Properties

Label 6025.2.a.h.1.11
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-2.02418\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.02418 q^{2}\) \(-2.93498 q^{3}\) \(+2.09729 q^{4}\) \(-5.94092 q^{6}\) \(-0.381245 q^{7}\) \(+0.196936 q^{8}\) \(+5.61411 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.02418 q^{2}\) \(-2.93498 q^{3}\) \(+2.09729 q^{4}\) \(-5.94092 q^{6}\) \(-0.381245 q^{7}\) \(+0.196936 q^{8}\) \(+5.61411 q^{9}\) \(+0.280814 q^{11}\) \(-6.15551 q^{12}\) \(+4.00528 q^{13}\) \(-0.771706 q^{14}\) \(-3.79595 q^{16}\) \(-2.60326 q^{17}\) \(+11.3640 q^{18}\) \(-3.86940 q^{19}\) \(+1.11895 q^{21}\) \(+0.568418 q^{22}\) \(-0.698450 q^{23}\) \(-0.578002 q^{24}\) \(+8.10740 q^{26}\) \(-7.67238 q^{27}\) \(-0.799581 q^{28}\) \(+1.62690 q^{29}\) \(+9.73691 q^{31}\) \(-8.07755 q^{32}\) \(-0.824185 q^{33}\) \(-5.26945 q^{34}\) \(+11.7744 q^{36}\) \(-4.41735 q^{37}\) \(-7.83234 q^{38}\) \(-11.7554 q^{39}\) \(-0.0157665 q^{41}\) \(+2.26494 q^{42}\) \(+12.2173 q^{43}\) \(+0.588950 q^{44}\) \(-1.41379 q^{46}\) \(-7.71890 q^{47}\) \(+11.1410 q^{48}\) \(-6.85465 q^{49}\) \(+7.64051 q^{51}\) \(+8.40025 q^{52}\) \(+4.91852 q^{53}\) \(-15.5302 q^{54}\) \(-0.0750807 q^{56}\) \(+11.3566 q^{57}\) \(+3.29313 q^{58}\) \(-14.1596 q^{59}\) \(-6.97043 q^{61}\) \(+19.7092 q^{62}\) \(-2.14035 q^{63}\) \(-8.75848 q^{64}\) \(-1.66830 q^{66}\) \(+2.97942 q^{67}\) \(-5.45979 q^{68}\) \(+2.04994 q^{69}\) \(+7.28180 q^{71}\) \(+1.10562 q^{72}\) \(+0.165424 q^{73}\) \(-8.94150 q^{74}\) \(-8.11525 q^{76}\) \(-0.107059 q^{77}\) \(-23.7951 q^{78}\) \(+11.1633 q^{79}\) \(+5.67594 q^{81}\) \(-0.0319141 q^{82}\) \(+14.6259 q^{83}\) \(+2.34676 q^{84}\) \(+24.7300 q^{86}\) \(-4.77491 q^{87}\) \(+0.0553024 q^{88}\) \(+14.3374 q^{89}\) \(-1.52699 q^{91}\) \(-1.46485 q^{92}\) \(-28.5777 q^{93}\) \(-15.6244 q^{94}\) \(+23.7074 q^{96}\) \(-8.75687 q^{97}\) \(-13.8750 q^{98}\) \(+1.57652 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.02418 1.43131 0.715655 0.698454i \(-0.246129\pi\)
0.715655 + 0.698454i \(0.246129\pi\)
\(3\) −2.93498 −1.69451 −0.847256 0.531185i \(-0.821747\pi\)
−0.847256 + 0.531185i \(0.821747\pi\)
\(4\) 2.09729 1.04865
\(5\) 0 0
\(6\) −5.94092 −2.42537
\(7\) −0.381245 −0.144097 −0.0720485 0.997401i \(-0.522954\pi\)
−0.0720485 + 0.997401i \(0.522954\pi\)
\(8\) 0.196936 0.0696273
\(9\) 5.61411 1.87137
\(10\) 0 0
\(11\) 0.280814 0.0846688 0.0423344 0.999103i \(-0.486521\pi\)
0.0423344 + 0.999103i \(0.486521\pi\)
\(12\) −6.15551 −1.77694
\(13\) 4.00528 1.11087 0.555433 0.831561i \(-0.312553\pi\)
0.555433 + 0.831561i \(0.312553\pi\)
\(14\) −0.771706 −0.206247
\(15\) 0 0
\(16\) −3.79595 −0.948988
\(17\) −2.60326 −0.631383 −0.315691 0.948862i \(-0.602236\pi\)
−0.315691 + 0.948862i \(0.602236\pi\)
\(18\) 11.3640 2.67851
\(19\) −3.86940 −0.887700 −0.443850 0.896101i \(-0.646388\pi\)
−0.443850 + 0.896101i \(0.646388\pi\)
\(20\) 0 0
\(21\) 1.11895 0.244174
\(22\) 0.568418 0.121187
\(23\) −0.698450 −0.145637 −0.0728185 0.997345i \(-0.523199\pi\)
−0.0728185 + 0.997345i \(0.523199\pi\)
\(24\) −0.578002 −0.117984
\(25\) 0 0
\(26\) 8.10740 1.58999
\(27\) −7.67238 −1.47655
\(28\) −0.799581 −0.151107
\(29\) 1.62690 0.302107 0.151054 0.988526i \(-0.451733\pi\)
0.151054 + 0.988526i \(0.451733\pi\)
\(30\) 0 0
\(31\) 9.73691 1.74880 0.874401 0.485205i \(-0.161255\pi\)
0.874401 + 0.485205i \(0.161255\pi\)
\(32\) −8.07755 −1.42792
\(33\) −0.824185 −0.143472
\(34\) −5.26945 −0.903704
\(35\) 0 0
\(36\) 11.7744 1.96241
\(37\) −4.41735 −0.726208 −0.363104 0.931749i \(-0.618283\pi\)
−0.363104 + 0.931749i \(0.618283\pi\)
\(38\) −7.83234 −1.27057
\(39\) −11.7554 −1.88238
\(40\) 0 0
\(41\) −0.0157665 −0.00246231 −0.00123116 0.999999i \(-0.500392\pi\)
−0.00123116 + 0.999999i \(0.500392\pi\)
\(42\) 2.26494 0.349488
\(43\) 12.2173 1.86312 0.931562 0.363583i \(-0.118447\pi\)
0.931562 + 0.363583i \(0.118447\pi\)
\(44\) 0.588950 0.0887875
\(45\) 0 0
\(46\) −1.41379 −0.208452
\(47\) −7.71890 −1.12592 −0.562958 0.826485i \(-0.690337\pi\)
−0.562958 + 0.826485i \(0.690337\pi\)
\(48\) 11.1410 1.60807
\(49\) −6.85465 −0.979236
\(50\) 0 0
\(51\) 7.64051 1.06989
\(52\) 8.40025 1.16491
\(53\) 4.91852 0.675611 0.337806 0.941216i \(-0.390315\pi\)
0.337806 + 0.941216i \(0.390315\pi\)
\(54\) −15.5302 −2.11340
\(55\) 0 0
\(56\) −0.0750807 −0.0100331
\(57\) 11.3566 1.50422
\(58\) 3.29313 0.432409
\(59\) −14.1596 −1.84342 −0.921709 0.387882i \(-0.873207\pi\)
−0.921709 + 0.387882i \(0.873207\pi\)
\(60\) 0 0
\(61\) −6.97043 −0.892472 −0.446236 0.894915i \(-0.647236\pi\)
−0.446236 + 0.894915i \(0.647236\pi\)
\(62\) 19.7092 2.50308
\(63\) −2.14035 −0.269659
\(64\) −8.75848 −1.09481
\(65\) 0 0
\(66\) −1.66830 −0.205353
\(67\) 2.97942 0.363994 0.181997 0.983299i \(-0.441744\pi\)
0.181997 + 0.983299i \(0.441744\pi\)
\(68\) −5.45979 −0.662097
\(69\) 2.04994 0.246784
\(70\) 0 0
\(71\) 7.28180 0.864191 0.432095 0.901828i \(-0.357774\pi\)
0.432095 + 0.901828i \(0.357774\pi\)
\(72\) 1.10562 0.130298
\(73\) 0.165424 0.0193614 0.00968072 0.999953i \(-0.496918\pi\)
0.00968072 + 0.999953i \(0.496918\pi\)
\(74\) −8.94150 −1.03943
\(75\) 0 0
\(76\) −8.11525 −0.930883
\(77\) −0.107059 −0.0122005
\(78\) −23.7951 −2.69426
\(79\) 11.1633 1.25597 0.627986 0.778225i \(-0.283880\pi\)
0.627986 + 0.778225i \(0.283880\pi\)
\(80\) 0 0
\(81\) 5.67594 0.630660
\(82\) −0.0319141 −0.00352433
\(83\) 14.6259 1.60540 0.802701 0.596382i \(-0.203396\pi\)
0.802701 + 0.596382i \(0.203396\pi\)
\(84\) 2.34676 0.256052
\(85\) 0 0
\(86\) 24.7300 2.66671
\(87\) −4.77491 −0.511924
\(88\) 0.0553024 0.00589525
\(89\) 14.3374 1.51976 0.759878 0.650066i \(-0.225259\pi\)
0.759878 + 0.650066i \(0.225259\pi\)
\(90\) 0 0
\(91\) −1.52699 −0.160072
\(92\) −1.46485 −0.152722
\(93\) −28.5777 −2.96337
\(94\) −15.6244 −1.61154
\(95\) 0 0
\(96\) 23.7074 2.41963
\(97\) −8.75687 −0.889126 −0.444563 0.895748i \(-0.646641\pi\)
−0.444563 + 0.895748i \(0.646641\pi\)
\(98\) −13.8750 −1.40159
\(99\) 1.57652 0.158447
\(100\) 0 0
\(101\) −5.97227 −0.594263 −0.297132 0.954837i \(-0.596030\pi\)
−0.297132 + 0.954837i \(0.596030\pi\)
\(102\) 15.4658 1.53134
\(103\) 17.0246 1.67749 0.838743 0.544527i \(-0.183291\pi\)
0.838743 + 0.544527i \(0.183291\pi\)
\(104\) 0.788783 0.0773466
\(105\) 0 0
\(106\) 9.95596 0.967008
\(107\) 6.06814 0.586629 0.293315 0.956016i \(-0.405242\pi\)
0.293315 + 0.956016i \(0.405242\pi\)
\(108\) −16.0912 −1.54838
\(109\) −10.0495 −0.962568 −0.481284 0.876565i \(-0.659829\pi\)
−0.481284 + 0.876565i \(0.659829\pi\)
\(110\) 0 0
\(111\) 12.9648 1.23057
\(112\) 1.44719 0.136746
\(113\) −3.24797 −0.305543 −0.152772 0.988262i \(-0.548820\pi\)
−0.152772 + 0.988262i \(0.548820\pi\)
\(114\) 22.9878 2.15300
\(115\) 0 0
\(116\) 3.41208 0.316803
\(117\) 22.4861 2.07884
\(118\) −28.6615 −2.63850
\(119\) 0.992478 0.0909803
\(120\) 0 0
\(121\) −10.9211 −0.992831
\(122\) −14.1094 −1.27740
\(123\) 0.0462743 0.00417241
\(124\) 20.4211 1.83387
\(125\) 0 0
\(126\) −4.33245 −0.385965
\(127\) −0.309449 −0.0274591 −0.0137296 0.999906i \(-0.504370\pi\)
−0.0137296 + 0.999906i \(0.504370\pi\)
\(128\) −1.57362 −0.139090
\(129\) −35.8576 −3.15709
\(130\) 0 0
\(131\) 17.9939 1.57214 0.786068 0.618141i \(-0.212114\pi\)
0.786068 + 0.618141i \(0.212114\pi\)
\(132\) −1.72856 −0.150452
\(133\) 1.47519 0.127915
\(134\) 6.03088 0.520989
\(135\) 0 0
\(136\) −0.512674 −0.0439615
\(137\) 8.91168 0.761377 0.380688 0.924703i \(-0.375687\pi\)
0.380688 + 0.924703i \(0.375687\pi\)
\(138\) 4.14944 0.353224
\(139\) 7.82985 0.664119 0.332059 0.943258i \(-0.392257\pi\)
0.332059 + 0.943258i \(0.392257\pi\)
\(140\) 0 0
\(141\) 22.6548 1.90788
\(142\) 14.7396 1.23692
\(143\) 1.12474 0.0940557
\(144\) −21.3109 −1.77591
\(145\) 0 0
\(146\) 0.334848 0.0277122
\(147\) 20.1183 1.65933
\(148\) −9.26447 −0.761535
\(149\) 20.5561 1.68402 0.842010 0.539462i \(-0.181372\pi\)
0.842010 + 0.539462i \(0.181372\pi\)
\(150\) 0 0
\(151\) 10.5866 0.861524 0.430762 0.902466i \(-0.358245\pi\)
0.430762 + 0.902466i \(0.358245\pi\)
\(152\) −0.762022 −0.0618082
\(153\) −14.6150 −1.18155
\(154\) −0.216706 −0.0174627
\(155\) 0 0
\(156\) −24.6546 −1.97395
\(157\) −7.79923 −0.622447 −0.311223 0.950337i \(-0.600739\pi\)
−0.311223 + 0.950337i \(0.600739\pi\)
\(158\) 22.5965 1.79768
\(159\) −14.4358 −1.14483
\(160\) 0 0
\(161\) 0.266280 0.0209858
\(162\) 11.4891 0.902669
\(163\) −17.1362 −1.34221 −0.671104 0.741363i \(-0.734180\pi\)
−0.671104 + 0.741363i \(0.734180\pi\)
\(164\) −0.0330669 −0.00258209
\(165\) 0 0
\(166\) 29.6054 2.29783
\(167\) 1.88493 0.145860 0.0729302 0.997337i \(-0.476765\pi\)
0.0729302 + 0.997337i \(0.476765\pi\)
\(168\) 0.220360 0.0170012
\(169\) 3.04231 0.234024
\(170\) 0 0
\(171\) −21.7232 −1.66122
\(172\) 25.6233 1.95376
\(173\) 9.95946 0.757203 0.378602 0.925560i \(-0.376405\pi\)
0.378602 + 0.925560i \(0.376405\pi\)
\(174\) −9.66526 −0.732722
\(175\) 0 0
\(176\) −1.06596 −0.0803496
\(177\) 41.5581 3.12369
\(178\) 29.0213 2.17524
\(179\) 25.8971 1.93564 0.967820 0.251643i \(-0.0809708\pi\)
0.967820 + 0.251643i \(0.0809708\pi\)
\(180\) 0 0
\(181\) −8.61696 −0.640494 −0.320247 0.947334i \(-0.603766\pi\)
−0.320247 + 0.947334i \(0.603766\pi\)
\(182\) −3.09090 −0.229113
\(183\) 20.4581 1.51230
\(184\) −0.137550 −0.0101403
\(185\) 0 0
\(186\) −57.8462 −4.24149
\(187\) −0.731033 −0.0534584
\(188\) −16.1888 −1.18069
\(189\) 2.92505 0.212766
\(190\) 0 0
\(191\) −7.40808 −0.536030 −0.268015 0.963415i \(-0.586368\pi\)
−0.268015 + 0.963415i \(0.586368\pi\)
\(192\) 25.7060 1.85517
\(193\) 13.0485 0.939252 0.469626 0.882865i \(-0.344389\pi\)
0.469626 + 0.882865i \(0.344389\pi\)
\(194\) −17.7255 −1.27261
\(195\) 0 0
\(196\) −14.3762 −1.02687
\(197\) 2.32016 0.165305 0.0826524 0.996578i \(-0.473661\pi\)
0.0826524 + 0.996578i \(0.473661\pi\)
\(198\) 3.19116 0.226786
\(199\) 21.5958 1.53089 0.765444 0.643502i \(-0.222519\pi\)
0.765444 + 0.643502i \(0.222519\pi\)
\(200\) 0 0
\(201\) −8.74455 −0.616793
\(202\) −12.0889 −0.850574
\(203\) −0.620245 −0.0435327
\(204\) 16.0244 1.12193
\(205\) 0 0
\(206\) 34.4609 2.40100
\(207\) −3.92118 −0.272541
\(208\) −15.2039 −1.05420
\(209\) −1.08658 −0.0751605
\(210\) 0 0
\(211\) 20.1477 1.38702 0.693512 0.720445i \(-0.256062\pi\)
0.693512 + 0.720445i \(0.256062\pi\)
\(212\) 10.3156 0.708477
\(213\) −21.3719 −1.46438
\(214\) 12.2830 0.839648
\(215\) 0 0
\(216\) −1.51096 −0.102808
\(217\) −3.71215 −0.251997
\(218\) −20.3420 −1.37773
\(219\) −0.485517 −0.0328082
\(220\) 0 0
\(221\) −10.4268 −0.701382
\(222\) 26.2431 1.76132
\(223\) 7.96809 0.533583 0.266792 0.963754i \(-0.414036\pi\)
0.266792 + 0.963754i \(0.414036\pi\)
\(224\) 3.07952 0.205759
\(225\) 0 0
\(226\) −6.57447 −0.437327
\(227\) 19.2441 1.27728 0.638639 0.769506i \(-0.279498\pi\)
0.638639 + 0.769506i \(0.279498\pi\)
\(228\) 23.8181 1.57739
\(229\) 12.7475 0.842380 0.421190 0.906972i \(-0.361612\pi\)
0.421190 + 0.906972i \(0.361612\pi\)
\(230\) 0 0
\(231\) 0.314216 0.0206739
\(232\) 0.320394 0.0210349
\(233\) 10.2413 0.670931 0.335465 0.942053i \(-0.391106\pi\)
0.335465 + 0.942053i \(0.391106\pi\)
\(234\) 45.5159 2.97547
\(235\) 0 0
\(236\) −29.6967 −1.93309
\(237\) −32.7641 −2.12826
\(238\) 2.00895 0.130221
\(239\) 22.4264 1.45064 0.725321 0.688411i \(-0.241691\pi\)
0.725321 + 0.688411i \(0.241691\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −22.1063 −1.42105
\(243\) 6.35836 0.407889
\(244\) −14.6190 −0.935887
\(245\) 0 0
\(246\) 0.0936674 0.00597202
\(247\) −15.4980 −0.986116
\(248\) 1.91755 0.121764
\(249\) −42.9267 −2.72037
\(250\) 0 0
\(251\) 14.0729 0.888274 0.444137 0.895959i \(-0.353510\pi\)
0.444137 + 0.895959i \(0.353510\pi\)
\(252\) −4.48894 −0.282777
\(253\) −0.196135 −0.0123309
\(254\) −0.626379 −0.0393025
\(255\) 0 0
\(256\) 14.3317 0.895730
\(257\) −1.46464 −0.0913619 −0.0456809 0.998956i \(-0.514546\pi\)
−0.0456809 + 0.998956i \(0.514546\pi\)
\(258\) −72.5821 −4.51877
\(259\) 1.68409 0.104644
\(260\) 0 0
\(261\) 9.13358 0.565355
\(262\) 36.4229 2.25021
\(263\) −8.09273 −0.499019 −0.249509 0.968372i \(-0.580269\pi\)
−0.249509 + 0.968372i \(0.580269\pi\)
\(264\) −0.162311 −0.00998958
\(265\) 0 0
\(266\) 2.98604 0.183086
\(267\) −42.0799 −2.57525
\(268\) 6.24872 0.381701
\(269\) −25.2517 −1.53962 −0.769812 0.638271i \(-0.779650\pi\)
−0.769812 + 0.638271i \(0.779650\pi\)
\(270\) 0 0
\(271\) 6.04109 0.366970 0.183485 0.983023i \(-0.441262\pi\)
0.183485 + 0.983023i \(0.441262\pi\)
\(272\) 9.88184 0.599175
\(273\) 4.48170 0.271245
\(274\) 18.0388 1.08977
\(275\) 0 0
\(276\) 4.29932 0.258789
\(277\) 17.9271 1.07714 0.538568 0.842582i \(-0.318966\pi\)
0.538568 + 0.842582i \(0.318966\pi\)
\(278\) 15.8490 0.950559
\(279\) 54.6641 3.27266
\(280\) 0 0
\(281\) 4.13276 0.246540 0.123270 0.992373i \(-0.460662\pi\)
0.123270 + 0.992373i \(0.460662\pi\)
\(282\) 45.8574 2.73077
\(283\) −13.7771 −0.818962 −0.409481 0.912319i \(-0.634290\pi\)
−0.409481 + 0.912319i \(0.634290\pi\)
\(284\) 15.2721 0.906230
\(285\) 0 0
\(286\) 2.27668 0.134623
\(287\) 0.00601088 0.000354811 0
\(288\) −45.3483 −2.67217
\(289\) −10.2230 −0.601356
\(290\) 0 0
\(291\) 25.7013 1.50663
\(292\) 0.346943 0.0203033
\(293\) −21.6053 −1.26220 −0.631098 0.775703i \(-0.717395\pi\)
−0.631098 + 0.775703i \(0.717395\pi\)
\(294\) 40.7229 2.37501
\(295\) 0 0
\(296\) −0.869934 −0.0505639
\(297\) −2.15451 −0.125018
\(298\) 41.6091 2.41035
\(299\) −2.79749 −0.161783
\(300\) 0 0
\(301\) −4.65779 −0.268470
\(302\) 21.4291 1.23311
\(303\) 17.5285 1.00699
\(304\) 14.6880 0.842417
\(305\) 0 0
\(306\) −29.5833 −1.69117
\(307\) −20.3178 −1.15960 −0.579800 0.814759i \(-0.696869\pi\)
−0.579800 + 0.814759i \(0.696869\pi\)
\(308\) −0.224534 −0.0127940
\(309\) −49.9670 −2.84252
\(310\) 0 0
\(311\) 20.4778 1.16119 0.580595 0.814193i \(-0.302820\pi\)
0.580595 + 0.814193i \(0.302820\pi\)
\(312\) −2.31506 −0.131065
\(313\) −1.98489 −0.112192 −0.0560962 0.998425i \(-0.517865\pi\)
−0.0560962 + 0.998425i \(0.517865\pi\)
\(314\) −15.7870 −0.890913
\(315\) 0 0
\(316\) 23.4127 1.31707
\(317\) 28.5808 1.60526 0.802630 0.596477i \(-0.203433\pi\)
0.802630 + 0.596477i \(0.203433\pi\)
\(318\) −29.2206 −1.63861
\(319\) 0.456856 0.0255790
\(320\) 0 0
\(321\) −17.8099 −0.994051
\(322\) 0.538999 0.0300372
\(323\) 10.0730 0.560479
\(324\) 11.9041 0.661339
\(325\) 0 0
\(326\) −34.6867 −1.92112
\(327\) 29.4951 1.63108
\(328\) −0.00310498 −0.000171444 0
\(329\) 2.94279 0.162241
\(330\) 0 0
\(331\) −23.4089 −1.28667 −0.643334 0.765585i \(-0.722449\pi\)
−0.643334 + 0.765585i \(0.722449\pi\)
\(332\) 30.6748 1.68350
\(333\) −24.7995 −1.35900
\(334\) 3.81544 0.208771
\(335\) 0 0
\(336\) −4.24746 −0.231718
\(337\) −2.23389 −0.121688 −0.0608440 0.998147i \(-0.519379\pi\)
−0.0608440 + 0.998147i \(0.519379\pi\)
\(338\) 6.15817 0.334960
\(339\) 9.53273 0.517747
\(340\) 0 0
\(341\) 2.73427 0.148069
\(342\) −43.9717 −2.37772
\(343\) 5.28201 0.285202
\(344\) 2.40603 0.129724
\(345\) 0 0
\(346\) 20.1597 1.08379
\(347\) −17.2084 −0.923793 −0.461897 0.886934i \(-0.652831\pi\)
−0.461897 + 0.886934i \(0.652831\pi\)
\(348\) −10.0144 −0.536827
\(349\) 21.1996 1.13479 0.567394 0.823447i \(-0.307952\pi\)
0.567394 + 0.823447i \(0.307952\pi\)
\(350\) 0 0
\(351\) −30.7301 −1.64025
\(352\) −2.26829 −0.120900
\(353\) 9.42434 0.501607 0.250803 0.968038i \(-0.419305\pi\)
0.250803 + 0.968038i \(0.419305\pi\)
\(354\) 84.1209 4.47097
\(355\) 0 0
\(356\) 30.0696 1.59369
\(357\) −2.91290 −0.154167
\(358\) 52.4203 2.77050
\(359\) 8.50212 0.448725 0.224362 0.974506i \(-0.427970\pi\)
0.224362 + 0.974506i \(0.427970\pi\)
\(360\) 0 0
\(361\) −4.02777 −0.211988
\(362\) −17.4423 −0.916744
\(363\) 32.0533 1.68236
\(364\) −3.20255 −0.167859
\(365\) 0 0
\(366\) 41.4108 2.16458
\(367\) −5.48335 −0.286229 −0.143114 0.989706i \(-0.545712\pi\)
−0.143114 + 0.989706i \(0.545712\pi\)
\(368\) 2.65128 0.138208
\(369\) −0.0885148 −0.00460790
\(370\) 0 0
\(371\) −1.87516 −0.0973535
\(372\) −59.9357 −3.10752
\(373\) 23.6497 1.22454 0.612268 0.790650i \(-0.290257\pi\)
0.612268 + 0.790650i \(0.290257\pi\)
\(374\) −1.47974 −0.0765155
\(375\) 0 0
\(376\) −1.52013 −0.0783945
\(377\) 6.51618 0.335601
\(378\) 5.92082 0.304534
\(379\) 4.37392 0.224673 0.112336 0.993670i \(-0.464167\pi\)
0.112336 + 0.993670i \(0.464167\pi\)
\(380\) 0 0
\(381\) 0.908227 0.0465299
\(382\) −14.9953 −0.767224
\(383\) −22.2150 −1.13514 −0.567568 0.823327i \(-0.692115\pi\)
−0.567568 + 0.823327i \(0.692115\pi\)
\(384\) 4.61855 0.235689
\(385\) 0 0
\(386\) 26.4125 1.34436
\(387\) 68.5894 3.48660
\(388\) −18.3657 −0.932378
\(389\) −9.47112 −0.480205 −0.240102 0.970748i \(-0.577181\pi\)
−0.240102 + 0.970748i \(0.577181\pi\)
\(390\) 0 0
\(391\) 1.81825 0.0919527
\(392\) −1.34993 −0.0681815
\(393\) −52.8118 −2.66400
\(394\) 4.69642 0.236602
\(395\) 0 0
\(396\) 3.30643 0.166154
\(397\) −33.8693 −1.69985 −0.849925 0.526904i \(-0.823353\pi\)
−0.849925 + 0.526904i \(0.823353\pi\)
\(398\) 43.7138 2.19118
\(399\) −4.32964 −0.216753
\(400\) 0 0
\(401\) 26.1950 1.30812 0.654059 0.756444i \(-0.273065\pi\)
0.654059 + 0.756444i \(0.273065\pi\)
\(402\) −17.7005 −0.882822
\(403\) 38.9991 1.94268
\(404\) −12.5256 −0.623172
\(405\) 0 0
\(406\) −1.25549 −0.0623087
\(407\) −1.24046 −0.0614871
\(408\) 1.50469 0.0744932
\(409\) −23.3301 −1.15360 −0.576800 0.816885i \(-0.695699\pi\)
−0.576800 + 0.816885i \(0.695699\pi\)
\(410\) 0 0
\(411\) −26.1556 −1.29016
\(412\) 35.7056 1.75909
\(413\) 5.39826 0.265631
\(414\) −7.93716 −0.390090
\(415\) 0 0
\(416\) −32.3529 −1.58623
\(417\) −22.9805 −1.12536
\(418\) −2.19944 −0.107578
\(419\) −17.9680 −0.877794 −0.438897 0.898537i \(-0.644631\pi\)
−0.438897 + 0.898537i \(0.644631\pi\)
\(420\) 0 0
\(421\) 20.6124 1.00459 0.502294 0.864697i \(-0.332489\pi\)
0.502294 + 0.864697i \(0.332489\pi\)
\(422\) 40.7825 1.98526
\(423\) −43.3348 −2.10701
\(424\) 0.968633 0.0470410
\(425\) 0 0
\(426\) −43.2606 −2.09598
\(427\) 2.65744 0.128602
\(428\) 12.7267 0.615166
\(429\) −3.30110 −0.159378
\(430\) 0 0
\(431\) −4.74707 −0.228659 −0.114329 0.993443i \(-0.536472\pi\)
−0.114329 + 0.993443i \(0.536472\pi\)
\(432\) 29.1240 1.40123
\(433\) 40.8642 1.96381 0.981904 0.189378i \(-0.0606471\pi\)
0.981904 + 0.189378i \(0.0606471\pi\)
\(434\) −7.51404 −0.360685
\(435\) 0 0
\(436\) −21.0767 −1.00939
\(437\) 2.70258 0.129282
\(438\) −0.982772 −0.0469587
\(439\) −23.5388 −1.12344 −0.561722 0.827326i \(-0.689861\pi\)
−0.561722 + 0.827326i \(0.689861\pi\)
\(440\) 0 0
\(441\) −38.4828 −1.83251
\(442\) −21.1057 −1.00389
\(443\) −27.9145 −1.32626 −0.663129 0.748505i \(-0.730772\pi\)
−0.663129 + 0.748505i \(0.730772\pi\)
\(444\) 27.1910 1.29043
\(445\) 0 0
\(446\) 16.1288 0.763722
\(447\) −60.3317 −2.85359
\(448\) 3.33912 0.157759
\(449\) 23.7869 1.12258 0.561288 0.827621i \(-0.310306\pi\)
0.561288 + 0.827621i \(0.310306\pi\)
\(450\) 0 0
\(451\) −0.00442746 −0.000208481 0
\(452\) −6.81194 −0.320407
\(453\) −31.0714 −1.45986
\(454\) 38.9536 1.82818
\(455\) 0 0
\(456\) 2.23652 0.104735
\(457\) −33.9948 −1.59021 −0.795106 0.606471i \(-0.792585\pi\)
−0.795106 + 0.606471i \(0.792585\pi\)
\(458\) 25.8032 1.20571
\(459\) 19.9732 0.932268
\(460\) 0 0
\(461\) 18.0014 0.838410 0.419205 0.907892i \(-0.362309\pi\)
0.419205 + 0.907892i \(0.362309\pi\)
\(462\) 0.636029 0.0295908
\(463\) −11.9773 −0.556634 −0.278317 0.960489i \(-0.589777\pi\)
−0.278317 + 0.960489i \(0.589777\pi\)
\(464\) −6.17562 −0.286696
\(465\) 0 0
\(466\) 20.7302 0.960310
\(467\) −22.0474 −1.02023 −0.510117 0.860105i \(-0.670398\pi\)
−0.510117 + 0.860105i \(0.670398\pi\)
\(468\) 47.1600 2.17997
\(469\) −1.13589 −0.0524505
\(470\) 0 0
\(471\) 22.8906 1.05474
\(472\) −2.78852 −0.128352
\(473\) 3.43080 0.157748
\(474\) −66.3204 −3.04620
\(475\) 0 0
\(476\) 2.08152 0.0954061
\(477\) 27.6132 1.26432
\(478\) 45.3950 2.07632
\(479\) 14.1990 0.648769 0.324385 0.945925i \(-0.394843\pi\)
0.324385 + 0.945925i \(0.394843\pi\)
\(480\) 0 0
\(481\) −17.6927 −0.806720
\(482\) 2.02418 0.0921987
\(483\) −0.781528 −0.0355608
\(484\) −22.9048 −1.04113
\(485\) 0 0
\(486\) 12.8704 0.583815
\(487\) 40.8500 1.85109 0.925544 0.378639i \(-0.123608\pi\)
0.925544 + 0.378639i \(0.123608\pi\)
\(488\) −1.37273 −0.0621404
\(489\) 50.2944 2.27439
\(490\) 0 0
\(491\) 7.70287 0.347626 0.173813 0.984779i \(-0.444391\pi\)
0.173813 + 0.984779i \(0.444391\pi\)
\(492\) 0.0970507 0.00437539
\(493\) −4.23523 −0.190745
\(494\) −31.3708 −1.41144
\(495\) 0 0
\(496\) −36.9608 −1.65959
\(497\) −2.77615 −0.124527
\(498\) −86.8913 −3.89369
\(499\) −1.84960 −0.0827996 −0.0413998 0.999143i \(-0.513182\pi\)
−0.0413998 + 0.999143i \(0.513182\pi\)
\(500\) 0 0
\(501\) −5.53224 −0.247162
\(502\) 28.4860 1.27139
\(503\) −16.8921 −0.753181 −0.376590 0.926380i \(-0.622904\pi\)
−0.376590 + 0.926380i \(0.622904\pi\)
\(504\) −0.421511 −0.0187756
\(505\) 0 0
\(506\) −0.397012 −0.0176493
\(507\) −8.92911 −0.396556
\(508\) −0.649005 −0.0287949
\(509\) 2.10162 0.0931524 0.0465762 0.998915i \(-0.485169\pi\)
0.0465762 + 0.998915i \(0.485169\pi\)
\(510\) 0 0
\(511\) −0.0630671 −0.00278992
\(512\) 32.1571 1.42116
\(513\) 29.6875 1.31073
\(514\) −2.96470 −0.130767
\(515\) 0 0
\(516\) −75.2039 −3.31067
\(517\) −2.16758 −0.0953300
\(518\) 3.40890 0.149778
\(519\) −29.2308 −1.28309
\(520\) 0 0
\(521\) −1.90175 −0.0833170 −0.0416585 0.999132i \(-0.513264\pi\)
−0.0416585 + 0.999132i \(0.513264\pi\)
\(522\) 18.4880 0.809197
\(523\) −2.87743 −0.125821 −0.0629105 0.998019i \(-0.520038\pi\)
−0.0629105 + 0.998019i \(0.520038\pi\)
\(524\) 37.7385 1.64861
\(525\) 0 0
\(526\) −16.3811 −0.714250
\(527\) −25.3477 −1.10416
\(528\) 3.12857 0.136153
\(529\) −22.5122 −0.978790
\(530\) 0 0
\(531\) −79.4934 −3.44972
\(532\) 3.09390 0.134137
\(533\) −0.0631492 −0.00273530
\(534\) −85.1771 −3.68597
\(535\) 0 0
\(536\) 0.586755 0.0253439
\(537\) −76.0075 −3.27997
\(538\) −51.1139 −2.20368
\(539\) −1.92489 −0.0829107
\(540\) 0 0
\(541\) 3.56338 0.153202 0.0766009 0.997062i \(-0.475593\pi\)
0.0766009 + 0.997062i \(0.475593\pi\)
\(542\) 12.2282 0.525247
\(543\) 25.2906 1.08532
\(544\) 21.0279 0.901565
\(545\) 0 0
\(546\) 9.07175 0.388235
\(547\) −8.83030 −0.377557 −0.188778 0.982020i \(-0.560453\pi\)
−0.188778 + 0.982020i \(0.560453\pi\)
\(548\) 18.6904 0.798414
\(549\) −39.1328 −1.67015
\(550\) 0 0
\(551\) −6.29511 −0.268181
\(552\) 0.403706 0.0171829
\(553\) −4.25595 −0.180982
\(554\) 36.2876 1.54171
\(555\) 0 0
\(556\) 16.4215 0.696425
\(557\) 8.23306 0.348846 0.174423 0.984671i \(-0.444194\pi\)
0.174423 + 0.984671i \(0.444194\pi\)
\(558\) 110.650 4.68418
\(559\) 48.9338 2.06968
\(560\) 0 0
\(561\) 2.14557 0.0905859
\(562\) 8.36544 0.352875
\(563\) 40.7923 1.71919 0.859596 0.510974i \(-0.170715\pi\)
0.859596 + 0.510974i \(0.170715\pi\)
\(564\) 47.5138 2.00069
\(565\) 0 0
\(566\) −27.8872 −1.17219
\(567\) −2.16392 −0.0908761
\(568\) 1.43405 0.0601712
\(569\) 17.6055 0.738063 0.369031 0.929417i \(-0.379689\pi\)
0.369031 + 0.929417i \(0.379689\pi\)
\(570\) 0 0
\(571\) 16.2781 0.681216 0.340608 0.940205i \(-0.389367\pi\)
0.340608 + 0.940205i \(0.389367\pi\)
\(572\) 2.35891 0.0986311
\(573\) 21.7426 0.908309
\(574\) 0.0121671 0.000507845 0
\(575\) 0 0
\(576\) −49.1711 −2.04880
\(577\) −25.7002 −1.06991 −0.534956 0.844880i \(-0.679672\pi\)
−0.534956 + 0.844880i \(0.679672\pi\)
\(578\) −20.6933 −0.860726
\(579\) −38.2971 −1.59157
\(580\) 0 0
\(581\) −5.57604 −0.231333
\(582\) 52.0239 2.15646
\(583\) 1.38119 0.0572032
\(584\) 0.0325779 0.00134808
\(585\) 0 0
\(586\) −43.7329 −1.80659
\(587\) −35.7831 −1.47693 −0.738464 0.674293i \(-0.764448\pi\)
−0.738464 + 0.674293i \(0.764448\pi\)
\(588\) 42.1939 1.74005
\(589\) −37.6760 −1.55241
\(590\) 0 0
\(591\) −6.80964 −0.280111
\(592\) 16.7680 0.689162
\(593\) 5.87794 0.241378 0.120689 0.992690i \(-0.461490\pi\)
0.120689 + 0.992690i \(0.461490\pi\)
\(594\) −4.36112 −0.178939
\(595\) 0 0
\(596\) 43.1121 1.76594
\(597\) −63.3834 −2.59411
\(598\) −5.66262 −0.231562
\(599\) 21.9834 0.898218 0.449109 0.893477i \(-0.351741\pi\)
0.449109 + 0.893477i \(0.351741\pi\)
\(600\) 0 0
\(601\) 21.9020 0.893400 0.446700 0.894684i \(-0.352599\pi\)
0.446700 + 0.894684i \(0.352599\pi\)
\(602\) −9.42818 −0.384264
\(603\) 16.7268 0.681169
\(604\) 22.2031 0.903433
\(605\) 0 0
\(606\) 35.4808 1.44131
\(607\) −23.4846 −0.953209 −0.476604 0.879118i \(-0.658133\pi\)
−0.476604 + 0.879118i \(0.658133\pi\)
\(608\) 31.2552 1.26757
\(609\) 1.82041 0.0737667
\(610\) 0 0
\(611\) −30.9164 −1.25074
\(612\) −30.6519 −1.23903
\(613\) −8.60887 −0.347709 −0.173854 0.984771i \(-0.555622\pi\)
−0.173854 + 0.984771i \(0.555622\pi\)
\(614\) −41.1269 −1.65975
\(615\) 0 0
\(616\) −0.0210837 −0.000849488 0
\(617\) 33.1258 1.33360 0.666798 0.745238i \(-0.267664\pi\)
0.666798 + 0.745238i \(0.267664\pi\)
\(618\) −101.142 −4.06853
\(619\) −15.7965 −0.634915 −0.317457 0.948273i \(-0.602829\pi\)
−0.317457 + 0.948273i \(0.602829\pi\)
\(620\) 0 0
\(621\) 5.35878 0.215040
\(622\) 41.4507 1.66202
\(623\) −5.46604 −0.218992
\(624\) 44.6231 1.78635
\(625\) 0 0
\(626\) −4.01776 −0.160582
\(627\) 3.18910 0.127360
\(628\) −16.3573 −0.652726
\(629\) 11.4995 0.458515
\(630\) 0 0
\(631\) −41.7674 −1.66273 −0.831367 0.555724i \(-0.812441\pi\)
−0.831367 + 0.555724i \(0.812441\pi\)
\(632\) 2.19846 0.0874499
\(633\) −59.1331 −2.35033
\(634\) 57.8527 2.29762
\(635\) 0 0
\(636\) −30.2760 −1.20052
\(637\) −27.4548 −1.08780
\(638\) 0.924758 0.0366115
\(639\) 40.8809 1.61722
\(640\) 0 0
\(641\) 12.5409 0.495337 0.247669 0.968845i \(-0.420336\pi\)
0.247669 + 0.968845i \(0.420336\pi\)
\(642\) −36.0503 −1.42279
\(643\) 15.0272 0.592616 0.296308 0.955092i \(-0.404244\pi\)
0.296308 + 0.955092i \(0.404244\pi\)
\(644\) 0.558468 0.0220067
\(645\) 0 0
\(646\) 20.3896 0.802218
\(647\) −0.131198 −0.00515792 −0.00257896 0.999997i \(-0.500821\pi\)
−0.00257896 + 0.999997i \(0.500821\pi\)
\(648\) 1.11779 0.0439111
\(649\) −3.97621 −0.156080
\(650\) 0 0
\(651\) 10.8951 0.427012
\(652\) −35.9396 −1.40750
\(653\) −29.9259 −1.17109 −0.585546 0.810639i \(-0.699120\pi\)
−0.585546 + 0.810639i \(0.699120\pi\)
\(654\) 59.7033 2.33458
\(655\) 0 0
\(656\) 0.0598488 0.00233670
\(657\) 0.928710 0.0362324
\(658\) 5.95672 0.232217
\(659\) −38.8457 −1.51321 −0.756606 0.653871i \(-0.773144\pi\)
−0.756606 + 0.653871i \(0.773144\pi\)
\(660\) 0 0
\(661\) −41.0165 −1.59536 −0.797678 0.603084i \(-0.793938\pi\)
−0.797678 + 0.603084i \(0.793938\pi\)
\(662\) −47.3837 −1.84162
\(663\) 30.6024 1.18850
\(664\) 2.88036 0.111780
\(665\) 0 0
\(666\) −50.1986 −1.94516
\(667\) −1.13631 −0.0439980
\(668\) 3.95325 0.152956
\(669\) −23.3862 −0.904163
\(670\) 0 0
\(671\) −1.95740 −0.0755645
\(672\) −9.03834 −0.348661
\(673\) −8.97729 −0.346049 −0.173024 0.984918i \(-0.555354\pi\)
−0.173024 + 0.984918i \(0.555354\pi\)
\(674\) −4.52180 −0.174173
\(675\) 0 0
\(676\) 6.38060 0.245408
\(677\) −4.52843 −0.174042 −0.0870209 0.996206i \(-0.527735\pi\)
−0.0870209 + 0.996206i \(0.527735\pi\)
\(678\) 19.2959 0.741056
\(679\) 3.33851 0.128120
\(680\) 0 0
\(681\) −56.4812 −2.16436
\(682\) 5.53464 0.211932
\(683\) −3.48350 −0.133292 −0.0666462 0.997777i \(-0.521230\pi\)
−0.0666462 + 0.997777i \(0.521230\pi\)
\(684\) −45.5600 −1.74203
\(685\) 0 0
\(686\) 10.6917 0.408212
\(687\) −37.4138 −1.42742
\(688\) −46.3763 −1.76808
\(689\) 19.7001 0.750514
\(690\) 0 0
\(691\) −44.5762 −1.69576 −0.847879 0.530190i \(-0.822121\pi\)
−0.847879 + 0.530190i \(0.822121\pi\)
\(692\) 20.8879 0.794038
\(693\) −0.601042 −0.0228317
\(694\) −34.8328 −1.32223
\(695\) 0 0
\(696\) −0.940350 −0.0356439
\(697\) 0.0410442 0.00155466
\(698\) 42.9117 1.62423
\(699\) −30.0581 −1.13690
\(700\) 0 0
\(701\) 8.90961 0.336511 0.168256 0.985743i \(-0.446187\pi\)
0.168256 + 0.985743i \(0.446187\pi\)
\(702\) −62.2031 −2.34770
\(703\) 17.0925 0.644655
\(704\) −2.45951 −0.0926962
\(705\) 0 0
\(706\) 19.0765 0.717955
\(707\) 2.27690 0.0856315
\(708\) 87.1594 3.27565
\(709\) −13.4817 −0.506315 −0.253158 0.967425i \(-0.581469\pi\)
−0.253158 + 0.967425i \(0.581469\pi\)
\(710\) 0 0
\(711\) 62.6721 2.35039
\(712\) 2.82354 0.105816
\(713\) −6.80075 −0.254690
\(714\) −5.89623 −0.220661
\(715\) 0 0
\(716\) 54.3138 2.02980
\(717\) −65.8210 −2.45813
\(718\) 17.2098 0.642264
\(719\) 25.1548 0.938118 0.469059 0.883167i \(-0.344593\pi\)
0.469059 + 0.883167i \(0.344593\pi\)
\(720\) 0 0
\(721\) −6.49055 −0.241721
\(722\) −8.15293 −0.303421
\(723\) −2.93498 −0.109153
\(724\) −18.0723 −0.671651
\(725\) 0 0
\(726\) 64.8816 2.40798
\(727\) 1.31218 0.0486659 0.0243330 0.999704i \(-0.492254\pi\)
0.0243330 + 0.999704i \(0.492254\pi\)
\(728\) −0.300719 −0.0111454
\(729\) −35.6895 −1.32183
\(730\) 0 0
\(731\) −31.8048 −1.17634
\(732\) 42.9066 1.58587
\(733\) −22.8551 −0.844173 −0.422087 0.906556i \(-0.638702\pi\)
−0.422087 + 0.906556i \(0.638702\pi\)
\(734\) −11.0993 −0.409682
\(735\) 0 0
\(736\) 5.64177 0.207958
\(737\) 0.836665 0.0308190
\(738\) −0.179170 −0.00659533
\(739\) 10.2085 0.375525 0.187762 0.982214i \(-0.439877\pi\)
0.187762 + 0.982214i \(0.439877\pi\)
\(740\) 0 0
\(741\) 45.4864 1.67099
\(742\) −3.79566 −0.139343
\(743\) −26.3806 −0.967810 −0.483905 0.875120i \(-0.660782\pi\)
−0.483905 + 0.875120i \(0.660782\pi\)
\(744\) −5.62796 −0.206331
\(745\) 0 0
\(746\) 47.8712 1.75269
\(747\) 82.1115 3.00430
\(748\) −1.53319 −0.0560589
\(749\) −2.31345 −0.0845315
\(750\) 0 0
\(751\) −31.8074 −1.16067 −0.580335 0.814378i \(-0.697078\pi\)
−0.580335 + 0.814378i \(0.697078\pi\)
\(752\) 29.3006 1.06848
\(753\) −41.3037 −1.50519
\(754\) 13.1899 0.480348
\(755\) 0 0
\(756\) 6.13469 0.223116
\(757\) 33.6767 1.22400 0.612000 0.790858i \(-0.290365\pi\)
0.612000 + 0.790858i \(0.290365\pi\)
\(758\) 8.85358 0.321576
\(759\) 0.575653 0.0208949
\(760\) 0 0
\(761\) −14.9020 −0.540197 −0.270098 0.962833i \(-0.587056\pi\)
−0.270098 + 0.962833i \(0.587056\pi\)
\(762\) 1.83841 0.0665986
\(763\) 3.83132 0.138703
\(764\) −15.5369 −0.562105
\(765\) 0 0
\(766\) −44.9672 −1.62473
\(767\) −56.7131 −2.04779
\(768\) −42.0632 −1.51782
\(769\) −23.5992 −0.851010 −0.425505 0.904956i \(-0.639904\pi\)
−0.425505 + 0.904956i \(0.639904\pi\)
\(770\) 0 0
\(771\) 4.29870 0.154814
\(772\) 27.3665 0.984943
\(773\) −30.4365 −1.09472 −0.547362 0.836896i \(-0.684368\pi\)
−0.547362 + 0.836896i \(0.684368\pi\)
\(774\) 138.837 4.99040
\(775\) 0 0
\(776\) −1.72454 −0.0619074
\(777\) −4.94277 −0.177321
\(778\) −19.1712 −0.687321
\(779\) 0.0610068 0.00218579
\(780\) 0 0
\(781\) 2.04483 0.0731699
\(782\) 3.68045 0.131613
\(783\) −12.4822 −0.446076
\(784\) 26.0199 0.929283
\(785\) 0 0
\(786\) −106.900 −3.81301
\(787\) −0.281399 −0.0100308 −0.00501539 0.999987i \(-0.501596\pi\)
−0.00501539 + 0.999987i \(0.501596\pi\)
\(788\) 4.86606 0.173346
\(789\) 23.7520 0.845593
\(790\) 0 0
\(791\) 1.23827 0.0440279
\(792\) 0.310474 0.0110322
\(793\) −27.9185 −0.991417
\(794\) −68.5574 −2.43301
\(795\) 0 0
\(796\) 45.2928 1.60536
\(797\) −26.6128 −0.942673 −0.471336 0.881954i \(-0.656228\pi\)
−0.471336 + 0.881954i \(0.656228\pi\)
\(798\) −8.76396 −0.310241
\(799\) 20.0943 0.710885
\(800\) 0 0
\(801\) 80.4915 2.84403
\(802\) 53.0234 1.87232
\(803\) 0.0464535 0.00163931
\(804\) −18.3399 −0.646798
\(805\) 0 0
\(806\) 78.9411 2.78058
\(807\) 74.1133 2.60891
\(808\) −1.17615 −0.0413769
\(809\) 13.2472 0.465748 0.232874 0.972507i \(-0.425187\pi\)
0.232874 + 0.972507i \(0.425187\pi\)
\(810\) 0 0
\(811\) 35.8348 1.25833 0.629165 0.777272i \(-0.283397\pi\)
0.629165 + 0.777272i \(0.283397\pi\)
\(812\) −1.30084 −0.0456504
\(813\) −17.7305 −0.621835
\(814\) −2.51090 −0.0880071
\(815\) 0 0
\(816\) −29.0030 −1.01531
\(817\) −47.2737 −1.65390
\(818\) −47.2243 −1.65116
\(819\) −8.57271 −0.299555
\(820\) 0 0
\(821\) −1.76973 −0.0617640 −0.0308820 0.999523i \(-0.509832\pi\)
−0.0308820 + 0.999523i \(0.509832\pi\)
\(822\) −52.9436 −1.84662
\(823\) 29.0119 1.01129 0.505645 0.862742i \(-0.331255\pi\)
0.505645 + 0.862742i \(0.331255\pi\)
\(824\) 3.35276 0.116799
\(825\) 0 0
\(826\) 10.9270 0.380200
\(827\) 15.9224 0.553675 0.276838 0.960917i \(-0.410714\pi\)
0.276838 + 0.960917i \(0.410714\pi\)
\(828\) −8.22386 −0.285799
\(829\) −31.0294 −1.07770 −0.538849 0.842403i \(-0.681141\pi\)
−0.538849 + 0.842403i \(0.681141\pi\)
\(830\) 0 0
\(831\) −52.6157 −1.82522
\(832\) −35.0802 −1.21619
\(833\) 17.8444 0.618273
\(834\) −46.5165 −1.61073
\(835\) 0 0
\(836\) −2.27888 −0.0788167
\(837\) −74.7053 −2.58219
\(838\) −36.3704 −1.25639
\(839\) −54.4602 −1.88017 −0.940087 0.340935i \(-0.889256\pi\)
−0.940087 + 0.340935i \(0.889256\pi\)
\(840\) 0 0
\(841\) −26.3532 −0.908731
\(842\) 41.7232 1.43788
\(843\) −12.1296 −0.417765
\(844\) 42.2556 1.45450
\(845\) 0 0
\(846\) −87.7172 −3.01578
\(847\) 4.16363 0.143064
\(848\) −18.6705 −0.641147
\(849\) 40.4355 1.38774
\(850\) 0 0
\(851\) 3.08530 0.105763
\(852\) −44.8232 −1.53562
\(853\) 5.82777 0.199539 0.0997694 0.995011i \(-0.468189\pi\)
0.0997694 + 0.995011i \(0.468189\pi\)
\(854\) 5.37912 0.184070
\(855\) 0 0
\(856\) 1.19503 0.0408454
\(857\) 48.9503 1.67211 0.836056 0.548644i \(-0.184856\pi\)
0.836056 + 0.548644i \(0.184856\pi\)
\(858\) −6.68200 −0.228120
\(859\) −23.1193 −0.788819 −0.394409 0.918935i \(-0.629051\pi\)
−0.394409 + 0.918935i \(0.629051\pi\)
\(860\) 0 0
\(861\) −0.0176418 −0.000601232 0
\(862\) −9.60892 −0.327281
\(863\) 24.5041 0.834129 0.417065 0.908877i \(-0.363059\pi\)
0.417065 + 0.908877i \(0.363059\pi\)
\(864\) 61.9740 2.10840
\(865\) 0 0
\(866\) 82.7164 2.81082
\(867\) 30.0045 1.01900
\(868\) −7.78545 −0.264255
\(869\) 3.13482 0.106342
\(870\) 0 0
\(871\) 11.9334 0.404349
\(872\) −1.97911 −0.0670210
\(873\) −49.1621 −1.66388
\(874\) 5.47050 0.185043
\(875\) 0 0
\(876\) −1.01827 −0.0344042
\(877\) 11.9231 0.402614 0.201307 0.979528i \(-0.435481\pi\)
0.201307 + 0.979528i \(0.435481\pi\)
\(878\) −47.6466 −1.60800
\(879\) 63.4112 2.13881
\(880\) 0 0
\(881\) −12.2901 −0.414063 −0.207032 0.978334i \(-0.566380\pi\)
−0.207032 + 0.978334i \(0.566380\pi\)
\(882\) −77.8960 −2.62289
\(883\) 48.1400 1.62004 0.810020 0.586403i \(-0.199456\pi\)
0.810020 + 0.586403i \(0.199456\pi\)
\(884\) −21.8680 −0.735501
\(885\) 0 0
\(886\) −56.5039 −1.89829
\(887\) −20.7341 −0.696184 −0.348092 0.937460i \(-0.613170\pi\)
−0.348092 + 0.937460i \(0.613170\pi\)
\(888\) 2.55324 0.0856811
\(889\) 0.117976 0.00395678
\(890\) 0 0
\(891\) 1.59389 0.0533972
\(892\) 16.7114 0.559540
\(893\) 29.8675 0.999477
\(894\) −122.122 −4.08437
\(895\) 0 0
\(896\) 0.599935 0.0200424
\(897\) 8.21059 0.274144
\(898\) 48.1490 1.60675
\(899\) 15.8410 0.528325
\(900\) 0 0
\(901\) −12.8042 −0.426569
\(902\) −0.00896195 −0.000298400 0
\(903\) 13.6705 0.454926
\(904\) −0.639641 −0.0212742
\(905\) 0 0
\(906\) −62.8940 −2.08951
\(907\) 7.02598 0.233294 0.116647 0.993173i \(-0.462785\pi\)
0.116647 + 0.993173i \(0.462785\pi\)
\(908\) 40.3606 1.33941
\(909\) −33.5290 −1.11209
\(910\) 0 0
\(911\) 58.0477 1.92320 0.961602 0.274446i \(-0.0884946\pi\)
0.961602 + 0.274446i \(0.0884946\pi\)
\(912\) −43.1091 −1.42749
\(913\) 4.10716 0.135927
\(914\) −68.8116 −2.27608
\(915\) 0 0
\(916\) 26.7353 0.883359
\(917\) −6.86008 −0.226540
\(918\) 40.4292 1.33436
\(919\) 17.9524 0.592194 0.296097 0.955158i \(-0.404315\pi\)
0.296097 + 0.955158i \(0.404315\pi\)
\(920\) 0 0
\(921\) 59.6324 1.96496
\(922\) 36.4381 1.20002
\(923\) 29.1657 0.960000
\(924\) 0.659003 0.0216796
\(925\) 0 0
\(926\) −24.2442 −0.796715
\(927\) 95.5782 3.13920
\(928\) −13.1413 −0.431385
\(929\) −20.8907 −0.685403 −0.342701 0.939444i \(-0.611342\pi\)
−0.342701 + 0.939444i \(0.611342\pi\)
\(930\) 0 0
\(931\) 26.5234 0.869268
\(932\) 21.4790 0.703569
\(933\) −60.1019 −1.96765
\(934\) −44.6279 −1.46027
\(935\) 0 0
\(936\) 4.42832 0.144744
\(937\) 39.5712 1.29273 0.646367 0.763027i \(-0.276288\pi\)
0.646367 + 0.763027i \(0.276288\pi\)
\(938\) −2.29924 −0.0750728
\(939\) 5.82561 0.190112
\(940\) 0 0
\(941\) −2.21402 −0.0721750 −0.0360875 0.999349i \(-0.511490\pi\)
−0.0360875 + 0.999349i \(0.511490\pi\)
\(942\) 46.3346 1.50966
\(943\) 0.0110121 0.000358603 0
\(944\) 53.7490 1.74938
\(945\) 0 0
\(946\) 6.94455 0.225787
\(947\) 27.2239 0.884659 0.442330 0.896853i \(-0.354152\pi\)
0.442330 + 0.896853i \(0.354152\pi\)
\(948\) −68.7159 −2.23179
\(949\) 0.662571 0.0215080
\(950\) 0 0
\(951\) −83.8842 −2.72013
\(952\) 0.195454 0.00633471
\(953\) 49.1033 1.59061 0.795305 0.606209i \(-0.207311\pi\)
0.795305 + 0.606209i \(0.207311\pi\)
\(954\) 55.8939 1.80963
\(955\) 0 0
\(956\) 47.0347 1.52121
\(957\) −1.34086 −0.0433440
\(958\) 28.7413 0.928590
\(959\) −3.39753 −0.109712
\(960\) 0 0
\(961\) 63.8075 2.05831
\(962\) −35.8132 −1.15467
\(963\) 34.0672 1.09780
\(964\) 2.09729 0.0675492
\(965\) 0 0
\(966\) −1.58195 −0.0508984
\(967\) 2.12457 0.0683214 0.0341607 0.999416i \(-0.489124\pi\)
0.0341607 + 0.999416i \(0.489124\pi\)
\(968\) −2.15076 −0.0691281
\(969\) −29.5642 −0.949738
\(970\) 0 0
\(971\) 32.0749 1.02933 0.514666 0.857391i \(-0.327916\pi\)
0.514666 + 0.857391i \(0.327916\pi\)
\(972\) 13.3353 0.427731
\(973\) −2.98509 −0.0956975
\(974\) 82.6876 2.64948
\(975\) 0 0
\(976\) 26.4594 0.846945
\(977\) 1.85481 0.0593406 0.0296703 0.999560i \(-0.490554\pi\)
0.0296703 + 0.999560i \(0.490554\pi\)
\(978\) 101.805 3.25535
\(979\) 4.02614 0.128676
\(980\) 0 0
\(981\) −56.4190 −1.80132
\(982\) 15.5920 0.497560
\(983\) 48.0786 1.53347 0.766734 0.641965i \(-0.221881\pi\)
0.766734 + 0.641965i \(0.221881\pi\)
\(984\) 0.00911306 0.000290514 0
\(985\) 0 0
\(986\) −8.57286 −0.273015
\(987\) −8.63703 −0.274920
\(988\) −32.5039 −1.03409
\(989\) −8.53319 −0.271340
\(990\) 0 0
\(991\) 45.7585 1.45357 0.726783 0.686867i \(-0.241015\pi\)
0.726783 + 0.686867i \(0.241015\pi\)
\(992\) −78.6504 −2.49715
\(993\) 68.7046 2.18028
\(994\) −5.61941 −0.178237
\(995\) 0 0
\(996\) −90.0299 −2.85271
\(997\) 17.8475 0.565235 0.282618 0.959233i \(-0.408797\pi\)
0.282618 + 0.959233i \(0.408797\pi\)
\(998\) −3.74393 −0.118512
\(999\) 33.8916 1.07228
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 \(a_p\))