Properties

Label 8002.2.a.d.1.8
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.80104 q^{3}\) \(+1.00000 q^{4}\) \(+0.676703 q^{5}\) \(-2.80104 q^{6}\) \(+3.76033 q^{7}\) \(+1.00000 q^{8}\) \(+4.84585 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.80104 q^{3}\) \(+1.00000 q^{4}\) \(+0.676703 q^{5}\) \(-2.80104 q^{6}\) \(+3.76033 q^{7}\) \(+1.00000 q^{8}\) \(+4.84585 q^{9}\) \(+0.676703 q^{10}\) \(-0.631840 q^{11}\) \(-2.80104 q^{12}\) \(-6.22087 q^{13}\) \(+3.76033 q^{14}\) \(-1.89548 q^{15}\) \(+1.00000 q^{16}\) \(+3.39684 q^{17}\) \(+4.84585 q^{18}\) \(+1.27370 q^{19}\) \(+0.676703 q^{20}\) \(-10.5329 q^{21}\) \(-0.631840 q^{22}\) \(+3.84216 q^{23}\) \(-2.80104 q^{24}\) \(-4.54207 q^{25}\) \(-6.22087 q^{26}\) \(-5.17032 q^{27}\) \(+3.76033 q^{28}\) \(+4.19303 q^{29}\) \(-1.89548 q^{30}\) \(-9.96120 q^{31}\) \(+1.00000 q^{32}\) \(+1.76981 q^{33}\) \(+3.39684 q^{34}\) \(+2.54463 q^{35}\) \(+4.84585 q^{36}\) \(-9.06735 q^{37}\) \(+1.27370 q^{38}\) \(+17.4249 q^{39}\) \(+0.676703 q^{40}\) \(+0.532380 q^{41}\) \(-10.5329 q^{42}\) \(-7.96327 q^{43}\) \(-0.631840 q^{44}\) \(+3.27920 q^{45}\) \(+3.84216 q^{46}\) \(-3.81367 q^{47}\) \(-2.80104 q^{48}\) \(+7.14011 q^{49}\) \(-4.54207 q^{50}\) \(-9.51470 q^{51}\) \(-6.22087 q^{52}\) \(+3.38497 q^{53}\) \(-5.17032 q^{54}\) \(-0.427568 q^{55}\) \(+3.76033 q^{56}\) \(-3.56770 q^{57}\) \(+4.19303 q^{58}\) \(-6.10929 q^{59}\) \(-1.89548 q^{60}\) \(-2.32597 q^{61}\) \(-9.96120 q^{62}\) \(+18.2220 q^{63}\) \(+1.00000 q^{64}\) \(-4.20968 q^{65}\) \(+1.76981 q^{66}\) \(+3.52438 q^{67}\) \(+3.39684 q^{68}\) \(-10.7621 q^{69}\) \(+2.54463 q^{70}\) \(-6.46908 q^{71}\) \(+4.84585 q^{72}\) \(+1.69845 q^{73}\) \(-9.06735 q^{74}\) \(+12.7226 q^{75}\) \(+1.27370 q^{76}\) \(-2.37593 q^{77}\) \(+17.4249 q^{78}\) \(-8.68079 q^{79}\) \(+0.676703 q^{80}\) \(-0.0552674 q^{81}\) \(+0.532380 q^{82}\) \(-12.7963 q^{83}\) \(-10.5329 q^{84}\) \(+2.29865 q^{85}\) \(-7.96327 q^{86}\) \(-11.7449 q^{87}\) \(-0.631840 q^{88}\) \(+4.85184 q^{89}\) \(+3.27920 q^{90}\) \(-23.3926 q^{91}\) \(+3.84216 q^{92}\) \(+27.9018 q^{93}\) \(-3.81367 q^{94}\) \(+0.861920 q^{95}\) \(-2.80104 q^{96}\) \(+2.77992 q^{97}\) \(+7.14011 q^{98}\) \(-3.06180 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.80104 −1.61718 −0.808592 0.588370i \(-0.799770\pi\)
−0.808592 + 0.588370i \(0.799770\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.676703 0.302631 0.151315 0.988486i \(-0.451649\pi\)
0.151315 + 0.988486i \(0.451649\pi\)
\(6\) −2.80104 −1.14352
\(7\) 3.76033 1.42127 0.710636 0.703559i \(-0.248407\pi\)
0.710636 + 0.703559i \(0.248407\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.84585 1.61528
\(10\) 0.676703 0.213992
\(11\) −0.631840 −0.190507 −0.0952534 0.995453i \(-0.530366\pi\)
−0.0952534 + 0.995453i \(0.530366\pi\)
\(12\) −2.80104 −0.808592
\(13\) −6.22087 −1.72536 −0.862680 0.505750i \(-0.831216\pi\)
−0.862680 + 0.505750i \(0.831216\pi\)
\(14\) 3.76033 1.00499
\(15\) −1.89548 −0.489410
\(16\) 1.00000 0.250000
\(17\) 3.39684 0.823855 0.411927 0.911217i \(-0.364856\pi\)
0.411927 + 0.911217i \(0.364856\pi\)
\(18\) 4.84585 1.14218
\(19\) 1.27370 0.292208 0.146104 0.989269i \(-0.453327\pi\)
0.146104 + 0.989269i \(0.453327\pi\)
\(20\) 0.676703 0.151315
\(21\) −10.5329 −2.29846
\(22\) −0.631840 −0.134709
\(23\) 3.84216 0.801147 0.400573 0.916265i \(-0.368811\pi\)
0.400573 + 0.916265i \(0.368811\pi\)
\(24\) −2.80104 −0.571761
\(25\) −4.54207 −0.908415
\(26\) −6.22087 −1.22001
\(27\) −5.17032 −0.995028
\(28\) 3.76033 0.710636
\(29\) 4.19303 0.778627 0.389313 0.921105i \(-0.372712\pi\)
0.389313 + 0.921105i \(0.372712\pi\)
\(30\) −1.89548 −0.346065
\(31\) −9.96120 −1.78908 −0.894542 0.446984i \(-0.852498\pi\)
−0.894542 + 0.446984i \(0.852498\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.76981 0.308085
\(34\) 3.39684 0.582553
\(35\) 2.54463 0.430121
\(36\) 4.84585 0.807642
\(37\) −9.06735 −1.49066 −0.745332 0.666694i \(-0.767709\pi\)
−0.745332 + 0.666694i \(0.767709\pi\)
\(38\) 1.27370 0.206622
\(39\) 17.4249 2.79022
\(40\) 0.676703 0.106996
\(41\) 0.532380 0.0831438 0.0415719 0.999136i \(-0.486763\pi\)
0.0415719 + 0.999136i \(0.486763\pi\)
\(42\) −10.5329 −1.62526
\(43\) −7.96327 −1.21439 −0.607194 0.794554i \(-0.707705\pi\)
−0.607194 + 0.794554i \(0.707705\pi\)
\(44\) −0.631840 −0.0952534
\(45\) 3.27920 0.488835
\(46\) 3.84216 0.566496
\(47\) −3.81367 −0.556281 −0.278140 0.960540i \(-0.589718\pi\)
−0.278140 + 0.960540i \(0.589718\pi\)
\(48\) −2.80104 −0.404296
\(49\) 7.14011 1.02002
\(50\) −4.54207 −0.642346
\(51\) −9.51470 −1.33233
\(52\) −6.22087 −0.862680
\(53\) 3.38497 0.464961 0.232481 0.972601i \(-0.425316\pi\)
0.232481 + 0.972601i \(0.425316\pi\)
\(54\) −5.17032 −0.703591
\(55\) −0.427568 −0.0576532
\(56\) 3.76033 0.502496
\(57\) −3.56770 −0.472554
\(58\) 4.19303 0.550572
\(59\) −6.10929 −0.795362 −0.397681 0.917524i \(-0.630185\pi\)
−0.397681 + 0.917524i \(0.630185\pi\)
\(60\) −1.89548 −0.244705
\(61\) −2.32597 −0.297810 −0.148905 0.988851i \(-0.547575\pi\)
−0.148905 + 0.988851i \(0.547575\pi\)
\(62\) −9.96120 −1.26507
\(63\) 18.2220 2.29576
\(64\) 1.00000 0.125000
\(65\) −4.20968 −0.522147
\(66\) 1.76981 0.217849
\(67\) 3.52438 0.430571 0.215286 0.976551i \(-0.430932\pi\)
0.215286 + 0.976551i \(0.430932\pi\)
\(68\) 3.39684 0.411927
\(69\) −10.7621 −1.29560
\(70\) 2.54463 0.304141
\(71\) −6.46908 −0.767738 −0.383869 0.923388i \(-0.625409\pi\)
−0.383869 + 0.923388i \(0.625409\pi\)
\(72\) 4.84585 0.571089
\(73\) 1.69845 0.198789 0.0993944 0.995048i \(-0.468309\pi\)
0.0993944 + 0.995048i \(0.468309\pi\)
\(74\) −9.06735 −1.05406
\(75\) 12.7226 1.46907
\(76\) 1.27370 0.146104
\(77\) −2.37593 −0.270762
\(78\) 17.4249 1.97299
\(79\) −8.68079 −0.976665 −0.488332 0.872658i \(-0.662395\pi\)
−0.488332 + 0.872658i \(0.662395\pi\)
\(80\) 0.676703 0.0756577
\(81\) −0.0552674 −0.00614083
\(82\) 0.532380 0.0587915
\(83\) −12.7963 −1.40458 −0.702290 0.711891i \(-0.747839\pi\)
−0.702290 + 0.711891i \(0.747839\pi\)
\(84\) −10.5329 −1.14923
\(85\) 2.29865 0.249324
\(86\) −7.96327 −0.858702
\(87\) −11.7449 −1.25918
\(88\) −0.631840 −0.0673544
\(89\) 4.85184 0.514294 0.257147 0.966372i \(-0.417217\pi\)
0.257147 + 0.966372i \(0.417217\pi\)
\(90\) 3.27920 0.345658
\(91\) −23.3926 −2.45221
\(92\) 3.84216 0.400573
\(93\) 27.9018 2.89328
\(94\) −3.81367 −0.393350
\(95\) 0.861920 0.0884311
\(96\) −2.80104 −0.285880
\(97\) 2.77992 0.282258 0.141129 0.989991i \(-0.454927\pi\)
0.141129 + 0.989991i \(0.454927\pi\)
\(98\) 7.14011 0.721260
\(99\) −3.06180 −0.307723
\(100\) −4.54207 −0.454207
\(101\) −5.96969 −0.594006 −0.297003 0.954877i \(-0.595987\pi\)
−0.297003 + 0.954877i \(0.595987\pi\)
\(102\) −9.51470 −0.942096
\(103\) 5.47500 0.539468 0.269734 0.962935i \(-0.413064\pi\)
0.269734 + 0.962935i \(0.413064\pi\)
\(104\) −6.22087 −0.610007
\(105\) −7.12762 −0.695585
\(106\) 3.38497 0.328777
\(107\) 14.9969 1.44981 0.724904 0.688850i \(-0.241884\pi\)
0.724904 + 0.688850i \(0.241884\pi\)
\(108\) −5.17032 −0.497514
\(109\) −12.1876 −1.16736 −0.583682 0.811982i \(-0.698389\pi\)
−0.583682 + 0.811982i \(0.698389\pi\)
\(110\) −0.427568 −0.0407670
\(111\) 25.3981 2.41068
\(112\) 3.76033 0.355318
\(113\) 15.6649 1.47363 0.736817 0.676092i \(-0.236328\pi\)
0.736817 + 0.676092i \(0.236328\pi\)
\(114\) −3.56770 −0.334146
\(115\) 2.60000 0.242452
\(116\) 4.19303 0.389313
\(117\) −30.1454 −2.78695
\(118\) −6.10929 −0.562406
\(119\) 12.7733 1.17092
\(120\) −1.89548 −0.173032
\(121\) −10.6008 −0.963707
\(122\) −2.32597 −0.210584
\(123\) −1.49122 −0.134459
\(124\) −9.96120 −0.894542
\(125\) −6.45715 −0.577545
\(126\) 18.2220 1.62335
\(127\) 4.99299 0.443056 0.221528 0.975154i \(-0.428896\pi\)
0.221528 + 0.975154i \(0.428896\pi\)
\(128\) 1.00000 0.0883883
\(129\) 22.3055 1.96389
\(130\) −4.20968 −0.369214
\(131\) −3.86571 −0.337749 −0.168874 0.985638i \(-0.554013\pi\)
−0.168874 + 0.985638i \(0.554013\pi\)
\(132\) 1.76981 0.154042
\(133\) 4.78956 0.415307
\(134\) 3.52438 0.304460
\(135\) −3.49877 −0.301126
\(136\) 3.39684 0.291277
\(137\) −9.58553 −0.818947 −0.409474 0.912322i \(-0.634288\pi\)
−0.409474 + 0.912322i \(0.634288\pi\)
\(138\) −10.7621 −0.916129
\(139\) −4.56613 −0.387294 −0.193647 0.981071i \(-0.562032\pi\)
−0.193647 + 0.981071i \(0.562032\pi\)
\(140\) 2.54463 0.215060
\(141\) 10.6823 0.899608
\(142\) −6.46908 −0.542873
\(143\) 3.93060 0.328693
\(144\) 4.84585 0.403821
\(145\) 2.83744 0.235636
\(146\) 1.69845 0.140565
\(147\) −19.9998 −1.64955
\(148\) −9.06735 −0.745332
\(149\) −0.673255 −0.0551552 −0.0275776 0.999620i \(-0.508779\pi\)
−0.0275776 + 0.999620i \(0.508779\pi\)
\(150\) 12.7226 1.03879
\(151\) 19.3660 1.57598 0.787990 0.615689i \(-0.211122\pi\)
0.787990 + 0.615689i \(0.211122\pi\)
\(152\) 1.27370 0.103311
\(153\) 16.4606 1.33076
\(154\) −2.37593 −0.191458
\(155\) −6.74077 −0.541432
\(156\) 17.4249 1.39511
\(157\) −16.9998 −1.35673 −0.678366 0.734724i \(-0.737312\pi\)
−0.678366 + 0.734724i \(0.737312\pi\)
\(158\) −8.68079 −0.690606
\(159\) −9.48145 −0.751928
\(160\) 0.676703 0.0534981
\(161\) 14.4478 1.13865
\(162\) −0.0552674 −0.00434222
\(163\) −13.0919 −1.02544 −0.512720 0.858556i \(-0.671362\pi\)
−0.512720 + 0.858556i \(0.671362\pi\)
\(164\) 0.532380 0.0415719
\(165\) 1.19764 0.0932359
\(166\) −12.7963 −0.993188
\(167\) −4.43489 −0.343182 −0.171591 0.985168i \(-0.554891\pi\)
−0.171591 + 0.985168i \(0.554891\pi\)
\(168\) −10.5329 −0.812628
\(169\) 25.6993 1.97687
\(170\) 2.29865 0.176299
\(171\) 6.17219 0.471999
\(172\) −7.96327 −0.607194
\(173\) 14.9456 1.13629 0.568146 0.822928i \(-0.307661\pi\)
0.568146 + 0.822928i \(0.307661\pi\)
\(174\) −11.7449 −0.890376
\(175\) −17.0797 −1.29110
\(176\) −0.631840 −0.0476267
\(177\) 17.1124 1.28625
\(178\) 4.85184 0.363661
\(179\) 4.46588 0.333795 0.166898 0.985974i \(-0.446625\pi\)
0.166898 + 0.985974i \(0.446625\pi\)
\(180\) 3.27920 0.244417
\(181\) 8.75756 0.650945 0.325472 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(182\) −23.3926 −1.73397
\(183\) 6.51516 0.481614
\(184\) 3.84216 0.283248
\(185\) −6.13590 −0.451121
\(186\) 27.9018 2.04586
\(187\) −2.14626 −0.156950
\(188\) −3.81367 −0.278140
\(189\) −19.4421 −1.41421
\(190\) 0.861920 0.0625303
\(191\) 16.4938 1.19345 0.596724 0.802447i \(-0.296469\pi\)
0.596724 + 0.802447i \(0.296469\pi\)
\(192\) −2.80104 −0.202148
\(193\) 10.3176 0.742678 0.371339 0.928497i \(-0.378899\pi\)
0.371339 + 0.928497i \(0.378899\pi\)
\(194\) 2.77992 0.199587
\(195\) 11.7915 0.844408
\(196\) 7.14011 0.510008
\(197\) −21.1641 −1.50788 −0.753939 0.656944i \(-0.771849\pi\)
−0.753939 + 0.656944i \(0.771849\pi\)
\(198\) −3.06180 −0.217593
\(199\) −0.760069 −0.0538799 −0.0269399 0.999637i \(-0.508576\pi\)
−0.0269399 + 0.999637i \(0.508576\pi\)
\(200\) −4.54207 −0.321173
\(201\) −9.87194 −0.696313
\(202\) −5.96969 −0.420026
\(203\) 15.7672 1.10664
\(204\) −9.51470 −0.666163
\(205\) 0.360263 0.0251619
\(206\) 5.47500 0.381462
\(207\) 18.6186 1.29408
\(208\) −6.22087 −0.431340
\(209\) −0.804778 −0.0556676
\(210\) −7.12762 −0.491853
\(211\) 20.5980 1.41802 0.709012 0.705196i \(-0.249141\pi\)
0.709012 + 0.705196i \(0.249141\pi\)
\(212\) 3.38497 0.232481
\(213\) 18.1202 1.24157
\(214\) 14.9969 1.02517
\(215\) −5.38877 −0.367511
\(216\) −5.17032 −0.351796
\(217\) −37.4574 −2.54278
\(218\) −12.1876 −0.825452
\(219\) −4.75744 −0.321478
\(220\) −0.427568 −0.0288266
\(221\) −21.1313 −1.42145
\(222\) 25.3981 1.70461
\(223\) 2.76363 0.185066 0.0925332 0.995710i \(-0.470504\pi\)
0.0925332 + 0.995710i \(0.470504\pi\)
\(224\) 3.76033 0.251248
\(225\) −22.0102 −1.46735
\(226\) 15.6649 1.04202
\(227\) 3.60460 0.239246 0.119623 0.992819i \(-0.461831\pi\)
0.119623 + 0.992819i \(0.461831\pi\)
\(228\) −3.56770 −0.236277
\(229\) −19.7873 −1.30758 −0.653791 0.756676i \(-0.726822\pi\)
−0.653791 + 0.756676i \(0.726822\pi\)
\(230\) 2.60000 0.171439
\(231\) 6.65508 0.437872
\(232\) 4.19303 0.275286
\(233\) −1.24894 −0.0818207 −0.0409103 0.999163i \(-0.513026\pi\)
−0.0409103 + 0.999163i \(0.513026\pi\)
\(234\) −30.1454 −1.97067
\(235\) −2.58072 −0.168348
\(236\) −6.10929 −0.397681
\(237\) 24.3153 1.57945
\(238\) 12.7733 0.827967
\(239\) 6.22948 0.402952 0.201476 0.979493i \(-0.435426\pi\)
0.201476 + 0.979493i \(0.435426\pi\)
\(240\) −1.89548 −0.122352
\(241\) −13.0332 −0.839542 −0.419771 0.907630i \(-0.637890\pi\)
−0.419771 + 0.907630i \(0.637890\pi\)
\(242\) −10.6008 −0.681444
\(243\) 15.6658 1.00496
\(244\) −2.32597 −0.148905
\(245\) 4.83174 0.308688
\(246\) −1.49122 −0.0950767
\(247\) −7.92356 −0.504164
\(248\) −9.96120 −0.632537
\(249\) 35.8431 2.27146
\(250\) −6.45715 −0.408386
\(251\) 13.6041 0.858683 0.429342 0.903142i \(-0.358746\pi\)
0.429342 + 0.903142i \(0.358746\pi\)
\(252\) 18.2220 1.14788
\(253\) −2.42763 −0.152624
\(254\) 4.99299 0.313288
\(255\) −6.43863 −0.403203
\(256\) 1.00000 0.0625000
\(257\) 3.05899 0.190815 0.0954074 0.995438i \(-0.469585\pi\)
0.0954074 + 0.995438i \(0.469585\pi\)
\(258\) 22.3055 1.38868
\(259\) −34.0963 −2.11864
\(260\) −4.20968 −0.261074
\(261\) 20.3188 1.25770
\(262\) −3.86571 −0.238824
\(263\) −12.8608 −0.793030 −0.396515 0.918028i \(-0.629780\pi\)
−0.396515 + 0.918028i \(0.629780\pi\)
\(264\) 1.76981 0.108924
\(265\) 2.29062 0.140712
\(266\) 4.78956 0.293667
\(267\) −13.5902 −0.831709
\(268\) 3.52438 0.215286
\(269\) −0.356613 −0.0217431 −0.0108715 0.999941i \(-0.503461\pi\)
−0.0108715 + 0.999941i \(0.503461\pi\)
\(270\) −3.49877 −0.212928
\(271\) −15.6107 −0.948285 −0.474142 0.880448i \(-0.657242\pi\)
−0.474142 + 0.880448i \(0.657242\pi\)
\(272\) 3.39684 0.205964
\(273\) 65.5236 3.96567
\(274\) −9.58553 −0.579083
\(275\) 2.86986 0.173059
\(276\) −10.7621 −0.647801
\(277\) −17.5079 −1.05195 −0.525975 0.850500i \(-0.676300\pi\)
−0.525975 + 0.850500i \(0.676300\pi\)
\(278\) −4.56613 −0.273858
\(279\) −48.2705 −2.88988
\(280\) 2.54463 0.152071
\(281\) 7.79420 0.464963 0.232482 0.972601i \(-0.425315\pi\)
0.232482 + 0.972601i \(0.425315\pi\)
\(282\) 10.6823 0.636119
\(283\) −15.3517 −0.912566 −0.456283 0.889835i \(-0.650819\pi\)
−0.456283 + 0.889835i \(0.650819\pi\)
\(284\) −6.46908 −0.383869
\(285\) −2.41428 −0.143009
\(286\) 3.93060 0.232421
\(287\) 2.00193 0.118170
\(288\) 4.84585 0.285545
\(289\) −5.46147 −0.321263
\(290\) 2.83744 0.166620
\(291\) −7.78668 −0.456463
\(292\) 1.69845 0.0993944
\(293\) −5.71102 −0.333641 −0.166821 0.985987i \(-0.553350\pi\)
−0.166821 + 0.985987i \(0.553350\pi\)
\(294\) −19.9998 −1.16641
\(295\) −4.13418 −0.240701
\(296\) −9.06735 −0.527029
\(297\) 3.26681 0.189560
\(298\) −0.673255 −0.0390006
\(299\) −23.9016 −1.38227
\(300\) 12.7226 0.734537
\(301\) −29.9446 −1.72598
\(302\) 19.3660 1.11439
\(303\) 16.7214 0.960617
\(304\) 1.27370 0.0730520
\(305\) −1.57399 −0.0901266
\(306\) 16.4606 0.940989
\(307\) −6.30793 −0.360013 −0.180006 0.983665i \(-0.557612\pi\)
−0.180006 + 0.983665i \(0.557612\pi\)
\(308\) −2.37593 −0.135381
\(309\) −15.3357 −0.872419
\(310\) −6.74077 −0.382850
\(311\) 18.4919 1.04858 0.524291 0.851539i \(-0.324330\pi\)
0.524291 + 0.851539i \(0.324330\pi\)
\(312\) 17.4249 0.986493
\(313\) −33.9583 −1.91944 −0.959719 0.280961i \(-0.909347\pi\)
−0.959719 + 0.280961i \(0.909347\pi\)
\(314\) −16.9998 −0.959355
\(315\) 12.3309 0.694768
\(316\) −8.68079 −0.488332
\(317\) 8.09258 0.454525 0.227262 0.973834i \(-0.427023\pi\)
0.227262 + 0.973834i \(0.427023\pi\)
\(318\) −9.48145 −0.531693
\(319\) −2.64932 −0.148334
\(320\) 0.676703 0.0378289
\(321\) −42.0071 −2.34461
\(322\) 14.4478 0.805146
\(323\) 4.32657 0.240737
\(324\) −0.0552674 −0.00307041
\(325\) 28.2557 1.56734
\(326\) −13.0919 −0.725096
\(327\) 34.1381 1.88784
\(328\) 0.532380 0.0293958
\(329\) −14.3407 −0.790626
\(330\) 1.19764 0.0659277
\(331\) −9.85515 −0.541688 −0.270844 0.962623i \(-0.587303\pi\)
−0.270844 + 0.962623i \(0.587303\pi\)
\(332\) −12.7963 −0.702290
\(333\) −43.9390 −2.40784
\(334\) −4.43489 −0.242666
\(335\) 2.38496 0.130304
\(336\) −10.5329 −0.574615
\(337\) −5.81069 −0.316529 −0.158264 0.987397i \(-0.550590\pi\)
−0.158264 + 0.987397i \(0.550590\pi\)
\(338\) 25.6993 1.39786
\(339\) −43.8782 −2.38314
\(340\) 2.29865 0.124662
\(341\) 6.29388 0.340833
\(342\) 6.17219 0.333754
\(343\) 0.526871 0.0284484
\(344\) −7.96327 −0.429351
\(345\) −7.28273 −0.392089
\(346\) 14.9456 0.803480
\(347\) −22.5232 −1.20911 −0.604555 0.796563i \(-0.706649\pi\)
−0.604555 + 0.796563i \(0.706649\pi\)
\(348\) −11.7449 −0.629591
\(349\) −5.10939 −0.273500 −0.136750 0.990606i \(-0.543666\pi\)
−0.136750 + 0.990606i \(0.543666\pi\)
\(350\) −17.0797 −0.912949
\(351\) 32.1639 1.71678
\(352\) −0.631840 −0.0336772
\(353\) −21.5775 −1.14845 −0.574226 0.818697i \(-0.694697\pi\)
−0.574226 + 0.818697i \(0.694697\pi\)
\(354\) 17.1124 0.909514
\(355\) −4.37764 −0.232341
\(356\) 4.85184 0.257147
\(357\) −35.7785 −1.89360
\(358\) 4.46588 0.236029
\(359\) −9.88203 −0.521553 −0.260777 0.965399i \(-0.583979\pi\)
−0.260777 + 0.965399i \(0.583979\pi\)
\(360\) 3.27920 0.172829
\(361\) −17.3777 −0.914615
\(362\) 8.75756 0.460287
\(363\) 29.6933 1.55849
\(364\) −23.3926 −1.22610
\(365\) 1.14935 0.0601596
\(366\) 6.51516 0.340553
\(367\) −1.69860 −0.0886663 −0.0443331 0.999017i \(-0.514116\pi\)
−0.0443331 + 0.999017i \(0.514116\pi\)
\(368\) 3.84216 0.200287
\(369\) 2.57983 0.134301
\(370\) −6.13590 −0.318990
\(371\) 12.7286 0.660837
\(372\) 27.9018 1.44664
\(373\) 11.9796 0.620282 0.310141 0.950691i \(-0.399624\pi\)
0.310141 + 0.950691i \(0.399624\pi\)
\(374\) −2.14626 −0.110980
\(375\) 18.0868 0.933997
\(376\) −3.81367 −0.196675
\(377\) −26.0843 −1.34341
\(378\) −19.4421 −0.999995
\(379\) −2.65510 −0.136383 −0.0681917 0.997672i \(-0.521723\pi\)
−0.0681917 + 0.997672i \(0.521723\pi\)
\(380\) 0.861920 0.0442156
\(381\) −13.9856 −0.716504
\(382\) 16.4938 0.843895
\(383\) −20.1176 −1.02796 −0.513981 0.857802i \(-0.671830\pi\)
−0.513981 + 0.857802i \(0.671830\pi\)
\(384\) −2.80104 −0.142940
\(385\) −1.60780 −0.0819410
\(386\) 10.3176 0.525153
\(387\) −38.5888 −1.96158
\(388\) 2.77992 0.141129
\(389\) 9.23455 0.468210 0.234105 0.972211i \(-0.424784\pi\)
0.234105 + 0.972211i \(0.424784\pi\)
\(390\) 11.7915 0.597087
\(391\) 13.0512 0.660029
\(392\) 7.14011 0.360630
\(393\) 10.8280 0.546202
\(394\) −21.1641 −1.06623
\(395\) −5.87432 −0.295569
\(396\) −3.06180 −0.153861
\(397\) −15.7963 −0.792795 −0.396397 0.918079i \(-0.629740\pi\)
−0.396397 + 0.918079i \(0.629740\pi\)
\(398\) −0.760069 −0.0380988
\(399\) −13.4158 −0.671628
\(400\) −4.54207 −0.227104
\(401\) 18.3253 0.915121 0.457560 0.889179i \(-0.348723\pi\)
0.457560 + 0.889179i \(0.348723\pi\)
\(402\) −9.87194 −0.492367
\(403\) 61.9674 3.08681
\(404\) −5.96969 −0.297003
\(405\) −0.0373996 −0.00185840
\(406\) 15.7672 0.782513
\(407\) 5.72911 0.283982
\(408\) −9.51470 −0.471048
\(409\) −32.7999 −1.62185 −0.810926 0.585149i \(-0.801036\pi\)
−0.810926 + 0.585149i \(0.801036\pi\)
\(410\) 0.360263 0.0177921
\(411\) 26.8495 1.32439
\(412\) 5.47500 0.269734
\(413\) −22.9730 −1.13043
\(414\) 18.6186 0.915052
\(415\) −8.65932 −0.425069
\(416\) −6.22087 −0.305003
\(417\) 12.7899 0.626326
\(418\) −0.804778 −0.0393630
\(419\) 29.1546 1.42429 0.712147 0.702030i \(-0.247723\pi\)
0.712147 + 0.702030i \(0.247723\pi\)
\(420\) −7.12762 −0.347792
\(421\) −14.9129 −0.726811 −0.363405 0.931631i \(-0.618386\pi\)
−0.363405 + 0.931631i \(0.618386\pi\)
\(422\) 20.5980 1.00269
\(423\) −18.4805 −0.898551
\(424\) 3.38497 0.164389
\(425\) −15.4287 −0.748402
\(426\) 18.1202 0.877925
\(427\) −8.74644 −0.423270
\(428\) 14.9969 0.724904
\(429\) −11.0098 −0.531557
\(430\) −5.38877 −0.259870
\(431\) 10.7514 0.517879 0.258939 0.965894i \(-0.416627\pi\)
0.258939 + 0.965894i \(0.416627\pi\)
\(432\) −5.17032 −0.248757
\(433\) 30.9398 1.48687 0.743435 0.668808i \(-0.233195\pi\)
0.743435 + 0.668808i \(0.233195\pi\)
\(434\) −37.4574 −1.79801
\(435\) −7.94779 −0.381067
\(436\) −12.1876 −0.583682
\(437\) 4.89378 0.234101
\(438\) −4.75744 −0.227319
\(439\) 11.9559 0.570622 0.285311 0.958435i \(-0.407903\pi\)
0.285311 + 0.958435i \(0.407903\pi\)
\(440\) −0.427568 −0.0203835
\(441\) 34.5999 1.64762
\(442\) −21.1313 −1.00511
\(443\) −3.58332 −0.170249 −0.0851244 0.996370i \(-0.527129\pi\)
−0.0851244 + 0.996370i \(0.527129\pi\)
\(444\) 25.3981 1.20534
\(445\) 3.28326 0.155641
\(446\) 2.76363 0.130862
\(447\) 1.88582 0.0891961
\(448\) 3.76033 0.177659
\(449\) −10.7821 −0.508837 −0.254419 0.967094i \(-0.581884\pi\)
−0.254419 + 0.967094i \(0.581884\pi\)
\(450\) −22.0102 −1.03757
\(451\) −0.336379 −0.0158395
\(452\) 15.6649 0.736817
\(453\) −54.2449 −2.54865
\(454\) 3.60460 0.169172
\(455\) −15.8298 −0.742113
\(456\) −3.56770 −0.167073
\(457\) −14.8925 −0.696642 −0.348321 0.937375i \(-0.613248\pi\)
−0.348321 + 0.937375i \(0.613248\pi\)
\(458\) −19.7873 −0.924599
\(459\) −17.5627 −0.819759
\(460\) 2.60000 0.121226
\(461\) −6.81045 −0.317194 −0.158597 0.987343i \(-0.550697\pi\)
−0.158597 + 0.987343i \(0.550697\pi\)
\(462\) 6.65508 0.309623
\(463\) 10.9756 0.510079 0.255040 0.966931i \(-0.417911\pi\)
0.255040 + 0.966931i \(0.417911\pi\)
\(464\) 4.19303 0.194657
\(465\) 18.8812 0.875595
\(466\) −1.24894 −0.0578560
\(467\) −6.92170 −0.320298 −0.160149 0.987093i \(-0.551197\pi\)
−0.160149 + 0.987093i \(0.551197\pi\)
\(468\) −30.1454 −1.39347
\(469\) 13.2528 0.611959
\(470\) −2.58072 −0.119040
\(471\) 47.6172 2.19409
\(472\) −6.10929 −0.281203
\(473\) 5.03151 0.231349
\(474\) 24.3153 1.11684
\(475\) −5.78526 −0.265446
\(476\) 12.7733 0.585461
\(477\) 16.4031 0.751045
\(478\) 6.22948 0.284930
\(479\) −30.6547 −1.40065 −0.700324 0.713825i \(-0.746961\pi\)
−0.700324 + 0.713825i \(0.746961\pi\)
\(480\) −1.89548 −0.0865162
\(481\) 56.4068 2.57193
\(482\) −13.0332 −0.593646
\(483\) −40.4690 −1.84140
\(484\) −10.6008 −0.481854
\(485\) 1.88118 0.0854200
\(486\) 15.6658 0.710613
\(487\) 27.5206 1.24708 0.623539 0.781792i \(-0.285694\pi\)
0.623539 + 0.781792i \(0.285694\pi\)
\(488\) −2.32597 −0.105292
\(489\) 36.6711 1.65833
\(490\) 4.83174 0.218276
\(491\) −5.76173 −0.260023 −0.130012 0.991512i \(-0.541501\pi\)
−0.130012 + 0.991512i \(0.541501\pi\)
\(492\) −1.49122 −0.0672294
\(493\) 14.2431 0.641475
\(494\) −7.92356 −0.356498
\(495\) −2.07193 −0.0931264
\(496\) −9.96120 −0.447271
\(497\) −24.3259 −1.09117
\(498\) 35.8431 1.60617
\(499\) 41.1456 1.84193 0.920965 0.389645i \(-0.127402\pi\)
0.920965 + 0.389645i \(0.127402\pi\)
\(500\) −6.45715 −0.288773
\(501\) 12.4223 0.554988
\(502\) 13.6041 0.607181
\(503\) 29.9578 1.33575 0.667877 0.744272i \(-0.267203\pi\)
0.667877 + 0.744272i \(0.267203\pi\)
\(504\) 18.2220 0.811674
\(505\) −4.03971 −0.179765
\(506\) −2.42763 −0.107921
\(507\) −71.9848 −3.19696
\(508\) 4.99299 0.221528
\(509\) 6.97677 0.309240 0.154620 0.987974i \(-0.450585\pi\)
0.154620 + 0.987974i \(0.450585\pi\)
\(510\) −6.43863 −0.285107
\(511\) 6.38675 0.282533
\(512\) 1.00000 0.0441942
\(513\) −6.58546 −0.290755
\(514\) 3.05899 0.134926
\(515\) 3.70495 0.163260
\(516\) 22.3055 0.981944
\(517\) 2.40963 0.105975
\(518\) −34.0963 −1.49810
\(519\) −41.8633 −1.83759
\(520\) −4.20968 −0.184607
\(521\) −38.9300 −1.70556 −0.852778 0.522274i \(-0.825084\pi\)
−0.852778 + 0.522274i \(0.825084\pi\)
\(522\) 20.3188 0.889331
\(523\) −20.7987 −0.909465 −0.454732 0.890628i \(-0.650265\pi\)
−0.454732 + 0.890628i \(0.650265\pi\)
\(524\) −3.86571 −0.168874
\(525\) 47.8410 2.08795
\(526\) −12.8608 −0.560757
\(527\) −33.8366 −1.47395
\(528\) 1.76981 0.0770212
\(529\) −8.23777 −0.358164
\(530\) 2.29062 0.0994981
\(531\) −29.6047 −1.28474
\(532\) 4.78956 0.207654
\(533\) −3.31187 −0.143453
\(534\) −13.5902 −0.588107
\(535\) 10.1485 0.438757
\(536\) 3.52438 0.152230
\(537\) −12.5091 −0.539809
\(538\) −0.356613 −0.0153747
\(539\) −4.51141 −0.194320
\(540\) −3.49877 −0.150563
\(541\) −23.4349 −1.00755 −0.503773 0.863836i \(-0.668055\pi\)
−0.503773 + 0.863836i \(0.668055\pi\)
\(542\) −15.6107 −0.670538
\(543\) −24.5303 −1.05270
\(544\) 3.39684 0.145638
\(545\) −8.24742 −0.353281
\(546\) 65.5236 2.80415
\(547\) −34.1967 −1.46214 −0.731072 0.682301i \(-0.760980\pi\)
−0.731072 + 0.682301i \(0.760980\pi\)
\(548\) −9.58553 −0.409474
\(549\) −11.2713 −0.481049
\(550\) 2.86986 0.122371
\(551\) 5.34069 0.227521
\(552\) −10.7621 −0.458064
\(553\) −32.6427 −1.38811
\(554\) −17.5079 −0.743841
\(555\) 17.1869 0.729545
\(556\) −4.56613 −0.193647
\(557\) −8.65534 −0.366739 −0.183369 0.983044i \(-0.558700\pi\)
−0.183369 + 0.983044i \(0.558700\pi\)
\(558\) −48.2705 −2.04345
\(559\) 49.5385 2.09526
\(560\) 2.54463 0.107530
\(561\) 6.01177 0.253817
\(562\) 7.79420 0.328779
\(563\) −24.9699 −1.05236 −0.526178 0.850374i \(-0.676375\pi\)
−0.526178 + 0.850374i \(0.676375\pi\)
\(564\) 10.6823 0.449804
\(565\) 10.6005 0.445967
\(566\) −15.3517 −0.645281
\(567\) −0.207824 −0.00872779
\(568\) −6.46908 −0.271436
\(569\) −23.0538 −0.966464 −0.483232 0.875492i \(-0.660537\pi\)
−0.483232 + 0.875492i \(0.660537\pi\)
\(570\) −2.41428 −0.101123
\(571\) 41.2184 1.72494 0.862469 0.506110i \(-0.168917\pi\)
0.862469 + 0.506110i \(0.168917\pi\)
\(572\) 3.93060 0.164346
\(573\) −46.1998 −1.93002
\(574\) 2.00193 0.0835588
\(575\) −17.4514 −0.727773
\(576\) 4.84585 0.201911
\(577\) −9.49822 −0.395416 −0.197708 0.980261i \(-0.563350\pi\)
−0.197708 + 0.980261i \(0.563350\pi\)
\(578\) −5.46147 −0.227167
\(579\) −28.9001 −1.20105
\(580\) 2.83744 0.117818
\(581\) −48.1185 −1.99629
\(582\) −7.78668 −0.322768
\(583\) −2.13876 −0.0885783
\(584\) 1.69845 0.0702824
\(585\) −20.3995 −0.843416
\(586\) −5.71102 −0.235920
\(587\) 35.6897 1.47307 0.736536 0.676399i \(-0.236460\pi\)
0.736536 + 0.676399i \(0.236460\pi\)
\(588\) −19.9998 −0.824777
\(589\) −12.6876 −0.522785
\(590\) −4.13418 −0.170201
\(591\) 59.2816 2.43852
\(592\) −9.06735 −0.372666
\(593\) −5.75974 −0.236524 −0.118262 0.992982i \(-0.537732\pi\)
−0.118262 + 0.992982i \(0.537732\pi\)
\(594\) 3.26681 0.134039
\(595\) 8.64370 0.354357
\(596\) −0.673255 −0.0275776
\(597\) 2.12899 0.0871337
\(598\) −23.9016 −0.977410
\(599\) 3.16499 0.129318 0.0646589 0.997907i \(-0.479404\pi\)
0.0646589 + 0.997907i \(0.479404\pi\)
\(600\) 12.7226 0.519396
\(601\) 16.7751 0.684272 0.342136 0.939650i \(-0.388850\pi\)
0.342136 + 0.939650i \(0.388850\pi\)
\(602\) −29.9446 −1.22045
\(603\) 17.0786 0.695495
\(604\) 19.3660 0.787990
\(605\) −7.17358 −0.291647
\(606\) 16.7214 0.679259
\(607\) −46.2442 −1.87699 −0.938497 0.345287i \(-0.887782\pi\)
−0.938497 + 0.345287i \(0.887782\pi\)
\(608\) 1.27370 0.0516556
\(609\) −44.1646 −1.78964
\(610\) −1.57399 −0.0637291
\(611\) 23.7243 0.959784
\(612\) 16.4606 0.665380
\(613\) −3.63707 −0.146900 −0.0734500 0.997299i \(-0.523401\pi\)
−0.0734500 + 0.997299i \(0.523401\pi\)
\(614\) −6.30793 −0.254567
\(615\) −1.00911 −0.0406914
\(616\) −2.37593 −0.0957289
\(617\) −29.5745 −1.19062 −0.595312 0.803495i \(-0.702971\pi\)
−0.595312 + 0.803495i \(0.702971\pi\)
\(618\) −15.3357 −0.616894
\(619\) −10.9005 −0.438129 −0.219065 0.975710i \(-0.570301\pi\)
−0.219065 + 0.975710i \(0.570301\pi\)
\(620\) −6.74077 −0.270716
\(621\) −19.8652 −0.797163
\(622\) 18.4919 0.741460
\(623\) 18.2446 0.730953
\(624\) 17.4249 0.697556
\(625\) 18.3408 0.733632
\(626\) −33.9583 −1.35725
\(627\) 2.25422 0.0900248
\(628\) −16.9998 −0.678366
\(629\) −30.8003 −1.22809
\(630\) 12.3309 0.491275
\(631\) 2.39342 0.0952807 0.0476404 0.998865i \(-0.484830\pi\)
0.0476404 + 0.998865i \(0.484830\pi\)
\(632\) −8.68079 −0.345303
\(633\) −57.6959 −2.29321
\(634\) 8.09258 0.321397
\(635\) 3.37877 0.134083
\(636\) −9.48145 −0.375964
\(637\) −44.4177 −1.75989
\(638\) −2.64932 −0.104888
\(639\) −31.3482 −1.24012
\(640\) 0.676703 0.0267490
\(641\) −34.1887 −1.35037 −0.675186 0.737647i \(-0.735937\pi\)
−0.675186 + 0.737647i \(0.735937\pi\)
\(642\) −42.0071 −1.65789
\(643\) 0.527584 0.0208059 0.0104029 0.999946i \(-0.496689\pi\)
0.0104029 + 0.999946i \(0.496689\pi\)
\(644\) 14.4478 0.569324
\(645\) 15.0942 0.594333
\(646\) 4.32657 0.170227
\(647\) −33.4190 −1.31384 −0.656918 0.753962i \(-0.728140\pi\)
−0.656918 + 0.753962i \(0.728140\pi\)
\(648\) −0.0552674 −0.00217111
\(649\) 3.86009 0.151522
\(650\) 28.2557 1.10828
\(651\) 104.920 4.11214
\(652\) −13.0919 −0.512720
\(653\) 6.97891 0.273106 0.136553 0.990633i \(-0.456398\pi\)
0.136553 + 0.990633i \(0.456398\pi\)
\(654\) 34.1381 1.33491
\(655\) −2.61594 −0.102213
\(656\) 0.532380 0.0207859
\(657\) 8.23045 0.321100
\(658\) −14.3407 −0.559057
\(659\) 2.15208 0.0838332 0.0419166 0.999121i \(-0.486654\pi\)
0.0419166 + 0.999121i \(0.486654\pi\)
\(660\) 1.19764 0.0466180
\(661\) 42.0362 1.63502 0.817509 0.575916i \(-0.195354\pi\)
0.817509 + 0.575916i \(0.195354\pi\)
\(662\) −9.85515 −0.383031
\(663\) 59.1898 2.29874
\(664\) −12.7963 −0.496594
\(665\) 3.24111 0.125685
\(666\) −43.9390 −1.70260
\(667\) 16.1103 0.623794
\(668\) −4.43489 −0.171591
\(669\) −7.74106 −0.299286
\(670\) 2.38496 0.0921389
\(671\) 1.46964 0.0567349
\(672\) −10.5329 −0.406314
\(673\) 5.86954 0.226254 0.113127 0.993581i \(-0.463913\pi\)
0.113127 + 0.993581i \(0.463913\pi\)
\(674\) −5.81069 −0.223820
\(675\) 23.4840 0.903898
\(676\) 25.6993 0.988433
\(677\) −36.6203 −1.40743 −0.703716 0.710481i \(-0.748477\pi\)
−0.703716 + 0.710481i \(0.748477\pi\)
\(678\) −43.8782 −1.68513
\(679\) 10.4534 0.401166
\(680\) 2.29865 0.0881493
\(681\) −10.0966 −0.386904
\(682\) 6.29388 0.241005
\(683\) −14.6062 −0.558892 −0.279446 0.960161i \(-0.590151\pi\)
−0.279446 + 0.960161i \(0.590151\pi\)
\(684\) 6.17219 0.235999
\(685\) −6.48656 −0.247839
\(686\) 0.526871 0.0201160
\(687\) 55.4251 2.11460
\(688\) −7.96327 −0.303597
\(689\) −21.0575 −0.802226
\(690\) −7.28273 −0.277249
\(691\) −9.52870 −0.362489 −0.181244 0.983438i \(-0.558012\pi\)
−0.181244 + 0.983438i \(0.558012\pi\)
\(692\) 14.9456 0.568146
\(693\) −11.5134 −0.437358
\(694\) −22.5232 −0.854970
\(695\) −3.08992 −0.117207
\(696\) −11.7449 −0.445188
\(697\) 1.80841 0.0684984
\(698\) −5.10939 −0.193393
\(699\) 3.49833 0.132319
\(700\) −17.0797 −0.645552
\(701\) 5.03585 0.190201 0.0951007 0.995468i \(-0.469683\pi\)
0.0951007 + 0.995468i \(0.469683\pi\)
\(702\) 32.1639 1.21395
\(703\) −11.5491 −0.435584
\(704\) −0.631840 −0.0238134
\(705\) 7.22871 0.272249
\(706\) −21.5775 −0.812078
\(707\) −22.4480 −0.844245
\(708\) 17.1124 0.643123
\(709\) 38.2526 1.43661 0.718303 0.695730i \(-0.244919\pi\)
0.718303 + 0.695730i \(0.244919\pi\)
\(710\) −4.37764 −0.164290
\(711\) −42.0658 −1.57759
\(712\) 4.85184 0.181831
\(713\) −38.2726 −1.43332
\(714\) −35.7785 −1.33898
\(715\) 2.65985 0.0994726
\(716\) 4.46588 0.166898
\(717\) −17.4491 −0.651647
\(718\) −9.88203 −0.368794
\(719\) 38.6953 1.44309 0.721545 0.692368i \(-0.243432\pi\)
0.721545 + 0.692368i \(0.243432\pi\)
\(720\) 3.27920 0.122209
\(721\) 20.5878 0.766731
\(722\) −17.3777 −0.646730
\(723\) 36.5066 1.35769
\(724\) 8.75756 0.325472
\(725\) −19.0451 −0.707316
\(726\) 29.6933 1.10202
\(727\) −2.53127 −0.0938796 −0.0469398 0.998898i \(-0.514947\pi\)
−0.0469398 + 0.998898i \(0.514947\pi\)
\(728\) −23.3926 −0.866986
\(729\) −43.7147 −1.61906
\(730\) 1.14935 0.0425393
\(731\) −27.0500 −1.00048
\(732\) 6.51516 0.240807
\(733\) −22.6497 −0.836587 −0.418293 0.908312i \(-0.637372\pi\)
−0.418293 + 0.908312i \(0.637372\pi\)
\(734\) −1.69860 −0.0626965
\(735\) −13.5339 −0.499206
\(736\) 3.84216 0.141624
\(737\) −2.22684 −0.0820267
\(738\) 2.57983 0.0949650
\(739\) −31.6763 −1.16523 −0.582616 0.812748i \(-0.697971\pi\)
−0.582616 + 0.812748i \(0.697971\pi\)
\(740\) −6.13590 −0.225560
\(741\) 22.1942 0.815326
\(742\) 12.7286 0.467282
\(743\) 44.8864 1.64672 0.823361 0.567517i \(-0.192096\pi\)
0.823361 + 0.567517i \(0.192096\pi\)
\(744\) 27.9018 1.02293
\(745\) −0.455594 −0.0166917
\(746\) 11.9796 0.438606
\(747\) −62.0091 −2.26880
\(748\) −2.14626 −0.0784750
\(749\) 56.3935 2.06057
\(750\) 18.0868 0.660435
\(751\) 41.5031 1.51447 0.757235 0.653143i \(-0.226550\pi\)
0.757235 + 0.653143i \(0.226550\pi\)
\(752\) −3.81367 −0.139070
\(753\) −38.1057 −1.38865
\(754\) −26.0843 −0.949935
\(755\) 13.1050 0.476940
\(756\) −19.4421 −0.707103
\(757\) 41.9409 1.52437 0.762184 0.647360i \(-0.224127\pi\)
0.762184 + 0.647360i \(0.224127\pi\)
\(758\) −2.65510 −0.0964376
\(759\) 6.79991 0.246821
\(760\) 0.861920 0.0312651
\(761\) −19.0384 −0.690143 −0.345071 0.938576i \(-0.612145\pi\)
−0.345071 + 0.938576i \(0.612145\pi\)
\(762\) −13.9856 −0.506645
\(763\) −45.8296 −1.65914
\(764\) 16.4938 0.596724
\(765\) 11.1389 0.402729
\(766\) −20.1176 −0.726879
\(767\) 38.0051 1.37229
\(768\) −2.80104 −0.101074
\(769\) 15.7182 0.566812 0.283406 0.959000i \(-0.408536\pi\)
0.283406 + 0.959000i \(0.408536\pi\)
\(770\) −1.60780 −0.0579410
\(771\) −8.56838 −0.308583
\(772\) 10.3176 0.371339
\(773\) −0.540300 −0.0194332 −0.00971662 0.999953i \(-0.503093\pi\)
−0.00971662 + 0.999953i \(0.503093\pi\)
\(774\) −38.5888 −1.38705
\(775\) 45.2445 1.62523
\(776\) 2.77992 0.0997933
\(777\) 95.5052 3.42623
\(778\) 9.23455 0.331075
\(779\) 0.678095 0.0242953
\(780\) 11.7915 0.422204
\(781\) 4.08742 0.146259
\(782\) 13.0512 0.466711
\(783\) −21.6793 −0.774755
\(784\) 7.14011 0.255004
\(785\) −11.5038 −0.410589
\(786\) 10.8280 0.386223
\(787\) 12.6465 0.450799 0.225400 0.974266i \(-0.427631\pi\)
0.225400 + 0.974266i \(0.427631\pi\)
\(788\) −21.1641 −0.753939
\(789\) 36.0236 1.28247
\(790\) −5.87432 −0.208999
\(791\) 58.9054 2.09444
\(792\) −3.06180 −0.108796
\(793\) 14.4696 0.513830
\(794\) −15.7963 −0.560590
\(795\) −6.41613 −0.227557
\(796\) −0.760069 −0.0269399
\(797\) −54.4649 −1.92924 −0.964622 0.263636i \(-0.915078\pi\)
−0.964622 + 0.263636i \(0.915078\pi\)
\(798\) −13.4158 −0.474913
\(799\) −12.9544 −0.458294
\(800\) −4.54207 −0.160587
\(801\) 23.5113 0.830732
\(802\) 18.3253 0.647088
\(803\) −1.07315 −0.0378706
\(804\) −9.87194 −0.348156
\(805\) 9.77688 0.344590
\(806\) 61.9674 2.18271
\(807\) 0.998889 0.0351626
\(808\) −5.96969 −0.210013
\(809\) 1.35956 0.0477996 0.0238998 0.999714i \(-0.492392\pi\)
0.0238998 + 0.999714i \(0.492392\pi\)
\(810\) −0.0373996 −0.00131409
\(811\) −9.33605 −0.327833 −0.163917 0.986474i \(-0.552413\pi\)
−0.163917 + 0.986474i \(0.552413\pi\)
\(812\) 15.7672 0.553320
\(813\) 43.7264 1.53355
\(814\) 5.72911 0.200805
\(815\) −8.85936 −0.310330
\(816\) −9.51470 −0.333081
\(817\) −10.1429 −0.354854
\(818\) −32.7999 −1.14682
\(819\) −113.357 −3.96101
\(820\) 0.360263 0.0125809
\(821\) −18.6988 −0.652593 −0.326296 0.945267i \(-0.605801\pi\)
−0.326296 + 0.945267i \(0.605801\pi\)
\(822\) 26.8495 0.936484
\(823\) 23.0774 0.804426 0.402213 0.915546i \(-0.368241\pi\)
0.402213 + 0.915546i \(0.368241\pi\)
\(824\) 5.47500 0.190731
\(825\) −8.03861 −0.279869
\(826\) −22.9730 −0.799332
\(827\) 20.6856 0.719309 0.359655 0.933086i \(-0.382895\pi\)
0.359655 + 0.933086i \(0.382895\pi\)
\(828\) 18.6186 0.647040
\(829\) −45.9765 −1.59683 −0.798416 0.602107i \(-0.794328\pi\)
−0.798416 + 0.602107i \(0.794328\pi\)
\(830\) −8.65932 −0.300569
\(831\) 49.0405 1.70120
\(832\) −6.22087 −0.215670
\(833\) 24.2538 0.840345
\(834\) 12.7899 0.442879
\(835\) −3.00110 −0.103857
\(836\) −0.804778 −0.0278338
\(837\) 51.5026 1.78019
\(838\) 29.1546 1.00713
\(839\) 45.6270 1.57522 0.787610 0.616174i \(-0.211318\pi\)
0.787610 + 0.616174i \(0.211318\pi\)
\(840\) −7.12762 −0.245926
\(841\) −11.4185 −0.393741
\(842\) −14.9129 −0.513933
\(843\) −21.8319 −0.751931
\(844\) 20.5980 0.709012
\(845\) 17.3908 0.598261
\(846\) −18.4805 −0.635372
\(847\) −39.8625 −1.36969
\(848\) 3.38497 0.116240
\(849\) 43.0009 1.47579
\(850\) −15.4287 −0.529200
\(851\) −34.8382 −1.19424
\(852\) 18.1202 0.620787
\(853\) −13.2743 −0.454502 −0.227251 0.973836i \(-0.572974\pi\)
−0.227251 + 0.973836i \(0.572974\pi\)
\(854\) −8.74644 −0.299297
\(855\) 4.17674 0.142841
\(856\) 14.9969 0.512585
\(857\) 24.7967 0.847039 0.423519 0.905887i \(-0.360795\pi\)
0.423519 + 0.905887i \(0.360795\pi\)
\(858\) −11.0098 −0.375868
\(859\) 1.35142 0.0461097 0.0230548 0.999734i \(-0.492661\pi\)
0.0230548 + 0.999734i \(0.492661\pi\)
\(860\) −5.38877 −0.183756
\(861\) −5.60749 −0.191103
\(862\) 10.7514 0.366196
\(863\) 33.6053 1.14394 0.571968 0.820276i \(-0.306180\pi\)
0.571968 + 0.820276i \(0.306180\pi\)
\(864\) −5.17032 −0.175898
\(865\) 10.1137 0.343877
\(866\) 30.9398 1.05138
\(867\) 15.2978 0.519542
\(868\) −37.4574 −1.27139
\(869\) 5.48487 0.186061
\(870\) −7.94779 −0.269455
\(871\) −21.9247 −0.742890
\(872\) −12.1876 −0.412726
\(873\) 13.4711 0.455927
\(874\) 4.89378 0.165535
\(875\) −24.2810 −0.820849
\(876\) −4.75744 −0.160739
\(877\) −1.06643 −0.0360108 −0.0180054 0.999838i \(-0.505732\pi\)
−0.0180054 + 0.999838i \(0.505732\pi\)
\(878\) 11.9559 0.403491
\(879\) 15.9968 0.539559
\(880\) −0.427568 −0.0144133
\(881\) 55.4004 1.86649 0.933244 0.359244i \(-0.116965\pi\)
0.933244 + 0.359244i \(0.116965\pi\)
\(882\) 34.5999 1.16504
\(883\) −47.3965 −1.59502 −0.797510 0.603306i \(-0.793850\pi\)
−0.797510 + 0.603306i \(0.793850\pi\)
\(884\) −21.1313 −0.710723
\(885\) 11.5800 0.389258
\(886\) −3.58332 −0.120384
\(887\) 22.8628 0.767657 0.383828 0.923404i \(-0.374605\pi\)
0.383828 + 0.923404i \(0.374605\pi\)
\(888\) 25.3981 0.852303
\(889\) 18.7753 0.629704
\(890\) 3.28326 0.110055
\(891\) 0.0349202 0.00116987
\(892\) 2.76363 0.0925332
\(893\) −4.85749 −0.162550
\(894\) 1.88582 0.0630712
\(895\) 3.02207 0.101017
\(896\) 3.76033 0.125624
\(897\) 66.9495 2.23538
\(898\) −10.7821 −0.359802
\(899\) −41.7676 −1.39303
\(900\) −22.0102 −0.733674
\(901\) 11.4982 0.383061
\(902\) −0.336379 −0.0112002
\(903\) 83.8761 2.79122
\(904\) 15.6649 0.521008
\(905\) 5.92627 0.196996
\(906\) −54.2449 −1.80217
\(907\) 20.5832 0.683453 0.341726 0.939799i \(-0.388988\pi\)
0.341726 + 0.939799i \(0.388988\pi\)
\(908\) 3.60460 0.119623
\(909\) −28.9282 −0.959489
\(910\) −15.8298 −0.524753
\(911\) 57.8412 1.91636 0.958182 0.286159i \(-0.0923786\pi\)
0.958182 + 0.286159i \(0.0923786\pi\)
\(912\) −3.56770 −0.118139
\(913\) 8.08523 0.267582
\(914\) −14.8925 −0.492601
\(915\) 4.40883 0.145751
\(916\) −19.7873 −0.653791
\(917\) −14.5364 −0.480033
\(918\) −17.5627 −0.579657
\(919\) 39.1324 1.29086 0.645430 0.763820i \(-0.276678\pi\)
0.645430 + 0.763820i \(0.276678\pi\)
\(920\) 2.60000 0.0857196
\(921\) 17.6688 0.582207
\(922\) −6.81045 −0.224290
\(923\) 40.2433 1.32462
\(924\) 6.65508 0.218936
\(925\) 41.1846 1.35414
\(926\) 10.9756 0.360681
\(927\) 26.5311 0.871395
\(928\) 4.19303 0.137643
\(929\) 10.1071 0.331602 0.165801 0.986159i \(-0.446979\pi\)
0.165801 + 0.986159i \(0.446979\pi\)
\(930\) 18.8812 0.619139
\(931\) 9.09440 0.298057
\(932\) −1.24894 −0.0409103
\(933\) −51.7968 −1.69575
\(934\) −6.92170 −0.226485
\(935\) −1.45238 −0.0474979
\(936\) −30.1454 −0.985334
\(937\) 53.9203 1.76150 0.880750 0.473582i \(-0.157039\pi\)
0.880750 + 0.473582i \(0.157039\pi\)
\(938\) 13.2528 0.432720
\(939\) 95.1188 3.10409
\(940\) −2.58072 −0.0841738
\(941\) 35.1814 1.14688 0.573440 0.819248i \(-0.305609\pi\)
0.573440 + 0.819248i \(0.305609\pi\)
\(942\) 47.6172 1.55145
\(943\) 2.04549 0.0666104
\(944\) −6.10929 −0.198840
\(945\) −13.1565 −0.427982
\(946\) 5.03151 0.163589
\(947\) −31.7472 −1.03164 −0.515822 0.856696i \(-0.672513\pi\)
−0.515822 + 0.856696i \(0.672513\pi\)
\(948\) 24.3153 0.789724
\(949\) −10.5659 −0.342982
\(950\) −5.78526 −0.187699
\(951\) −22.6677 −0.735050
\(952\) 12.7733 0.413984
\(953\) 42.7912 1.38614 0.693071 0.720869i \(-0.256257\pi\)
0.693071 + 0.720869i \(0.256257\pi\)
\(954\) 16.4031 0.531069
\(955\) 11.1614 0.361174
\(956\) 6.22948 0.201476
\(957\) 7.42088 0.239883
\(958\) −30.6547 −0.990408
\(959\) −36.0448 −1.16395
\(960\) −1.89548 −0.0611762
\(961\) 68.2255 2.20082
\(962\) 56.4068 1.81863
\(963\) 72.6729 2.34185
\(964\) −13.0332 −0.419771
\(965\) 6.98196 0.224757
\(966\) −40.4690 −1.30207
\(967\) −7.16842 −0.230521 −0.115260 0.993335i \(-0.536770\pi\)
−0.115260 + 0.993335i \(0.536770\pi\)
\(968\) −10.6008 −0.340722
\(969\) −12.1189 −0.389316
\(970\) 1.88118 0.0604011
\(971\) −55.7743 −1.78988 −0.894941 0.446185i \(-0.852782\pi\)
−0.894941 + 0.446185i \(0.852782\pi\)
\(972\) 15.6658 0.502479
\(973\) −17.1702 −0.550451
\(974\) 27.5206 0.881817
\(975\) −79.1454 −2.53468
\(976\) −2.32597 −0.0744526
\(977\) −44.4161 −1.42100 −0.710499 0.703698i \(-0.751531\pi\)
−0.710499 + 0.703698i \(0.751531\pi\)
\(978\) 36.6711 1.17261
\(979\) −3.06559 −0.0979766
\(980\) 4.83174 0.154344
\(981\) −59.0595 −1.88563
\(982\) −5.76173 −0.183864
\(983\) −1.42424 −0.0454262 −0.0227131 0.999742i \(-0.507230\pi\)
−0.0227131 + 0.999742i \(0.507230\pi\)
\(984\) −1.49122 −0.0475384
\(985\) −14.3218 −0.456331
\(986\) 14.2431 0.453592
\(987\) 40.1688 1.27859
\(988\) −7.92356 −0.252082
\(989\) −30.5962 −0.972903
\(990\) −2.07193 −0.0658503
\(991\) 49.3353 1.56719 0.783594 0.621273i \(-0.213384\pi\)
0.783594 + 0.621273i \(0.213384\pi\)
\(992\) −9.96120 −0.316268
\(993\) 27.6047 0.876009
\(994\) −24.3259 −0.771570
\(995\) −0.514341 −0.0163057
\(996\) 35.8431 1.13573
\(997\) 34.3648 1.08834 0.544172 0.838974i \(-0.316844\pi\)
0.544172 + 0.838974i \(0.316844\pi\)
\(998\) 41.1456 1.30244
\(999\) 46.8811 1.48325
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 \(a_p\))