Properties

Label 4006.2.a.g.1.1
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 1.1
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.34571 q^{3} +1.00000 q^{4} -3.64453 q^{5} +3.34571 q^{6} +5.09237 q^{7} -1.00000 q^{8} +8.19376 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.34571 q^{3} +1.00000 q^{4} -3.64453 q^{5} +3.34571 q^{6} +5.09237 q^{7} -1.00000 q^{8} +8.19376 q^{9} +3.64453 q^{10} -0.225781 q^{11} -3.34571 q^{12} -4.05580 q^{13} -5.09237 q^{14} +12.1935 q^{15} +1.00000 q^{16} +0.866411 q^{17} -8.19376 q^{18} -0.400561 q^{19} -3.64453 q^{20} -17.0376 q^{21} +0.225781 q^{22} +2.97729 q^{23} +3.34571 q^{24} +8.28261 q^{25} +4.05580 q^{26} -17.3768 q^{27} +5.09237 q^{28} -2.19058 q^{29} -12.1935 q^{30} -9.28273 q^{31} -1.00000 q^{32} +0.755399 q^{33} -0.866411 q^{34} -18.5593 q^{35} +8.19376 q^{36} +5.14177 q^{37} +0.400561 q^{38} +13.5695 q^{39} +3.64453 q^{40} -4.50642 q^{41} +17.0376 q^{42} +5.90255 q^{43} -0.225781 q^{44} -29.8624 q^{45} -2.97729 q^{46} -12.4279 q^{47} -3.34571 q^{48} +18.9322 q^{49} -8.28261 q^{50} -2.89876 q^{51} -4.05580 q^{52} -1.83001 q^{53} +17.3768 q^{54} +0.822867 q^{55} -5.09237 q^{56} +1.34016 q^{57} +2.19058 q^{58} +9.30416 q^{59} +12.1935 q^{60} -0.790477 q^{61} +9.28273 q^{62} +41.7257 q^{63} +1.00000 q^{64} +14.7815 q^{65} -0.755399 q^{66} -4.08274 q^{67} +0.866411 q^{68} -9.96114 q^{69} +18.5593 q^{70} -9.99418 q^{71} -8.19376 q^{72} +9.29518 q^{73} -5.14177 q^{74} -27.7112 q^{75} -0.400561 q^{76} -1.14976 q^{77} -13.5695 q^{78} +8.02468 q^{79} -3.64453 q^{80} +33.5565 q^{81} +4.50642 q^{82} +3.91707 q^{83} -17.0376 q^{84} -3.15766 q^{85} -5.90255 q^{86} +7.32903 q^{87} +0.225781 q^{88} -12.6557 q^{89} +29.8624 q^{90} -20.6536 q^{91} +2.97729 q^{92} +31.0573 q^{93} +12.4279 q^{94} +1.45986 q^{95} +3.34571 q^{96} +10.1195 q^{97} -18.9322 q^{98} -1.85000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −3.34571 −1.93165 −0.965823 0.259203i \(-0.916540\pi\)
−0.965823 + 0.259203i \(0.916540\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.64453 −1.62988 −0.814942 0.579543i \(-0.803231\pi\)
−0.814942 + 0.579543i \(0.803231\pi\)
\(6\) 3.34571 1.36588
\(7\) 5.09237 1.92473 0.962367 0.271753i \(-0.0876035\pi\)
0.962367 + 0.271753i \(0.0876035\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.19376 2.73125
\(10\) 3.64453 1.15250
\(11\) −0.225781 −0.0680756 −0.0340378 0.999421i \(-0.510837\pi\)
−0.0340378 + 0.999421i \(0.510837\pi\)
\(12\) −3.34571 −0.965823
\(13\) −4.05580 −1.12488 −0.562439 0.826839i \(-0.690137\pi\)
−0.562439 + 0.826839i \(0.690137\pi\)
\(14\) −5.09237 −1.36099
\(15\) 12.1935 3.14836
\(16\) 1.00000 0.250000
\(17\) 0.866411 0.210136 0.105068 0.994465i \(-0.466494\pi\)
0.105068 + 0.994465i \(0.466494\pi\)
\(18\) −8.19376 −1.93129
\(19\) −0.400561 −0.0918950 −0.0459475 0.998944i \(-0.514631\pi\)
−0.0459475 + 0.998944i \(0.514631\pi\)
\(20\) −3.64453 −0.814942
\(21\) −17.0376 −3.71790
\(22\) 0.225781 0.0481368
\(23\) 2.97729 0.620808 0.310404 0.950605i \(-0.399536\pi\)
0.310404 + 0.950605i \(0.399536\pi\)
\(24\) 3.34571 0.682940
\(25\) 8.28261 1.65652
\(26\) 4.05580 0.795409
\(27\) −17.3768 −3.34417
\(28\) 5.09237 0.962367
\(29\) −2.19058 −0.406780 −0.203390 0.979098i \(-0.565196\pi\)
−0.203390 + 0.979098i \(0.565196\pi\)
\(30\) −12.1935 −2.22623
\(31\) −9.28273 −1.66723 −0.833614 0.552348i \(-0.813732\pi\)
−0.833614 + 0.552348i \(0.813732\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.755399 0.131498
\(34\) −0.866411 −0.148588
\(35\) −18.5593 −3.13709
\(36\) 8.19376 1.36563
\(37\) 5.14177 0.845301 0.422651 0.906293i \(-0.361100\pi\)
0.422651 + 0.906293i \(0.361100\pi\)
\(38\) 0.400561 0.0649796
\(39\) 13.5695 2.17287
\(40\) 3.64453 0.576251
\(41\) −4.50642 −0.703785 −0.351892 0.936040i \(-0.614462\pi\)
−0.351892 + 0.936040i \(0.614462\pi\)
\(42\) 17.0376 2.62895
\(43\) 5.90255 0.900131 0.450065 0.892996i \(-0.351401\pi\)
0.450065 + 0.892996i \(0.351401\pi\)
\(44\) −0.225781 −0.0340378
\(45\) −29.8624 −4.45163
\(46\) −2.97729 −0.438977
\(47\) −12.4279 −1.81280 −0.906400 0.422421i \(-0.861180\pi\)
−0.906400 + 0.422421i \(0.861180\pi\)
\(48\) −3.34571 −0.482911
\(49\) 18.9322 2.70460
\(50\) −8.28261 −1.17134
\(51\) −2.89876 −0.405907
\(52\) −4.05580 −0.562439
\(53\) −1.83001 −0.251371 −0.125685 0.992070i \(-0.540113\pi\)
−0.125685 + 0.992070i \(0.540113\pi\)
\(54\) 17.3768 2.36469
\(55\) 0.822867 0.110955
\(56\) −5.09237 −0.680496
\(57\) 1.34016 0.177509
\(58\) 2.19058 0.287637
\(59\) 9.30416 1.21130 0.605650 0.795732i \(-0.292913\pi\)
0.605650 + 0.795732i \(0.292913\pi\)
\(60\) 12.1935 1.57418
\(61\) −0.790477 −0.101210 −0.0506051 0.998719i \(-0.516115\pi\)
−0.0506051 + 0.998719i \(0.516115\pi\)
\(62\) 9.28273 1.17891
\(63\) 41.7257 5.25694
\(64\) 1.00000 0.125000
\(65\) 14.7815 1.83342
\(66\) −0.755399 −0.0929831
\(67\) −4.08274 −0.498786 −0.249393 0.968402i \(-0.580231\pi\)
−0.249393 + 0.968402i \(0.580231\pi\)
\(68\) 0.866411 0.105068
\(69\) −9.96114 −1.19918
\(70\) 18.5593 2.21826
\(71\) −9.99418 −1.18609 −0.593046 0.805169i \(-0.702075\pi\)
−0.593046 + 0.805169i \(0.702075\pi\)
\(72\) −8.19376 −0.965644
\(73\) 9.29518 1.08792 0.543960 0.839111i \(-0.316925\pi\)
0.543960 + 0.839111i \(0.316925\pi\)
\(74\) −5.14177 −0.597718
\(75\) −27.7112 −3.19981
\(76\) −0.400561 −0.0459475
\(77\) −1.14976 −0.131028
\(78\) −13.5695 −1.53645
\(79\) 8.02468 0.902847 0.451424 0.892310i \(-0.350916\pi\)
0.451424 + 0.892310i \(0.350916\pi\)
\(80\) −3.64453 −0.407471
\(81\) 33.5565 3.72850
\(82\) 4.50642 0.497651
\(83\) 3.91707 0.429954 0.214977 0.976619i \(-0.431032\pi\)
0.214977 + 0.976619i \(0.431032\pi\)
\(84\) −17.0376 −1.85895
\(85\) −3.15766 −0.342496
\(86\) −5.90255 −0.636488
\(87\) 7.32903 0.785754
\(88\) 0.225781 0.0240684
\(89\) −12.6557 −1.34150 −0.670748 0.741685i \(-0.734027\pi\)
−0.670748 + 0.741685i \(0.734027\pi\)
\(90\) 29.8624 3.14778
\(91\) −20.6536 −2.16509
\(92\) 2.97729 0.310404
\(93\) 31.0573 3.22049
\(94\) 12.4279 1.28184
\(95\) 1.45986 0.149778
\(96\) 3.34571 0.341470
\(97\) 10.1195 1.02748 0.513738 0.857947i \(-0.328260\pi\)
0.513738 + 0.857947i \(0.328260\pi\)
\(98\) −18.9322 −1.91244
\(99\) −1.85000 −0.185932
\(100\) 8.28261 0.828261
\(101\) 15.5250 1.54480 0.772399 0.635138i \(-0.219057\pi\)
0.772399 + 0.635138i \(0.219057\pi\)
\(102\) 2.89876 0.287020
\(103\) 12.2172 1.20379 0.601896 0.798574i \(-0.294412\pi\)
0.601896 + 0.798574i \(0.294412\pi\)
\(104\) 4.05580 0.397704
\(105\) 62.0940 6.05975
\(106\) 1.83001 0.177746
\(107\) −1.19286 −0.115318 −0.0576591 0.998336i \(-0.518364\pi\)
−0.0576591 + 0.998336i \(0.518364\pi\)
\(108\) −17.3768 −1.67209
\(109\) −4.15216 −0.397705 −0.198853 0.980029i \(-0.563722\pi\)
−0.198853 + 0.980029i \(0.563722\pi\)
\(110\) −0.822867 −0.0784573
\(111\) −17.2028 −1.63282
\(112\) 5.09237 0.481183
\(113\) 10.4021 0.978551 0.489276 0.872129i \(-0.337261\pi\)
0.489276 + 0.872129i \(0.337261\pi\)
\(114\) −1.34016 −0.125518
\(115\) −10.8508 −1.01184
\(116\) −2.19058 −0.203390
\(117\) −33.2323 −3.07233
\(118\) −9.30416 −0.856518
\(119\) 4.41208 0.404455
\(120\) −12.1935 −1.11311
\(121\) −10.9490 −0.995366
\(122\) 0.790477 0.0715664
\(123\) 15.0772 1.35946
\(124\) −9.28273 −0.833614
\(125\) −11.9636 −1.07005
\(126\) −41.7257 −3.71722
\(127\) 4.03373 0.357935 0.178968 0.983855i \(-0.442724\pi\)
0.178968 + 0.983855i \(0.442724\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −19.7482 −1.73873
\(130\) −14.7815 −1.29642
\(131\) −0.688921 −0.0601913 −0.0300957 0.999547i \(-0.509581\pi\)
−0.0300957 + 0.999547i \(0.509581\pi\)
\(132\) 0.755399 0.0657490
\(133\) −2.03980 −0.176873
\(134\) 4.08274 0.352695
\(135\) 63.3304 5.45061
\(136\) −0.866411 −0.0742941
\(137\) 14.0944 1.20417 0.602084 0.798432i \(-0.294337\pi\)
0.602084 + 0.798432i \(0.294337\pi\)
\(138\) 9.96114 0.847949
\(139\) 11.0608 0.938169 0.469084 0.883153i \(-0.344584\pi\)
0.469084 + 0.883153i \(0.344584\pi\)
\(140\) −18.5593 −1.56855
\(141\) 41.5802 3.50169
\(142\) 9.99418 0.838693
\(143\) 0.915725 0.0765768
\(144\) 8.19376 0.682814
\(145\) 7.98362 0.663004
\(146\) −9.29518 −0.769275
\(147\) −63.3416 −5.22433
\(148\) 5.14177 0.422651
\(149\) −9.28809 −0.760910 −0.380455 0.924799i \(-0.624233\pi\)
−0.380455 + 0.924799i \(0.624233\pi\)
\(150\) 27.7112 2.26261
\(151\) 0.175333 0.0142684 0.00713421 0.999975i \(-0.497729\pi\)
0.00713421 + 0.999975i \(0.497729\pi\)
\(152\) 0.400561 0.0324898
\(153\) 7.09917 0.573934
\(154\) 1.14976 0.0926504
\(155\) 33.8312 2.71739
\(156\) 13.5695 1.08643
\(157\) −16.2661 −1.29817 −0.649087 0.760714i \(-0.724849\pi\)
−0.649087 + 0.760714i \(0.724849\pi\)
\(158\) −8.02468 −0.638409
\(159\) 6.12267 0.485559
\(160\) 3.64453 0.288125
\(161\) 15.1614 1.19489
\(162\) −33.5565 −2.63645
\(163\) 12.4851 0.977908 0.488954 0.872310i \(-0.337379\pi\)
0.488954 + 0.872310i \(0.337379\pi\)
\(164\) −4.50642 −0.351892
\(165\) −2.75307 −0.214327
\(166\) −3.91707 −0.304024
\(167\) −16.5947 −1.28413 −0.642067 0.766649i \(-0.721923\pi\)
−0.642067 + 0.766649i \(0.721923\pi\)
\(168\) 17.0376 1.31448
\(169\) 3.44955 0.265350
\(170\) 3.15766 0.242182
\(171\) −3.28210 −0.250989
\(172\) 5.90255 0.450065
\(173\) −11.0918 −0.843294 −0.421647 0.906760i \(-0.638548\pi\)
−0.421647 + 0.906760i \(0.638548\pi\)
\(174\) −7.32903 −0.555612
\(175\) 42.1781 3.18836
\(176\) −0.225781 −0.0170189
\(177\) −31.1290 −2.33980
\(178\) 12.6557 0.948581
\(179\) 18.2533 1.36431 0.682156 0.731207i \(-0.261042\pi\)
0.682156 + 0.731207i \(0.261042\pi\)
\(180\) −29.8624 −2.22581
\(181\) −25.5293 −1.89758 −0.948789 0.315912i \(-0.897690\pi\)
−0.948789 + 0.315912i \(0.897690\pi\)
\(182\) 20.6536 1.53095
\(183\) 2.64471 0.195502
\(184\) −2.97729 −0.219489
\(185\) −18.7393 −1.37774
\(186\) −31.0573 −2.27723
\(187\) −0.195619 −0.0143051
\(188\) −12.4279 −0.906400
\(189\) −88.4892 −6.43664
\(190\) −1.45986 −0.105909
\(191\) 4.04315 0.292552 0.146276 0.989244i \(-0.453271\pi\)
0.146276 + 0.989244i \(0.453271\pi\)
\(192\) −3.34571 −0.241456
\(193\) −3.19342 −0.229867 −0.114934 0.993373i \(-0.536666\pi\)
−0.114934 + 0.993373i \(0.536666\pi\)
\(194\) −10.1195 −0.726535
\(195\) −49.4546 −3.54152
\(196\) 18.9322 1.35230
\(197\) −6.83509 −0.486980 −0.243490 0.969903i \(-0.578292\pi\)
−0.243490 + 0.969903i \(0.578292\pi\)
\(198\) 1.85000 0.131474
\(199\) −25.4649 −1.80516 −0.902578 0.430527i \(-0.858328\pi\)
−0.902578 + 0.430527i \(0.858328\pi\)
\(200\) −8.28261 −0.585669
\(201\) 13.6597 0.963479
\(202\) −15.5250 −1.09234
\(203\) −11.1552 −0.782943
\(204\) −2.89876 −0.202954
\(205\) 16.4238 1.14709
\(206\) −12.2172 −0.851210
\(207\) 24.3952 1.69558
\(208\) −4.05580 −0.281219
\(209\) 0.0904392 0.00625581
\(210\) −62.0940 −4.28489
\(211\) −16.3806 −1.12769 −0.563845 0.825881i \(-0.690678\pi\)
−0.563845 + 0.825881i \(0.690678\pi\)
\(212\) −1.83001 −0.125685
\(213\) 33.4376 2.29111
\(214\) 1.19286 0.0815423
\(215\) −21.5120 −1.46711
\(216\) 17.3768 1.18234
\(217\) −47.2711 −3.20897
\(218\) 4.15216 0.281220
\(219\) −31.0990 −2.10147
\(220\) 0.822867 0.0554777
\(221\) −3.51399 −0.236377
\(222\) 17.2028 1.15458
\(223\) 6.01176 0.402577 0.201288 0.979532i \(-0.435487\pi\)
0.201288 + 0.979532i \(0.435487\pi\)
\(224\) −5.09237 −0.340248
\(225\) 67.8657 4.52438
\(226\) −10.4021 −0.691940
\(227\) 6.55876 0.435320 0.217660 0.976025i \(-0.430158\pi\)
0.217660 + 0.976025i \(0.430158\pi\)
\(228\) 1.34016 0.0887543
\(229\) 28.6438 1.89284 0.946418 0.322945i \(-0.104673\pi\)
0.946418 + 0.322945i \(0.104673\pi\)
\(230\) 10.8508 0.715482
\(231\) 3.84677 0.253099
\(232\) 2.19058 0.143818
\(233\) −1.09835 −0.0719551 −0.0359776 0.999353i \(-0.511454\pi\)
−0.0359776 + 0.999353i \(0.511454\pi\)
\(234\) 33.2323 2.17246
\(235\) 45.2940 2.95465
\(236\) 9.30416 0.605650
\(237\) −26.8482 −1.74398
\(238\) −4.41208 −0.285993
\(239\) −21.8676 −1.41450 −0.707249 0.706964i \(-0.750064\pi\)
−0.707249 + 0.706964i \(0.750064\pi\)
\(240\) 12.1935 0.787089
\(241\) −20.6562 −1.33058 −0.665291 0.746584i \(-0.731693\pi\)
−0.665291 + 0.746584i \(0.731693\pi\)
\(242\) 10.9490 0.703830
\(243\) −60.1397 −3.85797
\(244\) −0.790477 −0.0506051
\(245\) −68.9990 −4.40818
\(246\) −15.0772 −0.961285
\(247\) 1.62460 0.103371
\(248\) 9.28273 0.589454
\(249\) −13.1054 −0.830520
\(250\) 11.9636 0.756642
\(251\) 12.0655 0.761569 0.380784 0.924664i \(-0.375654\pi\)
0.380784 + 0.924664i \(0.375654\pi\)
\(252\) 41.7257 2.62847
\(253\) −0.672216 −0.0422619
\(254\) −4.03373 −0.253099
\(255\) 10.5646 0.661582
\(256\) 1.00000 0.0625000
\(257\) 29.6448 1.84919 0.924597 0.380948i \(-0.124402\pi\)
0.924597 + 0.380948i \(0.124402\pi\)
\(258\) 19.7482 1.22947
\(259\) 26.1838 1.62698
\(260\) 14.7815 0.916710
\(261\) −17.9491 −1.11102
\(262\) 0.688921 0.0425617
\(263\) −25.3004 −1.56009 −0.780043 0.625725i \(-0.784803\pi\)
−0.780043 + 0.625725i \(0.784803\pi\)
\(264\) −0.755399 −0.0464916
\(265\) 6.66952 0.409705
\(266\) 2.03980 0.125068
\(267\) 42.3421 2.59130
\(268\) −4.08274 −0.249393
\(269\) −13.3561 −0.814336 −0.407168 0.913353i \(-0.633484\pi\)
−0.407168 + 0.913353i \(0.633484\pi\)
\(270\) −63.3304 −3.85416
\(271\) −4.66595 −0.283436 −0.141718 0.989907i \(-0.545263\pi\)
−0.141718 + 0.989907i \(0.545263\pi\)
\(272\) 0.866411 0.0525339
\(273\) 69.1011 4.18219
\(274\) −14.0944 −0.851476
\(275\) −1.87006 −0.112769
\(276\) −9.96114 −0.599590
\(277\) 9.79161 0.588321 0.294160 0.955756i \(-0.404960\pi\)
0.294160 + 0.955756i \(0.404960\pi\)
\(278\) −11.0608 −0.663386
\(279\) −76.0605 −4.55362
\(280\) 18.5593 1.10913
\(281\) −18.8851 −1.12659 −0.563294 0.826256i \(-0.690466\pi\)
−0.563294 + 0.826256i \(0.690466\pi\)
\(282\) −41.5802 −2.47607
\(283\) −16.2713 −0.967226 −0.483613 0.875282i \(-0.660676\pi\)
−0.483613 + 0.875282i \(0.660676\pi\)
\(284\) −9.99418 −0.593046
\(285\) −4.88426 −0.289318
\(286\) −0.915725 −0.0541480
\(287\) −22.9484 −1.35460
\(288\) −8.19376 −0.482822
\(289\) −16.2493 −0.955843
\(290\) −7.98362 −0.468814
\(291\) −33.8568 −1.98472
\(292\) 9.29518 0.543960
\(293\) −0.296281 −0.0173089 −0.00865447 0.999963i \(-0.502755\pi\)
−0.00865447 + 0.999963i \(0.502755\pi\)
\(294\) 63.3416 3.69416
\(295\) −33.9093 −1.97428
\(296\) −5.14177 −0.298859
\(297\) 3.92336 0.227657
\(298\) 9.28809 0.538045
\(299\) −12.0753 −0.698333
\(300\) −27.7112 −1.59991
\(301\) 30.0580 1.73251
\(302\) −0.175333 −0.0100893
\(303\) −51.9422 −2.98400
\(304\) −0.400561 −0.0229738
\(305\) 2.88092 0.164961
\(306\) −7.09917 −0.405832
\(307\) 33.7428 1.92580 0.962902 0.269852i \(-0.0869748\pi\)
0.962902 + 0.269852i \(0.0869748\pi\)
\(308\) −1.14976 −0.0655138
\(309\) −40.8751 −2.32530
\(310\) −33.8312 −1.92148
\(311\) 29.1852 1.65494 0.827470 0.561510i \(-0.189779\pi\)
0.827470 + 0.561510i \(0.189779\pi\)
\(312\) −13.5695 −0.768224
\(313\) −14.9698 −0.846141 −0.423070 0.906097i \(-0.639048\pi\)
−0.423070 + 0.906097i \(0.639048\pi\)
\(314\) 16.2661 0.917947
\(315\) −152.070 −8.56820
\(316\) 8.02468 0.451424
\(317\) −13.0581 −0.733415 −0.366707 0.930336i \(-0.619515\pi\)
−0.366707 + 0.930336i \(0.619515\pi\)
\(318\) −6.12267 −0.343342
\(319\) 0.494591 0.0276918
\(320\) −3.64453 −0.203735
\(321\) 3.99097 0.222754
\(322\) −15.1614 −0.844914
\(323\) −0.347051 −0.0193104
\(324\) 33.5565 1.86425
\(325\) −33.5926 −1.86338
\(326\) −12.4851 −0.691485
\(327\) 13.8919 0.768226
\(328\) 4.50642 0.248826
\(329\) −63.2876 −3.48916
\(330\) 2.75307 0.151552
\(331\) −25.7235 −1.41389 −0.706946 0.707267i \(-0.749928\pi\)
−0.706946 + 0.707267i \(0.749928\pi\)
\(332\) 3.91707 0.214977
\(333\) 42.1304 2.30873
\(334\) 16.5947 0.908019
\(335\) 14.8797 0.812964
\(336\) −17.0376 −0.929476
\(337\) 24.5965 1.33986 0.669928 0.742426i \(-0.266325\pi\)
0.669928 + 0.742426i \(0.266325\pi\)
\(338\) −3.44955 −0.187631
\(339\) −34.8025 −1.89021
\(340\) −3.15766 −0.171248
\(341\) 2.09587 0.113498
\(342\) 3.28210 0.177476
\(343\) 60.7631 3.28090
\(344\) −5.90255 −0.318244
\(345\) 36.3037 1.95452
\(346\) 11.0918 0.596299
\(347\) 16.7055 0.896797 0.448399 0.893834i \(-0.351995\pi\)
0.448399 + 0.893834i \(0.351995\pi\)
\(348\) 7.32903 0.392877
\(349\) 14.6391 0.783615 0.391807 0.920047i \(-0.371850\pi\)
0.391807 + 0.920047i \(0.371850\pi\)
\(350\) −42.1781 −2.25451
\(351\) 70.4770 3.76178
\(352\) 0.225781 0.0120342
\(353\) −26.0658 −1.38734 −0.693670 0.720293i \(-0.744007\pi\)
−0.693670 + 0.720293i \(0.744007\pi\)
\(354\) 31.1290 1.65449
\(355\) 36.4241 1.93319
\(356\) −12.6557 −0.670748
\(357\) −14.7615 −0.781264
\(358\) −18.2533 −0.964714
\(359\) 1.94679 0.102748 0.0513738 0.998679i \(-0.483640\pi\)
0.0513738 + 0.998679i \(0.483640\pi\)
\(360\) 29.8624 1.57389
\(361\) −18.8396 −0.991555
\(362\) 25.5293 1.34179
\(363\) 36.6322 1.92269
\(364\) −20.6536 −1.08255
\(365\) −33.8766 −1.77318
\(366\) −2.64471 −0.138241
\(367\) 10.8315 0.565401 0.282700 0.959208i \(-0.408770\pi\)
0.282700 + 0.959208i \(0.408770\pi\)
\(368\) 2.97729 0.155202
\(369\) −36.9246 −1.92222
\(370\) 18.7393 0.974211
\(371\) −9.31907 −0.483822
\(372\) 31.0573 1.61025
\(373\) −36.4854 −1.88914 −0.944571 0.328307i \(-0.893522\pi\)
−0.944571 + 0.328307i \(0.893522\pi\)
\(374\) 0.195619 0.0101152
\(375\) 40.0266 2.06696
\(376\) 12.4279 0.640921
\(377\) 8.88455 0.457577
\(378\) 88.4892 4.55139
\(379\) −16.7914 −0.862518 −0.431259 0.902228i \(-0.641930\pi\)
−0.431259 + 0.902228i \(0.641930\pi\)
\(380\) 1.45986 0.0748891
\(381\) −13.4957 −0.691405
\(382\) −4.04315 −0.206866
\(383\) −10.2072 −0.521563 −0.260782 0.965398i \(-0.583980\pi\)
−0.260782 + 0.965398i \(0.583980\pi\)
\(384\) 3.34571 0.170735
\(385\) 4.19034 0.213560
\(386\) 3.19342 0.162541
\(387\) 48.3641 2.45849
\(388\) 10.1195 0.513738
\(389\) 19.7850 1.00314 0.501569 0.865118i \(-0.332757\pi\)
0.501569 + 0.865118i \(0.332757\pi\)
\(390\) 49.4546 2.50423
\(391\) 2.57956 0.130454
\(392\) −18.9322 −0.956221
\(393\) 2.30493 0.116268
\(394\) 6.83509 0.344347
\(395\) −29.2462 −1.47154
\(396\) −1.85000 −0.0929660
\(397\) −6.55430 −0.328951 −0.164476 0.986381i \(-0.552593\pi\)
−0.164476 + 0.986381i \(0.552593\pi\)
\(398\) 25.4649 1.27644
\(399\) 6.82459 0.341657
\(400\) 8.28261 0.414130
\(401\) −17.7763 −0.887707 −0.443854 0.896099i \(-0.646389\pi\)
−0.443854 + 0.896099i \(0.646389\pi\)
\(402\) −13.6597 −0.681282
\(403\) 37.6489 1.87543
\(404\) 15.5250 0.772399
\(405\) −122.298 −6.07702
\(406\) 11.1552 0.553624
\(407\) −1.16091 −0.0575444
\(408\) 2.89876 0.143510
\(409\) 28.7471 1.42145 0.710726 0.703469i \(-0.248366\pi\)
0.710726 + 0.703469i \(0.248366\pi\)
\(410\) −16.4238 −0.811113
\(411\) −47.1559 −2.32603
\(412\) 12.2172 0.601896
\(413\) 47.3802 2.33143
\(414\) −24.3952 −1.19896
\(415\) −14.2759 −0.700776
\(416\) 4.05580 0.198852
\(417\) −37.0064 −1.81221
\(418\) −0.0904392 −0.00442353
\(419\) 25.2111 1.23164 0.615821 0.787886i \(-0.288824\pi\)
0.615821 + 0.787886i \(0.288824\pi\)
\(420\) 62.0940 3.02988
\(421\) −12.9193 −0.629648 −0.314824 0.949150i \(-0.601946\pi\)
−0.314824 + 0.949150i \(0.601946\pi\)
\(422\) 16.3806 0.797397
\(423\) −101.832 −4.95122
\(424\) 1.83001 0.0888730
\(425\) 7.17614 0.348094
\(426\) −33.4376 −1.62006
\(427\) −4.02540 −0.194803
\(428\) −1.19286 −0.0576591
\(429\) −3.06375 −0.147919
\(430\) 21.5120 1.03740
\(431\) −14.8705 −0.716286 −0.358143 0.933667i \(-0.616590\pi\)
−0.358143 + 0.933667i \(0.616590\pi\)
\(432\) −17.3768 −0.836043
\(433\) 15.3636 0.738328 0.369164 0.929364i \(-0.379644\pi\)
0.369164 + 0.929364i \(0.379644\pi\)
\(434\) 47.2711 2.26908
\(435\) −26.7109 −1.28069
\(436\) −4.15216 −0.198853
\(437\) −1.19259 −0.0570491
\(438\) 31.0990 1.48597
\(439\) 33.0583 1.57779 0.788894 0.614530i \(-0.210654\pi\)
0.788894 + 0.614530i \(0.210654\pi\)
\(440\) −0.822867 −0.0392287
\(441\) 155.126 7.38695
\(442\) 3.51399 0.167144
\(443\) −3.60408 −0.171235 −0.0856175 0.996328i \(-0.527286\pi\)
−0.0856175 + 0.996328i \(0.527286\pi\)
\(444\) −17.2028 −0.816411
\(445\) 46.1239 2.18648
\(446\) −6.01176 −0.284665
\(447\) 31.0753 1.46981
\(448\) 5.09237 0.240592
\(449\) −2.73595 −0.129118 −0.0645588 0.997914i \(-0.520564\pi\)
−0.0645588 + 0.997914i \(0.520564\pi\)
\(450\) −67.8657 −3.19922
\(451\) 1.01747 0.0479106
\(452\) 10.4021 0.489276
\(453\) −0.586614 −0.0275615
\(454\) −6.55876 −0.307818
\(455\) 75.2728 3.52885
\(456\) −1.34016 −0.0627588
\(457\) −5.07560 −0.237426 −0.118713 0.992929i \(-0.537877\pi\)
−0.118713 + 0.992929i \(0.537877\pi\)
\(458\) −28.6438 −1.33844
\(459\) −15.0555 −0.702729
\(460\) −10.8508 −0.505922
\(461\) 25.3870 1.18239 0.591195 0.806528i \(-0.298656\pi\)
0.591195 + 0.806528i \(0.298656\pi\)
\(462\) −3.84677 −0.178968
\(463\) 17.4199 0.809572 0.404786 0.914411i \(-0.367346\pi\)
0.404786 + 0.914411i \(0.367346\pi\)
\(464\) −2.19058 −0.101695
\(465\) −113.189 −5.24903
\(466\) 1.09835 0.0508800
\(467\) 34.1750 1.58143 0.790715 0.612185i \(-0.209709\pi\)
0.790715 + 0.612185i \(0.209709\pi\)
\(468\) −33.2323 −1.53616
\(469\) −20.7908 −0.960031
\(470\) −45.2940 −2.08925
\(471\) 54.4215 2.50761
\(472\) −9.30416 −0.428259
\(473\) −1.33269 −0.0612770
\(474\) 26.8482 1.23318
\(475\) −3.31769 −0.152226
\(476\) 4.41208 0.202227
\(477\) −14.9946 −0.686558
\(478\) 21.8676 1.00020
\(479\) −43.0987 −1.96923 −0.984615 0.174740i \(-0.944092\pi\)
−0.984615 + 0.174740i \(0.944092\pi\)
\(480\) −12.1935 −0.556556
\(481\) −20.8540 −0.950860
\(482\) 20.6562 0.940864
\(483\) −50.7258 −2.30810
\(484\) −10.9490 −0.497683
\(485\) −36.8807 −1.67467
\(486\) 60.1397 2.72799
\(487\) 20.2072 0.915674 0.457837 0.889036i \(-0.348624\pi\)
0.457837 + 0.889036i \(0.348624\pi\)
\(488\) 0.790477 0.0357832
\(489\) −41.7715 −1.88897
\(490\) 68.9990 3.11706
\(491\) 8.40833 0.379463 0.189731 0.981836i \(-0.439238\pi\)
0.189731 + 0.981836i \(0.439238\pi\)
\(492\) 15.0772 0.679731
\(493\) −1.89794 −0.0854789
\(494\) −1.62460 −0.0730941
\(495\) 6.74238 0.303047
\(496\) −9.28273 −0.416807
\(497\) −50.8941 −2.28291
\(498\) 13.1054 0.587266
\(499\) 12.9379 0.579180 0.289590 0.957151i \(-0.406481\pi\)
0.289590 + 0.957151i \(0.406481\pi\)
\(500\) −11.9636 −0.535027
\(501\) 55.5209 2.48049
\(502\) −12.0655 −0.538511
\(503\) 13.0734 0.582912 0.291456 0.956584i \(-0.405860\pi\)
0.291456 + 0.956584i \(0.405860\pi\)
\(504\) −41.7257 −1.85861
\(505\) −56.5814 −2.51784
\(506\) 0.672216 0.0298837
\(507\) −11.5412 −0.512562
\(508\) 4.03373 0.178968
\(509\) −24.1204 −1.06912 −0.534560 0.845131i \(-0.679523\pi\)
−0.534560 + 0.845131i \(0.679523\pi\)
\(510\) −10.5646 −0.467809
\(511\) 47.3345 2.09395
\(512\) −1.00000 −0.0441942
\(513\) 6.96048 0.307313
\(514\) −29.6448 −1.30758
\(515\) −44.5258 −1.96204
\(516\) −19.7482 −0.869367
\(517\) 2.80599 0.123408
\(518\) −26.1838 −1.15045
\(519\) 37.1099 1.62894
\(520\) −14.7815 −0.648212
\(521\) −19.2528 −0.843482 −0.421741 0.906716i \(-0.638581\pi\)
−0.421741 + 0.906716i \(0.638581\pi\)
\(522\) 17.9491 0.785609
\(523\) −1.14698 −0.0501538 −0.0250769 0.999686i \(-0.507983\pi\)
−0.0250769 + 0.999686i \(0.507983\pi\)
\(524\) −0.688921 −0.0300957
\(525\) −141.116 −6.15879
\(526\) 25.3004 1.10315
\(527\) −8.04266 −0.350344
\(528\) 0.755399 0.0328745
\(529\) −14.1358 −0.614598
\(530\) −6.66952 −0.289705
\(531\) 76.2361 3.30837
\(532\) −2.03980 −0.0884367
\(533\) 18.2772 0.791672
\(534\) −42.3421 −1.83232
\(535\) 4.34742 0.187955
\(536\) 4.08274 0.176348
\(537\) −61.0701 −2.63537
\(538\) 13.3561 0.575822
\(539\) −4.27454 −0.184117
\(540\) 63.3304 2.72531
\(541\) −6.64322 −0.285614 −0.142807 0.989751i \(-0.545613\pi\)
−0.142807 + 0.989751i \(0.545613\pi\)
\(542\) 4.66595 0.200420
\(543\) 85.4136 3.66545
\(544\) −0.866411 −0.0371471
\(545\) 15.1327 0.648213
\(546\) −69.1011 −2.95725
\(547\) 37.3406 1.59657 0.798283 0.602282i \(-0.205742\pi\)
0.798283 + 0.602282i \(0.205742\pi\)
\(548\) 14.0944 0.602084
\(549\) −6.47698 −0.276431
\(550\) 1.87006 0.0797396
\(551\) 0.877459 0.0373810
\(552\) 9.96114 0.423974
\(553\) 40.8646 1.73774
\(554\) −9.79161 −0.416006
\(555\) 62.6963 2.66131
\(556\) 11.0608 0.469084
\(557\) −36.5932 −1.55050 −0.775252 0.631652i \(-0.782377\pi\)
−0.775252 + 0.631652i \(0.782377\pi\)
\(558\) 76.0605 3.21990
\(559\) −23.9396 −1.01254
\(560\) −18.5593 −0.784273
\(561\) 0.654486 0.0276324
\(562\) 18.8851 0.796618
\(563\) 4.53101 0.190959 0.0954797 0.995431i \(-0.469562\pi\)
0.0954797 + 0.995431i \(0.469562\pi\)
\(564\) 41.5802 1.75084
\(565\) −37.9109 −1.59492
\(566\) 16.2713 0.683932
\(567\) 170.882 7.17637
\(568\) 9.99418 0.419347
\(569\) −9.92421 −0.416044 −0.208022 0.978124i \(-0.566703\pi\)
−0.208022 + 0.978124i \(0.566703\pi\)
\(570\) 4.88426 0.204579
\(571\) 14.5818 0.610229 0.305115 0.952316i \(-0.401305\pi\)
0.305115 + 0.952316i \(0.401305\pi\)
\(572\) 0.915725 0.0382884
\(573\) −13.5272 −0.565108
\(574\) 22.9484 0.957846
\(575\) 24.6597 1.02838
\(576\) 8.19376 0.341407
\(577\) −26.4842 −1.10255 −0.551275 0.834324i \(-0.685859\pi\)
−0.551275 + 0.834324i \(0.685859\pi\)
\(578\) 16.2493 0.675883
\(579\) 10.6842 0.444022
\(580\) 7.98362 0.331502
\(581\) 19.9472 0.827548
\(582\) 33.8568 1.40341
\(583\) 0.413182 0.0171122
\(584\) −9.29518 −0.384637
\(585\) 121.116 5.00754
\(586\) 0.296281 0.0122393
\(587\) −26.0865 −1.07671 −0.538353 0.842720i \(-0.680953\pi\)
−0.538353 + 0.842720i \(0.680953\pi\)
\(588\) −63.3416 −2.61216
\(589\) 3.71830 0.153210
\(590\) 33.9093 1.39602
\(591\) 22.8682 0.940673
\(592\) 5.14177 0.211325
\(593\) −14.6531 −0.601730 −0.300865 0.953667i \(-0.597275\pi\)
−0.300865 + 0.953667i \(0.597275\pi\)
\(594\) −3.92336 −0.160978
\(595\) −16.0800 −0.659215
\(596\) −9.28809 −0.380455
\(597\) 85.1980 3.48692
\(598\) 12.0753 0.493796
\(599\) −2.09562 −0.0856249 −0.0428125 0.999083i \(-0.513632\pi\)
−0.0428125 + 0.999083i \(0.513632\pi\)
\(600\) 27.7112 1.13130
\(601\) 17.1605 0.699990 0.349995 0.936752i \(-0.386183\pi\)
0.349995 + 0.936752i \(0.386183\pi\)
\(602\) −30.0580 −1.22507
\(603\) −33.4530 −1.36231
\(604\) 0.175333 0.00713421
\(605\) 39.9041 1.62233
\(606\) 51.9422 2.11001
\(607\) 22.1521 0.899126 0.449563 0.893249i \(-0.351580\pi\)
0.449563 + 0.893249i \(0.351580\pi\)
\(608\) 0.400561 0.0162449
\(609\) 37.3221 1.51237
\(610\) −2.88092 −0.116645
\(611\) 50.4052 2.03918
\(612\) 7.09917 0.286967
\(613\) −13.3345 −0.538576 −0.269288 0.963060i \(-0.586788\pi\)
−0.269288 + 0.963060i \(0.586788\pi\)
\(614\) −33.7428 −1.36175
\(615\) −54.9492 −2.21577
\(616\) 1.14976 0.0463252
\(617\) 8.10512 0.326300 0.163150 0.986601i \(-0.447835\pi\)
0.163150 + 0.986601i \(0.447835\pi\)
\(618\) 40.8751 1.64424
\(619\) −24.3681 −0.979436 −0.489718 0.871881i \(-0.662900\pi\)
−0.489718 + 0.871881i \(0.662900\pi\)
\(620\) 33.8312 1.35869
\(621\) −51.7358 −2.07609
\(622\) −29.1852 −1.17022
\(623\) −64.4472 −2.58202
\(624\) 13.5695 0.543216
\(625\) 2.18853 0.0875412
\(626\) 14.9698 0.598312
\(627\) −0.302583 −0.0120840
\(628\) −16.2661 −0.649087
\(629\) 4.45488 0.177628
\(630\) 152.070 6.05863
\(631\) −28.1349 −1.12003 −0.560017 0.828481i \(-0.689205\pi\)
−0.560017 + 0.828481i \(0.689205\pi\)
\(632\) −8.02468 −0.319205
\(633\) 54.8048 2.17830
\(634\) 13.0581 0.518602
\(635\) −14.7010 −0.583393
\(636\) 6.12267 0.242780
\(637\) −76.7853 −3.04234
\(638\) −0.494591 −0.0195811
\(639\) −81.8900 −3.23952
\(640\) 3.64453 0.144063
\(641\) −28.2380 −1.11533 −0.557667 0.830065i \(-0.688303\pi\)
−0.557667 + 0.830065i \(0.688303\pi\)
\(642\) −3.99097 −0.157511
\(643\) −46.6720 −1.84057 −0.920283 0.391254i \(-0.872041\pi\)
−0.920283 + 0.391254i \(0.872041\pi\)
\(644\) 15.1614 0.597445
\(645\) 71.9730 2.83393
\(646\) 0.347051 0.0136545
\(647\) −16.3500 −0.642786 −0.321393 0.946946i \(-0.604151\pi\)
−0.321393 + 0.946946i \(0.604151\pi\)
\(648\) −33.5565 −1.31822
\(649\) −2.10071 −0.0824600
\(650\) 33.5926 1.31761
\(651\) 158.155 6.19859
\(652\) 12.4851 0.488954
\(653\) −30.5874 −1.19698 −0.598488 0.801131i \(-0.704232\pi\)
−0.598488 + 0.801131i \(0.704232\pi\)
\(654\) −13.8919 −0.543218
\(655\) 2.51079 0.0981048
\(656\) −4.50642 −0.175946
\(657\) 76.1626 2.97138
\(658\) 63.2876 2.46721
\(659\) 3.71700 0.144794 0.0723970 0.997376i \(-0.476935\pi\)
0.0723970 + 0.997376i \(0.476935\pi\)
\(660\) −2.75307 −0.107163
\(661\) 23.6062 0.918175 0.459088 0.888391i \(-0.348176\pi\)
0.459088 + 0.888391i \(0.348176\pi\)
\(662\) 25.7235 0.999773
\(663\) 11.7568 0.456596
\(664\) −3.91707 −0.152012
\(665\) 7.43413 0.288283
\(666\) −42.1304 −1.63252
\(667\) −6.52198 −0.252532
\(668\) −16.5947 −0.642067
\(669\) −20.1136 −0.777636
\(670\) −14.8797 −0.574852
\(671\) 0.178475 0.00688995
\(672\) 17.0376 0.657239
\(673\) 5.20959 0.200815 0.100408 0.994946i \(-0.467985\pi\)
0.100408 + 0.994946i \(0.467985\pi\)
\(674\) −24.5965 −0.947421
\(675\) −143.925 −5.53969
\(676\) 3.44955 0.132675
\(677\) −46.6202 −1.79176 −0.895880 0.444297i \(-0.853453\pi\)
−0.895880 + 0.444297i \(0.853453\pi\)
\(678\) 34.8025 1.33658
\(679\) 51.5320 1.97762
\(680\) 3.15766 0.121091
\(681\) −21.9437 −0.840885
\(682\) −2.09587 −0.0802549
\(683\) −4.70304 −0.179957 −0.0899785 0.995944i \(-0.528680\pi\)
−0.0899785 + 0.995944i \(0.528680\pi\)
\(684\) −3.28210 −0.125494
\(685\) −51.3676 −1.96266
\(686\) −60.7631 −2.31995
\(687\) −95.8338 −3.65629
\(688\) 5.90255 0.225033
\(689\) 7.42215 0.282761
\(690\) −36.3037 −1.38206
\(691\) −28.6239 −1.08891 −0.544453 0.838791i \(-0.683263\pi\)
−0.544453 + 0.838791i \(0.683263\pi\)
\(692\) −11.0918 −0.421647
\(693\) −9.42088 −0.357870
\(694\) −16.7055 −0.634131
\(695\) −40.3116 −1.52911
\(696\) −7.32903 −0.277806
\(697\) −3.90441 −0.147890
\(698\) −14.6391 −0.554099
\(699\) 3.67475 0.138992
\(700\) 42.1781 1.59418
\(701\) −29.2768 −1.10577 −0.552884 0.833258i \(-0.686473\pi\)
−0.552884 + 0.833258i \(0.686473\pi\)
\(702\) −70.4770 −2.65998
\(703\) −2.05959 −0.0776790
\(704\) −0.225781 −0.00850946
\(705\) −151.540 −5.70734
\(706\) 26.0658 0.980998
\(707\) 79.0591 2.97332
\(708\) −31.1290 −1.16990
\(709\) −38.6355 −1.45099 −0.725494 0.688228i \(-0.758389\pi\)
−0.725494 + 0.688228i \(0.758389\pi\)
\(710\) −36.4241 −1.36697
\(711\) 65.7524 2.46591
\(712\) 12.6557 0.474291
\(713\) −27.6374 −1.03503
\(714\) 14.7615 0.552437
\(715\) −3.33739 −0.124811
\(716\) 18.2533 0.682156
\(717\) 73.1626 2.73231
\(718\) −1.94679 −0.0726536
\(719\) −19.8083 −0.738723 −0.369362 0.929286i \(-0.620424\pi\)
−0.369362 + 0.929286i \(0.620424\pi\)
\(720\) −29.8624 −1.11291
\(721\) 62.2143 2.31698
\(722\) 18.8396 0.701135
\(723\) 69.1096 2.57021
\(724\) −25.5293 −0.948789
\(725\) −18.1437 −0.673839
\(726\) −36.6322 −1.35955
\(727\) −30.8120 −1.14275 −0.571377 0.820688i \(-0.693590\pi\)
−0.571377 + 0.820688i \(0.693590\pi\)
\(728\) 20.6536 0.765475
\(729\) 100.541 3.72373
\(730\) 33.8766 1.25383
\(731\) 5.11404 0.189149
\(732\) 2.64471 0.0977512
\(733\) 19.6630 0.726270 0.363135 0.931736i \(-0.381706\pi\)
0.363135 + 0.931736i \(0.381706\pi\)
\(734\) −10.8315 −0.399799
\(735\) 230.851 8.51505
\(736\) −2.97729 −0.109744
\(737\) 0.921807 0.0339552
\(738\) 36.9246 1.35921
\(739\) −50.5270 −1.85867 −0.929333 0.369243i \(-0.879617\pi\)
−0.929333 + 0.369243i \(0.879617\pi\)
\(740\) −18.7393 −0.688871
\(741\) −5.43543 −0.199675
\(742\) 9.31907 0.342114
\(743\) 1.93521 0.0709958 0.0354979 0.999370i \(-0.488698\pi\)
0.0354979 + 0.999370i \(0.488698\pi\)
\(744\) −31.0573 −1.13862
\(745\) 33.8507 1.24020
\(746\) 36.4854 1.33583
\(747\) 32.0956 1.17432
\(748\) −0.195619 −0.00715256
\(749\) −6.07449 −0.221957
\(750\) −40.0266 −1.46156
\(751\) −39.4628 −1.44002 −0.720010 0.693964i \(-0.755863\pi\)
−0.720010 + 0.693964i \(0.755863\pi\)
\(752\) −12.4279 −0.453200
\(753\) −40.3677 −1.47108
\(754\) −8.88455 −0.323556
\(755\) −0.639007 −0.0232559
\(756\) −88.4892 −3.21832
\(757\) −10.6029 −0.385369 −0.192685 0.981261i \(-0.561719\pi\)
−0.192685 + 0.981261i \(0.561719\pi\)
\(758\) 16.7914 0.609892
\(759\) 2.24904 0.0816350
\(760\) −1.45986 −0.0529546
\(761\) 3.73082 0.135242 0.0676211 0.997711i \(-0.478459\pi\)
0.0676211 + 0.997711i \(0.478459\pi\)
\(762\) 13.4957 0.488897
\(763\) −21.1443 −0.765477
\(764\) 4.04315 0.146276
\(765\) −25.8731 −0.935445
\(766\) 10.2072 0.368801
\(767\) −37.7359 −1.36256
\(768\) −3.34571 −0.120728
\(769\) −42.7266 −1.54076 −0.770380 0.637585i \(-0.779934\pi\)
−0.770380 + 0.637585i \(0.779934\pi\)
\(770\) −4.19034 −0.151009
\(771\) −99.1829 −3.57199
\(772\) −3.19342 −0.114934
\(773\) −6.58701 −0.236918 −0.118459 0.992959i \(-0.537795\pi\)
−0.118459 + 0.992959i \(0.537795\pi\)
\(774\) −48.3641 −1.73841
\(775\) −76.8852 −2.76180
\(776\) −10.1195 −0.363267
\(777\) −87.6032 −3.14275
\(778\) −19.7850 −0.709325
\(779\) 1.80510 0.0646743
\(780\) −49.4546 −1.77076
\(781\) 2.25650 0.0807439
\(782\) −2.57956 −0.0922447
\(783\) 38.0652 1.36034
\(784\) 18.9322 0.676150
\(785\) 59.2822 2.11587
\(786\) −2.30493 −0.0822141
\(787\) −16.4679 −0.587017 −0.293508 0.955957i \(-0.594823\pi\)
−0.293508 + 0.955957i \(0.594823\pi\)
\(788\) −6.83509 −0.243490
\(789\) 84.6476 3.01354
\(790\) 29.2462 1.04053
\(791\) 52.9715 1.88345
\(792\) 1.85000 0.0657369
\(793\) 3.20602 0.113849
\(794\) 6.55430 0.232604
\(795\) −22.3143 −0.791405
\(796\) −25.4649 −0.902578
\(797\) −16.4052 −0.581102 −0.290551 0.956859i \(-0.593839\pi\)
−0.290551 + 0.956859i \(0.593839\pi\)
\(798\) −6.82459 −0.241588
\(799\) −10.7677 −0.380934
\(800\) −8.28261 −0.292834
\(801\) −103.697 −3.66397
\(802\) 17.7763 0.627704
\(803\) −2.09868 −0.0740608
\(804\) 13.6597 0.481739
\(805\) −55.2564 −1.94753
\(806\) −37.6489 −1.32613
\(807\) 44.6856 1.57301
\(808\) −15.5250 −0.546168
\(809\) −15.5536 −0.546837 −0.273419 0.961895i \(-0.588154\pi\)
−0.273419 + 0.961895i \(0.588154\pi\)
\(810\) 122.298 4.29710
\(811\) 0.0117685 0.000413248 0 0.000206624 1.00000i \(-0.499934\pi\)
0.000206624 1.00000i \(0.499934\pi\)
\(812\) −11.1552 −0.391471
\(813\) 15.6109 0.547499
\(814\) 1.16091 0.0406900
\(815\) −45.5023 −1.59388
\(816\) −2.89876 −0.101477
\(817\) −2.36433 −0.0827175
\(818\) −28.7471 −1.00512
\(819\) −169.231 −5.91341
\(820\) 16.4238 0.573544
\(821\) −0.271600 −0.00947891 −0.00473945 0.999989i \(-0.501509\pi\)
−0.00473945 + 0.999989i \(0.501509\pi\)
\(822\) 47.1559 1.64475
\(823\) −36.1856 −1.26135 −0.630676 0.776046i \(-0.717222\pi\)
−0.630676 + 0.776046i \(0.717222\pi\)
\(824\) −12.2172 −0.425605
\(825\) 6.25667 0.217829
\(826\) −47.3802 −1.64857
\(827\) 25.2701 0.878729 0.439365 0.898309i \(-0.355204\pi\)
0.439365 + 0.898309i \(0.355204\pi\)
\(828\) 24.3952 0.847792
\(829\) −54.8501 −1.90502 −0.952512 0.304502i \(-0.901510\pi\)
−0.952512 + 0.304502i \(0.901510\pi\)
\(830\) 14.2759 0.495523
\(831\) −32.7599 −1.13643
\(832\) −4.05580 −0.140610
\(833\) 16.4031 0.568333
\(834\) 37.0064 1.28143
\(835\) 60.4798 2.09299
\(836\) 0.0904392 0.00312791
\(837\) 161.304 5.57549
\(838\) −25.2111 −0.870903
\(839\) 46.3934 1.60168 0.800839 0.598879i \(-0.204387\pi\)
0.800839 + 0.598879i \(0.204387\pi\)
\(840\) −62.0940 −2.14245
\(841\) −24.2014 −0.834530
\(842\) 12.9193 0.445228
\(843\) 63.1839 2.17617
\(844\) −16.3806 −0.563845
\(845\) −12.5720 −0.432490
\(846\) 101.832 3.50104
\(847\) −55.7564 −1.91581
\(848\) −1.83001 −0.0628427
\(849\) 54.4389 1.86834
\(850\) −7.17614 −0.246140
\(851\) 15.3085 0.524769
\(852\) 33.4376 1.14555
\(853\) −54.4289 −1.86361 −0.931806 0.362957i \(-0.881767\pi\)
−0.931806 + 0.362957i \(0.881767\pi\)
\(854\) 4.02540 0.137746
\(855\) 11.9617 0.409082
\(856\) 1.19286 0.0407712
\(857\) 41.7559 1.42635 0.713177 0.700984i \(-0.247255\pi\)
0.713177 + 0.700984i \(0.247255\pi\)
\(858\) 3.06375 0.104595
\(859\) −13.7299 −0.468460 −0.234230 0.972181i \(-0.575257\pi\)
−0.234230 + 0.972181i \(0.575257\pi\)
\(860\) −21.5120 −0.733554
\(861\) 76.7785 2.61660
\(862\) 14.8705 0.506490
\(863\) 25.7327 0.875950 0.437975 0.898987i \(-0.355696\pi\)
0.437975 + 0.898987i \(0.355696\pi\)
\(864\) 17.3768 0.591171
\(865\) 40.4244 1.37447
\(866\) −15.3636 −0.522077
\(867\) 54.3655 1.84635
\(868\) −47.2711 −1.60448
\(869\) −1.81182 −0.0614619
\(870\) 26.7109 0.905583
\(871\) 16.5588 0.561074
\(872\) 4.15216 0.140610
\(873\) 82.9165 2.80630
\(874\) 1.19259 0.0403398
\(875\) −60.9228 −2.05957
\(876\) −31.0990 −1.05074
\(877\) −39.9849 −1.35019 −0.675097 0.737729i \(-0.735898\pi\)
−0.675097 + 0.737729i \(0.735898\pi\)
\(878\) −33.0583 −1.11566
\(879\) 0.991271 0.0334348
\(880\) 0.822867 0.0277388
\(881\) 36.3809 1.22570 0.612852 0.790198i \(-0.290022\pi\)
0.612852 + 0.790198i \(0.290022\pi\)
\(882\) −155.126 −5.22336
\(883\) −12.8491 −0.432408 −0.216204 0.976348i \(-0.569368\pi\)
−0.216204 + 0.976348i \(0.569368\pi\)
\(884\) −3.51399 −0.118188
\(885\) 113.451 3.81360
\(886\) 3.60408 0.121081
\(887\) −23.9722 −0.804909 −0.402455 0.915440i \(-0.631843\pi\)
−0.402455 + 0.915440i \(0.631843\pi\)
\(888\) 17.2028 0.577290
\(889\) 20.5412 0.688931
\(890\) −46.1239 −1.54608
\(891\) −7.57643 −0.253820
\(892\) 6.01176 0.201288
\(893\) 4.97814 0.166587
\(894\) −31.0753 −1.03931
\(895\) −66.5246 −2.22367
\(896\) −5.09237 −0.170124
\(897\) 40.4004 1.34893
\(898\) 2.73595 0.0912999
\(899\) 20.3345 0.678194
\(900\) 67.8657 2.26219
\(901\) −1.58554 −0.0528219
\(902\) −1.01747 −0.0338779
\(903\) −100.565 −3.34660
\(904\) −10.4021 −0.345970
\(905\) 93.0423 3.09283
\(906\) 0.586614 0.0194889
\(907\) 30.7286 1.02033 0.510164 0.860077i \(-0.329585\pi\)
0.510164 + 0.860077i \(0.329585\pi\)
\(908\) 6.55876 0.217660
\(909\) 127.208 4.21924
\(910\) −75.2728 −2.49527
\(911\) 33.0407 1.09469 0.547343 0.836908i \(-0.315639\pi\)
0.547343 + 0.836908i \(0.315639\pi\)
\(912\) 1.34016 0.0443772
\(913\) −0.884402 −0.0292694
\(914\) 5.07560 0.167886
\(915\) −9.63871 −0.318646
\(916\) 28.6438 0.946418
\(917\) −3.50824 −0.115852
\(918\) 15.0555 0.496905
\(919\) −11.4572 −0.377937 −0.188968 0.981983i \(-0.560514\pi\)
−0.188968 + 0.981983i \(0.560514\pi\)
\(920\) 10.8508 0.357741
\(921\) −112.894 −3.71997
\(922\) −25.3870 −0.836077
\(923\) 40.5345 1.33421
\(924\) 3.84677 0.126549
\(925\) 42.5872 1.40026
\(926\) −17.4199 −0.572454
\(927\) 100.105 3.28786
\(928\) 2.19058 0.0719092
\(929\) −29.4185 −0.965189 −0.482595 0.875844i \(-0.660306\pi\)
−0.482595 + 0.875844i \(0.660306\pi\)
\(930\) 113.189 3.71162
\(931\) −7.58350 −0.248539
\(932\) −1.09835 −0.0359776
\(933\) −97.6451 −3.19676
\(934\) −34.1750 −1.11824
\(935\) 0.712941 0.0233157
\(936\) 33.2323 1.08623
\(937\) −28.8733 −0.943250 −0.471625 0.881799i \(-0.656332\pi\)
−0.471625 + 0.881799i \(0.656332\pi\)
\(938\) 20.7908 0.678844
\(939\) 50.0845 1.63444
\(940\) 45.2940 1.47733
\(941\) −15.2362 −0.496686 −0.248343 0.968672i \(-0.579886\pi\)
−0.248343 + 0.968672i \(0.579886\pi\)
\(942\) −54.4215 −1.77315
\(943\) −13.4169 −0.436915
\(944\) 9.30416 0.302825
\(945\) 322.501 10.4910
\(946\) 1.33269 0.0433294
\(947\) −17.6980 −0.575109 −0.287555 0.957764i \(-0.592842\pi\)
−0.287555 + 0.957764i \(0.592842\pi\)
\(948\) −26.8482 −0.871990
\(949\) −37.6995 −1.22378
\(950\) 3.31769 0.107640
\(951\) 43.6885 1.41670
\(952\) −4.41208 −0.142996
\(953\) 22.6190 0.732700 0.366350 0.930477i \(-0.380607\pi\)
0.366350 + 0.930477i \(0.380607\pi\)
\(954\) 14.9946 0.485470
\(955\) −14.7354 −0.476826
\(956\) −21.8676 −0.707249
\(957\) −1.65476 −0.0534907
\(958\) 43.0987 1.39246
\(959\) 71.7740 2.31770
\(960\) 12.1935 0.393545
\(961\) 55.1691 1.77965
\(962\) 20.8540 0.672360
\(963\) −9.77403 −0.314964
\(964\) −20.6562 −0.665291
\(965\) 11.6385 0.374657
\(966\) 50.7258 1.63208
\(967\) 41.7973 1.34411 0.672056 0.740501i \(-0.265412\pi\)
0.672056 + 0.740501i \(0.265412\pi\)
\(968\) 10.9490 0.351915
\(969\) 1.16113 0.0373009
\(970\) 36.8807 1.18417
\(971\) −22.8917 −0.734628 −0.367314 0.930097i \(-0.619723\pi\)
−0.367314 + 0.930097i \(0.619723\pi\)
\(972\) −60.1397 −1.92898
\(973\) 56.3259 1.80573
\(974\) −20.2072 −0.647479
\(975\) 112.391 3.59940
\(976\) −0.790477 −0.0253026
\(977\) −4.39443 −0.140590 −0.0702951 0.997526i \(-0.522394\pi\)
−0.0702951 + 0.997526i \(0.522394\pi\)
\(978\) 41.7715 1.33570
\(979\) 2.85741 0.0913232
\(980\) −68.9990 −2.20409
\(981\) −34.0219 −1.08623
\(982\) −8.40833 −0.268321
\(983\) 19.7597 0.630237 0.315118 0.949052i \(-0.397956\pi\)
0.315118 + 0.949052i \(0.397956\pi\)
\(984\) −15.0772 −0.480643
\(985\) 24.9107 0.793721
\(986\) 1.89794 0.0604427
\(987\) 211.742 6.73981
\(988\) 1.62460 0.0516853
\(989\) 17.5736 0.558808
\(990\) −6.74238 −0.214287
\(991\) −34.6916 −1.10202 −0.551008 0.834500i \(-0.685757\pi\)
−0.551008 + 0.834500i \(0.685757\pi\)
\(992\) 9.28273 0.294727
\(993\) 86.0634 2.73114
\(994\) 50.8941 1.61426
\(995\) 92.8075 2.94219
\(996\) −13.1054 −0.415260
\(997\) 21.8229 0.691138 0.345569 0.938393i \(-0.387686\pi\)
0.345569 + 0.938393i \(0.387686\pi\)
\(998\) −12.9379 −0.409542
\(999\) −89.3475 −2.82683
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.1.1 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.1 40 1.1 even 1 trivial