Properties

Label 4033.2.a.f.1.11
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
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 \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.15921 q^{2} -0.135675 q^{3} +2.66221 q^{4} -3.14294 q^{5} +0.292951 q^{6} +0.215452 q^{7} -1.42985 q^{8} -2.98159 q^{9} +O(q^{10})\) \(q-2.15921 q^{2} -0.135675 q^{3} +2.66221 q^{4} -3.14294 q^{5} +0.292951 q^{6} +0.215452 q^{7} -1.42985 q^{8} -2.98159 q^{9} +6.78628 q^{10} +6.40909 q^{11} -0.361194 q^{12} +6.09951 q^{13} -0.465208 q^{14} +0.426417 q^{15} -2.23707 q^{16} -1.51328 q^{17} +6.43790 q^{18} +0.941921 q^{19} -8.36715 q^{20} -0.0292314 q^{21} -13.8386 q^{22} +5.61733 q^{23} +0.193994 q^{24} +4.87806 q^{25} -13.1701 q^{26} +0.811551 q^{27} +0.573579 q^{28} +0.309118 q^{29} -0.920727 q^{30} +3.60497 q^{31} +7.69000 q^{32} -0.869551 q^{33} +3.26749 q^{34} -0.677153 q^{35} -7.93761 q^{36} +1.00000 q^{37} -2.03381 q^{38} -0.827549 q^{39} +4.49392 q^{40} +11.4789 q^{41} +0.0631169 q^{42} -3.97805 q^{43} +17.0623 q^{44} +9.37096 q^{45} -12.1290 q^{46} +0.788927 q^{47} +0.303514 q^{48} -6.95358 q^{49} -10.5328 q^{50} +0.205313 q^{51} +16.2381 q^{52} +8.30370 q^{53} -1.75231 q^{54} -20.1434 q^{55} -0.308063 q^{56} -0.127795 q^{57} -0.667451 q^{58} +13.6028 q^{59} +1.13521 q^{60} -7.36806 q^{61} -7.78390 q^{62} -0.642391 q^{63} -12.1302 q^{64} -19.1704 q^{65} +1.87755 q^{66} +8.94172 q^{67} -4.02865 q^{68} -0.762129 q^{69} +1.46212 q^{70} -1.27963 q^{71} +4.26322 q^{72} -10.6218 q^{73} -2.15921 q^{74} -0.661830 q^{75} +2.50759 q^{76} +1.38085 q^{77} +1.78686 q^{78} -7.77543 q^{79} +7.03097 q^{80} +8.83467 q^{81} -24.7854 q^{82} -5.35637 q^{83} -0.0778201 q^{84} +4.75613 q^{85} +8.58945 q^{86} -0.0419394 q^{87} -9.16400 q^{88} +5.06343 q^{89} -20.2339 q^{90} +1.31415 q^{91} +14.9545 q^{92} -0.489103 q^{93} -1.70346 q^{94} -2.96040 q^{95} -1.04334 q^{96} -9.73558 q^{97} +15.0143 q^{98} -19.1093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15921 −1.52680 −0.763398 0.645929i \(-0.776470\pi\)
−0.763398 + 0.645929i \(0.776470\pi\)
\(3\) −0.135675 −0.0783319 −0.0391659 0.999233i \(-0.512470\pi\)
−0.0391659 + 0.999233i \(0.512470\pi\)
\(4\) 2.66221 1.33110
\(5\) −3.14294 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(6\) 0.292951 0.119597
\(7\) 0.215452 0.0814333 0.0407167 0.999171i \(-0.487036\pi\)
0.0407167 + 0.999171i \(0.487036\pi\)
\(8\) −1.42985 −0.505527
\(9\) −2.98159 −0.993864
\(10\) 6.78628 2.14601
\(11\) 6.40909 1.93241 0.966206 0.257770i \(-0.0829877\pi\)
0.966206 + 0.257770i \(0.0829877\pi\)
\(12\) −0.361194 −0.104268
\(13\) 6.09951 1.69170 0.845849 0.533422i \(-0.179094\pi\)
0.845849 + 0.533422i \(0.179094\pi\)
\(14\) −0.465208 −0.124332
\(15\) 0.426417 0.110101
\(16\) −2.23707 −0.559268
\(17\) −1.51328 −0.367023 −0.183512 0.983018i \(-0.558746\pi\)
−0.183512 + 0.983018i \(0.558746\pi\)
\(18\) 6.43790 1.51743
\(19\) 0.941921 0.216092 0.108046 0.994146i \(-0.465541\pi\)
0.108046 + 0.994146i \(0.465541\pi\)
\(20\) −8.36715 −1.87095
\(21\) −0.0292314 −0.00637882
\(22\) −13.8386 −2.95040
\(23\) 5.61733 1.17129 0.585647 0.810566i \(-0.300841\pi\)
0.585647 + 0.810566i \(0.300841\pi\)
\(24\) 0.193994 0.0395988
\(25\) 4.87806 0.975613
\(26\) −13.1701 −2.58288
\(27\) 0.811551 0.156183
\(28\) 0.573579 0.108396
\(29\) 0.309118 0.0574017 0.0287008 0.999588i \(-0.490863\pi\)
0.0287008 + 0.999588i \(0.490863\pi\)
\(30\) −0.920727 −0.168101
\(31\) 3.60497 0.647471 0.323736 0.946148i \(-0.395061\pi\)
0.323736 + 0.946148i \(0.395061\pi\)
\(32\) 7.69000 1.35941
\(33\) −0.869551 −0.151369
\(34\) 3.26749 0.560369
\(35\) −0.677153 −0.114460
\(36\) −7.93761 −1.32294
\(37\) 1.00000 0.164399
\(38\) −2.03381 −0.329928
\(39\) −0.827549 −0.132514
\(40\) 4.49392 0.710551
\(41\) 11.4789 1.79271 0.896353 0.443342i \(-0.146207\pi\)
0.896353 + 0.443342i \(0.146207\pi\)
\(42\) 0.0631169 0.00973916
\(43\) −3.97805 −0.606646 −0.303323 0.952888i \(-0.598096\pi\)
−0.303323 + 0.952888i \(0.598096\pi\)
\(44\) 17.0623 2.57224
\(45\) 9.37096 1.39694
\(46\) −12.1290 −1.78833
\(47\) 0.788927 0.115077 0.0575384 0.998343i \(-0.481675\pi\)
0.0575384 + 0.998343i \(0.481675\pi\)
\(48\) 0.303514 0.0438085
\(49\) −6.95358 −0.993369
\(50\) −10.5328 −1.48956
\(51\) 0.205313 0.0287496
\(52\) 16.2381 2.25183
\(53\) 8.30370 1.14060 0.570300 0.821436i \(-0.306827\pi\)
0.570300 + 0.821436i \(0.306827\pi\)
\(54\) −1.75231 −0.238460
\(55\) −20.1434 −2.71613
\(56\) −0.308063 −0.0411667
\(57\) −0.127795 −0.0169269
\(58\) −0.667451 −0.0876406
\(59\) 13.6028 1.77093 0.885467 0.464703i \(-0.153839\pi\)
0.885467 + 0.464703i \(0.153839\pi\)
\(60\) 1.13521 0.146555
\(61\) −7.36806 −0.943383 −0.471692 0.881764i \(-0.656356\pi\)
−0.471692 + 0.881764i \(0.656356\pi\)
\(62\) −7.78390 −0.988556
\(63\) −0.642391 −0.0809337
\(64\) −12.1302 −1.51628
\(65\) −19.1704 −2.37779
\(66\) 1.87755 0.231110
\(67\) 8.94172 1.09241 0.546203 0.837653i \(-0.316073\pi\)
0.546203 + 0.837653i \(0.316073\pi\)
\(68\) −4.02865 −0.488546
\(69\) −0.762129 −0.0917496
\(70\) 1.46212 0.174757
\(71\) −1.27963 −0.151864 −0.0759320 0.997113i \(-0.524193\pi\)
−0.0759320 + 0.997113i \(0.524193\pi\)
\(72\) 4.26322 0.502425
\(73\) −10.6218 −1.24319 −0.621594 0.783339i \(-0.713515\pi\)
−0.621594 + 0.783339i \(0.713515\pi\)
\(74\) −2.15921 −0.251004
\(75\) −0.661830 −0.0764216
\(76\) 2.50759 0.287640
\(77\) 1.38085 0.157363
\(78\) 1.78686 0.202322
\(79\) −7.77543 −0.874804 −0.437402 0.899266i \(-0.644101\pi\)
−0.437402 + 0.899266i \(0.644101\pi\)
\(80\) 7.03097 0.786087
\(81\) 8.83467 0.981630
\(82\) −24.7854 −2.73709
\(83\) −5.35637 −0.587938 −0.293969 0.955815i \(-0.594976\pi\)
−0.293969 + 0.955815i \(0.594976\pi\)
\(84\) −0.0778201 −0.00849087
\(85\) 4.75613 0.515875
\(86\) 8.58945 0.926224
\(87\) −0.0419394 −0.00449638
\(88\) −9.16400 −0.976886
\(89\) 5.06343 0.536723 0.268361 0.963318i \(-0.413518\pi\)
0.268361 + 0.963318i \(0.413518\pi\)
\(90\) −20.2339 −2.13284
\(91\) 1.31415 0.137761
\(92\) 14.9545 1.55911
\(93\) −0.489103 −0.0507176
\(94\) −1.70346 −0.175699
\(95\) −2.96040 −0.303731
\(96\) −1.04334 −0.106485
\(97\) −9.73558 −0.988498 −0.494249 0.869320i \(-0.664557\pi\)
−0.494249 + 0.869320i \(0.664557\pi\)
\(98\) 15.0143 1.51667
\(99\) −19.1093 −1.92056
\(100\) 12.9864 1.29864
\(101\) −13.3935 −1.33270 −0.666350 0.745639i \(-0.732144\pi\)
−0.666350 + 0.745639i \(0.732144\pi\)
\(102\) −0.443315 −0.0438948
\(103\) −16.2053 −1.59675 −0.798376 0.602159i \(-0.794307\pi\)
−0.798376 + 0.602159i \(0.794307\pi\)
\(104\) −8.72135 −0.855199
\(105\) 0.0918726 0.00896585
\(106\) −17.9295 −1.74146
\(107\) −4.96272 −0.479764 −0.239882 0.970802i \(-0.577109\pi\)
−0.239882 + 0.970802i \(0.577109\pi\)
\(108\) 2.16052 0.207896
\(109\) −1.00000 −0.0957826
\(110\) 43.4938 4.14698
\(111\) −0.135675 −0.0128777
\(112\) −0.481982 −0.0455430
\(113\) −11.4705 −1.07905 −0.539525 0.841970i \(-0.681396\pi\)
−0.539525 + 0.841970i \(0.681396\pi\)
\(114\) 0.275937 0.0258438
\(115\) −17.6549 −1.64633
\(116\) 0.822935 0.0764076
\(117\) −18.1862 −1.68132
\(118\) −29.3714 −2.70385
\(119\) −0.326039 −0.0298879
\(120\) −0.609711 −0.0556587
\(121\) 30.0764 2.73422
\(122\) 15.9092 1.44035
\(123\) −1.55740 −0.140426
\(124\) 9.59717 0.861851
\(125\) 0.383238 0.0342779
\(126\) 1.38706 0.123569
\(127\) −7.87326 −0.698639 −0.349319 0.937004i \(-0.613587\pi\)
−0.349319 + 0.937004i \(0.613587\pi\)
\(128\) 10.8118 0.955633
\(129\) 0.539720 0.0475197
\(130\) 41.3929 3.63040
\(131\) 20.5299 1.79371 0.896853 0.442329i \(-0.145848\pi\)
0.896853 + 0.442329i \(0.145848\pi\)
\(132\) −2.31492 −0.201488
\(133\) 0.202939 0.0175971
\(134\) −19.3071 −1.66788
\(135\) −2.55066 −0.219525
\(136\) 2.16375 0.185540
\(137\) 7.14762 0.610662 0.305331 0.952246i \(-0.401233\pi\)
0.305331 + 0.952246i \(0.401233\pi\)
\(138\) 1.64560 0.140083
\(139\) −9.77207 −0.828856 −0.414428 0.910082i \(-0.636018\pi\)
−0.414428 + 0.910082i \(0.636018\pi\)
\(140\) −1.80272 −0.152358
\(141\) −0.107038 −0.00901419
\(142\) 2.76299 0.231865
\(143\) 39.0923 3.26906
\(144\) 6.67003 0.555836
\(145\) −0.971538 −0.0806818
\(146\) 22.9348 1.89809
\(147\) 0.943425 0.0778124
\(148\) 2.66221 0.218832
\(149\) 4.31774 0.353723 0.176861 0.984236i \(-0.443406\pi\)
0.176861 + 0.984236i \(0.443406\pi\)
\(150\) 1.42903 0.116680
\(151\) 13.3709 1.08811 0.544053 0.839051i \(-0.316889\pi\)
0.544053 + 0.839051i \(0.316889\pi\)
\(152\) −1.34680 −0.109240
\(153\) 4.51197 0.364771
\(154\) −2.98156 −0.240261
\(155\) −11.3302 −0.910063
\(156\) −2.20311 −0.176390
\(157\) 4.04462 0.322796 0.161398 0.986889i \(-0.448400\pi\)
0.161398 + 0.986889i \(0.448400\pi\)
\(158\) 16.7888 1.33565
\(159\) −1.12660 −0.0893454
\(160\) −24.1692 −1.91074
\(161\) 1.21027 0.0953823
\(162\) −19.0759 −1.49875
\(163\) 16.6323 1.30274 0.651372 0.758758i \(-0.274194\pi\)
0.651372 + 0.758758i \(0.274194\pi\)
\(164\) 30.5592 2.38628
\(165\) 2.73295 0.212760
\(166\) 11.5656 0.897661
\(167\) 8.54871 0.661519 0.330760 0.943715i \(-0.392695\pi\)
0.330760 + 0.943715i \(0.392695\pi\)
\(168\) 0.0417964 0.00322467
\(169\) 24.2040 1.86184
\(170\) −10.2695 −0.787635
\(171\) −2.80843 −0.214766
\(172\) −10.5904 −0.807509
\(173\) 13.1635 1.00080 0.500401 0.865794i \(-0.333186\pi\)
0.500401 + 0.865794i \(0.333186\pi\)
\(174\) 0.0905563 0.00686505
\(175\) 1.05099 0.0794474
\(176\) −14.3376 −1.08074
\(177\) −1.84556 −0.138720
\(178\) −10.9330 −0.819466
\(179\) −4.68878 −0.350456 −0.175228 0.984528i \(-0.556066\pi\)
−0.175228 + 0.984528i \(0.556066\pi\)
\(180\) 24.9474 1.85947
\(181\) 17.4209 1.29488 0.647441 0.762116i \(-0.275839\pi\)
0.647441 + 0.762116i \(0.275839\pi\)
\(182\) −2.83754 −0.210332
\(183\) 0.999660 0.0738970
\(184\) −8.03191 −0.592120
\(185\) −3.14294 −0.231073
\(186\) 1.05608 0.0774354
\(187\) −9.69871 −0.709240
\(188\) 2.10029 0.153179
\(189\) 0.174851 0.0127185
\(190\) 6.39214 0.463735
\(191\) −25.7363 −1.86221 −0.931106 0.364748i \(-0.881155\pi\)
−0.931106 + 0.364748i \(0.881155\pi\)
\(192\) 1.64577 0.118773
\(193\) 5.43046 0.390893 0.195447 0.980714i \(-0.437384\pi\)
0.195447 + 0.980714i \(0.437384\pi\)
\(194\) 21.0212 1.50923
\(195\) 2.60094 0.186257
\(196\) −18.5119 −1.32228
\(197\) −7.00772 −0.499279 −0.249640 0.968339i \(-0.580312\pi\)
−0.249640 + 0.968339i \(0.580312\pi\)
\(198\) 41.2610 2.93229
\(199\) −13.3484 −0.946242 −0.473121 0.880997i \(-0.656873\pi\)
−0.473121 + 0.880997i \(0.656873\pi\)
\(200\) −6.97488 −0.493198
\(201\) −1.21317 −0.0855701
\(202\) 28.9194 2.03476
\(203\) 0.0666001 0.00467441
\(204\) 0.546586 0.0382687
\(205\) −36.0775 −2.51976
\(206\) 34.9906 2.43791
\(207\) −16.7486 −1.16411
\(208\) −13.6450 −0.946112
\(209\) 6.03686 0.417578
\(210\) −0.198373 −0.0136890
\(211\) −22.5515 −1.55251 −0.776254 0.630420i \(-0.782883\pi\)
−0.776254 + 0.630420i \(0.782883\pi\)
\(212\) 22.1062 1.51826
\(213\) 0.173613 0.0118958
\(214\) 10.7156 0.732502
\(215\) 12.5028 0.852681
\(216\) −1.16039 −0.0789547
\(217\) 0.776699 0.0527257
\(218\) 2.15921 0.146240
\(219\) 1.44111 0.0973813
\(220\) −53.6258 −3.61545
\(221\) −9.23023 −0.620893
\(222\) 0.292951 0.0196616
\(223\) 27.2391 1.82406 0.912032 0.410120i \(-0.134513\pi\)
0.912032 + 0.410120i \(0.134513\pi\)
\(224\) 1.65683 0.110702
\(225\) −14.5444 −0.969627
\(226\) 24.7672 1.64749
\(227\) −25.8073 −1.71289 −0.856445 0.516239i \(-0.827332\pi\)
−0.856445 + 0.516239i \(0.827332\pi\)
\(228\) −0.340216 −0.0225314
\(229\) 19.5665 1.29299 0.646495 0.762919i \(-0.276234\pi\)
0.646495 + 0.762919i \(0.276234\pi\)
\(230\) 38.1207 2.51361
\(231\) −0.187347 −0.0123265
\(232\) −0.441990 −0.0290181
\(233\) −3.87374 −0.253777 −0.126889 0.991917i \(-0.540499\pi\)
−0.126889 + 0.991917i \(0.540499\pi\)
\(234\) 39.2680 2.56703
\(235\) −2.47955 −0.161748
\(236\) 36.2134 2.35729
\(237\) 1.05493 0.0685250
\(238\) 0.703987 0.0456327
\(239\) −19.7036 −1.27452 −0.637259 0.770650i \(-0.719932\pi\)
−0.637259 + 0.770650i \(0.719932\pi\)
\(240\) −0.953926 −0.0615756
\(241\) −3.83368 −0.246949 −0.123475 0.992348i \(-0.539404\pi\)
−0.123475 + 0.992348i \(0.539404\pi\)
\(242\) −64.9414 −4.17459
\(243\) −3.63329 −0.233076
\(244\) −19.6153 −1.25574
\(245\) 21.8547 1.39624
\(246\) 3.36276 0.214402
\(247\) 5.74525 0.365562
\(248\) −5.15454 −0.327314
\(249\) 0.726724 0.0460543
\(250\) −0.827493 −0.0523353
\(251\) 5.12914 0.323748 0.161874 0.986811i \(-0.448246\pi\)
0.161874 + 0.986811i \(0.448246\pi\)
\(252\) −1.71018 −0.107731
\(253\) 36.0019 2.26342
\(254\) 17.0001 1.06668
\(255\) −0.645287 −0.0404094
\(256\) 0.915568 0.0572230
\(257\) −27.1978 −1.69655 −0.848277 0.529553i \(-0.822360\pi\)
−0.848277 + 0.529553i \(0.822360\pi\)
\(258\) −1.16537 −0.0725529
\(259\) 0.215452 0.0133876
\(260\) −51.0355 −3.16509
\(261\) −0.921663 −0.0570495
\(262\) −44.3285 −2.73862
\(263\) 28.5341 1.75949 0.879744 0.475447i \(-0.157714\pi\)
0.879744 + 0.475447i \(0.157714\pi\)
\(264\) 1.24332 0.0765213
\(265\) −26.0980 −1.60319
\(266\) −0.438189 −0.0268671
\(267\) −0.686980 −0.0420425
\(268\) 23.8047 1.45410
\(269\) −5.56873 −0.339532 −0.169766 0.985484i \(-0.554301\pi\)
−0.169766 + 0.985484i \(0.554301\pi\)
\(270\) 5.50741 0.335170
\(271\) 2.58386 0.156958 0.0784792 0.996916i \(-0.474994\pi\)
0.0784792 + 0.996916i \(0.474994\pi\)
\(272\) 3.38530 0.205264
\(273\) −0.178297 −0.0107910
\(274\) −15.4332 −0.932356
\(275\) 31.2639 1.88529
\(276\) −2.02895 −0.122128
\(277\) 21.9033 1.31604 0.658022 0.752999i \(-0.271393\pi\)
0.658022 + 0.752999i \(0.271393\pi\)
\(278\) 21.1000 1.26549
\(279\) −10.7485 −0.643498
\(280\) 0.968225 0.0578625
\(281\) −6.60437 −0.393984 −0.196992 0.980405i \(-0.563117\pi\)
−0.196992 + 0.980405i \(0.563117\pi\)
\(282\) 0.231117 0.0137628
\(283\) 26.7604 1.59074 0.795369 0.606126i \(-0.207277\pi\)
0.795369 + 0.606126i \(0.207277\pi\)
\(284\) −3.40664 −0.202147
\(285\) 0.401652 0.0237918
\(286\) −84.4086 −4.99118
\(287\) 2.47316 0.145986
\(288\) −22.9285 −1.35107
\(289\) −14.7100 −0.865294
\(290\) 2.09776 0.123185
\(291\) 1.32087 0.0774309
\(292\) −28.2774 −1.65481
\(293\) 25.1790 1.47097 0.735486 0.677539i \(-0.236954\pi\)
0.735486 + 0.677539i \(0.236954\pi\)
\(294\) −2.03706 −0.118804
\(295\) −42.7528 −2.48916
\(296\) −1.42985 −0.0831081
\(297\) 5.20130 0.301810
\(298\) −9.32292 −0.540062
\(299\) 34.2629 1.98148
\(300\) −1.76193 −0.101725
\(301\) −0.857079 −0.0494012
\(302\) −28.8706 −1.66132
\(303\) 1.81716 0.104393
\(304\) −2.10714 −0.120853
\(305\) 23.1574 1.32599
\(306\) −9.74231 −0.556931
\(307\) 28.5667 1.63039 0.815193 0.579189i \(-0.196631\pi\)
0.815193 + 0.579189i \(0.196631\pi\)
\(308\) 3.67611 0.209466
\(309\) 2.19864 0.125077
\(310\) 24.4643 1.38948
\(311\) −11.7887 −0.668478 −0.334239 0.942488i \(-0.608479\pi\)
−0.334239 + 0.942488i \(0.608479\pi\)
\(312\) 1.18327 0.0669893
\(313\) 5.54193 0.313248 0.156624 0.987658i \(-0.449939\pi\)
0.156624 + 0.987658i \(0.449939\pi\)
\(314\) −8.73320 −0.492843
\(315\) 2.01900 0.113758
\(316\) −20.6998 −1.16445
\(317\) 12.0089 0.674486 0.337243 0.941418i \(-0.390506\pi\)
0.337243 + 0.941418i \(0.390506\pi\)
\(318\) 2.43258 0.136412
\(319\) 1.98116 0.110924
\(320\) 38.1246 2.13123
\(321\) 0.673316 0.0375808
\(322\) −2.61322 −0.145629
\(323\) −1.42539 −0.0793106
\(324\) 23.5197 1.30665
\(325\) 29.7538 1.65044
\(326\) −35.9128 −1.98902
\(327\) 0.135675 0.00750283
\(328\) −16.4131 −0.906260
\(329\) 0.169976 0.00937109
\(330\) −5.90102 −0.324840
\(331\) −32.5550 −1.78938 −0.894692 0.446684i \(-0.852605\pi\)
−0.894692 + 0.446684i \(0.852605\pi\)
\(332\) −14.2598 −0.782606
\(333\) −2.98159 −0.163390
\(334\) −18.4585 −1.01000
\(335\) −28.1033 −1.53545
\(336\) 0.0653928 0.00356747
\(337\) 26.7159 1.45531 0.727655 0.685944i \(-0.240610\pi\)
0.727655 + 0.685944i \(0.240610\pi\)
\(338\) −52.2616 −2.84265
\(339\) 1.55625 0.0845240
\(340\) 12.6618 0.686683
\(341\) 23.1045 1.25118
\(342\) 6.06399 0.327903
\(343\) −3.00633 −0.162327
\(344\) 5.68799 0.306676
\(345\) 2.39533 0.128960
\(346\) −28.4228 −1.52802
\(347\) −4.95830 −0.266175 −0.133088 0.991104i \(-0.542489\pi\)
−0.133088 + 0.991104i \(0.542489\pi\)
\(348\) −0.111651 −0.00598515
\(349\) −4.93248 −0.264030 −0.132015 0.991248i \(-0.542145\pi\)
−0.132015 + 0.991248i \(0.542145\pi\)
\(350\) −2.26931 −0.121300
\(351\) 4.95006 0.264215
\(352\) 49.2859 2.62695
\(353\) 29.9732 1.59531 0.797656 0.603113i \(-0.206073\pi\)
0.797656 + 0.603113i \(0.206073\pi\)
\(354\) 3.98495 0.211798
\(355\) 4.02180 0.213455
\(356\) 13.4799 0.714434
\(357\) 0.0442352 0.00234118
\(358\) 10.1241 0.535075
\(359\) 23.7562 1.25380 0.626902 0.779098i \(-0.284323\pi\)
0.626902 + 0.779098i \(0.284323\pi\)
\(360\) −13.3990 −0.706191
\(361\) −18.1128 −0.953304
\(362\) −37.6153 −1.97702
\(363\) −4.08061 −0.214176
\(364\) 3.49855 0.183374
\(365\) 33.3837 1.74738
\(366\) −2.15848 −0.112826
\(367\) −11.8751 −0.619874 −0.309937 0.950757i \(-0.600308\pi\)
−0.309937 + 0.950757i \(0.600308\pi\)
\(368\) −12.5664 −0.655066
\(369\) −34.2254 −1.78171
\(370\) 6.78628 0.352802
\(371\) 1.78905 0.0928829
\(372\) −1.30209 −0.0675104
\(373\) 16.3120 0.844601 0.422300 0.906456i \(-0.361223\pi\)
0.422300 + 0.906456i \(0.361223\pi\)
\(374\) 20.9416 1.08286
\(375\) −0.0519957 −0.00268505
\(376\) −1.12804 −0.0581744
\(377\) 1.88546 0.0971064
\(378\) −0.377540 −0.0194186
\(379\) −31.7353 −1.63013 −0.815066 0.579368i \(-0.803299\pi\)
−0.815066 + 0.579368i \(0.803299\pi\)
\(380\) −7.88120 −0.404297
\(381\) 1.06820 0.0547257
\(382\) 55.5702 2.84322
\(383\) −5.01688 −0.256351 −0.128175 0.991752i \(-0.540912\pi\)
−0.128175 + 0.991752i \(0.540912\pi\)
\(384\) −1.46688 −0.0748565
\(385\) −4.33994 −0.221184
\(386\) −11.7255 −0.596814
\(387\) 11.8609 0.602924
\(388\) −25.9181 −1.31579
\(389\) 18.8873 0.957627 0.478813 0.877917i \(-0.341067\pi\)
0.478813 + 0.877917i \(0.341067\pi\)
\(390\) −5.61598 −0.284376
\(391\) −8.50056 −0.429892
\(392\) 9.94254 0.502174
\(393\) −2.78539 −0.140504
\(394\) 15.1312 0.762297
\(395\) 24.4377 1.22959
\(396\) −50.8729 −2.55646
\(397\) 6.38387 0.320397 0.160199 0.987085i \(-0.448787\pi\)
0.160199 + 0.987085i \(0.448787\pi\)
\(398\) 28.8220 1.44472
\(399\) −0.0275337 −0.00137841
\(400\) −10.9126 −0.545629
\(401\) −0.364983 −0.0182264 −0.00911320 0.999958i \(-0.502901\pi\)
−0.00911320 + 0.999958i \(0.502901\pi\)
\(402\) 2.61949 0.130648
\(403\) 21.9885 1.09533
\(404\) −35.6562 −1.77396
\(405\) −27.7668 −1.37974
\(406\) −0.143804 −0.00713687
\(407\) 6.40909 0.317687
\(408\) −0.293566 −0.0145337
\(409\) 14.4559 0.714798 0.357399 0.933952i \(-0.383664\pi\)
0.357399 + 0.933952i \(0.383664\pi\)
\(410\) 77.8991 3.84716
\(411\) −0.969752 −0.0478343
\(412\) −43.1417 −2.12544
\(413\) 2.93075 0.144213
\(414\) 36.1638 1.77735
\(415\) 16.8347 0.826385
\(416\) 46.9052 2.29972
\(417\) 1.32582 0.0649258
\(418\) −13.0349 −0.637556
\(419\) −4.79350 −0.234178 −0.117089 0.993121i \(-0.537356\pi\)
−0.117089 + 0.993121i \(0.537356\pi\)
\(420\) 0.244584 0.0119345
\(421\) 17.3069 0.843488 0.421744 0.906715i \(-0.361418\pi\)
0.421744 + 0.906715i \(0.361418\pi\)
\(422\) 48.6935 2.37036
\(423\) −2.35226 −0.114371
\(424\) −11.8730 −0.576604
\(425\) −7.38185 −0.358073
\(426\) −0.374869 −0.0181624
\(427\) −1.58747 −0.0768228
\(428\) −13.2118 −0.638616
\(429\) −5.30383 −0.256071
\(430\) −26.9961 −1.30187
\(431\) −16.8484 −0.811558 −0.405779 0.913971i \(-0.633000\pi\)
−0.405779 + 0.913971i \(0.633000\pi\)
\(432\) −1.81550 −0.0873481
\(433\) 25.5437 1.22755 0.613775 0.789481i \(-0.289650\pi\)
0.613775 + 0.789481i \(0.289650\pi\)
\(434\) −1.67706 −0.0805014
\(435\) 0.131813 0.00631995
\(436\) −2.66221 −0.127497
\(437\) 5.29108 0.253107
\(438\) −3.11167 −0.148681
\(439\) −36.0917 −1.72256 −0.861282 0.508128i \(-0.830338\pi\)
−0.861282 + 0.508128i \(0.830338\pi\)
\(440\) 28.8019 1.37308
\(441\) 20.7327 0.987273
\(442\) 19.9300 0.947976
\(443\) 17.1547 0.815043 0.407521 0.913196i \(-0.366393\pi\)
0.407521 + 0.913196i \(0.366393\pi\)
\(444\) −0.361194 −0.0171415
\(445\) −15.9141 −0.754399
\(446\) −58.8150 −2.78497
\(447\) −0.585808 −0.0277077
\(448\) −2.61349 −0.123476
\(449\) 34.1085 1.60968 0.804840 0.593492i \(-0.202251\pi\)
0.804840 + 0.593492i \(0.202251\pi\)
\(450\) 31.4045 1.48042
\(451\) 73.5694 3.46425
\(452\) −30.5367 −1.43633
\(453\) −1.81409 −0.0852334
\(454\) 55.7234 2.61523
\(455\) −4.13030 −0.193632
\(456\) 0.182727 0.00855697
\(457\) 24.4800 1.14513 0.572564 0.819860i \(-0.305949\pi\)
0.572564 + 0.819860i \(0.305949\pi\)
\(458\) −42.2482 −1.97413
\(459\) −1.22810 −0.0573228
\(460\) −47.0010 −2.19143
\(461\) 22.2691 1.03718 0.518589 0.855024i \(-0.326458\pi\)
0.518589 + 0.855024i \(0.326458\pi\)
\(462\) 0.404522 0.0188201
\(463\) −4.73547 −0.220076 −0.110038 0.993927i \(-0.535097\pi\)
−0.110038 + 0.993927i \(0.535097\pi\)
\(464\) −0.691518 −0.0321029
\(465\) 1.53722 0.0712869
\(466\) 8.36424 0.387466
\(467\) 29.5509 1.36745 0.683725 0.729739i \(-0.260359\pi\)
0.683725 + 0.729739i \(0.260359\pi\)
\(468\) −48.4155 −2.23801
\(469\) 1.92652 0.0889582
\(470\) 5.35388 0.246956
\(471\) −0.548753 −0.0252852
\(472\) −19.4499 −0.895254
\(473\) −25.4956 −1.17229
\(474\) −2.27782 −0.104624
\(475\) 4.59475 0.210822
\(476\) −0.867982 −0.0397839
\(477\) −24.7582 −1.13360
\(478\) 42.5442 1.94593
\(479\) 17.2676 0.788976 0.394488 0.918901i \(-0.370922\pi\)
0.394488 + 0.918901i \(0.370922\pi\)
\(480\) 3.27915 0.149672
\(481\) 6.09951 0.278114
\(482\) 8.27775 0.377041
\(483\) −0.164203 −0.00747147
\(484\) 80.0696 3.63953
\(485\) 30.5983 1.38940
\(486\) 7.84506 0.355859
\(487\) −33.4329 −1.51499 −0.757494 0.652843i \(-0.773576\pi\)
−0.757494 + 0.652843i \(0.773576\pi\)
\(488\) 10.5352 0.476905
\(489\) −2.25659 −0.102046
\(490\) −47.1889 −2.13178
\(491\) 12.6270 0.569849 0.284924 0.958550i \(-0.408032\pi\)
0.284924 + 0.958550i \(0.408032\pi\)
\(492\) −4.14612 −0.186921
\(493\) −0.467780 −0.0210678
\(494\) −12.4052 −0.558138
\(495\) 60.0593 2.69947
\(496\) −8.06456 −0.362110
\(497\) −0.275699 −0.0123668
\(498\) −1.56915 −0.0703154
\(499\) −3.86740 −0.173128 −0.0865642 0.996246i \(-0.527589\pi\)
−0.0865642 + 0.996246i \(0.527589\pi\)
\(500\) 1.02026 0.0456274
\(501\) −1.15984 −0.0518180
\(502\) −11.0749 −0.494297
\(503\) 0.0290584 0.00129565 0.000647825 1.00000i \(-0.499794\pi\)
0.000647825 1.00000i \(0.499794\pi\)
\(504\) 0.918520 0.0409141
\(505\) 42.0949 1.87320
\(506\) −77.7359 −3.45578
\(507\) −3.28387 −0.145842
\(508\) −20.9602 −0.929961
\(509\) −26.6224 −1.18002 −0.590009 0.807396i \(-0.700876\pi\)
−0.590009 + 0.807396i \(0.700876\pi\)
\(510\) 1.39331 0.0616969
\(511\) −2.28849 −0.101237
\(512\) −23.6004 −1.04300
\(513\) 0.764417 0.0337498
\(514\) 58.7259 2.59029
\(515\) 50.9321 2.24434
\(516\) 1.43685 0.0632537
\(517\) 5.05630 0.222376
\(518\) −0.465208 −0.0204401
\(519\) −1.78596 −0.0783947
\(520\) 27.4107 1.20204
\(521\) −17.0833 −0.748435 −0.374217 0.927341i \(-0.622089\pi\)
−0.374217 + 0.927341i \(0.622089\pi\)
\(522\) 1.99007 0.0871029
\(523\) −26.7360 −1.16909 −0.584543 0.811363i \(-0.698726\pi\)
−0.584543 + 0.811363i \(0.698726\pi\)
\(524\) 54.6548 2.38761
\(525\) −0.142593 −0.00622326
\(526\) −61.6113 −2.68638
\(527\) −5.45531 −0.237637
\(528\) 1.94525 0.0846560
\(529\) 8.55435 0.371928
\(530\) 56.3512 2.44774
\(531\) −40.5580 −1.76007
\(532\) 0.540266 0.0234235
\(533\) 70.0157 3.03272
\(534\) 1.48334 0.0641903
\(535\) 15.5975 0.674340
\(536\) −12.7853 −0.552240
\(537\) 0.636149 0.0274519
\(538\) 12.0241 0.518395
\(539\) −44.5661 −1.91960
\(540\) −6.79037 −0.292211
\(541\) 11.9183 0.512409 0.256204 0.966623i \(-0.417528\pi\)
0.256204 + 0.966623i \(0.417528\pi\)
\(542\) −5.57911 −0.239643
\(543\) −2.36357 −0.101430
\(544\) −11.6371 −0.498936
\(545\) 3.14294 0.134629
\(546\) 0.384982 0.0164757
\(547\) 3.46419 0.148118 0.0740590 0.997254i \(-0.476405\pi\)
0.0740590 + 0.997254i \(0.476405\pi\)
\(548\) 19.0284 0.812855
\(549\) 21.9685 0.937595
\(550\) −67.5055 −2.87845
\(551\) 0.291164 0.0124040
\(552\) 1.08973 0.0463819
\(553\) −1.67523 −0.0712382
\(554\) −47.2940 −2.00933
\(555\) 0.426417 0.0181004
\(556\) −26.0153 −1.10329
\(557\) −13.2451 −0.561212 −0.280606 0.959823i \(-0.590535\pi\)
−0.280606 + 0.959823i \(0.590535\pi\)
\(558\) 23.2084 0.982490
\(559\) −24.2641 −1.02626
\(560\) 1.51484 0.0640137
\(561\) 1.31587 0.0555561
\(562\) 14.2603 0.601533
\(563\) 43.1107 1.81690 0.908450 0.417993i \(-0.137266\pi\)
0.908450 + 0.417993i \(0.137266\pi\)
\(564\) −0.284956 −0.0119988
\(565\) 36.0509 1.51667
\(566\) −57.7813 −2.42873
\(567\) 1.90345 0.0799374
\(568\) 1.82967 0.0767713
\(569\) −42.3754 −1.77647 −0.888235 0.459390i \(-0.848068\pi\)
−0.888235 + 0.459390i \(0.848068\pi\)
\(570\) −0.867252 −0.0363252
\(571\) −0.482562 −0.0201946 −0.0100973 0.999949i \(-0.503214\pi\)
−0.0100973 + 0.999949i \(0.503214\pi\)
\(572\) 104.072 4.35146
\(573\) 3.49176 0.145871
\(574\) −5.34008 −0.222891
\(575\) 27.4017 1.14273
\(576\) 36.1674 1.50697
\(577\) −37.0326 −1.54169 −0.770844 0.637023i \(-0.780165\pi\)
−0.770844 + 0.637023i \(0.780165\pi\)
\(578\) 31.7620 1.32113
\(579\) −0.736777 −0.0306194
\(580\) −2.58643 −0.107396
\(581\) −1.15404 −0.0478777
\(582\) −2.85205 −0.118221
\(583\) 53.2191 2.20411
\(584\) 15.1875 0.628465
\(585\) 57.1582 2.36320
\(586\) −54.3669 −2.24587
\(587\) 21.9665 0.906655 0.453327 0.891344i \(-0.350237\pi\)
0.453327 + 0.891344i \(0.350237\pi\)
\(588\) 2.51159 0.103576
\(589\) 3.39559 0.139913
\(590\) 92.3124 3.80044
\(591\) 0.950771 0.0391095
\(592\) −2.23707 −0.0919430
\(593\) −10.9162 −0.448275 −0.224137 0.974558i \(-0.571956\pi\)
−0.224137 + 0.974558i \(0.571956\pi\)
\(594\) −11.2307 −0.460802
\(595\) 1.02472 0.0420094
\(596\) 11.4947 0.470841
\(597\) 1.81104 0.0741209
\(598\) −73.9810 −3.02531
\(599\) −5.70872 −0.233252 −0.116626 0.993176i \(-0.537208\pi\)
−0.116626 + 0.993176i \(0.537208\pi\)
\(600\) 0.946315 0.0386331
\(601\) 14.7194 0.600417 0.300208 0.953874i \(-0.402944\pi\)
0.300208 + 0.953874i \(0.402944\pi\)
\(602\) 1.85062 0.0754255
\(603\) −26.6606 −1.08570
\(604\) 35.5960 1.44838
\(605\) −94.5283 −3.84312
\(606\) −3.92363 −0.159387
\(607\) −31.2488 −1.26835 −0.634174 0.773190i \(-0.718660\pi\)
−0.634174 + 0.773190i \(0.718660\pi\)
\(608\) 7.24338 0.293758
\(609\) −0.00903595 −0.000366155 0
\(610\) −50.0017 −2.02451
\(611\) 4.81207 0.194675
\(612\) 12.0118 0.485548
\(613\) 21.3293 0.861482 0.430741 0.902476i \(-0.358252\pi\)
0.430741 + 0.902476i \(0.358252\pi\)
\(614\) −61.6816 −2.48927
\(615\) 4.89481 0.197378
\(616\) −1.97441 −0.0795511
\(617\) −11.8392 −0.476626 −0.238313 0.971188i \(-0.576594\pi\)
−0.238313 + 0.971188i \(0.576594\pi\)
\(618\) −4.74734 −0.190966
\(619\) 22.4949 0.904146 0.452073 0.891981i \(-0.350685\pi\)
0.452073 + 0.891981i \(0.350685\pi\)
\(620\) −30.1633 −1.21139
\(621\) 4.55875 0.182936
\(622\) 25.4544 1.02063
\(623\) 1.09093 0.0437071
\(624\) 1.85129 0.0741107
\(625\) −25.5948 −1.02379
\(626\) −11.9662 −0.478266
\(627\) −0.819049 −0.0327097
\(628\) 10.7676 0.429674
\(629\) −1.51328 −0.0603382
\(630\) −4.35944 −0.173684
\(631\) 26.2358 1.04443 0.522214 0.852814i \(-0.325106\pi\)
0.522214 + 0.852814i \(0.325106\pi\)
\(632\) 11.1177 0.442237
\(633\) 3.05967 0.121611
\(634\) −25.9298 −1.02980
\(635\) 24.7452 0.981982
\(636\) −2.99925 −0.118928
\(637\) −42.4134 −1.68048
\(638\) −4.27775 −0.169358
\(639\) 3.81533 0.150932
\(640\) −33.9807 −1.34320
\(641\) −20.8763 −0.824563 −0.412282 0.911056i \(-0.635268\pi\)
−0.412282 + 0.911056i \(0.635268\pi\)
\(642\) −1.45383 −0.0573782
\(643\) 25.3355 0.999135 0.499568 0.866275i \(-0.333492\pi\)
0.499568 + 0.866275i \(0.333492\pi\)
\(644\) 3.22198 0.126964
\(645\) −1.69631 −0.0667921
\(646\) 3.07771 0.121091
\(647\) 27.4629 1.07968 0.539838 0.841769i \(-0.318485\pi\)
0.539838 + 0.841769i \(0.318485\pi\)
\(648\) −12.6322 −0.496240
\(649\) 87.1815 3.42217
\(650\) −64.2448 −2.51989
\(651\) −0.105378 −0.00413010
\(652\) 44.2787 1.73409
\(653\) 10.6541 0.416927 0.208463 0.978030i \(-0.433154\pi\)
0.208463 + 0.978030i \(0.433154\pi\)
\(654\) −0.292951 −0.0114553
\(655\) −64.5242 −2.52117
\(656\) −25.6791 −1.00260
\(657\) 31.6699 1.23556
\(658\) −0.367015 −0.0143077
\(659\) 11.0960 0.432238 0.216119 0.976367i \(-0.430660\pi\)
0.216119 + 0.976367i \(0.430660\pi\)
\(660\) 7.27567 0.283205
\(661\) −0.636140 −0.0247430 −0.0123715 0.999923i \(-0.503938\pi\)
−0.0123715 + 0.999923i \(0.503938\pi\)
\(662\) 70.2932 2.73202
\(663\) 1.25231 0.0486357
\(664\) 7.65878 0.297218
\(665\) −0.637825 −0.0247338
\(666\) 6.43790 0.249463
\(667\) 1.73641 0.0672342
\(668\) 22.7584 0.880550
\(669\) −3.69565 −0.142882
\(670\) 60.6810 2.34431
\(671\) −47.2225 −1.82301
\(672\) −0.224790 −0.00867146
\(673\) 7.63329 0.294242 0.147121 0.989119i \(-0.452999\pi\)
0.147121 + 0.989119i \(0.452999\pi\)
\(674\) −57.6854 −2.22196
\(675\) 3.95880 0.152374
\(676\) 64.4360 2.47831
\(677\) −0.859250 −0.0330237 −0.0165118 0.999864i \(-0.505256\pi\)
−0.0165118 + 0.999864i \(0.505256\pi\)
\(678\) −3.36028 −0.129051
\(679\) −2.09755 −0.0804967
\(680\) −6.80053 −0.260789
\(681\) 3.50140 0.134174
\(682\) −49.8877 −1.91030
\(683\) 1.62253 0.0620844 0.0310422 0.999518i \(-0.490117\pi\)
0.0310422 + 0.999518i \(0.490117\pi\)
\(684\) −7.47661 −0.285875
\(685\) −22.4645 −0.858326
\(686\) 6.49131 0.247840
\(687\) −2.65468 −0.101282
\(688\) 8.89917 0.339278
\(689\) 50.6485 1.92955
\(690\) −5.17202 −0.196895
\(691\) −0.186189 −0.00708295 −0.00354147 0.999994i \(-0.501127\pi\)
−0.00354147 + 0.999994i \(0.501127\pi\)
\(692\) 35.0440 1.33217
\(693\) −4.11714 −0.156397
\(694\) 10.7060 0.406395
\(695\) 30.7130 1.16501
\(696\) 0.0599669 0.00227304
\(697\) −17.3708 −0.657964
\(698\) 10.6503 0.403119
\(699\) 0.525569 0.0198788
\(700\) 2.79795 0.105753
\(701\) −19.0075 −0.717903 −0.358952 0.933356i \(-0.616866\pi\)
−0.358952 + 0.933356i \(0.616866\pi\)
\(702\) −10.6882 −0.403402
\(703\) 0.941921 0.0355252
\(704\) −77.7437 −2.93008
\(705\) 0.336412 0.0126700
\(706\) −64.7185 −2.43571
\(707\) −2.88565 −0.108526
\(708\) −4.91325 −0.184651
\(709\) 33.8296 1.27050 0.635249 0.772307i \(-0.280897\pi\)
0.635249 + 0.772307i \(0.280897\pi\)
\(710\) −8.68392 −0.325902
\(711\) 23.1832 0.869436
\(712\) −7.23993 −0.271328
\(713\) 20.2503 0.758379
\(714\) −0.0955133 −0.00357450
\(715\) −122.865 −4.59488
\(716\) −12.4825 −0.466493
\(717\) 2.67328 0.0998354
\(718\) −51.2947 −1.91430
\(719\) 38.9365 1.45209 0.726043 0.687649i \(-0.241357\pi\)
0.726043 + 0.687649i \(0.241357\pi\)
\(720\) −20.9635 −0.781264
\(721\) −3.49146 −0.130029
\(722\) 39.1094 1.45550
\(723\) 0.520134 0.0193440
\(724\) 46.3779 1.72362
\(725\) 1.50790 0.0560018
\(726\) 8.81091 0.327003
\(727\) −26.4963 −0.982694 −0.491347 0.870964i \(-0.663495\pi\)
−0.491347 + 0.870964i \(0.663495\pi\)
\(728\) −1.87904 −0.0696417
\(729\) −26.0111 −0.963373
\(730\) −72.0825 −2.66789
\(731\) 6.01988 0.222653
\(732\) 2.66130 0.0983645
\(733\) −40.2879 −1.48807 −0.744034 0.668142i \(-0.767090\pi\)
−0.744034 + 0.668142i \(0.767090\pi\)
\(734\) 25.6408 0.946421
\(735\) −2.96513 −0.109370
\(736\) 43.1973 1.59227
\(737\) 57.3083 2.11098
\(738\) 73.9001 2.72030
\(739\) −26.1948 −0.963592 −0.481796 0.876283i \(-0.660015\pi\)
−0.481796 + 0.876283i \(0.660015\pi\)
\(740\) −8.36715 −0.307583
\(741\) −0.779486 −0.0286351
\(742\) −3.86295 −0.141813
\(743\) −7.73748 −0.283861 −0.141930 0.989877i \(-0.545331\pi\)
−0.141930 + 0.989877i \(0.545331\pi\)
\(744\) 0.699342 0.0256391
\(745\) −13.5704 −0.497180
\(746\) −35.2210 −1.28953
\(747\) 15.9705 0.584330
\(748\) −25.8200 −0.944072
\(749\) −1.06923 −0.0390688
\(750\) 0.112270 0.00409952
\(751\) −22.5759 −0.823805 −0.411903 0.911228i \(-0.635136\pi\)
−0.411903 + 0.911228i \(0.635136\pi\)
\(752\) −1.76489 −0.0643588
\(753\) −0.695895 −0.0253598
\(754\) −4.07112 −0.148262
\(755\) −42.0238 −1.52940
\(756\) 0.465488 0.0169296
\(757\) −20.8059 −0.756205 −0.378102 0.925764i \(-0.623423\pi\)
−0.378102 + 0.925764i \(0.623423\pi\)
\(758\) 68.5233 2.48888
\(759\) −4.88455 −0.177298
\(760\) 4.23292 0.153544
\(761\) 48.4590 1.75664 0.878319 0.478074i \(-0.158665\pi\)
0.878319 + 0.478074i \(0.158665\pi\)
\(762\) −2.30648 −0.0835549
\(763\) −0.215452 −0.00779990
\(764\) −68.5153 −2.47880
\(765\) −14.1808 −0.512710
\(766\) 10.8325 0.391395
\(767\) 82.9703 2.99589
\(768\) −0.124219 −0.00448238
\(769\) −42.3172 −1.52600 −0.762998 0.646401i \(-0.776274\pi\)
−0.762998 + 0.646401i \(0.776274\pi\)
\(770\) 9.37085 0.337702
\(771\) 3.69006 0.132894
\(772\) 14.4570 0.520319
\(773\) −10.1730 −0.365898 −0.182949 0.983122i \(-0.558564\pi\)
−0.182949 + 0.983122i \(0.558564\pi\)
\(774\) −25.6102 −0.920541
\(775\) 17.5853 0.631681
\(776\) 13.9204 0.499712
\(777\) −0.0292314 −0.00104867
\(778\) −40.7818 −1.46210
\(779\) 10.8122 0.387388
\(780\) 6.92423 0.247927
\(781\) −8.20126 −0.293464
\(782\) 18.3545 0.656357
\(783\) 0.250865 0.00896517
\(784\) 15.5556 0.555559
\(785\) −12.7120 −0.453710
\(786\) 6.01425 0.214521
\(787\) 14.4841 0.516304 0.258152 0.966104i \(-0.416887\pi\)
0.258152 + 0.966104i \(0.416887\pi\)
\(788\) −18.6560 −0.664592
\(789\) −3.87136 −0.137824
\(790\) −52.7662 −1.87734
\(791\) −2.47134 −0.0878706
\(792\) 27.3233 0.970892
\(793\) −44.9415 −1.59592
\(794\) −13.7841 −0.489181
\(795\) 3.54084 0.125581
\(796\) −35.5362 −1.25955
\(797\) 34.4304 1.21959 0.609794 0.792560i \(-0.291252\pi\)
0.609794 + 0.792560i \(0.291252\pi\)
\(798\) 0.0594512 0.00210455
\(799\) −1.19386 −0.0422359
\(800\) 37.5123 1.32626
\(801\) −15.0971 −0.533430
\(802\) 0.788078 0.0278280
\(803\) −68.0761 −2.40235
\(804\) −3.22970 −0.113903
\(805\) −3.80379 −0.134066
\(806\) −47.4779 −1.67234
\(807\) 0.755537 0.0265962
\(808\) 19.1506 0.673715
\(809\) 44.0582 1.54901 0.774503 0.632571i \(-0.218000\pi\)
0.774503 + 0.632571i \(0.218000\pi\)
\(810\) 59.9545 2.10659
\(811\) −2.20246 −0.0773388 −0.0386694 0.999252i \(-0.512312\pi\)
−0.0386694 + 0.999252i \(0.512312\pi\)
\(812\) 0.177303 0.00622212
\(813\) −0.350565 −0.0122948
\(814\) −13.8386 −0.485042
\(815\) −52.2744 −1.83109
\(816\) −0.459300 −0.0160787
\(817\) −3.74701 −0.131091
\(818\) −31.2134 −1.09135
\(819\) −3.91827 −0.136915
\(820\) −96.0458 −3.35407
\(821\) −6.34252 −0.221356 −0.110678 0.993856i \(-0.535302\pi\)
−0.110678 + 0.993856i \(0.535302\pi\)
\(822\) 2.09390 0.0730332
\(823\) 5.51507 0.192243 0.0961217 0.995370i \(-0.469356\pi\)
0.0961217 + 0.995370i \(0.469356\pi\)
\(824\) 23.1710 0.807201
\(825\) −4.24173 −0.147678
\(826\) −6.32813 −0.220184
\(827\) −53.3974 −1.85681 −0.928405 0.371569i \(-0.878820\pi\)
−0.928405 + 0.371569i \(0.878820\pi\)
\(828\) −44.5882 −1.54955
\(829\) −39.4903 −1.37155 −0.685777 0.727812i \(-0.740538\pi\)
−0.685777 + 0.727812i \(0.740538\pi\)
\(830\) −36.3498 −1.26172
\(831\) −2.97173 −0.103088
\(832\) −73.9884 −2.56509
\(833\) 10.5227 0.364589
\(834\) −2.86274 −0.0991284
\(835\) −26.8681 −0.929808
\(836\) 16.0714 0.555839
\(837\) 2.92561 0.101124
\(838\) 10.3502 0.357542
\(839\) 37.6281 1.29907 0.649533 0.760334i \(-0.274965\pi\)
0.649533 + 0.760334i \(0.274965\pi\)
\(840\) −0.131364 −0.00453248
\(841\) −28.9044 −0.996705
\(842\) −37.3694 −1.28783
\(843\) 0.896047 0.0308615
\(844\) −60.0367 −2.06655
\(845\) −76.0716 −2.61694
\(846\) 5.07903 0.174621
\(847\) 6.48003 0.222656
\(848\) −18.5760 −0.637901
\(849\) −3.63070 −0.124605
\(850\) 15.9390 0.546703
\(851\) 5.61733 0.192559
\(852\) 0.462195 0.0158345
\(853\) −16.9514 −0.580406 −0.290203 0.956965i \(-0.593723\pi\)
−0.290203 + 0.956965i \(0.593723\pi\)
\(854\) 3.42768 0.117293
\(855\) 8.82671 0.301867
\(856\) 7.09592 0.242534
\(857\) −51.8794 −1.77217 −0.886084 0.463525i \(-0.846585\pi\)
−0.886084 + 0.463525i \(0.846585\pi\)
\(858\) 11.4521 0.390969
\(859\) 27.5784 0.940962 0.470481 0.882410i \(-0.344080\pi\)
0.470481 + 0.882410i \(0.344080\pi\)
\(860\) 33.2849 1.13501
\(861\) −0.335545 −0.0114353
\(862\) 36.3793 1.23908
\(863\) −0.959694 −0.0326683 −0.0163342 0.999867i \(-0.505200\pi\)
−0.0163342 + 0.999867i \(0.505200\pi\)
\(864\) 6.24083 0.212317
\(865\) −41.3721 −1.40669
\(866\) −55.1542 −1.87422
\(867\) 1.99578 0.0677801
\(868\) 2.06773 0.0701834
\(869\) −49.8334 −1.69048
\(870\) −0.284613 −0.00964928
\(871\) 54.5401 1.84802
\(872\) 1.42985 0.0484207
\(873\) 29.0275 0.982433
\(874\) −11.4246 −0.386442
\(875\) 0.0825696 0.00279136
\(876\) 3.83654 0.129625
\(877\) 24.7586 0.836039 0.418020 0.908438i \(-0.362724\pi\)
0.418020 + 0.908438i \(0.362724\pi\)
\(878\) 77.9297 2.63000
\(879\) −3.41615 −0.115224
\(880\) 45.0621 1.51904
\(881\) 11.3979 0.384004 0.192002 0.981395i \(-0.438502\pi\)
0.192002 + 0.981395i \(0.438502\pi\)
\(882\) −44.7664 −1.50736
\(883\) −4.91864 −0.165526 −0.0827628 0.996569i \(-0.526374\pi\)
−0.0827628 + 0.996569i \(0.526374\pi\)
\(884\) −24.5728 −0.826472
\(885\) 5.80047 0.194981
\(886\) −37.0406 −1.24440
\(887\) 24.5944 0.825799 0.412899 0.910777i \(-0.364516\pi\)
0.412899 + 0.910777i \(0.364516\pi\)
\(888\) 0.193994 0.00651001
\(889\) −1.69631 −0.0568925
\(890\) 34.3619 1.15181
\(891\) 56.6222 1.89691
\(892\) 72.5160 2.42802
\(893\) 0.743108 0.0248671
\(894\) 1.26488 0.0423041
\(895\) 14.7366 0.492589
\(896\) 2.32942 0.0778204
\(897\) −4.64861 −0.155213
\(898\) −73.6476 −2.45765
\(899\) 1.11436 0.0371659
\(900\) −38.7202 −1.29067
\(901\) −12.5658 −0.418627
\(902\) −158.852 −5.28919
\(903\) 0.116284 0.00386969
\(904\) 16.4010 0.545488
\(905\) −54.7527 −1.82004
\(906\) 3.91701 0.130134
\(907\) −0.681186 −0.0226184 −0.0113092 0.999936i \(-0.503600\pi\)
−0.0113092 + 0.999936i \(0.503600\pi\)
\(908\) −68.7043 −2.28003
\(909\) 39.9339 1.32452
\(910\) 8.91821 0.295636
\(911\) −32.0443 −1.06167 −0.530837 0.847474i \(-0.678123\pi\)
−0.530837 + 0.847474i \(0.678123\pi\)
\(912\) 0.285886 0.00946664
\(913\) −34.3294 −1.13614
\(914\) −52.8576 −1.74837
\(915\) −3.14187 −0.103867
\(916\) 52.0900 1.72110
\(917\) 4.42322 0.146067
\(918\) 2.65173 0.0875202
\(919\) −12.7384 −0.420200 −0.210100 0.977680i \(-0.567379\pi\)
−0.210100 + 0.977680i \(0.567379\pi\)
\(920\) 25.2438 0.832263
\(921\) −3.87578 −0.127711
\(922\) −48.0838 −1.58356
\(923\) −7.80511 −0.256908
\(924\) −0.498756 −0.0164079
\(925\) 4.87806 0.160390
\(926\) 10.2249 0.336011
\(927\) 48.3175 1.58695
\(928\) 2.37712 0.0780326
\(929\) −22.7956 −0.747899 −0.373949 0.927449i \(-0.621997\pi\)
−0.373949 + 0.927449i \(0.621997\pi\)
\(930\) −3.31919 −0.108840
\(931\) −6.54972 −0.214659
\(932\) −10.3127 −0.337804
\(933\) 1.59943 0.0523631
\(934\) −63.8066 −2.08782
\(935\) 30.4825 0.996883
\(936\) 26.0035 0.849951
\(937\) 7.34039 0.239800 0.119900 0.992786i \(-0.461743\pi\)
0.119900 + 0.992786i \(0.461743\pi\)
\(938\) −4.15976 −0.135821
\(939\) −0.751899 −0.0245373
\(940\) −6.60108 −0.215303
\(941\) 60.0308 1.95695 0.978474 0.206372i \(-0.0661656\pi\)
0.978474 + 0.206372i \(0.0661656\pi\)
\(942\) 1.18487 0.0386053
\(943\) 64.4808 2.09978
\(944\) −30.4304 −0.990425
\(945\) −0.549545 −0.0178767
\(946\) 55.0505 1.78985
\(947\) −1.45653 −0.0473308 −0.0236654 0.999720i \(-0.507534\pi\)
−0.0236654 + 0.999720i \(0.507534\pi\)
\(948\) 2.80844 0.0912138
\(949\) −64.7878 −2.10310
\(950\) −9.92105 −0.321881
\(951\) −1.62930 −0.0528337
\(952\) 0.466185 0.0151091
\(953\) 26.4407 0.856498 0.428249 0.903661i \(-0.359131\pi\)
0.428249 + 0.903661i \(0.359131\pi\)
\(954\) 53.4584 1.73078
\(955\) 80.8876 2.61746
\(956\) −52.4550 −1.69652
\(957\) −0.268794 −0.00868886
\(958\) −37.2844 −1.20460
\(959\) 1.53997 0.0497283
\(960\) −5.17254 −0.166943
\(961\) −18.0042 −0.580781
\(962\) −13.1701 −0.424622
\(963\) 14.7968 0.476821
\(964\) −10.2061 −0.328715
\(965\) −17.0676 −0.549426
\(966\) 0.354548 0.0114074
\(967\) −29.6811 −0.954481 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(968\) −43.0046 −1.38222
\(969\) 0.193389 0.00621255
\(970\) −66.0683 −2.12133
\(971\) 23.6579 0.759219 0.379610 0.925147i \(-0.376058\pi\)
0.379610 + 0.925147i \(0.376058\pi\)
\(972\) −9.67258 −0.310248
\(973\) −2.10541 −0.0674965
\(974\) 72.1887 2.31307
\(975\) −4.03684 −0.129282
\(976\) 16.4829 0.527604
\(977\) −7.16926 −0.229365 −0.114683 0.993402i \(-0.536585\pi\)
−0.114683 + 0.993402i \(0.536585\pi\)
\(978\) 4.87245 0.155804
\(979\) 32.4520 1.03717
\(980\) 58.1817 1.85854
\(981\) 2.98159 0.0951949
\(982\) −27.2644 −0.870042
\(983\) 34.9943 1.11615 0.558073 0.829792i \(-0.311541\pi\)
0.558073 + 0.829792i \(0.311541\pi\)
\(984\) 2.22684 0.0709890
\(985\) 22.0248 0.701769
\(986\) 1.01004 0.0321661
\(987\) −0.0230615 −0.000734055 0
\(988\) 15.2951 0.486600
\(989\) −22.3460 −0.710561
\(990\) −129.681 −4.12153
\(991\) 40.4662 1.28545 0.642726 0.766096i \(-0.277804\pi\)
0.642726 + 0.766096i \(0.277804\pi\)
\(992\) 27.7222 0.880181
\(993\) 4.41689 0.140166
\(994\) 0.595294 0.0188816
\(995\) 41.9532 1.33000
\(996\) 1.93469 0.0613030
\(997\) −8.77630 −0.277948 −0.138974 0.990296i \(-0.544380\pi\)
−0.138974 + 0.990296i \(0.544380\pi\)
\(998\) 8.35054 0.264332
\(999\) 0.811551 0.0256763
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 4033.2.a.f.1.11 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.11 85 1.1 even 1 trivial