Properties

Label 4006.2.a.g.1.11
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 1.11
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.82093 q^{3} +1.00000 q^{4} -3.80048 q^{5} +1.82093 q^{6} -3.54475 q^{7} -1.00000 q^{8} +0.315788 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.82093 q^{3} +1.00000 q^{4} -3.80048 q^{5} +1.82093 q^{6} -3.54475 q^{7} -1.00000 q^{8} +0.315788 q^{9} +3.80048 q^{10} -4.23704 q^{11} -1.82093 q^{12} +1.93193 q^{13} +3.54475 q^{14} +6.92040 q^{15} +1.00000 q^{16} -7.25106 q^{17} -0.315788 q^{18} +1.65314 q^{19} -3.80048 q^{20} +6.45474 q^{21} +4.23704 q^{22} +2.77810 q^{23} +1.82093 q^{24} +9.44361 q^{25} -1.93193 q^{26} +4.88776 q^{27} -3.54475 q^{28} +6.62357 q^{29} -6.92040 q^{30} -9.37689 q^{31} -1.00000 q^{32} +7.71535 q^{33} +7.25106 q^{34} +13.4717 q^{35} +0.315788 q^{36} -1.32098 q^{37} -1.65314 q^{38} -3.51791 q^{39} +3.80048 q^{40} +7.72437 q^{41} -6.45474 q^{42} +12.2401 q^{43} -4.23704 q^{44} -1.20015 q^{45} -2.77810 q^{46} +2.77894 q^{47} -1.82093 q^{48} +5.56523 q^{49} -9.44361 q^{50} +13.2037 q^{51} +1.93193 q^{52} -8.53389 q^{53} -4.88776 q^{54} +16.1028 q^{55} +3.54475 q^{56} -3.01025 q^{57} -6.62357 q^{58} -10.9129 q^{59} +6.92040 q^{60} -12.6169 q^{61} +9.37689 q^{62} -1.11939 q^{63} +1.00000 q^{64} -7.34226 q^{65} -7.71535 q^{66} +11.2323 q^{67} -7.25106 q^{68} -5.05873 q^{69} -13.4717 q^{70} -2.85150 q^{71} -0.315788 q^{72} +5.54156 q^{73} +1.32098 q^{74} -17.1962 q^{75} +1.65314 q^{76} +15.0192 q^{77} +3.51791 q^{78} +11.7255 q^{79} -3.80048 q^{80} -9.84764 q^{81} -7.72437 q^{82} +9.05386 q^{83} +6.45474 q^{84} +27.5575 q^{85} -12.2401 q^{86} -12.0611 q^{87} +4.23704 q^{88} -1.09101 q^{89} +1.20015 q^{90} -6.84821 q^{91} +2.77810 q^{92} +17.0747 q^{93} -2.77894 q^{94} -6.28271 q^{95} +1.82093 q^{96} -3.33585 q^{97} -5.56523 q^{98} -1.33801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −1.82093 −1.05131 −0.525657 0.850696i \(-0.676181\pi\)
−0.525657 + 0.850696i \(0.676181\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.80048 −1.69962 −0.849812 0.527086i \(-0.823285\pi\)
−0.849812 + 0.527086i \(0.823285\pi\)
\(6\) 1.82093 0.743392
\(7\) −3.54475 −1.33979 −0.669894 0.742457i \(-0.733661\pi\)
−0.669894 + 0.742457i \(0.733661\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.315788 0.105263
\(10\) 3.80048 1.20182
\(11\) −4.23704 −1.27752 −0.638758 0.769408i \(-0.720551\pi\)
−0.638758 + 0.769408i \(0.720551\pi\)
\(12\) −1.82093 −0.525657
\(13\) 1.93193 0.535821 0.267911 0.963444i \(-0.413667\pi\)
0.267911 + 0.963444i \(0.413667\pi\)
\(14\) 3.54475 0.947373
\(15\) 6.92040 1.78684
\(16\) 1.00000 0.250000
\(17\) −7.25106 −1.75864 −0.879320 0.476232i \(-0.842002\pi\)
−0.879320 + 0.476232i \(0.842002\pi\)
\(18\) −0.315788 −0.0744321
\(19\) 1.65314 0.379256 0.189628 0.981856i \(-0.439272\pi\)
0.189628 + 0.981856i \(0.439272\pi\)
\(20\) −3.80048 −0.849812
\(21\) 6.45474 1.40854
\(22\) 4.23704 0.903340
\(23\) 2.77810 0.579274 0.289637 0.957137i \(-0.406465\pi\)
0.289637 + 0.957137i \(0.406465\pi\)
\(24\) 1.82093 0.371696
\(25\) 9.44361 1.88872
\(26\) −1.93193 −0.378883
\(27\) 4.88776 0.940650
\(28\) −3.54475 −0.669894
\(29\) 6.62357 1.22997 0.614983 0.788540i \(-0.289163\pi\)
0.614983 + 0.788540i \(0.289163\pi\)
\(30\) −6.92040 −1.26349
\(31\) −9.37689 −1.68414 −0.842069 0.539369i \(-0.818663\pi\)
−0.842069 + 0.539369i \(0.818663\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.71535 1.34307
\(34\) 7.25106 1.24355
\(35\) 13.4717 2.27714
\(36\) 0.315788 0.0526314
\(37\) −1.32098 −0.217168 −0.108584 0.994087i \(-0.534632\pi\)
−0.108584 + 0.994087i \(0.534632\pi\)
\(38\) −1.65314 −0.268174
\(39\) −3.51791 −0.563317
\(40\) 3.80048 0.600908
\(41\) 7.72437 1.20634 0.603172 0.797611i \(-0.293903\pi\)
0.603172 + 0.797611i \(0.293903\pi\)
\(42\) −6.45474 −0.995988
\(43\) 12.2401 1.86659 0.933297 0.359106i \(-0.116918\pi\)
0.933297 + 0.359106i \(0.116918\pi\)
\(44\) −4.23704 −0.638758
\(45\) −1.20015 −0.178907
\(46\) −2.77810 −0.409609
\(47\) 2.77894 0.405350 0.202675 0.979246i \(-0.435036\pi\)
0.202675 + 0.979246i \(0.435036\pi\)
\(48\) −1.82093 −0.262829
\(49\) 5.56523 0.795033
\(50\) −9.44361 −1.33553
\(51\) 13.2037 1.84888
\(52\) 1.93193 0.267911
\(53\) −8.53389 −1.17222 −0.586110 0.810231i \(-0.699341\pi\)
−0.586110 + 0.810231i \(0.699341\pi\)
\(54\) −4.88776 −0.665140
\(55\) 16.1028 2.17130
\(56\) 3.54475 0.473687
\(57\) −3.01025 −0.398717
\(58\) −6.62357 −0.869718
\(59\) −10.9129 −1.42073 −0.710367 0.703831i \(-0.751471\pi\)
−0.710367 + 0.703831i \(0.751471\pi\)
\(60\) 6.92040 0.893420
\(61\) −12.6169 −1.61543 −0.807716 0.589572i \(-0.799296\pi\)
−0.807716 + 0.589572i \(0.799296\pi\)
\(62\) 9.37689 1.19087
\(63\) −1.11939 −0.141030
\(64\) 1.00000 0.125000
\(65\) −7.34226 −0.910695
\(66\) −7.71535 −0.949694
\(67\) 11.2323 1.37224 0.686119 0.727489i \(-0.259313\pi\)
0.686119 + 0.727489i \(0.259313\pi\)
\(68\) −7.25106 −0.879320
\(69\) −5.05873 −0.609000
\(70\) −13.4717 −1.61018
\(71\) −2.85150 −0.338410 −0.169205 0.985581i \(-0.554120\pi\)
−0.169205 + 0.985581i \(0.554120\pi\)
\(72\) −0.315788 −0.0372160
\(73\) 5.54156 0.648590 0.324295 0.945956i \(-0.394873\pi\)
0.324295 + 0.945956i \(0.394873\pi\)
\(74\) 1.32098 0.153561
\(75\) −17.1962 −1.98564
\(76\) 1.65314 0.189628
\(77\) 15.0192 1.71160
\(78\) 3.51791 0.398325
\(79\) 11.7255 1.31923 0.659613 0.751605i \(-0.270720\pi\)
0.659613 + 0.751605i \(0.270720\pi\)
\(80\) −3.80048 −0.424906
\(81\) −9.84764 −1.09418
\(82\) −7.72437 −0.853014
\(83\) 9.05386 0.993790 0.496895 0.867811i \(-0.334473\pi\)
0.496895 + 0.867811i \(0.334473\pi\)
\(84\) 6.45474 0.704270
\(85\) 27.5575 2.98903
\(86\) −12.2401 −1.31988
\(87\) −12.0611 −1.29308
\(88\) 4.23704 0.451670
\(89\) −1.09101 −0.115646 −0.0578232 0.998327i \(-0.518416\pi\)
−0.0578232 + 0.998327i \(0.518416\pi\)
\(90\) 1.20015 0.126507
\(91\) −6.84821 −0.717887
\(92\) 2.77810 0.289637
\(93\) 17.0747 1.77056
\(94\) −2.77894 −0.286626
\(95\) −6.28271 −0.644592
\(96\) 1.82093 0.185848
\(97\) −3.33585 −0.338704 −0.169352 0.985556i \(-0.554167\pi\)
−0.169352 + 0.985556i \(0.554167\pi\)
\(98\) −5.56523 −0.562173
\(99\) −1.33801 −0.134475
\(100\) 9.44361 0.944361
\(101\) 17.3615 1.72753 0.863765 0.503894i \(-0.168100\pi\)
0.863765 + 0.503894i \(0.168100\pi\)
\(102\) −13.2037 −1.30736
\(103\) 5.49812 0.541746 0.270873 0.962615i \(-0.412688\pi\)
0.270873 + 0.962615i \(0.412688\pi\)
\(104\) −1.93193 −0.189441
\(105\) −24.5311 −2.39399
\(106\) 8.53389 0.828885
\(107\) −10.1626 −0.982460 −0.491230 0.871030i \(-0.663453\pi\)
−0.491230 + 0.871030i \(0.663453\pi\)
\(108\) 4.88776 0.470325
\(109\) −6.14727 −0.588802 −0.294401 0.955682i \(-0.595120\pi\)
−0.294401 + 0.955682i \(0.595120\pi\)
\(110\) −16.1028 −1.53534
\(111\) 2.40541 0.228312
\(112\) −3.54475 −0.334947
\(113\) −8.41808 −0.791906 −0.395953 0.918271i \(-0.629586\pi\)
−0.395953 + 0.918271i \(0.629586\pi\)
\(114\) 3.01025 0.281936
\(115\) −10.5581 −0.984548
\(116\) 6.62357 0.614983
\(117\) 0.610082 0.0564021
\(118\) 10.9129 1.00461
\(119\) 25.7032 2.35620
\(120\) −6.92040 −0.631743
\(121\) 6.95249 0.632045
\(122\) 12.6169 1.14228
\(123\) −14.0655 −1.26825
\(124\) −9.37689 −0.842069
\(125\) −16.8878 −1.51049
\(126\) 1.11939 0.0997232
\(127\) 10.0912 0.895445 0.447722 0.894173i \(-0.352235\pi\)
0.447722 + 0.894173i \(0.352235\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −22.2883 −1.96238
\(130\) 7.34226 0.643959
\(131\) −20.2477 −1.76905 −0.884525 0.466493i \(-0.845517\pi\)
−0.884525 + 0.466493i \(0.845517\pi\)
\(132\) 7.71535 0.671535
\(133\) −5.85995 −0.508122
\(134\) −11.2323 −0.970319
\(135\) −18.5758 −1.59875
\(136\) 7.25106 0.621773
\(137\) 5.37282 0.459031 0.229515 0.973305i \(-0.426286\pi\)
0.229515 + 0.973305i \(0.426286\pi\)
\(138\) 5.05873 0.430628
\(139\) 1.01967 0.0864874 0.0432437 0.999065i \(-0.486231\pi\)
0.0432437 + 0.999065i \(0.486231\pi\)
\(140\) 13.4717 1.13857
\(141\) −5.06026 −0.426150
\(142\) 2.85150 0.239292
\(143\) −8.18567 −0.684520
\(144\) 0.315788 0.0263157
\(145\) −25.1727 −2.09048
\(146\) −5.54156 −0.458623
\(147\) −10.1339 −0.835829
\(148\) −1.32098 −0.108584
\(149\) −5.09976 −0.417789 −0.208895 0.977938i \(-0.566987\pi\)
−0.208895 + 0.977938i \(0.566987\pi\)
\(150\) 17.1962 1.40406
\(151\) −10.3479 −0.842104 −0.421052 0.907037i \(-0.638339\pi\)
−0.421052 + 0.907037i \(0.638339\pi\)
\(152\) −1.65314 −0.134087
\(153\) −2.28980 −0.185119
\(154\) −15.0192 −1.21028
\(155\) 35.6366 2.86240
\(156\) −3.51791 −0.281659
\(157\) 8.43226 0.672968 0.336484 0.941689i \(-0.390762\pi\)
0.336484 + 0.941689i \(0.390762\pi\)
\(158\) −11.7255 −0.932834
\(159\) 15.5396 1.23237
\(160\) 3.80048 0.300454
\(161\) −9.84767 −0.776105
\(162\) 9.84764 0.773704
\(163\) 22.8876 1.79270 0.896349 0.443349i \(-0.146210\pi\)
0.896349 + 0.443349i \(0.146210\pi\)
\(164\) 7.72437 0.603172
\(165\) −29.3220 −2.28272
\(166\) −9.05386 −0.702716
\(167\) −3.29537 −0.255004 −0.127502 0.991838i \(-0.540696\pi\)
−0.127502 + 0.991838i \(0.540696\pi\)
\(168\) −6.45474 −0.497994
\(169\) −9.26764 −0.712895
\(170\) −27.5575 −2.11356
\(171\) 0.522042 0.0399215
\(172\) 12.2401 0.933297
\(173\) −8.41833 −0.640034 −0.320017 0.947412i \(-0.603689\pi\)
−0.320017 + 0.947412i \(0.603689\pi\)
\(174\) 12.0611 0.914347
\(175\) −33.4752 −2.53049
\(176\) −4.23704 −0.319379
\(177\) 19.8716 1.49364
\(178\) 1.09101 0.0817743
\(179\) 18.2974 1.36761 0.683807 0.729663i \(-0.260323\pi\)
0.683807 + 0.729663i \(0.260323\pi\)
\(180\) −1.20015 −0.0894536
\(181\) −5.28677 −0.392962 −0.196481 0.980508i \(-0.562951\pi\)
−0.196481 + 0.980508i \(0.562951\pi\)
\(182\) 6.84821 0.507623
\(183\) 22.9745 1.69833
\(184\) −2.77810 −0.204804
\(185\) 5.02035 0.369104
\(186\) −17.0747 −1.25198
\(187\) 30.7230 2.24669
\(188\) 2.77894 0.202675
\(189\) −17.3259 −1.26027
\(190\) 6.28271 0.455795
\(191\) −14.4080 −1.04252 −0.521262 0.853397i \(-0.674539\pi\)
−0.521262 + 0.853397i \(0.674539\pi\)
\(192\) −1.82093 −0.131414
\(193\) 19.9624 1.43692 0.718461 0.695567i \(-0.244847\pi\)
0.718461 + 0.695567i \(0.244847\pi\)
\(194\) 3.33585 0.239500
\(195\) 13.3697 0.957427
\(196\) 5.56523 0.397516
\(197\) −6.27526 −0.447093 −0.223547 0.974693i \(-0.571764\pi\)
−0.223547 + 0.974693i \(0.571764\pi\)
\(198\) 1.33801 0.0950881
\(199\) 8.50276 0.602745 0.301372 0.953506i \(-0.402555\pi\)
0.301372 + 0.953506i \(0.402555\pi\)
\(200\) −9.44361 −0.667764
\(201\) −20.4532 −1.44266
\(202\) −17.3615 −1.22155
\(203\) −23.4789 −1.64789
\(204\) 13.2037 0.924442
\(205\) −29.3563 −2.05033
\(206\) −5.49812 −0.383072
\(207\) 0.877292 0.0609760
\(208\) 1.93193 0.133955
\(209\) −7.00441 −0.484505
\(210\) 24.5311 1.69280
\(211\) 3.50204 0.241090 0.120545 0.992708i \(-0.461536\pi\)
0.120545 + 0.992708i \(0.461536\pi\)
\(212\) −8.53389 −0.586110
\(213\) 5.19238 0.355776
\(214\) 10.1626 0.694704
\(215\) −46.5181 −3.17251
\(216\) −4.88776 −0.332570
\(217\) 33.2387 2.25639
\(218\) 6.14727 0.416346
\(219\) −10.0908 −0.681873
\(220\) 16.1028 1.08565
\(221\) −14.0085 −0.942317
\(222\) −2.40541 −0.161441
\(223\) 8.62891 0.577834 0.288917 0.957354i \(-0.406705\pi\)
0.288917 + 0.957354i \(0.406705\pi\)
\(224\) 3.54475 0.236843
\(225\) 2.98218 0.198812
\(226\) 8.41808 0.559962
\(227\) −18.6343 −1.23680 −0.618401 0.785863i \(-0.712219\pi\)
−0.618401 + 0.785863i \(0.712219\pi\)
\(228\) −3.01025 −0.199359
\(229\) 4.45951 0.294693 0.147346 0.989085i \(-0.452927\pi\)
0.147346 + 0.989085i \(0.452927\pi\)
\(230\) 10.5581 0.696181
\(231\) −27.3490 −1.79943
\(232\) −6.62357 −0.434859
\(233\) 27.1983 1.78182 0.890910 0.454180i \(-0.150068\pi\)
0.890910 + 0.454180i \(0.150068\pi\)
\(234\) −0.610082 −0.0398823
\(235\) −10.5613 −0.688943
\(236\) −10.9129 −0.710367
\(237\) −21.3514 −1.38692
\(238\) −25.7032 −1.66609
\(239\) 28.7485 1.85959 0.929794 0.368080i \(-0.119985\pi\)
0.929794 + 0.368080i \(0.119985\pi\)
\(240\) 6.92040 0.446710
\(241\) −12.7200 −0.819366 −0.409683 0.912228i \(-0.634361\pi\)
−0.409683 + 0.912228i \(0.634361\pi\)
\(242\) −6.95249 −0.446923
\(243\) 3.26859 0.209680
\(244\) −12.6169 −0.807716
\(245\) −21.1505 −1.35126
\(246\) 14.0655 0.896786
\(247\) 3.19375 0.203213
\(248\) 9.37689 0.595433
\(249\) −16.4864 −1.04479
\(250\) 16.8878 1.06808
\(251\) 5.69500 0.359465 0.179733 0.983716i \(-0.442477\pi\)
0.179733 + 0.983716i \(0.442477\pi\)
\(252\) −1.11939 −0.0705149
\(253\) −11.7709 −0.740032
\(254\) −10.0912 −0.633175
\(255\) −50.1802 −3.14241
\(256\) 1.00000 0.0625000
\(257\) −17.3344 −1.08129 −0.540645 0.841251i \(-0.681820\pi\)
−0.540645 + 0.841251i \(0.681820\pi\)
\(258\) 22.2883 1.38761
\(259\) 4.68254 0.290959
\(260\) −7.34226 −0.455348
\(261\) 2.09165 0.129470
\(262\) 20.2477 1.25091
\(263\) 0.573248 0.0353480 0.0176740 0.999844i \(-0.494374\pi\)
0.0176740 + 0.999844i \(0.494374\pi\)
\(264\) −7.71535 −0.474847
\(265\) 32.4329 1.99233
\(266\) 5.85995 0.359297
\(267\) 1.98665 0.121581
\(268\) 11.2323 0.686119
\(269\) −11.7841 −0.718490 −0.359245 0.933243i \(-0.616966\pi\)
−0.359245 + 0.933243i \(0.616966\pi\)
\(270\) 18.5758 1.13049
\(271\) 1.72211 0.104611 0.0523054 0.998631i \(-0.483343\pi\)
0.0523054 + 0.998631i \(0.483343\pi\)
\(272\) −7.25106 −0.439660
\(273\) 12.4701 0.754725
\(274\) −5.37282 −0.324584
\(275\) −40.0129 −2.41287
\(276\) −5.05873 −0.304500
\(277\) −0.604596 −0.0363266 −0.0181633 0.999835i \(-0.505782\pi\)
−0.0181633 + 0.999835i \(0.505782\pi\)
\(278\) −1.01967 −0.0611558
\(279\) −2.96111 −0.177277
\(280\) −13.4717 −0.805089
\(281\) 3.80725 0.227121 0.113561 0.993531i \(-0.463774\pi\)
0.113561 + 0.993531i \(0.463774\pi\)
\(282\) 5.06026 0.301334
\(283\) −0.610355 −0.0362818 −0.0181409 0.999835i \(-0.505775\pi\)
−0.0181409 + 0.999835i \(0.505775\pi\)
\(284\) −2.85150 −0.169205
\(285\) 11.4404 0.677669
\(286\) 8.18567 0.484029
\(287\) −27.3809 −1.61625
\(288\) −0.315788 −0.0186080
\(289\) 35.5778 2.09281
\(290\) 25.1727 1.47819
\(291\) 6.07435 0.356084
\(292\) 5.54156 0.324295
\(293\) −2.88815 −0.168728 −0.0843638 0.996435i \(-0.526886\pi\)
−0.0843638 + 0.996435i \(0.526886\pi\)
\(294\) 10.1339 0.591021
\(295\) 41.4741 2.41472
\(296\) 1.32098 0.0767804
\(297\) −20.7096 −1.20170
\(298\) 5.09976 0.295421
\(299\) 5.36710 0.310388
\(300\) −17.1962 −0.992821
\(301\) −43.3879 −2.50084
\(302\) 10.3479 0.595457
\(303\) −31.6140 −1.81618
\(304\) 1.65314 0.0948139
\(305\) 47.9503 2.74563
\(306\) 2.28980 0.130899
\(307\) −21.8437 −1.24668 −0.623342 0.781949i \(-0.714226\pi\)
−0.623342 + 0.781949i \(0.714226\pi\)
\(308\) 15.0192 0.855800
\(309\) −10.0117 −0.569546
\(310\) −35.6366 −2.02402
\(311\) 19.5894 1.11081 0.555407 0.831579i \(-0.312563\pi\)
0.555407 + 0.831579i \(0.312563\pi\)
\(312\) 3.51791 0.199163
\(313\) 25.3964 1.43549 0.717745 0.696306i \(-0.245174\pi\)
0.717745 + 0.696306i \(0.245174\pi\)
\(314\) −8.43226 −0.475860
\(315\) 4.25421 0.239698
\(316\) 11.7255 0.659613
\(317\) −5.85823 −0.329031 −0.164516 0.986374i \(-0.552606\pi\)
−0.164516 + 0.986374i \(0.552606\pi\)
\(318\) −15.5396 −0.871419
\(319\) −28.0643 −1.57130
\(320\) −3.80048 −0.212453
\(321\) 18.5055 1.03287
\(322\) 9.84767 0.548789
\(323\) −11.9870 −0.666974
\(324\) −9.84764 −0.547091
\(325\) 18.2444 1.01202
\(326\) −22.8876 −1.26763
\(327\) 11.1938 0.619016
\(328\) −7.72437 −0.426507
\(329\) −9.85064 −0.543083
\(330\) 29.3220 1.61412
\(331\) −32.5253 −1.78775 −0.893875 0.448316i \(-0.852024\pi\)
−0.893875 + 0.448316i \(0.852024\pi\)
\(332\) 9.05386 0.496895
\(333\) −0.417150 −0.0228597
\(334\) 3.29537 0.180315
\(335\) −42.6879 −2.33229
\(336\) 6.45474 0.352135
\(337\) −34.0500 −1.85482 −0.927412 0.374042i \(-0.877972\pi\)
−0.927412 + 0.374042i \(0.877972\pi\)
\(338\) 9.26764 0.504093
\(339\) 15.3287 0.832542
\(340\) 27.5575 1.49451
\(341\) 39.7302 2.15151
\(342\) −0.522042 −0.0282288
\(343\) 5.08590 0.274613
\(344\) −12.2401 −0.659940
\(345\) 19.2256 1.03507
\(346\) 8.41833 0.452572
\(347\) −6.91669 −0.371307 −0.185654 0.982615i \(-0.559440\pi\)
−0.185654 + 0.982615i \(0.559440\pi\)
\(348\) −12.0611 −0.646541
\(349\) −6.42314 −0.343823 −0.171911 0.985112i \(-0.554994\pi\)
−0.171911 + 0.985112i \(0.554994\pi\)
\(350\) 33.4752 1.78933
\(351\) 9.44282 0.504021
\(352\) 4.23704 0.225835
\(353\) 4.64082 0.247006 0.123503 0.992344i \(-0.460587\pi\)
0.123503 + 0.992344i \(0.460587\pi\)
\(354\) −19.8716 −1.05616
\(355\) 10.8370 0.575170
\(356\) −1.09101 −0.0578232
\(357\) −46.8037 −2.47711
\(358\) −18.2974 −0.967049
\(359\) −13.8789 −0.732501 −0.366251 0.930516i \(-0.619359\pi\)
−0.366251 + 0.930516i \(0.619359\pi\)
\(360\) 1.20015 0.0632533
\(361\) −16.2671 −0.856165
\(362\) 5.28677 0.277866
\(363\) −12.6600 −0.664478
\(364\) −6.84821 −0.358944
\(365\) −21.0606 −1.10236
\(366\) −22.9745 −1.20090
\(367\) 17.2289 0.899343 0.449672 0.893194i \(-0.351541\pi\)
0.449672 + 0.893194i \(0.351541\pi\)
\(368\) 2.77810 0.144819
\(369\) 2.43927 0.126983
\(370\) −5.02035 −0.260996
\(371\) 30.2505 1.57053
\(372\) 17.0747 0.885280
\(373\) 5.54848 0.287289 0.143645 0.989629i \(-0.454118\pi\)
0.143645 + 0.989629i \(0.454118\pi\)
\(374\) −30.7230 −1.58865
\(375\) 30.7516 1.58800
\(376\) −2.77894 −0.143313
\(377\) 12.7963 0.659042
\(378\) 17.3259 0.891147
\(379\) 26.7795 1.37557 0.687785 0.725915i \(-0.258583\pi\)
0.687785 + 0.725915i \(0.258583\pi\)
\(380\) −6.28271 −0.322296
\(381\) −18.3753 −0.941394
\(382\) 14.4080 0.737176
\(383\) 19.7557 1.00947 0.504736 0.863274i \(-0.331590\pi\)
0.504736 + 0.863274i \(0.331590\pi\)
\(384\) 1.82093 0.0929240
\(385\) −57.0802 −2.90908
\(386\) −19.9624 −1.01606
\(387\) 3.86527 0.196483
\(388\) −3.33585 −0.169352
\(389\) 5.74262 0.291162 0.145581 0.989346i \(-0.453495\pi\)
0.145581 + 0.989346i \(0.453495\pi\)
\(390\) −13.3697 −0.677003
\(391\) −20.1442 −1.01873
\(392\) −5.56523 −0.281086
\(393\) 36.8697 1.85983
\(394\) 6.27526 0.316143
\(395\) −44.5626 −2.24219
\(396\) −1.33801 −0.0672374
\(397\) −3.86966 −0.194213 −0.0971063 0.995274i \(-0.530959\pi\)
−0.0971063 + 0.995274i \(0.530959\pi\)
\(398\) −8.50276 −0.426205
\(399\) 10.6706 0.534197
\(400\) 9.44361 0.472181
\(401\) −13.3000 −0.664170 −0.332085 0.943250i \(-0.607752\pi\)
−0.332085 + 0.943250i \(0.607752\pi\)
\(402\) 20.4532 1.02011
\(403\) −18.1155 −0.902398
\(404\) 17.3615 0.863765
\(405\) 37.4257 1.85970
\(406\) 23.4789 1.16524
\(407\) 5.59704 0.277435
\(408\) −13.2037 −0.653679
\(409\) 13.1153 0.648509 0.324255 0.945970i \(-0.394887\pi\)
0.324255 + 0.945970i \(0.394887\pi\)
\(410\) 29.3563 1.44980
\(411\) −9.78353 −0.482586
\(412\) 5.49812 0.270873
\(413\) 38.6834 1.90348
\(414\) −0.877292 −0.0431166
\(415\) −34.4090 −1.68907
\(416\) −1.93193 −0.0947207
\(417\) −1.85675 −0.0909254
\(418\) 7.00441 0.342597
\(419\) 35.9124 1.75443 0.877217 0.480094i \(-0.159398\pi\)
0.877217 + 0.480094i \(0.159398\pi\)
\(420\) −24.5311 −1.19699
\(421\) −4.37921 −0.213429 −0.106715 0.994290i \(-0.534033\pi\)
−0.106715 + 0.994290i \(0.534033\pi\)
\(422\) −3.50204 −0.170477
\(423\) 0.877557 0.0426683
\(424\) 8.53389 0.414443
\(425\) −68.4762 −3.32158
\(426\) −5.19238 −0.251571
\(427\) 44.7238 2.16434
\(428\) −10.1626 −0.491230
\(429\) 14.9055 0.719646
\(430\) 46.5181 2.24330
\(431\) −6.34634 −0.305693 −0.152846 0.988250i \(-0.548844\pi\)
−0.152846 + 0.988250i \(0.548844\pi\)
\(432\) 4.88776 0.235163
\(433\) −12.1995 −0.586272 −0.293136 0.956071i \(-0.594699\pi\)
−0.293136 + 0.956071i \(0.594699\pi\)
\(434\) −33.2387 −1.59551
\(435\) 45.8378 2.19775
\(436\) −6.14727 −0.294401
\(437\) 4.59258 0.219693
\(438\) 10.0908 0.482157
\(439\) −32.3638 −1.54464 −0.772320 0.635233i \(-0.780904\pi\)
−0.772320 + 0.635233i \(0.780904\pi\)
\(440\) −16.1028 −0.767669
\(441\) 1.75743 0.0836874
\(442\) 14.0085 0.666319
\(443\) 11.8677 0.563852 0.281926 0.959436i \(-0.409027\pi\)
0.281926 + 0.959436i \(0.409027\pi\)
\(444\) 2.40541 0.114156
\(445\) 4.14634 0.196555
\(446\) −8.62891 −0.408591
\(447\) 9.28632 0.439228
\(448\) −3.54475 −0.167474
\(449\) −1.98188 −0.0935308 −0.0467654 0.998906i \(-0.514891\pi\)
−0.0467654 + 0.998906i \(0.514891\pi\)
\(450\) −2.98218 −0.140581
\(451\) −32.7285 −1.54112
\(452\) −8.41808 −0.395953
\(453\) 18.8429 0.885316
\(454\) 18.6343 0.874551
\(455\) 26.0264 1.22014
\(456\) 3.01025 0.140968
\(457\) 24.4134 1.14201 0.571006 0.820946i \(-0.306553\pi\)
0.571006 + 0.820946i \(0.306553\pi\)
\(458\) −4.45951 −0.208379
\(459\) −35.4414 −1.65427
\(460\) −10.5581 −0.492274
\(461\) −39.3419 −1.83234 −0.916168 0.400793i \(-0.868735\pi\)
−0.916168 + 0.400793i \(0.868735\pi\)
\(462\) 27.3490 1.27239
\(463\) 10.7789 0.500938 0.250469 0.968125i \(-0.419415\pi\)
0.250469 + 0.968125i \(0.419415\pi\)
\(464\) 6.62357 0.307492
\(465\) −64.8918 −3.00929
\(466\) −27.1983 −1.25994
\(467\) −4.75747 −0.220150 −0.110075 0.993923i \(-0.535109\pi\)
−0.110075 + 0.993923i \(0.535109\pi\)
\(468\) 0.610082 0.0282010
\(469\) −39.8155 −1.83851
\(470\) 10.5613 0.487156
\(471\) −15.3546 −0.707501
\(472\) 10.9129 0.502306
\(473\) −51.8616 −2.38460
\(474\) 21.3514 0.980702
\(475\) 15.6116 0.716309
\(476\) 25.7032 1.17810
\(477\) −2.69491 −0.123391
\(478\) −28.7485 −1.31493
\(479\) −20.4210 −0.933061 −0.466530 0.884505i \(-0.654496\pi\)
−0.466530 + 0.884505i \(0.654496\pi\)
\(480\) −6.92040 −0.315872
\(481\) −2.55204 −0.116363
\(482\) 12.7200 0.579379
\(483\) 17.9319 0.815930
\(484\) 6.95249 0.316022
\(485\) 12.6778 0.575669
\(486\) −3.26859 −0.148266
\(487\) 35.8756 1.62568 0.812840 0.582487i \(-0.197920\pi\)
0.812840 + 0.582487i \(0.197920\pi\)
\(488\) 12.6169 0.571141
\(489\) −41.6768 −1.88469
\(490\) 21.1505 0.955483
\(491\) 9.30422 0.419893 0.209947 0.977713i \(-0.432671\pi\)
0.209947 + 0.977713i \(0.432671\pi\)
\(492\) −14.0655 −0.634124
\(493\) −48.0279 −2.16307
\(494\) −3.19375 −0.143694
\(495\) 5.08507 0.228557
\(496\) −9.37689 −0.421035
\(497\) 10.1078 0.453398
\(498\) 16.4864 0.738775
\(499\) −21.5100 −0.962919 −0.481459 0.876468i \(-0.659893\pi\)
−0.481459 + 0.876468i \(0.659893\pi\)
\(500\) −16.8878 −0.755247
\(501\) 6.00065 0.268089
\(502\) −5.69500 −0.254180
\(503\) −35.4074 −1.57874 −0.789370 0.613918i \(-0.789593\pi\)
−0.789370 + 0.613918i \(0.789593\pi\)
\(504\) 1.11939 0.0498616
\(505\) −65.9818 −2.93615
\(506\) 11.7709 0.523281
\(507\) 16.8757 0.749477
\(508\) 10.0912 0.447722
\(509\) 3.08047 0.136539 0.0682697 0.997667i \(-0.478252\pi\)
0.0682697 + 0.997667i \(0.478252\pi\)
\(510\) 50.1802 2.22202
\(511\) −19.6434 −0.868974
\(512\) −1.00000 −0.0441942
\(513\) 8.08014 0.356747
\(514\) 17.3344 0.764588
\(515\) −20.8955 −0.920765
\(516\) −22.2883 −0.981189
\(517\) −11.7745 −0.517841
\(518\) −4.68254 −0.205739
\(519\) 15.3292 0.672877
\(520\) 7.34226 0.321979
\(521\) 18.2326 0.798786 0.399393 0.916780i \(-0.369221\pi\)
0.399393 + 0.916780i \(0.369221\pi\)
\(522\) −2.09165 −0.0915489
\(523\) −2.60504 −0.113911 −0.0569553 0.998377i \(-0.518139\pi\)
−0.0569553 + 0.998377i \(0.518139\pi\)
\(524\) −20.2477 −0.884525
\(525\) 60.9560 2.66034
\(526\) −0.573248 −0.0249948
\(527\) 67.9924 2.96179
\(528\) 7.71535 0.335768
\(529\) −15.2822 −0.664441
\(530\) −32.4329 −1.40879
\(531\) −3.44616 −0.149551
\(532\) −5.85995 −0.254061
\(533\) 14.9230 0.646385
\(534\) −1.98665 −0.0859706
\(535\) 38.6229 1.66981
\(536\) −11.2323 −0.485160
\(537\) −33.3184 −1.43779
\(538\) 11.7841 0.508050
\(539\) −23.5801 −1.01567
\(540\) −18.5758 −0.799376
\(541\) −30.9651 −1.33129 −0.665647 0.746267i \(-0.731844\pi\)
−0.665647 + 0.746267i \(0.731844\pi\)
\(542\) −1.72211 −0.0739710
\(543\) 9.62683 0.413127
\(544\) 7.25106 0.310887
\(545\) 23.3626 1.00074
\(546\) −12.4701 −0.533672
\(547\) −15.4319 −0.659821 −0.329910 0.944012i \(-0.607019\pi\)
−0.329910 + 0.944012i \(0.607019\pi\)
\(548\) 5.37282 0.229515
\(549\) −3.98428 −0.170045
\(550\) 40.0129 1.70616
\(551\) 10.9497 0.466472
\(552\) 5.05873 0.215314
\(553\) −41.5641 −1.76748
\(554\) 0.604596 0.0256868
\(555\) −9.14171 −0.388044
\(556\) 1.01967 0.0432437
\(557\) −20.9715 −0.888592 −0.444296 0.895880i \(-0.646546\pi\)
−0.444296 + 0.895880i \(0.646546\pi\)
\(558\) 2.96111 0.125354
\(559\) 23.6470 1.00016
\(560\) 13.4717 0.569284
\(561\) −55.9445 −2.36198
\(562\) −3.80725 −0.160599
\(563\) 1.78839 0.0753716 0.0376858 0.999290i \(-0.488001\pi\)
0.0376858 + 0.999290i \(0.488001\pi\)
\(564\) −5.06026 −0.213075
\(565\) 31.9927 1.34594
\(566\) 0.610355 0.0256551
\(567\) 34.9074 1.46597
\(568\) 2.85150 0.119646
\(569\) 16.6280 0.697081 0.348540 0.937294i \(-0.386677\pi\)
0.348540 + 0.937294i \(0.386677\pi\)
\(570\) −11.4404 −0.479185
\(571\) 17.3291 0.725201 0.362601 0.931945i \(-0.381889\pi\)
0.362601 + 0.931945i \(0.381889\pi\)
\(572\) −8.18567 −0.342260
\(573\) 26.2359 1.09602
\(574\) 27.3809 1.14286
\(575\) 26.2353 1.09409
\(576\) 0.315788 0.0131579
\(577\) −12.6121 −0.525049 −0.262524 0.964925i \(-0.584555\pi\)
−0.262524 + 0.964925i \(0.584555\pi\)
\(578\) −35.5778 −1.47984
\(579\) −36.3501 −1.51066
\(580\) −25.1727 −1.04524
\(581\) −32.0936 −1.33147
\(582\) −6.07435 −0.251790
\(583\) 36.1584 1.49753
\(584\) −5.54156 −0.229311
\(585\) −2.31860 −0.0958623
\(586\) 2.88815 0.119308
\(587\) 29.9048 1.23430 0.617151 0.786845i \(-0.288287\pi\)
0.617151 + 0.786845i \(0.288287\pi\)
\(588\) −10.1339 −0.417915
\(589\) −15.5013 −0.638719
\(590\) −41.4741 −1.70746
\(591\) 11.4268 0.470036
\(592\) −1.32098 −0.0542920
\(593\) −28.4837 −1.16968 −0.584842 0.811147i \(-0.698844\pi\)
−0.584842 + 0.811147i \(0.698844\pi\)
\(594\) 20.7096 0.849727
\(595\) −97.6842 −4.00466
\(596\) −5.09976 −0.208895
\(597\) −15.4829 −0.633675
\(598\) −5.36710 −0.219477
\(599\) 13.6918 0.559430 0.279715 0.960083i \(-0.409760\pi\)
0.279715 + 0.960083i \(0.409760\pi\)
\(600\) 17.1962 0.702030
\(601\) 33.9178 1.38353 0.691767 0.722121i \(-0.256833\pi\)
0.691767 + 0.722121i \(0.256833\pi\)
\(602\) 43.3879 1.76836
\(603\) 3.54702 0.144446
\(604\) −10.3479 −0.421052
\(605\) −26.4228 −1.07424
\(606\) 31.6140 1.28423
\(607\) 23.3715 0.948620 0.474310 0.880358i \(-0.342698\pi\)
0.474310 + 0.880358i \(0.342698\pi\)
\(608\) −1.65314 −0.0670436
\(609\) 42.7534 1.73246
\(610\) −47.9503 −1.94145
\(611\) 5.36872 0.217195
\(612\) −2.28980 −0.0925597
\(613\) −7.62645 −0.308029 −0.154015 0.988069i \(-0.549220\pi\)
−0.154015 + 0.988069i \(0.549220\pi\)
\(614\) 21.8437 0.881539
\(615\) 53.4558 2.15554
\(616\) −15.0192 −0.605142
\(617\) 27.2887 1.09860 0.549301 0.835625i \(-0.314894\pi\)
0.549301 + 0.835625i \(0.314894\pi\)
\(618\) 10.0117 0.402730
\(619\) 34.6326 1.39200 0.696001 0.718041i \(-0.254961\pi\)
0.696001 + 0.718041i \(0.254961\pi\)
\(620\) 35.6366 1.43120
\(621\) 13.5787 0.544895
\(622\) −19.5894 −0.785464
\(623\) 3.86734 0.154942
\(624\) −3.51791 −0.140829
\(625\) 16.9637 0.678550
\(626\) −25.3964 −1.01504
\(627\) 12.7545 0.509367
\(628\) 8.43226 0.336484
\(629\) 9.57850 0.381920
\(630\) −4.25421 −0.169492
\(631\) −26.4862 −1.05440 −0.527199 0.849742i \(-0.676758\pi\)
−0.527199 + 0.849742i \(0.676758\pi\)
\(632\) −11.7255 −0.466417
\(633\) −6.37697 −0.253462
\(634\) 5.85823 0.232660
\(635\) −38.3512 −1.52192
\(636\) 15.5396 0.616186
\(637\) 10.7516 0.425995
\(638\) 28.0643 1.11108
\(639\) −0.900469 −0.0356220
\(640\) 3.80048 0.150227
\(641\) 21.7321 0.858365 0.429183 0.903218i \(-0.358802\pi\)
0.429183 + 0.903218i \(0.358802\pi\)
\(642\) −18.5055 −0.730353
\(643\) 37.2441 1.46876 0.734382 0.678737i \(-0.237472\pi\)
0.734382 + 0.678737i \(0.237472\pi\)
\(644\) −9.84767 −0.388052
\(645\) 84.7062 3.33530
\(646\) 11.9870 0.471622
\(647\) 34.3429 1.35016 0.675079 0.737745i \(-0.264109\pi\)
0.675079 + 0.737745i \(0.264109\pi\)
\(648\) 9.84764 0.386852
\(649\) 46.2383 1.81501
\(650\) −18.2444 −0.715605
\(651\) −60.5254 −2.37218
\(652\) 22.8876 0.896349
\(653\) 28.8878 1.13047 0.565234 0.824931i \(-0.308786\pi\)
0.565234 + 0.824931i \(0.308786\pi\)
\(654\) −11.1938 −0.437711
\(655\) 76.9509 3.00672
\(656\) 7.72437 0.301586
\(657\) 1.74996 0.0682725
\(658\) 9.85064 0.384018
\(659\) −39.0221 −1.52008 −0.760042 0.649874i \(-0.774822\pi\)
−0.760042 + 0.649874i \(0.774822\pi\)
\(660\) −29.3220 −1.14136
\(661\) −2.31263 −0.0899511 −0.0449755 0.998988i \(-0.514321\pi\)
−0.0449755 + 0.998988i \(0.514321\pi\)
\(662\) 32.5253 1.26413
\(663\) 25.5086 0.990672
\(664\) −9.05386 −0.351358
\(665\) 22.2706 0.863617
\(666\) 0.417150 0.0161642
\(667\) 18.4010 0.712488
\(668\) −3.29537 −0.127502
\(669\) −15.7126 −0.607486
\(670\) 42.6879 1.64918
\(671\) 53.4584 2.06374
\(672\) −6.45474 −0.248997
\(673\) −38.9917 −1.50302 −0.751509 0.659723i \(-0.770674\pi\)
−0.751509 + 0.659723i \(0.770674\pi\)
\(674\) 34.0500 1.31156
\(675\) 46.1581 1.77663
\(676\) −9.26764 −0.356448
\(677\) 5.38730 0.207051 0.103525 0.994627i \(-0.466988\pi\)
0.103525 + 0.994627i \(0.466988\pi\)
\(678\) −15.3287 −0.588696
\(679\) 11.8247 0.453792
\(680\) −27.5575 −1.05678
\(681\) 33.9318 1.30027
\(682\) −39.7302 −1.52135
\(683\) 29.7789 1.13946 0.569729 0.821833i \(-0.307048\pi\)
0.569729 + 0.821833i \(0.307048\pi\)
\(684\) 0.522042 0.0199608
\(685\) −20.4193 −0.780180
\(686\) −5.08590 −0.194181
\(687\) −8.12045 −0.309815
\(688\) 12.2401 0.466648
\(689\) −16.4869 −0.628101
\(690\) −19.2256 −0.731905
\(691\) −2.89807 −0.110248 −0.0551238 0.998480i \(-0.517555\pi\)
−0.0551238 + 0.998480i \(0.517555\pi\)
\(692\) −8.41833 −0.320017
\(693\) 4.74290 0.180168
\(694\) 6.91669 0.262554
\(695\) −3.87523 −0.146996
\(696\) 12.0611 0.457174
\(697\) −56.0099 −2.12152
\(698\) 6.42314 0.243119
\(699\) −49.5262 −1.87325
\(700\) −33.4752 −1.26524
\(701\) 40.7677 1.53977 0.769887 0.638181i \(-0.220313\pi\)
0.769887 + 0.638181i \(0.220313\pi\)
\(702\) −9.44282 −0.356396
\(703\) −2.18376 −0.0823621
\(704\) −4.23704 −0.159689
\(705\) 19.2314 0.724296
\(706\) −4.64082 −0.174660
\(707\) −61.5420 −2.31453
\(708\) 19.8716 0.746820
\(709\) −12.9280 −0.485522 −0.242761 0.970086i \(-0.578053\pi\)
−0.242761 + 0.970086i \(0.578053\pi\)
\(710\) −10.8370 −0.406707
\(711\) 3.70279 0.138866
\(712\) 1.09101 0.0408872
\(713\) −26.0499 −0.975578
\(714\) 46.8037 1.75158
\(715\) 31.1094 1.16343
\(716\) 18.2974 0.683807
\(717\) −52.3491 −1.95501
\(718\) 13.8789 0.517957
\(719\) 18.6463 0.695391 0.347696 0.937607i \(-0.386964\pi\)
0.347696 + 0.937607i \(0.386964\pi\)
\(720\) −1.20015 −0.0447268
\(721\) −19.4894 −0.725825
\(722\) 16.2671 0.605400
\(723\) 23.1622 0.861412
\(724\) −5.28677 −0.196481
\(725\) 62.5504 2.32307
\(726\) 12.6600 0.469857
\(727\) 19.3731 0.718509 0.359254 0.933240i \(-0.383031\pi\)
0.359254 + 0.933240i \(0.383031\pi\)
\(728\) 6.84821 0.253811
\(729\) 23.5911 0.873743
\(730\) 21.0606 0.779486
\(731\) −88.7534 −3.28266
\(732\) 22.9745 0.849164
\(733\) −31.7529 −1.17282 −0.586410 0.810014i \(-0.699459\pi\)
−0.586410 + 0.810014i \(0.699459\pi\)
\(734\) −17.2289 −0.635932
\(735\) 38.5136 1.42060
\(736\) −2.77810 −0.102402
\(737\) −47.5915 −1.75306
\(738\) −2.43927 −0.0897907
\(739\) −8.70497 −0.320218 −0.160109 0.987099i \(-0.551185\pi\)
−0.160109 + 0.987099i \(0.551185\pi\)
\(740\) 5.02035 0.184552
\(741\) −5.81559 −0.213641
\(742\) −30.2505 −1.11053
\(743\) 16.4876 0.604872 0.302436 0.953170i \(-0.402200\pi\)
0.302436 + 0.953170i \(0.402200\pi\)
\(744\) −17.0747 −0.625988
\(745\) 19.3815 0.710084
\(746\) −5.54848 −0.203144
\(747\) 2.85910 0.104609
\(748\) 30.7230 1.12334
\(749\) 36.0240 1.31629
\(750\) −30.7516 −1.12289
\(751\) −12.5440 −0.457735 −0.228868 0.973458i \(-0.573502\pi\)
−0.228868 + 0.973458i \(0.573502\pi\)
\(752\) 2.77894 0.101338
\(753\) −10.3702 −0.377911
\(754\) −12.7963 −0.466013
\(755\) 39.3271 1.43126
\(756\) −17.3259 −0.630136
\(757\) 16.3930 0.595815 0.297908 0.954595i \(-0.403711\pi\)
0.297908 + 0.954595i \(0.403711\pi\)
\(758\) −26.7795 −0.972674
\(759\) 21.4340 0.778006
\(760\) 6.28271 0.227898
\(761\) 17.2389 0.624911 0.312455 0.949932i \(-0.398849\pi\)
0.312455 + 0.949932i \(0.398849\pi\)
\(762\) 18.3753 0.665666
\(763\) 21.7905 0.788870
\(764\) −14.4080 −0.521262
\(765\) 8.70233 0.314633
\(766\) −19.7557 −0.713804
\(767\) −21.0829 −0.761260
\(768\) −1.82093 −0.0657072
\(769\) −1.92188 −0.0693049 −0.0346524 0.999399i \(-0.511032\pi\)
−0.0346524 + 0.999399i \(0.511032\pi\)
\(770\) 57.0802 2.05703
\(771\) 31.5648 1.13678
\(772\) 19.9624 0.718461
\(773\) 0.651155 0.0234204 0.0117102 0.999931i \(-0.496272\pi\)
0.0117102 + 0.999931i \(0.496272\pi\)
\(774\) −3.86527 −0.138934
\(775\) −88.5517 −3.18087
\(776\) 3.33585 0.119750
\(777\) −8.52658 −0.305889
\(778\) −5.74262 −0.205883
\(779\) 12.7694 0.457513
\(780\) 13.3697 0.478714
\(781\) 12.0819 0.432324
\(782\) 20.1442 0.720354
\(783\) 32.3745 1.15697
\(784\) 5.56523 0.198758
\(785\) −32.0466 −1.14379
\(786\) −36.8697 −1.31510
\(787\) 20.8161 0.742015 0.371007 0.928630i \(-0.379012\pi\)
0.371007 + 0.928630i \(0.379012\pi\)
\(788\) −6.27526 −0.223547
\(789\) −1.04384 −0.0371618
\(790\) 44.5626 1.58547
\(791\) 29.8399 1.06099
\(792\) 1.33801 0.0475440
\(793\) −24.3750 −0.865583
\(794\) 3.86966 0.137329
\(795\) −59.0580 −2.09457
\(796\) 8.50276 0.301372
\(797\) −12.8114 −0.453801 −0.226901 0.973918i \(-0.572859\pi\)
−0.226901 + 0.973918i \(0.572859\pi\)
\(798\) −10.6706 −0.377734
\(799\) −20.1503 −0.712865
\(800\) −9.44361 −0.333882
\(801\) −0.344527 −0.0121733
\(802\) 13.3000 0.469639
\(803\) −23.4798 −0.828584
\(804\) −20.4532 −0.721328
\(805\) 37.4258 1.31909
\(806\) 18.1155 0.638092
\(807\) 21.4581 0.755360
\(808\) −17.3615 −0.610774
\(809\) 12.4630 0.438174 0.219087 0.975705i \(-0.429692\pi\)
0.219087 + 0.975705i \(0.429692\pi\)
\(810\) −37.4257 −1.31501
\(811\) −32.9912 −1.15848 −0.579238 0.815158i \(-0.696650\pi\)
−0.579238 + 0.815158i \(0.696650\pi\)
\(812\) −23.4789 −0.823947
\(813\) −3.13584 −0.109979
\(814\) −5.59704 −0.196176
\(815\) −86.9839 −3.04691
\(816\) 13.2037 0.462221
\(817\) 20.2345 0.707916
\(818\) −13.1153 −0.458565
\(819\) −2.16259 −0.0755668
\(820\) −29.3563 −1.02517
\(821\) 21.2066 0.740116 0.370058 0.929009i \(-0.379338\pi\)
0.370058 + 0.929009i \(0.379338\pi\)
\(822\) 9.78353 0.341240
\(823\) −3.53700 −0.123292 −0.0616461 0.998098i \(-0.519635\pi\)
−0.0616461 + 0.998098i \(0.519635\pi\)
\(824\) −5.49812 −0.191536
\(825\) 72.8608 2.53669
\(826\) −38.6834 −1.34597
\(827\) −47.9059 −1.66585 −0.832925 0.553386i \(-0.813335\pi\)
−0.832925 + 0.553386i \(0.813335\pi\)
\(828\) 0.877292 0.0304880
\(829\) 32.5398 1.13015 0.565077 0.825038i \(-0.308846\pi\)
0.565077 + 0.825038i \(0.308846\pi\)
\(830\) 34.4090 1.19435
\(831\) 1.10093 0.0381907
\(832\) 1.93193 0.0669777
\(833\) −40.3538 −1.39818
\(834\) 1.85675 0.0642940
\(835\) 12.5240 0.433410
\(836\) −7.00441 −0.242252
\(837\) −45.8320 −1.58419
\(838\) −35.9124 −1.24057
\(839\) −32.9144 −1.13633 −0.568165 0.822914i \(-0.692347\pi\)
−0.568165 + 0.822914i \(0.692347\pi\)
\(840\) 24.5311 0.846402
\(841\) 14.8717 0.512818
\(842\) 4.37921 0.150917
\(843\) −6.93274 −0.238776
\(844\) 3.50204 0.120545
\(845\) 35.2214 1.21165
\(846\) −0.877557 −0.0301710
\(847\) −24.6448 −0.846806
\(848\) −8.53389 −0.293055
\(849\) 1.11141 0.0381436
\(850\) 68.4762 2.34871
\(851\) −3.66982 −0.125800
\(852\) 5.19238 0.177888
\(853\) 3.99008 0.136618 0.0683088 0.997664i \(-0.478240\pi\)
0.0683088 + 0.997664i \(0.478240\pi\)
\(854\) −44.7238 −1.53042
\(855\) −1.98401 −0.0678516
\(856\) 10.1626 0.347352
\(857\) 24.7741 0.846269 0.423134 0.906067i \(-0.360930\pi\)
0.423134 + 0.906067i \(0.360930\pi\)
\(858\) −14.9055 −0.508867
\(859\) 45.9502 1.56780 0.783900 0.620887i \(-0.213227\pi\)
0.783900 + 0.620887i \(0.213227\pi\)
\(860\) −46.5181 −1.58625
\(861\) 49.8588 1.69918
\(862\) 6.34634 0.216157
\(863\) 17.8391 0.607251 0.303626 0.952791i \(-0.401803\pi\)
0.303626 + 0.952791i \(0.401803\pi\)
\(864\) −4.88776 −0.166285
\(865\) 31.9937 1.08782
\(866\) 12.1995 0.414557
\(867\) −64.7848 −2.20021
\(868\) 33.2387 1.12819
\(869\) −49.6816 −1.68533
\(870\) −45.8378 −1.55405
\(871\) 21.7000 0.735275
\(872\) 6.14727 0.208173
\(873\) −1.05342 −0.0356529
\(874\) −4.59258 −0.155346
\(875\) 59.8631 2.02374
\(876\) −10.0908 −0.340936
\(877\) 15.4239 0.520829 0.260414 0.965497i \(-0.416141\pi\)
0.260414 + 0.965497i \(0.416141\pi\)
\(878\) 32.3638 1.09223
\(879\) 5.25912 0.177386
\(880\) 16.1028 0.542824
\(881\) −10.0524 −0.338673 −0.169336 0.985558i \(-0.554162\pi\)
−0.169336 + 0.985558i \(0.554162\pi\)
\(882\) −1.75743 −0.0591759
\(883\) 38.3801 1.29159 0.645797 0.763510i \(-0.276525\pi\)
0.645797 + 0.763510i \(0.276525\pi\)
\(884\) −14.0085 −0.471158
\(885\) −75.5215 −2.53863
\(886\) −11.8677 −0.398704
\(887\) 4.83508 0.162346 0.0811730 0.996700i \(-0.474133\pi\)
0.0811730 + 0.996700i \(0.474133\pi\)
\(888\) −2.40541 −0.0807204
\(889\) −35.7706 −1.19971
\(890\) −4.14634 −0.138986
\(891\) 41.7248 1.39783
\(892\) 8.62891 0.288917
\(893\) 4.59397 0.153731
\(894\) −9.28632 −0.310581
\(895\) −69.5389 −2.32443
\(896\) 3.54475 0.118422
\(897\) −9.77312 −0.326315
\(898\) 1.98188 0.0661363
\(899\) −62.1085 −2.07143
\(900\) 2.98218 0.0994061
\(901\) 61.8798 2.06151
\(902\) 32.7285 1.08974
\(903\) 79.0064 2.62917
\(904\) 8.41808 0.279981
\(905\) 20.0922 0.667888
\(906\) −18.8429 −0.626013
\(907\) −33.0893 −1.09871 −0.549356 0.835588i \(-0.685127\pi\)
−0.549356 + 0.835588i \(0.685127\pi\)
\(908\) −18.6343 −0.618401
\(909\) 5.48255 0.181845
\(910\) −26.0264 −0.862768
\(911\) −27.4193 −0.908441 −0.454220 0.890889i \(-0.650082\pi\)
−0.454220 + 0.890889i \(0.650082\pi\)
\(912\) −3.01025 −0.0996793
\(913\) −38.3615 −1.26958
\(914\) −24.4134 −0.807524
\(915\) −87.3142 −2.88652
\(916\) 4.45951 0.147346
\(917\) 71.7730 2.37015
\(918\) 35.4414 1.16974
\(919\) 47.5869 1.56975 0.784874 0.619655i \(-0.212728\pi\)
0.784874 + 0.619655i \(0.212728\pi\)
\(920\) 10.5581 0.348090
\(921\) 39.7758 1.31066
\(922\) 39.3419 1.29566
\(923\) −5.50889 −0.181327
\(924\) −27.3490 −0.899715
\(925\) −12.4748 −0.410170
\(926\) −10.7789 −0.354216
\(927\) 1.73624 0.0570257
\(928\) −6.62357 −0.217429
\(929\) 0.714612 0.0234457 0.0117228 0.999931i \(-0.496268\pi\)
0.0117228 + 0.999931i \(0.496268\pi\)
\(930\) 64.8918 2.12789
\(931\) 9.20009 0.301521
\(932\) 27.1983 0.890910
\(933\) −35.6710 −1.16781
\(934\) 4.75747 0.155669
\(935\) −116.762 −3.81853
\(936\) −0.610082 −0.0199411
\(937\) 33.9434 1.10888 0.554442 0.832223i \(-0.312932\pi\)
0.554442 + 0.832223i \(0.312932\pi\)
\(938\) 39.8155 1.30002
\(939\) −46.2451 −1.50915
\(940\) −10.5613 −0.344471
\(941\) −35.6616 −1.16254 −0.581268 0.813713i \(-0.697443\pi\)
−0.581268 + 0.813713i \(0.697443\pi\)
\(942\) 15.3546 0.500279
\(943\) 21.4591 0.698804
\(944\) −10.9129 −0.355184
\(945\) 65.8466 2.14199
\(946\) 51.8616 1.68617
\(947\) 2.03154 0.0660163 0.0330082 0.999455i \(-0.489491\pi\)
0.0330082 + 0.999455i \(0.489491\pi\)
\(948\) −21.3514 −0.693461
\(949\) 10.7059 0.347529
\(950\) −15.6116 −0.506507
\(951\) 10.6674 0.345915
\(952\) −25.7032 −0.833044
\(953\) 29.6684 0.961052 0.480526 0.876980i \(-0.340446\pi\)
0.480526 + 0.876980i \(0.340446\pi\)
\(954\) 2.69491 0.0872508
\(955\) 54.7571 1.77190
\(956\) 28.7485 0.929794
\(957\) 51.1032 1.65193
\(958\) 20.4210 0.659774
\(959\) −19.0453 −0.615004
\(960\) 6.92040 0.223355
\(961\) 56.9260 1.83632
\(962\) 2.55204 0.0822812
\(963\) −3.20925 −0.103417
\(964\) −12.7200 −0.409683
\(965\) −75.8664 −2.44223
\(966\) −17.9319 −0.576950
\(967\) −13.9503 −0.448611 −0.224306 0.974519i \(-0.572011\pi\)
−0.224306 + 0.974519i \(0.572011\pi\)
\(968\) −6.95249 −0.223462
\(969\) 21.8275 0.701200
\(970\) −12.6778 −0.407060
\(971\) −19.6661 −0.631115 −0.315558 0.948906i \(-0.602192\pi\)
−0.315558 + 0.948906i \(0.602192\pi\)
\(972\) 3.26859 0.104840
\(973\) −3.61447 −0.115875
\(974\) −35.8756 −1.14953
\(975\) −33.2218 −1.06395
\(976\) −12.6169 −0.403858
\(977\) −2.46901 −0.0789905 −0.0394953 0.999220i \(-0.512575\pi\)
−0.0394953 + 0.999220i \(0.512575\pi\)
\(978\) 41.6768 1.33268
\(979\) 4.62263 0.147740
\(980\) −21.1505 −0.675628
\(981\) −1.94124 −0.0619790
\(982\) −9.30422 −0.296909
\(983\) −15.8743 −0.506311 −0.253155 0.967426i \(-0.581468\pi\)
−0.253155 + 0.967426i \(0.581468\pi\)
\(984\) 14.0655 0.448393
\(985\) 23.8490 0.759891
\(986\) 48.0279 1.52952
\(987\) 17.9373 0.570951
\(988\) 3.19375 0.101607
\(989\) 34.0042 1.08127
\(990\) −5.08507 −0.161614
\(991\) 56.4317 1.79261 0.896305 0.443437i \(-0.146241\pi\)
0.896305 + 0.443437i \(0.146241\pi\)
\(992\) 9.37689 0.297717
\(993\) 59.2263 1.87949
\(994\) −10.1078 −0.320601
\(995\) −32.3145 −1.02444
\(996\) −16.4864 −0.522393
\(997\) −35.6360 −1.12860 −0.564302 0.825568i \(-0.690855\pi\)
−0.564302 + 0.825568i \(0.690855\pi\)
\(998\) 21.5100 0.680886
\(999\) −6.45664 −0.204279
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.1.11 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.11 40 1.1 even 1 trivial