Properties

Label 8007.2.a.f.1.44
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 1.44
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.38551 q^{2} -1.00000 q^{3} +3.69065 q^{4} -1.70497 q^{5} -2.38551 q^{6} +3.54946 q^{7} +4.03306 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.38551 q^{2} -1.00000 q^{3} +3.69065 q^{4} -1.70497 q^{5} -2.38551 q^{6} +3.54946 q^{7} +4.03306 q^{8} +1.00000 q^{9} -4.06723 q^{10} +1.77305 q^{11} -3.69065 q^{12} -3.57101 q^{13} +8.46726 q^{14} +1.70497 q^{15} +2.23960 q^{16} -1.00000 q^{17} +2.38551 q^{18} -2.97373 q^{19} -6.29246 q^{20} -3.54946 q^{21} +4.22961 q^{22} -9.54123 q^{23} -4.03306 q^{24} -2.09307 q^{25} -8.51867 q^{26} -1.00000 q^{27} +13.0998 q^{28} -2.09288 q^{29} +4.06723 q^{30} +3.69825 q^{31} -2.72353 q^{32} -1.77305 q^{33} -2.38551 q^{34} -6.05173 q^{35} +3.69065 q^{36} -3.61193 q^{37} -7.09385 q^{38} +3.57101 q^{39} -6.87626 q^{40} -1.21726 q^{41} -8.46726 q^{42} -2.45179 q^{43} +6.54369 q^{44} -1.70497 q^{45} -22.7607 q^{46} -5.08516 q^{47} -2.23960 q^{48} +5.59865 q^{49} -4.99303 q^{50} +1.00000 q^{51} -13.1793 q^{52} +3.39762 q^{53} -2.38551 q^{54} -3.02299 q^{55} +14.3152 q^{56} +2.97373 q^{57} -4.99259 q^{58} -1.11134 q^{59} +6.29246 q^{60} +4.38285 q^{61} +8.82221 q^{62} +3.54946 q^{63} -10.9762 q^{64} +6.08847 q^{65} -4.22961 q^{66} -7.67085 q^{67} -3.69065 q^{68} +9.54123 q^{69} -14.4364 q^{70} +1.07669 q^{71} +4.03306 q^{72} -8.02295 q^{73} -8.61628 q^{74} +2.09307 q^{75} -10.9750 q^{76} +6.29335 q^{77} +8.51867 q^{78} +0.700468 q^{79} -3.81846 q^{80} +1.00000 q^{81} -2.90379 q^{82} +8.64683 q^{83} -13.0998 q^{84} +1.70497 q^{85} -5.84878 q^{86} +2.09288 q^{87} +7.15080 q^{88} +8.82373 q^{89} -4.06723 q^{90} -12.6751 q^{91} -35.2133 q^{92} -3.69825 q^{93} -12.1307 q^{94} +5.07012 q^{95} +2.72353 q^{96} -19.2592 q^{97} +13.3556 q^{98} +1.77305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.38551 1.68681 0.843405 0.537279i \(-0.180548\pi\)
0.843405 + 0.537279i \(0.180548\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.69065 1.84533
\(5\) −1.70497 −0.762487 −0.381243 0.924475i \(-0.624504\pi\)
−0.381243 + 0.924475i \(0.624504\pi\)
\(6\) −2.38551 −0.973880
\(7\) 3.54946 1.34157 0.670784 0.741652i \(-0.265958\pi\)
0.670784 + 0.741652i \(0.265958\pi\)
\(8\) 4.03306 1.42590
\(9\) 1.00000 0.333333
\(10\) −4.06723 −1.28617
\(11\) 1.77305 0.534593 0.267297 0.963614i \(-0.413870\pi\)
0.267297 + 0.963614i \(0.413870\pi\)
\(12\) −3.69065 −1.06540
\(13\) −3.57101 −0.990419 −0.495210 0.868773i \(-0.664909\pi\)
−0.495210 + 0.868773i \(0.664909\pi\)
\(14\) 8.46726 2.26297
\(15\) 1.70497 0.440222
\(16\) 2.23960 0.559901
\(17\) −1.00000 −0.242536
\(18\) 2.38551 0.562270
\(19\) −2.97373 −0.682220 −0.341110 0.940023i \(-0.610803\pi\)
−0.341110 + 0.940023i \(0.610803\pi\)
\(20\) −6.29246 −1.40704
\(21\) −3.54946 −0.774555
\(22\) 4.22961 0.901757
\(23\) −9.54123 −1.98948 −0.994742 0.102417i \(-0.967342\pi\)
−0.994742 + 0.102417i \(0.967342\pi\)
\(24\) −4.03306 −0.823245
\(25\) −2.09307 −0.418614
\(26\) −8.51867 −1.67065
\(27\) −1.00000 −0.192450
\(28\) 13.0998 2.47563
\(29\) −2.09288 −0.388639 −0.194319 0.980938i \(-0.562250\pi\)
−0.194319 + 0.980938i \(0.562250\pi\)
\(30\) 4.06723 0.742570
\(31\) 3.69825 0.664226 0.332113 0.943240i \(-0.392239\pi\)
0.332113 + 0.943240i \(0.392239\pi\)
\(32\) −2.72353 −0.481457
\(33\) −1.77305 −0.308648
\(34\) −2.38551 −0.409111
\(35\) −6.05173 −1.02293
\(36\) 3.69065 0.615108
\(37\) −3.61193 −0.593797 −0.296898 0.954909i \(-0.595952\pi\)
−0.296898 + 0.954909i \(0.595952\pi\)
\(38\) −7.09385 −1.15077
\(39\) 3.57101 0.571819
\(40\) −6.87626 −1.08723
\(41\) −1.21726 −0.190105 −0.0950523 0.995472i \(-0.530302\pi\)
−0.0950523 + 0.995472i \(0.530302\pi\)
\(42\) −8.46726 −1.30653
\(43\) −2.45179 −0.373895 −0.186948 0.982370i \(-0.559859\pi\)
−0.186948 + 0.982370i \(0.559859\pi\)
\(44\) 6.54369 0.986499
\(45\) −1.70497 −0.254162
\(46\) −22.7607 −3.35588
\(47\) −5.08516 −0.741747 −0.370873 0.928683i \(-0.620942\pi\)
−0.370873 + 0.928683i \(0.620942\pi\)
\(48\) −2.23960 −0.323259
\(49\) 5.59865 0.799807
\(50\) −4.99303 −0.706122
\(51\) 1.00000 0.140028
\(52\) −13.1793 −1.82765
\(53\) 3.39762 0.466699 0.233349 0.972393i \(-0.425031\pi\)
0.233349 + 0.972393i \(0.425031\pi\)
\(54\) −2.38551 −0.324627
\(55\) −3.02299 −0.407620
\(56\) 14.3152 1.91295
\(57\) 2.97373 0.393880
\(58\) −4.99259 −0.655560
\(59\) −1.11134 −0.144685 −0.0723423 0.997380i \(-0.523047\pi\)
−0.0723423 + 0.997380i \(0.523047\pi\)
\(60\) 6.29246 0.812353
\(61\) 4.38285 0.561167 0.280583 0.959830i \(-0.409472\pi\)
0.280583 + 0.959830i \(0.409472\pi\)
\(62\) 8.82221 1.12042
\(63\) 3.54946 0.447190
\(64\) −10.9762 −1.37203
\(65\) 6.08847 0.755182
\(66\) −4.22961 −0.520630
\(67\) −7.67085 −0.937144 −0.468572 0.883425i \(-0.655231\pi\)
−0.468572 + 0.883425i \(0.655231\pi\)
\(68\) −3.69065 −0.447557
\(69\) 9.54123 1.14863
\(70\) −14.4364 −1.72549
\(71\) 1.07669 0.127779 0.0638895 0.997957i \(-0.479649\pi\)
0.0638895 + 0.997957i \(0.479649\pi\)
\(72\) 4.03306 0.475301
\(73\) −8.02295 −0.939015 −0.469508 0.882928i \(-0.655569\pi\)
−0.469508 + 0.882928i \(0.655569\pi\)
\(74\) −8.61628 −1.00162
\(75\) 2.09307 0.241687
\(76\) −10.9750 −1.25892
\(77\) 6.29335 0.717194
\(78\) 8.51867 0.964549
\(79\) 0.700468 0.0788088 0.0394044 0.999223i \(-0.487454\pi\)
0.0394044 + 0.999223i \(0.487454\pi\)
\(80\) −3.81846 −0.426917
\(81\) 1.00000 0.111111
\(82\) −2.90379 −0.320670
\(83\) 8.64683 0.949113 0.474557 0.880225i \(-0.342608\pi\)
0.474557 + 0.880225i \(0.342608\pi\)
\(84\) −13.0998 −1.42931
\(85\) 1.70497 0.184930
\(86\) −5.84878 −0.630690
\(87\) 2.09288 0.224381
\(88\) 7.15080 0.762278
\(89\) 8.82373 0.935314 0.467657 0.883910i \(-0.345098\pi\)
0.467657 + 0.883910i \(0.345098\pi\)
\(90\) −4.06723 −0.428723
\(91\) −12.6751 −1.32872
\(92\) −35.2133 −3.67124
\(93\) −3.69825 −0.383491
\(94\) −12.1307 −1.25119
\(95\) 5.07012 0.520183
\(96\) 2.72353 0.277970
\(97\) −19.2592 −1.95548 −0.977738 0.209831i \(-0.932709\pi\)
−0.977738 + 0.209831i \(0.932709\pi\)
\(98\) 13.3556 1.34912
\(99\) 1.77305 0.178198
\(100\) −7.72479 −0.772479
\(101\) −5.15830 −0.513270 −0.256635 0.966508i \(-0.582614\pi\)
−0.256635 + 0.966508i \(0.582614\pi\)
\(102\) 2.38551 0.236201
\(103\) 18.7119 1.84374 0.921870 0.387500i \(-0.126661\pi\)
0.921870 + 0.387500i \(0.126661\pi\)
\(104\) −14.4021 −1.41224
\(105\) 6.05173 0.590588
\(106\) 8.10505 0.787232
\(107\) −6.27139 −0.606278 −0.303139 0.952946i \(-0.598035\pi\)
−0.303139 + 0.952946i \(0.598035\pi\)
\(108\) −3.69065 −0.355133
\(109\) −20.0664 −1.92201 −0.961006 0.276529i \(-0.910816\pi\)
−0.961006 + 0.276529i \(0.910816\pi\)
\(110\) −7.21138 −0.687578
\(111\) 3.61193 0.342829
\(112\) 7.94937 0.751145
\(113\) 17.2022 1.61825 0.809125 0.587636i \(-0.199941\pi\)
0.809125 + 0.587636i \(0.199941\pi\)
\(114\) 7.09385 0.664400
\(115\) 16.2675 1.51695
\(116\) −7.72411 −0.717165
\(117\) −3.57101 −0.330140
\(118\) −2.65112 −0.244055
\(119\) −3.54946 −0.325378
\(120\) 6.87626 0.627714
\(121\) −7.85631 −0.714210
\(122\) 10.4553 0.946581
\(123\) 1.21726 0.109757
\(124\) 13.6490 1.22571
\(125\) 12.0935 1.08167
\(126\) 8.46726 0.754324
\(127\) −1.55436 −0.137927 −0.0689637 0.997619i \(-0.521969\pi\)
−0.0689637 + 0.997619i \(0.521969\pi\)
\(128\) −20.7368 −1.83289
\(129\) 2.45179 0.215868
\(130\) 14.5241 1.27385
\(131\) 13.3128 1.16315 0.581574 0.813494i \(-0.302437\pi\)
0.581574 + 0.813494i \(0.302437\pi\)
\(132\) −6.54369 −0.569555
\(133\) −10.5551 −0.915245
\(134\) −18.2989 −1.58078
\(135\) 1.70497 0.146741
\(136\) −4.03306 −0.345832
\(137\) 10.3314 0.882670 0.441335 0.897342i \(-0.354505\pi\)
0.441335 + 0.897342i \(0.354505\pi\)
\(138\) 22.7607 1.93752
\(139\) 16.3890 1.39010 0.695049 0.718962i \(-0.255383\pi\)
0.695049 + 0.718962i \(0.255383\pi\)
\(140\) −22.3348 −1.88764
\(141\) 5.08516 0.428248
\(142\) 2.56844 0.215539
\(143\) −6.33156 −0.529472
\(144\) 2.23960 0.186634
\(145\) 3.56831 0.296332
\(146\) −19.1388 −1.58394
\(147\) −5.59865 −0.461769
\(148\) −13.3304 −1.09575
\(149\) 4.58577 0.375681 0.187840 0.982200i \(-0.439851\pi\)
0.187840 + 0.982200i \(0.439851\pi\)
\(150\) 4.99303 0.407680
\(151\) −14.6053 −1.18856 −0.594280 0.804258i \(-0.702563\pi\)
−0.594280 + 0.804258i \(0.702563\pi\)
\(152\) −11.9932 −0.972779
\(153\) −1.00000 −0.0808452
\(154\) 15.0128 1.20977
\(155\) −6.30542 −0.506463
\(156\) 13.1793 1.05519
\(157\) −1.00000 −0.0798087
\(158\) 1.67097 0.132935
\(159\) −3.39762 −0.269449
\(160\) 4.64355 0.367105
\(161\) −33.8662 −2.66903
\(162\) 2.38551 0.187423
\(163\) 5.03718 0.394542 0.197271 0.980349i \(-0.436792\pi\)
0.197271 + 0.980349i \(0.436792\pi\)
\(164\) −4.49249 −0.350805
\(165\) 3.02299 0.235340
\(166\) 20.6271 1.60097
\(167\) −13.9889 −1.08249 −0.541247 0.840863i \(-0.682048\pi\)
−0.541247 + 0.840863i \(0.682048\pi\)
\(168\) −14.3152 −1.10444
\(169\) −0.247902 −0.0190694
\(170\) 4.06723 0.311942
\(171\) −2.97373 −0.227407
\(172\) −9.04872 −0.689958
\(173\) 9.10778 0.692452 0.346226 0.938151i \(-0.387463\pi\)
0.346226 + 0.938151i \(0.387463\pi\)
\(174\) 4.99259 0.378488
\(175\) −7.42926 −0.561599
\(176\) 3.97092 0.299319
\(177\) 1.11134 0.0835337
\(178\) 21.0491 1.57770
\(179\) 13.0024 0.971845 0.485922 0.874002i \(-0.338484\pi\)
0.485922 + 0.874002i \(0.338484\pi\)
\(180\) −6.29246 −0.469012
\(181\) −4.06356 −0.302042 −0.151021 0.988531i \(-0.548256\pi\)
−0.151021 + 0.988531i \(0.548256\pi\)
\(182\) −30.2367 −2.24129
\(183\) −4.38285 −0.323990
\(184\) −38.4804 −2.83681
\(185\) 6.15823 0.452762
\(186\) −8.82221 −0.646876
\(187\) −1.77305 −0.129658
\(188\) −18.7675 −1.36876
\(189\) −3.54946 −0.258185
\(190\) 12.0948 0.877450
\(191\) −16.1191 −1.16634 −0.583168 0.812351i \(-0.698187\pi\)
−0.583168 + 0.812351i \(0.698187\pi\)
\(192\) 10.9762 0.792140
\(193\) −13.1424 −0.946008 −0.473004 0.881060i \(-0.656830\pi\)
−0.473004 + 0.881060i \(0.656830\pi\)
\(194\) −45.9430 −3.29851
\(195\) −6.08847 −0.436004
\(196\) 20.6627 1.47590
\(197\) 15.3852 1.09615 0.548075 0.836429i \(-0.315361\pi\)
0.548075 + 0.836429i \(0.315361\pi\)
\(198\) 4.22961 0.300586
\(199\) −15.5015 −1.09888 −0.549438 0.835535i \(-0.685158\pi\)
−0.549438 + 0.835535i \(0.685158\pi\)
\(200\) −8.44148 −0.596903
\(201\) 7.67085 0.541060
\(202\) −12.3052 −0.865788
\(203\) −7.42860 −0.521386
\(204\) 3.69065 0.258397
\(205\) 2.07540 0.144952
\(206\) 44.6374 3.11004
\(207\) −9.54123 −0.663161
\(208\) −7.99764 −0.554536
\(209\) −5.27255 −0.364710
\(210\) 14.4364 0.996209
\(211\) −3.80749 −0.262119 −0.131059 0.991375i \(-0.541838\pi\)
−0.131059 + 0.991375i \(0.541838\pi\)
\(212\) 12.5394 0.861211
\(213\) −1.07669 −0.0737733
\(214\) −14.9605 −1.02268
\(215\) 4.18024 0.285090
\(216\) −4.03306 −0.274415
\(217\) 13.1268 0.891104
\(218\) −47.8685 −3.24207
\(219\) 8.02295 0.542141
\(220\) −11.1568 −0.752192
\(221\) 3.57101 0.240212
\(222\) 8.61628 0.578287
\(223\) 21.5201 1.44109 0.720547 0.693406i \(-0.243891\pi\)
0.720547 + 0.693406i \(0.243891\pi\)
\(224\) −9.66707 −0.645908
\(225\) −2.09307 −0.139538
\(226\) 41.0361 2.72968
\(227\) −12.1500 −0.806423 −0.403212 0.915107i \(-0.632106\pi\)
−0.403212 + 0.915107i \(0.632106\pi\)
\(228\) 10.9750 0.726836
\(229\) 29.2181 1.93078 0.965392 0.260804i \(-0.0839875\pi\)
0.965392 + 0.260804i \(0.0839875\pi\)
\(230\) 38.8063 2.55881
\(231\) −6.29335 −0.414072
\(232\) −8.44073 −0.554161
\(233\) −16.9434 −1.11000 −0.554999 0.831851i \(-0.687281\pi\)
−0.554999 + 0.831851i \(0.687281\pi\)
\(234\) −8.51867 −0.556883
\(235\) 8.67006 0.565572
\(236\) −4.10158 −0.266990
\(237\) −0.700468 −0.0455003
\(238\) −8.46726 −0.548851
\(239\) −24.3448 −1.57474 −0.787368 0.616483i \(-0.788557\pi\)
−0.787368 + 0.616483i \(0.788557\pi\)
\(240\) 3.81846 0.246480
\(241\) 2.56042 0.164931 0.0824657 0.996594i \(-0.473720\pi\)
0.0824657 + 0.996594i \(0.473720\pi\)
\(242\) −18.7413 −1.20474
\(243\) −1.00000 −0.0641500
\(244\) 16.1756 1.03553
\(245\) −9.54554 −0.609842
\(246\) 2.90379 0.185139
\(247\) 10.6192 0.675684
\(248\) 14.9153 0.947121
\(249\) −8.64683 −0.547971
\(250\) 28.8491 1.82458
\(251\) −18.2472 −1.15175 −0.575876 0.817537i \(-0.695339\pi\)
−0.575876 + 0.817537i \(0.695339\pi\)
\(252\) 13.0998 0.825210
\(253\) −16.9170 −1.06356
\(254\) −3.70795 −0.232657
\(255\) −1.70497 −0.106770
\(256\) −27.5154 −1.71971
\(257\) 6.42815 0.400977 0.200488 0.979696i \(-0.435747\pi\)
0.200488 + 0.979696i \(0.435747\pi\)
\(258\) 5.84878 0.364129
\(259\) −12.8204 −0.796619
\(260\) 22.4704 1.39356
\(261\) −2.09288 −0.129546
\(262\) 31.7579 1.96201
\(263\) 10.3439 0.637830 0.318915 0.947783i \(-0.396682\pi\)
0.318915 + 0.947783i \(0.396682\pi\)
\(264\) −7.15080 −0.440101
\(265\) −5.79285 −0.355852
\(266\) −25.1793 −1.54384
\(267\) −8.82373 −0.540004
\(268\) −28.3104 −1.72934
\(269\) 3.22110 0.196394 0.0981970 0.995167i \(-0.468692\pi\)
0.0981970 + 0.995167i \(0.468692\pi\)
\(270\) 4.06723 0.247523
\(271\) 8.40771 0.510732 0.255366 0.966844i \(-0.417804\pi\)
0.255366 + 0.966844i \(0.417804\pi\)
\(272\) −2.23960 −0.135796
\(273\) 12.6751 0.767134
\(274\) 24.6456 1.48890
\(275\) −3.71111 −0.223788
\(276\) 35.2133 2.11959
\(277\) −20.6339 −1.23977 −0.619885 0.784693i \(-0.712821\pi\)
−0.619885 + 0.784693i \(0.712821\pi\)
\(278\) 39.0961 2.34483
\(279\) 3.69825 0.221409
\(280\) −24.4070 −1.45860
\(281\) 16.6593 0.993812 0.496906 0.867804i \(-0.334469\pi\)
0.496906 + 0.867804i \(0.334469\pi\)
\(282\) 12.1307 0.722372
\(283\) −7.82793 −0.465322 −0.232661 0.972558i \(-0.574743\pi\)
−0.232661 + 0.972558i \(0.574743\pi\)
\(284\) 3.97367 0.235794
\(285\) −5.07012 −0.300328
\(286\) −15.1040 −0.893118
\(287\) −4.32062 −0.255038
\(288\) −2.72353 −0.160486
\(289\) 1.00000 0.0588235
\(290\) 8.51223 0.499856
\(291\) 19.2592 1.12899
\(292\) −29.6099 −1.73279
\(293\) 4.88097 0.285149 0.142575 0.989784i \(-0.454462\pi\)
0.142575 + 0.989784i \(0.454462\pi\)
\(294\) −13.3556 −0.778916
\(295\) 1.89481 0.110320
\(296\) −14.5671 −0.846697
\(297\) −1.77305 −0.102883
\(298\) 10.9394 0.633702
\(299\) 34.0718 1.97042
\(300\) 7.72479 0.445991
\(301\) −8.70254 −0.501606
\(302\) −34.8410 −2.00488
\(303\) 5.15830 0.296336
\(304\) −6.65996 −0.381975
\(305\) −7.47264 −0.427882
\(306\) −2.38551 −0.136370
\(307\) −10.3444 −0.590389 −0.295194 0.955437i \(-0.595384\pi\)
−0.295194 + 0.955437i \(0.595384\pi\)
\(308\) 23.2266 1.32346
\(309\) −18.7119 −1.06448
\(310\) −15.0416 −0.854307
\(311\) 12.0298 0.682146 0.341073 0.940037i \(-0.389210\pi\)
0.341073 + 0.940037i \(0.389210\pi\)
\(312\) 14.4021 0.815358
\(313\) −21.9162 −1.23878 −0.619389 0.785085i \(-0.712619\pi\)
−0.619389 + 0.785085i \(0.712619\pi\)
\(314\) −2.38551 −0.134622
\(315\) −6.05173 −0.340976
\(316\) 2.58518 0.145428
\(317\) −14.7341 −0.827547 −0.413773 0.910380i \(-0.635789\pi\)
−0.413773 + 0.910380i \(0.635789\pi\)
\(318\) −8.10505 −0.454509
\(319\) −3.71078 −0.207764
\(320\) 18.7141 1.04615
\(321\) 6.27139 0.350035
\(322\) −80.7880 −4.50214
\(323\) 2.97373 0.165463
\(324\) 3.69065 0.205036
\(325\) 7.47437 0.414603
\(326\) 12.0162 0.665518
\(327\) 20.0664 1.10967
\(328\) −4.90930 −0.271071
\(329\) −18.0496 −0.995104
\(330\) 7.21138 0.396973
\(331\) −17.9044 −0.984116 −0.492058 0.870562i \(-0.663755\pi\)
−0.492058 + 0.870562i \(0.663755\pi\)
\(332\) 31.9124 1.75142
\(333\) −3.61193 −0.197932
\(334\) −33.3707 −1.82596
\(335\) 13.0786 0.714560
\(336\) −7.94937 −0.433674
\(337\) −4.44466 −0.242116 −0.121058 0.992645i \(-0.538629\pi\)
−0.121058 + 0.992645i \(0.538629\pi\)
\(338\) −0.591373 −0.0321665
\(339\) −17.2022 −0.934297
\(340\) 6.29246 0.341256
\(341\) 6.55717 0.355091
\(342\) −7.09385 −0.383591
\(343\) −4.97404 −0.268573
\(344\) −9.88824 −0.533138
\(345\) −16.2675 −0.875814
\(346\) 21.7267 1.16803
\(347\) −23.1104 −1.24063 −0.620316 0.784352i \(-0.712996\pi\)
−0.620316 + 0.784352i \(0.712996\pi\)
\(348\) 7.72411 0.414056
\(349\) 3.77827 0.202246 0.101123 0.994874i \(-0.467756\pi\)
0.101123 + 0.994874i \(0.467756\pi\)
\(350\) −17.7226 −0.947311
\(351\) 3.57101 0.190606
\(352\) −4.82895 −0.257384
\(353\) −10.2795 −0.547123 −0.273561 0.961855i \(-0.588202\pi\)
−0.273561 + 0.961855i \(0.588202\pi\)
\(354\) 2.65112 0.140905
\(355\) −1.83572 −0.0974299
\(356\) 32.5653 1.72596
\(357\) 3.54946 0.187857
\(358\) 31.0173 1.63932
\(359\) −20.0306 −1.05717 −0.528587 0.848879i \(-0.677278\pi\)
−0.528587 + 0.848879i \(0.677278\pi\)
\(360\) −6.87626 −0.362411
\(361\) −10.1570 −0.534576
\(362\) −9.69367 −0.509488
\(363\) 7.85631 0.412349
\(364\) −46.7795 −2.45191
\(365\) 13.6789 0.715987
\(366\) −10.4553 −0.546509
\(367\) −11.1774 −0.583456 −0.291728 0.956501i \(-0.594230\pi\)
−0.291728 + 0.956501i \(0.594230\pi\)
\(368\) −21.3685 −1.11391
\(369\) −1.21726 −0.0633682
\(370\) 14.6905 0.763724
\(371\) 12.0597 0.626109
\(372\) −13.6490 −0.707665
\(373\) 17.3225 0.896923 0.448462 0.893802i \(-0.351972\pi\)
0.448462 + 0.893802i \(0.351972\pi\)
\(374\) −4.22961 −0.218708
\(375\) −12.0935 −0.624505
\(376\) −20.5088 −1.05766
\(377\) 7.47371 0.384916
\(378\) −8.46726 −0.435509
\(379\) −2.96921 −0.152518 −0.0762590 0.997088i \(-0.524298\pi\)
−0.0762590 + 0.997088i \(0.524298\pi\)
\(380\) 18.7120 0.959908
\(381\) 1.55436 0.0796325
\(382\) −38.4522 −1.96739
\(383\) −9.07459 −0.463690 −0.231845 0.972753i \(-0.574476\pi\)
−0.231845 + 0.972753i \(0.574476\pi\)
\(384\) 20.7368 1.05822
\(385\) −10.7300 −0.546851
\(386\) −31.3512 −1.59574
\(387\) −2.45179 −0.124632
\(388\) −71.0790 −3.60849
\(389\) 27.0056 1.36924 0.684619 0.728901i \(-0.259969\pi\)
0.684619 + 0.728901i \(0.259969\pi\)
\(390\) −14.5241 −0.735456
\(391\) 9.54123 0.482521
\(392\) 22.5797 1.14045
\(393\) −13.3128 −0.671543
\(394\) 36.7015 1.84899
\(395\) −1.19428 −0.0600907
\(396\) 6.54369 0.328833
\(397\) 8.15106 0.409090 0.204545 0.978857i \(-0.434428\pi\)
0.204545 + 0.978857i \(0.434428\pi\)
\(398\) −36.9791 −1.85359
\(399\) 10.5551 0.528417
\(400\) −4.68764 −0.234382
\(401\) 4.37982 0.218718 0.109359 0.994002i \(-0.465120\pi\)
0.109359 + 0.994002i \(0.465120\pi\)
\(402\) 18.2989 0.912665
\(403\) −13.2065 −0.657862
\(404\) −19.0375 −0.947149
\(405\) −1.70497 −0.0847208
\(406\) −17.7210 −0.879478
\(407\) −6.40411 −0.317440
\(408\) 4.03306 0.199666
\(409\) 13.1244 0.648958 0.324479 0.945893i \(-0.394811\pi\)
0.324479 + 0.945893i \(0.394811\pi\)
\(410\) 4.95088 0.244507
\(411\) −10.3314 −0.509610
\(412\) 69.0591 3.40230
\(413\) −3.94467 −0.194104
\(414\) −22.7607 −1.11863
\(415\) −14.7426 −0.723686
\(416\) 9.72576 0.476845
\(417\) −16.3890 −0.802574
\(418\) −12.5777 −0.615196
\(419\) 22.2969 1.08927 0.544637 0.838672i \(-0.316667\pi\)
0.544637 + 0.838672i \(0.316667\pi\)
\(420\) 22.3348 1.08983
\(421\) 15.3130 0.746308 0.373154 0.927769i \(-0.378276\pi\)
0.373154 + 0.927769i \(0.378276\pi\)
\(422\) −9.08281 −0.442144
\(423\) −5.08516 −0.247249
\(424\) 13.7028 0.665467
\(425\) 2.09307 0.101529
\(426\) −2.56844 −0.124441
\(427\) 15.5567 0.752843
\(428\) −23.1455 −1.11878
\(429\) 6.33156 0.305691
\(430\) 9.97200 0.480893
\(431\) 8.59089 0.413809 0.206904 0.978361i \(-0.433661\pi\)
0.206904 + 0.978361i \(0.433661\pi\)
\(432\) −2.23960 −0.107753
\(433\) −27.5537 −1.32415 −0.662073 0.749439i \(-0.730323\pi\)
−0.662073 + 0.749439i \(0.730323\pi\)
\(434\) 31.3141 1.50312
\(435\) −3.56831 −0.171087
\(436\) −74.0580 −3.54674
\(437\) 28.3730 1.35726
\(438\) 19.1388 0.914488
\(439\) −17.7187 −0.845670 −0.422835 0.906207i \(-0.638965\pi\)
−0.422835 + 0.906207i \(0.638965\pi\)
\(440\) −12.1919 −0.581227
\(441\) 5.59865 0.266602
\(442\) 8.51867 0.405192
\(443\) 0.00601453 0.000285759 0 0.000142879 1.00000i \(-0.499955\pi\)
0.000142879 1.00000i \(0.499955\pi\)
\(444\) 13.3304 0.632631
\(445\) −15.0442 −0.713165
\(446\) 51.3364 2.43085
\(447\) −4.58577 −0.216899
\(448\) −38.9596 −1.84067
\(449\) −20.4710 −0.966088 −0.483044 0.875596i \(-0.660469\pi\)
−0.483044 + 0.875596i \(0.660469\pi\)
\(450\) −4.99303 −0.235374
\(451\) −2.15826 −0.101629
\(452\) 63.4875 2.98620
\(453\) 14.6053 0.686216
\(454\) −28.9839 −1.36028
\(455\) 21.6108 1.01313
\(456\) 11.9932 0.561634
\(457\) 17.3731 0.812678 0.406339 0.913722i \(-0.366805\pi\)
0.406339 + 0.913722i \(0.366805\pi\)
\(458\) 69.6999 3.25686
\(459\) 1.00000 0.0466760
\(460\) 60.0378 2.79927
\(461\) 12.9555 0.603396 0.301698 0.953404i \(-0.402447\pi\)
0.301698 + 0.953404i \(0.402447\pi\)
\(462\) −15.0128 −0.698460
\(463\) −35.9451 −1.67051 −0.835255 0.549862i \(-0.814680\pi\)
−0.835255 + 0.549862i \(0.814680\pi\)
\(464\) −4.68723 −0.217599
\(465\) 6.30542 0.292407
\(466\) −40.4186 −1.87236
\(467\) −4.61657 −0.213629 −0.106815 0.994279i \(-0.534065\pi\)
−0.106815 + 0.994279i \(0.534065\pi\)
\(468\) −13.1793 −0.609215
\(469\) −27.2274 −1.25724
\(470\) 20.6825 0.954012
\(471\) 1.00000 0.0460776
\(472\) −4.48212 −0.206306
\(473\) −4.34714 −0.199882
\(474\) −1.67097 −0.0767503
\(475\) 6.22422 0.285587
\(476\) −13.0998 −0.600429
\(477\) 3.39762 0.155566
\(478\) −58.0748 −2.65628
\(479\) −15.1629 −0.692810 −0.346405 0.938085i \(-0.612598\pi\)
−0.346405 + 0.938085i \(0.612598\pi\)
\(480\) −4.64355 −0.211948
\(481\) 12.8982 0.588108
\(482\) 6.10792 0.278208
\(483\) 33.8662 1.54096
\(484\) −28.9949 −1.31795
\(485\) 32.8364 1.49102
\(486\) −2.38551 −0.108209
\(487\) 5.78646 0.262210 0.131105 0.991369i \(-0.458148\pi\)
0.131105 + 0.991369i \(0.458148\pi\)
\(488\) 17.6763 0.800169
\(489\) −5.03718 −0.227789
\(490\) −22.7710 −1.02869
\(491\) 2.33360 0.105314 0.0526568 0.998613i \(-0.483231\pi\)
0.0526568 + 0.998613i \(0.483231\pi\)
\(492\) 4.49249 0.202537
\(493\) 2.09288 0.0942588
\(494\) 25.3322 1.13975
\(495\) −3.02299 −0.135873
\(496\) 8.28261 0.371900
\(497\) 3.82165 0.171424
\(498\) −20.6271 −0.924322
\(499\) 8.75409 0.391887 0.195943 0.980615i \(-0.437223\pi\)
0.195943 + 0.980615i \(0.437223\pi\)
\(500\) 44.6328 1.99604
\(501\) 13.9889 0.624979
\(502\) −43.5288 −1.94278
\(503\) 4.09764 0.182705 0.0913523 0.995819i \(-0.470881\pi\)
0.0913523 + 0.995819i \(0.470881\pi\)
\(504\) 14.3152 0.637649
\(505\) 8.79475 0.391361
\(506\) −40.3557 −1.79403
\(507\) 0.247902 0.0110097
\(508\) −5.73661 −0.254521
\(509\) 3.94586 0.174897 0.0874485 0.996169i \(-0.472129\pi\)
0.0874485 + 0.996169i \(0.472129\pi\)
\(510\) −4.06723 −0.180100
\(511\) −28.4771 −1.25975
\(512\) −24.1645 −1.06793
\(513\) 2.97373 0.131293
\(514\) 15.3344 0.676372
\(515\) −31.9033 −1.40583
\(516\) 9.04872 0.398348
\(517\) −9.01622 −0.396533
\(518\) −30.5831 −1.34374
\(519\) −9.10778 −0.399787
\(520\) 24.5552 1.07682
\(521\) 1.11211 0.0487224 0.0243612 0.999703i \(-0.492245\pi\)
0.0243612 + 0.999703i \(0.492245\pi\)
\(522\) −4.99259 −0.218520
\(523\) 17.2277 0.753314 0.376657 0.926353i \(-0.377074\pi\)
0.376657 + 0.926353i \(0.377074\pi\)
\(524\) 49.1330 2.14638
\(525\) 7.42926 0.324240
\(526\) 24.6754 1.07590
\(527\) −3.69825 −0.161098
\(528\) −3.97092 −0.172812
\(529\) 68.0350 2.95804
\(530\) −13.8189 −0.600254
\(531\) −1.11134 −0.0482282
\(532\) −38.9552 −1.68892
\(533\) 4.34686 0.188283
\(534\) −21.0491 −0.910883
\(535\) 10.6925 0.462279
\(536\) −30.9370 −1.33628
\(537\) −13.0024 −0.561095
\(538\) 7.68396 0.331279
\(539\) 9.92666 0.427571
\(540\) 6.29246 0.270784
\(541\) 17.9738 0.772756 0.386378 0.922341i \(-0.373726\pi\)
0.386378 + 0.922341i \(0.373726\pi\)
\(542\) 20.0567 0.861508
\(543\) 4.06356 0.174384
\(544\) 2.72353 0.116771
\(545\) 34.2126 1.46551
\(546\) 30.2367 1.29401
\(547\) −24.7584 −1.05859 −0.529297 0.848436i \(-0.677544\pi\)
−0.529297 + 0.848436i \(0.677544\pi\)
\(548\) 38.1296 1.62881
\(549\) 4.38285 0.187056
\(550\) −8.85288 −0.377488
\(551\) 6.22367 0.265137
\(552\) 38.4804 1.63783
\(553\) 2.48628 0.105727
\(554\) −49.2223 −2.09125
\(555\) −6.15823 −0.261402
\(556\) 60.4861 2.56518
\(557\) 43.5762 1.84638 0.923192 0.384340i \(-0.125571\pi\)
0.923192 + 0.384340i \(0.125571\pi\)
\(558\) 8.82221 0.373474
\(559\) 8.75538 0.370313
\(560\) −13.5535 −0.572738
\(561\) 1.77305 0.0748580
\(562\) 39.7410 1.67637
\(563\) −4.08073 −0.171982 −0.0859912 0.996296i \(-0.527406\pi\)
−0.0859912 + 0.996296i \(0.527406\pi\)
\(564\) 18.7675 0.790256
\(565\) −29.3293 −1.23389
\(566\) −18.6736 −0.784910
\(567\) 3.54946 0.149063
\(568\) 4.34234 0.182201
\(569\) 2.79788 0.117293 0.0586467 0.998279i \(-0.481321\pi\)
0.0586467 + 0.998279i \(0.481321\pi\)
\(570\) −12.0948 −0.506596
\(571\) 8.04086 0.336500 0.168250 0.985744i \(-0.446188\pi\)
0.168250 + 0.985744i \(0.446188\pi\)
\(572\) −23.3676 −0.977047
\(573\) 16.1191 0.673385
\(574\) −10.3069 −0.430201
\(575\) 19.9704 0.832825
\(576\) −10.9762 −0.457342
\(577\) −5.22192 −0.217391 −0.108696 0.994075i \(-0.534667\pi\)
−0.108696 + 0.994075i \(0.534667\pi\)
\(578\) 2.38551 0.0992241
\(579\) 13.1424 0.546178
\(580\) 13.1694 0.546829
\(581\) 30.6916 1.27330
\(582\) 45.9430 1.90440
\(583\) 6.02413 0.249494
\(584\) −32.3571 −1.33894
\(585\) 6.08847 0.251727
\(586\) 11.6436 0.480992
\(587\) −4.36699 −0.180245 −0.0901226 0.995931i \(-0.528726\pi\)
−0.0901226 + 0.995931i \(0.528726\pi\)
\(588\) −20.6627 −0.852113
\(589\) −10.9976 −0.453148
\(590\) 4.52009 0.186089
\(591\) −15.3852 −0.632862
\(592\) −8.08927 −0.332467
\(593\) 18.8680 0.774814 0.387407 0.921909i \(-0.373371\pi\)
0.387407 + 0.921909i \(0.373371\pi\)
\(594\) −4.22961 −0.173543
\(595\) 6.05173 0.248097
\(596\) 16.9245 0.693253
\(597\) 15.5015 0.634436
\(598\) 81.2786 3.32373
\(599\) 32.6871 1.33556 0.667780 0.744359i \(-0.267245\pi\)
0.667780 + 0.744359i \(0.267245\pi\)
\(600\) 8.44148 0.344622
\(601\) 37.8540 1.54410 0.772049 0.635563i \(-0.219232\pi\)
0.772049 + 0.635563i \(0.219232\pi\)
\(602\) −20.7600 −0.846114
\(603\) −7.67085 −0.312381
\(604\) −53.9030 −2.19328
\(605\) 13.3948 0.544576
\(606\) 12.3052 0.499863
\(607\) −32.1324 −1.30421 −0.652107 0.758127i \(-0.726115\pi\)
−0.652107 + 0.758127i \(0.726115\pi\)
\(608\) 8.09905 0.328460
\(609\) 7.42860 0.301022
\(610\) −17.8260 −0.721755
\(611\) 18.1591 0.734640
\(612\) −3.69065 −0.149186
\(613\) −5.85646 −0.236540 −0.118270 0.992981i \(-0.537735\pi\)
−0.118270 + 0.992981i \(0.537735\pi\)
\(614\) −24.6768 −0.995874
\(615\) −2.07540 −0.0836882
\(616\) 25.3815 1.02265
\(617\) 2.36074 0.0950398 0.0475199 0.998870i \(-0.484868\pi\)
0.0475199 + 0.998870i \(0.484868\pi\)
\(618\) −44.6374 −1.79558
\(619\) 16.8877 0.678773 0.339386 0.940647i \(-0.389781\pi\)
0.339386 + 0.940647i \(0.389781\pi\)
\(620\) −23.2711 −0.934589
\(621\) 9.54123 0.382876
\(622\) 28.6971 1.15065
\(623\) 31.3195 1.25479
\(624\) 7.99764 0.320162
\(625\) −10.1537 −0.406149
\(626\) −52.2813 −2.08958
\(627\) 5.27255 0.210565
\(628\) −3.69065 −0.147273
\(629\) 3.61193 0.144017
\(630\) −14.4364 −0.575162
\(631\) −8.41241 −0.334893 −0.167446 0.985881i \(-0.553552\pi\)
−0.167446 + 0.985881i \(0.553552\pi\)
\(632\) 2.82503 0.112374
\(633\) 3.80749 0.151334
\(634\) −35.1482 −1.39591
\(635\) 2.65015 0.105168
\(636\) −12.5394 −0.497220
\(637\) −19.9928 −0.792144
\(638\) −8.85210 −0.350458
\(639\) 1.07669 0.0425930
\(640\) 35.3557 1.39756
\(641\) 31.5324 1.24545 0.622727 0.782439i \(-0.286025\pi\)
0.622727 + 0.782439i \(0.286025\pi\)
\(642\) 14.9605 0.590442
\(643\) −33.3957 −1.31700 −0.658499 0.752582i \(-0.728808\pi\)
−0.658499 + 0.752582i \(0.728808\pi\)
\(644\) −124.988 −4.92523
\(645\) −4.18024 −0.164597
\(646\) 7.09385 0.279104
\(647\) −24.6816 −0.970335 −0.485168 0.874421i \(-0.661241\pi\)
−0.485168 + 0.874421i \(0.661241\pi\)
\(648\) 4.03306 0.158434
\(649\) −1.97046 −0.0773474
\(650\) 17.8302 0.699357
\(651\) −13.1268 −0.514479
\(652\) 18.5905 0.728059
\(653\) −36.2354 −1.41800 −0.709001 0.705207i \(-0.750854\pi\)
−0.709001 + 0.705207i \(0.750854\pi\)
\(654\) 47.8685 1.87181
\(655\) −22.6980 −0.886884
\(656\) −2.72618 −0.106440
\(657\) −8.02295 −0.313005
\(658\) −43.0574 −1.67855
\(659\) 13.6153 0.530376 0.265188 0.964197i \(-0.414566\pi\)
0.265188 + 0.964197i \(0.414566\pi\)
\(660\) 11.1568 0.434278
\(661\) 46.2084 1.79730 0.898649 0.438669i \(-0.144550\pi\)
0.898649 + 0.438669i \(0.144550\pi\)
\(662\) −42.7111 −1.66002
\(663\) −3.57101 −0.138686
\(664\) 34.8732 1.35334
\(665\) 17.9962 0.697862
\(666\) −8.61628 −0.333874
\(667\) 19.9687 0.773191
\(668\) −51.6282 −1.99755
\(669\) −21.5201 −0.832016
\(670\) 31.1991 1.20533
\(671\) 7.77099 0.299996
\(672\) 9.66707 0.372915
\(673\) 6.46465 0.249194 0.124597 0.992207i \(-0.460236\pi\)
0.124597 + 0.992207i \(0.460236\pi\)
\(674\) −10.6028 −0.408404
\(675\) 2.09307 0.0805623
\(676\) −0.914921 −0.0351893
\(677\) 10.8392 0.416583 0.208292 0.978067i \(-0.433210\pi\)
0.208292 + 0.978067i \(0.433210\pi\)
\(678\) −41.0361 −1.57598
\(679\) −68.3597 −2.62340
\(680\) 6.87626 0.263692
\(681\) 12.1500 0.465589
\(682\) 15.6422 0.598970
\(683\) 29.5459 1.13054 0.565271 0.824905i \(-0.308772\pi\)
0.565271 + 0.824905i \(0.308772\pi\)
\(684\) −10.9750 −0.419639
\(685\) −17.6147 −0.673025
\(686\) −11.8656 −0.453031
\(687\) −29.2181 −1.11474
\(688\) −5.49104 −0.209344
\(689\) −12.1329 −0.462228
\(690\) −38.8063 −1.47733
\(691\) 5.30148 0.201678 0.100839 0.994903i \(-0.467847\pi\)
0.100839 + 0.994903i \(0.467847\pi\)
\(692\) 33.6136 1.27780
\(693\) 6.29335 0.239065
\(694\) −55.1301 −2.09271
\(695\) −27.9428 −1.05993
\(696\) 8.44073 0.319945
\(697\) 1.21726 0.0461071
\(698\) 9.01310 0.341151
\(699\) 16.9434 0.640858
\(700\) −27.4188 −1.03633
\(701\) 44.3341 1.67448 0.837238 0.546839i \(-0.184169\pi\)
0.837238 + 0.546839i \(0.184169\pi\)
\(702\) 8.51867 0.321516
\(703\) 10.7409 0.405100
\(704\) −19.4613 −0.733477
\(705\) −8.67006 −0.326533
\(706\) −24.5218 −0.922891
\(707\) −18.3091 −0.688586
\(708\) 4.10158 0.154147
\(709\) −23.0112 −0.864202 −0.432101 0.901825i \(-0.642228\pi\)
−0.432101 + 0.901825i \(0.642228\pi\)
\(710\) −4.37912 −0.164346
\(711\) 0.700468 0.0262696
\(712\) 35.5867 1.33367
\(713\) −35.2859 −1.32147
\(714\) 8.46726 0.316879
\(715\) 10.7951 0.403715
\(716\) 47.9873 1.79337
\(717\) 24.3448 0.909174
\(718\) −47.7831 −1.78325
\(719\) −41.5951 −1.55124 −0.775618 0.631202i \(-0.782562\pi\)
−0.775618 + 0.631202i \(0.782562\pi\)
\(720\) −3.81846 −0.142306
\(721\) 66.4171 2.47350
\(722\) −24.2295 −0.901728
\(723\) −2.56042 −0.0952232
\(724\) −14.9972 −0.557367
\(725\) 4.38055 0.162690
\(726\) 18.7413 0.695555
\(727\) −13.3162 −0.493870 −0.246935 0.969032i \(-0.579423\pi\)
−0.246935 + 0.969032i \(0.579423\pi\)
\(728\) −51.1196 −1.89462
\(729\) 1.00000 0.0370370
\(730\) 32.6312 1.20773
\(731\) 2.45179 0.0906829
\(732\) −16.1756 −0.597866
\(733\) 48.9618 1.80844 0.904222 0.427062i \(-0.140452\pi\)
0.904222 + 0.427062i \(0.140452\pi\)
\(734\) −26.6638 −0.984178
\(735\) 9.54554 0.352093
\(736\) 25.9859 0.957851
\(737\) −13.6008 −0.500991
\(738\) −2.90379 −0.106890
\(739\) 31.5144 1.15928 0.579638 0.814874i \(-0.303194\pi\)
0.579638 + 0.814874i \(0.303194\pi\)
\(740\) 22.7279 0.835494
\(741\) −10.6192 −0.390106
\(742\) 28.7685 1.05613
\(743\) −15.7545 −0.577977 −0.288988 0.957333i \(-0.593319\pi\)
−0.288988 + 0.957333i \(0.593319\pi\)
\(744\) −14.9153 −0.546821
\(745\) −7.81861 −0.286452
\(746\) 41.3229 1.51294
\(747\) 8.64683 0.316371
\(748\) −6.54369 −0.239261
\(749\) −22.2600 −0.813364
\(750\) −28.8491 −1.05342
\(751\) −37.0370 −1.35150 −0.675750 0.737131i \(-0.736180\pi\)
−0.675750 + 0.737131i \(0.736180\pi\)
\(752\) −11.3887 −0.415304
\(753\) 18.2472 0.664964
\(754\) 17.8286 0.649279
\(755\) 24.9016 0.906262
\(756\) −13.0998 −0.476435
\(757\) −40.7252 −1.48018 −0.740091 0.672507i \(-0.765218\pi\)
−0.740091 + 0.672507i \(0.765218\pi\)
\(758\) −7.08307 −0.257269
\(759\) 16.9170 0.614049
\(760\) 20.4481 0.741731
\(761\) −24.6505 −0.893581 −0.446791 0.894639i \(-0.647433\pi\)
−0.446791 + 0.894639i \(0.647433\pi\)
\(762\) 3.70795 0.134325
\(763\) −71.2248 −2.57851
\(764\) −59.4899 −2.15227
\(765\) 1.70497 0.0616434
\(766\) −21.6475 −0.782157
\(767\) 3.96862 0.143298
\(768\) 27.5154 0.992875
\(769\) 43.5837 1.57167 0.785834 0.618437i \(-0.212234\pi\)
0.785834 + 0.618437i \(0.212234\pi\)
\(770\) −25.5965 −0.922433
\(771\) −6.42815 −0.231504
\(772\) −48.5039 −1.74569
\(773\) −7.03034 −0.252864 −0.126432 0.991975i \(-0.540353\pi\)
−0.126432 + 0.991975i \(0.540353\pi\)
\(774\) −5.84878 −0.210230
\(775\) −7.74070 −0.278054
\(776\) −77.6735 −2.78832
\(777\) 12.8204 0.459928
\(778\) 64.4221 2.30964
\(779\) 3.61981 0.129693
\(780\) −22.4704 −0.804570
\(781\) 1.90901 0.0683098
\(782\) 22.7607 0.813920
\(783\) 2.09288 0.0747936
\(784\) 12.5387 0.447812
\(785\) 1.70497 0.0608531
\(786\) −31.7579 −1.13277
\(787\) −0.0746412 −0.00266067 −0.00133034 0.999999i \(-0.500423\pi\)
−0.00133034 + 0.999999i \(0.500423\pi\)
\(788\) 56.7814 2.02275
\(789\) −10.3439 −0.368251
\(790\) −2.84896 −0.101362
\(791\) 61.0586 2.17099
\(792\) 7.15080 0.254093
\(793\) −15.6512 −0.555790
\(794\) 19.4444 0.690057
\(795\) 5.79285 0.205451
\(796\) −57.2108 −2.02778
\(797\) 13.0746 0.463128 0.231564 0.972820i \(-0.425616\pi\)
0.231564 + 0.972820i \(0.425616\pi\)
\(798\) 25.1793 0.891338
\(799\) 5.08516 0.179900
\(800\) 5.70055 0.201545
\(801\) 8.82373 0.311771
\(802\) 10.4481 0.368936
\(803\) −14.2251 −0.501991
\(804\) 28.3104 0.998432
\(805\) 57.7409 2.03510
\(806\) −31.5042 −1.10969
\(807\) −3.22110 −0.113388
\(808\) −20.8037 −0.731872
\(809\) −39.0955 −1.37452 −0.687262 0.726409i \(-0.741188\pi\)
−0.687262 + 0.726409i \(0.741188\pi\)
\(810\) −4.06723 −0.142908
\(811\) 45.3798 1.59350 0.796751 0.604308i \(-0.206550\pi\)
0.796751 + 0.604308i \(0.206550\pi\)
\(812\) −27.4164 −0.962127
\(813\) −8.40771 −0.294871
\(814\) −15.2771 −0.535460
\(815\) −8.58825 −0.300833
\(816\) 2.23960 0.0784018
\(817\) 7.29097 0.255079
\(818\) 31.3083 1.09467
\(819\) −12.6751 −0.442905
\(820\) 7.65958 0.267484
\(821\) −27.4974 −0.959666 −0.479833 0.877360i \(-0.659303\pi\)
−0.479833 + 0.877360i \(0.659303\pi\)
\(822\) −24.6456 −0.859615
\(823\) 43.6548 1.52171 0.760855 0.648921i \(-0.224780\pi\)
0.760855 + 0.648921i \(0.224780\pi\)
\(824\) 75.4663 2.62899
\(825\) 3.71111 0.129204
\(826\) −9.41004 −0.327417
\(827\) 4.23486 0.147260 0.0736302 0.997286i \(-0.476542\pi\)
0.0736302 + 0.997286i \(0.476542\pi\)
\(828\) −35.2133 −1.22375
\(829\) −22.8852 −0.794835 −0.397418 0.917638i \(-0.630094\pi\)
−0.397418 + 0.917638i \(0.630094\pi\)
\(830\) −35.1686 −1.22072
\(831\) 20.6339 0.715781
\(832\) 39.1962 1.35888
\(833\) −5.59865 −0.193982
\(834\) −39.0961 −1.35379
\(835\) 23.8507 0.825388
\(836\) −19.4591 −0.673009
\(837\) −3.69825 −0.127830
\(838\) 53.1894 1.83740
\(839\) −49.9417 −1.72418 −0.862090 0.506755i \(-0.830845\pi\)
−0.862090 + 0.506755i \(0.830845\pi\)
\(840\) 24.4070 0.842121
\(841\) −24.6198 −0.848960
\(842\) 36.5292 1.25888
\(843\) −16.6593 −0.573778
\(844\) −14.0521 −0.483694
\(845\) 0.422667 0.0145402
\(846\) −12.1307 −0.417062
\(847\) −27.8856 −0.958162
\(848\) 7.60931 0.261305
\(849\) 7.82793 0.268654
\(850\) 4.99303 0.171260
\(851\) 34.4622 1.18135
\(852\) −3.97367 −0.136136
\(853\) 9.30315 0.318534 0.159267 0.987236i \(-0.449087\pi\)
0.159267 + 0.987236i \(0.449087\pi\)
\(854\) 37.1107 1.26990
\(855\) 5.07012 0.173394
\(856\) −25.2929 −0.864494
\(857\) −8.87623 −0.303206 −0.151603 0.988441i \(-0.548444\pi\)
−0.151603 + 0.988441i \(0.548444\pi\)
\(858\) 15.1040 0.515642
\(859\) 52.2447 1.78257 0.891283 0.453447i \(-0.149806\pi\)
0.891283 + 0.453447i \(0.149806\pi\)
\(860\) 15.4278 0.526084
\(861\) 4.32062 0.147246
\(862\) 20.4936 0.698016
\(863\) 37.8548 1.28859 0.644296 0.764776i \(-0.277150\pi\)
0.644296 + 0.764776i \(0.277150\pi\)
\(864\) 2.72353 0.0926565
\(865\) −15.5285 −0.527985
\(866\) −65.7296 −2.23358
\(867\) −1.00000 −0.0339618
\(868\) 48.4464 1.64438
\(869\) 1.24196 0.0421307
\(870\) −8.51223 −0.288592
\(871\) 27.3927 0.928165
\(872\) −80.9290 −2.74060
\(873\) −19.2592 −0.651825
\(874\) 67.6840 2.28945
\(875\) 42.9253 1.45114
\(876\) 29.6099 1.00043
\(877\) −21.7686 −0.735072 −0.367536 0.930009i \(-0.619799\pi\)
−0.367536 + 0.930009i \(0.619799\pi\)
\(878\) −42.2682 −1.42648
\(879\) −4.88097 −0.164631
\(880\) −6.77030 −0.228227
\(881\) 30.6408 1.03231 0.516157 0.856494i \(-0.327362\pi\)
0.516157 + 0.856494i \(0.327362\pi\)
\(882\) 13.3556 0.449707
\(883\) 20.9770 0.705932 0.352966 0.935636i \(-0.385173\pi\)
0.352966 + 0.935636i \(0.385173\pi\)
\(884\) 13.1793 0.443269
\(885\) −1.89481 −0.0636934
\(886\) 0.0143477 0.000482021 0
\(887\) 4.63636 0.155674 0.0778369 0.996966i \(-0.475199\pi\)
0.0778369 + 0.996966i \(0.475199\pi\)
\(888\) 14.5671 0.488840
\(889\) −5.51715 −0.185039
\(890\) −35.8881 −1.20297
\(891\) 1.77305 0.0593993
\(892\) 79.4232 2.65929
\(893\) 15.1219 0.506034
\(894\) −10.9394 −0.365868
\(895\) −22.1687 −0.741019
\(896\) −73.6044 −2.45895
\(897\) −34.0718 −1.13762
\(898\) −48.8338 −1.62961
\(899\) −7.74001 −0.258144
\(900\) −7.72479 −0.257493
\(901\) −3.39762 −0.113191
\(902\) −5.14855 −0.171428
\(903\) 8.70254 0.289602
\(904\) 69.3777 2.30747
\(905\) 6.92827 0.230303
\(906\) 34.8410 1.15752
\(907\) 21.4210 0.711273 0.355636 0.934624i \(-0.384264\pi\)
0.355636 + 0.934624i \(0.384264\pi\)
\(908\) −44.8414 −1.48811
\(909\) −5.15830 −0.171090
\(910\) 51.5527 1.70895
\(911\) −8.15346 −0.270136 −0.135068 0.990836i \(-0.543125\pi\)
−0.135068 + 0.990836i \(0.543125\pi\)
\(912\) 6.65996 0.220533
\(913\) 15.3312 0.507389
\(914\) 41.4436 1.37083
\(915\) 7.47264 0.247038
\(916\) 107.834 3.56292
\(917\) 47.2533 1.56044
\(918\) 2.38551 0.0787335
\(919\) −14.9931 −0.494576 −0.247288 0.968942i \(-0.579539\pi\)
−0.247288 + 0.968942i \(0.579539\pi\)
\(920\) 65.6079 2.16303
\(921\) 10.3444 0.340861
\(922\) 30.9054 1.01781
\(923\) −3.84485 −0.126555
\(924\) −23.2266 −0.764098
\(925\) 7.56001 0.248572
\(926\) −85.7474 −2.81783
\(927\) 18.7119 0.614580
\(928\) 5.70004 0.187113
\(929\) 13.3305 0.437359 0.218679 0.975797i \(-0.429825\pi\)
0.218679 + 0.975797i \(0.429825\pi\)
\(930\) 15.0416 0.493234
\(931\) −16.6488 −0.545644
\(932\) −62.5321 −2.04831
\(933\) −12.0298 −0.393837
\(934\) −11.0129 −0.360352
\(935\) 3.02299 0.0988625
\(936\) −14.4021 −0.470747
\(937\) −27.7093 −0.905222 −0.452611 0.891708i \(-0.649507\pi\)
−0.452611 + 0.891708i \(0.649507\pi\)
\(938\) −64.9511 −2.12073
\(939\) 21.9162 0.715208
\(940\) 31.9981 1.04366
\(941\) −2.65246 −0.0864679 −0.0432339 0.999065i \(-0.513766\pi\)
−0.0432339 + 0.999065i \(0.513766\pi\)
\(942\) 2.38551 0.0777241
\(943\) 11.6142 0.378210
\(944\) −2.48897 −0.0810090
\(945\) 6.05173 0.196863
\(946\) −10.3701 −0.337162
\(947\) −24.1667 −0.785311 −0.392655 0.919686i \(-0.628444\pi\)
−0.392655 + 0.919686i \(0.628444\pi\)
\(948\) −2.58518 −0.0839629
\(949\) 28.6500 0.930019
\(950\) 14.8479 0.481730
\(951\) 14.7341 0.477784
\(952\) −14.3152 −0.463958
\(953\) 25.6950 0.832343 0.416172 0.909286i \(-0.363372\pi\)
0.416172 + 0.909286i \(0.363372\pi\)
\(954\) 8.10505 0.262411
\(955\) 27.4826 0.889316
\(956\) −89.8482 −2.90590
\(957\) 3.71078 0.119952
\(958\) −36.1712 −1.16864
\(959\) 36.6708 1.18416
\(960\) −18.7141 −0.603997
\(961\) −17.3229 −0.558804
\(962\) 30.7688 0.992026
\(963\) −6.27139 −0.202093
\(964\) 9.44963 0.304352
\(965\) 22.4074 0.721319
\(966\) 80.7880 2.59931
\(967\) 3.76872 0.121194 0.0605969 0.998162i \(-0.480700\pi\)
0.0605969 + 0.998162i \(0.480700\pi\)
\(968\) −31.6850 −1.01839
\(969\) −2.97373 −0.0955299
\(970\) 78.3315 2.51507
\(971\) 60.7894 1.95082 0.975412 0.220390i \(-0.0707331\pi\)
0.975412 + 0.220390i \(0.0707331\pi\)
\(972\) −3.69065 −0.118378
\(973\) 58.1721 1.86491
\(974\) 13.8037 0.442298
\(975\) −7.47437 −0.239371
\(976\) 9.81584 0.314197
\(977\) −1.18843 −0.0380213 −0.0190106 0.999819i \(-0.506052\pi\)
−0.0190106 + 0.999819i \(0.506052\pi\)
\(978\) −12.0162 −0.384237
\(979\) 15.6449 0.500013
\(980\) −35.2293 −1.12536
\(981\) −20.0664 −0.640670
\(982\) 5.56681 0.177644
\(983\) 21.0840 0.672476 0.336238 0.941777i \(-0.390845\pi\)
0.336238 + 0.941777i \(0.390845\pi\)
\(984\) 4.90930 0.156503
\(985\) −26.2313 −0.835799
\(986\) 4.99259 0.158997
\(987\) 18.0496 0.574524
\(988\) 39.1918 1.24686
\(989\) 23.3931 0.743858
\(990\) −7.21138 −0.229193
\(991\) −4.95893 −0.157526 −0.0787629 0.996893i \(-0.525097\pi\)
−0.0787629 + 0.996893i \(0.525097\pi\)
\(992\) −10.0723 −0.319796
\(993\) 17.9044 0.568180
\(994\) 9.11658 0.289160
\(995\) 26.4297 0.837878
\(996\) −31.9124 −1.01118
\(997\) −14.9758 −0.474288 −0.237144 0.971475i \(-0.576211\pi\)
−0.237144 + 0.971475i \(0.576211\pi\)
\(998\) 20.8830 0.661038
\(999\) 3.61193 0.114276
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.1.44 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.44 48 1.1 even 1 trivial