Properties

Label 8015.2.a.l.1.19
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.28523 q^{2}\) \(-0.829686 q^{3}\) \(-0.348175 q^{4}\) \(-1.00000 q^{5}\) \(+1.06634 q^{6}\) \(-1.00000 q^{7}\) \(+3.01795 q^{8}\) \(-2.31162 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.28523 q^{2}\) \(-0.829686 q^{3}\) \(-0.348175 q^{4}\) \(-1.00000 q^{5}\) \(+1.06634 q^{6}\) \(-1.00000 q^{7}\) \(+3.01795 q^{8}\) \(-2.31162 q^{9}\) \(+1.28523 q^{10}\) \(-2.11972 q^{11}\) \(+0.288876 q^{12}\) \(+3.07149 q^{13}\) \(+1.28523 q^{14}\) \(+0.829686 q^{15}\) \(-3.18242 q^{16}\) \(-6.86780 q^{17}\) \(+2.97097 q^{18}\) \(-3.15147 q^{19}\) \(+0.348175 q^{20}\) \(+0.829686 q^{21}\) \(+2.72434 q^{22}\) \(-0.512282 q^{23}\) \(-2.50395 q^{24}\) \(+1.00000 q^{25}\) \(-3.94759 q^{26}\) \(+4.40698 q^{27}\) \(+0.348175 q^{28}\) \(+3.17302 q^{29}\) \(-1.06634 q^{30}\) \(+3.72476 q^{31}\) \(-1.94575 q^{32}\) \(+1.75871 q^{33}\) \(+8.82673 q^{34}\) \(+1.00000 q^{35}\) \(+0.804849 q^{36}\) \(-5.59920 q^{37}\) \(+4.05038 q^{38}\) \(-2.54838 q^{39}\) \(-3.01795 q^{40}\) \(-7.64566 q^{41}\) \(-1.06634 q^{42}\) \(-5.76988 q^{43}\) \(+0.738035 q^{44}\) \(+2.31162 q^{45}\) \(+0.658402 q^{46}\) \(-10.3490 q^{47}\) \(+2.64041 q^{48}\) \(+1.00000 q^{49}\) \(-1.28523 q^{50}\) \(+5.69812 q^{51}\) \(-1.06942 q^{52}\) \(+5.76232 q^{53}\) \(-5.66400 q^{54}\) \(+2.11972 q^{55}\) \(-3.01795 q^{56}\) \(+2.61473 q^{57}\) \(-4.07808 q^{58}\) \(-0.788910 q^{59}\) \(-0.288876 q^{60}\) \(+5.99308 q^{61}\) \(-4.78719 q^{62}\) \(+2.31162 q^{63}\) \(+8.86559 q^{64}\) \(-3.07149 q^{65}\) \(-2.26035 q^{66}\) \(-11.9757 q^{67}\) \(+2.39120 q^{68}\) \(+0.425033 q^{69}\) \(-1.28523 q^{70}\) \(-15.5425 q^{71}\) \(-6.97636 q^{72}\) \(+9.76873 q^{73}\) \(+7.19628 q^{74}\) \(-0.829686 q^{75}\) \(+1.09726 q^{76}\) \(+2.11972 q^{77}\) \(+3.27526 q^{78}\) \(-9.51566 q^{79}\) \(+3.18242 q^{80}\) \(+3.27846 q^{81}\) \(+9.82645 q^{82}\) \(-2.71309 q^{83}\) \(-0.288876 q^{84}\) \(+6.86780 q^{85}\) \(+7.41564 q^{86}\) \(-2.63261 q^{87}\) \(-6.39723 q^{88}\) \(-16.0539 q^{89}\) \(-2.97097 q^{90}\) \(-3.07149 q^{91}\) \(+0.178364 q^{92}\) \(-3.09038 q^{93}\) \(+13.3009 q^{94}\) \(+3.15147 q^{95}\) \(+1.61436 q^{96}\) \(-0.759265 q^{97}\) \(-1.28523 q^{98}\) \(+4.90000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28523 −0.908797 −0.454399 0.890798i \(-0.650146\pi\)
−0.454399 + 0.890798i \(0.650146\pi\)
\(3\) −0.829686 −0.479019 −0.239510 0.970894i \(-0.576987\pi\)
−0.239510 + 0.970894i \(0.576987\pi\)
\(4\) −0.348175 −0.174088
\(5\) −1.00000 −0.447214
\(6\) 1.06634 0.435332
\(7\) −1.00000 −0.377964
\(8\) 3.01795 1.06701
\(9\) −2.31162 −0.770540
\(10\) 1.28523 0.406426
\(11\) −2.11972 −0.639121 −0.319560 0.947566i \(-0.603535\pi\)
−0.319560 + 0.947566i \(0.603535\pi\)
\(12\) 0.288876 0.0833913
\(13\) 3.07149 0.851879 0.425940 0.904752i \(-0.359944\pi\)
0.425940 + 0.904752i \(0.359944\pi\)
\(14\) 1.28523 0.343493
\(15\) 0.829686 0.214224
\(16\) −3.18242 −0.795606
\(17\) −6.86780 −1.66569 −0.832843 0.553509i \(-0.813288\pi\)
−0.832843 + 0.553509i \(0.813288\pi\)
\(18\) 2.97097 0.700265
\(19\) −3.15147 −0.722997 −0.361499 0.932373i \(-0.617735\pi\)
−0.361499 + 0.932373i \(0.617735\pi\)
\(20\) 0.348175 0.0778543
\(21\) 0.829686 0.181052
\(22\) 2.72434 0.580831
\(23\) −0.512282 −0.106818 −0.0534091 0.998573i \(-0.517009\pi\)
−0.0534091 + 0.998573i \(0.517009\pi\)
\(24\) −2.50395 −0.511117
\(25\) 1.00000 0.200000
\(26\) −3.94759 −0.774186
\(27\) 4.40698 0.848123
\(28\) 0.348175 0.0657989
\(29\) 3.17302 0.589216 0.294608 0.955618i \(-0.404811\pi\)
0.294608 + 0.955618i \(0.404811\pi\)
\(30\) −1.06634 −0.194686
\(31\) 3.72476 0.668987 0.334494 0.942398i \(-0.391435\pi\)
0.334494 + 0.942398i \(0.391435\pi\)
\(32\) −1.94575 −0.343963
\(33\) 1.75871 0.306151
\(34\) 8.82673 1.51377
\(35\) 1.00000 0.169031
\(36\) 0.804849 0.134141
\(37\) −5.59920 −0.920503 −0.460251 0.887789i \(-0.652241\pi\)
−0.460251 + 0.887789i \(0.652241\pi\)
\(38\) 4.05038 0.657058
\(39\) −2.54838 −0.408067
\(40\) −3.01795 −0.477180
\(41\) −7.64566 −1.19405 −0.597025 0.802222i \(-0.703651\pi\)
−0.597025 + 0.802222i \(0.703651\pi\)
\(42\) −1.06634 −0.164540
\(43\) −5.76988 −0.879898 −0.439949 0.898023i \(-0.645003\pi\)
−0.439949 + 0.898023i \(0.645003\pi\)
\(44\) 0.738035 0.111263
\(45\) 2.31162 0.344596
\(46\) 0.658402 0.0970760
\(47\) −10.3490 −1.50956 −0.754779 0.655979i \(-0.772256\pi\)
−0.754779 + 0.655979i \(0.772256\pi\)
\(48\) 2.64041 0.381111
\(49\) 1.00000 0.142857
\(50\) −1.28523 −0.181759
\(51\) 5.69812 0.797896
\(52\) −1.06942 −0.148302
\(53\) 5.76232 0.791516 0.395758 0.918355i \(-0.370482\pi\)
0.395758 + 0.918355i \(0.370482\pi\)
\(54\) −5.66400 −0.770772
\(55\) 2.11972 0.285824
\(56\) −3.01795 −0.403291
\(57\) 2.61473 0.346330
\(58\) −4.07808 −0.535478
\(59\) −0.788910 −0.102707 −0.0513537 0.998681i \(-0.516354\pi\)
−0.0513537 + 0.998681i \(0.516354\pi\)
\(60\) −0.288876 −0.0372937
\(61\) 5.99308 0.767335 0.383668 0.923471i \(-0.374661\pi\)
0.383668 + 0.923471i \(0.374661\pi\)
\(62\) −4.78719 −0.607974
\(63\) 2.31162 0.291237
\(64\) 8.86559 1.10820
\(65\) −3.07149 −0.380972
\(66\) −2.26035 −0.278230
\(67\) −11.9757 −1.46306 −0.731530 0.681810i \(-0.761193\pi\)
−0.731530 + 0.681810i \(0.761193\pi\)
\(68\) 2.39120 0.289975
\(69\) 0.425033 0.0511680
\(70\) −1.28523 −0.153615
\(71\) −15.5425 −1.84455 −0.922276 0.386533i \(-0.873673\pi\)
−0.922276 + 0.386533i \(0.873673\pi\)
\(72\) −6.97636 −0.822172
\(73\) 9.76873 1.14334 0.571672 0.820482i \(-0.306295\pi\)
0.571672 + 0.820482i \(0.306295\pi\)
\(74\) 7.19628 0.836550
\(75\) −0.829686 −0.0958039
\(76\) 1.09726 0.125865
\(77\) 2.11972 0.241565
\(78\) 3.27526 0.370850
\(79\) −9.51566 −1.07059 −0.535297 0.844664i \(-0.679800\pi\)
−0.535297 + 0.844664i \(0.679800\pi\)
\(80\) 3.18242 0.355806
\(81\) 3.27846 0.364273
\(82\) 9.82645 1.08515
\(83\) −2.71309 −0.297801 −0.148900 0.988852i \(-0.547573\pi\)
−0.148900 + 0.988852i \(0.547573\pi\)
\(84\) −0.288876 −0.0315190
\(85\) 6.86780 0.744918
\(86\) 7.41564 0.799649
\(87\) −2.63261 −0.282246
\(88\) −6.39723 −0.681947
\(89\) −16.0539 −1.70171 −0.850856 0.525399i \(-0.823916\pi\)
−0.850856 + 0.525399i \(0.823916\pi\)
\(90\) −2.97097 −0.313168
\(91\) −3.07149 −0.321980
\(92\) 0.178364 0.0185957
\(93\) −3.09038 −0.320458
\(94\) 13.3009 1.37188
\(95\) 3.15147 0.323334
\(96\) 1.61436 0.164765
\(97\) −0.759265 −0.0770917 −0.0385458 0.999257i \(-0.512273\pi\)
−0.0385458 + 0.999257i \(0.512273\pi\)
\(98\) −1.28523 −0.129828
\(99\) 4.90000 0.492468
\(100\) −0.348175 −0.0348175
\(101\) −4.01405 −0.399413 −0.199706 0.979856i \(-0.563999\pi\)
−0.199706 + 0.979856i \(0.563999\pi\)
\(102\) −7.32341 −0.725126
\(103\) −17.0160 −1.67664 −0.838320 0.545178i \(-0.816462\pi\)
−0.838320 + 0.545178i \(0.816462\pi\)
\(104\) 9.26963 0.908962
\(105\) −0.829686 −0.0809691
\(106\) −7.40593 −0.719327
\(107\) 1.70018 0.164363 0.0821814 0.996617i \(-0.473811\pi\)
0.0821814 + 0.996617i \(0.473811\pi\)
\(108\) −1.53440 −0.147648
\(109\) 11.6739 1.11816 0.559078 0.829115i \(-0.311155\pi\)
0.559078 + 0.829115i \(0.311155\pi\)
\(110\) −2.72434 −0.259756
\(111\) 4.64558 0.440939
\(112\) 3.18242 0.300711
\(113\) 4.59727 0.432475 0.216237 0.976341i \(-0.430622\pi\)
0.216237 + 0.976341i \(0.430622\pi\)
\(114\) −3.36054 −0.314744
\(115\) 0.512282 0.0477705
\(116\) −1.10477 −0.102575
\(117\) −7.10013 −0.656407
\(118\) 1.01393 0.0933402
\(119\) 6.86780 0.629570
\(120\) 2.50395 0.228579
\(121\) −6.50677 −0.591524
\(122\) −7.70250 −0.697352
\(123\) 6.34349 0.571974
\(124\) −1.29687 −0.116462
\(125\) −1.00000 −0.0894427
\(126\) −2.97097 −0.264675
\(127\) 20.5253 1.82132 0.910662 0.413152i \(-0.135572\pi\)
0.910662 + 0.413152i \(0.135572\pi\)
\(128\) −7.50285 −0.663165
\(129\) 4.78719 0.421488
\(130\) 3.94759 0.346226
\(131\) 13.3057 1.16252 0.581262 0.813717i \(-0.302559\pi\)
0.581262 + 0.813717i \(0.302559\pi\)
\(132\) −0.612337 −0.0532971
\(133\) 3.15147 0.273267
\(134\) 15.3915 1.32962
\(135\) −4.40698 −0.379292
\(136\) −20.7267 −1.77730
\(137\) −11.9618 −1.02197 −0.510983 0.859591i \(-0.670719\pi\)
−0.510983 + 0.859591i \(0.670719\pi\)
\(138\) −0.546267 −0.0465013
\(139\) −2.77551 −0.235416 −0.117708 0.993048i \(-0.537555\pi\)
−0.117708 + 0.993048i \(0.537555\pi\)
\(140\) −0.348175 −0.0294262
\(141\) 8.58643 0.723107
\(142\) 19.9757 1.67632
\(143\) −6.51072 −0.544454
\(144\) 7.35656 0.613047
\(145\) −3.17302 −0.263505
\(146\) −12.5551 −1.03907
\(147\) −0.829686 −0.0684313
\(148\) 1.94950 0.160248
\(149\) −11.2506 −0.921682 −0.460841 0.887483i \(-0.652452\pi\)
−0.460841 + 0.887483i \(0.652452\pi\)
\(150\) 1.06634 0.0870663
\(151\) 11.2784 0.917821 0.458911 0.888482i \(-0.348240\pi\)
0.458911 + 0.888482i \(0.348240\pi\)
\(152\) −9.51099 −0.771444
\(153\) 15.8758 1.28348
\(154\) −2.72434 −0.219534
\(155\) −3.72476 −0.299180
\(156\) 0.887281 0.0710393
\(157\) −16.1105 −1.28576 −0.642880 0.765967i \(-0.722261\pi\)
−0.642880 + 0.765967i \(0.722261\pi\)
\(158\) 12.2298 0.972954
\(159\) −4.78092 −0.379151
\(160\) 1.94575 0.153825
\(161\) 0.512282 0.0403735
\(162\) −4.21358 −0.331050
\(163\) −23.8170 −1.86549 −0.932744 0.360539i \(-0.882593\pi\)
−0.932744 + 0.360539i \(0.882593\pi\)
\(164\) 2.66203 0.207869
\(165\) −1.75871 −0.136915
\(166\) 3.48696 0.270641
\(167\) −0.127154 −0.00983946 −0.00491973 0.999988i \(-0.501566\pi\)
−0.00491973 + 0.999988i \(0.501566\pi\)
\(168\) 2.50395 0.193184
\(169\) −3.56592 −0.274302
\(170\) −8.82673 −0.676979
\(171\) 7.28501 0.557099
\(172\) 2.00893 0.153179
\(173\) 4.69164 0.356699 0.178349 0.983967i \(-0.442924\pi\)
0.178349 + 0.983967i \(0.442924\pi\)
\(174\) 3.38352 0.256504
\(175\) −1.00000 −0.0755929
\(176\) 6.74586 0.508488
\(177\) 0.654548 0.0491988
\(178\) 20.6330 1.54651
\(179\) 4.51041 0.337124 0.168562 0.985691i \(-0.446088\pi\)
0.168562 + 0.985691i \(0.446088\pi\)
\(180\) −0.804849 −0.0599899
\(181\) −11.0214 −0.819214 −0.409607 0.912262i \(-0.634334\pi\)
−0.409607 + 0.912262i \(0.634334\pi\)
\(182\) 3.94759 0.292615
\(183\) −4.97237 −0.367568
\(184\) −1.54604 −0.113976
\(185\) 5.59920 0.411661
\(186\) 3.97187 0.291231
\(187\) 14.5578 1.06458
\(188\) 3.60327 0.262795
\(189\) −4.40698 −0.320560
\(190\) −4.05038 −0.293845
\(191\) −15.9321 −1.15280 −0.576402 0.817166i \(-0.695544\pi\)
−0.576402 + 0.817166i \(0.695544\pi\)
\(192\) −7.35566 −0.530849
\(193\) 12.7166 0.915363 0.457681 0.889116i \(-0.348680\pi\)
0.457681 + 0.889116i \(0.348680\pi\)
\(194\) 0.975833 0.0700607
\(195\) 2.54838 0.182493
\(196\) −0.348175 −0.0248696
\(197\) −23.1318 −1.64807 −0.824037 0.566536i \(-0.808283\pi\)
−0.824037 + 0.566536i \(0.808283\pi\)
\(198\) −6.29764 −0.447554
\(199\) −16.3500 −1.15902 −0.579509 0.814966i \(-0.696756\pi\)
−0.579509 + 0.814966i \(0.696756\pi\)
\(200\) 3.01795 0.213402
\(201\) 9.93603 0.700834
\(202\) 5.15899 0.362985
\(203\) −3.17302 −0.222703
\(204\) −1.98394 −0.138904
\(205\) 7.64566 0.533996
\(206\) 21.8696 1.52373
\(207\) 1.18420 0.0823077
\(208\) −9.77480 −0.677760
\(209\) 6.68025 0.462083
\(210\) 1.06634 0.0735845
\(211\) −1.13399 −0.0780671 −0.0390335 0.999238i \(-0.512428\pi\)
−0.0390335 + 0.999238i \(0.512428\pi\)
\(212\) −2.00630 −0.137793
\(213\) 12.8954 0.883576
\(214\) −2.18513 −0.149372
\(215\) 5.76988 0.393502
\(216\) 13.3001 0.904954
\(217\) −3.72476 −0.252853
\(218\) −15.0037 −1.01618
\(219\) −8.10498 −0.547684
\(220\) −0.738035 −0.0497583
\(221\) −21.0944 −1.41896
\(222\) −5.97065 −0.400724
\(223\) 0.407893 0.0273145 0.0136573 0.999907i \(-0.495653\pi\)
0.0136573 + 0.999907i \(0.495653\pi\)
\(224\) 1.94575 0.130006
\(225\) −2.31162 −0.154108
\(226\) −5.90856 −0.393032
\(227\) 16.7163 1.10950 0.554751 0.832016i \(-0.312813\pi\)
0.554751 + 0.832016i \(0.312813\pi\)
\(228\) −0.910385 −0.0602917
\(229\) 1.00000 0.0660819
\(230\) −0.658402 −0.0434137
\(231\) −1.75871 −0.115714
\(232\) 9.57603 0.628697
\(233\) −25.0566 −1.64151 −0.820757 0.571278i \(-0.806448\pi\)
−0.820757 + 0.571278i \(0.806448\pi\)
\(234\) 9.12533 0.596541
\(235\) 10.3490 0.675095
\(236\) 0.274679 0.0178801
\(237\) 7.89501 0.512836
\(238\) −8.82673 −0.572152
\(239\) −9.02309 −0.583655 −0.291828 0.956471i \(-0.594263\pi\)
−0.291828 + 0.956471i \(0.594263\pi\)
\(240\) −2.64041 −0.170438
\(241\) 2.89667 0.186591 0.0932955 0.995638i \(-0.470260\pi\)
0.0932955 + 0.995638i \(0.470260\pi\)
\(242\) 8.36272 0.537576
\(243\) −15.9410 −1.02262
\(244\) −2.08664 −0.133583
\(245\) −1.00000 −0.0638877
\(246\) −8.15287 −0.519808
\(247\) −9.67973 −0.615906
\(248\) 11.2412 0.713815
\(249\) 2.25102 0.142652
\(250\) 1.28523 0.0812853
\(251\) −23.8655 −1.50638 −0.753188 0.657805i \(-0.771485\pi\)
−0.753188 + 0.657805i \(0.771485\pi\)
\(252\) −0.804849 −0.0507007
\(253\) 1.08590 0.0682697
\(254\) −26.3798 −1.65521
\(255\) −5.69812 −0.356830
\(256\) −8.08826 −0.505516
\(257\) −5.23631 −0.326632 −0.163316 0.986574i \(-0.552219\pi\)
−0.163316 + 0.986574i \(0.552219\pi\)
\(258\) −6.15265 −0.383047
\(259\) 5.59920 0.347917
\(260\) 1.06942 0.0663225
\(261\) −7.33483 −0.454014
\(262\) −17.1009 −1.05650
\(263\) 2.68393 0.165498 0.0827491 0.996570i \(-0.473630\pi\)
0.0827491 + 0.996570i \(0.473630\pi\)
\(264\) 5.30769 0.326666
\(265\) −5.76232 −0.353977
\(266\) −4.05038 −0.248345
\(267\) 13.3197 0.815153
\(268\) 4.16963 0.254700
\(269\) 13.5689 0.827312 0.413656 0.910433i \(-0.364252\pi\)
0.413656 + 0.910433i \(0.364252\pi\)
\(270\) 5.66400 0.344700
\(271\) −12.0364 −0.731159 −0.365579 0.930780i \(-0.619129\pi\)
−0.365579 + 0.930780i \(0.619129\pi\)
\(272\) 21.8563 1.32523
\(273\) 2.54838 0.154235
\(274\) 15.3737 0.928760
\(275\) −2.11972 −0.127824
\(276\) −0.147986 −0.00890771
\(277\) 5.00271 0.300584 0.150292 0.988642i \(-0.451979\pi\)
0.150292 + 0.988642i \(0.451979\pi\)
\(278\) 3.56718 0.213945
\(279\) −8.61024 −0.515482
\(280\) 3.01795 0.180357
\(281\) −0.978797 −0.0583901 −0.0291951 0.999574i \(-0.509294\pi\)
−0.0291951 + 0.999574i \(0.509294\pi\)
\(282\) −11.0356 −0.657158
\(283\) −20.8717 −1.24069 −0.620347 0.784327i \(-0.713008\pi\)
−0.620347 + 0.784327i \(0.713008\pi\)
\(284\) 5.41150 0.321113
\(285\) −2.61473 −0.154883
\(286\) 8.36780 0.494798
\(287\) 7.64566 0.451309
\(288\) 4.49783 0.265037
\(289\) 30.1667 1.77451
\(290\) 4.07808 0.239473
\(291\) 0.629952 0.0369284
\(292\) −3.40123 −0.199042
\(293\) 27.8956 1.62968 0.814840 0.579686i \(-0.196825\pi\)
0.814840 + 0.579686i \(0.196825\pi\)
\(294\) 1.06634 0.0621902
\(295\) 0.788910 0.0459321
\(296\) −16.8981 −0.982183
\(297\) −9.34158 −0.542053
\(298\) 14.4596 0.837622
\(299\) −1.57347 −0.0909962
\(300\) 0.288876 0.0166783
\(301\) 5.76988 0.332570
\(302\) −14.4953 −0.834113
\(303\) 3.33040 0.191326
\(304\) 10.0293 0.575221
\(305\) −5.99308 −0.343163
\(306\) −20.4041 −1.16642
\(307\) 24.8123 1.41611 0.708055 0.706157i \(-0.249573\pi\)
0.708055 + 0.706157i \(0.249573\pi\)
\(308\) −0.738035 −0.0420535
\(309\) 14.1180 0.803143
\(310\) 4.78719 0.271894
\(311\) −8.78571 −0.498192 −0.249096 0.968479i \(-0.580133\pi\)
−0.249096 + 0.968479i \(0.580133\pi\)
\(312\) −7.69088 −0.435410
\(313\) −7.29795 −0.412505 −0.206252 0.978499i \(-0.566127\pi\)
−0.206252 + 0.978499i \(0.566127\pi\)
\(314\) 20.7058 1.16850
\(315\) −2.31162 −0.130245
\(316\) 3.31311 0.186377
\(317\) −12.0895 −0.679012 −0.339506 0.940604i \(-0.610260\pi\)
−0.339506 + 0.940604i \(0.610260\pi\)
\(318\) 6.14459 0.344572
\(319\) −6.72593 −0.376580
\(320\) −8.86559 −0.495601
\(321\) −1.41062 −0.0787330
\(322\) −0.658402 −0.0366913
\(323\) 21.6437 1.20429
\(324\) −1.14148 −0.0634154
\(325\) 3.07149 0.170376
\(326\) 30.6104 1.69535
\(327\) −9.68567 −0.535619
\(328\) −23.0742 −1.27406
\(329\) 10.3490 0.570559
\(330\) 2.26035 0.124428
\(331\) −13.5342 −0.743907 −0.371953 0.928251i \(-0.621312\pi\)
−0.371953 + 0.928251i \(0.621312\pi\)
\(332\) 0.944632 0.0518434
\(333\) 12.9432 0.709285
\(334\) 0.163422 0.00894208
\(335\) 11.9757 0.654300
\(336\) −2.64041 −0.144046
\(337\) −14.4378 −0.786476 −0.393238 0.919437i \(-0.628645\pi\)
−0.393238 + 0.919437i \(0.628645\pi\)
\(338\) 4.58304 0.249285
\(339\) −3.81429 −0.207164
\(340\) −2.39120 −0.129681
\(341\) −7.89547 −0.427564
\(342\) −9.36294 −0.506290
\(343\) −1.00000 −0.0539949
\(344\) −17.4132 −0.938858
\(345\) −0.425033 −0.0228830
\(346\) −6.02985 −0.324167
\(347\) 10.6126 0.569716 0.284858 0.958570i \(-0.408054\pi\)
0.284858 + 0.958570i \(0.408054\pi\)
\(348\) 0.916610 0.0491355
\(349\) 8.40627 0.449977 0.224989 0.974361i \(-0.427765\pi\)
0.224989 + 0.974361i \(0.427765\pi\)
\(350\) 1.28523 0.0686986
\(351\) 13.5360 0.722499
\(352\) 4.12445 0.219834
\(353\) −2.25429 −0.119984 −0.0599920 0.998199i \(-0.519108\pi\)
−0.0599920 + 0.998199i \(0.519108\pi\)
\(354\) −0.841247 −0.0447118
\(355\) 15.5425 0.824908
\(356\) 5.58957 0.296247
\(357\) −5.69812 −0.301576
\(358\) −5.79693 −0.306377
\(359\) 31.0720 1.63992 0.819958 0.572424i \(-0.193997\pi\)
0.819958 + 0.572424i \(0.193997\pi\)
\(360\) 6.97636 0.367687
\(361\) −9.06822 −0.477275
\(362\) 14.1651 0.744500
\(363\) 5.39858 0.283352
\(364\) 1.06942 0.0560527
\(365\) −9.76873 −0.511319
\(366\) 6.39066 0.334045
\(367\) 3.23848 0.169047 0.0845237 0.996421i \(-0.473063\pi\)
0.0845237 + 0.996421i \(0.473063\pi\)
\(368\) 1.63030 0.0849852
\(369\) 17.6739 0.920064
\(370\) −7.19628 −0.374117
\(371\) −5.76232 −0.299165
\(372\) 1.07599 0.0557877
\(373\) 29.2902 1.51659 0.758294 0.651913i \(-0.226033\pi\)
0.758294 + 0.651913i \(0.226033\pi\)
\(374\) −18.7102 −0.967483
\(375\) 0.829686 0.0428448
\(376\) −31.2328 −1.61071
\(377\) 9.74592 0.501941
\(378\) 5.66400 0.291324
\(379\) 7.33776 0.376916 0.188458 0.982081i \(-0.439651\pi\)
0.188458 + 0.982081i \(0.439651\pi\)
\(380\) −1.09726 −0.0562885
\(381\) −17.0295 −0.872449
\(382\) 20.4764 1.04766
\(383\) 34.1527 1.74512 0.872560 0.488506i \(-0.162458\pi\)
0.872560 + 0.488506i \(0.162458\pi\)
\(384\) 6.22501 0.317669
\(385\) −2.11972 −0.108031
\(386\) −16.3438 −0.831879
\(387\) 13.3378 0.677997
\(388\) 0.264357 0.0134207
\(389\) −8.03852 −0.407569 −0.203785 0.979016i \(-0.565324\pi\)
−0.203785 + 0.979016i \(0.565324\pi\)
\(390\) −3.27526 −0.165849
\(391\) 3.51825 0.177926
\(392\) 3.01795 0.152430
\(393\) −11.0395 −0.556871
\(394\) 29.7298 1.49777
\(395\) 9.51566 0.478785
\(396\) −1.70606 −0.0857326
\(397\) 15.9574 0.800879 0.400440 0.916323i \(-0.368857\pi\)
0.400440 + 0.916323i \(0.368857\pi\)
\(398\) 21.0135 1.05331
\(399\) −2.61473 −0.130900
\(400\) −3.18242 −0.159121
\(401\) −7.11257 −0.355185 −0.177592 0.984104i \(-0.556831\pi\)
−0.177592 + 0.984104i \(0.556831\pi\)
\(402\) −12.7701 −0.636916
\(403\) 11.4406 0.569897
\(404\) 1.39759 0.0695328
\(405\) −3.27846 −0.162908
\(406\) 4.07808 0.202391
\(407\) 11.8688 0.588313
\(408\) 17.1967 0.851361
\(409\) −25.6282 −1.26723 −0.633615 0.773648i \(-0.718430\pi\)
−0.633615 + 0.773648i \(0.718430\pi\)
\(410\) −9.82645 −0.485294
\(411\) 9.92454 0.489542
\(412\) 5.92456 0.291882
\(413\) 0.788910 0.0388197
\(414\) −1.52198 −0.0748010
\(415\) 2.71309 0.133181
\(416\) −5.97636 −0.293015
\(417\) 2.30280 0.112769
\(418\) −8.58568 −0.419939
\(419\) −14.6556 −0.715975 −0.357987 0.933726i \(-0.616537\pi\)
−0.357987 + 0.933726i \(0.616537\pi\)
\(420\) 0.288876 0.0140957
\(421\) 33.3142 1.62363 0.811816 0.583913i \(-0.198479\pi\)
0.811816 + 0.583913i \(0.198479\pi\)
\(422\) 1.45744 0.0709471
\(423\) 23.9230 1.16318
\(424\) 17.3904 0.844553
\(425\) −6.86780 −0.333137
\(426\) −16.5736 −0.802991
\(427\) −5.99308 −0.290025
\(428\) −0.591961 −0.0286135
\(429\) 5.40185 0.260804
\(430\) −7.41564 −0.357614
\(431\) −0.525063 −0.0252914 −0.0126457 0.999920i \(-0.504025\pi\)
−0.0126457 + 0.999920i \(0.504025\pi\)
\(432\) −14.0249 −0.674772
\(433\) −17.1908 −0.826136 −0.413068 0.910700i \(-0.635543\pi\)
−0.413068 + 0.910700i \(0.635543\pi\)
\(434\) 4.78719 0.229793
\(435\) 2.63261 0.126224
\(436\) −4.06456 −0.194657
\(437\) 1.61444 0.0772292
\(438\) 10.4168 0.497734
\(439\) 37.5515 1.79224 0.896118 0.443816i \(-0.146376\pi\)
0.896118 + 0.443816i \(0.146376\pi\)
\(440\) 6.39723 0.304976
\(441\) −2.31162 −0.110077
\(442\) 27.1112 1.28955
\(443\) 23.0067 1.09308 0.546541 0.837432i \(-0.315944\pi\)
0.546541 + 0.837432i \(0.315944\pi\)
\(444\) −1.61747 −0.0767619
\(445\) 16.0539 0.761028
\(446\) −0.524238 −0.0248234
\(447\) 9.33443 0.441504
\(448\) −8.86559 −0.418860
\(449\) −9.83944 −0.464352 −0.232176 0.972674i \(-0.574585\pi\)
−0.232176 + 0.972674i \(0.574585\pi\)
\(450\) 2.97097 0.140053
\(451\) 16.2067 0.763143
\(452\) −1.60065 −0.0752884
\(453\) −9.35751 −0.439654
\(454\) −21.4844 −1.00831
\(455\) 3.07149 0.143994
\(456\) 7.89114 0.369536
\(457\) 2.68226 0.125471 0.0627354 0.998030i \(-0.480018\pi\)
0.0627354 + 0.998030i \(0.480018\pi\)
\(458\) −1.28523 −0.0600550
\(459\) −30.2662 −1.41271
\(460\) −0.178364 −0.00831625
\(461\) 5.15966 0.240309 0.120155 0.992755i \(-0.461661\pi\)
0.120155 + 0.992755i \(0.461661\pi\)
\(462\) 2.26035 0.105161
\(463\) 22.1578 1.02976 0.514879 0.857263i \(-0.327837\pi\)
0.514879 + 0.857263i \(0.327837\pi\)
\(464\) −10.0979 −0.468783
\(465\) 3.09038 0.143313
\(466\) 32.2036 1.49180
\(467\) 12.0699 0.558530 0.279265 0.960214i \(-0.409909\pi\)
0.279265 + 0.960214i \(0.409909\pi\)
\(468\) 2.47209 0.114272
\(469\) 11.9757 0.552984
\(470\) −13.3009 −0.613524
\(471\) 13.3667 0.615904
\(472\) −2.38089 −0.109590
\(473\) 12.2305 0.562361
\(474\) −10.1469 −0.466064
\(475\) −3.15147 −0.144599
\(476\) −2.39120 −0.109600
\(477\) −13.3203 −0.609895
\(478\) 11.5968 0.530425
\(479\) 1.77670 0.0811794 0.0405897 0.999176i \(-0.487076\pi\)
0.0405897 + 0.999176i \(0.487076\pi\)
\(480\) −1.61436 −0.0736851
\(481\) −17.1979 −0.784157
\(482\) −3.72290 −0.169573
\(483\) −0.425033 −0.0193397
\(484\) 2.26549 0.102977
\(485\) 0.759265 0.0344765
\(486\) 20.4879 0.929352
\(487\) 14.6185 0.662427 0.331214 0.943556i \(-0.392542\pi\)
0.331214 + 0.943556i \(0.392542\pi\)
\(488\) 18.0868 0.818752
\(489\) 19.7606 0.893605
\(490\) 1.28523 0.0580609
\(491\) 4.77155 0.215337 0.107668 0.994187i \(-0.465662\pi\)
0.107668 + 0.994187i \(0.465662\pi\)
\(492\) −2.20865 −0.0995735
\(493\) −21.7917 −0.981448
\(494\) 12.4407 0.559734
\(495\) −4.90000 −0.220239
\(496\) −11.8538 −0.532250
\(497\) 15.5425 0.697175
\(498\) −2.89308 −0.129642
\(499\) −0.0416221 −0.00186326 −0.000931630 1.00000i \(-0.500297\pi\)
−0.000931630 1.00000i \(0.500297\pi\)
\(500\) 0.348175 0.0155709
\(501\) 0.105498 0.00471329
\(502\) 30.6727 1.36899
\(503\) 7.28459 0.324804 0.162402 0.986725i \(-0.448076\pi\)
0.162402 + 0.986725i \(0.448076\pi\)
\(504\) 6.97636 0.310752
\(505\) 4.01405 0.178623
\(506\) −1.39563 −0.0620433
\(507\) 2.95860 0.131396
\(508\) −7.14639 −0.317070
\(509\) −24.6010 −1.09042 −0.545211 0.838299i \(-0.683550\pi\)
−0.545211 + 0.838299i \(0.683550\pi\)
\(510\) 7.32341 0.324286
\(511\) −9.76873 −0.432143
\(512\) 25.4010 1.12258
\(513\) −13.8885 −0.613191
\(514\) 6.72988 0.296842
\(515\) 17.0160 0.749816
\(516\) −1.66678 −0.0733758
\(517\) 21.9370 0.964790
\(518\) −7.19628 −0.316186
\(519\) −3.89259 −0.170866
\(520\) −9.26963 −0.406500
\(521\) −20.4969 −0.897987 −0.448993 0.893535i \(-0.648217\pi\)
−0.448993 + 0.893535i \(0.648217\pi\)
\(522\) 9.42696 0.412607
\(523\) 16.0003 0.699643 0.349822 0.936816i \(-0.386242\pi\)
0.349822 + 0.936816i \(0.386242\pi\)
\(524\) −4.63271 −0.202381
\(525\) 0.829686 0.0362105
\(526\) −3.44948 −0.150404
\(527\) −25.5809 −1.11432
\(528\) −5.59695 −0.243576
\(529\) −22.7376 −0.988590
\(530\) 7.40593 0.321693
\(531\) 1.82366 0.0791402
\(532\) −1.09726 −0.0475724
\(533\) −23.4836 −1.01719
\(534\) −17.1189 −0.740809
\(535\) −1.70018 −0.0735053
\(536\) −36.1420 −1.56110
\(537\) −3.74223 −0.161489
\(538\) −17.4392 −0.751858
\(539\) −2.11972 −0.0913030
\(540\) 1.53440 0.0660301
\(541\) 34.3532 1.47696 0.738481 0.674275i \(-0.235544\pi\)
0.738481 + 0.674275i \(0.235544\pi\)
\(542\) 15.4696 0.664475
\(543\) 9.14430 0.392420
\(544\) 13.3630 0.572935
\(545\) −11.6739 −0.500055
\(546\) −3.27526 −0.140168
\(547\) 2.07177 0.0885826 0.0442913 0.999019i \(-0.485897\pi\)
0.0442913 + 0.999019i \(0.485897\pi\)
\(548\) 4.16480 0.177912
\(549\) −13.8537 −0.591263
\(550\) 2.72434 0.116166
\(551\) −9.99969 −0.426001
\(552\) 1.28273 0.0545966
\(553\) 9.51566 0.404647
\(554\) −6.42965 −0.273170
\(555\) −4.64558 −0.197194
\(556\) 0.966364 0.0409829
\(557\) 44.3290 1.87828 0.939139 0.343537i \(-0.111625\pi\)
0.939139 + 0.343537i \(0.111625\pi\)
\(558\) 11.0662 0.468468
\(559\) −17.7221 −0.749567
\(560\) −3.18242 −0.134482
\(561\) −12.0784 −0.509952
\(562\) 1.25798 0.0530648
\(563\) −0.434764 −0.0183231 −0.00916157 0.999958i \(-0.502916\pi\)
−0.00916157 + 0.999958i \(0.502916\pi\)
\(564\) −2.98958 −0.125884
\(565\) −4.59727 −0.193409
\(566\) 26.8250 1.12754
\(567\) −3.27846 −0.137682
\(568\) −46.9064 −1.96815
\(569\) −32.2191 −1.35069 −0.675347 0.737500i \(-0.736006\pi\)
−0.675347 + 0.737500i \(0.736006\pi\)
\(570\) 3.36054 0.140758
\(571\) −30.2732 −1.26689 −0.633446 0.773787i \(-0.718360\pi\)
−0.633446 + 0.773787i \(0.718360\pi\)
\(572\) 2.26687 0.0947826
\(573\) 13.2186 0.552215
\(574\) −9.82645 −0.410148
\(575\) −0.512282 −0.0213636
\(576\) −20.4939 −0.853912
\(577\) −27.7311 −1.15446 −0.577231 0.816581i \(-0.695867\pi\)
−0.577231 + 0.816581i \(0.695867\pi\)
\(578\) −38.7713 −1.61267
\(579\) −10.5508 −0.438477
\(580\) 1.10477 0.0458730
\(581\) 2.71309 0.112558
\(582\) −0.809635 −0.0335604
\(583\) −12.2145 −0.505874
\(584\) 29.4816 1.21996
\(585\) 7.10013 0.293554
\(586\) −35.8524 −1.48105
\(587\) 43.0865 1.77837 0.889184 0.457549i \(-0.151273\pi\)
0.889184 + 0.457549i \(0.151273\pi\)
\(588\) 0.288876 0.0119130
\(589\) −11.7385 −0.483676
\(590\) −1.01393 −0.0417430
\(591\) 19.1921 0.789459
\(592\) 17.8190 0.732358
\(593\) −12.9793 −0.532997 −0.266499 0.963835i \(-0.585867\pi\)
−0.266499 + 0.963835i \(0.585867\pi\)
\(594\) 12.0061 0.492617
\(595\) −6.86780 −0.281552
\(596\) 3.91717 0.160453
\(597\) 13.5653 0.555192
\(598\) 2.02228 0.0826971
\(599\) −21.6877 −0.886136 −0.443068 0.896488i \(-0.646110\pi\)
−0.443068 + 0.896488i \(0.646110\pi\)
\(600\) −2.50395 −0.102223
\(601\) 28.1572 1.14856 0.574278 0.818660i \(-0.305283\pi\)
0.574278 + 0.818660i \(0.305283\pi\)
\(602\) −7.41564 −0.302239
\(603\) 27.6832 1.12735
\(604\) −3.92685 −0.159781
\(605\) 6.50677 0.264538
\(606\) −4.28034 −0.173877
\(607\) 39.8634 1.61801 0.809003 0.587804i \(-0.200007\pi\)
0.809003 + 0.587804i \(0.200007\pi\)
\(608\) 6.13197 0.248684
\(609\) 2.63261 0.106679
\(610\) 7.70250 0.311865
\(611\) −31.7869 −1.28596
\(612\) −5.52754 −0.223438
\(613\) 34.6287 1.39864 0.699319 0.714810i \(-0.253487\pi\)
0.699319 + 0.714810i \(0.253487\pi\)
\(614\) −31.8896 −1.28696
\(615\) −6.34349 −0.255794
\(616\) 6.39723 0.257752
\(617\) 10.7919 0.434465 0.217233 0.976120i \(-0.430297\pi\)
0.217233 + 0.976120i \(0.430297\pi\)
\(618\) −18.1449 −0.729895
\(619\) −7.55894 −0.303819 −0.151910 0.988394i \(-0.548542\pi\)
−0.151910 + 0.988394i \(0.548542\pi\)
\(620\) 1.29687 0.0520836
\(621\) −2.25761 −0.0905949
\(622\) 11.2917 0.452755
\(623\) 16.0539 0.643186
\(624\) 8.11001 0.324660
\(625\) 1.00000 0.0400000
\(626\) 9.37957 0.374883
\(627\) −5.54251 −0.221347
\(628\) 5.60929 0.223835
\(629\) 38.4542 1.53327
\(630\) 2.97097 0.118366
\(631\) −36.1018 −1.43719 −0.718595 0.695429i \(-0.755214\pi\)
−0.718595 + 0.695429i \(0.755214\pi\)
\(632\) −28.7178 −1.14233
\(633\) 0.940855 0.0373956
\(634\) 15.5378 0.617084
\(635\) −20.5253 −0.814521
\(636\) 1.66460 0.0660055
\(637\) 3.07149 0.121697
\(638\) 8.64440 0.342235
\(639\) 35.9283 1.42130
\(640\) 7.50285 0.296576
\(641\) −18.3572 −0.725067 −0.362534 0.931971i \(-0.618088\pi\)
−0.362534 + 0.931971i \(0.618088\pi\)
\(642\) 1.81297 0.0715523
\(643\) 15.1575 0.597753 0.298876 0.954292i \(-0.403388\pi\)
0.298876 + 0.954292i \(0.403388\pi\)
\(644\) −0.178364 −0.00702852
\(645\) −4.78719 −0.188495
\(646\) −27.8172 −1.09445
\(647\) −16.4182 −0.645467 −0.322733 0.946490i \(-0.604602\pi\)
−0.322733 + 0.946490i \(0.604602\pi\)
\(648\) 9.89422 0.388682
\(649\) 1.67227 0.0656424
\(650\) −3.94759 −0.154837
\(651\) 3.09038 0.121122
\(652\) 8.29247 0.324758
\(653\) 39.9952 1.56513 0.782567 0.622566i \(-0.213910\pi\)
0.782567 + 0.622566i \(0.213910\pi\)
\(654\) 12.4483 0.486769
\(655\) −13.3057 −0.519896
\(656\) 24.3317 0.949994
\(657\) −22.5816 −0.880993
\(658\) −13.3009 −0.518523
\(659\) −46.2910 −1.80324 −0.901621 0.432527i \(-0.857622\pi\)
−0.901621 + 0.432527i \(0.857622\pi\)
\(660\) 0.612337 0.0238352
\(661\) 1.10700 0.0430572 0.0215286 0.999768i \(-0.493147\pi\)
0.0215286 + 0.999768i \(0.493147\pi\)
\(662\) 17.3946 0.676060
\(663\) 17.5017 0.679711
\(664\) −8.18799 −0.317756
\(665\) −3.15147 −0.122209
\(666\) −16.6351 −0.644596
\(667\) −1.62548 −0.0629389
\(668\) 0.0442718 0.00171293
\(669\) −0.338423 −0.0130842
\(670\) −15.3915 −0.594626
\(671\) −12.7037 −0.490420
\(672\) −1.61436 −0.0622753
\(673\) 20.3284 0.783601 0.391801 0.920050i \(-0.371852\pi\)
0.391801 + 0.920050i \(0.371852\pi\)
\(674\) 18.5559 0.714747
\(675\) 4.40698 0.169625
\(676\) 1.24156 0.0477525
\(677\) 39.2118 1.50703 0.753516 0.657429i \(-0.228356\pi\)
0.753516 + 0.657429i \(0.228356\pi\)
\(678\) 4.90225 0.188270
\(679\) 0.759265 0.0291379
\(680\) 20.7267 0.794833
\(681\) −13.8693 −0.531473
\(682\) 10.1475 0.388569
\(683\) −4.94760 −0.189315 −0.0946573 0.995510i \(-0.530176\pi\)
−0.0946573 + 0.995510i \(0.530176\pi\)
\(684\) −2.53646 −0.0969839
\(685\) 11.9618 0.457037
\(686\) 1.28523 0.0490704
\(687\) −0.829686 −0.0316545
\(688\) 18.3622 0.700052
\(689\) 17.6989 0.674276
\(690\) 0.546267 0.0207960
\(691\) −1.07221 −0.0407888 −0.0203944 0.999792i \(-0.506492\pi\)
−0.0203944 + 0.999792i \(0.506492\pi\)
\(692\) −1.63351 −0.0620968
\(693\) −4.90000 −0.186136
\(694\) −13.6397 −0.517757
\(695\) 2.77551 0.105281
\(696\) −7.94510 −0.301158
\(697\) 52.5089 1.98891
\(698\) −10.8040 −0.408938
\(699\) 20.7891 0.786317
\(700\) 0.348175 0.0131598
\(701\) 6.44084 0.243267 0.121634 0.992575i \(-0.461187\pi\)
0.121634 + 0.992575i \(0.461187\pi\)
\(702\) −17.3969 −0.656605
\(703\) 17.6457 0.665521
\(704\) −18.7926 −0.708273
\(705\) −8.58643 −0.323383
\(706\) 2.89729 0.109041
\(707\) 4.01405 0.150964
\(708\) −0.227897 −0.00856490
\(709\) 17.9478 0.674045 0.337023 0.941497i \(-0.390580\pi\)
0.337023 + 0.941497i \(0.390580\pi\)
\(710\) −19.9757 −0.749675
\(711\) 21.9966 0.824937
\(712\) −48.4500 −1.81574
\(713\) −1.90813 −0.0714600
\(714\) 7.32341 0.274072
\(715\) 6.51072 0.243487
\(716\) −1.57041 −0.0586891
\(717\) 7.48634 0.279582
\(718\) −39.9347 −1.49035
\(719\) 20.0385 0.747311 0.373656 0.927568i \(-0.378104\pi\)
0.373656 + 0.927568i \(0.378104\pi\)
\(720\) −7.35656 −0.274163
\(721\) 17.0160 0.633711
\(722\) 11.6548 0.433746
\(723\) −2.40333 −0.0893807
\(724\) 3.83738 0.142615
\(725\) 3.17302 0.117843
\(726\) −6.93843 −0.257509
\(727\) −11.3970 −0.422692 −0.211346 0.977411i \(-0.567785\pi\)
−0.211346 + 0.977411i \(0.567785\pi\)
\(728\) −9.26963 −0.343555
\(729\) 3.39068 0.125581
\(730\) 12.5551 0.464685
\(731\) 39.6264 1.46563
\(732\) 1.73126 0.0639891
\(733\) −26.2293 −0.968800 −0.484400 0.874847i \(-0.660962\pi\)
−0.484400 + 0.874847i \(0.660962\pi\)
\(734\) −4.16220 −0.153630
\(735\) 0.829686 0.0306034
\(736\) 0.996772 0.0367415
\(737\) 25.3851 0.935072
\(738\) −22.7150 −0.836152
\(739\) 11.3041 0.415829 0.207914 0.978147i \(-0.433332\pi\)
0.207914 + 0.978147i \(0.433332\pi\)
\(740\) −1.94950 −0.0716651
\(741\) 8.03114 0.295031
\(742\) 7.40593 0.271880
\(743\) −17.7554 −0.651381 −0.325690 0.945476i \(-0.605597\pi\)
−0.325690 + 0.945476i \(0.605597\pi\)
\(744\) −9.32664 −0.341931
\(745\) 11.2506 0.412189
\(746\) −37.6447 −1.37827
\(747\) 6.27165 0.229468
\(748\) −5.06868 −0.185329
\(749\) −1.70018 −0.0621233
\(750\) −1.06634 −0.0389372
\(751\) 49.1304 1.79279 0.896397 0.443251i \(-0.146175\pi\)
0.896397 + 0.443251i \(0.146175\pi\)
\(752\) 32.9349 1.20101
\(753\) 19.8009 0.721583
\(754\) −12.5258 −0.456162
\(755\) −11.2784 −0.410462
\(756\) 1.53440 0.0558056
\(757\) 32.2813 1.17328 0.586642 0.809846i \(-0.300450\pi\)
0.586642 + 0.809846i \(0.300450\pi\)
\(758\) −9.43074 −0.342540
\(759\) −0.900953 −0.0327025
\(760\) 9.51099 0.345000
\(761\) 3.15537 0.114382 0.0571910 0.998363i \(-0.481786\pi\)
0.0571910 + 0.998363i \(0.481786\pi\)
\(762\) 21.8869 0.792880
\(763\) −11.6739 −0.422624
\(764\) 5.54715 0.200689
\(765\) −15.8758 −0.573989
\(766\) −43.8942 −1.58596
\(767\) −2.42313 −0.0874943
\(768\) 6.71072 0.242152
\(769\) 14.3547 0.517644 0.258822 0.965925i \(-0.416666\pi\)
0.258822 + 0.965925i \(0.416666\pi\)
\(770\) 2.72434 0.0981784
\(771\) 4.34450 0.156463
\(772\) −4.42761 −0.159353
\(773\) 9.99331 0.359435 0.179717 0.983718i \(-0.442482\pi\)
0.179717 + 0.983718i \(0.442482\pi\)
\(774\) −17.1421 −0.616162
\(775\) 3.72476 0.133797
\(776\) −2.29143 −0.0822574
\(777\) −4.64558 −0.166659
\(778\) 10.3314 0.370398
\(779\) 24.0951 0.863296
\(780\) −0.887281 −0.0317698
\(781\) 32.9457 1.17889
\(782\) −4.52177 −0.161698
\(783\) 13.9834 0.499727
\(784\) −3.18242 −0.113658
\(785\) 16.1105 0.575010
\(786\) 14.1884 0.506083
\(787\) −13.4187 −0.478327 −0.239163 0.970979i \(-0.576873\pi\)
−0.239163 + 0.970979i \(0.576873\pi\)
\(788\) 8.05392 0.286909
\(789\) −2.22682 −0.0792769
\(790\) −12.2298 −0.435118
\(791\) −4.59727 −0.163460
\(792\) 14.7880 0.525468
\(793\) 18.4077 0.653677
\(794\) −20.5090 −0.727837
\(795\) 4.78092 0.169562
\(796\) 5.69265 0.201771
\(797\) −3.57274 −0.126553 −0.0632765 0.997996i \(-0.520155\pi\)
−0.0632765 + 0.997996i \(0.520155\pi\)
\(798\) 3.36054 0.118962
\(799\) 71.0749 2.51445
\(800\) −1.94575 −0.0687926
\(801\) 37.1106 1.31124
\(802\) 9.14131 0.322791
\(803\) −20.7070 −0.730735
\(804\) −3.45948 −0.122006
\(805\) −0.512282 −0.0180556
\(806\) −14.7038 −0.517920
\(807\) −11.2579 −0.396298
\(808\) −12.1142 −0.426176
\(809\) −27.7845 −0.976851 −0.488425 0.872606i \(-0.662429\pi\)
−0.488425 + 0.872606i \(0.662429\pi\)
\(810\) 4.21358 0.148050
\(811\) −0.586590 −0.0205980 −0.0102990 0.999947i \(-0.503278\pi\)
−0.0102990 + 0.999947i \(0.503278\pi\)
\(812\) 1.10477 0.0387697
\(813\) 9.98643 0.350239
\(814\) −15.2541 −0.534657
\(815\) 23.8170 0.834272
\(816\) −18.1338 −0.634811
\(817\) 18.1836 0.636164
\(818\) 32.9382 1.15166
\(819\) 7.10013 0.248099
\(820\) −2.66203 −0.0929620
\(821\) 27.8267 0.971158 0.485579 0.874193i \(-0.338609\pi\)
0.485579 + 0.874193i \(0.338609\pi\)
\(822\) −12.7554 −0.444894
\(823\) −49.6784 −1.73168 −0.865840 0.500321i \(-0.833215\pi\)
−0.865840 + 0.500321i \(0.833215\pi\)
\(824\) −51.3536 −1.78899
\(825\) 1.75871 0.0612303
\(826\) −1.01393 −0.0352793
\(827\) −11.1529 −0.387823 −0.193912 0.981019i \(-0.562118\pi\)
−0.193912 + 0.981019i \(0.562118\pi\)
\(828\) −0.412309 −0.0143287
\(829\) 23.5046 0.816349 0.408174 0.912904i \(-0.366166\pi\)
0.408174 + 0.912904i \(0.366166\pi\)
\(830\) −3.48696 −0.121034
\(831\) −4.15068 −0.143985
\(832\) 27.2306 0.944051
\(833\) −6.86780 −0.237955
\(834\) −2.95964 −0.102484
\(835\) 0.127154 0.00440034
\(836\) −2.32590 −0.0804428
\(837\) 16.4150 0.567384
\(838\) 18.8359 0.650676
\(839\) −9.87033 −0.340761 −0.170381 0.985378i \(-0.554500\pi\)
−0.170381 + 0.985378i \(0.554500\pi\)
\(840\) −2.50395 −0.0863946
\(841\) −18.9319 −0.652825
\(842\) −42.8165 −1.47555
\(843\) 0.812094 0.0279700
\(844\) 0.394827 0.0135905
\(845\) 3.56592 0.122671
\(846\) −30.7466 −1.05709
\(847\) 6.50677 0.223575
\(848\) −18.3381 −0.629735
\(849\) 17.3170 0.594317
\(850\) 8.82673 0.302754
\(851\) 2.86837 0.0983264
\(852\) −4.48985 −0.153820
\(853\) 5.39797 0.184823 0.0924115 0.995721i \(-0.470542\pi\)
0.0924115 + 0.995721i \(0.470542\pi\)
\(854\) 7.70250 0.263574
\(855\) −7.28501 −0.249142
\(856\) 5.13107 0.175376
\(857\) −32.0359 −1.09433 −0.547163 0.837026i \(-0.684292\pi\)
−0.547163 + 0.837026i \(0.684292\pi\)
\(858\) −6.94264 −0.237018
\(859\) 9.28563 0.316822 0.158411 0.987373i \(-0.449363\pi\)
0.158411 + 0.987373i \(0.449363\pi\)
\(860\) −2.00893 −0.0685039
\(861\) −6.34349 −0.216186
\(862\) 0.674829 0.0229848
\(863\) 19.6009 0.667222 0.333611 0.942711i \(-0.391733\pi\)
0.333611 + 0.942711i \(0.391733\pi\)
\(864\) −8.57487 −0.291723
\(865\) −4.69164 −0.159521
\(866\) 22.0941 0.750790
\(867\) −25.0289 −0.850026
\(868\) 1.29687 0.0440186
\(869\) 20.1706 0.684240
\(870\) −3.38352 −0.114712
\(871\) −36.7832 −1.24635
\(872\) 35.2313 1.19308
\(873\) 1.75513 0.0594023
\(874\) −2.07493 −0.0701857
\(875\) 1.00000 0.0338062
\(876\) 2.82195 0.0953450
\(877\) 41.2933 1.39438 0.697188 0.716888i \(-0.254434\pi\)
0.697188 + 0.716888i \(0.254434\pi\)
\(878\) −48.2625 −1.62878
\(879\) −23.1446 −0.780649
\(880\) −6.74586 −0.227403
\(881\) 31.7879 1.07096 0.535481 0.844547i \(-0.320130\pi\)
0.535481 + 0.844547i \(0.320130\pi\)
\(882\) 2.97097 0.100038
\(883\) 2.44560 0.0823009 0.0411504 0.999153i \(-0.486898\pi\)
0.0411504 + 0.999153i \(0.486898\pi\)
\(884\) 7.34455 0.247024
\(885\) −0.654548 −0.0220024
\(886\) −29.5690 −0.993390
\(887\) −7.18207 −0.241150 −0.120575 0.992704i \(-0.538474\pi\)
−0.120575 + 0.992704i \(0.538474\pi\)
\(888\) 14.0201 0.470485
\(889\) −20.5253 −0.688396
\(890\) −20.6330 −0.691621
\(891\) −6.94942 −0.232814
\(892\) −0.142018 −0.00475512
\(893\) 32.6146 1.09141
\(894\) −11.9969 −0.401237
\(895\) −4.51041 −0.150766
\(896\) 7.50285 0.250653
\(897\) 1.30549 0.0435889
\(898\) 12.6460 0.422002
\(899\) 11.8188 0.394178
\(900\) 0.804849 0.0268283
\(901\) −39.5745 −1.31842
\(902\) −20.8294 −0.693542
\(903\) −4.78719 −0.159308
\(904\) 13.8743 0.461454
\(905\) 11.0214 0.366364
\(906\) 12.0266 0.399556
\(907\) −16.9745 −0.563629 −0.281814 0.959469i \(-0.590936\pi\)
−0.281814 + 0.959469i \(0.590936\pi\)
\(908\) −5.82022 −0.193151
\(909\) 9.27896 0.307764
\(910\) −3.94759 −0.130861
\(911\) −15.6286 −0.517800 −0.258900 0.965904i \(-0.583360\pi\)
−0.258900 + 0.965904i \(0.583360\pi\)
\(912\) −8.32119 −0.275542
\(913\) 5.75101 0.190331
\(914\) −3.44733 −0.114027
\(915\) 4.97237 0.164382
\(916\) −0.348175 −0.0115040
\(917\) −13.3057 −0.439393
\(918\) 38.8992 1.28386
\(919\) −42.8669 −1.41405 −0.707023 0.707190i \(-0.749962\pi\)
−0.707023 + 0.707190i \(0.749962\pi\)
\(920\) 1.54604 0.0509715
\(921\) −20.5864 −0.678345
\(922\) −6.63136 −0.218392
\(923\) −47.7386 −1.57134
\(924\) 0.612337 0.0201444
\(925\) −5.59920 −0.184101
\(926\) −28.4779 −0.935842
\(927\) 39.3346 1.29192
\(928\) −6.17390 −0.202668
\(929\) −4.58841 −0.150541 −0.0752704 0.997163i \(-0.523982\pi\)
−0.0752704 + 0.997163i \(0.523982\pi\)
\(930\) −3.97187 −0.130243
\(931\) −3.15147 −0.103285
\(932\) 8.72409 0.285767
\(933\) 7.28938 0.238644
\(934\) −15.5127 −0.507590
\(935\) −14.5578 −0.476092
\(936\) −21.4279 −0.700392
\(937\) 36.5381 1.19365 0.596825 0.802372i \(-0.296429\pi\)
0.596825 + 0.802372i \(0.296429\pi\)
\(938\) −15.3915 −0.502551
\(939\) 6.05501 0.197598
\(940\) −3.60327 −0.117526
\(941\) −40.5683 −1.32249 −0.661244 0.750171i \(-0.729971\pi\)
−0.661244 + 0.750171i \(0.729971\pi\)
\(942\) −17.1793 −0.559732
\(943\) 3.91673 0.127546
\(944\) 2.51065 0.0817146
\(945\) 4.40698 0.143359
\(946\) −15.7191 −0.511072
\(947\) −21.5637 −0.700725 −0.350363 0.936614i \(-0.613942\pi\)
−0.350363 + 0.936614i \(0.613942\pi\)
\(948\) −2.74884 −0.0892783
\(949\) 30.0046 0.973991
\(950\) 4.05038 0.131412
\(951\) 10.0305 0.325260
\(952\) 20.7267 0.671756
\(953\) 27.6494 0.895653 0.447826 0.894121i \(-0.352198\pi\)
0.447826 + 0.894121i \(0.352198\pi\)
\(954\) 17.1197 0.554271
\(955\) 15.9321 0.515549
\(956\) 3.14162 0.101607
\(957\) 5.58041 0.180389
\(958\) −2.28347 −0.0737756
\(959\) 11.9618 0.386267
\(960\) 7.35566 0.237403
\(961\) −17.1261 −0.552456
\(962\) 22.1033 0.712640
\(963\) −3.93018 −0.126648
\(964\) −1.00855 −0.0324832
\(965\) −12.7166 −0.409363
\(966\) 0.546267 0.0175758
\(967\) 31.2170 1.00387 0.501936 0.864905i \(-0.332621\pi\)
0.501936 + 0.864905i \(0.332621\pi\)
\(968\) −19.6371 −0.631161
\(969\) −17.9575 −0.576877
\(970\) −0.975833 −0.0313321
\(971\) 44.8773 1.44018 0.720090 0.693881i \(-0.244100\pi\)
0.720090 + 0.693881i \(0.244100\pi\)
\(972\) 5.55027 0.178025
\(973\) 2.77551 0.0889788
\(974\) −18.7882 −0.602012
\(975\) −2.54838 −0.0816134
\(976\) −19.0725 −0.610496
\(977\) 49.4673 1.58260 0.791299 0.611429i \(-0.209405\pi\)
0.791299 + 0.611429i \(0.209405\pi\)
\(978\) −25.3970 −0.812106
\(979\) 34.0299 1.08760
\(980\) 0.348175 0.0111220
\(981\) −26.9856 −0.861585
\(982\) −6.13255 −0.195698
\(983\) 15.3198 0.488626 0.244313 0.969696i \(-0.421438\pi\)
0.244313 + 0.969696i \(0.421438\pi\)
\(984\) 19.1444 0.610300
\(985\) 23.1318 0.737041
\(986\) 28.0074 0.891938
\(987\) −8.58643 −0.273309
\(988\) 3.37024 0.107222
\(989\) 2.95580 0.0939891
\(990\) 6.29764 0.200152
\(991\) −20.4127 −0.648431 −0.324215 0.945983i \(-0.605100\pi\)
−0.324215 + 0.945983i \(0.605100\pi\)
\(992\) −7.24745 −0.230107
\(993\) 11.2291 0.356346
\(994\) −19.9757 −0.633591
\(995\) 16.3500 0.518329
\(996\) −0.783748 −0.0248340
\(997\) −33.0932 −1.04807 −0.524036 0.851696i \(-0.675574\pi\)
−0.524036 + 0.851696i \(0.675574\pi\)
\(998\) 0.0534941 0.00169333
\(999\) −24.6755 −0.780700
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 \(a_p\))