Properties

Label 8042.2.a.a.1.8
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 1.8
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.51956 q^{3}\) \(+1.00000 q^{4}\) \(-0.909270 q^{5}\) \(-2.51956 q^{6}\) \(+0.00482385 q^{7}\) \(+1.00000 q^{8}\) \(+3.34819 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.51956 q^{3}\) \(+1.00000 q^{4}\) \(-0.909270 q^{5}\) \(-2.51956 q^{6}\) \(+0.00482385 q^{7}\) \(+1.00000 q^{8}\) \(+3.34819 q^{9}\) \(-0.909270 q^{10}\) \(+3.05966 q^{11}\) \(-2.51956 q^{12}\) \(+1.45203 q^{13}\) \(+0.00482385 q^{14}\) \(+2.29096 q^{15}\) \(+1.00000 q^{16}\) \(+2.08149 q^{17}\) \(+3.34819 q^{18}\) \(-5.78760 q^{19}\) \(-0.909270 q^{20}\) \(-0.0121540 q^{21}\) \(+3.05966 q^{22}\) \(+2.17008 q^{23}\) \(-2.51956 q^{24}\) \(-4.17323 q^{25}\) \(+1.45203 q^{26}\) \(-0.877281 q^{27}\) \(+0.00482385 q^{28}\) \(-3.09812 q^{29}\) \(+2.29096 q^{30}\) \(+4.31573 q^{31}\) \(+1.00000 q^{32}\) \(-7.70900 q^{33}\) \(+2.08149 q^{34}\) \(-0.00438618 q^{35}\) \(+3.34819 q^{36}\) \(-3.76423 q^{37}\) \(-5.78760 q^{38}\) \(-3.65848 q^{39}\) \(-0.909270 q^{40}\) \(-12.6995 q^{41}\) \(-0.0121540 q^{42}\) \(-11.8078 q^{43}\) \(+3.05966 q^{44}\) \(-3.04441 q^{45}\) \(+2.17008 q^{46}\) \(-7.36640 q^{47}\) \(-2.51956 q^{48}\) \(-6.99998 q^{49}\) \(-4.17323 q^{50}\) \(-5.24444 q^{51}\) \(+1.45203 q^{52}\) \(+10.1099 q^{53}\) \(-0.877281 q^{54}\) \(-2.78206 q^{55}\) \(+0.00482385 q^{56}\) \(+14.5822 q^{57}\) \(-3.09812 q^{58}\) \(+8.55161 q^{59}\) \(+2.29096 q^{60}\) \(+13.6179 q^{61}\) \(+4.31573 q^{62}\) \(+0.0161512 q^{63}\) \(+1.00000 q^{64}\) \(-1.32029 q^{65}\) \(-7.70900 q^{66}\) \(+11.6157 q^{67}\) \(+2.08149 q^{68}\) \(-5.46765 q^{69}\) \(-0.00438618 q^{70}\) \(+4.96073 q^{71}\) \(+3.34819 q^{72}\) \(+15.4576 q^{73}\) \(-3.76423 q^{74}\) \(+10.5147 q^{75}\) \(-5.78760 q^{76}\) \(+0.0147593 q^{77}\) \(-3.65848 q^{78}\) \(-6.72488 q^{79}\) \(-0.909270 q^{80}\) \(-7.83420 q^{81}\) \(-12.6995 q^{82}\) \(-1.12077 q^{83}\) \(-0.0121540 q^{84}\) \(-1.89264 q^{85}\) \(-11.8078 q^{86}\) \(+7.80591 q^{87}\) \(+3.05966 q^{88}\) \(+2.64423 q^{89}\) \(-3.04441 q^{90}\) \(+0.00700439 q^{91}\) \(+2.17008 q^{92}\) \(-10.8737 q^{93}\) \(-7.36640 q^{94}\) \(+5.26249 q^{95}\) \(-2.51956 q^{96}\) \(+12.7829 q^{97}\) \(-6.99998 q^{98}\) \(+10.2443 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.51956 −1.45467 −0.727335 0.686283i \(-0.759241\pi\)
−0.727335 + 0.686283i \(0.759241\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.909270 −0.406638 −0.203319 0.979113i \(-0.565173\pi\)
−0.203319 + 0.979113i \(0.565173\pi\)
\(6\) −2.51956 −1.02861
\(7\) 0.00482385 0.00182324 0.000911622 1.00000i \(-0.499710\pi\)
0.000911622 1.00000i \(0.499710\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.34819 1.11606
\(10\) −0.909270 −0.287536
\(11\) 3.05966 0.922522 0.461261 0.887265i \(-0.347397\pi\)
0.461261 + 0.887265i \(0.347397\pi\)
\(12\) −2.51956 −0.727335
\(13\) 1.45203 0.402721 0.201361 0.979517i \(-0.435464\pi\)
0.201361 + 0.979517i \(0.435464\pi\)
\(14\) 0.00482385 0.00128923
\(15\) 2.29096 0.591524
\(16\) 1.00000 0.250000
\(17\) 2.08149 0.504836 0.252418 0.967618i \(-0.418774\pi\)
0.252418 + 0.967618i \(0.418774\pi\)
\(18\) 3.34819 0.789175
\(19\) −5.78760 −1.32777 −0.663883 0.747836i \(-0.731093\pi\)
−0.663883 + 0.747836i \(0.731093\pi\)
\(20\) −0.909270 −0.203319
\(21\) −0.0121540 −0.00265222
\(22\) 3.05966 0.652322
\(23\) 2.17008 0.452493 0.226246 0.974070i \(-0.427355\pi\)
0.226246 + 0.974070i \(0.427355\pi\)
\(24\) −2.51956 −0.514303
\(25\) −4.17323 −0.834646
\(26\) 1.45203 0.284767
\(27\) −0.877281 −0.168833
\(28\) 0.00482385 0.000911622 0
\(29\) −3.09812 −0.575307 −0.287654 0.957735i \(-0.592875\pi\)
−0.287654 + 0.957735i \(0.592875\pi\)
\(30\) 2.29096 0.418270
\(31\) 4.31573 0.775128 0.387564 0.921843i \(-0.373317\pi\)
0.387564 + 0.921843i \(0.373317\pi\)
\(32\) 1.00000 0.176777
\(33\) −7.70900 −1.34196
\(34\) 2.08149 0.356973
\(35\) −0.00438618 −0.000741400 0
\(36\) 3.34819 0.558031
\(37\) −3.76423 −0.618835 −0.309418 0.950926i \(-0.600134\pi\)
−0.309418 + 0.950926i \(0.600134\pi\)
\(38\) −5.78760 −0.938873
\(39\) −3.65848 −0.585826
\(40\) −0.909270 −0.143768
\(41\) −12.6995 −1.98333 −0.991663 0.128855i \(-0.958870\pi\)
−0.991663 + 0.128855i \(0.958870\pi\)
\(42\) −0.0121540 −0.00187540
\(43\) −11.8078 −1.80067 −0.900335 0.435198i \(-0.856678\pi\)
−0.900335 + 0.435198i \(0.856678\pi\)
\(44\) 3.05966 0.461261
\(45\) −3.04441 −0.453833
\(46\) 2.17008 0.319961
\(47\) −7.36640 −1.07450 −0.537250 0.843423i \(-0.680537\pi\)
−0.537250 + 0.843423i \(0.680537\pi\)
\(48\) −2.51956 −0.363667
\(49\) −6.99998 −0.999997
\(50\) −4.17323 −0.590184
\(51\) −5.24444 −0.734369
\(52\) 1.45203 0.201361
\(53\) 10.1099 1.38870 0.694352 0.719636i \(-0.255691\pi\)
0.694352 + 0.719636i \(0.255691\pi\)
\(54\) −0.877281 −0.119383
\(55\) −2.78206 −0.375132
\(56\) 0.00482385 0.000644614 0
\(57\) 14.5822 1.93146
\(58\) −3.09812 −0.406804
\(59\) 8.55161 1.11332 0.556662 0.830739i \(-0.312082\pi\)
0.556662 + 0.830739i \(0.312082\pi\)
\(60\) 2.29096 0.295762
\(61\) 13.6179 1.74360 0.871798 0.489866i \(-0.162954\pi\)
0.871798 + 0.489866i \(0.162954\pi\)
\(62\) 4.31573 0.548098
\(63\) 0.0161512 0.00203485
\(64\) 1.00000 0.125000
\(65\) −1.32029 −0.163762
\(66\) −7.70900 −0.948912
\(67\) 11.6157 1.41908 0.709540 0.704665i \(-0.248903\pi\)
0.709540 + 0.704665i \(0.248903\pi\)
\(68\) 2.08149 0.252418
\(69\) −5.46765 −0.658227
\(70\) −0.00438618 −0.000524249 0
\(71\) 4.96073 0.588730 0.294365 0.955693i \(-0.404892\pi\)
0.294365 + 0.955693i \(0.404892\pi\)
\(72\) 3.34819 0.394588
\(73\) 15.4576 1.80917 0.904585 0.426294i \(-0.140181\pi\)
0.904585 + 0.426294i \(0.140181\pi\)
\(74\) −3.76423 −0.437582
\(75\) 10.5147 1.21413
\(76\) −5.78760 −0.663883
\(77\) 0.0147593 0.00168198
\(78\) −3.65848 −0.414242
\(79\) −6.72488 −0.756608 −0.378304 0.925681i \(-0.623493\pi\)
−0.378304 + 0.925681i \(0.623493\pi\)
\(80\) −0.909270 −0.101659
\(81\) −7.83420 −0.870467
\(82\) −12.6995 −1.40242
\(83\) −1.12077 −0.123020 −0.0615102 0.998106i \(-0.519592\pi\)
−0.0615102 + 0.998106i \(0.519592\pi\)
\(84\) −0.0121540 −0.00132611
\(85\) −1.89264 −0.205285
\(86\) −11.8078 −1.27327
\(87\) 7.80591 0.836882
\(88\) 3.05966 0.326161
\(89\) 2.64423 0.280288 0.140144 0.990131i \(-0.455243\pi\)
0.140144 + 0.990131i \(0.455243\pi\)
\(90\) −3.04441 −0.320909
\(91\) 0.00700439 0.000734259 0
\(92\) 2.17008 0.226246
\(93\) −10.8737 −1.12756
\(94\) −7.36640 −0.759786
\(95\) 5.26249 0.539920
\(96\) −2.51956 −0.257152
\(97\) 12.7829 1.29790 0.648952 0.760829i \(-0.275208\pi\)
0.648952 + 0.760829i \(0.275208\pi\)
\(98\) −6.99998 −0.707104
\(99\) 10.2443 1.02959
\(100\) −4.17323 −0.417323
\(101\) 4.31481 0.429340 0.214670 0.976687i \(-0.431132\pi\)
0.214670 + 0.976687i \(0.431132\pi\)
\(102\) −5.24444 −0.519277
\(103\) 3.31105 0.326248 0.163124 0.986606i \(-0.447843\pi\)
0.163124 + 0.986606i \(0.447843\pi\)
\(104\) 1.45203 0.142383
\(105\) 0.0110513 0.00107849
\(106\) 10.1099 0.981962
\(107\) −15.5758 −1.50577 −0.752884 0.658153i \(-0.771338\pi\)
−0.752884 + 0.658153i \(0.771338\pi\)
\(108\) −0.877281 −0.0844164
\(109\) −9.38773 −0.899182 −0.449591 0.893235i \(-0.648430\pi\)
−0.449591 + 0.893235i \(0.648430\pi\)
\(110\) −2.78206 −0.265259
\(111\) 9.48420 0.900200
\(112\) 0.00482385 0.000455811 0
\(113\) −4.89596 −0.460573 −0.230287 0.973123i \(-0.573966\pi\)
−0.230287 + 0.973123i \(0.573966\pi\)
\(114\) 14.5822 1.36575
\(115\) −1.97319 −0.184001
\(116\) −3.09812 −0.287654
\(117\) 4.86168 0.449462
\(118\) 8.55161 0.787240
\(119\) 0.0100408 0.000920438 0
\(120\) 2.29096 0.209135
\(121\) −1.63849 −0.148953
\(122\) 13.6179 1.23291
\(123\) 31.9971 2.88508
\(124\) 4.31573 0.387564
\(125\) 8.34094 0.746036
\(126\) 0.0161512 0.00143886
\(127\) 12.3403 1.09502 0.547512 0.836798i \(-0.315575\pi\)
0.547512 + 0.836798i \(0.315575\pi\)
\(128\) 1.00000 0.0883883
\(129\) 29.7504 2.61938
\(130\) −1.32029 −0.115797
\(131\) −12.4298 −1.08600 −0.542998 0.839734i \(-0.682711\pi\)
−0.542998 + 0.839734i \(0.682711\pi\)
\(132\) −7.70900 −0.670982
\(133\) −0.0279185 −0.00242084
\(134\) 11.6157 1.00344
\(135\) 0.797685 0.0686538
\(136\) 2.08149 0.178486
\(137\) 0.530161 0.0452947 0.0226474 0.999744i \(-0.492791\pi\)
0.0226474 + 0.999744i \(0.492791\pi\)
\(138\) −5.46765 −0.465437
\(139\) 2.48719 0.210960 0.105480 0.994421i \(-0.466362\pi\)
0.105480 + 0.994421i \(0.466362\pi\)
\(140\) −0.00438618 −0.000370700 0
\(141\) 18.5601 1.56304
\(142\) 4.96073 0.416295
\(143\) 4.44272 0.371519
\(144\) 3.34819 0.279016
\(145\) 2.81703 0.233942
\(146\) 15.4576 1.27928
\(147\) 17.6369 1.45466
\(148\) −3.76423 −0.309418
\(149\) −20.6331 −1.69033 −0.845164 0.534508i \(-0.820497\pi\)
−0.845164 + 0.534508i \(0.820497\pi\)
\(150\) 10.5147 0.858522
\(151\) −0.941015 −0.0765787 −0.0382893 0.999267i \(-0.512191\pi\)
−0.0382893 + 0.999267i \(0.512191\pi\)
\(152\) −5.78760 −0.469436
\(153\) 6.96922 0.563428
\(154\) 0.0147593 0.00118934
\(155\) −3.92416 −0.315196
\(156\) −3.65848 −0.292913
\(157\) −3.93743 −0.314241 −0.157121 0.987579i \(-0.550221\pi\)
−0.157121 + 0.987579i \(0.550221\pi\)
\(158\) −6.72488 −0.535003
\(159\) −25.4725 −2.02010
\(160\) −0.909270 −0.0718841
\(161\) 0.0104681 0.000825005 0
\(162\) −7.83420 −0.615513
\(163\) −21.0093 −1.64557 −0.822786 0.568351i \(-0.807582\pi\)
−0.822786 + 0.568351i \(0.807582\pi\)
\(164\) −12.6995 −0.991663
\(165\) 7.00956 0.545693
\(166\) −1.12077 −0.0869885
\(167\) −24.2258 −1.87465 −0.937325 0.348456i \(-0.886706\pi\)
−0.937325 + 0.348456i \(0.886706\pi\)
\(168\) −0.0121540 −0.000937700 0
\(169\) −10.8916 −0.837816
\(170\) −1.89264 −0.145159
\(171\) −19.3780 −1.48187
\(172\) −11.8078 −0.900335
\(173\) −12.0624 −0.917090 −0.458545 0.888671i \(-0.651629\pi\)
−0.458545 + 0.888671i \(0.651629\pi\)
\(174\) 7.80591 0.591765
\(175\) −0.0201310 −0.00152176
\(176\) 3.05966 0.230630
\(177\) −21.5463 −1.61952
\(178\) 2.64423 0.198194
\(179\) 0.744495 0.0556462 0.0278231 0.999613i \(-0.491142\pi\)
0.0278231 + 0.999613i \(0.491142\pi\)
\(180\) −3.04441 −0.226917
\(181\) −14.5856 −1.08414 −0.542070 0.840333i \(-0.682359\pi\)
−0.542070 + 0.840333i \(0.682359\pi\)
\(182\) 0.00700439 0.000519200 0
\(183\) −34.3112 −2.53635
\(184\) 2.17008 0.159980
\(185\) 3.42270 0.251642
\(186\) −10.8737 −0.797302
\(187\) 6.36865 0.465722
\(188\) −7.36640 −0.537250
\(189\) −0.00423187 −0.000307823 0
\(190\) 5.26249 0.381781
\(191\) 9.11568 0.659588 0.329794 0.944053i \(-0.393021\pi\)
0.329794 + 0.944053i \(0.393021\pi\)
\(192\) −2.51956 −0.181834
\(193\) −13.1995 −0.950121 −0.475061 0.879953i \(-0.657574\pi\)
−0.475061 + 0.879953i \(0.657574\pi\)
\(194\) 12.7829 0.917757
\(195\) 3.32655 0.238219
\(196\) −6.99998 −0.499998
\(197\) −9.82199 −0.699788 −0.349894 0.936789i \(-0.613782\pi\)
−0.349894 + 0.936789i \(0.613782\pi\)
\(198\) 10.2443 0.728032
\(199\) −3.36120 −0.238269 −0.119135 0.992878i \(-0.538012\pi\)
−0.119135 + 0.992878i \(0.538012\pi\)
\(200\) −4.17323 −0.295092
\(201\) −29.2664 −2.06429
\(202\) 4.31481 0.303589
\(203\) −0.0149449 −0.00104893
\(204\) −5.24444 −0.367184
\(205\) 11.5473 0.806496
\(206\) 3.31105 0.230692
\(207\) 7.26583 0.505010
\(208\) 1.45203 0.100680
\(209\) −17.7081 −1.22489
\(210\) 0.0110513 0.000762609 0
\(211\) 16.7356 1.15213 0.576063 0.817405i \(-0.304588\pi\)
0.576063 + 0.817405i \(0.304588\pi\)
\(212\) 10.1099 0.694352
\(213\) −12.4989 −0.856408
\(214\) −15.5758 −1.06474
\(215\) 10.7365 0.732220
\(216\) −0.877281 −0.0596914
\(217\) 0.0208184 0.00141325
\(218\) −9.38773 −0.635818
\(219\) −38.9462 −2.63174
\(220\) −2.78206 −0.187566
\(221\) 3.02239 0.203308
\(222\) 9.48420 0.636538
\(223\) 9.21293 0.616943 0.308472 0.951234i \(-0.400183\pi\)
0.308472 + 0.951234i \(0.400183\pi\)
\(224\) 0.00482385 0.000322307 0
\(225\) −13.9728 −0.931517
\(226\) −4.89596 −0.325674
\(227\) −6.50751 −0.431919 −0.215959 0.976402i \(-0.569288\pi\)
−0.215959 + 0.976402i \(0.569288\pi\)
\(228\) 14.5822 0.965731
\(229\) 5.19735 0.343451 0.171725 0.985145i \(-0.445066\pi\)
0.171725 + 0.985145i \(0.445066\pi\)
\(230\) −1.97319 −0.130108
\(231\) −0.0371871 −0.00244673
\(232\) −3.09812 −0.203402
\(233\) −16.1368 −1.05716 −0.528579 0.848884i \(-0.677275\pi\)
−0.528579 + 0.848884i \(0.677275\pi\)
\(234\) 4.86168 0.317818
\(235\) 6.69805 0.436932
\(236\) 8.55161 0.556662
\(237\) 16.9437 1.10061
\(238\) 0.0100408 0.000650848 0
\(239\) 17.1520 1.10947 0.554735 0.832027i \(-0.312820\pi\)
0.554735 + 0.832027i \(0.312820\pi\)
\(240\) 2.29096 0.147881
\(241\) −15.1272 −0.974428 −0.487214 0.873283i \(-0.661987\pi\)
−0.487214 + 0.873283i \(0.661987\pi\)
\(242\) −1.63849 −0.105326
\(243\) 22.3706 1.43507
\(244\) 13.6179 0.871798
\(245\) 6.36487 0.406636
\(246\) 31.9971 2.04006
\(247\) −8.40378 −0.534720
\(248\) 4.31573 0.274049
\(249\) 2.82385 0.178954
\(250\) 8.34094 0.527527
\(251\) 6.19085 0.390763 0.195382 0.980727i \(-0.437405\pi\)
0.195382 + 0.980727i \(0.437405\pi\)
\(252\) 0.0161512 0.00101743
\(253\) 6.63970 0.417434
\(254\) 12.3403 0.774299
\(255\) 4.76861 0.298622
\(256\) 1.00000 0.0625000
\(257\) 4.43236 0.276483 0.138242 0.990399i \(-0.455855\pi\)
0.138242 + 0.990399i \(0.455855\pi\)
\(258\) 29.7504 1.85218
\(259\) −0.0181581 −0.00112829
\(260\) −1.32029 −0.0818808
\(261\) −10.3731 −0.642079
\(262\) −12.4298 −0.767915
\(263\) −30.6784 −1.89171 −0.945855 0.324588i \(-0.894774\pi\)
−0.945855 + 0.324588i \(0.894774\pi\)
\(264\) −7.70900 −0.474456
\(265\) −9.19264 −0.564699
\(266\) −0.0279185 −0.00171179
\(267\) −6.66231 −0.407727
\(268\) 11.6157 0.709540
\(269\) −17.5567 −1.07045 −0.535227 0.844709i \(-0.679774\pi\)
−0.535227 + 0.844709i \(0.679774\pi\)
\(270\) 0.797685 0.0485456
\(271\) −13.8240 −0.839747 −0.419873 0.907583i \(-0.637926\pi\)
−0.419873 + 0.907583i \(0.637926\pi\)
\(272\) 2.08149 0.126209
\(273\) −0.0176480 −0.00106810
\(274\) 0.530161 0.0320282
\(275\) −12.7687 −0.769979
\(276\) −5.46765 −0.329114
\(277\) 18.9453 1.13831 0.569156 0.822229i \(-0.307270\pi\)
0.569156 + 0.822229i \(0.307270\pi\)
\(278\) 2.48719 0.149171
\(279\) 14.4499 0.865092
\(280\) −0.00438618 −0.000262124 0
\(281\) 3.09691 0.184746 0.0923730 0.995724i \(-0.470555\pi\)
0.0923730 + 0.995724i \(0.470555\pi\)
\(282\) 18.5601 1.10524
\(283\) 13.7990 0.820265 0.410133 0.912026i \(-0.365482\pi\)
0.410133 + 0.912026i \(0.365482\pi\)
\(284\) 4.96073 0.294365
\(285\) −13.2592 −0.785405
\(286\) 4.44272 0.262704
\(287\) −0.0612604 −0.00361609
\(288\) 3.34819 0.197294
\(289\) −12.6674 −0.745141
\(290\) 2.81703 0.165422
\(291\) −32.2072 −1.88802
\(292\) 15.4576 0.904585
\(293\) −29.6938 −1.73473 −0.867364 0.497674i \(-0.834188\pi\)
−0.867364 + 0.497674i \(0.834188\pi\)
\(294\) 17.6369 1.02860
\(295\) −7.77572 −0.452720
\(296\) −3.76423 −0.218791
\(297\) −2.68418 −0.155752
\(298\) −20.6331 −1.19524
\(299\) 3.15102 0.182228
\(300\) 10.5147 0.607067
\(301\) −0.0569590 −0.00328306
\(302\) −0.941015 −0.0541493
\(303\) −10.8714 −0.624548
\(304\) −5.78760 −0.331942
\(305\) −12.3824 −0.709012
\(306\) 6.96922 0.398404
\(307\) 10.1992 0.582097 0.291048 0.956708i \(-0.405996\pi\)
0.291048 + 0.956708i \(0.405996\pi\)
\(308\) 0.0147593 0.000840991 0
\(309\) −8.34240 −0.474583
\(310\) −3.92416 −0.222878
\(311\) 27.9822 1.58673 0.793364 0.608748i \(-0.208328\pi\)
0.793364 + 0.608748i \(0.208328\pi\)
\(312\) −3.65848 −0.207121
\(313\) 3.27472 0.185098 0.0925492 0.995708i \(-0.470498\pi\)
0.0925492 + 0.995708i \(0.470498\pi\)
\(314\) −3.93743 −0.222202
\(315\) −0.0146858 −0.000827449 0
\(316\) −6.72488 −0.378304
\(317\) 5.36778 0.301484 0.150742 0.988573i \(-0.451834\pi\)
0.150742 + 0.988573i \(0.451834\pi\)
\(318\) −25.4725 −1.42843
\(319\) −9.47920 −0.530733
\(320\) −0.909270 −0.0508297
\(321\) 39.2441 2.19039
\(322\) 0.0104681 0.000583366 0
\(323\) −12.0468 −0.670304
\(324\) −7.83420 −0.435233
\(325\) −6.05966 −0.336130
\(326\) −21.0093 −1.16360
\(327\) 23.6530 1.30801
\(328\) −12.6995 −0.701212
\(329\) −0.0355344 −0.00195908
\(330\) 7.00956 0.385864
\(331\) −22.9150 −1.25952 −0.629761 0.776789i \(-0.716847\pi\)
−0.629761 + 0.776789i \(0.716847\pi\)
\(332\) −1.12077 −0.0615102
\(333\) −12.6033 −0.690659
\(334\) −24.2258 −1.32558
\(335\) −10.5618 −0.577051
\(336\) −0.0121540 −0.000663054 0
\(337\) −30.9426 −1.68555 −0.842776 0.538265i \(-0.819080\pi\)
−0.842776 + 0.538265i \(0.819080\pi\)
\(338\) −10.8916 −0.592425
\(339\) 12.3357 0.669981
\(340\) −1.89264 −0.102643
\(341\) 13.2047 0.715073
\(342\) −19.3780 −1.04784
\(343\) −0.0675338 −0.00364648
\(344\) −11.8078 −0.636633
\(345\) 4.97157 0.267660
\(346\) −12.0624 −0.648481
\(347\) 7.59180 0.407549 0.203775 0.979018i \(-0.434679\pi\)
0.203775 + 0.979018i \(0.434679\pi\)
\(348\) 7.80591 0.418441
\(349\) 24.4006 1.30613 0.653066 0.757301i \(-0.273482\pi\)
0.653066 + 0.757301i \(0.273482\pi\)
\(350\) −0.0201310 −0.00107605
\(351\) −1.27384 −0.0679925
\(352\) 3.05966 0.163080
\(353\) 17.3119 0.921417 0.460709 0.887551i \(-0.347595\pi\)
0.460709 + 0.887551i \(0.347595\pi\)
\(354\) −21.5463 −1.14517
\(355\) −4.51064 −0.239400
\(356\) 2.64423 0.140144
\(357\) −0.0252984 −0.00133893
\(358\) 0.744495 0.0393478
\(359\) 24.9744 1.31810 0.659050 0.752099i \(-0.270959\pi\)
0.659050 + 0.752099i \(0.270959\pi\)
\(360\) −3.04441 −0.160454
\(361\) 14.4963 0.762964
\(362\) −14.5856 −0.766602
\(363\) 4.12826 0.216678
\(364\) 0.00700439 0.000367130 0
\(365\) −14.0551 −0.735677
\(366\) −34.3112 −1.79347
\(367\) −4.24439 −0.221555 −0.110778 0.993845i \(-0.535334\pi\)
−0.110778 + 0.993845i \(0.535334\pi\)
\(368\) 2.17008 0.113123
\(369\) −42.5203 −2.21352
\(370\) 3.42270 0.177938
\(371\) 0.0487687 0.00253195
\(372\) −10.8737 −0.563778
\(373\) −5.26135 −0.272423 −0.136211 0.990680i \(-0.543493\pi\)
−0.136211 + 0.990680i \(0.543493\pi\)
\(374\) 6.36865 0.329315
\(375\) −21.0155 −1.08524
\(376\) −7.36640 −0.379893
\(377\) −4.49857 −0.231688
\(378\) −0.00423187 −0.000217664 0
\(379\) 6.69263 0.343777 0.171889 0.985116i \(-0.445013\pi\)
0.171889 + 0.985116i \(0.445013\pi\)
\(380\) 5.26249 0.269960
\(381\) −31.0921 −1.59290
\(382\) 9.11568 0.466399
\(383\) 4.64020 0.237103 0.118552 0.992948i \(-0.462175\pi\)
0.118552 + 0.992948i \(0.462175\pi\)
\(384\) −2.51956 −0.128576
\(385\) −0.0134202 −0.000683958 0
\(386\) −13.1995 −0.671837
\(387\) −39.5347 −2.00966
\(388\) 12.7829 0.648952
\(389\) 12.0354 0.610217 0.305108 0.952318i \(-0.401307\pi\)
0.305108 + 0.952318i \(0.401307\pi\)
\(390\) 3.32655 0.168446
\(391\) 4.51700 0.228434
\(392\) −6.99998 −0.353552
\(393\) 31.3176 1.57977
\(394\) −9.82199 −0.494825
\(395\) 6.11473 0.307665
\(396\) 10.2443 0.514796
\(397\) −1.63041 −0.0818277 −0.0409138 0.999163i \(-0.513027\pi\)
−0.0409138 + 0.999163i \(0.513027\pi\)
\(398\) −3.36120 −0.168482
\(399\) 0.0703424 0.00352153
\(400\) −4.17323 −0.208661
\(401\) −33.0363 −1.64975 −0.824876 0.565313i \(-0.808755\pi\)
−0.824876 + 0.565313i \(0.808755\pi\)
\(402\) −29.2664 −1.45967
\(403\) 6.26658 0.312161
\(404\) 4.31481 0.214670
\(405\) 7.12340 0.353965
\(406\) −0.0149449 −0.000741702 0
\(407\) −11.5173 −0.570889
\(408\) −5.24444 −0.259639
\(409\) −14.6760 −0.725680 −0.362840 0.931851i \(-0.618193\pi\)
−0.362840 + 0.931851i \(0.618193\pi\)
\(410\) 11.5473 0.570279
\(411\) −1.33577 −0.0658889
\(412\) 3.31105 0.163124
\(413\) 0.0412517 0.00202986
\(414\) 7.26583 0.357096
\(415\) 1.01908 0.0500247
\(416\) 1.45203 0.0711917
\(417\) −6.26662 −0.306877
\(418\) −17.7081 −0.866131
\(419\) −3.01023 −0.147059 −0.0735297 0.997293i \(-0.523426\pi\)
−0.0735297 + 0.997293i \(0.523426\pi\)
\(420\) 0.0110513 0.000539246 0
\(421\) 30.4712 1.48508 0.742539 0.669803i \(-0.233622\pi\)
0.742539 + 0.669803i \(0.233622\pi\)
\(422\) 16.7356 0.814676
\(423\) −24.6641 −1.19921
\(424\) 10.1099 0.490981
\(425\) −8.68654 −0.421359
\(426\) −12.4989 −0.605572
\(427\) 0.0656908 0.00317900
\(428\) −15.5758 −0.752884
\(429\) −11.1937 −0.540438
\(430\) 10.7365 0.517758
\(431\) −28.1569 −1.35627 −0.678135 0.734938i \(-0.737211\pi\)
−0.678135 + 0.734938i \(0.737211\pi\)
\(432\) −0.877281 −0.0422082
\(433\) −24.9466 −1.19886 −0.599429 0.800428i \(-0.704606\pi\)
−0.599429 + 0.800428i \(0.704606\pi\)
\(434\) 0.0208184 0.000999317 0
\(435\) −7.09768 −0.340308
\(436\) −9.38773 −0.449591
\(437\) −12.5595 −0.600805
\(438\) −38.9462 −1.86092
\(439\) 2.28144 0.108887 0.0544437 0.998517i \(-0.482661\pi\)
0.0544437 + 0.998517i \(0.482661\pi\)
\(440\) −2.78206 −0.132629
\(441\) −23.4372 −1.11606
\(442\) 3.02239 0.143760
\(443\) 10.8977 0.517765 0.258882 0.965909i \(-0.416646\pi\)
0.258882 + 0.965909i \(0.416646\pi\)
\(444\) 9.48420 0.450100
\(445\) −2.40432 −0.113976
\(446\) 9.21293 0.436245
\(447\) 51.9863 2.45887
\(448\) 0.00482385 0.000227906 0
\(449\) −25.2566 −1.19193 −0.595966 0.803010i \(-0.703231\pi\)
−0.595966 + 0.803010i \(0.703231\pi\)
\(450\) −13.9728 −0.658682
\(451\) −38.8561 −1.82966
\(452\) −4.89596 −0.230287
\(453\) 2.37094 0.111397
\(454\) −6.50751 −0.305413
\(455\) −0.00636888 −0.000298578 0
\(456\) 14.5822 0.682875
\(457\) −28.0112 −1.31031 −0.655155 0.755494i \(-0.727397\pi\)
−0.655155 + 0.755494i \(0.727397\pi\)
\(458\) 5.19735 0.242856
\(459\) −1.82605 −0.0852328
\(460\) −1.97319 −0.0920003
\(461\) −42.3588 −1.97285 −0.986424 0.164220i \(-0.947489\pi\)
−0.986424 + 0.164220i \(0.947489\pi\)
\(462\) −0.0371871 −0.00173010
\(463\) −9.55174 −0.443907 −0.221953 0.975057i \(-0.571243\pi\)
−0.221953 + 0.975057i \(0.571243\pi\)
\(464\) −3.09812 −0.143827
\(465\) 9.88717 0.458507
\(466\) −16.1368 −0.747523
\(467\) 22.0439 1.02007 0.510034 0.860154i \(-0.329633\pi\)
0.510034 + 0.860154i \(0.329633\pi\)
\(468\) 4.86168 0.224731
\(469\) 0.0560322 0.00258733
\(470\) 6.69805 0.308958
\(471\) 9.92061 0.457117
\(472\) 8.55161 0.393620
\(473\) −36.1278 −1.66116
\(474\) 16.9437 0.778252
\(475\) 24.1530 1.10821
\(476\) 0.0100408 0.000460219 0
\(477\) 33.8499 1.54988
\(478\) 17.1520 0.784514
\(479\) 11.1450 0.509227 0.254614 0.967043i \(-0.418052\pi\)
0.254614 + 0.967043i \(0.418052\pi\)
\(480\) 2.29096 0.104568
\(481\) −5.46578 −0.249218
\(482\) −15.1272 −0.689025
\(483\) −0.0263751 −0.00120011
\(484\) −1.63849 −0.0744766
\(485\) −11.6231 −0.527777
\(486\) 22.3706 1.01475
\(487\) −21.3065 −0.965488 −0.482744 0.875762i \(-0.660360\pi\)
−0.482744 + 0.875762i \(0.660360\pi\)
\(488\) 13.6179 0.616454
\(489\) 52.9341 2.39376
\(490\) 6.36487 0.287535
\(491\) −16.8422 −0.760080 −0.380040 0.924970i \(-0.624090\pi\)
−0.380040 + 0.924970i \(0.624090\pi\)
\(492\) 31.9971 1.44254
\(493\) −6.44871 −0.290435
\(494\) −8.40378 −0.378104
\(495\) −9.31485 −0.418671
\(496\) 4.31573 0.193782
\(497\) 0.0239298 0.00107340
\(498\) 2.82385 0.126540
\(499\) −3.01941 −0.135167 −0.0675837 0.997714i \(-0.521529\pi\)
−0.0675837 + 0.997714i \(0.521529\pi\)
\(500\) 8.34094 0.373018
\(501\) 61.0384 2.72700
\(502\) 6.19085 0.276311
\(503\) 2.51457 0.112119 0.0560595 0.998427i \(-0.482146\pi\)
0.0560595 + 0.998427i \(0.482146\pi\)
\(504\) 0.0161512 0.000719430 0
\(505\) −3.92333 −0.174586
\(506\) 6.63970 0.295171
\(507\) 27.4421 1.21874
\(508\) 12.3403 0.547512
\(509\) 33.0177 1.46349 0.731743 0.681581i \(-0.238707\pi\)
0.731743 + 0.681581i \(0.238707\pi\)
\(510\) 4.76861 0.211158
\(511\) 0.0745649 0.00329856
\(512\) 1.00000 0.0441942
\(513\) 5.07735 0.224171
\(514\) 4.43236 0.195503
\(515\) −3.01064 −0.132665
\(516\) 29.7504 1.30969
\(517\) −22.5387 −0.991250
\(518\) −0.0181581 −0.000797820 0
\(519\) 30.3921 1.33406
\(520\) −1.32029 −0.0578985
\(521\) 19.7960 0.867280 0.433640 0.901086i \(-0.357229\pi\)
0.433640 + 0.901086i \(0.357229\pi\)
\(522\) −10.3731 −0.454018
\(523\) −34.9545 −1.52846 −0.764228 0.644946i \(-0.776880\pi\)
−0.764228 + 0.644946i \(0.776880\pi\)
\(524\) −12.4298 −0.542998
\(525\) 0.0507214 0.00221366
\(526\) −30.6784 −1.33764
\(527\) 8.98315 0.391312
\(528\) −7.70900 −0.335491
\(529\) −18.2908 −0.795250
\(530\) −9.19264 −0.399303
\(531\) 28.6324 1.24254
\(532\) −0.0279185 −0.00121042
\(533\) −18.4401 −0.798728
\(534\) −6.66231 −0.288306
\(535\) 14.1626 0.612302
\(536\) 11.6157 0.501720
\(537\) −1.87580 −0.0809467
\(538\) −17.5567 −0.756925
\(539\) −21.4175 −0.922519
\(540\) 0.797685 0.0343269
\(541\) −18.2568 −0.784921 −0.392460 0.919769i \(-0.628376\pi\)
−0.392460 + 0.919769i \(0.628376\pi\)
\(542\) −13.8240 −0.593791
\(543\) 36.7493 1.57706
\(544\) 2.08149 0.0892432
\(545\) 8.53598 0.365641
\(546\) −0.0176480 −0.000755264 0
\(547\) −0.439760 −0.0188028 −0.00940140 0.999956i \(-0.502993\pi\)
−0.00940140 + 0.999956i \(0.502993\pi\)
\(548\) 0.530161 0.0226474
\(549\) 45.5953 1.94596
\(550\) −12.7687 −0.544457
\(551\) 17.9307 0.763874
\(552\) −5.46765 −0.232718
\(553\) −0.0324398 −0.00137948
\(554\) 18.9453 0.804909
\(555\) −8.62370 −0.366055
\(556\) 2.48719 0.105480
\(557\) −10.4775 −0.443946 −0.221973 0.975053i \(-0.571250\pi\)
−0.221973 + 0.975053i \(0.571250\pi\)
\(558\) 14.4499 0.611712
\(559\) −17.1453 −0.725168
\(560\) −0.00438618 −0.000185350 0
\(561\) −16.0462 −0.677471
\(562\) 3.09691 0.130635
\(563\) 6.47141 0.272737 0.136369 0.990658i \(-0.456457\pi\)
0.136369 + 0.990658i \(0.456457\pi\)
\(564\) 18.5601 0.781521
\(565\) 4.45175 0.187286
\(566\) 13.7990 0.580015
\(567\) −0.0377910 −0.00158707
\(568\) 4.96073 0.208148
\(569\) −14.6877 −0.615739 −0.307870 0.951429i \(-0.599616\pi\)
−0.307870 + 0.951429i \(0.599616\pi\)
\(570\) −13.2592 −0.555365
\(571\) 45.6164 1.90898 0.954492 0.298235i \(-0.0963979\pi\)
0.954492 + 0.298235i \(0.0963979\pi\)
\(572\) 4.44272 0.185760
\(573\) −22.9675 −0.959482
\(574\) −0.0612604 −0.00255696
\(575\) −9.05623 −0.377671
\(576\) 3.34819 0.139508
\(577\) −39.7662 −1.65549 −0.827744 0.561107i \(-0.810376\pi\)
−0.827744 + 0.561107i \(0.810376\pi\)
\(578\) −12.6674 −0.526894
\(579\) 33.2570 1.38211
\(580\) 2.81703 0.116971
\(581\) −0.00540642 −0.000224296 0
\(582\) −32.2072 −1.33503
\(583\) 30.9329 1.28111
\(584\) 15.4576 0.639638
\(585\) −4.42058 −0.182768
\(586\) −29.6938 −1.22664
\(587\) −31.7503 −1.31048 −0.655238 0.755423i \(-0.727432\pi\)
−0.655238 + 0.755423i \(0.727432\pi\)
\(588\) 17.6369 0.727332
\(589\) −24.9777 −1.02919
\(590\) −7.77572 −0.320121
\(591\) 24.7471 1.01796
\(592\) −3.76423 −0.154709
\(593\) −36.0972 −1.48233 −0.741166 0.671322i \(-0.765727\pi\)
−0.741166 + 0.671322i \(0.765727\pi\)
\(594\) −2.68418 −0.110133
\(595\) −0.00912980 −0.000374285 0
\(596\) −20.6331 −0.845164
\(597\) 8.46876 0.346603
\(598\) 3.15102 0.128855
\(599\) −14.9244 −0.609794 −0.304897 0.952385i \(-0.598622\pi\)
−0.304897 + 0.952385i \(0.598622\pi\)
\(600\) 10.5147 0.429261
\(601\) 7.89652 0.322106 0.161053 0.986946i \(-0.448511\pi\)
0.161053 + 0.986946i \(0.448511\pi\)
\(602\) −0.0569590 −0.00232147
\(603\) 38.8914 1.58378
\(604\) −0.941015 −0.0382893
\(605\) 1.48983 0.0605700
\(606\) −10.8714 −0.441622
\(607\) −4.08812 −0.165932 −0.0829658 0.996552i \(-0.526439\pi\)
−0.0829658 + 0.996552i \(0.526439\pi\)
\(608\) −5.78760 −0.234718
\(609\) 0.0376545 0.00152584
\(610\) −12.3824 −0.501347
\(611\) −10.6962 −0.432724
\(612\) 6.96922 0.281714
\(613\) −27.2340 −1.09997 −0.549986 0.835174i \(-0.685367\pi\)
−0.549986 + 0.835174i \(0.685367\pi\)
\(614\) 10.1992 0.411605
\(615\) −29.0940 −1.17318
\(616\) 0.0147593 0.000594671 0
\(617\) −39.7334 −1.59961 −0.799803 0.600262i \(-0.795063\pi\)
−0.799803 + 0.600262i \(0.795063\pi\)
\(618\) −8.34240 −0.335581
\(619\) −12.8849 −0.517887 −0.258943 0.965892i \(-0.583374\pi\)
−0.258943 + 0.965892i \(0.583374\pi\)
\(620\) −3.92416 −0.157598
\(621\) −1.90377 −0.0763956
\(622\) 27.9822 1.12199
\(623\) 0.0127554 0.000511034 0
\(624\) −3.65848 −0.146457
\(625\) 13.2820 0.531279
\(626\) 3.27472 0.130884
\(627\) 44.6166 1.78182
\(628\) −3.93743 −0.157121
\(629\) −7.83520 −0.312410
\(630\) −0.0146858 −0.000585095 0
\(631\) 43.1708 1.71860 0.859301 0.511470i \(-0.170899\pi\)
0.859301 + 0.511470i \(0.170899\pi\)
\(632\) −6.72488 −0.267501
\(633\) −42.1664 −1.67596
\(634\) 5.36778 0.213182
\(635\) −11.2207 −0.445278
\(636\) −25.4725 −1.01005
\(637\) −10.1642 −0.402720
\(638\) −9.47920 −0.375285
\(639\) 16.6095 0.657060
\(640\) −0.909270 −0.0359420
\(641\) −0.858958 −0.0339268 −0.0169634 0.999856i \(-0.505400\pi\)
−0.0169634 + 0.999856i \(0.505400\pi\)
\(642\) 39.2441 1.54884
\(643\) −18.9536 −0.747455 −0.373728 0.927539i \(-0.621920\pi\)
−0.373728 + 0.927539i \(0.621920\pi\)
\(644\) 0.0104681 0.000412502 0
\(645\) −27.0512 −1.06514
\(646\) −12.0468 −0.473976
\(647\) 43.9905 1.72944 0.864722 0.502251i \(-0.167495\pi\)
0.864722 + 0.502251i \(0.167495\pi\)
\(648\) −7.83420 −0.307756
\(649\) 26.1650 1.02707
\(650\) −6.05966 −0.237679
\(651\) −0.0524533 −0.00205581
\(652\) −21.0093 −0.822786
\(653\) 13.5271 0.529356 0.264678 0.964337i \(-0.414734\pi\)
0.264678 + 0.964337i \(0.414734\pi\)
\(654\) 23.6530 0.924904
\(655\) 11.3020 0.441607
\(656\) −12.6995 −0.495832
\(657\) 51.7548 2.01915
\(658\) −0.0355344 −0.00138528
\(659\) 15.5526 0.605844 0.302922 0.953015i \(-0.402038\pi\)
0.302922 + 0.953015i \(0.402038\pi\)
\(660\) 7.00956 0.272847
\(661\) 5.45183 0.212051 0.106026 0.994363i \(-0.466187\pi\)
0.106026 + 0.994363i \(0.466187\pi\)
\(662\) −22.9150 −0.890616
\(663\) −7.61510 −0.295746
\(664\) −1.12077 −0.0434943
\(665\) 0.0253855 0.000984406 0
\(666\) −12.6033 −0.488369
\(667\) −6.72317 −0.260322
\(668\) −24.2258 −0.937325
\(669\) −23.2125 −0.897448
\(670\) −10.5618 −0.408037
\(671\) 41.6662 1.60850
\(672\) −0.0121540 −0.000468850 0
\(673\) 3.47368 0.133901 0.0669504 0.997756i \(-0.478673\pi\)
0.0669504 + 0.997756i \(0.478673\pi\)
\(674\) −30.9426 −1.19186
\(675\) 3.66109 0.140916
\(676\) −10.8916 −0.418908
\(677\) −37.2915 −1.43323 −0.716614 0.697470i \(-0.754309\pi\)
−0.716614 + 0.697470i \(0.754309\pi\)
\(678\) 12.3357 0.473748
\(679\) 0.0616627 0.00236640
\(680\) −1.89264 −0.0725793
\(681\) 16.3961 0.628299
\(682\) 13.2047 0.505633
\(683\) 33.9930 1.30071 0.650353 0.759632i \(-0.274621\pi\)
0.650353 + 0.759632i \(0.274621\pi\)
\(684\) −19.3780 −0.740935
\(685\) −0.482060 −0.0184186
\(686\) −0.0675338 −0.00257845
\(687\) −13.0950 −0.499607
\(688\) −11.8078 −0.450167
\(689\) 14.6799 0.559260
\(690\) 4.97157 0.189264
\(691\) −1.37786 −0.0524164 −0.0262082 0.999657i \(-0.508343\pi\)
−0.0262082 + 0.999657i \(0.508343\pi\)
\(692\) −12.0624 −0.458545
\(693\) 0.0494170 0.00187720
\(694\) 7.59180 0.288181
\(695\) −2.26152 −0.0857844
\(696\) 7.80591 0.295882
\(697\) −26.4339 −1.00125
\(698\) 24.4006 0.923575
\(699\) 40.6577 1.53781
\(700\) −0.0201310 −0.000760881 0
\(701\) 17.4152 0.657762 0.328881 0.944371i \(-0.393329\pi\)
0.328881 + 0.944371i \(0.393329\pi\)
\(702\) −1.27384 −0.0480780
\(703\) 21.7858 0.821668
\(704\) 3.05966 0.115315
\(705\) −16.8761 −0.635592
\(706\) 17.3119 0.651540
\(707\) 0.0208140 0.000782792 0
\(708\) −21.5463 −0.809760
\(709\) 7.29196 0.273855 0.136928 0.990581i \(-0.456277\pi\)
0.136928 + 0.990581i \(0.456277\pi\)
\(710\) −4.51064 −0.169281
\(711\) −22.5162 −0.844422
\(712\) 2.64423 0.0990969
\(713\) 9.36548 0.350740
\(714\) −0.0252984 −0.000946769 0
\(715\) −4.03963 −0.151074
\(716\) 0.744495 0.0278231
\(717\) −43.2155 −1.61391
\(718\) 24.9744 0.932038
\(719\) 2.69508 0.100509 0.0502547 0.998736i \(-0.483997\pi\)
0.0502547 + 0.998736i \(0.483997\pi\)
\(720\) −3.04441 −0.113458
\(721\) 0.0159720 0.000594830 0
\(722\) 14.4963 0.539497
\(723\) 38.1139 1.41747
\(724\) −14.5856 −0.542070
\(725\) 12.9292 0.480178
\(726\) 4.12826 0.153214
\(727\) −2.85675 −0.105951 −0.0529754 0.998596i \(-0.516871\pi\)
−0.0529754 + 0.998596i \(0.516871\pi\)
\(728\) 0.00700439 0.000259600 0
\(729\) −32.8615 −1.21709
\(730\) −14.0551 −0.520202
\(731\) −24.5778 −0.909042
\(732\) −34.3112 −1.26818
\(733\) 50.9565 1.88212 0.941060 0.338240i \(-0.109832\pi\)
0.941060 + 0.338240i \(0.109832\pi\)
\(734\) −4.24439 −0.156663
\(735\) −16.0367 −0.591522
\(736\) 2.17008 0.0799902
\(737\) 35.5400 1.30913
\(738\) −42.5203 −1.56519
\(739\) −49.0010 −1.80253 −0.901265 0.433268i \(-0.857360\pi\)
−0.901265 + 0.433268i \(0.857360\pi\)
\(740\) 3.42270 0.125821
\(741\) 21.1738 0.777840
\(742\) 0.0487687 0.00179036
\(743\) −21.4421 −0.786634 −0.393317 0.919403i \(-0.628672\pi\)
−0.393317 + 0.919403i \(0.628672\pi\)
\(744\) −10.8737 −0.398651
\(745\) 18.7610 0.687351
\(746\) −5.26135 −0.192632
\(747\) −3.75254 −0.137298
\(748\) 6.36865 0.232861
\(749\) −0.0751352 −0.00274538
\(750\) −21.0155 −0.767378
\(751\) 13.3972 0.488872 0.244436 0.969665i \(-0.421397\pi\)
0.244436 + 0.969665i \(0.421397\pi\)
\(752\) −7.36640 −0.268625
\(753\) −15.5982 −0.568431
\(754\) −4.49857 −0.163828
\(755\) 0.855636 0.0311398
\(756\) −0.00423187 −0.000153912 0
\(757\) −53.9187 −1.95971 −0.979854 0.199714i \(-0.935999\pi\)
−0.979854 + 0.199714i \(0.935999\pi\)
\(758\) 6.69263 0.243087
\(759\) −16.7291 −0.607229
\(760\) 5.26249 0.190891
\(761\) −39.4432 −1.42981 −0.714907 0.699220i \(-0.753531\pi\)
−0.714907 + 0.699220i \(0.753531\pi\)
\(762\) −31.0921 −1.12635
\(763\) −0.0452850 −0.00163943
\(764\) 9.11568 0.329794
\(765\) −6.33690 −0.229111
\(766\) 4.64020 0.167657
\(767\) 12.4172 0.448360
\(768\) −2.51956 −0.0909168
\(769\) −3.68605 −0.132922 −0.0664611 0.997789i \(-0.521171\pi\)
−0.0664611 + 0.997789i \(0.521171\pi\)
\(770\) −0.0134202 −0.000483631 0
\(771\) −11.1676 −0.402192
\(772\) −13.1995 −0.475061
\(773\) 23.9425 0.861153 0.430577 0.902554i \(-0.358310\pi\)
0.430577 + 0.902554i \(0.358310\pi\)
\(774\) −39.5347 −1.42104
\(775\) −18.0105 −0.646957
\(776\) 12.7829 0.458878
\(777\) 0.0457504 0.00164128
\(778\) 12.0354 0.431489
\(779\) 73.4996 2.63340
\(780\) 3.32655 0.119110
\(781\) 15.1781 0.543117
\(782\) 4.51700 0.161528
\(783\) 2.71792 0.0971307
\(784\) −6.99998 −0.249999
\(785\) 3.58019 0.127782
\(786\) 31.3176 1.11706
\(787\) −6.64066 −0.236714 −0.118357 0.992971i \(-0.537763\pi\)
−0.118357 + 0.992971i \(0.537763\pi\)
\(788\) −9.82199 −0.349894
\(789\) 77.2961 2.75181
\(790\) 6.11473 0.217552
\(791\) −0.0236174 −0.000839737 0
\(792\) 10.2443 0.364016
\(793\) 19.7736 0.702183
\(794\) −1.63041 −0.0578609
\(795\) 23.1614 0.821451
\(796\) −3.36120 −0.119135
\(797\) 17.0863 0.605229 0.302615 0.953113i \(-0.402140\pi\)
0.302615 + 0.953113i \(0.402140\pi\)
\(798\) 0.0703424 0.00249009
\(799\) −15.3331 −0.542446
\(800\) −4.17323 −0.147546
\(801\) 8.85339 0.312819
\(802\) −33.0363 −1.16655
\(803\) 47.2948 1.66900
\(804\) −29.2664 −1.03215
\(805\) −0.00951836 −0.000335478 0
\(806\) 6.26658 0.220731
\(807\) 44.2353 1.55716
\(808\) 4.31481 0.151795
\(809\) 1.20514 0.0423706 0.0211853 0.999776i \(-0.493256\pi\)
0.0211853 + 0.999776i \(0.493256\pi\)
\(810\) 7.12340 0.250291
\(811\) 25.0280 0.878851 0.439425 0.898279i \(-0.355182\pi\)
0.439425 + 0.898279i \(0.355182\pi\)
\(812\) −0.0149449 −0.000524463 0
\(813\) 34.8304 1.22155
\(814\) −11.5173 −0.403679
\(815\) 19.1031 0.669152
\(816\) −5.24444 −0.183592
\(817\) 68.3387 2.39087
\(818\) −14.6760 −0.513133
\(819\) 0.0234520 0.000819479 0
\(820\) 11.5473 0.403248
\(821\) 49.9093 1.74185 0.870923 0.491420i \(-0.163522\pi\)
0.870923 + 0.491420i \(0.163522\pi\)
\(822\) −1.33577 −0.0465905
\(823\) −16.2421 −0.566165 −0.283082 0.959096i \(-0.591357\pi\)
−0.283082 + 0.959096i \(0.591357\pi\)
\(824\) 3.31105 0.115346
\(825\) 32.1714 1.12006
\(826\) 0.0412517 0.00143533
\(827\) −27.6952 −0.963055 −0.481528 0.876431i \(-0.659918\pi\)
−0.481528 + 0.876431i \(0.659918\pi\)
\(828\) 7.26583 0.252505
\(829\) 22.8577 0.793882 0.396941 0.917844i \(-0.370072\pi\)
0.396941 + 0.917844i \(0.370072\pi\)
\(830\) 1.01908 0.0353728
\(831\) −47.7338 −1.65587
\(832\) 1.45203 0.0503402
\(833\) −14.5704 −0.504834
\(834\) −6.26662 −0.216995
\(835\) 22.0278 0.762304
\(836\) −17.7081 −0.612447
\(837\) −3.78611 −0.130867
\(838\) −3.01023 −0.103987
\(839\) 21.9530 0.757902 0.378951 0.925417i \(-0.376285\pi\)
0.378951 + 0.925417i \(0.376285\pi\)
\(840\) 0.0110513 0.000381304 0
\(841\) −19.4016 −0.669022
\(842\) 30.4712 1.05011
\(843\) −7.80285 −0.268744
\(844\) 16.7356 0.576063
\(845\) 9.90341 0.340688
\(846\) −24.6641 −0.847969
\(847\) −0.00790381 −0.000271578 0
\(848\) 10.1099 0.347176
\(849\) −34.7674 −1.19321
\(850\) −8.68654 −0.297946
\(851\) −8.16867 −0.280018
\(852\) −12.4989 −0.428204
\(853\) 7.52913 0.257792 0.128896 0.991658i \(-0.458857\pi\)
0.128896 + 0.991658i \(0.458857\pi\)
\(854\) 0.0656908 0.00224789
\(855\) 17.6198 0.602585
\(856\) −15.5758 −0.532369
\(857\) −30.7690 −1.05105 −0.525524 0.850779i \(-0.676131\pi\)
−0.525524 + 0.850779i \(0.676131\pi\)
\(858\) −11.1937 −0.382147
\(859\) −49.0163 −1.67242 −0.836208 0.548413i \(-0.815232\pi\)
−0.836208 + 0.548413i \(0.815232\pi\)
\(860\) 10.7365 0.366110
\(861\) 0.154349 0.00526021
\(862\) −28.1569 −0.959027
\(863\) 19.5655 0.666019 0.333009 0.942924i \(-0.391936\pi\)
0.333009 + 0.942924i \(0.391936\pi\)
\(864\) −0.877281 −0.0298457
\(865\) 10.9680 0.372924
\(866\) −24.9466 −0.847720
\(867\) 31.9163 1.08393
\(868\) 0.0208184 0.000706624 0
\(869\) −20.5758 −0.697987
\(870\) −7.09768 −0.240634
\(871\) 16.8663 0.571493
\(872\) −9.38773 −0.317909
\(873\) 42.7995 1.44854
\(874\) −12.5595 −0.424833
\(875\) 0.0402354 0.00136021
\(876\) −38.9462 −1.31587
\(877\) −15.8734 −0.536006 −0.268003 0.963418i \(-0.586364\pi\)
−0.268003 + 0.963418i \(0.586364\pi\)
\(878\) 2.28144 0.0769949
\(879\) 74.8153 2.52346
\(880\) −2.78206 −0.0937831
\(881\) −4.84391 −0.163195 −0.0815977 0.996665i \(-0.526002\pi\)
−0.0815977 + 0.996665i \(0.526002\pi\)
\(882\) −23.4372 −0.789173
\(883\) −30.0985 −1.01290 −0.506448 0.862270i \(-0.669042\pi\)
−0.506448 + 0.862270i \(0.669042\pi\)
\(884\) 3.02239 0.101654
\(885\) 19.5914 0.658558
\(886\) 10.8977 0.366115
\(887\) 49.4499 1.66037 0.830183 0.557490i \(-0.188236\pi\)
0.830183 + 0.557490i \(0.188236\pi\)
\(888\) 9.48420 0.318269
\(889\) 0.0595278 0.00199650
\(890\) −2.40432 −0.0805931
\(891\) −23.9700 −0.803025
\(892\) 9.21293 0.308472
\(893\) 42.6338 1.42669
\(894\) 51.9863 1.73868
\(895\) −0.676947 −0.0226278
\(896\) 0.00482385 0.000161154 0
\(897\) −7.93920 −0.265082
\(898\) −25.2566 −0.842823
\(899\) −13.3707 −0.445937
\(900\) −13.9728 −0.465758
\(901\) 21.0437 0.701067
\(902\) −38.8561 −1.29377
\(903\) 0.143512 0.00477577
\(904\) −4.89596 −0.162837
\(905\) 13.2623 0.440852
\(906\) 2.37094 0.0787693
\(907\) −19.0460 −0.632411 −0.316205 0.948691i \(-0.602409\pi\)
−0.316205 + 0.948691i \(0.602409\pi\)
\(908\) −6.50751 −0.215959
\(909\) 14.4468 0.479170
\(910\) −0.00636888 −0.000211126 0
\(911\) 38.7959 1.28537 0.642683 0.766132i \(-0.277821\pi\)
0.642683 + 0.766132i \(0.277821\pi\)
\(912\) 14.5822 0.482865
\(913\) −3.42917 −0.113489
\(914\) −28.0112 −0.926529
\(915\) 31.1981 1.03138
\(916\) 5.19735 0.171725
\(917\) −0.0599595 −0.00198004
\(918\) −1.82605 −0.0602687
\(919\) −25.4502 −0.839523 −0.419762 0.907634i \(-0.637886\pi\)
−0.419762 + 0.907634i \(0.637886\pi\)
\(920\) −1.97319 −0.0650541
\(921\) −25.6974 −0.846759
\(922\) −42.3588 −1.39501
\(923\) 7.20314 0.237094
\(924\) −0.0371871 −0.00122336
\(925\) 15.7090 0.516508
\(926\) −9.55174 −0.313890
\(927\) 11.0860 0.364113
\(928\) −3.09812 −0.101701
\(929\) 9.23192 0.302890 0.151445 0.988466i \(-0.451607\pi\)
0.151445 + 0.988466i \(0.451607\pi\)
\(930\) 9.88717 0.324213
\(931\) 40.5131 1.32776
\(932\) −16.1368 −0.528579
\(933\) −70.5030 −2.30816
\(934\) 22.0439 0.721297
\(935\) −5.79082 −0.189380
\(936\) 4.86168 0.158909
\(937\) 2.92926 0.0956947 0.0478473 0.998855i \(-0.484764\pi\)
0.0478473 + 0.998855i \(0.484764\pi\)
\(938\) 0.0560322 0.00182952
\(939\) −8.25087 −0.269257
\(940\) 6.69805 0.218466
\(941\) 39.0516 1.27305 0.636523 0.771258i \(-0.280372\pi\)
0.636523 + 0.771258i \(0.280372\pi\)
\(942\) 9.92061 0.323231
\(943\) −27.5589 −0.897441
\(944\) 8.55161 0.278331
\(945\) 0.00384791 0.000125173 0
\(946\) −36.1278 −1.17462
\(947\) 50.0727 1.62714 0.813572 0.581464i \(-0.197520\pi\)
0.813572 + 0.581464i \(0.197520\pi\)
\(948\) 16.9437 0.550307
\(949\) 22.4449 0.728591
\(950\) 24.1530 0.783626
\(951\) −13.5244 −0.438560
\(952\) 0.0100408 0.000325424 0
\(953\) −29.3196 −0.949754 −0.474877 0.880052i \(-0.657507\pi\)
−0.474877 + 0.880052i \(0.657507\pi\)
\(954\) 33.8499 1.09593
\(955\) −8.28861 −0.268213
\(956\) 17.1520 0.554735
\(957\) 23.8834 0.772042
\(958\) 11.1450 0.360078
\(959\) 0.00255742 8.25834e−5 0
\(960\) 2.29096 0.0739404
\(961\) −12.3745 −0.399176
\(962\) −5.46578 −0.176224
\(963\) −52.1506 −1.68053
\(964\) −15.1272 −0.487214
\(965\) 12.0019 0.386355
\(966\) −0.0263751 −0.000848605 0
\(967\) −31.9281 −1.02674 −0.513370 0.858168i \(-0.671603\pi\)
−0.513370 + 0.858168i \(0.671603\pi\)
\(968\) −1.63849 −0.0526629
\(969\) 30.3527 0.975070
\(970\) −11.6231 −0.373195
\(971\) 47.1387 1.51275 0.756376 0.654137i \(-0.226968\pi\)
0.756376 + 0.654137i \(0.226968\pi\)
\(972\) 22.3706 0.717537
\(973\) 0.0119978 0.000384632 0
\(974\) −21.3065 −0.682703
\(975\) 15.2677 0.488957
\(976\) 13.6179 0.435899
\(977\) 8.47638 0.271183 0.135592 0.990765i \(-0.456706\pi\)
0.135592 + 0.990765i \(0.456706\pi\)
\(978\) 52.9341 1.69265
\(979\) 8.09046 0.258572
\(980\) 6.36487 0.203318
\(981\) −31.4319 −1.00354
\(982\) −16.8422 −0.537457
\(983\) −45.1205 −1.43912 −0.719560 0.694430i \(-0.755657\pi\)
−0.719560 + 0.694430i \(0.755657\pi\)
\(984\) 31.9971 1.02003
\(985\) 8.93084 0.284560
\(986\) −6.44871 −0.205369
\(987\) 0.0895311 0.00284981
\(988\) −8.40378 −0.267360
\(989\) −25.6238 −0.814790
\(990\) −9.31485 −0.296045
\(991\) −23.0820 −0.733223 −0.366611 0.930374i \(-0.619482\pi\)
−0.366611 + 0.930374i \(0.619482\pi\)
\(992\) 4.31573 0.137025
\(993\) 57.7357 1.83219
\(994\) 0.0239298 0.000759008 0
\(995\) 3.05624 0.0968894
\(996\) 2.82385 0.0894770
\(997\) −12.8296 −0.406317 −0.203159 0.979146i \(-0.565121\pi\)
−0.203159 + 0.979146i \(0.565121\pi\)
\(998\) −3.01941 −0.0955778
\(999\) 3.30228 0.104480
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 \(a_p\))