Properties

Label 8002.2.a.e.1.9
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.50919 q^{3} +1.00000 q^{4} -3.69214 q^{5} +2.50919 q^{6} -2.32427 q^{7} -1.00000 q^{8} +3.29603 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.50919 q^{3} +1.00000 q^{4} -3.69214 q^{5} +2.50919 q^{6} -2.32427 q^{7} -1.00000 q^{8} +3.29603 q^{9} +3.69214 q^{10} +1.21449 q^{11} -2.50919 q^{12} -1.51284 q^{13} +2.32427 q^{14} +9.26428 q^{15} +1.00000 q^{16} +4.40033 q^{17} -3.29603 q^{18} +1.84008 q^{19} -3.69214 q^{20} +5.83203 q^{21} -1.21449 q^{22} +3.38598 q^{23} +2.50919 q^{24} +8.63189 q^{25} +1.51284 q^{26} -0.742794 q^{27} -2.32427 q^{28} -5.83234 q^{29} -9.26428 q^{30} -3.57673 q^{31} -1.00000 q^{32} -3.04738 q^{33} -4.40033 q^{34} +8.58153 q^{35} +3.29603 q^{36} +1.70011 q^{37} -1.84008 q^{38} +3.79599 q^{39} +3.69214 q^{40} +2.65356 q^{41} -5.83203 q^{42} +7.86167 q^{43} +1.21449 q^{44} -12.1694 q^{45} -3.38598 q^{46} +5.16719 q^{47} -2.50919 q^{48} -1.59777 q^{49} -8.63189 q^{50} -11.0413 q^{51} -1.51284 q^{52} +5.38323 q^{53} +0.742794 q^{54} -4.48406 q^{55} +2.32427 q^{56} -4.61712 q^{57} +5.83234 q^{58} -2.12801 q^{59} +9.26428 q^{60} +10.9496 q^{61} +3.57673 q^{62} -7.66086 q^{63} +1.00000 q^{64} +5.58560 q^{65} +3.04738 q^{66} -11.8691 q^{67} +4.40033 q^{68} -8.49607 q^{69} -8.58153 q^{70} +12.4845 q^{71} -3.29603 q^{72} +13.4429 q^{73} -1.70011 q^{74} -21.6591 q^{75} +1.84008 q^{76} -2.82280 q^{77} -3.79599 q^{78} -7.00049 q^{79} -3.69214 q^{80} -8.02428 q^{81} -2.65356 q^{82} -11.3465 q^{83} +5.83203 q^{84} -16.2466 q^{85} -7.86167 q^{86} +14.6344 q^{87} -1.21449 q^{88} -9.16985 q^{89} +12.1694 q^{90} +3.51624 q^{91} +3.38598 q^{92} +8.97468 q^{93} -5.16719 q^{94} -6.79385 q^{95} +2.50919 q^{96} -2.69458 q^{97} +1.59777 q^{98} +4.00299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.50919 −1.44868 −0.724340 0.689442i \(-0.757856\pi\)
−0.724340 + 0.689442i \(0.757856\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.69214 −1.65117 −0.825587 0.564274i \(-0.809156\pi\)
−0.825587 + 0.564274i \(0.809156\pi\)
\(6\) 2.50919 1.02437
\(7\) −2.32427 −0.878491 −0.439246 0.898367i \(-0.644754\pi\)
−0.439246 + 0.898367i \(0.644754\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.29603 1.09868
\(10\) 3.69214 1.16756
\(11\) 1.21449 0.366182 0.183091 0.983096i \(-0.441390\pi\)
0.183091 + 0.983096i \(0.441390\pi\)
\(12\) −2.50919 −0.724340
\(13\) −1.51284 −0.419585 −0.209793 0.977746i \(-0.567279\pi\)
−0.209793 + 0.977746i \(0.567279\pi\)
\(14\) 2.32427 0.621187
\(15\) 9.26428 2.39203
\(16\) 1.00000 0.250000
\(17\) 4.40033 1.06724 0.533618 0.845726i \(-0.320832\pi\)
0.533618 + 0.845726i \(0.320832\pi\)
\(18\) −3.29603 −0.776882
\(19\) 1.84008 0.422144 0.211072 0.977470i \(-0.432304\pi\)
0.211072 + 0.977470i \(0.432304\pi\)
\(20\) −3.69214 −0.825587
\(21\) 5.83203 1.27265
\(22\) −1.21449 −0.258930
\(23\) 3.38598 0.706026 0.353013 0.935618i \(-0.385157\pi\)
0.353013 + 0.935618i \(0.385157\pi\)
\(24\) 2.50919 0.512186
\(25\) 8.63189 1.72638
\(26\) 1.51284 0.296692
\(27\) −0.742794 −0.142951
\(28\) −2.32427 −0.439246
\(29\) −5.83234 −1.08304 −0.541519 0.840688i \(-0.682151\pi\)
−0.541519 + 0.840688i \(0.682151\pi\)
\(30\) −9.26428 −1.69142
\(31\) −3.57673 −0.642399 −0.321199 0.947012i \(-0.604086\pi\)
−0.321199 + 0.947012i \(0.604086\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.04738 −0.530481
\(34\) −4.40033 −0.754650
\(35\) 8.58153 1.45054
\(36\) 3.29603 0.549338
\(37\) 1.70011 0.279496 0.139748 0.990187i \(-0.455371\pi\)
0.139748 + 0.990187i \(0.455371\pi\)
\(38\) −1.84008 −0.298501
\(39\) 3.79599 0.607845
\(40\) 3.69214 0.583779
\(41\) 2.65356 0.414416 0.207208 0.978297i \(-0.433562\pi\)
0.207208 + 0.978297i \(0.433562\pi\)
\(42\) −5.83203 −0.899902
\(43\) 7.86167 1.19889 0.599447 0.800415i \(-0.295387\pi\)
0.599447 + 0.800415i \(0.295387\pi\)
\(44\) 1.21449 0.183091
\(45\) −12.1694 −1.81411
\(46\) −3.38598 −0.499236
\(47\) 5.16719 0.753712 0.376856 0.926272i \(-0.377005\pi\)
0.376856 + 0.926272i \(0.377005\pi\)
\(48\) −2.50919 −0.362170
\(49\) −1.59777 −0.228253
\(50\) −8.63189 −1.22073
\(51\) −11.0413 −1.54608
\(52\) −1.51284 −0.209793
\(53\) 5.38323 0.739444 0.369722 0.929142i \(-0.379453\pi\)
0.369722 + 0.929142i \(0.379453\pi\)
\(54\) 0.742794 0.101081
\(55\) −4.48406 −0.604630
\(56\) 2.32427 0.310594
\(57\) −4.61712 −0.611553
\(58\) 5.83234 0.765824
\(59\) −2.12801 −0.277043 −0.138521 0.990359i \(-0.544235\pi\)
−0.138521 + 0.990359i \(0.544235\pi\)
\(60\) 9.26428 1.19601
\(61\) 10.9496 1.40196 0.700978 0.713183i \(-0.252747\pi\)
0.700978 + 0.713183i \(0.252747\pi\)
\(62\) 3.57673 0.454245
\(63\) −7.66086 −0.965178
\(64\) 1.00000 0.125000
\(65\) 5.58560 0.692809
\(66\) 3.04738 0.375106
\(67\) −11.8691 −1.45004 −0.725019 0.688729i \(-0.758169\pi\)
−0.725019 + 0.688729i \(0.758169\pi\)
\(68\) 4.40033 0.533618
\(69\) −8.49607 −1.02281
\(70\) −8.58153 −1.02569
\(71\) 12.4845 1.48164 0.740821 0.671702i \(-0.234437\pi\)
0.740821 + 0.671702i \(0.234437\pi\)
\(72\) −3.29603 −0.388441
\(73\) 13.4429 1.57337 0.786684 0.617356i \(-0.211796\pi\)
0.786684 + 0.617356i \(0.211796\pi\)
\(74\) −1.70011 −0.197633
\(75\) −21.6591 −2.50097
\(76\) 1.84008 0.211072
\(77\) −2.82280 −0.321687
\(78\) −3.79599 −0.429811
\(79\) −7.00049 −0.787617 −0.393808 0.919193i \(-0.628843\pi\)
−0.393808 + 0.919193i \(0.628843\pi\)
\(80\) −3.69214 −0.412794
\(81\) −8.02428 −0.891586
\(82\) −2.65356 −0.293037
\(83\) −11.3465 −1.24544 −0.622722 0.782443i \(-0.713973\pi\)
−0.622722 + 0.782443i \(0.713973\pi\)
\(84\) 5.83203 0.636327
\(85\) −16.2466 −1.76219
\(86\) −7.86167 −0.847746
\(87\) 14.6344 1.56898
\(88\) −1.21449 −0.129465
\(89\) −9.16985 −0.972002 −0.486001 0.873958i \(-0.661545\pi\)
−0.486001 + 0.873958i \(0.661545\pi\)
\(90\) 12.1694 1.28277
\(91\) 3.51624 0.368602
\(92\) 3.38598 0.353013
\(93\) 8.97468 0.930631
\(94\) −5.16719 −0.532955
\(95\) −6.79385 −0.697034
\(96\) 2.50919 0.256093
\(97\) −2.69458 −0.273593 −0.136797 0.990599i \(-0.543681\pi\)
−0.136797 + 0.990599i \(0.543681\pi\)
\(98\) 1.59777 0.161399
\(99\) 4.00299 0.402315
\(100\) 8.63189 0.863189
\(101\) 13.4685 1.34017 0.670085 0.742284i \(-0.266257\pi\)
0.670085 + 0.742284i \(0.266257\pi\)
\(102\) 11.0413 1.09325
\(103\) −0.813326 −0.0801394 −0.0400697 0.999197i \(-0.512758\pi\)
−0.0400697 + 0.999197i \(0.512758\pi\)
\(104\) 1.51284 0.148346
\(105\) −21.5327 −2.10137
\(106\) −5.38323 −0.522866
\(107\) −18.9350 −1.83052 −0.915258 0.402869i \(-0.868013\pi\)
−0.915258 + 0.402869i \(0.868013\pi\)
\(108\) −0.742794 −0.0714754
\(109\) −13.0713 −1.25200 −0.626000 0.779823i \(-0.715309\pi\)
−0.626000 + 0.779823i \(0.715309\pi\)
\(110\) 4.48406 0.427538
\(111\) −4.26589 −0.404900
\(112\) −2.32427 −0.219623
\(113\) −13.3212 −1.25315 −0.626575 0.779361i \(-0.715544\pi\)
−0.626575 + 0.779361i \(0.715544\pi\)
\(114\) 4.61712 0.432433
\(115\) −12.5015 −1.16577
\(116\) −5.83234 −0.541519
\(117\) −4.98635 −0.460988
\(118\) 2.12801 0.195899
\(119\) −10.2275 −0.937557
\(120\) −9.26428 −0.845709
\(121\) −9.52502 −0.865911
\(122\) −10.9496 −0.991332
\(123\) −6.65828 −0.600357
\(124\) −3.57673 −0.321199
\(125\) −13.4095 −1.19938
\(126\) 7.66086 0.682484
\(127\) 17.2191 1.52795 0.763974 0.645247i \(-0.223245\pi\)
0.763974 + 0.645247i \(0.223245\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −19.7264 −1.73681
\(130\) −5.58560 −0.489890
\(131\) −13.0873 −1.14344 −0.571720 0.820448i \(-0.693724\pi\)
−0.571720 + 0.820448i \(0.693724\pi\)
\(132\) −3.04738 −0.265240
\(133\) −4.27685 −0.370850
\(134\) 11.8691 1.02533
\(135\) 2.74250 0.236037
\(136\) −4.40033 −0.377325
\(137\) 17.1461 1.46489 0.732444 0.680827i \(-0.238380\pi\)
0.732444 + 0.680827i \(0.238380\pi\)
\(138\) 8.49607 0.723233
\(139\) −2.52851 −0.214465 −0.107233 0.994234i \(-0.534199\pi\)
−0.107233 + 0.994234i \(0.534199\pi\)
\(140\) 8.58153 0.725271
\(141\) −12.9655 −1.09189
\(142\) −12.4845 −1.04768
\(143\) −1.83732 −0.153644
\(144\) 3.29603 0.274669
\(145\) 21.5338 1.78829
\(146\) −13.4429 −1.11254
\(147\) 4.00911 0.330666
\(148\) 1.70011 0.139748
\(149\) 0.193971 0.0158907 0.00794536 0.999968i \(-0.497471\pi\)
0.00794536 + 0.999968i \(0.497471\pi\)
\(150\) 21.6591 1.76845
\(151\) 10.2822 0.836752 0.418376 0.908274i \(-0.362599\pi\)
0.418376 + 0.908274i \(0.362599\pi\)
\(152\) −1.84008 −0.149251
\(153\) 14.5036 1.17255
\(154\) 2.82280 0.227467
\(155\) 13.2058 1.06071
\(156\) 3.79599 0.303923
\(157\) −21.7896 −1.73900 −0.869499 0.493935i \(-0.835558\pi\)
−0.869499 + 0.493935i \(0.835558\pi\)
\(158\) 7.00049 0.556929
\(159\) −13.5076 −1.07122
\(160\) 3.69214 0.291889
\(161\) −7.86993 −0.620238
\(162\) 8.02428 0.630447
\(163\) 23.9342 1.87467 0.937335 0.348429i \(-0.113285\pi\)
0.937335 + 0.348429i \(0.113285\pi\)
\(164\) 2.65356 0.207208
\(165\) 11.2513 0.875916
\(166\) 11.3465 0.880662
\(167\) 14.6972 1.13731 0.568653 0.822578i \(-0.307465\pi\)
0.568653 + 0.822578i \(0.307465\pi\)
\(168\) −5.83203 −0.449951
\(169\) −10.7113 −0.823948
\(170\) 16.2466 1.24606
\(171\) 6.06497 0.463800
\(172\) 7.86167 0.599447
\(173\) 10.3244 0.784950 0.392475 0.919763i \(-0.371619\pi\)
0.392475 + 0.919763i \(0.371619\pi\)
\(174\) −14.6344 −1.10943
\(175\) −20.0628 −1.51661
\(176\) 1.21449 0.0915454
\(177\) 5.33957 0.401347
\(178\) 9.16985 0.687309
\(179\) −10.2653 −0.767264 −0.383632 0.923486i \(-0.625327\pi\)
−0.383632 + 0.923486i \(0.625327\pi\)
\(180\) −12.1694 −0.907054
\(181\) −18.9276 −1.40688 −0.703440 0.710755i \(-0.748353\pi\)
−0.703440 + 0.710755i \(0.748353\pi\)
\(182\) −3.51624 −0.260641
\(183\) −27.4747 −2.03099
\(184\) −3.38598 −0.249618
\(185\) −6.27703 −0.461496
\(186\) −8.97468 −0.658056
\(187\) 5.34414 0.390802
\(188\) 5.16719 0.376856
\(189\) 1.72645 0.125581
\(190\) 6.79385 0.492878
\(191\) −10.0968 −0.730575 −0.365288 0.930895i \(-0.619029\pi\)
−0.365288 + 0.930895i \(0.619029\pi\)
\(192\) −2.50919 −0.181085
\(193\) −16.9104 −1.21724 −0.608618 0.793464i \(-0.708276\pi\)
−0.608618 + 0.793464i \(0.708276\pi\)
\(194\) 2.69458 0.193460
\(195\) −14.0153 −1.00366
\(196\) −1.59777 −0.114127
\(197\) 9.98318 0.711272 0.355636 0.934625i \(-0.384264\pi\)
0.355636 + 0.934625i \(0.384264\pi\)
\(198\) −4.00299 −0.284480
\(199\) 0.798766 0.0566230 0.0283115 0.999599i \(-0.490987\pi\)
0.0283115 + 0.999599i \(0.490987\pi\)
\(200\) −8.63189 −0.610367
\(201\) 29.7817 2.10064
\(202\) −13.4685 −0.947644
\(203\) 13.5559 0.951440
\(204\) −11.0413 −0.773042
\(205\) −9.79731 −0.684274
\(206\) 0.813326 0.0566671
\(207\) 11.1603 0.775694
\(208\) −1.51284 −0.104896
\(209\) 2.23476 0.154582
\(210\) 21.5327 1.48590
\(211\) −11.4585 −0.788835 −0.394418 0.918931i \(-0.629054\pi\)
−0.394418 + 0.918931i \(0.629054\pi\)
\(212\) 5.38323 0.369722
\(213\) −31.3261 −2.14643
\(214\) 18.9350 1.29437
\(215\) −29.0264 −1.97958
\(216\) 0.742794 0.0505407
\(217\) 8.31328 0.564342
\(218\) 13.0713 0.885298
\(219\) −33.7307 −2.27931
\(220\) −4.48406 −0.302315
\(221\) −6.65697 −0.447796
\(222\) 4.26589 0.286308
\(223\) −14.8652 −0.995446 −0.497723 0.867336i \(-0.665830\pi\)
−0.497723 + 0.867336i \(0.665830\pi\)
\(224\) 2.32427 0.155297
\(225\) 28.4510 1.89673
\(226\) 13.3212 0.886111
\(227\) 16.8836 1.12060 0.560301 0.828289i \(-0.310685\pi\)
0.560301 + 0.828289i \(0.310685\pi\)
\(228\) −4.61712 −0.305776
\(229\) −3.31633 −0.219149 −0.109575 0.993979i \(-0.534949\pi\)
−0.109575 + 0.993979i \(0.534949\pi\)
\(230\) 12.5015 0.824325
\(231\) 7.08293 0.466022
\(232\) 5.83234 0.382912
\(233\) 1.41856 0.0929333 0.0464666 0.998920i \(-0.485204\pi\)
0.0464666 + 0.998920i \(0.485204\pi\)
\(234\) 4.98635 0.325968
\(235\) −19.0780 −1.24451
\(236\) −2.12801 −0.138521
\(237\) 17.5656 1.14101
\(238\) 10.2275 0.662953
\(239\) 11.5402 0.746472 0.373236 0.927736i \(-0.378248\pi\)
0.373236 + 0.927736i \(0.378248\pi\)
\(240\) 9.26428 0.598006
\(241\) 28.5779 1.84086 0.920431 0.390906i \(-0.127838\pi\)
0.920431 + 0.390906i \(0.127838\pi\)
\(242\) 9.52502 0.612291
\(243\) 22.3628 1.43458
\(244\) 10.9496 0.700978
\(245\) 5.89920 0.376886
\(246\) 6.65828 0.424516
\(247\) −2.78375 −0.177126
\(248\) 3.57673 0.227122
\(249\) 28.4706 1.80425
\(250\) 13.4095 0.848089
\(251\) 20.8228 1.31432 0.657161 0.753751i \(-0.271757\pi\)
0.657161 + 0.753751i \(0.271757\pi\)
\(252\) −7.66086 −0.482589
\(253\) 4.11223 0.258534
\(254\) −17.2191 −1.08042
\(255\) 40.7658 2.55286
\(256\) 1.00000 0.0625000
\(257\) 2.04174 0.127360 0.0636800 0.997970i \(-0.479716\pi\)
0.0636800 + 0.997970i \(0.479716\pi\)
\(258\) 19.7264 1.22811
\(259\) −3.95150 −0.245534
\(260\) 5.58560 0.346404
\(261\) −19.2236 −1.18991
\(262\) 13.0873 0.808535
\(263\) −18.5902 −1.14632 −0.573160 0.819444i \(-0.694282\pi\)
−0.573160 + 0.819444i \(0.694282\pi\)
\(264\) 3.04738 0.187553
\(265\) −19.8756 −1.22095
\(266\) 4.27685 0.262231
\(267\) 23.0089 1.40812
\(268\) −11.8691 −0.725019
\(269\) 23.3760 1.42526 0.712630 0.701541i \(-0.247504\pi\)
0.712630 + 0.701541i \(0.247504\pi\)
\(270\) −2.74250 −0.166903
\(271\) 10.1022 0.613667 0.306833 0.951763i \(-0.400731\pi\)
0.306833 + 0.951763i \(0.400731\pi\)
\(272\) 4.40033 0.266809
\(273\) −8.82291 −0.533987
\(274\) −17.1461 −1.03583
\(275\) 10.4833 0.632168
\(276\) −8.49607 −0.511403
\(277\) −8.80553 −0.529073 −0.264537 0.964376i \(-0.585219\pi\)
−0.264537 + 0.964376i \(0.585219\pi\)
\(278\) 2.52851 0.151650
\(279\) −11.7890 −0.705789
\(280\) −8.58153 −0.512844
\(281\) −18.6722 −1.11389 −0.556946 0.830549i \(-0.688027\pi\)
−0.556946 + 0.830549i \(0.688027\pi\)
\(282\) 12.9655 0.772082
\(283\) −3.53530 −0.210152 −0.105076 0.994464i \(-0.533509\pi\)
−0.105076 + 0.994464i \(0.533509\pi\)
\(284\) 12.4845 0.740821
\(285\) 17.0471 1.00978
\(286\) 1.83732 0.108643
\(287\) −6.16759 −0.364061
\(288\) −3.29603 −0.194220
\(289\) 2.36287 0.138992
\(290\) −21.5338 −1.26451
\(291\) 6.76121 0.396349
\(292\) 13.4429 0.786684
\(293\) 11.0927 0.648045 0.324022 0.946049i \(-0.394965\pi\)
0.324022 + 0.946049i \(0.394965\pi\)
\(294\) −4.00911 −0.233816
\(295\) 7.85690 0.457446
\(296\) −1.70011 −0.0988166
\(297\) −0.902114 −0.0523459
\(298\) −0.193971 −0.0112364
\(299\) −5.12243 −0.296238
\(300\) −21.6591 −1.25049
\(301\) −18.2726 −1.05322
\(302\) −10.2822 −0.591673
\(303\) −33.7951 −1.94148
\(304\) 1.84008 0.105536
\(305\) −40.4275 −2.31487
\(306\) −14.5036 −0.829116
\(307\) −32.3668 −1.84727 −0.923635 0.383272i \(-0.874797\pi\)
−0.923635 + 0.383272i \(0.874797\pi\)
\(308\) −2.82280 −0.160844
\(309\) 2.04079 0.116096
\(310\) −13.2058 −0.750037
\(311\) 10.2327 0.580242 0.290121 0.956990i \(-0.406304\pi\)
0.290121 + 0.956990i \(0.406304\pi\)
\(312\) −3.79599 −0.214906
\(313\) 32.4146 1.83218 0.916090 0.400972i \(-0.131328\pi\)
0.916090 + 0.400972i \(0.131328\pi\)
\(314\) 21.7896 1.22966
\(315\) 28.2850 1.59368
\(316\) −7.00049 −0.393808
\(317\) 9.14630 0.513708 0.256854 0.966450i \(-0.417314\pi\)
0.256854 + 0.966450i \(0.417314\pi\)
\(318\) 13.5076 0.757466
\(319\) −7.08330 −0.396589
\(320\) −3.69214 −0.206397
\(321\) 47.5115 2.65183
\(322\) 7.86993 0.438574
\(323\) 8.09697 0.450528
\(324\) −8.02428 −0.445793
\(325\) −13.0586 −0.724363
\(326\) −23.9342 −1.32559
\(327\) 32.7983 1.81375
\(328\) −2.65356 −0.146518
\(329\) −12.0099 −0.662129
\(330\) −11.2513 −0.619366
\(331\) −4.76609 −0.261968 −0.130984 0.991384i \(-0.541814\pi\)
−0.130984 + 0.991384i \(0.541814\pi\)
\(332\) −11.3465 −0.622722
\(333\) 5.60360 0.307075
\(334\) −14.6972 −0.804197
\(335\) 43.8223 2.39427
\(336\) 5.83203 0.318163
\(337\) −26.6513 −1.45179 −0.725894 0.687807i \(-0.758574\pi\)
−0.725894 + 0.687807i \(0.758574\pi\)
\(338\) 10.7113 0.582619
\(339\) 33.4253 1.81542
\(340\) −16.2466 −0.881097
\(341\) −4.34389 −0.235235
\(342\) −6.06497 −0.327956
\(343\) 19.9835 1.07901
\(344\) −7.86167 −0.423873
\(345\) 31.3687 1.68883
\(346\) −10.3244 −0.555043
\(347\) −30.8312 −1.65511 −0.827553 0.561387i \(-0.810268\pi\)
−0.827553 + 0.561387i \(0.810268\pi\)
\(348\) 14.6344 0.784489
\(349\) −17.0144 −0.910757 −0.455379 0.890298i \(-0.650496\pi\)
−0.455379 + 0.890298i \(0.650496\pi\)
\(350\) 20.0628 1.07240
\(351\) 1.12373 0.0599800
\(352\) −1.21449 −0.0647324
\(353\) 34.0165 1.81051 0.905257 0.424864i \(-0.139678\pi\)
0.905257 + 0.424864i \(0.139678\pi\)
\(354\) −5.33957 −0.283795
\(355\) −46.0947 −2.44645
\(356\) −9.16985 −0.486001
\(357\) 25.6628 1.35822
\(358\) 10.2653 0.542537
\(359\) −10.9451 −0.577659 −0.288830 0.957381i \(-0.593266\pi\)
−0.288830 + 0.957381i \(0.593266\pi\)
\(360\) 12.1694 0.641384
\(361\) −15.6141 −0.821794
\(362\) 18.9276 0.994814
\(363\) 23.9001 1.25443
\(364\) 3.51624 0.184301
\(365\) −49.6329 −2.59791
\(366\) 27.4747 1.43612
\(367\) 23.5268 1.22809 0.614043 0.789272i \(-0.289542\pi\)
0.614043 + 0.789272i \(0.289542\pi\)
\(368\) 3.38598 0.176506
\(369\) 8.74621 0.455309
\(370\) 6.27703 0.326327
\(371\) −12.5121 −0.649595
\(372\) 8.97468 0.465316
\(373\) −8.38561 −0.434191 −0.217095 0.976150i \(-0.569658\pi\)
−0.217095 + 0.976150i \(0.569658\pi\)
\(374\) −5.34414 −0.276339
\(375\) 33.6469 1.73752
\(376\) −5.16719 −0.266477
\(377\) 8.82337 0.454427
\(378\) −1.72645 −0.0887991
\(379\) −29.8928 −1.53549 −0.767746 0.640754i \(-0.778622\pi\)
−0.767746 + 0.640754i \(0.778622\pi\)
\(380\) −6.79385 −0.348517
\(381\) −43.2060 −2.21351
\(382\) 10.0968 0.516595
\(383\) 13.5443 0.692079 0.346039 0.938220i \(-0.387526\pi\)
0.346039 + 0.938220i \(0.387526\pi\)
\(384\) 2.50919 0.128047
\(385\) 10.4222 0.531162
\(386\) 16.9104 0.860716
\(387\) 25.9123 1.31720
\(388\) −2.69458 −0.136797
\(389\) 15.4684 0.784280 0.392140 0.919905i \(-0.371735\pi\)
0.392140 + 0.919905i \(0.371735\pi\)
\(390\) 14.0153 0.709694
\(391\) 14.8994 0.753496
\(392\) 1.59777 0.0806997
\(393\) 32.8385 1.65648
\(394\) −9.98318 −0.502945
\(395\) 25.8468 1.30049
\(396\) 4.00299 0.201158
\(397\) 18.6320 0.935113 0.467557 0.883963i \(-0.345134\pi\)
0.467557 + 0.883963i \(0.345134\pi\)
\(398\) −0.798766 −0.0400385
\(399\) 10.7314 0.537244
\(400\) 8.63189 0.431595
\(401\) −26.5409 −1.32539 −0.662694 0.748891i \(-0.730587\pi\)
−0.662694 + 0.748891i \(0.730587\pi\)
\(402\) −29.7817 −1.48538
\(403\) 5.41100 0.269541
\(404\) 13.4685 0.670085
\(405\) 29.6268 1.47217
\(406\) −13.5559 −0.672769
\(407\) 2.06476 0.102346
\(408\) 11.0413 0.546623
\(409\) 5.83949 0.288744 0.144372 0.989523i \(-0.453884\pi\)
0.144372 + 0.989523i \(0.453884\pi\)
\(410\) 9.79731 0.483855
\(411\) −43.0227 −2.12215
\(412\) −0.813326 −0.0400697
\(413\) 4.94606 0.243380
\(414\) −11.1603 −0.548498
\(415\) 41.8930 2.05645
\(416\) 1.51284 0.0741729
\(417\) 6.34450 0.310691
\(418\) −2.23476 −0.109306
\(419\) 5.90643 0.288548 0.144274 0.989538i \(-0.453915\pi\)
0.144274 + 0.989538i \(0.453915\pi\)
\(420\) −21.5327 −1.05069
\(421\) −37.1517 −1.81066 −0.905331 0.424706i \(-0.860378\pi\)
−0.905331 + 0.424706i \(0.860378\pi\)
\(422\) 11.4585 0.557791
\(423\) 17.0312 0.828086
\(424\) −5.38323 −0.261433
\(425\) 37.9831 1.84245
\(426\) 31.3261 1.51775
\(427\) −25.4499 −1.23161
\(428\) −18.9350 −0.915258
\(429\) 4.61018 0.222582
\(430\) 29.0264 1.39978
\(431\) −16.1970 −0.780182 −0.390091 0.920776i \(-0.627556\pi\)
−0.390091 + 0.920776i \(0.627556\pi\)
\(432\) −0.742794 −0.0357377
\(433\) −41.1029 −1.97528 −0.987640 0.156740i \(-0.949901\pi\)
−0.987640 + 0.156740i \(0.949901\pi\)
\(434\) −8.31328 −0.399050
\(435\) −54.0324 −2.59066
\(436\) −13.0713 −0.626000
\(437\) 6.23049 0.298045
\(438\) 33.7307 1.61171
\(439\) 16.0877 0.767824 0.383912 0.923370i \(-0.374577\pi\)
0.383912 + 0.923370i \(0.374577\pi\)
\(440\) 4.48406 0.213769
\(441\) −5.26630 −0.250776
\(442\) 6.65697 0.316640
\(443\) 40.1459 1.90739 0.953696 0.300774i \(-0.0972448\pi\)
0.953696 + 0.300774i \(0.0972448\pi\)
\(444\) −4.26589 −0.202450
\(445\) 33.8564 1.60495
\(446\) 14.8652 0.703887
\(447\) −0.486710 −0.0230206
\(448\) −2.32427 −0.109811
\(449\) 18.0300 0.850891 0.425445 0.904984i \(-0.360117\pi\)
0.425445 + 0.904984i \(0.360117\pi\)
\(450\) −28.4510 −1.34119
\(451\) 3.22271 0.151752
\(452\) −13.3212 −0.626575
\(453\) −25.7999 −1.21219
\(454\) −16.8836 −0.792385
\(455\) −12.9824 −0.608626
\(456\) 4.61712 0.216216
\(457\) −19.4355 −0.909153 −0.454577 0.890708i \(-0.650209\pi\)
−0.454577 + 0.890708i \(0.650209\pi\)
\(458\) 3.31633 0.154962
\(459\) −3.26853 −0.152562
\(460\) −12.5015 −0.582886
\(461\) −1.89912 −0.0884509 −0.0442254 0.999022i \(-0.514082\pi\)
−0.0442254 + 0.999022i \(0.514082\pi\)
\(462\) −7.08293 −0.329528
\(463\) 30.4165 1.41357 0.706787 0.707426i \(-0.250144\pi\)
0.706787 + 0.707426i \(0.250144\pi\)
\(464\) −5.83234 −0.270760
\(465\) −33.1358 −1.53663
\(466\) −1.41856 −0.0657137
\(467\) −7.01036 −0.324401 −0.162200 0.986758i \(-0.551859\pi\)
−0.162200 + 0.986758i \(0.551859\pi\)
\(468\) −4.98635 −0.230494
\(469\) 27.5869 1.27385
\(470\) 19.0780 0.880002
\(471\) 54.6742 2.51925
\(472\) 2.12801 0.0979495
\(473\) 9.54790 0.439013
\(474\) −17.5656 −0.806813
\(475\) 15.8834 0.728781
\(476\) −10.2275 −0.468779
\(477\) 17.7433 0.812410
\(478\) −11.5402 −0.527836
\(479\) 17.6789 0.807768 0.403884 0.914810i \(-0.367660\pi\)
0.403884 + 0.914810i \(0.367660\pi\)
\(480\) −9.26428 −0.422854
\(481\) −2.57198 −0.117272
\(482\) −28.5779 −1.30169
\(483\) 19.7471 0.898526
\(484\) −9.52502 −0.432955
\(485\) 9.94877 0.451750
\(486\) −22.3628 −1.01440
\(487\) 36.8933 1.67179 0.835897 0.548887i \(-0.184948\pi\)
0.835897 + 0.548887i \(0.184948\pi\)
\(488\) −10.9496 −0.495666
\(489\) −60.0554 −2.71580
\(490\) −5.89920 −0.266499
\(491\) 37.1460 1.67637 0.838187 0.545382i \(-0.183616\pi\)
0.838187 + 0.545382i \(0.183616\pi\)
\(492\) −6.65828 −0.300178
\(493\) −25.6642 −1.15586
\(494\) 2.78375 0.125247
\(495\) −14.7796 −0.664293
\(496\) −3.57673 −0.160600
\(497\) −29.0174 −1.30161
\(498\) −28.4706 −1.27580
\(499\) 20.1331 0.901280 0.450640 0.892706i \(-0.351196\pi\)
0.450640 + 0.892706i \(0.351196\pi\)
\(500\) −13.4095 −0.599689
\(501\) −36.8781 −1.64759
\(502\) −20.8228 −0.929366
\(503\) 22.9342 1.02258 0.511292 0.859407i \(-0.329167\pi\)
0.511292 + 0.859407i \(0.329167\pi\)
\(504\) 7.66086 0.341242
\(505\) −49.7278 −2.21286
\(506\) −4.11223 −0.182811
\(507\) 26.8767 1.19364
\(508\) 17.2191 0.763974
\(509\) −3.08340 −0.136669 −0.0683347 0.997662i \(-0.521769\pi\)
−0.0683347 + 0.997662i \(0.521769\pi\)
\(510\) −40.7658 −1.80514
\(511\) −31.2448 −1.38219
\(512\) −1.00000 −0.0441942
\(513\) −1.36680 −0.0603458
\(514\) −2.04174 −0.0900572
\(515\) 3.00291 0.132324
\(516\) −19.7264 −0.868407
\(517\) 6.27549 0.275996
\(518\) 3.95150 0.173619
\(519\) −25.9059 −1.13714
\(520\) −5.58560 −0.244945
\(521\) −24.6477 −1.07983 −0.539917 0.841718i \(-0.681544\pi\)
−0.539917 + 0.841718i \(0.681544\pi\)
\(522\) 19.2236 0.841393
\(523\) 21.9461 0.959634 0.479817 0.877369i \(-0.340703\pi\)
0.479817 + 0.877369i \(0.340703\pi\)
\(524\) −13.0873 −0.571720
\(525\) 50.3415 2.19708
\(526\) 18.5902 0.810570
\(527\) −15.7388 −0.685591
\(528\) −3.04738 −0.132620
\(529\) −11.5351 −0.501527
\(530\) 19.8756 0.863343
\(531\) −7.01397 −0.304381
\(532\) −4.27685 −0.185425
\(533\) −4.01440 −0.173883
\(534\) −23.0089 −0.995692
\(535\) 69.9107 3.02250
\(536\) 11.8691 0.512666
\(537\) 25.7576 1.11152
\(538\) −23.3760 −1.00781
\(539\) −1.94047 −0.0835821
\(540\) 2.74250 0.118018
\(541\) 23.4737 1.00921 0.504607 0.863349i \(-0.331637\pi\)
0.504607 + 0.863349i \(0.331637\pi\)
\(542\) −10.1022 −0.433928
\(543\) 47.4930 2.03812
\(544\) −4.40033 −0.188662
\(545\) 48.2610 2.06727
\(546\) 8.82291 0.377586
\(547\) 2.91554 0.124659 0.0623297 0.998056i \(-0.480147\pi\)
0.0623297 + 0.998056i \(0.480147\pi\)
\(548\) 17.1461 0.732444
\(549\) 36.0903 1.54030
\(550\) −10.4833 −0.447011
\(551\) −10.7320 −0.457199
\(552\) 8.49607 0.361617
\(553\) 16.2710 0.691914
\(554\) 8.80553 0.374111
\(555\) 15.7502 0.668561
\(556\) −2.52851 −0.107233
\(557\) −25.0893 −1.06307 −0.531534 0.847037i \(-0.678384\pi\)
−0.531534 + 0.847037i \(0.678384\pi\)
\(558\) 11.7890 0.499068
\(559\) −11.8934 −0.503038
\(560\) 8.58153 0.362636
\(561\) −13.4095 −0.566148
\(562\) 18.6722 0.787641
\(563\) −3.78344 −0.159453 −0.0797264 0.996817i \(-0.525405\pi\)
−0.0797264 + 0.996817i \(0.525405\pi\)
\(564\) −12.9655 −0.545944
\(565\) 49.1836 2.06917
\(566\) 3.53530 0.148600
\(567\) 18.6506 0.783251
\(568\) −12.4845 −0.523840
\(569\) −13.5832 −0.569439 −0.284719 0.958611i \(-0.591900\pi\)
−0.284719 + 0.958611i \(0.591900\pi\)
\(570\) −17.0471 −0.714022
\(571\) 11.9627 0.500625 0.250312 0.968165i \(-0.419467\pi\)
0.250312 + 0.968165i \(0.419467\pi\)
\(572\) −1.83732 −0.0768222
\(573\) 25.3347 1.05837
\(574\) 6.16759 0.257430
\(575\) 29.2274 1.21887
\(576\) 3.29603 0.137335
\(577\) −17.9893 −0.748903 −0.374451 0.927247i \(-0.622169\pi\)
−0.374451 + 0.927247i \(0.622169\pi\)
\(578\) −2.36287 −0.0982825
\(579\) 42.4313 1.76339
\(580\) 21.5338 0.894143
\(581\) 26.3724 1.09411
\(582\) −6.76121 −0.280261
\(583\) 6.53787 0.270771
\(584\) −13.4429 −0.556270
\(585\) 18.4103 0.761172
\(586\) −11.0927 −0.458237
\(587\) −20.2323 −0.835076 −0.417538 0.908659i \(-0.637107\pi\)
−0.417538 + 0.908659i \(0.637107\pi\)
\(588\) 4.00911 0.165333
\(589\) −6.58148 −0.271185
\(590\) −7.85690 −0.323463
\(591\) −25.0497 −1.03041
\(592\) 1.70011 0.0698739
\(593\) 2.05939 0.0845690 0.0422845 0.999106i \(-0.486536\pi\)
0.0422845 + 0.999106i \(0.486536\pi\)
\(594\) 0.902114 0.0370142
\(595\) 37.7615 1.54807
\(596\) 0.193971 0.00794536
\(597\) −2.00426 −0.0820287
\(598\) 5.12243 0.209472
\(599\) 0.292320 0.0119439 0.00597194 0.999982i \(-0.498099\pi\)
0.00597194 + 0.999982i \(0.498099\pi\)
\(600\) 21.6591 0.884227
\(601\) 36.6086 1.49330 0.746648 0.665220i \(-0.231662\pi\)
0.746648 + 0.665220i \(0.231662\pi\)
\(602\) 18.2726 0.744737
\(603\) −39.1208 −1.59312
\(604\) 10.2822 0.418376
\(605\) 35.1677 1.42977
\(606\) 33.7951 1.37283
\(607\) −10.7173 −0.435003 −0.217501 0.976060i \(-0.569791\pi\)
−0.217501 + 0.976060i \(0.569791\pi\)
\(608\) −1.84008 −0.0746253
\(609\) −34.0144 −1.37833
\(610\) 40.4275 1.63686
\(611\) −7.81711 −0.316246
\(612\) 14.5036 0.586273
\(613\) −20.3254 −0.820935 −0.410467 0.911875i \(-0.634634\pi\)
−0.410467 + 0.911875i \(0.634634\pi\)
\(614\) 32.3668 1.30622
\(615\) 24.5833 0.991294
\(616\) 2.82280 0.113734
\(617\) 37.4009 1.50570 0.752851 0.658191i \(-0.228678\pi\)
0.752851 + 0.658191i \(0.228678\pi\)
\(618\) −2.04079 −0.0820926
\(619\) −36.2608 −1.45744 −0.728722 0.684809i \(-0.759885\pi\)
−0.728722 + 0.684809i \(0.759885\pi\)
\(620\) 13.2058 0.530357
\(621\) −2.51509 −0.100927
\(622\) −10.2327 −0.410293
\(623\) 21.3132 0.853895
\(624\) 3.79599 0.151961
\(625\) 6.35012 0.254005
\(626\) −32.4146 −1.29555
\(627\) −5.60744 −0.223939
\(628\) −21.7896 −0.869499
\(629\) 7.48102 0.298288
\(630\) −28.2850 −1.12690
\(631\) −4.28808 −0.170706 −0.0853529 0.996351i \(-0.527202\pi\)
−0.0853529 + 0.996351i \(0.527202\pi\)
\(632\) 7.00049 0.278465
\(633\) 28.7515 1.14277
\(634\) −9.14630 −0.363246
\(635\) −63.5753 −2.52291
\(636\) −13.5076 −0.535609
\(637\) 2.41717 0.0957716
\(638\) 7.08330 0.280431
\(639\) 41.1494 1.62785
\(640\) 3.69214 0.145945
\(641\) −4.37018 −0.172612 −0.0863059 0.996269i \(-0.527506\pi\)
−0.0863059 + 0.996269i \(0.527506\pi\)
\(642\) −47.5115 −1.87513
\(643\) −11.1269 −0.438801 −0.219401 0.975635i \(-0.570410\pi\)
−0.219401 + 0.975635i \(0.570410\pi\)
\(644\) −7.86993 −0.310119
\(645\) 72.8327 2.86778
\(646\) −8.09697 −0.318571
\(647\) −3.41131 −0.134112 −0.0670562 0.997749i \(-0.521361\pi\)
−0.0670562 + 0.997749i \(0.521361\pi\)
\(648\) 8.02428 0.315223
\(649\) −2.58444 −0.101448
\(650\) 13.0586 0.512202
\(651\) −20.8596 −0.817551
\(652\) 23.9342 0.937335
\(653\) 34.1849 1.33776 0.668880 0.743370i \(-0.266774\pi\)
0.668880 + 0.743370i \(0.266774\pi\)
\(654\) −32.7983 −1.28251
\(655\) 48.3201 1.88802
\(656\) 2.65356 0.103604
\(657\) 44.3081 1.72862
\(658\) 12.0099 0.468196
\(659\) 38.2622 1.49048 0.745241 0.666795i \(-0.232334\pi\)
0.745241 + 0.666795i \(0.232334\pi\)
\(660\) 11.2513 0.437958
\(661\) 11.0529 0.429909 0.214954 0.976624i \(-0.431040\pi\)
0.214954 + 0.976624i \(0.431040\pi\)
\(662\) 4.76609 0.185239
\(663\) 16.7036 0.648714
\(664\) 11.3465 0.440331
\(665\) 15.7907 0.612339
\(666\) −5.60360 −0.217135
\(667\) −19.7482 −0.764653
\(668\) 14.6972 0.568653
\(669\) 37.2995 1.44208
\(670\) −43.8223 −1.69300
\(671\) 13.2982 0.513371
\(672\) −5.83203 −0.224975
\(673\) −29.2303 −1.12675 −0.563373 0.826203i \(-0.690497\pi\)
−0.563373 + 0.826203i \(0.690497\pi\)
\(674\) 26.6513 1.02657
\(675\) −6.41172 −0.246787
\(676\) −10.7113 −0.411974
\(677\) −0.910983 −0.0350119 −0.0175060 0.999847i \(-0.505573\pi\)
−0.0175060 + 0.999847i \(0.505573\pi\)
\(678\) −33.4253 −1.28369
\(679\) 6.26293 0.240349
\(680\) 16.2466 0.623029
\(681\) −42.3641 −1.62339
\(682\) 4.34389 0.166336
\(683\) 34.7309 1.32894 0.664470 0.747315i \(-0.268657\pi\)
0.664470 + 0.747315i \(0.268657\pi\)
\(684\) 6.06497 0.231900
\(685\) −63.3057 −2.41879
\(686\) −19.9835 −0.762975
\(687\) 8.32130 0.317477
\(688\) 7.86167 0.299723
\(689\) −8.14395 −0.310260
\(690\) −31.3687 −1.19418
\(691\) 8.83052 0.335929 0.167964 0.985793i \(-0.446281\pi\)
0.167964 + 0.985793i \(0.446281\pi\)
\(692\) 10.3244 0.392475
\(693\) −9.30402 −0.353430
\(694\) 30.8312 1.17034
\(695\) 9.33559 0.354119
\(696\) −14.6344 −0.554717
\(697\) 11.6765 0.442280
\(698\) 17.0144 0.644003
\(699\) −3.55945 −0.134631
\(700\) −20.0628 −0.758304
\(701\) 17.4132 0.657687 0.328843 0.944384i \(-0.393341\pi\)
0.328843 + 0.944384i \(0.393341\pi\)
\(702\) −1.12373 −0.0424123
\(703\) 3.12834 0.117988
\(704\) 1.21449 0.0457727
\(705\) 47.8703 1.80290
\(706\) −34.0165 −1.28023
\(707\) −31.3045 −1.17733
\(708\) 5.33957 0.200673
\(709\) −9.30814 −0.349575 −0.174787 0.984606i \(-0.555924\pi\)
−0.174787 + 0.984606i \(0.555924\pi\)
\(710\) 46.0947 1.72990
\(711\) −23.0738 −0.865336
\(712\) 9.16985 0.343655
\(713\) −12.1107 −0.453550
\(714\) −25.6628 −0.960408
\(715\) 6.78364 0.253694
\(716\) −10.2653 −0.383632
\(717\) −28.9565 −1.08140
\(718\) 10.9451 0.408467
\(719\) −41.0909 −1.53243 −0.766217 0.642582i \(-0.777863\pi\)
−0.766217 + 0.642582i \(0.777863\pi\)
\(720\) −12.1694 −0.453527
\(721\) 1.89039 0.0704017
\(722\) 15.6141 0.581096
\(723\) −71.7072 −2.66682
\(724\) −18.9276 −0.703440
\(725\) −50.3441 −1.86973
\(726\) −23.9001 −0.887015
\(727\) 41.2270 1.52902 0.764512 0.644610i \(-0.222980\pi\)
0.764512 + 0.644610i \(0.222980\pi\)
\(728\) −3.51624 −0.130320
\(729\) −32.0397 −1.18666
\(730\) 49.6329 1.83700
\(731\) 34.5939 1.27950
\(732\) −27.4747 −1.01549
\(733\) 17.8158 0.658043 0.329022 0.944322i \(-0.393281\pi\)
0.329022 + 0.944322i \(0.393281\pi\)
\(734\) −23.5268 −0.868389
\(735\) −14.8022 −0.545987
\(736\) −3.38598 −0.124809
\(737\) −14.4148 −0.530977
\(738\) −8.74621 −0.321952
\(739\) −21.0947 −0.775982 −0.387991 0.921663i \(-0.626831\pi\)
−0.387991 + 0.921663i \(0.626831\pi\)
\(740\) −6.27703 −0.230748
\(741\) 6.98495 0.256598
\(742\) 12.5121 0.459333
\(743\) 14.0708 0.516209 0.258105 0.966117i \(-0.416902\pi\)
0.258105 + 0.966117i \(0.416902\pi\)
\(744\) −8.97468 −0.329028
\(745\) −0.716168 −0.0262384
\(746\) 8.38561 0.307019
\(747\) −37.3985 −1.36834
\(748\) 5.34414 0.195401
\(749\) 44.0100 1.60809
\(750\) −33.6469 −1.22861
\(751\) 18.4007 0.671450 0.335725 0.941960i \(-0.391019\pi\)
0.335725 + 0.941960i \(0.391019\pi\)
\(752\) 5.16719 0.188428
\(753\) −52.2483 −1.90403
\(754\) −8.82337 −0.321328
\(755\) −37.9633 −1.38162
\(756\) 1.72645 0.0627905
\(757\) −21.7375 −0.790064 −0.395032 0.918667i \(-0.629266\pi\)
−0.395032 + 0.918667i \(0.629266\pi\)
\(758\) 29.8928 1.08576
\(759\) −10.3184 −0.374533
\(760\) 6.79385 0.246439
\(761\) 9.12115 0.330642 0.165321 0.986240i \(-0.447134\pi\)
0.165321 + 0.986240i \(0.447134\pi\)
\(762\) 43.2060 1.56519
\(763\) 30.3812 1.09987
\(764\) −10.0968 −0.365288
\(765\) −53.5493 −1.93608
\(766\) −13.5443 −0.489374
\(767\) 3.21933 0.116243
\(768\) −2.50919 −0.0905426
\(769\) −48.6123 −1.75300 −0.876502 0.481397i \(-0.840129\pi\)
−0.876502 + 0.481397i \(0.840129\pi\)
\(770\) −10.4222 −0.375588
\(771\) −5.12311 −0.184504
\(772\) −16.9104 −0.608618
\(773\) −26.6898 −0.959965 −0.479983 0.877278i \(-0.659357\pi\)
−0.479983 + 0.877278i \(0.659357\pi\)
\(774\) −25.9123 −0.931398
\(775\) −30.8739 −1.10902
\(776\) 2.69458 0.0967298
\(777\) 9.91507 0.355701
\(778\) −15.4684 −0.554570
\(779\) 4.88277 0.174944
\(780\) −14.0153 −0.501829
\(781\) 15.1623 0.542550
\(782\) −14.8994 −0.532802
\(783\) 4.33223 0.154821
\(784\) −1.59777 −0.0570633
\(785\) 80.4502 2.87139
\(786\) −32.8385 −1.17131
\(787\) 12.5883 0.448726 0.224363 0.974506i \(-0.427970\pi\)
0.224363 + 0.974506i \(0.427970\pi\)
\(788\) 9.98318 0.355636
\(789\) 46.6463 1.66065
\(790\) −25.8468 −0.919587
\(791\) 30.9620 1.10088
\(792\) −4.00299 −0.142240
\(793\) −16.5650 −0.588240
\(794\) −18.6320 −0.661225
\(795\) 49.8718 1.76877
\(796\) 0.798766 0.0283115
\(797\) −0.0444540 −0.00157464 −0.000787320 1.00000i \(-0.500251\pi\)
−0.000787320 1.00000i \(0.500251\pi\)
\(798\) −10.7314 −0.379889
\(799\) 22.7373 0.804389
\(800\) −8.63189 −0.305184
\(801\) −30.2241 −1.06792
\(802\) 26.5409 0.937190
\(803\) 16.3262 0.576139
\(804\) 29.7817 1.05032
\(805\) 29.0569 1.02412
\(806\) −5.41100 −0.190594
\(807\) −58.6548 −2.06475
\(808\) −13.4685 −0.473822
\(809\) −21.0760 −0.740994 −0.370497 0.928834i \(-0.620813\pi\)
−0.370497 + 0.928834i \(0.620813\pi\)
\(810\) −29.6268 −1.04098
\(811\) −24.7779 −0.870071 −0.435036 0.900413i \(-0.643264\pi\)
−0.435036 + 0.900413i \(0.643264\pi\)
\(812\) 13.5559 0.475720
\(813\) −25.3484 −0.889008
\(814\) −2.06476 −0.0723697
\(815\) −88.3684 −3.09541
\(816\) −11.0413 −0.386521
\(817\) 14.4661 0.506106
\(818\) −5.83949 −0.204173
\(819\) 11.5896 0.404974
\(820\) −9.79731 −0.342137
\(821\) −39.2963 −1.37145 −0.685726 0.727860i \(-0.740515\pi\)
−0.685726 + 0.727860i \(0.740515\pi\)
\(822\) 43.0227 1.50059
\(823\) −43.3750 −1.51196 −0.755978 0.654597i \(-0.772838\pi\)
−0.755978 + 0.654597i \(0.772838\pi\)
\(824\) 0.813326 0.0283336
\(825\) −26.3046 −0.915810
\(826\) −4.94606 −0.172096
\(827\) −3.65692 −0.127164 −0.0635818 0.997977i \(-0.520252\pi\)
−0.0635818 + 0.997977i \(0.520252\pi\)
\(828\) 11.1603 0.387847
\(829\) 0.411757 0.0143009 0.00715045 0.999974i \(-0.497724\pi\)
0.00715045 + 0.999974i \(0.497724\pi\)
\(830\) −41.8930 −1.45413
\(831\) 22.0947 0.766458
\(832\) −1.51284 −0.0524481
\(833\) −7.03072 −0.243600
\(834\) −6.34450 −0.219692
\(835\) −54.2642 −1.87789
\(836\) 2.23476 0.0772908
\(837\) 2.65677 0.0918314
\(838\) −5.90643 −0.204034
\(839\) 42.5626 1.46942 0.734711 0.678380i \(-0.237318\pi\)
0.734711 + 0.678380i \(0.237318\pi\)
\(840\) 21.5327 0.742948
\(841\) 5.01619 0.172972
\(842\) 37.1517 1.28033
\(843\) 46.8522 1.61367
\(844\) −11.4585 −0.394418
\(845\) 39.5477 1.36048
\(846\) −17.0312 −0.585545
\(847\) 22.1387 0.760695
\(848\) 5.38323 0.184861
\(849\) 8.87073 0.304443
\(850\) −37.9831 −1.30281
\(851\) 5.75652 0.197331
\(852\) −31.3261 −1.07321
\(853\) −8.22454 −0.281603 −0.140801 0.990038i \(-0.544968\pi\)
−0.140801 + 0.990038i \(0.544968\pi\)
\(854\) 25.4499 0.870877
\(855\) −22.3927 −0.765815
\(856\) 18.9350 0.647185
\(857\) −6.44021 −0.219993 −0.109997 0.993932i \(-0.535084\pi\)
−0.109997 + 0.993932i \(0.535084\pi\)
\(858\) −4.61018 −0.157389
\(859\) 42.1664 1.43870 0.719350 0.694648i \(-0.244440\pi\)
0.719350 + 0.694648i \(0.244440\pi\)
\(860\) −29.0264 −0.989792
\(861\) 15.4756 0.527408
\(862\) 16.1970 0.551672
\(863\) 52.4475 1.78533 0.892667 0.450718i \(-0.148832\pi\)
0.892667 + 0.450718i \(0.148832\pi\)
\(864\) 0.742794 0.0252704
\(865\) −38.1191 −1.29609
\(866\) 41.1029 1.39673
\(867\) −5.92889 −0.201356
\(868\) 8.31328 0.282171
\(869\) −8.50201 −0.288411
\(870\) 54.0324 1.83187
\(871\) 17.9560 0.608414
\(872\) 13.0713 0.442649
\(873\) −8.88142 −0.300591
\(874\) −6.23049 −0.210750
\(875\) 31.1672 1.05364
\(876\) −33.7307 −1.13965
\(877\) 37.5461 1.26784 0.633922 0.773397i \(-0.281444\pi\)
0.633922 + 0.773397i \(0.281444\pi\)
\(878\) −16.0877 −0.542934
\(879\) −27.8338 −0.938810
\(880\) −4.48406 −0.151158
\(881\) 5.65461 0.190509 0.0952543 0.995453i \(-0.469634\pi\)
0.0952543 + 0.995453i \(0.469634\pi\)
\(882\) 5.26630 0.177326
\(883\) −10.4475 −0.351588 −0.175794 0.984427i \(-0.556249\pi\)
−0.175794 + 0.984427i \(0.556249\pi\)
\(884\) −6.65697 −0.223898
\(885\) −19.7144 −0.662694
\(886\) −40.1459 −1.34873
\(887\) 40.7281 1.36752 0.683758 0.729709i \(-0.260345\pi\)
0.683758 + 0.729709i \(0.260345\pi\)
\(888\) 4.26589 0.143154
\(889\) −40.0218 −1.34229
\(890\) −33.8564 −1.13487
\(891\) −9.74539 −0.326483
\(892\) −14.8652 −0.497723
\(893\) 9.50807 0.318175
\(894\) 0.486710 0.0162780
\(895\) 37.9009 1.26689
\(896\) 2.32427 0.0776484
\(897\) 12.8532 0.429154
\(898\) −18.0300 −0.601671
\(899\) 20.8607 0.695743
\(900\) 28.4510 0.948366
\(901\) 23.6880 0.789161
\(902\) −3.22271 −0.107305
\(903\) 45.8495 1.52578
\(904\) 13.3212 0.443056
\(905\) 69.8834 2.32300
\(906\) 25.7999 0.857146
\(907\) −57.4575 −1.90784 −0.953922 0.300053i \(-0.902996\pi\)
−0.953922 + 0.300053i \(0.902996\pi\)
\(908\) 16.8836 0.560301
\(909\) 44.3927 1.47241
\(910\) 12.9824 0.430364
\(911\) −54.1787 −1.79502 −0.897511 0.440992i \(-0.854627\pi\)
−0.897511 + 0.440992i \(0.854627\pi\)
\(912\) −4.61712 −0.152888
\(913\) −13.7802 −0.456059
\(914\) 19.4355 0.642868
\(915\) 101.440 3.35351
\(916\) −3.31633 −0.109575
\(917\) 30.4184 1.00450
\(918\) 3.26853 0.107878
\(919\) 27.4012 0.903882 0.451941 0.892048i \(-0.350732\pi\)
0.451941 + 0.892048i \(0.350732\pi\)
\(920\) 12.5015 0.412163
\(921\) 81.2144 2.67611
\(922\) 1.89912 0.0625442
\(923\) −18.8871 −0.621675
\(924\) 7.08293 0.233011
\(925\) 14.6751 0.482515
\(926\) −30.4165 −0.999548
\(927\) −2.68075 −0.0880473
\(928\) 5.83234 0.191456
\(929\) 43.3176 1.42121 0.710603 0.703593i \(-0.248422\pi\)
0.710603 + 0.703593i \(0.248422\pi\)
\(930\) 33.1358 1.08656
\(931\) −2.94004 −0.0963558
\(932\) 1.41856 0.0464666
\(933\) −25.6757 −0.840586
\(934\) 7.01036 0.229386
\(935\) −19.7313 −0.645283
\(936\) 4.98635 0.162984
\(937\) 1.16655 0.0381096 0.0190548 0.999818i \(-0.493934\pi\)
0.0190548 + 0.999818i \(0.493934\pi\)
\(938\) −27.5869 −0.900745
\(939\) −81.3343 −2.65424
\(940\) −19.0780 −0.622255
\(941\) −34.9273 −1.13860 −0.569299 0.822131i \(-0.692785\pi\)
−0.569299 + 0.822131i \(0.692785\pi\)
\(942\) −54.6742 −1.78138
\(943\) 8.98490 0.292589
\(944\) −2.12801 −0.0692607
\(945\) −6.37430 −0.207356
\(946\) −9.54790 −0.310429
\(947\) −45.2160 −1.46932 −0.734661 0.678434i \(-0.762659\pi\)
−0.734661 + 0.678434i \(0.762659\pi\)
\(948\) 17.5656 0.570503
\(949\) −20.3368 −0.660162
\(950\) −15.8834 −0.515326
\(951\) −22.9498 −0.744198
\(952\) 10.2275 0.331477
\(953\) 46.1715 1.49564 0.747821 0.663901i \(-0.231100\pi\)
0.747821 + 0.663901i \(0.231100\pi\)
\(954\) −17.7433 −0.574460
\(955\) 37.2786 1.20631
\(956\) 11.5402 0.373236
\(957\) 17.7733 0.574531
\(958\) −17.6789 −0.571178
\(959\) −39.8521 −1.28689
\(960\) 9.26428 0.299003
\(961\) −18.2070 −0.587324
\(962\) 2.57198 0.0829240
\(963\) −62.4103 −2.01114
\(964\) 28.5779 0.920431
\(965\) 62.4355 2.00987
\(966\) −19.7471 −0.635354
\(967\) 11.0874 0.356546 0.178273 0.983981i \(-0.442949\pi\)
0.178273 + 0.983981i \(0.442949\pi\)
\(968\) 9.52502 0.306146
\(969\) −20.3168 −0.652671
\(970\) −9.94877 −0.319436
\(971\) −40.7302 −1.30710 −0.653548 0.756885i \(-0.726720\pi\)
−0.653548 + 0.756885i \(0.726720\pi\)
\(972\) 22.3628 0.717288
\(973\) 5.87693 0.188406
\(974\) −36.8933 −1.18214
\(975\) 32.7666 1.04937
\(976\) 10.9496 0.350489
\(977\) −6.07444 −0.194339 −0.0971693 0.995268i \(-0.530979\pi\)
−0.0971693 + 0.995268i \(0.530979\pi\)
\(978\) 60.0554 1.92036
\(979\) −11.1367 −0.355929
\(980\) 5.89920 0.188443
\(981\) −43.0833 −1.37554
\(982\) −37.1460 −1.18538
\(983\) 6.82114 0.217560 0.108780 0.994066i \(-0.465306\pi\)
0.108780 + 0.994066i \(0.465306\pi\)
\(984\) 6.65828 0.212258
\(985\) −36.8593 −1.17443
\(986\) 25.6642 0.817315
\(987\) 30.1352 0.959214
\(988\) −2.78375 −0.0885628
\(989\) 26.6195 0.846450
\(990\) 14.7796 0.469726
\(991\) 42.4574 1.34870 0.674352 0.738410i \(-0.264423\pi\)
0.674352 + 0.738410i \(0.264423\pi\)
\(992\) 3.57673 0.113561
\(993\) 11.9590 0.379508
\(994\) 29.0174 0.920377
\(995\) −2.94916 −0.0934945
\(996\) 28.4706 0.902126
\(997\) −44.6702 −1.41472 −0.707359 0.706855i \(-0.750114\pi\)
−0.707359 + 0.706855i \(0.750114\pi\)
\(998\) −20.1331 −0.637301
\(999\) −1.26283 −0.0399541
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 \(a_p\))