Properties

Label 8002.2.a.d.1.11
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.64782 q^{3}\) \(+1.00000 q^{4}\) \(-0.675974 q^{5}\) \(-2.64782 q^{6}\) \(-0.999289 q^{7}\) \(+1.00000 q^{8}\) \(+4.01094 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.64782 q^{3}\) \(+1.00000 q^{4}\) \(-0.675974 q^{5}\) \(-2.64782 q^{6}\) \(-0.999289 q^{7}\) \(+1.00000 q^{8}\) \(+4.01094 q^{9}\) \(-0.675974 q^{10}\) \(-1.77569 q^{11}\) \(-2.64782 q^{12}\) \(+1.00412 q^{13}\) \(-0.999289 q^{14}\) \(+1.78986 q^{15}\) \(+1.00000 q^{16}\) \(-3.24084 q^{17}\) \(+4.01094 q^{18}\) \(-3.17784 q^{19}\) \(-0.675974 q^{20}\) \(+2.64594 q^{21}\) \(-1.77569 q^{22}\) \(+8.40714 q^{23}\) \(-2.64782 q^{24}\) \(-4.54306 q^{25}\) \(+1.00412 q^{26}\) \(-2.67680 q^{27}\) \(-0.999289 q^{28}\) \(+4.15832 q^{29}\) \(+1.78986 q^{30}\) \(-2.23231 q^{31}\) \(+1.00000 q^{32}\) \(+4.70171 q^{33}\) \(-3.24084 q^{34}\) \(+0.675494 q^{35}\) \(+4.01094 q^{36}\) \(+1.52693 q^{37}\) \(-3.17784 q^{38}\) \(-2.65872 q^{39}\) \(-0.675974 q^{40}\) \(+7.13965 q^{41}\) \(+2.64594 q^{42}\) \(+2.77622 q^{43}\) \(-1.77569 q^{44}\) \(-2.71130 q^{45}\) \(+8.40714 q^{46}\) \(+11.0813 q^{47}\) \(-2.64782 q^{48}\) \(-6.00142 q^{49}\) \(-4.54306 q^{50}\) \(+8.58115 q^{51}\) \(+1.00412 q^{52}\) \(-8.39649 q^{53}\) \(-2.67680 q^{54}\) \(+1.20032 q^{55}\) \(-0.999289 q^{56}\) \(+8.41435 q^{57}\) \(+4.15832 q^{58}\) \(-3.93445 q^{59}\) \(+1.78986 q^{60}\) \(-1.97459 q^{61}\) \(-2.23231 q^{62}\) \(-4.00809 q^{63}\) \(+1.00000 q^{64}\) \(-0.678759 q^{65}\) \(+4.70171 q^{66}\) \(-11.2348 q^{67}\) \(-3.24084 q^{68}\) \(-22.2606 q^{69}\) \(+0.675494 q^{70}\) \(+0.753276 q^{71}\) \(+4.01094 q^{72}\) \(+0.958508 q^{73}\) \(+1.52693 q^{74}\) \(+12.0292 q^{75}\) \(-3.17784 q^{76}\) \(+1.77443 q^{77}\) \(-2.65872 q^{78}\) \(+8.32703 q^{79}\) \(-0.675974 q^{80}\) \(-4.94516 q^{81}\) \(+7.13965 q^{82}\) \(+12.0952 q^{83}\) \(+2.64594 q^{84}\) \(+2.19072 q^{85}\) \(+2.77622 q^{86}\) \(-11.0105 q^{87}\) \(-1.77569 q^{88}\) \(+0.663771 q^{89}\) \(-2.71130 q^{90}\) \(-1.00341 q^{91}\) \(+8.40714 q^{92}\) \(+5.91074 q^{93}\) \(+11.0813 q^{94}\) \(+2.14814 q^{95}\) \(-2.64782 q^{96}\) \(+12.5368 q^{97}\) \(-6.00142 q^{98}\) \(-7.12219 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.64782 −1.52872 −0.764359 0.644790i \(-0.776945\pi\)
−0.764359 + 0.644790i \(0.776945\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.675974 −0.302305 −0.151152 0.988510i \(-0.548298\pi\)
−0.151152 + 0.988510i \(0.548298\pi\)
\(6\) −2.64782 −1.08097
\(7\) −0.999289 −0.377696 −0.188848 0.982006i \(-0.560475\pi\)
−0.188848 + 0.982006i \(0.560475\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.01094 1.33698
\(10\) −0.675974 −0.213762
\(11\) −1.77569 −0.535391 −0.267695 0.963504i \(-0.586262\pi\)
−0.267695 + 0.963504i \(0.586262\pi\)
\(12\) −2.64782 −0.764359
\(13\) 1.00412 0.278492 0.139246 0.990258i \(-0.455532\pi\)
0.139246 + 0.990258i \(0.455532\pi\)
\(14\) −0.999289 −0.267071
\(15\) 1.78986 0.462139
\(16\) 1.00000 0.250000
\(17\) −3.24084 −0.786019 −0.393009 0.919534i \(-0.628566\pi\)
−0.393009 + 0.919534i \(0.628566\pi\)
\(18\) 4.01094 0.945389
\(19\) −3.17784 −0.729047 −0.364523 0.931194i \(-0.618768\pi\)
−0.364523 + 0.931194i \(0.618768\pi\)
\(20\) −0.675974 −0.151152
\(21\) 2.64594 0.577391
\(22\) −1.77569 −0.378578
\(23\) 8.40714 1.75301 0.876505 0.481392i \(-0.159869\pi\)
0.876505 + 0.481392i \(0.159869\pi\)
\(24\) −2.64782 −0.540484
\(25\) −4.54306 −0.908612
\(26\) 1.00412 0.196924
\(27\) −2.67680 −0.515150
\(28\) −0.999289 −0.188848
\(29\) 4.15832 0.772181 0.386090 0.922461i \(-0.373825\pi\)
0.386090 + 0.922461i \(0.373825\pi\)
\(30\) 1.78986 0.326782
\(31\) −2.23231 −0.400934 −0.200467 0.979700i \(-0.564246\pi\)
−0.200467 + 0.979700i \(0.564246\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.70171 0.818462
\(34\) −3.24084 −0.555799
\(35\) 0.675494 0.114179
\(36\) 4.01094 0.668491
\(37\) 1.52693 0.251026 0.125513 0.992092i \(-0.459942\pi\)
0.125513 + 0.992092i \(0.459942\pi\)
\(38\) −3.17784 −0.515514
\(39\) −2.65872 −0.425737
\(40\) −0.675974 −0.106881
\(41\) 7.13965 1.11503 0.557513 0.830168i \(-0.311756\pi\)
0.557513 + 0.830168i \(0.311756\pi\)
\(42\) 2.64594 0.408277
\(43\) 2.77622 0.423369 0.211685 0.977338i \(-0.432105\pi\)
0.211685 + 0.977338i \(0.432105\pi\)
\(44\) −1.77569 −0.267695
\(45\) −2.71130 −0.404176
\(46\) 8.40714 1.23957
\(47\) 11.0813 1.61638 0.808189 0.588923i \(-0.200448\pi\)
0.808189 + 0.588923i \(0.200448\pi\)
\(48\) −2.64782 −0.382180
\(49\) −6.00142 −0.857346
\(50\) −4.54306 −0.642486
\(51\) 8.58115 1.20160
\(52\) 1.00412 0.139246
\(53\) −8.39649 −1.15335 −0.576673 0.816975i \(-0.695649\pi\)
−0.576673 + 0.816975i \(0.695649\pi\)
\(54\) −2.67680 −0.364266
\(55\) 1.20032 0.161851
\(56\) −0.999289 −0.133536
\(57\) 8.41435 1.11451
\(58\) 4.15832 0.546014
\(59\) −3.93445 −0.512222 −0.256111 0.966647i \(-0.582441\pi\)
−0.256111 + 0.966647i \(0.582441\pi\)
\(60\) 1.78986 0.231070
\(61\) −1.97459 −0.252821 −0.126410 0.991978i \(-0.540346\pi\)
−0.126410 + 0.991978i \(0.540346\pi\)
\(62\) −2.23231 −0.283503
\(63\) −4.00809 −0.504972
\(64\) 1.00000 0.125000
\(65\) −0.678759 −0.0841896
\(66\) 4.70171 0.578740
\(67\) −11.2348 −1.37256 −0.686278 0.727340i \(-0.740757\pi\)
−0.686278 + 0.727340i \(0.740757\pi\)
\(68\) −3.24084 −0.393009
\(69\) −22.2606 −2.67986
\(70\) 0.675494 0.0807370
\(71\) 0.753276 0.0893974 0.0446987 0.999001i \(-0.485767\pi\)
0.0446987 + 0.999001i \(0.485767\pi\)
\(72\) 4.01094 0.472694
\(73\) 0.958508 0.112185 0.0560925 0.998426i \(-0.482136\pi\)
0.0560925 + 0.998426i \(0.482136\pi\)
\(74\) 1.52693 0.177502
\(75\) 12.0292 1.38901
\(76\) −3.17784 −0.364523
\(77\) 1.77443 0.202215
\(78\) −2.65872 −0.301041
\(79\) 8.32703 0.936864 0.468432 0.883500i \(-0.344819\pi\)
0.468432 + 0.883500i \(0.344819\pi\)
\(80\) −0.675974 −0.0755762
\(81\) −4.94516 −0.549462
\(82\) 7.13965 0.788442
\(83\) 12.0952 1.32762 0.663811 0.747900i \(-0.268938\pi\)
0.663811 + 0.747900i \(0.268938\pi\)
\(84\) 2.64594 0.288695
\(85\) 2.19072 0.237617
\(86\) 2.77622 0.299367
\(87\) −11.0105 −1.18045
\(88\) −1.77569 −0.189289
\(89\) 0.663771 0.0703596 0.0351798 0.999381i \(-0.488800\pi\)
0.0351798 + 0.999381i \(0.488800\pi\)
\(90\) −2.71130 −0.285796
\(91\) −1.00341 −0.105185
\(92\) 8.40714 0.876505
\(93\) 5.91074 0.612916
\(94\) 11.0813 1.14295
\(95\) 2.14814 0.220394
\(96\) −2.64782 −0.270242
\(97\) 12.5368 1.27292 0.636458 0.771311i \(-0.280399\pi\)
0.636458 + 0.771311i \(0.280399\pi\)
\(98\) −6.00142 −0.606235
\(99\) −7.12219 −0.715807
\(100\) −4.54306 −0.454306
\(101\) −0.820120 −0.0816050 −0.0408025 0.999167i \(-0.512991\pi\)
−0.0408025 + 0.999167i \(0.512991\pi\)
\(102\) 8.58115 0.849661
\(103\) −19.6474 −1.93591 −0.967956 0.251122i \(-0.919201\pi\)
−0.967956 + 0.251122i \(0.919201\pi\)
\(104\) 1.00412 0.0984619
\(105\) −1.78859 −0.174548
\(106\) −8.39649 −0.815539
\(107\) 2.18068 0.210814 0.105407 0.994429i \(-0.466385\pi\)
0.105407 + 0.994429i \(0.466385\pi\)
\(108\) −2.67680 −0.257575
\(109\) 0.957011 0.0916651 0.0458325 0.998949i \(-0.485406\pi\)
0.0458325 + 0.998949i \(0.485406\pi\)
\(110\) 1.20032 0.114446
\(111\) −4.04303 −0.383747
\(112\) −0.999289 −0.0944240
\(113\) −15.6071 −1.46819 −0.734096 0.679046i \(-0.762394\pi\)
−0.734096 + 0.679046i \(0.762394\pi\)
\(114\) 8.41435 0.788076
\(115\) −5.68301 −0.529944
\(116\) 4.15832 0.386090
\(117\) 4.02746 0.372339
\(118\) −3.93445 −0.362195
\(119\) 3.23854 0.296876
\(120\) 1.78986 0.163391
\(121\) −7.84692 −0.713357
\(122\) −1.97459 −0.178771
\(123\) −18.9045 −1.70456
\(124\) −2.23231 −0.200467
\(125\) 6.45086 0.576983
\(126\) −4.00809 −0.357069
\(127\) 11.2992 1.00264 0.501322 0.865261i \(-0.332847\pi\)
0.501322 + 0.865261i \(0.332847\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.35092 −0.647213
\(130\) −0.678759 −0.0595311
\(131\) −5.39567 −0.471422 −0.235711 0.971823i \(-0.575742\pi\)
−0.235711 + 0.971823i \(0.575742\pi\)
\(132\) 4.70171 0.409231
\(133\) 3.17558 0.275358
\(134\) −11.2348 −0.970543
\(135\) 1.80945 0.155732
\(136\) −3.24084 −0.277900
\(137\) 22.0525 1.88407 0.942036 0.335511i \(-0.108909\pi\)
0.942036 + 0.335511i \(0.108909\pi\)
\(138\) −22.2606 −1.89495
\(139\) 5.75164 0.487848 0.243924 0.969794i \(-0.421565\pi\)
0.243924 + 0.969794i \(0.421565\pi\)
\(140\) 0.675494 0.0570897
\(141\) −29.3414 −2.47099
\(142\) 0.753276 0.0632135
\(143\) −1.78300 −0.149102
\(144\) 4.01094 0.334245
\(145\) −2.81092 −0.233434
\(146\) 0.958508 0.0793267
\(147\) 15.8907 1.31064
\(148\) 1.52693 0.125513
\(149\) 8.06859 0.661005 0.330502 0.943805i \(-0.392782\pi\)
0.330502 + 0.943805i \(0.392782\pi\)
\(150\) 12.0292 0.982180
\(151\) −0.119283 −0.00970714 −0.00485357 0.999988i \(-0.501545\pi\)
−0.00485357 + 0.999988i \(0.501545\pi\)
\(152\) −3.17784 −0.257757
\(153\) −12.9988 −1.05089
\(154\) 1.77443 0.142988
\(155\) 1.50898 0.121204
\(156\) −2.65872 −0.212868
\(157\) −10.7447 −0.857520 −0.428760 0.903418i \(-0.641049\pi\)
−0.428760 + 0.903418i \(0.641049\pi\)
\(158\) 8.32703 0.662463
\(159\) 22.2324 1.76314
\(160\) −0.675974 −0.0534405
\(161\) −8.40117 −0.662105
\(162\) −4.94516 −0.388528
\(163\) 2.11664 0.165788 0.0828940 0.996558i \(-0.473584\pi\)
0.0828940 + 0.996558i \(0.473584\pi\)
\(164\) 7.13965 0.557513
\(165\) −3.17823 −0.247425
\(166\) 12.0952 0.938771
\(167\) −22.9250 −1.77399 −0.886994 0.461780i \(-0.847211\pi\)
−0.886994 + 0.461780i \(0.847211\pi\)
\(168\) 2.64594 0.204139
\(169\) −11.9917 −0.922442
\(170\) 2.19072 0.168021
\(171\) −12.7461 −0.974722
\(172\) 2.77622 0.211685
\(173\) 18.6550 1.41831 0.709155 0.705052i \(-0.249077\pi\)
0.709155 + 0.705052i \(0.249077\pi\)
\(174\) −11.0105 −0.834702
\(175\) 4.53983 0.343179
\(176\) −1.77569 −0.133848
\(177\) 10.4177 0.783043
\(178\) 0.663771 0.0497517
\(179\) −10.4922 −0.784221 −0.392111 0.919918i \(-0.628255\pi\)
−0.392111 + 0.919918i \(0.628255\pi\)
\(180\) −2.71130 −0.202088
\(181\) −18.9162 −1.40603 −0.703015 0.711175i \(-0.748163\pi\)
−0.703015 + 0.711175i \(0.748163\pi\)
\(182\) −1.00341 −0.0743774
\(183\) 5.22837 0.386492
\(184\) 8.40714 0.619783
\(185\) −1.03216 −0.0758862
\(186\) 5.91074 0.433397
\(187\) 5.75472 0.420827
\(188\) 11.0813 0.808189
\(189\) 2.67490 0.194570
\(190\) 2.14814 0.155842
\(191\) 3.11891 0.225677 0.112838 0.993613i \(-0.464006\pi\)
0.112838 + 0.993613i \(0.464006\pi\)
\(192\) −2.64782 −0.191090
\(193\) 3.51877 0.253287 0.126643 0.991948i \(-0.459580\pi\)
0.126643 + 0.991948i \(0.459580\pi\)
\(194\) 12.5368 0.900088
\(195\) 1.79723 0.128702
\(196\) −6.00142 −0.428673
\(197\) −18.2977 −1.30365 −0.651827 0.758368i \(-0.725997\pi\)
−0.651827 + 0.758368i \(0.725997\pi\)
\(198\) −7.12219 −0.506152
\(199\) −6.62886 −0.469908 −0.234954 0.972007i \(-0.575494\pi\)
−0.234954 + 0.972007i \(0.575494\pi\)
\(200\) −4.54306 −0.321243
\(201\) 29.7478 2.09825
\(202\) −0.820120 −0.0577034
\(203\) −4.15536 −0.291649
\(204\) 8.58115 0.600801
\(205\) −4.82622 −0.337078
\(206\) −19.6474 −1.36890
\(207\) 33.7206 2.34374
\(208\) 1.00412 0.0696231
\(209\) 5.64286 0.390325
\(210\) −1.78859 −0.123424
\(211\) 11.7326 0.807703 0.403852 0.914825i \(-0.367671\pi\)
0.403852 + 0.914825i \(0.367671\pi\)
\(212\) −8.39649 −0.576673
\(213\) −1.99454 −0.136663
\(214\) 2.18068 0.149068
\(215\) −1.87665 −0.127987
\(216\) −2.67680 −0.182133
\(217\) 2.23072 0.151431
\(218\) 0.957011 0.0648170
\(219\) −2.53796 −0.171499
\(220\) 1.20032 0.0809256
\(221\) −3.25419 −0.218900
\(222\) −4.04303 −0.271350
\(223\) −0.662036 −0.0443332 −0.0221666 0.999754i \(-0.507056\pi\)
−0.0221666 + 0.999754i \(0.507056\pi\)
\(224\) −0.999289 −0.0667678
\(225\) −18.2220 −1.21480
\(226\) −15.6071 −1.03817
\(227\) 10.0944 0.669991 0.334996 0.942220i \(-0.391265\pi\)
0.334996 + 0.942220i \(0.391265\pi\)
\(228\) 8.41435 0.557254
\(229\) 7.12675 0.470949 0.235475 0.971881i \(-0.424336\pi\)
0.235475 + 0.971881i \(0.424336\pi\)
\(230\) −5.68301 −0.374727
\(231\) −4.69836 −0.309130
\(232\) 4.15832 0.273007
\(233\) −3.11727 −0.204219 −0.102110 0.994773i \(-0.532559\pi\)
−0.102110 + 0.994773i \(0.532559\pi\)
\(234\) 4.02746 0.263284
\(235\) −7.49069 −0.488639
\(236\) −3.93445 −0.256111
\(237\) −22.0485 −1.43220
\(238\) 3.23854 0.209923
\(239\) 15.8275 1.02380 0.511898 0.859046i \(-0.328943\pi\)
0.511898 + 0.859046i \(0.328943\pi\)
\(240\) 1.78986 0.115535
\(241\) −17.6675 −1.13806 −0.569032 0.822316i \(-0.692682\pi\)
−0.569032 + 0.822316i \(0.692682\pi\)
\(242\) −7.84692 −0.504419
\(243\) 21.1243 1.35512
\(244\) −1.97459 −0.126410
\(245\) 4.05681 0.259180
\(246\) −18.9045 −1.20531
\(247\) −3.19093 −0.203034
\(248\) −2.23231 −0.141752
\(249\) −32.0259 −2.02956
\(250\) 6.45086 0.407988
\(251\) −15.0190 −0.947992 −0.473996 0.880527i \(-0.657189\pi\)
−0.473996 + 0.880527i \(0.657189\pi\)
\(252\) −4.00809 −0.252486
\(253\) −14.9285 −0.938546
\(254\) 11.2992 0.708976
\(255\) −5.80064 −0.363250
\(256\) 1.00000 0.0625000
\(257\) −12.2957 −0.766987 −0.383494 0.923544i \(-0.625279\pi\)
−0.383494 + 0.923544i \(0.625279\pi\)
\(258\) −7.35092 −0.457649
\(259\) −1.52584 −0.0948113
\(260\) −0.678759 −0.0420948
\(261\) 16.6788 1.03239
\(262\) −5.39567 −0.333346
\(263\) 22.7772 1.40450 0.702250 0.711931i \(-0.252179\pi\)
0.702250 + 0.711931i \(0.252179\pi\)
\(264\) 4.70171 0.289370
\(265\) 5.67581 0.348662
\(266\) 3.17558 0.194707
\(267\) −1.75755 −0.107560
\(268\) −11.2348 −0.686278
\(269\) −18.8576 −1.14977 −0.574885 0.818234i \(-0.694953\pi\)
−0.574885 + 0.818234i \(0.694953\pi\)
\(270\) 1.80945 0.110119
\(271\) 12.2942 0.746819 0.373410 0.927667i \(-0.378189\pi\)
0.373410 + 0.927667i \(0.378189\pi\)
\(272\) −3.24084 −0.196505
\(273\) 2.65684 0.160799
\(274\) 22.0525 1.33224
\(275\) 8.06706 0.486462
\(276\) −22.2606 −1.33993
\(277\) −29.6731 −1.78288 −0.891441 0.453136i \(-0.850305\pi\)
−0.891441 + 0.453136i \(0.850305\pi\)
\(278\) 5.75164 0.344961
\(279\) −8.95366 −0.536041
\(280\) 0.675494 0.0403685
\(281\) 5.55595 0.331440 0.165720 0.986173i \(-0.447005\pi\)
0.165720 + 0.986173i \(0.447005\pi\)
\(282\) −29.3414 −1.74725
\(283\) −32.7588 −1.94731 −0.973655 0.228025i \(-0.926773\pi\)
−0.973655 + 0.228025i \(0.926773\pi\)
\(284\) 0.753276 0.0446987
\(285\) −5.68788 −0.336921
\(286\) −1.78300 −0.105431
\(287\) −7.13458 −0.421141
\(288\) 4.01094 0.236347
\(289\) −6.49697 −0.382175
\(290\) −2.81092 −0.165063
\(291\) −33.1951 −1.94593
\(292\) 0.958508 0.0560925
\(293\) −29.2191 −1.70700 −0.853500 0.521093i \(-0.825525\pi\)
−0.853500 + 0.521093i \(0.825525\pi\)
\(294\) 15.8907 0.926763
\(295\) 2.65959 0.154847
\(296\) 1.52693 0.0887509
\(297\) 4.75316 0.275807
\(298\) 8.06859 0.467401
\(299\) 8.44177 0.488200
\(300\) 12.0292 0.694506
\(301\) −2.77425 −0.159905
\(302\) −0.119283 −0.00686398
\(303\) 2.17153 0.124751
\(304\) −3.17784 −0.182262
\(305\) 1.33478 0.0764290
\(306\) −12.9988 −0.743093
\(307\) −14.8070 −0.845082 −0.422541 0.906344i \(-0.638862\pi\)
−0.422541 + 0.906344i \(0.638862\pi\)
\(308\) 1.77443 0.101107
\(309\) 52.0226 2.95946
\(310\) 1.50898 0.0857044
\(311\) −12.9873 −0.736443 −0.368222 0.929738i \(-0.620033\pi\)
−0.368222 + 0.929738i \(0.620033\pi\)
\(312\) −2.65872 −0.150521
\(313\) −26.2368 −1.48299 −0.741495 0.670959i \(-0.765883\pi\)
−0.741495 + 0.670959i \(0.765883\pi\)
\(314\) −10.7447 −0.606358
\(315\) 2.70937 0.152656
\(316\) 8.32703 0.468432
\(317\) −17.8514 −1.00263 −0.501317 0.865264i \(-0.667151\pi\)
−0.501317 + 0.865264i \(0.667151\pi\)
\(318\) 22.2324 1.24673
\(319\) −7.38389 −0.413418
\(320\) −0.675974 −0.0377881
\(321\) −5.77405 −0.322276
\(322\) −8.40117 −0.468179
\(323\) 10.2989 0.573044
\(324\) −4.94516 −0.274731
\(325\) −4.56177 −0.253042
\(326\) 2.11664 0.117230
\(327\) −2.53399 −0.140130
\(328\) 7.13965 0.394221
\(329\) −11.0735 −0.610499
\(330\) −3.17823 −0.174956
\(331\) 33.2198 1.82593 0.912964 0.408040i \(-0.133788\pi\)
0.912964 + 0.408040i \(0.133788\pi\)
\(332\) 12.0952 0.663811
\(333\) 6.12443 0.335616
\(334\) −22.9250 −1.25440
\(335\) 7.59447 0.414930
\(336\) 2.64594 0.144348
\(337\) −6.51251 −0.354759 −0.177379 0.984143i \(-0.556762\pi\)
−0.177379 + 0.984143i \(0.556762\pi\)
\(338\) −11.9917 −0.652265
\(339\) 41.3248 2.24445
\(340\) 2.19072 0.118809
\(341\) 3.96388 0.214656
\(342\) −12.7461 −0.689232
\(343\) 12.9922 0.701512
\(344\) 2.77622 0.149684
\(345\) 15.0476 0.810135
\(346\) 18.6550 1.00290
\(347\) −34.6642 −1.86087 −0.930437 0.366453i \(-0.880572\pi\)
−0.930437 + 0.366453i \(0.880572\pi\)
\(348\) −11.0105 −0.590223
\(349\) −19.6558 −1.05215 −0.526074 0.850439i \(-0.676337\pi\)
−0.526074 + 0.850439i \(0.676337\pi\)
\(350\) 4.53983 0.242664
\(351\) −2.68782 −0.143465
\(352\) −1.77569 −0.0946446
\(353\) −24.3355 −1.29525 −0.647624 0.761960i \(-0.724237\pi\)
−0.647624 + 0.761960i \(0.724237\pi\)
\(354\) 10.4177 0.553695
\(355\) −0.509195 −0.0270253
\(356\) 0.663771 0.0351798
\(357\) −8.57505 −0.453840
\(358\) −10.4922 −0.554528
\(359\) −1.38190 −0.0729337 −0.0364669 0.999335i \(-0.511610\pi\)
−0.0364669 + 0.999335i \(0.511610\pi\)
\(360\) −2.71130 −0.142898
\(361\) −8.90133 −0.468491
\(362\) −18.9162 −0.994214
\(363\) 20.7772 1.09052
\(364\) −1.00341 −0.0525927
\(365\) −0.647927 −0.0339140
\(366\) 5.22837 0.273291
\(367\) 30.4033 1.58704 0.793519 0.608545i \(-0.208246\pi\)
0.793519 + 0.608545i \(0.208246\pi\)
\(368\) 8.40714 0.438253
\(369\) 28.6367 1.49077
\(370\) −1.03216 −0.0536597
\(371\) 8.39052 0.435614
\(372\) 5.91074 0.306458
\(373\) 32.0524 1.65961 0.829806 0.558052i \(-0.188451\pi\)
0.829806 + 0.558052i \(0.188451\pi\)
\(374\) 5.75472 0.297570
\(375\) −17.0807 −0.882044
\(376\) 11.0813 0.571476
\(377\) 4.17545 0.215046
\(378\) 2.67490 0.137582
\(379\) 25.8904 1.32990 0.664950 0.746888i \(-0.268453\pi\)
0.664950 + 0.746888i \(0.268453\pi\)
\(380\) 2.14814 0.110197
\(381\) −29.9183 −1.53276
\(382\) 3.11891 0.159578
\(383\) −21.0970 −1.07800 −0.539002 0.842304i \(-0.681198\pi\)
−0.539002 + 0.842304i \(0.681198\pi\)
\(384\) −2.64782 −0.135121
\(385\) −1.19947 −0.0611306
\(386\) 3.51877 0.179101
\(387\) 11.1353 0.566037
\(388\) 12.5368 0.636458
\(389\) −7.11805 −0.360900 −0.180450 0.983584i \(-0.557755\pi\)
−0.180450 + 0.983584i \(0.557755\pi\)
\(390\) 1.79723 0.0910063
\(391\) −27.2462 −1.37790
\(392\) −6.00142 −0.303118
\(393\) 14.2868 0.720672
\(394\) −18.2977 −0.921822
\(395\) −5.62886 −0.283219
\(396\) −7.12219 −0.357904
\(397\) −27.9275 −1.40164 −0.700822 0.713337i \(-0.747183\pi\)
−0.700822 + 0.713337i \(0.747183\pi\)
\(398\) −6.62886 −0.332275
\(399\) −8.40837 −0.420945
\(400\) −4.54306 −0.227153
\(401\) −10.0662 −0.502680 −0.251340 0.967899i \(-0.580871\pi\)
−0.251340 + 0.967899i \(0.580871\pi\)
\(402\) 29.7478 1.48369
\(403\) −2.24150 −0.111657
\(404\) −0.820120 −0.0408025
\(405\) 3.34280 0.166105
\(406\) −4.15536 −0.206227
\(407\) −2.71135 −0.134397
\(408\) 8.58115 0.424830
\(409\) −27.3491 −1.35232 −0.676162 0.736753i \(-0.736358\pi\)
−0.676162 + 0.736753i \(0.736358\pi\)
\(410\) −4.82622 −0.238350
\(411\) −58.3910 −2.88022
\(412\) −19.6474 −0.967956
\(413\) 3.93165 0.193464
\(414\) 33.7206 1.65728
\(415\) −8.17605 −0.401347
\(416\) 1.00412 0.0492310
\(417\) −15.2293 −0.745782
\(418\) 5.64286 0.276001
\(419\) 0.124193 0.00606723 0.00303362 0.999995i \(-0.499034\pi\)
0.00303362 + 0.999995i \(0.499034\pi\)
\(420\) −1.78859 −0.0872740
\(421\) −14.8032 −0.721463 −0.360732 0.932670i \(-0.617473\pi\)
−0.360732 + 0.932670i \(0.617473\pi\)
\(422\) 11.7326 0.571132
\(423\) 44.4466 2.16107
\(424\) −8.39649 −0.407769
\(425\) 14.7233 0.714186
\(426\) −1.99454 −0.0966357
\(427\) 1.97319 0.0954894
\(428\) 2.18068 0.105407
\(429\) 4.72107 0.227935
\(430\) −1.87665 −0.0905002
\(431\) 1.54029 0.0741932 0.0370966 0.999312i \(-0.488189\pi\)
0.0370966 + 0.999312i \(0.488189\pi\)
\(432\) −2.67680 −0.128787
\(433\) −26.4020 −1.26880 −0.634400 0.773005i \(-0.718753\pi\)
−0.634400 + 0.773005i \(0.718753\pi\)
\(434\) 2.23072 0.107078
\(435\) 7.44280 0.356855
\(436\) 0.957011 0.0458325
\(437\) −26.7166 −1.27803
\(438\) −2.53796 −0.121268
\(439\) 1.28084 0.0611312 0.0305656 0.999533i \(-0.490269\pi\)
0.0305656 + 0.999533i \(0.490269\pi\)
\(440\) 1.20032 0.0572231
\(441\) −24.0714 −1.14626
\(442\) −3.25419 −0.154786
\(443\) −16.4162 −0.779956 −0.389978 0.920824i \(-0.627517\pi\)
−0.389978 + 0.920824i \(0.627517\pi\)
\(444\) −4.04303 −0.191874
\(445\) −0.448692 −0.0212700
\(446\) −0.662036 −0.0313483
\(447\) −21.3642 −1.01049
\(448\) −0.999289 −0.0472120
\(449\) 36.2018 1.70847 0.854234 0.519889i \(-0.174027\pi\)
0.854234 + 0.519889i \(0.174027\pi\)
\(450\) −18.2220 −0.858991
\(451\) −12.6778 −0.596975
\(452\) −15.6071 −0.734096
\(453\) 0.315840 0.0148395
\(454\) 10.0944 0.473755
\(455\) 0.678276 0.0317981
\(456\) 8.41435 0.394038
\(457\) 42.1247 1.97051 0.985256 0.171087i \(-0.0547278\pi\)
0.985256 + 0.171087i \(0.0547278\pi\)
\(458\) 7.12675 0.333011
\(459\) 8.67507 0.404917
\(460\) −5.68301 −0.264972
\(461\) −16.4873 −0.767888 −0.383944 0.923356i \(-0.625434\pi\)
−0.383944 + 0.923356i \(0.625434\pi\)
\(462\) −4.69836 −0.218588
\(463\) 10.5166 0.488747 0.244374 0.969681i \(-0.421418\pi\)
0.244374 + 0.969681i \(0.421418\pi\)
\(464\) 4.15832 0.193045
\(465\) −3.99551 −0.185287
\(466\) −3.11727 −0.144405
\(467\) −35.4620 −1.64098 −0.820492 0.571658i \(-0.806300\pi\)
−0.820492 + 0.571658i \(0.806300\pi\)
\(468\) 4.02746 0.186170
\(469\) 11.2269 0.518409
\(470\) −7.49069 −0.345520
\(471\) 28.4500 1.31091
\(472\) −3.93445 −0.181098
\(473\) −4.92970 −0.226668
\(474\) −22.0485 −1.01272
\(475\) 14.4371 0.662420
\(476\) 3.23854 0.148438
\(477\) −33.6778 −1.54200
\(478\) 15.8275 0.723933
\(479\) −29.1676 −1.33270 −0.666351 0.745638i \(-0.732145\pi\)
−0.666351 + 0.745638i \(0.732145\pi\)
\(480\) 1.78986 0.0816954
\(481\) 1.53322 0.0699087
\(482\) −17.6675 −0.804732
\(483\) 22.2448 1.01217
\(484\) −7.84692 −0.356678
\(485\) −8.47453 −0.384809
\(486\) 21.1243 0.958217
\(487\) −19.6810 −0.891830 −0.445915 0.895075i \(-0.647122\pi\)
−0.445915 + 0.895075i \(0.647122\pi\)
\(488\) −1.97459 −0.0893857
\(489\) −5.60448 −0.253443
\(490\) 4.05681 0.183268
\(491\) −14.4946 −0.654132 −0.327066 0.945002i \(-0.606060\pi\)
−0.327066 + 0.945002i \(0.606060\pi\)
\(492\) −18.9045 −0.852281
\(493\) −13.4764 −0.606948
\(494\) −3.19093 −0.143567
\(495\) 4.81442 0.216392
\(496\) −2.23231 −0.100234
\(497\) −0.752741 −0.0337650
\(498\) −32.0259 −1.43512
\(499\) 18.5198 0.829060 0.414530 0.910036i \(-0.363946\pi\)
0.414530 + 0.910036i \(0.363946\pi\)
\(500\) 6.45086 0.288491
\(501\) 60.7012 2.71193
\(502\) −15.0190 −0.670332
\(503\) −26.5307 −1.18294 −0.591472 0.806325i \(-0.701453\pi\)
−0.591472 + 0.806325i \(0.701453\pi\)
\(504\) −4.00809 −0.178535
\(505\) 0.554380 0.0246696
\(506\) −14.9285 −0.663652
\(507\) 31.7520 1.41015
\(508\) 11.2992 0.501322
\(509\) −34.9885 −1.55084 −0.775418 0.631448i \(-0.782461\pi\)
−0.775418 + 0.631448i \(0.782461\pi\)
\(510\) −5.80064 −0.256857
\(511\) −0.957827 −0.0423718
\(512\) 1.00000 0.0441942
\(513\) 8.50644 0.375568
\(514\) −12.2957 −0.542342
\(515\) 13.2811 0.585235
\(516\) −7.35092 −0.323606
\(517\) −19.6770 −0.865394
\(518\) −1.52584 −0.0670417
\(519\) −49.3950 −2.16820
\(520\) −0.678759 −0.0297655
\(521\) 7.75607 0.339800 0.169900 0.985461i \(-0.445656\pi\)
0.169900 + 0.985461i \(0.445656\pi\)
\(522\) 16.6788 0.730011
\(523\) −2.93779 −0.128461 −0.0642304 0.997935i \(-0.520459\pi\)
−0.0642304 + 0.997935i \(0.520459\pi\)
\(524\) −5.39567 −0.235711
\(525\) −12.0206 −0.524624
\(526\) 22.7772 0.993131
\(527\) 7.23454 0.315142
\(528\) 4.70171 0.204615
\(529\) 47.6801 2.07305
\(530\) 5.67581 0.246541
\(531\) −15.7809 −0.684831
\(532\) 3.17558 0.137679
\(533\) 7.16906 0.310526
\(534\) −1.75755 −0.0760564
\(535\) −1.47408 −0.0637302
\(536\) −11.2348 −0.485272
\(537\) 27.7814 1.19885
\(538\) −18.8576 −0.813010
\(539\) 10.6567 0.459015
\(540\) 1.80945 0.0778662
\(541\) −14.4463 −0.621096 −0.310548 0.950558i \(-0.600513\pi\)
−0.310548 + 0.950558i \(0.600513\pi\)
\(542\) 12.2942 0.528081
\(543\) 50.0867 2.14943
\(544\) −3.24084 −0.138950
\(545\) −0.646915 −0.0277108
\(546\) 2.65684 0.113702
\(547\) −22.4181 −0.958530 −0.479265 0.877670i \(-0.659097\pi\)
−0.479265 + 0.877670i \(0.659097\pi\)
\(548\) 22.0525 0.942036
\(549\) −7.91999 −0.338017
\(550\) 8.06706 0.343981
\(551\) −13.2145 −0.562956
\(552\) −22.2606 −0.947474
\(553\) −8.32111 −0.353850
\(554\) −29.6731 −1.26069
\(555\) 2.73298 0.116009
\(556\) 5.75164 0.243924
\(557\) −3.95791 −0.167702 −0.0838510 0.996478i \(-0.526722\pi\)
−0.0838510 + 0.996478i \(0.526722\pi\)
\(558\) −8.95366 −0.379039
\(559\) 2.78765 0.117905
\(560\) 0.675494 0.0285448
\(561\) −15.2375 −0.643326
\(562\) 5.55595 0.234363
\(563\) 28.2418 1.19025 0.595125 0.803633i \(-0.297102\pi\)
0.595125 + 0.803633i \(0.297102\pi\)
\(564\) −29.3414 −1.23549
\(565\) 10.5500 0.443842
\(566\) −32.7588 −1.37696
\(567\) 4.94164 0.207530
\(568\) 0.753276 0.0316068
\(569\) −6.40748 −0.268616 −0.134308 0.990940i \(-0.542881\pi\)
−0.134308 + 0.990940i \(0.542881\pi\)
\(570\) −5.68788 −0.238239
\(571\) 17.7442 0.742570 0.371285 0.928519i \(-0.378917\pi\)
0.371285 + 0.928519i \(0.378917\pi\)
\(572\) −1.78300 −0.0745511
\(573\) −8.25832 −0.344996
\(574\) −7.13458 −0.297791
\(575\) −38.1941 −1.59281
\(576\) 4.01094 0.167123
\(577\) 0.388267 0.0161637 0.00808187 0.999967i \(-0.497427\pi\)
0.00808187 + 0.999967i \(0.497427\pi\)
\(578\) −6.49697 −0.270238
\(579\) −9.31707 −0.387204
\(580\) −2.81092 −0.116717
\(581\) −12.0866 −0.501437
\(582\) −33.1951 −1.37598
\(583\) 14.9096 0.617491
\(584\) 0.958508 0.0396634
\(585\) −2.72246 −0.112560
\(586\) −29.2191 −1.20703
\(587\) −13.5651 −0.559891 −0.279946 0.960016i \(-0.590316\pi\)
−0.279946 + 0.960016i \(0.590316\pi\)
\(588\) 15.8907 0.655320
\(589\) 7.09391 0.292300
\(590\) 2.65959 0.109493
\(591\) 48.4489 1.99292
\(592\) 1.52693 0.0627564
\(593\) 21.4715 0.881728 0.440864 0.897574i \(-0.354672\pi\)
0.440864 + 0.897574i \(0.354672\pi\)
\(594\) 4.75316 0.195025
\(595\) −2.18917 −0.0897471
\(596\) 8.06859 0.330502
\(597\) 17.5520 0.718357
\(598\) 8.44177 0.345210
\(599\) 23.2629 0.950495 0.475247 0.879852i \(-0.342359\pi\)
0.475247 + 0.879852i \(0.342359\pi\)
\(600\) 12.0292 0.491090
\(601\) 28.3956 1.15828 0.579141 0.815227i \(-0.303388\pi\)
0.579141 + 0.815227i \(0.303388\pi\)
\(602\) −2.77425 −0.113070
\(603\) −45.0624 −1.83508
\(604\) −0.119283 −0.00485357
\(605\) 5.30432 0.215651
\(606\) 2.17153 0.0882123
\(607\) 30.7963 1.24998 0.624991 0.780632i \(-0.285103\pi\)
0.624991 + 0.780632i \(0.285103\pi\)
\(608\) −3.17784 −0.128878
\(609\) 11.0027 0.445850
\(610\) 1.33478 0.0540435
\(611\) 11.1270 0.450149
\(612\) −12.9988 −0.525446
\(613\) −18.2003 −0.735103 −0.367552 0.930003i \(-0.619804\pi\)
−0.367552 + 0.930003i \(0.619804\pi\)
\(614\) −14.8070 −0.597564
\(615\) 12.7790 0.515297
\(616\) 1.77443 0.0714938
\(617\) 9.74973 0.392509 0.196255 0.980553i \(-0.437122\pi\)
0.196255 + 0.980553i \(0.437122\pi\)
\(618\) 52.0226 2.09266
\(619\) 40.2360 1.61722 0.808610 0.588345i \(-0.200220\pi\)
0.808610 + 0.588345i \(0.200220\pi\)
\(620\) 1.50898 0.0606022
\(621\) −22.5042 −0.903063
\(622\) −12.9873 −0.520744
\(623\) −0.663299 −0.0265745
\(624\) −2.65872 −0.106434
\(625\) 18.3547 0.734187
\(626\) −26.2368 −1.04863
\(627\) −14.9413 −0.596697
\(628\) −10.7447 −0.428760
\(629\) −4.94853 −0.197311
\(630\) 2.70937 0.107944
\(631\) 46.6381 1.85663 0.928316 0.371791i \(-0.121256\pi\)
0.928316 + 0.371791i \(0.121256\pi\)
\(632\) 8.32703 0.331231
\(633\) −31.0657 −1.23475
\(634\) −17.8514 −0.708970
\(635\) −7.63798 −0.303104
\(636\) 22.2324 0.881571
\(637\) −6.02614 −0.238764
\(638\) −7.38389 −0.292331
\(639\) 3.02135 0.119523
\(640\) −0.675974 −0.0267202
\(641\) −10.1262 −0.399960 −0.199980 0.979800i \(-0.564088\pi\)
−0.199980 + 0.979800i \(0.564088\pi\)
\(642\) −5.77405 −0.227884
\(643\) −24.6692 −0.972857 −0.486428 0.873720i \(-0.661701\pi\)
−0.486428 + 0.873720i \(0.661701\pi\)
\(644\) −8.40117 −0.331052
\(645\) 4.96904 0.195656
\(646\) 10.2989 0.405203
\(647\) −34.7003 −1.36421 −0.682105 0.731254i \(-0.738935\pi\)
−0.682105 + 0.731254i \(0.738935\pi\)
\(648\) −4.94516 −0.194264
\(649\) 6.98636 0.274239
\(650\) −4.56177 −0.178927
\(651\) −5.90654 −0.231496
\(652\) 2.11664 0.0828940
\(653\) −4.13867 −0.161959 −0.0809793 0.996716i \(-0.525805\pi\)
−0.0809793 + 0.996716i \(0.525805\pi\)
\(654\) −2.53399 −0.0990870
\(655\) 3.64734 0.142513
\(656\) 7.13965 0.278756
\(657\) 3.84452 0.149989
\(658\) −11.0735 −0.431688
\(659\) −5.05728 −0.197004 −0.0985019 0.995137i \(-0.531405\pi\)
−0.0985019 + 0.995137i \(0.531405\pi\)
\(660\) −3.17823 −0.123713
\(661\) 40.0109 1.55624 0.778121 0.628114i \(-0.216173\pi\)
0.778121 + 0.628114i \(0.216173\pi\)
\(662\) 33.2198 1.29113
\(663\) 8.61650 0.334637
\(664\) 12.0952 0.469385
\(665\) −2.14661 −0.0832420
\(666\) 6.12443 0.237317
\(667\) 34.9596 1.35364
\(668\) −22.9250 −0.886994
\(669\) 1.75295 0.0677730
\(670\) 7.59447 0.293400
\(671\) 3.50627 0.135358
\(672\) 2.64594 0.102069
\(673\) 42.9421 1.65530 0.827649 0.561246i \(-0.189678\pi\)
0.827649 + 0.561246i \(0.189678\pi\)
\(674\) −6.51251 −0.250852
\(675\) 12.1608 0.468071
\(676\) −11.9917 −0.461221
\(677\) −38.7697 −1.49004 −0.745021 0.667041i \(-0.767560\pi\)
−0.745021 + 0.667041i \(0.767560\pi\)
\(678\) 41.3248 1.58707
\(679\) −12.5279 −0.480775
\(680\) 2.19072 0.0840104
\(681\) −26.7282 −1.02423
\(682\) 3.96388 0.151785
\(683\) −44.1884 −1.69082 −0.845412 0.534115i \(-0.820645\pi\)
−0.845412 + 0.534115i \(0.820645\pi\)
\(684\) −12.7461 −0.487361
\(685\) −14.9069 −0.569564
\(686\) 12.9922 0.496044
\(687\) −18.8704 −0.719949
\(688\) 2.77622 0.105842
\(689\) −8.43107 −0.321198
\(690\) 15.0476 0.572852
\(691\) −31.7649 −1.20839 −0.604196 0.796836i \(-0.706506\pi\)
−0.604196 + 0.796836i \(0.706506\pi\)
\(692\) 18.6550 0.709155
\(693\) 7.11713 0.270358
\(694\) −34.6642 −1.31584
\(695\) −3.88796 −0.147479
\(696\) −11.0105 −0.417351
\(697\) −23.1384 −0.876431
\(698\) −19.6558 −0.743982
\(699\) 8.25396 0.312194
\(700\) 4.53983 0.171589
\(701\) 16.8264 0.635524 0.317762 0.948170i \(-0.397069\pi\)
0.317762 + 0.948170i \(0.397069\pi\)
\(702\) −2.68782 −0.101445
\(703\) −4.85234 −0.183009
\(704\) −1.77569 −0.0669238
\(705\) 19.8340 0.746992
\(706\) −24.3355 −0.915879
\(707\) 0.819537 0.0308219
\(708\) 10.4177 0.391522
\(709\) −46.1542 −1.73336 −0.866679 0.498866i \(-0.833750\pi\)
−0.866679 + 0.498866i \(0.833750\pi\)
\(710\) −0.509195 −0.0191098
\(711\) 33.3992 1.25257
\(712\) 0.663771 0.0248759
\(713\) −18.7673 −0.702842
\(714\) −8.57505 −0.320913
\(715\) 1.20526 0.0450743
\(716\) −10.4922 −0.392111
\(717\) −41.9084 −1.56510
\(718\) −1.38190 −0.0515719
\(719\) −43.8635 −1.63583 −0.817916 0.575337i \(-0.804871\pi\)
−0.817916 + 0.575337i \(0.804871\pi\)
\(720\) −2.71130 −0.101044
\(721\) 19.6334 0.731186
\(722\) −8.90133 −0.331273
\(723\) 46.7803 1.73978
\(724\) −18.9162 −0.703015
\(725\) −18.8915 −0.701612
\(726\) 20.7772 0.771116
\(727\) −45.1451 −1.67434 −0.837169 0.546944i \(-0.815791\pi\)
−0.837169 + 0.546944i \(0.815791\pi\)
\(728\) −1.00341 −0.0371887
\(729\) −41.0978 −1.52214
\(730\) −0.647927 −0.0239809
\(731\) −8.99727 −0.332776
\(732\) 5.22837 0.193246
\(733\) 11.6790 0.431372 0.215686 0.976463i \(-0.430801\pi\)
0.215686 + 0.976463i \(0.430801\pi\)
\(734\) 30.4033 1.12221
\(735\) −10.7417 −0.396213
\(736\) 8.40714 0.309891
\(737\) 19.9496 0.734853
\(738\) 28.6367 1.05413
\(739\) 33.6614 1.23825 0.619127 0.785291i \(-0.287487\pi\)
0.619127 + 0.785291i \(0.287487\pi\)
\(740\) −1.03216 −0.0379431
\(741\) 8.44900 0.310382
\(742\) 8.39052 0.308026
\(743\) 35.2692 1.29390 0.646950 0.762532i \(-0.276044\pi\)
0.646950 + 0.762532i \(0.276044\pi\)
\(744\) 5.91074 0.216698
\(745\) −5.45416 −0.199825
\(746\) 32.0524 1.17352
\(747\) 48.5132 1.77501
\(748\) 5.75472 0.210414
\(749\) −2.17913 −0.0796237
\(750\) −17.0807 −0.623700
\(751\) −34.7979 −1.26979 −0.634896 0.772597i \(-0.718957\pi\)
−0.634896 + 0.772597i \(0.718957\pi\)
\(752\) 11.0813 0.404095
\(753\) 39.7677 1.44921
\(754\) 4.17545 0.152061
\(755\) 0.0806324 0.00293451
\(756\) 2.67490 0.0972850
\(757\) 2.85298 0.103693 0.0518467 0.998655i \(-0.483489\pi\)
0.0518467 + 0.998655i \(0.483489\pi\)
\(758\) 25.8904 0.940381
\(759\) 39.5279 1.43477
\(760\) 2.14814 0.0779212
\(761\) 27.7116 1.00455 0.502273 0.864709i \(-0.332497\pi\)
0.502273 + 0.864709i \(0.332497\pi\)
\(762\) −29.9183 −1.08382
\(763\) −0.956331 −0.0346215
\(764\) 3.11891 0.112838
\(765\) 8.78687 0.317690
\(766\) −21.0970 −0.762264
\(767\) −3.95066 −0.142650
\(768\) −2.64782 −0.0955449
\(769\) −0.893253 −0.0322115 −0.0161058 0.999870i \(-0.505127\pi\)
−0.0161058 + 0.999870i \(0.505127\pi\)
\(770\) −1.19947 −0.0432258
\(771\) 32.5569 1.17251
\(772\) 3.51877 0.126643
\(773\) 6.11956 0.220105 0.110053 0.993926i \(-0.464898\pi\)
0.110053 + 0.993926i \(0.464898\pi\)
\(774\) 11.1353 0.400249
\(775\) 10.1415 0.364293
\(776\) 12.5368 0.450044
\(777\) 4.04016 0.144940
\(778\) −7.11805 −0.255195
\(779\) −22.6887 −0.812906
\(780\) 1.79723 0.0643511
\(781\) −1.33758 −0.0478625
\(782\) −27.2462 −0.974322
\(783\) −11.1310 −0.397789
\(784\) −6.00142 −0.214336
\(785\) 7.26314 0.259232
\(786\) 14.2868 0.509592
\(787\) 48.9125 1.74354 0.871771 0.489913i \(-0.162972\pi\)
0.871771 + 0.489913i \(0.162972\pi\)
\(788\) −18.2977 −0.651827
\(789\) −60.3098 −2.14709
\(790\) −5.62886 −0.200266
\(791\) 15.5960 0.554530
\(792\) −7.12219 −0.253076
\(793\) −1.98273 −0.0704087
\(794\) −27.9275 −0.991111
\(795\) −15.0285 −0.533007
\(796\) −6.62886 −0.234954
\(797\) 26.2257 0.928963 0.464482 0.885583i \(-0.346241\pi\)
0.464482 + 0.885583i \(0.346241\pi\)
\(798\) −8.40837 −0.297653
\(799\) −35.9128 −1.27050
\(800\) −4.54306 −0.160621
\(801\) 2.66235 0.0940695
\(802\) −10.0662 −0.355448
\(803\) −1.70201 −0.0600628
\(804\) 29.7478 1.04913
\(805\) 5.67898 0.200158
\(806\) −2.24150 −0.0789535
\(807\) 49.9316 1.75768
\(808\) −0.820120 −0.0288517
\(809\) 7.94327 0.279270 0.139635 0.990203i \(-0.455407\pi\)
0.139635 + 0.990203i \(0.455407\pi\)
\(810\) 3.34280 0.117454
\(811\) 1.58185 0.0555461 0.0277731 0.999614i \(-0.491158\pi\)
0.0277731 + 0.999614i \(0.491158\pi\)
\(812\) −4.15536 −0.145825
\(813\) −32.5528 −1.14168
\(814\) −2.71135 −0.0950328
\(815\) −1.43079 −0.0501185
\(816\) 8.58115 0.300400
\(817\) −8.82238 −0.308656
\(818\) −27.3491 −0.956237
\(819\) −4.02460 −0.140631
\(820\) −4.82622 −0.168539
\(821\) 46.9363 1.63809 0.819044 0.573731i \(-0.194504\pi\)
0.819044 + 0.573731i \(0.194504\pi\)
\(822\) −58.3910 −2.03662
\(823\) 27.7022 0.965637 0.482818 0.875721i \(-0.339613\pi\)
0.482818 + 0.875721i \(0.339613\pi\)
\(824\) −19.6474 −0.684448
\(825\) −21.3601 −0.743664
\(826\) 3.93165 0.136800
\(827\) 2.58119 0.0897569 0.0448785 0.998992i \(-0.485710\pi\)
0.0448785 + 0.998992i \(0.485710\pi\)
\(828\) 33.7206 1.17187
\(829\) 24.2908 0.843654 0.421827 0.906676i \(-0.361389\pi\)
0.421827 + 0.906676i \(0.361389\pi\)
\(830\) −8.17605 −0.283795
\(831\) 78.5689 2.72553
\(832\) 1.00412 0.0348116
\(833\) 19.4496 0.673890
\(834\) −15.2293 −0.527348
\(835\) 15.4967 0.536286
\(836\) 5.64286 0.195162
\(837\) 5.97543 0.206541
\(838\) 0.124193 0.00429018
\(839\) −43.2157 −1.49197 −0.745985 0.665962i \(-0.768021\pi\)
−0.745985 + 0.665962i \(0.768021\pi\)
\(840\) −1.78859 −0.0617121
\(841\) −11.7084 −0.403737
\(842\) −14.8032 −0.510152
\(843\) −14.7111 −0.506679
\(844\) 11.7326 0.403852
\(845\) 8.10611 0.278859
\(846\) 44.4466 1.52811
\(847\) 7.84135 0.269432
\(848\) −8.39649 −0.288337
\(849\) 86.7395 2.97689
\(850\) 14.7233 0.505006
\(851\) 12.8371 0.440050
\(852\) −1.99454 −0.0683317
\(853\) −40.1372 −1.37427 −0.687135 0.726530i \(-0.741132\pi\)
−0.687135 + 0.726530i \(0.741132\pi\)
\(854\) 1.97319 0.0675212
\(855\) 8.61606 0.294663
\(856\) 2.18068 0.0745341
\(857\) 0.933967 0.0319037 0.0159518 0.999873i \(-0.494922\pi\)
0.0159518 + 0.999873i \(0.494922\pi\)
\(858\) 4.72107 0.161175
\(859\) 34.6405 1.18192 0.590958 0.806702i \(-0.298750\pi\)
0.590958 + 0.806702i \(0.298750\pi\)
\(860\) −1.87665 −0.0639933
\(861\) 18.8911 0.643806
\(862\) 1.54029 0.0524625
\(863\) 10.3125 0.351040 0.175520 0.984476i \(-0.443839\pi\)
0.175520 + 0.984476i \(0.443839\pi\)
\(864\) −2.67680 −0.0910665
\(865\) −12.6103 −0.428762
\(866\) −26.4020 −0.897177
\(867\) 17.2028 0.584238
\(868\) 2.23072 0.0757156
\(869\) −14.7862 −0.501588
\(870\) 7.44280 0.252335
\(871\) −11.2811 −0.382246
\(872\) 0.957011 0.0324085
\(873\) 50.2843 1.70187
\(874\) −26.7166 −0.903701
\(875\) −6.44628 −0.217924
\(876\) −2.53796 −0.0857496
\(877\) −24.8101 −0.837776 −0.418888 0.908038i \(-0.637580\pi\)
−0.418888 + 0.908038i \(0.637580\pi\)
\(878\) 1.28084 0.0432263
\(879\) 77.3670 2.60952
\(880\) 1.20032 0.0404628
\(881\) −8.83737 −0.297738 −0.148869 0.988857i \(-0.547563\pi\)
−0.148869 + 0.988857i \(0.547563\pi\)
\(882\) −24.0714 −0.810525
\(883\) 0.651910 0.0219385 0.0109693 0.999940i \(-0.496508\pi\)
0.0109693 + 0.999940i \(0.496508\pi\)
\(884\) −3.25419 −0.109450
\(885\) −7.04211 −0.236718
\(886\) −16.4162 −0.551512
\(887\) 50.6763 1.70154 0.850772 0.525535i \(-0.176135\pi\)
0.850772 + 0.525535i \(0.176135\pi\)
\(888\) −4.04303 −0.135675
\(889\) −11.2912 −0.378694
\(890\) −0.448692 −0.0150402
\(891\) 8.78107 0.294177
\(892\) −0.662036 −0.0221666
\(893\) −35.2147 −1.17841
\(894\) −21.3642 −0.714525
\(895\) 7.09244 0.237074
\(896\) −0.999289 −0.0333839
\(897\) −22.3523 −0.746321
\(898\) 36.2018 1.20807
\(899\) −9.28264 −0.309593
\(900\) −18.2220 −0.607399
\(901\) 27.2117 0.906552
\(902\) −12.6778 −0.422125
\(903\) 7.34570 0.244450
\(904\) −15.6071 −0.519084
\(905\) 12.7869 0.425050
\(906\) 0.315840 0.0104931
\(907\) 9.79119 0.325111 0.162555 0.986699i \(-0.448026\pi\)
0.162555 + 0.986699i \(0.448026\pi\)
\(908\) 10.0944 0.334996
\(909\) −3.28945 −0.109104
\(910\) 0.678276 0.0224846
\(911\) −2.61506 −0.0866409 −0.0433205 0.999061i \(-0.513794\pi\)
−0.0433205 + 0.999061i \(0.513794\pi\)
\(912\) 8.41435 0.278627
\(913\) −21.4773 −0.710797
\(914\) 42.1247 1.39336
\(915\) −3.53424 −0.116838
\(916\) 7.12675 0.235475
\(917\) 5.39184 0.178054
\(918\) 8.67507 0.286320
\(919\) −42.1602 −1.39074 −0.695369 0.718653i \(-0.744759\pi\)
−0.695369 + 0.718653i \(0.744759\pi\)
\(920\) −5.68301 −0.187363
\(921\) 39.2064 1.29189
\(922\) −16.4873 −0.542979
\(923\) 0.756378 0.0248965
\(924\) −4.69836 −0.154565
\(925\) −6.93693 −0.228085
\(926\) 10.5166 0.345596
\(927\) −78.8044 −2.58828
\(928\) 4.15832 0.136504
\(929\) 9.30964 0.305439 0.152720 0.988270i \(-0.451197\pi\)
0.152720 + 0.988270i \(0.451197\pi\)
\(930\) −3.99551 −0.131018
\(931\) 19.0716 0.625045
\(932\) −3.11727 −0.102110
\(933\) 34.3881 1.12581
\(934\) −35.4620 −1.16035
\(935\) −3.89005 −0.127218
\(936\) 4.02746 0.131642
\(937\) 35.5140 1.16019 0.580096 0.814548i \(-0.303015\pi\)
0.580096 + 0.814548i \(0.303015\pi\)
\(938\) 11.2269 0.366570
\(939\) 69.4702 2.26707
\(940\) −7.49069 −0.244320
\(941\) 2.85485 0.0930656 0.0465328 0.998917i \(-0.485183\pi\)
0.0465328 + 0.998917i \(0.485183\pi\)
\(942\) 28.4500 0.926951
\(943\) 60.0241 1.95465
\(944\) −3.93445 −0.128055
\(945\) −1.80816 −0.0588195
\(946\) −4.92970 −0.160279
\(947\) 7.29759 0.237140 0.118570 0.992946i \(-0.462169\pi\)
0.118570 + 0.992946i \(0.462169\pi\)
\(948\) −22.0485 −0.716101
\(949\) 0.962456 0.0312426
\(950\) 14.4371 0.468402
\(951\) 47.2673 1.53275
\(952\) 3.23854 0.104962
\(953\) −30.9193 −1.00158 −0.500788 0.865570i \(-0.666956\pi\)
−0.500788 + 0.865570i \(0.666956\pi\)
\(954\) −33.6778 −1.09036
\(955\) −2.10831 −0.0682232
\(956\) 15.8275 0.511898
\(957\) 19.5512 0.632000
\(958\) −29.1676 −0.942363
\(959\) −22.0368 −0.711607
\(960\) 1.78986 0.0577674
\(961\) −26.0168 −0.839252
\(962\) 1.53322 0.0494329
\(963\) 8.74659 0.281855
\(964\) −17.6675 −0.569032
\(965\) −2.37860 −0.0765698
\(966\) 22.2448 0.715714
\(967\) 6.55842 0.210905 0.105452 0.994424i \(-0.466371\pi\)
0.105452 + 0.994424i \(0.466371\pi\)
\(968\) −7.84692 −0.252210
\(969\) −27.2695 −0.876023
\(970\) −8.47453 −0.272101
\(971\) 28.1034 0.901880 0.450940 0.892554i \(-0.351089\pi\)
0.450940 + 0.892554i \(0.351089\pi\)
\(972\) 21.1243 0.677561
\(973\) −5.74755 −0.184258
\(974\) −19.6810 −0.630619
\(975\) 12.0787 0.386829
\(976\) −1.97459 −0.0632052
\(977\) −21.3900 −0.684326 −0.342163 0.939641i \(-0.611160\pi\)
−0.342163 + 0.939641i \(0.611160\pi\)
\(978\) −5.60448 −0.179211
\(979\) −1.17865 −0.0376699
\(980\) 4.05681 0.129590
\(981\) 3.83852 0.122554
\(982\) −14.4946 −0.462541
\(983\) 16.1687 0.515703 0.257851 0.966185i \(-0.416985\pi\)
0.257851 + 0.966185i \(0.416985\pi\)
\(984\) −18.9045 −0.602653
\(985\) 12.3687 0.394101
\(986\) −13.4764 −0.429177
\(987\) 29.3205 0.933282
\(988\) −3.19093 −0.101517
\(989\) 23.3401 0.742171
\(990\) 4.81442 0.153012
\(991\) −2.44333 −0.0776150 −0.0388075 0.999247i \(-0.512356\pi\)
−0.0388075 + 0.999247i \(0.512356\pi\)
\(992\) −2.23231 −0.0708758
\(993\) −87.9601 −2.79133
\(994\) −0.752741 −0.0238755
\(995\) 4.48094 0.142055
\(996\) −32.0259 −1.01478
\(997\) 29.9719 0.949220 0.474610 0.880196i \(-0.342589\pi\)
0.474610 + 0.880196i \(0.342589\pi\)
\(998\) 18.5198 0.586234
\(999\) −4.08728 −0.129316
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 \(a_p\))