Properties

Label 8043.2.a.t.1.5
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.45692 q^{2}\) \(-1.00000 q^{3}\) \(+4.03647 q^{4}\) \(-2.79922 q^{5}\) \(+2.45692 q^{6}\) \(+1.00000 q^{7}\) \(-5.00345 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.45692 q^{2}\) \(-1.00000 q^{3}\) \(+4.03647 q^{4}\) \(-2.79922 q^{5}\) \(+2.45692 q^{6}\) \(+1.00000 q^{7}\) \(-5.00345 q^{8}\) \(+1.00000 q^{9}\) \(+6.87748 q^{10}\) \(-0.984367 q^{11}\) \(-4.03647 q^{12}\) \(+4.11840 q^{13}\) \(-2.45692 q^{14}\) \(+2.79922 q^{15}\) \(+4.22016 q^{16}\) \(-1.41398 q^{17}\) \(-2.45692 q^{18}\) \(+7.64864 q^{19}\) \(-11.2990 q^{20}\) \(-1.00000 q^{21}\) \(+2.41851 q^{22}\) \(-3.00054 q^{23}\) \(+5.00345 q^{24}\) \(+2.83565 q^{25}\) \(-10.1186 q^{26}\) \(-1.00000 q^{27}\) \(+4.03647 q^{28}\) \(-2.48107 q^{29}\) \(-6.87748 q^{30}\) \(-1.69867 q^{31}\) \(-0.361700 q^{32}\) \(+0.984367 q^{33}\) \(+3.47404 q^{34}\) \(-2.79922 q^{35}\) \(+4.03647 q^{36}\) \(-4.85422 q^{37}\) \(-18.7921 q^{38}\) \(-4.11840 q^{39}\) \(+14.0058 q^{40}\) \(+2.85338 q^{41}\) \(+2.45692 q^{42}\) \(+7.04176 q^{43}\) \(-3.97337 q^{44}\) \(-2.79922 q^{45}\) \(+7.37209 q^{46}\) \(+9.67674 q^{47}\) \(-4.22016 q^{48}\) \(+1.00000 q^{49}\) \(-6.96697 q^{50}\) \(+1.41398 q^{51}\) \(+16.6238 q^{52}\) \(-2.69129 q^{53}\) \(+2.45692 q^{54}\) \(+2.75546 q^{55}\) \(-5.00345 q^{56}\) \(-7.64864 q^{57}\) \(+6.09580 q^{58}\) \(+8.15845 q^{59}\) \(+11.2990 q^{60}\) \(-7.43534 q^{61}\) \(+4.17350 q^{62}\) \(+1.00000 q^{63}\) \(-7.55165 q^{64}\) \(-11.5283 q^{65}\) \(-2.41851 q^{66}\) \(+6.56297 q^{67}\) \(-5.70748 q^{68}\) \(+3.00054 q^{69}\) \(+6.87748 q^{70}\) \(+14.0094 q^{71}\) \(-5.00345 q^{72}\) \(+5.55255 q^{73}\) \(+11.9264 q^{74}\) \(-2.83565 q^{75}\) \(+30.8735 q^{76}\) \(-0.984367 q^{77}\) \(+10.1186 q^{78}\) \(+9.46209 q^{79}\) \(-11.8132 q^{80}\) \(+1.00000 q^{81}\) \(-7.01053 q^{82}\) \(+12.1889 q^{83}\) \(-4.03647 q^{84}\) \(+3.95804 q^{85}\) \(-17.3011 q^{86}\) \(+2.48107 q^{87}\) \(+4.92523 q^{88}\) \(-8.31439 q^{89}\) \(+6.87748 q^{90}\) \(+4.11840 q^{91}\) \(-12.1116 q^{92}\) \(+1.69867 q^{93}\) \(-23.7750 q^{94}\) \(-21.4103 q^{95}\) \(+0.361700 q^{96}\) \(-7.65077 q^{97}\) \(-2.45692 q^{98}\) \(-0.984367 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45692 −1.73731 −0.868654 0.495420i \(-0.835014\pi\)
−0.868654 + 0.495420i \(0.835014\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.03647 2.01824
\(5\) −2.79922 −1.25185 −0.625925 0.779883i \(-0.715279\pi\)
−0.625925 + 0.779883i \(0.715279\pi\)
\(6\) 2.45692 1.00303
\(7\) 1.00000 0.377964
\(8\) −5.00345 −1.76899
\(9\) 1.00000 0.333333
\(10\) 6.87748 2.17485
\(11\) −0.984367 −0.296798 −0.148399 0.988928i \(-0.547412\pi\)
−0.148399 + 0.988928i \(0.547412\pi\)
\(12\) −4.03647 −1.16523
\(13\) 4.11840 1.14224 0.571120 0.820867i \(-0.306509\pi\)
0.571120 + 0.820867i \(0.306509\pi\)
\(14\) −2.45692 −0.656640
\(15\) 2.79922 0.722756
\(16\) 4.22016 1.05504
\(17\) −1.41398 −0.342940 −0.171470 0.985189i \(-0.554852\pi\)
−0.171470 + 0.985189i \(0.554852\pi\)
\(18\) −2.45692 −0.579102
\(19\) 7.64864 1.75472 0.877360 0.479833i \(-0.159303\pi\)
0.877360 + 0.479833i \(0.159303\pi\)
\(20\) −11.2990 −2.52653
\(21\) −1.00000 −0.218218
\(22\) 2.41851 0.515629
\(23\) −3.00054 −0.625655 −0.312828 0.949810i \(-0.601276\pi\)
−0.312828 + 0.949810i \(0.601276\pi\)
\(24\) 5.00345 1.02133
\(25\) 2.83565 0.567130
\(26\) −10.1186 −1.98442
\(27\) −1.00000 −0.192450
\(28\) 4.03647 0.762821
\(29\) −2.48107 −0.460723 −0.230362 0.973105i \(-0.573991\pi\)
−0.230362 + 0.973105i \(0.573991\pi\)
\(30\) −6.87748 −1.25565
\(31\) −1.69867 −0.305090 −0.152545 0.988297i \(-0.548747\pi\)
−0.152545 + 0.988297i \(0.548747\pi\)
\(32\) −0.361700 −0.0639401
\(33\) 0.984367 0.171356
\(34\) 3.47404 0.595792
\(35\) −2.79922 −0.473155
\(36\) 4.03647 0.672745
\(37\) −4.85422 −0.798029 −0.399014 0.916945i \(-0.630648\pi\)
−0.399014 + 0.916945i \(0.630648\pi\)
\(38\) −18.7921 −3.04849
\(39\) −4.11840 −0.659472
\(40\) 14.0058 2.21451
\(41\) 2.85338 0.445623 0.222811 0.974862i \(-0.428477\pi\)
0.222811 + 0.974862i \(0.428477\pi\)
\(42\) 2.45692 0.379111
\(43\) 7.04176 1.07386 0.536929 0.843628i \(-0.319584\pi\)
0.536929 + 0.843628i \(0.319584\pi\)
\(44\) −3.97337 −0.599008
\(45\) −2.79922 −0.417284
\(46\) 7.37209 1.08696
\(47\) 9.67674 1.41150 0.705749 0.708462i \(-0.250611\pi\)
0.705749 + 0.708462i \(0.250611\pi\)
\(48\) −4.22016 −0.609128
\(49\) 1.00000 0.142857
\(50\) −6.96697 −0.985279
\(51\) 1.41398 0.197997
\(52\) 16.6238 2.30531
\(53\) −2.69129 −0.369678 −0.184839 0.982769i \(-0.559176\pi\)
−0.184839 + 0.982769i \(0.559176\pi\)
\(54\) 2.45692 0.334345
\(55\) 2.75546 0.371546
\(56\) −5.00345 −0.668615
\(57\) −7.64864 −1.01309
\(58\) 6.09580 0.800418
\(59\) 8.15845 1.06214 0.531070 0.847328i \(-0.321790\pi\)
0.531070 + 0.847328i \(0.321790\pi\)
\(60\) 11.2990 1.45869
\(61\) −7.43534 −0.951998 −0.475999 0.879446i \(-0.657913\pi\)
−0.475999 + 0.879446i \(0.657913\pi\)
\(62\) 4.17350 0.530034
\(63\) 1.00000 0.125988
\(64\) −7.55165 −0.943956
\(65\) −11.5283 −1.42991
\(66\) −2.41851 −0.297698
\(67\) 6.56297 0.801794 0.400897 0.916123i \(-0.368698\pi\)
0.400897 + 0.916123i \(0.368698\pi\)
\(68\) −5.70748 −0.692134
\(69\) 3.00054 0.361222
\(70\) 6.87748 0.822016
\(71\) 14.0094 1.66261 0.831306 0.555815i \(-0.187594\pi\)
0.831306 + 0.555815i \(0.187594\pi\)
\(72\) −5.00345 −0.589663
\(73\) 5.55255 0.649877 0.324938 0.945735i \(-0.394656\pi\)
0.324938 + 0.945735i \(0.394656\pi\)
\(74\) 11.9264 1.38642
\(75\) −2.83565 −0.327433
\(76\) 30.8735 3.54144
\(77\) −0.984367 −0.112179
\(78\) 10.1186 1.14571
\(79\) 9.46209 1.06457 0.532284 0.846566i \(-0.321334\pi\)
0.532284 + 0.846566i \(0.321334\pi\)
\(80\) −11.8132 −1.32075
\(81\) 1.00000 0.111111
\(82\) −7.01053 −0.774184
\(83\) 12.1889 1.33791 0.668955 0.743303i \(-0.266742\pi\)
0.668955 + 0.743303i \(0.266742\pi\)
\(84\) −4.03647 −0.440415
\(85\) 3.95804 0.429310
\(86\) −17.3011 −1.86562
\(87\) 2.48107 0.265999
\(88\) 4.92523 0.525032
\(89\) −8.31439 −0.881324 −0.440662 0.897673i \(-0.645256\pi\)
−0.440662 + 0.897673i \(0.645256\pi\)
\(90\) 6.87748 0.724950
\(91\) 4.11840 0.431726
\(92\) −12.1116 −1.26272
\(93\) 1.69867 0.176144
\(94\) −23.7750 −2.45220
\(95\) −21.4103 −2.19665
\(96\) 0.361700 0.0369158
\(97\) −7.65077 −0.776818 −0.388409 0.921487i \(-0.626975\pi\)
−0.388409 + 0.921487i \(0.626975\pi\)
\(98\) −2.45692 −0.248187
\(99\) −0.984367 −0.0989326
\(100\) 11.4460 1.14460
\(101\) −17.3784 −1.72922 −0.864610 0.502444i \(-0.832434\pi\)
−0.864610 + 0.502444i \(0.832434\pi\)
\(102\) −3.47404 −0.343981
\(103\) 7.78687 0.767263 0.383631 0.923486i \(-0.374673\pi\)
0.383631 + 0.923486i \(0.374673\pi\)
\(104\) −20.6062 −2.02061
\(105\) 2.79922 0.273176
\(106\) 6.61230 0.642244
\(107\) −6.85574 −0.662770 −0.331385 0.943496i \(-0.607516\pi\)
−0.331385 + 0.943496i \(0.607516\pi\)
\(108\) −4.03647 −0.388410
\(109\) −16.2961 −1.56088 −0.780440 0.625231i \(-0.785005\pi\)
−0.780440 + 0.625231i \(0.785005\pi\)
\(110\) −6.76996 −0.645490
\(111\) 4.85422 0.460742
\(112\) 4.22016 0.398768
\(113\) −2.31882 −0.218136 −0.109068 0.994034i \(-0.534787\pi\)
−0.109068 + 0.994034i \(0.534787\pi\)
\(114\) 18.7921 1.76004
\(115\) 8.39917 0.783227
\(116\) −10.0148 −0.929848
\(117\) 4.11840 0.380746
\(118\) −20.0447 −1.84526
\(119\) −1.41398 −0.129619
\(120\) −14.0058 −1.27855
\(121\) −10.0310 −0.911911
\(122\) 18.2681 1.65391
\(123\) −2.85338 −0.257281
\(124\) −6.85662 −0.615743
\(125\) 6.05850 0.541889
\(126\) −2.45692 −0.218880
\(127\) 19.7333 1.75104 0.875522 0.483179i \(-0.160518\pi\)
0.875522 + 0.483179i \(0.160518\pi\)
\(128\) 19.2772 1.70388
\(129\) −7.04176 −0.619992
\(130\) 28.3242 2.48420
\(131\) 18.2284 1.59262 0.796310 0.604889i \(-0.206782\pi\)
0.796310 + 0.604889i \(0.206782\pi\)
\(132\) 3.97337 0.345837
\(133\) 7.64864 0.663222
\(134\) −16.1247 −1.39296
\(135\) 2.79922 0.240919
\(136\) 7.07477 0.606657
\(137\) −2.80549 −0.239689 −0.119845 0.992793i \(-0.538240\pi\)
−0.119845 + 0.992793i \(0.538240\pi\)
\(138\) −7.37209 −0.627554
\(139\) −12.2230 −1.03674 −0.518371 0.855156i \(-0.673461\pi\)
−0.518371 + 0.855156i \(0.673461\pi\)
\(140\) −11.2990 −0.954938
\(141\) −9.67674 −0.814929
\(142\) −34.4201 −2.88847
\(143\) −4.05402 −0.339014
\(144\) 4.22016 0.351680
\(145\) 6.94507 0.576757
\(146\) −13.6422 −1.12904
\(147\) −1.00000 −0.0824786
\(148\) −19.5939 −1.61061
\(149\) 23.6444 1.93703 0.968513 0.248963i \(-0.0800898\pi\)
0.968513 + 0.248963i \(0.0800898\pi\)
\(150\) 6.96697 0.568851
\(151\) −6.36352 −0.517856 −0.258928 0.965897i \(-0.583369\pi\)
−0.258928 + 0.965897i \(0.583369\pi\)
\(152\) −38.2696 −3.10408
\(153\) −1.41398 −0.114313
\(154\) 2.41851 0.194889
\(155\) 4.75495 0.381927
\(156\) −16.6238 −1.33097
\(157\) 9.84345 0.785593 0.392796 0.919625i \(-0.371508\pi\)
0.392796 + 0.919625i \(0.371508\pi\)
\(158\) −23.2476 −1.84948
\(159\) 2.69129 0.213433
\(160\) 1.01248 0.0800435
\(161\) −3.00054 −0.236475
\(162\) −2.45692 −0.193034
\(163\) −3.61022 −0.282774 −0.141387 0.989954i \(-0.545156\pi\)
−0.141387 + 0.989954i \(0.545156\pi\)
\(164\) 11.5176 0.899372
\(165\) −2.75546 −0.214512
\(166\) −29.9473 −2.32436
\(167\) −10.1072 −0.782120 −0.391060 0.920365i \(-0.627891\pi\)
−0.391060 + 0.920365i \(0.627891\pi\)
\(168\) 5.00345 0.386025
\(169\) 3.96123 0.304710
\(170\) −9.72460 −0.745843
\(171\) 7.64864 0.584906
\(172\) 28.4238 2.16730
\(173\) 0.0346365 0.00263337 0.00131668 0.999999i \(-0.499581\pi\)
0.00131668 + 0.999999i \(0.499581\pi\)
\(174\) −6.09580 −0.462121
\(175\) 2.83565 0.214355
\(176\) −4.15418 −0.313133
\(177\) −8.15845 −0.613227
\(178\) 20.4278 1.53113
\(179\) −15.2196 −1.13756 −0.568782 0.822489i \(-0.692585\pi\)
−0.568782 + 0.822489i \(0.692585\pi\)
\(180\) −11.2990 −0.842177
\(181\) 9.51027 0.706893 0.353446 0.935455i \(-0.385010\pi\)
0.353446 + 0.935455i \(0.385010\pi\)
\(182\) −10.1186 −0.750040
\(183\) 7.43534 0.549636
\(184\) 15.0131 1.10678
\(185\) 13.5880 0.999013
\(186\) −4.17350 −0.306016
\(187\) 1.39187 0.101784
\(188\) 39.0599 2.84874
\(189\) −1.00000 −0.0727393
\(190\) 52.6034 3.81625
\(191\) −9.31258 −0.673835 −0.336917 0.941534i \(-0.609384\pi\)
−0.336917 + 0.941534i \(0.609384\pi\)
\(192\) 7.55165 0.544993
\(193\) −3.50958 −0.252625 −0.126313 0.991990i \(-0.540314\pi\)
−0.126313 + 0.991990i \(0.540314\pi\)
\(194\) 18.7974 1.34957
\(195\) 11.5283 0.825561
\(196\) 4.03647 0.288319
\(197\) 18.2121 1.29756 0.648779 0.760977i \(-0.275280\pi\)
0.648779 + 0.760977i \(0.275280\pi\)
\(198\) 2.41851 0.171876
\(199\) −22.8073 −1.61676 −0.808382 0.588659i \(-0.799656\pi\)
−0.808382 + 0.588659i \(0.799656\pi\)
\(200\) −14.1880 −1.00325
\(201\) −6.56297 −0.462916
\(202\) 42.6975 3.00418
\(203\) −2.48107 −0.174137
\(204\) 5.70748 0.399604
\(205\) −7.98724 −0.557853
\(206\) −19.1317 −1.33297
\(207\) −3.00054 −0.208552
\(208\) 17.3803 1.20511
\(209\) −7.52907 −0.520797
\(210\) −6.87748 −0.474591
\(211\) −16.4783 −1.13441 −0.567207 0.823575i \(-0.691976\pi\)
−0.567207 + 0.823575i \(0.691976\pi\)
\(212\) −10.8633 −0.746097
\(213\) −14.0094 −0.959909
\(214\) 16.8440 1.15143
\(215\) −19.7114 −1.34431
\(216\) 5.00345 0.340442
\(217\) −1.69867 −0.115313
\(218\) 40.0382 2.71173
\(219\) −5.55255 −0.375206
\(220\) 11.1223 0.749868
\(221\) −5.82333 −0.391720
\(222\) −11.9264 −0.800451
\(223\) −12.9237 −0.865435 −0.432717 0.901530i \(-0.642445\pi\)
−0.432717 + 0.901530i \(0.642445\pi\)
\(224\) −0.361700 −0.0241671
\(225\) 2.83565 0.189043
\(226\) 5.69716 0.378969
\(227\) 0.269983 0.0179194 0.00895969 0.999960i \(-0.497148\pi\)
0.00895969 + 0.999960i \(0.497148\pi\)
\(228\) −30.8735 −2.04465
\(229\) −22.0587 −1.45768 −0.728840 0.684684i \(-0.759940\pi\)
−0.728840 + 0.684684i \(0.759940\pi\)
\(230\) −20.6361 −1.36071
\(231\) 0.984367 0.0647666
\(232\) 12.4139 0.815014
\(233\) −14.9230 −0.977640 −0.488820 0.872385i \(-0.662572\pi\)
−0.488820 + 0.872385i \(0.662572\pi\)
\(234\) −10.1186 −0.661473
\(235\) −27.0874 −1.76698
\(236\) 32.9314 2.14365
\(237\) −9.46209 −0.614629
\(238\) 3.47404 0.225188
\(239\) 18.5534 1.20012 0.600061 0.799954i \(-0.295143\pi\)
0.600061 + 0.799954i \(0.295143\pi\)
\(240\) 11.8132 0.762537
\(241\) 2.43794 0.157041 0.0785207 0.996912i \(-0.474980\pi\)
0.0785207 + 0.996912i \(0.474980\pi\)
\(242\) 24.6455 1.58427
\(243\) −1.00000 −0.0641500
\(244\) −30.0125 −1.92136
\(245\) −2.79922 −0.178836
\(246\) 7.01053 0.446975
\(247\) 31.5002 2.00431
\(248\) 8.49920 0.539700
\(249\) −12.1889 −0.772442
\(250\) −14.8853 −0.941427
\(251\) 1.35703 0.0856551 0.0428275 0.999082i \(-0.486363\pi\)
0.0428275 + 0.999082i \(0.486363\pi\)
\(252\) 4.03647 0.254274
\(253\) 2.95363 0.185693
\(254\) −48.4831 −3.04210
\(255\) −3.95804 −0.247862
\(256\) −32.2594 −2.01621
\(257\) −4.66411 −0.290939 −0.145470 0.989363i \(-0.546469\pi\)
−0.145470 + 0.989363i \(0.546469\pi\)
\(258\) 17.3011 1.07712
\(259\) −4.85422 −0.301627
\(260\) −46.5338 −2.88590
\(261\) −2.48107 −0.153574
\(262\) −44.7857 −2.76687
\(263\) 9.57669 0.590524 0.295262 0.955416i \(-0.404593\pi\)
0.295262 + 0.955416i \(0.404593\pi\)
\(264\) −4.92523 −0.303127
\(265\) 7.53353 0.462781
\(266\) −18.7921 −1.15222
\(267\) 8.31439 0.508832
\(268\) 26.4912 1.61821
\(269\) 10.3269 0.629639 0.314820 0.949152i \(-0.398056\pi\)
0.314820 + 0.949152i \(0.398056\pi\)
\(270\) −6.87748 −0.418550
\(271\) −12.6993 −0.771427 −0.385713 0.922619i \(-0.626045\pi\)
−0.385713 + 0.922619i \(0.626045\pi\)
\(272\) −5.96721 −0.361815
\(273\) −4.11840 −0.249257
\(274\) 6.89288 0.416414
\(275\) −2.79132 −0.168323
\(276\) 12.1116 0.729032
\(277\) 15.4665 0.929294 0.464647 0.885496i \(-0.346181\pi\)
0.464647 + 0.885496i \(0.346181\pi\)
\(278\) 30.0310 1.80114
\(279\) −1.69867 −0.101697
\(280\) 14.0058 0.837006
\(281\) 21.9734 1.31082 0.655411 0.755272i \(-0.272495\pi\)
0.655411 + 0.755272i \(0.272495\pi\)
\(282\) 23.7750 1.41578
\(283\) −22.6149 −1.34431 −0.672157 0.740409i \(-0.734632\pi\)
−0.672157 + 0.740409i \(0.734632\pi\)
\(284\) 56.5486 3.35554
\(285\) 21.4103 1.26823
\(286\) 9.96041 0.588971
\(287\) 2.85338 0.168430
\(288\) −0.361700 −0.0213134
\(289\) −15.0007 −0.882392
\(290\) −17.0635 −1.00200
\(291\) 7.65077 0.448496
\(292\) 22.4127 1.31160
\(293\) −5.75828 −0.336403 −0.168201 0.985753i \(-0.553796\pi\)
−0.168201 + 0.985753i \(0.553796\pi\)
\(294\) 2.45692 0.143291
\(295\) −22.8373 −1.32964
\(296\) 24.2879 1.41170
\(297\) 0.984367 0.0571187
\(298\) −58.0925 −3.36521
\(299\) −12.3574 −0.714648
\(300\) −11.4460 −0.660836
\(301\) 7.04176 0.405880
\(302\) 15.6347 0.899674
\(303\) 17.3784 0.998365
\(304\) 32.2785 1.85130
\(305\) 20.8132 1.19176
\(306\) 3.47404 0.198597
\(307\) 17.0315 0.972039 0.486020 0.873948i \(-0.338448\pi\)
0.486020 + 0.873948i \(0.338448\pi\)
\(308\) −3.97337 −0.226404
\(309\) −7.78687 −0.442979
\(310\) −11.6825 −0.663524
\(311\) 0.487175 0.0276252 0.0138126 0.999905i \(-0.495603\pi\)
0.0138126 + 0.999905i \(0.495603\pi\)
\(312\) 20.6062 1.16660
\(313\) 28.5388 1.61311 0.806553 0.591162i \(-0.201331\pi\)
0.806553 + 0.591162i \(0.201331\pi\)
\(314\) −24.1846 −1.36482
\(315\) −2.79922 −0.157718
\(316\) 38.1935 2.14855
\(317\) −32.6115 −1.83164 −0.915822 0.401583i \(-0.868460\pi\)
−0.915822 + 0.401583i \(0.868460\pi\)
\(318\) −6.61230 −0.370800
\(319\) 2.44228 0.136742
\(320\) 21.1388 1.18169
\(321\) 6.85574 0.382650
\(322\) 7.37209 0.410831
\(323\) −10.8150 −0.601763
\(324\) 4.03647 0.224248
\(325\) 11.6783 0.647798
\(326\) 8.87002 0.491265
\(327\) 16.2961 0.901174
\(328\) −14.2768 −0.788302
\(329\) 9.67674 0.533496
\(330\) 6.76996 0.372674
\(331\) 18.1294 0.996481 0.498241 0.867039i \(-0.333980\pi\)
0.498241 + 0.867039i \(0.333980\pi\)
\(332\) 49.2003 2.70022
\(333\) −4.85422 −0.266010
\(334\) 24.8326 1.35878
\(335\) −18.3712 −1.00373
\(336\) −4.22016 −0.230229
\(337\) 29.6809 1.61682 0.808411 0.588619i \(-0.200328\pi\)
0.808411 + 0.588619i \(0.200328\pi\)
\(338\) −9.73245 −0.529375
\(339\) 2.31882 0.125941
\(340\) 15.9765 0.866448
\(341\) 1.67211 0.0905499
\(342\) −18.7921 −1.01616
\(343\) 1.00000 0.0539949
\(344\) −35.2331 −1.89964
\(345\) −8.39917 −0.452196
\(346\) −0.0850993 −0.00457497
\(347\) −16.9246 −0.908558 −0.454279 0.890860i \(-0.650103\pi\)
−0.454279 + 0.890860i \(0.650103\pi\)
\(348\) 10.0148 0.536848
\(349\) 5.92140 0.316965 0.158483 0.987362i \(-0.449340\pi\)
0.158483 + 0.987362i \(0.449340\pi\)
\(350\) −6.96697 −0.372400
\(351\) −4.11840 −0.219824
\(352\) 0.356045 0.0189773
\(353\) 5.18274 0.275850 0.137925 0.990443i \(-0.455957\pi\)
0.137925 + 0.990443i \(0.455957\pi\)
\(354\) 20.0447 1.06536
\(355\) −39.2155 −2.08134
\(356\) −33.5608 −1.77872
\(357\) 1.41398 0.0748356
\(358\) 37.3933 1.97630
\(359\) −10.4370 −0.550846 −0.275423 0.961323i \(-0.588818\pi\)
−0.275423 + 0.961323i \(0.588818\pi\)
\(360\) 14.0058 0.738170
\(361\) 39.5017 2.07904
\(362\) −23.3660 −1.22809
\(363\) 10.0310 0.526492
\(364\) 16.6238 0.871325
\(365\) −15.5428 −0.813549
\(366\) −18.2681 −0.954887
\(367\) 19.9298 1.04033 0.520163 0.854067i \(-0.325871\pi\)
0.520163 + 0.854067i \(0.325871\pi\)
\(368\) −12.6627 −0.660091
\(369\) 2.85338 0.148541
\(370\) −33.3848 −1.73559
\(371\) −2.69129 −0.139725
\(372\) 6.85662 0.355499
\(373\) 2.61334 0.135313 0.0676567 0.997709i \(-0.478448\pi\)
0.0676567 + 0.997709i \(0.478448\pi\)
\(374\) −3.41972 −0.176830
\(375\) −6.05850 −0.312859
\(376\) −48.4171 −2.49692
\(377\) −10.2180 −0.526256
\(378\) 2.45692 0.126370
\(379\) −31.0034 −1.59254 −0.796269 0.604942i \(-0.793196\pi\)
−0.796269 + 0.604942i \(0.793196\pi\)
\(380\) −86.4219 −4.43335
\(381\) −19.7333 −1.01097
\(382\) 22.8803 1.17066
\(383\) −1.00000 −0.0510976
\(384\) −19.2772 −0.983737
\(385\) 2.75546 0.140431
\(386\) 8.62277 0.438887
\(387\) 7.04176 0.357953
\(388\) −30.8821 −1.56780
\(389\) 12.5464 0.636126 0.318063 0.948070i \(-0.396968\pi\)
0.318063 + 0.948070i \(0.396968\pi\)
\(390\) −28.3242 −1.43425
\(391\) 4.24269 0.214562
\(392\) −5.00345 −0.252713
\(393\) −18.2284 −0.919500
\(394\) −44.7457 −2.25426
\(395\) −26.4865 −1.33268
\(396\) −3.97337 −0.199669
\(397\) −16.5278 −0.829506 −0.414753 0.909934i \(-0.636132\pi\)
−0.414753 + 0.909934i \(0.636132\pi\)
\(398\) 56.0357 2.80881
\(399\) −7.64864 −0.382911
\(400\) 11.9669 0.598345
\(401\) −18.3159 −0.914654 −0.457327 0.889299i \(-0.651193\pi\)
−0.457327 + 0.889299i \(0.651193\pi\)
\(402\) 16.1247 0.804228
\(403\) −6.99580 −0.348485
\(404\) −70.1476 −3.48997
\(405\) −2.79922 −0.139095
\(406\) 6.09580 0.302529
\(407\) 4.77833 0.236853
\(408\) −7.07477 −0.350254
\(409\) 14.3630 0.710207 0.355103 0.934827i \(-0.384446\pi\)
0.355103 + 0.934827i \(0.384446\pi\)
\(410\) 19.6240 0.969163
\(411\) 2.80549 0.138385
\(412\) 31.4315 1.54852
\(413\) 8.15845 0.401451
\(414\) 7.37209 0.362318
\(415\) −34.1195 −1.67486
\(416\) −1.48963 −0.0730349
\(417\) 12.2230 0.598564
\(418\) 18.4983 0.904784
\(419\) 5.32951 0.260363 0.130182 0.991490i \(-0.458444\pi\)
0.130182 + 0.991490i \(0.458444\pi\)
\(420\) 11.2990 0.551334
\(421\) 9.38637 0.457464 0.228732 0.973489i \(-0.426542\pi\)
0.228732 + 0.973489i \(0.426542\pi\)
\(422\) 40.4860 1.97083
\(423\) 9.67674 0.470499
\(424\) 13.4658 0.653955
\(425\) −4.00955 −0.194492
\(426\) 34.4201 1.66766
\(427\) −7.43534 −0.359821
\(428\) −27.6730 −1.33763
\(429\) 4.05402 0.195730
\(430\) 48.4295 2.33548
\(431\) 15.2493 0.734535 0.367267 0.930115i \(-0.380293\pi\)
0.367267 + 0.930115i \(0.380293\pi\)
\(432\) −4.22016 −0.203043
\(433\) −25.2305 −1.21250 −0.606249 0.795275i \(-0.707327\pi\)
−0.606249 + 0.795275i \(0.707327\pi\)
\(434\) 4.17350 0.200334
\(435\) −6.94507 −0.332991
\(436\) −65.7786 −3.15022
\(437\) −22.9500 −1.09785
\(438\) 13.6422 0.651849
\(439\) 6.31008 0.301164 0.150582 0.988598i \(-0.451885\pi\)
0.150582 + 0.988598i \(0.451885\pi\)
\(440\) −13.7868 −0.657261
\(441\) 1.00000 0.0476190
\(442\) 14.3075 0.680537
\(443\) −34.4740 −1.63791 −0.818956 0.573857i \(-0.805447\pi\)
−0.818956 + 0.573857i \(0.805447\pi\)
\(444\) 19.5939 0.929886
\(445\) 23.2738 1.10329
\(446\) 31.7525 1.50353
\(447\) −23.6444 −1.11834
\(448\) −7.55165 −0.356782
\(449\) −24.9641 −1.17813 −0.589065 0.808086i \(-0.700504\pi\)
−0.589065 + 0.808086i \(0.700504\pi\)
\(450\) −6.96697 −0.328426
\(451\) −2.80877 −0.132260
\(452\) −9.35984 −0.440250
\(453\) 6.36352 0.298984
\(454\) −0.663327 −0.0311315
\(455\) −11.5283 −0.540456
\(456\) 38.2696 1.79214
\(457\) −28.9746 −1.35538 −0.677688 0.735349i \(-0.737018\pi\)
−0.677688 + 0.735349i \(0.737018\pi\)
\(458\) 54.1966 2.53244
\(459\) 1.41398 0.0659988
\(460\) 33.9030 1.58074
\(461\) 30.3866 1.41525 0.707623 0.706590i \(-0.249768\pi\)
0.707623 + 0.706590i \(0.249768\pi\)
\(462\) −2.41851 −0.112519
\(463\) 19.5012 0.906299 0.453150 0.891434i \(-0.350300\pi\)
0.453150 + 0.891434i \(0.350300\pi\)
\(464\) −10.4705 −0.486081
\(465\) −4.75495 −0.220505
\(466\) 36.6647 1.69846
\(467\) −13.0969 −0.606051 −0.303025 0.952982i \(-0.597997\pi\)
−0.303025 + 0.952982i \(0.597997\pi\)
\(468\) 16.6238 0.768436
\(469\) 6.56297 0.303050
\(470\) 66.5516 3.06979
\(471\) −9.84345 −0.453562
\(472\) −40.8204 −1.87891
\(473\) −6.93167 −0.318719
\(474\) 23.2476 1.06780
\(475\) 21.6889 0.995154
\(476\) −5.70748 −0.261602
\(477\) −2.69129 −0.123226
\(478\) −45.5844 −2.08498
\(479\) −1.59688 −0.0729632 −0.0364816 0.999334i \(-0.511615\pi\)
−0.0364816 + 0.999334i \(0.511615\pi\)
\(480\) −1.01248 −0.0462131
\(481\) −19.9916 −0.911540
\(482\) −5.98983 −0.272829
\(483\) 3.00054 0.136529
\(484\) −40.4899 −1.84045
\(485\) 21.4162 0.972460
\(486\) 2.45692 0.111448
\(487\) 3.18973 0.144540 0.0722702 0.997385i \(-0.476976\pi\)
0.0722702 + 0.997385i \(0.476976\pi\)
\(488\) 37.2024 1.68407
\(489\) 3.61022 0.163260
\(490\) 6.87748 0.310693
\(491\) 27.0604 1.22122 0.610609 0.791933i \(-0.290925\pi\)
0.610609 + 0.791933i \(0.290925\pi\)
\(492\) −11.5176 −0.519253
\(493\) 3.50818 0.158000
\(494\) −77.3935 −3.48210
\(495\) 2.75546 0.123849
\(496\) −7.16865 −0.321882
\(497\) 14.0094 0.628408
\(498\) 29.9473 1.34197
\(499\) 9.49967 0.425264 0.212632 0.977132i \(-0.431796\pi\)
0.212632 + 0.977132i \(0.431796\pi\)
\(500\) 24.4550 1.09366
\(501\) 10.1072 0.451557
\(502\) −3.33412 −0.148809
\(503\) −30.7234 −1.36989 −0.684945 0.728595i \(-0.740174\pi\)
−0.684945 + 0.728595i \(0.740174\pi\)
\(504\) −5.00345 −0.222872
\(505\) 48.6461 2.16472
\(506\) −7.25684 −0.322606
\(507\) −3.96123 −0.175925
\(508\) 79.6527 3.53402
\(509\) −21.5144 −0.953610 −0.476805 0.879009i \(-0.658205\pi\)
−0.476805 + 0.879009i \(0.658205\pi\)
\(510\) 9.72460 0.430613
\(511\) 5.55255 0.245630
\(512\) 40.7043 1.79889
\(513\) −7.64864 −0.337696
\(514\) 11.4594 0.505450
\(515\) −21.7972 −0.960498
\(516\) −28.4238 −1.25129
\(517\) −9.52546 −0.418929
\(518\) 11.9264 0.524018
\(519\) −0.0346365 −0.00152037
\(520\) 57.6815 2.52950
\(521\) −23.6374 −1.03557 −0.517787 0.855510i \(-0.673244\pi\)
−0.517787 + 0.855510i \(0.673244\pi\)
\(522\) 6.09580 0.266806
\(523\) 14.2272 0.622112 0.311056 0.950392i \(-0.399317\pi\)
0.311056 + 0.950392i \(0.399317\pi\)
\(524\) 73.5783 3.21428
\(525\) −2.83565 −0.123758
\(526\) −23.5292 −1.02592
\(527\) 2.40188 0.104627
\(528\) 4.15418 0.180788
\(529\) −13.9968 −0.608555
\(530\) −18.5093 −0.803993
\(531\) 8.15845 0.354047
\(532\) 30.8735 1.33854
\(533\) 11.7514 0.509008
\(534\) −20.4278 −0.883998
\(535\) 19.1908 0.829689
\(536\) −32.8375 −1.41836
\(537\) 15.2196 0.656772
\(538\) −25.3723 −1.09388
\(539\) −0.984367 −0.0423997
\(540\) 11.2990 0.486231
\(541\) −19.4255 −0.835166 −0.417583 0.908639i \(-0.637123\pi\)
−0.417583 + 0.908639i \(0.637123\pi\)
\(542\) 31.2012 1.34020
\(543\) −9.51027 −0.408125
\(544\) 0.511436 0.0219276
\(545\) 45.6163 1.95399
\(546\) 10.1186 0.433036
\(547\) 19.6489 0.840125 0.420063 0.907495i \(-0.362008\pi\)
0.420063 + 0.907495i \(0.362008\pi\)
\(548\) −11.3243 −0.483750
\(549\) −7.43534 −0.317333
\(550\) 6.85806 0.292429
\(551\) −18.9768 −0.808440
\(552\) −15.0131 −0.638998
\(553\) 9.46209 0.402369
\(554\) −38.0001 −1.61447
\(555\) −13.5880 −0.576780
\(556\) −49.3379 −2.09239
\(557\) 0.547473 0.0231972 0.0115986 0.999933i \(-0.496308\pi\)
0.0115986 + 0.999933i \(0.496308\pi\)
\(558\) 4.17350 0.176678
\(559\) 29.0008 1.22660
\(560\) −11.8132 −0.499197
\(561\) −1.39187 −0.0587649
\(562\) −53.9869 −2.27730
\(563\) −19.3828 −0.816888 −0.408444 0.912783i \(-0.633928\pi\)
−0.408444 + 0.912783i \(0.633928\pi\)
\(564\) −39.0599 −1.64472
\(565\) 6.49089 0.273074
\(566\) 55.5630 2.33549
\(567\) 1.00000 0.0419961
\(568\) −70.0955 −2.94114
\(569\) 8.21397 0.344347 0.172174 0.985067i \(-0.444921\pi\)
0.172174 + 0.985067i \(0.444921\pi\)
\(570\) −52.6034 −2.20331
\(571\) −16.4006 −0.686343 −0.343172 0.939273i \(-0.611501\pi\)
−0.343172 + 0.939273i \(0.611501\pi\)
\(572\) −16.3639 −0.684210
\(573\) 9.31258 0.389039
\(574\) −7.01053 −0.292614
\(575\) −8.50847 −0.354828
\(576\) −7.55165 −0.314652
\(577\) −26.0604 −1.08491 −0.542453 0.840086i \(-0.682504\pi\)
−0.542453 + 0.840086i \(0.682504\pi\)
\(578\) 36.8555 1.53299
\(579\) 3.50958 0.145853
\(580\) 28.0336 1.16403
\(581\) 12.1889 0.505682
\(582\) −18.7974 −0.779176
\(583\) 2.64922 0.109719
\(584\) −27.7819 −1.14962
\(585\) −11.5283 −0.476638
\(586\) 14.1477 0.584435
\(587\) −16.1899 −0.668230 −0.334115 0.942532i \(-0.608437\pi\)
−0.334115 + 0.942532i \(0.608437\pi\)
\(588\) −4.03647 −0.166461
\(589\) −12.9925 −0.535347
\(590\) 56.1096 2.30999
\(591\) −18.2121 −0.749145
\(592\) −20.4856 −0.841952
\(593\) 24.0417 0.987273 0.493637 0.869668i \(-0.335667\pi\)
0.493637 + 0.869668i \(0.335667\pi\)
\(594\) −2.41851 −0.0992328
\(595\) 3.95804 0.162264
\(596\) 95.4400 3.90938
\(597\) 22.8073 0.933439
\(598\) 30.3612 1.24156
\(599\) 12.6353 0.516266 0.258133 0.966109i \(-0.416893\pi\)
0.258133 + 0.966109i \(0.416893\pi\)
\(600\) 14.1880 0.579225
\(601\) 44.4543 1.81333 0.906664 0.421853i \(-0.138620\pi\)
0.906664 + 0.421853i \(0.138620\pi\)
\(602\) −17.3011 −0.705138
\(603\) 6.56297 0.267265
\(604\) −25.6862 −1.04515
\(605\) 28.0791 1.14158
\(606\) −42.6975 −1.73447
\(607\) 37.5003 1.52209 0.761044 0.648700i \(-0.224687\pi\)
0.761044 + 0.648700i \(0.224687\pi\)
\(608\) −2.76651 −0.112197
\(609\) 2.48107 0.100538
\(610\) −51.1364 −2.07045
\(611\) 39.8527 1.61227
\(612\) −5.70748 −0.230711
\(613\) 43.4573 1.75523 0.877613 0.479370i \(-0.159135\pi\)
0.877613 + 0.479370i \(0.159135\pi\)
\(614\) −41.8451 −1.68873
\(615\) 7.98724 0.322077
\(616\) 4.92523 0.198443
\(617\) −27.3678 −1.10178 −0.550892 0.834576i \(-0.685712\pi\)
−0.550892 + 0.834576i \(0.685712\pi\)
\(618\) 19.1317 0.769591
\(619\) 35.9429 1.44467 0.722334 0.691544i \(-0.243069\pi\)
0.722334 + 0.691544i \(0.243069\pi\)
\(620\) 19.1932 0.770818
\(621\) 3.00054 0.120407
\(622\) −1.19695 −0.0479934
\(623\) −8.31439 −0.333109
\(624\) −17.3803 −0.695769
\(625\) −31.1373 −1.24549
\(626\) −70.1175 −2.80246
\(627\) 7.52907 0.300682
\(628\) 39.7328 1.58551
\(629\) 6.86376 0.273676
\(630\) 6.87748 0.274005
\(631\) 10.8669 0.432603 0.216301 0.976327i \(-0.430601\pi\)
0.216301 + 0.976327i \(0.430601\pi\)
\(632\) −47.3431 −1.88321
\(633\) 16.4783 0.654955
\(634\) 80.1240 3.18213
\(635\) −55.2378 −2.19204
\(636\) 10.8633 0.430759
\(637\) 4.11840 0.163177
\(638\) −6.00050 −0.237562
\(639\) 14.0094 0.554204
\(640\) −53.9613 −2.13301
\(641\) −3.36714 −0.132994 −0.0664971 0.997787i \(-0.521182\pi\)
−0.0664971 + 0.997787i \(0.521182\pi\)
\(642\) −16.8440 −0.664781
\(643\) 50.4220 1.98845 0.994225 0.107311i \(-0.0342241\pi\)
0.994225 + 0.107311i \(0.0342241\pi\)
\(644\) −12.1116 −0.477263
\(645\) 19.7114 0.776137
\(646\) 26.5717 1.04545
\(647\) 37.9099 1.49039 0.745195 0.666847i \(-0.232356\pi\)
0.745195 + 0.666847i \(0.232356\pi\)
\(648\) −5.00345 −0.196554
\(649\) −8.03091 −0.315241
\(650\) −28.6928 −1.12542
\(651\) 1.69867 0.0665760
\(652\) −14.5725 −0.570705
\(653\) 19.4852 0.762515 0.381258 0.924469i \(-0.375491\pi\)
0.381258 + 0.924469i \(0.375491\pi\)
\(654\) −40.0382 −1.56562
\(655\) −51.0253 −1.99372
\(656\) 12.0417 0.470150
\(657\) 5.55255 0.216626
\(658\) −23.7750 −0.926846
\(659\) 37.0870 1.44471 0.722353 0.691525i \(-0.243061\pi\)
0.722353 + 0.691525i \(0.243061\pi\)
\(660\) −11.1223 −0.432937
\(661\) −24.5936 −0.956580 −0.478290 0.878202i \(-0.658743\pi\)
−0.478290 + 0.878202i \(0.658743\pi\)
\(662\) −44.5425 −1.73119
\(663\) 5.82333 0.226159
\(664\) −60.9868 −2.36675
\(665\) −21.4103 −0.830254
\(666\) 11.9264 0.462140
\(667\) 7.44454 0.288254
\(668\) −40.7975 −1.57850
\(669\) 12.9237 0.499659
\(670\) 45.1367 1.74378
\(671\) 7.31910 0.282551
\(672\) 0.361700 0.0139529
\(673\) −29.5007 −1.13717 −0.568585 0.822624i \(-0.692509\pi\)
−0.568585 + 0.822624i \(0.692509\pi\)
\(674\) −72.9237 −2.80891
\(675\) −2.83565 −0.109144
\(676\) 15.9894 0.614977
\(677\) 26.6087 1.02266 0.511328 0.859386i \(-0.329154\pi\)
0.511328 + 0.859386i \(0.329154\pi\)
\(678\) −5.69716 −0.218798
\(679\) −7.65077 −0.293610
\(680\) −19.8039 −0.759444
\(681\) −0.269983 −0.0103458
\(682\) −4.10825 −0.157313
\(683\) 48.8348 1.86861 0.934306 0.356471i \(-0.116020\pi\)
0.934306 + 0.356471i \(0.116020\pi\)
\(684\) 30.8735 1.18048
\(685\) 7.85320 0.300055
\(686\) −2.45692 −0.0938058
\(687\) 22.0587 0.841592
\(688\) 29.7173 1.13296
\(689\) −11.0838 −0.422260
\(690\) 20.6361 0.785604
\(691\) −38.2014 −1.45325 −0.726624 0.687035i \(-0.758912\pi\)
−0.726624 + 0.687035i \(0.758912\pi\)
\(692\) 0.139809 0.00531475
\(693\) −0.984367 −0.0373930
\(694\) 41.5823 1.57844
\(695\) 34.2149 1.29785
\(696\) −12.4139 −0.470548
\(697\) −4.03461 −0.152822
\(698\) −14.5484 −0.550666
\(699\) 14.9230 0.564441
\(700\) 11.4460 0.432619
\(701\) 44.9529 1.69785 0.848923 0.528517i \(-0.177252\pi\)
0.848923 + 0.528517i \(0.177252\pi\)
\(702\) 10.1186 0.381902
\(703\) −37.1282 −1.40032
\(704\) 7.43359 0.280164
\(705\) 27.0874 1.02017
\(706\) −12.7336 −0.479235
\(707\) −17.3784 −0.653583
\(708\) −32.9314 −1.23764
\(709\) −2.74087 −0.102936 −0.0514678 0.998675i \(-0.516390\pi\)
−0.0514678 + 0.998675i \(0.516390\pi\)
\(710\) 96.3494 3.61593
\(711\) 9.46209 0.354856
\(712\) 41.6007 1.55905
\(713\) 5.09692 0.190881
\(714\) −3.47404 −0.130013
\(715\) 11.3481 0.424395
\(716\) −61.4333 −2.29587
\(717\) −18.5534 −0.692891
\(718\) 25.6430 0.956988
\(719\) −38.4321 −1.43328 −0.716639 0.697445i \(-0.754320\pi\)
−0.716639 + 0.697445i \(0.754320\pi\)
\(720\) −11.8132 −0.440251
\(721\) 7.78687 0.289998
\(722\) −97.0528 −3.61193
\(723\) −2.43794 −0.0906679
\(724\) 38.3879 1.42668
\(725\) −7.03545 −0.261290
\(726\) −24.6455 −0.914678
\(727\) 3.18885 0.118268 0.0591339 0.998250i \(-0.481166\pi\)
0.0591339 + 0.998250i \(0.481166\pi\)
\(728\) −20.6062 −0.763718
\(729\) 1.00000 0.0370370
\(730\) 38.1875 1.41338
\(731\) −9.95689 −0.368269
\(732\) 30.0125 1.10930
\(733\) −5.90014 −0.217926 −0.108963 0.994046i \(-0.534753\pi\)
−0.108963 + 0.994046i \(0.534753\pi\)
\(734\) −48.9660 −1.80737
\(735\) 2.79922 0.103251
\(736\) 1.08529 0.0400045
\(737\) −6.46037 −0.237971
\(738\) −7.01053 −0.258061
\(739\) 2.89835 0.106617 0.0533087 0.998578i \(-0.483023\pi\)
0.0533087 + 0.998578i \(0.483023\pi\)
\(740\) 54.8478 2.01624
\(741\) −31.5002 −1.15719
\(742\) 6.61230 0.242745
\(743\) −17.0729 −0.626344 −0.313172 0.949696i \(-0.601392\pi\)
−0.313172 + 0.949696i \(0.601392\pi\)
\(744\) −8.49920 −0.311596
\(745\) −66.1860 −2.42487
\(746\) −6.42077 −0.235081
\(747\) 12.1889 0.445970
\(748\) 5.61825 0.205424
\(749\) −6.85574 −0.250503
\(750\) 14.8853 0.543533
\(751\) 45.9207 1.67567 0.837835 0.545924i \(-0.183821\pi\)
0.837835 + 0.545924i \(0.183821\pi\)
\(752\) 40.8374 1.48919
\(753\) −1.35703 −0.0494530
\(754\) 25.1049 0.914268
\(755\) 17.8129 0.648278
\(756\) −4.03647 −0.146805
\(757\) 17.1969 0.625033 0.312517 0.949912i \(-0.398828\pi\)
0.312517 + 0.949912i \(0.398828\pi\)
\(758\) 76.1730 2.76673
\(759\) −2.95363 −0.107210
\(760\) 107.125 3.88584
\(761\) −28.3587 −1.02800 −0.514002 0.857789i \(-0.671837\pi\)
−0.514002 + 0.857789i \(0.671837\pi\)
\(762\) 48.4831 1.75636
\(763\) −16.2961 −0.589957
\(764\) −37.5900 −1.35996
\(765\) 3.95804 0.143103
\(766\) 2.45692 0.0887722
\(767\) 33.5998 1.21322
\(768\) 32.2594 1.16406
\(769\) 23.5743 0.850110 0.425055 0.905167i \(-0.360255\pi\)
0.425055 + 0.905167i \(0.360255\pi\)
\(770\) −6.76996 −0.243972
\(771\) 4.66411 0.167974
\(772\) −14.1663 −0.509857
\(773\) −19.0351 −0.684645 −0.342323 0.939582i \(-0.611214\pi\)
−0.342323 + 0.939582i \(0.611214\pi\)
\(774\) −17.3011 −0.621874
\(775\) −4.81683 −0.173026
\(776\) 38.2803 1.37418
\(777\) 4.85422 0.174144
\(778\) −30.8255 −1.10515
\(779\) 21.8245 0.781943
\(780\) 46.5338 1.66618
\(781\) −13.7904 −0.493459
\(782\) −10.4240 −0.372761
\(783\) 2.48107 0.0886662
\(784\) 4.22016 0.150720
\(785\) −27.5540 −0.983445
\(786\) 44.7857 1.59745
\(787\) 34.4990 1.22976 0.614878 0.788622i \(-0.289205\pi\)
0.614878 + 0.788622i \(0.289205\pi\)
\(788\) 73.5126 2.61878
\(789\) −9.57669 −0.340939
\(790\) 65.0753 2.31528
\(791\) −2.31882 −0.0824477
\(792\) 4.92523 0.175011
\(793\) −30.6217 −1.08741
\(794\) 40.6075 1.44111
\(795\) −7.53353 −0.267187
\(796\) −92.0608 −3.26301
\(797\) 29.7462 1.05366 0.526832 0.849970i \(-0.323380\pi\)
0.526832 + 0.849970i \(0.323380\pi\)
\(798\) 18.7921 0.665234
\(799\) −13.6827 −0.484059
\(800\) −1.02565 −0.0362623
\(801\) −8.31439 −0.293775
\(802\) 45.0008 1.58903
\(803\) −5.46574 −0.192882
\(804\) −26.4912 −0.934274
\(805\) 8.39917 0.296032
\(806\) 17.1881 0.605426
\(807\) −10.3269 −0.363522
\(808\) 86.9522 3.05897
\(809\) −32.8674 −1.15555 −0.577777 0.816194i \(-0.696080\pi\)
−0.577777 + 0.816194i \(0.696080\pi\)
\(810\) 6.87748 0.241650
\(811\) 19.1632 0.672910 0.336455 0.941700i \(-0.390772\pi\)
0.336455 + 0.941700i \(0.390772\pi\)
\(812\) −10.0148 −0.351449
\(813\) 12.6993 0.445383
\(814\) −11.7400 −0.411487
\(815\) 10.1058 0.353991
\(816\) 5.96721 0.208894
\(817\) 53.8599 1.88432
\(818\) −35.2889 −1.23385
\(819\) 4.11840 0.143909
\(820\) −32.2403 −1.12588
\(821\) 34.3594 1.19915 0.599575 0.800318i \(-0.295336\pi\)
0.599575 + 0.800318i \(0.295336\pi\)
\(822\) −6.89288 −0.240417
\(823\) 9.59194 0.334354 0.167177 0.985927i \(-0.446535\pi\)
0.167177 + 0.985927i \(0.446535\pi\)
\(824\) −38.9612 −1.35728
\(825\) 2.79132 0.0971813
\(826\) −20.0447 −0.697444
\(827\) 10.9137 0.379506 0.189753 0.981832i \(-0.439231\pi\)
0.189753 + 0.981832i \(0.439231\pi\)
\(828\) −12.1116 −0.420907
\(829\) −38.1767 −1.32593 −0.662966 0.748650i \(-0.730702\pi\)
−0.662966 + 0.748650i \(0.730702\pi\)
\(830\) 83.8291 2.90975
\(831\) −15.4665 −0.536528
\(832\) −31.1007 −1.07822
\(833\) −1.41398 −0.0489914
\(834\) −30.0310 −1.03989
\(835\) 28.2923 0.979097
\(836\) −30.3909 −1.05109
\(837\) 1.69867 0.0587145
\(838\) −13.0942 −0.452331
\(839\) −34.0424 −1.17528 −0.587638 0.809124i \(-0.699942\pi\)
−0.587638 + 0.809124i \(0.699942\pi\)
\(840\) −14.0058 −0.483245
\(841\) −22.8443 −0.787734
\(842\) −23.0616 −0.794755
\(843\) −21.9734 −0.756804
\(844\) −66.5143 −2.28952
\(845\) −11.0884 −0.381452
\(846\) −23.7750 −0.817402
\(847\) −10.0310 −0.344670
\(848\) −11.3577 −0.390025
\(849\) 22.6149 0.776140
\(850\) 9.85115 0.337892
\(851\) 14.5653 0.499291
\(852\) −56.5486 −1.93732
\(853\) 44.3957 1.52008 0.760041 0.649876i \(-0.225179\pi\)
0.760041 + 0.649876i \(0.225179\pi\)
\(854\) 18.2681 0.625120
\(855\) −21.4103 −0.732215
\(856\) 34.3024 1.17243
\(857\) 3.70560 0.126581 0.0632905 0.997995i \(-0.479841\pi\)
0.0632905 + 0.997995i \(0.479841\pi\)
\(858\) −9.96041 −0.340043
\(859\) 14.6259 0.499031 0.249515 0.968371i \(-0.419729\pi\)
0.249515 + 0.968371i \(0.419729\pi\)
\(860\) −79.5647 −2.71313
\(861\) −2.85338 −0.0972429
\(862\) −37.4664 −1.27611
\(863\) 40.5646 1.38083 0.690417 0.723412i \(-0.257427\pi\)
0.690417 + 0.723412i \(0.257427\pi\)
\(864\) 0.361700 0.0123053
\(865\) −0.0969554 −0.00329658
\(866\) 61.9893 2.10648
\(867\) 15.0007 0.509449
\(868\) −6.85662 −0.232729
\(869\) −9.31417 −0.315961
\(870\) 17.0635 0.578507
\(871\) 27.0289 0.915841
\(872\) 81.5366 2.76118
\(873\) −7.65077 −0.258939
\(874\) 56.3865 1.90730
\(875\) 6.05850 0.204815
\(876\) −22.4127 −0.757255
\(877\) 44.0283 1.48673 0.743364 0.668887i \(-0.233229\pi\)
0.743364 + 0.668887i \(0.233229\pi\)
\(878\) −15.5034 −0.523214
\(879\) 5.75828 0.194222
\(880\) 11.6285 0.391996
\(881\) −10.4937 −0.353540 −0.176770 0.984252i \(-0.556565\pi\)
−0.176770 + 0.984252i \(0.556565\pi\)
\(882\) −2.45692 −0.0827289
\(883\) −18.8625 −0.634775 −0.317388 0.948296i \(-0.602806\pi\)
−0.317388 + 0.948296i \(0.602806\pi\)
\(884\) −23.5057 −0.790582
\(885\) 22.8373 0.767668
\(886\) 84.7001 2.84555
\(887\) 26.3462 0.884619 0.442310 0.896862i \(-0.354159\pi\)
0.442310 + 0.896862i \(0.354159\pi\)
\(888\) −24.2879 −0.815048
\(889\) 19.7333 0.661832
\(890\) −57.1820 −1.91675
\(891\) −0.984367 −0.0329775
\(892\) −52.1661 −1.74665
\(893\) 74.0139 2.47678
\(894\) 58.0925 1.94290
\(895\) 42.6029 1.42406
\(896\) 19.2772 0.644007
\(897\) 12.3574 0.412602
\(898\) 61.3349 2.04677
\(899\) 4.21451 0.140562
\(900\) 11.4460 0.381534
\(901\) 3.80543 0.126777
\(902\) 6.90093 0.229776
\(903\) −7.04176 −0.234335
\(904\) 11.6021 0.385880
\(905\) −26.6214 −0.884924
\(906\) −15.6347 −0.519427
\(907\) −13.5496 −0.449908 −0.224954 0.974369i \(-0.572223\pi\)
−0.224954 + 0.974369i \(0.572223\pi\)
\(908\) 1.08978 0.0361656
\(909\) −17.3784 −0.576406
\(910\) 28.3242 0.938938
\(911\) −2.70429 −0.0895972 −0.0447986 0.998996i \(-0.514265\pi\)
−0.0447986 + 0.998996i \(0.514265\pi\)
\(912\) −32.2785 −1.06885
\(913\) −11.9984 −0.397088
\(914\) 71.1885 2.35471
\(915\) −20.8132 −0.688062
\(916\) −89.0394 −2.94194
\(917\) 18.2284 0.601954
\(918\) −3.47404 −0.114660
\(919\) 48.6203 1.60384 0.801918 0.597434i \(-0.203813\pi\)
0.801918 + 0.597434i \(0.203813\pi\)
\(920\) −42.0249 −1.38552
\(921\) −17.0315 −0.561207
\(922\) −74.6576 −2.45872
\(923\) 57.6964 1.89910
\(924\) 3.97337 0.130714
\(925\) −13.7649 −0.452586
\(926\) −47.9130 −1.57452
\(927\) 7.78687 0.255754
\(928\) 0.897403 0.0294587
\(929\) 20.5529 0.674319 0.337160 0.941447i \(-0.390534\pi\)
0.337160 + 0.941447i \(0.390534\pi\)
\(930\) 11.6825 0.383086
\(931\) 7.64864 0.250674
\(932\) −60.2364 −1.97311
\(933\) −0.487175 −0.0159494
\(934\) 32.1780 1.05290
\(935\) −3.89616 −0.127418
\(936\) −20.6062 −0.673536
\(937\) 42.5885 1.39131 0.695653 0.718378i \(-0.255115\pi\)
0.695653 + 0.718378i \(0.255115\pi\)
\(938\) −16.1247 −0.526491
\(939\) −28.5388 −0.931327
\(940\) −109.337 −3.56619
\(941\) 3.51407 0.114556 0.0572778 0.998358i \(-0.481758\pi\)
0.0572778 + 0.998358i \(0.481758\pi\)
\(942\) 24.1846 0.787977
\(943\) −8.56167 −0.278806
\(944\) 34.4300 1.12060
\(945\) 2.79922 0.0910587
\(946\) 17.0306 0.553712
\(947\) 39.5180 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(948\) −38.1935 −1.24047
\(949\) 22.8676 0.742315
\(950\) −53.2879 −1.72889
\(951\) 32.6115 1.05750
\(952\) 7.07477 0.229295
\(953\) 26.3266 0.852803 0.426401 0.904534i \(-0.359781\pi\)
0.426401 + 0.904534i \(0.359781\pi\)
\(954\) 6.61230 0.214081
\(955\) 26.0680 0.843540
\(956\) 74.8904 2.42213
\(957\) −2.44228 −0.0789478
\(958\) 3.92341 0.126760
\(959\) −2.80549 −0.0905941
\(960\) −21.1388 −0.682250
\(961\) −28.1145 −0.906920
\(962\) 49.1179 1.58362
\(963\) −6.85574 −0.220923
\(964\) 9.84067 0.316947
\(965\) 9.82409 0.316249
\(966\) −7.37209 −0.237193
\(967\) 39.9678 1.28528 0.642639 0.766169i \(-0.277840\pi\)
0.642639 + 0.766169i \(0.277840\pi\)
\(968\) 50.1898 1.61316
\(969\) 10.8150 0.347428
\(970\) −52.6180 −1.68946
\(971\) −0.846076 −0.0271519 −0.0135759 0.999908i \(-0.504321\pi\)
−0.0135759 + 0.999908i \(0.504321\pi\)
\(972\) −4.03647 −0.129470
\(973\) −12.2230 −0.391852
\(974\) −7.83692 −0.251111
\(975\) −11.6783 −0.374006
\(976\) −31.3783 −1.00440
\(977\) 37.1676 1.18910 0.594548 0.804060i \(-0.297331\pi\)
0.594548 + 0.804060i \(0.297331\pi\)
\(978\) −8.87002 −0.283632
\(979\) 8.18441 0.261575
\(980\) −11.2990 −0.360933
\(981\) −16.2961 −0.520293
\(982\) −66.4852 −2.12163
\(983\) −11.1171 −0.354579 −0.177289 0.984159i \(-0.556733\pi\)
−0.177289 + 0.984159i \(0.556733\pi\)
\(984\) 14.2768 0.455126
\(985\) −50.9797 −1.62435
\(986\) −8.61933 −0.274495
\(987\) −9.67674 −0.308014
\(988\) 127.150 4.04517
\(989\) −21.1291 −0.671865
\(990\) −6.76996 −0.215163
\(991\) −14.1924 −0.450838 −0.225419 0.974262i \(-0.572375\pi\)
−0.225419 + 0.974262i \(0.572375\pi\)
\(992\) 0.614408 0.0195075
\(993\) −18.1294 −0.575319
\(994\) −34.4201 −1.09174
\(995\) 63.8426 2.02395
\(996\) −49.2003 −1.55897
\(997\) 49.1056 1.55519 0.777595 0.628766i \(-0.216440\pi\)
0.777595 + 0.628766i \(0.216440\pi\)
\(998\) −23.3400 −0.738814
\(999\) 4.85422 0.153581
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 \(a_p\))