Properties

Label 6039.2.a.j.1.7
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 1.7
Root \(-0.0561655\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.0561655 q^{2}\) \(-1.99685 q^{4}\) \(+2.87016 q^{5}\) \(+3.53988 q^{7}\) \(+0.224485 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.0561655 q^{2}\) \(-1.99685 q^{4}\) \(+2.87016 q^{5}\) \(+3.53988 q^{7}\) \(+0.224485 q^{8}\) \(-0.161204 q^{10}\) \(+1.00000 q^{11}\) \(+1.66374 q^{13}\) \(-0.198819 q^{14}\) \(+3.98108 q^{16}\) \(+6.51228 q^{17}\) \(-4.27158 q^{19}\) \(-5.73126 q^{20}\) \(-0.0561655 q^{22}\) \(+8.02418 q^{23}\) \(+3.23780 q^{25}\) \(-0.0934449 q^{26}\) \(-7.06858 q^{28}\) \(-3.26557 q^{29}\) \(+6.97737 q^{31}\) \(-0.672570 q^{32}\) \(-0.365766 q^{34}\) \(+10.1600 q^{35}\) \(+0.826353 q^{37}\) \(+0.239916 q^{38}\) \(+0.644307 q^{40}\) \(+11.9366 q^{41}\) \(-2.21299 q^{43}\) \(-1.99685 q^{44}\) \(-0.450683 q^{46}\) \(-10.4001 q^{47}\) \(+5.53072 q^{49}\) \(-0.181853 q^{50}\) \(-3.32224 q^{52}\) \(-8.11158 q^{53}\) \(+2.87016 q^{55}\) \(+0.794649 q^{56}\) \(+0.183413 q^{58}\) \(-2.00484 q^{59}\) \(+1.00000 q^{61}\) \(-0.391888 q^{62}\) \(-7.92439 q^{64}\) \(+4.77520 q^{65}\) \(+10.0237 q^{67}\) \(-13.0040 q^{68}\) \(-0.570642 q^{70}\) \(+2.13305 q^{71}\) \(+2.54693 q^{73}\) \(-0.0464125 q^{74}\) \(+8.52969 q^{76}\) \(+3.53988 q^{77}\) \(-6.81997 q^{79}\) \(+11.4263 q^{80}\) \(-0.670428 q^{82}\) \(-0.562991 q^{83}\) \(+18.6913 q^{85}\) \(+0.124294 q^{86}\) \(+0.224485 q^{88}\) \(-7.23252 q^{89}\) \(+5.88944 q^{91}\) \(-16.0231 q^{92}\) \(+0.584128 q^{94}\) \(-12.2601 q^{95}\) \(+11.1816 q^{97}\) \(-0.310636 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0561655 −0.0397150 −0.0198575 0.999803i \(-0.506321\pi\)
−0.0198575 + 0.999803i \(0.506321\pi\)
\(3\) 0 0
\(4\) −1.99685 −0.998423
\(5\) 2.87016 1.28357 0.641786 0.766883i \(-0.278194\pi\)
0.641786 + 0.766883i \(0.278194\pi\)
\(6\) 0 0
\(7\) 3.53988 1.33795 0.668974 0.743286i \(-0.266734\pi\)
0.668974 + 0.743286i \(0.266734\pi\)
\(8\) 0.224485 0.0793674
\(9\) 0 0
\(10\) −0.161204 −0.0509771
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.66374 0.461439 0.230719 0.973020i \(-0.425892\pi\)
0.230719 + 0.973020i \(0.425892\pi\)
\(14\) −0.198819 −0.0531366
\(15\) 0 0
\(16\) 3.98108 0.995271
\(17\) 6.51228 1.57946 0.789730 0.613455i \(-0.210221\pi\)
0.789730 + 0.613455i \(0.210221\pi\)
\(18\) 0 0
\(19\) −4.27158 −0.979968 −0.489984 0.871731i \(-0.662997\pi\)
−0.489984 + 0.871731i \(0.662997\pi\)
\(20\) −5.73126 −1.28155
\(21\) 0 0
\(22\) −0.0561655 −0.0119745
\(23\) 8.02418 1.67316 0.836579 0.547846i \(-0.184552\pi\)
0.836579 + 0.547846i \(0.184552\pi\)
\(24\) 0 0
\(25\) 3.23780 0.647559
\(26\) −0.0934449 −0.0183261
\(27\) 0 0
\(28\) −7.06858 −1.33584
\(29\) −3.26557 −0.606402 −0.303201 0.952927i \(-0.598055\pi\)
−0.303201 + 0.952927i \(0.598055\pi\)
\(30\) 0 0
\(31\) 6.97737 1.25317 0.626587 0.779352i \(-0.284451\pi\)
0.626587 + 0.779352i \(0.284451\pi\)
\(32\) −0.672570 −0.118895
\(33\) 0 0
\(34\) −0.365766 −0.0627283
\(35\) 10.1600 1.71735
\(36\) 0 0
\(37\) 0.826353 0.135852 0.0679258 0.997690i \(-0.478362\pi\)
0.0679258 + 0.997690i \(0.478362\pi\)
\(38\) 0.239916 0.0389194
\(39\) 0 0
\(40\) 0.644307 0.101874
\(41\) 11.9366 1.86419 0.932095 0.362214i \(-0.117979\pi\)
0.932095 + 0.362214i \(0.117979\pi\)
\(42\) 0 0
\(43\) −2.21299 −0.337477 −0.168739 0.985661i \(-0.553969\pi\)
−0.168739 + 0.985661i \(0.553969\pi\)
\(44\) −1.99685 −0.301036
\(45\) 0 0
\(46\) −0.450683 −0.0664495
\(47\) −10.4001 −1.51701 −0.758506 0.651666i \(-0.774070\pi\)
−0.758506 + 0.651666i \(0.774070\pi\)
\(48\) 0 0
\(49\) 5.53072 0.790103
\(50\) −0.181853 −0.0257178
\(51\) 0 0
\(52\) −3.32224 −0.460711
\(53\) −8.11158 −1.11421 −0.557106 0.830442i \(-0.688088\pi\)
−0.557106 + 0.830442i \(0.688088\pi\)
\(54\) 0 0
\(55\) 2.87016 0.387012
\(56\) 0.794649 0.106189
\(57\) 0 0
\(58\) 0.183413 0.0240833
\(59\) −2.00484 −0.261007 −0.130504 0.991448i \(-0.541659\pi\)
−0.130504 + 0.991448i \(0.541659\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −0.391888 −0.0497698
\(63\) 0 0
\(64\) −7.92439 −0.990549
\(65\) 4.77520 0.592291
\(66\) 0 0
\(67\) 10.0237 1.22459 0.612293 0.790631i \(-0.290247\pi\)
0.612293 + 0.790631i \(0.290247\pi\)
\(68\) −13.0040 −1.57697
\(69\) 0 0
\(70\) −0.570642 −0.0682047
\(71\) 2.13305 0.253146 0.126573 0.991957i \(-0.459602\pi\)
0.126573 + 0.991957i \(0.459602\pi\)
\(72\) 0 0
\(73\) 2.54693 0.298096 0.149048 0.988830i \(-0.452379\pi\)
0.149048 + 0.988830i \(0.452379\pi\)
\(74\) −0.0464125 −0.00539535
\(75\) 0 0
\(76\) 8.52969 0.978422
\(77\) 3.53988 0.403406
\(78\) 0 0
\(79\) −6.81997 −0.767306 −0.383653 0.923477i \(-0.625334\pi\)
−0.383653 + 0.923477i \(0.625334\pi\)
\(80\) 11.4263 1.27750
\(81\) 0 0
\(82\) −0.670428 −0.0740364
\(83\) −0.562991 −0.0617963 −0.0308982 0.999523i \(-0.509837\pi\)
−0.0308982 + 0.999523i \(0.509837\pi\)
\(84\) 0 0
\(85\) 18.6913 2.02735
\(86\) 0.124294 0.0134029
\(87\) 0 0
\(88\) 0.224485 0.0239302
\(89\) −7.23252 −0.766646 −0.383323 0.923614i \(-0.625220\pi\)
−0.383323 + 0.923614i \(0.625220\pi\)
\(90\) 0 0
\(91\) 5.88944 0.617381
\(92\) −16.0231 −1.67052
\(93\) 0 0
\(94\) 0.584128 0.0602482
\(95\) −12.2601 −1.25786
\(96\) 0 0
\(97\) 11.1816 1.13532 0.567660 0.823263i \(-0.307849\pi\)
0.567660 + 0.823263i \(0.307849\pi\)
\(98\) −0.310636 −0.0313789
\(99\) 0 0
\(100\) −6.46538 −0.646538
\(101\) −10.8938 −1.08398 −0.541989 0.840386i \(-0.682329\pi\)
−0.541989 + 0.840386i \(0.682329\pi\)
\(102\) 0 0
\(103\) −1.11625 −0.109988 −0.0549938 0.998487i \(-0.517514\pi\)
−0.0549938 + 0.998487i \(0.517514\pi\)
\(104\) 0.373485 0.0366232
\(105\) 0 0
\(106\) 0.455591 0.0442509
\(107\) 2.80022 0.270707 0.135354 0.990797i \(-0.456783\pi\)
0.135354 + 0.990797i \(0.456783\pi\)
\(108\) 0 0
\(109\) 10.6923 1.02414 0.512069 0.858944i \(-0.328879\pi\)
0.512069 + 0.858944i \(0.328879\pi\)
\(110\) −0.161204 −0.0153702
\(111\) 0 0
\(112\) 14.0925 1.33162
\(113\) −13.9443 −1.31177 −0.655885 0.754861i \(-0.727704\pi\)
−0.655885 + 0.754861i \(0.727704\pi\)
\(114\) 0 0
\(115\) 23.0307 2.14762
\(116\) 6.52085 0.605446
\(117\) 0 0
\(118\) 0.112603 0.0103659
\(119\) 23.0527 2.11323
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −0.0561655 −0.00508499
\(123\) 0 0
\(124\) −13.9327 −1.25120
\(125\) −5.05780 −0.452383
\(126\) 0 0
\(127\) −15.3492 −1.36202 −0.681012 0.732272i \(-0.738460\pi\)
−0.681012 + 0.732272i \(0.738460\pi\)
\(128\) 1.79022 0.158234
\(129\) 0 0
\(130\) −0.268202 −0.0235228
\(131\) −17.1289 −1.49656 −0.748280 0.663383i \(-0.769120\pi\)
−0.748280 + 0.663383i \(0.769120\pi\)
\(132\) 0 0
\(133\) −15.1209 −1.31115
\(134\) −0.562985 −0.0486345
\(135\) 0 0
\(136\) 1.46191 0.125358
\(137\) 1.15929 0.0990451 0.0495225 0.998773i \(-0.484230\pi\)
0.0495225 + 0.998773i \(0.484230\pi\)
\(138\) 0 0
\(139\) 7.66907 0.650482 0.325241 0.945631i \(-0.394555\pi\)
0.325241 + 0.945631i \(0.394555\pi\)
\(140\) −20.2879 −1.71464
\(141\) 0 0
\(142\) −0.119804 −0.0100537
\(143\) 1.66374 0.139129
\(144\) 0 0
\(145\) −9.37271 −0.778361
\(146\) −0.143050 −0.0118389
\(147\) 0 0
\(148\) −1.65010 −0.135637
\(149\) 1.19140 0.0976031 0.0488015 0.998808i \(-0.484460\pi\)
0.0488015 + 0.998808i \(0.484460\pi\)
\(150\) 0 0
\(151\) 11.2781 0.917798 0.458899 0.888488i \(-0.348244\pi\)
0.458899 + 0.888488i \(0.348244\pi\)
\(152\) −0.958906 −0.0777775
\(153\) 0 0
\(154\) −0.198819 −0.0160213
\(155\) 20.0262 1.60854
\(156\) 0 0
\(157\) 17.0614 1.36165 0.680825 0.732446i \(-0.261621\pi\)
0.680825 + 0.732446i \(0.261621\pi\)
\(158\) 0.383047 0.0304736
\(159\) 0 0
\(160\) −1.93038 −0.152610
\(161\) 28.4046 2.23860
\(162\) 0 0
\(163\) −18.8321 −1.47504 −0.737521 0.675325i \(-0.764004\pi\)
−0.737521 + 0.675325i \(0.764004\pi\)
\(164\) −23.8356 −1.86125
\(165\) 0 0
\(166\) 0.0316207 0.00245424
\(167\) −20.7776 −1.60782 −0.803911 0.594749i \(-0.797251\pi\)
−0.803911 + 0.594749i \(0.797251\pi\)
\(168\) 0 0
\(169\) −10.2320 −0.787074
\(170\) −1.04980 −0.0805163
\(171\) 0 0
\(172\) 4.41899 0.336945
\(173\) −8.58089 −0.652393 −0.326197 0.945302i \(-0.605767\pi\)
−0.326197 + 0.945302i \(0.605767\pi\)
\(174\) 0 0
\(175\) 11.4614 0.866400
\(176\) 3.98108 0.300085
\(177\) 0 0
\(178\) 0.406218 0.0304474
\(179\) −1.62970 −0.121810 −0.0609049 0.998144i \(-0.519399\pi\)
−0.0609049 + 0.998144i \(0.519399\pi\)
\(180\) 0 0
\(181\) −6.80075 −0.505496 −0.252748 0.967532i \(-0.581334\pi\)
−0.252748 + 0.967532i \(0.581334\pi\)
\(182\) −0.330783 −0.0245193
\(183\) 0 0
\(184\) 1.80131 0.132794
\(185\) 2.37176 0.174375
\(186\) 0 0
\(187\) 6.51228 0.476225
\(188\) 20.7674 1.51462
\(189\) 0 0
\(190\) 0.688595 0.0499559
\(191\) −21.1056 −1.52714 −0.763572 0.645723i \(-0.776556\pi\)
−0.763572 + 0.645723i \(0.776556\pi\)
\(192\) 0 0
\(193\) −15.3449 −1.10455 −0.552276 0.833661i \(-0.686241\pi\)
−0.552276 + 0.833661i \(0.686241\pi\)
\(194\) −0.628021 −0.0450893
\(195\) 0 0
\(196\) −11.0440 −0.788856
\(197\) −8.01939 −0.571358 −0.285679 0.958325i \(-0.592219\pi\)
−0.285679 + 0.958325i \(0.592219\pi\)
\(198\) 0 0
\(199\) 18.9435 1.34287 0.671435 0.741063i \(-0.265678\pi\)
0.671435 + 0.741063i \(0.265678\pi\)
\(200\) 0.726836 0.0513951
\(201\) 0 0
\(202\) 0.611859 0.0430502
\(203\) −11.5597 −0.811334
\(204\) 0 0
\(205\) 34.2600 2.39282
\(206\) 0.0626949 0.00436816
\(207\) 0 0
\(208\) 6.62349 0.459257
\(209\) −4.27158 −0.295471
\(210\) 0 0
\(211\) −14.2888 −0.983682 −0.491841 0.870685i \(-0.663676\pi\)
−0.491841 + 0.870685i \(0.663676\pi\)
\(212\) 16.1976 1.11245
\(213\) 0 0
\(214\) −0.157276 −0.0107511
\(215\) −6.35162 −0.433177
\(216\) 0 0
\(217\) 24.6990 1.67668
\(218\) −0.600540 −0.0406737
\(219\) 0 0
\(220\) −5.73126 −0.386401
\(221\) 10.8348 0.728824
\(222\) 0 0
\(223\) −2.84596 −0.190580 −0.0952899 0.995450i \(-0.530378\pi\)
−0.0952899 + 0.995450i \(0.530378\pi\)
\(224\) −2.38081 −0.159075
\(225\) 0 0
\(226\) 0.783189 0.0520970
\(227\) 19.4833 1.29315 0.646576 0.762849i \(-0.276200\pi\)
0.646576 + 0.762849i \(0.276200\pi\)
\(228\) 0 0
\(229\) −11.7161 −0.774219 −0.387109 0.922034i \(-0.626526\pi\)
−0.387109 + 0.922034i \(0.626526\pi\)
\(230\) −1.29353 −0.0852928
\(231\) 0 0
\(232\) −0.733072 −0.0481286
\(233\) 27.8004 1.82126 0.910632 0.413219i \(-0.135596\pi\)
0.910632 + 0.413219i \(0.135596\pi\)
\(234\) 0 0
\(235\) −29.8499 −1.94720
\(236\) 4.00335 0.260596
\(237\) 0 0
\(238\) −1.29476 −0.0839271
\(239\) −1.27569 −0.0825176 −0.0412588 0.999148i \(-0.513137\pi\)
−0.0412588 + 0.999148i \(0.513137\pi\)
\(240\) 0 0
\(241\) 14.9945 0.965878 0.482939 0.875654i \(-0.339569\pi\)
0.482939 + 0.875654i \(0.339569\pi\)
\(242\) −0.0561655 −0.00361046
\(243\) 0 0
\(244\) −1.99685 −0.127835
\(245\) 15.8740 1.01415
\(246\) 0 0
\(247\) −7.10681 −0.452195
\(248\) 1.56632 0.0994611
\(249\) 0 0
\(250\) 0.284074 0.0179664
\(251\) 25.6541 1.61927 0.809637 0.586931i \(-0.199664\pi\)
0.809637 + 0.586931i \(0.199664\pi\)
\(252\) 0 0
\(253\) 8.02418 0.504476
\(254\) 0.862098 0.0540929
\(255\) 0 0
\(256\) 15.7482 0.984264
\(257\) 23.5239 1.46738 0.733690 0.679485i \(-0.237797\pi\)
0.733690 + 0.679485i \(0.237797\pi\)
\(258\) 0 0
\(259\) 2.92519 0.181762
\(260\) −9.53533 −0.591356
\(261\) 0 0
\(262\) 0.962055 0.0594360
\(263\) 7.55266 0.465717 0.232859 0.972511i \(-0.425192\pi\)
0.232859 + 0.972511i \(0.425192\pi\)
\(264\) 0 0
\(265\) −23.2815 −1.43017
\(266\) 0.849271 0.0520722
\(267\) 0 0
\(268\) −20.0157 −1.22266
\(269\) −25.3390 −1.54495 −0.772474 0.635046i \(-0.780981\pi\)
−0.772474 + 0.635046i \(0.780981\pi\)
\(270\) 0 0
\(271\) −24.0494 −1.46090 −0.730449 0.682967i \(-0.760689\pi\)
−0.730449 + 0.682967i \(0.760689\pi\)
\(272\) 25.9259 1.57199
\(273\) 0 0
\(274\) −0.0651123 −0.00393358
\(275\) 3.23780 0.195246
\(276\) 0 0
\(277\) 25.9274 1.55782 0.778912 0.627133i \(-0.215772\pi\)
0.778912 + 0.627133i \(0.215772\pi\)
\(278\) −0.430738 −0.0258339
\(279\) 0 0
\(280\) 2.28077 0.136302
\(281\) 16.8801 1.00698 0.503491 0.864000i \(-0.332049\pi\)
0.503491 + 0.864000i \(0.332049\pi\)
\(282\) 0 0
\(283\) 14.2351 0.846191 0.423095 0.906085i \(-0.360944\pi\)
0.423095 + 0.906085i \(0.360944\pi\)
\(284\) −4.25937 −0.252747
\(285\) 0 0
\(286\) −0.0934449 −0.00552552
\(287\) 42.2542 2.49419
\(288\) 0 0
\(289\) 25.4098 1.49469
\(290\) 0.526423 0.0309126
\(291\) 0 0
\(292\) −5.08583 −0.297626
\(293\) −25.1762 −1.47081 −0.735406 0.677627i \(-0.763008\pi\)
−0.735406 + 0.677627i \(0.763008\pi\)
\(294\) 0 0
\(295\) −5.75419 −0.335022
\(296\) 0.185504 0.0107822
\(297\) 0 0
\(298\) −0.0669155 −0.00387631
\(299\) 13.3502 0.772060
\(300\) 0 0
\(301\) −7.83369 −0.451527
\(302\) −0.633440 −0.0364504
\(303\) 0 0
\(304\) −17.0055 −0.975333
\(305\) 2.87016 0.164345
\(306\) 0 0
\(307\) 20.2369 1.15498 0.577490 0.816398i \(-0.304032\pi\)
0.577490 + 0.816398i \(0.304032\pi\)
\(308\) −7.06858 −0.402770
\(309\) 0 0
\(310\) −1.12478 −0.0638832
\(311\) −20.5089 −1.16295 −0.581477 0.813563i \(-0.697525\pi\)
−0.581477 + 0.813563i \(0.697525\pi\)
\(312\) 0 0
\(313\) −10.5734 −0.597644 −0.298822 0.954309i \(-0.596594\pi\)
−0.298822 + 0.954309i \(0.596594\pi\)
\(314\) −0.958264 −0.0540780
\(315\) 0 0
\(316\) 13.6184 0.766096
\(317\) −20.3836 −1.14486 −0.572429 0.819955i \(-0.693999\pi\)
−0.572429 + 0.819955i \(0.693999\pi\)
\(318\) 0 0
\(319\) −3.26557 −0.182837
\(320\) −22.7442 −1.27144
\(321\) 0 0
\(322\) −1.59536 −0.0889059
\(323\) −27.8177 −1.54782
\(324\) 0 0
\(325\) 5.38686 0.298809
\(326\) 1.05771 0.0585813
\(327\) 0 0
\(328\) 2.67960 0.147956
\(329\) −36.8151 −2.02968
\(330\) 0 0
\(331\) 11.9595 0.657353 0.328676 0.944443i \(-0.393397\pi\)
0.328676 + 0.944443i \(0.393397\pi\)
\(332\) 1.12421 0.0616989
\(333\) 0 0
\(334\) 1.16699 0.0638547
\(335\) 28.7695 1.57185
\(336\) 0 0
\(337\) −17.6438 −0.961117 −0.480559 0.876963i \(-0.659566\pi\)
−0.480559 + 0.876963i \(0.659566\pi\)
\(338\) 0.574684 0.0312587
\(339\) 0 0
\(340\) −37.3236 −2.02415
\(341\) 6.97737 0.377846
\(342\) 0 0
\(343\) −5.20108 −0.280832
\(344\) −0.496782 −0.0267847
\(345\) 0 0
\(346\) 0.481950 0.0259098
\(347\) −0.648489 −0.0348127 −0.0174063 0.999848i \(-0.505541\pi\)
−0.0174063 + 0.999848i \(0.505541\pi\)
\(348\) 0 0
\(349\) −23.3381 −1.24926 −0.624631 0.780920i \(-0.714751\pi\)
−0.624631 + 0.780920i \(0.714751\pi\)
\(350\) −0.643735 −0.0344091
\(351\) 0 0
\(352\) −0.672570 −0.0358481
\(353\) 35.7398 1.90224 0.951119 0.308825i \(-0.0999356\pi\)
0.951119 + 0.308825i \(0.0999356\pi\)
\(354\) 0 0
\(355\) 6.12219 0.324932
\(356\) 14.4422 0.765437
\(357\) 0 0
\(358\) 0.0915332 0.00483768
\(359\) −10.9472 −0.577770 −0.288885 0.957364i \(-0.593285\pi\)
−0.288885 + 0.957364i \(0.593285\pi\)
\(360\) 0 0
\(361\) −0.753598 −0.0396631
\(362\) 0.381968 0.0200758
\(363\) 0 0
\(364\) −11.7603 −0.616407
\(365\) 7.31009 0.382628
\(366\) 0 0
\(367\) 17.0313 0.889025 0.444513 0.895773i \(-0.353377\pi\)
0.444513 + 0.895773i \(0.353377\pi\)
\(368\) 31.9449 1.66525
\(369\) 0 0
\(370\) −0.133211 −0.00692532
\(371\) −28.7140 −1.49076
\(372\) 0 0
\(373\) 26.7579 1.38547 0.692735 0.721192i \(-0.256406\pi\)
0.692735 + 0.721192i \(0.256406\pi\)
\(374\) −0.365766 −0.0189133
\(375\) 0 0
\(376\) −2.33467 −0.120401
\(377\) −5.43307 −0.279818
\(378\) 0 0
\(379\) 7.77600 0.399426 0.199713 0.979854i \(-0.435999\pi\)
0.199713 + 0.979854i \(0.435999\pi\)
\(380\) 24.4815 1.25588
\(381\) 0 0
\(382\) 1.18540 0.0606506
\(383\) 28.3894 1.45063 0.725316 0.688416i \(-0.241694\pi\)
0.725316 + 0.688416i \(0.241694\pi\)
\(384\) 0 0
\(385\) 10.1600 0.517801
\(386\) 0.861857 0.0438673
\(387\) 0 0
\(388\) −22.3279 −1.13353
\(389\) −32.7737 −1.66169 −0.830846 0.556503i \(-0.812143\pi\)
−0.830846 + 0.556503i \(0.812143\pi\)
\(390\) 0 0
\(391\) 52.2557 2.64269
\(392\) 1.24156 0.0627084
\(393\) 0 0
\(394\) 0.450413 0.0226915
\(395\) −19.5744 −0.984893
\(396\) 0 0
\(397\) 23.4981 1.17934 0.589668 0.807646i \(-0.299259\pi\)
0.589668 + 0.807646i \(0.299259\pi\)
\(398\) −1.06397 −0.0533321
\(399\) 0 0
\(400\) 12.8899 0.644497
\(401\) 5.67692 0.283492 0.141746 0.989903i \(-0.454728\pi\)
0.141746 + 0.989903i \(0.454728\pi\)
\(402\) 0 0
\(403\) 11.6086 0.578263
\(404\) 21.7533 1.08227
\(405\) 0 0
\(406\) 0.649258 0.0322221
\(407\) 0.826353 0.0409608
\(408\) 0 0
\(409\) 15.8544 0.783950 0.391975 0.919976i \(-0.371792\pi\)
0.391975 + 0.919976i \(0.371792\pi\)
\(410\) −1.92423 −0.0950311
\(411\) 0 0
\(412\) 2.22898 0.109814
\(413\) −7.09687 −0.349214
\(414\) 0 0
\(415\) −1.61587 −0.0793201
\(416\) −1.11898 −0.0548626
\(417\) 0 0
\(418\) 0.239916 0.0117347
\(419\) −9.40019 −0.459229 −0.229615 0.973282i \(-0.573747\pi\)
−0.229615 + 0.973282i \(0.573747\pi\)
\(420\) 0 0
\(421\) 19.3416 0.942650 0.471325 0.881960i \(-0.343776\pi\)
0.471325 + 0.881960i \(0.343776\pi\)
\(422\) 0.802538 0.0390669
\(423\) 0 0
\(424\) −1.82093 −0.0884321
\(425\) 21.0854 1.02279
\(426\) 0 0
\(427\) 3.53988 0.171307
\(428\) −5.59160 −0.270280
\(429\) 0 0
\(430\) 0.356742 0.0172036
\(431\) −22.0619 −1.06268 −0.531342 0.847158i \(-0.678312\pi\)
−0.531342 + 0.847158i \(0.678312\pi\)
\(432\) 0 0
\(433\) 16.4389 0.790005 0.395002 0.918680i \(-0.370744\pi\)
0.395002 + 0.918680i \(0.370744\pi\)
\(434\) −1.38723 −0.0665894
\(435\) 0 0
\(436\) −21.3509 −1.02252
\(437\) −34.2760 −1.63964
\(438\) 0 0
\(439\) 29.1315 1.39037 0.695185 0.718831i \(-0.255322\pi\)
0.695185 + 0.718831i \(0.255322\pi\)
\(440\) 0.644307 0.0307161
\(441\) 0 0
\(442\) −0.608540 −0.0289453
\(443\) 39.8835 1.89492 0.947461 0.319871i \(-0.103640\pi\)
0.947461 + 0.319871i \(0.103640\pi\)
\(444\) 0 0
\(445\) −20.7585 −0.984046
\(446\) 0.159845 0.00756888
\(447\) 0 0
\(448\) −28.0514 −1.32530
\(449\) 6.39145 0.301631 0.150816 0.988562i \(-0.451810\pi\)
0.150816 + 0.988562i \(0.451810\pi\)
\(450\) 0 0
\(451\) 11.9366 0.562074
\(452\) 27.8446 1.30970
\(453\) 0 0
\(454\) −1.09429 −0.0513576
\(455\) 16.9036 0.792453
\(456\) 0 0
\(457\) −6.55699 −0.306723 −0.153362 0.988170i \(-0.549010\pi\)
−0.153362 + 0.988170i \(0.549010\pi\)
\(458\) 0.658038 0.0307481
\(459\) 0 0
\(460\) −45.9887 −2.14423
\(461\) 7.90935 0.368375 0.184188 0.982891i \(-0.441035\pi\)
0.184188 + 0.982891i \(0.441035\pi\)
\(462\) 0 0
\(463\) 29.9602 1.39237 0.696184 0.717864i \(-0.254880\pi\)
0.696184 + 0.717864i \(0.254880\pi\)
\(464\) −13.0005 −0.603534
\(465\) 0 0
\(466\) −1.56142 −0.0723315
\(467\) −11.4395 −0.529355 −0.264678 0.964337i \(-0.585266\pi\)
−0.264678 + 0.964337i \(0.585266\pi\)
\(468\) 0 0
\(469\) 35.4826 1.63843
\(470\) 1.67654 0.0773329
\(471\) 0 0
\(472\) −0.450055 −0.0207155
\(473\) −2.21299 −0.101753
\(474\) 0 0
\(475\) −13.8305 −0.634587
\(476\) −46.0326 −2.10990
\(477\) 0 0
\(478\) 0.0716499 0.00327719
\(479\) −6.05533 −0.276675 −0.138338 0.990385i \(-0.544176\pi\)
−0.138338 + 0.990385i \(0.544176\pi\)
\(480\) 0 0
\(481\) 1.37484 0.0626872
\(482\) −0.842172 −0.0383599
\(483\) 0 0
\(484\) −1.99685 −0.0907657
\(485\) 32.0930 1.45727
\(486\) 0 0
\(487\) 5.74022 0.260114 0.130057 0.991507i \(-0.458484\pi\)
0.130057 + 0.991507i \(0.458484\pi\)
\(488\) 0.224485 0.0101620
\(489\) 0 0
\(490\) −0.891573 −0.0402772
\(491\) −5.78303 −0.260984 −0.130492 0.991449i \(-0.541656\pi\)
−0.130492 + 0.991449i \(0.541656\pi\)
\(492\) 0 0
\(493\) −21.2663 −0.957788
\(494\) 0.399158 0.0179590
\(495\) 0 0
\(496\) 27.7775 1.24725
\(497\) 7.55073 0.338697
\(498\) 0 0
\(499\) −9.90735 −0.443514 −0.221757 0.975102i \(-0.571179\pi\)
−0.221757 + 0.975102i \(0.571179\pi\)
\(500\) 10.0996 0.451670
\(501\) 0 0
\(502\) −1.44088 −0.0643095
\(503\) −33.8356 −1.50865 −0.754327 0.656499i \(-0.772037\pi\)
−0.754327 + 0.656499i \(0.772037\pi\)
\(504\) 0 0
\(505\) −31.2670 −1.39136
\(506\) −0.450683 −0.0200353
\(507\) 0 0
\(508\) 30.6501 1.35988
\(509\) 18.3516 0.813422 0.406711 0.913557i \(-0.366676\pi\)
0.406711 + 0.913557i \(0.366676\pi\)
\(510\) 0 0
\(511\) 9.01582 0.398836
\(512\) −4.46494 −0.197324
\(513\) 0 0
\(514\) −1.32123 −0.0582770
\(515\) −3.20382 −0.141177
\(516\) 0 0
\(517\) −10.4001 −0.457396
\(518\) −0.164295 −0.00721869
\(519\) 0 0
\(520\) 1.07196 0.0470086
\(521\) −14.9139 −0.653389 −0.326694 0.945130i \(-0.605935\pi\)
−0.326694 + 0.945130i \(0.605935\pi\)
\(522\) 0 0
\(523\) 12.6492 0.553112 0.276556 0.960998i \(-0.410807\pi\)
0.276556 + 0.960998i \(0.410807\pi\)
\(524\) 34.2038 1.49420
\(525\) 0 0
\(526\) −0.424199 −0.0184960
\(527\) 45.4386 1.97934
\(528\) 0 0
\(529\) 41.3875 1.79946
\(530\) 1.30762 0.0567993
\(531\) 0 0
\(532\) 30.1940 1.30908
\(533\) 19.8595 0.860210
\(534\) 0 0
\(535\) 8.03706 0.347472
\(536\) 2.25016 0.0971923
\(537\) 0 0
\(538\) 1.42318 0.0613577
\(539\) 5.53072 0.238225
\(540\) 0 0
\(541\) 16.0561 0.690305 0.345153 0.938547i \(-0.387827\pi\)
0.345153 + 0.938547i \(0.387827\pi\)
\(542\) 1.35075 0.0580196
\(543\) 0 0
\(544\) −4.37996 −0.187789
\(545\) 30.6886 1.31456
\(546\) 0 0
\(547\) 7.91664 0.338491 0.169246 0.985574i \(-0.445867\pi\)
0.169246 + 0.985574i \(0.445867\pi\)
\(548\) −2.31493 −0.0988889
\(549\) 0 0
\(550\) −0.181853 −0.00775422
\(551\) 13.9492 0.594254
\(552\) 0 0
\(553\) −24.1418 −1.02662
\(554\) −1.45622 −0.0618691
\(555\) 0 0
\(556\) −15.3140 −0.649456
\(557\) 30.0118 1.27164 0.635821 0.771837i \(-0.280662\pi\)
0.635821 + 0.771837i \(0.280662\pi\)
\(558\) 0 0
\(559\) −3.68184 −0.155725
\(560\) 40.4478 1.70923
\(561\) 0 0
\(562\) −0.948080 −0.0399923
\(563\) 0.239936 0.0101121 0.00505604 0.999987i \(-0.498391\pi\)
0.00505604 + 0.999987i \(0.498391\pi\)
\(564\) 0 0
\(565\) −40.0223 −1.68375
\(566\) −0.799524 −0.0336065
\(567\) 0 0
\(568\) 0.478838 0.0200916
\(569\) 7.76917 0.325701 0.162850 0.986651i \(-0.447931\pi\)
0.162850 + 0.986651i \(0.447931\pi\)
\(570\) 0 0
\(571\) −46.4165 −1.94247 −0.971235 0.238124i \(-0.923468\pi\)
−0.971235 + 0.238124i \(0.923468\pi\)
\(572\) −3.32224 −0.138910
\(573\) 0 0
\(574\) −2.37323 −0.0990567
\(575\) 25.9807 1.08347
\(576\) 0 0
\(577\) 41.0776 1.71008 0.855042 0.518559i \(-0.173531\pi\)
0.855042 + 0.518559i \(0.173531\pi\)
\(578\) −1.42715 −0.0593618
\(579\) 0 0
\(580\) 18.7159 0.777133
\(581\) −1.99292 −0.0826802
\(582\) 0 0
\(583\) −8.11158 −0.335947
\(584\) 0.571748 0.0236591
\(585\) 0 0
\(586\) 1.41404 0.0584133
\(587\) −32.5698 −1.34430 −0.672150 0.740415i \(-0.734629\pi\)
−0.672150 + 0.740415i \(0.734629\pi\)
\(588\) 0 0
\(589\) −29.8044 −1.22807
\(590\) 0.323187 0.0133054
\(591\) 0 0
\(592\) 3.28978 0.135209
\(593\) 37.9151 1.55699 0.778493 0.627653i \(-0.215984\pi\)
0.778493 + 0.627653i \(0.215984\pi\)
\(594\) 0 0
\(595\) 66.1647 2.71249
\(596\) −2.37904 −0.0974491
\(597\) 0 0
\(598\) −0.749820 −0.0306624
\(599\) 6.61867 0.270432 0.135216 0.990816i \(-0.456827\pi\)
0.135216 + 0.990816i \(0.456827\pi\)
\(600\) 0 0
\(601\) 28.1603 1.14868 0.574341 0.818616i \(-0.305258\pi\)
0.574341 + 0.818616i \(0.305258\pi\)
\(602\) 0.439984 0.0179324
\(603\) 0 0
\(604\) −22.5206 −0.916351
\(605\) 2.87016 0.116688
\(606\) 0 0
\(607\) −43.2487 −1.75541 −0.877705 0.479201i \(-0.840927\pi\)
−0.877705 + 0.479201i \(0.840927\pi\)
\(608\) 2.87293 0.116513
\(609\) 0 0
\(610\) −0.161204 −0.00652695
\(611\) −17.3031 −0.700009
\(612\) 0 0
\(613\) −28.6880 −1.15870 −0.579349 0.815079i \(-0.696693\pi\)
−0.579349 + 0.815079i \(0.696693\pi\)
\(614\) −1.13661 −0.0458700
\(615\) 0 0
\(616\) 0.794649 0.0320173
\(617\) 0.710736 0.0286132 0.0143066 0.999898i \(-0.495446\pi\)
0.0143066 + 0.999898i \(0.495446\pi\)
\(618\) 0 0
\(619\) −47.7932 −1.92097 −0.960486 0.278329i \(-0.910220\pi\)
−0.960486 + 0.278329i \(0.910220\pi\)
\(620\) −39.9891 −1.60600
\(621\) 0 0
\(622\) 1.15189 0.0461867
\(623\) −25.6022 −1.02573
\(624\) 0 0
\(625\) −30.7057 −1.22823
\(626\) 0.593861 0.0237355
\(627\) 0 0
\(628\) −34.0690 −1.35950
\(629\) 5.38144 0.214572
\(630\) 0 0
\(631\) −20.5702 −0.818889 −0.409444 0.912335i \(-0.634277\pi\)
−0.409444 + 0.912335i \(0.634277\pi\)
\(632\) −1.53098 −0.0608991
\(633\) 0 0
\(634\) 1.14486 0.0454680
\(635\) −44.0547 −1.74826
\(636\) 0 0
\(637\) 9.20169 0.364584
\(638\) 0.183413 0.00726138
\(639\) 0 0
\(640\) 5.13820 0.203105
\(641\) 13.0911 0.517069 0.258535 0.966002i \(-0.416760\pi\)
0.258535 + 0.966002i \(0.416760\pi\)
\(642\) 0 0
\(643\) 23.2585 0.917226 0.458613 0.888636i \(-0.348346\pi\)
0.458613 + 0.888636i \(0.348346\pi\)
\(644\) −56.7196 −2.23507
\(645\) 0 0
\(646\) 1.56240 0.0614717
\(647\) −30.4427 −1.19683 −0.598413 0.801188i \(-0.704202\pi\)
−0.598413 + 0.801188i \(0.704202\pi\)
\(648\) 0 0
\(649\) −2.00484 −0.0786967
\(650\) −0.302556 −0.0118672
\(651\) 0 0
\(652\) 37.6047 1.47271
\(653\) 28.5204 1.11609 0.558045 0.829811i \(-0.311552\pi\)
0.558045 + 0.829811i \(0.311552\pi\)
\(654\) 0 0
\(655\) −49.1627 −1.92094
\(656\) 47.5207 1.85537
\(657\) 0 0
\(658\) 2.06774 0.0806089
\(659\) −9.78396 −0.381129 −0.190564 0.981675i \(-0.561032\pi\)
−0.190564 + 0.981675i \(0.561032\pi\)
\(660\) 0 0
\(661\) −26.0822 −1.01448 −0.507239 0.861805i \(-0.669334\pi\)
−0.507239 + 0.861805i \(0.669334\pi\)
\(662\) −0.671711 −0.0261068
\(663\) 0 0
\(664\) −0.126383 −0.00490462
\(665\) −43.3992 −1.68295
\(666\) 0 0
\(667\) −26.2036 −1.01461
\(668\) 41.4897 1.60529
\(669\) 0 0
\(670\) −1.61586 −0.0624259
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −6.37530 −0.245750 −0.122875 0.992422i \(-0.539211\pi\)
−0.122875 + 0.992422i \(0.539211\pi\)
\(674\) 0.990972 0.0381708
\(675\) 0 0
\(676\) 20.4316 0.785833
\(677\) 22.2919 0.856747 0.428374 0.903602i \(-0.359087\pi\)
0.428374 + 0.903602i \(0.359087\pi\)
\(678\) 0 0
\(679\) 39.5815 1.51900
\(680\) 4.19591 0.160906
\(681\) 0 0
\(682\) −0.391888 −0.0150062
\(683\) −24.9233 −0.953662 −0.476831 0.878995i \(-0.658215\pi\)
−0.476831 + 0.878995i \(0.658215\pi\)
\(684\) 0 0
\(685\) 3.32735 0.127132
\(686\) 0.292121 0.0111532
\(687\) 0 0
\(688\) −8.81008 −0.335881
\(689\) −13.4956 −0.514141
\(690\) 0 0
\(691\) −0.490891 −0.0186744 −0.00933718 0.999956i \(-0.502972\pi\)
−0.00933718 + 0.999956i \(0.502972\pi\)
\(692\) 17.1347 0.651364
\(693\) 0 0
\(694\) 0.0364227 0.00138259
\(695\) 22.0114 0.834941
\(696\) 0 0
\(697\) 77.7347 2.94441
\(698\) 1.31080 0.0496145
\(699\) 0 0
\(700\) −22.8866 −0.865033
\(701\) 12.9149 0.487791 0.243895 0.969802i \(-0.421575\pi\)
0.243895 + 0.969802i \(0.421575\pi\)
\(702\) 0 0
\(703\) −3.52983 −0.133130
\(704\) −7.92439 −0.298662
\(705\) 0 0
\(706\) −2.00735 −0.0755474
\(707\) −38.5628 −1.45031
\(708\) 0 0
\(709\) −21.6649 −0.813642 −0.406821 0.913508i \(-0.633363\pi\)
−0.406821 + 0.913508i \(0.633363\pi\)
\(710\) −0.343856 −0.0129047
\(711\) 0 0
\(712\) −1.62359 −0.0608467
\(713\) 55.9877 2.09676
\(714\) 0 0
\(715\) 4.77520 0.178582
\(716\) 3.25427 0.121618
\(717\) 0 0
\(718\) 0.614854 0.0229462
\(719\) −3.05414 −0.113900 −0.0569502 0.998377i \(-0.518138\pi\)
−0.0569502 + 0.998377i \(0.518138\pi\)
\(720\) 0 0
\(721\) −3.95140 −0.147158
\(722\) 0.0423262 0.00157522
\(723\) 0 0
\(724\) 13.5800 0.504698
\(725\) −10.5733 −0.392681
\(726\) 0 0
\(727\) −11.0808 −0.410964 −0.205482 0.978661i \(-0.565876\pi\)
−0.205482 + 0.978661i \(0.565876\pi\)
\(728\) 1.32209 0.0489999
\(729\) 0 0
\(730\) −0.410575 −0.0151961
\(731\) −14.4116 −0.533032
\(732\) 0 0
\(733\) −10.7441 −0.396843 −0.198421 0.980117i \(-0.563581\pi\)
−0.198421 + 0.980117i \(0.563581\pi\)
\(734\) −0.956571 −0.0353077
\(735\) 0 0
\(736\) −5.39682 −0.198929
\(737\) 10.0237 0.369227
\(738\) 0 0
\(739\) −25.1340 −0.924569 −0.462284 0.886732i \(-0.652970\pi\)
−0.462284 + 0.886732i \(0.652970\pi\)
\(740\) −4.73604 −0.174100
\(741\) 0 0
\(742\) 1.61274 0.0592054
\(743\) 25.0852 0.920285 0.460143 0.887845i \(-0.347798\pi\)
0.460143 + 0.887845i \(0.347798\pi\)
\(744\) 0 0
\(745\) 3.41950 0.125281
\(746\) −1.50287 −0.0550240
\(747\) 0 0
\(748\) −13.0040 −0.475474
\(749\) 9.91242 0.362192
\(750\) 0 0
\(751\) 40.8602 1.49101 0.745505 0.666500i \(-0.232209\pi\)
0.745505 + 0.666500i \(0.232209\pi\)
\(752\) −41.4037 −1.50984
\(753\) 0 0
\(754\) 0.305151 0.0111130
\(755\) 32.3699 1.17806
\(756\) 0 0
\(757\) −23.1061 −0.839807 −0.419903 0.907569i \(-0.637936\pi\)
−0.419903 + 0.907569i \(0.637936\pi\)
\(758\) −0.436743 −0.0158632
\(759\) 0 0
\(760\) −2.75221 −0.0998331
\(761\) 24.9673 0.905066 0.452533 0.891748i \(-0.350521\pi\)
0.452533 + 0.891748i \(0.350521\pi\)
\(762\) 0 0
\(763\) 37.8495 1.37024
\(764\) 42.1445 1.52474
\(765\) 0 0
\(766\) −1.59451 −0.0576119
\(767\) −3.33553 −0.120439
\(768\) 0 0
\(769\) −39.7456 −1.43326 −0.716632 0.697452i \(-0.754317\pi\)
−0.716632 + 0.697452i \(0.754317\pi\)
\(770\) −0.570642 −0.0205645
\(771\) 0 0
\(772\) 30.6415 1.10281
\(773\) −47.6555 −1.71405 −0.857025 0.515276i \(-0.827690\pi\)
−0.857025 + 0.515276i \(0.827690\pi\)
\(774\) 0 0
\(775\) 22.5913 0.811504
\(776\) 2.51010 0.0901074
\(777\) 0 0
\(778\) 1.84075 0.0659941
\(779\) −50.9883 −1.82685
\(780\) 0 0
\(781\) 2.13305 0.0763265
\(782\) −2.93497 −0.104954
\(783\) 0 0
\(784\) 22.0182 0.786366
\(785\) 48.9690 1.74778
\(786\) 0 0
\(787\) 25.6637 0.914811 0.457405 0.889258i \(-0.348779\pi\)
0.457405 + 0.889258i \(0.348779\pi\)
\(788\) 16.0135 0.570457
\(789\) 0 0
\(790\) 1.09940 0.0391151
\(791\) −49.3611 −1.75508
\(792\) 0 0
\(793\) 1.66374 0.0590812
\(794\) −1.31978 −0.0468374
\(795\) 0 0
\(796\) −37.8273 −1.34075
\(797\) −8.44244 −0.299047 −0.149523 0.988758i \(-0.547774\pi\)
−0.149523 + 0.988758i \(0.547774\pi\)
\(798\) 0 0
\(799\) −67.7284 −2.39606
\(800\) −2.17764 −0.0769913
\(801\) 0 0
\(802\) −0.318848 −0.0112589
\(803\) 2.54693 0.0898793
\(804\) 0 0
\(805\) 81.5257 2.87340
\(806\) −0.652000 −0.0229657
\(807\) 0 0
\(808\) −2.44550 −0.0860325
\(809\) −14.1868 −0.498780 −0.249390 0.968403i \(-0.580230\pi\)
−0.249390 + 0.968403i \(0.580230\pi\)
\(810\) 0 0
\(811\) −2.52616 −0.0887054 −0.0443527 0.999016i \(-0.514123\pi\)
−0.0443527 + 0.999016i \(0.514123\pi\)
\(812\) 23.0830 0.810054
\(813\) 0 0
\(814\) −0.0464125 −0.00162676
\(815\) −54.0510 −1.89332
\(816\) 0 0
\(817\) 9.45295 0.330717
\(818\) −0.890471 −0.0311346
\(819\) 0 0
\(820\) −68.4120 −2.38905
\(821\) −14.9783 −0.522746 −0.261373 0.965238i \(-0.584175\pi\)
−0.261373 + 0.965238i \(0.584175\pi\)
\(822\) 0 0
\(823\) 1.14435 0.0398894 0.0199447 0.999801i \(-0.493651\pi\)
0.0199447 + 0.999801i \(0.493651\pi\)
\(824\) −0.250582 −0.00872944
\(825\) 0 0
\(826\) 0.398599 0.0138690
\(827\) −40.5209 −1.40905 −0.704525 0.709679i \(-0.748840\pi\)
−0.704525 + 0.709679i \(0.748840\pi\)
\(828\) 0 0
\(829\) −41.9288 −1.45625 −0.728124 0.685446i \(-0.759607\pi\)
−0.728124 + 0.685446i \(0.759607\pi\)
\(830\) 0.0907564 0.00315020
\(831\) 0 0
\(832\) −13.1841 −0.457078
\(833\) 36.0176 1.24794
\(834\) 0 0
\(835\) −59.6351 −2.06376
\(836\) 8.52969 0.295005
\(837\) 0 0
\(838\) 0.527967 0.0182383
\(839\) 17.9705 0.620412 0.310206 0.950669i \(-0.399602\pi\)
0.310206 + 0.950669i \(0.399602\pi\)
\(840\) 0 0
\(841\) −18.3360 −0.632277
\(842\) −1.08633 −0.0374374
\(843\) 0 0
\(844\) 28.5325 0.982130
\(845\) −29.3673 −1.01027
\(846\) 0 0
\(847\) 3.53988 0.121632
\(848\) −32.2929 −1.10894
\(849\) 0 0
\(850\) −1.18427 −0.0406203
\(851\) 6.63081 0.227301
\(852\) 0 0
\(853\) −29.2979 −1.00314 −0.501571 0.865117i \(-0.667244\pi\)
−0.501571 + 0.865117i \(0.667244\pi\)
\(854\) −0.198819 −0.00680345
\(855\) 0 0
\(856\) 0.628606 0.0214853
\(857\) −13.4529 −0.459543 −0.229772 0.973245i \(-0.573798\pi\)
−0.229772 + 0.973245i \(0.573798\pi\)
\(858\) 0 0
\(859\) 11.4298 0.389981 0.194990 0.980805i \(-0.437532\pi\)
0.194990 + 0.980805i \(0.437532\pi\)
\(860\) 12.6832 0.432493
\(861\) 0 0
\(862\) 1.23912 0.0422045
\(863\) −22.5690 −0.768259 −0.384129 0.923279i \(-0.625498\pi\)
−0.384129 + 0.923279i \(0.625498\pi\)
\(864\) 0 0
\(865\) −24.6285 −0.837394
\(866\) −0.923301 −0.0313751
\(867\) 0 0
\(868\) −49.3202 −1.67404
\(869\) −6.81997 −0.231352
\(870\) 0 0
\(871\) 16.6768 0.565072
\(872\) 2.40027 0.0812833
\(873\) 0 0
\(874\) 1.92513 0.0651184
\(875\) −17.9040 −0.605265
\(876\) 0 0
\(877\) 42.1546 1.42346 0.711729 0.702454i \(-0.247912\pi\)
0.711729 + 0.702454i \(0.247912\pi\)
\(878\) −1.63619 −0.0552186
\(879\) 0 0
\(880\) 11.4263 0.385181
\(881\) −4.79100 −0.161413 −0.0807065 0.996738i \(-0.525718\pi\)
−0.0807065 + 0.996738i \(0.525718\pi\)
\(882\) 0 0
\(883\) 35.8055 1.20495 0.602476 0.798137i \(-0.294181\pi\)
0.602476 + 0.798137i \(0.294181\pi\)
\(884\) −21.6353 −0.727675
\(885\) 0 0
\(886\) −2.24008 −0.0752569
\(887\) −17.9056 −0.601210 −0.300605 0.953749i \(-0.597189\pi\)
−0.300605 + 0.953749i \(0.597189\pi\)
\(888\) 0 0
\(889\) −54.3344 −1.82232
\(890\) 1.16591 0.0390814
\(891\) 0 0
\(892\) 5.68295 0.190279
\(893\) 44.4249 1.48662
\(894\) 0 0
\(895\) −4.67751 −0.156352
\(896\) 6.33714 0.211709
\(897\) 0 0
\(898\) −0.358979 −0.0119793
\(899\) −22.7851 −0.759927
\(900\) 0 0
\(901\) −52.8249 −1.75985
\(902\) −0.670428 −0.0223228
\(903\) 0 0
\(904\) −3.13029 −0.104112
\(905\) −19.5192 −0.648841
\(906\) 0 0
\(907\) 16.6708 0.553544 0.276772 0.960936i \(-0.410735\pi\)
0.276772 + 0.960936i \(0.410735\pi\)
\(908\) −38.9052 −1.29111
\(909\) 0 0
\(910\) −0.949400 −0.0314723
\(911\) 36.4248 1.20681 0.603403 0.797436i \(-0.293811\pi\)
0.603403 + 0.797436i \(0.293811\pi\)
\(912\) 0 0
\(913\) −0.562991 −0.0186323
\(914\) 0.368277 0.0121815
\(915\) 0 0
\(916\) 23.3952 0.772998
\(917\) −60.6342 −2.00232
\(918\) 0 0
\(919\) 4.21597 0.139072 0.0695359 0.997579i \(-0.477848\pi\)
0.0695359 + 0.997579i \(0.477848\pi\)
\(920\) 5.17004 0.170451
\(921\) 0 0
\(922\) −0.444233 −0.0146300
\(923\) 3.54884 0.116812
\(924\) 0 0
\(925\) 2.67556 0.0879719
\(926\) −1.68273 −0.0552979
\(927\) 0 0
\(928\) 2.19633 0.0720979
\(929\) −28.4286 −0.932713 −0.466356 0.884597i \(-0.654434\pi\)
−0.466356 + 0.884597i \(0.654434\pi\)
\(930\) 0 0
\(931\) −23.6249 −0.774275
\(932\) −55.5131 −1.81839
\(933\) 0 0
\(934\) 0.642503 0.0210234
\(935\) 18.6913 0.611270
\(936\) 0 0
\(937\) −20.5654 −0.671843 −0.335921 0.941890i \(-0.609048\pi\)
−0.335921 + 0.941890i \(0.609048\pi\)
\(938\) −1.99290 −0.0650704
\(939\) 0 0
\(940\) 59.6057 1.94412
\(941\) 7.87253 0.256637 0.128318 0.991733i \(-0.459042\pi\)
0.128318 + 0.991733i \(0.459042\pi\)
\(942\) 0 0
\(943\) 95.7818 3.11908
\(944\) −7.98142 −0.259773
\(945\) 0 0
\(946\) 0.124294 0.00404113
\(947\) −51.6536 −1.67852 −0.839258 0.543734i \(-0.817010\pi\)
−0.839258 + 0.543734i \(0.817010\pi\)
\(948\) 0 0
\(949\) 4.23744 0.137553
\(950\) 0.776798 0.0252026
\(951\) 0 0
\(952\) 5.17498 0.167722
\(953\) 50.9942 1.65186 0.825932 0.563769i \(-0.190649\pi\)
0.825932 + 0.563769i \(0.190649\pi\)
\(954\) 0 0
\(955\) −60.5762 −1.96020
\(956\) 2.54736 0.0823875
\(957\) 0 0
\(958\) 0.340101 0.0109882
\(959\) 4.10375 0.132517
\(960\) 0 0
\(961\) 17.6838 0.570444
\(962\) −0.0772185 −0.00248962
\(963\) 0 0
\(964\) −29.9416 −0.964355
\(965\) −44.0424 −1.41777
\(966\) 0 0
\(967\) 31.7512 1.02105 0.510524 0.859863i \(-0.329451\pi\)
0.510524 + 0.859863i \(0.329451\pi\)
\(968\) 0.224485 0.00721522
\(969\) 0 0
\(970\) −1.80252 −0.0578754
\(971\) −27.2104 −0.873222 −0.436611 0.899650i \(-0.643821\pi\)
−0.436611 + 0.899650i \(0.643821\pi\)
\(972\) 0 0
\(973\) 27.1476 0.870311
\(974\) −0.322402 −0.0103304
\(975\) 0 0
\(976\) 3.98108 0.127431
\(977\) −49.0474 −1.56916 −0.784582 0.620025i \(-0.787123\pi\)
−0.784582 + 0.620025i \(0.787123\pi\)
\(978\) 0 0
\(979\) −7.23252 −0.231152
\(980\) −31.6980 −1.01255
\(981\) 0 0
\(982\) 0.324807 0.0103650
\(983\) −29.9573 −0.955490 −0.477745 0.878499i \(-0.658546\pi\)
−0.477745 + 0.878499i \(0.658546\pi\)
\(984\) 0 0
\(985\) −23.0169 −0.733380
\(986\) 1.19444 0.0380386
\(987\) 0 0
\(988\) 14.1912 0.451482
\(989\) −17.7574 −0.564653
\(990\) 0 0
\(991\) −45.8678 −1.45704 −0.728519 0.685026i \(-0.759791\pi\)
−0.728519 + 0.685026i \(0.759791\pi\)
\(992\) −4.69277 −0.148996
\(993\) 0 0
\(994\) −0.424091 −0.0134513
\(995\) 54.3709 1.72367
\(996\) 0 0
\(997\) −17.7103 −0.560892 −0.280446 0.959870i \(-0.590482\pi\)
−0.280446 + 0.959870i \(0.590482\pi\)
\(998\) 0.556452 0.0176142
\(999\) 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 \(a_p\))