Properties

Label 8042.2.a.a.1.20
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.50743 q^{3}\) \(+1.00000 q^{4}\) \(-2.46037 q^{5}\) \(-1.50743 q^{6}\) \(-5.08447 q^{7}\) \(+1.00000 q^{8}\) \(-0.727642 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.50743 q^{3}\) \(+1.00000 q^{4}\) \(-2.46037 q^{5}\) \(-1.50743 q^{6}\) \(-5.08447 q^{7}\) \(+1.00000 q^{8}\) \(-0.727642 q^{9}\) \(-2.46037 q^{10}\) \(+6.13957 q^{11}\) \(-1.50743 q^{12}\) \(-1.35250 q^{13}\) \(-5.08447 q^{14}\) \(+3.70884 q^{15}\) \(+1.00000 q^{16}\) \(+7.01670 q^{17}\) \(-0.727642 q^{18}\) \(-5.54184 q^{19}\) \(-2.46037 q^{20}\) \(+7.66450 q^{21}\) \(+6.13957 q^{22}\) \(-8.72989 q^{23}\) \(-1.50743 q^{24}\) \(+1.05341 q^{25}\) \(-1.35250 q^{26}\) \(+5.61918 q^{27}\) \(-5.08447 q^{28}\) \(+3.89589 q^{29}\) \(+3.70884 q^{30}\) \(+2.99382 q^{31}\) \(+1.00000 q^{32}\) \(-9.25500 q^{33}\) \(+7.01670 q^{34}\) \(+12.5097 q^{35}\) \(-0.727642 q^{36}\) \(+2.45803 q^{37}\) \(-5.54184 q^{38}\) \(+2.03881 q^{39}\) \(-2.46037 q^{40}\) \(+3.56872 q^{41}\) \(+7.66450 q^{42}\) \(+2.60394 q^{43}\) \(+6.13957 q^{44}\) \(+1.79027 q^{45}\) \(-8.72989 q^{46}\) \(+7.26088 q^{47}\) \(-1.50743 q^{48}\) \(+18.8518 q^{49}\) \(+1.05341 q^{50}\) \(-10.5772 q^{51}\) \(-1.35250 q^{52}\) \(-11.4355 q^{53}\) \(+5.61918 q^{54}\) \(-15.1056 q^{55}\) \(-5.08447 q^{56}\) \(+8.35395 q^{57}\) \(+3.89589 q^{58}\) \(+7.78393 q^{59}\) \(+3.70884 q^{60}\) \(+0.118205 q^{61}\) \(+2.99382 q^{62}\) \(+3.69968 q^{63}\) \(+1.00000 q^{64}\) \(+3.32765 q^{65}\) \(-9.25500 q^{66}\) \(+3.26379 q^{67}\) \(+7.01670 q^{68}\) \(+13.1597 q^{69}\) \(+12.5097 q^{70}\) \(+12.1343 q^{71}\) \(-0.727642 q^{72}\) \(-7.86733 q^{73}\) \(+2.45803 q^{74}\) \(-1.58795 q^{75}\) \(-5.54184 q^{76}\) \(-31.2165 q^{77}\) \(+2.03881 q^{78}\) \(-13.3791 q^{79}\) \(-2.46037 q^{80}\) \(-6.28761 q^{81}\) \(+3.56872 q^{82}\) \(+11.8911 q^{83}\) \(+7.66450 q^{84}\) \(-17.2637 q^{85}\) \(+2.60394 q^{86}\) \(-5.87279 q^{87}\) \(+6.13957 q^{88}\) \(-17.2789 q^{89}\) \(+1.79027 q^{90}\) \(+6.87676 q^{91}\) \(-8.72989 q^{92}\) \(-4.51299 q^{93}\) \(+7.26088 q^{94}\) \(+13.6350 q^{95}\) \(-1.50743 q^{96}\) \(+7.57290 q^{97}\) \(+18.8518 q^{98}\) \(-4.46741 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.50743 −0.870318 −0.435159 0.900354i \(-0.643308\pi\)
−0.435159 + 0.900354i \(0.643308\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.46037 −1.10031 −0.550155 0.835063i \(-0.685431\pi\)
−0.550155 + 0.835063i \(0.685431\pi\)
\(6\) −1.50743 −0.615407
\(7\) −5.08447 −1.92175 −0.960875 0.276984i \(-0.910665\pi\)
−0.960875 + 0.276984i \(0.910665\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.727642 −0.242547
\(10\) −2.46037 −0.778037
\(11\) 6.13957 1.85115 0.925575 0.378564i \(-0.123582\pi\)
0.925575 + 0.378564i \(0.123582\pi\)
\(12\) −1.50743 −0.435159
\(13\) −1.35250 −0.375117 −0.187558 0.982253i \(-0.560057\pi\)
−0.187558 + 0.982253i \(0.560057\pi\)
\(14\) −5.08447 −1.35888
\(15\) 3.70884 0.957619
\(16\) 1.00000 0.250000
\(17\) 7.01670 1.70180 0.850900 0.525328i \(-0.176057\pi\)
0.850900 + 0.525328i \(0.176057\pi\)
\(18\) −0.727642 −0.171507
\(19\) −5.54184 −1.27138 −0.635692 0.771943i \(-0.719285\pi\)
−0.635692 + 0.771943i \(0.719285\pi\)
\(20\) −2.46037 −0.550155
\(21\) 7.66450 1.67253
\(22\) 6.13957 1.30896
\(23\) −8.72989 −1.82031 −0.910154 0.414269i \(-0.864037\pi\)
−0.910154 + 0.414269i \(0.864037\pi\)
\(24\) −1.50743 −0.307704
\(25\) 1.05341 0.210682
\(26\) −1.35250 −0.265248
\(27\) 5.61918 1.08141
\(28\) −5.08447 −0.960875
\(29\) 3.89589 0.723448 0.361724 0.932285i \(-0.382188\pi\)
0.361724 + 0.932285i \(0.382188\pi\)
\(30\) 3.70884 0.677139
\(31\) 2.99382 0.537706 0.268853 0.963181i \(-0.413355\pi\)
0.268853 + 0.963181i \(0.413355\pi\)
\(32\) 1.00000 0.176777
\(33\) −9.25500 −1.61109
\(34\) 7.01670 1.20335
\(35\) 12.5097 2.11452
\(36\) −0.727642 −0.121274
\(37\) 2.45803 0.404097 0.202049 0.979376i \(-0.435240\pi\)
0.202049 + 0.979376i \(0.435240\pi\)
\(38\) −5.54184 −0.899005
\(39\) 2.03881 0.326471
\(40\) −2.46037 −0.389018
\(41\) 3.56872 0.557341 0.278670 0.960387i \(-0.410106\pi\)
0.278670 + 0.960387i \(0.410106\pi\)
\(42\) 7.66450 1.18266
\(43\) 2.60394 0.397097 0.198549 0.980091i \(-0.436377\pi\)
0.198549 + 0.980091i \(0.436377\pi\)
\(44\) 6.13957 0.925575
\(45\) 1.79027 0.266877
\(46\) −8.72989 −1.28715
\(47\) 7.26088 1.05911 0.529554 0.848276i \(-0.322359\pi\)
0.529554 + 0.848276i \(0.322359\pi\)
\(48\) −1.50743 −0.217579
\(49\) 18.8518 2.69312
\(50\) 1.05341 0.148975
\(51\) −10.5772 −1.48111
\(52\) −1.35250 −0.187558
\(53\) −11.4355 −1.57079 −0.785395 0.618995i \(-0.787540\pi\)
−0.785395 + 0.618995i \(0.787540\pi\)
\(54\) 5.61918 0.764673
\(55\) −15.1056 −2.03684
\(56\) −5.08447 −0.679441
\(57\) 8.35395 1.10651
\(58\) 3.89589 0.511555
\(59\) 7.78393 1.01338 0.506691 0.862128i \(-0.330869\pi\)
0.506691 + 0.862128i \(0.330869\pi\)
\(60\) 3.70884 0.478810
\(61\) 0.118205 0.0151346 0.00756729 0.999971i \(-0.497591\pi\)
0.00756729 + 0.999971i \(0.497591\pi\)
\(62\) 2.99382 0.380216
\(63\) 3.69968 0.466115
\(64\) 1.00000 0.125000
\(65\) 3.32765 0.412745
\(66\) −9.25500 −1.13921
\(67\) 3.26379 0.398735 0.199367 0.979925i \(-0.436111\pi\)
0.199367 + 0.979925i \(0.436111\pi\)
\(68\) 7.01670 0.850900
\(69\) 13.1597 1.58425
\(70\) 12.5097 1.49519
\(71\) 12.1343 1.44008 0.720039 0.693934i \(-0.244124\pi\)
0.720039 + 0.693934i \(0.244124\pi\)
\(72\) −0.727642 −0.0857535
\(73\) −7.86733 −0.920801 −0.460401 0.887711i \(-0.652294\pi\)
−0.460401 + 0.887711i \(0.652294\pi\)
\(74\) 2.45803 0.285740
\(75\) −1.58795 −0.183361
\(76\) −5.54184 −0.635692
\(77\) −31.2165 −3.55745
\(78\) 2.03881 0.230850
\(79\) −13.3791 −1.50527 −0.752633 0.658440i \(-0.771217\pi\)
−0.752633 + 0.658440i \(0.771217\pi\)
\(80\) −2.46037 −0.275078
\(81\) −6.28761 −0.698623
\(82\) 3.56872 0.394100
\(83\) 11.8911 1.30522 0.652611 0.757693i \(-0.273673\pi\)
0.652611 + 0.757693i \(0.273673\pi\)
\(84\) 7.66450 0.836266
\(85\) −17.2637 −1.87251
\(86\) 2.60394 0.280790
\(87\) −5.87279 −0.629629
\(88\) 6.13957 0.654480
\(89\) −17.2789 −1.83156 −0.915779 0.401681i \(-0.868426\pi\)
−0.915779 + 0.401681i \(0.868426\pi\)
\(90\) 1.79027 0.188711
\(91\) 6.87676 0.720880
\(92\) −8.72989 −0.910154
\(93\) −4.51299 −0.467975
\(94\) 7.26088 0.748903
\(95\) 13.6350 1.39892
\(96\) −1.50743 −0.153852
\(97\) 7.57290 0.768912 0.384456 0.923143i \(-0.374389\pi\)
0.384456 + 0.923143i \(0.374389\pi\)
\(98\) 18.8518 1.90432
\(99\) −4.46741 −0.448992
\(100\) 1.05341 0.105341
\(101\) −16.5960 −1.65136 −0.825680 0.564139i \(-0.809208\pi\)
−0.825680 + 0.564139i \(0.809208\pi\)
\(102\) −10.5772 −1.04730
\(103\) 10.9796 1.08186 0.540928 0.841069i \(-0.318073\pi\)
0.540928 + 0.841069i \(0.318073\pi\)
\(104\) −1.35250 −0.132624
\(105\) −18.8575 −1.84030
\(106\) −11.4355 −1.11072
\(107\) −6.36100 −0.614941 −0.307471 0.951558i \(-0.599483\pi\)
−0.307471 + 0.951558i \(0.599483\pi\)
\(108\) 5.61918 0.540705
\(109\) 10.6018 1.01547 0.507735 0.861513i \(-0.330483\pi\)
0.507735 + 0.861513i \(0.330483\pi\)
\(110\) −15.1056 −1.44026
\(111\) −3.70531 −0.351693
\(112\) −5.08447 −0.480437
\(113\) −8.58785 −0.807877 −0.403939 0.914786i \(-0.632359\pi\)
−0.403939 + 0.914786i \(0.632359\pi\)
\(114\) 8.35395 0.782420
\(115\) 21.4788 2.00290
\(116\) 3.89589 0.361724
\(117\) 0.984138 0.0909836
\(118\) 7.78393 0.716569
\(119\) −35.6762 −3.27043
\(120\) 3.70884 0.338570
\(121\) 26.6943 2.42676
\(122\) 0.118205 0.0107018
\(123\) −5.37962 −0.485064
\(124\) 2.99382 0.268853
\(125\) 9.71006 0.868494
\(126\) 3.69968 0.329593
\(127\) 9.54416 0.846907 0.423454 0.905918i \(-0.360818\pi\)
0.423454 + 0.905918i \(0.360818\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.92527 −0.345601
\(130\) 3.32765 0.291855
\(131\) −1.83025 −0.159909 −0.0799547 0.996799i \(-0.525478\pi\)
−0.0799547 + 0.996799i \(0.525478\pi\)
\(132\) −9.25500 −0.805544
\(133\) 28.1773 2.44328
\(134\) 3.26379 0.281948
\(135\) −13.8252 −1.18989
\(136\) 7.01670 0.601677
\(137\) −4.67347 −0.399281 −0.199641 0.979869i \(-0.563978\pi\)
−0.199641 + 0.979869i \(0.563978\pi\)
\(138\) 13.1597 1.12023
\(139\) −19.8711 −1.68545 −0.842723 0.538347i \(-0.819049\pi\)
−0.842723 + 0.538347i \(0.819049\pi\)
\(140\) 12.5097 1.05726
\(141\) −10.9453 −0.921761
\(142\) 12.1343 1.01829
\(143\) −8.30378 −0.694397
\(144\) −0.727642 −0.0606369
\(145\) −9.58531 −0.796017
\(146\) −7.86733 −0.651105
\(147\) −28.4179 −2.34387
\(148\) 2.45803 0.202049
\(149\) −14.5346 −1.19072 −0.595362 0.803458i \(-0.702991\pi\)
−0.595362 + 0.803458i \(0.702991\pi\)
\(150\) −1.58795 −0.129656
\(151\) −4.73484 −0.385316 −0.192658 0.981266i \(-0.561711\pi\)
−0.192658 + 0.981266i \(0.561711\pi\)
\(152\) −5.54184 −0.449502
\(153\) −5.10565 −0.412767
\(154\) −31.2165 −2.51549
\(155\) −7.36590 −0.591644
\(156\) 2.03881 0.163235
\(157\) 6.50607 0.519241 0.259620 0.965711i \(-0.416403\pi\)
0.259620 + 0.965711i \(0.416403\pi\)
\(158\) −13.3791 −1.06438
\(159\) 17.2383 1.36709
\(160\) −2.46037 −0.194509
\(161\) 44.3869 3.49818
\(162\) −6.28761 −0.494001
\(163\) 6.56285 0.514042 0.257021 0.966406i \(-0.417259\pi\)
0.257021 + 0.966406i \(0.417259\pi\)
\(164\) 3.56872 0.278670
\(165\) 22.7707 1.77270
\(166\) 11.8911 0.922932
\(167\) −11.0561 −0.855550 −0.427775 0.903885i \(-0.640702\pi\)
−0.427775 + 0.903885i \(0.640702\pi\)
\(168\) 7.66450 0.591329
\(169\) −11.1707 −0.859287
\(170\) −17.2637 −1.32406
\(171\) 4.03247 0.308371
\(172\) 2.60394 0.198549
\(173\) −4.68551 −0.356233 −0.178116 0.984009i \(-0.557000\pi\)
−0.178116 + 0.984009i \(0.557000\pi\)
\(174\) −5.87279 −0.445215
\(175\) −5.35604 −0.404879
\(176\) 6.13957 0.462787
\(177\) −11.7338 −0.881964
\(178\) −17.2789 −1.29511
\(179\) 9.67377 0.723051 0.361526 0.932362i \(-0.382256\pi\)
0.361526 + 0.932362i \(0.382256\pi\)
\(180\) 1.79027 0.133439
\(181\) −12.8673 −0.956421 −0.478211 0.878245i \(-0.658714\pi\)
−0.478211 + 0.878245i \(0.658714\pi\)
\(182\) 6.87676 0.509739
\(183\) −0.178186 −0.0131719
\(184\) −8.72989 −0.643576
\(185\) −6.04765 −0.444632
\(186\) −4.51299 −0.330908
\(187\) 43.0795 3.15029
\(188\) 7.26088 0.529554
\(189\) −28.5705 −2.07820
\(190\) 13.6350 0.989184
\(191\) −2.18137 −0.157838 −0.0789192 0.996881i \(-0.525147\pi\)
−0.0789192 + 0.996881i \(0.525147\pi\)
\(192\) −1.50743 −0.108790
\(193\) −10.4373 −0.751293 −0.375647 0.926763i \(-0.622579\pi\)
−0.375647 + 0.926763i \(0.622579\pi\)
\(194\) 7.57290 0.543703
\(195\) −5.01622 −0.359219
\(196\) 18.8518 1.34656
\(197\) 6.26423 0.446308 0.223154 0.974783i \(-0.428365\pi\)
0.223154 + 0.974783i \(0.428365\pi\)
\(198\) −4.46741 −0.317485
\(199\) 4.27957 0.303370 0.151685 0.988429i \(-0.451530\pi\)
0.151685 + 0.988429i \(0.451530\pi\)
\(200\) 1.05341 0.0744875
\(201\) −4.91994 −0.347026
\(202\) −16.5960 −1.16769
\(203\) −19.8085 −1.39029
\(204\) −10.5772 −0.740553
\(205\) −8.78037 −0.613248
\(206\) 10.9796 0.764987
\(207\) 6.35224 0.441511
\(208\) −1.35250 −0.0937792
\(209\) −34.0245 −2.35352
\(210\) −18.8575 −1.30129
\(211\) −9.24903 −0.636730 −0.318365 0.947968i \(-0.603134\pi\)
−0.318365 + 0.947968i \(0.603134\pi\)
\(212\) −11.4355 −0.785395
\(213\) −18.2917 −1.25333
\(214\) −6.36100 −0.434829
\(215\) −6.40665 −0.436930
\(216\) 5.61918 0.382336
\(217\) −15.2220 −1.03334
\(218\) 10.6018 0.718046
\(219\) 11.8595 0.801390
\(220\) −15.1056 −1.01842
\(221\) −9.49010 −0.638373
\(222\) −3.70531 −0.248684
\(223\) 18.5235 1.24042 0.620212 0.784434i \(-0.287047\pi\)
0.620212 + 0.784434i \(0.287047\pi\)
\(224\) −5.08447 −0.339720
\(225\) −0.766507 −0.0511005
\(226\) −8.58785 −0.571256
\(227\) −14.0148 −0.930193 −0.465096 0.885260i \(-0.653980\pi\)
−0.465096 + 0.885260i \(0.653980\pi\)
\(228\) 8.35395 0.553254
\(229\) −19.3989 −1.28191 −0.640956 0.767577i \(-0.721462\pi\)
−0.640956 + 0.767577i \(0.721462\pi\)
\(230\) 21.4788 1.41627
\(231\) 47.0568 3.09611
\(232\) 3.89589 0.255777
\(233\) −16.1292 −1.05666 −0.528330 0.849039i \(-0.677182\pi\)
−0.528330 + 0.849039i \(0.677182\pi\)
\(234\) 0.984138 0.0643351
\(235\) −17.8644 −1.16535
\(236\) 7.78393 0.506691
\(237\) 20.1681 1.31006
\(238\) −35.6762 −2.31254
\(239\) −16.9585 −1.09695 −0.548476 0.836167i \(-0.684792\pi\)
−0.548476 + 0.836167i \(0.684792\pi\)
\(240\) 3.70884 0.239405
\(241\) 27.3400 1.76113 0.880564 0.473928i \(-0.157164\pi\)
0.880564 + 0.473928i \(0.157164\pi\)
\(242\) 26.6943 1.71598
\(243\) −7.37937 −0.473387
\(244\) 0.118205 0.00756729
\(245\) −46.3825 −2.96327
\(246\) −5.37962 −0.342992
\(247\) 7.49535 0.476918
\(248\) 2.99382 0.190108
\(249\) −17.9251 −1.13596
\(250\) 9.71006 0.614118
\(251\) 13.0250 0.822131 0.411065 0.911606i \(-0.365157\pi\)
0.411065 + 0.911606i \(0.365157\pi\)
\(252\) 3.69968 0.233058
\(253\) −53.5978 −3.36966
\(254\) 9.54416 0.598854
\(255\) 26.0238 1.62968
\(256\) 1.00000 0.0625000
\(257\) −3.52106 −0.219638 −0.109819 0.993952i \(-0.535027\pi\)
−0.109819 + 0.993952i \(0.535027\pi\)
\(258\) −3.92527 −0.244377
\(259\) −12.4978 −0.776573
\(260\) 3.32765 0.206372
\(261\) −2.83481 −0.175470
\(262\) −1.83025 −0.113073
\(263\) −14.7974 −0.912449 −0.456225 0.889865i \(-0.650799\pi\)
−0.456225 + 0.889865i \(0.650799\pi\)
\(264\) −9.25500 −0.569606
\(265\) 28.1356 1.72836
\(266\) 28.1773 1.72766
\(267\) 26.0468 1.59404
\(268\) 3.26379 0.199367
\(269\) 7.83519 0.477720 0.238860 0.971054i \(-0.423226\pi\)
0.238860 + 0.971054i \(0.423226\pi\)
\(270\) −13.8252 −0.841377
\(271\) 0.261639 0.0158934 0.00794672 0.999968i \(-0.497470\pi\)
0.00794672 + 0.999968i \(0.497470\pi\)
\(272\) 7.01670 0.425450
\(273\) −10.3663 −0.627395
\(274\) −4.67347 −0.282335
\(275\) 6.46750 0.390005
\(276\) 13.1597 0.792123
\(277\) −20.2781 −1.21839 −0.609196 0.793020i \(-0.708508\pi\)
−0.609196 + 0.793020i \(0.708508\pi\)
\(278\) −19.8711 −1.19179
\(279\) −2.17843 −0.130419
\(280\) 12.5097 0.747596
\(281\) 27.0775 1.61531 0.807653 0.589658i \(-0.200737\pi\)
0.807653 + 0.589658i \(0.200737\pi\)
\(282\) −10.9453 −0.651783
\(283\) 11.3312 0.673568 0.336784 0.941582i \(-0.390661\pi\)
0.336784 + 0.941582i \(0.390661\pi\)
\(284\) 12.1343 0.720039
\(285\) −20.5538 −1.21750
\(286\) −8.30378 −0.491013
\(287\) −18.1451 −1.07107
\(288\) −0.727642 −0.0428767
\(289\) 32.2341 1.89612
\(290\) −9.58531 −0.562869
\(291\) −11.4157 −0.669198
\(292\) −7.86733 −0.460401
\(293\) −23.4273 −1.36864 −0.684319 0.729183i \(-0.739900\pi\)
−0.684319 + 0.729183i \(0.739900\pi\)
\(294\) −28.4179 −1.65737
\(295\) −19.1513 −1.11503
\(296\) 2.45803 0.142870
\(297\) 34.4993 2.00185
\(298\) −14.5346 −0.841969
\(299\) 11.8072 0.682828
\(300\) −1.58795 −0.0916803
\(301\) −13.2397 −0.763121
\(302\) −4.73484 −0.272460
\(303\) 25.0173 1.43721
\(304\) −5.54184 −0.317846
\(305\) −0.290827 −0.0166527
\(306\) −5.10565 −0.291870
\(307\) −12.2086 −0.696779 −0.348390 0.937350i \(-0.613271\pi\)
−0.348390 + 0.937350i \(0.613271\pi\)
\(308\) −31.2165 −1.77872
\(309\) −16.5511 −0.941557
\(310\) −7.36590 −0.418355
\(311\) −0.714648 −0.0405240 −0.0202620 0.999795i \(-0.506450\pi\)
−0.0202620 + 0.999795i \(0.506450\pi\)
\(312\) 2.03881 0.115425
\(313\) −19.5181 −1.10323 −0.551614 0.834100i \(-0.685988\pi\)
−0.551614 + 0.834100i \(0.685988\pi\)
\(314\) 6.50607 0.367159
\(315\) −9.10256 −0.512871
\(316\) −13.3791 −0.752633
\(317\) −20.8123 −1.16894 −0.584468 0.811417i \(-0.698697\pi\)
−0.584468 + 0.811417i \(0.698697\pi\)
\(318\) 17.2383 0.966676
\(319\) 23.9191 1.33921
\(320\) −2.46037 −0.137539
\(321\) 9.58879 0.535194
\(322\) 44.3869 2.47358
\(323\) −38.8854 −2.16364
\(324\) −6.28761 −0.349312
\(325\) −1.42474 −0.0790305
\(326\) 6.56285 0.363483
\(327\) −15.9815 −0.883782
\(328\) 3.56872 0.197050
\(329\) −36.9177 −2.03534
\(330\) 22.7707 1.25349
\(331\) −24.3169 −1.33658 −0.668289 0.743902i \(-0.732973\pi\)
−0.668289 + 0.743902i \(0.732973\pi\)
\(332\) 11.8911 0.652611
\(333\) −1.78856 −0.0980127
\(334\) −11.0561 −0.604965
\(335\) −8.03012 −0.438732
\(336\) 7.66450 0.418133
\(337\) −17.2938 −0.942056 −0.471028 0.882118i \(-0.656117\pi\)
−0.471028 + 0.882118i \(0.656117\pi\)
\(338\) −11.1707 −0.607608
\(339\) 12.9456 0.703110
\(340\) −17.2637 −0.936253
\(341\) 18.3808 0.995375
\(342\) 4.03247 0.218051
\(343\) −60.2603 −3.25375
\(344\) 2.60394 0.140395
\(345\) −32.3778 −1.74316
\(346\) −4.68551 −0.251895
\(347\) −29.9903 −1.60996 −0.804982 0.593299i \(-0.797825\pi\)
−0.804982 + 0.593299i \(0.797825\pi\)
\(348\) −5.87279 −0.314815
\(349\) 1.14031 0.0610395 0.0305197 0.999534i \(-0.490284\pi\)
0.0305197 + 0.999534i \(0.490284\pi\)
\(350\) −5.35604 −0.286292
\(351\) −7.59995 −0.405655
\(352\) 6.13957 0.327240
\(353\) 4.30092 0.228915 0.114457 0.993428i \(-0.463487\pi\)
0.114457 + 0.993428i \(0.463487\pi\)
\(354\) −11.7338 −0.623643
\(355\) −29.8549 −1.58453
\(356\) −17.2789 −0.915779
\(357\) 53.7795 2.84631
\(358\) 9.67377 0.511275
\(359\) 6.62605 0.349710 0.174855 0.984594i \(-0.444054\pi\)
0.174855 + 0.984594i \(0.444054\pi\)
\(360\) 1.79027 0.0943554
\(361\) 11.7120 0.616419
\(362\) −12.8673 −0.676292
\(363\) −40.2399 −2.11205
\(364\) 6.87676 0.360440
\(365\) 19.3565 1.01317
\(366\) −0.178186 −0.00931393
\(367\) −4.25410 −0.222062 −0.111031 0.993817i \(-0.535415\pi\)
−0.111031 + 0.993817i \(0.535415\pi\)
\(368\) −8.72989 −0.455077
\(369\) −2.59675 −0.135182
\(370\) −6.04765 −0.314402
\(371\) 58.1436 3.01866
\(372\) −4.51299 −0.233988
\(373\) −11.8018 −0.611075 −0.305537 0.952180i \(-0.598836\pi\)
−0.305537 + 0.952180i \(0.598836\pi\)
\(374\) 43.0795 2.22759
\(375\) −14.6373 −0.755866
\(376\) 7.26088 0.374452
\(377\) −5.26920 −0.271377
\(378\) −28.5705 −1.46951
\(379\) 20.1557 1.03533 0.517665 0.855584i \(-0.326801\pi\)
0.517665 + 0.855584i \(0.326801\pi\)
\(380\) 13.6350 0.699459
\(381\) −14.3872 −0.737078
\(382\) −2.18137 −0.111609
\(383\) −19.1024 −0.976086 −0.488043 0.872820i \(-0.662289\pi\)
−0.488043 + 0.872820i \(0.662289\pi\)
\(384\) −1.50743 −0.0769259
\(385\) 76.8040 3.91429
\(386\) −10.4373 −0.531244
\(387\) −1.89474 −0.0963149
\(388\) 7.57290 0.384456
\(389\) −9.81847 −0.497816 −0.248908 0.968527i \(-0.580072\pi\)
−0.248908 + 0.968527i \(0.580072\pi\)
\(390\) −5.01622 −0.254006
\(391\) −61.2550 −3.09780
\(392\) 18.8518 0.952162
\(393\) 2.75897 0.139172
\(394\) 6.26423 0.315588
\(395\) 32.9175 1.65626
\(396\) −4.46741 −0.224496
\(397\) 8.71093 0.437189 0.218594 0.975816i \(-0.429853\pi\)
0.218594 + 0.975816i \(0.429853\pi\)
\(398\) 4.27957 0.214515
\(399\) −42.4754 −2.12643
\(400\) 1.05341 0.0526706
\(401\) 38.9361 1.94438 0.972188 0.234203i \(-0.0752481\pi\)
0.972188 + 0.234203i \(0.0752481\pi\)
\(402\) −4.91994 −0.245384
\(403\) −4.04915 −0.201703
\(404\) −16.5960 −0.825680
\(405\) 15.4698 0.768702
\(406\) −19.8085 −0.983080
\(407\) 15.0912 0.748044
\(408\) −10.5772 −0.523650
\(409\) 19.9201 0.984983 0.492492 0.870317i \(-0.336086\pi\)
0.492492 + 0.870317i \(0.336086\pi\)
\(410\) −8.78037 −0.433632
\(411\) 7.04495 0.347502
\(412\) 10.9796 0.540928
\(413\) −39.5772 −1.94747
\(414\) 6.35224 0.312196
\(415\) −29.2566 −1.43615
\(416\) −1.35250 −0.0663119
\(417\) 29.9544 1.46687
\(418\) −34.0245 −1.66419
\(419\) 38.0867 1.86066 0.930328 0.366730i \(-0.119523\pi\)
0.930328 + 0.366730i \(0.119523\pi\)
\(420\) −18.8575 −0.920152
\(421\) −3.33316 −0.162448 −0.0812240 0.996696i \(-0.525883\pi\)
−0.0812240 + 0.996696i \(0.525883\pi\)
\(422\) −9.24903 −0.450236
\(423\) −5.28333 −0.256884
\(424\) −11.4355 −0.555358
\(425\) 7.39147 0.358539
\(426\) −18.2917 −0.886235
\(427\) −0.601009 −0.0290849
\(428\) −6.36100 −0.307471
\(429\) 12.5174 0.604346
\(430\) −6.40665 −0.308956
\(431\) 2.96161 0.142656 0.0713280 0.997453i \(-0.477276\pi\)
0.0713280 + 0.997453i \(0.477276\pi\)
\(432\) 5.61918 0.270353
\(433\) 31.2183 1.50026 0.750128 0.661292i \(-0.229992\pi\)
0.750128 + 0.661292i \(0.229992\pi\)
\(434\) −15.2220 −0.730679
\(435\) 14.4492 0.692788
\(436\) 10.6018 0.507735
\(437\) 48.3797 2.31431
\(438\) 11.8595 0.566668
\(439\) 22.0650 1.05310 0.526552 0.850143i \(-0.323485\pi\)
0.526552 + 0.850143i \(0.323485\pi\)
\(440\) −15.1056 −0.720131
\(441\) −13.7174 −0.653209
\(442\) −9.49010 −0.451398
\(443\) −32.3480 −1.53690 −0.768451 0.639909i \(-0.778972\pi\)
−0.768451 + 0.639909i \(0.778972\pi\)
\(444\) −3.70531 −0.175846
\(445\) 42.5124 2.01528
\(446\) 18.5235 0.877112
\(447\) 21.9100 1.03631
\(448\) −5.08447 −0.240219
\(449\) −19.5080 −0.920639 −0.460319 0.887753i \(-0.652265\pi\)
−0.460319 + 0.887753i \(0.652265\pi\)
\(450\) −0.766507 −0.0361335
\(451\) 21.9104 1.03172
\(452\) −8.58785 −0.403939
\(453\) 7.13747 0.335347
\(454\) −14.0148 −0.657746
\(455\) −16.9194 −0.793192
\(456\) 8.35395 0.391210
\(457\) −37.6584 −1.76158 −0.880792 0.473503i \(-0.842989\pi\)
−0.880792 + 0.473503i \(0.842989\pi\)
\(458\) −19.3989 −0.906449
\(459\) 39.4281 1.84034
\(460\) 21.4788 1.00145
\(461\) 8.88393 0.413766 0.206883 0.978366i \(-0.433668\pi\)
0.206883 + 0.978366i \(0.433668\pi\)
\(462\) 47.0568 2.18928
\(463\) −3.30357 −0.153530 −0.0767650 0.997049i \(-0.524459\pi\)
−0.0767650 + 0.997049i \(0.524459\pi\)
\(464\) 3.89589 0.180862
\(465\) 11.1036 0.514918
\(466\) −16.1292 −0.747171
\(467\) 6.17430 0.285713 0.142856 0.989743i \(-0.454371\pi\)
0.142856 + 0.989743i \(0.454371\pi\)
\(468\) 0.984138 0.0454918
\(469\) −16.5946 −0.766268
\(470\) −17.8644 −0.824026
\(471\) −9.80747 −0.451904
\(472\) 7.78393 0.358285
\(473\) 15.9871 0.735087
\(474\) 20.1681 0.926352
\(475\) −5.83784 −0.267858
\(476\) −35.6762 −1.63522
\(477\) 8.32097 0.380991
\(478\) −16.9585 −0.775662
\(479\) −33.6049 −1.53545 −0.767724 0.640781i \(-0.778611\pi\)
−0.767724 + 0.640781i \(0.778611\pi\)
\(480\) 3.70884 0.169285
\(481\) −3.32449 −0.151584
\(482\) 27.3400 1.24530
\(483\) −66.9103 −3.04452
\(484\) 26.6943 1.21338
\(485\) −18.6321 −0.846042
\(486\) −7.37937 −0.334735
\(487\) 6.50466 0.294754 0.147377 0.989080i \(-0.452917\pi\)
0.147377 + 0.989080i \(0.452917\pi\)
\(488\) 0.118205 0.00535088
\(489\) −9.89306 −0.447380
\(490\) −46.3825 −2.09535
\(491\) 37.9220 1.71139 0.855697 0.517477i \(-0.173129\pi\)
0.855697 + 0.517477i \(0.173129\pi\)
\(492\) −5.37962 −0.242532
\(493\) 27.3363 1.23116
\(494\) 7.49535 0.337232
\(495\) 10.9915 0.494030
\(496\) 2.99382 0.134427
\(497\) −61.6965 −2.76747
\(498\) −17.9251 −0.803244
\(499\) −7.27918 −0.325861 −0.162930 0.986638i \(-0.552095\pi\)
−0.162930 + 0.986638i \(0.552095\pi\)
\(500\) 9.71006 0.434247
\(501\) 16.6664 0.744600
\(502\) 13.0250 0.581334
\(503\) −2.71900 −0.121234 −0.0606170 0.998161i \(-0.519307\pi\)
−0.0606170 + 0.998161i \(0.519307\pi\)
\(504\) 3.69968 0.164797
\(505\) 40.8322 1.81701
\(506\) −53.5978 −2.38271
\(507\) 16.8391 0.747853
\(508\) 9.54416 0.423454
\(509\) 0.244700 0.0108461 0.00542306 0.999985i \(-0.498274\pi\)
0.00542306 + 0.999985i \(0.498274\pi\)
\(510\) 26.0238 1.15235
\(511\) 40.0012 1.76955
\(512\) 1.00000 0.0441942
\(513\) −31.1406 −1.37489
\(514\) −3.52106 −0.155307
\(515\) −27.0139 −1.19038
\(516\) −3.92527 −0.172800
\(517\) 44.5787 1.96057
\(518\) −12.4978 −0.549120
\(519\) 7.06310 0.310036
\(520\) 3.32765 0.145927
\(521\) −10.2034 −0.447017 −0.223509 0.974702i \(-0.571751\pi\)
−0.223509 + 0.974702i \(0.571751\pi\)
\(522\) −2.83481 −0.124076
\(523\) −15.7765 −0.689860 −0.344930 0.938628i \(-0.612097\pi\)
−0.344930 + 0.938628i \(0.612097\pi\)
\(524\) −1.83025 −0.0799547
\(525\) 8.07388 0.352373
\(526\) −14.7974 −0.645199
\(527\) 21.0067 0.915068
\(528\) −9.25500 −0.402772
\(529\) 53.2110 2.31352
\(530\) 28.1356 1.22213
\(531\) −5.66392 −0.245793
\(532\) 28.1773 1.22164
\(533\) −4.82671 −0.209068
\(534\) 26.0468 1.12715
\(535\) 15.6504 0.676626
\(536\) 3.26379 0.140974
\(537\) −14.5826 −0.629284
\(538\) 7.83519 0.337799
\(539\) 115.742 4.98537
\(540\) −13.8252 −0.594944
\(541\) 29.0031 1.24694 0.623470 0.781847i \(-0.285722\pi\)
0.623470 + 0.781847i \(0.285722\pi\)
\(542\) 0.261639 0.0112384
\(543\) 19.3967 0.832390
\(544\) 7.01670 0.300838
\(545\) −26.0844 −1.11733
\(546\) −10.3663 −0.443635
\(547\) −28.7833 −1.23069 −0.615343 0.788260i \(-0.710982\pi\)
−0.615343 + 0.788260i \(0.710982\pi\)
\(548\) −4.67347 −0.199641
\(549\) −0.0860108 −0.00367085
\(550\) 6.46750 0.275775
\(551\) −21.5904 −0.919780
\(552\) 13.1597 0.560116
\(553\) 68.0256 2.89274
\(554\) −20.2781 −0.861533
\(555\) 9.11644 0.386971
\(556\) −19.8711 −0.842723
\(557\) 14.9313 0.632658 0.316329 0.948650i \(-0.397550\pi\)
0.316329 + 0.948650i \(0.397550\pi\)
\(558\) −2.17843 −0.0922203
\(559\) −3.52184 −0.148958
\(560\) 12.5097 0.528630
\(561\) −64.9395 −2.74175
\(562\) 27.0775 1.14219
\(563\) −15.5535 −0.655503 −0.327752 0.944764i \(-0.606291\pi\)
−0.327752 + 0.944764i \(0.606291\pi\)
\(564\) −10.9453 −0.460880
\(565\) 21.1293 0.888916
\(566\) 11.3312 0.476284
\(567\) 31.9692 1.34258
\(568\) 12.1343 0.509144
\(569\) −38.3983 −1.60974 −0.804870 0.593451i \(-0.797765\pi\)
−0.804870 + 0.593451i \(0.797765\pi\)
\(570\) −20.5538 −0.860904
\(571\) 9.72038 0.406785 0.203393 0.979097i \(-0.434803\pi\)
0.203393 + 0.979097i \(0.434803\pi\)
\(572\) −8.30378 −0.347199
\(573\) 3.28827 0.137369
\(574\) −18.1451 −0.757361
\(575\) −9.19618 −0.383507
\(576\) −0.727642 −0.0303184
\(577\) −34.3480 −1.42993 −0.714963 0.699162i \(-0.753557\pi\)
−0.714963 + 0.699162i \(0.753557\pi\)
\(578\) 32.2341 1.34076
\(579\) 15.7335 0.653863
\(580\) −9.58531 −0.398008
\(581\) −60.4602 −2.50831
\(582\) −11.4157 −0.473194
\(583\) −70.2092 −2.90777
\(584\) −7.86733 −0.325552
\(585\) −2.42134 −0.100110
\(586\) −23.4273 −0.967773
\(587\) 5.63871 0.232734 0.116367 0.993206i \(-0.462875\pi\)
0.116367 + 0.993206i \(0.462875\pi\)
\(588\) −28.4179 −1.17193
\(589\) −16.5913 −0.683631
\(590\) −19.1513 −0.788448
\(591\) −9.44292 −0.388430
\(592\) 2.45803 0.101024
\(593\) −3.03585 −0.124667 −0.0623337 0.998055i \(-0.519854\pi\)
−0.0623337 + 0.998055i \(0.519854\pi\)
\(594\) 34.4993 1.41552
\(595\) 87.7766 3.59849
\(596\) −14.5346 −0.595362
\(597\) −6.45116 −0.264029
\(598\) 11.8072 0.482833
\(599\) 21.2626 0.868766 0.434383 0.900728i \(-0.356966\pi\)
0.434383 + 0.900728i \(0.356966\pi\)
\(600\) −1.58795 −0.0648278
\(601\) 5.08342 0.207357 0.103678 0.994611i \(-0.466939\pi\)
0.103678 + 0.994611i \(0.466939\pi\)
\(602\) −13.2397 −0.539608
\(603\) −2.37487 −0.0967121
\(604\) −4.73484 −0.192658
\(605\) −65.6778 −2.67018
\(606\) 25.0173 1.01626
\(607\) −4.64678 −0.188607 −0.0943035 0.995543i \(-0.530062\pi\)
−0.0943035 + 0.995543i \(0.530062\pi\)
\(608\) −5.54184 −0.224751
\(609\) 29.8600 1.20999
\(610\) −0.290827 −0.0117753
\(611\) −9.82037 −0.397289
\(612\) −5.10565 −0.206383
\(613\) 32.1653 1.29914 0.649572 0.760300i \(-0.274948\pi\)
0.649572 + 0.760300i \(0.274948\pi\)
\(614\) −12.2086 −0.492697
\(615\) 13.2358 0.533720
\(616\) −31.2165 −1.25775
\(617\) −10.3097 −0.415051 −0.207526 0.978230i \(-0.566541\pi\)
−0.207526 + 0.978230i \(0.566541\pi\)
\(618\) −16.5511 −0.665782
\(619\) 15.1097 0.607309 0.303655 0.952782i \(-0.401793\pi\)
0.303655 + 0.952782i \(0.401793\pi\)
\(620\) −7.36590 −0.295822
\(621\) −49.0548 −1.96850
\(622\) −0.714648 −0.0286548
\(623\) 87.8540 3.51980
\(624\) 2.03881 0.0816177
\(625\) −29.1574 −1.16630
\(626\) −19.5181 −0.780100
\(627\) 51.2897 2.04831
\(628\) 6.50607 0.259620
\(629\) 17.2472 0.687692
\(630\) −9.10256 −0.362655
\(631\) −5.16314 −0.205541 −0.102771 0.994705i \(-0.532771\pi\)
−0.102771 + 0.994705i \(0.532771\pi\)
\(632\) −13.3791 −0.532192
\(633\) 13.9423 0.554157
\(634\) −20.8123 −0.826562
\(635\) −23.4821 −0.931861
\(636\) 17.2383 0.683543
\(637\) −25.4972 −1.01023
\(638\) 23.9191 0.946965
\(639\) −8.82944 −0.349287
\(640\) −2.46037 −0.0972546
\(641\) 25.3859 1.00268 0.501342 0.865249i \(-0.332840\pi\)
0.501342 + 0.865249i \(0.332840\pi\)
\(642\) 9.58879 0.378439
\(643\) −41.7951 −1.64824 −0.824120 0.566416i \(-0.808330\pi\)
−0.824120 + 0.566416i \(0.808330\pi\)
\(644\) 44.3869 1.74909
\(645\) 9.65761 0.380268
\(646\) −38.8854 −1.52993
\(647\) −22.1478 −0.870720 −0.435360 0.900256i \(-0.643379\pi\)
−0.435360 + 0.900256i \(0.643379\pi\)
\(648\) −6.28761 −0.247001
\(649\) 47.7900 1.87592
\(650\) −1.42474 −0.0558830
\(651\) 22.9462 0.899331
\(652\) 6.56285 0.257021
\(653\) −17.4592 −0.683230 −0.341615 0.939840i \(-0.610974\pi\)
−0.341615 + 0.939840i \(0.610974\pi\)
\(654\) −15.9815 −0.624928
\(655\) 4.50308 0.175950
\(656\) 3.56872 0.139335
\(657\) 5.72460 0.223338
\(658\) −36.9177 −1.43920
\(659\) −31.5496 −1.22900 −0.614499 0.788918i \(-0.710642\pi\)
−0.614499 + 0.788918i \(0.710642\pi\)
\(660\) 22.7707 0.886348
\(661\) 25.0337 0.973699 0.486850 0.873486i \(-0.338146\pi\)
0.486850 + 0.873486i \(0.338146\pi\)
\(662\) −24.3169 −0.945104
\(663\) 14.3057 0.555588
\(664\) 11.8911 0.461466
\(665\) −69.3266 −2.68837
\(666\) −1.78856 −0.0693055
\(667\) −34.0107 −1.31690
\(668\) −11.0561 −0.427775
\(669\) −27.9229 −1.07956
\(670\) −8.03012 −0.310230
\(671\) 0.725727 0.0280164
\(672\) 7.66450 0.295665
\(673\) −5.97534 −0.230333 −0.115166 0.993346i \(-0.536740\pi\)
−0.115166 + 0.993346i \(0.536740\pi\)
\(674\) −17.2938 −0.666134
\(675\) 5.91931 0.227834
\(676\) −11.1707 −0.429644
\(677\) 22.5056 0.864961 0.432481 0.901643i \(-0.357638\pi\)
0.432481 + 0.901643i \(0.357638\pi\)
\(678\) 12.9456 0.497174
\(679\) −38.5042 −1.47766
\(680\) −17.2637 −0.662031
\(681\) 21.1263 0.809563
\(682\) 18.3808 0.703836
\(683\) 3.34161 0.127863 0.0639315 0.997954i \(-0.479636\pi\)
0.0639315 + 0.997954i \(0.479636\pi\)
\(684\) 4.03247 0.154186
\(685\) 11.4985 0.439333
\(686\) −60.2603 −2.30075
\(687\) 29.2425 1.11567
\(688\) 2.60394 0.0992743
\(689\) 15.4666 0.589230
\(690\) −32.3778 −1.23260
\(691\) 32.4859 1.23582 0.617911 0.786248i \(-0.287979\pi\)
0.617911 + 0.786248i \(0.287979\pi\)
\(692\) −4.68551 −0.178116
\(693\) 22.7144 0.862849
\(694\) −29.9903 −1.13842
\(695\) 48.8903 1.85451
\(696\) −5.87279 −0.222608
\(697\) 25.0407 0.948482
\(698\) 1.14031 0.0431614
\(699\) 24.3137 0.919630
\(700\) −5.35604 −0.202439
\(701\) −29.6259 −1.11895 −0.559477 0.828846i \(-0.688998\pi\)
−0.559477 + 0.828846i \(0.688998\pi\)
\(702\) −7.59995 −0.286842
\(703\) −13.6220 −0.513763
\(704\) 6.13957 0.231394
\(705\) 26.9295 1.01422
\(706\) 4.30092 0.161867
\(707\) 84.3817 3.17350
\(708\) −11.7338 −0.440982
\(709\) −29.5063 −1.10813 −0.554066 0.832472i \(-0.686925\pi\)
−0.554066 + 0.832472i \(0.686925\pi\)
\(710\) −29.8549 −1.12043
\(711\) 9.73520 0.365098
\(712\) −17.2789 −0.647554
\(713\) −26.1357 −0.978791
\(714\) 53.7795 2.01265
\(715\) 20.4304 0.764052
\(716\) 9.67377 0.361526
\(717\) 25.5638 0.954696
\(718\) 6.62605 0.247282
\(719\) 50.6198 1.88780 0.943901 0.330229i \(-0.107126\pi\)
0.943901 + 0.330229i \(0.107126\pi\)
\(720\) 1.79027 0.0667193
\(721\) −55.8256 −2.07905
\(722\) 11.7120 0.435874
\(723\) −41.2133 −1.53274
\(724\) −12.8673 −0.478211
\(725\) 4.10397 0.152418
\(726\) −40.2399 −1.49344
\(727\) 42.2365 1.56647 0.783233 0.621729i \(-0.213569\pi\)
0.783233 + 0.621729i \(0.213569\pi\)
\(728\) 6.87676 0.254870
\(729\) 29.9867 1.11062
\(730\) 19.3565 0.716417
\(731\) 18.2711 0.675780
\(732\) −0.178186 −0.00658595
\(733\) 10.9034 0.402725 0.201363 0.979517i \(-0.435463\pi\)
0.201363 + 0.979517i \(0.435463\pi\)
\(734\) −4.25410 −0.157022
\(735\) 69.9185 2.57898
\(736\) −8.72989 −0.321788
\(737\) 20.0382 0.738118
\(738\) −2.59675 −0.0955878
\(739\) 48.4140 1.78094 0.890468 0.455045i \(-0.150377\pi\)
0.890468 + 0.455045i \(0.150377\pi\)
\(740\) −6.04765 −0.222316
\(741\) −11.2987 −0.415070
\(742\) 58.1436 2.13452
\(743\) 34.4891 1.26528 0.632641 0.774445i \(-0.281971\pi\)
0.632641 + 0.774445i \(0.281971\pi\)
\(744\) −4.51299 −0.165454
\(745\) 35.7606 1.31017
\(746\) −11.8018 −0.432095
\(747\) −8.65250 −0.316578
\(748\) 43.0795 1.57514
\(749\) 32.3423 1.18176
\(750\) −14.6373 −0.534478
\(751\) 23.9765 0.874916 0.437458 0.899239i \(-0.355879\pi\)
0.437458 + 0.899239i \(0.355879\pi\)
\(752\) 7.26088 0.264777
\(753\) −19.6343 −0.715515
\(754\) −5.26920 −0.191893
\(755\) 11.6495 0.423967
\(756\) −28.5705 −1.03910
\(757\) −21.5509 −0.783279 −0.391640 0.920119i \(-0.628092\pi\)
−0.391640 + 0.920119i \(0.628092\pi\)
\(758\) 20.1557 0.732089
\(759\) 80.7951 2.93268
\(760\) 13.6350 0.494592
\(761\) 12.6620 0.458997 0.229499 0.973309i \(-0.426291\pi\)
0.229499 + 0.973309i \(0.426291\pi\)
\(762\) −14.3872 −0.521193
\(763\) −53.9046 −1.95148
\(764\) −2.18137 −0.0789192
\(765\) 12.5618 0.454172
\(766\) −19.1024 −0.690197
\(767\) −10.5278 −0.380137
\(768\) −1.50743 −0.0543948
\(769\) −19.7506 −0.712223 −0.356112 0.934443i \(-0.615898\pi\)
−0.356112 + 0.934443i \(0.615898\pi\)
\(770\) 76.8040 2.76782
\(771\) 5.30777 0.191155
\(772\) −10.4373 −0.375647
\(773\) 5.20107 0.187070 0.0935348 0.995616i \(-0.470183\pi\)
0.0935348 + 0.995616i \(0.470183\pi\)
\(774\) −1.89474 −0.0681049
\(775\) 3.15373 0.113285
\(776\) 7.57290 0.271851
\(777\) 18.8396 0.675865
\(778\) −9.81847 −0.352009
\(779\) −19.7773 −0.708595
\(780\) −5.01622 −0.179610
\(781\) 74.4995 2.66580
\(782\) −61.2550 −2.19048
\(783\) 21.8917 0.782344
\(784\) 18.8518 0.673280
\(785\) −16.0073 −0.571326
\(786\) 2.75897 0.0984094
\(787\) −22.0891 −0.787390 −0.393695 0.919241i \(-0.628803\pi\)
−0.393695 + 0.919241i \(0.628803\pi\)
\(788\) 6.26423 0.223154
\(789\) 22.3062 0.794120
\(790\) 32.9175 1.17115
\(791\) 43.6647 1.55254
\(792\) −4.46741 −0.158742
\(793\) −0.159872 −0.00567724
\(794\) 8.71093 0.309139
\(795\) −42.4126 −1.50422
\(796\) 4.27957 0.151685
\(797\) −13.7660 −0.487617 −0.243809 0.969823i \(-0.578397\pi\)
−0.243809 + 0.969823i \(0.578397\pi\)
\(798\) −42.4754 −1.50361
\(799\) 50.9474 1.80239
\(800\) 1.05341 0.0372437
\(801\) 12.5729 0.444240
\(802\) 38.9361 1.37488
\(803\) −48.3020 −1.70454
\(804\) −4.91994 −0.173513
\(805\) −109.208 −3.84908
\(806\) −4.04915 −0.142625
\(807\) −11.8110 −0.415768
\(808\) −16.5960 −0.583844
\(809\) 9.91473 0.348583 0.174292 0.984694i \(-0.444236\pi\)
0.174292 + 0.984694i \(0.444236\pi\)
\(810\) 15.4698 0.543555
\(811\) −25.0294 −0.878902 −0.439451 0.898267i \(-0.644827\pi\)
−0.439451 + 0.898267i \(0.644827\pi\)
\(812\) −19.8085 −0.695143
\(813\) −0.394403 −0.0138323
\(814\) 15.0912 0.528947
\(815\) −16.1470 −0.565606
\(816\) −10.5772 −0.370276
\(817\) −14.4306 −0.504863
\(818\) 19.9201 0.696488
\(819\) −5.00382 −0.174848
\(820\) −8.78037 −0.306624
\(821\) −14.8924 −0.519749 −0.259874 0.965642i \(-0.583681\pi\)
−0.259874 + 0.965642i \(0.583681\pi\)
\(822\) 7.04495 0.245721
\(823\) 8.84132 0.308189 0.154094 0.988056i \(-0.450754\pi\)
0.154094 + 0.988056i \(0.450754\pi\)
\(824\) 10.9796 0.382494
\(825\) −9.74932 −0.339428
\(826\) −39.5772 −1.37707
\(827\) 19.6624 0.683728 0.341864 0.939749i \(-0.388942\pi\)
0.341864 + 0.939749i \(0.388942\pi\)
\(828\) 6.35224 0.220756
\(829\) 9.24352 0.321041 0.160520 0.987033i \(-0.448683\pi\)
0.160520 + 0.987033i \(0.448683\pi\)
\(830\) −29.2566 −1.01551
\(831\) 30.5679 1.06039
\(832\) −1.35250 −0.0468896
\(833\) 132.278 4.58315
\(834\) 29.9544 1.03724
\(835\) 27.2022 0.941370
\(836\) −34.0245 −1.17676
\(837\) 16.8228 0.581481
\(838\) 38.0867 1.31568
\(839\) 47.2432 1.63101 0.815507 0.578747i \(-0.196458\pi\)
0.815507 + 0.578747i \(0.196458\pi\)
\(840\) −18.8575 −0.650646
\(841\) −13.8221 −0.476623
\(842\) −3.33316 −0.114868
\(843\) −40.8175 −1.40583
\(844\) −9.24903 −0.318365
\(845\) 27.4841 0.945483
\(846\) −5.28333 −0.181644
\(847\) −135.726 −4.66362
\(848\) −11.4355 −0.392697
\(849\) −17.0810 −0.586218
\(850\) 7.39147 0.253525
\(851\) −21.4583 −0.735582
\(852\) −18.2917 −0.626663
\(853\) −45.7390 −1.56607 −0.783036 0.621976i \(-0.786330\pi\)
−0.783036 + 0.621976i \(0.786330\pi\)
\(854\) −0.601009 −0.0205661
\(855\) −9.92137 −0.339304
\(856\) −6.36100 −0.217415
\(857\) −5.43679 −0.185717 −0.0928585 0.995679i \(-0.529600\pi\)
−0.0928585 + 0.995679i \(0.529600\pi\)
\(858\) 12.5174 0.427337
\(859\) 41.9422 1.43105 0.715525 0.698587i \(-0.246188\pi\)
0.715525 + 0.698587i \(0.246188\pi\)
\(860\) −6.40665 −0.218465
\(861\) 27.3525 0.932171
\(862\) 2.96161 0.100873
\(863\) −14.5329 −0.494704 −0.247352 0.968926i \(-0.579560\pi\)
−0.247352 + 0.968926i \(0.579560\pi\)
\(864\) 5.61918 0.191168
\(865\) 11.5281 0.391967
\(866\) 31.2183 1.06084
\(867\) −48.5907 −1.65023
\(868\) −15.2220 −0.516668
\(869\) −82.1419 −2.78647
\(870\) 14.4492 0.489875
\(871\) −4.41428 −0.149572
\(872\) 10.6018 0.359023
\(873\) −5.51036 −0.186498
\(874\) 48.3797 1.63647
\(875\) −49.3705 −1.66903
\(876\) 11.8595 0.400695
\(877\) −14.2458 −0.481045 −0.240523 0.970644i \(-0.577319\pi\)
−0.240523 + 0.970644i \(0.577319\pi\)
\(878\) 22.0650 0.744657
\(879\) 35.3151 1.19115
\(880\) −15.1056 −0.509210
\(881\) −22.1206 −0.745262 −0.372631 0.927980i \(-0.621544\pi\)
−0.372631 + 0.927980i \(0.621544\pi\)
\(882\) −13.7174 −0.461889
\(883\) 46.1779 1.55401 0.777005 0.629495i \(-0.216738\pi\)
0.777005 + 0.629495i \(0.216738\pi\)
\(884\) −9.49010 −0.319187
\(885\) 28.8694 0.970434
\(886\) −32.3480 −1.08675
\(887\) −13.9149 −0.467216 −0.233608 0.972331i \(-0.575053\pi\)
−0.233608 + 0.972331i \(0.575053\pi\)
\(888\) −3.70531 −0.124342
\(889\) −48.5270 −1.62754
\(890\) 42.5124 1.42502
\(891\) −38.6032 −1.29326
\(892\) 18.5235 0.620212
\(893\) −40.2386 −1.34653
\(894\) 21.9100 0.732780
\(895\) −23.8010 −0.795581
\(896\) −5.08447 −0.169860
\(897\) −17.7986 −0.594277
\(898\) −19.5080 −0.650990
\(899\) 11.6636 0.389002
\(900\) −0.766507 −0.0255502
\(901\) −80.2396 −2.67317
\(902\) 21.9104 0.729537
\(903\) 19.9579 0.664158
\(904\) −8.58785 −0.285628
\(905\) 31.6584 1.05236
\(906\) 7.13747 0.237126
\(907\) 47.8753 1.58967 0.794837 0.606823i \(-0.207556\pi\)
0.794837 + 0.606823i \(0.207556\pi\)
\(908\) −14.0148 −0.465096
\(909\) 12.0759 0.400533
\(910\) −16.9194 −0.560871
\(911\) −48.5759 −1.60939 −0.804695 0.593688i \(-0.797671\pi\)
−0.804695 + 0.593688i \(0.797671\pi\)
\(912\) 8.35395 0.276627
\(913\) 73.0065 2.41616
\(914\) −37.6584 −1.24563
\(915\) 0.438403 0.0144932
\(916\) −19.3989 −0.640956
\(917\) 9.30583 0.307306
\(918\) 39.4281 1.30132
\(919\) −52.4784 −1.73110 −0.865551 0.500821i \(-0.833031\pi\)
−0.865551 + 0.500821i \(0.833031\pi\)
\(920\) 21.4788 0.708134
\(921\) 18.4036 0.606419
\(922\) 8.88393 0.292577
\(923\) −16.4117 −0.540197
\(924\) 47.0568 1.54805
\(925\) 2.58932 0.0851362
\(926\) −3.30357 −0.108562
\(927\) −7.98924 −0.262401
\(928\) 3.89589 0.127889
\(929\) −47.5590 −1.56036 −0.780181 0.625554i \(-0.784873\pi\)
−0.780181 + 0.625554i \(0.784873\pi\)
\(930\) 11.1036 0.364102
\(931\) −104.474 −3.42399
\(932\) −16.1292 −0.528330
\(933\) 1.07729 0.0352687
\(934\) 6.17430 0.202029
\(935\) −105.991 −3.46629
\(936\) 0.984138 0.0321676
\(937\) −3.73233 −0.121930 −0.0609649 0.998140i \(-0.519418\pi\)
−0.0609649 + 0.998140i \(0.519418\pi\)
\(938\) −16.5946 −0.541834
\(939\) 29.4222 0.960158
\(940\) −17.8644 −0.582674
\(941\) 25.0433 0.816389 0.408194 0.912895i \(-0.366159\pi\)
0.408194 + 0.912895i \(0.366159\pi\)
\(942\) −9.80747 −0.319545
\(943\) −31.1546 −1.01453
\(944\) 7.78393 0.253345
\(945\) 70.2940 2.28666
\(946\) 15.9871 0.519785
\(947\) −12.3962 −0.402821 −0.201410 0.979507i \(-0.564552\pi\)
−0.201410 + 0.979507i \(0.564552\pi\)
\(948\) 20.1681 0.655030
\(949\) 10.6406 0.345408
\(950\) −5.83784 −0.189404
\(951\) 31.3732 1.01734
\(952\) −35.6762 −1.15627
\(953\) 15.8362 0.512986 0.256493 0.966546i \(-0.417433\pi\)
0.256493 + 0.966546i \(0.417433\pi\)
\(954\) 8.32097 0.269401
\(955\) 5.36697 0.173671
\(956\) −16.9585 −0.548476
\(957\) −36.0564 −1.16554
\(958\) −33.6049 −1.08573
\(959\) 23.7621 0.767319
\(960\) 3.70884 0.119702
\(961\) −22.0370 −0.710872
\(962\) −3.32449 −0.107186
\(963\) 4.62853 0.149152
\(964\) 27.3400 0.880564
\(965\) 25.6796 0.826655
\(966\) −66.9103 −2.15280
\(967\) −59.3223 −1.90768 −0.953838 0.300321i \(-0.902906\pi\)
−0.953838 + 0.300321i \(0.902906\pi\)
\(968\) 26.6943 0.857988
\(969\) 58.6172 1.88306
\(970\) −18.6321 −0.598242
\(971\) 41.5975 1.33493 0.667464 0.744642i \(-0.267380\pi\)
0.667464 + 0.744642i \(0.267380\pi\)
\(972\) −7.37937 −0.236693
\(973\) 101.034 3.23900
\(974\) 6.50466 0.208423
\(975\) 2.14771 0.0687816
\(976\) 0.118205 0.00378365
\(977\) −23.5074 −0.752069 −0.376034 0.926606i \(-0.622713\pi\)
−0.376034 + 0.926606i \(0.622713\pi\)
\(978\) −9.89306 −0.316345
\(979\) −106.085 −3.39049
\(980\) −46.3825 −1.48163
\(981\) −7.71433 −0.246300
\(982\) 37.9220 1.21014
\(983\) 49.6256 1.58281 0.791406 0.611291i \(-0.209350\pi\)
0.791406 + 0.611291i \(0.209350\pi\)
\(984\) −5.37962 −0.171496
\(985\) −15.4123 −0.491077
\(986\) 27.3363 0.870564
\(987\) 55.6511 1.77139
\(988\) 7.49535 0.238459
\(989\) −22.7321 −0.722840
\(990\) 10.9915 0.349332
\(991\) 61.1688 1.94309 0.971545 0.236853i \(-0.0761161\pi\)
0.971545 + 0.236853i \(0.0761161\pi\)
\(992\) 2.99382 0.0950539
\(993\) 36.6561 1.16325
\(994\) −61.6965 −1.95690
\(995\) −10.5293 −0.333801
\(996\) −17.9251 −0.567979
\(997\) 8.88082 0.281258 0.140629 0.990062i \(-0.455087\pi\)
0.140629 + 0.990062i \(0.455087\pi\)
\(998\) −7.27918 −0.230418
\(999\) 13.8121 0.436995
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 \(a_p\))