Properties

Label 8001.2.a.v.1.3
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 1.3
Root \(2.42782\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42782 q^{2} +3.89430 q^{4} -4.13136 q^{5} +1.00000 q^{7} -4.59902 q^{8} +O(q^{10})\) \(q-2.42782 q^{2} +3.89430 q^{4} -4.13136 q^{5} +1.00000 q^{7} -4.59902 q^{8} +10.0302 q^{10} +4.39665 q^{11} +0.702420 q^{13} -2.42782 q^{14} +3.37699 q^{16} +0.979615 q^{17} -7.50347 q^{19} -16.0888 q^{20} -10.6743 q^{22} +4.28424 q^{23} +12.0682 q^{25} -1.70535 q^{26} +3.89430 q^{28} -8.97712 q^{29} -0.872190 q^{31} +0.999336 q^{32} -2.37833 q^{34} -4.13136 q^{35} +6.83153 q^{37} +18.2171 q^{38} +19.0002 q^{40} +4.36586 q^{41} -6.34656 q^{43} +17.1219 q^{44} -10.4014 q^{46} -2.85801 q^{47} +1.00000 q^{49} -29.2993 q^{50} +2.73544 q^{52} +5.93310 q^{53} -18.1642 q^{55} -4.59902 q^{56} +21.7948 q^{58} -5.83624 q^{59} +0.431173 q^{61} +2.11752 q^{62} -9.18018 q^{64} -2.90195 q^{65} +1.64991 q^{67} +3.81492 q^{68} +10.0302 q^{70} +15.5767 q^{71} -3.79200 q^{73} -16.5857 q^{74} -29.2208 q^{76} +4.39665 q^{77} +14.6779 q^{79} -13.9516 q^{80} -10.5995 q^{82} +5.45195 q^{83} -4.04715 q^{85} +15.4083 q^{86} -20.2203 q^{88} +12.1433 q^{89} +0.702420 q^{91} +16.6841 q^{92} +6.93874 q^{94} +30.9996 q^{95} +9.29248 q^{97} -2.42782 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + O(q^{10}) \) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + 9q^{11} + 24q^{13} - 4q^{14} + 20q^{16} - 17q^{17} + 23q^{19} - 5q^{20} - 3q^{22} + 17q^{23} + 38q^{25} - 28q^{26} + 22q^{28} - 2q^{29} + 16q^{31} - 17q^{32} + 29q^{34} - 5q^{35} + 56q^{37} - 2q^{38} - 13q^{40} + 7q^{41} + 19q^{43} + 29q^{44} + 10q^{46} - 25q^{47} + 19q^{49} + 9q^{50} + 16q^{52} - 18q^{53} + 10q^{55} - 9q^{56} + 31q^{58} - 11q^{59} + 26q^{61} - 26q^{62} + 45q^{64} - 27q^{65} + 24q^{67} - 14q^{68} + 32q^{71} + 51q^{73} + 12q^{76} + 9q^{77} + 30q^{79} + 30q^{80} - 52q^{82} - q^{83} + 44q^{85} + 24q^{86} - 30q^{88} - 5q^{89} + 24q^{91} + 88q^{92} + 7q^{94} + 24q^{95} + 5q^{97} - 4q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42782 −1.71673 −0.858363 0.513042i \(-0.828518\pi\)
−0.858363 + 0.513042i \(0.828518\pi\)
\(3\) 0 0
\(4\) 3.89430 1.94715
\(5\) −4.13136 −1.84760 −0.923801 0.382873i \(-0.874935\pi\)
−0.923801 + 0.382873i \(0.874935\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −4.59902 −1.62600
\(9\) 0 0
\(10\) 10.0302 3.17183
\(11\) 4.39665 1.32564 0.662820 0.748779i \(-0.269359\pi\)
0.662820 + 0.748779i \(0.269359\pi\)
\(12\) 0 0
\(13\) 0.702420 0.194816 0.0974081 0.995245i \(-0.468945\pi\)
0.0974081 + 0.995245i \(0.468945\pi\)
\(14\) −2.42782 −0.648862
\(15\) 0 0
\(16\) 3.37699 0.844246
\(17\) 0.979615 0.237592 0.118796 0.992919i \(-0.462097\pi\)
0.118796 + 0.992919i \(0.462097\pi\)
\(18\) 0 0
\(19\) −7.50347 −1.72141 −0.860707 0.509100i \(-0.829978\pi\)
−0.860707 + 0.509100i \(0.829978\pi\)
\(20\) −16.0888 −3.59756
\(21\) 0 0
\(22\) −10.6743 −2.27576
\(23\) 4.28424 0.893326 0.446663 0.894702i \(-0.352612\pi\)
0.446663 + 0.894702i \(0.352612\pi\)
\(24\) 0 0
\(25\) 12.0682 2.41363
\(26\) −1.70535 −0.334446
\(27\) 0 0
\(28\) 3.89430 0.735954
\(29\) −8.97712 −1.66701 −0.833505 0.552513i \(-0.813669\pi\)
−0.833505 + 0.552513i \(0.813669\pi\)
\(30\) 0 0
\(31\) −0.872190 −0.156650 −0.0783249 0.996928i \(-0.524957\pi\)
−0.0783249 + 0.996928i \(0.524957\pi\)
\(32\) 0.999336 0.176659
\(33\) 0 0
\(34\) −2.37833 −0.407880
\(35\) −4.13136 −0.698328
\(36\) 0 0
\(37\) 6.83153 1.12310 0.561548 0.827444i \(-0.310206\pi\)
0.561548 + 0.827444i \(0.310206\pi\)
\(38\) 18.2171 2.95520
\(39\) 0 0
\(40\) 19.0002 3.00420
\(41\) 4.36586 0.681833 0.340917 0.940094i \(-0.389263\pi\)
0.340917 + 0.940094i \(0.389263\pi\)
\(42\) 0 0
\(43\) −6.34656 −0.967841 −0.483921 0.875112i \(-0.660788\pi\)
−0.483921 + 0.875112i \(0.660788\pi\)
\(44\) 17.1219 2.58122
\(45\) 0 0
\(46\) −10.4014 −1.53360
\(47\) −2.85801 −0.416884 −0.208442 0.978035i \(-0.566839\pi\)
−0.208442 + 0.978035i \(0.566839\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −29.2993 −4.14355
\(51\) 0 0
\(52\) 2.73544 0.379337
\(53\) 5.93310 0.814974 0.407487 0.913211i \(-0.366405\pi\)
0.407487 + 0.913211i \(0.366405\pi\)
\(54\) 0 0
\(55\) −18.1642 −2.44926
\(56\) −4.59902 −0.614570
\(57\) 0 0
\(58\) 21.7948 2.86180
\(59\) −5.83624 −0.759814 −0.379907 0.925025i \(-0.624044\pi\)
−0.379907 + 0.925025i \(0.624044\pi\)
\(60\) 0 0
\(61\) 0.431173 0.0552061 0.0276030 0.999619i \(-0.491213\pi\)
0.0276030 + 0.999619i \(0.491213\pi\)
\(62\) 2.11752 0.268925
\(63\) 0 0
\(64\) −9.18018 −1.14752
\(65\) −2.90195 −0.359943
\(66\) 0 0
\(67\) 1.64991 0.201568 0.100784 0.994908i \(-0.467865\pi\)
0.100784 + 0.994908i \(0.467865\pi\)
\(68\) 3.81492 0.462627
\(69\) 0 0
\(70\) 10.0302 1.19884
\(71\) 15.5767 1.84862 0.924309 0.381645i \(-0.124642\pi\)
0.924309 + 0.381645i \(0.124642\pi\)
\(72\) 0 0
\(73\) −3.79200 −0.443821 −0.221910 0.975067i \(-0.571229\pi\)
−0.221910 + 0.975067i \(0.571229\pi\)
\(74\) −16.5857 −1.92805
\(75\) 0 0
\(76\) −29.2208 −3.35185
\(77\) 4.39665 0.501045
\(78\) 0 0
\(79\) 14.6779 1.65139 0.825697 0.564114i \(-0.190782\pi\)
0.825697 + 0.564114i \(0.190782\pi\)
\(80\) −13.9516 −1.55983
\(81\) 0 0
\(82\) −10.5995 −1.17052
\(83\) 5.45195 0.598429 0.299215 0.954186i \(-0.403275\pi\)
0.299215 + 0.954186i \(0.403275\pi\)
\(84\) 0 0
\(85\) −4.04715 −0.438975
\(86\) 15.4083 1.66152
\(87\) 0 0
\(88\) −20.2203 −2.15549
\(89\) 12.1433 1.28719 0.643593 0.765368i \(-0.277443\pi\)
0.643593 + 0.765368i \(0.277443\pi\)
\(90\) 0 0
\(91\) 0.702420 0.0736336
\(92\) 16.6841 1.73944
\(93\) 0 0
\(94\) 6.93874 0.715676
\(95\) 30.9996 3.18049
\(96\) 0 0
\(97\) 9.29248 0.943509 0.471754 0.881730i \(-0.343621\pi\)
0.471754 + 0.881730i \(0.343621\pi\)
\(98\) −2.42782 −0.245247
\(99\) 0 0
\(100\) 46.9971 4.69971
\(101\) −10.0187 −0.996893 −0.498447 0.866920i \(-0.666096\pi\)
−0.498447 + 0.866920i \(0.666096\pi\)
\(102\) 0 0
\(103\) −10.3855 −1.02332 −0.511659 0.859189i \(-0.670969\pi\)
−0.511659 + 0.859189i \(0.670969\pi\)
\(104\) −3.23045 −0.316771
\(105\) 0 0
\(106\) −14.4045 −1.39909
\(107\) 12.3554 1.19445 0.597223 0.802075i \(-0.296271\pi\)
0.597223 + 0.802075i \(0.296271\pi\)
\(108\) 0 0
\(109\) −12.4746 −1.19485 −0.597423 0.801926i \(-0.703809\pi\)
−0.597423 + 0.801926i \(0.703809\pi\)
\(110\) 44.0993 4.20470
\(111\) 0 0
\(112\) 3.37699 0.319095
\(113\) −17.5483 −1.65080 −0.825400 0.564548i \(-0.809051\pi\)
−0.825400 + 0.564548i \(0.809051\pi\)
\(114\) 0 0
\(115\) −17.6998 −1.65051
\(116\) −34.9596 −3.24592
\(117\) 0 0
\(118\) 14.1693 1.30439
\(119\) 0.979615 0.0898012
\(120\) 0 0
\(121\) 8.33054 0.757322
\(122\) −1.04681 −0.0947738
\(123\) 0 0
\(124\) −3.39657 −0.305021
\(125\) −29.2011 −2.61183
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 20.2891 1.79332
\(129\) 0 0
\(130\) 7.04541 0.617924
\(131\) −1.03408 −0.0903480 −0.0451740 0.998979i \(-0.514384\pi\)
−0.0451740 + 0.998979i \(0.514384\pi\)
\(132\) 0 0
\(133\) −7.50347 −0.650633
\(134\) −4.00567 −0.346037
\(135\) 0 0
\(136\) −4.50527 −0.386324
\(137\) −10.4831 −0.895629 −0.447815 0.894126i \(-0.647798\pi\)
−0.447815 + 0.894126i \(0.647798\pi\)
\(138\) 0 0
\(139\) 9.23389 0.783208 0.391604 0.920134i \(-0.371920\pi\)
0.391604 + 0.920134i \(0.371920\pi\)
\(140\) −16.0888 −1.35975
\(141\) 0 0
\(142\) −37.8175 −3.17357
\(143\) 3.08830 0.258256
\(144\) 0 0
\(145\) 37.0877 3.07997
\(146\) 9.20630 0.761919
\(147\) 0 0
\(148\) 26.6040 2.18684
\(149\) −11.0699 −0.906885 −0.453442 0.891286i \(-0.649804\pi\)
−0.453442 + 0.891286i \(0.649804\pi\)
\(150\) 0 0
\(151\) 12.6210 1.02708 0.513540 0.858066i \(-0.328334\pi\)
0.513540 + 0.858066i \(0.328334\pi\)
\(152\) 34.5086 2.79902
\(153\) 0 0
\(154\) −10.6743 −0.860157
\(155\) 3.60333 0.289427
\(156\) 0 0
\(157\) −0.436970 −0.0348740 −0.0174370 0.999848i \(-0.505551\pi\)
−0.0174370 + 0.999848i \(0.505551\pi\)
\(158\) −35.6353 −2.83499
\(159\) 0 0
\(160\) −4.12862 −0.326396
\(161\) 4.28424 0.337646
\(162\) 0 0
\(163\) −11.0335 −0.864209 −0.432105 0.901824i \(-0.642229\pi\)
−0.432105 + 0.901824i \(0.642229\pi\)
\(164\) 17.0020 1.32763
\(165\) 0 0
\(166\) −13.2363 −1.02734
\(167\) −22.0805 −1.70864 −0.854321 0.519746i \(-0.826027\pi\)
−0.854321 + 0.519746i \(0.826027\pi\)
\(168\) 0 0
\(169\) −12.5066 −0.962047
\(170\) 9.82574 0.753600
\(171\) 0 0
\(172\) −24.7154 −1.88453
\(173\) −7.62698 −0.579868 −0.289934 0.957047i \(-0.593633\pi\)
−0.289934 + 0.957047i \(0.593633\pi\)
\(174\) 0 0
\(175\) 12.0682 0.912267
\(176\) 14.8474 1.11917
\(177\) 0 0
\(178\) −29.4817 −2.20975
\(179\) 8.74055 0.653299 0.326650 0.945146i \(-0.394080\pi\)
0.326650 + 0.945146i \(0.394080\pi\)
\(180\) 0 0
\(181\) 1.99890 0.148577 0.0742884 0.997237i \(-0.476331\pi\)
0.0742884 + 0.997237i \(0.476331\pi\)
\(182\) −1.70535 −0.126409
\(183\) 0 0
\(184\) −19.7033 −1.45255
\(185\) −28.2235 −2.07504
\(186\) 0 0
\(187\) 4.30703 0.314961
\(188\) −11.1300 −0.811736
\(189\) 0 0
\(190\) −75.2613 −5.46003
\(191\) 5.03588 0.364383 0.182192 0.983263i \(-0.441681\pi\)
0.182192 + 0.983263i \(0.441681\pi\)
\(192\) 0 0
\(193\) 4.96100 0.357101 0.178550 0.983931i \(-0.442859\pi\)
0.178550 + 0.983931i \(0.442859\pi\)
\(194\) −22.5605 −1.61975
\(195\) 0 0
\(196\) 3.89430 0.278164
\(197\) −3.19173 −0.227401 −0.113701 0.993515i \(-0.536271\pi\)
−0.113701 + 0.993515i \(0.536271\pi\)
\(198\) 0 0
\(199\) −7.96090 −0.564333 −0.282167 0.959365i \(-0.591053\pi\)
−0.282167 + 0.959365i \(0.591053\pi\)
\(200\) −55.5017 −3.92457
\(201\) 0 0
\(202\) 24.3235 1.71139
\(203\) −8.97712 −0.630070
\(204\) 0 0
\(205\) −18.0370 −1.25976
\(206\) 25.2142 1.75676
\(207\) 0 0
\(208\) 2.37206 0.164473
\(209\) −32.9901 −2.28198
\(210\) 0 0
\(211\) −14.3101 −0.985151 −0.492575 0.870270i \(-0.663944\pi\)
−0.492575 + 0.870270i \(0.663944\pi\)
\(212\) 23.1053 1.58688
\(213\) 0 0
\(214\) −29.9968 −2.05054
\(215\) 26.2199 1.78819
\(216\) 0 0
\(217\) −0.872190 −0.0592081
\(218\) 30.2860 2.05123
\(219\) 0 0
\(220\) −70.7367 −4.76907
\(221\) 0.688101 0.0462867
\(222\) 0 0
\(223\) 13.2261 0.885686 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(224\) 0.999336 0.0667709
\(225\) 0 0
\(226\) 42.6040 2.83397
\(227\) −29.5131 −1.95885 −0.979426 0.201805i \(-0.935319\pi\)
−0.979426 + 0.201805i \(0.935319\pi\)
\(228\) 0 0
\(229\) −15.5215 −1.02569 −0.512845 0.858481i \(-0.671409\pi\)
−0.512845 + 0.858481i \(0.671409\pi\)
\(230\) 42.9718 2.83348
\(231\) 0 0
\(232\) 41.2860 2.71056
\(233\) 6.88255 0.450891 0.225445 0.974256i \(-0.427616\pi\)
0.225445 + 0.974256i \(0.427616\pi\)
\(234\) 0 0
\(235\) 11.8075 0.770236
\(236\) −22.7281 −1.47947
\(237\) 0 0
\(238\) −2.37833 −0.154164
\(239\) −5.00111 −0.323495 −0.161747 0.986832i \(-0.551713\pi\)
−0.161747 + 0.986832i \(0.551713\pi\)
\(240\) 0 0
\(241\) 15.5508 1.00171 0.500856 0.865530i \(-0.333019\pi\)
0.500856 + 0.865530i \(0.333019\pi\)
\(242\) −20.2250 −1.30011
\(243\) 0 0
\(244\) 1.67912 0.107495
\(245\) −4.13136 −0.263943
\(246\) 0 0
\(247\) −5.27059 −0.335360
\(248\) 4.01122 0.254713
\(249\) 0 0
\(250\) 70.8950 4.48380
\(251\) −24.6173 −1.55383 −0.776916 0.629605i \(-0.783217\pi\)
−0.776916 + 0.629605i \(0.783217\pi\)
\(252\) 0 0
\(253\) 18.8363 1.18423
\(254\) −2.42782 −0.152335
\(255\) 0 0
\(256\) −30.8980 −1.93112
\(257\) −10.9511 −0.683108 −0.341554 0.939862i \(-0.610953\pi\)
−0.341554 + 0.939862i \(0.610953\pi\)
\(258\) 0 0
\(259\) 6.83153 0.424491
\(260\) −11.3011 −0.700863
\(261\) 0 0
\(262\) 2.51056 0.155103
\(263\) 23.9422 1.47634 0.738171 0.674614i \(-0.235690\pi\)
0.738171 + 0.674614i \(0.235690\pi\)
\(264\) 0 0
\(265\) −24.5118 −1.50575
\(266\) 18.2171 1.11696
\(267\) 0 0
\(268\) 6.42523 0.392484
\(269\) 17.5905 1.07251 0.536257 0.844055i \(-0.319838\pi\)
0.536257 + 0.844055i \(0.319838\pi\)
\(270\) 0 0
\(271\) 7.00655 0.425617 0.212809 0.977094i \(-0.431739\pi\)
0.212809 + 0.977094i \(0.431739\pi\)
\(272\) 3.30815 0.200586
\(273\) 0 0
\(274\) 25.4510 1.53755
\(275\) 53.0595 3.19961
\(276\) 0 0
\(277\) 7.00516 0.420899 0.210449 0.977605i \(-0.432507\pi\)
0.210449 + 0.977605i \(0.432507\pi\)
\(278\) −22.4182 −1.34455
\(279\) 0 0
\(280\) 19.0002 1.13548
\(281\) 23.2539 1.38721 0.693607 0.720354i \(-0.256021\pi\)
0.693607 + 0.720354i \(0.256021\pi\)
\(282\) 0 0
\(283\) 30.2416 1.79768 0.898840 0.438278i \(-0.144411\pi\)
0.898840 + 0.438278i \(0.144411\pi\)
\(284\) 60.6605 3.59954
\(285\) 0 0
\(286\) −7.49782 −0.443355
\(287\) 4.36586 0.257709
\(288\) 0 0
\(289\) −16.0404 −0.943550
\(290\) −90.0423 −5.28747
\(291\) 0 0
\(292\) −14.7672 −0.864186
\(293\) 15.6762 0.915812 0.457906 0.889001i \(-0.348600\pi\)
0.457906 + 0.889001i \(0.348600\pi\)
\(294\) 0 0
\(295\) 24.1116 1.40383
\(296\) −31.4184 −1.82616
\(297\) 0 0
\(298\) 26.8758 1.55687
\(299\) 3.00934 0.174034
\(300\) 0 0
\(301\) −6.34656 −0.365810
\(302\) −30.6414 −1.76321
\(303\) 0 0
\(304\) −25.3391 −1.45330
\(305\) −1.78133 −0.101999
\(306\) 0 0
\(307\) −8.13944 −0.464543 −0.232271 0.972651i \(-0.574616\pi\)
−0.232271 + 0.972651i \(0.574616\pi\)
\(308\) 17.1219 0.975610
\(309\) 0 0
\(310\) −8.74823 −0.496866
\(311\) −10.5758 −0.599698 −0.299849 0.953987i \(-0.596936\pi\)
−0.299849 + 0.953987i \(0.596936\pi\)
\(312\) 0 0
\(313\) −21.2622 −1.20181 −0.600904 0.799321i \(-0.705193\pi\)
−0.600904 + 0.799321i \(0.705193\pi\)
\(314\) 1.06088 0.0598692
\(315\) 0 0
\(316\) 57.1602 3.21551
\(317\) 17.7625 0.997641 0.498820 0.866705i \(-0.333767\pi\)
0.498820 + 0.866705i \(0.333767\pi\)
\(318\) 0 0
\(319\) −39.4693 −2.20985
\(320\) 37.9266 2.12016
\(321\) 0 0
\(322\) −10.4014 −0.579645
\(323\) −7.35052 −0.408994
\(324\) 0 0
\(325\) 8.47692 0.470215
\(326\) 26.7873 1.48361
\(327\) 0 0
\(328\) −20.0787 −1.10866
\(329\) −2.85801 −0.157567
\(330\) 0 0
\(331\) −0.606407 −0.0333312 −0.0166656 0.999861i \(-0.505305\pi\)
−0.0166656 + 0.999861i \(0.505305\pi\)
\(332\) 21.2315 1.16523
\(333\) 0 0
\(334\) 53.6075 2.93327
\(335\) −6.81636 −0.372418
\(336\) 0 0
\(337\) 19.3425 1.05365 0.526827 0.849973i \(-0.323382\pi\)
0.526827 + 0.849973i \(0.323382\pi\)
\(338\) 30.3638 1.65157
\(339\) 0 0
\(340\) −15.7608 −0.854750
\(341\) −3.83471 −0.207661
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 29.1880 1.57371
\(345\) 0 0
\(346\) 18.5169 0.995475
\(347\) −17.3328 −0.930472 −0.465236 0.885187i \(-0.654031\pi\)
−0.465236 + 0.885187i \(0.654031\pi\)
\(348\) 0 0
\(349\) 28.3170 1.51578 0.757888 0.652385i \(-0.226231\pi\)
0.757888 + 0.652385i \(0.226231\pi\)
\(350\) −29.2993 −1.56611
\(351\) 0 0
\(352\) 4.39373 0.234187
\(353\) 9.94061 0.529085 0.264543 0.964374i \(-0.414779\pi\)
0.264543 + 0.964374i \(0.414779\pi\)
\(354\) 0 0
\(355\) −64.3531 −3.41551
\(356\) 47.2896 2.50635
\(357\) 0 0
\(358\) −21.2205 −1.12154
\(359\) −12.6698 −0.668689 −0.334344 0.942451i \(-0.608515\pi\)
−0.334344 + 0.942451i \(0.608515\pi\)
\(360\) 0 0
\(361\) 37.3021 1.96327
\(362\) −4.85296 −0.255066
\(363\) 0 0
\(364\) 2.73544 0.143376
\(365\) 15.6661 0.820004
\(366\) 0 0
\(367\) 13.6547 0.712772 0.356386 0.934339i \(-0.384009\pi\)
0.356386 + 0.934339i \(0.384009\pi\)
\(368\) 14.4678 0.754187
\(369\) 0 0
\(370\) 68.5216 3.56227
\(371\) 5.93310 0.308031
\(372\) 0 0
\(373\) −9.79015 −0.506915 −0.253457 0.967347i \(-0.581568\pi\)
−0.253457 + 0.967347i \(0.581568\pi\)
\(374\) −10.4567 −0.540702
\(375\) 0 0
\(376\) 13.1441 0.677853
\(377\) −6.30571 −0.324761
\(378\) 0 0
\(379\) −2.07864 −0.106772 −0.0533862 0.998574i \(-0.517001\pi\)
−0.0533862 + 0.998574i \(0.517001\pi\)
\(380\) 120.722 6.19289
\(381\) 0 0
\(382\) −12.2262 −0.625546
\(383\) 6.32519 0.323202 0.161601 0.986856i \(-0.448334\pi\)
0.161601 + 0.986856i \(0.448334\pi\)
\(384\) 0 0
\(385\) −18.1642 −0.925731
\(386\) −12.0444 −0.613044
\(387\) 0 0
\(388\) 36.1877 1.83715
\(389\) 10.0363 0.508859 0.254429 0.967091i \(-0.418112\pi\)
0.254429 + 0.967091i \(0.418112\pi\)
\(390\) 0 0
\(391\) 4.19691 0.212247
\(392\) −4.59902 −0.232286
\(393\) 0 0
\(394\) 7.74895 0.390386
\(395\) −60.6398 −3.05112
\(396\) 0 0
\(397\) −34.9023 −1.75170 −0.875848 0.482588i \(-0.839697\pi\)
−0.875848 + 0.482588i \(0.839697\pi\)
\(398\) 19.3276 0.968806
\(399\) 0 0
\(400\) 40.7540 2.03770
\(401\) 22.2029 1.10876 0.554380 0.832264i \(-0.312955\pi\)
0.554380 + 0.832264i \(0.312955\pi\)
\(402\) 0 0
\(403\) −0.612643 −0.0305179
\(404\) −39.0157 −1.94110
\(405\) 0 0
\(406\) 21.7948 1.08166
\(407\) 30.0359 1.48882
\(408\) 0 0
\(409\) 30.9983 1.53277 0.766384 0.642383i \(-0.222054\pi\)
0.766384 + 0.642383i \(0.222054\pi\)
\(410\) 43.7905 2.16266
\(411\) 0 0
\(412\) −40.4444 −1.99255
\(413\) −5.83624 −0.287183
\(414\) 0 0
\(415\) −22.5240 −1.10566
\(416\) 0.701953 0.0344161
\(417\) 0 0
\(418\) 80.0941 3.91753
\(419\) −21.8162 −1.06579 −0.532894 0.846182i \(-0.678896\pi\)
−0.532894 + 0.846182i \(0.678896\pi\)
\(420\) 0 0
\(421\) 0.803041 0.0391378 0.0195689 0.999809i \(-0.493771\pi\)
0.0195689 + 0.999809i \(0.493771\pi\)
\(422\) 34.7424 1.69123
\(423\) 0 0
\(424\) −27.2865 −1.32515
\(425\) 11.8222 0.573459
\(426\) 0 0
\(427\) 0.431173 0.0208659
\(428\) 48.1158 2.32577
\(429\) 0 0
\(430\) −63.6573 −3.06983
\(431\) 26.8778 1.29466 0.647328 0.762211i \(-0.275886\pi\)
0.647328 + 0.762211i \(0.275886\pi\)
\(432\) 0 0
\(433\) −0.181842 −0.00873876 −0.00436938 0.999990i \(-0.501391\pi\)
−0.00436938 + 0.999990i \(0.501391\pi\)
\(434\) 2.11752 0.101644
\(435\) 0 0
\(436\) −48.5797 −2.32655
\(437\) −32.1467 −1.53778
\(438\) 0 0
\(439\) 40.9576 1.95480 0.977401 0.211395i \(-0.0678008\pi\)
0.977401 + 0.211395i \(0.0678008\pi\)
\(440\) 83.5374 3.98249
\(441\) 0 0
\(442\) −1.67059 −0.0794616
\(443\) −2.65537 −0.126161 −0.0630803 0.998008i \(-0.520092\pi\)
−0.0630803 + 0.998008i \(0.520092\pi\)
\(444\) 0 0
\(445\) −50.1683 −2.37821
\(446\) −32.1106 −1.52048
\(447\) 0 0
\(448\) −9.18018 −0.433723
\(449\) −41.8175 −1.97349 −0.986744 0.162285i \(-0.948114\pi\)
−0.986744 + 0.162285i \(0.948114\pi\)
\(450\) 0 0
\(451\) 19.1952 0.903865
\(452\) −68.3382 −3.21436
\(453\) 0 0
\(454\) 71.6524 3.36281
\(455\) −2.90195 −0.136046
\(456\) 0 0
\(457\) −8.99792 −0.420905 −0.210452 0.977604i \(-0.567494\pi\)
−0.210452 + 0.977604i \(0.567494\pi\)
\(458\) 37.6834 1.76083
\(459\) 0 0
\(460\) −68.9282 −3.21379
\(461\) 8.15332 0.379738 0.189869 0.981809i \(-0.439194\pi\)
0.189869 + 0.981809i \(0.439194\pi\)
\(462\) 0 0
\(463\) −19.5221 −0.907270 −0.453635 0.891188i \(-0.649873\pi\)
−0.453635 + 0.891188i \(0.649873\pi\)
\(464\) −30.3156 −1.40737
\(465\) 0 0
\(466\) −16.7096 −0.774057
\(467\) −18.3081 −0.847197 −0.423598 0.905850i \(-0.639233\pi\)
−0.423598 + 0.905850i \(0.639233\pi\)
\(468\) 0 0
\(469\) 1.64991 0.0761856
\(470\) −28.6664 −1.32228
\(471\) 0 0
\(472\) 26.8410 1.23546
\(473\) −27.9036 −1.28301
\(474\) 0 0
\(475\) −90.5531 −4.15486
\(476\) 3.81492 0.174856
\(477\) 0 0
\(478\) 12.1418 0.555352
\(479\) −20.4221 −0.933111 −0.466555 0.884492i \(-0.654505\pi\)
−0.466555 + 0.884492i \(0.654505\pi\)
\(480\) 0 0
\(481\) 4.79860 0.218798
\(482\) −37.7544 −1.71967
\(483\) 0 0
\(484\) 32.4416 1.47462
\(485\) −38.3906 −1.74323
\(486\) 0 0
\(487\) −27.4355 −1.24322 −0.621610 0.783327i \(-0.713521\pi\)
−0.621610 + 0.783327i \(0.713521\pi\)
\(488\) −1.98298 −0.0897651
\(489\) 0 0
\(490\) 10.0302 0.453118
\(491\) −18.0466 −0.814431 −0.407215 0.913332i \(-0.633500\pi\)
−0.407215 + 0.913332i \(0.633500\pi\)
\(492\) 0 0
\(493\) −8.79412 −0.396067
\(494\) 12.7960 0.575721
\(495\) 0 0
\(496\) −2.94537 −0.132251
\(497\) 15.5767 0.698712
\(498\) 0 0
\(499\) 24.6544 1.10368 0.551842 0.833949i \(-0.313925\pi\)
0.551842 + 0.833949i \(0.313925\pi\)
\(500\) −113.718 −5.08563
\(501\) 0 0
\(502\) 59.7664 2.66750
\(503\) 13.5368 0.603577 0.301789 0.953375i \(-0.402416\pi\)
0.301789 + 0.953375i \(0.402416\pi\)
\(504\) 0 0
\(505\) 41.3907 1.84186
\(506\) −45.7312 −2.03300
\(507\) 0 0
\(508\) 3.89430 0.172782
\(509\) 44.1678 1.95770 0.978851 0.204576i \(-0.0655815\pi\)
0.978851 + 0.204576i \(0.0655815\pi\)
\(510\) 0 0
\(511\) −3.79200 −0.167748
\(512\) 34.4364 1.52189
\(513\) 0 0
\(514\) 26.5872 1.17271
\(515\) 42.9064 1.89068
\(516\) 0 0
\(517\) −12.5657 −0.552638
\(518\) −16.5857 −0.728735
\(519\) 0 0
\(520\) 13.3461 0.585267
\(521\) 44.2787 1.93989 0.969943 0.243331i \(-0.0782400\pi\)
0.969943 + 0.243331i \(0.0782400\pi\)
\(522\) 0 0
\(523\) 0.707142 0.0309212 0.0154606 0.999880i \(-0.495079\pi\)
0.0154606 + 0.999880i \(0.495079\pi\)
\(524\) −4.02702 −0.175921
\(525\) 0 0
\(526\) −58.1274 −2.53448
\(527\) −0.854410 −0.0372187
\(528\) 0 0
\(529\) −4.64527 −0.201968
\(530\) 59.5102 2.58496
\(531\) 0 0
\(532\) −29.2208 −1.26688
\(533\) 3.06667 0.132832
\(534\) 0 0
\(535\) −51.0448 −2.20686
\(536\) −7.58796 −0.327750
\(537\) 0 0
\(538\) −42.7066 −1.84121
\(539\) 4.39665 0.189377
\(540\) 0 0
\(541\) 29.3076 1.26003 0.630015 0.776583i \(-0.283049\pi\)
0.630015 + 0.776583i \(0.283049\pi\)
\(542\) −17.0106 −0.730669
\(543\) 0 0
\(544\) 0.978964 0.0419728
\(545\) 51.5370 2.20760
\(546\) 0 0
\(547\) 34.9550 1.49457 0.747285 0.664504i \(-0.231357\pi\)
0.747285 + 0.664504i \(0.231357\pi\)
\(548\) −40.8242 −1.74393
\(549\) 0 0
\(550\) −128.819 −5.49285
\(551\) 67.3595 2.86961
\(552\) 0 0
\(553\) 14.6779 0.624168
\(554\) −17.0072 −0.722569
\(555\) 0 0
\(556\) 35.9596 1.52502
\(557\) 0.580975 0.0246167 0.0123083 0.999924i \(-0.496082\pi\)
0.0123083 + 0.999924i \(0.496082\pi\)
\(558\) 0 0
\(559\) −4.45795 −0.188551
\(560\) −13.9516 −0.589561
\(561\) 0 0
\(562\) −56.4563 −2.38147
\(563\) 17.2618 0.727497 0.363748 0.931497i \(-0.381497\pi\)
0.363748 + 0.931497i \(0.381497\pi\)
\(564\) 0 0
\(565\) 72.4982 3.05002
\(566\) −73.4212 −3.08612
\(567\) 0 0
\(568\) −71.6377 −3.00585
\(569\) −13.6965 −0.574188 −0.287094 0.957902i \(-0.592689\pi\)
−0.287094 + 0.957902i \(0.592689\pi\)
\(570\) 0 0
\(571\) −40.5296 −1.69611 −0.848055 0.529909i \(-0.822226\pi\)
−0.848055 + 0.529909i \(0.822226\pi\)
\(572\) 12.0268 0.502864
\(573\) 0 0
\(574\) −10.5995 −0.442415
\(575\) 51.7029 2.15616
\(576\) 0 0
\(577\) −19.5066 −0.812069 −0.406035 0.913858i \(-0.633089\pi\)
−0.406035 + 0.913858i \(0.633089\pi\)
\(578\) 38.9431 1.61982
\(579\) 0 0
\(580\) 144.431 5.99716
\(581\) 5.45195 0.226185
\(582\) 0 0
\(583\) 26.0858 1.08036
\(584\) 17.4395 0.721652
\(585\) 0 0
\(586\) −38.0589 −1.57220
\(587\) −20.5249 −0.847155 −0.423578 0.905860i \(-0.639226\pi\)
−0.423578 + 0.905860i \(0.639226\pi\)
\(588\) 0 0
\(589\) 6.54445 0.269659
\(590\) −58.5387 −2.41000
\(591\) 0 0
\(592\) 23.0700 0.948170
\(593\) 24.3206 0.998726 0.499363 0.866393i \(-0.333567\pi\)
0.499363 + 0.866393i \(0.333567\pi\)
\(594\) 0 0
\(595\) −4.04715 −0.165917
\(596\) −43.1097 −1.76584
\(597\) 0 0
\(598\) −7.30612 −0.298770
\(599\) 38.6834 1.58056 0.790280 0.612746i \(-0.209935\pi\)
0.790280 + 0.612746i \(0.209935\pi\)
\(600\) 0 0
\(601\) 19.4855 0.794831 0.397416 0.917639i \(-0.369907\pi\)
0.397416 + 0.917639i \(0.369907\pi\)
\(602\) 15.4083 0.627995
\(603\) 0 0
\(604\) 49.1498 1.99988
\(605\) −34.4165 −1.39923
\(606\) 0 0
\(607\) −28.3703 −1.15152 −0.575758 0.817620i \(-0.695293\pi\)
−0.575758 + 0.817620i \(0.695293\pi\)
\(608\) −7.49849 −0.304104
\(609\) 0 0
\(610\) 4.32475 0.175104
\(611\) −2.00753 −0.0812158
\(612\) 0 0
\(613\) 29.5222 1.19239 0.596196 0.802839i \(-0.296678\pi\)
0.596196 + 0.802839i \(0.296678\pi\)
\(614\) 19.7611 0.797493
\(615\) 0 0
\(616\) −20.2203 −0.814699
\(617\) 31.1688 1.25481 0.627405 0.778693i \(-0.284117\pi\)
0.627405 + 0.778693i \(0.284117\pi\)
\(618\) 0 0
\(619\) 11.1738 0.449113 0.224556 0.974461i \(-0.427907\pi\)
0.224556 + 0.974461i \(0.427907\pi\)
\(620\) 14.0325 0.563557
\(621\) 0 0
\(622\) 25.6761 1.02952
\(623\) 12.1433 0.486511
\(624\) 0 0
\(625\) 60.2997 2.41199
\(626\) 51.6207 2.06318
\(627\) 0 0
\(628\) −1.70169 −0.0679050
\(629\) 6.69227 0.266838
\(630\) 0 0
\(631\) 7.63983 0.304137 0.152068 0.988370i \(-0.451407\pi\)
0.152068 + 0.988370i \(0.451407\pi\)
\(632\) −67.5040 −2.68517
\(633\) 0 0
\(634\) −43.1241 −1.71268
\(635\) −4.13136 −0.163948
\(636\) 0 0
\(637\) 0.702420 0.0278309
\(638\) 95.8242 3.79372
\(639\) 0 0
\(640\) −83.8218 −3.31335
\(641\) −11.2917 −0.445994 −0.222997 0.974819i \(-0.571584\pi\)
−0.222997 + 0.974819i \(0.571584\pi\)
\(642\) 0 0
\(643\) −20.4181 −0.805212 −0.402606 0.915373i \(-0.631896\pi\)
−0.402606 + 0.915373i \(0.631896\pi\)
\(644\) 16.6841 0.657447
\(645\) 0 0
\(646\) 17.8457 0.702130
\(647\) 25.7217 1.01122 0.505612 0.862761i \(-0.331267\pi\)
0.505612 + 0.862761i \(0.331267\pi\)
\(648\) 0 0
\(649\) −25.6599 −1.00724
\(650\) −20.5804 −0.807230
\(651\) 0 0
\(652\) −42.9677 −1.68275
\(653\) 23.4539 0.917821 0.458910 0.888483i \(-0.348240\pi\)
0.458910 + 0.888483i \(0.348240\pi\)
\(654\) 0 0
\(655\) 4.27216 0.166927
\(656\) 14.7435 0.575635
\(657\) 0 0
\(658\) 6.93874 0.270500
\(659\) 5.91947 0.230590 0.115295 0.993331i \(-0.463219\pi\)
0.115295 + 0.993331i \(0.463219\pi\)
\(660\) 0 0
\(661\) 37.2744 1.44981 0.724903 0.688851i \(-0.241885\pi\)
0.724903 + 0.688851i \(0.241885\pi\)
\(662\) 1.47225 0.0572205
\(663\) 0 0
\(664\) −25.0736 −0.973046
\(665\) 30.9996 1.20211
\(666\) 0 0
\(667\) −38.4601 −1.48918
\(668\) −85.9882 −3.32698
\(669\) 0 0
\(670\) 16.5489 0.639339
\(671\) 1.89572 0.0731834
\(672\) 0 0
\(673\) −19.6036 −0.755662 −0.377831 0.925875i \(-0.623330\pi\)
−0.377831 + 0.925875i \(0.623330\pi\)
\(674\) −46.9601 −1.80884
\(675\) 0 0
\(676\) −48.7045 −1.87325
\(677\) 17.6369 0.677839 0.338920 0.940815i \(-0.389939\pi\)
0.338920 + 0.940815i \(0.389939\pi\)
\(678\) 0 0
\(679\) 9.29248 0.356613
\(680\) 18.6129 0.713773
\(681\) 0 0
\(682\) 9.30999 0.356498
\(683\) −23.3875 −0.894896 −0.447448 0.894310i \(-0.647667\pi\)
−0.447448 + 0.894310i \(0.647667\pi\)
\(684\) 0 0
\(685\) 43.3094 1.65477
\(686\) −2.42782 −0.0926945
\(687\) 0 0
\(688\) −21.4322 −0.817097
\(689\) 4.16753 0.158770
\(690\) 0 0
\(691\) 47.8622 1.82077 0.910383 0.413767i \(-0.135787\pi\)
0.910383 + 0.413767i \(0.135787\pi\)
\(692\) −29.7018 −1.12909
\(693\) 0 0
\(694\) 42.0808 1.59737
\(695\) −38.1485 −1.44706
\(696\) 0 0
\(697\) 4.27687 0.161998
\(698\) −68.7486 −2.60217
\(699\) 0 0
\(700\) 46.9971 1.77632
\(701\) 18.8401 0.711580 0.355790 0.934566i \(-0.384212\pi\)
0.355790 + 0.934566i \(0.384212\pi\)
\(702\) 0 0
\(703\) −51.2602 −1.93331
\(704\) −40.3620 −1.52120
\(705\) 0 0
\(706\) −24.1340 −0.908295
\(707\) −10.0187 −0.376790
\(708\) 0 0
\(709\) −17.4274 −0.654499 −0.327250 0.944938i \(-0.606122\pi\)
−0.327250 + 0.944938i \(0.606122\pi\)
\(710\) 156.238 5.86350
\(711\) 0 0
\(712\) −55.8473 −2.09296
\(713\) −3.73667 −0.139939
\(714\) 0 0
\(715\) −12.7589 −0.477155
\(716\) 34.0383 1.27207
\(717\) 0 0
\(718\) 30.7601 1.14796
\(719\) −28.3723 −1.05811 −0.529055 0.848588i \(-0.677453\pi\)
−0.529055 + 0.848588i \(0.677453\pi\)
\(720\) 0 0
\(721\) −10.3855 −0.386778
\(722\) −90.5627 −3.37039
\(723\) 0 0
\(724\) 7.78431 0.289302
\(725\) −108.337 −4.02355
\(726\) 0 0
\(727\) −39.0293 −1.44752 −0.723758 0.690054i \(-0.757587\pi\)
−0.723758 + 0.690054i \(0.757587\pi\)
\(728\) −3.23045 −0.119728
\(729\) 0 0
\(730\) −38.0346 −1.40772
\(731\) −6.21719 −0.229951
\(732\) 0 0
\(733\) −39.4181 −1.45594 −0.727970 0.685609i \(-0.759536\pi\)
−0.727970 + 0.685609i \(0.759536\pi\)
\(734\) −33.1512 −1.22363
\(735\) 0 0
\(736\) 4.28140 0.157814
\(737\) 7.25406 0.267207
\(738\) 0 0
\(739\) 39.0447 1.43628 0.718141 0.695897i \(-0.244993\pi\)
0.718141 + 0.695897i \(0.244993\pi\)
\(740\) −109.911 −4.04041
\(741\) 0 0
\(742\) −14.4045 −0.528806
\(743\) −49.4864 −1.81548 −0.907741 0.419532i \(-0.862194\pi\)
−0.907741 + 0.419532i \(0.862194\pi\)
\(744\) 0 0
\(745\) 45.7339 1.67556
\(746\) 23.7687 0.870234
\(747\) 0 0
\(748\) 16.7729 0.613277
\(749\) 12.3554 0.451458
\(750\) 0 0
\(751\) 19.6553 0.717231 0.358616 0.933485i \(-0.383249\pi\)
0.358616 + 0.933485i \(0.383249\pi\)
\(752\) −9.65147 −0.351953
\(753\) 0 0
\(754\) 15.3091 0.557525
\(755\) −52.1418 −1.89763
\(756\) 0 0
\(757\) −31.7636 −1.15447 −0.577234 0.816579i \(-0.695868\pi\)
−0.577234 + 0.816579i \(0.695868\pi\)
\(758\) 5.04655 0.183299
\(759\) 0 0
\(760\) −142.568 −5.17147
\(761\) 17.6652 0.640365 0.320182 0.947356i \(-0.396256\pi\)
0.320182 + 0.947356i \(0.396256\pi\)
\(762\) 0 0
\(763\) −12.4746 −0.451610
\(764\) 19.6112 0.709509
\(765\) 0 0
\(766\) −15.3564 −0.554850
\(767\) −4.09949 −0.148024
\(768\) 0 0
\(769\) 45.2679 1.63240 0.816201 0.577769i \(-0.196076\pi\)
0.816201 + 0.577769i \(0.196076\pi\)
\(770\) 44.0993 1.58923
\(771\) 0 0
\(772\) 19.3196 0.695329
\(773\) 12.0686 0.434079 0.217039 0.976163i \(-0.430360\pi\)
0.217039 + 0.976163i \(0.430360\pi\)
\(774\) 0 0
\(775\) −10.5257 −0.378095
\(776\) −42.7363 −1.53415
\(777\) 0 0
\(778\) −24.3662 −0.873572
\(779\) −32.7591 −1.17372
\(780\) 0 0
\(781\) 68.4855 2.45060
\(782\) −10.1893 −0.364370
\(783\) 0 0
\(784\) 3.37699 0.120607
\(785\) 1.80528 0.0644333
\(786\) 0 0
\(787\) 24.7311 0.881569 0.440785 0.897613i \(-0.354700\pi\)
0.440785 + 0.897613i \(0.354700\pi\)
\(788\) −12.4296 −0.442785
\(789\) 0 0
\(790\) 147.222 5.23793
\(791\) −17.5483 −0.623944
\(792\) 0 0
\(793\) 0.302865 0.0107550
\(794\) 84.7364 3.00718
\(795\) 0 0
\(796\) −31.0022 −1.09884
\(797\) 16.3346 0.578603 0.289301 0.957238i \(-0.406577\pi\)
0.289301 + 0.957238i \(0.406577\pi\)
\(798\) 0 0
\(799\) −2.79975 −0.0990482
\(800\) 12.0601 0.426390
\(801\) 0 0
\(802\) −53.9046 −1.90344
\(803\) −16.6721 −0.588346
\(804\) 0 0
\(805\) −17.6998 −0.623834
\(806\) 1.48739 0.0523910
\(807\) 0 0
\(808\) 46.0760 1.62095
\(809\) 48.7035 1.71232 0.856162 0.516707i \(-0.172843\pi\)
0.856162 + 0.516707i \(0.172843\pi\)
\(810\) 0 0
\(811\) 5.69549 0.199996 0.0999978 0.994988i \(-0.468116\pi\)
0.0999978 + 0.994988i \(0.468116\pi\)
\(812\) −34.9596 −1.22684
\(813\) 0 0
\(814\) −72.9216 −2.55590
\(815\) 45.5833 1.59671
\(816\) 0 0
\(817\) 47.6212 1.66606
\(818\) −75.2582 −2.63134
\(819\) 0 0
\(820\) −70.2414 −2.45294
\(821\) 30.3036 1.05760 0.528802 0.848745i \(-0.322641\pi\)
0.528802 + 0.848745i \(0.322641\pi\)
\(822\) 0 0
\(823\) −1.13612 −0.0396027 −0.0198014 0.999804i \(-0.506303\pi\)
−0.0198014 + 0.999804i \(0.506303\pi\)
\(824\) 47.7633 1.66391
\(825\) 0 0
\(826\) 14.1693 0.493014
\(827\) 34.1644 1.18801 0.594006 0.804460i \(-0.297545\pi\)
0.594006 + 0.804460i \(0.297545\pi\)
\(828\) 0 0
\(829\) −16.2966 −0.566004 −0.283002 0.959119i \(-0.591330\pi\)
−0.283002 + 0.959119i \(0.591330\pi\)
\(830\) 54.6842 1.89811
\(831\) 0 0
\(832\) −6.44834 −0.223556
\(833\) 0.979615 0.0339417
\(834\) 0 0
\(835\) 91.2227 3.15689
\(836\) −128.474 −4.44335
\(837\) 0 0
\(838\) 52.9657 1.82967
\(839\) −26.2732 −0.907053 −0.453526 0.891243i \(-0.649834\pi\)
−0.453526 + 0.891243i \(0.649834\pi\)
\(840\) 0 0
\(841\) 51.5887 1.77892
\(842\) −1.94964 −0.0671890
\(843\) 0 0
\(844\) −55.7280 −1.91824
\(845\) 51.6693 1.77748
\(846\) 0 0
\(847\) 8.33054 0.286241
\(848\) 20.0360 0.688039
\(849\) 0 0
\(850\) −28.7020 −0.984472
\(851\) 29.2679 1.00329
\(852\) 0 0
\(853\) 49.7979 1.70505 0.852524 0.522689i \(-0.175071\pi\)
0.852524 + 0.522689i \(0.175071\pi\)
\(854\) −1.04681 −0.0358211
\(855\) 0 0
\(856\) −56.8230 −1.94217
\(857\) −31.7264 −1.08375 −0.541877 0.840458i \(-0.682286\pi\)
−0.541877 + 0.840458i \(0.682286\pi\)
\(858\) 0 0
\(859\) 2.93883 0.100272 0.0501359 0.998742i \(-0.484035\pi\)
0.0501359 + 0.998742i \(0.484035\pi\)
\(860\) 102.108 3.48187
\(861\) 0 0
\(862\) −65.2543 −2.22257
\(863\) −48.0520 −1.63571 −0.817854 0.575425i \(-0.804837\pi\)
−0.817854 + 0.575425i \(0.804837\pi\)
\(864\) 0 0
\(865\) 31.5098 1.07137
\(866\) 0.441479 0.0150021
\(867\) 0 0
\(868\) −3.39657 −0.115287
\(869\) 64.5336 2.18915
\(870\) 0 0
\(871\) 1.15893 0.0392688
\(872\) 57.3708 1.94282
\(873\) 0 0
\(874\) 78.0463 2.63996
\(875\) −29.2011 −0.987178
\(876\) 0 0
\(877\) 1.45427 0.0491073 0.0245537 0.999699i \(-0.492184\pi\)
0.0245537 + 0.999699i \(0.492184\pi\)
\(878\) −99.4377 −3.35586
\(879\) 0 0
\(880\) −61.3401 −2.06777
\(881\) −54.9217 −1.85036 −0.925179 0.379530i \(-0.876086\pi\)
−0.925179 + 0.379530i \(0.876086\pi\)
\(882\) 0 0
\(883\) 47.7578 1.60718 0.803590 0.595184i \(-0.202921\pi\)
0.803590 + 0.595184i \(0.202921\pi\)
\(884\) 2.67968 0.0901272
\(885\) 0 0
\(886\) 6.44676 0.216583
\(887\) 13.5209 0.453987 0.226994 0.973896i \(-0.427110\pi\)
0.226994 + 0.973896i \(0.427110\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 121.800 4.08273
\(891\) 0 0
\(892\) 51.5065 1.72456
\(893\) 21.4450 0.717630
\(894\) 0 0
\(895\) −36.1104 −1.20704
\(896\) 20.2891 0.677812
\(897\) 0 0
\(898\) 101.525 3.38794
\(899\) 7.82975 0.261137
\(900\) 0 0
\(901\) 5.81216 0.193631
\(902\) −46.6024 −1.55169
\(903\) 0 0
\(904\) 80.7048 2.68420
\(905\) −8.25817 −0.274511
\(906\) 0 0
\(907\) −51.1164 −1.69729 −0.848646 0.528962i \(-0.822581\pi\)
−0.848646 + 0.528962i \(0.822581\pi\)
\(908\) −114.933 −3.81418
\(909\) 0 0
\(910\) 7.04541 0.233553
\(911\) 33.9841 1.12594 0.562972 0.826476i \(-0.309658\pi\)
0.562972 + 0.826476i \(0.309658\pi\)
\(912\) 0 0
\(913\) 23.9703 0.793302
\(914\) 21.8453 0.722579
\(915\) 0 0
\(916\) −60.4455 −1.99717
\(917\) −1.03408 −0.0341483
\(918\) 0 0
\(919\) 35.3987 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(920\) 81.4016 2.68373
\(921\) 0 0
\(922\) −19.7948 −0.651907
\(923\) 10.9414 0.360141
\(924\) 0 0
\(925\) 82.4440 2.71074
\(926\) 47.3962 1.55754
\(927\) 0 0
\(928\) −8.97115 −0.294493
\(929\) 24.3384 0.798518 0.399259 0.916838i \(-0.369267\pi\)
0.399259 + 0.916838i \(0.369267\pi\)
\(930\) 0 0
\(931\) −7.50347 −0.245916
\(932\) 26.8027 0.877953
\(933\) 0 0
\(934\) 44.4487 1.45441
\(935\) −17.7939 −0.581922
\(936\) 0 0
\(937\) 6.36212 0.207841 0.103921 0.994586i \(-0.466861\pi\)
0.103921 + 0.994586i \(0.466861\pi\)
\(938\) −4.00567 −0.130790
\(939\) 0 0
\(940\) 45.9819 1.49977
\(941\) 21.9441 0.715358 0.357679 0.933845i \(-0.383568\pi\)
0.357679 + 0.933845i \(0.383568\pi\)
\(942\) 0 0
\(943\) 18.7044 0.609099
\(944\) −19.7089 −0.641470
\(945\) 0 0
\(946\) 67.7449 2.20258
\(947\) 25.7408 0.836463 0.418232 0.908340i \(-0.362650\pi\)
0.418232 + 0.908340i \(0.362650\pi\)
\(948\) 0 0
\(949\) −2.66358 −0.0864635
\(950\) 219.846 7.13276
\(951\) 0 0
\(952\) −4.50527 −0.146017
\(953\) −9.17939 −0.297350 −0.148675 0.988886i \(-0.547501\pi\)
−0.148675 + 0.988886i \(0.547501\pi\)
\(954\) 0 0
\(955\) −20.8050 −0.673235
\(956\) −19.4758 −0.629893
\(957\) 0 0
\(958\) 49.5812 1.60190
\(959\) −10.4831 −0.338516
\(960\) 0 0
\(961\) −30.2393 −0.975461
\(962\) −11.6501 −0.375616
\(963\) 0 0
\(964\) 60.5594 1.95049
\(965\) −20.4957 −0.659780
\(966\) 0 0
\(967\) 57.5730 1.85142 0.925711 0.378231i \(-0.123467\pi\)
0.925711 + 0.378231i \(0.123467\pi\)
\(968\) −38.3123 −1.23141
\(969\) 0 0
\(970\) 93.2055 2.99265
\(971\) 9.99471 0.320745 0.160373 0.987057i \(-0.448730\pi\)
0.160373 + 0.987057i \(0.448730\pi\)
\(972\) 0 0
\(973\) 9.23389 0.296025
\(974\) 66.6084 2.13427
\(975\) 0 0
\(976\) 1.45607 0.0466075
\(977\) −21.4270 −0.685510 −0.342755 0.939425i \(-0.611360\pi\)
−0.342755 + 0.939425i \(0.611360\pi\)
\(978\) 0 0
\(979\) 53.3898 1.70635
\(980\) −16.0888 −0.513937
\(981\) 0 0
\(982\) 43.8138 1.39816
\(983\) 5.16510 0.164741 0.0823705 0.996602i \(-0.473751\pi\)
0.0823705 + 0.996602i \(0.473751\pi\)
\(984\) 0 0
\(985\) 13.1862 0.420147
\(986\) 21.3505 0.679940
\(987\) 0 0
\(988\) −20.5253 −0.652996
\(989\) −27.1902 −0.864598
\(990\) 0 0
\(991\) 47.8521 1.52007 0.760036 0.649881i \(-0.225181\pi\)
0.760036 + 0.649881i \(0.225181\pi\)
\(992\) −0.871610 −0.0276736
\(993\) 0 0
\(994\) −37.8175 −1.19950
\(995\) 32.8894 1.04266
\(996\) 0 0
\(997\) 21.8952 0.693429 0.346714 0.937971i \(-0.387297\pi\)
0.346714 + 0.937971i \(0.387297\pi\)
\(998\) −59.8564 −1.89472
\(999\) 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 \(a_p\))