Properties

Label 8041.2.a.j.1.20
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.62861 q^{2}\) \(-2.08850 q^{3}\) \(+0.652359 q^{4}\) \(-3.32951 q^{5}\) \(+3.40134 q^{6}\) \(-5.07571 q^{7}\) \(+2.19478 q^{8}\) \(+1.36181 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.62861 q^{2}\) \(-2.08850 q^{3}\) \(+0.652359 q^{4}\) \(-3.32951 q^{5}\) \(+3.40134 q^{6}\) \(-5.07571 q^{7}\) \(+2.19478 q^{8}\) \(+1.36181 q^{9}\) \(+5.42246 q^{10}\) \(+1.00000 q^{11}\) \(-1.36245 q^{12}\) \(-0.291030 q^{13}\) \(+8.26634 q^{14}\) \(+6.95367 q^{15}\) \(-4.87915 q^{16}\) \(+1.00000 q^{17}\) \(-2.21786 q^{18}\) \(+7.07744 q^{19}\) \(-2.17204 q^{20}\) \(+10.6006 q^{21}\) \(-1.62861 q^{22}\) \(+1.66635 q^{23}\) \(-4.58378 q^{24}\) \(+6.08564 q^{25}\) \(+0.473973 q^{26}\) \(+3.42135 q^{27}\) \(-3.31119 q^{28}\) \(-4.92017 q^{29}\) \(-11.3248 q^{30}\) \(-5.61097 q^{31}\) \(+3.55666 q^{32}\) \(-2.08850 q^{33}\) \(-1.62861 q^{34}\) \(+16.8996 q^{35}\) \(+0.888390 q^{36}\) \(+8.06861 q^{37}\) \(-11.5264 q^{38}\) \(+0.607814 q^{39}\) \(-7.30753 q^{40}\) \(-2.39391 q^{41}\) \(-17.2642 q^{42}\) \(+1.00000 q^{43}\) \(+0.652359 q^{44}\) \(-4.53417 q^{45}\) \(-2.71383 q^{46}\) \(+6.60547 q^{47}\) \(+10.1901 q^{48}\) \(+18.7629 q^{49}\) \(-9.91112 q^{50}\) \(-2.08850 q^{51}\) \(-0.189856 q^{52}\) \(+9.64367 q^{53}\) \(-5.57203 q^{54}\) \(-3.32951 q^{55}\) \(-11.1401 q^{56}\) \(-14.7812 q^{57}\) \(+8.01303 q^{58}\) \(+13.7484 q^{59}\) \(+4.53629 q^{60}\) \(+14.9930 q^{61}\) \(+9.13806 q^{62}\) \(-6.91216 q^{63}\) \(+3.96590 q^{64}\) \(+0.968986 q^{65}\) \(+3.40134 q^{66}\) \(+1.40254 q^{67}\) \(+0.652359 q^{68}\) \(-3.48017 q^{69}\) \(-27.5229 q^{70}\) \(+7.30119 q^{71}\) \(+2.98887 q^{72}\) \(-12.2232 q^{73}\) \(-13.1406 q^{74}\) \(-12.7098 q^{75}\) \(+4.61703 q^{76}\) \(-5.07571 q^{77}\) \(-0.989890 q^{78}\) \(-6.07658 q^{79}\) \(+16.2452 q^{80}\) \(-11.2309 q^{81}\) \(+3.89874 q^{82}\) \(-1.31345 q^{83}\) \(+6.91540 q^{84}\) \(-3.32951 q^{85}\) \(-1.62861 q^{86}\) \(+10.2758 q^{87}\) \(+2.19478 q^{88}\) \(-4.77370 q^{89}\) \(+7.38437 q^{90}\) \(+1.47718 q^{91}\) \(+1.08706 q^{92}\) \(+11.7185 q^{93}\) \(-10.7577 q^{94}\) \(-23.5644 q^{95}\) \(-7.42806 q^{96}\) \(+1.25500 q^{97}\) \(-30.5573 q^{98}\) \(+1.36181 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.62861 −1.15160 −0.575799 0.817591i \(-0.695309\pi\)
−0.575799 + 0.817591i \(0.695309\pi\)
\(3\) −2.08850 −1.20579 −0.602897 0.797819i \(-0.705987\pi\)
−0.602897 + 0.797819i \(0.705987\pi\)
\(4\) 0.652359 0.326180
\(5\) −3.32951 −1.48900 −0.744501 0.667621i \(-0.767313\pi\)
−0.744501 + 0.667621i \(0.767313\pi\)
\(6\) 3.40134 1.38859
\(7\) −5.07571 −1.91844 −0.959219 0.282663i \(-0.908782\pi\)
−0.959219 + 0.282663i \(0.908782\pi\)
\(8\) 2.19478 0.775971
\(9\) 1.36181 0.453937
\(10\) 5.42246 1.71473
\(11\) 1.00000 0.301511
\(12\) −1.36245 −0.393305
\(13\) −0.291030 −0.0807171 −0.0403586 0.999185i \(-0.512850\pi\)
−0.0403586 + 0.999185i \(0.512850\pi\)
\(14\) 8.26634 2.20927
\(15\) 6.95367 1.79543
\(16\) −4.87915 −1.21979
\(17\) 1.00000 0.242536
\(18\) −2.21786 −0.522754
\(19\) 7.07744 1.62368 0.811838 0.583883i \(-0.198467\pi\)
0.811838 + 0.583883i \(0.198467\pi\)
\(20\) −2.17204 −0.485682
\(21\) 10.6006 2.31324
\(22\) −1.62861 −0.347220
\(23\) 1.66635 0.347459 0.173729 0.984793i \(-0.444418\pi\)
0.173729 + 0.984793i \(0.444418\pi\)
\(24\) −4.58378 −0.935660
\(25\) 6.08564 1.21713
\(26\) 0.473973 0.0929537
\(27\) 3.42135 0.658439
\(28\) −3.31119 −0.625756
\(29\) −4.92017 −0.913654 −0.456827 0.889556i \(-0.651014\pi\)
−0.456827 + 0.889556i \(0.651014\pi\)
\(30\) −11.3248 −2.06761
\(31\) −5.61097 −1.00776 −0.503880 0.863774i \(-0.668095\pi\)
−0.503880 + 0.863774i \(0.668095\pi\)
\(32\) 3.55666 0.628734
\(33\) −2.08850 −0.363560
\(34\) −1.62861 −0.279304
\(35\) 16.8996 2.85656
\(36\) 0.888390 0.148065
\(37\) 8.06861 1.32647 0.663236 0.748410i \(-0.269183\pi\)
0.663236 + 0.748410i \(0.269183\pi\)
\(38\) −11.5264 −1.86982
\(39\) 0.607814 0.0973281
\(40\) −7.30753 −1.15542
\(41\) −2.39391 −0.373866 −0.186933 0.982373i \(-0.559855\pi\)
−0.186933 + 0.982373i \(0.559855\pi\)
\(42\) −17.2642 −2.66392
\(43\) 1.00000 0.152499
\(44\) 0.652359 0.0983468
\(45\) −4.53417 −0.675914
\(46\) −2.71383 −0.400133
\(47\) 6.60547 0.963507 0.481753 0.876307i \(-0.340000\pi\)
0.481753 + 0.876307i \(0.340000\pi\)
\(48\) 10.1901 1.47081
\(49\) 18.7629 2.68041
\(50\) −9.91112 −1.40164
\(51\) −2.08850 −0.292448
\(52\) −0.189856 −0.0263283
\(53\) 9.64367 1.32466 0.662330 0.749212i \(-0.269568\pi\)
0.662330 + 0.749212i \(0.269568\pi\)
\(54\) −5.57203 −0.758257
\(55\) −3.32951 −0.448951
\(56\) −11.1401 −1.48865
\(57\) −14.7812 −1.95782
\(58\) 8.01303 1.05216
\(59\) 13.7484 1.78989 0.894947 0.446173i \(-0.147213\pi\)
0.894947 + 0.446173i \(0.147213\pi\)
\(60\) 4.53629 0.585632
\(61\) 14.9930 1.91966 0.959828 0.280590i \(-0.0905302\pi\)
0.959828 + 0.280590i \(0.0905302\pi\)
\(62\) 9.13806 1.16054
\(63\) −6.91216 −0.870851
\(64\) 3.96590 0.495737
\(65\) 0.968986 0.120188
\(66\) 3.40134 0.418676
\(67\) 1.40254 0.171347 0.0856735 0.996323i \(-0.472696\pi\)
0.0856735 + 0.996323i \(0.472696\pi\)
\(68\) 0.652359 0.0791102
\(69\) −3.48017 −0.418963
\(70\) −27.5229 −3.28961
\(71\) 7.30119 0.866492 0.433246 0.901276i \(-0.357368\pi\)
0.433246 + 0.901276i \(0.357368\pi\)
\(72\) 2.98887 0.352242
\(73\) −12.2232 −1.43061 −0.715307 0.698810i \(-0.753713\pi\)
−0.715307 + 0.698810i \(0.753713\pi\)
\(74\) −13.1406 −1.52756
\(75\) −12.7098 −1.46761
\(76\) 4.61703 0.529610
\(77\) −5.07571 −0.578431
\(78\) −0.989890 −0.112083
\(79\) −6.07658 −0.683668 −0.341834 0.939760i \(-0.611048\pi\)
−0.341834 + 0.939760i \(0.611048\pi\)
\(80\) 16.2452 1.81627
\(81\) −11.2309 −1.24788
\(82\) 3.89874 0.430544
\(83\) −1.31345 −0.144170 −0.0720851 0.997398i \(-0.522965\pi\)
−0.0720851 + 0.997398i \(0.522965\pi\)
\(84\) 6.91540 0.754532
\(85\) −3.32951 −0.361136
\(86\) −1.62861 −0.175617
\(87\) 10.2758 1.10168
\(88\) 2.19478 0.233964
\(89\) −4.77370 −0.506011 −0.253006 0.967465i \(-0.581419\pi\)
−0.253006 + 0.967465i \(0.581419\pi\)
\(90\) 7.38437 0.778381
\(91\) 1.47718 0.154851
\(92\) 1.08706 0.113334
\(93\) 11.7185 1.21515
\(94\) −10.7577 −1.10957
\(95\) −23.5644 −2.41766
\(96\) −7.42806 −0.758123
\(97\) 1.25500 0.127426 0.0637130 0.997968i \(-0.479706\pi\)
0.0637130 + 0.997968i \(0.479706\pi\)
\(98\) −30.5573 −3.08675
\(99\) 1.36181 0.136867
\(100\) 3.97003 0.397003
\(101\) 10.9162 1.08620 0.543099 0.839669i \(-0.317251\pi\)
0.543099 + 0.839669i \(0.317251\pi\)
\(102\) 3.40134 0.336783
\(103\) −11.9102 −1.17355 −0.586775 0.809750i \(-0.699603\pi\)
−0.586775 + 0.809750i \(0.699603\pi\)
\(104\) −0.638745 −0.0626341
\(105\) −35.2948 −3.44442
\(106\) −15.7057 −1.52548
\(107\) −12.9562 −1.25252 −0.626262 0.779613i \(-0.715416\pi\)
−0.626262 + 0.779613i \(0.715416\pi\)
\(108\) 2.23195 0.214769
\(109\) 19.3440 1.85281 0.926407 0.376523i \(-0.122880\pi\)
0.926407 + 0.376523i \(0.122880\pi\)
\(110\) 5.42246 0.517012
\(111\) −16.8513 −1.59945
\(112\) 24.7651 2.34009
\(113\) −10.0690 −0.947209 −0.473605 0.880738i \(-0.657047\pi\)
−0.473605 + 0.880738i \(0.657047\pi\)
\(114\) 24.0727 2.25462
\(115\) −5.54814 −0.517367
\(116\) −3.20972 −0.298015
\(117\) −0.396328 −0.0366405
\(118\) −22.3908 −2.06124
\(119\) −5.07571 −0.465290
\(120\) 15.2617 1.39320
\(121\) 1.00000 0.0909091
\(122\) −24.4177 −2.21067
\(123\) 4.99967 0.450805
\(124\) −3.66037 −0.328711
\(125\) −3.61466 −0.323305
\(126\) 11.2572 1.00287
\(127\) 14.7795 1.31147 0.655733 0.754993i \(-0.272360\pi\)
0.655733 + 0.754993i \(0.272360\pi\)
\(128\) −13.5722 −1.19962
\(129\) −2.08850 −0.183882
\(130\) −1.57810 −0.138408
\(131\) −21.9985 −1.92202 −0.961010 0.276514i \(-0.910821\pi\)
−0.961010 + 0.276514i \(0.910821\pi\)
\(132\) −1.36245 −0.118586
\(133\) −35.9230 −3.11492
\(134\) −2.28418 −0.197323
\(135\) −11.3914 −0.980417
\(136\) 2.19478 0.188201
\(137\) −11.4506 −0.978294 −0.489147 0.872201i \(-0.662692\pi\)
−0.489147 + 0.872201i \(0.662692\pi\)
\(138\) 5.66783 0.482478
\(139\) −6.06668 −0.514569 −0.257284 0.966336i \(-0.582828\pi\)
−0.257284 + 0.966336i \(0.582828\pi\)
\(140\) 11.0246 0.931752
\(141\) −13.7955 −1.16179
\(142\) −11.8908 −0.997851
\(143\) −0.291030 −0.0243371
\(144\) −6.64448 −0.553706
\(145\) 16.3818 1.36043
\(146\) 19.9067 1.64749
\(147\) −39.1861 −3.23202
\(148\) 5.26363 0.432668
\(149\) −6.38373 −0.522975 −0.261488 0.965207i \(-0.584213\pi\)
−0.261488 + 0.965207i \(0.584213\pi\)
\(150\) 20.6993 1.69009
\(151\) 1.42651 0.116088 0.0580439 0.998314i \(-0.481514\pi\)
0.0580439 + 0.998314i \(0.481514\pi\)
\(152\) 15.5334 1.25992
\(153\) 1.36181 0.110096
\(154\) 8.26634 0.666120
\(155\) 18.6818 1.50056
\(156\) 0.396513 0.0317464
\(157\) −1.02272 −0.0816221 −0.0408110 0.999167i \(-0.512994\pi\)
−0.0408110 + 0.999167i \(0.512994\pi\)
\(158\) 9.89635 0.787311
\(159\) −20.1408 −1.59727
\(160\) −11.8419 −0.936186
\(161\) −8.45793 −0.666578
\(162\) 18.2907 1.43705
\(163\) 19.0310 1.49063 0.745313 0.666715i \(-0.232300\pi\)
0.745313 + 0.666715i \(0.232300\pi\)
\(164\) −1.56169 −0.121947
\(165\) 6.95367 0.541342
\(166\) 2.13910 0.166026
\(167\) 1.56173 0.120850 0.0604252 0.998173i \(-0.480754\pi\)
0.0604252 + 0.998173i \(0.480754\pi\)
\(168\) 23.2659 1.79501
\(169\) −12.9153 −0.993485
\(170\) 5.42246 0.415884
\(171\) 9.63814 0.737047
\(172\) 0.652359 0.0497419
\(173\) 9.72343 0.739259 0.369629 0.929179i \(-0.379485\pi\)
0.369629 + 0.929179i \(0.379485\pi\)
\(174\) −16.7352 −1.26869
\(175\) −30.8890 −2.33499
\(176\) −4.87915 −0.367779
\(177\) −28.7135 −2.15824
\(178\) 7.77448 0.582722
\(179\) 3.23929 0.242116 0.121058 0.992645i \(-0.461371\pi\)
0.121058 + 0.992645i \(0.461371\pi\)
\(180\) −2.95791 −0.220469
\(181\) 11.2818 0.838572 0.419286 0.907854i \(-0.362280\pi\)
0.419286 + 0.907854i \(0.362280\pi\)
\(182\) −2.40575 −0.178326
\(183\) −31.3128 −2.31471
\(184\) 3.65727 0.269618
\(185\) −26.8645 −1.97512
\(186\) −19.0848 −1.39937
\(187\) 1.00000 0.0731272
\(188\) 4.30914 0.314276
\(189\) −17.3658 −1.26317
\(190\) 38.3771 2.78417
\(191\) 19.3859 1.40271 0.701357 0.712810i \(-0.252578\pi\)
0.701357 + 0.712810i \(0.252578\pi\)
\(192\) −8.28276 −0.597757
\(193\) −14.8428 −1.06841 −0.534205 0.845355i \(-0.679389\pi\)
−0.534205 + 0.845355i \(0.679389\pi\)
\(194\) −2.04390 −0.146744
\(195\) −2.02372 −0.144922
\(196\) 12.2401 0.874294
\(197\) 11.5745 0.824653 0.412326 0.911036i \(-0.364716\pi\)
0.412326 + 0.911036i \(0.364716\pi\)
\(198\) −2.21786 −0.157616
\(199\) −8.60612 −0.610072 −0.305036 0.952341i \(-0.598668\pi\)
−0.305036 + 0.952341i \(0.598668\pi\)
\(200\) 13.3566 0.944456
\(201\) −2.92919 −0.206609
\(202\) −17.7781 −1.25086
\(203\) 24.9734 1.75279
\(204\) −1.36245 −0.0953905
\(205\) 7.97055 0.556687
\(206\) 19.3971 1.35146
\(207\) 2.26926 0.157724
\(208\) 1.41998 0.0984576
\(209\) 7.07744 0.489557
\(210\) 57.4814 3.96659
\(211\) −4.22581 −0.290916 −0.145458 0.989364i \(-0.546466\pi\)
−0.145458 + 0.989364i \(0.546466\pi\)
\(212\) 6.29114 0.432077
\(213\) −15.2485 −1.04481
\(214\) 21.1005 1.44240
\(215\) −3.32951 −0.227071
\(216\) 7.50910 0.510929
\(217\) 28.4797 1.93333
\(218\) −31.5037 −2.13370
\(219\) 25.5280 1.72503
\(220\) −2.17204 −0.146439
\(221\) −0.291030 −0.0195768
\(222\) 27.4441 1.84193
\(223\) −27.5315 −1.84364 −0.921822 0.387613i \(-0.873300\pi\)
−0.921822 + 0.387613i \(0.873300\pi\)
\(224\) −18.0526 −1.20619
\(225\) 8.28750 0.552500
\(226\) 16.3984 1.09080
\(227\) 12.0603 0.800473 0.400236 0.916412i \(-0.368928\pi\)
0.400236 + 0.916412i \(0.368928\pi\)
\(228\) −9.64265 −0.638600
\(229\) 10.5284 0.695734 0.347867 0.937544i \(-0.386906\pi\)
0.347867 + 0.937544i \(0.386906\pi\)
\(230\) 9.03574 0.595799
\(231\) 10.6006 0.697468
\(232\) −10.7987 −0.708968
\(233\) −9.44338 −0.618656 −0.309328 0.950955i \(-0.600104\pi\)
−0.309328 + 0.950955i \(0.600104\pi\)
\(234\) 0.645462 0.0421952
\(235\) −21.9930 −1.43466
\(236\) 8.96892 0.583827
\(237\) 12.6909 0.824363
\(238\) 8.26634 0.535827
\(239\) 21.1275 1.36662 0.683312 0.730126i \(-0.260539\pi\)
0.683312 + 0.730126i \(0.260539\pi\)
\(240\) −33.9280 −2.19004
\(241\) 10.9561 0.705741 0.352871 0.935672i \(-0.385206\pi\)
0.352871 + 0.935672i \(0.385206\pi\)
\(242\) −1.62861 −0.104691
\(243\) 13.1916 0.846244
\(244\) 9.78081 0.626152
\(245\) −62.4711 −3.99113
\(246\) −8.14249 −0.519146
\(247\) −2.05974 −0.131058
\(248\) −12.3148 −0.781992
\(249\) 2.74314 0.173839
\(250\) 5.88686 0.372318
\(251\) 14.5228 0.916673 0.458336 0.888779i \(-0.348446\pi\)
0.458336 + 0.888779i \(0.348446\pi\)
\(252\) −4.50921 −0.284054
\(253\) 1.66635 0.104763
\(254\) −24.0700 −1.51028
\(255\) 6.95367 0.435456
\(256\) 14.1720 0.885748
\(257\) −21.4777 −1.33974 −0.669872 0.742476i \(-0.733651\pi\)
−0.669872 + 0.742476i \(0.733651\pi\)
\(258\) 3.40134 0.211758
\(259\) −40.9540 −2.54476
\(260\) 0.632127 0.0392029
\(261\) −6.70035 −0.414741
\(262\) 35.8269 2.21340
\(263\) −5.46042 −0.336704 −0.168352 0.985727i \(-0.553844\pi\)
−0.168352 + 0.985727i \(0.553844\pi\)
\(264\) −4.58378 −0.282112
\(265\) −32.1087 −1.97242
\(266\) 58.5045 3.58714
\(267\) 9.96985 0.610145
\(268\) 0.914957 0.0558899
\(269\) −0.0887634 −0.00541200 −0.00270600 0.999996i \(-0.500861\pi\)
−0.00270600 + 0.999996i \(0.500861\pi\)
\(270\) 18.5521 1.12905
\(271\) −16.3443 −0.992843 −0.496422 0.868082i \(-0.665353\pi\)
−0.496422 + 0.868082i \(0.665353\pi\)
\(272\) −4.87915 −0.295842
\(273\) −3.08509 −0.186718
\(274\) 18.6486 1.12660
\(275\) 6.08564 0.366978
\(276\) −2.27032 −0.136657
\(277\) 21.8189 1.31097 0.655486 0.755207i \(-0.272464\pi\)
0.655486 + 0.755207i \(0.272464\pi\)
\(278\) 9.88023 0.592577
\(279\) −7.64108 −0.457460
\(280\) 37.0909 2.21661
\(281\) 11.3532 0.677276 0.338638 0.940917i \(-0.390034\pi\)
0.338638 + 0.940917i \(0.390034\pi\)
\(282\) 22.4674 1.33792
\(283\) 27.6296 1.64241 0.821203 0.570636i \(-0.193303\pi\)
0.821203 + 0.570636i \(0.193303\pi\)
\(284\) 4.76300 0.282632
\(285\) 49.2141 2.91519
\(286\) 0.473973 0.0280266
\(287\) 12.1508 0.717239
\(288\) 4.84349 0.285406
\(289\) 1.00000 0.0588235
\(290\) −26.6795 −1.56667
\(291\) −2.62106 −0.153649
\(292\) −7.97390 −0.466637
\(293\) 13.6011 0.794584 0.397292 0.917692i \(-0.369950\pi\)
0.397292 + 0.917692i \(0.369950\pi\)
\(294\) 63.8188 3.72199
\(295\) −45.7756 −2.66516
\(296\) 17.7088 1.02930
\(297\) 3.42135 0.198527
\(298\) 10.3966 0.602258
\(299\) −0.484958 −0.0280459
\(300\) −8.29138 −0.478703
\(301\) −5.07571 −0.292559
\(302\) −2.32323 −0.133687
\(303\) −22.7983 −1.30973
\(304\) −34.5318 −1.98054
\(305\) −49.9193 −2.85837
\(306\) −2.21786 −0.126786
\(307\) −24.0368 −1.37185 −0.685926 0.727671i \(-0.740603\pi\)
−0.685926 + 0.727671i \(0.740603\pi\)
\(308\) −3.31119 −0.188672
\(309\) 24.8745 1.41506
\(310\) −30.4253 −1.72804
\(311\) 32.4528 1.84023 0.920115 0.391648i \(-0.128095\pi\)
0.920115 + 0.391648i \(0.128095\pi\)
\(312\) 1.33402 0.0755238
\(313\) 0.741689 0.0419227 0.0209614 0.999780i \(-0.493327\pi\)
0.0209614 + 0.999780i \(0.493327\pi\)
\(314\) 1.66561 0.0939959
\(315\) 23.0141 1.29670
\(316\) −3.96411 −0.222999
\(317\) −22.9895 −1.29122 −0.645609 0.763668i \(-0.723396\pi\)
−0.645609 + 0.763668i \(0.723396\pi\)
\(318\) 32.8014 1.83941
\(319\) −4.92017 −0.275477
\(320\) −13.2045 −0.738154
\(321\) 27.0590 1.51028
\(322\) 13.7746 0.767631
\(323\) 7.07744 0.393799
\(324\) −7.32658 −0.407032
\(325\) −1.77110 −0.0982431
\(326\) −30.9941 −1.71660
\(327\) −40.3998 −2.23411
\(328\) −5.25410 −0.290109
\(329\) −33.5275 −1.84843
\(330\) −11.3248 −0.623409
\(331\) 8.56674 0.470870 0.235435 0.971890i \(-0.424348\pi\)
0.235435 + 0.971890i \(0.424348\pi\)
\(332\) −0.856843 −0.0470254
\(333\) 10.9879 0.602135
\(334\) −2.54344 −0.139171
\(335\) −4.66976 −0.255136
\(336\) −51.7219 −2.82166
\(337\) −9.85838 −0.537020 −0.268510 0.963277i \(-0.586531\pi\)
−0.268510 + 0.963277i \(0.586531\pi\)
\(338\) 21.0339 1.14410
\(339\) 21.0290 1.14214
\(340\) −2.17204 −0.117795
\(341\) −5.61097 −0.303851
\(342\) −15.6967 −0.848782
\(343\) −59.7048 −3.22376
\(344\) 2.19478 0.118334
\(345\) 11.5873 0.623837
\(346\) −15.8356 −0.851330
\(347\) −32.9701 −1.76993 −0.884963 0.465661i \(-0.845817\pi\)
−0.884963 + 0.465661i \(0.845817\pi\)
\(348\) 6.70349 0.359345
\(349\) −6.16526 −0.330019 −0.165009 0.986292i \(-0.552765\pi\)
−0.165009 + 0.986292i \(0.552765\pi\)
\(350\) 50.3060 2.68897
\(351\) −0.995714 −0.0531473
\(352\) 3.55666 0.189570
\(353\) 9.70048 0.516304 0.258152 0.966104i \(-0.416886\pi\)
0.258152 + 0.966104i \(0.416886\pi\)
\(354\) 46.7631 2.48543
\(355\) −24.3094 −1.29021
\(356\) −3.11417 −0.165051
\(357\) 10.6006 0.561043
\(358\) −5.27553 −0.278821
\(359\) 22.9708 1.21235 0.606176 0.795331i \(-0.292703\pi\)
0.606176 + 0.795331i \(0.292703\pi\)
\(360\) −9.95148 −0.524489
\(361\) 31.0901 1.63632
\(362\) −18.3737 −0.965698
\(363\) −2.08850 −0.109618
\(364\) 0.963654 0.0505092
\(365\) 40.6972 2.13019
\(366\) 50.9962 2.66561
\(367\) 17.4307 0.909875 0.454938 0.890523i \(-0.349662\pi\)
0.454938 + 0.890523i \(0.349662\pi\)
\(368\) −8.13038 −0.423825
\(369\) −3.26005 −0.169712
\(370\) 43.7518 2.27455
\(371\) −48.9485 −2.54128
\(372\) 7.64466 0.396357
\(373\) −6.92606 −0.358618 −0.179309 0.983793i \(-0.557386\pi\)
−0.179309 + 0.983793i \(0.557386\pi\)
\(374\) −1.62861 −0.0842132
\(375\) 7.54920 0.389839
\(376\) 14.4975 0.747653
\(377\) 1.43192 0.0737475
\(378\) 28.2820 1.45467
\(379\) 14.6675 0.753419 0.376709 0.926331i \(-0.377056\pi\)
0.376709 + 0.926331i \(0.377056\pi\)
\(380\) −15.3725 −0.788590
\(381\) −30.8669 −1.58136
\(382\) −31.5720 −1.61536
\(383\) −0.404206 −0.0206540 −0.0103270 0.999947i \(-0.503287\pi\)
−0.0103270 + 0.999947i \(0.503287\pi\)
\(384\) 28.3455 1.44650
\(385\) 16.8996 0.861285
\(386\) 24.1731 1.23038
\(387\) 1.36181 0.0692248
\(388\) 0.818711 0.0415637
\(389\) 11.7715 0.596837 0.298418 0.954435i \(-0.403541\pi\)
0.298418 + 0.954435i \(0.403541\pi\)
\(390\) 3.29585 0.166892
\(391\) 1.66635 0.0842711
\(392\) 41.1803 2.07992
\(393\) 45.9438 2.31756
\(394\) −18.8504 −0.949669
\(395\) 20.2320 1.01798
\(396\) 0.888390 0.0446433
\(397\) −14.7110 −0.738325 −0.369162 0.929365i \(-0.620355\pi\)
−0.369162 + 0.929365i \(0.620355\pi\)
\(398\) 14.0160 0.702558
\(399\) 75.0251 3.75595
\(400\) −29.6927 −1.48464
\(401\) 36.0545 1.80048 0.900238 0.435398i \(-0.143392\pi\)
0.900238 + 0.435398i \(0.143392\pi\)
\(402\) 4.77049 0.237931
\(403\) 1.63296 0.0813435
\(404\) 7.12125 0.354296
\(405\) 37.3934 1.85809
\(406\) −40.6718 −2.01851
\(407\) 8.06861 0.399946
\(408\) −4.58378 −0.226931
\(409\) 26.8478 1.32754 0.663770 0.747937i \(-0.268956\pi\)
0.663770 + 0.747937i \(0.268956\pi\)
\(410\) −12.9809 −0.641080
\(411\) 23.9146 1.17962
\(412\) −7.76975 −0.382788
\(413\) −69.7831 −3.43380
\(414\) −3.69573 −0.181635
\(415\) 4.37316 0.214670
\(416\) −1.03509 −0.0507496
\(417\) 12.6702 0.620464
\(418\) −11.5264 −0.563773
\(419\) −7.71081 −0.376698 −0.188349 0.982102i \(-0.560314\pi\)
−0.188349 + 0.982102i \(0.560314\pi\)
\(420\) −23.0249 −1.12350
\(421\) 21.0274 1.02481 0.512405 0.858744i \(-0.328755\pi\)
0.512405 + 0.858744i \(0.328755\pi\)
\(422\) 6.88217 0.335019
\(423\) 8.99541 0.437372
\(424\) 21.1657 1.02790
\(425\) 6.08564 0.295197
\(426\) 24.8338 1.20320
\(427\) −76.1001 −3.68274
\(428\) −8.45209 −0.408547
\(429\) 0.607814 0.0293455
\(430\) 5.42246 0.261494
\(431\) 9.31784 0.448824 0.224412 0.974494i \(-0.427954\pi\)
0.224412 + 0.974494i \(0.427954\pi\)
\(432\) −16.6933 −0.803155
\(433\) −2.56641 −0.123334 −0.0616669 0.998097i \(-0.519642\pi\)
−0.0616669 + 0.998097i \(0.519642\pi\)
\(434\) −46.3822 −2.22642
\(435\) −34.2133 −1.64040
\(436\) 12.6192 0.604350
\(437\) 11.7935 0.564160
\(438\) −41.5751 −1.98654
\(439\) 3.05425 0.145772 0.0728858 0.997340i \(-0.476779\pi\)
0.0728858 + 0.997340i \(0.476779\pi\)
\(440\) −7.30753 −0.348373
\(441\) 25.5515 1.21674
\(442\) 0.473973 0.0225446
\(443\) 33.9273 1.61194 0.805968 0.591960i \(-0.201645\pi\)
0.805968 + 0.591960i \(0.201645\pi\)
\(444\) −10.9931 −0.521708
\(445\) 15.8941 0.753452
\(446\) 44.8380 2.12314
\(447\) 13.3324 0.630600
\(448\) −20.1298 −0.951042
\(449\) 4.81672 0.227315 0.113657 0.993520i \(-0.463743\pi\)
0.113657 + 0.993520i \(0.463743\pi\)
\(450\) −13.4971 −0.636258
\(451\) −2.39391 −0.112725
\(452\) −6.56859 −0.308960
\(453\) −2.97926 −0.139978
\(454\) −19.6415 −0.921823
\(455\) −4.91830 −0.230573
\(456\) −32.4414 −1.51921
\(457\) 14.9884 0.701129 0.350565 0.936539i \(-0.385990\pi\)
0.350565 + 0.936539i \(0.385990\pi\)
\(458\) −17.1466 −0.801206
\(459\) 3.42135 0.159695
\(460\) −3.61938 −0.168755
\(461\) −27.4947 −1.28056 −0.640279 0.768142i \(-0.721181\pi\)
−0.640279 + 0.768142i \(0.721181\pi\)
\(462\) −17.2642 −0.803204
\(463\) −38.9588 −1.81057 −0.905284 0.424808i \(-0.860342\pi\)
−0.905284 + 0.424808i \(0.860342\pi\)
\(464\) 24.0063 1.11446
\(465\) −39.0168 −1.80936
\(466\) 15.3795 0.712444
\(467\) 19.1118 0.884388 0.442194 0.896919i \(-0.354200\pi\)
0.442194 + 0.896919i \(0.354200\pi\)
\(468\) −0.258548 −0.0119514
\(469\) −7.11886 −0.328719
\(470\) 35.8179 1.65216
\(471\) 2.13595 0.0984193
\(472\) 30.1747 1.38891
\(473\) 1.00000 0.0459800
\(474\) −20.6685 −0.949335
\(475\) 43.0708 1.97622
\(476\) −3.31119 −0.151768
\(477\) 13.1329 0.601312
\(478\) −34.4084 −1.57380
\(479\) 15.3476 0.701250 0.350625 0.936516i \(-0.385969\pi\)
0.350625 + 0.936516i \(0.385969\pi\)
\(480\) 24.7318 1.12885
\(481\) −2.34821 −0.107069
\(482\) −17.8431 −0.812731
\(483\) 17.6643 0.803755
\(484\) 0.652359 0.0296527
\(485\) −4.17854 −0.189738
\(486\) −21.4840 −0.974534
\(487\) 8.22456 0.372690 0.186345 0.982484i \(-0.440336\pi\)
0.186345 + 0.982484i \(0.440336\pi\)
\(488\) 32.9063 1.48960
\(489\) −39.7462 −1.79739
\(490\) 101.741 4.59618
\(491\) 36.4639 1.64559 0.822797 0.568335i \(-0.192412\pi\)
0.822797 + 0.568335i \(0.192412\pi\)
\(492\) 3.26158 0.147043
\(493\) −4.92017 −0.221594
\(494\) 3.35451 0.150927
\(495\) −4.53417 −0.203796
\(496\) 27.3767 1.22925
\(497\) −37.0588 −1.66231
\(498\) −4.46750 −0.200193
\(499\) −33.1026 −1.48188 −0.740938 0.671573i \(-0.765619\pi\)
−0.740938 + 0.671573i \(0.765619\pi\)
\(500\) −2.35806 −0.105456
\(501\) −3.26167 −0.145721
\(502\) −23.6520 −1.05564
\(503\) −0.683501 −0.0304758 −0.0152379 0.999884i \(-0.504851\pi\)
−0.0152379 + 0.999884i \(0.504851\pi\)
\(504\) −15.1707 −0.675755
\(505\) −36.3455 −1.61735
\(506\) −2.71383 −0.120645
\(507\) 26.9735 1.19794
\(508\) 9.64153 0.427774
\(509\) −34.2606 −1.51857 −0.759286 0.650757i \(-0.774452\pi\)
−0.759286 + 0.650757i \(0.774452\pi\)
\(510\) −11.3248 −0.501470
\(511\) 62.0413 2.74455
\(512\) 4.06383 0.179598
\(513\) 24.2144 1.06909
\(514\) 34.9788 1.54285
\(515\) 39.6553 1.74742
\(516\) −1.36245 −0.0599785
\(517\) 6.60547 0.290508
\(518\) 66.6979 2.93054
\(519\) −20.3073 −0.891393
\(520\) 2.12671 0.0932624
\(521\) 8.32135 0.364565 0.182283 0.983246i \(-0.441651\pi\)
0.182283 + 0.983246i \(0.441651\pi\)
\(522\) 10.9122 0.477616
\(523\) 21.8533 0.955578 0.477789 0.878475i \(-0.341438\pi\)
0.477789 + 0.878475i \(0.341438\pi\)
\(524\) −14.3509 −0.626924
\(525\) 64.5115 2.81551
\(526\) 8.89287 0.387747
\(527\) −5.61097 −0.244418
\(528\) 10.1901 0.443466
\(529\) −20.2233 −0.879272
\(530\) 52.2924 2.27144
\(531\) 18.7228 0.812499
\(532\) −23.4347 −1.01602
\(533\) 0.696699 0.0301774
\(534\) −16.2370 −0.702642
\(535\) 43.1378 1.86501
\(536\) 3.07825 0.132960
\(537\) −6.76525 −0.291942
\(538\) 0.144561 0.00623245
\(539\) 18.7629 0.808173
\(540\) −7.43129 −0.319792
\(541\) −43.2293 −1.85857 −0.929287 0.369358i \(-0.879578\pi\)
−0.929287 + 0.369358i \(0.879578\pi\)
\(542\) 26.6184 1.14336
\(543\) −23.5621 −1.01114
\(544\) 3.55666 0.152490
\(545\) −64.4059 −2.75885
\(546\) 5.02440 0.215024
\(547\) 12.9473 0.553585 0.276792 0.960930i \(-0.410729\pi\)
0.276792 + 0.960930i \(0.410729\pi\)
\(548\) −7.46993 −0.319099
\(549\) 20.4176 0.871403
\(550\) −9.91112 −0.422612
\(551\) −34.8222 −1.48348
\(552\) −7.63820 −0.325103
\(553\) 30.8430 1.31158
\(554\) −35.5344 −1.50971
\(555\) 56.1065 2.38159
\(556\) −3.95765 −0.167842
\(557\) −45.2180 −1.91595 −0.957975 0.286852i \(-0.907391\pi\)
−0.957975 + 0.286852i \(0.907391\pi\)
\(558\) 12.4443 0.526810
\(559\) −0.291030 −0.0123092
\(560\) −82.4558 −3.48439
\(561\) −2.08850 −0.0881763
\(562\) −18.4899 −0.779950
\(563\) 28.6961 1.20940 0.604698 0.796455i \(-0.293294\pi\)
0.604698 + 0.796455i \(0.293294\pi\)
\(564\) −8.99962 −0.378952
\(565\) 33.5248 1.41040
\(566\) −44.9977 −1.89139
\(567\) 57.0048 2.39398
\(568\) 16.0245 0.672373
\(569\) 43.7394 1.83365 0.916826 0.399288i \(-0.130743\pi\)
0.916826 + 0.399288i \(0.130743\pi\)
\(570\) −80.1505 −3.35713
\(571\) −45.5937 −1.90804 −0.954019 0.299747i \(-0.903098\pi\)
−0.954019 + 0.299747i \(0.903098\pi\)
\(572\) −0.189856 −0.00793827
\(573\) −40.4873 −1.69138
\(574\) −19.7889 −0.825971
\(575\) 10.1408 0.422902
\(576\) 5.40081 0.225034
\(577\) −21.6913 −0.903020 −0.451510 0.892266i \(-0.649115\pi\)
−0.451510 + 0.892266i \(0.649115\pi\)
\(578\) −1.62861 −0.0677411
\(579\) 30.9992 1.28828
\(580\) 10.6868 0.443745
\(581\) 6.66671 0.276582
\(582\) 4.26868 0.176942
\(583\) 9.64367 0.399400
\(584\) −26.8271 −1.11011
\(585\) 1.31958 0.0545578
\(586\) −22.1508 −0.915042
\(587\) −46.4306 −1.91640 −0.958198 0.286106i \(-0.907639\pi\)
−0.958198 + 0.286106i \(0.907639\pi\)
\(588\) −25.5634 −1.05422
\(589\) −39.7113 −1.63628
\(590\) 74.5504 3.06919
\(591\) −24.1734 −0.994360
\(592\) −39.3679 −1.61801
\(593\) 7.37552 0.302876 0.151438 0.988467i \(-0.451610\pi\)
0.151438 + 0.988467i \(0.451610\pi\)
\(594\) −5.57203 −0.228623
\(595\) 16.8996 0.692818
\(596\) −4.16448 −0.170584
\(597\) 17.9738 0.735620
\(598\) 0.789806 0.0322976
\(599\) −5.20415 −0.212636 −0.106318 0.994332i \(-0.533906\pi\)
−0.106318 + 0.994332i \(0.533906\pi\)
\(600\) −27.8953 −1.13882
\(601\) −3.93573 −0.160542 −0.0802709 0.996773i \(-0.525579\pi\)
−0.0802709 + 0.996773i \(0.525579\pi\)
\(602\) 8.26634 0.336911
\(603\) 1.90999 0.0777808
\(604\) 0.930598 0.0378655
\(605\) −3.32951 −0.135364
\(606\) 37.1295 1.50828
\(607\) 10.2445 0.415813 0.207906 0.978149i \(-0.433335\pi\)
0.207906 + 0.978149i \(0.433335\pi\)
\(608\) 25.1720 1.02086
\(609\) −52.1568 −2.11350
\(610\) 81.2989 3.29170
\(611\) −1.92239 −0.0777715
\(612\) 0.888390 0.0359110
\(613\) 26.3194 1.06303 0.531515 0.847049i \(-0.321623\pi\)
0.531515 + 0.847049i \(0.321623\pi\)
\(614\) 39.1465 1.57982
\(615\) −16.6465 −0.671250
\(616\) −11.1401 −0.448846
\(617\) −9.39245 −0.378126 −0.189063 0.981965i \(-0.560545\pi\)
−0.189063 + 0.981965i \(0.560545\pi\)
\(618\) −40.5107 −1.62958
\(619\) 0.610849 0.0245521 0.0122761 0.999925i \(-0.496092\pi\)
0.0122761 + 0.999925i \(0.496092\pi\)
\(620\) 12.1872 0.489451
\(621\) 5.70118 0.228780
\(622\) −52.8529 −2.11921
\(623\) 24.2299 0.970752
\(624\) −2.96561 −0.118720
\(625\) −18.3932 −0.735726
\(626\) −1.20792 −0.0482782
\(627\) −14.7812 −0.590304
\(628\) −0.667182 −0.0266235
\(629\) 8.06861 0.321717
\(630\) −37.4810 −1.49328
\(631\) 12.2961 0.489501 0.244751 0.969586i \(-0.421294\pi\)
0.244751 + 0.969586i \(0.421294\pi\)
\(632\) −13.3367 −0.530507
\(633\) 8.82557 0.350785
\(634\) 37.4408 1.48696
\(635\) −49.2084 −1.95278
\(636\) −13.1390 −0.520996
\(637\) −5.46055 −0.216355
\(638\) 8.01303 0.317239
\(639\) 9.94285 0.393333
\(640\) 45.1888 1.78624
\(641\) 9.14232 0.361100 0.180550 0.983566i \(-0.442212\pi\)
0.180550 + 0.983566i \(0.442212\pi\)
\(642\) −44.0684 −1.73924
\(643\) 14.0019 0.552179 0.276090 0.961132i \(-0.410961\pi\)
0.276090 + 0.961132i \(0.410961\pi\)
\(644\) −5.51761 −0.217424
\(645\) 6.95367 0.273800
\(646\) −11.5264 −0.453499
\(647\) −26.7200 −1.05047 −0.525235 0.850957i \(-0.676023\pi\)
−0.525235 + 0.850957i \(0.676023\pi\)
\(648\) −24.6493 −0.968317
\(649\) 13.7484 0.539673
\(650\) 2.88443 0.113137
\(651\) −59.4796 −2.33119
\(652\) 12.4151 0.486212
\(653\) 9.86080 0.385883 0.192941 0.981210i \(-0.438197\pi\)
0.192941 + 0.981210i \(0.438197\pi\)
\(654\) 65.7953 2.57280
\(655\) 73.2443 2.86189
\(656\) 11.6802 0.456037
\(657\) −16.6457 −0.649409
\(658\) 54.6030 2.12865
\(659\) −27.6231 −1.07604 −0.538022 0.842931i \(-0.680828\pi\)
−0.538022 + 0.842931i \(0.680828\pi\)
\(660\) 4.53629 0.176575
\(661\) −14.3226 −0.557086 −0.278543 0.960424i \(-0.589852\pi\)
−0.278543 + 0.960424i \(0.589852\pi\)
\(662\) −13.9518 −0.542254
\(663\) 0.607814 0.0236055
\(664\) −2.88274 −0.111872
\(665\) 119.606 4.63813
\(666\) −17.8950 −0.693418
\(667\) −8.19875 −0.317457
\(668\) 1.01881 0.0394189
\(669\) 57.4994 2.22305
\(670\) 7.60520 0.293814
\(671\) 14.9930 0.578798
\(672\) 37.7027 1.45441
\(673\) −38.2857 −1.47581 −0.737903 0.674907i \(-0.764184\pi\)
−0.737903 + 0.674907i \(0.764184\pi\)
\(674\) 16.0554 0.618432
\(675\) 20.8211 0.801405
\(676\) −8.42542 −0.324054
\(677\) 25.7670 0.990307 0.495154 0.868806i \(-0.335112\pi\)
0.495154 + 0.868806i \(0.335112\pi\)
\(678\) −34.2480 −1.31529
\(679\) −6.37002 −0.244459
\(680\) −7.30753 −0.280231
\(681\) −25.1880 −0.965205
\(682\) 9.13806 0.349914
\(683\) 22.4740 0.859944 0.429972 0.902842i \(-0.358523\pi\)
0.429972 + 0.902842i \(0.358523\pi\)
\(684\) 6.28753 0.240410
\(685\) 38.1250 1.45668
\(686\) 97.2357 3.71248
\(687\) −21.9884 −0.838911
\(688\) −4.87915 −0.186016
\(689\) −2.80659 −0.106923
\(690\) −18.8711 −0.718410
\(691\) 10.1459 0.385970 0.192985 0.981202i \(-0.438183\pi\)
0.192985 + 0.981202i \(0.438183\pi\)
\(692\) 6.34317 0.241131
\(693\) −6.91216 −0.262571
\(694\) 53.6953 2.03824
\(695\) 20.1991 0.766194
\(696\) 22.5530 0.854869
\(697\) −2.39391 −0.0906758
\(698\) 10.0408 0.380049
\(699\) 19.7224 0.745971
\(700\) −20.1507 −0.761625
\(701\) 38.8986 1.46918 0.734589 0.678512i \(-0.237375\pi\)
0.734589 + 0.678512i \(0.237375\pi\)
\(702\) 1.62163 0.0612043
\(703\) 57.1051 2.15376
\(704\) 3.96590 0.149470
\(705\) 45.9322 1.72991
\(706\) −15.7983 −0.594576
\(707\) −55.4073 −2.08380
\(708\) −18.7315 −0.703974
\(709\) −39.1055 −1.46864 −0.734318 0.678805i \(-0.762498\pi\)
−0.734318 + 0.678805i \(0.762498\pi\)
\(710\) 39.5905 1.48580
\(711\) −8.27515 −0.310342
\(712\) −10.4772 −0.392650
\(713\) −9.34986 −0.350155
\(714\) −17.2642 −0.646097
\(715\) 0.968986 0.0362380
\(716\) 2.11318 0.0789733
\(717\) −44.1247 −1.64787
\(718\) −37.4104 −1.39614
\(719\) 34.7211 1.29488 0.647439 0.762117i \(-0.275840\pi\)
0.647439 + 0.762117i \(0.275840\pi\)
\(720\) 22.1229 0.824470
\(721\) 60.4529 2.25138
\(722\) −50.6336 −1.88439
\(723\) −22.8817 −0.850978
\(724\) 7.35981 0.273525
\(725\) −29.9424 −1.11203
\(726\) 3.40134 0.126235
\(727\) 7.13207 0.264514 0.132257 0.991215i \(-0.457778\pi\)
0.132257 + 0.991215i \(0.457778\pi\)
\(728\) 3.24209 0.120160
\(729\) 6.14203 0.227483
\(730\) −66.2797 −2.45312
\(731\) 1.00000 0.0369863
\(732\) −20.4272 −0.755010
\(733\) −36.6739 −1.35458 −0.677291 0.735716i \(-0.736846\pi\)
−0.677291 + 0.735716i \(0.736846\pi\)
\(734\) −28.3878 −1.04781
\(735\) 130.471 4.81248
\(736\) 5.92664 0.218459
\(737\) 1.40254 0.0516630
\(738\) 5.30935 0.195440
\(739\) −1.61499 −0.0594084 −0.0297042 0.999559i \(-0.509457\pi\)
−0.0297042 + 0.999559i \(0.509457\pi\)
\(740\) −17.5253 −0.644244
\(741\) 4.30177 0.158029
\(742\) 79.7178 2.92653
\(743\) −3.21151 −0.117819 −0.0589094 0.998263i \(-0.518762\pi\)
−0.0589094 + 0.998263i \(0.518762\pi\)
\(744\) 25.7195 0.942921
\(745\) 21.2547 0.778712
\(746\) 11.2798 0.412984
\(747\) −1.78868 −0.0654442
\(748\) 0.652359 0.0238526
\(749\) 65.7619 2.40289
\(750\) −12.2947 −0.448938
\(751\) 31.7034 1.15687 0.578436 0.815728i \(-0.303663\pi\)
0.578436 + 0.815728i \(0.303663\pi\)
\(752\) −32.2291 −1.17527
\(753\) −30.3308 −1.10532
\(754\) −2.33203 −0.0849275
\(755\) −4.74958 −0.172855
\(756\) −11.3287 −0.412022
\(757\) −17.5773 −0.638857 −0.319429 0.947610i \(-0.603491\pi\)
−0.319429 + 0.947610i \(0.603491\pi\)
\(758\) −23.8876 −0.867636
\(759\) −3.48017 −0.126322
\(760\) −51.7186 −1.87603
\(761\) −18.6364 −0.675569 −0.337784 0.941223i \(-0.609677\pi\)
−0.337784 + 0.941223i \(0.609677\pi\)
\(762\) 50.2700 1.82109
\(763\) −98.1843 −3.55451
\(764\) 12.6466 0.457537
\(765\) −4.53417 −0.163933
\(766\) 0.658293 0.0237851
\(767\) −4.00120 −0.144475
\(768\) −29.5981 −1.06803
\(769\) 4.64011 0.167327 0.0836633 0.996494i \(-0.473338\pi\)
0.0836633 + 0.996494i \(0.473338\pi\)
\(770\) −27.5229 −0.991855
\(771\) 44.8562 1.61546
\(772\) −9.68286 −0.348494
\(773\) −18.9078 −0.680068 −0.340034 0.940413i \(-0.610439\pi\)
−0.340034 + 0.940413i \(0.610439\pi\)
\(774\) −2.21786 −0.0797192
\(775\) −34.1464 −1.22657
\(776\) 2.75445 0.0988788
\(777\) 85.5321 3.06845
\(778\) −19.1711 −0.687316
\(779\) −16.9427 −0.607037
\(780\) −1.32019 −0.0472705
\(781\) 7.30119 0.261257
\(782\) −2.71383 −0.0970465
\(783\) −16.8336 −0.601585
\(784\) −91.5467 −3.26952
\(785\) 3.40516 0.121535
\(786\) −74.8244 −2.66890
\(787\) 30.0731 1.07199 0.535994 0.844222i \(-0.319937\pi\)
0.535994 + 0.844222i \(0.319937\pi\)
\(788\) 7.55076 0.268985
\(789\) 11.4041 0.405995
\(790\) −32.9500 −1.17231
\(791\) 51.1072 1.81716
\(792\) 2.98887 0.106205
\(793\) −4.36340 −0.154949
\(794\) 23.9585 0.850254
\(795\) 67.0589 2.37833
\(796\) −5.61428 −0.198993
\(797\) 31.1217 1.10239 0.551194 0.834377i \(-0.314172\pi\)
0.551194 + 0.834377i \(0.314172\pi\)
\(798\) −122.186 −4.32535
\(799\) 6.60547 0.233685
\(800\) 21.6445 0.765250
\(801\) −6.50088 −0.229697
\(802\) −58.7186 −2.07343
\(803\) −12.2232 −0.431347
\(804\) −1.91088 −0.0673916
\(805\) 28.1608 0.992537
\(806\) −2.65945 −0.0936750
\(807\) 0.185382 0.00652575
\(808\) 23.9585 0.842858
\(809\) 25.7767 0.906262 0.453131 0.891444i \(-0.350307\pi\)
0.453131 + 0.891444i \(0.350307\pi\)
\(810\) −60.8992 −2.13978
\(811\) 13.1142 0.460501 0.230250 0.973131i \(-0.426046\pi\)
0.230250 + 0.973131i \(0.426046\pi\)
\(812\) 16.2916 0.571724
\(813\) 34.1349 1.19716
\(814\) −13.1406 −0.460578
\(815\) −63.3640 −2.21955
\(816\) 10.1901 0.356724
\(817\) 7.07744 0.247608
\(818\) −43.7245 −1.52879
\(819\) 2.01164 0.0702926
\(820\) 5.19966 0.181580
\(821\) 20.0522 0.699828 0.349914 0.936782i \(-0.386211\pi\)
0.349914 + 0.936782i \(0.386211\pi\)
\(822\) −38.9475 −1.35845
\(823\) 13.8477 0.482702 0.241351 0.970438i \(-0.422410\pi\)
0.241351 + 0.970438i \(0.422410\pi\)
\(824\) −26.1403 −0.910641
\(825\) −12.7098 −0.442500
\(826\) 113.649 3.95436
\(827\) −32.5826 −1.13301 −0.566503 0.824059i \(-0.691704\pi\)
−0.566503 + 0.824059i \(0.691704\pi\)
\(828\) 1.48037 0.0514465
\(829\) −20.0534 −0.696482 −0.348241 0.937405i \(-0.613221\pi\)
−0.348241 + 0.937405i \(0.613221\pi\)
\(830\) −7.12215 −0.247214
\(831\) −45.5687 −1.58076
\(832\) −1.15419 −0.0400145
\(833\) 18.7629 0.650094
\(834\) −20.6348 −0.714525
\(835\) −5.19980 −0.179946
\(836\) 4.61703 0.159683
\(837\) −19.1971 −0.663548
\(838\) 12.5579 0.433805
\(839\) −8.47812 −0.292697 −0.146349 0.989233i \(-0.546752\pi\)
−0.146349 + 0.989233i \(0.546752\pi\)
\(840\) −77.4642 −2.67277
\(841\) −4.79188 −0.165237
\(842\) −34.2453 −1.18017
\(843\) −23.7111 −0.816654
\(844\) −2.75674 −0.0948910
\(845\) 43.0016 1.47930
\(846\) −14.6500 −0.503677
\(847\) −5.07571 −0.174404
\(848\) −47.0529 −1.61580
\(849\) −57.7042 −1.98040
\(850\) −9.91112 −0.339949
\(851\) 13.4452 0.460894
\(852\) −9.94750 −0.340796
\(853\) −47.7144 −1.63371 −0.816855 0.576842i \(-0.804285\pi\)
−0.816855 + 0.576842i \(0.804285\pi\)
\(854\) 123.937 4.24104
\(855\) −32.0903 −1.09746
\(856\) −28.4360 −0.971921
\(857\) −24.3088 −0.830373 −0.415186 0.909736i \(-0.636284\pi\)
−0.415186 + 0.909736i \(0.636284\pi\)
\(858\) −0.989890 −0.0337943
\(859\) 9.53462 0.325317 0.162658 0.986682i \(-0.447993\pi\)
0.162658 + 0.986682i \(0.447993\pi\)
\(860\) −2.17204 −0.0740658
\(861\) −25.3769 −0.864842
\(862\) −15.1751 −0.516866
\(863\) 29.5973 1.00750 0.503752 0.863848i \(-0.331953\pi\)
0.503752 + 0.863848i \(0.331953\pi\)
\(864\) 12.1686 0.413983
\(865\) −32.3743 −1.10076
\(866\) 4.17968 0.142031
\(867\) −2.08850 −0.0709290
\(868\) 18.5790 0.630611
\(869\) −6.07658 −0.206134
\(870\) 55.7199 1.88908
\(871\) −0.408179 −0.0138306
\(872\) 42.4557 1.43773
\(873\) 1.70907 0.0578434
\(874\) −19.2070 −0.649686
\(875\) 18.3470 0.620241
\(876\) 16.6535 0.562668
\(877\) −38.0420 −1.28459 −0.642294 0.766459i \(-0.722017\pi\)
−0.642294 + 0.766459i \(0.722017\pi\)
\(878\) −4.97418 −0.167870
\(879\) −28.4058 −0.958104
\(880\) 16.2452 0.547625
\(881\) −33.7151 −1.13589 −0.567946 0.823066i \(-0.692262\pi\)
−0.567946 + 0.823066i \(0.692262\pi\)
\(882\) −41.6133 −1.40119
\(883\) −21.0002 −0.706711 −0.353356 0.935489i \(-0.614959\pi\)
−0.353356 + 0.935489i \(0.614959\pi\)
\(884\) −0.189856 −0.00638554
\(885\) 95.6020 3.21363
\(886\) −55.2542 −1.85630
\(887\) 34.0722 1.14403 0.572016 0.820243i \(-0.306162\pi\)
0.572016 + 0.820243i \(0.306162\pi\)
\(888\) −36.9848 −1.24113
\(889\) −75.0164 −2.51597
\(890\) −25.8852 −0.867674
\(891\) −11.2309 −0.376249
\(892\) −17.9604 −0.601359
\(893\) 46.7498 1.56442
\(894\) −21.7132 −0.726198
\(895\) −10.7853 −0.360512
\(896\) 68.8886 2.30141
\(897\) 1.01283 0.0338175
\(898\) −7.84454 −0.261776
\(899\) 27.6070 0.920743
\(900\) 5.40643 0.180214
\(901\) 9.64367 0.321277
\(902\) 3.89874 0.129814
\(903\) 10.6006 0.352766
\(904\) −22.0991 −0.735007
\(905\) −37.5630 −1.24864
\(906\) 4.85205 0.161198
\(907\) 29.4640 0.978337 0.489168 0.872189i \(-0.337300\pi\)
0.489168 + 0.872189i \(0.337300\pi\)
\(908\) 7.86767 0.261098
\(909\) 14.8657 0.493066
\(910\) 8.00997 0.265528
\(911\) 3.26857 0.108293 0.0541463 0.998533i \(-0.482756\pi\)
0.0541463 + 0.998533i \(0.482756\pi\)
\(912\) 72.1196 2.38812
\(913\) −1.31345 −0.0434690
\(914\) −24.4103 −0.807420
\(915\) 104.256 3.44661
\(916\) 6.86828 0.226934
\(917\) 111.658 3.68728
\(918\) −5.57203 −0.183904
\(919\) −0.643250 −0.0212189 −0.0106094 0.999944i \(-0.503377\pi\)
−0.0106094 + 0.999944i \(0.503377\pi\)
\(920\) −12.1769 −0.401462
\(921\) 50.2007 1.65417
\(922\) 44.7781 1.47469
\(923\) −2.12486 −0.0699408
\(924\) 6.91540 0.227500
\(925\) 49.1027 1.61449
\(926\) 63.4485 2.08505
\(927\) −16.2195 −0.532718
\(928\) −17.4994 −0.574445
\(929\) 15.5564 0.510390 0.255195 0.966890i \(-0.417860\pi\)
0.255195 + 0.966890i \(0.417860\pi\)
\(930\) 63.5430 2.08366
\(931\) 132.793 4.35211
\(932\) −6.16047 −0.201793
\(933\) −67.7775 −2.21894
\(934\) −31.1256 −1.01846
\(935\) −3.32951 −0.108887
\(936\) −0.869851 −0.0284320
\(937\) −52.4852 −1.71462 −0.857309 0.514802i \(-0.827865\pi\)
−0.857309 + 0.514802i \(0.827865\pi\)
\(938\) 11.5938 0.378552
\(939\) −1.54901 −0.0505501
\(940\) −14.3473 −0.467958
\(941\) −16.1525 −0.526556 −0.263278 0.964720i \(-0.584804\pi\)
−0.263278 + 0.964720i \(0.584804\pi\)
\(942\) −3.47862 −0.113340
\(943\) −3.98910 −0.129903
\(944\) −67.0806 −2.18329
\(945\) 57.8195 1.88087
\(946\) −1.62861 −0.0529506
\(947\) −12.8320 −0.416984 −0.208492 0.978024i \(-0.566855\pi\)
−0.208492 + 0.978024i \(0.566855\pi\)
\(948\) 8.27902 0.268890
\(949\) 3.55731 0.115475
\(950\) −70.1453 −2.27581
\(951\) 48.0134 1.55694
\(952\) −11.1401 −0.361051
\(953\) −21.9532 −0.711133 −0.355566 0.934651i \(-0.615712\pi\)
−0.355566 + 0.934651i \(0.615712\pi\)
\(954\) −21.3883 −0.692471
\(955\) −64.5455 −2.08864
\(956\) 13.7827 0.445765
\(957\) 10.2758 0.332168
\(958\) −24.9952 −0.807558
\(959\) 58.1201 1.87680
\(960\) 27.5775 0.890062
\(961\) 0.482983 0.0155801
\(962\) 3.82430 0.123301
\(963\) −17.6439 −0.568567
\(964\) 7.14728 0.230198
\(965\) 49.4194 1.59087
\(966\) −28.7683 −0.925604
\(967\) −14.4592 −0.464977 −0.232488 0.972599i \(-0.574687\pi\)
−0.232488 + 0.972599i \(0.574687\pi\)
\(968\) 2.19478 0.0705428
\(969\) −14.7812 −0.474840
\(970\) 6.80519 0.218502
\(971\) −37.1369 −1.19178 −0.595890 0.803066i \(-0.703201\pi\)
−0.595890 + 0.803066i \(0.703201\pi\)
\(972\) 8.60569 0.276028
\(973\) 30.7927 0.987169
\(974\) −13.3946 −0.429190
\(975\) 3.69894 0.118461
\(976\) −73.1530 −2.34157
\(977\) −40.3189 −1.28992 −0.644958 0.764218i \(-0.723125\pi\)
−0.644958 + 0.764218i \(0.723125\pi\)
\(978\) 64.7310 2.06987
\(979\) −4.77370 −0.152568
\(980\) −40.7536 −1.30183
\(981\) 26.3428 0.841062
\(982\) −59.3854 −1.89506
\(983\) 28.5515 0.910651 0.455326 0.890325i \(-0.349523\pi\)
0.455326 + 0.890325i \(0.349523\pi\)
\(984\) 10.9732 0.349812
\(985\) −38.5376 −1.22791
\(986\) 8.01303 0.255187
\(987\) 70.0219 2.22882
\(988\) −1.34369 −0.0427486
\(989\) 1.66635 0.0529870
\(990\) 7.38437 0.234691
\(991\) 28.5652 0.907405 0.453702 0.891153i \(-0.350103\pi\)
0.453702 + 0.891153i \(0.350103\pi\)
\(992\) −19.9563 −0.633613
\(993\) −17.8916 −0.567772
\(994\) 60.3541 1.91432
\(995\) 28.6542 0.908398
\(996\) 1.78951 0.0567029
\(997\) 4.98477 0.157869 0.0789346 0.996880i \(-0.474848\pi\)
0.0789346 + 0.996880i \(0.474848\pi\)
\(998\) 53.9111 1.70653
\(999\) 27.6055 0.873401
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 \(a_p\))