Properties

Label 8002.2.a.d.1.13
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 1.13
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.42898 q^{3}\) \(+1.00000 q^{4}\) \(-1.63165 q^{5}\) \(-2.42898 q^{6}\) \(+3.93412 q^{7}\) \(+1.00000 q^{8}\) \(+2.89993 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.42898 q^{3}\) \(+1.00000 q^{4}\) \(-1.63165 q^{5}\) \(-2.42898 q^{6}\) \(+3.93412 q^{7}\) \(+1.00000 q^{8}\) \(+2.89993 q^{9}\) \(-1.63165 q^{10}\) \(-6.50822 q^{11}\) \(-2.42898 q^{12}\) \(+2.44292 q^{13}\) \(+3.93412 q^{14}\) \(+3.96325 q^{15}\) \(+1.00000 q^{16}\) \(-2.35205 q^{17}\) \(+2.89993 q^{18}\) \(+6.25808 q^{19}\) \(-1.63165 q^{20}\) \(-9.55589 q^{21}\) \(-6.50822 q^{22}\) \(-9.09408 q^{23}\) \(-2.42898 q^{24}\) \(-2.33771 q^{25}\) \(+2.44292 q^{26}\) \(+0.243076 q^{27}\) \(+3.93412 q^{28}\) \(+4.33849 q^{29}\) \(+3.96325 q^{30}\) \(+9.17000 q^{31}\) \(+1.00000 q^{32}\) \(+15.8083 q^{33}\) \(-2.35205 q^{34}\) \(-6.41912 q^{35}\) \(+2.89993 q^{36}\) \(+1.52912 q^{37}\) \(+6.25808 q^{38}\) \(-5.93380 q^{39}\) \(-1.63165 q^{40}\) \(+5.51590 q^{41}\) \(-9.55589 q^{42}\) \(-7.93779 q^{43}\) \(-6.50822 q^{44}\) \(-4.73167 q^{45}\) \(-9.09408 q^{46}\) \(-3.89046 q^{47}\) \(-2.42898 q^{48}\) \(+8.47732 q^{49}\) \(-2.33771 q^{50}\) \(+5.71307 q^{51}\) \(+2.44292 q^{52}\) \(-8.11651 q^{53}\) \(+0.243076 q^{54}\) \(+10.6192 q^{55}\) \(+3.93412 q^{56}\) \(-15.2007 q^{57}\) \(+4.33849 q^{58}\) \(+3.46092 q^{59}\) \(+3.96325 q^{60}\) \(-10.3917 q^{61}\) \(+9.17000 q^{62}\) \(+11.4087 q^{63}\) \(+1.00000 q^{64}\) \(-3.98600 q^{65}\) \(+15.8083 q^{66}\) \(+2.22144 q^{67}\) \(-2.35205 q^{68}\) \(+22.0893 q^{69}\) \(-6.41912 q^{70}\) \(-2.67169 q^{71}\) \(+2.89993 q^{72}\) \(-6.75657 q^{73}\) \(+1.52912 q^{74}\) \(+5.67824 q^{75}\) \(+6.25808 q^{76}\) \(-25.6041 q^{77}\) \(-5.93380 q^{78}\) \(+17.1301 q^{79}\) \(-1.63165 q^{80}\) \(-9.29021 q^{81}\) \(+5.51590 q^{82}\) \(-7.38539 q^{83}\) \(-9.55589 q^{84}\) \(+3.83773 q^{85}\) \(-7.93779 q^{86}\) \(-10.5381 q^{87}\) \(-6.50822 q^{88}\) \(+15.6397 q^{89}\) \(-4.73167 q^{90}\) \(+9.61075 q^{91}\) \(-9.09408 q^{92}\) \(-22.2737 q^{93}\) \(-3.89046 q^{94}\) \(-10.2110 q^{95}\) \(-2.42898 q^{96}\) \(-9.53508 q^{97}\) \(+8.47732 q^{98}\) \(-18.8734 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.42898 −1.40237 −0.701185 0.712979i \(-0.747345\pi\)
−0.701185 + 0.712979i \(0.747345\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.63165 −0.729697 −0.364849 0.931067i \(-0.618879\pi\)
−0.364849 + 0.931067i \(0.618879\pi\)
\(6\) −2.42898 −0.991625
\(7\) 3.93412 1.48696 0.743479 0.668759i \(-0.233174\pi\)
0.743479 + 0.668759i \(0.233174\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.89993 0.966642
\(10\) −1.63165 −0.515974
\(11\) −6.50822 −1.96230 −0.981152 0.193240i \(-0.938101\pi\)
−0.981152 + 0.193240i \(0.938101\pi\)
\(12\) −2.42898 −0.701185
\(13\) 2.44292 0.677545 0.338772 0.940868i \(-0.389988\pi\)
0.338772 + 0.940868i \(0.389988\pi\)
\(14\) 3.93412 1.05144
\(15\) 3.96325 1.02331
\(16\) 1.00000 0.250000
\(17\) −2.35205 −0.570456 −0.285228 0.958460i \(-0.592069\pi\)
−0.285228 + 0.958460i \(0.592069\pi\)
\(18\) 2.89993 0.683519
\(19\) 6.25808 1.43570 0.717851 0.696197i \(-0.245126\pi\)
0.717851 + 0.696197i \(0.245126\pi\)
\(20\) −1.63165 −0.364849
\(21\) −9.55589 −2.08527
\(22\) −6.50822 −1.38756
\(23\) −9.09408 −1.89625 −0.948123 0.317904i \(-0.897021\pi\)
−0.948123 + 0.317904i \(0.897021\pi\)
\(24\) −2.42898 −0.495813
\(25\) −2.33771 −0.467542
\(26\) 2.44292 0.479096
\(27\) 0.243076 0.0467800
\(28\) 3.93412 0.743479
\(29\) 4.33849 0.805637 0.402819 0.915280i \(-0.368031\pi\)
0.402819 + 0.915280i \(0.368031\pi\)
\(30\) 3.96325 0.723586
\(31\) 9.17000 1.64698 0.823490 0.567331i \(-0.192024\pi\)
0.823490 + 0.567331i \(0.192024\pi\)
\(32\) 1.00000 0.176777
\(33\) 15.8083 2.75188
\(34\) −2.35205 −0.403373
\(35\) −6.41912 −1.08503
\(36\) 2.89993 0.483321
\(37\) 1.52912 0.251385 0.125693 0.992069i \(-0.459885\pi\)
0.125693 + 0.992069i \(0.459885\pi\)
\(38\) 6.25808 1.01519
\(39\) −5.93380 −0.950168
\(40\) −1.63165 −0.257987
\(41\) 5.51590 0.861439 0.430720 0.902486i \(-0.358260\pi\)
0.430720 + 0.902486i \(0.358260\pi\)
\(42\) −9.55589 −1.47451
\(43\) −7.93779 −1.21050 −0.605251 0.796035i \(-0.706927\pi\)
−0.605251 + 0.796035i \(0.706927\pi\)
\(44\) −6.50822 −0.981152
\(45\) −4.73167 −0.705356
\(46\) −9.09408 −1.34085
\(47\) −3.89046 −0.567482 −0.283741 0.958901i \(-0.591576\pi\)
−0.283741 + 0.958901i \(0.591576\pi\)
\(48\) −2.42898 −0.350593
\(49\) 8.47732 1.21105
\(50\) −2.33771 −0.330602
\(51\) 5.71307 0.799990
\(52\) 2.44292 0.338772
\(53\) −8.11651 −1.11489 −0.557444 0.830214i \(-0.688218\pi\)
−0.557444 + 0.830214i \(0.688218\pi\)
\(54\) 0.243076 0.0330784
\(55\) 10.6192 1.43189
\(56\) 3.93412 0.525719
\(57\) −15.2007 −2.01339
\(58\) 4.33849 0.569672
\(59\) 3.46092 0.450573 0.225286 0.974293i \(-0.427668\pi\)
0.225286 + 0.974293i \(0.427668\pi\)
\(60\) 3.96325 0.511653
\(61\) −10.3917 −1.33052 −0.665261 0.746610i \(-0.731680\pi\)
−0.665261 + 0.746610i \(0.731680\pi\)
\(62\) 9.17000 1.16459
\(63\) 11.4087 1.43736
\(64\) 1.00000 0.125000
\(65\) −3.98600 −0.494403
\(66\) 15.8083 1.94587
\(67\) 2.22144 0.271392 0.135696 0.990751i \(-0.456673\pi\)
0.135696 + 0.990751i \(0.456673\pi\)
\(68\) −2.35205 −0.285228
\(69\) 22.0893 2.65924
\(70\) −6.41912 −0.767232
\(71\) −2.67169 −0.317071 −0.158536 0.987353i \(-0.550677\pi\)
−0.158536 + 0.987353i \(0.550677\pi\)
\(72\) 2.89993 0.341760
\(73\) −6.75657 −0.790796 −0.395398 0.918510i \(-0.629393\pi\)
−0.395398 + 0.918510i \(0.629393\pi\)
\(74\) 1.52912 0.177756
\(75\) 5.67824 0.655667
\(76\) 6.25808 0.717851
\(77\) −25.6041 −2.91786
\(78\) −5.93380 −0.671871
\(79\) 17.1301 1.92729 0.963645 0.267186i \(-0.0860937\pi\)
0.963645 + 0.267186i \(0.0860937\pi\)
\(80\) −1.63165 −0.182424
\(81\) −9.29021 −1.03225
\(82\) 5.51590 0.609130
\(83\) −7.38539 −0.810652 −0.405326 0.914172i \(-0.632842\pi\)
−0.405326 + 0.914172i \(0.632842\pi\)
\(84\) −9.55589 −1.04263
\(85\) 3.83773 0.416260
\(86\) −7.93779 −0.855954
\(87\) −10.5381 −1.12980
\(88\) −6.50822 −0.693779
\(89\) 15.6397 1.65780 0.828901 0.559396i \(-0.188967\pi\)
0.828901 + 0.559396i \(0.188967\pi\)
\(90\) −4.73167 −0.498762
\(91\) 9.61075 1.00748
\(92\) −9.09408 −0.948123
\(93\) −22.2737 −2.30968
\(94\) −3.89046 −0.401270
\(95\) −10.2110 −1.04763
\(96\) −2.42898 −0.247906
\(97\) −9.53508 −0.968141 −0.484070 0.875029i \(-0.660842\pi\)
−0.484070 + 0.875029i \(0.660842\pi\)
\(98\) 8.47732 0.856338
\(99\) −18.8734 −1.89685
\(100\) −2.33771 −0.233771
\(101\) 7.22405 0.718820 0.359410 0.933180i \(-0.382978\pi\)
0.359410 + 0.933180i \(0.382978\pi\)
\(102\) 5.71307 0.565678
\(103\) −13.2094 −1.30156 −0.650782 0.759265i \(-0.725559\pi\)
−0.650782 + 0.759265i \(0.725559\pi\)
\(104\) 2.44292 0.239548
\(105\) 15.5919 1.52161
\(106\) −8.11651 −0.788345
\(107\) 8.95921 0.866120 0.433060 0.901365i \(-0.357434\pi\)
0.433060 + 0.901365i \(0.357434\pi\)
\(108\) 0.243076 0.0233900
\(109\) −15.1403 −1.45018 −0.725090 0.688654i \(-0.758202\pi\)
−0.725090 + 0.688654i \(0.758202\pi\)
\(110\) 10.6192 1.01250
\(111\) −3.71419 −0.352535
\(112\) 3.93412 0.371740
\(113\) 4.09684 0.385398 0.192699 0.981258i \(-0.438276\pi\)
0.192699 + 0.981258i \(0.438276\pi\)
\(114\) −15.2007 −1.42368
\(115\) 14.8384 1.38369
\(116\) 4.33849 0.402819
\(117\) 7.08429 0.654943
\(118\) 3.46092 0.318603
\(119\) −9.25325 −0.848244
\(120\) 3.96325 0.361793
\(121\) 31.3570 2.85063
\(122\) −10.3917 −0.940822
\(123\) −13.3980 −1.20806
\(124\) 9.17000 0.823490
\(125\) 11.9726 1.07086
\(126\) 11.4087 1.01636
\(127\) −0.451099 −0.0400286 −0.0200143 0.999800i \(-0.506371\pi\)
−0.0200143 + 0.999800i \(0.506371\pi\)
\(128\) 1.00000 0.0883883
\(129\) 19.2807 1.69757
\(130\) −3.98600 −0.349595
\(131\) 6.87675 0.600825 0.300412 0.953809i \(-0.402876\pi\)
0.300412 + 0.953809i \(0.402876\pi\)
\(132\) 15.8083 1.37594
\(133\) 24.6200 2.13483
\(134\) 2.22144 0.191903
\(135\) −0.396615 −0.0341352
\(136\) −2.35205 −0.201687
\(137\) −19.6896 −1.68220 −0.841098 0.540883i \(-0.818090\pi\)
−0.841098 + 0.540883i \(0.818090\pi\)
\(138\) 22.0893 1.88037
\(139\) −11.5087 −0.976159 −0.488080 0.872799i \(-0.662302\pi\)
−0.488080 + 0.872799i \(0.662302\pi\)
\(140\) −6.41912 −0.542515
\(141\) 9.44983 0.795820
\(142\) −2.67169 −0.224203
\(143\) −15.8991 −1.32955
\(144\) 2.89993 0.241661
\(145\) −7.07891 −0.587871
\(146\) −6.75657 −0.559178
\(147\) −20.5912 −1.69833
\(148\) 1.52912 0.125693
\(149\) 2.39346 0.196080 0.0980398 0.995182i \(-0.468743\pi\)
0.0980398 + 0.995182i \(0.468743\pi\)
\(150\) 5.67824 0.463626
\(151\) 6.19252 0.503940 0.251970 0.967735i \(-0.418922\pi\)
0.251970 + 0.967735i \(0.418922\pi\)
\(152\) 6.25808 0.507597
\(153\) −6.82077 −0.551427
\(154\) −25.6041 −2.06324
\(155\) −14.9622 −1.20180
\(156\) −5.93380 −0.475084
\(157\) 7.02873 0.560954 0.280477 0.959861i \(-0.409507\pi\)
0.280477 + 0.959861i \(0.409507\pi\)
\(158\) 17.1301 1.36280
\(159\) 19.7148 1.56349
\(160\) −1.63165 −0.128993
\(161\) −35.7772 −2.81964
\(162\) −9.29021 −0.729907
\(163\) −7.85085 −0.614926 −0.307463 0.951560i \(-0.599480\pi\)
−0.307463 + 0.951560i \(0.599480\pi\)
\(164\) 5.51590 0.430720
\(165\) −25.7937 −2.00804
\(166\) −7.38539 −0.573218
\(167\) 8.77288 0.678866 0.339433 0.940630i \(-0.389765\pi\)
0.339433 + 0.940630i \(0.389765\pi\)
\(168\) −9.55589 −0.737253
\(169\) −7.03213 −0.540933
\(170\) 3.83773 0.294340
\(171\) 18.1480 1.38781
\(172\) −7.93779 −0.605251
\(173\) 20.0977 1.52800 0.764001 0.645215i \(-0.223232\pi\)
0.764001 + 0.645215i \(0.223232\pi\)
\(174\) −10.5381 −0.798890
\(175\) −9.19683 −0.695215
\(176\) −6.50822 −0.490576
\(177\) −8.40648 −0.631870
\(178\) 15.6397 1.17224
\(179\) −22.0836 −1.65060 −0.825301 0.564693i \(-0.808995\pi\)
−0.825301 + 0.564693i \(0.808995\pi\)
\(180\) −4.73167 −0.352678
\(181\) 0.504009 0.0374627 0.0187313 0.999825i \(-0.494037\pi\)
0.0187313 + 0.999825i \(0.494037\pi\)
\(182\) 9.61075 0.712396
\(183\) 25.2412 1.86589
\(184\) −9.09408 −0.670424
\(185\) −2.49499 −0.183435
\(186\) −22.2737 −1.63319
\(187\) 15.3077 1.11941
\(188\) −3.89046 −0.283741
\(189\) 0.956290 0.0695599
\(190\) −10.2110 −0.740785
\(191\) 13.0768 0.946203 0.473101 0.881008i \(-0.343134\pi\)
0.473101 + 0.881008i \(0.343134\pi\)
\(192\) −2.42898 −0.175296
\(193\) 6.83261 0.491822 0.245911 0.969292i \(-0.420913\pi\)
0.245911 + 0.969292i \(0.420913\pi\)
\(194\) −9.53508 −0.684579
\(195\) 9.68190 0.693335
\(196\) 8.47732 0.605523
\(197\) −25.5654 −1.82146 −0.910730 0.413002i \(-0.864480\pi\)
−0.910730 + 0.413002i \(0.864480\pi\)
\(198\) −18.8734 −1.34127
\(199\) 14.2658 1.01127 0.505637 0.862746i \(-0.331258\pi\)
0.505637 + 0.862746i \(0.331258\pi\)
\(200\) −2.33771 −0.165301
\(201\) −5.39582 −0.380592
\(202\) 7.22405 0.508282
\(203\) 17.0681 1.19795
\(204\) 5.71307 0.399995
\(205\) −9.00004 −0.628590
\(206\) −13.2094 −0.920345
\(207\) −26.3722 −1.83299
\(208\) 2.44292 0.169386
\(209\) −40.7290 −2.81728
\(210\) 15.5919 1.07594
\(211\) −20.9173 −1.44001 −0.720005 0.693969i \(-0.755860\pi\)
−0.720005 + 0.693969i \(0.755860\pi\)
\(212\) −8.11651 −0.557444
\(213\) 6.48947 0.444651
\(214\) 8.95921 0.612439
\(215\) 12.9517 0.883300
\(216\) 0.243076 0.0165392
\(217\) 36.0759 2.44899
\(218\) −15.1403 −1.02543
\(219\) 16.4115 1.10899
\(220\) 10.6192 0.715944
\(221\) −5.74587 −0.386509
\(222\) −3.71419 −0.249280
\(223\) −22.7105 −1.52081 −0.760405 0.649449i \(-0.774999\pi\)
−0.760405 + 0.649449i \(0.774999\pi\)
\(224\) 3.93412 0.262860
\(225\) −6.77919 −0.451946
\(226\) 4.09684 0.272518
\(227\) −25.5465 −1.69558 −0.847791 0.530330i \(-0.822068\pi\)
−0.847791 + 0.530330i \(0.822068\pi\)
\(228\) −15.2007 −1.00669
\(229\) 0.0691195 0.00456754 0.00228377 0.999997i \(-0.499273\pi\)
0.00228377 + 0.999997i \(0.499273\pi\)
\(230\) 14.8384 0.978414
\(231\) 62.1919 4.09192
\(232\) 4.33849 0.284836
\(233\) −4.53012 −0.296778 −0.148389 0.988929i \(-0.547409\pi\)
−0.148389 + 0.988929i \(0.547409\pi\)
\(234\) 7.08429 0.463115
\(235\) 6.34788 0.414090
\(236\) 3.46092 0.225286
\(237\) −41.6087 −2.70277
\(238\) −9.25325 −0.599799
\(239\) 3.09460 0.200173 0.100087 0.994979i \(-0.468088\pi\)
0.100087 + 0.994979i \(0.468088\pi\)
\(240\) 3.96325 0.255826
\(241\) 9.49765 0.611797 0.305899 0.952064i \(-0.401043\pi\)
0.305899 + 0.952064i \(0.401043\pi\)
\(242\) 31.3570 2.01570
\(243\) 21.8365 1.40081
\(244\) −10.3917 −0.665261
\(245\) −13.8320 −0.883697
\(246\) −13.3980 −0.854225
\(247\) 15.2880 0.972752
\(248\) 9.17000 0.582295
\(249\) 17.9389 1.13683
\(250\) 11.9726 0.757213
\(251\) 15.2680 0.963711 0.481855 0.876251i \(-0.339963\pi\)
0.481855 + 0.876251i \(0.339963\pi\)
\(252\) 11.4087 0.718678
\(253\) 59.1863 3.72101
\(254\) −0.451099 −0.0283045
\(255\) −9.32175 −0.583751
\(256\) 1.00000 0.0625000
\(257\) −22.4339 −1.39939 −0.699695 0.714442i \(-0.746681\pi\)
−0.699695 + 0.714442i \(0.746681\pi\)
\(258\) 19.2807 1.20036
\(259\) 6.01573 0.373799
\(260\) −3.98600 −0.247201
\(261\) 12.5813 0.778763
\(262\) 6.87675 0.424847
\(263\) 11.5457 0.711937 0.355969 0.934498i \(-0.384151\pi\)
0.355969 + 0.934498i \(0.384151\pi\)
\(264\) 15.8083 0.972935
\(265\) 13.2433 0.813531
\(266\) 24.6200 1.50955
\(267\) −37.9884 −2.32485
\(268\) 2.22144 0.135696
\(269\) −15.5778 −0.949795 −0.474898 0.880041i \(-0.657515\pi\)
−0.474898 + 0.880041i \(0.657515\pi\)
\(270\) −0.396615 −0.0241372
\(271\) 14.6625 0.890685 0.445342 0.895360i \(-0.353082\pi\)
0.445342 + 0.895360i \(0.353082\pi\)
\(272\) −2.35205 −0.142614
\(273\) −23.3443 −1.41286
\(274\) −19.6896 −1.18949
\(275\) 15.2143 0.917459
\(276\) 22.0893 1.32962
\(277\) −28.2531 −1.69757 −0.848783 0.528742i \(-0.822664\pi\)
−0.848783 + 0.528742i \(0.822664\pi\)
\(278\) −11.5087 −0.690249
\(279\) 26.5923 1.59204
\(280\) −6.41912 −0.383616
\(281\) 21.9228 1.30780 0.653902 0.756579i \(-0.273131\pi\)
0.653902 + 0.756579i \(0.273131\pi\)
\(282\) 9.44983 0.562729
\(283\) −10.8414 −0.644457 −0.322228 0.946662i \(-0.604432\pi\)
−0.322228 + 0.946662i \(0.604432\pi\)
\(284\) −2.67169 −0.158536
\(285\) 24.8023 1.46916
\(286\) −15.8991 −0.940132
\(287\) 21.7002 1.28092
\(288\) 2.89993 0.170880
\(289\) −11.4679 −0.674580
\(290\) −7.07891 −0.415688
\(291\) 23.1605 1.35769
\(292\) −6.75657 −0.395398
\(293\) −30.1137 −1.75926 −0.879632 0.475655i \(-0.842211\pi\)
−0.879632 + 0.475655i \(0.842211\pi\)
\(294\) −20.5912 −1.20090
\(295\) −5.64701 −0.328782
\(296\) 1.52912 0.0888781
\(297\) −1.58199 −0.0917965
\(298\) 2.39346 0.138649
\(299\) −22.2161 −1.28479
\(300\) 5.67824 0.327833
\(301\) −31.2282 −1.79997
\(302\) 6.19252 0.356339
\(303\) −17.5470 −1.00805
\(304\) 6.25808 0.358925
\(305\) 16.9557 0.970879
\(306\) −6.82077 −0.389917
\(307\) −22.2556 −1.27019 −0.635097 0.772433i \(-0.719040\pi\)
−0.635097 + 0.772433i \(0.719040\pi\)
\(308\) −25.6041 −1.45893
\(309\) 32.0854 1.82527
\(310\) −14.9622 −0.849799
\(311\) −5.16239 −0.292732 −0.146366 0.989230i \(-0.546758\pi\)
−0.146366 + 0.989230i \(0.546758\pi\)
\(312\) −5.93380 −0.335935
\(313\) −34.3839 −1.94349 −0.971745 0.236033i \(-0.924153\pi\)
−0.971745 + 0.236033i \(0.924153\pi\)
\(314\) 7.02873 0.396654
\(315\) −18.6150 −1.04884
\(316\) 17.1301 0.963645
\(317\) −15.6821 −0.880797 −0.440398 0.897802i \(-0.645163\pi\)
−0.440398 + 0.897802i \(0.645163\pi\)
\(318\) 19.7148 1.10555
\(319\) −28.2359 −1.58090
\(320\) −1.63165 −0.0912122
\(321\) −21.7617 −1.21462
\(322\) −35.7772 −1.99379
\(323\) −14.7193 −0.819004
\(324\) −9.29021 −0.516123
\(325\) −5.71084 −0.316780
\(326\) −7.85085 −0.434818
\(327\) 36.7755 2.03369
\(328\) 5.51590 0.304565
\(329\) −15.3055 −0.843822
\(330\) −25.7937 −1.41990
\(331\) −31.1154 −1.71026 −0.855128 0.518417i \(-0.826522\pi\)
−0.855128 + 0.518417i \(0.826522\pi\)
\(332\) −7.38539 −0.405326
\(333\) 4.43433 0.243000
\(334\) 8.77288 0.480030
\(335\) −3.62461 −0.198034
\(336\) −9.55589 −0.521317
\(337\) −16.3637 −0.891387 −0.445694 0.895186i \(-0.647043\pi\)
−0.445694 + 0.895186i \(0.647043\pi\)
\(338\) −7.03213 −0.382498
\(339\) −9.95113 −0.540471
\(340\) 3.83773 0.208130
\(341\) −59.6804 −3.23187
\(342\) 18.1480 0.981330
\(343\) 5.81195 0.313816
\(344\) −7.93779 −0.427977
\(345\) −36.0421 −1.94044
\(346\) 20.0977 1.08046
\(347\) 4.10189 0.220201 0.110100 0.993920i \(-0.464883\pi\)
0.110100 + 0.993920i \(0.464883\pi\)
\(348\) −10.5381 −0.564901
\(349\) −21.0142 −1.12486 −0.562432 0.826843i \(-0.690134\pi\)
−0.562432 + 0.826843i \(0.690134\pi\)
\(350\) −9.19683 −0.491591
\(351\) 0.593815 0.0316955
\(352\) −6.50822 −0.346889
\(353\) −15.0533 −0.801208 −0.400604 0.916251i \(-0.631200\pi\)
−0.400604 + 0.916251i \(0.631200\pi\)
\(354\) −8.40648 −0.446799
\(355\) 4.35927 0.231366
\(356\) 15.6397 0.828901
\(357\) 22.4759 1.18955
\(358\) −22.0836 −1.16715
\(359\) −8.27864 −0.436930 −0.218465 0.975845i \(-0.570105\pi\)
−0.218465 + 0.975845i \(0.570105\pi\)
\(360\) −4.73167 −0.249381
\(361\) 20.1636 1.06124
\(362\) 0.504009 0.0264901
\(363\) −76.1653 −3.99764
\(364\) 9.61075 0.503740
\(365\) 11.0244 0.577042
\(366\) 25.2412 1.31938
\(367\) 10.7723 0.562311 0.281156 0.959662i \(-0.409282\pi\)
0.281156 + 0.959662i \(0.409282\pi\)
\(368\) −9.09408 −0.474062
\(369\) 15.9957 0.832704
\(370\) −2.49499 −0.129708
\(371\) −31.9313 −1.65779
\(372\) −22.2737 −1.15484
\(373\) 0.104352 0.00540316 0.00270158 0.999996i \(-0.499140\pi\)
0.00270158 + 0.999996i \(0.499140\pi\)
\(374\) 15.3077 0.791540
\(375\) −29.0811 −1.50174
\(376\) −3.89046 −0.200635
\(377\) 10.5986 0.545855
\(378\) 0.956290 0.0491862
\(379\) 9.03615 0.464156 0.232078 0.972697i \(-0.425448\pi\)
0.232078 + 0.972697i \(0.425448\pi\)
\(380\) −10.2110 −0.523814
\(381\) 1.09571 0.0561349
\(382\) 13.0768 0.669066
\(383\) 27.7505 1.41798 0.708992 0.705216i \(-0.249150\pi\)
0.708992 + 0.705216i \(0.249150\pi\)
\(384\) −2.42898 −0.123953
\(385\) 41.7771 2.12916
\(386\) 6.83261 0.347771
\(387\) −23.0190 −1.17012
\(388\) −9.53508 −0.484070
\(389\) −25.7264 −1.30438 −0.652191 0.758055i \(-0.726150\pi\)
−0.652191 + 0.758055i \(0.726150\pi\)
\(390\) 9.68190 0.490262
\(391\) 21.3897 1.08172
\(392\) 8.47732 0.428169
\(393\) −16.7035 −0.842579
\(394\) −25.5654 −1.28797
\(395\) −27.9504 −1.40634
\(396\) −18.8734 −0.948423
\(397\) −21.5241 −1.08026 −0.540131 0.841581i \(-0.681625\pi\)
−0.540131 + 0.841581i \(0.681625\pi\)
\(398\) 14.2658 0.715079
\(399\) −59.8015 −2.99382
\(400\) −2.33771 −0.116885
\(401\) −11.7675 −0.587641 −0.293820 0.955861i \(-0.594927\pi\)
−0.293820 + 0.955861i \(0.594927\pi\)
\(402\) −5.39582 −0.269119
\(403\) 22.4016 1.11590
\(404\) 7.22405 0.359410
\(405\) 15.1584 0.753226
\(406\) 17.0681 0.847078
\(407\) −9.95183 −0.493294
\(408\) 5.71307 0.282839
\(409\) 25.5443 1.26309 0.631543 0.775341i \(-0.282422\pi\)
0.631543 + 0.775341i \(0.282422\pi\)
\(410\) −9.00004 −0.444480
\(411\) 47.8256 2.35906
\(412\) −13.2094 −0.650782
\(413\) 13.6157 0.669983
\(414\) −26.3722 −1.29612
\(415\) 12.0504 0.591531
\(416\) 2.44292 0.119774
\(417\) 27.9545 1.36894
\(418\) −40.7290 −1.99212
\(419\) −19.7092 −0.962856 −0.481428 0.876486i \(-0.659882\pi\)
−0.481428 + 0.876486i \(0.659882\pi\)
\(420\) 15.5919 0.760807
\(421\) 30.2532 1.47445 0.737225 0.675648i \(-0.236136\pi\)
0.737225 + 0.675648i \(0.236136\pi\)
\(422\) −20.9173 −1.01824
\(423\) −11.2820 −0.548552
\(424\) −8.11651 −0.394173
\(425\) 5.49841 0.266712
\(426\) 6.48947 0.314416
\(427\) −40.8823 −1.97843
\(428\) 8.95921 0.433060
\(429\) 38.6185 1.86452
\(430\) 12.9517 0.624587
\(431\) −34.8805 −1.68013 −0.840067 0.542483i \(-0.817484\pi\)
−0.840067 + 0.542483i \(0.817484\pi\)
\(432\) 0.243076 0.0116950
\(433\) 14.8819 0.715176 0.357588 0.933879i \(-0.383599\pi\)
0.357588 + 0.933879i \(0.383599\pi\)
\(434\) 36.0759 1.73170
\(435\) 17.1945 0.824413
\(436\) −15.1403 −0.725090
\(437\) −56.9115 −2.72244
\(438\) 16.4115 0.784174
\(439\) 10.0693 0.480581 0.240291 0.970701i \(-0.422757\pi\)
0.240291 + 0.970701i \(0.422757\pi\)
\(440\) 10.6192 0.506249
\(441\) 24.5836 1.17065
\(442\) −5.74587 −0.273303
\(443\) 26.5038 1.25923 0.629617 0.776905i \(-0.283212\pi\)
0.629617 + 0.776905i \(0.283212\pi\)
\(444\) −3.71419 −0.176268
\(445\) −25.5185 −1.20969
\(446\) −22.7105 −1.07537
\(447\) −5.81365 −0.274976
\(448\) 3.93412 0.185870
\(449\) −28.6134 −1.35035 −0.675174 0.737659i \(-0.735931\pi\)
−0.675174 + 0.737659i \(0.735931\pi\)
\(450\) −6.77919 −0.319574
\(451\) −35.8987 −1.69041
\(452\) 4.09684 0.192699
\(453\) −15.0415 −0.706710
\(454\) −25.5465 −1.19896
\(455\) −15.6814 −0.735156
\(456\) −15.2007 −0.711839
\(457\) 0.264389 0.0123676 0.00618379 0.999981i \(-0.498032\pi\)
0.00618379 + 0.999981i \(0.498032\pi\)
\(458\) 0.0691195 0.00322974
\(459\) −0.571726 −0.0266859
\(460\) 14.8384 0.691843
\(461\) −25.3513 −1.18073 −0.590364 0.807137i \(-0.701016\pi\)
−0.590364 + 0.807137i \(0.701016\pi\)
\(462\) 62.1919 2.89343
\(463\) 38.7891 1.80268 0.901342 0.433108i \(-0.142583\pi\)
0.901342 + 0.433108i \(0.142583\pi\)
\(464\) 4.33849 0.201409
\(465\) 36.3430 1.68536
\(466\) −4.53012 −0.209854
\(467\) −38.7430 −1.79281 −0.896406 0.443233i \(-0.853831\pi\)
−0.896406 + 0.443233i \(0.853831\pi\)
\(468\) 7.08429 0.327472
\(469\) 8.73941 0.403548
\(470\) 6.34788 0.292806
\(471\) −17.0726 −0.786665
\(472\) 3.46092 0.159302
\(473\) 51.6609 2.37537
\(474\) −41.6087 −1.91115
\(475\) −14.6296 −0.671251
\(476\) −9.25325 −0.424122
\(477\) −23.5373 −1.07770
\(478\) 3.09460 0.141544
\(479\) 7.52557 0.343852 0.171926 0.985110i \(-0.445001\pi\)
0.171926 + 0.985110i \(0.445001\pi\)
\(480\) 3.96325 0.180897
\(481\) 3.73551 0.170325
\(482\) 9.49765 0.432606
\(483\) 86.9020 3.95418
\(484\) 31.3570 1.42532
\(485\) 15.5579 0.706450
\(486\) 21.8365 0.990522
\(487\) −27.9026 −1.26439 −0.632193 0.774811i \(-0.717845\pi\)
−0.632193 + 0.774811i \(0.717845\pi\)
\(488\) −10.3917 −0.470411
\(489\) 19.0695 0.862354
\(490\) −13.8320 −0.624868
\(491\) −11.2908 −0.509548 −0.254774 0.967001i \(-0.582001\pi\)
−0.254774 + 0.967001i \(0.582001\pi\)
\(492\) −13.3980 −0.604028
\(493\) −10.2043 −0.459580
\(494\) 15.2880 0.687840
\(495\) 30.7948 1.38412
\(496\) 9.17000 0.411745
\(497\) −10.5108 −0.471472
\(498\) 17.9389 0.803863
\(499\) −10.2253 −0.457748 −0.228874 0.973456i \(-0.573504\pi\)
−0.228874 + 0.973456i \(0.573504\pi\)
\(500\) 11.9726 0.535431
\(501\) −21.3091 −0.952021
\(502\) 15.2680 0.681446
\(503\) −29.7579 −1.32684 −0.663420 0.748247i \(-0.730896\pi\)
−0.663420 + 0.748247i \(0.730896\pi\)
\(504\) 11.4087 0.508182
\(505\) −11.7871 −0.524521
\(506\) 59.1863 2.63115
\(507\) 17.0809 0.758589
\(508\) −0.451099 −0.0200143
\(509\) −13.5647 −0.601244 −0.300622 0.953743i \(-0.597194\pi\)
−0.300622 + 0.953743i \(0.597194\pi\)
\(510\) −9.32175 −0.412774
\(511\) −26.5812 −1.17588
\(512\) 1.00000 0.0441942
\(513\) 1.52119 0.0671621
\(514\) −22.4339 −0.989518
\(515\) 21.5532 0.949748
\(516\) 19.2807 0.848786
\(517\) 25.3200 1.11357
\(518\) 6.01573 0.264316
\(519\) −48.8169 −2.14282
\(520\) −3.98600 −0.174798
\(521\) −1.70687 −0.0747792 −0.0373896 0.999301i \(-0.511904\pi\)
−0.0373896 + 0.999301i \(0.511904\pi\)
\(522\) 12.5813 0.550669
\(523\) 21.2928 0.931070 0.465535 0.885030i \(-0.345862\pi\)
0.465535 + 0.885030i \(0.345862\pi\)
\(524\) 6.87675 0.300412
\(525\) 22.3389 0.974949
\(526\) 11.5457 0.503416
\(527\) −21.5683 −0.939529
\(528\) 15.8083 0.687969
\(529\) 59.7022 2.59575
\(530\) 13.2433 0.575253
\(531\) 10.0364 0.435543
\(532\) 24.6200 1.06741
\(533\) 13.4749 0.583664
\(534\) −37.9884 −1.64392
\(535\) −14.6183 −0.632005
\(536\) 2.22144 0.0959515
\(537\) 53.6404 2.31476
\(538\) −15.5778 −0.671607
\(539\) −55.1723 −2.37644
\(540\) −0.396615 −0.0170676
\(541\) 40.6056 1.74577 0.872886 0.487925i \(-0.162246\pi\)
0.872886 + 0.487925i \(0.162246\pi\)
\(542\) 14.6625 0.629809
\(543\) −1.22423 −0.0525365
\(544\) −2.35205 −0.100843
\(545\) 24.7038 1.05819
\(546\) −23.3443 −0.999044
\(547\) 12.7634 0.545726 0.272863 0.962053i \(-0.412029\pi\)
0.272863 + 0.962053i \(0.412029\pi\)
\(548\) −19.6896 −0.841098
\(549\) −30.1352 −1.28614
\(550\) 15.2143 0.648741
\(551\) 27.1506 1.15665
\(552\) 22.0893 0.940183
\(553\) 67.3920 2.86580
\(554\) −28.2531 −1.20036
\(555\) 6.06027 0.257244
\(556\) −11.5087 −0.488080
\(557\) −1.40014 −0.0593260 −0.0296630 0.999560i \(-0.509443\pi\)
−0.0296630 + 0.999560i \(0.509443\pi\)
\(558\) 26.5923 1.12574
\(559\) −19.3914 −0.820169
\(560\) −6.41912 −0.271257
\(561\) −37.1819 −1.56982
\(562\) 21.9228 0.924757
\(563\) 29.1661 1.22920 0.614602 0.788837i \(-0.289317\pi\)
0.614602 + 0.788837i \(0.289317\pi\)
\(564\) 9.44983 0.397910
\(565\) −6.68462 −0.281224
\(566\) −10.8414 −0.455700
\(567\) −36.5488 −1.53491
\(568\) −2.67169 −0.112102
\(569\) −6.70361 −0.281030 −0.140515 0.990079i \(-0.544876\pi\)
−0.140515 + 0.990079i \(0.544876\pi\)
\(570\) 24.8023 1.03885
\(571\) 0.996288 0.0416934 0.0208467 0.999783i \(-0.493364\pi\)
0.0208467 + 0.999783i \(0.493364\pi\)
\(572\) −15.8991 −0.664774
\(573\) −31.7632 −1.32693
\(574\) 21.7002 0.905750
\(575\) 21.2593 0.886574
\(576\) 2.89993 0.120830
\(577\) 39.9708 1.66401 0.832004 0.554770i \(-0.187194\pi\)
0.832004 + 0.554770i \(0.187194\pi\)
\(578\) −11.4679 −0.477000
\(579\) −16.5963 −0.689717
\(580\) −7.07891 −0.293936
\(581\) −29.0550 −1.20541
\(582\) 23.1605 0.960033
\(583\) 52.8241 2.18775
\(584\) −6.75657 −0.279589
\(585\) −11.5591 −0.477910
\(586\) −30.1137 −1.24399
\(587\) 3.85518 0.159120 0.0795601 0.996830i \(-0.474648\pi\)
0.0795601 + 0.996830i \(0.474648\pi\)
\(588\) −20.5912 −0.849167
\(589\) 57.3866 2.36457
\(590\) −5.64701 −0.232484
\(591\) 62.0978 2.55436
\(592\) 1.52912 0.0628463
\(593\) −3.95459 −0.162395 −0.0811977 0.996698i \(-0.525875\pi\)
−0.0811977 + 0.996698i \(0.525875\pi\)
\(594\) −1.58199 −0.0649099
\(595\) 15.0981 0.618961
\(596\) 2.39346 0.0980398
\(597\) −34.6512 −1.41818
\(598\) −22.2161 −0.908485
\(599\) −27.6817 −1.13104 −0.565521 0.824734i \(-0.691325\pi\)
−0.565521 + 0.824734i \(0.691325\pi\)
\(600\) 5.67824 0.231813
\(601\) −41.7687 −1.70378 −0.851891 0.523718i \(-0.824544\pi\)
−0.851891 + 0.523718i \(0.824544\pi\)
\(602\) −31.2282 −1.27277
\(603\) 6.44201 0.262339
\(604\) 6.19252 0.251970
\(605\) −51.1637 −2.08010
\(606\) −17.5470 −0.712800
\(607\) −30.6562 −1.24430 −0.622148 0.782900i \(-0.713740\pi\)
−0.622148 + 0.782900i \(0.713740\pi\)
\(608\) 6.25808 0.253799
\(609\) −41.4581 −1.67997
\(610\) 16.9557 0.686515
\(611\) −9.50409 −0.384494
\(612\) −6.82077 −0.275713
\(613\) 17.5748 0.709841 0.354920 0.934897i \(-0.384508\pi\)
0.354920 + 0.934897i \(0.384508\pi\)
\(614\) −22.2556 −0.898162
\(615\) 21.8609 0.881516
\(616\) −25.6041 −1.03162
\(617\) 10.0730 0.405522 0.202761 0.979228i \(-0.435009\pi\)
0.202761 + 0.979228i \(0.435009\pi\)
\(618\) 32.0854 1.29066
\(619\) −12.2522 −0.492459 −0.246230 0.969212i \(-0.579192\pi\)
−0.246230 + 0.969212i \(0.579192\pi\)
\(620\) −14.9622 −0.600898
\(621\) −2.21055 −0.0887063
\(622\) −5.16239 −0.206993
\(623\) 61.5284 2.46508
\(624\) −5.93380 −0.237542
\(625\) −7.84657 −0.313863
\(626\) −34.3839 −1.37426
\(627\) 98.9297 3.95087
\(628\) 7.02873 0.280477
\(629\) −3.59656 −0.143404
\(630\) −18.6150 −0.741639
\(631\) −38.5619 −1.53513 −0.767563 0.640973i \(-0.778531\pi\)
−0.767563 + 0.640973i \(0.778531\pi\)
\(632\) 17.1301 0.681400
\(633\) 50.8077 2.01943
\(634\) −15.6821 −0.622817
\(635\) 0.736037 0.0292088
\(636\) 19.7148 0.781743
\(637\) 20.7094 0.820537
\(638\) −28.2359 −1.11787
\(639\) −7.74770 −0.306494
\(640\) −1.63165 −0.0644967
\(641\) 18.1661 0.717519 0.358759 0.933430i \(-0.383200\pi\)
0.358759 + 0.933430i \(0.383200\pi\)
\(642\) −21.7617 −0.858867
\(643\) −7.80555 −0.307821 −0.153910 0.988085i \(-0.549187\pi\)
−0.153910 + 0.988085i \(0.549187\pi\)
\(644\) −35.7772 −1.40982
\(645\) −31.4594 −1.23871
\(646\) −14.7193 −0.579123
\(647\) −6.58881 −0.259033 −0.129516 0.991577i \(-0.541342\pi\)
−0.129516 + 0.991577i \(0.541342\pi\)
\(648\) −9.29021 −0.364954
\(649\) −22.5244 −0.884160
\(650\) −5.71084 −0.223998
\(651\) −87.6275 −3.43439
\(652\) −7.85085 −0.307463
\(653\) 35.6242 1.39408 0.697041 0.717031i \(-0.254499\pi\)
0.697041 + 0.717031i \(0.254499\pi\)
\(654\) 36.7755 1.43804
\(655\) −11.2205 −0.438420
\(656\) 5.51590 0.215360
\(657\) −19.5936 −0.764417
\(658\) −15.3055 −0.596672
\(659\) 0.604088 0.0235319 0.0117660 0.999931i \(-0.496255\pi\)
0.0117660 + 0.999931i \(0.496255\pi\)
\(660\) −25.7937 −1.00402
\(661\) −23.8552 −0.927858 −0.463929 0.885872i \(-0.653561\pi\)
−0.463929 + 0.885872i \(0.653561\pi\)
\(662\) −31.1154 −1.20933
\(663\) 13.9566 0.542029
\(664\) −7.38539 −0.286609
\(665\) −40.1714 −1.55778
\(666\) 4.43433 0.171827
\(667\) −39.4546 −1.52769
\(668\) 8.77288 0.339433
\(669\) 55.1633 2.13274
\(670\) −3.62461 −0.140031
\(671\) 67.6316 2.61089
\(672\) −9.55589 −0.368626
\(673\) 28.6740 1.10530 0.552651 0.833413i \(-0.313616\pi\)
0.552651 + 0.833413i \(0.313616\pi\)
\(674\) −16.3637 −0.630306
\(675\) −0.568241 −0.0218716
\(676\) −7.03213 −0.270467
\(677\) −26.4862 −1.01795 −0.508973 0.860783i \(-0.669975\pi\)
−0.508973 + 0.860783i \(0.669975\pi\)
\(678\) −9.95113 −0.382171
\(679\) −37.5122 −1.43959
\(680\) 3.83773 0.147170
\(681\) 62.0519 2.37783
\(682\) −59.6804 −2.28528
\(683\) 26.9505 1.03123 0.515615 0.856820i \(-0.327563\pi\)
0.515615 + 0.856820i \(0.327563\pi\)
\(684\) 18.1480 0.693905
\(685\) 32.1266 1.22749
\(686\) 5.81195 0.221901
\(687\) −0.167890 −0.00640539
\(688\) −7.93779 −0.302625
\(689\) −19.8280 −0.755387
\(690\) −36.0421 −1.37210
\(691\) −0.960197 −0.0365276 −0.0182638 0.999833i \(-0.505814\pi\)
−0.0182638 + 0.999833i \(0.505814\pi\)
\(692\) 20.0977 0.764001
\(693\) −74.2501 −2.82053
\(694\) 4.10189 0.155705
\(695\) 18.7783 0.712301
\(696\) −10.5381 −0.399445
\(697\) −12.9737 −0.491413
\(698\) −21.0142 −0.795399
\(699\) 11.0036 0.416193
\(700\) −9.19683 −0.347608
\(701\) −17.0425 −0.643685 −0.321842 0.946793i \(-0.604302\pi\)
−0.321842 + 0.946793i \(0.604302\pi\)
\(702\) 0.593815 0.0224121
\(703\) 9.56933 0.360914
\(704\) −6.50822 −0.245288
\(705\) −15.4188 −0.580707
\(706\) −15.0533 −0.566540
\(707\) 28.4203 1.06886
\(708\) −8.40648 −0.315935
\(709\) −28.3692 −1.06543 −0.532715 0.846295i \(-0.678828\pi\)
−0.532715 + 0.846295i \(0.678828\pi\)
\(710\) 4.35927 0.163600
\(711\) 49.6761 1.86300
\(712\) 15.6397 0.586121
\(713\) −83.3926 −3.12308
\(714\) 22.4759 0.841140
\(715\) 25.9418 0.970168
\(716\) −22.0836 −0.825301
\(717\) −7.51671 −0.280717
\(718\) −8.27864 −0.308956
\(719\) 24.8035 0.925014 0.462507 0.886616i \(-0.346950\pi\)
0.462507 + 0.886616i \(0.346950\pi\)
\(720\) −4.73167 −0.176339
\(721\) −51.9675 −1.93537
\(722\) 20.1636 0.750410
\(723\) −23.0696 −0.857966
\(724\) 0.504009 0.0187313
\(725\) −10.1421 −0.376669
\(726\) −76.1653 −2.82676
\(727\) 30.3174 1.12441 0.562206 0.826998i \(-0.309953\pi\)
0.562206 + 0.826998i \(0.309953\pi\)
\(728\) 9.61075 0.356198
\(729\) −25.1696 −0.932209
\(730\) 11.0244 0.408030
\(731\) 18.6701 0.690538
\(732\) 25.2412 0.932943
\(733\) −42.1520 −1.55692 −0.778460 0.627694i \(-0.783999\pi\)
−0.778460 + 0.627694i \(0.783999\pi\)
\(734\) 10.7723 0.397614
\(735\) 33.5977 1.23927
\(736\) −9.09408 −0.335212
\(737\) −14.4576 −0.532553
\(738\) 15.9957 0.588810
\(739\) 3.94245 0.145025 0.0725126 0.997367i \(-0.476898\pi\)
0.0725126 + 0.997367i \(0.476898\pi\)
\(740\) −2.49499 −0.0917176
\(741\) −37.1342 −1.36416
\(742\) −31.9313 −1.17224
\(743\) 22.2927 0.817840 0.408920 0.912570i \(-0.365906\pi\)
0.408920 + 0.912570i \(0.365906\pi\)
\(744\) −22.2737 −0.816594
\(745\) −3.90529 −0.143079
\(746\) 0.104352 0.00382061
\(747\) −21.4171 −0.783610
\(748\) 15.3077 0.559704
\(749\) 35.2466 1.28788
\(750\) −29.0811 −1.06189
\(751\) 21.3230 0.778086 0.389043 0.921219i \(-0.372806\pi\)
0.389043 + 0.921219i \(0.372806\pi\)
\(752\) −3.89046 −0.141870
\(753\) −37.0857 −1.35148
\(754\) 10.5986 0.385978
\(755\) −10.1040 −0.367724
\(756\) 0.956290 0.0347799
\(757\) −5.03001 −0.182819 −0.0914095 0.995813i \(-0.529137\pi\)
−0.0914095 + 0.995813i \(0.529137\pi\)
\(758\) 9.03615 0.328208
\(759\) −143.762 −5.21823
\(760\) −10.2110 −0.370392
\(761\) −34.9027 −1.26522 −0.632612 0.774469i \(-0.718017\pi\)
−0.632612 + 0.774469i \(0.718017\pi\)
\(762\) 1.09571 0.0396934
\(763\) −59.5639 −2.15636
\(764\) 13.0768 0.473101
\(765\) 11.1291 0.402374
\(766\) 27.7505 1.00267
\(767\) 8.45475 0.305283
\(768\) −2.42898 −0.0876481
\(769\) 21.1588 0.763005 0.381503 0.924368i \(-0.375407\pi\)
0.381503 + 0.924368i \(0.375407\pi\)
\(770\) 41.7771 1.50554
\(771\) 54.4915 1.96246
\(772\) 6.83261 0.245911
\(773\) 28.3876 1.02103 0.510515 0.859869i \(-0.329455\pi\)
0.510515 + 0.859869i \(0.329455\pi\)
\(774\) −23.0190 −0.827401
\(775\) −21.4368 −0.770032
\(776\) −9.53508 −0.342289
\(777\) −14.6121 −0.524205
\(778\) −25.7264 −0.922338
\(779\) 34.5190 1.23677
\(780\) 9.68190 0.346668
\(781\) 17.3880 0.622190
\(782\) 21.3897 0.764895
\(783\) 1.05458 0.0376877
\(784\) 8.47732 0.302761
\(785\) −11.4684 −0.409326
\(786\) −16.7035 −0.595793
\(787\) −8.25891 −0.294398 −0.147199 0.989107i \(-0.547026\pi\)
−0.147199 + 0.989107i \(0.547026\pi\)
\(788\) −25.5654 −0.910730
\(789\) −28.0442 −0.998399
\(790\) −27.9504 −0.994431
\(791\) 16.1175 0.573071
\(792\) −18.8734 −0.670636
\(793\) −25.3862 −0.901489
\(794\) −21.5241 −0.763861
\(795\) −32.1677 −1.14087
\(796\) 14.2658 0.505637
\(797\) −15.8016 −0.559721 −0.279861 0.960041i \(-0.590288\pi\)
−0.279861 + 0.960041i \(0.590288\pi\)
\(798\) −59.8015 −2.11695
\(799\) 9.15055 0.323723
\(800\) −2.33771 −0.0826505
\(801\) 45.3539 1.60250
\(802\) −11.7675 −0.415525
\(803\) 43.9733 1.55178
\(804\) −5.39582 −0.190296
\(805\) 58.3760 2.05748
\(806\) 22.4016 0.789062
\(807\) 37.8381 1.33196
\(808\) 7.22405 0.254141
\(809\) 36.4376 1.28108 0.640539 0.767926i \(-0.278711\pi\)
0.640539 + 0.767926i \(0.278711\pi\)
\(810\) 15.1584 0.532612
\(811\) 49.4947 1.73800 0.868998 0.494816i \(-0.164765\pi\)
0.868998 + 0.494816i \(0.164765\pi\)
\(812\) 17.0681 0.598974
\(813\) −35.6149 −1.24907
\(814\) −9.95183 −0.348812
\(815\) 12.8099 0.448710
\(816\) 5.71307 0.199998
\(817\) −49.6753 −1.73792
\(818\) 25.5443 0.893137
\(819\) 27.8705 0.973873
\(820\) −9.00004 −0.314295
\(821\) −7.75605 −0.270688 −0.135344 0.990799i \(-0.543214\pi\)
−0.135344 + 0.990799i \(0.543214\pi\)
\(822\) 47.8256 1.66811
\(823\) −47.1461 −1.64341 −0.821705 0.569914i \(-0.806977\pi\)
−0.821705 + 0.569914i \(0.806977\pi\)
\(824\) −13.2094 −0.460172
\(825\) −36.9553 −1.28662
\(826\) 13.6157 0.473750
\(827\) −40.4001 −1.40485 −0.702425 0.711758i \(-0.747899\pi\)
−0.702425 + 0.711758i \(0.747899\pi\)
\(828\) −26.3722 −0.916496
\(829\) −36.0373 −1.25163 −0.625814 0.779973i \(-0.715233\pi\)
−0.625814 + 0.779973i \(0.715233\pi\)
\(830\) 12.0504 0.418275
\(831\) 68.6262 2.38062
\(832\) 2.44292 0.0846931
\(833\) −19.9391 −0.690848
\(834\) 27.9545 0.967984
\(835\) −14.3143 −0.495366
\(836\) −40.7290 −1.40864
\(837\) 2.22900 0.0770457
\(838\) −19.7092 −0.680842
\(839\) −55.0706 −1.90125 −0.950623 0.310347i \(-0.899555\pi\)
−0.950623 + 0.310347i \(0.899555\pi\)
\(840\) 15.5919 0.537971
\(841\) −10.1775 −0.350949
\(842\) 30.2532 1.04259
\(843\) −53.2500 −1.83403
\(844\) −20.9173 −0.720005
\(845\) 11.4740 0.394718
\(846\) −11.2820 −0.387885
\(847\) 123.362 4.23877
\(848\) −8.11651 −0.278722
\(849\) 26.3336 0.903767
\(850\) 5.49841 0.188594
\(851\) −13.9059 −0.476688
\(852\) 6.48947 0.222326
\(853\) 15.9079 0.544677 0.272338 0.962202i \(-0.412203\pi\)
0.272338 + 0.962202i \(0.412203\pi\)
\(854\) −40.8823 −1.39896
\(855\) −29.6112 −1.01268
\(856\) 8.95921 0.306220
\(857\) −50.3694 −1.72059 −0.860293 0.509801i \(-0.829719\pi\)
−0.860293 + 0.509801i \(0.829719\pi\)
\(858\) 38.6185 1.31841
\(859\) 29.0510 0.991206 0.495603 0.868549i \(-0.334947\pi\)
0.495603 + 0.868549i \(0.334947\pi\)
\(860\) 12.9517 0.441650
\(861\) −52.7094 −1.79633
\(862\) −34.8805 −1.18803
\(863\) 24.6713 0.839822 0.419911 0.907565i \(-0.362061\pi\)
0.419911 + 0.907565i \(0.362061\pi\)
\(864\) 0.243076 0.00826961
\(865\) −32.7925 −1.11498
\(866\) 14.8819 0.505706
\(867\) 27.8552 0.946011
\(868\) 36.0759 1.22450
\(869\) −111.487 −3.78193
\(870\) 17.1945 0.582948
\(871\) 5.42680 0.183880
\(872\) −15.1403 −0.512716
\(873\) −27.6510 −0.935846
\(874\) −56.9115 −1.92506
\(875\) 47.1016 1.59233
\(876\) 16.4115 0.554495
\(877\) −34.2934 −1.15801 −0.579004 0.815325i \(-0.696558\pi\)
−0.579004 + 0.815325i \(0.696558\pi\)
\(878\) 10.0693 0.339822
\(879\) 73.1456 2.46714
\(880\) 10.6192 0.357972
\(881\) −2.98833 −0.100680 −0.0503398 0.998732i \(-0.516030\pi\)
−0.0503398 + 0.998732i \(0.516030\pi\)
\(882\) 24.5836 0.827773
\(883\) 48.0252 1.61618 0.808089 0.589061i \(-0.200502\pi\)
0.808089 + 0.589061i \(0.200502\pi\)
\(884\) −5.74587 −0.193255
\(885\) 13.7165 0.461074
\(886\) 26.5038 0.890414
\(887\) 19.1642 0.643471 0.321735 0.946830i \(-0.395734\pi\)
0.321735 + 0.946830i \(0.395734\pi\)
\(888\) −3.71419 −0.124640
\(889\) −1.77468 −0.0595209
\(890\) −25.5185 −0.855382
\(891\) 60.4627 2.02558
\(892\) −22.7105 −0.760405
\(893\) −24.3468 −0.814735
\(894\) −5.81365 −0.194438
\(895\) 36.0327 1.20444
\(896\) 3.93412 0.131430
\(897\) 53.9624 1.80175
\(898\) −28.6134 −0.954840
\(899\) 39.7839 1.32687
\(900\) −6.77919 −0.225973
\(901\) 19.0904 0.635994
\(902\) −35.8987 −1.19530
\(903\) 75.8527 2.52422
\(904\) 4.09684 0.136259
\(905\) −0.822367 −0.0273364
\(906\) −15.0415 −0.499720
\(907\) 3.57374 0.118664 0.0593321 0.998238i \(-0.481103\pi\)
0.0593321 + 0.998238i \(0.481103\pi\)
\(908\) −25.5465 −0.847791
\(909\) 20.9492 0.694842
\(910\) −15.6814 −0.519834
\(911\) 20.0567 0.664507 0.332253 0.943190i \(-0.392191\pi\)
0.332253 + 0.943190i \(0.392191\pi\)
\(912\) −15.2007 −0.503346
\(913\) 48.0658 1.59075
\(914\) 0.264389 0.00874520
\(915\) −41.1849 −1.36153
\(916\) 0.0691195 0.00228377
\(917\) 27.0540 0.893401
\(918\) −0.571726 −0.0188698
\(919\) −0.392125 −0.0129350 −0.00646751 0.999979i \(-0.502059\pi\)
−0.00646751 + 0.999979i \(0.502059\pi\)
\(920\) 14.8384 0.489207
\(921\) 54.0583 1.78128
\(922\) −25.3513 −0.834901
\(923\) −6.52673 −0.214830
\(924\) 62.1919 2.04596
\(925\) −3.57463 −0.117533
\(926\) 38.7891 1.27469
\(927\) −38.3064 −1.25815
\(928\) 4.33849 0.142418
\(929\) −19.3263 −0.634075 −0.317037 0.948413i \(-0.602688\pi\)
−0.317037 + 0.948413i \(0.602688\pi\)
\(930\) 36.3430 1.19173
\(931\) 53.0517 1.73870
\(932\) −4.53012 −0.148389
\(933\) 12.5393 0.410519
\(934\) −38.7430 −1.26771
\(935\) −24.9768 −0.816828
\(936\) 7.08429 0.231557
\(937\) 54.2433 1.77205 0.886026 0.463636i \(-0.153455\pi\)
0.886026 + 0.463636i \(0.153455\pi\)
\(938\) 8.73941 0.285352
\(939\) 83.5176 2.72549
\(940\) 6.34788 0.207045
\(941\) 29.0862 0.948183 0.474092 0.880476i \(-0.342777\pi\)
0.474092 + 0.880476i \(0.342777\pi\)
\(942\) −17.0726 −0.556256
\(943\) −50.1620 −1.63350
\(944\) 3.46092 0.112643
\(945\) −1.56033 −0.0507576
\(946\) 51.6609 1.67964
\(947\) 51.9951 1.68961 0.844807 0.535072i \(-0.179715\pi\)
0.844807 + 0.535072i \(0.179715\pi\)
\(948\) −41.6087 −1.35139
\(949\) −16.5058 −0.535800
\(950\) −14.6296 −0.474646
\(951\) 38.0916 1.23520
\(952\) −9.25325 −0.299900
\(953\) 3.97607 0.128798 0.0643988 0.997924i \(-0.479487\pi\)
0.0643988 + 0.997924i \(0.479487\pi\)
\(954\) −23.5373 −0.762048
\(955\) −21.3368 −0.690442
\(956\) 3.09460 0.100087
\(957\) 68.5842 2.21701
\(958\) 7.52557 0.243140
\(959\) −77.4613 −2.50136
\(960\) 3.96325 0.127913
\(961\) 53.0888 1.71254
\(962\) 3.73551 0.120438
\(963\) 25.9811 0.837228
\(964\) 9.49765 0.305899
\(965\) −11.1484 −0.358881
\(966\) 86.9020 2.79603
\(967\) 50.2201 1.61497 0.807485 0.589889i \(-0.200828\pi\)
0.807485 + 0.589889i \(0.200828\pi\)
\(968\) 31.3570 1.00785
\(969\) 35.7529 1.14855
\(970\) 15.5579 0.499535
\(971\) −1.89168 −0.0607070 −0.0303535 0.999539i \(-0.509663\pi\)
−0.0303535 + 0.999539i \(0.509663\pi\)
\(972\) 21.8365 0.700405
\(973\) −45.2768 −1.45151
\(974\) −27.9026 −0.894055
\(975\) 13.8715 0.444243
\(976\) −10.3917 −0.332631
\(977\) 41.2310 1.31910 0.659548 0.751663i \(-0.270748\pi\)
0.659548 + 0.751663i \(0.270748\pi\)
\(978\) 19.0695 0.609776
\(979\) −101.786 −3.25311
\(980\) −13.8320 −0.441848
\(981\) −43.9059 −1.40181
\(982\) −11.2908 −0.360305
\(983\) −11.6824 −0.372610 −0.186305 0.982492i \(-0.559651\pi\)
−0.186305 + 0.982492i \(0.559651\pi\)
\(984\) −13.3980 −0.427113
\(985\) 41.7139 1.32911
\(986\) −10.2043 −0.324972
\(987\) 37.1768 1.18335
\(988\) 15.2880 0.486376
\(989\) 72.1869 2.29541
\(990\) 30.7948 0.978723
\(991\) 27.6633 0.878754 0.439377 0.898303i \(-0.355199\pi\)
0.439377 + 0.898303i \(0.355199\pi\)
\(992\) 9.17000 0.291148
\(993\) 75.5785 2.39841
\(994\) −10.5108 −0.333381
\(995\) −23.2768 −0.737924
\(996\) 17.9389 0.568417
\(997\) 5.23529 0.165803 0.0829017 0.996558i \(-0.473581\pi\)
0.0829017 + 0.996558i \(0.473581\pi\)
\(998\) −10.2253 −0.323677
\(999\) 0.371691 0.0117598
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 \(a_p\))