Properties

Label 6047.2.a.a.1.3
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77438 q^{2}\) \(-3.26218 q^{3}\) \(+5.69718 q^{4}\) \(+2.18536 q^{5}\) \(+9.05052 q^{6}\) \(+2.86186 q^{7}\) \(-10.2574 q^{8}\) \(+7.64181 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77438 q^{2}\) \(-3.26218 q^{3}\) \(+5.69718 q^{4}\) \(+2.18536 q^{5}\) \(+9.05052 q^{6}\) \(+2.86186 q^{7}\) \(-10.2574 q^{8}\) \(+7.64181 q^{9}\) \(-6.06301 q^{10}\) \(+1.00872 q^{11}\) \(-18.5852 q^{12}\) \(-0.310734 q^{13}\) \(-7.93988 q^{14}\) \(-7.12903 q^{15}\) \(+17.0635 q^{16}\) \(-2.88986 q^{17}\) \(-21.2013 q^{18}\) \(-0.819136 q^{19}\) \(+12.4504 q^{20}\) \(-9.33590 q^{21}\) \(-2.79857 q^{22}\) \(+5.98245 q^{23}\) \(+33.4614 q^{24}\) \(-0.224208 q^{25}\) \(+0.862095 q^{26}\) \(-15.1424 q^{27}\) \(+16.3045 q^{28}\) \(+4.28435 q^{29}\) \(+19.7786 q^{30}\) \(-5.07960 q^{31}\) \(-26.8259 q^{32}\) \(-3.29063 q^{33}\) \(+8.01758 q^{34}\) \(+6.25419 q^{35}\) \(+43.5368 q^{36}\) \(-6.54106 q^{37}\) \(+2.27259 q^{38}\) \(+1.01367 q^{39}\) \(-22.4161 q^{40}\) \(+5.84478 q^{41}\) \(+25.9013 q^{42}\) \(+8.07457 q^{43}\) \(+5.74686 q^{44}\) \(+16.7001 q^{45}\) \(-16.5976 q^{46}\) \(+0.356923 q^{47}\) \(-55.6643 q^{48}\) \(+1.19024 q^{49}\) \(+0.622037 q^{50}\) \(+9.42725 q^{51}\) \(-1.77031 q^{52}\) \(+5.30402 q^{53}\) \(+42.0108 q^{54}\) \(+2.20442 q^{55}\) \(-29.3552 q^{56}\) \(+2.67217 q^{57}\) \(-11.8864 q^{58}\) \(+7.92929 q^{59}\) \(-40.6154 q^{60}\) \(-11.3369 q^{61}\) \(+14.0927 q^{62}\) \(+21.8698 q^{63}\) \(+40.2982 q^{64}\) \(-0.679066 q^{65}\) \(+9.12944 q^{66}\) \(-8.70340 q^{67}\) \(-16.4641 q^{68}\) \(-19.5158 q^{69}\) \(-17.3515 q^{70}\) \(-2.88126 q^{71}\) \(-78.3850 q^{72}\) \(-6.95310 q^{73}\) \(+18.1474 q^{74}\) \(+0.731405 q^{75}\) \(-4.66677 q^{76}\) \(+2.88682 q^{77}\) \(-2.81231 q^{78}\) \(-16.6345 q^{79}\) \(+37.2899 q^{80}\) \(+26.4718 q^{81}\) \(-16.2156 q^{82}\) \(-17.8718 q^{83}\) \(-53.1883 q^{84}\) \(-6.31539 q^{85}\) \(-22.4019 q^{86}\) \(-13.9763 q^{87}\) \(-10.3468 q^{88}\) \(-0.0355791 q^{89}\) \(-46.3324 q^{90}\) \(-0.889278 q^{91}\) \(+34.0831 q^{92}\) \(+16.5706 q^{93}\) \(-0.990239 q^{94}\) \(-1.79011 q^{95}\) \(+87.5109 q^{96}\) \(-11.4073 q^{97}\) \(-3.30218 q^{98}\) \(+7.70845 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77438 −1.96178 −0.980891 0.194556i \(-0.937673\pi\)
−0.980891 + 0.194556i \(0.937673\pi\)
\(3\) −3.26218 −1.88342 −0.941710 0.336426i \(-0.890782\pi\)
−0.941710 + 0.336426i \(0.890782\pi\)
\(4\) 5.69718 2.84859
\(5\) 2.18536 0.977322 0.488661 0.872474i \(-0.337485\pi\)
0.488661 + 0.872474i \(0.337485\pi\)
\(6\) 9.05052 3.69486
\(7\) 2.86186 1.08168 0.540841 0.841125i \(-0.318106\pi\)
0.540841 + 0.841125i \(0.318106\pi\)
\(8\) −10.2574 −3.62653
\(9\) 7.64181 2.54727
\(10\) −6.06301 −1.91729
\(11\) 1.00872 0.304141 0.152070 0.988370i \(-0.451406\pi\)
0.152070 + 0.988370i \(0.451406\pi\)
\(12\) −18.5852 −5.36509
\(13\) −0.310734 −0.0861822 −0.0430911 0.999071i \(-0.513721\pi\)
−0.0430911 + 0.999071i \(0.513721\pi\)
\(14\) −7.93988 −2.12202
\(15\) −7.12903 −1.84071
\(16\) 17.0635 4.26588
\(17\) −2.88986 −0.700895 −0.350447 0.936582i \(-0.613970\pi\)
−0.350447 + 0.936582i \(0.613970\pi\)
\(18\) −21.2013 −4.99719
\(19\) −0.819136 −0.187923 −0.0939614 0.995576i \(-0.529953\pi\)
−0.0939614 + 0.995576i \(0.529953\pi\)
\(20\) 12.4504 2.78399
\(21\) −9.33590 −2.03726
\(22\) −2.79857 −0.596658
\(23\) 5.98245 1.24743 0.623714 0.781653i \(-0.285623\pi\)
0.623714 + 0.781653i \(0.285623\pi\)
\(24\) 33.4614 6.83029
\(25\) −0.224208 −0.0448415
\(26\) 0.862095 0.169071
\(27\) −15.1424 −2.91416
\(28\) 16.3045 3.08127
\(29\) 4.28435 0.795584 0.397792 0.917476i \(-0.369777\pi\)
0.397792 + 0.917476i \(0.369777\pi\)
\(30\) 19.7786 3.61107
\(31\) −5.07960 −0.912323 −0.456161 0.889897i \(-0.650776\pi\)
−0.456161 + 0.889897i \(0.650776\pi\)
\(32\) −26.8259 −4.74220
\(33\) −3.29063 −0.572824
\(34\) 8.01758 1.37500
\(35\) 6.25419 1.05715
\(36\) 43.5368 7.25613
\(37\) −6.54106 −1.07534 −0.537672 0.843154i \(-0.680696\pi\)
−0.537672 + 0.843154i \(0.680696\pi\)
\(38\) 2.27259 0.368664
\(39\) 1.01367 0.162317
\(40\) −22.4161 −3.54429
\(41\) 5.84478 0.912801 0.456400 0.889775i \(-0.349138\pi\)
0.456400 + 0.889775i \(0.349138\pi\)
\(42\) 25.9013 3.99666
\(43\) 8.07457 1.23136 0.615680 0.787996i \(-0.288881\pi\)
0.615680 + 0.787996i \(0.288881\pi\)
\(44\) 5.74686 0.866372
\(45\) 16.7001 2.48950
\(46\) −16.5976 −2.44718
\(47\) 0.356923 0.0520625 0.0260313 0.999661i \(-0.491713\pi\)
0.0260313 + 0.999661i \(0.491713\pi\)
\(48\) −55.6643 −8.03444
\(49\) 1.19024 0.170034
\(50\) 0.622037 0.0879693
\(51\) 9.42725 1.32008
\(52\) −1.77031 −0.245498
\(53\) 5.30402 0.728563 0.364281 0.931289i \(-0.381315\pi\)
0.364281 + 0.931289i \(0.381315\pi\)
\(54\) 42.0108 5.71695
\(55\) 2.20442 0.297243
\(56\) −29.3552 −3.92275
\(57\) 2.67217 0.353937
\(58\) −11.8864 −1.56076
\(59\) 7.92929 1.03231 0.516153 0.856496i \(-0.327364\pi\)
0.516153 + 0.856496i \(0.327364\pi\)
\(60\) −40.6154 −5.24342
\(61\) −11.3369 −1.45154 −0.725770 0.687938i \(-0.758516\pi\)
−0.725770 + 0.687938i \(0.758516\pi\)
\(62\) 14.0927 1.78978
\(63\) 21.8698 2.75533
\(64\) 40.2982 5.03728
\(65\) −0.679066 −0.0842278
\(66\) 9.12944 1.12376
\(67\) −8.70340 −1.06329 −0.531644 0.846968i \(-0.678426\pi\)
−0.531644 + 0.846968i \(0.678426\pi\)
\(68\) −16.4641 −1.99656
\(69\) −19.5158 −2.34943
\(70\) −17.3515 −2.07390
\(71\) −2.88126 −0.341943 −0.170971 0.985276i \(-0.554691\pi\)
−0.170971 + 0.985276i \(0.554691\pi\)
\(72\) −78.3850 −9.23776
\(73\) −6.95310 −0.813799 −0.406899 0.913473i \(-0.633390\pi\)
−0.406899 + 0.913473i \(0.633390\pi\)
\(74\) 18.1474 2.10959
\(75\) 0.731405 0.0844554
\(76\) −4.66677 −0.535315
\(77\) 2.88682 0.328983
\(78\) −2.81231 −0.318431
\(79\) −16.6345 −1.87153 −0.935765 0.352624i \(-0.885290\pi\)
−0.935765 + 0.352624i \(0.885290\pi\)
\(80\) 37.2899 4.16914
\(81\) 26.4718 2.94131
\(82\) −16.2156 −1.79072
\(83\) −17.8718 −1.96168 −0.980840 0.194814i \(-0.937590\pi\)
−0.980840 + 0.194814i \(0.937590\pi\)
\(84\) −53.1883 −5.80332
\(85\) −6.31539 −0.685000
\(86\) −22.4019 −2.41566
\(87\) −13.9763 −1.49842
\(88\) −10.3468 −1.10298
\(89\) −0.0355791 −0.00377138 −0.00188569 0.999998i \(-0.500600\pi\)
−0.00188569 + 0.999998i \(0.500600\pi\)
\(90\) −46.3324 −4.88386
\(91\) −0.889278 −0.0932217
\(92\) 34.0831 3.55341
\(93\) 16.5706 1.71829
\(94\) −0.990239 −0.102135
\(95\) −1.79011 −0.183661
\(96\) 87.5109 8.93155
\(97\) −11.4073 −1.15824 −0.579119 0.815243i \(-0.696604\pi\)
−0.579119 + 0.815243i \(0.696604\pi\)
\(98\) −3.30218 −0.333570
\(99\) 7.70845 0.774728
\(100\) −1.27735 −0.127735
\(101\) 12.6784 1.26155 0.630774 0.775966i \(-0.282737\pi\)
0.630774 + 0.775966i \(0.282737\pi\)
\(102\) −26.1548 −2.58971
\(103\) −1.59186 −0.156850 −0.0784252 0.996920i \(-0.524989\pi\)
−0.0784252 + 0.996920i \(0.524989\pi\)
\(104\) 3.18732 0.312543
\(105\) −20.4023 −1.99106
\(106\) −14.7154 −1.42928
\(107\) 3.14382 0.303925 0.151962 0.988386i \(-0.451441\pi\)
0.151962 + 0.988386i \(0.451441\pi\)
\(108\) −86.2691 −8.30125
\(109\) −14.3122 −1.37086 −0.685430 0.728139i \(-0.740386\pi\)
−0.685430 + 0.728139i \(0.740386\pi\)
\(110\) −6.11589 −0.583127
\(111\) 21.3381 2.02532
\(112\) 48.8334 4.61432
\(113\) −8.72018 −0.820326 −0.410163 0.912012i \(-0.634528\pi\)
−0.410163 + 0.912012i \(0.634528\pi\)
\(114\) −7.41361 −0.694348
\(115\) 13.0738 1.21914
\(116\) 24.4087 2.26629
\(117\) −2.37457 −0.219529
\(118\) −21.9989 −2.02516
\(119\) −8.27038 −0.758145
\(120\) 73.1252 6.67539
\(121\) −9.98248 −0.907499
\(122\) 31.4528 2.84761
\(123\) −19.0667 −1.71919
\(124\) −28.9394 −2.59884
\(125\) −11.4168 −1.02115
\(126\) −60.6751 −5.40537
\(127\) −10.4477 −0.927087 −0.463544 0.886074i \(-0.653422\pi\)
−0.463544 + 0.886074i \(0.653422\pi\)
\(128\) −58.1507 −5.13985
\(129\) −26.3407 −2.31917
\(130\) 1.88399 0.165237
\(131\) 15.6713 1.36920 0.684602 0.728917i \(-0.259976\pi\)
0.684602 + 0.728917i \(0.259976\pi\)
\(132\) −18.7473 −1.63174
\(133\) −2.34425 −0.203272
\(134\) 24.1465 2.08594
\(135\) −33.0916 −2.84807
\(136\) 29.6424 2.54182
\(137\) −11.0694 −0.945721 −0.472860 0.881137i \(-0.656779\pi\)
−0.472860 + 0.881137i \(0.656779\pi\)
\(138\) 54.1443 4.60907
\(139\) 16.4646 1.39651 0.698253 0.715851i \(-0.253961\pi\)
0.698253 + 0.715851i \(0.253961\pi\)
\(140\) 35.6313 3.01139
\(141\) −1.16435 −0.0980556
\(142\) 7.99371 0.670818
\(143\) −0.313444 −0.0262115
\(144\) 130.396 10.8663
\(145\) 9.36284 0.777541
\(146\) 19.2905 1.59650
\(147\) −3.88278 −0.320246
\(148\) −37.2656 −3.06322
\(149\) −8.52165 −0.698121 −0.349060 0.937100i \(-0.613499\pi\)
−0.349060 + 0.937100i \(0.613499\pi\)
\(150\) −2.02920 −0.165683
\(151\) 0.452528 0.0368262 0.0184131 0.999830i \(-0.494139\pi\)
0.0184131 + 0.999830i \(0.494139\pi\)
\(152\) 8.40220 0.681508
\(153\) −22.0838 −1.78537
\(154\) −8.00912 −0.645393
\(155\) −11.1007 −0.891633
\(156\) 5.77507 0.462376
\(157\) −22.5475 −1.79949 −0.899743 0.436421i \(-0.856246\pi\)
−0.899743 + 0.436421i \(0.856246\pi\)
\(158\) 46.1505 3.67154
\(159\) −17.3027 −1.37219
\(160\) −58.6242 −4.63465
\(161\) 17.1209 1.34932
\(162\) −73.4429 −5.77022
\(163\) −20.6365 −1.61638 −0.808189 0.588923i \(-0.799552\pi\)
−0.808189 + 0.588923i \(0.799552\pi\)
\(164\) 33.2988 2.60020
\(165\) −7.19120 −0.559834
\(166\) 49.5830 3.84839
\(167\) −1.02741 −0.0795034 −0.0397517 0.999210i \(-0.512657\pi\)
−0.0397517 + 0.999210i \(0.512657\pi\)
\(168\) 95.7619 7.38819
\(169\) −12.9034 −0.992573
\(170\) 17.5213 1.34382
\(171\) −6.25968 −0.478690
\(172\) 46.0023 3.50764
\(173\) −13.2993 −1.01113 −0.505563 0.862790i \(-0.668715\pi\)
−0.505563 + 0.862790i \(0.668715\pi\)
\(174\) 38.7756 2.93957
\(175\) −0.641650 −0.0485042
\(176\) 17.2123 1.29743
\(177\) −25.8668 −1.94427
\(178\) 0.0987100 0.00739863
\(179\) −6.91430 −0.516799 −0.258400 0.966038i \(-0.583195\pi\)
−0.258400 + 0.966038i \(0.583195\pi\)
\(180\) 95.1435 7.09158
\(181\) 4.37093 0.324889 0.162444 0.986718i \(-0.448062\pi\)
0.162444 + 0.986718i \(0.448062\pi\)
\(182\) 2.46719 0.182881
\(183\) 36.9829 2.73386
\(184\) −61.3643 −4.52384
\(185\) −14.2946 −1.05096
\(186\) −45.9730 −3.37091
\(187\) −2.91506 −0.213171
\(188\) 2.03345 0.148305
\(189\) −43.3355 −3.15219
\(190\) 4.96643 0.360303
\(191\) 5.48129 0.396612 0.198306 0.980140i \(-0.436456\pi\)
0.198306 + 0.980140i \(0.436456\pi\)
\(192\) −131.460 −9.48731
\(193\) 23.0753 1.66100 0.830500 0.557019i \(-0.188055\pi\)
0.830500 + 0.557019i \(0.188055\pi\)
\(194\) 31.6483 2.27221
\(195\) 2.21523 0.158636
\(196\) 6.78102 0.484358
\(197\) −22.1917 −1.58109 −0.790547 0.612402i \(-0.790203\pi\)
−0.790547 + 0.612402i \(0.790203\pi\)
\(198\) −21.3862 −1.51985
\(199\) 23.9947 1.70094 0.850471 0.526022i \(-0.176317\pi\)
0.850471 + 0.526022i \(0.176317\pi\)
\(200\) 2.29978 0.162619
\(201\) 28.3920 2.00262
\(202\) −35.1747 −2.47488
\(203\) 12.2612 0.860568
\(204\) 53.7088 3.76036
\(205\) 12.7729 0.892100
\(206\) 4.41642 0.307706
\(207\) 45.7167 3.17753
\(208\) −5.30222 −0.367643
\(209\) −0.826279 −0.0571549
\(210\) 56.6037 3.90603
\(211\) 16.2234 1.11687 0.558434 0.829549i \(-0.311402\pi\)
0.558434 + 0.829549i \(0.311402\pi\)
\(212\) 30.2180 2.07538
\(213\) 9.39919 0.644022
\(214\) −8.72215 −0.596234
\(215\) 17.6458 1.20344
\(216\) 155.322 10.5683
\(217\) −14.5371 −0.986843
\(218\) 39.7075 2.68933
\(219\) 22.6823 1.53272
\(220\) 12.5590 0.846725
\(221\) 0.897980 0.0604046
\(222\) −59.2001 −3.97325
\(223\) 14.5458 0.974058 0.487029 0.873386i \(-0.338081\pi\)
0.487029 + 0.873386i \(0.338081\pi\)
\(224\) −76.7720 −5.12954
\(225\) −1.71335 −0.114223
\(226\) 24.1931 1.60930
\(227\) 3.16511 0.210075 0.105038 0.994468i \(-0.466504\pi\)
0.105038 + 0.994468i \(0.466504\pi\)
\(228\) 15.2238 1.00822
\(229\) 19.7124 1.30263 0.651316 0.758807i \(-0.274217\pi\)
0.651316 + 0.758807i \(0.274217\pi\)
\(230\) −36.2717 −2.39168
\(231\) −9.41731 −0.619613
\(232\) −43.9462 −2.88521
\(233\) −4.35047 −0.285009 −0.142504 0.989794i \(-0.545516\pi\)
−0.142504 + 0.989794i \(0.545516\pi\)
\(234\) 6.58797 0.430669
\(235\) 0.780004 0.0508819
\(236\) 45.1746 2.94062
\(237\) 54.2648 3.52488
\(238\) 22.9452 1.48731
\(239\) −26.9472 −1.74307 −0.871535 0.490334i \(-0.836875\pi\)
−0.871535 + 0.490334i \(0.836875\pi\)
\(240\) −121.646 −7.85224
\(241\) 1.58736 0.102251 0.0511253 0.998692i \(-0.483719\pi\)
0.0511253 + 0.998692i \(0.483719\pi\)
\(242\) 27.6952 1.78031
\(243\) −40.9286 −2.62557
\(244\) −64.5883 −4.13484
\(245\) 2.60110 0.166178
\(246\) 52.8983 3.37267
\(247\) 0.254534 0.0161956
\(248\) 52.1034 3.30857
\(249\) 58.3009 3.69467
\(250\) 31.6744 2.00327
\(251\) −12.9515 −0.817492 −0.408746 0.912648i \(-0.634034\pi\)
−0.408746 + 0.912648i \(0.634034\pi\)
\(252\) 124.596 7.84882
\(253\) 6.03462 0.379393
\(254\) 28.9860 1.81874
\(255\) 20.6019 1.29014
\(256\) 80.7358 5.04599
\(257\) −2.31137 −0.144179 −0.0720896 0.997398i \(-0.522967\pi\)
−0.0720896 + 0.997398i \(0.522967\pi\)
\(258\) 73.0791 4.54970
\(259\) −18.7196 −1.16318
\(260\) −3.86876 −0.239930
\(261\) 32.7402 2.02657
\(262\) −43.4780 −2.68608
\(263\) 10.5650 0.651467 0.325734 0.945462i \(-0.394389\pi\)
0.325734 + 0.945462i \(0.394389\pi\)
\(264\) 33.7532 2.07737
\(265\) 11.5912 0.712040
\(266\) 6.50385 0.398776
\(267\) 0.116065 0.00710309
\(268\) −49.5848 −3.02888
\(269\) −1.58441 −0.0966032 −0.0483016 0.998833i \(-0.515381\pi\)
−0.0483016 + 0.998833i \(0.515381\pi\)
\(270\) 91.8087 5.58730
\(271\) −7.62050 −0.462912 −0.231456 0.972845i \(-0.574349\pi\)
−0.231456 + 0.972845i \(0.574349\pi\)
\(272\) −49.3112 −2.98993
\(273\) 2.90098 0.175576
\(274\) 30.7107 1.85530
\(275\) −0.226163 −0.0136381
\(276\) −111.185 −6.69256
\(277\) 2.50785 0.150682 0.0753410 0.997158i \(-0.475995\pi\)
0.0753410 + 0.997158i \(0.475995\pi\)
\(278\) −45.6789 −2.73964
\(279\) −38.8173 −2.32393
\(280\) −64.1516 −3.83379
\(281\) −10.1495 −0.605471 −0.302736 0.953075i \(-0.597900\pi\)
−0.302736 + 0.953075i \(0.597900\pi\)
\(282\) 3.23034 0.192364
\(283\) 16.5050 0.981120 0.490560 0.871407i \(-0.336792\pi\)
0.490560 + 0.871407i \(0.336792\pi\)
\(284\) −16.4151 −0.974055
\(285\) 5.83965 0.345911
\(286\) 0.869613 0.0514213
\(287\) 16.7269 0.987359
\(288\) −204.999 −12.0797
\(289\) −8.64869 −0.508747
\(290\) −25.9761 −1.52537
\(291\) 37.2127 2.18145
\(292\) −39.6131 −2.31818
\(293\) 7.84290 0.458187 0.229093 0.973404i \(-0.426424\pi\)
0.229093 + 0.973404i \(0.426424\pi\)
\(294\) 10.7723 0.628253
\(295\) 17.3283 1.00890
\(296\) 67.0942 3.89977
\(297\) −15.2745 −0.886314
\(298\) 23.6423 1.36956
\(299\) −1.85895 −0.107506
\(300\) 4.16695 0.240579
\(301\) 23.1083 1.33194
\(302\) −1.25549 −0.0722450
\(303\) −41.3592 −2.37603
\(304\) −13.9773 −0.801656
\(305\) −24.7752 −1.41862
\(306\) 61.2688 3.50250
\(307\) 0.329612 0.0188120 0.00940598 0.999956i \(-0.497006\pi\)
0.00940598 + 0.999956i \(0.497006\pi\)
\(308\) 16.4467 0.937139
\(309\) 5.19292 0.295415
\(310\) 30.7977 1.74919
\(311\) −17.4194 −0.987765 −0.493882 0.869529i \(-0.664423\pi\)
−0.493882 + 0.869529i \(0.664423\pi\)
\(312\) −10.3976 −0.588649
\(313\) −13.6638 −0.772323 −0.386162 0.922431i \(-0.626199\pi\)
−0.386162 + 0.922431i \(0.626199\pi\)
\(314\) 62.5553 3.53020
\(315\) 47.7933 2.69285
\(316\) −94.7699 −5.33123
\(317\) −7.30849 −0.410486 −0.205243 0.978711i \(-0.565798\pi\)
−0.205243 + 0.978711i \(0.565798\pi\)
\(318\) 48.0041 2.69194
\(319\) 4.32171 0.241969
\(320\) 88.0661 4.92304
\(321\) −10.2557 −0.572418
\(322\) −47.5000 −2.64707
\(323\) 2.36719 0.131714
\(324\) 150.815 8.37860
\(325\) 0.0696690 0.00386454
\(326\) 57.2536 3.17098
\(327\) 46.6889 2.58190
\(328\) −59.9521 −3.31030
\(329\) 1.02146 0.0563151
\(330\) 19.9511 1.09827
\(331\) −9.14908 −0.502879 −0.251439 0.967873i \(-0.580904\pi\)
−0.251439 + 0.967873i \(0.580904\pi\)
\(332\) −101.819 −5.58803
\(333\) −49.9856 −2.73919
\(334\) 2.85043 0.155968
\(335\) −19.0200 −1.03918
\(336\) −159.303 −8.69071
\(337\) 5.95989 0.324656 0.162328 0.986737i \(-0.448100\pi\)
0.162328 + 0.986737i \(0.448100\pi\)
\(338\) 35.7991 1.94721
\(339\) 28.4468 1.54502
\(340\) −35.9799 −1.95128
\(341\) −5.12389 −0.277474
\(342\) 17.3667 0.939086
\(343\) −16.6267 −0.897758
\(344\) −82.8240 −4.46557
\(345\) −42.6491 −2.29615
\(346\) 36.8973 1.98361
\(347\) 12.0883 0.648932 0.324466 0.945897i \(-0.394815\pi\)
0.324466 + 0.945897i \(0.394815\pi\)
\(348\) −79.6256 −4.26838
\(349\) −11.5816 −0.619948 −0.309974 0.950745i \(-0.600320\pi\)
−0.309974 + 0.950745i \(0.600320\pi\)
\(350\) 1.78018 0.0951547
\(351\) 4.70527 0.251149
\(352\) −27.0598 −1.44229
\(353\) −20.2605 −1.07836 −0.539180 0.842190i \(-0.681266\pi\)
−0.539180 + 0.842190i \(0.681266\pi\)
\(354\) 71.7642 3.81423
\(355\) −6.29659 −0.334188
\(356\) −0.202701 −0.0107431
\(357\) 26.9795 1.42790
\(358\) 19.1829 1.01385
\(359\) 0.617077 0.0325681 0.0162841 0.999867i \(-0.494816\pi\)
0.0162841 + 0.999867i \(0.494816\pi\)
\(360\) −171.299 −9.02827
\(361\) −18.3290 −0.964685
\(362\) −12.1266 −0.637361
\(363\) 32.5646 1.70920
\(364\) −5.06638 −0.265550
\(365\) −15.1950 −0.795344
\(366\) −102.605 −5.36324
\(367\) 14.5716 0.760629 0.380315 0.924857i \(-0.375816\pi\)
0.380315 + 0.924857i \(0.375816\pi\)
\(368\) 102.082 5.32138
\(369\) 44.6647 2.32515
\(370\) 39.6586 2.06175
\(371\) 15.1794 0.788073
\(372\) 94.4055 4.89470
\(373\) −0.455180 −0.0235683 −0.0117842 0.999931i \(-0.503751\pi\)
−0.0117842 + 0.999931i \(0.503751\pi\)
\(374\) 8.08749 0.418194
\(375\) 37.2435 1.92325
\(376\) −3.66109 −0.188807
\(377\) −1.33129 −0.0685651
\(378\) 120.229 6.18391
\(379\) −37.8095 −1.94214 −0.971072 0.238789i \(-0.923250\pi\)
−0.971072 + 0.238789i \(0.923250\pi\)
\(380\) −10.1986 −0.523175
\(381\) 34.0824 1.74609
\(382\) −15.2072 −0.778067
\(383\) 31.5926 1.61431 0.807154 0.590341i \(-0.201007\pi\)
0.807154 + 0.590341i \(0.201007\pi\)
\(384\) 189.698 9.68049
\(385\) 6.30873 0.321523
\(386\) −64.0198 −3.25852
\(387\) 61.7043 3.13661
\(388\) −64.9896 −3.29935
\(389\) 33.4195 1.69444 0.847218 0.531245i \(-0.178276\pi\)
0.847218 + 0.531245i \(0.178276\pi\)
\(390\) −6.14590 −0.311210
\(391\) −17.2885 −0.874315
\(392\) −12.2088 −0.616635
\(393\) −51.1225 −2.57879
\(394\) 61.5682 3.10176
\(395\) −36.3524 −1.82909
\(396\) 43.9164 2.20688
\(397\) 23.8153 1.19526 0.597628 0.801773i \(-0.296110\pi\)
0.597628 + 0.801773i \(0.296110\pi\)
\(398\) −66.5705 −3.33688
\(399\) 7.64737 0.382847
\(400\) −3.82577 −0.191289
\(401\) −13.4744 −0.672879 −0.336440 0.941705i \(-0.609223\pi\)
−0.336440 + 0.941705i \(0.609223\pi\)
\(402\) −78.7703 −3.92870
\(403\) 1.57841 0.0786260
\(404\) 72.2312 3.59364
\(405\) 57.8504 2.87461
\(406\) −34.0172 −1.68825
\(407\) −6.59810 −0.327056
\(408\) −96.6989 −4.78731
\(409\) 23.0857 1.14151 0.570756 0.821119i \(-0.306650\pi\)
0.570756 + 0.821119i \(0.306650\pi\)
\(410\) −35.4370 −1.75011
\(411\) 36.1103 1.78119
\(412\) −9.06910 −0.446803
\(413\) 22.6925 1.11663
\(414\) −126.836 −6.23363
\(415\) −39.0562 −1.91719
\(416\) 8.33573 0.408693
\(417\) −53.7103 −2.63021
\(418\) 2.29241 0.112126
\(419\) −4.23010 −0.206654 −0.103327 0.994647i \(-0.532949\pi\)
−0.103327 + 0.994647i \(0.532949\pi\)
\(420\) −116.236 −5.67171
\(421\) 20.9144 1.01930 0.509652 0.860380i \(-0.329774\pi\)
0.509652 + 0.860380i \(0.329774\pi\)
\(422\) −45.0100 −2.19105
\(423\) 2.72754 0.132617
\(424\) −54.4054 −2.64216
\(425\) 0.647929 0.0314292
\(426\) −26.0769 −1.26343
\(427\) −32.4446 −1.57010
\(428\) 17.9109 0.865757
\(429\) 1.02251 0.0493673
\(430\) −48.9562 −2.36088
\(431\) −31.8792 −1.53557 −0.767784 0.640709i \(-0.778641\pi\)
−0.767784 + 0.640709i \(0.778641\pi\)
\(432\) −258.383 −12.4315
\(433\) −6.16704 −0.296369 −0.148184 0.988960i \(-0.547343\pi\)
−0.148184 + 0.988960i \(0.547343\pi\)
\(434\) 40.3314 1.93597
\(435\) −30.5433 −1.46444
\(436\) −81.5392 −3.90502
\(437\) −4.90044 −0.234420
\(438\) −62.9292 −3.00687
\(439\) 8.98601 0.428879 0.214439 0.976737i \(-0.431208\pi\)
0.214439 + 0.976737i \(0.431208\pi\)
\(440\) −22.6115 −1.07796
\(441\) 9.09559 0.433123
\(442\) −2.49134 −0.118501
\(443\) 22.6312 1.07524 0.537621 0.843187i \(-0.319323\pi\)
0.537621 + 0.843187i \(0.319323\pi\)
\(444\) 121.567 5.76932
\(445\) −0.0777532 −0.00368585
\(446\) −40.3555 −1.91089
\(447\) 27.7991 1.31485
\(448\) 115.328 5.44873
\(449\) −0.171548 −0.00809587 −0.00404794 0.999992i \(-0.501289\pi\)
−0.00404794 + 0.999992i \(0.501289\pi\)
\(450\) 4.75349 0.224082
\(451\) 5.89574 0.277620
\(452\) −49.6805 −2.33677
\(453\) −1.47623 −0.0693592
\(454\) −8.78121 −0.412122
\(455\) −1.94339 −0.0911076
\(456\) −27.4095 −1.28357
\(457\) −3.51690 −0.164513 −0.0822567 0.996611i \(-0.526213\pi\)
−0.0822567 + 0.996611i \(0.526213\pi\)
\(458\) −54.6897 −2.55548
\(459\) 43.7595 2.04252
\(460\) 74.4838 3.47283
\(461\) −20.3090 −0.945884 −0.472942 0.881093i \(-0.656808\pi\)
−0.472942 + 0.881093i \(0.656808\pi\)
\(462\) 26.1272 1.21555
\(463\) 18.1645 0.844175 0.422087 0.906555i \(-0.361298\pi\)
0.422087 + 0.906555i \(0.361298\pi\)
\(464\) 73.1061 3.39386
\(465\) 36.2126 1.67932
\(466\) 12.0699 0.559125
\(467\) 22.1828 1.02650 0.513249 0.858240i \(-0.328442\pi\)
0.513249 + 0.858240i \(0.328442\pi\)
\(468\) −13.5284 −0.625349
\(469\) −24.9079 −1.15014
\(470\) −2.16403 −0.0998191
\(471\) 73.5539 3.38919
\(472\) −81.3338 −3.74369
\(473\) 8.14498 0.374507
\(474\) −150.551 −6.91504
\(475\) 0.183657 0.00842674
\(476\) −47.1179 −2.15964
\(477\) 40.5323 1.85585
\(478\) 74.7618 3.41952
\(479\) −22.6777 −1.03617 −0.518085 0.855329i \(-0.673355\pi\)
−0.518085 + 0.855329i \(0.673355\pi\)
\(480\) 191.243 8.72900
\(481\) 2.03253 0.0926756
\(482\) −4.40393 −0.200594
\(483\) −55.8515 −2.54133
\(484\) −56.8720 −2.58509
\(485\) −24.9291 −1.13197
\(486\) 113.551 5.15080
\(487\) −37.7175 −1.70914 −0.854572 0.519333i \(-0.826181\pi\)
−0.854572 + 0.519333i \(0.826181\pi\)
\(488\) 116.287 5.26406
\(489\) 67.3201 3.04432
\(490\) −7.21644 −0.326006
\(491\) −6.09245 −0.274949 −0.137474 0.990505i \(-0.543898\pi\)
−0.137474 + 0.990505i \(0.543898\pi\)
\(492\) −108.626 −4.89726
\(493\) −12.3812 −0.557620
\(494\) −0.706173 −0.0317722
\(495\) 16.8457 0.757159
\(496\) −86.6759 −3.89186
\(497\) −8.24577 −0.369873
\(498\) −161.749 −7.24814
\(499\) −39.0019 −1.74596 −0.872982 0.487752i \(-0.837817\pi\)
−0.872982 + 0.487752i \(0.837817\pi\)
\(500\) −65.0434 −2.90883
\(501\) 3.35160 0.149738
\(502\) 35.9324 1.60374
\(503\) −6.74645 −0.300809 −0.150405 0.988625i \(-0.548058\pi\)
−0.150405 + 0.988625i \(0.548058\pi\)
\(504\) −224.327 −9.99231
\(505\) 27.7069 1.23294
\(506\) −16.7423 −0.744287
\(507\) 42.0933 1.86943
\(508\) −59.5227 −2.64089
\(509\) −28.5549 −1.26567 −0.632837 0.774285i \(-0.718110\pi\)
−0.632837 + 0.774285i \(0.718110\pi\)
\(510\) −57.1575 −2.53098
\(511\) −19.8988 −0.880271
\(512\) −107.690 −4.75928
\(513\) 12.4037 0.547637
\(514\) 6.41262 0.282848
\(515\) −3.47878 −0.153293
\(516\) −150.068 −6.60636
\(517\) 0.360035 0.0158343
\(518\) 51.9353 2.28191
\(519\) 43.3847 1.90438
\(520\) 6.96544 0.305455
\(521\) 14.1306 0.619071 0.309536 0.950888i \(-0.399826\pi\)
0.309536 + 0.950888i \(0.399826\pi\)
\(522\) −90.8337 −3.97568
\(523\) −2.72062 −0.118965 −0.0594823 0.998229i \(-0.518945\pi\)
−0.0594823 + 0.998229i \(0.518945\pi\)
\(524\) 89.2820 3.90030
\(525\) 2.09318 0.0913538
\(526\) −29.3114 −1.27804
\(527\) 14.6793 0.639442
\(528\) −56.1497 −2.44360
\(529\) 12.7897 0.556074
\(530\) −32.1583 −1.39687
\(531\) 60.5941 2.62956
\(532\) −13.3556 −0.579040
\(533\) −1.81617 −0.0786672
\(534\) −0.322010 −0.0139347
\(535\) 6.87038 0.297032
\(536\) 89.2741 3.85605
\(537\) 22.5557 0.973350
\(538\) 4.39575 0.189514
\(539\) 1.20062 0.0517143
\(540\) −188.529 −8.11299
\(541\) 13.9598 0.600177 0.300089 0.953911i \(-0.402984\pi\)
0.300089 + 0.953911i \(0.402984\pi\)
\(542\) 21.1422 0.908133
\(543\) −14.2588 −0.611902
\(544\) 77.5232 3.32378
\(545\) −31.2773 −1.33977
\(546\) −8.04843 −0.344441
\(547\) 17.1894 0.734965 0.367483 0.930030i \(-0.380220\pi\)
0.367483 + 0.930030i \(0.380220\pi\)
\(548\) −63.0643 −2.69397
\(549\) −86.6343 −3.69746
\(550\) 0.627461 0.0267550
\(551\) −3.50947 −0.149508
\(552\) 200.181 8.52028
\(553\) −47.6057 −2.02440
\(554\) −6.95772 −0.295605
\(555\) 46.6315 1.97939
\(556\) 93.8016 3.97807
\(557\) −3.53460 −0.149766 −0.0748829 0.997192i \(-0.523858\pi\)
−0.0748829 + 0.997192i \(0.523858\pi\)
\(558\) 107.694 4.55905
\(559\) −2.50905 −0.106121
\(560\) 106.719 4.50968
\(561\) 9.50946 0.401490
\(562\) 28.1587 1.18780
\(563\) 28.8229 1.21474 0.607369 0.794420i \(-0.292225\pi\)
0.607369 + 0.794420i \(0.292225\pi\)
\(564\) −6.63349 −0.279320
\(565\) −19.0567 −0.801723
\(566\) −45.7911 −1.92474
\(567\) 75.7586 3.18156
\(568\) 29.5542 1.24007
\(569\) 18.7969 0.788005 0.394003 0.919109i \(-0.371090\pi\)
0.394003 + 0.919109i \(0.371090\pi\)
\(570\) −16.2014 −0.678602
\(571\) 10.8066 0.452244 0.226122 0.974099i \(-0.427395\pi\)
0.226122 + 0.974099i \(0.427395\pi\)
\(572\) −1.78575 −0.0746659
\(573\) −17.8810 −0.746987
\(574\) −46.4068 −1.93698
\(575\) −1.34131 −0.0559365
\(576\) 307.951 12.8313
\(577\) 14.1539 0.589235 0.294618 0.955615i \(-0.404808\pi\)
0.294618 + 0.955615i \(0.404808\pi\)
\(578\) 23.9948 0.998050
\(579\) −75.2759 −3.12836
\(580\) 53.3418 2.21490
\(581\) −51.1465 −2.12191
\(582\) −103.242 −4.27953
\(583\) 5.35027 0.221585
\(584\) 71.3207 2.95127
\(585\) −5.18929 −0.214551
\(586\) −21.7592 −0.898863
\(587\) 21.2805 0.878339 0.439170 0.898404i \(-0.355273\pi\)
0.439170 + 0.898404i \(0.355273\pi\)
\(588\) −22.1209 −0.912250
\(589\) 4.16088 0.171446
\(590\) −48.0754 −1.97923
\(591\) 72.3933 2.97786
\(592\) −111.614 −4.58729
\(593\) −14.3680 −0.590022 −0.295011 0.955494i \(-0.595323\pi\)
−0.295011 + 0.955494i \(0.595323\pi\)
\(594\) 42.3771 1.73876
\(595\) −18.0737 −0.740951
\(596\) −48.5494 −1.98866
\(597\) −78.2751 −3.20359
\(598\) 5.15744 0.210903
\(599\) 47.7184 1.94972 0.974860 0.222819i \(-0.0715259\pi\)
0.974860 + 0.222819i \(0.0715259\pi\)
\(600\) −7.50230 −0.306280
\(601\) −25.6015 −1.04431 −0.522153 0.852852i \(-0.674871\pi\)
−0.522153 + 0.852852i \(0.674871\pi\)
\(602\) −64.1111 −2.61297
\(603\) −66.5097 −2.70848
\(604\) 2.57814 0.104903
\(605\) −21.8153 −0.886918
\(606\) 114.746 4.66124
\(607\) 39.3364 1.59662 0.798308 0.602249i \(-0.205729\pi\)
0.798308 + 0.602249i \(0.205729\pi\)
\(608\) 21.9741 0.891166
\(609\) −39.9982 −1.62081
\(610\) 68.7357 2.78303
\(611\) −0.110908 −0.00448686
\(612\) −125.815 −5.08578
\(613\) 23.1516 0.935086 0.467543 0.883970i \(-0.345139\pi\)
0.467543 + 0.883970i \(0.345139\pi\)
\(614\) −0.914470 −0.0369050
\(615\) −41.6676 −1.68020
\(616\) −29.6112 −1.19307
\(617\) −18.9182 −0.761617 −0.380809 0.924654i \(-0.624354\pi\)
−0.380809 + 0.924654i \(0.624354\pi\)
\(618\) −14.4071 −0.579540
\(619\) −3.95811 −0.159090 −0.0795449 0.996831i \(-0.525347\pi\)
−0.0795449 + 0.996831i \(0.525347\pi\)
\(620\) −63.2430 −2.53990
\(621\) −90.5887 −3.63520
\(622\) 48.3281 1.93778
\(623\) −0.101822 −0.00407943
\(624\) 17.2968 0.692426
\(625\) −23.8287 −0.953148
\(626\) 37.9086 1.51513
\(627\) 2.69547 0.107647
\(628\) −128.457 −5.12600
\(629\) 18.9028 0.753703
\(630\) −132.597 −5.28278
\(631\) 3.24478 0.129173 0.0645863 0.997912i \(-0.479427\pi\)
0.0645863 + 0.997912i \(0.479427\pi\)
\(632\) 170.627 6.78717
\(633\) −52.9238 −2.10353
\(634\) 20.2765 0.805284
\(635\) −22.8321 −0.906063
\(636\) −98.5764 −3.90881
\(637\) −0.369849 −0.0146539
\(638\) −11.9901 −0.474691
\(639\) −22.0181 −0.871021
\(640\) −127.080 −5.02329
\(641\) 39.6131 1.56462 0.782312 0.622887i \(-0.214040\pi\)
0.782312 + 0.622887i \(0.214040\pi\)
\(642\) 28.4532 1.12296
\(643\) 20.8230 0.821180 0.410590 0.911820i \(-0.365323\pi\)
0.410590 + 0.911820i \(0.365323\pi\)
\(644\) 97.5411 3.84366
\(645\) −57.5638 −2.26657
\(646\) −6.56749 −0.258394
\(647\) 15.1733 0.596526 0.298263 0.954484i \(-0.403593\pi\)
0.298263 + 0.954484i \(0.403593\pi\)
\(648\) −271.532 −10.6668
\(649\) 7.99844 0.313966
\(650\) −0.193288 −0.00758139
\(651\) 47.4226 1.85864
\(652\) −117.570 −4.60440
\(653\) −26.4551 −1.03527 −0.517635 0.855602i \(-0.673187\pi\)
−0.517635 + 0.855602i \(0.673187\pi\)
\(654\) −129.533 −5.06513
\(655\) 34.2473 1.33815
\(656\) 99.7325 3.89390
\(657\) −53.1343 −2.07297
\(658\) −2.83392 −0.110478
\(659\) 2.44877 0.0953907 0.0476953 0.998862i \(-0.484812\pi\)
0.0476953 + 0.998862i \(0.484812\pi\)
\(660\) −40.9696 −1.59474
\(661\) 27.8714 1.08407 0.542037 0.840355i \(-0.317653\pi\)
0.542037 + 0.840355i \(0.317653\pi\)
\(662\) 25.3830 0.986539
\(663\) −2.92937 −0.113767
\(664\) 183.318 7.11410
\(665\) −5.12303 −0.198663
\(666\) 138.679 5.37370
\(667\) 25.6309 0.992433
\(668\) −5.85334 −0.226473
\(669\) −47.4510 −1.83456
\(670\) 52.7688 2.03864
\(671\) −11.4357 −0.441472
\(672\) 250.444 9.66109
\(673\) −44.9781 −1.73378 −0.866889 0.498502i \(-0.833884\pi\)
−0.866889 + 0.498502i \(0.833884\pi\)
\(674\) −16.5350 −0.636904
\(675\) 3.39504 0.130675
\(676\) −73.5133 −2.82743
\(677\) 38.5268 1.48070 0.740352 0.672220i \(-0.234659\pi\)
0.740352 + 0.672220i \(0.234659\pi\)
\(678\) −78.9222 −3.03099
\(679\) −32.6462 −1.25285
\(680\) 64.7794 2.48418
\(681\) −10.3251 −0.395660
\(682\) 14.2156 0.544344
\(683\) 0.0349168 0.00133605 0.000668026 1.00000i \(-0.499787\pi\)
0.000668026 1.00000i \(0.499787\pi\)
\(684\) −35.6626 −1.36359
\(685\) −24.1906 −0.924274
\(686\) 46.1288 1.76121
\(687\) −64.3054 −2.45340
\(688\) 137.781 5.25283
\(689\) −1.64814 −0.0627891
\(690\) 118.325 4.50454
\(691\) 35.7472 1.35989 0.679943 0.733265i \(-0.262005\pi\)
0.679943 + 0.733265i \(0.262005\pi\)
\(692\) −75.7685 −2.88029
\(693\) 22.0605 0.838009
\(694\) −33.5374 −1.27306
\(695\) 35.9810 1.36484
\(696\) 143.360 5.43406
\(697\) −16.8906 −0.639777
\(698\) 32.1317 1.21620
\(699\) 14.1920 0.536791
\(700\) −3.65560 −0.138169
\(701\) −22.0960 −0.834554 −0.417277 0.908779i \(-0.637015\pi\)
−0.417277 + 0.908779i \(0.637015\pi\)
\(702\) −13.0542 −0.492699
\(703\) 5.35802 0.202082
\(704\) 40.6496 1.53204
\(705\) −2.54451 −0.0958319
\(706\) 56.2105 2.11551
\(707\) 36.2838 1.36459
\(708\) −147.368 −5.53842
\(709\) −27.6601 −1.03880 −0.519399 0.854532i \(-0.673844\pi\)
−0.519399 + 0.854532i \(0.673844\pi\)
\(710\) 17.4691 0.655605
\(711\) −127.118 −4.76729
\(712\) 0.364949 0.0136770
\(713\) −30.3884 −1.13806
\(714\) −74.8513 −2.80124
\(715\) −0.684988 −0.0256171
\(716\) −39.3920 −1.47215
\(717\) 87.9066 3.28293
\(718\) −1.71201 −0.0638915
\(719\) 9.99841 0.372878 0.186439 0.982467i \(-0.440305\pi\)
0.186439 + 0.982467i \(0.440305\pi\)
\(720\) 284.962 10.6199
\(721\) −4.55567 −0.169662
\(722\) 50.8516 1.89250
\(723\) −5.17824 −0.192581
\(724\) 24.9020 0.925475
\(725\) −0.960583 −0.0356752
\(726\) −90.3467 −3.35308
\(727\) −50.3564 −1.86761 −0.933807 0.357778i \(-0.883535\pi\)
−0.933807 + 0.357778i \(0.883535\pi\)
\(728\) 9.12167 0.338072
\(729\) 54.1009 2.00374
\(730\) 42.1568 1.56029
\(731\) −23.3344 −0.863054
\(732\) 210.699 7.78764
\(733\) 35.7919 1.32200 0.661002 0.750385i \(-0.270132\pi\)
0.661002 + 0.750385i \(0.270132\pi\)
\(734\) −40.4270 −1.49219
\(735\) −8.48526 −0.312983
\(736\) −160.485 −5.91554
\(737\) −8.77929 −0.323389
\(738\) −123.917 −4.56144
\(739\) 16.4371 0.604650 0.302325 0.953205i \(-0.402237\pi\)
0.302325 + 0.953205i \(0.402237\pi\)
\(740\) −81.4388 −2.99375
\(741\) −0.830335 −0.0305031
\(742\) −42.1133 −1.54603
\(743\) 46.7796 1.71618 0.858089 0.513500i \(-0.171652\pi\)
0.858089 + 0.513500i \(0.171652\pi\)
\(744\) −169.971 −6.23143
\(745\) −18.6229 −0.682289
\(746\) 1.26284 0.0462359
\(747\) −136.573 −4.99693
\(748\) −16.6076 −0.607236
\(749\) 8.99718 0.328750
\(750\) −103.328 −3.77299
\(751\) −38.4969 −1.40477 −0.702385 0.711797i \(-0.747882\pi\)
−0.702385 + 0.711797i \(0.747882\pi\)
\(752\) 6.09036 0.222093
\(753\) 42.2501 1.53968
\(754\) 3.69352 0.134510
\(755\) 0.988936 0.0359911
\(756\) −246.890 −8.97930
\(757\) −48.4461 −1.76080 −0.880402 0.474228i \(-0.842727\pi\)
−0.880402 + 0.474228i \(0.842727\pi\)
\(758\) 104.898 3.81006
\(759\) −19.6860 −0.714557
\(760\) 18.3618 0.666053
\(761\) −5.33776 −0.193494 −0.0967469 0.995309i \(-0.530844\pi\)
−0.0967469 + 0.995309i \(0.530844\pi\)
\(762\) −94.5575 −3.42546
\(763\) −40.9595 −1.48283
\(764\) 31.2279 1.12979
\(765\) −48.2610 −1.74488
\(766\) −87.6500 −3.16692
\(767\) −2.46390 −0.0889664
\(768\) −263.375 −9.50371
\(769\) 53.0873 1.91438 0.957188 0.289468i \(-0.0934784\pi\)
0.957188 + 0.289468i \(0.0934784\pi\)
\(770\) −17.5028 −0.630757
\(771\) 7.54010 0.271550
\(772\) 131.464 4.73151
\(773\) −12.4277 −0.446995 −0.223498 0.974704i \(-0.571747\pi\)
−0.223498 + 0.974704i \(0.571747\pi\)
\(774\) −171.191 −6.15334
\(775\) 1.13888 0.0409099
\(776\) 117.009 4.20039
\(777\) 61.0667 2.19076
\(778\) −92.7184 −3.32412
\(779\) −4.78767 −0.171536
\(780\) 12.6206 0.451890
\(781\) −2.90639 −0.103999
\(782\) 47.9648 1.71522
\(783\) −64.8754 −2.31846
\(784\) 20.3097 0.725346
\(785\) −49.2743 −1.75868
\(786\) 141.833 5.05902
\(787\) 23.1385 0.824798 0.412399 0.911003i \(-0.364691\pi\)
0.412399 + 0.911003i \(0.364691\pi\)
\(788\) −126.430 −4.50389
\(789\) −34.4650 −1.22699
\(790\) 100.855 3.58827
\(791\) −24.9559 −0.887331
\(792\) −79.0685 −2.80958
\(793\) 3.52276 0.125097
\(794\) −66.0727 −2.34483
\(795\) −37.8125 −1.34107
\(796\) 136.702 4.84529
\(797\) 15.9583 0.565271 0.282636 0.959227i \(-0.408791\pi\)
0.282636 + 0.959227i \(0.408791\pi\)
\(798\) −21.2167 −0.751063
\(799\) −1.03146 −0.0364903
\(800\) 6.01457 0.212647
\(801\) −0.271889 −0.00960672
\(802\) 37.3831 1.32004
\(803\) −7.01373 −0.247509
\(804\) 161.755 5.70464
\(805\) 37.4154 1.31872
\(806\) −4.37910 −0.154247
\(807\) 5.16863 0.181944
\(808\) −130.047 −4.57505
\(809\) −6.87759 −0.241803 −0.120902 0.992664i \(-0.538579\pi\)
−0.120902 + 0.992664i \(0.538579\pi\)
\(810\) −160.499 −5.63936
\(811\) −1.45082 −0.0509453 −0.0254726 0.999676i \(-0.508109\pi\)
−0.0254726 + 0.999676i \(0.508109\pi\)
\(812\) 69.8543 2.45141
\(813\) 24.8594 0.871858
\(814\) 18.3056 0.641613
\(815\) −45.0982 −1.57972
\(816\) 160.862 5.63130
\(817\) −6.61417 −0.231401
\(818\) −64.0484 −2.23940
\(819\) −6.79569 −0.237461
\(820\) 72.7697 2.54123
\(821\) 29.4821 1.02893 0.514466 0.857511i \(-0.327990\pi\)
0.514466 + 0.857511i \(0.327990\pi\)
\(822\) −100.184 −3.49431
\(823\) −20.9623 −0.730698 −0.365349 0.930871i \(-0.619050\pi\)
−0.365349 + 0.930871i \(0.619050\pi\)
\(824\) 16.3283 0.568823
\(825\) 0.737783 0.0256863
\(826\) −62.9577 −2.19058
\(827\) −51.9104 −1.80510 −0.902550 0.430585i \(-0.858307\pi\)
−0.902550 + 0.430585i \(0.858307\pi\)
\(828\) 260.457 9.05149
\(829\) 35.9236 1.24768 0.623840 0.781552i \(-0.285572\pi\)
0.623840 + 0.781552i \(0.285572\pi\)
\(830\) 108.357 3.76112
\(831\) −8.18105 −0.283798
\(832\) −12.5220 −0.434124
\(833\) −3.43963 −0.119176
\(834\) 149.013 5.15989
\(835\) −2.24526 −0.0777004
\(836\) −4.70746 −0.162811
\(837\) 76.9174 2.65865
\(838\) 11.7359 0.405410
\(839\) −1.52939 −0.0528003 −0.0264002 0.999651i \(-0.508404\pi\)
−0.0264002 + 0.999651i \(0.508404\pi\)
\(840\) 209.274 7.22064
\(841\) −10.6444 −0.367047
\(842\) −58.0244 −1.99965
\(843\) 33.1096 1.14036
\(844\) 92.4279 3.18150
\(845\) −28.1987 −0.970063
\(846\) −7.56722 −0.260166
\(847\) −28.5685 −0.981624
\(848\) 90.5052 3.10796
\(849\) −53.8422 −1.84786
\(850\) −1.79760 −0.0616572
\(851\) −39.1316 −1.34141
\(852\) 53.5489 1.83456
\(853\) −24.1138 −0.825642 −0.412821 0.910812i \(-0.635456\pi\)
−0.412821 + 0.910812i \(0.635456\pi\)
\(854\) 90.0136 3.08020
\(855\) −13.6797 −0.467834
\(856\) −32.2474 −1.10219
\(857\) 7.86522 0.268671 0.134335 0.990936i \(-0.457110\pi\)
0.134335 + 0.990936i \(0.457110\pi\)
\(858\) −2.83683 −0.0968478
\(859\) 44.2552 1.50997 0.754985 0.655742i \(-0.227644\pi\)
0.754985 + 0.655742i \(0.227644\pi\)
\(860\) 100.531 3.42810
\(861\) −54.5662 −1.85961
\(862\) 88.4451 3.01245
\(863\) −15.5694 −0.529989 −0.264994 0.964250i \(-0.585370\pi\)
−0.264994 + 0.964250i \(0.585370\pi\)
\(864\) 406.209 13.8195
\(865\) −29.0637 −0.988196
\(866\) 17.1097 0.581411
\(867\) 28.2136 0.958184
\(868\) −82.8205 −2.81111
\(869\) −16.7796 −0.569208
\(870\) 84.7386 2.87291
\(871\) 2.70444 0.0916366
\(872\) 146.806 4.97147
\(873\) −87.1726 −2.95035
\(874\) 13.5957 0.459881
\(875\) −32.6732 −1.10456
\(876\) 129.225 4.36611
\(877\) 18.8844 0.637681 0.318840 0.947808i \(-0.396707\pi\)
0.318840 + 0.947808i \(0.396707\pi\)
\(878\) −24.9306 −0.841367
\(879\) −25.5849 −0.862958
\(880\) 37.6151 1.26800
\(881\) −15.9961 −0.538923 −0.269462 0.963011i \(-0.586846\pi\)
−0.269462 + 0.963011i \(0.586846\pi\)
\(882\) −25.2346 −0.849694
\(883\) −5.71942 −0.192474 −0.0962370 0.995358i \(-0.530681\pi\)
−0.0962370 + 0.995358i \(0.530681\pi\)
\(884\) 5.11595 0.172068
\(885\) −56.5282 −1.90017
\(886\) −62.7876 −2.10939
\(887\) 48.9667 1.64414 0.822071 0.569385i \(-0.192819\pi\)
0.822071 + 0.569385i \(0.192819\pi\)
\(888\) −218.873 −7.34491
\(889\) −29.9000 −1.00281
\(890\) 0.215717 0.00723084
\(891\) 26.7027 0.894573
\(892\) 82.8700 2.77469
\(893\) −0.292368 −0.00978373
\(894\) −77.1254 −2.57946
\(895\) −15.1102 −0.505079
\(896\) −166.419 −5.55968
\(897\) 6.06424 0.202479
\(898\) 0.475941 0.0158823
\(899\) −21.7628 −0.725829
\(900\) −9.76127 −0.325376
\(901\) −15.3279 −0.510646
\(902\) −16.3570 −0.544630
\(903\) −75.3833 −2.50860
\(904\) 89.4463 2.97494
\(905\) 9.55205 0.317521
\(906\) 4.09562 0.136068
\(907\) 37.1397 1.23320 0.616602 0.787275i \(-0.288509\pi\)
0.616602 + 0.787275i \(0.288509\pi\)
\(908\) 18.0322 0.598419
\(909\) 96.8859 3.21350
\(910\) 5.39171 0.178733
\(911\) −10.4871 −0.347453 −0.173726 0.984794i \(-0.555581\pi\)
−0.173726 + 0.984794i \(0.555581\pi\)
\(912\) 45.5966 1.50985
\(913\) −18.0276 −0.596627
\(914\) 9.75720 0.322740
\(915\) 80.8210 2.67186
\(916\) 112.305 3.71067
\(917\) 44.8490 1.48104
\(918\) −121.405 −4.00698
\(919\) −56.6739 −1.86950 −0.934750 0.355307i \(-0.884376\pi\)
−0.934750 + 0.355307i \(0.884376\pi\)
\(920\) −134.103 −4.42125
\(921\) −1.07525 −0.0354308
\(922\) 56.3449 1.85562
\(923\) 0.895307 0.0294694
\(924\) −53.6521 −1.76503
\(925\) 1.46656 0.0482201
\(926\) −50.3952 −1.65609
\(927\) −12.1647 −0.399540
\(928\) −114.932 −3.77281
\(929\) 2.95513 0.0969545 0.0484773 0.998824i \(-0.484563\pi\)
0.0484773 + 0.998824i \(0.484563\pi\)
\(930\) −100.468 −3.29446
\(931\) −0.974969 −0.0319533
\(932\) −24.7854 −0.811874
\(933\) 56.8253 1.86038
\(934\) −61.5436 −2.01377
\(935\) −6.37046 −0.208336
\(936\) 24.3569 0.796131
\(937\) 55.1764 1.80253 0.901267 0.433264i \(-0.142638\pi\)
0.901267 + 0.433264i \(0.142638\pi\)
\(938\) 69.1040 2.25632
\(939\) 44.5737 1.45461
\(940\) 4.44383 0.144942
\(941\) 12.9030 0.420625 0.210312 0.977634i \(-0.432552\pi\)
0.210312 + 0.977634i \(0.432552\pi\)
\(942\) −204.067 −6.64885
\(943\) 34.9661 1.13865
\(944\) 135.302 4.40369
\(945\) −94.7035 −3.08071
\(946\) −22.5973 −0.734700
\(947\) −31.6465 −1.02837 −0.514186 0.857679i \(-0.671906\pi\)
−0.514186 + 0.857679i \(0.671906\pi\)
\(948\) 309.156 10.0409
\(949\) 2.16057 0.0701350
\(950\) −0.509533 −0.0165314
\(951\) 23.8416 0.773117
\(952\) 84.8325 2.74944
\(953\) −32.8076 −1.06274 −0.531371 0.847139i \(-0.678323\pi\)
−0.531371 + 0.847139i \(0.678323\pi\)
\(954\) −112.452 −3.64077
\(955\) 11.9786 0.387618
\(956\) −153.523 −4.96529
\(957\) −14.0982 −0.455730
\(958\) 62.9165 2.03274
\(959\) −31.6790 −1.02297
\(960\) −287.287 −9.27216
\(961\) −5.19767 −0.167667
\(962\) −5.63902 −0.181809
\(963\) 24.0245 0.774178
\(964\) 9.04346 0.291270
\(965\) 50.4279 1.62333
\(966\) 154.953 4.98554
\(967\) 15.2763 0.491254 0.245627 0.969364i \(-0.421006\pi\)
0.245627 + 0.969364i \(0.421006\pi\)
\(968\) 102.394 3.29107
\(969\) −7.72220 −0.248073
\(970\) 69.1628 2.22068
\(971\) −21.6320 −0.694203 −0.347101 0.937828i \(-0.612834\pi\)
−0.347101 + 0.937828i \(0.612834\pi\)
\(972\) −233.178 −7.47918
\(973\) 47.1193 1.51057
\(974\) 104.643 3.35297
\(975\) −0.227273 −0.00727855
\(976\) −193.447 −6.19209
\(977\) −25.1584 −0.804889 −0.402445 0.915444i \(-0.631839\pi\)
−0.402445 + 0.915444i \(0.631839\pi\)
\(978\) −186.771 −5.97229
\(979\) −0.0358894 −0.00114703
\(980\) 14.8190 0.473374
\(981\) −109.371 −3.49195
\(982\) 16.9028 0.539389
\(983\) 24.2438 0.773258 0.386629 0.922235i \(-0.373639\pi\)
0.386629 + 0.922235i \(0.373639\pi\)
\(984\) 195.575 6.23469
\(985\) −48.4968 −1.54524
\(986\) 34.3501 1.09393
\(987\) −3.33219 −0.106065
\(988\) 1.45013 0.0461346
\(989\) 48.3057 1.53603
\(990\) −46.7364 −1.48538
\(991\) 5.90834 0.187685 0.0938423 0.995587i \(-0.470085\pi\)
0.0938423 + 0.995587i \(0.470085\pi\)
\(992\) 136.265 4.32641
\(993\) 29.8459 0.947132
\(994\) 22.8769 0.725611
\(995\) 52.4371 1.66237
\(996\) 332.151 10.5246
\(997\) 43.7386 1.38522 0.692608 0.721314i \(-0.256461\pi\)
0.692608 + 0.721314i \(0.256461\pi\)
\(998\) 108.206 3.42520
\(999\) 99.0475 3.13372
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 \(a_p\))