Properties

Label 6039.2.a.j.1.5
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.5
Root \(-1.18140\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.18140 q^{2}\) \(-0.604292 q^{4}\) \(+2.90081 q^{5}\) \(-0.528840 q^{7}\) \(+3.07671 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.18140 q^{2}\) \(-0.604292 q^{4}\) \(+2.90081 q^{5}\) \(-0.528840 q^{7}\) \(+3.07671 q^{8}\) \(-3.42702 q^{10}\) \(+1.00000 q^{11}\) \(-0.150802 q^{13}\) \(+0.624772 q^{14}\) \(-2.42625 q^{16}\) \(-0.0673519 q^{17}\) \(-0.482246 q^{19}\) \(-1.75293 q^{20}\) \(-1.18140 q^{22}\) \(+4.10835 q^{23}\) \(+3.41469 q^{25}\) \(+0.178158 q^{26}\) \(+0.319574 q^{28}\) \(+5.83447 q^{29}\) \(-2.84419 q^{31}\) \(-3.28705 q^{32}\) \(+0.0795696 q^{34}\) \(-1.53406 q^{35}\) \(+6.02828 q^{37}\) \(+0.569726 q^{38}\) \(+8.92495 q^{40}\) \(-11.4101 q^{41}\) \(+11.3555 q^{43}\) \(-0.604292 q^{44}\) \(-4.85361 q^{46}\) \(+3.90970 q^{47}\) \(-6.72033 q^{49}\) \(-4.03411 q^{50}\) \(+0.0911284 q^{52}\) \(+0.588357 q^{53}\) \(+2.90081 q^{55}\) \(-1.62709 q^{56}\) \(-6.89285 q^{58}\) \(-11.9392 q^{59}\) \(+1.00000 q^{61}\) \(+3.36013 q^{62}\) \(+8.73582 q^{64}\) \(-0.437448 q^{65}\) \(+9.38126 q^{67}\) \(+0.0407002 q^{68}\) \(+1.81234 q^{70}\) \(-12.6773 q^{71}\) \(+13.0690 q^{73}\) \(-7.12182 q^{74}\) \(+0.291417 q^{76}\) \(-0.528840 q^{77}\) \(+9.65447 q^{79}\) \(-7.03808 q^{80}\) \(+13.4799 q^{82}\) \(+11.6417 q^{83}\) \(-0.195375 q^{85}\) \(-13.4154 q^{86}\) \(+3.07671 q^{88}\) \(+12.7098 q^{89}\) \(+0.0797502 q^{91}\) \(-2.48264 q^{92}\) \(-4.61892 q^{94}\) \(-1.39890 q^{95}\) \(-1.66875 q^{97}\) \(+7.93940 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18140 −0.835377 −0.417688 0.908590i \(-0.637160\pi\)
−0.417688 + 0.908590i \(0.637160\pi\)
\(3\) 0 0
\(4\) −0.604292 −0.302146
\(5\) 2.90081 1.29728 0.648640 0.761095i \(-0.275338\pi\)
0.648640 + 0.761095i \(0.275338\pi\)
\(6\) 0 0
\(7\) −0.528840 −0.199883 −0.0999414 0.994993i \(-0.531866\pi\)
−0.0999414 + 0.994993i \(0.531866\pi\)
\(8\) 3.07671 1.08778
\(9\) 0 0
\(10\) −3.42702 −1.08372
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −0.150802 −0.0418250 −0.0209125 0.999781i \(-0.506657\pi\)
−0.0209125 + 0.999781i \(0.506657\pi\)
\(14\) 0.624772 0.166977
\(15\) 0 0
\(16\) −2.42625 −0.606562
\(17\) −0.0673519 −0.0163352 −0.00816762 0.999967i \(-0.502600\pi\)
−0.00816762 + 0.999967i \(0.502600\pi\)
\(18\) 0 0
\(19\) −0.482246 −0.110635 −0.0553174 0.998469i \(-0.517617\pi\)
−0.0553174 + 0.998469i \(0.517617\pi\)
\(20\) −1.75293 −0.391968
\(21\) 0 0
\(22\) −1.18140 −0.251876
\(23\) 4.10835 0.856651 0.428325 0.903625i \(-0.359104\pi\)
0.428325 + 0.903625i \(0.359104\pi\)
\(24\) 0 0
\(25\) 3.41469 0.682937
\(26\) 0.178158 0.0349396
\(27\) 0 0
\(28\) 0.319574 0.0603937
\(29\) 5.83447 1.08343 0.541717 0.840561i \(-0.317774\pi\)
0.541717 + 0.840561i \(0.317774\pi\)
\(30\) 0 0
\(31\) −2.84419 −0.510832 −0.255416 0.966831i \(-0.582213\pi\)
−0.255416 + 0.966831i \(0.582213\pi\)
\(32\) −3.28705 −0.581074
\(33\) 0 0
\(34\) 0.0795696 0.0136461
\(35\) −1.53406 −0.259304
\(36\) 0 0
\(37\) 6.02828 0.991043 0.495522 0.868596i \(-0.334977\pi\)
0.495522 + 0.868596i \(0.334977\pi\)
\(38\) 0.569726 0.0924217
\(39\) 0 0
\(40\) 8.92495 1.41116
\(41\) −11.4101 −1.78196 −0.890982 0.454038i \(-0.849983\pi\)
−0.890982 + 0.454038i \(0.849983\pi\)
\(42\) 0 0
\(43\) 11.3555 1.73170 0.865849 0.500305i \(-0.166779\pi\)
0.865849 + 0.500305i \(0.166779\pi\)
\(44\) −0.604292 −0.0911004
\(45\) 0 0
\(46\) −4.85361 −0.715626
\(47\) 3.90970 0.570288 0.285144 0.958485i \(-0.407959\pi\)
0.285144 + 0.958485i \(0.407959\pi\)
\(48\) 0 0
\(49\) −6.72033 −0.960047
\(50\) −4.03411 −0.570510
\(51\) 0 0
\(52\) 0.0911284 0.0126372
\(53\) 0.588357 0.0808171 0.0404085 0.999183i \(-0.487134\pi\)
0.0404085 + 0.999183i \(0.487134\pi\)
\(54\) 0 0
\(55\) 2.90081 0.391145
\(56\) −1.62709 −0.217429
\(57\) 0 0
\(58\) −6.89285 −0.905076
\(59\) −11.9392 −1.55435 −0.777176 0.629284i \(-0.783348\pi\)
−0.777176 + 0.629284i \(0.783348\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 3.36013 0.426738
\(63\) 0 0
\(64\) 8.73582 1.09198
\(65\) −0.437448 −0.0542587
\(66\) 0 0
\(67\) 9.38126 1.14610 0.573052 0.819519i \(-0.305759\pi\)
0.573052 + 0.819519i \(0.305759\pi\)
\(68\) 0.0407002 0.00493562
\(69\) 0 0
\(70\) 1.81234 0.216617
\(71\) −12.6773 −1.50452 −0.752258 0.658869i \(-0.771035\pi\)
−0.752258 + 0.658869i \(0.771035\pi\)
\(72\) 0 0
\(73\) 13.0690 1.52961 0.764806 0.644261i \(-0.222835\pi\)
0.764806 + 0.644261i \(0.222835\pi\)
\(74\) −7.12182 −0.827894
\(75\) 0 0
\(76\) 0.291417 0.0334278
\(77\) −0.528840 −0.0602669
\(78\) 0 0
\(79\) 9.65447 1.08621 0.543107 0.839664i \(-0.317248\pi\)
0.543107 + 0.839664i \(0.317248\pi\)
\(80\) −7.03808 −0.786881
\(81\) 0 0
\(82\) 13.4799 1.48861
\(83\) 11.6417 1.27784 0.638919 0.769274i \(-0.279382\pi\)
0.638919 + 0.769274i \(0.279382\pi\)
\(84\) 0 0
\(85\) −0.195375 −0.0211914
\(86\) −13.4154 −1.44662
\(87\) 0 0
\(88\) 3.07671 0.327979
\(89\) 12.7098 1.34724 0.673620 0.739078i \(-0.264738\pi\)
0.673620 + 0.739078i \(0.264738\pi\)
\(90\) 0 0
\(91\) 0.0797502 0.00836009
\(92\) −2.48264 −0.258833
\(93\) 0 0
\(94\) −4.61892 −0.476406
\(95\) −1.39890 −0.143524
\(96\) 0 0
\(97\) −1.66875 −0.169436 −0.0847178 0.996405i \(-0.526999\pi\)
−0.0847178 + 0.996405i \(0.526999\pi\)
\(98\) 7.93940 0.802001
\(99\) 0 0
\(100\) −2.06347 −0.206347
\(101\) −7.21215 −0.717636 −0.358818 0.933408i \(-0.616820\pi\)
−0.358818 + 0.933408i \(0.616820\pi\)
\(102\) 0 0
\(103\) 10.7724 1.06143 0.530717 0.847549i \(-0.321923\pi\)
0.530717 + 0.847549i \(0.321923\pi\)
\(104\) −0.463975 −0.0454965
\(105\) 0 0
\(106\) −0.695086 −0.0675127
\(107\) 2.91453 0.281759 0.140879 0.990027i \(-0.455007\pi\)
0.140879 + 0.990027i \(0.455007\pi\)
\(108\) 0 0
\(109\) −15.6562 −1.49960 −0.749798 0.661667i \(-0.769849\pi\)
−0.749798 + 0.661667i \(0.769849\pi\)
\(110\) −3.42702 −0.326753
\(111\) 0 0
\(112\) 1.28310 0.121241
\(113\) 17.6863 1.66379 0.831895 0.554933i \(-0.187256\pi\)
0.831895 + 0.554933i \(0.187256\pi\)
\(114\) 0 0
\(115\) 11.9175 1.11132
\(116\) −3.52572 −0.327355
\(117\) 0 0
\(118\) 14.1050 1.29847
\(119\) 0.0356184 0.00326513
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −1.18140 −0.106959
\(123\) 0 0
\(124\) 1.71872 0.154346
\(125\) −4.59869 −0.411319
\(126\) 0 0
\(127\) −20.8464 −1.84981 −0.924907 0.380192i \(-0.875858\pi\)
−0.924907 + 0.380192i \(0.875858\pi\)
\(128\) −3.74641 −0.331139
\(129\) 0 0
\(130\) 0.516801 0.0453265
\(131\) 8.61884 0.753031 0.376516 0.926410i \(-0.377122\pi\)
0.376516 + 0.926410i \(0.377122\pi\)
\(132\) 0 0
\(133\) 0.255031 0.0221140
\(134\) −11.0830 −0.957428
\(135\) 0 0
\(136\) −0.207222 −0.0177692
\(137\) −3.31289 −0.283039 −0.141520 0.989935i \(-0.545199\pi\)
−0.141520 + 0.989935i \(0.545199\pi\)
\(138\) 0 0
\(139\) 16.9686 1.43926 0.719628 0.694360i \(-0.244312\pi\)
0.719628 + 0.694360i \(0.244312\pi\)
\(140\) 0.927022 0.0783476
\(141\) 0 0
\(142\) 14.9769 1.25684
\(143\) −0.150802 −0.0126107
\(144\) 0 0
\(145\) 16.9247 1.40552
\(146\) −15.4397 −1.27780
\(147\) 0 0
\(148\) −3.64284 −0.299440
\(149\) 10.5728 0.866156 0.433078 0.901356i \(-0.357427\pi\)
0.433078 + 0.901356i \(0.357427\pi\)
\(150\) 0 0
\(151\) −11.7619 −0.957168 −0.478584 0.878042i \(-0.658850\pi\)
−0.478584 + 0.878042i \(0.658850\pi\)
\(152\) −1.48373 −0.120347
\(153\) 0 0
\(154\) 0.624772 0.0503456
\(155\) −8.25046 −0.662693
\(156\) 0 0
\(157\) 14.7885 1.18025 0.590126 0.807311i \(-0.299078\pi\)
0.590126 + 0.807311i \(0.299078\pi\)
\(158\) −11.4058 −0.907397
\(159\) 0 0
\(160\) −9.53511 −0.753817
\(161\) −2.17266 −0.171230
\(162\) 0 0
\(163\) −20.8054 −1.62961 −0.814803 0.579739i \(-0.803155\pi\)
−0.814803 + 0.579739i \(0.803155\pi\)
\(164\) 6.89505 0.538413
\(165\) 0 0
\(166\) −13.7535 −1.06748
\(167\) 13.2699 1.02686 0.513430 0.858132i \(-0.328375\pi\)
0.513430 + 0.858132i \(0.328375\pi\)
\(168\) 0 0
\(169\) −12.9773 −0.998251
\(170\) 0.230816 0.0177028
\(171\) 0 0
\(172\) −6.86204 −0.523226
\(173\) −12.4101 −0.943521 −0.471760 0.881727i \(-0.656381\pi\)
−0.471760 + 0.881727i \(0.656381\pi\)
\(174\) 0 0
\(175\) −1.80582 −0.136507
\(176\) −2.42625 −0.182885
\(177\) 0 0
\(178\) −15.0154 −1.12545
\(179\) −8.62506 −0.644668 −0.322334 0.946626i \(-0.604467\pi\)
−0.322334 + 0.946626i \(0.604467\pi\)
\(180\) 0 0
\(181\) −1.29192 −0.0960277 −0.0480139 0.998847i \(-0.515289\pi\)
−0.0480139 + 0.998847i \(0.515289\pi\)
\(182\) −0.0942169 −0.00698382
\(183\) 0 0
\(184\) 12.6402 0.931849
\(185\) 17.4869 1.28566
\(186\) 0 0
\(187\) −0.0673519 −0.00492526
\(188\) −2.36260 −0.172310
\(189\) 0 0
\(190\) 1.65266 0.119897
\(191\) −9.07558 −0.656686 −0.328343 0.944559i \(-0.606490\pi\)
−0.328343 + 0.944559i \(0.606490\pi\)
\(192\) 0 0
\(193\) 21.0767 1.51713 0.758566 0.651596i \(-0.225900\pi\)
0.758566 + 0.651596i \(0.225900\pi\)
\(194\) 1.97146 0.141543
\(195\) 0 0
\(196\) 4.06104 0.290074
\(197\) −6.18993 −0.441014 −0.220507 0.975385i \(-0.570771\pi\)
−0.220507 + 0.975385i \(0.570771\pi\)
\(198\) 0 0
\(199\) −20.3389 −1.44179 −0.720894 0.693045i \(-0.756269\pi\)
−0.720894 + 0.693045i \(0.756269\pi\)
\(200\) 10.5060 0.742887
\(201\) 0 0
\(202\) 8.52045 0.599496
\(203\) −3.08550 −0.216560
\(204\) 0 0
\(205\) −33.0986 −2.31171
\(206\) −12.7265 −0.886697
\(207\) 0 0
\(208\) 0.365883 0.0253694
\(209\) −0.482246 −0.0333576
\(210\) 0 0
\(211\) 28.7585 1.97981 0.989907 0.141717i \(-0.0452623\pi\)
0.989907 + 0.141717i \(0.0452623\pi\)
\(212\) −0.355539 −0.0244185
\(213\) 0 0
\(214\) −3.44323 −0.235374
\(215\) 32.9401 2.24650
\(216\) 0 0
\(217\) 1.50412 0.102107
\(218\) 18.4963 1.25273
\(219\) 0 0
\(220\) −1.75293 −0.118183
\(221\) 0.0101568 0.000683220 0
\(222\) 0 0
\(223\) −21.4498 −1.43639 −0.718194 0.695843i \(-0.755031\pi\)
−0.718194 + 0.695843i \(0.755031\pi\)
\(224\) 1.73833 0.116147
\(225\) 0 0
\(226\) −20.8946 −1.38989
\(227\) −20.1374 −1.33657 −0.668283 0.743908i \(-0.732970\pi\)
−0.668283 + 0.743908i \(0.732970\pi\)
\(228\) 0 0
\(229\) 23.4322 1.54844 0.774221 0.632915i \(-0.218142\pi\)
0.774221 + 0.632915i \(0.218142\pi\)
\(230\) −14.0794 −0.928368
\(231\) 0 0
\(232\) 17.9510 1.17854
\(233\) 1.49700 0.0980719 0.0490360 0.998797i \(-0.484385\pi\)
0.0490360 + 0.998797i \(0.484385\pi\)
\(234\) 0 0
\(235\) 11.3413 0.739824
\(236\) 7.21476 0.469641
\(237\) 0 0
\(238\) −0.0420796 −0.00272761
\(239\) −11.3579 −0.734680 −0.367340 0.930087i \(-0.619731\pi\)
−0.367340 + 0.930087i \(0.619731\pi\)
\(240\) 0 0
\(241\) 19.2590 1.24058 0.620290 0.784373i \(-0.287015\pi\)
0.620290 + 0.784373i \(0.287015\pi\)
\(242\) −1.18140 −0.0759433
\(243\) 0 0
\(244\) −0.604292 −0.0386858
\(245\) −19.4944 −1.24545
\(246\) 0 0
\(247\) 0.0727237 0.00462730
\(248\) −8.75077 −0.555675
\(249\) 0 0
\(250\) 5.43290 0.343607
\(251\) 9.41617 0.594344 0.297172 0.954824i \(-0.403957\pi\)
0.297172 + 0.954824i \(0.403957\pi\)
\(252\) 0 0
\(253\) 4.10835 0.258290
\(254\) 24.6279 1.54529
\(255\) 0 0
\(256\) −13.0456 −0.815353
\(257\) −15.6633 −0.977049 −0.488524 0.872550i \(-0.662465\pi\)
−0.488524 + 0.872550i \(0.662465\pi\)
\(258\) 0 0
\(259\) −3.18800 −0.198092
\(260\) 0.264346 0.0163940
\(261\) 0 0
\(262\) −10.1823 −0.629065
\(263\) 7.59913 0.468582 0.234291 0.972166i \(-0.424723\pi\)
0.234291 + 0.972166i \(0.424723\pi\)
\(264\) 0 0
\(265\) 1.70671 0.104842
\(266\) −0.301294 −0.0184735
\(267\) 0 0
\(268\) −5.66902 −0.346290
\(269\) 24.2461 1.47831 0.739154 0.673536i \(-0.235226\pi\)
0.739154 + 0.673536i \(0.235226\pi\)
\(270\) 0 0
\(271\) 3.99382 0.242607 0.121304 0.992615i \(-0.461293\pi\)
0.121304 + 0.992615i \(0.461293\pi\)
\(272\) 0.163412 0.00990833
\(273\) 0 0
\(274\) 3.91385 0.236445
\(275\) 3.41469 0.205913
\(276\) 0 0
\(277\) 7.93878 0.476995 0.238497 0.971143i \(-0.423345\pi\)
0.238497 + 0.971143i \(0.423345\pi\)
\(278\) −20.0467 −1.20232
\(279\) 0 0
\(280\) −4.71987 −0.282066
\(281\) −3.12368 −0.186343 −0.0931717 0.995650i \(-0.529701\pi\)
−0.0931717 + 0.995650i \(0.529701\pi\)
\(282\) 0 0
\(283\) 5.18624 0.308290 0.154145 0.988048i \(-0.450738\pi\)
0.154145 + 0.988048i \(0.450738\pi\)
\(284\) 7.66077 0.454583
\(285\) 0 0
\(286\) 0.178158 0.0105347
\(287\) 6.03414 0.356184
\(288\) 0 0
\(289\) −16.9955 −0.999733
\(290\) −19.9948 −1.17414
\(291\) 0 0
\(292\) −7.89749 −0.462166
\(293\) 22.5194 1.31560 0.657799 0.753194i \(-0.271488\pi\)
0.657799 + 0.753194i \(0.271488\pi\)
\(294\) 0 0
\(295\) −34.6333 −2.01643
\(296\) 18.5473 1.07804
\(297\) 0 0
\(298\) −12.4907 −0.723567
\(299\) −0.619548 −0.0358294
\(300\) 0 0
\(301\) −6.00525 −0.346137
\(302\) 13.8955 0.799596
\(303\) 0 0
\(304\) 1.17005 0.0671069
\(305\) 2.90081 0.166100
\(306\) 0 0
\(307\) −6.51791 −0.371997 −0.185998 0.982550i \(-0.559552\pi\)
−0.185998 + 0.982550i \(0.559552\pi\)
\(308\) 0.319574 0.0182094
\(309\) 0 0
\(310\) 9.74711 0.553598
\(311\) −17.4530 −0.989667 −0.494834 0.868988i \(-0.664771\pi\)
−0.494834 + 0.868988i \(0.664771\pi\)
\(312\) 0 0
\(313\) 20.6548 1.16748 0.583739 0.811941i \(-0.301589\pi\)
0.583739 + 0.811941i \(0.301589\pi\)
\(314\) −17.4712 −0.985955
\(315\) 0 0
\(316\) −5.83412 −0.328195
\(317\) 13.7550 0.772558 0.386279 0.922382i \(-0.373760\pi\)
0.386279 + 0.922382i \(0.373760\pi\)
\(318\) 0 0
\(319\) 5.83447 0.326668
\(320\) 25.3409 1.41660
\(321\) 0 0
\(322\) 2.56678 0.143041
\(323\) 0.0324802 0.00180724
\(324\) 0 0
\(325\) −0.514942 −0.0285638
\(326\) 24.5795 1.36133
\(327\) 0 0
\(328\) −35.1057 −1.93839
\(329\) −2.06761 −0.113991
\(330\) 0 0
\(331\) 26.0426 1.43143 0.715716 0.698392i \(-0.246101\pi\)
0.715716 + 0.698392i \(0.246101\pi\)
\(332\) −7.03495 −0.386093
\(333\) 0 0
\(334\) −15.6771 −0.857814
\(335\) 27.2132 1.48682
\(336\) 0 0
\(337\) 32.9988 1.79756 0.898781 0.438399i \(-0.144454\pi\)
0.898781 + 0.438399i \(0.144454\pi\)
\(338\) 15.3313 0.833915
\(339\) 0 0
\(340\) 0.118063 0.00640289
\(341\) −2.84419 −0.154022
\(342\) 0 0
\(343\) 7.25586 0.391780
\(344\) 34.9376 1.88371
\(345\) 0 0
\(346\) 14.6613 0.788195
\(347\) −26.3834 −1.41633 −0.708166 0.706045i \(-0.750477\pi\)
−0.708166 + 0.706045i \(0.750477\pi\)
\(348\) 0 0
\(349\) −14.5133 −0.776881 −0.388441 0.921474i \(-0.626986\pi\)
−0.388441 + 0.921474i \(0.626986\pi\)
\(350\) 2.13340 0.114035
\(351\) 0 0
\(352\) −3.28705 −0.175201
\(353\) −34.6089 −1.84205 −0.921024 0.389507i \(-0.872645\pi\)
−0.921024 + 0.389507i \(0.872645\pi\)
\(354\) 0 0
\(355\) −36.7743 −1.95178
\(356\) −7.68045 −0.407063
\(357\) 0 0
\(358\) 10.1897 0.538540
\(359\) −19.3153 −1.01942 −0.509712 0.860345i \(-0.670248\pi\)
−0.509712 + 0.860345i \(0.670248\pi\)
\(360\) 0 0
\(361\) −18.7674 −0.987760
\(362\) 1.52628 0.0802193
\(363\) 0 0
\(364\) −0.0481924 −0.00252597
\(365\) 37.9107 1.98434
\(366\) 0 0
\(367\) 14.0802 0.734979 0.367489 0.930028i \(-0.380217\pi\)
0.367489 + 0.930028i \(0.380217\pi\)
\(368\) −9.96788 −0.519612
\(369\) 0 0
\(370\) −20.6590 −1.07401
\(371\) −0.311147 −0.0161539
\(372\) 0 0
\(373\) 26.0491 1.34877 0.674386 0.738379i \(-0.264409\pi\)
0.674386 + 0.738379i \(0.264409\pi\)
\(374\) 0.0795696 0.00411445
\(375\) 0 0
\(376\) 12.0290 0.620349
\(377\) −0.879850 −0.0453146
\(378\) 0 0
\(379\) 14.8469 0.762635 0.381317 0.924444i \(-0.375470\pi\)
0.381317 + 0.924444i \(0.375470\pi\)
\(380\) 0.845345 0.0433653
\(381\) 0 0
\(382\) 10.7219 0.548580
\(383\) −11.6961 −0.597643 −0.298821 0.954309i \(-0.596593\pi\)
−0.298821 + 0.954309i \(0.596593\pi\)
\(384\) 0 0
\(385\) −1.53406 −0.0781831
\(386\) −24.9000 −1.26738
\(387\) 0 0
\(388\) 1.00841 0.0511943
\(389\) 14.7146 0.746059 0.373029 0.927820i \(-0.378319\pi\)
0.373029 + 0.927820i \(0.378319\pi\)
\(390\) 0 0
\(391\) −0.276705 −0.0139936
\(392\) −20.6765 −1.04432
\(393\) 0 0
\(394\) 7.31279 0.368413
\(395\) 28.0058 1.40912
\(396\) 0 0
\(397\) 29.4067 1.47588 0.737940 0.674867i \(-0.235799\pi\)
0.737940 + 0.674867i \(0.235799\pi\)
\(398\) 24.0284 1.20444
\(399\) 0 0
\(400\) −8.28488 −0.414244
\(401\) 17.6578 0.881786 0.440893 0.897560i \(-0.354662\pi\)
0.440893 + 0.897560i \(0.354662\pi\)
\(402\) 0 0
\(403\) 0.428910 0.0213656
\(404\) 4.35824 0.216831
\(405\) 0 0
\(406\) 3.64522 0.180909
\(407\) 6.02828 0.298811
\(408\) 0 0
\(409\) −11.0602 −0.546893 −0.273447 0.961887i \(-0.588164\pi\)
−0.273447 + 0.961887i \(0.588164\pi\)
\(410\) 39.1027 1.93115
\(411\) 0 0
\(412\) −6.50965 −0.320708
\(413\) 6.31393 0.310688
\(414\) 0 0
\(415\) 33.7702 1.65771
\(416\) 0.495694 0.0243034
\(417\) 0 0
\(418\) 0.569726 0.0278662
\(419\) −9.64189 −0.471037 −0.235519 0.971870i \(-0.575679\pi\)
−0.235519 + 0.971870i \(0.575679\pi\)
\(420\) 0 0
\(421\) 31.6981 1.54487 0.772435 0.635094i \(-0.219039\pi\)
0.772435 + 0.635094i \(0.219039\pi\)
\(422\) −33.9753 −1.65389
\(423\) 0 0
\(424\) 1.81021 0.0879114
\(425\) −0.229986 −0.0111559
\(426\) 0 0
\(427\) −0.528840 −0.0255924
\(428\) −1.76123 −0.0851322
\(429\) 0 0
\(430\) −38.9155 −1.87667
\(431\) 19.2048 0.925061 0.462530 0.886603i \(-0.346942\pi\)
0.462530 + 0.886603i \(0.346942\pi\)
\(432\) 0 0
\(433\) −13.3020 −0.639254 −0.319627 0.947544i \(-0.603558\pi\)
−0.319627 + 0.947544i \(0.603558\pi\)
\(434\) −1.77697 −0.0852975
\(435\) 0 0
\(436\) 9.46094 0.453097
\(437\) −1.98124 −0.0947753
\(438\) 0 0
\(439\) 37.7505 1.80174 0.900868 0.434094i \(-0.142931\pi\)
0.900868 + 0.434094i \(0.142931\pi\)
\(440\) 8.92495 0.425480
\(441\) 0 0
\(442\) −0.0119993 −0.000570746 0
\(443\) −12.5575 −0.596623 −0.298311 0.954469i \(-0.596423\pi\)
−0.298311 + 0.954469i \(0.596423\pi\)
\(444\) 0 0
\(445\) 36.8688 1.74775
\(446\) 25.3409 1.19992
\(447\) 0 0
\(448\) −4.61985 −0.218268
\(449\) 27.8448 1.31408 0.657040 0.753856i \(-0.271808\pi\)
0.657040 + 0.753856i \(0.271808\pi\)
\(450\) 0 0
\(451\) −11.4101 −0.537282
\(452\) −10.6877 −0.502707
\(453\) 0 0
\(454\) 23.7903 1.11654
\(455\) 0.231340 0.0108454
\(456\) 0 0
\(457\) −15.9549 −0.746338 −0.373169 0.927763i \(-0.621729\pi\)
−0.373169 + 0.927763i \(0.621729\pi\)
\(458\) −27.6828 −1.29353
\(459\) 0 0
\(460\) −7.20167 −0.335780
\(461\) 21.5790 1.00503 0.502517 0.864568i \(-0.332408\pi\)
0.502517 + 0.864568i \(0.332408\pi\)
\(462\) 0 0
\(463\) −1.41157 −0.0656011 −0.0328006 0.999462i \(-0.510443\pi\)
−0.0328006 + 0.999462i \(0.510443\pi\)
\(464\) −14.1559 −0.657170
\(465\) 0 0
\(466\) −1.76856 −0.0819270
\(467\) 1.05698 0.0489112 0.0244556 0.999701i \(-0.492215\pi\)
0.0244556 + 0.999701i \(0.492215\pi\)
\(468\) 0 0
\(469\) −4.96119 −0.229086
\(470\) −13.3986 −0.618032
\(471\) 0 0
\(472\) −36.7335 −1.69080
\(473\) 11.3555 0.522127
\(474\) 0 0
\(475\) −1.64672 −0.0755566
\(476\) −0.0215239 −0.000986546 0
\(477\) 0 0
\(478\) 13.4182 0.613734
\(479\) 24.6689 1.12715 0.563575 0.826065i \(-0.309426\pi\)
0.563575 + 0.826065i \(0.309426\pi\)
\(480\) 0 0
\(481\) −0.909077 −0.0414503
\(482\) −22.7526 −1.03635
\(483\) 0 0
\(484\) −0.604292 −0.0274678
\(485\) −4.84072 −0.219806
\(486\) 0 0
\(487\) 8.86822 0.401857 0.200929 0.979606i \(-0.435604\pi\)
0.200929 + 0.979606i \(0.435604\pi\)
\(488\) 3.07671 0.139276
\(489\) 0 0
\(490\) 23.0307 1.04042
\(491\) −14.8167 −0.668670 −0.334335 0.942454i \(-0.608512\pi\)
−0.334335 + 0.942454i \(0.608512\pi\)
\(492\) 0 0
\(493\) −0.392963 −0.0176981
\(494\) −0.0859158 −0.00386553
\(495\) 0 0
\(496\) 6.90072 0.309852
\(497\) 6.70425 0.300727
\(498\) 0 0
\(499\) −1.89914 −0.0850174 −0.0425087 0.999096i \(-0.513535\pi\)
−0.0425087 + 0.999096i \(0.513535\pi\)
\(500\) 2.77895 0.124278
\(501\) 0 0
\(502\) −11.1243 −0.496501
\(503\) −22.0264 −0.982109 −0.491055 0.871129i \(-0.663388\pi\)
−0.491055 + 0.871129i \(0.663388\pi\)
\(504\) 0 0
\(505\) −20.9211 −0.930976
\(506\) −4.85361 −0.215769
\(507\) 0 0
\(508\) 12.5973 0.558914
\(509\) 32.0102 1.41882 0.709412 0.704794i \(-0.248960\pi\)
0.709412 + 0.704794i \(0.248960\pi\)
\(510\) 0 0
\(511\) −6.91142 −0.305743
\(512\) 22.9049 1.01227
\(513\) 0 0
\(514\) 18.5046 0.816204
\(515\) 31.2486 1.37698
\(516\) 0 0
\(517\) 3.90970 0.171948
\(518\) 3.76630 0.165482
\(519\) 0 0
\(520\) −1.34590 −0.0590217
\(521\) −28.1925 −1.23514 −0.617569 0.786517i \(-0.711882\pi\)
−0.617569 + 0.786517i \(0.711882\pi\)
\(522\) 0 0
\(523\) −8.41440 −0.367936 −0.183968 0.982932i \(-0.558894\pi\)
−0.183968 + 0.982932i \(0.558894\pi\)
\(524\) −5.20829 −0.227525
\(525\) 0 0
\(526\) −8.97762 −0.391443
\(527\) 0.191562 0.00834457
\(528\) 0 0
\(529\) −6.12144 −0.266150
\(530\) −2.01631 −0.0875829
\(531\) 0 0
\(532\) −0.154113 −0.00668165
\(533\) 1.72067 0.0745306
\(534\) 0 0
\(535\) 8.45450 0.365520
\(536\) 28.8634 1.24671
\(537\) 0 0
\(538\) −28.6443 −1.23494
\(539\) −6.72033 −0.289465
\(540\) 0 0
\(541\) 27.0427 1.16266 0.581329 0.813669i \(-0.302533\pi\)
0.581329 + 0.813669i \(0.302533\pi\)
\(542\) −4.71830 −0.202668
\(543\) 0 0
\(544\) 0.221389 0.00949199
\(545\) −45.4158 −1.94540
\(546\) 0 0
\(547\) 16.9856 0.726253 0.363126 0.931740i \(-0.381709\pi\)
0.363126 + 0.931740i \(0.381709\pi\)
\(548\) 2.00195 0.0855192
\(549\) 0 0
\(550\) −4.03411 −0.172015
\(551\) −2.81365 −0.119865
\(552\) 0 0
\(553\) −5.10567 −0.217115
\(554\) −9.37888 −0.398470
\(555\) 0 0
\(556\) −10.2540 −0.434865
\(557\) 29.1185 1.23379 0.616896 0.787045i \(-0.288390\pi\)
0.616896 + 0.787045i \(0.288390\pi\)
\(558\) 0 0
\(559\) −1.71243 −0.0724282
\(560\) 3.72202 0.157284
\(561\) 0 0
\(562\) 3.69032 0.155667
\(563\) −33.1163 −1.39569 −0.697843 0.716250i \(-0.745857\pi\)
−0.697843 + 0.716250i \(0.745857\pi\)
\(564\) 0 0
\(565\) 51.3046 2.15840
\(566\) −6.12703 −0.257538
\(567\) 0 0
\(568\) −39.0043 −1.63659
\(569\) 9.13425 0.382928 0.191464 0.981500i \(-0.438677\pi\)
0.191464 + 0.981500i \(0.438677\pi\)
\(570\) 0 0
\(571\) 31.6452 1.32431 0.662156 0.749366i \(-0.269642\pi\)
0.662156 + 0.749366i \(0.269642\pi\)
\(572\) 0.0911284 0.00381027
\(573\) 0 0
\(574\) −7.12874 −0.297548
\(575\) 14.0287 0.585039
\(576\) 0 0
\(577\) −5.78481 −0.240825 −0.120412 0.992724i \(-0.538422\pi\)
−0.120412 + 0.992724i \(0.538422\pi\)
\(578\) 20.0785 0.835154
\(579\) 0 0
\(580\) −10.2274 −0.424671
\(581\) −6.15657 −0.255418
\(582\) 0 0
\(583\) 0.588357 0.0243673
\(584\) 40.2096 1.66388
\(585\) 0 0
\(586\) −26.6044 −1.09902
\(587\) 8.04522 0.332062 0.166031 0.986121i \(-0.446905\pi\)
0.166031 + 0.986121i \(0.446905\pi\)
\(588\) 0 0
\(589\) 1.37160 0.0565158
\(590\) 40.9158 1.68448
\(591\) 0 0
\(592\) −14.6261 −0.601129
\(593\) 7.77065 0.319103 0.159551 0.987190i \(-0.448995\pi\)
0.159551 + 0.987190i \(0.448995\pi\)
\(594\) 0 0
\(595\) 0.103322 0.00423579
\(596\) −6.38905 −0.261706
\(597\) 0 0
\(598\) 0.731935 0.0299310
\(599\) −5.13824 −0.209943 −0.104971 0.994475i \(-0.533475\pi\)
−0.104971 + 0.994475i \(0.533475\pi\)
\(600\) 0 0
\(601\) −18.9195 −0.771744 −0.385872 0.922552i \(-0.626099\pi\)
−0.385872 + 0.922552i \(0.626099\pi\)
\(602\) 7.09461 0.289155
\(603\) 0 0
\(604\) 7.10760 0.289204
\(605\) 2.90081 0.117935
\(606\) 0 0
\(607\) 31.8620 1.29324 0.646620 0.762812i \(-0.276182\pi\)
0.646620 + 0.762812i \(0.276182\pi\)
\(608\) 1.58517 0.0642870
\(609\) 0 0
\(610\) −3.42702 −0.138756
\(611\) −0.589591 −0.0238523
\(612\) 0 0
\(613\) −14.7696 −0.596539 −0.298269 0.954482i \(-0.596409\pi\)
−0.298269 + 0.954482i \(0.596409\pi\)
\(614\) 7.70027 0.310758
\(615\) 0 0
\(616\) −1.62709 −0.0655573
\(617\) 45.2708 1.82253 0.911266 0.411817i \(-0.135106\pi\)
0.911266 + 0.411817i \(0.135106\pi\)
\(618\) 0 0
\(619\) 39.0064 1.56780 0.783900 0.620887i \(-0.213227\pi\)
0.783900 + 0.620887i \(0.213227\pi\)
\(620\) 4.98569 0.200230
\(621\) 0 0
\(622\) 20.6190 0.826745
\(623\) −6.72147 −0.269290
\(624\) 0 0
\(625\) −30.4133 −1.21653
\(626\) −24.4016 −0.975284
\(627\) 0 0
\(628\) −8.93657 −0.356608
\(629\) −0.406016 −0.0161889
\(630\) 0 0
\(631\) −37.8923 −1.50847 −0.754235 0.656605i \(-0.771992\pi\)
−0.754235 + 0.656605i \(0.771992\pi\)
\(632\) 29.7040 1.18156
\(633\) 0 0
\(634\) −16.2502 −0.645377
\(635\) −60.4713 −2.39973
\(636\) 0 0
\(637\) 1.01344 0.0401539
\(638\) −6.89285 −0.272891
\(639\) 0 0
\(640\) −10.8676 −0.429580
\(641\) 15.2355 0.601767 0.300883 0.953661i \(-0.402719\pi\)
0.300883 + 0.953661i \(0.402719\pi\)
\(642\) 0 0
\(643\) 0.685252 0.0270237 0.0135118 0.999909i \(-0.495699\pi\)
0.0135118 + 0.999909i \(0.495699\pi\)
\(644\) 1.31292 0.0517363
\(645\) 0 0
\(646\) −0.0383721 −0.00150973
\(647\) −32.3211 −1.27067 −0.635337 0.772235i \(-0.719139\pi\)
−0.635337 + 0.772235i \(0.719139\pi\)
\(648\) 0 0
\(649\) −11.9392 −0.468655
\(650\) 0.608353 0.0238616
\(651\) 0 0
\(652\) 12.5725 0.492378
\(653\) 19.3514 0.757281 0.378640 0.925544i \(-0.376392\pi\)
0.378640 + 0.925544i \(0.376392\pi\)
\(654\) 0 0
\(655\) 25.0016 0.976893
\(656\) 27.6838 1.08087
\(657\) 0 0
\(658\) 2.44267 0.0952253
\(659\) −35.8402 −1.39613 −0.698067 0.716032i \(-0.745956\pi\)
−0.698067 + 0.716032i \(0.745956\pi\)
\(660\) 0 0
\(661\) 22.2012 0.863526 0.431763 0.901987i \(-0.357892\pi\)
0.431763 + 0.901987i \(0.357892\pi\)
\(662\) −30.7668 −1.19578
\(663\) 0 0
\(664\) 35.8180 1.39001
\(665\) 0.739796 0.0286880
\(666\) 0 0
\(667\) 23.9701 0.928125
\(668\) −8.01892 −0.310261
\(669\) 0 0
\(670\) −32.1497 −1.24205
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −1.26748 −0.0488576 −0.0244288 0.999702i \(-0.507777\pi\)
−0.0244288 + 0.999702i \(0.507777\pi\)
\(674\) −38.9849 −1.50164
\(675\) 0 0
\(676\) 7.84205 0.301617
\(677\) −22.7065 −0.872681 −0.436340 0.899782i \(-0.643726\pi\)
−0.436340 + 0.899782i \(0.643726\pi\)
\(678\) 0 0
\(679\) 0.882501 0.0338673
\(680\) −0.601112 −0.0230516
\(681\) 0 0
\(682\) 3.36013 0.128666
\(683\) 34.5294 1.32123 0.660616 0.750724i \(-0.270295\pi\)
0.660616 + 0.750724i \(0.270295\pi\)
\(684\) 0 0
\(685\) −9.61006 −0.367182
\(686\) −8.57208 −0.327284
\(687\) 0 0
\(688\) −27.5513 −1.05038
\(689\) −0.0887255 −0.00338017
\(690\) 0 0
\(691\) −22.4560 −0.854265 −0.427132 0.904189i \(-0.640476\pi\)
−0.427132 + 0.904189i \(0.640476\pi\)
\(692\) 7.49931 0.285081
\(693\) 0 0
\(694\) 31.1693 1.18317
\(695\) 49.2226 1.86712
\(696\) 0 0
\(697\) 0.768494 0.0291088
\(698\) 17.1461 0.648988
\(699\) 0 0
\(700\) 1.09124 0.0412451
\(701\) 31.5776 1.19267 0.596335 0.802736i \(-0.296623\pi\)
0.596335 + 0.802736i \(0.296623\pi\)
\(702\) 0 0
\(703\) −2.90711 −0.109644
\(704\) 8.73582 0.329244
\(705\) 0 0
\(706\) 40.8870 1.53880
\(707\) 3.81408 0.143443
\(708\) 0 0
\(709\) −9.16530 −0.344210 −0.172105 0.985079i \(-0.555057\pi\)
−0.172105 + 0.985079i \(0.555057\pi\)
\(710\) 43.4453 1.63047
\(711\) 0 0
\(712\) 39.1045 1.46550
\(713\) −11.6850 −0.437605
\(714\) 0 0
\(715\) −0.437448 −0.0163596
\(716\) 5.21205 0.194784
\(717\) 0 0
\(718\) 22.8191 0.851603
\(719\) 3.15397 0.117623 0.0588116 0.998269i \(-0.481269\pi\)
0.0588116 + 0.998269i \(0.481269\pi\)
\(720\) 0 0
\(721\) −5.69686 −0.212162
\(722\) 22.1719 0.825152
\(723\) 0 0
\(724\) 0.780697 0.0290144
\(725\) 19.9229 0.739917
\(726\) 0 0
\(727\) 39.5017 1.46504 0.732519 0.680747i \(-0.238345\pi\)
0.732519 + 0.680747i \(0.238345\pi\)
\(728\) 0.245368 0.00909396
\(729\) 0 0
\(730\) −44.7877 −1.65767
\(731\) −0.764815 −0.0282877
\(732\) 0 0
\(733\) 23.5163 0.868595 0.434297 0.900770i \(-0.356997\pi\)
0.434297 + 0.900770i \(0.356997\pi\)
\(734\) −16.6343 −0.613984
\(735\) 0 0
\(736\) −13.5044 −0.497778
\(737\) 9.38126 0.345563
\(738\) 0 0
\(739\) 28.9368 1.06446 0.532228 0.846601i \(-0.321355\pi\)
0.532228 + 0.846601i \(0.321355\pi\)
\(740\) −10.5672 −0.388457
\(741\) 0 0
\(742\) 0.367589 0.0134946
\(743\) 36.1642 1.32674 0.663369 0.748293i \(-0.269126\pi\)
0.663369 + 0.748293i \(0.269126\pi\)
\(744\) 0 0
\(745\) 30.6696 1.12365
\(746\) −30.7744 −1.12673
\(747\) 0 0
\(748\) 0.0407002 0.00148815
\(749\) −1.54132 −0.0563187
\(750\) 0 0
\(751\) −37.9916 −1.38633 −0.693167 0.720777i \(-0.743785\pi\)
−0.693167 + 0.720777i \(0.743785\pi\)
\(752\) −9.48590 −0.345915
\(753\) 0 0
\(754\) 1.03946 0.0378548
\(755\) −34.1189 −1.24172
\(756\) 0 0
\(757\) −6.48633 −0.235750 −0.117875 0.993028i \(-0.537608\pi\)
−0.117875 + 0.993028i \(0.537608\pi\)
\(758\) −17.5402 −0.637087
\(759\) 0 0
\(760\) −4.30402 −0.156123
\(761\) 0.142118 0.00515178 0.00257589 0.999997i \(-0.499180\pi\)
0.00257589 + 0.999997i \(0.499180\pi\)
\(762\) 0 0
\(763\) 8.27965 0.299743
\(764\) 5.48430 0.198415
\(765\) 0 0
\(766\) 13.8178 0.499257
\(767\) 1.80046 0.0650107
\(768\) 0 0
\(769\) 37.9256 1.36763 0.683816 0.729655i \(-0.260319\pi\)
0.683816 + 0.729655i \(0.260319\pi\)
\(770\) 1.81234 0.0653124
\(771\) 0 0
\(772\) −12.7365 −0.458395
\(773\) −7.81766 −0.281182 −0.140591 0.990068i \(-0.544900\pi\)
−0.140591 + 0.990068i \(0.544900\pi\)
\(774\) 0 0
\(775\) −9.71203 −0.348867
\(776\) −5.13426 −0.184309
\(777\) 0 0
\(778\) −17.3838 −0.623240
\(779\) 5.50249 0.197147
\(780\) 0 0
\(781\) −12.6773 −0.453629
\(782\) 0.326900 0.0116899
\(783\) 0 0
\(784\) 16.3052 0.582328
\(785\) 42.8986 1.53112
\(786\) 0 0
\(787\) 20.2740 0.722692 0.361346 0.932432i \(-0.382317\pi\)
0.361346 + 0.932432i \(0.382317\pi\)
\(788\) 3.74052 0.133251
\(789\) 0 0
\(790\) −33.0860 −1.17715
\(791\) −9.35324 −0.332563
\(792\) 0 0
\(793\) −0.150802 −0.00535514
\(794\) −34.7411 −1.23292
\(795\) 0 0
\(796\) 12.2906 0.435630
\(797\) −5.99639 −0.212403 −0.106201 0.994345i \(-0.533869\pi\)
−0.106201 + 0.994345i \(0.533869\pi\)
\(798\) 0 0
\(799\) −0.263326 −0.00931579
\(800\) −11.2243 −0.396837
\(801\) 0 0
\(802\) −20.8609 −0.736624
\(803\) 13.0690 0.461195
\(804\) 0 0
\(805\) −6.30247 −0.222133
\(806\) −0.506715 −0.0178483
\(807\) 0 0
\(808\) −22.1897 −0.780632
\(809\) 38.7682 1.36302 0.681508 0.731811i \(-0.261324\pi\)
0.681508 + 0.731811i \(0.261324\pi\)
\(810\) 0 0
\(811\) −20.8789 −0.733159 −0.366579 0.930387i \(-0.619471\pi\)
−0.366579 + 0.930387i \(0.619471\pi\)
\(812\) 1.86454 0.0654326
\(813\) 0 0
\(814\) −7.12182 −0.249620
\(815\) −60.3525 −2.11406
\(816\) 0 0
\(817\) −5.47615 −0.191586
\(818\) 13.0666 0.456862
\(819\) 0 0
\(820\) 20.0012 0.698473
\(821\) −33.6755 −1.17528 −0.587642 0.809121i \(-0.699944\pi\)
−0.587642 + 0.809121i \(0.699944\pi\)
\(822\) 0 0
\(823\) −48.6794 −1.69686 −0.848428 0.529311i \(-0.822450\pi\)
−0.848428 + 0.529311i \(0.822450\pi\)
\(824\) 33.1435 1.15461
\(825\) 0 0
\(826\) −7.45928 −0.259542
\(827\) −2.49408 −0.0867276 −0.0433638 0.999059i \(-0.513807\pi\)
−0.0433638 + 0.999059i \(0.513807\pi\)
\(828\) 0 0
\(829\) 20.9559 0.727829 0.363915 0.931432i \(-0.381440\pi\)
0.363915 + 0.931432i \(0.381440\pi\)
\(830\) −39.8962 −1.38482
\(831\) 0 0
\(832\) −1.31738 −0.0456719
\(833\) 0.452627 0.0156826
\(834\) 0 0
\(835\) 38.4936 1.33212
\(836\) 0.291417 0.0100789
\(837\) 0 0
\(838\) 11.3909 0.393493
\(839\) −46.2064 −1.59522 −0.797611 0.603172i \(-0.793903\pi\)
−0.797611 + 0.603172i \(0.793903\pi\)
\(840\) 0 0
\(841\) 5.04106 0.173830
\(842\) −37.4481 −1.29055
\(843\) 0 0
\(844\) −17.3785 −0.598193
\(845\) −37.6445 −1.29501
\(846\) 0 0
\(847\) −0.528840 −0.0181712
\(848\) −1.42750 −0.0490206
\(849\) 0 0
\(850\) 0.271705 0.00931941
\(851\) 24.7663 0.848978
\(852\) 0 0
\(853\) −12.1396 −0.415653 −0.207826 0.978166i \(-0.566639\pi\)
−0.207826 + 0.978166i \(0.566639\pi\)
\(854\) 0.624772 0.0213793
\(855\) 0 0
\(856\) 8.96718 0.306492
\(857\) 39.4393 1.34722 0.673610 0.739087i \(-0.264743\pi\)
0.673610 + 0.739087i \(0.264743\pi\)
\(858\) 0 0
\(859\) −25.7414 −0.878285 −0.439143 0.898417i \(-0.644718\pi\)
−0.439143 + 0.898417i \(0.644718\pi\)
\(860\) −19.9055 −0.678770
\(861\) 0 0
\(862\) −22.6885 −0.772774
\(863\) −15.9889 −0.544269 −0.272134 0.962259i \(-0.587730\pi\)
−0.272134 + 0.962259i \(0.587730\pi\)
\(864\) 0 0
\(865\) −35.9992 −1.22401
\(866\) 15.7150 0.534018
\(867\) 0 0
\(868\) −0.908930 −0.0308511
\(869\) 9.65447 0.327506
\(870\) 0 0
\(871\) −1.41471 −0.0479357
\(872\) −48.1698 −1.63123
\(873\) 0 0
\(874\) 2.34063 0.0791731
\(875\) 2.43197 0.0822157
\(876\) 0 0
\(877\) 49.8159 1.68216 0.841082 0.540908i \(-0.181919\pi\)
0.841082 + 0.540908i \(0.181919\pi\)
\(878\) −44.5985 −1.50513
\(879\) 0 0
\(880\) −7.03808 −0.237254
\(881\) −26.3085 −0.886355 −0.443178 0.896434i \(-0.646149\pi\)
−0.443178 + 0.896434i \(0.646149\pi\)
\(882\) 0 0
\(883\) −27.4250 −0.922925 −0.461462 0.887160i \(-0.652675\pi\)
−0.461462 + 0.887160i \(0.652675\pi\)
\(884\) −0.00613767 −0.000206432 0
\(885\) 0 0
\(886\) 14.8354 0.498405
\(887\) 32.1898 1.08083 0.540413 0.841400i \(-0.318268\pi\)
0.540413 + 0.841400i \(0.318268\pi\)
\(888\) 0 0
\(889\) 11.0244 0.369746
\(890\) −43.5568 −1.46003
\(891\) 0 0
\(892\) 12.9620 0.433998
\(893\) −1.88544 −0.0630937
\(894\) 0 0
\(895\) −25.0197 −0.836315
\(896\) 1.98125 0.0661889
\(897\) 0 0
\(898\) −32.8959 −1.09775
\(899\) −16.5944 −0.553453
\(900\) 0 0
\(901\) −0.0396270 −0.00132017
\(902\) 13.4799 0.448833
\(903\) 0 0
\(904\) 54.4158 1.80984
\(905\) −3.74762 −0.124575
\(906\) 0 0
\(907\) −1.28331 −0.0426114 −0.0213057 0.999773i \(-0.506782\pi\)
−0.0213057 + 0.999773i \(0.506782\pi\)
\(908\) 12.1689 0.403838
\(909\) 0 0
\(910\) −0.273305 −0.00905998
\(911\) 49.4716 1.63907 0.819534 0.573030i \(-0.194232\pi\)
0.819534 + 0.573030i \(0.194232\pi\)
\(912\) 0 0
\(913\) 11.6417 0.385283
\(914\) 18.8491 0.623473
\(915\) 0 0
\(916\) −14.1599 −0.467856
\(917\) −4.55799 −0.150518
\(918\) 0 0
\(919\) −29.7366 −0.980921 −0.490461 0.871463i \(-0.663171\pi\)
−0.490461 + 0.871463i \(0.663171\pi\)
\(920\) 36.6668 1.20887
\(921\) 0 0
\(922\) −25.4934 −0.839581
\(923\) 1.91176 0.0629263
\(924\) 0 0
\(925\) 20.5847 0.676820
\(926\) 1.66763 0.0548017
\(927\) 0 0
\(928\) −19.1782 −0.629556
\(929\) −9.03584 −0.296456 −0.148228 0.988953i \(-0.547357\pi\)
−0.148228 + 0.988953i \(0.547357\pi\)
\(930\) 0 0
\(931\) 3.24085 0.106215
\(932\) −0.904626 −0.0296320
\(933\) 0 0
\(934\) −1.24872 −0.0408593
\(935\) −0.195375 −0.00638944
\(936\) 0 0
\(937\) −16.0261 −0.523551 −0.261776 0.965129i \(-0.584308\pi\)
−0.261776 + 0.965129i \(0.584308\pi\)
\(938\) 5.86115 0.191373
\(939\) 0 0
\(940\) −6.85344 −0.223535
\(941\) 3.42319 0.111593 0.0557963 0.998442i \(-0.482230\pi\)
0.0557963 + 0.998442i \(0.482230\pi\)
\(942\) 0 0
\(943\) −46.8769 −1.52652
\(944\) 28.9675 0.942811
\(945\) 0 0
\(946\) −13.4154 −0.436173
\(947\) −26.8391 −0.872153 −0.436076 0.899910i \(-0.643632\pi\)
−0.436076 + 0.899910i \(0.643632\pi\)
\(948\) 0 0
\(949\) −1.97083 −0.0639760
\(950\) 1.94543 0.0631182
\(951\) 0 0
\(952\) 0.109588 0.00355175
\(953\) −5.87575 −0.190334 −0.0951671 0.995461i \(-0.530339\pi\)
−0.0951671 + 0.995461i \(0.530339\pi\)
\(954\) 0 0
\(955\) −26.3265 −0.851906
\(956\) 6.86347 0.221980
\(957\) 0 0
\(958\) −29.1438 −0.941595
\(959\) 1.75199 0.0565747
\(960\) 0 0
\(961\) −22.9106 −0.739050
\(962\) 1.07398 0.0346267
\(963\) 0 0
\(964\) −11.6380 −0.374836
\(965\) 61.1394 1.96815
\(966\) 0 0
\(967\) 41.7810 1.34359 0.671793 0.740739i \(-0.265525\pi\)
0.671793 + 0.740739i \(0.265525\pi\)
\(968\) 3.07671 0.0988893
\(969\) 0 0
\(970\) 5.71883 0.183620
\(971\) −30.2221 −0.969873 −0.484937 0.874549i \(-0.661157\pi\)
−0.484937 + 0.874549i \(0.661157\pi\)
\(972\) 0 0
\(973\) −8.97366 −0.287682
\(974\) −10.4769 −0.335702
\(975\) 0 0
\(976\) −2.42625 −0.0776623
\(977\) −12.5432 −0.401292 −0.200646 0.979664i \(-0.564304\pi\)
−0.200646 + 0.979664i \(0.564304\pi\)
\(978\) 0 0
\(979\) 12.7098 0.406208
\(980\) 11.7803 0.376308
\(981\) 0 0
\(982\) 17.5045 0.558591
\(983\) −35.7613 −1.14061 −0.570304 0.821434i \(-0.693175\pi\)
−0.570304 + 0.821434i \(0.693175\pi\)
\(984\) 0 0
\(985\) −17.9558 −0.572119
\(986\) 0.464246 0.0147846
\(987\) 0 0
\(988\) −0.0439463 −0.00139812
\(989\) 46.6524 1.48346
\(990\) 0 0
\(991\) 26.5390 0.843039 0.421519 0.906819i \(-0.361497\pi\)
0.421519 + 0.906819i \(0.361497\pi\)
\(992\) 9.34902 0.296832
\(993\) 0 0
\(994\) −7.92041 −0.251220
\(995\) −58.9993 −1.87040
\(996\) 0 0
\(997\) −0.481491 −0.0152490 −0.00762448 0.999971i \(-0.502427\pi\)
−0.00762448 + 0.999971i \(0.502427\pi\)
\(998\) 2.24365 0.0710216
\(999\) 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 \(a_p\))