.106064
\(407\) 27.3302 1.35471
\(408\) 0 0
\(409\) −6.89619 −0.340995 −0.170497 0.985358i \(-0.554537\pi\)
−0.170497 + 0.985358i \(0.554537\pi\)
\(410\) 12.3470 0.609776
\(411\) 0 0
\(412\) 6.94103 0.341960
\(413\) −3.57241 −0.175787
\(414\) 0 0
\(415\) 9.37377 0.460140
\(416\) 3.61369 0.177176
\(417\) 0 0
\(418\) −9.06900 −0.443579
\(419\) 3.01240 0.147165 0.0735827 0.997289i \(-0.476557\pi\)
0.0735827 + 0.997289i \(0.476557\pi\)
\(420\) 0 0
\(421\) −38.9520 −1.89840 −0.949201 0.314670i \(-0.898106\pi\)
−0.949201 + 0.314670i \(0.898106\pi\)
\(422\) −13.3550 −0.650113
\(423\) 0 0
\(424\) −12.8841 −0.625705
\(425\) −25.2363 −1.22414
\(426\) 0 0
\(427\) 5.69337 0.275522
\(428\) −14.3087 −0.691636
\(429\) 0 0
\(430\) −8.00720 −0.386142
\(431\) −5.42792 −0.261454 −0.130727 0.991418i \(-0.541731\pi\)
−0.130727 + 0.991418i \(0.541731\pi\)
\(432\) 0 0
\(433\) 22.8723 1.09917 0.549587 0.835436i \(-0.314785\pi\)
0.549587 + 0.835436i \(0.314785\pi\)
\(434\) 1.66790 0.0800615
\(435\) 0 0
\(436\) −7.75669 −0.371478
\(437\) 4.03471 0.193006
\(438\) 0 0
\(439\) −7.90666 −0.377364 −0.188682 0.982038i \(-0.560422\pi\)
−0.188682 + 0.982038i \(0.560422\pi\)
\(440\) −4.54236 −0.216549
\(441\) 0 0
\(442\) 25.1234 1.19500
\(443\) −10.0631 −0.478110 −0.239055 0.971006i \(-0.576838\pi\)
−0.239055 + 0.971006i \(0.576838\pi\)
\(444\) 0 0
\(445\) −18.3278 −0.868821
\(446\) −18.7279 −0.886792
\(447\) 0 0
\(448\) 0.506529 0.0239312
\(449\) 13.1764 0.621831 0.310915 0.950438i \(-0.399364\pi\)
0.310915 + 0.950438i \(0.399364\pi\)
\(450\) 0 0
\(451\) −40.9356 −1.92758
\(452\) −1.71654 −0.0807393
\(453\) 0 0
\(454\) −8.54460 −0.401018
\(455\) 2.14253 0.100443
\(456\) 0 0
\(457\) 15.0444 0.703749 0.351874 0.936047i \(-0.385544\pi\)
0.351874 + 0.936047i \(0.385544\pi\)
\(458\) 5.34208 0.249619
\(459\) 0 0
\(460\) 2.02085 0.0942227
\(461\) −0.361142 −0.0168201 −0.00841003 0.999965i \(-0.502677\pi\)
−0.00841003 + 0.999965i \(0.502677\pi\)
\(462\) 0 0
\(463\) 3.07957 0.143120 0.0715599 0.997436i \(-0.477202\pi\)
0.0715599 + 0.997436i \(0.477202\pi\)
\(464\) 4.21919 0.195871
\(465\) 0 0
\(466\) −14.8123 −0.686167
\(467\) 25.3161 1.17149 0.585746 0.810495i \(-0.300802\pi\)
0.585746 + 0.810495i \(0.300802\pi\)
\(468\) 0 0
\(469\) −2.53766 −0.117178
\(470\) −4.88898 −0.225512
\(471\) 0 0
\(472\) 7.05273 0.324628
\(473\) 26.5473 1.22064
\(474\) 0 0
\(475\) 8.48296 0.389225
\(476\) 3.52153 0.161409
\(477\) 0 0
\(478\) −6.91374 −0.316227
\(479\) 11.9963 0.548123 0.274062 0.961712i \(-0.411633\pi\)
0.274062 + 0.961712i \(0.411633\pi\)
\(480\) 0 0
\(481\) 25.4498 1.16041
\(482\) −8.56369 −0.390065
\(483\) 0 0
\(484\) 4.05985 0.184539
\(485\) −1.19588 −0.0543021
\(486\) 0 0
\(487\) −15.3061 −0.693585 −0.346792 0.937942i \(-0.612729\pi\)
−0.346792 + 0.937942i \(0.612729\pi\)
\(488\) −11.2400 −0.508810
\(489\) 0 0
\(490\) −7.89318 −0.356578
\(491\) 18.7839 0.847706 0.423853 0.905731i \(-0.360677\pi\)
0.423853 + 0.905731i \(0.360677\pi\)
\(492\) 0 0
\(493\) 29.3329 1.32109
\(494\) −8.44501 −0.379959
\(495\) 0 0
\(496\) −3.29279 −0.147851
\(497\) −0.467939 −0.0209899
\(498\) 0 0
\(499\) −2.22731 −0.0997079 −0.0498540 0.998757i \(-0.515876\pi\)
−0.0498540 + 0.998757i \(0.515876\pi\)
\(500\) 10.1013 0.451745
\(501\) 0 0
\(502\) −16.1199 −0.719468
\(503\) 10.4225 0.464716 0.232358 0.972630i \(-0.425356\pi\)
0.232358 + 0.972630i \(0.425356\pi\)
\(504\) 0 0
\(505\) 5.05907 0.225126
\(506\) −6.69998 −0.297850
\(507\) 0 0
\(508\) 3.86129 0.171317
\(509\) 25.1510 1.11480 0.557400 0.830244i \(-0.311799\pi\)
0.557400 + 0.830244i \(0.311799\pi\)
\(510\) 0 0
\(511\) 1.25077 0.0553307
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −2.39190 −0.105502
\(515\) −8.12447 −0.358007
\(516\) 0 0
\(517\) 16.2090 0.712873
\(518\) 3.56727 0.156737
\(519\) 0 0
\(520\) −4.22983 −0.185490
\(521\) 30.0875 1.31816 0.659078 0.752074i \(-0.270947\pi\)
0.659078 + 0.752074i \(0.270947\pi\)
\(522\) 0 0
\(523\) −23.8359 −1.04227 −0.521137 0.853473i \(-0.674492\pi\)
−0.521137 + 0.853473i \(0.674492\pi\)
\(524\) −7.45036 −0.325470
\(525\) 0 0
\(526\) 28.7218 1.25233
\(527\) −22.8924 −0.997209
\(528\) 0 0
\(529\) −20.0192 −0.870402
\(530\) 15.0808 0.655067
\(531\) 0 0
\(532\) −1.18373 −0.0513212
\(533\) −38.1191 −1.65112
\(534\) 0 0
\(535\) 16.7483 0.724093
\(536\) 5.00991 0.216395
\(537\) 0 0
\(538\) 10.6420 0.458808
\(539\) 26.1692 1.12719
\(540\) 0 0
\(541\) −16.0897 −0.691750 −0.345875 0.938281i \(-0.612418\pi\)
−0.345875 + 0.938281i \(0.612418\pi\)
\(542\) 16.2311 0.697185
\(543\) 0 0
\(544\) −6.95227 −0.298076
\(545\) 9.07921 0.388910
\(546\) 0 0
\(547\) −1.17274 −0.0501429 −0.0250715 0.999686i \(-0.507981\pi\)
−0.0250715 + 0.999686i \(0.507981\pi\)
\(548\) −11.7309 −0.501117
\(549\) 0 0
\(550\) −14.0867 −0.600658
\(551\) −9.86001 −0.420051
\(552\) 0 0
\(553\) −3.95489 −0.168179
\(554\) 17.4271 0.740404
\(555\) 0 0
\(556\) −0.614537 −0.0260622
\(557\) −32.1956 −1.36417 −0.682086 0.731272i \(-0.738927\pi\)
−0.682086 + 0.731272i \(0.738927\pi\)
\(558\) 0 0
\(559\) 24.7207 1.04557
\(560\) −0.592892 −0.0250542
\(561\) 0 0
\(562\) −10.0480 −0.423850
\(563\) 39.9085 1.68194 0.840970 0.541081i \(-0.181985\pi\)
0.840970 + 0.541081i \(0.181985\pi\)
\(564\) 0 0
\(565\) 2.00921 0.0845282
\(566\) 2.11210 0.0887780
\(567\) 0 0
\(568\) 0.923816 0.0387624
\(569\) 45.1626 1.89331 0.946657 0.322244i \(-0.104437\pi\)
0.946657 + 0.322244i \(0.104437\pi\)
\(570\) 0 0
\(571\) 8.79540 0.368076 0.184038 0.982919i \(-0.441083\pi\)
0.184038 + 0.982919i \(0.441083\pi\)
\(572\) 14.0237 0.586359
\(573\) 0 0
\(574\) −5.34312 −0.223018
\(575\) 6.26703 0.261353
\(576\) 0 0
\(577\) 20.4382 0.850855 0.425427 0.904993i \(-0.360124\pi\)
0.425427 + 0.904993i \(0.360124\pi\)
\(578\) −31.3341 −1.30333
\(579\) 0 0
\(580\) −4.93855 −0.205062
\(581\) −4.05646 −0.168290
\(582\) 0 0
\(583\) −49.9992 −2.07075
\(584\) −2.46929 −0.102180
\(585\) 0 0
\(586\) 17.4877 0.722409
\(587\) −40.4128 −1.66801 −0.834007 0.551753i \(-0.813959\pi\)
−0.834007 + 0.551753i \(0.813959\pi\)
\(588\) 0 0
\(589\) 7.69509 0.317071
\(590\) −8.25522 −0.339862
\(591\) 0 0
\(592\) −7.04259 −0.289449
\(593\) 17.1642 0.704850 0.352425 0.935840i \(-0.385357\pi\)
0.352425 + 0.935840i \(0.385357\pi\)
\(594\) 0 0
\(595\) −4.12195 −0.168983
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −6.23900 −0.255131
\(599\) 11.0793 0.452689 0.226345 0.974047i \(-0.427322\pi\)
0.226345 + 0.974047i \(0.427322\pi\)
\(600\) 0 0
\(601\) −11.3103 −0.461358 −0.230679 0.973030i \(-0.574095\pi\)
−0.230679 + 0.973030i \(0.574095\pi\)
\(602\) 3.46508 0.141226
\(603\) 0 0
\(604\) 17.5323 0.713378
\(605\) −4.75206 −0.193199
\(606\) 0 0
\(607\) −10.9521 −0.444533 −0.222267 0.974986i \(-0.571346\pi\)
−0.222267 + 0.974986i \(0.571346\pi\)
\(608\) 2.33695 0.0947757
\(609\) 0 0
\(610\) 13.1564 0.532687
\(611\) 15.0938 0.610629
\(612\) 0 0
\(613\) 6.68464 0.269990 0.134995 0.990846i \(-0.456898\pi\)
0.134995 + 0.990846i \(0.456898\pi\)
\(614\) −14.4985 −0.585112
\(615\) 0 0
\(616\) 1.96569 0.0791998
\(617\) 21.3178 0.858222 0.429111 0.903252i \(-0.358827\pi\)
0.429111 + 0.903252i \(0.358827\pi\)
\(618\) 0 0
\(619\) −27.6883 −1.11289 −0.556443 0.830885i \(-0.687834\pi\)
−0.556443 + 0.830885i \(0.687834\pi\)
\(620\) 3.85422 0.154789
\(621\) 0 0
\(622\) 27.0815 1.08587
\(623\) 7.93127 0.317760
\(624\) 0 0
\(625\) 6.32605 0.253042
\(626\) −20.4400 −0.816946
\(627\) 0 0
\(628\) 22.2770 0.888950
\(629\) −48.9620 −1.95224
\(630\) 0 0
\(631\) 37.1206 1.47775 0.738874 0.673843i \(-0.235358\pi\)
0.738874 + 0.673843i \(0.235358\pi\)
\(632\) 7.80783 0.310579
\(633\) 0 0
\(634\) 10.5261 0.418046
\(635\) −4.51964 −0.179356
\(636\) 0 0
\(637\) 24.3687 0.965523
\(638\) 16.3734 0.648229
\(639\) 0 0
\(640\) 1.17050 0.0462681
\(641\) −8.02175 −0.316840 −0.158420 0.987372i \(-0.550640\pi\)
−0.158420 + 0.987372i \(0.550640\pi\)
\(642\) 0 0
\(643\) 1.00334 0.0395677 0.0197839 0.999804i \(-0.493702\pi\)
0.0197839 + 0.999804i \(0.493702\pi\)
\(644\) −0.874515 −0.0344607
\(645\) 0 0
\(646\) 16.2471 0.639234
\(647\) 27.4169 1.07787 0.538935 0.842347i \(-0.318827\pi\)
0.538935 + 0.842347i \(0.318827\pi\)
\(648\) 0 0
\(649\) 27.3696 1.07435
\(650\) −13.1175 −0.514509
\(651\) 0 0
\(652\) 13.4831 0.528038
\(653\) 39.3088 1.53827 0.769137 0.639084i \(-0.220686\pi\)
0.769137 + 0.639084i \(0.220686\pi\)
\(654\) 0 0
\(655\) 8.72064 0.340744
\(656\) 10.5485 0.411850
\(657\) 0 0
\(658\) 2.11568 0.0824780
\(659\) 36.5849 1.42515 0.712573 0.701598i \(-0.247530\pi\)
0.712573 + 0.701598i \(0.247530\pi\)
\(660\) 0 0
\(661\) −13.5700 −0.527810 −0.263905 0.964549i \(-0.585011\pi\)
−0.263905 + 0.964549i \(0.585011\pi\)
\(662\) 10.1909 0.396079
\(663\) 0 0
\(664\) 8.00835 0.310784
\(665\) 1.38556 0.0537296
\(666\) 0 0
\(667\) −7.28437 −0.282052
\(668\) 12.6208 0.488313
\(669\) 0 0
\(670\) −5.86410 −0.226550
\(671\) −43.6190 −1.68389
\(672\) 0 0
\(673\) −1.54169 −0.0594279 −0.0297139 0.999558i \(-0.509460\pi\)
−0.0297139 + 0.999558i \(0.509460\pi\)
\(674\) 14.6134 0.562886
\(675\) 0 0
\(676\) 0.0587896 0.00226114
\(677\) −2.97532 −0.114351 −0.0571755 0.998364i \(-0.518209\pi\)
−0.0571755 + 0.998364i \(0.518209\pi\)
\(678\) 0 0
\(679\) 0.517512 0.0198603
\(680\) 8.13763 0.312064
\(681\) 0 0
\(682\) −12.7784 −0.489309
\(683\) 6.60805 0.252850 0.126425 0.991976i \(-0.459650\pi\)
0.126425 + 0.991976i \(0.459650\pi\)
\(684\) 0 0
\(685\) 13.7310 0.524633
\(686\) 6.96144 0.265789
\(687\) 0 0
\(688\) −6.84084 −0.260805
\(689\) −46.5590 −1.77376
\(690\) 0 0
\(691\) −16.9869 −0.646212 −0.323106 0.946363i \(-0.604727\pi\)
−0.323106 + 0.946363i \(0.604727\pi\)
\(692\) 13.5303 0.514346
\(693\) 0 0
\(694\) −18.1962 −0.690717
\(695\) 0.719316 0.0272852
\(696\) 0 0
\(697\) 73.3361 2.77780
\(698\) −18.9456 −0.717101
\(699\) 0 0
\(700\) −1.83866 −0.0694950
\(701\) 16.5146 0.623747 0.311873 0.950124i \(-0.399044\pi\)
0.311873 + 0.950124i \(0.399044\pi\)
\(702\) 0 0
\(703\) 16.4582 0.620731
\(704\) −3.88070 −0.146259
\(705\) 0 0
\(706\) −36.1335 −1.35990
\(707\) −2.18929 −0.0823367
\(708\) 0 0
\(709\) −1.25383 −0.0470885 −0.0235442 0.999723i \(-0.507495\pi\)
−0.0235442 + 0.999723i \(0.507495\pi\)
\(710\) −1.08133 −0.0405814
\(711\) 0 0
\(712\) −15.6581 −0.586812
\(713\) 5.68497 0.212904
\(714\) 0 0
\(715\) −16.4147 −0.613875
\(716\) −7.23353 −0.270330
\(717\) 0 0
\(718\) −13.2222 −0.493449
\(719\) 50.6632 1.88942 0.944709 0.327909i \(-0.106344\pi\)
0.944709 + 0.327909i \(0.106344\pi\)
\(720\) 0 0
\(721\) 3.51583 0.130936
\(722\) 13.5387 0.503857
\(723\) 0 0
\(724\) 3.30723 0.122912
\(725\) −15.3154 −0.568798
\(726\) 0 0
\(727\) 20.3402 0.754378 0.377189 0.926136i \(-0.376891\pi\)
0.377189 + 0.926136i \(0.376891\pi\)
\(728\) 1.83044 0.0678406
\(729\) 0 0
\(730\) 2.89031 0.106975
\(731\) −47.5594 −1.75905
\(732\) 0 0
\(733\) 17.1935 0.635058 0.317529 0.948249i \(-0.397147\pi\)
0.317529 + 0.948249i \(0.397147\pi\)
\(734\) 2.09001 0.0771437
\(735\) 0 0
\(736\) 1.72649 0.0636391
\(737\) 19.4420 0.716154
\(738\) 0 0
\(739\) 40.2873 1.48199 0.740996 0.671509i \(-0.234354\pi\)
0.740996 + 0.671509i \(0.234354\pi\)
\(740\) 8.24335 0.303032
\(741\) 0 0
\(742\) −6.52614 −0.239582
\(743\) −13.2514 −0.486145 −0.243073 0.970008i \(-0.578155\pi\)
−0.243073 + 0.970008i \(0.578155\pi\)
\(744\) 0 0
\(745\) −1.17050 −0.0428838
\(746\) 15.6737 0.573854
\(747\) 0 0
\(748\) −26.9797 −0.986476
\(749\) −7.24776 −0.264827
\(750\) 0 0
\(751\) 38.9147 1.42002 0.710010 0.704192i \(-0.248691\pi\)
0.710010 + 0.704192i \(0.248691\pi\)
\(752\) −4.17683 −0.152313
\(753\) 0 0
\(754\) 15.2468 0.555257
\(755\) −20.5215 −0.746855
\(756\) 0 0
\(757\) 5.51490 0.200442 0.100221 0.994965i \(-0.468045\pi\)
0.100221 + 0.994965i \(0.468045\pi\)
\(758\) −29.1521 −1.05885
\(759\) 0 0
\(760\) −2.73540 −0.0992232
\(761\) −40.3355 −1.46216 −0.731081 0.682291i \(-0.760984\pi\)
−0.731081 + 0.682291i \(0.760984\pi\)
\(762\) 0 0
\(763\) −3.92899 −0.142239
\(764\) 12.7158 0.460042
\(765\) 0 0
\(766\) 13.1248 0.474219
\(767\) 25.4864 0.920262
\(768\) 0 0
\(769\) 15.9355 0.574648 0.287324 0.957833i \(-0.407234\pi\)
0.287324 + 0.957833i \(0.407234\pi\)
\(770\) −2.30084 −0.0829164
\(771\) 0 0
\(772\) −3.36901 −0.121253
\(773\) −26.9572 −0.969584 −0.484792 0.874629i \(-0.661105\pi\)
−0.484792 + 0.874629i \(0.661105\pi\)
\(774\) 0 0
\(775\) 11.9526 0.429351
\(776\) −1.02168 −0.0366763
\(777\) 0 0
\(778\) −32.1642 −1.15314
\(779\) −24.6513 −0.883225
\(780\) 0 0
\(781\) 3.58505 0.128283
\(782\) 12.0030 0.429227
\(783\) 0 0
\(784\) −6.74343 −0.240837
\(785\) −26.0752 −0.930665
\(786\) 0 0
\(787\) 51.2529 1.82697 0.913484 0.406875i \(-0.133381\pi\)
0.913484 + 0.406875i \(0.133381\pi\)
\(788\) −0.815685 −0.0290576
\(789\) 0 0
\(790\) −9.13906 −0.325153
\(791\) −0.869478 −0.0309151
\(792\) 0 0
\(793\) −40.6179 −1.44238
\(794\) −33.8252 −1.20041
\(795\) 0 0
\(796\) 5.35685 0.189868
\(797\) −10.0808 −0.357082 −0.178541 0.983933i \(-0.557138\pi\)
−0.178541 + 0.983933i \(0.557138\pi\)
\(798\) 0 0
\(799\) −29.0385 −1.02731
\(800\) 3.62993 0.128337
\(801\) 0 0
\(802\) 9.59093 0.338667
\(803\) −9.58260 −0.338163
\(804\) 0 0
\(805\) 1.02362 0.0360778
\(806\) −11.8992 −0.419130
\(807\) 0 0
\(808\) 4.32214 0.152052
\(809\) −8.55995 −0.300952 −0.150476 0.988614i \(-0.548081\pi\)
−0.150476 + 0.988614i \(0.548081\pi\)
\(810\) 0 0
\(811\) −7.01809 −0.246439 −0.123219 0.992379i \(-0.539322\pi\)
−0.123219 + 0.992379i \(0.539322\pi\)
\(812\) 2.13714 0.0749989
\(813\) 0 0
\(814\) −27.3302 −0.957923
\(815\) −15.7819 −0.552817
\(816\) 0 0
\(817\) 15.9867 0.559303
\(818\) 6.89619 0.241120
\(819\) 0 0
\(820\) −12.3470 −0.431177
\(821\) −16.3421 −0.570344 −0.285172 0.958476i \(-0.592051\pi\)
−0.285172 + 0.958476i \(0.592051\pi\)
\(822\) 0 0
\(823\) 30.5614 1.06530 0.532652 0.846335i \(-0.321196\pi\)
0.532652 + 0.846335i \(0.321196\pi\)
\(824\) −6.94103 −0.241802
\(825\) 0 0
\(826\) 3.57241 0.124300
\(827\) −3.44532 −0.119805 −0.0599027 0.998204i \(-0.519079\pi\)
−0.0599027 + 0.998204i \(0.519079\pi\)
\(828\) 0 0
\(829\) −12.4705 −0.433120 −0.216560 0.976269i \(-0.569484\pi\)
−0.216560 + 0.976269i \(0.569484\pi\)
\(830\) −9.37377 −0.325368
\(831\) 0 0
\(832\) −3.61369 −0.125282
\(833\) −46.8822 −1.62437
\(834\) 0 0
\(835\) −14.7726 −0.511228
\(836\) 9.06900 0.313658
\(837\) 0 0
\(838\) −3.01240 −0.104062
\(839\) 30.3546 1.04796 0.523979 0.851731i \(-0.324447\pi\)
0.523979 + 0.851731i \(0.324447\pi\)
\(840\) 0 0
\(841\) −11.1985 −0.386154
\(842\) 38.9520 1.34237
\(843\) 0 0
\(844\) 13.3550 0.459699
\(845\) −0.0688132 −0.00236724
\(846\) 0 0
\(847\) 2.05643 0.0706598
\(848\) 12.8841 0.442440
\(849\) 0 0
\(850\) 25.2363 0.865597
\(851\) 12.1589 0.416803
\(852\) 0 0
\(853\) −41.6101 −1.42470 −0.712351 0.701824i \(-0.752369\pi\)
−0.712351 + 0.701824i \(0.752369\pi\)
\(854\) −5.69337 −0.194823
\(855\) 0 0
\(856\) 14.3087 0.489061
\(857\) 39.6564 1.35464 0.677318 0.735690i \(-0.263142\pi\)
0.677318 + 0.735690i \(0.263142\pi\)
\(858\) 0 0
\(859\) 46.6299 1.59099 0.795497 0.605958i \(-0.207210\pi\)
0.795497 + 0.605958i \(0.207210\pi\)
\(860\) 8.00720 0.273043
\(861\) 0 0
\(862\) 5.42792 0.184876
\(863\) 32.8049 1.11669 0.558346 0.829608i \(-0.311436\pi\)
0.558346 + 0.829608i \(0.311436\pi\)
\(864\) 0 0
\(865\) −15.8372 −0.538482
\(866\) −22.8723 −0.777234
\(867\) 0 0
\(868\) −1.66790 −0.0566121
\(869\) 30.2999 1.02785
\(870\) 0 0
\(871\) 18.1043 0.613440
\(872\) 7.75669 0.262675
\(873\) 0 0
\(874\) −4.03471 −0.136476
\(875\) 5.11661 0.172973
\(876\) 0 0
\(877\) −39.7704 −1.34295 −0.671475 0.741027i \(-0.734339\pi\)
−0.671475 + 0.741027i \(0.734339\pi\)
\(878\) 7.90666 0.266837
\(879\) 0 0
\(880\) 4.54236 0.153123
\(881\) 27.5405 0.927861 0.463931 0.885871i \(-0.346439\pi\)
0.463931 + 0.885871i \(0.346439\pi\)
\(882\) 0 0
\(883\) 47.8260 1.60947 0.804737 0.593632i \(-0.202306\pi\)
0.804737 + 0.593632i \(0.202306\pi\)
\(884\) −25.1234 −0.844991
\(885\) 0 0
\(886\) 10.0631 0.338075
\(887\) −45.4546 −1.52622 −0.763108 0.646271i \(-0.776327\pi\)
−0.763108 + 0.646271i \(0.776327\pi\)
\(888\) 0 0
\(889\) 1.95585 0.0655972
\(890\) 18.3278 0.614349
\(891\) 0 0
\(892\) 18.7279 0.627057
\(893\) 9.76103 0.326640
\(894\) 0 0
\(895\) 8.46684 0.283015
\(896\) −0.506529 −0.0169219
\(897\) 0 0
\(898\) −13.1764 −0.439701
\(899\) −13.8929 −0.463355
\(900\) 0 0
\(901\) 89.5735 2.98412
\(902\) 40.9356 1.36301
\(903\) 0 0
\(904\) 1.71654 0.0570913
\(905\) −3.87111 −0.128680
\(906\) 0 0
\(907\) −12.7377 −0.422947 −0.211473 0.977384i \(-0.567826\pi\)
−0.211473 + 0.977384i \(0.567826\pi\)
\(908\) 8.54460 0.283562
\(909\) 0 0
\(910\) −2.14253 −0.0710242
\(911\) 39.3617 1.30411 0.652055 0.758171i \(-0.273907\pi\)
0.652055 + 0.758171i \(0.273907\pi\)
\(912\) 0 0
\(913\) 31.0780 1.02853
\(914\) −15.0444 −0.497626
\(915\) 0 0
\(916\) −5.34208 −0.176507
\(917\) −3.77382 −0.124623
\(918\) 0 0
\(919\) −21.2378 −0.700570 −0.350285 0.936643i \(-0.613915\pi\)
−0.350285 + 0.936643i \(0.613915\pi\)
\(920\) −2.02085 −0.0666255
\(921\) 0 0
\(922\) 0.361142 0.0118936
\(923\) 3.33839 0.109884
\(924\) 0 0
\(925\) 25.5641 0.840543
\(926\) −3.07957 −0.101201
\(927\) 0 0
\(928\) −4.21919 −0.138502
\(929\) 28.3154 0.928997 0.464498 0.885574i \(-0.346235\pi\)
0.464498 + 0.885574i \(0.346235\pi\)
\(930\) 0 0
\(931\) 15.7590 0.516482
\(932\) 14.8123 0.485194
\(933\) 0 0
\(934\) −25.3161 −0.828369
\(935\) 31.5797 1.03277
\(936\) 0 0
\(937\) 40.8706 1.33519 0.667593 0.744527i \(-0.267325\pi\)
0.667593 + 0.744527i \(0.267325\pi\)
\(938\) 2.53766 0.0828576
\(939\) 0 0
\(940\) 4.88898 0.159461
\(941\) −16.4529 −0.536349 −0.268174 0.963370i \(-0.586420\pi\)
−0.268174 + 0.963370i \(0.586420\pi\)
\(942\) 0 0
\(943\) −18.2119 −0.593060
\(944\) −7.05273 −0.229547
\(945\) 0 0
\(946\) −26.5473 −0.863126
\(947\) −17.3768 −0.564671 −0.282335 0.959316i \(-0.591109\pi\)
−0.282335 + 0.959316i \(0.591109\pi\)
\(948\) 0 0
\(949\) −8.92328 −0.289662
\(950\) −8.48296 −0.275223
\(951\) 0 0
\(952\) −3.52153 −0.114133
\(953\) −47.2562 −1.53078 −0.765389 0.643568i \(-0.777453\pi\)
−0.765389 + 0.643568i \(0.777453\pi\)
\(954\) 0 0
\(955\) −14.8838 −0.481630
\(956\) 6.91374 0.223606
\(957\) 0 0
\(958\) −11.9963 −0.387582
\(959\) −5.94202 −0.191878
\(960\) 0 0
\(961\) −20.1575 −0.650242
\(962\) −25.4498 −0.820534
\(963\) 0 0
\(964\) 8.56369 0.275818
\(965\) 3.94342 0.126943
\(966\) 0 0
\(967\) −45.1307 −1.45131 −0.725653 0.688061i \(-0.758462\pi\)
−0.725653 + 0.688061i \(0.758462\pi\)
\(968\) −4.05985 −0.130489
\(969\) 0 0
\(970\) 1.19588 0.0383974
\(971\) 7.05507 0.226408 0.113204 0.993572i \(-0.463889\pi\)
0.113204 + 0.993572i \(0.463889\pi\)
\(972\) 0 0
\(973\) −0.311281 −0.00997921
\(974\) 15.3061 0.490438
\(975\) 0 0
\(976\) 11.2400 0.359783
\(977\) −5.88708 −0.188344 −0.0941721 0.995556i \(-0.530020\pi\)
−0.0941721 + 0.995556i \(0.530020\pi\)
\(978\) 0 0
\(979\) −60.7644 −1.94204
\(980\) 7.89318 0.252138
\(981\) 0 0
\(982\) −18.7839 −0.599419
\(983\) −21.2758 −0.678593 −0.339297 0.940679i \(-0.610189\pi\)
−0.339297 + 0.940679i \(0.610189\pi\)
\(984\) 0 0
\(985\) 0.954758 0.0304211
\(986\) −29.3329 −0.934151
\(987\) 0 0
\(988\) 8.44501 0.268672
\(989\) 11.8106 0.375556
\(990\) 0 0
\(991\) −33.3295 −1.05875 −0.529373 0.848389i \(-0.677573\pi\)
−0.529373 + 0.848389i \(0.677573\pi\)
\(992\) 3.29279 0.104546
\(993\) 0 0
\(994\) 0.467939 0.0148421
\(995\) −6.27019 −0.198778
\(996\) 0 0
\(997\) −2.18494 −0.0691979 −0.0345989 0.999401i \(-0.511015\pi\)
−0.0345989 + 0.999401i \(0.511015\pi\)
\(998\) 2.22731 0.0705042
\(999\) 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 \(a_p\))