Properties

Label 8003.2.a.c.1.1
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 1.1
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79279 q^{2}\) \(+3.40925 q^{3}\) \(+5.79969 q^{4}\) \(+2.64273 q^{5}\) \(-9.52131 q^{6}\) \(+3.16263 q^{7}\) \(-10.6117 q^{8}\) \(+8.62295 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79279 q^{2}\) \(+3.40925 q^{3}\) \(+5.79969 q^{4}\) \(+2.64273 q^{5}\) \(-9.52131 q^{6}\) \(+3.16263 q^{7}\) \(-10.6117 q^{8}\) \(+8.62295 q^{9}\) \(-7.38060 q^{10}\) \(+1.52129 q^{11}\) \(+19.7726 q^{12}\) \(-3.08710 q^{13}\) \(-8.83256 q^{14}\) \(+9.00972 q^{15}\) \(+18.0370 q^{16}\) \(-0.165772 q^{17}\) \(-24.0821 q^{18}\) \(-3.02173 q^{19}\) \(+15.3270 q^{20}\) \(+10.7822 q^{21}\) \(-4.24863 q^{22}\) \(-3.71651 q^{23}\) \(-36.1780 q^{24}\) \(+1.98403 q^{25}\) \(+8.62164 q^{26}\) \(+19.1700 q^{27}\) \(+18.3423 q^{28}\) \(+4.48131 q^{29}\) \(-25.1623 q^{30}\) \(-2.77064 q^{31}\) \(-29.1502 q^{32}\) \(+5.18643 q^{33}\) \(+0.462967 q^{34}\) \(+8.35797 q^{35}\) \(+50.0105 q^{36}\) \(+1.05579 q^{37}\) \(+8.43906 q^{38}\) \(-10.5247 q^{39}\) \(-28.0440 q^{40}\) \(+7.11352 q^{41}\) \(-30.1124 q^{42}\) \(-7.56573 q^{43}\) \(+8.82298 q^{44}\) \(+22.7881 q^{45}\) \(+10.3794 q^{46}\) \(+2.34704 q^{47}\) \(+61.4927 q^{48}\) \(+3.00221 q^{49}\) \(-5.54098 q^{50}\) \(-0.565157 q^{51}\) \(-17.9042 q^{52}\) \(-1.00000 q^{53}\) \(-53.5379 q^{54}\) \(+4.02035 q^{55}\) \(-33.5610 q^{56}\) \(-10.3018 q^{57}\) \(-12.5154 q^{58}\) \(-9.08942 q^{59}\) \(+52.2536 q^{60}\) \(+6.11238 q^{61}\) \(+7.73783 q^{62}\) \(+27.2712 q^{63}\) \(+45.3364 q^{64}\) \(-8.15838 q^{65}\) \(-14.4846 q^{66}\) \(+5.99829 q^{67}\) \(-0.961426 q^{68}\) \(-12.6705 q^{69}\) \(-23.3421 q^{70}\) \(+12.3581 q^{71}\) \(-91.5046 q^{72}\) \(+10.5006 q^{73}\) \(-2.94862 q^{74}\) \(+6.76404 q^{75}\) \(-17.5251 q^{76}\) \(+4.81126 q^{77}\) \(+29.3933 q^{78}\) \(+8.53624 q^{79}\) \(+47.6670 q^{80}\) \(+39.4865 q^{81}\) \(-19.8666 q^{82}\) \(-5.34613 q^{83}\) \(+62.5332 q^{84}\) \(-0.438091 q^{85}\) \(+21.1295 q^{86}\) \(+15.2779 q^{87}\) \(-16.1435 q^{88}\) \(-15.1104 q^{89}\) \(-63.6426 q^{90}\) \(-9.76335 q^{91}\) \(-21.5546 q^{92}\) \(-9.44580 q^{93}\) \(-6.55480 q^{94}\) \(-7.98561 q^{95}\) \(-99.3801 q^{96}\) \(+17.3610 q^{97}\) \(-8.38454 q^{98}\) \(+13.1180 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79279 −1.97480 −0.987401 0.158236i \(-0.949419\pi\)
−0.987401 + 0.158236i \(0.949419\pi\)
\(3\) 3.40925 1.96833 0.984164 0.177259i \(-0.0567229\pi\)
0.984164 + 0.177259i \(0.0567229\pi\)
\(4\) 5.79969 2.89985
\(5\) 2.64273 1.18187 0.590933 0.806721i \(-0.298760\pi\)
0.590933 + 0.806721i \(0.298760\pi\)
\(6\) −9.52131 −3.88706
\(7\) 3.16263 1.19536 0.597680 0.801735i \(-0.296089\pi\)
0.597680 + 0.801735i \(0.296089\pi\)
\(8\) −10.6117 −3.75182
\(9\) 8.62295 2.87432
\(10\) −7.38060 −2.33395
\(11\) 1.52129 0.458685 0.229342 0.973346i \(-0.426342\pi\)
0.229342 + 0.973346i \(0.426342\pi\)
\(12\) 19.7726 5.70785
\(13\) −3.08710 −0.856208 −0.428104 0.903729i \(-0.640818\pi\)
−0.428104 + 0.903729i \(0.640818\pi\)
\(14\) −8.83256 −2.36060
\(15\) 9.00972 2.32630
\(16\) 18.0370 4.50926
\(17\) −0.165772 −0.0402056 −0.0201028 0.999798i \(-0.506399\pi\)
−0.0201028 + 0.999798i \(0.506399\pi\)
\(18\) −24.0821 −5.67621
\(19\) −3.02173 −0.693232 −0.346616 0.938007i \(-0.612669\pi\)
−0.346616 + 0.938007i \(0.612669\pi\)
\(20\) 15.3270 3.42723
\(21\) 10.7822 2.35286
\(22\) −4.24863 −0.905812
\(23\) −3.71651 −0.774946 −0.387473 0.921881i \(-0.626652\pi\)
−0.387473 + 0.921881i \(0.626652\pi\)
\(24\) −36.1780 −7.38481
\(25\) 1.98403 0.396806
\(26\) 8.62164 1.69084
\(27\) 19.1700 3.68927
\(28\) 18.3423 3.46636
\(29\) 4.48131 0.832159 0.416079 0.909328i \(-0.363404\pi\)
0.416079 + 0.909328i \(0.363404\pi\)
\(30\) −25.1623 −4.59398
\(31\) −2.77064 −0.497622 −0.248811 0.968552i \(-0.580040\pi\)
−0.248811 + 0.968552i \(0.580040\pi\)
\(32\) −29.1502 −5.15307
\(33\) 5.18643 0.902842
\(34\) 0.462967 0.0793981
\(35\) 8.35797 1.41275
\(36\) 50.0105 8.33508
\(37\) 1.05579 0.173572 0.0867858 0.996227i \(-0.472340\pi\)
0.0867858 + 0.996227i \(0.472340\pi\)
\(38\) 8.43906 1.36900
\(39\) −10.5247 −1.68530
\(40\) −28.0440 −4.43414
\(41\) 7.11352 1.11095 0.555473 0.831535i \(-0.312537\pi\)
0.555473 + 0.831535i \(0.312537\pi\)
\(42\) −30.1124 −4.64644
\(43\) −7.56573 −1.15376 −0.576881 0.816828i \(-0.695730\pi\)
−0.576881 + 0.816828i \(0.695730\pi\)
\(44\) 8.82298 1.33011
\(45\) 22.7881 3.39706
\(46\) 10.3794 1.53037
\(47\) 2.34704 0.342351 0.171176 0.985241i \(-0.445243\pi\)
0.171176 + 0.985241i \(0.445243\pi\)
\(48\) 61.4927 8.87570
\(49\) 3.00221 0.428886
\(50\) −5.54098 −0.783613
\(51\) −0.565157 −0.0791378
\(52\) −17.9042 −2.48287
\(53\) −1.00000 −0.137361
\(54\) −53.5379 −7.28559
\(55\) 4.02035 0.542104
\(56\) −33.5610 −4.48478
\(57\) −10.3018 −1.36451
\(58\) −12.5154 −1.64335
\(59\) −9.08942 −1.18334 −0.591671 0.806180i \(-0.701531\pi\)
−0.591671 + 0.806180i \(0.701531\pi\)
\(60\) 52.2536 6.74591
\(61\) 6.11238 0.782610 0.391305 0.920261i \(-0.372024\pi\)
0.391305 + 0.920261i \(0.372024\pi\)
\(62\) 7.73783 0.982706
\(63\) 27.2712 3.43585
\(64\) 45.3364 5.66705
\(65\) −8.15838 −1.01192
\(66\) −14.4846 −1.78294
\(67\) 5.99829 0.732807 0.366404 0.930456i \(-0.380589\pi\)
0.366404 + 0.930456i \(0.380589\pi\)
\(68\) −0.961426 −0.116590
\(69\) −12.6705 −1.52535
\(70\) −23.3421 −2.78991
\(71\) 12.3581 1.46663 0.733317 0.679887i \(-0.237971\pi\)
0.733317 + 0.679887i \(0.237971\pi\)
\(72\) −91.5046 −10.7839
\(73\) 10.5006 1.22901 0.614503 0.788914i \(-0.289356\pi\)
0.614503 + 0.788914i \(0.289356\pi\)
\(74\) −2.94862 −0.342770
\(75\) 6.76404 0.781044
\(76\) −17.5251 −2.01026
\(77\) 4.81126 0.548294
\(78\) 29.3933 3.32813
\(79\) 8.53624 0.960402 0.480201 0.877158i \(-0.340564\pi\)
0.480201 + 0.877158i \(0.340564\pi\)
\(80\) 47.6670 5.32933
\(81\) 39.4865 4.38738
\(82\) −19.8666 −2.19390
\(83\) −5.34613 −0.586814 −0.293407 0.955988i \(-0.594789\pi\)
−0.293407 + 0.955988i \(0.594789\pi\)
\(84\) 62.5332 6.82294
\(85\) −0.438091 −0.0475176
\(86\) 21.1295 2.27845
\(87\) 15.2779 1.63796
\(88\) −16.1435 −1.72090
\(89\) −15.1104 −1.60169 −0.800847 0.598869i \(-0.795617\pi\)
−0.800847 + 0.598869i \(0.795617\pi\)
\(90\) −63.6426 −6.70852
\(91\) −9.76335 −1.02348
\(92\) −21.5546 −2.24722
\(93\) −9.44580 −0.979484
\(94\) −6.55480 −0.676076
\(95\) −7.98561 −0.819307
\(96\) −99.3801 −10.1429
\(97\) 17.3610 1.76274 0.881370 0.472427i \(-0.156622\pi\)
0.881370 + 0.472427i \(0.156622\pi\)
\(98\) −8.38454 −0.846966
\(99\) 13.1180 1.31841
\(100\) 11.5067 1.15067
\(101\) −15.7977 −1.57193 −0.785965 0.618271i \(-0.787833\pi\)
−0.785965 + 0.618271i \(0.787833\pi\)
\(102\) 1.57837 0.156282
\(103\) 11.1528 1.09891 0.549457 0.835522i \(-0.314835\pi\)
0.549457 + 0.835522i \(0.314835\pi\)
\(104\) 32.7595 3.21234
\(105\) 28.4944 2.78077
\(106\) 2.79279 0.271260
\(107\) −6.56524 −0.634686 −0.317343 0.948311i \(-0.602791\pi\)
−0.317343 + 0.948311i \(0.602791\pi\)
\(108\) 111.180 10.6983
\(109\) 0.943928 0.0904120 0.0452060 0.998978i \(-0.485606\pi\)
0.0452060 + 0.998978i \(0.485606\pi\)
\(110\) −11.2280 −1.07055
\(111\) 3.59946 0.341646
\(112\) 57.0444 5.39019
\(113\) 19.0630 1.79330 0.896648 0.442745i \(-0.145995\pi\)
0.896648 + 0.442745i \(0.145995\pi\)
\(114\) 28.7708 2.69463
\(115\) −9.82174 −0.915882
\(116\) 25.9902 2.41313
\(117\) −26.6199 −2.46101
\(118\) 25.3849 2.33686
\(119\) −0.524275 −0.0480602
\(120\) −95.6089 −8.72785
\(121\) −8.68569 −0.789608
\(122\) −17.0706 −1.54550
\(123\) 24.2517 2.18671
\(124\) −16.0689 −1.44303
\(125\) −7.97040 −0.712895
\(126\) −76.1627 −6.78512
\(127\) −8.89800 −0.789569 −0.394785 0.918774i \(-0.629181\pi\)
−0.394785 + 0.918774i \(0.629181\pi\)
\(128\) −68.3147 −6.03822
\(129\) −25.7934 −2.27098
\(130\) 22.7847 1.99835
\(131\) −18.9361 −1.65446 −0.827228 0.561866i \(-0.810084\pi\)
−0.827228 + 0.561866i \(0.810084\pi\)
\(132\) 30.0797 2.61810
\(133\) −9.55659 −0.828662
\(134\) −16.7520 −1.44715
\(135\) 50.6612 4.36022
\(136\) 1.75913 0.150844
\(137\) 8.91004 0.761236 0.380618 0.924732i \(-0.375711\pi\)
0.380618 + 0.924732i \(0.375711\pi\)
\(138\) 35.3861 3.01226
\(139\) 7.03516 0.596715 0.298357 0.954454i \(-0.403561\pi\)
0.298357 + 0.954454i \(0.403561\pi\)
\(140\) 48.4736 4.09677
\(141\) 8.00164 0.673860
\(142\) −34.5135 −2.89631
\(143\) −4.69636 −0.392730
\(144\) 155.532 12.9610
\(145\) 11.8429 0.983500
\(146\) −29.3261 −2.42705
\(147\) 10.2353 0.844190
\(148\) 6.12328 0.503331
\(149\) −5.43878 −0.445562 −0.222781 0.974868i \(-0.571514\pi\)
−0.222781 + 0.974868i \(0.571514\pi\)
\(150\) −18.8906 −1.54241
\(151\) 1.00000 0.0813788
\(152\) 32.0658 2.60088
\(153\) −1.42944 −0.115564
\(154\) −13.4368 −1.08277
\(155\) −7.32206 −0.588122
\(156\) −61.0399 −4.88711
\(157\) 4.11878 0.328715 0.164357 0.986401i \(-0.447445\pi\)
0.164357 + 0.986401i \(0.447445\pi\)
\(158\) −23.8400 −1.89660
\(159\) −3.40925 −0.270371
\(160\) −77.0361 −6.09024
\(161\) −11.7539 −0.926340
\(162\) −110.277 −8.66422
\(163\) 18.3424 1.43669 0.718344 0.695688i \(-0.244900\pi\)
0.718344 + 0.695688i \(0.244900\pi\)
\(164\) 41.2562 3.22157
\(165\) 13.7064 1.06704
\(166\) 14.9306 1.15884
\(167\) −17.2435 −1.33434 −0.667170 0.744906i \(-0.732494\pi\)
−0.667170 + 0.744906i \(0.732494\pi\)
\(168\) −114.418 −8.82751
\(169\) −3.46980 −0.266908
\(170\) 1.22350 0.0938379
\(171\) −26.0562 −1.99257
\(172\) −43.8789 −3.34573
\(173\) 7.72314 0.587179 0.293590 0.955932i \(-0.405150\pi\)
0.293590 + 0.955932i \(0.405150\pi\)
\(174\) −42.6680 −3.23465
\(175\) 6.27474 0.474326
\(176\) 27.4395 2.06833
\(177\) −30.9880 −2.32920
\(178\) 42.2001 3.16303
\(179\) 1.89969 0.141990 0.0709948 0.997477i \(-0.477383\pi\)
0.0709948 + 0.997477i \(0.477383\pi\)
\(180\) 132.164 9.85094
\(181\) −11.1133 −0.826042 −0.413021 0.910722i \(-0.635526\pi\)
−0.413021 + 0.910722i \(0.635526\pi\)
\(182\) 27.2670 2.02117
\(183\) 20.8386 1.54043
\(184\) 39.4387 2.90746
\(185\) 2.79018 0.205138
\(186\) 26.3802 1.93429
\(187\) −0.252186 −0.0184417
\(188\) 13.6121 0.992765
\(189\) 60.6276 4.41001
\(190\) 22.3022 1.61797
\(191\) −26.6640 −1.92934 −0.964669 0.263465i \(-0.915135\pi\)
−0.964669 + 0.263465i \(0.915135\pi\)
\(192\) 154.563 11.1546
\(193\) 20.2688 1.45898 0.729491 0.683990i \(-0.239757\pi\)
0.729491 + 0.683990i \(0.239757\pi\)
\(194\) −48.4856 −3.48106
\(195\) −27.8139 −1.99180
\(196\) 17.4119 1.24370
\(197\) 26.6551 1.89910 0.949548 0.313623i \(-0.101543\pi\)
0.949548 + 0.313623i \(0.101543\pi\)
\(198\) −36.6358 −2.60359
\(199\) −0.956757 −0.0678227 −0.0339114 0.999425i \(-0.510796\pi\)
−0.0339114 + 0.999425i \(0.510796\pi\)
\(200\) −21.0540 −1.48874
\(201\) 20.4496 1.44241
\(202\) 44.1197 3.10425
\(203\) 14.1727 0.994730
\(204\) −3.27774 −0.229487
\(205\) 18.7991 1.31299
\(206\) −31.1473 −2.17014
\(207\) −32.0473 −2.22744
\(208\) −55.6821 −3.86086
\(209\) −4.59691 −0.317975
\(210\) −79.5789 −5.49146
\(211\) 7.98963 0.550029 0.275015 0.961440i \(-0.411317\pi\)
0.275015 + 0.961440i \(0.411317\pi\)
\(212\) −5.79969 −0.398324
\(213\) 42.1317 2.88682
\(214\) 18.3354 1.25338
\(215\) −19.9942 −1.36359
\(216\) −203.427 −13.8415
\(217\) −8.76251 −0.594838
\(218\) −2.63620 −0.178546
\(219\) 35.7992 2.41909
\(220\) 23.3168 1.57202
\(221\) 0.511755 0.0344244
\(222\) −10.0526 −0.674683
\(223\) 28.3393 1.89774 0.948871 0.315664i \(-0.102227\pi\)
0.948871 + 0.315664i \(0.102227\pi\)
\(224\) −92.1911 −6.15978
\(225\) 17.1082 1.14055
\(226\) −53.2390 −3.54140
\(227\) −25.1412 −1.66868 −0.834340 0.551250i \(-0.814151\pi\)
−0.834340 + 0.551250i \(0.814151\pi\)
\(228\) −59.7473 −3.95686
\(229\) 8.54268 0.564516 0.282258 0.959338i \(-0.408917\pi\)
0.282258 + 0.959338i \(0.408917\pi\)
\(230\) 27.4301 1.80869
\(231\) 16.4028 1.07922
\(232\) −47.5546 −3.12211
\(233\) −9.52413 −0.623947 −0.311973 0.950091i \(-0.600990\pi\)
−0.311973 + 0.950091i \(0.600990\pi\)
\(234\) 74.3440 4.86002
\(235\) 6.20260 0.404613
\(236\) −52.7158 −3.43151
\(237\) 29.1021 1.89039
\(238\) 1.46419 0.0949093
\(239\) 8.73804 0.565217 0.282608 0.959235i \(-0.408800\pi\)
0.282608 + 0.959235i \(0.408800\pi\)
\(240\) 162.509 10.4899
\(241\) 24.3057 1.56567 0.782834 0.622230i \(-0.213773\pi\)
0.782834 + 0.622230i \(0.213773\pi\)
\(242\) 24.2573 1.55932
\(243\) 77.1089 4.94654
\(244\) 35.4499 2.26945
\(245\) 7.93402 0.506886
\(246\) −67.7301 −4.31831
\(247\) 9.32838 0.593551
\(248\) 29.4014 1.86699
\(249\) −18.2263 −1.15504
\(250\) 22.2597 1.40783
\(251\) −13.9737 −0.882013 −0.441006 0.897504i \(-0.645378\pi\)
−0.441006 + 0.897504i \(0.645378\pi\)
\(252\) 158.164 9.96342
\(253\) −5.65388 −0.355456
\(254\) 24.8503 1.55924
\(255\) −1.49356 −0.0935302
\(256\) 100.116 6.25725
\(257\) 6.25915 0.390435 0.195217 0.980760i \(-0.437459\pi\)
0.195217 + 0.980760i \(0.437459\pi\)
\(258\) 72.0357 4.48475
\(259\) 3.33908 0.207481
\(260\) −47.3161 −2.93442
\(261\) 38.6422 2.39189
\(262\) 52.8846 3.26722
\(263\) −24.2409 −1.49476 −0.747378 0.664399i \(-0.768687\pi\)
−0.747378 + 0.664399i \(0.768687\pi\)
\(264\) −55.0371 −3.38730
\(265\) −2.64273 −0.162342
\(266\) 26.6896 1.63644
\(267\) −51.5149 −3.15266
\(268\) 34.7882 2.12503
\(269\) 11.6427 0.709867 0.354933 0.934892i \(-0.384504\pi\)
0.354933 + 0.934892i \(0.384504\pi\)
\(270\) −141.486 −8.61058
\(271\) −5.06948 −0.307949 −0.153975 0.988075i \(-0.549207\pi\)
−0.153975 + 0.988075i \(0.549207\pi\)
\(272\) −2.99003 −0.181297
\(273\) −33.2857 −2.01454
\(274\) −24.8839 −1.50329
\(275\) 3.01827 0.182009
\(276\) −73.4850 −4.42328
\(277\) 20.3679 1.22379 0.611895 0.790939i \(-0.290408\pi\)
0.611895 + 0.790939i \(0.290408\pi\)
\(278\) −19.6477 −1.17839
\(279\) −23.8911 −1.43032
\(280\) −88.6927 −5.30040
\(281\) −3.12641 −0.186506 −0.0932530 0.995642i \(-0.529727\pi\)
−0.0932530 + 0.995642i \(0.529727\pi\)
\(282\) −22.3469 −1.33074
\(283\) −2.96933 −0.176508 −0.0882541 0.996098i \(-0.528129\pi\)
−0.0882541 + 0.996098i \(0.528129\pi\)
\(284\) 71.6730 4.25301
\(285\) −27.2249 −1.61266
\(286\) 13.1160 0.775563
\(287\) 22.4974 1.32798
\(288\) −251.361 −14.8116
\(289\) −16.9725 −0.998384
\(290\) −33.0748 −1.94222
\(291\) 59.1878 3.46965
\(292\) 60.9004 3.56393
\(293\) −0.910323 −0.0531816 −0.0265908 0.999646i \(-0.508465\pi\)
−0.0265908 + 0.999646i \(0.508465\pi\)
\(294\) −28.5849 −1.66711
\(295\) −24.0209 −1.39855
\(296\) −11.2038 −0.651209
\(297\) 29.1631 1.69221
\(298\) 15.1894 0.879897
\(299\) 11.4733 0.663515
\(300\) 39.2293 2.26491
\(301\) −23.9276 −1.37916
\(302\) −2.79279 −0.160707
\(303\) −53.8582 −3.09407
\(304\) −54.5030 −3.12596
\(305\) 16.1534 0.924940
\(306\) 3.99214 0.228215
\(307\) 5.71222 0.326013 0.163007 0.986625i \(-0.447881\pi\)
0.163007 + 0.986625i \(0.447881\pi\)
\(308\) 27.9038 1.58997
\(309\) 38.0225 2.16302
\(310\) 20.4490 1.16143
\(311\) 5.42274 0.307495 0.153748 0.988110i \(-0.450866\pi\)
0.153748 + 0.988110i \(0.450866\pi\)
\(312\) 111.685 6.32294
\(313\) −2.82638 −0.159756 −0.0798782 0.996805i \(-0.525453\pi\)
−0.0798782 + 0.996805i \(0.525453\pi\)
\(314\) −11.5029 −0.649147
\(315\) 72.0704 4.06071
\(316\) 49.5076 2.78502
\(317\) 2.52393 0.141758 0.0708791 0.997485i \(-0.477420\pi\)
0.0708791 + 0.997485i \(0.477420\pi\)
\(318\) 9.52131 0.533929
\(319\) 6.81735 0.381699
\(320\) 119.812 6.69768
\(321\) −22.3825 −1.24927
\(322\) 32.8263 1.82934
\(323\) 0.500917 0.0278718
\(324\) 229.009 12.7227
\(325\) −6.12490 −0.339748
\(326\) −51.2266 −2.83718
\(327\) 3.21808 0.177960
\(328\) −75.4869 −4.16807
\(329\) 7.42282 0.409233
\(330\) −38.2790 −2.10719
\(331\) 14.9839 0.823587 0.411794 0.911277i \(-0.364902\pi\)
0.411794 + 0.911277i \(0.364902\pi\)
\(332\) −31.0059 −1.70167
\(333\) 9.10407 0.498900
\(334\) 48.1574 2.63506
\(335\) 15.8519 0.866079
\(336\) 194.478 10.6097
\(337\) 13.7625 0.749693 0.374846 0.927087i \(-0.377695\pi\)
0.374846 + 0.927087i \(0.377695\pi\)
\(338\) 9.69043 0.527090
\(339\) 64.9904 3.52979
\(340\) −2.54079 −0.137794
\(341\) −4.21494 −0.228252
\(342\) 72.7696 3.93493
\(343\) −12.6435 −0.682686
\(344\) 80.2856 4.32871
\(345\) −33.4847 −1.80276
\(346\) −21.5691 −1.15956
\(347\) −4.05674 −0.217777 −0.108889 0.994054i \(-0.534729\pi\)
−0.108889 + 0.994054i \(0.534729\pi\)
\(348\) 88.6071 4.74984
\(349\) −2.03062 −0.108697 −0.0543484 0.998522i \(-0.517308\pi\)
−0.0543484 + 0.998522i \(0.517308\pi\)
\(350\) −17.5240 −0.936700
\(351\) −59.1798 −3.15879
\(352\) −44.3457 −2.36364
\(353\) 30.4506 1.62072 0.810362 0.585930i \(-0.199271\pi\)
0.810362 + 0.585930i \(0.199271\pi\)
\(354\) 86.5432 4.59972
\(355\) 32.6591 1.73336
\(356\) −87.6354 −4.64467
\(357\) −1.78738 −0.0945982
\(358\) −5.30544 −0.280401
\(359\) −4.58939 −0.242219 −0.121109 0.992639i \(-0.538645\pi\)
−0.121109 + 0.992639i \(0.538645\pi\)
\(360\) −241.822 −12.7451
\(361\) −9.86916 −0.519430
\(362\) 31.0370 1.63127
\(363\) −29.6117 −1.55421
\(364\) −56.6244 −2.96793
\(365\) 27.7504 1.45252
\(366\) −58.1979 −3.04205
\(367\) −18.9786 −0.990674 −0.495337 0.868701i \(-0.664955\pi\)
−0.495337 + 0.868701i \(0.664955\pi\)
\(368\) −67.0348 −3.49443
\(369\) 61.3396 3.19321
\(370\) −7.79240 −0.405108
\(371\) −3.16263 −0.164195
\(372\) −54.7827 −2.84035
\(373\) 9.81235 0.508064 0.254032 0.967196i \(-0.418243\pi\)
0.254032 + 0.967196i \(0.418243\pi\)
\(374\) 0.704304 0.0364187
\(375\) −27.1731 −1.40321
\(376\) −24.9062 −1.28444
\(377\) −13.8343 −0.712501
\(378\) −169.320 −8.70890
\(379\) −33.1417 −1.70237 −0.851186 0.524864i \(-0.824116\pi\)
−0.851186 + 0.524864i \(0.824116\pi\)
\(380\) −46.3141 −2.37586
\(381\) −30.3354 −1.55413
\(382\) 74.4670 3.81006
\(383\) 2.76840 0.141459 0.0707293 0.997496i \(-0.477467\pi\)
0.0707293 + 0.997496i \(0.477467\pi\)
\(384\) −232.902 −11.8852
\(385\) 12.7149 0.648009
\(386\) −56.6067 −2.88120
\(387\) −65.2389 −3.31628
\(388\) 100.688 5.11167
\(389\) −26.7282 −1.35517 −0.677587 0.735442i \(-0.736974\pi\)
−0.677587 + 0.735442i \(0.736974\pi\)
\(390\) 77.6785 3.93340
\(391\) 0.616093 0.0311572
\(392\) −31.8586 −1.60910
\(393\) −64.5579 −3.25651
\(394\) −74.4421 −3.75034
\(395\) 22.5590 1.13507
\(396\) 76.0802 3.82317
\(397\) 8.72177 0.437733 0.218866 0.975755i \(-0.429764\pi\)
0.218866 + 0.975755i \(0.429764\pi\)
\(398\) 2.67202 0.133936
\(399\) −32.5808 −1.63108
\(400\) 35.7860 1.78930
\(401\) 14.7502 0.736588 0.368294 0.929709i \(-0.379942\pi\)
0.368294 + 0.929709i \(0.379942\pi\)
\(402\) −57.1116 −2.84847
\(403\) 8.55326 0.426068
\(404\) −91.6218 −4.55835
\(405\) 104.352 5.18530
\(406\) −39.5815 −1.96439
\(407\) 1.60617 0.0796146
\(408\) 5.99730 0.296911
\(409\) −38.6742 −1.91232 −0.956158 0.292850i \(-0.905396\pi\)
−0.956158 + 0.292850i \(0.905396\pi\)
\(410\) −52.5021 −2.59289
\(411\) 30.3765 1.49836
\(412\) 64.6825 3.18668
\(413\) −28.7464 −1.41452
\(414\) 89.5015 4.39876
\(415\) −14.1284 −0.693535
\(416\) 89.9896 4.41210
\(417\) 23.9846 1.17453
\(418\) 12.8382 0.627938
\(419\) 0.373425 0.0182430 0.00912151 0.999958i \(-0.497096\pi\)
0.00912151 + 0.999958i \(0.497096\pi\)
\(420\) 165.259 8.06379
\(421\) −11.0816 −0.540085 −0.270042 0.962848i \(-0.587038\pi\)
−0.270042 + 0.962848i \(0.587038\pi\)
\(422\) −22.3134 −1.08620
\(423\) 20.2384 0.984026
\(424\) 10.6117 0.515352
\(425\) −0.328896 −0.0159538
\(426\) −117.665 −5.70089
\(427\) 19.3312 0.935501
\(428\) −38.0764 −1.84049
\(429\) −16.0111 −0.773021
\(430\) 55.8396 2.69283
\(431\) −24.7324 −1.19132 −0.595658 0.803238i \(-0.703109\pi\)
−0.595658 + 0.803238i \(0.703109\pi\)
\(432\) 345.770 16.6359
\(433\) −38.9077 −1.86978 −0.934892 0.354933i \(-0.884504\pi\)
−0.934892 + 0.354933i \(0.884504\pi\)
\(434\) 24.4719 1.17469
\(435\) 40.3754 1.93585
\(436\) 5.47449 0.262181
\(437\) 11.2303 0.537218
\(438\) −99.9799 −4.77722
\(439\) −19.1826 −0.915534 −0.457767 0.889072i \(-0.651351\pi\)
−0.457767 + 0.889072i \(0.651351\pi\)
\(440\) −42.6629 −2.03387
\(441\) 25.8879 1.23276
\(442\) −1.42922 −0.0679813
\(443\) 3.51378 0.166945 0.0834723 0.996510i \(-0.473399\pi\)
0.0834723 + 0.996510i \(0.473399\pi\)
\(444\) 20.8758 0.990720
\(445\) −39.9326 −1.89299
\(446\) −79.1459 −3.74767
\(447\) −18.5421 −0.877013
\(448\) 143.382 6.77416
\(449\) −31.5482 −1.48885 −0.744425 0.667706i \(-0.767277\pi\)
−0.744425 + 0.667706i \(0.767277\pi\)
\(450\) −47.7796 −2.25235
\(451\) 10.8217 0.509574
\(452\) 110.559 5.20028
\(453\) 3.40925 0.160180
\(454\) 70.2142 3.29531
\(455\) −25.8019 −1.20961
\(456\) 109.320 5.11939
\(457\) −11.3458 −0.530736 −0.265368 0.964147i \(-0.585493\pi\)
−0.265368 + 0.964147i \(0.585493\pi\)
\(458\) −23.8579 −1.11481
\(459\) −3.17785 −0.148329
\(460\) −56.9631 −2.65592
\(461\) −11.7202 −0.545865 −0.272932 0.962033i \(-0.587994\pi\)
−0.272932 + 0.962033i \(0.587994\pi\)
\(462\) −45.8095 −2.13125
\(463\) 6.64387 0.308767 0.154383 0.988011i \(-0.450661\pi\)
0.154383 + 0.988011i \(0.450661\pi\)
\(464\) 80.8296 3.75242
\(465\) −24.9627 −1.15762
\(466\) 26.5989 1.23217
\(467\) −18.6131 −0.861310 −0.430655 0.902517i \(-0.641717\pi\)
−0.430655 + 0.902517i \(0.641717\pi\)
\(468\) −154.387 −7.13656
\(469\) 18.9703 0.875969
\(470\) −17.3226 −0.799031
\(471\) 14.0419 0.647019
\(472\) 96.4546 4.43968
\(473\) −11.5096 −0.529213
\(474\) −81.2762 −3.73314
\(475\) −5.99519 −0.275078
\(476\) −3.04063 −0.139367
\(477\) −8.62295 −0.394818
\(478\) −24.4035 −1.11619
\(479\) 6.64345 0.303547 0.151773 0.988415i \(-0.451502\pi\)
0.151773 + 0.988415i \(0.451502\pi\)
\(480\) −262.635 −11.9876
\(481\) −3.25935 −0.148613
\(482\) −67.8808 −3.09189
\(483\) −40.0721 −1.82334
\(484\) −50.3743 −2.28974
\(485\) 45.8804 2.08332
\(486\) −215.349 −9.76844
\(487\) −31.8382 −1.44273 −0.721364 0.692556i \(-0.756485\pi\)
−0.721364 + 0.692556i \(0.756485\pi\)
\(488\) −64.8631 −2.93621
\(489\) 62.5338 2.82788
\(490\) −22.1581 −1.00100
\(491\) −7.05164 −0.318236 −0.159118 0.987260i \(-0.550865\pi\)
−0.159118 + 0.987260i \(0.550865\pi\)
\(492\) 140.653 6.34111
\(493\) −0.742876 −0.0334574
\(494\) −26.0522 −1.17215
\(495\) 34.6673 1.55818
\(496\) −49.9742 −2.24391
\(497\) 39.0840 1.75316
\(498\) 50.9022 2.28098
\(499\) 28.8664 1.29224 0.646119 0.763236i \(-0.276391\pi\)
0.646119 + 0.763236i \(0.276391\pi\)
\(500\) −46.2259 −2.06728
\(501\) −58.7872 −2.62642
\(502\) 39.0257 1.74180
\(503\) 6.00702 0.267840 0.133920 0.990992i \(-0.457244\pi\)
0.133920 + 0.990992i \(0.457244\pi\)
\(504\) −289.395 −12.8907
\(505\) −41.7491 −1.85781
\(506\) 15.7901 0.701956
\(507\) −11.8294 −0.525362
\(508\) −51.6056 −2.28963
\(509\) −5.41661 −0.240087 −0.120043 0.992769i \(-0.538303\pi\)
−0.120043 + 0.992769i \(0.538303\pi\)
\(510\) 4.17120 0.184704
\(511\) 33.2096 1.46911
\(512\) −142.974 −6.31861
\(513\) −57.9266 −2.55752
\(514\) −17.4805 −0.771032
\(515\) 29.4737 1.29877
\(516\) −149.594 −6.58550
\(517\) 3.57052 0.157031
\(518\) −9.32537 −0.409733
\(519\) 26.3301 1.15576
\(520\) 86.5747 3.79655
\(521\) −5.00854 −0.219428 −0.109714 0.993963i \(-0.534994\pi\)
−0.109714 + 0.993963i \(0.534994\pi\)
\(522\) −107.920 −4.72351
\(523\) 0.0363510 0.00158952 0.000794759 1.00000i \(-0.499747\pi\)
0.000794759 1.00000i \(0.499747\pi\)
\(524\) −109.824 −4.79767
\(525\) 21.3921 0.933629
\(526\) 67.6997 2.95185
\(527\) 0.459295 0.0200072
\(528\) 93.5479 4.07115
\(529\) −9.18753 −0.399458
\(530\) 7.38060 0.320593
\(531\) −78.3776 −3.40130
\(532\) −55.4253 −2.40299
\(533\) −21.9602 −0.951201
\(534\) 143.870 6.22588
\(535\) −17.3502 −0.750113
\(536\) −63.6523 −2.74936
\(537\) 6.47651 0.279482
\(538\) −32.5156 −1.40185
\(539\) 4.56721 0.196724
\(540\) 293.819 12.6440
\(541\) 20.7724 0.893074 0.446537 0.894765i \(-0.352657\pi\)
0.446537 + 0.894765i \(0.352657\pi\)
\(542\) 14.1580 0.608139
\(543\) −37.8878 −1.62592
\(544\) 4.83228 0.207182
\(545\) 2.49455 0.106855
\(546\) 92.9599 3.97832
\(547\) −41.2983 −1.76579 −0.882895 0.469571i \(-0.844409\pi\)
−0.882895 + 0.469571i \(0.844409\pi\)
\(548\) 51.6755 2.20747
\(549\) 52.7068 2.24947
\(550\) −8.42941 −0.359431
\(551\) −13.5413 −0.576879
\(552\) 134.456 5.72283
\(553\) 26.9969 1.14803
\(554\) −56.8833 −2.41674
\(555\) 9.51241 0.403780
\(556\) 40.8018 1.73038
\(557\) −14.6650 −0.621374 −0.310687 0.950512i \(-0.600559\pi\)
−0.310687 + 0.950512i \(0.600559\pi\)
\(558\) 66.7230 2.82461
\(559\) 23.3562 0.987861
\(560\) 150.753 6.37048
\(561\) −0.859765 −0.0362993
\(562\) 8.73141 0.368312
\(563\) 28.0238 1.18106 0.590532 0.807014i \(-0.298918\pi\)
0.590532 + 0.807014i \(0.298918\pi\)
\(564\) 46.4070 1.95409
\(565\) 50.3784 2.11943
\(566\) 8.29272 0.348569
\(567\) 124.881 5.24451
\(568\) −131.141 −5.50255
\(569\) −18.7602 −0.786467 −0.393234 0.919439i \(-0.628644\pi\)
−0.393234 + 0.919439i \(0.628644\pi\)
\(570\) 76.0335 3.18469
\(571\) −39.0729 −1.63515 −0.817575 0.575822i \(-0.804682\pi\)
−0.817575 + 0.575822i \(0.804682\pi\)
\(572\) −27.2375 −1.13886
\(573\) −90.9040 −3.79757
\(574\) −62.8306 −2.62250
\(575\) −7.37367 −0.307503
\(576\) 390.933 16.2889
\(577\) −42.0695 −1.75138 −0.875689 0.482876i \(-0.839592\pi\)
−0.875689 + 0.482876i \(0.839592\pi\)
\(578\) 47.4007 1.97161
\(579\) 69.1014 2.87176
\(580\) 68.6852 2.85200
\(581\) −16.9078 −0.701454
\(582\) −165.299 −6.85188
\(583\) −1.52129 −0.0630052
\(584\) −111.430 −4.61101
\(585\) −70.3493 −2.90859
\(586\) 2.54234 0.105023
\(587\) 23.2407 0.959247 0.479624 0.877474i \(-0.340773\pi\)
0.479624 + 0.877474i \(0.340773\pi\)
\(588\) 59.3613 2.44802
\(589\) 8.37213 0.344968
\(590\) 67.0853 2.76186
\(591\) 90.8737 3.73804
\(592\) 19.0434 0.782679
\(593\) −12.4341 −0.510607 −0.255304 0.966861i \(-0.582175\pi\)
−0.255304 + 0.966861i \(0.582175\pi\)
\(594\) −81.4464 −3.34179
\(595\) −1.38552 −0.0568006
\(596\) −31.5432 −1.29206
\(597\) −3.26182 −0.133497
\(598\) −32.0424 −1.31031
\(599\) −14.4548 −0.590606 −0.295303 0.955404i \(-0.595421\pi\)
−0.295303 + 0.955404i \(0.595421\pi\)
\(600\) −71.7783 −2.93034
\(601\) 29.8521 1.21769 0.608846 0.793288i \(-0.291633\pi\)
0.608846 + 0.793288i \(0.291633\pi\)
\(602\) 66.8247 2.72357
\(603\) 51.7229 2.10632
\(604\) 5.79969 0.235986
\(605\) −22.9539 −0.933211
\(606\) 150.415 6.11019
\(607\) −11.2942 −0.458416 −0.229208 0.973377i \(-0.573614\pi\)
−0.229208 + 0.973377i \(0.573614\pi\)
\(608\) 88.0839 3.57227
\(609\) 48.3183 1.95796
\(610\) −45.1130 −1.82657
\(611\) −7.24556 −0.293124
\(612\) −8.29033 −0.335117
\(613\) −5.16448 −0.208592 −0.104296 0.994546i \(-0.533259\pi\)
−0.104296 + 0.994546i \(0.533259\pi\)
\(614\) −15.9530 −0.643812
\(615\) 64.0908 2.58439
\(616\) −51.0558 −2.05710
\(617\) −34.9324 −1.40632 −0.703162 0.711029i \(-0.748229\pi\)
−0.703162 + 0.711029i \(0.748229\pi\)
\(618\) −106.189 −4.27154
\(619\) −13.6582 −0.548971 −0.274485 0.961591i \(-0.588507\pi\)
−0.274485 + 0.961591i \(0.588507\pi\)
\(620\) −42.4657 −1.70546
\(621\) −71.2456 −2.85899
\(622\) −15.1446 −0.607243
\(623\) −47.7884 −1.91460
\(624\) −189.834 −7.59945
\(625\) −30.9838 −1.23935
\(626\) 7.89349 0.315487
\(627\) −15.6720 −0.625879
\(628\) 23.8877 0.953222
\(629\) −0.175021 −0.00697855
\(630\) −201.278 −8.01909
\(631\) −28.4436 −1.13232 −0.566161 0.824294i \(-0.691572\pi\)
−0.566161 + 0.824294i \(0.691572\pi\)
\(632\) −90.5844 −3.60326
\(633\) 27.2386 1.08264
\(634\) −7.04882 −0.279944
\(635\) −23.5150 −0.933165
\(636\) −19.7726 −0.784033
\(637\) −9.26811 −0.367216
\(638\) −19.0395 −0.753779
\(639\) 106.563 4.21557
\(640\) −180.537 −7.13637
\(641\) −3.66442 −0.144736 −0.0723680 0.997378i \(-0.523056\pi\)
−0.0723680 + 0.997378i \(0.523056\pi\)
\(642\) 62.5097 2.46706
\(643\) −0.0230049 −0.000907224 0 −0.000453612 1.00000i \(-0.500144\pi\)
−0.000453612 1.00000i \(0.500144\pi\)
\(644\) −68.1692 −2.68624
\(645\) −68.1651 −2.68400
\(646\) −1.39896 −0.0550413
\(647\) −1.71975 −0.0676105 −0.0338052 0.999428i \(-0.510763\pi\)
−0.0338052 + 0.999428i \(0.510763\pi\)
\(648\) −419.020 −16.4607
\(649\) −13.8276 −0.542780
\(650\) 17.1056 0.670936
\(651\) −29.8735 −1.17084
\(652\) 106.380 4.16618
\(653\) 8.44514 0.330484 0.165242 0.986253i \(-0.447160\pi\)
0.165242 + 0.986253i \(0.447160\pi\)
\(654\) −8.98744 −0.351437
\(655\) −50.0431 −1.95534
\(656\) 128.307 5.00954
\(657\) 90.5465 3.53256
\(658\) −20.7304 −0.808154
\(659\) 8.85856 0.345080 0.172540 0.985002i \(-0.444803\pi\)
0.172540 + 0.985002i \(0.444803\pi\)
\(660\) 79.4926 3.09425
\(661\) −39.5463 −1.53817 −0.769087 0.639144i \(-0.779289\pi\)
−0.769087 + 0.639144i \(0.779289\pi\)
\(662\) −41.8468 −1.62642
\(663\) 1.74470 0.0677584
\(664\) 56.7318 2.20162
\(665\) −25.2555 −0.979367
\(666\) −25.4258 −0.985229
\(667\) −16.6549 −0.644879
\(668\) −100.007 −3.86938
\(669\) 96.6157 3.73538
\(670\) −44.2709 −1.71034
\(671\) 9.29868 0.358971
\(672\) −314.302 −12.1245
\(673\) 10.7219 0.413298 0.206649 0.978415i \(-0.433744\pi\)
0.206649 + 0.978415i \(0.433744\pi\)
\(674\) −38.4359 −1.48050
\(675\) 38.0339 1.46392
\(676\) −20.1238 −0.773991
\(677\) −48.9632 −1.88181 −0.940903 0.338675i \(-0.890021\pi\)
−0.940903 + 0.338675i \(0.890021\pi\)
\(678\) −181.505 −6.97065
\(679\) 54.9063 2.10711
\(680\) 4.64891 0.178277
\(681\) −85.7125 −3.28451
\(682\) 11.7714 0.450752
\(683\) 21.0604 0.805852 0.402926 0.915233i \(-0.367993\pi\)
0.402926 + 0.915233i \(0.367993\pi\)
\(684\) −151.118 −5.77814
\(685\) 23.5469 0.899679
\(686\) 35.3108 1.34817
\(687\) 29.1241 1.11115
\(688\) −136.463 −5.20261
\(689\) 3.08710 0.117609
\(690\) 93.5159 3.56009
\(691\) −36.9792 −1.40676 −0.703378 0.710816i \(-0.748326\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(692\) 44.7918 1.70273
\(693\) 41.4872 1.57597
\(694\) 11.3296 0.430067
\(695\) 18.5920 0.705236
\(696\) −162.125 −6.14534
\(697\) −1.17922 −0.0446662
\(698\) 5.67111 0.214655
\(699\) −32.4701 −1.22813
\(700\) 36.3915 1.37547
\(701\) 42.3310 1.59882 0.799410 0.600785i \(-0.205145\pi\)
0.799410 + 0.600785i \(0.205145\pi\)
\(702\) 165.277 6.23798
\(703\) −3.19032 −0.120325
\(704\) 68.9695 2.59939
\(705\) 21.1462 0.796411
\(706\) −85.0423 −3.20061
\(707\) −49.9622 −1.87902
\(708\) −179.721 −6.75433
\(709\) −45.2746 −1.70032 −0.850161 0.526523i \(-0.823495\pi\)
−0.850161 + 0.526523i \(0.823495\pi\)
\(710\) −91.2100 −3.42305
\(711\) 73.6076 2.76050
\(712\) 160.347 6.00927
\(713\) 10.2971 0.385631
\(714\) 4.99178 0.186813
\(715\) −12.4112 −0.464153
\(716\) 11.0176 0.411748
\(717\) 29.7901 1.11253
\(718\) 12.8172 0.478334
\(719\) −3.29101 −0.122734 −0.0613669 0.998115i \(-0.519546\pi\)
−0.0613669 + 0.998115i \(0.519546\pi\)
\(720\) 411.030 15.3182
\(721\) 35.2720 1.31360
\(722\) 27.5625 1.02577
\(723\) 82.8641 3.08175
\(724\) −64.4534 −2.39539
\(725\) 8.89105 0.330205
\(726\) 82.6992 3.06926
\(727\) 0.291756 0.0108206 0.00541031 0.999985i \(-0.498278\pi\)
0.00541031 + 0.999985i \(0.498278\pi\)
\(728\) 103.606 3.83990
\(729\) 144.424 5.34903
\(730\) −77.5010 −2.86844
\(731\) 1.25419 0.0463877
\(732\) 120.857 4.46702
\(733\) 32.0074 1.18222 0.591109 0.806591i \(-0.298690\pi\)
0.591109 + 0.806591i \(0.298690\pi\)
\(734\) 53.0033 1.95639
\(735\) 27.0490 0.997718
\(736\) 108.337 3.99336
\(737\) 9.12510 0.336128
\(738\) −171.309 −6.30596
\(739\) −13.9514 −0.513211 −0.256606 0.966516i \(-0.582604\pi\)
−0.256606 + 0.966516i \(0.582604\pi\)
\(740\) 16.1822 0.594869
\(741\) 31.8027 1.16830
\(742\) 8.83256 0.324253
\(743\) −21.3794 −0.784333 −0.392166 0.919894i \(-0.628274\pi\)
−0.392166 + 0.919894i \(0.628274\pi\)
\(744\) 100.236 3.67485
\(745\) −14.3732 −0.526595
\(746\) −27.4039 −1.00333
\(747\) −46.0994 −1.68669
\(748\) −1.46260 −0.0534781
\(749\) −20.7634 −0.758678
\(750\) 75.8887 2.77106
\(751\) −34.7134 −1.26671 −0.633354 0.773862i \(-0.718322\pi\)
−0.633354 + 0.773862i \(0.718322\pi\)
\(752\) 42.3337 1.54375
\(753\) −47.6398 −1.73609
\(754\) 38.6362 1.40705
\(755\) 2.64273 0.0961788
\(756\) 351.621 12.7883
\(757\) 35.9194 1.30551 0.652756 0.757568i \(-0.273613\pi\)
0.652756 + 0.757568i \(0.273613\pi\)
\(758\) 92.5578 3.36185
\(759\) −19.2754 −0.699654
\(760\) 84.7413 3.07389
\(761\) −21.1632 −0.767165 −0.383582 0.923507i \(-0.625310\pi\)
−0.383582 + 0.923507i \(0.625310\pi\)
\(762\) 84.7206 3.06910
\(763\) 2.98529 0.108075
\(764\) −154.643 −5.59478
\(765\) −3.77763 −0.136581
\(766\) −7.73157 −0.279353
\(767\) 28.0600 1.01319
\(768\) 341.320 12.3163
\(769\) −24.0963 −0.868934 −0.434467 0.900688i \(-0.643063\pi\)
−0.434467 + 0.900688i \(0.643063\pi\)
\(770\) −35.5100 −1.27969
\(771\) 21.3390 0.768504
\(772\) 117.553 4.23082
\(773\) −30.0257 −1.07995 −0.539974 0.841682i \(-0.681566\pi\)
−0.539974 + 0.841682i \(0.681566\pi\)
\(774\) 182.199 6.54900
\(775\) −5.49703 −0.197459
\(776\) −184.230 −6.61348
\(777\) 11.3838 0.408390
\(778\) 74.6464 2.67620
\(779\) −21.4951 −0.770143
\(780\) −161.312 −5.77590
\(781\) 18.8002 0.672723
\(782\) −1.72062 −0.0615293
\(783\) 85.9069 3.07006
\(784\) 54.1509 1.93396
\(785\) 10.8848 0.388497
\(786\) 180.297 6.43097
\(787\) −19.9602 −0.711504 −0.355752 0.934580i \(-0.615775\pi\)
−0.355752 + 0.934580i \(0.615775\pi\)
\(788\) 154.591 5.50708
\(789\) −82.6431 −2.94217
\(790\) −63.0026 −2.24153
\(791\) 60.2891 2.14363
\(792\) −139.205 −4.94642
\(793\) −18.8695 −0.670077
\(794\) −24.3581 −0.864436
\(795\) −9.00972 −0.319542
\(796\) −5.54889 −0.196675
\(797\) 40.1578 1.42246 0.711231 0.702959i \(-0.248138\pi\)
0.711231 + 0.702959i \(0.248138\pi\)
\(798\) 90.9913 3.22106
\(799\) −0.389074 −0.0137644
\(800\) −57.8348 −2.04477
\(801\) −130.296 −4.60378
\(802\) −41.1941 −1.45462
\(803\) 15.9745 0.563727
\(804\) 118.602 4.18275
\(805\) −31.0625 −1.09481
\(806\) −23.8875 −0.841400
\(807\) 39.6928 1.39725
\(808\) 167.641 5.89760
\(809\) −4.83199 −0.169884 −0.0849419 0.996386i \(-0.527070\pi\)
−0.0849419 + 0.996386i \(0.527070\pi\)
\(810\) −291.434 −10.2399
\(811\) 41.0673 1.44207 0.721034 0.692900i \(-0.243667\pi\)
0.721034 + 0.692900i \(0.243667\pi\)
\(812\) 82.1974 2.88456
\(813\) −17.2831 −0.606145
\(814\) −4.48569 −0.157223
\(815\) 48.4741 1.69797
\(816\) −10.1938 −0.356853
\(817\) 22.8616 0.799825
\(818\) 108.009 3.77645
\(819\) −84.1889 −2.94180
\(820\) 109.029 3.80746
\(821\) 13.2896 0.463809 0.231905 0.972739i \(-0.425504\pi\)
0.231905 + 0.972739i \(0.425504\pi\)
\(822\) −84.8353 −2.95897
\(823\) −46.0569 −1.60544 −0.802721 0.596355i \(-0.796615\pi\)
−0.802721 + 0.596355i \(0.796615\pi\)
\(824\) −118.350 −4.12292
\(825\) 10.2900 0.358253
\(826\) 80.2828 2.79340
\(827\) −51.4982 −1.79077 −0.895385 0.445294i \(-0.853099\pi\)
−0.895385 + 0.445294i \(0.853099\pi\)
\(828\) −185.865 −6.45924
\(829\) 13.1520 0.456787 0.228393 0.973569i \(-0.426653\pi\)
0.228393 + 0.973569i \(0.426653\pi\)
\(830\) 39.4576 1.36959
\(831\) 69.4392 2.40882
\(832\) −139.958 −4.85217
\(833\) −0.497681 −0.0172436
\(834\) −66.9840 −2.31947
\(835\) −45.5698 −1.57701
\(836\) −26.6606 −0.922078
\(837\) −53.1133 −1.83586
\(838\) −1.04290 −0.0360263
\(839\) −3.44491 −0.118931 −0.0594657 0.998230i \(-0.518940\pi\)
−0.0594657 + 0.998230i \(0.518940\pi\)
\(840\) −302.375 −10.4329
\(841\) −8.91783 −0.307512
\(842\) 30.9487 1.06656
\(843\) −10.6587 −0.367105
\(844\) 46.3374 1.59500
\(845\) −9.16975 −0.315449
\(846\) −56.5217 −1.94326
\(847\) −27.4696 −0.943866
\(848\) −18.0370 −0.619394
\(849\) −10.1232 −0.347426
\(850\) 0.918539 0.0315056
\(851\) −3.92388 −0.134509
\(852\) 244.351 8.37132
\(853\) 39.1765 1.34138 0.670688 0.741739i \(-0.265999\pi\)
0.670688 + 0.741739i \(0.265999\pi\)
\(854\) −53.9880 −1.84743
\(855\) −68.8596 −2.35495
\(856\) 69.6687 2.38123
\(857\) −2.13667 −0.0729873 −0.0364936 0.999334i \(-0.511619\pi\)
−0.0364936 + 0.999334i \(0.511619\pi\)
\(858\) 44.7155 1.52656
\(859\) −19.1467 −0.653276 −0.326638 0.945149i \(-0.605916\pi\)
−0.326638 + 0.945149i \(0.605916\pi\)
\(860\) −115.960 −3.95421
\(861\) 76.6992 2.61390
\(862\) 69.0723 2.35261
\(863\) 31.1734 1.06116 0.530578 0.847636i \(-0.321975\pi\)
0.530578 + 0.847636i \(0.321975\pi\)
\(864\) −558.810 −19.0111
\(865\) 20.4102 0.693967
\(866\) 108.661 3.69245
\(867\) −57.8635 −1.96515
\(868\) −50.8198 −1.72494
\(869\) 12.9861 0.440522
\(870\) −112.760 −3.82292
\(871\) −18.5173 −0.627436
\(872\) −10.0167 −0.339209
\(873\) 149.703 5.06667
\(874\) −31.3639 −1.06090
\(875\) −25.2074 −0.852166
\(876\) 207.625 7.01498
\(877\) 36.5162 1.23306 0.616532 0.787330i \(-0.288537\pi\)
0.616532 + 0.787330i \(0.288537\pi\)
\(878\) 53.5729 1.80800
\(879\) −3.10351 −0.104679
\(880\) 72.5151 2.44448
\(881\) −45.7898 −1.54270 −0.771348 0.636414i \(-0.780417\pi\)
−0.771348 + 0.636414i \(0.780417\pi\)
\(882\) −72.2995 −2.43445
\(883\) 19.7147 0.663454 0.331727 0.943375i \(-0.392369\pi\)
0.331727 + 0.943375i \(0.392369\pi\)
\(884\) 2.96802 0.0998253
\(885\) −81.8931 −2.75281
\(886\) −9.81325 −0.329683
\(887\) −13.6433 −0.458096 −0.229048 0.973415i \(-0.573561\pi\)
−0.229048 + 0.973415i \(0.573561\pi\)
\(888\) −38.1966 −1.28179
\(889\) −28.1410 −0.943820
\(890\) 111.523 3.73828
\(891\) 60.0702 2.01243
\(892\) 164.359 5.50316
\(893\) −7.09212 −0.237329
\(894\) 51.7843 1.73193
\(895\) 5.02037 0.167813
\(896\) −216.054 −7.21785
\(897\) 39.1151 1.30602
\(898\) 88.1075 2.94019
\(899\) −12.4161 −0.414101
\(900\) 99.2222 3.30741
\(901\) 0.165772 0.00552266
\(902\) −30.2228 −1.00631
\(903\) −81.5750 −2.71464
\(904\) −202.292 −6.72812
\(905\) −29.3693 −0.976270
\(906\) −9.52131 −0.316324
\(907\) 8.33806 0.276861 0.138430 0.990372i \(-0.455794\pi\)
0.138430 + 0.990372i \(0.455794\pi\)
\(908\) −145.811 −4.83892
\(909\) −136.223 −4.51823
\(910\) 72.0594 2.38875
\(911\) 40.2144 1.33236 0.666182 0.745789i \(-0.267927\pi\)
0.666182 + 0.745789i \(0.267927\pi\)
\(912\) −185.814 −6.15292
\(913\) −8.13298 −0.269163
\(914\) 31.6866 1.04810
\(915\) 55.0708 1.82059
\(916\) 49.5449 1.63701
\(917\) −59.8879 −1.97767
\(918\) 8.87508 0.292921
\(919\) 29.2563 0.965077 0.482539 0.875875i \(-0.339715\pi\)
0.482539 + 0.875875i \(0.339715\pi\)
\(920\) 104.226 3.43623
\(921\) 19.4744 0.641702
\(922\) 32.7321 1.07797
\(923\) −38.1506 −1.25574
\(924\) 95.1309 3.12958
\(925\) 2.09473 0.0688742
\(926\) −18.5549 −0.609753
\(927\) 96.1696 3.15863
\(928\) −130.631 −4.28818
\(929\) −38.7575 −1.27159 −0.635796 0.771857i \(-0.719328\pi\)
−0.635796 + 0.771857i \(0.719328\pi\)
\(930\) 69.7157 2.28607
\(931\) −9.07185 −0.297318
\(932\) −55.2370 −1.80935
\(933\) 18.4875 0.605252
\(934\) 51.9825 1.70092
\(935\) −0.666461 −0.0217956
\(936\) 282.484 9.23328
\(937\) 15.8952 0.519272 0.259636 0.965707i \(-0.416397\pi\)
0.259636 + 0.965707i \(0.416397\pi\)
\(938\) −52.9802 −1.72987
\(939\) −9.63582 −0.314453
\(940\) 35.9732 1.17332
\(941\) 40.8553 1.33184 0.665922 0.746021i \(-0.268038\pi\)
0.665922 + 0.746021i \(0.268038\pi\)
\(942\) −39.2162 −1.27773
\(943\) −26.4375 −0.860923
\(944\) −163.946 −5.33599
\(945\) 160.223 5.21204
\(946\) 32.1440 1.04509
\(947\) −27.1367 −0.881824 −0.440912 0.897550i \(-0.645345\pi\)
−0.440912 + 0.897550i \(0.645345\pi\)
\(948\) 168.783 5.48183
\(949\) −32.4165 −1.05229
\(950\) 16.7433 0.543225
\(951\) 8.60470 0.279027
\(952\) 5.56347 0.180313
\(953\) −32.7334 −1.06034 −0.530169 0.847892i \(-0.677871\pi\)
−0.530169 + 0.847892i \(0.677871\pi\)
\(954\) 24.0821 0.779687
\(955\) −70.4657 −2.28022
\(956\) 50.6779 1.63904
\(957\) 23.2420 0.751308
\(958\) −18.5538 −0.599445
\(959\) 28.1791 0.909952
\(960\) 408.468 13.1832
\(961\) −23.3235 −0.752372
\(962\) 9.10268 0.293482
\(963\) −56.6118 −1.82429
\(964\) 140.966 4.54020
\(965\) 53.5651 1.72432
\(966\) 111.913 3.60074
\(967\) −12.3713 −0.397834 −0.198917 0.980016i \(-0.563742\pi\)
−0.198917 + 0.980016i \(0.563742\pi\)
\(968\) 92.1704 2.96247
\(969\) 1.70775 0.0548609
\(970\) −128.134 −4.11415
\(971\) −30.1248 −0.966752 −0.483376 0.875413i \(-0.660590\pi\)
−0.483376 + 0.875413i \(0.660590\pi\)
\(972\) 447.208 14.3442
\(973\) 22.2496 0.713289
\(974\) 88.9176 2.84910
\(975\) −20.8813 −0.668736
\(976\) 110.249 3.52899
\(977\) 48.6443 1.55627 0.778134 0.628098i \(-0.216166\pi\)
0.778134 + 0.628098i \(0.216166\pi\)
\(978\) −174.644 −5.58450
\(979\) −22.9872 −0.734673
\(980\) 46.0149 1.46989
\(981\) 8.13945 0.259873
\(982\) 19.6938 0.628454
\(983\) −53.2984 −1.69996 −0.849978 0.526819i \(-0.823385\pi\)
−0.849978 + 0.526819i \(0.823385\pi\)
\(984\) −257.353 −8.20413
\(985\) 70.4422 2.24447
\(986\) 2.07470 0.0660718
\(987\) 25.3062 0.805505
\(988\) 54.1017 1.72121
\(989\) 28.1181 0.894104
\(990\) −96.8185 −3.07709
\(991\) 21.7853 0.692033 0.346017 0.938228i \(-0.387534\pi\)
0.346017 + 0.938228i \(0.387534\pi\)
\(992\) 80.7648 2.56428
\(993\) 51.0836 1.62109
\(994\) −109.153 −3.46214
\(995\) −2.52845 −0.0801573
\(996\) −105.707 −3.34944
\(997\) −43.3661 −1.37342 −0.686709 0.726932i \(-0.740945\pi\)
−0.686709 + 0.726932i \(0.740945\pi\)
\(998\) −80.6179 −2.55192
\(999\) 20.2396 0.640353
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 \(a_p\))