Properties

Label 8021.2.a.a.1.3
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59685 q^{2} -2.33995 q^{3} +4.74363 q^{4} -3.06624 q^{5} +6.07651 q^{6} +0.887424 q^{7} -7.12481 q^{8} +2.47538 q^{9} +O(q^{10})\) \(q-2.59685 q^{2} -2.33995 q^{3} +4.74363 q^{4} -3.06624 q^{5} +6.07651 q^{6} +0.887424 q^{7} -7.12481 q^{8} +2.47538 q^{9} +7.96257 q^{10} +4.07583 q^{11} -11.0999 q^{12} +1.00000 q^{13} -2.30451 q^{14} +7.17486 q^{15} +9.01480 q^{16} +3.26610 q^{17} -6.42820 q^{18} -1.22112 q^{19} -14.5451 q^{20} -2.07653 q^{21} -10.5843 q^{22} +7.32658 q^{23} +16.6717 q^{24} +4.40182 q^{25} -2.59685 q^{26} +1.22758 q^{27} +4.20961 q^{28} -2.76340 q^{29} -18.6320 q^{30} +2.45502 q^{31} -9.16047 q^{32} -9.53726 q^{33} -8.48157 q^{34} -2.72105 q^{35} +11.7423 q^{36} -4.89092 q^{37} +3.17107 q^{38} -2.33995 q^{39} +21.8464 q^{40} +0.0195808 q^{41} +5.39244 q^{42} -4.44762 q^{43} +19.3343 q^{44} -7.59011 q^{45} -19.0260 q^{46} +11.0886 q^{47} -21.0942 q^{48} -6.21248 q^{49} -11.4309 q^{50} -7.64251 q^{51} +4.74363 q^{52} -0.247069 q^{53} -3.18785 q^{54} -12.4975 q^{55} -6.32273 q^{56} +2.85737 q^{57} +7.17615 q^{58} +3.31595 q^{59} +34.0349 q^{60} -14.3544 q^{61} -6.37533 q^{62} +2.19671 q^{63} +5.75877 q^{64} -3.06624 q^{65} +24.7668 q^{66} -3.17161 q^{67} +15.4932 q^{68} -17.1439 q^{69} +7.06617 q^{70} +7.07369 q^{71} -17.6366 q^{72} -2.77198 q^{73} +12.7010 q^{74} -10.3001 q^{75} -5.79255 q^{76} +3.61699 q^{77} +6.07651 q^{78} +4.65029 q^{79} -27.6415 q^{80} -10.2986 q^{81} -0.0508483 q^{82} -3.62454 q^{83} -9.85030 q^{84} -10.0146 q^{85} +11.5498 q^{86} +6.46624 q^{87} -29.0395 q^{88} -10.6903 q^{89} +19.7104 q^{90} +0.887424 q^{91} +34.7546 q^{92} -5.74464 q^{93} -28.7954 q^{94} +3.74425 q^{95} +21.4351 q^{96} +14.7700 q^{97} +16.1329 q^{98} +10.0892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} + O(q^{10}) \) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} - 33q^{10} - 47q^{11} - 53q^{12} + 134q^{13} - 28q^{14} - 30q^{15} + 30q^{16} - 17q^{17} - 14q^{18} - 87q^{19} - 12q^{20} - 24q^{21} - 52q^{22} - 44q^{23} - 36q^{24} + 58q^{25} - 6q^{26} - 117q^{27} - 71q^{28} - 42q^{29} - 21q^{30} - 82q^{31} - 31q^{32} + 12q^{33} - 30q^{34} - 54q^{35} + 32q^{36} - 55q^{37} - 12q^{38} - 33q^{39} - 86q^{40} - 16q^{41} + 6q^{42} - 148q^{43} - 54q^{44} - 24q^{45} - 57q^{46} - 21q^{47} - 82q^{48} + 12q^{49} - 17q^{50} - 123q^{51} + 98q^{52} - 17q^{53} - 10q^{54} - 148q^{55} - 47q^{56} - q^{57} - 58q^{58} - 64q^{59} - 16q^{60} - 112q^{61} - 15q^{62} - 58q^{63} - 65q^{64} - 8q^{65} - 20q^{66} - 110q^{67} - 8q^{68} - 57q^{69} - 40q^{70} - 78q^{71} - 28q^{72} - 43q^{73} - 52q^{74} - 150q^{75} - 96q^{76} - 24q^{77} - 16q^{78} - 228q^{79} + 20q^{80} + 54q^{81} - 89q^{82} - 12q^{83} + 6q^{84} - 77q^{85} + 29q^{86} - 77q^{87} - 95q^{88} - 32q^{89} - 46q^{90} - 32q^{91} - 62q^{92} - 9q^{93} - 87q^{94} - 61q^{95} - 54q^{96} - 38q^{97} + 6q^{98} - 193q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59685 −1.83625 −0.918125 0.396290i \(-0.870298\pi\)
−0.918125 + 0.396290i \(0.870298\pi\)
\(3\) −2.33995 −1.35097 −0.675486 0.737373i \(-0.736066\pi\)
−0.675486 + 0.737373i \(0.736066\pi\)
\(4\) 4.74363 2.37182
\(5\) −3.06624 −1.37126 −0.685632 0.727948i \(-0.740474\pi\)
−0.685632 + 0.727948i \(0.740474\pi\)
\(6\) 6.07651 2.48072
\(7\) 0.887424 0.335415 0.167707 0.985837i \(-0.446364\pi\)
0.167707 + 0.985837i \(0.446364\pi\)
\(8\) −7.12481 −2.51900
\(9\) 2.47538 0.825127
\(10\) 7.96257 2.51798
\(11\) 4.07583 1.22891 0.614455 0.788952i \(-0.289376\pi\)
0.614455 + 0.788952i \(0.289376\pi\)
\(12\) −11.0999 −3.20426
\(13\) 1.00000 0.277350
\(14\) −2.30451 −0.615905
\(15\) 7.17486 1.85254
\(16\) 9.01480 2.25370
\(17\) 3.26610 0.792145 0.396072 0.918219i \(-0.370373\pi\)
0.396072 + 0.918219i \(0.370373\pi\)
\(18\) −6.42820 −1.51514
\(19\) −1.22112 −0.280144 −0.140072 0.990141i \(-0.544733\pi\)
−0.140072 + 0.990141i \(0.544733\pi\)
\(20\) −14.5451 −3.25239
\(21\) −2.07653 −0.453136
\(22\) −10.5843 −2.25659
\(23\) 7.32658 1.52770 0.763849 0.645395i \(-0.223307\pi\)
0.763849 + 0.645395i \(0.223307\pi\)
\(24\) 16.6717 3.40310
\(25\) 4.40182 0.880365
\(26\) −2.59685 −0.509284
\(27\) 1.22758 0.236249
\(28\) 4.20961 0.795542
\(29\) −2.76340 −0.513151 −0.256576 0.966524i \(-0.582594\pi\)
−0.256576 + 0.966524i \(0.582594\pi\)
\(30\) −18.6320 −3.40173
\(31\) 2.45502 0.440935 0.220468 0.975394i \(-0.429242\pi\)
0.220468 + 0.975394i \(0.429242\pi\)
\(32\) −9.16047 −1.61936
\(33\) −9.53726 −1.66022
\(34\) −8.48157 −1.45458
\(35\) −2.72105 −0.459942
\(36\) 11.7423 1.95705
\(37\) −4.89092 −0.804062 −0.402031 0.915626i \(-0.631696\pi\)
−0.402031 + 0.915626i \(0.631696\pi\)
\(38\) 3.17107 0.514415
\(39\) −2.33995 −0.374692
\(40\) 21.8464 3.45421
\(41\) 0.0195808 0.00305800 0.00152900 0.999999i \(-0.499513\pi\)
0.00152900 + 0.999999i \(0.499513\pi\)
\(42\) 5.39244 0.832071
\(43\) −4.44762 −0.678255 −0.339128 0.940740i \(-0.610132\pi\)
−0.339128 + 0.940740i \(0.610132\pi\)
\(44\) 19.3343 2.91475
\(45\) −7.59011 −1.13147
\(46\) −19.0260 −2.80524
\(47\) 11.0886 1.61744 0.808719 0.588195i \(-0.200161\pi\)
0.808719 + 0.588195i \(0.200161\pi\)
\(48\) −21.0942 −3.04469
\(49\) −6.21248 −0.887497
\(50\) −11.4309 −1.61657
\(51\) −7.64251 −1.07017
\(52\) 4.74363 0.657824
\(53\) −0.247069 −0.0339375 −0.0169688 0.999856i \(-0.505402\pi\)
−0.0169688 + 0.999856i \(0.505402\pi\)
\(54\) −3.18785 −0.433812
\(55\) −12.4975 −1.68516
\(56\) −6.32273 −0.844910
\(57\) 2.85737 0.378467
\(58\) 7.17615 0.942274
\(59\) 3.31595 0.431700 0.215850 0.976427i \(-0.430748\pi\)
0.215850 + 0.976427i \(0.430748\pi\)
\(60\) 34.0349 4.39389
\(61\) −14.3544 −1.83790 −0.918948 0.394378i \(-0.870960\pi\)
−0.918948 + 0.394378i \(0.870960\pi\)
\(62\) −6.37533 −0.809668
\(63\) 2.19671 0.276760
\(64\) 5.75877 0.719847
\(65\) −3.06624 −0.380320
\(66\) 24.7668 3.04859
\(67\) −3.17161 −0.387474 −0.193737 0.981053i \(-0.562061\pi\)
−0.193737 + 0.981053i \(0.562061\pi\)
\(68\) 15.4932 1.87882
\(69\) −17.1439 −2.06388
\(70\) 7.06617 0.844569
\(71\) 7.07369 0.839492 0.419746 0.907642i \(-0.362119\pi\)
0.419746 + 0.907642i \(0.362119\pi\)
\(72\) −17.6366 −2.07850
\(73\) −2.77198 −0.324436 −0.162218 0.986755i \(-0.551865\pi\)
−0.162218 + 0.986755i \(0.551865\pi\)
\(74\) 12.7010 1.47646
\(75\) −10.3001 −1.18935
\(76\) −5.79255 −0.664451
\(77\) 3.61699 0.412194
\(78\) 6.07651 0.688029
\(79\) 4.65029 0.523199 0.261599 0.965177i \(-0.415750\pi\)
0.261599 + 0.965177i \(0.415750\pi\)
\(80\) −27.6415 −3.09042
\(81\) −10.2986 −1.14429
\(82\) −0.0508483 −0.00561526
\(83\) −3.62454 −0.397845 −0.198922 0.980015i \(-0.563744\pi\)
−0.198922 + 0.980015i \(0.563744\pi\)
\(84\) −9.85030 −1.07476
\(85\) −10.0146 −1.08624
\(86\) 11.5498 1.24545
\(87\) 6.46624 0.693253
\(88\) −29.0395 −3.09563
\(89\) −10.6903 −1.13317 −0.566587 0.824002i \(-0.691737\pi\)
−0.566587 + 0.824002i \(0.691737\pi\)
\(90\) 19.7104 2.07766
\(91\) 0.887424 0.0930273
\(92\) 34.7546 3.62342
\(93\) −5.74464 −0.595692
\(94\) −28.7954 −2.97002
\(95\) 3.74425 0.384152
\(96\) 21.4351 2.18771
\(97\) 14.7700 1.49967 0.749833 0.661627i \(-0.230134\pi\)
0.749833 + 0.661627i \(0.230134\pi\)
\(98\) 16.1329 1.62967
\(99\) 10.0892 1.01401
\(100\) 20.8806 2.08806
\(101\) −17.3846 −1.72983 −0.864915 0.501919i \(-0.832627\pi\)
−0.864915 + 0.501919i \(0.832627\pi\)
\(102\) 19.8465 1.96509
\(103\) −9.88251 −0.973753 −0.486876 0.873471i \(-0.661864\pi\)
−0.486876 + 0.873471i \(0.661864\pi\)
\(104\) −7.12481 −0.698645
\(105\) 6.36714 0.621369
\(106\) 0.641602 0.0623179
\(107\) 1.12246 0.108512 0.0542560 0.998527i \(-0.482721\pi\)
0.0542560 + 0.998527i \(0.482721\pi\)
\(108\) 5.82321 0.560338
\(109\) −15.4286 −1.47779 −0.738894 0.673821i \(-0.764652\pi\)
−0.738894 + 0.673821i \(0.764652\pi\)
\(110\) 32.4541 3.09438
\(111\) 11.4445 1.08627
\(112\) 7.99995 0.755924
\(113\) 7.91491 0.744573 0.372286 0.928118i \(-0.378574\pi\)
0.372286 + 0.928118i \(0.378574\pi\)
\(114\) −7.42015 −0.694961
\(115\) −22.4651 −2.09488
\(116\) −13.1086 −1.21710
\(117\) 2.47538 0.228849
\(118\) −8.61102 −0.792709
\(119\) 2.89841 0.265697
\(120\) −51.1195 −4.66655
\(121\) 5.61242 0.510220
\(122\) 37.2763 3.37484
\(123\) −0.0458181 −0.00413127
\(124\) 11.6457 1.04582
\(125\) 1.83415 0.164051
\(126\) −5.70453 −0.508200
\(127\) −0.733112 −0.0650532 −0.0325266 0.999471i \(-0.510355\pi\)
−0.0325266 + 0.999471i \(0.510355\pi\)
\(128\) 3.36626 0.297538
\(129\) 10.4072 0.916305
\(130\) 7.96257 0.698363
\(131\) 14.5403 1.27039 0.635197 0.772350i \(-0.280919\pi\)
0.635197 + 0.772350i \(0.280919\pi\)
\(132\) −45.2413 −3.93775
\(133\) −1.08365 −0.0939645
\(134\) 8.23620 0.711500
\(135\) −3.76406 −0.323959
\(136\) −23.2703 −1.99541
\(137\) −14.8050 −1.26488 −0.632439 0.774610i \(-0.717946\pi\)
−0.632439 + 0.774610i \(0.717946\pi\)
\(138\) 44.5201 3.78980
\(139\) 5.74221 0.487048 0.243524 0.969895i \(-0.421697\pi\)
0.243524 + 0.969895i \(0.421697\pi\)
\(140\) −12.9077 −1.09090
\(141\) −25.9468 −2.18512
\(142\) −18.3693 −1.54152
\(143\) 4.07583 0.340838
\(144\) 22.3151 1.85959
\(145\) 8.47326 0.703666
\(146\) 7.19843 0.595746
\(147\) 14.5369 1.19898
\(148\) −23.2007 −1.90709
\(149\) −9.60935 −0.787229 −0.393614 0.919276i \(-0.628775\pi\)
−0.393614 + 0.919276i \(0.628775\pi\)
\(150\) 26.7477 2.18394
\(151\) −16.3885 −1.33368 −0.666840 0.745201i \(-0.732354\pi\)
−0.666840 + 0.745201i \(0.732354\pi\)
\(152\) 8.70025 0.705684
\(153\) 8.08483 0.653620
\(154\) −9.39279 −0.756892
\(155\) −7.52769 −0.604639
\(156\) −11.0999 −0.888702
\(157\) −24.9215 −1.98895 −0.994475 0.104977i \(-0.966523\pi\)
−0.994475 + 0.104977i \(0.966523\pi\)
\(158\) −12.0761 −0.960724
\(159\) 0.578130 0.0458487
\(160\) 28.0882 2.22057
\(161\) 6.50178 0.512412
\(162\) 26.7440 2.10121
\(163\) 5.63390 0.441281 0.220641 0.975355i \(-0.429185\pi\)
0.220641 + 0.975355i \(0.429185\pi\)
\(164\) 0.0928839 0.00725302
\(165\) 29.2435 2.27661
\(166\) 9.41238 0.730542
\(167\) 19.0423 1.47354 0.736770 0.676143i \(-0.236350\pi\)
0.736770 + 0.676143i \(0.236350\pi\)
\(168\) 14.7949 1.14145
\(169\) 1.00000 0.0769231
\(170\) 26.0065 1.99461
\(171\) −3.02274 −0.231155
\(172\) −21.0979 −1.60870
\(173\) 2.32303 0.176617 0.0883083 0.996093i \(-0.471854\pi\)
0.0883083 + 0.996093i \(0.471854\pi\)
\(174\) −16.7918 −1.27299
\(175\) 3.90628 0.295287
\(176\) 36.7428 2.76959
\(177\) −7.75916 −0.583214
\(178\) 27.7612 2.08079
\(179\) −11.2701 −0.842367 −0.421184 0.906975i \(-0.638385\pi\)
−0.421184 + 0.906975i \(0.638385\pi\)
\(180\) −36.0047 −2.68363
\(181\) 23.0241 1.71137 0.855684 0.517499i \(-0.173137\pi\)
0.855684 + 0.517499i \(0.173137\pi\)
\(182\) −2.30451 −0.170821
\(183\) 33.5887 2.48295
\(184\) −52.2005 −3.84827
\(185\) 14.9967 1.10258
\(186\) 14.9180 1.09384
\(187\) 13.3121 0.973475
\(188\) 52.6003 3.83627
\(189\) 1.08939 0.0792412
\(190\) −9.72326 −0.705399
\(191\) −6.79401 −0.491598 −0.245799 0.969321i \(-0.579050\pi\)
−0.245799 + 0.969321i \(0.579050\pi\)
\(192\) −13.4753 −0.972493
\(193\) 17.5471 1.26307 0.631534 0.775348i \(-0.282425\pi\)
0.631534 + 0.775348i \(0.282425\pi\)
\(194\) −38.3555 −2.75376
\(195\) 7.17486 0.513802
\(196\) −29.4697 −2.10498
\(197\) 7.22353 0.514655 0.257328 0.966324i \(-0.417158\pi\)
0.257328 + 0.966324i \(0.417158\pi\)
\(198\) −26.2003 −1.86197
\(199\) −5.60785 −0.397530 −0.198765 0.980047i \(-0.563693\pi\)
−0.198765 + 0.980047i \(0.563693\pi\)
\(200\) −31.3622 −2.21764
\(201\) 7.42142 0.523467
\(202\) 45.1451 3.17640
\(203\) −2.45231 −0.172118
\(204\) −36.2533 −2.53824
\(205\) −0.0600393 −0.00419333
\(206\) 25.6634 1.78805
\(207\) 18.1361 1.26055
\(208\) 9.01480 0.625064
\(209\) −4.97709 −0.344272
\(210\) −16.5345 −1.14099
\(211\) −13.2555 −0.912546 −0.456273 0.889840i \(-0.650816\pi\)
−0.456273 + 0.889840i \(0.650816\pi\)
\(212\) −1.17201 −0.0804937
\(213\) −16.5521 −1.13413
\(214\) −2.91485 −0.199255
\(215\) 13.6375 0.930067
\(216\) −8.74630 −0.595110
\(217\) 2.17865 0.147896
\(218\) 40.0657 2.71359
\(219\) 6.48631 0.438304
\(220\) −59.2835 −3.99689
\(221\) 3.26610 0.219701
\(222\) −29.7197 −1.99466
\(223\) −3.48626 −0.233457 −0.116729 0.993164i \(-0.537241\pi\)
−0.116729 + 0.993164i \(0.537241\pi\)
\(224\) −8.12922 −0.543156
\(225\) 10.8962 0.726413
\(226\) −20.5539 −1.36722
\(227\) 6.17481 0.409837 0.204918 0.978779i \(-0.434307\pi\)
0.204918 + 0.978779i \(0.434307\pi\)
\(228\) 13.5543 0.897655
\(229\) 11.0873 0.732669 0.366334 0.930483i \(-0.380613\pi\)
0.366334 + 0.930483i \(0.380613\pi\)
\(230\) 58.3384 3.84672
\(231\) −8.46359 −0.556863
\(232\) 19.6887 1.29263
\(233\) −26.2264 −1.71815 −0.859073 0.511854i \(-0.828959\pi\)
−0.859073 + 0.511854i \(0.828959\pi\)
\(234\) −6.42820 −0.420224
\(235\) −34.0003 −2.21794
\(236\) 15.7296 1.02391
\(237\) −10.8815 −0.706827
\(238\) −7.52674 −0.487886
\(239\) 7.66439 0.495768 0.247884 0.968790i \(-0.420265\pi\)
0.247884 + 0.968790i \(0.420265\pi\)
\(240\) 64.6799 4.17507
\(241\) −16.4630 −1.06047 −0.530237 0.847849i \(-0.677897\pi\)
−0.530237 + 0.847849i \(0.677897\pi\)
\(242\) −14.5746 −0.936892
\(243\) 20.4156 1.30966
\(244\) −68.0922 −4.35915
\(245\) 19.0489 1.21699
\(246\) 0.118983 0.00758606
\(247\) −1.22112 −0.0776981
\(248\) −17.4916 −1.11072
\(249\) 8.48125 0.537477
\(250\) −4.76301 −0.301239
\(251\) −24.0528 −1.51820 −0.759100 0.650974i \(-0.774361\pi\)
−0.759100 + 0.650974i \(0.774361\pi\)
\(252\) 10.4204 0.656423
\(253\) 29.8619 1.87740
\(254\) 1.90378 0.119454
\(255\) 23.4338 1.46748
\(256\) −20.2592 −1.26620
\(257\) −5.85859 −0.365449 −0.182724 0.983164i \(-0.558492\pi\)
−0.182724 + 0.983164i \(0.558492\pi\)
\(258\) −27.0260 −1.68256
\(259\) −4.34032 −0.269694
\(260\) −14.5451 −0.902050
\(261\) −6.84048 −0.423415
\(262\) −37.7590 −2.33276
\(263\) 8.89663 0.548590 0.274295 0.961646i \(-0.411556\pi\)
0.274295 + 0.961646i \(0.411556\pi\)
\(264\) 67.9512 4.18211
\(265\) 0.757573 0.0465373
\(266\) 2.81408 0.172542
\(267\) 25.0149 1.53089
\(268\) −15.0450 −0.919018
\(269\) −2.42854 −0.148071 −0.0740353 0.997256i \(-0.523588\pi\)
−0.0740353 + 0.997256i \(0.523588\pi\)
\(270\) 9.77471 0.594870
\(271\) 23.6721 1.43798 0.718988 0.695023i \(-0.244606\pi\)
0.718988 + 0.695023i \(0.244606\pi\)
\(272\) 29.4432 1.78526
\(273\) −2.07653 −0.125677
\(274\) 38.4464 2.32263
\(275\) 17.9411 1.08189
\(276\) −81.3242 −4.89514
\(277\) 15.3855 0.924428 0.462214 0.886768i \(-0.347055\pi\)
0.462214 + 0.886768i \(0.347055\pi\)
\(278\) −14.9117 −0.894342
\(279\) 6.07712 0.363828
\(280\) 19.3870 1.15859
\(281\) 15.7240 0.938012 0.469006 0.883195i \(-0.344612\pi\)
0.469006 + 0.883195i \(0.344612\pi\)
\(282\) 67.3800 4.01242
\(283\) −15.9649 −0.949016 −0.474508 0.880251i \(-0.657374\pi\)
−0.474508 + 0.880251i \(0.657374\pi\)
\(284\) 33.5550 1.99112
\(285\) −8.76137 −0.518979
\(286\) −10.5843 −0.625865
\(287\) 0.0173764 0.00102570
\(288\) −22.6757 −1.33618
\(289\) −6.33261 −0.372507
\(290\) −22.0038 −1.29211
\(291\) −34.5611 −2.02601
\(292\) −13.1493 −0.769503
\(293\) −12.2974 −0.718423 −0.359212 0.933256i \(-0.616954\pi\)
−0.359212 + 0.933256i \(0.616954\pi\)
\(294\) −37.7502 −2.20164
\(295\) −10.1675 −0.591974
\(296\) 34.8469 2.02543
\(297\) 5.00343 0.290328
\(298\) 24.9541 1.44555
\(299\) 7.32658 0.423707
\(300\) −48.8597 −2.82092
\(301\) −3.94692 −0.227497
\(302\) 42.5586 2.44897
\(303\) 40.6791 2.33695
\(304\) −11.0082 −0.631361
\(305\) 44.0141 2.52024
\(306\) −20.9951 −1.20021
\(307\) 17.2333 0.983559 0.491779 0.870720i \(-0.336347\pi\)
0.491779 + 0.870720i \(0.336347\pi\)
\(308\) 17.1577 0.977650
\(309\) 23.1246 1.31551
\(310\) 19.5483 1.11027
\(311\) 1.80395 0.102293 0.0511464 0.998691i \(-0.483712\pi\)
0.0511464 + 0.998691i \(0.483712\pi\)
\(312\) 16.6717 0.943850
\(313\) 24.7695 1.40005 0.700026 0.714117i \(-0.253172\pi\)
0.700026 + 0.714117i \(0.253172\pi\)
\(314\) 64.7173 3.65221
\(315\) −6.73565 −0.379511
\(316\) 22.0593 1.24093
\(317\) −18.5509 −1.04192 −0.520960 0.853581i \(-0.674426\pi\)
−0.520960 + 0.853581i \(0.674426\pi\)
\(318\) −1.50132 −0.0841897
\(319\) −11.2632 −0.630617
\(320\) −17.6578 −0.987100
\(321\) −2.62649 −0.146597
\(322\) −16.8842 −0.940918
\(323\) −3.98830 −0.221915
\(324\) −48.8529 −2.71405
\(325\) 4.40182 0.244169
\(326\) −14.6304 −0.810303
\(327\) 36.1021 1.99645
\(328\) −0.139509 −0.00770310
\(329\) 9.84029 0.542513
\(330\) −75.9411 −4.18042
\(331\) 0.581248 0.0319483 0.0159741 0.999872i \(-0.494915\pi\)
0.0159741 + 0.999872i \(0.494915\pi\)
\(332\) −17.1935 −0.943615
\(333\) −12.1069 −0.663454
\(334\) −49.4501 −2.70579
\(335\) 9.72492 0.531329
\(336\) −18.7195 −1.02123
\(337\) 16.5184 0.899813 0.449906 0.893076i \(-0.351457\pi\)
0.449906 + 0.893076i \(0.351457\pi\)
\(338\) −2.59685 −0.141250
\(339\) −18.5205 −1.00590
\(340\) −47.5058 −2.57636
\(341\) 10.0063 0.541870
\(342\) 7.84960 0.424458
\(343\) −11.7251 −0.633094
\(344\) 31.6884 1.70853
\(345\) 52.5672 2.83012
\(346\) −6.03256 −0.324312
\(347\) 17.6662 0.948374 0.474187 0.880424i \(-0.342742\pi\)
0.474187 + 0.880424i \(0.342742\pi\)
\(348\) 30.6735 1.64427
\(349\) 1.49985 0.0802849 0.0401424 0.999194i \(-0.487219\pi\)
0.0401424 + 0.999194i \(0.487219\pi\)
\(350\) −10.1440 −0.542222
\(351\) 1.22758 0.0655236
\(352\) −37.3365 −1.99004
\(353\) −23.9661 −1.27559 −0.637793 0.770208i \(-0.720152\pi\)
−0.637793 + 0.770208i \(0.720152\pi\)
\(354\) 20.1494 1.07093
\(355\) −21.6896 −1.15117
\(356\) −50.7111 −2.68768
\(357\) −6.78215 −0.358949
\(358\) 29.2668 1.54680
\(359\) 21.5530 1.13752 0.568762 0.822502i \(-0.307423\pi\)
0.568762 + 0.822502i \(0.307423\pi\)
\(360\) 54.0781 2.85017
\(361\) −17.5089 −0.921519
\(362\) −59.7901 −3.14250
\(363\) −13.1328 −0.689294
\(364\) 4.20961 0.220644
\(365\) 8.49957 0.444888
\(366\) −87.2248 −4.55932
\(367\) −18.0907 −0.944327 −0.472163 0.881511i \(-0.656527\pi\)
−0.472163 + 0.881511i \(0.656527\pi\)
\(368\) 66.0477 3.44297
\(369\) 0.0484698 0.00252324
\(370\) −38.9443 −2.02462
\(371\) −0.219255 −0.0113832
\(372\) −27.2505 −1.41287
\(373\) 22.0427 1.14133 0.570664 0.821183i \(-0.306686\pi\)
0.570664 + 0.821183i \(0.306686\pi\)
\(374\) −34.5695 −1.78754
\(375\) −4.29182 −0.221629
\(376\) −79.0042 −4.07433
\(377\) −2.76340 −0.142323
\(378\) −2.82897 −0.145507
\(379\) 8.62140 0.442851 0.221426 0.975177i \(-0.428929\pi\)
0.221426 + 0.975177i \(0.428929\pi\)
\(380\) 17.7613 0.911138
\(381\) 1.71545 0.0878850
\(382\) 17.6430 0.902696
\(383\) 24.1392 1.23345 0.616727 0.787177i \(-0.288458\pi\)
0.616727 + 0.787177i \(0.288458\pi\)
\(384\) −7.87690 −0.401966
\(385\) −11.0906 −0.565227
\(386\) −45.5672 −2.31931
\(387\) −11.0096 −0.559647
\(388\) 70.0635 3.55693
\(389\) −8.97952 −0.455280 −0.227640 0.973745i \(-0.573101\pi\)
−0.227640 + 0.973745i \(0.573101\pi\)
\(390\) −18.6320 −0.943470
\(391\) 23.9293 1.21016
\(392\) 44.2627 2.23561
\(393\) −34.0237 −1.71627
\(394\) −18.7584 −0.945036
\(395\) −14.2589 −0.717444
\(396\) 47.8597 2.40504
\(397\) 15.2818 0.766974 0.383487 0.923546i \(-0.374723\pi\)
0.383487 + 0.923546i \(0.374723\pi\)
\(398\) 14.5628 0.729965
\(399\) 2.53569 0.126943
\(400\) 39.6816 1.98408
\(401\) −12.9257 −0.645481 −0.322740 0.946488i \(-0.604604\pi\)
−0.322740 + 0.946488i \(0.604604\pi\)
\(402\) −19.2723 −0.961216
\(403\) 2.45502 0.122294
\(404\) −82.4660 −4.10284
\(405\) 31.5781 1.56913
\(406\) 6.36828 0.316053
\(407\) −19.9346 −0.988121
\(408\) 54.4514 2.69575
\(409\) −2.03362 −0.100556 −0.0502781 0.998735i \(-0.516011\pi\)
−0.0502781 + 0.998735i \(0.516011\pi\)
\(410\) 0.155913 0.00770000
\(411\) 34.6431 1.70882
\(412\) −46.8790 −2.30956
\(413\) 2.94265 0.144798
\(414\) −47.0967 −2.31468
\(415\) 11.1137 0.545550
\(416\) −9.16047 −0.449129
\(417\) −13.4365 −0.657989
\(418\) 12.9247 0.632170
\(419\) 1.71646 0.0838543 0.0419272 0.999121i \(-0.486650\pi\)
0.0419272 + 0.999121i \(0.486650\pi\)
\(420\) 30.2034 1.47377
\(421\) 30.6462 1.49361 0.746803 0.665045i \(-0.231588\pi\)
0.746803 + 0.665045i \(0.231588\pi\)
\(422\) 34.4226 1.67566
\(423\) 27.4485 1.33459
\(424\) 1.76032 0.0854887
\(425\) 14.3768 0.697377
\(426\) 42.9833 2.08255
\(427\) −12.7385 −0.616457
\(428\) 5.32452 0.257370
\(429\) −9.53726 −0.460463
\(430\) −35.4145 −1.70784
\(431\) −30.3466 −1.46174 −0.730872 0.682514i \(-0.760887\pi\)
−0.730872 + 0.682514i \(0.760887\pi\)
\(432\) 11.0664 0.532433
\(433\) −27.9847 −1.34486 −0.672429 0.740162i \(-0.734749\pi\)
−0.672429 + 0.740162i \(0.734749\pi\)
\(434\) −5.65762 −0.271575
\(435\) −19.8270 −0.950633
\(436\) −73.1875 −3.50504
\(437\) −8.94664 −0.427976
\(438\) −16.8440 −0.804837
\(439\) 31.0430 1.48160 0.740801 0.671725i \(-0.234446\pi\)
0.740801 + 0.671725i \(0.234446\pi\)
\(440\) 89.0422 4.24492
\(441\) −15.3783 −0.732298
\(442\) −8.48157 −0.403427
\(443\) −29.9436 −1.42266 −0.711332 0.702856i \(-0.751908\pi\)
−0.711332 + 0.702856i \(0.751908\pi\)
\(444\) 54.2887 2.57643
\(445\) 32.7792 1.55388
\(446\) 9.05329 0.428686
\(447\) 22.4854 1.06352
\(448\) 5.11047 0.241447
\(449\) 16.0487 0.757383 0.378691 0.925523i \(-0.376374\pi\)
0.378691 + 0.925523i \(0.376374\pi\)
\(450\) −28.2958 −1.33388
\(451\) 0.0798079 0.00375801
\(452\) 37.5455 1.76599
\(453\) 38.3484 1.80177
\(454\) −16.0351 −0.752563
\(455\) −2.72105 −0.127565
\(456\) −20.3582 −0.953359
\(457\) −1.39851 −0.0654196 −0.0327098 0.999465i \(-0.510414\pi\)
−0.0327098 + 0.999465i \(0.510414\pi\)
\(458\) −28.7920 −1.34536
\(459\) 4.00941 0.187143
\(460\) −106.566 −4.96867
\(461\) 12.9088 0.601223 0.300612 0.953747i \(-0.402809\pi\)
0.300612 + 0.953747i \(0.402809\pi\)
\(462\) 21.9787 1.02254
\(463\) −29.2290 −1.35839 −0.679194 0.733959i \(-0.737670\pi\)
−0.679194 + 0.733959i \(0.737670\pi\)
\(464\) −24.9115 −1.15649
\(465\) 17.6145 0.816851
\(466\) 68.1059 3.15495
\(467\) 15.4186 0.713489 0.356744 0.934202i \(-0.383887\pi\)
0.356744 + 0.934202i \(0.383887\pi\)
\(468\) 11.7423 0.542788
\(469\) −2.81456 −0.129964
\(470\) 88.2937 4.07269
\(471\) 58.3151 2.68702
\(472\) −23.6255 −1.08745
\(473\) −18.1278 −0.833515
\(474\) 28.2575 1.29791
\(475\) −5.37516 −0.246629
\(476\) 13.7490 0.630185
\(477\) −0.611590 −0.0280028
\(478\) −19.9033 −0.910354
\(479\) 10.1582 0.464141 0.232070 0.972699i \(-0.425450\pi\)
0.232070 + 0.972699i \(0.425450\pi\)
\(480\) −65.7251 −2.99992
\(481\) −4.89092 −0.223007
\(482\) 42.7519 1.94730
\(483\) −15.2139 −0.692255
\(484\) 26.6233 1.21015
\(485\) −45.2884 −2.05644
\(486\) −53.0162 −2.40486
\(487\) 4.99619 0.226399 0.113199 0.993572i \(-0.463890\pi\)
0.113199 + 0.993572i \(0.463890\pi\)
\(488\) 102.273 4.62966
\(489\) −13.1831 −0.596159
\(490\) −49.4673 −2.23470
\(491\) −25.8974 −1.16873 −0.584366 0.811490i \(-0.698657\pi\)
−0.584366 + 0.811490i \(0.698657\pi\)
\(492\) −0.217344 −0.00979863
\(493\) −9.02554 −0.406490
\(494\) 3.17107 0.142673
\(495\) −30.9360 −1.39047
\(496\) 22.1316 0.993736
\(497\) 6.27736 0.281578
\(498\) −22.0245 −0.986943
\(499\) −1.71131 −0.0766087 −0.0383044 0.999266i \(-0.512196\pi\)
−0.0383044 + 0.999266i \(0.512196\pi\)
\(500\) 8.70053 0.389099
\(501\) −44.5582 −1.99071
\(502\) 62.4615 2.78780
\(503\) 25.9781 1.15831 0.579154 0.815218i \(-0.303383\pi\)
0.579154 + 0.815218i \(0.303383\pi\)
\(504\) −15.6512 −0.697158
\(505\) 53.3052 2.37205
\(506\) −77.5470 −3.44738
\(507\) −2.33995 −0.103921
\(508\) −3.47762 −0.154294
\(509\) −26.3414 −1.16756 −0.583781 0.811911i \(-0.698427\pi\)
−0.583781 + 0.811911i \(0.698427\pi\)
\(510\) −60.8540 −2.69466
\(511\) −2.45992 −0.108821
\(512\) 45.8777 2.02753
\(513\) −1.49903 −0.0661837
\(514\) 15.2139 0.671055
\(515\) 30.3022 1.33527
\(516\) 49.3680 2.17331
\(517\) 45.1953 1.98769
\(518\) 11.2712 0.495226
\(519\) −5.43578 −0.238604
\(520\) 21.8464 0.958027
\(521\) 37.7638 1.65446 0.827232 0.561861i \(-0.189914\pi\)
0.827232 + 0.561861i \(0.189914\pi\)
\(522\) 17.7637 0.777496
\(523\) 9.99220 0.436928 0.218464 0.975845i \(-0.429895\pi\)
0.218464 + 0.975845i \(0.429895\pi\)
\(524\) 68.9739 3.01314
\(525\) −9.14052 −0.398925
\(526\) −23.1032 −1.00735
\(527\) 8.01835 0.349285
\(528\) −85.9765 −3.74165
\(529\) 30.6788 1.33386
\(530\) −1.96730 −0.0854542
\(531\) 8.20824 0.356207
\(532\) −5.14045 −0.222867
\(533\) 0.0195808 0.000848137 0
\(534\) −64.9600 −2.81109
\(535\) −3.44172 −0.148798
\(536\) 22.5971 0.976047
\(537\) 26.3715 1.13802
\(538\) 6.30655 0.271895
\(539\) −25.3210 −1.09065
\(540\) −17.8553 −0.768372
\(541\) −24.6408 −1.05939 −0.529695 0.848188i \(-0.677693\pi\)
−0.529695 + 0.848188i \(0.677693\pi\)
\(542\) −61.4728 −2.64048
\(543\) −53.8753 −2.31201
\(544\) −29.9190 −1.28277
\(545\) 47.3077 2.02644
\(546\) 5.39244 0.230775
\(547\) 36.4970 1.56050 0.780250 0.625468i \(-0.215092\pi\)
0.780250 + 0.625468i \(0.215092\pi\)
\(548\) −70.2296 −3.00006
\(549\) −35.5327 −1.51650
\(550\) −46.5904 −1.98662
\(551\) 3.37445 0.143756
\(552\) 122.147 5.19891
\(553\) 4.12678 0.175489
\(554\) −39.9540 −1.69748
\(555\) −35.0917 −1.48956
\(556\) 27.2390 1.15519
\(557\) −29.5295 −1.25121 −0.625603 0.780142i \(-0.715147\pi\)
−0.625603 + 0.780142i \(0.715147\pi\)
\(558\) −15.7814 −0.668079
\(559\) −4.44762 −0.188114
\(560\) −24.5298 −1.03657
\(561\) −31.1496 −1.31514
\(562\) −40.8328 −1.72243
\(563\) −32.7793 −1.38148 −0.690741 0.723103i \(-0.742715\pi\)
−0.690741 + 0.723103i \(0.742715\pi\)
\(564\) −123.082 −5.18269
\(565\) −24.2690 −1.02101
\(566\) 41.4585 1.74263
\(567\) −9.13925 −0.383812
\(568\) −50.3987 −2.11468
\(569\) 4.26047 0.178608 0.0893041 0.996004i \(-0.471536\pi\)
0.0893041 + 0.996004i \(0.471536\pi\)
\(570\) 22.7520 0.952975
\(571\) 2.15887 0.0903460 0.0451730 0.998979i \(-0.485616\pi\)
0.0451730 + 0.998979i \(0.485616\pi\)
\(572\) 19.3343 0.808406
\(573\) 15.8977 0.664135
\(574\) −0.0451240 −0.00188344
\(575\) 32.2503 1.34493
\(576\) 14.2552 0.593965
\(577\) 12.4251 0.517266 0.258633 0.965976i \(-0.416728\pi\)
0.258633 + 0.965976i \(0.416728\pi\)
\(578\) 16.4449 0.684016
\(579\) −41.0594 −1.70637
\(580\) 40.1940 1.66897
\(581\) −3.21650 −0.133443
\(582\) 89.7501 3.72026
\(583\) −1.00701 −0.0417062
\(584\) 19.7499 0.817255
\(585\) −7.59011 −0.313813
\(586\) 31.9346 1.31921
\(587\) 12.3634 0.510293 0.255146 0.966902i \(-0.417876\pi\)
0.255146 + 0.966902i \(0.417876\pi\)
\(588\) 68.9578 2.84377
\(589\) −2.99788 −0.123526
\(590\) 26.4035 1.08701
\(591\) −16.9027 −0.695285
\(592\) −44.0907 −1.81212
\(593\) −44.6152 −1.83213 −0.916063 0.401035i \(-0.868651\pi\)
−0.916063 + 0.401035i \(0.868651\pi\)
\(594\) −12.9932 −0.533115
\(595\) −8.88722 −0.364341
\(596\) −45.5833 −1.86716
\(597\) 13.1221 0.537052
\(598\) −19.0260 −0.778033
\(599\) 15.1494 0.618988 0.309494 0.950901i \(-0.399840\pi\)
0.309494 + 0.950901i \(0.399840\pi\)
\(600\) 73.3860 2.99597
\(601\) −15.3552 −0.626351 −0.313176 0.949695i \(-0.601393\pi\)
−0.313176 + 0.949695i \(0.601393\pi\)
\(602\) 10.2496 0.417741
\(603\) −7.85095 −0.319715
\(604\) −77.7412 −3.16325
\(605\) −17.2090 −0.699647
\(606\) −105.637 −4.29123
\(607\) −12.1459 −0.492985 −0.246493 0.969145i \(-0.579278\pi\)
−0.246493 + 0.969145i \(0.579278\pi\)
\(608\) 11.1860 0.453654
\(609\) 5.73829 0.232527
\(610\) −114.298 −4.62780
\(611\) 11.0886 0.448597
\(612\) 38.3515 1.55027
\(613\) −37.2908 −1.50616 −0.753081 0.657928i \(-0.771433\pi\)
−0.753081 + 0.657928i \(0.771433\pi\)
\(614\) −44.7524 −1.80606
\(615\) 0.140489 0.00566507
\(616\) −25.7704 −1.03832
\(617\) 1.00000 0.0402585
\(618\) −60.0512 −2.41561
\(619\) −1.80833 −0.0726830 −0.0363415 0.999339i \(-0.511570\pi\)
−0.0363415 + 0.999339i \(0.511570\pi\)
\(620\) −35.7086 −1.43409
\(621\) 8.99399 0.360916
\(622\) −4.68460 −0.187835
\(623\) −9.48687 −0.380083
\(624\) −21.0942 −0.844444
\(625\) −27.6331 −1.10532
\(626\) −64.3226 −2.57085
\(627\) 11.6461 0.465102
\(628\) −118.218 −4.71742
\(629\) −15.9742 −0.636934
\(630\) 17.4915 0.696877
\(631\) −9.67808 −0.385278 −0.192639 0.981270i \(-0.561705\pi\)
−0.192639 + 0.981270i \(0.561705\pi\)
\(632\) −33.1324 −1.31794
\(633\) 31.0172 1.23282
\(634\) 48.1738 1.91323
\(635\) 2.24790 0.0892051
\(636\) 2.74244 0.108745
\(637\) −6.21248 −0.246147
\(638\) 29.2488 1.15797
\(639\) 17.5101 0.692688
\(640\) −10.3218 −0.408004
\(641\) −28.0104 −1.10634 −0.553172 0.833067i \(-0.686583\pi\)
−0.553172 + 0.833067i \(0.686583\pi\)
\(642\) 6.82061 0.269188
\(643\) 23.6779 0.933766 0.466883 0.884319i \(-0.345377\pi\)
0.466883 + 0.884319i \(0.345377\pi\)
\(644\) 30.8421 1.21535
\(645\) −31.9110 −1.25650
\(646\) 10.3570 0.407491
\(647\) −10.3090 −0.405288 −0.202644 0.979252i \(-0.564953\pi\)
−0.202644 + 0.979252i \(0.564953\pi\)
\(648\) 73.3758 2.88247
\(649\) 13.5153 0.530520
\(650\) −11.4309 −0.448356
\(651\) −5.09793 −0.199804
\(652\) 26.7252 1.04664
\(653\) 23.0902 0.903591 0.451795 0.892122i \(-0.350784\pi\)
0.451795 + 0.892122i \(0.350784\pi\)
\(654\) −93.7518 −3.66599
\(655\) −44.5841 −1.74204
\(656\) 0.176517 0.00689181
\(657\) −6.86172 −0.267701
\(658\) −25.5538 −0.996189
\(659\) 6.31945 0.246171 0.123086 0.992396i \(-0.460721\pi\)
0.123086 + 0.992396i \(0.460721\pi\)
\(660\) 138.721 5.39969
\(661\) −5.03170 −0.195711 −0.0978553 0.995201i \(-0.531198\pi\)
−0.0978553 + 0.995201i \(0.531198\pi\)
\(662\) −1.50942 −0.0586651
\(663\) −7.64251 −0.296811
\(664\) 25.8241 1.00217
\(665\) 3.32274 0.128850
\(666\) 31.4398 1.21827
\(667\) −20.2463 −0.783940
\(668\) 90.3299 3.49497
\(669\) 8.15768 0.315394
\(670\) −25.2542 −0.975654
\(671\) −58.5063 −2.25861
\(672\) 19.0220 0.733789
\(673\) −36.4348 −1.40446 −0.702229 0.711951i \(-0.747812\pi\)
−0.702229 + 0.711951i \(0.747812\pi\)
\(674\) −42.8957 −1.65228
\(675\) 5.40361 0.207985
\(676\) 4.74363 0.182447
\(677\) 15.1154 0.580931 0.290466 0.956885i \(-0.406190\pi\)
0.290466 + 0.956885i \(0.406190\pi\)
\(678\) 48.0951 1.84708
\(679\) 13.1073 0.503010
\(680\) 71.3524 2.73624
\(681\) −14.4488 −0.553678
\(682\) −25.9848 −0.995009
\(683\) −5.08117 −0.194426 −0.0972128 0.995264i \(-0.530993\pi\)
−0.0972128 + 0.995264i \(0.530993\pi\)
\(684\) −14.3388 −0.548257
\(685\) 45.3958 1.73448
\(686\) 30.4483 1.16252
\(687\) −25.9437 −0.989815
\(688\) −40.0944 −1.52858
\(689\) −0.247069 −0.00941258
\(690\) −136.509 −5.19681
\(691\) 9.10662 0.346432 0.173216 0.984884i \(-0.444584\pi\)
0.173216 + 0.984884i \(0.444584\pi\)
\(692\) 11.0196 0.418902
\(693\) 8.95343 0.340113
\(694\) −45.8766 −1.74145
\(695\) −17.6070 −0.667871
\(696\) −46.0707 −1.74631
\(697\) 0.0639526 0.00242238
\(698\) −3.89487 −0.147423
\(699\) 61.3684 2.32117
\(700\) 18.5300 0.700368
\(701\) −32.8097 −1.23921 −0.619603 0.784916i \(-0.712706\pi\)
−0.619603 + 0.784916i \(0.712706\pi\)
\(702\) −3.18785 −0.120318
\(703\) 5.97241 0.225254
\(704\) 23.4718 0.884627
\(705\) 79.5591 2.99637
\(706\) 62.2363 2.34229
\(707\) −15.4275 −0.580210
\(708\) −36.8066 −1.38328
\(709\) −19.4051 −0.728774 −0.364387 0.931248i \(-0.618722\pi\)
−0.364387 + 0.931248i \(0.618722\pi\)
\(710\) 56.3247 2.11383
\(711\) 11.5112 0.431705
\(712\) 76.1667 2.85447
\(713\) 17.9869 0.673616
\(714\) 17.6122 0.659121
\(715\) −12.4975 −0.467379
\(716\) −53.4613 −1.99794
\(717\) −17.9343 −0.669769
\(718\) −55.9699 −2.08878
\(719\) 15.3845 0.573745 0.286873 0.957969i \(-0.407384\pi\)
0.286873 + 0.957969i \(0.407384\pi\)
\(720\) −68.4233 −2.54999
\(721\) −8.76998 −0.326611
\(722\) 45.4679 1.69214
\(723\) 38.5226 1.43267
\(724\) 109.218 4.05905
\(725\) −12.1640 −0.451760
\(726\) 34.1039 1.26572
\(727\) −32.5409 −1.20688 −0.603438 0.797410i \(-0.706203\pi\)
−0.603438 + 0.797410i \(0.706203\pi\)
\(728\) −6.32273 −0.234336
\(729\) −16.8756 −0.625021
\(730\) −22.0721 −0.816925
\(731\) −14.5264 −0.537276
\(732\) 159.333 5.88910
\(733\) −9.93639 −0.367009 −0.183505 0.983019i \(-0.558744\pi\)
−0.183505 + 0.983019i \(0.558744\pi\)
\(734\) 46.9788 1.73402
\(735\) −44.5736 −1.64412
\(736\) −67.1149 −2.47389
\(737\) −12.9270 −0.476171
\(738\) −0.125869 −0.00463330
\(739\) 47.8304 1.75947 0.879734 0.475466i \(-0.157720\pi\)
0.879734 + 0.475466i \(0.157720\pi\)
\(740\) 71.1390 2.61512
\(741\) 2.85737 0.104968
\(742\) 0.569373 0.0209023
\(743\) 43.2154 1.58542 0.792709 0.609600i \(-0.208670\pi\)
0.792709 + 0.609600i \(0.208670\pi\)
\(744\) 40.9295 1.50055
\(745\) 29.4646 1.07950
\(746\) −57.2416 −2.09577
\(747\) −8.97211 −0.328272
\(748\) 63.1476 2.30890
\(749\) 0.996094 0.0363965
\(750\) 11.1452 0.406966
\(751\) −38.5102 −1.40526 −0.702629 0.711556i \(-0.747991\pi\)
−0.702629 + 0.711556i \(0.747991\pi\)
\(752\) 99.9615 3.64522
\(753\) 56.2824 2.05105
\(754\) 7.17615 0.261340
\(755\) 50.2512 1.82883
\(756\) 5.16765 0.187946
\(757\) −28.3330 −1.02978 −0.514891 0.857256i \(-0.672168\pi\)
−0.514891 + 0.857256i \(0.672168\pi\)
\(758\) −22.3885 −0.813186
\(759\) −69.8755 −2.53632
\(760\) −26.6771 −0.967679
\(761\) 41.0389 1.48766 0.743829 0.668369i \(-0.233007\pi\)
0.743829 + 0.668369i \(0.233007\pi\)
\(762\) −4.45476 −0.161379
\(763\) −13.6917 −0.495672
\(764\) −32.2283 −1.16598
\(765\) −24.7900 −0.896286
\(766\) −62.6858 −2.26493
\(767\) 3.31595 0.119732
\(768\) 47.4056 1.71060
\(769\) −16.1649 −0.582920 −0.291460 0.956583i \(-0.594141\pi\)
−0.291460 + 0.956583i \(0.594141\pi\)
\(770\) 28.8005 1.03790
\(771\) 13.7088 0.493711
\(772\) 83.2371 2.99577
\(773\) −22.7398 −0.817895 −0.408947 0.912558i \(-0.634104\pi\)
−0.408947 + 0.912558i \(0.634104\pi\)
\(774\) 28.5902 1.02765
\(775\) 10.8066 0.388184
\(776\) −105.233 −3.77766
\(777\) 10.1561 0.364350
\(778\) 23.3185 0.836007
\(779\) −0.0239105 −0.000856681 0
\(780\) 34.0349 1.21864
\(781\) 28.8312 1.03166
\(782\) −62.1409 −2.22215
\(783\) −3.39231 −0.121231
\(784\) −56.0042 −2.00015
\(785\) 76.4152 2.72737
\(786\) 88.3544 3.15150
\(787\) 20.1167 0.717082 0.358541 0.933514i \(-0.383274\pi\)
0.358541 + 0.933514i \(0.383274\pi\)
\(788\) 34.2658 1.22067
\(789\) −20.8177 −0.741130
\(790\) 37.0283 1.31741
\(791\) 7.02388 0.249741
\(792\) −71.8839 −2.55428
\(793\) −14.3544 −0.509741
\(794\) −39.6847 −1.40836
\(795\) −1.77269 −0.0628707
\(796\) −26.6016 −0.942869
\(797\) −20.1054 −0.712169 −0.356085 0.934454i \(-0.615889\pi\)
−0.356085 + 0.934454i \(0.615889\pi\)
\(798\) −6.58482 −0.233100
\(799\) 36.2164 1.28125
\(800\) −40.3228 −1.42563
\(801\) −26.4627 −0.935013
\(802\) 33.5662 1.18526
\(803\) −11.2981 −0.398703
\(804\) 35.2045 1.24157
\(805\) −19.9360 −0.702653
\(806\) −6.37533 −0.224562
\(807\) 5.68266 0.200039
\(808\) 123.862 4.35744
\(809\) −43.9073 −1.54370 −0.771849 0.635805i \(-0.780668\pi\)
−0.771849 + 0.635805i \(0.780668\pi\)
\(810\) −82.0035 −2.88131
\(811\) 1.92974 0.0677624 0.0338812 0.999426i \(-0.489213\pi\)
0.0338812 + 0.999426i \(0.489213\pi\)
\(812\) −11.6329 −0.408233
\(813\) −55.3915 −1.94267
\(814\) 51.7671 1.81444
\(815\) −17.2749 −0.605113
\(816\) −68.8957 −2.41183
\(817\) 5.43108 0.190009
\(818\) 5.28102 0.184647
\(819\) 2.19671 0.0767593
\(820\) −0.284804 −0.00994580
\(821\) −15.1450 −0.528564 −0.264282 0.964445i \(-0.585135\pi\)
−0.264282 + 0.964445i \(0.585135\pi\)
\(822\) −89.9629 −3.13782
\(823\) 12.3029 0.428851 0.214425 0.976740i \(-0.431212\pi\)
0.214425 + 0.976740i \(0.431212\pi\)
\(824\) 70.4110 2.45288
\(825\) −41.9814 −1.46160
\(826\) −7.64163 −0.265886
\(827\) 14.1604 0.492404 0.246202 0.969219i \(-0.420817\pi\)
0.246202 + 0.969219i \(0.420817\pi\)
\(828\) 86.0310 2.98978
\(829\) −32.1756 −1.11750 −0.558752 0.829335i \(-0.688720\pi\)
−0.558752 + 0.829335i \(0.688720\pi\)
\(830\) −28.8606 −1.00177
\(831\) −36.0015 −1.24888
\(832\) 5.75877 0.199650
\(833\) −20.2906 −0.703026
\(834\) 34.8926 1.20823
\(835\) −58.3884 −2.02061
\(836\) −23.6095 −0.816551
\(837\) 3.01375 0.104170
\(838\) −4.45738 −0.153978
\(839\) −41.0663 −1.41777 −0.708883 0.705326i \(-0.750800\pi\)
−0.708883 + 0.705326i \(0.750800\pi\)
\(840\) −45.3647 −1.56523
\(841\) −21.3636 −0.736676
\(842\) −79.5837 −2.74264
\(843\) −36.7933 −1.26723
\(844\) −62.8792 −2.16439
\(845\) −3.06624 −0.105482
\(846\) −71.2797 −2.45065
\(847\) 4.98060 0.171135
\(848\) −2.22728 −0.0764850
\(849\) 37.3571 1.28209
\(850\) −37.3344 −1.28056
\(851\) −35.8337 −1.22836
\(852\) −78.5171 −2.68995
\(853\) −45.6107 −1.56168 −0.780841 0.624730i \(-0.785209\pi\)
−0.780841 + 0.624730i \(0.785209\pi\)
\(854\) 33.0799 1.13197
\(855\) 9.26844 0.316974
\(856\) −7.99728 −0.273342
\(857\) 10.8468 0.370518 0.185259 0.982690i \(-0.440688\pi\)
0.185259 + 0.982690i \(0.440688\pi\)
\(858\) 24.7668 0.845526
\(859\) −39.0237 −1.33147 −0.665737 0.746187i \(-0.731883\pi\)
−0.665737 + 0.746187i \(0.731883\pi\)
\(860\) 64.6911 2.20595
\(861\) −0.0406600 −0.00138569
\(862\) 78.8056 2.68413
\(863\) −52.0840 −1.77296 −0.886481 0.462766i \(-0.846857\pi\)
−0.886481 + 0.462766i \(0.846857\pi\)
\(864\) −11.2452 −0.382571
\(865\) −7.12296 −0.242188
\(866\) 72.6720 2.46950
\(867\) 14.8180 0.503246
\(868\) 10.3347 0.350783
\(869\) 18.9538 0.642964
\(870\) 51.4878 1.74560
\(871\) −3.17161 −0.107466
\(872\) 109.926 3.72255
\(873\) 36.5614 1.23742
\(874\) 23.2331 0.785871
\(875\) 1.62767 0.0550252
\(876\) 30.7687 1.03958
\(877\) −27.2025 −0.918562 −0.459281 0.888291i \(-0.651893\pi\)
−0.459281 + 0.888291i \(0.651893\pi\)
\(878\) −80.6140 −2.72059
\(879\) 28.7754 0.970570
\(880\) −112.662 −3.79785
\(881\) −26.0402 −0.877317 −0.438658 0.898654i \(-0.644546\pi\)
−0.438658 + 0.898654i \(0.644546\pi\)
\(882\) 39.9350 1.34468
\(883\) −39.1282 −1.31677 −0.658385 0.752681i \(-0.728760\pi\)
−0.658385 + 0.752681i \(0.728760\pi\)
\(884\) 15.4932 0.521092
\(885\) 23.7915 0.799741
\(886\) 77.7591 2.61237
\(887\) 1.86334 0.0625649 0.0312825 0.999511i \(-0.490041\pi\)
0.0312825 + 0.999511i \(0.490041\pi\)
\(888\) −81.5401 −2.73631
\(889\) −0.650581 −0.0218198
\(890\) −85.1226 −2.85332
\(891\) −41.9755 −1.40623
\(892\) −16.5375 −0.553718
\(893\) −13.5405 −0.453116
\(894\) −58.3913 −1.95290
\(895\) 34.5568 1.15511
\(896\) 2.98730 0.0997987
\(897\) −17.1439 −0.572417
\(898\) −41.6760 −1.39074
\(899\) −6.78423 −0.226267
\(900\) 51.6876 1.72292
\(901\) −0.806952 −0.0268835
\(902\) −0.207249 −0.00690064
\(903\) 9.23561 0.307342
\(904\) −56.3923 −1.87558
\(905\) −70.5974 −2.34674
\(906\) −99.5851 −3.30849
\(907\) −23.6070 −0.783856 −0.391928 0.919996i \(-0.628192\pi\)
−0.391928 + 0.919996i \(0.628192\pi\)
\(908\) 29.2911 0.972058
\(909\) −43.0334 −1.42733
\(910\) 7.06617 0.234241
\(911\) −33.8862 −1.12270 −0.561351 0.827578i \(-0.689718\pi\)
−0.561351 + 0.827578i \(0.689718\pi\)
\(912\) 25.7586 0.852952
\(913\) −14.7730 −0.488915
\(914\) 3.63173 0.120127
\(915\) −102.991 −3.40478
\(916\) 52.5940 1.73776
\(917\) 12.9034 0.426109
\(918\) −10.4118 −0.343642
\(919\) 50.0168 1.64990 0.824951 0.565205i \(-0.191203\pi\)
0.824951 + 0.565205i \(0.191203\pi\)
\(920\) 160.059 5.27700
\(921\) −40.3252 −1.32876
\(922\) −33.5222 −1.10400
\(923\) 7.07369 0.232833
\(924\) −40.1482 −1.32078
\(925\) −21.5290 −0.707868
\(926\) 75.9034 2.49434
\(927\) −24.4630 −0.803470
\(928\) 25.3141 0.830975
\(929\) 28.0237 0.919429 0.459715 0.888067i \(-0.347952\pi\)
0.459715 + 0.888067i \(0.347952\pi\)
\(930\) −45.7421 −1.49994
\(931\) 7.58619 0.248627
\(932\) −124.408 −4.07513
\(933\) −4.22117 −0.138195
\(934\) −40.0399 −1.31014
\(935\) −40.8180 −1.33489
\(936\) −17.6366 −0.576471
\(937\) 23.6168 0.771527 0.385764 0.922598i \(-0.373938\pi\)
0.385764 + 0.922598i \(0.373938\pi\)
\(938\) 7.30900 0.238647
\(939\) −57.9594 −1.89143
\(940\) −161.285 −5.26054
\(941\) −13.9230 −0.453875 −0.226938 0.973909i \(-0.572871\pi\)
−0.226938 + 0.973909i \(0.572871\pi\)
\(942\) −151.436 −4.93404
\(943\) 0.143460 0.00467170
\(944\) 29.8926 0.972921
\(945\) −3.34032 −0.108661
\(946\) 47.0751 1.53054
\(947\) 2.68819 0.0873544 0.0436772 0.999046i \(-0.486093\pi\)
0.0436772 + 0.999046i \(0.486093\pi\)
\(948\) −51.6177 −1.67646
\(949\) −2.77198 −0.0899824
\(950\) 13.9585 0.452873
\(951\) 43.4082 1.40761
\(952\) −20.6506 −0.669291
\(953\) 37.8558 1.22627 0.613135 0.789978i \(-0.289908\pi\)
0.613135 + 0.789978i \(0.289908\pi\)
\(954\) 1.58821 0.0514201
\(955\) 20.8321 0.674110
\(956\) 36.3570 1.17587
\(957\) 26.3553 0.851946
\(958\) −26.3794 −0.852278
\(959\) −13.1383 −0.424259
\(960\) 41.3184 1.33354
\(961\) −24.9729 −0.805576
\(962\) 12.7010 0.409496
\(963\) 2.77851 0.0895361
\(964\) −78.0944 −2.51525
\(965\) −53.8036 −1.73200
\(966\) 39.5082 1.27115
\(967\) −55.4438 −1.78295 −0.891476 0.453067i \(-0.850330\pi\)
−0.891476 + 0.453067i \(0.850330\pi\)
\(968\) −39.9874 −1.28524
\(969\) 9.33243 0.299801
\(970\) 117.607 3.77614
\(971\) 13.7628 0.441671 0.220835 0.975311i \(-0.429122\pi\)
0.220835 + 0.975311i \(0.429122\pi\)
\(972\) 96.8440 3.10627
\(973\) 5.09577 0.163363
\(974\) −12.9743 −0.415725
\(975\) −10.3001 −0.329866
\(976\) −129.402 −4.14207
\(977\) 13.3040 0.425634 0.212817 0.977092i \(-0.431736\pi\)
0.212817 + 0.977092i \(0.431736\pi\)
\(978\) 34.2345 1.09470
\(979\) −43.5721 −1.39257
\(980\) 90.3612 2.88648
\(981\) −38.1916 −1.21936
\(982\) 67.2516 2.14608
\(983\) 34.2403 1.09210 0.546049 0.837753i \(-0.316131\pi\)
0.546049 + 0.837753i \(0.316131\pi\)
\(984\) 0.326445 0.0104067
\(985\) −22.1491 −0.705728
\(986\) 23.4380 0.746418
\(987\) −23.0258 −0.732920
\(988\) −5.79255 −0.184286
\(989\) −32.5858 −1.03617
\(990\) 80.3363 2.55325
\(991\) 3.97272 0.126198 0.0630988 0.998007i \(-0.479902\pi\)
0.0630988 + 0.998007i \(0.479902\pi\)
\(992\) −22.4892 −0.714032
\(993\) −1.36009 −0.0431613
\(994\) −16.3014 −0.517048
\(995\) 17.1950 0.545119
\(996\) 40.2319 1.27480
\(997\) −15.0808 −0.477615 −0.238807 0.971067i \(-0.576756\pi\)
−0.238807 + 0.971067i \(0.576756\pi\)
\(998\) 4.44401 0.140673
\(999\) −6.00401 −0.189959
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 \(a_p\))