Properties

Label 8027.2.a.f.1.2
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.77938 q^{2} +1.07296 q^{3} +5.72495 q^{4} +0.733926 q^{5} -2.98217 q^{6} -2.15808 q^{7} -10.3531 q^{8} -1.84875 q^{9} +O(q^{10})\) \(q-2.77938 q^{2} +1.07296 q^{3} +5.72495 q^{4} +0.733926 q^{5} -2.98217 q^{6} -2.15808 q^{7} -10.3531 q^{8} -1.84875 q^{9} -2.03986 q^{10} -2.49200 q^{11} +6.14265 q^{12} -5.66398 q^{13} +5.99813 q^{14} +0.787474 q^{15} +17.3252 q^{16} -6.34198 q^{17} +5.13839 q^{18} -6.25095 q^{19} +4.20170 q^{20} -2.31554 q^{21} +6.92623 q^{22} +1.00000 q^{23} -11.1084 q^{24} -4.46135 q^{25} +15.7424 q^{26} -5.20252 q^{27} -12.3549 q^{28} -4.49732 q^{29} -2.18869 q^{30} -0.531708 q^{31} -27.4472 q^{32} -2.67382 q^{33} +17.6268 q^{34} -1.58387 q^{35} -10.5840 q^{36} +5.87088 q^{37} +17.3738 q^{38} -6.07723 q^{39} -7.59839 q^{40} -10.2857 q^{41} +6.43576 q^{42} +10.2016 q^{43} -14.2666 q^{44} -1.35685 q^{45} -2.77938 q^{46} +0.810322 q^{47} +18.5893 q^{48} -2.34269 q^{49} +12.3998 q^{50} -6.80469 q^{51} -32.4260 q^{52} -1.04820 q^{53} +14.4598 q^{54} -1.82895 q^{55} +22.3428 q^{56} -6.70702 q^{57} +12.4998 q^{58} +8.71970 q^{59} +4.50826 q^{60} -1.25973 q^{61} +1.47782 q^{62} +3.98976 q^{63} +41.6358 q^{64} -4.15695 q^{65} +7.43157 q^{66} +6.08227 q^{67} -36.3075 q^{68} +1.07296 q^{69} +4.40218 q^{70} -9.04273 q^{71} +19.1403 q^{72} -2.30362 q^{73} -16.3174 q^{74} -4.78686 q^{75} -35.7864 q^{76} +5.37795 q^{77} +16.8909 q^{78} -2.45578 q^{79} +12.7154 q^{80} -0.0358428 q^{81} +28.5878 q^{82} +0.414136 q^{83} -13.2563 q^{84} -4.65454 q^{85} -28.3542 q^{86} -4.82545 q^{87} +25.7999 q^{88} -7.75727 q^{89} +3.77120 q^{90} +12.2233 q^{91} +5.72495 q^{92} -0.570502 q^{93} -2.25219 q^{94} -4.58774 q^{95} -29.4498 q^{96} -14.0088 q^{97} +6.51121 q^{98} +4.60711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77938 −1.96532 −0.982659 0.185420i \(-0.940635\pi\)
−0.982659 + 0.185420i \(0.940635\pi\)
\(3\) 1.07296 0.619474 0.309737 0.950822i \(-0.399759\pi\)
0.309737 + 0.950822i \(0.399759\pi\)
\(4\) 5.72495 2.86248
\(5\) 0.733926 0.328222 0.164111 0.986442i \(-0.447525\pi\)
0.164111 + 0.986442i \(0.447525\pi\)
\(6\) −2.98217 −1.21746
\(7\) −2.15808 −0.815678 −0.407839 0.913054i \(-0.633718\pi\)
−0.407839 + 0.913054i \(0.633718\pi\)
\(8\) −10.3531 −3.66036
\(9\) −1.84875 −0.616252
\(10\) −2.03986 −0.645060
\(11\) −2.49200 −0.751368 −0.375684 0.926748i \(-0.622592\pi\)
−0.375684 + 0.926748i \(0.622592\pi\)
\(12\) 6.14265 1.77323
\(13\) −5.66398 −1.57091 −0.785453 0.618921i \(-0.787570\pi\)
−0.785453 + 0.618921i \(0.787570\pi\)
\(14\) 5.99813 1.60307
\(15\) 0.787474 0.203325
\(16\) 17.3252 4.33130
\(17\) −6.34198 −1.53816 −0.769078 0.639155i \(-0.779284\pi\)
−0.769078 + 0.639155i \(0.779284\pi\)
\(18\) 5.13839 1.21113
\(19\) −6.25095 −1.43407 −0.717033 0.697039i \(-0.754500\pi\)
−0.717033 + 0.697039i \(0.754500\pi\)
\(20\) 4.20170 0.939528
\(21\) −2.31554 −0.505292
\(22\) 6.92623 1.47668
\(23\) 1.00000 0.208514
\(24\) −11.1084 −2.26750
\(25\) −4.46135 −0.892270
\(26\) 15.7424 3.08733
\(27\) −5.20252 −1.00123
\(28\) −12.3549 −2.33486
\(29\) −4.49732 −0.835131 −0.417565 0.908647i \(-0.637117\pi\)
−0.417565 + 0.908647i \(0.637117\pi\)
\(30\) −2.18869 −0.399598
\(31\) −0.531708 −0.0954977 −0.0477488 0.998859i \(-0.515205\pi\)
−0.0477488 + 0.998859i \(0.515205\pi\)
\(32\) −27.4472 −4.85202
\(33\) −2.67382 −0.465453
\(34\) 17.6268 3.02297
\(35\) −1.58387 −0.267723
\(36\) −10.5840 −1.76401
\(37\) 5.87088 0.965166 0.482583 0.875850i \(-0.339699\pi\)
0.482583 + 0.875850i \(0.339699\pi\)
\(38\) 17.3738 2.81840
\(39\) −6.07723 −0.973136
\(40\) −7.59839 −1.20141
\(41\) −10.2857 −1.60635 −0.803176 0.595742i \(-0.796858\pi\)
−0.803176 + 0.595742i \(0.796858\pi\)
\(42\) 6.43576 0.993059
\(43\) 10.2016 1.55574 0.777868 0.628428i \(-0.216301\pi\)
0.777868 + 0.628428i \(0.216301\pi\)
\(44\) −14.2666 −2.15077
\(45\) −1.35685 −0.202267
\(46\) −2.77938 −0.409797
\(47\) 0.810322 0.118198 0.0590988 0.998252i \(-0.481177\pi\)
0.0590988 + 0.998252i \(0.481177\pi\)
\(48\) 18.5893 2.68313
\(49\) −2.34269 −0.334669
\(50\) 12.3998 1.75360
\(51\) −6.80469 −0.952848
\(52\) −32.4260 −4.49668
\(53\) −1.04820 −0.143981 −0.0719903 0.997405i \(-0.522935\pi\)
−0.0719903 + 0.997405i \(0.522935\pi\)
\(54\) 14.4598 1.96773
\(55\) −1.82895 −0.246615
\(56\) 22.3428 2.98568
\(57\) −6.70702 −0.888367
\(58\) 12.4998 1.64130
\(59\) 8.71970 1.13521 0.567604 0.823301i \(-0.307870\pi\)
0.567604 + 0.823301i \(0.307870\pi\)
\(60\) 4.50826 0.582013
\(61\) −1.25973 −0.161292 −0.0806459 0.996743i \(-0.525698\pi\)
−0.0806459 + 0.996743i \(0.525698\pi\)
\(62\) 1.47782 0.187683
\(63\) 3.98976 0.502663
\(64\) 41.6358 5.20447
\(65\) −4.15695 −0.515606
\(66\) 7.43157 0.914764
\(67\) 6.08227 0.743068 0.371534 0.928419i \(-0.378832\pi\)
0.371534 + 0.928419i \(0.378832\pi\)
\(68\) −36.3075 −4.40293
\(69\) 1.07296 0.129169
\(70\) 4.40218 0.526162
\(71\) −9.04273 −1.07318 −0.536588 0.843845i \(-0.680287\pi\)
−0.536588 + 0.843845i \(0.680287\pi\)
\(72\) 19.1403 2.25570
\(73\) −2.30362 −0.269619 −0.134809 0.990872i \(-0.543042\pi\)
−0.134809 + 0.990872i \(0.543042\pi\)
\(74\) −16.3174 −1.89686
\(75\) −4.78686 −0.552739
\(76\) −35.7864 −4.10498
\(77\) 5.37795 0.612874
\(78\) 16.8909 1.91252
\(79\) −2.45578 −0.276297 −0.138148 0.990412i \(-0.544115\pi\)
−0.138148 + 0.990412i \(0.544115\pi\)
\(80\) 12.7154 1.42163
\(81\) −0.0358428 −0.00398253
\(82\) 28.5878 3.15699
\(83\) 0.414136 0.0454573 0.0227286 0.999742i \(-0.492765\pi\)
0.0227286 + 0.999742i \(0.492765\pi\)
\(84\) −13.2563 −1.44639
\(85\) −4.65454 −0.504856
\(86\) −28.3542 −3.05752
\(87\) −4.82545 −0.517342
\(88\) 25.7999 2.75028
\(89\) −7.75727 −0.822269 −0.411135 0.911575i \(-0.634867\pi\)
−0.411135 + 0.911575i \(0.634867\pi\)
\(90\) 3.77120 0.397520
\(91\) 12.2233 1.28135
\(92\) 5.72495 0.596868
\(93\) −0.570502 −0.0591584
\(94\) −2.25219 −0.232296
\(95\) −4.58774 −0.470692
\(96\) −29.4498 −3.00570
\(97\) −14.0088 −1.42238 −0.711189 0.703001i \(-0.751843\pi\)
−0.711189 + 0.703001i \(0.751843\pi\)
\(98\) 6.51121 0.657732
\(99\) 4.60711 0.463032
\(100\) −25.5410 −2.55410
\(101\) −16.1286 −1.60485 −0.802427 0.596750i \(-0.796458\pi\)
−0.802427 + 0.596750i \(0.796458\pi\)
\(102\) 18.9128 1.87265
\(103\) −3.61298 −0.355997 −0.177999 0.984031i \(-0.556962\pi\)
−0.177999 + 0.984031i \(0.556962\pi\)
\(104\) 58.6396 5.75008
\(105\) −1.69943 −0.165848
\(106\) 2.91333 0.282968
\(107\) 8.62515 0.833824 0.416912 0.908947i \(-0.363112\pi\)
0.416912 + 0.908947i \(0.363112\pi\)
\(108\) −29.7842 −2.86599
\(109\) −2.38299 −0.228249 −0.114125 0.993466i \(-0.536406\pi\)
−0.114125 + 0.993466i \(0.536406\pi\)
\(110\) 5.08334 0.484678
\(111\) 6.29922 0.597896
\(112\) −37.3892 −3.53295
\(113\) −15.7369 −1.48040 −0.740201 0.672385i \(-0.765270\pi\)
−0.740201 + 0.672385i \(0.765270\pi\)
\(114\) 18.6414 1.74592
\(115\) 0.733926 0.0684390
\(116\) −25.7469 −2.39054
\(117\) 10.4713 0.968073
\(118\) −24.2354 −2.23105
\(119\) 13.6865 1.25464
\(120\) −8.15277 −0.744243
\(121\) −4.78991 −0.435447
\(122\) 3.50127 0.316990
\(123\) −11.0361 −0.995094
\(124\) −3.04401 −0.273360
\(125\) −6.94394 −0.621084
\(126\) −11.0891 −0.987893
\(127\) −8.74485 −0.775980 −0.387990 0.921664i \(-0.626831\pi\)
−0.387990 + 0.921664i \(0.626831\pi\)
\(128\) −60.8273 −5.37642
\(129\) 10.9460 0.963738
\(130\) 11.5537 1.01333
\(131\) −4.68062 −0.408948 −0.204474 0.978872i \(-0.565548\pi\)
−0.204474 + 0.978872i \(0.565548\pi\)
\(132\) −15.3075 −1.33235
\(133\) 13.4901 1.16974
\(134\) −16.9050 −1.46037
\(135\) −3.81827 −0.328624
\(136\) 65.6589 5.63020
\(137\) 3.36342 0.287356 0.143678 0.989624i \(-0.454107\pi\)
0.143678 + 0.989624i \(0.454107\pi\)
\(138\) −2.98217 −0.253859
\(139\) −18.1258 −1.53741 −0.768704 0.639604i \(-0.779098\pi\)
−0.768704 + 0.639604i \(0.779098\pi\)
\(140\) −9.06760 −0.766352
\(141\) 0.869444 0.0732204
\(142\) 25.1332 2.10913
\(143\) 14.1147 1.18033
\(144\) −32.0300 −2.66917
\(145\) −3.30070 −0.274108
\(146\) 6.40265 0.529887
\(147\) −2.51361 −0.207319
\(148\) 33.6105 2.76277
\(149\) 13.5979 1.11398 0.556990 0.830519i \(-0.311956\pi\)
0.556990 + 0.830519i \(0.311956\pi\)
\(150\) 13.3045 1.08631
\(151\) 16.5747 1.34883 0.674415 0.738353i \(-0.264396\pi\)
0.674415 + 0.738353i \(0.264396\pi\)
\(152\) 64.7165 5.24920
\(153\) 11.7248 0.947891
\(154\) −14.9474 −1.20449
\(155\) −0.390235 −0.0313444
\(156\) −34.7919 −2.78558
\(157\) −4.11891 −0.328725 −0.164362 0.986400i \(-0.552557\pi\)
−0.164362 + 0.986400i \(0.552557\pi\)
\(158\) 6.82555 0.543011
\(159\) −1.12467 −0.0891923
\(160\) −20.1442 −1.59254
\(161\) −2.15808 −0.170081
\(162\) 0.0996207 0.00782694
\(163\) 13.5000 1.05740 0.528701 0.848808i \(-0.322679\pi\)
0.528701 + 0.848808i \(0.322679\pi\)
\(164\) −58.8850 −4.59815
\(165\) −1.96239 −0.152772
\(166\) −1.15104 −0.0893380
\(167\) −10.8543 −0.839932 −0.419966 0.907540i \(-0.637958\pi\)
−0.419966 + 0.907540i \(0.637958\pi\)
\(168\) 23.9729 1.84955
\(169\) 19.0807 1.46775
\(170\) 12.9367 0.992203
\(171\) 11.5565 0.883745
\(172\) 58.4039 4.45326
\(173\) 1.92183 0.146114 0.0730572 0.997328i \(-0.476724\pi\)
0.0730572 + 0.997328i \(0.476724\pi\)
\(174\) 13.4117 1.01674
\(175\) 9.62796 0.727805
\(176\) −43.1745 −3.25440
\(177\) 9.35590 0.703233
\(178\) 21.5604 1.61602
\(179\) 15.2725 1.14152 0.570761 0.821116i \(-0.306648\pi\)
0.570761 + 0.821116i \(0.306648\pi\)
\(180\) −7.76790 −0.578985
\(181\) −20.7905 −1.54535 −0.772674 0.634803i \(-0.781081\pi\)
−0.772674 + 0.634803i \(0.781081\pi\)
\(182\) −33.9733 −2.51827
\(183\) −1.35164 −0.0999162
\(184\) −10.3531 −0.763238
\(185\) 4.30879 0.316789
\(186\) 1.58564 0.116265
\(187\) 15.8042 1.15572
\(188\) 4.63906 0.338338
\(189\) 11.2275 0.816678
\(190\) 12.7511 0.925059
\(191\) −5.27262 −0.381514 −0.190757 0.981637i \(-0.561094\pi\)
−0.190757 + 0.981637i \(0.561094\pi\)
\(192\) 44.6736 3.22404
\(193\) 8.48768 0.610957 0.305478 0.952199i \(-0.401184\pi\)
0.305478 + 0.952199i \(0.401184\pi\)
\(194\) 38.9358 2.79542
\(195\) −4.46024 −0.319405
\(196\) −13.4118 −0.957984
\(197\) −25.1915 −1.79482 −0.897410 0.441199i \(-0.854553\pi\)
−0.897410 + 0.441199i \(0.854553\pi\)
\(198\) −12.8049 −0.910004
\(199\) −3.70561 −0.262684 −0.131342 0.991337i \(-0.541929\pi\)
−0.131342 + 0.991337i \(0.541929\pi\)
\(200\) 46.1887 3.26603
\(201\) 6.52604 0.460312
\(202\) 44.8275 3.15405
\(203\) 9.70557 0.681198
\(204\) −38.9566 −2.72751
\(205\) −7.54893 −0.527240
\(206\) 10.0418 0.699648
\(207\) −1.84875 −0.128497
\(208\) −98.1296 −6.80407
\(209\) 15.5774 1.07751
\(210\) 4.72337 0.325944
\(211\) −21.3792 −1.47181 −0.735903 0.677087i \(-0.763242\pi\)
−0.735903 + 0.677087i \(0.763242\pi\)
\(212\) −6.00087 −0.412141
\(213\) −9.70250 −0.664804
\(214\) −23.9726 −1.63873
\(215\) 7.48725 0.510626
\(216\) 53.8621 3.66485
\(217\) 1.14747 0.0778953
\(218\) 6.62324 0.448583
\(219\) −2.47170 −0.167022
\(220\) −10.4706 −0.705931
\(221\) 35.9208 2.41630
\(222\) −17.5079 −1.17506
\(223\) 7.10724 0.475936 0.237968 0.971273i \(-0.423519\pi\)
0.237968 + 0.971273i \(0.423519\pi\)
\(224\) 59.2332 3.95769
\(225\) 8.24795 0.549863
\(226\) 43.7388 2.90946
\(227\) 9.81408 0.651383 0.325692 0.945476i \(-0.394403\pi\)
0.325692 + 0.945476i \(0.394403\pi\)
\(228\) −38.3974 −2.54293
\(229\) −10.8468 −0.716775 −0.358388 0.933573i \(-0.616673\pi\)
−0.358388 + 0.933573i \(0.616673\pi\)
\(230\) −2.03986 −0.134504
\(231\) 5.77033 0.379660
\(232\) 46.5610 3.05688
\(233\) 2.92032 0.191317 0.0956584 0.995414i \(-0.469504\pi\)
0.0956584 + 0.995414i \(0.469504\pi\)
\(234\) −29.1038 −1.90257
\(235\) 0.594717 0.0387950
\(236\) 49.9199 3.24951
\(237\) −2.63496 −0.171159
\(238\) −38.0400 −2.46577
\(239\) 7.40108 0.478736 0.239368 0.970929i \(-0.423060\pi\)
0.239368 + 0.970929i \(0.423060\pi\)
\(240\) 13.6431 0.880662
\(241\) 26.5264 1.70872 0.854358 0.519684i \(-0.173950\pi\)
0.854358 + 0.519684i \(0.173950\pi\)
\(242\) 13.3130 0.855791
\(243\) 15.5691 0.998759
\(244\) −7.21190 −0.461694
\(245\) −1.71936 −0.109846
\(246\) 30.6736 1.95568
\(247\) 35.4053 2.25278
\(248\) 5.50481 0.349556
\(249\) 0.444351 0.0281596
\(250\) 19.2998 1.22063
\(251\) −0.250558 −0.0158151 −0.00790756 0.999969i \(-0.502517\pi\)
−0.00790756 + 0.999969i \(0.502517\pi\)
\(252\) 22.8412 1.43886
\(253\) −2.49200 −0.156671
\(254\) 24.3053 1.52505
\(255\) −4.99414 −0.312745
\(256\) 85.7905 5.36191
\(257\) 10.7268 0.669118 0.334559 0.942375i \(-0.391413\pi\)
0.334559 + 0.942375i \(0.391413\pi\)
\(258\) −30.4230 −1.89405
\(259\) −12.6698 −0.787265
\(260\) −23.7983 −1.47591
\(261\) 8.31443 0.514651
\(262\) 13.0092 0.803713
\(263\) 8.48462 0.523184 0.261592 0.965179i \(-0.415752\pi\)
0.261592 + 0.965179i \(0.415752\pi\)
\(264\) 27.6823 1.70373
\(265\) −0.769298 −0.0472576
\(266\) −37.4940 −2.29890
\(267\) −8.32325 −0.509375
\(268\) 34.8207 2.12702
\(269\) −16.4049 −1.00022 −0.500111 0.865961i \(-0.666708\pi\)
−0.500111 + 0.865961i \(0.666708\pi\)
\(270\) 10.6124 0.645852
\(271\) 24.8720 1.51086 0.755432 0.655227i \(-0.227427\pi\)
0.755432 + 0.655227i \(0.227427\pi\)
\(272\) −109.876 −6.66221
\(273\) 13.1152 0.793766
\(274\) −9.34821 −0.564746
\(275\) 11.1177 0.670423
\(276\) 6.14265 0.369744
\(277\) 17.1419 1.02996 0.514979 0.857203i \(-0.327800\pi\)
0.514979 + 0.857203i \(0.327800\pi\)
\(278\) 50.3784 3.02150
\(279\) 0.982998 0.0588506
\(280\) 16.3979 0.979964
\(281\) −23.0529 −1.37522 −0.687610 0.726080i \(-0.741340\pi\)
−0.687610 + 0.726080i \(0.741340\pi\)
\(282\) −2.41652 −0.143901
\(283\) −19.4824 −1.15811 −0.579054 0.815289i \(-0.696578\pi\)
−0.579054 + 0.815289i \(0.696578\pi\)
\(284\) −51.7692 −3.07194
\(285\) −4.92246 −0.291581
\(286\) −39.2300 −2.31972
\(287\) 22.1973 1.31027
\(288\) 50.7431 2.99007
\(289\) 23.2207 1.36592
\(290\) 9.17390 0.538710
\(291\) −15.0309 −0.881126
\(292\) −13.1881 −0.771778
\(293\) 7.29960 0.426447 0.213224 0.977003i \(-0.431604\pi\)
0.213224 + 0.977003i \(0.431604\pi\)
\(294\) 6.98628 0.407448
\(295\) 6.39962 0.372600
\(296\) −60.7816 −3.53286
\(297\) 12.9647 0.752289
\(298\) −37.7936 −2.18933
\(299\) −5.66398 −0.327557
\(300\) −27.4045 −1.58220
\(301\) −22.0160 −1.26898
\(302\) −46.0674 −2.65088
\(303\) −17.3053 −0.994166
\(304\) −108.299 −6.21137
\(305\) −0.924549 −0.0529395
\(306\) −32.5876 −1.86291
\(307\) 32.9419 1.88009 0.940047 0.341044i \(-0.110780\pi\)
0.940047 + 0.341044i \(0.110780\pi\)
\(308\) 30.7885 1.75434
\(309\) −3.87658 −0.220531
\(310\) 1.08461 0.0616018
\(311\) −14.0869 −0.798793 −0.399397 0.916778i \(-0.630780\pi\)
−0.399397 + 0.916778i \(0.630780\pi\)
\(312\) 62.9180 3.56203
\(313\) 23.2143 1.31215 0.656075 0.754695i \(-0.272215\pi\)
0.656075 + 0.754695i \(0.272215\pi\)
\(314\) 11.4480 0.646049
\(315\) 2.92819 0.164985
\(316\) −14.0592 −0.790893
\(317\) −3.85515 −0.216527 −0.108263 0.994122i \(-0.534529\pi\)
−0.108263 + 0.994122i \(0.534529\pi\)
\(318\) 3.12589 0.175291
\(319\) 11.2073 0.627490
\(320\) 30.5576 1.70822
\(321\) 9.25445 0.516533
\(322\) 5.99813 0.334263
\(323\) 39.6434 2.20582
\(324\) −0.205198 −0.0113999
\(325\) 25.2690 1.40167
\(326\) −37.5216 −2.07813
\(327\) −2.55686 −0.141395
\(328\) 106.488 5.87983
\(329\) −1.74874 −0.0964112
\(330\) 5.45423 0.300245
\(331\) 9.56895 0.525957 0.262979 0.964802i \(-0.415295\pi\)
0.262979 + 0.964802i \(0.415295\pi\)
\(332\) 2.37091 0.130120
\(333\) −10.8538 −0.594785
\(334\) 30.1682 1.65073
\(335\) 4.46394 0.243891
\(336\) −40.1171 −2.18857
\(337\) 19.9366 1.08602 0.543008 0.839727i \(-0.317285\pi\)
0.543008 + 0.839727i \(0.317285\pi\)
\(338\) −53.0325 −2.88459
\(339\) −16.8851 −0.917072
\(340\) −26.6471 −1.44514
\(341\) 1.32502 0.0717539
\(342\) −32.1198 −1.73684
\(343\) 20.1623 1.08866
\(344\) −105.618 −5.69455
\(345\) 0.787474 0.0423962
\(346\) −5.34151 −0.287161
\(347\) −30.1310 −1.61751 −0.808757 0.588142i \(-0.799859\pi\)
−0.808757 + 0.588142i \(0.799859\pi\)
\(348\) −27.6255 −1.48088
\(349\) −1.00000 −0.0535288
\(350\) −26.7598 −1.43037
\(351\) 29.4670 1.57283
\(352\) 68.3985 3.64565
\(353\) −20.7845 −1.10625 −0.553124 0.833099i \(-0.686565\pi\)
−0.553124 + 0.833099i \(0.686565\pi\)
\(354\) −26.0036 −1.38208
\(355\) −6.63670 −0.352240
\(356\) −44.4100 −2.35373
\(357\) 14.6851 0.777217
\(358\) −42.4481 −2.24345
\(359\) −13.8233 −0.729567 −0.364783 0.931092i \(-0.618857\pi\)
−0.364783 + 0.931092i \(0.618857\pi\)
\(360\) 14.0476 0.740371
\(361\) 20.0743 1.05654
\(362\) 57.7848 3.03710
\(363\) −5.13939 −0.269748
\(364\) 69.9780 3.66785
\(365\) −1.69069 −0.0884948
\(366\) 3.75672 0.196367
\(367\) 15.7662 0.822990 0.411495 0.911412i \(-0.365007\pi\)
0.411495 + 0.911412i \(0.365007\pi\)
\(368\) 17.3252 0.903138
\(369\) 19.0157 0.989917
\(370\) −11.9758 −0.622591
\(371\) 2.26209 0.117442
\(372\) −3.26610 −0.169339
\(373\) 26.3868 1.36626 0.683129 0.730297i \(-0.260619\pi\)
0.683129 + 0.730297i \(0.260619\pi\)
\(374\) −43.9260 −2.27136
\(375\) −7.45057 −0.384746
\(376\) −8.38932 −0.432646
\(377\) 25.4727 1.31191
\(378\) −31.2054 −1.60503
\(379\) −7.81830 −0.401599 −0.200800 0.979632i \(-0.564354\pi\)
−0.200800 + 0.979632i \(0.564354\pi\)
\(380\) −26.2646 −1.34734
\(381\) −9.38289 −0.480700
\(382\) 14.6546 0.749796
\(383\) 2.84229 0.145234 0.0726172 0.997360i \(-0.476865\pi\)
0.0726172 + 0.997360i \(0.476865\pi\)
\(384\) −65.2653 −3.33055
\(385\) 3.94702 0.201159
\(386\) −23.5905 −1.20072
\(387\) −18.8603 −0.958724
\(388\) −80.1997 −4.07152
\(389\) −29.4065 −1.49097 −0.745484 0.666524i \(-0.767781\pi\)
−0.745484 + 0.666524i \(0.767781\pi\)
\(390\) 12.3967 0.627732
\(391\) −6.34198 −0.320728
\(392\) 24.2540 1.22501
\(393\) −5.02212 −0.253333
\(394\) 70.0167 3.52739
\(395\) −1.80236 −0.0906867
\(396\) 26.3755 1.32542
\(397\) −20.5940 −1.03358 −0.516791 0.856112i \(-0.672873\pi\)
−0.516791 + 0.856112i \(0.672873\pi\)
\(398\) 10.2993 0.516257
\(399\) 14.4743 0.724621
\(400\) −77.2938 −3.86469
\(401\) 2.43088 0.121392 0.0606962 0.998156i \(-0.480668\pi\)
0.0606962 + 0.998156i \(0.480668\pi\)
\(402\) −18.1384 −0.904659
\(403\) 3.01159 0.150018
\(404\) −92.3354 −4.59386
\(405\) −0.0263060 −0.00130715
\(406\) −26.9755 −1.33877
\(407\) −14.6303 −0.725195
\(408\) 70.4494 3.48777
\(409\) −22.3476 −1.10502 −0.552510 0.833506i \(-0.686330\pi\)
−0.552510 + 0.833506i \(0.686330\pi\)
\(410\) 20.9813 1.03619
\(411\) 3.60882 0.178010
\(412\) −20.6841 −1.01903
\(413\) −18.8178 −0.925965
\(414\) 5.13839 0.252538
\(415\) 0.303945 0.0149201
\(416\) 155.460 7.62207
\(417\) −19.4483 −0.952385
\(418\) −43.2955 −2.11765
\(419\) −34.7494 −1.69762 −0.848810 0.528698i \(-0.822680\pi\)
−0.848810 + 0.528698i \(0.822680\pi\)
\(420\) −9.72918 −0.474735
\(421\) 2.64290 0.128807 0.0644036 0.997924i \(-0.479486\pi\)
0.0644036 + 0.997924i \(0.479486\pi\)
\(422\) 59.4210 2.89257
\(423\) −1.49809 −0.0728395
\(424\) 10.8520 0.527021
\(425\) 28.2938 1.37245
\(426\) 26.9669 1.30655
\(427\) 2.71860 0.131562
\(428\) 49.3786 2.38680
\(429\) 15.1445 0.731183
\(430\) −20.8099 −1.00354
\(431\) −0.616863 −0.0297132 −0.0148566 0.999890i \(-0.504729\pi\)
−0.0148566 + 0.999890i \(0.504729\pi\)
\(432\) −90.1348 −4.33661
\(433\) 22.7536 1.09347 0.546733 0.837307i \(-0.315871\pi\)
0.546733 + 0.837307i \(0.315871\pi\)
\(434\) −3.18926 −0.153089
\(435\) −3.54152 −0.169803
\(436\) −13.6425 −0.653358
\(437\) −6.25095 −0.299023
\(438\) 6.86979 0.328251
\(439\) −19.2503 −0.918765 −0.459383 0.888239i \(-0.651929\pi\)
−0.459383 + 0.888239i \(0.651929\pi\)
\(440\) 18.9352 0.902701
\(441\) 4.33105 0.206241
\(442\) −99.8377 −4.74879
\(443\) −21.1932 −1.00692 −0.503461 0.864018i \(-0.667940\pi\)
−0.503461 + 0.864018i \(0.667940\pi\)
\(444\) 36.0628 1.71146
\(445\) −5.69327 −0.269887
\(446\) −19.7537 −0.935365
\(447\) 14.5900 0.690082
\(448\) −89.8534 −4.24517
\(449\) 30.8234 1.45465 0.727323 0.686296i \(-0.240764\pi\)
0.727323 + 0.686296i \(0.240764\pi\)
\(450\) −22.9242 −1.08066
\(451\) 25.6319 1.20696
\(452\) −90.0930 −4.23762
\(453\) 17.7840 0.835565
\(454\) −27.2771 −1.28018
\(455\) 8.97103 0.420568
\(456\) 69.4383 3.25174
\(457\) 25.1681 1.17731 0.588656 0.808383i \(-0.299657\pi\)
0.588656 + 0.808383i \(0.299657\pi\)
\(458\) 30.1473 1.40869
\(459\) 32.9943 1.54004
\(460\) 4.20170 0.195905
\(461\) −26.5726 −1.23761 −0.618805 0.785545i \(-0.712383\pi\)
−0.618805 + 0.785545i \(0.712383\pi\)
\(462\) −16.0379 −0.746153
\(463\) 21.7853 1.01245 0.506224 0.862402i \(-0.331041\pi\)
0.506224 + 0.862402i \(0.331041\pi\)
\(464\) −77.9169 −3.61720
\(465\) −0.418707 −0.0194171
\(466\) −8.11669 −0.375998
\(467\) −23.7522 −1.09912 −0.549561 0.835454i \(-0.685205\pi\)
−0.549561 + 0.835454i \(0.685205\pi\)
\(468\) 59.9478 2.77109
\(469\) −13.1260 −0.606104
\(470\) −1.65294 −0.0762446
\(471\) −4.41943 −0.203636
\(472\) −90.2757 −4.15528
\(473\) −25.4225 −1.16893
\(474\) 7.32355 0.336382
\(475\) 27.8877 1.27957
\(476\) 78.3546 3.59138
\(477\) 1.93786 0.0887283
\(478\) −20.5704 −0.940868
\(479\) 26.0076 1.18832 0.594160 0.804347i \(-0.297485\pi\)
0.594160 + 0.804347i \(0.297485\pi\)
\(480\) −21.6140 −0.986537
\(481\) −33.2526 −1.51619
\(482\) −73.7270 −3.35817
\(483\) −2.31554 −0.105361
\(484\) −27.4220 −1.24646
\(485\) −10.2814 −0.466855
\(486\) −43.2725 −1.96288
\(487\) −34.8165 −1.57769 −0.788844 0.614594i \(-0.789320\pi\)
−0.788844 + 0.614594i \(0.789320\pi\)
\(488\) 13.0421 0.590387
\(489\) 14.4850 0.655033
\(490\) 4.77875 0.215882
\(491\) −11.9085 −0.537421 −0.268711 0.963221i \(-0.586598\pi\)
−0.268711 + 0.963221i \(0.586598\pi\)
\(492\) −63.1813 −2.84843
\(493\) 28.5219 1.28456
\(494\) −98.4047 −4.42744
\(495\) 3.38128 0.151977
\(496\) −9.21195 −0.413629
\(497\) 19.5150 0.875365
\(498\) −1.23502 −0.0553426
\(499\) −4.57926 −0.204996 −0.102498 0.994733i \(-0.532684\pi\)
−0.102498 + 0.994733i \(0.532684\pi\)
\(500\) −39.7537 −1.77784
\(501\) −11.6462 −0.520316
\(502\) 0.696397 0.0310817
\(503\) −39.4638 −1.75960 −0.879802 0.475339i \(-0.842325\pi\)
−0.879802 + 0.475339i \(0.842325\pi\)
\(504\) −41.3063 −1.83993
\(505\) −11.8372 −0.526748
\(506\) 6.92623 0.307908
\(507\) 20.4728 0.909231
\(508\) −50.0639 −2.22123
\(509\) −34.6796 −1.53715 −0.768573 0.639762i \(-0.779033\pi\)
−0.768573 + 0.639762i \(0.779033\pi\)
\(510\) 13.8806 0.614644
\(511\) 4.97141 0.219922
\(512\) −116.790 −5.16144
\(513\) 32.5207 1.43582
\(514\) −29.8138 −1.31503
\(515\) −2.65166 −0.116846
\(516\) 62.6651 2.75868
\(517\) −2.01933 −0.0888099
\(518\) 35.2143 1.54723
\(519\) 2.06205 0.0905141
\(520\) 43.0371 1.88730
\(521\) −8.22397 −0.360299 −0.180149 0.983639i \(-0.557658\pi\)
−0.180149 + 0.983639i \(0.557658\pi\)
\(522\) −23.1090 −1.01145
\(523\) 9.77095 0.427254 0.213627 0.976915i \(-0.431472\pi\)
0.213627 + 0.976915i \(0.431472\pi\)
\(524\) −26.7963 −1.17060
\(525\) 10.3304 0.450857
\(526\) −23.5820 −1.02822
\(527\) 3.37208 0.146890
\(528\) −46.3245 −2.01602
\(529\) 1.00000 0.0434783
\(530\) 2.13817 0.0928763
\(531\) −16.1206 −0.699574
\(532\) 77.2299 3.34834
\(533\) 58.2579 2.52343
\(534\) 23.1335 1.00108
\(535\) 6.33022 0.273679
\(536\) −62.9702 −2.71990
\(537\) 16.3868 0.707144
\(538\) 45.5954 1.96576
\(539\) 5.83798 0.251460
\(540\) −21.8594 −0.940680
\(541\) −2.26469 −0.0973667 −0.0486833 0.998814i \(-0.515503\pi\)
−0.0486833 + 0.998814i \(0.515503\pi\)
\(542\) −69.1286 −2.96933
\(543\) −22.3074 −0.957304
\(544\) 174.069 7.46316
\(545\) −1.74894 −0.0749164
\(546\) −36.4520 −1.56000
\(547\) −16.6070 −0.710063 −0.355032 0.934854i \(-0.615530\pi\)
−0.355032 + 0.934854i \(0.615530\pi\)
\(548\) 19.2554 0.822550
\(549\) 2.32893 0.0993964
\(550\) −30.9003 −1.31760
\(551\) 28.1125 1.19763
\(552\) −11.1084 −0.472806
\(553\) 5.29977 0.225369
\(554\) −47.6439 −2.02419
\(555\) 4.62317 0.196242
\(556\) −103.769 −4.40080
\(557\) 0.177868 0.00753652 0.00376826 0.999993i \(-0.498801\pi\)
0.00376826 + 0.999993i \(0.498801\pi\)
\(558\) −2.73213 −0.115660
\(559\) −57.7819 −2.44391
\(560\) −27.4409 −1.15959
\(561\) 16.9573 0.715939
\(562\) 64.0727 2.70275
\(563\) 23.6017 0.994692 0.497346 0.867552i \(-0.334308\pi\)
0.497346 + 0.867552i \(0.334308\pi\)
\(564\) 4.97753 0.209592
\(565\) −11.5497 −0.485901
\(566\) 54.1489 2.27605
\(567\) 0.0773516 0.00324846
\(568\) 93.6200 3.92821
\(569\) −23.9893 −1.00568 −0.502842 0.864378i \(-0.667712\pi\)
−0.502842 + 0.864378i \(0.667712\pi\)
\(570\) 13.6814 0.573050
\(571\) 7.76209 0.324833 0.162417 0.986722i \(-0.448071\pi\)
0.162417 + 0.986722i \(0.448071\pi\)
\(572\) 80.8059 3.37866
\(573\) −5.65732 −0.236338
\(574\) −61.6948 −2.57509
\(575\) −4.46135 −0.186051
\(576\) −76.9743 −3.20726
\(577\) −42.3041 −1.76114 −0.880570 0.473915i \(-0.842840\pi\)
−0.880570 + 0.473915i \(0.842840\pi\)
\(578\) −64.5391 −2.68447
\(579\) 9.10695 0.378472
\(580\) −18.8964 −0.784628
\(581\) −0.893738 −0.0370785
\(582\) 41.7766 1.73169
\(583\) 2.61211 0.108182
\(584\) 23.8496 0.986903
\(585\) 7.68517 0.317743
\(586\) −20.2884 −0.838105
\(587\) −12.7211 −0.525055 −0.262528 0.964925i \(-0.584556\pi\)
−0.262528 + 0.964925i \(0.584556\pi\)
\(588\) −14.3903 −0.593446
\(589\) 3.32368 0.136950
\(590\) −17.7870 −0.732278
\(591\) −27.0295 −1.11184
\(592\) 101.714 4.18043
\(593\) 35.3328 1.45094 0.725472 0.688252i \(-0.241622\pi\)
0.725472 + 0.688252i \(0.241622\pi\)
\(594\) −36.0339 −1.47849
\(595\) 10.0449 0.411800
\(596\) 77.8471 3.18874
\(597\) −3.97597 −0.162726
\(598\) 15.7424 0.643753
\(599\) 15.6172 0.638101 0.319050 0.947738i \(-0.396636\pi\)
0.319050 + 0.947738i \(0.396636\pi\)
\(600\) 49.5586 2.02322
\(601\) −23.7703 −0.969611 −0.484806 0.874622i \(-0.661110\pi\)
−0.484806 + 0.874622i \(0.661110\pi\)
\(602\) 61.1907 2.49395
\(603\) −11.2446 −0.457917
\(604\) 94.8894 3.86099
\(605\) −3.51544 −0.142923
\(606\) 48.0981 1.95385
\(607\) 11.6679 0.473584 0.236792 0.971560i \(-0.423904\pi\)
0.236792 + 0.971560i \(0.423904\pi\)
\(608\) 171.571 6.95812
\(609\) 10.4137 0.421985
\(610\) 2.56967 0.104043
\(611\) −4.58965 −0.185677
\(612\) 67.1237 2.71332
\(613\) −4.56271 −0.184286 −0.0921431 0.995746i \(-0.529372\pi\)
−0.0921431 + 0.995746i \(0.529372\pi\)
\(614\) −91.5581 −3.69499
\(615\) −8.09970 −0.326612
\(616\) −55.6783 −2.24334
\(617\) 4.45037 0.179165 0.0895825 0.995979i \(-0.471447\pi\)
0.0895825 + 0.995979i \(0.471447\pi\)
\(618\) 10.7745 0.433414
\(619\) 17.8374 0.716945 0.358473 0.933540i \(-0.383298\pi\)
0.358473 + 0.933540i \(0.383298\pi\)
\(620\) −2.23408 −0.0897227
\(621\) −5.20252 −0.208770
\(622\) 39.1528 1.56988
\(623\) 16.7408 0.670707
\(624\) −105.289 −4.21494
\(625\) 17.2104 0.688417
\(626\) −64.5214 −2.57879
\(627\) 16.7139 0.667490
\(628\) −23.5806 −0.940967
\(629\) −37.2330 −1.48458
\(630\) −8.13856 −0.324248
\(631\) 36.4207 1.44989 0.724943 0.688809i \(-0.241866\pi\)
0.724943 + 0.688809i \(0.241866\pi\)
\(632\) 25.4249 1.01135
\(633\) −22.9391 −0.911746
\(634\) 10.7149 0.425544
\(635\) −6.41808 −0.254694
\(636\) −6.43870 −0.255311
\(637\) 13.2689 0.525734
\(638\) −31.1494 −1.23322
\(639\) 16.7178 0.661346
\(640\) −44.6427 −1.76466
\(641\) 25.8592 1.02138 0.510688 0.859766i \(-0.329391\pi\)
0.510688 + 0.859766i \(0.329391\pi\)
\(642\) −25.7216 −1.01515
\(643\) −4.03188 −0.159002 −0.0795010 0.996835i \(-0.525333\pi\)
−0.0795010 + 0.996835i \(0.525333\pi\)
\(644\) −12.3549 −0.486852
\(645\) 8.03353 0.316320
\(646\) −110.184 −4.33513
\(647\) 45.2789 1.78010 0.890048 0.455867i \(-0.150671\pi\)
0.890048 + 0.455867i \(0.150671\pi\)
\(648\) 0.371083 0.0145775
\(649\) −21.7295 −0.852959
\(650\) −70.2322 −2.75473
\(651\) 1.23119 0.0482542
\(652\) 77.2869 3.02679
\(653\) 13.4356 0.525774 0.262887 0.964827i \(-0.415325\pi\)
0.262887 + 0.964827i \(0.415325\pi\)
\(654\) 7.10648 0.277885
\(655\) −3.43523 −0.134226
\(656\) −178.201 −6.95759
\(657\) 4.25884 0.166153
\(658\) 4.86042 0.189479
\(659\) −4.85141 −0.188984 −0.0944921 0.995526i \(-0.530123\pi\)
−0.0944921 + 0.995526i \(0.530123\pi\)
\(660\) −11.2346 −0.437306
\(661\) 25.3089 0.984402 0.492201 0.870482i \(-0.336192\pi\)
0.492201 + 0.870482i \(0.336192\pi\)
\(662\) −26.5958 −1.03367
\(663\) 38.5417 1.49683
\(664\) −4.28757 −0.166390
\(665\) 9.90070 0.383933
\(666\) 30.1669 1.16894
\(667\) −4.49732 −0.174137
\(668\) −62.1404 −2.40428
\(669\) 7.62579 0.294830
\(670\) −12.4070 −0.479324
\(671\) 3.13925 0.121189
\(672\) 63.5550 2.45169
\(673\) −12.7372 −0.490983 −0.245492 0.969399i \(-0.578949\pi\)
−0.245492 + 0.969399i \(0.578949\pi\)
\(674\) −55.4114 −2.13437
\(675\) 23.2103 0.893365
\(676\) 109.236 4.20139
\(677\) −37.1815 −1.42900 −0.714500 0.699636i \(-0.753346\pi\)
−0.714500 + 0.699636i \(0.753346\pi\)
\(678\) 46.9301 1.80234
\(679\) 30.2321 1.16020
\(680\) 48.1888 1.84796
\(681\) 10.5301 0.403515
\(682\) −3.68273 −0.141019
\(683\) −8.61310 −0.329571 −0.164786 0.986329i \(-0.552693\pi\)
−0.164786 + 0.986329i \(0.552693\pi\)
\(684\) 66.1603 2.52970
\(685\) 2.46850 0.0943165
\(686\) −56.0386 −2.13956
\(687\) −11.6382 −0.444024
\(688\) 176.745 6.73836
\(689\) 5.93696 0.226180
\(690\) −2.18869 −0.0833220
\(691\) −24.0088 −0.913338 −0.456669 0.889637i \(-0.650958\pi\)
−0.456669 + 0.889637i \(0.650958\pi\)
\(692\) 11.0024 0.418249
\(693\) −9.94251 −0.377685
\(694\) 83.7454 3.17893
\(695\) −13.3030 −0.504611
\(696\) 49.9582 1.89366
\(697\) 65.2315 2.47082
\(698\) 2.77938 0.105201
\(699\) 3.13339 0.118516
\(700\) 55.1196 2.08333
\(701\) 0.139269 0.00526012 0.00263006 0.999997i \(-0.499163\pi\)
0.00263006 + 0.999997i \(0.499163\pi\)
\(702\) −81.9000 −3.09112
\(703\) −36.6986 −1.38411
\(704\) −103.757 −3.91047
\(705\) 0.638108 0.0240325
\(706\) 57.7681 2.17413
\(707\) 34.8068 1.30904
\(708\) 53.5621 2.01299
\(709\) −15.5777 −0.585033 −0.292517 0.956260i \(-0.594493\pi\)
−0.292517 + 0.956260i \(0.594493\pi\)
\(710\) 18.4459 0.692263
\(711\) 4.54013 0.170268
\(712\) 80.3115 3.00980
\(713\) −0.531708 −0.0199126
\(714\) −40.8154 −1.52748
\(715\) 10.3591 0.387409
\(716\) 87.4345 3.26758
\(717\) 7.94107 0.296565
\(718\) 38.4202 1.43383
\(719\) −2.52288 −0.0940877 −0.0470438 0.998893i \(-0.514980\pi\)
−0.0470438 + 0.998893i \(0.514980\pi\)
\(720\) −23.5077 −0.876080
\(721\) 7.79710 0.290379
\(722\) −55.7942 −2.07645
\(723\) 28.4618 1.05851
\(724\) −119.025 −4.42352
\(725\) 20.0641 0.745162
\(726\) 14.2843 0.530141
\(727\) −27.1085 −1.00540 −0.502700 0.864461i \(-0.667660\pi\)
−0.502700 + 0.864461i \(0.667660\pi\)
\(728\) −126.549 −4.69022
\(729\) 16.8126 0.622688
\(730\) 4.69907 0.173920
\(731\) −64.6986 −2.39296
\(732\) −7.73808 −0.286008
\(733\) −8.67264 −0.320331 −0.160166 0.987090i \(-0.551203\pi\)
−0.160166 + 0.987090i \(0.551203\pi\)
\(734\) −43.8203 −1.61744
\(735\) −1.84480 −0.0680467
\(736\) −27.4472 −1.01172
\(737\) −15.1571 −0.558317
\(738\) −52.8518 −1.94550
\(739\) 7.03904 0.258935 0.129468 0.991584i \(-0.458673\pi\)
0.129468 + 0.991584i \(0.458673\pi\)
\(740\) 24.6676 0.906800
\(741\) 37.9885 1.39554
\(742\) −6.28721 −0.230811
\(743\) 43.2112 1.58527 0.792633 0.609700i \(-0.208710\pi\)
0.792633 + 0.609700i \(0.208710\pi\)
\(744\) 5.90645 0.216541
\(745\) 9.97983 0.365633
\(746\) −73.3391 −2.68513
\(747\) −0.765635 −0.0280131
\(748\) 90.4785 3.30822
\(749\) −18.6138 −0.680132
\(750\) 20.7080 0.756148
\(751\) −7.78872 −0.284214 −0.142107 0.989851i \(-0.545388\pi\)
−0.142107 + 0.989851i \(0.545388\pi\)
\(752\) 14.0390 0.511949
\(753\) −0.268839 −0.00979706
\(754\) −70.7984 −2.57833
\(755\) 12.1646 0.442715
\(756\) 64.2768 2.33772
\(757\) 35.3499 1.28481 0.642406 0.766364i \(-0.277936\pi\)
0.642406 + 0.766364i \(0.277936\pi\)
\(758\) 21.7300 0.789271
\(759\) −2.67382 −0.0970537
\(760\) 47.4971 1.72290
\(761\) −45.1325 −1.63605 −0.818026 0.575181i \(-0.804931\pi\)
−0.818026 + 0.575181i \(0.804931\pi\)
\(762\) 26.0786 0.944728
\(763\) 5.14269 0.186178
\(764\) −30.1855 −1.09207
\(765\) 8.60511 0.311118
\(766\) −7.89982 −0.285432
\(767\) −49.3883 −1.78331
\(768\) 92.0499 3.32157
\(769\) 35.5296 1.28123 0.640615 0.767862i \(-0.278679\pi\)
0.640615 + 0.767862i \(0.278679\pi\)
\(770\) −10.9703 −0.395341
\(771\) 11.5094 0.414502
\(772\) 48.5916 1.74885
\(773\) −33.7122 −1.21255 −0.606273 0.795257i \(-0.707336\pi\)
−0.606273 + 0.795257i \(0.707336\pi\)
\(774\) 52.4200 1.88420
\(775\) 2.37214 0.0852097
\(776\) 145.034 5.20642
\(777\) −13.5942 −0.487691
\(778\) 81.7318 2.93023
\(779\) 64.2952 2.30362
\(780\) −25.5347 −0.914288
\(781\) 22.5345 0.806349
\(782\) 17.6268 0.630332
\(783\) 23.3974 0.836155
\(784\) −40.5875 −1.44955
\(785\) −3.02297 −0.107895
\(786\) 13.9584 0.497879
\(787\) −10.1125 −0.360471 −0.180236 0.983623i \(-0.557686\pi\)
−0.180236 + 0.983623i \(0.557686\pi\)
\(788\) −144.220 −5.13763
\(789\) 9.10367 0.324099
\(790\) 5.00945 0.178228
\(791\) 33.9615 1.20753
\(792\) −47.6977 −1.69486
\(793\) 7.13509 0.253374
\(794\) 57.2384 2.03132
\(795\) −0.825427 −0.0292749
\(796\) −21.2144 −0.751926
\(797\) −46.4061 −1.64379 −0.821893 0.569641i \(-0.807082\pi\)
−0.821893 + 0.569641i \(0.807082\pi\)
\(798\) −40.2296 −1.42411
\(799\) −5.13904 −0.181806
\(800\) 122.452 4.32932
\(801\) 14.3413 0.506725
\(802\) −6.75635 −0.238575
\(803\) 5.74064 0.202583
\(804\) 37.3613 1.31763
\(805\) −1.58387 −0.0558242
\(806\) −8.37035 −0.294833
\(807\) −17.6018 −0.619612
\(808\) 166.980 5.87435
\(809\) −20.1895 −0.709826 −0.354913 0.934899i \(-0.615490\pi\)
−0.354913 + 0.934899i \(0.615490\pi\)
\(810\) 0.0731143 0.00256897
\(811\) −3.88458 −0.136406 −0.0682030 0.997671i \(-0.521727\pi\)
−0.0682030 + 0.997671i \(0.521727\pi\)
\(812\) 55.5640 1.94991
\(813\) 26.6866 0.935941
\(814\) 40.6630 1.42524
\(815\) 9.90800 0.347062
\(816\) −117.893 −4.12707
\(817\) −63.7699 −2.23103
\(818\) 62.1126 2.17172
\(819\) −22.5979 −0.789636
\(820\) −43.2173 −1.50921
\(821\) −28.6055 −0.998340 −0.499170 0.866504i \(-0.666362\pi\)
−0.499170 + 0.866504i \(0.666362\pi\)
\(822\) −10.0303 −0.349846
\(823\) −34.1518 −1.19046 −0.595228 0.803557i \(-0.702938\pi\)
−0.595228 + 0.803557i \(0.702938\pi\)
\(824\) 37.4054 1.30308
\(825\) 11.9289 0.415310
\(826\) 52.3019 1.81982
\(827\) 11.1702 0.388426 0.194213 0.980959i \(-0.437785\pi\)
0.194213 + 0.980959i \(0.437785\pi\)
\(828\) −10.5840 −0.367821
\(829\) −0.377626 −0.0131155 −0.00655774 0.999978i \(-0.502087\pi\)
−0.00655774 + 0.999978i \(0.502087\pi\)
\(830\) −0.844779 −0.0293227
\(831\) 18.3926 0.638032
\(832\) −235.824 −8.17573
\(833\) 14.8573 0.514773
\(834\) 54.0541 1.87174
\(835\) −7.96626 −0.275684
\(836\) 89.1799 3.08435
\(837\) 2.76623 0.0956148
\(838\) 96.5818 3.33636
\(839\) −47.2668 −1.63183 −0.815915 0.578172i \(-0.803766\pi\)
−0.815915 + 0.578172i \(0.803766\pi\)
\(840\) 17.5943 0.607063
\(841\) −8.77415 −0.302557
\(842\) −7.34563 −0.253147
\(843\) −24.7348 −0.851913
\(844\) −122.395 −4.21301
\(845\) 14.0038 0.481746
\(846\) 4.16375 0.143153
\(847\) 10.3370 0.355184
\(848\) −18.1602 −0.623623
\(849\) −20.9038 −0.717418
\(850\) −78.6392 −2.69730
\(851\) 5.87088 0.201251
\(852\) −55.5464 −1.90299
\(853\) −49.9716 −1.71099 −0.855497 0.517807i \(-0.826749\pi\)
−0.855497 + 0.517807i \(0.826749\pi\)
\(854\) −7.55602 −0.258562
\(855\) 8.48160 0.290064
\(856\) −89.2967 −3.05210
\(857\) 8.23835 0.281417 0.140708 0.990051i \(-0.455062\pi\)
0.140708 + 0.990051i \(0.455062\pi\)
\(858\) −42.0923 −1.43701
\(859\) 48.0245 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(860\) 42.8642 1.46166
\(861\) 23.8169 0.811676
\(862\) 1.71450 0.0583960
\(863\) −10.9120 −0.371450 −0.185725 0.982602i \(-0.559463\pi\)
−0.185725 + 0.982602i \(0.559463\pi\)
\(864\) 142.795 4.85797
\(865\) 1.41048 0.0479579
\(866\) −63.2408 −2.14901
\(867\) 24.9149 0.846153
\(868\) 6.56921 0.222974
\(869\) 6.11982 0.207601
\(870\) 9.84323 0.333717
\(871\) −34.4499 −1.16729
\(872\) 24.6713 0.835475
\(873\) 25.8988 0.876542
\(874\) 17.3738 0.587676
\(875\) 14.9856 0.506605
\(876\) −14.1504 −0.478097
\(877\) −27.7805 −0.938079 −0.469040 0.883177i \(-0.655400\pi\)
−0.469040 + 0.883177i \(0.655400\pi\)
\(878\) 53.5038 1.80567
\(879\) 7.83219 0.264173
\(880\) −31.6869 −1.06816
\(881\) −8.55089 −0.288087 −0.144043 0.989571i \(-0.546011\pi\)
−0.144043 + 0.989571i \(0.546011\pi\)
\(882\) −12.0376 −0.405328
\(883\) 1.42088 0.0478165 0.0239082 0.999714i \(-0.492389\pi\)
0.0239082 + 0.999714i \(0.492389\pi\)
\(884\) 205.645 6.91660
\(885\) 6.86654 0.230816
\(886\) 58.9041 1.97892
\(887\) 2.42617 0.0814628 0.0407314 0.999170i \(-0.487031\pi\)
0.0407314 + 0.999170i \(0.487031\pi\)
\(888\) −65.2163 −2.18852
\(889\) 18.8721 0.632950
\(890\) 15.8238 0.530413
\(891\) 0.0893204 0.00299234
\(892\) 40.6886 1.36236
\(893\) −5.06528 −0.169503
\(894\) −40.5511 −1.35623
\(895\) 11.2089 0.374672
\(896\) 131.270 4.38543
\(897\) −6.07723 −0.202913
\(898\) −85.6699 −2.85884
\(899\) 2.39126 0.0797530
\(900\) 47.2191 1.57397
\(901\) 6.64763 0.221465
\(902\) −71.2409 −2.37206
\(903\) −23.6223 −0.786100
\(904\) 162.925 5.41881
\(905\) −15.2587 −0.507217
\(906\) −49.4285 −1.64215
\(907\) −40.2815 −1.33753 −0.668763 0.743475i \(-0.733176\pi\)
−0.668763 + 0.743475i \(0.733176\pi\)
\(908\) 56.1852 1.86457
\(909\) 29.8178 0.988994
\(910\) −24.9339 −0.826551
\(911\) −39.4654 −1.30755 −0.653774 0.756690i \(-0.726815\pi\)
−0.653774 + 0.756690i \(0.726815\pi\)
\(912\) −116.201 −3.84778
\(913\) −1.03203 −0.0341551
\(914\) −69.9516 −2.31379
\(915\) −0.992005 −0.0327947
\(916\) −62.0973 −2.05175
\(917\) 10.1012 0.333570
\(918\) −91.7037 −3.02667
\(919\) −30.4427 −1.00421 −0.502105 0.864807i \(-0.667441\pi\)
−0.502105 + 0.864807i \(0.667441\pi\)
\(920\) −7.59839 −0.250511
\(921\) 35.3454 1.16467
\(922\) 73.8554 2.43230
\(923\) 51.2179 1.68586
\(924\) 33.0349 1.08677
\(925\) −26.1921 −0.861189
\(926\) −60.5496 −1.98978
\(927\) 6.67951 0.219384
\(928\) 123.439 4.05207
\(929\) 44.3241 1.45423 0.727113 0.686517i \(-0.240861\pi\)
0.727113 + 0.686517i \(0.240861\pi\)
\(930\) 1.16375 0.0381607
\(931\) 14.6440 0.479938
\(932\) 16.7187 0.547640
\(933\) −15.1147 −0.494832
\(934\) 66.0165 2.16013
\(935\) 11.5991 0.379333
\(936\) −108.410 −3.54350
\(937\) −11.1132 −0.363054 −0.181527 0.983386i \(-0.558104\pi\)
−0.181527 + 0.983386i \(0.558104\pi\)
\(938\) 36.4823 1.19119
\(939\) 24.9081 0.812844
\(940\) 3.40473 0.111050
\(941\) 34.5270 1.12555 0.562774 0.826610i \(-0.309734\pi\)
0.562774 + 0.826610i \(0.309734\pi\)
\(942\) 12.2833 0.400211
\(943\) −10.2857 −0.334948
\(944\) 151.071 4.91693
\(945\) 8.24014 0.268052
\(946\) 70.6589 2.29732
\(947\) 52.1941 1.69608 0.848040 0.529932i \(-0.177782\pi\)
0.848040 + 0.529932i \(0.177782\pi\)
\(948\) −15.0850 −0.489938
\(949\) 13.0477 0.423546
\(950\) −77.5105 −2.51477
\(951\) −4.13642 −0.134133
\(952\) −141.697 −4.59243
\(953\) −37.4211 −1.21219 −0.606094 0.795393i \(-0.707265\pi\)
−0.606094 + 0.795393i \(0.707265\pi\)
\(954\) −5.38604 −0.174379
\(955\) −3.86972 −0.125221
\(956\) 42.3708 1.37037
\(957\) 12.0250 0.388714
\(958\) −72.2851 −2.33543
\(959\) −7.25853 −0.234390
\(960\) 32.7871 1.05820
\(961\) −30.7173 −0.990880
\(962\) 92.4215 2.97979
\(963\) −15.9458 −0.513845
\(964\) 151.863 4.89116
\(965\) 6.22933 0.200529
\(966\) 6.43576 0.207067
\(967\) −22.7597 −0.731902 −0.365951 0.930634i \(-0.619256\pi\)
−0.365951 + 0.930634i \(0.619256\pi\)
\(968\) 49.5903 1.59389
\(969\) 42.5358 1.36645
\(970\) 28.5760 0.917519
\(971\) 7.31002 0.234590 0.117295 0.993097i \(-0.462578\pi\)
0.117295 + 0.993097i \(0.462578\pi\)
\(972\) 89.1325 2.85893
\(973\) 39.1169 1.25403
\(974\) 96.7684 3.10066
\(975\) 27.1127 0.868301
\(976\) −21.8251 −0.698603
\(977\) −1.09574 −0.0350558 −0.0175279 0.999846i \(-0.505580\pi\)
−0.0175279 + 0.999846i \(0.505580\pi\)
\(978\) −40.2592 −1.28735
\(979\) 19.3312 0.617826
\(980\) −9.84325 −0.314431
\(981\) 4.40557 0.140659
\(982\) 33.0981 1.05620
\(983\) 31.9922 1.02039 0.510196 0.860058i \(-0.329573\pi\)
0.510196 + 0.860058i \(0.329573\pi\)
\(984\) 114.258 3.64240
\(985\) −18.4887 −0.589099
\(986\) −79.2731 −2.52457
\(987\) −1.87633 −0.0597243
\(988\) 202.694 6.44854
\(989\) 10.2016 0.324393
\(990\) −9.39785 −0.298683
\(991\) 52.4198 1.66517 0.832585 0.553897i \(-0.186860\pi\)
0.832585 + 0.553897i \(0.186860\pi\)
\(992\) 14.5939 0.463357
\(993\) 10.2671 0.325817
\(994\) −54.2395 −1.72037
\(995\) −2.71964 −0.0862185
\(996\) 2.54389 0.0806063
\(997\) 45.2745 1.43386 0.716929 0.697146i \(-0.245547\pi\)
0.716929 + 0.697146i \(0.245547\pi\)
\(998\) 12.7275 0.402883
\(999\) −30.5434 −0.966350
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 \(a_p\))