Properties

Label 4012.2.a.g.1.3
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.36915\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.36915 q^{3}\) \(+2.61284 q^{5}\) \(-2.25519 q^{7}\) \(+2.61289 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.36915 q^{3}\) \(+2.61284 q^{5}\) \(-2.25519 q^{7}\) \(+2.61289 q^{9}\) \(-6.06042 q^{11}\) \(+5.42929 q^{13}\) \(-6.19022 q^{15}\) \(-1.00000 q^{17}\) \(-4.71401 q^{19}\) \(+5.34289 q^{21}\) \(+9.23431 q^{23}\) \(+1.82693 q^{25}\) \(+0.917132 q^{27}\) \(+4.85561 q^{29}\) \(-0.261418 q^{31}\) \(+14.3581 q^{33}\) \(-5.89245 q^{35}\) \(+4.91282 q^{37}\) \(-12.8628 q^{39}\) \(-5.42987 q^{41}\) \(-5.25368 q^{43}\) \(+6.82705 q^{45}\) \(-1.34302 q^{47}\) \(-1.91412 q^{49}\) \(+2.36915 q^{51}\) \(+5.39130 q^{53}\) \(-15.8349 q^{55}\) \(+11.1682 q^{57}\) \(+1.00000 q^{59}\) \(-12.6581 q^{61}\) \(-5.89256 q^{63}\) \(+14.1859 q^{65}\) \(-3.44937 q^{67}\) \(-21.8775 q^{69}\) \(-2.07941 q^{71}\) \(-0.551991 q^{73}\) \(-4.32827 q^{75}\) \(+13.6674 q^{77}\) \(+15.1411 q^{79}\) \(-10.0115 q^{81}\) \(+7.01331 q^{83}\) \(-2.61284 q^{85}\) \(-11.5037 q^{87}\) \(-8.76169 q^{89}\) \(-12.2441 q^{91}\) \(+0.619339 q^{93}\) \(-12.3170 q^{95}\) \(-1.65497 q^{97}\) \(-15.8352 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.36915 −1.36783 −0.683916 0.729561i \(-0.739724\pi\)
−0.683916 + 0.729561i \(0.739724\pi\)
\(4\) 0 0
\(5\) 2.61284 1.16850 0.584249 0.811575i \(-0.301389\pi\)
0.584249 + 0.811575i \(0.301389\pi\)
\(6\) 0 0
\(7\) −2.25519 −0.852382 −0.426191 0.904633i \(-0.640145\pi\)
−0.426191 + 0.904633i \(0.640145\pi\)
\(8\) 0 0
\(9\) 2.61289 0.870962
\(10\) 0 0
\(11\) −6.06042 −1.82729 −0.913643 0.406517i \(-0.866743\pi\)
−0.913643 + 0.406517i \(0.866743\pi\)
\(12\) 0 0
\(13\) 5.42929 1.50581 0.752907 0.658127i \(-0.228651\pi\)
0.752907 + 0.658127i \(0.228651\pi\)
\(14\) 0 0
\(15\) −6.19022 −1.59831
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −4.71401 −1.08147 −0.540734 0.841193i \(-0.681854\pi\)
−0.540734 + 0.841193i \(0.681854\pi\)
\(20\) 0 0
\(21\) 5.34289 1.16591
\(22\) 0 0
\(23\) 9.23431 1.92549 0.962744 0.270415i \(-0.0871609\pi\)
0.962744 + 0.270415i \(0.0871609\pi\)
\(24\) 0 0
\(25\) 1.82693 0.365385
\(26\) 0 0
\(27\) 0.917132 0.176502
\(28\) 0 0
\(29\) 4.85561 0.901664 0.450832 0.892609i \(-0.351127\pi\)
0.450832 + 0.892609i \(0.351127\pi\)
\(30\) 0 0
\(31\) −0.261418 −0.0469521 −0.0234760 0.999724i \(-0.507473\pi\)
−0.0234760 + 0.999724i \(0.507473\pi\)
\(32\) 0 0
\(33\) 14.3581 2.49942
\(34\) 0 0
\(35\) −5.89245 −0.996006
\(36\) 0 0
\(37\) 4.91282 0.807663 0.403832 0.914833i \(-0.367678\pi\)
0.403832 + 0.914833i \(0.367678\pi\)
\(38\) 0 0
\(39\) −12.8628 −2.05970
\(40\) 0 0
\(41\) −5.42987 −0.848003 −0.424001 0.905662i \(-0.639375\pi\)
−0.424001 + 0.905662i \(0.639375\pi\)
\(42\) 0 0
\(43\) −5.25368 −0.801179 −0.400589 0.916258i \(-0.631195\pi\)
−0.400589 + 0.916258i \(0.631195\pi\)
\(44\) 0 0
\(45\) 6.82705 1.01772
\(46\) 0 0
\(47\) −1.34302 −0.195899 −0.0979495 0.995191i \(-0.531228\pi\)
−0.0979495 + 0.995191i \(0.531228\pi\)
\(48\) 0 0
\(49\) −1.91412 −0.273445
\(50\) 0 0
\(51\) 2.36915 0.331748
\(52\) 0 0
\(53\) 5.39130 0.740553 0.370276 0.928922i \(-0.379263\pi\)
0.370276 + 0.928922i \(0.379263\pi\)
\(54\) 0 0
\(55\) −15.8349 −2.13518
\(56\) 0 0
\(57\) 11.1682 1.47927
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −12.6581 −1.62070 −0.810350 0.585946i \(-0.800723\pi\)
−0.810350 + 0.585946i \(0.800723\pi\)
\(62\) 0 0
\(63\) −5.89256 −0.742392
\(64\) 0 0
\(65\) 14.1859 1.75954
\(66\) 0 0
\(67\) −3.44937 −0.421407 −0.210704 0.977550i \(-0.567576\pi\)
−0.210704 + 0.977550i \(0.567576\pi\)
\(68\) 0 0
\(69\) −21.8775 −2.63374
\(70\) 0 0
\(71\) −2.07941 −0.246780 −0.123390 0.992358i \(-0.539377\pi\)
−0.123390 + 0.992358i \(0.539377\pi\)
\(72\) 0 0
\(73\) −0.551991 −0.0646057 −0.0323029 0.999478i \(-0.510284\pi\)
−0.0323029 + 0.999478i \(0.510284\pi\)
\(74\) 0 0
\(75\) −4.32827 −0.499786
\(76\) 0 0
\(77\) 13.6674 1.55755
\(78\) 0 0
\(79\) 15.1411 1.70350 0.851752 0.523945i \(-0.175540\pi\)
0.851752 + 0.523945i \(0.175540\pi\)
\(80\) 0 0
\(81\) −10.0115 −1.11239
\(82\) 0 0
\(83\) 7.01331 0.769811 0.384906 0.922956i \(-0.374234\pi\)
0.384906 + 0.922956i \(0.374234\pi\)
\(84\) 0 0
\(85\) −2.61284 −0.283402
\(86\) 0 0
\(87\) −11.5037 −1.23332
\(88\) 0 0
\(89\) −8.76169 −0.928737 −0.464369 0.885642i \(-0.653719\pi\)
−0.464369 + 0.885642i \(0.653719\pi\)
\(90\) 0 0
\(91\) −12.2441 −1.28353
\(92\) 0 0
\(93\) 0.619339 0.0642225
\(94\) 0 0
\(95\) −12.3170 −1.26369
\(96\) 0 0
\(97\) −1.65497 −0.168037 −0.0840184 0.996464i \(-0.526775\pi\)
−0.0840184 + 0.996464i \(0.526775\pi\)
\(98\) 0 0
\(99\) −15.8352 −1.59150
\(100\) 0 0
\(101\) −10.3274 −1.02761 −0.513806 0.857906i \(-0.671765\pi\)
−0.513806 + 0.857906i \(0.671765\pi\)
\(102\) 0 0
\(103\) 6.42576 0.633149 0.316574 0.948568i \(-0.397467\pi\)
0.316574 + 0.948568i \(0.397467\pi\)
\(104\) 0 0
\(105\) 13.9601 1.36237
\(106\) 0 0
\(107\) −10.5279 −1.01777 −0.508887 0.860833i \(-0.669943\pi\)
−0.508887 + 0.860833i \(0.669943\pi\)
\(108\) 0 0
\(109\) −0.328812 −0.0314945 −0.0157473 0.999876i \(-0.505013\pi\)
−0.0157473 + 0.999876i \(0.505013\pi\)
\(110\) 0 0
\(111\) −11.6392 −1.10475
\(112\) 0 0
\(113\) −2.58368 −0.243052 −0.121526 0.992588i \(-0.538779\pi\)
−0.121526 + 0.992588i \(0.538779\pi\)
\(114\) 0 0
\(115\) 24.1278 2.24993
\(116\) 0 0
\(117\) 14.1861 1.31151
\(118\) 0 0
\(119\) 2.25519 0.206733
\(120\) 0 0
\(121\) 25.7287 2.33897
\(122\) 0 0
\(123\) 12.8642 1.15992
\(124\) 0 0
\(125\) −8.29073 −0.741545
\(126\) 0 0
\(127\) 2.01055 0.178407 0.0892037 0.996013i \(-0.471568\pi\)
0.0892037 + 0.996013i \(0.471568\pi\)
\(128\) 0 0
\(129\) 12.4468 1.09588
\(130\) 0 0
\(131\) 13.4608 1.17607 0.588036 0.808835i \(-0.299901\pi\)
0.588036 + 0.808835i \(0.299901\pi\)
\(132\) 0 0
\(133\) 10.6310 0.921824
\(134\) 0 0
\(135\) 2.39632 0.206242
\(136\) 0 0
\(137\) −19.1535 −1.63639 −0.818197 0.574939i \(-0.805026\pi\)
−0.818197 + 0.574939i \(0.805026\pi\)
\(138\) 0 0
\(139\) 14.2452 1.20826 0.604129 0.796886i \(-0.293521\pi\)
0.604129 + 0.796886i \(0.293521\pi\)
\(140\) 0 0
\(141\) 3.18181 0.267957
\(142\) 0 0
\(143\) −32.9038 −2.75155
\(144\) 0 0
\(145\) 12.6869 1.05359
\(146\) 0 0
\(147\) 4.53483 0.374027
\(148\) 0 0
\(149\) 6.55596 0.537085 0.268543 0.963268i \(-0.413458\pi\)
0.268543 + 0.963268i \(0.413458\pi\)
\(150\) 0 0
\(151\) −22.2739 −1.81262 −0.906311 0.422612i \(-0.861113\pi\)
−0.906311 + 0.422612i \(0.861113\pi\)
\(152\) 0 0
\(153\) −2.61289 −0.211239
\(154\) 0 0
\(155\) −0.683043 −0.0548633
\(156\) 0 0
\(157\) −9.47766 −0.756400 −0.378200 0.925724i \(-0.623457\pi\)
−0.378200 + 0.925724i \(0.623457\pi\)
\(158\) 0 0
\(159\) −12.7728 −1.01295
\(160\) 0 0
\(161\) −20.8251 −1.64125
\(162\) 0 0
\(163\) 4.15317 0.325301 0.162651 0.986684i \(-0.447996\pi\)
0.162651 + 0.986684i \(0.447996\pi\)
\(164\) 0 0
\(165\) 37.5153 2.92056
\(166\) 0 0
\(167\) −4.32048 −0.334329 −0.167164 0.985929i \(-0.553461\pi\)
−0.167164 + 0.985929i \(0.553461\pi\)
\(168\) 0 0
\(169\) 16.4772 1.26748
\(170\) 0 0
\(171\) −12.3172 −0.941918
\(172\) 0 0
\(173\) 6.97592 0.530369 0.265185 0.964198i \(-0.414567\pi\)
0.265185 + 0.964198i \(0.414567\pi\)
\(174\) 0 0
\(175\) −4.12007 −0.311448
\(176\) 0 0
\(177\) −2.36915 −0.178076
\(178\) 0 0
\(179\) −18.5731 −1.38822 −0.694109 0.719870i \(-0.744201\pi\)
−0.694109 + 0.719870i \(0.744201\pi\)
\(180\) 0 0
\(181\) −23.3636 −1.73660 −0.868300 0.496039i \(-0.834787\pi\)
−0.868300 + 0.496039i \(0.834787\pi\)
\(182\) 0 0
\(183\) 29.9889 2.21685
\(184\) 0 0
\(185\) 12.8364 0.943752
\(186\) 0 0
\(187\) 6.06042 0.443182
\(188\) 0 0
\(189\) −2.06831 −0.150447
\(190\) 0 0
\(191\) 3.19794 0.231395 0.115697 0.993285i \(-0.463090\pi\)
0.115697 + 0.993285i \(0.463090\pi\)
\(192\) 0 0
\(193\) −20.6927 −1.48950 −0.744748 0.667346i \(-0.767430\pi\)
−0.744748 + 0.667346i \(0.767430\pi\)
\(194\) 0 0
\(195\) −33.6085 −2.40675
\(196\) 0 0
\(197\) 1.44238 0.102765 0.0513827 0.998679i \(-0.483637\pi\)
0.0513827 + 0.998679i \(0.483637\pi\)
\(198\) 0 0
\(199\) −6.29939 −0.446552 −0.223276 0.974755i \(-0.571675\pi\)
−0.223276 + 0.974755i \(0.571675\pi\)
\(200\) 0 0
\(201\) 8.17208 0.576414
\(202\) 0 0
\(203\) −10.9503 −0.768562
\(204\) 0 0
\(205\) −14.1874 −0.990889
\(206\) 0 0
\(207\) 24.1282 1.67703
\(208\) 0 0
\(209\) 28.5689 1.97615
\(210\) 0 0
\(211\) 2.51274 0.172984 0.0864920 0.996253i \(-0.472434\pi\)
0.0864920 + 0.996253i \(0.472434\pi\)
\(212\) 0 0
\(213\) 4.92644 0.337554
\(214\) 0 0
\(215\) −13.7270 −0.936175
\(216\) 0 0
\(217\) 0.589547 0.0400211
\(218\) 0 0
\(219\) 1.30775 0.0883697
\(220\) 0 0
\(221\) −5.42929 −0.365214
\(222\) 0 0
\(223\) −1.19251 −0.0798561 −0.0399280 0.999203i \(-0.512713\pi\)
−0.0399280 + 0.999203i \(0.512713\pi\)
\(224\) 0 0
\(225\) 4.77355 0.318237
\(226\) 0 0
\(227\) −29.2551 −1.94173 −0.970865 0.239629i \(-0.922974\pi\)
−0.970865 + 0.239629i \(0.922974\pi\)
\(228\) 0 0
\(229\) −16.7652 −1.10787 −0.553937 0.832559i \(-0.686875\pi\)
−0.553937 + 0.832559i \(0.686875\pi\)
\(230\) 0 0
\(231\) −32.3802 −2.13046
\(232\) 0 0
\(233\) 11.8680 0.777498 0.388749 0.921344i \(-0.372907\pi\)
0.388749 + 0.921344i \(0.372907\pi\)
\(234\) 0 0
\(235\) −3.50908 −0.228907
\(236\) 0 0
\(237\) −35.8715 −2.33011
\(238\) 0 0
\(239\) −19.0664 −1.23330 −0.616652 0.787236i \(-0.711511\pi\)
−0.616652 + 0.787236i \(0.711511\pi\)
\(240\) 0 0
\(241\) 10.4893 0.675677 0.337838 0.941204i \(-0.390304\pi\)
0.337838 + 0.941204i \(0.390304\pi\)
\(242\) 0 0
\(243\) 20.9673 1.34506
\(244\) 0 0
\(245\) −5.00128 −0.319520
\(246\) 0 0
\(247\) −25.5937 −1.62849
\(248\) 0 0
\(249\) −16.6156 −1.05297
\(250\) 0 0
\(251\) −1.91962 −0.121165 −0.0605825 0.998163i \(-0.519296\pi\)
−0.0605825 + 0.998163i \(0.519296\pi\)
\(252\) 0 0
\(253\) −55.9638 −3.51842
\(254\) 0 0
\(255\) 6.19022 0.387646
\(256\) 0 0
\(257\) −15.0099 −0.936293 −0.468146 0.883651i \(-0.655078\pi\)
−0.468146 + 0.883651i \(0.655078\pi\)
\(258\) 0 0
\(259\) −11.0794 −0.688438
\(260\) 0 0
\(261\) 12.6872 0.785315
\(262\) 0 0
\(263\) −7.83895 −0.483370 −0.241685 0.970355i \(-0.577700\pi\)
−0.241685 + 0.970355i \(0.577700\pi\)
\(264\) 0 0
\(265\) 14.0866 0.865334
\(266\) 0 0
\(267\) 20.7578 1.27036
\(268\) 0 0
\(269\) −8.83638 −0.538764 −0.269382 0.963033i \(-0.586819\pi\)
−0.269382 + 0.963033i \(0.586819\pi\)
\(270\) 0 0
\(271\) −27.0201 −1.64136 −0.820678 0.571391i \(-0.806404\pi\)
−0.820678 + 0.571391i \(0.806404\pi\)
\(272\) 0 0
\(273\) 29.0081 1.75565
\(274\) 0 0
\(275\) −11.0720 −0.667664
\(276\) 0 0
\(277\) −24.5367 −1.47427 −0.737133 0.675748i \(-0.763821\pi\)
−0.737133 + 0.675748i \(0.763821\pi\)
\(278\) 0 0
\(279\) −0.683055 −0.0408935
\(280\) 0 0
\(281\) 12.8388 0.765896 0.382948 0.923770i \(-0.374909\pi\)
0.382948 + 0.923770i \(0.374909\pi\)
\(282\) 0 0
\(283\) 32.3095 1.92060 0.960302 0.278964i \(-0.0899911\pi\)
0.960302 + 0.278964i \(0.0899911\pi\)
\(284\) 0 0
\(285\) 29.1808 1.72852
\(286\) 0 0
\(287\) 12.2454 0.722822
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 3.92088 0.229846
\(292\) 0 0
\(293\) 7.83519 0.457737 0.228868 0.973457i \(-0.426497\pi\)
0.228868 + 0.973457i \(0.426497\pi\)
\(294\) 0 0
\(295\) 2.61284 0.152125
\(296\) 0 0
\(297\) −5.55821 −0.322520
\(298\) 0 0
\(299\) 50.1358 2.89943
\(300\) 0 0
\(301\) 11.8481 0.682910
\(302\) 0 0
\(303\) 24.4671 1.40560
\(304\) 0 0
\(305\) −33.0735 −1.89378
\(306\) 0 0
\(307\) −23.2355 −1.32612 −0.663059 0.748567i \(-0.730742\pi\)
−0.663059 + 0.748567i \(0.730742\pi\)
\(308\) 0 0
\(309\) −15.2236 −0.866041
\(310\) 0 0
\(311\) 24.8702 1.41026 0.705129 0.709079i \(-0.250889\pi\)
0.705129 + 0.709079i \(0.250889\pi\)
\(312\) 0 0
\(313\) −19.7144 −1.11432 −0.557162 0.830404i \(-0.688110\pi\)
−0.557162 + 0.830404i \(0.688110\pi\)
\(314\) 0 0
\(315\) −15.3963 −0.867483
\(316\) 0 0
\(317\) 1.20697 0.0677904 0.0338952 0.999425i \(-0.489209\pi\)
0.0338952 + 0.999425i \(0.489209\pi\)
\(318\) 0 0
\(319\) −29.4270 −1.64760
\(320\) 0 0
\(321\) 24.9423 1.39214
\(322\) 0 0
\(323\) 4.71401 0.262295
\(324\) 0 0
\(325\) 9.91892 0.550203
\(326\) 0 0
\(327\) 0.779007 0.0430792
\(328\) 0 0
\(329\) 3.02876 0.166981
\(330\) 0 0
\(331\) −22.7735 −1.25175 −0.625873 0.779925i \(-0.715257\pi\)
−0.625873 + 0.779925i \(0.715257\pi\)
\(332\) 0 0
\(333\) 12.8366 0.703444
\(334\) 0 0
\(335\) −9.01264 −0.492413
\(336\) 0 0
\(337\) −31.6281 −1.72289 −0.861447 0.507848i \(-0.830441\pi\)
−0.861447 + 0.507848i \(0.830441\pi\)
\(338\) 0 0
\(339\) 6.12112 0.332454
\(340\) 0 0
\(341\) 1.58430 0.0857948
\(342\) 0 0
\(343\) 20.1030 1.08546
\(344\) 0 0
\(345\) −57.1624 −3.07752
\(346\) 0 0
\(347\) 12.3370 0.662283 0.331141 0.943581i \(-0.392566\pi\)
0.331141 + 0.943581i \(0.392566\pi\)
\(348\) 0 0
\(349\) 17.5046 0.936999 0.468499 0.883464i \(-0.344795\pi\)
0.468499 + 0.883464i \(0.344795\pi\)
\(350\) 0 0
\(351\) 4.97938 0.265779
\(352\) 0 0
\(353\) −12.6537 −0.673488 −0.336744 0.941596i \(-0.609326\pi\)
−0.336744 + 0.941596i \(0.609326\pi\)
\(354\) 0 0
\(355\) −5.43316 −0.288362
\(356\) 0 0
\(357\) −5.34289 −0.282776
\(358\) 0 0
\(359\) 26.6098 1.40441 0.702206 0.711974i \(-0.252199\pi\)
0.702206 + 0.711974i \(0.252199\pi\)
\(360\) 0 0
\(361\) 3.22193 0.169575
\(362\) 0 0
\(363\) −60.9553 −3.19932
\(364\) 0 0
\(365\) −1.44226 −0.0754916
\(366\) 0 0
\(367\) 16.8798 0.881119 0.440560 0.897723i \(-0.354780\pi\)
0.440560 + 0.897723i \(0.354780\pi\)
\(368\) 0 0
\(369\) −14.1876 −0.738578
\(370\) 0 0
\(371\) −12.1584 −0.631234
\(372\) 0 0
\(373\) −28.4599 −1.47360 −0.736800 0.676111i \(-0.763664\pi\)
−0.736800 + 0.676111i \(0.763664\pi\)
\(374\) 0 0
\(375\) 19.6420 1.01431
\(376\) 0 0
\(377\) 26.3625 1.35774
\(378\) 0 0
\(379\) 29.1179 1.49569 0.747843 0.663876i \(-0.231090\pi\)
0.747843 + 0.663876i \(0.231090\pi\)
\(380\) 0 0
\(381\) −4.76330 −0.244031
\(382\) 0 0
\(383\) −32.0664 −1.63852 −0.819258 0.573425i \(-0.805614\pi\)
−0.819258 + 0.573425i \(0.805614\pi\)
\(384\) 0 0
\(385\) 35.7107 1.81999
\(386\) 0 0
\(387\) −13.7273 −0.697796
\(388\) 0 0
\(389\) −19.3753 −0.982369 −0.491184 0.871056i \(-0.663436\pi\)
−0.491184 + 0.871056i \(0.663436\pi\)
\(390\) 0 0
\(391\) −9.23431 −0.466999
\(392\) 0 0
\(393\) −31.8906 −1.60867
\(394\) 0 0
\(395\) 39.5612 1.99054
\(396\) 0 0
\(397\) 6.83768 0.343173 0.171587 0.985169i \(-0.445111\pi\)
0.171587 + 0.985169i \(0.445111\pi\)
\(398\) 0 0
\(399\) −25.1865 −1.26090
\(400\) 0 0
\(401\) −10.4316 −0.520930 −0.260465 0.965483i \(-0.583876\pi\)
−0.260465 + 0.965483i \(0.583876\pi\)
\(402\) 0 0
\(403\) −1.41931 −0.0707011
\(404\) 0 0
\(405\) −26.1584 −1.29982
\(406\) 0 0
\(407\) −29.7738 −1.47583
\(408\) 0 0
\(409\) −13.7407 −0.679436 −0.339718 0.940527i \(-0.610332\pi\)
−0.339718 + 0.940527i \(0.610332\pi\)
\(410\) 0 0
\(411\) 45.3776 2.23831
\(412\) 0 0
\(413\) −2.25519 −0.110971
\(414\) 0 0
\(415\) 18.3247 0.899522
\(416\) 0 0
\(417\) −33.7490 −1.65269
\(418\) 0 0
\(419\) −9.01763 −0.440540 −0.220270 0.975439i \(-0.570694\pi\)
−0.220270 + 0.975439i \(0.570694\pi\)
\(420\) 0 0
\(421\) 40.4142 1.96967 0.984833 0.173507i \(-0.0555100\pi\)
0.984833 + 0.173507i \(0.0555100\pi\)
\(422\) 0 0
\(423\) −3.50915 −0.170621
\(424\) 0 0
\(425\) −1.82693 −0.0886190
\(426\) 0 0
\(427\) 28.5464 1.38146
\(428\) 0 0
\(429\) 77.9541 3.76366
\(430\) 0 0
\(431\) −10.1119 −0.487074 −0.243537 0.969892i \(-0.578308\pi\)
−0.243537 + 0.969892i \(0.578308\pi\)
\(432\) 0 0
\(433\) 14.9409 0.718014 0.359007 0.933335i \(-0.383115\pi\)
0.359007 + 0.933335i \(0.383115\pi\)
\(434\) 0 0
\(435\) −30.0573 −1.44114
\(436\) 0 0
\(437\) −43.5307 −2.08236
\(438\) 0 0
\(439\) −22.7125 −1.08401 −0.542004 0.840376i \(-0.682334\pi\)
−0.542004 + 0.840376i \(0.682334\pi\)
\(440\) 0 0
\(441\) −5.00137 −0.238160
\(442\) 0 0
\(443\) −1.53378 −0.0728720 −0.0364360 0.999336i \(-0.511601\pi\)
−0.0364360 + 0.999336i \(0.511601\pi\)
\(444\) 0 0
\(445\) −22.8929 −1.08523
\(446\) 0 0
\(447\) −15.5321 −0.734642
\(448\) 0 0
\(449\) −13.8416 −0.653228 −0.326614 0.945158i \(-0.605908\pi\)
−0.326614 + 0.945158i \(0.605908\pi\)
\(450\) 0 0
\(451\) 32.9073 1.54954
\(452\) 0 0
\(453\) 52.7702 2.47936
\(454\) 0 0
\(455\) −31.9918 −1.49980
\(456\) 0 0
\(457\) −30.4282 −1.42337 −0.711685 0.702499i \(-0.752068\pi\)
−0.711685 + 0.702499i \(0.752068\pi\)
\(458\) 0 0
\(459\) −0.917132 −0.0428081
\(460\) 0 0
\(461\) 16.5661 0.771561 0.385780 0.922591i \(-0.373932\pi\)
0.385780 + 0.922591i \(0.373932\pi\)
\(462\) 0 0
\(463\) 14.7244 0.684300 0.342150 0.939645i \(-0.388845\pi\)
0.342150 + 0.939645i \(0.388845\pi\)
\(464\) 0 0
\(465\) 1.61823 0.0750438
\(466\) 0 0
\(467\) −0.384116 −0.0177747 −0.00888737 0.999961i \(-0.502829\pi\)
−0.00888737 + 0.999961i \(0.502829\pi\)
\(468\) 0 0
\(469\) 7.77898 0.359200
\(470\) 0 0
\(471\) 22.4540 1.03463
\(472\) 0 0
\(473\) 31.8395 1.46398
\(474\) 0 0
\(475\) −8.61216 −0.395153
\(476\) 0 0
\(477\) 14.0869 0.644993
\(478\) 0 0
\(479\) 29.5628 1.35076 0.675380 0.737469i \(-0.263979\pi\)
0.675380 + 0.737469i \(0.263979\pi\)
\(480\) 0 0
\(481\) 26.6731 1.21619
\(482\) 0 0
\(483\) 49.3379 2.24495
\(484\) 0 0
\(485\) −4.32417 −0.196351
\(486\) 0 0
\(487\) 8.39436 0.380385 0.190192 0.981747i \(-0.439089\pi\)
0.190192 + 0.981747i \(0.439089\pi\)
\(488\) 0 0
\(489\) −9.83949 −0.444957
\(490\) 0 0
\(491\) −42.2433 −1.90642 −0.953208 0.302316i \(-0.902240\pi\)
−0.953208 + 0.302316i \(0.902240\pi\)
\(492\) 0 0
\(493\) −4.85561 −0.218686
\(494\) 0 0
\(495\) −41.3748 −1.85966
\(496\) 0 0
\(497\) 4.68946 0.210351
\(498\) 0 0
\(499\) −10.8615 −0.486227 −0.243114 0.969998i \(-0.578169\pi\)
−0.243114 + 0.969998i \(0.578169\pi\)
\(500\) 0 0
\(501\) 10.2359 0.457305
\(502\) 0 0
\(503\) −36.9612 −1.64802 −0.824008 0.566578i \(-0.808267\pi\)
−0.824008 + 0.566578i \(0.808267\pi\)
\(504\) 0 0
\(505\) −26.9838 −1.20076
\(506\) 0 0
\(507\) −39.0370 −1.73369
\(508\) 0 0
\(509\) 9.67091 0.428655 0.214328 0.976762i \(-0.431244\pi\)
0.214328 + 0.976762i \(0.431244\pi\)
\(510\) 0 0
\(511\) 1.24485 0.0550687
\(512\) 0 0
\(513\) −4.32337 −0.190882
\(514\) 0 0
\(515\) 16.7895 0.739833
\(516\) 0 0
\(517\) 8.13924 0.357963
\(518\) 0 0
\(519\) −16.5270 −0.725456
\(520\) 0 0
\(521\) 6.39688 0.280253 0.140126 0.990134i \(-0.455249\pi\)
0.140126 + 0.990134i \(0.455249\pi\)
\(522\) 0 0
\(523\) −23.1391 −1.01180 −0.505902 0.862591i \(-0.668840\pi\)
−0.505902 + 0.862591i \(0.668840\pi\)
\(524\) 0 0
\(525\) 9.76107 0.426008
\(526\) 0 0
\(527\) 0.261418 0.0113875
\(528\) 0 0
\(529\) 62.2726 2.70750
\(530\) 0 0
\(531\) 2.61289 0.113390
\(532\) 0 0
\(533\) −29.4803 −1.27693
\(534\) 0 0
\(535\) −27.5078 −1.18927
\(536\) 0 0
\(537\) 44.0025 1.89885
\(538\) 0 0
\(539\) 11.6004 0.499663
\(540\) 0 0
\(541\) −26.6644 −1.14639 −0.573196 0.819418i \(-0.694297\pi\)
−0.573196 + 0.819418i \(0.694297\pi\)
\(542\) 0 0
\(543\) 55.3519 2.37538
\(544\) 0 0
\(545\) −0.859134 −0.0368012
\(546\) 0 0
\(547\) 21.5239 0.920294 0.460147 0.887843i \(-0.347797\pi\)
0.460147 + 0.887843i \(0.347797\pi\)
\(548\) 0 0
\(549\) −33.0741 −1.41157
\(550\) 0 0
\(551\) −22.8894 −0.975121
\(552\) 0 0
\(553\) −34.1460 −1.45204
\(554\) 0 0
\(555\) −30.4114 −1.29089
\(556\) 0 0
\(557\) 28.3005 1.19913 0.599565 0.800326i \(-0.295340\pi\)
0.599565 + 0.800326i \(0.295340\pi\)
\(558\) 0 0
\(559\) −28.5238 −1.20643
\(560\) 0 0
\(561\) −14.3581 −0.606198
\(562\) 0 0
\(563\) −0.369301 −0.0155642 −0.00778209 0.999970i \(-0.502477\pi\)
−0.00778209 + 0.999970i \(0.502477\pi\)
\(564\) 0 0
\(565\) −6.75073 −0.284005
\(566\) 0 0
\(567\) 22.5778 0.948179
\(568\) 0 0
\(569\) 14.2674 0.598120 0.299060 0.954234i \(-0.403327\pi\)
0.299060 + 0.954234i \(0.403327\pi\)
\(570\) 0 0
\(571\) 29.6239 1.23972 0.619860 0.784713i \(-0.287189\pi\)
0.619860 + 0.784713i \(0.287189\pi\)
\(572\) 0 0
\(573\) −7.57640 −0.316509
\(574\) 0 0
\(575\) 16.8704 0.703545
\(576\) 0 0
\(577\) −10.7653 −0.448167 −0.224084 0.974570i \(-0.571939\pi\)
−0.224084 + 0.974570i \(0.571939\pi\)
\(578\) 0 0
\(579\) 49.0243 2.03738
\(580\) 0 0
\(581\) −15.8164 −0.656173
\(582\) 0 0
\(583\) −32.6736 −1.35320
\(584\) 0 0
\(585\) 37.0660 1.53249
\(586\) 0 0
\(587\) −9.82168 −0.405384 −0.202692 0.979243i \(-0.564969\pi\)
−0.202692 + 0.979243i \(0.564969\pi\)
\(588\) 0 0
\(589\) 1.23233 0.0507772
\(590\) 0 0
\(591\) −3.41722 −0.140566
\(592\) 0 0
\(593\) 33.6900 1.38348 0.691741 0.722146i \(-0.256844\pi\)
0.691741 + 0.722146i \(0.256844\pi\)
\(594\) 0 0
\(595\) 5.89245 0.241567
\(596\) 0 0
\(597\) 14.9242 0.610808
\(598\) 0 0
\(599\) −9.78884 −0.399961 −0.199981 0.979800i \(-0.564088\pi\)
−0.199981 + 0.979800i \(0.564088\pi\)
\(600\) 0 0
\(601\) 2.64087 0.107723 0.0538616 0.998548i \(-0.482847\pi\)
0.0538616 + 0.998548i \(0.482847\pi\)
\(602\) 0 0
\(603\) −9.01281 −0.367030
\(604\) 0 0
\(605\) 67.2250 2.73308
\(606\) 0 0
\(607\) 15.4789 0.628268 0.314134 0.949379i \(-0.398286\pi\)
0.314134 + 0.949379i \(0.398286\pi\)
\(608\) 0 0
\(609\) 25.9430 1.05126
\(610\) 0 0
\(611\) −7.29162 −0.294987
\(612\) 0 0
\(613\) 16.0780 0.649382 0.324691 0.945820i \(-0.394740\pi\)
0.324691 + 0.945820i \(0.394740\pi\)
\(614\) 0 0
\(615\) 33.6120 1.35537
\(616\) 0 0
\(617\) −42.1336 −1.69623 −0.848116 0.529810i \(-0.822263\pi\)
−0.848116 + 0.529810i \(0.822263\pi\)
\(618\) 0 0
\(619\) −17.6412 −0.709061 −0.354530 0.935045i \(-0.615359\pi\)
−0.354530 + 0.935045i \(0.615359\pi\)
\(620\) 0 0
\(621\) 8.46909 0.339853
\(622\) 0 0
\(623\) 19.7593 0.791639
\(624\) 0 0
\(625\) −30.7970 −1.23188
\(626\) 0 0
\(627\) −67.6841 −2.70304
\(628\) 0 0
\(629\) −4.91282 −0.195887
\(630\) 0 0
\(631\) 40.2793 1.60350 0.801748 0.597663i \(-0.203904\pi\)
0.801748 + 0.597663i \(0.203904\pi\)
\(632\) 0 0
\(633\) −5.95306 −0.236613
\(634\) 0 0
\(635\) 5.25324 0.208468
\(636\) 0 0
\(637\) −10.3923 −0.411758
\(638\) 0 0
\(639\) −5.43326 −0.214936
\(640\) 0 0
\(641\) −6.22392 −0.245830 −0.122915 0.992417i \(-0.539224\pi\)
−0.122915 + 0.992417i \(0.539224\pi\)
\(642\) 0 0
\(643\) 40.6123 1.60159 0.800796 0.598937i \(-0.204410\pi\)
0.800796 + 0.598937i \(0.204410\pi\)
\(644\) 0 0
\(645\) 32.5214 1.28053
\(646\) 0 0
\(647\) −42.4761 −1.66991 −0.834953 0.550321i \(-0.814505\pi\)
−0.834953 + 0.550321i \(0.814505\pi\)
\(648\) 0 0
\(649\) −6.06042 −0.237892
\(650\) 0 0
\(651\) −1.39673 −0.0547421
\(652\) 0 0
\(653\) −1.45550 −0.0569582 −0.0284791 0.999594i \(-0.509066\pi\)
−0.0284791 + 0.999594i \(0.509066\pi\)
\(654\) 0 0
\(655\) 35.1708 1.37424
\(656\) 0 0
\(657\) −1.44229 −0.0562691
\(658\) 0 0
\(659\) −12.1468 −0.473172 −0.236586 0.971611i \(-0.576028\pi\)
−0.236586 + 0.971611i \(0.576028\pi\)
\(660\) 0 0
\(661\) −24.1812 −0.940541 −0.470271 0.882522i \(-0.655844\pi\)
−0.470271 + 0.882522i \(0.655844\pi\)
\(662\) 0 0
\(663\) 12.8628 0.499550
\(664\) 0 0
\(665\) 27.7771 1.07715
\(666\) 0 0
\(667\) 44.8382 1.73614
\(668\) 0 0
\(669\) 2.82523 0.109230
\(670\) 0 0
\(671\) 76.7133 2.96148
\(672\) 0 0
\(673\) 28.6407 1.10402 0.552009 0.833838i \(-0.313861\pi\)
0.552009 + 0.833838i \(0.313861\pi\)
\(674\) 0 0
\(675\) 1.67553 0.0644913
\(676\) 0 0
\(677\) 30.3915 1.16804 0.584020 0.811739i \(-0.301479\pi\)
0.584020 + 0.811739i \(0.301479\pi\)
\(678\) 0 0
\(679\) 3.73228 0.143232
\(680\) 0 0
\(681\) 69.3098 2.65596
\(682\) 0 0
\(683\) −42.1625 −1.61330 −0.806651 0.591028i \(-0.798722\pi\)
−0.806651 + 0.591028i \(0.798722\pi\)
\(684\) 0 0
\(685\) −50.0450 −1.91212
\(686\) 0 0
\(687\) 39.7192 1.51538
\(688\) 0 0
\(689\) 29.2710 1.11513
\(690\) 0 0
\(691\) −6.37017 −0.242333 −0.121166 0.992632i \(-0.538663\pi\)
−0.121166 + 0.992632i \(0.538663\pi\)
\(692\) 0 0
\(693\) 35.7114 1.35656
\(694\) 0 0
\(695\) 37.2203 1.41185
\(696\) 0 0
\(697\) 5.42987 0.205671
\(698\) 0 0
\(699\) −28.1171 −1.06349
\(700\) 0 0
\(701\) −27.0562 −1.02190 −0.510948 0.859611i \(-0.670706\pi\)
−0.510948 + 0.859611i \(0.670706\pi\)
\(702\) 0 0
\(703\) −23.1591 −0.873463
\(704\) 0 0
\(705\) 8.31355 0.313107
\(706\) 0 0
\(707\) 23.2902 0.875918
\(708\) 0 0
\(709\) 26.8377 1.00791 0.503955 0.863730i \(-0.331878\pi\)
0.503955 + 0.863730i \(0.331878\pi\)
\(710\) 0 0
\(711\) 39.5619 1.48369
\(712\) 0 0
\(713\) −2.41402 −0.0904056
\(714\) 0 0
\(715\) −85.9723 −3.21518
\(716\) 0 0
\(717\) 45.1712 1.68695
\(718\) 0 0
\(719\) −14.3047 −0.533476 −0.266738 0.963769i \(-0.585946\pi\)
−0.266738 + 0.963769i \(0.585946\pi\)
\(720\) 0 0
\(721\) −14.4913 −0.539685
\(722\) 0 0
\(723\) −24.8508 −0.924211
\(724\) 0 0
\(725\) 8.87084 0.329455
\(726\) 0 0
\(727\) −23.1343 −0.858005 −0.429003 0.903303i \(-0.641135\pi\)
−0.429003 + 0.903303i \(0.641135\pi\)
\(728\) 0 0
\(729\) −19.6404 −0.727422
\(730\) 0 0
\(731\) 5.25368 0.194314
\(732\) 0 0
\(733\) 45.4479 1.67866 0.839329 0.543624i \(-0.182948\pi\)
0.839329 + 0.543624i \(0.182948\pi\)
\(734\) 0 0
\(735\) 11.8488 0.437049
\(736\) 0 0
\(737\) 20.9046 0.770032
\(738\) 0 0
\(739\) −39.6465 −1.45842 −0.729210 0.684290i \(-0.760112\pi\)
−0.729210 + 0.684290i \(0.760112\pi\)
\(740\) 0 0
\(741\) 60.6355 2.22750
\(742\) 0 0
\(743\) −42.5081 −1.55947 −0.779736 0.626108i \(-0.784647\pi\)
−0.779736 + 0.626108i \(0.784647\pi\)
\(744\) 0 0
\(745\) 17.1297 0.627582
\(746\) 0 0
\(747\) 18.3250 0.670476
\(748\) 0 0
\(749\) 23.7425 0.867533
\(750\) 0 0
\(751\) 15.6674 0.571712 0.285856 0.958273i \(-0.407722\pi\)
0.285856 + 0.958273i \(0.407722\pi\)
\(752\) 0 0
\(753\) 4.54786 0.165733
\(754\) 0 0
\(755\) −58.1980 −2.11804
\(756\) 0 0
\(757\) 42.5551 1.54669 0.773345 0.633985i \(-0.218582\pi\)
0.773345 + 0.633985i \(0.218582\pi\)
\(758\) 0 0
\(759\) 132.587 4.81260
\(760\) 0 0
\(761\) 36.1326 1.30981 0.654903 0.755713i \(-0.272709\pi\)
0.654903 + 0.755713i \(0.272709\pi\)
\(762\) 0 0
\(763\) 0.741535 0.0268454
\(764\) 0 0
\(765\) −6.82705 −0.246833
\(766\) 0 0
\(767\) 5.42929 0.196040
\(768\) 0 0
\(769\) 23.5262 0.848378 0.424189 0.905574i \(-0.360559\pi\)
0.424189 + 0.905574i \(0.360559\pi\)
\(770\) 0 0
\(771\) 35.5608 1.28069
\(772\) 0 0
\(773\) −8.44290 −0.303670 −0.151835 0.988406i \(-0.548518\pi\)
−0.151835 + 0.988406i \(0.548518\pi\)
\(774\) 0 0
\(775\) −0.477592 −0.0171556
\(776\) 0 0
\(777\) 26.2487 0.941666
\(778\) 0 0
\(779\) 25.5965 0.917089
\(780\) 0 0
\(781\) 12.6021 0.450938
\(782\) 0 0
\(783\) 4.45323 0.159146
\(784\) 0 0
\(785\) −24.7636 −0.883851
\(786\) 0 0
\(787\) 52.5998 1.87498 0.937491 0.348009i \(-0.113142\pi\)
0.937491 + 0.348009i \(0.113142\pi\)
\(788\) 0 0
\(789\) 18.5717 0.661169
\(790\) 0 0
\(791\) 5.82668 0.207173
\(792\) 0 0
\(793\) −68.7244 −2.44047
\(794\) 0 0
\(795\) −33.3733 −1.18363
\(796\) 0 0
\(797\) −5.46355 −0.193529 −0.0967645 0.995307i \(-0.530849\pi\)
−0.0967645 + 0.995307i \(0.530849\pi\)
\(798\) 0 0
\(799\) 1.34302 0.0475125
\(800\) 0 0
\(801\) −22.8933 −0.808895
\(802\) 0 0
\(803\) 3.34530 0.118053
\(804\) 0 0
\(805\) −54.4127 −1.91780
\(806\) 0 0
\(807\) 20.9347 0.736938
\(808\) 0 0
\(809\) 7.54210 0.265166 0.132583 0.991172i \(-0.457673\pi\)
0.132583 + 0.991172i \(0.457673\pi\)
\(810\) 0 0
\(811\) −37.2599 −1.30837 −0.654187 0.756333i \(-0.726989\pi\)
−0.654187 + 0.756333i \(0.726989\pi\)
\(812\) 0 0
\(813\) 64.0148 2.24510
\(814\) 0 0
\(815\) 10.8516 0.380114
\(816\) 0 0
\(817\) 24.7659 0.866450
\(818\) 0 0
\(819\) −31.9924 −1.11790
\(820\) 0 0
\(821\) 42.2056 1.47299 0.736494 0.676445i \(-0.236480\pi\)
0.736494 + 0.676445i \(0.236480\pi\)
\(822\) 0 0
\(823\) −8.40358 −0.292930 −0.146465 0.989216i \(-0.546790\pi\)
−0.146465 + 0.989216i \(0.546790\pi\)
\(824\) 0 0
\(825\) 26.2311 0.913251
\(826\) 0 0
\(827\) 40.2908 1.40105 0.700525 0.713628i \(-0.252949\pi\)
0.700525 + 0.713628i \(0.252949\pi\)
\(828\) 0 0
\(829\) 32.4352 1.12652 0.563261 0.826279i \(-0.309547\pi\)
0.563261 + 0.826279i \(0.309547\pi\)
\(830\) 0 0
\(831\) 58.1311 2.01655
\(832\) 0 0
\(833\) 1.91412 0.0663202
\(834\) 0 0
\(835\) −11.2887 −0.390662
\(836\) 0 0
\(837\) −0.239755 −0.00828714
\(838\) 0 0
\(839\) −38.7784 −1.33878 −0.669390 0.742911i \(-0.733445\pi\)
−0.669390 + 0.742911i \(0.733445\pi\)
\(840\) 0 0
\(841\) −5.42307 −0.187002
\(842\) 0 0
\(843\) −30.4170 −1.04762
\(844\) 0 0
\(845\) 43.0522 1.48104
\(846\) 0 0
\(847\) −58.0232 −1.99370
\(848\) 0 0
\(849\) −76.5463 −2.62706
\(850\) 0 0
\(851\) 45.3666 1.55515
\(852\) 0 0
\(853\) 25.0484 0.857640 0.428820 0.903390i \(-0.358929\pi\)
0.428820 + 0.903390i \(0.358929\pi\)
\(854\) 0 0
\(855\) −32.1828 −1.10063
\(856\) 0 0
\(857\) 36.6693 1.25260 0.626300 0.779582i \(-0.284569\pi\)
0.626300 + 0.779582i \(0.284569\pi\)
\(858\) 0 0
\(859\) −12.8294 −0.437734 −0.218867 0.975755i \(-0.570236\pi\)
−0.218867 + 0.975755i \(0.570236\pi\)
\(860\) 0 0
\(861\) −29.0112 −0.988699
\(862\) 0 0
\(863\) −35.0474 −1.19303 −0.596513 0.802603i \(-0.703448\pi\)
−0.596513 + 0.802603i \(0.703448\pi\)
\(864\) 0 0
\(865\) 18.2270 0.619735
\(866\) 0 0
\(867\) −2.36915 −0.0804607
\(868\) 0 0
\(869\) −91.7613 −3.11279
\(870\) 0 0
\(871\) −18.7276 −0.634561
\(872\) 0 0
\(873\) −4.32425 −0.146354
\(874\) 0 0
\(875\) 18.6972 0.632080
\(876\) 0 0
\(877\) 15.6076 0.527032 0.263516 0.964655i \(-0.415118\pi\)
0.263516 + 0.964655i \(0.415118\pi\)
\(878\) 0 0
\(879\) −18.5628 −0.626106
\(880\) 0 0
\(881\) 20.6422 0.695453 0.347726 0.937596i \(-0.386954\pi\)
0.347726 + 0.937596i \(0.386954\pi\)
\(882\) 0 0
\(883\) 19.8510 0.668040 0.334020 0.942566i \(-0.391595\pi\)
0.334020 + 0.942566i \(0.391595\pi\)
\(884\) 0 0
\(885\) −6.19022 −0.208082
\(886\) 0 0
\(887\) −0.0138328 −0.000464460 0 −0.000232230 1.00000i \(-0.500074\pi\)
−0.000232230 1.00000i \(0.500074\pi\)
\(888\) 0 0
\(889\) −4.53417 −0.152071
\(890\) 0 0
\(891\) 60.6738 2.03265
\(892\) 0 0
\(893\) 6.33099 0.211859
\(894\) 0 0
\(895\) −48.5285 −1.62213
\(896\) 0 0
\(897\) −118.779 −3.96593
\(898\) 0 0
\(899\) −1.26934 −0.0423350
\(900\) 0 0
\(901\) −5.39130 −0.179610
\(902\) 0 0
\(903\) −28.0698 −0.934106
\(904\) 0 0
\(905\) −61.0452 −2.02921
\(906\) 0 0
\(907\) 5.63211 0.187011 0.0935056 0.995619i \(-0.470193\pi\)
0.0935056 + 0.995619i \(0.470193\pi\)
\(908\) 0 0
\(909\) −26.9842 −0.895011
\(910\) 0 0
\(911\) 13.6162 0.451124 0.225562 0.974229i \(-0.427578\pi\)
0.225562 + 0.974229i \(0.427578\pi\)
\(912\) 0 0
\(913\) −42.5036 −1.40667
\(914\) 0 0
\(915\) 78.3562 2.59038
\(916\) 0 0
\(917\) −30.3566 −1.00246
\(918\) 0 0
\(919\) 14.6397 0.482918 0.241459 0.970411i \(-0.422374\pi\)
0.241459 + 0.970411i \(0.422374\pi\)
\(920\) 0 0
\(921\) 55.0483 1.81390
\(922\) 0 0
\(923\) −11.2897 −0.371605
\(924\) 0 0
\(925\) 8.97537 0.295108
\(926\) 0 0
\(927\) 16.7898 0.551449
\(928\) 0 0
\(929\) −54.5903 −1.79105 −0.895525 0.445012i \(-0.853200\pi\)
−0.895525 + 0.445012i \(0.853200\pi\)
\(930\) 0 0
\(931\) 9.02317 0.295722
\(932\) 0 0
\(933\) −58.9213 −1.92900
\(934\) 0 0
\(935\) 15.8349 0.517857
\(936\) 0 0
\(937\) 23.6633 0.773047 0.386524 0.922280i \(-0.373676\pi\)
0.386524 + 0.922280i \(0.373676\pi\)
\(938\) 0 0
\(939\) 46.7064 1.52421
\(940\) 0 0
\(941\) 8.03358 0.261887 0.130944 0.991390i \(-0.458199\pi\)
0.130944 + 0.991390i \(0.458199\pi\)
\(942\) 0 0
\(943\) −50.1411 −1.63282
\(944\) 0 0
\(945\) −5.40416 −0.175797
\(946\) 0 0
\(947\) 57.9876 1.88435 0.942173 0.335128i \(-0.108780\pi\)
0.942173 + 0.335128i \(0.108780\pi\)
\(948\) 0 0
\(949\) −2.99692 −0.0972842
\(950\) 0 0
\(951\) −2.85950 −0.0927258
\(952\) 0 0
\(953\) 30.7105 0.994809 0.497405 0.867519i \(-0.334286\pi\)
0.497405 + 0.867519i \(0.334286\pi\)
\(954\) 0 0
\(955\) 8.35569 0.270384
\(956\) 0 0
\(957\) 69.7171 2.25364
\(958\) 0 0
\(959\) 43.1948 1.39483
\(960\) 0 0
\(961\) −30.9317 −0.997796
\(962\) 0 0
\(963\) −27.5083 −0.886443
\(964\) 0 0
\(965\) −54.0668 −1.74047
\(966\) 0 0
\(967\) −27.3529 −0.879610 −0.439805 0.898093i \(-0.644953\pi\)
−0.439805 + 0.898093i \(0.644953\pi\)
\(968\) 0 0
\(969\) −11.1682 −0.358775
\(970\) 0 0
\(971\) 13.1142 0.420855 0.210428 0.977609i \(-0.432514\pi\)
0.210428 + 0.977609i \(0.432514\pi\)
\(972\) 0 0
\(973\) −32.1256 −1.02990
\(974\) 0 0
\(975\) −23.4994 −0.752584
\(976\) 0 0
\(977\) −19.5068 −0.624078 −0.312039 0.950069i \(-0.601012\pi\)
−0.312039 + 0.950069i \(0.601012\pi\)
\(978\) 0 0
\(979\) 53.0996 1.69707
\(980\) 0 0
\(981\) −0.859149 −0.0274305
\(982\) 0 0
\(983\) 17.2597 0.550500 0.275250 0.961373i \(-0.411239\pi\)
0.275250 + 0.961373i \(0.411239\pi\)
\(984\) 0 0
\(985\) 3.76871 0.120081
\(986\) 0 0
\(987\) −7.17559 −0.228401
\(988\) 0 0
\(989\) −48.5141 −1.54266
\(990\) 0 0
\(991\) −41.2804 −1.31132 −0.655658 0.755058i \(-0.727609\pi\)
−0.655658 + 0.755058i \(0.727609\pi\)
\(992\) 0 0
\(993\) 53.9540 1.71218
\(994\) 0 0
\(995\) −16.4593 −0.521795
\(996\) 0 0
\(997\) 29.9074 0.947178 0.473589 0.880746i \(-0.342958\pi\)
0.473589 + 0.880746i \(0.342958\pi\)
\(998\) 0 0
\(999\) 4.50571 0.142554
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 \(a_p\))