Properties

Label 4003.2.a.c.1.15
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.39320 q^{2} +3.24043 q^{3} +3.72738 q^{4} +2.56572 q^{5} -7.75497 q^{6} -2.79627 q^{7} -4.13396 q^{8} +7.50035 q^{9} +O(q^{10})\) \(q-2.39320 q^{2} +3.24043 q^{3} +3.72738 q^{4} +2.56572 q^{5} -7.75497 q^{6} -2.79627 q^{7} -4.13396 q^{8} +7.50035 q^{9} -6.14026 q^{10} +3.51490 q^{11} +12.0783 q^{12} +1.02927 q^{13} +6.69203 q^{14} +8.31401 q^{15} +2.43862 q^{16} -3.64469 q^{17} -17.9498 q^{18} +2.31545 q^{19} +9.56340 q^{20} -9.06112 q^{21} -8.41183 q^{22} +2.99496 q^{23} -13.3958 q^{24} +1.58289 q^{25} -2.46325 q^{26} +14.5831 q^{27} -10.4228 q^{28} -4.24330 q^{29} -19.8970 q^{30} +3.21604 q^{31} +2.43184 q^{32} +11.3898 q^{33} +8.72245 q^{34} -7.17444 q^{35} +27.9567 q^{36} +3.62174 q^{37} -5.54132 q^{38} +3.33529 q^{39} -10.6066 q^{40} -5.65051 q^{41} +21.6850 q^{42} +8.47151 q^{43} +13.1014 q^{44} +19.2438 q^{45} -7.16753 q^{46} +10.2753 q^{47} +7.90215 q^{48} +0.819148 q^{49} -3.78818 q^{50} -11.8103 q^{51} +3.83650 q^{52} -5.05786 q^{53} -34.9001 q^{54} +9.01822 q^{55} +11.5597 q^{56} +7.50304 q^{57} +10.1550 q^{58} -0.487214 q^{59} +30.9895 q^{60} +3.39301 q^{61} -7.69660 q^{62} -20.9730 q^{63} -10.6971 q^{64} +2.64082 q^{65} -27.2579 q^{66} +0.382019 q^{67} -13.5852 q^{68} +9.70495 q^{69} +17.1698 q^{70} -5.02956 q^{71} -31.0062 q^{72} -9.64474 q^{73} -8.66754 q^{74} +5.12925 q^{75} +8.63057 q^{76} -9.82861 q^{77} -7.98199 q^{78} +9.13895 q^{79} +6.25679 q^{80} +24.7543 q^{81} +13.5228 q^{82} -7.62765 q^{83} -33.7742 q^{84} -9.35124 q^{85} -20.2740 q^{86} -13.7501 q^{87} -14.5305 q^{88} +8.23006 q^{89} -46.0541 q^{90} -2.87813 q^{91} +11.1634 q^{92} +10.4213 q^{93} -24.5909 q^{94} +5.94079 q^{95} +7.88021 q^{96} +5.19890 q^{97} -1.96038 q^{98} +26.3630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39320 −1.69224 −0.846122 0.532989i \(-0.821069\pi\)
−0.846122 + 0.532989i \(0.821069\pi\)
\(3\) 3.24043 1.87086 0.935430 0.353512i \(-0.115013\pi\)
0.935430 + 0.353512i \(0.115013\pi\)
\(4\) 3.72738 1.86369
\(5\) 2.56572 1.14742 0.573711 0.819058i \(-0.305503\pi\)
0.573711 + 0.819058i \(0.305503\pi\)
\(6\) −7.75497 −3.16595
\(7\) −2.79627 −1.05689 −0.528446 0.848967i \(-0.677225\pi\)
−0.528446 + 0.848967i \(0.677225\pi\)
\(8\) −4.13396 −1.46158
\(9\) 7.50035 2.50012
\(10\) −6.14026 −1.94172
\(11\) 3.51490 1.05978 0.529891 0.848066i \(-0.322233\pi\)
0.529891 + 0.848066i \(0.322233\pi\)
\(12\) 12.0783 3.48671
\(13\) 1.02927 0.285469 0.142735 0.989761i \(-0.454410\pi\)
0.142735 + 0.989761i \(0.454410\pi\)
\(14\) 6.69203 1.78852
\(15\) 8.31401 2.14667
\(16\) 2.43862 0.609654
\(17\) −3.64469 −0.883967 −0.441984 0.897023i \(-0.645725\pi\)
−0.441984 + 0.897023i \(0.645725\pi\)
\(18\) −17.9498 −4.23081
\(19\) 2.31545 0.531201 0.265600 0.964083i \(-0.414430\pi\)
0.265600 + 0.964083i \(0.414430\pi\)
\(20\) 9.56340 2.13844
\(21\) −9.06112 −1.97730
\(22\) −8.41183 −1.79341
\(23\) 2.99496 0.624493 0.312246 0.950001i \(-0.398919\pi\)
0.312246 + 0.950001i \(0.398919\pi\)
\(24\) −13.3958 −2.73441
\(25\) 1.58289 0.316579
\(26\) −2.46325 −0.483084
\(27\) 14.5831 2.80651
\(28\) −10.4228 −1.96972
\(29\) −4.24330 −0.787961 −0.393980 0.919119i \(-0.628902\pi\)
−0.393980 + 0.919119i \(0.628902\pi\)
\(30\) −19.8970 −3.63269
\(31\) 3.21604 0.577617 0.288809 0.957387i \(-0.406741\pi\)
0.288809 + 0.957387i \(0.406741\pi\)
\(32\) 2.43184 0.429893
\(33\) 11.3898 1.98270
\(34\) 8.72245 1.49589
\(35\) −7.17444 −1.21270
\(36\) 27.9567 4.65945
\(37\) 3.62174 0.595411 0.297705 0.954658i \(-0.403779\pi\)
0.297705 + 0.954658i \(0.403779\pi\)
\(38\) −5.54132 −0.898922
\(39\) 3.33529 0.534073
\(40\) −10.6066 −1.67705
\(41\) −5.65051 −0.882462 −0.441231 0.897394i \(-0.645458\pi\)
−0.441231 + 0.897394i \(0.645458\pi\)
\(42\) 21.6850 3.34607
\(43\) 8.47151 1.29189 0.645946 0.763383i \(-0.276463\pi\)
0.645946 + 0.763383i \(0.276463\pi\)
\(44\) 13.1014 1.97511
\(45\) 19.2438 2.86869
\(46\) −7.16753 −1.05679
\(47\) 10.2753 1.49881 0.749407 0.662110i \(-0.230339\pi\)
0.749407 + 0.662110i \(0.230339\pi\)
\(48\) 7.90215 1.14058
\(49\) 0.819148 0.117021
\(50\) −3.78818 −0.535729
\(51\) −11.8103 −1.65378
\(52\) 3.83650 0.532027
\(53\) −5.05786 −0.694751 −0.347375 0.937726i \(-0.612927\pi\)
−0.347375 + 0.937726i \(0.612927\pi\)
\(54\) −34.9001 −4.74930
\(55\) 9.01822 1.21602
\(56\) 11.5597 1.54473
\(57\) 7.50304 0.993802
\(58\) 10.1550 1.33342
\(59\) −0.487214 −0.0634299 −0.0317150 0.999497i \(-0.510097\pi\)
−0.0317150 + 0.999497i \(0.510097\pi\)
\(60\) 30.9895 4.00073
\(61\) 3.39301 0.434430 0.217215 0.976124i \(-0.430303\pi\)
0.217215 + 0.976124i \(0.430303\pi\)
\(62\) −7.69660 −0.977470
\(63\) −20.9730 −2.64236
\(64\) −10.6971 −1.33714
\(65\) 2.64082 0.327554
\(66\) −27.2579 −3.35522
\(67\) 0.382019 0.0466710 0.0233355 0.999728i \(-0.492571\pi\)
0.0233355 + 0.999728i \(0.492571\pi\)
\(68\) −13.5852 −1.64744
\(69\) 9.70495 1.16834
\(70\) 17.1698 2.05219
\(71\) −5.02956 −0.596899 −0.298450 0.954425i \(-0.596469\pi\)
−0.298450 + 0.954425i \(0.596469\pi\)
\(72\) −31.0062 −3.65411
\(73\) −9.64474 −1.12883 −0.564416 0.825491i \(-0.690899\pi\)
−0.564416 + 0.825491i \(0.690899\pi\)
\(74\) −8.66754 −1.00758
\(75\) 5.12925 0.592275
\(76\) 8.63057 0.989994
\(77\) −9.82861 −1.12007
\(78\) −7.98199 −0.903783
\(79\) 9.13895 1.02821 0.514106 0.857727i \(-0.328124\pi\)
0.514106 + 0.857727i \(0.328124\pi\)
\(80\) 6.25679 0.699531
\(81\) 24.7543 2.75047
\(82\) 13.5228 1.49334
\(83\) −7.62765 −0.837243 −0.418622 0.908161i \(-0.637487\pi\)
−0.418622 + 0.908161i \(0.637487\pi\)
\(84\) −33.7742 −3.68507
\(85\) −9.35124 −1.01428
\(86\) −20.2740 −2.18620
\(87\) −13.7501 −1.47416
\(88\) −14.5305 −1.54895
\(89\) 8.23006 0.872385 0.436192 0.899853i \(-0.356327\pi\)
0.436192 + 0.899853i \(0.356327\pi\)
\(90\) −46.0541 −4.85453
\(91\) −2.87813 −0.301710
\(92\) 11.1634 1.16386
\(93\) 10.4213 1.08064
\(94\) −24.5909 −2.53636
\(95\) 5.94079 0.609512
\(96\) 7.88021 0.804270
\(97\) 5.19890 0.527868 0.263934 0.964541i \(-0.414980\pi\)
0.263934 + 0.964541i \(0.414980\pi\)
\(98\) −1.96038 −0.198028
\(99\) 26.3630 2.64958
\(100\) 5.90005 0.590005
\(101\) 0.980373 0.0975508 0.0487754 0.998810i \(-0.484468\pi\)
0.0487754 + 0.998810i \(0.484468\pi\)
\(102\) 28.2645 2.79860
\(103\) 9.87016 0.972536 0.486268 0.873810i \(-0.338358\pi\)
0.486268 + 0.873810i \(0.338358\pi\)
\(104\) −4.25498 −0.417235
\(105\) −23.2482 −2.26880
\(106\) 12.1045 1.17569
\(107\) −0.364181 −0.0352067 −0.0176033 0.999845i \(-0.505604\pi\)
−0.0176033 + 0.999845i \(0.505604\pi\)
\(108\) 54.3566 5.23047
\(109\) −4.06581 −0.389434 −0.194717 0.980859i \(-0.562379\pi\)
−0.194717 + 0.980859i \(0.562379\pi\)
\(110\) −21.5824 −2.05780
\(111\) 11.7360 1.11393
\(112\) −6.81904 −0.644339
\(113\) −8.80074 −0.827904 −0.413952 0.910299i \(-0.635852\pi\)
−0.413952 + 0.910299i \(0.635852\pi\)
\(114\) −17.9562 −1.68176
\(115\) 7.68422 0.716557
\(116\) −15.8164 −1.46852
\(117\) 7.71992 0.713707
\(118\) 1.16600 0.107339
\(119\) 10.1916 0.934258
\(120\) −34.3698 −3.13752
\(121\) 1.35450 0.123136
\(122\) −8.12013 −0.735162
\(123\) −18.3101 −1.65096
\(124\) 11.9874 1.07650
\(125\) −8.76732 −0.784173
\(126\) 50.1926 4.47151
\(127\) 1.96533 0.174395 0.0871975 0.996191i \(-0.472209\pi\)
0.0871975 + 0.996191i \(0.472209\pi\)
\(128\) 20.7366 1.83287
\(129\) 27.4513 2.41695
\(130\) −6.32001 −0.554301
\(131\) 16.1691 1.41270 0.706351 0.707861i \(-0.250340\pi\)
0.706351 + 0.707861i \(0.250340\pi\)
\(132\) 42.4540 3.69515
\(133\) −6.47463 −0.561422
\(134\) −0.914245 −0.0789788
\(135\) 37.4160 3.22025
\(136\) 15.0670 1.29199
\(137\) 7.28342 0.622265 0.311132 0.950367i \(-0.399292\pi\)
0.311132 + 0.950367i \(0.399292\pi\)
\(138\) −23.2258 −1.97711
\(139\) −1.44687 −0.122722 −0.0613611 0.998116i \(-0.519544\pi\)
−0.0613611 + 0.998116i \(0.519544\pi\)
\(140\) −26.7419 −2.26010
\(141\) 33.2965 2.80407
\(142\) 12.0367 1.01010
\(143\) 3.61779 0.302535
\(144\) 18.2905 1.52421
\(145\) −10.8871 −0.904124
\(146\) 23.0817 1.91026
\(147\) 2.65439 0.218930
\(148\) 13.4996 1.10966
\(149\) 2.08460 0.170777 0.0853886 0.996348i \(-0.472787\pi\)
0.0853886 + 0.996348i \(0.472787\pi\)
\(150\) −12.2753 −1.00227
\(151\) −10.8854 −0.885841 −0.442921 0.896561i \(-0.646058\pi\)
−0.442921 + 0.896561i \(0.646058\pi\)
\(152\) −9.57199 −0.776391
\(153\) −27.3365 −2.21002
\(154\) 23.5218 1.89544
\(155\) 8.25144 0.662771
\(156\) 12.4319 0.995348
\(157\) 6.84560 0.546338 0.273169 0.961966i \(-0.411928\pi\)
0.273169 + 0.961966i \(0.411928\pi\)
\(158\) −21.8713 −1.73999
\(159\) −16.3896 −1.29978
\(160\) 6.23942 0.493269
\(161\) −8.37474 −0.660022
\(162\) −59.2418 −4.65447
\(163\) 5.76269 0.451369 0.225685 0.974200i \(-0.427538\pi\)
0.225685 + 0.974200i \(0.427538\pi\)
\(164\) −21.0616 −1.64464
\(165\) 29.2229 2.27500
\(166\) 18.2545 1.41682
\(167\) 8.27564 0.640388 0.320194 0.947352i \(-0.396252\pi\)
0.320194 + 0.947352i \(0.396252\pi\)
\(168\) 37.4583 2.88997
\(169\) −11.9406 −0.918507
\(170\) 22.3793 1.71642
\(171\) 17.3667 1.32806
\(172\) 31.5765 2.40769
\(173\) 20.1595 1.53270 0.766349 0.642424i \(-0.222071\pi\)
0.766349 + 0.642424i \(0.222071\pi\)
\(174\) 32.9067 2.49465
\(175\) −4.42621 −0.334590
\(176\) 8.57148 0.646100
\(177\) −1.57878 −0.118668
\(178\) −19.6961 −1.47629
\(179\) 19.4815 1.45611 0.728057 0.685517i \(-0.240424\pi\)
0.728057 + 0.685517i \(0.240424\pi\)
\(180\) 71.7289 5.34636
\(181\) −11.8313 −0.879416 −0.439708 0.898141i \(-0.644918\pi\)
−0.439708 + 0.898141i \(0.644918\pi\)
\(182\) 6.88793 0.510568
\(183\) 10.9948 0.812758
\(184\) −12.3811 −0.912744
\(185\) 9.29236 0.683188
\(186\) −24.9403 −1.82871
\(187\) −12.8107 −0.936812
\(188\) 38.3002 2.79333
\(189\) −40.7782 −2.96618
\(190\) −14.2175 −1.03144
\(191\) 18.8169 1.36154 0.680772 0.732496i \(-0.261645\pi\)
0.680772 + 0.732496i \(0.261645\pi\)
\(192\) −34.6632 −2.50160
\(193\) −23.4427 −1.68744 −0.843720 0.536784i \(-0.819639\pi\)
−0.843720 + 0.536784i \(0.819639\pi\)
\(194\) −12.4420 −0.893282
\(195\) 8.55740 0.612808
\(196\) 3.05328 0.218091
\(197\) 26.0328 1.85476 0.927379 0.374124i \(-0.122057\pi\)
0.927379 + 0.374124i \(0.122057\pi\)
\(198\) −63.0917 −4.48373
\(199\) −27.0208 −1.91546 −0.957728 0.287677i \(-0.907117\pi\)
−0.957728 + 0.287677i \(0.907117\pi\)
\(200\) −6.54363 −0.462704
\(201\) 1.23790 0.0873149
\(202\) −2.34622 −0.165080
\(203\) 11.8654 0.832790
\(204\) −44.0217 −3.08213
\(205\) −14.4976 −1.01256
\(206\) −23.6212 −1.64577
\(207\) 22.4633 1.56131
\(208\) 2.51000 0.174038
\(209\) 8.13857 0.562957
\(210\) 55.6376 3.83936
\(211\) −16.7660 −1.15422 −0.577109 0.816667i \(-0.695819\pi\)
−0.577109 + 0.816667i \(0.695819\pi\)
\(212\) −18.8526 −1.29480
\(213\) −16.2979 −1.11671
\(214\) 0.871555 0.0595783
\(215\) 21.7355 1.48235
\(216\) −60.2858 −4.10193
\(217\) −8.99292 −0.610479
\(218\) 9.73027 0.659017
\(219\) −31.2531 −2.11189
\(220\) 33.6144 2.26628
\(221\) −3.75139 −0.252346
\(222\) −28.0865 −1.88504
\(223\) 16.6625 1.11581 0.557903 0.829906i \(-0.311606\pi\)
0.557903 + 0.829906i \(0.311606\pi\)
\(224\) −6.80010 −0.454351
\(225\) 11.8723 0.791485
\(226\) 21.0619 1.40102
\(227\) −17.2095 −1.14223 −0.571116 0.820870i \(-0.693489\pi\)
−0.571116 + 0.820870i \(0.693489\pi\)
\(228\) 27.9667 1.85214
\(229\) −23.7039 −1.56640 −0.783199 0.621771i \(-0.786413\pi\)
−0.783199 + 0.621771i \(0.786413\pi\)
\(230\) −18.3898 −1.21259
\(231\) −31.8489 −2.09550
\(232\) 17.5416 1.15167
\(233\) −5.94633 −0.389557 −0.194779 0.980847i \(-0.562399\pi\)
−0.194779 + 0.980847i \(0.562399\pi\)
\(234\) −18.4753 −1.20777
\(235\) 26.3636 1.71977
\(236\) −1.81603 −0.118214
\(237\) 29.6141 1.92364
\(238\) −24.3904 −1.58099
\(239\) −7.67611 −0.496526 −0.248263 0.968693i \(-0.579860\pi\)
−0.248263 + 0.968693i \(0.579860\pi\)
\(240\) 20.2747 1.30872
\(241\) −13.2541 −0.853770 −0.426885 0.904306i \(-0.640389\pi\)
−0.426885 + 0.904306i \(0.640389\pi\)
\(242\) −3.24158 −0.208377
\(243\) 36.4651 2.33924
\(244\) 12.6470 0.809643
\(245\) 2.10170 0.134273
\(246\) 43.8196 2.79383
\(247\) 2.38323 0.151642
\(248\) −13.2950 −0.844232
\(249\) −24.7168 −1.56637
\(250\) 20.9819 1.32701
\(251\) −12.1700 −0.768161 −0.384081 0.923300i \(-0.625482\pi\)
−0.384081 + 0.923300i \(0.625482\pi\)
\(252\) −78.1746 −4.92453
\(253\) 10.5270 0.661826
\(254\) −4.70342 −0.295119
\(255\) −30.3020 −1.89758
\(256\) −28.2325 −1.76453
\(257\) 16.8474 1.05091 0.525457 0.850820i \(-0.323894\pi\)
0.525457 + 0.850820i \(0.323894\pi\)
\(258\) −65.6963 −4.09007
\(259\) −10.1274 −0.629285
\(260\) 9.84336 0.610460
\(261\) −31.8262 −1.97000
\(262\) −38.6959 −2.39064
\(263\) −10.6177 −0.654718 −0.327359 0.944900i \(-0.606159\pi\)
−0.327359 + 0.944900i \(0.606159\pi\)
\(264\) −47.0848 −2.89787
\(265\) −12.9770 −0.797173
\(266\) 15.4951 0.950063
\(267\) 26.6689 1.63211
\(268\) 1.42393 0.0869804
\(269\) −18.0469 −1.10034 −0.550170 0.835053i \(-0.685437\pi\)
−0.550170 + 0.835053i \(0.685437\pi\)
\(270\) −89.5437 −5.44946
\(271\) −23.0879 −1.40249 −0.701244 0.712921i \(-0.747372\pi\)
−0.701244 + 0.712921i \(0.747372\pi\)
\(272\) −8.88800 −0.538914
\(273\) −9.32637 −0.564458
\(274\) −17.4307 −1.05302
\(275\) 5.56371 0.335504
\(276\) 36.1741 2.17742
\(277\) 19.4987 1.17156 0.585782 0.810469i \(-0.300788\pi\)
0.585782 + 0.810469i \(0.300788\pi\)
\(278\) 3.46265 0.207676
\(279\) 24.1214 1.44411
\(280\) 29.6589 1.77246
\(281\) 0.311221 0.0185659 0.00928294 0.999957i \(-0.497045\pi\)
0.00928294 + 0.999957i \(0.497045\pi\)
\(282\) −79.6850 −4.74517
\(283\) −7.03041 −0.417915 −0.208957 0.977925i \(-0.567007\pi\)
−0.208957 + 0.977925i \(0.567007\pi\)
\(284\) −18.7471 −1.11244
\(285\) 19.2507 1.14031
\(286\) −8.65808 −0.511963
\(287\) 15.8004 0.932667
\(288\) 18.2397 1.07478
\(289\) −3.71624 −0.218602
\(290\) 26.0549 1.53000
\(291\) 16.8466 0.987568
\(292\) −35.9496 −2.10379
\(293\) 3.91062 0.228461 0.114230 0.993454i \(-0.463560\pi\)
0.114230 + 0.993454i \(0.463560\pi\)
\(294\) −6.35247 −0.370484
\(295\) −1.25005 −0.0727809
\(296\) −14.9721 −0.870238
\(297\) 51.2580 2.97429
\(298\) −4.98886 −0.288997
\(299\) 3.08264 0.178274
\(300\) 19.1187 1.10382
\(301\) −23.6887 −1.36539
\(302\) 26.0509 1.49906
\(303\) 3.17683 0.182504
\(304\) 5.64649 0.323849
\(305\) 8.70549 0.498475
\(306\) 65.4215 3.73990
\(307\) 25.2624 1.44180 0.720902 0.693037i \(-0.243728\pi\)
0.720902 + 0.693037i \(0.243728\pi\)
\(308\) −36.6350 −2.08747
\(309\) 31.9835 1.81948
\(310\) −19.7473 −1.12157
\(311\) 21.0704 1.19479 0.597395 0.801947i \(-0.296202\pi\)
0.597395 + 0.801947i \(0.296202\pi\)
\(312\) −13.7880 −0.780589
\(313\) −8.77657 −0.496081 −0.248041 0.968750i \(-0.579787\pi\)
−0.248041 + 0.968750i \(0.579787\pi\)
\(314\) −16.3829 −0.924538
\(315\) −53.8109 −3.03190
\(316\) 34.0644 1.91627
\(317\) −31.9380 −1.79382 −0.896908 0.442216i \(-0.854192\pi\)
−0.896908 + 0.442216i \(0.854192\pi\)
\(318\) 39.2236 2.19955
\(319\) −14.9148 −0.835066
\(320\) −27.4457 −1.53426
\(321\) −1.18010 −0.0658668
\(322\) 20.0424 1.11692
\(323\) −8.43910 −0.469564
\(324\) 92.2686 5.12603
\(325\) 1.62923 0.0903736
\(326\) −13.7913 −0.763827
\(327\) −13.1749 −0.728576
\(328\) 23.3590 1.28979
\(329\) −28.7327 −1.58408
\(330\) −69.9360 −3.84985
\(331\) −8.71438 −0.478986 −0.239493 0.970898i \(-0.576981\pi\)
−0.239493 + 0.970898i \(0.576981\pi\)
\(332\) −28.4312 −1.56036
\(333\) 27.1643 1.48860
\(334\) −19.8052 −1.08369
\(335\) 0.980151 0.0535514
\(336\) −22.0966 −1.20547
\(337\) 25.4145 1.38442 0.692208 0.721698i \(-0.256638\pi\)
0.692208 + 0.721698i \(0.256638\pi\)
\(338\) 28.5762 1.55434
\(339\) −28.5181 −1.54889
\(340\) −34.8556 −1.89031
\(341\) 11.3040 0.612148
\(342\) −41.5619 −2.24741
\(343\) 17.2834 0.933213
\(344\) −35.0209 −1.88820
\(345\) 24.9001 1.34058
\(346\) −48.2456 −2.59370
\(347\) −5.40936 −0.290390 −0.145195 0.989403i \(-0.546381\pi\)
−0.145195 + 0.989403i \(0.546381\pi\)
\(348\) −51.2519 −2.74739
\(349\) 4.76821 0.255237 0.127618 0.991823i \(-0.459267\pi\)
0.127618 + 0.991823i \(0.459267\pi\)
\(350\) 10.5928 0.566208
\(351\) 15.0100 0.801173
\(352\) 8.54768 0.455593
\(353\) −24.2744 −1.29199 −0.645997 0.763340i \(-0.723558\pi\)
−0.645997 + 0.763340i \(0.723558\pi\)
\(354\) 3.77833 0.200816
\(355\) −12.9044 −0.684896
\(356\) 30.6766 1.62586
\(357\) 33.0250 1.74787
\(358\) −46.6230 −2.46410
\(359\) 15.2658 0.805699 0.402849 0.915266i \(-0.368020\pi\)
0.402849 + 0.915266i \(0.368020\pi\)
\(360\) −79.5531 −4.19281
\(361\) −13.6387 −0.717826
\(362\) 28.3147 1.48819
\(363\) 4.38915 0.230371
\(364\) −10.7279 −0.562295
\(365\) −24.7457 −1.29525
\(366\) −26.3127 −1.37538
\(367\) 0.287626 0.0150140 0.00750698 0.999972i \(-0.497610\pi\)
0.00750698 + 0.999972i \(0.497610\pi\)
\(368\) 7.30356 0.380725
\(369\) −42.3809 −2.20626
\(370\) −22.2384 −1.15612
\(371\) 14.1432 0.734277
\(372\) 38.8443 2.01398
\(373\) −1.93480 −0.100180 −0.0500902 0.998745i \(-0.515951\pi\)
−0.0500902 + 0.998745i \(0.515951\pi\)
\(374\) 30.6585 1.58531
\(375\) −28.4098 −1.46708
\(376\) −42.4779 −2.19063
\(377\) −4.36752 −0.224939
\(378\) 97.5903 5.01950
\(379\) −19.8120 −1.01767 −0.508836 0.860863i \(-0.669924\pi\)
−0.508836 + 0.860863i \(0.669924\pi\)
\(380\) 22.1436 1.13594
\(381\) 6.36851 0.326269
\(382\) −45.0325 −2.30406
\(383\) −36.9164 −1.88634 −0.943171 0.332308i \(-0.892173\pi\)
−0.943171 + 0.332308i \(0.892173\pi\)
\(384\) 67.1953 3.42905
\(385\) −25.2174 −1.28520
\(386\) 56.1029 2.85556
\(387\) 63.5393 3.22988
\(388\) 19.3783 0.983784
\(389\) 10.2935 0.521899 0.260950 0.965352i \(-0.415964\pi\)
0.260950 + 0.965352i \(0.415964\pi\)
\(390\) −20.4795 −1.03702
\(391\) −10.9157 −0.552031
\(392\) −3.38633 −0.171035
\(393\) 52.3948 2.64297
\(394\) −62.3015 −3.13870
\(395\) 23.4479 1.17979
\(396\) 98.2649 4.93800
\(397\) 23.3327 1.17103 0.585517 0.810660i \(-0.300892\pi\)
0.585517 + 0.810660i \(0.300892\pi\)
\(398\) 64.6661 3.24142
\(399\) −20.9806 −1.05034
\(400\) 3.86007 0.193004
\(401\) 19.8949 0.993504 0.496752 0.867893i \(-0.334526\pi\)
0.496752 + 0.867893i \(0.334526\pi\)
\(402\) −2.96254 −0.147758
\(403\) 3.31018 0.164892
\(404\) 3.65423 0.181805
\(405\) 63.5124 3.15595
\(406\) −28.3963 −1.40928
\(407\) 12.7300 0.631005
\(408\) 48.8235 2.41713
\(409\) −1.15423 −0.0570729 −0.0285365 0.999593i \(-0.509085\pi\)
−0.0285365 + 0.999593i \(0.509085\pi\)
\(410\) 34.6956 1.71349
\(411\) 23.6014 1.16417
\(412\) 36.7899 1.81251
\(413\) 1.36238 0.0670386
\(414\) −53.7590 −2.64211
\(415\) −19.5704 −0.960672
\(416\) 2.50303 0.122721
\(417\) −4.68849 −0.229596
\(418\) −19.4772 −0.952660
\(419\) 3.46098 0.169080 0.0845399 0.996420i \(-0.473058\pi\)
0.0845399 + 0.996420i \(0.473058\pi\)
\(420\) −86.6551 −4.22834
\(421\) 23.6303 1.15167 0.575834 0.817566i \(-0.304677\pi\)
0.575834 + 0.817566i \(0.304677\pi\)
\(422\) 40.1243 1.95322
\(423\) 77.0688 3.74721
\(424\) 20.9090 1.01543
\(425\) −5.76916 −0.279845
\(426\) 39.0041 1.88975
\(427\) −9.48778 −0.459146
\(428\) −1.35744 −0.0656144
\(429\) 11.7232 0.566001
\(430\) −52.0172 −2.50849
\(431\) −29.3418 −1.41334 −0.706671 0.707542i \(-0.749804\pi\)
−0.706671 + 0.707542i \(0.749804\pi\)
\(432\) 35.5625 1.71100
\(433\) −17.4920 −0.840610 −0.420305 0.907383i \(-0.638077\pi\)
−0.420305 + 0.907383i \(0.638077\pi\)
\(434\) 21.5218 1.03308
\(435\) −35.2788 −1.69149
\(436\) −15.1548 −0.725784
\(437\) 6.93469 0.331731
\(438\) 74.7947 3.57383
\(439\) 26.6785 1.27329 0.636647 0.771155i \(-0.280321\pi\)
0.636647 + 0.771155i \(0.280321\pi\)
\(440\) −37.2810 −1.77730
\(441\) 6.14390 0.292567
\(442\) 8.97780 0.427030
\(443\) −17.4828 −0.830631 −0.415316 0.909677i \(-0.636329\pi\)
−0.415316 + 0.909677i \(0.636329\pi\)
\(444\) 43.7445 2.07602
\(445\) 21.1160 1.00099
\(446\) −39.8767 −1.88822
\(447\) 6.75500 0.319500
\(448\) 29.9120 1.41321
\(449\) −32.5296 −1.53517 −0.767584 0.640949i \(-0.778541\pi\)
−0.767584 + 0.640949i \(0.778541\pi\)
\(450\) −28.4127 −1.33939
\(451\) −19.8610 −0.935217
\(452\) −32.8037 −1.54296
\(453\) −35.2733 −1.65728
\(454\) 41.1856 1.93294
\(455\) −7.38447 −0.346189
\(456\) −31.0173 −1.45252
\(457\) 20.3357 0.951263 0.475632 0.879645i \(-0.342220\pi\)
0.475632 + 0.879645i \(0.342220\pi\)
\(458\) 56.7281 2.65073
\(459\) −53.1507 −2.48086
\(460\) 28.6420 1.33544
\(461\) 36.5773 1.70358 0.851788 0.523887i \(-0.175519\pi\)
0.851788 + 0.523887i \(0.175519\pi\)
\(462\) 76.2206 3.54610
\(463\) −11.8926 −0.552697 −0.276349 0.961057i \(-0.589124\pi\)
−0.276349 + 0.961057i \(0.589124\pi\)
\(464\) −10.3478 −0.480383
\(465\) 26.7382 1.23995
\(466\) 14.2307 0.659226
\(467\) 19.7127 0.912195 0.456097 0.889930i \(-0.349247\pi\)
0.456097 + 0.889930i \(0.349247\pi\)
\(468\) 28.7751 1.33013
\(469\) −1.06823 −0.0493262
\(470\) −63.0933 −2.91028
\(471\) 22.1827 1.02212
\(472\) 2.01413 0.0927077
\(473\) 29.7765 1.36912
\(474\) −70.8723 −3.25527
\(475\) 3.66511 0.168167
\(476\) 37.9878 1.74117
\(477\) −37.9358 −1.73696
\(478\) 18.3704 0.840244
\(479\) −31.6469 −1.44598 −0.722992 0.690857i \(-0.757234\pi\)
−0.722992 + 0.690857i \(0.757234\pi\)
\(480\) 20.2184 0.922838
\(481\) 3.72777 0.169972
\(482\) 31.7196 1.44479
\(483\) −27.1377 −1.23481
\(484\) 5.04874 0.229488
\(485\) 13.3389 0.605688
\(486\) −87.2681 −3.95856
\(487\) −14.4351 −0.654118 −0.327059 0.945004i \(-0.606058\pi\)
−0.327059 + 0.945004i \(0.606058\pi\)
\(488\) −14.0266 −0.634953
\(489\) 18.6736 0.844448
\(490\) −5.02978 −0.227222
\(491\) −25.8128 −1.16492 −0.582459 0.812860i \(-0.697909\pi\)
−0.582459 + 0.812860i \(0.697909\pi\)
\(492\) −68.2486 −3.07689
\(493\) 15.4655 0.696532
\(494\) −5.70354 −0.256615
\(495\) 67.6399 3.04019
\(496\) 7.84268 0.352147
\(497\) 14.0640 0.630858
\(498\) 59.1522 2.65067
\(499\) −14.8504 −0.664793 −0.332397 0.943140i \(-0.607857\pi\)
−0.332397 + 0.943140i \(0.607857\pi\)
\(500\) −32.6792 −1.46146
\(501\) 26.8166 1.19808
\(502\) 29.1251 1.29992
\(503\) 18.5348 0.826426 0.413213 0.910634i \(-0.364407\pi\)
0.413213 + 0.910634i \(0.364407\pi\)
\(504\) 86.7018 3.86201
\(505\) 2.51536 0.111932
\(506\) −25.1931 −1.11997
\(507\) −38.6926 −1.71840
\(508\) 7.32555 0.325019
\(509\) 1.60638 0.0712015 0.0356008 0.999366i \(-0.488666\pi\)
0.0356008 + 0.999366i \(0.488666\pi\)
\(510\) 72.5185 3.21118
\(511\) 26.9693 1.19305
\(512\) 26.0926 1.15314
\(513\) 33.7664 1.49082
\(514\) −40.3192 −1.77840
\(515\) 25.3240 1.11591
\(516\) 102.321 4.50445
\(517\) 36.1168 1.58841
\(518\) 24.2368 1.06490
\(519\) 65.3254 2.86746
\(520\) −10.9171 −0.478745
\(521\) 26.0587 1.14165 0.570826 0.821071i \(-0.306623\pi\)
0.570826 + 0.821071i \(0.306623\pi\)
\(522\) 76.1664 3.33371
\(523\) −6.65022 −0.290794 −0.145397 0.989373i \(-0.546446\pi\)
−0.145397 + 0.989373i \(0.546446\pi\)
\(524\) 60.2685 2.63284
\(525\) −14.3428 −0.625971
\(526\) 25.4103 1.10794
\(527\) −11.7215 −0.510595
\(528\) 27.7752 1.20876
\(529\) −14.0302 −0.610009
\(530\) 31.0566 1.34901
\(531\) −3.65428 −0.158582
\(532\) −24.1334 −1.04632
\(533\) −5.81593 −0.251916
\(534\) −63.8239 −2.76193
\(535\) −0.934384 −0.0403969
\(536\) −1.57925 −0.0682133
\(537\) 63.1282 2.72418
\(538\) 43.1898 1.86204
\(539\) 2.87922 0.124017
\(540\) 139.464 6.00156
\(541\) −5.19518 −0.223358 −0.111679 0.993744i \(-0.535623\pi\)
−0.111679 + 0.993744i \(0.535623\pi\)
\(542\) 55.2538 2.37335
\(543\) −38.3385 −1.64526
\(544\) −8.86332 −0.380012
\(545\) −10.4317 −0.446845
\(546\) 22.3198 0.955201
\(547\) −6.07215 −0.259626 −0.129813 0.991538i \(-0.541438\pi\)
−0.129813 + 0.991538i \(0.541438\pi\)
\(548\) 27.1481 1.15971
\(549\) 25.4488 1.08613
\(550\) −13.3150 −0.567755
\(551\) −9.82515 −0.418565
\(552\) −40.1199 −1.70762
\(553\) −25.5550 −1.08671
\(554\) −46.6642 −1.98257
\(555\) 30.1112 1.27815
\(556\) −5.39305 −0.228716
\(557\) −0.316767 −0.0134218 −0.00671092 0.999977i \(-0.502136\pi\)
−0.00671092 + 0.999977i \(0.502136\pi\)
\(558\) −57.7273 −2.44379
\(559\) 8.71951 0.368796
\(560\) −17.4957 −0.739329
\(561\) −41.5121 −1.75264
\(562\) −0.744813 −0.0314180
\(563\) 30.7402 1.29554 0.647772 0.761834i \(-0.275701\pi\)
0.647772 + 0.761834i \(0.275701\pi\)
\(564\) 124.109 5.22592
\(565\) −22.5802 −0.949956
\(566\) 16.8252 0.707214
\(567\) −69.2197 −2.90695
\(568\) 20.7920 0.872414
\(569\) 22.2385 0.932287 0.466143 0.884709i \(-0.345643\pi\)
0.466143 + 0.884709i \(0.345643\pi\)
\(570\) −46.0706 −1.92969
\(571\) −24.6105 −1.02992 −0.514958 0.857215i \(-0.672193\pi\)
−0.514958 + 0.857215i \(0.672193\pi\)
\(572\) 13.4849 0.563832
\(573\) 60.9748 2.54726
\(574\) −37.8134 −1.57830
\(575\) 4.74071 0.197701
\(576\) −80.2321 −3.34300
\(577\) −18.3153 −0.762474 −0.381237 0.924477i \(-0.624502\pi\)
−0.381237 + 0.924477i \(0.624502\pi\)
\(578\) 8.89368 0.369928
\(579\) −75.9642 −3.15696
\(580\) −40.5804 −1.68501
\(581\) 21.3290 0.884876
\(582\) −40.3173 −1.67121
\(583\) −17.7779 −0.736284
\(584\) 39.8710 1.64987
\(585\) 19.8071 0.818924
\(586\) −9.35886 −0.386611
\(587\) −30.9110 −1.27583 −0.637917 0.770105i \(-0.720204\pi\)
−0.637917 + 0.770105i \(0.720204\pi\)
\(588\) 9.89392 0.408019
\(589\) 7.44657 0.306831
\(590\) 2.99162 0.123163
\(591\) 84.3572 3.46999
\(592\) 8.83204 0.362995
\(593\) 36.4996 1.49886 0.749429 0.662084i \(-0.230328\pi\)
0.749429 + 0.662084i \(0.230328\pi\)
\(594\) −122.670 −5.03322
\(595\) 26.1486 1.07199
\(596\) 7.77011 0.318276
\(597\) −87.5589 −3.58355
\(598\) −7.37735 −0.301682
\(599\) −28.0381 −1.14561 −0.572804 0.819692i \(-0.694144\pi\)
−0.572804 + 0.819692i \(0.694144\pi\)
\(600\) −21.2041 −0.865655
\(601\) 47.5005 1.93759 0.968794 0.247868i \(-0.0797300\pi\)
0.968794 + 0.247868i \(0.0797300\pi\)
\(602\) 56.6916 2.31058
\(603\) 2.86528 0.116683
\(604\) −40.5740 −1.65093
\(605\) 3.47526 0.141289
\(606\) −7.60277 −0.308841
\(607\) −7.03650 −0.285603 −0.142801 0.989751i \(-0.545611\pi\)
−0.142801 + 0.989751i \(0.545611\pi\)
\(608\) 5.63081 0.228360
\(609\) 38.4490 1.55803
\(610\) −20.8339 −0.843541
\(611\) 10.5762 0.427865
\(612\) −101.893 −4.11880
\(613\) 19.1407 0.773087 0.386544 0.922271i \(-0.373669\pi\)
0.386544 + 0.922271i \(0.373669\pi\)
\(614\) −60.4580 −2.43989
\(615\) −46.9784 −1.89435
\(616\) 40.6311 1.63708
\(617\) 4.21003 0.169489 0.0847447 0.996403i \(-0.472993\pi\)
0.0847447 + 0.996403i \(0.472993\pi\)
\(618\) −76.5428 −3.07900
\(619\) −16.9723 −0.682176 −0.341088 0.940031i \(-0.610795\pi\)
−0.341088 + 0.940031i \(0.610795\pi\)
\(620\) 30.7563 1.23520
\(621\) 43.6757 1.75265
\(622\) −50.4255 −2.02188
\(623\) −23.0135 −0.922017
\(624\) 8.13348 0.325600
\(625\) −30.4089 −1.21636
\(626\) 21.0040 0.839491
\(627\) 26.3724 1.05321
\(628\) 25.5162 1.01821
\(629\) −13.2001 −0.526324
\(630\) 128.780 5.13071
\(631\) −36.1788 −1.44026 −0.720128 0.693841i \(-0.755917\pi\)
−0.720128 + 0.693841i \(0.755917\pi\)
\(632\) −37.7801 −1.50281
\(633\) −54.3289 −2.15938
\(634\) 76.4339 3.03558
\(635\) 5.04248 0.200105
\(636\) −61.0904 −2.42239
\(637\) 0.843128 0.0334060
\(638\) 35.6939 1.41314
\(639\) −37.7235 −1.49232
\(640\) 53.2042 2.10308
\(641\) −21.9630 −0.867485 −0.433743 0.901037i \(-0.642807\pi\)
−0.433743 + 0.901037i \(0.642807\pi\)
\(642\) 2.82421 0.111463
\(643\) −18.7695 −0.740196 −0.370098 0.928993i \(-0.620676\pi\)
−0.370098 + 0.928993i \(0.620676\pi\)
\(644\) −31.2158 −1.23008
\(645\) 70.4322 2.77326
\(646\) 20.1964 0.794617
\(647\) −29.1688 −1.14674 −0.573372 0.819295i \(-0.694365\pi\)
−0.573372 + 0.819295i \(0.694365\pi\)
\(648\) −102.333 −4.02003
\(649\) −1.71251 −0.0672218
\(650\) −3.89907 −0.152934
\(651\) −29.1409 −1.14212
\(652\) 21.4798 0.841213
\(653\) 42.2753 1.65436 0.827179 0.561938i \(-0.189944\pi\)
0.827179 + 0.561938i \(0.189944\pi\)
\(654\) 31.5302 1.23293
\(655\) 41.4854 1.62097
\(656\) −13.7794 −0.537997
\(657\) −72.3390 −2.82221
\(658\) 68.7629 2.68066
\(659\) 0.760019 0.0296061 0.0148031 0.999890i \(-0.495288\pi\)
0.0148031 + 0.999890i \(0.495288\pi\)
\(660\) 108.925 4.23989
\(661\) 10.2330 0.398019 0.199010 0.979998i \(-0.436228\pi\)
0.199010 + 0.979998i \(0.436228\pi\)
\(662\) 20.8552 0.810561
\(663\) −12.1561 −0.472103
\(664\) 31.5324 1.22370
\(665\) −16.6121 −0.644188
\(666\) −65.0096 −2.51907
\(667\) −12.7085 −0.492076
\(668\) 30.8465 1.19349
\(669\) 53.9937 2.08752
\(670\) −2.34569 −0.0906220
\(671\) 11.9261 0.460401
\(672\) −22.0352 −0.850027
\(673\) −19.4212 −0.748631 −0.374316 0.927301i \(-0.622122\pi\)
−0.374316 + 0.927301i \(0.622122\pi\)
\(674\) −60.8219 −2.34277
\(675\) 23.0834 0.888482
\(676\) −44.5072 −1.71181
\(677\) −7.74032 −0.297485 −0.148742 0.988876i \(-0.547522\pi\)
−0.148742 + 0.988876i \(0.547522\pi\)
\(678\) 68.2495 2.62111
\(679\) −14.5375 −0.557900
\(680\) 38.6577 1.48245
\(681\) −55.7659 −2.13696
\(682\) −27.0528 −1.03590
\(683\) −21.0024 −0.803633 −0.401817 0.915720i \(-0.631621\pi\)
−0.401817 + 0.915720i \(0.631621\pi\)
\(684\) 64.7323 2.47510
\(685\) 18.6872 0.714001
\(686\) −41.3624 −1.57923
\(687\) −76.8107 −2.93051
\(688\) 20.6588 0.787608
\(689\) −5.20593 −0.198330
\(690\) −59.5909 −2.26859
\(691\) −3.77905 −0.143762 −0.0718810 0.997413i \(-0.522900\pi\)
−0.0718810 + 0.997413i \(0.522900\pi\)
\(692\) 75.1422 2.85648
\(693\) −73.7181 −2.80032
\(694\) 12.9457 0.491411
\(695\) −3.71227 −0.140814
\(696\) 56.8424 2.15460
\(697\) 20.5944 0.780068
\(698\) −11.4113 −0.431923
\(699\) −19.2686 −0.728807
\(700\) −16.4982 −0.623572
\(701\) 32.7511 1.23699 0.618496 0.785788i \(-0.287742\pi\)
0.618496 + 0.785788i \(0.287742\pi\)
\(702\) −35.9218 −1.35578
\(703\) 8.38596 0.316283
\(704\) −37.5992 −1.41707
\(705\) 85.4293 3.21745
\(706\) 58.0933 2.18637
\(707\) −2.74139 −0.103101
\(708\) −5.88472 −0.221161
\(709\) −8.26321 −0.310331 −0.155166 0.987888i \(-0.549591\pi\)
−0.155166 + 0.987888i \(0.549591\pi\)
\(710\) 30.8828 1.15901
\(711\) 68.5454 2.57065
\(712\) −34.0228 −1.27506
\(713\) 9.63191 0.360718
\(714\) −79.0352 −2.95782
\(715\) 9.28223 0.347136
\(716\) 72.6149 2.71375
\(717\) −24.8739 −0.928931
\(718\) −36.5341 −1.36344
\(719\) 42.8474 1.59794 0.798969 0.601372i \(-0.205379\pi\)
0.798969 + 0.601372i \(0.205379\pi\)
\(720\) 46.9282 1.74891
\(721\) −27.5997 −1.02787
\(722\) 32.6400 1.21474
\(723\) −42.9488 −1.59728
\(724\) −44.0999 −1.63896
\(725\) −6.71669 −0.249452
\(726\) −10.5041 −0.389844
\(727\) −43.6731 −1.61975 −0.809874 0.586604i \(-0.800464\pi\)
−0.809874 + 0.586604i \(0.800464\pi\)
\(728\) 11.8981 0.440973
\(729\) 43.8997 1.62592
\(730\) 59.2212 2.19187
\(731\) −30.8760 −1.14199
\(732\) 40.9818 1.51473
\(733\) −48.5002 −1.79140 −0.895699 0.444662i \(-0.853324\pi\)
−0.895699 + 0.444662i \(0.853324\pi\)
\(734\) −0.688345 −0.0254073
\(735\) 6.81041 0.251206
\(736\) 7.28328 0.268465
\(737\) 1.34276 0.0494611
\(738\) 101.426 3.73353
\(739\) 41.5990 1.53024 0.765122 0.643886i \(-0.222679\pi\)
0.765122 + 0.643886i \(0.222679\pi\)
\(740\) 34.6362 1.27325
\(741\) 7.72269 0.283700
\(742\) −33.8474 −1.24258
\(743\) −10.9455 −0.401552 −0.200776 0.979637i \(-0.564346\pi\)
−0.200776 + 0.979637i \(0.564346\pi\)
\(744\) −43.0814 −1.57944
\(745\) 5.34849 0.195954
\(746\) 4.63036 0.169530
\(747\) −57.2101 −2.09321
\(748\) −47.7504 −1.74593
\(749\) 1.01835 0.0372097
\(750\) 67.9903 2.48265
\(751\) −5.11517 −0.186655 −0.0933276 0.995635i \(-0.529750\pi\)
−0.0933276 + 0.995635i \(0.529750\pi\)
\(752\) 25.0576 0.913758
\(753\) −39.4359 −1.43712
\(754\) 10.4523 0.380651
\(755\) −27.9288 −1.01643
\(756\) −151.996 −5.52804
\(757\) −37.9332 −1.37871 −0.689353 0.724425i \(-0.742105\pi\)
−0.689353 + 0.724425i \(0.742105\pi\)
\(758\) 47.4139 1.72215
\(759\) 34.1119 1.23818
\(760\) −24.5590 −0.890848
\(761\) 28.7658 1.04276 0.521379 0.853325i \(-0.325418\pi\)
0.521379 + 0.853325i \(0.325418\pi\)
\(762\) −15.2411 −0.552127
\(763\) 11.3691 0.411590
\(764\) 70.1378 2.53750
\(765\) −70.1376 −2.53583
\(766\) 88.3482 3.19215
\(767\) −0.501477 −0.0181073
\(768\) −91.4852 −3.30119
\(769\) −12.0086 −0.433043 −0.216521 0.976278i \(-0.569471\pi\)
−0.216521 + 0.976278i \(0.569471\pi\)
\(770\) 60.3502 2.17487
\(771\) 54.5928 1.96611
\(772\) −87.3798 −3.14487
\(773\) 52.3196 1.88180 0.940902 0.338678i \(-0.109980\pi\)
0.940902 + 0.338678i \(0.109980\pi\)
\(774\) −152.062 −5.46575
\(775\) 5.09065 0.182861
\(776\) −21.4921 −0.771520
\(777\) −32.8170 −1.17730
\(778\) −24.6343 −0.883181
\(779\) −13.0835 −0.468765
\(780\) 31.8967 1.14208
\(781\) −17.6784 −0.632583
\(782\) 26.1234 0.934172
\(783\) −61.8803 −2.21142
\(784\) 1.99759 0.0713424
\(785\) 17.5639 0.626881
\(786\) −125.391 −4.47255
\(787\) 25.7897 0.919302 0.459651 0.888100i \(-0.347974\pi\)
0.459651 + 0.888100i \(0.347974\pi\)
\(788\) 97.0341 3.45670
\(789\) −34.4060 −1.22489
\(790\) −56.1155 −1.99650
\(791\) 24.6093 0.875005
\(792\) −108.984 −3.87256
\(793\) 3.49233 0.124016
\(794\) −55.8397 −1.98168
\(795\) −42.0511 −1.49140
\(796\) −100.717 −3.56982
\(797\) 45.2666 1.60342 0.801712 0.597710i \(-0.203923\pi\)
0.801712 + 0.597710i \(0.203923\pi\)
\(798\) 50.2106 1.77744
\(799\) −37.4505 −1.32490
\(800\) 3.84935 0.136095
\(801\) 61.7284 2.18107
\(802\) −47.6124 −1.68125
\(803\) −33.9003 −1.19631
\(804\) 4.61414 0.162728
\(805\) −21.4872 −0.757324
\(806\) −7.92192 −0.279038
\(807\) −58.4796 −2.05858
\(808\) −4.05283 −0.142578
\(809\) −16.1748 −0.568677 −0.284338 0.958724i \(-0.591774\pi\)
−0.284338 + 0.958724i \(0.591774\pi\)
\(810\) −151.997 −5.34065
\(811\) −19.5970 −0.688142 −0.344071 0.938944i \(-0.611806\pi\)
−0.344071 + 0.938944i \(0.611806\pi\)
\(812\) 44.2270 1.55206
\(813\) −74.8145 −2.62386
\(814\) −30.4655 −1.06781
\(815\) 14.7854 0.517911
\(816\) −28.8009 −1.00823
\(817\) 19.6154 0.686254
\(818\) 2.76229 0.0965813
\(819\) −21.5870 −0.754311
\(820\) −54.0381 −1.88709
\(821\) −10.2871 −0.359021 −0.179511 0.983756i \(-0.557451\pi\)
−0.179511 + 0.983756i \(0.557451\pi\)
\(822\) −56.4827 −1.97006
\(823\) 51.2301 1.78577 0.892884 0.450286i \(-0.148678\pi\)
0.892884 + 0.450286i \(0.148678\pi\)
\(824\) −40.8029 −1.42144
\(825\) 18.0288 0.627682
\(826\) −3.26045 −0.113446
\(827\) −50.6261 −1.76044 −0.880221 0.474564i \(-0.842606\pi\)
−0.880221 + 0.474564i \(0.842606\pi\)
\(828\) 83.7292 2.90979
\(829\) 53.2843 1.85064 0.925320 0.379186i \(-0.123796\pi\)
0.925320 + 0.379186i \(0.123796\pi\)
\(830\) 46.8357 1.62569
\(831\) 63.1841 2.19183
\(832\) −11.0103 −0.381712
\(833\) −2.98554 −0.103443
\(834\) 11.2205 0.388533
\(835\) 21.2329 0.734796
\(836\) 30.3356 1.04918
\(837\) 46.8997 1.62109
\(838\) −8.28279 −0.286124
\(839\) 25.0546 0.864980 0.432490 0.901639i \(-0.357635\pi\)
0.432490 + 0.901639i \(0.357635\pi\)
\(840\) 96.1074 3.31602
\(841\) −10.9944 −0.379118
\(842\) −56.5518 −1.94891
\(843\) 1.00849 0.0347342
\(844\) −62.4933 −2.15111
\(845\) −30.6362 −1.05392
\(846\) −184.441 −6.34120
\(847\) −3.78755 −0.130142
\(848\) −12.3342 −0.423558
\(849\) −22.7815 −0.781860
\(850\) 13.8067 0.473567
\(851\) 10.8470 0.371830
\(852\) −60.7486 −2.08121
\(853\) 33.6958 1.15372 0.576861 0.816842i \(-0.304277\pi\)
0.576861 + 0.816842i \(0.304277\pi\)
\(854\) 22.7061 0.776987
\(855\) 44.5580 1.52385
\(856\) 1.50551 0.0514573
\(857\) −5.19775 −0.177552 −0.0887758 0.996052i \(-0.528295\pi\)
−0.0887758 + 0.996052i \(0.528295\pi\)
\(858\) −28.0559 −0.957812
\(859\) 46.5223 1.58732 0.793660 0.608362i \(-0.208173\pi\)
0.793660 + 0.608362i \(0.208173\pi\)
\(860\) 81.0164 2.76264
\(861\) 51.2000 1.74489
\(862\) 70.2205 2.39172
\(863\) 26.9573 0.917637 0.458818 0.888530i \(-0.348273\pi\)
0.458818 + 0.888530i \(0.348273\pi\)
\(864\) 35.4637 1.20650
\(865\) 51.7235 1.75865
\(866\) 41.8617 1.42252
\(867\) −12.0422 −0.408974
\(868\) −33.5201 −1.13774
\(869\) 32.1225 1.08968
\(870\) 84.4291 2.86241
\(871\) 0.393202 0.0133231
\(872\) 16.8079 0.569187
\(873\) 38.9936 1.31973
\(874\) −16.5961 −0.561370
\(875\) 24.5158 0.828786
\(876\) −116.492 −3.93590
\(877\) −42.2271 −1.42591 −0.712953 0.701212i \(-0.752643\pi\)
−0.712953 + 0.701212i \(0.752643\pi\)
\(878\) −63.8468 −2.15473
\(879\) 12.6721 0.427418
\(880\) 21.9920 0.741350
\(881\) 40.1694 1.35334 0.676671 0.736286i \(-0.263422\pi\)
0.676671 + 0.736286i \(0.263422\pi\)
\(882\) −14.7036 −0.495095
\(883\) 20.2122 0.680194 0.340097 0.940390i \(-0.389540\pi\)
0.340097 + 0.940390i \(0.389540\pi\)
\(884\) −13.9829 −0.470294
\(885\) −4.05070 −0.136163
\(886\) 41.8397 1.40563
\(887\) 31.7475 1.06598 0.532989 0.846122i \(-0.321069\pi\)
0.532989 + 0.846122i \(0.321069\pi\)
\(888\) −48.5161 −1.62809
\(889\) −5.49561 −0.184317
\(890\) −50.5347 −1.69393
\(891\) 87.0086 2.91490
\(892\) 62.1076 2.07952
\(893\) 23.7921 0.796171
\(894\) −16.1660 −0.540673
\(895\) 49.9839 1.67078
\(896\) −57.9852 −1.93715
\(897\) 9.98906 0.333525
\(898\) 77.8497 2.59788
\(899\) −13.6466 −0.455140
\(900\) 44.2525 1.47508
\(901\) 18.4343 0.614137
\(902\) 47.5312 1.58262
\(903\) −76.7613 −2.55446
\(904\) 36.3819 1.21005
\(905\) −30.3558 −1.00906
\(906\) 84.4159 2.80453
\(907\) 40.6477 1.34968 0.674842 0.737963i \(-0.264212\pi\)
0.674842 + 0.737963i \(0.264212\pi\)
\(908\) −64.1462 −2.12877
\(909\) 7.35315 0.243889
\(910\) 17.6725 0.585837
\(911\) 17.7696 0.588734 0.294367 0.955692i \(-0.404891\pi\)
0.294367 + 0.955692i \(0.404891\pi\)
\(912\) 18.2970 0.605876
\(913\) −26.8104 −0.887295
\(914\) −48.6673 −1.60977
\(915\) 28.2095 0.932577
\(916\) −88.3535 −2.91928
\(917\) −45.2133 −1.49307
\(918\) 127.200 4.19823
\(919\) −39.6066 −1.30650 −0.653251 0.757142i \(-0.726595\pi\)
−0.653251 + 0.757142i \(0.726595\pi\)
\(920\) −31.7663 −1.04730
\(921\) 81.8611 2.69741
\(922\) −87.5366 −2.88287
\(923\) −5.17680 −0.170396
\(924\) −118.713 −3.90537
\(925\) 5.73284 0.188494
\(926\) 28.4614 0.935299
\(927\) 74.0297 2.43145
\(928\) −10.3190 −0.338739
\(929\) −42.8988 −1.40746 −0.703732 0.710466i \(-0.748484\pi\)
−0.703732 + 0.710466i \(0.748484\pi\)
\(930\) −63.9896 −2.09830
\(931\) 1.89670 0.0621617
\(932\) −22.1643 −0.726015
\(933\) 68.2769 2.23529
\(934\) −47.1763 −1.54366
\(935\) −32.8686 −1.07492
\(936\) −31.9139 −1.04314
\(937\) −5.07215 −0.165700 −0.0828500 0.996562i \(-0.526402\pi\)
−0.0828500 + 0.996562i \(0.526402\pi\)
\(938\) 2.55648 0.0834720
\(939\) −28.4398 −0.928099
\(940\) 98.2673 3.20513
\(941\) −43.7577 −1.42646 −0.713231 0.700929i \(-0.752769\pi\)
−0.713231 + 0.700929i \(0.752769\pi\)
\(942\) −53.0874 −1.72968
\(943\) −16.9231 −0.551091
\(944\) −1.18813 −0.0386703
\(945\) −104.625 −3.40346
\(946\) −71.2609 −2.31689
\(947\) 49.6028 1.61187 0.805936 0.592002i \(-0.201662\pi\)
0.805936 + 0.592002i \(0.201662\pi\)
\(948\) 110.383 3.58507
\(949\) −9.92708 −0.322247
\(950\) −8.77133 −0.284580
\(951\) −103.493 −3.35598
\(952\) −42.1315 −1.36549
\(953\) −1.93027 −0.0625275 −0.0312637 0.999511i \(-0.509953\pi\)
−0.0312637 + 0.999511i \(0.509953\pi\)
\(954\) 90.7877 2.93936
\(955\) 48.2788 1.56227
\(956\) −28.6118 −0.925372
\(957\) −48.3302 −1.56229
\(958\) 75.7372 2.44696
\(959\) −20.3664 −0.657667
\(960\) −88.9358 −2.87039
\(961\) −20.6571 −0.666358
\(962\) −8.92127 −0.287633
\(963\) −2.73148 −0.0880209
\(964\) −49.4030 −1.59116
\(965\) −60.1472 −1.93621
\(966\) 64.9458 2.08960
\(967\) 12.8335 0.412697 0.206349 0.978479i \(-0.433842\pi\)
0.206349 + 0.978479i \(0.433842\pi\)
\(968\) −5.59945 −0.179973
\(969\) −27.3463 −0.878489
\(970\) −31.9226 −1.02497
\(971\) −9.00915 −0.289117 −0.144559 0.989496i \(-0.546176\pi\)
−0.144559 + 0.989496i \(0.546176\pi\)
\(972\) 135.919 4.35962
\(973\) 4.04586 0.129704
\(974\) 34.5461 1.10693
\(975\) 5.27941 0.169076
\(976\) 8.27424 0.264852
\(977\) −2.46127 −0.0787430 −0.0393715 0.999225i \(-0.512536\pi\)
−0.0393715 + 0.999225i \(0.512536\pi\)
\(978\) −44.6895 −1.42901
\(979\) 28.9278 0.924537
\(980\) 7.83385 0.250243
\(981\) −30.4950 −0.973631
\(982\) 61.7752 1.97132
\(983\) −40.2839 −1.28486 −0.642428 0.766346i \(-0.722073\pi\)
−0.642428 + 0.766346i \(0.722073\pi\)
\(984\) 75.6932 2.41301
\(985\) 66.7927 2.12819
\(986\) −37.0120 −1.17870
\(987\) −93.1061 −2.96360
\(988\) 8.88322 0.282613
\(989\) 25.3718 0.806778
\(990\) −161.875 −5.14474
\(991\) 9.57445 0.304142 0.152071 0.988370i \(-0.451406\pi\)
0.152071 + 0.988370i \(0.451406\pi\)
\(992\) 7.82090 0.248314
\(993\) −28.2383 −0.896115
\(994\) −33.6580 −1.06757
\(995\) −69.3277 −2.19784
\(996\) −92.1291 −2.91922
\(997\) 9.22173 0.292055 0.146028 0.989281i \(-0.453351\pi\)
0.146028 + 0.989281i \(0.453351\pi\)
\(998\) 35.5398 1.12499
\(999\) 52.8161 1.67103
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 4003.2.a.c.1.15 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.15 179 1.1 even 1 trivial