Properties

Label 8003.2.a.c.1.2
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.76521 q^{2}\) \(+1.30852 q^{3}\) \(+5.64636 q^{4}\) \(-2.58270 q^{5}\) \(-3.61833 q^{6}\) \(-0.870652 q^{7}\) \(-10.0829 q^{8}\) \(-1.28777 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.76521 q^{2}\) \(+1.30852 q^{3}\) \(+5.64636 q^{4}\) \(-2.58270 q^{5}\) \(-3.61833 q^{6}\) \(-0.870652 q^{7}\) \(-10.0829 q^{8}\) \(-1.28777 q^{9}\) \(+7.14170 q^{10}\) \(-1.36817 q^{11}\) \(+7.38839 q^{12}\) \(-1.36903 q^{13}\) \(+2.40753 q^{14}\) \(-3.37952 q^{15}\) \(+16.5887 q^{16}\) \(+6.73794 q^{17}\) \(+3.56095 q^{18}\) \(+0.887237 q^{19}\) \(-14.5829 q^{20}\) \(-1.13927 q^{21}\) \(+3.78328 q^{22}\) \(-8.40069 q^{23}\) \(-13.1938 q^{24}\) \(+1.67034 q^{25}\) \(+3.78564 q^{26}\) \(-5.61064 q^{27}\) \(-4.91602 q^{28}\) \(-5.53716 q^{29}\) \(+9.34506 q^{30}\) \(+9.82817 q^{31}\) \(-25.7053 q^{32}\) \(-1.79029 q^{33}\) \(-18.6318 q^{34}\) \(+2.24863 q^{35}\) \(-7.27122 q^{36}\) \(-1.35972 q^{37}\) \(-2.45339 q^{38}\) \(-1.79140 q^{39}\) \(+26.0412 q^{40}\) \(-9.71324 q^{41}\) \(+3.15031 q^{42}\) \(-2.00043 q^{43}\) \(-7.72521 q^{44}\) \(+3.32593 q^{45}\) \(+23.2296 q^{46}\) \(+4.14628 q^{47}\) \(+21.7067 q^{48}\) \(-6.24197 q^{49}\) \(-4.61883 q^{50}\) \(+8.81674 q^{51}\) \(-7.73002 q^{52}\) \(-1.00000 q^{53}\) \(+15.5146 q^{54}\) \(+3.53358 q^{55}\) \(+8.77873 q^{56}\) \(+1.16097 q^{57}\) \(+15.3114 q^{58}\) \(-9.95832 q^{59}\) \(-19.0820 q^{60}\) \(-11.1445 q^{61}\) \(-27.1769 q^{62}\) \(+1.12120 q^{63}\) \(+37.9029 q^{64}\) \(+3.53578 q^{65}\) \(+4.95051 q^{66}\) \(+3.20481 q^{67}\) \(+38.0449 q^{68}\) \(-10.9925 q^{69}\) \(-6.21793 q^{70}\) \(+13.5027 q^{71}\) \(+12.9845 q^{72}\) \(+4.99035 q^{73}\) \(+3.75991 q^{74}\) \(+2.18567 q^{75}\) \(+5.00966 q^{76}\) \(+1.19120 q^{77}\) \(+4.95359 q^{78}\) \(+10.3250 q^{79}\) \(-42.8436 q^{80}\) \(-3.47833 q^{81}\) \(+26.8591 q^{82}\) \(+13.0696 q^{83}\) \(-6.43271 q^{84}\) \(-17.4021 q^{85}\) \(+5.53161 q^{86}\) \(-7.24550 q^{87}\) \(+13.7952 q^{88}\) \(+0.764070 q^{89}\) \(-9.19687 q^{90}\) \(+1.19195 q^{91}\) \(-47.4334 q^{92}\) \(+12.8604 q^{93}\) \(-11.4653 q^{94}\) \(-2.29147 q^{95}\) \(-33.6359 q^{96}\) \(-7.44042 q^{97}\) \(+17.2603 q^{98}\) \(+1.76190 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76521 −1.95530 −0.977648 0.210249i \(-0.932573\pi\)
−0.977648 + 0.210249i \(0.932573\pi\)
\(3\) 1.30852 0.755475 0.377738 0.925913i \(-0.376702\pi\)
0.377738 + 0.925913i \(0.376702\pi\)
\(4\) 5.64636 2.82318
\(5\) −2.58270 −1.15502 −0.577509 0.816384i \(-0.695975\pi\)
−0.577509 + 0.816384i \(0.695975\pi\)
\(6\) −3.61833 −1.47718
\(7\) −0.870652 −0.329075 −0.164538 0.986371i \(-0.552613\pi\)
−0.164538 + 0.986371i \(0.552613\pi\)
\(8\) −10.0829 −3.56486
\(9\) −1.28777 −0.429257
\(10\) 7.14170 2.25840
\(11\) −1.36817 −0.412520 −0.206260 0.978497i \(-0.566129\pi\)
−0.206260 + 0.978497i \(0.566129\pi\)
\(12\) 7.38839 2.13284
\(13\) −1.36903 −0.379700 −0.189850 0.981813i \(-0.560800\pi\)
−0.189850 + 0.981813i \(0.560800\pi\)
\(14\) 2.40753 0.643440
\(15\) −3.37952 −0.872588
\(16\) 16.5887 4.14717
\(17\) 6.73794 1.63419 0.817095 0.576503i \(-0.195583\pi\)
0.817095 + 0.576503i \(0.195583\pi\)
\(18\) 3.56095 0.839324
\(19\) 0.887237 0.203546 0.101773 0.994808i \(-0.467548\pi\)
0.101773 + 0.994808i \(0.467548\pi\)
\(20\) −14.5829 −3.26083
\(21\) −1.13927 −0.248608
\(22\) 3.78328 0.806599
\(23\) −8.40069 −1.75167 −0.875833 0.482615i \(-0.839687\pi\)
−0.875833 + 0.482615i \(0.839687\pi\)
\(24\) −13.1938 −2.69316
\(25\) 1.67034 0.334067
\(26\) 3.78564 0.742425
\(27\) −5.61064 −1.07977
\(28\) −4.91602 −0.929040
\(29\) −5.53716 −1.02823 −0.514113 0.857723i \(-0.671879\pi\)
−0.514113 + 0.857723i \(0.671879\pi\)
\(30\) 9.34506 1.70617
\(31\) 9.82817 1.76519 0.882596 0.470132i \(-0.155794\pi\)
0.882596 + 0.470132i \(0.155794\pi\)
\(32\) −25.7053 −4.54409
\(33\) −1.79029 −0.311649
\(34\) −18.6318 −3.19533
\(35\) 2.24863 0.380088
\(36\) −7.27122 −1.21187
\(37\) −1.35972 −0.223537 −0.111768 0.993734i \(-0.535651\pi\)
−0.111768 + 0.993734i \(0.535651\pi\)
\(38\) −2.45339 −0.397993
\(39\) −1.79140 −0.286854
\(40\) 26.0412 4.11748
\(41\) −9.71324 −1.51695 −0.758476 0.651701i \(-0.774056\pi\)
−0.758476 + 0.651701i \(0.774056\pi\)
\(42\) 3.15031 0.486103
\(43\) −2.00043 −0.305063 −0.152532 0.988299i \(-0.548743\pi\)
−0.152532 + 0.988299i \(0.548743\pi\)
\(44\) −7.72521 −1.16462
\(45\) 3.32593 0.495800
\(46\) 23.2296 3.42502
\(47\) 4.14628 0.604797 0.302398 0.953182i \(-0.402213\pi\)
0.302398 + 0.953182i \(0.402213\pi\)
\(48\) 21.7067 3.13309
\(49\) −6.24197 −0.891709
\(50\) −4.61883 −0.653201
\(51\) 8.81674 1.23459
\(52\) −7.73002 −1.07196
\(53\) −1.00000 −0.137361
\(54\) 15.5146 2.11127
\(55\) 3.53358 0.476468
\(56\) 8.77873 1.17311
\(57\) 1.16097 0.153774
\(58\) 15.3114 2.01048
\(59\) −9.95832 −1.29646 −0.648232 0.761443i \(-0.724491\pi\)
−0.648232 + 0.761443i \(0.724491\pi\)
\(60\) −19.0820 −2.46347
\(61\) −11.1445 −1.42690 −0.713452 0.700704i \(-0.752869\pi\)
−0.713452 + 0.700704i \(0.752869\pi\)
\(62\) −27.1769 −3.45147
\(63\) 1.12120 0.141258
\(64\) 37.9029 4.73787
\(65\) 3.53578 0.438560
\(66\) 4.95051 0.609366
\(67\) 3.20481 0.391530 0.195765 0.980651i \(-0.437281\pi\)
0.195765 + 0.980651i \(0.437281\pi\)
\(68\) 38.0449 4.61362
\(69\) −10.9925 −1.32334
\(70\) −6.21793 −0.743185
\(71\) 13.5027 1.60248 0.801238 0.598346i \(-0.204175\pi\)
0.801238 + 0.598346i \(0.204175\pi\)
\(72\) 12.9845 1.53024
\(73\) 4.99035 0.584076 0.292038 0.956407i \(-0.405667\pi\)
0.292038 + 0.956407i \(0.405667\pi\)
\(74\) 3.75991 0.437080
\(75\) 2.18567 0.252380
\(76\) 5.00966 0.574648
\(77\) 1.19120 0.135750
\(78\) 4.95359 0.560884
\(79\) 10.3250 1.16165 0.580827 0.814027i \(-0.302729\pi\)
0.580827 + 0.814027i \(0.302729\pi\)
\(80\) −42.8436 −4.79006
\(81\) −3.47833 −0.386482
\(82\) 26.8591 2.96609
\(83\) 13.0696 1.43457 0.717285 0.696780i \(-0.245385\pi\)
0.717285 + 0.696780i \(0.245385\pi\)
\(84\) −6.43271 −0.701867
\(85\) −17.4021 −1.88752
\(86\) 5.53161 0.596489
\(87\) −7.24550 −0.776799
\(88\) 13.7952 1.47058
\(89\) 0.764070 0.0809913 0.0404957 0.999180i \(-0.487106\pi\)
0.0404957 + 0.999180i \(0.487106\pi\)
\(90\) −9.19687 −0.969435
\(91\) 1.19195 0.124950
\(92\) −47.4334 −4.94527
\(93\) 12.8604 1.33356
\(94\) −11.4653 −1.18256
\(95\) −2.29147 −0.235099
\(96\) −33.6359 −3.43295
\(97\) −7.44042 −0.755460 −0.377730 0.925916i \(-0.623295\pi\)
−0.377730 + 0.925916i \(0.623295\pi\)
\(98\) 17.2603 1.74356
\(99\) 1.76190 0.177077
\(100\) 9.43133 0.943133
\(101\) −15.0436 −1.49689 −0.748446 0.663196i \(-0.769199\pi\)
−0.748446 + 0.663196i \(0.769199\pi\)
\(102\) −24.3801 −2.41399
\(103\) 9.12994 0.899600 0.449800 0.893129i \(-0.351495\pi\)
0.449800 + 0.893129i \(0.351495\pi\)
\(104\) 13.8038 1.35358
\(105\) 2.94238 0.287147
\(106\) 2.76521 0.268581
\(107\) 0.948839 0.0917277 0.0458639 0.998948i \(-0.485396\pi\)
0.0458639 + 0.998948i \(0.485396\pi\)
\(108\) −31.6797 −3.04838
\(109\) −17.8479 −1.70952 −0.854760 0.519023i \(-0.826296\pi\)
−0.854760 + 0.519023i \(0.826296\pi\)
\(110\) −9.77109 −0.931637
\(111\) −1.77922 −0.168876
\(112\) −14.4430 −1.36473
\(113\) −13.8273 −1.30077 −0.650383 0.759606i \(-0.725392\pi\)
−0.650383 + 0.759606i \(0.725392\pi\)
\(114\) −3.21032 −0.300674
\(115\) 21.6965 2.02321
\(116\) −31.2648 −2.90287
\(117\) 1.76299 0.162989
\(118\) 27.5368 2.53497
\(119\) −5.86640 −0.537772
\(120\) 34.0755 3.11065
\(121\) −9.12810 −0.829827
\(122\) 30.8168 2.79002
\(123\) −12.7100 −1.14602
\(124\) 55.4934 4.98346
\(125\) 8.59952 0.769164
\(126\) −3.10035 −0.276201
\(127\) −12.4913 −1.10842 −0.554212 0.832376i \(-0.686980\pi\)
−0.554212 + 0.832376i \(0.686980\pi\)
\(128\) −53.3989 −4.71984
\(129\) −2.61761 −0.230468
\(130\) −9.77717 −0.857514
\(131\) −13.4412 −1.17436 −0.587180 0.809456i \(-0.699762\pi\)
−0.587180 + 0.809456i \(0.699762\pi\)
\(132\) −10.1086 −0.879841
\(133\) −0.772474 −0.0669820
\(134\) −8.86196 −0.765556
\(135\) 14.4906 1.24715
\(136\) −67.9383 −5.82566
\(137\) −14.4835 −1.23741 −0.618703 0.785625i \(-0.712342\pi\)
−0.618703 + 0.785625i \(0.712342\pi\)
\(138\) 30.3965 2.58752
\(139\) 14.0154 1.18877 0.594386 0.804180i \(-0.297395\pi\)
0.594386 + 0.804180i \(0.297395\pi\)
\(140\) 12.6966 1.07306
\(141\) 5.42550 0.456909
\(142\) −37.3377 −3.13331
\(143\) 1.87307 0.156634
\(144\) −21.3624 −1.78020
\(145\) 14.3008 1.18762
\(146\) −13.7993 −1.14204
\(147\) −8.16775 −0.673664
\(148\) −7.67747 −0.631084
\(149\) 19.5312 1.60006 0.800029 0.599962i \(-0.204818\pi\)
0.800029 + 0.599962i \(0.204818\pi\)
\(150\) −6.04383 −0.493477
\(151\) 1.00000 0.0813788
\(152\) −8.94596 −0.725613
\(153\) −8.67692 −0.701488
\(154\) −3.29392 −0.265432
\(155\) −25.3832 −2.03883
\(156\) −10.1149 −0.809840
\(157\) 12.5422 1.00098 0.500488 0.865743i \(-0.333154\pi\)
0.500488 + 0.865743i \(0.333154\pi\)
\(158\) −28.5508 −2.27138
\(159\) −1.30852 −0.103773
\(160\) 66.3889 5.24851
\(161\) 7.31408 0.576430
\(162\) 9.61831 0.755686
\(163\) 2.55442 0.200077 0.100039 0.994984i \(-0.468103\pi\)
0.100039 + 0.994984i \(0.468103\pi\)
\(164\) −54.8445 −4.28263
\(165\) 4.62377 0.359960
\(166\) −36.1400 −2.80501
\(167\) 0.587083 0.0454298 0.0227149 0.999742i \(-0.492769\pi\)
0.0227149 + 0.999742i \(0.492769\pi\)
\(168\) 11.4872 0.886254
\(169\) −11.1258 −0.855828
\(170\) 48.1203 3.69066
\(171\) −1.14256 −0.0873736
\(172\) −11.2952 −0.861250
\(173\) 6.03433 0.458781 0.229391 0.973334i \(-0.426327\pi\)
0.229391 + 0.973334i \(0.426327\pi\)
\(174\) 20.0353 1.51887
\(175\) −1.45428 −0.109933
\(176\) −22.6962 −1.71079
\(177\) −13.0307 −0.979446
\(178\) −2.11281 −0.158362
\(179\) 4.56945 0.341537 0.170769 0.985311i \(-0.445375\pi\)
0.170769 + 0.985311i \(0.445375\pi\)
\(180\) 18.7794 1.39973
\(181\) 15.6096 1.16025 0.580125 0.814527i \(-0.303004\pi\)
0.580125 + 0.814527i \(0.303004\pi\)
\(182\) −3.29597 −0.244314
\(183\) −14.5828 −1.07799
\(184\) 84.7037 6.24444
\(185\) 3.51175 0.258189
\(186\) −35.5616 −2.60750
\(187\) −9.21868 −0.674137
\(188\) 23.4114 1.70745
\(189\) 4.88492 0.355325
\(190\) 6.33638 0.459689
\(191\) −14.7198 −1.06509 −0.532544 0.846402i \(-0.678764\pi\)
−0.532544 + 0.846402i \(0.678764\pi\)
\(192\) 49.5968 3.57934
\(193\) 10.1684 0.731938 0.365969 0.930627i \(-0.380738\pi\)
0.365969 + 0.930627i \(0.380738\pi\)
\(194\) 20.5743 1.47715
\(195\) 4.62665 0.331321
\(196\) −35.2444 −2.51746
\(197\) −16.2865 −1.16037 −0.580183 0.814486i \(-0.697019\pi\)
−0.580183 + 0.814486i \(0.697019\pi\)
\(198\) −4.87200 −0.346238
\(199\) −1.90904 −0.135328 −0.0676640 0.997708i \(-0.521555\pi\)
−0.0676640 + 0.997708i \(0.521555\pi\)
\(200\) −16.8419 −1.19090
\(201\) 4.19356 0.295791
\(202\) 41.5986 2.92686
\(203\) 4.82094 0.338364
\(204\) 49.7825 3.48547
\(205\) 25.0864 1.75211
\(206\) −25.2462 −1.75898
\(207\) 10.8182 0.751914
\(208\) −22.7104 −1.57468
\(209\) −1.21390 −0.0839669
\(210\) −8.13630 −0.561458
\(211\) 2.76745 0.190519 0.0952597 0.995452i \(-0.469632\pi\)
0.0952597 + 0.995452i \(0.469632\pi\)
\(212\) −5.64636 −0.387794
\(213\) 17.6686 1.21063
\(214\) −2.62373 −0.179355
\(215\) 5.16652 0.352354
\(216\) 56.5718 3.84922
\(217\) −8.55692 −0.580881
\(218\) 49.3532 3.34262
\(219\) 6.52998 0.441255
\(220\) 19.9519 1.34516
\(221\) −9.22442 −0.620501
\(222\) 4.91992 0.330203
\(223\) 6.70188 0.448791 0.224396 0.974498i \(-0.427959\pi\)
0.224396 + 0.974498i \(0.427959\pi\)
\(224\) 22.3803 1.49535
\(225\) −2.15101 −0.143401
\(226\) 38.2354 2.54338
\(227\) 3.85759 0.256037 0.128019 0.991772i \(-0.459138\pi\)
0.128019 + 0.991772i \(0.459138\pi\)
\(228\) 6.55525 0.434132
\(229\) −27.9711 −1.84838 −0.924192 0.381929i \(-0.875260\pi\)
−0.924192 + 0.381929i \(0.875260\pi\)
\(230\) −59.9952 −3.95597
\(231\) 1.55872 0.102556
\(232\) 55.8309 3.66548
\(233\) 4.11746 0.269744 0.134872 0.990863i \(-0.456938\pi\)
0.134872 + 0.990863i \(0.456938\pi\)
\(234\) −4.87504 −0.318691
\(235\) −10.7086 −0.698551
\(236\) −56.2283 −3.66015
\(237\) 13.5105 0.877601
\(238\) 16.2218 1.05150
\(239\) 15.5130 1.00346 0.501728 0.865026i \(-0.332698\pi\)
0.501728 + 0.865026i \(0.332698\pi\)
\(240\) −56.0618 −3.61877
\(241\) −13.8534 −0.892373 −0.446186 0.894940i \(-0.647218\pi\)
−0.446186 + 0.894940i \(0.647218\pi\)
\(242\) 25.2411 1.62256
\(243\) 12.2804 0.787791
\(244\) −62.9258 −4.02841
\(245\) 16.1211 1.02994
\(246\) 35.1457 2.24081
\(247\) −1.21465 −0.0772864
\(248\) −99.0969 −6.29266
\(249\) 17.1018 1.08378
\(250\) −23.7794 −1.50394
\(251\) 9.19677 0.580495 0.290248 0.956952i \(-0.406262\pi\)
0.290248 + 0.956952i \(0.406262\pi\)
\(252\) 6.33070 0.398797
\(253\) 11.4936 0.722597
\(254\) 34.5410 2.16730
\(255\) −22.7710 −1.42597
\(256\) 71.8531 4.49082
\(257\) −4.59812 −0.286823 −0.143411 0.989663i \(-0.545807\pi\)
−0.143411 + 0.989663i \(0.545807\pi\)
\(258\) 7.23824 0.450633
\(259\) 1.18384 0.0735604
\(260\) 19.9643 1.23813
\(261\) 7.13060 0.441373
\(262\) 37.1676 2.29622
\(263\) −20.1315 −1.24136 −0.620679 0.784065i \(-0.713143\pi\)
−0.620679 + 0.784065i \(0.713143\pi\)
\(264\) 18.0514 1.11098
\(265\) 2.58270 0.158654
\(266\) 2.13605 0.130970
\(267\) 0.999803 0.0611869
\(268\) 18.0955 1.10536
\(269\) −23.2392 −1.41692 −0.708458 0.705753i \(-0.750609\pi\)
−0.708458 + 0.705753i \(0.750609\pi\)
\(270\) −40.0695 −2.43855
\(271\) 5.21526 0.316805 0.158402 0.987375i \(-0.449366\pi\)
0.158402 + 0.987375i \(0.449366\pi\)
\(272\) 111.774 6.77727
\(273\) 1.55969 0.0943965
\(274\) 40.0498 2.41950
\(275\) −2.28531 −0.137810
\(276\) −62.0676 −3.73603
\(277\) −15.5892 −0.936663 −0.468331 0.883553i \(-0.655145\pi\)
−0.468331 + 0.883553i \(0.655145\pi\)
\(278\) −38.7555 −2.32440
\(279\) −12.6564 −0.757721
\(280\) −22.6728 −1.35496
\(281\) 17.7271 1.05751 0.528754 0.848775i \(-0.322660\pi\)
0.528754 + 0.848775i \(0.322660\pi\)
\(282\) −15.0026 −0.893393
\(283\) 24.9313 1.48201 0.741006 0.671499i \(-0.234349\pi\)
0.741006 + 0.671499i \(0.234349\pi\)
\(284\) 76.2411 4.52408
\(285\) −2.99843 −0.177612
\(286\) −5.17942 −0.306265
\(287\) 8.45685 0.499192
\(288\) 33.1025 1.95058
\(289\) 28.3998 1.67058
\(290\) −39.5447 −2.32215
\(291\) −9.73595 −0.570731
\(292\) 28.1773 1.64895
\(293\) 16.0157 0.935650 0.467825 0.883821i \(-0.345038\pi\)
0.467825 + 0.883821i \(0.345038\pi\)
\(294\) 22.5855 1.31721
\(295\) 25.7194 1.49744
\(296\) 13.7100 0.796877
\(297\) 7.67634 0.445426
\(298\) −54.0077 −3.12858
\(299\) 11.5008 0.665107
\(300\) 12.3411 0.712514
\(301\) 1.74168 0.100389
\(302\) −2.76521 −0.159120
\(303\) −19.6848 −1.13086
\(304\) 14.7181 0.844141
\(305\) 28.7828 1.64810
\(306\) 23.9935 1.37162
\(307\) −7.35235 −0.419621 −0.209810 0.977742i \(-0.567285\pi\)
−0.209810 + 0.977742i \(0.567285\pi\)
\(308\) 6.72597 0.383248
\(309\) 11.9467 0.679625
\(310\) 70.1898 3.98651
\(311\) 5.84369 0.331365 0.165683 0.986179i \(-0.447017\pi\)
0.165683 + 0.986179i \(0.447017\pi\)
\(312\) 18.0626 1.02259
\(313\) −11.6986 −0.661244 −0.330622 0.943763i \(-0.607258\pi\)
−0.330622 + 0.943763i \(0.607258\pi\)
\(314\) −34.6818 −1.95721
\(315\) −2.89572 −0.163155
\(316\) 58.2988 3.27956
\(317\) 13.4761 0.756892 0.378446 0.925623i \(-0.376459\pi\)
0.378446 + 0.925623i \(0.376459\pi\)
\(318\) 3.61833 0.202906
\(319\) 7.57581 0.424164
\(320\) −97.8919 −5.47232
\(321\) 1.24158 0.0692980
\(322\) −20.2249 −1.12709
\(323\) 5.97815 0.332633
\(324\) −19.6399 −1.09111
\(325\) −2.28674 −0.126845
\(326\) −7.06349 −0.391211
\(327\) −23.3544 −1.29150
\(328\) 97.9380 5.40772
\(329\) −3.60996 −0.199024
\(330\) −12.7857 −0.703829
\(331\) 12.6596 0.695837 0.347919 0.937525i \(-0.386889\pi\)
0.347919 + 0.937525i \(0.386889\pi\)
\(332\) 73.7954 4.05005
\(333\) 1.75101 0.0959546
\(334\) −1.62340 −0.0888288
\(335\) −8.27706 −0.452224
\(336\) −18.8989 −1.03102
\(337\) −2.57834 −0.140451 −0.0702255 0.997531i \(-0.522372\pi\)
−0.0702255 + 0.997531i \(0.522372\pi\)
\(338\) 30.7650 1.67340
\(339\) −18.0934 −0.982697
\(340\) −98.2584 −5.32881
\(341\) −13.4467 −0.728177
\(342\) 3.15941 0.170841
\(343\) 11.5291 0.622515
\(344\) 20.1703 1.08751
\(345\) 28.3903 1.52848
\(346\) −16.6862 −0.897053
\(347\) 19.8839 1.06742 0.533712 0.845666i \(-0.320797\pi\)
0.533712 + 0.845666i \(0.320797\pi\)
\(348\) −40.9107 −2.19304
\(349\) 9.17365 0.491054 0.245527 0.969390i \(-0.421039\pi\)
0.245527 + 0.969390i \(0.421039\pi\)
\(350\) 4.02139 0.214952
\(351\) 7.68111 0.409988
\(352\) 35.1693 1.87453
\(353\) 9.53825 0.507670 0.253835 0.967248i \(-0.418308\pi\)
0.253835 + 0.967248i \(0.418308\pi\)
\(354\) 36.0325 1.91511
\(355\) −34.8734 −1.85089
\(356\) 4.31422 0.228653
\(357\) −7.67631 −0.406273
\(358\) −12.6355 −0.667806
\(359\) 21.4229 1.13066 0.565330 0.824865i \(-0.308749\pi\)
0.565330 + 0.824865i \(0.308749\pi\)
\(360\) −33.5351 −1.76746
\(361\) −18.2128 −0.958569
\(362\) −43.1637 −2.26863
\(363\) −11.9443 −0.626914
\(364\) 6.73015 0.352756
\(365\) −12.8886 −0.674618
\(366\) 40.3244 2.10779
\(367\) 27.3120 1.42568 0.712838 0.701329i \(-0.247410\pi\)
0.712838 + 0.701329i \(0.247410\pi\)
\(368\) −139.356 −7.26446
\(369\) 12.5084 0.651162
\(370\) −9.71071 −0.504836
\(371\) 0.870652 0.0452020
\(372\) 72.6144 3.76488
\(373\) 33.2452 1.72137 0.860686 0.509136i \(-0.170035\pi\)
0.860686 + 0.509136i \(0.170035\pi\)
\(374\) 25.4915 1.31814
\(375\) 11.2527 0.581085
\(376\) −41.8067 −2.15602
\(377\) 7.58052 0.390417
\(378\) −13.5078 −0.694766
\(379\) −17.6342 −0.905809 −0.452904 0.891559i \(-0.649612\pi\)
−0.452904 + 0.891559i \(0.649612\pi\)
\(380\) −12.9385 −0.663729
\(381\) −16.3451 −0.837387
\(382\) 40.7033 2.08256
\(383\) −22.6558 −1.15766 −0.578829 0.815449i \(-0.696490\pi\)
−0.578829 + 0.815449i \(0.696490\pi\)
\(384\) −69.8736 −3.56572
\(385\) −3.07652 −0.156794
\(386\) −28.1178 −1.43116
\(387\) 2.57610 0.130951
\(388\) −42.0113 −2.13280
\(389\) 22.0901 1.12001 0.560006 0.828489i \(-0.310799\pi\)
0.560006 + 0.828489i \(0.310799\pi\)
\(390\) −12.7936 −0.647831
\(391\) −56.6034 −2.86255
\(392\) 62.9374 3.17882
\(393\) −17.5881 −0.887200
\(394\) 45.0355 2.26886
\(395\) −26.6664 −1.34173
\(396\) 9.94830 0.499921
\(397\) 30.3661 1.52403 0.762016 0.647558i \(-0.224210\pi\)
0.762016 + 0.647558i \(0.224210\pi\)
\(398\) 5.27888 0.264606
\(399\) −1.01080 −0.0506033
\(400\) 27.7087 1.38544
\(401\) 26.3611 1.31641 0.658206 0.752838i \(-0.271316\pi\)
0.658206 + 0.752838i \(0.271316\pi\)
\(402\) −11.5961 −0.578359
\(403\) −13.4550 −0.670243
\(404\) −84.9415 −4.22600
\(405\) 8.98349 0.446393
\(406\) −13.3309 −0.661601
\(407\) 1.86033 0.0922134
\(408\) −88.8987 −4.40114
\(409\) 5.34941 0.264511 0.132256 0.991216i \(-0.457778\pi\)
0.132256 + 0.991216i \(0.457778\pi\)
\(410\) −69.3690 −3.42589
\(411\) −18.9519 −0.934830
\(412\) 51.5510 2.53973
\(413\) 8.67023 0.426634
\(414\) −29.9145 −1.47022
\(415\) −33.7547 −1.65695
\(416\) 35.1912 1.72539
\(417\) 18.3395 0.898088
\(418\) 3.35667 0.164180
\(419\) 5.73842 0.280340 0.140170 0.990127i \(-0.455235\pi\)
0.140170 + 0.990127i \(0.455235\pi\)
\(420\) 16.6138 0.810669
\(421\) 6.94429 0.338444 0.169222 0.985578i \(-0.445874\pi\)
0.169222 + 0.985578i \(0.445874\pi\)
\(422\) −7.65258 −0.372522
\(423\) −5.33946 −0.259613
\(424\) 10.0829 0.489671
\(425\) 11.2546 0.545930
\(426\) −48.8572 −2.36714
\(427\) 9.70296 0.469559
\(428\) 5.35749 0.258964
\(429\) 2.45095 0.118333
\(430\) −14.2865 −0.688956
\(431\) −35.1784 −1.69448 −0.847241 0.531209i \(-0.821738\pi\)
−0.847241 + 0.531209i \(0.821738\pi\)
\(432\) −93.0732 −4.47799
\(433\) −1.91625 −0.0920890 −0.0460445 0.998939i \(-0.514662\pi\)
−0.0460445 + 0.998939i \(0.514662\pi\)
\(434\) 23.6616 1.13580
\(435\) 18.7129 0.897217
\(436\) −100.776 −4.82629
\(437\) −7.45340 −0.356545
\(438\) −18.0567 −0.862784
\(439\) −26.8615 −1.28203 −0.641014 0.767529i \(-0.721486\pi\)
−0.641014 + 0.767529i \(0.721486\pi\)
\(440\) −35.6289 −1.69854
\(441\) 8.03822 0.382772
\(442\) 25.5074 1.21326
\(443\) 25.6380 1.21810 0.609048 0.793133i \(-0.291552\pi\)
0.609048 + 0.793133i \(0.291552\pi\)
\(444\) −10.0461 −0.476769
\(445\) −1.97336 −0.0935464
\(446\) −18.5321 −0.877519
\(447\) 25.5570 1.20880
\(448\) −33.0003 −1.55912
\(449\) −28.3608 −1.33843 −0.669214 0.743070i \(-0.733369\pi\)
−0.669214 + 0.743070i \(0.733369\pi\)
\(450\) 5.94799 0.280391
\(451\) 13.2894 0.625774
\(452\) −78.0741 −3.67230
\(453\) 1.30852 0.0614797
\(454\) −10.6670 −0.500628
\(455\) −3.07844 −0.144319
\(456\) −11.7060 −0.548183
\(457\) −9.26310 −0.433309 −0.216655 0.976248i \(-0.569515\pi\)
−0.216655 + 0.976248i \(0.569515\pi\)
\(458\) 77.3459 3.61414
\(459\) −37.8042 −1.76455
\(460\) 122.506 5.71188
\(461\) 2.52915 0.117794 0.0588972 0.998264i \(-0.481242\pi\)
0.0588972 + 0.998264i \(0.481242\pi\)
\(462\) −4.31017 −0.200527
\(463\) 13.4133 0.623368 0.311684 0.950186i \(-0.399107\pi\)
0.311684 + 0.950186i \(0.399107\pi\)
\(464\) −91.8543 −4.26423
\(465\) −33.2145 −1.54029
\(466\) −11.3856 −0.527429
\(467\) 8.95977 0.414609 0.207304 0.978276i \(-0.433531\pi\)
0.207304 + 0.978276i \(0.433531\pi\)
\(468\) 9.95449 0.460147
\(469\) −2.79027 −0.128843
\(470\) 29.6115 1.36587
\(471\) 16.4117 0.756213
\(472\) 100.409 4.62171
\(473\) 2.73694 0.125845
\(474\) −37.3593 −1.71597
\(475\) 1.48198 0.0679981
\(476\) −33.1238 −1.51823
\(477\) 1.28777 0.0589630
\(478\) −42.8968 −1.96205
\(479\) −26.3714 −1.20494 −0.602471 0.798141i \(-0.705817\pi\)
−0.602471 + 0.798141i \(0.705817\pi\)
\(480\) 86.8714 3.96512
\(481\) 1.86149 0.0848767
\(482\) 38.3074 1.74485
\(483\) 9.57063 0.435479
\(484\) −51.5406 −2.34275
\(485\) 19.2164 0.872570
\(486\) −33.9580 −1.54036
\(487\) 21.7392 0.985095 0.492548 0.870285i \(-0.336066\pi\)
0.492548 + 0.870285i \(0.336066\pi\)
\(488\) 112.369 5.08671
\(489\) 3.34251 0.151154
\(490\) −44.5782 −2.01384
\(491\) −23.5346 −1.06210 −0.531051 0.847340i \(-0.678203\pi\)
−0.531051 + 0.847340i \(0.678203\pi\)
\(492\) −71.7652 −3.23542
\(493\) −37.3091 −1.68032
\(494\) 3.35876 0.151118
\(495\) −4.55045 −0.204527
\(496\) 163.037 7.32056
\(497\) −11.7561 −0.527335
\(498\) −47.2900 −2.11911
\(499\) −8.52970 −0.381842 −0.190921 0.981605i \(-0.561147\pi\)
−0.190921 + 0.981605i \(0.561147\pi\)
\(500\) 48.5560 2.17149
\(501\) 0.768211 0.0343211
\(502\) −25.4310 −1.13504
\(503\) 17.3956 0.775629 0.387815 0.921737i \(-0.373230\pi\)
0.387815 + 0.921737i \(0.373230\pi\)
\(504\) −11.3050 −0.503565
\(505\) 38.8530 1.72894
\(506\) −31.7822 −1.41289
\(507\) −14.5583 −0.646557
\(508\) −70.5304 −3.12928
\(509\) 42.4568 1.88186 0.940931 0.338598i \(-0.109953\pi\)
0.940931 + 0.338598i \(0.109953\pi\)
\(510\) 62.9665 2.78820
\(511\) −4.34485 −0.192205
\(512\) −91.8908 −4.06104
\(513\) −4.97797 −0.219783
\(514\) 12.7147 0.560823
\(515\) −23.5799 −1.03905
\(516\) −14.7800 −0.650653
\(517\) −5.67283 −0.249491
\(518\) −3.27357 −0.143832
\(519\) 7.89605 0.346598
\(520\) −35.6511 −1.56340
\(521\) −17.4569 −0.764802 −0.382401 0.923997i \(-0.624903\pi\)
−0.382401 + 0.923997i \(0.624903\pi\)
\(522\) −19.7176 −0.863014
\(523\) 26.8010 1.17193 0.585964 0.810337i \(-0.300716\pi\)
0.585964 + 0.810337i \(0.300716\pi\)
\(524\) −75.8937 −3.31543
\(525\) −1.90296 −0.0830520
\(526\) 55.6676 2.42722
\(527\) 66.2216 2.88466
\(528\) −29.6985 −1.29246
\(529\) 47.5716 2.06833
\(530\) −7.14170 −0.310215
\(531\) 12.8240 0.556516
\(532\) −4.36167 −0.189102
\(533\) 13.2977 0.575986
\(534\) −2.76466 −0.119639
\(535\) −2.45057 −0.105947
\(536\) −32.3139 −1.39575
\(537\) 5.97923 0.258023
\(538\) 64.2610 2.77049
\(539\) 8.54010 0.367848
\(540\) 81.8192 3.52094
\(541\) −7.92219 −0.340602 −0.170301 0.985392i \(-0.554474\pi\)
−0.170301 + 0.985392i \(0.554474\pi\)
\(542\) −14.4213 −0.619447
\(543\) 20.4255 0.876540
\(544\) −173.200 −7.42591
\(545\) 46.0958 1.97453
\(546\) −4.31285 −0.184573
\(547\) 12.9126 0.552103 0.276051 0.961143i \(-0.410974\pi\)
0.276051 + 0.961143i \(0.410974\pi\)
\(548\) −81.7789 −3.49342
\(549\) 14.3515 0.612508
\(550\) 6.31936 0.269458
\(551\) −4.91278 −0.209291
\(552\) 110.837 4.71752
\(553\) −8.98949 −0.382272
\(554\) 43.1073 1.83145
\(555\) 4.59520 0.195055
\(556\) 79.1361 3.35612
\(557\) 40.2565 1.70572 0.852861 0.522138i \(-0.174865\pi\)
0.852861 + 0.522138i \(0.174865\pi\)
\(558\) 34.9977 1.48157
\(559\) 2.73865 0.115832
\(560\) 37.3019 1.57629
\(561\) −12.0628 −0.509294
\(562\) −49.0190 −2.06774
\(563\) −17.5566 −0.739923 −0.369961 0.929047i \(-0.620629\pi\)
−0.369961 + 0.929047i \(0.620629\pi\)
\(564\) 30.6343 1.28994
\(565\) 35.7118 1.50241
\(566\) −68.9401 −2.89777
\(567\) 3.02842 0.127182
\(568\) −136.147 −5.71260
\(569\) −46.4680 −1.94804 −0.974021 0.226458i \(-0.927285\pi\)
−0.974021 + 0.226458i \(0.927285\pi\)
\(570\) 8.29129 0.347284
\(571\) 13.9275 0.582848 0.291424 0.956594i \(-0.405871\pi\)
0.291424 + 0.956594i \(0.405871\pi\)
\(572\) 10.5760 0.442205
\(573\) −19.2612 −0.804648
\(574\) −23.3849 −0.976068
\(575\) −14.0320 −0.585174
\(576\) −48.8103 −2.03376
\(577\) 5.83135 0.242762 0.121381 0.992606i \(-0.461268\pi\)
0.121381 + 0.992606i \(0.461268\pi\)
\(578\) −78.5314 −3.26647
\(579\) 13.3056 0.552961
\(580\) 80.7477 3.35286
\(581\) −11.3790 −0.472082
\(582\) 26.9219 1.11595
\(583\) 1.36817 0.0566640
\(584\) −50.3174 −2.08215
\(585\) −4.55328 −0.188255
\(586\) −44.2868 −1.82947
\(587\) −35.8149 −1.47824 −0.739120 0.673573i \(-0.764759\pi\)
−0.739120 + 0.673573i \(0.764759\pi\)
\(588\) −46.1181 −1.90188
\(589\) 8.71992 0.359298
\(590\) −71.1193 −2.92794
\(591\) −21.3112 −0.876628
\(592\) −22.5560 −0.927045
\(593\) 29.8483 1.22572 0.612862 0.790190i \(-0.290018\pi\)
0.612862 + 0.790190i \(0.290018\pi\)
\(594\) −21.2267 −0.870940
\(595\) 15.1511 0.621136
\(596\) 110.280 4.51725
\(597\) −2.49802 −0.102237
\(598\) −31.8020 −1.30048
\(599\) 25.2684 1.03244 0.516219 0.856457i \(-0.327339\pi\)
0.516219 + 0.856457i \(0.327339\pi\)
\(600\) −22.0380 −0.899698
\(601\) −37.5848 −1.53312 −0.766559 0.642174i \(-0.778033\pi\)
−0.766559 + 0.642174i \(0.778033\pi\)
\(602\) −4.81611 −0.196290
\(603\) −4.12706 −0.168067
\(604\) 5.64636 0.229747
\(605\) 23.5751 0.958466
\(606\) 54.4326 2.21117
\(607\) −8.59207 −0.348741 −0.174371 0.984680i \(-0.555789\pi\)
−0.174371 + 0.984680i \(0.555789\pi\)
\(608\) −22.8066 −0.924932
\(609\) 6.30831 0.255625
\(610\) −79.5905 −3.22252
\(611\) −5.67636 −0.229641
\(612\) −48.9931 −1.98043
\(613\) 10.6718 0.431029 0.215514 0.976501i \(-0.430857\pi\)
0.215514 + 0.976501i \(0.430857\pi\)
\(614\) 20.3308 0.820483
\(615\) 32.8261 1.32367
\(616\) −12.0108 −0.483931
\(617\) −17.9580 −0.722962 −0.361481 0.932380i \(-0.617729\pi\)
−0.361481 + 0.932380i \(0.617729\pi\)
\(618\) −33.0352 −1.32887
\(619\) −16.6603 −0.669635 −0.334818 0.942283i \(-0.608675\pi\)
−0.334818 + 0.942283i \(0.608675\pi\)
\(620\) −143.323 −5.75599
\(621\) 47.1333 1.89139
\(622\) −16.1590 −0.647917
\(623\) −0.665239 −0.0266523
\(624\) −29.7170 −1.18963
\(625\) −30.5617 −1.22247
\(626\) 32.3490 1.29293
\(627\) −1.58841 −0.0634349
\(628\) 70.8178 2.82594
\(629\) −9.16171 −0.365301
\(630\) 8.00727 0.319017
\(631\) 5.08332 0.202364 0.101182 0.994868i \(-0.467738\pi\)
0.101182 + 0.994868i \(0.467738\pi\)
\(632\) −104.107 −4.14113
\(633\) 3.62127 0.143933
\(634\) −37.2641 −1.47995
\(635\) 32.2613 1.28025
\(636\) −7.38839 −0.292969
\(637\) 8.54541 0.338582
\(638\) −20.9487 −0.829366
\(639\) −17.3884 −0.687874
\(640\) 137.913 5.45150
\(641\) 12.2158 0.482497 0.241248 0.970463i \(-0.422443\pi\)
0.241248 + 0.970463i \(0.422443\pi\)
\(642\) −3.43321 −0.135498
\(643\) 45.6046 1.79847 0.899235 0.437466i \(-0.144124\pi\)
0.899235 + 0.437466i \(0.144124\pi\)
\(644\) 41.2979 1.62737
\(645\) 6.76051 0.266195
\(646\) −16.5308 −0.650396
\(647\) −42.2217 −1.65991 −0.829954 0.557832i \(-0.811633\pi\)
−0.829954 + 0.557832i \(0.811633\pi\)
\(648\) 35.0719 1.37775
\(649\) 13.6247 0.534817
\(650\) 6.32329 0.248020
\(651\) −11.1969 −0.438842
\(652\) 14.4232 0.564855
\(653\) 22.4025 0.876678 0.438339 0.898810i \(-0.355567\pi\)
0.438339 + 0.898810i \(0.355567\pi\)
\(654\) 64.5797 2.52527
\(655\) 34.7145 1.35641
\(656\) −161.130 −6.29106
\(657\) −6.42642 −0.250719
\(658\) 9.98230 0.389150
\(659\) 28.4806 1.10945 0.554723 0.832035i \(-0.312824\pi\)
0.554723 + 0.832035i \(0.312824\pi\)
\(660\) 26.1075 1.01623
\(661\) −5.23118 −0.203469 −0.101735 0.994812i \(-0.532439\pi\)
−0.101735 + 0.994812i \(0.532439\pi\)
\(662\) −35.0065 −1.36057
\(663\) −12.0703 −0.468773
\(664\) −131.780 −5.11404
\(665\) 1.99507 0.0773655
\(666\) −4.84190 −0.187620
\(667\) 46.5160 1.80111
\(668\) 3.31488 0.128257
\(669\) 8.76956 0.339051
\(670\) 22.8878 0.884232
\(671\) 15.2476 0.588627
\(672\) 29.2851 1.12970
\(673\) −32.8740 −1.26720 −0.633599 0.773661i \(-0.718423\pi\)
−0.633599 + 0.773661i \(0.718423\pi\)
\(674\) 7.12964 0.274623
\(675\) −9.37166 −0.360715
\(676\) −62.8201 −2.41616
\(677\) −12.3787 −0.475754 −0.237877 0.971295i \(-0.576451\pi\)
−0.237877 + 0.971295i \(0.576451\pi\)
\(678\) 50.0319 1.92146
\(679\) 6.47801 0.248603
\(680\) 175.464 6.72874
\(681\) 5.04774 0.193430
\(682\) 37.1828 1.42380
\(683\) 49.0448 1.87665 0.938324 0.345758i \(-0.112378\pi\)
0.938324 + 0.345758i \(0.112378\pi\)
\(684\) −6.45130 −0.246671
\(685\) 37.4065 1.42923
\(686\) −31.8804 −1.21720
\(687\) −36.6008 −1.39641
\(688\) −33.1846 −1.26515
\(689\) 1.36903 0.0521557
\(690\) −78.5050 −2.98863
\(691\) −14.4057 −0.548019 −0.274009 0.961727i \(-0.588350\pi\)
−0.274009 + 0.961727i \(0.588350\pi\)
\(692\) 34.0720 1.29522
\(693\) −1.53400 −0.0582717
\(694\) −54.9831 −2.08713
\(695\) −36.1976 −1.37305
\(696\) 73.0560 2.76918
\(697\) −65.4472 −2.47899
\(698\) −25.3670 −0.960156
\(699\) 5.38779 0.203785
\(700\) −8.21140 −0.310362
\(701\) 13.0627 0.493370 0.246685 0.969096i \(-0.420659\pi\)
0.246685 + 0.969096i \(0.420659\pi\)
\(702\) −21.2399 −0.801647
\(703\) −1.20639 −0.0455000
\(704\) −51.8578 −1.95447
\(705\) −14.0124 −0.527738
\(706\) −26.3752 −0.992644
\(707\) 13.0977 0.492590
\(708\) −73.5760 −2.76515
\(709\) 34.1811 1.28370 0.641849 0.766831i \(-0.278168\pi\)
0.641849 + 0.766831i \(0.278168\pi\)
\(710\) 96.4322 3.61903
\(711\) −13.2962 −0.498648
\(712\) −7.70408 −0.288723
\(713\) −82.5635 −3.09203
\(714\) 21.2266 0.794385
\(715\) −4.83757 −0.180915
\(716\) 25.8008 0.964221
\(717\) 20.2992 0.758086
\(718\) −59.2388 −2.21077
\(719\) 0.827451 0.0308587 0.0154294 0.999881i \(-0.495088\pi\)
0.0154294 + 0.999881i \(0.495088\pi\)
\(720\) 55.1727 2.05617
\(721\) −7.94900 −0.296036
\(722\) 50.3622 1.87429
\(723\) −18.1274 −0.674166
\(724\) 88.1373 3.27560
\(725\) −9.24893 −0.343497
\(726\) 33.0285 1.22580
\(727\) 16.2689 0.603380 0.301690 0.953406i \(-0.402449\pi\)
0.301690 + 0.953406i \(0.402449\pi\)
\(728\) −12.0183 −0.445428
\(729\) 26.5042 0.981638
\(730\) 35.6395 1.31908
\(731\) −13.4788 −0.498532
\(732\) −82.3397 −3.04336
\(733\) 1.37090 0.0506355 0.0253177 0.999679i \(-0.491940\pi\)
0.0253177 + 0.999679i \(0.491940\pi\)
\(734\) −75.5233 −2.78762
\(735\) 21.0948 0.778095
\(736\) 215.942 7.95972
\(737\) −4.38474 −0.161514
\(738\) −34.5884 −1.27322
\(739\) 39.2350 1.44328 0.721641 0.692267i \(-0.243388\pi\)
0.721641 + 0.692267i \(0.243388\pi\)
\(740\) 19.8286 0.728914
\(741\) −1.58940 −0.0583879
\(742\) −2.40753 −0.0883833
\(743\) 18.4725 0.677689 0.338844 0.940842i \(-0.389964\pi\)
0.338844 + 0.940842i \(0.389964\pi\)
\(744\) −129.671 −4.75395
\(745\) −50.4432 −1.84810
\(746\) −91.9299 −3.36579
\(747\) −16.8306 −0.615799
\(748\) −52.0520 −1.90321
\(749\) −0.826108 −0.0301853
\(750\) −31.1159 −1.13619
\(751\) 52.2716 1.90742 0.953710 0.300729i \(-0.0972300\pi\)
0.953710 + 0.300729i \(0.0972300\pi\)
\(752\) 68.7813 2.50820
\(753\) 12.0342 0.438550
\(754\) −20.9617 −0.763380
\(755\) −2.58270 −0.0939941
\(756\) 27.5820 1.00315
\(757\) −26.1702 −0.951171 −0.475586 0.879669i \(-0.657764\pi\)
−0.475586 + 0.879669i \(0.657764\pi\)
\(758\) 48.7622 1.77112
\(759\) 15.0396 0.545904
\(760\) 23.1047 0.838097
\(761\) 50.2203 1.82048 0.910242 0.414078i \(-0.135896\pi\)
0.910242 + 0.414078i \(0.135896\pi\)
\(762\) 45.1977 1.63734
\(763\) 15.5393 0.562561
\(764\) −83.1134 −3.00694
\(765\) 22.4099 0.810231
\(766\) 62.6479 2.26356
\(767\) 13.6332 0.492266
\(768\) 94.0214 3.39270
\(769\) −31.7406 −1.14459 −0.572297 0.820047i \(-0.693947\pi\)
−0.572297 + 0.820047i \(0.693947\pi\)
\(770\) 8.50722 0.306579
\(771\) −6.01673 −0.216687
\(772\) 57.4146 2.06640
\(773\) −17.3338 −0.623454 −0.311727 0.950172i \(-0.600907\pi\)
−0.311727 + 0.950172i \(0.600907\pi\)
\(774\) −7.12345 −0.256047
\(775\) 16.4164 0.589693
\(776\) 75.0213 2.69311
\(777\) 1.54908 0.0555731
\(778\) −61.0837 −2.18996
\(779\) −8.61794 −0.308770
\(780\) 26.1237 0.935380
\(781\) −18.4741 −0.661053
\(782\) 156.520 5.59714
\(783\) 31.0670 1.11025
\(784\) −103.546 −3.69807
\(785\) −32.3927 −1.15615
\(786\) 48.6346 1.73474
\(787\) 0.346255 0.0123426 0.00617132 0.999981i \(-0.498036\pi\)
0.00617132 + 0.999981i \(0.498036\pi\)
\(788\) −91.9595 −3.27592
\(789\) −26.3424 −0.937816
\(790\) 73.7381 2.62348
\(791\) 12.0388 0.428050
\(792\) −17.7651 −0.631255
\(793\) 15.2571 0.541795
\(794\) −83.9686 −2.97993
\(795\) 3.37952 0.119859
\(796\) −10.7791 −0.382056
\(797\) 49.1718 1.74176 0.870878 0.491500i \(-0.163551\pi\)
0.870878 + 0.491500i \(0.163551\pi\)
\(798\) 2.79507 0.0989444
\(799\) 27.9374 0.988353
\(800\) −42.9364 −1.51803
\(801\) −0.983948 −0.0347661
\(802\) −72.8939 −2.57397
\(803\) −6.82767 −0.240943
\(804\) 23.6784 0.835072
\(805\) −18.8901 −0.665787
\(806\) 37.2059 1.31052
\(807\) −30.4089 −1.07045
\(808\) 151.683 5.33621
\(809\) −12.5616 −0.441643 −0.220821 0.975314i \(-0.570874\pi\)
−0.220821 + 0.975314i \(0.570874\pi\)
\(810\) −24.8412 −0.872831
\(811\) 46.0556 1.61723 0.808615 0.588338i \(-0.200218\pi\)
0.808615 + 0.588338i \(0.200218\pi\)
\(812\) 27.2208 0.955262
\(813\) 6.82429 0.239338
\(814\) −5.14421 −0.180304
\(815\) −6.59730 −0.231093
\(816\) 146.258 5.12006
\(817\) −1.77486 −0.0620945
\(818\) −14.7922 −0.517198
\(819\) −1.53495 −0.0536356
\(820\) 141.647 4.94652
\(821\) −11.1068 −0.387631 −0.193815 0.981038i \(-0.562086\pi\)
−0.193815 + 0.981038i \(0.562086\pi\)
\(822\) 52.4060 1.82787
\(823\) −14.1847 −0.494446 −0.247223 0.968959i \(-0.579518\pi\)
−0.247223 + 0.968959i \(0.579518\pi\)
\(824\) −92.0567 −3.20695
\(825\) −2.99038 −0.104112
\(826\) −23.9750 −0.834196
\(827\) 46.1191 1.60372 0.801859 0.597513i \(-0.203844\pi\)
0.801859 + 0.597513i \(0.203844\pi\)
\(828\) 61.0833 2.12279
\(829\) 29.6375 1.02935 0.514676 0.857385i \(-0.327912\pi\)
0.514676 + 0.857385i \(0.327912\pi\)
\(830\) 93.3388 3.23984
\(831\) −20.3988 −0.707626
\(832\) −51.8901 −1.79897
\(833\) −42.0580 −1.45722
\(834\) −50.7124 −1.75603
\(835\) −1.51626 −0.0524723
\(836\) −6.85409 −0.237054
\(837\) −55.1424 −1.90600
\(838\) −15.8679 −0.548148
\(839\) 48.4413 1.67238 0.836190 0.548441i \(-0.184778\pi\)
0.836190 + 0.548441i \(0.184778\pi\)
\(840\) −29.6679 −1.02364
\(841\) 1.66017 0.0572474
\(842\) −19.2024 −0.661758
\(843\) 23.1962 0.798921
\(844\) 15.6261 0.537871
\(845\) 28.7345 0.988497
\(846\) 14.7647 0.507621
\(847\) 7.94740 0.273076
\(848\) −16.5887 −0.569658
\(849\) 32.6231 1.11962
\(850\) −31.1214 −1.06745
\(851\) 11.4226 0.391561
\(852\) 99.7632 3.41783
\(853\) −3.01383 −0.103192 −0.0515958 0.998668i \(-0.516431\pi\)
−0.0515958 + 0.998668i \(0.516431\pi\)
\(854\) −26.8307 −0.918127
\(855\) 2.95088 0.100918
\(856\) −9.56709 −0.326996
\(857\) −27.3996 −0.935952 −0.467976 0.883741i \(-0.655017\pi\)
−0.467976 + 0.883741i \(0.655017\pi\)
\(858\) −6.77738 −0.231376
\(859\) 37.5914 1.28260 0.641301 0.767290i \(-0.278395\pi\)
0.641301 + 0.767290i \(0.278395\pi\)
\(860\) 29.1721 0.994759
\(861\) 11.0660 0.377127
\(862\) 97.2754 3.31321
\(863\) −28.7670 −0.979240 −0.489620 0.871936i \(-0.662864\pi\)
−0.489620 + 0.871936i \(0.662864\pi\)
\(864\) 144.223 4.90656
\(865\) −15.5849 −0.529901
\(866\) 5.29882 0.180061
\(867\) 37.1618 1.26208
\(868\) −48.3155 −1.63993
\(869\) −14.1264 −0.479206
\(870\) −51.7451 −1.75432
\(871\) −4.38747 −0.148664
\(872\) 179.960 6.09420
\(873\) 9.58155 0.324286
\(874\) 20.6102 0.697150
\(875\) −7.48719 −0.253113
\(876\) 36.8706 1.24574
\(877\) 4.66782 0.157621 0.0788105 0.996890i \(-0.474888\pi\)
0.0788105 + 0.996890i \(0.474888\pi\)
\(878\) 74.2775 2.50674
\(879\) 20.9570 0.706861
\(880\) 58.6175 1.97600
\(881\) 36.6606 1.23513 0.617563 0.786521i \(-0.288120\pi\)
0.617563 + 0.786521i \(0.288120\pi\)
\(882\) −22.2273 −0.748433
\(883\) −17.8823 −0.601786 −0.300893 0.953658i \(-0.597285\pi\)
−0.300893 + 0.953658i \(0.597285\pi\)
\(884\) −52.0844 −1.75179
\(885\) 33.6543 1.13128
\(886\) −70.8943 −2.38174
\(887\) −45.5159 −1.52827 −0.764137 0.645054i \(-0.776835\pi\)
−0.764137 + 0.645054i \(0.776835\pi\)
\(888\) 17.9398 0.602021
\(889\) 10.8756 0.364755
\(890\) 5.45676 0.182911
\(891\) 4.75897 0.159431
\(892\) 37.8412 1.26702
\(893\) 3.67873 0.123104
\(894\) −70.6703 −2.36357
\(895\) −11.8015 −0.394482
\(896\) 46.4919 1.55318
\(897\) 15.0490 0.502472
\(898\) 78.4234 2.61702
\(899\) −54.4202 −1.81502
\(900\) −12.1454 −0.404846
\(901\) −6.73794 −0.224473
\(902\) −36.7479 −1.22357
\(903\) 2.27903 0.0758413
\(904\) 139.420 4.63705
\(905\) −40.3148 −1.34011
\(906\) −3.61833 −0.120211
\(907\) −2.40569 −0.0798795 −0.0399397 0.999202i \(-0.512717\pi\)
−0.0399397 + 0.999202i \(0.512717\pi\)
\(908\) 21.7813 0.722839
\(909\) 19.3727 0.642551
\(910\) 8.51251 0.282187
\(911\) 14.2468 0.472016 0.236008 0.971751i \(-0.424161\pi\)
0.236008 + 0.971751i \(0.424161\pi\)
\(912\) 19.2590 0.637728
\(913\) −17.8814 −0.591789
\(914\) 25.6144 0.847248
\(915\) 37.6630 1.24510
\(916\) −157.935 −5.21832
\(917\) 11.7026 0.386453
\(918\) 104.536 3.45021
\(919\) −6.97491 −0.230081 −0.115041 0.993361i \(-0.536700\pi\)
−0.115041 + 0.993361i \(0.536700\pi\)
\(920\) −218.764 −7.21244
\(921\) −9.62071 −0.317013
\(922\) −6.99363 −0.230323
\(923\) −18.4855 −0.608459
\(924\) 8.80108 0.289534
\(925\) −2.27119 −0.0746763
\(926\) −37.0905 −1.21887
\(927\) −11.7573 −0.386159
\(928\) 142.334 4.67235
\(929\) −48.1874 −1.58098 −0.790488 0.612477i \(-0.790173\pi\)
−0.790488 + 0.612477i \(0.790173\pi\)
\(930\) 91.8449 3.01171
\(931\) −5.53810 −0.181504
\(932\) 23.2487 0.761536
\(933\) 7.64660 0.250338
\(934\) −24.7756 −0.810683
\(935\) 23.8091 0.778640
\(936\) −17.7761 −0.581032
\(937\) −50.7779 −1.65884 −0.829421 0.558624i \(-0.811329\pi\)
−0.829421 + 0.558624i \(0.811329\pi\)
\(938\) 7.71568 0.251926
\(939\) −15.3079 −0.499553
\(940\) −60.4646 −1.97214
\(941\) 56.6747 1.84754 0.923771 0.382944i \(-0.125090\pi\)
0.923771 + 0.382944i \(0.125090\pi\)
\(942\) −45.3819 −1.47862
\(943\) 81.5979 2.65719
\(944\) −165.196 −5.37666
\(945\) −12.6163 −0.410407
\(946\) −7.56821 −0.246064
\(947\) 26.0117 0.845268 0.422634 0.906301i \(-0.361106\pi\)
0.422634 + 0.906301i \(0.361106\pi\)
\(948\) 76.2852 2.47763
\(949\) −6.83192 −0.221773
\(950\) −4.09799 −0.132956
\(951\) 17.6337 0.571813
\(952\) 59.1506 1.91708
\(953\) 52.6861 1.70667 0.853335 0.521363i \(-0.174576\pi\)
0.853335 + 0.521363i \(0.174576\pi\)
\(954\) −3.56095 −0.115290
\(955\) 38.0169 1.23020
\(956\) 87.5923 2.83294
\(957\) 9.91311 0.320445
\(958\) 72.9225 2.35602
\(959\) 12.6101 0.407200
\(960\) −128.094 −4.13421
\(961\) 65.5930 2.11590
\(962\) −5.14741 −0.165959
\(963\) −1.22189 −0.0393748
\(964\) −78.2211 −2.51933
\(965\) −26.2620 −0.845402
\(966\) −26.4648 −0.851490
\(967\) 18.2872 0.588076 0.294038 0.955794i \(-0.405001\pi\)
0.294038 + 0.955794i \(0.405001\pi\)
\(968\) 92.0381 2.95822
\(969\) 7.82254 0.251296
\(970\) −53.1372 −1.70613
\(971\) −30.3126 −0.972779 −0.486389 0.873742i \(-0.661686\pi\)
−0.486389 + 0.873742i \(0.661686\pi\)
\(972\) 69.3399 2.22408
\(973\) −12.2025 −0.391195
\(974\) −60.1132 −1.92615
\(975\) −2.99224 −0.0958285
\(976\) −184.872 −5.91762
\(977\) 29.2865 0.936959 0.468479 0.883474i \(-0.344802\pi\)
0.468479 + 0.883474i \(0.344802\pi\)
\(978\) −9.24273 −0.295550
\(979\) −1.04538 −0.0334105
\(980\) 91.0257 2.90771
\(981\) 22.9840 0.733823
\(982\) 65.0780 2.07672
\(983\) −37.2045 −1.18664 −0.593319 0.804968i \(-0.702183\pi\)
−0.593319 + 0.804968i \(0.702183\pi\)
\(984\) 128.154 4.08540
\(985\) 42.0631 1.34024
\(986\) 103.167 3.28551
\(987\) −4.72372 −0.150358
\(988\) −6.85836 −0.218193
\(989\) 16.8050 0.534369
\(990\) 12.5829 0.399911
\(991\) 45.0889 1.43230 0.716149 0.697948i \(-0.245903\pi\)
0.716149 + 0.697948i \(0.245903\pi\)
\(992\) −252.636 −8.02119
\(993\) 16.5654 0.525688
\(994\) 32.5082 1.03110
\(995\) 4.93047 0.156306
\(996\) 96.5629 3.05971
\(997\) 3.27822 0.103822 0.0519112 0.998652i \(-0.483469\pi\)
0.0519112 + 0.998652i \(0.483469\pi\)
\(998\) 23.5864 0.746614
\(999\) 7.62890 0.241368
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 \(a_p\))