Properties

Label 4006.2.a.g.1.4
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.86035 q^{3} +1.00000 q^{4} -2.90727 q^{5} +2.86035 q^{6} +0.924767 q^{7} -1.00000 q^{8} +5.18162 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.86035 q^{3} +1.00000 q^{4} -2.90727 q^{5} +2.86035 q^{6} +0.924767 q^{7} -1.00000 q^{8} +5.18162 q^{9} +2.90727 q^{10} -1.96179 q^{11} -2.86035 q^{12} +4.75038 q^{13} -0.924767 q^{14} +8.31583 q^{15} +1.00000 q^{16} -3.12285 q^{17} -5.18162 q^{18} -2.40612 q^{19} -2.90727 q^{20} -2.64516 q^{21} +1.96179 q^{22} -5.24942 q^{23} +2.86035 q^{24} +3.45224 q^{25} -4.75038 q^{26} -6.24021 q^{27} +0.924767 q^{28} -6.70446 q^{29} -8.31583 q^{30} +5.39883 q^{31} -1.00000 q^{32} +5.61140 q^{33} +3.12285 q^{34} -2.68855 q^{35} +5.18162 q^{36} -1.56509 q^{37} +2.40612 q^{38} -13.5878 q^{39} +2.90727 q^{40} +2.11925 q^{41} +2.64516 q^{42} +0.246973 q^{43} -1.96179 q^{44} -15.0644 q^{45} +5.24942 q^{46} +10.1832 q^{47} -2.86035 q^{48} -6.14481 q^{49} -3.45224 q^{50} +8.93246 q^{51} +4.75038 q^{52} +0.976945 q^{53} +6.24021 q^{54} +5.70345 q^{55} -0.924767 q^{56} +6.88237 q^{57} +6.70446 q^{58} +7.22403 q^{59} +8.31583 q^{60} +1.80157 q^{61} -5.39883 q^{62} +4.79179 q^{63} +1.00000 q^{64} -13.8107 q^{65} -5.61140 q^{66} +6.89869 q^{67} -3.12285 q^{68} +15.0152 q^{69} +2.68855 q^{70} +13.6869 q^{71} -5.18162 q^{72} +8.90678 q^{73} +1.56509 q^{74} -9.87461 q^{75} -2.40612 q^{76} -1.81419 q^{77} +13.5878 q^{78} -2.07547 q^{79} -2.90727 q^{80} +2.30435 q^{81} -2.11925 q^{82} -8.77630 q^{83} -2.64516 q^{84} +9.07899 q^{85} -0.246973 q^{86} +19.1771 q^{87} +1.96179 q^{88} +8.42300 q^{89} +15.0644 q^{90} +4.39299 q^{91} -5.24942 q^{92} -15.4426 q^{93} -10.1832 q^{94} +6.99526 q^{95} +2.86035 q^{96} +8.08147 q^{97} +6.14481 q^{98} -10.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.86035 −1.65143 −0.825713 0.564090i \(-0.809227\pi\)
−0.825713 + 0.564090i \(0.809227\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.90727 −1.30017 −0.650086 0.759861i \(-0.725267\pi\)
−0.650086 + 0.759861i \(0.725267\pi\)
\(6\) 2.86035 1.16773
\(7\) 0.924767 0.349529 0.174765 0.984610i \(-0.444084\pi\)
0.174765 + 0.984610i \(0.444084\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.18162 1.72721
\(10\) 2.90727 0.919360
\(11\) −1.96179 −0.591501 −0.295750 0.955265i \(-0.595570\pi\)
−0.295750 + 0.955265i \(0.595570\pi\)
\(12\) −2.86035 −0.825713
\(13\) 4.75038 1.31752 0.658759 0.752354i \(-0.271082\pi\)
0.658759 + 0.752354i \(0.271082\pi\)
\(14\) −0.924767 −0.247154
\(15\) 8.31583 2.14714
\(16\) 1.00000 0.250000
\(17\) −3.12285 −0.757403 −0.378702 0.925519i \(-0.623629\pi\)
−0.378702 + 0.925519i \(0.623629\pi\)
\(18\) −5.18162 −1.22132
\(19\) −2.40612 −0.552003 −0.276001 0.961157i \(-0.589009\pi\)
−0.276001 + 0.961157i \(0.589009\pi\)
\(20\) −2.90727 −0.650086
\(21\) −2.64516 −0.577221
\(22\) 1.96179 0.418254
\(23\) −5.24942 −1.09458 −0.547290 0.836943i \(-0.684341\pi\)
−0.547290 + 0.836943i \(0.684341\pi\)
\(24\) 2.86035 0.583867
\(25\) 3.45224 0.690447
\(26\) −4.75038 −0.931626
\(27\) −6.24021 −1.20093
\(28\) 0.924767 0.174765
\(29\) −6.70446 −1.24499 −0.622494 0.782625i \(-0.713880\pi\)
−0.622494 + 0.782625i \(0.713880\pi\)
\(30\) −8.31583 −1.51826
\(31\) 5.39883 0.969659 0.484830 0.874609i \(-0.338882\pi\)
0.484830 + 0.874609i \(0.338882\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.61140 0.976820
\(34\) 3.12285 0.535565
\(35\) −2.68855 −0.454448
\(36\) 5.18162 0.863604
\(37\) −1.56509 −0.257299 −0.128649 0.991690i \(-0.541064\pi\)
−0.128649 + 0.991690i \(0.541064\pi\)
\(38\) 2.40612 0.390325
\(39\) −13.5878 −2.17578
\(40\) 2.90727 0.459680
\(41\) 2.11925 0.330972 0.165486 0.986212i \(-0.447081\pi\)
0.165486 + 0.986212i \(0.447081\pi\)
\(42\) 2.64516 0.408157
\(43\) 0.246973 0.0376630 0.0188315 0.999823i \(-0.494005\pi\)
0.0188315 + 0.999823i \(0.494005\pi\)
\(44\) −1.96179 −0.295750
\(45\) −15.0644 −2.24567
\(46\) 5.24942 0.773985
\(47\) 10.1832 1.48538 0.742689 0.669637i \(-0.233550\pi\)
0.742689 + 0.669637i \(0.233550\pi\)
\(48\) −2.86035 −0.412856
\(49\) −6.14481 −0.877829
\(50\) −3.45224 −0.488220
\(51\) 8.93246 1.25080
\(52\) 4.75038 0.658759
\(53\) 0.976945 0.134194 0.0670968 0.997746i \(-0.478626\pi\)
0.0670968 + 0.997746i \(0.478626\pi\)
\(54\) 6.24021 0.849186
\(55\) 5.70345 0.769053
\(56\) −0.924767 −0.123577
\(57\) 6.88237 0.911592
\(58\) 6.70446 0.880339
\(59\) 7.22403 0.940489 0.470244 0.882536i \(-0.344166\pi\)
0.470244 + 0.882536i \(0.344166\pi\)
\(60\) 8.31583 1.07357
\(61\) 1.80157 0.230667 0.115333 0.993327i \(-0.463206\pi\)
0.115333 + 0.993327i \(0.463206\pi\)
\(62\) −5.39883 −0.685653
\(63\) 4.79179 0.603709
\(64\) 1.00000 0.125000
\(65\) −13.8107 −1.71300
\(66\) −5.61140 −0.690716
\(67\) 6.89869 0.842809 0.421404 0.906873i \(-0.361537\pi\)
0.421404 + 0.906873i \(0.361537\pi\)
\(68\) −3.12285 −0.378702
\(69\) 15.0152 1.80762
\(70\) 2.68855 0.321343
\(71\) 13.6869 1.62433 0.812167 0.583426i \(-0.198288\pi\)
0.812167 + 0.583426i \(0.198288\pi\)
\(72\) −5.18162 −0.610660
\(73\) 8.90678 1.04246 0.521230 0.853416i \(-0.325473\pi\)
0.521230 + 0.853416i \(0.325473\pi\)
\(74\) 1.56509 0.181938
\(75\) −9.87461 −1.14022
\(76\) −2.40612 −0.276001
\(77\) −1.81419 −0.206747
\(78\) 13.5878 1.53851
\(79\) −2.07547 −0.233509 −0.116754 0.993161i \(-0.537249\pi\)
−0.116754 + 0.993161i \(0.537249\pi\)
\(80\) −2.90727 −0.325043
\(81\) 2.30435 0.256039
\(82\) −2.11925 −0.234032
\(83\) −8.77630 −0.963325 −0.481662 0.876357i \(-0.659967\pi\)
−0.481662 + 0.876357i \(0.659967\pi\)
\(84\) −2.64516 −0.288611
\(85\) 9.07899 0.984754
\(86\) −0.246973 −0.0266318
\(87\) 19.1771 2.05601
\(88\) 1.96179 0.209127
\(89\) 8.42300 0.892836 0.446418 0.894824i \(-0.352699\pi\)
0.446418 + 0.894824i \(0.352699\pi\)
\(90\) 15.0644 1.58793
\(91\) 4.39299 0.460511
\(92\) −5.24942 −0.547290
\(93\) −15.4426 −1.60132
\(94\) −10.1832 −1.05032
\(95\) 6.99526 0.717699
\(96\) 2.86035 0.291934
\(97\) 8.08147 0.820549 0.410275 0.911962i \(-0.365433\pi\)
0.410275 + 0.911962i \(0.365433\pi\)
\(98\) 6.14481 0.620719
\(99\) −10.1652 −1.02164
\(100\) 3.45224 0.345224
\(101\) −15.8267 −1.57482 −0.787408 0.616432i \(-0.788578\pi\)
−0.787408 + 0.616432i \(0.788578\pi\)
\(102\) −8.93246 −0.884446
\(103\) 6.34543 0.625233 0.312617 0.949879i \(-0.398794\pi\)
0.312617 + 0.949879i \(0.398794\pi\)
\(104\) −4.75038 −0.465813
\(105\) 7.69020 0.750487
\(106\) −0.976945 −0.0948892
\(107\) 5.74011 0.554918 0.277459 0.960738i \(-0.410508\pi\)
0.277459 + 0.960738i \(0.410508\pi\)
\(108\) −6.24021 −0.600465
\(109\) 2.46460 0.236066 0.118033 0.993010i \(-0.462341\pi\)
0.118033 + 0.993010i \(0.462341\pi\)
\(110\) −5.70345 −0.543802
\(111\) 4.47670 0.424910
\(112\) 0.924767 0.0873823
\(113\) 3.31855 0.312183 0.156092 0.987743i \(-0.450111\pi\)
0.156092 + 0.987743i \(0.450111\pi\)
\(114\) −6.88237 −0.644593
\(115\) 15.2615 1.42314
\(116\) −6.70446 −0.622494
\(117\) 24.6147 2.27563
\(118\) −7.22403 −0.665026
\(119\) −2.88791 −0.264734
\(120\) −8.31583 −0.759128
\(121\) −7.15140 −0.650127
\(122\) −1.80157 −0.163106
\(123\) −6.06181 −0.546575
\(124\) 5.39883 0.484830
\(125\) 4.49978 0.402472
\(126\) −4.79179 −0.426887
\(127\) 10.7675 0.955464 0.477732 0.878506i \(-0.341459\pi\)
0.477732 + 0.878506i \(0.341459\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.706430 −0.0621977
\(130\) 13.8107 1.21127
\(131\) −16.1817 −1.41380 −0.706900 0.707314i \(-0.749907\pi\)
−0.706900 + 0.707314i \(0.749907\pi\)
\(132\) 5.61140 0.488410
\(133\) −2.22510 −0.192941
\(134\) −6.89869 −0.595956
\(135\) 18.1420 1.56142
\(136\) 3.12285 0.267782
\(137\) −14.6083 −1.24807 −0.624036 0.781396i \(-0.714508\pi\)
−0.624036 + 0.781396i \(0.714508\pi\)
\(138\) −15.0152 −1.27818
\(139\) −12.4414 −1.05527 −0.527635 0.849471i \(-0.676921\pi\)
−0.527635 + 0.849471i \(0.676921\pi\)
\(140\) −2.68855 −0.227224
\(141\) −29.1277 −2.45299
\(142\) −13.6869 −1.14858
\(143\) −9.31923 −0.779313
\(144\) 5.18162 0.431802
\(145\) 19.4917 1.61870
\(146\) −8.90678 −0.737130
\(147\) 17.5763 1.44967
\(148\) −1.56509 −0.128649
\(149\) 16.3480 1.33928 0.669638 0.742687i \(-0.266449\pi\)
0.669638 + 0.742687i \(0.266449\pi\)
\(150\) 9.87461 0.806259
\(151\) 24.4659 1.99101 0.995504 0.0947174i \(-0.0301947\pi\)
0.995504 + 0.0947174i \(0.0301947\pi\)
\(152\) 2.40612 0.195162
\(153\) −16.1814 −1.30819
\(154\) 1.81419 0.146192
\(155\) −15.6959 −1.26072
\(156\) −13.5878 −1.08789
\(157\) −2.38955 −0.190707 −0.0953535 0.995443i \(-0.530398\pi\)
−0.0953535 + 0.995443i \(0.530398\pi\)
\(158\) 2.07547 0.165115
\(159\) −2.79441 −0.221611
\(160\) 2.90727 0.229840
\(161\) −4.85449 −0.382588
\(162\) −2.30435 −0.181047
\(163\) 17.0078 1.33215 0.666076 0.745884i \(-0.267973\pi\)
0.666076 + 0.745884i \(0.267973\pi\)
\(164\) 2.11925 0.165486
\(165\) −16.3139 −1.27003
\(166\) 8.77630 0.681173
\(167\) −11.1082 −0.859579 −0.429789 0.902929i \(-0.641412\pi\)
−0.429789 + 0.902929i \(0.641412\pi\)
\(168\) 2.64516 0.204079
\(169\) 9.56611 0.735855
\(170\) −9.07899 −0.696326
\(171\) −12.4676 −0.953424
\(172\) 0.246973 0.0188315
\(173\) −7.43749 −0.565462 −0.282731 0.959199i \(-0.591240\pi\)
−0.282731 + 0.959199i \(0.591240\pi\)
\(174\) −19.1771 −1.45382
\(175\) 3.19251 0.241331
\(176\) −1.96179 −0.147875
\(177\) −20.6633 −1.55315
\(178\) −8.42300 −0.631331
\(179\) −2.56601 −0.191792 −0.0958962 0.995391i \(-0.530572\pi\)
−0.0958962 + 0.995391i \(0.530572\pi\)
\(180\) −15.0644 −1.12283
\(181\) −17.2955 −1.28556 −0.642781 0.766050i \(-0.722220\pi\)
−0.642781 + 0.766050i \(0.722220\pi\)
\(182\) −4.39299 −0.325630
\(183\) −5.15311 −0.380929
\(184\) 5.24942 0.386993
\(185\) 4.55014 0.334533
\(186\) 15.4426 1.13230
\(187\) 6.12637 0.448005
\(188\) 10.1832 0.742689
\(189\) −5.77074 −0.419760
\(190\) −6.99526 −0.507490
\(191\) 7.03698 0.509178 0.254589 0.967049i \(-0.418060\pi\)
0.254589 + 0.967049i \(0.418060\pi\)
\(192\) −2.86035 −0.206428
\(193\) −22.5963 −1.62652 −0.813258 0.581903i \(-0.802308\pi\)
−0.813258 + 0.581903i \(0.802308\pi\)
\(194\) −8.08147 −0.580216
\(195\) 39.5033 2.82889
\(196\) −6.14481 −0.438915
\(197\) 5.69244 0.405570 0.202785 0.979223i \(-0.435001\pi\)
0.202785 + 0.979223i \(0.435001\pi\)
\(198\) 10.1652 0.722412
\(199\) −26.8035 −1.90005 −0.950026 0.312170i \(-0.898944\pi\)
−0.950026 + 0.312170i \(0.898944\pi\)
\(200\) −3.45224 −0.244110
\(201\) −19.7327 −1.39184
\(202\) 15.8267 1.11356
\(203\) −6.20007 −0.435159
\(204\) 8.93246 0.625398
\(205\) −6.16124 −0.430320
\(206\) −6.34543 −0.442107
\(207\) −27.2005 −1.89057
\(208\) 4.75038 0.329380
\(209\) 4.72030 0.326510
\(210\) −7.69020 −0.530674
\(211\) 9.11175 0.627279 0.313639 0.949542i \(-0.398452\pi\)
0.313639 + 0.949542i \(0.398452\pi\)
\(212\) 0.976945 0.0670968
\(213\) −39.1493 −2.68247
\(214\) −5.74011 −0.392386
\(215\) −0.718018 −0.0489684
\(216\) 6.24021 0.424593
\(217\) 4.99266 0.338924
\(218\) −2.46460 −0.166924
\(219\) −25.4765 −1.72155
\(220\) 5.70345 0.384526
\(221\) −14.8347 −0.997892
\(222\) −4.47670 −0.300457
\(223\) 11.2314 0.752113 0.376057 0.926597i \(-0.377280\pi\)
0.376057 + 0.926597i \(0.377280\pi\)
\(224\) −0.924767 −0.0617886
\(225\) 17.8882 1.19255
\(226\) −3.31855 −0.220747
\(227\) −9.49489 −0.630198 −0.315099 0.949059i \(-0.602038\pi\)
−0.315099 + 0.949059i \(0.602038\pi\)
\(228\) 6.88237 0.455796
\(229\) −9.64030 −0.637049 −0.318524 0.947915i \(-0.603187\pi\)
−0.318524 + 0.947915i \(0.603187\pi\)
\(230\) −15.2615 −1.00631
\(231\) 5.18924 0.341427
\(232\) 6.70446 0.440170
\(233\) 10.6424 0.697205 0.348603 0.937271i \(-0.386656\pi\)
0.348603 + 0.937271i \(0.386656\pi\)
\(234\) −24.6147 −1.60911
\(235\) −29.6054 −1.93125
\(236\) 7.22403 0.470244
\(237\) 5.93658 0.385622
\(238\) 2.88791 0.187195
\(239\) 6.03473 0.390354 0.195177 0.980768i \(-0.437472\pi\)
0.195177 + 0.980768i \(0.437472\pi\)
\(240\) 8.31583 0.536784
\(241\) −8.99086 −0.579152 −0.289576 0.957155i \(-0.593514\pi\)
−0.289576 + 0.957155i \(0.593514\pi\)
\(242\) 7.15140 0.459709
\(243\) 12.1294 0.778101
\(244\) 1.80157 0.115333
\(245\) 17.8646 1.14133
\(246\) 6.06181 0.386487
\(247\) −11.4300 −0.727274
\(248\) −5.39883 −0.342826
\(249\) 25.1033 1.59086
\(250\) −4.49978 −0.284591
\(251\) −9.62109 −0.607278 −0.303639 0.952787i \(-0.598202\pi\)
−0.303639 + 0.952787i \(0.598202\pi\)
\(252\) 4.79179 0.301855
\(253\) 10.2982 0.647445
\(254\) −10.7675 −0.675615
\(255\) −25.9691 −1.62625
\(256\) 1.00000 0.0625000
\(257\) 27.6742 1.72627 0.863135 0.504973i \(-0.168498\pi\)
0.863135 + 0.504973i \(0.168498\pi\)
\(258\) 0.706430 0.0439804
\(259\) −1.44734 −0.0899334
\(260\) −13.8107 −0.856500
\(261\) −34.7400 −2.15035
\(262\) 16.1817 0.999707
\(263\) 9.78791 0.603548 0.301774 0.953379i \(-0.402421\pi\)
0.301774 + 0.953379i \(0.402421\pi\)
\(264\) −5.61140 −0.345358
\(265\) −2.84024 −0.174475
\(266\) 2.22510 0.136430
\(267\) −24.0928 −1.47445
\(268\) 6.89869 0.421404
\(269\) −14.1504 −0.862764 −0.431382 0.902169i \(-0.641974\pi\)
−0.431382 + 0.902169i \(0.641974\pi\)
\(270\) −18.1420 −1.10409
\(271\) −14.9984 −0.911085 −0.455543 0.890214i \(-0.650555\pi\)
−0.455543 + 0.890214i \(0.650555\pi\)
\(272\) −3.12285 −0.189351
\(273\) −12.5655 −0.760500
\(274\) 14.6083 0.882520
\(275\) −6.77255 −0.408400
\(276\) 15.0152 0.903809
\(277\) −6.51546 −0.391476 −0.195738 0.980656i \(-0.562710\pi\)
−0.195738 + 0.980656i \(0.562710\pi\)
\(278\) 12.4414 0.746188
\(279\) 27.9747 1.67480
\(280\) 2.68855 0.160672
\(281\) 27.8508 1.66144 0.830719 0.556691i \(-0.187929\pi\)
0.830719 + 0.556691i \(0.187929\pi\)
\(282\) 29.1277 1.73453
\(283\) 7.40071 0.439927 0.219963 0.975508i \(-0.429406\pi\)
0.219963 + 0.975508i \(0.429406\pi\)
\(284\) 13.6869 0.812167
\(285\) −20.0089 −1.18523
\(286\) 9.31923 0.551058
\(287\) 1.95981 0.115684
\(288\) −5.18162 −0.305330
\(289\) −7.24779 −0.426341
\(290\) −19.4917 −1.14459
\(291\) −23.1159 −1.35508
\(292\) 8.90678 0.521230
\(293\) 28.9410 1.69075 0.845376 0.534172i \(-0.179377\pi\)
0.845376 + 0.534172i \(0.179377\pi\)
\(294\) −17.5763 −1.02507
\(295\) −21.0022 −1.22280
\(296\) 1.56509 0.0909689
\(297\) 12.2420 0.710351
\(298\) −16.3480 −0.947012
\(299\) −24.9368 −1.44213
\(300\) −9.87461 −0.570111
\(301\) 0.228392 0.0131643
\(302\) −24.4659 −1.40786
\(303\) 45.2700 2.60069
\(304\) −2.40612 −0.138001
\(305\) −5.23764 −0.299907
\(306\) 16.1814 0.925032
\(307\) 22.1714 1.26539 0.632696 0.774401i \(-0.281948\pi\)
0.632696 + 0.774401i \(0.281948\pi\)
\(308\) −1.81419 −0.103373
\(309\) −18.1502 −1.03253
\(310\) 15.6959 0.891466
\(311\) −1.02105 −0.0578982 −0.0289491 0.999581i \(-0.509216\pi\)
−0.0289491 + 0.999581i \(0.509216\pi\)
\(312\) 13.5878 0.769256
\(313\) −25.1728 −1.42285 −0.711424 0.702763i \(-0.751950\pi\)
−0.711424 + 0.702763i \(0.751950\pi\)
\(314\) 2.38955 0.134850
\(315\) −13.9311 −0.784926
\(316\) −2.07547 −0.116754
\(317\) −11.7399 −0.659378 −0.329689 0.944090i \(-0.606944\pi\)
−0.329689 + 0.944090i \(0.606944\pi\)
\(318\) 2.79441 0.156703
\(319\) 13.1527 0.736411
\(320\) −2.90727 −0.162521
\(321\) −16.4187 −0.916405
\(322\) 4.85449 0.270530
\(323\) 7.51397 0.418089
\(324\) 2.30435 0.128019
\(325\) 16.3994 0.909677
\(326\) −17.0078 −0.941974
\(327\) −7.04962 −0.389845
\(328\) −2.11925 −0.117016
\(329\) 9.41712 0.519183
\(330\) 16.3139 0.898049
\(331\) −3.72572 −0.204784 −0.102392 0.994744i \(-0.532650\pi\)
−0.102392 + 0.994744i \(0.532650\pi\)
\(332\) −8.77630 −0.481662
\(333\) −8.10970 −0.444409
\(334\) 11.1082 0.607814
\(335\) −20.0564 −1.09580
\(336\) −2.64516 −0.144305
\(337\) 0.392319 0.0213710 0.0106855 0.999943i \(-0.496599\pi\)
0.0106855 + 0.999943i \(0.496599\pi\)
\(338\) −9.56611 −0.520328
\(339\) −9.49223 −0.515547
\(340\) 9.07899 0.492377
\(341\) −10.5914 −0.573554
\(342\) 12.4676 0.674172
\(343\) −12.1559 −0.656356
\(344\) −0.246973 −0.0133159
\(345\) −43.6533 −2.35021
\(346\) 7.43749 0.399842
\(347\) −26.2281 −1.40800 −0.703998 0.710202i \(-0.748604\pi\)
−0.703998 + 0.710202i \(0.748604\pi\)
\(348\) 19.1771 1.02800
\(349\) −5.24597 −0.280810 −0.140405 0.990094i \(-0.544840\pi\)
−0.140405 + 0.990094i \(0.544840\pi\)
\(350\) −3.19251 −0.170647
\(351\) −29.6434 −1.58225
\(352\) 1.96179 0.104564
\(353\) −6.45299 −0.343458 −0.171729 0.985144i \(-0.554935\pi\)
−0.171729 + 0.985144i \(0.554935\pi\)
\(354\) 20.6633 1.09824
\(355\) −39.7915 −2.11191
\(356\) 8.42300 0.446418
\(357\) 8.26045 0.437189
\(358\) 2.56601 0.135618
\(359\) −30.6743 −1.61893 −0.809463 0.587170i \(-0.800242\pi\)
−0.809463 + 0.587170i \(0.800242\pi\)
\(360\) 15.0644 0.793963
\(361\) −13.2106 −0.695293
\(362\) 17.2955 0.909030
\(363\) 20.4555 1.07364
\(364\) 4.39299 0.230255
\(365\) −25.8944 −1.35538
\(366\) 5.15311 0.269358
\(367\) −3.99356 −0.208462 −0.104231 0.994553i \(-0.533238\pi\)
−0.104231 + 0.994553i \(0.533238\pi\)
\(368\) −5.24942 −0.273645
\(369\) 10.9812 0.571657
\(370\) −4.55014 −0.236550
\(371\) 0.903446 0.0469046
\(372\) −15.4426 −0.800660
\(373\) −8.77963 −0.454592 −0.227296 0.973826i \(-0.572989\pi\)
−0.227296 + 0.973826i \(0.572989\pi\)
\(374\) −6.12637 −0.316787
\(375\) −12.8709 −0.664653
\(376\) −10.1832 −0.525160
\(377\) −31.8488 −1.64029
\(378\) 5.77074 0.296815
\(379\) 0.346627 0.0178050 0.00890252 0.999960i \(-0.497166\pi\)
0.00890252 + 0.999960i \(0.497166\pi\)
\(380\) 6.99526 0.358849
\(381\) −30.7990 −1.57788
\(382\) −7.03698 −0.360043
\(383\) −11.3843 −0.581711 −0.290855 0.956767i \(-0.593940\pi\)
−0.290855 + 0.956767i \(0.593940\pi\)
\(384\) 2.86035 0.145967
\(385\) 5.27436 0.268806
\(386\) 22.5963 1.15012
\(387\) 1.27972 0.0650519
\(388\) 8.08147 0.410275
\(389\) 6.21366 0.315045 0.157522 0.987515i \(-0.449649\pi\)
0.157522 + 0.987515i \(0.449649\pi\)
\(390\) −39.5033 −2.00033
\(391\) 16.3932 0.829039
\(392\) 6.14481 0.310360
\(393\) 46.2853 2.33478
\(394\) −5.69244 −0.286781
\(395\) 6.03396 0.303601
\(396\) −10.1652 −0.510822
\(397\) −26.0825 −1.30904 −0.654522 0.756043i \(-0.727130\pi\)
−0.654522 + 0.756043i \(0.727130\pi\)
\(398\) 26.8035 1.34354
\(399\) 6.36459 0.318628
\(400\) 3.45224 0.172612
\(401\) −11.2005 −0.559328 −0.279664 0.960098i \(-0.590223\pi\)
−0.279664 + 0.960098i \(0.590223\pi\)
\(402\) 19.7327 0.984177
\(403\) 25.6465 1.27754
\(404\) −15.8267 −0.787408
\(405\) −6.69937 −0.332894
\(406\) 6.20007 0.307704
\(407\) 3.07037 0.152192
\(408\) −8.93246 −0.442223
\(409\) −33.1316 −1.63825 −0.819125 0.573615i \(-0.805541\pi\)
−0.819125 + 0.573615i \(0.805541\pi\)
\(410\) 6.16124 0.304282
\(411\) 41.7849 2.06110
\(412\) 6.34543 0.312617
\(413\) 6.68055 0.328728
\(414\) 27.2005 1.33683
\(415\) 25.5151 1.25249
\(416\) −4.75038 −0.232907
\(417\) 35.5869 1.74270
\(418\) −4.72030 −0.230878
\(419\) 4.70544 0.229876 0.114938 0.993373i \(-0.463333\pi\)
0.114938 + 0.993373i \(0.463333\pi\)
\(420\) 7.69020 0.375243
\(421\) 0.481440 0.0234640 0.0117320 0.999931i \(-0.496266\pi\)
0.0117320 + 0.999931i \(0.496266\pi\)
\(422\) −9.11175 −0.443553
\(423\) 52.7657 2.56556
\(424\) −0.976945 −0.0474446
\(425\) −10.7808 −0.522947
\(426\) 39.1493 1.89679
\(427\) 1.66603 0.0806248
\(428\) 5.74011 0.277459
\(429\) 26.6563 1.28698
\(430\) 0.718018 0.0346259
\(431\) 3.93910 0.189740 0.0948700 0.995490i \(-0.469756\pi\)
0.0948700 + 0.995490i \(0.469756\pi\)
\(432\) −6.24021 −0.300232
\(433\) −20.7600 −0.997662 −0.498831 0.866699i \(-0.666237\pi\)
−0.498831 + 0.866699i \(0.666237\pi\)
\(434\) −4.99266 −0.239655
\(435\) −55.7532 −2.67316
\(436\) 2.46460 0.118033
\(437\) 12.6308 0.604212
\(438\) 25.4765 1.21732
\(439\) −27.9455 −1.33376 −0.666882 0.745163i \(-0.732371\pi\)
−0.666882 + 0.745163i \(0.732371\pi\)
\(440\) −5.70345 −0.271901
\(441\) −31.8401 −1.51619
\(442\) 14.8347 0.705617
\(443\) 16.1926 0.769333 0.384667 0.923056i \(-0.374316\pi\)
0.384667 + 0.923056i \(0.374316\pi\)
\(444\) 4.47670 0.212455
\(445\) −24.4880 −1.16084
\(446\) −11.2314 −0.531824
\(447\) −46.7609 −2.21172
\(448\) 0.924767 0.0436911
\(449\) 6.35882 0.300091 0.150046 0.988679i \(-0.452058\pi\)
0.150046 + 0.988679i \(0.452058\pi\)
\(450\) −17.8882 −0.843257
\(451\) −4.15752 −0.195770
\(452\) 3.31855 0.156092
\(453\) −69.9812 −3.28800
\(454\) 9.49489 0.445617
\(455\) −12.7716 −0.598743
\(456\) −6.88237 −0.322296
\(457\) −6.02019 −0.281613 −0.140806 0.990037i \(-0.544969\pi\)
−0.140806 + 0.990037i \(0.544969\pi\)
\(458\) 9.64030 0.450461
\(459\) 19.4873 0.909588
\(460\) 15.2615 0.711571
\(461\) 20.1400 0.938011 0.469006 0.883195i \(-0.344612\pi\)
0.469006 + 0.883195i \(0.344612\pi\)
\(462\) −5.18924 −0.241425
\(463\) 24.5324 1.14012 0.570059 0.821604i \(-0.306920\pi\)
0.570059 + 0.821604i \(0.306920\pi\)
\(464\) −6.70446 −0.311247
\(465\) 44.8958 2.08199
\(466\) −10.6424 −0.492998
\(467\) −33.1166 −1.53245 −0.766226 0.642571i \(-0.777868\pi\)
−0.766226 + 0.642571i \(0.777868\pi\)
\(468\) 24.6147 1.13781
\(469\) 6.37968 0.294586
\(470\) 29.6054 1.36560
\(471\) 6.83497 0.314939
\(472\) −7.22403 −0.332513
\(473\) −0.484508 −0.0222777
\(474\) −5.93658 −0.272676
\(475\) −8.30651 −0.381129
\(476\) −2.88791 −0.132367
\(477\) 5.06216 0.231780
\(478\) −6.03473 −0.276022
\(479\) 11.4385 0.522637 0.261319 0.965253i \(-0.415843\pi\)
0.261319 + 0.965253i \(0.415843\pi\)
\(480\) −8.31583 −0.379564
\(481\) −7.43476 −0.338996
\(482\) 8.99086 0.409523
\(483\) 13.8856 0.631815
\(484\) −7.15140 −0.325063
\(485\) −23.4950 −1.06686
\(486\) −12.1294 −0.550200
\(487\) 21.3072 0.965520 0.482760 0.875753i \(-0.339634\pi\)
0.482760 + 0.875753i \(0.339634\pi\)
\(488\) −1.80157 −0.0815530
\(489\) −48.6483 −2.19995
\(490\) −17.8646 −0.807042
\(491\) −10.6261 −0.479548 −0.239774 0.970829i \(-0.577073\pi\)
−0.239774 + 0.970829i \(0.577073\pi\)
\(492\) −6.06181 −0.273288
\(493\) 20.9371 0.942958
\(494\) 11.4300 0.514260
\(495\) 29.5531 1.32831
\(496\) 5.39883 0.242415
\(497\) 12.6572 0.567752
\(498\) −25.1033 −1.12491
\(499\) −14.2070 −0.635993 −0.317996 0.948092i \(-0.603010\pi\)
−0.317996 + 0.948092i \(0.603010\pi\)
\(500\) 4.49978 0.201236
\(501\) 31.7734 1.41953
\(502\) 9.62109 0.429410
\(503\) 42.8787 1.91187 0.955934 0.293581i \(-0.0948471\pi\)
0.955934 + 0.293581i \(0.0948471\pi\)
\(504\) −4.79179 −0.213443
\(505\) 46.0126 2.04753
\(506\) −10.2982 −0.457813
\(507\) −27.3625 −1.21521
\(508\) 10.7675 0.477732
\(509\) −20.6702 −0.916192 −0.458096 0.888903i \(-0.651468\pi\)
−0.458096 + 0.888903i \(0.651468\pi\)
\(510\) 25.9691 1.14993
\(511\) 8.23670 0.364370
\(512\) −1.00000 −0.0441942
\(513\) 15.0147 0.662917
\(514\) −27.6742 −1.22066
\(515\) −18.4479 −0.812911
\(516\) −0.706430 −0.0310989
\(517\) −19.9773 −0.878602
\(518\) 1.44734 0.0635925
\(519\) 21.2739 0.933819
\(520\) 13.8107 0.605637
\(521\) −22.0184 −0.964645 −0.482322 0.875994i \(-0.660207\pi\)
−0.482322 + 0.875994i \(0.660207\pi\)
\(522\) 34.7400 1.52053
\(523\) −15.9562 −0.697715 −0.348858 0.937176i \(-0.613430\pi\)
−0.348858 + 0.937176i \(0.613430\pi\)
\(524\) −16.1817 −0.706900
\(525\) −9.13172 −0.398541
\(526\) −9.78791 −0.426773
\(527\) −16.8598 −0.734423
\(528\) 5.61140 0.244205
\(529\) 4.55644 0.198106
\(530\) 2.84024 0.123372
\(531\) 37.4322 1.62442
\(532\) −2.22510 −0.0964705
\(533\) 10.0673 0.436061
\(534\) 24.0928 1.04260
\(535\) −16.6881 −0.721488
\(536\) −6.89869 −0.297978
\(537\) 7.33969 0.316731
\(538\) 14.1504 0.610067
\(539\) 12.0548 0.519237
\(540\) 18.1420 0.780708
\(541\) 21.3231 0.916750 0.458375 0.888759i \(-0.348432\pi\)
0.458375 + 0.888759i \(0.348432\pi\)
\(542\) 14.9984 0.644235
\(543\) 49.4712 2.12301
\(544\) 3.12285 0.133891
\(545\) −7.16526 −0.306926
\(546\) 12.5655 0.537755
\(547\) −6.58830 −0.281695 −0.140848 0.990031i \(-0.544983\pi\)
−0.140848 + 0.990031i \(0.544983\pi\)
\(548\) −14.6083 −0.624036
\(549\) 9.33503 0.398409
\(550\) 6.77255 0.288782
\(551\) 16.1318 0.687237
\(552\) −15.0152 −0.639090
\(553\) −1.91933 −0.0816180
\(554\) 6.51546 0.276815
\(555\) −13.0150 −0.552456
\(556\) −12.4414 −0.527635
\(557\) −8.20766 −0.347770 −0.173885 0.984766i \(-0.555632\pi\)
−0.173885 + 0.984766i \(0.555632\pi\)
\(558\) −27.9747 −1.18426
\(559\) 1.17322 0.0496217
\(560\) −2.68855 −0.113612
\(561\) −17.5236 −0.739846
\(562\) −27.8508 −1.17481
\(563\) −24.2028 −1.02003 −0.510013 0.860167i \(-0.670359\pi\)
−0.510013 + 0.860167i \(0.670359\pi\)
\(564\) −29.1277 −1.22650
\(565\) −9.64793 −0.405892
\(566\) −7.40071 −0.311075
\(567\) 2.13099 0.0894930
\(568\) −13.6869 −0.574288
\(569\) −43.8335 −1.83760 −0.918798 0.394727i \(-0.870839\pi\)
−0.918798 + 0.394727i \(0.870839\pi\)
\(570\) 20.0089 0.838082
\(571\) −20.6604 −0.864610 −0.432305 0.901727i \(-0.642300\pi\)
−0.432305 + 0.901727i \(0.642300\pi\)
\(572\) −9.31923 −0.389657
\(573\) −20.1282 −0.840869
\(574\) −1.95981 −0.0818011
\(575\) −18.1222 −0.755750
\(576\) 5.18162 0.215901
\(577\) 38.8143 1.61586 0.807930 0.589279i \(-0.200588\pi\)
0.807930 + 0.589279i \(0.200588\pi\)
\(578\) 7.24779 0.301468
\(579\) 64.6334 2.68607
\(580\) 19.4917 0.809349
\(581\) −8.11604 −0.336710
\(582\) 23.1159 0.958184
\(583\) −1.91656 −0.0793756
\(584\) −8.90678 −0.368565
\(585\) −71.5616 −2.95871
\(586\) −28.9410 −1.19554
\(587\) −24.1509 −0.996815 −0.498407 0.866943i \(-0.666082\pi\)
−0.498407 + 0.866943i \(0.666082\pi\)
\(588\) 17.5763 0.724835
\(589\) −12.9903 −0.535255
\(590\) 21.0022 0.864648
\(591\) −16.2824 −0.669768
\(592\) −1.56509 −0.0643247
\(593\) 8.60652 0.353427 0.176714 0.984262i \(-0.443453\pi\)
0.176714 + 0.984262i \(0.443453\pi\)
\(594\) −12.2420 −0.502294
\(595\) 8.39595 0.344200
\(596\) 16.3480 0.669638
\(597\) 76.6676 3.13780
\(598\) 24.9368 1.01974
\(599\) 43.4943 1.77713 0.888565 0.458750i \(-0.151703\pi\)
0.888565 + 0.458750i \(0.151703\pi\)
\(600\) 9.87461 0.403129
\(601\) 41.7126 1.70149 0.850747 0.525576i \(-0.176150\pi\)
0.850747 + 0.525576i \(0.176150\pi\)
\(602\) −0.228392 −0.00930858
\(603\) 35.7464 1.45571
\(604\) 24.4659 0.995504
\(605\) 20.7911 0.845277
\(606\) −45.2700 −1.83897
\(607\) 12.5991 0.511381 0.255690 0.966759i \(-0.417697\pi\)
0.255690 + 0.966759i \(0.417697\pi\)
\(608\) 2.40612 0.0975812
\(609\) 17.7344 0.718633
\(610\) 5.23764 0.212066
\(611\) 48.3742 1.95701
\(612\) −16.1814 −0.654096
\(613\) −17.0227 −0.687542 −0.343771 0.939054i \(-0.611704\pi\)
−0.343771 + 0.939054i \(0.611704\pi\)
\(614\) −22.1714 −0.894767
\(615\) 17.6233 0.710642
\(616\) 1.81419 0.0730960
\(617\) 0.633973 0.0255228 0.0127614 0.999919i \(-0.495938\pi\)
0.0127614 + 0.999919i \(0.495938\pi\)
\(618\) 18.1502 0.730107
\(619\) −38.6596 −1.55386 −0.776931 0.629586i \(-0.783225\pi\)
−0.776931 + 0.629586i \(0.783225\pi\)
\(620\) −15.6959 −0.630362
\(621\) 32.7575 1.31451
\(622\) 1.02105 0.0409402
\(623\) 7.78931 0.312072
\(624\) −13.5878 −0.543946
\(625\) −30.3432 −1.21373
\(626\) 25.1728 1.00611
\(627\) −13.5017 −0.539207
\(628\) −2.38955 −0.0953535
\(629\) 4.88754 0.194879
\(630\) 13.9311 0.555026
\(631\) −4.95319 −0.197183 −0.0985917 0.995128i \(-0.531434\pi\)
−0.0985917 + 0.995128i \(0.531434\pi\)
\(632\) 2.07547 0.0825577
\(633\) −26.0628 −1.03590
\(634\) 11.7399 0.466251
\(635\) −31.3042 −1.24227
\(636\) −2.79441 −0.110805
\(637\) −29.1902 −1.15656
\(638\) −13.1527 −0.520721
\(639\) 70.9202 2.80556
\(640\) 2.90727 0.114920
\(641\) 6.03197 0.238248 0.119124 0.992879i \(-0.461991\pi\)
0.119124 + 0.992879i \(0.461991\pi\)
\(642\) 16.4187 0.647996
\(643\) 16.8039 0.662679 0.331340 0.943512i \(-0.392499\pi\)
0.331340 + 0.943512i \(0.392499\pi\)
\(644\) −4.85449 −0.191294
\(645\) 2.05379 0.0808677
\(646\) −7.51397 −0.295633
\(647\) 18.9646 0.745576 0.372788 0.927917i \(-0.378402\pi\)
0.372788 + 0.927917i \(0.378402\pi\)
\(648\) −2.30435 −0.0905234
\(649\) −14.1720 −0.556300
\(650\) −16.3994 −0.643239
\(651\) −14.2808 −0.559708
\(652\) 17.0078 0.666076
\(653\) −5.59835 −0.219080 −0.109540 0.993982i \(-0.534938\pi\)
−0.109540 + 0.993982i \(0.534938\pi\)
\(654\) 7.04962 0.275662
\(655\) 47.0445 1.83818
\(656\) 2.11925 0.0827429
\(657\) 46.1516 1.80054
\(658\) −9.41712 −0.367118
\(659\) 27.7703 1.08178 0.540890 0.841094i \(-0.318088\pi\)
0.540890 + 0.841094i \(0.318088\pi\)
\(660\) −16.3139 −0.635017
\(661\) −32.7324 −1.27314 −0.636571 0.771218i \(-0.719648\pi\)
−0.636571 + 0.771218i \(0.719648\pi\)
\(662\) 3.72572 0.144804
\(663\) 42.4326 1.64795
\(664\) 8.77630 0.340587
\(665\) 6.46899 0.250857
\(666\) 8.10970 0.314244
\(667\) 35.1946 1.36274
\(668\) −11.1082 −0.429789
\(669\) −32.1259 −1.24206
\(670\) 20.0564 0.774845
\(671\) −3.53429 −0.136440
\(672\) 2.64516 0.102039
\(673\) −1.26633 −0.0488134 −0.0244067 0.999702i \(-0.507770\pi\)
−0.0244067 + 0.999702i \(0.507770\pi\)
\(674\) −0.392319 −0.0151115
\(675\) −21.5427 −0.829178
\(676\) 9.56611 0.367927
\(677\) −22.2235 −0.854119 −0.427059 0.904224i \(-0.640450\pi\)
−0.427059 + 0.904224i \(0.640450\pi\)
\(678\) 9.49223 0.364547
\(679\) 7.47348 0.286806
\(680\) −9.07899 −0.348163
\(681\) 27.1587 1.04073
\(682\) 10.5914 0.405564
\(683\) 4.75350 0.181888 0.0909438 0.995856i \(-0.471012\pi\)
0.0909438 + 0.995856i \(0.471012\pi\)
\(684\) −12.4676 −0.476712
\(685\) 42.4703 1.62271
\(686\) 12.1559 0.464114
\(687\) 27.5747 1.05204
\(688\) 0.246973 0.00941576
\(689\) 4.64086 0.176803
\(690\) 43.6533 1.66185
\(691\) −25.4118 −0.966711 −0.483355 0.875424i \(-0.660582\pi\)
−0.483355 + 0.875424i \(0.660582\pi\)
\(692\) −7.43749 −0.282731
\(693\) −9.40047 −0.357095
\(694\) 26.2281 0.995604
\(695\) 36.1707 1.37203
\(696\) −19.1771 −0.726908
\(697\) −6.61811 −0.250679
\(698\) 5.24597 0.198563
\(699\) −30.4410 −1.15138
\(700\) 3.19251 0.120666
\(701\) −48.4592 −1.83028 −0.915139 0.403138i \(-0.867920\pi\)
−0.915139 + 0.403138i \(0.867920\pi\)
\(702\) 29.6434 1.11882
\(703\) 3.76580 0.142030
\(704\) −1.96179 −0.0739376
\(705\) 84.6820 3.18931
\(706\) 6.45299 0.242862
\(707\) −14.6360 −0.550444
\(708\) −20.6633 −0.776574
\(709\) −12.0723 −0.453386 −0.226693 0.973966i \(-0.572791\pi\)
−0.226693 + 0.973966i \(0.572791\pi\)
\(710\) 39.7915 1.49335
\(711\) −10.7543 −0.403318
\(712\) −8.42300 −0.315665
\(713\) −28.3408 −1.06137
\(714\) −8.26045 −0.309139
\(715\) 27.0935 1.01324
\(716\) −2.56601 −0.0958962
\(717\) −17.2614 −0.644641
\(718\) 30.6743 1.14475
\(719\) −40.0619 −1.49406 −0.747028 0.664793i \(-0.768520\pi\)
−0.747028 + 0.664793i \(0.768520\pi\)
\(720\) −15.0644 −0.561417
\(721\) 5.86804 0.218537
\(722\) 13.2106 0.491646
\(723\) 25.7171 0.956427
\(724\) −17.2955 −0.642781
\(725\) −23.1454 −0.859598
\(726\) −20.4555 −0.759176
\(727\) 50.9079 1.88807 0.944034 0.329848i \(-0.106997\pi\)
0.944034 + 0.329848i \(0.106997\pi\)
\(728\) −4.39299 −0.162815
\(729\) −41.6074 −1.54101
\(730\) 25.8944 0.958396
\(731\) −0.771260 −0.0285261
\(732\) −5.15311 −0.190465
\(733\) 13.9213 0.514197 0.257098 0.966385i \(-0.417234\pi\)
0.257098 + 0.966385i \(0.417234\pi\)
\(734\) 3.99356 0.147405
\(735\) −51.0992 −1.88482
\(736\) 5.24942 0.193496
\(737\) −13.5337 −0.498522
\(738\) −10.9812 −0.404222
\(739\) 24.9402 0.917440 0.458720 0.888581i \(-0.348308\pi\)
0.458720 + 0.888581i \(0.348308\pi\)
\(740\) 4.55014 0.167266
\(741\) 32.6939 1.20104
\(742\) −0.903446 −0.0331665
\(743\) −16.3152 −0.598547 −0.299274 0.954167i \(-0.596744\pi\)
−0.299274 + 0.954167i \(0.596744\pi\)
\(744\) 15.4426 0.566152
\(745\) −47.5280 −1.74129
\(746\) 8.77963 0.321445
\(747\) −45.4755 −1.66386
\(748\) 6.12637 0.224002
\(749\) 5.30827 0.193960
\(750\) 12.8709 0.469981
\(751\) 8.63544 0.315112 0.157556 0.987510i \(-0.449639\pi\)
0.157556 + 0.987510i \(0.449639\pi\)
\(752\) 10.1832 0.371344
\(753\) 27.5197 1.00287
\(754\) 31.8488 1.15986
\(755\) −71.1291 −2.58865
\(756\) −5.77074 −0.209880
\(757\) −6.09659 −0.221584 −0.110792 0.993844i \(-0.535339\pi\)
−0.110792 + 0.993844i \(0.535339\pi\)
\(758\) −0.346627 −0.0125901
\(759\) −29.4566 −1.06921
\(760\) −6.99526 −0.253745
\(761\) 0.318396 0.0115418 0.00577091 0.999983i \(-0.498163\pi\)
0.00577091 + 0.999983i \(0.498163\pi\)
\(762\) 30.7990 1.11573
\(763\) 2.27918 0.0825118
\(764\) 7.03698 0.254589
\(765\) 47.0439 1.70088
\(766\) 11.3843 0.411332
\(767\) 34.3169 1.23911
\(768\) −2.86035 −0.103214
\(769\) −29.6649 −1.06974 −0.534872 0.844933i \(-0.679640\pi\)
−0.534872 + 0.844933i \(0.679640\pi\)
\(770\) −5.27436 −0.190075
\(771\) −79.1580 −2.85081
\(772\) −22.5963 −0.813258
\(773\) 12.5021 0.449671 0.224835 0.974397i \(-0.427816\pi\)
0.224835 + 0.974397i \(0.427816\pi\)
\(774\) −1.27972 −0.0459986
\(775\) 18.6380 0.669498
\(776\) −8.08147 −0.290108
\(777\) 4.13991 0.148518
\(778\) −6.21366 −0.222770
\(779\) −5.09919 −0.182697
\(780\) 39.5033 1.41445
\(781\) −26.8507 −0.960794
\(782\) −16.3932 −0.586219
\(783\) 41.8373 1.49514
\(784\) −6.14481 −0.219457
\(785\) 6.94708 0.247952
\(786\) −46.2853 −1.65094
\(787\) 20.5767 0.733479 0.366740 0.930324i \(-0.380474\pi\)
0.366740 + 0.930324i \(0.380474\pi\)
\(788\) 5.69244 0.202785
\(789\) −27.9969 −0.996715
\(790\) −6.03396 −0.214679
\(791\) 3.06889 0.109117
\(792\) 10.1652 0.361206
\(793\) 8.55812 0.303908
\(794\) 26.0825 0.925633
\(795\) 8.12410 0.288132
\(796\) −26.8035 −0.950026
\(797\) −24.1437 −0.855214 −0.427607 0.903965i \(-0.640643\pi\)
−0.427607 + 0.903965i \(0.640643\pi\)
\(798\) −6.36459 −0.225304
\(799\) −31.8007 −1.12503
\(800\) −3.45224 −0.122055
\(801\) 43.6448 1.54211
\(802\) 11.2005 0.395505
\(803\) −17.4732 −0.616616
\(804\) −19.7327 −0.695918
\(805\) 14.1133 0.497430
\(806\) −25.6465 −0.903360
\(807\) 40.4751 1.42479
\(808\) 15.8267 0.556782
\(809\) −7.60139 −0.267251 −0.133625 0.991032i \(-0.542662\pi\)
−0.133625 + 0.991032i \(0.542662\pi\)
\(810\) 6.69937 0.235392
\(811\) −16.7616 −0.588580 −0.294290 0.955716i \(-0.595083\pi\)
−0.294290 + 0.955716i \(0.595083\pi\)
\(812\) −6.20007 −0.217580
\(813\) 42.9006 1.50459
\(814\) −3.07037 −0.107616
\(815\) −49.4463 −1.73203
\(816\) 8.93246 0.312699
\(817\) −0.594248 −0.0207901
\(818\) 33.1316 1.15842
\(819\) 22.7628 0.795398
\(820\) −6.16124 −0.215160
\(821\) −10.1763 −0.355156 −0.177578 0.984107i \(-0.556826\pi\)
−0.177578 + 0.984107i \(0.556826\pi\)
\(822\) −41.7849 −1.45742
\(823\) −36.4234 −1.26964 −0.634820 0.772660i \(-0.718926\pi\)
−0.634820 + 0.772660i \(0.718926\pi\)
\(824\) −6.34543 −0.221053
\(825\) 19.3719 0.674442
\(826\) −6.68055 −0.232446
\(827\) −34.4459 −1.19780 −0.598900 0.800824i \(-0.704395\pi\)
−0.598900 + 0.800824i \(0.704395\pi\)
\(828\) −27.2005 −0.945284
\(829\) 19.9394 0.692524 0.346262 0.938138i \(-0.387451\pi\)
0.346262 + 0.938138i \(0.387451\pi\)
\(830\) −25.5151 −0.885642
\(831\) 18.6365 0.646494
\(832\) 4.75038 0.164690
\(833\) 19.1893 0.664871
\(834\) −35.5869 −1.23227
\(835\) 32.2946 1.11760
\(836\) 4.72030 0.163255
\(837\) −33.6899 −1.16449
\(838\) −4.70544 −0.162547
\(839\) 9.69550 0.334726 0.167363 0.985895i \(-0.446475\pi\)
0.167363 + 0.985895i \(0.446475\pi\)
\(840\) −7.69020 −0.265337
\(841\) 15.9498 0.549994
\(842\) −0.481440 −0.0165915
\(843\) −79.6631 −2.74374
\(844\) 9.11175 0.313639
\(845\) −27.8113 −0.956738
\(846\) −52.7657 −1.81412
\(847\) −6.61337 −0.227238
\(848\) 0.976945 0.0335484
\(849\) −21.1686 −0.726506
\(850\) 10.7808 0.369779
\(851\) 8.21581 0.281634
\(852\) −39.1493 −1.34123
\(853\) 20.0790 0.687492 0.343746 0.939063i \(-0.388304\pi\)
0.343746 + 0.939063i \(0.388304\pi\)
\(854\) −1.66603 −0.0570103
\(855\) 36.2468 1.23961
\(856\) −5.74011 −0.196193
\(857\) 20.9821 0.716733 0.358367 0.933581i \(-0.383334\pi\)
0.358367 + 0.933581i \(0.383334\pi\)
\(858\) −26.6563 −0.910031
\(859\) −21.9135 −0.747680 −0.373840 0.927493i \(-0.621959\pi\)
−0.373840 + 0.927493i \(0.621959\pi\)
\(860\) −0.718018 −0.0244842
\(861\) −5.60576 −0.191044
\(862\) −3.93910 −0.134166
\(863\) 30.8113 1.04883 0.524414 0.851463i \(-0.324284\pi\)
0.524414 + 0.851463i \(0.324284\pi\)
\(864\) 6.24021 0.212296
\(865\) 21.6228 0.735198
\(866\) 20.7600 0.705454
\(867\) 20.7312 0.704070
\(868\) 4.99266 0.169462
\(869\) 4.07163 0.138120
\(870\) 55.7532 1.89021
\(871\) 32.7714 1.11042
\(872\) −2.46460 −0.0834618
\(873\) 41.8751 1.41726
\(874\) −12.6308 −0.427242
\(875\) 4.16124 0.140676
\(876\) −25.4765 −0.860773
\(877\) 17.7004 0.597701 0.298850 0.954300i \(-0.403397\pi\)
0.298850 + 0.954300i \(0.403397\pi\)
\(878\) 27.9455 0.943113
\(879\) −82.7815 −2.79215
\(880\) 5.70345 0.192263
\(881\) −0.849879 −0.0286332 −0.0143166 0.999898i \(-0.504557\pi\)
−0.0143166 + 0.999898i \(0.504557\pi\)
\(882\) 31.8401 1.07211
\(883\) −15.8989 −0.535040 −0.267520 0.963552i \(-0.586204\pi\)
−0.267520 + 0.963552i \(0.586204\pi\)
\(884\) −14.8347 −0.498946
\(885\) 60.0738 2.01936
\(886\) −16.1926 −0.544001
\(887\) −8.57797 −0.288020 −0.144010 0.989576i \(-0.546000\pi\)
−0.144010 + 0.989576i \(0.546000\pi\)
\(888\) −4.47670 −0.150228
\(889\) 9.95746 0.333962
\(890\) 24.4880 0.820838
\(891\) −4.52064 −0.151447
\(892\) 11.2314 0.376057
\(893\) −24.5021 −0.819933
\(894\) 46.7609 1.56392
\(895\) 7.46009 0.249363
\(896\) −0.924767 −0.0308943
\(897\) 71.3279 2.38157
\(898\) −6.35882 −0.212197
\(899\) −36.1963 −1.20721
\(900\) 17.8882 0.596273
\(901\) −3.05085 −0.101639
\(902\) 4.15752 0.138430
\(903\) −0.653283 −0.0217399
\(904\) −3.31855 −0.110373
\(905\) 50.2827 1.67145
\(906\) 69.9812 2.32497
\(907\) 41.9823 1.39400 0.697000 0.717071i \(-0.254518\pi\)
0.697000 + 0.717071i \(0.254518\pi\)
\(908\) −9.49489 −0.315099
\(909\) −82.0081 −2.72004
\(910\) 12.7716 0.423376
\(911\) 8.97259 0.297275 0.148638 0.988892i \(-0.452511\pi\)
0.148638 + 0.988892i \(0.452511\pi\)
\(912\) 6.88237 0.227898
\(913\) 17.2172 0.569807
\(914\) 6.02019 0.199130
\(915\) 14.9815 0.495273
\(916\) −9.64030 −0.318524
\(917\) −14.9643 −0.494164
\(918\) −19.4873 −0.643176
\(919\) 14.1904 0.468097 0.234049 0.972225i \(-0.424803\pi\)
0.234049 + 0.972225i \(0.424803\pi\)
\(920\) −15.2615 −0.503157
\(921\) −63.4182 −2.08970
\(922\) −20.1400 −0.663274
\(923\) 65.0179 2.14009
\(924\) 5.18924 0.170713
\(925\) −5.40305 −0.177651
\(926\) −24.5324 −0.806185
\(927\) 32.8796 1.07991
\(928\) 6.70446 0.220085
\(929\) −35.1994 −1.15485 −0.577427 0.816442i \(-0.695943\pi\)
−0.577427 + 0.816442i \(0.695943\pi\)
\(930\) −44.8958 −1.47219
\(931\) 14.7852 0.484564
\(932\) 10.6424 0.348603
\(933\) 2.92055 0.0956146
\(934\) 33.1166 1.08361
\(935\) −17.8110 −0.582483
\(936\) −24.6147 −0.804556
\(937\) 3.34155 0.109164 0.0545819 0.998509i \(-0.482617\pi\)
0.0545819 + 0.998509i \(0.482617\pi\)
\(938\) −6.37968 −0.208304
\(939\) 72.0030 2.34973
\(940\) −29.6054 −0.965623
\(941\) 5.63570 0.183719 0.0918593 0.995772i \(-0.470719\pi\)
0.0918593 + 0.995772i \(0.470719\pi\)
\(942\) −6.83497 −0.222695
\(943\) −11.1249 −0.362275
\(944\) 7.22403 0.235122
\(945\) 16.7771 0.545760
\(946\) 0.484508 0.0157527
\(947\) 13.7554 0.446990 0.223495 0.974705i \(-0.428253\pi\)
0.223495 + 0.974705i \(0.428253\pi\)
\(948\) 5.93658 0.192811
\(949\) 42.3106 1.37346
\(950\) 8.30651 0.269499
\(951\) 33.5802 1.08891
\(952\) 2.88791 0.0935977
\(953\) 16.7347 0.542090 0.271045 0.962567i \(-0.412631\pi\)
0.271045 + 0.962567i \(0.412631\pi\)
\(954\) −5.06216 −0.163893
\(955\) −20.4584 −0.662018
\(956\) 6.03473 0.195177
\(957\) −37.6214 −1.21613
\(958\) −11.4385 −0.369560
\(959\) −13.5093 −0.436237
\(960\) 8.31583 0.268392
\(961\) −1.85260 −0.0597613
\(962\) 7.43476 0.239706
\(963\) 29.7431 0.958458
\(964\) −8.99086 −0.289576
\(965\) 65.6936 2.11475
\(966\) −13.8856 −0.446761
\(967\) −10.1650 −0.326885 −0.163443 0.986553i \(-0.552260\pi\)
−0.163443 + 0.986553i \(0.552260\pi\)
\(968\) 7.15140 0.229855
\(969\) −21.4926 −0.690443
\(970\) 23.4950 0.754380
\(971\) 22.7207 0.729142 0.364571 0.931176i \(-0.381216\pi\)
0.364571 + 0.931176i \(0.381216\pi\)
\(972\) 12.1294 0.389050
\(973\) −11.5054 −0.368847
\(974\) −21.3072 −0.682726
\(975\) −46.9082 −1.50226
\(976\) 1.80157 0.0576667
\(977\) −23.5699 −0.754069 −0.377034 0.926199i \(-0.623056\pi\)
−0.377034 + 0.926199i \(0.623056\pi\)
\(978\) 48.6483 1.55560
\(979\) −16.5241 −0.528113
\(980\) 17.8646 0.570665
\(981\) 12.7706 0.407734
\(982\) 10.6261 0.339091
\(983\) −35.1370 −1.12069 −0.560347 0.828258i \(-0.689332\pi\)
−0.560347 + 0.828258i \(0.689332\pi\)
\(984\) 6.06181 0.193243
\(985\) −16.5495 −0.527310
\(986\) −20.9371 −0.666772
\(987\) −26.9363 −0.857392
\(988\) −11.4300 −0.363637
\(989\) −1.29647 −0.0412252
\(990\) −29.5531 −0.939260
\(991\) −42.0035 −1.33428 −0.667142 0.744931i \(-0.732483\pi\)
−0.667142 + 0.744931i \(0.732483\pi\)
\(992\) −5.39883 −0.171413
\(993\) 10.6569 0.338185
\(994\) −12.6572 −0.401461
\(995\) 77.9252 2.47039
\(996\) 25.1033 0.795430
\(997\) 35.3169 1.11850 0.559248 0.829000i \(-0.311090\pi\)
0.559248 + 0.829000i \(0.311090\pi\)
\(998\) 14.2070 0.449715
\(999\) 9.76648 0.308998
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 4006.2.a.g.1.4 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.4 40 1.1 even 1 trivial