Properties

Label 8042.2.a.a.1.14
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.07802 q^{3}\) \(+1.00000 q^{4}\) \(-3.66993 q^{5}\) \(-2.07802 q^{6}\) \(-3.45056 q^{7}\) \(+1.00000 q^{8}\) \(+1.31817 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.07802 q^{3}\) \(+1.00000 q^{4}\) \(-3.66993 q^{5}\) \(-2.07802 q^{6}\) \(-3.45056 q^{7}\) \(+1.00000 q^{8}\) \(+1.31817 q^{9}\) \(-3.66993 q^{10}\) \(-0.0411660 q^{11}\) \(-2.07802 q^{12}\) \(-1.28748 q^{13}\) \(-3.45056 q^{14}\) \(+7.62619 q^{15}\) \(+1.00000 q^{16}\) \(-3.99294 q^{17}\) \(+1.31817 q^{18}\) \(+4.34352 q^{19}\) \(-3.66993 q^{20}\) \(+7.17034 q^{21}\) \(-0.0411660 q^{22}\) \(-2.81157 q^{23}\) \(-2.07802 q^{24}\) \(+8.46842 q^{25}\) \(-1.28748 q^{26}\) \(+3.49488 q^{27}\) \(-3.45056 q^{28}\) \(-2.72765 q^{29}\) \(+7.62619 q^{30}\) \(+8.98284 q^{31}\) \(+1.00000 q^{32}\) \(+0.0855438 q^{33}\) \(-3.99294 q^{34}\) \(+12.6633 q^{35}\) \(+1.31817 q^{36}\) \(+8.77471 q^{37}\) \(+4.34352 q^{38}\) \(+2.67542 q^{39}\) \(-3.66993 q^{40}\) \(+0.445901 q^{41}\) \(+7.17034 q^{42}\) \(-9.80961 q^{43}\) \(-0.0411660 q^{44}\) \(-4.83758 q^{45}\) \(-2.81157 q^{46}\) \(+5.77836 q^{47}\) \(-2.07802 q^{48}\) \(+4.90639 q^{49}\) \(+8.46842 q^{50}\) \(+8.29742 q^{51}\) \(-1.28748 q^{52}\) \(+7.93141 q^{53}\) \(+3.49488 q^{54}\) \(+0.151077 q^{55}\) \(-3.45056 q^{56}\) \(-9.02591 q^{57}\) \(-2.72765 q^{58}\) \(-4.48136 q^{59}\) \(+7.62619 q^{60}\) \(+7.09875 q^{61}\) \(+8.98284 q^{62}\) \(-4.54842 q^{63}\) \(+1.00000 q^{64}\) \(+4.72498 q^{65}\) \(+0.0855438 q^{66}\) \(-10.4509 q^{67}\) \(-3.99294 q^{68}\) \(+5.84250 q^{69}\) \(+12.6633 q^{70}\) \(+7.58055 q^{71}\) \(+1.31817 q^{72}\) \(-3.83122 q^{73}\) \(+8.77471 q^{74}\) \(-17.5975 q^{75}\) \(+4.34352 q^{76}\) \(+0.142046 q^{77}\) \(+2.67542 q^{78}\) \(-1.20276 q^{79}\) \(-3.66993 q^{80}\) \(-11.2169 q^{81}\) \(+0.445901 q^{82}\) \(+4.24142 q^{83}\) \(+7.17034 q^{84}\) \(+14.6538 q^{85}\) \(-9.80961 q^{86}\) \(+5.66811 q^{87}\) \(-0.0411660 q^{88}\) \(+7.73181 q^{89}\) \(-4.83758 q^{90}\) \(+4.44255 q^{91}\) \(-2.81157 q^{92}\) \(-18.6665 q^{93}\) \(+5.77836 q^{94}\) \(-15.9404 q^{95}\) \(-2.07802 q^{96}\) \(+12.0758 q^{97}\) \(+4.90639 q^{98}\) \(-0.0542636 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.07802 −1.19975 −0.599873 0.800096i \(-0.704782\pi\)
−0.599873 + 0.800096i \(0.704782\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.66993 −1.64124 −0.820622 0.571471i \(-0.806373\pi\)
−0.820622 + 0.571471i \(0.806373\pi\)
\(6\) −2.07802 −0.848348
\(7\) −3.45056 −1.30419 −0.652095 0.758137i \(-0.726110\pi\)
−0.652095 + 0.758137i \(0.726110\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.31817 0.439389
\(10\) −3.66993 −1.16054
\(11\) −0.0411660 −0.0124120 −0.00620601 0.999981i \(-0.501975\pi\)
−0.00620601 + 0.999981i \(0.501975\pi\)
\(12\) −2.07802 −0.599873
\(13\) −1.28748 −0.357084 −0.178542 0.983932i \(-0.557138\pi\)
−0.178542 + 0.983932i \(0.557138\pi\)
\(14\) −3.45056 −0.922202
\(15\) 7.62619 1.96908
\(16\) 1.00000 0.250000
\(17\) −3.99294 −0.968431 −0.484216 0.874949i \(-0.660895\pi\)
−0.484216 + 0.874949i \(0.660895\pi\)
\(18\) 1.31817 0.310695
\(19\) 4.34352 0.996471 0.498235 0.867042i \(-0.333982\pi\)
0.498235 + 0.867042i \(0.333982\pi\)
\(20\) −3.66993 −0.820622
\(21\) 7.17034 1.56470
\(22\) −0.0411660 −0.00877662
\(23\) −2.81157 −0.586253 −0.293127 0.956074i \(-0.594696\pi\)
−0.293127 + 0.956074i \(0.594696\pi\)
\(24\) −2.07802 −0.424174
\(25\) 8.46842 1.69368
\(26\) −1.28748 −0.252496
\(27\) 3.49488 0.672591
\(28\) −3.45056 −0.652095
\(29\) −2.72765 −0.506512 −0.253256 0.967399i \(-0.581501\pi\)
−0.253256 + 0.967399i \(0.581501\pi\)
\(30\) 7.62619 1.39235
\(31\) 8.98284 1.61337 0.806683 0.590984i \(-0.201260\pi\)
0.806683 + 0.590984i \(0.201260\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.0855438 0.0148913
\(34\) −3.99294 −0.684784
\(35\) 12.6633 2.14050
\(36\) 1.31817 0.219694
\(37\) 8.77471 1.44255 0.721277 0.692647i \(-0.243555\pi\)
0.721277 + 0.692647i \(0.243555\pi\)
\(38\) 4.34352 0.704611
\(39\) 2.67542 0.428410
\(40\) −3.66993 −0.580268
\(41\) 0.445901 0.0696380 0.0348190 0.999394i \(-0.488915\pi\)
0.0348190 + 0.999394i \(0.488915\pi\)
\(42\) 7.17034 1.10641
\(43\) −9.80961 −1.49595 −0.747976 0.663726i \(-0.768974\pi\)
−0.747976 + 0.663726i \(0.768974\pi\)
\(44\) −0.0411660 −0.00620601
\(45\) −4.83758 −0.721144
\(46\) −2.81157 −0.414544
\(47\) 5.77836 0.842860 0.421430 0.906861i \(-0.361528\pi\)
0.421430 + 0.906861i \(0.361528\pi\)
\(48\) −2.07802 −0.299936
\(49\) 4.90639 0.700914
\(50\) 8.46842 1.19761
\(51\) 8.29742 1.16187
\(52\) −1.28748 −0.178542
\(53\) 7.93141 1.08946 0.544731 0.838611i \(-0.316632\pi\)
0.544731 + 0.838611i \(0.316632\pi\)
\(54\) 3.49488 0.475594
\(55\) 0.151077 0.0203712
\(56\) −3.45056 −0.461101
\(57\) −9.02591 −1.19551
\(58\) −2.72765 −0.358158
\(59\) −4.48136 −0.583424 −0.291712 0.956506i \(-0.594225\pi\)
−0.291712 + 0.956506i \(0.594225\pi\)
\(60\) 7.62619 0.984538
\(61\) 7.09875 0.908902 0.454451 0.890772i \(-0.349836\pi\)
0.454451 + 0.890772i \(0.349836\pi\)
\(62\) 8.98284 1.14082
\(63\) −4.54842 −0.573047
\(64\) 1.00000 0.125000
\(65\) 4.72498 0.586062
\(66\) 0.0855438 0.0105297
\(67\) −10.4509 −1.27678 −0.638391 0.769713i \(-0.720400\pi\)
−0.638391 + 0.769713i \(0.720400\pi\)
\(68\) −3.99294 −0.484216
\(69\) 5.84250 0.703354
\(70\) 12.6633 1.51356
\(71\) 7.58055 0.899646 0.449823 0.893118i \(-0.351487\pi\)
0.449823 + 0.893118i \(0.351487\pi\)
\(72\) 1.31817 0.155347
\(73\) −3.83122 −0.448410 −0.224205 0.974542i \(-0.571979\pi\)
−0.224205 + 0.974542i \(0.571979\pi\)
\(74\) 8.77471 1.02004
\(75\) −17.5975 −2.03199
\(76\) 4.34352 0.498235
\(77\) 0.142046 0.0161876
\(78\) 2.67542 0.302931
\(79\) −1.20276 −0.135321 −0.0676604 0.997708i \(-0.521553\pi\)
−0.0676604 + 0.997708i \(0.521553\pi\)
\(80\) −3.66993 −0.410311
\(81\) −11.2169 −1.24633
\(82\) 0.445901 0.0492415
\(83\) 4.24142 0.465556 0.232778 0.972530i \(-0.425218\pi\)
0.232778 + 0.972530i \(0.425218\pi\)
\(84\) 7.17034 0.782348
\(85\) 14.6538 1.58943
\(86\) −9.80961 −1.05780
\(87\) 5.66811 0.607685
\(88\) −0.0411660 −0.00438831
\(89\) 7.73181 0.819570 0.409785 0.912182i \(-0.365604\pi\)
0.409785 + 0.912182i \(0.365604\pi\)
\(90\) −4.83758 −0.509926
\(91\) 4.44255 0.465706
\(92\) −2.81157 −0.293127
\(93\) −18.6665 −1.93563
\(94\) 5.77836 0.595992
\(95\) −15.9404 −1.63545
\(96\) −2.07802 −0.212087
\(97\) 12.0758 1.22611 0.613057 0.790038i \(-0.289939\pi\)
0.613057 + 0.790038i \(0.289939\pi\)
\(98\) 4.90639 0.495621
\(99\) −0.0542636 −0.00545370
\(100\) 8.46842 0.846842
\(101\) 5.35286 0.532630 0.266315 0.963886i \(-0.414194\pi\)
0.266315 + 0.963886i \(0.414194\pi\)
\(102\) 8.29742 0.821567
\(103\) −17.2376 −1.69847 −0.849236 0.528014i \(-0.822937\pi\)
−0.849236 + 0.528014i \(0.822937\pi\)
\(104\) −1.28748 −0.126248
\(105\) −26.3147 −2.56805
\(106\) 7.93141 0.770366
\(107\) 6.06603 0.586425 0.293212 0.956047i \(-0.405276\pi\)
0.293212 + 0.956047i \(0.405276\pi\)
\(108\) 3.49488 0.336295
\(109\) −17.9980 −1.72390 −0.861949 0.506995i \(-0.830756\pi\)
−0.861949 + 0.506995i \(0.830756\pi\)
\(110\) 0.151077 0.0144046
\(111\) −18.2340 −1.73070
\(112\) −3.45056 −0.326048
\(113\) 7.54476 0.709751 0.354876 0.934914i \(-0.384523\pi\)
0.354876 + 0.934914i \(0.384523\pi\)
\(114\) −9.02591 −0.845354
\(115\) 10.3183 0.962185
\(116\) −2.72765 −0.253256
\(117\) −1.69712 −0.156899
\(118\) −4.48136 −0.412543
\(119\) 13.7779 1.26302
\(120\) 7.62619 0.696173
\(121\) −10.9983 −0.999846
\(122\) 7.09875 0.642691
\(123\) −0.926591 −0.0835479
\(124\) 8.98284 0.806683
\(125\) −12.7289 −1.13850
\(126\) −4.54842 −0.405205
\(127\) −14.4684 −1.28386 −0.641932 0.766762i \(-0.721867\pi\)
−0.641932 + 0.766762i \(0.721867\pi\)
\(128\) 1.00000 0.0883883
\(129\) 20.3846 1.79476
\(130\) 4.72498 0.414408
\(131\) 13.9591 1.21961 0.609806 0.792551i \(-0.291247\pi\)
0.609806 + 0.792551i \(0.291247\pi\)
\(132\) 0.0855438 0.00744563
\(133\) −14.9876 −1.29959
\(134\) −10.4509 −0.902821
\(135\) −12.8260 −1.10389
\(136\) −3.99294 −0.342392
\(137\) 17.7070 1.51282 0.756408 0.654101i \(-0.226953\pi\)
0.756408 + 0.654101i \(0.226953\pi\)
\(138\) 5.84250 0.497347
\(139\) −10.8347 −0.918990 −0.459495 0.888180i \(-0.651970\pi\)
−0.459495 + 0.888180i \(0.651970\pi\)
\(140\) 12.6633 1.07025
\(141\) −12.0075 −1.01122
\(142\) 7.58055 0.636146
\(143\) 0.0530006 0.00443213
\(144\) 1.31817 0.109847
\(145\) 10.0103 0.831310
\(146\) −3.83122 −0.317074
\(147\) −10.1956 −0.840918
\(148\) 8.77471 0.721277
\(149\) −13.2508 −1.08555 −0.542774 0.839879i \(-0.682626\pi\)
−0.542774 + 0.839879i \(0.682626\pi\)
\(150\) −17.5975 −1.43683
\(151\) 10.1082 0.822592 0.411296 0.911502i \(-0.365076\pi\)
0.411296 + 0.911502i \(0.365076\pi\)
\(152\) 4.34352 0.352306
\(153\) −5.26336 −0.425518
\(154\) 0.142046 0.0114464
\(155\) −32.9664 −2.64793
\(156\) 2.67542 0.214205
\(157\) 3.55120 0.283416 0.141708 0.989908i \(-0.454741\pi\)
0.141708 + 0.989908i \(0.454741\pi\)
\(158\) −1.20276 −0.0956862
\(159\) −16.4816 −1.30708
\(160\) −3.66993 −0.290134
\(161\) 9.70151 0.764586
\(162\) −11.2169 −0.881286
\(163\) 2.35726 0.184635 0.0923175 0.995730i \(-0.470573\pi\)
0.0923175 + 0.995730i \(0.470573\pi\)
\(164\) 0.445901 0.0348190
\(165\) −0.313940 −0.0244402
\(166\) 4.24142 0.329198
\(167\) −1.22613 −0.0948810 −0.0474405 0.998874i \(-0.515106\pi\)
−0.0474405 + 0.998874i \(0.515106\pi\)
\(168\) 7.17034 0.553204
\(169\) −11.3424 −0.872491
\(170\) 14.6538 1.12390
\(171\) 5.72547 0.437838
\(172\) −9.80961 −0.747976
\(173\) −13.1214 −0.997599 −0.498800 0.866717i \(-0.666226\pi\)
−0.498800 + 0.866717i \(0.666226\pi\)
\(174\) 5.66811 0.429698
\(175\) −29.2208 −2.20889
\(176\) −0.0411660 −0.00310300
\(177\) 9.31236 0.699960
\(178\) 7.73181 0.579523
\(179\) −3.60509 −0.269457 −0.134729 0.990883i \(-0.543016\pi\)
−0.134729 + 0.990883i \(0.543016\pi\)
\(180\) −4.83758 −0.360572
\(181\) 11.5782 0.860603 0.430301 0.902685i \(-0.358407\pi\)
0.430301 + 0.902685i \(0.358407\pi\)
\(182\) 4.44255 0.329304
\(183\) −14.7513 −1.09045
\(184\) −2.81157 −0.207272
\(185\) −32.2026 −2.36758
\(186\) −18.6665 −1.36870
\(187\) 0.164374 0.0120202
\(188\) 5.77836 0.421430
\(189\) −12.0593 −0.877187
\(190\) −15.9404 −1.15644
\(191\) −5.72854 −0.414503 −0.207251 0.978288i \(-0.566452\pi\)
−0.207251 + 0.978288i \(0.566452\pi\)
\(192\) −2.07802 −0.149968
\(193\) −13.8501 −0.996955 −0.498478 0.866903i \(-0.666107\pi\)
−0.498478 + 0.866903i \(0.666107\pi\)
\(194\) 12.0758 0.866994
\(195\) −9.81861 −0.703125
\(196\) 4.90639 0.350457
\(197\) 7.70435 0.548913 0.274456 0.961600i \(-0.411502\pi\)
0.274456 + 0.961600i \(0.411502\pi\)
\(198\) −0.0542636 −0.00385635
\(199\) −0.384256 −0.0272392 −0.0136196 0.999907i \(-0.504335\pi\)
−0.0136196 + 0.999907i \(0.504335\pi\)
\(200\) 8.46842 0.598807
\(201\) 21.7172 1.53181
\(202\) 5.35286 0.376626
\(203\) 9.41193 0.660588
\(204\) 8.29742 0.580935
\(205\) −1.63643 −0.114293
\(206\) −17.2376 −1.20100
\(207\) −3.70612 −0.257593
\(208\) −1.28748 −0.0892710
\(209\) −0.178805 −0.0123682
\(210\) −26.3147 −1.81589
\(211\) 21.3716 1.47129 0.735643 0.677370i \(-0.236880\pi\)
0.735643 + 0.677370i \(0.236880\pi\)
\(212\) 7.93141 0.544731
\(213\) −15.7525 −1.07935
\(214\) 6.06603 0.414665
\(215\) 36.0006 2.45522
\(216\) 3.49488 0.237797
\(217\) −30.9959 −2.10414
\(218\) −17.9980 −1.21898
\(219\) 7.96135 0.537978
\(220\) 0.151077 0.0101856
\(221\) 5.14085 0.345811
\(222\) −18.2340 −1.22379
\(223\) −7.32606 −0.490589 −0.245295 0.969449i \(-0.578885\pi\)
−0.245295 + 0.969449i \(0.578885\pi\)
\(224\) −3.45056 −0.230551
\(225\) 11.1628 0.744185
\(226\) 7.54476 0.501870
\(227\) 3.35917 0.222956 0.111478 0.993767i \(-0.464442\pi\)
0.111478 + 0.993767i \(0.464442\pi\)
\(228\) −9.02591 −0.597756
\(229\) 4.02544 0.266008 0.133004 0.991115i \(-0.457538\pi\)
0.133004 + 0.991115i \(0.457538\pi\)
\(230\) 10.3183 0.680367
\(231\) −0.295174 −0.0194210
\(232\) −2.72765 −0.179079
\(233\) 2.12563 0.139255 0.0696273 0.997573i \(-0.477819\pi\)
0.0696273 + 0.997573i \(0.477819\pi\)
\(234\) −1.69712 −0.110944
\(235\) −21.2062 −1.38334
\(236\) −4.48136 −0.291712
\(237\) 2.49935 0.162350
\(238\) 13.7779 0.893089
\(239\) 0.817349 0.0528699 0.0264350 0.999651i \(-0.491585\pi\)
0.0264350 + 0.999651i \(0.491585\pi\)
\(240\) 7.62619 0.492269
\(241\) 25.8208 1.66326 0.831631 0.555329i \(-0.187407\pi\)
0.831631 + 0.555329i \(0.187407\pi\)
\(242\) −10.9983 −0.706998
\(243\) 12.8244 0.822683
\(244\) 7.09875 0.454451
\(245\) −18.0061 −1.15037
\(246\) −0.926591 −0.0590773
\(247\) −5.59221 −0.355824
\(248\) 8.98284 0.570411
\(249\) −8.81375 −0.558549
\(250\) −12.7289 −0.805043
\(251\) 19.2137 1.21276 0.606380 0.795175i \(-0.292621\pi\)
0.606380 + 0.795175i \(0.292621\pi\)
\(252\) −4.54842 −0.286523
\(253\) 0.115741 0.00727658
\(254\) −14.4684 −0.907828
\(255\) −30.4510 −1.90691
\(256\) 1.00000 0.0625000
\(257\) 20.3353 1.26848 0.634242 0.773135i \(-0.281312\pi\)
0.634242 + 0.773135i \(0.281312\pi\)
\(258\) 20.3846 1.26909
\(259\) −30.2777 −1.88137
\(260\) 4.72498 0.293031
\(261\) −3.59550 −0.222556
\(262\) 13.9591 0.862396
\(263\) 16.2149 0.999851 0.499925 0.866069i \(-0.333361\pi\)
0.499925 + 0.866069i \(0.333361\pi\)
\(264\) 0.0855438 0.00526486
\(265\) −29.1077 −1.78807
\(266\) −14.9876 −0.918948
\(267\) −16.0668 −0.983275
\(268\) −10.4509 −0.638391
\(269\) 0.420135 0.0256161 0.0128080 0.999918i \(-0.495923\pi\)
0.0128080 + 0.999918i \(0.495923\pi\)
\(270\) −12.8260 −0.780565
\(271\) −23.0699 −1.40140 −0.700698 0.713458i \(-0.747128\pi\)
−0.700698 + 0.713458i \(0.747128\pi\)
\(272\) −3.99294 −0.242108
\(273\) −9.23170 −0.558728
\(274\) 17.7070 1.06972
\(275\) −0.348611 −0.0210220
\(276\) 5.84250 0.351677
\(277\) −26.8417 −1.61276 −0.806381 0.591396i \(-0.798577\pi\)
−0.806381 + 0.591396i \(0.798577\pi\)
\(278\) −10.8347 −0.649824
\(279\) 11.8409 0.708895
\(280\) 12.6633 0.756780
\(281\) −17.3013 −1.03211 −0.516055 0.856556i \(-0.672600\pi\)
−0.516055 + 0.856556i \(0.672600\pi\)
\(282\) −12.0075 −0.715039
\(283\) −33.2822 −1.97842 −0.989212 0.146492i \(-0.953202\pi\)
−0.989212 + 0.146492i \(0.953202\pi\)
\(284\) 7.58055 0.449823
\(285\) 33.1245 1.96213
\(286\) 0.0530006 0.00313399
\(287\) −1.53861 −0.0908213
\(288\) 1.31817 0.0776737
\(289\) −1.05639 −0.0621407
\(290\) 10.0103 0.587825
\(291\) −25.0938 −1.47103
\(292\) −3.83122 −0.224205
\(293\) 6.49404 0.379386 0.189693 0.981843i \(-0.439251\pi\)
0.189693 + 0.981843i \(0.439251\pi\)
\(294\) −10.1956 −0.594619
\(295\) 16.4463 0.957541
\(296\) 8.77471 0.510020
\(297\) −0.143870 −0.00834821
\(298\) −13.2508 −0.767599
\(299\) 3.61985 0.209342
\(300\) −17.5975 −1.01599
\(301\) 33.8487 1.95101
\(302\) 10.1082 0.581661
\(303\) −11.1234 −0.639020
\(304\) 4.34352 0.249118
\(305\) −26.0519 −1.49173
\(306\) −5.26336 −0.300886
\(307\) −6.26311 −0.357455 −0.178727 0.983899i \(-0.557198\pi\)
−0.178727 + 0.983899i \(0.557198\pi\)
\(308\) 0.142046 0.00809382
\(309\) 35.8201 2.03773
\(310\) −32.9664 −1.87237
\(311\) −27.9835 −1.58680 −0.793400 0.608701i \(-0.791691\pi\)
−0.793400 + 0.608701i \(0.791691\pi\)
\(312\) 2.67542 0.151466
\(313\) 2.37282 0.134119 0.0670597 0.997749i \(-0.478638\pi\)
0.0670597 + 0.997749i \(0.478638\pi\)
\(314\) 3.55120 0.200406
\(315\) 16.6924 0.940509
\(316\) −1.20276 −0.0676604
\(317\) 0.321234 0.0180423 0.00902116 0.999959i \(-0.497128\pi\)
0.00902116 + 0.999959i \(0.497128\pi\)
\(318\) −16.4816 −0.924243
\(319\) 0.112286 0.00628684
\(320\) −3.66993 −0.205156
\(321\) −12.6053 −0.703560
\(322\) 9.70151 0.540644
\(323\) −17.3434 −0.965014
\(324\) −11.2169 −0.623163
\(325\) −10.9030 −0.604787
\(326\) 2.35726 0.130557
\(327\) 37.4002 2.06824
\(328\) 0.445901 0.0246208
\(329\) −19.9386 −1.09925
\(330\) −0.313940 −0.0172818
\(331\) 21.4885 1.18111 0.590557 0.806996i \(-0.298908\pi\)
0.590557 + 0.806996i \(0.298908\pi\)
\(332\) 4.24142 0.232778
\(333\) 11.5665 0.633842
\(334\) −1.22613 −0.0670910
\(335\) 38.3541 2.09551
\(336\) 7.17034 0.391174
\(337\) −25.7783 −1.40423 −0.702117 0.712061i \(-0.747762\pi\)
−0.702117 + 0.712061i \(0.747762\pi\)
\(338\) −11.3424 −0.616944
\(339\) −15.6782 −0.851521
\(340\) 14.6538 0.794716
\(341\) −0.369788 −0.0200251
\(342\) 5.72547 0.309598
\(343\) 7.22412 0.390066
\(344\) −9.80961 −0.528899
\(345\) −21.4416 −1.15438
\(346\) −13.1214 −0.705409
\(347\) −7.15996 −0.384367 −0.192183 0.981359i \(-0.561557\pi\)
−0.192183 + 0.981359i \(0.561557\pi\)
\(348\) 5.66811 0.303843
\(349\) −13.5643 −0.726082 −0.363041 0.931773i \(-0.618261\pi\)
−0.363041 + 0.931773i \(0.618261\pi\)
\(350\) −29.2208 −1.56192
\(351\) −4.49961 −0.240171
\(352\) −0.0411660 −0.00219416
\(353\) −8.32890 −0.443303 −0.221651 0.975126i \(-0.571145\pi\)
−0.221651 + 0.975126i \(0.571145\pi\)
\(354\) 9.31236 0.494947
\(355\) −27.8201 −1.47654
\(356\) 7.73181 0.409785
\(357\) −28.6308 −1.51530
\(358\) −3.60509 −0.190535
\(359\) 29.6768 1.56628 0.783140 0.621845i \(-0.213617\pi\)
0.783140 + 0.621845i \(0.213617\pi\)
\(360\) −4.83758 −0.254963
\(361\) −0.133871 −0.00704582
\(362\) 11.5782 0.608538
\(363\) 22.8547 1.19956
\(364\) 4.44255 0.232853
\(365\) 14.0603 0.735951
\(366\) −14.7513 −0.771065
\(367\) −0.0919967 −0.00480219 −0.00240110 0.999997i \(-0.500764\pi\)
−0.00240110 + 0.999997i \(0.500764\pi\)
\(368\) −2.81157 −0.146563
\(369\) 0.587771 0.0305982
\(370\) −32.2026 −1.67413
\(371\) −27.3678 −1.42087
\(372\) −18.6665 −0.967814
\(373\) −21.5505 −1.11584 −0.557921 0.829894i \(-0.688401\pi\)
−0.557921 + 0.829894i \(0.688401\pi\)
\(374\) 0.164374 0.00849956
\(375\) 26.4508 1.36591
\(376\) 5.77836 0.297996
\(377\) 3.51181 0.180867
\(378\) −12.0593 −0.620265
\(379\) 26.9935 1.38656 0.693281 0.720667i \(-0.256164\pi\)
0.693281 + 0.720667i \(0.256164\pi\)
\(380\) −15.9404 −0.817726
\(381\) 30.0656 1.54031
\(382\) −5.72854 −0.293098
\(383\) −7.01748 −0.358576 −0.179288 0.983797i \(-0.557379\pi\)
−0.179288 + 0.983797i \(0.557379\pi\)
\(384\) −2.07802 −0.106043
\(385\) −0.521299 −0.0265679
\(386\) −13.8501 −0.704954
\(387\) −12.9307 −0.657304
\(388\) 12.0758 0.613057
\(389\) 14.4447 0.732373 0.366187 0.930541i \(-0.380663\pi\)
0.366187 + 0.930541i \(0.380663\pi\)
\(390\) −9.81861 −0.497184
\(391\) 11.2264 0.567746
\(392\) 4.90639 0.247810
\(393\) −29.0073 −1.46322
\(394\) 7.70435 0.388140
\(395\) 4.41404 0.222094
\(396\) −0.0542636 −0.00272685
\(397\) −20.9947 −1.05369 −0.526847 0.849960i \(-0.676626\pi\)
−0.526847 + 0.849960i \(0.676626\pi\)
\(398\) −0.384256 −0.0192610
\(399\) 31.1445 1.55917
\(400\) 8.46842 0.423421
\(401\) −30.2401 −1.51012 −0.755060 0.655655i \(-0.772393\pi\)
−0.755060 + 0.655655i \(0.772393\pi\)
\(402\) 21.7172 1.08315
\(403\) −11.5653 −0.576107
\(404\) 5.35286 0.266315
\(405\) 41.1654 2.04553
\(406\) 9.41193 0.467106
\(407\) −0.361220 −0.0179050
\(408\) 8.29742 0.410783
\(409\) 4.69838 0.232320 0.116160 0.993231i \(-0.462941\pi\)
0.116160 + 0.993231i \(0.462941\pi\)
\(410\) −1.63643 −0.0808174
\(411\) −36.7956 −1.81499
\(412\) −17.2376 −0.849236
\(413\) 15.4632 0.760896
\(414\) −3.70612 −0.182146
\(415\) −15.5657 −0.764091
\(416\) −1.28748 −0.0631241
\(417\) 22.5148 1.10255
\(418\) −0.178805 −0.00874565
\(419\) 27.6248 1.34956 0.674779 0.738020i \(-0.264239\pi\)
0.674779 + 0.738020i \(0.264239\pi\)
\(420\) −26.3147 −1.28402
\(421\) −4.20494 −0.204936 −0.102468 0.994736i \(-0.532674\pi\)
−0.102468 + 0.994736i \(0.532674\pi\)
\(422\) 21.3716 1.04036
\(423\) 7.61683 0.370343
\(424\) 7.93141 0.385183
\(425\) −33.8139 −1.64022
\(426\) −15.7525 −0.763213
\(427\) −24.4947 −1.18538
\(428\) 6.06603 0.293212
\(429\) −0.110136 −0.00531743
\(430\) 36.0006 1.73610
\(431\) 27.4258 1.32105 0.660527 0.750803i \(-0.270333\pi\)
0.660527 + 0.750803i \(0.270333\pi\)
\(432\) 3.49488 0.168148
\(433\) −17.7193 −0.851534 −0.425767 0.904833i \(-0.639996\pi\)
−0.425767 + 0.904833i \(0.639996\pi\)
\(434\) −30.9959 −1.48785
\(435\) −20.8016 −0.997360
\(436\) −17.9980 −0.861949
\(437\) −12.2121 −0.584184
\(438\) 7.96135 0.380408
\(439\) −11.2775 −0.538247 −0.269124 0.963106i \(-0.586734\pi\)
−0.269124 + 0.963106i \(0.586734\pi\)
\(440\) 0.151077 0.00720229
\(441\) 6.46744 0.307973
\(442\) 5.14085 0.244526
\(443\) 6.29496 0.299083 0.149541 0.988755i \(-0.452220\pi\)
0.149541 + 0.988755i \(0.452220\pi\)
\(444\) −18.2340 −0.865349
\(445\) −28.3752 −1.34511
\(446\) −7.32606 −0.346899
\(447\) 27.5354 1.30238
\(448\) −3.45056 −0.163024
\(449\) 30.4039 1.43485 0.717425 0.696636i \(-0.245321\pi\)
0.717425 + 0.696636i \(0.245321\pi\)
\(450\) 11.1628 0.526218
\(451\) −0.0183560 −0.000864348 0
\(452\) 7.54476 0.354876
\(453\) −21.0050 −0.986901
\(454\) 3.35917 0.157653
\(455\) −16.3039 −0.764337
\(456\) −9.02591 −0.422677
\(457\) −35.3996 −1.65592 −0.827962 0.560785i \(-0.810500\pi\)
−0.827962 + 0.560785i \(0.810500\pi\)
\(458\) 4.02544 0.188096
\(459\) −13.9549 −0.651358
\(460\) 10.3183 0.481092
\(461\) 0.985230 0.0458867 0.0229434 0.999737i \(-0.492696\pi\)
0.0229434 + 0.999737i \(0.492696\pi\)
\(462\) −0.295174 −0.0137328
\(463\) −31.2127 −1.45058 −0.725288 0.688446i \(-0.758293\pi\)
−0.725288 + 0.688446i \(0.758293\pi\)
\(464\) −2.72765 −0.126628
\(465\) 68.5049 3.17684
\(466\) 2.12563 0.0984679
\(467\) −41.4673 −1.91888 −0.959440 0.281913i \(-0.909031\pi\)
−0.959440 + 0.281913i \(0.909031\pi\)
\(468\) −1.69712 −0.0784493
\(469\) 36.0615 1.66517
\(470\) −21.2062 −0.978169
\(471\) −7.37946 −0.340027
\(472\) −4.48136 −0.206272
\(473\) 0.403823 0.0185678
\(474\) 2.49935 0.114799
\(475\) 36.7827 1.68771
\(476\) 13.7779 0.631510
\(477\) 10.4549 0.478697
\(478\) 0.817349 0.0373847
\(479\) 25.1228 1.14789 0.573946 0.818893i \(-0.305412\pi\)
0.573946 + 0.818893i \(0.305412\pi\)
\(480\) 7.62619 0.348087
\(481\) −11.2973 −0.515113
\(482\) 25.8208 1.17610
\(483\) −20.1599 −0.917308
\(484\) −10.9983 −0.499923
\(485\) −44.3175 −2.01235
\(486\) 12.8244 0.581725
\(487\) −1.05337 −0.0477326 −0.0238663 0.999715i \(-0.507598\pi\)
−0.0238663 + 0.999715i \(0.507598\pi\)
\(488\) 7.09875 0.321345
\(489\) −4.89844 −0.221515
\(490\) −18.0061 −0.813435
\(491\) −11.2134 −0.506054 −0.253027 0.967459i \(-0.581426\pi\)
−0.253027 + 0.967459i \(0.581426\pi\)
\(492\) −0.926591 −0.0417739
\(493\) 10.8914 0.490522
\(494\) −5.59221 −0.251605
\(495\) 0.199144 0.00895085
\(496\) 8.98284 0.403342
\(497\) −26.1572 −1.17331
\(498\) −8.81375 −0.394954
\(499\) 14.7997 0.662524 0.331262 0.943539i \(-0.392526\pi\)
0.331262 + 0.943539i \(0.392526\pi\)
\(500\) −12.7289 −0.569252
\(501\) 2.54793 0.113833
\(502\) 19.2137 0.857551
\(503\) 31.2459 1.39319 0.696594 0.717466i \(-0.254698\pi\)
0.696594 + 0.717466i \(0.254698\pi\)
\(504\) −4.54842 −0.202603
\(505\) −19.6447 −0.874176
\(506\) 0.115741 0.00514532
\(507\) 23.5697 1.04677
\(508\) −14.4684 −0.641932
\(509\) −17.5494 −0.777861 −0.388931 0.921267i \(-0.627155\pi\)
−0.388931 + 0.921267i \(0.627155\pi\)
\(510\) −30.4510 −1.34839
\(511\) 13.2199 0.584812
\(512\) 1.00000 0.0441942
\(513\) 15.1801 0.670217
\(514\) 20.3353 0.896953
\(515\) 63.2609 2.78761
\(516\) 20.3846 0.897381
\(517\) −0.237872 −0.0104616
\(518\) −30.2777 −1.33033
\(519\) 27.2665 1.19687
\(520\) 4.72498 0.207204
\(521\) −22.8519 −1.00116 −0.500580 0.865690i \(-0.666880\pi\)
−0.500580 + 0.865690i \(0.666880\pi\)
\(522\) −3.59550 −0.157371
\(523\) 30.8207 1.34769 0.673847 0.738871i \(-0.264641\pi\)
0.673847 + 0.738871i \(0.264641\pi\)
\(524\) 13.9591 0.609806
\(525\) 60.7214 2.65010
\(526\) 16.2149 0.707001
\(527\) −35.8680 −1.56243
\(528\) 0.0855438 0.00372281
\(529\) −15.0951 −0.656307
\(530\) −29.1077 −1.26436
\(531\) −5.90718 −0.256350
\(532\) −14.9876 −0.649794
\(533\) −0.574090 −0.0248666
\(534\) −16.0668 −0.695280
\(535\) −22.2619 −0.962466
\(536\) −10.4509 −0.451410
\(537\) 7.49145 0.323280
\(538\) 0.420135 0.0181133
\(539\) −0.201977 −0.00869975
\(540\) −12.8260 −0.551943
\(541\) 20.3551 0.875134 0.437567 0.899186i \(-0.355840\pi\)
0.437567 + 0.899186i \(0.355840\pi\)
\(542\) −23.0699 −0.990936
\(543\) −24.0598 −1.03250
\(544\) −3.99294 −0.171196
\(545\) 66.0516 2.82934
\(546\) −9.23170 −0.395080
\(547\) 20.3339 0.869416 0.434708 0.900571i \(-0.356852\pi\)
0.434708 + 0.900571i \(0.356852\pi\)
\(548\) 17.7070 0.756408
\(549\) 9.35733 0.399361
\(550\) −0.348611 −0.0148648
\(551\) −11.8476 −0.504724
\(552\) 5.84250 0.248673
\(553\) 4.15019 0.176484
\(554\) −26.8417 −1.14039
\(555\) 66.9177 2.84050
\(556\) −10.8347 −0.459495
\(557\) −45.6190 −1.93294 −0.966469 0.256782i \(-0.917338\pi\)
−0.966469 + 0.256782i \(0.917338\pi\)
\(558\) 11.8409 0.501264
\(559\) 12.6297 0.534180
\(560\) 12.6633 0.535124
\(561\) −0.341572 −0.0144212
\(562\) −17.3013 −0.729812
\(563\) 29.8794 1.25926 0.629632 0.776893i \(-0.283206\pi\)
0.629632 + 0.776893i \(0.283206\pi\)
\(564\) −12.0075 −0.505609
\(565\) −27.6888 −1.16488
\(566\) −33.2822 −1.39896
\(567\) 38.7048 1.62545
\(568\) 7.58055 0.318073
\(569\) −29.2356 −1.22562 −0.612811 0.790229i \(-0.709961\pi\)
−0.612811 + 0.790229i \(0.709961\pi\)
\(570\) 33.1245 1.38743
\(571\) −20.3269 −0.850655 −0.425327 0.905040i \(-0.639841\pi\)
−0.425327 + 0.905040i \(0.639841\pi\)
\(572\) 0.0530006 0.00221607
\(573\) 11.9040 0.497298
\(574\) −1.53861 −0.0642203
\(575\) −23.8096 −0.992927
\(576\) 1.31817 0.0549236
\(577\) 10.7226 0.446386 0.223193 0.974774i \(-0.428352\pi\)
0.223193 + 0.974774i \(0.428352\pi\)
\(578\) −1.05639 −0.0439401
\(579\) 28.7809 1.19609
\(580\) 10.0103 0.415655
\(581\) −14.6353 −0.607174
\(582\) −25.0938 −1.04017
\(583\) −0.326504 −0.0135224
\(584\) −3.83122 −0.158537
\(585\) 6.22831 0.257509
\(586\) 6.49404 0.268266
\(587\) 5.29535 0.218563 0.109281 0.994011i \(-0.465145\pi\)
0.109281 + 0.994011i \(0.465145\pi\)
\(588\) −10.1956 −0.420459
\(589\) 39.0171 1.60767
\(590\) 16.4463 0.677084
\(591\) −16.0098 −0.658555
\(592\) 8.77471 0.360639
\(593\) 19.4576 0.799027 0.399513 0.916727i \(-0.369179\pi\)
0.399513 + 0.916727i \(0.369179\pi\)
\(594\) −0.143870 −0.00590308
\(595\) −50.5640 −2.07292
\(596\) −13.2508 −0.542774
\(597\) 0.798492 0.0326801
\(598\) 3.61985 0.148027
\(599\) 18.2888 0.747259 0.373629 0.927578i \(-0.378113\pi\)
0.373629 + 0.927578i \(0.378113\pi\)
\(600\) −17.5975 −0.718416
\(601\) −0.625965 −0.0255337 −0.0127668 0.999919i \(-0.504064\pi\)
−0.0127668 + 0.999919i \(0.504064\pi\)
\(602\) 33.8487 1.37957
\(603\) −13.7760 −0.561003
\(604\) 10.1082 0.411296
\(605\) 40.3631 1.64099
\(606\) −11.1234 −0.451855
\(607\) 8.69823 0.353050 0.176525 0.984296i \(-0.443514\pi\)
0.176525 + 0.984296i \(0.443514\pi\)
\(608\) 4.34352 0.176153
\(609\) −19.5582 −0.792538
\(610\) −26.0519 −1.05481
\(611\) −7.43955 −0.300972
\(612\) −5.26336 −0.212759
\(613\) 28.3724 1.14595 0.572975 0.819573i \(-0.305789\pi\)
0.572975 + 0.819573i \(0.305789\pi\)
\(614\) −6.26311 −0.252759
\(615\) 3.40053 0.137122
\(616\) 0.142046 0.00572319
\(617\) 16.5979 0.668208 0.334104 0.942536i \(-0.391566\pi\)
0.334104 + 0.942536i \(0.391566\pi\)
\(618\) 35.8201 1.44089
\(619\) 41.6792 1.67523 0.837614 0.546263i \(-0.183950\pi\)
0.837614 + 0.546263i \(0.183950\pi\)
\(620\) −32.9664 −1.32396
\(621\) −9.82612 −0.394308
\(622\) −27.9835 −1.12204
\(623\) −26.6791 −1.06888
\(624\) 2.67542 0.107102
\(625\) 4.37198 0.174879
\(626\) 2.37282 0.0948368
\(627\) 0.371561 0.0148387
\(628\) 3.55120 0.141708
\(629\) −35.0370 −1.39701
\(630\) 16.6924 0.665041
\(631\) −23.1327 −0.920897 −0.460449 0.887686i \(-0.652311\pi\)
−0.460449 + 0.887686i \(0.652311\pi\)
\(632\) −1.20276 −0.0478431
\(633\) −44.4107 −1.76517
\(634\) 0.321234 0.0127578
\(635\) 53.0981 2.10713
\(636\) −16.4816 −0.653539
\(637\) −6.31691 −0.250285
\(638\) 0.112286 0.00444546
\(639\) 9.99242 0.395294
\(640\) −3.66993 −0.145067
\(641\) −39.9116 −1.57641 −0.788207 0.615410i \(-0.788990\pi\)
−0.788207 + 0.615410i \(0.788990\pi\)
\(642\) −12.6053 −0.497492
\(643\) 12.5138 0.493496 0.246748 0.969080i \(-0.420638\pi\)
0.246748 + 0.969080i \(0.420638\pi\)
\(644\) 9.70151 0.382293
\(645\) −74.8100 −2.94564
\(646\) −17.3434 −0.682368
\(647\) 40.4521 1.59034 0.795169 0.606388i \(-0.207382\pi\)
0.795169 + 0.606388i \(0.207382\pi\)
\(648\) −11.2169 −0.440643
\(649\) 0.184480 0.00724147
\(650\) −10.9030 −0.427649
\(651\) 64.4100 2.52443
\(652\) 2.35726 0.0923175
\(653\) −42.5996 −1.66705 −0.833526 0.552480i \(-0.813681\pi\)
−0.833526 + 0.552480i \(0.813681\pi\)
\(654\) 37.4002 1.46247
\(655\) −51.2290 −2.00168
\(656\) 0.445901 0.0174095
\(657\) −5.05018 −0.197026
\(658\) −19.9386 −0.777287
\(659\) 7.20073 0.280501 0.140250 0.990116i \(-0.455209\pi\)
0.140250 + 0.990116i \(0.455209\pi\)
\(660\) −0.313940 −0.0122201
\(661\) 5.49090 0.213571 0.106786 0.994282i \(-0.465944\pi\)
0.106786 + 0.994282i \(0.465944\pi\)
\(662\) 21.4885 0.835173
\(663\) −10.6828 −0.414885
\(664\) 4.24142 0.164599
\(665\) 55.0034 2.13294
\(666\) 11.5665 0.448194
\(667\) 7.66898 0.296944
\(668\) −1.22613 −0.0474405
\(669\) 15.2237 0.588582
\(670\) 38.3541 1.48175
\(671\) −0.292227 −0.0112813
\(672\) 7.17034 0.276602
\(673\) 6.34218 0.244473 0.122237 0.992501i \(-0.460993\pi\)
0.122237 + 0.992501i \(0.460993\pi\)
\(674\) −25.7783 −0.992944
\(675\) 29.5961 1.13916
\(676\) −11.3424 −0.436246
\(677\) −29.6556 −1.13976 −0.569879 0.821729i \(-0.693010\pi\)
−0.569879 + 0.821729i \(0.693010\pi\)
\(678\) −15.6782 −0.602116
\(679\) −41.6684 −1.59909
\(680\) 14.6538 0.561949
\(681\) −6.98041 −0.267490
\(682\) −0.369788 −0.0141599
\(683\) −12.0924 −0.462702 −0.231351 0.972870i \(-0.574315\pi\)
−0.231351 + 0.972870i \(0.574315\pi\)
\(684\) 5.72547 0.218919
\(685\) −64.9837 −2.48290
\(686\) 7.22412 0.275818
\(687\) −8.36494 −0.319142
\(688\) −9.80961 −0.373988
\(689\) −10.2116 −0.389029
\(690\) −21.4416 −0.816267
\(691\) 43.8358 1.66759 0.833795 0.552074i \(-0.186163\pi\)
0.833795 + 0.552074i \(0.186163\pi\)
\(692\) −13.1214 −0.498800
\(693\) 0.187240 0.00711266
\(694\) −7.15996 −0.271788
\(695\) 39.7627 1.50829
\(696\) 5.66811 0.214849
\(697\) −1.78046 −0.0674396
\(698\) −13.5643 −0.513417
\(699\) −4.41710 −0.167070
\(700\) −29.2208 −1.10444
\(701\) −25.8701 −0.977101 −0.488551 0.872536i \(-0.662474\pi\)
−0.488551 + 0.872536i \(0.662474\pi\)
\(702\) −4.49961 −0.169827
\(703\) 38.1131 1.43746
\(704\) −0.0411660 −0.00155150
\(705\) 44.0669 1.65965
\(706\) −8.32890 −0.313462
\(707\) −18.4704 −0.694651
\(708\) 9.31236 0.349980
\(709\) 16.0301 0.602024 0.301012 0.953620i \(-0.402676\pi\)
0.301012 + 0.953620i \(0.402676\pi\)
\(710\) −27.8201 −1.04407
\(711\) −1.58543 −0.0594584
\(712\) 7.73181 0.289762
\(713\) −25.2559 −0.945841
\(714\) −28.6308 −1.07148
\(715\) −0.194509 −0.00727421
\(716\) −3.60509 −0.134729
\(717\) −1.69847 −0.0634304
\(718\) 29.6768 1.10753
\(719\) 0.101795 0.00379630 0.00189815 0.999998i \(-0.499396\pi\)
0.00189815 + 0.999998i \(0.499396\pi\)
\(720\) −4.83758 −0.180286
\(721\) 59.4795 2.21513
\(722\) −0.133871 −0.00498215
\(723\) −53.6561 −1.99549
\(724\) 11.5782 0.430301
\(725\) −23.0989 −0.857871
\(726\) 22.8547 0.848217
\(727\) −12.1973 −0.452374 −0.226187 0.974084i \(-0.572626\pi\)
−0.226187 + 0.974084i \(0.572626\pi\)
\(728\) 4.44255 0.164652
\(729\) 7.00154 0.259316
\(730\) 14.0603 0.520396
\(731\) 39.1692 1.44873
\(732\) −14.7513 −0.545225
\(733\) 34.5973 1.27788 0.638940 0.769256i \(-0.279373\pi\)
0.638940 + 0.769256i \(0.279373\pi\)
\(734\) −0.0919967 −0.00339566
\(735\) 37.4171 1.38015
\(736\) −2.81157 −0.103636
\(737\) 0.430222 0.0158474
\(738\) 0.587771 0.0216362
\(739\) −20.8959 −0.768668 −0.384334 0.923194i \(-0.625569\pi\)
−0.384334 + 0.923194i \(0.625569\pi\)
\(740\) −32.2026 −1.18379
\(741\) 11.6207 0.426898
\(742\) −27.3678 −1.00470
\(743\) −39.9977 −1.46737 −0.733686 0.679488i \(-0.762202\pi\)
−0.733686 + 0.679488i \(0.762202\pi\)
\(744\) −18.6665 −0.684348
\(745\) 48.6296 1.78165
\(746\) −21.5505 −0.789020
\(747\) 5.59089 0.204560
\(748\) 0.164374 0.00601009
\(749\) −20.9312 −0.764810
\(750\) 26.4508 0.965847
\(751\) 19.7539 0.720829 0.360414 0.932792i \(-0.382635\pi\)
0.360414 + 0.932792i \(0.382635\pi\)
\(752\) 5.77836 0.210715
\(753\) −39.9265 −1.45500
\(754\) 3.51181 0.127892
\(755\) −37.0964 −1.35007
\(756\) −12.0593 −0.438593
\(757\) −37.1317 −1.34958 −0.674788 0.738012i \(-0.735765\pi\)
−0.674788 + 0.738012i \(0.735765\pi\)
\(758\) 26.9935 0.980447
\(759\) −0.240512 −0.00873005
\(760\) −15.9404 −0.578220
\(761\) 39.1816 1.42033 0.710165 0.704035i \(-0.248620\pi\)
0.710165 + 0.704035i \(0.248620\pi\)
\(762\) 30.0656 1.08916
\(763\) 62.1033 2.24829
\(764\) −5.72854 −0.207251
\(765\) 19.3162 0.698379
\(766\) −7.01748 −0.253552
\(767\) 5.76969 0.208331
\(768\) −2.07802 −0.0749841
\(769\) 27.1506 0.979076 0.489538 0.871982i \(-0.337166\pi\)
0.489538 + 0.871982i \(0.337166\pi\)
\(770\) −0.521299 −0.0187863
\(771\) −42.2572 −1.52186
\(772\) −13.8501 −0.498478
\(773\) −4.52177 −0.162637 −0.0813185 0.996688i \(-0.525913\pi\)
−0.0813185 + 0.996688i \(0.525913\pi\)
\(774\) −12.9307 −0.464784
\(775\) 76.0704 2.73253
\(776\) 12.0758 0.433497
\(777\) 62.9177 2.25716
\(778\) 14.4447 0.517866
\(779\) 1.93678 0.0693923
\(780\) −9.81861 −0.351563
\(781\) −0.312061 −0.0111664
\(782\) 11.2264 0.401457
\(783\) −9.53282 −0.340675
\(784\) 4.90639 0.175228
\(785\) −13.0327 −0.465155
\(786\) −29.0073 −1.03466
\(787\) 17.5622 0.626023 0.313012 0.949749i \(-0.398662\pi\)
0.313012 + 0.949749i \(0.398662\pi\)
\(788\) 7.70435 0.274456
\(789\) −33.6948 −1.19957
\(790\) 4.41404 0.157044
\(791\) −26.0337 −0.925651
\(792\) −0.0542636 −0.00192817
\(793\) −9.13953 −0.324554
\(794\) −20.9947 −0.745074
\(795\) 60.4864 2.14523
\(796\) −0.384256 −0.0136196
\(797\) −38.5622 −1.36594 −0.682972 0.730445i \(-0.739313\pi\)
−0.682972 + 0.730445i \(0.739313\pi\)
\(798\) 31.1445 1.10250
\(799\) −23.0727 −0.816252
\(800\) 8.46842 0.299404
\(801\) 10.1918 0.360110
\(802\) −30.2401 −1.06782
\(803\) 0.157716 0.00556567
\(804\) 21.7172 0.765906
\(805\) −35.6039 −1.25487
\(806\) −11.5653 −0.407369
\(807\) −0.873049 −0.0307328
\(808\) 5.35286 0.188313
\(809\) 22.2328 0.781664 0.390832 0.920462i \(-0.372187\pi\)
0.390832 + 0.920462i \(0.372187\pi\)
\(810\) 41.1654 1.44641
\(811\) −22.5824 −0.792975 −0.396488 0.918040i \(-0.629771\pi\)
−0.396488 + 0.918040i \(0.629771\pi\)
\(812\) 9.41193 0.330294
\(813\) 47.9397 1.68132
\(814\) −0.361220 −0.0126608
\(815\) −8.65100 −0.303031
\(816\) 8.29742 0.290468
\(817\) −42.6082 −1.49067
\(818\) 4.69838 0.164275
\(819\) 5.85601 0.204626
\(820\) −1.63643 −0.0571465
\(821\) 36.4722 1.27289 0.636444 0.771323i \(-0.280405\pi\)
0.636444 + 0.771323i \(0.280405\pi\)
\(822\) −36.7956 −1.28339
\(823\) −41.4219 −1.44388 −0.721938 0.691958i \(-0.756748\pi\)
−0.721938 + 0.691958i \(0.756748\pi\)
\(824\) −17.2376 −0.600500
\(825\) 0.724420 0.0252211
\(826\) 15.4632 0.538035
\(827\) 10.3127 0.358608 0.179304 0.983794i \(-0.442615\pi\)
0.179304 + 0.983794i \(0.442615\pi\)
\(828\) −3.70612 −0.128796
\(829\) −1.45972 −0.0506982 −0.0253491 0.999679i \(-0.508070\pi\)
−0.0253491 + 0.999679i \(0.508070\pi\)
\(830\) −15.5657 −0.540294
\(831\) 55.7776 1.93490
\(832\) −1.28748 −0.0446355
\(833\) −19.5910 −0.678787
\(834\) 22.5148 0.779623
\(835\) 4.49983 0.155723
\(836\) −0.178805 −0.00618411
\(837\) 31.3940 1.08514
\(838\) 27.6248 0.954282
\(839\) −41.5883 −1.43579 −0.717894 0.696153i \(-0.754894\pi\)
−0.717894 + 0.696153i \(0.754894\pi\)
\(840\) −26.3147 −0.907943
\(841\) −21.5599 −0.743446
\(842\) −4.20494 −0.144912
\(843\) 35.9525 1.23827
\(844\) 21.3716 0.735643
\(845\) 41.6258 1.43197
\(846\) 7.61683 0.261872
\(847\) 37.9504 1.30399
\(848\) 7.93141 0.272366
\(849\) 69.1611 2.37360
\(850\) −33.8139 −1.15981
\(851\) −24.6707 −0.845702
\(852\) −15.7525 −0.539673
\(853\) 36.7505 1.25831 0.629157 0.777279i \(-0.283400\pi\)
0.629157 + 0.777279i \(0.283400\pi\)
\(854\) −24.4947 −0.838191
\(855\) −21.0121 −0.718599
\(856\) 6.06603 0.207332
\(857\) −40.0036 −1.36650 −0.683249 0.730186i \(-0.739433\pi\)
−0.683249 + 0.730186i \(0.739433\pi\)
\(858\) −0.110136 −0.00375999
\(859\) −11.6933 −0.398971 −0.199485 0.979901i \(-0.563927\pi\)
−0.199485 + 0.979901i \(0.563927\pi\)
\(860\) 36.0006 1.22761
\(861\) 3.19726 0.108962
\(862\) 27.4258 0.934126
\(863\) −13.9631 −0.475311 −0.237655 0.971350i \(-0.576379\pi\)
−0.237655 + 0.971350i \(0.576379\pi\)
\(864\) 3.49488 0.118898
\(865\) 48.1546 1.63730
\(866\) −17.7193 −0.602125
\(867\) 2.19520 0.0745530
\(868\) −30.9959 −1.05207
\(869\) 0.0495127 0.00167960
\(870\) −20.8016 −0.705240
\(871\) 13.4554 0.455918
\(872\) −17.9980 −0.609490
\(873\) 15.9179 0.538741
\(874\) −12.2121 −0.413081
\(875\) 43.9217 1.48483
\(876\) 7.96135 0.268989
\(877\) 46.4762 1.56939 0.784695 0.619882i \(-0.212820\pi\)
0.784695 + 0.619882i \(0.212820\pi\)
\(878\) −11.2775 −0.380598
\(879\) −13.4947 −0.455166
\(880\) 0.151077 0.00509279
\(881\) −25.6684 −0.864792 −0.432396 0.901684i \(-0.642332\pi\)
−0.432396 + 0.901684i \(0.642332\pi\)
\(882\) 6.46744 0.217770
\(883\) −2.14740 −0.0722658 −0.0361329 0.999347i \(-0.511504\pi\)
−0.0361329 + 0.999347i \(0.511504\pi\)
\(884\) 5.14085 0.172906
\(885\) −34.1758 −1.14881
\(886\) 6.29496 0.211483
\(887\) −40.5477 −1.36146 −0.680729 0.732535i \(-0.738337\pi\)
−0.680729 + 0.732535i \(0.738337\pi\)
\(888\) −18.2340 −0.611894
\(889\) 49.9242 1.67440
\(890\) −28.3752 −0.951139
\(891\) 0.461756 0.0154694
\(892\) −7.32606 −0.245295
\(893\) 25.0984 0.839886
\(894\) 27.5354 0.920923
\(895\) 13.2304 0.442245
\(896\) −3.45056 −0.115275
\(897\) −7.52213 −0.251157
\(898\) 30.4039 1.01459
\(899\) −24.5021 −0.817189
\(900\) 11.1628 0.372092
\(901\) −31.6697 −1.05507
\(902\) −0.0183560 −0.000611187 0
\(903\) −70.3383 −2.34071
\(904\) 7.54476 0.250935
\(905\) −42.4913 −1.41246
\(906\) −21.0050 −0.697844
\(907\) 27.3524 0.908223 0.454112 0.890945i \(-0.349957\pi\)
0.454112 + 0.890945i \(0.349957\pi\)
\(908\) 3.35917 0.111478
\(909\) 7.05596 0.234031
\(910\) −16.3039 −0.540468
\(911\) 36.5608 1.21131 0.605656 0.795726i \(-0.292911\pi\)
0.605656 + 0.795726i \(0.292911\pi\)
\(912\) −9.02591 −0.298878
\(913\) −0.174602 −0.00577849
\(914\) −35.3996 −1.17091
\(915\) 54.1364 1.78970
\(916\) 4.02544 0.133004
\(917\) −48.1668 −1.59061
\(918\) −13.9549 −0.460580
\(919\) −42.6438 −1.40669 −0.703345 0.710849i \(-0.748311\pi\)
−0.703345 + 0.710849i \(0.748311\pi\)
\(920\) 10.3183 0.340184
\(921\) 13.0149 0.428855
\(922\) 0.985230 0.0324468
\(923\) −9.75984 −0.321249
\(924\) −0.295174 −0.00971052
\(925\) 74.3079 2.44323
\(926\) −31.2127 −1.02571
\(927\) −22.7220 −0.746289
\(928\) −2.72765 −0.0895395
\(929\) 27.3470 0.897224 0.448612 0.893727i \(-0.351918\pi\)
0.448612 + 0.893727i \(0.351918\pi\)
\(930\) 68.5049 2.24636
\(931\) 21.3110 0.698440
\(932\) 2.12563 0.0696273
\(933\) 58.1503 1.90376
\(934\) −41.4673 −1.35685
\(935\) −0.603240 −0.0197281
\(936\) −1.69712 −0.0554720
\(937\) 15.0547 0.491816 0.245908 0.969293i \(-0.420914\pi\)
0.245908 + 0.969293i \(0.420914\pi\)
\(938\) 36.0615 1.17745
\(939\) −4.93076 −0.160909
\(940\) −21.2062 −0.691670
\(941\) 49.2447 1.60533 0.802666 0.596429i \(-0.203414\pi\)
0.802666 + 0.596429i \(0.203414\pi\)
\(942\) −7.37946 −0.240436
\(943\) −1.25368 −0.0408255
\(944\) −4.48136 −0.145856
\(945\) 44.2569 1.43968
\(946\) 0.403823 0.0131294
\(947\) 38.9341 1.26519 0.632594 0.774484i \(-0.281990\pi\)
0.632594 + 0.774484i \(0.281990\pi\)
\(948\) 2.49935 0.0811752
\(949\) 4.93263 0.160120
\(950\) 36.7827 1.19339
\(951\) −0.667531 −0.0216462
\(952\) 13.7779 0.446545
\(953\) −48.4828 −1.57051 −0.785256 0.619171i \(-0.787469\pi\)
−0.785256 + 0.619171i \(0.787469\pi\)
\(954\) 10.4549 0.338490
\(955\) 21.0234 0.680301
\(956\) 0.817349 0.0264350
\(957\) −0.233334 −0.00754260
\(958\) 25.1228 0.811682
\(959\) −61.0993 −1.97300
\(960\) 7.62619 0.246134
\(961\) 49.6915 1.60295
\(962\) −11.2973 −0.364240
\(963\) 7.99603 0.257668
\(964\) 25.8208 0.831631
\(965\) 50.8291 1.63625
\(966\) −20.1599 −0.648635
\(967\) −17.5222 −0.563476 −0.281738 0.959491i \(-0.590911\pi\)
−0.281738 + 0.959491i \(0.590911\pi\)
\(968\) −10.9983 −0.353499
\(969\) 36.0400 1.15777
\(970\) −44.3175 −1.42295
\(971\) 41.9650 1.34672 0.673360 0.739315i \(-0.264850\pi\)
0.673360 + 0.739315i \(0.264850\pi\)
\(972\) 12.8244 0.411342
\(973\) 37.3859 1.19854
\(974\) −1.05337 −0.0337520
\(975\) 22.6565 0.725590
\(976\) 7.09875 0.227225
\(977\) 13.2720 0.424607 0.212304 0.977204i \(-0.431903\pi\)
0.212304 + 0.977204i \(0.431903\pi\)
\(978\) −4.89844 −0.156635
\(979\) −0.318288 −0.0101725
\(980\) −18.0061 −0.575185
\(981\) −23.7244 −0.757461
\(982\) −11.2134 −0.357834
\(983\) −13.9796 −0.445879 −0.222939 0.974832i \(-0.571565\pi\)
−0.222939 + 0.974832i \(0.571565\pi\)
\(984\) −0.926591 −0.0295386
\(985\) −28.2745 −0.900900
\(986\) 10.8914 0.346852
\(987\) 41.4328 1.31882
\(988\) −5.59221 −0.177912
\(989\) 27.5804 0.877007
\(990\) 0.199144 0.00632921
\(991\) 36.1350 1.14787 0.573933 0.818902i \(-0.305417\pi\)
0.573933 + 0.818902i \(0.305417\pi\)
\(992\) 8.98284 0.285206
\(993\) −44.6535 −1.41704
\(994\) −26.1572 −0.829655
\(995\) 1.41020 0.0447062
\(996\) −8.81375 −0.279274
\(997\) 55.1563 1.74682 0.873409 0.486988i \(-0.161904\pi\)
0.873409 + 0.486988i \(0.161904\pi\)
\(998\) 14.7997 0.468475
\(999\) 30.6666 0.970249
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 \(a_p\))