Properties

Label 8003.2.a.c.1.7
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 1.7
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65004 q^{2}\) \(-0.851556 q^{3}\) \(+5.02269 q^{4}\) \(-0.493922 q^{5}\) \(+2.25665 q^{6}\) \(+4.68994 q^{7}\) \(-8.01024 q^{8}\) \(-2.27485 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65004 q^{2}\) \(-0.851556 q^{3}\) \(+5.02269 q^{4}\) \(-0.493922 q^{5}\) \(+2.25665 q^{6}\) \(+4.68994 q^{7}\) \(-8.01024 q^{8}\) \(-2.27485 q^{9}\) \(+1.30891 q^{10}\) \(-6.10353 q^{11}\) \(-4.27710 q^{12}\) \(-1.88903 q^{13}\) \(-12.4285 q^{14}\) \(+0.420603 q^{15}\) \(+11.1820 q^{16}\) \(-0.365382 q^{17}\) \(+6.02844 q^{18}\) \(-1.92390 q^{19}\) \(-2.48082 q^{20}\) \(-3.99374 q^{21}\) \(+16.1746 q^{22}\) \(-5.59813 q^{23}\) \(+6.82117 q^{24}\) \(-4.75604 q^{25}\) \(+5.00601 q^{26}\) \(+4.49183 q^{27}\) \(+23.5561 q^{28}\) \(+4.25229 q^{29}\) \(-1.11461 q^{30}\) \(-0.539420 q^{31}\) \(-13.6123 q^{32}\) \(+5.19749 q^{33}\) \(+0.968276 q^{34}\) \(-2.31646 q^{35}\) \(-11.4259 q^{36}\) \(-7.84073 q^{37}\) \(+5.09842 q^{38}\) \(+1.60862 q^{39}\) \(+3.95644 q^{40}\) \(-2.57678 q^{41}\) \(+10.5836 q^{42}\) \(-1.65675 q^{43}\) \(-30.6561 q^{44}\) \(+1.12360 q^{45}\) \(+14.8352 q^{46}\) \(-4.53476 q^{47}\) \(-9.52214 q^{48}\) \(+14.9955 q^{49}\) \(+12.6037 q^{50}\) \(+0.311144 q^{51}\) \(-9.48804 q^{52}\) \(-1.00000 q^{53}\) \(-11.9035 q^{54}\) \(+3.01467 q^{55}\) \(-37.5675 q^{56}\) \(+1.63831 q^{57}\) \(-11.2687 q^{58}\) \(-7.19531 q^{59}\) \(+2.11256 q^{60}\) \(-1.86182 q^{61}\) \(+1.42948 q^{62}\) \(-10.6689 q^{63}\) \(+13.7091 q^{64}\) \(+0.933037 q^{65}\) \(-13.7735 q^{66}\) \(-3.62113 q^{67}\) \(-1.83520 q^{68}\) \(+4.76712 q^{69}\) \(+6.13872 q^{70}\) \(+0.316144 q^{71}\) \(+18.2221 q^{72}\) \(+3.71369 q^{73}\) \(+20.7782 q^{74}\) \(+4.05003 q^{75}\) \(-9.66318 q^{76}\) \(-28.6252 q^{77}\) \(-4.26290 q^{78}\) \(-12.7904 q^{79}\) \(-5.52307 q^{80}\) \(+2.99951 q^{81}\) \(+6.82857 q^{82}\) \(-2.32400 q^{83}\) \(-20.0593 q^{84}\) \(+0.180471 q^{85}\) \(+4.39045 q^{86}\) \(-3.62107 q^{87}\) \(+48.8907 q^{88}\) \(-11.0332 q^{89}\) \(-2.97758 q^{90}\) \(-8.85945 q^{91}\) \(-28.1177 q^{92}\) \(+0.459346 q^{93}\) \(+12.0173 q^{94}\) \(+0.950260 q^{95}\) \(+11.5917 q^{96}\) \(+6.51641 q^{97}\) \(-39.7386 q^{98}\) \(+13.8846 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65004 −1.87386 −0.936929 0.349519i \(-0.886345\pi\)
−0.936929 + 0.349519i \(0.886345\pi\)
\(3\) −0.851556 −0.491646 −0.245823 0.969315i \(-0.579058\pi\)
−0.245823 + 0.969315i \(0.579058\pi\)
\(4\) 5.02269 2.51135
\(5\) −0.493922 −0.220889 −0.110444 0.993882i \(-0.535227\pi\)
−0.110444 + 0.993882i \(0.535227\pi\)
\(6\) 2.25665 0.921275
\(7\) 4.68994 1.77263 0.886315 0.463084i \(-0.153257\pi\)
0.886315 + 0.463084i \(0.153257\pi\)
\(8\) −8.01024 −2.83205
\(9\) −2.27485 −0.758284
\(10\) 1.30891 0.413914
\(11\) −6.10353 −1.84028 −0.920141 0.391586i \(-0.871926\pi\)
−0.920141 + 0.391586i \(0.871926\pi\)
\(12\) −4.27710 −1.23469
\(13\) −1.88903 −0.523924 −0.261962 0.965078i \(-0.584370\pi\)
−0.261962 + 0.965078i \(0.584370\pi\)
\(14\) −12.4285 −3.32166
\(15\) 0.420603 0.108599
\(16\) 11.1820 2.79551
\(17\) −0.365382 −0.0886182 −0.0443091 0.999018i \(-0.514109\pi\)
−0.0443091 + 0.999018i \(0.514109\pi\)
\(18\) 6.02844 1.42092
\(19\) −1.92390 −0.441374 −0.220687 0.975345i \(-0.570830\pi\)
−0.220687 + 0.975345i \(0.570830\pi\)
\(20\) −2.48082 −0.554728
\(21\) −3.99374 −0.871506
\(22\) 16.1746 3.44843
\(23\) −5.59813 −1.16729 −0.583645 0.812009i \(-0.698374\pi\)
−0.583645 + 0.812009i \(0.698374\pi\)
\(24\) 6.82117 1.39237
\(25\) −4.75604 −0.951208
\(26\) 5.00601 0.981759
\(27\) 4.49183 0.864453
\(28\) 23.5561 4.45169
\(29\) 4.25229 0.789631 0.394815 0.918760i \(-0.370809\pi\)
0.394815 + 0.918760i \(0.370809\pi\)
\(30\) −1.11461 −0.203499
\(31\) −0.539420 −0.0968827 −0.0484413 0.998826i \(-0.515425\pi\)
−0.0484413 + 0.998826i \(0.515425\pi\)
\(32\) −13.6123 −2.40635
\(33\) 5.19749 0.904768
\(34\) 0.968276 0.166058
\(35\) −2.31646 −0.391554
\(36\) −11.4259 −1.90431
\(37\) −7.84073 −1.28901 −0.644504 0.764601i \(-0.722936\pi\)
−0.644504 + 0.764601i \(0.722936\pi\)
\(38\) 5.09842 0.827072
\(39\) 1.60862 0.257585
\(40\) 3.95644 0.625568
\(41\) −2.57678 −0.402426 −0.201213 0.979547i \(-0.564488\pi\)
−0.201213 + 0.979547i \(0.564488\pi\)
\(42\) 10.5836 1.63308
\(43\) −1.65675 −0.252652 −0.126326 0.991989i \(-0.540319\pi\)
−0.126326 + 0.991989i \(0.540319\pi\)
\(44\) −30.6561 −4.62159
\(45\) 1.12360 0.167496
\(46\) 14.8352 2.18734
\(47\) −4.53476 −0.661463 −0.330731 0.943725i \(-0.607295\pi\)
−0.330731 + 0.943725i \(0.607295\pi\)
\(48\) −9.52214 −1.37440
\(49\) 14.9955 2.14221
\(50\) 12.6037 1.78243
\(51\) 0.311144 0.0435688
\(52\) −9.48804 −1.31575
\(53\) −1.00000 −0.137361
\(54\) −11.9035 −1.61986
\(55\) 3.01467 0.406498
\(56\) −37.5675 −5.02017
\(57\) 1.63831 0.217000
\(58\) −11.2687 −1.47966
\(59\) −7.19531 −0.936749 −0.468374 0.883530i \(-0.655160\pi\)
−0.468374 + 0.883530i \(0.655160\pi\)
\(60\) 2.11256 0.272730
\(61\) −1.86182 −0.238382 −0.119191 0.992871i \(-0.538030\pi\)
−0.119191 + 0.992871i \(0.538030\pi\)
\(62\) 1.42948 0.181544
\(63\) −10.6689 −1.34416
\(64\) 13.7091 1.71364
\(65\) 0.933037 0.115729
\(66\) −13.7735 −1.69541
\(67\) −3.62113 −0.442392 −0.221196 0.975229i \(-0.570996\pi\)
−0.221196 + 0.975229i \(0.570996\pi\)
\(68\) −1.83520 −0.222551
\(69\) 4.76712 0.573894
\(70\) 6.13872 0.733717
\(71\) 0.316144 0.0375194 0.0187597 0.999824i \(-0.494028\pi\)
0.0187597 + 0.999824i \(0.494028\pi\)
\(72\) 18.2221 2.14750
\(73\) 3.71369 0.434655 0.217327 0.976099i \(-0.430266\pi\)
0.217327 + 0.976099i \(0.430266\pi\)
\(74\) 20.7782 2.41542
\(75\) 4.05003 0.467658
\(76\) −9.66318 −1.10844
\(77\) −28.6252 −3.26214
\(78\) −4.26290 −0.482678
\(79\) −12.7904 −1.43903 −0.719517 0.694474i \(-0.755637\pi\)
−0.719517 + 0.694474i \(0.755637\pi\)
\(80\) −5.52307 −0.617497
\(81\) 2.99951 0.333279
\(82\) 6.82857 0.754090
\(83\) −2.32400 −0.255092 −0.127546 0.991833i \(-0.540710\pi\)
−0.127546 + 0.991833i \(0.540710\pi\)
\(84\) −20.0593 −2.18865
\(85\) 0.180471 0.0195748
\(86\) 4.39045 0.473434
\(87\) −3.62107 −0.388219
\(88\) 48.8907 5.21177
\(89\) −11.0332 −1.16952 −0.584760 0.811207i \(-0.698811\pi\)
−0.584760 + 0.811207i \(0.698811\pi\)
\(90\) −2.97758 −0.313865
\(91\) −8.85945 −0.928723
\(92\) −28.1177 −2.93147
\(93\) 0.459346 0.0476320
\(94\) 12.0173 1.23949
\(95\) 0.950260 0.0974946
\(96\) 11.5917 1.18307
\(97\) 6.51641 0.661641 0.330820 0.943694i \(-0.392675\pi\)
0.330820 + 0.943694i \(0.392675\pi\)
\(98\) −39.7386 −4.01421
\(99\) 13.8846 1.39546
\(100\) −23.8881 −2.38881
\(101\) 11.1695 1.11141 0.555703 0.831381i \(-0.312449\pi\)
0.555703 + 0.831381i \(0.312449\pi\)
\(102\) −0.824542 −0.0816418
\(103\) −13.2927 −1.30977 −0.654884 0.755730i \(-0.727282\pi\)
−0.654884 + 0.755730i \(0.727282\pi\)
\(104\) 15.1316 1.48378
\(105\) 1.97260 0.192506
\(106\) 2.65004 0.257394
\(107\) −2.97117 −0.287233 −0.143617 0.989633i \(-0.545873\pi\)
−0.143617 + 0.989633i \(0.545873\pi\)
\(108\) 22.5611 2.17094
\(109\) 8.39739 0.804324 0.402162 0.915569i \(-0.368259\pi\)
0.402162 + 0.915569i \(0.368259\pi\)
\(110\) −7.98898 −0.761720
\(111\) 6.67682 0.633736
\(112\) 52.4431 4.95541
\(113\) −12.7160 −1.19622 −0.598112 0.801413i \(-0.704082\pi\)
−0.598112 + 0.801413i \(0.704082\pi\)
\(114\) −4.34159 −0.406627
\(115\) 2.76504 0.257841
\(116\) 21.3580 1.98304
\(117\) 4.29728 0.397283
\(118\) 19.0678 1.75534
\(119\) −1.71362 −0.157087
\(120\) −3.36913 −0.307558
\(121\) 26.2530 2.38664
\(122\) 4.93389 0.446693
\(123\) 2.19428 0.197851
\(124\) −2.70934 −0.243306
\(125\) 4.81873 0.431000
\(126\) 28.2730 2.51876
\(127\) 5.67529 0.503601 0.251800 0.967779i \(-0.418977\pi\)
0.251800 + 0.967779i \(0.418977\pi\)
\(128\) −9.10497 −0.804773
\(129\) 1.41082 0.124215
\(130\) −2.47258 −0.216860
\(131\) 9.41565 0.822649 0.411325 0.911489i \(-0.365066\pi\)
0.411325 + 0.911489i \(0.365066\pi\)
\(132\) 26.1054 2.27218
\(133\) −9.02299 −0.782392
\(134\) 9.59614 0.828980
\(135\) −2.21862 −0.190948
\(136\) 2.92680 0.250971
\(137\) −5.32292 −0.454768 −0.227384 0.973805i \(-0.573017\pi\)
−0.227384 + 0.973805i \(0.573017\pi\)
\(138\) −12.6330 −1.07540
\(139\) 9.38432 0.795967 0.397984 0.917393i \(-0.369710\pi\)
0.397984 + 0.917393i \(0.369710\pi\)
\(140\) −11.6349 −0.983327
\(141\) 3.86160 0.325206
\(142\) −0.837794 −0.0703061
\(143\) 11.5298 0.964168
\(144\) −25.4375 −2.11979
\(145\) −2.10030 −0.174421
\(146\) −9.84141 −0.814481
\(147\) −12.7695 −1.05321
\(148\) −39.3816 −3.23714
\(149\) −14.6227 −1.19794 −0.598970 0.800771i \(-0.704423\pi\)
−0.598970 + 0.800771i \(0.704423\pi\)
\(150\) −10.7327 −0.876324
\(151\) 1.00000 0.0813788
\(152\) 15.4109 1.24999
\(153\) 0.831191 0.0671978
\(154\) 75.8577 6.11279
\(155\) 0.266432 0.0214003
\(156\) 8.07960 0.646885
\(157\) 0.375571 0.0299738 0.0149869 0.999888i \(-0.495229\pi\)
0.0149869 + 0.999888i \(0.495229\pi\)
\(158\) 33.8951 2.69655
\(159\) 0.851556 0.0675328
\(160\) 6.72345 0.531535
\(161\) −26.2549 −2.06917
\(162\) −7.94881 −0.624518
\(163\) −8.99459 −0.704511 −0.352255 0.935904i \(-0.614585\pi\)
−0.352255 + 0.935904i \(0.614585\pi\)
\(164\) −12.9424 −1.01063
\(165\) −2.56716 −0.199853
\(166\) 6.15868 0.478006
\(167\) 21.1748 1.63855 0.819277 0.573398i \(-0.194375\pi\)
0.819277 + 0.573398i \(0.194375\pi\)
\(168\) 31.9909 2.46815
\(169\) −9.43155 −0.725504
\(170\) −0.478253 −0.0366804
\(171\) 4.37660 0.334687
\(172\) −8.32135 −0.634497
\(173\) 6.60857 0.502441 0.251220 0.967930i \(-0.419168\pi\)
0.251220 + 0.967930i \(0.419168\pi\)
\(174\) 9.59595 0.727467
\(175\) −22.3055 −1.68614
\(176\) −68.2499 −5.14453
\(177\) 6.12721 0.460549
\(178\) 29.2384 2.19151
\(179\) 4.02808 0.301073 0.150536 0.988604i \(-0.451900\pi\)
0.150536 + 0.988604i \(0.451900\pi\)
\(180\) 5.64350 0.420642
\(181\) 11.1220 0.826693 0.413346 0.910574i \(-0.364360\pi\)
0.413346 + 0.910574i \(0.364360\pi\)
\(182\) 23.4779 1.74030
\(183\) 1.58544 0.117199
\(184\) 44.8424 3.30582
\(185\) 3.87271 0.284727
\(186\) −1.21728 −0.0892556
\(187\) 2.23012 0.163083
\(188\) −22.7767 −1.66116
\(189\) 21.0664 1.53236
\(190\) −2.51822 −0.182691
\(191\) −9.36635 −0.677725 −0.338863 0.940836i \(-0.610042\pi\)
−0.338863 + 0.940836i \(0.610042\pi\)
\(192\) −11.6741 −0.842504
\(193\) 20.6882 1.48917 0.744583 0.667529i \(-0.232648\pi\)
0.744583 + 0.667529i \(0.232648\pi\)
\(194\) −17.2687 −1.23982
\(195\) −0.794533 −0.0568977
\(196\) 75.3178 5.37984
\(197\) 8.27169 0.589334 0.294667 0.955600i \(-0.404791\pi\)
0.294667 + 0.955600i \(0.404791\pi\)
\(198\) −36.7948 −2.61489
\(199\) 12.8090 0.908008 0.454004 0.891000i \(-0.349995\pi\)
0.454004 + 0.891000i \(0.349995\pi\)
\(200\) 38.0970 2.69387
\(201\) 3.08360 0.217500
\(202\) −29.5996 −2.08262
\(203\) 19.9430 1.39972
\(204\) 1.56278 0.109416
\(205\) 1.27273 0.0888915
\(206\) 35.2261 2.45432
\(207\) 12.7349 0.885138
\(208\) −21.1233 −1.46464
\(209\) 11.7426 0.812253
\(210\) −5.22746 −0.360729
\(211\) 20.1936 1.39018 0.695092 0.718921i \(-0.255363\pi\)
0.695092 + 0.718921i \(0.255363\pi\)
\(212\) −5.02269 −0.344960
\(213\) −0.269215 −0.0184463
\(214\) 7.87370 0.538235
\(215\) 0.818306 0.0558080
\(216\) −35.9807 −2.44817
\(217\) −2.52984 −0.171737
\(218\) −22.2534 −1.50719
\(219\) −3.16241 −0.213696
\(220\) 15.1418 1.02086
\(221\) 0.690220 0.0464292
\(222\) −17.6938 −1.18753
\(223\) 17.4811 1.17062 0.585311 0.810809i \(-0.300973\pi\)
0.585311 + 0.810809i \(0.300973\pi\)
\(224\) −63.8411 −4.26556
\(225\) 10.8193 0.721286
\(226\) 33.6980 2.24155
\(227\) 7.55328 0.501329 0.250665 0.968074i \(-0.419351\pi\)
0.250665 + 0.968074i \(0.419351\pi\)
\(228\) 8.22874 0.544961
\(229\) 12.9974 0.858894 0.429447 0.903092i \(-0.358708\pi\)
0.429447 + 0.903092i \(0.358708\pi\)
\(230\) −7.32746 −0.483158
\(231\) 24.3759 1.60382
\(232\) −34.0619 −2.23627
\(233\) −6.25731 −0.409930 −0.204965 0.978769i \(-0.565708\pi\)
−0.204965 + 0.978769i \(0.565708\pi\)
\(234\) −11.3879 −0.744453
\(235\) 2.23982 0.146110
\(236\) −36.1398 −2.35250
\(237\) 10.8918 0.707496
\(238\) 4.54115 0.294359
\(239\) 20.3259 1.31477 0.657385 0.753554i \(-0.271662\pi\)
0.657385 + 0.753554i \(0.271662\pi\)
\(240\) 4.70320 0.303590
\(241\) 4.11784 0.265253 0.132627 0.991166i \(-0.457659\pi\)
0.132627 + 0.991166i \(0.457659\pi\)
\(242\) −69.5715 −4.47223
\(243\) −16.0297 −1.02831
\(244\) −9.35135 −0.598659
\(245\) −7.40661 −0.473191
\(246\) −5.81491 −0.370745
\(247\) 3.63432 0.231246
\(248\) 4.32088 0.274376
\(249\) 1.97902 0.125415
\(250\) −12.7698 −0.807633
\(251\) −22.3853 −1.41295 −0.706475 0.707738i \(-0.749716\pi\)
−0.706475 + 0.707738i \(0.749716\pi\)
\(252\) −53.5867 −3.37564
\(253\) 34.1683 2.14814
\(254\) −15.0397 −0.943677
\(255\) −0.153681 −0.00962386
\(256\) −3.28975 −0.205609
\(257\) −25.2767 −1.57672 −0.788358 0.615217i \(-0.789069\pi\)
−0.788358 + 0.615217i \(0.789069\pi\)
\(258\) −3.73871 −0.232762
\(259\) −36.7725 −2.28493
\(260\) 4.68636 0.290635
\(261\) −9.67334 −0.598765
\(262\) −24.9518 −1.54153
\(263\) −9.89773 −0.610320 −0.305160 0.952301i \(-0.598710\pi\)
−0.305160 + 0.952301i \(0.598710\pi\)
\(264\) −41.6332 −2.56235
\(265\) 0.493922 0.0303414
\(266\) 23.9112 1.46609
\(267\) 9.39541 0.574989
\(268\) −18.1878 −1.11100
\(269\) −17.5990 −1.07303 −0.536515 0.843891i \(-0.680260\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(270\) 5.87941 0.357810
\(271\) −21.1707 −1.28603 −0.643014 0.765854i \(-0.722316\pi\)
−0.643014 + 0.765854i \(0.722316\pi\)
\(272\) −4.08572 −0.247733
\(273\) 7.54432 0.456603
\(274\) 14.1059 0.852171
\(275\) 29.0286 1.75049
\(276\) 23.9438 1.44125
\(277\) 13.4478 0.808001 0.404001 0.914759i \(-0.367619\pi\)
0.404001 + 0.914759i \(0.367619\pi\)
\(278\) −24.8688 −1.49153
\(279\) 1.22710 0.0734646
\(280\) 18.5554 1.10890
\(281\) −20.7878 −1.24009 −0.620047 0.784564i \(-0.712887\pi\)
−0.620047 + 0.784564i \(0.712887\pi\)
\(282\) −10.2334 −0.609389
\(283\) −33.2101 −1.97413 −0.987067 0.160307i \(-0.948751\pi\)
−0.987067 + 0.160307i \(0.948751\pi\)
\(284\) 1.58790 0.0942242
\(285\) −0.809199 −0.0479328
\(286\) −30.5543 −1.80671
\(287\) −12.0850 −0.713352
\(288\) 30.9661 1.82469
\(289\) −16.8665 −0.992147
\(290\) 5.56588 0.326840
\(291\) −5.54909 −0.325293
\(292\) 18.6527 1.09157
\(293\) 3.84636 0.224707 0.112353 0.993668i \(-0.464161\pi\)
0.112353 + 0.993668i \(0.464161\pi\)
\(294\) 33.8397 1.97357
\(295\) 3.55392 0.206917
\(296\) 62.8061 3.65053
\(297\) −27.4160 −1.59084
\(298\) 38.7507 2.24477
\(299\) 10.5751 0.611571
\(300\) 20.3421 1.17445
\(301\) −7.77006 −0.447859
\(302\) −2.65004 −0.152492
\(303\) −9.51145 −0.546418
\(304\) −21.5132 −1.23387
\(305\) 0.919595 0.0526558
\(306\) −2.20269 −0.125919
\(307\) 9.36853 0.534690 0.267345 0.963601i \(-0.413854\pi\)
0.267345 + 0.963601i \(0.413854\pi\)
\(308\) −143.775 −8.19236
\(309\) 11.3195 0.643942
\(310\) −0.706053 −0.0401011
\(311\) −29.0297 −1.64612 −0.823062 0.567951i \(-0.807736\pi\)
−0.823062 + 0.567951i \(0.807736\pi\)
\(312\) −12.8854 −0.729494
\(313\) −3.32230 −0.187788 −0.0938939 0.995582i \(-0.529931\pi\)
−0.0938939 + 0.995582i \(0.529931\pi\)
\(314\) −0.995277 −0.0561667
\(315\) 5.26962 0.296909
\(316\) −64.2423 −3.61391
\(317\) 23.4006 1.31431 0.657155 0.753756i \(-0.271760\pi\)
0.657155 + 0.753756i \(0.271760\pi\)
\(318\) −2.25665 −0.126547
\(319\) −25.9540 −1.45314
\(320\) −6.77124 −0.378524
\(321\) 2.53011 0.141217
\(322\) 69.5763 3.87734
\(323\) 0.702961 0.0391138
\(324\) 15.0656 0.836979
\(325\) 8.98433 0.498361
\(326\) 23.8360 1.32015
\(327\) −7.15084 −0.395443
\(328\) 20.6407 1.13969
\(329\) −21.2677 −1.17253
\(330\) 6.80306 0.374496
\(331\) −1.08898 −0.0598559 −0.0299280 0.999552i \(-0.509528\pi\)
−0.0299280 + 0.999552i \(0.509528\pi\)
\(332\) −11.6727 −0.640624
\(333\) 17.8365 0.977434
\(334\) −56.1139 −3.07042
\(335\) 1.78856 0.0977195
\(336\) −44.6582 −2.43631
\(337\) −15.3967 −0.838712 −0.419356 0.907822i \(-0.637744\pi\)
−0.419356 + 0.907822i \(0.637744\pi\)
\(338\) 24.9939 1.35949
\(339\) 10.8284 0.588119
\(340\) 0.906448 0.0491590
\(341\) 3.29236 0.178291
\(342\) −11.5981 −0.627156
\(343\) 37.4984 2.02472
\(344\) 13.2710 0.715523
\(345\) −2.35459 −0.126767
\(346\) −17.5130 −0.941503
\(347\) −3.36141 −0.180450 −0.0902250 0.995921i \(-0.528759\pi\)
−0.0902250 + 0.995921i \(0.528759\pi\)
\(348\) −18.1875 −0.974952
\(349\) 7.04139 0.376917 0.188459 0.982081i \(-0.439651\pi\)
0.188459 + 0.982081i \(0.439651\pi\)
\(350\) 59.1105 3.15959
\(351\) −8.48523 −0.452908
\(352\) 83.0833 4.42836
\(353\) −15.2204 −0.810102 −0.405051 0.914294i \(-0.632746\pi\)
−0.405051 + 0.914294i \(0.632746\pi\)
\(354\) −16.2373 −0.863004
\(355\) −0.156151 −0.00828762
\(356\) −55.4165 −2.93707
\(357\) 1.45924 0.0772313
\(358\) −10.6746 −0.564168
\(359\) 37.3964 1.97371 0.986853 0.161620i \(-0.0516718\pi\)
0.986853 + 0.161620i \(0.0516718\pi\)
\(360\) −9.00031 −0.474358
\(361\) −15.2986 −0.805189
\(362\) −29.4737 −1.54910
\(363\) −22.3559 −1.17338
\(364\) −44.4983 −2.33234
\(365\) −1.83427 −0.0960103
\(366\) −4.20148 −0.219615
\(367\) 13.5707 0.708386 0.354193 0.935172i \(-0.384756\pi\)
0.354193 + 0.935172i \(0.384756\pi\)
\(368\) −62.5985 −3.26317
\(369\) 5.86181 0.305153
\(370\) −10.2628 −0.533539
\(371\) −4.68994 −0.243489
\(372\) 2.30715 0.119620
\(373\) 25.9115 1.34165 0.670824 0.741616i \(-0.265940\pi\)
0.670824 + 0.741616i \(0.265940\pi\)
\(374\) −5.90990 −0.305594
\(375\) −4.10342 −0.211899
\(376\) 36.3245 1.87329
\(377\) −8.03273 −0.413707
\(378\) −55.8267 −2.87142
\(379\) 17.3681 0.892140 0.446070 0.894998i \(-0.352823\pi\)
0.446070 + 0.894998i \(0.352823\pi\)
\(380\) 4.77286 0.244843
\(381\) −4.83283 −0.247593
\(382\) 24.8212 1.26996
\(383\) −1.83259 −0.0936411 −0.0468205 0.998903i \(-0.514909\pi\)
−0.0468205 + 0.998903i \(0.514909\pi\)
\(384\) 7.75339 0.395664
\(385\) 14.1386 0.720570
\(386\) −54.8244 −2.79049
\(387\) 3.76886 0.191582
\(388\) 32.7299 1.66161
\(389\) 11.7497 0.595736 0.297868 0.954607i \(-0.403725\pi\)
0.297868 + 0.954607i \(0.403725\pi\)
\(390\) 2.10554 0.106618
\(391\) 2.04546 0.103443
\(392\) −120.118 −6.06685
\(393\) −8.01795 −0.404452
\(394\) −21.9203 −1.10433
\(395\) 6.31748 0.317867
\(396\) 69.7382 3.50448
\(397\) 15.7363 0.789780 0.394890 0.918728i \(-0.370783\pi\)
0.394890 + 0.918728i \(0.370783\pi\)
\(398\) −33.9444 −1.70148
\(399\) 7.68358 0.384660
\(400\) −53.1823 −2.65911
\(401\) 9.62963 0.480881 0.240440 0.970664i \(-0.422708\pi\)
0.240440 + 0.970664i \(0.422708\pi\)
\(402\) −8.17165 −0.407565
\(403\) 1.01898 0.0507591
\(404\) 56.1009 2.79112
\(405\) −1.48153 −0.0736176
\(406\) −52.8496 −2.62288
\(407\) 47.8561 2.37214
\(408\) −2.49234 −0.123389
\(409\) −7.41399 −0.366598 −0.183299 0.983057i \(-0.558678\pi\)
−0.183299 + 0.983057i \(0.558678\pi\)
\(410\) −3.37279 −0.166570
\(411\) 4.53277 0.223585
\(412\) −66.7651 −3.28928
\(413\) −33.7455 −1.66051
\(414\) −33.7480 −1.65862
\(415\) 1.14788 0.0563470
\(416\) 25.7142 1.26074
\(417\) −7.99127 −0.391334
\(418\) −31.1183 −1.52205
\(419\) 36.3461 1.77562 0.887812 0.460207i \(-0.152225\pi\)
0.887812 + 0.460207i \(0.152225\pi\)
\(420\) 9.90776 0.483449
\(421\) −4.72614 −0.230338 −0.115169 0.993346i \(-0.536741\pi\)
−0.115169 + 0.993346i \(0.536741\pi\)
\(422\) −53.5138 −2.60501
\(423\) 10.3159 0.501577
\(424\) 8.01024 0.389012
\(425\) 1.73777 0.0842944
\(426\) 0.713428 0.0345657
\(427\) −8.73182 −0.422562
\(428\) −14.9233 −0.721343
\(429\) −9.81825 −0.474030
\(430\) −2.16854 −0.104576
\(431\) 22.1144 1.06521 0.532607 0.846363i \(-0.321212\pi\)
0.532607 + 0.846363i \(0.321212\pi\)
\(432\) 50.2279 2.41659
\(433\) 17.2282 0.827934 0.413967 0.910292i \(-0.364143\pi\)
0.413967 + 0.910292i \(0.364143\pi\)
\(434\) 6.70418 0.321811
\(435\) 1.78853 0.0857532
\(436\) 42.1775 2.01993
\(437\) 10.7703 0.515212
\(438\) 8.38051 0.400436
\(439\) −28.4781 −1.35918 −0.679592 0.733591i \(-0.737843\pi\)
−0.679592 + 0.733591i \(0.737843\pi\)
\(440\) −24.1482 −1.15122
\(441\) −34.1125 −1.62441
\(442\) −1.82911 −0.0870018
\(443\) 35.0044 1.66311 0.831555 0.555442i \(-0.187451\pi\)
0.831555 + 0.555442i \(0.187451\pi\)
\(444\) 33.5356 1.59153
\(445\) 5.44956 0.258334
\(446\) −46.3256 −2.19358
\(447\) 12.4521 0.588962
\(448\) 64.2949 3.03765
\(449\) −15.3300 −0.723465 −0.361733 0.932282i \(-0.617815\pi\)
−0.361733 + 0.932282i \(0.617815\pi\)
\(450\) −28.6715 −1.35159
\(451\) 15.7275 0.740578
\(452\) −63.8687 −3.00413
\(453\) −0.851556 −0.0400096
\(454\) −20.0165 −0.939420
\(455\) 4.37588 0.205145
\(456\) −13.1233 −0.614554
\(457\) −15.4767 −0.723970 −0.361985 0.932184i \(-0.617901\pi\)
−0.361985 + 0.932184i \(0.617901\pi\)
\(458\) −34.4437 −1.60945
\(459\) −1.64124 −0.0766063
\(460\) 13.8879 0.647529
\(461\) −29.3381 −1.36641 −0.683207 0.730225i \(-0.739415\pi\)
−0.683207 + 0.730225i \(0.739415\pi\)
\(462\) −64.5971 −3.00533
\(463\) −35.6005 −1.65450 −0.827248 0.561837i \(-0.810095\pi\)
−0.827248 + 0.561837i \(0.810095\pi\)
\(464\) 47.5493 2.20742
\(465\) −0.226881 −0.0105214
\(466\) 16.5821 0.768151
\(467\) −2.08640 −0.0965472 −0.0482736 0.998834i \(-0.515372\pi\)
−0.0482736 + 0.998834i \(0.515372\pi\)
\(468\) 21.5839 0.997716
\(469\) −16.9829 −0.784197
\(470\) −5.93560 −0.273789
\(471\) −0.319820 −0.0147365
\(472\) 57.6361 2.65292
\(473\) 10.1120 0.464951
\(474\) −28.8636 −1.32575
\(475\) 9.15017 0.419838
\(476\) −8.60698 −0.394500
\(477\) 2.27485 0.104158
\(478\) −53.8643 −2.46369
\(479\) −9.90491 −0.452567 −0.226283 0.974061i \(-0.572658\pi\)
−0.226283 + 0.974061i \(0.572658\pi\)
\(480\) −5.72539 −0.261327
\(481\) 14.8114 0.675342
\(482\) −10.9124 −0.497047
\(483\) 22.3575 1.01730
\(484\) 131.861 5.99368
\(485\) −3.21860 −0.146149
\(486\) 42.4794 1.92691
\(487\) −6.89602 −0.312489 −0.156244 0.987718i \(-0.549939\pi\)
−0.156244 + 0.987718i \(0.549939\pi\)
\(488\) 14.9136 0.675108
\(489\) 7.65940 0.346370
\(490\) 19.6278 0.886693
\(491\) 4.85311 0.219018 0.109509 0.993986i \(-0.465072\pi\)
0.109509 + 0.993986i \(0.465072\pi\)
\(492\) 11.0212 0.496873
\(493\) −1.55371 −0.0699757
\(494\) −9.63109 −0.433323
\(495\) −6.85793 −0.308241
\(496\) −6.03182 −0.270837
\(497\) 1.48270 0.0665080
\(498\) −5.24446 −0.235010
\(499\) 38.4464 1.72110 0.860549 0.509367i \(-0.170121\pi\)
0.860549 + 0.509367i \(0.170121\pi\)
\(500\) 24.2030 1.08239
\(501\) −18.0315 −0.805589
\(502\) 59.3219 2.64767
\(503\) −0.353789 −0.0157747 −0.00788733 0.999969i \(-0.502511\pi\)
−0.00788733 + 0.999969i \(0.502511\pi\)
\(504\) 85.4606 3.80672
\(505\) −5.51686 −0.245497
\(506\) −90.5473 −4.02532
\(507\) 8.03149 0.356691
\(508\) 28.5053 1.26472
\(509\) 1.26228 0.0559494 0.0279747 0.999609i \(-0.491094\pi\)
0.0279747 + 0.999609i \(0.491094\pi\)
\(510\) 0.407260 0.0180338
\(511\) 17.4170 0.770481
\(512\) 26.9279 1.19006
\(513\) −8.64186 −0.381547
\(514\) 66.9841 2.95454
\(515\) 6.56556 0.289313
\(516\) 7.08609 0.311948
\(517\) 27.6780 1.21728
\(518\) 97.4485 4.28164
\(519\) −5.62757 −0.247023
\(520\) −7.47385 −0.327750
\(521\) −30.8053 −1.34960 −0.674802 0.737999i \(-0.735771\pi\)
−0.674802 + 0.737999i \(0.735771\pi\)
\(522\) 25.6347 1.12200
\(523\) 3.82421 0.167221 0.0836105 0.996499i \(-0.473355\pi\)
0.0836105 + 0.996499i \(0.473355\pi\)
\(524\) 47.2919 2.06596
\(525\) 18.9944 0.828984
\(526\) 26.2293 1.14365
\(527\) 0.197094 0.00858557
\(528\) 58.1186 2.52929
\(529\) 8.33904 0.362567
\(530\) −1.30891 −0.0568555
\(531\) 16.3683 0.710322
\(532\) −45.3197 −1.96486
\(533\) 4.86764 0.210841
\(534\) −24.8982 −1.07745
\(535\) 1.46753 0.0634467
\(536\) 29.0062 1.25288
\(537\) −3.43013 −0.148021
\(538\) 46.6380 2.01071
\(539\) −91.5254 −3.94228
\(540\) −11.1434 −0.479537
\(541\) −16.3988 −0.705039 −0.352520 0.935804i \(-0.614675\pi\)
−0.352520 + 0.935804i \(0.614675\pi\)
\(542\) 56.1031 2.40983
\(543\) −9.47101 −0.406440
\(544\) 4.97371 0.213246
\(545\) −4.14766 −0.177666
\(546\) −19.9927 −0.855609
\(547\) 9.49316 0.405898 0.202949 0.979189i \(-0.434947\pi\)
0.202949 + 0.979189i \(0.434947\pi\)
\(548\) −26.7354 −1.14208
\(549\) 4.23537 0.180761
\(550\) −76.9269 −3.28017
\(551\) −8.18100 −0.348523
\(552\) −38.1858 −1.62529
\(553\) −59.9863 −2.55088
\(554\) −35.6372 −1.51408
\(555\) −3.29783 −0.139985
\(556\) 47.1345 1.99895
\(557\) 14.3081 0.606255 0.303128 0.952950i \(-0.401969\pi\)
0.303128 + 0.952950i \(0.401969\pi\)
\(558\) −3.25186 −0.137662
\(559\) 3.12966 0.132371
\(560\) −25.9028 −1.09459
\(561\) −1.89907 −0.0801789
\(562\) 55.0884 2.32376
\(563\) 5.73632 0.241757 0.120878 0.992667i \(-0.461429\pi\)
0.120878 + 0.992667i \(0.461429\pi\)
\(564\) 19.3956 0.816704
\(565\) 6.28074 0.264233
\(566\) 88.0079 3.69925
\(567\) 14.0675 0.590780
\(568\) −2.53239 −0.106257
\(569\) 14.2455 0.597204 0.298602 0.954378i \(-0.403480\pi\)
0.298602 + 0.954378i \(0.403480\pi\)
\(570\) 2.14441 0.0898193
\(571\) −17.6283 −0.737722 −0.368861 0.929485i \(-0.620252\pi\)
−0.368861 + 0.929485i \(0.620252\pi\)
\(572\) 57.9105 2.42136
\(573\) 7.97597 0.333201
\(574\) 32.0256 1.33672
\(575\) 26.6249 1.11034
\(576\) −31.1862 −1.29943
\(577\) −0.902406 −0.0375676 −0.0187838 0.999824i \(-0.505979\pi\)
−0.0187838 + 0.999824i \(0.505979\pi\)
\(578\) 44.6968 1.85914
\(579\) −17.6171 −0.732143
\(580\) −10.5492 −0.438031
\(581\) −10.8994 −0.452184
\(582\) 14.7053 0.609553
\(583\) 6.10353 0.252782
\(584\) −29.7476 −1.23096
\(585\) −2.12252 −0.0877554
\(586\) −10.1930 −0.421069
\(587\) −14.2569 −0.588447 −0.294223 0.955737i \(-0.595061\pi\)
−0.294223 + 0.955737i \(0.595061\pi\)
\(588\) −64.1373 −2.64498
\(589\) 1.03779 0.0427615
\(590\) −9.41802 −0.387734
\(591\) −7.04381 −0.289744
\(592\) −87.6754 −3.60344
\(593\) 38.6368 1.58663 0.793313 0.608815i \(-0.208355\pi\)
0.793313 + 0.608815i \(0.208355\pi\)
\(594\) 72.6534 2.98101
\(595\) 0.846395 0.0346988
\(596\) −73.4454 −3.00844
\(597\) −10.9076 −0.446418
\(598\) −28.0243 −1.14600
\(599\) −37.4739 −1.53114 −0.765572 0.643350i \(-0.777544\pi\)
−0.765572 + 0.643350i \(0.777544\pi\)
\(600\) −32.4418 −1.32443
\(601\) −19.6052 −0.799713 −0.399856 0.916578i \(-0.630940\pi\)
−0.399856 + 0.916578i \(0.630940\pi\)
\(602\) 20.5909 0.839224
\(603\) 8.23755 0.335459
\(604\) 5.02269 0.204370
\(605\) −12.9670 −0.527182
\(606\) 25.2057 1.02391
\(607\) −0.395047 −0.0160345 −0.00801723 0.999968i \(-0.502552\pi\)
−0.00801723 + 0.999968i \(0.502552\pi\)
\(608\) 26.1889 1.06210
\(609\) −16.9826 −0.688168
\(610\) −2.43696 −0.0986696
\(611\) 8.56632 0.346556
\(612\) 4.17482 0.168757
\(613\) 27.3613 1.10511 0.552556 0.833476i \(-0.313653\pi\)
0.552556 + 0.833476i \(0.313653\pi\)
\(614\) −24.8269 −1.00193
\(615\) −1.08380 −0.0437031
\(616\) 229.294 9.23853
\(617\) 28.5308 1.14861 0.574303 0.818643i \(-0.305273\pi\)
0.574303 + 0.818643i \(0.305273\pi\)
\(618\) −29.9970 −1.20666
\(619\) −17.0164 −0.683945 −0.341973 0.939710i \(-0.611095\pi\)
−0.341973 + 0.939710i \(0.611095\pi\)
\(620\) 1.33820 0.0537435
\(621\) −25.1458 −1.00907
\(622\) 76.9298 3.08461
\(623\) −51.7451 −2.07312
\(624\) 17.9877 0.720083
\(625\) 21.4001 0.856005
\(626\) 8.80423 0.351888
\(627\) −9.99948 −0.399341
\(628\) 1.88638 0.0752746
\(629\) 2.86486 0.114230
\(630\) −13.9647 −0.556366
\(631\) −15.6008 −0.621058 −0.310529 0.950564i \(-0.600506\pi\)
−0.310529 + 0.950564i \(0.600506\pi\)
\(632\) 102.454 4.07542
\(633\) −17.1960 −0.683479
\(634\) −62.0125 −2.46283
\(635\) −2.80315 −0.111240
\(636\) 4.27710 0.169598
\(637\) −28.3270 −1.12236
\(638\) 68.7790 2.72299
\(639\) −0.719182 −0.0284504
\(640\) 4.49715 0.177765
\(641\) 13.6920 0.540800 0.270400 0.962748i \(-0.412844\pi\)
0.270400 + 0.962748i \(0.412844\pi\)
\(642\) −6.70489 −0.264621
\(643\) −3.87942 −0.152989 −0.0764946 0.997070i \(-0.524373\pi\)
−0.0764946 + 0.997070i \(0.524373\pi\)
\(644\) −131.870 −5.19641
\(645\) −0.696834 −0.0274378
\(646\) −1.86287 −0.0732937
\(647\) 13.5149 0.531325 0.265662 0.964066i \(-0.414409\pi\)
0.265662 + 0.964066i \(0.414409\pi\)
\(648\) −24.0268 −0.943862
\(649\) 43.9167 1.72388
\(650\) −23.8088 −0.933858
\(651\) 2.15430 0.0844338
\(652\) −45.1771 −1.76927
\(653\) 22.2678 0.871405 0.435703 0.900091i \(-0.356500\pi\)
0.435703 + 0.900091i \(0.356500\pi\)
\(654\) 18.9500 0.741003
\(655\) −4.65060 −0.181714
\(656\) −28.8137 −1.12499
\(657\) −8.44810 −0.329592
\(658\) 56.3603 2.19715
\(659\) −34.7186 −1.35245 −0.676223 0.736697i \(-0.736384\pi\)
−0.676223 + 0.736697i \(0.736384\pi\)
\(660\) −12.8940 −0.501900
\(661\) 1.57901 0.0614166 0.0307083 0.999528i \(-0.490224\pi\)
0.0307083 + 0.999528i \(0.490224\pi\)
\(662\) 2.88585 0.112162
\(663\) −0.587761 −0.0228267
\(664\) 18.6158 0.722433
\(665\) 4.45666 0.172822
\(666\) −47.2674 −1.83157
\(667\) −23.8049 −0.921729
\(668\) 106.354 4.11498
\(669\) −14.8861 −0.575531
\(670\) −4.73975 −0.183112
\(671\) 11.3637 0.438689
\(672\) 54.3642 2.09715
\(673\) −16.2056 −0.624681 −0.312340 0.949970i \(-0.601113\pi\)
−0.312340 + 0.949970i \(0.601113\pi\)
\(674\) 40.8018 1.57163
\(675\) −21.3633 −0.822275
\(676\) −47.3718 −1.82199
\(677\) 45.9766 1.76702 0.883511 0.468410i \(-0.155173\pi\)
0.883511 + 0.468410i \(0.155173\pi\)
\(678\) −28.6957 −1.10205
\(679\) 30.5615 1.17284
\(680\) −1.44561 −0.0554367
\(681\) −6.43204 −0.246476
\(682\) −8.72488 −0.334093
\(683\) 6.98130 0.267132 0.133566 0.991040i \(-0.457357\pi\)
0.133566 + 0.991040i \(0.457357\pi\)
\(684\) 21.9823 0.840515
\(685\) 2.62911 0.100453
\(686\) −99.3721 −3.79404
\(687\) −11.0680 −0.422272
\(688\) −18.5259 −0.706292
\(689\) 1.88903 0.0719665
\(690\) 6.23974 0.237543
\(691\) −24.2430 −0.922249 −0.461124 0.887335i \(-0.652554\pi\)
−0.461124 + 0.887335i \(0.652554\pi\)
\(692\) 33.1928 1.26180
\(693\) 65.1180 2.47363
\(694\) 8.90786 0.338138
\(695\) −4.63512 −0.175820
\(696\) 29.0056 1.09945
\(697\) 0.941512 0.0356623
\(698\) −18.6600 −0.706290
\(699\) 5.32845 0.201541
\(700\) −112.034 −4.23448
\(701\) 24.5747 0.928172 0.464086 0.885790i \(-0.346383\pi\)
0.464086 + 0.885790i \(0.346383\pi\)
\(702\) 22.4862 0.848685
\(703\) 15.0848 0.568935
\(704\) −83.6740 −3.15358
\(705\) −1.90733 −0.0718343
\(706\) 40.3347 1.51802
\(707\) 52.3842 1.97011
\(708\) 30.7751 1.15660
\(709\) −32.3302 −1.21418 −0.607092 0.794631i \(-0.707664\pi\)
−0.607092 + 0.794631i \(0.707664\pi\)
\(710\) 0.413805 0.0155298
\(711\) 29.0963 1.09120
\(712\) 88.3788 3.31213
\(713\) 3.01974 0.113090
\(714\) −3.86705 −0.144721
\(715\) −5.69481 −0.212974
\(716\) 20.2318 0.756098
\(717\) −17.3086 −0.646402
\(718\) −99.1018 −3.69845
\(719\) 19.6843 0.734102 0.367051 0.930201i \(-0.380367\pi\)
0.367051 + 0.930201i \(0.380367\pi\)
\(720\) 12.5642 0.468239
\(721\) −62.3419 −2.32173
\(722\) 40.5418 1.50881
\(723\) −3.50657 −0.130411
\(724\) 55.8624 2.07611
\(725\) −20.2241 −0.751103
\(726\) 59.2440 2.19875
\(727\) 17.7409 0.657974 0.328987 0.944334i \(-0.393293\pi\)
0.328987 + 0.944334i \(0.393293\pi\)
\(728\) 70.9664 2.63019
\(729\) 4.65169 0.172285
\(730\) 4.86089 0.179910
\(731\) 0.605348 0.0223896
\(732\) 7.96319 0.294328
\(733\) −14.2305 −0.525614 −0.262807 0.964848i \(-0.584648\pi\)
−0.262807 + 0.964848i \(0.584648\pi\)
\(734\) −35.9629 −1.32741
\(735\) 6.30715 0.232643
\(736\) 76.2037 2.80890
\(737\) 22.1017 0.814126
\(738\) −15.5340 −0.571814
\(739\) 15.7298 0.578630 0.289315 0.957234i \(-0.406572\pi\)
0.289315 + 0.957234i \(0.406572\pi\)
\(740\) 19.4514 0.715049
\(741\) −3.09483 −0.113691
\(742\) 12.4285 0.456265
\(743\) 21.6632 0.794747 0.397373 0.917657i \(-0.369922\pi\)
0.397373 + 0.917657i \(0.369922\pi\)
\(744\) −3.67947 −0.134896
\(745\) 7.22249 0.264612
\(746\) −68.6665 −2.51406
\(747\) 5.28675 0.193432
\(748\) 11.2012 0.409557
\(749\) −13.9346 −0.509158
\(750\) 10.8742 0.397070
\(751\) −22.9959 −0.839132 −0.419566 0.907725i \(-0.637818\pi\)
−0.419566 + 0.907725i \(0.637818\pi\)
\(752\) −50.7079 −1.84913
\(753\) 19.0624 0.694671
\(754\) 21.2870 0.775228
\(755\) −0.493922 −0.0179757
\(756\) 105.810 3.84827
\(757\) 28.0600 1.01986 0.509929 0.860216i \(-0.329672\pi\)
0.509929 + 0.860216i \(0.329672\pi\)
\(758\) −46.0261 −1.67174
\(759\) −29.0962 −1.05613
\(760\) −7.61181 −0.276109
\(761\) 49.3032 1.78724 0.893620 0.448823i \(-0.148157\pi\)
0.893620 + 0.448823i \(0.148157\pi\)
\(762\) 12.8072 0.463955
\(763\) 39.3832 1.42577
\(764\) −47.0443 −1.70200
\(765\) −0.410544 −0.0148432
\(766\) 4.85643 0.175470
\(767\) 13.5922 0.490785
\(768\) 2.80141 0.101087
\(769\) −29.2106 −1.05336 −0.526680 0.850064i \(-0.676563\pi\)
−0.526680 + 0.850064i \(0.676563\pi\)
\(770\) −37.4678 −1.35025
\(771\) 21.5245 0.775186
\(772\) 103.910 3.73981
\(773\) −26.3542 −0.947893 −0.473947 0.880554i \(-0.657171\pi\)
−0.473947 + 0.880554i \(0.657171\pi\)
\(774\) −9.98763 −0.358998
\(775\) 2.56550 0.0921556
\(776\) −52.1980 −1.87380
\(777\) 31.3139 1.12338
\(778\) −31.1372 −1.11632
\(779\) 4.95749 0.177620
\(780\) −3.99069 −0.142890
\(781\) −1.92959 −0.0690463
\(782\) −5.42054 −0.193838
\(783\) 19.1006 0.682599
\(784\) 167.680 5.98859
\(785\) −0.185503 −0.00662088
\(786\) 21.2479 0.757886
\(787\) 18.5046 0.659617 0.329809 0.944048i \(-0.393016\pi\)
0.329809 + 0.944048i \(0.393016\pi\)
\(788\) 41.5462 1.48002
\(789\) 8.42847 0.300061
\(790\) −16.7415 −0.595637
\(791\) −59.6374 −2.12046
\(792\) −111.219 −3.95200
\(793\) 3.51704 0.124894
\(794\) −41.7017 −1.47994
\(795\) −0.420603 −0.0149172
\(796\) 64.3358 2.28032
\(797\) −40.0113 −1.41727 −0.708637 0.705573i \(-0.750690\pi\)
−0.708637 + 0.705573i \(0.750690\pi\)
\(798\) −20.3618 −0.720799
\(799\) 1.65692 0.0586177
\(800\) 64.7409 2.28894
\(801\) 25.0990 0.886828
\(802\) −25.5189 −0.901103
\(803\) −22.6666 −0.799887
\(804\) 15.4880 0.546218
\(805\) 12.9679 0.457057
\(806\) −2.70034 −0.0951155
\(807\) 14.9865 0.527551
\(808\) −89.4703 −3.14755
\(809\) −0.207180 −0.00728408 −0.00364204 0.999993i \(-0.501159\pi\)
−0.00364204 + 0.999993i \(0.501159\pi\)
\(810\) 3.92610 0.137949
\(811\) −54.9165 −1.92838 −0.964189 0.265216i \(-0.914557\pi\)
−0.964189 + 0.265216i \(0.914557\pi\)
\(812\) 100.167 3.51519
\(813\) 18.0280 0.632271
\(814\) −126.820 −4.44505
\(815\) 4.44263 0.155619
\(816\) 3.47922 0.121797
\(817\) 3.18743 0.111514
\(818\) 19.6473 0.686953
\(819\) 20.1539 0.704236
\(820\) 6.39254 0.223237
\(821\) 50.5332 1.76362 0.881811 0.471603i \(-0.156324\pi\)
0.881811 + 0.471603i \(0.156324\pi\)
\(822\) −12.0120 −0.418967
\(823\) −34.8676 −1.21541 −0.607705 0.794163i \(-0.707910\pi\)
−0.607705 + 0.794163i \(0.707910\pi\)
\(824\) 106.478 3.70932
\(825\) −24.7195 −0.860622
\(826\) 89.4269 3.11156
\(827\) 24.9528 0.867694 0.433847 0.900986i \(-0.357156\pi\)
0.433847 + 0.900986i \(0.357156\pi\)
\(828\) 63.9636 2.22289
\(829\) −40.9995 −1.42397 −0.711985 0.702194i \(-0.752204\pi\)
−0.711985 + 0.702194i \(0.752204\pi\)
\(830\) −3.04191 −0.105586
\(831\) −11.4516 −0.397251
\(832\) −25.8970 −0.897817
\(833\) −5.47909 −0.189839
\(834\) 21.1772 0.733305
\(835\) −10.4587 −0.361938
\(836\) 58.9795 2.03985
\(837\) −2.42298 −0.0837505
\(838\) −96.3185 −3.32727
\(839\) −22.9893 −0.793678 −0.396839 0.917888i \(-0.629893\pi\)
−0.396839 + 0.917888i \(0.629893\pi\)
\(840\) −15.8010 −0.545186
\(841\) −10.9180 −0.376483
\(842\) 12.5244 0.431621
\(843\) 17.7020 0.609688
\(844\) 101.426 3.49123
\(845\) 4.65845 0.160256
\(846\) −27.3375 −0.939884
\(847\) 123.125 4.23063
\(848\) −11.1820 −0.383993
\(849\) 28.2802 0.970575
\(850\) −4.60516 −0.157956
\(851\) 43.8934 1.50465
\(852\) −1.35218 −0.0463250
\(853\) −17.1989 −0.588880 −0.294440 0.955670i \(-0.595133\pi\)
−0.294440 + 0.955670i \(0.595133\pi\)
\(854\) 23.1396 0.791822
\(855\) −2.16170 −0.0739286
\(856\) 23.7998 0.813459
\(857\) 47.9179 1.63684 0.818422 0.574618i \(-0.194849\pi\)
0.818422 + 0.574618i \(0.194849\pi\)
\(858\) 26.0187 0.888264
\(859\) 41.9550 1.43149 0.715743 0.698364i \(-0.246088\pi\)
0.715743 + 0.698364i \(0.246088\pi\)
\(860\) 4.11010 0.140153
\(861\) 10.2910 0.350717
\(862\) −58.6040 −1.99606
\(863\) −44.9833 −1.53125 −0.765624 0.643288i \(-0.777570\pi\)
−0.765624 + 0.643288i \(0.777570\pi\)
\(864\) −61.1444 −2.08017
\(865\) −3.26412 −0.110984
\(866\) −45.6553 −1.55143
\(867\) 14.3628 0.487785
\(868\) −12.7066 −0.431291
\(869\) 78.0667 2.64823
\(870\) −4.73966 −0.160689
\(871\) 6.84045 0.231780
\(872\) −67.2651 −2.27788
\(873\) −14.8239 −0.501712
\(874\) −28.5416 −0.965434
\(875\) 22.5995 0.764003
\(876\) −15.8838 −0.536665
\(877\) −17.1959 −0.580664 −0.290332 0.956926i \(-0.593766\pi\)
−0.290332 + 0.956926i \(0.593766\pi\)
\(878\) 75.4679 2.54692
\(879\) −3.27539 −0.110476
\(880\) 33.7102 1.13637
\(881\) −8.84278 −0.297921 −0.148960 0.988843i \(-0.547593\pi\)
−0.148960 + 0.988843i \(0.547593\pi\)
\(882\) 90.3995 3.04391
\(883\) 6.31514 0.212521 0.106261 0.994338i \(-0.466112\pi\)
0.106261 + 0.994338i \(0.466112\pi\)
\(884\) 3.46676 0.116600
\(885\) −3.02636 −0.101730
\(886\) −92.7630 −3.11643
\(887\) 36.1368 1.21335 0.606677 0.794949i \(-0.292502\pi\)
0.606677 + 0.794949i \(0.292502\pi\)
\(888\) −53.4829 −1.79477
\(889\) 26.6168 0.892698
\(890\) −14.4415 −0.484081
\(891\) −18.3076 −0.613328
\(892\) 87.8022 2.93984
\(893\) 8.72444 0.291952
\(894\) −32.9984 −1.10363
\(895\) −1.98956 −0.0665036
\(896\) −42.7017 −1.42656
\(897\) −9.00525 −0.300677
\(898\) 40.6249 1.35567
\(899\) −2.29377 −0.0765015
\(900\) 54.3420 1.81140
\(901\) 0.365382 0.0121727
\(902\) −41.6784 −1.38774
\(903\) 6.61664 0.220188
\(904\) 101.859 3.38776
\(905\) −5.49341 −0.182607
\(906\) 2.25665 0.0749723
\(907\) 29.3011 0.972927 0.486463 0.873701i \(-0.338287\pi\)
0.486463 + 0.873701i \(0.338287\pi\)
\(908\) 37.9378 1.25901
\(909\) −25.4089 −0.842761
\(910\) −11.5962 −0.384412
\(911\) 33.0124 1.09375 0.546874 0.837215i \(-0.315818\pi\)
0.546874 + 0.837215i \(0.315818\pi\)
\(912\) 18.3197 0.606626
\(913\) 14.1846 0.469441
\(914\) 41.0139 1.35662
\(915\) −0.783086 −0.0258880
\(916\) 65.2821 2.15698
\(917\) 44.1588 1.45825
\(918\) 4.34934 0.143549
\(919\) −38.8358 −1.28107 −0.640537 0.767927i \(-0.721288\pi\)
−0.640537 + 0.767927i \(0.721288\pi\)
\(920\) −22.1486 −0.730219
\(921\) −7.97782 −0.262878
\(922\) 77.7471 2.56046
\(923\) −0.597207 −0.0196573
\(924\) 122.433 4.02774
\(925\) 37.2908 1.22611
\(926\) 94.3426 3.10029
\(927\) 30.2389 0.993176
\(928\) −57.8837 −1.90013
\(929\) −1.11650 −0.0366312 −0.0183156 0.999832i \(-0.505830\pi\)
−0.0183156 + 0.999832i \(0.505830\pi\)
\(930\) 0.601244 0.0197156
\(931\) −28.8499 −0.945518
\(932\) −31.4285 −1.02948
\(933\) 24.7204 0.809311
\(934\) 5.52905 0.180916
\(935\) −1.10151 −0.0360231
\(936\) −34.4222 −1.12513
\(937\) 5.76560 0.188354 0.0941770 0.995555i \(-0.469978\pi\)
0.0941770 + 0.995555i \(0.469978\pi\)
\(938\) 45.0053 1.46947
\(939\) 2.82913 0.0923251
\(940\) 11.2499 0.366932
\(941\) 7.29849 0.237924 0.118962 0.992899i \(-0.462043\pi\)
0.118962 + 0.992899i \(0.462043\pi\)
\(942\) 0.847534 0.0276141
\(943\) 14.4252 0.469748
\(944\) −80.4583 −2.61869
\(945\) −10.4052 −0.338480
\(946\) −26.7972 −0.871253
\(947\) 29.1982 0.948815 0.474407 0.880305i \(-0.342662\pi\)
0.474407 + 0.880305i \(0.342662\pi\)
\(948\) 54.7060 1.77677
\(949\) −7.01529 −0.227726
\(950\) −24.2483 −0.786718
\(951\) −19.9269 −0.646175
\(952\) 13.7265 0.444879
\(953\) −11.0857 −0.359102 −0.179551 0.983749i \(-0.557464\pi\)
−0.179551 + 0.983749i \(0.557464\pi\)
\(954\) −6.02844 −0.195178
\(955\) 4.62625 0.149702
\(956\) 102.091 3.30184
\(957\) 22.1013 0.714433
\(958\) 26.2484 0.848046
\(959\) −24.9642 −0.806135
\(960\) 5.76609 0.186100
\(961\) −30.7090 −0.990614
\(962\) −39.2508 −1.26550
\(963\) 6.75897 0.217805
\(964\) 20.6826 0.666143
\(965\) −10.2183 −0.328940
\(966\) −59.2481 −1.90628
\(967\) −52.5166 −1.68882 −0.844410 0.535697i \(-0.820049\pi\)
−0.844410 + 0.535697i \(0.820049\pi\)
\(968\) −210.293 −6.75908
\(969\) −0.598610 −0.0192301
\(970\) 8.52941 0.273863
\(971\) −18.3920 −0.590227 −0.295114 0.955462i \(-0.595357\pi\)
−0.295114 + 0.955462i \(0.595357\pi\)
\(972\) −80.5125 −2.58244
\(973\) 44.0118 1.41095
\(974\) 18.2747 0.585559
\(975\) −7.65066 −0.245017
\(976\) −20.8190 −0.666399
\(977\) 23.3472 0.746944 0.373472 0.927642i \(-0.378167\pi\)
0.373472 + 0.927642i \(0.378167\pi\)
\(978\) −20.2977 −0.649048
\(979\) 67.3416 2.15225
\(980\) −37.2011 −1.18835
\(981\) −19.1028 −0.609906
\(982\) −12.8609 −0.410408
\(983\) −14.5159 −0.462986 −0.231493 0.972837i \(-0.574361\pi\)
−0.231493 + 0.972837i \(0.574361\pi\)
\(984\) −17.5767 −0.560324
\(985\) −4.08557 −0.130177
\(986\) 4.11739 0.131125
\(987\) 18.1107 0.576469
\(988\) 18.2541 0.580740
\(989\) 9.27470 0.294918
\(990\) 18.1738 0.577600
\(991\) 8.48021 0.269383 0.134691 0.990888i \(-0.456996\pi\)
0.134691 + 0.990888i \(0.456996\pi\)
\(992\) 7.34277 0.233133
\(993\) 0.927330 0.0294279
\(994\) −3.92920 −0.124627
\(995\) −6.32667 −0.200569
\(996\) 9.93998 0.314960
\(997\) −17.6544 −0.559119 −0.279560 0.960128i \(-0.590188\pi\)
−0.279560 + 0.960128i \(0.590188\pi\)
\(998\) −101.884 −3.22509
\(999\) −35.2192 −1.11429
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 \(a_p\))