Properties

Label 6039.2.a.j.1.12
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 1.12
Root \(1.93923\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.93923 q^{2}\) \(+1.76061 q^{4}\) \(-3.07794 q^{5}\) \(-3.15900 q^{7}\) \(-0.464237 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.93923 q^{2}\) \(+1.76061 q^{4}\) \(-3.07794 q^{5}\) \(-3.15900 q^{7}\) \(-0.464237 q^{8}\) \(-5.96883 q^{10}\) \(+1.00000 q^{11}\) \(-4.31016 q^{13}\) \(-6.12601 q^{14}\) \(-4.42148 q^{16}\) \(+3.81369 q^{17}\) \(-4.23281 q^{19}\) \(-5.41904 q^{20}\) \(+1.93923 q^{22}\) \(-6.48918 q^{23}\) \(+4.47371 q^{25}\) \(-8.35838 q^{26}\) \(-5.56175 q^{28}\) \(+3.27479 q^{29}\) \(+10.0842 q^{31}\) \(-7.64578 q^{32}\) \(+7.39562 q^{34}\) \(+9.72319 q^{35}\) \(-1.85262 q^{37}\) \(-8.20839 q^{38}\) \(+1.42889 q^{40}\) \(+10.7788 q^{41}\) \(+10.4003 q^{43}\) \(+1.76061 q^{44}\) \(-12.5840 q^{46}\) \(-10.3730 q^{47}\) \(+2.97925 q^{49}\) \(+8.67555 q^{50}\) \(-7.58850 q^{52}\) \(-8.28262 q^{53}\) \(-3.07794 q^{55}\) \(+1.46652 q^{56}\) \(+6.35056 q^{58}\) \(+10.0151 q^{59}\) \(+1.00000 q^{61}\) \(+19.5555 q^{62}\) \(-5.98396 q^{64}\) \(+13.2664 q^{65}\) \(-5.80576 q^{67}\) \(+6.71441 q^{68}\) \(+18.8555 q^{70}\) \(+3.40168 q^{71}\) \(+11.2828 q^{73}\) \(-3.59265 q^{74}\) \(-7.45232 q^{76}\) \(-3.15900 q^{77}\) \(+4.26886 q^{79}\) \(+13.6090 q^{80}\) \(+20.9026 q^{82}\) \(-17.4095 q^{83}\) \(-11.7383 q^{85}\) \(+20.1685 q^{86}\) \(-0.464237 q^{88}\) \(+9.75884 q^{89}\) \(+13.6158 q^{91}\) \(-11.4249 q^{92}\) \(-20.1156 q^{94}\) \(+13.0283 q^{95}\) \(+0.814992 q^{97}\) \(+5.77745 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93923 1.37124 0.685621 0.727959i \(-0.259531\pi\)
0.685621 + 0.727959i \(0.259531\pi\)
\(3\) 0 0
\(4\) 1.76061 0.880304
\(5\) −3.07794 −1.37650 −0.688248 0.725475i \(-0.741620\pi\)
−0.688248 + 0.725475i \(0.741620\pi\)
\(6\) 0 0
\(7\) −3.15900 −1.19399 −0.596994 0.802246i \(-0.703638\pi\)
−0.596994 + 0.802246i \(0.703638\pi\)
\(8\) −0.464237 −0.164132
\(9\) 0 0
\(10\) −5.96883 −1.88751
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −4.31016 −1.19542 −0.597711 0.801711i \(-0.703923\pi\)
−0.597711 + 0.801711i \(0.703923\pi\)
\(14\) −6.12601 −1.63725
\(15\) 0 0
\(16\) −4.42148 −1.10537
\(17\) 3.81369 0.924956 0.462478 0.886631i \(-0.346960\pi\)
0.462478 + 0.886631i \(0.346960\pi\)
\(18\) 0 0
\(19\) −4.23281 −0.971073 −0.485537 0.874216i \(-0.661376\pi\)
−0.485537 + 0.874216i \(0.661376\pi\)
\(20\) −5.41904 −1.21173
\(21\) 0 0
\(22\) 1.93923 0.413445
\(23\) −6.48918 −1.35309 −0.676544 0.736402i \(-0.736523\pi\)
−0.676544 + 0.736402i \(0.736523\pi\)
\(24\) 0 0
\(25\) 4.47371 0.894742
\(26\) −8.35838 −1.63921
\(27\) 0 0
\(28\) −5.56175 −1.05107
\(29\) 3.27479 0.608113 0.304056 0.952654i \(-0.401659\pi\)
0.304056 + 0.952654i \(0.401659\pi\)
\(30\) 0 0
\(31\) 10.0842 1.81117 0.905585 0.424164i \(-0.139432\pi\)
0.905585 + 0.424164i \(0.139432\pi\)
\(32\) −7.64578 −1.35160
\(33\) 0 0
\(34\) 7.39562 1.26834
\(35\) 9.72319 1.64352
\(36\) 0 0
\(37\) −1.85262 −0.304569 −0.152284 0.988337i \(-0.548663\pi\)
−0.152284 + 0.988337i \(0.548663\pi\)
\(38\) −8.20839 −1.33158
\(39\) 0 0
\(40\) 1.42889 0.225928
\(41\) 10.7788 1.68337 0.841685 0.539969i \(-0.181564\pi\)
0.841685 + 0.539969i \(0.181564\pi\)
\(42\) 0 0
\(43\) 10.4003 1.58603 0.793013 0.609205i \(-0.208511\pi\)
0.793013 + 0.609205i \(0.208511\pi\)
\(44\) 1.76061 0.265422
\(45\) 0 0
\(46\) −12.5840 −1.85541
\(47\) −10.3730 −1.51305 −0.756527 0.653962i \(-0.773106\pi\)
−0.756527 + 0.653962i \(0.773106\pi\)
\(48\) 0 0
\(49\) 2.97925 0.425607
\(50\) 8.67555 1.22691
\(51\) 0 0
\(52\) −7.58850 −1.05234
\(53\) −8.28262 −1.13771 −0.568853 0.822439i \(-0.692613\pi\)
−0.568853 + 0.822439i \(0.692613\pi\)
\(54\) 0 0
\(55\) −3.07794 −0.415029
\(56\) 1.46652 0.195972
\(57\) 0 0
\(58\) 6.35056 0.833869
\(59\) 10.0151 1.30385 0.651925 0.758283i \(-0.273962\pi\)
0.651925 + 0.758283i \(0.273962\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 19.5555 2.48355
\(63\) 0 0
\(64\) −5.98396 −0.747995
\(65\) 13.2664 1.64550
\(66\) 0 0
\(67\) −5.80576 −0.709287 −0.354643 0.935002i \(-0.615398\pi\)
−0.354643 + 0.935002i \(0.615398\pi\)
\(68\) 6.71441 0.814242
\(69\) 0 0
\(70\) 18.8555 2.25366
\(71\) 3.40168 0.403705 0.201853 0.979416i \(-0.435304\pi\)
0.201853 + 0.979416i \(0.435304\pi\)
\(72\) 0 0
\(73\) 11.2828 1.32055 0.660276 0.751023i \(-0.270439\pi\)
0.660276 + 0.751023i \(0.270439\pi\)
\(74\) −3.59265 −0.417638
\(75\) 0 0
\(76\) −7.45232 −0.854840
\(77\) −3.15900 −0.360001
\(78\) 0 0
\(79\) 4.26886 0.480284 0.240142 0.970738i \(-0.422806\pi\)
0.240142 + 0.970738i \(0.422806\pi\)
\(80\) 13.6090 1.52154
\(81\) 0 0
\(82\) 20.9026 2.30831
\(83\) −17.4095 −1.91094 −0.955469 0.295092i \(-0.904650\pi\)
−0.955469 + 0.295092i \(0.904650\pi\)
\(84\) 0 0
\(85\) −11.7383 −1.27320
\(86\) 20.1685 2.17483
\(87\) 0 0
\(88\) −0.464237 −0.0494878
\(89\) 9.75884 1.03444 0.517218 0.855854i \(-0.326968\pi\)
0.517218 + 0.855854i \(0.326968\pi\)
\(90\) 0 0
\(91\) 13.6158 1.42732
\(92\) −11.4249 −1.19113
\(93\) 0 0
\(94\) −20.1156 −2.07476
\(95\) 13.0283 1.33668
\(96\) 0 0
\(97\) 0.814992 0.0827499 0.0413749 0.999144i \(-0.486826\pi\)
0.0413749 + 0.999144i \(0.486826\pi\)
\(98\) 5.77745 0.583610
\(99\) 0 0
\(100\) 7.87645 0.787645
\(101\) −8.64218 −0.859929 −0.429965 0.902846i \(-0.641474\pi\)
−0.429965 + 0.902846i \(0.641474\pi\)
\(102\) 0 0
\(103\) 1.53886 0.151629 0.0758143 0.997122i \(-0.475844\pi\)
0.0758143 + 0.997122i \(0.475844\pi\)
\(104\) 2.00093 0.196208
\(105\) 0 0
\(106\) −16.0619 −1.56007
\(107\) 1.27301 0.123067 0.0615333 0.998105i \(-0.480401\pi\)
0.0615333 + 0.998105i \(0.480401\pi\)
\(108\) 0 0
\(109\) 10.8977 1.04381 0.521905 0.853004i \(-0.325222\pi\)
0.521905 + 0.853004i \(0.325222\pi\)
\(110\) −5.96883 −0.569105
\(111\) 0 0
\(112\) 13.9674 1.31980
\(113\) 12.6330 1.18841 0.594206 0.804313i \(-0.297466\pi\)
0.594206 + 0.804313i \(0.297466\pi\)
\(114\) 0 0
\(115\) 19.9733 1.86252
\(116\) 5.76561 0.535324
\(117\) 0 0
\(118\) 19.4215 1.78789
\(119\) −12.0474 −1.10439
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 1.93923 0.175570
\(123\) 0 0
\(124\) 17.7543 1.59438
\(125\) 1.61989 0.144887
\(126\) 0 0
\(127\) 12.4848 1.10784 0.553921 0.832569i \(-0.313131\pi\)
0.553921 + 0.832569i \(0.313131\pi\)
\(128\) 3.68729 0.325913
\(129\) 0 0
\(130\) 25.7266 2.25637
\(131\) −0.0498953 −0.00435938 −0.00217969 0.999998i \(-0.500694\pi\)
−0.00217969 + 0.999998i \(0.500694\pi\)
\(132\) 0 0
\(133\) 13.3714 1.15945
\(134\) −11.2587 −0.972604
\(135\) 0 0
\(136\) −1.77045 −0.151815
\(137\) −0.243742 −0.0208243 −0.0104121 0.999946i \(-0.503314\pi\)
−0.0104121 + 0.999946i \(0.503314\pi\)
\(138\) 0 0
\(139\) −21.1871 −1.79706 −0.898531 0.438910i \(-0.855365\pi\)
−0.898531 + 0.438910i \(0.855365\pi\)
\(140\) 17.1187 1.44680
\(141\) 0 0
\(142\) 6.59664 0.553578
\(143\) −4.31016 −0.360434
\(144\) 0 0
\(145\) −10.0796 −0.837065
\(146\) 21.8799 1.81080
\(147\) 0 0
\(148\) −3.26174 −0.268113
\(149\) −13.4964 −1.10567 −0.552834 0.833291i \(-0.686454\pi\)
−0.552834 + 0.833291i \(0.686454\pi\)
\(150\) 0 0
\(151\) 2.14503 0.174560 0.0872801 0.996184i \(-0.472182\pi\)
0.0872801 + 0.996184i \(0.472182\pi\)
\(152\) 1.96503 0.159385
\(153\) 0 0
\(154\) −6.12601 −0.493648
\(155\) −31.0385 −2.49307
\(156\) 0 0
\(157\) −2.78006 −0.221873 −0.110936 0.993828i \(-0.535385\pi\)
−0.110936 + 0.993828i \(0.535385\pi\)
\(158\) 8.27830 0.658586
\(159\) 0 0
\(160\) 23.5332 1.86047
\(161\) 20.4993 1.61557
\(162\) 0 0
\(163\) 16.8129 1.31689 0.658444 0.752630i \(-0.271215\pi\)
0.658444 + 0.752630i \(0.271215\pi\)
\(164\) 18.9773 1.48188
\(165\) 0 0
\(166\) −33.7609 −2.62036
\(167\) −14.1771 −1.09706 −0.548529 0.836132i \(-0.684812\pi\)
−0.548529 + 0.836132i \(0.684812\pi\)
\(168\) 0 0
\(169\) 5.57746 0.429036
\(170\) −22.7633 −1.74586
\(171\) 0 0
\(172\) 18.3108 1.39618
\(173\) −19.2019 −1.45989 −0.729945 0.683505i \(-0.760455\pi\)
−0.729945 + 0.683505i \(0.760455\pi\)
\(174\) 0 0
\(175\) −14.1324 −1.06831
\(176\) −4.42148 −0.333281
\(177\) 0 0
\(178\) 18.9246 1.41846
\(179\) 6.27478 0.468999 0.234500 0.972116i \(-0.424655\pi\)
0.234500 + 0.972116i \(0.424655\pi\)
\(180\) 0 0
\(181\) 14.9701 1.11272 0.556359 0.830942i \(-0.312198\pi\)
0.556359 + 0.830942i \(0.312198\pi\)
\(182\) 26.4041 1.95720
\(183\) 0 0
\(184\) 3.01251 0.222085
\(185\) 5.70225 0.419238
\(186\) 0 0
\(187\) 3.81369 0.278885
\(188\) −18.2627 −1.33195
\(189\) 0 0
\(190\) 25.2649 1.83291
\(191\) 1.11274 0.0805152 0.0402576 0.999189i \(-0.487182\pi\)
0.0402576 + 0.999189i \(0.487182\pi\)
\(192\) 0 0
\(193\) −16.4747 −1.18587 −0.592937 0.805249i \(-0.702032\pi\)
−0.592937 + 0.805249i \(0.702032\pi\)
\(194\) 1.58046 0.113470
\(195\) 0 0
\(196\) 5.24529 0.374664
\(197\) −25.4239 −1.81138 −0.905690 0.423941i \(-0.860646\pi\)
−0.905690 + 0.423941i \(0.860646\pi\)
\(198\) 0 0
\(199\) −8.05688 −0.571137 −0.285569 0.958358i \(-0.592182\pi\)
−0.285569 + 0.958358i \(0.592182\pi\)
\(200\) −2.07686 −0.146856
\(201\) 0 0
\(202\) −16.7592 −1.17917
\(203\) −10.3450 −0.726079
\(204\) 0 0
\(205\) −33.1766 −2.31715
\(206\) 2.98420 0.207919
\(207\) 0 0
\(208\) 19.0573 1.32138
\(209\) −4.23281 −0.292790
\(210\) 0 0
\(211\) 21.8405 1.50356 0.751780 0.659414i \(-0.229196\pi\)
0.751780 + 0.659414i \(0.229196\pi\)
\(212\) −14.5825 −1.00153
\(213\) 0 0
\(214\) 2.46866 0.168754
\(215\) −32.0114 −2.18316
\(216\) 0 0
\(217\) −31.8559 −2.16252
\(218\) 21.1331 1.43132
\(219\) 0 0
\(220\) −5.41904 −0.365352
\(221\) −16.4376 −1.10571
\(222\) 0 0
\(223\) 12.6761 0.848852 0.424426 0.905463i \(-0.360476\pi\)
0.424426 + 0.905463i \(0.360476\pi\)
\(224\) 24.1530 1.61379
\(225\) 0 0
\(226\) 24.4983 1.62960
\(227\) −18.0164 −1.19579 −0.597897 0.801573i \(-0.703997\pi\)
−0.597897 + 0.801573i \(0.703997\pi\)
\(228\) 0 0
\(229\) 21.1854 1.39997 0.699984 0.714159i \(-0.253191\pi\)
0.699984 + 0.714159i \(0.253191\pi\)
\(230\) 38.7328 2.55397
\(231\) 0 0
\(232\) −1.52028 −0.0998110
\(233\) 28.3068 1.85444 0.927221 0.374516i \(-0.122191\pi\)
0.927221 + 0.374516i \(0.122191\pi\)
\(234\) 0 0
\(235\) 31.9274 2.08271
\(236\) 17.6326 1.14778
\(237\) 0 0
\(238\) −23.3627 −1.51438
\(239\) −4.89918 −0.316902 −0.158451 0.987367i \(-0.550650\pi\)
−0.158451 + 0.987367i \(0.550650\pi\)
\(240\) 0 0
\(241\) 27.3485 1.76167 0.880836 0.473422i \(-0.156981\pi\)
0.880836 + 0.473422i \(0.156981\pi\)
\(242\) 1.93923 0.124658
\(243\) 0 0
\(244\) 1.76061 0.112711
\(245\) −9.16995 −0.585847
\(246\) 0 0
\(247\) 18.2441 1.16084
\(248\) −4.68144 −0.297272
\(249\) 0 0
\(250\) 3.14134 0.198676
\(251\) −2.95590 −0.186575 −0.0932874 0.995639i \(-0.529738\pi\)
−0.0932874 + 0.995639i \(0.529738\pi\)
\(252\) 0 0
\(253\) −6.48918 −0.407971
\(254\) 24.2108 1.51912
\(255\) 0 0
\(256\) 19.1184 1.19490
\(257\) −8.57140 −0.534669 −0.267335 0.963604i \(-0.586143\pi\)
−0.267335 + 0.963604i \(0.586143\pi\)
\(258\) 0 0
\(259\) 5.85242 0.363652
\(260\) 23.3569 1.44854
\(261\) 0 0
\(262\) −0.0967585 −0.00597776
\(263\) 1.84001 0.113460 0.0567300 0.998390i \(-0.481933\pi\)
0.0567300 + 0.998390i \(0.481933\pi\)
\(264\) 0 0
\(265\) 25.4934 1.56605
\(266\) 25.9303 1.58989
\(267\) 0 0
\(268\) −10.2217 −0.624388
\(269\) 8.65480 0.527692 0.263846 0.964565i \(-0.415009\pi\)
0.263846 + 0.964565i \(0.415009\pi\)
\(270\) 0 0
\(271\) 18.4447 1.12044 0.560219 0.828344i \(-0.310717\pi\)
0.560219 + 0.828344i \(0.310717\pi\)
\(272\) −16.8621 −1.02242
\(273\) 0 0
\(274\) −0.472671 −0.0285551
\(275\) 4.47371 0.269775
\(276\) 0 0
\(277\) 8.09606 0.486445 0.243223 0.969971i \(-0.421795\pi\)
0.243223 + 0.969971i \(0.421795\pi\)
\(278\) −41.0865 −2.46421
\(279\) 0 0
\(280\) −4.51386 −0.269755
\(281\) 17.8764 1.06642 0.533208 0.845984i \(-0.320986\pi\)
0.533208 + 0.845984i \(0.320986\pi\)
\(282\) 0 0
\(283\) 17.7034 1.05236 0.526179 0.850374i \(-0.323624\pi\)
0.526179 + 0.850374i \(0.323624\pi\)
\(284\) 5.98903 0.355383
\(285\) 0 0
\(286\) −8.35838 −0.494241
\(287\) −34.0503 −2.00992
\(288\) 0 0
\(289\) −2.45576 −0.144456
\(290\) −19.5466 −1.14782
\(291\) 0 0
\(292\) 19.8646 1.16249
\(293\) 13.3362 0.779109 0.389554 0.921003i \(-0.372629\pi\)
0.389554 + 0.921003i \(0.372629\pi\)
\(294\) 0 0
\(295\) −30.8258 −1.79474
\(296\) 0.860054 0.0499896
\(297\) 0 0
\(298\) −26.1726 −1.51614
\(299\) 27.9694 1.61751
\(300\) 0 0
\(301\) −32.8544 −1.89370
\(302\) 4.15971 0.239364
\(303\) 0 0
\(304\) 18.7153 1.07339
\(305\) −3.07794 −0.176242
\(306\) 0 0
\(307\) −32.1020 −1.83216 −0.916080 0.400996i \(-0.868664\pi\)
−0.916080 + 0.400996i \(0.868664\pi\)
\(308\) −5.56175 −0.316910
\(309\) 0 0
\(310\) −60.1907 −3.41860
\(311\) −19.1427 −1.08548 −0.542742 0.839899i \(-0.682614\pi\)
−0.542742 + 0.839899i \(0.682614\pi\)
\(312\) 0 0
\(313\) 7.12592 0.402781 0.201390 0.979511i \(-0.435454\pi\)
0.201390 + 0.979511i \(0.435454\pi\)
\(314\) −5.39117 −0.304241
\(315\) 0 0
\(316\) 7.51579 0.422796
\(317\) 30.7643 1.72789 0.863947 0.503584i \(-0.167985\pi\)
0.863947 + 0.503584i \(0.167985\pi\)
\(318\) 0 0
\(319\) 3.27479 0.183353
\(320\) 18.4183 1.02961
\(321\) 0 0
\(322\) 39.7528 2.21534
\(323\) −16.1426 −0.898200
\(324\) 0 0
\(325\) −19.2824 −1.06959
\(326\) 32.6040 1.80577
\(327\) 0 0
\(328\) −5.00393 −0.276296
\(329\) 32.7682 1.80657
\(330\) 0 0
\(331\) −1.20244 −0.0660920 −0.0330460 0.999454i \(-0.510521\pi\)
−0.0330460 + 0.999454i \(0.510521\pi\)
\(332\) −30.6512 −1.68221
\(333\) 0 0
\(334\) −27.4926 −1.50433
\(335\) 17.8698 0.976331
\(336\) 0 0
\(337\) −27.8849 −1.51898 −0.759492 0.650516i \(-0.774553\pi\)
−0.759492 + 0.650516i \(0.774553\pi\)
\(338\) 10.8160 0.588312
\(339\) 0 0
\(340\) −20.6666 −1.12080
\(341\) 10.0842 0.546089
\(342\) 0 0
\(343\) 12.7015 0.685818
\(344\) −4.82818 −0.260318
\(345\) 0 0
\(346\) −37.2368 −2.00186
\(347\) −8.66808 −0.465327 −0.232663 0.972557i \(-0.574744\pi\)
−0.232663 + 0.972557i \(0.574744\pi\)
\(348\) 0 0
\(349\) −3.27364 −0.175234 −0.0876170 0.996154i \(-0.527925\pi\)
−0.0876170 + 0.996154i \(0.527925\pi\)
\(350\) −27.4060 −1.46491
\(351\) 0 0
\(352\) −7.64578 −0.407521
\(353\) −23.4498 −1.24811 −0.624054 0.781381i \(-0.714515\pi\)
−0.624054 + 0.781381i \(0.714515\pi\)
\(354\) 0 0
\(355\) −10.4702 −0.555699
\(356\) 17.1815 0.910617
\(357\) 0 0
\(358\) 12.1682 0.643111
\(359\) 26.9502 1.42238 0.711188 0.703001i \(-0.248157\pi\)
0.711188 + 0.703001i \(0.248157\pi\)
\(360\) 0 0
\(361\) −1.08332 −0.0570167
\(362\) 29.0304 1.52580
\(363\) 0 0
\(364\) 23.9720 1.25648
\(365\) −34.7278 −1.81774
\(366\) 0 0
\(367\) −6.45575 −0.336987 −0.168494 0.985703i \(-0.553890\pi\)
−0.168494 + 0.985703i \(0.553890\pi\)
\(368\) 28.6918 1.49566
\(369\) 0 0
\(370\) 11.0580 0.574877
\(371\) 26.1648 1.35841
\(372\) 0 0
\(373\) 9.95114 0.515250 0.257625 0.966245i \(-0.417060\pi\)
0.257625 + 0.966245i \(0.417060\pi\)
\(374\) 7.39562 0.382418
\(375\) 0 0
\(376\) 4.81552 0.248341
\(377\) −14.1148 −0.726952
\(378\) 0 0
\(379\) −5.99448 −0.307916 −0.153958 0.988077i \(-0.549202\pi\)
−0.153958 + 0.988077i \(0.549202\pi\)
\(380\) 22.9378 1.17668
\(381\) 0 0
\(382\) 2.15786 0.110406
\(383\) −2.43976 −0.124666 −0.0623329 0.998055i \(-0.519854\pi\)
−0.0623329 + 0.998055i \(0.519854\pi\)
\(384\) 0 0
\(385\) 9.72319 0.495540
\(386\) −31.9482 −1.62612
\(387\) 0 0
\(388\) 1.43488 0.0728450
\(389\) 1.63009 0.0826491 0.0413245 0.999146i \(-0.486842\pi\)
0.0413245 + 0.999146i \(0.486842\pi\)
\(390\) 0 0
\(391\) −24.7477 −1.25155
\(392\) −1.38308 −0.0698559
\(393\) 0 0
\(394\) −49.3028 −2.48384
\(395\) −13.1393 −0.661110
\(396\) 0 0
\(397\) −29.1550 −1.46325 −0.731624 0.681709i \(-0.761237\pi\)
−0.731624 + 0.681709i \(0.761237\pi\)
\(398\) −15.6241 −0.783167
\(399\) 0 0
\(400\) −19.7804 −0.989020
\(401\) 28.8479 1.44059 0.720297 0.693666i \(-0.244005\pi\)
0.720297 + 0.693666i \(0.244005\pi\)
\(402\) 0 0
\(403\) −43.4644 −2.16512
\(404\) −15.2155 −0.756999
\(405\) 0 0
\(406\) −20.0614 −0.995630
\(407\) −1.85262 −0.0918310
\(408\) 0 0
\(409\) 19.7104 0.974619 0.487309 0.873229i \(-0.337978\pi\)
0.487309 + 0.873229i \(0.337978\pi\)
\(410\) −64.3370 −3.17738
\(411\) 0 0
\(412\) 2.70933 0.133479
\(413\) −31.6375 −1.55678
\(414\) 0 0
\(415\) 53.5853 2.63040
\(416\) 32.9545 1.61573
\(417\) 0 0
\(418\) −8.20839 −0.401485
\(419\) 6.33286 0.309381 0.154690 0.987963i \(-0.450562\pi\)
0.154690 + 0.987963i \(0.450562\pi\)
\(420\) 0 0
\(421\) 30.9731 1.50954 0.754768 0.655992i \(-0.227750\pi\)
0.754768 + 0.655992i \(0.227750\pi\)
\(422\) 42.3537 2.06174
\(423\) 0 0
\(424\) 3.84510 0.186734
\(425\) 17.0613 0.827597
\(426\) 0 0
\(427\) −3.15900 −0.152874
\(428\) 2.24127 0.108336
\(429\) 0 0
\(430\) −62.0774 −2.99364
\(431\) 0.711680 0.0342804 0.0171402 0.999853i \(-0.494544\pi\)
0.0171402 + 0.999853i \(0.494544\pi\)
\(432\) 0 0
\(433\) 38.6317 1.85652 0.928259 0.371934i \(-0.121305\pi\)
0.928259 + 0.371934i \(0.121305\pi\)
\(434\) −61.7758 −2.96533
\(435\) 0 0
\(436\) 19.1866 0.918870
\(437\) 27.4675 1.31395
\(438\) 0 0
\(439\) 10.1209 0.483043 0.241522 0.970395i \(-0.422353\pi\)
0.241522 + 0.970395i \(0.422353\pi\)
\(440\) 1.42889 0.0681197
\(441\) 0 0
\(442\) −31.8763 −1.51620
\(443\) 27.6987 1.31600 0.658002 0.753016i \(-0.271402\pi\)
0.658002 + 0.753016i \(0.271402\pi\)
\(444\) 0 0
\(445\) −30.0371 −1.42390
\(446\) 24.5818 1.16398
\(447\) 0 0
\(448\) 18.9033 0.893097
\(449\) −20.3574 −0.960727 −0.480364 0.877069i \(-0.659495\pi\)
−0.480364 + 0.877069i \(0.659495\pi\)
\(450\) 0 0
\(451\) 10.7788 0.507555
\(452\) 22.2418 1.04616
\(453\) 0 0
\(454\) −34.9380 −1.63972
\(455\) −41.9085 −1.96470
\(456\) 0 0
\(457\) −29.6278 −1.38593 −0.692964 0.720972i \(-0.743696\pi\)
−0.692964 + 0.720972i \(0.743696\pi\)
\(458\) 41.0832 1.91969
\(459\) 0 0
\(460\) 35.1651 1.63958
\(461\) −13.6161 −0.634163 −0.317081 0.948398i \(-0.602703\pi\)
−0.317081 + 0.948398i \(0.602703\pi\)
\(462\) 0 0
\(463\) −16.1578 −0.750914 −0.375457 0.926840i \(-0.622514\pi\)
−0.375457 + 0.926840i \(0.622514\pi\)
\(464\) −14.4794 −0.672189
\(465\) 0 0
\(466\) 54.8934 2.54289
\(467\) 12.4292 0.575155 0.287577 0.957757i \(-0.407150\pi\)
0.287577 + 0.957757i \(0.407150\pi\)
\(468\) 0 0
\(469\) 18.3404 0.846880
\(470\) 61.9145 2.85590
\(471\) 0 0
\(472\) −4.64936 −0.214004
\(473\) 10.4003 0.478205
\(474\) 0 0
\(475\) −18.9364 −0.868860
\(476\) −21.2108 −0.972196
\(477\) 0 0
\(478\) −9.50063 −0.434549
\(479\) −29.1644 −1.33255 −0.666277 0.745704i \(-0.732113\pi\)
−0.666277 + 0.745704i \(0.732113\pi\)
\(480\) 0 0
\(481\) 7.98509 0.364089
\(482\) 53.0350 2.41568
\(483\) 0 0
\(484\) 1.76061 0.0800276
\(485\) −2.50850 −0.113905
\(486\) 0 0
\(487\) 36.8143 1.66822 0.834108 0.551601i \(-0.185983\pi\)
0.834108 + 0.551601i \(0.185983\pi\)
\(488\) −0.464237 −0.0210150
\(489\) 0 0
\(490\) −17.7826 −0.803337
\(491\) −38.5259 −1.73865 −0.869326 0.494239i \(-0.835447\pi\)
−0.869326 + 0.494239i \(0.835447\pi\)
\(492\) 0 0
\(493\) 12.4890 0.562477
\(494\) 35.3794 1.59180
\(495\) 0 0
\(496\) −44.5869 −2.00201
\(497\) −10.7459 −0.482019
\(498\) 0 0
\(499\) 1.68198 0.0752959 0.0376480 0.999291i \(-0.488013\pi\)
0.0376480 + 0.999291i \(0.488013\pi\)
\(500\) 2.85199 0.127545
\(501\) 0 0
\(502\) −5.73217 −0.255839
\(503\) −20.1033 −0.896360 −0.448180 0.893943i \(-0.647928\pi\)
−0.448180 + 0.893943i \(0.647928\pi\)
\(504\) 0 0
\(505\) 26.6001 1.18369
\(506\) −12.5840 −0.559427
\(507\) 0 0
\(508\) 21.9807 0.975238
\(509\) −32.9375 −1.45993 −0.729964 0.683485i \(-0.760463\pi\)
−0.729964 + 0.683485i \(0.760463\pi\)
\(510\) 0 0
\(511\) −35.6423 −1.57672
\(512\) 29.7004 1.31259
\(513\) 0 0
\(514\) −16.6219 −0.733161
\(515\) −4.73652 −0.208716
\(516\) 0 0
\(517\) −10.3730 −0.456203
\(518\) 11.3492 0.498654
\(519\) 0 0
\(520\) −6.15875 −0.270079
\(521\) −6.18719 −0.271066 −0.135533 0.990773i \(-0.543275\pi\)
−0.135533 + 0.990773i \(0.543275\pi\)
\(522\) 0 0
\(523\) 19.2567 0.842035 0.421017 0.907053i \(-0.361673\pi\)
0.421017 + 0.907053i \(0.361673\pi\)
\(524\) −0.0878461 −0.00383757
\(525\) 0 0
\(526\) 3.56820 0.155581
\(527\) 38.4579 1.67525
\(528\) 0 0
\(529\) 19.1095 0.830846
\(530\) 49.4376 2.14743
\(531\) 0 0
\(532\) 23.5418 1.02067
\(533\) −46.4585 −2.01234
\(534\) 0 0
\(535\) −3.91825 −0.169401
\(536\) 2.69525 0.116417
\(537\) 0 0
\(538\) 16.7836 0.723594
\(539\) 2.97925 0.128325
\(540\) 0 0
\(541\) −32.4081 −1.39333 −0.696666 0.717395i \(-0.745334\pi\)
−0.696666 + 0.717395i \(0.745334\pi\)
\(542\) 35.7686 1.53639
\(543\) 0 0
\(544\) −29.1586 −1.25017
\(545\) −33.5425 −1.43680
\(546\) 0 0
\(547\) −10.6214 −0.454140 −0.227070 0.973878i \(-0.572915\pi\)
−0.227070 + 0.973878i \(0.572915\pi\)
\(548\) −0.429133 −0.0183317
\(549\) 0 0
\(550\) 8.67555 0.369927
\(551\) −13.8615 −0.590522
\(552\) 0 0
\(553\) −13.4853 −0.573454
\(554\) 15.7001 0.667034
\(555\) 0 0
\(556\) −37.3021 −1.58196
\(557\) 33.3894 1.41475 0.707376 0.706837i \(-0.249879\pi\)
0.707376 + 0.706837i \(0.249879\pi\)
\(558\) 0 0
\(559\) −44.8268 −1.89597
\(560\) −42.9909 −1.81670
\(561\) 0 0
\(562\) 34.6664 1.46231
\(563\) −8.93867 −0.376720 −0.188360 0.982100i \(-0.560317\pi\)
−0.188360 + 0.982100i \(0.560317\pi\)
\(564\) 0 0
\(565\) −38.8836 −1.63585
\(566\) 34.3309 1.44304
\(567\) 0 0
\(568\) −1.57918 −0.0662611
\(569\) 2.35475 0.0987163 0.0493582 0.998781i \(-0.484282\pi\)
0.0493582 + 0.998781i \(0.484282\pi\)
\(570\) 0 0
\(571\) 4.24507 0.177651 0.0888253 0.996047i \(-0.471689\pi\)
0.0888253 + 0.996047i \(0.471689\pi\)
\(572\) −7.58850 −0.317291
\(573\) 0 0
\(574\) −66.0313 −2.75609
\(575\) −29.0307 −1.21066
\(576\) 0 0
\(577\) −8.98406 −0.374011 −0.187006 0.982359i \(-0.559878\pi\)
−0.187006 + 0.982359i \(0.559878\pi\)
\(578\) −4.76227 −0.198084
\(579\) 0 0
\(580\) −17.7462 −0.736871
\(581\) 54.9964 2.28164
\(582\) 0 0
\(583\) −8.28262 −0.343031
\(584\) −5.23789 −0.216745
\(585\) 0 0
\(586\) 25.8619 1.06835
\(587\) −0.0674569 −0.00278424 −0.00139212 0.999999i \(-0.500443\pi\)
−0.00139212 + 0.999999i \(0.500443\pi\)
\(588\) 0 0
\(589\) −42.6844 −1.75878
\(590\) −59.7782 −2.46103
\(591\) 0 0
\(592\) 8.19132 0.336661
\(593\) 19.4214 0.797540 0.398770 0.917051i \(-0.369437\pi\)
0.398770 + 0.917051i \(0.369437\pi\)
\(594\) 0 0
\(595\) 37.0813 1.52018
\(596\) −23.7619 −0.973324
\(597\) 0 0
\(598\) 54.2390 2.21800
\(599\) 19.6058 0.801070 0.400535 0.916282i \(-0.368824\pi\)
0.400535 + 0.916282i \(0.368824\pi\)
\(600\) 0 0
\(601\) 32.7244 1.33485 0.667427 0.744675i \(-0.267395\pi\)
0.667427 + 0.744675i \(0.267395\pi\)
\(602\) −63.7122 −2.59672
\(603\) 0 0
\(604\) 3.77656 0.153666
\(605\) −3.07794 −0.125136
\(606\) 0 0
\(607\) −6.92562 −0.281102 −0.140551 0.990073i \(-0.544887\pi\)
−0.140551 + 0.990073i \(0.544887\pi\)
\(608\) 32.3631 1.31250
\(609\) 0 0
\(610\) −5.96883 −0.241671
\(611\) 44.7092 1.80874
\(612\) 0 0
\(613\) 10.1296 0.409131 0.204566 0.978853i \(-0.434422\pi\)
0.204566 + 0.978853i \(0.434422\pi\)
\(614\) −62.2532 −2.51233
\(615\) 0 0
\(616\) 1.46652 0.0590878
\(617\) −3.90198 −0.157088 −0.0785439 0.996911i \(-0.525027\pi\)
−0.0785439 + 0.996911i \(0.525027\pi\)
\(618\) 0 0
\(619\) 8.08612 0.325009 0.162504 0.986708i \(-0.448043\pi\)
0.162504 + 0.986708i \(0.448043\pi\)
\(620\) −54.6466 −2.19466
\(621\) 0 0
\(622\) −37.1221 −1.48846
\(623\) −30.8281 −1.23510
\(624\) 0 0
\(625\) −27.3545 −1.09418
\(626\) 13.8188 0.552310
\(627\) 0 0
\(628\) −4.89459 −0.195315
\(629\) −7.06532 −0.281713
\(630\) 0 0
\(631\) 14.8852 0.592569 0.296284 0.955100i \(-0.404252\pi\)
0.296284 + 0.955100i \(0.404252\pi\)
\(632\) −1.98176 −0.0788302
\(633\) 0 0
\(634\) 59.6589 2.36936
\(635\) −38.4273 −1.52494
\(636\) 0 0
\(637\) −12.8410 −0.508780
\(638\) 6.35056 0.251421
\(639\) 0 0
\(640\) −11.3492 −0.448618
\(641\) −6.49332 −0.256471 −0.128235 0.991744i \(-0.540931\pi\)
−0.128235 + 0.991744i \(0.540931\pi\)
\(642\) 0 0
\(643\) −0.679815 −0.0268093 −0.0134046 0.999910i \(-0.504267\pi\)
−0.0134046 + 0.999910i \(0.504267\pi\)
\(644\) 36.0912 1.42219
\(645\) 0 0
\(646\) −31.3043 −1.23165
\(647\) −9.53160 −0.374726 −0.187363 0.982291i \(-0.559994\pi\)
−0.187363 + 0.982291i \(0.559994\pi\)
\(648\) 0 0
\(649\) 10.0151 0.393126
\(650\) −37.3930 −1.46667
\(651\) 0 0
\(652\) 29.6009 1.15926
\(653\) 15.7563 0.616591 0.308296 0.951291i \(-0.400241\pi\)
0.308296 + 0.951291i \(0.400241\pi\)
\(654\) 0 0
\(655\) 0.153575 0.00600066
\(656\) −47.6583 −1.86075
\(657\) 0 0
\(658\) 63.5450 2.47724
\(659\) −22.5633 −0.878941 −0.439470 0.898257i \(-0.644834\pi\)
−0.439470 + 0.898257i \(0.644834\pi\)
\(660\) 0 0
\(661\) −47.5006 −1.84756 −0.923779 0.382927i \(-0.874916\pi\)
−0.923779 + 0.382927i \(0.874916\pi\)
\(662\) −2.33180 −0.0906281
\(663\) 0 0
\(664\) 8.08211 0.313647
\(665\) −41.1564 −1.59598
\(666\) 0 0
\(667\) −21.2507 −0.822830
\(668\) −24.9603 −0.965744
\(669\) 0 0
\(670\) 34.6536 1.33879
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 6.74671 0.260067 0.130033 0.991510i \(-0.458492\pi\)
0.130033 + 0.991510i \(0.458492\pi\)
\(674\) −54.0751 −2.08290
\(675\) 0 0
\(676\) 9.81973 0.377682
\(677\) −31.7778 −1.22132 −0.610660 0.791893i \(-0.709096\pi\)
−0.610660 + 0.791893i \(0.709096\pi\)
\(678\) 0 0
\(679\) −2.57456 −0.0988024
\(680\) 5.44935 0.208973
\(681\) 0 0
\(682\) 19.5555 0.748819
\(683\) 4.24491 0.162427 0.0812135 0.996697i \(-0.474120\pi\)
0.0812135 + 0.996697i \(0.474120\pi\)
\(684\) 0 0
\(685\) 0.750222 0.0286645
\(686\) 24.6312 0.940422
\(687\) 0 0
\(688\) −45.9845 −1.75314
\(689\) 35.6994 1.36004
\(690\) 0 0
\(691\) 39.5060 1.50288 0.751440 0.659801i \(-0.229359\pi\)
0.751440 + 0.659801i \(0.229359\pi\)
\(692\) −33.8069 −1.28515
\(693\) 0 0
\(694\) −16.8094 −0.638076
\(695\) 65.2125 2.47365
\(696\) 0 0
\(697\) 41.1071 1.55704
\(698\) −6.34834 −0.240288
\(699\) 0 0
\(700\) −24.8817 −0.940438
\(701\) 2.69413 0.101756 0.0508779 0.998705i \(-0.483798\pi\)
0.0508779 + 0.998705i \(0.483798\pi\)
\(702\) 0 0
\(703\) 7.84179 0.295759
\(704\) −5.98396 −0.225529
\(705\) 0 0
\(706\) −45.4746 −1.71146
\(707\) 27.3006 1.02675
\(708\) 0 0
\(709\) 44.7755 1.68158 0.840790 0.541362i \(-0.182091\pi\)
0.840790 + 0.541362i \(0.182091\pi\)
\(710\) −20.3041 −0.761997
\(711\) 0 0
\(712\) −4.53041 −0.169784
\(713\) −65.4380 −2.45067
\(714\) 0 0
\(715\) 13.2664 0.496135
\(716\) 11.0474 0.412862
\(717\) 0 0
\(718\) 52.2626 1.95042
\(719\) 28.5746 1.06565 0.532827 0.846224i \(-0.321130\pi\)
0.532827 + 0.846224i \(0.321130\pi\)
\(720\) 0 0
\(721\) −4.86126 −0.181043
\(722\) −2.10080 −0.0781836
\(723\) 0 0
\(724\) 26.3564 0.979529
\(725\) 14.6504 0.544104
\(726\) 0 0
\(727\) −25.0251 −0.928130 −0.464065 0.885801i \(-0.653610\pi\)
−0.464065 + 0.885801i \(0.653610\pi\)
\(728\) −6.32094 −0.234270
\(729\) 0 0
\(730\) −67.3451 −2.49256
\(731\) 39.6634 1.46700
\(732\) 0 0
\(733\) −0.528034 −0.0195034 −0.00975169 0.999952i \(-0.503104\pi\)
−0.00975169 + 0.999952i \(0.503104\pi\)
\(734\) −12.5192 −0.462091
\(735\) 0 0
\(736\) 49.6148 1.82883
\(737\) −5.80576 −0.213858
\(738\) 0 0
\(739\) 20.9456 0.770496 0.385248 0.922813i \(-0.374116\pi\)
0.385248 + 0.922813i \(0.374116\pi\)
\(740\) 10.0394 0.369057
\(741\) 0 0
\(742\) 50.7395 1.86270
\(743\) 17.0344 0.624932 0.312466 0.949929i \(-0.398845\pi\)
0.312466 + 0.949929i \(0.398845\pi\)
\(744\) 0 0
\(745\) 41.5411 1.52195
\(746\) 19.2975 0.706533
\(747\) 0 0
\(748\) 6.71441 0.245503
\(749\) −4.02143 −0.146940
\(750\) 0 0
\(751\) −10.2079 −0.372491 −0.186246 0.982503i \(-0.559632\pi\)
−0.186246 + 0.982503i \(0.559632\pi\)
\(752\) 45.8639 1.67248
\(753\) 0 0
\(754\) −27.3719 −0.996826
\(755\) −6.60228 −0.240281
\(756\) 0 0
\(757\) 18.2567 0.663549 0.331775 0.943359i \(-0.392353\pi\)
0.331775 + 0.943359i \(0.392353\pi\)
\(758\) −11.6247 −0.422227
\(759\) 0 0
\(760\) −6.04823 −0.219392
\(761\) −5.09224 −0.184594 −0.0922968 0.995732i \(-0.529421\pi\)
−0.0922968 + 0.995732i \(0.529421\pi\)
\(762\) 0 0
\(763\) −34.4258 −1.24630
\(764\) 1.95910 0.0708779
\(765\) 0 0
\(766\) −4.73125 −0.170947
\(767\) −43.1665 −1.55865
\(768\) 0 0
\(769\) −9.02962 −0.325617 −0.162808 0.986658i \(-0.552055\pi\)
−0.162808 + 0.986658i \(0.552055\pi\)
\(770\) 18.8555 0.679505
\(771\) 0 0
\(772\) −29.0054 −1.04393
\(773\) 9.13122 0.328427 0.164214 0.986425i \(-0.447491\pi\)
0.164214 + 0.986425i \(0.447491\pi\)
\(774\) 0 0
\(775\) 45.1137 1.62053
\(776\) −0.378349 −0.0135819
\(777\) 0 0
\(778\) 3.16113 0.113332
\(779\) −45.6247 −1.63468
\(780\) 0 0
\(781\) 3.40168 0.121722
\(782\) −47.9915 −1.71617
\(783\) 0 0
\(784\) −13.1727 −0.470453
\(785\) 8.55685 0.305407
\(786\) 0 0
\(787\) 28.3647 1.01109 0.505546 0.862800i \(-0.331291\pi\)
0.505546 + 0.862800i \(0.331291\pi\)
\(788\) −44.7615 −1.59456
\(789\) 0 0
\(790\) −25.4801 −0.906541
\(791\) −39.9076 −1.41895
\(792\) 0 0
\(793\) −4.31016 −0.153058
\(794\) −56.5382 −2.00647
\(795\) 0 0
\(796\) −14.1850 −0.502774
\(797\) −36.2460 −1.28390 −0.641950 0.766747i \(-0.721874\pi\)
−0.641950 + 0.766747i \(0.721874\pi\)
\(798\) 0 0
\(799\) −39.5593 −1.39951
\(800\) −34.2050 −1.20933
\(801\) 0 0
\(802\) 55.9426 1.97540
\(803\) 11.2828 0.398162
\(804\) 0 0
\(805\) −63.0956 −2.22383
\(806\) −84.2874 −2.96890
\(807\) 0 0
\(808\) 4.01202 0.141142
\(809\) 53.3004 1.87394 0.936971 0.349408i \(-0.113617\pi\)
0.936971 + 0.349408i \(0.113617\pi\)
\(810\) 0 0
\(811\) 13.8664 0.486914 0.243457 0.969912i \(-0.421719\pi\)
0.243457 + 0.969912i \(0.421719\pi\)
\(812\) −18.2135 −0.639170
\(813\) 0 0
\(814\) −3.59265 −0.125922
\(815\) −51.7491 −1.81269
\(816\) 0 0
\(817\) −44.0224 −1.54015
\(818\) 38.2231 1.33644
\(819\) 0 0
\(820\) −58.4109 −2.03980
\(821\) 42.4160 1.48033 0.740164 0.672427i \(-0.234748\pi\)
0.740164 + 0.672427i \(0.234748\pi\)
\(822\) 0 0
\(823\) 35.8679 1.25028 0.625138 0.780514i \(-0.285043\pi\)
0.625138 + 0.780514i \(0.285043\pi\)
\(824\) −0.714396 −0.0248871
\(825\) 0 0
\(826\) −61.3524 −2.13472
\(827\) 7.27629 0.253022 0.126511 0.991965i \(-0.459622\pi\)
0.126511 + 0.991965i \(0.459622\pi\)
\(828\) 0 0
\(829\) −21.2488 −0.738000 −0.369000 0.929429i \(-0.620300\pi\)
−0.369000 + 0.929429i \(0.620300\pi\)
\(830\) 103.914 3.60691
\(831\) 0 0
\(832\) 25.7918 0.894171
\(833\) 11.3619 0.393668
\(834\) 0 0
\(835\) 43.6363 1.51010
\(836\) −7.45232 −0.257744
\(837\) 0 0
\(838\) 12.2809 0.424236
\(839\) −27.7675 −0.958641 −0.479320 0.877640i \(-0.659117\pi\)
−0.479320 + 0.877640i \(0.659117\pi\)
\(840\) 0 0
\(841\) −18.2758 −0.630199
\(842\) 60.0639 2.06994
\(843\) 0 0
\(844\) 38.4525 1.32359
\(845\) −17.1671 −0.590566
\(846\) 0 0
\(847\) −3.15900 −0.108544
\(848\) 36.6214 1.25758
\(849\) 0 0
\(850\) 33.0859 1.13484
\(851\) 12.0220 0.412108
\(852\) 0 0
\(853\) −7.41186 −0.253777 −0.126889 0.991917i \(-0.540499\pi\)
−0.126889 + 0.991917i \(0.540499\pi\)
\(854\) −6.12601 −0.209628
\(855\) 0 0
\(856\) −0.590978 −0.0201992
\(857\) 13.6447 0.466095 0.233047 0.972465i \(-0.425130\pi\)
0.233047 + 0.972465i \(0.425130\pi\)
\(858\) 0 0
\(859\) −39.3829 −1.34373 −0.671864 0.740675i \(-0.734506\pi\)
−0.671864 + 0.740675i \(0.734506\pi\)
\(860\) −56.3595 −1.92184
\(861\) 0 0
\(862\) 1.38011 0.0470068
\(863\) 48.1420 1.63877 0.819387 0.573241i \(-0.194314\pi\)
0.819387 + 0.573241i \(0.194314\pi\)
\(864\) 0 0
\(865\) 59.1022 2.00953
\(866\) 74.9156 2.54574
\(867\) 0 0
\(868\) −56.0857 −1.90367
\(869\) 4.26886 0.144811
\(870\) 0 0
\(871\) 25.0238 0.847898
\(872\) −5.05911 −0.171323
\(873\) 0 0
\(874\) 53.2657 1.80174
\(875\) −5.11722 −0.172994
\(876\) 0 0
\(877\) 37.6587 1.27164 0.635822 0.771836i \(-0.280661\pi\)
0.635822 + 0.771836i \(0.280661\pi\)
\(878\) 19.6267 0.662369
\(879\) 0 0
\(880\) 13.6090 0.458760
\(881\) −32.6783 −1.10096 −0.550480 0.834848i \(-0.685555\pi\)
−0.550480 + 0.834848i \(0.685555\pi\)
\(882\) 0 0
\(883\) −2.47331 −0.0832335 −0.0416167 0.999134i \(-0.513251\pi\)
−0.0416167 + 0.999134i \(0.513251\pi\)
\(884\) −28.9402 −0.973364
\(885\) 0 0
\(886\) 53.7141 1.80456
\(887\) −2.57792 −0.0865580 −0.0432790 0.999063i \(-0.513780\pi\)
−0.0432790 + 0.999063i \(0.513780\pi\)
\(888\) 0 0
\(889\) −39.4393 −1.32275
\(890\) −58.2489 −1.95251
\(891\) 0 0
\(892\) 22.3176 0.747248
\(893\) 43.9068 1.46929
\(894\) 0 0
\(895\) −19.3134 −0.645576
\(896\) −11.6481 −0.389136
\(897\) 0 0
\(898\) −39.4777 −1.31739
\(899\) 33.0235 1.10140
\(900\) 0 0
\(901\) −31.5874 −1.05233
\(902\) 20.9026 0.695981
\(903\) 0 0
\(904\) −5.86470 −0.195057
\(905\) −46.0770 −1.53165
\(906\) 0 0
\(907\) 8.34904 0.277225 0.138613 0.990347i \(-0.455736\pi\)
0.138613 + 0.990347i \(0.455736\pi\)
\(908\) −31.7199 −1.05266
\(909\) 0 0
\(910\) −81.2702 −2.69408
\(911\) 8.66605 0.287119 0.143560 0.989642i \(-0.454145\pi\)
0.143560 + 0.989642i \(0.454145\pi\)
\(912\) 0 0
\(913\) −17.4095 −0.576169
\(914\) −57.4550 −1.90044
\(915\) 0 0
\(916\) 37.2991 1.23240
\(917\) 0.157619 0.00520504
\(918\) 0 0
\(919\) 17.4019 0.574035 0.287017 0.957925i \(-0.407336\pi\)
0.287017 + 0.957925i \(0.407336\pi\)
\(920\) −9.27234 −0.305700
\(921\) 0 0
\(922\) −26.4046 −0.869591
\(923\) −14.6618 −0.482599
\(924\) 0 0
\(925\) −8.28809 −0.272511
\(926\) −31.3336 −1.02969
\(927\) 0 0
\(928\) −25.0383 −0.821922
\(929\) −7.38998 −0.242458 −0.121229 0.992625i \(-0.538683\pi\)
−0.121229 + 0.992625i \(0.538683\pi\)
\(930\) 0 0
\(931\) −12.6106 −0.413296
\(932\) 49.8372 1.63247
\(933\) 0 0
\(934\) 24.1031 0.788676
\(935\) −11.7383 −0.383884
\(936\) 0 0
\(937\) 41.9703 1.37111 0.685555 0.728021i \(-0.259560\pi\)
0.685555 + 0.728021i \(0.259560\pi\)
\(938\) 35.5662 1.16128
\(939\) 0 0
\(940\) 56.2116 1.83342
\(941\) 51.7763 1.68786 0.843929 0.536454i \(-0.180237\pi\)
0.843929 + 0.536454i \(0.180237\pi\)
\(942\) 0 0
\(943\) −69.9458 −2.27775
\(944\) −44.2814 −1.44124
\(945\) 0 0
\(946\) 20.1685 0.655734
\(947\) −22.0964 −0.718037 −0.359019 0.933330i \(-0.616889\pi\)
−0.359019 + 0.933330i \(0.616889\pi\)
\(948\) 0 0
\(949\) −48.6307 −1.57862
\(950\) −36.7219 −1.19142
\(951\) 0 0
\(952\) 5.59286 0.181266
\(953\) 36.4561 1.18093 0.590464 0.807064i \(-0.298945\pi\)
0.590464 + 0.807064i \(0.298945\pi\)
\(954\) 0 0
\(955\) −3.42495 −0.110829
\(956\) −8.62553 −0.278970
\(957\) 0 0
\(958\) −56.5564 −1.82725
\(959\) 0.769979 0.0248639
\(960\) 0 0
\(961\) 70.6905 2.28034
\(962\) 15.4849 0.499253
\(963\) 0 0
\(964\) 48.1500 1.55081
\(965\) 50.7081 1.63235
\(966\) 0 0
\(967\) 1.95027 0.0627164 0.0313582 0.999508i \(-0.490017\pi\)
0.0313582 + 0.999508i \(0.490017\pi\)
\(968\) −0.464237 −0.0149211
\(969\) 0 0
\(970\) −4.86455 −0.156191
\(971\) 40.8271 1.31020 0.655102 0.755540i \(-0.272626\pi\)
0.655102 + 0.755540i \(0.272626\pi\)
\(972\) 0 0
\(973\) 66.9298 2.14567
\(974\) 71.3914 2.28753
\(975\) 0 0
\(976\) −4.42148 −0.141528
\(977\) 29.4296 0.941535 0.470767 0.882257i \(-0.343977\pi\)
0.470767 + 0.882257i \(0.343977\pi\)
\(978\) 0 0
\(979\) 9.75884 0.311894
\(980\) −16.1447 −0.515723
\(981\) 0 0
\(982\) −74.7106 −2.38411
\(983\) −12.2766 −0.391562 −0.195781 0.980648i \(-0.562724\pi\)
−0.195781 + 0.980648i \(0.562724\pi\)
\(984\) 0 0
\(985\) 78.2533 2.49336
\(986\) 24.2191 0.771292
\(987\) 0 0
\(988\) 32.1207 1.02189
\(989\) −67.4892 −2.14603
\(990\) 0 0
\(991\) −30.0821 −0.955588 −0.477794 0.878472i \(-0.658563\pi\)
−0.477794 + 0.878472i \(0.658563\pi\)
\(992\) −77.1014 −2.44797
\(993\) 0 0
\(994\) −20.8387 −0.660965
\(995\) 24.7986 0.786168
\(996\) 0 0
\(997\) 28.9187 0.915866 0.457933 0.888987i \(-0.348590\pi\)
0.457933 + 0.888987i \(0.348590\pi\)
\(998\) 3.26175 0.103249
\(999\) 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 \(a_p\))