Properties

Label 8002.2.a.d.1.18
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.99879 q^{3}\) \(+1.00000 q^{4}\) \(+2.05838 q^{5}\) \(-1.99879 q^{6}\) \(+2.31041 q^{7}\) \(+1.00000 q^{8}\) \(+0.995149 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.99879 q^{3}\) \(+1.00000 q^{4}\) \(+2.05838 q^{5}\) \(-1.99879 q^{6}\) \(+2.31041 q^{7}\) \(+1.00000 q^{8}\) \(+0.995149 q^{9}\) \(+2.05838 q^{10}\) \(-3.05453 q^{11}\) \(-1.99879 q^{12}\) \(-1.17980 q^{13}\) \(+2.31041 q^{14}\) \(-4.11426 q^{15}\) \(+1.00000 q^{16}\) \(+0.133866 q^{17}\) \(+0.995149 q^{18}\) \(-2.51765 q^{19}\) \(+2.05838 q^{20}\) \(-4.61802 q^{21}\) \(-3.05453 q^{22}\) \(-1.56784 q^{23}\) \(-1.99879 q^{24}\) \(-0.763082 q^{25}\) \(-1.17980 q^{26}\) \(+4.00727 q^{27}\) \(+2.31041 q^{28}\) \(-6.46205 q^{29}\) \(-4.11426 q^{30}\) \(+3.37485 q^{31}\) \(+1.00000 q^{32}\) \(+6.10535 q^{33}\) \(+0.133866 q^{34}\) \(+4.75570 q^{35}\) \(+0.995149 q^{36}\) \(+5.00901 q^{37}\) \(-2.51765 q^{38}\) \(+2.35817 q^{39}\) \(+2.05838 q^{40}\) \(-0.906925 q^{41}\) \(-4.61802 q^{42}\) \(+11.9374 q^{43}\) \(-3.05453 q^{44}\) \(+2.04839 q^{45}\) \(-1.56784 q^{46}\) \(-3.39371 q^{47}\) \(-1.99879 q^{48}\) \(-1.66199 q^{49}\) \(-0.763082 q^{50}\) \(-0.267570 q^{51}\) \(-1.17980 q^{52}\) \(-11.2280 q^{53}\) \(+4.00727 q^{54}\) \(-6.28737 q^{55}\) \(+2.31041 q^{56}\) \(+5.03225 q^{57}\) \(-6.46205 q^{58}\) \(-13.9430 q^{59}\) \(-4.11426 q^{60}\) \(-0.114241 q^{61}\) \(+3.37485 q^{62}\) \(+2.29921 q^{63}\) \(+1.00000 q^{64}\) \(-2.42848 q^{65}\) \(+6.10535 q^{66}\) \(-10.6053 q^{67}\) \(+0.133866 q^{68}\) \(+3.13378 q^{69}\) \(+4.75570 q^{70}\) \(-14.0887 q^{71}\) \(+0.995149 q^{72}\) \(+10.2490 q^{73}\) \(+5.00901 q^{74}\) \(+1.52524 q^{75}\) \(-2.51765 q^{76}\) \(-7.05723 q^{77}\) \(+2.35817 q^{78}\) \(+2.04015 q^{79}\) \(+2.05838 q^{80}\) \(-10.9951 q^{81}\) \(-0.906925 q^{82}\) \(-11.3749 q^{83}\) \(-4.61802 q^{84}\) \(+0.275547 q^{85}\) \(+11.9374 q^{86}\) \(+12.9163 q^{87}\) \(-3.05453 q^{88}\) \(+0.534851 q^{89}\) \(+2.04839 q^{90}\) \(-2.72583 q^{91}\) \(-1.56784 q^{92}\) \(-6.74561 q^{93}\) \(-3.39371 q^{94}\) \(-5.18228 q^{95}\) \(-1.99879 q^{96}\) \(+2.81200 q^{97}\) \(-1.66199 q^{98}\) \(-3.03971 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.99879 −1.15400 −0.577000 0.816744i \(-0.695777\pi\)
−0.577000 + 0.816744i \(0.695777\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.05838 0.920534 0.460267 0.887780i \(-0.347754\pi\)
0.460267 + 0.887780i \(0.347754\pi\)
\(6\) −1.99879 −0.816001
\(7\) 2.31041 0.873254 0.436627 0.899643i \(-0.356173\pi\)
0.436627 + 0.899643i \(0.356173\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.995149 0.331716
\(10\) 2.05838 0.650916
\(11\) −3.05453 −0.920975 −0.460488 0.887666i \(-0.652325\pi\)
−0.460488 + 0.887666i \(0.652325\pi\)
\(12\) −1.99879 −0.577000
\(13\) −1.17980 −0.327218 −0.163609 0.986525i \(-0.552314\pi\)
−0.163609 + 0.986525i \(0.552314\pi\)
\(14\) 2.31041 0.617484
\(15\) −4.11426 −1.06230
\(16\) 1.00000 0.250000
\(17\) 0.133866 0.0324673 0.0162336 0.999868i \(-0.494832\pi\)
0.0162336 + 0.999868i \(0.494832\pi\)
\(18\) 0.995149 0.234559
\(19\) −2.51765 −0.577589 −0.288795 0.957391i \(-0.593254\pi\)
−0.288795 + 0.957391i \(0.593254\pi\)
\(20\) 2.05838 0.460267
\(21\) −4.61802 −1.00774
\(22\) −3.05453 −0.651228
\(23\) −1.56784 −0.326917 −0.163459 0.986550i \(-0.552265\pi\)
−0.163459 + 0.986550i \(0.552265\pi\)
\(24\) −1.99879 −0.408001
\(25\) −0.763082 −0.152616
\(26\) −1.17980 −0.231378
\(27\) 4.00727 0.771199
\(28\) 2.31041 0.436627
\(29\) −6.46205 −1.19997 −0.599986 0.800011i \(-0.704827\pi\)
−0.599986 + 0.800011i \(0.704827\pi\)
\(30\) −4.11426 −0.751157
\(31\) 3.37485 0.606141 0.303070 0.952968i \(-0.401988\pi\)
0.303070 + 0.952968i \(0.401988\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.10535 1.06281
\(34\) 0.133866 0.0229578
\(35\) 4.75570 0.803861
\(36\) 0.995149 0.165858
\(37\) 5.00901 0.823476 0.411738 0.911302i \(-0.364922\pi\)
0.411738 + 0.911302i \(0.364922\pi\)
\(38\) −2.51765 −0.408417
\(39\) 2.35817 0.377610
\(40\) 2.05838 0.325458
\(41\) −0.906925 −0.141638 −0.0708189 0.997489i \(-0.522561\pi\)
−0.0708189 + 0.997489i \(0.522561\pi\)
\(42\) −4.61802 −0.712577
\(43\) 11.9374 1.82044 0.910219 0.414128i \(-0.135913\pi\)
0.910219 + 0.414128i \(0.135913\pi\)
\(44\) −3.05453 −0.460488
\(45\) 2.04839 0.305356
\(46\) −1.56784 −0.231165
\(47\) −3.39371 −0.495024 −0.247512 0.968885i \(-0.579613\pi\)
−0.247512 + 0.968885i \(0.579613\pi\)
\(48\) −1.99879 −0.288500
\(49\) −1.66199 −0.237427
\(50\) −0.763082 −0.107916
\(51\) −0.267570 −0.0374673
\(52\) −1.17980 −0.163609
\(53\) −11.2280 −1.54228 −0.771141 0.636664i \(-0.780314\pi\)
−0.771141 + 0.636664i \(0.780314\pi\)
\(54\) 4.00727 0.545320
\(55\) −6.28737 −0.847789
\(56\) 2.31041 0.308742
\(57\) 5.03225 0.666538
\(58\) −6.46205 −0.848508
\(59\) −13.9430 −1.81522 −0.907611 0.419812i \(-0.862096\pi\)
−0.907611 + 0.419812i \(0.862096\pi\)
\(60\) −4.11426 −0.531148
\(61\) −0.114241 −0.0146270 −0.00731351 0.999973i \(-0.502328\pi\)
−0.00731351 + 0.999973i \(0.502328\pi\)
\(62\) 3.37485 0.428606
\(63\) 2.29921 0.289673
\(64\) 1.00000 0.125000
\(65\) −2.42848 −0.301216
\(66\) 6.10535 0.751517
\(67\) −10.6053 −1.29564 −0.647822 0.761792i \(-0.724320\pi\)
−0.647822 + 0.761792i \(0.724320\pi\)
\(68\) 0.133866 0.0162336
\(69\) 3.13378 0.377262
\(70\) 4.75570 0.568415
\(71\) −14.0887 −1.67203 −0.836013 0.548710i \(-0.815119\pi\)
−0.836013 + 0.548710i \(0.815119\pi\)
\(72\) 0.995149 0.117279
\(73\) 10.2490 1.19956 0.599779 0.800166i \(-0.295255\pi\)
0.599779 + 0.800166i \(0.295255\pi\)
\(74\) 5.00901 0.582285
\(75\) 1.52524 0.176119
\(76\) −2.51765 −0.288795
\(77\) −7.05723 −0.804246
\(78\) 2.35817 0.267011
\(79\) 2.04015 0.229535 0.114768 0.993392i \(-0.463388\pi\)
0.114768 + 0.993392i \(0.463388\pi\)
\(80\) 2.05838 0.230134
\(81\) −10.9951 −1.22168
\(82\) −0.906925 −0.100153
\(83\) −11.3749 −1.24856 −0.624280 0.781200i \(-0.714608\pi\)
−0.624280 + 0.781200i \(0.714608\pi\)
\(84\) −4.61802 −0.503868
\(85\) 0.275547 0.0298873
\(86\) 11.9374 1.28724
\(87\) 12.9163 1.38477
\(88\) −3.05453 −0.325614
\(89\) 0.534851 0.0566941 0.0283470 0.999598i \(-0.490976\pi\)
0.0283470 + 0.999598i \(0.490976\pi\)
\(90\) 2.04839 0.215919
\(91\) −2.72583 −0.285745
\(92\) −1.56784 −0.163459
\(93\) −6.74561 −0.699487
\(94\) −3.39371 −0.350035
\(95\) −5.18228 −0.531691
\(96\) −1.99879 −0.204000
\(97\) 2.81200 0.285515 0.142758 0.989758i \(-0.454403\pi\)
0.142758 + 0.989758i \(0.454403\pi\)
\(98\) −1.66199 −0.167886
\(99\) −3.03971 −0.305503
\(100\) −0.763082 −0.0763082
\(101\) −6.93643 −0.690200 −0.345100 0.938566i \(-0.612155\pi\)
−0.345100 + 0.938566i \(0.612155\pi\)
\(102\) −0.267570 −0.0264934
\(103\) 15.9364 1.57026 0.785132 0.619329i \(-0.212595\pi\)
0.785132 + 0.619329i \(0.212595\pi\)
\(104\) −1.17980 −0.115689
\(105\) −9.50564 −0.927655
\(106\) −11.2280 −1.09056
\(107\) 7.05246 0.681787 0.340894 0.940102i \(-0.389270\pi\)
0.340894 + 0.940102i \(0.389270\pi\)
\(108\) 4.00727 0.385600
\(109\) −1.17890 −0.112918 −0.0564592 0.998405i \(-0.517981\pi\)
−0.0564592 + 0.998405i \(0.517981\pi\)
\(110\) −6.28737 −0.599478
\(111\) −10.0119 −0.950291
\(112\) 2.31041 0.218314
\(113\) 0.694134 0.0652987 0.0326493 0.999467i \(-0.489606\pi\)
0.0326493 + 0.999467i \(0.489606\pi\)
\(114\) 5.03225 0.471313
\(115\) −3.22721 −0.300938
\(116\) −6.46205 −0.599986
\(117\) −1.17408 −0.108544
\(118\) −13.9430 −1.28356
\(119\) 0.309286 0.0283522
\(120\) −4.11426 −0.375579
\(121\) −1.66985 −0.151805
\(122\) −0.114241 −0.0103429
\(123\) 1.81275 0.163450
\(124\) 3.37485 0.303070
\(125\) −11.8626 −1.06102
\(126\) 2.29921 0.204830
\(127\) 2.41691 0.214466 0.107233 0.994234i \(-0.465801\pi\)
0.107233 + 0.994234i \(0.465801\pi\)
\(128\) 1.00000 0.0883883
\(129\) −23.8603 −2.10079
\(130\) −2.42848 −0.212992
\(131\) 3.83531 0.335092 0.167546 0.985864i \(-0.446416\pi\)
0.167546 + 0.985864i \(0.446416\pi\)
\(132\) 6.10535 0.531403
\(133\) −5.81682 −0.504382
\(134\) −10.6053 −0.916158
\(135\) 8.24847 0.709916
\(136\) 0.133866 0.0114789
\(137\) −10.9150 −0.932528 −0.466264 0.884646i \(-0.654400\pi\)
−0.466264 + 0.884646i \(0.654400\pi\)
\(138\) 3.13378 0.266765
\(139\) 3.28500 0.278630 0.139315 0.990248i \(-0.455510\pi\)
0.139315 + 0.990248i \(0.455510\pi\)
\(140\) 4.75570 0.401930
\(141\) 6.78331 0.571257
\(142\) −14.0887 −1.18230
\(143\) 3.60374 0.301360
\(144\) 0.995149 0.0829291
\(145\) −13.3013 −1.10462
\(146\) 10.2490 0.848216
\(147\) 3.32196 0.273991
\(148\) 5.00901 0.411738
\(149\) −12.1043 −0.991621 −0.495810 0.868431i \(-0.665129\pi\)
−0.495810 + 0.868431i \(0.665129\pi\)
\(150\) 1.52524 0.124535
\(151\) −9.04117 −0.735760 −0.367880 0.929873i \(-0.619916\pi\)
−0.367880 + 0.929873i \(0.619916\pi\)
\(152\) −2.51765 −0.204209
\(153\) 0.133217 0.0107699
\(154\) −7.05723 −0.568688
\(155\) 6.94671 0.557974
\(156\) 2.35817 0.188805
\(157\) −2.02690 −0.161764 −0.0808821 0.996724i \(-0.525774\pi\)
−0.0808821 + 0.996724i \(0.525774\pi\)
\(158\) 2.04015 0.162306
\(159\) 22.4423 1.77979
\(160\) 2.05838 0.162729
\(161\) −3.62236 −0.285482
\(162\) −10.9951 −0.863859
\(163\) 11.6588 0.913187 0.456594 0.889675i \(-0.349069\pi\)
0.456594 + 0.889675i \(0.349069\pi\)
\(164\) −0.906925 −0.0708189
\(165\) 12.5671 0.978349
\(166\) −11.3749 −0.882866
\(167\) 10.3272 0.799143 0.399572 0.916702i \(-0.369159\pi\)
0.399572 + 0.916702i \(0.369159\pi\)
\(168\) −4.61802 −0.356288
\(169\) −11.6081 −0.892928
\(170\) 0.275547 0.0211335
\(171\) −2.50544 −0.191596
\(172\) 11.9374 0.910219
\(173\) −19.3822 −1.47360 −0.736802 0.676108i \(-0.763665\pi\)
−0.736802 + 0.676108i \(0.763665\pi\)
\(174\) 12.9163 0.979179
\(175\) −1.76304 −0.133273
\(176\) −3.05453 −0.230244
\(177\) 27.8691 2.09477
\(178\) 0.534851 0.0400887
\(179\) −25.1615 −1.88066 −0.940330 0.340263i \(-0.889484\pi\)
−0.940330 + 0.340263i \(0.889484\pi\)
\(180\) 2.04839 0.152678
\(181\) 13.1748 0.979276 0.489638 0.871926i \(-0.337129\pi\)
0.489638 + 0.871926i \(0.337129\pi\)
\(182\) −2.72583 −0.202052
\(183\) 0.228343 0.0168796
\(184\) −1.56784 −0.115583
\(185\) 10.3104 0.758038
\(186\) −6.74561 −0.494612
\(187\) −0.408898 −0.0299016
\(188\) −3.39371 −0.247512
\(189\) 9.25845 0.673453
\(190\) −5.18228 −0.375962
\(191\) 8.61139 0.623098 0.311549 0.950230i \(-0.399152\pi\)
0.311549 + 0.950230i \(0.399152\pi\)
\(192\) −1.99879 −0.144250
\(193\) −1.18576 −0.0853530 −0.0426765 0.999089i \(-0.513588\pi\)
−0.0426765 + 0.999089i \(0.513588\pi\)
\(194\) 2.81200 0.201890
\(195\) 4.85401 0.347603
\(196\) −1.66199 −0.118713
\(197\) 21.8995 1.56028 0.780139 0.625606i \(-0.215148\pi\)
0.780139 + 0.625606i \(0.215148\pi\)
\(198\) −3.03971 −0.216023
\(199\) −14.8077 −1.04969 −0.524844 0.851198i \(-0.675876\pi\)
−0.524844 + 0.851198i \(0.675876\pi\)
\(200\) −0.763082 −0.0539581
\(201\) 21.1977 1.49517
\(202\) −6.93643 −0.488045
\(203\) −14.9300 −1.04788
\(204\) −0.267570 −0.0187336
\(205\) −1.86679 −0.130383
\(206\) 15.9364 1.11034
\(207\) −1.56023 −0.108444
\(208\) −1.17980 −0.0818046
\(209\) 7.69024 0.531945
\(210\) −9.50564 −0.655951
\(211\) 12.9449 0.891164 0.445582 0.895241i \(-0.352997\pi\)
0.445582 + 0.895241i \(0.352997\pi\)
\(212\) −11.2280 −0.771141
\(213\) 28.1604 1.92952
\(214\) 7.05246 0.482096
\(215\) 24.5717 1.67578
\(216\) 4.00727 0.272660
\(217\) 7.79730 0.529315
\(218\) −1.17890 −0.0798454
\(219\) −20.4856 −1.38429
\(220\) −6.28737 −0.423895
\(221\) −0.157936 −0.0106239
\(222\) −10.0119 −0.671957
\(223\) 14.4248 0.965956 0.482978 0.875632i \(-0.339555\pi\)
0.482978 + 0.875632i \(0.339555\pi\)
\(224\) 2.31041 0.154371
\(225\) −0.759381 −0.0506254
\(226\) 0.694134 0.0461731
\(227\) 11.5492 0.766547 0.383273 0.923635i \(-0.374797\pi\)
0.383273 + 0.923635i \(0.374797\pi\)
\(228\) 5.03225 0.333269
\(229\) −2.62170 −0.173247 −0.0866234 0.996241i \(-0.527608\pi\)
−0.0866234 + 0.996241i \(0.527608\pi\)
\(230\) −3.22721 −0.212796
\(231\) 14.1059 0.928100
\(232\) −6.46205 −0.424254
\(233\) 27.3261 1.79019 0.895097 0.445872i \(-0.147106\pi\)
0.895097 + 0.445872i \(0.147106\pi\)
\(234\) −1.17408 −0.0767520
\(235\) −6.98554 −0.455686
\(236\) −13.9430 −0.907611
\(237\) −4.07783 −0.264884
\(238\) 0.309286 0.0200480
\(239\) −7.37212 −0.476863 −0.238431 0.971159i \(-0.576633\pi\)
−0.238431 + 0.971159i \(0.576633\pi\)
\(240\) −4.11426 −0.265574
\(241\) −1.77515 −0.114348 −0.0571739 0.998364i \(-0.518209\pi\)
−0.0571739 + 0.998364i \(0.518209\pi\)
\(242\) −1.66985 −0.107342
\(243\) 9.95510 0.638620
\(244\) −0.114241 −0.00731351
\(245\) −3.42100 −0.218560
\(246\) 1.81275 0.115577
\(247\) 2.97033 0.188998
\(248\) 3.37485 0.214303
\(249\) 22.7361 1.44084
\(250\) −11.8626 −0.750257
\(251\) −15.2230 −0.960865 −0.480432 0.877032i \(-0.659520\pi\)
−0.480432 + 0.877032i \(0.659520\pi\)
\(252\) 2.29921 0.144836
\(253\) 4.78901 0.301083
\(254\) 2.41691 0.151650
\(255\) −0.550760 −0.0344899
\(256\) 1.00000 0.0625000
\(257\) −18.5499 −1.15711 −0.578555 0.815643i \(-0.696383\pi\)
−0.578555 + 0.815643i \(0.696383\pi\)
\(258\) −23.8603 −1.48548
\(259\) 11.5729 0.719104
\(260\) −2.42848 −0.150608
\(261\) −6.43070 −0.398050
\(262\) 3.83531 0.236946
\(263\) 1.58811 0.0979273 0.0489636 0.998801i \(-0.484408\pi\)
0.0489636 + 0.998801i \(0.484408\pi\)
\(264\) 6.10535 0.375759
\(265\) −23.1114 −1.41972
\(266\) −5.81682 −0.356652
\(267\) −1.06905 −0.0654249
\(268\) −10.6053 −0.647822
\(269\) 4.93143 0.300675 0.150337 0.988635i \(-0.451964\pi\)
0.150337 + 0.988635i \(0.451964\pi\)
\(270\) 8.24847 0.501986
\(271\) −8.46366 −0.514131 −0.257065 0.966394i \(-0.582756\pi\)
−0.257065 + 0.966394i \(0.582756\pi\)
\(272\) 0.133866 0.00811682
\(273\) 5.44836 0.329750
\(274\) −10.9150 −0.659397
\(275\) 2.33086 0.140556
\(276\) 3.13378 0.188631
\(277\) −8.86433 −0.532606 −0.266303 0.963889i \(-0.585802\pi\)
−0.266303 + 0.963889i \(0.585802\pi\)
\(278\) 3.28500 0.197021
\(279\) 3.35848 0.201067
\(280\) 4.75570 0.284208
\(281\) 1.22720 0.0732089 0.0366044 0.999330i \(-0.488346\pi\)
0.0366044 + 0.999330i \(0.488346\pi\)
\(282\) 6.78331 0.403940
\(283\) −3.26756 −0.194236 −0.0971181 0.995273i \(-0.530962\pi\)
−0.0971181 + 0.995273i \(0.530962\pi\)
\(284\) −14.0887 −0.836013
\(285\) 10.3583 0.613571
\(286\) 3.60374 0.213094
\(287\) −2.09537 −0.123686
\(288\) 0.995149 0.0586397
\(289\) −16.9821 −0.998946
\(290\) −13.3013 −0.781081
\(291\) −5.62059 −0.329485
\(292\) 10.2490 0.599779
\(293\) 1.98823 0.116154 0.0580768 0.998312i \(-0.481503\pi\)
0.0580768 + 0.998312i \(0.481503\pi\)
\(294\) 3.32196 0.193741
\(295\) −28.6999 −1.67097
\(296\) 5.00901 0.291143
\(297\) −12.2403 −0.710256
\(298\) −12.1043 −0.701182
\(299\) 1.84974 0.106973
\(300\) 1.52524 0.0880597
\(301\) 27.5804 1.58971
\(302\) −9.04117 −0.520261
\(303\) 13.8644 0.796491
\(304\) −2.51765 −0.144397
\(305\) −0.235150 −0.0134647
\(306\) 0.133217 0.00761549
\(307\) −12.3062 −0.702351 −0.351176 0.936310i \(-0.614218\pi\)
−0.351176 + 0.936310i \(0.614218\pi\)
\(308\) −7.05723 −0.402123
\(309\) −31.8535 −1.81208
\(310\) 6.94671 0.394547
\(311\) 15.4280 0.874839 0.437419 0.899258i \(-0.355893\pi\)
0.437419 + 0.899258i \(0.355893\pi\)
\(312\) 2.35817 0.133505
\(313\) −19.7519 −1.11644 −0.558222 0.829691i \(-0.688516\pi\)
−0.558222 + 0.829691i \(0.688516\pi\)
\(314\) −2.02690 −0.114385
\(315\) 4.73263 0.266654
\(316\) 2.04015 0.114768
\(317\) −9.83219 −0.552231 −0.276116 0.961124i \(-0.589047\pi\)
−0.276116 + 0.961124i \(0.589047\pi\)
\(318\) 22.4423 1.25850
\(319\) 19.7385 1.10514
\(320\) 2.05838 0.115067
\(321\) −14.0964 −0.786782
\(322\) −3.62236 −0.201866
\(323\) −0.337028 −0.0187528
\(324\) −10.9951 −0.610840
\(325\) 0.900287 0.0499389
\(326\) 11.6588 0.645721
\(327\) 2.35638 0.130308
\(328\) −0.906925 −0.0500766
\(329\) −7.84088 −0.432282
\(330\) 12.5671 0.691797
\(331\) 6.83200 0.375520 0.187760 0.982215i \(-0.439877\pi\)
0.187760 + 0.982215i \(0.439877\pi\)
\(332\) −11.3749 −0.624280
\(333\) 4.98471 0.273160
\(334\) 10.3272 0.565080
\(335\) −21.8297 −1.19268
\(336\) −4.61802 −0.251934
\(337\) −11.9388 −0.650347 −0.325174 0.945654i \(-0.605423\pi\)
−0.325174 + 0.945654i \(0.605423\pi\)
\(338\) −11.6081 −0.631396
\(339\) −1.38743 −0.0753547
\(340\) 0.275547 0.0149436
\(341\) −10.3086 −0.558241
\(342\) −2.50544 −0.135479
\(343\) −20.0128 −1.08059
\(344\) 11.9374 0.643622
\(345\) 6.45050 0.347283
\(346\) −19.3822 −1.04200
\(347\) −11.7684 −0.631761 −0.315881 0.948799i \(-0.602300\pi\)
−0.315881 + 0.948799i \(0.602300\pi\)
\(348\) 12.9163 0.692384
\(349\) −11.2253 −0.600877 −0.300438 0.953801i \(-0.597133\pi\)
−0.300438 + 0.953801i \(0.597133\pi\)
\(350\) −1.76304 −0.0942382
\(351\) −4.72779 −0.252351
\(352\) −3.05453 −0.162807
\(353\) −11.7271 −0.624172 −0.312086 0.950054i \(-0.601028\pi\)
−0.312086 + 0.950054i \(0.601028\pi\)
\(354\) 27.8691 1.48122
\(355\) −28.9999 −1.53916
\(356\) 0.534851 0.0283470
\(357\) −0.618197 −0.0327184
\(358\) −25.1615 −1.32983
\(359\) 7.88693 0.416256 0.208128 0.978102i \(-0.433263\pi\)
0.208128 + 0.978102i \(0.433263\pi\)
\(360\) 2.04839 0.107960
\(361\) −12.6614 −0.666391
\(362\) 13.1748 0.692453
\(363\) 3.33768 0.175183
\(364\) −2.72583 −0.142872
\(365\) 21.0964 1.10423
\(366\) 0.228343 0.0119357
\(367\) −1.79646 −0.0937747 −0.0468873 0.998900i \(-0.514930\pi\)
−0.0468873 + 0.998900i \(0.514930\pi\)
\(368\) −1.56784 −0.0817293
\(369\) −0.902525 −0.0469836
\(370\) 10.3104 0.536014
\(371\) −25.9413 −1.34680
\(372\) −6.74561 −0.349743
\(373\) 13.8286 0.716016 0.358008 0.933719i \(-0.383456\pi\)
0.358008 + 0.933719i \(0.383456\pi\)
\(374\) −0.408898 −0.0211436
\(375\) 23.7108 1.22442
\(376\) −3.39371 −0.175017
\(377\) 7.62394 0.392653
\(378\) 9.25845 0.476203
\(379\) −3.65081 −0.187530 −0.0937648 0.995594i \(-0.529890\pi\)
−0.0937648 + 0.995594i \(0.529890\pi\)
\(380\) −5.18228 −0.265845
\(381\) −4.83088 −0.247494
\(382\) 8.61139 0.440597
\(383\) 13.4424 0.686873 0.343437 0.939176i \(-0.388409\pi\)
0.343437 + 0.939176i \(0.388409\pi\)
\(384\) −1.99879 −0.102000
\(385\) −14.5264 −0.740336
\(386\) −1.18576 −0.0603537
\(387\) 11.8795 0.603869
\(388\) 2.81200 0.142758
\(389\) −31.4414 −1.59414 −0.797072 0.603884i \(-0.793619\pi\)
−0.797072 + 0.603884i \(0.793619\pi\)
\(390\) 4.85401 0.245793
\(391\) −0.209881 −0.0106141
\(392\) −1.66199 −0.0839431
\(393\) −7.66596 −0.386697
\(394\) 21.8995 1.10328
\(395\) 4.19941 0.211295
\(396\) −3.03971 −0.152751
\(397\) −20.6448 −1.03613 −0.518066 0.855340i \(-0.673348\pi\)
−0.518066 + 0.855340i \(0.673348\pi\)
\(398\) −14.8077 −0.742242
\(399\) 11.6266 0.582057
\(400\) −0.763082 −0.0381541
\(401\) −23.1779 −1.15745 −0.578724 0.815524i \(-0.696449\pi\)
−0.578724 + 0.815524i \(0.696449\pi\)
\(402\) 21.1977 1.05725
\(403\) −3.98166 −0.198340
\(404\) −6.93643 −0.345100
\(405\) −22.6321 −1.12460
\(406\) −14.9300 −0.740964
\(407\) −15.3002 −0.758401
\(408\) −0.267570 −0.0132467
\(409\) 12.5721 0.621652 0.310826 0.950467i \(-0.399394\pi\)
0.310826 + 0.950467i \(0.399394\pi\)
\(410\) −1.86679 −0.0921944
\(411\) 21.8167 1.07614
\(412\) 15.9364 0.785132
\(413\) −32.2141 −1.58515
\(414\) −1.56023 −0.0766813
\(415\) −23.4139 −1.14934
\(416\) −1.17980 −0.0578446
\(417\) −6.56601 −0.321539
\(418\) 7.69024 0.376142
\(419\) 12.3554 0.603599 0.301799 0.953371i \(-0.402413\pi\)
0.301799 + 0.953371i \(0.402413\pi\)
\(420\) −9.50564 −0.463828
\(421\) −21.8116 −1.06303 −0.531516 0.847048i \(-0.678377\pi\)
−0.531516 + 0.847048i \(0.678377\pi\)
\(422\) 12.9449 0.630148
\(423\) −3.37725 −0.164207
\(424\) −11.2280 −0.545279
\(425\) −0.102151 −0.00495504
\(426\) 28.1604 1.36438
\(427\) −0.263943 −0.0127731
\(428\) 7.05246 0.340894
\(429\) −7.20311 −0.347770
\(430\) 24.5717 1.18495
\(431\) 14.8941 0.717425 0.358713 0.933448i \(-0.383216\pi\)
0.358713 + 0.933448i \(0.383216\pi\)
\(432\) 4.00727 0.192800
\(433\) 6.86545 0.329932 0.164966 0.986299i \(-0.447248\pi\)
0.164966 + 0.986299i \(0.447248\pi\)
\(434\) 7.79730 0.374282
\(435\) 26.5865 1.27473
\(436\) −1.17890 −0.0564592
\(437\) 3.94727 0.188824
\(438\) −20.4856 −0.978841
\(439\) 11.9953 0.572506 0.286253 0.958154i \(-0.407590\pi\)
0.286253 + 0.958154i \(0.407590\pi\)
\(440\) −6.28737 −0.299739
\(441\) −1.65393 −0.0787584
\(442\) −0.157936 −0.00751223
\(443\) 34.4921 1.63877 0.819385 0.573244i \(-0.194315\pi\)
0.819385 + 0.573244i \(0.194315\pi\)
\(444\) −10.0119 −0.475146
\(445\) 1.10092 0.0521888
\(446\) 14.4248 0.683034
\(447\) 24.1939 1.14433
\(448\) 2.31041 0.109157
\(449\) 3.34325 0.157778 0.0788888 0.996883i \(-0.474863\pi\)
0.0788888 + 0.996883i \(0.474863\pi\)
\(450\) −0.759381 −0.0357975
\(451\) 2.77023 0.130445
\(452\) 0.694134 0.0326493
\(453\) 18.0714 0.849067
\(454\) 11.5492 0.542030
\(455\) −5.61079 −0.263038
\(456\) 5.03225 0.235657
\(457\) −4.44436 −0.207898 −0.103949 0.994583i \(-0.533148\pi\)
−0.103949 + 0.994583i \(0.533148\pi\)
\(458\) −2.62170 −0.122504
\(459\) 0.536437 0.0250388
\(460\) −3.22721 −0.150469
\(461\) −1.34714 −0.0627425 −0.0313713 0.999508i \(-0.509987\pi\)
−0.0313713 + 0.999508i \(0.509987\pi\)
\(462\) 14.1059 0.656266
\(463\) −3.14173 −0.146008 −0.0730042 0.997332i \(-0.523259\pi\)
−0.0730042 + 0.997332i \(0.523259\pi\)
\(464\) −6.46205 −0.299993
\(465\) −13.8850 −0.643902
\(466\) 27.3261 1.26586
\(467\) −17.2444 −0.797976 −0.398988 0.916956i \(-0.630638\pi\)
−0.398988 + 0.916956i \(0.630638\pi\)
\(468\) −1.17408 −0.0542718
\(469\) −24.5026 −1.13143
\(470\) −6.98554 −0.322219
\(471\) 4.05134 0.186676
\(472\) −13.9430 −0.641778
\(473\) −36.4632 −1.67658
\(474\) −4.07783 −0.187301
\(475\) 1.92118 0.0881496
\(476\) 0.309286 0.0141761
\(477\) −11.1735 −0.511600
\(478\) −7.37212 −0.337193
\(479\) 38.4726 1.75786 0.878930 0.476951i \(-0.158258\pi\)
0.878930 + 0.476951i \(0.158258\pi\)
\(480\) −4.11426 −0.187789
\(481\) −5.90964 −0.269456
\(482\) −1.77515 −0.0808561
\(483\) 7.24032 0.329446
\(484\) −1.66985 −0.0759023
\(485\) 5.78816 0.262827
\(486\) 9.95510 0.451573
\(487\) −16.0693 −0.728169 −0.364084 0.931366i \(-0.618618\pi\)
−0.364084 + 0.931366i \(0.618618\pi\)
\(488\) −0.114241 −0.00517143
\(489\) −23.3034 −1.05382
\(490\) −3.42100 −0.154545
\(491\) −19.2444 −0.868488 −0.434244 0.900795i \(-0.642984\pi\)
−0.434244 + 0.900795i \(0.642984\pi\)
\(492\) 1.81275 0.0817251
\(493\) −0.865049 −0.0389598
\(494\) 2.97033 0.133642
\(495\) −6.25687 −0.281226
\(496\) 3.37485 0.151535
\(497\) −32.5508 −1.46010
\(498\) 22.7361 1.01883
\(499\) 10.1059 0.452403 0.226202 0.974080i \(-0.427369\pi\)
0.226202 + 0.974080i \(0.427369\pi\)
\(500\) −11.8626 −0.530512
\(501\) −20.6419 −0.922212
\(502\) −15.2230 −0.679434
\(503\) 30.3869 1.35489 0.677443 0.735576i \(-0.263088\pi\)
0.677443 + 0.735576i \(0.263088\pi\)
\(504\) 2.29921 0.102415
\(505\) −14.2778 −0.635353
\(506\) 4.78901 0.212898
\(507\) 23.2020 1.03044
\(508\) 2.41691 0.107233
\(509\) −21.5598 −0.955621 −0.477810 0.878463i \(-0.658569\pi\)
−0.477810 + 0.878463i \(0.658569\pi\)
\(510\) −0.550760 −0.0243880
\(511\) 23.6795 1.04752
\(512\) 1.00000 0.0441942
\(513\) −10.0889 −0.445436
\(514\) −18.5499 −0.818200
\(515\) 32.8032 1.44548
\(516\) −23.8603 −1.05039
\(517\) 10.3662 0.455905
\(518\) 11.5729 0.508483
\(519\) 38.7410 1.70054
\(520\) −2.42848 −0.106496
\(521\) −25.2085 −1.10440 −0.552201 0.833711i \(-0.686212\pi\)
−0.552201 + 0.833711i \(0.686212\pi\)
\(522\) −6.43070 −0.281464
\(523\) −4.26413 −0.186457 −0.0932287 0.995645i \(-0.529719\pi\)
−0.0932287 + 0.995645i \(0.529719\pi\)
\(524\) 3.83531 0.167546
\(525\) 3.52393 0.153797
\(526\) 1.58811 0.0692450
\(527\) 0.451778 0.0196798
\(528\) 6.10535 0.265701
\(529\) −20.5419 −0.893125
\(530\) −23.1114 −1.00390
\(531\) −13.8754 −0.602139
\(532\) −5.81682 −0.252191
\(533\) 1.06999 0.0463465
\(534\) −1.06905 −0.0462624
\(535\) 14.5166 0.627608
\(536\) −10.6053 −0.458079
\(537\) 50.2925 2.17028
\(538\) 4.93143 0.212609
\(539\) 5.07659 0.218664
\(540\) 8.24847 0.354958
\(541\) −15.1448 −0.651128 −0.325564 0.945520i \(-0.605554\pi\)
−0.325564 + 0.945520i \(0.605554\pi\)
\(542\) −8.46366 −0.363545
\(543\) −26.3336 −1.13008
\(544\) 0.133866 0.00573946
\(545\) −2.42663 −0.103945
\(546\) 5.44836 0.233168
\(547\) 22.4040 0.957927 0.478963 0.877835i \(-0.341013\pi\)
0.478963 + 0.877835i \(0.341013\pi\)
\(548\) −10.9150 −0.466264
\(549\) −0.113686 −0.00485202
\(550\) 2.33086 0.0993881
\(551\) 16.2692 0.693091
\(552\) 3.13378 0.133382
\(553\) 4.71360 0.200443
\(554\) −8.86433 −0.376609
\(555\) −20.6083 −0.874776
\(556\) 3.28500 0.139315
\(557\) 3.07380 0.130241 0.0651206 0.997877i \(-0.479257\pi\)
0.0651206 + 0.997877i \(0.479257\pi\)
\(558\) 3.35848 0.142176
\(559\) −14.0838 −0.595681
\(560\) 4.75570 0.200965
\(561\) 0.817300 0.0345064
\(562\) 1.22720 0.0517665
\(563\) −14.5243 −0.612127 −0.306063 0.952011i \(-0.599012\pi\)
−0.306063 + 0.952011i \(0.599012\pi\)
\(564\) 6.78331 0.285629
\(565\) 1.42879 0.0601097
\(566\) −3.26756 −0.137346
\(567\) −25.4033 −1.06684
\(568\) −14.0887 −0.591150
\(569\) −10.8718 −0.455769 −0.227884 0.973688i \(-0.573181\pi\)
−0.227884 + 0.973688i \(0.573181\pi\)
\(570\) 10.3583 0.433860
\(571\) −5.45313 −0.228206 −0.114103 0.993469i \(-0.536399\pi\)
−0.114103 + 0.993469i \(0.536399\pi\)
\(572\) 3.60374 0.150680
\(573\) −17.2123 −0.719056
\(574\) −2.09537 −0.0874591
\(575\) 1.19639 0.0498929
\(576\) 0.995149 0.0414645
\(577\) −28.8939 −1.20287 −0.601435 0.798922i \(-0.705404\pi\)
−0.601435 + 0.798922i \(0.705404\pi\)
\(578\) −16.9821 −0.706361
\(579\) 2.37009 0.0984974
\(580\) −13.3013 −0.552308
\(581\) −26.2808 −1.09031
\(582\) −5.62059 −0.232981
\(583\) 34.2962 1.42040
\(584\) 10.2490 0.424108
\(585\) −2.41670 −0.0999182
\(586\) 1.98823 0.0821330
\(587\) 2.18944 0.0903677 0.0451839 0.998979i \(-0.485613\pi\)
0.0451839 + 0.998979i \(0.485613\pi\)
\(588\) 3.32196 0.136995
\(589\) −8.49670 −0.350100
\(590\) −28.6999 −1.18156
\(591\) −43.7725 −1.80056
\(592\) 5.00901 0.205869
\(593\) −24.9483 −1.02451 −0.512253 0.858835i \(-0.671189\pi\)
−0.512253 + 0.858835i \(0.671189\pi\)
\(594\) −12.2403 −0.502227
\(595\) 0.636627 0.0260992
\(596\) −12.1043 −0.495810
\(597\) 29.5974 1.21134
\(598\) 1.84974 0.0756416
\(599\) −2.89609 −0.118331 −0.0591655 0.998248i \(-0.518844\pi\)
−0.0591655 + 0.998248i \(0.518844\pi\)
\(600\) 1.52524 0.0622676
\(601\) 31.9769 1.30436 0.652182 0.758062i \(-0.273854\pi\)
0.652182 + 0.758062i \(0.273854\pi\)
\(602\) 27.5804 1.12409
\(603\) −10.5539 −0.429786
\(604\) −9.04117 −0.367880
\(605\) −3.43718 −0.139741
\(606\) 13.8644 0.563204
\(607\) −22.3191 −0.905905 −0.452953 0.891535i \(-0.649629\pi\)
−0.452953 + 0.891535i \(0.649629\pi\)
\(608\) −2.51765 −0.102104
\(609\) 29.8419 1.20925
\(610\) −0.235150 −0.00952096
\(611\) 4.00391 0.161981
\(612\) 0.133217 0.00538496
\(613\) −11.1096 −0.448711 −0.224356 0.974507i \(-0.572028\pi\)
−0.224356 + 0.974507i \(0.572028\pi\)
\(614\) −12.3062 −0.496637
\(615\) 3.73132 0.150461
\(616\) −7.05723 −0.284344
\(617\) 22.8667 0.920578 0.460289 0.887769i \(-0.347746\pi\)
0.460289 + 0.887769i \(0.347746\pi\)
\(618\) −31.8535 −1.28134
\(619\) −27.6211 −1.11019 −0.555093 0.831788i \(-0.687318\pi\)
−0.555093 + 0.831788i \(0.687318\pi\)
\(620\) 6.94671 0.278987
\(621\) −6.28276 −0.252118
\(622\) 15.4280 0.618604
\(623\) 1.23573 0.0495083
\(624\) 2.35817 0.0944025
\(625\) −20.6023 −0.824092
\(626\) −19.7519 −0.789445
\(627\) −15.3712 −0.613865
\(628\) −2.02690 −0.0808821
\(629\) 0.670536 0.0267360
\(630\) 4.73263 0.188553
\(631\) 31.2957 1.24586 0.622930 0.782277i \(-0.285942\pi\)
0.622930 + 0.782277i \(0.285942\pi\)
\(632\) 2.04015 0.0811529
\(633\) −25.8741 −1.02840
\(634\) −9.83219 −0.390486
\(635\) 4.97491 0.197423
\(636\) 22.4423 0.889897
\(637\) 1.96082 0.0776904
\(638\) 19.7385 0.781455
\(639\) −14.0204 −0.554638
\(640\) 2.05838 0.0813645
\(641\) 36.8362 1.45494 0.727471 0.686138i \(-0.240696\pi\)
0.727471 + 0.686138i \(0.240696\pi\)
\(642\) −14.0964 −0.556339
\(643\) 30.8316 1.21588 0.607940 0.793983i \(-0.291996\pi\)
0.607940 + 0.793983i \(0.291996\pi\)
\(644\) −3.62236 −0.142741
\(645\) −49.1136 −1.93384
\(646\) −0.337028 −0.0132602
\(647\) −10.2856 −0.404368 −0.202184 0.979348i \(-0.564804\pi\)
−0.202184 + 0.979348i \(0.564804\pi\)
\(648\) −10.9951 −0.431929
\(649\) 42.5893 1.67177
\(650\) 0.900287 0.0353122
\(651\) −15.5851 −0.610830
\(652\) 11.6588 0.456594
\(653\) 15.7195 0.615152 0.307576 0.951524i \(-0.400482\pi\)
0.307576 + 0.951524i \(0.400482\pi\)
\(654\) 2.35638 0.0921416
\(655\) 7.89451 0.308464
\(656\) −0.906925 −0.0354095
\(657\) 10.1993 0.397913
\(658\) −7.84088 −0.305669
\(659\) −11.1967 −0.436161 −0.218080 0.975931i \(-0.569979\pi\)
−0.218080 + 0.975931i \(0.569979\pi\)
\(660\) 12.5671 0.489175
\(661\) −15.4849 −0.602294 −0.301147 0.953578i \(-0.597370\pi\)
−0.301147 + 0.953578i \(0.597370\pi\)
\(662\) 6.83200 0.265533
\(663\) 0.315680 0.0122600
\(664\) −11.3749 −0.441433
\(665\) −11.9732 −0.464301
\(666\) 4.98471 0.193154
\(667\) 10.1315 0.392291
\(668\) 10.3272 0.399572
\(669\) −28.8321 −1.11471
\(670\) −21.8297 −0.843355
\(671\) 0.348951 0.0134711
\(672\) −4.61802 −0.178144
\(673\) 27.6145 1.06446 0.532230 0.846600i \(-0.321354\pi\)
0.532230 + 0.846600i \(0.321354\pi\)
\(674\) −11.9388 −0.459865
\(675\) −3.05788 −0.117698
\(676\) −11.6081 −0.446464
\(677\) 36.0282 1.38468 0.692339 0.721573i \(-0.256580\pi\)
0.692339 + 0.721573i \(0.256580\pi\)
\(678\) −1.38743 −0.0532838
\(679\) 6.49688 0.249327
\(680\) 0.275547 0.0105667
\(681\) −23.0844 −0.884595
\(682\) −10.3086 −0.394736
\(683\) −36.8052 −1.40831 −0.704156 0.710046i \(-0.748674\pi\)
−0.704156 + 0.710046i \(0.748674\pi\)
\(684\) −2.50544 −0.0957979
\(685\) −22.4671 −0.858424
\(686\) −20.0128 −0.764091
\(687\) 5.24022 0.199927
\(688\) 11.9374 0.455109
\(689\) 13.2468 0.504663
\(690\) 6.45050 0.245566
\(691\) 10.3573 0.394009 0.197004 0.980403i \(-0.436879\pi\)
0.197004 + 0.980403i \(0.436879\pi\)
\(692\) −19.3822 −0.736802
\(693\) −7.02299 −0.266781
\(694\) −11.7684 −0.446723
\(695\) 6.76177 0.256488
\(696\) 12.9163 0.489589
\(697\) −0.121406 −0.00459860
\(698\) −11.2253 −0.424884
\(699\) −54.6191 −2.06588
\(700\) −1.76304 −0.0666365
\(701\) 35.9180 1.35660 0.678302 0.734783i \(-0.262716\pi\)
0.678302 + 0.734783i \(0.262716\pi\)
\(702\) −4.72779 −0.178439
\(703\) −12.6109 −0.475631
\(704\) −3.05453 −0.115122
\(705\) 13.9626 0.525862
\(706\) −11.7271 −0.441357
\(707\) −16.0260 −0.602720
\(708\) 27.8691 1.04738
\(709\) −19.6049 −0.736278 −0.368139 0.929771i \(-0.620005\pi\)
−0.368139 + 0.929771i \(0.620005\pi\)
\(710\) −28.9999 −1.08835
\(711\) 2.03026 0.0761406
\(712\) 0.534851 0.0200444
\(713\) −5.29122 −0.198158
\(714\) −0.618197 −0.0231354
\(715\) 7.41786 0.277412
\(716\) −25.1615 −0.940330
\(717\) 14.7353 0.550300
\(718\) 7.88693 0.294338
\(719\) −24.1943 −0.902297 −0.451148 0.892449i \(-0.648986\pi\)
−0.451148 + 0.892449i \(0.648986\pi\)
\(720\) 2.04839 0.0763391
\(721\) 36.8198 1.37124
\(722\) −12.6614 −0.471210
\(723\) 3.54816 0.131957
\(724\) 13.1748 0.489638
\(725\) 4.93107 0.183135
\(726\) 3.33768 0.123873
\(727\) 37.8695 1.40450 0.702252 0.711929i \(-0.252178\pi\)
0.702252 + 0.711929i \(0.252178\pi\)
\(728\) −2.72583 −0.101026
\(729\) 13.0872 0.484713
\(730\) 21.0964 0.780812
\(731\) 1.59801 0.0591047
\(732\) 0.228343 0.00843979
\(733\) 2.80019 0.103427 0.0517136 0.998662i \(-0.483532\pi\)
0.0517136 + 0.998662i \(0.483532\pi\)
\(734\) −1.79646 −0.0663087
\(735\) 6.83785 0.252218
\(736\) −1.56784 −0.0577913
\(737\) 32.3942 1.19326
\(738\) −0.902525 −0.0332224
\(739\) 7.65527 0.281604 0.140802 0.990038i \(-0.455032\pi\)
0.140802 + 0.990038i \(0.455032\pi\)
\(740\) 10.3104 0.379019
\(741\) −5.93706 −0.218103
\(742\) −25.9413 −0.952335
\(743\) −13.2583 −0.486400 −0.243200 0.969976i \(-0.578197\pi\)
−0.243200 + 0.969976i \(0.578197\pi\)
\(744\) −6.74561 −0.247306
\(745\) −24.9152 −0.912821
\(746\) 13.8286 0.506299
\(747\) −11.3197 −0.414168
\(748\) −0.408898 −0.0149508
\(749\) 16.2941 0.595373
\(750\) 23.7108 0.865796
\(751\) −2.79614 −0.102033 −0.0510163 0.998698i \(-0.516246\pi\)
−0.0510163 + 0.998698i \(0.516246\pi\)
\(752\) −3.39371 −0.123756
\(753\) 30.4274 1.10884
\(754\) 7.62394 0.277648
\(755\) −18.6101 −0.677292
\(756\) 9.25845 0.336727
\(757\) −27.3903 −0.995519 −0.497759 0.867315i \(-0.665844\pi\)
−0.497759 + 0.867315i \(0.665844\pi\)
\(758\) −3.65081 −0.132604
\(759\) −9.57221 −0.347449
\(760\) −5.18228 −0.187981
\(761\) 0.387886 0.0140608 0.00703042 0.999975i \(-0.497762\pi\)
0.00703042 + 0.999975i \(0.497762\pi\)
\(762\) −4.83088 −0.175004
\(763\) −2.72375 −0.0986065
\(764\) 8.61139 0.311549
\(765\) 0.274210 0.00991409
\(766\) 13.4424 0.485693
\(767\) 16.4500 0.593974
\(768\) −1.99879 −0.0721250
\(769\) 12.9538 0.467127 0.233563 0.972342i \(-0.424961\pi\)
0.233563 + 0.972342i \(0.424961\pi\)
\(770\) −14.5264 −0.523496
\(771\) 37.0773 1.33530
\(772\) −1.18576 −0.0426765
\(773\) 21.4322 0.770864 0.385432 0.922736i \(-0.374053\pi\)
0.385432 + 0.922736i \(0.374053\pi\)
\(774\) 11.8795 0.427000
\(775\) −2.57529 −0.0925071
\(776\) 2.81200 0.100945
\(777\) −23.1317 −0.829846
\(778\) −31.4414 −1.12723
\(779\) 2.28332 0.0818085
\(780\) 4.85401 0.173802
\(781\) 43.0345 1.53989
\(782\) −0.209881 −0.00750531
\(783\) −25.8952 −0.925418
\(784\) −1.66199 −0.0593567
\(785\) −4.17213 −0.148910
\(786\) −7.66596 −0.273436
\(787\) −24.1541 −0.861000 −0.430500 0.902591i \(-0.641663\pi\)
−0.430500 + 0.902591i \(0.641663\pi\)
\(788\) 21.8995 0.780139
\(789\) −3.17430 −0.113008
\(790\) 4.19941 0.149408
\(791\) 1.60374 0.0570223
\(792\) −3.03971 −0.108011
\(793\) 0.134781 0.00478623
\(794\) −20.6448 −0.732656
\(795\) 46.1948 1.63836
\(796\) −14.8077 −0.524844
\(797\) 35.3332 1.25156 0.625782 0.779998i \(-0.284780\pi\)
0.625782 + 0.779998i \(0.284780\pi\)
\(798\) 11.6266 0.411576
\(799\) −0.454303 −0.0160721
\(800\) −0.763082 −0.0269790
\(801\) 0.532256 0.0188063
\(802\) −23.1779 −0.818439
\(803\) −31.3060 −1.10476
\(804\) 21.1977 0.747586
\(805\) −7.45618 −0.262796
\(806\) −3.98166 −0.140248
\(807\) −9.85688 −0.346979
\(808\) −6.93643 −0.244023
\(809\) −29.0498 −1.02134 −0.510668 0.859778i \(-0.670602\pi\)
−0.510668 + 0.859778i \(0.670602\pi\)
\(810\) −22.6321 −0.795212
\(811\) 48.0953 1.68886 0.844428 0.535669i \(-0.179941\pi\)
0.844428 + 0.535669i \(0.179941\pi\)
\(812\) −14.9300 −0.523940
\(813\) 16.9170 0.593307
\(814\) −15.3002 −0.536270
\(815\) 23.9982 0.840620
\(816\) −0.267570 −0.00936681
\(817\) −30.0542 −1.05146
\(818\) 12.5721 0.439574
\(819\) −2.71261 −0.0947863
\(820\) −1.86679 −0.0651913
\(821\) −34.9974 −1.22142 −0.610709 0.791855i \(-0.709115\pi\)
−0.610709 + 0.791855i \(0.709115\pi\)
\(822\) 21.8167 0.760944
\(823\) 6.38339 0.222511 0.111256 0.993792i \(-0.464513\pi\)
0.111256 + 0.993792i \(0.464513\pi\)
\(824\) 15.9364 0.555172
\(825\) −4.65889 −0.162202
\(826\) −32.2141 −1.12087
\(827\) −24.4635 −0.850680 −0.425340 0.905034i \(-0.639845\pi\)
−0.425340 + 0.905034i \(0.639845\pi\)
\(828\) −1.56023 −0.0542219
\(829\) −6.55621 −0.227706 −0.113853 0.993498i \(-0.536319\pi\)
−0.113853 + 0.993498i \(0.536319\pi\)
\(830\) −23.4139 −0.812708
\(831\) 17.7179 0.614627
\(832\) −1.17980 −0.0409023
\(833\) −0.222484 −0.00770861
\(834\) −6.56601 −0.227362
\(835\) 21.2573 0.735639
\(836\) 7.69024 0.265973
\(837\) 13.5239 0.467456
\(838\) 12.3554 0.426809
\(839\) 2.50184 0.0863731 0.0431865 0.999067i \(-0.486249\pi\)
0.0431865 + 0.999067i \(0.486249\pi\)
\(840\) −9.50564 −0.327976
\(841\) 12.7580 0.439932
\(842\) −21.8116 −0.751677
\(843\) −2.45292 −0.0844831
\(844\) 12.9449 0.445582
\(845\) −23.8938 −0.821971
\(846\) −3.37725 −0.116112
\(847\) −3.85805 −0.132564
\(848\) −11.2280 −0.385571
\(849\) 6.53115 0.224149
\(850\) −0.102151 −0.00350374
\(851\) −7.85332 −0.269208
\(852\) 28.1604 0.964759
\(853\) 14.5627 0.498617 0.249309 0.968424i \(-0.419797\pi\)
0.249309 + 0.968424i \(0.419797\pi\)
\(854\) −0.263943 −0.00903195
\(855\) −5.15714 −0.176370
\(856\) 7.05246 0.241048
\(857\) −26.9155 −0.919417 −0.459709 0.888070i \(-0.652046\pi\)
−0.459709 + 0.888070i \(0.652046\pi\)
\(858\) −7.20311 −0.245910
\(859\) 5.76283 0.196625 0.0983127 0.995156i \(-0.468655\pi\)
0.0983127 + 0.995156i \(0.468655\pi\)
\(860\) 24.5717 0.837888
\(861\) 4.18820 0.142734
\(862\) 14.8941 0.507296
\(863\) −11.1285 −0.378820 −0.189410 0.981898i \(-0.560657\pi\)
−0.189410 + 0.981898i \(0.560657\pi\)
\(864\) 4.00727 0.136330
\(865\) −39.8960 −1.35650
\(866\) 6.86545 0.233297
\(867\) 33.9436 1.15278
\(868\) 7.79730 0.264658
\(869\) −6.23171 −0.211396
\(870\) 26.5865 0.901368
\(871\) 12.5122 0.423958
\(872\) −1.17890 −0.0399227
\(873\) 2.79836 0.0947101
\(874\) 3.94727 0.133519
\(875\) −27.4075 −0.926543
\(876\) −20.4856 −0.692145
\(877\) 39.6363 1.33842 0.669211 0.743073i \(-0.266632\pi\)
0.669211 + 0.743073i \(0.266632\pi\)
\(878\) 11.9953 0.404823
\(879\) −3.97405 −0.134041
\(880\) −6.28737 −0.211947
\(881\) −5.63151 −0.189730 −0.0948651 0.995490i \(-0.530242\pi\)
−0.0948651 + 0.995490i \(0.530242\pi\)
\(882\) −1.65393 −0.0556906
\(883\) 4.80069 0.161556 0.0807781 0.996732i \(-0.474259\pi\)
0.0807781 + 0.996732i \(0.474259\pi\)
\(884\) −0.157936 −0.00531195
\(885\) 57.3650 1.92831
\(886\) 34.4921 1.15878
\(887\) 31.1995 1.04758 0.523789 0.851848i \(-0.324518\pi\)
0.523789 + 0.851848i \(0.324518\pi\)
\(888\) −10.0119 −0.335979
\(889\) 5.58406 0.187283
\(890\) 1.10092 0.0369031
\(891\) 33.5849 1.12514
\(892\) 14.4248 0.482978
\(893\) 8.54418 0.285920
\(894\) 24.1939 0.809164
\(895\) −51.7919 −1.73121
\(896\) 2.31041 0.0771855
\(897\) −3.69724 −0.123447
\(898\) 3.34325 0.111566
\(899\) −21.8084 −0.727352
\(900\) −0.759381 −0.0253127
\(901\) −1.50305 −0.0500737
\(902\) 2.77023 0.0922385
\(903\) −55.1272 −1.83452
\(904\) 0.694134 0.0230866
\(905\) 27.1187 0.901457
\(906\) 18.0714 0.600381
\(907\) 20.8151 0.691153 0.345577 0.938391i \(-0.387683\pi\)
0.345577 + 0.938391i \(0.387683\pi\)
\(908\) 11.5492 0.383273
\(909\) −6.90278 −0.228951
\(910\) −5.61079 −0.185996
\(911\) 13.5482 0.448871 0.224436 0.974489i \(-0.427946\pi\)
0.224436 + 0.974489i \(0.427946\pi\)
\(912\) 5.03225 0.166634
\(913\) 34.7451 1.14989
\(914\) −4.44436 −0.147006
\(915\) 0.470015 0.0155382
\(916\) −2.62170 −0.0866234
\(917\) 8.86115 0.292621
\(918\) 0.536437 0.0177051
\(919\) −0.485829 −0.0160260 −0.00801301 0.999968i \(-0.502551\pi\)
−0.00801301 + 0.999968i \(0.502551\pi\)
\(920\) −3.22721 −0.106398
\(921\) 24.5974 0.810513
\(922\) −1.34714 −0.0443657
\(923\) 16.6219 0.547118
\(924\) 14.1059 0.464050
\(925\) −3.82229 −0.125676
\(926\) −3.14173 −0.103244
\(927\) 15.8591 0.520882
\(928\) −6.46205 −0.212127
\(929\) −45.4186 −1.49014 −0.745068 0.666989i \(-0.767583\pi\)
−0.745068 + 0.666989i \(0.767583\pi\)
\(930\) −13.8850 −0.455307
\(931\) 4.18431 0.137135
\(932\) 27.3261 0.895097
\(933\) −30.8372 −1.00956
\(934\) −17.2444 −0.564254
\(935\) −0.841666 −0.0275254
\(936\) −1.17408 −0.0383760
\(937\) −48.0337 −1.56919 −0.784596 0.620007i \(-0.787130\pi\)
−0.784596 + 0.620007i \(0.787130\pi\)
\(938\) −24.5026 −0.800039
\(939\) 39.4799 1.28838
\(940\) −6.98554 −0.227843
\(941\) −58.5051 −1.90721 −0.953605 0.301059i \(-0.902660\pi\)
−0.953605 + 0.301059i \(0.902660\pi\)
\(942\) 4.05134 0.132000
\(943\) 1.42191 0.0463039
\(944\) −13.9430 −0.453806
\(945\) 19.0574 0.619937
\(946\) −36.4632 −1.18552
\(947\) 35.1193 1.14122 0.570611 0.821220i \(-0.306706\pi\)
0.570611 + 0.821220i \(0.306706\pi\)
\(948\) −4.07783 −0.132442
\(949\) −12.0918 −0.392518
\(950\) 1.92118 0.0623312
\(951\) 19.6525 0.637275
\(952\) 0.309286 0.0100240
\(953\) 56.5572 1.83207 0.916033 0.401102i \(-0.131373\pi\)
0.916033 + 0.401102i \(0.131373\pi\)
\(954\) −11.1735 −0.361756
\(955\) 17.7255 0.573583
\(956\) −7.37212 −0.238431
\(957\) −39.4531 −1.27534
\(958\) 38.4726 1.24299
\(959\) −25.2181 −0.814334
\(960\) −4.11426 −0.132787
\(961\) −19.6104 −0.632593
\(962\) −5.90964 −0.190534
\(963\) 7.01825 0.226160
\(964\) −1.77515 −0.0571739
\(965\) −2.44075 −0.0785704
\(966\) 7.24032 0.232954
\(967\) −13.4723 −0.433240 −0.216620 0.976256i \(-0.569503\pi\)
−0.216620 + 0.976256i \(0.569503\pi\)
\(968\) −1.66985 −0.0536710
\(969\) 0.673648 0.0216407
\(970\) 5.78816 0.185847
\(971\) 60.1256 1.92952 0.964761 0.263128i \(-0.0847542\pi\)
0.964761 + 0.263128i \(0.0847542\pi\)
\(972\) 9.95510 0.319310
\(973\) 7.58971 0.243315
\(974\) −16.0693 −0.514893
\(975\) −1.79948 −0.0576295
\(976\) −0.114241 −0.00365675
\(977\) 52.1944 1.66985 0.834923 0.550367i \(-0.185512\pi\)
0.834923 + 0.550367i \(0.185512\pi\)
\(978\) −23.3034 −0.745162
\(979\) −1.63372 −0.0522138
\(980\) −3.42100 −0.109280
\(981\) −1.17318 −0.0374569
\(982\) −19.2444 −0.614114
\(983\) 25.2508 0.805375 0.402687 0.915338i \(-0.368076\pi\)
0.402687 + 0.915338i \(0.368076\pi\)
\(984\) 1.81275 0.0577884
\(985\) 45.0775 1.43629
\(986\) −0.865049 −0.0275488
\(987\) 15.6722 0.498853
\(988\) 2.97033 0.0944989
\(989\) −18.7159 −0.595132
\(990\) −6.25687 −0.198857
\(991\) −3.89647 −0.123775 −0.0618877 0.998083i \(-0.519712\pi\)
−0.0618877 + 0.998083i \(0.519712\pi\)
\(992\) 3.37485 0.107152
\(993\) −13.6557 −0.433351
\(994\) −32.5508 −1.03245
\(995\) −30.4798 −0.966274
\(996\) 22.7361 0.720420
\(997\) 56.7553 1.79746 0.898729 0.438505i \(-0.144492\pi\)
0.898729 + 0.438505i \(0.144492\pi\)
\(998\) 10.1059 0.319898
\(999\) 20.0724 0.635064
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 \(a_p\))