Properties

Label 8003.2.a.c.1.9
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58576 q^{2}\) \(+1.51660 q^{3}\) \(+4.68613 q^{4}\) \(-3.91728 q^{5}\) \(-3.92157 q^{6}\) \(-1.90750 q^{7}\) \(-6.94569 q^{8}\) \(-0.699911 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58576 q^{2}\) \(+1.51660 q^{3}\) \(+4.68613 q^{4}\) \(-3.91728 q^{5}\) \(-3.92157 q^{6}\) \(-1.90750 q^{7}\) \(-6.94569 q^{8}\) \(-0.699911 q^{9}\) \(+10.1291 q^{10}\) \(+3.75612 q^{11}\) \(+7.10701 q^{12}\) \(+0.142589 q^{13}\) \(+4.93232 q^{14}\) \(-5.94096 q^{15}\) \(+8.58758 q^{16}\) \(+0.966060 q^{17}\) \(+1.80980 q^{18}\) \(+3.91278 q^{19}\) \(-18.3569 q^{20}\) \(-2.89292 q^{21}\) \(-9.71241 q^{22}\) \(+8.94661 q^{23}\) \(-10.5339 q^{24}\) \(+10.3451 q^{25}\) \(-0.368700 q^{26}\) \(-5.61130 q^{27}\) \(-8.93879 q^{28}\) \(-1.33204 q^{29}\) \(+15.3619 q^{30}\) \(+5.78221 q^{31}\) \(-8.31402 q^{32}\) \(+5.69655 q^{33}\) \(-2.49799 q^{34}\) \(+7.47220 q^{35}\) \(-3.27988 q^{36}\) \(+8.39609 q^{37}\) \(-10.1175 q^{38}\) \(+0.216251 q^{39}\) \(+27.2082 q^{40}\) \(-7.06425 q^{41}\) \(+7.48038 q^{42}\) \(-10.2633 q^{43}\) \(+17.6017 q^{44}\) \(+2.74175 q^{45}\) \(-23.1338 q^{46}\) \(-5.88279 q^{47}\) \(+13.0240 q^{48}\) \(-3.36145 q^{49}\) \(-26.7498 q^{50}\) \(+1.46513 q^{51}\) \(+0.668190 q^{52}\) \(-1.00000 q^{53}\) \(+14.5095 q^{54}\) \(-14.7138 q^{55}\) \(+13.2489 q^{56}\) \(+5.93414 q^{57}\) \(+3.44432 q^{58}\) \(+10.5720 q^{59}\) \(-27.8401 q^{60}\) \(+10.9931 q^{61}\) \(-14.9514 q^{62}\) \(+1.33508 q^{63}\) \(+4.32286 q^{64}\) \(-0.558560 q^{65}\) \(-14.7299 q^{66}\) \(+4.88864 q^{67}\) \(+4.52709 q^{68}\) \(+13.5685 q^{69}\) \(-19.3213 q^{70}\) \(-5.62361 q^{71}\) \(+4.86136 q^{72}\) \(+2.67486 q^{73}\) \(-21.7102 q^{74}\) \(+15.6894 q^{75}\) \(+18.3358 q^{76}\) \(-7.16479 q^{77}\) \(-0.559172 q^{78}\) \(-12.4486 q^{79}\) \(-33.6400 q^{80}\) \(-6.41039 q^{81}\) \(+18.2664 q^{82}\) \(-4.48555 q^{83}\) \(-13.5566 q^{84}\) \(-3.78433 q^{85}\) \(+26.5383 q^{86}\) \(-2.02017 q^{87}\) \(-26.0888 q^{88}\) \(-4.37845 q^{89}\) \(-7.08949 q^{90}\) \(-0.271988 q^{91}\) \(+41.9250 q^{92}\) \(+8.76932 q^{93}\) \(+15.2114 q^{94}\) \(-15.3274 q^{95}\) \(-12.6091 q^{96}\) \(+7.22950 q^{97}\) \(+8.69190 q^{98}\) \(-2.62895 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58576 −1.82841 −0.914203 0.405257i \(-0.867182\pi\)
−0.914203 + 0.405257i \(0.867182\pi\)
\(3\) 1.51660 0.875612 0.437806 0.899069i \(-0.355756\pi\)
0.437806 + 0.899069i \(0.355756\pi\)
\(4\) 4.68613 2.34307
\(5\) −3.91728 −1.75186 −0.875930 0.482438i \(-0.839751\pi\)
−0.875930 + 0.482438i \(0.839751\pi\)
\(6\) −3.92157 −1.60097
\(7\) −1.90750 −0.720966 −0.360483 0.932766i \(-0.617388\pi\)
−0.360483 + 0.932766i \(0.617388\pi\)
\(8\) −6.94569 −2.45567
\(9\) −0.699911 −0.233304
\(10\) 10.1291 3.20311
\(11\) 3.75612 1.13251 0.566256 0.824229i \(-0.308391\pi\)
0.566256 + 0.824229i \(0.308391\pi\)
\(12\) 7.10701 2.05162
\(13\) 0.142589 0.0395470 0.0197735 0.999804i \(-0.493705\pi\)
0.0197735 + 0.999804i \(0.493705\pi\)
\(14\) 4.93232 1.31822
\(15\) −5.94096 −1.53395
\(16\) 8.58758 2.14690
\(17\) 0.966060 0.234304 0.117152 0.993114i \(-0.462624\pi\)
0.117152 + 0.993114i \(0.462624\pi\)
\(18\) 1.80980 0.426574
\(19\) 3.91278 0.897653 0.448826 0.893619i \(-0.351842\pi\)
0.448826 + 0.893619i \(0.351842\pi\)
\(20\) −18.3569 −4.10473
\(21\) −2.89292 −0.631287
\(22\) −9.71241 −2.07069
\(23\) 8.94661 1.86550 0.932749 0.360527i \(-0.117403\pi\)
0.932749 + 0.360527i \(0.117403\pi\)
\(24\) −10.5339 −2.15021
\(25\) 10.3451 2.06901
\(26\) −0.368700 −0.0723080
\(27\) −5.61130 −1.07990
\(28\) −8.93879 −1.68927
\(29\) −1.33204 −0.247353 −0.123677 0.992323i \(-0.539469\pi\)
−0.123677 + 0.992323i \(0.539469\pi\)
\(30\) 15.3619 2.80468
\(31\) 5.78221 1.03851 0.519257 0.854618i \(-0.326209\pi\)
0.519257 + 0.854618i \(0.326209\pi\)
\(32\) −8.31402 −1.46972
\(33\) 5.69655 0.991641
\(34\) −2.49799 −0.428403
\(35\) 7.47220 1.26303
\(36\) −3.27988 −0.546646
\(37\) 8.39609 1.38031 0.690155 0.723662i \(-0.257543\pi\)
0.690155 + 0.723662i \(0.257543\pi\)
\(38\) −10.1175 −1.64127
\(39\) 0.216251 0.0346278
\(40\) 27.2082 4.30199
\(41\) −7.06425 −1.10325 −0.551626 0.834092i \(-0.685992\pi\)
−0.551626 + 0.834092i \(0.685992\pi\)
\(42\) 7.48038 1.15425
\(43\) −10.2633 −1.56514 −0.782568 0.622565i \(-0.786091\pi\)
−0.782568 + 0.622565i \(0.786091\pi\)
\(44\) 17.6017 2.65355
\(45\) 2.74175 0.408716
\(46\) −23.1338 −3.41089
\(47\) −5.88279 −0.858092 −0.429046 0.903283i \(-0.641150\pi\)
−0.429046 + 0.903283i \(0.641150\pi\)
\(48\) 13.0240 1.87985
\(49\) −3.36145 −0.480207
\(50\) −26.7498 −3.78300
\(51\) 1.46513 0.205159
\(52\) 0.668190 0.0926613
\(53\) −1.00000 −0.137361
\(54\) 14.5095 1.97449
\(55\) −14.7138 −1.98400
\(56\) 13.2489 1.77046
\(57\) 5.93414 0.785995
\(58\) 3.44432 0.452262
\(59\) 10.5720 1.37636 0.688179 0.725541i \(-0.258411\pi\)
0.688179 + 0.725541i \(0.258411\pi\)
\(60\) −27.8401 −3.59415
\(61\) 10.9931 1.40752 0.703761 0.710437i \(-0.251503\pi\)
0.703761 + 0.710437i \(0.251503\pi\)
\(62\) −14.9514 −1.89883
\(63\) 1.33508 0.168204
\(64\) 4.32286 0.540357
\(65\) −0.558560 −0.0692808
\(66\) −14.7299 −1.81312
\(67\) 4.88864 0.597243 0.298621 0.954372i \(-0.403473\pi\)
0.298621 + 0.954372i \(0.403473\pi\)
\(68\) 4.52709 0.548990
\(69\) 13.5685 1.63345
\(70\) −19.3213 −2.30934
\(71\) −5.62361 −0.667400 −0.333700 0.942679i \(-0.608297\pi\)
−0.333700 + 0.942679i \(0.608297\pi\)
\(72\) 4.86136 0.572917
\(73\) 2.67486 0.313068 0.156534 0.987673i \(-0.449968\pi\)
0.156534 + 0.987673i \(0.449968\pi\)
\(74\) −21.7102 −2.52377
\(75\) 15.6894 1.81165
\(76\) 18.3358 2.10326
\(77\) −7.16479 −0.816503
\(78\) −0.559172 −0.0633137
\(79\) −12.4486 −1.40058 −0.700288 0.713860i \(-0.746945\pi\)
−0.700288 + 0.713860i \(0.746945\pi\)
\(80\) −33.6400 −3.76106
\(81\) −6.41039 −0.712266
\(82\) 18.2664 2.01719
\(83\) −4.48555 −0.492353 −0.246177 0.969225i \(-0.579174\pi\)
−0.246177 + 0.969225i \(0.579174\pi\)
\(84\) −13.5566 −1.47915
\(85\) −3.78433 −0.410468
\(86\) 26.5383 2.86170
\(87\) −2.02017 −0.216585
\(88\) −26.0888 −2.78108
\(89\) −4.37845 −0.464115 −0.232057 0.972702i \(-0.574546\pi\)
−0.232057 + 0.972702i \(0.574546\pi\)
\(90\) −7.08949 −0.747298
\(91\) −0.271988 −0.0285121
\(92\) 41.9250 4.37099
\(93\) 8.76932 0.909336
\(94\) 15.2114 1.56894
\(95\) −15.3274 −1.57256
\(96\) −12.6091 −1.28691
\(97\) 7.22950 0.734045 0.367022 0.930212i \(-0.380377\pi\)
0.367022 + 0.930212i \(0.380377\pi\)
\(98\) 8.69190 0.878014
\(99\) −2.62895 −0.264219
\(100\) 48.4784 4.84784
\(101\) −12.0889 −1.20289 −0.601446 0.798913i \(-0.705409\pi\)
−0.601446 + 0.798913i \(0.705409\pi\)
\(102\) −3.78847 −0.375114
\(103\) 2.36405 0.232937 0.116468 0.993194i \(-0.462843\pi\)
0.116468 + 0.993194i \(0.462843\pi\)
\(104\) −0.990377 −0.0971144
\(105\) 11.3324 1.10593
\(106\) 2.58576 0.251151
\(107\) 9.13710 0.883317 0.441658 0.897183i \(-0.354390\pi\)
0.441658 + 0.897183i \(0.354390\pi\)
\(108\) −26.2953 −2.53027
\(109\) 9.16055 0.877422 0.438711 0.898628i \(-0.355435\pi\)
0.438711 + 0.898628i \(0.355435\pi\)
\(110\) 38.0462 3.62756
\(111\) 12.7336 1.20862
\(112\) −16.3808 −1.54784
\(113\) 5.92505 0.557382 0.278691 0.960381i \(-0.410100\pi\)
0.278691 + 0.960381i \(0.410100\pi\)
\(114\) −15.3442 −1.43712
\(115\) −35.0464 −3.26809
\(116\) −6.24211 −0.579565
\(117\) −0.0997995 −0.00922647
\(118\) −27.3366 −2.51654
\(119\) −1.84276 −0.168925
\(120\) 41.2641 3.76688
\(121\) 3.10843 0.282584
\(122\) −28.4255 −2.57352
\(123\) −10.7137 −0.966020
\(124\) 27.0962 2.43331
\(125\) −20.9381 −1.87276
\(126\) −3.45219 −0.307545
\(127\) 17.4134 1.54519 0.772595 0.634899i \(-0.218958\pi\)
0.772595 + 0.634899i \(0.218958\pi\)
\(128\) 5.45018 0.481732
\(129\) −15.5653 −1.37045
\(130\) 1.44430 0.126673
\(131\) −12.0533 −1.05310 −0.526550 0.850144i \(-0.676515\pi\)
−0.526550 + 0.850144i \(0.676515\pi\)
\(132\) 26.6948 2.32348
\(133\) −7.46361 −0.647177
\(134\) −12.6408 −1.09200
\(135\) 21.9810 1.89183
\(136\) −6.70995 −0.575373
\(137\) −5.13529 −0.438737 −0.219369 0.975642i \(-0.570400\pi\)
−0.219369 + 0.975642i \(0.570400\pi\)
\(138\) −35.0848 −2.98661
\(139\) −15.2916 −1.29702 −0.648509 0.761207i \(-0.724607\pi\)
−0.648509 + 0.761207i \(0.724607\pi\)
\(140\) 35.0157 2.95937
\(141\) −8.92186 −0.751356
\(142\) 14.5413 1.22028
\(143\) 0.535580 0.0447875
\(144\) −6.01055 −0.500879
\(145\) 5.21796 0.433328
\(146\) −6.91653 −0.572416
\(147\) −5.09799 −0.420475
\(148\) 39.3452 3.23416
\(149\) −22.5918 −1.85079 −0.925395 0.379005i \(-0.876266\pi\)
−0.925395 + 0.379005i \(0.876266\pi\)
\(150\) −40.5689 −3.31244
\(151\) 1.00000 0.0813788
\(152\) −27.1769 −2.20434
\(153\) −0.676156 −0.0546640
\(154\) 18.5264 1.49290
\(155\) −22.6505 −1.81933
\(156\) 1.01338 0.0811353
\(157\) 7.94569 0.634135 0.317067 0.948403i \(-0.397302\pi\)
0.317067 + 0.948403i \(0.397302\pi\)
\(158\) 32.1890 2.56082
\(159\) −1.51660 −0.120275
\(160\) 32.5683 2.57475
\(161\) −17.0656 −1.34496
\(162\) 16.5757 1.30231
\(163\) 16.5204 1.29398 0.646989 0.762499i \(-0.276028\pi\)
0.646989 + 0.762499i \(0.276028\pi\)
\(164\) −33.1040 −2.58499
\(165\) −22.3150 −1.73722
\(166\) 11.5985 0.900221
\(167\) −25.1452 −1.94579 −0.972897 0.231240i \(-0.925722\pi\)
−0.972897 + 0.231240i \(0.925722\pi\)
\(168\) 20.0933 1.55023
\(169\) −12.9797 −0.998436
\(170\) 9.78534 0.750501
\(171\) −2.73860 −0.209426
\(172\) −48.0951 −3.66722
\(173\) −10.5848 −0.804745 −0.402372 0.915476i \(-0.631814\pi\)
−0.402372 + 0.915476i \(0.631814\pi\)
\(174\) 5.22368 0.396006
\(175\) −19.7332 −1.49169
\(176\) 32.2560 2.43139
\(177\) 16.0335 1.20515
\(178\) 11.3216 0.848590
\(179\) −24.0504 −1.79761 −0.898807 0.438344i \(-0.855565\pi\)
−0.898807 + 0.438344i \(0.855565\pi\)
\(180\) 12.8482 0.957648
\(181\) 6.86739 0.510449 0.255225 0.966882i \(-0.417851\pi\)
0.255225 + 0.966882i \(0.417851\pi\)
\(182\) 0.703294 0.0521316
\(183\) 16.6722 1.23244
\(184\) −62.1404 −4.58105
\(185\) −32.8898 −2.41811
\(186\) −22.6753 −1.66264
\(187\) 3.62863 0.265352
\(188\) −27.5675 −2.01057
\(189\) 10.7035 0.778568
\(190\) 39.6330 2.87528
\(191\) 15.7699 1.14107 0.570533 0.821275i \(-0.306737\pi\)
0.570533 + 0.821275i \(0.306737\pi\)
\(192\) 6.55607 0.473143
\(193\) 18.8268 1.35519 0.677593 0.735437i \(-0.263023\pi\)
0.677593 + 0.735437i \(0.263023\pi\)
\(194\) −18.6937 −1.34213
\(195\) −0.847114 −0.0606631
\(196\) −15.7522 −1.12516
\(197\) −6.29805 −0.448718 −0.224359 0.974507i \(-0.572029\pi\)
−0.224359 + 0.974507i \(0.572029\pi\)
\(198\) 6.79782 0.483100
\(199\) 17.5297 1.24265 0.621325 0.783553i \(-0.286595\pi\)
0.621325 + 0.783553i \(0.286595\pi\)
\(200\) −71.8536 −5.08082
\(201\) 7.41414 0.522953
\(202\) 31.2590 2.19937
\(203\) 2.54086 0.178333
\(204\) 6.86580 0.480702
\(205\) 27.6727 1.93274
\(206\) −6.11285 −0.425902
\(207\) −6.26184 −0.435228
\(208\) 1.22449 0.0849033
\(209\) 14.6969 1.01660
\(210\) −29.3027 −2.02208
\(211\) −16.3640 −1.12654 −0.563271 0.826273i \(-0.690457\pi\)
−0.563271 + 0.826273i \(0.690457\pi\)
\(212\) −4.68613 −0.321845
\(213\) −8.52879 −0.584383
\(214\) −23.6263 −1.61506
\(215\) 40.2041 2.74190
\(216\) 38.9743 2.65187
\(217\) −11.0295 −0.748734
\(218\) −23.6870 −1.60428
\(219\) 4.05670 0.274126
\(220\) −68.9507 −4.64865
\(221\) 0.137749 0.00926602
\(222\) −32.9259 −2.20984
\(223\) −14.1502 −0.947565 −0.473782 0.880642i \(-0.657112\pi\)
−0.473782 + 0.880642i \(0.657112\pi\)
\(224\) 15.8590 1.05962
\(225\) −7.24063 −0.482709
\(226\) −15.3207 −1.01912
\(227\) 25.6179 1.70032 0.850160 0.526525i \(-0.176505\pi\)
0.850160 + 0.526525i \(0.176505\pi\)
\(228\) 27.8082 1.84164
\(229\) 21.4403 1.41681 0.708407 0.705804i \(-0.249414\pi\)
0.708407 + 0.705804i \(0.249414\pi\)
\(230\) 90.6214 5.97540
\(231\) −10.8661 −0.714940
\(232\) 9.25192 0.607418
\(233\) 5.55659 0.364025 0.182012 0.983296i \(-0.441739\pi\)
0.182012 + 0.983296i \(0.441739\pi\)
\(234\) 0.258057 0.0168697
\(235\) 23.0445 1.50326
\(236\) 49.5418 3.22490
\(237\) −18.8796 −1.22636
\(238\) 4.76492 0.308864
\(239\) 3.49503 0.226075 0.113037 0.993591i \(-0.463942\pi\)
0.113037 + 0.993591i \(0.463942\pi\)
\(240\) −51.0185 −3.29323
\(241\) 27.1249 1.74727 0.873633 0.486585i \(-0.161758\pi\)
0.873633 + 0.486585i \(0.161758\pi\)
\(242\) −8.03763 −0.516679
\(243\) 7.11188 0.456227
\(244\) 51.5151 3.29792
\(245\) 13.1677 0.841256
\(246\) 27.7030 1.76628
\(247\) 0.557918 0.0354995
\(248\) −40.1614 −2.55025
\(249\) −6.80280 −0.431110
\(250\) 54.1409 3.42417
\(251\) −2.17259 −0.137132 −0.0685662 0.997647i \(-0.521842\pi\)
−0.0685662 + 0.997647i \(0.521842\pi\)
\(252\) 6.25636 0.394114
\(253\) 33.6045 2.11270
\(254\) −45.0268 −2.82524
\(255\) −5.73932 −0.359410
\(256\) −22.7386 −1.42116
\(257\) −5.50631 −0.343474 −0.171737 0.985143i \(-0.554938\pi\)
−0.171737 + 0.985143i \(0.554938\pi\)
\(258\) 40.2482 2.50574
\(259\) −16.0155 −0.995157
\(260\) −2.61749 −0.162330
\(261\) 0.932308 0.0577084
\(262\) 31.1668 1.92549
\(263\) −4.71111 −0.290499 −0.145250 0.989395i \(-0.546399\pi\)
−0.145250 + 0.989395i \(0.546399\pi\)
\(264\) −39.5664 −2.43514
\(265\) 3.91728 0.240637
\(266\) 19.2991 1.18330
\(267\) −6.64037 −0.406384
\(268\) 22.9088 1.39938
\(269\) −4.71700 −0.287601 −0.143800 0.989607i \(-0.545932\pi\)
−0.143800 + 0.989607i \(0.545932\pi\)
\(270\) −56.8376 −3.45903
\(271\) 18.7886 1.14132 0.570662 0.821185i \(-0.306687\pi\)
0.570662 + 0.821185i \(0.306687\pi\)
\(272\) 8.29612 0.503026
\(273\) −0.412498 −0.0249655
\(274\) 13.2786 0.802190
\(275\) 38.8573 2.34318
\(276\) 63.5837 3.82729
\(277\) 26.3472 1.58305 0.791526 0.611136i \(-0.209287\pi\)
0.791526 + 0.611136i \(0.209287\pi\)
\(278\) 39.5404 2.37147
\(279\) −4.04703 −0.242289
\(280\) −51.8996 −3.10159
\(281\) −4.57799 −0.273100 −0.136550 0.990633i \(-0.543601\pi\)
−0.136550 + 0.990633i \(0.543601\pi\)
\(282\) 23.0697 1.37378
\(283\) −19.9392 −1.18526 −0.592631 0.805474i \(-0.701911\pi\)
−0.592631 + 0.805474i \(0.701911\pi\)
\(284\) −26.3530 −1.56376
\(285\) −23.2457 −1.37695
\(286\) −1.38488 −0.0818897
\(287\) 13.4751 0.795407
\(288\) 5.81908 0.342892
\(289\) −16.0667 −0.945102
\(290\) −13.4924 −0.792300
\(291\) 10.9643 0.642738
\(292\) 12.5347 0.733540
\(293\) 17.2198 1.00599 0.502996 0.864289i \(-0.332231\pi\)
0.502996 + 0.864289i \(0.332231\pi\)
\(294\) 13.1822 0.768800
\(295\) −41.4135 −2.41119
\(296\) −58.3166 −3.38959
\(297\) −21.0767 −1.22299
\(298\) 58.4168 3.38399
\(299\) 1.27569 0.0737749
\(300\) 73.5225 4.24483
\(301\) 19.5772 1.12841
\(302\) −2.58576 −0.148794
\(303\) −18.3341 −1.05327
\(304\) 33.6013 1.92717
\(305\) −43.0630 −2.46578
\(306\) 1.74837 0.0999479
\(307\) 24.9304 1.42286 0.711428 0.702759i \(-0.248049\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(308\) −33.5752 −1.91312
\(309\) 3.58532 0.203962
\(310\) 58.5687 3.32648
\(311\) 23.5635 1.33616 0.668081 0.744088i \(-0.267116\pi\)
0.668081 + 0.744088i \(0.267116\pi\)
\(312\) −1.50201 −0.0850346
\(313\) 0.606690 0.0342922 0.0171461 0.999853i \(-0.494542\pi\)
0.0171461 + 0.999853i \(0.494542\pi\)
\(314\) −20.5456 −1.15946
\(315\) −5.22988 −0.294670
\(316\) −58.3358 −3.28164
\(317\) −3.08402 −0.173216 −0.0866080 0.996242i \(-0.527603\pi\)
−0.0866080 + 0.996242i \(0.527603\pi\)
\(318\) 3.92157 0.219911
\(319\) −5.00329 −0.280131
\(320\) −16.9338 −0.946631
\(321\) 13.8574 0.773443
\(322\) 44.1276 2.45913
\(323\) 3.77998 0.210324
\(324\) −30.0399 −1.66889
\(325\) 1.47509 0.0818233
\(326\) −42.7177 −2.36592
\(327\) 13.8929 0.768281
\(328\) 49.0661 2.70922
\(329\) 11.2214 0.618656
\(330\) 57.7010 3.17634
\(331\) −3.76482 −0.206933 −0.103467 0.994633i \(-0.532993\pi\)
−0.103467 + 0.994633i \(0.532993\pi\)
\(332\) −21.0199 −1.15362
\(333\) −5.87652 −0.322031
\(334\) 65.0193 3.55770
\(335\) −19.1502 −1.04629
\(336\) −24.8432 −1.35531
\(337\) 30.3197 1.65162 0.825810 0.563948i \(-0.190718\pi\)
0.825810 + 0.563948i \(0.190718\pi\)
\(338\) 33.5623 1.82555
\(339\) 8.98595 0.488050
\(340\) −17.7339 −0.961753
\(341\) 21.7187 1.17613
\(342\) 7.08135 0.382915
\(343\) 19.7644 1.06718
\(344\) 71.2855 3.84346
\(345\) −53.1515 −2.86158
\(346\) 27.3696 1.47140
\(347\) −7.44001 −0.399401 −0.199700 0.979857i \(-0.563997\pi\)
−0.199700 + 0.979857i \(0.563997\pi\)
\(348\) −9.46681 −0.507474
\(349\) −8.69386 −0.465372 −0.232686 0.972552i \(-0.574751\pi\)
−0.232686 + 0.972552i \(0.574751\pi\)
\(350\) 51.0252 2.72741
\(351\) −0.800109 −0.0427066
\(352\) −31.2284 −1.66448
\(353\) 18.5627 0.987991 0.493995 0.869464i \(-0.335536\pi\)
0.493995 + 0.869464i \(0.335536\pi\)
\(354\) −41.4588 −2.20351
\(355\) 22.0292 1.16919
\(356\) −20.5180 −1.08745
\(357\) −2.79473 −0.147913
\(358\) 62.1886 3.28677
\(359\) 28.2132 1.48904 0.744519 0.667602i \(-0.232679\pi\)
0.744519 + 0.667602i \(0.232679\pi\)
\(360\) −19.0433 −1.00367
\(361\) −3.69017 −0.194219
\(362\) −17.7574 −0.933308
\(363\) 4.71425 0.247434
\(364\) −1.27457 −0.0668057
\(365\) −10.4782 −0.548452
\(366\) −43.1102 −2.25340
\(367\) 3.67470 0.191818 0.0959089 0.995390i \(-0.469424\pi\)
0.0959089 + 0.995390i \(0.469424\pi\)
\(368\) 76.8298 4.00503
\(369\) 4.94435 0.257393
\(370\) 85.0451 4.42128
\(371\) 1.90750 0.0990323
\(372\) 41.0942 2.13064
\(373\) −31.7582 −1.64438 −0.822189 0.569215i \(-0.807247\pi\)
−0.822189 + 0.569215i \(0.807247\pi\)
\(374\) −9.38276 −0.485171
\(375\) −31.7549 −1.63981
\(376\) 40.8600 2.10719
\(377\) −0.189934 −0.00978208
\(378\) −27.6768 −1.42354
\(379\) 6.69828 0.344068 0.172034 0.985091i \(-0.444966\pi\)
0.172034 + 0.985091i \(0.444966\pi\)
\(380\) −71.8264 −3.68462
\(381\) 26.4093 1.35299
\(382\) −40.7770 −2.08633
\(383\) 18.4508 0.942793 0.471396 0.881921i \(-0.343750\pi\)
0.471396 + 0.881921i \(0.343750\pi\)
\(384\) 8.26577 0.421811
\(385\) 28.0665 1.43040
\(386\) −48.6816 −2.47783
\(387\) 7.18339 0.365152
\(388\) 33.8784 1.71992
\(389\) 31.1220 1.57795 0.788974 0.614427i \(-0.210613\pi\)
0.788974 + 0.614427i \(0.210613\pi\)
\(390\) 2.19043 0.110917
\(391\) 8.64296 0.437093
\(392\) 23.3476 1.17923
\(393\) −18.2801 −0.922107
\(394\) 16.2852 0.820438
\(395\) 48.7646 2.45361
\(396\) −12.3196 −0.619084
\(397\) 5.73702 0.287933 0.143966 0.989583i \(-0.454014\pi\)
0.143966 + 0.989583i \(0.454014\pi\)
\(398\) −45.3276 −2.27207
\(399\) −11.3194 −0.566676
\(400\) 88.8392 4.44196
\(401\) −0.256250 −0.0127965 −0.00639826 0.999980i \(-0.502037\pi\)
−0.00639826 + 0.999980i \(0.502037\pi\)
\(402\) −19.1712 −0.956170
\(403\) 0.824478 0.0410702
\(404\) −56.6503 −2.81846
\(405\) 25.1113 1.24779
\(406\) −6.57004 −0.326066
\(407\) 31.5367 1.56322
\(408\) −10.1763 −0.503804
\(409\) −38.3070 −1.89416 −0.947079 0.321002i \(-0.895980\pi\)
−0.947079 + 0.321002i \(0.895980\pi\)
\(410\) −71.5547 −3.53384
\(411\) −7.78820 −0.384164
\(412\) 11.0782 0.545786
\(413\) −20.1661 −0.992307
\(414\) 16.1916 0.795773
\(415\) 17.5711 0.862534
\(416\) −1.18549 −0.0581232
\(417\) −23.1913 −1.13568
\(418\) −38.0025 −1.85876
\(419\) 34.8432 1.70220 0.851101 0.525002i \(-0.175936\pi\)
0.851101 + 0.525002i \(0.175936\pi\)
\(420\) 53.1050 2.59126
\(421\) 2.30563 0.112370 0.0561848 0.998420i \(-0.482106\pi\)
0.0561848 + 0.998420i \(0.482106\pi\)
\(422\) 42.3132 2.05977
\(423\) 4.11743 0.200196
\(424\) 6.94569 0.337312
\(425\) 9.99396 0.484778
\(426\) 22.0534 1.06849
\(427\) −20.9693 −1.01478
\(428\) 42.8177 2.06967
\(429\) 0.812263 0.0392164
\(430\) −103.958 −5.01330
\(431\) −3.04894 −0.146862 −0.0734312 0.997300i \(-0.523395\pi\)
−0.0734312 + 0.997300i \(0.523395\pi\)
\(432\) −48.1875 −2.31842
\(433\) −16.6336 −0.799358 −0.399679 0.916655i \(-0.630878\pi\)
−0.399679 + 0.916655i \(0.630878\pi\)
\(434\) 28.5197 1.36899
\(435\) 7.91358 0.379427
\(436\) 42.9276 2.05586
\(437\) 35.0061 1.67457
\(438\) −10.4896 −0.501214
\(439\) −15.1998 −0.725447 −0.362724 0.931897i \(-0.618153\pi\)
−0.362724 + 0.931897i \(0.618153\pi\)
\(440\) 102.197 4.87206
\(441\) 2.35272 0.112034
\(442\) −0.356186 −0.0169420
\(443\) −5.99981 −0.285060 −0.142530 0.989791i \(-0.545524\pi\)
−0.142530 + 0.989791i \(0.545524\pi\)
\(444\) 59.6711 2.83187
\(445\) 17.1516 0.813064
\(446\) 36.5889 1.73253
\(447\) −34.2628 −1.62057
\(448\) −8.24584 −0.389579
\(449\) −28.4475 −1.34252 −0.671260 0.741222i \(-0.734247\pi\)
−0.671260 + 0.741222i \(0.734247\pi\)
\(450\) 18.7225 0.882588
\(451\) −26.5342 −1.24945
\(452\) 27.7656 1.30598
\(453\) 1.51660 0.0712563
\(454\) −66.2416 −3.10887
\(455\) 1.06545 0.0499491
\(456\) −41.2166 −1.93015
\(457\) −17.1863 −0.803942 −0.401971 0.915653i \(-0.631675\pi\)
−0.401971 + 0.915653i \(0.631675\pi\)
\(458\) −55.4393 −2.59051
\(459\) −5.42085 −0.253024
\(460\) −164.232 −7.65736
\(461\) 0.275645 0.0128381 0.00641904 0.999979i \(-0.497957\pi\)
0.00641904 + 0.999979i \(0.497957\pi\)
\(462\) 28.0972 1.30720
\(463\) 0.821586 0.0381823 0.0190912 0.999818i \(-0.493923\pi\)
0.0190912 + 0.999818i \(0.493923\pi\)
\(464\) −11.4390 −0.531041
\(465\) −34.3519 −1.59303
\(466\) −14.3680 −0.665585
\(467\) 18.6468 0.862872 0.431436 0.902144i \(-0.358007\pi\)
0.431436 + 0.902144i \(0.358007\pi\)
\(468\) −0.467674 −0.0216182
\(469\) −9.32508 −0.430592
\(470\) −59.5875 −2.74857
\(471\) 12.0505 0.555256
\(472\) −73.4298 −3.37988
\(473\) −38.5501 −1.77254
\(474\) 48.8180 2.24229
\(475\) 40.4780 1.85726
\(476\) −8.63540 −0.395803
\(477\) 0.699911 0.0320467
\(478\) −9.03730 −0.413356
\(479\) 18.2930 0.835828 0.417914 0.908487i \(-0.362761\pi\)
0.417914 + 0.908487i \(0.362761\pi\)
\(480\) 49.3933 2.25448
\(481\) 1.19719 0.0545871
\(482\) −70.1383 −3.19471
\(483\) −25.8818 −1.17766
\(484\) 14.5665 0.662114
\(485\) −28.3200 −1.28594
\(486\) −18.3896 −0.834169
\(487\) 26.4988 1.20077 0.600387 0.799709i \(-0.295013\pi\)
0.600387 + 0.799709i \(0.295013\pi\)
\(488\) −76.3546 −3.45641
\(489\) 25.0549 1.13302
\(490\) −34.0486 −1.53816
\(491\) 27.5508 1.24335 0.621675 0.783276i \(-0.286453\pi\)
0.621675 + 0.783276i \(0.286453\pi\)
\(492\) −50.2057 −2.26345
\(493\) −1.28683 −0.0579558
\(494\) −1.44264 −0.0649074
\(495\) 10.2983 0.462876
\(496\) 49.6552 2.22958
\(497\) 10.7270 0.481173
\(498\) 17.5904 0.788244
\(499\) 7.01388 0.313984 0.156992 0.987600i \(-0.449820\pi\)
0.156992 + 0.987600i \(0.449820\pi\)
\(500\) −98.1189 −4.38801
\(501\) −38.1353 −1.70376
\(502\) 5.61778 0.250734
\(503\) 16.2687 0.725385 0.362693 0.931909i \(-0.381857\pi\)
0.362693 + 0.931909i \(0.381857\pi\)
\(504\) −9.27304 −0.413054
\(505\) 47.3557 2.10730
\(506\) −86.8931 −3.86287
\(507\) −19.6850 −0.874242
\(508\) 81.6016 3.62049
\(509\) −7.12948 −0.316009 −0.158004 0.987438i \(-0.550506\pi\)
−0.158004 + 0.987438i \(0.550506\pi\)
\(510\) 14.8405 0.657148
\(511\) −5.10229 −0.225712
\(512\) 47.8960 2.11672
\(513\) −21.9558 −0.969371
\(514\) 14.2380 0.628011
\(515\) −9.26063 −0.408072
\(516\) −72.9413 −3.21106
\(517\) −22.0964 −0.971800
\(518\) 41.4122 1.81955
\(519\) −16.0529 −0.704644
\(520\) 3.87958 0.170131
\(521\) 29.9032 1.31008 0.655041 0.755593i \(-0.272651\pi\)
0.655041 + 0.755593i \(0.272651\pi\)
\(522\) −2.41072 −0.105514
\(523\) −15.4246 −0.674471 −0.337235 0.941420i \(-0.609492\pi\)
−0.337235 + 0.941420i \(0.609492\pi\)
\(524\) −56.4833 −2.46748
\(525\) −29.9275 −1.30614
\(526\) 12.1818 0.531151
\(527\) 5.58596 0.243328
\(528\) 48.9196 2.12895
\(529\) 57.0419 2.48008
\(530\) −10.1291 −0.439981
\(531\) −7.39946 −0.321109
\(532\) −34.9755 −1.51638
\(533\) −1.00728 −0.0436303
\(534\) 17.1704 0.743035
\(535\) −35.7926 −1.54745
\(536\) −33.9550 −1.46663
\(537\) −36.4750 −1.57401
\(538\) 12.1970 0.525851
\(539\) −12.6260 −0.543841
\(540\) 103.006 4.43267
\(541\) −22.2568 −0.956894 −0.478447 0.878116i \(-0.658800\pi\)
−0.478447 + 0.878116i \(0.658800\pi\)
\(542\) −48.5826 −2.08680
\(543\) 10.4151 0.446956
\(544\) −8.03184 −0.344362
\(545\) −35.8844 −1.53712
\(546\) 1.06662 0.0456471
\(547\) −35.8183 −1.53148 −0.765740 0.643150i \(-0.777627\pi\)
−0.765740 + 0.643150i \(0.777627\pi\)
\(548\) −24.0646 −1.02799
\(549\) −7.69419 −0.328380
\(550\) −100.476 −4.28429
\(551\) −5.21197 −0.222037
\(552\) −94.2424 −4.01122
\(553\) 23.7457 1.00977
\(554\) −68.1275 −2.89446
\(555\) −49.8809 −2.11732
\(556\) −71.6585 −3.03900
\(557\) −9.46947 −0.401234 −0.200617 0.979670i \(-0.564295\pi\)
−0.200617 + 0.979670i \(0.564295\pi\)
\(558\) 10.4646 0.443003
\(559\) −1.46343 −0.0618964
\(560\) 64.1681 2.71160
\(561\) 5.50320 0.232345
\(562\) 11.8376 0.499337
\(563\) 16.6832 0.703115 0.351558 0.936166i \(-0.385652\pi\)
0.351558 + 0.936166i \(0.385652\pi\)
\(564\) −41.8090 −1.76048
\(565\) −23.2101 −0.976455
\(566\) 51.5579 2.16714
\(567\) 12.2278 0.513520
\(568\) 39.0598 1.63891
\(569\) −46.6921 −1.95743 −0.978717 0.205216i \(-0.934210\pi\)
−0.978717 + 0.205216i \(0.934210\pi\)
\(570\) 60.1076 2.51763
\(571\) 17.6507 0.738658 0.369329 0.929299i \(-0.379587\pi\)
0.369329 + 0.929299i \(0.379587\pi\)
\(572\) 2.50980 0.104940
\(573\) 23.9166 0.999131
\(574\) −34.8432 −1.45433
\(575\) 92.5534 3.85974
\(576\) −3.02562 −0.126067
\(577\) −7.85004 −0.326802 −0.163401 0.986560i \(-0.552246\pi\)
−0.163401 + 0.986560i \(0.552246\pi\)
\(578\) 41.5446 1.72803
\(579\) 28.5529 1.18662
\(580\) 24.4521 1.01532
\(581\) 8.55618 0.354970
\(582\) −28.3510 −1.17519
\(583\) −3.75612 −0.155563
\(584\) −18.5787 −0.768793
\(585\) 0.390942 0.0161635
\(586\) −44.5262 −1.83936
\(587\) −34.9831 −1.44391 −0.721954 0.691941i \(-0.756756\pi\)
−0.721954 + 0.691941i \(0.756756\pi\)
\(588\) −23.8899 −0.985202
\(589\) 22.6245 0.932226
\(590\) 107.085 4.40863
\(591\) −9.55165 −0.392902
\(592\) 72.1021 2.96338
\(593\) −8.61073 −0.353600 −0.176800 0.984247i \(-0.556575\pi\)
−0.176800 + 0.984247i \(0.556575\pi\)
\(594\) 54.4992 2.23613
\(595\) 7.21859 0.295933
\(596\) −105.868 −4.33652
\(597\) 26.5857 1.08808
\(598\) −3.29861 −0.134890
\(599\) −19.6518 −0.802950 −0.401475 0.915870i \(-0.631502\pi\)
−0.401475 + 0.915870i \(0.631502\pi\)
\(600\) −108.974 −4.44883
\(601\) −27.8365 −1.13547 −0.567737 0.823210i \(-0.692181\pi\)
−0.567737 + 0.823210i \(0.692181\pi\)
\(602\) −50.6218 −2.06319
\(603\) −3.42162 −0.139339
\(604\) 4.68613 0.190676
\(605\) −12.1766 −0.495048
\(606\) 47.4075 1.92580
\(607\) 28.8503 1.17100 0.585499 0.810673i \(-0.300898\pi\)
0.585499 + 0.810673i \(0.300898\pi\)
\(608\) −32.5309 −1.31930
\(609\) 3.85348 0.156151
\(610\) 111.350 4.50845
\(611\) −0.838819 −0.0339350
\(612\) −3.16856 −0.128081
\(613\) 45.9035 1.85402 0.927012 0.375033i \(-0.122369\pi\)
0.927012 + 0.375033i \(0.122369\pi\)
\(614\) −64.4640 −2.60156
\(615\) 41.9685 1.69233
\(616\) 49.7644 2.00506
\(617\) 30.4913 1.22753 0.613766 0.789488i \(-0.289654\pi\)
0.613766 + 0.789488i \(0.289654\pi\)
\(618\) −9.27077 −0.372925
\(619\) 31.7620 1.27662 0.638311 0.769779i \(-0.279634\pi\)
0.638311 + 0.769779i \(0.279634\pi\)
\(620\) −106.143 −4.26282
\(621\) −50.2021 −2.01454
\(622\) −60.9294 −2.44305
\(623\) 8.35188 0.334611
\(624\) 1.85707 0.0743423
\(625\) 30.2952 1.21181
\(626\) −1.56875 −0.0627000
\(627\) 22.2893 0.890150
\(628\) 37.2345 1.48582
\(629\) 8.11113 0.323412
\(630\) 13.5232 0.538777
\(631\) −10.4816 −0.417265 −0.208632 0.977994i \(-0.566901\pi\)
−0.208632 + 0.977994i \(0.566901\pi\)
\(632\) 86.4641 3.43936
\(633\) −24.8176 −0.986413
\(634\) 7.97453 0.316709
\(635\) −68.2132 −2.70696
\(636\) −7.10701 −0.281811
\(637\) −0.479305 −0.0189908
\(638\) 12.9373 0.512192
\(639\) 3.93603 0.155707
\(640\) −21.3499 −0.843928
\(641\) 6.16145 0.243363 0.121681 0.992569i \(-0.461171\pi\)
0.121681 + 0.992569i \(0.461171\pi\)
\(642\) −35.8318 −1.41417
\(643\) −11.0271 −0.434866 −0.217433 0.976075i \(-0.569768\pi\)
−0.217433 + 0.976075i \(0.569768\pi\)
\(644\) −79.9719 −3.15133
\(645\) 60.9738 2.40084
\(646\) −9.77410 −0.384557
\(647\) 20.1232 0.791125 0.395562 0.918439i \(-0.370550\pi\)
0.395562 + 0.918439i \(0.370550\pi\)
\(648\) 44.5246 1.74909
\(649\) 39.7097 1.55874
\(650\) −3.81423 −0.149606
\(651\) −16.7275 −0.655601
\(652\) 77.4169 3.03188
\(653\) −17.9445 −0.702224 −0.351112 0.936333i \(-0.614196\pi\)
−0.351112 + 0.936333i \(0.614196\pi\)
\(654\) −35.9237 −1.40473
\(655\) 47.2161 1.84488
\(656\) −60.6649 −2.36857
\(657\) −1.87216 −0.0730401
\(658\) −29.0158 −1.13115
\(659\) −8.14962 −0.317464 −0.158732 0.987322i \(-0.550741\pi\)
−0.158732 + 0.987322i \(0.550741\pi\)
\(660\) −104.571 −4.07042
\(661\) 4.92480 0.191553 0.0957763 0.995403i \(-0.469467\pi\)
0.0957763 + 0.995403i \(0.469467\pi\)
\(662\) 9.73490 0.378358
\(663\) 0.208911 0.00811344
\(664\) 31.1552 1.20906
\(665\) 29.2371 1.13376
\(666\) 15.1952 0.588804
\(667\) −11.9172 −0.461437
\(668\) −117.834 −4.55912
\(669\) −21.4602 −0.829699
\(670\) 49.5177 1.91304
\(671\) 41.2914 1.59404
\(672\) 24.0518 0.927818
\(673\) −10.5249 −0.405704 −0.202852 0.979209i \(-0.565021\pi\)
−0.202852 + 0.979209i \(0.565021\pi\)
\(674\) −78.3994 −3.01983
\(675\) −58.0493 −2.23432
\(676\) −60.8245 −2.33940
\(677\) 18.6657 0.717381 0.358691 0.933457i \(-0.383223\pi\)
0.358691 + 0.933457i \(0.383223\pi\)
\(678\) −23.2355 −0.892353
\(679\) −13.7903 −0.529222
\(680\) 26.2847 1.00797
\(681\) 38.8522 1.48882
\(682\) −56.1591 −2.15044
\(683\) −37.7647 −1.44503 −0.722513 0.691357i \(-0.757013\pi\)
−0.722513 + 0.691357i \(0.757013\pi\)
\(684\) −12.8334 −0.490699
\(685\) 20.1164 0.768606
\(686\) −51.1060 −1.95124
\(687\) 32.5164 1.24058
\(688\) −88.1368 −3.36018
\(689\) −0.142589 −0.00543220
\(690\) 137.437 5.23213
\(691\) −9.96020 −0.378904 −0.189452 0.981890i \(-0.560671\pi\)
−0.189452 + 0.981890i \(0.560671\pi\)
\(692\) −49.6016 −1.88557
\(693\) 5.01472 0.190493
\(694\) 19.2380 0.730266
\(695\) 59.9015 2.27219
\(696\) 14.0315 0.531862
\(697\) −6.82449 −0.258496
\(698\) 22.4802 0.850888
\(699\) 8.42715 0.318744
\(700\) −92.4724 −3.49513
\(701\) −8.51557 −0.321629 −0.160814 0.986985i \(-0.551412\pi\)
−0.160814 + 0.986985i \(0.551412\pi\)
\(702\) 2.06889 0.0780850
\(703\) 32.8520 1.23904
\(704\) 16.2372 0.611961
\(705\) 34.9494 1.31627
\(706\) −47.9985 −1.80645
\(707\) 23.0596 0.867245
\(708\) 75.1353 2.82376
\(709\) 14.2980 0.536973 0.268487 0.963283i \(-0.413476\pi\)
0.268487 + 0.963283i \(0.413476\pi\)
\(710\) −56.9623 −2.13776
\(711\) 8.71291 0.326760
\(712\) 30.4113 1.13971
\(713\) 51.7312 1.93735
\(714\) 7.22650 0.270445
\(715\) −2.09802 −0.0784614
\(716\) −112.704 −4.21193
\(717\) 5.30058 0.197954
\(718\) −72.9525 −2.72256
\(719\) −8.40001 −0.313268 −0.156634 0.987657i \(-0.550064\pi\)
−0.156634 + 0.987657i \(0.550064\pi\)
\(720\) 23.5450 0.877470
\(721\) −4.50942 −0.167939
\(722\) 9.54188 0.355112
\(723\) 41.1377 1.52993
\(724\) 32.1815 1.19602
\(725\) −13.7800 −0.511777
\(726\) −12.1899 −0.452410
\(727\) 27.9374 1.03614 0.518069 0.855339i \(-0.326651\pi\)
0.518069 + 0.855339i \(0.326651\pi\)
\(728\) 1.88914 0.0700162
\(729\) 30.0171 1.11174
\(730\) 27.0940 1.00279
\(731\) −9.91495 −0.366718
\(732\) 78.1280 2.88770
\(733\) −43.6711 −1.61303 −0.806514 0.591215i \(-0.798648\pi\)
−0.806514 + 0.591215i \(0.798648\pi\)
\(734\) −9.50188 −0.350721
\(735\) 19.9703 0.736614
\(736\) −74.3823 −2.74177
\(737\) 18.3623 0.676385
\(738\) −12.7849 −0.470618
\(739\) 2.08967 0.0768698 0.0384349 0.999261i \(-0.487763\pi\)
0.0384349 + 0.999261i \(0.487763\pi\)
\(740\) −154.126 −5.66579
\(741\) 0.846141 0.0310838
\(742\) −4.93232 −0.181071
\(743\) 18.9152 0.693931 0.346965 0.937878i \(-0.387212\pi\)
0.346965 + 0.937878i \(0.387212\pi\)
\(744\) −60.9089 −2.23303
\(745\) 88.4982 3.24232
\(746\) 82.1190 3.00659
\(747\) 3.13949 0.114868
\(748\) 17.0043 0.621738
\(749\) −17.4290 −0.636842
\(750\) 82.1103 2.99825
\(751\) 0.164356 0.00599743 0.00299871 0.999996i \(-0.499045\pi\)
0.00299871 + 0.999996i \(0.499045\pi\)
\(752\) −50.5189 −1.84223
\(753\) −3.29495 −0.120075
\(754\) 0.491122 0.0178856
\(755\) −3.91728 −0.142564
\(756\) 50.1582 1.82424
\(757\) −41.5741 −1.51104 −0.755518 0.655128i \(-0.772615\pi\)
−0.755518 + 0.655128i \(0.772615\pi\)
\(758\) −17.3201 −0.629095
\(759\) 50.9648 1.84990
\(760\) 106.460 3.86170
\(761\) −6.44288 −0.233554 −0.116777 0.993158i \(-0.537256\pi\)
−0.116777 + 0.993158i \(0.537256\pi\)
\(762\) −68.2879 −2.47381
\(763\) −17.4737 −0.632592
\(764\) 73.8996 2.67359
\(765\) 2.64869 0.0957637
\(766\) −47.7093 −1.72381
\(767\) 1.50745 0.0544308
\(768\) −34.4854 −1.24438
\(769\) 38.0509 1.37215 0.686075 0.727531i \(-0.259332\pi\)
0.686075 + 0.727531i \(0.259332\pi\)
\(770\) −72.5730 −2.61535
\(771\) −8.35090 −0.300750
\(772\) 88.2251 3.17529
\(773\) 26.9944 0.970921 0.485460 0.874259i \(-0.338652\pi\)
0.485460 + 0.874259i \(0.338652\pi\)
\(774\) −18.5745 −0.667646
\(775\) 59.8173 2.14870
\(776\) −50.2139 −1.80257
\(777\) −24.2892 −0.871371
\(778\) −80.4739 −2.88513
\(779\) −27.6409 −0.990337
\(780\) −3.96969 −0.142138
\(781\) −21.1229 −0.755838
\(782\) −22.3486 −0.799184
\(783\) 7.47446 0.267116
\(784\) −28.8667 −1.03096
\(785\) −31.1255 −1.11092
\(786\) 47.2678 1.68599
\(787\) 5.34202 0.190423 0.0952113 0.995457i \(-0.469647\pi\)
0.0952113 + 0.995457i \(0.469647\pi\)
\(788\) −29.5135 −1.05138
\(789\) −7.14489 −0.254365
\(790\) −126.093 −4.48620
\(791\) −11.3020 −0.401853
\(792\) 18.2599 0.648836
\(793\) 1.56749 0.0556633
\(794\) −14.8345 −0.526458
\(795\) 5.94096 0.210704
\(796\) 82.1467 2.91161
\(797\) 23.2653 0.824101 0.412050 0.911161i \(-0.364813\pi\)
0.412050 + 0.911161i \(0.364813\pi\)
\(798\) 29.2691 1.03611
\(799\) −5.68312 −0.201054
\(800\) −86.0091 −3.04088
\(801\) 3.06453 0.108280
\(802\) 0.662600 0.0233972
\(803\) 10.0471 0.354554
\(804\) 34.7436 1.22531
\(805\) 66.8509 2.35618
\(806\) −2.13190 −0.0750929
\(807\) −7.15382 −0.251827
\(808\) 83.9658 2.95391
\(809\) 14.1968 0.499134 0.249567 0.968358i \(-0.419712\pi\)
0.249567 + 0.968358i \(0.419712\pi\)
\(810\) −64.9317 −2.28147
\(811\) 37.6255 1.32121 0.660604 0.750734i \(-0.270300\pi\)
0.660604 + 0.750734i \(0.270300\pi\)
\(812\) 11.9068 0.417847
\(813\) 28.4948 0.999357
\(814\) −81.5463 −2.85820
\(815\) −64.7151 −2.26687
\(816\) 12.5819 0.440456
\(817\) −40.1579 −1.40495
\(818\) 99.0524 3.46329
\(819\) 0.190367 0.00665197
\(820\) 129.678 4.52854
\(821\) 49.9913 1.74471 0.872354 0.488875i \(-0.162593\pi\)
0.872354 + 0.488875i \(0.162593\pi\)
\(822\) 20.1384 0.702407
\(823\) 40.3708 1.40724 0.703619 0.710578i \(-0.251566\pi\)
0.703619 + 0.710578i \(0.251566\pi\)
\(824\) −16.4199 −0.572015
\(825\) 58.9312 2.05172
\(826\) 52.1445 1.81434
\(827\) 18.0366 0.627195 0.313598 0.949556i \(-0.398466\pi\)
0.313598 + 0.949556i \(0.398466\pi\)
\(828\) −29.3438 −1.01977
\(829\) −23.6846 −0.822601 −0.411300 0.911500i \(-0.634925\pi\)
−0.411300 + 0.911500i \(0.634925\pi\)
\(830\) −45.4347 −1.57706
\(831\) 39.9583 1.38614
\(832\) 0.616391 0.0213695
\(833\) −3.24736 −0.112514
\(834\) 59.9671 2.07649
\(835\) 98.5007 3.40876
\(836\) 68.8714 2.38197
\(837\) −32.4457 −1.12149
\(838\) −90.0960 −3.11232
\(839\) 21.8035 0.752739 0.376370 0.926470i \(-0.377172\pi\)
0.376370 + 0.926470i \(0.377172\pi\)
\(840\) −78.7111 −2.71579
\(841\) −27.2257 −0.938816
\(842\) −5.96180 −0.205457
\(843\) −6.94300 −0.239130
\(844\) −76.6837 −2.63956
\(845\) 50.8450 1.74912
\(846\) −10.6467 −0.366040
\(847\) −5.92932 −0.203734
\(848\) −8.58758 −0.294899
\(849\) −30.2399 −1.03783
\(850\) −25.8419 −0.886371
\(851\) 75.1166 2.57496
\(852\) −39.9671 −1.36925
\(853\) 32.2129 1.10295 0.551474 0.834192i \(-0.314065\pi\)
0.551474 + 0.834192i \(0.314065\pi\)
\(854\) 54.2215 1.85542
\(855\) 10.7279 0.366885
\(856\) −63.4634 −2.16914
\(857\) 41.0072 1.40078 0.700390 0.713760i \(-0.253009\pi\)
0.700390 + 0.713760i \(0.253009\pi\)
\(858\) −2.10031 −0.0717036
\(859\) −24.6072 −0.839588 −0.419794 0.907619i \(-0.637898\pi\)
−0.419794 + 0.907619i \(0.637898\pi\)
\(860\) 188.402 6.42445
\(861\) 20.4363 0.696468
\(862\) 7.88382 0.268524
\(863\) −20.0106 −0.681170 −0.340585 0.940214i \(-0.610625\pi\)
−0.340585 + 0.940214i \(0.610625\pi\)
\(864\) 46.6525 1.58715
\(865\) 41.4635 1.40980
\(866\) 43.0103 1.46155
\(867\) −24.3669 −0.827542
\(868\) −51.6859 −1.75433
\(869\) −46.7584 −1.58617
\(870\) −20.4626 −0.693747
\(871\) 0.697066 0.0236192
\(872\) −63.6263 −2.15466
\(873\) −5.06001 −0.171255
\(874\) −90.5173 −3.06179
\(875\) 39.9395 1.35020
\(876\) 19.0102 0.642297
\(877\) 48.7666 1.64673 0.823366 0.567511i \(-0.192094\pi\)
0.823366 + 0.567511i \(0.192094\pi\)
\(878\) 39.3030 1.32641
\(879\) 26.1156 0.880858
\(880\) −126.356 −4.25945
\(881\) 40.1845 1.35385 0.676925 0.736052i \(-0.263312\pi\)
0.676925 + 0.736052i \(0.263312\pi\)
\(882\) −6.08356 −0.204844
\(883\) −15.2135 −0.511977 −0.255988 0.966680i \(-0.582401\pi\)
−0.255988 + 0.966680i \(0.582401\pi\)
\(884\) 0.645511 0.0217109
\(885\) −62.8079 −2.11126
\(886\) 15.5140 0.521204
\(887\) 41.2413 1.38475 0.692374 0.721539i \(-0.256565\pi\)
0.692374 + 0.721539i \(0.256565\pi\)
\(888\) −88.4433 −2.96796
\(889\) −33.2161 −1.11403
\(890\) −44.3499 −1.48661
\(891\) −24.0782 −0.806650
\(892\) −66.3095 −2.22021
\(893\) −23.0180 −0.770269
\(894\) 88.5951 2.96306
\(895\) 94.2123 3.14917
\(896\) −10.3962 −0.347313
\(897\) 1.93471 0.0645981
\(898\) 73.5583 2.45467
\(899\) −7.70212 −0.256880
\(900\) −33.9306 −1.13102
\(901\) −0.966060 −0.0321841
\(902\) 68.6109 2.28449
\(903\) 29.6909 0.988050
\(904\) −41.1535 −1.36875
\(905\) −26.9015 −0.894236
\(906\) −3.92157 −0.130285
\(907\) −11.4689 −0.380819 −0.190409 0.981705i \(-0.560982\pi\)
−0.190409 + 0.981705i \(0.560982\pi\)
\(908\) 120.049 3.98396
\(909\) 8.46117 0.280639
\(910\) −2.75500 −0.0913273
\(911\) −12.6546 −0.419265 −0.209632 0.977780i \(-0.567227\pi\)
−0.209632 + 0.977780i \(0.567227\pi\)
\(912\) 50.9599 1.68745
\(913\) −16.8483 −0.557596
\(914\) 44.4396 1.46993
\(915\) −65.3095 −2.15907
\(916\) 100.472 3.31969
\(917\) 22.9916 0.759250
\(918\) 14.0170 0.462630
\(919\) −5.85207 −0.193042 −0.0965209 0.995331i \(-0.530771\pi\)
−0.0965209 + 0.995331i \(0.530771\pi\)
\(920\) 243.421 8.02536
\(921\) 37.8096 1.24587
\(922\) −0.712751 −0.0234732
\(923\) −0.801863 −0.0263937
\(924\) −50.9202 −1.67515
\(925\) 86.8582 2.85588
\(926\) −2.12442 −0.0698128
\(927\) −1.65462 −0.0543450
\(928\) 11.0746 0.363541
\(929\) −12.8196 −0.420596 −0.210298 0.977637i \(-0.567443\pi\)
−0.210298 + 0.977637i \(0.567443\pi\)
\(930\) 88.8255 2.91270
\(931\) −13.1526 −0.431060
\(932\) 26.0389 0.852934
\(933\) 35.7365 1.16996
\(934\) −48.2161 −1.57768
\(935\) −14.2144 −0.464860
\(936\) 0.693176 0.0226572
\(937\) −35.8178 −1.17012 −0.585058 0.810992i \(-0.698928\pi\)
−0.585058 + 0.810992i \(0.698928\pi\)
\(938\) 24.1124 0.787297
\(939\) 0.920109 0.0300266
\(940\) 107.990 3.52223
\(941\) 52.9402 1.72580 0.862900 0.505375i \(-0.168646\pi\)
0.862900 + 0.505375i \(0.168646\pi\)
\(942\) −31.1596 −1.01523
\(943\) −63.2012 −2.05811
\(944\) 90.7879 2.95490
\(945\) −41.9288 −1.36394
\(946\) 99.6812 3.24091
\(947\) −26.0614 −0.846883 −0.423441 0.905924i \(-0.639178\pi\)
−0.423441 + 0.905924i \(0.639178\pi\)
\(948\) −88.4723 −2.87345
\(949\) 0.381405 0.0123809
\(950\) −104.666 −3.39582
\(951\) −4.67724 −0.151670
\(952\) 12.7992 0.414825
\(953\) −30.6756 −0.993679 −0.496839 0.867843i \(-0.665506\pi\)
−0.496839 + 0.867843i \(0.665506\pi\)
\(954\) −1.80980 −0.0585944
\(955\) −61.7749 −1.99899
\(956\) 16.3782 0.529708
\(957\) −7.58801 −0.245286
\(958\) −47.3012 −1.52823
\(959\) 9.79555 0.316315
\(960\) −25.6819 −0.828881
\(961\) 2.43391 0.0785132
\(962\) −3.09564 −0.0998073
\(963\) −6.39516 −0.206081
\(964\) 127.111 4.09396
\(965\) −73.7500 −2.37410
\(966\) 66.9241 2.15325
\(967\) −17.3466 −0.557830 −0.278915 0.960316i \(-0.589975\pi\)
−0.278915 + 0.960316i \(0.589975\pi\)
\(968\) −21.5902 −0.693934
\(969\) 5.73273 0.184162
\(970\) 73.2286 2.35123
\(971\) 14.9833 0.480838 0.240419 0.970669i \(-0.422715\pi\)
0.240419 + 0.970669i \(0.422715\pi\)
\(972\) 33.3272 1.06897
\(973\) 29.1687 0.935106
\(974\) −68.5194 −2.19550
\(975\) 2.23713 0.0716455
\(976\) 94.4041 3.02180
\(977\) 41.3195 1.32193 0.660964 0.750417i \(-0.270148\pi\)
0.660964 + 0.750417i \(0.270148\pi\)
\(978\) −64.7859 −2.07163
\(979\) −16.4460 −0.525615
\(980\) 61.7058 1.97112
\(981\) −6.41158 −0.204706
\(982\) −71.2396 −2.27335
\(983\) −49.6718 −1.58429 −0.792143 0.610336i \(-0.791034\pi\)
−0.792143 + 0.610336i \(0.791034\pi\)
\(984\) 74.4139 2.37223
\(985\) 24.6712 0.786091
\(986\) 3.32742 0.105967
\(987\) 17.0184 0.541702
\(988\) 2.61448 0.0831777
\(989\) −91.8216 −2.91976
\(990\) −26.6290 −0.846324
\(991\) −4.59118 −0.145844 −0.0729219 0.997338i \(-0.523232\pi\)
−0.0729219 + 0.997338i \(0.523232\pi\)
\(992\) −48.0734 −1.52633
\(993\) −5.70974 −0.181193
\(994\) −27.7375 −0.879779
\(995\) −68.6688 −2.17695
\(996\) −31.8789 −1.01012
\(997\) −7.02084 −0.222352 −0.111176 0.993801i \(-0.535462\pi\)
−0.111176 + 0.993801i \(0.535462\pi\)
\(998\) −18.1362 −0.574091
\(999\) −47.1130 −1.49059
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 \(a_p\))