Properties

Label 4031.2.a.c.1.13
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.77273 q^{2}\) \(-1.39503 q^{3}\) \(+1.14258 q^{4}\) \(-2.16266 q^{5}\) \(+2.47302 q^{6}\) \(+3.73562 q^{7}\) \(+1.51997 q^{8}\) \(-1.05388 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.77273 q^{2}\) \(-1.39503 q^{3}\) \(+1.14258 q^{4}\) \(-2.16266 q^{5}\) \(+2.47302 q^{6}\) \(+3.73562 q^{7}\) \(+1.51997 q^{8}\) \(-1.05388 q^{9}\) \(+3.83382 q^{10}\) \(+5.45206 q^{11}\) \(-1.59394 q^{12}\) \(+3.93093 q^{13}\) \(-6.62225 q^{14}\) \(+3.01698 q^{15}\) \(-4.97967 q^{16}\) \(-1.81906 q^{17}\) \(+1.86825 q^{18}\) \(+1.77289 q^{19}\) \(-2.47102 q^{20}\) \(-5.21131 q^{21}\) \(-9.66504 q^{22}\) \(-3.66238 q^{23}\) \(-2.12041 q^{24}\) \(-0.322895 q^{25}\) \(-6.96848 q^{26}\) \(+5.65530 q^{27}\) \(+4.26825 q^{28}\) \(-1.00000 q^{29}\) \(-5.34831 q^{30}\) \(-8.07220 q^{31}\) \(+5.78768 q^{32}\) \(-7.60580 q^{33}\) \(+3.22470 q^{34}\) \(-8.07888 q^{35}\) \(-1.20415 q^{36}\) \(-7.62182 q^{37}\) \(-3.14286 q^{38}\) \(-5.48377 q^{39}\) \(-3.28719 q^{40}\) \(+5.37965 q^{41}\) \(+9.23826 q^{42}\) \(-7.92755 q^{43}\) \(+6.22942 q^{44}\) \(+2.27919 q^{45}\) \(+6.49242 q^{46}\) \(+5.26609 q^{47}\) \(+6.94680 q^{48}\) \(+6.95483 q^{49}\) \(+0.572407 q^{50}\) \(+2.53765 q^{51}\) \(+4.49140 q^{52}\) \(-1.41840 q^{53}\) \(-10.0253 q^{54}\) \(-11.7910 q^{55}\) \(+5.67804 q^{56}\) \(-2.47324 q^{57}\) \(+1.77273 q^{58}\) \(-5.15127 q^{59}\) \(+3.44715 q^{60}\) \(-12.7156 q^{61}\) \(+14.3099 q^{62}\) \(-3.93691 q^{63}\) \(-0.300666 q^{64}\) \(-8.50126 q^{65}\) \(+13.4831 q^{66}\) \(+6.96779 q^{67}\) \(-2.07842 q^{68}\) \(+5.10914 q^{69}\) \(+14.3217 q^{70}\) \(+13.5512 q^{71}\) \(-1.60188 q^{72}\) \(-11.1071 q^{73}\) \(+13.5115 q^{74}\) \(+0.450449 q^{75}\) \(+2.02567 q^{76}\) \(+20.3668 q^{77}\) \(+9.72126 q^{78}\) \(-3.72137 q^{79}\) \(+10.7693 q^{80}\) \(-4.72768 q^{81}\) \(-9.53669 q^{82}\) \(-6.14188 q^{83}\) \(-5.95434 q^{84}\) \(+3.93401 q^{85}\) \(+14.0534 q^{86}\) \(+1.39503 q^{87}\) \(+8.28699 q^{88}\) \(+4.02014 q^{89}\) \(-4.04040 q^{90}\) \(+14.6844 q^{91}\) \(-4.18457 q^{92}\) \(+11.2610 q^{93}\) \(-9.33537 q^{94}\) \(-3.83416 q^{95}\) \(-8.07400 q^{96}\) \(+10.5701 q^{97}\) \(-12.3291 q^{98}\) \(-5.74584 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.77273 −1.25351 −0.626756 0.779216i \(-0.715618\pi\)
−0.626756 + 0.779216i \(0.715618\pi\)
\(3\) −1.39503 −0.805423 −0.402711 0.915327i \(-0.631932\pi\)
−0.402711 + 0.915327i \(0.631932\pi\)
\(4\) 1.14258 0.571291
\(5\) −2.16266 −0.967172 −0.483586 0.875297i \(-0.660666\pi\)
−0.483586 + 0.875297i \(0.660666\pi\)
\(6\) 2.47302 1.00961
\(7\) 3.73562 1.41193 0.705965 0.708246i \(-0.250513\pi\)
0.705965 + 0.708246i \(0.250513\pi\)
\(8\) 1.51997 0.537392
\(9\) −1.05388 −0.351295
\(10\) 3.83382 1.21236
\(11\) 5.45206 1.64386 0.821929 0.569590i \(-0.192898\pi\)
0.821929 + 0.569590i \(0.192898\pi\)
\(12\) −1.59394 −0.460131
\(13\) 3.93093 1.09024 0.545121 0.838357i \(-0.316484\pi\)
0.545121 + 0.838357i \(0.316484\pi\)
\(14\) −6.62225 −1.76987
\(15\) 3.01698 0.778982
\(16\) −4.97967 −1.24492
\(17\) −1.81906 −0.441187 −0.220593 0.975366i \(-0.570799\pi\)
−0.220593 + 0.975366i \(0.570799\pi\)
\(18\) 1.86825 0.440352
\(19\) 1.77289 0.406729 0.203364 0.979103i \(-0.434812\pi\)
0.203364 + 0.979103i \(0.434812\pi\)
\(20\) −2.47102 −0.552536
\(21\) −5.21131 −1.13720
\(22\) −9.66504 −2.06059
\(23\) −3.66238 −0.763659 −0.381830 0.924233i \(-0.624706\pi\)
−0.381830 + 0.924233i \(0.624706\pi\)
\(24\) −2.12041 −0.432828
\(25\) −0.322895 −0.0645790
\(26\) −6.96848 −1.36663
\(27\) 5.65530 1.08836
\(28\) 4.26825 0.806623
\(29\) −1.00000 −0.185695
\(30\) −5.34831 −0.976463
\(31\) −8.07220 −1.44981 −0.724905 0.688849i \(-0.758117\pi\)
−0.724905 + 0.688849i \(0.758117\pi\)
\(32\) 5.78768 1.02313
\(33\) −7.60580 −1.32400
\(34\) 3.22470 0.553032
\(35\) −8.07888 −1.36558
\(36\) −1.20415 −0.200691
\(37\) −7.62182 −1.25302 −0.626510 0.779414i \(-0.715517\pi\)
−0.626510 + 0.779414i \(0.715517\pi\)
\(38\) −3.14286 −0.509839
\(39\) −5.48377 −0.878106
\(40\) −3.28719 −0.519750
\(41\) 5.37965 0.840161 0.420080 0.907487i \(-0.362002\pi\)
0.420080 + 0.907487i \(0.362002\pi\)
\(42\) 9.23826 1.42549
\(43\) −7.92755 −1.20894 −0.604470 0.796628i \(-0.706615\pi\)
−0.604470 + 0.796628i \(0.706615\pi\)
\(44\) 6.22942 0.939121
\(45\) 2.27919 0.339762
\(46\) 6.49242 0.957255
\(47\) 5.26609 0.768138 0.384069 0.923304i \(-0.374522\pi\)
0.384069 + 0.923304i \(0.374522\pi\)
\(48\) 6.94680 1.00268
\(49\) 6.95483 0.993548
\(50\) 0.572407 0.0809505
\(51\) 2.53765 0.355342
\(52\) 4.49140 0.622846
\(53\) −1.41840 −0.194832 −0.0974162 0.995244i \(-0.531058\pi\)
−0.0974162 + 0.995244i \(0.531058\pi\)
\(54\) −10.0253 −1.36428
\(55\) −11.7910 −1.58989
\(56\) 5.67804 0.758760
\(57\) −2.47324 −0.327589
\(58\) 1.77273 0.232771
\(59\) −5.15127 −0.670638 −0.335319 0.942105i \(-0.608844\pi\)
−0.335319 + 0.942105i \(0.608844\pi\)
\(60\) 3.44715 0.445025
\(61\) −12.7156 −1.62807 −0.814034 0.580818i \(-0.802733\pi\)
−0.814034 + 0.580818i \(0.802733\pi\)
\(62\) 14.3099 1.81735
\(63\) −3.93691 −0.496003
\(64\) −0.300666 −0.0375832
\(65\) −8.50126 −1.05445
\(66\) 13.4831 1.65965
\(67\) 6.96779 0.851251 0.425626 0.904899i \(-0.360054\pi\)
0.425626 + 0.904899i \(0.360054\pi\)
\(68\) −2.07842 −0.252046
\(69\) 5.10914 0.615068
\(70\) 14.3217 1.71177
\(71\) 13.5512 1.60824 0.804118 0.594470i \(-0.202638\pi\)
0.804118 + 0.594470i \(0.202638\pi\)
\(72\) −1.60188 −0.188783
\(73\) −11.1071 −1.29999 −0.649996 0.759938i \(-0.725229\pi\)
−0.649996 + 0.759938i \(0.725229\pi\)
\(74\) 13.5115 1.57067
\(75\) 0.450449 0.0520134
\(76\) 2.02567 0.232360
\(77\) 20.3668 2.32101
\(78\) 9.72126 1.10072
\(79\) −3.72137 −0.418687 −0.209344 0.977842i \(-0.567133\pi\)
−0.209344 + 0.977842i \(0.567133\pi\)
\(80\) 10.7693 1.20405
\(81\) −4.72768 −0.525298
\(82\) −9.53669 −1.05315
\(83\) −6.14188 −0.674159 −0.337079 0.941476i \(-0.609439\pi\)
−0.337079 + 0.941476i \(0.609439\pi\)
\(84\) −5.95434 −0.649672
\(85\) 3.93401 0.426703
\(86\) 14.0534 1.51542
\(87\) 1.39503 0.149563
\(88\) 8.28699 0.883396
\(89\) 4.02014 0.426134 0.213067 0.977038i \(-0.431655\pi\)
0.213067 + 0.977038i \(0.431655\pi\)
\(90\) −4.04040 −0.425896
\(91\) 14.6844 1.53935
\(92\) −4.18457 −0.436271
\(93\) 11.2610 1.16771
\(94\) −9.33537 −0.962870
\(95\) −3.83416 −0.393377
\(96\) −8.07400 −0.824049
\(97\) 10.5701 1.07323 0.536616 0.843827i \(-0.319702\pi\)
0.536616 + 0.843827i \(0.319702\pi\)
\(98\) −12.3291 −1.24542
\(99\) −5.74584 −0.577478
\(100\) −0.368934 −0.0368934
\(101\) 14.7059 1.46329 0.731644 0.681687i \(-0.238754\pi\)
0.731644 + 0.681687i \(0.238754\pi\)
\(102\) −4.49857 −0.445425
\(103\) −9.88718 −0.974213 −0.487106 0.873343i \(-0.661948\pi\)
−0.487106 + 0.873343i \(0.661948\pi\)
\(104\) 5.97490 0.585887
\(105\) 11.2703 1.09987
\(106\) 2.51445 0.244225
\(107\) −4.44211 −0.429435 −0.214718 0.976676i \(-0.568883\pi\)
−0.214718 + 0.976676i \(0.568883\pi\)
\(108\) 6.46164 0.621772
\(109\) −15.5199 −1.48654 −0.743268 0.668993i \(-0.766725\pi\)
−0.743268 + 0.668993i \(0.766725\pi\)
\(110\) 20.9022 1.99295
\(111\) 10.6327 1.00921
\(112\) −18.6021 −1.75774
\(113\) 1.29751 0.122059 0.0610296 0.998136i \(-0.480562\pi\)
0.0610296 + 0.998136i \(0.480562\pi\)
\(114\) 4.38439 0.410636
\(115\) 7.92049 0.738589
\(116\) −1.14258 −0.106086
\(117\) −4.14274 −0.382996
\(118\) 9.13183 0.840653
\(119\) −6.79531 −0.622925
\(120\) 4.58574 0.418618
\(121\) 18.7249 1.70227
\(122\) 22.5414 2.04080
\(123\) −7.50479 −0.676684
\(124\) −9.22315 −0.828263
\(125\) 11.5116 1.02963
\(126\) 6.97908 0.621746
\(127\) −5.71551 −0.507169 −0.253585 0.967313i \(-0.581610\pi\)
−0.253585 + 0.967313i \(0.581610\pi\)
\(128\) −11.0424 −0.976016
\(129\) 11.0592 0.973707
\(130\) 15.0705 1.32177
\(131\) −20.6216 −1.80172 −0.900859 0.434112i \(-0.857062\pi\)
−0.900859 + 0.434112i \(0.857062\pi\)
\(132\) −8.69025 −0.756389
\(133\) 6.62284 0.574273
\(134\) −12.3520 −1.06705
\(135\) −12.2305 −1.05263
\(136\) −2.76492 −0.237090
\(137\) 4.99492 0.426745 0.213373 0.976971i \(-0.431555\pi\)
0.213373 + 0.976971i \(0.431555\pi\)
\(138\) −9.05714 −0.770995
\(139\) −1.00000 −0.0848189
\(140\) −9.23077 −0.780143
\(141\) −7.34637 −0.618676
\(142\) −24.0227 −2.01594
\(143\) 21.4316 1.79220
\(144\) 5.24799 0.437333
\(145\) 2.16266 0.179599
\(146\) 19.6900 1.62955
\(147\) −9.70222 −0.800226
\(148\) −8.70855 −0.715839
\(149\) 14.1402 1.15841 0.579205 0.815182i \(-0.303363\pi\)
0.579205 + 0.815182i \(0.303363\pi\)
\(150\) −0.798526 −0.0651994
\(151\) −12.8175 −1.04307 −0.521535 0.853230i \(-0.674640\pi\)
−0.521535 + 0.853230i \(0.674640\pi\)
\(152\) 2.69475 0.218573
\(153\) 1.91708 0.154986
\(154\) −36.1049 −2.90942
\(155\) 17.4574 1.40222
\(156\) −6.26565 −0.501654
\(157\) −14.6799 −1.17158 −0.585791 0.810462i \(-0.699216\pi\)
−0.585791 + 0.810462i \(0.699216\pi\)
\(158\) 6.59700 0.524829
\(159\) 1.97872 0.156922
\(160\) −12.5168 −0.989539
\(161\) −13.6812 −1.07823
\(162\) 8.38091 0.658467
\(163\) 2.80863 0.219989 0.109994 0.993932i \(-0.464917\pi\)
0.109994 + 0.993932i \(0.464917\pi\)
\(164\) 6.14669 0.479976
\(165\) 16.4488 1.28054
\(166\) 10.8879 0.845066
\(167\) −17.7861 −1.37633 −0.688165 0.725554i \(-0.741583\pi\)
−0.688165 + 0.725554i \(0.741583\pi\)
\(168\) −7.92105 −0.611122
\(169\) 2.45217 0.188629
\(170\) −6.97395 −0.534877
\(171\) −1.86842 −0.142882
\(172\) −9.05787 −0.690656
\(173\) −14.5083 −1.10304 −0.551522 0.834160i \(-0.685953\pi\)
−0.551522 + 0.834160i \(0.685953\pi\)
\(174\) −2.47302 −0.187479
\(175\) −1.20621 −0.0911811
\(176\) −27.1495 −2.04647
\(177\) 7.18619 0.540147
\(178\) −7.12664 −0.534164
\(179\) −5.34156 −0.399247 −0.199624 0.979873i \(-0.563972\pi\)
−0.199624 + 0.979873i \(0.563972\pi\)
\(180\) 2.60416 0.194103
\(181\) 12.4045 0.922018 0.461009 0.887396i \(-0.347488\pi\)
0.461009 + 0.887396i \(0.347488\pi\)
\(182\) −26.0316 −1.92959
\(183\) 17.7387 1.31128
\(184\) −5.56672 −0.410384
\(185\) 16.4834 1.21188
\(186\) −19.9627 −1.46374
\(187\) −9.91761 −0.725248
\(188\) 6.01694 0.438830
\(189\) 21.1260 1.53669
\(190\) 6.79694 0.493102
\(191\) 23.2478 1.68216 0.841078 0.540914i \(-0.181922\pi\)
0.841078 + 0.540914i \(0.181922\pi\)
\(192\) 0.419438 0.0302704
\(193\) 13.0720 0.940943 0.470472 0.882415i \(-0.344084\pi\)
0.470472 + 0.882415i \(0.344084\pi\)
\(194\) −18.7380 −1.34531
\(195\) 11.8595 0.849279
\(196\) 7.94647 0.567605
\(197\) 5.68340 0.404926 0.202463 0.979290i \(-0.435105\pi\)
0.202463 + 0.979290i \(0.435105\pi\)
\(198\) 10.1858 0.723875
\(199\) 7.62027 0.540186 0.270093 0.962834i \(-0.412945\pi\)
0.270093 + 0.962834i \(0.412945\pi\)
\(200\) −0.490792 −0.0347042
\(201\) −9.72030 −0.685617
\(202\) −26.0696 −1.83425
\(203\) −3.73562 −0.262189
\(204\) 2.89947 0.203003
\(205\) −11.6344 −0.812580
\(206\) 17.5273 1.22119
\(207\) 3.85972 0.268269
\(208\) −19.5747 −1.35726
\(209\) 9.66590 0.668604
\(210\) −19.9792 −1.37870
\(211\) −25.7623 −1.77355 −0.886774 0.462203i \(-0.847059\pi\)
−0.886774 + 0.462203i \(0.847059\pi\)
\(212\) −1.62064 −0.111306
\(213\) −18.9044 −1.29531
\(214\) 7.87467 0.538302
\(215\) 17.1446 1.16925
\(216\) 8.59591 0.584877
\(217\) −30.1547 −2.04703
\(218\) 27.5126 1.86339
\(219\) 15.4948 1.04704
\(220\) −13.4721 −0.908291
\(221\) −7.15058 −0.481000
\(222\) −18.8489 −1.26506
\(223\) 0.340185 0.0227804 0.0113902 0.999935i \(-0.496374\pi\)
0.0113902 + 0.999935i \(0.496374\pi\)
\(224\) 21.6205 1.44458
\(225\) 0.340294 0.0226863
\(226\) −2.30013 −0.153002
\(227\) 2.92280 0.193993 0.0969966 0.995285i \(-0.469076\pi\)
0.0969966 + 0.995285i \(0.469076\pi\)
\(228\) −2.82588 −0.187148
\(229\) 17.1639 1.13422 0.567111 0.823642i \(-0.308061\pi\)
0.567111 + 0.823642i \(0.308061\pi\)
\(230\) −14.0409 −0.925830
\(231\) −28.4124 −1.86940
\(232\) −1.51997 −0.0997912
\(233\) −7.73633 −0.506824 −0.253412 0.967358i \(-0.581553\pi\)
−0.253412 + 0.967358i \(0.581553\pi\)
\(234\) 7.34397 0.480090
\(235\) −11.3888 −0.742922
\(236\) −5.88575 −0.383129
\(237\) 5.19144 0.337220
\(238\) 12.0463 0.780843
\(239\) 11.4269 0.739142 0.369571 0.929203i \(-0.379505\pi\)
0.369571 + 0.929203i \(0.379505\pi\)
\(240\) −15.0236 −0.969768
\(241\) 7.36721 0.474564 0.237282 0.971441i \(-0.423744\pi\)
0.237282 + 0.971441i \(0.423744\pi\)
\(242\) −33.1943 −2.13381
\(243\) −10.3706 −0.665277
\(244\) −14.5286 −0.930100
\(245\) −15.0410 −0.960931
\(246\) 13.3040 0.848232
\(247\) 6.96910 0.443433
\(248\) −12.2695 −0.779116
\(249\) 8.56812 0.542983
\(250\) −20.4070 −1.29065
\(251\) −27.2651 −1.72096 −0.860478 0.509487i \(-0.829835\pi\)
−0.860478 + 0.509487i \(0.829835\pi\)
\(252\) −4.49824 −0.283362
\(253\) −19.9675 −1.25535
\(254\) 10.1321 0.635742
\(255\) −5.48807 −0.343676
\(256\) 20.1765 1.26103
\(257\) −20.4871 −1.27795 −0.638975 0.769227i \(-0.720641\pi\)
−0.638975 + 0.769227i \(0.720641\pi\)
\(258\) −19.6050 −1.22055
\(259\) −28.4722 −1.76918
\(260\) −9.71338 −0.602399
\(261\) 1.05388 0.0652338
\(262\) 36.5566 2.25847
\(263\) −10.3135 −0.635957 −0.317979 0.948098i \(-0.603004\pi\)
−0.317979 + 0.948098i \(0.603004\pi\)
\(264\) −11.5606 −0.711507
\(265\) 3.06752 0.188436
\(266\) −11.7405 −0.719858
\(267\) −5.60823 −0.343218
\(268\) 7.96127 0.486312
\(269\) −16.5722 −1.01042 −0.505211 0.862996i \(-0.668585\pi\)
−0.505211 + 0.862996i \(0.668585\pi\)
\(270\) 21.6814 1.31949
\(271\) −17.6684 −1.07328 −0.536640 0.843811i \(-0.680307\pi\)
−0.536640 + 0.843811i \(0.680307\pi\)
\(272\) 9.05831 0.549241
\(273\) −20.4853 −1.23982
\(274\) −8.85466 −0.534930
\(275\) −1.76044 −0.106159
\(276\) 5.83761 0.351383
\(277\) 8.40696 0.505125 0.252563 0.967581i \(-0.418727\pi\)
0.252563 + 0.967581i \(0.418727\pi\)
\(278\) 1.77273 0.106321
\(279\) 8.50716 0.509311
\(280\) −12.2797 −0.733851
\(281\) −29.6127 −1.76655 −0.883273 0.468858i \(-0.844665\pi\)
−0.883273 + 0.468858i \(0.844665\pi\)
\(282\) 13.0232 0.775517
\(283\) 0.0946396 0.00562574 0.00281287 0.999996i \(-0.499105\pi\)
0.00281287 + 0.999996i \(0.499105\pi\)
\(284\) 15.4834 0.918770
\(285\) 5.34878 0.316834
\(286\) −37.9926 −2.24655
\(287\) 20.0963 1.18625
\(288\) −6.09954 −0.359419
\(289\) −13.6910 −0.805354
\(290\) −3.83382 −0.225130
\(291\) −14.7456 −0.864405
\(292\) −12.6908 −0.742673
\(293\) 18.2997 1.06908 0.534540 0.845143i \(-0.320485\pi\)
0.534540 + 0.845143i \(0.320485\pi\)
\(294\) 17.1994 1.00309
\(295\) 11.1405 0.648622
\(296\) −11.5850 −0.673362
\(297\) 30.8330 1.78911
\(298\) −25.0668 −1.45208
\(299\) −14.3965 −0.832574
\(300\) 0.514675 0.0297148
\(301\) −29.6143 −1.70694
\(302\) 22.7219 1.30750
\(303\) −20.5151 −1.17856
\(304\) −8.82841 −0.506344
\(305\) 27.4996 1.57462
\(306\) −3.39846 −0.194277
\(307\) 28.1543 1.60685 0.803427 0.595404i \(-0.203008\pi\)
0.803427 + 0.595404i \(0.203008\pi\)
\(308\) 23.2707 1.32597
\(309\) 13.7929 0.784653
\(310\) −30.9474 −1.75769
\(311\) 6.28781 0.356549 0.178275 0.983981i \(-0.442948\pi\)
0.178275 + 0.983981i \(0.442948\pi\)
\(312\) −8.33519 −0.471887
\(313\) 27.1107 1.53239 0.766195 0.642609i \(-0.222148\pi\)
0.766195 + 0.642609i \(0.222148\pi\)
\(314\) 26.0235 1.46859
\(315\) 8.51419 0.479720
\(316\) −4.25197 −0.239192
\(317\) 6.71602 0.377209 0.188605 0.982053i \(-0.439604\pi\)
0.188605 + 0.982053i \(0.439604\pi\)
\(318\) −3.50774 −0.196704
\(319\) −5.45206 −0.305257
\(320\) 0.650238 0.0363494
\(321\) 6.19689 0.345877
\(322\) 24.2532 1.35158
\(323\) −3.22499 −0.179443
\(324\) −5.40176 −0.300098
\(325\) −1.26928 −0.0704068
\(326\) −4.97895 −0.275759
\(327\) 21.6508 1.19729
\(328\) 8.17693 0.451495
\(329\) 19.6721 1.08456
\(330\) −29.1593 −1.60517
\(331\) −6.60045 −0.362794 −0.181397 0.983410i \(-0.558062\pi\)
−0.181397 + 0.983410i \(0.558062\pi\)
\(332\) −7.01760 −0.385141
\(333\) 8.03251 0.440179
\(334\) 31.5300 1.72525
\(335\) −15.0690 −0.823306
\(336\) 25.9506 1.41572
\(337\) 4.53428 0.246998 0.123499 0.992345i \(-0.460588\pi\)
0.123499 + 0.992345i \(0.460588\pi\)
\(338\) −4.34705 −0.236448
\(339\) −1.81006 −0.0983092
\(340\) 4.49493 0.243772
\(341\) −44.0101 −2.38328
\(342\) 3.31221 0.179104
\(343\) −0.168724 −0.00911022
\(344\) −12.0497 −0.649674
\(345\) −11.0493 −0.594877
\(346\) 25.7193 1.38268
\(347\) 28.0089 1.50360 0.751798 0.659394i \(-0.229187\pi\)
0.751798 + 0.659394i \(0.229187\pi\)
\(348\) 1.59394 0.0854441
\(349\) −8.55451 −0.457913 −0.228956 0.973437i \(-0.573531\pi\)
−0.228956 + 0.973437i \(0.573531\pi\)
\(350\) 2.13829 0.114297
\(351\) 22.2306 1.18658
\(352\) 31.5548 1.68187
\(353\) −7.09717 −0.377744 −0.188872 0.982002i \(-0.560483\pi\)
−0.188872 + 0.982002i \(0.560483\pi\)
\(354\) −12.7392 −0.677081
\(355\) −29.3067 −1.55544
\(356\) 4.59334 0.243447
\(357\) 9.47968 0.501718
\(358\) 9.46917 0.500461
\(359\) −15.3399 −0.809610 −0.404805 0.914403i \(-0.632661\pi\)
−0.404805 + 0.914403i \(0.632661\pi\)
\(360\) 3.46431 0.182585
\(361\) −15.8569 −0.834572
\(362\) −21.9898 −1.15576
\(363\) −26.1219 −1.37104
\(364\) 16.7782 0.879415
\(365\) 24.0210 1.25732
\(366\) −31.4460 −1.64371
\(367\) 34.3142 1.79119 0.895594 0.444872i \(-0.146751\pi\)
0.895594 + 0.444872i \(0.146751\pi\)
\(368\) 18.2374 0.950693
\(369\) −5.66953 −0.295144
\(370\) −29.2207 −1.51911
\(371\) −5.29860 −0.275090
\(372\) 12.8666 0.667102
\(373\) 25.8444 1.33817 0.669086 0.743185i \(-0.266686\pi\)
0.669086 + 0.743185i \(0.266686\pi\)
\(374\) 17.5813 0.909106
\(375\) −16.0591 −0.829288
\(376\) 8.00432 0.412791
\(377\) −3.93093 −0.202453
\(378\) −37.4508 −1.92626
\(379\) 4.07128 0.209127 0.104564 0.994518i \(-0.466655\pi\)
0.104564 + 0.994518i \(0.466655\pi\)
\(380\) −4.38084 −0.224732
\(381\) 7.97332 0.408486
\(382\) −41.2122 −2.10860
\(383\) 13.9396 0.712279 0.356139 0.934433i \(-0.384093\pi\)
0.356139 + 0.934433i \(0.384093\pi\)
\(384\) 15.4044 0.786105
\(385\) −44.0465 −2.24482
\(386\) −23.1732 −1.17948
\(387\) 8.35471 0.424694
\(388\) 12.0772 0.613128
\(389\) −21.1005 −1.06984 −0.534920 0.844903i \(-0.679658\pi\)
−0.534920 + 0.844903i \(0.679658\pi\)
\(390\) −21.0238 −1.06458
\(391\) 6.66208 0.336916
\(392\) 10.5712 0.533924
\(393\) 28.7678 1.45114
\(394\) −10.0752 −0.507579
\(395\) 8.04807 0.404942
\(396\) −6.56509 −0.329908
\(397\) −25.4364 −1.27662 −0.638309 0.769780i \(-0.720366\pi\)
−0.638309 + 0.769780i \(0.720366\pi\)
\(398\) −13.5087 −0.677130
\(399\) −9.23908 −0.462532
\(400\) 1.60791 0.0803956
\(401\) −2.51858 −0.125772 −0.0628859 0.998021i \(-0.520030\pi\)
−0.0628859 + 0.998021i \(0.520030\pi\)
\(402\) 17.2315 0.859429
\(403\) −31.7312 −1.58065
\(404\) 16.8026 0.835963
\(405\) 10.2244 0.508053
\(406\) 6.62225 0.328657
\(407\) −41.5546 −2.05979
\(408\) 3.85716 0.190958
\(409\) −7.24837 −0.358409 −0.179204 0.983812i \(-0.557352\pi\)
−0.179204 + 0.983812i \(0.557352\pi\)
\(410\) 20.6246 1.01858
\(411\) −6.96808 −0.343710
\(412\) −11.2969 −0.556559
\(413\) −19.2432 −0.946895
\(414\) −6.84226 −0.336279
\(415\) 13.2828 0.652027
\(416\) 22.7509 1.11546
\(417\) 1.39503 0.0683150
\(418\) −17.1351 −0.838103
\(419\) 25.1094 1.22667 0.613337 0.789821i \(-0.289827\pi\)
0.613337 + 0.789821i \(0.289827\pi\)
\(420\) 12.8772 0.628345
\(421\) 11.6449 0.567538 0.283769 0.958893i \(-0.408415\pi\)
0.283769 + 0.958893i \(0.408415\pi\)
\(422\) 45.6696 2.22316
\(423\) −5.54985 −0.269843
\(424\) −2.15593 −0.104701
\(425\) 0.587365 0.0284914
\(426\) 33.5125 1.62369
\(427\) −47.5007 −2.29872
\(428\) −5.07547 −0.245332
\(429\) −29.8978 −1.44348
\(430\) −30.3928 −1.46567
\(431\) −28.8899 −1.39158 −0.695789 0.718246i \(-0.744945\pi\)
−0.695789 + 0.718246i \(0.744945\pi\)
\(432\) −28.1615 −1.35492
\(433\) 10.1554 0.488035 0.244018 0.969771i \(-0.421535\pi\)
0.244018 + 0.969771i \(0.421535\pi\)
\(434\) 53.4562 2.56598
\(435\) −3.01698 −0.144653
\(436\) −17.7328 −0.849245
\(437\) −6.49300 −0.310602
\(438\) −27.4682 −1.31248
\(439\) −20.0788 −0.958310 −0.479155 0.877730i \(-0.659057\pi\)
−0.479155 + 0.877730i \(0.659057\pi\)
\(440\) −17.9219 −0.854395
\(441\) −7.32958 −0.349028
\(442\) 12.6761 0.602939
\(443\) −14.2968 −0.679263 −0.339631 0.940559i \(-0.610302\pi\)
−0.339631 + 0.940559i \(0.610302\pi\)
\(444\) 12.1487 0.576553
\(445\) −8.69421 −0.412145
\(446\) −0.603056 −0.0285555
\(447\) −19.7260 −0.933009
\(448\) −1.12317 −0.0530649
\(449\) 21.7782 1.02778 0.513888 0.857857i \(-0.328205\pi\)
0.513888 + 0.857857i \(0.328205\pi\)
\(450\) −0.603250 −0.0284375
\(451\) 29.3302 1.38110
\(452\) 1.48251 0.0697313
\(453\) 17.8808 0.840112
\(454\) −5.18135 −0.243173
\(455\) −31.7575 −1.48881
\(456\) −3.75926 −0.176043
\(457\) −6.89700 −0.322628 −0.161314 0.986903i \(-0.551573\pi\)
−0.161314 + 0.986903i \(0.551573\pi\)
\(458\) −30.4270 −1.42176
\(459\) −10.2873 −0.480171
\(460\) 9.04981 0.421949
\(461\) −0.316932 −0.0147610 −0.00738049 0.999973i \(-0.502349\pi\)
−0.00738049 + 0.999973i \(0.502349\pi\)
\(462\) 50.3675 2.34331
\(463\) −31.4197 −1.46020 −0.730098 0.683342i \(-0.760526\pi\)
−0.730098 + 0.683342i \(0.760526\pi\)
\(464\) 4.97967 0.231175
\(465\) −24.3537 −1.12938
\(466\) 13.7144 0.635309
\(467\) 15.0087 0.694519 0.347260 0.937769i \(-0.387112\pi\)
0.347260 + 0.937769i \(0.387112\pi\)
\(468\) −4.73342 −0.218802
\(469\) 26.0290 1.20191
\(470\) 20.1893 0.931261
\(471\) 20.4789 0.943618
\(472\) −7.82980 −0.360396
\(473\) −43.2215 −1.98733
\(474\) −9.20303 −0.422709
\(475\) −0.572457 −0.0262661
\(476\) −7.76419 −0.355871
\(477\) 1.49483 0.0684436
\(478\) −20.2568 −0.926523
\(479\) −23.9979 −1.09649 −0.548247 0.836317i \(-0.684704\pi\)
−0.548247 + 0.836317i \(0.684704\pi\)
\(480\) 17.4613 0.796997
\(481\) −29.9608 −1.36610
\(482\) −13.0601 −0.594871
\(483\) 19.0858 0.868434
\(484\) 21.3948 0.972490
\(485\) −22.8596 −1.03800
\(486\) 18.3844 0.833932
\(487\) −22.5092 −1.01999 −0.509995 0.860177i \(-0.670353\pi\)
−0.509995 + 0.860177i \(0.670353\pi\)
\(488\) −19.3274 −0.874910
\(489\) −3.91813 −0.177184
\(490\) 26.6636 1.20454
\(491\) 8.62984 0.389459 0.194730 0.980857i \(-0.437617\pi\)
0.194730 + 0.980857i \(0.437617\pi\)
\(492\) −8.57484 −0.386584
\(493\) 1.81906 0.0819263
\(494\) −12.3543 −0.555848
\(495\) 12.4263 0.558520
\(496\) 40.1969 1.80489
\(497\) 50.6222 2.27072
\(498\) −15.1890 −0.680635
\(499\) −11.5217 −0.515780 −0.257890 0.966174i \(-0.583027\pi\)
−0.257890 + 0.966174i \(0.583027\pi\)
\(500\) 13.1530 0.588219
\(501\) 24.8122 1.10853
\(502\) 48.3337 2.15724
\(503\) −27.8681 −1.24258 −0.621288 0.783582i \(-0.713390\pi\)
−0.621288 + 0.783582i \(0.713390\pi\)
\(504\) −5.98399 −0.266548
\(505\) −31.8038 −1.41525
\(506\) 35.3971 1.57359
\(507\) −3.42086 −0.151926
\(508\) −6.53043 −0.289741
\(509\) 33.1858 1.47093 0.735466 0.677561i \(-0.236963\pi\)
0.735466 + 0.677561i \(0.236963\pi\)
\(510\) 9.72888 0.430802
\(511\) −41.4920 −1.83550
\(512\) −13.6828 −0.604700
\(513\) 10.0262 0.442669
\(514\) 36.3182 1.60193
\(515\) 21.3826 0.942231
\(516\) 12.6360 0.556270
\(517\) 28.7110 1.26271
\(518\) 50.4736 2.21768
\(519\) 20.2395 0.888417
\(520\) −12.9217 −0.566654
\(521\) 6.50743 0.285096 0.142548 0.989788i \(-0.454471\pi\)
0.142548 + 0.989788i \(0.454471\pi\)
\(522\) −1.86825 −0.0817713
\(523\) −43.0607 −1.88291 −0.941455 0.337137i \(-0.890541\pi\)
−0.941455 + 0.337137i \(0.890541\pi\)
\(524\) −23.5619 −1.02931
\(525\) 1.68271 0.0734393
\(526\) 18.2831 0.797180
\(527\) 14.6838 0.639637
\(528\) 37.8744 1.64827
\(529\) −9.58697 −0.416825
\(530\) −5.43790 −0.236207
\(531\) 5.42884 0.235592
\(532\) 7.56713 0.328077
\(533\) 21.1470 0.915979
\(534\) 9.94189 0.430228
\(535\) 9.60678 0.415337
\(536\) 10.5909 0.457456
\(537\) 7.45166 0.321563
\(538\) 29.3780 1.26658
\(539\) 37.9182 1.63325
\(540\) −13.9743 −0.601360
\(541\) 16.9080 0.726932 0.363466 0.931607i \(-0.381593\pi\)
0.363466 + 0.931607i \(0.381593\pi\)
\(542\) 31.3214 1.34537
\(543\) −17.3047 −0.742614
\(544\) −10.5281 −0.451390
\(545\) 33.5643 1.43774
\(546\) 36.3149 1.55413
\(547\) −6.58138 −0.281400 −0.140700 0.990052i \(-0.544935\pi\)
−0.140700 + 0.990052i \(0.544935\pi\)
\(548\) 5.70711 0.243796
\(549\) 13.4008 0.571931
\(550\) 3.12079 0.133071
\(551\) −1.77289 −0.0755277
\(552\) 7.76576 0.330533
\(553\) −13.9016 −0.591157
\(554\) −14.9033 −0.633180
\(555\) −22.9949 −0.976079
\(556\) −1.14258 −0.0484563
\(557\) −27.4639 −1.16368 −0.581841 0.813302i \(-0.697667\pi\)
−0.581841 + 0.813302i \(0.697667\pi\)
\(558\) −15.0809 −0.638427
\(559\) −31.1626 −1.31804
\(560\) 40.2301 1.70003
\(561\) 13.8354 0.584131
\(562\) 52.4954 2.21439
\(563\) 12.2906 0.517987 0.258993 0.965879i \(-0.416609\pi\)
0.258993 + 0.965879i \(0.416609\pi\)
\(564\) −8.39383 −0.353444
\(565\) −2.80607 −0.118052
\(566\) −0.167771 −0.00705193
\(567\) −17.6608 −0.741684
\(568\) 20.5975 0.864253
\(569\) −41.3392 −1.73303 −0.866514 0.499152i \(-0.833645\pi\)
−0.866514 + 0.499152i \(0.833645\pi\)
\(570\) −9.48196 −0.397156
\(571\) −18.0905 −0.757064 −0.378532 0.925588i \(-0.623571\pi\)
−0.378532 + 0.925588i \(0.623571\pi\)
\(572\) 24.4874 1.02387
\(573\) −32.4315 −1.35485
\(574\) −35.6254 −1.48698
\(575\) 1.18256 0.0493164
\(576\) 0.316867 0.0132028
\(577\) −27.2262 −1.13344 −0.566721 0.823910i \(-0.691788\pi\)
−0.566721 + 0.823910i \(0.691788\pi\)
\(578\) 24.2705 1.00952
\(579\) −18.2359 −0.757857
\(580\) 2.47102 0.102603
\(581\) −22.9437 −0.951865
\(582\) 26.1401 1.08354
\(583\) −7.73321 −0.320277
\(584\) −16.8825 −0.698605
\(585\) 8.95934 0.370423
\(586\) −32.4405 −1.34010
\(587\) −34.0089 −1.40370 −0.701849 0.712326i \(-0.747642\pi\)
−0.701849 + 0.712326i \(0.747642\pi\)
\(588\) −11.0856 −0.457162
\(589\) −14.3111 −0.589680
\(590\) −19.7490 −0.813055
\(591\) −7.92853 −0.326136
\(592\) 37.9542 1.55991
\(593\) 8.73057 0.358522 0.179261 0.983802i \(-0.442629\pi\)
0.179261 + 0.983802i \(0.442629\pi\)
\(594\) −54.6587 −2.24267
\(595\) 14.6959 0.602475
\(596\) 16.1563 0.661789
\(597\) −10.6305 −0.435078
\(598\) 25.5212 1.04364
\(599\) 31.3108 1.27933 0.639663 0.768655i \(-0.279074\pi\)
0.639663 + 0.768655i \(0.279074\pi\)
\(600\) 0.684671 0.0279516
\(601\) −14.9545 −0.610007 −0.305004 0.952351i \(-0.598658\pi\)
−0.305004 + 0.952351i \(0.598658\pi\)
\(602\) 52.4982 2.13967
\(603\) −7.34324 −0.299040
\(604\) −14.6450 −0.595896
\(605\) −40.4957 −1.64639
\(606\) 36.3679 1.47734
\(607\) −8.82904 −0.358360 −0.179180 0.983816i \(-0.557344\pi\)
−0.179180 + 0.983816i \(0.557344\pi\)
\(608\) 10.2609 0.416135
\(609\) 5.21131 0.211173
\(610\) −48.7494 −1.97380
\(611\) 20.7006 0.837457
\(612\) 2.19042 0.0885423
\(613\) 25.3203 1.02268 0.511339 0.859379i \(-0.329150\pi\)
0.511339 + 0.859379i \(0.329150\pi\)
\(614\) −49.9101 −2.01421
\(615\) 16.2303 0.654470
\(616\) 30.9570 1.24729
\(617\) 16.2437 0.653946 0.326973 0.945034i \(-0.393971\pi\)
0.326973 + 0.945034i \(0.393971\pi\)
\(618\) −24.4512 −0.983571
\(619\) −1.01566 −0.0408230 −0.0204115 0.999792i \(-0.506498\pi\)
−0.0204115 + 0.999792i \(0.506498\pi\)
\(620\) 19.9466 0.801073
\(621\) −20.7119 −0.831138
\(622\) −11.1466 −0.446939
\(623\) 15.0177 0.601672
\(624\) 27.3074 1.09317
\(625\) −23.2813 −0.931251
\(626\) −48.0601 −1.92087
\(627\) −13.4842 −0.538509
\(628\) −16.7730 −0.669314
\(629\) 13.8645 0.552815
\(630\) −15.0934 −0.601335
\(631\) 38.4311 1.52992 0.764959 0.644079i \(-0.222759\pi\)
0.764959 + 0.644079i \(0.222759\pi\)
\(632\) −5.65639 −0.224999
\(633\) 35.9392 1.42846
\(634\) −11.9057 −0.472836
\(635\) 12.3607 0.490520
\(636\) 2.26084 0.0896483
\(637\) 27.3389 1.08321
\(638\) 9.66504 0.382643
\(639\) −14.2814 −0.564964
\(640\) 23.8809 0.943975
\(641\) −43.4914 −1.71781 −0.858903 0.512138i \(-0.828854\pi\)
−0.858903 + 0.512138i \(0.828854\pi\)
\(642\) −10.9854 −0.433560
\(643\) 45.0616 1.77706 0.888529 0.458821i \(-0.151728\pi\)
0.888529 + 0.458821i \(0.151728\pi\)
\(644\) −15.6319 −0.615985
\(645\) −23.9173 −0.941742
\(646\) 5.71705 0.224934
\(647\) −2.12450 −0.0835227 −0.0417613 0.999128i \(-0.513297\pi\)
−0.0417613 + 0.999128i \(0.513297\pi\)
\(648\) −7.18595 −0.282291
\(649\) −28.0850 −1.10243
\(650\) 2.25009 0.0882557
\(651\) 42.0667 1.64873
\(652\) 3.20909 0.125678
\(653\) 15.6984 0.614327 0.307164 0.951657i \(-0.400620\pi\)
0.307164 + 0.951657i \(0.400620\pi\)
\(654\) −38.3810 −1.50082
\(655\) 44.5976 1.74257
\(656\) −26.7889 −1.04593
\(657\) 11.7056 0.456680
\(658\) −34.8734 −1.35951
\(659\) 14.5096 0.565214 0.282607 0.959236i \(-0.408801\pi\)
0.282607 + 0.959236i \(0.408801\pi\)
\(660\) 18.7941 0.731558
\(661\) −48.8269 −1.89914 −0.949572 0.313548i \(-0.898482\pi\)
−0.949572 + 0.313548i \(0.898482\pi\)
\(662\) 11.7008 0.454766
\(663\) 9.97530 0.387408
\(664\) −9.33549 −0.362287
\(665\) −14.3230 −0.555420
\(666\) −14.2395 −0.551769
\(667\) 3.66238 0.141808
\(668\) −20.3221 −0.786285
\(669\) −0.474569 −0.0183479
\(670\) 26.7133 1.03202
\(671\) −69.3263 −2.67631
\(672\) −30.1614 −1.16350
\(673\) −38.2960 −1.47620 −0.738101 0.674691i \(-0.764277\pi\)
−0.738101 + 0.674691i \(0.764277\pi\)
\(674\) −8.03806 −0.309615
\(675\) −1.82607 −0.0702854
\(676\) 2.80181 0.107762
\(677\) 40.6909 1.56388 0.781939 0.623356i \(-0.214231\pi\)
0.781939 + 0.623356i \(0.214231\pi\)
\(678\) 3.20876 0.123232
\(679\) 39.4859 1.51533
\(680\) 5.97959 0.229307
\(681\) −4.07740 −0.156246
\(682\) 78.0182 2.98747
\(683\) 7.05178 0.269829 0.134914 0.990857i \(-0.456924\pi\)
0.134914 + 0.990857i \(0.456924\pi\)
\(684\) −2.13482 −0.0816270
\(685\) −10.8023 −0.412736
\(686\) 0.299102 0.0114198
\(687\) −23.9442 −0.913528
\(688\) 39.4766 1.50503
\(689\) −5.57563 −0.212415
\(690\) 19.5875 0.745685
\(691\) −43.1729 −1.64237 −0.821187 0.570659i \(-0.806688\pi\)
−0.821187 + 0.570659i \(0.806688\pi\)
\(692\) −16.5769 −0.630159
\(693\) −21.4642 −0.815359
\(694\) −49.6523 −1.88477
\(695\) 2.16266 0.0820344
\(696\) 2.12041 0.0803741
\(697\) −9.78590 −0.370668
\(698\) 15.1649 0.573999
\(699\) 10.7924 0.408207
\(700\) −1.37820 −0.0520909
\(701\) −19.3060 −0.729178 −0.364589 0.931169i \(-0.618791\pi\)
−0.364589 + 0.931169i \(0.618791\pi\)
\(702\) −39.4088 −1.48739
\(703\) −13.5126 −0.509639
\(704\) −1.63925 −0.0617814
\(705\) 15.8877 0.598366
\(706\) 12.5814 0.473507
\(707\) 54.9354 2.06606
\(708\) 8.21081 0.308581
\(709\) −5.60958 −0.210672 −0.105336 0.994437i \(-0.533592\pi\)
−0.105336 + 0.994437i \(0.533592\pi\)
\(710\) 51.9530 1.94976
\(711\) 3.92189 0.147082
\(712\) 6.11051 0.229001
\(713\) 29.5635 1.10716
\(714\) −16.8049 −0.628909
\(715\) −46.3494 −1.73337
\(716\) −6.10317 −0.228086
\(717\) −15.9408 −0.595322
\(718\) 27.1936 1.01486
\(719\) 40.7256 1.51881 0.759404 0.650619i \(-0.225490\pi\)
0.759404 + 0.650619i \(0.225490\pi\)
\(720\) −11.3496 −0.422976
\(721\) −36.9347 −1.37552
\(722\) 28.1100 1.04615
\(723\) −10.2775 −0.382224
\(724\) 14.1731 0.526740
\(725\) 0.322895 0.0119920
\(726\) 46.3072 1.71862
\(727\) 41.6231 1.54372 0.771858 0.635795i \(-0.219328\pi\)
0.771858 + 0.635795i \(0.219328\pi\)
\(728\) 22.3199 0.827232
\(729\) 28.6504 1.06113
\(730\) −42.5828 −1.57606
\(731\) 14.4207 0.533368
\(732\) 20.2679 0.749123
\(733\) 17.1924 0.635017 0.317509 0.948255i \(-0.397154\pi\)
0.317509 + 0.948255i \(0.397154\pi\)
\(734\) −60.8300 −2.24528
\(735\) 20.9826 0.773956
\(736\) −21.1967 −0.781320
\(737\) 37.9888 1.39934
\(738\) 10.0506 0.369966
\(739\) −4.14398 −0.152439 −0.0762195 0.997091i \(-0.524285\pi\)
−0.0762195 + 0.997091i \(0.524285\pi\)
\(740\) 18.8336 0.692339
\(741\) −9.72212 −0.357151
\(742\) 9.39301 0.344828
\(743\) −32.3530 −1.18692 −0.593458 0.804865i \(-0.702238\pi\)
−0.593458 + 0.804865i \(0.702238\pi\)
\(744\) 17.1164 0.627518
\(745\) −30.5804 −1.12038
\(746\) −45.8152 −1.67741
\(747\) 6.47282 0.236828
\(748\) −11.3317 −0.414327
\(749\) −16.5940 −0.606332
\(750\) 28.4685 1.03952
\(751\) 47.3663 1.72842 0.864211 0.503129i \(-0.167818\pi\)
0.864211 + 0.503129i \(0.167818\pi\)
\(752\) −26.2234 −0.956269
\(753\) 38.0357 1.38610
\(754\) 6.96848 0.253777
\(755\) 27.7198 1.00883
\(756\) 24.1382 0.877899
\(757\) 20.4474 0.743175 0.371587 0.928398i \(-0.378814\pi\)
0.371587 + 0.928398i \(0.378814\pi\)
\(758\) −7.21728 −0.262144
\(759\) 27.8553 1.01108
\(760\) −5.82782 −0.211397
\(761\) −29.4092 −1.06608 −0.533041 0.846090i \(-0.678951\pi\)
−0.533041 + 0.846090i \(0.678951\pi\)
\(762\) −14.1346 −0.512041
\(763\) −57.9764 −2.09889
\(764\) 26.5626 0.961000
\(765\) −4.14599 −0.149898
\(766\) −24.7111 −0.892849
\(767\) −20.2493 −0.731158
\(768\) −28.1468 −1.01566
\(769\) −32.0952 −1.15738 −0.578691 0.815547i \(-0.696436\pi\)
−0.578691 + 0.815547i \(0.696436\pi\)
\(770\) 78.0827 2.81390
\(771\) 28.5802 1.02929
\(772\) 14.9358 0.537552
\(773\) −28.7423 −1.03379 −0.516893 0.856050i \(-0.672912\pi\)
−0.516893 + 0.856050i \(0.672912\pi\)
\(774\) −14.8107 −0.532359
\(775\) 2.60647 0.0936273
\(776\) 16.0663 0.576746
\(777\) 39.7197 1.42493
\(778\) 37.4056 1.34106
\(779\) 9.53753 0.341718
\(780\) 13.5505 0.485185
\(781\) 73.8821 2.64371
\(782\) −11.8101 −0.422328
\(783\) −5.65530 −0.202104
\(784\) −34.6328 −1.23689
\(785\) 31.7476 1.13312
\(786\) −50.9977 −1.81903
\(787\) −15.8626 −0.565441 −0.282720 0.959202i \(-0.591237\pi\)
−0.282720 + 0.959202i \(0.591237\pi\)
\(788\) 6.49375 0.231330
\(789\) 14.3877 0.512214
\(790\) −14.2671 −0.507600
\(791\) 4.84699 0.172339
\(792\) −8.73352 −0.310332
\(793\) −49.9841 −1.77499
\(794\) 45.0920 1.60026
\(795\) −4.27929 −0.151771
\(796\) 8.70678 0.308604
\(797\) 22.7866 0.807142 0.403571 0.914948i \(-0.367769\pi\)
0.403571 + 0.914948i \(0.367769\pi\)
\(798\) 16.3784 0.579790
\(799\) −9.57933 −0.338892
\(800\) −1.86881 −0.0660725
\(801\) −4.23676 −0.149699
\(802\) 4.46477 0.157656
\(803\) −60.5567 −2.13700
\(804\) −11.1062 −0.391687
\(805\) 29.5879 1.04284
\(806\) 56.2510 1.98136
\(807\) 23.1187 0.813817
\(808\) 22.3525 0.786359
\(809\) 14.1227 0.496529 0.248265 0.968692i \(-0.420140\pi\)
0.248265 + 0.968692i \(0.420140\pi\)
\(810\) −18.1251 −0.636850
\(811\) −17.8637 −0.627281 −0.313641 0.949542i \(-0.601549\pi\)
−0.313641 + 0.949542i \(0.601549\pi\)
\(812\) −4.26825 −0.149786
\(813\) 24.6480 0.864444
\(814\) 73.6652 2.58196
\(815\) −6.07412 −0.212767
\(816\) −12.6366 −0.442371
\(817\) −14.0547 −0.491711
\(818\) 12.8494 0.449270
\(819\) −15.4757 −0.540764
\(820\) −13.2932 −0.464219
\(821\) −8.90320 −0.310724 −0.155362 0.987858i \(-0.549654\pi\)
−0.155362 + 0.987858i \(0.549654\pi\)
\(822\) 12.3525 0.430845
\(823\) 7.92475 0.276239 0.138120 0.990416i \(-0.455894\pi\)
0.138120 + 0.990416i \(0.455894\pi\)
\(824\) −15.0283 −0.523534
\(825\) 2.45588 0.0855026
\(826\) 34.1130 1.18694
\(827\) 39.2178 1.36374 0.681869 0.731475i \(-0.261168\pi\)
0.681869 + 0.731475i \(0.261168\pi\)
\(828\) 4.41005 0.153260
\(829\) −40.4664 −1.40545 −0.702727 0.711459i \(-0.748035\pi\)
−0.702727 + 0.711459i \(0.748035\pi\)
\(830\) −23.5469 −0.817323
\(831\) −11.7280 −0.406839
\(832\) −1.18189 −0.0409748
\(833\) −12.6513 −0.438340
\(834\) −2.47302 −0.0856337
\(835\) 38.4653 1.33115
\(836\) 11.0441 0.381968
\(837\) −45.6507 −1.57792
\(838\) −44.5123 −1.53765
\(839\) −22.7643 −0.785912 −0.392956 0.919557i \(-0.628548\pi\)
−0.392956 + 0.919557i \(0.628548\pi\)
\(840\) 17.1306 0.591060
\(841\) 1.00000 0.0344828
\(842\) −20.6433 −0.711416
\(843\) 41.3107 1.42282
\(844\) −29.4355 −1.01321
\(845\) −5.30322 −0.182436
\(846\) 9.83840 0.338251
\(847\) 69.9492 2.40348
\(848\) 7.06317 0.242550
\(849\) −0.132025 −0.00453110
\(850\) −1.04124 −0.0357143
\(851\) 27.9140 0.956880
\(852\) −21.5998 −0.739998
\(853\) −3.83624 −0.131350 −0.0656751 0.997841i \(-0.520920\pi\)
−0.0656751 + 0.997841i \(0.520920\pi\)
\(854\) 84.2060 2.88147
\(855\) 4.04076 0.138191
\(856\) −6.75189 −0.230775
\(857\) −39.8323 −1.36064 −0.680322 0.732913i \(-0.738160\pi\)
−0.680322 + 0.732913i \(0.738160\pi\)
\(858\) 53.0009 1.80942
\(859\) 14.0912 0.480787 0.240393 0.970676i \(-0.422724\pi\)
0.240393 + 0.970676i \(0.422724\pi\)
\(860\) 19.5891 0.667983
\(861\) −28.0350 −0.955431
\(862\) 51.2141 1.74436
\(863\) −40.5117 −1.37903 −0.689517 0.724269i \(-0.742177\pi\)
−0.689517 + 0.724269i \(0.742177\pi\)
\(864\) 32.7311 1.11353
\(865\) 31.3765 1.06683
\(866\) −18.0027 −0.611758
\(867\) 19.0994 0.648651
\(868\) −34.4542 −1.16945
\(869\) −20.2891 −0.688262
\(870\) 5.34831 0.181325
\(871\) 27.3899 0.928070
\(872\) −23.5898 −0.798853
\(873\) −11.1397 −0.377020
\(874\) 11.5103 0.389343
\(875\) 43.0030 1.45377
\(876\) 17.7041 0.598166
\(877\) 5.64130 0.190493 0.0952466 0.995454i \(-0.469636\pi\)
0.0952466 + 0.995454i \(0.469636\pi\)
\(878\) 35.5944 1.20125
\(879\) −25.5287 −0.861060
\(880\) 58.7151 1.97929
\(881\) −23.0396 −0.776222 −0.388111 0.921613i \(-0.626872\pi\)
−0.388111 + 0.921613i \(0.626872\pi\)
\(882\) 12.9934 0.437510
\(883\) −8.33649 −0.280545 −0.140273 0.990113i \(-0.544798\pi\)
−0.140273 + 0.990113i \(0.544798\pi\)
\(884\) −8.17013 −0.274791
\(885\) −15.5413 −0.522415
\(886\) 25.3445 0.851464
\(887\) 33.6630 1.13029 0.565146 0.824991i \(-0.308820\pi\)
0.565146 + 0.824991i \(0.308820\pi\)
\(888\) 16.1614 0.542341
\(889\) −21.3509 −0.716088
\(890\) 15.4125 0.516628
\(891\) −25.7756 −0.863515
\(892\) 0.388689 0.0130143
\(893\) 9.33620 0.312424
\(894\) 34.9690 1.16954
\(895\) 11.5520 0.386141
\(896\) −41.2500 −1.37807
\(897\) 20.0836 0.670574
\(898\) −38.6069 −1.28833
\(899\) 8.07220 0.269223
\(900\) 0.388813 0.0129604
\(901\) 2.58016 0.0859574
\(902\) −51.9946 −1.73123
\(903\) 41.3129 1.37481
\(904\) 1.97218 0.0655936
\(905\) −26.8267 −0.891749
\(906\) −31.6978 −1.05309
\(907\) 51.6497 1.71500 0.857501 0.514483i \(-0.172016\pi\)
0.857501 + 0.514483i \(0.172016\pi\)
\(908\) 3.33954 0.110827
\(909\) −15.4983 −0.514045
\(910\) 56.2975 1.86624
\(911\) 14.8868 0.493221 0.246610 0.969115i \(-0.420683\pi\)
0.246610 + 0.969115i \(0.420683\pi\)
\(912\) 12.3159 0.407821
\(913\) −33.4859 −1.10822
\(914\) 12.2265 0.404418
\(915\) −38.3628 −1.26823
\(916\) 19.6111 0.647970
\(917\) −77.0344 −2.54390
\(918\) 18.2367 0.601900
\(919\) −28.3293 −0.934498 −0.467249 0.884126i \(-0.654755\pi\)
−0.467249 + 0.884126i \(0.654755\pi\)
\(920\) 12.0389 0.396912
\(921\) −39.2762 −1.29420
\(922\) 0.561835 0.0185031
\(923\) 53.2689 1.75337
\(924\) −32.4634 −1.06797
\(925\) 2.46105 0.0809188
\(926\) 55.6987 1.83037
\(927\) 10.4199 0.342236
\(928\) −5.78768 −0.189990
\(929\) −4.84591 −0.158989 −0.0794947 0.996835i \(-0.525331\pi\)
−0.0794947 + 0.996835i \(0.525331\pi\)
\(930\) 43.1726 1.41569
\(931\) 12.3302 0.404105
\(932\) −8.83939 −0.289544
\(933\) −8.77171 −0.287173
\(934\) −26.6064 −0.870588
\(935\) 21.4484 0.701439
\(936\) −6.29685 −0.205819
\(937\) 0.553136 0.0180702 0.00903509 0.999959i \(-0.497124\pi\)
0.00903509 + 0.999959i \(0.497124\pi\)
\(938\) −46.1425 −1.50661
\(939\) −37.8204 −1.23422
\(940\) −13.0126 −0.424424
\(941\) 49.5592 1.61558 0.807792 0.589468i \(-0.200663\pi\)
0.807792 + 0.589468i \(0.200663\pi\)
\(942\) −36.3036 −1.18284
\(943\) −19.7023 −0.641596
\(944\) 25.6516 0.834889
\(945\) −45.6885 −1.48625
\(946\) 76.6201 2.49113
\(947\) −5.00757 −0.162724 −0.0813621 0.996685i \(-0.525927\pi\)
−0.0813621 + 0.996685i \(0.525927\pi\)
\(948\) 5.93164 0.192651
\(949\) −43.6613 −1.41731
\(950\) 1.01481 0.0329249
\(951\) −9.36907 −0.303813
\(952\) −10.3287 −0.334755
\(953\) −25.2521 −0.817997 −0.408999 0.912535i \(-0.634122\pi\)
−0.408999 + 0.912535i \(0.634122\pi\)
\(954\) −2.64993 −0.0857948
\(955\) −50.2772 −1.62693
\(956\) 13.0561 0.422265
\(957\) 7.60580 0.245861
\(958\) 42.5419 1.37447
\(959\) 18.6591 0.602534
\(960\) −0.907103 −0.0292766
\(961\) 34.1605 1.10195
\(962\) 53.1125 1.71242
\(963\) 4.68147 0.150858
\(964\) 8.41764 0.271114
\(965\) −28.2703 −0.910054
\(966\) −33.8340 −1.08859
\(967\) −23.2433 −0.747454 −0.373727 0.927539i \(-0.621920\pi\)
−0.373727 + 0.927539i \(0.621920\pi\)
\(968\) 28.4614 0.914785
\(969\) 4.49897 0.144528
\(970\) 40.5239 1.30114
\(971\) −5.37637 −0.172536 −0.0862680 0.996272i \(-0.527494\pi\)
−0.0862680 + 0.996272i \(0.527494\pi\)
\(972\) −11.8493 −0.380066
\(973\) −3.73562 −0.119758
\(974\) 39.9029 1.27857
\(975\) 1.77068 0.0567072
\(976\) 63.3196 2.02681
\(977\) 45.4013 1.45252 0.726259 0.687421i \(-0.241257\pi\)
0.726259 + 0.687421i \(0.241257\pi\)
\(978\) 6.94580 0.222102
\(979\) 21.9181 0.700504
\(980\) −17.1855 −0.548971
\(981\) 16.3562 0.522212
\(982\) −15.2984 −0.488192
\(983\) −23.4219 −0.747043 −0.373522 0.927621i \(-0.621850\pi\)
−0.373522 + 0.927621i \(0.621850\pi\)
\(984\) −11.4071 −0.363645
\(985\) −12.2913 −0.391632
\(986\) −3.22470 −0.102696
\(987\) −27.4432 −0.873527
\(988\) 7.96276 0.253329
\(989\) 29.0337 0.923218
\(990\) −22.0285 −0.700112
\(991\) −17.4885 −0.555542 −0.277771 0.960647i \(-0.589596\pi\)
−0.277771 + 0.960647i \(0.589596\pi\)
\(992\) −46.7193 −1.48334
\(993\) 9.20784 0.292202
\(994\) −89.7397 −2.84637
\(995\) −16.4801 −0.522453
\(996\) 9.78978 0.310201
\(997\) 12.1176 0.383769 0.191884 0.981418i \(-0.438540\pi\)
0.191884 + 0.981418i \(0.438540\pi\)
\(998\) 20.4248 0.646537
\(999\) −43.1037 −1.36374
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 \(a_p\))