Properties

Label 6039.2.a.j.1.8
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(0.179763\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.179763 q^{2}\) \(-1.96769 q^{4}\) \(-2.20477 q^{5}\) \(+3.17177 q^{7}\) \(-0.713244 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.179763 q^{2}\) \(-1.96769 q^{4}\) \(-2.20477 q^{5}\) \(+3.17177 q^{7}\) \(-0.713244 q^{8}\) \(-0.396336 q^{10}\) \(+1.00000 q^{11}\) \(+5.02358 q^{13}\) \(+0.570167 q^{14}\) \(+3.80716 q^{16}\) \(-1.08785 q^{17}\) \(+3.53893 q^{19}\) \(+4.33828 q^{20}\) \(+0.179763 q^{22}\) \(-1.91419 q^{23}\) \(-0.139010 q^{25}\) \(+0.903056 q^{26}\) \(-6.24104 q^{28}\) \(+5.13495 q^{29}\) \(-0.976010 q^{31}\) \(+2.11088 q^{32}\) \(-0.195555 q^{34}\) \(-6.99300 q^{35}\) \(+7.67629 q^{37}\) \(+0.636169 q^{38}\) \(+1.57254 q^{40}\) \(+2.80345 q^{41}\) \(-7.46749 q^{43}\) \(-1.96769 q^{44}\) \(-0.344102 q^{46}\) \(-5.09413 q^{47}\) \(+3.06010 q^{49}\) \(-0.0249889 q^{50}\) \(-9.88482 q^{52}\) \(+10.9620 q^{53}\) \(-2.20477 q^{55}\) \(-2.26224 q^{56}\) \(+0.923076 q^{58}\) \(-8.89797 q^{59}\) \(+1.00000 q^{61}\) \(-0.175451 q^{62}\) \(-7.23485 q^{64}\) \(-11.0758 q^{65}\) \(-6.12066 q^{67}\) \(+2.14054 q^{68}\) \(-1.25709 q^{70}\) \(-10.4162 q^{71}\) \(+12.2613 q^{73}\) \(+1.37992 q^{74}\) \(-6.96349 q^{76}\) \(+3.17177 q^{77}\) \(+15.6773 q^{79}\) \(-8.39388 q^{80}\) \(+0.503958 q^{82}\) \(-10.7598 q^{83}\) \(+2.39845 q^{85}\) \(-1.34238 q^{86}\) \(-0.713244 q^{88}\) \(+14.2391 q^{89}\) \(+15.9336 q^{91}\) \(+3.76653 q^{92}\) \(-0.915737 q^{94}\) \(-7.80250 q^{95}\) \(-13.8759 q^{97}\) \(+0.550094 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.179763 0.127112 0.0635560 0.997978i \(-0.479756\pi\)
0.0635560 + 0.997978i \(0.479756\pi\)
\(3\) 0 0
\(4\) −1.96769 −0.983843
\(5\) −2.20477 −0.986001 −0.493001 0.870029i \(-0.664100\pi\)
−0.493001 + 0.870029i \(0.664100\pi\)
\(6\) 0 0
\(7\) 3.17177 1.19881 0.599407 0.800444i \(-0.295403\pi\)
0.599407 + 0.800444i \(0.295403\pi\)
\(8\) −0.713244 −0.252170
\(9\) 0 0
\(10\) −0.396336 −0.125332
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 5.02358 1.39329 0.696645 0.717416i \(-0.254675\pi\)
0.696645 + 0.717416i \(0.254675\pi\)
\(14\) 0.570167 0.152384
\(15\) 0 0
\(16\) 3.80716 0.951789
\(17\) −1.08785 −0.263842 −0.131921 0.991260i \(-0.542114\pi\)
−0.131921 + 0.991260i \(0.542114\pi\)
\(18\) 0 0
\(19\) 3.53893 0.811885 0.405943 0.913899i \(-0.366943\pi\)
0.405943 + 0.913899i \(0.366943\pi\)
\(20\) 4.33828 0.970070
\(21\) 0 0
\(22\) 0.179763 0.0383257
\(23\) −1.91419 −0.399137 −0.199568 0.979884i \(-0.563954\pi\)
−0.199568 + 0.979884i \(0.563954\pi\)
\(24\) 0 0
\(25\) −0.139010 −0.0278020
\(26\) 0.903056 0.177104
\(27\) 0 0
\(28\) −6.24104 −1.17944
\(29\) 5.13495 0.953537 0.476768 0.879029i \(-0.341808\pi\)
0.476768 + 0.879029i \(0.341808\pi\)
\(30\) 0 0
\(31\) −0.976010 −0.175297 −0.0876483 0.996151i \(-0.527935\pi\)
−0.0876483 + 0.996151i \(0.527935\pi\)
\(32\) 2.11088 0.373154
\(33\) 0 0
\(34\) −0.195555 −0.0335374
\(35\) −6.99300 −1.18203
\(36\) 0 0
\(37\) 7.67629 1.26197 0.630987 0.775793i \(-0.282650\pi\)
0.630987 + 0.775793i \(0.282650\pi\)
\(38\) 0.636169 0.103200
\(39\) 0 0
\(40\) 1.57254 0.248640
\(41\) 2.80345 0.437826 0.218913 0.975744i \(-0.429749\pi\)
0.218913 + 0.975744i \(0.429749\pi\)
\(42\) 0 0
\(43\) −7.46749 −1.13878 −0.569391 0.822067i \(-0.692821\pi\)
−0.569391 + 0.822067i \(0.692821\pi\)
\(44\) −1.96769 −0.296640
\(45\) 0 0
\(46\) −0.344102 −0.0507350
\(47\) −5.09413 −0.743055 −0.371527 0.928422i \(-0.621166\pi\)
−0.371527 + 0.928422i \(0.621166\pi\)
\(48\) 0 0
\(49\) 3.06010 0.437157
\(50\) −0.0249889 −0.00353396
\(51\) 0 0
\(52\) −9.88482 −1.37078
\(53\) 10.9620 1.50574 0.752870 0.658169i \(-0.228669\pi\)
0.752870 + 0.658169i \(0.228669\pi\)
\(54\) 0 0
\(55\) −2.20477 −0.297290
\(56\) −2.26224 −0.302305
\(57\) 0 0
\(58\) 0.923076 0.121206
\(59\) −8.89797 −1.15842 −0.579209 0.815179i \(-0.696638\pi\)
−0.579209 + 0.815179i \(0.696638\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −0.175451 −0.0222823
\(63\) 0 0
\(64\) −7.23485 −0.904356
\(65\) −11.0758 −1.37379
\(66\) 0 0
\(67\) −6.12066 −0.747757 −0.373879 0.927478i \(-0.621972\pi\)
−0.373879 + 0.927478i \(0.621972\pi\)
\(68\) 2.14054 0.259579
\(69\) 0 0
\(70\) −1.25709 −0.150250
\(71\) −10.4162 −1.23618 −0.618091 0.786107i \(-0.712093\pi\)
−0.618091 + 0.786107i \(0.712093\pi\)
\(72\) 0 0
\(73\) 12.2613 1.43508 0.717538 0.696519i \(-0.245269\pi\)
0.717538 + 0.696519i \(0.245269\pi\)
\(74\) 1.37992 0.160412
\(75\) 0 0
\(76\) −6.96349 −0.798767
\(77\) 3.17177 0.361456
\(78\) 0 0
\(79\) 15.6773 1.76384 0.881918 0.471402i \(-0.156252\pi\)
0.881918 + 0.471402i \(0.156252\pi\)
\(80\) −8.39388 −0.938465
\(81\) 0 0
\(82\) 0.503958 0.0556529
\(83\) −10.7598 −1.18105 −0.590523 0.807021i \(-0.701078\pi\)
−0.590523 + 0.807021i \(0.701078\pi\)
\(84\) 0 0
\(85\) 2.39845 0.260148
\(86\) −1.34238 −0.144753
\(87\) 0 0
\(88\) −0.713244 −0.0760321
\(89\) 14.2391 1.50934 0.754669 0.656106i \(-0.227797\pi\)
0.754669 + 0.656106i \(0.227797\pi\)
\(90\) 0 0
\(91\) 15.9336 1.67030
\(92\) 3.76653 0.392688
\(93\) 0 0
\(94\) −0.915737 −0.0944511
\(95\) −7.80250 −0.800520
\(96\) 0 0
\(97\) −13.8759 −1.40888 −0.704440 0.709763i \(-0.748802\pi\)
−0.704440 + 0.709763i \(0.748802\pi\)
\(98\) 0.550094 0.0555678
\(99\) 0 0
\(100\) 0.273528 0.0273528
\(101\) 3.48657 0.346927 0.173463 0.984840i \(-0.444504\pi\)
0.173463 + 0.984840i \(0.444504\pi\)
\(102\) 0 0
\(103\) −19.2415 −1.89592 −0.947960 0.318389i \(-0.896858\pi\)
−0.947960 + 0.318389i \(0.896858\pi\)
\(104\) −3.58304 −0.351346
\(105\) 0 0
\(106\) 1.97056 0.191398
\(107\) −2.82984 −0.273571 −0.136786 0.990601i \(-0.543677\pi\)
−0.136786 + 0.990601i \(0.543677\pi\)
\(108\) 0 0
\(109\) 7.46781 0.715287 0.357643 0.933858i \(-0.383580\pi\)
0.357643 + 0.933858i \(0.383580\pi\)
\(110\) −0.396336 −0.0377892
\(111\) 0 0
\(112\) 12.0754 1.14102
\(113\) 9.07728 0.853919 0.426959 0.904271i \(-0.359585\pi\)
0.426959 + 0.904271i \(0.359585\pi\)
\(114\) 0 0
\(115\) 4.22035 0.393549
\(116\) −10.1040 −0.938130
\(117\) 0 0
\(118\) −1.59953 −0.147249
\(119\) −3.45039 −0.316297
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0.179763 0.0162750
\(123\) 0 0
\(124\) 1.92048 0.172464
\(125\) 11.3303 1.01341
\(126\) 0 0
\(127\) 8.94879 0.794077 0.397039 0.917802i \(-0.370038\pi\)
0.397039 + 0.917802i \(0.370038\pi\)
\(128\) −5.52231 −0.488108
\(129\) 0 0
\(130\) −1.99103 −0.174625
\(131\) −13.9885 −1.22218 −0.611090 0.791561i \(-0.709268\pi\)
−0.611090 + 0.791561i \(0.709268\pi\)
\(132\) 0 0
\(133\) 11.2246 0.973300
\(134\) −1.10027 −0.0950488
\(135\) 0 0
\(136\) 0.775901 0.0665329
\(137\) −19.7992 −1.69156 −0.845781 0.533530i \(-0.820865\pi\)
−0.845781 + 0.533530i \(0.820865\pi\)
\(138\) 0 0
\(139\) −4.24898 −0.360394 −0.180197 0.983631i \(-0.557674\pi\)
−0.180197 + 0.983631i \(0.557674\pi\)
\(140\) 13.7600 1.16293
\(141\) 0 0
\(142\) −1.87246 −0.157133
\(143\) 5.02358 0.420093
\(144\) 0 0
\(145\) −11.3214 −0.940188
\(146\) 2.20413 0.182415
\(147\) 0 0
\(148\) −15.1045 −1.24158
\(149\) −4.17125 −0.341722 −0.170861 0.985295i \(-0.554655\pi\)
−0.170861 + 0.985295i \(0.554655\pi\)
\(150\) 0 0
\(151\) 18.0934 1.47242 0.736212 0.676751i \(-0.236613\pi\)
0.736212 + 0.676751i \(0.236613\pi\)
\(152\) −2.52412 −0.204733
\(153\) 0 0
\(154\) 0.570167 0.0459454
\(155\) 2.15187 0.172843
\(156\) 0 0
\(157\) 19.5799 1.56265 0.781323 0.624126i \(-0.214545\pi\)
0.781323 + 0.624126i \(0.214545\pi\)
\(158\) 2.81821 0.224205
\(159\) 0 0
\(160\) −4.65399 −0.367930
\(161\) −6.07137 −0.478491
\(162\) 0 0
\(163\) 14.3214 1.12174 0.560870 0.827904i \(-0.310467\pi\)
0.560870 + 0.827904i \(0.310467\pi\)
\(164\) −5.51632 −0.430752
\(165\) 0 0
\(166\) −1.93422 −0.150125
\(167\) −0.178130 −0.0137841 −0.00689205 0.999976i \(-0.502194\pi\)
−0.00689205 + 0.999976i \(0.502194\pi\)
\(168\) 0 0
\(169\) 12.2363 0.941258
\(170\) 0.431153 0.0330679
\(171\) 0 0
\(172\) 14.6937 1.12038
\(173\) −0.504790 −0.0383785 −0.0191892 0.999816i \(-0.506108\pi\)
−0.0191892 + 0.999816i \(0.506108\pi\)
\(174\) 0 0
\(175\) −0.440907 −0.0333294
\(176\) 3.80716 0.286975
\(177\) 0 0
\(178\) 2.55966 0.191855
\(179\) −12.0518 −0.900795 −0.450397 0.892828i \(-0.648718\pi\)
−0.450397 + 0.892828i \(0.648718\pi\)
\(180\) 0 0
\(181\) 23.8425 1.77220 0.886098 0.463497i \(-0.153406\pi\)
0.886098 + 0.463497i \(0.153406\pi\)
\(182\) 2.86428 0.212315
\(183\) 0 0
\(184\) 1.36529 0.100650
\(185\) −16.9244 −1.24431
\(186\) 0 0
\(187\) −1.08785 −0.0795512
\(188\) 10.0236 0.731049
\(189\) 0 0
\(190\) −1.40260 −0.101756
\(191\) 26.0154 1.88241 0.941205 0.337836i \(-0.109695\pi\)
0.941205 + 0.337836i \(0.109695\pi\)
\(192\) 0 0
\(193\) −3.89975 −0.280710 −0.140355 0.990101i \(-0.544824\pi\)
−0.140355 + 0.990101i \(0.544824\pi\)
\(194\) −2.49437 −0.179086
\(195\) 0 0
\(196\) −6.02131 −0.430093
\(197\) 21.9665 1.56505 0.782526 0.622618i \(-0.213931\pi\)
0.782526 + 0.622618i \(0.213931\pi\)
\(198\) 0 0
\(199\) 1.14129 0.0809040 0.0404520 0.999181i \(-0.487120\pi\)
0.0404520 + 0.999181i \(0.487120\pi\)
\(200\) 0.0991481 0.00701083
\(201\) 0 0
\(202\) 0.626758 0.0440985
\(203\) 16.2869 1.14311
\(204\) 0 0
\(205\) −6.18096 −0.431697
\(206\) −3.45892 −0.240994
\(207\) 0 0
\(208\) 19.1255 1.32612
\(209\) 3.53893 0.244793
\(210\) 0 0
\(211\) 9.40163 0.647235 0.323617 0.946188i \(-0.395101\pi\)
0.323617 + 0.946188i \(0.395101\pi\)
\(212\) −21.5697 −1.48141
\(213\) 0 0
\(214\) −0.508702 −0.0347742
\(215\) 16.4641 1.12284
\(216\) 0 0
\(217\) −3.09568 −0.210148
\(218\) 1.34244 0.0909215
\(219\) 0 0
\(220\) 4.33828 0.292487
\(221\) −5.46488 −0.367608
\(222\) 0 0
\(223\) 2.42729 0.162543 0.0812715 0.996692i \(-0.474102\pi\)
0.0812715 + 0.996692i \(0.474102\pi\)
\(224\) 6.69520 0.447342
\(225\) 0 0
\(226\) 1.63176 0.108543
\(227\) 19.4929 1.29379 0.646893 0.762581i \(-0.276068\pi\)
0.646893 + 0.762581i \(0.276068\pi\)
\(228\) 0 0
\(229\) 14.8284 0.979889 0.489944 0.871754i \(-0.337017\pi\)
0.489944 + 0.871754i \(0.337017\pi\)
\(230\) 0.758664 0.0500248
\(231\) 0 0
\(232\) −3.66248 −0.240453
\(233\) 9.17826 0.601288 0.300644 0.953736i \(-0.402798\pi\)
0.300644 + 0.953736i \(0.402798\pi\)
\(234\) 0 0
\(235\) 11.2314 0.732653
\(236\) 17.5084 1.13970
\(237\) 0 0
\(238\) −0.620255 −0.0402051
\(239\) −17.9788 −1.16296 −0.581478 0.813562i \(-0.697525\pi\)
−0.581478 + 0.813562i \(0.697525\pi\)
\(240\) 0 0
\(241\) −11.8019 −0.760226 −0.380113 0.924940i \(-0.624115\pi\)
−0.380113 + 0.924940i \(0.624115\pi\)
\(242\) 0.179763 0.0115556
\(243\) 0 0
\(244\) −1.96769 −0.125968
\(245\) −6.74680 −0.431037
\(246\) 0 0
\(247\) 17.7781 1.13119
\(248\) 0.696134 0.0442045
\(249\) 0 0
\(250\) 2.03677 0.128817
\(251\) 17.0765 1.07786 0.538929 0.842351i \(-0.318829\pi\)
0.538929 + 0.842351i \(0.318829\pi\)
\(252\) 0 0
\(253\) −1.91419 −0.120344
\(254\) 1.60867 0.100937
\(255\) 0 0
\(256\) 13.4770 0.842312
\(257\) −18.9734 −1.18353 −0.591763 0.806112i \(-0.701568\pi\)
−0.591763 + 0.806112i \(0.701568\pi\)
\(258\) 0 0
\(259\) 24.3474 1.51287
\(260\) 21.7937 1.35159
\(261\) 0 0
\(262\) −2.51462 −0.155354
\(263\) −14.6726 −0.904753 −0.452376 0.891827i \(-0.649424\pi\)
−0.452376 + 0.891827i \(0.649424\pi\)
\(264\) 0 0
\(265\) −24.1685 −1.48466
\(266\) 2.01778 0.123718
\(267\) 0 0
\(268\) 12.0435 0.735675
\(269\) 16.9485 1.03337 0.516685 0.856176i \(-0.327166\pi\)
0.516685 + 0.856176i \(0.327166\pi\)
\(270\) 0 0
\(271\) 6.59936 0.400883 0.200441 0.979706i \(-0.435762\pi\)
0.200441 + 0.979706i \(0.435762\pi\)
\(272\) −4.14160 −0.251121
\(273\) 0 0
\(274\) −3.55918 −0.215018
\(275\) −0.139010 −0.00838262
\(276\) 0 0
\(277\) −19.7287 −1.18538 −0.592692 0.805429i \(-0.701935\pi\)
−0.592692 + 0.805429i \(0.701935\pi\)
\(278\) −0.763811 −0.0458104
\(279\) 0 0
\(280\) 4.98772 0.298073
\(281\) 23.8313 1.42165 0.710827 0.703367i \(-0.248321\pi\)
0.710827 + 0.703367i \(0.248321\pi\)
\(282\) 0 0
\(283\) −14.5254 −0.863447 −0.431724 0.902006i \(-0.642094\pi\)
−0.431724 + 0.902006i \(0.642094\pi\)
\(284\) 20.4959 1.21621
\(285\) 0 0
\(286\) 0.903056 0.0533988
\(287\) 8.89190 0.524872
\(288\) 0 0
\(289\) −15.8166 −0.930388
\(290\) −2.03517 −0.119509
\(291\) 0 0
\(292\) −24.1264 −1.41189
\(293\) 3.05620 0.178545 0.0892724 0.996007i \(-0.471546\pi\)
0.0892724 + 0.996007i \(0.471546\pi\)
\(294\) 0 0
\(295\) 19.6179 1.14220
\(296\) −5.47507 −0.318232
\(297\) 0 0
\(298\) −0.749838 −0.0434369
\(299\) −9.61610 −0.556113
\(300\) 0 0
\(301\) −23.6851 −1.36519
\(302\) 3.25254 0.187163
\(303\) 0 0
\(304\) 13.4732 0.772743
\(305\) −2.20477 −0.126244
\(306\) 0 0
\(307\) −18.3076 −1.04487 −0.522436 0.852679i \(-0.674976\pi\)
−0.522436 + 0.852679i \(0.674976\pi\)
\(308\) −6.24104 −0.355616
\(309\) 0 0
\(310\) 0.386828 0.0219704
\(311\) 20.8499 1.18229 0.591145 0.806565i \(-0.298676\pi\)
0.591145 + 0.806565i \(0.298676\pi\)
\(312\) 0 0
\(313\) −3.49928 −0.197791 −0.0988956 0.995098i \(-0.531531\pi\)
−0.0988956 + 0.995098i \(0.531531\pi\)
\(314\) 3.51975 0.198631
\(315\) 0 0
\(316\) −30.8480 −1.73534
\(317\) 18.4416 1.03578 0.517891 0.855447i \(-0.326717\pi\)
0.517891 + 0.855447i \(0.326717\pi\)
\(318\) 0 0
\(319\) 5.13495 0.287502
\(320\) 15.9512 0.891696
\(321\) 0 0
\(322\) −1.09141 −0.0608219
\(323\) −3.84981 −0.214209
\(324\) 0 0
\(325\) −0.698328 −0.0387362
\(326\) 2.57447 0.142587
\(327\) 0 0
\(328\) −1.99955 −0.110407
\(329\) −16.1574 −0.890785
\(330\) 0 0
\(331\) 6.78274 0.372813 0.186407 0.982473i \(-0.440316\pi\)
0.186407 + 0.982473i \(0.440316\pi\)
\(332\) 21.1720 1.16196
\(333\) 0 0
\(334\) −0.0320212 −0.00175212
\(335\) 13.4946 0.737289
\(336\) 0 0
\(337\) 35.9736 1.95961 0.979803 0.199965i \(-0.0640827\pi\)
0.979803 + 0.199965i \(0.0640827\pi\)
\(338\) 2.19965 0.119645
\(339\) 0 0
\(340\) −4.71939 −0.255945
\(341\) −0.976010 −0.0528539
\(342\) 0 0
\(343\) −12.4964 −0.674745
\(344\) 5.32615 0.287167
\(345\) 0 0
\(346\) −0.0907427 −0.00487836
\(347\) 8.50844 0.456757 0.228379 0.973572i \(-0.426658\pi\)
0.228379 + 0.973572i \(0.426658\pi\)
\(348\) 0 0
\(349\) 13.9195 0.745096 0.372548 0.928013i \(-0.378484\pi\)
0.372548 + 0.928013i \(0.378484\pi\)
\(350\) −0.0792589 −0.00423657
\(351\) 0 0
\(352\) 2.11088 0.112510
\(353\) 21.3602 1.13689 0.568444 0.822722i \(-0.307546\pi\)
0.568444 + 0.822722i \(0.307546\pi\)
\(354\) 0 0
\(355\) 22.9654 1.21888
\(356\) −28.0180 −1.48495
\(357\) 0 0
\(358\) −2.16647 −0.114502
\(359\) 10.1841 0.537495 0.268748 0.963211i \(-0.413390\pi\)
0.268748 + 0.963211i \(0.413390\pi\)
\(360\) 0 0
\(361\) −6.47601 −0.340842
\(362\) 4.28600 0.225267
\(363\) 0 0
\(364\) −31.3523 −1.64331
\(365\) −27.0333 −1.41499
\(366\) 0 0
\(367\) −7.71600 −0.402772 −0.201386 0.979512i \(-0.564545\pi\)
−0.201386 + 0.979512i \(0.564545\pi\)
\(368\) −7.28763 −0.379894
\(369\) 0 0
\(370\) −3.04239 −0.158166
\(371\) 34.7688 1.80510
\(372\) 0 0
\(373\) −17.3992 −0.900897 −0.450448 0.892802i \(-0.648736\pi\)
−0.450448 + 0.892802i \(0.648736\pi\)
\(374\) −0.195555 −0.0101119
\(375\) 0 0
\(376\) 3.63336 0.187376
\(377\) 25.7958 1.32855
\(378\) 0 0
\(379\) −2.31368 −0.118846 −0.0594230 0.998233i \(-0.518926\pi\)
−0.0594230 + 0.998233i \(0.518926\pi\)
\(380\) 15.3529 0.787585
\(381\) 0 0
\(382\) 4.67662 0.239277
\(383\) 8.99228 0.459484 0.229742 0.973252i \(-0.426212\pi\)
0.229742 + 0.973252i \(0.426212\pi\)
\(384\) 0 0
\(385\) −6.99300 −0.356396
\(386\) −0.701032 −0.0356816
\(387\) 0 0
\(388\) 27.3033 1.38612
\(389\) 7.65447 0.388097 0.194048 0.980992i \(-0.437838\pi\)
0.194048 + 0.980992i \(0.437838\pi\)
\(390\) 0 0
\(391\) 2.08235 0.105309
\(392\) −2.18260 −0.110238
\(393\) 0 0
\(394\) 3.94878 0.198937
\(395\) −34.5648 −1.73914
\(396\) 0 0
\(397\) 26.1237 1.31111 0.655555 0.755147i \(-0.272435\pi\)
0.655555 + 0.755147i \(0.272435\pi\)
\(398\) 0.205162 0.0102839
\(399\) 0 0
\(400\) −0.529232 −0.0264616
\(401\) 27.3416 1.36537 0.682686 0.730712i \(-0.260812\pi\)
0.682686 + 0.730712i \(0.260812\pi\)
\(402\) 0 0
\(403\) −4.90306 −0.244239
\(404\) −6.86047 −0.341321
\(405\) 0 0
\(406\) 2.92778 0.145303
\(407\) 7.67629 0.380500
\(408\) 0 0
\(409\) −24.2671 −1.19993 −0.599965 0.800027i \(-0.704819\pi\)
−0.599965 + 0.800027i \(0.704819\pi\)
\(410\) −1.11111 −0.0548738
\(411\) 0 0
\(412\) 37.8612 1.86529
\(413\) −28.2223 −1.38873
\(414\) 0 0
\(415\) 23.7229 1.16451
\(416\) 10.6042 0.519911
\(417\) 0 0
\(418\) 0.636169 0.0311161
\(419\) −16.5732 −0.809655 −0.404828 0.914393i \(-0.632668\pi\)
−0.404828 + 0.914393i \(0.632668\pi\)
\(420\) 0 0
\(421\) 0.423105 0.0206209 0.0103104 0.999947i \(-0.496718\pi\)
0.0103104 + 0.999947i \(0.496718\pi\)
\(422\) 1.69007 0.0822713
\(423\) 0 0
\(424\) −7.81856 −0.379703
\(425\) 0.151222 0.00733532
\(426\) 0 0
\(427\) 3.17177 0.153493
\(428\) 5.56824 0.269151
\(429\) 0 0
\(430\) 2.95964 0.142726
\(431\) −24.3394 −1.17239 −0.586195 0.810170i \(-0.699375\pi\)
−0.586195 + 0.810170i \(0.699375\pi\)
\(432\) 0 0
\(433\) 5.45603 0.262200 0.131100 0.991369i \(-0.458149\pi\)
0.131100 + 0.991369i \(0.458149\pi\)
\(434\) −0.556489 −0.0267123
\(435\) 0 0
\(436\) −14.6943 −0.703730
\(437\) −6.77419 −0.324053
\(438\) 0 0
\(439\) 5.71582 0.272801 0.136401 0.990654i \(-0.456447\pi\)
0.136401 + 0.990654i \(0.456447\pi\)
\(440\) 1.57254 0.0749677
\(441\) 0 0
\(442\) −0.982386 −0.0467273
\(443\) −15.1986 −0.722106 −0.361053 0.932545i \(-0.617583\pi\)
−0.361053 + 0.932545i \(0.617583\pi\)
\(444\) 0 0
\(445\) −31.3938 −1.48821
\(446\) 0.436337 0.0206612
\(447\) 0 0
\(448\) −22.9473 −1.08416
\(449\) 1.16467 0.0549641 0.0274820 0.999622i \(-0.491251\pi\)
0.0274820 + 0.999622i \(0.491251\pi\)
\(450\) 0 0
\(451\) 2.80345 0.132010
\(452\) −17.8612 −0.840122
\(453\) 0 0
\(454\) 3.50410 0.164456
\(455\) −35.1299 −1.64691
\(456\) 0 0
\(457\) 15.8354 0.740748 0.370374 0.928883i \(-0.379230\pi\)
0.370374 + 0.928883i \(0.379230\pi\)
\(458\) 2.66560 0.124556
\(459\) 0 0
\(460\) −8.30431 −0.387191
\(461\) −14.3447 −0.668097 −0.334048 0.942556i \(-0.608415\pi\)
−0.334048 + 0.942556i \(0.608415\pi\)
\(462\) 0 0
\(463\) 24.6422 1.14522 0.572611 0.819827i \(-0.305931\pi\)
0.572611 + 0.819827i \(0.305931\pi\)
\(464\) 19.5496 0.907566
\(465\) 0 0
\(466\) 1.64992 0.0764309
\(467\) 9.26543 0.428753 0.214377 0.976751i \(-0.431228\pi\)
0.214377 + 0.976751i \(0.431228\pi\)
\(468\) 0 0
\(469\) −19.4133 −0.896422
\(470\) 2.01899 0.0931289
\(471\) 0 0
\(472\) 6.34643 0.292118
\(473\) −7.46749 −0.343356
\(474\) 0 0
\(475\) −0.491946 −0.0225720
\(476\) 6.78929 0.311187
\(477\) 0 0
\(478\) −3.23194 −0.147825
\(479\) −4.42880 −0.202357 −0.101178 0.994868i \(-0.532261\pi\)
−0.101178 + 0.994868i \(0.532261\pi\)
\(480\) 0 0
\(481\) 38.5625 1.75830
\(482\) −2.12154 −0.0966337
\(483\) 0 0
\(484\) −1.96769 −0.0894402
\(485\) 30.5930 1.38916
\(486\) 0 0
\(487\) 24.2935 1.10084 0.550422 0.834886i \(-0.314467\pi\)
0.550422 + 0.834886i \(0.314467\pi\)
\(488\) −0.713244 −0.0322871
\(489\) 0 0
\(490\) −1.21283 −0.0547899
\(491\) 42.5903 1.92207 0.961037 0.276420i \(-0.0891481\pi\)
0.961037 + 0.276420i \(0.0891481\pi\)
\(492\) 0 0
\(493\) −5.58604 −0.251583
\(494\) 3.19585 0.143788
\(495\) 0 0
\(496\) −3.71582 −0.166845
\(497\) −33.0379 −1.48195
\(498\) 0 0
\(499\) 29.9642 1.34138 0.670690 0.741737i \(-0.265998\pi\)
0.670690 + 0.741737i \(0.265998\pi\)
\(500\) −22.2945 −0.997040
\(501\) 0 0
\(502\) 3.06973 0.137009
\(503\) −23.4580 −1.04594 −0.522970 0.852351i \(-0.675176\pi\)
−0.522970 + 0.852351i \(0.675176\pi\)
\(504\) 0 0
\(505\) −7.68707 −0.342070
\(506\) −0.344102 −0.0152972
\(507\) 0 0
\(508\) −17.6084 −0.781247
\(509\) −12.5052 −0.554284 −0.277142 0.960829i \(-0.589387\pi\)
−0.277142 + 0.960829i \(0.589387\pi\)
\(510\) 0 0
\(511\) 38.8900 1.72039
\(512\) 13.4673 0.595176
\(513\) 0 0
\(514\) −3.41072 −0.150440
\(515\) 42.4230 1.86938
\(516\) 0 0
\(517\) −5.09413 −0.224039
\(518\) 4.37677 0.192304
\(519\) 0 0
\(520\) 7.89976 0.346428
\(521\) 17.7110 0.775931 0.387966 0.921674i \(-0.373178\pi\)
0.387966 + 0.921674i \(0.373178\pi\)
\(522\) 0 0
\(523\) −24.7263 −1.08121 −0.540603 0.841278i \(-0.681804\pi\)
−0.540603 + 0.841278i \(0.681804\pi\)
\(524\) 27.5249 1.20243
\(525\) 0 0
\(526\) −2.63760 −0.115005
\(527\) 1.06175 0.0462505
\(528\) 0 0
\(529\) −19.3359 −0.840690
\(530\) −4.34462 −0.188718
\(531\) 0 0
\(532\) −22.0866 −0.957574
\(533\) 14.0834 0.610019
\(534\) 0 0
\(535\) 6.23914 0.269742
\(536\) 4.36552 0.188562
\(537\) 0 0
\(538\) 3.04672 0.131354
\(539\) 3.06010 0.131808
\(540\) 0 0
\(541\) −14.3455 −0.616759 −0.308380 0.951263i \(-0.599787\pi\)
−0.308380 + 0.951263i \(0.599787\pi\)
\(542\) 1.18632 0.0509570
\(543\) 0 0
\(544\) −2.29631 −0.0984535
\(545\) −16.4648 −0.705273
\(546\) 0 0
\(547\) −13.1006 −0.560142 −0.280071 0.959979i \(-0.590358\pi\)
−0.280071 + 0.959979i \(0.590358\pi\)
\(548\) 38.9586 1.66423
\(549\) 0 0
\(550\) −0.0249889 −0.00106553
\(551\) 18.1722 0.774162
\(552\) 0 0
\(553\) 49.7248 2.11451
\(554\) −3.54650 −0.150676
\(555\) 0 0
\(556\) 8.36066 0.354571
\(557\) −26.6862 −1.13073 −0.565365 0.824841i \(-0.691265\pi\)
−0.565365 + 0.824841i \(0.691265\pi\)
\(558\) 0 0
\(559\) −37.5135 −1.58665
\(560\) −26.6234 −1.12505
\(561\) 0 0
\(562\) 4.28399 0.180709
\(563\) 35.8990 1.51296 0.756482 0.654015i \(-0.226917\pi\)
0.756482 + 0.654015i \(0.226917\pi\)
\(564\) 0 0
\(565\) −20.0133 −0.841965
\(566\) −2.61114 −0.109754
\(567\) 0 0
\(568\) 7.42933 0.311728
\(569\) −43.3017 −1.81530 −0.907650 0.419727i \(-0.862126\pi\)
−0.907650 + 0.419727i \(0.862126\pi\)
\(570\) 0 0
\(571\) 18.0647 0.755983 0.377992 0.925809i \(-0.376615\pi\)
0.377992 + 0.925809i \(0.376615\pi\)
\(572\) −9.88482 −0.413305
\(573\) 0 0
\(574\) 1.59844 0.0667175
\(575\) 0.266092 0.0110968
\(576\) 0 0
\(577\) 40.3884 1.68139 0.840696 0.541507i \(-0.182146\pi\)
0.840696 + 0.541507i \(0.182146\pi\)
\(578\) −2.84324 −0.118263
\(579\) 0 0
\(580\) 22.2769 0.924997
\(581\) −34.1277 −1.41585
\(582\) 0 0
\(583\) 10.9620 0.453998
\(584\) −8.74530 −0.361883
\(585\) 0 0
\(586\) 0.549392 0.0226952
\(587\) −8.96421 −0.369992 −0.184996 0.982739i \(-0.559227\pi\)
−0.184996 + 0.982739i \(0.559227\pi\)
\(588\) 0 0
\(589\) −3.45403 −0.142321
\(590\) 3.52659 0.145187
\(591\) 0 0
\(592\) 29.2248 1.20113
\(593\) 26.1692 1.07464 0.537321 0.843378i \(-0.319436\pi\)
0.537321 + 0.843378i \(0.319436\pi\)
\(594\) 0 0
\(595\) 7.60731 0.311869
\(596\) 8.20770 0.336201
\(597\) 0 0
\(598\) −1.72862 −0.0706886
\(599\) −25.8018 −1.05423 −0.527116 0.849794i \(-0.676726\pi\)
−0.527116 + 0.849794i \(0.676726\pi\)
\(600\) 0 0
\(601\) −20.9671 −0.855267 −0.427633 0.903952i \(-0.640653\pi\)
−0.427633 + 0.903952i \(0.640653\pi\)
\(602\) −4.25772 −0.173532
\(603\) 0 0
\(604\) −35.6022 −1.44863
\(605\) −2.20477 −0.0896365
\(606\) 0 0
\(607\) 15.8671 0.644025 0.322013 0.946735i \(-0.395641\pi\)
0.322013 + 0.946735i \(0.395641\pi\)
\(608\) 7.47023 0.302958
\(609\) 0 0
\(610\) −0.396336 −0.0160472
\(611\) −25.5908 −1.03529
\(612\) 0 0
\(613\) −30.5257 −1.23292 −0.616462 0.787385i \(-0.711434\pi\)
−0.616462 + 0.787385i \(0.711434\pi\)
\(614\) −3.29104 −0.132816
\(615\) 0 0
\(616\) −2.26224 −0.0911484
\(617\) −39.2025 −1.57823 −0.789116 0.614244i \(-0.789461\pi\)
−0.789116 + 0.614244i \(0.789461\pi\)
\(618\) 0 0
\(619\) −5.80498 −0.233322 −0.116661 0.993172i \(-0.537219\pi\)
−0.116661 + 0.993172i \(0.537219\pi\)
\(620\) −4.23421 −0.170050
\(621\) 0 0
\(622\) 3.74805 0.150283
\(623\) 45.1630 1.80942
\(624\) 0 0
\(625\) −24.2856 −0.971425
\(626\) −0.629043 −0.0251416
\(627\) 0 0
\(628\) −38.5271 −1.53740
\(629\) −8.35063 −0.332961
\(630\) 0 0
\(631\) −10.9232 −0.434845 −0.217423 0.976078i \(-0.569765\pi\)
−0.217423 + 0.976078i \(0.569765\pi\)
\(632\) −11.1818 −0.444787
\(633\) 0 0
\(634\) 3.31512 0.131660
\(635\) −19.7300 −0.782961
\(636\) 0 0
\(637\) 15.3726 0.609086
\(638\) 0.923076 0.0365449
\(639\) 0 0
\(640\) 12.1754 0.481275
\(641\) 20.5925 0.813355 0.406677 0.913572i \(-0.366687\pi\)
0.406677 + 0.913572i \(0.366687\pi\)
\(642\) 0 0
\(643\) −32.4513 −1.27975 −0.639877 0.768477i \(-0.721015\pi\)
−0.639877 + 0.768477i \(0.721015\pi\)
\(644\) 11.9465 0.470760
\(645\) 0 0
\(646\) −0.692055 −0.0272285
\(647\) −24.4762 −0.962258 −0.481129 0.876650i \(-0.659773\pi\)
−0.481129 + 0.876650i \(0.659773\pi\)
\(648\) 0 0
\(649\) −8.89797 −0.349276
\(650\) −0.125534 −0.00492384
\(651\) 0 0
\(652\) −28.1800 −1.10362
\(653\) −9.38845 −0.367399 −0.183699 0.982982i \(-0.558807\pi\)
−0.183699 + 0.982982i \(0.558807\pi\)
\(654\) 0 0
\(655\) 30.8413 1.20507
\(656\) 10.6732 0.416718
\(657\) 0 0
\(658\) −2.90450 −0.113229
\(659\) −5.44984 −0.212296 −0.106148 0.994350i \(-0.533852\pi\)
−0.106148 + 0.994350i \(0.533852\pi\)
\(660\) 0 0
\(661\) 5.23046 0.203441 0.101721 0.994813i \(-0.467565\pi\)
0.101721 + 0.994813i \(0.467565\pi\)
\(662\) 1.21929 0.0473890
\(663\) 0 0
\(664\) 7.67439 0.297824
\(665\) −24.7477 −0.959675
\(666\) 0 0
\(667\) −9.82929 −0.380592
\(668\) 0.350503 0.0135614
\(669\) 0 0
\(670\) 2.42584 0.0937182
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −50.7702 −1.95705 −0.978523 0.206136i \(-0.933911\pi\)
−0.978523 + 0.206136i \(0.933911\pi\)
\(674\) 6.46673 0.249089
\(675\) 0 0
\(676\) −24.0773 −0.926049
\(677\) 38.0216 1.46129 0.730645 0.682757i \(-0.239219\pi\)
0.730645 + 0.682757i \(0.239219\pi\)
\(678\) 0 0
\(679\) −44.0110 −1.68899
\(680\) −1.71068 −0.0656015
\(681\) 0 0
\(682\) −0.175451 −0.00671836
\(683\) −20.3542 −0.778831 −0.389416 0.921062i \(-0.627323\pi\)
−0.389416 + 0.921062i \(0.627323\pi\)
\(684\) 0 0
\(685\) 43.6527 1.66788
\(686\) −2.24640 −0.0857681
\(687\) 0 0
\(688\) −28.4299 −1.08388
\(689\) 55.0683 2.09793
\(690\) 0 0
\(691\) −2.62631 −0.0999094 −0.0499547 0.998751i \(-0.515908\pi\)
−0.0499547 + 0.998751i \(0.515908\pi\)
\(692\) 0.993268 0.0377584
\(693\) 0 0
\(694\) 1.52951 0.0580593
\(695\) 9.36801 0.355349
\(696\) 0 0
\(697\) −3.04973 −0.115517
\(698\) 2.50222 0.0947106
\(699\) 0 0
\(700\) 0.867566 0.0327909
\(701\) −36.7376 −1.38756 −0.693780 0.720187i \(-0.744056\pi\)
−0.693780 + 0.720187i \(0.744056\pi\)
\(702\) 0 0
\(703\) 27.1658 1.02458
\(704\) −7.23485 −0.272674
\(705\) 0 0
\(706\) 3.83978 0.144512
\(707\) 11.0586 0.415901
\(708\) 0 0
\(709\) 29.6385 1.11310 0.556549 0.830815i \(-0.312125\pi\)
0.556549 + 0.830815i \(0.312125\pi\)
\(710\) 4.12833 0.154934
\(711\) 0 0
\(712\) −10.1559 −0.380610
\(713\) 1.86827 0.0699673
\(714\) 0 0
\(715\) −11.0758 −0.414212
\(716\) 23.7142 0.886240
\(717\) 0 0
\(718\) 1.83072 0.0683220
\(719\) −20.2891 −0.756655 −0.378327 0.925672i \(-0.623501\pi\)
−0.378327 + 0.925672i \(0.623501\pi\)
\(720\) 0 0
\(721\) −61.0295 −2.27286
\(722\) −1.16415 −0.0433251
\(723\) 0 0
\(724\) −46.9145 −1.74356
\(725\) −0.713810 −0.0265102
\(726\) 0 0
\(727\) −12.1406 −0.450271 −0.225136 0.974327i \(-0.572283\pi\)
−0.225136 + 0.974327i \(0.572283\pi\)
\(728\) −11.3646 −0.421199
\(729\) 0 0
\(730\) −4.85959 −0.179862
\(731\) 8.12349 0.300458
\(732\) 0 0
\(733\) 3.41541 0.126151 0.0630755 0.998009i \(-0.479909\pi\)
0.0630755 + 0.998009i \(0.479909\pi\)
\(734\) −1.38705 −0.0511971
\(735\) 0 0
\(736\) −4.04062 −0.148939
\(737\) −6.12066 −0.225457
\(738\) 0 0
\(739\) 11.0875 0.407862 0.203931 0.978985i \(-0.434628\pi\)
0.203931 + 0.978985i \(0.434628\pi\)
\(740\) 33.3019 1.22420
\(741\) 0 0
\(742\) 6.25015 0.229450
\(743\) 15.5926 0.572036 0.286018 0.958224i \(-0.407668\pi\)
0.286018 + 0.958224i \(0.407668\pi\)
\(744\) 0 0
\(745\) 9.19662 0.336938
\(746\) −3.12774 −0.114515
\(747\) 0 0
\(748\) 2.14054 0.0782659
\(749\) −8.97560 −0.327961
\(750\) 0 0
\(751\) 2.31000 0.0842932 0.0421466 0.999111i \(-0.486580\pi\)
0.0421466 + 0.999111i \(0.486580\pi\)
\(752\) −19.3941 −0.707231
\(753\) 0 0
\(754\) 4.63715 0.168875
\(755\) −39.8918 −1.45181
\(756\) 0 0
\(757\) 23.7474 0.863116 0.431558 0.902085i \(-0.357964\pi\)
0.431558 + 0.902085i \(0.357964\pi\)
\(758\) −0.415916 −0.0151067
\(759\) 0 0
\(760\) 5.56509 0.201867
\(761\) 7.80814 0.283045 0.141523 0.989935i \(-0.454800\pi\)
0.141523 + 0.989935i \(0.454800\pi\)
\(762\) 0 0
\(763\) 23.6862 0.857496
\(764\) −51.1902 −1.85199
\(765\) 0 0
\(766\) 1.61648 0.0584059
\(767\) −44.6997 −1.61401
\(768\) 0 0
\(769\) −24.6045 −0.887261 −0.443630 0.896210i \(-0.646310\pi\)
−0.443630 + 0.896210i \(0.646310\pi\)
\(770\) −1.25709 −0.0453022
\(771\) 0 0
\(772\) 7.67348 0.276175
\(773\) 0.312960 0.0112564 0.00562819 0.999984i \(-0.498208\pi\)
0.00562819 + 0.999984i \(0.498208\pi\)
\(774\) 0 0
\(775\) 0.135675 0.00487359
\(776\) 9.89688 0.355277
\(777\) 0 0
\(778\) 1.37599 0.0493317
\(779\) 9.92122 0.355464
\(780\) 0 0
\(781\) −10.4162 −0.372723
\(782\) 0.374330 0.0133860
\(783\) 0 0
\(784\) 11.6503 0.416081
\(785\) −43.1691 −1.54077
\(786\) 0 0
\(787\) 9.32767 0.332495 0.166248 0.986084i \(-0.446835\pi\)
0.166248 + 0.986084i \(0.446835\pi\)
\(788\) −43.2233 −1.53976
\(789\) 0 0
\(790\) −6.21349 −0.221066
\(791\) 28.7910 1.02369
\(792\) 0 0
\(793\) 5.02358 0.178393
\(794\) 4.69608 0.166658
\(795\) 0 0
\(796\) −2.24570 −0.0795968
\(797\) −10.3564 −0.366842 −0.183421 0.983034i \(-0.558717\pi\)
−0.183421 + 0.983034i \(0.558717\pi\)
\(798\) 0 0
\(799\) 5.54163 0.196049
\(800\) −0.293433 −0.0103744
\(801\) 0 0
\(802\) 4.91501 0.173555
\(803\) 12.2613 0.432692
\(804\) 0 0
\(805\) 13.3859 0.471793
\(806\) −0.881391 −0.0310457
\(807\) 0 0
\(808\) −2.48678 −0.0874845
\(809\) 21.7280 0.763917 0.381958 0.924180i \(-0.375250\pi\)
0.381958 + 0.924180i \(0.375250\pi\)
\(810\) 0 0
\(811\) 13.2505 0.465286 0.232643 0.972562i \(-0.425263\pi\)
0.232643 + 0.972562i \(0.425263\pi\)
\(812\) −32.0474 −1.12464
\(813\) 0 0
\(814\) 1.37992 0.0483660
\(815\) −31.5754 −1.10604
\(816\) 0 0
\(817\) −26.4269 −0.924560
\(818\) −4.36233 −0.152525
\(819\) 0 0
\(820\) 12.1622 0.424722
\(821\) 16.6433 0.580856 0.290428 0.956897i \(-0.406202\pi\)
0.290428 + 0.956897i \(0.406202\pi\)
\(822\) 0 0
\(823\) −19.5756 −0.682364 −0.341182 0.939997i \(-0.610827\pi\)
−0.341182 + 0.939997i \(0.610827\pi\)
\(824\) 13.7239 0.478094
\(825\) 0 0
\(826\) −5.07333 −0.176524
\(827\) −20.1005 −0.698964 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(828\) 0 0
\(829\) 55.2719 1.91967 0.959835 0.280564i \(-0.0905214\pi\)
0.959835 + 0.280564i \(0.0905214\pi\)
\(830\) 4.26451 0.148023
\(831\) 0 0
\(832\) −36.3449 −1.26003
\(833\) −3.32892 −0.115340
\(834\) 0 0
\(835\) 0.392734 0.0135911
\(836\) −6.96349 −0.240837
\(837\) 0 0
\(838\) −2.97926 −0.102917
\(839\) 9.09374 0.313951 0.156975 0.987603i \(-0.449826\pi\)
0.156975 + 0.987603i \(0.449826\pi\)
\(840\) 0 0
\(841\) −2.63226 −0.0907676
\(842\) 0.0760589 0.00262116
\(843\) 0 0
\(844\) −18.4994 −0.636777
\(845\) −26.9783 −0.928081
\(846\) 0 0
\(847\) 3.17177 0.108983
\(848\) 41.7339 1.43315
\(849\) 0 0
\(850\) 0.0271841 0.000932407 0
\(851\) −14.6939 −0.503700
\(852\) 0 0
\(853\) −30.4639 −1.04307 −0.521533 0.853231i \(-0.674639\pi\)
−0.521533 + 0.853231i \(0.674639\pi\)
\(854\) 0.570167 0.0195107
\(855\) 0 0
\(856\) 2.01837 0.0689865
\(857\) 36.7917 1.25678 0.628391 0.777898i \(-0.283714\pi\)
0.628391 + 0.777898i \(0.283714\pi\)
\(858\) 0 0
\(859\) −19.7020 −0.672225 −0.336112 0.941822i \(-0.609112\pi\)
−0.336112 + 0.941822i \(0.609112\pi\)
\(860\) −32.3961 −1.10470
\(861\) 0 0
\(862\) −4.37534 −0.149025
\(863\) 40.6000 1.38204 0.691020 0.722836i \(-0.257162\pi\)
0.691020 + 0.722836i \(0.257162\pi\)
\(864\) 0 0
\(865\) 1.11294 0.0378412
\(866\) 0.980794 0.0333287
\(867\) 0 0
\(868\) 6.09131 0.206753
\(869\) 15.6773 0.531817
\(870\) 0 0
\(871\) −30.7476 −1.04184
\(872\) −5.32638 −0.180374
\(873\) 0 0
\(874\) −1.21775 −0.0411910
\(875\) 35.9371 1.21490
\(876\) 0 0
\(877\) 32.5425 1.09888 0.549441 0.835532i \(-0.314841\pi\)
0.549441 + 0.835532i \(0.314841\pi\)
\(878\) 1.02750 0.0346763
\(879\) 0 0
\(880\) −8.39388 −0.282958
\(881\) −9.99390 −0.336703 −0.168352 0.985727i \(-0.553844\pi\)
−0.168352 + 0.985727i \(0.553844\pi\)
\(882\) 0 0
\(883\) −47.6765 −1.60444 −0.802221 0.597028i \(-0.796348\pi\)
−0.802221 + 0.597028i \(0.796348\pi\)
\(884\) 10.7532 0.361668
\(885\) 0 0
\(886\) −2.73215 −0.0917883
\(887\) 32.5954 1.09445 0.547224 0.836986i \(-0.315685\pi\)
0.547224 + 0.836986i \(0.315685\pi\)
\(888\) 0 0
\(889\) 28.3835 0.951951
\(890\) −5.64346 −0.189169
\(891\) 0 0
\(892\) −4.77613 −0.159917
\(893\) −18.0277 −0.603275
\(894\) 0 0
\(895\) 26.5714 0.888185
\(896\) −17.5155 −0.585151
\(897\) 0 0
\(898\) 0.209365 0.00698659
\(899\) −5.01177 −0.167152
\(900\) 0 0
\(901\) −11.9249 −0.397277
\(902\) 0.503958 0.0167800
\(903\) 0 0
\(904\) −6.47432 −0.215333
\(905\) −52.5671 −1.74739
\(906\) 0 0
\(907\) 11.8687 0.394094 0.197047 0.980394i \(-0.436865\pi\)
0.197047 + 0.980394i \(0.436865\pi\)
\(908\) −38.3558 −1.27288
\(909\) 0 0
\(910\) −6.31507 −0.209342
\(911\) 22.8072 0.755636 0.377818 0.925880i \(-0.376674\pi\)
0.377818 + 0.925880i \(0.376674\pi\)
\(912\) 0 0
\(913\) −10.7598 −0.356099
\(914\) 2.84662 0.0941579
\(915\) 0 0
\(916\) −29.1776 −0.964056
\(917\) −44.3682 −1.46517
\(918\) 0 0
\(919\) 55.9065 1.84419 0.922093 0.386969i \(-0.126478\pi\)
0.922093 + 0.386969i \(0.126478\pi\)
\(920\) −3.01014 −0.0992413
\(921\) 0 0
\(922\) −2.57864 −0.0849231
\(923\) −52.3268 −1.72236
\(924\) 0 0
\(925\) −1.06708 −0.0350854
\(926\) 4.42977 0.145571
\(927\) 0 0
\(928\) 10.8392 0.355816
\(929\) 42.5584 1.39630 0.698149 0.715953i \(-0.254007\pi\)
0.698149 + 0.715953i \(0.254007\pi\)
\(930\) 0 0
\(931\) 10.8295 0.354921
\(932\) −18.0599 −0.591573
\(933\) 0 0
\(934\) 1.66559 0.0544996
\(935\) 2.39845 0.0784376
\(936\) 0 0
\(937\) −18.2206 −0.595242 −0.297621 0.954684i \(-0.596193\pi\)
−0.297621 + 0.954684i \(0.596193\pi\)
\(938\) −3.48980 −0.113946
\(939\) 0 0
\(940\) −22.0998 −0.720815
\(941\) 30.8164 1.00458 0.502292 0.864698i \(-0.332490\pi\)
0.502292 + 0.864698i \(0.332490\pi\)
\(942\) 0 0
\(943\) −5.36635 −0.174752
\(944\) −33.8760 −1.10257
\(945\) 0 0
\(946\) −1.34238 −0.0436446
\(947\) 52.0370 1.69098 0.845488 0.533994i \(-0.179310\pi\)
0.845488 + 0.533994i \(0.179310\pi\)
\(948\) 0 0
\(949\) 61.5956 1.99948
\(950\) −0.0884339 −0.00286917
\(951\) 0 0
\(952\) 2.46098 0.0797607
\(953\) 19.4381 0.629662 0.314831 0.949148i \(-0.398052\pi\)
0.314831 + 0.949148i \(0.398052\pi\)
\(954\) 0 0
\(955\) −57.3579 −1.85606
\(956\) 35.3767 1.14416
\(957\) 0 0
\(958\) −0.796135 −0.0257220
\(959\) −62.7985 −2.02787
\(960\) 0 0
\(961\) −30.0474 −0.969271
\(962\) 6.93212 0.223500
\(963\) 0 0
\(964\) 23.2224 0.747942
\(965\) 8.59803 0.276781
\(966\) 0 0
\(967\) −30.8565 −0.992280 −0.496140 0.868243i \(-0.665250\pi\)
−0.496140 + 0.868243i \(0.665250\pi\)
\(968\) −0.713244 −0.0229245
\(969\) 0 0
\(970\) 5.49951 0.176578
\(971\) 5.96171 0.191320 0.0956601 0.995414i \(-0.469504\pi\)
0.0956601 + 0.995414i \(0.469504\pi\)
\(972\) 0 0
\(973\) −13.4768 −0.432046
\(974\) 4.36708 0.139930
\(975\) 0 0
\(976\) 3.80716 0.121864
\(977\) −4.76596 −0.152477 −0.0762383 0.997090i \(-0.524291\pi\)
−0.0762383 + 0.997090i \(0.524291\pi\)
\(978\) 0 0
\(979\) 14.2391 0.455083
\(980\) 13.2756 0.424073
\(981\) 0 0
\(982\) 7.65618 0.244318
\(983\) −52.1600 −1.66365 −0.831823 0.555042i \(-0.812702\pi\)
−0.831823 + 0.555042i \(0.812702\pi\)
\(984\) 0 0
\(985\) −48.4311 −1.54314
\(986\) −1.00417 −0.0319791
\(987\) 0 0
\(988\) −34.9817 −1.11291
\(989\) 14.2942 0.454530
\(990\) 0 0
\(991\) 20.1207 0.639156 0.319578 0.947560i \(-0.396459\pi\)
0.319578 + 0.947560i \(0.396459\pi\)
\(992\) −2.06024 −0.0654126
\(993\) 0 0
\(994\) −5.93900 −0.188374
\(995\) −2.51628 −0.0797714
\(996\) 0 0
\(997\) 15.9577 0.505384 0.252692 0.967547i \(-0.418684\pi\)
0.252692 + 0.967547i \(0.418684\pi\)
\(998\) 5.38646 0.170505
\(999\) 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 \(a_p\))