Properties

Label 8001.2.a.u.1.13
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
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: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(1.60620\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.60620 q^{2} +0.579871 q^{4} +3.54808 q^{5} +1.00000 q^{7} -2.28101 q^{8} +O(q^{10})\) \(q+1.60620 q^{2} +0.579871 q^{4} +3.54808 q^{5} +1.00000 q^{7} -2.28101 q^{8} +5.69892 q^{10} +2.78529 q^{11} +2.43579 q^{13} +1.60620 q^{14} -4.82349 q^{16} +6.06028 q^{17} -1.93658 q^{19} +2.05743 q^{20} +4.47373 q^{22} -3.19860 q^{23} +7.58887 q^{25} +3.91236 q^{26} +0.579871 q^{28} -2.42395 q^{29} +3.23823 q^{31} -3.18546 q^{32} +9.73400 q^{34} +3.54808 q^{35} -1.06507 q^{37} -3.11054 q^{38} -8.09320 q^{40} +3.51151 q^{41} +5.82642 q^{43} +1.61511 q^{44} -5.13759 q^{46} +2.39519 q^{47} +1.00000 q^{49} +12.1892 q^{50} +1.41244 q^{52} -11.1491 q^{53} +9.88243 q^{55} -2.28101 q^{56} -3.89334 q^{58} +2.80705 q^{59} +8.16721 q^{61} +5.20123 q^{62} +4.53050 q^{64} +8.64238 q^{65} +5.97952 q^{67} +3.51418 q^{68} +5.69892 q^{70} -12.1587 q^{71} +2.47476 q^{73} -1.71072 q^{74} -1.12297 q^{76} +2.78529 q^{77} -3.02097 q^{79} -17.1141 q^{80} +5.64018 q^{82} +10.1939 q^{83} +21.5023 q^{85} +9.35838 q^{86} -6.35327 q^{88} +2.30092 q^{89} +2.43579 q^{91} -1.85478 q^{92} +3.84715 q^{94} -6.87116 q^{95} -0.707978 q^{97} +1.60620 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} + O(q^{10}) \) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} - 4q^{10} + 9q^{11} - 25q^{13} + 6q^{14} + 34q^{16} + 17q^{17} - 5q^{19} + 21q^{20} + 5q^{22} + 14q^{23} + 28q^{25} + 8q^{26} + 22q^{28} + 17q^{29} + 5q^{31} + 53q^{32} - 19q^{34} + 10q^{35} - 15q^{37} + 22q^{38} - q^{40} + 17q^{41} + q^{43} + 33q^{44} + 10q^{46} + 31q^{47} + 18q^{49} + 35q^{50} - 70q^{52} + 35q^{53} + 4q^{55} + 21q^{56} + 3q^{58} + 46q^{59} - 5q^{61} + 10q^{62} + 63q^{64} + 12q^{65} + 6q^{67} + 56q^{68} - 4q^{70} + 22q^{71} - 16q^{73} - 18q^{74} + 32q^{76} + 9q^{77} + 46q^{79} + 30q^{80} - 12q^{82} + 46q^{83} + 4q^{85} - 18q^{86} + 30q^{88} + 42q^{89} - 25q^{91} + 48q^{92} + 3q^{94} + 2q^{95} - 35q^{97} + 6q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.60620 1.13575 0.567877 0.823114i \(-0.307765\pi\)
0.567877 + 0.823114i \(0.307765\pi\)
\(3\) 0 0
\(4\) 0.579871 0.289935
\(5\) 3.54808 1.58675 0.793375 0.608733i \(-0.208322\pi\)
0.793375 + 0.608733i \(0.208322\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.28101 −0.806458
\(9\) 0 0
\(10\) 5.69892 1.80216
\(11\) 2.78529 0.839796 0.419898 0.907571i \(-0.362066\pi\)
0.419898 + 0.907571i \(0.362066\pi\)
\(12\) 0 0
\(13\) 2.43579 0.675567 0.337784 0.941224i \(-0.390323\pi\)
0.337784 + 0.941224i \(0.390323\pi\)
\(14\) 1.60620 0.429274
\(15\) 0 0
\(16\) −4.82349 −1.20587
\(17\) 6.06028 1.46983 0.734917 0.678158i \(-0.237221\pi\)
0.734917 + 0.678158i \(0.237221\pi\)
\(18\) 0 0
\(19\) −1.93658 −0.444283 −0.222141 0.975014i \(-0.571305\pi\)
−0.222141 + 0.975014i \(0.571305\pi\)
\(20\) 2.05743 0.460055
\(21\) 0 0
\(22\) 4.47373 0.953802
\(23\) −3.19860 −0.666955 −0.333477 0.942758i \(-0.608222\pi\)
−0.333477 + 0.942758i \(0.608222\pi\)
\(24\) 0 0
\(25\) 7.58887 1.51777
\(26\) 3.91236 0.767277
\(27\) 0 0
\(28\) 0.579871 0.109585
\(29\) −2.42395 −0.450116 −0.225058 0.974345i \(-0.572257\pi\)
−0.225058 + 0.974345i \(0.572257\pi\)
\(30\) 0 0
\(31\) 3.23823 0.581603 0.290801 0.956783i \(-0.406078\pi\)
0.290801 + 0.956783i \(0.406078\pi\)
\(32\) −3.18546 −0.563116
\(33\) 0 0
\(34\) 9.73400 1.66937
\(35\) 3.54808 0.599735
\(36\) 0 0
\(37\) −1.06507 −0.175097 −0.0875484 0.996160i \(-0.527903\pi\)
−0.0875484 + 0.996160i \(0.527903\pi\)
\(38\) −3.11054 −0.504596
\(39\) 0 0
\(40\) −8.09320 −1.27965
\(41\) 3.51151 0.548406 0.274203 0.961672i \(-0.411586\pi\)
0.274203 + 0.961672i \(0.411586\pi\)
\(42\) 0 0
\(43\) 5.82642 0.888521 0.444260 0.895898i \(-0.353466\pi\)
0.444260 + 0.895898i \(0.353466\pi\)
\(44\) 1.61511 0.243487
\(45\) 0 0
\(46\) −5.13759 −0.757496
\(47\) 2.39519 0.349375 0.174687 0.984624i \(-0.444109\pi\)
0.174687 + 0.984624i \(0.444109\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 12.1892 1.72382
\(51\) 0 0
\(52\) 1.41244 0.195871
\(53\) −11.1491 −1.53145 −0.765723 0.643171i \(-0.777619\pi\)
−0.765723 + 0.643171i \(0.777619\pi\)
\(54\) 0 0
\(55\) 9.88243 1.33255
\(56\) −2.28101 −0.304813
\(57\) 0 0
\(58\) −3.89334 −0.511221
\(59\) 2.80705 0.365447 0.182723 0.983164i \(-0.441509\pi\)
0.182723 + 0.983164i \(0.441509\pi\)
\(60\) 0 0
\(61\) 8.16721 1.04570 0.522852 0.852423i \(-0.324868\pi\)
0.522852 + 0.852423i \(0.324868\pi\)
\(62\) 5.20123 0.660557
\(63\) 0 0
\(64\) 4.53050 0.566312
\(65\) 8.64238 1.07196
\(66\) 0 0
\(67\) 5.97952 0.730515 0.365257 0.930907i \(-0.380981\pi\)
0.365257 + 0.930907i \(0.380981\pi\)
\(68\) 3.51418 0.426157
\(69\) 0 0
\(70\) 5.69892 0.681151
\(71\) −12.1587 −1.44297 −0.721484 0.692431i \(-0.756540\pi\)
−0.721484 + 0.692431i \(0.756540\pi\)
\(72\) 0 0
\(73\) 2.47476 0.289649 0.144824 0.989457i \(-0.453738\pi\)
0.144824 + 0.989457i \(0.453738\pi\)
\(74\) −1.71072 −0.198867
\(75\) 0 0
\(76\) −1.12297 −0.128813
\(77\) 2.78529 0.317413
\(78\) 0 0
\(79\) −3.02097 −0.339885 −0.169943 0.985454i \(-0.554358\pi\)
−0.169943 + 0.985454i \(0.554358\pi\)
\(80\) −17.1141 −1.91342
\(81\) 0 0
\(82\) 5.64018 0.622854
\(83\) 10.1939 1.11893 0.559465 0.828854i \(-0.311007\pi\)
0.559465 + 0.828854i \(0.311007\pi\)
\(84\) 0 0
\(85\) 21.5023 2.33226
\(86\) 9.35838 1.00914
\(87\) 0 0
\(88\) −6.35327 −0.677261
\(89\) 2.30092 0.243897 0.121949 0.992536i \(-0.461086\pi\)
0.121949 + 0.992536i \(0.461086\pi\)
\(90\) 0 0
\(91\) 2.43579 0.255340
\(92\) −1.85478 −0.193374
\(93\) 0 0
\(94\) 3.84715 0.396804
\(95\) −6.87116 −0.704966
\(96\) 0 0
\(97\) −0.707978 −0.0718843 −0.0359422 0.999354i \(-0.511443\pi\)
−0.0359422 + 0.999354i \(0.511443\pi\)
\(98\) 1.60620 0.162250
\(99\) 0 0
\(100\) 4.40057 0.440057
\(101\) −11.1926 −1.11371 −0.556853 0.830611i \(-0.687991\pi\)
−0.556853 + 0.830611i \(0.687991\pi\)
\(102\) 0 0
\(103\) 9.42373 0.928548 0.464274 0.885692i \(-0.346315\pi\)
0.464274 + 0.885692i \(0.346315\pi\)
\(104\) −5.55606 −0.544817
\(105\) 0 0
\(106\) −17.9076 −1.73934
\(107\) 6.56198 0.634371 0.317185 0.948364i \(-0.397262\pi\)
0.317185 + 0.948364i \(0.397262\pi\)
\(108\) 0 0
\(109\) −15.5034 −1.48495 −0.742476 0.669872i \(-0.766349\pi\)
−0.742476 + 0.669872i \(0.766349\pi\)
\(110\) 15.8731 1.51344
\(111\) 0 0
\(112\) −4.82349 −0.455777
\(113\) −14.8683 −1.39869 −0.699344 0.714786i \(-0.746524\pi\)
−0.699344 + 0.714786i \(0.746524\pi\)
\(114\) 0 0
\(115\) −11.3489 −1.05829
\(116\) −1.40558 −0.130505
\(117\) 0 0
\(118\) 4.50868 0.415057
\(119\) 6.06028 0.555545
\(120\) 0 0
\(121\) −3.24216 −0.294742
\(122\) 13.1182 1.18766
\(123\) 0 0
\(124\) 1.87775 0.168627
\(125\) 9.18552 0.821578
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 13.6478 1.20631
\(129\) 0 0
\(130\) 13.8814 1.21748
\(131\) 16.9371 1.47981 0.739903 0.672714i \(-0.234871\pi\)
0.739903 + 0.672714i \(0.234871\pi\)
\(132\) 0 0
\(133\) −1.93658 −0.167923
\(134\) 9.60429 0.829684
\(135\) 0 0
\(136\) −13.8235 −1.18536
\(137\) 8.14622 0.695979 0.347989 0.937498i \(-0.386865\pi\)
0.347989 + 0.937498i \(0.386865\pi\)
\(138\) 0 0
\(139\) −10.0461 −0.852099 −0.426050 0.904700i \(-0.640095\pi\)
−0.426050 + 0.904700i \(0.640095\pi\)
\(140\) 2.05743 0.173884
\(141\) 0 0
\(142\) −19.5292 −1.63886
\(143\) 6.78439 0.567339
\(144\) 0 0
\(145\) −8.60037 −0.714222
\(146\) 3.97495 0.328969
\(147\) 0 0
\(148\) −0.617604 −0.0507667
\(149\) 4.50378 0.368964 0.184482 0.982836i \(-0.440939\pi\)
0.184482 + 0.982836i \(0.440939\pi\)
\(150\) 0 0
\(151\) −13.3733 −1.08831 −0.544154 0.838986i \(-0.683149\pi\)
−0.544154 + 0.838986i \(0.683149\pi\)
\(152\) 4.41736 0.358296
\(153\) 0 0
\(154\) 4.47373 0.360503
\(155\) 11.4895 0.922858
\(156\) 0 0
\(157\) −7.76796 −0.619951 −0.309975 0.950745i \(-0.600321\pi\)
−0.309975 + 0.950745i \(0.600321\pi\)
\(158\) −4.85227 −0.386026
\(159\) 0 0
\(160\) −11.3023 −0.893524
\(161\) −3.19860 −0.252085
\(162\) 0 0
\(163\) 11.3737 0.890858 0.445429 0.895317i \(-0.353051\pi\)
0.445429 + 0.895317i \(0.353051\pi\)
\(164\) 2.03622 0.159002
\(165\) 0 0
\(166\) 16.3735 1.27083
\(167\) −2.47601 −0.191600 −0.0957998 0.995401i \(-0.530541\pi\)
−0.0957998 + 0.995401i \(0.530541\pi\)
\(168\) 0 0
\(169\) −7.06692 −0.543609
\(170\) 34.5370 2.64887
\(171\) 0 0
\(172\) 3.37857 0.257614
\(173\) 10.7831 0.819820 0.409910 0.912126i \(-0.365560\pi\)
0.409910 + 0.912126i \(0.365560\pi\)
\(174\) 0 0
\(175\) 7.58887 0.573665
\(176\) −13.4348 −1.01269
\(177\) 0 0
\(178\) 3.69573 0.277007
\(179\) 12.0233 0.898667 0.449333 0.893364i \(-0.351662\pi\)
0.449333 + 0.893364i \(0.351662\pi\)
\(180\) 0 0
\(181\) 17.0378 1.26641 0.633204 0.773985i \(-0.281739\pi\)
0.633204 + 0.773985i \(0.281739\pi\)
\(182\) 3.91236 0.290004
\(183\) 0 0
\(184\) 7.29604 0.537871
\(185\) −3.77896 −0.277835
\(186\) 0 0
\(187\) 16.8796 1.23436
\(188\) 1.38890 0.101296
\(189\) 0 0
\(190\) −11.0364 −0.800667
\(191\) −13.9297 −1.00792 −0.503959 0.863727i \(-0.668124\pi\)
−0.503959 + 0.863727i \(0.668124\pi\)
\(192\) 0 0
\(193\) −23.5610 −1.69596 −0.847979 0.530030i \(-0.822181\pi\)
−0.847979 + 0.530030i \(0.822181\pi\)
\(194\) −1.13715 −0.0816428
\(195\) 0 0
\(196\) 0.579871 0.0414193
\(197\) 6.52931 0.465194 0.232597 0.972573i \(-0.425278\pi\)
0.232597 + 0.972573i \(0.425278\pi\)
\(198\) 0 0
\(199\) 19.0272 1.34881 0.674403 0.738364i \(-0.264401\pi\)
0.674403 + 0.738364i \(0.264401\pi\)
\(200\) −17.3103 −1.22402
\(201\) 0 0
\(202\) −17.9776 −1.26490
\(203\) −2.42395 −0.170128
\(204\) 0 0
\(205\) 12.4591 0.870182
\(206\) 15.1364 1.05460
\(207\) 0 0
\(208\) −11.7490 −0.814648
\(209\) −5.39395 −0.373107
\(210\) 0 0
\(211\) −12.5670 −0.865151 −0.432575 0.901598i \(-0.642395\pi\)
−0.432575 + 0.901598i \(0.642395\pi\)
\(212\) −6.46503 −0.444020
\(213\) 0 0
\(214\) 10.5398 0.720489
\(215\) 20.6726 1.40986
\(216\) 0 0
\(217\) 3.23823 0.219825
\(218\) −24.9015 −1.68654
\(219\) 0 0
\(220\) 5.73053 0.386352
\(221\) 14.7616 0.992971
\(222\) 0 0
\(223\) 27.9633 1.87256 0.936280 0.351255i \(-0.114245\pi\)
0.936280 + 0.351255i \(0.114245\pi\)
\(224\) −3.18546 −0.212838
\(225\) 0 0
\(226\) −23.8814 −1.58856
\(227\) 17.2281 1.14347 0.571733 0.820440i \(-0.306271\pi\)
0.571733 + 0.820440i \(0.306271\pi\)
\(228\) 0 0
\(229\) −17.7667 −1.17406 −0.587030 0.809565i \(-0.699703\pi\)
−0.587030 + 0.809565i \(0.699703\pi\)
\(230\) −18.2286 −1.20196
\(231\) 0 0
\(232\) 5.52905 0.363000
\(233\) −14.0286 −0.919043 −0.459521 0.888167i \(-0.651979\pi\)
−0.459521 + 0.888167i \(0.651979\pi\)
\(234\) 0 0
\(235\) 8.49834 0.554370
\(236\) 1.62773 0.105956
\(237\) 0 0
\(238\) 9.73400 0.630962
\(239\) 21.4428 1.38702 0.693510 0.720447i \(-0.256063\pi\)
0.693510 + 0.720447i \(0.256063\pi\)
\(240\) 0 0
\(241\) −4.57437 −0.294661 −0.147331 0.989087i \(-0.547068\pi\)
−0.147331 + 0.989087i \(0.547068\pi\)
\(242\) −5.20755 −0.334754
\(243\) 0 0
\(244\) 4.73593 0.303187
\(245\) 3.54808 0.226679
\(246\) 0 0
\(247\) −4.71712 −0.300143
\(248\) −7.38642 −0.469038
\(249\) 0 0
\(250\) 14.7538 0.933110
\(251\) −11.2949 −0.712925 −0.356462 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(252\) 0 0
\(253\) −8.90903 −0.560106
\(254\) 1.60620 0.100782
\(255\) 0 0
\(256\) 12.8601 0.803755
\(257\) 27.1572 1.69402 0.847010 0.531576i \(-0.178400\pi\)
0.847010 + 0.531576i \(0.178400\pi\)
\(258\) 0 0
\(259\) −1.06507 −0.0661803
\(260\) 5.01147 0.310798
\(261\) 0 0
\(262\) 27.2044 1.68069
\(263\) −1.15314 −0.0711058 −0.0355529 0.999368i \(-0.511319\pi\)
−0.0355529 + 0.999368i \(0.511319\pi\)
\(264\) 0 0
\(265\) −39.5579 −2.43002
\(266\) −3.11054 −0.190719
\(267\) 0 0
\(268\) 3.46735 0.211802
\(269\) −15.9024 −0.969584 −0.484792 0.874629i \(-0.661105\pi\)
−0.484792 + 0.874629i \(0.661105\pi\)
\(270\) 0 0
\(271\) 3.54720 0.215477 0.107739 0.994179i \(-0.465639\pi\)
0.107739 + 0.994179i \(0.465639\pi\)
\(272\) −29.2317 −1.77243
\(273\) 0 0
\(274\) 13.0844 0.790460
\(275\) 21.1372 1.27462
\(276\) 0 0
\(277\) 0.879357 0.0528355 0.0264177 0.999651i \(-0.491590\pi\)
0.0264177 + 0.999651i \(0.491590\pi\)
\(278\) −16.1360 −0.967774
\(279\) 0 0
\(280\) −8.09320 −0.483661
\(281\) −15.5204 −0.925868 −0.462934 0.886393i \(-0.653203\pi\)
−0.462934 + 0.886393i \(0.653203\pi\)
\(282\) 0 0
\(283\) −27.1358 −1.61306 −0.806528 0.591196i \(-0.798656\pi\)
−0.806528 + 0.591196i \(0.798656\pi\)
\(284\) −7.05046 −0.418368
\(285\) 0 0
\(286\) 10.8971 0.644357
\(287\) 3.51151 0.207278
\(288\) 0 0
\(289\) 19.7270 1.16041
\(290\) −13.8139 −0.811180
\(291\) 0 0
\(292\) 1.43504 0.0839794
\(293\) 13.8186 0.807294 0.403647 0.914915i \(-0.367742\pi\)
0.403647 + 0.914915i \(0.367742\pi\)
\(294\) 0 0
\(295\) 9.95964 0.579873
\(296\) 2.42944 0.141208
\(297\) 0 0
\(298\) 7.23396 0.419052
\(299\) −7.79113 −0.450573
\(300\) 0 0
\(301\) 5.82642 0.335829
\(302\) −21.4802 −1.23605
\(303\) 0 0
\(304\) 9.34110 0.535749
\(305\) 28.9779 1.65927
\(306\) 0 0
\(307\) −24.8063 −1.41577 −0.707885 0.706328i \(-0.750350\pi\)
−0.707885 + 0.706328i \(0.750350\pi\)
\(308\) 1.61511 0.0920293
\(309\) 0 0
\(310\) 18.4544 1.04814
\(311\) 14.3789 0.815355 0.407677 0.913126i \(-0.366339\pi\)
0.407677 + 0.913126i \(0.366339\pi\)
\(312\) 0 0
\(313\) 5.43949 0.307458 0.153729 0.988113i \(-0.450872\pi\)
0.153729 + 0.988113i \(0.450872\pi\)
\(314\) −12.4769 −0.704111
\(315\) 0 0
\(316\) −1.75177 −0.0985448
\(317\) 0.807453 0.0453511 0.0226755 0.999743i \(-0.492782\pi\)
0.0226755 + 0.999743i \(0.492782\pi\)
\(318\) 0 0
\(319\) −6.75141 −0.378006
\(320\) 16.0746 0.898596
\(321\) 0 0
\(322\) −5.13759 −0.286307
\(323\) −11.7362 −0.653022
\(324\) 0 0
\(325\) 18.4849 1.02536
\(326\) 18.2684 1.01180
\(327\) 0 0
\(328\) −8.00978 −0.442266
\(329\) 2.39519 0.132051
\(330\) 0 0
\(331\) −4.60565 −0.253150 −0.126575 0.991957i \(-0.540398\pi\)
−0.126575 + 0.991957i \(0.540398\pi\)
\(332\) 5.91117 0.324417
\(333\) 0 0
\(334\) −3.97697 −0.217610
\(335\) 21.2158 1.15914
\(336\) 0 0
\(337\) 3.71254 0.202235 0.101118 0.994874i \(-0.467758\pi\)
0.101118 + 0.994874i \(0.467758\pi\)
\(338\) −11.3509 −0.617406
\(339\) 0 0
\(340\) 12.4686 0.676204
\(341\) 9.01940 0.488428
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −13.2901 −0.716555
\(345\) 0 0
\(346\) 17.3197 0.931113
\(347\) 5.38943 0.289320 0.144660 0.989481i \(-0.453791\pi\)
0.144660 + 0.989481i \(0.453791\pi\)
\(348\) 0 0
\(349\) 16.3138 0.873257 0.436629 0.899642i \(-0.356172\pi\)
0.436629 + 0.899642i \(0.356172\pi\)
\(350\) 12.1892 0.651542
\(351\) 0 0
\(352\) −8.87244 −0.472903
\(353\) −3.10479 −0.165251 −0.0826256 0.996581i \(-0.526331\pi\)
−0.0826256 + 0.996581i \(0.526331\pi\)
\(354\) 0 0
\(355\) −43.1399 −2.28963
\(356\) 1.33424 0.0707144
\(357\) 0 0
\(358\) 19.3119 1.02066
\(359\) 0.513047 0.0270776 0.0135388 0.999908i \(-0.495690\pi\)
0.0135388 + 0.999908i \(0.495690\pi\)
\(360\) 0 0
\(361\) −15.2496 −0.802613
\(362\) 27.3660 1.43833
\(363\) 0 0
\(364\) 1.41244 0.0740322
\(365\) 8.78064 0.459600
\(366\) 0 0
\(367\) 2.45004 0.127891 0.0639456 0.997953i \(-0.479632\pi\)
0.0639456 + 0.997953i \(0.479632\pi\)
\(368\) 15.4284 0.804262
\(369\) 0 0
\(370\) −6.06976 −0.315552
\(371\) −11.1491 −0.578832
\(372\) 0 0
\(373\) −28.9564 −1.49930 −0.749652 0.661832i \(-0.769779\pi\)
−0.749652 + 0.661832i \(0.769779\pi\)
\(374\) 27.1120 1.40193
\(375\) 0 0
\(376\) −5.46346 −0.281756
\(377\) −5.90424 −0.304084
\(378\) 0 0
\(379\) 10.9005 0.559919 0.279959 0.960012i \(-0.409679\pi\)
0.279959 + 0.960012i \(0.409679\pi\)
\(380\) −3.98438 −0.204395
\(381\) 0 0
\(382\) −22.3739 −1.14475
\(383\) 16.5606 0.846208 0.423104 0.906081i \(-0.360941\pi\)
0.423104 + 0.906081i \(0.360941\pi\)
\(384\) 0 0
\(385\) 9.88243 0.503655
\(386\) −37.8436 −1.92619
\(387\) 0 0
\(388\) −0.410536 −0.0208418
\(389\) 12.9612 0.657157 0.328578 0.944477i \(-0.393431\pi\)
0.328578 + 0.944477i \(0.393431\pi\)
\(390\) 0 0
\(391\) −19.3844 −0.980312
\(392\) −2.28101 −0.115208
\(393\) 0 0
\(394\) 10.4874 0.528346
\(395\) −10.7186 −0.539313
\(396\) 0 0
\(397\) −31.8068 −1.59634 −0.798168 0.602435i \(-0.794197\pi\)
−0.798168 + 0.602435i \(0.794197\pi\)
\(398\) 30.5615 1.53191
\(399\) 0 0
\(400\) −36.6049 −1.83024
\(401\) −36.4319 −1.81932 −0.909660 0.415353i \(-0.863658\pi\)
−0.909660 + 0.415353i \(0.863658\pi\)
\(402\) 0 0
\(403\) 7.88765 0.392912
\(404\) −6.49027 −0.322903
\(405\) 0 0
\(406\) −3.89334 −0.193223
\(407\) −2.96653 −0.147046
\(408\) 0 0
\(409\) −0.0186891 −0.000924115 0 −0.000462058 1.00000i \(-0.500147\pi\)
−0.000462058 1.00000i \(0.500147\pi\)
\(410\) 20.0118 0.988313
\(411\) 0 0
\(412\) 5.46455 0.269219
\(413\) 2.80705 0.138126
\(414\) 0 0
\(415\) 36.1689 1.77546
\(416\) −7.75913 −0.380423
\(417\) 0 0
\(418\) −8.66375 −0.423758
\(419\) 20.4211 0.997637 0.498819 0.866706i \(-0.333767\pi\)
0.498819 + 0.866706i \(0.333767\pi\)
\(420\) 0 0
\(421\) 20.7357 1.01060 0.505299 0.862944i \(-0.331382\pi\)
0.505299 + 0.862944i \(0.331382\pi\)
\(422\) −20.1852 −0.982598
\(423\) 0 0
\(424\) 25.4312 1.23505
\(425\) 45.9907 2.23087
\(426\) 0 0
\(427\) 8.16721 0.395239
\(428\) 3.80510 0.183927
\(429\) 0 0
\(430\) 33.2043 1.60125
\(431\) −26.7720 −1.28956 −0.644782 0.764367i \(-0.723052\pi\)
−0.644782 + 0.764367i \(0.723052\pi\)
\(432\) 0 0
\(433\) −7.45697 −0.358359 −0.179179 0.983816i \(-0.557344\pi\)
−0.179179 + 0.983816i \(0.557344\pi\)
\(434\) 5.20123 0.249667
\(435\) 0 0
\(436\) −8.98995 −0.430540
\(437\) 6.19436 0.296317
\(438\) 0 0
\(439\) 0.491516 0.0234588 0.0117294 0.999931i \(-0.496266\pi\)
0.0117294 + 0.999931i \(0.496266\pi\)
\(440\) −22.5419 −1.07464
\(441\) 0 0
\(442\) 23.7100 1.12777
\(443\) −16.3582 −0.777203 −0.388602 0.921406i \(-0.627042\pi\)
−0.388602 + 0.921406i \(0.627042\pi\)
\(444\) 0 0
\(445\) 8.16385 0.387004
\(446\) 44.9146 2.12677
\(447\) 0 0
\(448\) 4.53050 0.214046
\(449\) −21.0828 −0.994957 −0.497478 0.867476i \(-0.665741\pi\)
−0.497478 + 0.867476i \(0.665741\pi\)
\(450\) 0 0
\(451\) 9.78057 0.460549
\(452\) −8.62167 −0.405529
\(453\) 0 0
\(454\) 27.6717 1.29870
\(455\) 8.64238 0.405161
\(456\) 0 0
\(457\) 9.58237 0.448245 0.224122 0.974561i \(-0.428049\pi\)
0.224122 + 0.974561i \(0.428049\pi\)
\(458\) −28.5369 −1.33344
\(459\) 0 0
\(460\) −6.58089 −0.306836
\(461\) 26.0159 1.21168 0.605841 0.795586i \(-0.292837\pi\)
0.605841 + 0.795586i \(0.292837\pi\)
\(462\) 0 0
\(463\) −15.0319 −0.698590 −0.349295 0.937013i \(-0.613579\pi\)
−0.349295 + 0.937013i \(0.613579\pi\)
\(464\) 11.6919 0.542783
\(465\) 0 0
\(466\) −22.5327 −1.04381
\(467\) 7.12952 0.329915 0.164957 0.986301i \(-0.447251\pi\)
0.164957 + 0.986301i \(0.447251\pi\)
\(468\) 0 0
\(469\) 5.97952 0.276109
\(470\) 13.6500 0.629628
\(471\) 0 0
\(472\) −6.40290 −0.294718
\(473\) 16.2283 0.746177
\(474\) 0 0
\(475\) −14.6965 −0.674321
\(476\) 3.51418 0.161072
\(477\) 0 0
\(478\) 34.4414 1.57531
\(479\) 2.79072 0.127511 0.0637557 0.997966i \(-0.479692\pi\)
0.0637557 + 0.997966i \(0.479692\pi\)
\(480\) 0 0
\(481\) −2.59429 −0.118290
\(482\) −7.34735 −0.334662
\(483\) 0 0
\(484\) −1.88004 −0.0854561
\(485\) −2.51196 −0.114062
\(486\) 0 0
\(487\) 32.2763 1.46258 0.731289 0.682067i \(-0.238919\pi\)
0.731289 + 0.682067i \(0.238919\pi\)
\(488\) −18.6295 −0.843317
\(489\) 0 0
\(490\) 5.69892 0.257451
\(491\) 30.0985 1.35833 0.679163 0.733987i \(-0.262343\pi\)
0.679163 + 0.733987i \(0.262343\pi\)
\(492\) 0 0
\(493\) −14.6898 −0.661596
\(494\) −7.57662 −0.340888
\(495\) 0 0
\(496\) −15.6196 −0.701339
\(497\) −12.1587 −0.545391
\(498\) 0 0
\(499\) 31.8366 1.42520 0.712602 0.701569i \(-0.247517\pi\)
0.712602 + 0.701569i \(0.247517\pi\)
\(500\) 5.32642 0.238205
\(501\) 0 0
\(502\) −18.1418 −0.809707
\(503\) 42.3948 1.89029 0.945145 0.326651i \(-0.105920\pi\)
0.945145 + 0.326651i \(0.105920\pi\)
\(504\) 0 0
\(505\) −39.7123 −1.76717
\(506\) −14.3097 −0.636142
\(507\) 0 0
\(508\) 0.579871 0.0257276
\(509\) −15.5022 −0.687125 −0.343562 0.939130i \(-0.611634\pi\)
−0.343562 + 0.939130i \(0.611634\pi\)
\(510\) 0 0
\(511\) 2.47476 0.109477
\(512\) −6.63978 −0.293440
\(513\) 0 0
\(514\) 43.6199 1.92399
\(515\) 33.4362 1.47337
\(516\) 0 0
\(517\) 6.67131 0.293404
\(518\) −1.71072 −0.0751645
\(519\) 0 0
\(520\) −19.7133 −0.864487
\(521\) −37.1898 −1.62931 −0.814657 0.579943i \(-0.803075\pi\)
−0.814657 + 0.579943i \(0.803075\pi\)
\(522\) 0 0
\(523\) −43.4445 −1.89970 −0.949848 0.312712i \(-0.898763\pi\)
−0.949848 + 0.312712i \(0.898763\pi\)
\(524\) 9.82136 0.429048
\(525\) 0 0
\(526\) −1.85217 −0.0807586
\(527\) 19.6246 0.854859
\(528\) 0 0
\(529\) −12.7689 −0.555172
\(530\) −63.5378 −2.75990
\(531\) 0 0
\(532\) −1.12297 −0.0486869
\(533\) 8.55331 0.370485
\(534\) 0 0
\(535\) 23.2824 1.00659
\(536\) −13.6393 −0.589130
\(537\) 0 0
\(538\) −25.5423 −1.10121
\(539\) 2.78529 0.119971
\(540\) 0 0
\(541\) −5.77004 −0.248074 −0.124037 0.992278i \(-0.539584\pi\)
−0.124037 + 0.992278i \(0.539584\pi\)
\(542\) 5.69751 0.244729
\(543\) 0 0
\(544\) −19.3048 −0.827686
\(545\) −55.0072 −2.35625
\(546\) 0 0
\(547\) −34.9425 −1.49403 −0.747016 0.664806i \(-0.768514\pi\)
−0.747016 + 0.664806i \(0.768514\pi\)
\(548\) 4.72376 0.201789
\(549\) 0 0
\(550\) 33.9505 1.44766
\(551\) 4.69419 0.199979
\(552\) 0 0
\(553\) −3.02097 −0.128465
\(554\) 1.41242 0.0600080
\(555\) 0 0
\(556\) −5.82544 −0.247054
\(557\) 17.9223 0.759392 0.379696 0.925111i \(-0.376029\pi\)
0.379696 + 0.925111i \(0.376029\pi\)
\(558\) 0 0
\(559\) 14.1919 0.600255
\(560\) −17.1141 −0.723204
\(561\) 0 0
\(562\) −24.9288 −1.05156
\(563\) −17.5956 −0.741568 −0.370784 0.928719i \(-0.620911\pi\)
−0.370784 + 0.928719i \(0.620911\pi\)
\(564\) 0 0
\(565\) −52.7537 −2.21937
\(566\) −43.5855 −1.83203
\(567\) 0 0
\(568\) 27.7340 1.16369
\(569\) −32.1201 −1.34654 −0.673272 0.739395i \(-0.735112\pi\)
−0.673272 + 0.739395i \(0.735112\pi\)
\(570\) 0 0
\(571\) 17.9633 0.751739 0.375870 0.926673i \(-0.377344\pi\)
0.375870 + 0.926673i \(0.377344\pi\)
\(572\) 3.93407 0.164492
\(573\) 0 0
\(574\) 5.64018 0.235416
\(575\) −24.2738 −1.01229
\(576\) 0 0
\(577\) −29.0564 −1.20963 −0.604816 0.796365i \(-0.706753\pi\)
−0.604816 + 0.796365i \(0.706753\pi\)
\(578\) 31.6854 1.31794
\(579\) 0 0
\(580\) −4.98711 −0.207078
\(581\) 10.1939 0.422916
\(582\) 0 0
\(583\) −31.0535 −1.28610
\(584\) −5.64494 −0.233589
\(585\) 0 0
\(586\) 22.1955 0.916886
\(587\) 6.10638 0.252037 0.126019 0.992028i \(-0.459780\pi\)
0.126019 + 0.992028i \(0.459780\pi\)
\(588\) 0 0
\(589\) −6.27110 −0.258396
\(590\) 15.9971 0.658592
\(591\) 0 0
\(592\) 5.13736 0.211144
\(593\) 9.02500 0.370612 0.185306 0.982681i \(-0.440672\pi\)
0.185306 + 0.982681i \(0.440672\pi\)
\(594\) 0 0
\(595\) 21.5023 0.881510
\(596\) 2.61161 0.106976
\(597\) 0 0
\(598\) −12.5141 −0.511739
\(599\) −5.06194 −0.206825 −0.103413 0.994639i \(-0.532976\pi\)
−0.103413 + 0.994639i \(0.532976\pi\)
\(600\) 0 0
\(601\) −8.99790 −0.367032 −0.183516 0.983017i \(-0.558748\pi\)
−0.183516 + 0.983017i \(0.558748\pi\)
\(602\) 9.35838 0.381419
\(603\) 0 0
\(604\) −7.75481 −0.315539
\(605\) −11.5034 −0.467682
\(606\) 0 0
\(607\) 12.7806 0.518749 0.259375 0.965777i \(-0.416484\pi\)
0.259375 + 0.965777i \(0.416484\pi\)
\(608\) 6.16892 0.250183
\(609\) 0 0
\(610\) 46.5443 1.88452
\(611\) 5.83419 0.236026
\(612\) 0 0
\(613\) −17.1381 −0.692201 −0.346101 0.938197i \(-0.612494\pi\)
−0.346101 + 0.938197i \(0.612494\pi\)
\(614\) −39.8438 −1.60797
\(615\) 0 0
\(616\) −6.35327 −0.255980
\(617\) 45.8447 1.84564 0.922820 0.385232i \(-0.125879\pi\)
0.922820 + 0.385232i \(0.125879\pi\)
\(618\) 0 0
\(619\) 46.5262 1.87005 0.935023 0.354587i \(-0.115378\pi\)
0.935023 + 0.354587i \(0.115378\pi\)
\(620\) 6.66242 0.267569
\(621\) 0 0
\(622\) 23.0954 0.926042
\(623\) 2.30092 0.0921845
\(624\) 0 0
\(625\) −5.35340 −0.214136
\(626\) 8.73690 0.349197
\(627\) 0 0
\(628\) −4.50441 −0.179746
\(629\) −6.45463 −0.257363
\(630\) 0 0
\(631\) −13.7725 −0.548273 −0.274136 0.961691i \(-0.588392\pi\)
−0.274136 + 0.961691i \(0.588392\pi\)
\(632\) 6.89085 0.274103
\(633\) 0 0
\(634\) 1.29693 0.0515076
\(635\) 3.54808 0.140801
\(636\) 0 0
\(637\) 2.43579 0.0965096
\(638\) −10.8441 −0.429322
\(639\) 0 0
\(640\) 48.4235 1.91411
\(641\) 0.860650 0.0339937 0.0169968 0.999856i \(-0.494589\pi\)
0.0169968 + 0.999856i \(0.494589\pi\)
\(642\) 0 0
\(643\) −41.6792 −1.64367 −0.821834 0.569727i \(-0.807049\pi\)
−0.821834 + 0.569727i \(0.807049\pi\)
\(644\) −1.85478 −0.0730884
\(645\) 0 0
\(646\) −18.8507 −0.741672
\(647\) −19.3518 −0.760798 −0.380399 0.924822i \(-0.624213\pi\)
−0.380399 + 0.924822i \(0.624213\pi\)
\(648\) 0 0
\(649\) 7.81845 0.306901
\(650\) 29.6904 1.16455
\(651\) 0 0
\(652\) 6.59529 0.258291
\(653\) −8.67139 −0.339338 −0.169669 0.985501i \(-0.554270\pi\)
−0.169669 + 0.985501i \(0.554270\pi\)
\(654\) 0 0
\(655\) 60.0944 2.34808
\(656\) −16.9377 −0.661308
\(657\) 0 0
\(658\) 3.84715 0.149978
\(659\) −22.3147 −0.869257 −0.434629 0.900610i \(-0.643120\pi\)
−0.434629 + 0.900610i \(0.643120\pi\)
\(660\) 0 0
\(661\) −0.0803059 −0.00312354 −0.00156177 0.999999i \(-0.500497\pi\)
−0.00156177 + 0.999999i \(0.500497\pi\)
\(662\) −7.39759 −0.287516
\(663\) 0 0
\(664\) −23.2525 −0.902370
\(665\) −6.87116 −0.266452
\(666\) 0 0
\(667\) 7.75325 0.300207
\(668\) −1.43577 −0.0555515
\(669\) 0 0
\(670\) 34.0768 1.31650
\(671\) 22.7481 0.878179
\(672\) 0 0
\(673\) 36.2767 1.39836 0.699182 0.714944i \(-0.253548\pi\)
0.699182 + 0.714944i \(0.253548\pi\)
\(674\) 5.96308 0.229689
\(675\) 0 0
\(676\) −4.09790 −0.157612
\(677\) −10.2419 −0.393629 −0.196815 0.980441i \(-0.563060\pi\)
−0.196815 + 0.980441i \(0.563060\pi\)
\(678\) 0 0
\(679\) −0.707978 −0.0271697
\(680\) −49.0470 −1.88087
\(681\) 0 0
\(682\) 14.4869 0.554734
\(683\) −2.86486 −0.109621 −0.0548104 0.998497i \(-0.517455\pi\)
−0.0548104 + 0.998497i \(0.517455\pi\)
\(684\) 0 0
\(685\) 28.9034 1.10434
\(686\) 1.60620 0.0613249
\(687\) 0 0
\(688\) −28.1037 −1.07144
\(689\) −27.1569 −1.03459
\(690\) 0 0
\(691\) −4.83501 −0.183932 −0.0919662 0.995762i \(-0.529315\pi\)
−0.0919662 + 0.995762i \(0.529315\pi\)
\(692\) 6.25278 0.237695
\(693\) 0 0
\(694\) 8.65649 0.328596
\(695\) −35.6444 −1.35207
\(696\) 0 0
\(697\) 21.2807 0.806065
\(698\) 26.2032 0.991804
\(699\) 0 0
\(700\) 4.40057 0.166326
\(701\) 25.9468 0.979998 0.489999 0.871723i \(-0.336997\pi\)
0.489999 + 0.871723i \(0.336997\pi\)
\(702\) 0 0
\(703\) 2.06260 0.0777925
\(704\) 12.6187 0.475587
\(705\) 0 0
\(706\) −4.98691 −0.187685
\(707\) −11.1926 −0.420942
\(708\) 0 0
\(709\) −25.5065 −0.957918 −0.478959 0.877837i \(-0.658986\pi\)
−0.478959 + 0.877837i \(0.658986\pi\)
\(710\) −69.2912 −2.60045
\(711\) 0 0
\(712\) −5.24842 −0.196693
\(713\) −10.3578 −0.387903
\(714\) 0 0
\(715\) 24.0715 0.900225
\(716\) 6.97199 0.260555
\(717\) 0 0
\(718\) 0.824054 0.0307534
\(719\) −39.6442 −1.47848 −0.739240 0.673442i \(-0.764815\pi\)
−0.739240 + 0.673442i \(0.764815\pi\)
\(720\) 0 0
\(721\) 9.42373 0.350958
\(722\) −24.4939 −0.911570
\(723\) 0 0
\(724\) 9.87971 0.367177
\(725\) −18.3951 −0.683175
\(726\) 0 0
\(727\) 15.1557 0.562094 0.281047 0.959694i \(-0.409318\pi\)
0.281047 + 0.959694i \(0.409318\pi\)
\(728\) −5.55606 −0.205921
\(729\) 0 0
\(730\) 14.1034 0.521992
\(731\) 35.3097 1.30598
\(732\) 0 0
\(733\) −8.36022 −0.308792 −0.154396 0.988009i \(-0.549343\pi\)
−0.154396 + 0.988009i \(0.549343\pi\)
\(734\) 3.93525 0.145253
\(735\) 0 0
\(736\) 10.1890 0.375573
\(737\) 16.6547 0.613484
\(738\) 0 0
\(739\) −24.2136 −0.890712 −0.445356 0.895354i \(-0.646923\pi\)
−0.445356 + 0.895354i \(0.646923\pi\)
\(740\) −2.19131 −0.0805541
\(741\) 0 0
\(742\) −17.9076 −0.657410
\(743\) −28.8264 −1.05754 −0.528768 0.848766i \(-0.677346\pi\)
−0.528768 + 0.848766i \(0.677346\pi\)
\(744\) 0 0
\(745\) 15.9798 0.585454
\(746\) −46.5097 −1.70284
\(747\) 0 0
\(748\) 9.78800 0.357885
\(749\) 6.56198 0.239770
\(750\) 0 0
\(751\) −11.1065 −0.405283 −0.202641 0.979253i \(-0.564953\pi\)
−0.202641 + 0.979253i \(0.564953\pi\)
\(752\) −11.5532 −0.421302
\(753\) 0 0
\(754\) −9.48338 −0.345364
\(755\) −47.4497 −1.72687
\(756\) 0 0
\(757\) −15.6799 −0.569897 −0.284949 0.958543i \(-0.591977\pi\)
−0.284949 + 0.958543i \(0.591977\pi\)
\(758\) 17.5083 0.635930
\(759\) 0 0
\(760\) 15.6732 0.568525
\(761\) −26.4513 −0.958857 −0.479429 0.877581i \(-0.659156\pi\)
−0.479429 + 0.877581i \(0.659156\pi\)
\(762\) 0 0
\(763\) −15.5034 −0.561259
\(764\) −8.07743 −0.292231
\(765\) 0 0
\(766\) 26.5996 0.961083
\(767\) 6.83739 0.246884
\(768\) 0 0
\(769\) −8.07969 −0.291361 −0.145681 0.989332i \(-0.546537\pi\)
−0.145681 + 0.989332i \(0.546537\pi\)
\(770\) 15.8731 0.572028
\(771\) 0 0
\(772\) −13.6623 −0.491718
\(773\) −42.2559 −1.51984 −0.759919 0.650018i \(-0.774761\pi\)
−0.759919 + 0.650018i \(0.774761\pi\)
\(774\) 0 0
\(775\) 24.5745 0.882742
\(776\) 1.61490 0.0579717
\(777\) 0 0
\(778\) 20.8182 0.746368
\(779\) −6.80033 −0.243647
\(780\) 0 0
\(781\) −33.8654 −1.21180
\(782\) −31.1352 −1.11339
\(783\) 0 0
\(784\) −4.82349 −0.172268
\(785\) −27.5613 −0.983707
\(786\) 0 0
\(787\) −32.9478 −1.17446 −0.587231 0.809420i \(-0.699782\pi\)
−0.587231 + 0.809420i \(0.699782\pi\)
\(788\) 3.78616 0.134876
\(789\) 0 0
\(790\) −17.2162 −0.612526
\(791\) −14.8683 −0.528654
\(792\) 0 0
\(793\) 19.8936 0.706444
\(794\) −51.0879 −1.81304
\(795\) 0 0
\(796\) 11.0333 0.391067
\(797\) 10.7795 0.381831 0.190915 0.981607i \(-0.438854\pi\)
0.190915 + 0.981607i \(0.438854\pi\)
\(798\) 0 0
\(799\) 14.5155 0.513523
\(800\) −24.1741 −0.854683
\(801\) 0 0
\(802\) −58.5168 −2.06630
\(803\) 6.89292 0.243246
\(804\) 0 0
\(805\) −11.3489 −0.399996
\(806\) 12.6691 0.446251
\(807\) 0 0
\(808\) 25.5304 0.898158
\(809\) 11.5058 0.404521 0.202260 0.979332i \(-0.435171\pi\)
0.202260 + 0.979332i \(0.435171\pi\)
\(810\) 0 0
\(811\) 7.28050 0.255653 0.127826 0.991797i \(-0.459200\pi\)
0.127826 + 0.991797i \(0.459200\pi\)
\(812\) −1.40558 −0.0493261
\(813\) 0 0
\(814\) −4.76484 −0.167008
\(815\) 40.3549 1.41357
\(816\) 0 0
\(817\) −11.2834 −0.394755
\(818\) −0.0300184 −0.00104957
\(819\) 0 0
\(820\) 7.22468 0.252297
\(821\) 23.7546 0.829041 0.414521 0.910040i \(-0.363949\pi\)
0.414521 + 0.910040i \(0.363949\pi\)
\(822\) 0 0
\(823\) 54.5319 1.90086 0.950431 0.310936i \(-0.100642\pi\)
0.950431 + 0.310936i \(0.100642\pi\)
\(824\) −21.4956 −0.748835
\(825\) 0 0
\(826\) 4.50868 0.156877
\(827\) −16.7507 −0.582478 −0.291239 0.956650i \(-0.594068\pi\)
−0.291239 + 0.956650i \(0.594068\pi\)
\(828\) 0 0
\(829\) 17.2568 0.599355 0.299677 0.954041i \(-0.403121\pi\)
0.299677 + 0.954041i \(0.403121\pi\)
\(830\) 58.0944 2.01649
\(831\) 0 0
\(832\) 11.0353 0.382582
\(833\) 6.06028 0.209976
\(834\) 0 0
\(835\) −8.78509 −0.304021
\(836\) −3.12779 −0.108177
\(837\) 0 0
\(838\) 32.8004 1.13307
\(839\) 4.63330 0.159959 0.0799796 0.996797i \(-0.474514\pi\)
0.0799796 + 0.996797i \(0.474514\pi\)
\(840\) 0 0
\(841\) −23.1245 −0.797395
\(842\) 33.3057 1.14779
\(843\) 0 0
\(844\) −7.28726 −0.250838
\(845\) −25.0740 −0.862572
\(846\) 0 0
\(847\) −3.24216 −0.111402
\(848\) 53.7776 1.84673
\(849\) 0 0
\(850\) 73.8701 2.53372
\(851\) 3.40674 0.116782
\(852\) 0 0
\(853\) −36.0413 −1.23403 −0.617016 0.786951i \(-0.711659\pi\)
−0.617016 + 0.786951i \(0.711659\pi\)
\(854\) 13.1182 0.448894
\(855\) 0 0
\(856\) −14.9679 −0.511594
\(857\) 38.5445 1.31665 0.658327 0.752732i \(-0.271264\pi\)
0.658327 + 0.752732i \(0.271264\pi\)
\(858\) 0 0
\(859\) −29.3488 −1.00137 −0.500685 0.865630i \(-0.666918\pi\)
−0.500685 + 0.865630i \(0.666918\pi\)
\(860\) 11.9874 0.408768
\(861\) 0 0
\(862\) −43.0012 −1.46463
\(863\) 2.89395 0.0985111 0.0492555 0.998786i \(-0.484315\pi\)
0.0492555 + 0.998786i \(0.484315\pi\)
\(864\) 0 0
\(865\) 38.2591 1.30085
\(866\) −11.9774 −0.407007
\(867\) 0 0
\(868\) 1.87775 0.0637351
\(869\) −8.41427 −0.285434
\(870\) 0 0
\(871\) 14.5649 0.493512
\(872\) 35.3633 1.19755
\(873\) 0 0
\(874\) 9.94937 0.336542
\(875\) 9.18552 0.310527
\(876\) 0 0
\(877\) −20.8638 −0.704519 −0.352259 0.935902i \(-0.614587\pi\)
−0.352259 + 0.935902i \(0.614587\pi\)
\(878\) 0.789471 0.0266434
\(879\) 0 0
\(880\) −47.6678 −1.60688
\(881\) 37.4032 1.26015 0.630074 0.776535i \(-0.283025\pi\)
0.630074 + 0.776535i \(0.283025\pi\)
\(882\) 0 0
\(883\) 0.668193 0.0224865 0.0112433 0.999937i \(-0.496421\pi\)
0.0112433 + 0.999937i \(0.496421\pi\)
\(884\) 8.55981 0.287897
\(885\) 0 0
\(886\) −26.2746 −0.882711
\(887\) −15.8528 −0.532286 −0.266143 0.963934i \(-0.585749\pi\)
−0.266143 + 0.963934i \(0.585749\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 13.1128 0.439541
\(891\) 0 0
\(892\) 16.2151 0.542921
\(893\) −4.63849 −0.155221
\(894\) 0 0
\(895\) 42.6598 1.42596
\(896\) 13.6478 0.455941
\(897\) 0 0
\(898\) −33.8631 −1.13003
\(899\) −7.84931 −0.261789
\(900\) 0 0
\(901\) −67.5666 −2.25097
\(902\) 15.7095 0.523070
\(903\) 0 0
\(904\) 33.9146 1.12798
\(905\) 60.4514 2.00947
\(906\) 0 0
\(907\) −3.26158 −0.108299 −0.0541496 0.998533i \(-0.517245\pi\)
−0.0541496 + 0.998533i \(0.517245\pi\)
\(908\) 9.99005 0.331531
\(909\) 0 0
\(910\) 13.8814 0.460163
\(911\) −50.2514 −1.66490 −0.832451 0.554099i \(-0.813063\pi\)
−0.832451 + 0.554099i \(0.813063\pi\)
\(912\) 0 0
\(913\) 28.3931 0.939674
\(914\) 15.3912 0.509095
\(915\) 0 0
\(916\) −10.3024 −0.340401
\(917\) 16.9371 0.559314
\(918\) 0 0
\(919\) 22.1516 0.730713 0.365356 0.930868i \(-0.380947\pi\)
0.365356 + 0.930868i \(0.380947\pi\)
\(920\) 25.8869 0.853466
\(921\) 0 0
\(922\) 41.7867 1.37617
\(923\) −29.6160 −0.974822
\(924\) 0 0
\(925\) −8.08269 −0.265757
\(926\) −24.1442 −0.793426
\(927\) 0 0
\(928\) 7.72141 0.253468
\(929\) −17.8794 −0.586605 −0.293302 0.956020i \(-0.594754\pi\)
−0.293302 + 0.956020i \(0.594754\pi\)
\(930\) 0 0
\(931\) −1.93658 −0.0634690
\(932\) −8.13477 −0.266463
\(933\) 0 0
\(934\) 11.4514 0.374702
\(935\) 59.8903 1.95862
\(936\) 0 0
\(937\) −41.2241 −1.34673 −0.673366 0.739310i \(-0.735152\pi\)
−0.673366 + 0.739310i \(0.735152\pi\)
\(938\) 9.60429 0.313591
\(939\) 0 0
\(940\) 4.92794 0.160732
\(941\) −18.6993 −0.609581 −0.304791 0.952419i \(-0.598586\pi\)
−0.304791 + 0.952419i \(0.598586\pi\)
\(942\) 0 0
\(943\) −11.2319 −0.365762
\(944\) −13.5398 −0.440682
\(945\) 0 0
\(946\) 26.0658 0.847473
\(947\) −35.5049 −1.15376 −0.576878 0.816830i \(-0.695729\pi\)
−0.576878 + 0.816830i \(0.695729\pi\)
\(948\) 0 0
\(949\) 6.02799 0.195677
\(950\) −23.6055 −0.765862
\(951\) 0 0
\(952\) −13.8235 −0.448024
\(953\) −8.77896 −0.284378 −0.142189 0.989839i \(-0.545414\pi\)
−0.142189 + 0.989839i \(0.545414\pi\)
\(954\) 0 0
\(955\) −49.4237 −1.59931
\(956\) 12.4341 0.402146
\(957\) 0 0
\(958\) 4.48245 0.144821
\(959\) 8.14622 0.263055
\(960\) 0 0
\(961\) −20.5139 −0.661738
\(962\) −4.16695 −0.134348
\(963\) 0 0
\(964\) −2.65255 −0.0854327
\(965\) −83.5963 −2.69106
\(966\) 0 0
\(967\) 27.9391 0.898461 0.449230 0.893416i \(-0.351698\pi\)
0.449230 + 0.893416i \(0.351698\pi\)
\(968\) 7.39540 0.237697
\(969\) 0 0
\(970\) −4.03471 −0.129547
\(971\) −59.3843 −1.90573 −0.952867 0.303389i \(-0.901882\pi\)
−0.952867 + 0.303389i \(0.901882\pi\)
\(972\) 0 0
\(973\) −10.0461 −0.322063
\(974\) 51.8421 1.66113
\(975\) 0 0
\(976\) −39.3945 −1.26099
\(977\) 15.7565 0.504094 0.252047 0.967715i \(-0.418896\pi\)
0.252047 + 0.967715i \(0.418896\pi\)
\(978\) 0 0
\(979\) 6.40873 0.204824
\(980\) 2.05743 0.0657221
\(981\) 0 0
\(982\) 48.3442 1.54272
\(983\) 38.6686 1.23334 0.616668 0.787223i \(-0.288482\pi\)
0.616668 + 0.787223i \(0.288482\pi\)
\(984\) 0 0
\(985\) 23.1665 0.738146
\(986\) −23.5947 −0.751410
\(987\) 0 0
\(988\) −2.73532 −0.0870221
\(989\) −18.6364 −0.592603
\(990\) 0 0
\(991\) 41.4853 1.31783 0.658913 0.752219i \(-0.271017\pi\)
0.658913 + 0.752219i \(0.271017\pi\)
\(992\) −10.3153 −0.327510
\(993\) 0 0
\(994\) −19.5292 −0.619429
\(995\) 67.5102 2.14022
\(996\) 0 0
\(997\) 60.2478 1.90807 0.954034 0.299698i \(-0.0968859\pi\)
0.954034 + 0.299698i \(0.0968859\pi\)
\(998\) 51.1359 1.61868
\(999\) 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 \(a_p\))