Properties

Label 8002.2.a.e.1.4
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 1.4
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.93461 q^{3} +1.00000 q^{4} +1.73622 q^{5} +2.93461 q^{6} -0.969734 q^{7} -1.00000 q^{8} +5.61192 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.93461 q^{3} +1.00000 q^{4} +1.73622 q^{5} +2.93461 q^{6} -0.969734 q^{7} -1.00000 q^{8} +5.61192 q^{9} -1.73622 q^{10} -5.59748 q^{11} -2.93461 q^{12} -5.07738 q^{13} +0.969734 q^{14} -5.09513 q^{15} +1.00000 q^{16} +4.63902 q^{17} -5.61192 q^{18} +1.16072 q^{19} +1.73622 q^{20} +2.84579 q^{21} +5.59748 q^{22} +8.33406 q^{23} +2.93461 q^{24} -1.98553 q^{25} +5.07738 q^{26} -7.66495 q^{27} -0.969734 q^{28} -5.44758 q^{29} +5.09513 q^{30} +6.78772 q^{31} -1.00000 q^{32} +16.4264 q^{33} -4.63902 q^{34} -1.68367 q^{35} +5.61192 q^{36} -11.1148 q^{37} -1.16072 q^{38} +14.9001 q^{39} -1.73622 q^{40} -5.20560 q^{41} -2.84579 q^{42} +0.841312 q^{43} -5.59748 q^{44} +9.74354 q^{45} -8.33406 q^{46} -0.998598 q^{47} -2.93461 q^{48} -6.05962 q^{49} +1.98553 q^{50} -13.6137 q^{51} -5.07738 q^{52} -2.85680 q^{53} +7.66495 q^{54} -9.71846 q^{55} +0.969734 q^{56} -3.40627 q^{57} +5.44758 q^{58} +6.29475 q^{59} -5.09513 q^{60} -3.58449 q^{61} -6.78772 q^{62} -5.44207 q^{63} +1.00000 q^{64} -8.81546 q^{65} -16.4264 q^{66} +8.13548 q^{67} +4.63902 q^{68} -24.4572 q^{69} +1.68367 q^{70} -9.51758 q^{71} -5.61192 q^{72} +8.69676 q^{73} +11.1148 q^{74} +5.82675 q^{75} +1.16072 q^{76} +5.42806 q^{77} -14.9001 q^{78} +13.9628 q^{79} +1.73622 q^{80} +5.65787 q^{81} +5.20560 q^{82} -17.3624 q^{83} +2.84579 q^{84} +8.05437 q^{85} -0.841312 q^{86} +15.9865 q^{87} +5.59748 q^{88} -7.79136 q^{89} -9.74354 q^{90} +4.92370 q^{91} +8.33406 q^{92} -19.9193 q^{93} +0.998598 q^{94} +2.01527 q^{95} +2.93461 q^{96} -1.51463 q^{97} +6.05962 q^{98} -31.4126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.93461 −1.69430 −0.847148 0.531357i \(-0.821682\pi\)
−0.847148 + 0.531357i \(0.821682\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.73622 0.776462 0.388231 0.921562i \(-0.373086\pi\)
0.388231 + 0.921562i \(0.373086\pi\)
\(6\) 2.93461 1.19805
\(7\) −0.969734 −0.366525 −0.183262 0.983064i \(-0.558666\pi\)
−0.183262 + 0.983064i \(0.558666\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.61192 1.87064
\(10\) −1.73622 −0.549042
\(11\) −5.59748 −1.68770 −0.843851 0.536577i \(-0.819717\pi\)
−0.843851 + 0.536577i \(0.819717\pi\)
\(12\) −2.93461 −0.847148
\(13\) −5.07738 −1.40821 −0.704106 0.710095i \(-0.748652\pi\)
−0.704106 + 0.710095i \(0.748652\pi\)
\(14\) 0.969734 0.259172
\(15\) −5.09513 −1.31556
\(16\) 1.00000 0.250000
\(17\) 4.63902 1.12513 0.562564 0.826754i \(-0.309815\pi\)
0.562564 + 0.826754i \(0.309815\pi\)
\(18\) −5.61192 −1.32274
\(19\) 1.16072 0.266288 0.133144 0.991097i \(-0.457493\pi\)
0.133144 + 0.991097i \(0.457493\pi\)
\(20\) 1.73622 0.388231
\(21\) 2.84579 0.621002
\(22\) 5.59748 1.19339
\(23\) 8.33406 1.73777 0.868886 0.495012i \(-0.164836\pi\)
0.868886 + 0.495012i \(0.164836\pi\)
\(24\) 2.93461 0.599024
\(25\) −1.98553 −0.397106
\(26\) 5.07738 0.995756
\(27\) −7.66495 −1.47512
\(28\) −0.969734 −0.183262
\(29\) −5.44758 −1.01159 −0.505795 0.862654i \(-0.668801\pi\)
−0.505795 + 0.862654i \(0.668801\pi\)
\(30\) 5.09513 0.930239
\(31\) 6.78772 1.21911 0.609555 0.792744i \(-0.291348\pi\)
0.609555 + 0.792744i \(0.291348\pi\)
\(32\) −1.00000 −0.176777
\(33\) 16.4264 2.85947
\(34\) −4.63902 −0.795585
\(35\) −1.68367 −0.284593
\(36\) 5.61192 0.935320
\(37\) −11.1148 −1.82727 −0.913633 0.406539i \(-0.866735\pi\)
−0.913633 + 0.406539i \(0.866735\pi\)
\(38\) −1.16072 −0.188294
\(39\) 14.9001 2.38593
\(40\) −1.73622 −0.274521
\(41\) −5.20560 −0.812978 −0.406489 0.913656i \(-0.633247\pi\)
−0.406489 + 0.913656i \(0.633247\pi\)
\(42\) −2.84579 −0.439114
\(43\) 0.841312 0.128299 0.0641494 0.997940i \(-0.479567\pi\)
0.0641494 + 0.997940i \(0.479567\pi\)
\(44\) −5.59748 −0.843851
\(45\) 9.74354 1.45248
\(46\) −8.33406 −1.22879
\(47\) −0.998598 −0.145660 −0.0728302 0.997344i \(-0.523203\pi\)
−0.0728302 + 0.997344i \(0.523203\pi\)
\(48\) −2.93461 −0.423574
\(49\) −6.05962 −0.865660
\(50\) 1.98553 0.280796
\(51\) −13.6137 −1.90630
\(52\) −5.07738 −0.704106
\(53\) −2.85680 −0.392412 −0.196206 0.980563i \(-0.562862\pi\)
−0.196206 + 0.980563i \(0.562862\pi\)
\(54\) 7.66495 1.04307
\(55\) −9.71846 −1.31044
\(56\) 0.969734 0.129586
\(57\) −3.40627 −0.451171
\(58\) 5.44758 0.715303
\(59\) 6.29475 0.819507 0.409753 0.912196i \(-0.365615\pi\)
0.409753 + 0.912196i \(0.365615\pi\)
\(60\) −5.09513 −0.657779
\(61\) −3.58449 −0.458947 −0.229474 0.973315i \(-0.573700\pi\)
−0.229474 + 0.973315i \(0.573700\pi\)
\(62\) −6.78772 −0.862041
\(63\) −5.44207 −0.685636
\(64\) 1.00000 0.125000
\(65\) −8.81546 −1.09342
\(66\) −16.4264 −2.02195
\(67\) 8.13548 0.993907 0.496953 0.867777i \(-0.334452\pi\)
0.496953 + 0.867777i \(0.334452\pi\)
\(68\) 4.63902 0.562564
\(69\) −24.4572 −2.94430
\(70\) 1.68367 0.201237
\(71\) −9.51758 −1.12953 −0.564765 0.825252i \(-0.691033\pi\)
−0.564765 + 0.825252i \(0.691033\pi\)
\(72\) −5.61192 −0.661371
\(73\) 8.69676 1.01788 0.508939 0.860802i \(-0.330038\pi\)
0.508939 + 0.860802i \(0.330038\pi\)
\(74\) 11.1148 1.29207
\(75\) 5.82675 0.672815
\(76\) 1.16072 0.133144
\(77\) 5.42806 0.618585
\(78\) −14.9001 −1.68710
\(79\) 13.9628 1.57094 0.785469 0.618901i \(-0.212422\pi\)
0.785469 + 0.618901i \(0.212422\pi\)
\(80\) 1.73622 0.194116
\(81\) 5.65787 0.628652
\(82\) 5.20560 0.574862
\(83\) −17.3624 −1.90577 −0.952884 0.303334i \(-0.901900\pi\)
−0.952884 + 0.303334i \(0.901900\pi\)
\(84\) 2.84579 0.310501
\(85\) 8.05437 0.873619
\(86\) −0.841312 −0.0907210
\(87\) 15.9865 1.71393
\(88\) 5.59748 0.596693
\(89\) −7.79136 −0.825882 −0.412941 0.910758i \(-0.635498\pi\)
−0.412941 + 0.910758i \(0.635498\pi\)
\(90\) −9.74354 −1.02706
\(91\) 4.92370 0.516144
\(92\) 8.33406 0.868886
\(93\) −19.9193 −2.06553
\(94\) 0.998598 0.102997
\(95\) 2.01527 0.206763
\(96\) 2.93461 0.299512
\(97\) −1.51463 −0.153787 −0.0768937 0.997039i \(-0.524500\pi\)
−0.0768937 + 0.997039i \(0.524500\pi\)
\(98\) 6.05962 0.612114
\(99\) −31.4126 −3.15708
\(100\) −1.98553 −0.198553
\(101\) −1.08327 −0.107789 −0.0538946 0.998547i \(-0.517164\pi\)
−0.0538946 + 0.998547i \(0.517164\pi\)
\(102\) 13.6137 1.34796
\(103\) 0.0218735 0.00215526 0.00107763 0.999999i \(-0.499657\pi\)
0.00107763 + 0.999999i \(0.499657\pi\)
\(104\) 5.07738 0.497878
\(105\) 4.94092 0.482184
\(106\) 2.85680 0.277477
\(107\) 12.2708 1.18626 0.593131 0.805106i \(-0.297892\pi\)
0.593131 + 0.805106i \(0.297892\pi\)
\(108\) −7.66495 −0.737560
\(109\) −1.36902 −0.131128 −0.0655641 0.997848i \(-0.520885\pi\)
−0.0655641 + 0.997848i \(0.520885\pi\)
\(110\) 9.71846 0.926619
\(111\) 32.6177 3.09593
\(112\) −0.969734 −0.0916312
\(113\) −2.41954 −0.227611 −0.113806 0.993503i \(-0.536304\pi\)
−0.113806 + 0.993503i \(0.536304\pi\)
\(114\) 3.40627 0.319026
\(115\) 14.4698 1.34932
\(116\) −5.44758 −0.505795
\(117\) −28.4938 −2.63425
\(118\) −6.29475 −0.579479
\(119\) −4.49861 −0.412387
\(120\) 5.09513 0.465120
\(121\) 20.3317 1.84834
\(122\) 3.58449 0.324525
\(123\) 15.2764 1.37742
\(124\) 6.78772 0.609555
\(125\) −12.1284 −1.08480
\(126\) 5.44207 0.484818
\(127\) 2.56016 0.227178 0.113589 0.993528i \(-0.463765\pi\)
0.113589 + 0.993528i \(0.463765\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.46892 −0.217376
\(130\) 8.81546 0.773167
\(131\) −1.62071 −0.141602 −0.0708009 0.997490i \(-0.522555\pi\)
−0.0708009 + 0.997490i \(0.522555\pi\)
\(132\) 16.4264 1.42973
\(133\) −1.12559 −0.0976013
\(134\) −8.13548 −0.702798
\(135\) −13.3081 −1.14538
\(136\) −4.63902 −0.397792
\(137\) 4.22758 0.361187 0.180593 0.983558i \(-0.442198\pi\)
0.180593 + 0.983558i \(0.442198\pi\)
\(138\) 24.4572 2.08194
\(139\) −12.2166 −1.03620 −0.518098 0.855321i \(-0.673360\pi\)
−0.518098 + 0.855321i \(0.673360\pi\)
\(140\) −1.68367 −0.142296
\(141\) 2.93049 0.246792
\(142\) 9.51758 0.798698
\(143\) 28.4205 2.37664
\(144\) 5.61192 0.467660
\(145\) −9.45822 −0.785462
\(146\) −8.69676 −0.719749
\(147\) 17.7826 1.46668
\(148\) −11.1148 −0.913633
\(149\) −3.67818 −0.301328 −0.150664 0.988585i \(-0.548141\pi\)
−0.150664 + 0.988585i \(0.548141\pi\)
\(150\) −5.82675 −0.475752
\(151\) −0.832853 −0.0677766 −0.0338883 0.999426i \(-0.510789\pi\)
−0.0338883 + 0.999426i \(0.510789\pi\)
\(152\) −1.16072 −0.0941471
\(153\) 26.0338 2.10471
\(154\) −5.42806 −0.437406
\(155\) 11.7850 0.946594
\(156\) 14.9001 1.19296
\(157\) 15.6537 1.24930 0.624650 0.780905i \(-0.285242\pi\)
0.624650 + 0.780905i \(0.285242\pi\)
\(158\) −13.9628 −1.11082
\(159\) 8.38359 0.664862
\(160\) −1.73622 −0.137260
\(161\) −8.08182 −0.636937
\(162\) −5.65787 −0.444524
\(163\) −10.3750 −0.812637 −0.406318 0.913732i \(-0.633188\pi\)
−0.406318 + 0.913732i \(0.633188\pi\)
\(164\) −5.20560 −0.406489
\(165\) 28.5199 2.22027
\(166\) 17.3624 1.34758
\(167\) 0.599480 0.0463892 0.0231946 0.999731i \(-0.492616\pi\)
0.0231946 + 0.999731i \(0.492616\pi\)
\(168\) −2.84579 −0.219557
\(169\) 12.7798 0.983058
\(170\) −8.05437 −0.617742
\(171\) 6.51389 0.498129
\(172\) 0.841312 0.0641494
\(173\) −13.4289 −1.02098 −0.510489 0.859884i \(-0.670536\pi\)
−0.510489 + 0.859884i \(0.670536\pi\)
\(174\) −15.9865 −1.21193
\(175\) 1.92544 0.145549
\(176\) −5.59748 −0.421926
\(177\) −18.4726 −1.38849
\(178\) 7.79136 0.583987
\(179\) −6.70467 −0.501131 −0.250565 0.968100i \(-0.580616\pi\)
−0.250565 + 0.968100i \(0.580616\pi\)
\(180\) 9.74354 0.726241
\(181\) −21.0383 −1.56377 −0.781883 0.623425i \(-0.785741\pi\)
−0.781883 + 0.623425i \(0.785741\pi\)
\(182\) −4.92370 −0.364969
\(183\) 10.5191 0.777593
\(184\) −8.33406 −0.614395
\(185\) −19.2978 −1.41880
\(186\) 19.9193 1.46055
\(187\) −25.9668 −1.89888
\(188\) −0.998598 −0.0728302
\(189\) 7.43296 0.540668
\(190\) −2.01527 −0.146203
\(191\) −17.6389 −1.27631 −0.638153 0.769910i \(-0.720301\pi\)
−0.638153 + 0.769910i \(0.720301\pi\)
\(192\) −2.93461 −0.211787
\(193\) −8.84040 −0.636346 −0.318173 0.948033i \(-0.603069\pi\)
−0.318173 + 0.948033i \(0.603069\pi\)
\(194\) 1.51463 0.108744
\(195\) 25.8699 1.85258
\(196\) −6.05962 −0.432830
\(197\) 6.41973 0.457387 0.228693 0.973499i \(-0.426555\pi\)
0.228693 + 0.973499i \(0.426555\pi\)
\(198\) 31.4126 2.23239
\(199\) 16.7976 1.19075 0.595375 0.803448i \(-0.297003\pi\)
0.595375 + 0.803448i \(0.297003\pi\)
\(200\) 1.98553 0.140398
\(201\) −23.8744 −1.68397
\(202\) 1.08327 0.0762185
\(203\) 5.28270 0.370773
\(204\) −13.6137 −0.953149
\(205\) −9.03807 −0.631246
\(206\) −0.0218735 −0.00152400
\(207\) 46.7701 3.25075
\(208\) −5.07738 −0.352053
\(209\) −6.49712 −0.449415
\(210\) −4.94092 −0.340956
\(211\) 15.0713 1.03755 0.518775 0.854911i \(-0.326388\pi\)
0.518775 + 0.854911i \(0.326388\pi\)
\(212\) −2.85680 −0.196206
\(213\) 27.9304 1.91376
\(214\) −12.2708 −0.838814
\(215\) 1.46070 0.0996192
\(216\) 7.66495 0.521534
\(217\) −6.58228 −0.446834
\(218\) 1.36902 0.0927216
\(219\) −25.5216 −1.72459
\(220\) −9.71846 −0.655219
\(221\) −23.5540 −1.58442
\(222\) −32.6177 −2.18915
\(223\) −20.7382 −1.38873 −0.694366 0.719622i \(-0.744315\pi\)
−0.694366 + 0.719622i \(0.744315\pi\)
\(224\) 0.969734 0.0647931
\(225\) −11.1426 −0.742842
\(226\) 2.41954 0.160946
\(227\) 17.3460 1.15129 0.575646 0.817699i \(-0.304751\pi\)
0.575646 + 0.817699i \(0.304751\pi\)
\(228\) −3.40627 −0.225586
\(229\) 20.7031 1.36810 0.684049 0.729436i \(-0.260217\pi\)
0.684049 + 0.729436i \(0.260217\pi\)
\(230\) −14.4698 −0.954110
\(231\) −15.9292 −1.04807
\(232\) 5.44758 0.357651
\(233\) 9.04071 0.592277 0.296138 0.955145i \(-0.404301\pi\)
0.296138 + 0.955145i \(0.404301\pi\)
\(234\) 28.4938 1.86270
\(235\) −1.73379 −0.113100
\(236\) 6.29475 0.409753
\(237\) −40.9753 −2.66163
\(238\) 4.49861 0.291602
\(239\) −1.12309 −0.0726465 −0.0363232 0.999340i \(-0.511565\pi\)
−0.0363232 + 0.999340i \(0.511565\pi\)
\(240\) −5.09513 −0.328889
\(241\) −26.8969 −1.73258 −0.866291 0.499540i \(-0.833502\pi\)
−0.866291 + 0.499540i \(0.833502\pi\)
\(242\) −20.3317 −1.30697
\(243\) 6.39123 0.409998
\(244\) −3.58449 −0.229474
\(245\) −10.5208 −0.672152
\(246\) −15.2764 −0.973986
\(247\) −5.89343 −0.374990
\(248\) −6.78772 −0.431021
\(249\) 50.9518 3.22894
\(250\) 12.1284 0.767070
\(251\) −14.5477 −0.918246 −0.459123 0.888373i \(-0.651836\pi\)
−0.459123 + 0.888373i \(0.651836\pi\)
\(252\) −5.44207 −0.342818
\(253\) −46.6497 −2.93284
\(254\) −2.56016 −0.160639
\(255\) −23.6364 −1.48017
\(256\) 1.00000 0.0625000
\(257\) −1.83563 −0.114503 −0.0572517 0.998360i \(-0.518234\pi\)
−0.0572517 + 0.998360i \(0.518234\pi\)
\(258\) 2.46892 0.153708
\(259\) 10.7784 0.669739
\(260\) −8.81546 −0.546711
\(261\) −30.5714 −1.89232
\(262\) 1.62071 0.100128
\(263\) 4.52022 0.278729 0.139364 0.990241i \(-0.455494\pi\)
0.139364 + 0.990241i \(0.455494\pi\)
\(264\) −16.4264 −1.01097
\(265\) −4.96004 −0.304693
\(266\) 1.12559 0.0690145
\(267\) 22.8646 1.39929
\(268\) 8.13548 0.496953
\(269\) 15.9214 0.970746 0.485373 0.874307i \(-0.338684\pi\)
0.485373 + 0.874307i \(0.338684\pi\)
\(270\) 13.3081 0.809903
\(271\) 26.9178 1.63514 0.817569 0.575831i \(-0.195321\pi\)
0.817569 + 0.575831i \(0.195321\pi\)
\(272\) 4.63902 0.281282
\(273\) −14.4491 −0.874501
\(274\) −4.22758 −0.255397
\(275\) 11.1140 0.670197
\(276\) −24.4572 −1.47215
\(277\) −19.0216 −1.14290 −0.571448 0.820638i \(-0.693618\pi\)
−0.571448 + 0.820638i \(0.693618\pi\)
\(278\) 12.2166 0.732701
\(279\) 38.0921 2.28052
\(280\) 1.68367 0.100619
\(281\) 33.4586 1.99597 0.997986 0.0634286i \(-0.0202035\pi\)
0.997986 + 0.0634286i \(0.0202035\pi\)
\(282\) −2.93049 −0.174508
\(283\) −12.1836 −0.724237 −0.362118 0.932132i \(-0.617946\pi\)
−0.362118 + 0.932132i \(0.617946\pi\)
\(284\) −9.51758 −0.564765
\(285\) −5.91404 −0.350317
\(286\) −28.4205 −1.68054
\(287\) 5.04804 0.297976
\(288\) −5.61192 −0.330685
\(289\) 4.52048 0.265911
\(290\) 9.45822 0.555406
\(291\) 4.44484 0.260561
\(292\) 8.69676 0.508939
\(293\) 9.28817 0.542620 0.271310 0.962492i \(-0.412543\pi\)
0.271310 + 0.962492i \(0.412543\pi\)
\(294\) −17.7826 −1.03710
\(295\) 10.9291 0.636316
\(296\) 11.1148 0.646036
\(297\) 42.9044 2.48957
\(298\) 3.67818 0.213071
\(299\) −42.3152 −2.44715
\(300\) 5.82675 0.336408
\(301\) −0.815848 −0.0470247
\(302\) 0.832853 0.0479253
\(303\) 3.17897 0.182627
\(304\) 1.16072 0.0665721
\(305\) −6.22348 −0.356355
\(306\) −26.0338 −1.48825
\(307\) −5.68571 −0.324501 −0.162250 0.986750i \(-0.551875\pi\)
−0.162250 + 0.986750i \(0.551875\pi\)
\(308\) 5.42806 0.309292
\(309\) −0.0641901 −0.00365165
\(310\) −11.7850 −0.669343
\(311\) −18.2473 −1.03471 −0.517355 0.855771i \(-0.673083\pi\)
−0.517355 + 0.855771i \(0.673083\pi\)
\(312\) −14.9001 −0.843552
\(313\) 8.12769 0.459404 0.229702 0.973261i \(-0.426225\pi\)
0.229702 + 0.973261i \(0.426225\pi\)
\(314\) −15.6537 −0.883388
\(315\) −9.44864 −0.532370
\(316\) 13.9628 0.785469
\(317\) 20.5473 1.15405 0.577026 0.816726i \(-0.304213\pi\)
0.577026 + 0.816726i \(0.304213\pi\)
\(318\) −8.38359 −0.470128
\(319\) 30.4927 1.70726
\(320\) 1.73622 0.0970578
\(321\) −36.0099 −2.00988
\(322\) 8.08182 0.450382
\(323\) 5.38462 0.299608
\(324\) 5.65787 0.314326
\(325\) 10.0813 0.559209
\(326\) 10.3750 0.574621
\(327\) 4.01753 0.222170
\(328\) 5.20560 0.287431
\(329\) 0.968374 0.0533882
\(330\) −28.5199 −1.56997
\(331\) −19.4503 −1.06908 −0.534541 0.845142i \(-0.679516\pi\)
−0.534541 + 0.845142i \(0.679516\pi\)
\(332\) −17.3624 −0.952884
\(333\) −62.3755 −3.41816
\(334\) −0.599480 −0.0328021
\(335\) 14.1250 0.771731
\(336\) 2.84579 0.155250
\(337\) −8.05826 −0.438961 −0.219481 0.975617i \(-0.570436\pi\)
−0.219481 + 0.975617i \(0.570436\pi\)
\(338\) −12.7798 −0.695127
\(339\) 7.10041 0.385641
\(340\) 8.05437 0.436809
\(341\) −37.9941 −2.05750
\(342\) −6.51389 −0.352231
\(343\) 12.6643 0.683811
\(344\) −0.841312 −0.0453605
\(345\) −42.4632 −2.28614
\(346\) 13.4289 0.721941
\(347\) 27.7871 1.49169 0.745846 0.666119i \(-0.232046\pi\)
0.745846 + 0.666119i \(0.232046\pi\)
\(348\) 15.9865 0.856967
\(349\) −22.2523 −1.19114 −0.595568 0.803305i \(-0.703073\pi\)
−0.595568 + 0.803305i \(0.703073\pi\)
\(350\) −1.92544 −0.102919
\(351\) 38.9179 2.07728
\(352\) 5.59748 0.298346
\(353\) 17.8198 0.948451 0.474226 0.880403i \(-0.342728\pi\)
0.474226 + 0.880403i \(0.342728\pi\)
\(354\) 18.4726 0.981809
\(355\) −16.5246 −0.877037
\(356\) −7.79136 −0.412941
\(357\) 13.2017 0.698706
\(358\) 6.70467 0.354353
\(359\) −32.7383 −1.72786 −0.863930 0.503611i \(-0.832004\pi\)
−0.863930 + 0.503611i \(0.832004\pi\)
\(360\) −9.74354 −0.513530
\(361\) −17.6527 −0.929091
\(362\) 21.0383 1.10575
\(363\) −59.6656 −3.13163
\(364\) 4.92370 0.258072
\(365\) 15.0995 0.790344
\(366\) −10.5191 −0.549841
\(367\) −35.4344 −1.84966 −0.924829 0.380383i \(-0.875792\pi\)
−0.924829 + 0.380383i \(0.875792\pi\)
\(368\) 8.33406 0.434443
\(369\) −29.2134 −1.52079
\(370\) 19.2978 1.00325
\(371\) 2.77034 0.143829
\(372\) −19.9193 −1.03277
\(373\) 10.5647 0.547021 0.273510 0.961869i \(-0.411815\pi\)
0.273510 + 0.961869i \(0.411815\pi\)
\(374\) 25.9668 1.34271
\(375\) 35.5922 1.83797
\(376\) 0.998598 0.0514987
\(377\) 27.6594 1.42453
\(378\) −7.43296 −0.382310
\(379\) −17.8530 −0.917046 −0.458523 0.888683i \(-0.651621\pi\)
−0.458523 + 0.888683i \(0.651621\pi\)
\(380\) 2.01527 0.103381
\(381\) −7.51307 −0.384906
\(382\) 17.6389 0.902484
\(383\) 21.5663 1.10199 0.550993 0.834510i \(-0.314249\pi\)
0.550993 + 0.834510i \(0.314249\pi\)
\(384\) 2.93461 0.149756
\(385\) 9.42432 0.480308
\(386\) 8.84040 0.449964
\(387\) 4.72137 0.240001
\(388\) −1.51463 −0.0768937
\(389\) −4.28700 −0.217359 −0.108680 0.994077i \(-0.534662\pi\)
−0.108680 + 0.994077i \(0.534662\pi\)
\(390\) −25.8699 −1.30997
\(391\) 38.6619 1.95521
\(392\) 6.05962 0.306057
\(393\) 4.75614 0.239915
\(394\) −6.41973 −0.323421
\(395\) 24.2425 1.21977
\(396\) −31.4126 −1.57854
\(397\) 21.9150 1.09988 0.549942 0.835203i \(-0.314650\pi\)
0.549942 + 0.835203i \(0.314650\pi\)
\(398\) −16.7976 −0.841988
\(399\) 3.30317 0.165365
\(400\) −1.98553 −0.0992765
\(401\) −12.2197 −0.610225 −0.305112 0.952316i \(-0.598694\pi\)
−0.305112 + 0.952316i \(0.598694\pi\)
\(402\) 23.8744 1.19075
\(403\) −34.4638 −1.71677
\(404\) −1.08327 −0.0538946
\(405\) 9.82332 0.488125
\(406\) −5.28270 −0.262176
\(407\) 62.2150 3.08388
\(408\) 13.6137 0.673978
\(409\) 12.8807 0.636909 0.318454 0.947938i \(-0.396836\pi\)
0.318454 + 0.947938i \(0.396836\pi\)
\(410\) 9.03807 0.446359
\(411\) −12.4063 −0.611957
\(412\) 0.0218735 0.00107763
\(413\) −6.10423 −0.300370
\(414\) −46.7701 −2.29862
\(415\) −30.1450 −1.47976
\(416\) 5.07738 0.248939
\(417\) 35.8508 1.75562
\(418\) 6.49712 0.317785
\(419\) 20.2844 0.990957 0.495479 0.868620i \(-0.334993\pi\)
0.495479 + 0.868620i \(0.334993\pi\)
\(420\) 4.94092 0.241092
\(421\) −18.3081 −0.892284 −0.446142 0.894962i \(-0.647202\pi\)
−0.446142 + 0.894962i \(0.647202\pi\)
\(422\) −15.0713 −0.733659
\(423\) −5.60405 −0.272478
\(424\) 2.85680 0.138739
\(425\) −9.21091 −0.446795
\(426\) −27.9304 −1.35323
\(427\) 3.47600 0.168216
\(428\) 12.2708 0.593131
\(429\) −83.4030 −4.02673
\(430\) −1.46070 −0.0704414
\(431\) 7.43296 0.358033 0.179017 0.983846i \(-0.442708\pi\)
0.179017 + 0.983846i \(0.442708\pi\)
\(432\) −7.66495 −0.368780
\(433\) −2.68774 −0.129165 −0.0645823 0.997912i \(-0.520571\pi\)
−0.0645823 + 0.997912i \(0.520571\pi\)
\(434\) 6.58228 0.315960
\(435\) 27.7561 1.33081
\(436\) −1.36902 −0.0655641
\(437\) 9.67354 0.462748
\(438\) 25.5216 1.21947
\(439\) −40.8831 −1.95124 −0.975621 0.219463i \(-0.929569\pi\)
−0.975621 + 0.219463i \(0.929569\pi\)
\(440\) 9.71846 0.463310
\(441\) −34.0061 −1.61934
\(442\) 23.5540 1.12035
\(443\) 3.69104 0.175367 0.0876833 0.996148i \(-0.472054\pi\)
0.0876833 + 0.996148i \(0.472054\pi\)
\(444\) 32.6177 1.54797
\(445\) −13.5275 −0.641266
\(446\) 20.7382 0.981982
\(447\) 10.7940 0.510539
\(448\) −0.969734 −0.0458156
\(449\) 17.2332 0.813287 0.406644 0.913587i \(-0.366699\pi\)
0.406644 + 0.913587i \(0.366699\pi\)
\(450\) 11.1426 0.525269
\(451\) 29.1382 1.37206
\(452\) −2.41954 −0.113806
\(453\) 2.44410 0.114834
\(454\) −17.3460 −0.814087
\(455\) 8.54864 0.400767
\(456\) 3.40627 0.159513
\(457\) 39.1433 1.83105 0.915524 0.402264i \(-0.131777\pi\)
0.915524 + 0.402264i \(0.131777\pi\)
\(458\) −20.7031 −0.967391
\(459\) −35.5579 −1.65970
\(460\) 14.4698 0.674658
\(461\) −7.39099 −0.344233 −0.172116 0.985077i \(-0.555061\pi\)
−0.172116 + 0.985077i \(0.555061\pi\)
\(462\) 15.9292 0.741095
\(463\) 26.8790 1.24917 0.624586 0.780956i \(-0.285268\pi\)
0.624586 + 0.780956i \(0.285268\pi\)
\(464\) −5.44758 −0.252898
\(465\) −34.5843 −1.60381
\(466\) −9.04071 −0.418803
\(467\) −21.2586 −0.983730 −0.491865 0.870671i \(-0.663685\pi\)
−0.491865 + 0.870671i \(0.663685\pi\)
\(468\) −28.4938 −1.31713
\(469\) −7.88924 −0.364291
\(470\) 1.73379 0.0799737
\(471\) −45.9374 −2.11668
\(472\) −6.29475 −0.289739
\(473\) −4.70922 −0.216530
\(474\) 40.9753 1.88206
\(475\) −2.30465 −0.105745
\(476\) −4.49861 −0.206194
\(477\) −16.0321 −0.734061
\(478\) 1.12309 0.0513688
\(479\) 32.8925 1.50290 0.751448 0.659792i \(-0.229356\pi\)
0.751448 + 0.659792i \(0.229356\pi\)
\(480\) 5.09513 0.232560
\(481\) 56.4342 2.57318
\(482\) 26.8969 1.22512
\(483\) 23.7170 1.07916
\(484\) 20.3317 0.924170
\(485\) −2.62973 −0.119410
\(486\) −6.39123 −0.289912
\(487\) 38.1817 1.73018 0.865088 0.501620i \(-0.167262\pi\)
0.865088 + 0.501620i \(0.167262\pi\)
\(488\) 3.58449 0.162262
\(489\) 30.4467 1.37685
\(490\) 10.5208 0.475283
\(491\) 37.9964 1.71475 0.857376 0.514691i \(-0.172093\pi\)
0.857376 + 0.514691i \(0.172093\pi\)
\(492\) 15.2764 0.688712
\(493\) −25.2714 −1.13817
\(494\) 5.89343 0.265158
\(495\) −54.5392 −2.45136
\(496\) 6.78772 0.304778
\(497\) 9.22952 0.414001
\(498\) −50.9518 −2.28320
\(499\) 19.9074 0.891176 0.445588 0.895238i \(-0.352995\pi\)
0.445588 + 0.895238i \(0.352995\pi\)
\(500\) −12.1284 −0.542400
\(501\) −1.75924 −0.0785970
\(502\) 14.5477 0.649298
\(503\) 8.32446 0.371169 0.185585 0.982628i \(-0.440582\pi\)
0.185585 + 0.982628i \(0.440582\pi\)
\(504\) 5.44207 0.242409
\(505\) −1.88080 −0.0836943
\(506\) 46.6497 2.07383
\(507\) −37.5036 −1.66559
\(508\) 2.56016 0.113589
\(509\) 20.3976 0.904106 0.452053 0.891991i \(-0.350692\pi\)
0.452053 + 0.891991i \(0.350692\pi\)
\(510\) 23.6364 1.04664
\(511\) −8.43354 −0.373078
\(512\) −1.00000 −0.0441942
\(513\) −8.89689 −0.392807
\(514\) 1.83563 0.0809661
\(515\) 0.0379773 0.00167348
\(516\) −2.46892 −0.108688
\(517\) 5.58963 0.245831
\(518\) −10.7784 −0.473577
\(519\) 39.4085 1.72984
\(520\) 8.81546 0.386583
\(521\) −34.4011 −1.50714 −0.753569 0.657369i \(-0.771669\pi\)
−0.753569 + 0.657369i \(0.771669\pi\)
\(522\) 30.5714 1.33807
\(523\) 38.5727 1.68667 0.843333 0.537391i \(-0.180590\pi\)
0.843333 + 0.537391i \(0.180590\pi\)
\(524\) −1.62071 −0.0708009
\(525\) −5.65040 −0.246604
\(526\) −4.52022 −0.197091
\(527\) 31.4884 1.37165
\(528\) 16.4264 0.714867
\(529\) 46.4566 2.01985
\(530\) 4.96004 0.215451
\(531\) 35.3256 1.53300
\(532\) −1.12559 −0.0488006
\(533\) 26.4308 1.14484
\(534\) −22.8646 −0.989447
\(535\) 21.3048 0.921087
\(536\) −8.13548 −0.351399
\(537\) 19.6756 0.849064
\(538\) −15.9214 −0.686421
\(539\) 33.9186 1.46098
\(540\) −13.3081 −0.572688
\(541\) 15.3445 0.659712 0.329856 0.944031i \(-0.393000\pi\)
0.329856 + 0.944031i \(0.393000\pi\)
\(542\) −26.9178 −1.15622
\(543\) 61.7392 2.64948
\(544\) −4.63902 −0.198896
\(545\) −2.37692 −0.101816
\(546\) 14.4491 0.618366
\(547\) −21.9635 −0.939089 −0.469545 0.882909i \(-0.655582\pi\)
−0.469545 + 0.882909i \(0.655582\pi\)
\(548\) 4.22758 0.180593
\(549\) −20.1159 −0.858525
\(550\) −11.1140 −0.473901
\(551\) −6.32314 −0.269375
\(552\) 24.4572 1.04097
\(553\) −13.5402 −0.575788
\(554\) 19.0216 0.808150
\(555\) 56.6315 2.40387
\(556\) −12.2166 −0.518098
\(557\) 15.5796 0.660130 0.330065 0.943958i \(-0.392929\pi\)
0.330065 + 0.943958i \(0.392929\pi\)
\(558\) −38.0921 −1.61257
\(559\) −4.27166 −0.180672
\(560\) −1.68367 −0.0711482
\(561\) 76.2023 3.21726
\(562\) −33.4586 −1.41137
\(563\) 6.33660 0.267056 0.133528 0.991045i \(-0.457369\pi\)
0.133528 + 0.991045i \(0.457369\pi\)
\(564\) 2.93049 0.123396
\(565\) −4.20086 −0.176732
\(566\) 12.1836 0.512113
\(567\) −5.48663 −0.230417
\(568\) 9.51758 0.399349
\(569\) −7.83139 −0.328309 −0.164154 0.986435i \(-0.552490\pi\)
−0.164154 + 0.986435i \(0.552490\pi\)
\(570\) 5.91404 0.247712
\(571\) −18.9693 −0.793839 −0.396919 0.917853i \(-0.629921\pi\)
−0.396919 + 0.917853i \(0.629921\pi\)
\(572\) 28.4205 1.18832
\(573\) 51.7632 2.16244
\(574\) −5.04804 −0.210701
\(575\) −16.5475 −0.690080
\(576\) 5.61192 0.233830
\(577\) −24.5903 −1.02371 −0.511853 0.859073i \(-0.671041\pi\)
−0.511853 + 0.859073i \(0.671041\pi\)
\(578\) −4.52048 −0.188027
\(579\) 25.9431 1.07816
\(580\) −9.45822 −0.392731
\(581\) 16.8369 0.698511
\(582\) −4.44484 −0.184245
\(583\) 15.9909 0.662275
\(584\) −8.69676 −0.359874
\(585\) −49.4716 −2.04540
\(586\) −9.28817 −0.383691
\(587\) 47.0341 1.94131 0.970653 0.240483i \(-0.0773057\pi\)
0.970653 + 0.240483i \(0.0773057\pi\)
\(588\) 17.7826 0.733342
\(589\) 7.87867 0.324635
\(590\) −10.9291 −0.449944
\(591\) −18.8394 −0.774948
\(592\) −11.1148 −0.456817
\(593\) 19.9052 0.817409 0.408705 0.912667i \(-0.365981\pi\)
0.408705 + 0.912667i \(0.365981\pi\)
\(594\) −42.9044 −1.76039
\(595\) −7.81059 −0.320203
\(596\) −3.67818 −0.150664
\(597\) −49.2944 −2.01748
\(598\) 42.3152 1.73040
\(599\) −29.5929 −1.20913 −0.604566 0.796555i \(-0.706653\pi\)
−0.604566 + 0.796555i \(0.706653\pi\)
\(600\) −5.82675 −0.237876
\(601\) −17.5753 −0.716913 −0.358457 0.933546i \(-0.616697\pi\)
−0.358457 + 0.933546i \(0.616697\pi\)
\(602\) 0.815848 0.0332515
\(603\) 45.6556 1.85924
\(604\) −0.832853 −0.0338883
\(605\) 35.3004 1.43517
\(606\) −3.17897 −0.129137
\(607\) 34.7179 1.40916 0.704578 0.709627i \(-0.251136\pi\)
0.704578 + 0.709627i \(0.251136\pi\)
\(608\) −1.16072 −0.0470736
\(609\) −15.5027 −0.628199
\(610\) 6.22348 0.251981
\(611\) 5.07026 0.205121
\(612\) 26.0338 1.05235
\(613\) −10.0265 −0.404967 −0.202484 0.979286i \(-0.564901\pi\)
−0.202484 + 0.979286i \(0.564901\pi\)
\(614\) 5.68571 0.229457
\(615\) 26.5232 1.06952
\(616\) −5.42806 −0.218703
\(617\) 23.7495 0.956120 0.478060 0.878327i \(-0.341340\pi\)
0.478060 + 0.878327i \(0.341340\pi\)
\(618\) 0.0641901 0.00258211
\(619\) 19.9963 0.803720 0.401860 0.915701i \(-0.368364\pi\)
0.401860 + 0.915701i \(0.368364\pi\)
\(620\) 11.7850 0.473297
\(621\) −63.8802 −2.56342
\(622\) 18.2473 0.731651
\(623\) 7.55554 0.302706
\(624\) 14.9001 0.596482
\(625\) −11.1300 −0.445201
\(626\) −8.12769 −0.324848
\(627\) 19.0665 0.761443
\(628\) 15.6537 0.624650
\(629\) −51.5619 −2.05591
\(630\) 9.44864 0.376443
\(631\) 22.2279 0.884877 0.442439 0.896799i \(-0.354113\pi\)
0.442439 + 0.896799i \(0.354113\pi\)
\(632\) −13.9628 −0.555410
\(633\) −44.2283 −1.75792
\(634\) −20.5473 −0.816037
\(635\) 4.44501 0.176395
\(636\) 8.38359 0.332431
\(637\) 30.7670 1.21903
\(638\) −30.4927 −1.20722
\(639\) −53.4119 −2.11294
\(640\) −1.73622 −0.0686302
\(641\) 11.5431 0.455926 0.227963 0.973670i \(-0.426794\pi\)
0.227963 + 0.973670i \(0.426794\pi\)
\(642\) 36.0099 1.42120
\(643\) −45.0879 −1.77809 −0.889047 0.457816i \(-0.848632\pi\)
−0.889047 + 0.457816i \(0.848632\pi\)
\(644\) −8.08182 −0.318468
\(645\) −4.28659 −0.168784
\(646\) −5.38462 −0.211855
\(647\) 5.54638 0.218051 0.109025 0.994039i \(-0.465227\pi\)
0.109025 + 0.994039i \(0.465227\pi\)
\(648\) −5.65787 −0.222262
\(649\) −35.2347 −1.38308
\(650\) −10.0813 −0.395421
\(651\) 19.3164 0.757070
\(652\) −10.3750 −0.406318
\(653\) 46.1850 1.80736 0.903679 0.428211i \(-0.140856\pi\)
0.903679 + 0.428211i \(0.140856\pi\)
\(654\) −4.01753 −0.157098
\(655\) −2.81391 −0.109948
\(656\) −5.20560 −0.203244
\(657\) 48.8055 1.90408
\(658\) −0.968374 −0.0377511
\(659\) −10.2559 −0.399514 −0.199757 0.979845i \(-0.564015\pi\)
−0.199757 + 0.979845i \(0.564015\pi\)
\(660\) 28.5199 1.11013
\(661\) 33.1065 1.28769 0.643847 0.765154i \(-0.277337\pi\)
0.643847 + 0.765154i \(0.277337\pi\)
\(662\) 19.4503 0.755956
\(663\) 69.1219 2.68447
\(664\) 17.3624 0.673791
\(665\) −1.95428 −0.0757837
\(666\) 62.3755 2.41700
\(667\) −45.4005 −1.75791
\(668\) 0.599480 0.0231946
\(669\) 60.8585 2.35292
\(670\) −14.1250 −0.545696
\(671\) 20.0641 0.774566
\(672\) −2.84579 −0.109779
\(673\) 39.6904 1.52995 0.764977 0.644057i \(-0.222750\pi\)
0.764977 + 0.644057i \(0.222750\pi\)
\(674\) 8.05826 0.310392
\(675\) 15.2190 0.585780
\(676\) 12.7798 0.491529
\(677\) 26.2019 1.00702 0.503510 0.863989i \(-0.332042\pi\)
0.503510 + 0.863989i \(0.332042\pi\)
\(678\) −7.10041 −0.272689
\(679\) 1.46879 0.0563669
\(680\) −8.05437 −0.308871
\(681\) −50.9036 −1.95063
\(682\) 37.9941 1.45487
\(683\) 30.1594 1.15402 0.577009 0.816738i \(-0.304220\pi\)
0.577009 + 0.816738i \(0.304220\pi\)
\(684\) 6.51389 0.249065
\(685\) 7.34002 0.280448
\(686\) −12.6643 −0.483527
\(687\) −60.7554 −2.31796
\(688\) 0.841312 0.0320747
\(689\) 14.5051 0.552599
\(690\) 42.4632 1.61654
\(691\) 40.0267 1.52269 0.761343 0.648349i \(-0.224540\pi\)
0.761343 + 0.648349i \(0.224540\pi\)
\(692\) −13.4289 −0.510489
\(693\) 30.4618 1.15715
\(694\) −27.7871 −1.05479
\(695\) −21.2107 −0.804567
\(696\) −15.9865 −0.605967
\(697\) −24.1489 −0.914703
\(698\) 22.2523 0.842260
\(699\) −26.5309 −1.00349
\(700\) 1.92544 0.0727746
\(701\) −29.3923 −1.11013 −0.555067 0.831806i \(-0.687307\pi\)
−0.555067 + 0.831806i \(0.687307\pi\)
\(702\) −38.9179 −1.46886
\(703\) −12.9012 −0.486580
\(704\) −5.59748 −0.210963
\(705\) 5.08799 0.191625
\(706\) −17.8198 −0.670656
\(707\) 1.05048 0.0395074
\(708\) −18.4726 −0.694244
\(709\) 4.92938 0.185127 0.0925634 0.995707i \(-0.470494\pi\)
0.0925634 + 0.995707i \(0.470494\pi\)
\(710\) 16.5246 0.620159
\(711\) 78.3581 2.93866
\(712\) 7.79136 0.291993
\(713\) 56.5693 2.11854
\(714\) −13.2017 −0.494060
\(715\) 49.3443 1.84537
\(716\) −6.70467 −0.250565
\(717\) 3.29582 0.123085
\(718\) 32.7383 1.22178
\(719\) 41.5432 1.54930 0.774650 0.632390i \(-0.217926\pi\)
0.774650 + 0.632390i \(0.217926\pi\)
\(720\) 9.74354 0.363120
\(721\) −0.0212115 −0.000789956 0
\(722\) 17.6527 0.656966
\(723\) 78.9318 2.93551
\(724\) −21.0383 −0.781883
\(725\) 10.8163 0.401709
\(726\) 59.6656 2.21440
\(727\) −41.9372 −1.55536 −0.777681 0.628659i \(-0.783604\pi\)
−0.777681 + 0.628659i \(0.783604\pi\)
\(728\) −4.92370 −0.182485
\(729\) −35.7294 −1.32331
\(730\) −15.0995 −0.558858
\(731\) 3.90286 0.144352
\(732\) 10.5191 0.388796
\(733\) −31.9386 −1.17968 −0.589839 0.807521i \(-0.700809\pi\)
−0.589839 + 0.807521i \(0.700809\pi\)
\(734\) 35.4344 1.30791
\(735\) 30.8745 1.13882
\(736\) −8.33406 −0.307198
\(737\) −45.5381 −1.67742
\(738\) 29.2134 1.07536
\(739\) 2.94365 0.108284 0.0541419 0.998533i \(-0.482758\pi\)
0.0541419 + 0.998533i \(0.482758\pi\)
\(740\) −19.2978 −0.709402
\(741\) 17.2949 0.635344
\(742\) −2.77034 −0.101702
\(743\) 28.7128 1.05337 0.526686 0.850060i \(-0.323434\pi\)
0.526686 + 0.850060i \(0.323434\pi\)
\(744\) 19.9193 0.730277
\(745\) −6.38614 −0.233970
\(746\) −10.5647 −0.386802
\(747\) −97.4362 −3.56501
\(748\) −25.9668 −0.949440
\(749\) −11.8994 −0.434794
\(750\) −35.5922 −1.29964
\(751\) −38.8152 −1.41638 −0.708192 0.706019i \(-0.750489\pi\)
−0.708192 + 0.706019i \(0.750489\pi\)
\(752\) −0.998598 −0.0364151
\(753\) 42.6919 1.55578
\(754\) −27.6594 −1.00730
\(755\) −1.44602 −0.0526260
\(756\) 7.43296 0.270334
\(757\) 5.40087 0.196298 0.0981490 0.995172i \(-0.468708\pi\)
0.0981490 + 0.995172i \(0.468708\pi\)
\(758\) 17.8530 0.648449
\(759\) 136.899 4.96910
\(760\) −2.01527 −0.0731017
\(761\) −33.5624 −1.21664 −0.608318 0.793693i \(-0.708155\pi\)
−0.608318 + 0.793693i \(0.708155\pi\)
\(762\) 7.51307 0.272170
\(763\) 1.32758 0.0480617
\(764\) −17.6389 −0.638153
\(765\) 45.2005 1.63423
\(766\) −21.5663 −0.779222
\(767\) −31.9608 −1.15404
\(768\) −2.93461 −0.105894
\(769\) 43.7374 1.57721 0.788605 0.614900i \(-0.210804\pi\)
0.788605 + 0.614900i \(0.210804\pi\)
\(770\) −9.42432 −0.339629
\(771\) 5.38685 0.194003
\(772\) −8.84040 −0.318173
\(773\) −28.7498 −1.03406 −0.517029 0.855968i \(-0.672962\pi\)
−0.517029 + 0.855968i \(0.672962\pi\)
\(774\) −4.72137 −0.169706
\(775\) −13.4772 −0.484116
\(776\) 1.51463 0.0543720
\(777\) −31.6304 −1.13474
\(778\) 4.28700 0.153696
\(779\) −6.04226 −0.216486
\(780\) 25.8699 0.926291
\(781\) 53.2744 1.90631
\(782\) −38.6619 −1.38255
\(783\) 41.7555 1.49222
\(784\) −6.05962 −0.216415
\(785\) 27.1783 0.970034
\(786\) −4.75614 −0.169646
\(787\) 0.501539 0.0178779 0.00893897 0.999960i \(-0.497155\pi\)
0.00893897 + 0.999960i \(0.497155\pi\)
\(788\) 6.41973 0.228693
\(789\) −13.2651 −0.472249
\(790\) −24.2425 −0.862511
\(791\) 2.34631 0.0834252
\(792\) 31.4126 1.11620
\(793\) 18.1998 0.646295
\(794\) −21.9150 −0.777736
\(795\) 14.5558 0.516240
\(796\) 16.7976 0.595375
\(797\) 2.00065 0.0708665 0.0354332 0.999372i \(-0.488719\pi\)
0.0354332 + 0.999372i \(0.488719\pi\)
\(798\) −3.30317 −0.116931
\(799\) −4.63251 −0.163887
\(800\) 1.98553 0.0701991
\(801\) −43.7245 −1.54493
\(802\) 12.2197 0.431494
\(803\) −48.6799 −1.71788
\(804\) −23.8744 −0.841986
\(805\) −14.0318 −0.494557
\(806\) 34.4638 1.21394
\(807\) −46.7231 −1.64473
\(808\) 1.08327 0.0381092
\(809\) 10.7594 0.378282 0.189141 0.981950i \(-0.439430\pi\)
0.189141 + 0.981950i \(0.439430\pi\)
\(810\) −9.82332 −0.345156
\(811\) −11.2000 −0.393284 −0.196642 0.980475i \(-0.563004\pi\)
−0.196642 + 0.980475i \(0.563004\pi\)
\(812\) 5.28270 0.185387
\(813\) −78.9931 −2.77041
\(814\) −62.2150 −2.18063
\(815\) −18.0134 −0.630982
\(816\) −13.6137 −0.476575
\(817\) 0.976530 0.0341645
\(818\) −12.8807 −0.450363
\(819\) 27.6314 0.965520
\(820\) −9.03807 −0.315623
\(821\) 37.9997 1.32620 0.663100 0.748531i \(-0.269241\pi\)
0.663100 + 0.748531i \(0.269241\pi\)
\(822\) 12.4063 0.432719
\(823\) 37.6727 1.31319 0.656594 0.754245i \(-0.271997\pi\)
0.656594 + 0.754245i \(0.271997\pi\)
\(824\) −0.0218735 −0.000762000 0
\(825\) −32.6151 −1.13551
\(826\) 6.10423 0.212393
\(827\) −34.8576 −1.21212 −0.606059 0.795420i \(-0.707251\pi\)
−0.606059 + 0.795420i \(0.707251\pi\)
\(828\) 46.7701 1.62537
\(829\) 52.1624 1.81168 0.905838 0.423624i \(-0.139242\pi\)
0.905838 + 0.423624i \(0.139242\pi\)
\(830\) 30.1450 1.04635
\(831\) 55.8209 1.93640
\(832\) −5.07738 −0.176026
\(833\) −28.1107 −0.973977
\(834\) −35.8508 −1.24141
\(835\) 1.04083 0.0360195
\(836\) −6.49712 −0.224708
\(837\) −52.0276 −1.79834
\(838\) −20.2844 −0.700713
\(839\) −20.4438 −0.705798 −0.352899 0.935661i \(-0.614804\pi\)
−0.352899 + 0.935661i \(0.614804\pi\)
\(840\) −4.94092 −0.170478
\(841\) 0.676151 0.0233156
\(842\) 18.3081 0.630940
\(843\) −98.1878 −3.38177
\(844\) 15.0713 0.518775
\(845\) 22.1885 0.763308
\(846\) 5.60405 0.192671
\(847\) −19.7164 −0.677462
\(848\) −2.85680 −0.0981030
\(849\) 35.7539 1.22707
\(850\) 9.21091 0.315932
\(851\) −92.6317 −3.17537
\(852\) 27.9304 0.956879
\(853\) 10.2350 0.350438 0.175219 0.984529i \(-0.443937\pi\)
0.175219 + 0.984529i \(0.443937\pi\)
\(854\) −3.47600 −0.118946
\(855\) 11.3096 0.386779
\(856\) −12.2708 −0.419407
\(857\) −31.4030 −1.07271 −0.536354 0.843993i \(-0.680199\pi\)
−0.536354 + 0.843993i \(0.680199\pi\)
\(858\) 83.4030 2.84733
\(859\) −22.0748 −0.753184 −0.376592 0.926379i \(-0.622904\pi\)
−0.376592 + 0.926379i \(0.622904\pi\)
\(860\) 1.46070 0.0498096
\(861\) −14.8140 −0.504860
\(862\) −7.43296 −0.253168
\(863\) −17.4248 −0.593147 −0.296574 0.955010i \(-0.595844\pi\)
−0.296574 + 0.955010i \(0.595844\pi\)
\(864\) 7.66495 0.260767
\(865\) −23.3155 −0.792752
\(866\) 2.68774 0.0913331
\(867\) −13.2658 −0.450532
\(868\) −6.58228 −0.223417
\(869\) −78.1564 −2.65128
\(870\) −27.7561 −0.941021
\(871\) −41.3069 −1.39963
\(872\) 1.36902 0.0463608
\(873\) −8.49998 −0.287681
\(874\) −9.67354 −0.327213
\(875\) 11.7614 0.397606
\(876\) −25.5216 −0.862294
\(877\) −1.96363 −0.0663069 −0.0331535 0.999450i \(-0.510555\pi\)
−0.0331535 + 0.999450i \(0.510555\pi\)
\(878\) 40.8831 1.37974
\(879\) −27.2571 −0.919360
\(880\) −9.71846 −0.327609
\(881\) 13.1791 0.444014 0.222007 0.975045i \(-0.428739\pi\)
0.222007 + 0.975045i \(0.428739\pi\)
\(882\) 34.0061 1.14504
\(883\) 34.7747 1.17026 0.585131 0.810939i \(-0.301043\pi\)
0.585131 + 0.810939i \(0.301043\pi\)
\(884\) −23.5540 −0.792208
\(885\) −32.0726 −1.07811
\(886\) −3.69104 −0.124003
\(887\) 41.7789 1.40280 0.701398 0.712770i \(-0.252559\pi\)
0.701398 + 0.712770i \(0.252559\pi\)
\(888\) −32.6177 −1.09458
\(889\) −2.48267 −0.0832662
\(890\) 13.5275 0.453444
\(891\) −31.6698 −1.06098
\(892\) −20.7382 −0.694366
\(893\) −1.15910 −0.0387877
\(894\) −10.7940 −0.361006
\(895\) −11.6408 −0.389109
\(896\) 0.969734 0.0323965
\(897\) 124.178 4.14620
\(898\) −17.2332 −0.575081
\(899\) −36.9767 −1.23324
\(900\) −11.1426 −0.371421
\(901\) −13.2528 −0.441513
\(902\) −29.1382 −0.970196
\(903\) 2.39419 0.0796738
\(904\) 2.41954 0.0804728
\(905\) −36.5272 −1.21421
\(906\) −2.44410 −0.0811996
\(907\) −29.4064 −0.976423 −0.488211 0.872725i \(-0.662350\pi\)
−0.488211 + 0.872725i \(0.662350\pi\)
\(908\) 17.3460 0.575646
\(909\) −6.07921 −0.201635
\(910\) −8.54864 −0.283385
\(911\) −12.9355 −0.428571 −0.214285 0.976771i \(-0.568742\pi\)
−0.214285 + 0.976771i \(0.568742\pi\)
\(912\) −3.40627 −0.112793
\(913\) 97.1855 3.21637
\(914\) −39.1433 −1.29475
\(915\) 18.2635 0.603771
\(916\) 20.7031 0.684049
\(917\) 1.57165 0.0519006
\(918\) 35.5579 1.17358
\(919\) −0.578930 −0.0190971 −0.00954856 0.999954i \(-0.503039\pi\)
−0.00954856 + 0.999954i \(0.503039\pi\)
\(920\) −14.4698 −0.477055
\(921\) 16.6853 0.549800
\(922\) 7.39099 0.243409
\(923\) 48.3244 1.59062
\(924\) −15.9292 −0.524033
\(925\) 22.0688 0.725619
\(926\) −26.8790 −0.883298
\(927\) 0.122752 0.00403171
\(928\) 5.44758 0.178826
\(929\) 17.3036 0.567712 0.283856 0.958867i \(-0.408386\pi\)
0.283856 + 0.958867i \(0.408386\pi\)
\(930\) 34.5843 1.13406
\(931\) −7.03354 −0.230515
\(932\) 9.04071 0.296138
\(933\) 53.5487 1.75311
\(934\) 21.2586 0.695602
\(935\) −45.0841 −1.47441
\(936\) 28.4938 0.931350
\(937\) −17.8150 −0.581989 −0.290995 0.956725i \(-0.593986\pi\)
−0.290995 + 0.956725i \(0.593986\pi\)
\(938\) 7.88924 0.257593
\(939\) −23.8516 −0.778367
\(940\) −1.73379 −0.0565499
\(941\) −20.4653 −0.667150 −0.333575 0.942724i \(-0.608255\pi\)
−0.333575 + 0.942724i \(0.608255\pi\)
\(942\) 45.9374 1.49672
\(943\) −43.3838 −1.41277
\(944\) 6.29475 0.204877
\(945\) 12.9053 0.419809
\(946\) 4.70922 0.153110
\(947\) 14.1382 0.459431 0.229716 0.973258i \(-0.426220\pi\)
0.229716 + 0.973258i \(0.426220\pi\)
\(948\) −40.9753 −1.33082
\(949\) −44.1567 −1.43339
\(950\) 2.30465 0.0747728
\(951\) −60.2982 −1.95530
\(952\) 4.49861 0.145801
\(953\) 30.4788 0.987305 0.493652 0.869659i \(-0.335661\pi\)
0.493652 + 0.869659i \(0.335661\pi\)
\(954\) 16.0321 0.519060
\(955\) −30.6250 −0.991003
\(956\) −1.12309 −0.0363232
\(957\) −89.4841 −2.89261
\(958\) −32.8925 −1.06271
\(959\) −4.09963 −0.132384
\(960\) −5.09513 −0.164445
\(961\) 15.0732 0.486231
\(962\) −56.4342 −1.81951
\(963\) 68.8626 2.21907
\(964\) −26.8969 −0.866291
\(965\) −15.3489 −0.494098
\(966\) −23.7170 −0.763081
\(967\) 5.03801 0.162011 0.0810057 0.996714i \(-0.474187\pi\)
0.0810057 + 0.996714i \(0.474187\pi\)
\(968\) −20.3317 −0.653487
\(969\) −15.8017 −0.507625
\(970\) 2.62973 0.0844357
\(971\) 36.0266 1.15615 0.578074 0.815984i \(-0.303804\pi\)
0.578074 + 0.815984i \(0.303804\pi\)
\(972\) 6.39123 0.204999
\(973\) 11.8468 0.379791
\(974\) −38.1817 −1.22342
\(975\) −29.5846 −0.947466
\(976\) −3.58449 −0.114737
\(977\) −36.1702 −1.15719 −0.578594 0.815616i \(-0.696398\pi\)
−0.578594 + 0.815616i \(0.696398\pi\)
\(978\) −30.4467 −0.973578
\(979\) 43.6119 1.39384
\(980\) −10.5208 −0.336076
\(981\) −7.68282 −0.245293
\(982\) −37.9964 −1.21251
\(983\) 39.4426 1.25802 0.629012 0.777396i \(-0.283460\pi\)
0.629012 + 0.777396i \(0.283460\pi\)
\(984\) −15.2764 −0.486993
\(985\) 11.1461 0.355143
\(986\) 25.2714 0.804806
\(987\) −2.84180 −0.0904554
\(988\) −5.89343 −0.187495
\(989\) 7.01154 0.222954
\(990\) 54.5392 1.73337
\(991\) −50.6112 −1.60772 −0.803858 0.594821i \(-0.797223\pi\)
−0.803858 + 0.594821i \(0.797223\pi\)
\(992\) −6.78772 −0.215510
\(993\) 57.0789 1.81134
\(994\) −9.22952 −0.292743
\(995\) 29.1644 0.924573
\(996\) 50.9518 1.61447
\(997\) 39.3897 1.24748 0.623742 0.781631i \(-0.285612\pi\)
0.623742 + 0.781631i \(0.285612\pi\)
\(998\) −19.9074 −0.630157
\(999\) 85.1946 2.69544
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 \(a_p\))