Properties

Label 8001.2.a.v.1.4
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.26573\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.26573 q^{2}\) \(+3.13354 q^{4}\) \(+0.263451 q^{5}\) \(+1.00000 q^{7}\) \(-2.56830 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.26573 q^{2}\) \(+3.13354 q^{4}\) \(+0.263451 q^{5}\) \(+1.00000 q^{7}\) \(-2.56830 q^{8}\) \(-0.596909 q^{10}\) \(-2.11462 q^{11}\) \(+5.02935 q^{13}\) \(-2.26573 q^{14}\) \(-0.448003 q^{16}\) \(-0.600740 q^{17}\) \(-0.662362 q^{19}\) \(+0.825534 q^{20}\) \(+4.79117 q^{22}\) \(+0.862531 q^{23}\) \(-4.93059 q^{25}\) \(-11.3952 q^{26}\) \(+3.13354 q^{28}\) \(-7.49718 q^{29}\) \(-6.27258 q^{31}\) \(+6.15165 q^{32}\) \(+1.36112 q^{34}\) \(+0.263451 q^{35}\) \(+1.88794 q^{37}\) \(+1.50074 q^{38}\) \(-0.676621 q^{40}\) \(-9.92148 q^{41}\) \(-0.837435 q^{43}\) \(-6.62626 q^{44}\) \(-1.95426 q^{46}\) \(+6.32880 q^{47}\) \(+1.00000 q^{49}\) \(+11.1714 q^{50}\) \(+15.7597 q^{52}\) \(-2.22979 q^{53}\) \(-0.557099 q^{55}\) \(-2.56830 q^{56}\) \(+16.9866 q^{58}\) \(+8.92253 q^{59}\) \(+12.6716 q^{61}\) \(+14.2120 q^{62}\) \(-13.0420 q^{64}\) \(+1.32499 q^{65}\) \(-6.63659 q^{67}\) \(-1.88244 q^{68}\) \(-0.596909 q^{70}\) \(-3.04160 q^{71}\) \(+3.58423 q^{73}\) \(-4.27757 q^{74}\) \(-2.07554 q^{76}\) \(-2.11462 q^{77}\) \(-6.24082 q^{79}\) \(-0.118027 q^{80}\) \(+22.4794 q^{82}\) \(+15.5940 q^{83}\) \(-0.158265 q^{85}\) \(+1.89740 q^{86}\) \(+5.43098 q^{88}\) \(-10.2988 q^{89}\) \(+5.02935 q^{91}\) \(+2.70278 q^{92}\) \(-14.3394 q^{94}\) \(-0.174500 q^{95}\) \(+10.8058 q^{97}\) \(-2.26573 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26573 −1.60211 −0.801057 0.598588i \(-0.795729\pi\)
−0.801057 + 0.598588i \(0.795729\pi\)
\(3\) 0 0
\(4\) 3.13354 1.56677
\(5\) 0.263451 0.117819 0.0589094 0.998263i \(-0.481238\pi\)
0.0589094 + 0.998263i \(0.481238\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.56830 −0.908031
\(9\) 0 0
\(10\) −0.596909 −0.188759
\(11\) −2.11462 −0.637583 −0.318791 0.947825i \(-0.603277\pi\)
−0.318791 + 0.947825i \(0.603277\pi\)
\(12\) 0 0
\(13\) 5.02935 1.39489 0.697445 0.716638i \(-0.254320\pi\)
0.697445 + 0.716638i \(0.254320\pi\)
\(14\) −2.26573 −0.605542
\(15\) 0 0
\(16\) −0.448003 −0.112001
\(17\) −0.600740 −0.145701 −0.0728504 0.997343i \(-0.523210\pi\)
−0.0728504 + 0.997343i \(0.523210\pi\)
\(18\) 0 0
\(19\) −0.662362 −0.151956 −0.0759782 0.997109i \(-0.524208\pi\)
−0.0759782 + 0.997109i \(0.524208\pi\)
\(20\) 0.825534 0.184595
\(21\) 0 0
\(22\) 4.79117 1.02148
\(23\) 0.862531 0.179850 0.0899251 0.995949i \(-0.471337\pi\)
0.0899251 + 0.995949i \(0.471337\pi\)
\(24\) 0 0
\(25\) −4.93059 −0.986119
\(26\) −11.3952 −2.23477
\(27\) 0 0
\(28\) 3.13354 0.592184
\(29\) −7.49718 −1.39219 −0.696095 0.717949i \(-0.745081\pi\)
−0.696095 + 0.717949i \(0.745081\pi\)
\(30\) 0 0
\(31\) −6.27258 −1.12659 −0.563294 0.826256i \(-0.690466\pi\)
−0.563294 + 0.826256i \(0.690466\pi\)
\(32\) 6.15165 1.08747
\(33\) 0 0
\(34\) 1.36112 0.233429
\(35\) 0.263451 0.0445313
\(36\) 0 0
\(37\) 1.88794 0.310376 0.155188 0.987885i \(-0.450402\pi\)
0.155188 + 0.987885i \(0.450402\pi\)
\(38\) 1.50074 0.243451
\(39\) 0 0
\(40\) −0.676621 −0.106983
\(41\) −9.92148 −1.54948 −0.774738 0.632283i \(-0.782118\pi\)
−0.774738 + 0.632283i \(0.782118\pi\)
\(42\) 0 0
\(43\) −0.837435 −0.127708 −0.0638538 0.997959i \(-0.520339\pi\)
−0.0638538 + 0.997959i \(0.520339\pi\)
\(44\) −6.62626 −0.998946
\(45\) 0 0
\(46\) −1.95426 −0.288140
\(47\) 6.32880 0.923150 0.461575 0.887101i \(-0.347284\pi\)
0.461575 + 0.887101i \(0.347284\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 11.1714 1.57988
\(51\) 0 0
\(52\) 15.7597 2.18547
\(53\) −2.22979 −0.306285 −0.153143 0.988204i \(-0.548939\pi\)
−0.153143 + 0.988204i \(0.548939\pi\)
\(54\) 0 0
\(55\) −0.557099 −0.0751192
\(56\) −2.56830 −0.343204
\(57\) 0 0
\(58\) 16.9866 2.23045
\(59\) 8.92253 1.16161 0.580807 0.814041i \(-0.302737\pi\)
0.580807 + 0.814041i \(0.302737\pi\)
\(60\) 0 0
\(61\) 12.6716 1.62243 0.811215 0.584748i \(-0.198806\pi\)
0.811215 + 0.584748i \(0.198806\pi\)
\(62\) 14.2120 1.80492
\(63\) 0 0
\(64\) −13.0420 −1.63025
\(65\) 1.32499 0.164344
\(66\) 0 0
\(67\) −6.63659 −0.810788 −0.405394 0.914142i \(-0.632866\pi\)
−0.405394 + 0.914142i \(0.632866\pi\)
\(68\) −1.88244 −0.228280
\(69\) 0 0
\(70\) −0.596909 −0.0713443
\(71\) −3.04160 −0.360971 −0.180486 0.983578i \(-0.557767\pi\)
−0.180486 + 0.983578i \(0.557767\pi\)
\(72\) 0 0
\(73\) 3.58423 0.419502 0.209751 0.977755i \(-0.432735\pi\)
0.209751 + 0.977755i \(0.432735\pi\)
\(74\) −4.27757 −0.497257
\(75\) 0 0
\(76\) −2.07554 −0.238081
\(77\) −2.11462 −0.240984
\(78\) 0 0
\(79\) −6.24082 −0.702147 −0.351073 0.936348i \(-0.614183\pi\)
−0.351073 + 0.936348i \(0.614183\pi\)
\(80\) −0.118027 −0.0131958
\(81\) 0 0
\(82\) 22.4794 2.48244
\(83\) 15.5940 1.71166 0.855832 0.517254i \(-0.173046\pi\)
0.855832 + 0.517254i \(0.173046\pi\)
\(84\) 0 0
\(85\) −0.158265 −0.0171663
\(86\) 1.89740 0.204602
\(87\) 0 0
\(88\) 5.43098 0.578945
\(89\) −10.2988 −1.09167 −0.545837 0.837891i \(-0.683788\pi\)
−0.545837 + 0.837891i \(0.683788\pi\)
\(90\) 0 0
\(91\) 5.02935 0.527219
\(92\) 2.70278 0.281784
\(93\) 0 0
\(94\) −14.3394 −1.47899
\(95\) −0.174500 −0.0179033
\(96\) 0 0
\(97\) 10.8058 1.09716 0.548580 0.836098i \(-0.315169\pi\)
0.548580 + 0.836098i \(0.315169\pi\)
\(98\) −2.26573 −0.228873
\(99\) 0 0
\(100\) −15.4502 −1.54502
\(101\) 11.1783 1.11229 0.556143 0.831086i \(-0.312281\pi\)
0.556143 + 0.831086i \(0.312281\pi\)
\(102\) 0 0
\(103\) 8.91300 0.878224 0.439112 0.898432i \(-0.355293\pi\)
0.439112 + 0.898432i \(0.355293\pi\)
\(104\) −12.9169 −1.26660
\(105\) 0 0
\(106\) 5.05210 0.490704
\(107\) −1.40233 −0.135568 −0.0677840 0.997700i \(-0.521593\pi\)
−0.0677840 + 0.997700i \(0.521593\pi\)
\(108\) 0 0
\(109\) −7.84506 −0.751421 −0.375710 0.926737i \(-0.622601\pi\)
−0.375710 + 0.926737i \(0.622601\pi\)
\(110\) 1.26224 0.120350
\(111\) 0 0
\(112\) −0.448003 −0.0423323
\(113\) 5.51409 0.518722 0.259361 0.965780i \(-0.416488\pi\)
0.259361 + 0.965780i \(0.416488\pi\)
\(114\) 0 0
\(115\) 0.227234 0.0211897
\(116\) −23.4927 −2.18124
\(117\) 0 0
\(118\) −20.2161 −1.86104
\(119\) −0.600740 −0.0550697
\(120\) 0 0
\(121\) −6.52837 −0.593488
\(122\) −28.7104 −2.59932
\(123\) 0 0
\(124\) −19.6554 −1.76511
\(125\) −2.61622 −0.234002
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 17.2464 1.52438
\(129\) 0 0
\(130\) −3.00206 −0.263298
\(131\) −4.56918 −0.399211 −0.199606 0.979876i \(-0.563966\pi\)
−0.199606 + 0.979876i \(0.563966\pi\)
\(132\) 0 0
\(133\) −0.662362 −0.0574341
\(134\) 15.0367 1.29898
\(135\) 0 0
\(136\) 1.54288 0.132301
\(137\) 11.8489 1.01232 0.506158 0.862441i \(-0.331065\pi\)
0.506158 + 0.862441i \(0.331065\pi\)
\(138\) 0 0
\(139\) 15.4594 1.31125 0.655623 0.755088i \(-0.272406\pi\)
0.655623 + 0.755088i \(0.272406\pi\)
\(140\) 0.825534 0.0697703
\(141\) 0 0
\(142\) 6.89144 0.578317
\(143\) −10.6352 −0.889358
\(144\) 0 0
\(145\) −1.97514 −0.164026
\(146\) −8.12090 −0.672090
\(147\) 0 0
\(148\) 5.91594 0.486287
\(149\) 19.2171 1.57433 0.787163 0.616745i \(-0.211549\pi\)
0.787163 + 0.616745i \(0.211549\pi\)
\(150\) 0 0
\(151\) −19.4578 −1.58345 −0.791725 0.610878i \(-0.790817\pi\)
−0.791725 + 0.610878i \(0.790817\pi\)
\(152\) 1.70115 0.137981
\(153\) 0 0
\(154\) 4.79117 0.386083
\(155\) −1.65252 −0.132733
\(156\) 0 0
\(157\) 20.3132 1.62117 0.810583 0.585623i \(-0.199150\pi\)
0.810583 + 0.585623i \(0.199150\pi\)
\(158\) 14.1400 1.12492
\(159\) 0 0
\(160\) 1.62066 0.128124
\(161\) 0.862531 0.0679770
\(162\) 0 0
\(163\) 18.2949 1.43297 0.716483 0.697605i \(-0.245751\pi\)
0.716483 + 0.697605i \(0.245751\pi\)
\(164\) −31.0894 −2.42767
\(165\) 0 0
\(166\) −35.3318 −2.74228
\(167\) −0.426687 −0.0330181 −0.0165090 0.999864i \(-0.505255\pi\)
−0.0165090 + 0.999864i \(0.505255\pi\)
\(168\) 0 0
\(169\) 12.2944 0.945720
\(170\) 0.358587 0.0275024
\(171\) 0 0
\(172\) −2.62414 −0.200089
\(173\) 18.0358 1.37124 0.685620 0.727960i \(-0.259531\pi\)
0.685620 + 0.727960i \(0.259531\pi\)
\(174\) 0 0
\(175\) −4.93059 −0.372718
\(176\) 0.947357 0.0714097
\(177\) 0 0
\(178\) 23.3344 1.74899
\(179\) 3.90602 0.291950 0.145975 0.989288i \(-0.453368\pi\)
0.145975 + 0.989288i \(0.453368\pi\)
\(180\) 0 0
\(181\) −19.6214 −1.45845 −0.729223 0.684276i \(-0.760118\pi\)
−0.729223 + 0.684276i \(0.760118\pi\)
\(182\) −11.3952 −0.844665
\(183\) 0 0
\(184\) −2.21524 −0.163310
\(185\) 0.497380 0.0365681
\(186\) 0 0
\(187\) 1.27034 0.0928963
\(188\) 19.8316 1.44636
\(189\) 0 0
\(190\) 0.395370 0.0286832
\(191\) 18.2968 1.32391 0.661957 0.749542i \(-0.269726\pi\)
0.661957 + 0.749542i \(0.269726\pi\)
\(192\) 0 0
\(193\) −8.29105 −0.596803 −0.298401 0.954440i \(-0.596453\pi\)
−0.298401 + 0.954440i \(0.596453\pi\)
\(194\) −24.4830 −1.75778
\(195\) 0 0
\(196\) 3.13354 0.223824
\(197\) 22.0383 1.57016 0.785082 0.619391i \(-0.212621\pi\)
0.785082 + 0.619391i \(0.212621\pi\)
\(198\) 0 0
\(199\) −7.76159 −0.550204 −0.275102 0.961415i \(-0.588712\pi\)
−0.275102 + 0.961415i \(0.588712\pi\)
\(200\) 12.6632 0.895427
\(201\) 0 0
\(202\) −25.3271 −1.78201
\(203\) −7.49718 −0.526199
\(204\) 0 0
\(205\) −2.61382 −0.182557
\(206\) −20.1945 −1.40702
\(207\) 0 0
\(208\) −2.25316 −0.156229
\(209\) 1.40065 0.0968847
\(210\) 0 0
\(211\) −6.35929 −0.437792 −0.218896 0.975748i \(-0.570246\pi\)
−0.218896 + 0.975748i \(0.570246\pi\)
\(212\) −6.98714 −0.479878
\(213\) 0 0
\(214\) 3.17729 0.217195
\(215\) −0.220623 −0.0150464
\(216\) 0 0
\(217\) −6.27258 −0.425811
\(218\) 17.7748 1.20386
\(219\) 0 0
\(220\) −1.74569 −0.117695
\(221\) −3.02133 −0.203237
\(222\) 0 0
\(223\) −10.9206 −0.731298 −0.365649 0.930753i \(-0.619153\pi\)
−0.365649 + 0.930753i \(0.619153\pi\)
\(224\) 6.15165 0.411025
\(225\) 0 0
\(226\) −12.4934 −0.831051
\(227\) −1.39196 −0.0923874 −0.0461937 0.998933i \(-0.514709\pi\)
−0.0461937 + 0.998933i \(0.514709\pi\)
\(228\) 0 0
\(229\) 5.71394 0.377588 0.188794 0.982017i \(-0.439542\pi\)
0.188794 + 0.982017i \(0.439542\pi\)
\(230\) −0.514852 −0.0339484
\(231\) 0 0
\(232\) 19.2550 1.26415
\(233\) −14.1302 −0.925697 −0.462849 0.886437i \(-0.653173\pi\)
−0.462849 + 0.886437i \(0.653173\pi\)
\(234\) 0 0
\(235\) 1.66733 0.108764
\(236\) 27.9591 1.81998
\(237\) 0 0
\(238\) 1.36112 0.0882280
\(239\) 23.6713 1.53117 0.765585 0.643335i \(-0.222450\pi\)
0.765585 + 0.643335i \(0.222450\pi\)
\(240\) 0 0
\(241\) 18.5876 1.19734 0.598668 0.800997i \(-0.295697\pi\)
0.598668 + 0.800997i \(0.295697\pi\)
\(242\) 14.7915 0.950836
\(243\) 0 0
\(244\) 39.7069 2.54198
\(245\) 0.263451 0.0168313
\(246\) 0 0
\(247\) −3.33125 −0.211963
\(248\) 16.1099 1.02298
\(249\) 0 0
\(250\) 5.92766 0.374898
\(251\) 23.4333 1.47910 0.739548 0.673104i \(-0.235039\pi\)
0.739548 + 0.673104i \(0.235039\pi\)
\(252\) 0 0
\(253\) −1.82393 −0.114669
\(254\) −2.26573 −0.142165
\(255\) 0 0
\(256\) −12.9916 −0.811976
\(257\) 7.24896 0.452178 0.226089 0.974107i \(-0.427406\pi\)
0.226089 + 0.974107i \(0.427406\pi\)
\(258\) 0 0
\(259\) 1.88794 0.117311
\(260\) 4.15190 0.257490
\(261\) 0 0
\(262\) 10.3525 0.639582
\(263\) 3.53120 0.217743 0.108871 0.994056i \(-0.465276\pi\)
0.108871 + 0.994056i \(0.465276\pi\)
\(264\) 0 0
\(265\) −0.587440 −0.0360861
\(266\) 1.50074 0.0920160
\(267\) 0 0
\(268\) −20.7960 −1.27032
\(269\) 17.7944 1.08494 0.542472 0.840074i \(-0.317488\pi\)
0.542472 + 0.840074i \(0.317488\pi\)
\(270\) 0 0
\(271\) 12.7007 0.771511 0.385756 0.922601i \(-0.373941\pi\)
0.385756 + 0.922601i \(0.373941\pi\)
\(272\) 0.269133 0.0163186
\(273\) 0 0
\(274\) −26.8463 −1.62185
\(275\) 10.4263 0.628732
\(276\) 0 0
\(277\) −5.23820 −0.314733 −0.157366 0.987540i \(-0.550300\pi\)
−0.157366 + 0.987540i \(0.550300\pi\)
\(278\) −35.0268 −2.10077
\(279\) 0 0
\(280\) −0.676621 −0.0404358
\(281\) −17.9732 −1.07219 −0.536096 0.844157i \(-0.680101\pi\)
−0.536096 + 0.844157i \(0.680101\pi\)
\(282\) 0 0
\(283\) −14.1901 −0.843514 −0.421757 0.906709i \(-0.638586\pi\)
−0.421757 + 0.906709i \(0.638586\pi\)
\(284\) −9.53097 −0.565559
\(285\) 0 0
\(286\) 24.0965 1.42485
\(287\) −9.92148 −0.585647
\(288\) 0 0
\(289\) −16.6391 −0.978771
\(290\) 4.47513 0.262789
\(291\) 0 0
\(292\) 11.2313 0.657263
\(293\) −20.3093 −1.18648 −0.593241 0.805025i \(-0.702152\pi\)
−0.593241 + 0.805025i \(0.702152\pi\)
\(294\) 0 0
\(295\) 2.35065 0.136860
\(296\) −4.84880 −0.281831
\(297\) 0 0
\(298\) −43.5408 −2.52225
\(299\) 4.33797 0.250871
\(300\) 0 0
\(301\) −0.837435 −0.0482690
\(302\) 44.0861 2.53687
\(303\) 0 0
\(304\) 0.296740 0.0170192
\(305\) 3.33834 0.191153
\(306\) 0 0
\(307\) −17.4945 −0.998463 −0.499231 0.866469i \(-0.666384\pi\)
−0.499231 + 0.866469i \(0.666384\pi\)
\(308\) −6.62626 −0.377566
\(309\) 0 0
\(310\) 3.74416 0.212654
\(311\) −9.84459 −0.558235 −0.279118 0.960257i \(-0.590042\pi\)
−0.279118 + 0.960257i \(0.590042\pi\)
\(312\) 0 0
\(313\) 22.4434 1.26857 0.634287 0.773097i \(-0.281294\pi\)
0.634287 + 0.773097i \(0.281294\pi\)
\(314\) −46.0242 −2.59729
\(315\) 0 0
\(316\) −19.5559 −1.10010
\(317\) −14.8472 −0.833905 −0.416952 0.908928i \(-0.636902\pi\)
−0.416952 + 0.908928i \(0.636902\pi\)
\(318\) 0 0
\(319\) 15.8537 0.887637
\(320\) −3.43592 −0.192074
\(321\) 0 0
\(322\) −1.95426 −0.108907
\(323\) 0.397908 0.0221402
\(324\) 0 0
\(325\) −24.7977 −1.37553
\(326\) −41.4513 −2.29577
\(327\) 0 0
\(328\) 25.4813 1.40697
\(329\) 6.32880 0.348918
\(330\) 0 0
\(331\) 27.0357 1.48601 0.743007 0.669284i \(-0.233399\pi\)
0.743007 + 0.669284i \(0.233399\pi\)
\(332\) 48.8644 2.68178
\(333\) 0 0
\(334\) 0.966759 0.0528987
\(335\) −1.74841 −0.0955261
\(336\) 0 0
\(337\) 12.7721 0.695742 0.347871 0.937542i \(-0.386905\pi\)
0.347871 + 0.937542i \(0.386905\pi\)
\(338\) −27.8557 −1.51515
\(339\) 0 0
\(340\) −0.495931 −0.0268956
\(341\) 13.2641 0.718294
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 2.15079 0.115963
\(345\) 0 0
\(346\) −40.8644 −2.19688
\(347\) 1.00797 0.0541108 0.0270554 0.999634i \(-0.491387\pi\)
0.0270554 + 0.999634i \(0.491387\pi\)
\(348\) 0 0
\(349\) 21.1658 1.13298 0.566490 0.824068i \(-0.308301\pi\)
0.566490 + 0.824068i \(0.308301\pi\)
\(350\) 11.1714 0.597137
\(351\) 0 0
\(352\) −13.0084 −0.693351
\(353\) −25.1557 −1.33890 −0.669450 0.742857i \(-0.733470\pi\)
−0.669450 + 0.742857i \(0.733470\pi\)
\(354\) 0 0
\(355\) −0.801311 −0.0425292
\(356\) −32.2718 −1.71040
\(357\) 0 0
\(358\) −8.84999 −0.467737
\(359\) −24.8593 −1.31202 −0.656012 0.754750i \(-0.727758\pi\)
−0.656012 + 0.754750i \(0.727758\pi\)
\(360\) 0 0
\(361\) −18.5613 −0.976909
\(362\) 44.4568 2.33660
\(363\) 0 0
\(364\) 15.7597 0.826031
\(365\) 0.944267 0.0494252
\(366\) 0 0
\(367\) 17.4263 0.909648 0.454824 0.890581i \(-0.349702\pi\)
0.454824 + 0.890581i \(0.349702\pi\)
\(368\) −0.386416 −0.0201433
\(369\) 0 0
\(370\) −1.12693 −0.0585862
\(371\) −2.22979 −0.115765
\(372\) 0 0
\(373\) −3.72752 −0.193004 −0.0965018 0.995333i \(-0.530765\pi\)
−0.0965018 + 0.995333i \(0.530765\pi\)
\(374\) −2.87825 −0.148831
\(375\) 0 0
\(376\) −16.2543 −0.838249
\(377\) −37.7059 −1.94195
\(378\) 0 0
\(379\) −24.7896 −1.27336 −0.636678 0.771130i \(-0.719692\pi\)
−0.636678 + 0.771130i \(0.719692\pi\)
\(380\) −0.546803 −0.0280504
\(381\) 0 0
\(382\) −41.4558 −2.12106
\(383\) 12.0043 0.613393 0.306696 0.951807i \(-0.400776\pi\)
0.306696 + 0.951807i \(0.400776\pi\)
\(384\) 0 0
\(385\) −0.557099 −0.0283924
\(386\) 18.7853 0.956146
\(387\) 0 0
\(388\) 33.8603 1.71900
\(389\) 3.92849 0.199182 0.0995911 0.995028i \(-0.468247\pi\)
0.0995911 + 0.995028i \(0.468247\pi\)
\(390\) 0 0
\(391\) −0.518157 −0.0262043
\(392\) −2.56830 −0.129719
\(393\) 0 0
\(394\) −49.9329 −2.51558
\(395\) −1.64415 −0.0827261
\(396\) 0 0
\(397\) −8.49822 −0.426514 −0.213257 0.976996i \(-0.568407\pi\)
−0.213257 + 0.976996i \(0.568407\pi\)
\(398\) 17.5857 0.881490
\(399\) 0 0
\(400\) 2.20892 0.110446
\(401\) 22.7863 1.13790 0.568948 0.822374i \(-0.307351\pi\)
0.568948 + 0.822374i \(0.307351\pi\)
\(402\) 0 0
\(403\) −31.5470 −1.57147
\(404\) 35.0278 1.74270
\(405\) 0 0
\(406\) 16.9866 0.843031
\(407\) −3.99228 −0.197890
\(408\) 0 0
\(409\) −0.459834 −0.0227373 −0.0113687 0.999935i \(-0.503619\pi\)
−0.0113687 + 0.999935i \(0.503619\pi\)
\(410\) 5.92222 0.292478
\(411\) 0 0
\(412\) 27.9293 1.37598
\(413\) 8.92253 0.439049
\(414\) 0 0
\(415\) 4.10825 0.201666
\(416\) 30.9388 1.51690
\(417\) 0 0
\(418\) −3.17349 −0.155220
\(419\) 7.58777 0.370687 0.185343 0.982674i \(-0.440660\pi\)
0.185343 + 0.982674i \(0.440660\pi\)
\(420\) 0 0
\(421\) −7.86449 −0.383292 −0.191646 0.981464i \(-0.561383\pi\)
−0.191646 + 0.981464i \(0.561383\pi\)
\(422\) 14.4085 0.701393
\(423\) 0 0
\(424\) 5.72677 0.278116
\(425\) 2.96200 0.143678
\(426\) 0 0
\(427\) 12.6716 0.613221
\(428\) −4.39425 −0.212404
\(429\) 0 0
\(430\) 0.499873 0.0241060
\(431\) −28.4816 −1.37191 −0.685954 0.727645i \(-0.740615\pi\)
−0.685954 + 0.727645i \(0.740615\pi\)
\(432\) 0 0
\(433\) 3.03914 0.146052 0.0730260 0.997330i \(-0.476734\pi\)
0.0730260 + 0.997330i \(0.476734\pi\)
\(434\) 14.2120 0.682197
\(435\) 0 0
\(436\) −24.5828 −1.17730
\(437\) −0.571308 −0.0273294
\(438\) 0 0
\(439\) 34.0162 1.62350 0.811752 0.584002i \(-0.198514\pi\)
0.811752 + 0.584002i \(0.198514\pi\)
\(440\) 1.43080 0.0682106
\(441\) 0 0
\(442\) 6.84553 0.325609
\(443\) 20.9252 0.994186 0.497093 0.867697i \(-0.334401\pi\)
0.497093 + 0.867697i \(0.334401\pi\)
\(444\) 0 0
\(445\) −2.71324 −0.128620
\(446\) 24.7432 1.17162
\(447\) 0 0
\(448\) −13.0420 −0.616176
\(449\) −2.80824 −0.132529 −0.0662646 0.997802i \(-0.521108\pi\)
−0.0662646 + 0.997802i \(0.521108\pi\)
\(450\) 0 0
\(451\) 20.9802 0.987919
\(452\) 17.2786 0.812718
\(453\) 0 0
\(454\) 3.15380 0.148015
\(455\) 1.32499 0.0621163
\(456\) 0 0
\(457\) −7.78721 −0.364271 −0.182135 0.983273i \(-0.558301\pi\)
−0.182135 + 0.983273i \(0.558301\pi\)
\(458\) −12.9463 −0.604939
\(459\) 0 0
\(460\) 0.712048 0.0331994
\(461\) 2.68061 0.124849 0.0624243 0.998050i \(-0.480117\pi\)
0.0624243 + 0.998050i \(0.480117\pi\)
\(462\) 0 0
\(463\) 4.95916 0.230472 0.115236 0.993338i \(-0.463238\pi\)
0.115236 + 0.993338i \(0.463238\pi\)
\(464\) 3.35876 0.155926
\(465\) 0 0
\(466\) 32.0151 1.48307
\(467\) 39.4769 1.82677 0.913386 0.407095i \(-0.133458\pi\)
0.913386 + 0.407095i \(0.133458\pi\)
\(468\) 0 0
\(469\) −6.63659 −0.306449
\(470\) −3.77772 −0.174253
\(471\) 0 0
\(472\) −22.9157 −1.05478
\(473\) 1.77086 0.0814242
\(474\) 0 0
\(475\) 3.26584 0.149847
\(476\) −1.88244 −0.0862816
\(477\) 0 0
\(478\) −53.6328 −2.45311
\(479\) −31.0109 −1.41692 −0.708462 0.705749i \(-0.750610\pi\)
−0.708462 + 0.705749i \(0.750610\pi\)
\(480\) 0 0
\(481\) 9.49512 0.432940
\(482\) −42.1146 −1.91827
\(483\) 0 0
\(484\) −20.4569 −0.929860
\(485\) 2.84679 0.129266
\(486\) 0 0
\(487\) 39.6366 1.79611 0.898053 0.439887i \(-0.144981\pi\)
0.898053 + 0.439887i \(0.144981\pi\)
\(488\) −32.5444 −1.47322
\(489\) 0 0
\(490\) −0.596909 −0.0269656
\(491\) −16.5621 −0.747438 −0.373719 0.927542i \(-0.621918\pi\)
−0.373719 + 0.927542i \(0.621918\pi\)
\(492\) 0 0
\(493\) 4.50385 0.202843
\(494\) 7.54773 0.339588
\(495\) 0 0
\(496\) 2.81013 0.126179
\(497\) −3.04160 −0.136434
\(498\) 0 0
\(499\) 39.7879 1.78115 0.890576 0.454834i \(-0.150301\pi\)
0.890576 + 0.454834i \(0.150301\pi\)
\(500\) −8.19804 −0.366628
\(501\) 0 0
\(502\) −53.0935 −2.36968
\(503\) −18.0707 −0.805734 −0.402867 0.915259i \(-0.631986\pi\)
−0.402867 + 0.915259i \(0.631986\pi\)
\(504\) 0 0
\(505\) 2.94494 0.131048
\(506\) 4.13253 0.183713
\(507\) 0 0
\(508\) 3.13354 0.139028
\(509\) −23.0487 −1.02162 −0.510808 0.859695i \(-0.670654\pi\)
−0.510808 + 0.859695i \(0.670654\pi\)
\(510\) 0 0
\(511\) 3.58423 0.158557
\(512\) −5.05717 −0.223497
\(513\) 0 0
\(514\) −16.4242 −0.724441
\(515\) 2.34814 0.103471
\(516\) 0 0
\(517\) −13.3830 −0.588585
\(518\) −4.27757 −0.187946
\(519\) 0 0
\(520\) −3.40296 −0.149230
\(521\) −23.3186 −1.02161 −0.510803 0.859698i \(-0.670652\pi\)
−0.510803 + 0.859698i \(0.670652\pi\)
\(522\) 0 0
\(523\) 5.13133 0.224377 0.112189 0.993687i \(-0.464214\pi\)
0.112189 + 0.993687i \(0.464214\pi\)
\(524\) −14.3177 −0.625473
\(525\) 0 0
\(526\) −8.00074 −0.348849
\(527\) 3.76819 0.164145
\(528\) 0 0
\(529\) −22.2560 −0.967654
\(530\) 1.33098 0.0578141
\(531\) 0 0
\(532\) −2.07554 −0.0899861
\(533\) −49.8986 −2.16135
\(534\) 0 0
\(535\) −0.369444 −0.0159725
\(536\) 17.0447 0.736221
\(537\) 0 0
\(538\) −40.3173 −1.73820
\(539\) −2.11462 −0.0910832
\(540\) 0 0
\(541\) 31.1702 1.34011 0.670055 0.742312i \(-0.266271\pi\)
0.670055 + 0.742312i \(0.266271\pi\)
\(542\) −28.7763 −1.23605
\(543\) 0 0
\(544\) −3.69554 −0.158445
\(545\) −2.06679 −0.0885315
\(546\) 0 0
\(547\) −7.59702 −0.324825 −0.162413 0.986723i \(-0.551928\pi\)
−0.162413 + 0.986723i \(0.551928\pi\)
\(548\) 37.1289 1.58607
\(549\) 0 0
\(550\) −23.6233 −1.00730
\(551\) 4.96585 0.211552
\(552\) 0 0
\(553\) −6.24082 −0.265387
\(554\) 11.8684 0.504238
\(555\) 0 0
\(556\) 48.4425 2.05442
\(557\) 11.1855 0.473947 0.236973 0.971516i \(-0.423845\pi\)
0.236973 + 0.971516i \(0.423845\pi\)
\(558\) 0 0
\(559\) −4.21176 −0.178138
\(560\) −0.118027 −0.00498754
\(561\) 0 0
\(562\) 40.7225 1.71777
\(563\) 28.2073 1.18879 0.594397 0.804172i \(-0.297391\pi\)
0.594397 + 0.804172i \(0.297391\pi\)
\(564\) 0 0
\(565\) 1.45269 0.0611152
\(566\) 32.1510 1.35141
\(567\) 0 0
\(568\) 7.81173 0.327773
\(569\) −24.8095 −1.04007 −0.520035 0.854145i \(-0.674081\pi\)
−0.520035 + 0.854145i \(0.674081\pi\)
\(570\) 0 0
\(571\) −21.0354 −0.880304 −0.440152 0.897923i \(-0.645076\pi\)
−0.440152 + 0.897923i \(0.645076\pi\)
\(572\) −33.3258 −1.39342
\(573\) 0 0
\(574\) 22.4794 0.938273
\(575\) −4.25279 −0.177354
\(576\) 0 0
\(577\) −13.9122 −0.579171 −0.289585 0.957152i \(-0.593517\pi\)
−0.289585 + 0.957152i \(0.593517\pi\)
\(578\) 37.6998 1.56810
\(579\) 0 0
\(580\) −6.18917 −0.256991
\(581\) 15.5940 0.646948
\(582\) 0 0
\(583\) 4.71516 0.195282
\(584\) −9.20537 −0.380921
\(585\) 0 0
\(586\) 46.0154 1.90088
\(587\) −27.0344 −1.11583 −0.557914 0.829899i \(-0.688398\pi\)
−0.557914 + 0.829899i \(0.688398\pi\)
\(588\) 0 0
\(589\) 4.15472 0.171192
\(590\) −5.32594 −0.219265
\(591\) 0 0
\(592\) −0.845803 −0.0347623
\(593\) 29.7989 1.22369 0.611847 0.790976i \(-0.290427\pi\)
0.611847 + 0.790976i \(0.290427\pi\)
\(594\) 0 0
\(595\) −0.158265 −0.00648825
\(596\) 60.2176 2.46661
\(597\) 0 0
\(598\) −9.82868 −0.401924
\(599\) −29.2831 −1.19648 −0.598238 0.801319i \(-0.704132\pi\)
−0.598238 + 0.801319i \(0.704132\pi\)
\(600\) 0 0
\(601\) −6.01295 −0.245274 −0.122637 0.992452i \(-0.539135\pi\)
−0.122637 + 0.992452i \(0.539135\pi\)
\(602\) 1.89740 0.0773324
\(603\) 0 0
\(604\) −60.9717 −2.48090
\(605\) −1.71990 −0.0699241
\(606\) 0 0
\(607\) 8.18284 0.332131 0.166066 0.986115i \(-0.446894\pi\)
0.166066 + 0.986115i \(0.446894\pi\)
\(608\) −4.07462 −0.165248
\(609\) 0 0
\(610\) −7.56378 −0.306249
\(611\) 31.8298 1.28769
\(612\) 0 0
\(613\) −33.3302 −1.34619 −0.673097 0.739555i \(-0.735036\pi\)
−0.673097 + 0.739555i \(0.735036\pi\)
\(614\) 39.6378 1.59965
\(615\) 0 0
\(616\) 5.43098 0.218821
\(617\) 15.3915 0.619638 0.309819 0.950796i \(-0.399732\pi\)
0.309819 + 0.950796i \(0.399732\pi\)
\(618\) 0 0
\(619\) 16.0862 0.646558 0.323279 0.946304i \(-0.395215\pi\)
0.323279 + 0.946304i \(0.395215\pi\)
\(620\) −5.17823 −0.207963
\(621\) 0 0
\(622\) 22.3052 0.894357
\(623\) −10.2988 −0.412614
\(624\) 0 0
\(625\) 23.9637 0.958549
\(626\) −50.8507 −2.03240
\(627\) 0 0
\(628\) 63.6521 2.54000
\(629\) −1.13416 −0.0452220
\(630\) 0 0
\(631\) 2.67650 0.106550 0.0532749 0.998580i \(-0.483034\pi\)
0.0532749 + 0.998580i \(0.483034\pi\)
\(632\) 16.0283 0.637571
\(633\) 0 0
\(634\) 33.6399 1.33601
\(635\) 0.263451 0.0104547
\(636\) 0 0
\(637\) 5.02935 0.199270
\(638\) −35.9202 −1.42210
\(639\) 0 0
\(640\) 4.54357 0.179600
\(641\) 47.2540 1.86642 0.933210 0.359333i \(-0.116996\pi\)
0.933210 + 0.359333i \(0.116996\pi\)
\(642\) 0 0
\(643\) 14.0330 0.553409 0.276704 0.960955i \(-0.410758\pi\)
0.276704 + 0.960955i \(0.410758\pi\)
\(644\) 2.70278 0.106504
\(645\) 0 0
\(646\) −0.901552 −0.0354711
\(647\) 18.8486 0.741017 0.370508 0.928829i \(-0.379183\pi\)
0.370508 + 0.928829i \(0.379183\pi\)
\(648\) 0 0
\(649\) −18.8678 −0.740625
\(650\) 56.1849 2.20375
\(651\) 0 0
\(652\) 57.3277 2.24513
\(653\) −42.9357 −1.68020 −0.840101 0.542429i \(-0.817505\pi\)
−0.840101 + 0.542429i \(0.817505\pi\)
\(654\) 0 0
\(655\) −1.20376 −0.0470346
\(656\) 4.44485 0.173542
\(657\) 0 0
\(658\) −14.3394 −0.559007
\(659\) 6.16411 0.240120 0.120060 0.992767i \(-0.461691\pi\)
0.120060 + 0.992767i \(0.461691\pi\)
\(660\) 0 0
\(661\) 17.9305 0.697416 0.348708 0.937231i \(-0.386620\pi\)
0.348708 + 0.937231i \(0.386620\pi\)
\(662\) −61.2555 −2.38076
\(663\) 0 0
\(664\) −40.0501 −1.55424
\(665\) −0.174500 −0.00676682
\(666\) 0 0
\(667\) −6.46655 −0.250386
\(668\) −1.33704 −0.0517317
\(669\) 0 0
\(670\) 3.96144 0.153044
\(671\) −26.7956 −1.03443
\(672\) 0 0
\(673\) 27.6482 1.06576 0.532879 0.846191i \(-0.321110\pi\)
0.532879 + 0.846191i \(0.321110\pi\)
\(674\) −28.9382 −1.11466
\(675\) 0 0
\(676\) 38.5249 1.48173
\(677\) 44.0086 1.69139 0.845694 0.533668i \(-0.179187\pi\)
0.845694 + 0.533668i \(0.179187\pi\)
\(678\) 0 0
\(679\) 10.8058 0.414688
\(680\) 0.406473 0.0155875
\(681\) 0 0
\(682\) −30.0530 −1.15079
\(683\) −12.3742 −0.473484 −0.236742 0.971573i \(-0.576080\pi\)
−0.236742 + 0.971573i \(0.576080\pi\)
\(684\) 0 0
\(685\) 3.12159 0.119270
\(686\) −2.26573 −0.0865060
\(687\) 0 0
\(688\) 0.375173 0.0143034
\(689\) −11.2144 −0.427234
\(690\) 0 0
\(691\) 29.0744 1.10604 0.553021 0.833168i \(-0.313475\pi\)
0.553021 + 0.833168i \(0.313475\pi\)
\(692\) 56.5160 2.14842
\(693\) 0 0
\(694\) −2.28380 −0.0866918
\(695\) 4.07278 0.154489
\(696\) 0 0
\(697\) 5.96023 0.225760
\(698\) −47.9561 −1.81516
\(699\) 0 0
\(700\) −15.4502 −0.583963
\(701\) −9.79244 −0.369855 −0.184928 0.982752i \(-0.559205\pi\)
−0.184928 + 0.982752i \(0.559205\pi\)
\(702\) 0 0
\(703\) −1.25050 −0.0471635
\(704\) 27.5789 1.03942
\(705\) 0 0
\(706\) 56.9960 2.14507
\(707\) 11.1783 0.420405
\(708\) 0 0
\(709\) 0.289511 0.0108728 0.00543641 0.999985i \(-0.498270\pi\)
0.00543641 + 0.999985i \(0.498270\pi\)
\(710\) 1.81556 0.0681366
\(711\) 0 0
\(712\) 26.4505 0.991275
\(713\) −5.41030 −0.202617
\(714\) 0 0
\(715\) −2.80185 −0.104783
\(716\) 12.2397 0.457418
\(717\) 0 0
\(718\) 56.3246 2.10201
\(719\) 35.0204 1.30604 0.653021 0.757340i \(-0.273501\pi\)
0.653021 + 0.757340i \(0.273501\pi\)
\(720\) 0 0
\(721\) 8.91300 0.331938
\(722\) 42.0549 1.56512
\(723\) 0 0
\(724\) −61.4844 −2.28505
\(725\) 36.9655 1.37287
\(726\) 0 0
\(727\) 17.1376 0.635597 0.317798 0.948158i \(-0.397057\pi\)
0.317798 + 0.948158i \(0.397057\pi\)
\(728\) −12.9169 −0.478731
\(729\) 0 0
\(730\) −2.13946 −0.0791848
\(731\) 0.503081 0.0186071
\(732\) 0 0
\(733\) 15.9224 0.588106 0.294053 0.955789i \(-0.404996\pi\)
0.294053 + 0.955789i \(0.404996\pi\)
\(734\) −39.4834 −1.45736
\(735\) 0 0
\(736\) 5.30599 0.195581
\(737\) 14.0339 0.516944
\(738\) 0 0
\(739\) −26.5239 −0.975697 −0.487848 0.872928i \(-0.662218\pi\)
−0.487848 + 0.872928i \(0.662218\pi\)
\(740\) 1.55856 0.0572938
\(741\) 0 0
\(742\) 5.05210 0.185469
\(743\) 23.2387 0.852544 0.426272 0.904595i \(-0.359827\pi\)
0.426272 + 0.904595i \(0.359827\pi\)
\(744\) 0 0
\(745\) 5.06276 0.185485
\(746\) 8.44556 0.309214
\(747\) 0 0
\(748\) 3.98066 0.145547
\(749\) −1.40233 −0.0512399
\(750\) 0 0
\(751\) −3.26661 −0.119200 −0.0596001 0.998222i \(-0.518983\pi\)
−0.0596001 + 0.998222i \(0.518983\pi\)
\(752\) −2.83532 −0.103393
\(753\) 0 0
\(754\) 85.4315 3.11123
\(755\) −5.12616 −0.186560
\(756\) 0 0
\(757\) 5.68679 0.206690 0.103345 0.994646i \(-0.467045\pi\)
0.103345 + 0.994646i \(0.467045\pi\)
\(758\) 56.1666 2.04006
\(759\) 0 0
\(760\) 0.448168 0.0162568
\(761\) 41.2816 1.49646 0.748229 0.663440i \(-0.230904\pi\)
0.748229 + 0.663440i \(0.230904\pi\)
\(762\) 0 0
\(763\) −7.84506 −0.284010
\(764\) 57.3339 2.07427
\(765\) 0 0
\(766\) −27.1986 −0.982726
\(767\) 44.8745 1.62033
\(768\) 0 0
\(769\) −15.3798 −0.554611 −0.277306 0.960782i \(-0.589441\pi\)
−0.277306 + 0.960782i \(0.589441\pi\)
\(770\) 1.26224 0.0454879
\(771\) 0 0
\(772\) −25.9803 −0.935053
\(773\) −43.4059 −1.56120 −0.780602 0.625029i \(-0.785087\pi\)
−0.780602 + 0.625029i \(0.785087\pi\)
\(774\) 0 0
\(775\) 30.9276 1.11095
\(776\) −27.7525 −0.996256
\(777\) 0 0
\(778\) −8.90090 −0.319113
\(779\) 6.57162 0.235453
\(780\) 0 0
\(781\) 6.43183 0.230149
\(782\) 1.17400 0.0419823
\(783\) 0 0
\(784\) −0.448003 −0.0160001
\(785\) 5.35152 0.191004
\(786\) 0 0
\(787\) 3.18555 0.113553 0.0567763 0.998387i \(-0.481918\pi\)
0.0567763 + 0.998387i \(0.481918\pi\)
\(788\) 69.0580 2.46009
\(789\) 0 0
\(790\) 3.72520 0.132537
\(791\) 5.51409 0.196058
\(792\) 0 0
\(793\) 63.7299 2.26311
\(794\) 19.2547 0.683324
\(795\) 0 0
\(796\) −24.3212 −0.862044
\(797\) −44.1424 −1.56361 −0.781803 0.623526i \(-0.785700\pi\)
−0.781803 + 0.623526i \(0.785700\pi\)
\(798\) 0 0
\(799\) −3.80196 −0.134504
\(800\) −30.3313 −1.07237
\(801\) 0 0
\(802\) −51.6278 −1.82304
\(803\) −7.57929 −0.267467
\(804\) 0 0
\(805\) 0.227234 0.00800896
\(806\) 71.4771 2.51767
\(807\) 0 0
\(808\) −28.7093 −1.00999
\(809\) −31.3325 −1.10159 −0.550797 0.834639i \(-0.685676\pi\)
−0.550797 + 0.834639i \(0.685676\pi\)
\(810\) 0 0
\(811\) −6.35201 −0.223049 −0.111525 0.993762i \(-0.535573\pi\)
−0.111525 + 0.993762i \(0.535573\pi\)
\(812\) −23.4927 −0.824433
\(813\) 0 0
\(814\) 9.04544 0.317043
\(815\) 4.81980 0.168830
\(816\) 0 0
\(817\) 0.554686 0.0194060
\(818\) 1.04186 0.0364278
\(819\) 0 0
\(820\) −8.19052 −0.286025
\(821\) −19.9589 −0.696571 −0.348285 0.937389i \(-0.613236\pi\)
−0.348285 + 0.937389i \(0.613236\pi\)
\(822\) 0 0
\(823\) −3.54944 −0.123726 −0.0618629 0.998085i \(-0.519704\pi\)
−0.0618629 + 0.998085i \(0.519704\pi\)
\(824\) −22.8913 −0.797455
\(825\) 0 0
\(826\) −20.2161 −0.703407
\(827\) 33.1724 1.15352 0.576758 0.816915i \(-0.304317\pi\)
0.576758 + 0.816915i \(0.304317\pi\)
\(828\) 0 0
\(829\) 17.7237 0.615570 0.307785 0.951456i \(-0.400412\pi\)
0.307785 + 0.951456i \(0.400412\pi\)
\(830\) −9.30819 −0.323092
\(831\) 0 0
\(832\) −65.5928 −2.27402
\(833\) −0.600740 −0.0208144
\(834\) 0 0
\(835\) −0.112411 −0.00389015
\(836\) 4.38898 0.151796
\(837\) 0 0
\(838\) −17.1919 −0.593883
\(839\) −38.2507 −1.32056 −0.660280 0.751019i \(-0.729562\pi\)
−0.660280 + 0.751019i \(0.729562\pi\)
\(840\) 0 0
\(841\) 27.2077 0.938196
\(842\) 17.8188 0.614078
\(843\) 0 0
\(844\) −19.9271 −0.685919
\(845\) 3.23896 0.111424
\(846\) 0 0
\(847\) −6.52837 −0.224318
\(848\) 0.998952 0.0343041
\(849\) 0 0
\(850\) −6.71111 −0.230189
\(851\) 1.62841 0.0558211
\(852\) 0 0
\(853\) 29.5909 1.01317 0.506587 0.862189i \(-0.330907\pi\)
0.506587 + 0.862189i \(0.330907\pi\)
\(854\) −28.7104 −0.982450
\(855\) 0 0
\(856\) 3.60159 0.123100
\(857\) 15.8769 0.542344 0.271172 0.962531i \(-0.412589\pi\)
0.271172 + 0.962531i \(0.412589\pi\)
\(858\) 0 0
\(859\) 42.5121 1.45049 0.725247 0.688489i \(-0.241726\pi\)
0.725247 + 0.688489i \(0.241726\pi\)
\(860\) −0.691331 −0.0235742
\(861\) 0 0
\(862\) 64.5316 2.19795
\(863\) −44.1539 −1.50302 −0.751508 0.659724i \(-0.770673\pi\)
−0.751508 + 0.659724i \(0.770673\pi\)
\(864\) 0 0
\(865\) 4.75156 0.161558
\(866\) −6.88589 −0.233992
\(867\) 0 0
\(868\) −19.6554 −0.667147
\(869\) 13.1970 0.447677
\(870\) 0 0
\(871\) −33.3777 −1.13096
\(872\) 20.1485 0.682313
\(873\) 0 0
\(874\) 1.29443 0.0437848
\(875\) −2.61622 −0.0884445
\(876\) 0 0
\(877\) 4.55932 0.153957 0.0769786 0.997033i \(-0.475473\pi\)
0.0769786 + 0.997033i \(0.475473\pi\)
\(878\) −77.0716 −2.60104
\(879\) 0 0
\(880\) 0.249582 0.00841340
\(881\) −30.1946 −1.01728 −0.508642 0.860978i \(-0.669852\pi\)
−0.508642 + 0.860978i \(0.669852\pi\)
\(882\) 0 0
\(883\) 50.7580 1.70814 0.854071 0.520156i \(-0.174126\pi\)
0.854071 + 0.520156i \(0.174126\pi\)
\(884\) −9.46747 −0.318425
\(885\) 0 0
\(886\) −47.4109 −1.59280
\(887\) 41.3459 1.38826 0.694129 0.719851i \(-0.255790\pi\)
0.694129 + 0.719851i \(0.255790\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 6.14747 0.206064
\(891\) 0 0
\(892\) −34.2202 −1.14578
\(893\) −4.19196 −0.140279
\(894\) 0 0
\(895\) 1.02904 0.0343971
\(896\) 17.2464 0.576160
\(897\) 0 0
\(898\) 6.36273 0.212327
\(899\) 47.0267 1.56843
\(900\) 0 0
\(901\) 1.33952 0.0446260
\(902\) −47.5355 −1.58276
\(903\) 0 0
\(904\) −14.1618 −0.471015
\(905\) −5.16927 −0.171832
\(906\) 0 0
\(907\) 6.47378 0.214958 0.107479 0.994207i \(-0.465722\pi\)
0.107479 + 0.994207i \(0.465722\pi\)
\(908\) −4.36175 −0.144750
\(909\) 0 0
\(910\) −3.00206 −0.0995175
\(911\) 17.7715 0.588797 0.294399 0.955683i \(-0.404881\pi\)
0.294399 + 0.955683i \(0.404881\pi\)
\(912\) 0 0
\(913\) −32.9754 −1.09133
\(914\) 17.6437 0.583603
\(915\) 0 0
\(916\) 17.9049 0.591593
\(917\) −4.56918 −0.150888
\(918\) 0 0
\(919\) −1.18053 −0.0389421 −0.0194710 0.999810i \(-0.506198\pi\)
−0.0194710 + 0.999810i \(0.506198\pi\)
\(920\) −0.583606 −0.0192409
\(921\) 0 0
\(922\) −6.07355 −0.200022
\(923\) −15.2973 −0.503515
\(924\) 0 0
\(925\) −9.30867 −0.306067
\(926\) −11.2361 −0.369242
\(927\) 0 0
\(928\) −46.1200 −1.51396
\(929\) 29.3261 0.962159 0.481080 0.876677i \(-0.340245\pi\)
0.481080 + 0.876677i \(0.340245\pi\)
\(930\) 0 0
\(931\) −0.662362 −0.0217081
\(932\) −44.2774 −1.45036
\(933\) 0 0
\(934\) −89.4440 −2.92670
\(935\) 0.334672 0.0109449
\(936\) 0 0
\(937\) 24.0660 0.786202 0.393101 0.919495i \(-0.371402\pi\)
0.393101 + 0.919495i \(0.371402\pi\)
\(938\) 15.0367 0.490966
\(939\) 0 0
\(940\) 5.22464 0.170409
\(941\) 33.5049 1.09223 0.546115 0.837710i \(-0.316106\pi\)
0.546115 + 0.837710i \(0.316106\pi\)
\(942\) 0 0
\(943\) −8.55758 −0.278673
\(944\) −3.99732 −0.130102
\(945\) 0 0
\(946\) −4.01229 −0.130451
\(947\) −0.188355 −0.00612073 −0.00306036 0.999995i \(-0.500974\pi\)
−0.00306036 + 0.999995i \(0.500974\pi\)
\(948\) 0 0
\(949\) 18.0263 0.585159
\(950\) −7.39952 −0.240072
\(951\) 0 0
\(952\) 1.54288 0.0500050
\(953\) 38.4600 1.24584 0.622921 0.782285i \(-0.285946\pi\)
0.622921 + 0.782285i \(0.285946\pi\)
\(954\) 0 0
\(955\) 4.82032 0.155982
\(956\) 74.1750 2.39899
\(957\) 0 0
\(958\) 70.2623 2.27007
\(959\) 11.8489 0.382620
\(960\) 0 0
\(961\) 8.34528 0.269203
\(962\) −21.5134 −0.693619
\(963\) 0 0
\(964\) 58.2452 1.87595
\(965\) −2.18428 −0.0703146
\(966\) 0 0
\(967\) 31.6878 1.01901 0.509505 0.860468i \(-0.329829\pi\)
0.509505 + 0.860468i \(0.329829\pi\)
\(968\) 16.7668 0.538906
\(969\) 0 0
\(970\) −6.45006 −0.207099
\(971\) 8.21103 0.263504 0.131752 0.991283i \(-0.457940\pi\)
0.131752 + 0.991283i \(0.457940\pi\)
\(972\) 0 0
\(973\) 15.4594 0.495604
\(974\) −89.8059 −2.87757
\(975\) 0 0
\(976\) −5.67691 −0.181713
\(977\) −37.8453 −1.21078 −0.605389 0.795929i \(-0.706983\pi\)
−0.605389 + 0.795929i \(0.706983\pi\)
\(978\) 0 0
\(979\) 21.7782 0.696033
\(980\) 0.825534 0.0263707
\(981\) 0 0
\(982\) 37.5253 1.19748
\(983\) 54.3534 1.73360 0.866802 0.498652i \(-0.166171\pi\)
0.866802 + 0.498652i \(0.166171\pi\)
\(984\) 0 0
\(985\) 5.80601 0.184995
\(986\) −10.2045 −0.324978
\(987\) 0 0
\(988\) −10.4386 −0.332097
\(989\) −0.722314 −0.0229682
\(990\) 0 0
\(991\) 11.9772 0.380469 0.190235 0.981739i \(-0.439075\pi\)
0.190235 + 0.981739i \(0.439075\pi\)
\(992\) −38.5868 −1.22513
\(993\) 0 0
\(994\) 6.89144 0.218583
\(995\) −2.04480 −0.0648244
\(996\) 0 0
\(997\) −41.7518 −1.32229 −0.661146 0.750258i \(-0.729929\pi\)
−0.661146 + 0.750258i \(0.729929\pi\)
\(998\) −90.1488 −2.85361
\(999\) 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 \(a_p\))