Properties

Label 8003.2.a.c.1.16
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 1.16
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.39169 q^{2}\) \(-2.70490 q^{3}\) \(+3.72019 q^{4}\) \(+3.87028 q^{5}\) \(+6.46929 q^{6}\) \(-0.448223 q^{7}\) \(-4.11416 q^{8}\) \(+4.31650 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.39169 q^{2}\) \(-2.70490 q^{3}\) \(+3.72019 q^{4}\) \(+3.87028 q^{5}\) \(+6.46929 q^{6}\) \(-0.448223 q^{7}\) \(-4.11416 q^{8}\) \(+4.31650 q^{9}\) \(-9.25652 q^{10}\) \(+1.05036 q^{11}\) \(-10.0627 q^{12}\) \(-1.18419 q^{13}\) \(+1.07201 q^{14}\) \(-10.4687 q^{15}\) \(+2.39942 q^{16}\) \(+4.93717 q^{17}\) \(-10.3237 q^{18}\) \(-3.82010 q^{19}\) \(+14.3982 q^{20}\) \(+1.21240 q^{21}\) \(-2.51213 q^{22}\) \(-1.26401 q^{23}\) \(+11.1284 q^{24}\) \(+9.97908 q^{25}\) \(+2.83223 q^{26}\) \(-3.56101 q^{27}\) \(-1.66747 q^{28}\) \(+7.55593 q^{29}\) \(+25.0380 q^{30}\) \(-5.15642 q^{31}\) \(+2.48964 q^{32}\) \(-2.84111 q^{33}\) \(-11.8082 q^{34}\) \(-1.73475 q^{35}\) \(+16.0582 q^{36}\) \(+3.83586 q^{37}\) \(+9.13651 q^{38}\) \(+3.20313 q^{39}\) \(-15.9229 q^{40}\) \(-3.73658 q^{41}\) \(-2.89968 q^{42}\) \(-10.6396 q^{43}\) \(+3.90752 q^{44}\) \(+16.7061 q^{45}\) \(+3.02313 q^{46}\) \(-6.33948 q^{47}\) \(-6.49020 q^{48}\) \(-6.79910 q^{49}\) \(-23.8669 q^{50}\) \(-13.3546 q^{51}\) \(-4.40543 q^{52}\) \(-1.00000 q^{53}\) \(+8.51683 q^{54}\) \(+4.06517 q^{55}\) \(+1.84406 q^{56}\) \(+10.3330 q^{57}\) \(-18.0715 q^{58}\) \(-2.84970 q^{59}\) \(-38.9457 q^{60}\) \(-15.1761 q^{61}\) \(+12.3326 q^{62}\) \(-1.93475 q^{63}\) \(-10.7533 q^{64}\) \(-4.58317 q^{65}\) \(+6.79506 q^{66}\) \(+14.2853 q^{67}\) \(+18.3672 q^{68}\) \(+3.41903 q^{69}\) \(+4.14898 q^{70}\) \(+13.8121 q^{71}\) \(-17.7588 q^{72}\) \(+10.5536 q^{73}\) \(-9.17419 q^{74}\) \(-26.9925 q^{75}\) \(-14.2115 q^{76}\) \(-0.470793 q^{77}\) \(-7.66090 q^{78}\) \(-14.9888 q^{79}\) \(+9.28643 q^{80}\) \(-3.31733 q^{81}\) \(+8.93673 q^{82}\) \(+8.77655 q^{83}\) \(+4.51035 q^{84}\) \(+19.1082 q^{85}\) \(+25.4466 q^{86}\) \(-20.4381 q^{87}\) \(-4.32133 q^{88}\) \(+5.60844 q^{89}\) \(-39.9558 q^{90}\) \(+0.530783 q^{91}\) \(-4.70236 q^{92}\) \(+13.9476 q^{93}\) \(+15.1621 q^{94}\) \(-14.7849 q^{95}\) \(-6.73425 q^{96}\) \(-0.789133 q^{97}\) \(+16.2613 q^{98}\) \(+4.53386 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39169 −1.69118 −0.845591 0.533832i \(-0.820751\pi\)
−0.845591 + 0.533832i \(0.820751\pi\)
\(3\) −2.70490 −1.56168 −0.780838 0.624733i \(-0.785208\pi\)
−0.780838 + 0.624733i \(0.785208\pi\)
\(4\) 3.72019 1.86009
\(5\) 3.87028 1.73084 0.865421 0.501045i \(-0.167051\pi\)
0.865421 + 0.501045i \(0.167051\pi\)
\(6\) 6.46929 2.64108
\(7\) −0.448223 −0.169412 −0.0847061 0.996406i \(-0.526995\pi\)
−0.0847061 + 0.996406i \(0.526995\pi\)
\(8\) −4.11416 −1.45457
\(9\) 4.31650 1.43883
\(10\) −9.25652 −2.92717
\(11\) 1.05036 0.316694 0.158347 0.987384i \(-0.449384\pi\)
0.158347 + 0.987384i \(0.449384\pi\)
\(12\) −10.0627 −2.90486
\(13\) −1.18419 −0.328437 −0.164218 0.986424i \(-0.552510\pi\)
−0.164218 + 0.986424i \(0.552510\pi\)
\(14\) 1.07201 0.286507
\(15\) −10.4687 −2.70302
\(16\) 2.39942 0.599855
\(17\) 4.93717 1.19744 0.598719 0.800959i \(-0.295677\pi\)
0.598719 + 0.800959i \(0.295677\pi\)
\(18\) −10.3237 −2.43333
\(19\) −3.82010 −0.876392 −0.438196 0.898879i \(-0.644382\pi\)
−0.438196 + 0.898879i \(0.644382\pi\)
\(20\) 14.3982 3.21953
\(21\) 1.21240 0.264567
\(22\) −2.51213 −0.535587
\(23\) −1.26401 −0.263565 −0.131782 0.991279i \(-0.542070\pi\)
−0.131782 + 0.991279i \(0.542070\pi\)
\(24\) 11.1284 2.27157
\(25\) 9.97908 1.99582
\(26\) 2.83223 0.555446
\(27\) −3.56101 −0.685316
\(28\) −1.66747 −0.315123
\(29\) 7.55593 1.40310 0.701551 0.712619i \(-0.252491\pi\)
0.701551 + 0.712619i \(0.252491\pi\)
\(30\) 25.0380 4.57129
\(31\) −5.15642 −0.926120 −0.463060 0.886327i \(-0.653249\pi\)
−0.463060 + 0.886327i \(0.653249\pi\)
\(32\) 2.48964 0.440111
\(33\) −2.84111 −0.494574
\(34\) −11.8082 −2.02509
\(35\) −1.73475 −0.293226
\(36\) 16.0582 2.67637
\(37\) 3.83586 0.630611 0.315306 0.948990i \(-0.397893\pi\)
0.315306 + 0.948990i \(0.397893\pi\)
\(38\) 9.13651 1.48214
\(39\) 3.20313 0.512912
\(40\) −15.9229 −2.51764
\(41\) −3.73658 −0.583555 −0.291778 0.956486i \(-0.594247\pi\)
−0.291778 + 0.956486i \(0.594247\pi\)
\(42\) −2.89968 −0.447431
\(43\) −10.6396 −1.62252 −0.811261 0.584684i \(-0.801219\pi\)
−0.811261 + 0.584684i \(0.801219\pi\)
\(44\) 3.90752 0.589081
\(45\) 16.7061 2.49039
\(46\) 3.02313 0.445736
\(47\) −6.33948 −0.924709 −0.462354 0.886695i \(-0.652995\pi\)
−0.462354 + 0.886695i \(0.652995\pi\)
\(48\) −6.49020 −0.936779
\(49\) −6.79910 −0.971299
\(50\) −23.8669 −3.37529
\(51\) −13.3546 −1.87001
\(52\) −4.40543 −0.610923
\(53\) −1.00000 −0.137361
\(54\) 8.51683 1.15899
\(55\) 4.06517 0.548148
\(56\) 1.84406 0.246423
\(57\) 10.3330 1.36864
\(58\) −18.0715 −2.37290
\(59\) −2.84970 −0.370999 −0.185499 0.982644i \(-0.559390\pi\)
−0.185499 + 0.982644i \(0.559390\pi\)
\(60\) −38.9457 −5.02786
\(61\) −15.1761 −1.94310 −0.971550 0.236835i \(-0.923890\pi\)
−0.971550 + 0.236835i \(0.923890\pi\)
\(62\) 12.3326 1.56624
\(63\) −1.93475 −0.243756
\(64\) −10.7533 −1.34416
\(65\) −4.58317 −0.568472
\(66\) 6.79506 0.836414
\(67\) 14.2853 1.74522 0.872612 0.488415i \(-0.162425\pi\)
0.872612 + 0.488415i \(0.162425\pi\)
\(68\) 18.3672 2.22735
\(69\) 3.41903 0.411603
\(70\) 4.14898 0.495898
\(71\) 13.8121 1.63919 0.819595 0.572944i \(-0.194199\pi\)
0.819595 + 0.572944i \(0.194199\pi\)
\(72\) −17.7588 −2.09289
\(73\) 10.5536 1.23521 0.617605 0.786488i \(-0.288103\pi\)
0.617605 + 0.786488i \(0.288103\pi\)
\(74\) −9.17419 −1.06648
\(75\) −26.9925 −3.11682
\(76\) −14.2115 −1.63017
\(77\) −0.470793 −0.0536519
\(78\) −7.66090 −0.867426
\(79\) −14.9888 −1.68637 −0.843184 0.537626i \(-0.819321\pi\)
−0.843184 + 0.537626i \(0.819321\pi\)
\(80\) 9.28643 1.03825
\(81\) −3.31733 −0.368592
\(82\) 8.93673 0.986897
\(83\) 8.77655 0.963352 0.481676 0.876349i \(-0.340028\pi\)
0.481676 + 0.876349i \(0.340028\pi\)
\(84\) 4.51035 0.492120
\(85\) 19.1082 2.07258
\(86\) 25.4466 2.74398
\(87\) −20.4381 −2.19119
\(88\) −4.32133 −0.460655
\(89\) 5.60844 0.594494 0.297247 0.954801i \(-0.403932\pi\)
0.297247 + 0.954801i \(0.403932\pi\)
\(90\) −39.9558 −4.21171
\(91\) 0.530783 0.0556412
\(92\) −4.70236 −0.490255
\(93\) 13.9476 1.44630
\(94\) 15.1621 1.56385
\(95\) −14.7849 −1.51690
\(96\) −6.73425 −0.687311
\(97\) −0.789133 −0.0801243 −0.0400622 0.999197i \(-0.512756\pi\)
−0.0400622 + 0.999197i \(0.512756\pi\)
\(98\) 16.2613 1.64264
\(99\) 4.53386 0.455670
\(100\) 37.1241 3.71241
\(101\) 4.23498 0.421396 0.210698 0.977551i \(-0.432426\pi\)
0.210698 + 0.977551i \(0.432426\pi\)
\(102\) 31.9400 3.16253
\(103\) 10.3585 1.02066 0.510329 0.859979i \(-0.329524\pi\)
0.510329 + 0.859979i \(0.329524\pi\)
\(104\) 4.87196 0.477735
\(105\) 4.69233 0.457924
\(106\) 2.39169 0.232302
\(107\) −4.66932 −0.451400 −0.225700 0.974197i \(-0.572467\pi\)
−0.225700 + 0.974197i \(0.572467\pi\)
\(108\) −13.2476 −1.27475
\(109\) 6.48667 0.621310 0.310655 0.950523i \(-0.399452\pi\)
0.310655 + 0.950523i \(0.399452\pi\)
\(110\) −9.72264 −0.927017
\(111\) −10.3756 −0.984811
\(112\) −1.07547 −0.101623
\(113\) 10.2030 0.959821 0.479911 0.877317i \(-0.340669\pi\)
0.479911 + 0.877317i \(0.340669\pi\)
\(114\) −24.7134 −2.31462
\(115\) −4.89208 −0.456189
\(116\) 28.1095 2.60990
\(117\) −5.11158 −0.472565
\(118\) 6.81559 0.627426
\(119\) −2.21295 −0.202861
\(120\) 43.0700 3.93174
\(121\) −9.89675 −0.899705
\(122\) 36.2965 3.28613
\(123\) 10.1071 0.911324
\(124\) −19.1828 −1.72267
\(125\) 19.2705 1.72360
\(126\) 4.62733 0.412236
\(127\) 17.4823 1.55130 0.775652 0.631161i \(-0.217421\pi\)
0.775652 + 0.631161i \(0.217421\pi\)
\(128\) 20.7393 1.83311
\(129\) 28.7791 2.53386
\(130\) 10.9615 0.961389
\(131\) 1.59621 0.139462 0.0697309 0.997566i \(-0.477786\pi\)
0.0697309 + 0.997566i \(0.477786\pi\)
\(132\) −10.5695 −0.919953
\(133\) 1.71226 0.148472
\(134\) −34.1660 −2.95149
\(135\) −13.7821 −1.18617
\(136\) −20.3123 −1.74176
\(137\) 16.3099 1.39345 0.696723 0.717340i \(-0.254641\pi\)
0.696723 + 0.717340i \(0.254641\pi\)
\(138\) −8.17726 −0.696095
\(139\) −3.52706 −0.299161 −0.149581 0.988750i \(-0.547792\pi\)
−0.149581 + 0.988750i \(0.547792\pi\)
\(140\) −6.45359 −0.545428
\(141\) 17.1477 1.44410
\(142\) −33.0342 −2.77217
\(143\) −1.24383 −0.104014
\(144\) 10.3571 0.863091
\(145\) 29.2436 2.42855
\(146\) −25.2411 −2.08897
\(147\) 18.3909 1.51686
\(148\) 14.2701 1.17300
\(149\) 0.588110 0.0481798 0.0240899 0.999710i \(-0.492331\pi\)
0.0240899 + 0.999710i \(0.492331\pi\)
\(150\) 64.5576 5.27111
\(151\) 1.00000 0.0813788
\(152\) 15.7165 1.27478
\(153\) 21.3113 1.72291
\(154\) 1.12599 0.0907350
\(155\) −19.9568 −1.60297
\(156\) 11.9163 0.954064
\(157\) 13.3085 1.06213 0.531067 0.847330i \(-0.321791\pi\)
0.531067 + 0.847330i \(0.321791\pi\)
\(158\) 35.8485 2.85195
\(159\) 2.70490 0.214513
\(160\) 9.63563 0.761763
\(161\) 0.566559 0.0446511
\(162\) 7.93402 0.623355
\(163\) −21.5246 −1.68594 −0.842968 0.537964i \(-0.819193\pi\)
−0.842968 + 0.537964i \(0.819193\pi\)
\(164\) −13.9008 −1.08547
\(165\) −10.9959 −0.856029
\(166\) −20.9908 −1.62920
\(167\) −14.8656 −1.15034 −0.575169 0.818035i \(-0.695064\pi\)
−0.575169 + 0.818035i \(0.695064\pi\)
\(168\) −4.98800 −0.384833
\(169\) −11.5977 −0.892129
\(170\) −45.7010 −3.50510
\(171\) −16.4895 −1.26098
\(172\) −39.5813 −3.01804
\(173\) 20.9921 1.59600 0.797999 0.602658i \(-0.205892\pi\)
0.797999 + 0.602658i \(0.205892\pi\)
\(174\) 48.8816 3.70570
\(175\) −4.47285 −0.338116
\(176\) 2.52024 0.189970
\(177\) 7.70815 0.579380
\(178\) −13.4137 −1.00540
\(179\) 7.23183 0.540532 0.270266 0.962786i \(-0.412888\pi\)
0.270266 + 0.962786i \(0.412888\pi\)
\(180\) 62.1497 4.63237
\(181\) −1.10604 −0.0822113 −0.0411057 0.999155i \(-0.513088\pi\)
−0.0411057 + 0.999155i \(0.513088\pi\)
\(182\) −1.26947 −0.0940993
\(183\) 41.0499 3.03449
\(184\) 5.20034 0.383374
\(185\) 14.8459 1.09149
\(186\) −33.3584 −2.44596
\(187\) 5.18578 0.379222
\(188\) −23.5841 −1.72005
\(189\) 1.59612 0.116101
\(190\) 35.3609 2.56535
\(191\) 18.4150 1.33246 0.666230 0.745746i \(-0.267907\pi\)
0.666230 + 0.745746i \(0.267907\pi\)
\(192\) 29.0866 2.09915
\(193\) −25.1176 −1.80800 −0.904002 0.427528i \(-0.859385\pi\)
−0.904002 + 0.427528i \(0.859385\pi\)
\(194\) 1.88736 0.135505
\(195\) 12.3970 0.887769
\(196\) −25.2939 −1.80671
\(197\) 5.07158 0.361335 0.180668 0.983544i \(-0.442174\pi\)
0.180668 + 0.983544i \(0.442174\pi\)
\(198\) −10.8436 −0.770621
\(199\) 24.3833 1.72848 0.864241 0.503077i \(-0.167799\pi\)
0.864241 + 0.503077i \(0.167799\pi\)
\(200\) −41.0555 −2.90306
\(201\) −38.6403 −2.72547
\(202\) −10.1288 −0.712657
\(203\) −3.38674 −0.237703
\(204\) −49.6814 −3.47840
\(205\) −14.4616 −1.01004
\(206\) −24.7744 −1.72612
\(207\) −5.45611 −0.379226
\(208\) −2.84138 −0.197014
\(209\) −4.01247 −0.277548
\(210\) −11.2226 −0.774433
\(211\) 16.4126 1.12989 0.564944 0.825129i \(-0.308898\pi\)
0.564944 + 0.825129i \(0.308898\pi\)
\(212\) −3.72019 −0.255504
\(213\) −37.3603 −2.55988
\(214\) 11.1676 0.763400
\(215\) −41.1782 −2.80833
\(216\) 14.6505 0.996843
\(217\) 2.31122 0.156896
\(218\) −15.5141 −1.05075
\(219\) −28.5466 −1.92900
\(220\) 15.1232 1.01961
\(221\) −5.84656 −0.393283
\(222\) 24.8153 1.66549
\(223\) −12.3841 −0.829299 −0.414650 0.909981i \(-0.636096\pi\)
−0.414650 + 0.909981i \(0.636096\pi\)
\(224\) −1.11592 −0.0745602
\(225\) 43.0747 2.87165
\(226\) −24.4025 −1.62323
\(227\) 24.8458 1.64908 0.824538 0.565807i \(-0.191435\pi\)
0.824538 + 0.565807i \(0.191435\pi\)
\(228\) 38.4407 2.54580
\(229\) −7.16757 −0.473646 −0.236823 0.971553i \(-0.576106\pi\)
−0.236823 + 0.971553i \(0.576106\pi\)
\(230\) 11.7004 0.771498
\(231\) 1.27345 0.0837869
\(232\) −31.0863 −2.04092
\(233\) 11.4617 0.750878 0.375439 0.926847i \(-0.377492\pi\)
0.375439 + 0.926847i \(0.377492\pi\)
\(234\) 12.2253 0.799194
\(235\) −24.5356 −1.60053
\(236\) −10.6014 −0.690093
\(237\) 40.5431 2.63356
\(238\) 5.29269 0.343074
\(239\) 24.2458 1.56833 0.784164 0.620554i \(-0.213092\pi\)
0.784164 + 0.620554i \(0.213092\pi\)
\(240\) −25.1189 −1.62142
\(241\) 24.2028 1.55904 0.779521 0.626376i \(-0.215463\pi\)
0.779521 + 0.626376i \(0.215463\pi\)
\(242\) 23.6700 1.52156
\(243\) 19.6561 1.26094
\(244\) −56.4579 −3.61435
\(245\) −26.3144 −1.68117
\(246\) −24.1730 −1.54121
\(247\) 4.52375 0.287839
\(248\) 21.2143 1.34711
\(249\) −23.7397 −1.50444
\(250\) −46.0890 −2.91492
\(251\) −19.3814 −1.22334 −0.611671 0.791112i \(-0.709502\pi\)
−0.611671 + 0.791112i \(0.709502\pi\)
\(252\) −7.19765 −0.453409
\(253\) −1.32766 −0.0834694
\(254\) −41.8123 −2.62353
\(255\) −51.6859 −3.23670
\(256\) −28.0954 −1.75596
\(257\) 25.8622 1.61324 0.806621 0.591069i \(-0.201294\pi\)
0.806621 + 0.591069i \(0.201294\pi\)
\(258\) −68.8306 −4.28521
\(259\) −1.71932 −0.106833
\(260\) −17.0502 −1.05741
\(261\) 32.6152 2.01883
\(262\) −3.81765 −0.235855
\(263\) −19.8085 −1.22144 −0.610722 0.791845i \(-0.709121\pi\)
−0.610722 + 0.791845i \(0.709121\pi\)
\(264\) 11.6888 0.719394
\(265\) −3.87028 −0.237750
\(266\) −4.09519 −0.251092
\(267\) −15.1703 −0.928407
\(268\) 53.1439 3.24628
\(269\) −27.2617 −1.66218 −0.831088 0.556141i \(-0.812281\pi\)
−0.831088 + 0.556141i \(0.812281\pi\)
\(270\) 32.9625 2.00604
\(271\) −14.4840 −0.879842 −0.439921 0.898036i \(-0.644994\pi\)
−0.439921 + 0.898036i \(0.644994\pi\)
\(272\) 11.8463 0.718289
\(273\) −1.43572 −0.0868935
\(274\) −39.0082 −2.35657
\(275\) 10.4816 0.632063
\(276\) 12.7194 0.765620
\(277\) 7.69069 0.462089 0.231044 0.972943i \(-0.425786\pi\)
0.231044 + 0.972943i \(0.425786\pi\)
\(278\) 8.43564 0.505936
\(279\) −22.2577 −1.33253
\(280\) 7.13703 0.426519
\(281\) −10.4230 −0.621787 −0.310893 0.950445i \(-0.600628\pi\)
−0.310893 + 0.950445i \(0.600628\pi\)
\(282\) −41.0120 −2.44223
\(283\) 3.74403 0.222560 0.111280 0.993789i \(-0.464505\pi\)
0.111280 + 0.993789i \(0.464505\pi\)
\(284\) 51.3834 3.04905
\(285\) 39.9917 2.36890
\(286\) 2.97485 0.175906
\(287\) 1.67482 0.0988614
\(288\) 10.7466 0.633247
\(289\) 7.37560 0.433859
\(290\) −69.9417 −4.10712
\(291\) 2.13453 0.125128
\(292\) 39.2615 2.29761
\(293\) −3.97012 −0.231937 −0.115968 0.993253i \(-0.536997\pi\)
−0.115968 + 0.993253i \(0.536997\pi\)
\(294\) −43.9853 −2.56528
\(295\) −11.0291 −0.642141
\(296\) −15.7813 −0.917271
\(297\) −3.74032 −0.217036
\(298\) −1.40658 −0.0814808
\(299\) 1.49684 0.0865643
\(300\) −100.417 −5.79758
\(301\) 4.76891 0.274875
\(302\) −2.39169 −0.137626
\(303\) −11.4552 −0.658084
\(304\) −9.16603 −0.525708
\(305\) −58.7358 −3.36320
\(306\) −50.9700 −2.91376
\(307\) 17.2052 0.981954 0.490977 0.871172i \(-0.336640\pi\)
0.490977 + 0.871172i \(0.336640\pi\)
\(308\) −1.75144 −0.0997975
\(309\) −28.0189 −1.59394
\(310\) 47.7305 2.71091
\(311\) 5.78665 0.328131 0.164066 0.986449i \(-0.447539\pi\)
0.164066 + 0.986449i \(0.447539\pi\)
\(312\) −13.1782 −0.746068
\(313\) −17.7720 −1.00453 −0.502266 0.864713i \(-0.667500\pi\)
−0.502266 + 0.864713i \(0.667500\pi\)
\(314\) −31.8298 −1.79626
\(315\) −7.48804 −0.421903
\(316\) −55.7610 −3.13680
\(317\) −17.4780 −0.981660 −0.490830 0.871255i \(-0.663306\pi\)
−0.490830 + 0.871255i \(0.663306\pi\)
\(318\) −6.46929 −0.362780
\(319\) 7.93642 0.444354
\(320\) −41.6183 −2.32653
\(321\) 12.6301 0.704941
\(322\) −1.35503 −0.0755131
\(323\) −18.8605 −1.04943
\(324\) −12.3411 −0.685615
\(325\) −11.8172 −0.655499
\(326\) 51.4801 2.85122
\(327\) −17.5458 −0.970286
\(328\) 15.3729 0.848824
\(329\) 2.84150 0.156657
\(330\) 26.2988 1.44770
\(331\) 29.1935 1.60462 0.802309 0.596908i \(-0.203604\pi\)
0.802309 + 0.596908i \(0.203604\pi\)
\(332\) 32.6504 1.79192
\(333\) 16.5575 0.907345
\(334\) 35.5540 1.94543
\(335\) 55.2880 3.02071
\(336\) 2.90905 0.158702
\(337\) 29.1847 1.58979 0.794896 0.606745i \(-0.207525\pi\)
0.794896 + 0.606745i \(0.207525\pi\)
\(338\) 27.7381 1.50875
\(339\) −27.5982 −1.49893
\(340\) 71.0862 3.85519
\(341\) −5.41607 −0.293297
\(342\) 39.4377 2.13255
\(343\) 6.18507 0.333962
\(344\) 43.7729 2.36008
\(345\) 13.2326 0.712420
\(346\) −50.2066 −2.69912
\(347\) −22.5446 −1.21026 −0.605130 0.796127i \(-0.706879\pi\)
−0.605130 + 0.796127i \(0.706879\pi\)
\(348\) −76.0334 −4.07582
\(349\) 15.5629 0.833060 0.416530 0.909122i \(-0.363246\pi\)
0.416530 + 0.909122i \(0.363246\pi\)
\(350\) 10.6977 0.571815
\(351\) 4.21692 0.225083
\(352\) 2.61501 0.139381
\(353\) −0.142293 −0.00757352 −0.00378676 0.999993i \(-0.501205\pi\)
−0.00378676 + 0.999993i \(0.501205\pi\)
\(354\) −18.4355 −0.979837
\(355\) 53.4565 2.83718
\(356\) 20.8645 1.10581
\(357\) 5.98581 0.316803
\(358\) −17.2963 −0.914138
\(359\) −19.8288 −1.04652 −0.523261 0.852173i \(-0.675285\pi\)
−0.523261 + 0.852173i \(0.675285\pi\)
\(360\) −68.7314 −3.62246
\(361\) −4.40681 −0.231937
\(362\) 2.64531 0.139034
\(363\) 26.7698 1.40505
\(364\) 1.97461 0.103498
\(365\) 40.8456 2.13796
\(366\) −98.1786 −5.13188
\(367\) 14.5906 0.761623 0.380812 0.924653i \(-0.375645\pi\)
0.380812 + 0.924653i \(0.375645\pi\)
\(368\) −3.03289 −0.158101
\(369\) −16.1289 −0.839638
\(370\) −35.5067 −1.84591
\(371\) 0.448223 0.0232706
\(372\) 51.8877 2.69025
\(373\) −24.6611 −1.27690 −0.638452 0.769662i \(-0.720425\pi\)
−0.638452 + 0.769662i \(0.720425\pi\)
\(374\) −12.4028 −0.641333
\(375\) −52.1247 −2.69171
\(376\) 26.0816 1.34506
\(377\) −8.94770 −0.460830
\(378\) −3.81744 −0.196348
\(379\) 27.3965 1.40726 0.703631 0.710565i \(-0.251561\pi\)
0.703631 + 0.710565i \(0.251561\pi\)
\(380\) −55.0025 −2.82157
\(381\) −47.2879 −2.42263
\(382\) −44.0429 −2.25343
\(383\) −3.00462 −0.153529 −0.0767644 0.997049i \(-0.524459\pi\)
−0.0767644 + 0.997049i \(0.524459\pi\)
\(384\) −56.0977 −2.86273
\(385\) −1.82210 −0.0928629
\(386\) 60.0735 3.05766
\(387\) −45.9258 −2.33454
\(388\) −2.93572 −0.149039
\(389\) 32.5015 1.64789 0.823945 0.566670i \(-0.191769\pi\)
0.823945 + 0.566670i \(0.191769\pi\)
\(390\) −29.6499 −1.50138
\(391\) −6.24064 −0.315602
\(392\) 27.9725 1.41283
\(393\) −4.31760 −0.217794
\(394\) −12.1297 −0.611083
\(395\) −58.0107 −2.91884
\(396\) 16.8668 0.847589
\(397\) 6.67097 0.334806 0.167403 0.985889i \(-0.446462\pi\)
0.167403 + 0.985889i \(0.446462\pi\)
\(398\) −58.3172 −2.92318
\(399\) −4.63149 −0.231864
\(400\) 23.9440 1.19720
\(401\) 3.37448 0.168514 0.0842569 0.996444i \(-0.473148\pi\)
0.0842569 + 0.996444i \(0.473148\pi\)
\(402\) 92.4156 4.60927
\(403\) 6.10621 0.304172
\(404\) 15.7549 0.783836
\(405\) −12.8390 −0.637974
\(406\) 8.10004 0.401998
\(407\) 4.02901 0.199711
\(408\) 54.9427 2.72007
\(409\) −7.74593 −0.383012 −0.191506 0.981491i \(-0.561337\pi\)
−0.191506 + 0.981491i \(0.561337\pi\)
\(410\) 34.5877 1.70816
\(411\) −44.1166 −2.17611
\(412\) 38.5357 1.89852
\(413\) 1.27730 0.0628517
\(414\) 13.0493 0.641339
\(415\) 33.9677 1.66741
\(416\) −2.94822 −0.144549
\(417\) 9.54035 0.467193
\(418\) 9.59658 0.469384
\(419\) −35.1455 −1.71697 −0.858486 0.512837i \(-0.828594\pi\)
−0.858486 + 0.512837i \(0.828594\pi\)
\(420\) 17.4563 0.851782
\(421\) 2.27247 0.110753 0.0553767 0.998466i \(-0.482364\pi\)
0.0553767 + 0.998466i \(0.482364\pi\)
\(422\) −39.2538 −1.91085
\(423\) −27.3644 −1.33050
\(424\) 4.11416 0.199801
\(425\) 49.2684 2.38987
\(426\) 89.3542 4.32923
\(427\) 6.80227 0.329185
\(428\) −17.3707 −0.839647
\(429\) 3.36443 0.162436
\(430\) 98.4856 4.74940
\(431\) 2.13556 0.102866 0.0514331 0.998676i \(-0.483621\pi\)
0.0514331 + 0.998676i \(0.483621\pi\)
\(432\) −8.54435 −0.411090
\(433\) 29.4260 1.41412 0.707061 0.707153i \(-0.250021\pi\)
0.707061 + 0.707153i \(0.250021\pi\)
\(434\) −5.52774 −0.265340
\(435\) −79.1011 −3.79261
\(436\) 24.1316 1.15570
\(437\) 4.82866 0.230986
\(438\) 68.2746 3.26229
\(439\) 8.95868 0.427574 0.213787 0.976880i \(-0.431420\pi\)
0.213787 + 0.976880i \(0.431420\pi\)
\(440\) −16.7248 −0.797321
\(441\) −29.3483 −1.39754
\(442\) 13.9832 0.665112
\(443\) −10.3797 −0.493153 −0.246576 0.969123i \(-0.579306\pi\)
−0.246576 + 0.969123i \(0.579306\pi\)
\(444\) −38.5993 −1.83184
\(445\) 21.7063 1.02898
\(446\) 29.6189 1.40250
\(447\) −1.59078 −0.0752413
\(448\) 4.81987 0.227718
\(449\) −24.7946 −1.17013 −0.585065 0.810986i \(-0.698931\pi\)
−0.585065 + 0.810986i \(0.698931\pi\)
\(450\) −103.021 −4.85648
\(451\) −3.92473 −0.184808
\(452\) 37.9572 1.78536
\(453\) −2.70490 −0.127087
\(454\) −59.4235 −2.78888
\(455\) 2.05428 0.0963061
\(456\) −42.5116 −1.99079
\(457\) 10.3022 0.481916 0.240958 0.970536i \(-0.422538\pi\)
0.240958 + 0.970536i \(0.422538\pi\)
\(458\) 17.1426 0.801021
\(459\) −17.5813 −0.820624
\(460\) −18.1995 −0.848554
\(461\) −14.7074 −0.684994 −0.342497 0.939519i \(-0.611273\pi\)
−0.342497 + 0.939519i \(0.611273\pi\)
\(462\) −3.04570 −0.141699
\(463\) −20.3812 −0.947196 −0.473598 0.880741i \(-0.657045\pi\)
−0.473598 + 0.880741i \(0.657045\pi\)
\(464\) 18.1299 0.841657
\(465\) 53.9812 2.50332
\(466\) −27.4127 −1.26987
\(467\) 37.1890 1.72090 0.860451 0.509533i \(-0.170182\pi\)
0.860451 + 0.509533i \(0.170182\pi\)
\(468\) −19.0160 −0.879016
\(469\) −6.40298 −0.295662
\(470\) 58.6816 2.70678
\(471\) −35.9982 −1.65871
\(472\) 11.7241 0.539645
\(473\) −11.1754 −0.513843
\(474\) −96.9667 −4.45383
\(475\) −38.1211 −1.74912
\(476\) −8.23259 −0.377340
\(477\) −4.31650 −0.197639
\(478\) −57.9884 −2.65233
\(479\) −13.3152 −0.608386 −0.304193 0.952610i \(-0.598387\pi\)
−0.304193 + 0.952610i \(0.598387\pi\)
\(480\) −26.0634 −1.18963
\(481\) −4.54240 −0.207116
\(482\) −57.8857 −2.63662
\(483\) −1.53249 −0.0697306
\(484\) −36.8178 −1.67354
\(485\) −3.05417 −0.138683
\(486\) −47.0112 −2.13247
\(487\) −38.6096 −1.74957 −0.874783 0.484515i \(-0.838996\pi\)
−0.874783 + 0.484515i \(0.838996\pi\)
\(488\) 62.4368 2.82638
\(489\) 58.2219 2.63289
\(490\) 62.9360 2.84316
\(491\) −34.0796 −1.53799 −0.768996 0.639253i \(-0.779244\pi\)
−0.768996 + 0.639253i \(0.779244\pi\)
\(492\) 37.6002 1.69515
\(493\) 37.3049 1.68013
\(494\) −10.8194 −0.486788
\(495\) 17.5473 0.788693
\(496\) −12.3724 −0.555538
\(497\) −6.19088 −0.277699
\(498\) 56.7781 2.54429
\(499\) 17.5904 0.787456 0.393728 0.919227i \(-0.371185\pi\)
0.393728 + 0.919227i \(0.371185\pi\)
\(500\) 71.6897 3.20606
\(501\) 40.2101 1.79646
\(502\) 46.3543 2.06889
\(503\) −2.42370 −0.108068 −0.0540338 0.998539i \(-0.517208\pi\)
−0.0540338 + 0.998539i \(0.517208\pi\)
\(504\) 7.95988 0.354561
\(505\) 16.3906 0.729370
\(506\) 3.17536 0.141162
\(507\) 31.3706 1.39322
\(508\) 65.0374 2.88557
\(509\) 22.4246 0.993954 0.496977 0.867764i \(-0.334443\pi\)
0.496977 + 0.867764i \(0.334443\pi\)
\(510\) 123.617 5.47384
\(511\) −4.73038 −0.209260
\(512\) 25.7169 1.13654
\(513\) 13.6034 0.600605
\(514\) −61.8545 −2.72828
\(515\) 40.0905 1.76660
\(516\) 107.064 4.71321
\(517\) −6.65871 −0.292850
\(518\) 4.11208 0.180674
\(519\) −56.7815 −2.49243
\(520\) 18.8559 0.826885
\(521\) 16.5027 0.722997 0.361499 0.932373i \(-0.382265\pi\)
0.361499 + 0.932373i \(0.382265\pi\)
\(522\) −78.0055 −3.41421
\(523\) 14.6709 0.641512 0.320756 0.947162i \(-0.396063\pi\)
0.320756 + 0.947162i \(0.396063\pi\)
\(524\) 5.93821 0.259412
\(525\) 12.0986 0.528028
\(526\) 47.3758 2.06568
\(527\) −25.4581 −1.10897
\(528\) −6.81701 −0.296672
\(529\) −21.4023 −0.930534
\(530\) 9.25652 0.402078
\(531\) −12.3007 −0.533806
\(532\) 6.36992 0.276171
\(533\) 4.42483 0.191661
\(534\) 36.2827 1.57010
\(535\) −18.0716 −0.781303
\(536\) −58.7718 −2.53856
\(537\) −19.5614 −0.844136
\(538\) 65.2016 2.81104
\(539\) −7.14147 −0.307605
\(540\) −51.2720 −2.20639
\(541\) 6.83314 0.293780 0.146890 0.989153i \(-0.453074\pi\)
0.146890 + 0.989153i \(0.453074\pi\)
\(542\) 34.6413 1.48797
\(543\) 2.99173 0.128387
\(544\) 12.2918 0.527006
\(545\) 25.1052 1.07539
\(546\) 3.43379 0.146953
\(547\) −18.1637 −0.776623 −0.388311 0.921528i \(-0.626941\pi\)
−0.388311 + 0.921528i \(0.626941\pi\)
\(548\) 60.6757 2.59194
\(549\) −65.5076 −2.79580
\(550\) −25.0687 −1.06893
\(551\) −28.8645 −1.22967
\(552\) −14.0664 −0.598707
\(553\) 6.71830 0.285691
\(554\) −18.3938 −0.781476
\(555\) −40.1566 −1.70455
\(556\) −13.1213 −0.556468
\(557\) −8.68874 −0.368154 −0.184077 0.982912i \(-0.558930\pi\)
−0.184077 + 0.982912i \(0.558930\pi\)
\(558\) 53.2335 2.25355
\(559\) 12.5993 0.532896
\(560\) −4.16239 −0.175893
\(561\) −14.0270 −0.592222
\(562\) 24.9287 1.05155
\(563\) −9.24161 −0.389487 −0.194744 0.980854i \(-0.562388\pi\)
−0.194744 + 0.980854i \(0.562388\pi\)
\(564\) 63.7926 2.68615
\(565\) 39.4886 1.66130
\(566\) −8.95457 −0.376389
\(567\) 1.48690 0.0624440
\(568\) −56.8250 −2.38432
\(569\) −7.89008 −0.330769 −0.165385 0.986229i \(-0.552887\pi\)
−0.165385 + 0.986229i \(0.552887\pi\)
\(570\) −95.6477 −4.00624
\(571\) 7.40686 0.309967 0.154984 0.987917i \(-0.450467\pi\)
0.154984 + 0.987917i \(0.450467\pi\)
\(572\) −4.62726 −0.193476
\(573\) −49.8107 −2.08087
\(574\) −4.00565 −0.167192
\(575\) −12.6137 −0.526027
\(576\) −46.4166 −1.93403
\(577\) 46.4834 1.93513 0.967566 0.252620i \(-0.0812922\pi\)
0.967566 + 0.252620i \(0.0812922\pi\)
\(578\) −17.6402 −0.733734
\(579\) 67.9407 2.82352
\(580\) 108.792 4.51733
\(581\) −3.93385 −0.163204
\(582\) −5.10513 −0.211615
\(583\) −1.05036 −0.0435013
\(584\) −43.4194 −1.79671
\(585\) −19.7832 −0.817937
\(586\) 9.49530 0.392247
\(587\) −8.39052 −0.346314 −0.173157 0.984894i \(-0.555397\pi\)
−0.173157 + 0.984894i \(0.555397\pi\)
\(588\) 68.4176 2.82149
\(589\) 19.6981 0.811644
\(590\) 26.3783 1.08598
\(591\) −13.7181 −0.564289
\(592\) 9.20383 0.378275
\(593\) 23.3843 0.960278 0.480139 0.877193i \(-0.340586\pi\)
0.480139 + 0.877193i \(0.340586\pi\)
\(594\) 8.94570 0.367046
\(595\) −8.56474 −0.351120
\(596\) 2.18788 0.0896190
\(597\) −65.9543 −2.69933
\(598\) −3.57997 −0.146396
\(599\) −11.7449 −0.479883 −0.239942 0.970787i \(-0.577128\pi\)
−0.239942 + 0.970787i \(0.577128\pi\)
\(600\) 111.051 4.53365
\(601\) −11.9460 −0.487289 −0.243645 0.969865i \(-0.578343\pi\)
−0.243645 + 0.969865i \(0.578343\pi\)
\(602\) −11.4058 −0.464864
\(603\) 61.6624 2.51109
\(604\) 3.72019 0.151372
\(605\) −38.3032 −1.55725
\(606\) 27.3973 1.11294
\(607\) 17.7751 0.721470 0.360735 0.932668i \(-0.382526\pi\)
0.360735 + 0.932668i \(0.382526\pi\)
\(608\) −9.51070 −0.385710
\(609\) 9.16081 0.371215
\(610\) 140.478 5.68778
\(611\) 7.50718 0.303708
\(612\) 79.2819 3.20478
\(613\) −40.4649 −1.63436 −0.817182 0.576380i \(-0.804465\pi\)
−0.817182 + 0.576380i \(0.804465\pi\)
\(614\) −41.1496 −1.66066
\(615\) 39.1172 1.57736
\(616\) 1.93692 0.0780406
\(617\) −46.9633 −1.89067 −0.945336 0.326097i \(-0.894266\pi\)
−0.945336 + 0.326097i \(0.894266\pi\)
\(618\) 67.0124 2.69564
\(619\) 35.1944 1.41458 0.707291 0.706922i \(-0.249917\pi\)
0.707291 + 0.706922i \(0.249917\pi\)
\(620\) −74.2430 −2.98167
\(621\) 4.50115 0.180625
\(622\) −13.8399 −0.554929
\(623\) −2.51383 −0.100715
\(624\) 7.68565 0.307672
\(625\) 24.6867 0.987468
\(626\) 42.5051 1.69885
\(627\) 10.8533 0.433440
\(628\) 49.5101 1.97567
\(629\) 18.9383 0.755118
\(630\) 17.9091 0.713515
\(631\) 28.4848 1.13396 0.566981 0.823731i \(-0.308111\pi\)
0.566981 + 0.823731i \(0.308111\pi\)
\(632\) 61.6661 2.45295
\(633\) −44.3944 −1.76452
\(634\) 41.8019 1.66016
\(635\) 67.6614 2.68506
\(636\) 10.0627 0.399014
\(637\) 8.05145 0.319010
\(638\) −18.9815 −0.751483
\(639\) 59.6197 2.35852
\(640\) 80.2669 3.17283
\(641\) 24.5148 0.968276 0.484138 0.874992i \(-0.339133\pi\)
0.484138 + 0.874992i \(0.339133\pi\)
\(642\) −30.2072 −1.19218
\(643\) −48.8650 −1.92705 −0.963524 0.267620i \(-0.913763\pi\)
−0.963524 + 0.267620i \(0.913763\pi\)
\(644\) 2.10770 0.0830552
\(645\) 111.383 4.38571
\(646\) 45.1085 1.77477
\(647\) 45.3741 1.78384 0.891920 0.452192i \(-0.149358\pi\)
0.891920 + 0.452192i \(0.149358\pi\)
\(648\) 13.6480 0.536144
\(649\) −2.99319 −0.117493
\(650\) 28.2630 1.10857
\(651\) −6.25164 −0.245021
\(652\) −80.0755 −3.13600
\(653\) −6.56459 −0.256892 −0.128446 0.991716i \(-0.540999\pi\)
−0.128446 + 0.991716i \(0.540999\pi\)
\(654\) 41.9642 1.64093
\(655\) 6.17780 0.241386
\(656\) −8.96561 −0.350048
\(657\) 45.5548 1.77726
\(658\) −6.79599 −0.264935
\(659\) 6.21299 0.242024 0.121012 0.992651i \(-0.461386\pi\)
0.121012 + 0.992651i \(0.461386\pi\)
\(660\) −40.9068 −1.59229
\(661\) −15.9371 −0.619880 −0.309940 0.950756i \(-0.600309\pi\)
−0.309940 + 0.950756i \(0.600309\pi\)
\(662\) −69.8218 −2.71370
\(663\) 15.8144 0.614180
\(664\) −36.1081 −1.40127
\(665\) 6.62692 0.256981
\(666\) −39.6004 −1.53448
\(667\) −9.55079 −0.369808
\(668\) −55.3030 −2.13974
\(669\) 33.4977 1.29510
\(670\) −132.232 −5.10856
\(671\) −15.9403 −0.615368
\(672\) 3.01844 0.116439
\(673\) 0.102951 0.00396847 0.00198424 0.999998i \(-0.499368\pi\)
0.00198424 + 0.999998i \(0.499368\pi\)
\(674\) −69.8008 −2.68863
\(675\) −35.5356 −1.36777
\(676\) −43.1456 −1.65944
\(677\) 14.3249 0.550551 0.275276 0.961365i \(-0.411231\pi\)
0.275276 + 0.961365i \(0.411231\pi\)
\(678\) 66.0064 2.53496
\(679\) 0.353707 0.0135740
\(680\) −78.6142 −3.01472
\(681\) −67.2055 −2.57532
\(682\) 12.9536 0.496018
\(683\) 43.0990 1.64914 0.824569 0.565762i \(-0.191418\pi\)
0.824569 + 0.565762i \(0.191418\pi\)
\(684\) −61.3439 −2.34554
\(685\) 63.1238 2.41184
\(686\) −14.7928 −0.564791
\(687\) 19.3876 0.739682
\(688\) −25.5288 −0.973278
\(689\) 1.18419 0.0451142
\(690\) −31.6483 −1.20483
\(691\) 13.0820 0.497661 0.248831 0.968547i \(-0.419954\pi\)
0.248831 + 0.968547i \(0.419954\pi\)
\(692\) 78.0945 2.96871
\(693\) −2.03218 −0.0771961
\(694\) 53.9198 2.04677
\(695\) −13.6507 −0.517801
\(696\) 84.0854 3.18725
\(697\) −18.4481 −0.698771
\(698\) −37.2215 −1.40886
\(699\) −31.0027 −1.17263
\(700\) −16.6398 −0.628927
\(701\) 34.2201 1.29247 0.646237 0.763137i \(-0.276342\pi\)
0.646237 + 0.763137i \(0.276342\pi\)
\(702\) −10.0856 −0.380656
\(703\) −14.6534 −0.552663
\(704\) −11.2948 −0.425688
\(705\) 66.3664 2.49950
\(706\) 0.340322 0.0128082
\(707\) −1.89821 −0.0713896
\(708\) 28.6758 1.07770
\(709\) 25.8747 0.971747 0.485873 0.874029i \(-0.338502\pi\)
0.485873 + 0.874029i \(0.338502\pi\)
\(710\) −127.852 −4.79818
\(711\) −64.6990 −2.42640
\(712\) −23.0740 −0.864735
\(713\) 6.51778 0.244093
\(714\) −14.3162 −0.535771
\(715\) −4.81396 −0.180032
\(716\) 26.9038 1.00544
\(717\) −65.5824 −2.44922
\(718\) 47.4243 1.76986
\(719\) 36.1869 1.34954 0.674772 0.738026i \(-0.264242\pi\)
0.674772 + 0.738026i \(0.264242\pi\)
\(720\) 40.0849 1.49387
\(721\) −4.64293 −0.172912
\(722\) 10.5397 0.392248
\(723\) −65.4663 −2.43472
\(724\) −4.11468 −0.152921
\(725\) 75.4013 2.80033
\(726\) −64.0250 −2.37619
\(727\) 28.7514 1.06633 0.533165 0.846012i \(-0.321003\pi\)
0.533165 + 0.846012i \(0.321003\pi\)
\(728\) −2.18372 −0.0809342
\(729\) −43.2158 −1.60058
\(730\) −97.6900 −3.61567
\(731\) −52.5294 −1.94287
\(732\) 152.713 5.64444
\(733\) −44.2125 −1.63303 −0.816513 0.577327i \(-0.804096\pi\)
−0.816513 + 0.577327i \(0.804096\pi\)
\(734\) −34.8962 −1.28804
\(735\) 71.1780 2.62544
\(736\) −3.14694 −0.115998
\(737\) 15.0046 0.552702
\(738\) 38.5754 1.41998
\(739\) −10.6665 −0.392375 −0.196188 0.980566i \(-0.562856\pi\)
−0.196188 + 0.980566i \(0.562856\pi\)
\(740\) 55.2294 2.03027
\(741\) −12.2363 −0.449512
\(742\) −1.07201 −0.0393547
\(743\) 39.1946 1.43791 0.718956 0.695056i \(-0.244620\pi\)
0.718956 + 0.695056i \(0.244620\pi\)
\(744\) −57.3827 −2.10375
\(745\) 2.27615 0.0833917
\(746\) 58.9817 2.15947
\(747\) 37.8840 1.38610
\(748\) 19.2921 0.705388
\(749\) 2.09290 0.0764727
\(750\) 124.666 4.55217
\(751\) −42.5715 −1.55346 −0.776728 0.629836i \(-0.783122\pi\)
−0.776728 + 0.629836i \(0.783122\pi\)
\(752\) −15.2111 −0.554691
\(753\) 52.4247 1.91046
\(754\) 21.4001 0.779347
\(755\) 3.87028 0.140854
\(756\) 5.93788 0.215959
\(757\) −2.67333 −0.0971637 −0.0485818 0.998819i \(-0.515470\pi\)
−0.0485818 + 0.998819i \(0.515470\pi\)
\(758\) −65.5239 −2.37994
\(759\) 3.59120 0.130352
\(760\) 60.8273 2.20644
\(761\) 14.5742 0.528315 0.264158 0.964479i \(-0.414906\pi\)
0.264158 + 0.964479i \(0.414906\pi\)
\(762\) 113.098 4.09711
\(763\) −2.90747 −0.105258
\(764\) 68.5071 2.47850
\(765\) 82.4807 2.98209
\(766\) 7.18612 0.259645
\(767\) 3.37459 0.121850
\(768\) 75.9952 2.74224
\(769\) 3.55851 0.128323 0.0641615 0.997940i \(-0.479563\pi\)
0.0641615 + 0.997940i \(0.479563\pi\)
\(770\) 4.35791 0.157048
\(771\) −69.9548 −2.51936
\(772\) −93.4422 −3.36306
\(773\) −24.1279 −0.867820 −0.433910 0.900956i \(-0.642866\pi\)
−0.433910 + 0.900956i \(0.642866\pi\)
\(774\) 109.840 3.94813
\(775\) −51.4564 −1.84837
\(776\) 3.24662 0.116547
\(777\) 4.65059 0.166839
\(778\) −77.7335 −2.78688
\(779\) 14.2741 0.511423
\(780\) 46.1193 1.65133
\(781\) 14.5076 0.519122
\(782\) 14.9257 0.533741
\(783\) −26.9067 −0.961568
\(784\) −16.3139 −0.582639
\(785\) 51.5076 1.83839
\(786\) 10.3264 0.368329
\(787\) −10.2574 −0.365637 −0.182819 0.983147i \(-0.558522\pi\)
−0.182819 + 0.983147i \(0.558522\pi\)
\(788\) 18.8672 0.672117
\(789\) 53.5800 1.90750
\(790\) 138.744 4.93628
\(791\) −4.57323 −0.162605
\(792\) −18.6530 −0.662806
\(793\) 17.9714 0.638185
\(794\) −15.9549 −0.566218
\(795\) 10.4687 0.371288
\(796\) 90.7103 3.21514
\(797\) −13.6241 −0.482590 −0.241295 0.970452i \(-0.577572\pi\)
−0.241295 + 0.970452i \(0.577572\pi\)
\(798\) 11.0771 0.392125
\(799\) −31.2991 −1.10728
\(800\) 24.8444 0.878381
\(801\) 24.2088 0.855378
\(802\) −8.07073 −0.284987
\(803\) 11.0851 0.391184
\(804\) −143.749 −5.06964
\(805\) 2.19274 0.0772840
\(806\) −14.6042 −0.514410
\(807\) 73.7403 2.59578
\(808\) −17.4234 −0.612952
\(809\) −36.9906 −1.30052 −0.650261 0.759711i \(-0.725340\pi\)
−0.650261 + 0.759711i \(0.725340\pi\)
\(810\) 30.7069 1.07893
\(811\) −34.3246 −1.20530 −0.602650 0.798006i \(-0.705888\pi\)
−0.602650 + 0.798006i \(0.705888\pi\)
\(812\) −12.5993 −0.442149
\(813\) 39.1779 1.37403
\(814\) −9.63616 −0.337747
\(815\) −83.3062 −2.91809
\(816\) −32.0432 −1.12174
\(817\) 40.6443 1.42197
\(818\) 18.5259 0.647742
\(819\) 2.29112 0.0800584
\(820\) −53.7999 −1.87877
\(821\) 14.7819 0.515893 0.257947 0.966159i \(-0.416954\pi\)
0.257947 + 0.966159i \(0.416954\pi\)
\(822\) 105.513 3.68020
\(823\) 26.9333 0.938835 0.469417 0.882976i \(-0.344464\pi\)
0.469417 + 0.882976i \(0.344464\pi\)
\(824\) −42.6167 −1.48462
\(825\) −28.3517 −0.987079
\(826\) −3.05490 −0.106294
\(827\) 47.7838 1.66161 0.830803 0.556567i \(-0.187882\pi\)
0.830803 + 0.556567i \(0.187882\pi\)
\(828\) −20.2977 −0.705395
\(829\) 28.8466 1.00188 0.500942 0.865481i \(-0.332987\pi\)
0.500942 + 0.865481i \(0.332987\pi\)
\(830\) −81.2403 −2.81989
\(831\) −20.8026 −0.721633
\(832\) 12.7340 0.441472
\(833\) −33.5683 −1.16307
\(834\) −22.8176 −0.790108
\(835\) −57.5342 −1.99105
\(836\) −14.9271 −0.516266
\(837\) 18.3620 0.634685
\(838\) 84.0573 2.90371
\(839\) −23.6771 −0.817424 −0.408712 0.912663i \(-0.634022\pi\)
−0.408712 + 0.912663i \(0.634022\pi\)
\(840\) −19.3050 −0.666085
\(841\) 28.0921 0.968695
\(842\) −5.43505 −0.187304
\(843\) 28.1933 0.971030
\(844\) 61.0578 2.10170
\(845\) −44.8863 −1.54414
\(846\) 65.4472 2.25012
\(847\) 4.43595 0.152421
\(848\) −2.39942 −0.0823964
\(849\) −10.1272 −0.347566
\(850\) −117.835 −4.04170
\(851\) −4.84857 −0.166207
\(852\) −138.987 −4.76162
\(853\) 21.3528 0.731107 0.365553 0.930790i \(-0.380880\pi\)
0.365553 + 0.930790i \(0.380880\pi\)
\(854\) −16.2689 −0.556711
\(855\) −63.8189 −2.18256
\(856\) 19.2103 0.656595
\(857\) 47.6593 1.62801 0.814006 0.580857i \(-0.197282\pi\)
0.814006 + 0.580857i \(0.197282\pi\)
\(858\) −8.04667 −0.274709
\(859\) 15.5311 0.529914 0.264957 0.964260i \(-0.414642\pi\)
0.264957 + 0.964260i \(0.414642\pi\)
\(860\) −153.191 −5.22376
\(861\) −4.53022 −0.154389
\(862\) −5.10759 −0.173965
\(863\) 25.8022 0.878318 0.439159 0.898409i \(-0.355277\pi\)
0.439159 + 0.898409i \(0.355277\pi\)
\(864\) −8.86564 −0.301615
\(865\) 81.2453 2.76242
\(866\) −70.3778 −2.39154
\(867\) −19.9503 −0.677547
\(868\) 8.59819 0.291842
\(869\) −15.7435 −0.534063
\(870\) 189.185 6.41399
\(871\) −16.9165 −0.573195
\(872\) −26.6872 −0.903742
\(873\) −3.40629 −0.115286
\(874\) −11.5487 −0.390639
\(875\) −8.63746 −0.291999
\(876\) −106.199 −3.58812
\(877\) −49.9200 −1.68568 −0.842840 0.538164i \(-0.819118\pi\)
−0.842840 + 0.538164i \(0.819118\pi\)
\(878\) −21.4264 −0.723106
\(879\) 10.7388 0.362210
\(880\) 9.75405 0.328809
\(881\) 32.6794 1.10100 0.550499 0.834836i \(-0.314437\pi\)
0.550499 + 0.834836i \(0.314437\pi\)
\(882\) 70.1921 2.36349
\(883\) 38.1763 1.28473 0.642367 0.766397i \(-0.277952\pi\)
0.642367 + 0.766397i \(0.277952\pi\)
\(884\) −21.7503 −0.731542
\(885\) 29.8327 1.00282
\(886\) 24.8250 0.834011
\(887\) −25.1764 −0.845341 −0.422670 0.906283i \(-0.638907\pi\)
−0.422670 + 0.906283i \(0.638907\pi\)
\(888\) 42.6869 1.43248
\(889\) −7.83596 −0.262810
\(890\) −51.9147 −1.74018
\(891\) −3.48437 −0.116731
\(892\) −46.0711 −1.54257
\(893\) 24.2175 0.810407
\(894\) 3.80466 0.127247
\(895\) 27.9892 0.935576
\(896\) −9.29582 −0.310551
\(897\) −4.04880 −0.135185
\(898\) 59.3011 1.97890
\(899\) −38.9616 −1.29944
\(900\) 160.246 5.34153
\(901\) −4.93717 −0.164481
\(902\) 9.38675 0.312545
\(903\) −12.8994 −0.429266
\(904\) −41.9769 −1.39613
\(905\) −4.28069 −0.142295
\(906\) 6.46929 0.214928
\(907\) 22.8623 0.759131 0.379566 0.925165i \(-0.376073\pi\)
0.379566 + 0.925165i \(0.376073\pi\)
\(908\) 92.4311 3.06743
\(909\) 18.2803 0.606319
\(910\) −4.91320 −0.162871
\(911\) 27.1210 0.898558 0.449279 0.893391i \(-0.351681\pi\)
0.449279 + 0.893391i \(0.351681\pi\)
\(912\) 24.7932 0.820986
\(913\) 9.21850 0.305088
\(914\) −24.6396 −0.815007
\(915\) 158.875 5.25223
\(916\) −26.6647 −0.881026
\(917\) −0.715459 −0.0236265
\(918\) 42.0490 1.38782
\(919\) 9.82933 0.324240 0.162120 0.986771i \(-0.448167\pi\)
0.162120 + 0.986771i \(0.448167\pi\)
\(920\) 20.1268 0.663561
\(921\) −46.5385 −1.53349
\(922\) 35.1757 1.15845
\(923\) −16.3562 −0.538370
\(924\) 4.73747 0.155851
\(925\) 38.2784 1.25858
\(926\) 48.7456 1.60188
\(927\) 44.7126 1.46856
\(928\) 18.8116 0.617521
\(929\) 20.1498 0.661095 0.330547 0.943789i \(-0.392767\pi\)
0.330547 + 0.943789i \(0.392767\pi\)
\(930\) −129.106 −4.23357
\(931\) 25.9733 0.851239
\(932\) 42.6395 1.39670
\(933\) −15.6523 −0.512435
\(934\) −88.9447 −2.91036
\(935\) 20.0704 0.656373
\(936\) 21.0298 0.687381
\(937\) −9.61016 −0.313950 −0.156975 0.987603i \(-0.550174\pi\)
−0.156975 + 0.987603i \(0.550174\pi\)
\(938\) 15.3140 0.500018
\(939\) 48.0715 1.56876
\(940\) −91.2770 −2.97713
\(941\) 19.3603 0.631129 0.315564 0.948904i \(-0.397806\pi\)
0.315564 + 0.948904i \(0.397806\pi\)
\(942\) 86.0966 2.80518
\(943\) 4.72308 0.153804
\(944\) −6.83761 −0.222545
\(945\) 6.17745 0.200952
\(946\) 26.7280 0.869002
\(947\) −16.0894 −0.522837 −0.261418 0.965226i \(-0.584190\pi\)
−0.261418 + 0.965226i \(0.584190\pi\)
\(948\) 150.828 4.89867
\(949\) −12.4976 −0.405688
\(950\) 91.1740 2.95807
\(951\) 47.2762 1.53304
\(952\) 9.10442 0.295076
\(953\) −59.4118 −1.92454 −0.962268 0.272104i \(-0.912280\pi\)
−0.962268 + 0.272104i \(0.912280\pi\)
\(954\) 10.3237 0.334243
\(955\) 71.2711 2.30628
\(956\) 90.1987 2.91724
\(957\) −21.4672 −0.693937
\(958\) 31.8458 1.02889
\(959\) −7.31045 −0.236067
\(960\) 112.573 3.63329
\(961\) −4.41133 −0.142301
\(962\) 10.8640 0.350270
\(963\) −20.1551 −0.649490
\(964\) 90.0391 2.89996
\(965\) −97.2122 −3.12937
\(966\) 3.66523 0.117927
\(967\) 41.8590 1.34610 0.673048 0.739599i \(-0.264985\pi\)
0.673048 + 0.739599i \(0.264985\pi\)
\(968\) 40.7168 1.30869
\(969\) 51.0158 1.63886
\(970\) 7.30463 0.234537
\(971\) 37.4824 1.20287 0.601433 0.798923i \(-0.294597\pi\)
0.601433 + 0.798923i \(0.294597\pi\)
\(972\) 73.1242 2.34546
\(973\) 1.58091 0.0506816
\(974\) 92.3422 2.95883
\(975\) 31.9643 1.02368
\(976\) −36.4138 −1.16558
\(977\) −14.8910 −0.476407 −0.238203 0.971215i \(-0.576558\pi\)
−0.238203 + 0.971215i \(0.576558\pi\)
\(978\) −139.249 −4.45269
\(979\) 5.89086 0.188273
\(980\) −97.8946 −3.12713
\(981\) 27.9997 0.893962
\(982\) 81.5080 2.60102
\(983\) 8.80561 0.280855 0.140428 0.990091i \(-0.455152\pi\)
0.140428 + 0.990091i \(0.455152\pi\)
\(984\) −41.5821 −1.32559
\(985\) 19.6285 0.625415
\(986\) −89.2218 −2.84140
\(987\) −7.68598 −0.244648
\(988\) 16.8292 0.535408
\(989\) 13.4486 0.427640
\(990\) −41.9678 −1.33382
\(991\) −37.3228 −1.18560 −0.592798 0.805351i \(-0.701977\pi\)
−0.592798 + 0.805351i \(0.701977\pi\)
\(992\) −12.8377 −0.407596
\(993\) −78.9655 −2.50590
\(994\) 14.8067 0.469639
\(995\) 94.3701 2.99173
\(996\) −88.3162 −2.79841
\(997\) −10.7722 −0.341161 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(998\) −42.0709 −1.33173
\(999\) −13.6595 −0.432168
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 \(a_p\))