Properties

Label 6040.2.a.p.1.4
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.44352\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.44352 q^{3}\) \(+1.00000 q^{5}\) \(-4.90700 q^{7}\) \(+2.97081 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.44352 q^{3}\) \(+1.00000 q^{5}\) \(-4.90700 q^{7}\) \(+2.97081 q^{9}\) \(-4.55796 q^{11}\) \(+3.11931 q^{13}\) \(-2.44352 q^{15}\) \(-4.54495 q^{17}\) \(-0.659498 q^{19}\) \(+11.9904 q^{21}\) \(+9.23979 q^{23}\) \(+1.00000 q^{25}\) \(+0.0713283 q^{27}\) \(+6.59821 q^{29}\) \(-8.71715 q^{31}\) \(+11.1375 q^{33}\) \(-4.90700 q^{35}\) \(+1.00732 q^{37}\) \(-7.62211 q^{39}\) \(-6.56419 q^{41}\) \(+4.24344 q^{43}\) \(+2.97081 q^{45}\) \(+5.91958 q^{47}\) \(+17.0787 q^{49}\) \(+11.1057 q^{51}\) \(+5.36874 q^{53}\) \(-4.55796 q^{55}\) \(+1.61150 q^{57}\) \(+11.2380 q^{59}\) \(+2.04081 q^{61}\) \(-14.5778 q^{63}\) \(+3.11931 q^{65}\) \(-11.9435 q^{67}\) \(-22.5776 q^{69}\) \(+7.82263 q^{71}\) \(+5.78308 q^{73}\) \(-2.44352 q^{75}\) \(+22.3659 q^{77}\) \(-12.3011 q^{79}\) \(-9.08672 q^{81}\) \(+3.88380 q^{83}\) \(-4.54495 q^{85}\) \(-16.1229 q^{87}\) \(-1.09325 q^{89}\) \(-15.3065 q^{91}\) \(+21.3006 q^{93}\) \(-0.659498 q^{95}\) \(+0.995271 q^{97}\) \(-13.5408 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.44352 −1.41077 −0.705385 0.708825i \(-0.749226\pi\)
−0.705385 + 0.708825i \(0.749226\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.90700 −1.85467 −0.927336 0.374229i \(-0.877908\pi\)
−0.927336 + 0.374229i \(0.877908\pi\)
\(8\) 0 0
\(9\) 2.97081 0.990270
\(10\) 0 0
\(11\) −4.55796 −1.37428 −0.687138 0.726527i \(-0.741133\pi\)
−0.687138 + 0.726527i \(0.741133\pi\)
\(12\) 0 0
\(13\) 3.11931 0.865141 0.432571 0.901600i \(-0.357607\pi\)
0.432571 + 0.901600i \(0.357607\pi\)
\(14\) 0 0
\(15\) −2.44352 −0.630915
\(16\) 0 0
\(17\) −4.54495 −1.10231 −0.551156 0.834402i \(-0.685813\pi\)
−0.551156 + 0.834402i \(0.685813\pi\)
\(18\) 0 0
\(19\) −0.659498 −0.151299 −0.0756496 0.997134i \(-0.524103\pi\)
−0.0756496 + 0.997134i \(0.524103\pi\)
\(20\) 0 0
\(21\) 11.9904 2.61652
\(22\) 0 0
\(23\) 9.23979 1.92663 0.963315 0.268374i \(-0.0864864\pi\)
0.963315 + 0.268374i \(0.0864864\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0.0713283 0.0137271
\(28\) 0 0
\(29\) 6.59821 1.22526 0.612628 0.790371i \(-0.290112\pi\)
0.612628 + 0.790371i \(0.290112\pi\)
\(30\) 0 0
\(31\) −8.71715 −1.56565 −0.782823 0.622245i \(-0.786221\pi\)
−0.782823 + 0.622245i \(0.786221\pi\)
\(32\) 0 0
\(33\) 11.1375 1.93879
\(34\) 0 0
\(35\) −4.90700 −0.829435
\(36\) 0 0
\(37\) 1.00732 0.165602 0.0828012 0.996566i \(-0.473613\pi\)
0.0828012 + 0.996566i \(0.473613\pi\)
\(38\) 0 0
\(39\) −7.62211 −1.22051
\(40\) 0 0
\(41\) −6.56419 −1.02515 −0.512577 0.858641i \(-0.671309\pi\)
−0.512577 + 0.858641i \(0.671309\pi\)
\(42\) 0 0
\(43\) 4.24344 0.647118 0.323559 0.946208i \(-0.395121\pi\)
0.323559 + 0.946208i \(0.395121\pi\)
\(44\) 0 0
\(45\) 2.97081 0.442862
\(46\) 0 0
\(47\) 5.91958 0.863460 0.431730 0.902003i \(-0.357903\pi\)
0.431730 + 0.902003i \(0.357903\pi\)
\(48\) 0 0
\(49\) 17.0787 2.43981
\(50\) 0 0
\(51\) 11.1057 1.55511
\(52\) 0 0
\(53\) 5.36874 0.737453 0.368727 0.929538i \(-0.379794\pi\)
0.368727 + 0.929538i \(0.379794\pi\)
\(54\) 0 0
\(55\) −4.55796 −0.614595
\(56\) 0 0
\(57\) 1.61150 0.213448
\(58\) 0 0
\(59\) 11.2380 1.46306 0.731531 0.681809i \(-0.238806\pi\)
0.731531 + 0.681809i \(0.238806\pi\)
\(60\) 0 0
\(61\) 2.04081 0.261298 0.130649 0.991429i \(-0.458294\pi\)
0.130649 + 0.991429i \(0.458294\pi\)
\(62\) 0 0
\(63\) −14.5778 −1.83663
\(64\) 0 0
\(65\) 3.11931 0.386903
\(66\) 0 0
\(67\) −11.9435 −1.45913 −0.729564 0.683913i \(-0.760277\pi\)
−0.729564 + 0.683913i \(0.760277\pi\)
\(68\) 0 0
\(69\) −22.5776 −2.71803
\(70\) 0 0
\(71\) 7.82263 0.928375 0.464188 0.885737i \(-0.346346\pi\)
0.464188 + 0.885737i \(0.346346\pi\)
\(72\) 0 0
\(73\) 5.78308 0.676858 0.338429 0.940992i \(-0.390104\pi\)
0.338429 + 0.940992i \(0.390104\pi\)
\(74\) 0 0
\(75\) −2.44352 −0.282154
\(76\) 0 0
\(77\) 22.3659 2.54883
\(78\) 0 0
\(79\) −12.3011 −1.38399 −0.691993 0.721904i \(-0.743267\pi\)
−0.691993 + 0.721904i \(0.743267\pi\)
\(80\) 0 0
\(81\) −9.08672 −1.00964
\(82\) 0 0
\(83\) 3.88380 0.426302 0.213151 0.977019i \(-0.431627\pi\)
0.213151 + 0.977019i \(0.431627\pi\)
\(84\) 0 0
\(85\) −4.54495 −0.492969
\(86\) 0 0
\(87\) −16.1229 −1.72855
\(88\) 0 0
\(89\) −1.09325 −0.115884 −0.0579421 0.998320i \(-0.518454\pi\)
−0.0579421 + 0.998320i \(0.518454\pi\)
\(90\) 0 0
\(91\) −15.3065 −1.60455
\(92\) 0 0
\(93\) 21.3006 2.20876
\(94\) 0 0
\(95\) −0.659498 −0.0676631
\(96\) 0 0
\(97\) 0.995271 0.101054 0.0505272 0.998723i \(-0.483910\pi\)
0.0505272 + 0.998723i \(0.483910\pi\)
\(98\) 0 0
\(99\) −13.5408 −1.36090
\(100\) 0 0
\(101\) −12.6516 −1.25888 −0.629441 0.777048i \(-0.716716\pi\)
−0.629441 + 0.777048i \(0.716716\pi\)
\(102\) 0 0
\(103\) 12.9853 1.27948 0.639739 0.768592i \(-0.279043\pi\)
0.639739 + 0.768592i \(0.279043\pi\)
\(104\) 0 0
\(105\) 11.9904 1.17014
\(106\) 0 0
\(107\) −3.68720 −0.356455 −0.178228 0.983989i \(-0.557036\pi\)
−0.178228 + 0.983989i \(0.557036\pi\)
\(108\) 0 0
\(109\) −0.860710 −0.0824411 −0.0412206 0.999150i \(-0.513125\pi\)
−0.0412206 + 0.999150i \(0.513125\pi\)
\(110\) 0 0
\(111\) −2.46141 −0.233627
\(112\) 0 0
\(113\) −0.987609 −0.0929064 −0.0464532 0.998920i \(-0.514792\pi\)
−0.0464532 + 0.998920i \(0.514792\pi\)
\(114\) 0 0
\(115\) 9.23979 0.861615
\(116\) 0 0
\(117\) 9.26688 0.856723
\(118\) 0 0
\(119\) 22.3021 2.04443
\(120\) 0 0
\(121\) 9.77498 0.888634
\(122\) 0 0
\(123\) 16.0398 1.44626
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.821329 0.0728812 0.0364406 0.999336i \(-0.488398\pi\)
0.0364406 + 0.999336i \(0.488398\pi\)
\(128\) 0 0
\(129\) −10.3689 −0.912934
\(130\) 0 0
\(131\) −9.77119 −0.853713 −0.426856 0.904319i \(-0.640379\pi\)
−0.426856 + 0.904319i \(0.640379\pi\)
\(132\) 0 0
\(133\) 3.23616 0.280611
\(134\) 0 0
\(135\) 0.0713283 0.00613896
\(136\) 0 0
\(137\) −20.5205 −1.75318 −0.876591 0.481237i \(-0.840188\pi\)
−0.876591 + 0.481237i \(0.840188\pi\)
\(138\) 0 0
\(139\) −5.99207 −0.508240 −0.254120 0.967173i \(-0.581786\pi\)
−0.254120 + 0.967173i \(0.581786\pi\)
\(140\) 0 0
\(141\) −14.4646 −1.21814
\(142\) 0 0
\(143\) −14.2177 −1.18894
\(144\) 0 0
\(145\) 6.59821 0.547951
\(146\) 0 0
\(147\) −41.7322 −3.44201
\(148\) 0 0
\(149\) −7.43163 −0.608823 −0.304412 0.952541i \(-0.598460\pi\)
−0.304412 + 0.952541i \(0.598460\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −13.5022 −1.09159
\(154\) 0 0
\(155\) −8.71715 −0.700178
\(156\) 0 0
\(157\) 19.6466 1.56797 0.783984 0.620781i \(-0.213184\pi\)
0.783984 + 0.620781i \(0.213184\pi\)
\(158\) 0 0
\(159\) −13.1186 −1.04038
\(160\) 0 0
\(161\) −45.3397 −3.57327
\(162\) 0 0
\(163\) −20.2618 −1.58703 −0.793513 0.608554i \(-0.791750\pi\)
−0.793513 + 0.608554i \(0.791750\pi\)
\(164\) 0 0
\(165\) 11.1375 0.867052
\(166\) 0 0
\(167\) −18.8685 −1.46009 −0.730043 0.683401i \(-0.760500\pi\)
−0.730043 + 0.683401i \(0.760500\pi\)
\(168\) 0 0
\(169\) −3.26990 −0.251531
\(170\) 0 0
\(171\) −1.95924 −0.149827
\(172\) 0 0
\(173\) 19.6606 1.49477 0.747384 0.664392i \(-0.231309\pi\)
0.747384 + 0.664392i \(0.231309\pi\)
\(174\) 0 0
\(175\) −4.90700 −0.370935
\(176\) 0 0
\(177\) −27.4603 −2.06404
\(178\) 0 0
\(179\) −3.10016 −0.231717 −0.115858 0.993266i \(-0.536962\pi\)
−0.115858 + 0.993266i \(0.536962\pi\)
\(180\) 0 0
\(181\) 20.1645 1.49882 0.749408 0.662109i \(-0.230338\pi\)
0.749408 + 0.662109i \(0.230338\pi\)
\(182\) 0 0
\(183\) −4.98676 −0.368632
\(184\) 0 0
\(185\) 1.00732 0.0740597
\(186\) 0 0
\(187\) 20.7157 1.51488
\(188\) 0 0
\(189\) −0.350008 −0.0254594
\(190\) 0 0
\(191\) 26.0368 1.88396 0.941980 0.335670i \(-0.108963\pi\)
0.941980 + 0.335670i \(0.108963\pi\)
\(192\) 0 0
\(193\) −0.537494 −0.0386896 −0.0193448 0.999813i \(-0.506158\pi\)
−0.0193448 + 0.999813i \(0.506158\pi\)
\(194\) 0 0
\(195\) −7.62211 −0.545831
\(196\) 0 0
\(197\) 25.7975 1.83800 0.918998 0.394262i \(-0.129000\pi\)
0.918998 + 0.394262i \(0.129000\pi\)
\(198\) 0 0
\(199\) 20.6942 1.46697 0.733485 0.679706i \(-0.237893\pi\)
0.733485 + 0.679706i \(0.237893\pi\)
\(200\) 0 0
\(201\) 29.1842 2.05849
\(202\) 0 0
\(203\) −32.3774 −2.27245
\(204\) 0 0
\(205\) −6.56419 −0.458463
\(206\) 0 0
\(207\) 27.4497 1.90788
\(208\) 0 0
\(209\) 3.00596 0.207927
\(210\) 0 0
\(211\) −18.6906 −1.28672 −0.643359 0.765565i \(-0.722460\pi\)
−0.643359 + 0.765565i \(0.722460\pi\)
\(212\) 0 0
\(213\) −19.1148 −1.30972
\(214\) 0 0
\(215\) 4.24344 0.289400
\(216\) 0 0
\(217\) 42.7751 2.90376
\(218\) 0 0
\(219\) −14.1311 −0.954890
\(220\) 0 0
\(221\) −14.1771 −0.953655
\(222\) 0 0
\(223\) 12.2346 0.819290 0.409645 0.912245i \(-0.365653\pi\)
0.409645 + 0.912245i \(0.365653\pi\)
\(224\) 0 0
\(225\) 2.97081 0.198054
\(226\) 0 0
\(227\) −5.43786 −0.360923 −0.180462 0.983582i \(-0.557759\pi\)
−0.180462 + 0.983582i \(0.557759\pi\)
\(228\) 0 0
\(229\) −23.9167 −1.58046 −0.790230 0.612810i \(-0.790039\pi\)
−0.790230 + 0.612810i \(0.790039\pi\)
\(230\) 0 0
\(231\) −54.6516 −3.59581
\(232\) 0 0
\(233\) 1.60310 0.105022 0.0525112 0.998620i \(-0.483277\pi\)
0.0525112 + 0.998620i \(0.483277\pi\)
\(234\) 0 0
\(235\) 5.91958 0.386151
\(236\) 0 0
\(237\) 30.0581 1.95248
\(238\) 0 0
\(239\) −15.3589 −0.993482 −0.496741 0.867899i \(-0.665470\pi\)
−0.496741 + 0.867899i \(0.665470\pi\)
\(240\) 0 0
\(241\) −12.6833 −0.817002 −0.408501 0.912758i \(-0.633948\pi\)
−0.408501 + 0.912758i \(0.633948\pi\)
\(242\) 0 0
\(243\) 21.9896 1.41064
\(244\) 0 0
\(245\) 17.0787 1.09112
\(246\) 0 0
\(247\) −2.05718 −0.130895
\(248\) 0 0
\(249\) −9.49015 −0.601414
\(250\) 0 0
\(251\) 22.5468 1.42314 0.711570 0.702615i \(-0.247984\pi\)
0.711570 + 0.702615i \(0.247984\pi\)
\(252\) 0 0
\(253\) −42.1146 −2.64772
\(254\) 0 0
\(255\) 11.1057 0.695465
\(256\) 0 0
\(257\) 20.0366 1.24985 0.624924 0.780686i \(-0.285130\pi\)
0.624924 + 0.780686i \(0.285130\pi\)
\(258\) 0 0
\(259\) −4.94292 −0.307138
\(260\) 0 0
\(261\) 19.6020 1.21333
\(262\) 0 0
\(263\) 15.3583 0.947035 0.473517 0.880784i \(-0.342984\pi\)
0.473517 + 0.880784i \(0.342984\pi\)
\(264\) 0 0
\(265\) 5.36874 0.329799
\(266\) 0 0
\(267\) 2.67138 0.163486
\(268\) 0 0
\(269\) −8.01918 −0.488938 −0.244469 0.969657i \(-0.578614\pi\)
−0.244469 + 0.969657i \(0.578614\pi\)
\(270\) 0 0
\(271\) −1.72618 −0.104858 −0.0524290 0.998625i \(-0.516696\pi\)
−0.0524290 + 0.998625i \(0.516696\pi\)
\(272\) 0 0
\(273\) 37.4017 2.26366
\(274\) 0 0
\(275\) −4.55796 −0.274855
\(276\) 0 0
\(277\) −3.90954 −0.234902 −0.117451 0.993079i \(-0.537472\pi\)
−0.117451 + 0.993079i \(0.537472\pi\)
\(278\) 0 0
\(279\) −25.8970 −1.55041
\(280\) 0 0
\(281\) −25.7769 −1.53772 −0.768862 0.639415i \(-0.779177\pi\)
−0.768862 + 0.639415i \(0.779177\pi\)
\(282\) 0 0
\(283\) 23.4564 1.39434 0.697169 0.716907i \(-0.254443\pi\)
0.697169 + 0.716907i \(0.254443\pi\)
\(284\) 0 0
\(285\) 1.61150 0.0954570
\(286\) 0 0
\(287\) 32.2105 1.90133
\(288\) 0 0
\(289\) 3.65655 0.215091
\(290\) 0 0
\(291\) −2.43197 −0.142565
\(292\) 0 0
\(293\) −29.6302 −1.73102 −0.865508 0.500895i \(-0.833004\pi\)
−0.865508 + 0.500895i \(0.833004\pi\)
\(294\) 0 0
\(295\) 11.2380 0.654301
\(296\) 0 0
\(297\) −0.325111 −0.0188649
\(298\) 0 0
\(299\) 28.8218 1.66681
\(300\) 0 0
\(301\) −20.8226 −1.20019
\(302\) 0 0
\(303\) 30.9145 1.77599
\(304\) 0 0
\(305\) 2.04081 0.116856
\(306\) 0 0
\(307\) 18.8553 1.07613 0.538064 0.842904i \(-0.319156\pi\)
0.538064 + 0.842904i \(0.319156\pi\)
\(308\) 0 0
\(309\) −31.7298 −1.80505
\(310\) 0 0
\(311\) −8.79397 −0.498661 −0.249330 0.968419i \(-0.580210\pi\)
−0.249330 + 0.968419i \(0.580210\pi\)
\(312\) 0 0
\(313\) −6.25931 −0.353797 −0.176899 0.984229i \(-0.556606\pi\)
−0.176899 + 0.984229i \(0.556606\pi\)
\(314\) 0 0
\(315\) −14.5778 −0.821364
\(316\) 0 0
\(317\) −25.7840 −1.44817 −0.724087 0.689709i \(-0.757739\pi\)
−0.724087 + 0.689709i \(0.757739\pi\)
\(318\) 0 0
\(319\) −30.0744 −1.68384
\(320\) 0 0
\(321\) 9.00976 0.502876
\(322\) 0 0
\(323\) 2.99738 0.166779
\(324\) 0 0
\(325\) 3.11931 0.173028
\(326\) 0 0
\(327\) 2.10317 0.116305
\(328\) 0 0
\(329\) −29.0474 −1.60143
\(330\) 0 0
\(331\) −15.5427 −0.854302 −0.427151 0.904180i \(-0.640483\pi\)
−0.427151 + 0.904180i \(0.640483\pi\)
\(332\) 0 0
\(333\) 2.99256 0.163991
\(334\) 0 0
\(335\) −11.9435 −0.652542
\(336\) 0 0
\(337\) −7.18169 −0.391211 −0.195606 0.980683i \(-0.562667\pi\)
−0.195606 + 0.980683i \(0.562667\pi\)
\(338\) 0 0
\(339\) 2.41325 0.131070
\(340\) 0 0
\(341\) 39.7324 2.15163
\(342\) 0 0
\(343\) −49.4561 −2.67038
\(344\) 0 0
\(345\) −22.5776 −1.21554
\(346\) 0 0
\(347\) −26.2473 −1.40903 −0.704514 0.709691i \(-0.748835\pi\)
−0.704514 + 0.709691i \(0.748835\pi\)
\(348\) 0 0
\(349\) −31.6220 −1.69269 −0.846344 0.532636i \(-0.821202\pi\)
−0.846344 + 0.532636i \(0.821202\pi\)
\(350\) 0 0
\(351\) 0.222495 0.0118759
\(352\) 0 0
\(353\) −8.96351 −0.477080 −0.238540 0.971133i \(-0.576669\pi\)
−0.238540 + 0.971133i \(0.576669\pi\)
\(354\) 0 0
\(355\) 7.82263 0.415182
\(356\) 0 0
\(357\) −54.4956 −2.88422
\(358\) 0 0
\(359\) 30.7553 1.62320 0.811601 0.584212i \(-0.198596\pi\)
0.811601 + 0.584212i \(0.198596\pi\)
\(360\) 0 0
\(361\) −18.5651 −0.977109
\(362\) 0 0
\(363\) −23.8854 −1.25366
\(364\) 0 0
\(365\) 5.78308 0.302700
\(366\) 0 0
\(367\) 3.04193 0.158787 0.0793936 0.996843i \(-0.474702\pi\)
0.0793936 + 0.996843i \(0.474702\pi\)
\(368\) 0 0
\(369\) −19.5010 −1.01518
\(370\) 0 0
\(371\) −26.3444 −1.36773
\(372\) 0 0
\(373\) −8.42720 −0.436344 −0.218172 0.975910i \(-0.570009\pi\)
−0.218172 + 0.975910i \(0.570009\pi\)
\(374\) 0 0
\(375\) −2.44352 −0.126183
\(376\) 0 0
\(377\) 20.5819 1.06002
\(378\) 0 0
\(379\) −32.6655 −1.67792 −0.838958 0.544196i \(-0.816835\pi\)
−0.838958 + 0.544196i \(0.816835\pi\)
\(380\) 0 0
\(381\) −2.00694 −0.102818
\(382\) 0 0
\(383\) −1.55770 −0.0795945 −0.0397973 0.999208i \(-0.512671\pi\)
−0.0397973 + 0.999208i \(0.512671\pi\)
\(384\) 0 0
\(385\) 22.3659 1.13987
\(386\) 0 0
\(387\) 12.6064 0.640821
\(388\) 0 0
\(389\) 1.08604 0.0550643 0.0275322 0.999621i \(-0.491235\pi\)
0.0275322 + 0.999621i \(0.491235\pi\)
\(390\) 0 0
\(391\) −41.9944 −2.12375
\(392\) 0 0
\(393\) 23.8761 1.20439
\(394\) 0 0
\(395\) −12.3011 −0.618937
\(396\) 0 0
\(397\) 10.5760 0.530795 0.265398 0.964139i \(-0.414497\pi\)
0.265398 + 0.964139i \(0.414497\pi\)
\(398\) 0 0
\(399\) −7.90763 −0.395877
\(400\) 0 0
\(401\) 9.18627 0.458740 0.229370 0.973339i \(-0.426333\pi\)
0.229370 + 0.973339i \(0.426333\pi\)
\(402\) 0 0
\(403\) −27.1915 −1.35450
\(404\) 0 0
\(405\) −9.08672 −0.451523
\(406\) 0 0
\(407\) −4.59132 −0.227583
\(408\) 0 0
\(409\) −35.8039 −1.77039 −0.885194 0.465222i \(-0.845974\pi\)
−0.885194 + 0.465222i \(0.845974\pi\)
\(410\) 0 0
\(411\) 50.1422 2.47333
\(412\) 0 0
\(413\) −55.1448 −2.71350
\(414\) 0 0
\(415\) 3.88380 0.190648
\(416\) 0 0
\(417\) 14.6418 0.717010
\(418\) 0 0
\(419\) −24.7415 −1.20870 −0.604352 0.796718i \(-0.706568\pi\)
−0.604352 + 0.796718i \(0.706568\pi\)
\(420\) 0 0
\(421\) −2.91112 −0.141879 −0.0709396 0.997481i \(-0.522600\pi\)
−0.0709396 + 0.997481i \(0.522600\pi\)
\(422\) 0 0
\(423\) 17.5859 0.855058
\(424\) 0 0
\(425\) −4.54495 −0.220462
\(426\) 0 0
\(427\) −10.0142 −0.484623
\(428\) 0 0
\(429\) 34.7413 1.67732
\(430\) 0 0
\(431\) 6.40292 0.308418 0.154209 0.988038i \(-0.450717\pi\)
0.154209 + 0.988038i \(0.450717\pi\)
\(432\) 0 0
\(433\) −27.8646 −1.33909 −0.669543 0.742774i \(-0.733510\pi\)
−0.669543 + 0.742774i \(0.733510\pi\)
\(434\) 0 0
\(435\) −16.1229 −0.773033
\(436\) 0 0
\(437\) −6.09362 −0.291498
\(438\) 0 0
\(439\) −0.0872818 −0.00416573 −0.00208287 0.999998i \(-0.500663\pi\)
−0.00208287 + 0.999998i \(0.500663\pi\)
\(440\) 0 0
\(441\) 50.7375 2.41607
\(442\) 0 0
\(443\) 16.2609 0.772581 0.386290 0.922377i \(-0.373756\pi\)
0.386290 + 0.922377i \(0.373756\pi\)
\(444\) 0 0
\(445\) −1.09325 −0.0518250
\(446\) 0 0
\(447\) 18.1594 0.858909
\(448\) 0 0
\(449\) 24.7882 1.16983 0.584914 0.811095i \(-0.301128\pi\)
0.584914 + 0.811095i \(0.301128\pi\)
\(450\) 0 0
\(451\) 29.9193 1.40884
\(452\) 0 0
\(453\) −2.44352 −0.114807
\(454\) 0 0
\(455\) −15.3065 −0.717578
\(456\) 0 0
\(457\) −28.8553 −1.34979 −0.674897 0.737912i \(-0.735812\pi\)
−0.674897 + 0.737912i \(0.735812\pi\)
\(458\) 0 0
\(459\) −0.324183 −0.0151316
\(460\) 0 0
\(461\) −4.01283 −0.186896 −0.0934481 0.995624i \(-0.529789\pi\)
−0.0934481 + 0.995624i \(0.529789\pi\)
\(462\) 0 0
\(463\) −0.278363 −0.0129366 −0.00646832 0.999979i \(-0.502059\pi\)
−0.00646832 + 0.999979i \(0.502059\pi\)
\(464\) 0 0
\(465\) 21.3006 0.987790
\(466\) 0 0
\(467\) 23.1235 1.07003 0.535014 0.844843i \(-0.320306\pi\)
0.535014 + 0.844843i \(0.320306\pi\)
\(468\) 0 0
\(469\) 58.6067 2.70621
\(470\) 0 0
\(471\) −48.0069 −2.21204
\(472\) 0 0
\(473\) −19.3414 −0.889318
\(474\) 0 0
\(475\) −0.659498 −0.0302598
\(476\) 0 0
\(477\) 15.9495 0.730278
\(478\) 0 0
\(479\) −0.851379 −0.0389005 −0.0194503 0.999811i \(-0.506192\pi\)
−0.0194503 + 0.999811i \(0.506192\pi\)
\(480\) 0 0
\(481\) 3.14214 0.143269
\(482\) 0 0
\(483\) 110.789 5.04106
\(484\) 0 0
\(485\) 0.995271 0.0451929
\(486\) 0 0
\(487\) 14.6366 0.663247 0.331623 0.943412i \(-0.392404\pi\)
0.331623 + 0.943412i \(0.392404\pi\)
\(488\) 0 0
\(489\) 49.5102 2.23893
\(490\) 0 0
\(491\) −38.5616 −1.74026 −0.870131 0.492821i \(-0.835966\pi\)
−0.870131 + 0.492821i \(0.835966\pi\)
\(492\) 0 0
\(493\) −29.9885 −1.35061
\(494\) 0 0
\(495\) −13.5408 −0.608615
\(496\) 0 0
\(497\) −38.3857 −1.72183
\(498\) 0 0
\(499\) 21.6585 0.969568 0.484784 0.874634i \(-0.338898\pi\)
0.484784 + 0.874634i \(0.338898\pi\)
\(500\) 0 0
\(501\) 46.1056 2.05984
\(502\) 0 0
\(503\) 5.07601 0.226328 0.113164 0.993576i \(-0.463901\pi\)
0.113164 + 0.993576i \(0.463901\pi\)
\(504\) 0 0
\(505\) −12.6516 −0.562989
\(506\) 0 0
\(507\) 7.99008 0.354852
\(508\) 0 0
\(509\) −12.1392 −0.538063 −0.269031 0.963131i \(-0.586703\pi\)
−0.269031 + 0.963131i \(0.586703\pi\)
\(510\) 0 0
\(511\) −28.3776 −1.25535
\(512\) 0 0
\(513\) −0.0470409 −0.00207691
\(514\) 0 0
\(515\) 12.9853 0.572200
\(516\) 0 0
\(517\) −26.9812 −1.18663
\(518\) 0 0
\(519\) −48.0412 −2.10877
\(520\) 0 0
\(521\) −29.1155 −1.27557 −0.637787 0.770213i \(-0.720150\pi\)
−0.637787 + 0.770213i \(0.720150\pi\)
\(522\) 0 0
\(523\) −14.6340 −0.639901 −0.319950 0.947434i \(-0.603666\pi\)
−0.319950 + 0.947434i \(0.603666\pi\)
\(524\) 0 0
\(525\) 11.9904 0.523303
\(526\) 0 0
\(527\) 39.6190 1.72583
\(528\) 0 0
\(529\) 62.3737 2.71190
\(530\) 0 0
\(531\) 33.3859 1.44883
\(532\) 0 0
\(533\) −20.4757 −0.886903
\(534\) 0 0
\(535\) −3.68720 −0.159412
\(536\) 0 0
\(537\) 7.57531 0.326899
\(538\) 0 0
\(539\) −77.8439 −3.35297
\(540\) 0 0
\(541\) −20.4516 −0.879282 −0.439641 0.898173i \(-0.644894\pi\)
−0.439641 + 0.898173i \(0.644894\pi\)
\(542\) 0 0
\(543\) −49.2724 −2.11448
\(544\) 0 0
\(545\) −0.860710 −0.0368688
\(546\) 0 0
\(547\) −26.5793 −1.13645 −0.568224 0.822874i \(-0.692369\pi\)
−0.568224 + 0.822874i \(0.692369\pi\)
\(548\) 0 0
\(549\) 6.06285 0.258756
\(550\) 0 0
\(551\) −4.35151 −0.185380
\(552\) 0 0
\(553\) 60.3617 2.56684
\(554\) 0 0
\(555\) −2.46141 −0.104481
\(556\) 0 0
\(557\) 16.4379 0.696495 0.348248 0.937403i \(-0.386777\pi\)
0.348248 + 0.937403i \(0.386777\pi\)
\(558\) 0 0
\(559\) 13.2366 0.559848
\(560\) 0 0
\(561\) −50.6193 −2.13715
\(562\) 0 0
\(563\) −31.4472 −1.32534 −0.662671 0.748910i \(-0.730577\pi\)
−0.662671 + 0.748910i \(0.730577\pi\)
\(564\) 0 0
\(565\) −0.987609 −0.0415490
\(566\) 0 0
\(567\) 44.5886 1.87254
\(568\) 0 0
\(569\) 39.8445 1.67037 0.835184 0.549971i \(-0.185361\pi\)
0.835184 + 0.549971i \(0.185361\pi\)
\(570\) 0 0
\(571\) 35.8060 1.49843 0.749217 0.662325i \(-0.230430\pi\)
0.749217 + 0.662325i \(0.230430\pi\)
\(572\) 0 0
\(573\) −63.6216 −2.65783
\(574\) 0 0
\(575\) 9.23979 0.385326
\(576\) 0 0
\(577\) 38.8692 1.61815 0.809073 0.587708i \(-0.199970\pi\)
0.809073 + 0.587708i \(0.199970\pi\)
\(578\) 0 0
\(579\) 1.31338 0.0545822
\(580\) 0 0
\(581\) −19.0578 −0.790651
\(582\) 0 0
\(583\) −24.4705 −1.01346
\(584\) 0 0
\(585\) 9.26688 0.383138
\(586\) 0 0
\(587\) −29.9688 −1.23694 −0.618472 0.785807i \(-0.712248\pi\)
−0.618472 + 0.785807i \(0.712248\pi\)
\(588\) 0 0
\(589\) 5.74894 0.236881
\(590\) 0 0
\(591\) −63.0368 −2.59299
\(592\) 0 0
\(593\) 17.1766 0.705359 0.352680 0.935744i \(-0.385271\pi\)
0.352680 + 0.935744i \(0.385271\pi\)
\(594\) 0 0
\(595\) 22.3021 0.914296
\(596\) 0 0
\(597\) −50.5667 −2.06956
\(598\) 0 0
\(599\) 8.35518 0.341384 0.170692 0.985324i \(-0.445400\pi\)
0.170692 + 0.985324i \(0.445400\pi\)
\(600\) 0 0
\(601\) 6.21168 0.253380 0.126690 0.991942i \(-0.459565\pi\)
0.126690 + 0.991942i \(0.459565\pi\)
\(602\) 0 0
\(603\) −35.4818 −1.44493
\(604\) 0 0
\(605\) 9.77498 0.397409
\(606\) 0 0
\(607\) −22.1313 −0.898281 −0.449141 0.893461i \(-0.648270\pi\)
−0.449141 + 0.893461i \(0.648270\pi\)
\(608\) 0 0
\(609\) 79.1150 3.20590
\(610\) 0 0
\(611\) 18.4650 0.747014
\(612\) 0 0
\(613\) −0.776065 −0.0313450 −0.0156725 0.999877i \(-0.504989\pi\)
−0.0156725 + 0.999877i \(0.504989\pi\)
\(614\) 0 0
\(615\) 16.0398 0.646785
\(616\) 0 0
\(617\) 18.0896 0.728262 0.364131 0.931348i \(-0.381366\pi\)
0.364131 + 0.931348i \(0.381366\pi\)
\(618\) 0 0
\(619\) −8.50175 −0.341714 −0.170857 0.985296i \(-0.554654\pi\)
−0.170857 + 0.985296i \(0.554654\pi\)
\(620\) 0 0
\(621\) 0.659059 0.0264471
\(622\) 0 0
\(623\) 5.36458 0.214927
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −7.34515 −0.293337
\(628\) 0 0
\(629\) −4.57822 −0.182545
\(630\) 0 0
\(631\) 13.3616 0.531916 0.265958 0.963985i \(-0.414312\pi\)
0.265958 + 0.963985i \(0.414312\pi\)
\(632\) 0 0
\(633\) 45.6710 1.81526
\(634\) 0 0
\(635\) 0.821329 0.0325934
\(636\) 0 0
\(637\) 53.2737 2.11078
\(638\) 0 0
\(639\) 23.2395 0.919342
\(640\) 0 0
\(641\) 14.9085 0.588852 0.294426 0.955674i \(-0.404871\pi\)
0.294426 + 0.955674i \(0.404871\pi\)
\(642\) 0 0
\(643\) −23.8380 −0.940079 −0.470039 0.882645i \(-0.655760\pi\)
−0.470039 + 0.882645i \(0.655760\pi\)
\(644\) 0 0
\(645\) −10.3689 −0.408276
\(646\) 0 0
\(647\) 0.797347 0.0313470 0.0156735 0.999877i \(-0.495011\pi\)
0.0156735 + 0.999877i \(0.495011\pi\)
\(648\) 0 0
\(649\) −51.2223 −2.01065
\(650\) 0 0
\(651\) −104.522 −4.09654
\(652\) 0 0
\(653\) −24.8601 −0.972850 −0.486425 0.873722i \(-0.661699\pi\)
−0.486425 + 0.873722i \(0.661699\pi\)
\(654\) 0 0
\(655\) −9.77119 −0.381792
\(656\) 0 0
\(657\) 17.1804 0.670272
\(658\) 0 0
\(659\) −4.59726 −0.179084 −0.0895420 0.995983i \(-0.528540\pi\)
−0.0895420 + 0.995983i \(0.528540\pi\)
\(660\) 0 0
\(661\) −42.3397 −1.64682 −0.823412 0.567444i \(-0.807932\pi\)
−0.823412 + 0.567444i \(0.807932\pi\)
\(662\) 0 0
\(663\) 34.6421 1.34539
\(664\) 0 0
\(665\) 3.23616 0.125493
\(666\) 0 0
\(667\) 60.9661 2.36062
\(668\) 0 0
\(669\) −29.8956 −1.15583
\(670\) 0 0
\(671\) −9.30191 −0.359096
\(672\) 0 0
\(673\) 23.1313 0.891648 0.445824 0.895121i \(-0.352911\pi\)
0.445824 + 0.895121i \(0.352911\pi\)
\(674\) 0 0
\(675\) 0.0713283 0.00274543
\(676\) 0 0
\(677\) −31.4287 −1.20790 −0.603951 0.797022i \(-0.706408\pi\)
−0.603951 + 0.797022i \(0.706408\pi\)
\(678\) 0 0
\(679\) −4.88380 −0.187423
\(680\) 0 0
\(681\) 13.2875 0.509180
\(682\) 0 0
\(683\) −51.3739 −1.96577 −0.982884 0.184226i \(-0.941022\pi\)
−0.982884 + 0.184226i \(0.941022\pi\)
\(684\) 0 0
\(685\) −20.5205 −0.784047
\(686\) 0 0
\(687\) 58.4411 2.22967
\(688\) 0 0
\(689\) 16.7468 0.638001
\(690\) 0 0
\(691\) 31.4053 1.19471 0.597356 0.801976i \(-0.296218\pi\)
0.597356 + 0.801976i \(0.296218\pi\)
\(692\) 0 0
\(693\) 66.4449 2.52403
\(694\) 0 0
\(695\) −5.99207 −0.227292
\(696\) 0 0
\(697\) 29.8339 1.13004
\(698\) 0 0
\(699\) −3.91721 −0.148162
\(700\) 0 0
\(701\) 30.2348 1.14195 0.570977 0.820966i \(-0.306565\pi\)
0.570977 + 0.820966i \(0.306565\pi\)
\(702\) 0 0
\(703\) −0.664326 −0.0250555
\(704\) 0 0
\(705\) −14.4646 −0.544770
\(706\) 0 0
\(707\) 62.0815 2.33481
\(708\) 0 0
\(709\) −9.32406 −0.350172 −0.175086 0.984553i \(-0.556020\pi\)
−0.175086 + 0.984553i \(0.556020\pi\)
\(710\) 0 0
\(711\) −36.5443 −1.37052
\(712\) 0 0
\(713\) −80.5446 −3.01642
\(714\) 0 0
\(715\) −14.2177 −0.531711
\(716\) 0 0
\(717\) 37.5298 1.40157
\(718\) 0 0
\(719\) 1.57759 0.0588341 0.0294170 0.999567i \(-0.490635\pi\)
0.0294170 + 0.999567i \(0.490635\pi\)
\(720\) 0 0
\(721\) −63.7188 −2.37301
\(722\) 0 0
\(723\) 30.9919 1.15260
\(724\) 0 0
\(725\) 6.59821 0.245051
\(726\) 0 0
\(727\) 16.4423 0.609813 0.304906 0.952382i \(-0.401375\pi\)
0.304906 + 0.952382i \(0.401375\pi\)
\(728\) 0 0
\(729\) −26.4720 −0.980446
\(730\) 0 0
\(731\) −19.2862 −0.713326
\(732\) 0 0
\(733\) 23.7228 0.876222 0.438111 0.898921i \(-0.355648\pi\)
0.438111 + 0.898921i \(0.355648\pi\)
\(734\) 0 0
\(735\) −41.7322 −1.53931
\(736\) 0 0
\(737\) 54.4379 2.00524
\(738\) 0 0
\(739\) −27.4891 −1.01120 −0.505601 0.862768i \(-0.668729\pi\)
−0.505601 + 0.862768i \(0.668729\pi\)
\(740\) 0 0
\(741\) 5.02677 0.184663
\(742\) 0 0
\(743\) −22.3533 −0.820064 −0.410032 0.912071i \(-0.634483\pi\)
−0.410032 + 0.912071i \(0.634483\pi\)
\(744\) 0 0
\(745\) −7.43163 −0.272274
\(746\) 0 0
\(747\) 11.5380 0.422154
\(748\) 0 0
\(749\) 18.0931 0.661108
\(750\) 0 0
\(751\) 27.5418 1.00501 0.502507 0.864573i \(-0.332411\pi\)
0.502507 + 0.864573i \(0.332411\pi\)
\(752\) 0 0
\(753\) −55.0936 −2.00772
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −0.0171918 −0.000624848 0 −0.000312424 1.00000i \(-0.500099\pi\)
−0.000312424 1.00000i \(0.500099\pi\)
\(758\) 0 0
\(759\) 102.908 3.73532
\(760\) 0 0
\(761\) −19.8740 −0.720433 −0.360216 0.932869i \(-0.617297\pi\)
−0.360216 + 0.932869i \(0.617297\pi\)
\(762\) 0 0
\(763\) 4.22351 0.152901
\(764\) 0 0
\(765\) −13.5022 −0.488172
\(766\) 0 0
\(767\) 35.0548 1.26575
\(768\) 0 0
\(769\) 31.1662 1.12388 0.561940 0.827178i \(-0.310055\pi\)
0.561940 + 0.827178i \(0.310055\pi\)
\(770\) 0 0
\(771\) −48.9599 −1.76325
\(772\) 0 0
\(773\) 49.5132 1.78087 0.890434 0.455113i \(-0.150401\pi\)
0.890434 + 0.455113i \(0.150401\pi\)
\(774\) 0 0
\(775\) −8.71715 −0.313129
\(776\) 0 0
\(777\) 12.0782 0.433301
\(778\) 0 0
\(779\) 4.32907 0.155105
\(780\) 0 0
\(781\) −35.6552 −1.27584
\(782\) 0 0
\(783\) 0.470639 0.0168193
\(784\) 0 0
\(785\) 19.6466 0.701217
\(786\) 0 0
\(787\) 45.0522 1.60594 0.802968 0.596022i \(-0.203253\pi\)
0.802968 + 0.596022i \(0.203253\pi\)
\(788\) 0 0
\(789\) −37.5284 −1.33605
\(790\) 0 0
\(791\) 4.84620 0.172311
\(792\) 0 0
\(793\) 6.36591 0.226060
\(794\) 0 0
\(795\) −13.1186 −0.465270
\(796\) 0 0
\(797\) 0.404496 0.0143280 0.00716399 0.999974i \(-0.497720\pi\)
0.00716399 + 0.999974i \(0.497720\pi\)
\(798\) 0 0
\(799\) −26.9042 −0.951801
\(800\) 0 0
\(801\) −3.24784 −0.114757
\(802\) 0 0
\(803\) −26.3590 −0.930190
\(804\) 0 0
\(805\) −45.3397 −1.59801
\(806\) 0 0
\(807\) 19.5950 0.689778
\(808\) 0 0
\(809\) 2.67030 0.0938828 0.0469414 0.998898i \(-0.485053\pi\)
0.0469414 + 0.998898i \(0.485053\pi\)
\(810\) 0 0
\(811\) 8.37223 0.293989 0.146994 0.989137i \(-0.453040\pi\)
0.146994 + 0.989137i \(0.453040\pi\)
\(812\) 0 0
\(813\) 4.21796 0.147930
\(814\) 0 0
\(815\) −20.2618 −0.709739
\(816\) 0 0
\(817\) −2.79854 −0.0979084
\(818\) 0 0
\(819\) −45.4726 −1.58894
\(820\) 0 0
\(821\) −38.6690 −1.34956 −0.674778 0.738020i \(-0.735761\pi\)
−0.674778 + 0.738020i \(0.735761\pi\)
\(822\) 0 0
\(823\) −9.91401 −0.345581 −0.172790 0.984959i \(-0.555278\pi\)
−0.172790 + 0.984959i \(0.555278\pi\)
\(824\) 0 0
\(825\) 11.1375 0.387757
\(826\) 0 0
\(827\) −23.8640 −0.829831 −0.414915 0.909860i \(-0.636189\pi\)
−0.414915 + 0.909860i \(0.636189\pi\)
\(828\) 0 0
\(829\) 30.1061 1.04563 0.522814 0.852447i \(-0.324882\pi\)
0.522814 + 0.852447i \(0.324882\pi\)
\(830\) 0 0
\(831\) 9.55306 0.331392
\(832\) 0 0
\(833\) −77.6217 −2.68943
\(834\) 0 0
\(835\) −18.8685 −0.652970
\(836\) 0 0
\(837\) −0.621779 −0.0214918
\(838\) 0 0
\(839\) 10.5196 0.363177 0.181588 0.983375i \(-0.441876\pi\)
0.181588 + 0.983375i \(0.441876\pi\)
\(840\) 0 0
\(841\) 14.5364 0.501254
\(842\) 0 0
\(843\) 62.9866 2.16937
\(844\) 0 0
\(845\) −3.26990 −0.112488
\(846\) 0 0
\(847\) −47.9658 −1.64813
\(848\) 0 0
\(849\) −57.3163 −1.96709
\(850\) 0 0
\(851\) 9.30743 0.319054
\(852\) 0 0
\(853\) 26.4542 0.905776 0.452888 0.891567i \(-0.350394\pi\)
0.452888 + 0.891567i \(0.350394\pi\)
\(854\) 0 0
\(855\) −1.95924 −0.0670047
\(856\) 0 0
\(857\) 38.1461 1.30305 0.651524 0.758628i \(-0.274130\pi\)
0.651524 + 0.758628i \(0.274130\pi\)
\(858\) 0 0
\(859\) −26.2063 −0.894148 −0.447074 0.894497i \(-0.647534\pi\)
−0.447074 + 0.894497i \(0.647534\pi\)
\(860\) 0 0
\(861\) −78.7071 −2.68233
\(862\) 0 0
\(863\) 3.93531 0.133959 0.0669797 0.997754i \(-0.478664\pi\)
0.0669797 + 0.997754i \(0.478664\pi\)
\(864\) 0 0
\(865\) 19.6606 0.668481
\(866\) 0 0
\(867\) −8.93486 −0.303444
\(868\) 0 0
\(869\) 56.0681 1.90198
\(870\) 0 0
\(871\) −37.2554 −1.26235
\(872\) 0 0
\(873\) 2.95676 0.100071
\(874\) 0 0
\(875\) −4.90700 −0.165887
\(876\) 0 0
\(877\) 45.4315 1.53411 0.767057 0.641579i \(-0.221720\pi\)
0.767057 + 0.641579i \(0.221720\pi\)
\(878\) 0 0
\(879\) 72.4022 2.44206
\(880\) 0 0
\(881\) −13.0379 −0.439257 −0.219628 0.975584i \(-0.570484\pi\)
−0.219628 + 0.975584i \(0.570484\pi\)
\(882\) 0 0
\(883\) 44.1661 1.48631 0.743154 0.669121i \(-0.233329\pi\)
0.743154 + 0.669121i \(0.233329\pi\)
\(884\) 0 0
\(885\) −27.4603 −0.923068
\(886\) 0 0
\(887\) −40.1853 −1.34929 −0.674646 0.738142i \(-0.735704\pi\)
−0.674646 + 0.738142i \(0.735704\pi\)
\(888\) 0 0
\(889\) −4.03026 −0.135171
\(890\) 0 0
\(891\) 41.4169 1.38752
\(892\) 0 0
\(893\) −3.90395 −0.130641
\(894\) 0 0
\(895\) −3.10016 −0.103627
\(896\) 0 0
\(897\) −70.4267 −2.35148
\(898\) 0 0
\(899\) −57.5176 −1.91832
\(900\) 0 0
\(901\) −24.4006 −0.812903
\(902\) 0 0
\(903\) 50.8804 1.69319
\(904\) 0 0
\(905\) 20.1645 0.670291
\(906\) 0 0
\(907\) −44.5559 −1.47946 −0.739728 0.672906i \(-0.765046\pi\)
−0.739728 + 0.672906i \(0.765046\pi\)
\(908\) 0 0
\(909\) −37.5855 −1.24663
\(910\) 0 0
\(911\) 0.356378 0.0118073 0.00590367 0.999983i \(-0.498121\pi\)
0.00590367 + 0.999983i \(0.498121\pi\)
\(912\) 0 0
\(913\) −17.7022 −0.585857
\(914\) 0 0
\(915\) −4.98676 −0.164857
\(916\) 0 0
\(917\) 47.9472 1.58336
\(918\) 0 0
\(919\) 3.29330 0.108636 0.0543181 0.998524i \(-0.482702\pi\)
0.0543181 + 0.998524i \(0.482702\pi\)
\(920\) 0 0
\(921\) −46.0733 −1.51817
\(922\) 0 0
\(923\) 24.4012 0.803176
\(924\) 0 0
\(925\) 1.00732 0.0331205
\(926\) 0 0
\(927\) 38.5768 1.26703
\(928\) 0 0
\(929\) −54.4247 −1.78562 −0.892809 0.450436i \(-0.851269\pi\)
−0.892809 + 0.450436i \(0.851269\pi\)
\(930\) 0 0
\(931\) −11.2634 −0.369142
\(932\) 0 0
\(933\) 21.4883 0.703495
\(934\) 0 0
\(935\) 20.7157 0.677475
\(936\) 0 0
\(937\) −18.4535 −0.602851 −0.301425 0.953490i \(-0.597462\pi\)
−0.301425 + 0.953490i \(0.597462\pi\)
\(938\) 0 0
\(939\) 15.2948 0.499126
\(940\) 0 0
\(941\) 16.2609 0.530090 0.265045 0.964236i \(-0.414613\pi\)
0.265045 + 0.964236i \(0.414613\pi\)
\(942\) 0 0
\(943\) −60.6517 −1.97509
\(944\) 0 0
\(945\) −0.350008 −0.0113858
\(946\) 0 0
\(947\) −27.6991 −0.900099 −0.450050 0.893003i \(-0.648594\pi\)
−0.450050 + 0.893003i \(0.648594\pi\)
\(948\) 0 0
\(949\) 18.0392 0.585578
\(950\) 0 0
\(951\) 63.0038 2.04304
\(952\) 0 0
\(953\) −7.04323 −0.228153 −0.114076 0.993472i \(-0.536391\pi\)
−0.114076 + 0.993472i \(0.536391\pi\)
\(954\) 0 0
\(955\) 26.0368 0.842532
\(956\) 0 0
\(957\) 73.4874 2.37551
\(958\) 0 0
\(959\) 100.694 3.25158
\(960\) 0 0
\(961\) 44.9886 1.45125
\(962\) 0 0
\(963\) −10.9540 −0.352987
\(964\) 0 0
\(965\) −0.537494 −0.0173025
\(966\) 0 0
\(967\) −21.9286 −0.705175 −0.352588 0.935779i \(-0.614698\pi\)
−0.352588 + 0.935779i \(0.614698\pi\)
\(968\) 0 0
\(969\) −7.32418 −0.235287
\(970\) 0 0
\(971\) 23.2670 0.746673 0.373336 0.927696i \(-0.378214\pi\)
0.373336 + 0.927696i \(0.378214\pi\)
\(972\) 0 0
\(973\) 29.4031 0.942620
\(974\) 0 0
\(975\) −7.62211 −0.244103
\(976\) 0 0
\(977\) 27.9216 0.893292 0.446646 0.894711i \(-0.352618\pi\)
0.446646 + 0.894711i \(0.352618\pi\)
\(978\) 0 0
\(979\) 4.98298 0.159257
\(980\) 0 0
\(981\) −2.55701 −0.0816389
\(982\) 0 0
\(983\) −4.15409 −0.132495 −0.0662474 0.997803i \(-0.521103\pi\)
−0.0662474 + 0.997803i \(0.521103\pi\)
\(984\) 0 0
\(985\) 25.7975 0.821977
\(986\) 0 0
\(987\) 70.9780 2.25926
\(988\) 0 0
\(989\) 39.2085 1.24676
\(990\) 0 0
\(991\) −14.1314 −0.448900 −0.224450 0.974486i \(-0.572058\pi\)
−0.224450 + 0.974486i \(0.572058\pi\)
\(992\) 0 0
\(993\) 37.9788 1.20522
\(994\) 0 0
\(995\) 20.6942 0.656049
\(996\) 0 0
\(997\) 2.90142 0.0918887 0.0459444 0.998944i \(-0.485370\pi\)
0.0459444 + 0.998944i \(0.485370\pi\)
\(998\) 0 0
\(999\) 0.0718505 0.00227325
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 \(a_p\))