Properties

Label 8011.2.a.b.1.17
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57524 q^{2} +0.178143 q^{3} +4.63185 q^{4} -1.43369 q^{5} -0.458760 q^{6} +4.00928 q^{7} -6.77765 q^{8} -2.96827 q^{9} +O(q^{10})\) \(q-2.57524 q^{2} +0.178143 q^{3} +4.63185 q^{4} -1.43369 q^{5} -0.458760 q^{6} +4.00928 q^{7} -6.77765 q^{8} -2.96827 q^{9} +3.69209 q^{10} +3.24857 q^{11} +0.825131 q^{12} +0.109242 q^{13} -10.3249 q^{14} -0.255401 q^{15} +8.19036 q^{16} +4.02676 q^{17} +7.64399 q^{18} +0.800935 q^{19} -6.64064 q^{20} +0.714224 q^{21} -8.36584 q^{22} +2.16360 q^{23} -1.20739 q^{24} -2.94453 q^{25} -0.281325 q^{26} -1.06320 q^{27} +18.5704 q^{28} +1.12086 q^{29} +0.657719 q^{30} -9.40104 q^{31} -7.53682 q^{32} +0.578709 q^{33} -10.3699 q^{34} -5.74806 q^{35} -13.7486 q^{36} -9.59768 q^{37} -2.06260 q^{38} +0.0194607 q^{39} +9.71704 q^{40} +2.07739 q^{41} -1.83930 q^{42} +4.11530 q^{43} +15.0469 q^{44} +4.25557 q^{45} -5.57180 q^{46} +10.7434 q^{47} +1.45905 q^{48} +9.07433 q^{49} +7.58288 q^{50} +0.717338 q^{51} +0.505995 q^{52} +8.93327 q^{53} +2.73800 q^{54} -4.65744 q^{55} -27.1735 q^{56} +0.142681 q^{57} -2.88649 q^{58} +3.20813 q^{59} -1.18298 q^{60} -8.18150 q^{61} +24.2099 q^{62} -11.9006 q^{63} +3.02841 q^{64} -0.156620 q^{65} -1.49031 q^{66} +5.25878 q^{67} +18.6514 q^{68} +0.385430 q^{69} +14.8026 q^{70} -6.13821 q^{71} +20.1179 q^{72} +2.04661 q^{73} +24.7163 q^{74} -0.524547 q^{75} +3.70981 q^{76} +13.0244 q^{77} -0.0501160 q^{78} +1.93328 q^{79} -11.7424 q^{80} +8.71539 q^{81} -5.34979 q^{82} +10.7876 q^{83} +3.30818 q^{84} -5.77313 q^{85} -10.5979 q^{86} +0.199674 q^{87} -22.0177 q^{88} +1.83270 q^{89} -10.9591 q^{90} +0.437983 q^{91} +10.0215 q^{92} -1.67473 q^{93} -27.6668 q^{94} -1.14829 q^{95} -1.34263 q^{96} +1.53650 q^{97} -23.3686 q^{98} -9.64262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + O(q^{10}) \) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + 21q^{10} + 70q^{11} + 20q^{12} + 53q^{13} + 69q^{14} + 28q^{15} + 449q^{16} + 88q^{17} + 86q^{18} + 44q^{19} + 136q^{20} + 125q^{21} + 17q^{22} + 104q^{23} + 84q^{24} + 444q^{25} + 100q^{26} + 32q^{27} + 46q^{28} + 373q^{29} + 99q^{30} + 30q^{31} + 221q^{32} + 56q^{33} + 26q^{34} + 164q^{35} + 599q^{36} + 81q^{37} + 66q^{38} + 143q^{39} + 42q^{40} + 182q^{41} + 32q^{42} + 40q^{43} + 184q^{44} + 198q^{45} + 54q^{46} + 66q^{47} + 5q^{48} + 479q^{49} + 184q^{50} + 123q^{51} + 64q^{52} + 221q^{53} + 67q^{54} + 38q^{55} + 174q^{56} + 84q^{57} + 44q^{58} + 127q^{59} + 29q^{60} + 174q^{61} + 86q^{62} + 48q^{63} + 549q^{64} + 202q^{65} + 32q^{66} + 29q^{67} + 172q^{68} + 249q^{69} + 12q^{70} + 185q^{71} + 218q^{72} + 57q^{73} + 272q^{74} + 24q^{75} + 84q^{76} + 384q^{77} + 12q^{78} + 93q^{79} + 215q^{80} + 702q^{81} + 48q^{82} + 121q^{83} + 179q^{84} + 177q^{85} + 209q^{86} + 91q^{87} + 36q^{88} + 186q^{89} + 66q^{90} + 32q^{91} + 272q^{92} + 220q^{93} + 60q^{94} + 170q^{95} + 162q^{96} + 22q^{97} + 196q^{98} + 152q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57524 −1.82097 −0.910484 0.413544i \(-0.864291\pi\)
−0.910484 + 0.413544i \(0.864291\pi\)
\(3\) 0.178143 0.102851 0.0514254 0.998677i \(-0.483624\pi\)
0.0514254 + 0.998677i \(0.483624\pi\)
\(4\) 4.63185 2.31593
\(5\) −1.43369 −0.641165 −0.320583 0.947221i \(-0.603879\pi\)
−0.320583 + 0.947221i \(0.603879\pi\)
\(6\) −0.458760 −0.187288
\(7\) 4.00928 1.51537 0.757683 0.652623i \(-0.226331\pi\)
0.757683 + 0.652623i \(0.226331\pi\)
\(8\) −6.77765 −2.39626
\(9\) −2.96827 −0.989422
\(10\) 3.69209 1.16754
\(11\) 3.24857 0.979481 0.489740 0.871868i \(-0.337092\pi\)
0.489740 + 0.871868i \(0.337092\pi\)
\(12\) 0.825131 0.238195
\(13\) 0.109242 0.0302984 0.0151492 0.999885i \(-0.495178\pi\)
0.0151492 + 0.999885i \(0.495178\pi\)
\(14\) −10.3249 −2.75943
\(15\) −0.255401 −0.0659443
\(16\) 8.19036 2.04759
\(17\) 4.02676 0.976633 0.488317 0.872667i \(-0.337611\pi\)
0.488317 + 0.872667i \(0.337611\pi\)
\(18\) 7.64399 1.80171
\(19\) 0.800935 0.183747 0.0918735 0.995771i \(-0.470714\pi\)
0.0918735 + 0.995771i \(0.470714\pi\)
\(20\) −6.64064 −1.48489
\(21\) 0.714224 0.155856
\(22\) −8.36584 −1.78360
\(23\) 2.16360 0.451143 0.225571 0.974227i \(-0.427575\pi\)
0.225571 + 0.974227i \(0.427575\pi\)
\(24\) −1.20739 −0.246457
\(25\) −2.94453 −0.588907
\(26\) −0.281325 −0.0551724
\(27\) −1.06320 −0.204613
\(28\) 18.5704 3.50948
\(29\) 1.12086 0.208139 0.104069 0.994570i \(-0.466814\pi\)
0.104069 + 0.994570i \(0.466814\pi\)
\(30\) 0.657719 0.120083
\(31\) −9.40104 −1.68848 −0.844239 0.535967i \(-0.819947\pi\)
−0.844239 + 0.535967i \(0.819947\pi\)
\(32\) −7.53682 −1.33234
\(33\) 0.578709 0.100740
\(34\) −10.3699 −1.77842
\(35\) −5.74806 −0.971600
\(36\) −13.7486 −2.29143
\(37\) −9.59768 −1.57785 −0.788924 0.614491i \(-0.789362\pi\)
−0.788924 + 0.614491i \(0.789362\pi\)
\(38\) −2.06260 −0.334598
\(39\) 0.0194607 0.00311621
\(40\) 9.71704 1.53640
\(41\) 2.07739 0.324435 0.162217 0.986755i \(-0.448135\pi\)
0.162217 + 0.986755i \(0.448135\pi\)
\(42\) −1.83930 −0.283810
\(43\) 4.11530 0.627577 0.313789 0.949493i \(-0.398402\pi\)
0.313789 + 0.949493i \(0.398402\pi\)
\(44\) 15.0469 2.26841
\(45\) 4.25557 0.634383
\(46\) −5.57180 −0.821517
\(47\) 10.7434 1.56709 0.783543 0.621337i \(-0.213410\pi\)
0.783543 + 0.621337i \(0.213410\pi\)
\(48\) 1.45905 0.210596
\(49\) 9.07433 1.29633
\(50\) 7.58288 1.07238
\(51\) 0.717338 0.100447
\(52\) 0.505995 0.0701689
\(53\) 8.93327 1.22708 0.613539 0.789664i \(-0.289745\pi\)
0.613539 + 0.789664i \(0.289745\pi\)
\(54\) 2.73800 0.372595
\(55\) −4.65744 −0.628009
\(56\) −27.1735 −3.63121
\(57\) 0.142681 0.0188985
\(58\) −2.88649 −0.379015
\(59\) 3.20813 0.417662 0.208831 0.977952i \(-0.433034\pi\)
0.208831 + 0.977952i \(0.433034\pi\)
\(60\) −1.18298 −0.152722
\(61\) −8.18150 −1.04753 −0.523767 0.851862i \(-0.675474\pi\)
−0.523767 + 0.851862i \(0.675474\pi\)
\(62\) 24.2099 3.07466
\(63\) −11.9006 −1.49934
\(64\) 3.02841 0.378551
\(65\) −0.156620 −0.0194263
\(66\) −1.49031 −0.183445
\(67\) 5.25878 0.642462 0.321231 0.947001i \(-0.395903\pi\)
0.321231 + 0.947001i \(0.395903\pi\)
\(68\) 18.6514 2.26181
\(69\) 0.385430 0.0464004
\(70\) 14.8026 1.76925
\(71\) −6.13821 −0.728472 −0.364236 0.931307i \(-0.618670\pi\)
−0.364236 + 0.931307i \(0.618670\pi\)
\(72\) 20.1179 2.37091
\(73\) 2.04661 0.239538 0.119769 0.992802i \(-0.461785\pi\)
0.119769 + 0.992802i \(0.461785\pi\)
\(74\) 24.7163 2.87321
\(75\) −0.524547 −0.0605695
\(76\) 3.70981 0.425545
\(77\) 13.0244 1.48427
\(78\) −0.0501160 −0.00567452
\(79\) 1.93328 0.217511 0.108756 0.994069i \(-0.465313\pi\)
0.108756 + 0.994069i \(0.465313\pi\)
\(80\) −11.7424 −1.31284
\(81\) 8.71539 0.968377
\(82\) −5.34979 −0.590785
\(83\) 10.7876 1.18409 0.592047 0.805903i \(-0.298320\pi\)
0.592047 + 0.805903i \(0.298320\pi\)
\(84\) 3.30818 0.360952
\(85\) −5.77313 −0.626183
\(86\) −10.5979 −1.14280
\(87\) 0.199674 0.0214072
\(88\) −22.0177 −2.34709
\(89\) 1.83270 0.194266 0.0971331 0.995271i \(-0.469033\pi\)
0.0971331 + 0.995271i \(0.469033\pi\)
\(90\) −10.9591 −1.15519
\(91\) 0.437983 0.0459131
\(92\) 10.0215 1.04481
\(93\) −1.67473 −0.173661
\(94\) −27.6668 −2.85361
\(95\) −1.14829 −0.117812
\(96\) −1.34263 −0.137032
\(97\) 1.53650 0.156008 0.0780041 0.996953i \(-0.475145\pi\)
0.0780041 + 0.996953i \(0.475145\pi\)
\(98\) −23.3686 −2.36058
\(99\) −9.64262 −0.969120
\(100\) −13.6387 −1.36387
\(101\) −18.6319 −1.85395 −0.926974 0.375127i \(-0.877599\pi\)
−0.926974 + 0.375127i \(0.877599\pi\)
\(102\) −1.84732 −0.182912
\(103\) −13.5484 −1.33496 −0.667482 0.744626i \(-0.732628\pi\)
−0.667482 + 0.744626i \(0.732628\pi\)
\(104\) −0.740407 −0.0726029
\(105\) −1.02398 −0.0999298
\(106\) −23.0053 −2.23447
\(107\) −6.05270 −0.585136 −0.292568 0.956245i \(-0.594510\pi\)
−0.292568 + 0.956245i \(0.594510\pi\)
\(108\) −4.92460 −0.473870
\(109\) 18.5890 1.78051 0.890254 0.455465i \(-0.150527\pi\)
0.890254 + 0.455465i \(0.150527\pi\)
\(110\) 11.9940 1.14359
\(111\) −1.70976 −0.162283
\(112\) 32.8374 3.10285
\(113\) 2.75737 0.259391 0.129696 0.991554i \(-0.458600\pi\)
0.129696 + 0.991554i \(0.458600\pi\)
\(114\) −0.367437 −0.0344136
\(115\) −3.10194 −0.289257
\(116\) 5.19167 0.482035
\(117\) −0.324260 −0.0299779
\(118\) −8.26169 −0.760550
\(119\) 16.1444 1.47996
\(120\) 1.73102 0.158020
\(121\) −0.446790 −0.0406172
\(122\) 21.0693 1.90753
\(123\) 0.370073 0.0333683
\(124\) −43.5443 −3.91039
\(125\) 11.3900 1.01875
\(126\) 30.6469 2.73024
\(127\) 7.04726 0.625343 0.312672 0.949861i \(-0.398776\pi\)
0.312672 + 0.949861i \(0.398776\pi\)
\(128\) 7.27478 0.643006
\(129\) 0.733110 0.0645468
\(130\) 0.403333 0.0353747
\(131\) 7.12786 0.622764 0.311382 0.950285i \(-0.399208\pi\)
0.311382 + 0.950285i \(0.399208\pi\)
\(132\) 2.68050 0.233307
\(133\) 3.21117 0.278444
\(134\) −13.5426 −1.16990
\(135\) 1.52430 0.131191
\(136\) −27.2920 −2.34027
\(137\) −3.94505 −0.337048 −0.168524 0.985698i \(-0.553900\pi\)
−0.168524 + 0.985698i \(0.553900\pi\)
\(138\) −0.992575 −0.0844936
\(139\) 13.1177 1.11263 0.556314 0.830972i \(-0.312215\pi\)
0.556314 + 0.830972i \(0.312215\pi\)
\(140\) −26.6242 −2.25015
\(141\) 1.91386 0.161176
\(142\) 15.8074 1.32652
\(143\) 0.354882 0.0296767
\(144\) −24.3112 −2.02593
\(145\) −1.60697 −0.133452
\(146\) −5.27051 −0.436191
\(147\) 1.61652 0.133329
\(148\) −44.4550 −3.65418
\(149\) 0.552167 0.0452353 0.0226176 0.999744i \(-0.492800\pi\)
0.0226176 + 0.999744i \(0.492800\pi\)
\(150\) 1.35083 0.110295
\(151\) 4.37735 0.356224 0.178112 0.984010i \(-0.443001\pi\)
0.178112 + 0.984010i \(0.443001\pi\)
\(152\) −5.42845 −0.440306
\(153\) −11.9525 −0.966302
\(154\) −33.5410 −2.70281
\(155\) 13.4782 1.08259
\(156\) 0.0901393 0.00721692
\(157\) 10.9416 0.873239 0.436619 0.899646i \(-0.356176\pi\)
0.436619 + 0.899646i \(0.356176\pi\)
\(158\) −4.97866 −0.396081
\(159\) 1.59140 0.126206
\(160\) 10.8055 0.854247
\(161\) 8.67450 0.683646
\(162\) −22.4442 −1.76338
\(163\) −0.365656 −0.0286404 −0.0143202 0.999897i \(-0.504558\pi\)
−0.0143202 + 0.999897i \(0.504558\pi\)
\(164\) 9.62219 0.751367
\(165\) −0.829689 −0.0645912
\(166\) −27.7807 −2.15620
\(167\) 6.93449 0.536607 0.268304 0.963334i \(-0.413537\pi\)
0.268304 + 0.963334i \(0.413537\pi\)
\(168\) −4.84076 −0.373473
\(169\) −12.9881 −0.999082
\(170\) 14.8672 1.14026
\(171\) −2.37739 −0.181803
\(172\) 19.0615 1.45342
\(173\) 16.3378 1.24214 0.621068 0.783757i \(-0.286699\pi\)
0.621068 + 0.783757i \(0.286699\pi\)
\(174\) −0.514207 −0.0389819
\(175\) −11.8055 −0.892409
\(176\) 26.6070 2.00557
\(177\) 0.571504 0.0429569
\(178\) −4.71965 −0.353753
\(179\) −0.905544 −0.0676836 −0.0338418 0.999427i \(-0.510774\pi\)
−0.0338418 + 0.999427i \(0.510774\pi\)
\(180\) 19.7112 1.46918
\(181\) 20.2103 1.50222 0.751110 0.660177i \(-0.229519\pi\)
0.751110 + 0.660177i \(0.229519\pi\)
\(182\) −1.12791 −0.0836064
\(183\) −1.45747 −0.107740
\(184\) −14.6642 −1.08106
\(185\) 13.7601 1.01166
\(186\) 4.31282 0.316231
\(187\) 13.0812 0.956593
\(188\) 49.7619 3.62926
\(189\) −4.26268 −0.310064
\(190\) 2.95712 0.214532
\(191\) 14.3439 1.03789 0.518945 0.854807i \(-0.326325\pi\)
0.518945 + 0.854807i \(0.326325\pi\)
\(192\) 0.539488 0.0389342
\(193\) −21.3381 −1.53595 −0.767975 0.640479i \(-0.778736\pi\)
−0.767975 + 0.640479i \(0.778736\pi\)
\(194\) −3.95686 −0.284086
\(195\) −0.0279007 −0.00199801
\(196\) 42.0309 3.00221
\(197\) −14.5274 −1.03503 −0.517516 0.855673i \(-0.673143\pi\)
−0.517516 + 0.855673i \(0.673143\pi\)
\(198\) 24.8320 1.76474
\(199\) 13.1015 0.928738 0.464369 0.885642i \(-0.346281\pi\)
0.464369 + 0.885642i \(0.346281\pi\)
\(200\) 19.9570 1.41117
\(201\) 0.936813 0.0660777
\(202\) 47.9817 3.37598
\(203\) 4.49385 0.315407
\(204\) 3.32260 0.232629
\(205\) −2.97834 −0.208016
\(206\) 34.8904 2.43093
\(207\) −6.42215 −0.446370
\(208\) 0.894735 0.0620387
\(209\) 2.60189 0.179977
\(210\) 2.63698 0.181969
\(211\) −19.0591 −1.31208 −0.656041 0.754725i \(-0.727770\pi\)
−0.656041 + 0.754725i \(0.727770\pi\)
\(212\) 41.3776 2.84182
\(213\) −1.09348 −0.0749239
\(214\) 15.5871 1.06551
\(215\) −5.90006 −0.402381
\(216\) 7.20602 0.490307
\(217\) −37.6914 −2.55866
\(218\) −47.8712 −3.24225
\(219\) 0.364589 0.0246366
\(220\) −21.5726 −1.45442
\(221\) 0.439893 0.0295904
\(222\) 4.40303 0.295512
\(223\) 1.49026 0.0997951 0.0498976 0.998754i \(-0.484111\pi\)
0.0498976 + 0.998754i \(0.484111\pi\)
\(224\) −30.2172 −2.01897
\(225\) 8.74016 0.582677
\(226\) −7.10088 −0.472343
\(227\) −2.41143 −0.160052 −0.0800260 0.996793i \(-0.525500\pi\)
−0.0800260 + 0.996793i \(0.525500\pi\)
\(228\) 0.660876 0.0437676
\(229\) 13.1561 0.869376 0.434688 0.900581i \(-0.356859\pi\)
0.434688 + 0.900581i \(0.356859\pi\)
\(230\) 7.98823 0.526728
\(231\) 2.32021 0.152658
\(232\) −7.59682 −0.498755
\(233\) −0.359749 −0.0235679 −0.0117840 0.999931i \(-0.503751\pi\)
−0.0117840 + 0.999931i \(0.503751\pi\)
\(234\) 0.835048 0.0545888
\(235\) −15.4027 −1.00476
\(236\) 14.8596 0.967275
\(237\) 0.344400 0.0223712
\(238\) −41.5757 −2.69495
\(239\) 10.7586 0.695916 0.347958 0.937510i \(-0.386875\pi\)
0.347958 + 0.937510i \(0.386875\pi\)
\(240\) −2.09183 −0.135027
\(241\) −8.04907 −0.518486 −0.259243 0.965812i \(-0.583473\pi\)
−0.259243 + 0.965812i \(0.583473\pi\)
\(242\) 1.15059 0.0739627
\(243\) 4.74219 0.304212
\(244\) −37.8955 −2.42601
\(245\) −13.0098 −0.831163
\(246\) −0.953025 −0.0607627
\(247\) 0.0874960 0.00556724
\(248\) 63.7170 4.04603
\(249\) 1.92173 0.121785
\(250\) −29.3320 −1.85512
\(251\) −13.9814 −0.882498 −0.441249 0.897385i \(-0.645464\pi\)
−0.441249 + 0.897385i \(0.645464\pi\)
\(252\) −55.1219 −3.47235
\(253\) 7.02862 0.441886
\(254\) −18.1484 −1.13873
\(255\) −1.02844 −0.0644034
\(256\) −24.7911 −1.54944
\(257\) 29.4420 1.83654 0.918269 0.395956i \(-0.129587\pi\)
0.918269 + 0.395956i \(0.129587\pi\)
\(258\) −1.88793 −0.117538
\(259\) −38.4798 −2.39102
\(260\) −0.725440 −0.0449898
\(261\) −3.32702 −0.205937
\(262\) −18.3559 −1.13403
\(263\) 8.53217 0.526116 0.263058 0.964780i \(-0.415269\pi\)
0.263058 + 0.964780i \(0.415269\pi\)
\(264\) −3.92229 −0.241400
\(265\) −12.8075 −0.786760
\(266\) −8.26953 −0.507038
\(267\) 0.326483 0.0199804
\(268\) 24.3579 1.48789
\(269\) −22.9832 −1.40131 −0.700654 0.713501i \(-0.747108\pi\)
−0.700654 + 0.713501i \(0.747108\pi\)
\(270\) −3.92544 −0.238895
\(271\) 32.3247 1.96359 0.981793 0.189956i \(-0.0608346\pi\)
0.981793 + 0.189956i \(0.0608346\pi\)
\(272\) 32.9806 1.99974
\(273\) 0.0780236 0.00472220
\(274\) 10.1594 0.613755
\(275\) −9.56553 −0.576823
\(276\) 1.78526 0.107460
\(277\) −16.6530 −1.00058 −0.500292 0.865857i \(-0.666774\pi\)
−0.500292 + 0.865857i \(0.666774\pi\)
\(278\) −33.7812 −2.02606
\(279\) 27.9048 1.67062
\(280\) 38.9584 2.32821
\(281\) 10.9350 0.652325 0.326162 0.945314i \(-0.394244\pi\)
0.326162 + 0.945314i \(0.394244\pi\)
\(282\) −4.92864 −0.293496
\(283\) −5.02256 −0.298560 −0.149280 0.988795i \(-0.547696\pi\)
−0.149280 + 0.988795i \(0.547696\pi\)
\(284\) −28.4313 −1.68709
\(285\) −0.204560 −0.0121171
\(286\) −0.913905 −0.0540403
\(287\) 8.32886 0.491637
\(288\) 22.3713 1.31824
\(289\) −0.785194 −0.0461879
\(290\) 4.13833 0.243011
\(291\) 0.273717 0.0160456
\(292\) 9.47961 0.554752
\(293\) −22.9620 −1.34145 −0.670727 0.741704i \(-0.734018\pi\)
−0.670727 + 0.741704i \(0.734018\pi\)
\(294\) −4.16294 −0.242787
\(295\) −4.59946 −0.267791
\(296\) 65.0497 3.78094
\(297\) −3.45389 −0.200415
\(298\) −1.42196 −0.0823720
\(299\) 0.236357 0.0136689
\(300\) −2.42963 −0.140275
\(301\) 16.4994 0.951009
\(302\) −11.2727 −0.648673
\(303\) −3.31914 −0.190680
\(304\) 6.55994 0.376238
\(305\) 11.7297 0.671642
\(306\) 30.7805 1.75961
\(307\) −6.84208 −0.390498 −0.195249 0.980754i \(-0.562551\pi\)
−0.195249 + 0.980754i \(0.562551\pi\)
\(308\) 60.3272 3.43746
\(309\) −2.41355 −0.137302
\(310\) −34.7095 −1.97137
\(311\) 26.3220 1.49258 0.746291 0.665620i \(-0.231833\pi\)
0.746291 + 0.665620i \(0.231833\pi\)
\(312\) −0.131898 −0.00746726
\(313\) 22.2969 1.26029 0.630146 0.776476i \(-0.282995\pi\)
0.630146 + 0.776476i \(0.282995\pi\)
\(314\) −28.1774 −1.59014
\(315\) 17.0618 0.961322
\(316\) 8.95468 0.503740
\(317\) −19.1219 −1.07399 −0.536996 0.843585i \(-0.680441\pi\)
−0.536996 + 0.843585i \(0.680441\pi\)
\(318\) −4.09823 −0.229817
\(319\) 3.64120 0.203868
\(320\) −4.34179 −0.242714
\(321\) −1.07824 −0.0601817
\(322\) −22.3389 −1.24490
\(323\) 3.22517 0.179453
\(324\) 40.3684 2.24269
\(325\) −0.321668 −0.0178429
\(326\) 0.941652 0.0521533
\(327\) 3.31150 0.183127
\(328\) −14.0799 −0.777430
\(329\) 43.0733 2.37471
\(330\) 2.13665 0.117619
\(331\) 30.8192 1.69398 0.846989 0.531611i \(-0.178413\pi\)
0.846989 + 0.531611i \(0.178413\pi\)
\(332\) 49.9666 2.74227
\(333\) 28.4884 1.56116
\(334\) −17.8580 −0.977145
\(335\) −7.53945 −0.411924
\(336\) 5.84975 0.319130
\(337\) −7.98837 −0.435154 −0.217577 0.976043i \(-0.569815\pi\)
−0.217577 + 0.976043i \(0.569815\pi\)
\(338\) 33.4474 1.81930
\(339\) 0.491205 0.0266786
\(340\) −26.7403 −1.45019
\(341\) −30.5400 −1.65383
\(342\) 6.12234 0.331058
\(343\) 8.31656 0.449052
\(344\) −27.8920 −1.50384
\(345\) −0.552587 −0.0297503
\(346\) −42.0736 −2.26189
\(347\) −1.72126 −0.0924020 −0.0462010 0.998932i \(-0.514711\pi\)
−0.0462010 + 0.998932i \(0.514711\pi\)
\(348\) 0.924858 0.0495776
\(349\) −32.6175 −1.74597 −0.872987 0.487744i \(-0.837820\pi\)
−0.872987 + 0.487744i \(0.837820\pi\)
\(350\) 30.4019 1.62505
\(351\) −0.116147 −0.00619946
\(352\) −24.4839 −1.30500
\(353\) 3.78629 0.201524 0.100762 0.994911i \(-0.467872\pi\)
0.100762 + 0.994911i \(0.467872\pi\)
\(354\) −1.47176 −0.0782231
\(355\) 8.80029 0.467071
\(356\) 8.48881 0.449906
\(357\) 2.87601 0.152215
\(358\) 2.33199 0.123250
\(359\) −10.4953 −0.553922 −0.276961 0.960881i \(-0.589327\pi\)
−0.276961 + 0.960881i \(0.589327\pi\)
\(360\) −28.8428 −1.52015
\(361\) −18.3585 −0.966237
\(362\) −52.0464 −2.73550
\(363\) −0.0795923 −0.00417751
\(364\) 2.02868 0.106331
\(365\) −2.93421 −0.153583
\(366\) 3.75334 0.196190
\(367\) −5.67748 −0.296362 −0.148181 0.988960i \(-0.547342\pi\)
−0.148181 + 0.988960i \(0.547342\pi\)
\(368\) 17.7207 0.923755
\(369\) −6.16626 −0.321003
\(370\) −35.4355 −1.84220
\(371\) 35.8160 1.85947
\(372\) −7.75709 −0.402186
\(373\) −1.03621 −0.0536528 −0.0268264 0.999640i \(-0.508540\pi\)
−0.0268264 + 0.999640i \(0.508540\pi\)
\(374\) −33.6873 −1.74193
\(375\) 2.02904 0.104779
\(376\) −72.8150 −3.75515
\(377\) 0.122446 0.00630628
\(378\) 10.9774 0.564617
\(379\) 3.49439 0.179495 0.0897473 0.995965i \(-0.471394\pi\)
0.0897473 + 0.995965i \(0.471394\pi\)
\(380\) −5.31872 −0.272844
\(381\) 1.25542 0.0643170
\(382\) −36.9390 −1.88997
\(383\) 0.802352 0.0409983 0.0204991 0.999790i \(-0.493474\pi\)
0.0204991 + 0.999790i \(0.493474\pi\)
\(384\) 1.29595 0.0661336
\(385\) −18.6730 −0.951664
\(386\) 54.9507 2.79692
\(387\) −12.2153 −0.620938
\(388\) 7.11685 0.361303
\(389\) −2.08570 −0.105749 −0.0528746 0.998601i \(-0.516838\pi\)
−0.0528746 + 0.998601i \(0.516838\pi\)
\(390\) 0.0718508 0.00363831
\(391\) 8.71232 0.440601
\(392\) −61.5026 −3.10635
\(393\) 1.26978 0.0640517
\(394\) 37.4115 1.88476
\(395\) −2.77173 −0.139461
\(396\) −44.6632 −2.24441
\(397\) 32.4801 1.63013 0.815066 0.579368i \(-0.196701\pi\)
0.815066 + 0.579368i \(0.196701\pi\)
\(398\) −33.7394 −1.69120
\(399\) 0.572047 0.0286382
\(400\) −24.1168 −1.20584
\(401\) 1.52539 0.0761742 0.0380871 0.999274i \(-0.487874\pi\)
0.0380871 + 0.999274i \(0.487874\pi\)
\(402\) −2.41252 −0.120325
\(403\) −1.02699 −0.0511582
\(404\) −86.3004 −4.29361
\(405\) −12.4952 −0.620890
\(406\) −11.5727 −0.574346
\(407\) −31.1787 −1.54547
\(408\) −4.86187 −0.240698
\(409\) −18.3103 −0.905386 −0.452693 0.891666i \(-0.649537\pi\)
−0.452693 + 0.891666i \(0.649537\pi\)
\(410\) 7.66993 0.378791
\(411\) −0.702782 −0.0346657
\(412\) −62.7542 −3.09168
\(413\) 12.8623 0.632911
\(414\) 16.5386 0.812827
\(415\) −15.4661 −0.759200
\(416\) −0.823341 −0.0403676
\(417\) 2.33682 0.114435
\(418\) −6.70049 −0.327732
\(419\) −4.08632 −0.199630 −0.0998148 0.995006i \(-0.531825\pi\)
−0.0998148 + 0.995006i \(0.531825\pi\)
\(420\) −4.74290 −0.231430
\(421\) −0.284669 −0.0138739 −0.00693696 0.999976i \(-0.502208\pi\)
−0.00693696 + 0.999976i \(0.502208\pi\)
\(422\) 49.0817 2.38926
\(423\) −31.8893 −1.55051
\(424\) −60.5466 −2.94040
\(425\) −11.8569 −0.575146
\(426\) 2.81597 0.136434
\(427\) −32.8019 −1.58740
\(428\) −28.0352 −1.35513
\(429\) 0.0632196 0.00305227
\(430\) 15.1941 0.732723
\(431\) 7.82709 0.377018 0.188509 0.982072i \(-0.439635\pi\)
0.188509 + 0.982072i \(0.439635\pi\)
\(432\) −8.70801 −0.418964
\(433\) −19.2305 −0.924158 −0.462079 0.886839i \(-0.652896\pi\)
−0.462079 + 0.886839i \(0.652896\pi\)
\(434\) 97.0644 4.65924
\(435\) −0.286270 −0.0137256
\(436\) 86.1017 4.12353
\(437\) 1.73291 0.0828961
\(438\) −0.938904 −0.0448625
\(439\) 27.0140 1.28931 0.644654 0.764475i \(-0.277001\pi\)
0.644654 + 0.764475i \(0.277001\pi\)
\(440\) 31.5665 1.50487
\(441\) −26.9350 −1.28262
\(442\) −1.13283 −0.0538832
\(443\) 25.3502 1.20442 0.602211 0.798337i \(-0.294286\pi\)
0.602211 + 0.798337i \(0.294286\pi\)
\(444\) −7.91934 −0.375835
\(445\) −2.62753 −0.124557
\(446\) −3.83777 −0.181724
\(447\) 0.0983644 0.00465248
\(448\) 12.1417 0.573643
\(449\) −16.0981 −0.759716 −0.379858 0.925045i \(-0.624027\pi\)
−0.379858 + 0.925045i \(0.624027\pi\)
\(450\) −22.5080 −1.06104
\(451\) 6.74856 0.317777
\(452\) 12.7717 0.600731
\(453\) 0.779794 0.0366379
\(454\) 6.21000 0.291450
\(455\) −0.627932 −0.0294379
\(456\) −0.967040 −0.0452858
\(457\) −18.0394 −0.843847 −0.421923 0.906631i \(-0.638645\pi\)
−0.421923 + 0.906631i \(0.638645\pi\)
\(458\) −33.8800 −1.58311
\(459\) −4.28126 −0.199832
\(460\) −14.3677 −0.669898
\(461\) −29.4735 −1.37272 −0.686360 0.727262i \(-0.740792\pi\)
−0.686360 + 0.727262i \(0.740792\pi\)
\(462\) −5.97509 −0.277986
\(463\) 30.9655 1.43909 0.719544 0.694446i \(-0.244351\pi\)
0.719544 + 0.694446i \(0.244351\pi\)
\(464\) 9.18027 0.426183
\(465\) 2.40104 0.111346
\(466\) 0.926440 0.0429165
\(467\) −14.5535 −0.673454 −0.336727 0.941602i \(-0.609320\pi\)
−0.336727 + 0.941602i \(0.609320\pi\)
\(468\) −1.50193 −0.0694266
\(469\) 21.0839 0.973564
\(470\) 39.6656 1.82964
\(471\) 1.94917 0.0898132
\(472\) −21.7435 −1.00083
\(473\) 13.3688 0.614700
\(474\) −0.886913 −0.0407372
\(475\) −2.35838 −0.108210
\(476\) 74.7786 3.42747
\(477\) −26.5163 −1.21410
\(478\) −27.7060 −1.26724
\(479\) 29.7211 1.35799 0.678996 0.734142i \(-0.262416\pi\)
0.678996 + 0.734142i \(0.262416\pi\)
\(480\) 1.92491 0.0878599
\(481\) −1.04847 −0.0478063
\(482\) 20.7283 0.944147
\(483\) 1.54530 0.0703135
\(484\) −2.06946 −0.0940666
\(485\) −2.20287 −0.100027
\(486\) −12.2123 −0.553960
\(487\) 27.8799 1.26336 0.631680 0.775229i \(-0.282366\pi\)
0.631680 + 0.775229i \(0.282366\pi\)
\(488\) 55.4513 2.51016
\(489\) −0.0651390 −0.00294569
\(490\) 33.5033 1.51352
\(491\) −7.54215 −0.340373 −0.170186 0.985412i \(-0.554437\pi\)
−0.170186 + 0.985412i \(0.554437\pi\)
\(492\) 1.71412 0.0772786
\(493\) 4.51345 0.203275
\(494\) −0.225323 −0.0101378
\(495\) 13.8245 0.621366
\(496\) −76.9979 −3.45731
\(497\) −24.6098 −1.10390
\(498\) −4.94892 −0.221767
\(499\) −2.45075 −0.109711 −0.0548553 0.998494i \(-0.517470\pi\)
−0.0548553 + 0.998494i \(0.517470\pi\)
\(500\) 52.7568 2.35936
\(501\) 1.23533 0.0551905
\(502\) 36.0054 1.60700
\(503\) 12.0785 0.538554 0.269277 0.963063i \(-0.413215\pi\)
0.269277 + 0.963063i \(0.413215\pi\)
\(504\) 80.6581 3.59280
\(505\) 26.7124 1.18869
\(506\) −18.1004 −0.804660
\(507\) −2.31373 −0.102756
\(508\) 32.6419 1.44825
\(509\) −33.2006 −1.47159 −0.735795 0.677205i \(-0.763191\pi\)
−0.735795 + 0.677205i \(0.763191\pi\)
\(510\) 2.64848 0.117277
\(511\) 8.20544 0.362987
\(512\) 49.2935 2.17848
\(513\) −0.851556 −0.0375971
\(514\) −75.8201 −3.34428
\(515\) 19.4242 0.855933
\(516\) 3.39566 0.149486
\(517\) 34.9007 1.53493
\(518\) 99.0946 4.35397
\(519\) 2.91045 0.127755
\(520\) 1.06151 0.0465504
\(521\) 14.9950 0.656944 0.328472 0.944514i \(-0.393466\pi\)
0.328472 + 0.944514i \(0.393466\pi\)
\(522\) 8.56786 0.375005
\(523\) 40.4068 1.76687 0.883434 0.468556i \(-0.155226\pi\)
0.883434 + 0.468556i \(0.155226\pi\)
\(524\) 33.0152 1.44228
\(525\) −2.10306 −0.0917849
\(526\) −21.9724 −0.958040
\(527\) −37.8558 −1.64902
\(528\) 4.73983 0.206275
\(529\) −18.3188 −0.796470
\(530\) 32.9824 1.43267
\(531\) −9.52257 −0.413244
\(532\) 14.8737 0.644856
\(533\) 0.226940 0.00982985
\(534\) −0.840771 −0.0363837
\(535\) 8.67769 0.375169
\(536\) −35.6421 −1.53951
\(537\) −0.161316 −0.00696130
\(538\) 59.1871 2.55174
\(539\) 29.4786 1.26973
\(540\) 7.06035 0.303829
\(541\) 38.8209 1.66904 0.834520 0.550978i \(-0.185745\pi\)
0.834520 + 0.550978i \(0.185745\pi\)
\(542\) −83.2438 −3.57563
\(543\) 3.60032 0.154504
\(544\) −30.3490 −1.30120
\(545\) −26.6509 −1.14160
\(546\) −0.200929 −0.00859898
\(547\) −37.3858 −1.59850 −0.799250 0.600999i \(-0.794770\pi\)
−0.799250 + 0.600999i \(0.794770\pi\)
\(548\) −18.2729 −0.780580
\(549\) 24.2848 1.03645
\(550\) 24.6335 1.05038
\(551\) 0.897738 0.0382449
\(552\) −2.61231 −0.111187
\(553\) 7.75107 0.329609
\(554\) 42.8855 1.82203
\(555\) 2.45126 0.104050
\(556\) 60.7592 2.57677
\(557\) −11.6757 −0.494716 −0.247358 0.968924i \(-0.579562\pi\)
−0.247358 + 0.968924i \(0.579562\pi\)
\(558\) −71.8615 −3.04214
\(559\) 0.449565 0.0190146
\(560\) −47.0787 −1.98944
\(561\) 2.33032 0.0983863
\(562\) −28.1601 −1.18786
\(563\) −24.2102 −1.02034 −0.510169 0.860074i \(-0.670417\pi\)
−0.510169 + 0.860074i \(0.670417\pi\)
\(564\) 8.86471 0.373272
\(565\) −3.95321 −0.166313
\(566\) 12.9343 0.543669
\(567\) 34.9425 1.46745
\(568\) 41.6027 1.74561
\(569\) 30.9493 1.29746 0.648731 0.761018i \(-0.275300\pi\)
0.648731 + 0.761018i \(0.275300\pi\)
\(570\) 0.526790 0.0220648
\(571\) −2.44057 −0.102135 −0.0510674 0.998695i \(-0.516262\pi\)
−0.0510674 + 0.998695i \(0.516262\pi\)
\(572\) 1.64376 0.0687291
\(573\) 2.55527 0.106748
\(574\) −21.4488 −0.895255
\(575\) −6.37081 −0.265681
\(576\) −8.98911 −0.374546
\(577\) −29.4018 −1.22401 −0.612007 0.790853i \(-0.709637\pi\)
−0.612007 + 0.790853i \(0.709637\pi\)
\(578\) 2.02206 0.0841066
\(579\) −3.80123 −0.157974
\(580\) −7.44325 −0.309064
\(581\) 43.2505 1.79433
\(582\) −0.704886 −0.0292184
\(583\) 29.0204 1.20190
\(584\) −13.8712 −0.573995
\(585\) 0.464889 0.0192208
\(586\) 59.1326 2.44275
\(587\) 37.2187 1.53618 0.768091 0.640341i \(-0.221207\pi\)
0.768091 + 0.640341i \(0.221207\pi\)
\(588\) 7.48751 0.308780
\(589\) −7.52962 −0.310253
\(590\) 11.8447 0.487638
\(591\) −2.58795 −0.106454
\(592\) −78.6084 −3.23079
\(593\) −14.8068 −0.608042 −0.304021 0.952665i \(-0.598329\pi\)
−0.304021 + 0.952665i \(0.598329\pi\)
\(594\) 8.89459 0.364949
\(595\) −23.1461 −0.948897
\(596\) 2.55755 0.104762
\(597\) 2.33393 0.0955213
\(598\) −0.608677 −0.0248906
\(599\) −23.1142 −0.944420 −0.472210 0.881486i \(-0.656544\pi\)
−0.472210 + 0.881486i \(0.656544\pi\)
\(600\) 3.55520 0.145140
\(601\) −0.164513 −0.00671063 −0.00335531 0.999994i \(-0.501068\pi\)
−0.00335531 + 0.999994i \(0.501068\pi\)
\(602\) −42.4898 −1.73176
\(603\) −15.6094 −0.635666
\(604\) 20.2753 0.824989
\(605\) 0.640558 0.0260424
\(606\) 8.54759 0.347222
\(607\) 16.4064 0.665917 0.332958 0.942942i \(-0.391953\pi\)
0.332958 + 0.942942i \(0.391953\pi\)
\(608\) −6.03650 −0.244813
\(609\) 0.800547 0.0324398
\(610\) −30.2068 −1.22304
\(611\) 1.17364 0.0474802
\(612\) −55.3622 −2.23788
\(613\) −11.9747 −0.483652 −0.241826 0.970320i \(-0.577746\pi\)
−0.241826 + 0.970320i \(0.577746\pi\)
\(614\) 17.6200 0.711084
\(615\) −0.530569 −0.0213946
\(616\) −88.2750 −3.55670
\(617\) −29.6207 −1.19248 −0.596241 0.802805i \(-0.703340\pi\)
−0.596241 + 0.802805i \(0.703340\pi\)
\(618\) 6.21547 0.250023
\(619\) 15.3324 0.616260 0.308130 0.951344i \(-0.400297\pi\)
0.308130 + 0.951344i \(0.400297\pi\)
\(620\) 62.4289 2.50721
\(621\) −2.30035 −0.0923099
\(622\) −67.7853 −2.71794
\(623\) 7.34782 0.294384
\(624\) 0.159390 0.00638072
\(625\) −1.60704 −0.0642818
\(626\) −57.4197 −2.29495
\(627\) 0.463508 0.0185107
\(628\) 50.6801 2.02236
\(629\) −38.6475 −1.54098
\(630\) −43.9381 −1.75054
\(631\) 18.0358 0.717993 0.358997 0.933339i \(-0.383119\pi\)
0.358997 + 0.933339i \(0.383119\pi\)
\(632\) −13.1031 −0.521214
\(633\) −3.39524 −0.134949
\(634\) 49.2434 1.95570
\(635\) −10.1036 −0.400948
\(636\) 7.37111 0.292284
\(637\) 0.991301 0.0392768
\(638\) −9.37696 −0.371238
\(639\) 18.2198 0.720766
\(640\) −10.4298 −0.412273
\(641\) 39.6015 1.56417 0.782083 0.623174i \(-0.214157\pi\)
0.782083 + 0.623174i \(0.214157\pi\)
\(642\) 2.77673 0.109589
\(643\) −41.8858 −1.65182 −0.825908 0.563805i \(-0.809337\pi\)
−0.825908 + 0.563805i \(0.809337\pi\)
\(644\) 40.1790 1.58327
\(645\) −1.05105 −0.0413851
\(646\) −8.30559 −0.326779
\(647\) 14.5489 0.571977 0.285988 0.958233i \(-0.407678\pi\)
0.285988 + 0.958233i \(0.407678\pi\)
\(648\) −59.0699 −2.32048
\(649\) 10.4218 0.409092
\(650\) 0.828372 0.0324914
\(651\) −6.71445 −0.263160
\(652\) −1.69367 −0.0663291
\(653\) 3.87731 0.151731 0.0758655 0.997118i \(-0.475828\pi\)
0.0758655 + 0.997118i \(0.475828\pi\)
\(654\) −8.52791 −0.333468
\(655\) −10.2191 −0.399295
\(656\) 17.0146 0.664309
\(657\) −6.07489 −0.237004
\(658\) −110.924 −4.32427
\(659\) 24.1717 0.941595 0.470797 0.882241i \(-0.343966\pi\)
0.470797 + 0.882241i \(0.343966\pi\)
\(660\) −3.84300 −0.149589
\(661\) −11.8517 −0.460979 −0.230490 0.973075i \(-0.574033\pi\)
−0.230490 + 0.973075i \(0.574033\pi\)
\(662\) −79.3668 −3.08468
\(663\) 0.0783638 0.00304340
\(664\) −73.1146 −2.83740
\(665\) −4.60382 −0.178529
\(666\) −73.3645 −2.84282
\(667\) 2.42510 0.0939004
\(668\) 32.1196 1.24274
\(669\) 0.265479 0.0102640
\(670\) 19.4159 0.750101
\(671\) −26.5782 −1.02604
\(672\) −5.38298 −0.207653
\(673\) 6.67425 0.257273 0.128637 0.991692i \(-0.458940\pi\)
0.128637 + 0.991692i \(0.458940\pi\)
\(674\) 20.5720 0.792403
\(675\) 3.13064 0.120498
\(676\) −60.1588 −2.31380
\(677\) 29.5146 1.13434 0.567169 0.823601i \(-0.308038\pi\)
0.567169 + 0.823601i \(0.308038\pi\)
\(678\) −1.26497 −0.0485808
\(679\) 6.16027 0.236409
\(680\) 39.1282 1.50050
\(681\) −0.429578 −0.0164615
\(682\) 78.6477 3.01157
\(683\) 47.7648 1.82767 0.913835 0.406086i \(-0.133107\pi\)
0.913835 + 0.406086i \(0.133107\pi\)
\(684\) −11.0117 −0.421043
\(685\) 5.65598 0.216104
\(686\) −21.4171 −0.817709
\(687\) 2.34365 0.0894160
\(688\) 33.7058 1.28502
\(689\) 0.975892 0.0371785
\(690\) 1.42304 0.0541744
\(691\) 15.9512 0.606810 0.303405 0.952862i \(-0.401876\pi\)
0.303405 + 0.952862i \(0.401876\pi\)
\(692\) 75.6741 2.87670
\(693\) −38.6600 −1.46857
\(694\) 4.43265 0.168261
\(695\) −18.8067 −0.713379
\(696\) −1.35332 −0.0512974
\(697\) 8.36517 0.316854
\(698\) 83.9978 3.17936
\(699\) −0.0640867 −0.00242398
\(700\) −54.6812 −2.06675
\(701\) 17.9075 0.676357 0.338179 0.941082i \(-0.390189\pi\)
0.338179 + 0.941082i \(0.390189\pi\)
\(702\) 0.299106 0.0112890
\(703\) −7.68711 −0.289925
\(704\) 9.83799 0.370783
\(705\) −2.74388 −0.103340
\(706\) −9.75060 −0.366969
\(707\) −74.7007 −2.80941
\(708\) 2.64712 0.0994850
\(709\) 44.0267 1.65346 0.826729 0.562600i \(-0.190199\pi\)
0.826729 + 0.562600i \(0.190199\pi\)
\(710\) −22.6628 −0.850522
\(711\) −5.73850 −0.215210
\(712\) −12.4214 −0.465512
\(713\) −20.3401 −0.761744
\(714\) −7.40641 −0.277178
\(715\) −0.508790 −0.0190277
\(716\) −4.19435 −0.156750
\(717\) 1.91657 0.0715755
\(718\) 27.0280 1.00867
\(719\) −23.5998 −0.880126 −0.440063 0.897967i \(-0.645044\pi\)
−0.440063 + 0.897967i \(0.645044\pi\)
\(720\) 34.8546 1.29896
\(721\) −54.3194 −2.02296
\(722\) 47.2775 1.75949
\(723\) −1.43388 −0.0533267
\(724\) 93.6112 3.47903
\(725\) −3.30042 −0.122574
\(726\) 0.204969 0.00760712
\(727\) −17.2165 −0.638525 −0.319262 0.947666i \(-0.603435\pi\)
−0.319262 + 0.947666i \(0.603435\pi\)
\(728\) −2.96850 −0.110020
\(729\) −25.3014 −0.937089
\(730\) 7.55628 0.279670
\(731\) 16.5713 0.612912
\(732\) −6.75080 −0.249517
\(733\) 21.7761 0.804318 0.402159 0.915570i \(-0.368260\pi\)
0.402159 + 0.915570i \(0.368260\pi\)
\(734\) 14.6209 0.539666
\(735\) −2.31759 −0.0854858
\(736\) −16.3067 −0.601073
\(737\) 17.0835 0.629279
\(738\) 15.8796 0.584536
\(739\) 27.5149 1.01215 0.506076 0.862489i \(-0.331095\pi\)
0.506076 + 0.862489i \(0.331095\pi\)
\(740\) 63.7347 2.34293
\(741\) 0.0155868 0.000572595 0
\(742\) −92.2347 −3.38604
\(743\) −46.5260 −1.70687 −0.853437 0.521197i \(-0.825486\pi\)
−0.853437 + 0.521197i \(0.825486\pi\)
\(744\) 11.3507 0.416137
\(745\) −0.791635 −0.0290033
\(746\) 2.66848 0.0977000
\(747\) −32.0205 −1.17157
\(748\) 60.5903 2.21540
\(749\) −24.2670 −0.886695
\(750\) −5.22527 −0.190800
\(751\) −11.4830 −0.419022 −0.209511 0.977806i \(-0.567187\pi\)
−0.209511 + 0.977806i \(0.567187\pi\)
\(752\) 87.9923 3.20875
\(753\) −2.49068 −0.0907655
\(754\) −0.315327 −0.0114835
\(755\) −6.27577 −0.228399
\(756\) −19.7441 −0.718086
\(757\) 23.0164 0.836546 0.418273 0.908321i \(-0.362635\pi\)
0.418273 + 0.908321i \(0.362635\pi\)
\(758\) −8.99888 −0.326854
\(759\) 1.25210 0.0454483
\(760\) 7.78272 0.282309
\(761\) 8.76873 0.317866 0.158933 0.987289i \(-0.449195\pi\)
0.158933 + 0.987289i \(0.449195\pi\)
\(762\) −3.23300 −0.117119
\(763\) 74.5287 2.69812
\(764\) 66.4390 2.40368
\(765\) 17.1362 0.619559
\(766\) −2.06625 −0.0746566
\(767\) 0.350463 0.0126545
\(768\) −4.41636 −0.159361
\(769\) −31.0232 −1.11873 −0.559363 0.828923i \(-0.688954\pi\)
−0.559363 + 0.828923i \(0.688954\pi\)
\(770\) 48.0874 1.73295
\(771\) 5.24487 0.188889
\(772\) −98.8350 −3.55715
\(773\) −28.9616 −1.04168 −0.520838 0.853656i \(-0.674380\pi\)
−0.520838 + 0.853656i \(0.674380\pi\)
\(774\) 31.4573 1.13071
\(775\) 27.6817 0.994356
\(776\) −10.4139 −0.373836
\(777\) −6.85489 −0.245918
\(778\) 5.37118 0.192566
\(779\) 1.66386 0.0596139
\(780\) −0.129232 −0.00462724
\(781\) −19.9404 −0.713524
\(782\) −22.4363 −0.802320
\(783\) −1.19170 −0.0425880
\(784\) 74.3220 2.65436
\(785\) −15.6869 −0.559890
\(786\) −3.26998 −0.116636
\(787\) 14.7106 0.524378 0.262189 0.965017i \(-0.415556\pi\)
0.262189 + 0.965017i \(0.415556\pi\)
\(788\) −67.2887 −2.39706
\(789\) 1.51994 0.0541114
\(790\) 7.13786 0.253954
\(791\) 11.0551 0.393072
\(792\) 65.3543 2.32226
\(793\) −0.893766 −0.0317386
\(794\) −83.6441 −2.96842
\(795\) −2.28157 −0.0809189
\(796\) 60.6840 2.15089
\(797\) −51.7450 −1.83290 −0.916451 0.400146i \(-0.868959\pi\)
−0.916451 + 0.400146i \(0.868959\pi\)
\(798\) −1.47316 −0.0521492
\(799\) 43.2611 1.53047
\(800\) 22.1924 0.784621
\(801\) −5.43995 −0.192211
\(802\) −3.92824 −0.138711
\(803\) 6.64856 0.234623
\(804\) 4.33918 0.153031
\(805\) −12.4365 −0.438330
\(806\) 2.64475 0.0931574
\(807\) −4.09428 −0.144126
\(808\) 126.281 4.44254
\(809\) −30.2174 −1.06239 −0.531194 0.847250i \(-0.678257\pi\)
−0.531194 + 0.847250i \(0.678257\pi\)
\(810\) 32.1780 1.13062
\(811\) −23.1150 −0.811679 −0.405839 0.913944i \(-0.633021\pi\)
−0.405839 + 0.913944i \(0.633021\pi\)
\(812\) 20.8149 0.730459
\(813\) 5.75841 0.201956
\(814\) 80.2927 2.81426
\(815\) 0.524238 0.0183632
\(816\) 5.87526 0.205675
\(817\) 3.29608 0.115315
\(818\) 47.1534 1.64868
\(819\) −1.30005 −0.0454275
\(820\) −13.7952 −0.481750
\(821\) 43.4539 1.51655 0.758276 0.651934i \(-0.226042\pi\)
0.758276 + 0.651934i \(0.226042\pi\)
\(822\) 1.80983 0.0631251
\(823\) 32.5375 1.13419 0.567093 0.823654i \(-0.308068\pi\)
0.567093 + 0.823654i \(0.308068\pi\)
\(824\) 91.8264 3.19892
\(825\) −1.70403 −0.0593267
\(826\) −33.1234 −1.15251
\(827\) 22.3875 0.778489 0.389245 0.921134i \(-0.372736\pi\)
0.389245 + 0.921134i \(0.372736\pi\)
\(828\) −29.7465 −1.03376
\(829\) 18.1641 0.630866 0.315433 0.948948i \(-0.397850\pi\)
0.315433 + 0.948948i \(0.397850\pi\)
\(830\) 39.8288 1.38248
\(831\) −2.96662 −0.102911
\(832\) 0.330830 0.0114695
\(833\) 36.5401 1.26604
\(834\) −6.01787 −0.208382
\(835\) −9.94191 −0.344054
\(836\) 12.0516 0.416813
\(837\) 9.99522 0.345485
\(838\) 10.5232 0.363519
\(839\) −1.39539 −0.0481741 −0.0240870 0.999710i \(-0.507668\pi\)
−0.0240870 + 0.999710i \(0.507668\pi\)
\(840\) 6.94015 0.239458
\(841\) −27.7437 −0.956678
\(842\) 0.733090 0.0252640
\(843\) 1.94798 0.0670921
\(844\) −88.2789 −3.03869
\(845\) 18.6209 0.640577
\(846\) 82.1225 2.82343
\(847\) −1.79130 −0.0615500
\(848\) 73.1667 2.51255
\(849\) −0.894732 −0.0307071
\(850\) 30.5344 1.04732
\(851\) −20.7656 −0.711835
\(852\) −5.06483 −0.173518
\(853\) 55.2005 1.89003 0.945014 0.327030i \(-0.106048\pi\)
0.945014 + 0.327030i \(0.106048\pi\)
\(854\) 84.4727 2.89060
\(855\) 3.40843 0.116566
\(856\) 41.0231 1.40214
\(857\) −29.8711 −1.02038 −0.510189 0.860062i \(-0.670425\pi\)
−0.510189 + 0.860062i \(0.670425\pi\)
\(858\) −0.162806 −0.00555809
\(859\) 51.6157 1.76111 0.880553 0.473949i \(-0.157172\pi\)
0.880553 + 0.473949i \(0.157172\pi\)
\(860\) −27.3282 −0.931884
\(861\) 1.48373 0.0505652
\(862\) −20.1566 −0.686537
\(863\) 22.1500 0.753996 0.376998 0.926214i \(-0.376956\pi\)
0.376998 + 0.926214i \(0.376956\pi\)
\(864\) 8.01317 0.272614
\(865\) −23.4233 −0.796415
\(866\) 49.5231 1.68286
\(867\) −0.139877 −0.00475046
\(868\) −174.581 −5.92567
\(869\) 6.28041 0.213048
\(870\) 0.737213 0.0249939
\(871\) 0.574481 0.0194656
\(872\) −125.990 −4.26656
\(873\) −4.56075 −0.154358
\(874\) −4.46265 −0.150951
\(875\) 45.6657 1.54378
\(876\) 1.68872 0.0570567
\(877\) 23.4426 0.791599 0.395800 0.918337i \(-0.370468\pi\)
0.395800 + 0.918337i \(0.370468\pi\)
\(878\) −69.5675 −2.34779
\(879\) −4.09051 −0.137970
\(880\) −38.1461 −1.28591
\(881\) 46.4242 1.56407 0.782035 0.623235i \(-0.214182\pi\)
0.782035 + 0.623235i \(0.214182\pi\)
\(882\) 69.3641 2.33561
\(883\) −35.8348 −1.20594 −0.602968 0.797765i \(-0.706015\pi\)
−0.602968 + 0.797765i \(0.706015\pi\)
\(884\) 2.03752 0.0685292
\(885\) −0.819359 −0.0275425
\(886\) −65.2827 −2.19322
\(887\) 51.3009 1.72252 0.861259 0.508167i \(-0.169677\pi\)
0.861259 + 0.508167i \(0.169677\pi\)
\(888\) 11.5881 0.388872
\(889\) 28.2544 0.947623
\(890\) 6.76651 0.226814
\(891\) 28.3126 0.948507
\(892\) 6.90266 0.231118
\(893\) 8.60476 0.287947
\(894\) −0.253312 −0.00847202
\(895\) 1.29827 0.0433964
\(896\) 29.1666 0.974389
\(897\) 0.0421053 0.00140586
\(898\) 41.4564 1.38342
\(899\) −10.5373 −0.351438
\(900\) 40.4831 1.34944
\(901\) 35.9721 1.19841
\(902\) −17.3792 −0.578663
\(903\) 2.93924 0.0978119
\(904\) −18.6885 −0.621569
\(905\) −28.9753 −0.963172
\(906\) −2.00816 −0.0667165
\(907\) −7.91590 −0.262843 −0.131422 0.991327i \(-0.541954\pi\)
−0.131422 + 0.991327i \(0.541954\pi\)
\(908\) −11.1694 −0.370668
\(909\) 55.3045 1.83434
\(910\) 1.61708 0.0536055
\(911\) 46.2018 1.53073 0.765367 0.643594i \(-0.222558\pi\)
0.765367 + 0.643594i \(0.222558\pi\)
\(912\) 1.16861 0.0386964
\(913\) 35.0443 1.15980
\(914\) 46.4557 1.53662
\(915\) 2.08956 0.0690789
\(916\) 60.9369 2.01341
\(917\) 28.5776 0.943715
\(918\) 11.0253 0.363888
\(919\) 50.7856 1.67526 0.837632 0.546235i \(-0.183939\pi\)
0.837632 + 0.546235i \(0.183939\pi\)
\(920\) 21.0238 0.693136
\(921\) −1.21887 −0.0401630
\(922\) 75.9014 2.49968
\(923\) −0.670553 −0.0220715
\(924\) 10.7469 0.353546
\(925\) 28.2607 0.929206
\(926\) −79.7436 −2.62054
\(927\) 40.2153 1.32084
\(928\) −8.44775 −0.277311
\(929\) 16.4618 0.540093 0.270046 0.962847i \(-0.412961\pi\)
0.270046 + 0.962847i \(0.412961\pi\)
\(930\) −6.18325 −0.202757
\(931\) 7.26794 0.238197
\(932\) −1.66630 −0.0545816
\(933\) 4.68906 0.153513
\(934\) 37.4786 1.22634
\(935\) −18.7544 −0.613335
\(936\) 2.19772 0.0718349
\(937\) 13.0454 0.426173 0.213087 0.977033i \(-0.431648\pi\)
0.213087 + 0.977033i \(0.431648\pi\)
\(938\) −54.2961 −1.77283
\(939\) 3.97202 0.129622
\(940\) −71.3431 −2.32695
\(941\) −10.2707 −0.334814 −0.167407 0.985888i \(-0.553539\pi\)
−0.167407 + 0.985888i \(0.553539\pi\)
\(942\) −5.01959 −0.163547
\(943\) 4.49466 0.146366
\(944\) 26.2757 0.855201
\(945\) 6.11136 0.198802
\(946\) −34.4279 −1.11935
\(947\) 52.7465 1.71403 0.857016 0.515291i \(-0.172316\pi\)
0.857016 + 0.515291i \(0.172316\pi\)
\(948\) 1.59521 0.0518101
\(949\) 0.223577 0.00725761
\(950\) 6.07339 0.197047
\(951\) −3.40642 −0.110461
\(952\) −109.421 −3.54636
\(953\) 21.6341 0.700796 0.350398 0.936601i \(-0.386046\pi\)
0.350398 + 0.936601i \(0.386046\pi\)
\(954\) 68.2858 2.21083
\(955\) −20.5647 −0.665460
\(956\) 49.8323 1.61169
\(957\) 0.648654 0.0209680
\(958\) −76.5389 −2.47286
\(959\) −15.8168 −0.510752
\(960\) −0.773459 −0.0249633
\(961\) 57.3796 1.85096
\(962\) 2.70007 0.0870537
\(963\) 17.9660 0.578947
\(964\) −37.2821 −1.20078
\(965\) 30.5922 0.984799
\(966\) −3.97951 −0.128039
\(967\) −31.9608 −1.02779 −0.513895 0.857853i \(-0.671798\pi\)
−0.513895 + 0.857853i \(0.671798\pi\)
\(968\) 3.02818 0.0973295
\(969\) 0.574541 0.0184569
\(970\) 5.67291 0.182146
\(971\) 56.7996 1.82279 0.911393 0.411536i \(-0.135008\pi\)
0.911393 + 0.411536i \(0.135008\pi\)
\(972\) 21.9651 0.704532
\(973\) 52.5925 1.68604
\(974\) −71.7975 −2.30054
\(975\) −0.0573028 −0.00183516
\(976\) −67.0094 −2.14492
\(977\) 17.5072 0.560105 0.280053 0.959985i \(-0.409648\pi\)
0.280053 + 0.959985i \(0.409648\pi\)
\(978\) 0.167748 0.00536401
\(979\) 5.95367 0.190280
\(980\) −60.2593 −1.92491
\(981\) −55.1772 −1.76167
\(982\) 19.4228 0.619808
\(983\) 9.56460 0.305063 0.152532 0.988299i \(-0.451257\pi\)
0.152532 + 0.988299i \(0.451257\pi\)
\(984\) −2.50822 −0.0799592
\(985\) 20.8277 0.663627
\(986\) −11.6232 −0.370158
\(987\) 7.67320 0.244240
\(988\) 0.405269 0.0128933
\(989\) 8.90388 0.283127
\(990\) −35.6014 −1.13149
\(991\) −23.3498 −0.741732 −0.370866 0.928686i \(-0.620939\pi\)
−0.370866 + 0.928686i \(0.620939\pi\)
\(992\) 70.8540 2.24962
\(993\) 5.49022 0.174227
\(994\) 63.3761 2.01017
\(995\) −18.7834 −0.595474
\(996\) 8.90119 0.282045
\(997\) −38.5827 −1.22193 −0.610964 0.791659i \(-0.709218\pi\)
−0.610964 + 0.791659i \(0.709218\pi\)
\(998\) 6.31127 0.199780
\(999\) 10.2043 0.322849
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 \(a_p\))