Properties

Label 8001.2.a.u.1.17
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Root \(2.73355\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.73355 q^{2} +5.47227 q^{4} -4.25416 q^{5} +1.00000 q^{7} +9.49162 q^{8} +O(q^{10})\) \(q+2.73355 q^{2} +5.47227 q^{4} -4.25416 q^{5} +1.00000 q^{7} +9.49162 q^{8} -11.6289 q^{10} -0.824446 q^{11} -6.07408 q^{13} +2.73355 q^{14} +15.0012 q^{16} +0.158117 q^{17} +2.99692 q^{19} -23.2799 q^{20} -2.25366 q^{22} +7.25197 q^{23} +13.0978 q^{25} -16.6038 q^{26} +5.47227 q^{28} +8.45102 q^{29} +3.64198 q^{31} +22.0233 q^{32} +0.432220 q^{34} -4.25416 q^{35} -7.96478 q^{37} +8.19223 q^{38} -40.3788 q^{40} +2.33165 q^{41} -7.65441 q^{43} -4.51159 q^{44} +19.8236 q^{46} +1.87334 q^{47} +1.00000 q^{49} +35.8035 q^{50} -33.2390 q^{52} +4.08642 q^{53} +3.50732 q^{55} +9.49162 q^{56} +23.1013 q^{58} +5.07072 q^{59} -10.9691 q^{61} +9.95552 q^{62} +30.1993 q^{64} +25.8401 q^{65} -8.96906 q^{67} +0.865260 q^{68} -11.6289 q^{70} +13.5264 q^{71} +3.98307 q^{73} -21.7721 q^{74} +16.4000 q^{76} -0.824446 q^{77} +10.1633 q^{79} -63.8175 q^{80} +6.37367 q^{82} +14.9750 q^{83} -0.672655 q^{85} -20.9237 q^{86} -7.82533 q^{88} +2.30581 q^{89} -6.07408 q^{91} +39.6847 q^{92} +5.12087 q^{94} -12.7494 q^{95} +12.0013 q^{97} +2.73355 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} + O(q^{10}) \) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} - 4q^{10} + 9q^{11} - 25q^{13} + 6q^{14} + 34q^{16} + 17q^{17} - 5q^{19} + 21q^{20} + 5q^{22} + 14q^{23} + 28q^{25} + 8q^{26} + 22q^{28} + 17q^{29} + 5q^{31} + 53q^{32} - 19q^{34} + 10q^{35} - 15q^{37} + 22q^{38} - q^{40} + 17q^{41} + q^{43} + 33q^{44} + 10q^{46} + 31q^{47} + 18q^{49} + 35q^{50} - 70q^{52} + 35q^{53} + 4q^{55} + 21q^{56} + 3q^{58} + 46q^{59} - 5q^{61} + 10q^{62} + 63q^{64} + 12q^{65} + 6q^{67} + 56q^{68} - 4q^{70} + 22q^{71} - 16q^{73} - 18q^{74} + 32q^{76} + 9q^{77} + 46q^{79} + 30q^{80} - 12q^{82} + 46q^{83} + 4q^{85} - 18q^{86} + 30q^{88} + 42q^{89} - 25q^{91} + 48q^{92} + 3q^{94} + 2q^{95} - 35q^{97} + 6q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.73355 1.93291 0.966454 0.256838i \(-0.0826808\pi\)
0.966454 + 0.256838i \(0.0826808\pi\)
\(3\) 0 0
\(4\) 5.47227 2.73614
\(5\) −4.25416 −1.90252 −0.951258 0.308396i \(-0.900208\pi\)
−0.951258 + 0.308396i \(0.900208\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 9.49162 3.35579
\(9\) 0 0
\(10\) −11.6289 −3.67739
\(11\) −0.824446 −0.248580 −0.124290 0.992246i \(-0.539665\pi\)
−0.124290 + 0.992246i \(0.539665\pi\)
\(12\) 0 0
\(13\) −6.07408 −1.68465 −0.842324 0.538972i \(-0.818813\pi\)
−0.842324 + 0.538972i \(0.818813\pi\)
\(14\) 2.73355 0.730571
\(15\) 0 0
\(16\) 15.0012 3.75031
\(17\) 0.158117 0.0383490 0.0191745 0.999816i \(-0.493896\pi\)
0.0191745 + 0.999816i \(0.493896\pi\)
\(18\) 0 0
\(19\) 2.99692 0.687542 0.343771 0.939054i \(-0.388296\pi\)
0.343771 + 0.939054i \(0.388296\pi\)
\(20\) −23.2799 −5.20554
\(21\) 0 0
\(22\) −2.25366 −0.480482
\(23\) 7.25197 1.51214 0.756070 0.654491i \(-0.227117\pi\)
0.756070 + 0.654491i \(0.227117\pi\)
\(24\) 0 0
\(25\) 13.0978 2.61957
\(26\) −16.6038 −3.25627
\(27\) 0 0
\(28\) 5.47227 1.03416
\(29\) 8.45102 1.56932 0.784658 0.619929i \(-0.212839\pi\)
0.784658 + 0.619929i \(0.212839\pi\)
\(30\) 0 0
\(31\) 3.64198 0.654119 0.327059 0.945004i \(-0.393942\pi\)
0.327059 + 0.945004i \(0.393942\pi\)
\(32\) 22.0233 3.89321
\(33\) 0 0
\(34\) 0.432220 0.0741252
\(35\) −4.25416 −0.719084
\(36\) 0 0
\(37\) −7.96478 −1.30940 −0.654701 0.755888i \(-0.727206\pi\)
−0.654701 + 0.755888i \(0.727206\pi\)
\(38\) 8.19223 1.32896
\(39\) 0 0
\(40\) −40.3788 −6.38445
\(41\) 2.33165 0.364142 0.182071 0.983285i \(-0.441720\pi\)
0.182071 + 0.983285i \(0.441720\pi\)
\(42\) 0 0
\(43\) −7.65441 −1.16729 −0.583643 0.812010i \(-0.698373\pi\)
−0.583643 + 0.812010i \(0.698373\pi\)
\(44\) −4.51159 −0.680148
\(45\) 0 0
\(46\) 19.8236 2.92283
\(47\) 1.87334 0.273255 0.136628 0.990622i \(-0.456374\pi\)
0.136628 + 0.990622i \(0.456374\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 35.8035 5.06339
\(51\) 0 0
\(52\) −33.2390 −4.60942
\(53\) 4.08642 0.561312 0.280656 0.959808i \(-0.409448\pi\)
0.280656 + 0.959808i \(0.409448\pi\)
\(54\) 0 0
\(55\) 3.50732 0.472927
\(56\) 9.49162 1.26837
\(57\) 0 0
\(58\) 23.1013 3.03334
\(59\) 5.07072 0.660152 0.330076 0.943954i \(-0.392926\pi\)
0.330076 + 0.943954i \(0.392926\pi\)
\(60\) 0 0
\(61\) −10.9691 −1.40445 −0.702224 0.711956i \(-0.747809\pi\)
−0.702224 + 0.711956i \(0.747809\pi\)
\(62\) 9.95552 1.26435
\(63\) 0 0
\(64\) 30.1993 3.77491
\(65\) 25.8401 3.20507
\(66\) 0 0
\(67\) −8.96906 −1.09574 −0.547872 0.836562i \(-0.684562\pi\)
−0.547872 + 0.836562i \(0.684562\pi\)
\(68\) 0.865260 0.104928
\(69\) 0 0
\(70\) −11.6289 −1.38992
\(71\) 13.5264 1.60529 0.802643 0.596459i \(-0.203426\pi\)
0.802643 + 0.596459i \(0.203426\pi\)
\(72\) 0 0
\(73\) 3.98307 0.466183 0.233091 0.972455i \(-0.425116\pi\)
0.233091 + 0.972455i \(0.425116\pi\)
\(74\) −21.7721 −2.53096
\(75\) 0 0
\(76\) 16.4000 1.88121
\(77\) −0.824446 −0.0939544
\(78\) 0 0
\(79\) 10.1633 1.14346 0.571732 0.820441i \(-0.306272\pi\)
0.571732 + 0.820441i \(0.306272\pi\)
\(80\) −63.8175 −7.13502
\(81\) 0 0
\(82\) 6.37367 0.703854
\(83\) 14.9750 1.64372 0.821859 0.569691i \(-0.192937\pi\)
0.821859 + 0.569691i \(0.192937\pi\)
\(84\) 0 0
\(85\) −0.672655 −0.0729596
\(86\) −20.9237 −2.25626
\(87\) 0 0
\(88\) −7.82533 −0.834183
\(89\) 2.30581 0.244415 0.122208 0.992505i \(-0.461003\pi\)
0.122208 + 0.992505i \(0.461003\pi\)
\(90\) 0 0
\(91\) −6.07408 −0.636737
\(92\) 39.6847 4.13742
\(93\) 0 0
\(94\) 5.12087 0.528177
\(95\) −12.7494 −1.30806
\(96\) 0 0
\(97\) 12.0013 1.21854 0.609272 0.792961i \(-0.291462\pi\)
0.609272 + 0.792961i \(0.291462\pi\)
\(98\) 2.73355 0.276130
\(99\) 0 0
\(100\) 71.6750 7.16750
\(101\) 14.7534 1.46802 0.734008 0.679140i \(-0.237647\pi\)
0.734008 + 0.679140i \(0.237647\pi\)
\(102\) 0 0
\(103\) 20.0095 1.97159 0.985797 0.167943i \(-0.0537124\pi\)
0.985797 + 0.167943i \(0.0537124\pi\)
\(104\) −57.6529 −5.65333
\(105\) 0 0
\(106\) 11.1704 1.08497
\(107\) −3.53204 −0.341455 −0.170728 0.985318i \(-0.554612\pi\)
−0.170728 + 0.985318i \(0.554612\pi\)
\(108\) 0 0
\(109\) −7.28193 −0.697483 −0.348741 0.937219i \(-0.613391\pi\)
−0.348741 + 0.937219i \(0.613391\pi\)
\(110\) 9.58743 0.914125
\(111\) 0 0
\(112\) 15.0012 1.41748
\(113\) 0.617948 0.0581316 0.0290658 0.999578i \(-0.490747\pi\)
0.0290658 + 0.999578i \(0.490747\pi\)
\(114\) 0 0
\(115\) −30.8510 −2.87687
\(116\) 46.2463 4.29386
\(117\) 0 0
\(118\) 13.8611 1.27601
\(119\) 0.158117 0.0144946
\(120\) 0 0
\(121\) −10.3203 −0.938208
\(122\) −29.9845 −2.71467
\(123\) 0 0
\(124\) 19.9299 1.78976
\(125\) −34.4495 −3.08125
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 38.5045 3.40334
\(129\) 0 0
\(130\) 70.6351 6.19510
\(131\) −5.77893 −0.504907 −0.252454 0.967609i \(-0.581237\pi\)
−0.252454 + 0.967609i \(0.581237\pi\)
\(132\) 0 0
\(133\) 2.99692 0.259866
\(134\) −24.5173 −2.11797
\(135\) 0 0
\(136\) 1.50079 0.128691
\(137\) −10.6326 −0.908402 −0.454201 0.890899i \(-0.650075\pi\)
−0.454201 + 0.890899i \(0.650075\pi\)
\(138\) 0 0
\(139\) 11.1927 0.949357 0.474678 0.880159i \(-0.342564\pi\)
0.474678 + 0.880159i \(0.342564\pi\)
\(140\) −23.2799 −1.96751
\(141\) 0 0
\(142\) 36.9750 3.10287
\(143\) 5.00775 0.418769
\(144\) 0 0
\(145\) −35.9520 −2.98565
\(146\) 10.8879 0.901088
\(147\) 0 0
\(148\) −43.5855 −3.58270
\(149\) 5.51178 0.451543 0.225771 0.974180i \(-0.427510\pi\)
0.225771 + 0.974180i \(0.427510\pi\)
\(150\) 0 0
\(151\) −9.28026 −0.755217 −0.377608 0.925965i \(-0.623253\pi\)
−0.377608 + 0.925965i \(0.623253\pi\)
\(152\) 28.4457 2.30725
\(153\) 0 0
\(154\) −2.25366 −0.181605
\(155\) −15.4936 −1.24447
\(156\) 0 0
\(157\) 6.26218 0.499777 0.249888 0.968275i \(-0.419606\pi\)
0.249888 + 0.968275i \(0.419606\pi\)
\(158\) 27.7819 2.21021
\(159\) 0 0
\(160\) −93.6906 −7.40689
\(161\) 7.25197 0.571535
\(162\) 0 0
\(163\) 9.87167 0.773209 0.386605 0.922246i \(-0.373648\pi\)
0.386605 + 0.922246i \(0.373648\pi\)
\(164\) 12.7594 0.996343
\(165\) 0 0
\(166\) 40.9348 3.17716
\(167\) 3.42627 0.265132 0.132566 0.991174i \(-0.457678\pi\)
0.132566 + 0.991174i \(0.457678\pi\)
\(168\) 0 0
\(169\) 23.8945 1.83804
\(170\) −1.83873 −0.141024
\(171\) 0 0
\(172\) −41.8870 −3.19385
\(173\) 24.0689 1.82992 0.914961 0.403542i \(-0.132221\pi\)
0.914961 + 0.403542i \(0.132221\pi\)
\(174\) 0 0
\(175\) 13.0978 0.990104
\(176\) −12.3677 −0.932251
\(177\) 0 0
\(178\) 6.30304 0.472433
\(179\) −1.62717 −0.121620 −0.0608101 0.998149i \(-0.519368\pi\)
−0.0608101 + 0.998149i \(0.519368\pi\)
\(180\) 0 0
\(181\) −21.3974 −1.59046 −0.795229 0.606309i \(-0.792650\pi\)
−0.795229 + 0.606309i \(0.792650\pi\)
\(182\) −16.6038 −1.23075
\(183\) 0 0
\(184\) 68.8329 5.07443
\(185\) 33.8834 2.49116
\(186\) 0 0
\(187\) −0.130359 −0.00953280
\(188\) 10.2514 0.747663
\(189\) 0 0
\(190\) −34.8510 −2.52836
\(191\) −3.16587 −0.229074 −0.114537 0.993419i \(-0.536538\pi\)
−0.114537 + 0.993419i \(0.536538\pi\)
\(192\) 0 0
\(193\) 17.9622 1.29295 0.646474 0.762936i \(-0.276243\pi\)
0.646474 + 0.762936i \(0.276243\pi\)
\(194\) 32.8060 2.35534
\(195\) 0 0
\(196\) 5.47227 0.390877
\(197\) −3.38471 −0.241150 −0.120575 0.992704i \(-0.538474\pi\)
−0.120575 + 0.992704i \(0.538474\pi\)
\(198\) 0 0
\(199\) −8.58653 −0.608683 −0.304342 0.952563i \(-0.598436\pi\)
−0.304342 + 0.952563i \(0.598436\pi\)
\(200\) 124.320 8.79073
\(201\) 0 0
\(202\) 40.3291 2.83754
\(203\) 8.45102 0.593146
\(204\) 0 0
\(205\) −9.91919 −0.692787
\(206\) 54.6969 3.81091
\(207\) 0 0
\(208\) −91.1187 −6.31794
\(209\) −2.47080 −0.170909
\(210\) 0 0
\(211\) −1.57255 −0.108259 −0.0541293 0.998534i \(-0.517238\pi\)
−0.0541293 + 0.998534i \(0.517238\pi\)
\(212\) 22.3620 1.53583
\(213\) 0 0
\(214\) −9.65500 −0.660002
\(215\) 32.5630 2.22078
\(216\) 0 0
\(217\) 3.64198 0.247234
\(218\) −19.9055 −1.34817
\(219\) 0 0
\(220\) 19.1930 1.29399
\(221\) −0.960416 −0.0646046
\(222\) 0 0
\(223\) 20.6473 1.38264 0.691322 0.722546i \(-0.257028\pi\)
0.691322 + 0.722546i \(0.257028\pi\)
\(224\) 22.0233 1.47149
\(225\) 0 0
\(226\) 1.68919 0.112363
\(227\) −16.1218 −1.07004 −0.535021 0.844839i \(-0.679696\pi\)
−0.535021 + 0.844839i \(0.679696\pi\)
\(228\) 0 0
\(229\) 0.466165 0.0308051 0.0154025 0.999881i \(-0.495097\pi\)
0.0154025 + 0.999881i \(0.495097\pi\)
\(230\) −84.3326 −5.56073
\(231\) 0 0
\(232\) 80.2139 5.26630
\(233\) −15.7869 −1.03423 −0.517117 0.855914i \(-0.672995\pi\)
−0.517117 + 0.855914i \(0.672995\pi\)
\(234\) 0 0
\(235\) −7.96949 −0.519872
\(236\) 27.7484 1.80627
\(237\) 0 0
\(238\) 0.432220 0.0280167
\(239\) −21.2755 −1.37620 −0.688100 0.725616i \(-0.741555\pi\)
−0.688100 + 0.725616i \(0.741555\pi\)
\(240\) 0 0
\(241\) 0.979158 0.0630731 0.0315366 0.999503i \(-0.489960\pi\)
0.0315366 + 0.999503i \(0.489960\pi\)
\(242\) −28.2110 −1.81347
\(243\) 0 0
\(244\) −60.0258 −3.84276
\(245\) −4.25416 −0.271788
\(246\) 0 0
\(247\) −18.2036 −1.15827
\(248\) 34.5683 2.19509
\(249\) 0 0
\(250\) −94.1692 −5.95578
\(251\) −22.4410 −1.41646 −0.708232 0.705980i \(-0.750507\pi\)
−0.708232 + 0.705980i \(0.750507\pi\)
\(252\) 0 0
\(253\) −5.97886 −0.375887
\(254\) 2.73355 0.171518
\(255\) 0 0
\(256\) 44.8552 2.80345
\(257\) −1.84487 −0.115080 −0.0575400 0.998343i \(-0.518326\pi\)
−0.0575400 + 0.998343i \(0.518326\pi\)
\(258\) 0 0
\(259\) −7.96478 −0.494908
\(260\) 141.404 8.76950
\(261\) 0 0
\(262\) −15.7970 −0.975939
\(263\) −10.0151 −0.617555 −0.308778 0.951134i \(-0.599920\pi\)
−0.308778 + 0.951134i \(0.599920\pi\)
\(264\) 0 0
\(265\) −17.3843 −1.06791
\(266\) 8.19223 0.502298
\(267\) 0 0
\(268\) −49.0811 −2.99811
\(269\) −5.91408 −0.360588 −0.180294 0.983613i \(-0.557705\pi\)
−0.180294 + 0.983613i \(0.557705\pi\)
\(270\) 0 0
\(271\) 5.40067 0.328067 0.164034 0.986455i \(-0.447549\pi\)
0.164034 + 0.986455i \(0.447549\pi\)
\(272\) 2.37195 0.143821
\(273\) 0 0
\(274\) −29.0646 −1.75586
\(275\) −10.7985 −0.651172
\(276\) 0 0
\(277\) −29.8821 −1.79544 −0.897719 0.440568i \(-0.854777\pi\)
−0.897719 + 0.440568i \(0.854777\pi\)
\(278\) 30.5959 1.83502
\(279\) 0 0
\(280\) −40.3788 −2.41310
\(281\) −9.16406 −0.546682 −0.273341 0.961917i \(-0.588129\pi\)
−0.273341 + 0.961917i \(0.588129\pi\)
\(282\) 0 0
\(283\) −17.9317 −1.06593 −0.532966 0.846137i \(-0.678923\pi\)
−0.532966 + 0.846137i \(0.678923\pi\)
\(284\) 74.0201 4.39228
\(285\) 0 0
\(286\) 13.6889 0.809443
\(287\) 2.33165 0.137633
\(288\) 0 0
\(289\) −16.9750 −0.998529
\(290\) −98.2764 −5.77099
\(291\) 0 0
\(292\) 21.7964 1.27554
\(293\) 10.8736 0.635241 0.317621 0.948218i \(-0.397116\pi\)
0.317621 + 0.948218i \(0.397116\pi\)
\(294\) 0 0
\(295\) −21.5716 −1.25595
\(296\) −75.5987 −4.39408
\(297\) 0 0
\(298\) 15.0667 0.872791
\(299\) −44.0490 −2.54742
\(300\) 0 0
\(301\) −7.65441 −0.441193
\(302\) −25.3680 −1.45976
\(303\) 0 0
\(304\) 44.9575 2.57849
\(305\) 46.6642 2.67198
\(306\) 0 0
\(307\) 15.4755 0.883234 0.441617 0.897204i \(-0.354405\pi\)
0.441617 + 0.897204i \(0.354405\pi\)
\(308\) −4.51159 −0.257072
\(309\) 0 0
\(310\) −42.3523 −2.40545
\(311\) 6.68109 0.378850 0.189425 0.981895i \(-0.439338\pi\)
0.189425 + 0.981895i \(0.439338\pi\)
\(312\) 0 0
\(313\) −2.10828 −0.119167 −0.0595837 0.998223i \(-0.518977\pi\)
−0.0595837 + 0.998223i \(0.518977\pi\)
\(314\) 17.1180 0.966022
\(315\) 0 0
\(316\) 55.6165 3.12867
\(317\) 14.5298 0.816073 0.408037 0.912966i \(-0.366214\pi\)
0.408037 + 0.912966i \(0.366214\pi\)
\(318\) 0 0
\(319\) −6.96741 −0.390100
\(320\) −128.472 −7.18182
\(321\) 0 0
\(322\) 19.8236 1.10473
\(323\) 0.473865 0.0263666
\(324\) 0 0
\(325\) −79.5573 −4.41305
\(326\) 26.9847 1.49454
\(327\) 0 0
\(328\) 22.1311 1.22199
\(329\) 1.87334 0.103281
\(330\) 0 0
\(331\) 3.02729 0.166395 0.0831976 0.996533i \(-0.473487\pi\)
0.0831976 + 0.996533i \(0.473487\pi\)
\(332\) 81.9472 4.49744
\(333\) 0 0
\(334\) 9.36585 0.512477
\(335\) 38.1558 2.08467
\(336\) 0 0
\(337\) 23.2809 1.26819 0.634095 0.773255i \(-0.281373\pi\)
0.634095 + 0.773255i \(0.281373\pi\)
\(338\) 65.3166 3.55276
\(339\) 0 0
\(340\) −3.68095 −0.199628
\(341\) −3.00262 −0.162601
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −72.6527 −3.91717
\(345\) 0 0
\(346\) 65.7934 3.53707
\(347\) −12.7330 −0.683545 −0.341772 0.939783i \(-0.611027\pi\)
−0.341772 + 0.939783i \(0.611027\pi\)
\(348\) 0 0
\(349\) −4.43634 −0.237472 −0.118736 0.992926i \(-0.537884\pi\)
−0.118736 + 0.992926i \(0.537884\pi\)
\(350\) 35.8035 1.91378
\(351\) 0 0
\(352\) −18.1570 −0.967773
\(353\) −30.1229 −1.60328 −0.801640 0.597808i \(-0.796039\pi\)
−0.801640 + 0.597808i \(0.796039\pi\)
\(354\) 0 0
\(355\) −57.5433 −3.05408
\(356\) 12.6180 0.668754
\(357\) 0 0
\(358\) −4.44794 −0.235081
\(359\) −16.9749 −0.895899 −0.447950 0.894059i \(-0.647846\pi\)
−0.447950 + 0.894059i \(0.647846\pi\)
\(360\) 0 0
\(361\) −10.0184 −0.527286
\(362\) −58.4909 −3.07421
\(363\) 0 0
\(364\) −33.2390 −1.74220
\(365\) −16.9446 −0.886920
\(366\) 0 0
\(367\) −30.7822 −1.60682 −0.803409 0.595428i \(-0.796983\pi\)
−0.803409 + 0.595428i \(0.796983\pi\)
\(368\) 108.788 5.67099
\(369\) 0 0
\(370\) 92.6219 4.81518
\(371\) 4.08642 0.212156
\(372\) 0 0
\(373\) −18.9019 −0.978701 −0.489350 0.872087i \(-0.662766\pi\)
−0.489350 + 0.872087i \(0.662766\pi\)
\(374\) −0.356342 −0.0184260
\(375\) 0 0
\(376\) 17.7810 0.916987
\(377\) −51.3322 −2.64374
\(378\) 0 0
\(379\) 27.2163 1.39801 0.699004 0.715117i \(-0.253627\pi\)
0.699004 + 0.715117i \(0.253627\pi\)
\(380\) −69.7681 −3.57903
\(381\) 0 0
\(382\) −8.65404 −0.442779
\(383\) −22.7566 −1.16281 −0.581403 0.813616i \(-0.697496\pi\)
−0.581403 + 0.813616i \(0.697496\pi\)
\(384\) 0 0
\(385\) 3.50732 0.178750
\(386\) 49.1005 2.49915
\(387\) 0 0
\(388\) 65.6742 3.33410
\(389\) 29.3879 1.49003 0.745014 0.667049i \(-0.232443\pi\)
0.745014 + 0.667049i \(0.232443\pi\)
\(390\) 0 0
\(391\) 1.14666 0.0579891
\(392\) 9.49162 0.479399
\(393\) 0 0
\(394\) −9.25226 −0.466122
\(395\) −43.2364 −2.17546
\(396\) 0 0
\(397\) 13.9738 0.701326 0.350663 0.936502i \(-0.385956\pi\)
0.350663 + 0.936502i \(0.385956\pi\)
\(398\) −23.4717 −1.17653
\(399\) 0 0
\(400\) 196.484 9.82418
\(401\) 13.0010 0.649240 0.324620 0.945844i \(-0.394764\pi\)
0.324620 + 0.945844i \(0.394764\pi\)
\(402\) 0 0
\(403\) −22.1217 −1.10196
\(404\) 80.7346 4.01669
\(405\) 0 0
\(406\) 23.1013 1.14650
\(407\) 6.56654 0.325491
\(408\) 0 0
\(409\) 20.1740 0.997539 0.498769 0.866735i \(-0.333785\pi\)
0.498769 + 0.866735i \(0.333785\pi\)
\(410\) −27.1146 −1.33909
\(411\) 0 0
\(412\) 109.497 5.39455
\(413\) 5.07072 0.249514
\(414\) 0 0
\(415\) −63.7059 −3.12720
\(416\) −133.771 −6.55868
\(417\) 0 0
\(418\) −6.75405 −0.330352
\(419\) 10.2203 0.499296 0.249648 0.968337i \(-0.419685\pi\)
0.249648 + 0.968337i \(0.419685\pi\)
\(420\) 0 0
\(421\) 17.7217 0.863705 0.431852 0.901944i \(-0.357860\pi\)
0.431852 + 0.901944i \(0.357860\pi\)
\(422\) −4.29863 −0.209254
\(423\) 0 0
\(424\) 38.7867 1.88365
\(425\) 2.07099 0.100458
\(426\) 0 0
\(427\) −10.9691 −0.530831
\(428\) −19.3283 −0.934269
\(429\) 0 0
\(430\) 89.0125 4.29257
\(431\) −9.52244 −0.458680 −0.229340 0.973346i \(-0.573657\pi\)
−0.229340 + 0.973346i \(0.573657\pi\)
\(432\) 0 0
\(433\) −4.07745 −0.195950 −0.0979748 0.995189i \(-0.531236\pi\)
−0.0979748 + 0.995189i \(0.531236\pi\)
\(434\) 9.95552 0.477880
\(435\) 0 0
\(436\) −39.8487 −1.90841
\(437\) 21.7336 1.03966
\(438\) 0 0
\(439\) 17.8790 0.853320 0.426660 0.904412i \(-0.359690\pi\)
0.426660 + 0.904412i \(0.359690\pi\)
\(440\) 33.2902 1.58705
\(441\) 0 0
\(442\) −2.62534 −0.124875
\(443\) −13.3161 −0.632666 −0.316333 0.948648i \(-0.602452\pi\)
−0.316333 + 0.948648i \(0.602452\pi\)
\(444\) 0 0
\(445\) −9.80927 −0.465004
\(446\) 56.4403 2.67253
\(447\) 0 0
\(448\) 30.1993 1.42678
\(449\) 9.52844 0.449675 0.224837 0.974396i \(-0.427815\pi\)
0.224837 + 0.974396i \(0.427815\pi\)
\(450\) 0 0
\(451\) −1.92232 −0.0905184
\(452\) 3.38158 0.159056
\(453\) 0 0
\(454\) −44.0697 −2.06829
\(455\) 25.8401 1.21140
\(456\) 0 0
\(457\) −16.6666 −0.779630 −0.389815 0.920893i \(-0.627461\pi\)
−0.389815 + 0.920893i \(0.627461\pi\)
\(458\) 1.27428 0.0595434
\(459\) 0 0
\(460\) −168.825 −7.87151
\(461\) −6.78637 −0.316073 −0.158036 0.987433i \(-0.550516\pi\)
−0.158036 + 0.987433i \(0.550516\pi\)
\(462\) 0 0
\(463\) −33.8866 −1.57484 −0.787422 0.616415i \(-0.788585\pi\)
−0.787422 + 0.616415i \(0.788585\pi\)
\(464\) 126.776 5.88541
\(465\) 0 0
\(466\) −43.1542 −1.99908
\(467\) −13.2514 −0.613200 −0.306600 0.951838i \(-0.599191\pi\)
−0.306600 + 0.951838i \(0.599191\pi\)
\(468\) 0 0
\(469\) −8.96906 −0.414153
\(470\) −21.7850 −1.00487
\(471\) 0 0
\(472\) 48.1294 2.21533
\(473\) 6.31064 0.290164
\(474\) 0 0
\(475\) 39.2532 1.80106
\(476\) 0.865260 0.0396591
\(477\) 0 0
\(478\) −58.1576 −2.66007
\(479\) 31.4248 1.43584 0.717919 0.696127i \(-0.245095\pi\)
0.717919 + 0.696127i \(0.245095\pi\)
\(480\) 0 0
\(481\) 48.3787 2.20588
\(482\) 2.67657 0.121915
\(483\) 0 0
\(484\) −56.4754 −2.56707
\(485\) −51.0553 −2.31830
\(486\) 0 0
\(487\) −6.66403 −0.301976 −0.150988 0.988536i \(-0.548245\pi\)
−0.150988 + 0.988536i \(0.548245\pi\)
\(488\) −104.114 −4.71304
\(489\) 0 0
\(490\) −11.6289 −0.525341
\(491\) −2.68603 −0.121219 −0.0606095 0.998162i \(-0.519304\pi\)
−0.0606095 + 0.998162i \(0.519304\pi\)
\(492\) 0 0
\(493\) 1.33625 0.0601817
\(494\) −49.7603 −2.23882
\(495\) 0 0
\(496\) 54.6342 2.45315
\(497\) 13.5264 0.606741
\(498\) 0 0
\(499\) 9.17753 0.410843 0.205421 0.978674i \(-0.434144\pi\)
0.205421 + 0.978674i \(0.434144\pi\)
\(500\) −188.517 −8.43073
\(501\) 0 0
\(502\) −61.3435 −2.73789
\(503\) −7.82917 −0.349085 −0.174543 0.984650i \(-0.555845\pi\)
−0.174543 + 0.984650i \(0.555845\pi\)
\(504\) 0 0
\(505\) −62.7632 −2.79293
\(506\) −16.3435 −0.726556
\(507\) 0 0
\(508\) 5.47227 0.242793
\(509\) −13.5889 −0.602318 −0.301159 0.953574i \(-0.597374\pi\)
−0.301159 + 0.953574i \(0.597374\pi\)
\(510\) 0 0
\(511\) 3.98307 0.176200
\(512\) 45.6048 2.01546
\(513\) 0 0
\(514\) −5.04304 −0.222439
\(515\) −85.1235 −3.75099
\(516\) 0 0
\(517\) −1.54447 −0.0679257
\(518\) −21.7721 −0.956611
\(519\) 0 0
\(520\) 245.264 10.7555
\(521\) 35.6930 1.56374 0.781869 0.623443i \(-0.214266\pi\)
0.781869 + 0.623443i \(0.214266\pi\)
\(522\) 0 0
\(523\) −38.0116 −1.66213 −0.831066 0.556173i \(-0.812269\pi\)
−0.831066 + 0.556173i \(0.812269\pi\)
\(524\) −31.6239 −1.38149
\(525\) 0 0
\(526\) −27.3766 −1.19368
\(527\) 0.575859 0.0250848
\(528\) 0 0
\(529\) 29.5910 1.28657
\(530\) −47.5206 −2.06417
\(531\) 0 0
\(532\) 16.4000 0.711030
\(533\) −14.1626 −0.613451
\(534\) 0 0
\(535\) 15.0259 0.649624
\(536\) −85.1309 −3.67709
\(537\) 0 0
\(538\) −16.1664 −0.696983
\(539\) −0.824446 −0.0355114
\(540\) 0 0
\(541\) −18.2336 −0.783922 −0.391961 0.919982i \(-0.628203\pi\)
−0.391961 + 0.919982i \(0.628203\pi\)
\(542\) 14.7630 0.634124
\(543\) 0 0
\(544\) 3.48226 0.149301
\(545\) 30.9785 1.32697
\(546\) 0 0
\(547\) 20.9218 0.894550 0.447275 0.894396i \(-0.352394\pi\)
0.447275 + 0.894396i \(0.352394\pi\)
\(548\) −58.1844 −2.48551
\(549\) 0 0
\(550\) −29.5181 −1.25866
\(551\) 25.3271 1.07897
\(552\) 0 0
\(553\) 10.1633 0.432188
\(554\) −81.6840 −3.47042
\(555\) 0 0
\(556\) 61.2498 2.59757
\(557\) 25.8713 1.09620 0.548101 0.836412i \(-0.315351\pi\)
0.548101 + 0.836412i \(0.315351\pi\)
\(558\) 0 0
\(559\) 46.4935 1.96646
\(560\) −63.8175 −2.69678
\(561\) 0 0
\(562\) −25.0504 −1.05669
\(563\) 5.55729 0.234212 0.117106 0.993119i \(-0.462638\pi\)
0.117106 + 0.993119i \(0.462638\pi\)
\(564\) 0 0
\(565\) −2.62885 −0.110596
\(566\) −49.0173 −2.06035
\(567\) 0 0
\(568\) 128.387 5.38701
\(569\) 46.5246 1.95041 0.975207 0.221295i \(-0.0710283\pi\)
0.975207 + 0.221295i \(0.0710283\pi\)
\(570\) 0 0
\(571\) 20.3185 0.850303 0.425151 0.905122i \(-0.360221\pi\)
0.425151 + 0.905122i \(0.360221\pi\)
\(572\) 27.4038 1.14581
\(573\) 0 0
\(574\) 6.37367 0.266032
\(575\) 94.9851 3.96115
\(576\) 0 0
\(577\) −25.7829 −1.07336 −0.536679 0.843787i \(-0.680321\pi\)
−0.536679 + 0.843787i \(0.680321\pi\)
\(578\) −46.4019 −1.93007
\(579\) 0 0
\(580\) −196.739 −8.16914
\(581\) 14.9750 0.621267
\(582\) 0 0
\(583\) −3.36903 −0.139531
\(584\) 37.8057 1.56441
\(585\) 0 0
\(586\) 29.7234 1.22786
\(587\) −10.4729 −0.432264 −0.216132 0.976364i \(-0.569344\pi\)
−0.216132 + 0.976364i \(0.569344\pi\)
\(588\) 0 0
\(589\) 10.9147 0.449734
\(590\) −58.9671 −2.42764
\(591\) 0 0
\(592\) −119.482 −4.91066
\(593\) 0.853843 0.0350631 0.0175316 0.999846i \(-0.494419\pi\)
0.0175316 + 0.999846i \(0.494419\pi\)
\(594\) 0 0
\(595\) −0.672655 −0.0275762
\(596\) 30.1620 1.23548
\(597\) 0 0
\(598\) −120.410 −4.92393
\(599\) −25.2120 −1.03013 −0.515066 0.857150i \(-0.672233\pi\)
−0.515066 + 0.857150i \(0.672233\pi\)
\(600\) 0 0
\(601\) 4.40447 0.179662 0.0898310 0.995957i \(-0.471367\pi\)
0.0898310 + 0.995957i \(0.471367\pi\)
\(602\) −20.9237 −0.852785
\(603\) 0 0
\(604\) −50.7841 −2.06638
\(605\) 43.9041 1.78496
\(606\) 0 0
\(607\) −30.6486 −1.24399 −0.621995 0.783021i \(-0.713678\pi\)
−0.621995 + 0.783021i \(0.713678\pi\)
\(608\) 66.0022 2.67674
\(609\) 0 0
\(610\) 127.559 5.16470
\(611\) −11.3788 −0.460338
\(612\) 0 0
\(613\) 18.9715 0.766253 0.383127 0.923696i \(-0.374847\pi\)
0.383127 + 0.923696i \(0.374847\pi\)
\(614\) 42.3030 1.70721
\(615\) 0 0
\(616\) −7.82533 −0.315291
\(617\) 32.5842 1.31179 0.655896 0.754851i \(-0.272291\pi\)
0.655896 + 0.754851i \(0.272291\pi\)
\(618\) 0 0
\(619\) 11.4269 0.459286 0.229643 0.973275i \(-0.426244\pi\)
0.229643 + 0.973275i \(0.426244\pi\)
\(620\) −84.7849 −3.40504
\(621\) 0 0
\(622\) 18.2631 0.732282
\(623\) 2.30581 0.0923803
\(624\) 0 0
\(625\) 81.0642 3.24257
\(626\) −5.76309 −0.230340
\(627\) 0 0
\(628\) 34.2684 1.36746
\(629\) −1.25937 −0.0502143
\(630\) 0 0
\(631\) −8.98000 −0.357488 −0.178744 0.983896i \(-0.557203\pi\)
−0.178744 + 0.983896i \(0.557203\pi\)
\(632\) 96.4664 3.83723
\(633\) 0 0
\(634\) 39.7178 1.57739
\(635\) −4.25416 −0.168821
\(636\) 0 0
\(637\) −6.07408 −0.240664
\(638\) −19.0457 −0.754028
\(639\) 0 0
\(640\) −163.804 −6.47492
\(641\) −47.3990 −1.87215 −0.936075 0.351801i \(-0.885569\pi\)
−0.936075 + 0.351801i \(0.885569\pi\)
\(642\) 0 0
\(643\) −31.5756 −1.24522 −0.622610 0.782532i \(-0.713928\pi\)
−0.622610 + 0.782532i \(0.713928\pi\)
\(644\) 39.6847 1.56380
\(645\) 0 0
\(646\) 1.29533 0.0509641
\(647\) 25.6927 1.01009 0.505043 0.863094i \(-0.331477\pi\)
0.505043 + 0.863094i \(0.331477\pi\)
\(648\) 0 0
\(649\) −4.18054 −0.164100
\(650\) −217.474 −8.53002
\(651\) 0 0
\(652\) 54.0205 2.11561
\(653\) 44.9646 1.75960 0.879801 0.475343i \(-0.157676\pi\)
0.879801 + 0.475343i \(0.157676\pi\)
\(654\) 0 0
\(655\) 24.5845 0.960594
\(656\) 34.9776 1.36564
\(657\) 0 0
\(658\) 5.12087 0.199632
\(659\) −22.2509 −0.866774 −0.433387 0.901208i \(-0.642682\pi\)
−0.433387 + 0.901208i \(0.642682\pi\)
\(660\) 0 0
\(661\) 1.25962 0.0489934 0.0244967 0.999700i \(-0.492202\pi\)
0.0244967 + 0.999700i \(0.492202\pi\)
\(662\) 8.27525 0.321627
\(663\) 0 0
\(664\) 142.137 5.51598
\(665\) −12.7494 −0.494400
\(666\) 0 0
\(667\) 61.2865 2.37302
\(668\) 18.7495 0.725438
\(669\) 0 0
\(670\) 104.301 4.02948
\(671\) 9.04342 0.349117
\(672\) 0 0
\(673\) −7.14715 −0.275503 −0.137751 0.990467i \(-0.543987\pi\)
−0.137751 + 0.990467i \(0.543987\pi\)
\(674\) 63.6393 2.45129
\(675\) 0 0
\(676\) 130.757 5.02912
\(677\) −43.3438 −1.66584 −0.832919 0.553394i \(-0.813332\pi\)
−0.832919 + 0.553394i \(0.813332\pi\)
\(678\) 0 0
\(679\) 12.0013 0.460566
\(680\) −6.38458 −0.244838
\(681\) 0 0
\(682\) −8.20779 −0.314293
\(683\) −10.7838 −0.412630 −0.206315 0.978486i \(-0.566147\pi\)
−0.206315 + 0.978486i \(0.566147\pi\)
\(684\) 0 0
\(685\) 45.2326 1.72825
\(686\) 2.73355 0.104367
\(687\) 0 0
\(688\) −114.825 −4.37768
\(689\) −24.8212 −0.945613
\(690\) 0 0
\(691\) −27.4142 −1.04289 −0.521443 0.853286i \(-0.674606\pi\)
−0.521443 + 0.853286i \(0.674606\pi\)
\(692\) 131.711 5.00692
\(693\) 0 0
\(694\) −34.8063 −1.32123
\(695\) −47.6157 −1.80617
\(696\) 0 0
\(697\) 0.368673 0.0139645
\(698\) −12.1269 −0.459011
\(699\) 0 0
\(700\) 71.6750 2.70906
\(701\) 40.6532 1.53545 0.767726 0.640778i \(-0.221388\pi\)
0.767726 + 0.640778i \(0.221388\pi\)
\(702\) 0 0
\(703\) −23.8699 −0.900269
\(704\) −24.8977 −0.938366
\(705\) 0 0
\(706\) −82.3423 −3.09899
\(707\) 14.7534 0.554858
\(708\) 0 0
\(709\) −1.15285 −0.0432962 −0.0216481 0.999766i \(-0.506891\pi\)
−0.0216481 + 0.999766i \(0.506891\pi\)
\(710\) −157.297 −5.90326
\(711\) 0 0
\(712\) 21.8859 0.820208
\(713\) 26.4115 0.989119
\(714\) 0 0
\(715\) −21.3038 −0.796715
\(716\) −8.90431 −0.332770
\(717\) 0 0
\(718\) −46.4016 −1.73169
\(719\) 3.46292 0.129145 0.0645726 0.997913i \(-0.479432\pi\)
0.0645726 + 0.997913i \(0.479432\pi\)
\(720\) 0 0
\(721\) 20.0095 0.745192
\(722\) −27.3859 −1.01920
\(723\) 0 0
\(724\) −117.093 −4.35171
\(725\) 110.690 4.11093
\(726\) 0 0
\(727\) −17.7957 −0.660005 −0.330002 0.943980i \(-0.607050\pi\)
−0.330002 + 0.943980i \(0.607050\pi\)
\(728\) −57.6529 −2.13676
\(729\) 0 0
\(730\) −46.3188 −1.71434
\(731\) −1.21029 −0.0447643
\(732\) 0 0
\(733\) 28.8583 1.06591 0.532953 0.846145i \(-0.321082\pi\)
0.532953 + 0.846145i \(0.321082\pi\)
\(734\) −84.1445 −3.10583
\(735\) 0 0
\(736\) 159.712 5.88707
\(737\) 7.39451 0.272380
\(738\) 0 0
\(739\) −54.0990 −1.99006 −0.995031 0.0995614i \(-0.968256\pi\)
−0.995031 + 0.0995614i \(0.968256\pi\)
\(740\) 185.419 6.81615
\(741\) 0 0
\(742\) 11.1704 0.410079
\(743\) 11.4467 0.419938 0.209969 0.977708i \(-0.432664\pi\)
0.209969 + 0.977708i \(0.432664\pi\)
\(744\) 0 0
\(745\) −23.4480 −0.859067
\(746\) −51.6691 −1.89174
\(747\) 0 0
\(748\) −0.713360 −0.0260830
\(749\) −3.53204 −0.129058
\(750\) 0 0
\(751\) 27.0757 0.988005 0.494003 0.869460i \(-0.335533\pi\)
0.494003 + 0.869460i \(0.335533\pi\)
\(752\) 28.1024 1.02479
\(753\) 0 0
\(754\) −140.319 −5.11011
\(755\) 39.4797 1.43681
\(756\) 0 0
\(757\) −8.33274 −0.302859 −0.151429 0.988468i \(-0.548388\pi\)
−0.151429 + 0.988468i \(0.548388\pi\)
\(758\) 74.3971 2.70222
\(759\) 0 0
\(760\) −121.012 −4.38958
\(761\) −29.5344 −1.07062 −0.535310 0.844656i \(-0.679805\pi\)
−0.535310 + 0.844656i \(0.679805\pi\)
\(762\) 0 0
\(763\) −7.28193 −0.263624
\(764\) −17.3245 −0.626778
\(765\) 0 0
\(766\) −62.2061 −2.24760
\(767\) −30.8000 −1.11212
\(768\) 0 0
\(769\) −16.5765 −0.597763 −0.298881 0.954290i \(-0.596613\pi\)
−0.298881 + 0.954290i \(0.596613\pi\)
\(770\) 9.58743 0.345507
\(771\) 0 0
\(772\) 98.2942 3.53768
\(773\) 14.6432 0.526678 0.263339 0.964703i \(-0.415176\pi\)
0.263339 + 0.964703i \(0.415176\pi\)
\(774\) 0 0
\(775\) 47.7021 1.71351
\(776\) 113.911 4.08918
\(777\) 0 0
\(778\) 80.3333 2.88009
\(779\) 6.98777 0.250363
\(780\) 0 0
\(781\) −11.1518 −0.399042
\(782\) 3.13445 0.112088
\(783\) 0 0
\(784\) 15.0012 0.535758
\(785\) −26.6403 −0.950833
\(786\) 0 0
\(787\) 16.1508 0.575713 0.287857 0.957674i \(-0.407057\pi\)
0.287857 + 0.957674i \(0.407057\pi\)
\(788\) −18.5220 −0.659821
\(789\) 0 0
\(790\) −118.189 −4.20496
\(791\) 0.617948 0.0219717
\(792\) 0 0
\(793\) 66.6271 2.36600
\(794\) 38.1981 1.35560
\(795\) 0 0
\(796\) −46.9878 −1.66544
\(797\) −17.4408 −0.617783 −0.308892 0.951097i \(-0.599958\pi\)
−0.308892 + 0.951097i \(0.599958\pi\)
\(798\) 0 0
\(799\) 0.296207 0.0104791
\(800\) 288.458 10.1985
\(801\) 0 0
\(802\) 35.5389 1.25492
\(803\) −3.28382 −0.115884
\(804\) 0 0
\(805\) −30.8510 −1.08735
\(806\) −60.4706 −2.12999
\(807\) 0 0
\(808\) 140.034 4.92636
\(809\) 16.1442 0.567600 0.283800 0.958883i \(-0.408405\pi\)
0.283800 + 0.958883i \(0.408405\pi\)
\(810\) 0 0
\(811\) −20.7568 −0.728870 −0.364435 0.931229i \(-0.618738\pi\)
−0.364435 + 0.931229i \(0.618738\pi\)
\(812\) 46.2463 1.62293
\(813\) 0 0
\(814\) 17.9499 0.629145
\(815\) −41.9956 −1.47104
\(816\) 0 0
\(817\) −22.9397 −0.802558
\(818\) 55.1465 1.92815
\(819\) 0 0
\(820\) −54.2805 −1.89556
\(821\) 34.1101 1.19045 0.595225 0.803559i \(-0.297063\pi\)
0.595225 + 0.803559i \(0.297063\pi\)
\(822\) 0 0
\(823\) 40.0748 1.39692 0.698460 0.715649i \(-0.253869\pi\)
0.698460 + 0.715649i \(0.253869\pi\)
\(824\) 189.922 6.61626
\(825\) 0 0
\(826\) 13.8611 0.482288
\(827\) −17.2128 −0.598547 −0.299274 0.954167i \(-0.596744\pi\)
−0.299274 + 0.954167i \(0.596744\pi\)
\(828\) 0 0
\(829\) 1.98879 0.0690734 0.0345367 0.999403i \(-0.489004\pi\)
0.0345367 + 0.999403i \(0.489004\pi\)
\(830\) −174.143 −6.04459
\(831\) 0 0
\(832\) −183.433 −6.35939
\(833\) 0.158117 0.00547843
\(834\) 0 0
\(835\) −14.5759 −0.504419
\(836\) −13.5209 −0.467630
\(837\) 0 0
\(838\) 27.9377 0.965093
\(839\) 40.5028 1.39831 0.699157 0.714969i \(-0.253559\pi\)
0.699157 + 0.714969i \(0.253559\pi\)
\(840\) 0 0
\(841\) 42.4198 1.46275
\(842\) 48.4432 1.66946
\(843\) 0 0
\(844\) −8.60541 −0.296210
\(845\) −101.651 −3.49689
\(846\) 0 0
\(847\) −10.3203 −0.354609
\(848\) 61.3013 2.10509
\(849\) 0 0
\(850\) 5.66115 0.194176
\(851\) −57.7604 −1.98000
\(852\) 0 0
\(853\) 15.5137 0.531179 0.265590 0.964086i \(-0.414433\pi\)
0.265590 + 0.964086i \(0.414433\pi\)
\(854\) −29.9845 −1.02605
\(855\) 0 0
\(856\) −33.5248 −1.14585
\(857\) 35.7100 1.21983 0.609914 0.792467i \(-0.291204\pi\)
0.609914 + 0.792467i \(0.291204\pi\)
\(858\) 0 0
\(859\) −5.81711 −0.198477 −0.0992386 0.995064i \(-0.531641\pi\)
−0.0992386 + 0.995064i \(0.531641\pi\)
\(860\) 178.194 6.07636
\(861\) 0 0
\(862\) −26.0300 −0.886587
\(863\) 32.7541 1.11496 0.557481 0.830190i \(-0.311768\pi\)
0.557481 + 0.830190i \(0.311768\pi\)
\(864\) 0 0
\(865\) −102.393 −3.48146
\(866\) −11.1459 −0.378753
\(867\) 0 0
\(868\) 19.9299 0.676465
\(869\) −8.37911 −0.284242
\(870\) 0 0
\(871\) 54.4788 1.84594
\(872\) −69.1173 −2.34061
\(873\) 0 0
\(874\) 59.4098 2.00957
\(875\) −34.4495 −1.16460
\(876\) 0 0
\(877\) −17.7749 −0.600216 −0.300108 0.953905i \(-0.597023\pi\)
−0.300108 + 0.953905i \(0.597023\pi\)
\(878\) 48.8732 1.64939
\(879\) 0 0
\(880\) 52.6141 1.77362
\(881\) 25.2583 0.850974 0.425487 0.904965i \(-0.360103\pi\)
0.425487 + 0.904965i \(0.360103\pi\)
\(882\) 0 0
\(883\) −11.7438 −0.395212 −0.197606 0.980282i \(-0.563317\pi\)
−0.197606 + 0.980282i \(0.563317\pi\)
\(884\) −5.25566 −0.176767
\(885\) 0 0
\(886\) −36.4001 −1.22288
\(887\) 14.7378 0.494848 0.247424 0.968907i \(-0.420416\pi\)
0.247424 + 0.968907i \(0.420416\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −26.8141 −0.898811
\(891\) 0 0
\(892\) 112.988 3.78311
\(893\) 5.61427 0.187874
\(894\) 0 0
\(895\) 6.92222 0.231384
\(896\) 38.5045 1.28634
\(897\) 0 0
\(898\) 26.0464 0.869180
\(899\) 30.7785 1.02652
\(900\) 0 0
\(901\) 0.646132 0.0215258
\(902\) −5.25474 −0.174964
\(903\) 0 0
\(904\) 5.86532 0.195078
\(905\) 91.0280 3.02587
\(906\) 0 0
\(907\) 30.1984 1.00272 0.501361 0.865238i \(-0.332833\pi\)
0.501361 + 0.865238i \(0.332833\pi\)
\(908\) −88.2229 −2.92778
\(909\) 0 0
\(910\) 70.6351 2.34153
\(911\) −25.3123 −0.838636 −0.419318 0.907840i \(-0.637731\pi\)
−0.419318 + 0.907840i \(0.637731\pi\)
\(912\) 0 0
\(913\) −12.3461 −0.408595
\(914\) −45.5589 −1.50695
\(915\) 0 0
\(916\) 2.55098 0.0842869
\(917\) −5.77893 −0.190837
\(918\) 0 0
\(919\) −11.7299 −0.386933 −0.193467 0.981107i \(-0.561973\pi\)
−0.193467 + 0.981107i \(0.561973\pi\)
\(920\) −292.826 −9.65418
\(921\) 0 0
\(922\) −18.5509 −0.610940
\(923\) −82.1604 −2.70434
\(924\) 0 0
\(925\) −104.321 −3.43007
\(926\) −92.6306 −3.04403
\(927\) 0 0
\(928\) 186.119 6.10967
\(929\) −29.3813 −0.963971 −0.481985 0.876179i \(-0.660084\pi\)
−0.481985 + 0.876179i \(0.660084\pi\)
\(930\) 0 0
\(931\) 2.99692 0.0982202
\(932\) −86.3903 −2.82981
\(933\) 0 0
\(934\) −36.2232 −1.18526
\(935\) 0.554568 0.0181363
\(936\) 0 0
\(937\) −44.3816 −1.44988 −0.724941 0.688811i \(-0.758133\pi\)
−0.724941 + 0.688811i \(0.758133\pi\)
\(938\) −24.5173 −0.800519
\(939\) 0 0
\(940\) −43.6112 −1.42244
\(941\) 55.8015 1.81908 0.909538 0.415620i \(-0.136435\pi\)
0.909538 + 0.415620i \(0.136435\pi\)
\(942\) 0 0
\(943\) 16.9090 0.550634
\(944\) 76.0670 2.47577
\(945\) 0 0
\(946\) 17.2504 0.560860
\(947\) −33.7324 −1.09615 −0.548077 0.836428i \(-0.684640\pi\)
−0.548077 + 0.836428i \(0.684640\pi\)
\(948\) 0 0
\(949\) −24.1935 −0.785353
\(950\) 107.301 3.48129
\(951\) 0 0
\(952\) 1.50079 0.0486408
\(953\) 47.4188 1.53605 0.768023 0.640423i \(-0.221241\pi\)
0.768023 + 0.640423i \(0.221241\pi\)
\(954\) 0 0
\(955\) 13.4681 0.435817
\(956\) −116.425 −3.76547
\(957\) 0 0
\(958\) 85.9012 2.77534
\(959\) −10.6326 −0.343344
\(960\) 0 0
\(961\) −17.7360 −0.572128
\(962\) 132.246 4.26377
\(963\) 0 0
\(964\) 5.35822 0.172577
\(965\) −76.4141 −2.45986
\(966\) 0 0
\(967\) −1.40282 −0.0451117 −0.0225558 0.999746i \(-0.507180\pi\)
−0.0225558 + 0.999746i \(0.507180\pi\)
\(968\) −97.9562 −3.14843
\(969\) 0 0
\(970\) −139.562 −4.48106
\(971\) 5.29054 0.169781 0.0848907 0.996390i \(-0.472946\pi\)
0.0848907 + 0.996390i \(0.472946\pi\)
\(972\) 0 0
\(973\) 11.1927 0.358823
\(974\) −18.2164 −0.583692
\(975\) 0 0
\(976\) −164.550 −5.26711
\(977\) −41.5812 −1.33030 −0.665149 0.746710i \(-0.731632\pi\)
−0.665149 + 0.746710i \(0.731632\pi\)
\(978\) 0 0
\(979\) −1.90102 −0.0607567
\(980\) −23.2799 −0.743649
\(981\) 0 0
\(982\) −7.34240 −0.234305
\(983\) −42.2822 −1.34859 −0.674296 0.738461i \(-0.735553\pi\)
−0.674296 + 0.738461i \(0.735553\pi\)
\(984\) 0 0
\(985\) 14.3991 0.458793
\(986\) 3.65270 0.116326
\(987\) 0 0
\(988\) −99.6149 −3.16917
\(989\) −55.5095 −1.76510
\(990\) 0 0
\(991\) 38.2496 1.21504 0.607519 0.794305i \(-0.292165\pi\)
0.607519 + 0.794305i \(0.292165\pi\)
\(992\) 80.2084 2.54662
\(993\) 0 0
\(994\) 36.9750 1.17278
\(995\) 36.5284 1.15803
\(996\) 0 0
\(997\) 11.6674 0.369512 0.184756 0.982784i \(-0.440851\pi\)
0.184756 + 0.982784i \(0.440851\pi\)
\(998\) 25.0872 0.794121
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))