Properties

Label 6026.2.a.i.1.7
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.97733 q^{3}\) \(+1.00000 q^{4}\) \(-3.11644 q^{5}\) \(+1.97733 q^{6}\) \(-3.94255 q^{7}\) \(-1.00000 q^{8}\) \(+0.909824 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.97733 q^{3}\) \(+1.00000 q^{4}\) \(-3.11644 q^{5}\) \(+1.97733 q^{6}\) \(-3.94255 q^{7}\) \(-1.00000 q^{8}\) \(+0.909824 q^{9}\) \(+3.11644 q^{10}\) \(-4.52506 q^{11}\) \(-1.97733 q^{12}\) \(-5.66517 q^{13}\) \(+3.94255 q^{14}\) \(+6.16222 q^{15}\) \(+1.00000 q^{16}\) \(+1.59542 q^{17}\) \(-0.909824 q^{18}\) \(-6.00815 q^{19}\) \(-3.11644 q^{20}\) \(+7.79571 q^{21}\) \(+4.52506 q^{22}\) \(+1.00000 q^{23}\) \(+1.97733 q^{24}\) \(+4.71218 q^{25}\) \(+5.66517 q^{26}\) \(+4.13296 q^{27}\) \(-3.94255 q^{28}\) \(-5.05182 q^{29}\) \(-6.16222 q^{30}\) \(+3.72512 q^{31}\) \(-1.00000 q^{32}\) \(+8.94753 q^{33}\) \(-1.59542 q^{34}\) \(+12.2867 q^{35}\) \(+0.909824 q^{36}\) \(+3.72100 q^{37}\) \(+6.00815 q^{38}\) \(+11.2019 q^{39}\) \(+3.11644 q^{40}\) \(+2.67619 q^{41}\) \(-7.79571 q^{42}\) \(+6.70351 q^{43}\) \(-4.52506 q^{44}\) \(-2.83541 q^{45}\) \(-1.00000 q^{46}\) \(-2.96233 q^{47}\) \(-1.97733 q^{48}\) \(+8.54368 q^{49}\) \(-4.71218 q^{50}\) \(-3.15466 q^{51}\) \(-5.66517 q^{52}\) \(-2.04095 q^{53}\) \(-4.13296 q^{54}\) \(+14.1021 q^{55}\) \(+3.94255 q^{56}\) \(+11.8801 q^{57}\) \(+5.05182 q^{58}\) \(+1.88037 q^{59}\) \(+6.16222 q^{60}\) \(+2.55870 q^{61}\) \(-3.72512 q^{62}\) \(-3.58702 q^{63}\) \(+1.00000 q^{64}\) \(+17.6551 q^{65}\) \(-8.94753 q^{66}\) \(+4.61407 q^{67}\) \(+1.59542 q^{68}\) \(-1.97733 q^{69}\) \(-12.2867 q^{70}\) \(+5.59111 q^{71}\) \(-0.909824 q^{72}\) \(-13.5640 q^{73}\) \(-3.72100 q^{74}\) \(-9.31752 q^{75}\) \(-6.00815 q^{76}\) \(+17.8403 q^{77}\) \(-11.2019 q^{78}\) \(-14.9962 q^{79}\) \(-3.11644 q^{80}\) \(-10.9017 q^{81}\) \(-2.67619 q^{82}\) \(-9.80877 q^{83}\) \(+7.79571 q^{84}\) \(-4.97201 q^{85}\) \(-6.70351 q^{86}\) \(+9.98911 q^{87}\) \(+4.52506 q^{88}\) \(-0.355681 q^{89}\) \(+2.83541 q^{90}\) \(+22.3352 q^{91}\) \(+1.00000 q^{92}\) \(-7.36577 q^{93}\) \(+2.96233 q^{94}\) \(+18.7240 q^{95}\) \(+1.97733 q^{96}\) \(+14.7960 q^{97}\) \(-8.54368 q^{98}\) \(-4.11701 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.97733 −1.14161 −0.570805 0.821085i \(-0.693369\pi\)
−0.570805 + 0.821085i \(0.693369\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.11644 −1.39371 −0.696856 0.717211i \(-0.745419\pi\)
−0.696856 + 0.717211i \(0.745419\pi\)
\(6\) 1.97733 0.807241
\(7\) −3.94255 −1.49014 −0.745071 0.666985i \(-0.767585\pi\)
−0.745071 + 0.666985i \(0.767585\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.909824 0.303275
\(10\) 3.11644 0.985504
\(11\) −4.52506 −1.36436 −0.682179 0.731185i \(-0.738968\pi\)
−0.682179 + 0.731185i \(0.738968\pi\)
\(12\) −1.97733 −0.570805
\(13\) −5.66517 −1.57123 −0.785617 0.618713i \(-0.787655\pi\)
−0.785617 + 0.618713i \(0.787655\pi\)
\(14\) 3.94255 1.05369
\(15\) 6.16222 1.59108
\(16\) 1.00000 0.250000
\(17\) 1.59542 0.386945 0.193473 0.981106i \(-0.438025\pi\)
0.193473 + 0.981106i \(0.438025\pi\)
\(18\) −0.909824 −0.214447
\(19\) −6.00815 −1.37836 −0.689182 0.724588i \(-0.742030\pi\)
−0.689182 + 0.724588i \(0.742030\pi\)
\(20\) −3.11644 −0.696856
\(21\) 7.79571 1.70116
\(22\) 4.52506 0.964747
\(23\) 1.00000 0.208514
\(24\) 1.97733 0.403620
\(25\) 4.71218 0.942435
\(26\) 5.66517 1.11103
\(27\) 4.13296 0.795389
\(28\) −3.94255 −0.745071
\(29\) −5.05182 −0.938100 −0.469050 0.883172i \(-0.655404\pi\)
−0.469050 + 0.883172i \(0.655404\pi\)
\(30\) −6.16222 −1.12506
\(31\) 3.72512 0.669051 0.334525 0.942387i \(-0.391424\pi\)
0.334525 + 0.942387i \(0.391424\pi\)
\(32\) −1.00000 −0.176777
\(33\) 8.94753 1.55757
\(34\) −1.59542 −0.273612
\(35\) 12.2867 2.07683
\(36\) 0.909824 0.151637
\(37\) 3.72100 0.611728 0.305864 0.952075i \(-0.401055\pi\)
0.305864 + 0.952075i \(0.401055\pi\)
\(38\) 6.00815 0.974651
\(39\) 11.2019 1.79374
\(40\) 3.11644 0.492752
\(41\) 2.67619 0.417950 0.208975 0.977921i \(-0.432987\pi\)
0.208975 + 0.977921i \(0.432987\pi\)
\(42\) −7.79571 −1.20290
\(43\) 6.70351 1.02228 0.511138 0.859499i \(-0.329224\pi\)
0.511138 + 0.859499i \(0.329224\pi\)
\(44\) −4.52506 −0.682179
\(45\) −2.83541 −0.422678
\(46\) −1.00000 −0.147442
\(47\) −2.96233 −0.432101 −0.216050 0.976382i \(-0.569318\pi\)
−0.216050 + 0.976382i \(0.569318\pi\)
\(48\) −1.97733 −0.285403
\(49\) 8.54368 1.22053
\(50\) −4.71218 −0.666402
\(51\) −3.15466 −0.441741
\(52\) −5.66517 −0.785617
\(53\) −2.04095 −0.280346 −0.140173 0.990127i \(-0.544766\pi\)
−0.140173 + 0.990127i \(0.544766\pi\)
\(54\) −4.13296 −0.562425
\(55\) 14.1021 1.90152
\(56\) 3.94255 0.526845
\(57\) 11.8801 1.57356
\(58\) 5.05182 0.663337
\(59\) 1.88037 0.244803 0.122402 0.992481i \(-0.460940\pi\)
0.122402 + 0.992481i \(0.460940\pi\)
\(60\) 6.16222 0.795539
\(61\) 2.55870 0.327608 0.163804 0.986493i \(-0.447623\pi\)
0.163804 + 0.986493i \(0.447623\pi\)
\(62\) −3.72512 −0.473090
\(63\) −3.58702 −0.451922
\(64\) 1.00000 0.125000
\(65\) 17.6551 2.18985
\(66\) −8.94753 −1.10136
\(67\) 4.61407 0.563698 0.281849 0.959459i \(-0.409052\pi\)
0.281849 + 0.959459i \(0.409052\pi\)
\(68\) 1.59542 0.193473
\(69\) −1.97733 −0.238042
\(70\) −12.2867 −1.46854
\(71\) 5.59111 0.663543 0.331772 0.943360i \(-0.392354\pi\)
0.331772 + 0.943360i \(0.392354\pi\)
\(72\) −0.909824 −0.107224
\(73\) −13.5640 −1.58755 −0.793773 0.608215i \(-0.791886\pi\)
−0.793773 + 0.608215i \(0.791886\pi\)
\(74\) −3.72100 −0.432557
\(75\) −9.31752 −1.07589
\(76\) −6.00815 −0.689182
\(77\) 17.8403 2.03309
\(78\) −11.2019 −1.26836
\(79\) −14.9962 −1.68720 −0.843601 0.536971i \(-0.819568\pi\)
−0.843601 + 0.536971i \(0.819568\pi\)
\(80\) −3.11644 −0.348428
\(81\) −10.9017 −1.21130
\(82\) −2.67619 −0.295535
\(83\) −9.80877 −1.07665 −0.538326 0.842737i \(-0.680943\pi\)
−0.538326 + 0.842737i \(0.680943\pi\)
\(84\) 7.79571 0.850581
\(85\) −4.97201 −0.539290
\(86\) −6.70351 −0.722858
\(87\) 9.98911 1.07095
\(88\) 4.52506 0.482373
\(89\) −0.355681 −0.0377021 −0.0188511 0.999822i \(-0.506001\pi\)
−0.0188511 + 0.999822i \(0.506001\pi\)
\(90\) 2.83541 0.298878
\(91\) 22.3352 2.34136
\(92\) 1.00000 0.104257
\(93\) −7.36577 −0.763795
\(94\) 2.96233 0.305541
\(95\) 18.7240 1.92104
\(96\) 1.97733 0.201810
\(97\) 14.7960 1.50231 0.751154 0.660127i \(-0.229497\pi\)
0.751154 + 0.660127i \(0.229497\pi\)
\(98\) −8.54368 −0.863042
\(99\) −4.11701 −0.413775
\(100\) 4.71218 0.471218
\(101\) 12.7490 1.26858 0.634288 0.773097i \(-0.281294\pi\)
0.634288 + 0.773097i \(0.281294\pi\)
\(102\) 3.15466 0.312358
\(103\) 3.90007 0.384285 0.192142 0.981367i \(-0.438456\pi\)
0.192142 + 0.981367i \(0.438456\pi\)
\(104\) 5.66517 0.555515
\(105\) −24.2948 −2.37093
\(106\) 2.04095 0.198234
\(107\) 5.66895 0.548038 0.274019 0.961724i \(-0.411647\pi\)
0.274019 + 0.961724i \(0.411647\pi\)
\(108\) 4.13296 0.397695
\(109\) −9.26812 −0.887725 −0.443862 0.896095i \(-0.646392\pi\)
−0.443862 + 0.896095i \(0.646392\pi\)
\(110\) −14.1021 −1.34458
\(111\) −7.35763 −0.698356
\(112\) −3.94255 −0.372536
\(113\) −1.54825 −0.145648 −0.0728238 0.997345i \(-0.523201\pi\)
−0.0728238 + 0.997345i \(0.523201\pi\)
\(114\) −11.8801 −1.11267
\(115\) −3.11644 −0.290609
\(116\) −5.05182 −0.469050
\(117\) −5.15430 −0.476515
\(118\) −1.88037 −0.173102
\(119\) −6.29000 −0.576604
\(120\) −6.16222 −0.562531
\(121\) 9.47620 0.861473
\(122\) −2.55870 −0.231654
\(123\) −5.29170 −0.477136
\(124\) 3.72512 0.334525
\(125\) 0.896982 0.0802285
\(126\) 3.58702 0.319557
\(127\) −6.92755 −0.614721 −0.307360 0.951593i \(-0.599446\pi\)
−0.307360 + 0.951593i \(0.599446\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −13.2550 −1.16704
\(130\) −17.6551 −1.54846
\(131\) 1.00000 0.0873704
\(132\) 8.94753 0.778783
\(133\) 23.6874 2.05396
\(134\) −4.61407 −0.398595
\(135\) −12.8801 −1.10854
\(136\) −1.59542 −0.136806
\(137\) 17.0067 1.45298 0.726492 0.687175i \(-0.241149\pi\)
0.726492 + 0.687175i \(0.241149\pi\)
\(138\) 1.97733 0.168321
\(139\) −21.7796 −1.84732 −0.923662 0.383209i \(-0.874819\pi\)
−0.923662 + 0.383209i \(0.874819\pi\)
\(140\) 12.2867 1.03842
\(141\) 5.85750 0.493291
\(142\) −5.59111 −0.469196
\(143\) 25.6352 2.14373
\(144\) 0.909824 0.0758186
\(145\) 15.7437 1.30744
\(146\) 13.5640 1.12256
\(147\) −16.8937 −1.39337
\(148\) 3.72100 0.305864
\(149\) −15.8438 −1.29798 −0.648988 0.760799i \(-0.724808\pi\)
−0.648988 + 0.760799i \(0.724808\pi\)
\(150\) 9.31752 0.760772
\(151\) −4.72329 −0.384376 −0.192188 0.981358i \(-0.561558\pi\)
−0.192188 + 0.981358i \(0.561558\pi\)
\(152\) 6.00815 0.487325
\(153\) 1.45155 0.117351
\(154\) −17.8403 −1.43761
\(155\) −11.6091 −0.932464
\(156\) 11.2019 0.896869
\(157\) 6.34927 0.506727 0.253363 0.967371i \(-0.418463\pi\)
0.253363 + 0.967371i \(0.418463\pi\)
\(158\) 14.9962 1.19303
\(159\) 4.03562 0.320046
\(160\) 3.11644 0.246376
\(161\) −3.94255 −0.310716
\(162\) 10.9017 0.856518
\(163\) −17.4955 −1.37035 −0.685176 0.728378i \(-0.740275\pi\)
−0.685176 + 0.728378i \(0.740275\pi\)
\(164\) 2.67619 0.208975
\(165\) −27.8844 −2.17080
\(166\) 9.80877 0.761308
\(167\) 6.62277 0.512485 0.256243 0.966612i \(-0.417515\pi\)
0.256243 + 0.966612i \(0.417515\pi\)
\(168\) −7.79571 −0.601452
\(169\) 19.0941 1.46878
\(170\) 4.97201 0.381336
\(171\) −5.46636 −0.418023
\(172\) 6.70351 0.511138
\(173\) 16.2181 1.23304 0.616519 0.787340i \(-0.288543\pi\)
0.616519 + 0.787340i \(0.288543\pi\)
\(174\) −9.98911 −0.757273
\(175\) −18.5780 −1.40436
\(176\) −4.52506 −0.341089
\(177\) −3.71810 −0.279470
\(178\) 0.355681 0.0266594
\(179\) −10.3870 −0.776359 −0.388180 0.921584i \(-0.626896\pi\)
−0.388180 + 0.921584i \(0.626896\pi\)
\(180\) −2.83541 −0.211339
\(181\) 6.04645 0.449429 0.224715 0.974425i \(-0.427855\pi\)
0.224715 + 0.974425i \(0.427855\pi\)
\(182\) −22.3352 −1.65559
\(183\) −5.05939 −0.374001
\(184\) −1.00000 −0.0737210
\(185\) −11.5963 −0.852574
\(186\) 7.36577 0.540085
\(187\) −7.21936 −0.527932
\(188\) −2.96233 −0.216050
\(189\) −16.2944 −1.18524
\(190\) −18.7240 −1.35838
\(191\) −6.52512 −0.472141 −0.236070 0.971736i \(-0.575860\pi\)
−0.236070 + 0.971736i \(0.575860\pi\)
\(192\) −1.97733 −0.142701
\(193\) −14.8862 −1.07153 −0.535764 0.844368i \(-0.679976\pi\)
−0.535764 + 0.844368i \(0.679976\pi\)
\(194\) −14.7960 −1.06229
\(195\) −34.9100 −2.49996
\(196\) 8.54368 0.610263
\(197\) 15.8551 1.12963 0.564813 0.825219i \(-0.308948\pi\)
0.564813 + 0.825219i \(0.308948\pi\)
\(198\) 4.11701 0.292583
\(199\) 24.2691 1.72039 0.860194 0.509967i \(-0.170342\pi\)
0.860194 + 0.509967i \(0.170342\pi\)
\(200\) −4.71218 −0.333201
\(201\) −9.12353 −0.643524
\(202\) −12.7490 −0.897018
\(203\) 19.9171 1.39790
\(204\) −3.15466 −0.220870
\(205\) −8.34017 −0.582503
\(206\) −3.90007 −0.271730
\(207\) 0.909824 0.0632371
\(208\) −5.66517 −0.392809
\(209\) 27.1873 1.88058
\(210\) 24.2948 1.67650
\(211\) 10.0122 0.689268 0.344634 0.938737i \(-0.388003\pi\)
0.344634 + 0.938737i \(0.388003\pi\)
\(212\) −2.04095 −0.140173
\(213\) −11.0555 −0.757508
\(214\) −5.66895 −0.387521
\(215\) −20.8911 −1.42476
\(216\) −4.13296 −0.281213
\(217\) −14.6864 −0.996981
\(218\) 9.26812 0.627716
\(219\) 26.8205 1.81236
\(220\) 14.1021 0.950762
\(221\) −9.03830 −0.607982
\(222\) 7.35763 0.493812
\(223\) 11.1823 0.748820 0.374410 0.927263i \(-0.377845\pi\)
0.374410 + 0.927263i \(0.377845\pi\)
\(224\) 3.94255 0.263423
\(225\) 4.28725 0.285817
\(226\) 1.54825 0.102988
\(227\) −24.6608 −1.63680 −0.818399 0.574651i \(-0.805138\pi\)
−0.818399 + 0.574651i \(0.805138\pi\)
\(228\) 11.8801 0.786778
\(229\) 16.5997 1.09694 0.548469 0.836171i \(-0.315211\pi\)
0.548469 + 0.836171i \(0.315211\pi\)
\(230\) 3.11644 0.205492
\(231\) −35.2761 −2.32099
\(232\) 5.05182 0.331669
\(233\) −0.350756 −0.0229788 −0.0114894 0.999934i \(-0.503657\pi\)
−0.0114894 + 0.999934i \(0.503657\pi\)
\(234\) 5.15430 0.336947
\(235\) 9.23193 0.602225
\(236\) 1.88037 0.122402
\(237\) 29.6523 1.92613
\(238\) 6.29000 0.407720
\(239\) −11.9578 −0.773486 −0.386743 0.922188i \(-0.626400\pi\)
−0.386743 + 0.922188i \(0.626400\pi\)
\(240\) 6.16222 0.397769
\(241\) −5.56516 −0.358484 −0.179242 0.983805i \(-0.557364\pi\)
−0.179242 + 0.983805i \(0.557364\pi\)
\(242\) −9.47620 −0.609153
\(243\) 9.15732 0.587443
\(244\) 2.55870 0.163804
\(245\) −26.6258 −1.70106
\(246\) 5.29170 0.337386
\(247\) 34.0372 2.16573
\(248\) −3.72512 −0.236545
\(249\) 19.3951 1.22912
\(250\) −0.896982 −0.0567301
\(251\) −9.51128 −0.600347 −0.300173 0.953885i \(-0.597045\pi\)
−0.300173 + 0.953885i \(0.597045\pi\)
\(252\) −3.58702 −0.225961
\(253\) −4.52506 −0.284488
\(254\) 6.92755 0.434673
\(255\) 9.83130 0.615660
\(256\) 1.00000 0.0625000
\(257\) 3.21716 0.200681 0.100341 0.994953i \(-0.468007\pi\)
0.100341 + 0.994953i \(0.468007\pi\)
\(258\) 13.2550 0.825223
\(259\) −14.6702 −0.911563
\(260\) 17.6551 1.09493
\(261\) −4.59627 −0.284502
\(262\) −1.00000 −0.0617802
\(263\) 22.4649 1.38525 0.692624 0.721299i \(-0.256455\pi\)
0.692624 + 0.721299i \(0.256455\pi\)
\(264\) −8.94753 −0.550682
\(265\) 6.36048 0.390721
\(266\) −23.6874 −1.45237
\(267\) 0.703298 0.0430412
\(268\) 4.61407 0.281849
\(269\) 4.02909 0.245658 0.122829 0.992428i \(-0.460803\pi\)
0.122829 + 0.992428i \(0.460803\pi\)
\(270\) 12.8801 0.783859
\(271\) −14.0411 −0.852934 −0.426467 0.904503i \(-0.640242\pi\)
−0.426467 + 0.904503i \(0.640242\pi\)
\(272\) 1.59542 0.0967363
\(273\) −44.1640 −2.67293
\(274\) −17.0067 −1.02742
\(275\) −21.3229 −1.28582
\(276\) −1.97733 −0.119021
\(277\) −0.490680 −0.0294821 −0.0147410 0.999891i \(-0.504692\pi\)
−0.0147410 + 0.999891i \(0.504692\pi\)
\(278\) 21.7796 1.30625
\(279\) 3.38920 0.202906
\(280\) −12.2867 −0.734271
\(281\) 23.1767 1.38261 0.691304 0.722564i \(-0.257036\pi\)
0.691304 + 0.722564i \(0.257036\pi\)
\(282\) −5.85750 −0.348809
\(283\) 11.4998 0.683592 0.341796 0.939774i \(-0.388965\pi\)
0.341796 + 0.939774i \(0.388965\pi\)
\(284\) 5.59111 0.331772
\(285\) −37.0235 −2.19308
\(286\) −25.6352 −1.51584
\(287\) −10.5510 −0.622806
\(288\) −0.909824 −0.0536119
\(289\) −14.4546 −0.850273
\(290\) −15.7437 −0.924501
\(291\) −29.2566 −1.71505
\(292\) −13.5640 −0.793773
\(293\) −7.09097 −0.414259 −0.207129 0.978314i \(-0.566412\pi\)
−0.207129 + 0.978314i \(0.566412\pi\)
\(294\) 16.8937 0.985258
\(295\) −5.86005 −0.341185
\(296\) −3.72100 −0.216279
\(297\) −18.7019 −1.08520
\(298\) 15.8438 0.917808
\(299\) −5.66517 −0.327625
\(300\) −9.31752 −0.537947
\(301\) −26.4289 −1.52334
\(302\) 4.72329 0.271795
\(303\) −25.2090 −1.44822
\(304\) −6.00815 −0.344591
\(305\) −7.97404 −0.456592
\(306\) −1.45155 −0.0829794
\(307\) −13.5874 −0.775472 −0.387736 0.921771i \(-0.626743\pi\)
−0.387736 + 0.921771i \(0.626743\pi\)
\(308\) 17.8403 1.01654
\(309\) −7.71171 −0.438704
\(310\) 11.6091 0.659352
\(311\) 24.9892 1.41701 0.708503 0.705708i \(-0.249371\pi\)
0.708503 + 0.705708i \(0.249371\pi\)
\(312\) −11.2019 −0.634182
\(313\) 25.5324 1.44317 0.721587 0.692324i \(-0.243413\pi\)
0.721587 + 0.692324i \(0.243413\pi\)
\(314\) −6.34927 −0.358310
\(315\) 11.1787 0.629850
\(316\) −14.9962 −0.843601
\(317\) 18.1255 1.01803 0.509016 0.860757i \(-0.330009\pi\)
0.509016 + 0.860757i \(0.330009\pi\)
\(318\) −4.03562 −0.226306
\(319\) 22.8598 1.27990
\(320\) −3.11644 −0.174214
\(321\) −11.2094 −0.625646
\(322\) 3.94255 0.219710
\(323\) −9.58550 −0.533352
\(324\) −10.9017 −0.605650
\(325\) −26.6953 −1.48079
\(326\) 17.4955 0.968985
\(327\) 18.3261 1.01344
\(328\) −2.67619 −0.147768
\(329\) 11.6791 0.643892
\(330\) 27.8844 1.53499
\(331\) −34.6744 −1.90588 −0.952938 0.303165i \(-0.901957\pi\)
−0.952938 + 0.303165i \(0.901957\pi\)
\(332\) −9.80877 −0.538326
\(333\) 3.38545 0.185522
\(334\) −6.62277 −0.362382
\(335\) −14.3795 −0.785634
\(336\) 7.79571 0.425291
\(337\) 2.21349 0.120577 0.0602883 0.998181i \(-0.480798\pi\)
0.0602883 + 0.998181i \(0.480798\pi\)
\(338\) −19.0941 −1.03858
\(339\) 3.06141 0.166273
\(340\) −4.97201 −0.269645
\(341\) −16.8564 −0.912825
\(342\) 5.46636 0.295587
\(343\) −6.08604 −0.328615
\(344\) −6.70351 −0.361429
\(345\) 6.16222 0.331763
\(346\) −16.2181 −0.871889
\(347\) −16.0471 −0.861451 −0.430726 0.902483i \(-0.641742\pi\)
−0.430726 + 0.902483i \(0.641742\pi\)
\(348\) 9.98911 0.535473
\(349\) 0.832866 0.0445823 0.0222911 0.999752i \(-0.492904\pi\)
0.0222911 + 0.999752i \(0.492904\pi\)
\(350\) 18.5780 0.993035
\(351\) −23.4139 −1.24974
\(352\) 4.52506 0.241187
\(353\) −1.78388 −0.0949462 −0.0474731 0.998873i \(-0.515117\pi\)
−0.0474731 + 0.998873i \(0.515117\pi\)
\(354\) 3.71810 0.197615
\(355\) −17.4243 −0.924788
\(356\) −0.355681 −0.0188511
\(357\) 12.4374 0.658257
\(358\) 10.3870 0.548969
\(359\) 23.3295 1.23129 0.615643 0.788025i \(-0.288896\pi\)
0.615643 + 0.788025i \(0.288896\pi\)
\(360\) 2.83541 0.149439
\(361\) 17.0979 0.899889
\(362\) −6.04645 −0.317794
\(363\) −18.7375 −0.983466
\(364\) 22.3352 1.17068
\(365\) 42.2713 2.21258
\(366\) 5.05939 0.264459
\(367\) 15.1016 0.788299 0.394149 0.919046i \(-0.371039\pi\)
0.394149 + 0.919046i \(0.371039\pi\)
\(368\) 1.00000 0.0521286
\(369\) 2.43486 0.126754
\(370\) 11.5963 0.602861
\(371\) 8.04653 0.417755
\(372\) −7.36577 −0.381898
\(373\) 23.2013 1.20132 0.600660 0.799505i \(-0.294905\pi\)
0.600660 + 0.799505i \(0.294905\pi\)
\(374\) 7.21936 0.373304
\(375\) −1.77363 −0.0915897
\(376\) 2.96233 0.152771
\(377\) 28.6194 1.47398
\(378\) 16.2944 0.838094
\(379\) −11.2140 −0.576027 −0.288013 0.957626i \(-0.592995\pi\)
−0.288013 + 0.957626i \(0.592995\pi\)
\(380\) 18.7240 0.960522
\(381\) 13.6980 0.701772
\(382\) 6.52512 0.333854
\(383\) 30.6759 1.56747 0.783733 0.621098i \(-0.213313\pi\)
0.783733 + 0.621098i \(0.213313\pi\)
\(384\) 1.97733 0.100905
\(385\) −55.5981 −2.83354
\(386\) 14.8862 0.757685
\(387\) 6.09901 0.310030
\(388\) 14.7960 0.751154
\(389\) −23.4690 −1.18993 −0.594963 0.803753i \(-0.702833\pi\)
−0.594963 + 0.803753i \(0.702833\pi\)
\(390\) 34.9100 1.76774
\(391\) 1.59542 0.0806836
\(392\) −8.54368 −0.431521
\(393\) −1.97733 −0.0997430
\(394\) −15.8551 −0.798766
\(395\) 46.7346 2.35147
\(396\) −4.11701 −0.206887
\(397\) 7.94589 0.398793 0.199396 0.979919i \(-0.436102\pi\)
0.199396 + 0.979919i \(0.436102\pi\)
\(398\) −24.2691 −1.21650
\(399\) −46.8378 −2.34482
\(400\) 4.71218 0.235609
\(401\) 4.89362 0.244376 0.122188 0.992507i \(-0.461009\pi\)
0.122188 + 0.992507i \(0.461009\pi\)
\(402\) 9.12353 0.455040
\(403\) −21.1034 −1.05124
\(404\) 12.7490 0.634288
\(405\) 33.9744 1.68820
\(406\) −19.9171 −0.988467
\(407\) −16.8378 −0.834616
\(408\) 3.15466 0.156179
\(409\) −0.0432583 −0.00213899 −0.00106949 0.999999i \(-0.500340\pi\)
−0.00106949 + 0.999999i \(0.500340\pi\)
\(410\) 8.34017 0.411892
\(411\) −33.6279 −1.65874
\(412\) 3.90007 0.192142
\(413\) −7.41344 −0.364792
\(414\) −0.909824 −0.0447154
\(415\) 30.5684 1.50054
\(416\) 5.66517 0.277758
\(417\) 43.0654 2.10892
\(418\) −27.1873 −1.32977
\(419\) −8.25349 −0.403209 −0.201605 0.979467i \(-0.564616\pi\)
−0.201605 + 0.979467i \(0.564616\pi\)
\(420\) −24.2948 −1.18547
\(421\) −9.71405 −0.473434 −0.236717 0.971579i \(-0.576071\pi\)
−0.236717 + 0.971579i \(0.576071\pi\)
\(422\) −10.0122 −0.487386
\(423\) −2.69520 −0.131045
\(424\) 2.04095 0.0991172
\(425\) 7.51788 0.364671
\(426\) 11.0555 0.535639
\(427\) −10.0878 −0.488183
\(428\) 5.66895 0.274019
\(429\) −50.6893 −2.44730
\(430\) 20.8911 1.00746
\(431\) −5.93987 −0.286114 −0.143057 0.989714i \(-0.545693\pi\)
−0.143057 + 0.989714i \(0.545693\pi\)
\(432\) 4.13296 0.198847
\(433\) 12.8952 0.619704 0.309852 0.950785i \(-0.399720\pi\)
0.309852 + 0.950785i \(0.399720\pi\)
\(434\) 14.6864 0.704972
\(435\) −31.1304 −1.49259
\(436\) −9.26812 −0.443862
\(437\) −6.00815 −0.287409
\(438\) −26.8205 −1.28153
\(439\) −29.7579 −1.42027 −0.710134 0.704067i \(-0.751365\pi\)
−0.710134 + 0.704067i \(0.751365\pi\)
\(440\) −14.1021 −0.672290
\(441\) 7.77324 0.370154
\(442\) 9.03830 0.429908
\(443\) −27.7112 −1.31660 −0.658299 0.752756i \(-0.728724\pi\)
−0.658299 + 0.752756i \(0.728724\pi\)
\(444\) −7.35763 −0.349178
\(445\) 1.10846 0.0525460
\(446\) −11.1823 −0.529496
\(447\) 31.3284 1.48178
\(448\) −3.94255 −0.186268
\(449\) −7.22774 −0.341098 −0.170549 0.985349i \(-0.554554\pi\)
−0.170549 + 0.985349i \(0.554554\pi\)
\(450\) −4.28725 −0.202103
\(451\) −12.1099 −0.570234
\(452\) −1.54825 −0.0728238
\(453\) 9.33950 0.438808
\(454\) 24.6608 1.15739
\(455\) −69.6062 −3.26319
\(456\) −11.8801 −0.556336
\(457\) −36.5408 −1.70930 −0.854652 0.519200i \(-0.826230\pi\)
−0.854652 + 0.519200i \(0.826230\pi\)
\(458\) −16.5997 −0.775652
\(459\) 6.59379 0.307772
\(460\) −3.11644 −0.145305
\(461\) −4.30028 −0.200284 −0.100142 0.994973i \(-0.531930\pi\)
−0.100142 + 0.994973i \(0.531930\pi\)
\(462\) 35.2761 1.64119
\(463\) 18.5138 0.860409 0.430204 0.902732i \(-0.358442\pi\)
0.430204 + 0.902732i \(0.358442\pi\)
\(464\) −5.05182 −0.234525
\(465\) 22.9550 1.06451
\(466\) 0.350756 0.0162485
\(467\) 14.3610 0.664547 0.332273 0.943183i \(-0.392184\pi\)
0.332273 + 0.943183i \(0.392184\pi\)
\(468\) −5.15430 −0.238258
\(469\) −18.1912 −0.839991
\(470\) −9.23193 −0.425837
\(471\) −12.5546 −0.578485
\(472\) −1.88037 −0.0865509
\(473\) −30.3338 −1.39475
\(474\) −29.6523 −1.36198
\(475\) −28.3115 −1.29902
\(476\) −6.29000 −0.288302
\(477\) −1.85690 −0.0850217
\(478\) 11.9578 0.546937
\(479\) 19.0808 0.871826 0.435913 0.899989i \(-0.356426\pi\)
0.435913 + 0.899989i \(0.356426\pi\)
\(480\) −6.16222 −0.281265
\(481\) −21.0801 −0.961169
\(482\) 5.56516 0.253486
\(483\) 7.79571 0.354717
\(484\) 9.47620 0.430736
\(485\) −46.1109 −2.09379
\(486\) −9.15732 −0.415385
\(487\) −36.4821 −1.65316 −0.826580 0.562819i \(-0.809717\pi\)
−0.826580 + 0.562819i \(0.809717\pi\)
\(488\) −2.55870 −0.115827
\(489\) 34.5943 1.56441
\(490\) 26.6258 1.20283
\(491\) 15.9047 0.717770 0.358885 0.933382i \(-0.383157\pi\)
0.358885 + 0.933382i \(0.383157\pi\)
\(492\) −5.29170 −0.238568
\(493\) −8.05976 −0.362993
\(494\) −34.0372 −1.53141
\(495\) 12.8304 0.576684
\(496\) 3.72512 0.167263
\(497\) −22.0432 −0.988774
\(498\) −19.3951 −0.869117
\(499\) −26.2569 −1.17542 −0.587711 0.809071i \(-0.699971\pi\)
−0.587711 + 0.809071i \(0.699971\pi\)
\(500\) 0.896982 0.0401142
\(501\) −13.0954 −0.585059
\(502\) 9.51128 0.424509
\(503\) −11.6417 −0.519080 −0.259540 0.965732i \(-0.583571\pi\)
−0.259540 + 0.965732i \(0.583571\pi\)
\(504\) 3.58702 0.159779
\(505\) −39.7315 −1.76803
\(506\) 4.52506 0.201164
\(507\) −37.7553 −1.67677
\(508\) −6.92755 −0.307360
\(509\) 21.3295 0.945412 0.472706 0.881220i \(-0.343277\pi\)
0.472706 + 0.881220i \(0.343277\pi\)
\(510\) −9.83130 −0.435337
\(511\) 53.4767 2.36567
\(512\) −1.00000 −0.0441942
\(513\) −24.8315 −1.09634
\(514\) −3.21716 −0.141903
\(515\) −12.1543 −0.535583
\(516\) −13.2550 −0.583521
\(517\) 13.4048 0.589540
\(518\) 14.6702 0.644572
\(519\) −32.0684 −1.40765
\(520\) −17.6551 −0.774229
\(521\) 14.1911 0.621724 0.310862 0.950455i \(-0.399382\pi\)
0.310862 + 0.950455i \(0.399382\pi\)
\(522\) 4.59627 0.201173
\(523\) −38.7652 −1.69509 −0.847543 0.530727i \(-0.821919\pi\)
−0.847543 + 0.530727i \(0.821919\pi\)
\(524\) 1.00000 0.0436852
\(525\) 36.7348 1.60324
\(526\) −22.4649 −0.979518
\(527\) 5.94311 0.258886
\(528\) 8.94753 0.389391
\(529\) 1.00000 0.0434783
\(530\) −6.36048 −0.276282
\(531\) 1.71080 0.0742425
\(532\) 23.6874 1.02698
\(533\) −15.1611 −0.656698
\(534\) −0.703298 −0.0304347
\(535\) −17.6669 −0.763807
\(536\) −4.61407 −0.199297
\(537\) 20.5385 0.886300
\(538\) −4.02909 −0.173706
\(539\) −38.6607 −1.66523
\(540\) −12.8801 −0.554272
\(541\) −39.2996 −1.68962 −0.844810 0.535066i \(-0.820287\pi\)
−0.844810 + 0.535066i \(0.820287\pi\)
\(542\) 14.0411 0.603116
\(543\) −11.9558 −0.513073
\(544\) −1.59542 −0.0684029
\(545\) 28.8835 1.23723
\(546\) 44.1640 1.89004
\(547\) 4.02526 0.172108 0.0860539 0.996290i \(-0.472574\pi\)
0.0860539 + 0.996290i \(0.472574\pi\)
\(548\) 17.0067 0.726492
\(549\) 2.32797 0.0993553
\(550\) 21.3229 0.909212
\(551\) 30.3521 1.29304
\(552\) 1.97733 0.0841606
\(553\) 59.1231 2.51417
\(554\) 0.490680 0.0208470
\(555\) 22.9296 0.973307
\(556\) −21.7796 −0.923662
\(557\) 39.2374 1.66254 0.831272 0.555866i \(-0.187613\pi\)
0.831272 + 0.555866i \(0.187613\pi\)
\(558\) −3.38920 −0.143476
\(559\) −37.9765 −1.60624
\(560\) 12.2867 0.519208
\(561\) 14.2750 0.602692
\(562\) −23.1767 −0.977652
\(563\) 5.68412 0.239557 0.119779 0.992801i \(-0.461782\pi\)
0.119779 + 0.992801i \(0.461782\pi\)
\(564\) 5.85750 0.246645
\(565\) 4.82504 0.202991
\(566\) −11.4998 −0.483372
\(567\) 42.9804 1.80501
\(568\) −5.59111 −0.234598
\(569\) −29.3431 −1.23013 −0.615063 0.788478i \(-0.710870\pi\)
−0.615063 + 0.788478i \(0.710870\pi\)
\(570\) 37.0235 1.55074
\(571\) 11.0184 0.461104 0.230552 0.973060i \(-0.425947\pi\)
0.230552 + 0.973060i \(0.425947\pi\)
\(572\) 25.6352 1.07186
\(573\) 12.9023 0.539001
\(574\) 10.5510 0.440390
\(575\) 4.71218 0.196511
\(576\) 0.909824 0.0379093
\(577\) 11.9946 0.499340 0.249670 0.968331i \(-0.419678\pi\)
0.249670 + 0.968331i \(0.419678\pi\)
\(578\) 14.4546 0.601234
\(579\) 29.4348 1.22327
\(580\) 15.7437 0.653721
\(581\) 38.6715 1.60437
\(582\) 29.2566 1.21272
\(583\) 9.23542 0.382492
\(584\) 13.5640 0.561282
\(585\) 16.0631 0.664126
\(586\) 7.09097 0.292925
\(587\) 1.99332 0.0822732 0.0411366 0.999154i \(-0.486902\pi\)
0.0411366 + 0.999154i \(0.486902\pi\)
\(588\) −16.8937 −0.696683
\(589\) −22.3811 −0.922196
\(590\) 5.86005 0.241254
\(591\) −31.3506 −1.28959
\(592\) 3.72100 0.152932
\(593\) −28.3687 −1.16496 −0.582481 0.812844i \(-0.697918\pi\)
−0.582481 + 0.812844i \(0.697918\pi\)
\(594\) 18.7019 0.767349
\(595\) 19.6024 0.803620
\(596\) −15.8438 −0.648988
\(597\) −47.9879 −1.96401
\(598\) 5.66517 0.231666
\(599\) 34.7442 1.41961 0.709806 0.704398i \(-0.248783\pi\)
0.709806 + 0.704398i \(0.248783\pi\)
\(600\) 9.31752 0.380386
\(601\) 15.4051 0.628388 0.314194 0.949359i \(-0.398266\pi\)
0.314194 + 0.949359i \(0.398266\pi\)
\(602\) 26.4289 1.07716
\(603\) 4.19799 0.170955
\(604\) −4.72329 −0.192188
\(605\) −29.5320 −1.20065
\(606\) 25.2090 1.02405
\(607\) 42.5316 1.72631 0.863153 0.504942i \(-0.168486\pi\)
0.863153 + 0.504942i \(0.168486\pi\)
\(608\) 6.00815 0.243663
\(609\) −39.3825 −1.59586
\(610\) 7.97404 0.322859
\(611\) 16.7821 0.678932
\(612\) 1.45155 0.0586753
\(613\) −43.7597 −1.76744 −0.883719 0.468018i \(-0.844968\pi\)
−0.883719 + 0.468018i \(0.844968\pi\)
\(614\) 13.5874 0.548341
\(615\) 16.4912 0.664991
\(616\) −17.8403 −0.718805
\(617\) 33.3336 1.34196 0.670979 0.741476i \(-0.265874\pi\)
0.670979 + 0.741476i \(0.265874\pi\)
\(618\) 7.71171 0.310210
\(619\) 10.4754 0.421044 0.210522 0.977589i \(-0.432484\pi\)
0.210522 + 0.977589i \(0.432484\pi\)
\(620\) −11.6091 −0.466232
\(621\) 4.13296 0.165850
\(622\) −24.9892 −1.00197
\(623\) 1.40229 0.0561816
\(624\) 11.2019 0.448435
\(625\) −26.3563 −1.05425
\(626\) −25.5324 −1.02048
\(627\) −53.7581 −2.14689
\(628\) 6.34927 0.253363
\(629\) 5.93654 0.236705
\(630\) −11.1787 −0.445371
\(631\) −39.8346 −1.58579 −0.792895 0.609359i \(-0.791427\pi\)
−0.792895 + 0.609359i \(0.791427\pi\)
\(632\) 14.9962 0.596516
\(633\) −19.7974 −0.786876
\(634\) −18.1255 −0.719857
\(635\) 21.5893 0.856744
\(636\) 4.03562 0.160023
\(637\) −48.4014 −1.91773
\(638\) −22.8598 −0.905029
\(639\) 5.08693 0.201236
\(640\) 3.11644 0.123188
\(641\) 20.4704 0.808532 0.404266 0.914642i \(-0.367527\pi\)
0.404266 + 0.914642i \(0.367527\pi\)
\(642\) 11.2094 0.442398
\(643\) −28.6994 −1.13179 −0.565897 0.824476i \(-0.691470\pi\)
−0.565897 + 0.824476i \(0.691470\pi\)
\(644\) −3.94255 −0.155358
\(645\) 41.3085 1.62652
\(646\) 9.58550 0.377136
\(647\) −28.2430 −1.11035 −0.555173 0.831735i \(-0.687348\pi\)
−0.555173 + 0.831735i \(0.687348\pi\)
\(648\) 10.9017 0.428259
\(649\) −8.50878 −0.333999
\(650\) 26.6953 1.04707
\(651\) 29.0399 1.13816
\(652\) −17.4955 −0.685176
\(653\) 17.9053 0.700690 0.350345 0.936621i \(-0.386064\pi\)
0.350345 + 0.936621i \(0.386064\pi\)
\(654\) −18.3261 −0.716607
\(655\) −3.11644 −0.121769
\(656\) 2.67619 0.104488
\(657\) −12.3408 −0.481462
\(658\) −11.6791 −0.455300
\(659\) −4.99041 −0.194399 −0.0971993 0.995265i \(-0.530988\pi\)
−0.0971993 + 0.995265i \(0.530988\pi\)
\(660\) −27.8844 −1.08540
\(661\) 5.56723 0.216540 0.108270 0.994122i \(-0.465469\pi\)
0.108270 + 0.994122i \(0.465469\pi\)
\(662\) 34.6744 1.34766
\(663\) 17.8717 0.694078
\(664\) 9.80877 0.380654
\(665\) −73.8204 −2.86263
\(666\) −3.38545 −0.131184
\(667\) −5.05182 −0.195607
\(668\) 6.62277 0.256243
\(669\) −22.1110 −0.854861
\(670\) 14.3795 0.555527
\(671\) −11.5783 −0.446975
\(672\) −7.79571 −0.300726
\(673\) 35.3453 1.36246 0.681230 0.732069i \(-0.261445\pi\)
0.681230 + 0.732069i \(0.261445\pi\)
\(674\) −2.21349 −0.0852606
\(675\) 19.4753 0.749603
\(676\) 19.0941 0.734389
\(677\) 32.6139 1.25345 0.626727 0.779239i \(-0.284394\pi\)
0.626727 + 0.779239i \(0.284394\pi\)
\(678\) −3.06141 −0.117573
\(679\) −58.3340 −2.23865
\(680\) 4.97201 0.190668
\(681\) 48.7625 1.86858
\(682\) 16.8564 0.645464
\(683\) 33.5964 1.28553 0.642766 0.766063i \(-0.277787\pi\)
0.642766 + 0.766063i \(0.277787\pi\)
\(684\) −5.46636 −0.209011
\(685\) −53.0005 −2.02504
\(686\) 6.08604 0.232366
\(687\) −32.8230 −1.25228
\(688\) 6.70351 0.255569
\(689\) 11.5623 0.440489
\(690\) −6.16222 −0.234592
\(691\) 19.3313 0.735396 0.367698 0.929945i \(-0.380146\pi\)
0.367698 + 0.929945i \(0.380146\pi\)
\(692\) 16.2181 0.616519
\(693\) 16.2315 0.616584
\(694\) 16.0471 0.609138
\(695\) 67.8748 2.57464
\(696\) −9.98911 −0.378636
\(697\) 4.26963 0.161724
\(698\) −0.832866 −0.0315244
\(699\) 0.693559 0.0262328
\(700\) −18.5780 −0.702182
\(701\) −2.76789 −0.104542 −0.0522709 0.998633i \(-0.516646\pi\)
−0.0522709 + 0.998633i \(0.516646\pi\)
\(702\) 23.4139 0.883702
\(703\) −22.3563 −0.843185
\(704\) −4.52506 −0.170545
\(705\) −18.2545 −0.687506
\(706\) 1.78388 0.0671371
\(707\) −50.2636 −1.89036
\(708\) −3.71810 −0.139735
\(709\) 26.9589 1.01246 0.506231 0.862398i \(-0.331038\pi\)
0.506231 + 0.862398i \(0.331038\pi\)
\(710\) 17.4243 0.653924
\(711\) −13.6439 −0.511685
\(712\) 0.355681 0.0133297
\(713\) 3.72512 0.139507
\(714\) −12.4374 −0.465458
\(715\) −79.8906 −2.98774
\(716\) −10.3870 −0.388180
\(717\) 23.6445 0.883019
\(718\) −23.3295 −0.870651
\(719\) 11.9081 0.444096 0.222048 0.975036i \(-0.428726\pi\)
0.222048 + 0.975036i \(0.428726\pi\)
\(720\) −2.83541 −0.105669
\(721\) −15.3762 −0.572639
\(722\) −17.0979 −0.636318
\(723\) 11.0041 0.409249
\(724\) 6.04645 0.224715
\(725\) −23.8051 −0.884099
\(726\) 18.7375 0.695416
\(727\) 48.3390 1.79280 0.896398 0.443251i \(-0.146175\pi\)
0.896398 + 0.443251i \(0.146175\pi\)
\(728\) −22.3352 −0.827797
\(729\) 14.5980 0.540668
\(730\) −42.2713 −1.56453
\(731\) 10.6949 0.395565
\(732\) −5.05939 −0.187001
\(733\) −20.4702 −0.756085 −0.378042 0.925788i \(-0.623403\pi\)
−0.378042 + 0.925788i \(0.623403\pi\)
\(734\) −15.1016 −0.557412
\(735\) 52.6480 1.94195
\(736\) −1.00000 −0.0368605
\(737\) −20.8790 −0.769086
\(738\) −2.43486 −0.0896284
\(739\) 28.3826 1.04407 0.522035 0.852924i \(-0.325173\pi\)
0.522035 + 0.852924i \(0.325173\pi\)
\(740\) −11.5963 −0.426287
\(741\) −67.3027 −2.47243
\(742\) −8.04653 −0.295397
\(743\) 39.3924 1.44517 0.722583 0.691284i \(-0.242955\pi\)
0.722583 + 0.691284i \(0.242955\pi\)
\(744\) 7.36577 0.270042
\(745\) 49.3763 1.80901
\(746\) −23.2013 −0.849461
\(747\) −8.92425 −0.326521
\(748\) −7.21936 −0.263966
\(749\) −22.3501 −0.816655
\(750\) 1.77363 0.0647637
\(751\) −39.3187 −1.43476 −0.717380 0.696682i \(-0.754659\pi\)
−0.717380 + 0.696682i \(0.754659\pi\)
\(752\) −2.96233 −0.108025
\(753\) 18.8069 0.685362
\(754\) −28.6194 −1.04226
\(755\) 14.7198 0.535710
\(756\) −16.2944 −0.592622
\(757\) −0.804958 −0.0292567 −0.0146283 0.999893i \(-0.504657\pi\)
−0.0146283 + 0.999893i \(0.504657\pi\)
\(758\) 11.2140 0.407313
\(759\) 8.94753 0.324775
\(760\) −18.7240 −0.679192
\(761\) 45.8676 1.66270 0.831350 0.555750i \(-0.187569\pi\)
0.831350 + 0.555750i \(0.187569\pi\)
\(762\) −13.6980 −0.496227
\(763\) 36.5400 1.32284
\(764\) −6.52512 −0.236070
\(765\) −4.52365 −0.163553
\(766\) −30.6759 −1.10837
\(767\) −10.6526 −0.384643
\(768\) −1.97733 −0.0713507
\(769\) −38.1167 −1.37452 −0.687262 0.726410i \(-0.741187\pi\)
−0.687262 + 0.726410i \(0.741187\pi\)
\(770\) 55.5981 2.00362
\(771\) −6.36138 −0.229100
\(772\) −14.8862 −0.535764
\(773\) −44.4507 −1.59878 −0.799390 0.600812i \(-0.794844\pi\)
−0.799390 + 0.600812i \(0.794844\pi\)
\(774\) −6.09901 −0.219225
\(775\) 17.5534 0.630537
\(776\) −14.7960 −0.531146
\(777\) 29.0078 1.04065
\(778\) 23.4690 0.841404
\(779\) −16.0789 −0.576088
\(780\) −34.9100 −1.24998
\(781\) −25.3001 −0.905310
\(782\) −1.59542 −0.0570520
\(783\) −20.8790 −0.746155
\(784\) 8.54368 0.305131
\(785\) −19.7871 −0.706232
\(786\) 1.97733 0.0705289
\(787\) 3.59343 0.128092 0.0640460 0.997947i \(-0.479600\pi\)
0.0640460 + 0.997947i \(0.479600\pi\)
\(788\) 15.8551 0.564813
\(789\) −44.4206 −1.58141
\(790\) −46.7346 −1.66274
\(791\) 6.10407 0.217036
\(792\) 4.11701 0.146292
\(793\) −14.4955 −0.514750
\(794\) −7.94589 −0.281989
\(795\) −12.5768 −0.446052
\(796\) 24.2691 0.860194
\(797\) 20.5921 0.729409 0.364705 0.931123i \(-0.381170\pi\)
0.364705 + 0.931123i \(0.381170\pi\)
\(798\) 46.8378 1.65804
\(799\) −4.72615 −0.167199
\(800\) −4.71218 −0.166601
\(801\) −0.323607 −0.0114341
\(802\) −4.89362 −0.172800
\(803\) 61.3779 2.16598
\(804\) −9.12353 −0.321762
\(805\) 12.2867 0.433049
\(806\) 21.1034 0.743336
\(807\) −7.96682 −0.280445
\(808\) −12.7490 −0.448509
\(809\) 33.2797 1.17005 0.585027 0.811014i \(-0.301084\pi\)
0.585027 + 0.811014i \(0.301084\pi\)
\(810\) −33.9744 −1.19374
\(811\) −17.4713 −0.613500 −0.306750 0.951790i \(-0.599242\pi\)
−0.306750 + 0.951790i \(0.599242\pi\)
\(812\) 19.9171 0.698952
\(813\) 27.7638 0.973719
\(814\) 16.8378 0.590163
\(815\) 54.5235 1.90988
\(816\) −3.15466 −0.110435
\(817\) −40.2757 −1.40907
\(818\) 0.0432583 0.00151249
\(819\) 20.3211 0.710076
\(820\) −8.34017 −0.291251
\(821\) 9.97398 0.348094 0.174047 0.984737i \(-0.444315\pi\)
0.174047 + 0.984737i \(0.444315\pi\)
\(822\) 33.6279 1.17291
\(823\) 36.5017 1.27237 0.636185 0.771537i \(-0.280512\pi\)
0.636185 + 0.771537i \(0.280512\pi\)
\(824\) −3.90007 −0.135865
\(825\) 42.1624 1.46790
\(826\) 7.41344 0.257947
\(827\) −2.20329 −0.0766158 −0.0383079 0.999266i \(-0.512197\pi\)
−0.0383079 + 0.999266i \(0.512197\pi\)
\(828\) 0.909824 0.0316186
\(829\) −55.8744 −1.94060 −0.970299 0.241909i \(-0.922226\pi\)
−0.970299 + 0.241909i \(0.922226\pi\)
\(830\) −30.5684 −1.06104
\(831\) 0.970235 0.0336571
\(832\) −5.66517 −0.196404
\(833\) 13.6307 0.472277
\(834\) −43.0654 −1.49123
\(835\) −20.6394 −0.714257
\(836\) 27.1873 0.940291
\(837\) 15.3958 0.532156
\(838\) 8.25349 0.285112
\(839\) −24.0039 −0.828708 −0.414354 0.910116i \(-0.635992\pi\)
−0.414354 + 0.910116i \(0.635992\pi\)
\(840\) 24.2948 0.838251
\(841\) −3.47907 −0.119968
\(842\) 9.71405 0.334768
\(843\) −45.8280 −1.57840
\(844\) 10.0122 0.344634
\(845\) −59.5056 −2.04706
\(846\) 2.69520 0.0926629
\(847\) −37.3604 −1.28372
\(848\) −2.04095 −0.0700864
\(849\) −22.7389 −0.780395
\(850\) −7.51788 −0.257861
\(851\) 3.72100 0.127554
\(852\) −11.0555 −0.378754
\(853\) −7.28720 −0.249509 −0.124754 0.992188i \(-0.539814\pi\)
−0.124754 + 0.992188i \(0.539814\pi\)
\(854\) 10.0878 0.345198
\(855\) 17.0356 0.582604
\(856\) −5.66895 −0.193761
\(857\) −46.5179 −1.58902 −0.794510 0.607250i \(-0.792272\pi\)
−0.794510 + 0.607250i \(0.792272\pi\)
\(858\) 50.6893 1.73050
\(859\) −22.0739 −0.753150 −0.376575 0.926386i \(-0.622898\pi\)
−0.376575 + 0.926386i \(0.622898\pi\)
\(860\) −20.8911 −0.712380
\(861\) 20.8628 0.711001
\(862\) 5.93987 0.202313
\(863\) −20.9086 −0.711738 −0.355869 0.934536i \(-0.615815\pi\)
−0.355869 + 0.934536i \(0.615815\pi\)
\(864\) −4.13296 −0.140606
\(865\) −50.5426 −1.71850
\(866\) −12.8952 −0.438197
\(867\) 28.5816 0.970681
\(868\) −14.6864 −0.498491
\(869\) 67.8586 2.30195
\(870\) 31.1304 1.05542
\(871\) −26.1395 −0.885703
\(872\) 9.26812 0.313858
\(873\) 13.4618 0.455612
\(874\) 6.00815 0.203229
\(875\) −3.53639 −0.119552
\(876\) 26.8205 0.906179
\(877\) −4.40947 −0.148897 −0.0744485 0.997225i \(-0.523720\pi\)
−0.0744485 + 0.997225i \(0.523720\pi\)
\(878\) 29.7579 1.00428
\(879\) 14.0212 0.472922
\(880\) 14.1021 0.475381
\(881\) 24.8428 0.836974 0.418487 0.908223i \(-0.362560\pi\)
0.418487 + 0.908223i \(0.362560\pi\)
\(882\) −7.77324 −0.261739
\(883\) 13.9687 0.470085 0.235043 0.971985i \(-0.424477\pi\)
0.235043 + 0.971985i \(0.424477\pi\)
\(884\) −9.03830 −0.303991
\(885\) 11.5872 0.389501
\(886\) 27.7112 0.930976
\(887\) −46.7212 −1.56874 −0.784372 0.620291i \(-0.787014\pi\)
−0.784372 + 0.620291i \(0.787014\pi\)
\(888\) 7.35763 0.246906
\(889\) 27.3122 0.916022
\(890\) −1.10846 −0.0371556
\(891\) 49.3308 1.65265
\(892\) 11.1823 0.374410
\(893\) 17.7982 0.595593
\(894\) −31.3284 −1.04778
\(895\) 32.3704 1.08202
\(896\) 3.94255 0.131711
\(897\) 11.2019 0.374020
\(898\) 7.22774 0.241193
\(899\) −18.8186 −0.627637
\(900\) 4.28725 0.142908
\(901\) −3.25616 −0.108478
\(902\) 12.1099 0.403216
\(903\) 52.2586 1.73906
\(904\) 1.54825 0.0514942
\(905\) −18.8434 −0.626375
\(906\) −9.33950 −0.310284
\(907\) −9.55540 −0.317282 −0.158641 0.987336i \(-0.550711\pi\)
−0.158641 + 0.987336i \(0.550711\pi\)
\(908\) −24.6608 −0.818399
\(909\) 11.5994 0.384726
\(910\) 69.6062 2.30742
\(911\) −16.8585 −0.558548 −0.279274 0.960211i \(-0.590094\pi\)
−0.279274 + 0.960211i \(0.590094\pi\)
\(912\) 11.8801 0.393389
\(913\) 44.3853 1.46894
\(914\) 36.5408 1.20866
\(915\) 15.7673 0.521250
\(916\) 16.5997 0.548469
\(917\) −3.94255 −0.130194
\(918\) −6.59379 −0.217628
\(919\) −39.6299 −1.30727 −0.653635 0.756810i \(-0.726757\pi\)
−0.653635 + 0.756810i \(0.726757\pi\)
\(920\) 3.11644 0.102746
\(921\) 26.8667 0.885287
\(922\) 4.30028 0.141622
\(923\) −31.6746 −1.04258
\(924\) −35.2761 −1.16050
\(925\) 17.5340 0.576514
\(926\) −18.5138 −0.608401
\(927\) 3.54837 0.116544
\(928\) 5.05182 0.165834
\(929\) −10.5940 −0.347578 −0.173789 0.984783i \(-0.555601\pi\)
−0.173789 + 0.984783i \(0.555601\pi\)
\(930\) −22.9550 −0.752723
\(931\) −51.3317 −1.68233
\(932\) −0.350756 −0.0114894
\(933\) −49.4118 −1.61767
\(934\) −14.3610 −0.469905
\(935\) 22.4987 0.735785
\(936\) 5.15430 0.168474
\(937\) 30.0662 0.982219 0.491110 0.871098i \(-0.336591\pi\)
0.491110 + 0.871098i \(0.336591\pi\)
\(938\) 18.1912 0.593963
\(939\) −50.4858 −1.64754
\(940\) 9.23193 0.301112
\(941\) 32.7494 1.06760 0.533801 0.845610i \(-0.320763\pi\)
0.533801 + 0.845610i \(0.320763\pi\)
\(942\) 12.5546 0.409050
\(943\) 2.67619 0.0871486
\(944\) 1.88037 0.0612008
\(945\) 50.7805 1.65189
\(946\) 30.3338 0.986238
\(947\) −44.7569 −1.45440 −0.727202 0.686423i \(-0.759180\pi\)
−0.727202 + 0.686423i \(0.759180\pi\)
\(948\) 29.6523 0.963063
\(949\) 76.8423 2.49441
\(950\) 28.3115 0.918546
\(951\) −35.8401 −1.16220
\(952\) 6.29000 0.203860
\(953\) 21.2296 0.687694 0.343847 0.939026i \(-0.388270\pi\)
0.343847 + 0.939026i \(0.388270\pi\)
\(954\) 1.85690 0.0601194
\(955\) 20.3351 0.658029
\(956\) −11.9578 −0.386743
\(957\) −45.2014 −1.46115
\(958\) −19.0808 −0.616474
\(959\) −67.0499 −2.16515
\(960\) 6.16222 0.198885
\(961\) −17.1235 −0.552371
\(962\) 21.0801 0.679649
\(963\) 5.15774 0.166206
\(964\) −5.56516 −0.179242
\(965\) 46.3917 1.49340
\(966\) −7.79571 −0.250823
\(967\) −6.33670 −0.203774 −0.101887 0.994796i \(-0.532488\pi\)
−0.101887 + 0.994796i \(0.532488\pi\)
\(968\) −9.47620 −0.304577
\(969\) 18.9537 0.608880
\(970\) 46.1109 1.48053
\(971\) 47.5951 1.52740 0.763700 0.645572i \(-0.223381\pi\)
0.763700 + 0.645572i \(0.223381\pi\)
\(972\) 9.15732 0.293721
\(973\) 85.8672 2.75278
\(974\) 36.4821 1.16896
\(975\) 52.7853 1.69048
\(976\) 2.55870 0.0819021
\(977\) 29.3380 0.938606 0.469303 0.883037i \(-0.344505\pi\)
0.469303 + 0.883037i \(0.344505\pi\)
\(978\) −34.5943 −1.10620
\(979\) 1.60948 0.0514392
\(980\) −26.6258 −0.850531
\(981\) −8.43235 −0.269224
\(982\) −15.9047 −0.507540
\(983\) −38.5444 −1.22938 −0.614688 0.788770i \(-0.710718\pi\)
−0.614688 + 0.788770i \(0.710718\pi\)
\(984\) 5.29170 0.168693
\(985\) −49.4113 −1.57437
\(986\) 8.05976 0.256675
\(987\) −23.0935 −0.735074
\(988\) 34.0372 1.08287
\(989\) 6.70351 0.213159
\(990\) −12.8304 −0.407777
\(991\) −32.7952 −1.04177 −0.520887 0.853626i \(-0.674399\pi\)
−0.520887 + 0.853626i \(0.674399\pi\)
\(992\) −3.72512 −0.118273
\(993\) 68.5626 2.17577
\(994\) 22.0432 0.699169
\(995\) −75.6330 −2.39773
\(996\) 19.3951 0.614559
\(997\) −28.8581 −0.913945 −0.456972 0.889481i \(-0.651066\pi\)
−0.456972 + 0.889481i \(0.651066\pi\)
\(998\) 26.2569 0.831149
\(999\) 15.3787 0.486562
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 \(a_p\))