Properties

Label 8007.2.a.f.1.17
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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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: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.980818 q^{2} -1.00000 q^{3} -1.03800 q^{4} +1.00436 q^{5} +0.980818 q^{6} -3.53145 q^{7} +2.97972 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.980818 q^{2} -1.00000 q^{3} -1.03800 q^{4} +1.00436 q^{5} +0.980818 q^{6} -3.53145 q^{7} +2.97972 q^{8} +1.00000 q^{9} -0.985094 q^{10} +6.32698 q^{11} +1.03800 q^{12} +3.86467 q^{13} +3.46371 q^{14} -1.00436 q^{15} -0.846572 q^{16} -1.00000 q^{17} -0.980818 q^{18} -2.59733 q^{19} -1.04252 q^{20} +3.53145 q^{21} -6.20562 q^{22} +6.45448 q^{23} -2.97972 q^{24} -3.99126 q^{25} -3.79054 q^{26} -1.00000 q^{27} +3.66564 q^{28} -7.53770 q^{29} +0.985094 q^{30} -4.09152 q^{31} -5.12911 q^{32} -6.32698 q^{33} +0.980818 q^{34} -3.54685 q^{35} -1.03800 q^{36} +6.50621 q^{37} +2.54751 q^{38} -3.86467 q^{39} +2.99271 q^{40} -9.61376 q^{41} -3.46371 q^{42} +7.33861 q^{43} -6.56738 q^{44} +1.00436 q^{45} -6.33067 q^{46} -4.71120 q^{47} +0.846572 q^{48} +5.47117 q^{49} +3.91470 q^{50} +1.00000 q^{51} -4.01151 q^{52} +2.16439 q^{53} +0.980818 q^{54} +6.35456 q^{55} -10.5227 q^{56} +2.59733 q^{57} +7.39311 q^{58} +3.64108 q^{59} +1.04252 q^{60} +7.27575 q^{61} +4.01303 q^{62} -3.53145 q^{63} +6.72387 q^{64} +3.88152 q^{65} +6.20562 q^{66} -6.61390 q^{67} +1.03800 q^{68} -6.45448 q^{69} +3.47881 q^{70} -11.6229 q^{71} +2.97972 q^{72} -10.8308 q^{73} -6.38141 q^{74} +3.99126 q^{75} +2.69602 q^{76} -22.3434 q^{77} +3.79054 q^{78} -16.2317 q^{79} -0.850263 q^{80} +1.00000 q^{81} +9.42935 q^{82} -8.05337 q^{83} -3.66564 q^{84} -1.00436 q^{85} -7.19784 q^{86} +7.53770 q^{87} +18.8526 q^{88} +2.16759 q^{89} -0.985094 q^{90} -13.6479 q^{91} -6.69972 q^{92} +4.09152 q^{93} +4.62082 q^{94} -2.60865 q^{95} +5.12911 q^{96} +3.94258 q^{97} -5.36622 q^{98} +6.32698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.980818 −0.693543 −0.346772 0.937950i \(-0.612722\pi\)
−0.346772 + 0.937950i \(0.612722\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.03800 −0.518998
\(5\) 1.00436 0.449163 0.224582 0.974455i \(-0.427898\pi\)
0.224582 + 0.974455i \(0.427898\pi\)
\(6\) 0.980818 0.400417
\(7\) −3.53145 −1.33476 −0.667382 0.744716i \(-0.732585\pi\)
−0.667382 + 0.744716i \(0.732585\pi\)
\(8\) 2.97972 1.05349
\(9\) 1.00000 0.333333
\(10\) −0.985094 −0.311514
\(11\) 6.32698 1.90766 0.953828 0.300353i \(-0.0971046\pi\)
0.953828 + 0.300353i \(0.0971046\pi\)
\(12\) 1.03800 0.299644
\(13\) 3.86467 1.07187 0.535933 0.844260i \(-0.319960\pi\)
0.535933 + 0.844260i \(0.319960\pi\)
\(14\) 3.46371 0.925716
\(15\) −1.00436 −0.259325
\(16\) −0.846572 −0.211643
\(17\) −1.00000 −0.242536
\(18\) −0.980818 −0.231181
\(19\) −2.59733 −0.595868 −0.297934 0.954586i \(-0.596298\pi\)
−0.297934 + 0.954586i \(0.596298\pi\)
\(20\) −1.04252 −0.233115
\(21\) 3.53145 0.770626
\(22\) −6.20562 −1.32304
\(23\) 6.45448 1.34585 0.672926 0.739710i \(-0.265037\pi\)
0.672926 + 0.739710i \(0.265037\pi\)
\(24\) −2.97972 −0.608233
\(25\) −3.99126 −0.798252
\(26\) −3.79054 −0.743385
\(27\) −1.00000 −0.192450
\(28\) 3.66564 0.692740
\(29\) −7.53770 −1.39972 −0.699858 0.714282i \(-0.746753\pi\)
−0.699858 + 0.714282i \(0.746753\pi\)
\(30\) 0.985094 0.179853
\(31\) −4.09152 −0.734858 −0.367429 0.930051i \(-0.619762\pi\)
−0.367429 + 0.930051i \(0.619762\pi\)
\(32\) −5.12911 −0.906707
\(33\) −6.32698 −1.10139
\(34\) 0.980818 0.168209
\(35\) −3.54685 −0.599527
\(36\) −1.03800 −0.172999
\(37\) 6.50621 1.06961 0.534807 0.844974i \(-0.320384\pi\)
0.534807 + 0.844974i \(0.320384\pi\)
\(38\) 2.54751 0.413260
\(39\) −3.86467 −0.618842
\(40\) 2.99271 0.473189
\(41\) −9.61376 −1.50142 −0.750709 0.660633i \(-0.770288\pi\)
−0.750709 + 0.660633i \(0.770288\pi\)
\(42\) −3.46371 −0.534463
\(43\) 7.33861 1.11913 0.559564 0.828787i \(-0.310969\pi\)
0.559564 + 0.828787i \(0.310969\pi\)
\(44\) −6.56738 −0.990070
\(45\) 1.00436 0.149721
\(46\) −6.33067 −0.933406
\(47\) −4.71120 −0.687198 −0.343599 0.939116i \(-0.611646\pi\)
−0.343599 + 0.939116i \(0.611646\pi\)
\(48\) 0.846572 0.122192
\(49\) 5.47117 0.781595
\(50\) 3.91470 0.553622
\(51\) 1.00000 0.140028
\(52\) −4.01151 −0.556297
\(53\) 2.16439 0.297301 0.148651 0.988890i \(-0.452507\pi\)
0.148651 + 0.988890i \(0.452507\pi\)
\(54\) 0.980818 0.133472
\(55\) 6.35456 0.856849
\(56\) −10.5227 −1.40616
\(57\) 2.59733 0.344025
\(58\) 7.39311 0.970764
\(59\) 3.64108 0.474028 0.237014 0.971506i \(-0.423831\pi\)
0.237014 + 0.971506i \(0.423831\pi\)
\(60\) 1.04252 0.134589
\(61\) 7.27575 0.931564 0.465782 0.884899i \(-0.345773\pi\)
0.465782 + 0.884899i \(0.345773\pi\)
\(62\) 4.01303 0.509656
\(63\) −3.53145 −0.444921
\(64\) 6.72387 0.840483
\(65\) 3.88152 0.481443
\(66\) 6.20562 0.763858
\(67\) −6.61390 −0.808016 −0.404008 0.914755i \(-0.632383\pi\)
−0.404008 + 0.914755i \(0.632383\pi\)
\(68\) 1.03800 0.125876
\(69\) −6.45448 −0.777028
\(70\) 3.47881 0.415798
\(71\) −11.6229 −1.37939 −0.689695 0.724100i \(-0.742255\pi\)
−0.689695 + 0.724100i \(0.742255\pi\)
\(72\) 2.97972 0.351164
\(73\) −10.8308 −1.26765 −0.633826 0.773476i \(-0.718516\pi\)
−0.633826 + 0.773476i \(0.718516\pi\)
\(74\) −6.38141 −0.741824
\(75\) 3.99126 0.460871
\(76\) 2.69602 0.309254
\(77\) −22.3434 −2.54627
\(78\) 3.79054 0.429194
\(79\) −16.2317 −1.82621 −0.913103 0.407728i \(-0.866321\pi\)
−0.913103 + 0.407728i \(0.866321\pi\)
\(80\) −0.850263 −0.0950623
\(81\) 1.00000 0.111111
\(82\) 9.42935 1.04130
\(83\) −8.05337 −0.883972 −0.441986 0.897022i \(-0.645726\pi\)
−0.441986 + 0.897022i \(0.645726\pi\)
\(84\) −3.66564 −0.399954
\(85\) −1.00436 −0.108938
\(86\) −7.19784 −0.776163
\(87\) 7.53770 0.808127
\(88\) 18.8526 2.00970
\(89\) 2.16759 0.229764 0.114882 0.993379i \(-0.463351\pi\)
0.114882 + 0.993379i \(0.463351\pi\)
\(90\) −0.985094 −0.103838
\(91\) −13.6479 −1.43069
\(92\) −6.69972 −0.698494
\(93\) 4.09152 0.424271
\(94\) 4.62082 0.476602
\(95\) −2.60865 −0.267642
\(96\) 5.12911 0.523488
\(97\) 3.94258 0.400308 0.200154 0.979764i \(-0.435856\pi\)
0.200154 + 0.979764i \(0.435856\pi\)
\(98\) −5.36622 −0.542070
\(99\) 6.32698 0.635885
\(100\) 4.14291 0.414291
\(101\) −12.4762 −1.24143 −0.620715 0.784037i \(-0.713157\pi\)
−0.620715 + 0.784037i \(0.713157\pi\)
\(102\) −0.980818 −0.0971155
\(103\) 5.58186 0.549997 0.274998 0.961445i \(-0.411323\pi\)
0.274998 + 0.961445i \(0.411323\pi\)
\(104\) 11.5156 1.12920
\(105\) 3.54685 0.346137
\(106\) −2.12287 −0.206191
\(107\) 8.77058 0.847884 0.423942 0.905689i \(-0.360646\pi\)
0.423942 + 0.905689i \(0.360646\pi\)
\(108\) 1.03800 0.0998812
\(109\) 8.70332 0.833626 0.416813 0.908992i \(-0.363147\pi\)
0.416813 + 0.908992i \(0.363147\pi\)
\(110\) −6.23267 −0.594262
\(111\) −6.50621 −0.617542
\(112\) 2.98963 0.282494
\(113\) −8.93732 −0.840753 −0.420376 0.907350i \(-0.638102\pi\)
−0.420376 + 0.907350i \(0.638102\pi\)
\(114\) −2.54751 −0.238596
\(115\) 6.48262 0.604507
\(116\) 7.82411 0.726450
\(117\) 3.86467 0.357289
\(118\) −3.57124 −0.328759
\(119\) 3.53145 0.323728
\(120\) −2.99271 −0.273196
\(121\) 29.0307 2.63915
\(122\) −7.13619 −0.646080
\(123\) 9.61376 0.866844
\(124\) 4.24698 0.381390
\(125\) −9.03046 −0.807709
\(126\) 3.46371 0.308572
\(127\) 7.22565 0.641173 0.320587 0.947219i \(-0.396120\pi\)
0.320587 + 0.947219i \(0.396120\pi\)
\(128\) 3.66333 0.323796
\(129\) −7.33861 −0.646129
\(130\) −3.80706 −0.333901
\(131\) 15.2193 1.32971 0.664856 0.746971i \(-0.268493\pi\)
0.664856 + 0.746971i \(0.268493\pi\)
\(132\) 6.56738 0.571617
\(133\) 9.17235 0.795343
\(134\) 6.48703 0.560394
\(135\) −1.00436 −0.0864415
\(136\) −2.97972 −0.255509
\(137\) 17.4584 1.49157 0.745787 0.666185i \(-0.232074\pi\)
0.745787 + 0.666185i \(0.232074\pi\)
\(138\) 6.33067 0.538902
\(139\) 23.1304 1.96189 0.980946 0.194278i \(-0.0622365\pi\)
0.980946 + 0.194278i \(0.0622365\pi\)
\(140\) 3.68162 0.311153
\(141\) 4.71120 0.396754
\(142\) 11.4000 0.956666
\(143\) 24.4517 2.04475
\(144\) −0.846572 −0.0705477
\(145\) −7.57056 −0.628701
\(146\) 10.6231 0.879171
\(147\) −5.47117 −0.451254
\(148\) −6.75342 −0.555128
\(149\) 7.85577 0.643570 0.321785 0.946813i \(-0.395717\pi\)
0.321785 + 0.946813i \(0.395717\pi\)
\(150\) −3.91470 −0.319634
\(151\) −1.61453 −0.131388 −0.0656941 0.997840i \(-0.520926\pi\)
−0.0656941 + 0.997840i \(0.520926\pi\)
\(152\) −7.73932 −0.627741
\(153\) −1.00000 −0.0808452
\(154\) 21.9148 1.76595
\(155\) −4.10936 −0.330071
\(156\) 4.01151 0.321178
\(157\) −1.00000 −0.0798087
\(158\) 15.9203 1.26655
\(159\) −2.16439 −0.171647
\(160\) −5.15147 −0.407259
\(161\) −22.7937 −1.79639
\(162\) −0.980818 −0.0770603
\(163\) −21.9925 −1.72258 −0.861291 0.508112i \(-0.830344\pi\)
−0.861291 + 0.508112i \(0.830344\pi\)
\(164\) 9.97905 0.779233
\(165\) −6.35456 −0.494702
\(166\) 7.89889 0.613073
\(167\) 0.0214142 0.00165708 0.000828541 1.00000i \(-0.499736\pi\)
0.000828541 1.00000i \(0.499736\pi\)
\(168\) 10.5227 0.811848
\(169\) 1.93567 0.148897
\(170\) 0.985094 0.0755533
\(171\) −2.59733 −0.198623
\(172\) −7.61745 −0.580825
\(173\) 5.93545 0.451264 0.225632 0.974213i \(-0.427555\pi\)
0.225632 + 0.974213i \(0.427555\pi\)
\(174\) −7.39311 −0.560471
\(175\) 14.0950 1.06548
\(176\) −5.35624 −0.403742
\(177\) −3.64108 −0.273680
\(178\) −2.12601 −0.159351
\(179\) −14.6954 −1.09838 −0.549191 0.835697i \(-0.685064\pi\)
−0.549191 + 0.835697i \(0.685064\pi\)
\(180\) −1.04252 −0.0777050
\(181\) −4.11606 −0.305944 −0.152972 0.988230i \(-0.548885\pi\)
−0.152972 + 0.988230i \(0.548885\pi\)
\(182\) 13.3861 0.992244
\(183\) −7.27575 −0.537839
\(184\) 19.2325 1.41784
\(185\) 6.53457 0.480431
\(186\) −4.01303 −0.294250
\(187\) −6.32698 −0.462675
\(188\) 4.89020 0.356655
\(189\) 3.53145 0.256875
\(190\) 2.55861 0.185621
\(191\) −7.47583 −0.540932 −0.270466 0.962730i \(-0.587178\pi\)
−0.270466 + 0.962730i \(0.587178\pi\)
\(192\) −6.72387 −0.485253
\(193\) 2.58077 0.185768 0.0928839 0.995677i \(-0.470391\pi\)
0.0928839 + 0.995677i \(0.470391\pi\)
\(194\) −3.86695 −0.277631
\(195\) −3.88152 −0.277961
\(196\) −5.67905 −0.405646
\(197\) −20.6346 −1.47016 −0.735079 0.677982i \(-0.762855\pi\)
−0.735079 + 0.677982i \(0.762855\pi\)
\(198\) −6.20562 −0.441014
\(199\) −13.6167 −0.965264 −0.482632 0.875823i \(-0.660319\pi\)
−0.482632 + 0.875823i \(0.660319\pi\)
\(200\) −11.8928 −0.840951
\(201\) 6.61390 0.466508
\(202\) 12.2369 0.860984
\(203\) 26.6191 1.86829
\(204\) −1.03800 −0.0726743
\(205\) −9.65568 −0.674382
\(206\) −5.47478 −0.381446
\(207\) 6.45448 0.448617
\(208\) −3.27172 −0.226853
\(209\) −16.4332 −1.13671
\(210\) −3.47881 −0.240061
\(211\) −22.0131 −1.51544 −0.757722 0.652578i \(-0.773688\pi\)
−0.757722 + 0.652578i \(0.773688\pi\)
\(212\) −2.24662 −0.154299
\(213\) 11.6229 0.796391
\(214\) −8.60234 −0.588044
\(215\) 7.37061 0.502671
\(216\) −2.97972 −0.202744
\(217\) 14.4490 0.980863
\(218\) −8.53637 −0.578156
\(219\) 10.8308 0.731879
\(220\) −6.59601 −0.444703
\(221\) −3.86467 −0.259966
\(222\) 6.38141 0.428292
\(223\) 17.6054 1.17895 0.589474 0.807787i \(-0.299335\pi\)
0.589474 + 0.807787i \(0.299335\pi\)
\(224\) 18.1132 1.21024
\(225\) −3.99126 −0.266084
\(226\) 8.76589 0.583098
\(227\) −21.1832 −1.40598 −0.702991 0.711199i \(-0.748152\pi\)
−0.702991 + 0.711199i \(0.748152\pi\)
\(228\) −2.69602 −0.178548
\(229\) −18.7107 −1.23644 −0.618220 0.786005i \(-0.712146\pi\)
−0.618220 + 0.786005i \(0.712146\pi\)
\(230\) −6.35827 −0.419252
\(231\) 22.3434 1.47009
\(232\) −22.4603 −1.47459
\(233\) −1.35758 −0.0889379 −0.0444689 0.999011i \(-0.514160\pi\)
−0.0444689 + 0.999011i \(0.514160\pi\)
\(234\) −3.79054 −0.247795
\(235\) −4.73173 −0.308664
\(236\) −3.77943 −0.246020
\(237\) 16.2317 1.05436
\(238\) −3.46371 −0.224519
\(239\) 15.1210 0.978094 0.489047 0.872257i \(-0.337345\pi\)
0.489047 + 0.872257i \(0.337345\pi\)
\(240\) 0.850263 0.0548842
\(241\) 16.4242 1.05797 0.528987 0.848630i \(-0.322572\pi\)
0.528987 + 0.848630i \(0.322572\pi\)
\(242\) −28.4738 −1.83037
\(243\) −1.00000 −0.0641500
\(244\) −7.55220 −0.483480
\(245\) 5.49502 0.351064
\(246\) −9.42935 −0.601193
\(247\) −10.0378 −0.638691
\(248\) −12.1916 −0.774166
\(249\) 8.05337 0.510361
\(250\) 8.85724 0.560181
\(251\) 7.14002 0.450674 0.225337 0.974281i \(-0.427652\pi\)
0.225337 + 0.974281i \(0.427652\pi\)
\(252\) 3.66564 0.230913
\(253\) 40.8373 2.56742
\(254\) −7.08705 −0.444681
\(255\) 1.00436 0.0628954
\(256\) −17.0408 −1.06505
\(257\) −9.05691 −0.564955 −0.282477 0.959274i \(-0.591156\pi\)
−0.282477 + 0.959274i \(0.591156\pi\)
\(258\) 7.19784 0.448118
\(259\) −22.9764 −1.42768
\(260\) −4.02900 −0.249868
\(261\) −7.53770 −0.466572
\(262\) −14.9273 −0.922213
\(263\) 5.55816 0.342731 0.171365 0.985208i \(-0.445182\pi\)
0.171365 + 0.985208i \(0.445182\pi\)
\(264\) −18.8526 −1.16030
\(265\) 2.17382 0.133537
\(266\) −8.99640 −0.551605
\(267\) −2.16759 −0.132654
\(268\) 6.86520 0.419359
\(269\) 12.5220 0.763478 0.381739 0.924270i \(-0.375325\pi\)
0.381739 + 0.924270i \(0.375325\pi\)
\(270\) 0.985094 0.0599509
\(271\) 2.37609 0.144337 0.0721686 0.997392i \(-0.477008\pi\)
0.0721686 + 0.997392i \(0.477008\pi\)
\(272\) 0.846572 0.0513310
\(273\) 13.6479 0.826009
\(274\) −17.1235 −1.03447
\(275\) −25.2526 −1.52279
\(276\) 6.69972 0.403276
\(277\) −21.2558 −1.27714 −0.638569 0.769564i \(-0.720473\pi\)
−0.638569 + 0.769564i \(0.720473\pi\)
\(278\) −22.6867 −1.36066
\(279\) −4.09152 −0.244953
\(280\) −10.5686 −0.631596
\(281\) −8.43216 −0.503020 −0.251510 0.967855i \(-0.580927\pi\)
−0.251510 + 0.967855i \(0.580927\pi\)
\(282\) −4.62082 −0.275166
\(283\) 5.80167 0.344873 0.172437 0.985021i \(-0.444836\pi\)
0.172437 + 0.985021i \(0.444836\pi\)
\(284\) 12.0646 0.715900
\(285\) 2.60865 0.154523
\(286\) −23.9826 −1.41812
\(287\) 33.9506 2.00404
\(288\) −5.12911 −0.302236
\(289\) 1.00000 0.0588235
\(290\) 7.42535 0.436031
\(291\) −3.94258 −0.231118
\(292\) 11.2424 0.657909
\(293\) −25.3292 −1.47975 −0.739874 0.672745i \(-0.765115\pi\)
−0.739874 + 0.672745i \(0.765115\pi\)
\(294\) 5.36622 0.312964
\(295\) 3.65695 0.212916
\(296\) 19.3867 1.12683
\(297\) −6.32698 −0.367129
\(298\) −7.70508 −0.446343
\(299\) 24.9444 1.44257
\(300\) −4.14291 −0.239191
\(301\) −25.9160 −1.49377
\(302\) 1.58356 0.0911234
\(303\) 12.4762 0.716739
\(304\) 2.19883 0.126111
\(305\) 7.30747 0.418424
\(306\) 0.980818 0.0560696
\(307\) −8.84271 −0.504680 −0.252340 0.967639i \(-0.581200\pi\)
−0.252340 + 0.967639i \(0.581200\pi\)
\(308\) 23.1924 1.32151
\(309\) −5.58186 −0.317541
\(310\) 4.03053 0.228919
\(311\) 11.1415 0.631776 0.315888 0.948796i \(-0.397698\pi\)
0.315888 + 0.948796i \(0.397698\pi\)
\(312\) −11.5156 −0.651945
\(313\) −17.4045 −0.983760 −0.491880 0.870663i \(-0.663690\pi\)
−0.491880 + 0.870663i \(0.663690\pi\)
\(314\) 0.980818 0.0553508
\(315\) −3.54685 −0.199842
\(316\) 16.8484 0.947798
\(317\) 30.5137 1.71382 0.856910 0.515466i \(-0.172381\pi\)
0.856910 + 0.515466i \(0.172381\pi\)
\(318\) 2.12287 0.119045
\(319\) −47.6909 −2.67018
\(320\) 6.75318 0.377514
\(321\) −8.77058 −0.489526
\(322\) 22.3565 1.24588
\(323\) 2.59733 0.144519
\(324\) −1.03800 −0.0576664
\(325\) −15.4249 −0.855620
\(326\) 21.5706 1.19468
\(327\) −8.70332 −0.481294
\(328\) −28.6463 −1.58173
\(329\) 16.6374 0.917248
\(330\) 6.23267 0.343097
\(331\) 18.7043 1.02808 0.514040 0.857766i \(-0.328148\pi\)
0.514040 + 0.857766i \(0.328148\pi\)
\(332\) 8.35936 0.458780
\(333\) 6.50621 0.356538
\(334\) −0.0210034 −0.00114926
\(335\) −6.64273 −0.362931
\(336\) −2.98963 −0.163098
\(337\) −18.1160 −0.986842 −0.493421 0.869791i \(-0.664254\pi\)
−0.493421 + 0.869791i \(0.664254\pi\)
\(338\) −1.89854 −0.103267
\(339\) 8.93732 0.485409
\(340\) 1.04252 0.0565387
\(341\) −25.8870 −1.40186
\(342\) 2.54751 0.137753
\(343\) 5.39900 0.291519
\(344\) 21.8670 1.17899
\(345\) −6.48262 −0.349012
\(346\) −5.82159 −0.312971
\(347\) −12.5427 −0.673325 −0.336663 0.941625i \(-0.609298\pi\)
−0.336663 + 0.941625i \(0.609298\pi\)
\(348\) −7.82411 −0.419416
\(349\) −6.54338 −0.350259 −0.175129 0.984545i \(-0.556034\pi\)
−0.175129 + 0.984545i \(0.556034\pi\)
\(350\) −13.8246 −0.738955
\(351\) −3.86467 −0.206281
\(352\) −32.4518 −1.72969
\(353\) 7.74439 0.412192 0.206096 0.978532i \(-0.433924\pi\)
0.206096 + 0.978532i \(0.433924\pi\)
\(354\) 3.57124 0.189809
\(355\) −11.6736 −0.619571
\(356\) −2.24995 −0.119247
\(357\) −3.53145 −0.186904
\(358\) 14.4135 0.761776
\(359\) −5.80074 −0.306151 −0.153076 0.988214i \(-0.548918\pi\)
−0.153076 + 0.988214i \(0.548918\pi\)
\(360\) 2.99271 0.157730
\(361\) −12.2539 −0.644941
\(362\) 4.03711 0.212186
\(363\) −29.0307 −1.52371
\(364\) 14.1665 0.742525
\(365\) −10.8780 −0.569383
\(366\) 7.13619 0.373014
\(367\) −9.02968 −0.471345 −0.235673 0.971832i \(-0.575729\pi\)
−0.235673 + 0.971832i \(0.575729\pi\)
\(368\) −5.46418 −0.284840
\(369\) −9.61376 −0.500472
\(370\) −6.40923 −0.333200
\(371\) −7.64343 −0.396827
\(372\) −4.24698 −0.220196
\(373\) −1.15360 −0.0597310 −0.0298655 0.999554i \(-0.509508\pi\)
−0.0298655 + 0.999554i \(0.509508\pi\)
\(374\) 6.20562 0.320885
\(375\) 9.03046 0.466331
\(376\) −14.0380 −0.723957
\(377\) −29.1307 −1.50031
\(378\) −3.46371 −0.178154
\(379\) 18.2491 0.937394 0.468697 0.883359i \(-0.344724\pi\)
0.468697 + 0.883359i \(0.344724\pi\)
\(380\) 2.70777 0.138906
\(381\) −7.22565 −0.370181
\(382\) 7.33242 0.375159
\(383\) −23.5927 −1.20553 −0.602764 0.797919i \(-0.705934\pi\)
−0.602764 + 0.797919i \(0.705934\pi\)
\(384\) −3.66333 −0.186943
\(385\) −22.4408 −1.14369
\(386\) −2.53126 −0.128838
\(387\) 7.33861 0.373043
\(388\) −4.09238 −0.207759
\(389\) 13.8726 0.703370 0.351685 0.936118i \(-0.385609\pi\)
0.351685 + 0.936118i \(0.385609\pi\)
\(390\) 3.80706 0.192778
\(391\) −6.45448 −0.326417
\(392\) 16.3026 0.823403
\(393\) −15.2193 −0.767710
\(394\) 20.2388 1.01962
\(395\) −16.3024 −0.820265
\(396\) −6.56738 −0.330023
\(397\) 19.8767 0.997581 0.498791 0.866722i \(-0.333778\pi\)
0.498791 + 0.866722i \(0.333778\pi\)
\(398\) 13.3555 0.669452
\(399\) −9.17235 −0.459192
\(400\) 3.37889 0.168945
\(401\) −23.1378 −1.15544 −0.577722 0.816233i \(-0.696058\pi\)
−0.577722 + 0.816233i \(0.696058\pi\)
\(402\) −6.48703 −0.323544
\(403\) −15.8124 −0.787670
\(404\) 12.9503 0.644299
\(405\) 1.00436 0.0499070
\(406\) −26.1084 −1.29574
\(407\) 41.1647 2.04046
\(408\) 2.97972 0.147518
\(409\) 30.7047 1.51825 0.759125 0.650945i \(-0.225627\pi\)
0.759125 + 0.650945i \(0.225627\pi\)
\(410\) 9.47046 0.467713
\(411\) −17.4584 −0.861160
\(412\) −5.79394 −0.285447
\(413\) −12.8583 −0.632716
\(414\) −6.33067 −0.311135
\(415\) −8.08848 −0.397048
\(416\) −19.8223 −0.971869
\(417\) −23.1304 −1.13270
\(418\) 16.1180 0.788358
\(419\) 27.4810 1.34254 0.671268 0.741215i \(-0.265750\pi\)
0.671268 + 0.741215i \(0.265750\pi\)
\(420\) −3.68162 −0.179644
\(421\) −32.6641 −1.59195 −0.795975 0.605329i \(-0.793041\pi\)
−0.795975 + 0.605329i \(0.793041\pi\)
\(422\) 21.5908 1.05103
\(423\) −4.71120 −0.229066
\(424\) 6.44926 0.313204
\(425\) 3.99126 0.193605
\(426\) −11.4000 −0.552331
\(427\) −25.6940 −1.24342
\(428\) −9.10382 −0.440050
\(429\) −24.4517 −1.18054
\(430\) −7.22922 −0.348624
\(431\) −0.416855 −0.0200792 −0.0100396 0.999950i \(-0.503196\pi\)
−0.0100396 + 0.999950i \(0.503196\pi\)
\(432\) 0.846572 0.0407307
\(433\) 6.04143 0.290332 0.145166 0.989407i \(-0.453628\pi\)
0.145166 + 0.989407i \(0.453628\pi\)
\(434\) −14.1718 −0.680270
\(435\) 7.57056 0.362981
\(436\) −9.03401 −0.432650
\(437\) −16.7644 −0.801950
\(438\) −10.6231 −0.507590
\(439\) −5.79669 −0.276661 −0.138330 0.990386i \(-0.544174\pi\)
−0.138330 + 0.990386i \(0.544174\pi\)
\(440\) 18.9348 0.902682
\(441\) 5.47117 0.260532
\(442\) 3.79054 0.180297
\(443\) −18.3239 −0.870596 −0.435298 0.900287i \(-0.643357\pi\)
−0.435298 + 0.900287i \(0.643357\pi\)
\(444\) 6.75342 0.320503
\(445\) 2.17704 0.103202
\(446\) −17.2677 −0.817651
\(447\) −7.85577 −0.371565
\(448\) −23.7450 −1.12185
\(449\) −30.6524 −1.44658 −0.723289 0.690546i \(-0.757370\pi\)
−0.723289 + 0.690546i \(0.757370\pi\)
\(450\) 3.91470 0.184541
\(451\) −60.8261 −2.86419
\(452\) 9.27691 0.436349
\(453\) 1.61453 0.0758570
\(454\) 20.7769 0.975109
\(455\) −13.7074 −0.642613
\(456\) 7.73932 0.362427
\(457\) −40.9890 −1.91739 −0.958693 0.284444i \(-0.908191\pi\)
−0.958693 + 0.284444i \(0.908191\pi\)
\(458\) 18.3518 0.857524
\(459\) 1.00000 0.0466760
\(460\) −6.72893 −0.313738
\(461\) 29.9443 1.39465 0.697323 0.716757i \(-0.254375\pi\)
0.697323 + 0.716757i \(0.254375\pi\)
\(462\) −21.9148 −1.01957
\(463\) −1.03311 −0.0480129 −0.0240065 0.999712i \(-0.507642\pi\)
−0.0240065 + 0.999712i \(0.507642\pi\)
\(464\) 6.38121 0.296240
\(465\) 4.10936 0.190567
\(466\) 1.33154 0.0616822
\(467\) −29.8673 −1.38209 −0.691046 0.722811i \(-0.742850\pi\)
−0.691046 + 0.722811i \(0.742850\pi\)
\(468\) −4.01151 −0.185432
\(469\) 23.3567 1.07851
\(470\) 4.64097 0.214072
\(471\) 1.00000 0.0460776
\(472\) 10.8494 0.499384
\(473\) 46.4312 2.13491
\(474\) −15.9203 −0.731245
\(475\) 10.3666 0.475653
\(476\) −3.66564 −0.168014
\(477\) 2.16439 0.0991004
\(478\) −14.8309 −0.678350
\(479\) 18.3559 0.838701 0.419350 0.907824i \(-0.362258\pi\)
0.419350 + 0.907824i \(0.362258\pi\)
\(480\) 5.15147 0.235131
\(481\) 25.1443 1.14648
\(482\) −16.1091 −0.733751
\(483\) 22.7937 1.03715
\(484\) −30.1337 −1.36971
\(485\) 3.95977 0.179804
\(486\) 0.980818 0.0444908
\(487\) 6.50618 0.294823 0.147412 0.989075i \(-0.452906\pi\)
0.147412 + 0.989075i \(0.452906\pi\)
\(488\) 21.6797 0.981394
\(489\) 21.9925 0.994533
\(490\) −5.38961 −0.243478
\(491\) −34.8722 −1.57376 −0.786880 0.617106i \(-0.788305\pi\)
−0.786880 + 0.617106i \(0.788305\pi\)
\(492\) −9.97905 −0.449890
\(493\) 7.53770 0.339481
\(494\) 9.84527 0.442960
\(495\) 6.35456 0.285616
\(496\) 3.46377 0.155528
\(497\) 41.0459 1.84116
\(498\) −7.89889 −0.353958
\(499\) 31.2012 1.39676 0.698379 0.715728i \(-0.253905\pi\)
0.698379 + 0.715728i \(0.253905\pi\)
\(500\) 9.37358 0.419199
\(501\) −0.0214142 −0.000956716 0
\(502\) −7.00306 −0.312562
\(503\) 32.9316 1.46835 0.734173 0.678963i \(-0.237570\pi\)
0.734173 + 0.678963i \(0.237570\pi\)
\(504\) −10.5227 −0.468720
\(505\) −12.5306 −0.557604
\(506\) −40.0540 −1.78062
\(507\) −1.93567 −0.0859660
\(508\) −7.50020 −0.332768
\(509\) 13.7677 0.610243 0.305121 0.952313i \(-0.401303\pi\)
0.305121 + 0.952313i \(0.401303\pi\)
\(510\) −0.985094 −0.0436207
\(511\) 38.2486 1.69202
\(512\) 9.38726 0.414862
\(513\) 2.59733 0.114675
\(514\) 8.88319 0.391821
\(515\) 5.60619 0.247038
\(516\) 7.61745 0.335340
\(517\) −29.8076 −1.31094
\(518\) 22.5356 0.990160
\(519\) −5.93545 −0.260537
\(520\) 11.5658 0.507196
\(521\) 10.9548 0.479940 0.239970 0.970780i \(-0.422862\pi\)
0.239970 + 0.970780i \(0.422862\pi\)
\(522\) 7.39311 0.323588
\(523\) 28.5644 1.24903 0.624516 0.781012i \(-0.285296\pi\)
0.624516 + 0.781012i \(0.285296\pi\)
\(524\) −15.7975 −0.690118
\(525\) −14.0950 −0.615154
\(526\) −5.45155 −0.237699
\(527\) 4.09152 0.178229
\(528\) 5.35624 0.233101
\(529\) 18.6603 0.811316
\(530\) −2.13212 −0.0926135
\(531\) 3.64108 0.158009
\(532\) −9.52086 −0.412782
\(533\) −37.1540 −1.60932
\(534\) 2.12601 0.0920015
\(535\) 8.80881 0.380838
\(536\) −19.7076 −0.851237
\(537\) 14.6954 0.634151
\(538\) −12.2818 −0.529505
\(539\) 34.6160 1.49101
\(540\) 1.04252 0.0448630
\(541\) 3.26376 0.140320 0.0701599 0.997536i \(-0.477649\pi\)
0.0701599 + 0.997536i \(0.477649\pi\)
\(542\) −2.33051 −0.100104
\(543\) 4.11606 0.176637
\(544\) 5.12911 0.219909
\(545\) 8.74126 0.374434
\(546\) −13.3861 −0.572872
\(547\) −15.6784 −0.670361 −0.335180 0.942154i \(-0.608797\pi\)
−0.335180 + 0.942154i \(0.608797\pi\)
\(548\) −18.1218 −0.774124
\(549\) 7.27575 0.310521
\(550\) 24.7682 1.05612
\(551\) 19.5779 0.834046
\(552\) −19.2325 −0.818591
\(553\) 57.3214 2.43756
\(554\) 20.8481 0.885751
\(555\) −6.53457 −0.277377
\(556\) −24.0092 −1.01822
\(557\) −44.5967 −1.88962 −0.944811 0.327615i \(-0.893755\pi\)
−0.944811 + 0.327615i \(0.893755\pi\)
\(558\) 4.01303 0.169885
\(559\) 28.3613 1.19956
\(560\) 3.00266 0.126886
\(561\) 6.32698 0.267125
\(562\) 8.27041 0.348866
\(563\) 18.1585 0.765290 0.382645 0.923895i \(-0.375013\pi\)
0.382645 + 0.923895i \(0.375013\pi\)
\(564\) −4.89020 −0.205915
\(565\) −8.97629 −0.377635
\(566\) −5.69038 −0.239184
\(567\) −3.53145 −0.148307
\(568\) −34.6331 −1.45317
\(569\) −17.4367 −0.730984 −0.365492 0.930814i \(-0.619099\pi\)
−0.365492 + 0.930814i \(0.619099\pi\)
\(570\) −2.55861 −0.107169
\(571\) 20.6732 0.865147 0.432574 0.901599i \(-0.357606\pi\)
0.432574 + 0.901599i \(0.357606\pi\)
\(572\) −25.3807 −1.06122
\(573\) 7.47583 0.312307
\(574\) −33.2993 −1.38989
\(575\) −25.7615 −1.07433
\(576\) 6.72387 0.280161
\(577\) −33.5049 −1.39483 −0.697413 0.716669i \(-0.745666\pi\)
−0.697413 + 0.716669i \(0.745666\pi\)
\(578\) −0.980818 −0.0407967
\(579\) −2.58077 −0.107253
\(580\) 7.85822 0.326295
\(581\) 28.4401 1.17989
\(582\) 3.86695 0.160290
\(583\) 13.6940 0.567148
\(584\) −32.2728 −1.33546
\(585\) 3.88152 0.160481
\(586\) 24.8433 1.02627
\(587\) −14.9112 −0.615452 −0.307726 0.951475i \(-0.599568\pi\)
−0.307726 + 0.951475i \(0.599568\pi\)
\(588\) 5.67905 0.234200
\(589\) 10.6270 0.437879
\(590\) −3.58681 −0.147666
\(591\) 20.6346 0.848796
\(592\) −5.50798 −0.226376
\(593\) −22.1437 −0.909332 −0.454666 0.890662i \(-0.650241\pi\)
−0.454666 + 0.890662i \(0.650241\pi\)
\(594\) 6.20562 0.254619
\(595\) 3.54685 0.145407
\(596\) −8.15426 −0.334011
\(597\) 13.6167 0.557295
\(598\) −24.4659 −1.00049
\(599\) 11.8283 0.483289 0.241645 0.970365i \(-0.422313\pi\)
0.241645 + 0.970365i \(0.422313\pi\)
\(600\) 11.8928 0.485523
\(601\) −9.44203 −0.385149 −0.192574 0.981282i \(-0.561684\pi\)
−0.192574 + 0.981282i \(0.561684\pi\)
\(602\) 25.4189 1.03599
\(603\) −6.61390 −0.269339
\(604\) 1.67587 0.0681902
\(605\) 29.1572 1.18541
\(606\) −12.2369 −0.497090
\(607\) −22.1184 −0.897756 −0.448878 0.893593i \(-0.648176\pi\)
−0.448878 + 0.893593i \(0.648176\pi\)
\(608\) 13.3220 0.540278
\(609\) −26.6191 −1.07866
\(610\) −7.16730 −0.290195
\(611\) −18.2072 −0.736585
\(612\) 1.03800 0.0419585
\(613\) −0.434638 −0.0175549 −0.00877744 0.999961i \(-0.502794\pi\)
−0.00877744 + 0.999961i \(0.502794\pi\)
\(614\) 8.67309 0.350017
\(615\) 9.65568 0.389354
\(616\) −66.5772 −2.68247
\(617\) −13.4147 −0.540056 −0.270028 0.962853i \(-0.587033\pi\)
−0.270028 + 0.962853i \(0.587033\pi\)
\(618\) 5.47478 0.220228
\(619\) −38.8737 −1.56246 −0.781232 0.624241i \(-0.785409\pi\)
−0.781232 + 0.624241i \(0.785409\pi\)
\(620\) 4.26550 0.171306
\(621\) −6.45448 −0.259009
\(622\) −10.9278 −0.438164
\(623\) −7.65475 −0.306681
\(624\) 3.27172 0.130974
\(625\) 10.8865 0.435459
\(626\) 17.0706 0.682280
\(627\) 16.4332 0.656281
\(628\) 1.03800 0.0414206
\(629\) −6.50621 −0.259420
\(630\) 3.47881 0.138599
\(631\) −43.6469 −1.73755 −0.868777 0.495204i \(-0.835093\pi\)
−0.868777 + 0.495204i \(0.835093\pi\)
\(632\) −48.3659 −1.92389
\(633\) 22.0131 0.874942
\(634\) −29.9284 −1.18861
\(635\) 7.25716 0.287991
\(636\) 2.24662 0.0890844
\(637\) 21.1442 0.837766
\(638\) 46.7761 1.85188
\(639\) −11.6229 −0.459796
\(640\) 3.67930 0.145437
\(641\) −7.34221 −0.290000 −0.145000 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(642\) 8.60234 0.339507
\(643\) 1.32896 0.0524089 0.0262044 0.999657i \(-0.491658\pi\)
0.0262044 + 0.999657i \(0.491658\pi\)
\(644\) 23.6598 0.932325
\(645\) −7.37061 −0.290217
\(646\) −2.54751 −0.100230
\(647\) −30.2272 −1.18835 −0.594177 0.804334i \(-0.702522\pi\)
−0.594177 + 0.804334i \(0.702522\pi\)
\(648\) 2.97972 0.117055
\(649\) 23.0370 0.904283
\(650\) 15.1290 0.593409
\(651\) −14.4490 −0.566301
\(652\) 22.8281 0.894017
\(653\) −42.1752 −1.65044 −0.825222 0.564809i \(-0.808950\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(654\) 8.53637 0.333798
\(655\) 15.2856 0.597258
\(656\) 8.13874 0.317765
\(657\) −10.8308 −0.422551
\(658\) −16.3182 −0.636151
\(659\) 2.87875 0.112140 0.0560701 0.998427i \(-0.482143\pi\)
0.0560701 + 0.998427i \(0.482143\pi\)
\(660\) 6.59601 0.256749
\(661\) −4.30998 −0.167639 −0.0838193 0.996481i \(-0.526712\pi\)
−0.0838193 + 0.996481i \(0.526712\pi\)
\(662\) −18.3455 −0.713017
\(663\) 3.86467 0.150091
\(664\) −23.9968 −0.931256
\(665\) 9.21233 0.357239
\(666\) −6.38141 −0.247275
\(667\) −48.6519 −1.88381
\(668\) −0.0222279 −0.000860022 0
\(669\) −17.6054 −0.680666
\(670\) 6.51531 0.251708
\(671\) 46.0335 1.77710
\(672\) −18.1132 −0.698732
\(673\) −36.1438 −1.39324 −0.696620 0.717440i \(-0.745314\pi\)
−0.696620 + 0.717440i \(0.745314\pi\)
\(674\) 17.7685 0.684417
\(675\) 3.99126 0.153624
\(676\) −2.00921 −0.0772775
\(677\) 0.978831 0.0376195 0.0188098 0.999823i \(-0.494012\pi\)
0.0188098 + 0.999823i \(0.494012\pi\)
\(678\) −8.76589 −0.336652
\(679\) −13.9230 −0.534317
\(680\) −2.99271 −0.114765
\(681\) 21.1832 0.811744
\(682\) 25.3904 0.972248
\(683\) −20.5167 −0.785048 −0.392524 0.919742i \(-0.628398\pi\)
−0.392524 + 0.919742i \(0.628398\pi\)
\(684\) 2.69602 0.103085
\(685\) 17.5345 0.669960
\(686\) −5.29544 −0.202181
\(687\) 18.7107 0.713859
\(688\) −6.21266 −0.236856
\(689\) 8.36463 0.318667
\(690\) 6.35827 0.242055
\(691\) 8.25164 0.313907 0.156954 0.987606i \(-0.449833\pi\)
0.156954 + 0.987606i \(0.449833\pi\)
\(692\) −6.16097 −0.234205
\(693\) −22.3434 −0.848757
\(694\) 12.3021 0.466980
\(695\) 23.2312 0.881210
\(696\) 22.4603 0.851354
\(697\) 9.61376 0.364147
\(698\) 6.41786 0.242920
\(699\) 1.35758 0.0513483
\(700\) −14.6305 −0.552981
\(701\) −10.3876 −0.392333 −0.196166 0.980571i \(-0.562849\pi\)
−0.196166 + 0.980571i \(0.562849\pi\)
\(702\) 3.79054 0.143065
\(703\) −16.8988 −0.637349
\(704\) 42.5418 1.60335
\(705\) 4.73173 0.178207
\(706\) −7.59584 −0.285873
\(707\) 44.0592 1.65701
\(708\) 3.77943 0.142040
\(709\) −7.12066 −0.267422 −0.133711 0.991020i \(-0.542689\pi\)
−0.133711 + 0.991020i \(0.542689\pi\)
\(710\) 11.4497 0.429699
\(711\) −16.2317 −0.608736
\(712\) 6.45882 0.242054
\(713\) −26.4086 −0.989010
\(714\) 3.46371 0.129626
\(715\) 24.5583 0.918428
\(716\) 15.2537 0.570058
\(717\) −15.1210 −0.564703
\(718\) 5.68947 0.212329
\(719\) 23.3538 0.870948 0.435474 0.900201i \(-0.356581\pi\)
0.435474 + 0.900201i \(0.356581\pi\)
\(720\) −0.850263 −0.0316874
\(721\) −19.7121 −0.734116
\(722\) 12.0188 0.447295
\(723\) −16.4242 −0.610822
\(724\) 4.27246 0.158785
\(725\) 30.0849 1.11733
\(726\) 28.4738 1.05676
\(727\) 23.5558 0.873636 0.436818 0.899550i \(-0.356105\pi\)
0.436818 + 0.899550i \(0.356105\pi\)
\(728\) −40.6669 −1.50722
\(729\) 1.00000 0.0370370
\(730\) 10.6694 0.394891
\(731\) −7.33861 −0.271428
\(732\) 7.55220 0.279137
\(733\) −17.3075 −0.639266 −0.319633 0.947541i \(-0.603560\pi\)
−0.319633 + 0.947541i \(0.603560\pi\)
\(734\) 8.85647 0.326898
\(735\) −5.49502 −0.202687
\(736\) −33.1057 −1.22029
\(737\) −41.8460 −1.54142
\(738\) 9.42935 0.347099
\(739\) 35.2270 1.29584 0.647922 0.761706i \(-0.275638\pi\)
0.647922 + 0.761706i \(0.275638\pi\)
\(740\) −6.78286 −0.249343
\(741\) 10.0378 0.368748
\(742\) 7.49681 0.275217
\(743\) 30.3847 1.11471 0.557353 0.830275i \(-0.311817\pi\)
0.557353 + 0.830275i \(0.311817\pi\)
\(744\) 12.1916 0.446965
\(745\) 7.89002 0.289068
\(746\) 1.13147 0.0414260
\(747\) −8.05337 −0.294657
\(748\) 6.56738 0.240127
\(749\) −30.9729 −1.13172
\(750\) −8.85724 −0.323421
\(751\) −22.9662 −0.838047 −0.419024 0.907975i \(-0.637628\pi\)
−0.419024 + 0.907975i \(0.637628\pi\)
\(752\) 3.98837 0.145441
\(753\) −7.14002 −0.260197
\(754\) 28.5719 1.04053
\(755\) −1.62156 −0.0590148
\(756\) −3.66564 −0.133318
\(757\) −52.4501 −1.90633 −0.953165 0.302451i \(-0.902195\pi\)
−0.953165 + 0.302451i \(0.902195\pi\)
\(758\) −17.8991 −0.650123
\(759\) −40.8373 −1.48230
\(760\) −7.77306 −0.281958
\(761\) 21.3685 0.774609 0.387304 0.921952i \(-0.373406\pi\)
0.387304 + 0.921952i \(0.373406\pi\)
\(762\) 7.08705 0.256737
\(763\) −30.7354 −1.11269
\(764\) 7.75988 0.280743
\(765\) −1.00436 −0.0363127
\(766\) 23.1401 0.836086
\(767\) 14.0716 0.508095
\(768\) 17.0408 0.614907
\(769\) 6.12609 0.220913 0.110456 0.993881i \(-0.464769\pi\)
0.110456 + 0.993881i \(0.464769\pi\)
\(770\) 22.0104 0.793199
\(771\) 9.05691 0.326177
\(772\) −2.67883 −0.0964131
\(773\) −6.32525 −0.227504 −0.113752 0.993509i \(-0.536287\pi\)
−0.113752 + 0.993509i \(0.536287\pi\)
\(774\) −7.19784 −0.258721
\(775\) 16.3303 0.586602
\(776\) 11.7478 0.421721
\(777\) 22.9764 0.824273
\(778\) −13.6065 −0.487818
\(779\) 24.9701 0.894647
\(780\) 4.02900 0.144261
\(781\) −73.5381 −2.63140
\(782\) 6.33067 0.226384
\(783\) 7.53770 0.269376
\(784\) −4.63174 −0.165419
\(785\) −1.00436 −0.0358471
\(786\) 14.9273 0.532440
\(787\) 26.4440 0.942626 0.471313 0.881966i \(-0.343780\pi\)
0.471313 + 0.881966i \(0.343780\pi\)
\(788\) 21.4187 0.763009
\(789\) −5.55816 −0.197876
\(790\) 15.9897 0.568889
\(791\) 31.5617 1.12221
\(792\) 18.8526 0.669899
\(793\) 28.1184 0.998512
\(794\) −19.4954 −0.691866
\(795\) −2.17382 −0.0770975
\(796\) 14.1341 0.500970
\(797\) −44.0474 −1.56024 −0.780119 0.625631i \(-0.784841\pi\)
−0.780119 + 0.625631i \(0.784841\pi\)
\(798\) 8.99640 0.318469
\(799\) 4.71120 0.166670
\(800\) 20.4716 0.723781
\(801\) 2.16759 0.0765881
\(802\) 22.6939 0.801351
\(803\) −68.5264 −2.41824
\(804\) −6.86520 −0.242117
\(805\) −22.8931 −0.806874
\(806\) 15.5091 0.546283
\(807\) −12.5220 −0.440794
\(808\) −37.1756 −1.30783
\(809\) −2.28286 −0.0802612 −0.0401306 0.999194i \(-0.512777\pi\)
−0.0401306 + 0.999194i \(0.512777\pi\)
\(810\) −0.985094 −0.0346127
\(811\) 30.9797 1.08784 0.543922 0.839136i \(-0.316939\pi\)
0.543922 + 0.839136i \(0.316939\pi\)
\(812\) −27.6305 −0.969639
\(813\) −2.37609 −0.0833332
\(814\) −40.3750 −1.41514
\(815\) −22.0883 −0.773721
\(816\) −0.846572 −0.0296360
\(817\) −19.0608 −0.666853
\(818\) −30.1157 −1.05297
\(819\) −13.6479 −0.476896
\(820\) 10.0226 0.350003
\(821\) 14.3457 0.500669 0.250334 0.968159i \(-0.419459\pi\)
0.250334 + 0.968159i \(0.419459\pi\)
\(822\) 17.1235 0.597252
\(823\) −17.0771 −0.595272 −0.297636 0.954679i \(-0.596198\pi\)
−0.297636 + 0.954679i \(0.596198\pi\)
\(824\) 16.6324 0.579416
\(825\) 25.2526 0.879184
\(826\) 12.6117 0.438816
\(827\) 17.7657 0.617774 0.308887 0.951099i \(-0.400043\pi\)
0.308887 + 0.951099i \(0.400043\pi\)
\(828\) −6.69972 −0.232831
\(829\) 54.5361 1.89412 0.947058 0.321063i \(-0.104040\pi\)
0.947058 + 0.321063i \(0.104040\pi\)
\(830\) 7.93332 0.275370
\(831\) 21.2558 0.737356
\(832\) 25.9855 0.900886
\(833\) −5.47117 −0.189565
\(834\) 22.6867 0.785576
\(835\) 0.0215076 0.000744300 0
\(836\) 17.0576 0.589951
\(837\) 4.09152 0.141424
\(838\) −26.9539 −0.931106
\(839\) −8.42316 −0.290800 −0.145400 0.989373i \(-0.546447\pi\)
−0.145400 + 0.989373i \(0.546447\pi\)
\(840\) 10.5686 0.364652
\(841\) 27.8170 0.959206
\(842\) 32.0375 1.10409
\(843\) 8.43216 0.290419
\(844\) 22.8495 0.786512
\(845\) 1.94411 0.0668793
\(846\) 4.62082 0.158867
\(847\) −102.520 −3.52264
\(848\) −1.83231 −0.0629217
\(849\) −5.80167 −0.199113
\(850\) −3.91470 −0.134273
\(851\) 41.9942 1.43954
\(852\) −12.0646 −0.413325
\(853\) −26.0950 −0.893476 −0.446738 0.894665i \(-0.647414\pi\)
−0.446738 + 0.894665i \(0.647414\pi\)
\(854\) 25.2011 0.862364
\(855\) −2.60865 −0.0892140
\(856\) 26.1339 0.893237
\(857\) −36.1183 −1.23378 −0.616889 0.787051i \(-0.711607\pi\)
−0.616889 + 0.787051i \(0.711607\pi\)
\(858\) 23.9826 0.818754
\(859\) −16.6305 −0.567425 −0.283712 0.958909i \(-0.591566\pi\)
−0.283712 + 0.958909i \(0.591566\pi\)
\(860\) −7.65066 −0.260885
\(861\) −33.9506 −1.15703
\(862\) 0.408859 0.0139258
\(863\) 25.9834 0.884485 0.442243 0.896895i \(-0.354183\pi\)
0.442243 + 0.896895i \(0.354183\pi\)
\(864\) 5.12911 0.174496
\(865\) 5.96132 0.202691
\(866\) −5.92554 −0.201358
\(867\) −1.00000 −0.0339618
\(868\) −14.9980 −0.509066
\(869\) −102.698 −3.48377
\(870\) −7.42535 −0.251743
\(871\) −25.5605 −0.866085
\(872\) 25.9335 0.878218
\(873\) 3.94258 0.133436
\(874\) 16.4428 0.556187
\(875\) 31.8907 1.07810
\(876\) −11.2424 −0.379844
\(877\) 3.16815 0.106981 0.0534904 0.998568i \(-0.482965\pi\)
0.0534904 + 0.998568i \(0.482965\pi\)
\(878\) 5.68550 0.191876
\(879\) 25.3292 0.854333
\(880\) −5.37960 −0.181346
\(881\) −42.5202 −1.43254 −0.716271 0.697822i \(-0.754153\pi\)
−0.716271 + 0.697822i \(0.754153\pi\)
\(882\) −5.36622 −0.180690
\(883\) −37.8272 −1.27299 −0.636493 0.771283i \(-0.719616\pi\)
−0.636493 + 0.771283i \(0.719616\pi\)
\(884\) 4.01151 0.134922
\(885\) −3.65695 −0.122927
\(886\) 17.9724 0.603796
\(887\) 1.25871 0.0422633 0.0211317 0.999777i \(-0.493273\pi\)
0.0211317 + 0.999777i \(0.493273\pi\)
\(888\) −19.3867 −0.650575
\(889\) −25.5171 −0.855815
\(890\) −2.13528 −0.0715748
\(891\) 6.32698 0.211962
\(892\) −18.2744 −0.611872
\(893\) 12.2365 0.409480
\(894\) 7.70508 0.257696
\(895\) −14.7594 −0.493353
\(896\) −12.9369 −0.432191
\(897\) −24.9444 −0.832870
\(898\) 30.0645 1.00326
\(899\) 30.8406 1.02859
\(900\) 4.14291 0.138097
\(901\) −2.16439 −0.0721061
\(902\) 59.6593 1.98644
\(903\) 25.9160 0.862429
\(904\) −26.6307 −0.885725
\(905\) −4.13401 −0.137419
\(906\) −1.58356 −0.0526101
\(907\) 0.600796 0.0199491 0.00997455 0.999950i \(-0.496825\pi\)
0.00997455 + 0.999950i \(0.496825\pi\)
\(908\) 21.9881 0.729702
\(909\) −12.4762 −0.413810
\(910\) 13.4445 0.445680
\(911\) 45.7317 1.51516 0.757580 0.652743i \(-0.226382\pi\)
0.757580 + 0.652743i \(0.226382\pi\)
\(912\) −2.19883 −0.0728104
\(913\) −50.9535 −1.68631
\(914\) 40.2028 1.32979
\(915\) −7.30747 −0.241577
\(916\) 19.4217 0.641710
\(917\) −53.7461 −1.77485
\(918\) −0.980818 −0.0323718
\(919\) 8.86669 0.292485 0.146243 0.989249i \(-0.453282\pi\)
0.146243 + 0.989249i \(0.453282\pi\)
\(920\) 19.3164 0.636842
\(921\) 8.84271 0.291377
\(922\) −29.3699 −0.967246
\(923\) −44.9188 −1.47852
\(924\) −23.1924 −0.762974
\(925\) −25.9680 −0.853822
\(926\) 1.01330 0.0332990
\(927\) 5.58186 0.183332
\(928\) 38.6617 1.26913
\(929\) 14.2950 0.469004 0.234502 0.972116i \(-0.424654\pi\)
0.234502 + 0.972116i \(0.424654\pi\)
\(930\) −4.03053 −0.132166
\(931\) −14.2104 −0.465728
\(932\) 1.40916 0.0461586
\(933\) −11.1415 −0.364756
\(934\) 29.2944 0.958541
\(935\) −6.35456 −0.207816
\(936\) 11.5156 0.376400
\(937\) 10.1695 0.332222 0.166111 0.986107i \(-0.446879\pi\)
0.166111 + 0.986107i \(0.446879\pi\)
\(938\) −22.9086 −0.747994
\(939\) 17.4045 0.567974
\(940\) 4.91152 0.160196
\(941\) 53.2669 1.73645 0.868225 0.496170i \(-0.165261\pi\)
0.868225 + 0.496170i \(0.165261\pi\)
\(942\) −0.980818 −0.0319568
\(943\) −62.0518 −2.02068
\(944\) −3.08244 −0.100325
\(945\) 3.54685 0.115379
\(946\) −45.5406 −1.48065
\(947\) −6.12953 −0.199183 −0.0995915 0.995028i \(-0.531754\pi\)
−0.0995915 + 0.995028i \(0.531754\pi\)
\(948\) −16.8484 −0.547211
\(949\) −41.8575 −1.35875
\(950\) −10.1678 −0.329886
\(951\) −30.5137 −0.989474
\(952\) 10.5227 0.341044
\(953\) 20.2026 0.654426 0.327213 0.944951i \(-0.393890\pi\)
0.327213 + 0.944951i \(0.393890\pi\)
\(954\) −2.12287 −0.0687304
\(955\) −7.50842 −0.242967
\(956\) −15.6955 −0.507629
\(957\) 47.6909 1.54163
\(958\) −18.0038 −0.581675
\(959\) −61.6536 −1.99090
\(960\) −6.75318 −0.217958
\(961\) −14.2595 −0.459983
\(962\) −24.6620 −0.795136
\(963\) 8.77058 0.282628
\(964\) −17.0482 −0.549087
\(965\) 2.59202 0.0834401
\(966\) −22.3565 −0.719307
\(967\) 51.5095 1.65644 0.828218 0.560407i \(-0.189355\pi\)
0.828218 + 0.560407i \(0.189355\pi\)
\(968\) 86.5033 2.78032
\(969\) −2.59733 −0.0834382
\(970\) −3.88381 −0.124702
\(971\) 4.84236 0.155399 0.0776993 0.996977i \(-0.475243\pi\)
0.0776993 + 0.996977i \(0.475243\pi\)
\(972\) 1.03800 0.0332937
\(973\) −81.6839 −2.61866
\(974\) −6.38138 −0.204473
\(975\) 15.4249 0.493992
\(976\) −6.15945 −0.197159
\(977\) 8.04118 0.257260 0.128630 0.991693i \(-0.458942\pi\)
0.128630 + 0.991693i \(0.458942\pi\)
\(978\) −21.5706 −0.689752
\(979\) 13.7143 0.438311
\(980\) −5.70381 −0.182201
\(981\) 8.70332 0.277875
\(982\) 34.2033 1.09147
\(983\) 58.1175 1.85366 0.926830 0.375481i \(-0.122523\pi\)
0.926830 + 0.375481i \(0.122523\pi\)
\(984\) 28.6463 0.913212
\(985\) −20.7246 −0.660341
\(986\) −7.39311 −0.235445
\(987\) −16.6374 −0.529573
\(988\) 10.4192 0.331479
\(989\) 47.3669 1.50618
\(990\) −6.23267 −0.198087
\(991\) −53.8212 −1.70969 −0.854843 0.518887i \(-0.826347\pi\)
−0.854843 + 0.518887i \(0.826347\pi\)
\(992\) 20.9858 0.666301
\(993\) −18.7043 −0.593562
\(994\) −40.2585 −1.27692
\(995\) −13.6761 −0.433561
\(996\) −8.35936 −0.264877
\(997\) −46.4864 −1.47224 −0.736119 0.676852i \(-0.763344\pi\)
−0.736119 + 0.676852i \(0.763344\pi\)
\(998\) −30.6027 −0.968712
\(999\) −6.50621 −0.205847
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8007.2.a.f.1.17 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.17 48 1.1 even 1 trivial