Properties

Label 4031.2.a.c.1.6
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31412 q^{2}\) \(+0.311751 q^{3}\) \(+3.35513 q^{4}\) \(+1.29585 q^{5}\) \(-0.721429 q^{6}\) \(-1.13716 q^{7}\) \(-3.13593 q^{8}\) \(-2.90281 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31412 q^{2}\) \(+0.311751 q^{3}\) \(+3.35513 q^{4}\) \(+1.29585 q^{5}\) \(-0.721429 q^{6}\) \(-1.13716 q^{7}\) \(-3.13593 q^{8}\) \(-2.90281 q^{9}\) \(-2.99874 q^{10}\) \(+2.78758 q^{11}\) \(+1.04597 q^{12}\) \(+3.93476 q^{13}\) \(+2.63152 q^{14}\) \(+0.403982 q^{15}\) \(+0.546648 q^{16}\) \(-3.61518 q^{17}\) \(+6.71744 q^{18}\) \(+4.23592 q^{19}\) \(+4.34773 q^{20}\) \(-0.354511 q^{21}\) \(-6.45077 q^{22}\) \(-0.383069 q^{23}\) \(-0.977632 q^{24}\) \(-3.32078 q^{25}\) \(-9.10550 q^{26}\) \(-1.84021 q^{27}\) \(-3.81532 q^{28}\) \(-1.00000 q^{29}\) \(-0.934860 q^{30}\) \(-10.0360 q^{31}\) \(+5.00686 q^{32}\) \(+0.869031 q^{33}\) \(+8.36595 q^{34}\) \(-1.47358 q^{35}\) \(-9.73931 q^{36}\) \(+3.45191 q^{37}\) \(-9.80241 q^{38}\) \(+1.22667 q^{39}\) \(-4.06368 q^{40}\) \(+2.80806 q^{41}\) \(+0.820379 q^{42}\) \(+4.55341 q^{43}\) \(+9.35268 q^{44}\) \(-3.76159 q^{45}\) \(+0.886466 q^{46}\) \(-11.7839 q^{47}\) \(+0.170418 q^{48}\) \(-5.70687 q^{49}\) \(+7.68468 q^{50}\) \(-1.12704 q^{51}\) \(+13.2017 q^{52}\) \(+0.380395 q^{53}\) \(+4.25846 q^{54}\) \(+3.61227 q^{55}\) \(+3.56605 q^{56}\) \(+1.32055 q^{57}\) \(+2.31412 q^{58}\) \(+6.87739 q^{59}\) \(+1.35541 q^{60}\) \(+2.49126 q^{61}\) \(+23.2244 q^{62}\) \(+3.30096 q^{63}\) \(-12.6797 q^{64}\) \(+5.09885 q^{65}\) \(-2.01104 q^{66}\) \(-9.83620 q^{67}\) \(-12.1294 q^{68}\) \(-0.119422 q^{69}\) \(+3.41004 q^{70}\) \(+3.25521 q^{71}\) \(+9.10302 q^{72}\) \(-1.79064 q^{73}\) \(-7.98813 q^{74}\) \(-1.03526 q^{75}\) \(+14.2121 q^{76}\) \(-3.16992 q^{77}\) \(-2.83865 q^{78}\) \(-8.48872 q^{79}\) \(+0.708371 q^{80}\) \(+8.13475 q^{81}\) \(-6.49817 q^{82}\) \(+11.7202 q^{83}\) \(-1.18943 q^{84}\) \(-4.68472 q^{85}\) \(-10.5371 q^{86}\) \(-0.311751 q^{87}\) \(-8.74165 q^{88}\) \(-14.2658 q^{89}\) \(+8.70477 q^{90}\) \(-4.47445 q^{91}\) \(-1.28525 q^{92}\) \(-3.12873 q^{93}\) \(+27.2694 q^{94}\) \(+5.48910 q^{95}\) \(+1.56090 q^{96}\) \(-3.70766 q^{97}\) \(+13.2064 q^{98}\) \(-8.09180 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31412 −1.63633 −0.818164 0.574986i \(-0.805008\pi\)
−0.818164 + 0.574986i \(0.805008\pi\)
\(3\) 0.311751 0.179990 0.0899949 0.995942i \(-0.471315\pi\)
0.0899949 + 0.995942i \(0.471315\pi\)
\(4\) 3.35513 1.67757
\(5\) 1.29585 0.579520 0.289760 0.957099i \(-0.406425\pi\)
0.289760 + 0.957099i \(0.406425\pi\)
\(6\) −0.721429 −0.294522
\(7\) −1.13716 −0.429806 −0.214903 0.976635i \(-0.568943\pi\)
−0.214903 + 0.976635i \(0.568943\pi\)
\(8\) −3.13593 −1.10872
\(9\) −2.90281 −0.967604
\(10\) −2.99874 −0.948284
\(11\) 2.78758 0.840486 0.420243 0.907412i \(-0.361945\pi\)
0.420243 + 0.907412i \(0.361945\pi\)
\(12\) 1.04597 0.301945
\(13\) 3.93476 1.09131 0.545654 0.838011i \(-0.316281\pi\)
0.545654 + 0.838011i \(0.316281\pi\)
\(14\) 2.63152 0.703303
\(15\) 0.403982 0.104308
\(16\) 0.546648 0.136662
\(17\) −3.61518 −0.876811 −0.438405 0.898777i \(-0.644457\pi\)
−0.438405 + 0.898777i \(0.644457\pi\)
\(18\) 6.71744 1.58332
\(19\) 4.23592 0.971787 0.485893 0.874018i \(-0.338494\pi\)
0.485893 + 0.874018i \(0.338494\pi\)
\(20\) 4.34773 0.972183
\(21\) −0.354511 −0.0773606
\(22\) −6.45077 −1.37531
\(23\) −0.383069 −0.0798754 −0.0399377 0.999202i \(-0.512716\pi\)
−0.0399377 + 0.999202i \(0.512716\pi\)
\(24\) −0.977632 −0.199558
\(25\) −3.32078 −0.664157
\(26\) −9.10550 −1.78574
\(27\) −1.84021 −0.354149
\(28\) −3.81532 −0.721027
\(29\) −1.00000 −0.185695
\(30\) −0.934860 −0.170681
\(31\) −10.0360 −1.80251 −0.901257 0.433284i \(-0.857355\pi\)
−0.901257 + 0.433284i \(0.857355\pi\)
\(32\) 5.00686 0.885096
\(33\) 0.869031 0.151279
\(34\) 8.36595 1.43475
\(35\) −1.47358 −0.249081
\(36\) −9.73931 −1.62322
\(37\) 3.45191 0.567491 0.283745 0.958900i \(-0.408423\pi\)
0.283745 + 0.958900i \(0.408423\pi\)
\(38\) −9.80241 −1.59016
\(39\) 1.22667 0.196424
\(40\) −4.06368 −0.642525
\(41\) 2.80806 0.438545 0.219272 0.975664i \(-0.429632\pi\)
0.219272 + 0.975664i \(0.429632\pi\)
\(42\) 0.820379 0.126587
\(43\) 4.55341 0.694389 0.347194 0.937793i \(-0.387134\pi\)
0.347194 + 0.937793i \(0.387134\pi\)
\(44\) 9.35268 1.40997
\(45\) −3.76159 −0.560745
\(46\) 0.886466 0.130702
\(47\) −11.7839 −1.71886 −0.859432 0.511250i \(-0.829183\pi\)
−0.859432 + 0.511250i \(0.829183\pi\)
\(48\) 0.170418 0.0245977
\(49\) −5.70687 −0.815267
\(50\) 7.68468 1.08678
\(51\) −1.12704 −0.157817
\(52\) 13.2017 1.83074
\(53\) 0.380395 0.0522513 0.0261257 0.999659i \(-0.491683\pi\)
0.0261257 + 0.999659i \(0.491683\pi\)
\(54\) 4.25846 0.579503
\(55\) 3.61227 0.487078
\(56\) 3.56605 0.476534
\(57\) 1.32055 0.174912
\(58\) 2.31412 0.303858
\(59\) 6.87739 0.895360 0.447680 0.894194i \(-0.352250\pi\)
0.447680 + 0.894194i \(0.352250\pi\)
\(60\) 1.35541 0.174983
\(61\) 2.49126 0.318973 0.159487 0.987200i \(-0.449016\pi\)
0.159487 + 0.987200i \(0.449016\pi\)
\(62\) 23.2244 2.94950
\(63\) 3.30096 0.415882
\(64\) −12.6797 −1.58497
\(65\) 5.09885 0.632434
\(66\) −2.01104 −0.247542
\(67\) −9.83620 −1.20168 −0.600842 0.799368i \(-0.705168\pi\)
−0.600842 + 0.799368i \(0.705168\pi\)
\(68\) −12.1294 −1.47091
\(69\) −0.119422 −0.0143768
\(70\) 3.41004 0.407578
\(71\) 3.25521 0.386322 0.193161 0.981167i \(-0.438126\pi\)
0.193161 + 0.981167i \(0.438126\pi\)
\(72\) 9.10302 1.07280
\(73\) −1.79064 −0.209579 −0.104789 0.994494i \(-0.533417\pi\)
−0.104789 + 0.994494i \(0.533417\pi\)
\(74\) −7.98813 −0.928601
\(75\) −1.03526 −0.119541
\(76\) 14.2121 1.63024
\(77\) −3.16992 −0.361246
\(78\) −2.83865 −0.321414
\(79\) −8.48872 −0.955055 −0.477528 0.878617i \(-0.658467\pi\)
−0.477528 + 0.878617i \(0.658467\pi\)
\(80\) 0.708371 0.0791983
\(81\) 8.13475 0.903861
\(82\) −6.49817 −0.717603
\(83\) 11.7202 1.28646 0.643231 0.765673i \(-0.277594\pi\)
0.643231 + 0.765673i \(0.277594\pi\)
\(84\) −1.18943 −0.129778
\(85\) −4.68472 −0.508129
\(86\) −10.5371 −1.13625
\(87\) −0.311751 −0.0334233
\(88\) −8.74165 −0.931863
\(89\) −14.2658 −1.51217 −0.756086 0.654472i \(-0.772891\pi\)
−0.756086 + 0.654472i \(0.772891\pi\)
\(90\) 8.70477 0.917563
\(91\) −4.47445 −0.469050
\(92\) −1.28525 −0.133996
\(93\) −3.12873 −0.324434
\(94\) 27.2694 2.81262
\(95\) 5.48910 0.563170
\(96\) 1.56090 0.159308
\(97\) −3.70766 −0.376456 −0.188228 0.982125i \(-0.560274\pi\)
−0.188228 + 0.982125i \(0.560274\pi\)
\(98\) 13.2064 1.33404
\(99\) −8.09180 −0.813257
\(100\) −11.1417 −1.11417
\(101\) 6.81077 0.677697 0.338848 0.940841i \(-0.389963\pi\)
0.338848 + 0.940841i \(0.389963\pi\)
\(102\) 2.60810 0.258240
\(103\) 0.353928 0.0348736 0.0174368 0.999848i \(-0.494449\pi\)
0.0174368 + 0.999848i \(0.494449\pi\)
\(104\) −12.3392 −1.20995
\(105\) −0.459391 −0.0448320
\(106\) −0.880279 −0.0855002
\(107\) −10.9921 −1.06265 −0.531324 0.847169i \(-0.678305\pi\)
−0.531324 + 0.847169i \(0.678305\pi\)
\(108\) −6.17415 −0.594108
\(109\) 2.39166 0.229079 0.114540 0.993419i \(-0.463461\pi\)
0.114540 + 0.993419i \(0.463461\pi\)
\(110\) −8.35920 −0.797019
\(111\) 1.07614 0.102143
\(112\) −0.621625 −0.0587381
\(113\) −4.07855 −0.383678 −0.191839 0.981426i \(-0.561445\pi\)
−0.191839 + 0.981426i \(0.561445\pi\)
\(114\) −3.05592 −0.286213
\(115\) −0.496398 −0.0462894
\(116\) −3.35513 −0.311516
\(117\) −11.4219 −1.05595
\(118\) −15.9151 −1.46510
\(119\) 4.11104 0.376858
\(120\) −1.26686 −0.115648
\(121\) −3.22942 −0.293584
\(122\) −5.76507 −0.521945
\(123\) 0.875416 0.0789336
\(124\) −33.6720 −3.02384
\(125\) −10.7825 −0.964412
\(126\) −7.63880 −0.680518
\(127\) −3.37957 −0.299889 −0.149944 0.988694i \(-0.547909\pi\)
−0.149944 + 0.988694i \(0.547909\pi\)
\(128\) 19.3287 1.70843
\(129\) 1.41953 0.124983
\(130\) −11.7993 −1.03487
\(131\) −9.87230 −0.862547 −0.431273 0.902221i \(-0.641936\pi\)
−0.431273 + 0.902221i \(0.641936\pi\)
\(132\) 2.91571 0.253780
\(133\) −4.81691 −0.417679
\(134\) 22.7621 1.96635
\(135\) −2.38463 −0.205236
\(136\) 11.3370 0.972137
\(137\) −7.89475 −0.674494 −0.337247 0.941416i \(-0.609496\pi\)
−0.337247 + 0.941416i \(0.609496\pi\)
\(138\) 0.276357 0.0235251
\(139\) −1.00000 −0.0848189
\(140\) −4.94406 −0.417850
\(141\) −3.67366 −0.309378
\(142\) −7.53293 −0.632149
\(143\) 10.9685 0.917228
\(144\) −1.58681 −0.132235
\(145\) −1.29585 −0.107614
\(146\) 4.14375 0.342939
\(147\) −1.77912 −0.146740
\(148\) 11.5816 0.952004
\(149\) −2.67103 −0.218820 −0.109410 0.993997i \(-0.534896\pi\)
−0.109410 + 0.993997i \(0.534896\pi\)
\(150\) 2.39571 0.195609
\(151\) −6.10750 −0.497021 −0.248511 0.968629i \(-0.579941\pi\)
−0.248511 + 0.968629i \(0.579941\pi\)
\(152\) −13.2836 −1.07744
\(153\) 10.4942 0.848405
\(154\) 7.33555 0.591116
\(155\) −13.0051 −1.04459
\(156\) 4.11563 0.329514
\(157\) 2.32296 0.185392 0.0926960 0.995694i \(-0.470452\pi\)
0.0926960 + 0.995694i \(0.470452\pi\)
\(158\) 19.6439 1.56278
\(159\) 0.118589 0.00940470
\(160\) 6.48812 0.512931
\(161\) 0.435610 0.0343309
\(162\) −18.8247 −1.47901
\(163\) 16.8464 1.31951 0.659756 0.751480i \(-0.270660\pi\)
0.659756 + 0.751480i \(0.270660\pi\)
\(164\) 9.42140 0.735688
\(165\) 1.12613 0.0876691
\(166\) −27.1219 −2.10507
\(167\) 3.54358 0.274211 0.137105 0.990556i \(-0.456220\pi\)
0.137105 + 0.990556i \(0.456220\pi\)
\(168\) 1.11172 0.0857713
\(169\) 2.48236 0.190951
\(170\) 10.8410 0.831465
\(171\) −12.2961 −0.940304
\(172\) 15.2773 1.16488
\(173\) 19.2566 1.46405 0.732027 0.681276i \(-0.238575\pi\)
0.732027 + 0.681276i \(0.238575\pi\)
\(174\) 0.721429 0.0546914
\(175\) 3.77626 0.285458
\(176\) 1.52382 0.114862
\(177\) 2.14404 0.161156
\(178\) 33.0127 2.47441
\(179\) −3.76009 −0.281042 −0.140521 0.990078i \(-0.544878\pi\)
−0.140521 + 0.990078i \(0.544878\pi\)
\(180\) −12.6206 −0.940687
\(181\) −5.05011 −0.375372 −0.187686 0.982229i \(-0.560099\pi\)
−0.187686 + 0.982229i \(0.560099\pi\)
\(182\) 10.3544 0.767519
\(183\) 0.776655 0.0574120
\(184\) 1.20128 0.0885594
\(185\) 4.47315 0.328872
\(186\) 7.24024 0.530880
\(187\) −10.0776 −0.736947
\(188\) −39.5367 −2.88351
\(189\) 2.09261 0.152215
\(190\) −12.7024 −0.921530
\(191\) 23.4484 1.69666 0.848332 0.529465i \(-0.177607\pi\)
0.848332 + 0.529465i \(0.177607\pi\)
\(192\) −3.95293 −0.285278
\(193\) 4.99663 0.359666 0.179833 0.983697i \(-0.442444\pi\)
0.179833 + 0.983697i \(0.442444\pi\)
\(194\) 8.57996 0.616005
\(195\) 1.58957 0.113832
\(196\) −19.1473 −1.36766
\(197\) −14.1743 −1.00988 −0.504939 0.863155i \(-0.668485\pi\)
−0.504939 + 0.863155i \(0.668485\pi\)
\(198\) 18.7254 1.33075
\(199\) −2.26467 −0.160538 −0.0802692 0.996773i \(-0.525578\pi\)
−0.0802692 + 0.996773i \(0.525578\pi\)
\(200\) 10.4138 0.736364
\(201\) −3.06645 −0.216291
\(202\) −15.7609 −1.10893
\(203\) 1.13716 0.0798129
\(204\) −3.78136 −0.264748
\(205\) 3.63881 0.254145
\(206\) −0.819031 −0.0570646
\(207\) 1.11198 0.0772877
\(208\) 2.15093 0.149140
\(209\) 11.8079 0.816773
\(210\) 1.06308 0.0733598
\(211\) 13.4434 0.925479 0.462740 0.886494i \(-0.346867\pi\)
0.462740 + 0.886494i \(0.346867\pi\)
\(212\) 1.27628 0.0876550
\(213\) 1.01482 0.0695340
\(214\) 25.4370 1.73884
\(215\) 5.90052 0.402412
\(216\) 5.77077 0.392651
\(217\) 11.4125 0.774731
\(218\) −5.53457 −0.374849
\(219\) −0.558235 −0.0377220
\(220\) 12.1196 0.817105
\(221\) −14.2249 −0.956870
\(222\) −2.49031 −0.167139
\(223\) −2.36637 −0.158464 −0.0792318 0.996856i \(-0.525247\pi\)
−0.0792318 + 0.996856i \(0.525247\pi\)
\(224\) −5.69360 −0.380419
\(225\) 9.63961 0.642641
\(226\) 9.43824 0.627822
\(227\) −18.6957 −1.24088 −0.620438 0.784255i \(-0.713045\pi\)
−0.620438 + 0.784255i \(0.713045\pi\)
\(228\) 4.43063 0.293426
\(229\) −25.3115 −1.67263 −0.836317 0.548246i \(-0.815296\pi\)
−0.836317 + 0.548246i \(0.815296\pi\)
\(230\) 1.14872 0.0757445
\(231\) −0.988226 −0.0650205
\(232\) 3.13593 0.205884
\(233\) 25.9601 1.70070 0.850352 0.526215i \(-0.176389\pi\)
0.850352 + 0.526215i \(0.176389\pi\)
\(234\) 26.4315 1.72788
\(235\) −15.2702 −0.996115
\(236\) 23.0746 1.50203
\(237\) −2.64637 −0.171900
\(238\) −9.51342 −0.616663
\(239\) −8.50889 −0.550395 −0.275197 0.961388i \(-0.588743\pi\)
−0.275197 + 0.961388i \(0.588743\pi\)
\(240\) 0.220836 0.0142549
\(241\) −7.50867 −0.483676 −0.241838 0.970317i \(-0.577750\pi\)
−0.241838 + 0.970317i \(0.577750\pi\)
\(242\) 7.47326 0.480399
\(243\) 8.05665 0.516834
\(244\) 8.35851 0.535099
\(245\) −7.39522 −0.472463
\(246\) −2.02581 −0.129161
\(247\) 16.6673 1.06052
\(248\) 31.4722 1.99848
\(249\) 3.65379 0.231550
\(250\) 24.9518 1.57809
\(251\) 5.84509 0.368939 0.184469 0.982838i \(-0.440943\pi\)
0.184469 + 0.982838i \(0.440943\pi\)
\(252\) 11.0751 0.697669
\(253\) −1.06783 −0.0671341
\(254\) 7.82072 0.490716
\(255\) −1.46047 −0.0914580
\(256\) −19.3693 −1.21058
\(257\) 16.5272 1.03094 0.515468 0.856909i \(-0.327618\pi\)
0.515468 + 0.856909i \(0.327618\pi\)
\(258\) −3.28496 −0.204513
\(259\) −3.92537 −0.243911
\(260\) 17.1073 1.06095
\(261\) 2.90281 0.179679
\(262\) 22.8456 1.41141
\(263\) −5.36913 −0.331075 −0.165537 0.986204i \(-0.552936\pi\)
−0.165537 + 0.986204i \(0.552936\pi\)
\(264\) −2.72522 −0.167726
\(265\) 0.492933 0.0302807
\(266\) 11.1469 0.683460
\(267\) −4.44738 −0.272175
\(268\) −33.0018 −2.01590
\(269\) 15.9452 0.972196 0.486098 0.873904i \(-0.338420\pi\)
0.486098 + 0.873904i \(0.338420\pi\)
\(270\) 5.51830 0.335833
\(271\) −6.23858 −0.378967 −0.189483 0.981884i \(-0.560681\pi\)
−0.189483 + 0.981884i \(0.560681\pi\)
\(272\) −1.97623 −0.119827
\(273\) −1.39492 −0.0844242
\(274\) 18.2694 1.10369
\(275\) −9.25694 −0.558214
\(276\) −0.400678 −0.0241180
\(277\) −10.6406 −0.639329 −0.319664 0.947531i \(-0.603570\pi\)
−0.319664 + 0.947531i \(0.603570\pi\)
\(278\) 2.31412 0.138791
\(279\) 29.1325 1.74412
\(280\) 4.62106 0.276161
\(281\) −6.35189 −0.378922 −0.189461 0.981888i \(-0.560674\pi\)
−0.189461 + 0.981888i \(0.560674\pi\)
\(282\) 8.50127 0.506243
\(283\) −10.8965 −0.647730 −0.323865 0.946103i \(-0.604982\pi\)
−0.323865 + 0.946103i \(0.604982\pi\)
\(284\) 10.9216 0.648081
\(285\) 1.71123 0.101365
\(286\) −25.3823 −1.50088
\(287\) −3.19321 −0.188489
\(288\) −14.5340 −0.856422
\(289\) −3.93045 −0.231203
\(290\) 2.99874 0.176092
\(291\) −1.15587 −0.0677582
\(292\) −6.00784 −0.351582
\(293\) 2.69708 0.157565 0.0787826 0.996892i \(-0.474897\pi\)
0.0787826 + 0.996892i \(0.474897\pi\)
\(294\) 4.11710 0.240114
\(295\) 8.91204 0.518879
\(296\) −10.8250 −0.629188
\(297\) −5.12972 −0.297657
\(298\) 6.18108 0.358060
\(299\) −1.50729 −0.0871686
\(300\) −3.47343 −0.200539
\(301\) −5.17795 −0.298452
\(302\) 14.1335 0.813290
\(303\) 2.12327 0.121978
\(304\) 2.31556 0.132806
\(305\) 3.22829 0.184851
\(306\) −24.2848 −1.38827
\(307\) −15.7417 −0.898427 −0.449213 0.893424i \(-0.648296\pi\)
−0.449213 + 0.893424i \(0.648296\pi\)
\(308\) −10.6355 −0.606013
\(309\) 0.110338 0.00627689
\(310\) 30.0953 1.70930
\(311\) −17.8191 −1.01043 −0.505214 0.862994i \(-0.668586\pi\)
−0.505214 + 0.862994i \(0.668586\pi\)
\(312\) −3.84675 −0.217779
\(313\) −13.6759 −0.773009 −0.386504 0.922288i \(-0.626318\pi\)
−0.386504 + 0.922288i \(0.626318\pi\)
\(314\) −5.37559 −0.303362
\(315\) 4.27753 0.241012
\(316\) −28.4808 −1.60217
\(317\) 20.8956 1.17361 0.586806 0.809728i \(-0.300385\pi\)
0.586806 + 0.809728i \(0.300385\pi\)
\(318\) −0.274428 −0.0153892
\(319\) −2.78758 −0.156074
\(320\) −16.4310 −0.918521
\(321\) −3.42681 −0.191266
\(322\) −1.00805 −0.0561766
\(323\) −15.3136 −0.852073
\(324\) 27.2931 1.51629
\(325\) −13.0665 −0.724799
\(326\) −38.9845 −2.15915
\(327\) 0.745603 0.0412319
\(328\) −8.80588 −0.486223
\(329\) 13.4002 0.738777
\(330\) −2.60599 −0.143455
\(331\) −25.3733 −1.39464 −0.697322 0.716758i \(-0.745625\pi\)
−0.697322 + 0.716758i \(0.745625\pi\)
\(332\) 39.3229 2.15812
\(333\) −10.0203 −0.549106
\(334\) −8.20026 −0.448698
\(335\) −12.7462 −0.696399
\(336\) −0.193793 −0.0105722
\(337\) 2.82593 0.153938 0.0769690 0.997033i \(-0.475476\pi\)
0.0769690 + 0.997033i \(0.475476\pi\)
\(338\) −5.74448 −0.312458
\(339\) −1.27149 −0.0690581
\(340\) −15.7178 −0.852420
\(341\) −27.9760 −1.51499
\(342\) 28.4545 1.53865
\(343\) 14.4497 0.780212
\(344\) −14.2792 −0.769883
\(345\) −0.154753 −0.00833161
\(346\) −44.5620 −2.39567
\(347\) −4.66332 −0.250340 −0.125170 0.992135i \(-0.539948\pi\)
−0.125170 + 0.992135i \(0.539948\pi\)
\(348\) −1.04597 −0.0560697
\(349\) −9.24866 −0.495069 −0.247535 0.968879i \(-0.579620\pi\)
−0.247535 + 0.968879i \(0.579620\pi\)
\(350\) −8.73870 −0.467103
\(351\) −7.24079 −0.386485
\(352\) 13.9570 0.743911
\(353\) 13.4304 0.714828 0.357414 0.933946i \(-0.383658\pi\)
0.357414 + 0.933946i \(0.383658\pi\)
\(354\) −4.96155 −0.263703
\(355\) 4.21824 0.223881
\(356\) −47.8636 −2.53677
\(357\) 1.28162 0.0678306
\(358\) 8.70128 0.459877
\(359\) −4.02047 −0.212192 −0.106096 0.994356i \(-0.533835\pi\)
−0.106096 + 0.994356i \(0.533835\pi\)
\(360\) 11.7961 0.621709
\(361\) −1.05698 −0.0556306
\(362\) 11.6865 0.614231
\(363\) −1.00678 −0.0528421
\(364\) −15.0124 −0.786862
\(365\) −2.32040 −0.121455
\(366\) −1.79727 −0.0939447
\(367\) 10.6338 0.555078 0.277539 0.960714i \(-0.410481\pi\)
0.277539 + 0.960714i \(0.410481\pi\)
\(368\) −0.209404 −0.0109159
\(369\) −8.15126 −0.424338
\(370\) −10.3514 −0.538142
\(371\) −0.432570 −0.0224579
\(372\) −10.4973 −0.544260
\(373\) −12.5870 −0.651729 −0.325864 0.945416i \(-0.605655\pi\)
−0.325864 + 0.945416i \(0.605655\pi\)
\(374\) 23.3207 1.20589
\(375\) −3.36144 −0.173584
\(376\) 36.9536 1.90574
\(377\) −3.93476 −0.202651
\(378\) −4.84254 −0.249074
\(379\) −3.89244 −0.199941 −0.0999706 0.994990i \(-0.531875\pi\)
−0.0999706 + 0.994990i \(0.531875\pi\)
\(380\) 18.4166 0.944754
\(381\) −1.05359 −0.0539769
\(382\) −54.2622 −2.77630
\(383\) −15.5423 −0.794175 −0.397087 0.917781i \(-0.629979\pi\)
−0.397087 + 0.917781i \(0.629979\pi\)
\(384\) 6.02575 0.307500
\(385\) −4.10772 −0.209349
\(386\) −11.5628 −0.588530
\(387\) −13.2177 −0.671893
\(388\) −12.4397 −0.631530
\(389\) −16.6122 −0.842274 −0.421137 0.906997i \(-0.638369\pi\)
−0.421137 + 0.906997i \(0.638369\pi\)
\(390\) −3.67845 −0.186266
\(391\) 1.38486 0.0700356
\(392\) 17.8964 0.903903
\(393\) −3.07770 −0.155250
\(394\) 32.8010 1.65249
\(395\) −11.0001 −0.553473
\(396\) −27.1491 −1.36429
\(397\) −26.7036 −1.34022 −0.670108 0.742264i \(-0.733752\pi\)
−0.670108 + 0.742264i \(0.733752\pi\)
\(398\) 5.24072 0.262693
\(399\) −1.50168 −0.0751780
\(400\) −1.81530 −0.0907649
\(401\) 6.88089 0.343615 0.171808 0.985131i \(-0.445039\pi\)
0.171808 + 0.985131i \(0.445039\pi\)
\(402\) 7.09612 0.353922
\(403\) −39.4892 −1.96710
\(404\) 22.8510 1.13688
\(405\) 10.5414 0.523805
\(406\) −2.63152 −0.130600
\(407\) 9.62247 0.476968
\(408\) 3.53432 0.174975
\(409\) −25.7580 −1.27365 −0.636826 0.771007i \(-0.719753\pi\)
−0.636826 + 0.771007i \(0.719753\pi\)
\(410\) −8.42062 −0.415865
\(411\) −2.46120 −0.121402
\(412\) 1.18748 0.0585028
\(413\) −7.82069 −0.384831
\(414\) −2.57324 −0.126468
\(415\) 15.1876 0.745530
\(416\) 19.7008 0.965912
\(417\) −0.311751 −0.0152665
\(418\) −27.3250 −1.33651
\(419\) −22.2355 −1.08628 −0.543138 0.839644i \(-0.682764\pi\)
−0.543138 + 0.839644i \(0.682764\pi\)
\(420\) −1.54132 −0.0752087
\(421\) 11.3874 0.554987 0.277493 0.960728i \(-0.410496\pi\)
0.277493 + 0.960728i \(0.410496\pi\)
\(422\) −31.1095 −1.51439
\(423\) 34.2065 1.66318
\(424\) −1.19289 −0.0579320
\(425\) 12.0052 0.582340
\(426\) −2.34840 −0.113780
\(427\) −2.83296 −0.137097
\(428\) −36.8800 −1.78266
\(429\) 3.41943 0.165092
\(430\) −13.6545 −0.658478
\(431\) −36.4535 −1.75590 −0.877952 0.478749i \(-0.841091\pi\)
−0.877952 + 0.478749i \(0.841091\pi\)
\(432\) −1.00595 −0.0483986
\(433\) −16.3500 −0.785729 −0.392865 0.919596i \(-0.628516\pi\)
−0.392865 + 0.919596i \(0.628516\pi\)
\(434\) −26.4099 −1.26771
\(435\) −0.403982 −0.0193694
\(436\) 8.02433 0.384296
\(437\) −1.62265 −0.0776218
\(438\) 1.29182 0.0617256
\(439\) −23.9011 −1.14074 −0.570369 0.821389i \(-0.693200\pi\)
−0.570369 + 0.821389i \(0.693200\pi\)
\(440\) −11.3278 −0.540033
\(441\) 16.5660 0.788855
\(442\) 32.9180 1.56575
\(443\) 16.4236 0.780309 0.390155 0.920749i \(-0.372422\pi\)
0.390155 + 0.920749i \(0.372422\pi\)
\(444\) 3.61059 0.171351
\(445\) −18.4863 −0.876333
\(446\) 5.47605 0.259298
\(447\) −0.832698 −0.0393853
\(448\) 14.4189 0.681229
\(449\) −10.6997 −0.504951 −0.252475 0.967603i \(-0.581245\pi\)
−0.252475 + 0.967603i \(0.581245\pi\)
\(450\) −22.3072 −1.05157
\(451\) 7.82767 0.368591
\(452\) −13.6841 −0.643645
\(453\) −1.90402 −0.0894588
\(454\) 43.2640 2.03048
\(455\) −5.79820 −0.271824
\(456\) −4.14117 −0.193928
\(457\) −33.1942 −1.55276 −0.776381 0.630264i \(-0.782947\pi\)
−0.776381 + 0.630264i \(0.782947\pi\)
\(458\) 58.5738 2.73698
\(459\) 6.65269 0.310521
\(460\) −1.66548 −0.0776535
\(461\) 31.2733 1.45654 0.728271 0.685289i \(-0.240324\pi\)
0.728271 + 0.685289i \(0.240324\pi\)
\(462\) 2.28687 0.106395
\(463\) −2.15877 −0.100326 −0.0501632 0.998741i \(-0.515974\pi\)
−0.0501632 + 0.998741i \(0.515974\pi\)
\(464\) −0.546648 −0.0253775
\(465\) −4.05435 −0.188016
\(466\) −60.0747 −2.78291
\(467\) 13.9210 0.644187 0.322094 0.946708i \(-0.395613\pi\)
0.322094 + 0.946708i \(0.395613\pi\)
\(468\) −38.3219 −1.77143
\(469\) 11.1853 0.516490
\(470\) 35.3369 1.62997
\(471\) 0.724185 0.0333687
\(472\) −21.5670 −0.992704
\(473\) 12.6930 0.583624
\(474\) 6.12401 0.281285
\(475\) −14.0666 −0.645419
\(476\) 13.7931 0.632205
\(477\) −1.10422 −0.0505586
\(478\) 19.6906 0.900626
\(479\) 21.6989 0.991447 0.495724 0.868480i \(-0.334903\pi\)
0.495724 + 0.868480i \(0.334903\pi\)
\(480\) 2.02268 0.0923223
\(481\) 13.5825 0.619307
\(482\) 17.3759 0.791453
\(483\) 0.135802 0.00617921
\(484\) −10.8351 −0.492506
\(485\) −4.80456 −0.218164
\(486\) −18.6440 −0.845710
\(487\) 4.77561 0.216403 0.108202 0.994129i \(-0.465491\pi\)
0.108202 + 0.994129i \(0.465491\pi\)
\(488\) −7.81243 −0.353652
\(489\) 5.25189 0.237499
\(490\) 17.1134 0.773104
\(491\) 13.1760 0.594623 0.297311 0.954781i \(-0.403910\pi\)
0.297311 + 0.954781i \(0.403910\pi\)
\(492\) 2.93714 0.132416
\(493\) 3.61518 0.162820
\(494\) −38.5702 −1.73535
\(495\) −10.4857 −0.471298
\(496\) −5.48614 −0.246335
\(497\) −3.70169 −0.166043
\(498\) −8.45530 −0.378891
\(499\) −17.2531 −0.772355 −0.386178 0.922424i \(-0.626205\pi\)
−0.386178 + 0.922424i \(0.626205\pi\)
\(500\) −36.1765 −1.61786
\(501\) 1.10472 0.0493551
\(502\) −13.5262 −0.603704
\(503\) 4.26936 0.190362 0.0951808 0.995460i \(-0.469657\pi\)
0.0951808 + 0.995460i \(0.469657\pi\)
\(504\) −10.3516 −0.461096
\(505\) 8.82570 0.392739
\(506\) 2.47109 0.109853
\(507\) 0.773881 0.0343693
\(508\) −11.3389 −0.503083
\(509\) −7.43591 −0.329591 −0.164795 0.986328i \(-0.552696\pi\)
−0.164795 + 0.986328i \(0.552696\pi\)
\(510\) 3.37969 0.149655
\(511\) 2.03624 0.0900782
\(512\) 6.16549 0.272479
\(513\) −7.79498 −0.344157
\(514\) −38.2458 −1.68695
\(515\) 0.458637 0.0202099
\(516\) 4.76272 0.209667
\(517\) −32.8486 −1.44468
\(518\) 9.08377 0.399118
\(519\) 6.00328 0.263515
\(520\) −15.9896 −0.701192
\(521\) −26.6066 −1.16565 −0.582827 0.812596i \(-0.698054\pi\)
−0.582827 + 0.812596i \(0.698054\pi\)
\(522\) −6.71744 −0.294014
\(523\) 0.223778 0.00978514 0.00489257 0.999988i \(-0.498443\pi\)
0.00489257 + 0.999988i \(0.498443\pi\)
\(524\) −33.1229 −1.44698
\(525\) 1.17725 0.0513796
\(526\) 12.4248 0.541747
\(527\) 36.2819 1.58046
\(528\) 0.475053 0.0206740
\(529\) −22.8533 −0.993620
\(530\) −1.14071 −0.0495491
\(531\) −19.9638 −0.866354
\(532\) −16.1614 −0.700685
\(533\) 11.0490 0.478587
\(534\) 10.2918 0.445368
\(535\) −14.2441 −0.615825
\(536\) 30.8457 1.33233
\(537\) −1.17221 −0.0505847
\(538\) −36.8990 −1.59083
\(539\) −15.9083 −0.685220
\(540\) −8.00074 −0.344297
\(541\) −19.8094 −0.851671 −0.425836 0.904801i \(-0.640020\pi\)
−0.425836 + 0.904801i \(0.640020\pi\)
\(542\) 14.4368 0.620113
\(543\) −1.57438 −0.0675630
\(544\) −18.1007 −0.776062
\(545\) 3.09922 0.132756
\(546\) 3.22800 0.138146
\(547\) −2.27235 −0.0971586 −0.0485793 0.998819i \(-0.515469\pi\)
−0.0485793 + 0.998819i \(0.515469\pi\)
\(548\) −26.4879 −1.13151
\(549\) −7.23166 −0.308640
\(550\) 21.4216 0.913421
\(551\) −4.23592 −0.180456
\(552\) 0.374500 0.0159398
\(553\) 9.65302 0.410488
\(554\) 24.6235 1.04615
\(555\) 1.39451 0.0591936
\(556\) −3.35513 −0.142289
\(557\) −3.27832 −0.138907 −0.0694535 0.997585i \(-0.522126\pi\)
−0.0694535 + 0.997585i \(0.522126\pi\)
\(558\) −67.4161 −2.85395
\(559\) 17.9166 0.757792
\(560\) −0.805530 −0.0340399
\(561\) −3.14170 −0.132643
\(562\) 14.6990 0.620040
\(563\) 23.6327 0.995998 0.497999 0.867178i \(-0.334068\pi\)
0.497999 + 0.867178i \(0.334068\pi\)
\(564\) −12.3256 −0.519002
\(565\) −5.28517 −0.222349
\(566\) 25.2158 1.05990
\(567\) −9.25050 −0.388484
\(568\) −10.2081 −0.428323
\(569\) 2.04529 0.0857432 0.0428716 0.999081i \(-0.486349\pi\)
0.0428716 + 0.999081i \(0.486349\pi\)
\(570\) −3.95999 −0.165866
\(571\) −44.1233 −1.84650 −0.923251 0.384197i \(-0.874478\pi\)
−0.923251 + 0.384197i \(0.874478\pi\)
\(572\) 36.8006 1.53871
\(573\) 7.31006 0.305382
\(574\) 7.38945 0.308430
\(575\) 1.27209 0.0530498
\(576\) 36.8069 1.53362
\(577\) 31.7503 1.32178 0.660891 0.750482i \(-0.270179\pi\)
0.660891 + 0.750482i \(0.270179\pi\)
\(578\) 9.09552 0.378324
\(579\) 1.55771 0.0647361
\(580\) −4.34773 −0.180530
\(581\) −13.3278 −0.552928
\(582\) 2.67482 0.110875
\(583\) 1.06038 0.0439165
\(584\) 5.61533 0.232364
\(585\) −14.8010 −0.611945
\(586\) −6.24136 −0.257828
\(587\) 32.8234 1.35477 0.677384 0.735630i \(-0.263114\pi\)
0.677384 + 0.735630i \(0.263114\pi\)
\(588\) −5.96920 −0.246166
\(589\) −42.5116 −1.75166
\(590\) −20.6235 −0.849056
\(591\) −4.41887 −0.181768
\(592\) 1.88698 0.0775544
\(593\) −7.81354 −0.320864 −0.160432 0.987047i \(-0.551289\pi\)
−0.160432 + 0.987047i \(0.551289\pi\)
\(594\) 11.8708 0.487064
\(595\) 5.32727 0.218397
\(596\) −8.96167 −0.367084
\(597\) −0.706015 −0.0288953
\(598\) 3.48803 0.142636
\(599\) −2.23550 −0.0913399 −0.0456700 0.998957i \(-0.514542\pi\)
−0.0456700 + 0.998957i \(0.514542\pi\)
\(600\) 3.24650 0.132538
\(601\) −6.43562 −0.262514 −0.131257 0.991348i \(-0.541901\pi\)
−0.131257 + 0.991348i \(0.541901\pi\)
\(602\) 11.9824 0.488366
\(603\) 28.5526 1.16275
\(604\) −20.4915 −0.833786
\(605\) −4.18483 −0.170138
\(606\) −4.91348 −0.199597
\(607\) −24.5469 −0.996329 −0.498164 0.867083i \(-0.665992\pi\)
−0.498164 + 0.867083i \(0.665992\pi\)
\(608\) 21.2087 0.860125
\(609\) 0.354511 0.0143655
\(610\) −7.47064 −0.302477
\(611\) −46.3670 −1.87581
\(612\) 35.2094 1.42326
\(613\) −5.78251 −0.233554 −0.116777 0.993158i \(-0.537256\pi\)
−0.116777 + 0.993158i \(0.537256\pi\)
\(614\) 36.4281 1.47012
\(615\) 1.13440 0.0457436
\(616\) 9.94065 0.400520
\(617\) 0.963831 0.0388024 0.0194012 0.999812i \(-0.493824\pi\)
0.0194012 + 0.999812i \(0.493824\pi\)
\(618\) −0.255334 −0.0102710
\(619\) 2.86259 0.115057 0.0575285 0.998344i \(-0.481678\pi\)
0.0575285 + 0.998344i \(0.481678\pi\)
\(620\) −43.6337 −1.75237
\(621\) 0.704927 0.0282878
\(622\) 41.2354 1.65339
\(623\) 16.2225 0.649940
\(624\) 0.670555 0.0268437
\(625\) 2.63153 0.105261
\(626\) 31.6477 1.26489
\(627\) 3.68114 0.147011
\(628\) 7.79382 0.311007
\(629\) −12.4793 −0.497582
\(630\) −9.89870 −0.394374
\(631\) −4.96291 −0.197570 −0.0987851 0.995109i \(-0.531496\pi\)
−0.0987851 + 0.995109i \(0.531496\pi\)
\(632\) 26.6200 1.05889
\(633\) 4.19099 0.166577
\(634\) −48.3548 −1.92041
\(635\) −4.37940 −0.173791
\(636\) 0.397881 0.0157770
\(637\) −22.4552 −0.889707
\(638\) 6.45077 0.255389
\(639\) −9.44925 −0.373807
\(640\) 25.0470 0.990069
\(641\) −24.8544 −0.981691 −0.490846 0.871247i \(-0.663312\pi\)
−0.490846 + 0.871247i \(0.663312\pi\)
\(642\) 7.93003 0.312973
\(643\) −18.8363 −0.742830 −0.371415 0.928467i \(-0.621127\pi\)
−0.371415 + 0.928467i \(0.621127\pi\)
\(644\) 1.46153 0.0575923
\(645\) 1.83950 0.0724301
\(646\) 35.4375 1.39427
\(647\) 8.58381 0.337464 0.168732 0.985662i \(-0.446033\pi\)
0.168732 + 0.985662i \(0.446033\pi\)
\(648\) −25.5100 −1.00213
\(649\) 19.1713 0.752537
\(650\) 30.2374 1.18601
\(651\) 3.55786 0.139444
\(652\) 56.5219 2.21357
\(653\) −8.16296 −0.319441 −0.159721 0.987162i \(-0.551059\pi\)
−0.159721 + 0.987162i \(0.551059\pi\)
\(654\) −1.72541 −0.0674689
\(655\) −12.7930 −0.499863
\(656\) 1.53502 0.0599324
\(657\) 5.19790 0.202789
\(658\) −31.0096 −1.20888
\(659\) −24.3059 −0.946823 −0.473411 0.880842i \(-0.656978\pi\)
−0.473411 + 0.880842i \(0.656978\pi\)
\(660\) 3.77831 0.147071
\(661\) −10.9894 −0.427437 −0.213719 0.976895i \(-0.568558\pi\)
−0.213719 + 0.976895i \(0.568558\pi\)
\(662\) 58.7168 2.28209
\(663\) −4.43463 −0.172227
\(664\) −36.7538 −1.42632
\(665\) −6.24198 −0.242053
\(666\) 23.1880 0.898518
\(667\) 0.383069 0.0148325
\(668\) 11.8892 0.460006
\(669\) −0.737718 −0.0285218
\(670\) 29.4962 1.13954
\(671\) 6.94458 0.268093
\(672\) −1.77499 −0.0684716
\(673\) −23.9288 −0.922386 −0.461193 0.887300i \(-0.652578\pi\)
−0.461193 + 0.887300i \(0.652578\pi\)
\(674\) −6.53952 −0.251893
\(675\) 6.11094 0.235210
\(676\) 8.32866 0.320333
\(677\) 33.6028 1.29146 0.645731 0.763565i \(-0.276553\pi\)
0.645731 + 0.763565i \(0.276553\pi\)
\(678\) 2.94239 0.113002
\(679\) 4.21620 0.161803
\(680\) 14.6910 0.563373
\(681\) −5.82841 −0.223345
\(682\) 64.7398 2.47902
\(683\) 21.7767 0.833263 0.416632 0.909075i \(-0.363210\pi\)
0.416632 + 0.909075i \(0.363210\pi\)
\(684\) −41.2550 −1.57742
\(685\) −10.2304 −0.390883
\(686\) −33.4384 −1.27668
\(687\) −7.89091 −0.301057
\(688\) 2.48911 0.0948965
\(689\) 1.49677 0.0570222
\(690\) 0.358116 0.0136332
\(691\) 16.2195 0.617021 0.308510 0.951221i \(-0.400170\pi\)
0.308510 + 0.951221i \(0.400170\pi\)
\(692\) 64.6085 2.45605
\(693\) 9.20167 0.349542
\(694\) 10.7915 0.409638
\(695\) −1.29585 −0.0491542
\(696\) 0.977632 0.0370570
\(697\) −10.1516 −0.384521
\(698\) 21.4025 0.810095
\(699\) 8.09310 0.306109
\(700\) 12.6699 0.478875
\(701\) 28.2550 1.06718 0.533589 0.845744i \(-0.320843\pi\)
0.533589 + 0.845744i \(0.320843\pi\)
\(702\) 16.7560 0.632416
\(703\) 14.6220 0.551480
\(704\) −35.3458 −1.33214
\(705\) −4.76049 −0.179291
\(706\) −31.0795 −1.16969
\(707\) −7.74493 −0.291278
\(708\) 7.19353 0.270349
\(709\) −32.7292 −1.22917 −0.614585 0.788850i \(-0.710677\pi\)
−0.614585 + 0.788850i \(0.710677\pi\)
\(710\) −9.76151 −0.366343
\(711\) 24.6411 0.924115
\(712\) 44.7366 1.67657
\(713\) 3.84447 0.143977
\(714\) −2.96582 −0.110993
\(715\) 14.2134 0.531552
\(716\) −12.6156 −0.471467
\(717\) −2.65266 −0.0990654
\(718\) 9.30383 0.347216
\(719\) 9.90783 0.369500 0.184750 0.982786i \(-0.440852\pi\)
0.184750 + 0.982786i \(0.440852\pi\)
\(720\) −2.05627 −0.0766325
\(721\) −0.402473 −0.0149889
\(722\) 2.44598 0.0910298
\(723\) −2.34084 −0.0870568
\(724\) −16.9438 −0.629710
\(725\) 3.32078 0.123331
\(726\) 2.32980 0.0864670
\(727\) 41.0757 1.52341 0.761706 0.647923i \(-0.224362\pi\)
0.761706 + 0.647923i \(0.224362\pi\)
\(728\) 14.0316 0.520045
\(729\) −21.8926 −0.810836
\(730\) 5.36966 0.198740
\(731\) −16.4614 −0.608848
\(732\) 2.60578 0.0963123
\(733\) −4.60030 −0.169916 −0.0849581 0.996385i \(-0.527076\pi\)
−0.0849581 + 0.996385i \(0.527076\pi\)
\(734\) −24.6078 −0.908289
\(735\) −2.30547 −0.0850386
\(736\) −1.91797 −0.0706974
\(737\) −27.4191 −1.01000
\(738\) 18.8630 0.694355
\(739\) 22.5825 0.830709 0.415355 0.909660i \(-0.363657\pi\)
0.415355 + 0.909660i \(0.363657\pi\)
\(740\) 15.0080 0.551705
\(741\) 5.19607 0.190882
\(742\) 1.00102 0.0367485
\(743\) −36.8186 −1.35074 −0.675372 0.737477i \(-0.736017\pi\)
−0.675372 + 0.737477i \(0.736017\pi\)
\(744\) 9.81149 0.359707
\(745\) −3.46125 −0.126810
\(746\) 29.1277 1.06644
\(747\) −34.0216 −1.24478
\(748\) −33.8117 −1.23628
\(749\) 12.4998 0.456732
\(750\) 7.77877 0.284041
\(751\) 4.12722 0.150604 0.0753022 0.997161i \(-0.476008\pi\)
0.0753022 + 0.997161i \(0.476008\pi\)
\(752\) −6.44166 −0.234903
\(753\) 1.82221 0.0664052
\(754\) 9.10550 0.331603
\(755\) −7.91438 −0.288034
\(756\) 7.02099 0.255351
\(757\) −19.2373 −0.699192 −0.349596 0.936900i \(-0.613681\pi\)
−0.349596 + 0.936900i \(0.613681\pi\)
\(758\) 9.00756 0.327169
\(759\) −0.332899 −0.0120835
\(760\) −17.2134 −0.624397
\(761\) 4.51141 0.163538 0.0817692 0.996651i \(-0.473943\pi\)
0.0817692 + 0.996651i \(0.473943\pi\)
\(762\) 2.43812 0.0883238
\(763\) −2.71970 −0.0984596
\(764\) 78.6723 2.84627
\(765\) 13.5989 0.491668
\(766\) 35.9667 1.29953
\(767\) 27.0609 0.977113
\(768\) −6.03841 −0.217893
\(769\) 15.5928 0.562291 0.281145 0.959665i \(-0.409286\pi\)
0.281145 + 0.959665i \(0.409286\pi\)
\(770\) 9.50574 0.342563
\(771\) 5.15237 0.185558
\(772\) 16.7644 0.603363
\(773\) −41.1797 −1.48113 −0.740566 0.671984i \(-0.765442\pi\)
−0.740566 + 0.671984i \(0.765442\pi\)
\(774\) 30.5873 1.09944
\(775\) 33.3273 1.19715
\(776\) 11.6270 0.417384
\(777\) −1.22374 −0.0439015
\(778\) 38.4427 1.37824
\(779\) 11.8947 0.426172
\(780\) 5.33323 0.190960
\(781\) 9.07413 0.324698
\(782\) −3.20474 −0.114601
\(783\) 1.84021 0.0657637
\(784\) −3.11965 −0.111416
\(785\) 3.01019 0.107438
\(786\) 7.12216 0.254039
\(787\) −19.5882 −0.698246 −0.349123 0.937077i \(-0.613520\pi\)
−0.349123 + 0.937077i \(0.613520\pi\)
\(788\) −47.5567 −1.69414
\(789\) −1.67383 −0.0595901
\(790\) 25.4554 0.905663
\(791\) 4.63796 0.164907
\(792\) 25.3754 0.901674
\(793\) 9.80253 0.348098
\(794\) 61.7953 2.19303
\(795\) 0.153673 0.00545021
\(796\) −7.59828 −0.269314
\(797\) 17.2477 0.610944 0.305472 0.952201i \(-0.401186\pi\)
0.305472 + 0.952201i \(0.401186\pi\)
\(798\) 3.47506 0.123016
\(799\) 42.6011 1.50712
\(800\) −16.6267 −0.587843
\(801\) 41.4109 1.46318
\(802\) −15.9232 −0.562267
\(803\) −4.99155 −0.176148
\(804\) −10.2883 −0.362842
\(805\) 0.564484 0.0198954
\(806\) 91.3826 3.21881
\(807\) 4.97094 0.174985
\(808\) −21.3581 −0.751376
\(809\) 6.65883 0.234112 0.117056 0.993125i \(-0.462654\pi\)
0.117056 + 0.993125i \(0.462654\pi\)
\(810\) −24.3940 −0.857116
\(811\) 21.7342 0.763189 0.381595 0.924330i \(-0.375375\pi\)
0.381595 + 0.924330i \(0.375375\pi\)
\(812\) 3.81532 0.133891
\(813\) −1.94489 −0.0682101
\(814\) −22.2675 −0.780476
\(815\) 21.8303 0.764683
\(816\) −0.616093 −0.0215676
\(817\) 19.2879 0.674798
\(818\) 59.6071 2.08411
\(819\) 12.9885 0.453855
\(820\) 12.2087 0.426346
\(821\) 13.3231 0.464980 0.232490 0.972599i \(-0.425313\pi\)
0.232490 + 0.972599i \(0.425313\pi\)
\(822\) 5.69550 0.198653
\(823\) 18.7951 0.655157 0.327578 0.944824i \(-0.393767\pi\)
0.327578 + 0.944824i \(0.393767\pi\)
\(824\) −1.10990 −0.0386651
\(825\) −2.88586 −0.100473
\(826\) 18.0980 0.629709
\(827\) 27.6050 0.959919 0.479959 0.877291i \(-0.340651\pi\)
0.479959 + 0.877291i \(0.340651\pi\)
\(828\) 3.73083 0.129655
\(829\) −26.1151 −0.907016 −0.453508 0.891252i \(-0.649828\pi\)
−0.453508 + 0.891252i \(0.649828\pi\)
\(830\) −35.1458 −1.21993
\(831\) −3.31721 −0.115073
\(832\) −49.8918 −1.72969
\(833\) 20.6314 0.714835
\(834\) 0.721429 0.0249810
\(835\) 4.59193 0.158910
\(836\) 39.6172 1.37019
\(837\) 18.4683 0.638358
\(838\) 51.4555 1.77750
\(839\) 30.7252 1.06075 0.530377 0.847762i \(-0.322051\pi\)
0.530377 + 0.847762i \(0.322051\pi\)
\(840\) 1.44062 0.0497061
\(841\) 1.00000 0.0344828
\(842\) −26.3517 −0.908140
\(843\) −1.98021 −0.0682020
\(844\) 45.1042 1.55255
\(845\) 3.21676 0.110660
\(846\) −79.1579 −2.72150
\(847\) 3.67237 0.126184
\(848\) 0.207942 0.00714076
\(849\) −3.39700 −0.116585
\(850\) −27.7815 −0.952898
\(851\) −1.32232 −0.0453286
\(852\) 3.40484 0.116648
\(853\) 34.0611 1.16623 0.583115 0.812390i \(-0.301834\pi\)
0.583115 + 0.812390i \(0.301834\pi\)
\(854\) 6.55580 0.224335
\(855\) −15.9338 −0.544925
\(856\) 34.4705 1.17818
\(857\) −14.9393 −0.510315 −0.255158 0.966899i \(-0.582127\pi\)
−0.255158 + 0.966899i \(0.582127\pi\)
\(858\) −7.91296 −0.270144
\(859\) −39.4619 −1.34642 −0.673211 0.739450i \(-0.735086\pi\)
−0.673211 + 0.739450i \(0.735086\pi\)
\(860\) 19.7970 0.675073
\(861\) −0.995487 −0.0339261
\(862\) 84.3577 2.87323
\(863\) −5.79967 −0.197423 −0.0987116 0.995116i \(-0.531472\pi\)
−0.0987116 + 0.995116i \(0.531472\pi\)
\(864\) −9.21367 −0.313455
\(865\) 24.9536 0.848448
\(866\) 37.8357 1.28571
\(867\) −1.22532 −0.0416142
\(868\) 38.2905 1.29966
\(869\) −23.6629 −0.802710
\(870\) 0.934860 0.0316947
\(871\) −38.7031 −1.31141
\(872\) −7.50008 −0.253985
\(873\) 10.7626 0.364260
\(874\) 3.75500 0.127015
\(875\) 12.2614 0.414510
\(876\) −1.87295 −0.0632812
\(877\) 1.22011 0.0412001 0.0206001 0.999788i \(-0.493442\pi\)
0.0206001 + 0.999788i \(0.493442\pi\)
\(878\) 55.3099 1.86662
\(879\) 0.840819 0.0283601
\(880\) 1.97464 0.0665650
\(881\) 23.8129 0.802277 0.401139 0.916017i \(-0.368615\pi\)
0.401139 + 0.916017i \(0.368615\pi\)
\(882\) −38.3356 −1.29083
\(883\) 47.8692 1.61093 0.805464 0.592645i \(-0.201916\pi\)
0.805464 + 0.592645i \(0.201916\pi\)
\(884\) −47.7264 −1.60521
\(885\) 2.77834 0.0933929
\(886\) −38.0061 −1.27684
\(887\) −26.7351 −0.897676 −0.448838 0.893613i \(-0.648162\pi\)
−0.448838 + 0.893613i \(0.648162\pi\)
\(888\) −3.37470 −0.113247
\(889\) 3.84311 0.128894
\(890\) 42.7794 1.43397
\(891\) 22.6762 0.759682
\(892\) −7.93947 −0.265833
\(893\) −49.9158 −1.67037
\(894\) 1.92696 0.0644472
\(895\) −4.87249 −0.162870
\(896\) −21.9798 −0.734293
\(897\) −0.469898 −0.0156895
\(898\) 24.7604 0.826264
\(899\) 10.0360 0.334719
\(900\) 32.3422 1.07807
\(901\) −1.37520 −0.0458145
\(902\) −18.1141 −0.603135
\(903\) −1.61423 −0.0537184
\(904\) 12.7901 0.425391
\(905\) −6.54416 −0.217535
\(906\) 4.40613 0.146384
\(907\) 56.4278 1.87365 0.936827 0.349792i \(-0.113748\pi\)
0.936827 + 0.349792i \(0.113748\pi\)
\(908\) −62.7265 −2.08165
\(909\) −19.7704 −0.655742
\(910\) 13.4177 0.444792
\(911\) 8.50374 0.281741 0.140871 0.990028i \(-0.455010\pi\)
0.140871 + 0.990028i \(0.455010\pi\)
\(912\) 0.721878 0.0239038
\(913\) 32.6710 1.08125
\(914\) 76.8153 2.54083
\(915\) 1.00642 0.0332714
\(916\) −84.9236 −2.80595
\(917\) 11.2264 0.370727
\(918\) −15.3951 −0.508114
\(919\) 15.7155 0.518406 0.259203 0.965823i \(-0.416540\pi\)
0.259203 + 0.965823i \(0.416540\pi\)
\(920\) 1.55667 0.0513219
\(921\) −4.90750 −0.161708
\(922\) −72.3700 −2.38338
\(923\) 12.8085 0.421596
\(924\) −3.31563 −0.109076
\(925\) −11.4631 −0.376903
\(926\) 4.99564 0.164167
\(927\) −1.02739 −0.0337438
\(928\) −5.00686 −0.164358
\(929\) −17.4172 −0.571440 −0.285720 0.958313i \(-0.592233\pi\)
−0.285720 + 0.958313i \(0.592233\pi\)
\(930\) 9.38224 0.307656
\(931\) −24.1738 −0.792266
\(932\) 87.0996 2.85304
\(933\) −5.55513 −0.181867
\(934\) −32.2148 −1.05410
\(935\) −13.0590 −0.427075
\(936\) 35.8182 1.17076
\(937\) −6.07434 −0.198440 −0.0992200 0.995066i \(-0.531635\pi\)
−0.0992200 + 0.995066i \(0.531635\pi\)
\(938\) −25.8841 −0.845147
\(939\) −4.26349 −0.139134
\(940\) −51.2334 −1.67105
\(941\) −29.2591 −0.953821 −0.476910 0.878952i \(-0.658243\pi\)
−0.476910 + 0.878952i \(0.658243\pi\)
\(942\) −1.67585 −0.0546020
\(943\) −1.07568 −0.0350289
\(944\) 3.75951 0.122362
\(945\) 2.71170 0.0882116
\(946\) −29.3730 −0.955000
\(947\) 3.77521 0.122678 0.0613389 0.998117i \(-0.480463\pi\)
0.0613389 + 0.998117i \(0.480463\pi\)
\(948\) −8.87892 −0.288374
\(949\) −7.04575 −0.228715
\(950\) 32.5517 1.05612
\(951\) 6.51422 0.211238
\(952\) −12.8919 −0.417830
\(953\) −21.5188 −0.697061 −0.348530 0.937297i \(-0.613319\pi\)
−0.348530 + 0.937297i \(0.613319\pi\)
\(954\) 2.55528 0.0827303
\(955\) 30.3855 0.983250
\(956\) −28.5485 −0.923323
\(957\) −0.869031 −0.0280918
\(958\) −50.2137 −1.62233
\(959\) 8.97759 0.289901
\(960\) −5.12239 −0.165324
\(961\) 69.7209 2.24906
\(962\) −31.4314 −1.01339
\(963\) 31.9080 1.02822
\(964\) −25.1926 −0.811399
\(965\) 6.47487 0.208433
\(966\) −0.314262 −0.0101112
\(967\) −30.8925 −0.993435 −0.496718 0.867912i \(-0.665462\pi\)
−0.496718 + 0.867912i \(0.665462\pi\)
\(968\) 10.1273 0.325502
\(969\) −4.77404 −0.153364
\(970\) 11.1183 0.356987
\(971\) −42.9351 −1.37785 −0.688926 0.724831i \(-0.741918\pi\)
−0.688926 + 0.724831i \(0.741918\pi\)
\(972\) 27.0311 0.867024
\(973\) 1.13716 0.0364556
\(974\) −11.0513 −0.354107
\(975\) −4.07350 −0.130456
\(976\) 1.36184 0.0435915
\(977\) −19.3023 −0.617536 −0.308768 0.951137i \(-0.599917\pi\)
−0.308768 + 0.951137i \(0.599917\pi\)
\(978\) −12.1535 −0.388625
\(979\) −39.7670 −1.27096
\(980\) −24.8119 −0.792588
\(981\) −6.94253 −0.221658
\(982\) −30.4907 −0.972997
\(983\) 10.6594 0.339981 0.169991 0.985446i \(-0.445626\pi\)
0.169991 + 0.985446i \(0.445626\pi\)
\(984\) −2.74525 −0.0875152
\(985\) −18.3677 −0.585245
\(986\) −8.36595 −0.266426
\(987\) 4.17753 0.132972
\(988\) 55.9211 1.77909
\(989\) −1.74427 −0.0554646
\(990\) 24.2652 0.771198
\(991\) 40.8739 1.29840 0.649202 0.760616i \(-0.275103\pi\)
0.649202 + 0.760616i \(0.275103\pi\)
\(992\) −50.2487 −1.59540
\(993\) −7.91017 −0.251022
\(994\) 8.56613 0.271701
\(995\) −2.93467 −0.0930352
\(996\) 12.2590 0.388440
\(997\) 12.9519 0.410189 0.205095 0.978742i \(-0.434250\pi\)
0.205095 + 0.978742i \(0.434250\pi\)
\(998\) 39.9257 1.26383
\(999\) −6.35224 −0.200976
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 \(a_p\))