Properties

Label 8043.2.a.t.1.4
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.55848 q^{2}\) \(-1.00000 q^{3}\) \(+4.54580 q^{4}\) \(+3.55238 q^{5}\) \(+2.55848 q^{6}\) \(+1.00000 q^{7}\) \(-6.51338 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.55848 q^{2}\) \(-1.00000 q^{3}\) \(+4.54580 q^{4}\) \(+3.55238 q^{5}\) \(+2.55848 q^{6}\) \(+1.00000 q^{7}\) \(-6.51338 q^{8}\) \(+1.00000 q^{9}\) \(-9.08869 q^{10}\) \(-1.59905 q^{11}\) \(-4.54580 q^{12}\) \(+3.71849 q^{13}\) \(-2.55848 q^{14}\) \(-3.55238 q^{15}\) \(+7.57272 q^{16}\) \(+2.71431 q^{17}\) \(-2.55848 q^{18}\) \(+1.03969 q^{19}\) \(+16.1484 q^{20}\) \(-1.00000 q^{21}\) \(+4.09113 q^{22}\) \(+3.04813 q^{23}\) \(+6.51338 q^{24}\) \(+7.61944 q^{25}\) \(-9.51366 q^{26}\) \(-1.00000 q^{27}\) \(+4.54580 q^{28}\) \(+7.73676 q^{29}\) \(+9.08869 q^{30}\) \(+8.27017 q^{31}\) \(-6.34787 q^{32}\) \(+1.59905 q^{33}\) \(-6.94450 q^{34}\) \(+3.55238 q^{35}\) \(+4.54580 q^{36}\) \(+6.82052 q^{37}\) \(-2.66003 q^{38}\) \(-3.71849 q^{39}\) \(-23.1380 q^{40}\) \(+0.500993 q^{41}\) \(+2.55848 q^{42}\) \(+11.4404 q^{43}\) \(-7.26897 q^{44}\) \(+3.55238 q^{45}\) \(-7.79857 q^{46}\) \(-6.65378 q^{47}\) \(-7.57272 q^{48}\) \(+1.00000 q^{49}\) \(-19.4942 q^{50}\) \(-2.71431 q^{51}\) \(+16.9035 q^{52}\) \(+13.8620 q^{53}\) \(+2.55848 q^{54}\) \(-5.68044 q^{55}\) \(-6.51338 q^{56}\) \(-1.03969 q^{57}\) \(-19.7943 q^{58}\) \(-7.73203 q^{59}\) \(-16.1484 q^{60}\) \(+6.96622 q^{61}\) \(-21.1590 q^{62}\) \(+1.00000 q^{63}\) \(+1.09544 q^{64}\) \(+13.2095 q^{65}\) \(-4.09113 q^{66}\) \(-10.4775 q^{67}\) \(+12.3387 q^{68}\) \(-3.04813 q^{69}\) \(-9.08869 q^{70}\) \(+15.8202 q^{71}\) \(-6.51338 q^{72}\) \(+1.90550 q^{73}\) \(-17.4501 q^{74}\) \(-7.61944 q^{75}\) \(+4.72624 q^{76}\) \(-1.59905 q^{77}\) \(+9.51366 q^{78}\) \(-7.08096 q^{79}\) \(+26.9012 q^{80}\) \(+1.00000 q^{81}\) \(-1.28178 q^{82}\) \(-16.1031 q^{83}\) \(-4.54580 q^{84}\) \(+9.64228 q^{85}\) \(-29.2699 q^{86}\) \(-7.73676 q^{87}\) \(+10.4152 q^{88}\) \(-3.81355 q^{89}\) \(-9.08869 q^{90}\) \(+3.71849 q^{91}\) \(+13.8562 q^{92}\) \(-8.27017 q^{93}\) \(+17.0235 q^{94}\) \(+3.69339 q^{95}\) \(+6.34787 q^{96}\) \(-11.7860 q^{97}\) \(-2.55848 q^{98}\) \(-1.59905 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55848 −1.80912 −0.904558 0.426350i \(-0.859799\pi\)
−0.904558 + 0.426350i \(0.859799\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.54580 2.27290
\(5\) 3.55238 1.58867 0.794337 0.607477i \(-0.207818\pi\)
0.794337 + 0.607477i \(0.207818\pi\)
\(6\) 2.55848 1.04449
\(7\) 1.00000 0.377964
\(8\) −6.51338 −2.30283
\(9\) 1.00000 0.333333
\(10\) −9.08869 −2.87410
\(11\) −1.59905 −0.482132 −0.241066 0.970509i \(-0.577497\pi\)
−0.241066 + 0.970509i \(0.577497\pi\)
\(12\) −4.54580 −1.31226
\(13\) 3.71849 1.03132 0.515661 0.856793i \(-0.327546\pi\)
0.515661 + 0.856793i \(0.327546\pi\)
\(14\) −2.55848 −0.683782
\(15\) −3.55238 −0.917222
\(16\) 7.57272 1.89318
\(17\) 2.71431 0.658317 0.329159 0.944275i \(-0.393235\pi\)
0.329159 + 0.944275i \(0.393235\pi\)
\(18\) −2.55848 −0.603039
\(19\) 1.03969 0.238522 0.119261 0.992863i \(-0.461947\pi\)
0.119261 + 0.992863i \(0.461947\pi\)
\(20\) 16.1484 3.61090
\(21\) −1.00000 −0.218218
\(22\) 4.09113 0.872232
\(23\) 3.04813 0.635579 0.317790 0.948161i \(-0.397059\pi\)
0.317790 + 0.948161i \(0.397059\pi\)
\(24\) 6.51338 1.32954
\(25\) 7.61944 1.52389
\(26\) −9.51366 −1.86578
\(27\) −1.00000 −0.192450
\(28\) 4.54580 0.859076
\(29\) 7.73676 1.43668 0.718340 0.695692i \(-0.244902\pi\)
0.718340 + 0.695692i \(0.244902\pi\)
\(30\) 9.08869 1.65936
\(31\) 8.27017 1.48537 0.742683 0.669643i \(-0.233553\pi\)
0.742683 + 0.669643i \(0.233553\pi\)
\(32\) −6.34787 −1.12216
\(33\) 1.59905 0.278359
\(34\) −6.94450 −1.19097
\(35\) 3.55238 0.600463
\(36\) 4.54580 0.757634
\(37\) 6.82052 1.12129 0.560643 0.828057i \(-0.310554\pi\)
0.560643 + 0.828057i \(0.310554\pi\)
\(38\) −2.66003 −0.431514
\(39\) −3.71849 −0.595434
\(40\) −23.1380 −3.65844
\(41\) 0.500993 0.0782420 0.0391210 0.999234i \(-0.487544\pi\)
0.0391210 + 0.999234i \(0.487544\pi\)
\(42\) 2.55848 0.394782
\(43\) 11.4404 1.74464 0.872319 0.488937i \(-0.162615\pi\)
0.872319 + 0.488937i \(0.162615\pi\)
\(44\) −7.26897 −1.09584
\(45\) 3.55238 0.529558
\(46\) −7.79857 −1.14984
\(47\) −6.65378 −0.970553 −0.485277 0.874361i \(-0.661281\pi\)
−0.485277 + 0.874361i \(0.661281\pi\)
\(48\) −7.57272 −1.09303
\(49\) 1.00000 0.142857
\(50\) −19.4942 −2.75689
\(51\) −2.71431 −0.380080
\(52\) 16.9035 2.34409
\(53\) 13.8620 1.90409 0.952044 0.305960i \(-0.0989773\pi\)
0.952044 + 0.305960i \(0.0989773\pi\)
\(54\) 2.55848 0.348165
\(55\) −5.68044 −0.765951
\(56\) −6.51338 −0.870387
\(57\) −1.03969 −0.137711
\(58\) −19.7943 −2.59912
\(59\) −7.73203 −1.00663 −0.503313 0.864104i \(-0.667886\pi\)
−0.503313 + 0.864104i \(0.667886\pi\)
\(60\) −16.1484 −2.08475
\(61\) 6.96622 0.891933 0.445966 0.895050i \(-0.352860\pi\)
0.445966 + 0.895050i \(0.352860\pi\)
\(62\) −21.1590 −2.68720
\(63\) 1.00000 0.125988
\(64\) 1.09544 0.136930
\(65\) 13.2095 1.63844
\(66\) −4.09113 −0.503584
\(67\) −10.4775 −1.28003 −0.640015 0.768363i \(-0.721072\pi\)
−0.640015 + 0.768363i \(0.721072\pi\)
\(68\) 12.3387 1.49629
\(69\) −3.04813 −0.366952
\(70\) −9.08869 −1.08631
\(71\) 15.8202 1.87751 0.938755 0.344586i \(-0.111981\pi\)
0.938755 + 0.344586i \(0.111981\pi\)
\(72\) −6.51338 −0.767609
\(73\) 1.90550 0.223022 0.111511 0.993763i \(-0.464431\pi\)
0.111511 + 0.993763i \(0.464431\pi\)
\(74\) −17.4501 −2.02854
\(75\) −7.61944 −0.879817
\(76\) 4.72624 0.542137
\(77\) −1.59905 −0.182229
\(78\) 9.51366 1.07721
\(79\) −7.08096 −0.796670 −0.398335 0.917240i \(-0.630412\pi\)
−0.398335 + 0.917240i \(0.630412\pi\)
\(80\) 26.9012 3.00765
\(81\) 1.00000 0.111111
\(82\) −1.28178 −0.141549
\(83\) −16.1031 −1.76755 −0.883773 0.467916i \(-0.845005\pi\)
−0.883773 + 0.467916i \(0.845005\pi\)
\(84\) −4.54580 −0.495988
\(85\) 9.64228 1.04585
\(86\) −29.2699 −3.15625
\(87\) −7.73676 −0.829468
\(88\) 10.4152 1.11027
\(89\) −3.81355 −0.404236 −0.202118 0.979361i \(-0.564782\pi\)
−0.202118 + 0.979361i \(0.564782\pi\)
\(90\) −9.08869 −0.958032
\(91\) 3.71849 0.389803
\(92\) 13.8562 1.44461
\(93\) −8.27017 −0.857577
\(94\) 17.0235 1.75584
\(95\) 3.69339 0.378934
\(96\) 6.34787 0.647877
\(97\) −11.7860 −1.19668 −0.598341 0.801242i \(-0.704173\pi\)
−0.598341 + 0.801242i \(0.704173\pi\)
\(98\) −2.55848 −0.258445
\(99\) −1.59905 −0.160711
\(100\) 34.6365 3.46365
\(101\) −3.13057 −0.311504 −0.155752 0.987796i \(-0.549780\pi\)
−0.155752 + 0.987796i \(0.549780\pi\)
\(102\) 6.94450 0.687608
\(103\) 1.97999 0.195094 0.0975470 0.995231i \(-0.468900\pi\)
0.0975470 + 0.995231i \(0.468900\pi\)
\(104\) −24.2199 −2.37496
\(105\) −3.55238 −0.346677
\(106\) −35.4655 −3.44472
\(107\) −16.7934 −1.62348 −0.811738 0.584022i \(-0.801478\pi\)
−0.811738 + 0.584022i \(0.801478\pi\)
\(108\) −4.54580 −0.437420
\(109\) 15.5866 1.49292 0.746461 0.665430i \(-0.231752\pi\)
0.746461 + 0.665430i \(0.231752\pi\)
\(110\) 14.5333 1.38569
\(111\) −6.82052 −0.647375
\(112\) 7.57272 0.715555
\(113\) −8.79725 −0.827576 −0.413788 0.910373i \(-0.635794\pi\)
−0.413788 + 0.910373i \(0.635794\pi\)
\(114\) 2.66003 0.249135
\(115\) 10.8281 1.00973
\(116\) 35.1698 3.26543
\(117\) 3.71849 0.343774
\(118\) 19.7822 1.82110
\(119\) 2.71431 0.248820
\(120\) 23.1380 2.11220
\(121\) −8.44304 −0.767549
\(122\) −17.8229 −1.61361
\(123\) −0.500993 −0.0451731
\(124\) 37.5946 3.37609
\(125\) 9.30525 0.832287
\(126\) −2.55848 −0.227927
\(127\) 13.6682 1.21286 0.606429 0.795138i \(-0.292601\pi\)
0.606429 + 0.795138i \(0.292601\pi\)
\(128\) 9.89308 0.874433
\(129\) −11.4404 −1.00727
\(130\) −33.7962 −2.96412
\(131\) 5.20953 0.455159 0.227580 0.973759i \(-0.426919\pi\)
0.227580 + 0.973759i \(0.426919\pi\)
\(132\) 7.26897 0.632682
\(133\) 1.03969 0.0901528
\(134\) 26.8064 2.31572
\(135\) −3.55238 −0.305741
\(136\) −17.6793 −1.51599
\(137\) 11.0237 0.941814 0.470907 0.882183i \(-0.343927\pi\)
0.470907 + 0.882183i \(0.343927\pi\)
\(138\) 7.79857 0.663859
\(139\) −4.31470 −0.365968 −0.182984 0.983116i \(-0.558576\pi\)
−0.182984 + 0.983116i \(0.558576\pi\)
\(140\) 16.1484 1.36479
\(141\) 6.65378 0.560349
\(142\) −40.4756 −3.39663
\(143\) −5.94605 −0.497233
\(144\) 7.57272 0.631060
\(145\) 27.4840 2.28242
\(146\) −4.87519 −0.403473
\(147\) −1.00000 −0.0824786
\(148\) 31.0047 2.54857
\(149\) −2.30263 −0.188638 −0.0943192 0.995542i \(-0.530067\pi\)
−0.0943192 + 0.995542i \(0.530067\pi\)
\(150\) 19.4942 1.59169
\(151\) −8.87322 −0.722093 −0.361046 0.932548i \(-0.617580\pi\)
−0.361046 + 0.932548i \(0.617580\pi\)
\(152\) −6.77191 −0.549275
\(153\) 2.71431 0.219439
\(154\) 4.09113 0.329673
\(155\) 29.3788 2.35976
\(156\) −16.9035 −1.35336
\(157\) 7.81294 0.623540 0.311770 0.950158i \(-0.399078\pi\)
0.311770 + 0.950158i \(0.399078\pi\)
\(158\) 18.1165 1.44127
\(159\) −13.8620 −1.09933
\(160\) −22.5501 −1.78274
\(161\) 3.04813 0.240226
\(162\) −2.55848 −0.201013
\(163\) 20.7196 1.62288 0.811441 0.584434i \(-0.198683\pi\)
0.811441 + 0.584434i \(0.198683\pi\)
\(164\) 2.27742 0.177836
\(165\) 5.68044 0.442222
\(166\) 41.1994 3.19770
\(167\) −15.1567 −1.17286 −0.586429 0.810001i \(-0.699467\pi\)
−0.586429 + 0.810001i \(0.699467\pi\)
\(168\) 6.51338 0.502518
\(169\) 0.827139 0.0636261
\(170\) −24.6695 −1.89207
\(171\) 1.03969 0.0795073
\(172\) 52.0056 3.96539
\(173\) −12.2564 −0.931839 −0.465920 0.884827i \(-0.654276\pi\)
−0.465920 + 0.884827i \(0.654276\pi\)
\(174\) 19.7943 1.50060
\(175\) 7.61944 0.575975
\(176\) −12.1092 −0.912762
\(177\) 7.73203 0.581175
\(178\) 9.75689 0.731310
\(179\) −5.31786 −0.397476 −0.198738 0.980053i \(-0.563684\pi\)
−0.198738 + 0.980053i \(0.563684\pi\)
\(180\) 16.1484 1.20363
\(181\) 4.35552 0.323743 0.161872 0.986812i \(-0.448247\pi\)
0.161872 + 0.986812i \(0.448247\pi\)
\(182\) −9.51366 −0.705199
\(183\) −6.96622 −0.514958
\(184\) −19.8536 −1.46363
\(185\) 24.2291 1.78136
\(186\) 21.1590 1.55146
\(187\) −4.34032 −0.317396
\(188\) −30.2468 −2.20597
\(189\) −1.00000 −0.0727393
\(190\) −9.44945 −0.685535
\(191\) 4.76255 0.344606 0.172303 0.985044i \(-0.444879\pi\)
0.172303 + 0.985044i \(0.444879\pi\)
\(192\) −1.09544 −0.0790566
\(193\) 6.87865 0.495136 0.247568 0.968871i \(-0.420369\pi\)
0.247568 + 0.968871i \(0.420369\pi\)
\(194\) 30.1541 2.16494
\(195\) −13.2095 −0.945951
\(196\) 4.54580 0.324700
\(197\) −18.3570 −1.30789 −0.653943 0.756544i \(-0.726886\pi\)
−0.653943 + 0.756544i \(0.726886\pi\)
\(198\) 4.09113 0.290744
\(199\) −1.30520 −0.0925235 −0.0462618 0.998929i \(-0.514731\pi\)
−0.0462618 + 0.998929i \(0.514731\pi\)
\(200\) −49.6283 −3.50925
\(201\) 10.4775 0.739025
\(202\) 8.00950 0.563546
\(203\) 7.73676 0.543014
\(204\) −12.3387 −0.863883
\(205\) 1.77972 0.124301
\(206\) −5.06575 −0.352948
\(207\) 3.04813 0.211860
\(208\) 28.1591 1.95248
\(209\) −1.66252 −0.114999
\(210\) 9.08869 0.627179
\(211\) −17.4286 −1.19984 −0.599918 0.800061i \(-0.704800\pi\)
−0.599918 + 0.800061i \(0.704800\pi\)
\(212\) 63.0138 4.32781
\(213\) −15.8202 −1.08398
\(214\) 42.9654 2.93706
\(215\) 40.6406 2.77166
\(216\) 6.51338 0.443179
\(217\) 8.27017 0.561416
\(218\) −39.8778 −2.70087
\(219\) −1.90550 −0.128762
\(220\) −25.8222 −1.74093
\(221\) 10.0931 0.678937
\(222\) 17.4501 1.17118
\(223\) 3.53637 0.236813 0.118407 0.992965i \(-0.462221\pi\)
0.118407 + 0.992965i \(0.462221\pi\)
\(224\) −6.34787 −0.424135
\(225\) 7.61944 0.507963
\(226\) 22.5076 1.49718
\(227\) −1.71958 −0.114133 −0.0570663 0.998370i \(-0.518175\pi\)
−0.0570663 + 0.998370i \(0.518175\pi\)
\(228\) −4.72624 −0.313003
\(229\) −7.53757 −0.498097 −0.249048 0.968491i \(-0.580118\pi\)
−0.249048 + 0.968491i \(0.580118\pi\)
\(230\) −27.7035 −1.82672
\(231\) 1.59905 0.105210
\(232\) −50.3924 −3.30843
\(233\) 11.8519 0.776447 0.388223 0.921565i \(-0.373089\pi\)
0.388223 + 0.921565i \(0.373089\pi\)
\(234\) −9.51366 −0.621927
\(235\) −23.6368 −1.54189
\(236\) −35.1483 −2.28796
\(237\) 7.08096 0.459958
\(238\) −6.94450 −0.450145
\(239\) 2.29552 0.148485 0.0742425 0.997240i \(-0.476346\pi\)
0.0742425 + 0.997240i \(0.476346\pi\)
\(240\) −26.9012 −1.73647
\(241\) −9.25898 −0.596424 −0.298212 0.954500i \(-0.596390\pi\)
−0.298212 + 0.954500i \(0.596390\pi\)
\(242\) 21.6013 1.38859
\(243\) −1.00000 −0.0641500
\(244\) 31.6671 2.02728
\(245\) 3.55238 0.226954
\(246\) 1.28178 0.0817233
\(247\) 3.86608 0.245993
\(248\) −53.8667 −3.42054
\(249\) 16.1031 1.02049
\(250\) −23.8073 −1.50570
\(251\) −20.0498 −1.26553 −0.632765 0.774344i \(-0.718080\pi\)
−0.632765 + 0.774344i \(0.718080\pi\)
\(252\) 4.54580 0.286359
\(253\) −4.87411 −0.306433
\(254\) −34.9698 −2.19420
\(255\) −9.64228 −0.603823
\(256\) −27.5021 −1.71888
\(257\) −10.3896 −0.648084 −0.324042 0.946043i \(-0.605042\pi\)
−0.324042 + 0.946043i \(0.605042\pi\)
\(258\) 29.2699 1.82226
\(259\) 6.82052 0.423806
\(260\) 60.0478 3.72400
\(261\) 7.73676 0.478893
\(262\) −13.3285 −0.823436
\(263\) −26.4874 −1.63328 −0.816640 0.577147i \(-0.804166\pi\)
−0.816640 + 0.577147i \(0.804166\pi\)
\(264\) −10.4152 −0.641012
\(265\) 49.2431 3.02498
\(266\) −2.66003 −0.163097
\(267\) 3.81355 0.233386
\(268\) −47.6286 −2.90938
\(269\) −28.3791 −1.73030 −0.865151 0.501511i \(-0.832778\pi\)
−0.865151 + 0.501511i \(0.832778\pi\)
\(270\) 9.08869 0.553120
\(271\) −26.8832 −1.63304 −0.816520 0.577317i \(-0.804100\pi\)
−0.816520 + 0.577317i \(0.804100\pi\)
\(272\) 20.5547 1.24631
\(273\) −3.71849 −0.225053
\(274\) −28.2038 −1.70385
\(275\) −12.1839 −0.734715
\(276\) −13.8562 −0.834046
\(277\) 19.2208 1.15487 0.577434 0.816437i \(-0.304054\pi\)
0.577434 + 0.816437i \(0.304054\pi\)
\(278\) 11.0391 0.662079
\(279\) 8.27017 0.495122
\(280\) −23.1380 −1.38276
\(281\) 16.0403 0.956887 0.478443 0.878118i \(-0.341201\pi\)
0.478443 + 0.878118i \(0.341201\pi\)
\(282\) −17.0235 −1.01374
\(283\) 28.0068 1.66483 0.832415 0.554153i \(-0.186958\pi\)
0.832415 + 0.554153i \(0.186958\pi\)
\(284\) 71.9154 4.26739
\(285\) −3.69339 −0.218777
\(286\) 15.2128 0.899553
\(287\) 0.500993 0.0295727
\(288\) −6.34787 −0.374052
\(289\) −9.63252 −0.566619
\(290\) −70.3170 −4.12916
\(291\) 11.7860 0.690905
\(292\) 8.66204 0.506908
\(293\) 9.16667 0.535523 0.267761 0.963485i \(-0.413716\pi\)
0.267761 + 0.963485i \(0.413716\pi\)
\(294\) 2.55848 0.149213
\(295\) −27.4672 −1.59920
\(296\) −44.4246 −2.58213
\(297\) 1.59905 0.0927863
\(298\) 5.89121 0.341269
\(299\) 11.3344 0.655487
\(300\) −34.6365 −1.99974
\(301\) 11.4404 0.659411
\(302\) 22.7019 1.30635
\(303\) 3.13057 0.179847
\(304\) 7.87330 0.451565
\(305\) 24.7467 1.41699
\(306\) −6.94450 −0.396991
\(307\) −10.7189 −0.611759 −0.305880 0.952070i \(-0.598951\pi\)
−0.305880 + 0.952070i \(0.598951\pi\)
\(308\) −7.26897 −0.414188
\(309\) −1.97999 −0.112638
\(310\) −75.1650 −4.26909
\(311\) 31.7612 1.80101 0.900506 0.434844i \(-0.143197\pi\)
0.900506 + 0.434844i \(0.143197\pi\)
\(312\) 24.2199 1.37118
\(313\) 13.1052 0.740747 0.370374 0.928883i \(-0.379230\pi\)
0.370374 + 0.928883i \(0.379230\pi\)
\(314\) −19.9892 −1.12806
\(315\) 3.55238 0.200154
\(316\) −32.1886 −1.81075
\(317\) −33.1956 −1.86445 −0.932224 0.361882i \(-0.882134\pi\)
−0.932224 + 0.361882i \(0.882134\pi\)
\(318\) 35.4655 1.98881
\(319\) −12.3715 −0.692669
\(320\) 3.89143 0.217537
\(321\) 16.7934 0.937314
\(322\) −7.79857 −0.434597
\(323\) 2.82205 0.157023
\(324\) 4.54580 0.252545
\(325\) 28.3328 1.57162
\(326\) −53.0106 −2.93598
\(327\) −15.5866 −0.861939
\(328\) −3.26316 −0.180178
\(329\) −6.65378 −0.366835
\(330\) −14.5333 −0.800031
\(331\) −0.00736511 −0.000404823 0 −0.000202411 1.00000i \(-0.500064\pi\)
−0.000202411 1.00000i \(0.500064\pi\)
\(332\) −73.2016 −4.01746
\(333\) 6.82052 0.373762
\(334\) 38.7779 2.12184
\(335\) −37.2201 −2.03355
\(336\) −7.57272 −0.413126
\(337\) 14.7457 0.803252 0.401626 0.915804i \(-0.368445\pi\)
0.401626 + 0.915804i \(0.368445\pi\)
\(338\) −2.11622 −0.115107
\(339\) 8.79725 0.477801
\(340\) 43.8319 2.37712
\(341\) −13.2244 −0.716142
\(342\) −2.66003 −0.143838
\(343\) 1.00000 0.0539949
\(344\) −74.5154 −4.01760
\(345\) −10.8281 −0.582967
\(346\) 31.3578 1.68581
\(347\) −13.1170 −0.704155 −0.352077 0.935971i \(-0.614525\pi\)
−0.352077 + 0.935971i \(0.614525\pi\)
\(348\) −35.1698 −1.88530
\(349\) −25.6281 −1.37184 −0.685919 0.727678i \(-0.740600\pi\)
−0.685919 + 0.727678i \(0.740600\pi\)
\(350\) −19.4942 −1.04201
\(351\) −3.71849 −0.198478
\(352\) 10.1506 0.541027
\(353\) −24.1173 −1.28364 −0.641818 0.766857i \(-0.721819\pi\)
−0.641818 + 0.766857i \(0.721819\pi\)
\(354\) −19.7822 −1.05141
\(355\) 56.1994 2.98275
\(356\) −17.3357 −0.918788
\(357\) −2.71431 −0.143657
\(358\) 13.6056 0.719079
\(359\) −6.48500 −0.342265 −0.171133 0.985248i \(-0.554743\pi\)
−0.171133 + 0.985248i \(0.554743\pi\)
\(360\) −23.1380 −1.21948
\(361\) −17.9190 −0.943107
\(362\) −11.1435 −0.585689
\(363\) 8.44304 0.443145
\(364\) 16.9035 0.885984
\(365\) 6.76908 0.354310
\(366\) 17.8229 0.931618
\(367\) 24.8129 1.29522 0.647610 0.761972i \(-0.275769\pi\)
0.647610 + 0.761972i \(0.275769\pi\)
\(368\) 23.0826 1.20327
\(369\) 0.500993 0.0260807
\(370\) −61.9896 −3.22269
\(371\) 13.8620 0.719678
\(372\) −37.5946 −1.94919
\(373\) −5.45384 −0.282389 −0.141195 0.989982i \(-0.545094\pi\)
−0.141195 + 0.989982i \(0.545094\pi\)
\(374\) 11.1046 0.574205
\(375\) −9.30525 −0.480521
\(376\) 43.3386 2.23502
\(377\) 28.7690 1.48168
\(378\) 2.55848 0.131594
\(379\) −5.84207 −0.300087 −0.150043 0.988679i \(-0.547941\pi\)
−0.150043 + 0.988679i \(0.547941\pi\)
\(380\) 16.7894 0.861279
\(381\) −13.6682 −0.700244
\(382\) −12.1849 −0.623433
\(383\) −1.00000 −0.0510976
\(384\) −9.89308 −0.504854
\(385\) −5.68044 −0.289502
\(386\) −17.5989 −0.895758
\(387\) 11.4404 0.581546
\(388\) −53.5766 −2.71994
\(389\) −30.8769 −1.56552 −0.782760 0.622324i \(-0.786189\pi\)
−0.782760 + 0.622324i \(0.786189\pi\)
\(390\) 33.7962 1.71134
\(391\) 8.27358 0.418413
\(392\) −6.51338 −0.328975
\(393\) −5.20953 −0.262786
\(394\) 46.9661 2.36612
\(395\) −25.1543 −1.26565
\(396\) −7.26897 −0.365279
\(397\) 29.9851 1.50491 0.752455 0.658644i \(-0.228870\pi\)
0.752455 + 0.658644i \(0.228870\pi\)
\(398\) 3.33934 0.167386
\(399\) −1.03969 −0.0520497
\(400\) 57.6999 2.88499
\(401\) −34.5655 −1.72612 −0.863060 0.505102i \(-0.831455\pi\)
−0.863060 + 0.505102i \(0.831455\pi\)
\(402\) −26.8064 −1.33698
\(403\) 30.7525 1.53189
\(404\) −14.2310 −0.708017
\(405\) 3.55238 0.176519
\(406\) −19.7943 −0.982376
\(407\) −10.9064 −0.540608
\(408\) 17.6793 0.875257
\(409\) −9.10775 −0.450349 −0.225175 0.974318i \(-0.572295\pi\)
−0.225175 + 0.974318i \(0.572295\pi\)
\(410\) −4.55338 −0.224875
\(411\) −11.0237 −0.543757
\(412\) 9.00064 0.443430
\(413\) −7.73203 −0.380468
\(414\) −7.79857 −0.383279
\(415\) −57.2044 −2.80806
\(416\) −23.6045 −1.15730
\(417\) 4.31470 0.211292
\(418\) 4.25352 0.208046
\(419\) 2.57151 0.125626 0.0628132 0.998025i \(-0.479993\pi\)
0.0628132 + 0.998025i \(0.479993\pi\)
\(420\) −16.1484 −0.787963
\(421\) −12.9324 −0.630288 −0.315144 0.949044i \(-0.602053\pi\)
−0.315144 + 0.949044i \(0.602053\pi\)
\(422\) 44.5907 2.17064
\(423\) −6.65378 −0.323518
\(424\) −90.2883 −4.38479
\(425\) 20.6815 1.00320
\(426\) 40.4756 1.96105
\(427\) 6.96622 0.337119
\(428\) −76.3393 −3.69000
\(429\) 5.94605 0.287078
\(430\) −103.978 −5.01426
\(431\) −15.9417 −0.767887 −0.383944 0.923357i \(-0.625434\pi\)
−0.383944 + 0.923357i \(0.625434\pi\)
\(432\) −7.57272 −0.364343
\(433\) 35.1364 1.68855 0.844274 0.535912i \(-0.180032\pi\)
0.844274 + 0.535912i \(0.180032\pi\)
\(434\) −21.1590 −1.01567
\(435\) −27.4840 −1.31775
\(436\) 70.8534 3.39326
\(437\) 3.16912 0.151600
\(438\) 4.87519 0.232945
\(439\) −24.8569 −1.18636 −0.593178 0.805071i \(-0.702127\pi\)
−0.593178 + 0.805071i \(0.702127\pi\)
\(440\) 36.9989 1.76385
\(441\) 1.00000 0.0476190
\(442\) −25.8230 −1.22828
\(443\) 17.9854 0.854511 0.427255 0.904131i \(-0.359480\pi\)
0.427255 + 0.904131i \(0.359480\pi\)
\(444\) −31.0047 −1.47142
\(445\) −13.5472 −0.642199
\(446\) −9.04773 −0.428422
\(447\) 2.30263 0.108910
\(448\) 1.09544 0.0517547
\(449\) 17.2059 0.811997 0.405998 0.913874i \(-0.366924\pi\)
0.405998 + 0.913874i \(0.366924\pi\)
\(450\) −19.4942 −0.918963
\(451\) −0.801114 −0.0377230
\(452\) −39.9906 −1.88100
\(453\) 8.87322 0.416900
\(454\) 4.39950 0.206479
\(455\) 13.2095 0.619271
\(456\) 6.77191 0.317124
\(457\) −21.5416 −1.00767 −0.503836 0.863800i \(-0.668078\pi\)
−0.503836 + 0.863800i \(0.668078\pi\)
\(458\) 19.2847 0.901115
\(459\) −2.71431 −0.126693
\(460\) 49.2226 2.29501
\(461\) −5.20012 −0.242194 −0.121097 0.992641i \(-0.538641\pi\)
−0.121097 + 0.992641i \(0.538641\pi\)
\(462\) −4.09113 −0.190337
\(463\) −0.961649 −0.0446916 −0.0223458 0.999750i \(-0.507113\pi\)
−0.0223458 + 0.999750i \(0.507113\pi\)
\(464\) 58.5883 2.71989
\(465\) −29.3788 −1.36241
\(466\) −30.3229 −1.40468
\(467\) 8.56194 0.396199 0.198100 0.980182i \(-0.436523\pi\)
0.198100 + 0.980182i \(0.436523\pi\)
\(468\) 16.9035 0.781365
\(469\) −10.4775 −0.483806
\(470\) 60.4741 2.78946
\(471\) −7.81294 −0.360001
\(472\) 50.3617 2.31808
\(473\) −18.2937 −0.841146
\(474\) −18.1165 −0.832117
\(475\) 7.92187 0.363480
\(476\) 12.3387 0.565544
\(477\) 13.8620 0.634696
\(478\) −5.87304 −0.268627
\(479\) −28.6941 −1.31107 −0.655534 0.755166i \(-0.727556\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(480\) 22.5501 1.02927
\(481\) 25.3620 1.15641
\(482\) 23.6889 1.07900
\(483\) −3.04813 −0.138695
\(484\) −38.3804 −1.74456
\(485\) −41.8682 −1.90114
\(486\) 2.55848 0.116055
\(487\) 43.2664 1.96059 0.980295 0.197541i \(-0.0632956\pi\)
0.980295 + 0.197541i \(0.0632956\pi\)
\(488\) −45.3736 −2.05397
\(489\) −20.7196 −0.936972
\(490\) −9.08869 −0.410585
\(491\) −6.20509 −0.280032 −0.140016 0.990149i \(-0.544715\pi\)
−0.140016 + 0.990149i \(0.544715\pi\)
\(492\) −2.27742 −0.102674
\(493\) 21.0000 0.945791
\(494\) −9.89128 −0.445030
\(495\) −5.68044 −0.255317
\(496\) 62.6277 2.81207
\(497\) 15.8202 0.709632
\(498\) −41.1994 −1.84619
\(499\) −29.3188 −1.31249 −0.656244 0.754549i \(-0.727856\pi\)
−0.656244 + 0.754549i \(0.727856\pi\)
\(500\) 42.2998 1.89171
\(501\) 15.1567 0.677149
\(502\) 51.2968 2.28949
\(503\) 10.4901 0.467732 0.233866 0.972269i \(-0.424862\pi\)
0.233866 + 0.972269i \(0.424862\pi\)
\(504\) −6.51338 −0.290129
\(505\) −11.1210 −0.494878
\(506\) 12.4703 0.554373
\(507\) −0.827139 −0.0367345
\(508\) 62.1330 2.75671
\(509\) −20.4149 −0.904872 −0.452436 0.891797i \(-0.649445\pi\)
−0.452436 + 0.891797i \(0.649445\pi\)
\(510\) 24.6695 1.09239
\(511\) 1.90550 0.0842945
\(512\) 50.5773 2.23522
\(513\) −1.03969 −0.0459036
\(514\) 26.5815 1.17246
\(515\) 7.03368 0.309941
\(516\) −52.0056 −2.28942
\(517\) 10.6397 0.467934
\(518\) −17.4501 −0.766715
\(519\) 12.2564 0.537998
\(520\) −86.0384 −3.77303
\(521\) 0.789813 0.0346024 0.0173012 0.999850i \(-0.494493\pi\)
0.0173012 + 0.999850i \(0.494493\pi\)
\(522\) −19.7943 −0.866374
\(523\) −1.35522 −0.0592596 −0.0296298 0.999561i \(-0.509433\pi\)
−0.0296298 + 0.999561i \(0.509433\pi\)
\(524\) 23.6815 1.03453
\(525\) −7.61944 −0.332540
\(526\) 67.7673 2.95479
\(527\) 22.4478 0.977842
\(528\) 12.1092 0.526983
\(529\) −13.7089 −0.596039
\(530\) −125.987 −5.47254
\(531\) −7.73203 −0.335542
\(532\) 4.72624 0.204908
\(533\) 1.86294 0.0806928
\(534\) −9.75689 −0.422222
\(535\) −59.6565 −2.57918
\(536\) 68.2439 2.94769
\(537\) 5.31786 0.229483
\(538\) 72.6072 3.13032
\(539\) −1.59905 −0.0688760
\(540\) −16.1484 −0.694918
\(541\) −3.61096 −0.155247 −0.0776236 0.996983i \(-0.524733\pi\)
−0.0776236 + 0.996983i \(0.524733\pi\)
\(542\) 68.7801 2.95436
\(543\) −4.35552 −0.186913
\(544\) −17.2301 −0.738734
\(545\) 55.3694 2.37177
\(546\) 9.51366 0.407147
\(547\) 14.8002 0.632810 0.316405 0.948624i \(-0.397524\pi\)
0.316405 + 0.948624i \(0.397524\pi\)
\(548\) 50.1114 2.14065
\(549\) 6.96622 0.297311
\(550\) 31.1721 1.32918
\(551\) 8.04385 0.342680
\(552\) 19.8536 0.845027
\(553\) −7.08096 −0.301113
\(554\) −49.1761 −2.08929
\(555\) −24.2291 −1.02847
\(556\) −19.6138 −0.831810
\(557\) 13.9396 0.590639 0.295319 0.955399i \(-0.404574\pi\)
0.295319 + 0.955399i \(0.404574\pi\)
\(558\) −21.1590 −0.895733
\(559\) 42.5408 1.79929
\(560\) 26.9012 1.13678
\(561\) 4.34032 0.183248
\(562\) −41.0388 −1.73112
\(563\) 38.2550 1.61226 0.806128 0.591741i \(-0.201559\pi\)
0.806128 + 0.591741i \(0.201559\pi\)
\(564\) 30.2468 1.27362
\(565\) −31.2512 −1.31475
\(566\) −71.6547 −3.01187
\(567\) 1.00000 0.0419961
\(568\) −103.043 −4.32358
\(569\) 17.7973 0.746102 0.373051 0.927811i \(-0.378312\pi\)
0.373051 + 0.927811i \(0.378312\pi\)
\(570\) 9.44945 0.395794
\(571\) −41.8234 −1.75026 −0.875128 0.483892i \(-0.839223\pi\)
−0.875128 + 0.483892i \(0.839223\pi\)
\(572\) −27.0296 −1.13016
\(573\) −4.76255 −0.198959
\(574\) −1.28178 −0.0535005
\(575\) 23.2250 0.968551
\(576\) 1.09544 0.0456434
\(577\) 1.37013 0.0570394 0.0285197 0.999593i \(-0.490921\pi\)
0.0285197 + 0.999593i \(0.490921\pi\)
\(578\) 24.6446 1.02508
\(579\) −6.87865 −0.285867
\(580\) 124.937 5.18771
\(581\) −16.1031 −0.668070
\(582\) −30.1541 −1.24993
\(583\) −22.1660 −0.918022
\(584\) −12.4113 −0.513582
\(585\) 13.2095 0.546145
\(586\) −23.4527 −0.968822
\(587\) −9.80599 −0.404737 −0.202368 0.979309i \(-0.564864\pi\)
−0.202368 + 0.979309i \(0.564864\pi\)
\(588\) −4.54580 −0.187466
\(589\) 8.59843 0.354292
\(590\) 70.2741 2.89314
\(591\) 18.3570 0.755108
\(592\) 51.6499 2.12280
\(593\) −46.1043 −1.89328 −0.946639 0.322296i \(-0.895545\pi\)
−0.946639 + 0.322296i \(0.895545\pi\)
\(594\) −4.09113 −0.167861
\(595\) 9.64228 0.395295
\(596\) −10.4673 −0.428757
\(597\) 1.30520 0.0534185
\(598\) −28.9989 −1.18585
\(599\) 28.8668 1.17947 0.589734 0.807598i \(-0.299233\pi\)
0.589734 + 0.807598i \(0.299233\pi\)
\(600\) 49.6283 2.02607
\(601\) 29.7081 1.21182 0.605909 0.795534i \(-0.292810\pi\)
0.605909 + 0.795534i \(0.292810\pi\)
\(602\) −29.2699 −1.19295
\(603\) −10.4775 −0.426676
\(604\) −40.3359 −1.64125
\(605\) −29.9929 −1.21939
\(606\) −8.00950 −0.325364
\(607\) 1.97026 0.0799704 0.0399852 0.999200i \(-0.487269\pi\)
0.0399852 + 0.999200i \(0.487269\pi\)
\(608\) −6.59983 −0.267659
\(609\) −7.73676 −0.313509
\(610\) −63.3138 −2.56350
\(611\) −24.7420 −1.00095
\(612\) 12.3387 0.498763
\(613\) −10.8390 −0.437783 −0.218892 0.975749i \(-0.570244\pi\)
−0.218892 + 0.975749i \(0.570244\pi\)
\(614\) 27.4240 1.10674
\(615\) −1.77972 −0.0717653
\(616\) 10.4152 0.419641
\(617\) −29.8250 −1.20071 −0.600354 0.799734i \(-0.704974\pi\)
−0.600354 + 0.799734i \(0.704974\pi\)
\(618\) 5.06575 0.203775
\(619\) −40.0962 −1.61160 −0.805802 0.592185i \(-0.798266\pi\)
−0.805802 + 0.592185i \(0.798266\pi\)
\(620\) 133.550 5.36351
\(621\) −3.04813 −0.122317
\(622\) −81.2602 −3.25824
\(623\) −3.81355 −0.152787
\(624\) −28.1591 −1.12726
\(625\) −5.04135 −0.201654
\(626\) −33.5292 −1.34010
\(627\) 1.66252 0.0663947
\(628\) 35.5161 1.41725
\(629\) 18.5130 0.738162
\(630\) −9.08869 −0.362102
\(631\) 36.5753 1.45604 0.728020 0.685556i \(-0.240441\pi\)
0.728020 + 0.685556i \(0.240441\pi\)
\(632\) 46.1210 1.83459
\(633\) 17.4286 0.692726
\(634\) 84.9301 3.37300
\(635\) 48.5548 1.92684
\(636\) −63.0138 −2.49866
\(637\) 3.71849 0.147332
\(638\) 31.6521 1.25312
\(639\) 15.8202 0.625837
\(640\) 35.1440 1.38919
\(641\) 2.55550 0.100936 0.0504680 0.998726i \(-0.483929\pi\)
0.0504680 + 0.998726i \(0.483929\pi\)
\(642\) −42.9654 −1.69571
\(643\) 15.2678 0.602102 0.301051 0.953608i \(-0.402663\pi\)
0.301051 + 0.953608i \(0.402663\pi\)
\(644\) 13.8562 0.546011
\(645\) −40.6406 −1.60022
\(646\) −7.22015 −0.284073
\(647\) 12.9048 0.507340 0.253670 0.967291i \(-0.418362\pi\)
0.253670 + 0.967291i \(0.418362\pi\)
\(648\) −6.51338 −0.255870
\(649\) 12.3639 0.485326
\(650\) −72.4887 −2.84324
\(651\) −8.27017 −0.324133
\(652\) 94.1871 3.68865
\(653\) 11.3501 0.444164 0.222082 0.975028i \(-0.428715\pi\)
0.222082 + 0.975028i \(0.428715\pi\)
\(654\) 39.8778 1.55935
\(655\) 18.5063 0.723100
\(656\) 3.79388 0.148126
\(657\) 1.90550 0.0743408
\(658\) 17.0235 0.663646
\(659\) −26.1746 −1.01962 −0.509809 0.860287i \(-0.670284\pi\)
−0.509809 + 0.860287i \(0.670284\pi\)
\(660\) 25.8222 1.00513
\(661\) 19.3722 0.753493 0.376746 0.926316i \(-0.377043\pi\)
0.376746 + 0.926316i \(0.377043\pi\)
\(662\) 0.0188435 0.000732372 0
\(663\) −10.0931 −0.391985
\(664\) 104.886 4.07035
\(665\) 3.69339 0.143223
\(666\) −17.4501 −0.676179
\(667\) 23.5827 0.913124
\(668\) −68.8992 −2.66579
\(669\) −3.53637 −0.136724
\(670\) 95.2267 3.67893
\(671\) −11.1393 −0.430029
\(672\) 6.34787 0.244874
\(673\) 40.0119 1.54235 0.771173 0.636626i \(-0.219670\pi\)
0.771173 + 0.636626i \(0.219670\pi\)
\(674\) −37.7267 −1.45318
\(675\) −7.61944 −0.293272
\(676\) 3.76001 0.144616
\(677\) 29.8781 1.14831 0.574154 0.818747i \(-0.305331\pi\)
0.574154 + 0.818747i \(0.305331\pi\)
\(678\) −22.5076 −0.864398
\(679\) −11.7860 −0.452303
\(680\) −62.8038 −2.40842
\(681\) 1.71958 0.0658944
\(682\) 33.8344 1.29558
\(683\) 34.2084 1.30895 0.654475 0.756084i \(-0.272890\pi\)
0.654475 + 0.756084i \(0.272890\pi\)
\(684\) 4.72624 0.180712
\(685\) 39.1603 1.49624
\(686\) −2.55848 −0.0976831
\(687\) 7.53757 0.287576
\(688\) 86.6346 3.30291
\(689\) 51.5456 1.96373
\(690\) 27.7035 1.05466
\(691\) −3.38017 −0.128588 −0.0642938 0.997931i \(-0.520479\pi\)
−0.0642938 + 0.997931i \(0.520479\pi\)
\(692\) −55.7153 −2.11798
\(693\) −1.59905 −0.0607429
\(694\) 33.5594 1.27390
\(695\) −15.3275 −0.581405
\(696\) 50.3924 1.91012
\(697\) 1.35985 0.0515081
\(698\) 65.5688 2.48182
\(699\) −11.8519 −0.448282
\(700\) 34.6365 1.30914
\(701\) 41.8071 1.57903 0.789516 0.613729i \(-0.210331\pi\)
0.789516 + 0.613729i \(0.210331\pi\)
\(702\) 9.51366 0.359070
\(703\) 7.09124 0.267451
\(704\) −1.75166 −0.0660183
\(705\) 23.6368 0.890213
\(706\) 61.7036 2.32225
\(707\) −3.13057 −0.117737
\(708\) 35.1483 1.32095
\(709\) −46.8010 −1.75765 −0.878823 0.477147i \(-0.841671\pi\)
−0.878823 + 0.477147i \(0.841671\pi\)
\(710\) −143.785 −5.39615
\(711\) −7.08096 −0.265557
\(712\) 24.8391 0.930885
\(713\) 25.2086 0.944068
\(714\) 6.94450 0.259891
\(715\) −21.1226 −0.789942
\(716\) −24.1739 −0.903423
\(717\) −2.29552 −0.0857279
\(718\) 16.5917 0.619197
\(719\) −38.3986 −1.43203 −0.716013 0.698087i \(-0.754035\pi\)
−0.716013 + 0.698087i \(0.754035\pi\)
\(720\) 26.9012 1.00255
\(721\) 1.97999 0.0737386
\(722\) 45.8454 1.70619
\(723\) 9.25898 0.344345
\(724\) 19.7993 0.735836
\(725\) 58.9498 2.18934
\(726\) −21.6013 −0.801700
\(727\) −50.5319 −1.87412 −0.937061 0.349165i \(-0.886465\pi\)
−0.937061 + 0.349165i \(0.886465\pi\)
\(728\) −24.2199 −0.897649
\(729\) 1.00000 0.0370370
\(730\) −17.3185 −0.640988
\(731\) 31.0527 1.14853
\(732\) −31.6671 −1.17045
\(733\) −37.5500 −1.38694 −0.693471 0.720485i \(-0.743919\pi\)
−0.693471 + 0.720485i \(0.743919\pi\)
\(734\) −63.4831 −2.34320
\(735\) −3.55238 −0.131032
\(736\) −19.3491 −0.713219
\(737\) 16.7540 0.617143
\(738\) −1.28178 −0.0471830
\(739\) 14.6248 0.537983 0.268992 0.963143i \(-0.413310\pi\)
0.268992 + 0.963143i \(0.413310\pi\)
\(740\) 110.141 4.04885
\(741\) −3.86608 −0.142024
\(742\) −35.4655 −1.30198
\(743\) 46.2516 1.69681 0.848403 0.529351i \(-0.177565\pi\)
0.848403 + 0.529351i \(0.177565\pi\)
\(744\) 53.8667 1.97485
\(745\) −8.17981 −0.299685
\(746\) 13.9535 0.510875
\(747\) −16.1031 −0.589182
\(748\) −19.7302 −0.721409
\(749\) −16.7934 −0.613616
\(750\) 23.8073 0.869319
\(751\) 31.0900 1.13449 0.567245 0.823549i \(-0.308009\pi\)
0.567245 + 0.823549i \(0.308009\pi\)
\(752\) −50.3872 −1.83743
\(753\) 20.0498 0.730654
\(754\) −73.6049 −2.68053
\(755\) −31.5211 −1.14717
\(756\) −4.54580 −0.165329
\(757\) 42.2710 1.53637 0.768184 0.640230i \(-0.221161\pi\)
0.768184 + 0.640230i \(0.221161\pi\)
\(758\) 14.9468 0.542892
\(759\) 4.87411 0.176919
\(760\) −24.0564 −0.872619
\(761\) −8.40649 −0.304735 −0.152368 0.988324i \(-0.548690\pi\)
−0.152368 + 0.988324i \(0.548690\pi\)
\(762\) 34.9698 1.26682
\(763\) 15.5866 0.564271
\(764\) 21.6496 0.783256
\(765\) 9.64228 0.348617
\(766\) 2.55848 0.0924415
\(767\) −28.7515 −1.03816
\(768\) 27.5021 0.992397
\(769\) −26.7663 −0.965217 −0.482608 0.875836i \(-0.660311\pi\)
−0.482608 + 0.875836i \(0.660311\pi\)
\(770\) 14.5333 0.523743
\(771\) 10.3896 0.374171
\(772\) 31.2690 1.12539
\(773\) 12.0509 0.433441 0.216721 0.976234i \(-0.430464\pi\)
0.216721 + 0.976234i \(0.430464\pi\)
\(774\) −29.2699 −1.05208
\(775\) 63.0140 2.26353
\(776\) 76.7664 2.75575
\(777\) −6.82052 −0.244685
\(778\) 78.9978 2.83221
\(779\) 0.520879 0.0186624
\(780\) −60.0478 −2.15005
\(781\) −25.2973 −0.905207
\(782\) −21.1678 −0.756957
\(783\) −7.73676 −0.276489
\(784\) 7.57272 0.270454
\(785\) 27.7546 0.990603
\(786\) 13.3285 0.475411
\(787\) 1.12847 0.0402256 0.0201128 0.999798i \(-0.493597\pi\)
0.0201128 + 0.999798i \(0.493597\pi\)
\(788\) −83.4475 −2.97270
\(789\) 26.4874 0.942975
\(790\) 64.3567 2.28971
\(791\) −8.79725 −0.312794
\(792\) 10.4152 0.370089
\(793\) 25.9038 0.919870
\(794\) −76.7162 −2.72256
\(795\) −49.2431 −1.74647
\(796\) −5.93320 −0.210297
\(797\) 40.2066 1.42419 0.712095 0.702083i \(-0.247746\pi\)
0.712095 + 0.702083i \(0.247746\pi\)
\(798\) 2.66003 0.0941640
\(799\) −18.0604 −0.638932
\(800\) −48.3672 −1.71004
\(801\) −3.81355 −0.134745
\(802\) 88.4350 3.12275
\(803\) −3.04700 −0.107526
\(804\) 47.6286 1.67973
\(805\) 10.8281 0.381642
\(806\) −78.6796 −2.77137
\(807\) 28.3791 0.998991
\(808\) 20.3906 0.717339
\(809\) 46.7869 1.64494 0.822469 0.568809i \(-0.192596\pi\)
0.822469 + 0.568809i \(0.192596\pi\)
\(810\) −9.08869 −0.319344
\(811\) 30.5910 1.07419 0.537097 0.843520i \(-0.319521\pi\)
0.537097 + 0.843520i \(0.319521\pi\)
\(812\) 35.1698 1.23422
\(813\) 26.8832 0.942836
\(814\) 27.9036 0.978022
\(815\) 73.6039 2.57823
\(816\) −20.5547 −0.719559
\(817\) 11.8945 0.416134
\(818\) 23.3020 0.814734
\(819\) 3.71849 0.129934
\(820\) 8.09026 0.282524
\(821\) −48.7632 −1.70185 −0.850924 0.525289i \(-0.823957\pi\)
−0.850924 + 0.525289i \(0.823957\pi\)
\(822\) 28.2038 0.983719
\(823\) −1.88548 −0.0657237 −0.0328619 0.999460i \(-0.510462\pi\)
−0.0328619 + 0.999460i \(0.510462\pi\)
\(824\) −12.8964 −0.449268
\(825\) 12.1839 0.424188
\(826\) 19.7822 0.688312
\(827\) −43.7034 −1.51972 −0.759859 0.650088i \(-0.774732\pi\)
−0.759859 + 0.650088i \(0.774732\pi\)
\(828\) 13.8562 0.481536
\(829\) −21.0053 −0.729543 −0.364771 0.931097i \(-0.618853\pi\)
−0.364771 + 0.931097i \(0.618853\pi\)
\(830\) 146.356 5.08010
\(831\) −19.2208 −0.666764
\(832\) 4.07338 0.141219
\(833\) 2.71431 0.0940453
\(834\) −11.0391 −0.382252
\(835\) −53.8423 −1.86329
\(836\) −7.55749 −0.261381
\(837\) −8.27017 −0.285859
\(838\) −6.57915 −0.227273
\(839\) 48.9656 1.69048 0.845240 0.534388i \(-0.179458\pi\)
0.845240 + 0.534388i \(0.179458\pi\)
\(840\) 23.1380 0.798338
\(841\) 30.8575 1.06405
\(842\) 33.0873 1.14026
\(843\) −16.0403 −0.552459
\(844\) −79.2271 −2.72711
\(845\) 2.93832 0.101081
\(846\) 17.0235 0.585281
\(847\) −8.44304 −0.290106
\(848\) 104.973 3.60478
\(849\) −28.0068 −0.961190
\(850\) −52.9132 −1.81491
\(851\) 20.7898 0.712666
\(852\) −71.9154 −2.46378
\(853\) −23.3560 −0.799694 −0.399847 0.916582i \(-0.630937\pi\)
−0.399847 + 0.916582i \(0.630937\pi\)
\(854\) −17.8229 −0.609887
\(855\) 3.69339 0.126311
\(856\) 109.382 3.73858
\(857\) 11.4905 0.392506 0.196253 0.980553i \(-0.437123\pi\)
0.196253 + 0.980553i \(0.437123\pi\)
\(858\) −15.2128 −0.519357
\(859\) −14.7448 −0.503087 −0.251544 0.967846i \(-0.580938\pi\)
−0.251544 + 0.967846i \(0.580938\pi\)
\(860\) 184.744 6.29972
\(861\) −0.500993 −0.0170738
\(862\) 40.7866 1.38920
\(863\) −19.3803 −0.659712 −0.329856 0.944031i \(-0.607000\pi\)
−0.329856 + 0.944031i \(0.607000\pi\)
\(864\) 6.34787 0.215959
\(865\) −43.5396 −1.48039
\(866\) −89.8957 −3.05478
\(867\) 9.63252 0.327137
\(868\) 37.5946 1.27604
\(869\) 11.3228 0.384100
\(870\) 70.3170 2.38397
\(871\) −38.9604 −1.32012
\(872\) −101.521 −3.43794
\(873\) −11.7860 −0.398894
\(874\) −8.10812 −0.274261
\(875\) 9.30525 0.314575
\(876\) −8.66204 −0.292663
\(877\) 18.5870 0.627639 0.313820 0.949483i \(-0.398391\pi\)
0.313820 + 0.949483i \(0.398391\pi\)
\(878\) 63.5959 2.14626
\(879\) −9.16667 −0.309184
\(880\) −43.0164 −1.45008
\(881\) 13.9901 0.471337 0.235669 0.971833i \(-0.424272\pi\)
0.235669 + 0.971833i \(0.424272\pi\)
\(882\) −2.55848 −0.0861484
\(883\) −37.2229 −1.25265 −0.626325 0.779562i \(-0.715442\pi\)
−0.626325 + 0.779562i \(0.715442\pi\)
\(884\) 45.8814 1.54316
\(885\) 27.4672 0.923298
\(886\) −46.0152 −1.54591
\(887\) 23.2403 0.780333 0.390166 0.920744i \(-0.372417\pi\)
0.390166 + 0.920744i \(0.372417\pi\)
\(888\) 44.4246 1.49079
\(889\) 13.6682 0.458417
\(890\) 34.6602 1.16181
\(891\) −1.59905 −0.0535702
\(892\) 16.0757 0.538253
\(893\) −6.91788 −0.231498
\(894\) −5.89121 −0.197032
\(895\) −18.8911 −0.631459
\(896\) 9.89308 0.330505
\(897\) −11.3344 −0.378446
\(898\) −44.0209 −1.46900
\(899\) 63.9843 2.13400
\(900\) 34.6365 1.15455
\(901\) 37.6257 1.25349
\(902\) 2.04963 0.0682452
\(903\) −11.4404 −0.380711
\(904\) 57.2998 1.90576
\(905\) 15.4725 0.514323
\(906\) −22.7019 −0.754221
\(907\) −16.7305 −0.555528 −0.277764 0.960649i \(-0.589593\pi\)
−0.277764 + 0.960649i \(0.589593\pi\)
\(908\) −7.81687 −0.259412
\(909\) −3.13057 −0.103835
\(910\) −33.7962 −1.12033
\(911\) −53.5197 −1.77319 −0.886593 0.462551i \(-0.846934\pi\)
−0.886593 + 0.462551i \(0.846934\pi\)
\(912\) −7.87330 −0.260711
\(913\) 25.7497 0.852190
\(914\) 55.1136 1.82299
\(915\) −24.7467 −0.818100
\(916\) −34.2643 −1.13213
\(917\) 5.20953 0.172034
\(918\) 6.94450 0.229203
\(919\) −20.7607 −0.684833 −0.342416 0.939548i \(-0.611245\pi\)
−0.342416 + 0.939548i \(0.611245\pi\)
\(920\) −70.5277 −2.32523
\(921\) 10.7189 0.353199
\(922\) 13.3044 0.438157
\(923\) 58.8271 1.93632
\(924\) 7.26897 0.239131
\(925\) 51.9685 1.70871
\(926\) 2.46036 0.0808523
\(927\) 1.97999 0.0650313
\(928\) −49.1120 −1.61218
\(929\) −41.9540 −1.37647 −0.688233 0.725489i \(-0.741614\pi\)
−0.688233 + 0.725489i \(0.741614\pi\)
\(930\) 75.1650 2.46476
\(931\) 1.03969 0.0340746
\(932\) 53.8766 1.76479
\(933\) −31.7612 −1.03981
\(934\) −21.9055 −0.716771
\(935\) −15.4185 −0.504238
\(936\) −24.2199 −0.791652
\(937\) −43.6871 −1.42719 −0.713597 0.700556i \(-0.752935\pi\)
−0.713597 + 0.700556i \(0.752935\pi\)
\(938\) 26.8064 0.875261
\(939\) −13.1052 −0.427671
\(940\) −107.448 −3.50457
\(941\) −7.98130 −0.260183 −0.130091 0.991502i \(-0.541527\pi\)
−0.130091 + 0.991502i \(0.541527\pi\)
\(942\) 19.9892 0.651284
\(943\) 1.52709 0.0497290
\(944\) −58.5525 −1.90572
\(945\) −3.55238 −0.115559
\(946\) 46.8040 1.52173
\(947\) −47.8121 −1.55368 −0.776842 0.629695i \(-0.783180\pi\)
−0.776842 + 0.629695i \(0.783180\pi\)
\(948\) 32.1886 1.04544
\(949\) 7.08559 0.230008
\(950\) −20.2679 −0.657578
\(951\) 33.1956 1.07644
\(952\) −17.6793 −0.572990
\(953\) −29.0952 −0.942484 −0.471242 0.882004i \(-0.656194\pi\)
−0.471242 + 0.882004i \(0.656194\pi\)
\(954\) −35.4655 −1.14824
\(955\) 16.9184 0.547467
\(956\) 10.4350 0.337492
\(957\) 12.3715 0.399913
\(958\) 73.4132 2.37187
\(959\) 11.0237 0.355972
\(960\) −3.89143 −0.125595
\(961\) 37.3957 1.20631
\(962\) −64.8881 −2.09208
\(963\) −16.7934 −0.541159
\(964\) −42.0895 −1.35561
\(965\) 24.4356 0.786610
\(966\) 7.79857 0.250915
\(967\) −4.60559 −0.148106 −0.0740529 0.997254i \(-0.523593\pi\)
−0.0740529 + 0.997254i \(0.523593\pi\)
\(968\) 54.9927 1.76753
\(969\) −2.82205 −0.0906573
\(970\) 107.119 3.43938
\(971\) −30.6355 −0.983139 −0.491570 0.870838i \(-0.663577\pi\)
−0.491570 + 0.870838i \(0.663577\pi\)
\(972\) −4.54580 −0.145807
\(973\) −4.31470 −0.138323
\(974\) −110.696 −3.54693
\(975\) −28.3328 −0.907375
\(976\) 52.7532 1.68859
\(977\) 16.5895 0.530746 0.265373 0.964146i \(-0.414505\pi\)
0.265373 + 0.964146i \(0.414505\pi\)
\(978\) 53.0106 1.69509
\(979\) 6.09806 0.194895
\(980\) 16.1484 0.515843
\(981\) 15.5866 0.497640
\(982\) 15.8756 0.506610
\(983\) 15.3648 0.490060 0.245030 0.969515i \(-0.421202\pi\)
0.245030 + 0.969515i \(0.421202\pi\)
\(984\) 3.26316 0.104026
\(985\) −65.2113 −2.07780
\(986\) −53.7279 −1.71105
\(987\) 6.65378 0.211792
\(988\) 17.5745 0.559118
\(989\) 34.8717 1.10886
\(990\) 14.5333 0.461898
\(991\) 28.3203 0.899625 0.449813 0.893123i \(-0.351491\pi\)
0.449813 + 0.893123i \(0.351491\pi\)
\(992\) −52.4980 −1.66681
\(993\) 0.00736511 0.000233725 0
\(994\) −40.4756 −1.28381
\(995\) −4.63659 −0.146990
\(996\) 73.2016 2.31948
\(997\) −14.4552 −0.457800 −0.228900 0.973450i \(-0.573513\pi\)
−0.228900 + 0.973450i \(0.573513\pi\)
\(998\) 75.0114 2.37444
\(999\) −6.82052 −0.215792
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 \(a_p\))