Properties

Label 8047.2.a.b.1.18
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.23848 q^{2} +1.32587 q^{3} +3.01078 q^{4} +3.90699 q^{5} -2.96792 q^{6} -1.03210 q^{7} -2.26261 q^{8} -1.24208 q^{9} +O(q^{10})\) \(q-2.23848 q^{2} +1.32587 q^{3} +3.01078 q^{4} +3.90699 q^{5} -2.96792 q^{6} -1.03210 q^{7} -2.26261 q^{8} -1.24208 q^{9} -8.74571 q^{10} -3.76952 q^{11} +3.99190 q^{12} +1.00000 q^{13} +2.31032 q^{14} +5.18015 q^{15} -0.956754 q^{16} -1.19568 q^{17} +2.78036 q^{18} +5.93474 q^{19} +11.7631 q^{20} -1.36842 q^{21} +8.43798 q^{22} +5.47097 q^{23} -2.99993 q^{24} +10.2646 q^{25} -2.23848 q^{26} -5.62443 q^{27} -3.10742 q^{28} -8.46985 q^{29} -11.5957 q^{30} -6.03126 q^{31} +6.66690 q^{32} -4.99788 q^{33} +2.67650 q^{34} -4.03239 q^{35} -3.73962 q^{36} +4.09348 q^{37} -13.2848 q^{38} +1.32587 q^{39} -8.84002 q^{40} -5.95287 q^{41} +3.06318 q^{42} -0.0499133 q^{43} -11.3492 q^{44} -4.85278 q^{45} -12.2466 q^{46} -11.3673 q^{47} -1.26853 q^{48} -5.93478 q^{49} -22.9771 q^{50} -1.58531 q^{51} +3.01078 q^{52} -2.35755 q^{53} +12.5902 q^{54} -14.7275 q^{55} +2.33523 q^{56} +7.86868 q^{57} +18.9596 q^{58} -2.92248 q^{59} +15.5963 q^{60} +11.4918 q^{61} +13.5008 q^{62} +1.28194 q^{63} -13.0102 q^{64} +3.90699 q^{65} +11.1876 q^{66} +2.07218 q^{67} -3.59992 q^{68} +7.25377 q^{69} +9.02642 q^{70} -15.5903 q^{71} +2.81034 q^{72} -11.0783 q^{73} -9.16317 q^{74} +13.6095 q^{75} +17.8682 q^{76} +3.89050 q^{77} -2.96792 q^{78} -11.3917 q^{79} -3.73803 q^{80} -3.73102 q^{81} +13.3254 q^{82} +14.0645 q^{83} -4.12002 q^{84} -4.67150 q^{85} +0.111730 q^{86} -11.2299 q^{87} +8.52896 q^{88} -1.14619 q^{89} +10.8628 q^{90} -1.03210 q^{91} +16.4719 q^{92} -7.99665 q^{93} +25.4453 q^{94} +23.1870 q^{95} +8.83943 q^{96} +0.332148 q^{97} +13.2849 q^{98} +4.68202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23848 −1.58284 −0.791421 0.611271i \(-0.790659\pi\)
−0.791421 + 0.611271i \(0.790659\pi\)
\(3\) 1.32587 0.765490 0.382745 0.923854i \(-0.374979\pi\)
0.382745 + 0.923854i \(0.374979\pi\)
\(4\) 3.01078 1.50539
\(5\) 3.90699 1.74726 0.873630 0.486591i \(-0.161760\pi\)
0.873630 + 0.486591i \(0.161760\pi\)
\(6\) −2.96792 −1.21165
\(7\) −1.03210 −0.390096 −0.195048 0.980794i \(-0.562486\pi\)
−0.195048 + 0.980794i \(0.562486\pi\)
\(8\) −2.26261 −0.799955
\(9\) −1.24208 −0.414025
\(10\) −8.74571 −2.76564
\(11\) −3.76952 −1.13655 −0.568276 0.822838i \(-0.692389\pi\)
−0.568276 + 0.822838i \(0.692389\pi\)
\(12\) 3.99190 1.15236
\(13\) 1.00000 0.277350
\(14\) 2.31032 0.617460
\(15\) 5.18015 1.33751
\(16\) −0.956754 −0.239188
\(17\) −1.19568 −0.289994 −0.144997 0.989432i \(-0.546317\pi\)
−0.144997 + 0.989432i \(0.546317\pi\)
\(18\) 2.78036 0.655337
\(19\) 5.93474 1.36152 0.680761 0.732505i \(-0.261649\pi\)
0.680761 + 0.732505i \(0.261649\pi\)
\(20\) 11.7631 2.63031
\(21\) −1.36842 −0.298614
\(22\) 8.43798 1.79898
\(23\) 5.47097 1.14078 0.570388 0.821376i \(-0.306793\pi\)
0.570388 + 0.821376i \(0.306793\pi\)
\(24\) −2.99993 −0.612357
\(25\) 10.2646 2.05292
\(26\) −2.23848 −0.439002
\(27\) −5.62443 −1.08242
\(28\) −3.10742 −0.587246
\(29\) −8.46985 −1.57281 −0.786406 0.617710i \(-0.788060\pi\)
−0.786406 + 0.617710i \(0.788060\pi\)
\(30\) −11.5957 −2.11707
\(31\) −6.03126 −1.08325 −0.541623 0.840621i \(-0.682190\pi\)
−0.541623 + 0.840621i \(0.682190\pi\)
\(32\) 6.66690 1.17855
\(33\) −4.99788 −0.870019
\(34\) 2.67650 0.459015
\(35\) −4.03239 −0.681598
\(36\) −3.73962 −0.623270
\(37\) 4.09348 0.672964 0.336482 0.941690i \(-0.390763\pi\)
0.336482 + 0.941690i \(0.390763\pi\)
\(38\) −13.2848 −2.15508
\(39\) 1.32587 0.212309
\(40\) −8.84002 −1.39773
\(41\) −5.95287 −0.929682 −0.464841 0.885394i \(-0.653889\pi\)
−0.464841 + 0.885394i \(0.653889\pi\)
\(42\) 3.06318 0.472659
\(43\) −0.0499133 −0.00761171 −0.00380586 0.999993i \(-0.501211\pi\)
−0.00380586 + 0.999993i \(0.501211\pi\)
\(44\) −11.3492 −1.71095
\(45\) −4.85278 −0.723410
\(46\) −12.2466 −1.80567
\(47\) −11.3673 −1.65808 −0.829042 0.559186i \(-0.811114\pi\)
−0.829042 + 0.559186i \(0.811114\pi\)
\(48\) −1.26853 −0.183096
\(49\) −5.93478 −0.847825
\(50\) −22.9771 −3.24945
\(51\) −1.58531 −0.221988
\(52\) 3.01078 0.417520
\(53\) −2.35755 −0.323835 −0.161917 0.986804i \(-0.551768\pi\)
−0.161917 + 0.986804i \(0.551768\pi\)
\(54\) 12.5902 1.71330
\(55\) −14.7275 −1.98585
\(56\) 2.33523 0.312059
\(57\) 7.86868 1.04223
\(58\) 18.9596 2.48951
\(59\) −2.92248 −0.380474 −0.190237 0.981738i \(-0.560926\pi\)
−0.190237 + 0.981738i \(0.560926\pi\)
\(60\) 15.5963 2.01348
\(61\) 11.4918 1.47137 0.735685 0.677324i \(-0.236860\pi\)
0.735685 + 0.677324i \(0.236860\pi\)
\(62\) 13.5008 1.71461
\(63\) 1.28194 0.161509
\(64\) −13.0102 −1.62627
\(65\) 3.90699 0.484603
\(66\) 11.1876 1.37710
\(67\) 2.07218 0.253157 0.126579 0.991957i \(-0.459600\pi\)
0.126579 + 0.991957i \(0.459600\pi\)
\(68\) −3.59992 −0.436555
\(69\) 7.25377 0.873252
\(70\) 9.02642 1.07886
\(71\) −15.5903 −1.85023 −0.925113 0.379692i \(-0.876030\pi\)
−0.925113 + 0.379692i \(0.876030\pi\)
\(72\) 2.81034 0.331201
\(73\) −11.0783 −1.29662 −0.648308 0.761378i \(-0.724523\pi\)
−0.648308 + 0.761378i \(0.724523\pi\)
\(74\) −9.16317 −1.06520
\(75\) 13.6095 1.57149
\(76\) 17.8682 2.04962
\(77\) 3.89050 0.443364
\(78\) −2.96792 −0.336051
\(79\) −11.3917 −1.28167 −0.640833 0.767680i \(-0.721411\pi\)
−0.640833 + 0.767680i \(0.721411\pi\)
\(80\) −3.73803 −0.417924
\(81\) −3.73102 −0.414558
\(82\) 13.3254 1.47154
\(83\) 14.0645 1.54378 0.771889 0.635757i \(-0.219312\pi\)
0.771889 + 0.635757i \(0.219312\pi\)
\(84\) −4.12002 −0.449531
\(85\) −4.67150 −0.506695
\(86\) 0.111730 0.0120481
\(87\) −11.2299 −1.20397
\(88\) 8.52896 0.909190
\(89\) −1.14619 −0.121496 −0.0607480 0.998153i \(-0.519349\pi\)
−0.0607480 + 0.998153i \(0.519349\pi\)
\(90\) 10.8628 1.14504
\(91\) −1.03210 −0.108193
\(92\) 16.4719 1.71731
\(93\) −7.99665 −0.829214
\(94\) 25.4453 2.62449
\(95\) 23.1870 2.37893
\(96\) 8.83943 0.902170
\(97\) 0.332148 0.0337246 0.0168623 0.999858i \(-0.494632\pi\)
0.0168623 + 0.999858i \(0.494632\pi\)
\(98\) 13.2849 1.34197
\(99\) 4.68202 0.470561
\(100\) 30.9044 3.09044
\(101\) 3.65611 0.363796 0.181898 0.983317i \(-0.441776\pi\)
0.181898 + 0.983317i \(0.441776\pi\)
\(102\) 3.54868 0.351372
\(103\) 12.6244 1.24392 0.621959 0.783049i \(-0.286337\pi\)
0.621959 + 0.783049i \(0.286337\pi\)
\(104\) −2.26261 −0.221868
\(105\) −5.34641 −0.521757
\(106\) 5.27732 0.512579
\(107\) 6.73786 0.651373 0.325687 0.945478i \(-0.394405\pi\)
0.325687 + 0.945478i \(0.394405\pi\)
\(108\) −16.9339 −1.62947
\(109\) −13.6342 −1.30592 −0.652958 0.757394i \(-0.726472\pi\)
−0.652958 + 0.757394i \(0.726472\pi\)
\(110\) 32.9671 3.14329
\(111\) 5.42741 0.515147
\(112\) 0.987462 0.0933064
\(113\) −11.5464 −1.08619 −0.543096 0.839671i \(-0.682748\pi\)
−0.543096 + 0.839671i \(0.682748\pi\)
\(114\) −17.6139 −1.64969
\(115\) 21.3750 1.99323
\(116\) −25.5009 −2.36770
\(117\) −1.24208 −0.114830
\(118\) 6.54190 0.602231
\(119\) 1.23405 0.113125
\(120\) −11.7207 −1.06995
\(121\) 3.20925 0.291750
\(122\) −25.7241 −2.32895
\(123\) −7.89272 −0.711662
\(124\) −18.1588 −1.63071
\(125\) 20.5687 1.83972
\(126\) −2.86960 −0.255644
\(127\) 12.9198 1.14644 0.573222 0.819400i \(-0.305693\pi\)
0.573222 + 0.819400i \(0.305693\pi\)
\(128\) 15.7892 1.39559
\(129\) −0.0661785 −0.00582669
\(130\) −8.74571 −0.767050
\(131\) −13.2359 −1.15643 −0.578214 0.815885i \(-0.696250\pi\)
−0.578214 + 0.815885i \(0.696250\pi\)
\(132\) −15.0475 −1.30972
\(133\) −6.12522 −0.531124
\(134\) −4.63853 −0.400708
\(135\) −21.9746 −1.89127
\(136\) 2.70536 0.231982
\(137\) 10.3092 0.880777 0.440389 0.897807i \(-0.354841\pi\)
0.440389 + 0.897807i \(0.354841\pi\)
\(138\) −16.2374 −1.38222
\(139\) −9.66127 −0.819458 −0.409729 0.912207i \(-0.634377\pi\)
−0.409729 + 0.912207i \(0.634377\pi\)
\(140\) −12.1406 −1.02607
\(141\) −15.0715 −1.26925
\(142\) 34.8985 2.92862
\(143\) −3.76952 −0.315223
\(144\) 1.18836 0.0990301
\(145\) −33.0916 −2.74811
\(146\) 24.7985 2.05234
\(147\) −7.86873 −0.649002
\(148\) 12.3246 1.01307
\(149\) 16.5334 1.35447 0.677235 0.735767i \(-0.263178\pi\)
0.677235 + 0.735767i \(0.263178\pi\)
\(150\) −30.4645 −2.48742
\(151\) −22.1723 −1.80436 −0.902180 0.431360i \(-0.858034\pi\)
−0.902180 + 0.431360i \(0.858034\pi\)
\(152\) −13.4280 −1.08916
\(153\) 1.48512 0.120065
\(154\) −8.70880 −0.701775
\(155\) −23.5641 −1.89271
\(156\) 3.99190 0.319608
\(157\) −18.3149 −1.46169 −0.730845 0.682543i \(-0.760874\pi\)
−0.730845 + 0.682543i \(0.760874\pi\)
\(158\) 25.5001 2.02868
\(159\) −3.12580 −0.247892
\(160\) 26.0475 2.05924
\(161\) −5.64656 −0.445011
\(162\) 8.35181 0.656180
\(163\) 7.27759 0.570025 0.285012 0.958524i \(-0.408002\pi\)
0.285012 + 0.958524i \(0.408002\pi\)
\(164\) −17.9228 −1.39954
\(165\) −19.5267 −1.52015
\(166\) −31.4830 −2.44356
\(167\) 3.84224 0.297321 0.148661 0.988888i \(-0.452504\pi\)
0.148661 + 0.988888i \(0.452504\pi\)
\(168\) 3.09621 0.238878
\(169\) 1.00000 0.0769231
\(170\) 10.4571 0.802019
\(171\) −7.37140 −0.563705
\(172\) −0.150278 −0.0114586
\(173\) 5.35078 0.406812 0.203406 0.979094i \(-0.434799\pi\)
0.203406 + 0.979094i \(0.434799\pi\)
\(174\) 25.1379 1.90570
\(175\) −10.5940 −0.800834
\(176\) 3.60650 0.271850
\(177\) −3.87482 −0.291249
\(178\) 2.56572 0.192309
\(179\) −20.2863 −1.51627 −0.758136 0.652097i \(-0.773890\pi\)
−0.758136 + 0.652097i \(0.773890\pi\)
\(180\) −14.6107 −1.08901
\(181\) 7.59052 0.564199 0.282100 0.959385i \(-0.408969\pi\)
0.282100 + 0.959385i \(0.408969\pi\)
\(182\) 2.31032 0.171253
\(183\) 15.2366 1.12632
\(184\) −12.3787 −0.912569
\(185\) 15.9932 1.17584
\(186\) 17.9003 1.31252
\(187\) 4.50712 0.329593
\(188\) −34.2243 −2.49607
\(189\) 5.80495 0.422248
\(190\) −51.9035 −3.76548
\(191\) 14.5409 1.05214 0.526071 0.850441i \(-0.323665\pi\)
0.526071 + 0.850441i \(0.323665\pi\)
\(192\) −17.2498 −1.24490
\(193\) −20.2721 −1.45922 −0.729608 0.683866i \(-0.760297\pi\)
−0.729608 + 0.683866i \(0.760297\pi\)
\(194\) −0.743507 −0.0533807
\(195\) 5.18015 0.370959
\(196\) −17.8683 −1.27631
\(197\) −19.6310 −1.39865 −0.699326 0.714803i \(-0.746516\pi\)
−0.699326 + 0.714803i \(0.746516\pi\)
\(198\) −10.4806 −0.744824
\(199\) 13.5115 0.957806 0.478903 0.877868i \(-0.341035\pi\)
0.478903 + 0.877868i \(0.341035\pi\)
\(200\) −23.2248 −1.64224
\(201\) 2.74744 0.193789
\(202\) −8.18412 −0.575832
\(203\) 8.74169 0.613547
\(204\) −4.77302 −0.334178
\(205\) −23.2578 −1.62440
\(206\) −28.2594 −1.96893
\(207\) −6.79535 −0.472310
\(208\) −0.956754 −0.0663389
\(209\) −22.3711 −1.54744
\(210\) 11.9678 0.825859
\(211\) 9.47000 0.651942 0.325971 0.945380i \(-0.394309\pi\)
0.325971 + 0.945380i \(0.394309\pi\)
\(212\) −7.09807 −0.487498
\(213\) −20.6706 −1.41633
\(214\) −15.0825 −1.03102
\(215\) −0.195011 −0.0132996
\(216\) 12.7259 0.865889
\(217\) 6.22484 0.422570
\(218\) 30.5198 2.06706
\(219\) −14.6883 −0.992546
\(220\) −44.3412 −2.98948
\(221\) −1.19568 −0.0804299
\(222\) −12.1491 −0.815397
\(223\) 21.4757 1.43812 0.719059 0.694949i \(-0.244573\pi\)
0.719059 + 0.694949i \(0.244573\pi\)
\(224\) −6.88088 −0.459748
\(225\) −12.7494 −0.849960
\(226\) 25.8463 1.71927
\(227\) 18.2247 1.20962 0.604808 0.796371i \(-0.293250\pi\)
0.604808 + 0.796371i \(0.293250\pi\)
\(228\) 23.6909 1.56897
\(229\) −18.8810 −1.24769 −0.623847 0.781546i \(-0.714431\pi\)
−0.623847 + 0.781546i \(0.714431\pi\)
\(230\) −47.8475 −3.15497
\(231\) 5.15829 0.339390
\(232\) 19.1640 1.25818
\(233\) −13.0345 −0.853920 −0.426960 0.904271i \(-0.640415\pi\)
−0.426960 + 0.904271i \(0.640415\pi\)
\(234\) 2.78036 0.181758
\(235\) −44.4118 −2.89710
\(236\) −8.79895 −0.572763
\(237\) −15.1039 −0.981103
\(238\) −2.76240 −0.179060
\(239\) −26.4703 −1.71222 −0.856110 0.516794i \(-0.827125\pi\)
−0.856110 + 0.516794i \(0.827125\pi\)
\(240\) −4.95613 −0.319917
\(241\) 20.8309 1.34184 0.670918 0.741531i \(-0.265900\pi\)
0.670918 + 0.741531i \(0.265900\pi\)
\(242\) −7.18383 −0.461794
\(243\) 11.9264 0.765082
\(244\) 34.5992 2.21499
\(245\) −23.1871 −1.48137
\(246\) 17.6677 1.12645
\(247\) 5.93474 0.377618
\(248\) 13.6464 0.866548
\(249\) 18.6476 1.18175
\(250\) −46.0426 −2.91199
\(251\) 3.58261 0.226132 0.113066 0.993587i \(-0.463933\pi\)
0.113066 + 0.993587i \(0.463933\pi\)
\(252\) 3.85965 0.243135
\(253\) −20.6229 −1.29655
\(254\) −28.9206 −1.81464
\(255\) −6.19379 −0.387870
\(256\) −9.32347 −0.582717
\(257\) −18.8765 −1.17749 −0.588743 0.808320i \(-0.700377\pi\)
−0.588743 + 0.808320i \(0.700377\pi\)
\(258\) 0.148139 0.00922273
\(259\) −4.22487 −0.262520
\(260\) 11.7631 0.729517
\(261\) 10.5202 0.651184
\(262\) 29.6283 1.83044
\(263\) −8.91152 −0.549508 −0.274754 0.961515i \(-0.588596\pi\)
−0.274754 + 0.961515i \(0.588596\pi\)
\(264\) 11.3083 0.695976
\(265\) −9.21093 −0.565823
\(266\) 13.7112 0.840686
\(267\) −1.51970 −0.0930040
\(268\) 6.23888 0.381101
\(269\) −9.72144 −0.592727 −0.296363 0.955075i \(-0.595774\pi\)
−0.296363 + 0.955075i \(0.595774\pi\)
\(270\) 49.1897 2.99359
\(271\) 24.2752 1.47462 0.737308 0.675557i \(-0.236097\pi\)
0.737308 + 0.675557i \(0.236097\pi\)
\(272\) 1.14397 0.0693633
\(273\) −1.36842 −0.0828207
\(274\) −23.0770 −1.39413
\(275\) −38.6925 −2.33325
\(276\) 21.8395 1.31459
\(277\) −14.4959 −0.870972 −0.435486 0.900196i \(-0.643423\pi\)
−0.435486 + 0.900196i \(0.643423\pi\)
\(278\) 21.6265 1.29707
\(279\) 7.49128 0.448491
\(280\) 9.12374 0.545248
\(281\) 12.1992 0.727743 0.363871 0.931449i \(-0.381455\pi\)
0.363871 + 0.931449i \(0.381455\pi\)
\(282\) 33.7372 2.00902
\(283\) −23.3560 −1.38837 −0.694186 0.719796i \(-0.744235\pi\)
−0.694186 + 0.719796i \(0.744235\pi\)
\(284\) −46.9390 −2.78531
\(285\) 30.7429 1.82105
\(286\) 8.43798 0.498948
\(287\) 6.14393 0.362665
\(288\) −8.28079 −0.487950
\(289\) −15.5704 −0.915903
\(290\) 74.0749 4.34983
\(291\) 0.440385 0.0258158
\(292\) −33.3543 −1.95191
\(293\) −1.33650 −0.0780791 −0.0390395 0.999238i \(-0.512430\pi\)
−0.0390395 + 0.999238i \(0.512430\pi\)
\(294\) 17.6140 1.02727
\(295\) −11.4181 −0.664788
\(296\) −9.26197 −0.538341
\(297\) 21.2014 1.23023
\(298\) −37.0097 −2.14391
\(299\) 5.47097 0.316394
\(300\) 40.9752 2.36570
\(301\) 0.0515153 0.00296929
\(302\) 49.6323 2.85602
\(303\) 4.84752 0.278482
\(304\) −5.67809 −0.325661
\(305\) 44.8982 2.57087
\(306\) −3.32441 −0.190044
\(307\) 29.8792 1.70530 0.852648 0.522485i \(-0.174995\pi\)
0.852648 + 0.522485i \(0.174995\pi\)
\(308\) 11.7135 0.667436
\(309\) 16.7383 0.952207
\(310\) 52.7477 2.99587
\(311\) 16.7174 0.947958 0.473979 0.880536i \(-0.342817\pi\)
0.473979 + 0.880536i \(0.342817\pi\)
\(312\) −2.99993 −0.169837
\(313\) −28.2330 −1.59583 −0.797913 0.602773i \(-0.794063\pi\)
−0.797913 + 0.602773i \(0.794063\pi\)
\(314\) 40.9976 2.31363
\(315\) 5.00853 0.282199
\(316\) −34.2979 −1.92941
\(317\) 33.5934 1.88680 0.943398 0.331663i \(-0.107610\pi\)
0.943398 + 0.331663i \(0.107610\pi\)
\(318\) 6.99703 0.392374
\(319\) 31.9272 1.78758
\(320\) −50.8307 −2.84153
\(321\) 8.93350 0.498620
\(322\) 12.6397 0.704383
\(323\) −7.09603 −0.394834
\(324\) −11.2333 −0.624072
\(325\) 10.2646 0.569377
\(326\) −16.2907 −0.902260
\(327\) −18.0771 −0.999666
\(328\) 13.4690 0.743704
\(329\) 11.7321 0.646811
\(330\) 43.7100 2.40616
\(331\) 14.4142 0.792274 0.396137 0.918191i \(-0.370351\pi\)
0.396137 + 0.918191i \(0.370351\pi\)
\(332\) 42.3451 2.32399
\(333\) −5.08441 −0.278624
\(334\) −8.60076 −0.470613
\(335\) 8.09599 0.442331
\(336\) 1.30924 0.0714251
\(337\) 15.5676 0.848022 0.424011 0.905657i \(-0.360622\pi\)
0.424011 + 0.905657i \(0.360622\pi\)
\(338\) −2.23848 −0.121757
\(339\) −15.3090 −0.831468
\(340\) −14.0649 −0.762775
\(341\) 22.7349 1.23117
\(342\) 16.5007 0.892256
\(343\) 13.3499 0.720828
\(344\) 0.112935 0.00608903
\(345\) 28.3404 1.52580
\(346\) −11.9776 −0.643920
\(347\) −29.3825 −1.57733 −0.788666 0.614821i \(-0.789228\pi\)
−0.788666 + 0.614821i \(0.789228\pi\)
\(348\) −33.8108 −1.81245
\(349\) −4.65305 −0.249072 −0.124536 0.992215i \(-0.539744\pi\)
−0.124536 + 0.992215i \(0.539744\pi\)
\(350\) 23.7145 1.26759
\(351\) −5.62443 −0.300210
\(352\) −25.1310 −1.33949
\(353\) −11.1882 −0.595487 −0.297744 0.954646i \(-0.596234\pi\)
−0.297744 + 0.954646i \(0.596234\pi\)
\(354\) 8.67370 0.461002
\(355\) −60.9111 −3.23283
\(356\) −3.45093 −0.182899
\(357\) 1.63619 0.0865964
\(358\) 45.4105 2.40002
\(359\) −1.40414 −0.0741078 −0.0370539 0.999313i \(-0.511797\pi\)
−0.0370539 + 0.999313i \(0.511797\pi\)
\(360\) 10.9800 0.578695
\(361\) 16.2211 0.853744
\(362\) −16.9912 −0.893039
\(363\) 4.25504 0.223331
\(364\) −3.10742 −0.162873
\(365\) −43.2828 −2.26552
\(366\) −34.1067 −1.78279
\(367\) 12.8753 0.672087 0.336043 0.941847i \(-0.390911\pi\)
0.336043 + 0.941847i \(0.390911\pi\)
\(368\) −5.23437 −0.272860
\(369\) 7.39391 0.384912
\(370\) −35.8004 −1.86118
\(371\) 2.43322 0.126326
\(372\) −24.0762 −1.24829
\(373\) 0.326143 0.0168871 0.00844353 0.999964i \(-0.497312\pi\)
0.00844353 + 0.999964i \(0.497312\pi\)
\(374\) −10.0891 −0.521695
\(375\) 27.2714 1.40829
\(376\) 25.7197 1.32639
\(377\) −8.46985 −0.436219
\(378\) −12.9943 −0.668352
\(379\) −36.6353 −1.88183 −0.940915 0.338643i \(-0.890032\pi\)
−0.940915 + 0.338643i \(0.890032\pi\)
\(380\) 69.8110 3.58123
\(381\) 17.1299 0.877592
\(382\) −32.5494 −1.66537
\(383\) 15.3572 0.784717 0.392358 0.919812i \(-0.371659\pi\)
0.392358 + 0.919812i \(0.371659\pi\)
\(384\) 20.9344 1.06831
\(385\) 15.2002 0.774672
\(386\) 45.3786 2.30971
\(387\) 0.0619961 0.00315144
\(388\) 1.00003 0.0507687
\(389\) −12.3326 −0.625289 −0.312645 0.949870i \(-0.601215\pi\)
−0.312645 + 0.949870i \(0.601215\pi\)
\(390\) −11.5957 −0.587169
\(391\) −6.54151 −0.330818
\(392\) 13.4281 0.678222
\(393\) −17.5491 −0.885234
\(394\) 43.9436 2.21385
\(395\) −44.5073 −2.23940
\(396\) 14.0966 0.708378
\(397\) 13.4070 0.672878 0.336439 0.941705i \(-0.390777\pi\)
0.336439 + 0.941705i \(0.390777\pi\)
\(398\) −30.2452 −1.51606
\(399\) −8.12123 −0.406570
\(400\) −9.82068 −0.491034
\(401\) 5.26038 0.262691 0.131345 0.991337i \(-0.458070\pi\)
0.131345 + 0.991337i \(0.458070\pi\)
\(402\) −6.15008 −0.306738
\(403\) −6.03126 −0.300439
\(404\) 11.0077 0.547656
\(405\) −14.5771 −0.724340
\(406\) −19.5681 −0.971148
\(407\) −15.4304 −0.764859
\(408\) 3.58694 0.177580
\(409\) −10.7035 −0.529253 −0.264627 0.964351i \(-0.585249\pi\)
−0.264627 + 0.964351i \(0.585249\pi\)
\(410\) 52.0621 2.57116
\(411\) 13.6687 0.674226
\(412\) 38.0093 1.87258
\(413\) 3.01628 0.148421
\(414\) 15.2112 0.747592
\(415\) 54.9498 2.69738
\(416\) 6.66690 0.326872
\(417\) −12.8096 −0.627287
\(418\) 50.0772 2.44936
\(419\) 4.24356 0.207311 0.103656 0.994613i \(-0.466946\pi\)
0.103656 + 0.994613i \(0.466946\pi\)
\(420\) −16.0969 −0.785448
\(421\) 17.0084 0.828937 0.414469 0.910064i \(-0.363967\pi\)
0.414469 + 0.910064i \(0.363967\pi\)
\(422\) −21.1984 −1.03192
\(423\) 14.1190 0.686489
\(424\) 5.33423 0.259053
\(425\) −12.2731 −0.595334
\(426\) 46.2708 2.24183
\(427\) −11.8606 −0.573975
\(428\) 20.2862 0.980571
\(429\) −4.99788 −0.241300
\(430\) 0.436528 0.0210512
\(431\) −27.9992 −1.34867 −0.674336 0.738425i \(-0.735570\pi\)
−0.674336 + 0.738425i \(0.735570\pi\)
\(432\) 5.38120 0.258903
\(433\) −22.4619 −1.07945 −0.539726 0.841841i \(-0.681472\pi\)
−0.539726 + 0.841841i \(0.681472\pi\)
\(434\) −13.9342 −0.668861
\(435\) −43.8751 −2.10365
\(436\) −41.0495 −1.96592
\(437\) 32.4688 1.55319
\(438\) 32.8795 1.57104
\(439\) −34.0975 −1.62738 −0.813692 0.581296i \(-0.802546\pi\)
−0.813692 + 0.581296i \(0.802546\pi\)
\(440\) 33.3226 1.58859
\(441\) 7.37144 0.351021
\(442\) 2.67650 0.127308
\(443\) −25.9131 −1.23117 −0.615584 0.788071i \(-0.711080\pi\)
−0.615584 + 0.788071i \(0.711080\pi\)
\(444\) 16.3408 0.775498
\(445\) −4.47816 −0.212285
\(446\) −48.0728 −2.27632
\(447\) 21.9211 1.03683
\(448\) 13.4278 0.634403
\(449\) 11.2111 0.529087 0.264543 0.964374i \(-0.414779\pi\)
0.264543 + 0.964374i \(0.414779\pi\)
\(450\) 28.5392 1.34535
\(451\) 22.4394 1.05663
\(452\) −34.7636 −1.63514
\(453\) −29.3976 −1.38122
\(454\) −40.7956 −1.91463
\(455\) −4.03239 −0.189041
\(456\) −17.8038 −0.833738
\(457\) 24.0944 1.12709 0.563545 0.826086i \(-0.309437\pi\)
0.563545 + 0.826086i \(0.309437\pi\)
\(458\) 42.2648 1.97490
\(459\) 6.72500 0.313896
\(460\) 64.3555 3.00059
\(461\) −26.7250 −1.24471 −0.622353 0.782737i \(-0.713823\pi\)
−0.622353 + 0.782737i \(0.713823\pi\)
\(462\) −11.5467 −0.537202
\(463\) −17.9898 −0.836059 −0.418029 0.908434i \(-0.637279\pi\)
−0.418029 + 0.908434i \(0.637279\pi\)
\(464\) 8.10356 0.376198
\(465\) −31.2429 −1.44885
\(466\) 29.1775 1.35162
\(467\) −11.3932 −0.527214 −0.263607 0.964630i \(-0.584912\pi\)
−0.263607 + 0.964630i \(0.584912\pi\)
\(468\) −3.73962 −0.172864
\(469\) −2.13869 −0.0987555
\(470\) 99.4148 4.58566
\(471\) −24.2832 −1.11891
\(472\) 6.61244 0.304362
\(473\) 0.188149 0.00865110
\(474\) 33.8097 1.55293
\(475\) 60.9177 2.79509
\(476\) 3.71547 0.170298
\(477\) 2.92826 0.134076
\(478\) 59.2531 2.71017
\(479\) 2.37177 0.108369 0.0541844 0.998531i \(-0.482744\pi\)
0.0541844 + 0.998531i \(0.482744\pi\)
\(480\) 34.5356 1.57633
\(481\) 4.09348 0.186647
\(482\) −46.6295 −2.12392
\(483\) −7.48659 −0.340652
\(484\) 9.66234 0.439197
\(485\) 1.29770 0.0589256
\(486\) −26.6971 −1.21100
\(487\) 3.72897 0.168976 0.0844879 0.996425i \(-0.473075\pi\)
0.0844879 + 0.996425i \(0.473075\pi\)
\(488\) −26.0014 −1.17703
\(489\) 9.64912 0.436348
\(490\) 51.9039 2.34478
\(491\) −15.0464 −0.679032 −0.339516 0.940600i \(-0.610263\pi\)
−0.339516 + 0.940600i \(0.610263\pi\)
\(492\) −23.7632 −1.07133
\(493\) 10.1272 0.456106
\(494\) −13.2848 −0.597711
\(495\) 18.2926 0.822192
\(496\) 5.77043 0.259100
\(497\) 16.0907 0.721765
\(498\) −41.7423 −1.87052
\(499\) −4.53998 −0.203237 −0.101619 0.994823i \(-0.532402\pi\)
−0.101619 + 0.994823i \(0.532402\pi\)
\(500\) 61.9279 2.76950
\(501\) 5.09430 0.227596
\(502\) −8.01958 −0.357932
\(503\) 3.13257 0.139675 0.0698373 0.997558i \(-0.477752\pi\)
0.0698373 + 0.997558i \(0.477752\pi\)
\(504\) −2.90054 −0.129200
\(505\) 14.2844 0.635647
\(506\) 46.1639 2.05223
\(507\) 1.32587 0.0588838
\(508\) 38.8986 1.72585
\(509\) 4.02397 0.178359 0.0891796 0.996016i \(-0.471575\pi\)
0.0891796 + 0.996016i \(0.471575\pi\)
\(510\) 13.8647 0.613938
\(511\) 11.4339 0.505804
\(512\) −10.7081 −0.473236
\(513\) −33.3795 −1.47374
\(514\) 42.2547 1.86377
\(515\) 49.3234 2.17345
\(516\) −0.199249 −0.00877145
\(517\) 42.8490 1.88450
\(518\) 9.45727 0.415528
\(519\) 7.09442 0.311411
\(520\) −8.84002 −0.387660
\(521\) −28.8083 −1.26212 −0.631058 0.775736i \(-0.717379\pi\)
−0.631058 + 0.775736i \(0.717379\pi\)
\(522\) −23.5492 −1.03072
\(523\) 28.2127 1.23366 0.616828 0.787098i \(-0.288417\pi\)
0.616828 + 0.787098i \(0.288417\pi\)
\(524\) −39.8505 −1.74088
\(525\) −14.0463 −0.613030
\(526\) 19.9482 0.869784
\(527\) 7.21144 0.314135
\(528\) 4.78174 0.208098
\(529\) 6.93146 0.301368
\(530\) 20.6185 0.895609
\(531\) 3.62994 0.157526
\(532\) −18.4417 −0.799549
\(533\) −5.95287 −0.257847
\(534\) 3.40181 0.147211
\(535\) 26.3247 1.13812
\(536\) −4.68854 −0.202514
\(537\) −26.8970 −1.16069
\(538\) 21.7612 0.938193
\(539\) 22.3712 0.963597
\(540\) −66.1607 −2.84711
\(541\) 10.6367 0.457306 0.228653 0.973508i \(-0.426568\pi\)
0.228653 + 0.973508i \(0.426568\pi\)
\(542\) −54.3396 −2.33408
\(543\) 10.0640 0.431889
\(544\) −7.97146 −0.341774
\(545\) −53.2686 −2.28178
\(546\) 3.06318 0.131092
\(547\) 1.20662 0.0515912 0.0257956 0.999667i \(-0.491788\pi\)
0.0257956 + 0.999667i \(0.491788\pi\)
\(548\) 31.0389 1.32591
\(549\) −14.2736 −0.609184
\(550\) 86.6123 3.69316
\(551\) −50.2663 −2.14142
\(552\) −16.4125 −0.698562
\(553\) 11.7573 0.499972
\(554\) 32.4487 1.37861
\(555\) 21.2049 0.900096
\(556\) −29.0880 −1.23360
\(557\) −10.0578 −0.426161 −0.213080 0.977035i \(-0.568350\pi\)
−0.213080 + 0.977035i \(0.568350\pi\)
\(558\) −16.7691 −0.709891
\(559\) −0.0499133 −0.00211111
\(560\) 3.85800 0.163030
\(561\) 5.97585 0.252300
\(562\) −27.3076 −1.15190
\(563\) 29.9102 1.26056 0.630282 0.776366i \(-0.282939\pi\)
0.630282 + 0.776366i \(0.282939\pi\)
\(564\) −45.3769 −1.91071
\(565\) −45.1116 −1.89786
\(566\) 52.2819 2.19757
\(567\) 3.85077 0.161717
\(568\) 35.2748 1.48010
\(569\) 26.7110 1.11978 0.559892 0.828566i \(-0.310843\pi\)
0.559892 + 0.828566i \(0.310843\pi\)
\(570\) −68.8172 −2.88244
\(571\) 2.79583 0.117002 0.0585009 0.998287i \(-0.481368\pi\)
0.0585009 + 0.998287i \(0.481368\pi\)
\(572\) −11.3492 −0.474534
\(573\) 19.2793 0.805403
\(574\) −13.7531 −0.574041
\(575\) 56.1572 2.34192
\(576\) 16.1597 0.673319
\(577\) −18.2546 −0.759948 −0.379974 0.924997i \(-0.624067\pi\)
−0.379974 + 0.924997i \(0.624067\pi\)
\(578\) 34.8539 1.44973
\(579\) −26.8781 −1.11701
\(580\) −99.6317 −4.13698
\(581\) −14.5159 −0.602221
\(582\) −0.985791 −0.0408624
\(583\) 8.88682 0.368055
\(584\) 25.0659 1.03723
\(585\) −4.85278 −0.200638
\(586\) 2.99172 0.123587
\(587\) 7.62208 0.314597 0.157298 0.987551i \(-0.449722\pi\)
0.157298 + 0.987551i \(0.449722\pi\)
\(588\) −23.6910 −0.977002
\(589\) −35.7940 −1.47486
\(590\) 25.5592 1.05225
\(591\) −26.0281 −1.07065
\(592\) −3.91645 −0.160965
\(593\) 14.7775 0.606841 0.303421 0.952857i \(-0.401871\pi\)
0.303421 + 0.952857i \(0.401871\pi\)
\(594\) −47.4588 −1.94726
\(595\) 4.82144 0.197660
\(596\) 49.7785 2.03901
\(597\) 17.9145 0.733191
\(598\) −12.2466 −0.500802
\(599\) −7.58443 −0.309891 −0.154946 0.987923i \(-0.549520\pi\)
−0.154946 + 0.987923i \(0.549520\pi\)
\(600\) −30.7930 −1.25712
\(601\) 9.09656 0.371056 0.185528 0.982639i \(-0.440600\pi\)
0.185528 + 0.982639i \(0.440600\pi\)
\(602\) −0.115316 −0.00469993
\(603\) −2.57380 −0.104813
\(604\) −66.7561 −2.71627
\(605\) 12.5385 0.509763
\(606\) −10.8511 −0.440794
\(607\) 29.2873 1.18873 0.594367 0.804194i \(-0.297403\pi\)
0.594367 + 0.804194i \(0.297403\pi\)
\(608\) 39.5663 1.60463
\(609\) 11.5903 0.469664
\(610\) −100.504 −4.06928
\(611\) −11.3673 −0.459870
\(612\) 4.47138 0.180745
\(613\) 8.42301 0.340202 0.170101 0.985427i \(-0.445591\pi\)
0.170101 + 0.985427i \(0.445591\pi\)
\(614\) −66.8840 −2.69922
\(615\) −30.8368 −1.24346
\(616\) −8.80270 −0.354671
\(617\) −6.87233 −0.276670 −0.138335 0.990386i \(-0.544175\pi\)
−0.138335 + 0.990386i \(0.544175\pi\)
\(618\) −37.4683 −1.50719
\(619\) 1.00000 0.0401934
\(620\) −70.9464 −2.84927
\(621\) −30.7711 −1.23480
\(622\) −37.4216 −1.50047
\(623\) 1.18298 0.0473951
\(624\) −1.26853 −0.0507818
\(625\) 29.0388 1.16155
\(626\) 63.1990 2.52594
\(627\) −29.6611 −1.18455
\(628\) −55.1423 −2.20042
\(629\) −4.89448 −0.195156
\(630\) −11.2115 −0.446676
\(631\) −49.0171 −1.95134 −0.975671 0.219241i \(-0.929642\pi\)
−0.975671 + 0.219241i \(0.929642\pi\)
\(632\) 25.7750 1.02528
\(633\) 12.5560 0.499055
\(634\) −75.1982 −2.98650
\(635\) 50.4775 2.00314
\(636\) −9.41110 −0.373175
\(637\) −5.93478 −0.235144
\(638\) −71.4684 −2.82946
\(639\) 19.3643 0.766040
\(640\) 61.6884 2.43845
\(641\) 6.97605 0.275537 0.137769 0.990464i \(-0.456007\pi\)
0.137769 + 0.990464i \(0.456007\pi\)
\(642\) −19.9974 −0.789236
\(643\) 12.3210 0.485893 0.242947 0.970040i \(-0.421886\pi\)
0.242947 + 0.970040i \(0.421886\pi\)
\(644\) −17.0006 −0.669916
\(645\) −0.258559 −0.0101807
\(646\) 15.8843 0.624960
\(647\) −4.35098 −0.171055 −0.0855273 0.996336i \(-0.527257\pi\)
−0.0855273 + 0.996336i \(0.527257\pi\)
\(648\) 8.44186 0.331628
\(649\) 11.0163 0.432429
\(650\) −22.9771 −0.901234
\(651\) 8.25331 0.323473
\(652\) 21.9112 0.858111
\(653\) −48.6301 −1.90304 −0.951521 0.307583i \(-0.900480\pi\)
−0.951521 + 0.307583i \(0.900480\pi\)
\(654\) 40.4652 1.58231
\(655\) −51.7127 −2.02058
\(656\) 5.69543 0.222369
\(657\) 13.7601 0.536832
\(658\) −26.2620 −1.02380
\(659\) −31.2362 −1.21679 −0.608394 0.793635i \(-0.708186\pi\)
−0.608394 + 0.793635i \(0.708186\pi\)
\(660\) −58.7906 −2.28842
\(661\) −26.7161 −1.03914 −0.519568 0.854429i \(-0.673907\pi\)
−0.519568 + 0.854429i \(0.673907\pi\)
\(662\) −32.2658 −1.25405
\(663\) −1.58531 −0.0615683
\(664\) −31.8225 −1.23495
\(665\) −23.9312 −0.928012
\(666\) 11.3813 0.441018
\(667\) −46.3382 −1.79422
\(668\) 11.5681 0.447585
\(669\) 28.4739 1.10087
\(670\) −18.1227 −0.700141
\(671\) −43.3184 −1.67229
\(672\) −9.12313 −0.351933
\(673\) 39.8203 1.53496 0.767480 0.641073i \(-0.221510\pi\)
0.767480 + 0.641073i \(0.221510\pi\)
\(674\) −34.8478 −1.34229
\(675\) −57.7325 −2.22212
\(676\) 3.01078 0.115799
\(677\) 32.4723 1.24801 0.624006 0.781420i \(-0.285504\pi\)
0.624006 + 0.781420i \(0.285504\pi\)
\(678\) 34.2688 1.31608
\(679\) −0.342809 −0.0131558
\(680\) 10.5698 0.405333
\(681\) 24.1635 0.925949
\(682\) −50.8916 −1.94874
\(683\) −41.2303 −1.57764 −0.788818 0.614627i \(-0.789306\pi\)
−0.788818 + 0.614627i \(0.789306\pi\)
\(684\) −22.1937 −0.848596
\(685\) 40.2781 1.53895
\(686\) −29.8835 −1.14096
\(687\) −25.0338 −0.955098
\(688\) 0.0477548 0.00182063
\(689\) −2.35755 −0.0898155
\(690\) −63.4394 −2.41510
\(691\) 43.8536 1.66827 0.834135 0.551560i \(-0.185967\pi\)
0.834135 + 0.551560i \(0.185967\pi\)
\(692\) 16.1100 0.612411
\(693\) −4.83230 −0.183564
\(694\) 65.7720 2.49667
\(695\) −37.7465 −1.43181
\(696\) 25.4089 0.963123
\(697\) 7.11771 0.269602
\(698\) 10.4157 0.394242
\(699\) −17.2820 −0.653667
\(700\) −31.8963 −1.20557
\(701\) −0.400398 −0.0151228 −0.00756141 0.999971i \(-0.502407\pi\)
−0.00756141 + 0.999971i \(0.502407\pi\)
\(702\) 12.5902 0.475185
\(703\) 24.2938 0.916256
\(704\) 49.0421 1.84835
\(705\) −58.8841 −2.21770
\(706\) 25.0445 0.942563
\(707\) −3.77345 −0.141915
\(708\) −11.6662 −0.438444
\(709\) 23.4093 0.879154 0.439577 0.898205i \(-0.355128\pi\)
0.439577 + 0.898205i \(0.355128\pi\)
\(710\) 136.348 5.11706
\(711\) 14.1494 0.530642
\(712\) 2.59339 0.0971914
\(713\) −32.9968 −1.23574
\(714\) −3.66258 −0.137068
\(715\) −14.7275 −0.550776
\(716\) −61.0777 −2.28258
\(717\) −35.0961 −1.31069
\(718\) 3.14314 0.117301
\(719\) 7.12733 0.265805 0.132902 0.991129i \(-0.457570\pi\)
0.132902 + 0.991129i \(0.457570\pi\)
\(720\) 4.64292 0.173031
\(721\) −13.0296 −0.485247
\(722\) −36.3107 −1.35134
\(723\) 27.6190 1.02716
\(724\) 22.8534 0.849340
\(725\) −86.9395 −3.22885
\(726\) −9.52480 −0.353499
\(727\) 38.7900 1.43864 0.719321 0.694677i \(-0.244453\pi\)
0.719321 + 0.694677i \(0.244453\pi\)
\(728\) 2.33523 0.0865495
\(729\) 27.0060 1.00022
\(730\) 96.8875 3.58597
\(731\) 0.0596802 0.00220735
\(732\) 45.8740 1.69555
\(733\) 33.5070 1.23761 0.618805 0.785544i \(-0.287617\pi\)
0.618805 + 0.785544i \(0.287617\pi\)
\(734\) −28.8211 −1.06381
\(735\) −30.7431 −1.13397
\(736\) 36.4744 1.34446
\(737\) −7.81112 −0.287726
\(738\) −16.5511 −0.609255
\(739\) 21.6782 0.797444 0.398722 0.917072i \(-0.369454\pi\)
0.398722 + 0.917072i \(0.369454\pi\)
\(740\) 48.1521 1.77010
\(741\) 7.86868 0.289063
\(742\) −5.44670 −0.199955
\(743\) 52.1191 1.91206 0.956032 0.293263i \(-0.0947411\pi\)
0.956032 + 0.293263i \(0.0947411\pi\)
\(744\) 18.0933 0.663334
\(745\) 64.5959 2.36661
\(746\) −0.730065 −0.0267296
\(747\) −17.4692 −0.639163
\(748\) 13.5700 0.496167
\(749\) −6.95411 −0.254098
\(750\) −61.0464 −2.22910
\(751\) −51.4811 −1.87857 −0.939285 0.343137i \(-0.888510\pi\)
−0.939285 + 0.343137i \(0.888510\pi\)
\(752\) 10.8757 0.396595
\(753\) 4.75006 0.173102
\(754\) 18.9596 0.690467
\(755\) −86.6272 −3.15269
\(756\) 17.4774 0.635648
\(757\) −36.3738 −1.32203 −0.661014 0.750374i \(-0.729874\pi\)
−0.661014 + 0.750374i \(0.729874\pi\)
\(758\) 82.0073 2.97864
\(759\) −27.3432 −0.992496
\(760\) −52.4632 −1.90304
\(761\) 50.0496 1.81430 0.907149 0.420810i \(-0.138254\pi\)
0.907149 + 0.420810i \(0.138254\pi\)
\(762\) −38.3449 −1.38909
\(763\) 14.0718 0.509432
\(764\) 43.7794 1.58388
\(765\) 5.80236 0.209785
\(766\) −34.3768 −1.24208
\(767\) −2.92248 −0.105525
\(768\) −12.3617 −0.446064
\(769\) 7.18707 0.259172 0.129586 0.991568i \(-0.458635\pi\)
0.129586 + 0.991568i \(0.458635\pi\)
\(770\) −34.0252 −1.22618
\(771\) −25.0278 −0.901353
\(772\) −61.0348 −2.19669
\(773\) −40.9826 −1.47404 −0.737021 0.675869i \(-0.763768\pi\)
−0.737021 + 0.675869i \(0.763768\pi\)
\(774\) −0.138777 −0.00498824
\(775\) −61.9084 −2.22382
\(776\) −0.751524 −0.0269781
\(777\) −5.60161 −0.200957
\(778\) 27.6063 0.989734
\(779\) −35.3287 −1.26578
\(780\) 15.5963 0.558438
\(781\) 58.7678 2.10288
\(782\) 14.6430 0.523633
\(783\) 47.6381 1.70245
\(784\) 5.67812 0.202790
\(785\) −71.5563 −2.55395
\(786\) 39.2832 1.40119
\(787\) 17.1646 0.611850 0.305925 0.952056i \(-0.401034\pi\)
0.305925 + 0.952056i \(0.401034\pi\)
\(788\) −59.1047 −2.10552
\(789\) −11.8155 −0.420643
\(790\) 99.6286 3.54463
\(791\) 11.9170 0.423718
\(792\) −10.5936 −0.376428
\(793\) 11.4918 0.408085
\(794\) −30.0113 −1.06506
\(795\) −12.2125 −0.433132
\(796\) 40.6802 1.44187
\(797\) 5.73226 0.203047 0.101524 0.994833i \(-0.467628\pi\)
0.101524 + 0.994833i \(0.467628\pi\)
\(798\) 18.1792 0.643536
\(799\) 13.5916 0.480835
\(800\) 68.4330 2.41947
\(801\) 1.42366 0.0503024
\(802\) −11.7752 −0.415798
\(803\) 41.7598 1.47367
\(804\) 8.27193 0.291729
\(805\) −22.0611 −0.777550
\(806\) 13.5008 0.475547
\(807\) −12.8893 −0.453726
\(808\) −8.27236 −0.291021
\(809\) 11.0768 0.389438 0.194719 0.980859i \(-0.437621\pi\)
0.194719 + 0.980859i \(0.437621\pi\)
\(810\) 32.6304 1.14652
\(811\) 38.1818 1.34074 0.670372 0.742025i \(-0.266135\pi\)
0.670372 + 0.742025i \(0.266135\pi\)
\(812\) 26.3193 0.923628
\(813\) 32.1857 1.12880
\(814\) 34.5407 1.21065
\(815\) 28.4335 0.995982
\(816\) 1.51675 0.0530969
\(817\) −0.296223 −0.0103635
\(818\) 23.9595 0.837725
\(819\) 1.28194 0.0447946
\(820\) −70.0242 −2.44535
\(821\) 22.3533 0.780136 0.390068 0.920786i \(-0.372451\pi\)
0.390068 + 0.920786i \(0.372451\pi\)
\(822\) −30.5970 −1.06719
\(823\) −29.5354 −1.02954 −0.514770 0.857328i \(-0.672123\pi\)
−0.514770 + 0.857328i \(0.672123\pi\)
\(824\) −28.5641 −0.995079
\(825\) −51.3012 −1.78608
\(826\) −6.75187 −0.234928
\(827\) −42.0989 −1.46392 −0.731961 0.681347i \(-0.761395\pi\)
−0.731961 + 0.681347i \(0.761395\pi\)
\(828\) −20.4593 −0.711011
\(829\) −49.5363 −1.72047 −0.860234 0.509899i \(-0.829683\pi\)
−0.860234 + 0.509899i \(0.829683\pi\)
\(830\) −123.004 −4.26953
\(831\) −19.2196 −0.666720
\(832\) −13.0102 −0.451048
\(833\) 7.09608 0.245865
\(834\) 28.6739 0.992896
\(835\) 15.0116 0.519498
\(836\) −67.3545 −2.32950
\(837\) 33.9224 1.17253
\(838\) −9.49910 −0.328141
\(839\) −21.5369 −0.743538 −0.371769 0.928325i \(-0.621249\pi\)
−0.371769 + 0.928325i \(0.621249\pi\)
\(840\) 12.0969 0.417382
\(841\) 42.7383 1.47374
\(842\) −38.0729 −1.31208
\(843\) 16.1745 0.557080
\(844\) 28.5121 0.981427
\(845\) 3.90699 0.134405
\(846\) −31.6050 −1.08660
\(847\) −3.31225 −0.113810
\(848\) 2.25560 0.0774575
\(849\) −30.9670 −1.06278
\(850\) 27.4731 0.942321
\(851\) 22.3953 0.767701
\(852\) −62.2348 −2.13213
\(853\) −45.9227 −1.57236 −0.786182 0.617995i \(-0.787945\pi\)
−0.786182 + 0.617995i \(0.787945\pi\)
\(854\) 26.5497 0.908512
\(855\) −28.8000 −0.984939
\(856\) −15.2452 −0.521069
\(857\) −43.5480 −1.48757 −0.743786 0.668417i \(-0.766972\pi\)
−0.743786 + 0.668417i \(0.766972\pi\)
\(858\) 11.1876 0.381940
\(859\) −37.8011 −1.28976 −0.644878 0.764286i \(-0.723092\pi\)
−0.644878 + 0.764286i \(0.723092\pi\)
\(860\) −0.587136 −0.0200212
\(861\) 8.14604 0.277616
\(862\) 62.6755 2.13474
\(863\) −2.80812 −0.0955896 −0.0477948 0.998857i \(-0.515219\pi\)
−0.0477948 + 0.998857i \(0.515219\pi\)
\(864\) −37.4975 −1.27569
\(865\) 20.9054 0.710806
\(866\) 50.2805 1.70860
\(867\) −20.6442 −0.701115
\(868\) 18.7416 0.636133
\(869\) 42.9412 1.45668
\(870\) 98.2135 3.32975
\(871\) 2.07218 0.0702132
\(872\) 30.8489 1.04467
\(873\) −0.412553 −0.0139628
\(874\) −72.6806 −2.45846
\(875\) −21.2289 −0.717667
\(876\) −44.2234 −1.49417
\(877\) −0.199904 −0.00675028 −0.00337514 0.999994i \(-0.501074\pi\)
−0.00337514 + 0.999994i \(0.501074\pi\)
\(878\) 76.3265 2.57589
\(879\) −1.77202 −0.0597687
\(880\) 14.0906 0.474993
\(881\) −31.5566 −1.06317 −0.531584 0.847006i \(-0.678403\pi\)
−0.531584 + 0.847006i \(0.678403\pi\)
\(882\) −16.5008 −0.555611
\(883\) 44.5139 1.49801 0.749005 0.662564i \(-0.230532\pi\)
0.749005 + 0.662564i \(0.230532\pi\)
\(884\) −3.59992 −0.121079
\(885\) −15.1389 −0.508888
\(886\) 58.0059 1.94875
\(887\) 18.6140 0.624998 0.312499 0.949918i \(-0.398834\pi\)
0.312499 + 0.949918i \(0.398834\pi\)
\(888\) −12.2801 −0.412095
\(889\) −13.3344 −0.447223
\(890\) 10.0243 0.336014
\(891\) 14.0641 0.471166
\(892\) 64.6586 2.16493
\(893\) −67.4617 −2.25752
\(894\) −49.0699 −1.64114
\(895\) −79.2585 −2.64932
\(896\) −16.2960 −0.544411
\(897\) 7.25377 0.242196
\(898\) −25.0959 −0.837461
\(899\) 51.0839 1.70374
\(900\) −38.3857 −1.27952
\(901\) 2.81887 0.0939102
\(902\) −50.2302 −1.67248
\(903\) 0.0683025 0.00227297
\(904\) 26.1250 0.868904
\(905\) 29.6561 0.985803
\(906\) 65.8058 2.18625
\(907\) 38.1532 1.26686 0.633428 0.773801i \(-0.281647\pi\)
0.633428 + 0.773801i \(0.281647\pi\)
\(908\) 54.8706 1.82094
\(909\) −4.54116 −0.150621
\(910\) 9.02642 0.299223
\(911\) −13.3450 −0.442139 −0.221069 0.975258i \(-0.570955\pi\)
−0.221069 + 0.975258i \(0.570955\pi\)
\(912\) −7.52839 −0.249290
\(913\) −53.0163 −1.75458
\(914\) −53.9348 −1.78401
\(915\) 59.5291 1.96797
\(916\) −56.8467 −1.87827
\(917\) 13.6607 0.451117
\(918\) −15.0538 −0.496848
\(919\) −0.672650 −0.0221887 −0.0110943 0.999938i \(-0.503532\pi\)
−0.0110943 + 0.999938i \(0.503532\pi\)
\(920\) −48.3634 −1.59449
\(921\) 39.6159 1.30539
\(922\) 59.8233 1.97017
\(923\) −15.5903 −0.513160
\(924\) 15.5305 0.510915
\(925\) 42.0179 1.38154
\(926\) 40.2698 1.32335
\(927\) −15.6805 −0.515014
\(928\) −56.4676 −1.85364
\(929\) −39.7353 −1.30367 −0.651837 0.758359i \(-0.726001\pi\)
−0.651837 + 0.758359i \(0.726001\pi\)
\(930\) 69.9365 2.29331
\(931\) −35.2214 −1.15433
\(932\) −39.2441 −1.28548
\(933\) 22.1651 0.725653
\(934\) 25.5034 0.834497
\(935\) 17.6093 0.575886
\(936\) 2.81034 0.0918588
\(937\) −7.21086 −0.235569 −0.117784 0.993039i \(-0.537579\pi\)
−0.117784 + 0.993039i \(0.537579\pi\)
\(938\) 4.78741 0.156314
\(939\) −37.4333 −1.22159
\(940\) −133.714 −4.36128
\(941\) −1.52336 −0.0496600 −0.0248300 0.999692i \(-0.507904\pi\)
−0.0248300 + 0.999692i \(0.507904\pi\)
\(942\) 54.3573 1.77106
\(943\) −32.5679 −1.06056
\(944\) 2.79609 0.0910051
\(945\) 22.6799 0.737777
\(946\) −0.421168 −0.0136933
\(947\) −4.31072 −0.140080 −0.0700398 0.997544i \(-0.522313\pi\)
−0.0700398 + 0.997544i \(0.522313\pi\)
\(948\) −45.4745 −1.47694
\(949\) −11.0783 −0.359616
\(950\) −136.363 −4.42419
\(951\) 44.5404 1.44432
\(952\) −2.79219 −0.0904953
\(953\) −4.38181 −0.141941 −0.0709704 0.997478i \(-0.522610\pi\)
−0.0709704 + 0.997478i \(0.522610\pi\)
\(954\) −6.55484 −0.212221
\(955\) 56.8111 1.83836
\(956\) −79.6962 −2.57756
\(957\) 42.3313 1.36838
\(958\) −5.30915 −0.171531
\(959\) −10.6401 −0.343587
\(960\) −67.3948 −2.17516
\(961\) 5.37612 0.173423
\(962\) −9.16317 −0.295432
\(963\) −8.36893 −0.269685
\(964\) 62.7173 2.01999
\(965\) −79.2028 −2.54963
\(966\) 16.7586 0.539198
\(967\) 19.2219 0.618134 0.309067 0.951040i \(-0.399983\pi\)
0.309067 + 0.951040i \(0.399983\pi\)
\(968\) −7.26129 −0.233387
\(969\) −9.40840 −0.302241
\(970\) −2.90488 −0.0932699
\(971\) −7.62570 −0.244720 −0.122360 0.992486i \(-0.539046\pi\)
−0.122360 + 0.992486i \(0.539046\pi\)
\(972\) 35.9079 1.15175
\(973\) 9.97135 0.319667
\(974\) −8.34722 −0.267462
\(975\) 13.6095 0.435852
\(976\) −10.9948 −0.351935
\(977\) 13.5509 0.433533 0.216766 0.976223i \(-0.430449\pi\)
0.216766 + 0.976223i \(0.430449\pi\)
\(978\) −21.5993 −0.690671
\(979\) 4.32059 0.138087
\(980\) −69.8114 −2.23004
\(981\) 16.9347 0.540683
\(982\) 33.6809 1.07480
\(983\) −62.3913 −1.98997 −0.994986 0.100013i \(-0.968112\pi\)
−0.994986 + 0.100013i \(0.968112\pi\)
\(984\) 17.8582 0.569298
\(985\) −76.6982 −2.44381
\(986\) −22.6695 −0.721945
\(987\) 15.5552 0.495128
\(988\) 17.8682 0.568464
\(989\) −0.273074 −0.00868325
\(990\) −40.9476 −1.30140
\(991\) −1.75024 −0.0555983 −0.0277991 0.999614i \(-0.508850\pi\)
−0.0277991 + 0.999614i \(0.508850\pi\)
\(992\) −40.2098 −1.27666
\(993\) 19.1113 0.606478
\(994\) −36.0186 −1.14244
\(995\) 52.7894 1.67354
\(996\) 56.1440 1.77899
\(997\) 38.5253 1.22011 0.610054 0.792359i \(-0.291148\pi\)
0.610054 + 0.792359i \(0.291148\pi\)
\(998\) 10.1626 0.321693
\(999\) −23.0235 −0.728431
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 \(a_p\))