Properties

Label 8007.2.a.e.1.14
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.42820 q^{2}\) \(+1.00000 q^{3}\) \(+0.0397473 q^{4}\) \(-3.43580 q^{5}\) \(-1.42820 q^{6}\) \(+0.0177517 q^{7}\) \(+2.79963 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.42820 q^{2}\) \(+1.00000 q^{3}\) \(+0.0397473 q^{4}\) \(-3.43580 q^{5}\) \(-1.42820 q^{6}\) \(+0.0177517 q^{7}\) \(+2.79963 q^{8}\) \(+1.00000 q^{9}\) \(+4.90700 q^{10}\) \(-2.14032 q^{11}\) \(+0.0397473 q^{12}\) \(-1.57212 q^{13}\) \(-0.0253529 q^{14}\) \(-3.43580 q^{15}\) \(-4.07791 q^{16}\) \(-1.00000 q^{17}\) \(-1.42820 q^{18}\) \(-1.12471 q^{19}\) \(-0.136564 q^{20}\) \(+0.0177517 q^{21}\) \(+3.05680 q^{22}\) \(+2.11501 q^{23}\) \(+2.79963 q^{24}\) \(+6.80471 q^{25}\) \(+2.24530 q^{26}\) \(+1.00000 q^{27}\) \(+0.000705581 q^{28}\) \(+7.22554 q^{29}\) \(+4.90700 q^{30}\) \(-2.53455 q^{31}\) \(+0.224811 q^{32}\) \(-2.14032 q^{33}\) \(+1.42820 q^{34}\) \(-0.0609912 q^{35}\) \(+0.0397473 q^{36}\) \(+5.42717 q^{37}\) \(+1.60630 q^{38}\) \(-1.57212 q^{39}\) \(-9.61895 q^{40}\) \(+9.59589 q^{41}\) \(-0.0253529 q^{42}\) \(-11.5802 q^{43}\) \(-0.0850718 q^{44}\) \(-3.43580 q^{45}\) \(-3.02066 q^{46}\) \(-10.9992 q^{47}\) \(-4.07791 q^{48}\) \(-6.99968 q^{49}\) \(-9.71846 q^{50}\) \(-1.00000 q^{51}\) \(-0.0624875 q^{52}\) \(-4.78120 q^{53}\) \(-1.42820 q^{54}\) \(+7.35370 q^{55}\) \(+0.0496981 q^{56}\) \(-1.12471 q^{57}\) \(-10.3195 q^{58}\) \(+1.42869 q^{59}\) \(-0.136564 q^{60}\) \(+10.4637 q^{61}\) \(+3.61984 q^{62}\) \(+0.0177517 q^{63}\) \(+7.83475 q^{64}\) \(+5.40149 q^{65}\) \(+3.05680 q^{66}\) \(+13.3878 q^{67}\) \(-0.0397473 q^{68}\) \(+2.11501 q^{69}\) \(+0.0871075 q^{70}\) \(-5.47570 q^{71}\) \(+2.79963 q^{72}\) \(+10.9506 q^{73}\) \(-7.75107 q^{74}\) \(+6.80471 q^{75}\) \(-0.0447041 q^{76}\) \(-0.0379943 q^{77}\) \(+2.24530 q^{78}\) \(+3.38850 q^{79}\) \(+14.0109 q^{80}\) \(+1.00000 q^{81}\) \(-13.7048 q^{82}\) \(+8.56257 q^{83}\) \(+0.000705581 q^{84}\) \(+3.43580 q^{85}\) \(+16.5389 q^{86}\) \(+7.22554 q^{87}\) \(-5.99209 q^{88}\) \(-8.56091 q^{89}\) \(+4.90700 q^{90}\) \(-0.0279078 q^{91}\) \(+0.0840660 q^{92}\) \(-2.53455 q^{93}\) \(+15.7090 q^{94}\) \(+3.86427 q^{95}\) \(+0.224811 q^{96}\) \(+15.4548 q^{97}\) \(+9.99693 q^{98}\) \(-2.14032 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.42820 −1.00989 −0.504944 0.863152i \(-0.668487\pi\)
−0.504944 + 0.863152i \(0.668487\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.0397473 0.0198736
\(5\) −3.43580 −1.53654 −0.768268 0.640129i \(-0.778881\pi\)
−0.768268 + 0.640129i \(0.778881\pi\)
\(6\) −1.42820 −0.583059
\(7\) 0.0177517 0.00670951 0.00335475 0.999994i \(-0.498932\pi\)
0.00335475 + 0.999994i \(0.498932\pi\)
\(8\) 2.79963 0.989818
\(9\) 1.00000 0.333333
\(10\) 4.90700 1.55173
\(11\) −2.14032 −0.645330 −0.322665 0.946513i \(-0.604579\pi\)
−0.322665 + 0.946513i \(0.604579\pi\)
\(12\) 0.0397473 0.0114741
\(13\) −1.57212 −0.436028 −0.218014 0.975946i \(-0.569958\pi\)
−0.218014 + 0.975946i \(0.569958\pi\)
\(14\) −0.0253529 −0.00677585
\(15\) −3.43580 −0.887119
\(16\) −4.07791 −1.01948
\(17\) −1.00000 −0.242536
\(18\) −1.42820 −0.336629
\(19\) −1.12471 −0.258026 −0.129013 0.991643i \(-0.541181\pi\)
−0.129013 + 0.991643i \(0.541181\pi\)
\(20\) −0.136564 −0.0305366
\(21\) 0.0177517 0.00387374
\(22\) 3.05680 0.651711
\(23\) 2.11501 0.441011 0.220505 0.975386i \(-0.429229\pi\)
0.220505 + 0.975386i \(0.429229\pi\)
\(24\) 2.79963 0.571472
\(25\) 6.80471 1.36094
\(26\) 2.24530 0.440339
\(27\) 1.00000 0.192450
\(28\) 0.000705581 0 0.000133342 0
\(29\) 7.22554 1.34175 0.670874 0.741571i \(-0.265919\pi\)
0.670874 + 0.741571i \(0.265919\pi\)
\(30\) 4.90700 0.895891
\(31\) −2.53455 −0.455219 −0.227610 0.973752i \(-0.573091\pi\)
−0.227610 + 0.973752i \(0.573091\pi\)
\(32\) 0.224811 0.0397414
\(33\) −2.14032 −0.372582
\(34\) 1.42820 0.244934
\(35\) −0.0609912 −0.0103094
\(36\) 0.0397473 0.00662455
\(37\) 5.42717 0.892222 0.446111 0.894978i \(-0.352809\pi\)
0.446111 + 0.894978i \(0.352809\pi\)
\(38\) 1.60630 0.260577
\(39\) −1.57212 −0.251741
\(40\) −9.61895 −1.52089
\(41\) 9.59589 1.49863 0.749313 0.662216i \(-0.230384\pi\)
0.749313 + 0.662216i \(0.230384\pi\)
\(42\) −0.0253529 −0.00391204
\(43\) −11.5802 −1.76597 −0.882986 0.469400i \(-0.844470\pi\)
−0.882986 + 0.469400i \(0.844470\pi\)
\(44\) −0.0850718 −0.0128251
\(45\) −3.43580 −0.512179
\(46\) −3.02066 −0.445371
\(47\) −10.9992 −1.60439 −0.802197 0.597059i \(-0.796336\pi\)
−0.802197 + 0.597059i \(0.796336\pi\)
\(48\) −4.07791 −0.588596
\(49\) −6.99968 −0.999955
\(50\) −9.71846 −1.37440
\(51\) −1.00000 −0.140028
\(52\) −0.0624875 −0.00866546
\(53\) −4.78120 −0.656749 −0.328374 0.944548i \(-0.606501\pi\)
−0.328374 + 0.944548i \(0.606501\pi\)
\(54\) −1.42820 −0.194353
\(55\) 7.35370 0.991573
\(56\) 0.0496981 0.00664119
\(57\) −1.12471 −0.148971
\(58\) −10.3195 −1.35502
\(59\) 1.42869 0.185999 0.0929997 0.995666i \(-0.470354\pi\)
0.0929997 + 0.995666i \(0.470354\pi\)
\(60\) −0.136564 −0.0176303
\(61\) 10.4637 1.33974 0.669872 0.742477i \(-0.266349\pi\)
0.669872 + 0.742477i \(0.266349\pi\)
\(62\) 3.61984 0.459720
\(63\) 0.0177517 0.00223650
\(64\) 7.83475 0.979344
\(65\) 5.40149 0.669972
\(66\) 3.05680 0.376266
\(67\) 13.3878 1.63558 0.817790 0.575517i \(-0.195199\pi\)
0.817790 + 0.575517i \(0.195199\pi\)
\(68\) −0.0397473 −0.00482007
\(69\) 2.11501 0.254618
\(70\) 0.0871075 0.0104113
\(71\) −5.47570 −0.649846 −0.324923 0.945740i \(-0.605338\pi\)
−0.324923 + 0.945740i \(0.605338\pi\)
\(72\) 2.79963 0.329939
\(73\) 10.9506 1.28167 0.640833 0.767680i \(-0.278589\pi\)
0.640833 + 0.767680i \(0.278589\pi\)
\(74\) −7.75107 −0.901044
\(75\) 6.80471 0.785740
\(76\) −0.0447041 −0.00512791
\(77\) −0.0379943 −0.00432985
\(78\) 2.24530 0.254230
\(79\) 3.38850 0.381236 0.190618 0.981664i \(-0.438951\pi\)
0.190618 + 0.981664i \(0.438951\pi\)
\(80\) 14.0109 1.56647
\(81\) 1.00000 0.111111
\(82\) −13.7048 −1.51345
\(83\) 8.56257 0.939864 0.469932 0.882703i \(-0.344278\pi\)
0.469932 + 0.882703i \(0.344278\pi\)
\(84\) 0.000705581 0 7.69852e−5 0
\(85\) 3.43580 0.372665
\(86\) 16.5389 1.78343
\(87\) 7.22554 0.774659
\(88\) −5.99209 −0.638759
\(89\) −8.56091 −0.907455 −0.453727 0.891141i \(-0.649906\pi\)
−0.453727 + 0.891141i \(0.649906\pi\)
\(90\) 4.90700 0.517243
\(91\) −0.0279078 −0.00292553
\(92\) 0.0840660 0.00876449
\(93\) −2.53455 −0.262821
\(94\) 15.7090 1.62026
\(95\) 3.86427 0.396465
\(96\) 0.224811 0.0229447
\(97\) 15.4548 1.56920 0.784600 0.620002i \(-0.212868\pi\)
0.784600 + 0.620002i \(0.212868\pi\)
\(98\) 9.99693 1.00984
\(99\) −2.14032 −0.215110
\(100\) 0.270469 0.0270469
\(101\) −10.8054 −1.07518 −0.537588 0.843207i \(-0.680665\pi\)
−0.537588 + 0.843207i \(0.680665\pi\)
\(102\) 1.42820 0.141413
\(103\) 13.8359 1.36329 0.681645 0.731683i \(-0.261265\pi\)
0.681645 + 0.731683i \(0.261265\pi\)
\(104\) −4.40135 −0.431588
\(105\) −0.0609912 −0.00595213
\(106\) 6.82850 0.663242
\(107\) −16.7030 −1.61474 −0.807368 0.590049i \(-0.799109\pi\)
−0.807368 + 0.590049i \(0.799109\pi\)
\(108\) 0.0397473 0.00382468
\(109\) 5.21370 0.499382 0.249691 0.968326i \(-0.419671\pi\)
0.249691 + 0.968326i \(0.419671\pi\)
\(110\) −10.5025 −1.00138
\(111\) 5.42717 0.515124
\(112\) −0.0723899 −0.00684020
\(113\) −6.98038 −0.656659 −0.328329 0.944563i \(-0.606486\pi\)
−0.328329 + 0.944563i \(0.606486\pi\)
\(114\) 1.60630 0.150444
\(115\) −7.26676 −0.677629
\(116\) 0.287195 0.0266654
\(117\) −1.57212 −0.145343
\(118\) −2.04045 −0.187839
\(119\) −0.0177517 −0.00162729
\(120\) −9.61895 −0.878086
\(121\) −6.41904 −0.583549
\(122\) −14.9443 −1.35299
\(123\) 9.59589 0.865233
\(124\) −0.100742 −0.00904686
\(125\) −6.20061 −0.554600
\(126\) −0.0253529 −0.00225862
\(127\) 13.9141 1.23468 0.617339 0.786697i \(-0.288211\pi\)
0.617339 + 0.786697i \(0.288211\pi\)
\(128\) −11.6392 −1.02877
\(129\) −11.5802 −1.01958
\(130\) −7.71439 −0.676597
\(131\) 12.3653 1.08036 0.540181 0.841549i \(-0.318356\pi\)
0.540181 + 0.841549i \(0.318356\pi\)
\(132\) −0.0850718 −0.00740455
\(133\) −0.0199655 −0.00173122
\(134\) −19.1204 −1.65175
\(135\) −3.43580 −0.295706
\(136\) −2.79963 −0.240066
\(137\) −18.1813 −1.55334 −0.776668 0.629911i \(-0.783091\pi\)
−0.776668 + 0.629911i \(0.783091\pi\)
\(138\) −3.02066 −0.257135
\(139\) 2.53697 0.215183 0.107592 0.994195i \(-0.465686\pi\)
0.107592 + 0.994195i \(0.465686\pi\)
\(140\) −0.00242423 −0.000204885 0
\(141\) −10.9992 −0.926298
\(142\) 7.82038 0.656272
\(143\) 3.36484 0.281382
\(144\) −4.07791 −0.339826
\(145\) −24.8255 −2.06164
\(146\) −15.6396 −1.29434
\(147\) −6.99968 −0.577324
\(148\) 0.215715 0.0177317
\(149\) 4.95984 0.406326 0.203163 0.979145i \(-0.434878\pi\)
0.203163 + 0.979145i \(0.434878\pi\)
\(150\) −9.71846 −0.793509
\(151\) 8.66297 0.704982 0.352491 0.935815i \(-0.385335\pi\)
0.352491 + 0.935815i \(0.385335\pi\)
\(152\) −3.14876 −0.255398
\(153\) −1.00000 −0.0808452
\(154\) 0.0542633 0.00437266
\(155\) 8.70821 0.699460
\(156\) −0.0624875 −0.00500301
\(157\) 1.00000 0.0798087
\(158\) −4.83945 −0.385006
\(159\) −4.78120 −0.379174
\(160\) −0.772407 −0.0610641
\(161\) 0.0375451 0.00295896
\(162\) −1.42820 −0.112210
\(163\) 3.88060 0.303952 0.151976 0.988384i \(-0.451436\pi\)
0.151976 + 0.988384i \(0.451436\pi\)
\(164\) 0.381411 0.0297832
\(165\) 7.35370 0.572485
\(166\) −12.2290 −0.949157
\(167\) 1.37018 0.106028 0.0530138 0.998594i \(-0.483117\pi\)
0.0530138 + 0.998594i \(0.483117\pi\)
\(168\) 0.0496981 0.00383429
\(169\) −10.5284 −0.809880
\(170\) −4.90700 −0.376349
\(171\) −1.12471 −0.0860085
\(172\) −0.460283 −0.0350963
\(173\) −23.8813 −1.81566 −0.907831 0.419336i \(-0.862263\pi\)
−0.907831 + 0.419336i \(0.862263\pi\)
\(174\) −10.3195 −0.782319
\(175\) 0.120795 0.00913125
\(176\) 8.72804 0.657900
\(177\) 1.42869 0.107387
\(178\) 12.2267 0.916428
\(179\) 21.4147 1.60061 0.800305 0.599593i \(-0.204671\pi\)
0.800305 + 0.599593i \(0.204671\pi\)
\(180\) −0.136564 −0.0101789
\(181\) 9.64664 0.717029 0.358515 0.933524i \(-0.383283\pi\)
0.358515 + 0.933524i \(0.383283\pi\)
\(182\) 0.0398578 0.00295446
\(183\) 10.4637 0.773501
\(184\) 5.92125 0.436520
\(185\) −18.6467 −1.37093
\(186\) 3.61984 0.265420
\(187\) 2.14032 0.156516
\(188\) −0.437187 −0.0318852
\(189\) 0.0177517 0.00129125
\(190\) −5.51894 −0.400386
\(191\) −11.3109 −0.818424 −0.409212 0.912439i \(-0.634196\pi\)
−0.409212 + 0.912439i \(0.634196\pi\)
\(192\) 7.83475 0.565425
\(193\) −17.7254 −1.27590 −0.637949 0.770078i \(-0.720217\pi\)
−0.637949 + 0.770078i \(0.720217\pi\)
\(194\) −22.0725 −1.58472
\(195\) 5.40149 0.386809
\(196\) −0.278218 −0.0198727
\(197\) −13.1545 −0.937218 −0.468609 0.883406i \(-0.655245\pi\)
−0.468609 + 0.883406i \(0.655245\pi\)
\(198\) 3.05680 0.217237
\(199\) 19.7186 1.39781 0.698907 0.715213i \(-0.253670\pi\)
0.698907 + 0.715213i \(0.253670\pi\)
\(200\) 19.0506 1.34708
\(201\) 13.3878 0.944303
\(202\) 15.4322 1.08581
\(203\) 0.128265 0.00900247
\(204\) −0.0397473 −0.00278287
\(205\) −32.9696 −2.30269
\(206\) −19.7604 −1.37677
\(207\) 2.11501 0.147004
\(208\) 6.41098 0.444521
\(209\) 2.40723 0.166512
\(210\) 0.0871075 0.00601099
\(211\) 7.41727 0.510626 0.255313 0.966858i \(-0.417822\pi\)
0.255313 + 0.966858i \(0.417822\pi\)
\(212\) −0.190040 −0.0130520
\(213\) −5.47570 −0.375189
\(214\) 23.8551 1.63070
\(215\) 39.7874 2.71348
\(216\) 2.79963 0.190491
\(217\) −0.0449926 −0.00305430
\(218\) −7.44620 −0.504320
\(219\) 10.9506 0.739970
\(220\) 0.292290 0.0197062
\(221\) 1.57212 0.105752
\(222\) −7.75107 −0.520218
\(223\) −5.73344 −0.383939 −0.191970 0.981401i \(-0.561488\pi\)
−0.191970 + 0.981401i \(0.561488\pi\)
\(224\) 0.00399078 0.000266645 0
\(225\) 6.80471 0.453647
\(226\) 9.96935 0.663152
\(227\) −17.6673 −1.17262 −0.586311 0.810086i \(-0.699420\pi\)
−0.586311 + 0.810086i \(0.699420\pi\)
\(228\) −0.0447041 −0.00296060
\(229\) −10.6572 −0.704245 −0.352122 0.935954i \(-0.614540\pi\)
−0.352122 + 0.935954i \(0.614540\pi\)
\(230\) 10.3784 0.684329
\(231\) −0.0379943 −0.00249984
\(232\) 20.2288 1.32809
\(233\) 5.83796 0.382457 0.191229 0.981546i \(-0.438753\pi\)
0.191229 + 0.981546i \(0.438753\pi\)
\(234\) 2.24530 0.146780
\(235\) 37.7909 2.46521
\(236\) 0.0567865 0.00369649
\(237\) 3.38850 0.220107
\(238\) 0.0253529 0.00164339
\(239\) −1.52807 −0.0988425 −0.0494212 0.998778i \(-0.515738\pi\)
−0.0494212 + 0.998778i \(0.515738\pi\)
\(240\) 14.0109 0.904399
\(241\) −14.1203 −0.909567 −0.454784 0.890602i \(-0.650283\pi\)
−0.454784 + 0.890602i \(0.650283\pi\)
\(242\) 9.16765 0.589319
\(243\) 1.00000 0.0641500
\(244\) 0.415905 0.0266256
\(245\) 24.0495 1.53647
\(246\) −13.7048 −0.873788
\(247\) 1.76818 0.112506
\(248\) −7.09580 −0.450584
\(249\) 8.56257 0.542631
\(250\) 8.85570 0.560083
\(251\) −9.25544 −0.584198 −0.292099 0.956388i \(-0.594354\pi\)
−0.292099 + 0.956388i \(0.594354\pi\)
\(252\) 0.000705581 0 4.44474e−5 0
\(253\) −4.52680 −0.284598
\(254\) −19.8721 −1.24689
\(255\) 3.43580 0.215158
\(256\) 0.953560 0.0595975
\(257\) 14.2047 0.886063 0.443032 0.896506i \(-0.353903\pi\)
0.443032 + 0.896506i \(0.353903\pi\)
\(258\) 16.5389 1.02967
\(259\) 0.0963415 0.00598637
\(260\) 0.214695 0.0133148
\(261\) 7.22554 0.447250
\(262\) −17.6601 −1.09104
\(263\) −19.5083 −1.20293 −0.601467 0.798898i \(-0.705417\pi\)
−0.601467 + 0.798898i \(0.705417\pi\)
\(264\) −5.99209 −0.368788
\(265\) 16.4272 1.00912
\(266\) 0.0285146 0.00174834
\(267\) −8.56091 −0.523919
\(268\) 0.532129 0.0325049
\(269\) −4.24273 −0.258684 −0.129342 0.991600i \(-0.541286\pi\)
−0.129342 + 0.991600i \(0.541286\pi\)
\(270\) 4.90700 0.298630
\(271\) −3.73401 −0.226825 −0.113412 0.993548i \(-0.536178\pi\)
−0.113412 + 0.993548i \(0.536178\pi\)
\(272\) 4.07791 0.247260
\(273\) −0.0279078 −0.00168906
\(274\) 25.9665 1.56869
\(275\) −14.5642 −0.878257
\(276\) 0.0840660 0.00506018
\(277\) 9.99835 0.600743 0.300371 0.953822i \(-0.402889\pi\)
0.300371 + 0.953822i \(0.402889\pi\)
\(278\) −3.62330 −0.217311
\(279\) −2.53455 −0.151740
\(280\) −0.170753 −0.0102044
\(281\) 17.1755 1.02461 0.512303 0.858805i \(-0.328793\pi\)
0.512303 + 0.858805i \(0.328793\pi\)
\(282\) 15.7090 0.935457
\(283\) −17.4753 −1.03880 −0.519401 0.854531i \(-0.673845\pi\)
−0.519401 + 0.854531i \(0.673845\pi\)
\(284\) −0.217644 −0.0129148
\(285\) 3.86427 0.228899
\(286\) −4.80566 −0.284164
\(287\) 0.170343 0.0100550
\(288\) 0.224811 0.0132471
\(289\) 1.00000 0.0588235
\(290\) 35.4557 2.08203
\(291\) 15.4548 0.905978
\(292\) 0.435255 0.0254714
\(293\) 21.0171 1.22783 0.613916 0.789371i \(-0.289593\pi\)
0.613916 + 0.789371i \(0.289593\pi\)
\(294\) 9.99693 0.583033
\(295\) −4.90869 −0.285795
\(296\) 15.1941 0.883137
\(297\) −2.14032 −0.124194
\(298\) −7.08362 −0.410343
\(299\) −3.32506 −0.192293
\(300\) 0.270469 0.0156155
\(301\) −0.205569 −0.0118488
\(302\) −12.3724 −0.711953
\(303\) −10.8054 −0.620754
\(304\) 4.58646 0.263052
\(305\) −35.9513 −2.05856
\(306\) 1.42820 0.0816446
\(307\) 10.8947 0.621795 0.310898 0.950443i \(-0.399370\pi\)
0.310898 + 0.950443i \(0.399370\pi\)
\(308\) −0.00151017 −8.60498e−5 0
\(309\) 13.8359 0.787096
\(310\) −12.4370 −0.706376
\(311\) 16.3943 0.929634 0.464817 0.885407i \(-0.346120\pi\)
0.464817 + 0.885407i \(0.346120\pi\)
\(312\) −4.40135 −0.249178
\(313\) 11.8995 0.672599 0.336300 0.941755i \(-0.390825\pi\)
0.336300 + 0.941755i \(0.390825\pi\)
\(314\) −1.42820 −0.0805978
\(315\) −0.0609912 −0.00343647
\(316\) 0.134684 0.00757655
\(317\) −12.2961 −0.690620 −0.345310 0.938489i \(-0.612226\pi\)
−0.345310 + 0.938489i \(0.612226\pi\)
\(318\) 6.82850 0.382923
\(319\) −15.4650 −0.865871
\(320\) −26.9186 −1.50480
\(321\) −16.7030 −0.932268
\(322\) −0.0536217 −0.00298822
\(323\) 1.12471 0.0625804
\(324\) 0.0397473 0.00220818
\(325\) −10.6978 −0.593409
\(326\) −5.54226 −0.306957
\(327\) 5.21370 0.288318
\(328\) 26.8649 1.48337
\(329\) −0.195254 −0.0107647
\(330\) −10.5025 −0.578146
\(331\) 2.79942 0.153870 0.0769351 0.997036i \(-0.475487\pi\)
0.0769351 + 0.997036i \(0.475487\pi\)
\(332\) 0.340339 0.0186785
\(333\) 5.42717 0.297407
\(334\) −1.95689 −0.107076
\(335\) −45.9978 −2.51313
\(336\) −0.0723899 −0.00394919
\(337\) 1.24402 0.0677659 0.0338830 0.999426i \(-0.489213\pi\)
0.0338830 + 0.999426i \(0.489213\pi\)
\(338\) 15.0367 0.817888
\(339\) −6.98038 −0.379122
\(340\) 0.136564 0.00740620
\(341\) 5.42475 0.293767
\(342\) 1.60630 0.0868590
\(343\) −0.248518 −0.0134187
\(344\) −32.4204 −1.74799
\(345\) −7.26676 −0.391229
\(346\) 34.1072 1.83362
\(347\) 4.98828 0.267785 0.133892 0.990996i \(-0.457252\pi\)
0.133892 + 0.990996i \(0.457252\pi\)
\(348\) 0.287195 0.0153953
\(349\) −16.7777 −0.898090 −0.449045 0.893509i \(-0.648236\pi\)
−0.449045 + 0.893509i \(0.648236\pi\)
\(350\) −0.172519 −0.00922154
\(351\) −1.57212 −0.0839136
\(352\) −0.481168 −0.0256463
\(353\) −6.47133 −0.344434 −0.172217 0.985059i \(-0.555093\pi\)
−0.172217 + 0.985059i \(0.555093\pi\)
\(354\) −2.04045 −0.108449
\(355\) 18.8134 0.998512
\(356\) −0.340273 −0.0180344
\(357\) −0.0177517 −0.000939519 0
\(358\) −30.5844 −1.61644
\(359\) −20.7359 −1.09440 −0.547199 0.837002i \(-0.684306\pi\)
−0.547199 + 0.837002i \(0.684306\pi\)
\(360\) −9.61895 −0.506963
\(361\) −17.7350 −0.933423
\(362\) −13.7773 −0.724119
\(363\) −6.41904 −0.336912
\(364\) −0.00110926 −5.81410e−5 0
\(365\) −37.6239 −1.96933
\(366\) −14.9443 −0.781150
\(367\) −22.6049 −1.17997 −0.589984 0.807415i \(-0.700866\pi\)
−0.589984 + 0.807415i \(0.700866\pi\)
\(368\) −8.62484 −0.449601
\(369\) 9.59589 0.499542
\(370\) 26.6311 1.38449
\(371\) −0.0848744 −0.00440646
\(372\) −0.100742 −0.00522321
\(373\) −33.3360 −1.72607 −0.863037 0.505141i \(-0.831440\pi\)
−0.863037 + 0.505141i \(0.831440\pi\)
\(374\) −3.05680 −0.158063
\(375\) −6.20061 −0.320198
\(376\) −30.7936 −1.58806
\(377\) −11.3594 −0.585040
\(378\) −0.0253529 −0.00130401
\(379\) −6.55025 −0.336464 −0.168232 0.985747i \(-0.553806\pi\)
−0.168232 + 0.985747i \(0.553806\pi\)
\(380\) 0.153594 0.00787921
\(381\) 13.9141 0.712842
\(382\) 16.1541 0.826517
\(383\) −18.1074 −0.925243 −0.462622 0.886556i \(-0.653091\pi\)
−0.462622 + 0.886556i \(0.653091\pi\)
\(384\) −11.6392 −0.593960
\(385\) 0.130541 0.00665297
\(386\) 25.3153 1.28851
\(387\) −11.5802 −0.588657
\(388\) 0.614287 0.0311857
\(389\) 16.1574 0.819215 0.409607 0.912262i \(-0.365666\pi\)
0.409607 + 0.912262i \(0.365666\pi\)
\(390\) −7.71439 −0.390634
\(391\) −2.11501 −0.106961
\(392\) −19.5965 −0.989773
\(393\) 12.3653 0.623747
\(394\) 18.7872 0.946485
\(395\) −11.6422 −0.585783
\(396\) −0.0850718 −0.00427502
\(397\) −31.6739 −1.58967 −0.794833 0.606828i \(-0.792441\pi\)
−0.794833 + 0.606828i \(0.792441\pi\)
\(398\) −28.1620 −1.41164
\(399\) −0.0199655 −0.000999523 0
\(400\) −27.7490 −1.38745
\(401\) 18.7676 0.937208 0.468604 0.883408i \(-0.344757\pi\)
0.468604 + 0.883408i \(0.344757\pi\)
\(402\) −19.1204 −0.953640
\(403\) 3.98462 0.198488
\(404\) −0.429485 −0.0213677
\(405\) −3.43580 −0.170726
\(406\) −0.183188 −0.00909149
\(407\) −11.6159 −0.575778
\(408\) −2.79963 −0.138602
\(409\) −33.6880 −1.66577 −0.832883 0.553450i \(-0.813311\pi\)
−0.832883 + 0.553450i \(0.813311\pi\)
\(410\) 47.0870 2.32546
\(411\) −18.1813 −0.896818
\(412\) 0.549939 0.0270935
\(413\) 0.0253616 0.00124796
\(414\) −3.02066 −0.148457
\(415\) −29.4193 −1.44413
\(416\) −0.353431 −0.0173284
\(417\) 2.53697 0.124236
\(418\) −3.43800 −0.168158
\(419\) −26.0118 −1.27076 −0.635379 0.772200i \(-0.719156\pi\)
−0.635379 + 0.772200i \(0.719156\pi\)
\(420\) −0.00242423 −0.000118291 0
\(421\) 34.0339 1.65871 0.829355 0.558722i \(-0.188708\pi\)
0.829355 + 0.558722i \(0.188708\pi\)
\(422\) −10.5933 −0.515675
\(423\) −10.9992 −0.534798
\(424\) −13.3856 −0.650061
\(425\) −6.80471 −0.330077
\(426\) 7.82038 0.378899
\(427\) 0.185749 0.00898902
\(428\) −0.663897 −0.0320907
\(429\) 3.36484 0.162456
\(430\) −56.8243 −2.74031
\(431\) 28.8515 1.38973 0.694864 0.719141i \(-0.255465\pi\)
0.694864 + 0.719141i \(0.255465\pi\)
\(432\) −4.07791 −0.196199
\(433\) 6.65932 0.320026 0.160013 0.987115i \(-0.448846\pi\)
0.160013 + 0.987115i \(0.448846\pi\)
\(434\) 0.0642583 0.00308450
\(435\) −24.8255 −1.19029
\(436\) 0.207230 0.00992454
\(437\) −2.37877 −0.113792
\(438\) −15.6396 −0.747287
\(439\) −11.9295 −0.569365 −0.284682 0.958622i \(-0.591888\pi\)
−0.284682 + 0.958622i \(0.591888\pi\)
\(440\) 20.5876 0.981477
\(441\) −6.99968 −0.333318
\(442\) −2.24530 −0.106798
\(443\) 22.8934 1.08770 0.543850 0.839183i \(-0.316966\pi\)
0.543850 + 0.839183i \(0.316966\pi\)
\(444\) 0.215715 0.0102374
\(445\) 29.4136 1.39434
\(446\) 8.18848 0.387736
\(447\) 4.95984 0.234592
\(448\) 0.139080 0.00657092
\(449\) 31.9959 1.50998 0.754991 0.655735i \(-0.227641\pi\)
0.754991 + 0.655735i \(0.227641\pi\)
\(450\) −9.71846 −0.458133
\(451\) −20.5383 −0.967109
\(452\) −0.277451 −0.0130502
\(453\) 8.66297 0.407022
\(454\) 25.2324 1.18422
\(455\) 0.0958856 0.00449519
\(456\) −3.14876 −0.147454
\(457\) 22.5887 1.05666 0.528329 0.849040i \(-0.322819\pi\)
0.528329 + 0.849040i \(0.322819\pi\)
\(458\) 15.2205 0.711208
\(459\) −1.00000 −0.0466760
\(460\) −0.288834 −0.0134669
\(461\) −15.1682 −0.706452 −0.353226 0.935538i \(-0.614915\pi\)
−0.353226 + 0.935538i \(0.614915\pi\)
\(462\) 0.0542633 0.00252456
\(463\) −0.911350 −0.0423540 −0.0211770 0.999776i \(-0.506741\pi\)
−0.0211770 + 0.999776i \(0.506741\pi\)
\(464\) −29.4651 −1.36788
\(465\) 8.70821 0.403834
\(466\) −8.33776 −0.386239
\(467\) 1.81262 0.0838781 0.0419391 0.999120i \(-0.486646\pi\)
0.0419391 + 0.999120i \(0.486646\pi\)
\(468\) −0.0624875 −0.00288849
\(469\) 0.237656 0.0109739
\(470\) −53.9729 −2.48959
\(471\) 1.00000 0.0460776
\(472\) 3.99980 0.184106
\(473\) 24.7854 1.13963
\(474\) −4.83945 −0.222283
\(475\) −7.65331 −0.351158
\(476\) −0.000705581 0 −3.23403e−5 0
\(477\) −4.78120 −0.218916
\(478\) 2.18238 0.0998198
\(479\) −35.9876 −1.64432 −0.822159 0.569259i \(-0.807230\pi\)
−0.822159 + 0.569259i \(0.807230\pi\)
\(480\) −0.772407 −0.0352554
\(481\) −8.53217 −0.389034
\(482\) 20.1665 0.918561
\(483\) 0.0375451 0.00170836
\(484\) −0.255139 −0.0115972
\(485\) −53.0997 −2.41113
\(486\) −1.42820 −0.0647843
\(487\) 3.92136 0.177694 0.0888469 0.996045i \(-0.471682\pi\)
0.0888469 + 0.996045i \(0.471682\pi\)
\(488\) 29.2945 1.32610
\(489\) 3.88060 0.175487
\(490\) −34.3474 −1.55166
\(491\) −21.6489 −0.977000 −0.488500 0.872564i \(-0.662456\pi\)
−0.488500 + 0.872564i \(0.662456\pi\)
\(492\) 0.381411 0.0171953
\(493\) −7.22554 −0.325422
\(494\) −2.52530 −0.113619
\(495\) 7.35370 0.330524
\(496\) 10.3357 0.464086
\(497\) −0.0972029 −0.00436015
\(498\) −12.2290 −0.547996
\(499\) −3.63515 −0.162732 −0.0813658 0.996684i \(-0.525928\pi\)
−0.0813658 + 0.996684i \(0.525928\pi\)
\(500\) −0.246457 −0.0110219
\(501\) 1.37018 0.0612151
\(502\) 13.2186 0.589975
\(503\) −15.9087 −0.709333 −0.354666 0.934993i \(-0.615406\pi\)
−0.354666 + 0.934993i \(0.615406\pi\)
\(504\) 0.0496981 0.00221373
\(505\) 37.1251 1.65205
\(506\) 6.46517 0.287412
\(507\) −10.5284 −0.467584
\(508\) 0.553048 0.0245375
\(509\) −19.1996 −0.851005 −0.425503 0.904957i \(-0.639903\pi\)
−0.425503 + 0.904957i \(0.639903\pi\)
\(510\) −4.90700 −0.217285
\(511\) 0.194391 0.00859935
\(512\) 21.9165 0.968583
\(513\) −1.12471 −0.0496570
\(514\) −20.2871 −0.894824
\(515\) −47.5373 −2.09474
\(516\) −0.460283 −0.0202628
\(517\) 23.5417 1.03536
\(518\) −0.137595 −0.00604556
\(519\) −23.8813 −1.04827
\(520\) 15.1222 0.663151
\(521\) −6.79497 −0.297693 −0.148847 0.988860i \(-0.547556\pi\)
−0.148847 + 0.988860i \(0.547556\pi\)
\(522\) −10.3195 −0.451672
\(523\) 23.7900 1.04026 0.520131 0.854086i \(-0.325883\pi\)
0.520131 + 0.854086i \(0.325883\pi\)
\(524\) 0.491487 0.0214707
\(525\) 0.120795 0.00527193
\(526\) 27.8617 1.21483
\(527\) 2.53455 0.110407
\(528\) 8.72804 0.379839
\(529\) −18.5267 −0.805510
\(530\) −23.4613 −1.01910
\(531\) 1.42869 0.0619998
\(532\) −0.000793572 0 −3.44057e−5 0
\(533\) −15.0859 −0.653443
\(534\) 12.2267 0.529100
\(535\) 57.3880 2.48110
\(536\) 37.4808 1.61893
\(537\) 21.4147 0.924112
\(538\) 6.05946 0.261242
\(539\) 14.9816 0.645301
\(540\) −0.136564 −0.00587676
\(541\) 18.4019 0.791162 0.395581 0.918431i \(-0.370543\pi\)
0.395581 + 0.918431i \(0.370543\pi\)
\(542\) 5.33290 0.229068
\(543\) 9.64664 0.413977
\(544\) −0.224811 −0.00963871
\(545\) −17.9132 −0.767318
\(546\) 0.0398578 0.00170576
\(547\) −21.1291 −0.903413 −0.451707 0.892166i \(-0.649185\pi\)
−0.451707 + 0.892166i \(0.649185\pi\)
\(548\) −0.722658 −0.0308704
\(549\) 10.4637 0.446581
\(550\) 20.8006 0.886941
\(551\) −8.12662 −0.346205
\(552\) 5.92125 0.252025
\(553\) 0.0601517 0.00255791
\(554\) −14.2796 −0.606683
\(555\) −18.6467 −0.791507
\(556\) 0.100838 0.00427648
\(557\) −34.6864 −1.46971 −0.734855 0.678224i \(-0.762750\pi\)
−0.734855 + 0.678224i \(0.762750\pi\)
\(558\) 3.61984 0.153240
\(559\) 18.2056 0.770013
\(560\) 0.248717 0.0105102
\(561\) 2.14032 0.0903643
\(562\) −24.5300 −1.03474
\(563\) 13.5564 0.571332 0.285666 0.958329i \(-0.407785\pi\)
0.285666 + 0.958329i \(0.407785\pi\)
\(564\) −0.437187 −0.0184089
\(565\) 23.9832 1.00898
\(566\) 24.9582 1.04907
\(567\) 0.0177517 0.000745501 0
\(568\) −15.3299 −0.643229
\(569\) −35.1773 −1.47471 −0.737354 0.675506i \(-0.763925\pi\)
−0.737354 + 0.675506i \(0.763925\pi\)
\(570\) −5.51894 −0.231163
\(571\) −33.0205 −1.38186 −0.690932 0.722920i \(-0.742799\pi\)
−0.690932 + 0.722920i \(0.742799\pi\)
\(572\) 0.133743 0.00559209
\(573\) −11.3109 −0.472518
\(574\) −0.243284 −0.0101545
\(575\) 14.3920 0.600190
\(576\) 7.83475 0.326448
\(577\) −12.2284 −0.509074 −0.254537 0.967063i \(-0.581923\pi\)
−0.254537 + 0.967063i \(0.581923\pi\)
\(578\) −1.42820 −0.0594052
\(579\) −17.7254 −0.736640
\(580\) −0.986745 −0.0409724
\(581\) 0.152000 0.00630602
\(582\) −22.0725 −0.914937
\(583\) 10.2333 0.423820
\(584\) 30.6575 1.26862
\(585\) 5.40149 0.223324
\(586\) −30.0166 −1.23997
\(587\) −5.87170 −0.242351 −0.121175 0.992631i \(-0.538666\pi\)
−0.121175 + 0.992631i \(0.538666\pi\)
\(588\) −0.278218 −0.0114735
\(589\) 2.85063 0.117458
\(590\) 7.01057 0.288621
\(591\) −13.1545 −0.541103
\(592\) −22.1315 −0.909601
\(593\) −29.9397 −1.22948 −0.614739 0.788731i \(-0.710738\pi\)
−0.614739 + 0.788731i \(0.710738\pi\)
\(594\) 3.05680 0.125422
\(595\) 0.0609912 0.00250040
\(596\) 0.197140 0.00807517
\(597\) 19.7186 0.807028
\(598\) 4.74884 0.194194
\(599\) −25.8178 −1.05489 −0.527444 0.849590i \(-0.676850\pi\)
−0.527444 + 0.849590i \(0.676850\pi\)
\(600\) 19.0506 0.777739
\(601\) −44.8575 −1.82977 −0.914887 0.403709i \(-0.867721\pi\)
−0.914887 + 0.403709i \(0.867721\pi\)
\(602\) 0.293593 0.0119660
\(603\) 13.3878 0.545193
\(604\) 0.344329 0.0140106
\(605\) 22.0545 0.896643
\(606\) 15.4322 0.626891
\(607\) 30.1202 1.22254 0.611271 0.791421i \(-0.290659\pi\)
0.611271 + 0.791421i \(0.290659\pi\)
\(608\) −0.252847 −0.0102543
\(609\) 0.128265 0.00519758
\(610\) 51.3455 2.07892
\(611\) 17.2920 0.699561
\(612\) −0.0397473 −0.00160669
\(613\) 36.1798 1.46129 0.730645 0.682758i \(-0.239220\pi\)
0.730645 + 0.682758i \(0.239220\pi\)
\(614\) −15.5598 −0.627944
\(615\) −32.9696 −1.32946
\(616\) −0.106370 −0.00428576
\(617\) −31.0597 −1.25042 −0.625209 0.780457i \(-0.714986\pi\)
−0.625209 + 0.780457i \(0.714986\pi\)
\(618\) −19.7604 −0.794878
\(619\) −35.1436 −1.41254 −0.706269 0.707943i \(-0.749623\pi\)
−0.706269 + 0.707943i \(0.749623\pi\)
\(620\) 0.346128 0.0139008
\(621\) 2.11501 0.0848726
\(622\) −23.4143 −0.938826
\(623\) −0.151971 −0.00608857
\(624\) 6.41098 0.256644
\(625\) −12.7195 −0.508780
\(626\) −16.9948 −0.679250
\(627\) 2.40723 0.0961356
\(628\) 0.0397473 0.00158609
\(629\) −5.42717 −0.216396
\(630\) 0.0871075 0.00347045
\(631\) 20.8299 0.829225 0.414612 0.909998i \(-0.363917\pi\)
0.414612 + 0.909998i \(0.363917\pi\)
\(632\) 9.48655 0.377355
\(633\) 7.41727 0.294810
\(634\) 17.5613 0.697449
\(635\) −47.8061 −1.89713
\(636\) −0.190040 −0.00753557
\(637\) 11.0044 0.436008
\(638\) 22.0870 0.874433
\(639\) −5.47570 −0.216615
\(640\) 39.9899 1.58074
\(641\) −46.0706 −1.81968 −0.909839 0.414960i \(-0.863795\pi\)
−0.909839 + 0.414960i \(0.863795\pi\)
\(642\) 23.8551 0.941486
\(643\) 13.5403 0.533979 0.266990 0.963699i \(-0.413971\pi\)
0.266990 + 0.963699i \(0.413971\pi\)
\(644\) 0.00149231 5.88054e−5 0
\(645\) 39.7874 1.56663
\(646\) −1.60630 −0.0631992
\(647\) −49.3679 −1.94085 −0.970427 0.241397i \(-0.922395\pi\)
−0.970427 + 0.241397i \(0.922395\pi\)
\(648\) 2.79963 0.109980
\(649\) −3.05785 −0.120031
\(650\) 15.2786 0.599276
\(651\) −0.0449926 −0.00176340
\(652\) 0.154243 0.00604063
\(653\) 8.33714 0.326258 0.163129 0.986605i \(-0.447841\pi\)
0.163129 + 0.986605i \(0.447841\pi\)
\(654\) −7.44620 −0.291169
\(655\) −42.4847 −1.66001
\(656\) −39.1312 −1.52782
\(657\) 10.9506 0.427222
\(658\) 0.278861 0.0108711
\(659\) 14.8314 0.577749 0.288874 0.957367i \(-0.406719\pi\)
0.288874 + 0.957367i \(0.406719\pi\)
\(660\) 0.292290 0.0113774
\(661\) −38.9353 −1.51441 −0.757203 0.653179i \(-0.773435\pi\)
−0.757203 + 0.653179i \(0.773435\pi\)
\(662\) −3.99813 −0.155392
\(663\) 1.57212 0.0610561
\(664\) 23.9720 0.930294
\(665\) 0.0685973 0.00266009
\(666\) −7.75107 −0.300348
\(667\) 15.2821 0.591726
\(668\) 0.0544609 0.00210715
\(669\) −5.73344 −0.221667
\(670\) 65.6939 2.53798
\(671\) −22.3957 −0.864577
\(672\) 0.00399078 0.000153948 0
\(673\) −17.3054 −0.667076 −0.333538 0.942737i \(-0.608242\pi\)
−0.333538 + 0.942737i \(0.608242\pi\)
\(674\) −1.77670 −0.0684360
\(675\) 6.80471 0.261913
\(676\) −0.418477 −0.0160953
\(677\) −16.4340 −0.631611 −0.315806 0.948824i \(-0.602275\pi\)
−0.315806 + 0.948824i \(0.602275\pi\)
\(678\) 9.96935 0.382871
\(679\) 0.274349 0.0105286
\(680\) 9.61895 0.368870
\(681\) −17.6673 −0.677013
\(682\) −7.74761 −0.296671
\(683\) 7.26276 0.277902 0.138951 0.990299i \(-0.455627\pi\)
0.138951 + 0.990299i \(0.455627\pi\)
\(684\) −0.0447041 −0.00170930
\(685\) 62.4673 2.38675
\(686\) 0.354933 0.0135514
\(687\) −10.6572 −0.406596
\(688\) 47.2233 1.80037
\(689\) 7.51663 0.286361
\(690\) 10.3784 0.395098
\(691\) −12.3929 −0.471447 −0.235724 0.971820i \(-0.575746\pi\)
−0.235724 + 0.971820i \(0.575746\pi\)
\(692\) −0.949217 −0.0360838
\(693\) −0.0379943 −0.00144328
\(694\) −7.12425 −0.270433
\(695\) −8.71653 −0.330637
\(696\) 20.2288 0.766771
\(697\) −9.59589 −0.363470
\(698\) 23.9619 0.906970
\(699\) 5.83796 0.220812
\(700\) 0.00480127 0.000181471 0
\(701\) 20.5757 0.777132 0.388566 0.921421i \(-0.372971\pi\)
0.388566 + 0.921421i \(0.372971\pi\)
\(702\) 2.24530 0.0847434
\(703\) −6.10398 −0.230216
\(704\) −16.7689 −0.632001
\(705\) 37.7909 1.42329
\(706\) 9.24233 0.347840
\(707\) −0.191814 −0.00721391
\(708\) 0.0567865 0.00213417
\(709\) −0.00689544 −0.000258964 0 −0.000129482 1.00000i \(-0.500041\pi\)
−0.000129482 1.00000i \(0.500041\pi\)
\(710\) −26.8692 −1.00838
\(711\) 3.38850 0.127079
\(712\) −23.9674 −0.898215
\(713\) −5.36061 −0.200756
\(714\) 0.0253529 0.000948809 0
\(715\) −11.5609 −0.432354
\(716\) 0.851176 0.0318099
\(717\) −1.52807 −0.0570667
\(718\) 29.6149 1.10522
\(719\) 22.3294 0.832748 0.416374 0.909194i \(-0.363301\pi\)
0.416374 + 0.909194i \(0.363301\pi\)
\(720\) 14.0109 0.522155
\(721\) 0.245610 0.00914700
\(722\) 25.3291 0.942652
\(723\) −14.1203 −0.525139
\(724\) 0.383428 0.0142500
\(725\) 49.1677 1.82604
\(726\) 9.16765 0.340243
\(727\) 16.6132 0.616149 0.308075 0.951362i \(-0.400315\pi\)
0.308075 + 0.951362i \(0.400315\pi\)
\(728\) −0.0781315 −0.00289574
\(729\) 1.00000 0.0370370
\(730\) 53.7344 1.98880
\(731\) 11.5802 0.428311
\(732\) 0.415905 0.0153723
\(733\) −34.4739 −1.27332 −0.636660 0.771144i \(-0.719685\pi\)
−0.636660 + 0.771144i \(0.719685\pi\)
\(734\) 32.2843 1.19164
\(735\) 24.0495 0.887079
\(736\) 0.475479 0.0175264
\(737\) −28.6542 −1.05549
\(738\) −13.7048 −0.504482
\(739\) −11.3500 −0.417515 −0.208758 0.977967i \(-0.566942\pi\)
−0.208758 + 0.977967i \(0.566942\pi\)
\(740\) −0.741154 −0.0272454
\(741\) 1.76818 0.0649556
\(742\) 0.121217 0.00445003
\(743\) 38.9822 1.43012 0.715058 0.699065i \(-0.246400\pi\)
0.715058 + 0.699065i \(0.246400\pi\)
\(744\) −7.09580 −0.260145
\(745\) −17.0410 −0.624334
\(746\) 47.6104 1.74314
\(747\) 8.56257 0.313288
\(748\) 0.0850718 0.00311053
\(749\) −0.296506 −0.0108341
\(750\) 8.85570 0.323364
\(751\) 4.25670 0.155329 0.0776645 0.996980i \(-0.475254\pi\)
0.0776645 + 0.996980i \(0.475254\pi\)
\(752\) 44.8537 1.63565
\(753\) −9.25544 −0.337287
\(754\) 16.2235 0.590825
\(755\) −29.7642 −1.08323
\(756\) 0.000705581 0 2.56617e−5 0
\(757\) 9.05927 0.329265 0.164632 0.986355i \(-0.447356\pi\)
0.164632 + 0.986355i \(0.447356\pi\)
\(758\) 9.35505 0.339791
\(759\) −4.52680 −0.164313
\(760\) 10.8185 0.392429
\(761\) 7.34113 0.266116 0.133058 0.991108i \(-0.457520\pi\)
0.133058 + 0.991108i \(0.457520\pi\)
\(762\) −19.8721 −0.719890
\(763\) 0.0925520 0.00335061
\(764\) −0.449575 −0.0162651
\(765\) 3.43580 0.124222
\(766\) 25.8609 0.934392
\(767\) −2.24607 −0.0811010
\(768\) 0.953560 0.0344086
\(769\) −30.9731 −1.11692 −0.558460 0.829532i \(-0.688607\pi\)
−0.558460 + 0.829532i \(0.688607\pi\)
\(770\) −0.186438 −0.00671875
\(771\) 14.2047 0.511569
\(772\) −0.704534 −0.0253567
\(773\) 39.3182 1.41418 0.707089 0.707124i \(-0.250008\pi\)
0.707089 + 0.707124i \(0.250008\pi\)
\(774\) 16.5389 0.594478
\(775\) −17.2469 −0.619526
\(776\) 43.2678 1.55322
\(777\) 0.0963415 0.00345623
\(778\) −23.0760 −0.827315
\(779\) −10.7926 −0.386684
\(780\) 0.214695 0.00768730
\(781\) 11.7197 0.419365
\(782\) 3.02066 0.108018
\(783\) 7.22554 0.258220
\(784\) 28.5441 1.01943
\(785\) −3.43580 −0.122629
\(786\) −17.6601 −0.629915
\(787\) 20.9054 0.745196 0.372598 0.927993i \(-0.378467\pi\)
0.372598 + 0.927993i \(0.378467\pi\)
\(788\) −0.522855 −0.0186259
\(789\) −19.5083 −0.694514
\(790\) 16.6274 0.591575
\(791\) −0.123913 −0.00440586
\(792\) −5.99209 −0.212920
\(793\) −16.4503 −0.584166
\(794\) 45.2365 1.60538
\(795\) 16.4272 0.582614
\(796\) 0.783760 0.0277796
\(797\) −47.2798 −1.67474 −0.837369 0.546638i \(-0.815907\pi\)
−0.837369 + 0.546638i \(0.815907\pi\)
\(798\) 0.0285146 0.00100941
\(799\) 10.9992 0.389123
\(800\) 1.52978 0.0540858
\(801\) −8.56091 −0.302485
\(802\) −26.8038 −0.946475
\(803\) −23.4377 −0.827098
\(804\) 0.532129 0.0187667
\(805\) −0.128997 −0.00454655
\(806\) −5.69083 −0.200451
\(807\) −4.24273 −0.149351
\(808\) −30.2511 −1.06423
\(809\) −21.2575 −0.747375 −0.373687 0.927555i \(-0.621907\pi\)
−0.373687 + 0.927555i \(0.621907\pi\)
\(810\) 4.90700 0.172414
\(811\) −32.9937 −1.15857 −0.579283 0.815126i \(-0.696667\pi\)
−0.579283 + 0.815126i \(0.696667\pi\)
\(812\) 0.00509820 0.000178912 0
\(813\) −3.73401 −0.130957
\(814\) 16.5898 0.581471
\(815\) −13.3330 −0.467033
\(816\) 4.07791 0.142756
\(817\) 13.0244 0.455666
\(818\) 48.1131 1.68224
\(819\) −0.0279078 −0.000975178 0
\(820\) −1.31045 −0.0457629
\(821\) −9.92574 −0.346411 −0.173205 0.984886i \(-0.555412\pi\)
−0.173205 + 0.984886i \(0.555412\pi\)
\(822\) 25.9665 0.905686
\(823\) 24.3703 0.849495 0.424747 0.905312i \(-0.360363\pi\)
0.424747 + 0.905312i \(0.360363\pi\)
\(824\) 38.7353 1.34941
\(825\) −14.5642 −0.507062
\(826\) −0.0362214 −0.00126030
\(827\) 41.9660 1.45930 0.729650 0.683821i \(-0.239683\pi\)
0.729650 + 0.683821i \(0.239683\pi\)
\(828\) 0.0840660 0.00292150
\(829\) 39.9557 1.38772 0.693860 0.720110i \(-0.255909\pi\)
0.693860 + 0.720110i \(0.255909\pi\)
\(830\) 42.0165 1.45841
\(831\) 9.99835 0.346839
\(832\) −12.3172 −0.427022
\(833\) 6.99968 0.242525
\(834\) −3.62330 −0.125465
\(835\) −4.70766 −0.162915
\(836\) 0.0956809 0.00330919
\(837\) −2.53455 −0.0876069
\(838\) 37.1499 1.28332
\(839\) 6.13011 0.211635 0.105817 0.994386i \(-0.466254\pi\)
0.105817 + 0.994386i \(0.466254\pi\)
\(840\) −0.170753 −0.00589153
\(841\) 23.2084 0.800289
\(842\) −48.6071 −1.67511
\(843\) 17.1755 0.591556
\(844\) 0.294816 0.0101480
\(845\) 36.1736 1.24441
\(846\) 15.7090 0.540086
\(847\) −0.113949 −0.00391532
\(848\) 19.4973 0.669541
\(849\) −17.4753 −0.599752
\(850\) 9.71846 0.333341
\(851\) 11.4785 0.393479
\(852\) −0.217644 −0.00745637
\(853\) 2.89569 0.0991466 0.0495733 0.998770i \(-0.484214\pi\)
0.0495733 + 0.998770i \(0.484214\pi\)
\(854\) −0.265286 −0.00907790
\(855\) 3.86427 0.132155
\(856\) −46.7620 −1.59829
\(857\) 15.3289 0.523625 0.261813 0.965119i \(-0.415680\pi\)
0.261813 + 0.965119i \(0.415680\pi\)
\(858\) −4.80566 −0.164062
\(859\) −7.10231 −0.242328 −0.121164 0.992633i \(-0.538663\pi\)
−0.121164 + 0.992633i \(0.538663\pi\)
\(860\) 1.58144 0.0539267
\(861\) 0.170343 0.00580528
\(862\) −41.2056 −1.40347
\(863\) 15.8374 0.539112 0.269556 0.962985i \(-0.413123\pi\)
0.269556 + 0.962985i \(0.413123\pi\)
\(864\) 0.224811 0.00764824
\(865\) 82.0514 2.78983
\(866\) −9.51082 −0.323191
\(867\) 1.00000 0.0339618
\(868\) −0.00178833 −6.07000e−5 0
\(869\) −7.25248 −0.246023
\(870\) 35.4557 1.20206
\(871\) −21.0472 −0.713159
\(872\) 14.5964 0.494297
\(873\) 15.4548 0.523067
\(874\) 3.39735 0.114917
\(875\) −0.110071 −0.00372109
\(876\) 0.435255 0.0147059
\(877\) −33.2347 −1.12226 −0.561128 0.827729i \(-0.689632\pi\)
−0.561128 + 0.827729i \(0.689632\pi\)
\(878\) 17.0377 0.574995
\(879\) 21.0171 0.708890
\(880\) −29.9878 −1.01089
\(881\) −13.1617 −0.443430 −0.221715 0.975111i \(-0.571165\pi\)
−0.221715 + 0.975111i \(0.571165\pi\)
\(882\) 9.99693 0.336614
\(883\) −7.78730 −0.262063 −0.131032 0.991378i \(-0.541829\pi\)
−0.131032 + 0.991378i \(0.541829\pi\)
\(884\) 0.0624875 0.00210168
\(885\) −4.90869 −0.165004
\(886\) −32.6963 −1.09845
\(887\) 23.2948 0.782162 0.391081 0.920356i \(-0.372101\pi\)
0.391081 + 0.920356i \(0.372101\pi\)
\(888\) 15.1941 0.509879
\(889\) 0.246999 0.00828408
\(890\) −42.0084 −1.40812
\(891\) −2.14032 −0.0717034
\(892\) −0.227889 −0.00763027
\(893\) 12.3709 0.413975
\(894\) −7.08362 −0.236912
\(895\) −73.5766 −2.45939
\(896\) −0.206615 −0.00690254
\(897\) −3.32506 −0.111020
\(898\) −45.6965 −1.52491
\(899\) −18.3135 −0.610789
\(900\) 0.270469 0.00901562
\(901\) 4.78120 0.159285
\(902\) 29.3327 0.976672
\(903\) −0.205569 −0.00684091
\(904\) −19.5425 −0.649972
\(905\) −33.1439 −1.10174
\(906\) −12.3724 −0.411046
\(907\) −37.0970 −1.23179 −0.615893 0.787830i \(-0.711204\pi\)
−0.615893 + 0.787830i \(0.711204\pi\)
\(908\) −0.702228 −0.0233043
\(909\) −10.8054 −0.358392
\(910\) −0.136944 −0.00453963
\(911\) −38.7110 −1.28255 −0.641276 0.767310i \(-0.721595\pi\)
−0.641276 + 0.767310i \(0.721595\pi\)
\(912\) 4.58646 0.151873
\(913\) −18.3266 −0.606523
\(914\) −32.2612 −1.06711
\(915\) −35.9513 −1.18851
\(916\) −0.423593 −0.0139959
\(917\) 0.219505 0.00724870
\(918\) 1.42820 0.0471375
\(919\) 1.12584 0.0371381 0.0185691 0.999828i \(-0.494089\pi\)
0.0185691 + 0.999828i \(0.494089\pi\)
\(920\) −20.3442 −0.670729
\(921\) 10.8947 0.358994
\(922\) 21.6631 0.713437
\(923\) 8.60847 0.283351
\(924\) −0.00151017 −4.96809e−5 0
\(925\) 36.9303 1.21426
\(926\) 1.30159 0.0427728
\(927\) 13.8359 0.454430
\(928\) 1.62438 0.0533230
\(929\) 52.9710 1.73792 0.868961 0.494881i \(-0.164788\pi\)
0.868961 + 0.494881i \(0.164788\pi\)
\(930\) −12.4370 −0.407827
\(931\) 7.87260 0.258014
\(932\) 0.232043 0.00760082
\(933\) 16.3943 0.536725
\(934\) −2.58878 −0.0847075
\(935\) −7.35370 −0.240492
\(936\) −4.40135 −0.143863
\(937\) −2.48383 −0.0811433 −0.0405716 0.999177i \(-0.512918\pi\)
−0.0405716 + 0.999177i \(0.512918\pi\)
\(938\) −0.339420 −0.0110824
\(939\) 11.8995 0.388325
\(940\) 1.50209 0.0489927
\(941\) −15.5052 −0.505456 −0.252728 0.967537i \(-0.581328\pi\)
−0.252728 + 0.967537i \(0.581328\pi\)
\(942\) −1.42820 −0.0465332
\(943\) 20.2954 0.660911
\(944\) −5.82607 −0.189622
\(945\) −0.0609912 −0.00198404
\(946\) −35.3985 −1.15090
\(947\) −52.1726 −1.69538 −0.847692 0.530489i \(-0.822008\pi\)
−0.847692 + 0.530489i \(0.822008\pi\)
\(948\) 0.134684 0.00437433
\(949\) −17.2156 −0.558842
\(950\) 10.9304 0.354630
\(951\) −12.2961 −0.398730
\(952\) −0.0496981 −0.00161073
\(953\) 16.1006 0.521550 0.260775 0.965400i \(-0.416022\pi\)
0.260775 + 0.965400i \(0.416022\pi\)
\(954\) 6.82850 0.221081
\(955\) 38.8618 1.25754
\(956\) −0.0607365 −0.00196436
\(957\) −15.4650 −0.499911
\(958\) 51.3974 1.66058
\(959\) −0.322749 −0.0104221
\(960\) −26.9186 −0.868795
\(961\) −24.5760 −0.792776
\(962\) 12.1856 0.392880
\(963\) −16.7030 −0.538245
\(964\) −0.561243 −0.0180764
\(965\) 60.9007 1.96046
\(966\) −0.0536217 −0.00172525
\(967\) −30.0760 −0.967179 −0.483589 0.875295i \(-0.660667\pi\)
−0.483589 + 0.875295i \(0.660667\pi\)
\(968\) −17.9709 −0.577607
\(969\) 1.12471 0.0361308
\(970\) 75.8368 2.43497
\(971\) −54.2862 −1.74213 −0.871064 0.491169i \(-0.836570\pi\)
−0.871064 + 0.491169i \(0.836570\pi\)
\(972\) 0.0397473 0.00127489
\(973\) 0.0450356 0.00144377
\(974\) −5.60047 −0.179451
\(975\) −10.6978 −0.342605
\(976\) −42.6702 −1.36584
\(977\) −52.6742 −1.68520 −0.842599 0.538541i \(-0.818976\pi\)
−0.842599 + 0.538541i \(0.818976\pi\)
\(978\) −5.54226 −0.177222
\(979\) 18.3231 0.585608
\(980\) 0.955902 0.0305352
\(981\) 5.21370 0.166461
\(982\) 30.9189 0.986660
\(983\) 57.1798 1.82375 0.911876 0.410465i \(-0.134634\pi\)
0.911876 + 0.410465i \(0.134634\pi\)
\(984\) 26.8649 0.856423
\(985\) 45.1961 1.44007
\(986\) 10.3195 0.328640
\(987\) −0.195254 −0.00621500
\(988\) 0.0702802 0.00223591
\(989\) −24.4924 −0.778812
\(990\) −10.5025 −0.333793
\(991\) −37.7418 −1.19891 −0.599454 0.800409i \(-0.704616\pi\)
−0.599454 + 0.800409i \(0.704616\pi\)
\(992\) −0.569796 −0.0180911
\(993\) 2.79942 0.0888370
\(994\) 0.138825 0.00440326
\(995\) −67.7491 −2.14779
\(996\) 0.340339 0.0107840
\(997\) 23.7173 0.751135 0.375568 0.926795i \(-0.377448\pi\)
0.375568 + 0.926795i \(0.377448\pi\)
\(998\) 5.19171 0.164341
\(999\) 5.42717 0.171708
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 \(a_p\))