Properties

Label 8001.2.a.o.1.8
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.305711\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.305711 q^{2} -1.90654 q^{4} +0.276458 q^{5} +1.00000 q^{7} -1.19427 q^{8} +O(q^{10})\) \(q+0.305711 q^{2} -1.90654 q^{4} +0.276458 q^{5} +1.00000 q^{7} -1.19427 q^{8} +0.0845162 q^{10} +5.49757 q^{11} +5.85411 q^{13} +0.305711 q^{14} +3.44798 q^{16} -1.15122 q^{17} -6.10623 q^{19} -0.527078 q^{20} +1.68067 q^{22} -4.90674 q^{23} -4.92357 q^{25} +1.78966 q^{26} -1.90654 q^{28} -5.37546 q^{29} -9.23065 q^{31} +3.44263 q^{32} -0.351941 q^{34} +0.276458 q^{35} +3.98305 q^{37} -1.86674 q^{38} -0.330166 q^{40} -1.75449 q^{41} -10.6978 q^{43} -10.4813 q^{44} -1.50004 q^{46} +2.53420 q^{47} +1.00000 q^{49} -1.50519 q^{50} -11.1611 q^{52} +6.75216 q^{53} +1.51985 q^{55} -1.19427 q^{56} -1.64334 q^{58} -10.1143 q^{59} +6.36077 q^{61} -2.82191 q^{62} -5.84351 q^{64} +1.61841 q^{65} +3.74324 q^{67} +2.19485 q^{68} +0.0845162 q^{70} -10.2468 q^{71} +0.769235 q^{73} +1.21766 q^{74} +11.6418 q^{76} +5.49757 q^{77} -0.396745 q^{79} +0.953221 q^{80} -0.536368 q^{82} +2.27133 q^{83} -0.318264 q^{85} -3.27044 q^{86} -6.56559 q^{88} +6.61497 q^{89} +5.85411 q^{91} +9.35489 q^{92} +0.774732 q^{94} -1.68811 q^{95} +6.50324 q^{97} +0.305711 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13q - 4q^{2} + 10q^{4} - 12q^{5} + 13q^{7} - 9q^{8} + O(q^{10}) \) \( 13q - 4q^{2} + 10q^{4} - 12q^{5} + 13q^{7} - 9q^{8} + 6q^{10} - 3q^{11} + 21q^{13} - 4q^{14} + 8q^{16} - 17q^{17} + 5q^{19} - 29q^{20} + q^{22} - 4q^{23} + q^{25} - 22q^{26} + 10q^{28} - 21q^{29} - 7q^{31} - 12q^{32} + 2q^{34} - 12q^{35} + 7q^{37} + 9q^{38} + 29q^{40} - 21q^{41} - 9q^{43} + 2q^{44} - 28q^{46} - 23q^{47} + 13q^{49} - 15q^{50} + 15q^{52} - 31q^{53} - 8q^{55} - 9q^{56} - 25q^{58} - 28q^{59} + 29q^{61} + 3q^{62} + 9q^{64} - 30q^{65} - 18q^{67} - 34q^{68} + 6q^{70} - 10q^{71} + 24q^{73} + 19q^{74} - 3q^{77} - 28q^{79} - 26q^{80} + 18q^{82} - 26q^{83} + 20q^{85} + 2q^{86} - 17q^{88} - 44q^{89} + 21q^{91} - 6q^{92} - 9q^{94} + 2q^{95} + 17q^{97} - 4q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.305711 0.216170 0.108085 0.994142i \(-0.465528\pi\)
0.108085 + 0.994142i \(0.465528\pi\)
\(3\) 0 0
\(4\) −1.90654 −0.953270
\(5\) 0.276458 0.123636 0.0618178 0.998087i \(-0.480310\pi\)
0.0618178 + 0.998087i \(0.480310\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.19427 −0.422239
\(9\) 0 0
\(10\) 0.0845162 0.0267264
\(11\) 5.49757 1.65758 0.828790 0.559560i \(-0.189030\pi\)
0.828790 + 0.559560i \(0.189030\pi\)
\(12\) 0 0
\(13\) 5.85411 1.62364 0.811819 0.583910i \(-0.198478\pi\)
0.811819 + 0.583910i \(0.198478\pi\)
\(14\) 0.305711 0.0817047
\(15\) 0 0
\(16\) 3.44798 0.861995
\(17\) −1.15122 −0.279213 −0.139606 0.990207i \(-0.544584\pi\)
−0.139606 + 0.990207i \(0.544584\pi\)
\(18\) 0 0
\(19\) −6.10623 −1.40087 −0.700433 0.713718i \(-0.747010\pi\)
−0.700433 + 0.713718i \(0.747010\pi\)
\(20\) −0.527078 −0.117858
\(21\) 0 0
\(22\) 1.68067 0.358319
\(23\) −4.90674 −1.02313 −0.511563 0.859246i \(-0.670933\pi\)
−0.511563 + 0.859246i \(0.670933\pi\)
\(24\) 0 0
\(25\) −4.92357 −0.984714
\(26\) 1.78966 0.350982
\(27\) 0 0
\(28\) −1.90654 −0.360302
\(29\) −5.37546 −0.998198 −0.499099 0.866545i \(-0.666336\pi\)
−0.499099 + 0.866545i \(0.666336\pi\)
\(30\) 0 0
\(31\) −9.23065 −1.65787 −0.828937 0.559342i \(-0.811054\pi\)
−0.828937 + 0.559342i \(0.811054\pi\)
\(32\) 3.44263 0.608577
\(33\) 0 0
\(34\) −0.351941 −0.0603574
\(35\) 0.276458 0.0467299
\(36\) 0 0
\(37\) 3.98305 0.654810 0.327405 0.944884i \(-0.393826\pi\)
0.327405 + 0.944884i \(0.393826\pi\)
\(38\) −1.86674 −0.302825
\(39\) 0 0
\(40\) −0.330166 −0.0522038
\(41\) −1.75449 −0.274006 −0.137003 0.990571i \(-0.543747\pi\)
−0.137003 + 0.990571i \(0.543747\pi\)
\(42\) 0 0
\(43\) −10.6978 −1.63140 −0.815701 0.578474i \(-0.803649\pi\)
−0.815701 + 0.578474i \(0.803649\pi\)
\(44\) −10.4813 −1.58012
\(45\) 0 0
\(46\) −1.50004 −0.221169
\(47\) 2.53420 0.369651 0.184825 0.982771i \(-0.440828\pi\)
0.184825 + 0.982771i \(0.440828\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.50519 −0.212866
\(51\) 0 0
\(52\) −11.1611 −1.54777
\(53\) 6.75216 0.927481 0.463740 0.885971i \(-0.346507\pi\)
0.463740 + 0.885971i \(0.346507\pi\)
\(54\) 0 0
\(55\) 1.51985 0.204936
\(56\) −1.19427 −0.159591
\(57\) 0 0
\(58\) −1.64334 −0.215781
\(59\) −10.1143 −1.31678 −0.658388 0.752679i \(-0.728761\pi\)
−0.658388 + 0.752679i \(0.728761\pi\)
\(60\) 0 0
\(61\) 6.36077 0.814413 0.407206 0.913336i \(-0.366503\pi\)
0.407206 + 0.913336i \(0.366503\pi\)
\(62\) −2.82191 −0.358383
\(63\) 0 0
\(64\) −5.84351 −0.730439
\(65\) 1.61841 0.200740
\(66\) 0 0
\(67\) 3.74324 0.457310 0.228655 0.973508i \(-0.426567\pi\)
0.228655 + 0.973508i \(0.426567\pi\)
\(68\) 2.19485 0.266165
\(69\) 0 0
\(70\) 0.0845162 0.0101016
\(71\) −10.2468 −1.21607 −0.608036 0.793910i \(-0.708042\pi\)
−0.608036 + 0.793910i \(0.708042\pi\)
\(72\) 0 0
\(73\) 0.769235 0.0900321 0.0450161 0.998986i \(-0.485666\pi\)
0.0450161 + 0.998986i \(0.485666\pi\)
\(74\) 1.21766 0.141550
\(75\) 0 0
\(76\) 11.6418 1.33540
\(77\) 5.49757 0.626506
\(78\) 0 0
\(79\) −0.396745 −0.0446372 −0.0223186 0.999751i \(-0.507105\pi\)
−0.0223186 + 0.999751i \(0.507105\pi\)
\(80\) 0.953221 0.106573
\(81\) 0 0
\(82\) −0.536368 −0.0592319
\(83\) 2.27133 0.249311 0.124656 0.992200i \(-0.460217\pi\)
0.124656 + 0.992200i \(0.460217\pi\)
\(84\) 0 0
\(85\) −0.318264 −0.0345206
\(86\) −3.27044 −0.352661
\(87\) 0 0
\(88\) −6.56559 −0.699895
\(89\) 6.61497 0.701185 0.350593 0.936528i \(-0.385980\pi\)
0.350593 + 0.936528i \(0.385980\pi\)
\(90\) 0 0
\(91\) 5.85411 0.613677
\(92\) 9.35489 0.975315
\(93\) 0 0
\(94\) 0.774732 0.0799075
\(95\) −1.68811 −0.173197
\(96\) 0 0
\(97\) 6.50324 0.660304 0.330152 0.943928i \(-0.392900\pi\)
0.330152 + 0.943928i \(0.392900\pi\)
\(98\) 0.305711 0.0308815
\(99\) 0 0
\(100\) 9.38699 0.938699
\(101\) −6.45399 −0.642196 −0.321098 0.947046i \(-0.604052\pi\)
−0.321098 + 0.947046i \(0.604052\pi\)
\(102\) 0 0
\(103\) −7.17745 −0.707215 −0.353608 0.935394i \(-0.615045\pi\)
−0.353608 + 0.935394i \(0.615045\pi\)
\(104\) −6.99140 −0.685563
\(105\) 0 0
\(106\) 2.06421 0.200494
\(107\) −2.58615 −0.250012 −0.125006 0.992156i \(-0.539895\pi\)
−0.125006 + 0.992156i \(0.539895\pi\)
\(108\) 0 0
\(109\) 16.7781 1.60705 0.803524 0.595272i \(-0.202956\pi\)
0.803524 + 0.595272i \(0.202956\pi\)
\(110\) 0.464633 0.0443011
\(111\) 0 0
\(112\) 3.44798 0.325803
\(113\) −10.3192 −0.970744 −0.485372 0.874308i \(-0.661316\pi\)
−0.485372 + 0.874308i \(0.661316\pi\)
\(114\) 0 0
\(115\) −1.35651 −0.126495
\(116\) 10.2485 0.951553
\(117\) 0 0
\(118\) −3.09207 −0.284648
\(119\) −1.15122 −0.105532
\(120\) 0 0
\(121\) 19.2233 1.74757
\(122\) 1.94456 0.176052
\(123\) 0 0
\(124\) 17.5986 1.58040
\(125\) −2.74345 −0.245381
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −8.67168 −0.766476
\(129\) 0 0
\(130\) 0.494767 0.0433939
\(131\) −11.9275 −1.04211 −0.521056 0.853522i \(-0.674462\pi\)
−0.521056 + 0.853522i \(0.674462\pi\)
\(132\) 0 0
\(133\) −6.10623 −0.529477
\(134\) 1.14435 0.0988568
\(135\) 0 0
\(136\) 1.37487 0.117894
\(137\) −8.19429 −0.700086 −0.350043 0.936734i \(-0.613833\pi\)
−0.350043 + 0.936734i \(0.613833\pi\)
\(138\) 0 0
\(139\) −13.5478 −1.14911 −0.574553 0.818467i \(-0.694824\pi\)
−0.574553 + 0.818467i \(0.694824\pi\)
\(140\) −0.527078 −0.0445462
\(141\) 0 0
\(142\) −3.13256 −0.262878
\(143\) 32.1834 2.69131
\(144\) 0 0
\(145\) −1.48609 −0.123413
\(146\) 0.235164 0.0194623
\(147\) 0 0
\(148\) −7.59385 −0.624211
\(149\) −4.98742 −0.408585 −0.204293 0.978910i \(-0.565489\pi\)
−0.204293 + 0.978910i \(0.565489\pi\)
\(150\) 0 0
\(151\) 4.17561 0.339806 0.169903 0.985461i \(-0.445655\pi\)
0.169903 + 0.985461i \(0.445655\pi\)
\(152\) 7.29250 0.591500
\(153\) 0 0
\(154\) 1.68067 0.135432
\(155\) −2.55189 −0.204972
\(156\) 0 0
\(157\) 5.35019 0.426991 0.213496 0.976944i \(-0.431515\pi\)
0.213496 + 0.976944i \(0.431515\pi\)
\(158\) −0.121289 −0.00964925
\(159\) 0 0
\(160\) 0.951742 0.0752418
\(161\) −4.90674 −0.386705
\(162\) 0 0
\(163\) −7.82336 −0.612773 −0.306386 0.951907i \(-0.599120\pi\)
−0.306386 + 0.951907i \(0.599120\pi\)
\(164\) 3.34501 0.261202
\(165\) 0 0
\(166\) 0.694371 0.0538937
\(167\) −8.35675 −0.646665 −0.323332 0.946285i \(-0.604803\pi\)
−0.323332 + 0.946285i \(0.604803\pi\)
\(168\) 0 0
\(169\) 21.2706 1.63620
\(170\) −0.0972969 −0.00746233
\(171\) 0 0
\(172\) 20.3958 1.55517
\(173\) −7.00766 −0.532783 −0.266391 0.963865i \(-0.585831\pi\)
−0.266391 + 0.963865i \(0.585831\pi\)
\(174\) 0 0
\(175\) −4.92357 −0.372187
\(176\) 18.9555 1.42883
\(177\) 0 0
\(178\) 2.02227 0.151575
\(179\) −25.1904 −1.88282 −0.941410 0.337263i \(-0.890499\pi\)
−0.941410 + 0.337263i \(0.890499\pi\)
\(180\) 0 0
\(181\) 16.9017 1.25629 0.628147 0.778095i \(-0.283814\pi\)
0.628147 + 0.778095i \(0.283814\pi\)
\(182\) 1.78966 0.132659
\(183\) 0 0
\(184\) 5.85998 0.432003
\(185\) 1.10115 0.0809578
\(186\) 0 0
\(187\) −6.32893 −0.462817
\(188\) −4.83155 −0.352377
\(189\) 0 0
\(190\) −0.516075 −0.0374400
\(191\) 21.8166 1.57859 0.789296 0.614013i \(-0.210446\pi\)
0.789296 + 0.614013i \(0.210446\pi\)
\(192\) 0 0
\(193\) −17.6982 −1.27395 −0.636973 0.770886i \(-0.719814\pi\)
−0.636973 + 0.770886i \(0.719814\pi\)
\(194\) 1.98811 0.142738
\(195\) 0 0
\(196\) −1.90654 −0.136181
\(197\) −9.11313 −0.649284 −0.324642 0.945837i \(-0.605244\pi\)
−0.324642 + 0.945837i \(0.605244\pi\)
\(198\) 0 0
\(199\) −0.0226194 −0.00160344 −0.000801722 1.00000i \(-0.500255\pi\)
−0.000801722 1.00000i \(0.500255\pi\)
\(200\) 5.88008 0.415785
\(201\) 0 0
\(202\) −1.97306 −0.138824
\(203\) −5.37546 −0.377283
\(204\) 0 0
\(205\) −0.485043 −0.0338769
\(206\) −2.19423 −0.152879
\(207\) 0 0
\(208\) 20.1848 1.39957
\(209\) −33.5694 −2.32205
\(210\) 0 0
\(211\) 13.0645 0.899399 0.449700 0.893180i \(-0.351531\pi\)
0.449700 + 0.893180i \(0.351531\pi\)
\(212\) −12.8733 −0.884140
\(213\) 0 0
\(214\) −0.790614 −0.0540452
\(215\) −2.95750 −0.201700
\(216\) 0 0
\(217\) −9.23065 −0.626618
\(218\) 5.12924 0.347396
\(219\) 0 0
\(220\) −2.89765 −0.195359
\(221\) −6.73938 −0.453340
\(222\) 0 0
\(223\) 14.4547 0.967958 0.483979 0.875080i \(-0.339191\pi\)
0.483979 + 0.875080i \(0.339191\pi\)
\(224\) 3.44263 0.230020
\(225\) 0 0
\(226\) −3.15468 −0.209846
\(227\) −5.34653 −0.354862 −0.177431 0.984133i \(-0.556779\pi\)
−0.177431 + 0.984133i \(0.556779\pi\)
\(228\) 0 0
\(229\) 12.2399 0.808839 0.404419 0.914574i \(-0.367474\pi\)
0.404419 + 0.914574i \(0.367474\pi\)
\(230\) −0.414698 −0.0273444
\(231\) 0 0
\(232\) 6.41976 0.421478
\(233\) −20.6821 −1.35493 −0.677465 0.735555i \(-0.736921\pi\)
−0.677465 + 0.735555i \(0.736921\pi\)
\(234\) 0 0
\(235\) 0.700599 0.0457020
\(236\) 19.2834 1.25524
\(237\) 0 0
\(238\) −0.351941 −0.0228130
\(239\) −19.8538 −1.28424 −0.642119 0.766605i \(-0.721944\pi\)
−0.642119 + 0.766605i \(0.721944\pi\)
\(240\) 0 0
\(241\) 3.39756 0.218856 0.109428 0.993995i \(-0.465098\pi\)
0.109428 + 0.993995i \(0.465098\pi\)
\(242\) 5.87676 0.377773
\(243\) 0 0
\(244\) −12.1271 −0.776356
\(245\) 0.276458 0.0176622
\(246\) 0 0
\(247\) −35.7465 −2.27450
\(248\) 11.0239 0.700019
\(249\) 0 0
\(250\) −0.838702 −0.0530442
\(251\) −16.9646 −1.07080 −0.535398 0.844600i \(-0.679839\pi\)
−0.535398 + 0.844600i \(0.679839\pi\)
\(252\) 0 0
\(253\) −26.9751 −1.69591
\(254\) −0.305711 −0.0191820
\(255\) 0 0
\(256\) 9.03599 0.564749
\(257\) 9.88570 0.616653 0.308327 0.951281i \(-0.400231\pi\)
0.308327 + 0.951281i \(0.400231\pi\)
\(258\) 0 0
\(259\) 3.98305 0.247495
\(260\) −3.08557 −0.191359
\(261\) 0 0
\(262\) −3.64637 −0.225274
\(263\) −15.4492 −0.952640 −0.476320 0.879272i \(-0.658030\pi\)
−0.476320 + 0.879272i \(0.658030\pi\)
\(264\) 0 0
\(265\) 1.86669 0.114670
\(266\) −1.86674 −0.114457
\(267\) 0 0
\(268\) −7.13664 −0.435940
\(269\) 20.0563 1.22285 0.611427 0.791301i \(-0.290596\pi\)
0.611427 + 0.791301i \(0.290596\pi\)
\(270\) 0 0
\(271\) 1.52170 0.0924367 0.0462183 0.998931i \(-0.485283\pi\)
0.0462183 + 0.998931i \(0.485283\pi\)
\(272\) −3.96939 −0.240680
\(273\) 0 0
\(274\) −2.50509 −0.151338
\(275\) −27.0677 −1.63224
\(276\) 0 0
\(277\) −2.88589 −0.173396 −0.0866981 0.996235i \(-0.527632\pi\)
−0.0866981 + 0.996235i \(0.527632\pi\)
\(278\) −4.14170 −0.248403
\(279\) 0 0
\(280\) −0.330166 −0.0197312
\(281\) 1.40750 0.0839643 0.0419822 0.999118i \(-0.486633\pi\)
0.0419822 + 0.999118i \(0.486633\pi\)
\(282\) 0 0
\(283\) 18.7659 1.11552 0.557759 0.830003i \(-0.311661\pi\)
0.557759 + 0.830003i \(0.311661\pi\)
\(284\) 19.5359 1.15924
\(285\) 0 0
\(286\) 9.83881 0.581781
\(287\) −1.75449 −0.103564
\(288\) 0 0
\(289\) −15.6747 −0.922040
\(290\) −0.454313 −0.0266782
\(291\) 0 0
\(292\) −1.46658 −0.0858250
\(293\) −12.6713 −0.740266 −0.370133 0.928979i \(-0.620688\pi\)
−0.370133 + 0.928979i \(0.620688\pi\)
\(294\) 0 0
\(295\) −2.79619 −0.162800
\(296\) −4.75685 −0.276486
\(297\) 0 0
\(298\) −1.52471 −0.0883240
\(299\) −28.7246 −1.66118
\(300\) 0 0
\(301\) −10.6978 −0.616612
\(302\) 1.27653 0.0734560
\(303\) 0 0
\(304\) −21.0542 −1.20754
\(305\) 1.75848 0.100690
\(306\) 0 0
\(307\) −8.37854 −0.478189 −0.239094 0.970996i \(-0.576851\pi\)
−0.239094 + 0.970996i \(0.576851\pi\)
\(308\) −10.4813 −0.597230
\(309\) 0 0
\(310\) −0.780139 −0.0443089
\(311\) −26.6946 −1.51371 −0.756856 0.653581i \(-0.773266\pi\)
−0.756856 + 0.653581i \(0.773266\pi\)
\(312\) 0 0
\(313\) −4.74932 −0.268447 −0.134224 0.990951i \(-0.542854\pi\)
−0.134224 + 0.990951i \(0.542854\pi\)
\(314\) 1.63561 0.0923028
\(315\) 0 0
\(316\) 0.756410 0.0425514
\(317\) 12.7833 0.717979 0.358990 0.933342i \(-0.383121\pi\)
0.358990 + 0.933342i \(0.383121\pi\)
\(318\) 0 0
\(319\) −29.5520 −1.65459
\(320\) −1.61548 −0.0903083
\(321\) 0 0
\(322\) −1.50004 −0.0835941
\(323\) 7.02963 0.391139
\(324\) 0 0
\(325\) −28.8231 −1.59882
\(326\) −2.39169 −0.132463
\(327\) 0 0
\(328\) 2.09534 0.115696
\(329\) 2.53420 0.139715
\(330\) 0 0
\(331\) 30.0111 1.64956 0.824780 0.565454i \(-0.191299\pi\)
0.824780 + 0.565454i \(0.191299\pi\)
\(332\) −4.33039 −0.237661
\(333\) 0 0
\(334\) −2.55475 −0.139790
\(335\) 1.03485 0.0565398
\(336\) 0 0
\(337\) −33.6687 −1.83405 −0.917026 0.398827i \(-0.869418\pi\)
−0.917026 + 0.398827i \(0.869418\pi\)
\(338\) 6.50265 0.353698
\(339\) 0 0
\(340\) 0.606784 0.0329075
\(341\) −50.7462 −2.74806
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 12.7761 0.688842
\(345\) 0 0
\(346\) −2.14232 −0.115172
\(347\) −10.1973 −0.547418 −0.273709 0.961813i \(-0.588251\pi\)
−0.273709 + 0.961813i \(0.588251\pi\)
\(348\) 0 0
\(349\) −21.7938 −1.16660 −0.583299 0.812258i \(-0.698238\pi\)
−0.583299 + 0.812258i \(0.698238\pi\)
\(350\) −1.50519 −0.0804558
\(351\) 0 0
\(352\) 18.9261 1.00876
\(353\) −10.8660 −0.578340 −0.289170 0.957278i \(-0.593379\pi\)
−0.289170 + 0.957278i \(0.593379\pi\)
\(354\) 0 0
\(355\) −2.83281 −0.150350
\(356\) −12.6117 −0.668419
\(357\) 0 0
\(358\) −7.70099 −0.407010
\(359\) 32.9974 1.74153 0.870767 0.491696i \(-0.163623\pi\)
0.870767 + 0.491696i \(0.163623\pi\)
\(360\) 0 0
\(361\) 18.2861 0.962424
\(362\) 5.16703 0.271573
\(363\) 0 0
\(364\) −11.1611 −0.585000
\(365\) 0.212661 0.0111312
\(366\) 0 0
\(367\) −11.0294 −0.575732 −0.287866 0.957671i \(-0.592946\pi\)
−0.287866 + 0.957671i \(0.592946\pi\)
\(368\) −16.9183 −0.881929
\(369\) 0 0
\(370\) 0.336632 0.0175007
\(371\) 6.75216 0.350555
\(372\) 0 0
\(373\) −33.0143 −1.70942 −0.854708 0.519109i \(-0.826264\pi\)
−0.854708 + 0.519109i \(0.826264\pi\)
\(374\) −1.93482 −0.100047
\(375\) 0 0
\(376\) −3.02652 −0.156081
\(377\) −31.4685 −1.62071
\(378\) 0 0
\(379\) −5.90961 −0.303556 −0.151778 0.988415i \(-0.548500\pi\)
−0.151778 + 0.988415i \(0.548500\pi\)
\(380\) 3.21846 0.165104
\(381\) 0 0
\(382\) 6.66956 0.341245
\(383\) −24.2106 −1.23710 −0.618551 0.785745i \(-0.712280\pi\)
−0.618551 + 0.785745i \(0.712280\pi\)
\(384\) 0 0
\(385\) 1.51985 0.0774585
\(386\) −5.41054 −0.275389
\(387\) 0 0
\(388\) −12.3987 −0.629448
\(389\) 32.5969 1.65273 0.826363 0.563137i \(-0.190406\pi\)
0.826363 + 0.563137i \(0.190406\pi\)
\(390\) 0 0
\(391\) 5.64875 0.285669
\(392\) −1.19427 −0.0603199
\(393\) 0 0
\(394\) −2.78598 −0.140356
\(395\) −0.109683 −0.00551876
\(396\) 0 0
\(397\) 12.9830 0.651597 0.325799 0.945439i \(-0.394367\pi\)
0.325799 + 0.945439i \(0.394367\pi\)
\(398\) −0.00691498 −0.000346617 0
\(399\) 0 0
\(400\) −16.9764 −0.848819
\(401\) 36.1973 1.80760 0.903802 0.427950i \(-0.140764\pi\)
0.903802 + 0.427950i \(0.140764\pi\)
\(402\) 0 0
\(403\) −54.0372 −2.69179
\(404\) 12.3048 0.612186
\(405\) 0 0
\(406\) −1.64334 −0.0815574
\(407\) 21.8971 1.08540
\(408\) 0 0
\(409\) −9.96969 −0.492969 −0.246485 0.969147i \(-0.579276\pi\)
−0.246485 + 0.969147i \(0.579276\pi\)
\(410\) −0.148283 −0.00732318
\(411\) 0 0
\(412\) 13.6841 0.674167
\(413\) −10.1143 −0.497694
\(414\) 0 0
\(415\) 0.627928 0.0308237
\(416\) 20.1535 0.988108
\(417\) 0 0
\(418\) −10.2625 −0.501957
\(419\) −5.11772 −0.250017 −0.125008 0.992156i \(-0.539896\pi\)
−0.125008 + 0.992156i \(0.539896\pi\)
\(420\) 0 0
\(421\) −32.5904 −1.58836 −0.794179 0.607684i \(-0.792099\pi\)
−0.794179 + 0.607684i \(0.792099\pi\)
\(422\) 3.99397 0.194423
\(423\) 0 0
\(424\) −8.06392 −0.391619
\(425\) 5.66813 0.274945
\(426\) 0 0
\(427\) 6.36077 0.307819
\(428\) 4.93060 0.238329
\(429\) 0 0
\(430\) −0.904139 −0.0436014
\(431\) 5.40245 0.260227 0.130113 0.991499i \(-0.458466\pi\)
0.130113 + 0.991499i \(0.458466\pi\)
\(432\) 0 0
\(433\) −15.1606 −0.728572 −0.364286 0.931287i \(-0.618687\pi\)
−0.364286 + 0.931287i \(0.618687\pi\)
\(434\) −2.82191 −0.135456
\(435\) 0 0
\(436\) −31.9881 −1.53195
\(437\) 29.9617 1.43326
\(438\) 0 0
\(439\) 25.7263 1.22785 0.613925 0.789364i \(-0.289590\pi\)
0.613925 + 0.789364i \(0.289590\pi\)
\(440\) −1.81511 −0.0865319
\(441\) 0 0
\(442\) −2.06030 −0.0979986
\(443\) −28.5560 −1.35674 −0.678368 0.734722i \(-0.737312\pi\)
−0.678368 + 0.734722i \(0.737312\pi\)
\(444\) 0 0
\(445\) 1.82876 0.0866915
\(446\) 4.41896 0.209244
\(447\) 0 0
\(448\) −5.84351 −0.276080
\(449\) 33.0302 1.55879 0.779396 0.626532i \(-0.215526\pi\)
0.779396 + 0.626532i \(0.215526\pi\)
\(450\) 0 0
\(451\) −9.64545 −0.454186
\(452\) 19.6739 0.925382
\(453\) 0 0
\(454\) −1.63449 −0.0767106
\(455\) 1.61841 0.0758724
\(456\) 0 0
\(457\) 26.3102 1.23074 0.615370 0.788239i \(-0.289007\pi\)
0.615370 + 0.788239i \(0.289007\pi\)
\(458\) 3.74189 0.174847
\(459\) 0 0
\(460\) 2.58623 0.120584
\(461\) −16.9634 −0.790064 −0.395032 0.918667i \(-0.629267\pi\)
−0.395032 + 0.918667i \(0.629267\pi\)
\(462\) 0 0
\(463\) 23.7165 1.10220 0.551099 0.834440i \(-0.314209\pi\)
0.551099 + 0.834440i \(0.314209\pi\)
\(464\) −18.5345 −0.860441
\(465\) 0 0
\(466\) −6.32275 −0.292896
\(467\) 34.2579 1.58526 0.792632 0.609700i \(-0.208710\pi\)
0.792632 + 0.609700i \(0.208710\pi\)
\(468\) 0 0
\(469\) 3.74324 0.172847
\(470\) 0.214181 0.00987942
\(471\) 0 0
\(472\) 12.0793 0.555994
\(473\) −58.8120 −2.70418
\(474\) 0 0
\(475\) 30.0645 1.37945
\(476\) 2.19485 0.100601
\(477\) 0 0
\(478\) −6.06953 −0.277614
\(479\) −23.5026 −1.07386 −0.536932 0.843626i \(-0.680417\pi\)
−0.536932 + 0.843626i \(0.680417\pi\)
\(480\) 0 0
\(481\) 23.3172 1.06317
\(482\) 1.03867 0.0473102
\(483\) 0 0
\(484\) −36.6499 −1.66591
\(485\) 1.79787 0.0816371
\(486\) 0 0
\(487\) −0.487332 −0.0220831 −0.0110416 0.999939i \(-0.503515\pi\)
−0.0110416 + 0.999939i \(0.503515\pi\)
\(488\) −7.59649 −0.343877
\(489\) 0 0
\(490\) 0.0845162 0.00381805
\(491\) −15.3844 −0.694290 −0.347145 0.937811i \(-0.612849\pi\)
−0.347145 + 0.937811i \(0.612849\pi\)
\(492\) 0 0
\(493\) 6.18835 0.278709
\(494\) −10.9281 −0.491679
\(495\) 0 0
\(496\) −31.8271 −1.42908
\(497\) −10.2468 −0.459632
\(498\) 0 0
\(499\) −3.97860 −0.178107 −0.0890533 0.996027i \(-0.528384\pi\)
−0.0890533 + 0.996027i \(0.528384\pi\)
\(500\) 5.23050 0.233915
\(501\) 0 0
\(502\) −5.18627 −0.231474
\(503\) 39.1786 1.74689 0.873445 0.486924i \(-0.161881\pi\)
0.873445 + 0.486924i \(0.161881\pi\)
\(504\) 0 0
\(505\) −1.78426 −0.0793983
\(506\) −8.24659 −0.366606
\(507\) 0 0
\(508\) 1.90654 0.0845891
\(509\) −28.7484 −1.27425 −0.637126 0.770760i \(-0.719877\pi\)
−0.637126 + 0.770760i \(0.719877\pi\)
\(510\) 0 0
\(511\) 0.769235 0.0340290
\(512\) 20.1058 0.888558
\(513\) 0 0
\(514\) 3.02217 0.133302
\(515\) −1.98426 −0.0874370
\(516\) 0 0
\(517\) 13.9319 0.612726
\(518\) 1.21766 0.0535010
\(519\) 0 0
\(520\) −1.93283 −0.0847600
\(521\) −28.5996 −1.25297 −0.626487 0.779432i \(-0.715508\pi\)
−0.626487 + 0.779432i \(0.715508\pi\)
\(522\) 0 0
\(523\) 41.7036 1.82357 0.911785 0.410667i \(-0.134704\pi\)
0.911785 + 0.410667i \(0.134704\pi\)
\(524\) 22.7403 0.993415
\(525\) 0 0
\(526\) −4.72300 −0.205933
\(527\) 10.6265 0.462899
\(528\) 0 0
\(529\) 1.07606 0.0467851
\(530\) 0.570667 0.0247882
\(531\) 0 0
\(532\) 11.6418 0.504735
\(533\) −10.2710 −0.444886
\(534\) 0 0
\(535\) −0.714961 −0.0309104
\(536\) −4.47045 −0.193094
\(537\) 0 0
\(538\) 6.13142 0.264344
\(539\) 5.49757 0.236797
\(540\) 0 0
\(541\) 16.8941 0.726333 0.363166 0.931724i \(-0.381696\pi\)
0.363166 + 0.931724i \(0.381696\pi\)
\(542\) 0.465200 0.0199821
\(543\) 0 0
\(544\) −3.96323 −0.169922
\(545\) 4.63843 0.198688
\(546\) 0 0
\(547\) −12.9628 −0.554250 −0.277125 0.960834i \(-0.589382\pi\)
−0.277125 + 0.960834i \(0.589382\pi\)
\(548\) 15.6228 0.667371
\(549\) 0 0
\(550\) −8.27488 −0.352842
\(551\) 32.8238 1.39834
\(552\) 0 0
\(553\) −0.396745 −0.0168713
\(554\) −0.882248 −0.0374831
\(555\) 0 0
\(556\) 25.8294 1.09541
\(557\) 32.8548 1.39210 0.696052 0.717992i \(-0.254938\pi\)
0.696052 + 0.717992i \(0.254938\pi\)
\(558\) 0 0
\(559\) −62.6262 −2.64881
\(560\) 0.953221 0.0402809
\(561\) 0 0
\(562\) 0.430288 0.0181506
\(563\) −37.3311 −1.57332 −0.786660 0.617386i \(-0.788192\pi\)
−0.786660 + 0.617386i \(0.788192\pi\)
\(564\) 0 0
\(565\) −2.85281 −0.120019
\(566\) 5.73694 0.241142
\(567\) 0 0
\(568\) 12.2375 0.513473
\(569\) 20.1928 0.846526 0.423263 0.906007i \(-0.360885\pi\)
0.423263 + 0.906007i \(0.360885\pi\)
\(570\) 0 0
\(571\) 22.1763 0.928048 0.464024 0.885823i \(-0.346405\pi\)
0.464024 + 0.885823i \(0.346405\pi\)
\(572\) −61.3589 −2.56554
\(573\) 0 0
\(574\) −0.536368 −0.0223876
\(575\) 24.1587 1.00749
\(576\) 0 0
\(577\) 35.6411 1.48376 0.741878 0.670535i \(-0.233935\pi\)
0.741878 + 0.670535i \(0.233935\pi\)
\(578\) −4.79192 −0.199318
\(579\) 0 0
\(580\) 2.83329 0.117646
\(581\) 2.27133 0.0942308
\(582\) 0 0
\(583\) 37.1205 1.53737
\(584\) −0.918676 −0.0380151
\(585\) 0 0
\(586\) −3.87376 −0.160023
\(587\) −3.23639 −0.133580 −0.0667900 0.997767i \(-0.521276\pi\)
−0.0667900 + 0.997767i \(0.521276\pi\)
\(588\) 0 0
\(589\) 56.3645 2.32246
\(590\) −0.854825 −0.0351926
\(591\) 0 0
\(592\) 13.7335 0.564443
\(593\) −18.1133 −0.743825 −0.371912 0.928268i \(-0.621298\pi\)
−0.371912 + 0.928268i \(0.621298\pi\)
\(594\) 0 0
\(595\) −0.318264 −0.0130476
\(596\) 9.50872 0.389492
\(597\) 0 0
\(598\) −8.78141 −0.359099
\(599\) 22.2405 0.908721 0.454361 0.890818i \(-0.349868\pi\)
0.454361 + 0.890818i \(0.349868\pi\)
\(600\) 0 0
\(601\) 34.6167 1.41205 0.706023 0.708189i \(-0.250488\pi\)
0.706023 + 0.708189i \(0.250488\pi\)
\(602\) −3.27044 −0.133293
\(603\) 0 0
\(604\) −7.96097 −0.323927
\(605\) 5.31442 0.216062
\(606\) 0 0
\(607\) −39.8677 −1.61818 −0.809089 0.587686i \(-0.800039\pi\)
−0.809089 + 0.587686i \(0.800039\pi\)
\(608\) −21.0215 −0.852534
\(609\) 0 0
\(610\) 0.537588 0.0217663
\(611\) 14.8355 0.600179
\(612\) 0 0
\(613\) −15.6926 −0.633818 −0.316909 0.948456i \(-0.602645\pi\)
−0.316909 + 0.948456i \(0.602645\pi\)
\(614\) −2.56141 −0.103370
\(615\) 0 0
\(616\) −6.56559 −0.264535
\(617\) −26.1395 −1.05234 −0.526169 0.850380i \(-0.676372\pi\)
−0.526169 + 0.850380i \(0.676372\pi\)
\(618\) 0 0
\(619\) 4.72169 0.189781 0.0948904 0.995488i \(-0.469750\pi\)
0.0948904 + 0.995488i \(0.469750\pi\)
\(620\) 4.86527 0.195394
\(621\) 0 0
\(622\) −8.16084 −0.327220
\(623\) 6.61497 0.265023
\(624\) 0 0
\(625\) 23.8594 0.954376
\(626\) −1.45192 −0.0580303
\(627\) 0 0
\(628\) −10.2003 −0.407038
\(629\) −4.58538 −0.182831
\(630\) 0 0
\(631\) −8.69806 −0.346264 −0.173132 0.984899i \(-0.555389\pi\)
−0.173132 + 0.984899i \(0.555389\pi\)
\(632\) 0.473821 0.0188476
\(633\) 0 0
\(634\) 3.90798 0.155206
\(635\) −0.276458 −0.0109709
\(636\) 0 0
\(637\) 5.85411 0.231948
\(638\) −9.03436 −0.357674
\(639\) 0 0
\(640\) −2.39735 −0.0947637
\(641\) 0.289431 0.0114318 0.00571592 0.999984i \(-0.498181\pi\)
0.00571592 + 0.999984i \(0.498181\pi\)
\(642\) 0 0
\(643\) 25.5065 1.00588 0.502939 0.864322i \(-0.332252\pi\)
0.502939 + 0.864322i \(0.332252\pi\)
\(644\) 9.35489 0.368634
\(645\) 0 0
\(646\) 2.14904 0.0845527
\(647\) 7.05434 0.277335 0.138667 0.990339i \(-0.455718\pi\)
0.138667 + 0.990339i \(0.455718\pi\)
\(648\) 0 0
\(649\) −55.6043 −2.18266
\(650\) −8.81154 −0.345617
\(651\) 0 0
\(652\) 14.9156 0.584138
\(653\) −29.0397 −1.13641 −0.568206 0.822886i \(-0.692362\pi\)
−0.568206 + 0.822886i \(0.692362\pi\)
\(654\) 0 0
\(655\) −3.29746 −0.128842
\(656\) −6.04946 −0.236192
\(657\) 0 0
\(658\) 0.774732 0.0302022
\(659\) −5.95542 −0.231990 −0.115995 0.993250i \(-0.537006\pi\)
−0.115995 + 0.993250i \(0.537006\pi\)
\(660\) 0 0
\(661\) 18.6354 0.724832 0.362416 0.932016i \(-0.381952\pi\)
0.362416 + 0.932016i \(0.381952\pi\)
\(662\) 9.17473 0.356586
\(663\) 0 0
\(664\) −2.71259 −0.105269
\(665\) −1.68811 −0.0654623
\(666\) 0 0
\(667\) 26.3760 1.02128
\(668\) 15.9325 0.616446
\(669\) 0 0
\(670\) 0.316364 0.0122222
\(671\) 34.9688 1.34995
\(672\) 0 0
\(673\) 21.1789 0.816387 0.408193 0.912896i \(-0.366159\pi\)
0.408193 + 0.912896i \(0.366159\pi\)
\(674\) −10.2929 −0.396468
\(675\) 0 0
\(676\) −40.5532 −1.55974
\(677\) −21.4495 −0.824370 −0.412185 0.911100i \(-0.635234\pi\)
−0.412185 + 0.911100i \(0.635234\pi\)
\(678\) 0 0
\(679\) 6.50324 0.249571
\(680\) 0.380094 0.0145760
\(681\) 0 0
\(682\) −15.5137 −0.594048
\(683\) −42.3011 −1.61861 −0.809303 0.587391i \(-0.800155\pi\)
−0.809303 + 0.587391i \(0.800155\pi\)
\(684\) 0 0
\(685\) −2.26538 −0.0865556
\(686\) 0.305711 0.0116721
\(687\) 0 0
\(688\) −36.8859 −1.40626
\(689\) 39.5279 1.50589
\(690\) 0 0
\(691\) −13.9263 −0.529782 −0.264891 0.964278i \(-0.585336\pi\)
−0.264891 + 0.964278i \(0.585336\pi\)
\(692\) 13.3604 0.507886
\(693\) 0 0
\(694\) −3.11742 −0.118336
\(695\) −3.74538 −0.142071
\(696\) 0 0
\(697\) 2.01981 0.0765059
\(698\) −6.66261 −0.252184
\(699\) 0 0
\(700\) 9.38699 0.354795
\(701\) 34.0403 1.28568 0.642842 0.765999i \(-0.277755\pi\)
0.642842 + 0.765999i \(0.277755\pi\)
\(702\) 0 0
\(703\) −24.3214 −0.917300
\(704\) −32.1251 −1.21076
\(705\) 0 0
\(706\) −3.32186 −0.125020
\(707\) −6.45399 −0.242727
\(708\) 0 0
\(709\) −34.3771 −1.29106 −0.645529 0.763736i \(-0.723363\pi\)
−0.645529 + 0.763736i \(0.723363\pi\)
\(710\) −0.866020 −0.0325012
\(711\) 0 0
\(712\) −7.90007 −0.296068
\(713\) 45.2924 1.69621
\(714\) 0 0
\(715\) 8.89734 0.332742
\(716\) 48.0266 1.79484
\(717\) 0 0
\(718\) 10.0877 0.376468
\(719\) 40.4073 1.50694 0.753469 0.657484i \(-0.228379\pi\)
0.753469 + 0.657484i \(0.228379\pi\)
\(720\) 0 0
\(721\) −7.17745 −0.267302
\(722\) 5.59025 0.208047
\(723\) 0 0
\(724\) −32.2238 −1.19759
\(725\) 26.4665 0.982940
\(726\) 0 0
\(727\) 3.23987 0.120160 0.0600800 0.998194i \(-0.480864\pi\)
0.0600800 + 0.998194i \(0.480864\pi\)
\(728\) −6.99140 −0.259118
\(729\) 0 0
\(730\) 0.0650128 0.00240623
\(731\) 12.3156 0.455508
\(732\) 0 0
\(733\) 8.50412 0.314107 0.157053 0.987590i \(-0.449801\pi\)
0.157053 + 0.987590i \(0.449801\pi\)
\(734\) −3.37182 −0.124456
\(735\) 0 0
\(736\) −16.8921 −0.622650
\(737\) 20.5787 0.758027
\(738\) 0 0
\(739\) −17.5860 −0.646913 −0.323456 0.946243i \(-0.604845\pi\)
−0.323456 + 0.946243i \(0.604845\pi\)
\(740\) −2.09938 −0.0771747
\(741\) 0 0
\(742\) 2.06421 0.0757795
\(743\) 26.7552 0.981551 0.490776 0.871286i \(-0.336713\pi\)
0.490776 + 0.871286i \(0.336713\pi\)
\(744\) 0 0
\(745\) −1.37881 −0.0505157
\(746\) −10.0928 −0.369525
\(747\) 0 0
\(748\) 12.0664 0.441190
\(749\) −2.58615 −0.0944958
\(750\) 0 0
\(751\) −26.4154 −0.963910 −0.481955 0.876196i \(-0.660073\pi\)
−0.481955 + 0.876196i \(0.660073\pi\)
\(752\) 8.73786 0.318637
\(753\) 0 0
\(754\) −9.62027 −0.350350
\(755\) 1.15438 0.0420122
\(756\) 0 0
\(757\) −46.7851 −1.70043 −0.850217 0.526433i \(-0.823529\pi\)
−0.850217 + 0.526433i \(0.823529\pi\)
\(758\) −1.80663 −0.0656199
\(759\) 0 0
\(760\) 2.01607 0.0731305
\(761\) 27.0165 0.979349 0.489674 0.871905i \(-0.337116\pi\)
0.489674 + 0.871905i \(0.337116\pi\)
\(762\) 0 0
\(763\) 16.7781 0.607407
\(764\) −41.5942 −1.50482
\(765\) 0 0
\(766\) −7.40143 −0.267425
\(767\) −59.2105 −2.13797
\(768\) 0 0
\(769\) 8.57917 0.309373 0.154686 0.987964i \(-0.450563\pi\)
0.154686 + 0.987964i \(0.450563\pi\)
\(770\) 0.464633 0.0167442
\(771\) 0 0
\(772\) 33.7424 1.21441
\(773\) −37.9118 −1.36359 −0.681796 0.731542i \(-0.738801\pi\)
−0.681796 + 0.731542i \(0.738801\pi\)
\(774\) 0 0
\(775\) 45.4478 1.63253
\(776\) −7.76664 −0.278806
\(777\) 0 0
\(778\) 9.96522 0.357270
\(779\) 10.7133 0.383845
\(780\) 0 0
\(781\) −56.3325 −2.01573
\(782\) 1.72688 0.0617532
\(783\) 0 0
\(784\) 3.44798 0.123142
\(785\) 1.47910 0.0527913
\(786\) 0 0
\(787\) −40.7590 −1.45290 −0.726450 0.687219i \(-0.758831\pi\)
−0.726450 + 0.687219i \(0.758831\pi\)
\(788\) 17.3746 0.618943
\(789\) 0 0
\(790\) −0.0335313 −0.00119299
\(791\) −10.3192 −0.366907
\(792\) 0 0
\(793\) 37.2366 1.32231
\(794\) 3.96904 0.140856
\(795\) 0 0
\(796\) 0.0431247 0.00152852
\(797\) 5.07686 0.179831 0.0899157 0.995949i \(-0.471340\pi\)
0.0899157 + 0.995949i \(0.471340\pi\)
\(798\) 0 0
\(799\) −2.91743 −0.103211
\(800\) −16.9500 −0.599274
\(801\) 0 0
\(802\) 11.0659 0.390750
\(803\) 4.22892 0.149235
\(804\) 0 0
\(805\) −1.35651 −0.0478105
\(806\) −16.5198 −0.581884
\(807\) 0 0
\(808\) 7.70782 0.271160
\(809\) −50.5158 −1.77604 −0.888021 0.459803i \(-0.847920\pi\)
−0.888021 + 0.459803i \(0.847920\pi\)
\(810\) 0 0
\(811\) −16.8436 −0.591458 −0.295729 0.955272i \(-0.595563\pi\)
−0.295729 + 0.955272i \(0.595563\pi\)
\(812\) 10.2485 0.359653
\(813\) 0 0
\(814\) 6.69418 0.234631
\(815\) −2.16283 −0.0757606
\(816\) 0 0
\(817\) 65.3234 2.28537
\(818\) −3.04784 −0.106565
\(819\) 0 0
\(820\) 0.924755 0.0322938
\(821\) 15.9626 0.557100 0.278550 0.960422i \(-0.410146\pi\)
0.278550 + 0.960422i \(0.410146\pi\)
\(822\) 0 0
\(823\) 35.8972 1.25130 0.625650 0.780104i \(-0.284834\pi\)
0.625650 + 0.780104i \(0.284834\pi\)
\(824\) 8.57183 0.298614
\(825\) 0 0
\(826\) −3.09207 −0.107587
\(827\) 20.2205 0.703137 0.351568 0.936162i \(-0.385648\pi\)
0.351568 + 0.936162i \(0.385648\pi\)
\(828\) 0 0
\(829\) −30.6787 −1.06552 −0.532758 0.846268i \(-0.678844\pi\)
−0.532758 + 0.846268i \(0.678844\pi\)
\(830\) 0.191964 0.00666318
\(831\) 0 0
\(832\) −34.2085 −1.18597
\(833\) −1.15122 −0.0398875
\(834\) 0 0
\(835\) −2.31029 −0.0799508
\(836\) 64.0015 2.21354
\(837\) 0 0
\(838\) −1.56454 −0.0540462
\(839\) −32.8827 −1.13524 −0.567618 0.823292i \(-0.692135\pi\)
−0.567618 + 0.823292i \(0.692135\pi\)
\(840\) 0 0
\(841\) −0.104428 −0.00360097
\(842\) −9.96323 −0.343356
\(843\) 0 0
\(844\) −24.9081 −0.857371
\(845\) 5.88042 0.202293
\(846\) 0 0
\(847\) 19.2233 0.660519
\(848\) 23.2813 0.799484
\(849\) 0 0
\(850\) 1.73281 0.0594348
\(851\) −19.5438 −0.669952
\(852\) 0 0
\(853\) 8.11977 0.278016 0.139008 0.990291i \(-0.455609\pi\)
0.139008 + 0.990291i \(0.455609\pi\)
\(854\) 1.94456 0.0665413
\(855\) 0 0
\(856\) 3.08856 0.105565
\(857\) 39.4412 1.34729 0.673644 0.739056i \(-0.264728\pi\)
0.673644 + 0.739056i \(0.264728\pi\)
\(858\) 0 0
\(859\) 50.5091 1.72335 0.861675 0.507461i \(-0.169416\pi\)
0.861675 + 0.507461i \(0.169416\pi\)
\(860\) 5.63859 0.192274
\(861\) 0 0
\(862\) 1.65159 0.0562533
\(863\) −18.8260 −0.640844 −0.320422 0.947275i \(-0.603825\pi\)
−0.320422 + 0.947275i \(0.603825\pi\)
\(864\) 0 0
\(865\) −1.93732 −0.0658710
\(866\) −4.63476 −0.157496
\(867\) 0 0
\(868\) 17.5986 0.597336
\(869\) −2.18113 −0.0739898
\(870\) 0 0
\(871\) 21.9133 0.742505
\(872\) −20.0376 −0.678558
\(873\) 0 0
\(874\) 9.15961 0.309828
\(875\) −2.74345 −0.0927455
\(876\) 0 0
\(877\) 51.8551 1.75102 0.875511 0.483197i \(-0.160525\pi\)
0.875511 + 0.483197i \(0.160525\pi\)
\(878\) 7.86482 0.265425
\(879\) 0 0
\(880\) 5.24040 0.176654
\(881\) −18.0437 −0.607907 −0.303953 0.952687i \(-0.598307\pi\)
−0.303953 + 0.952687i \(0.598307\pi\)
\(882\) 0 0
\(883\) −38.3129 −1.28933 −0.644665 0.764465i \(-0.723003\pi\)
−0.644665 + 0.764465i \(0.723003\pi\)
\(884\) 12.8489 0.432156
\(885\) 0 0
\(886\) −8.72988 −0.293286
\(887\) 39.8828 1.33913 0.669567 0.742751i \(-0.266480\pi\)
0.669567 + 0.742751i \(0.266480\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 0.559072 0.0187401
\(891\) 0 0
\(892\) −27.5585 −0.922726
\(893\) −15.4744 −0.517831
\(894\) 0 0
\(895\) −6.96409 −0.232784
\(896\) −8.67168 −0.289701
\(897\) 0 0
\(898\) 10.0977 0.336965
\(899\) 49.6190 1.65489
\(900\) 0 0
\(901\) −7.77324 −0.258964
\(902\) −2.94872 −0.0981816
\(903\) 0 0
\(904\) 12.3239 0.409886
\(905\) 4.67261 0.155323
\(906\) 0 0
\(907\) 15.9249 0.528779 0.264389 0.964416i \(-0.414830\pi\)
0.264389 + 0.964416i \(0.414830\pi\)
\(908\) 10.1934 0.338279
\(909\) 0 0
\(910\) 0.494767 0.0164014
\(911\) −30.4445 −1.00867 −0.504335 0.863508i \(-0.668262\pi\)
−0.504335 + 0.863508i \(0.668262\pi\)
\(912\) 0 0
\(913\) 12.4868 0.413253
\(914\) 8.04332 0.266049
\(915\) 0 0
\(916\) −23.3360 −0.771042
\(917\) −11.9275 −0.393881
\(918\) 0 0
\(919\) −32.5351 −1.07323 −0.536617 0.843826i \(-0.680298\pi\)
−0.536617 + 0.843826i \(0.680298\pi\)
\(920\) 1.62004 0.0534110
\(921\) 0 0
\(922\) −5.18590 −0.170788
\(923\) −59.9859 −1.97446
\(924\) 0 0
\(925\) −19.6108 −0.644800
\(926\) 7.25038 0.238262
\(927\) 0 0
\(928\) −18.5057 −0.607480
\(929\) −24.8695 −0.815942 −0.407971 0.912995i \(-0.633764\pi\)
−0.407971 + 0.912995i \(0.633764\pi\)
\(930\) 0 0
\(931\) −6.10623 −0.200124
\(932\) 39.4313 1.29161
\(933\) 0 0
\(934\) 10.4730 0.342687
\(935\) −1.74968 −0.0572207
\(936\) 0 0
\(937\) −49.0788 −1.60333 −0.801667 0.597770i \(-0.796053\pi\)
−0.801667 + 0.597770i \(0.796053\pi\)
\(938\) 1.14435 0.0373644
\(939\) 0 0
\(940\) −1.33572 −0.0435664
\(941\) −41.2182 −1.34367 −0.671837 0.740699i \(-0.734495\pi\)
−0.671837 + 0.740699i \(0.734495\pi\)
\(942\) 0 0
\(943\) 8.60884 0.280342
\(944\) −34.8740 −1.13505
\(945\) 0 0
\(946\) −17.9795 −0.584563
\(947\) 7.08226 0.230143 0.115071 0.993357i \(-0.463290\pi\)
0.115071 + 0.993357i \(0.463290\pi\)
\(948\) 0 0
\(949\) 4.50318 0.146180
\(950\) 9.19103 0.298197
\(951\) 0 0
\(952\) 1.37487 0.0445599
\(953\) −11.4314 −0.370300 −0.185150 0.982710i \(-0.559277\pi\)
−0.185150 + 0.982710i \(0.559277\pi\)
\(954\) 0 0
\(955\) 6.03136 0.195170
\(956\) 37.8522 1.22423
\(957\) 0 0
\(958\) −7.18501 −0.232137
\(959\) −8.19429 −0.264608
\(960\) 0 0
\(961\) 54.2049 1.74855
\(962\) 7.12833 0.229827
\(963\) 0 0
\(964\) −6.47759 −0.208629
\(965\) −4.89281 −0.157505
\(966\) 0 0
\(967\) 45.9374 1.47725 0.738624 0.674117i \(-0.235476\pi\)
0.738624 + 0.674117i \(0.235476\pi\)
\(968\) −22.9578 −0.737892
\(969\) 0 0
\(970\) 0.549629 0.0176475
\(971\) −21.6154 −0.693671 −0.346835 0.937926i \(-0.612744\pi\)
−0.346835 + 0.937926i \(0.612744\pi\)
\(972\) 0 0
\(973\) −13.5478 −0.434321
\(974\) −0.148983 −0.00477371
\(975\) 0 0
\(976\) 21.9318 0.702020
\(977\) −20.9557 −0.670432 −0.335216 0.942141i \(-0.608809\pi\)
−0.335216 + 0.942141i \(0.608809\pi\)
\(978\) 0 0
\(979\) 36.3662 1.16227
\(980\) −0.527078 −0.0168369
\(981\) 0 0
\(982\) −4.70319 −0.150085
\(983\) 41.0432 1.30908 0.654538 0.756029i \(-0.272863\pi\)
0.654538 + 0.756029i \(0.272863\pi\)
\(984\) 0 0
\(985\) −2.51940 −0.0802746
\(986\) 1.89185 0.0602487
\(987\) 0 0
\(988\) 68.1522 2.16821
\(989\) 52.4914 1.66913
\(990\) 0 0
\(991\) −57.2547 −1.81875 −0.909377 0.415973i \(-0.863441\pi\)
−0.909377 + 0.415973i \(0.863441\pi\)
\(992\) −31.7777 −1.00894
\(993\) 0 0
\(994\) −3.13256 −0.0993587
\(995\) −0.00625330 −0.000198243 0
\(996\) 0 0
\(997\) −6.92036 −0.219170 −0.109585 0.993977i \(-0.534952\pi\)
−0.109585 + 0.993977i \(0.534952\pi\)
\(998\) −1.21630 −0.0385013
\(999\) 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 \(a_p\))