Properties

Label 4003.2.a.b.1.13
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45287 q^{2} -0.154053 q^{3} +4.01656 q^{4} -1.18015 q^{5} +0.377872 q^{6} +4.09823 q^{7} -4.94635 q^{8} -2.97627 q^{9} +O(q^{10})\) \(q-2.45287 q^{2} -0.154053 q^{3} +4.01656 q^{4} -1.18015 q^{5} +0.377872 q^{6} +4.09823 q^{7} -4.94635 q^{8} -2.97627 q^{9} +2.89476 q^{10} +5.48058 q^{11} -0.618764 q^{12} -3.18906 q^{13} -10.0524 q^{14} +0.181806 q^{15} +4.09963 q^{16} -0.192870 q^{17} +7.30039 q^{18} +6.80476 q^{19} -4.74015 q^{20} -0.631346 q^{21} -13.4431 q^{22} -2.66990 q^{23} +0.762001 q^{24} -3.60724 q^{25} +7.82234 q^{26} +0.920663 q^{27} +16.4608 q^{28} -9.24117 q^{29} -0.445946 q^{30} +4.63160 q^{31} -0.163149 q^{32} -0.844301 q^{33} +0.473085 q^{34} -4.83654 q^{35} -11.9544 q^{36} -5.89403 q^{37} -16.6912 q^{38} +0.491285 q^{39} +5.83745 q^{40} +4.56265 q^{41} +1.54861 q^{42} -4.29737 q^{43} +22.0131 q^{44} +3.51245 q^{45} +6.54892 q^{46} -5.19678 q^{47} -0.631561 q^{48} +9.79553 q^{49} +8.84809 q^{50} +0.0297123 q^{51} -12.8090 q^{52} -7.66747 q^{53} -2.25826 q^{54} -6.46792 q^{55} -20.2713 q^{56} -1.04830 q^{57} +22.6674 q^{58} -7.73668 q^{59} +0.730235 q^{60} +1.67991 q^{61} -11.3607 q^{62} -12.1974 q^{63} -7.79908 q^{64} +3.76357 q^{65} +2.07096 q^{66} -1.81328 q^{67} -0.774674 q^{68} +0.411307 q^{69} +11.8634 q^{70} -6.15697 q^{71} +14.7217 q^{72} -4.56558 q^{73} +14.4573 q^{74} +0.555707 q^{75} +27.3317 q^{76} +22.4607 q^{77} -1.20506 q^{78} +9.09484 q^{79} -4.83819 q^{80} +8.78697 q^{81} -11.1916 q^{82} -15.1678 q^{83} -2.53584 q^{84} +0.227616 q^{85} +10.5409 q^{86} +1.42363 q^{87} -27.1089 q^{88} -7.31368 q^{89} -8.61557 q^{90} -13.0695 q^{91} -10.7238 q^{92} -0.713512 q^{93} +12.7470 q^{94} -8.03065 q^{95} +0.0251336 q^{96} +2.45124 q^{97} -24.0271 q^{98} -16.3117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45287 −1.73444 −0.867220 0.497926i \(-0.834095\pi\)
−0.867220 + 0.497926i \(0.834095\pi\)
\(3\) −0.154053 −0.0889426 −0.0444713 0.999011i \(-0.514160\pi\)
−0.0444713 + 0.999011i \(0.514160\pi\)
\(4\) 4.01656 2.00828
\(5\) −1.18015 −0.527780 −0.263890 0.964553i \(-0.585006\pi\)
−0.263890 + 0.964553i \(0.585006\pi\)
\(6\) 0.377872 0.154266
\(7\) 4.09823 1.54899 0.774494 0.632582i \(-0.218005\pi\)
0.774494 + 0.632582i \(0.218005\pi\)
\(8\) −4.94635 −1.74880
\(9\) −2.97627 −0.992089
\(10\) 2.89476 0.915402
\(11\) 5.48058 1.65246 0.826229 0.563335i \(-0.190482\pi\)
0.826229 + 0.563335i \(0.190482\pi\)
\(12\) −0.618764 −0.178622
\(13\) −3.18906 −0.884486 −0.442243 0.896895i \(-0.645817\pi\)
−0.442243 + 0.896895i \(0.645817\pi\)
\(14\) −10.0524 −2.68662
\(15\) 0.181806 0.0469421
\(16\) 4.09963 1.02491
\(17\) −0.192870 −0.0467779 −0.0233889 0.999726i \(-0.507446\pi\)
−0.0233889 + 0.999726i \(0.507446\pi\)
\(18\) 7.30039 1.72072
\(19\) 6.80476 1.56112 0.780560 0.625081i \(-0.214934\pi\)
0.780560 + 0.625081i \(0.214934\pi\)
\(20\) −4.74015 −1.05993
\(21\) −0.631346 −0.137771
\(22\) −13.4431 −2.86609
\(23\) −2.66990 −0.556713 −0.278357 0.960478i \(-0.589790\pi\)
−0.278357 + 0.960478i \(0.589790\pi\)
\(24\) 0.762001 0.155543
\(25\) −3.60724 −0.721448
\(26\) 7.82234 1.53409
\(27\) 0.920663 0.177182
\(28\) 16.4608 3.11080
\(29\) −9.24117 −1.71604 −0.858022 0.513614i \(-0.828306\pi\)
−0.858022 + 0.513614i \(0.828306\pi\)
\(30\) −0.445946 −0.0814183
\(31\) 4.63160 0.831859 0.415930 0.909397i \(-0.363456\pi\)
0.415930 + 0.909397i \(0.363456\pi\)
\(32\) −0.163149 −0.0288409
\(33\) −0.844301 −0.146974
\(34\) 0.473085 0.0811334
\(35\) −4.83654 −0.817524
\(36\) −11.9544 −1.99239
\(37\) −5.89403 −0.968973 −0.484486 0.874799i \(-0.660994\pi\)
−0.484486 + 0.874799i \(0.660994\pi\)
\(38\) −16.6912 −2.70767
\(39\) 0.491285 0.0786685
\(40\) 5.83745 0.922982
\(41\) 4.56265 0.712566 0.356283 0.934378i \(-0.384044\pi\)
0.356283 + 0.934378i \(0.384044\pi\)
\(42\) 1.54861 0.238955
\(43\) −4.29737 −0.655344 −0.327672 0.944792i \(-0.606264\pi\)
−0.327672 + 0.944792i \(0.606264\pi\)
\(44\) 22.0131 3.31860
\(45\) 3.51245 0.523605
\(46\) 6.54892 0.965586
\(47\) −5.19678 −0.758029 −0.379014 0.925391i \(-0.623737\pi\)
−0.379014 + 0.925391i \(0.623737\pi\)
\(48\) −0.631561 −0.0911580
\(49\) 9.79553 1.39936
\(50\) 8.84809 1.25131
\(51\) 0.0297123 0.00416055
\(52\) −12.8090 −1.77630
\(53\) −7.66747 −1.05321 −0.526604 0.850111i \(-0.676535\pi\)
−0.526604 + 0.850111i \(0.676535\pi\)
\(54\) −2.25826 −0.307311
\(55\) −6.46792 −0.872134
\(56\) −20.2713 −2.70887
\(57\) −1.04830 −0.138850
\(58\) 22.6674 2.97637
\(59\) −7.73668 −1.00723 −0.503615 0.863928i \(-0.667997\pi\)
−0.503615 + 0.863928i \(0.667997\pi\)
\(60\) 0.730235 0.0942729
\(61\) 1.67991 0.215091 0.107545 0.994200i \(-0.465701\pi\)
0.107545 + 0.994200i \(0.465701\pi\)
\(62\) −11.3607 −1.44281
\(63\) −12.1974 −1.53673
\(64\) −7.79908 −0.974885
\(65\) 3.76357 0.466814
\(66\) 2.07096 0.254917
\(67\) −1.81328 −0.221528 −0.110764 0.993847i \(-0.535330\pi\)
−0.110764 + 0.993847i \(0.535330\pi\)
\(68\) −0.774674 −0.0939431
\(69\) 0.411307 0.0495156
\(70\) 11.8634 1.41795
\(71\) −6.15697 −0.730698 −0.365349 0.930871i \(-0.619050\pi\)
−0.365349 + 0.930871i \(0.619050\pi\)
\(72\) 14.7217 1.73497
\(73\) −4.56558 −0.534360 −0.267180 0.963647i \(-0.586092\pi\)
−0.267180 + 0.963647i \(0.586092\pi\)
\(74\) 14.4573 1.68062
\(75\) 0.555707 0.0641675
\(76\) 27.3317 3.13517
\(77\) 22.4607 2.55963
\(78\) −1.20506 −0.136446
\(79\) 9.09484 1.02325 0.511625 0.859209i \(-0.329044\pi\)
0.511625 + 0.859209i \(0.329044\pi\)
\(80\) −4.83819 −0.540926
\(81\) 8.78697 0.976330
\(82\) −11.1916 −1.23590
\(83\) −15.1678 −1.66489 −0.832444 0.554109i \(-0.813059\pi\)
−0.832444 + 0.554109i \(0.813059\pi\)
\(84\) −2.53584 −0.276683
\(85\) 0.227616 0.0246884
\(86\) 10.5409 1.13665
\(87\) 1.42363 0.152629
\(88\) −27.1089 −2.88982
\(89\) −7.31368 −0.775248 −0.387624 0.921817i \(-0.626704\pi\)
−0.387624 + 0.921817i \(0.626704\pi\)
\(90\) −8.61557 −0.908161
\(91\) −13.0695 −1.37006
\(92\) −10.7238 −1.11804
\(93\) −0.713512 −0.0739877
\(94\) 12.7470 1.31475
\(95\) −8.03065 −0.823928
\(96\) 0.0251336 0.00256519
\(97\) 2.45124 0.248886 0.124443 0.992227i \(-0.460286\pi\)
0.124443 + 0.992227i \(0.460286\pi\)
\(98\) −24.0271 −2.42711
\(99\) −16.3117 −1.63938
\(100\) −14.4887 −1.44887
\(101\) −18.7995 −1.87062 −0.935308 0.353834i \(-0.884878\pi\)
−0.935308 + 0.353834i \(0.884878\pi\)
\(102\) −0.0728802 −0.00721622
\(103\) 0.771377 0.0760060 0.0380030 0.999278i \(-0.487900\pi\)
0.0380030 + 0.999278i \(0.487900\pi\)
\(104\) 15.7742 1.54679
\(105\) 0.745084 0.0727128
\(106\) 18.8073 1.82673
\(107\) 6.21860 0.601175 0.300588 0.953754i \(-0.402817\pi\)
0.300588 + 0.953754i \(0.402817\pi\)
\(108\) 3.69790 0.355830
\(109\) −10.9029 −1.04431 −0.522153 0.852852i \(-0.674871\pi\)
−0.522153 + 0.852852i \(0.674871\pi\)
\(110\) 15.8649 1.51266
\(111\) 0.907994 0.0861830
\(112\) 16.8013 1.58757
\(113\) 18.5806 1.74791 0.873957 0.486003i \(-0.161546\pi\)
0.873957 + 0.486003i \(0.161546\pi\)
\(114\) 2.57133 0.240827
\(115\) 3.15089 0.293822
\(116\) −37.1177 −3.44629
\(117\) 9.49149 0.877489
\(118\) 18.9770 1.74698
\(119\) −0.790427 −0.0724583
\(120\) −0.899277 −0.0820924
\(121\) 19.0368 1.73061
\(122\) −4.12060 −0.373062
\(123\) −0.702890 −0.0633775
\(124\) 18.6031 1.67061
\(125\) 10.1579 0.908546
\(126\) 29.9187 2.66537
\(127\) −8.00695 −0.710502 −0.355251 0.934771i \(-0.615605\pi\)
−0.355251 + 0.934771i \(0.615605\pi\)
\(128\) 19.4564 1.71972
\(129\) 0.662024 0.0582880
\(130\) −9.23155 −0.809660
\(131\) −7.53027 −0.657923 −0.328961 0.944343i \(-0.606699\pi\)
−0.328961 + 0.944343i \(0.606699\pi\)
\(132\) −3.39118 −0.295165
\(133\) 27.8875 2.41815
\(134\) 4.44774 0.384226
\(135\) −1.08652 −0.0935129
\(136\) 0.954004 0.0818052
\(137\) −7.41725 −0.633698 −0.316849 0.948476i \(-0.602625\pi\)
−0.316849 + 0.948476i \(0.602625\pi\)
\(138\) −1.00888 −0.0858817
\(139\) 5.13575 0.435609 0.217805 0.975992i \(-0.430110\pi\)
0.217805 + 0.975992i \(0.430110\pi\)
\(140\) −19.4262 −1.64182
\(141\) 0.800581 0.0674211
\(142\) 15.1022 1.26735
\(143\) −17.4779 −1.46158
\(144\) −12.2016 −1.01680
\(145\) 10.9060 0.905693
\(146\) 11.1988 0.926816
\(147\) −1.50903 −0.124463
\(148\) −23.6737 −1.94597
\(149\) −0.175622 −0.0143875 −0.00719377 0.999974i \(-0.502290\pi\)
−0.00719377 + 0.999974i \(0.502290\pi\)
\(150\) −1.36308 −0.111295
\(151\) 11.8629 0.965388 0.482694 0.875789i \(-0.339658\pi\)
0.482694 + 0.875789i \(0.339658\pi\)
\(152\) −33.6588 −2.73009
\(153\) 0.574033 0.0464078
\(154\) −55.0931 −4.43953
\(155\) −5.46599 −0.439039
\(156\) 1.97327 0.157988
\(157\) 9.01649 0.719594 0.359797 0.933031i \(-0.382846\pi\)
0.359797 + 0.933031i \(0.382846\pi\)
\(158\) −22.3084 −1.77476
\(159\) 1.18120 0.0936751
\(160\) 0.192541 0.0152217
\(161\) −10.9419 −0.862342
\(162\) −21.5533 −1.69339
\(163\) 8.57431 0.671592 0.335796 0.941935i \(-0.390995\pi\)
0.335796 + 0.941935i \(0.390995\pi\)
\(164\) 18.3262 1.43103
\(165\) 0.996403 0.0775699
\(166\) 37.2047 2.88765
\(167\) −19.3151 −1.49465 −0.747324 0.664460i \(-0.768662\pi\)
−0.747324 + 0.664460i \(0.768662\pi\)
\(168\) 3.12286 0.240934
\(169\) −2.82990 −0.217685
\(170\) −0.558312 −0.0428206
\(171\) −20.2528 −1.54877
\(172\) −17.2607 −1.31611
\(173\) −13.7794 −1.04763 −0.523815 0.851832i \(-0.675492\pi\)
−0.523815 + 0.851832i \(0.675492\pi\)
\(174\) −3.49198 −0.264726
\(175\) −14.7833 −1.11751
\(176\) 22.4684 1.69362
\(177\) 1.19186 0.0895856
\(178\) 17.9395 1.34462
\(179\) 3.01303 0.225204 0.112602 0.993640i \(-0.464081\pi\)
0.112602 + 0.993640i \(0.464081\pi\)
\(180\) 14.1080 1.05154
\(181\) 12.3330 0.916706 0.458353 0.888770i \(-0.348440\pi\)
0.458353 + 0.888770i \(0.348440\pi\)
\(182\) 32.0578 2.37628
\(183\) −0.258796 −0.0191307
\(184\) 13.2063 0.973581
\(185\) 6.95585 0.511404
\(186\) 1.75015 0.128327
\(187\) −1.05704 −0.0772984
\(188\) −20.8732 −1.52233
\(189\) 3.77309 0.274452
\(190\) 19.6981 1.42905
\(191\) 9.79911 0.709039 0.354519 0.935049i \(-0.384644\pi\)
0.354519 + 0.935049i \(0.384644\pi\)
\(192\) 1.20147 0.0867089
\(193\) −9.11411 −0.656048 −0.328024 0.944669i \(-0.606383\pi\)
−0.328024 + 0.944669i \(0.606383\pi\)
\(194\) −6.01256 −0.431677
\(195\) −0.579790 −0.0415197
\(196\) 39.3443 2.81031
\(197\) 23.5975 1.68125 0.840625 0.541618i \(-0.182188\pi\)
0.840625 + 0.541618i \(0.182188\pi\)
\(198\) 40.0104 2.84341
\(199\) −12.0048 −0.850997 −0.425499 0.904959i \(-0.639901\pi\)
−0.425499 + 0.904959i \(0.639901\pi\)
\(200\) 17.8427 1.26167
\(201\) 0.279342 0.0197033
\(202\) 46.1126 3.24447
\(203\) −37.8725 −2.65813
\(204\) 0.119341 0.00835554
\(205\) −5.38462 −0.376078
\(206\) −1.89209 −0.131828
\(207\) 7.94635 0.552309
\(208\) −13.0740 −0.906517
\(209\) 37.2941 2.57968
\(210\) −1.82759 −0.126116
\(211\) 4.08280 0.281071 0.140536 0.990076i \(-0.455118\pi\)
0.140536 + 0.990076i \(0.455118\pi\)
\(212\) −30.7969 −2.11514
\(213\) 0.948500 0.0649902
\(214\) −15.2534 −1.04270
\(215\) 5.07155 0.345877
\(216\) −4.55392 −0.309855
\(217\) 18.9814 1.28854
\(218\) 26.7433 1.81129
\(219\) 0.703342 0.0475274
\(220\) −25.9788 −1.75149
\(221\) 0.615074 0.0413744
\(222\) −2.22719 −0.149479
\(223\) 13.9434 0.933719 0.466860 0.884331i \(-0.345385\pi\)
0.466860 + 0.884331i \(0.345385\pi\)
\(224\) −0.668623 −0.0446742
\(225\) 10.7361 0.715741
\(226\) −45.5757 −3.03165
\(227\) 7.01701 0.465735 0.232868 0.972508i \(-0.425189\pi\)
0.232868 + 0.972508i \(0.425189\pi\)
\(228\) −4.21054 −0.278850
\(229\) −21.7982 −1.44046 −0.720232 0.693733i \(-0.755965\pi\)
−0.720232 + 0.693733i \(0.755965\pi\)
\(230\) −7.72872 −0.509617
\(231\) −3.46014 −0.227661
\(232\) 45.7101 3.00102
\(233\) 3.49397 0.228898 0.114449 0.993429i \(-0.463490\pi\)
0.114449 + 0.993429i \(0.463490\pi\)
\(234\) −23.2814 −1.52195
\(235\) 6.13299 0.400072
\(236\) −31.0748 −2.02280
\(237\) −1.40109 −0.0910105
\(238\) 1.93881 0.125675
\(239\) −5.25990 −0.340235 −0.170117 0.985424i \(-0.554415\pi\)
−0.170117 + 0.985424i \(0.554415\pi\)
\(240\) 0.745338 0.0481114
\(241\) 22.9316 1.47715 0.738576 0.674170i \(-0.235499\pi\)
0.738576 + 0.674170i \(0.235499\pi\)
\(242\) −46.6946 −3.00165
\(243\) −4.11565 −0.264019
\(244\) 6.74746 0.431962
\(245\) −11.5602 −0.738555
\(246\) 1.72410 0.109924
\(247\) −21.7008 −1.38079
\(248\) −22.9095 −1.45476
\(249\) 2.33665 0.148079
\(250\) −24.9159 −1.57582
\(251\) 15.8844 1.00261 0.501307 0.865270i \(-0.332853\pi\)
0.501307 + 0.865270i \(0.332853\pi\)
\(252\) −48.9918 −3.08619
\(253\) −14.6326 −0.919945
\(254\) 19.6400 1.23232
\(255\) −0.0350650 −0.00219585
\(256\) −32.1259 −2.00787
\(257\) 6.40882 0.399772 0.199886 0.979819i \(-0.435943\pi\)
0.199886 + 0.979819i \(0.435943\pi\)
\(258\) −1.62386 −0.101097
\(259\) −24.1551 −1.50093
\(260\) 15.1166 0.937493
\(261\) 27.5042 1.70247
\(262\) 18.4708 1.14113
\(263\) −20.9579 −1.29232 −0.646161 0.763201i \(-0.723627\pi\)
−0.646161 + 0.763201i \(0.723627\pi\)
\(264\) 4.17621 0.257028
\(265\) 9.04878 0.555862
\(266\) −68.4044 −4.19414
\(267\) 1.12670 0.0689526
\(268\) −7.28316 −0.444890
\(269\) 1.52770 0.0931453 0.0465726 0.998915i \(-0.485170\pi\)
0.0465726 + 0.998915i \(0.485170\pi\)
\(270\) 2.66509 0.162192
\(271\) −8.25345 −0.501361 −0.250681 0.968070i \(-0.580654\pi\)
−0.250681 + 0.968070i \(0.580654\pi\)
\(272\) −0.790697 −0.0479430
\(273\) 2.01340 0.121856
\(274\) 18.1935 1.09911
\(275\) −19.7698 −1.19216
\(276\) 1.65204 0.0994411
\(277\) −21.2202 −1.27500 −0.637500 0.770451i \(-0.720031\pi\)
−0.637500 + 0.770451i \(0.720031\pi\)
\(278\) −12.5973 −0.755537
\(279\) −13.7849 −0.825278
\(280\) 23.9232 1.42969
\(281\) 23.2045 1.38426 0.692132 0.721771i \(-0.256672\pi\)
0.692132 + 0.721771i \(0.256672\pi\)
\(282\) −1.96372 −0.116938
\(283\) 3.64808 0.216856 0.108428 0.994104i \(-0.465418\pi\)
0.108428 + 0.994104i \(0.465418\pi\)
\(284\) −24.7298 −1.46745
\(285\) 1.23715 0.0732823
\(286\) 42.8710 2.53501
\(287\) 18.6988 1.10376
\(288\) 0.485575 0.0286128
\(289\) −16.9628 −0.997812
\(290\) −26.7509 −1.57087
\(291\) −0.377621 −0.0221365
\(292\) −18.3379 −1.07315
\(293\) −19.9772 −1.16708 −0.583541 0.812083i \(-0.698333\pi\)
−0.583541 + 0.812083i \(0.698333\pi\)
\(294\) 3.70146 0.215873
\(295\) 9.13045 0.531596
\(296\) 29.1540 1.69454
\(297\) 5.04577 0.292785
\(298\) 0.430778 0.0249543
\(299\) 8.51448 0.492405
\(300\) 2.23203 0.128866
\(301\) −17.6117 −1.01512
\(302\) −29.0981 −1.67441
\(303\) 2.89612 0.166378
\(304\) 27.8970 1.60000
\(305\) −1.98255 −0.113520
\(306\) −1.40803 −0.0804916
\(307\) −4.63766 −0.264685 −0.132342 0.991204i \(-0.542250\pi\)
−0.132342 + 0.991204i \(0.542250\pi\)
\(308\) 90.2148 5.14046
\(309\) −0.118833 −0.00676018
\(310\) 13.4073 0.761486
\(311\) −0.0269580 −0.00152865 −0.000764325 1.00000i \(-0.500243\pi\)
−0.000764325 1.00000i \(0.500243\pi\)
\(312\) −2.43007 −0.137576
\(313\) 0.0974778 0.00550977 0.00275489 0.999996i \(-0.499123\pi\)
0.00275489 + 0.999996i \(0.499123\pi\)
\(314\) −22.1163 −1.24809
\(315\) 14.3948 0.811057
\(316\) 36.5300 2.05497
\(317\) 19.1623 1.07626 0.538131 0.842861i \(-0.319131\pi\)
0.538131 + 0.842861i \(0.319131\pi\)
\(318\) −2.89732 −0.162474
\(319\) −50.6470 −2.83569
\(320\) 9.20410 0.514525
\(321\) −0.957995 −0.0534701
\(322\) 26.8390 1.49568
\(323\) −1.31244 −0.0730259
\(324\) 35.2934 1.96074
\(325\) 11.5037 0.638111
\(326\) −21.0317 −1.16484
\(327\) 1.67962 0.0928834
\(328\) −22.5685 −1.24614
\(329\) −21.2976 −1.17418
\(330\) −2.44404 −0.134540
\(331\) 27.4329 1.50785 0.753924 0.656962i \(-0.228159\pi\)
0.753924 + 0.656962i \(0.228159\pi\)
\(332\) −60.9226 −3.34356
\(333\) 17.5422 0.961308
\(334\) 47.3774 2.59238
\(335\) 2.13995 0.116918
\(336\) −2.58829 −0.141203
\(337\) −26.6037 −1.44919 −0.724597 0.689173i \(-0.757974\pi\)
−0.724597 + 0.689173i \(0.757974\pi\)
\(338\) 6.94137 0.377561
\(339\) −2.86240 −0.155464
\(340\) 0.914234 0.0495813
\(341\) 25.3838 1.37461
\(342\) 49.6774 2.68625
\(343\) 11.4567 0.618605
\(344\) 21.2563 1.14606
\(345\) −0.485405 −0.0261333
\(346\) 33.7991 1.81705
\(347\) −7.03327 −0.377566 −0.188783 0.982019i \(-0.560454\pi\)
−0.188783 + 0.982019i \(0.560454\pi\)
\(348\) 5.71810 0.306523
\(349\) 0.0147714 0.000790697 0 0.000395349 1.00000i \(-0.499874\pi\)
0.000395349 1.00000i \(0.499874\pi\)
\(350\) 36.2615 1.93826
\(351\) −2.93605 −0.156715
\(352\) −0.894151 −0.0476584
\(353\) −34.8482 −1.85478 −0.927392 0.374090i \(-0.877955\pi\)
−0.927392 + 0.374090i \(0.877955\pi\)
\(354\) −2.92347 −0.155381
\(355\) 7.26616 0.385648
\(356\) −29.3758 −1.55692
\(357\) 0.121768 0.00644463
\(358\) −7.39056 −0.390603
\(359\) −36.5280 −1.92787 −0.963936 0.266133i \(-0.914254\pi\)
−0.963936 + 0.266133i \(0.914254\pi\)
\(360\) −17.3738 −0.915680
\(361\) 27.3048 1.43710
\(362\) −30.2512 −1.58997
\(363\) −2.93267 −0.153925
\(364\) −52.4945 −2.75146
\(365\) 5.38807 0.282025
\(366\) 0.634791 0.0331811
\(367\) −1.89373 −0.0988519 −0.0494259 0.998778i \(-0.515739\pi\)
−0.0494259 + 0.998778i \(0.515739\pi\)
\(368\) −10.9456 −0.570580
\(369\) −13.5797 −0.706929
\(370\) −17.0618 −0.887000
\(371\) −31.4231 −1.63141
\(372\) −2.86586 −0.148588
\(373\) 29.4413 1.52441 0.762206 0.647334i \(-0.224116\pi\)
0.762206 + 0.647334i \(0.224116\pi\)
\(374\) 2.59278 0.134069
\(375\) −1.56485 −0.0808085
\(376\) 25.7051 1.32564
\(377\) 29.4707 1.51782
\(378\) −9.25490 −0.476021
\(379\) −11.1366 −0.572051 −0.286025 0.958222i \(-0.592334\pi\)
−0.286025 + 0.958222i \(0.592334\pi\)
\(380\) −32.2556 −1.65468
\(381\) 1.23350 0.0631939
\(382\) −24.0359 −1.22979
\(383\) −0.293213 −0.0149825 −0.00749123 0.999972i \(-0.502385\pi\)
−0.00749123 + 0.999972i \(0.502385\pi\)
\(384\) −2.99732 −0.152956
\(385\) −26.5070 −1.35092
\(386\) 22.3557 1.13788
\(387\) 12.7901 0.650159
\(388\) 9.84554 0.499832
\(389\) −24.2789 −1.23099 −0.615494 0.788141i \(-0.711044\pi\)
−0.615494 + 0.788141i \(0.711044\pi\)
\(390\) 1.42215 0.0720133
\(391\) 0.514945 0.0260419
\(392\) −48.4521 −2.44720
\(393\) 1.16006 0.0585174
\(394\) −57.8815 −2.91603
\(395\) −10.7333 −0.540050
\(396\) −65.5168 −3.29234
\(397\) −12.7662 −0.640717 −0.320358 0.947296i \(-0.603803\pi\)
−0.320358 + 0.947296i \(0.603803\pi\)
\(398\) 29.4462 1.47600
\(399\) −4.29616 −0.215077
\(400\) −14.7884 −0.739418
\(401\) −0.156996 −0.00784002 −0.00392001 0.999992i \(-0.501248\pi\)
−0.00392001 + 0.999992i \(0.501248\pi\)
\(402\) −0.685189 −0.0341741
\(403\) −14.7704 −0.735768
\(404\) −75.5092 −3.75672
\(405\) −10.3700 −0.515288
\(406\) 92.8962 4.61036
\(407\) −32.3027 −1.60119
\(408\) −0.146967 −0.00727597
\(409\) 9.35103 0.462379 0.231189 0.972909i \(-0.425738\pi\)
0.231189 + 0.972909i \(0.425738\pi\)
\(410\) 13.2078 0.652285
\(411\) 1.14265 0.0563628
\(412\) 3.09828 0.152641
\(413\) −31.7067 −1.56019
\(414\) −19.4913 −0.957947
\(415\) 17.9004 0.878694
\(416\) 0.520292 0.0255094
\(417\) −0.791179 −0.0387442
\(418\) −91.4774 −4.47430
\(419\) −26.8069 −1.30960 −0.654800 0.755802i \(-0.727247\pi\)
−0.654800 + 0.755802i \(0.727247\pi\)
\(420\) 2.99267 0.146028
\(421\) −2.74086 −0.133581 −0.0667906 0.997767i \(-0.521276\pi\)
−0.0667906 + 0.997767i \(0.521276\pi\)
\(422\) −10.0146 −0.487501
\(423\) 15.4670 0.752032
\(424\) 37.9260 1.84185
\(425\) 0.695729 0.0337478
\(426\) −2.32655 −0.112722
\(427\) 6.88467 0.333172
\(428\) 24.9774 1.20733
\(429\) 2.69252 0.129996
\(430\) −12.4399 −0.599903
\(431\) 6.83256 0.329113 0.164556 0.986368i \(-0.447381\pi\)
0.164556 + 0.986368i \(0.447381\pi\)
\(432\) 3.77438 0.181595
\(433\) −10.9181 −0.524689 −0.262345 0.964974i \(-0.584496\pi\)
−0.262345 + 0.964974i \(0.584496\pi\)
\(434\) −46.5588 −2.23489
\(435\) −1.68010 −0.0805547
\(436\) −43.7921 −2.09726
\(437\) −18.1681 −0.869096
\(438\) −1.72520 −0.0824334
\(439\) 36.1942 1.72745 0.863727 0.503959i \(-0.168124\pi\)
0.863727 + 0.503959i \(0.168124\pi\)
\(440\) 31.9926 1.52519
\(441\) −29.1541 −1.38829
\(442\) −1.50870 −0.0717614
\(443\) 17.3906 0.826251 0.413126 0.910674i \(-0.364437\pi\)
0.413126 + 0.910674i \(0.364437\pi\)
\(444\) 3.64701 0.173080
\(445\) 8.63125 0.409161
\(446\) −34.2013 −1.61948
\(447\) 0.0270552 0.00127967
\(448\) −31.9625 −1.51009
\(449\) −6.52024 −0.307709 −0.153855 0.988094i \(-0.549169\pi\)
−0.153855 + 0.988094i \(0.549169\pi\)
\(450\) −26.3343 −1.24141
\(451\) 25.0060 1.17748
\(452\) 74.6300 3.51030
\(453\) −1.82751 −0.0858641
\(454\) −17.2118 −0.807789
\(455\) 15.4240 0.723089
\(456\) 5.18524 0.242821
\(457\) −14.9429 −0.698999 −0.349499 0.936937i \(-0.613648\pi\)
−0.349499 + 0.936937i \(0.613648\pi\)
\(458\) 53.4681 2.49840
\(459\) −0.177568 −0.00828818
\(460\) 12.6557 0.590077
\(461\) −17.3974 −0.810276 −0.405138 0.914255i \(-0.632777\pi\)
−0.405138 + 0.914255i \(0.632777\pi\)
\(462\) 8.48727 0.394864
\(463\) −1.81386 −0.0842972 −0.0421486 0.999111i \(-0.513420\pi\)
−0.0421486 + 0.999111i \(0.513420\pi\)
\(464\) −37.8854 −1.75879
\(465\) 0.842052 0.0390492
\(466\) −8.57025 −0.397009
\(467\) −21.8978 −1.01331 −0.506655 0.862149i \(-0.669118\pi\)
−0.506655 + 0.862149i \(0.669118\pi\)
\(468\) 38.1232 1.76224
\(469\) −7.43126 −0.343144
\(470\) −15.0434 −0.693901
\(471\) −1.38902 −0.0640026
\(472\) 38.2683 1.76144
\(473\) −23.5521 −1.08293
\(474\) 3.43668 0.157852
\(475\) −24.5464 −1.12627
\(476\) −3.17480 −0.145517
\(477\) 22.8205 1.04488
\(478\) 12.9018 0.590117
\(479\) 7.21751 0.329776 0.164888 0.986312i \(-0.447274\pi\)
0.164888 + 0.986312i \(0.447274\pi\)
\(480\) −0.0296615 −0.00135385
\(481\) 18.7964 0.857043
\(482\) −56.2481 −2.56203
\(483\) 1.68563 0.0766990
\(484\) 76.4623 3.47556
\(485\) −2.89283 −0.131357
\(486\) 10.0951 0.457925
\(487\) −27.3996 −1.24160 −0.620798 0.783971i \(-0.713191\pi\)
−0.620798 + 0.783971i \(0.713191\pi\)
\(488\) −8.30943 −0.376150
\(489\) −1.32090 −0.0597332
\(490\) 28.3557 1.28098
\(491\) −33.6499 −1.51860 −0.759300 0.650740i \(-0.774459\pi\)
−0.759300 + 0.650740i \(0.774459\pi\)
\(492\) −2.82320 −0.127280
\(493\) 1.78235 0.0802729
\(494\) 53.2292 2.39489
\(495\) 19.2503 0.865234
\(496\) 18.9878 0.852579
\(497\) −25.2327 −1.13184
\(498\) −5.73150 −0.256835
\(499\) 5.45861 0.244361 0.122181 0.992508i \(-0.461011\pi\)
0.122181 + 0.992508i \(0.461011\pi\)
\(500\) 40.7996 1.82461
\(501\) 2.97555 0.132938
\(502\) −38.9623 −1.73897
\(503\) −34.3253 −1.53049 −0.765244 0.643740i \(-0.777382\pi\)
−0.765244 + 0.643740i \(0.777382\pi\)
\(504\) 60.3329 2.68744
\(505\) 22.1862 0.987274
\(506\) 35.8919 1.59559
\(507\) 0.435955 0.0193614
\(508\) −32.1604 −1.42689
\(509\) −4.96106 −0.219895 −0.109948 0.993937i \(-0.535068\pi\)
−0.109948 + 0.993937i \(0.535068\pi\)
\(510\) 0.0860097 0.00380858
\(511\) −18.7108 −0.827717
\(512\) 39.8876 1.76280
\(513\) 6.26489 0.276602
\(514\) −15.7200 −0.693379
\(515\) −0.910342 −0.0401145
\(516\) 2.65906 0.117059
\(517\) −28.4814 −1.25261
\(518\) 59.2493 2.60327
\(519\) 2.12276 0.0931790
\(520\) −18.6160 −0.816364
\(521\) −18.2186 −0.798172 −0.399086 0.916914i \(-0.630672\pi\)
−0.399086 + 0.916914i \(0.630672\pi\)
\(522\) −67.4642 −2.95283
\(523\) −20.2083 −0.883649 −0.441825 0.897101i \(-0.645669\pi\)
−0.441825 + 0.897101i \(0.645669\pi\)
\(524\) −30.2458 −1.32129
\(525\) 2.27742 0.0993946
\(526\) 51.4071 2.24145
\(527\) −0.893296 −0.0389126
\(528\) −3.46132 −0.150635
\(529\) −15.8716 −0.690070
\(530\) −22.1955 −0.964110
\(531\) 23.0264 0.999262
\(532\) 112.012 4.85633
\(533\) −14.5506 −0.630255
\(534\) −2.76363 −0.119594
\(535\) −7.33890 −0.317288
\(536\) 8.96914 0.387408
\(537\) −0.464167 −0.0200303
\(538\) −3.74724 −0.161555
\(539\) 53.6852 2.31238
\(540\) −4.36408 −0.187800
\(541\) −45.7308 −1.96612 −0.983060 0.183282i \(-0.941328\pi\)
−0.983060 + 0.183282i \(0.941328\pi\)
\(542\) 20.2446 0.869581
\(543\) −1.89994 −0.0815342
\(544\) 0.0314666 0.00134912
\(545\) 12.8671 0.551164
\(546\) −4.93860 −0.211353
\(547\) −12.0802 −0.516514 −0.258257 0.966076i \(-0.583148\pi\)
−0.258257 + 0.966076i \(0.583148\pi\)
\(548\) −29.7918 −1.27264
\(549\) −4.99986 −0.213389
\(550\) 48.4926 2.06773
\(551\) −62.8840 −2.67895
\(552\) −2.03447 −0.0865928
\(553\) 37.2728 1.58500
\(554\) 52.0504 2.21141
\(555\) −1.07157 −0.0454857
\(556\) 20.6281 0.874825
\(557\) −32.4836 −1.37637 −0.688187 0.725533i \(-0.741593\pi\)
−0.688187 + 0.725533i \(0.741593\pi\)
\(558\) 33.8125 1.43140
\(559\) 13.7046 0.579642
\(560\) −19.8280 −0.837887
\(561\) 0.162840 0.00687513
\(562\) −56.9176 −2.40092
\(563\) 7.29351 0.307385 0.153692 0.988119i \(-0.450884\pi\)
0.153692 + 0.988119i \(0.450884\pi\)
\(564\) 3.21558 0.135400
\(565\) −21.9279 −0.922514
\(566\) −8.94827 −0.376124
\(567\) 36.0111 1.51232
\(568\) 30.4546 1.27784
\(569\) −4.49709 −0.188528 −0.0942638 0.995547i \(-0.530050\pi\)
−0.0942638 + 0.995547i \(0.530050\pi\)
\(570\) −3.03456 −0.127104
\(571\) 20.8980 0.874554 0.437277 0.899327i \(-0.355943\pi\)
0.437277 + 0.899327i \(0.355943\pi\)
\(572\) −70.2010 −2.93525
\(573\) −1.50958 −0.0630638
\(574\) −45.8657 −1.91440
\(575\) 9.63099 0.401640
\(576\) 23.2122 0.967173
\(577\) −24.8696 −1.03534 −0.517668 0.855582i \(-0.673200\pi\)
−0.517668 + 0.855582i \(0.673200\pi\)
\(578\) 41.6075 1.73064
\(579\) 1.40406 0.0583506
\(580\) 43.8046 1.81889
\(581\) −62.1614 −2.57889
\(582\) 0.926254 0.0383945
\(583\) −42.0222 −1.74038
\(584\) 22.5830 0.934490
\(585\) −11.2014 −0.463121
\(586\) 49.0015 2.02423
\(587\) 42.8556 1.76884 0.884421 0.466691i \(-0.154554\pi\)
0.884421 + 0.466691i \(0.154554\pi\)
\(588\) −6.06112 −0.249956
\(589\) 31.5169 1.29863
\(590\) −22.3958 −0.922020
\(591\) −3.63526 −0.149535
\(592\) −24.1634 −0.993108
\(593\) 37.5717 1.54288 0.771442 0.636299i \(-0.219536\pi\)
0.771442 + 0.636299i \(0.219536\pi\)
\(594\) −12.3766 −0.507818
\(595\) 0.932824 0.0382421
\(596\) −0.705398 −0.0288942
\(597\) 1.84938 0.0756899
\(598\) −20.8849 −0.854047
\(599\) −6.82934 −0.279039 −0.139520 0.990219i \(-0.544556\pi\)
−0.139520 + 0.990219i \(0.544556\pi\)
\(600\) −2.74872 −0.112216
\(601\) −0.673297 −0.0274643 −0.0137322 0.999906i \(-0.504371\pi\)
−0.0137322 + 0.999906i \(0.504371\pi\)
\(602\) 43.1990 1.76066
\(603\) 5.39681 0.219775
\(604\) 47.6480 1.93877
\(605\) −22.4663 −0.913384
\(606\) −7.10379 −0.288572
\(607\) −19.9964 −0.811627 −0.405814 0.913956i \(-0.633012\pi\)
−0.405814 + 0.913956i \(0.633012\pi\)
\(608\) −1.11019 −0.0450241
\(609\) 5.83438 0.236421
\(610\) 4.86293 0.196894
\(611\) 16.5728 0.670466
\(612\) 2.30564 0.0931999
\(613\) −3.20002 −0.129248 −0.0646238 0.997910i \(-0.520585\pi\)
−0.0646238 + 0.997910i \(0.520585\pi\)
\(614\) 11.3756 0.459080
\(615\) 0.829517 0.0334494
\(616\) −111.099 −4.47629
\(617\) 48.3916 1.94817 0.974086 0.226177i \(-0.0726226\pi\)
0.974086 + 0.226177i \(0.0726226\pi\)
\(618\) 0.291482 0.0117251
\(619\) 3.61406 0.145261 0.0726306 0.997359i \(-0.476861\pi\)
0.0726306 + 0.997359i \(0.476861\pi\)
\(620\) −21.9545 −0.881712
\(621\) −2.45808 −0.0986394
\(622\) 0.0661245 0.00265135
\(623\) −29.9732 −1.20085
\(624\) 2.01409 0.0806280
\(625\) 6.04840 0.241936
\(626\) −0.239100 −0.00955636
\(627\) −5.74527 −0.229444
\(628\) 36.2153 1.44515
\(629\) 1.13678 0.0453265
\(630\) −35.3086 −1.40673
\(631\) −9.82783 −0.391240 −0.195620 0.980680i \(-0.562672\pi\)
−0.195620 + 0.980680i \(0.562672\pi\)
\(632\) −44.9863 −1.78946
\(633\) −0.628968 −0.0249992
\(634\) −47.0026 −1.86671
\(635\) 9.44942 0.374989
\(636\) 4.74435 0.188126
\(637\) −31.2385 −1.23772
\(638\) 124.230 4.91833
\(639\) 18.3248 0.724917
\(640\) −22.9615 −0.907634
\(641\) −3.71444 −0.146712 −0.0733558 0.997306i \(-0.523371\pi\)
−0.0733558 + 0.997306i \(0.523371\pi\)
\(642\) 2.34984 0.0927406
\(643\) −35.9366 −1.41720 −0.708601 0.705609i \(-0.750673\pi\)
−0.708601 + 0.705609i \(0.750673\pi\)
\(644\) −43.9488 −1.73182
\(645\) −0.781289 −0.0307632
\(646\) 3.21923 0.126659
\(647\) −28.7054 −1.12853 −0.564263 0.825595i \(-0.690839\pi\)
−0.564263 + 0.825595i \(0.690839\pi\)
\(648\) −43.4635 −1.70741
\(649\) −42.4015 −1.66440
\(650\) −28.2171 −1.10676
\(651\) −2.92414 −0.114606
\(652\) 34.4392 1.34874
\(653\) −3.77911 −0.147888 −0.0739440 0.997262i \(-0.523559\pi\)
−0.0739440 + 0.997262i \(0.523559\pi\)
\(654\) −4.11989 −0.161101
\(655\) 8.88687 0.347239
\(656\) 18.7052 0.730315
\(657\) 13.5884 0.530133
\(658\) 52.2403 2.03654
\(659\) 17.4480 0.679678 0.339839 0.940484i \(-0.389627\pi\)
0.339839 + 0.940484i \(0.389627\pi\)
\(660\) 4.00211 0.155782
\(661\) −47.2122 −1.83634 −0.918172 0.396183i \(-0.870335\pi\)
−0.918172 + 0.396183i \(0.870335\pi\)
\(662\) −67.2892 −2.61527
\(663\) −0.0947541 −0.00367995
\(664\) 75.0256 2.91156
\(665\) −32.9115 −1.27625
\(666\) −43.0287 −1.66733
\(667\) 24.6730 0.955344
\(668\) −77.5803 −3.00167
\(669\) −2.14803 −0.0830474
\(670\) −5.24901 −0.202787
\(671\) 9.20689 0.355428
\(672\) 0.103003 0.00397344
\(673\) 26.5048 1.02169 0.510843 0.859674i \(-0.329333\pi\)
0.510843 + 0.859674i \(0.329333\pi\)
\(674\) 65.2553 2.51354
\(675\) −3.32105 −0.127827
\(676\) −11.3665 −0.437172
\(677\) −41.5900 −1.59843 −0.799216 0.601044i \(-0.794752\pi\)
−0.799216 + 0.601044i \(0.794752\pi\)
\(678\) 7.02108 0.269643
\(679\) 10.0457 0.385520
\(680\) −1.12587 −0.0431751
\(681\) −1.08099 −0.0414237
\(682\) −62.2632 −2.38418
\(683\) 37.9879 1.45357 0.726784 0.686866i \(-0.241014\pi\)
0.726784 + 0.686866i \(0.241014\pi\)
\(684\) −81.3466 −3.11036
\(685\) 8.75348 0.334453
\(686\) −28.1018 −1.07293
\(687\) 3.35808 0.128119
\(688\) −17.6177 −0.671667
\(689\) 24.4520 0.931548
\(690\) 1.19063 0.0453267
\(691\) −32.6194 −1.24090 −0.620450 0.784246i \(-0.713050\pi\)
−0.620450 + 0.784246i \(0.713050\pi\)
\(692\) −55.3459 −2.10394
\(693\) −66.8491 −2.53939
\(694\) 17.2517 0.654865
\(695\) −6.06097 −0.229906
\(696\) −7.04179 −0.266918
\(697\) −0.879999 −0.0333323
\(698\) −0.0362324 −0.00137142
\(699\) −0.538257 −0.0203588
\(700\) −59.3781 −2.24428
\(701\) 33.4148 1.26206 0.631029 0.775759i \(-0.282633\pi\)
0.631029 + 0.775759i \(0.282633\pi\)
\(702\) 7.20174 0.271812
\(703\) −40.1075 −1.51268
\(704\) −42.7435 −1.61096
\(705\) −0.944807 −0.0355835
\(706\) 85.4781 3.21701
\(707\) −77.0446 −2.89756
\(708\) 4.78717 0.179913
\(709\) 3.88843 0.146033 0.0730166 0.997331i \(-0.476737\pi\)
0.0730166 + 0.997331i \(0.476737\pi\)
\(710\) −17.8229 −0.668882
\(711\) −27.0687 −1.01515
\(712\) 36.1760 1.35575
\(713\) −12.3659 −0.463107
\(714\) −0.298680 −0.0111778
\(715\) 20.6266 0.771390
\(716\) 12.1020 0.452273
\(717\) 0.810304 0.0302614
\(718\) 89.5983 3.34378
\(719\) 33.0481 1.23249 0.616244 0.787555i \(-0.288654\pi\)
0.616244 + 0.787555i \(0.288654\pi\)
\(720\) 14.3997 0.536647
\(721\) 3.16128 0.117732
\(722\) −66.9751 −2.49255
\(723\) −3.53268 −0.131382
\(724\) 49.5363 1.84100
\(725\) 33.3352 1.23804
\(726\) 7.19346 0.266974
\(727\) 39.1541 1.45215 0.726073 0.687618i \(-0.241343\pi\)
0.726073 + 0.687618i \(0.241343\pi\)
\(728\) 64.6464 2.39596
\(729\) −25.7269 −0.952848
\(730\) −13.2162 −0.489155
\(731\) 0.828835 0.0306556
\(732\) −1.03947 −0.0384198
\(733\) −28.0029 −1.03431 −0.517155 0.855892i \(-0.673009\pi\)
−0.517155 + 0.855892i \(0.673009\pi\)
\(734\) 4.64507 0.171453
\(735\) 1.78089 0.0656890
\(736\) 0.435592 0.0160561
\(737\) −9.93784 −0.366065
\(738\) 33.3091 1.22613
\(739\) 50.6121 1.86179 0.930897 0.365281i \(-0.119027\pi\)
0.930897 + 0.365281i \(0.119027\pi\)
\(740\) 27.9386 1.02704
\(741\) 3.34308 0.122811
\(742\) 77.0767 2.82958
\(743\) −45.8270 −1.68123 −0.840615 0.541633i \(-0.817806\pi\)
−0.840615 + 0.541633i \(0.817806\pi\)
\(744\) 3.52928 0.129390
\(745\) 0.207261 0.00759346
\(746\) −72.2156 −2.64400
\(747\) 45.1436 1.65172
\(748\) −4.24567 −0.155237
\(749\) 25.4853 0.931212
\(750\) 3.83837 0.140157
\(751\) 13.0035 0.474506 0.237253 0.971448i \(-0.423753\pi\)
0.237253 + 0.971448i \(0.423753\pi\)
\(752\) −21.3049 −0.776910
\(753\) −2.44704 −0.0891751
\(754\) −72.2876 −2.63256
\(755\) −14.0000 −0.509512
\(756\) 15.1549 0.551177
\(757\) 12.8466 0.466917 0.233458 0.972367i \(-0.424996\pi\)
0.233458 + 0.972367i \(0.424996\pi\)
\(758\) 27.3167 0.992188
\(759\) 2.25420 0.0818223
\(760\) 39.7225 1.44089
\(761\) 5.92289 0.214704 0.107352 0.994221i \(-0.465763\pi\)
0.107352 + 0.994221i \(0.465763\pi\)
\(762\) −3.02560 −0.109606
\(763\) −44.6826 −1.61762
\(764\) 39.3587 1.42395
\(765\) −0.677446 −0.0244931
\(766\) 0.719212 0.0259862
\(767\) 24.6727 0.890880
\(768\) 4.94909 0.178585
\(769\) −31.8209 −1.14749 −0.573746 0.819033i \(-0.694510\pi\)
−0.573746 + 0.819033i \(0.694510\pi\)
\(770\) 65.0183 2.34310
\(771\) −0.987300 −0.0355567
\(772\) −36.6074 −1.31753
\(773\) 53.0471 1.90797 0.953986 0.299851i \(-0.0969370\pi\)
0.953986 + 0.299851i \(0.0969370\pi\)
\(774\) −31.3725 −1.12766
\(775\) −16.7073 −0.600143
\(776\) −12.1247 −0.435251
\(777\) 3.72117 0.133496
\(778\) 59.5529 2.13508
\(779\) 31.0477 1.11240
\(780\) −2.32876 −0.0833831
\(781\) −33.7438 −1.20745
\(782\) −1.26309 −0.0451681
\(783\) −8.50801 −0.304051
\(784\) 40.1581 1.43422
\(785\) −10.6408 −0.379787
\(786\) −2.84548 −0.101495
\(787\) −37.7856 −1.34691 −0.673455 0.739228i \(-0.735191\pi\)
−0.673455 + 0.739228i \(0.735191\pi\)
\(788\) 94.7806 3.37642
\(789\) 3.22864 0.114943
\(790\) 26.3273 0.936685
\(791\) 76.1476 2.70750
\(792\) 80.6833 2.86696
\(793\) −5.35734 −0.190245
\(794\) 31.3138 1.11128
\(795\) −1.39399 −0.0494399
\(796\) −48.2180 −1.70904
\(797\) 12.2357 0.433411 0.216706 0.976237i \(-0.430469\pi\)
0.216706 + 0.976237i \(0.430469\pi\)
\(798\) 10.5379 0.373038
\(799\) 1.00230 0.0354590
\(800\) 0.588518 0.0208072
\(801\) 21.7675 0.769116
\(802\) 0.385091 0.0135980
\(803\) −25.0220 −0.883008
\(804\) 1.12199 0.0395697
\(805\) 12.9131 0.455127
\(806\) 36.2299 1.27614
\(807\) −0.235346 −0.00828458
\(808\) 92.9888 3.27133
\(809\) 17.0387 0.599050 0.299525 0.954088i \(-0.403172\pi\)
0.299525 + 0.954088i \(0.403172\pi\)
\(810\) 25.4361 0.893735
\(811\) 29.3552 1.03080 0.515400 0.856950i \(-0.327644\pi\)
0.515400 + 0.856950i \(0.327644\pi\)
\(812\) −152.117 −5.33827
\(813\) 1.27147 0.0445924
\(814\) 79.2343 2.77716
\(815\) −10.1190 −0.354453
\(816\) 0.121809 0.00426418
\(817\) −29.2426 −1.02307
\(818\) −22.9368 −0.801967
\(819\) 38.8984 1.35922
\(820\) −21.6276 −0.755270
\(821\) 52.4593 1.83084 0.915421 0.402497i \(-0.131858\pi\)
0.915421 + 0.402497i \(0.131858\pi\)
\(822\) −2.80277 −0.0977578
\(823\) 22.6140 0.788276 0.394138 0.919051i \(-0.371043\pi\)
0.394138 + 0.919051i \(0.371043\pi\)
\(824\) −3.81550 −0.132919
\(825\) 3.04560 0.106034
\(826\) 77.7724 2.70605
\(827\) −0.426064 −0.0148157 −0.00740785 0.999973i \(-0.502358\pi\)
−0.00740785 + 0.999973i \(0.502358\pi\)
\(828\) 31.9170 1.10919
\(829\) 27.4947 0.954930 0.477465 0.878651i \(-0.341556\pi\)
0.477465 + 0.878651i \(0.341556\pi\)
\(830\) −43.9072 −1.52404
\(831\) 3.26904 0.113402
\(832\) 24.8717 0.862272
\(833\) −1.88926 −0.0654591
\(834\) 1.94066 0.0671995
\(835\) 22.7948 0.788845
\(836\) 149.794 5.18073
\(837\) 4.26414 0.147390
\(838\) 65.7537 2.27142
\(839\) 18.4382 0.636558 0.318279 0.947997i \(-0.396895\pi\)
0.318279 + 0.947997i \(0.396895\pi\)
\(840\) −3.68545 −0.127160
\(841\) 56.3993 1.94480
\(842\) 6.72296 0.231688
\(843\) −3.57473 −0.123120
\(844\) 16.3988 0.564470
\(845\) 3.33971 0.114890
\(846\) −37.9385 −1.30435
\(847\) 78.0171 2.68070
\(848\) −31.4338 −1.07944
\(849\) −0.561999 −0.0192877
\(850\) −1.70653 −0.0585336
\(851\) 15.7365 0.539440
\(852\) 3.80971 0.130518
\(853\) −21.4491 −0.734404 −0.367202 0.930141i \(-0.619684\pi\)
−0.367202 + 0.930141i \(0.619684\pi\)
\(854\) −16.8872 −0.577867
\(855\) 23.9014 0.817410
\(856\) −30.7594 −1.05134
\(857\) −12.9996 −0.444056 −0.222028 0.975040i \(-0.571268\pi\)
−0.222028 + 0.975040i \(0.571268\pi\)
\(858\) −6.60441 −0.225471
\(859\) 3.77899 0.128938 0.0644688 0.997920i \(-0.479465\pi\)
0.0644688 + 0.997920i \(0.479465\pi\)
\(860\) 20.3702 0.694618
\(861\) −2.88061 −0.0981709
\(862\) −16.7594 −0.570826
\(863\) 26.5162 0.902621 0.451311 0.892367i \(-0.350957\pi\)
0.451311 + 0.892367i \(0.350957\pi\)
\(864\) −0.150205 −0.00511008
\(865\) 16.2618 0.552918
\(866\) 26.7806 0.910041
\(867\) 2.61317 0.0887480
\(868\) 76.2398 2.58775
\(869\) 49.8450 1.69088
\(870\) 4.12107 0.139717
\(871\) 5.78267 0.195938
\(872\) 53.9295 1.82628
\(873\) −7.29554 −0.246917
\(874\) 44.5639 1.50740
\(875\) 41.6293 1.40733
\(876\) 2.82501 0.0954484
\(877\) 11.9881 0.404811 0.202405 0.979302i \(-0.435124\pi\)
0.202405 + 0.979302i \(0.435124\pi\)
\(878\) −88.7796 −2.99617
\(879\) 3.07756 0.103803
\(880\) −26.5161 −0.893857
\(881\) 12.2562 0.412923 0.206462 0.978455i \(-0.433805\pi\)
0.206462 + 0.978455i \(0.433805\pi\)
\(882\) 71.5112 2.40791
\(883\) −9.64087 −0.324441 −0.162221 0.986755i \(-0.551866\pi\)
−0.162221 + 0.986755i \(0.551866\pi\)
\(884\) 2.47048 0.0830913
\(885\) −1.40658 −0.0472815
\(886\) −42.6568 −1.43308
\(887\) 8.66172 0.290832 0.145416 0.989371i \(-0.453548\pi\)
0.145416 + 0.989371i \(0.453548\pi\)
\(888\) −4.49126 −0.150717
\(889\) −32.8144 −1.10056
\(890\) −21.1713 −0.709664
\(891\) 48.1577 1.61334
\(892\) 56.0045 1.87517
\(893\) −35.3629 −1.18337
\(894\) −0.0663628 −0.00221950
\(895\) −3.55583 −0.118858
\(896\) 79.7370 2.66383
\(897\) −1.31168 −0.0437958
\(898\) 15.9933 0.533703
\(899\) −42.8014 −1.42751
\(900\) 43.1223 1.43741
\(901\) 1.47883 0.0492669
\(902\) −61.3363 −2.04228
\(903\) 2.71313 0.0902873
\(904\) −91.9061 −3.05675
\(905\) −14.5548 −0.483819
\(906\) 4.48265 0.148926
\(907\) −26.1870 −0.869525 −0.434762 0.900545i \(-0.643168\pi\)
−0.434762 + 0.900545i \(0.643168\pi\)
\(908\) 28.1842 0.935326
\(909\) 55.9522 1.85582
\(910\) −37.8331 −1.25415
\(911\) 39.6510 1.31370 0.656848 0.754023i \(-0.271889\pi\)
0.656848 + 0.754023i \(0.271889\pi\)
\(912\) −4.29763 −0.142309
\(913\) −83.1286 −2.75116
\(914\) 36.6529 1.21237
\(915\) 0.305418 0.0100968
\(916\) −87.5537 −2.89286
\(917\) −30.8608 −1.01911
\(918\) 0.435552 0.0143753
\(919\) 44.1429 1.45614 0.728069 0.685503i \(-0.240418\pi\)
0.728069 + 0.685503i \(0.240418\pi\)
\(920\) −15.5854 −0.513836
\(921\) 0.714445 0.0235418
\(922\) 42.6734 1.40538
\(923\) 19.6349 0.646292
\(924\) −13.8979 −0.457206
\(925\) 21.2612 0.699064
\(926\) 4.44916 0.146208
\(927\) −2.29582 −0.0754048
\(928\) 1.50769 0.0494923
\(929\) 26.8196 0.879921 0.439961 0.898017i \(-0.354992\pi\)
0.439961 + 0.898017i \(0.354992\pi\)
\(930\) −2.06544 −0.0677285
\(931\) 66.6562 2.18457
\(932\) 14.0337 0.459691
\(933\) 0.00415297 0.000135962 0
\(934\) 53.7124 1.75752
\(935\) 1.24747 0.0407966
\(936\) −46.9483 −1.53455
\(937\) 39.5638 1.29249 0.646246 0.763129i \(-0.276338\pi\)
0.646246 + 0.763129i \(0.276338\pi\)
\(938\) 18.2279 0.595162
\(939\) −0.0150168 −0.000490053 0
\(940\) 24.6335 0.803457
\(941\) −18.0284 −0.587709 −0.293854 0.955850i \(-0.594938\pi\)
−0.293854 + 0.955850i \(0.594938\pi\)
\(942\) 3.40708 0.111009
\(943\) −12.1818 −0.396695
\(944\) −31.7175 −1.03232
\(945\) −4.45282 −0.144850
\(946\) 57.7702 1.87827
\(947\) −14.3579 −0.466568 −0.233284 0.972409i \(-0.574947\pi\)
−0.233284 + 0.972409i \(0.574947\pi\)
\(948\) −5.62755 −0.182774
\(949\) 14.5599 0.472634
\(950\) 60.2091 1.95344
\(951\) −2.95201 −0.0957256
\(952\) 3.90973 0.126715
\(953\) −17.8983 −0.579784 −0.289892 0.957059i \(-0.593619\pi\)
−0.289892 + 0.957059i \(0.593619\pi\)
\(954\) −55.9756 −1.81228
\(955\) −11.5644 −0.374217
\(956\) −21.1267 −0.683287
\(957\) 7.80233 0.252213
\(958\) −17.7036 −0.571977
\(959\) −30.3976 −0.981590
\(960\) −1.41792 −0.0457632
\(961\) −9.54833 −0.308011
\(962\) −46.1051 −1.48649
\(963\) −18.5082 −0.596419
\(964\) 92.1060 2.96654
\(965\) 10.7560 0.346249
\(966\) −4.13463 −0.133030
\(967\) −45.4824 −1.46261 −0.731307 0.682048i \(-0.761090\pi\)
−0.731307 + 0.682048i \(0.761090\pi\)
\(968\) −94.1625 −3.02650
\(969\) 0.202185 0.00649511
\(970\) 7.09574 0.227830
\(971\) −37.2870 −1.19660 −0.598299 0.801273i \(-0.704156\pi\)
−0.598299 + 0.801273i \(0.704156\pi\)
\(972\) −16.5308 −0.530224
\(973\) 21.0475 0.674753
\(974\) 67.2076 2.15347
\(975\) −1.77218 −0.0567553
\(976\) 6.88702 0.220448
\(977\) 54.3149 1.73769 0.868844 0.495086i \(-0.164864\pi\)
0.868844 + 0.495086i \(0.164864\pi\)
\(978\) 3.23999 0.103604
\(979\) −40.0832 −1.28106
\(980\) −46.4323 −1.48322
\(981\) 32.4499 1.03605
\(982\) 82.5389 2.63392
\(983\) −28.5523 −0.910677 −0.455339 0.890318i \(-0.650482\pi\)
−0.455339 + 0.890318i \(0.650482\pi\)
\(984\) 3.47674 0.110835
\(985\) −27.8486 −0.887330
\(986\) −4.37186 −0.139228
\(987\) 3.28097 0.104434
\(988\) −87.1625 −2.77301
\(989\) 11.4736 0.364839
\(990\) −47.2183 −1.50070
\(991\) −28.2039 −0.895928 −0.447964 0.894052i \(-0.647851\pi\)
−0.447964 + 0.894052i \(0.647851\pi\)
\(992\) −0.755640 −0.0239916
\(993\) −4.22612 −0.134112
\(994\) 61.8925 1.96311
\(995\) 14.1675 0.449139
\(996\) 9.38531 0.297385
\(997\) 32.1059 1.01680 0.508402 0.861120i \(-0.330237\pi\)
0.508402 + 0.861120i \(0.330237\pi\)
\(998\) −13.3893 −0.423829
\(999\) −5.42642 −0.171684
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 \(a_p\))