Properties

Label 8008.2.a.p.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.82075\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.82075 q^{3} -1.92109 q^{5} -1.00000 q^{7} +4.95665 q^{9} +O(q^{10})\) \(q-2.82075 q^{3} -1.92109 q^{5} -1.00000 q^{7} +4.95665 q^{9} +1.00000 q^{11} +1.00000 q^{13} +5.41891 q^{15} -0.965104 q^{17} +3.09750 q^{19} +2.82075 q^{21} -3.72460 q^{23} -1.30943 q^{25} -5.51924 q^{27} -0.786974 q^{29} +2.78741 q^{31} -2.82075 q^{33} +1.92109 q^{35} -10.8226 q^{37} -2.82075 q^{39} -4.59093 q^{41} -4.94708 q^{43} -9.52216 q^{45} -0.799126 q^{47} +1.00000 q^{49} +2.72232 q^{51} -1.50368 q^{53} -1.92109 q^{55} -8.73730 q^{57} +3.65311 q^{59} +14.3415 q^{61} -4.95665 q^{63} -1.92109 q^{65} +12.8578 q^{67} +10.5062 q^{69} +4.44026 q^{71} -1.16794 q^{73} +3.69358 q^{75} -1.00000 q^{77} +9.23904 q^{79} +0.698463 q^{81} +6.28506 q^{83} +1.85405 q^{85} +2.21986 q^{87} +4.46976 q^{89} -1.00000 q^{91} -7.86259 q^{93} -5.95057 q^{95} +7.50530 q^{97} +4.95665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.82075 −1.62856 −0.814282 0.580470i \(-0.802869\pi\)
−0.814282 + 0.580470i \(0.802869\pi\)
\(4\) 0 0
\(5\) −1.92109 −0.859136 −0.429568 0.903035i \(-0.641334\pi\)
−0.429568 + 0.903035i \(0.641334\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 4.95665 1.65222
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 5.41891 1.39916
\(16\) 0 0
\(17\) −0.965104 −0.234072 −0.117036 0.993128i \(-0.537339\pi\)
−0.117036 + 0.993128i \(0.537339\pi\)
\(18\) 0 0
\(19\) 3.09750 0.710616 0.355308 0.934749i \(-0.384376\pi\)
0.355308 + 0.934749i \(0.384376\pi\)
\(20\) 0 0
\(21\) 2.82075 0.615539
\(22\) 0 0
\(23\) −3.72460 −0.776632 −0.388316 0.921526i \(-0.626943\pi\)
−0.388316 + 0.921526i \(0.626943\pi\)
\(24\) 0 0
\(25\) −1.30943 −0.261886
\(26\) 0 0
\(27\) −5.51924 −1.06218
\(28\) 0 0
\(29\) −0.786974 −0.146137 −0.0730687 0.997327i \(-0.523279\pi\)
−0.0730687 + 0.997327i \(0.523279\pi\)
\(30\) 0 0
\(31\) 2.78741 0.500633 0.250317 0.968164i \(-0.419465\pi\)
0.250317 + 0.968164i \(0.419465\pi\)
\(32\) 0 0
\(33\) −2.82075 −0.491030
\(34\) 0 0
\(35\) 1.92109 0.324723
\(36\) 0 0
\(37\) −10.8226 −1.77922 −0.889612 0.456716i \(-0.849025\pi\)
−0.889612 + 0.456716i \(0.849025\pi\)
\(38\) 0 0
\(39\) −2.82075 −0.451682
\(40\) 0 0
\(41\) −4.59093 −0.716983 −0.358492 0.933533i \(-0.616709\pi\)
−0.358492 + 0.933533i \(0.616709\pi\)
\(42\) 0 0
\(43\) −4.94708 −0.754423 −0.377212 0.926127i \(-0.623117\pi\)
−0.377212 + 0.926127i \(0.623117\pi\)
\(44\) 0 0
\(45\) −9.52216 −1.41948
\(46\) 0 0
\(47\) −0.799126 −0.116564 −0.0582822 0.998300i \(-0.518562\pi\)
−0.0582822 + 0.998300i \(0.518562\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 2.72232 0.381201
\(52\) 0 0
\(53\) −1.50368 −0.206547 −0.103273 0.994653i \(-0.532932\pi\)
−0.103273 + 0.994653i \(0.532932\pi\)
\(54\) 0 0
\(55\) −1.92109 −0.259039
\(56\) 0 0
\(57\) −8.73730 −1.15728
\(58\) 0 0
\(59\) 3.65311 0.475595 0.237798 0.971315i \(-0.423575\pi\)
0.237798 + 0.971315i \(0.423575\pi\)
\(60\) 0 0
\(61\) 14.3415 1.83624 0.918122 0.396298i \(-0.129705\pi\)
0.918122 + 0.396298i \(0.129705\pi\)
\(62\) 0 0
\(63\) −4.95665 −0.624480
\(64\) 0 0
\(65\) −1.92109 −0.238281
\(66\) 0 0
\(67\) 12.8578 1.57083 0.785413 0.618972i \(-0.212451\pi\)
0.785413 + 0.618972i \(0.212451\pi\)
\(68\) 0 0
\(69\) 10.5062 1.26480
\(70\) 0 0
\(71\) 4.44026 0.526962 0.263481 0.964665i \(-0.415129\pi\)
0.263481 + 0.964665i \(0.415129\pi\)
\(72\) 0 0
\(73\) −1.16794 −0.136697 −0.0683484 0.997662i \(-0.521773\pi\)
−0.0683484 + 0.997662i \(0.521773\pi\)
\(74\) 0 0
\(75\) 3.69358 0.426498
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.23904 1.03947 0.519737 0.854327i \(-0.326030\pi\)
0.519737 + 0.854327i \(0.326030\pi\)
\(80\) 0 0
\(81\) 0.698463 0.0776070
\(82\) 0 0
\(83\) 6.28506 0.689875 0.344938 0.938626i \(-0.387900\pi\)
0.344938 + 0.938626i \(0.387900\pi\)
\(84\) 0 0
\(85\) 1.85405 0.201100
\(86\) 0 0
\(87\) 2.21986 0.237994
\(88\) 0 0
\(89\) 4.46976 0.473793 0.236897 0.971535i \(-0.423870\pi\)
0.236897 + 0.971535i \(0.423870\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −7.86259 −0.815313
\(94\) 0 0
\(95\) −5.95057 −0.610516
\(96\) 0 0
\(97\) 7.50530 0.762048 0.381024 0.924565i \(-0.375572\pi\)
0.381024 + 0.924565i \(0.375572\pi\)
\(98\) 0 0
\(99\) 4.95665 0.498163
\(100\) 0 0
\(101\) 1.12014 0.111459 0.0557293 0.998446i \(-0.482252\pi\)
0.0557293 + 0.998446i \(0.482252\pi\)
\(102\) 0 0
\(103\) 0.999512 0.0984849 0.0492424 0.998787i \(-0.484319\pi\)
0.0492424 + 0.998787i \(0.484319\pi\)
\(104\) 0 0
\(105\) −5.41891 −0.528832
\(106\) 0 0
\(107\) 5.56947 0.538421 0.269210 0.963081i \(-0.413237\pi\)
0.269210 + 0.963081i \(0.413237\pi\)
\(108\) 0 0
\(109\) 1.41533 0.135564 0.0677821 0.997700i \(-0.478408\pi\)
0.0677821 + 0.997700i \(0.478408\pi\)
\(110\) 0 0
\(111\) 30.5279 2.89758
\(112\) 0 0
\(113\) 0.238232 0.0224110 0.0112055 0.999937i \(-0.496433\pi\)
0.0112055 + 0.999937i \(0.496433\pi\)
\(114\) 0 0
\(115\) 7.15527 0.667233
\(116\) 0 0
\(117\) 4.95665 0.458243
\(118\) 0 0
\(119\) 0.965104 0.0884709
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 12.9499 1.16765
\(124\) 0 0
\(125\) 12.1210 1.08413
\(126\) 0 0
\(127\) −2.54582 −0.225905 −0.112952 0.993600i \(-0.536031\pi\)
−0.112952 + 0.993600i \(0.536031\pi\)
\(128\) 0 0
\(129\) 13.9545 1.22863
\(130\) 0 0
\(131\) 7.05388 0.616300 0.308150 0.951338i \(-0.400290\pi\)
0.308150 + 0.951338i \(0.400290\pi\)
\(132\) 0 0
\(133\) −3.09750 −0.268588
\(134\) 0 0
\(135\) 10.6029 0.912556
\(136\) 0 0
\(137\) −19.1999 −1.64036 −0.820180 0.572106i \(-0.806127\pi\)
−0.820180 + 0.572106i \(0.806127\pi\)
\(138\) 0 0
\(139\) 14.8024 1.25552 0.627762 0.778406i \(-0.283971\pi\)
0.627762 + 0.778406i \(0.283971\pi\)
\(140\) 0 0
\(141\) 2.25414 0.189833
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.51185 0.125552
\(146\) 0 0
\(147\) −2.82075 −0.232652
\(148\) 0 0
\(149\) −11.2743 −0.923623 −0.461811 0.886978i \(-0.652800\pi\)
−0.461811 + 0.886978i \(0.652800\pi\)
\(150\) 0 0
\(151\) 4.09117 0.332934 0.166467 0.986047i \(-0.446764\pi\)
0.166467 + 0.986047i \(0.446764\pi\)
\(152\) 0 0
\(153\) −4.78369 −0.386738
\(154\) 0 0
\(155\) −5.35485 −0.430112
\(156\) 0 0
\(157\) −12.6226 −1.00739 −0.503696 0.863881i \(-0.668027\pi\)
−0.503696 + 0.863881i \(0.668027\pi\)
\(158\) 0 0
\(159\) 4.24152 0.336374
\(160\) 0 0
\(161\) 3.72460 0.293539
\(162\) 0 0
\(163\) −1.58008 −0.123762 −0.0618808 0.998084i \(-0.519710\pi\)
−0.0618808 + 0.998084i \(0.519710\pi\)
\(164\) 0 0
\(165\) 5.41891 0.421862
\(166\) 0 0
\(167\) −10.4625 −0.809611 −0.404805 0.914403i \(-0.632661\pi\)
−0.404805 + 0.914403i \(0.632661\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 15.3533 1.17409
\(172\) 0 0
\(173\) 8.90837 0.677291 0.338645 0.940914i \(-0.390031\pi\)
0.338645 + 0.940914i \(0.390031\pi\)
\(174\) 0 0
\(175\) 1.30943 0.0989836
\(176\) 0 0
\(177\) −10.3045 −0.774537
\(178\) 0 0
\(179\) −17.8195 −1.33189 −0.665947 0.745999i \(-0.731972\pi\)
−0.665947 + 0.745999i \(0.731972\pi\)
\(180\) 0 0
\(181\) −15.2593 −1.13421 −0.567106 0.823645i \(-0.691937\pi\)
−0.567106 + 0.823645i \(0.691937\pi\)
\(182\) 0 0
\(183\) −40.4539 −2.99044
\(184\) 0 0
\(185\) 20.7911 1.52860
\(186\) 0 0
\(187\) −0.965104 −0.0705754
\(188\) 0 0
\(189\) 5.51924 0.401466
\(190\) 0 0
\(191\) 12.6559 0.915751 0.457876 0.889016i \(-0.348611\pi\)
0.457876 + 0.889016i \(0.348611\pi\)
\(192\) 0 0
\(193\) −16.9963 −1.22342 −0.611711 0.791081i \(-0.709518\pi\)
−0.611711 + 0.791081i \(0.709518\pi\)
\(194\) 0 0
\(195\) 5.41891 0.388056
\(196\) 0 0
\(197\) 9.70263 0.691284 0.345642 0.938367i \(-0.387661\pi\)
0.345642 + 0.938367i \(0.387661\pi\)
\(198\) 0 0
\(199\) −18.9379 −1.34247 −0.671235 0.741245i \(-0.734236\pi\)
−0.671235 + 0.741245i \(0.734236\pi\)
\(200\) 0 0
\(201\) −36.2686 −2.55819
\(202\) 0 0
\(203\) 0.786974 0.0552348
\(204\) 0 0
\(205\) 8.81958 0.615986
\(206\) 0 0
\(207\) −18.4615 −1.28317
\(208\) 0 0
\(209\) 3.09750 0.214259
\(210\) 0 0
\(211\) 11.8938 0.818804 0.409402 0.912354i \(-0.365737\pi\)
0.409402 + 0.912354i \(0.365737\pi\)
\(212\) 0 0
\(213\) −12.5249 −0.858192
\(214\) 0 0
\(215\) 9.50377 0.648152
\(216\) 0 0
\(217\) −2.78741 −0.189222
\(218\) 0 0
\(219\) 3.29447 0.222619
\(220\) 0 0
\(221\) −0.965104 −0.0649199
\(222\) 0 0
\(223\) 0.973431 0.0651857 0.0325929 0.999469i \(-0.489624\pi\)
0.0325929 + 0.999469i \(0.489624\pi\)
\(224\) 0 0
\(225\) −6.49039 −0.432693
\(226\) 0 0
\(227\) −2.50622 −0.166344 −0.0831719 0.996535i \(-0.526505\pi\)
−0.0831719 + 0.996535i \(0.526505\pi\)
\(228\) 0 0
\(229\) 28.9136 1.91066 0.955332 0.295534i \(-0.0954974\pi\)
0.955332 + 0.295534i \(0.0954974\pi\)
\(230\) 0 0
\(231\) 2.82075 0.185592
\(232\) 0 0
\(233\) 7.98505 0.523118 0.261559 0.965187i \(-0.415763\pi\)
0.261559 + 0.965187i \(0.415763\pi\)
\(234\) 0 0
\(235\) 1.53519 0.100145
\(236\) 0 0
\(237\) −26.0611 −1.69285
\(238\) 0 0
\(239\) 6.12982 0.396505 0.198253 0.980151i \(-0.436473\pi\)
0.198253 + 0.980151i \(0.436473\pi\)
\(240\) 0 0
\(241\) −6.12777 −0.394725 −0.197362 0.980331i \(-0.563238\pi\)
−0.197362 + 0.980331i \(0.563238\pi\)
\(242\) 0 0
\(243\) 14.5875 0.935791
\(244\) 0 0
\(245\) −1.92109 −0.122734
\(246\) 0 0
\(247\) 3.09750 0.197089
\(248\) 0 0
\(249\) −17.7286 −1.12351
\(250\) 0 0
\(251\) 16.1518 1.01949 0.509747 0.860324i \(-0.329739\pi\)
0.509747 + 0.860324i \(0.329739\pi\)
\(252\) 0 0
\(253\) −3.72460 −0.234163
\(254\) 0 0
\(255\) −5.22981 −0.327504
\(256\) 0 0
\(257\) −7.69320 −0.479889 −0.239944 0.970787i \(-0.577129\pi\)
−0.239944 + 0.970787i \(0.577129\pi\)
\(258\) 0 0
\(259\) 10.8226 0.672484
\(260\) 0 0
\(261\) −3.90076 −0.241451
\(262\) 0 0
\(263\) −13.1633 −0.811681 −0.405841 0.913944i \(-0.633021\pi\)
−0.405841 + 0.913944i \(0.633021\pi\)
\(264\) 0 0
\(265\) 2.88870 0.177452
\(266\) 0 0
\(267\) −12.6081 −0.771602
\(268\) 0 0
\(269\) −1.62237 −0.0989175 −0.0494587 0.998776i \(-0.515750\pi\)
−0.0494587 + 0.998776i \(0.515750\pi\)
\(270\) 0 0
\(271\) −3.46096 −0.210239 −0.105119 0.994460i \(-0.533522\pi\)
−0.105119 + 0.994460i \(0.533522\pi\)
\(272\) 0 0
\(273\) 2.82075 0.170720
\(274\) 0 0
\(275\) −1.30943 −0.0789616
\(276\) 0 0
\(277\) −1.41294 −0.0848954 −0.0424477 0.999099i \(-0.513516\pi\)
−0.0424477 + 0.999099i \(0.513516\pi\)
\(278\) 0 0
\(279\) 13.8162 0.827155
\(280\) 0 0
\(281\) −7.83859 −0.467611 −0.233806 0.972283i \(-0.575118\pi\)
−0.233806 + 0.972283i \(0.575118\pi\)
\(282\) 0 0
\(283\) 11.6854 0.694627 0.347313 0.937749i \(-0.387094\pi\)
0.347313 + 0.937749i \(0.387094\pi\)
\(284\) 0 0
\(285\) 16.7851 0.994263
\(286\) 0 0
\(287\) 4.59093 0.270994
\(288\) 0 0
\(289\) −16.0686 −0.945210
\(290\) 0 0
\(291\) −21.1706 −1.24104
\(292\) 0 0
\(293\) −27.1820 −1.58799 −0.793996 0.607923i \(-0.792003\pi\)
−0.793996 + 0.607923i \(0.792003\pi\)
\(294\) 0 0
\(295\) −7.01795 −0.408601
\(296\) 0 0
\(297\) −5.51924 −0.320259
\(298\) 0 0
\(299\) −3.72460 −0.215399
\(300\) 0 0
\(301\) 4.94708 0.285145
\(302\) 0 0
\(303\) −3.15965 −0.181517
\(304\) 0 0
\(305\) −27.5513 −1.57758
\(306\) 0 0
\(307\) 24.7444 1.41224 0.706118 0.708094i \(-0.250445\pi\)
0.706118 + 0.708094i \(0.250445\pi\)
\(308\) 0 0
\(309\) −2.81938 −0.160389
\(310\) 0 0
\(311\) −19.2913 −1.09391 −0.546956 0.837161i \(-0.684214\pi\)
−0.546956 + 0.837161i \(0.684214\pi\)
\(312\) 0 0
\(313\) 11.9577 0.675892 0.337946 0.941166i \(-0.390268\pi\)
0.337946 + 0.941166i \(0.390268\pi\)
\(314\) 0 0
\(315\) 9.52216 0.536513
\(316\) 0 0
\(317\) 15.9623 0.896531 0.448266 0.893900i \(-0.352042\pi\)
0.448266 + 0.893900i \(0.352042\pi\)
\(318\) 0 0
\(319\) −0.786974 −0.0440621
\(320\) 0 0
\(321\) −15.7101 −0.876852
\(322\) 0 0
\(323\) −2.98941 −0.166335
\(324\) 0 0
\(325\) −1.30943 −0.0726341
\(326\) 0 0
\(327\) −3.99230 −0.220775
\(328\) 0 0
\(329\) 0.799126 0.0440572
\(330\) 0 0
\(331\) −34.4160 −1.89168 −0.945838 0.324640i \(-0.894757\pi\)
−0.945838 + 0.324640i \(0.894757\pi\)
\(332\) 0 0
\(333\) −53.6439 −2.93967
\(334\) 0 0
\(335\) −24.7009 −1.34955
\(336\) 0 0
\(337\) 7.86366 0.428361 0.214180 0.976794i \(-0.431292\pi\)
0.214180 + 0.976794i \(0.431292\pi\)
\(338\) 0 0
\(339\) −0.671995 −0.0364978
\(340\) 0 0
\(341\) 2.78741 0.150947
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −20.1833 −1.08663
\(346\) 0 0
\(347\) 9.82358 0.527357 0.263679 0.964611i \(-0.415064\pi\)
0.263679 + 0.964611i \(0.415064\pi\)
\(348\) 0 0
\(349\) −23.4893 −1.25735 −0.628676 0.777667i \(-0.716403\pi\)
−0.628676 + 0.777667i \(0.716403\pi\)
\(350\) 0 0
\(351\) −5.51924 −0.294595
\(352\) 0 0
\(353\) −12.6559 −0.673607 −0.336804 0.941575i \(-0.609346\pi\)
−0.336804 + 0.941575i \(0.609346\pi\)
\(354\) 0 0
\(355\) −8.53013 −0.452732
\(356\) 0 0
\(357\) −2.72232 −0.144081
\(358\) 0 0
\(359\) −15.4424 −0.815019 −0.407509 0.913201i \(-0.633603\pi\)
−0.407509 + 0.913201i \(0.633603\pi\)
\(360\) 0 0
\(361\) −9.40547 −0.495025
\(362\) 0 0
\(363\) −2.82075 −0.148051
\(364\) 0 0
\(365\) 2.24371 0.117441
\(366\) 0 0
\(367\) 10.5254 0.549423 0.274712 0.961527i \(-0.411418\pi\)
0.274712 + 0.961527i \(0.411418\pi\)
\(368\) 0 0
\(369\) −22.7557 −1.18461
\(370\) 0 0
\(371\) 1.50368 0.0780673
\(372\) 0 0
\(373\) 31.1512 1.61295 0.806474 0.591270i \(-0.201373\pi\)
0.806474 + 0.591270i \(0.201373\pi\)
\(374\) 0 0
\(375\) −34.1902 −1.76558
\(376\) 0 0
\(377\) −0.786974 −0.0405312
\(378\) 0 0
\(379\) 17.2227 0.884669 0.442334 0.896850i \(-0.354150\pi\)
0.442334 + 0.896850i \(0.354150\pi\)
\(380\) 0 0
\(381\) 7.18113 0.367900
\(382\) 0 0
\(383\) 13.2561 0.677353 0.338677 0.940903i \(-0.390021\pi\)
0.338677 + 0.940903i \(0.390021\pi\)
\(384\) 0 0
\(385\) 1.92109 0.0979076
\(386\) 0 0
\(387\) −24.5210 −1.24647
\(388\) 0 0
\(389\) −25.5281 −1.29433 −0.647163 0.762352i \(-0.724045\pi\)
−0.647163 + 0.762352i \(0.724045\pi\)
\(390\) 0 0
\(391\) 3.59462 0.181788
\(392\) 0 0
\(393\) −19.8973 −1.00368
\(394\) 0 0
\(395\) −17.7490 −0.893049
\(396\) 0 0
\(397\) −3.14865 −0.158026 −0.0790131 0.996874i \(-0.525177\pi\)
−0.0790131 + 0.996874i \(0.525177\pi\)
\(398\) 0 0
\(399\) 8.73730 0.437412
\(400\) 0 0
\(401\) −17.3655 −0.867192 −0.433596 0.901107i \(-0.642756\pi\)
−0.433596 + 0.901107i \(0.642756\pi\)
\(402\) 0 0
\(403\) 2.78741 0.138851
\(404\) 0 0
\(405\) −1.34181 −0.0666749
\(406\) 0 0
\(407\) −10.8226 −0.536456
\(408\) 0 0
\(409\) 11.4713 0.567220 0.283610 0.958940i \(-0.408468\pi\)
0.283610 + 0.958940i \(0.408468\pi\)
\(410\) 0 0
\(411\) 54.1582 2.67143
\(412\) 0 0
\(413\) −3.65311 −0.179758
\(414\) 0 0
\(415\) −12.0741 −0.592696
\(416\) 0 0
\(417\) −41.7539 −2.04470
\(418\) 0 0
\(419\) 30.9086 1.50998 0.754992 0.655734i \(-0.227641\pi\)
0.754992 + 0.655734i \(0.227641\pi\)
\(420\) 0 0
\(421\) 11.0837 0.540186 0.270093 0.962834i \(-0.412945\pi\)
0.270093 + 0.962834i \(0.412945\pi\)
\(422\) 0 0
\(423\) −3.96099 −0.192590
\(424\) 0 0
\(425\) 1.26374 0.0613002
\(426\) 0 0
\(427\) −14.3415 −0.694035
\(428\) 0 0
\(429\) −2.82075 −0.136187
\(430\) 0 0
\(431\) −0.506075 −0.0243768 −0.0121884 0.999926i \(-0.503880\pi\)
−0.0121884 + 0.999926i \(0.503880\pi\)
\(432\) 0 0
\(433\) 16.2174 0.779360 0.389680 0.920950i \(-0.372586\pi\)
0.389680 + 0.920950i \(0.372586\pi\)
\(434\) 0 0
\(435\) −4.26454 −0.204469
\(436\) 0 0
\(437\) −11.5370 −0.551888
\(438\) 0 0
\(439\) 6.42312 0.306559 0.153279 0.988183i \(-0.451017\pi\)
0.153279 + 0.988183i \(0.451017\pi\)
\(440\) 0 0
\(441\) 4.95665 0.236031
\(442\) 0 0
\(443\) −16.8382 −0.800009 −0.400005 0.916513i \(-0.630991\pi\)
−0.400005 + 0.916513i \(0.630991\pi\)
\(444\) 0 0
\(445\) −8.58678 −0.407053
\(446\) 0 0
\(447\) 31.8019 1.50418
\(448\) 0 0
\(449\) 34.9320 1.64854 0.824272 0.566194i \(-0.191585\pi\)
0.824272 + 0.566194i \(0.191585\pi\)
\(450\) 0 0
\(451\) −4.59093 −0.216179
\(452\) 0 0
\(453\) −11.5402 −0.542205
\(454\) 0 0
\(455\) 1.92109 0.0900619
\(456\) 0 0
\(457\) −27.7876 −1.29985 −0.649925 0.759998i \(-0.725200\pi\)
−0.649925 + 0.759998i \(0.725200\pi\)
\(458\) 0 0
\(459\) 5.32664 0.248626
\(460\) 0 0
\(461\) −21.2125 −0.987963 −0.493981 0.869472i \(-0.664459\pi\)
−0.493981 + 0.869472i \(0.664459\pi\)
\(462\) 0 0
\(463\) −32.8563 −1.52696 −0.763481 0.645830i \(-0.776511\pi\)
−0.763481 + 0.645830i \(0.776511\pi\)
\(464\) 0 0
\(465\) 15.1047 0.700464
\(466\) 0 0
\(467\) −25.1183 −1.16233 −0.581167 0.813784i \(-0.697404\pi\)
−0.581167 + 0.813784i \(0.697404\pi\)
\(468\) 0 0
\(469\) −12.8578 −0.593716
\(470\) 0 0
\(471\) 35.6052 1.64060
\(472\) 0 0
\(473\) −4.94708 −0.227467
\(474\) 0 0
\(475\) −4.05596 −0.186100
\(476\) 0 0
\(477\) −7.45323 −0.341260
\(478\) 0 0
\(479\) −18.8332 −0.860512 −0.430256 0.902707i \(-0.641577\pi\)
−0.430256 + 0.902707i \(0.641577\pi\)
\(480\) 0 0
\(481\) −10.8226 −0.493468
\(482\) 0 0
\(483\) −10.5062 −0.478048
\(484\) 0 0
\(485\) −14.4183 −0.654702
\(486\) 0 0
\(487\) −23.9582 −1.08565 −0.542824 0.839847i \(-0.682645\pi\)
−0.542824 + 0.839847i \(0.682645\pi\)
\(488\) 0 0
\(489\) 4.45703 0.201554
\(490\) 0 0
\(491\) −6.97873 −0.314946 −0.157473 0.987523i \(-0.550335\pi\)
−0.157473 + 0.987523i \(0.550335\pi\)
\(492\) 0 0
\(493\) 0.759512 0.0342067
\(494\) 0 0
\(495\) −9.52216 −0.427989
\(496\) 0 0
\(497\) −4.44026 −0.199173
\(498\) 0 0
\(499\) 12.2887 0.550116 0.275058 0.961428i \(-0.411303\pi\)
0.275058 + 0.961428i \(0.411303\pi\)
\(500\) 0 0
\(501\) 29.5121 1.31850
\(502\) 0 0
\(503\) −1.30018 −0.0579722 −0.0289861 0.999580i \(-0.509228\pi\)
−0.0289861 + 0.999580i \(0.509228\pi\)
\(504\) 0 0
\(505\) −2.15189 −0.0957581
\(506\) 0 0
\(507\) −2.82075 −0.125274
\(508\) 0 0
\(509\) −24.7209 −1.09574 −0.547868 0.836565i \(-0.684560\pi\)
−0.547868 + 0.836565i \(0.684560\pi\)
\(510\) 0 0
\(511\) 1.16794 0.0516665
\(512\) 0 0
\(513\) −17.0959 −0.754801
\(514\) 0 0
\(515\) −1.92015 −0.0846119
\(516\) 0 0
\(517\) −0.799126 −0.0351455
\(518\) 0 0
\(519\) −25.1283 −1.10301
\(520\) 0 0
\(521\) 6.00539 0.263101 0.131550 0.991309i \(-0.458004\pi\)
0.131550 + 0.991309i \(0.458004\pi\)
\(522\) 0 0
\(523\) −11.7372 −0.513230 −0.256615 0.966514i \(-0.582607\pi\)
−0.256615 + 0.966514i \(0.582607\pi\)
\(524\) 0 0
\(525\) −3.69358 −0.161201
\(526\) 0 0
\(527\) −2.69014 −0.117184
\(528\) 0 0
\(529\) −9.12737 −0.396842
\(530\) 0 0
\(531\) 18.1072 0.785787
\(532\) 0 0
\(533\) −4.59093 −0.198855
\(534\) 0 0
\(535\) −10.6994 −0.462576
\(536\) 0 0
\(537\) 50.2645 2.16907
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −36.1370 −1.55365 −0.776826 0.629715i \(-0.783172\pi\)
−0.776826 + 0.629715i \(0.783172\pi\)
\(542\) 0 0
\(543\) 43.0426 1.84714
\(544\) 0 0
\(545\) −2.71897 −0.116468
\(546\) 0 0
\(547\) 6.13682 0.262392 0.131196 0.991356i \(-0.458118\pi\)
0.131196 + 0.991356i \(0.458118\pi\)
\(548\) 0 0
\(549\) 71.0860 3.03388
\(550\) 0 0
\(551\) −2.43766 −0.103848
\(552\) 0 0
\(553\) −9.23904 −0.392884
\(554\) 0 0
\(555\) −58.6467 −2.48941
\(556\) 0 0
\(557\) 2.07144 0.0877696 0.0438848 0.999037i \(-0.486027\pi\)
0.0438848 + 0.999037i \(0.486027\pi\)
\(558\) 0 0
\(559\) −4.94708 −0.209239
\(560\) 0 0
\(561\) 2.72232 0.114937
\(562\) 0 0
\(563\) −12.3135 −0.518953 −0.259476 0.965749i \(-0.583550\pi\)
−0.259476 + 0.965749i \(0.583550\pi\)
\(564\) 0 0
\(565\) −0.457665 −0.0192541
\(566\) 0 0
\(567\) −0.698463 −0.0293327
\(568\) 0 0
\(569\) 3.27822 0.137430 0.0687150 0.997636i \(-0.478110\pi\)
0.0687150 + 0.997636i \(0.478110\pi\)
\(570\) 0 0
\(571\) −12.5889 −0.526828 −0.263414 0.964683i \(-0.584849\pi\)
−0.263414 + 0.964683i \(0.584849\pi\)
\(572\) 0 0
\(573\) −35.6993 −1.49136
\(574\) 0 0
\(575\) 4.87710 0.203389
\(576\) 0 0
\(577\) 30.3850 1.26494 0.632471 0.774584i \(-0.282041\pi\)
0.632471 + 0.774584i \(0.282041\pi\)
\(578\) 0 0
\(579\) 47.9424 1.99242
\(580\) 0 0
\(581\) −6.28506 −0.260748
\(582\) 0 0
\(583\) −1.50368 −0.0622762
\(584\) 0 0
\(585\) −9.52216 −0.393693
\(586\) 0 0
\(587\) −23.1269 −0.954549 −0.477275 0.878754i \(-0.658375\pi\)
−0.477275 + 0.878754i \(0.658375\pi\)
\(588\) 0 0
\(589\) 8.63400 0.355758
\(590\) 0 0
\(591\) −27.3687 −1.12580
\(592\) 0 0
\(593\) −15.0928 −0.619785 −0.309893 0.950772i \(-0.600293\pi\)
−0.309893 + 0.950772i \(0.600293\pi\)
\(594\) 0 0
\(595\) −1.85405 −0.0760085
\(596\) 0 0
\(597\) 53.4190 2.18630
\(598\) 0 0
\(599\) −45.8369 −1.87285 −0.936423 0.350873i \(-0.885885\pi\)
−0.936423 + 0.350873i \(0.885885\pi\)
\(600\) 0 0
\(601\) −22.0710 −0.900295 −0.450147 0.892954i \(-0.648629\pi\)
−0.450147 + 0.892954i \(0.648629\pi\)
\(602\) 0 0
\(603\) 63.7315 2.59535
\(604\) 0 0
\(605\) −1.92109 −0.0781032
\(606\) 0 0
\(607\) 0.770767 0.0312845 0.0156422 0.999878i \(-0.495021\pi\)
0.0156422 + 0.999878i \(0.495021\pi\)
\(608\) 0 0
\(609\) −2.21986 −0.0899533
\(610\) 0 0
\(611\) −0.799126 −0.0323292
\(612\) 0 0
\(613\) −22.3061 −0.900935 −0.450467 0.892793i \(-0.648743\pi\)
−0.450467 + 0.892793i \(0.648743\pi\)
\(614\) 0 0
\(615\) −24.8779 −1.00317
\(616\) 0 0
\(617\) 8.72611 0.351300 0.175650 0.984453i \(-0.443797\pi\)
0.175650 + 0.984453i \(0.443797\pi\)
\(618\) 0 0
\(619\) 3.10198 0.124679 0.0623396 0.998055i \(-0.480144\pi\)
0.0623396 + 0.998055i \(0.480144\pi\)
\(620\) 0 0
\(621\) 20.5570 0.824922
\(622\) 0 0
\(623\) −4.46976 −0.179077
\(624\) 0 0
\(625\) −16.7382 −0.669530
\(626\) 0 0
\(627\) −8.73730 −0.348934
\(628\) 0 0
\(629\) 10.4449 0.416467
\(630\) 0 0
\(631\) 21.7298 0.865048 0.432524 0.901622i \(-0.357623\pi\)
0.432524 + 0.901622i \(0.357623\pi\)
\(632\) 0 0
\(633\) −33.5495 −1.33347
\(634\) 0 0
\(635\) 4.89074 0.194083
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) 22.0089 0.870657
\(640\) 0 0
\(641\) −4.59909 −0.181653 −0.0908265 0.995867i \(-0.528951\pi\)
−0.0908265 + 0.995867i \(0.528951\pi\)
\(642\) 0 0
\(643\) 24.7546 0.976226 0.488113 0.872780i \(-0.337685\pi\)
0.488113 + 0.872780i \(0.337685\pi\)
\(644\) 0 0
\(645\) −26.8078 −1.05556
\(646\) 0 0
\(647\) −27.5816 −1.08434 −0.542172 0.840268i \(-0.682398\pi\)
−0.542172 + 0.840268i \(0.682398\pi\)
\(648\) 0 0
\(649\) 3.65311 0.143397
\(650\) 0 0
\(651\) 7.86259 0.308159
\(652\) 0 0
\(653\) −13.5587 −0.530595 −0.265297 0.964167i \(-0.585470\pi\)
−0.265297 + 0.964167i \(0.585470\pi\)
\(654\) 0 0
\(655\) −13.5511 −0.529485
\(656\) 0 0
\(657\) −5.78906 −0.225853
\(658\) 0 0
\(659\) 27.9805 1.08997 0.544983 0.838447i \(-0.316536\pi\)
0.544983 + 0.838447i \(0.316536\pi\)
\(660\) 0 0
\(661\) −2.77272 −0.107846 −0.0539232 0.998545i \(-0.517173\pi\)
−0.0539232 + 0.998545i \(0.517173\pi\)
\(662\) 0 0
\(663\) 2.72232 0.105726
\(664\) 0 0
\(665\) 5.95057 0.230753
\(666\) 0 0
\(667\) 2.93116 0.113495
\(668\) 0 0
\(669\) −2.74581 −0.106159
\(670\) 0 0
\(671\) 14.3415 0.553648
\(672\) 0 0
\(673\) −11.0314 −0.425229 −0.212614 0.977136i \(-0.568198\pi\)
−0.212614 + 0.977136i \(0.568198\pi\)
\(674\) 0 0
\(675\) 7.22706 0.278170
\(676\) 0 0
\(677\) −4.07374 −0.156567 −0.0782834 0.996931i \(-0.524944\pi\)
−0.0782834 + 0.996931i \(0.524944\pi\)
\(678\) 0 0
\(679\) −7.50530 −0.288027
\(680\) 0 0
\(681\) 7.06944 0.270901
\(682\) 0 0
\(683\) −17.4545 −0.667878 −0.333939 0.942595i \(-0.608378\pi\)
−0.333939 + 0.942595i \(0.608378\pi\)
\(684\) 0 0
\(685\) 36.8847 1.40929
\(686\) 0 0
\(687\) −81.5582 −3.11164
\(688\) 0 0
\(689\) −1.50368 −0.0572857
\(690\) 0 0
\(691\) 2.95460 0.112398 0.0561992 0.998420i \(-0.482102\pi\)
0.0561992 + 0.998420i \(0.482102\pi\)
\(692\) 0 0
\(693\) −4.95665 −0.188288
\(694\) 0 0
\(695\) −28.4367 −1.07866
\(696\) 0 0
\(697\) 4.43073 0.167826
\(698\) 0 0
\(699\) −22.5239 −0.851931
\(700\) 0 0
\(701\) 33.6736 1.27184 0.635918 0.771757i \(-0.280622\pi\)
0.635918 + 0.771757i \(0.280622\pi\)
\(702\) 0 0
\(703\) −33.5231 −1.26435
\(704\) 0 0
\(705\) −4.33039 −0.163092
\(706\) 0 0
\(707\) −1.12014 −0.0421274
\(708\) 0 0
\(709\) 4.54524 0.170700 0.0853500 0.996351i \(-0.472799\pi\)
0.0853500 + 0.996351i \(0.472799\pi\)
\(710\) 0 0
\(711\) 45.7947 1.71744
\(712\) 0 0
\(713\) −10.3820 −0.388808
\(714\) 0 0
\(715\) −1.92109 −0.0718445
\(716\) 0 0
\(717\) −17.2907 −0.645734
\(718\) 0 0
\(719\) 4.41887 0.164796 0.0823979 0.996600i \(-0.473742\pi\)
0.0823979 + 0.996600i \(0.473742\pi\)
\(720\) 0 0
\(721\) −0.999512 −0.0372238
\(722\) 0 0
\(723\) 17.2849 0.642834
\(724\) 0 0
\(725\) 1.03049 0.0382713
\(726\) 0 0
\(727\) 29.7898 1.10484 0.552422 0.833565i \(-0.313704\pi\)
0.552422 + 0.833565i \(0.313704\pi\)
\(728\) 0 0
\(729\) −43.2432 −1.60160
\(730\) 0 0
\(731\) 4.77445 0.176589
\(732\) 0 0
\(733\) 15.3862 0.568301 0.284150 0.958780i \(-0.408288\pi\)
0.284150 + 0.958780i \(0.408288\pi\)
\(734\) 0 0
\(735\) 5.41891 0.199880
\(736\) 0 0
\(737\) 12.8578 0.473622
\(738\) 0 0
\(739\) −2.58332 −0.0950291 −0.0475146 0.998871i \(-0.515130\pi\)
−0.0475146 + 0.998871i \(0.515130\pi\)
\(740\) 0 0
\(741\) −8.73730 −0.320973
\(742\) 0 0
\(743\) 1.52107 0.0558028 0.0279014 0.999611i \(-0.491118\pi\)
0.0279014 + 0.999611i \(0.491118\pi\)
\(744\) 0 0
\(745\) 21.6588 0.793517
\(746\) 0 0
\(747\) 31.1529 1.13982
\(748\) 0 0
\(749\) −5.56947 −0.203504
\(750\) 0 0
\(751\) 9.78675 0.357124 0.178562 0.983929i \(-0.442856\pi\)
0.178562 + 0.983929i \(0.442856\pi\)
\(752\) 0 0
\(753\) −45.5603 −1.66031
\(754\) 0 0
\(755\) −7.85948 −0.286036
\(756\) 0 0
\(757\) −37.0214 −1.34557 −0.672784 0.739839i \(-0.734902\pi\)
−0.672784 + 0.739839i \(0.734902\pi\)
\(758\) 0 0
\(759\) 10.5062 0.381350
\(760\) 0 0
\(761\) 9.66051 0.350193 0.175097 0.984551i \(-0.443976\pi\)
0.175097 + 0.984551i \(0.443976\pi\)
\(762\) 0 0
\(763\) −1.41533 −0.0512384
\(764\) 0 0
\(765\) 9.18987 0.332261
\(766\) 0 0
\(767\) 3.65311 0.131906
\(768\) 0 0
\(769\) −22.6345 −0.816222 −0.408111 0.912932i \(-0.633812\pi\)
−0.408111 + 0.912932i \(0.633812\pi\)
\(770\) 0 0
\(771\) 21.7006 0.781529
\(772\) 0 0
\(773\) −10.4568 −0.376107 −0.188053 0.982159i \(-0.560218\pi\)
−0.188053 + 0.982159i \(0.560218\pi\)
\(774\) 0 0
\(775\) −3.64991 −0.131109
\(776\) 0 0
\(777\) −30.5279 −1.09518
\(778\) 0 0
\(779\) −14.2204 −0.509500
\(780\) 0 0
\(781\) 4.44026 0.158885
\(782\) 0 0
\(783\) 4.34350 0.155224
\(784\) 0 0
\(785\) 24.2491 0.865487
\(786\) 0 0
\(787\) 18.3322 0.653471 0.326735 0.945116i \(-0.394051\pi\)
0.326735 + 0.945116i \(0.394051\pi\)
\(788\) 0 0
\(789\) 37.1303 1.32187
\(790\) 0 0
\(791\) −0.238232 −0.00847057
\(792\) 0 0
\(793\) 14.3415 0.509282
\(794\) 0 0
\(795\) −8.14832 −0.288991
\(796\) 0 0
\(797\) −41.3042 −1.46307 −0.731535 0.681804i \(-0.761196\pi\)
−0.731535 + 0.681804i \(0.761196\pi\)
\(798\) 0 0
\(799\) 0.771239 0.0272845
\(800\) 0 0
\(801\) 22.1550 0.782810
\(802\) 0 0
\(803\) −1.16794 −0.0412156
\(804\) 0 0
\(805\) −7.15527 −0.252190
\(806\) 0 0
\(807\) 4.57630 0.161093
\(808\) 0 0
\(809\) 7.79972 0.274224 0.137112 0.990556i \(-0.456218\pi\)
0.137112 + 0.990556i \(0.456218\pi\)
\(810\) 0 0
\(811\) 49.1702 1.72660 0.863300 0.504692i \(-0.168394\pi\)
0.863300 + 0.504692i \(0.168394\pi\)
\(812\) 0 0
\(813\) 9.76253 0.342387
\(814\) 0 0
\(815\) 3.03548 0.106328
\(816\) 0 0
\(817\) −15.3236 −0.536105
\(818\) 0 0
\(819\) −4.95665 −0.173200
\(820\) 0 0
\(821\) 22.3354 0.779511 0.389755 0.920918i \(-0.372560\pi\)
0.389755 + 0.920918i \(0.372560\pi\)
\(822\) 0 0
\(823\) −43.1116 −1.50277 −0.751387 0.659861i \(-0.770615\pi\)
−0.751387 + 0.659861i \(0.770615\pi\)
\(824\) 0 0
\(825\) 3.69358 0.128594
\(826\) 0 0
\(827\) −21.2067 −0.737431 −0.368715 0.929542i \(-0.620202\pi\)
−0.368715 + 0.929542i \(0.620202\pi\)
\(828\) 0 0
\(829\) 6.96521 0.241912 0.120956 0.992658i \(-0.461404\pi\)
0.120956 + 0.992658i \(0.461404\pi\)
\(830\) 0 0
\(831\) 3.98556 0.138258
\(832\) 0 0
\(833\) −0.965104 −0.0334389
\(834\) 0 0
\(835\) 20.0993 0.695565
\(836\) 0 0
\(837\) −15.3844 −0.531762
\(838\) 0 0
\(839\) −18.8012 −0.649090 −0.324545 0.945870i \(-0.605211\pi\)
−0.324545 + 0.945870i \(0.605211\pi\)
\(840\) 0 0
\(841\) −28.3807 −0.978644
\(842\) 0 0
\(843\) 22.1107 0.761535
\(844\) 0 0
\(845\) −1.92109 −0.0660874
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −32.9617 −1.13124
\(850\) 0 0
\(851\) 40.3098 1.38180
\(852\) 0 0
\(853\) 21.1583 0.724448 0.362224 0.932091i \(-0.382018\pi\)
0.362224 + 0.932091i \(0.382018\pi\)
\(854\) 0 0
\(855\) −29.4949 −1.00871
\(856\) 0 0
\(857\) −21.4458 −0.732575 −0.366288 0.930502i \(-0.619371\pi\)
−0.366288 + 0.930502i \(0.619371\pi\)
\(858\) 0 0
\(859\) −27.6487 −0.943360 −0.471680 0.881770i \(-0.656352\pi\)
−0.471680 + 0.881770i \(0.656352\pi\)
\(860\) 0 0
\(861\) −12.9499 −0.441331
\(862\) 0 0
\(863\) −7.47498 −0.254451 −0.127226 0.991874i \(-0.540607\pi\)
−0.127226 + 0.991874i \(0.540607\pi\)
\(864\) 0 0
\(865\) −17.1137 −0.581885
\(866\) 0 0
\(867\) 45.3255 1.53933
\(868\) 0 0
\(869\) 9.23904 0.313413
\(870\) 0 0
\(871\) 12.8578 0.435669
\(872\) 0 0
\(873\) 37.2012 1.25907
\(874\) 0 0
\(875\) −12.1210 −0.409763
\(876\) 0 0
\(877\) −19.3194 −0.652368 −0.326184 0.945306i \(-0.605763\pi\)
−0.326184 + 0.945306i \(0.605763\pi\)
\(878\) 0 0
\(879\) 76.6739 2.58614
\(880\) 0 0
\(881\) −17.5591 −0.591579 −0.295790 0.955253i \(-0.595583\pi\)
−0.295790 + 0.955253i \(0.595583\pi\)
\(882\) 0 0
\(883\) 48.9084 1.64590 0.822950 0.568114i \(-0.192327\pi\)
0.822950 + 0.568114i \(0.192327\pi\)
\(884\) 0 0
\(885\) 19.7959 0.665432
\(886\) 0 0
\(887\) 17.9645 0.603187 0.301594 0.953437i \(-0.402481\pi\)
0.301594 + 0.953437i \(0.402481\pi\)
\(888\) 0 0
\(889\) 2.54582 0.0853840
\(890\) 0 0
\(891\) 0.698463 0.0233994
\(892\) 0 0
\(893\) −2.47529 −0.0828326
\(894\) 0 0
\(895\) 34.2328 1.14428
\(896\) 0 0
\(897\) 10.5062 0.350791
\(898\) 0 0
\(899\) −2.19362 −0.0731612
\(900\) 0 0
\(901\) 1.45121 0.0483468
\(902\) 0 0
\(903\) −13.9545 −0.464377
\(904\) 0 0
\(905\) 29.3144 0.974442
\(906\) 0 0
\(907\) 21.3944 0.710390 0.355195 0.934792i \(-0.384414\pi\)
0.355195 + 0.934792i \(0.384414\pi\)
\(908\) 0 0
\(909\) 5.55217 0.184154
\(910\) 0 0
\(911\) −47.8635 −1.58579 −0.792894 0.609359i \(-0.791427\pi\)
−0.792894 + 0.609359i \(0.791427\pi\)
\(912\) 0 0
\(913\) 6.28506 0.208005
\(914\) 0 0
\(915\) 77.7154 2.56919
\(916\) 0 0
\(917\) −7.05388 −0.232940
\(918\) 0 0
\(919\) 44.9869 1.48398 0.741991 0.670410i \(-0.233882\pi\)
0.741991 + 0.670410i \(0.233882\pi\)
\(920\) 0 0
\(921\) −69.7978 −2.29992
\(922\) 0 0
\(923\) 4.44026 0.146153
\(924\) 0 0
\(925\) 14.1714 0.465954
\(926\) 0 0
\(927\) 4.95424 0.162719
\(928\) 0 0
\(929\) 21.9391 0.719800 0.359900 0.932991i \(-0.382811\pi\)
0.359900 + 0.932991i \(0.382811\pi\)
\(930\) 0 0
\(931\) 3.09750 0.101517
\(932\) 0 0
\(933\) 54.4162 1.78151
\(934\) 0 0
\(935\) 1.85405 0.0606338
\(936\) 0 0
\(937\) −54.4149 −1.77766 −0.888829 0.458238i \(-0.848481\pi\)
−0.888829 + 0.458238i \(0.848481\pi\)
\(938\) 0 0
\(939\) −33.7299 −1.10073
\(940\) 0 0
\(941\) −20.7915 −0.677782 −0.338891 0.940826i \(-0.610052\pi\)
−0.338891 + 0.940826i \(0.610052\pi\)
\(942\) 0 0
\(943\) 17.0994 0.556833
\(944\) 0 0
\(945\) −10.6029 −0.344914
\(946\) 0 0
\(947\) 47.0249 1.52810 0.764052 0.645154i \(-0.223207\pi\)
0.764052 + 0.645154i \(0.223207\pi\)
\(948\) 0 0
\(949\) −1.16794 −0.0379129
\(950\) 0 0
\(951\) −45.0257 −1.46006
\(952\) 0 0
\(953\) −13.8050 −0.447187 −0.223594 0.974682i \(-0.571779\pi\)
−0.223594 + 0.974682i \(0.571779\pi\)
\(954\) 0 0
\(955\) −24.3131 −0.786754
\(956\) 0 0
\(957\) 2.21986 0.0717579
\(958\) 0 0
\(959\) 19.1999 0.619998
\(960\) 0 0
\(961\) −23.2304 −0.749367
\(962\) 0 0
\(963\) 27.6059 0.889588
\(964\) 0 0
\(965\) 32.6514 1.05109
\(966\) 0 0
\(967\) 26.2050 0.842697 0.421348 0.906899i \(-0.361557\pi\)
0.421348 + 0.906899i \(0.361557\pi\)
\(968\) 0 0
\(969\) 8.43240 0.270888
\(970\) 0 0
\(971\) −11.9621 −0.383883 −0.191942 0.981406i \(-0.561478\pi\)
−0.191942 + 0.981406i \(0.561478\pi\)
\(972\) 0 0
\(973\) −14.8024 −0.474543
\(974\) 0 0
\(975\) 3.69358 0.118289
\(976\) 0 0
\(977\) 19.7252 0.631064 0.315532 0.948915i \(-0.397817\pi\)
0.315532 + 0.948915i \(0.397817\pi\)
\(978\) 0 0
\(979\) 4.46976 0.142854
\(980\) 0 0
\(981\) 7.01531 0.223982
\(982\) 0 0
\(983\) 3.94017 0.125672 0.0628360 0.998024i \(-0.479985\pi\)
0.0628360 + 0.998024i \(0.479985\pi\)
\(984\) 0 0
\(985\) −18.6396 −0.593907
\(986\) 0 0
\(987\) −2.25414 −0.0717500
\(988\) 0 0
\(989\) 18.4259 0.585909
\(990\) 0 0
\(991\) −34.6737 −1.10145 −0.550723 0.834688i \(-0.685648\pi\)
−0.550723 + 0.834688i \(0.685648\pi\)
\(992\) 0 0
\(993\) 97.0791 3.08071
\(994\) 0 0
\(995\) 36.3813 1.15336
\(996\) 0 0
\(997\) −23.9427 −0.758274 −0.379137 0.925341i \(-0.623779\pi\)
−0.379137 + 0.925341i \(0.623779\pi\)
\(998\) 0 0
\(999\) 59.7326 1.88985
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 \(a_p\))