Properties

Label 4003.2.a.c.1.10
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 1.10
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54699 q^{2} -0.919443 q^{3} +4.48717 q^{4} -0.00498874 q^{5} +2.34182 q^{6} -0.132134 q^{7} -6.33481 q^{8} -2.15462 q^{9} +O(q^{10})\) \(q-2.54699 q^{2} -0.919443 q^{3} +4.48717 q^{4} -0.00498874 q^{5} +2.34182 q^{6} -0.132134 q^{7} -6.33481 q^{8} -2.15462 q^{9} +0.0127063 q^{10} +5.60667 q^{11} -4.12570 q^{12} +4.28134 q^{13} +0.336545 q^{14} +0.00458687 q^{15} +7.16038 q^{16} -5.76338 q^{17} +5.48781 q^{18} -6.95640 q^{19} -0.0223854 q^{20} +0.121490 q^{21} -14.2801 q^{22} +6.39969 q^{23} +5.82450 q^{24} -4.99998 q^{25} -10.9045 q^{26} +4.73938 q^{27} -0.592909 q^{28} +1.11344 q^{29} -0.0116827 q^{30} +6.59694 q^{31} -5.56780 q^{32} -5.15501 q^{33} +14.6793 q^{34} +0.000659184 q^{35} -9.66817 q^{36} +3.65341 q^{37} +17.7179 q^{38} -3.93645 q^{39} +0.0316028 q^{40} -3.61946 q^{41} -0.309434 q^{42} +1.54973 q^{43} +25.1581 q^{44} +0.0107489 q^{45} -16.3000 q^{46} -0.423887 q^{47} -6.58356 q^{48} -6.98254 q^{49} +12.7349 q^{50} +5.29910 q^{51} +19.2111 q^{52} -0.698466 q^{53} -12.0712 q^{54} -0.0279702 q^{55} +0.837046 q^{56} +6.39602 q^{57} -2.83592 q^{58} +0.427629 q^{59} +0.0205821 q^{60} -8.82156 q^{61} -16.8024 q^{62} +0.284700 q^{63} -0.139594 q^{64} -0.0213585 q^{65} +13.1298 q^{66} +14.5095 q^{67} -25.8613 q^{68} -5.88415 q^{69} -0.00167894 q^{70} +11.4271 q^{71} +13.6491 q^{72} -7.78949 q^{73} -9.30520 q^{74} +4.59719 q^{75} -31.2146 q^{76} -0.740833 q^{77} +10.0261 q^{78} +8.90525 q^{79} -0.0357213 q^{80} +2.10628 q^{81} +9.21874 q^{82} +3.14039 q^{83} +0.545146 q^{84} +0.0287520 q^{85} -3.94716 q^{86} -1.02374 q^{87} -35.5172 q^{88} +9.35921 q^{89} -0.0273773 q^{90} -0.565712 q^{91} +28.7165 q^{92} -6.06551 q^{93} +1.07964 q^{94} +0.0347037 q^{95} +5.11928 q^{96} -8.80504 q^{97} +17.7845 q^{98} -12.0803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54699 −1.80100 −0.900498 0.434860i \(-0.856798\pi\)
−0.900498 + 0.434860i \(0.856798\pi\)
\(3\) −0.919443 −0.530841 −0.265420 0.964133i \(-0.585511\pi\)
−0.265420 + 0.964133i \(0.585511\pi\)
\(4\) 4.48717 2.24359
\(5\) −0.00498874 −0.00223103 −0.00111552 0.999999i \(-0.500355\pi\)
−0.00111552 + 0.999999i \(0.500355\pi\)
\(6\) 2.34182 0.956042
\(7\) −0.132134 −0.0499420 −0.0249710 0.999688i \(-0.507949\pi\)
−0.0249710 + 0.999688i \(0.507949\pi\)
\(8\) −6.33481 −2.23969
\(9\) −2.15462 −0.718208
\(10\) 0.0127063 0.00401808
\(11\) 5.60667 1.69047 0.845237 0.534392i \(-0.179459\pi\)
0.845237 + 0.534392i \(0.179459\pi\)
\(12\) −4.12570 −1.19099
\(13\) 4.28134 1.18743 0.593715 0.804675i \(-0.297661\pi\)
0.593715 + 0.804675i \(0.297661\pi\)
\(14\) 0.336545 0.0899454
\(15\) 0.00458687 0.00118432
\(16\) 7.16038 1.79009
\(17\) −5.76338 −1.39783 −0.698913 0.715207i \(-0.746332\pi\)
−0.698913 + 0.715207i \(0.746332\pi\)
\(18\) 5.48781 1.29349
\(19\) −6.95640 −1.59591 −0.797954 0.602718i \(-0.794084\pi\)
−0.797954 + 0.602718i \(0.794084\pi\)
\(20\) −0.0223854 −0.00500552
\(21\) 0.121490 0.0265113
\(22\) −14.2801 −3.04454
\(23\) 6.39969 1.33443 0.667214 0.744866i \(-0.267487\pi\)
0.667214 + 0.744866i \(0.267487\pi\)
\(24\) 5.82450 1.18892
\(25\) −4.99998 −0.999995
\(26\) −10.9045 −2.13856
\(27\) 4.73938 0.912095
\(28\) −0.592909 −0.112049
\(29\) 1.11344 0.206760 0.103380 0.994642i \(-0.467034\pi\)
0.103380 + 0.994642i \(0.467034\pi\)
\(30\) −0.0116827 −0.00213296
\(31\) 6.59694 1.18485 0.592423 0.805627i \(-0.298172\pi\)
0.592423 + 0.805627i \(0.298172\pi\)
\(32\) −5.56780 −0.984258
\(33\) −5.15501 −0.897372
\(34\) 14.6793 2.51748
\(35\) 0.000659184 0 0.000111422 0
\(36\) −9.66817 −1.61136
\(37\) 3.65341 0.600616 0.300308 0.953842i \(-0.402911\pi\)
0.300308 + 0.953842i \(0.402911\pi\)
\(38\) 17.7179 2.87423
\(39\) −3.93645 −0.630336
\(40\) 0.0316028 0.00499683
\(41\) −3.61946 −0.565265 −0.282632 0.959228i \(-0.591208\pi\)
−0.282632 + 0.959228i \(0.591208\pi\)
\(42\) −0.309434 −0.0477467
\(43\) 1.54973 0.236332 0.118166 0.992994i \(-0.462299\pi\)
0.118166 + 0.992994i \(0.462299\pi\)
\(44\) 25.1581 3.79272
\(45\) 0.0107489 0.00160235
\(46\) −16.3000 −2.40330
\(47\) −0.423887 −0.0618303 −0.0309152 0.999522i \(-0.509842\pi\)
−0.0309152 + 0.999522i \(0.509842\pi\)
\(48\) −6.58356 −0.950255
\(49\) −6.98254 −0.997506
\(50\) 12.7349 1.80099
\(51\) 5.29910 0.742023
\(52\) 19.2111 2.66410
\(53\) −0.698466 −0.0959417 −0.0479709 0.998849i \(-0.515275\pi\)
−0.0479709 + 0.998849i \(0.515275\pi\)
\(54\) −12.0712 −1.64268
\(55\) −0.0279702 −0.00377150
\(56\) 0.837046 0.111855
\(57\) 6.39602 0.847173
\(58\) −2.83592 −0.372374
\(59\) 0.427629 0.0556726 0.0278363 0.999612i \(-0.491138\pi\)
0.0278363 + 0.999612i \(0.491138\pi\)
\(60\) 0.0205821 0.00265713
\(61\) −8.82156 −1.12949 −0.564743 0.825267i \(-0.691025\pi\)
−0.564743 + 0.825267i \(0.691025\pi\)
\(62\) −16.8024 −2.13390
\(63\) 0.284700 0.0358688
\(64\) −0.139594 −0.0174493
\(65\) −0.0213585 −0.00264920
\(66\) 13.1298 1.61616
\(67\) 14.5095 1.77262 0.886308 0.463096i \(-0.153262\pi\)
0.886308 + 0.463096i \(0.153262\pi\)
\(68\) −25.8613 −3.13614
\(69\) −5.88415 −0.708368
\(70\) −0.00167894 −0.000200671 0
\(71\) 11.4271 1.35615 0.678073 0.734994i \(-0.262815\pi\)
0.678073 + 0.734994i \(0.262815\pi\)
\(72\) 13.6491 1.60857
\(73\) −7.78949 −0.911691 −0.455846 0.890059i \(-0.650663\pi\)
−0.455846 + 0.890059i \(0.650663\pi\)
\(74\) −9.30520 −1.08171
\(75\) 4.59719 0.530838
\(76\) −31.2146 −3.58056
\(77\) −0.740833 −0.0844257
\(78\) 10.0261 1.13523
\(79\) 8.90525 1.00192 0.500960 0.865471i \(-0.332981\pi\)
0.500960 + 0.865471i \(0.332981\pi\)
\(80\) −0.0357213 −0.00399376
\(81\) 2.10628 0.234031
\(82\) 9.21874 1.01804
\(83\) 3.14039 0.344702 0.172351 0.985036i \(-0.444864\pi\)
0.172351 + 0.985036i \(0.444864\pi\)
\(84\) 0.545146 0.0594803
\(85\) 0.0287520 0.00311860
\(86\) −3.94716 −0.425633
\(87\) −1.02374 −0.109757
\(88\) −35.5172 −3.78615
\(89\) 9.35921 0.992074 0.496037 0.868301i \(-0.334788\pi\)
0.496037 + 0.868301i \(0.334788\pi\)
\(90\) −0.0273773 −0.00288582
\(91\) −0.565712 −0.0593027
\(92\) 28.7165 2.99390
\(93\) −6.06551 −0.628964
\(94\) 1.07964 0.111356
\(95\) 0.0347037 0.00356053
\(96\) 5.11928 0.522484
\(97\) −8.80504 −0.894016 −0.447008 0.894530i \(-0.647510\pi\)
−0.447008 + 0.894530i \(0.647510\pi\)
\(98\) 17.7845 1.79650
\(99\) −12.0803 −1.21411
\(100\) −22.4358 −2.24358
\(101\) 3.60218 0.358431 0.179215 0.983810i \(-0.442644\pi\)
0.179215 + 0.983810i \(0.442644\pi\)
\(102\) −13.4968 −1.33638
\(103\) −1.56121 −0.153830 −0.0769151 0.997038i \(-0.524507\pi\)
−0.0769151 + 0.997038i \(0.524507\pi\)
\(104\) −27.1215 −2.65948
\(105\) −0.000606082 0 −5.91476e−5 0
\(106\) 1.77899 0.172791
\(107\) 9.60061 0.928126 0.464063 0.885802i \(-0.346391\pi\)
0.464063 + 0.885802i \(0.346391\pi\)
\(108\) 21.2664 2.04636
\(109\) −13.3335 −1.27712 −0.638559 0.769573i \(-0.720469\pi\)
−0.638559 + 0.769573i \(0.720469\pi\)
\(110\) 0.0712400 0.00679246
\(111\) −3.35910 −0.318832
\(112\) −0.946131 −0.0894010
\(113\) 5.39416 0.507440 0.253720 0.967278i \(-0.418346\pi\)
0.253720 + 0.967278i \(0.418346\pi\)
\(114\) −16.2906 −1.52576
\(115\) −0.0319264 −0.00297715
\(116\) 4.99619 0.463884
\(117\) −9.22468 −0.852822
\(118\) −1.08917 −0.100266
\(119\) 0.761540 0.0698103
\(120\) −0.0290569 −0.00265252
\(121\) 20.4347 1.85770
\(122\) 22.4685 2.03420
\(123\) 3.32789 0.300066
\(124\) 29.6016 2.65830
\(125\) 0.0498873 0.00446206
\(126\) −0.725128 −0.0645995
\(127\) −16.5934 −1.47242 −0.736211 0.676752i \(-0.763387\pi\)
−0.736211 + 0.676752i \(0.763387\pi\)
\(128\) 11.4912 1.01568
\(129\) −1.42489 −0.125455
\(130\) 0.0544000 0.00477119
\(131\) −18.2276 −1.59255 −0.796275 0.604934i \(-0.793199\pi\)
−0.796275 + 0.604934i \(0.793199\pi\)
\(132\) −23.1314 −2.01333
\(133\) 0.919179 0.0797029
\(134\) −36.9556 −3.19247
\(135\) −0.0236436 −0.00203491
\(136\) 36.5100 3.13070
\(137\) 13.6741 1.16826 0.584131 0.811660i \(-0.301436\pi\)
0.584131 + 0.811660i \(0.301436\pi\)
\(138\) 14.9869 1.27577
\(139\) 6.72038 0.570016 0.285008 0.958525i \(-0.408004\pi\)
0.285008 + 0.958525i \(0.408004\pi\)
\(140\) 0.00295787 0.000249986 0
\(141\) 0.389740 0.0328221
\(142\) −29.1047 −2.44241
\(143\) 24.0041 2.00732
\(144\) −15.4279 −1.28566
\(145\) −0.00555466 −0.000461289 0
\(146\) 19.8398 1.64195
\(147\) 6.42005 0.529517
\(148\) 16.3935 1.34753
\(149\) 8.80851 0.721621 0.360810 0.932639i \(-0.382500\pi\)
0.360810 + 0.932639i \(0.382500\pi\)
\(150\) −11.7090 −0.956037
\(151\) 3.55247 0.289096 0.144548 0.989498i \(-0.453827\pi\)
0.144548 + 0.989498i \(0.453827\pi\)
\(152\) 44.0675 3.57435
\(153\) 12.4179 1.00393
\(154\) 1.88690 0.152050
\(155\) −0.0329104 −0.00264343
\(156\) −17.6635 −1.41421
\(157\) −9.58055 −0.764612 −0.382306 0.924036i \(-0.624870\pi\)
−0.382306 + 0.924036i \(0.624870\pi\)
\(158\) −22.6816 −1.80445
\(159\) 0.642200 0.0509298
\(160\) 0.0277764 0.00219591
\(161\) −0.845618 −0.0666440
\(162\) −5.36468 −0.421489
\(163\) 18.8960 1.48005 0.740024 0.672580i \(-0.234814\pi\)
0.740024 + 0.672580i \(0.234814\pi\)
\(164\) −16.2411 −1.26822
\(165\) 0.0257170 0.00200207
\(166\) −7.99855 −0.620808
\(167\) −23.5498 −1.82233 −0.911167 0.412037i \(-0.864818\pi\)
−0.911167 + 0.412037i \(0.864818\pi\)
\(168\) −0.769616 −0.0593772
\(169\) 5.32988 0.409991
\(170\) −0.0732312 −0.00561658
\(171\) 14.9884 1.14619
\(172\) 6.95392 0.530231
\(173\) 21.1821 1.61044 0.805221 0.592974i \(-0.202046\pi\)
0.805221 + 0.592974i \(0.202046\pi\)
\(174\) 2.60747 0.197671
\(175\) 0.660668 0.0499418
\(176\) 40.1459 3.02611
\(177\) −0.393181 −0.0295533
\(178\) −23.8378 −1.78672
\(179\) −21.2330 −1.58703 −0.793515 0.608550i \(-0.791751\pi\)
−0.793515 + 0.608550i \(0.791751\pi\)
\(180\) 0.0482320 0.00359500
\(181\) −14.7425 −1.09580 −0.547900 0.836544i \(-0.684572\pi\)
−0.547900 + 0.836544i \(0.684572\pi\)
\(182\) 1.44086 0.106804
\(183\) 8.11092 0.599577
\(184\) −40.5408 −2.98871
\(185\) −0.0182259 −0.00134000
\(186\) 15.4488 1.13276
\(187\) −32.3134 −2.36299
\(188\) −1.90206 −0.138722
\(189\) −0.626235 −0.0455519
\(190\) −0.0883901 −0.00641249
\(191\) −8.37038 −0.605659 −0.302830 0.953045i \(-0.597931\pi\)
−0.302830 + 0.953045i \(0.597931\pi\)
\(192\) 0.128349 0.00926280
\(193\) 5.05503 0.363869 0.181935 0.983311i \(-0.441764\pi\)
0.181935 + 0.983311i \(0.441764\pi\)
\(194\) 22.4264 1.61012
\(195\) 0.0196379 0.00140630
\(196\) −31.3319 −2.23799
\(197\) −10.0050 −0.712829 −0.356415 0.934328i \(-0.616001\pi\)
−0.356415 + 0.934328i \(0.616001\pi\)
\(198\) 30.7683 2.18661
\(199\) −1.14529 −0.0811871 −0.0405936 0.999176i \(-0.512925\pi\)
−0.0405936 + 0.999176i \(0.512925\pi\)
\(200\) 31.6739 2.23968
\(201\) −13.3406 −0.940977
\(202\) −9.17474 −0.645532
\(203\) −0.147123 −0.0103260
\(204\) 23.7780 1.66479
\(205\) 0.0180566 0.00126112
\(206\) 3.97638 0.277047
\(207\) −13.7889 −0.958396
\(208\) 30.6560 2.12561
\(209\) −39.0022 −2.69784
\(210\) 0.00154369 0.000106525 0
\(211\) −20.8380 −1.43455 −0.717275 0.696791i \(-0.754611\pi\)
−0.717275 + 0.696791i \(0.754611\pi\)
\(212\) −3.13414 −0.215254
\(213\) −10.5066 −0.719898
\(214\) −24.4527 −1.67155
\(215\) −0.00773122 −0.000527265 0
\(216\) −30.0231 −2.04281
\(217\) −0.871682 −0.0591736
\(218\) 33.9603 2.30008
\(219\) 7.16200 0.483963
\(220\) −0.125507 −0.00846170
\(221\) −24.6750 −1.65982
\(222\) 8.55560 0.574214
\(223\) 14.8917 0.997225 0.498612 0.866825i \(-0.333843\pi\)
0.498612 + 0.866825i \(0.333843\pi\)
\(224\) 0.735698 0.0491559
\(225\) 10.7731 0.718204
\(226\) −13.7389 −0.913897
\(227\) 16.1586 1.07248 0.536240 0.844065i \(-0.319844\pi\)
0.536240 + 0.844065i \(0.319844\pi\)
\(228\) 28.7000 1.90071
\(229\) −4.63145 −0.306055 −0.153027 0.988222i \(-0.548902\pi\)
−0.153027 + 0.988222i \(0.548902\pi\)
\(230\) 0.0813163 0.00536184
\(231\) 0.681154 0.0448166
\(232\) −7.05342 −0.463080
\(233\) −10.2327 −0.670368 −0.335184 0.942153i \(-0.608799\pi\)
−0.335184 + 0.942153i \(0.608799\pi\)
\(234\) 23.4952 1.53593
\(235\) 0.00211466 0.000137946 0
\(236\) 1.91885 0.124906
\(237\) −8.18787 −0.531860
\(238\) −1.93964 −0.125728
\(239\) 21.4387 1.38675 0.693377 0.720575i \(-0.256122\pi\)
0.693377 + 0.720575i \(0.256122\pi\)
\(240\) 0.0328437 0.00212005
\(241\) −4.76917 −0.307209 −0.153605 0.988132i \(-0.549088\pi\)
−0.153605 + 0.988132i \(0.549088\pi\)
\(242\) −52.0471 −3.34571
\(243\) −16.1548 −1.03633
\(244\) −39.5839 −2.53410
\(245\) 0.0348341 0.00222547
\(246\) −8.47611 −0.540417
\(247\) −29.7827 −1.89503
\(248\) −41.7904 −2.65369
\(249\) −2.88741 −0.182982
\(250\) −0.127063 −0.00803615
\(251\) −9.18029 −0.579455 −0.289728 0.957109i \(-0.593565\pi\)
−0.289728 + 0.957109i \(0.593565\pi\)
\(252\) 1.27750 0.0804747
\(253\) 35.8809 2.25581
\(254\) 42.2631 2.65183
\(255\) −0.0264359 −0.00165548
\(256\) −28.9887 −1.81179
\(257\) 19.2786 1.20257 0.601284 0.799036i \(-0.294656\pi\)
0.601284 + 0.799036i \(0.294656\pi\)
\(258\) 3.62919 0.225943
\(259\) −0.482740 −0.0299960
\(260\) −0.0958393 −0.00594370
\(261\) −2.39904 −0.148497
\(262\) 46.4255 2.86818
\(263\) 9.27487 0.571913 0.285957 0.958243i \(-0.407689\pi\)
0.285957 + 0.958243i \(0.407689\pi\)
\(264\) 32.6560 2.00984
\(265\) 0.00348447 0.000214049 0
\(266\) −2.34114 −0.143545
\(267\) −8.60526 −0.526633
\(268\) 65.1066 3.97702
\(269\) 16.6379 1.01443 0.507215 0.861820i \(-0.330675\pi\)
0.507215 + 0.861820i \(0.330675\pi\)
\(270\) 0.0602200 0.00366487
\(271\) −7.42833 −0.451239 −0.225619 0.974216i \(-0.572441\pi\)
−0.225619 + 0.974216i \(0.572441\pi\)
\(272\) −41.2680 −2.50224
\(273\) 0.520140 0.0314803
\(274\) −34.8280 −2.10403
\(275\) −28.0332 −1.69047
\(276\) −26.4032 −1.58929
\(277\) 24.5833 1.47707 0.738534 0.674216i \(-0.235518\pi\)
0.738534 + 0.674216i \(0.235518\pi\)
\(278\) −17.1168 −1.02660
\(279\) −14.2139 −0.850966
\(280\) −0.00417581 −0.000249552 0
\(281\) 3.44674 0.205615 0.102808 0.994701i \(-0.467217\pi\)
0.102808 + 0.994701i \(0.467217\pi\)
\(282\) −0.992666 −0.0591124
\(283\) −13.1816 −0.783567 −0.391784 0.920057i \(-0.628142\pi\)
−0.391784 + 0.920057i \(0.628142\pi\)
\(284\) 51.2754 3.04263
\(285\) −0.0319081 −0.00189007
\(286\) −61.1382 −3.61517
\(287\) 0.478255 0.0282305
\(288\) 11.9965 0.706902
\(289\) 16.2166 0.953917
\(290\) 0.0141477 0.000830780 0
\(291\) 8.09573 0.474580
\(292\) −34.9528 −2.04546
\(293\) 14.2934 0.835029 0.417514 0.908670i \(-0.362901\pi\)
0.417514 + 0.908670i \(0.362901\pi\)
\(294\) −16.3518 −0.953658
\(295\) −0.00213333 −0.000124207 0
\(296\) −23.1436 −1.34520
\(297\) 26.5722 1.54187
\(298\) −22.4352 −1.29964
\(299\) 27.3992 1.58454
\(300\) 20.6284 1.19098
\(301\) −0.204773 −0.0118029
\(302\) −9.04812 −0.520661
\(303\) −3.31200 −0.190270
\(304\) −49.8105 −2.85683
\(305\) 0.0440085 0.00251992
\(306\) −31.6284 −1.80807
\(307\) −10.0890 −0.575807 −0.287903 0.957659i \(-0.592958\pi\)
−0.287903 + 0.957659i \(0.592958\pi\)
\(308\) −3.32424 −0.189416
\(309\) 1.43544 0.0816593
\(310\) 0.0838227 0.00476081
\(311\) −13.3890 −0.759221 −0.379611 0.925146i \(-0.623942\pi\)
−0.379611 + 0.925146i \(0.623942\pi\)
\(312\) 24.9367 1.41176
\(313\) 14.1061 0.797323 0.398662 0.917098i \(-0.369475\pi\)
0.398662 + 0.917098i \(0.369475\pi\)
\(314\) 24.4016 1.37706
\(315\) −0.00142029 −8.00245e−5 0
\(316\) 39.9594 2.24789
\(317\) 15.1958 0.853484 0.426742 0.904373i \(-0.359661\pi\)
0.426742 + 0.904373i \(0.359661\pi\)
\(318\) −1.63568 −0.0917243
\(319\) 6.24268 0.349523
\(320\) 0.000696400 0 3.89300e−5 0
\(321\) −8.82722 −0.492687
\(322\) 2.15378 0.120026
\(323\) 40.0924 2.23080
\(324\) 9.45123 0.525069
\(325\) −21.4066 −1.18742
\(326\) −48.1280 −2.66556
\(327\) 12.2594 0.677946
\(328\) 22.9286 1.26602
\(329\) 0.0560100 0.00308793
\(330\) −0.0655011 −0.00360572
\(331\) 33.0920 1.81890 0.909451 0.415811i \(-0.136502\pi\)
0.909451 + 0.415811i \(0.136502\pi\)
\(332\) 14.0915 0.773370
\(333\) −7.87172 −0.431367
\(334\) 59.9810 3.28202
\(335\) −0.0723841 −0.00395477
\(336\) 0.869914 0.0474577
\(337\) 9.44809 0.514670 0.257335 0.966322i \(-0.417156\pi\)
0.257335 + 0.966322i \(0.417156\pi\)
\(338\) −13.5752 −0.738391
\(339\) −4.95962 −0.269370
\(340\) 0.129015 0.00699684
\(341\) 36.9868 2.00295
\(342\) −38.1754 −2.06429
\(343\) 1.84757 0.0997595
\(344\) −9.81727 −0.529312
\(345\) 0.0293545 0.00158039
\(346\) −53.9506 −2.90040
\(347\) 29.5273 1.58511 0.792554 0.609801i \(-0.208751\pi\)
0.792554 + 0.609801i \(0.208751\pi\)
\(348\) −4.59371 −0.246249
\(349\) −22.2461 −1.19081 −0.595405 0.803426i \(-0.703008\pi\)
−0.595405 + 0.803426i \(0.703008\pi\)
\(350\) −1.68272 −0.0899450
\(351\) 20.2909 1.08305
\(352\) −31.2168 −1.66386
\(353\) 32.4164 1.72535 0.862674 0.505760i \(-0.168788\pi\)
0.862674 + 0.505760i \(0.168788\pi\)
\(354\) 1.00143 0.0532254
\(355\) −0.0570068 −0.00302561
\(356\) 41.9964 2.22580
\(357\) −0.700193 −0.0370581
\(358\) 54.0804 2.85824
\(359\) 11.1652 0.589276 0.294638 0.955609i \(-0.404801\pi\)
0.294638 + 0.955609i \(0.404801\pi\)
\(360\) −0.0680921 −0.00358877
\(361\) 29.3916 1.54692
\(362\) 37.5490 1.97353
\(363\) −18.7886 −0.986144
\(364\) −2.53845 −0.133051
\(365\) 0.0388598 0.00203401
\(366\) −20.6585 −1.07984
\(367\) 4.41283 0.230348 0.115174 0.993345i \(-0.463258\pi\)
0.115174 + 0.993345i \(0.463258\pi\)
\(368\) 45.8242 2.38875
\(369\) 7.79858 0.405978
\(370\) 0.0464213 0.00241333
\(371\) 0.0922913 0.00479153
\(372\) −27.2170 −1.41114
\(373\) −30.0648 −1.55670 −0.778348 0.627833i \(-0.783942\pi\)
−0.778348 + 0.627833i \(0.783942\pi\)
\(374\) 82.3019 4.25573
\(375\) −0.0458685 −0.00236864
\(376\) 2.68525 0.138481
\(377\) 4.76701 0.245513
\(378\) 1.59502 0.0820388
\(379\) 2.03871 0.104721 0.0523607 0.998628i \(-0.483325\pi\)
0.0523607 + 0.998628i \(0.483325\pi\)
\(380\) 0.155722 0.00798835
\(381\) 15.2566 0.781622
\(382\) 21.3193 1.09079
\(383\) 10.9931 0.561720 0.280860 0.959749i \(-0.409380\pi\)
0.280860 + 0.959749i \(0.409380\pi\)
\(384\) −10.5655 −0.539167
\(385\) 0.00369582 0.000188357 0
\(386\) −12.8751 −0.655327
\(387\) −3.33909 −0.169736
\(388\) −39.5097 −2.00580
\(389\) 33.0476 1.67558 0.837789 0.545994i \(-0.183848\pi\)
0.837789 + 0.545994i \(0.183848\pi\)
\(390\) −0.0500177 −0.00253274
\(391\) −36.8839 −1.86530
\(392\) 44.2331 2.23411
\(393\) 16.7592 0.845391
\(394\) 25.4828 1.28380
\(395\) −0.0444260 −0.00223532
\(396\) −54.2062 −2.72397
\(397\) −30.4586 −1.52867 −0.764337 0.644818i \(-0.776933\pi\)
−0.764337 + 0.644818i \(0.776933\pi\)
\(398\) 2.91703 0.146218
\(399\) −0.845133 −0.0423096
\(400\) −35.8017 −1.79009
\(401\) −9.58603 −0.478704 −0.239352 0.970933i \(-0.576935\pi\)
−0.239352 + 0.970933i \(0.576935\pi\)
\(402\) 33.9785 1.69470
\(403\) 28.2437 1.40692
\(404\) 16.1636 0.804170
\(405\) −0.0105077 −0.000522131 0
\(406\) 0.374722 0.0185971
\(407\) 20.4834 1.01533
\(408\) −33.5688 −1.66190
\(409\) 8.78053 0.434169 0.217085 0.976153i \(-0.430345\pi\)
0.217085 + 0.976153i \(0.430345\pi\)
\(410\) −0.0459899 −0.00227128
\(411\) −12.5726 −0.620161
\(412\) −7.00540 −0.345131
\(413\) −0.0565045 −0.00278040
\(414\) 35.1203 1.72607
\(415\) −0.0156666 −0.000769043 0
\(416\) −23.8377 −1.16874
\(417\) −6.17901 −0.302587
\(418\) 99.3384 4.85880
\(419\) 5.01986 0.245236 0.122618 0.992454i \(-0.460871\pi\)
0.122618 + 0.992454i \(0.460871\pi\)
\(420\) −0.00271960 −0.000132703 0
\(421\) −7.15490 −0.348708 −0.174354 0.984683i \(-0.555784\pi\)
−0.174354 + 0.984683i \(0.555784\pi\)
\(422\) 53.0743 2.58362
\(423\) 0.913318 0.0444070
\(424\) 4.42465 0.214880
\(425\) 28.8168 1.39782
\(426\) 26.7601 1.29653
\(427\) 1.16563 0.0564088
\(428\) 43.0796 2.08233
\(429\) −22.0704 −1.06557
\(430\) 0.0196914 0.000949602 0
\(431\) 15.2131 0.732791 0.366395 0.930459i \(-0.380592\pi\)
0.366395 + 0.930459i \(0.380592\pi\)
\(432\) 33.9358 1.63274
\(433\) 37.7158 1.81251 0.906254 0.422734i \(-0.138930\pi\)
0.906254 + 0.422734i \(0.138930\pi\)
\(434\) 2.22017 0.106571
\(435\) 0.00510719 0.000244871 0
\(436\) −59.8297 −2.86532
\(437\) −44.5188 −2.12962
\(438\) −18.2416 −0.871615
\(439\) −6.55294 −0.312755 −0.156377 0.987697i \(-0.549982\pi\)
−0.156377 + 0.987697i \(0.549982\pi\)
\(440\) 0.177186 0.00844702
\(441\) 15.0448 0.716417
\(442\) 62.8471 2.98933
\(443\) 37.4385 1.77876 0.889379 0.457171i \(-0.151137\pi\)
0.889379 + 0.457171i \(0.151137\pi\)
\(444\) −15.0729 −0.715326
\(445\) −0.0466907 −0.00221335
\(446\) −37.9292 −1.79600
\(447\) −8.09892 −0.383066
\(448\) 0.0184452 0.000871454 0
\(449\) 0.596286 0.0281405 0.0140702 0.999901i \(-0.495521\pi\)
0.0140702 + 0.999901i \(0.495521\pi\)
\(450\) −27.4389 −1.29348
\(451\) −20.2931 −0.955565
\(452\) 24.2045 1.13849
\(453\) −3.26630 −0.153464
\(454\) −41.1557 −1.93153
\(455\) 0.00282219 0.000132306 0
\(456\) −40.5176 −1.89741
\(457\) 36.3978 1.70262 0.851309 0.524664i \(-0.175809\pi\)
0.851309 + 0.524664i \(0.175809\pi\)
\(458\) 11.7963 0.551203
\(459\) −27.3149 −1.27495
\(460\) −0.143259 −0.00667950
\(461\) −36.4399 −1.69718 −0.848589 0.529053i \(-0.822547\pi\)
−0.848589 + 0.529053i \(0.822547\pi\)
\(462\) −1.73489 −0.0807145
\(463\) 38.0092 1.76644 0.883218 0.468962i \(-0.155372\pi\)
0.883218 + 0.468962i \(0.155372\pi\)
\(464\) 7.97263 0.370120
\(465\) 0.0302593 0.00140324
\(466\) 26.0627 1.20733
\(467\) 12.9150 0.597633 0.298816 0.954311i \(-0.403408\pi\)
0.298816 + 0.954311i \(0.403408\pi\)
\(468\) −41.3927 −1.91338
\(469\) −1.91720 −0.0885281
\(470\) −0.00538604 −0.000248439 0
\(471\) 8.80878 0.405887
\(472\) −2.70895 −0.124690
\(473\) 8.68884 0.399513
\(474\) 20.8545 0.957877
\(475\) 34.7818 1.59590
\(476\) 3.41716 0.156625
\(477\) 1.50493 0.0689061
\(478\) −54.6042 −2.49754
\(479\) 21.7375 0.993211 0.496606 0.867976i \(-0.334580\pi\)
0.496606 + 0.867976i \(0.334580\pi\)
\(480\) −0.0255388 −0.00116568
\(481\) 15.6415 0.713190
\(482\) 12.1471 0.553283
\(483\) 0.777498 0.0353774
\(484\) 91.6941 4.16791
\(485\) 0.0439261 0.00199458
\(486\) 41.1460 1.86642
\(487\) 33.8375 1.53332 0.766661 0.642052i \(-0.221917\pi\)
0.766661 + 0.642052i \(0.221917\pi\)
\(488\) 55.8829 2.52970
\(489\) −17.3738 −0.785670
\(490\) −0.0887222 −0.00400806
\(491\) −2.50531 −0.113063 −0.0565315 0.998401i \(-0.518004\pi\)
−0.0565315 + 0.998401i \(0.518004\pi\)
\(492\) 14.9328 0.673223
\(493\) −6.41717 −0.289015
\(494\) 75.8564 3.41294
\(495\) 0.0602653 0.00270872
\(496\) 47.2366 2.12099
\(497\) −1.50991 −0.0677287
\(498\) 7.35421 0.329550
\(499\) 18.9020 0.846169 0.423084 0.906090i \(-0.360947\pi\)
0.423084 + 0.906090i \(0.360947\pi\)
\(500\) 0.223853 0.0100110
\(501\) 21.6527 0.967369
\(502\) 23.3821 1.04360
\(503\) 11.4790 0.511824 0.255912 0.966700i \(-0.417624\pi\)
0.255912 + 0.966700i \(0.417624\pi\)
\(504\) −1.80352 −0.0803351
\(505\) −0.0179704 −0.000799671 0
\(506\) −91.3885 −4.06271
\(507\) −4.90052 −0.217640
\(508\) −74.4572 −3.30351
\(509\) −3.17455 −0.140709 −0.0703547 0.997522i \(-0.522413\pi\)
−0.0703547 + 0.997522i \(0.522413\pi\)
\(510\) 0.0673320 0.00298151
\(511\) 1.02926 0.0455317
\(512\) 50.8517 2.24735
\(513\) −32.9691 −1.45562
\(514\) −49.1025 −2.16582
\(515\) 0.00778845 0.000343200 0
\(516\) −6.39373 −0.281468
\(517\) −2.37659 −0.104523
\(518\) 1.22954 0.0540227
\(519\) −19.4757 −0.854889
\(520\) 0.135302 0.00593339
\(521\) 9.39862 0.411761 0.205880 0.978577i \(-0.433994\pi\)
0.205880 + 0.978577i \(0.433994\pi\)
\(522\) 6.11034 0.267442
\(523\) 19.3112 0.844421 0.422211 0.906498i \(-0.361254\pi\)
0.422211 + 0.906498i \(0.361254\pi\)
\(524\) −81.7903 −3.57303
\(525\) −0.607447 −0.0265111
\(526\) −23.6230 −1.03001
\(527\) −38.0207 −1.65621
\(528\) −36.9118 −1.60638
\(529\) 17.9560 0.780696
\(530\) −0.00887492 −0.000385502 0
\(531\) −0.921381 −0.0399845
\(532\) 4.12452 0.178820
\(533\) −15.4961 −0.671212
\(534\) 21.9175 0.948465
\(535\) −0.0478950 −0.00207068
\(536\) −91.9149 −3.97012
\(537\) 19.5226 0.842461
\(538\) −42.3766 −1.82698
\(539\) −39.1488 −1.68626
\(540\) −0.106093 −0.00456551
\(541\) −3.83761 −0.164992 −0.0824959 0.996591i \(-0.526289\pi\)
−0.0824959 + 0.996591i \(0.526289\pi\)
\(542\) 18.9199 0.812679
\(543\) 13.5549 0.581695
\(544\) 32.0894 1.37582
\(545\) 0.0665174 0.00284929
\(546\) −1.32479 −0.0566959
\(547\) −33.3107 −1.42426 −0.712131 0.702047i \(-0.752270\pi\)
−0.712131 + 0.702047i \(0.752270\pi\)
\(548\) 61.3583 2.62110
\(549\) 19.0071 0.811205
\(550\) 71.4004 3.04452
\(551\) −7.74552 −0.329970
\(552\) 37.2750 1.58653
\(553\) −1.17669 −0.0500379
\(554\) −62.6135 −2.66019
\(555\) 0.0167577 0.000711324 0
\(556\) 30.1555 1.27888
\(557\) −10.9936 −0.465813 −0.232907 0.972499i \(-0.574824\pi\)
−0.232907 + 0.972499i \(0.574824\pi\)
\(558\) 36.2028 1.53259
\(559\) 6.63493 0.280628
\(560\) 0.00472000 0.000199457 0
\(561\) 29.7103 1.25437
\(562\) −8.77883 −0.370313
\(563\) 26.2323 1.10556 0.552779 0.833328i \(-0.313567\pi\)
0.552779 + 0.833328i \(0.313567\pi\)
\(564\) 1.74883 0.0736391
\(565\) −0.0269101 −0.00113212
\(566\) 33.5735 1.41120
\(567\) −0.278311 −0.0116880
\(568\) −72.3885 −3.03735
\(569\) 1.61722 0.0677972 0.0338986 0.999425i \(-0.489208\pi\)
0.0338986 + 0.999425i \(0.489208\pi\)
\(570\) 0.0812697 0.00340401
\(571\) 31.1273 1.30264 0.651318 0.758805i \(-0.274216\pi\)
0.651318 + 0.758805i \(0.274216\pi\)
\(572\) 107.710 4.50360
\(573\) 7.69609 0.321509
\(574\) −1.21811 −0.0508430
\(575\) −31.9983 −1.33442
\(576\) 0.300773 0.0125322
\(577\) −29.8247 −1.24162 −0.620808 0.783962i \(-0.713195\pi\)
−0.620808 + 0.783962i \(0.713195\pi\)
\(578\) −41.3035 −1.71800
\(579\) −4.64781 −0.193157
\(580\) −0.0249247 −0.00103494
\(581\) −0.414953 −0.0172151
\(582\) −20.6198 −0.854717
\(583\) −3.91607 −0.162187
\(584\) 49.3450 2.04191
\(585\) 0.0460196 0.00190267
\(586\) −36.4052 −1.50388
\(587\) −7.69834 −0.317745 −0.158872 0.987299i \(-0.550786\pi\)
−0.158872 + 0.987299i \(0.550786\pi\)
\(588\) 28.8079 1.18802
\(589\) −45.8910 −1.89091
\(590\) 0.00543359 0.000223697 0
\(591\) 9.19906 0.378399
\(592\) 26.1598 1.07516
\(593\) 15.4321 0.633722 0.316861 0.948472i \(-0.397371\pi\)
0.316861 + 0.948472i \(0.397371\pi\)
\(594\) −67.6791 −2.77691
\(595\) −0.00379913 −0.000155749 0
\(596\) 39.5253 1.61902
\(597\) 1.05303 0.0430974
\(598\) −69.7857 −2.85375
\(599\) −19.0519 −0.778441 −0.389221 0.921145i \(-0.627256\pi\)
−0.389221 + 0.921145i \(0.627256\pi\)
\(600\) −29.1224 −1.18892
\(601\) 34.9430 1.42536 0.712678 0.701492i \(-0.247482\pi\)
0.712678 + 0.701492i \(0.247482\pi\)
\(602\) 0.521555 0.0212570
\(603\) −31.2625 −1.27311
\(604\) 15.9406 0.648612
\(605\) −0.101944 −0.00414460
\(606\) 8.43565 0.342675
\(607\) −6.67583 −0.270963 −0.135482 0.990780i \(-0.543258\pi\)
−0.135482 + 0.990780i \(0.543258\pi\)
\(608\) 38.7319 1.57079
\(609\) 0.135271 0.00548148
\(610\) −0.112089 −0.00453837
\(611\) −1.81481 −0.0734192
\(612\) 55.7214 2.25240
\(613\) 16.2939 0.658105 0.329052 0.944312i \(-0.393271\pi\)
0.329052 + 0.944312i \(0.393271\pi\)
\(614\) 25.6965 1.03703
\(615\) −0.0166020 −0.000669457 0
\(616\) 4.69304 0.189088
\(617\) −41.7478 −1.68070 −0.840352 0.542040i \(-0.817652\pi\)
−0.840352 + 0.542040i \(0.817652\pi\)
\(618\) −3.65605 −0.147068
\(619\) 9.76112 0.392333 0.196166 0.980571i \(-0.437151\pi\)
0.196166 + 0.980571i \(0.437151\pi\)
\(620\) −0.147675 −0.00593077
\(621\) 30.3306 1.21712
\(622\) 34.1017 1.36735
\(623\) −1.23667 −0.0495462
\(624\) −28.1865 −1.12836
\(625\) 24.9996 0.999985
\(626\) −35.9281 −1.43598
\(627\) 35.8603 1.43212
\(628\) −42.9896 −1.71547
\(629\) −21.0560 −0.839557
\(630\) 0.00361748 0.000144124 0
\(631\) −6.55693 −0.261027 −0.130514 0.991447i \(-0.541663\pi\)
−0.130514 + 0.991447i \(0.541663\pi\)
\(632\) −56.4131 −2.24399
\(633\) 19.1594 0.761517
\(634\) −38.7037 −1.53712
\(635\) 0.0827800 0.00328502
\(636\) 2.88166 0.114265
\(637\) −29.8946 −1.18447
\(638\) −15.9001 −0.629489
\(639\) −24.6211 −0.973995
\(640\) −0.0573264 −0.00226603
\(641\) 34.3272 1.35584 0.677922 0.735134i \(-0.262881\pi\)
0.677922 + 0.735134i \(0.262881\pi\)
\(642\) 22.4829 0.887328
\(643\) −2.32588 −0.0917238 −0.0458619 0.998948i \(-0.514603\pi\)
−0.0458619 + 0.998948i \(0.514603\pi\)
\(644\) −3.79443 −0.149522
\(645\) 0.00710842 0.000279894 0
\(646\) −102.115 −4.01767
\(647\) −17.8101 −0.700186 −0.350093 0.936715i \(-0.613850\pi\)
−0.350093 + 0.936715i \(0.613850\pi\)
\(648\) −13.3429 −0.524158
\(649\) 2.39758 0.0941131
\(650\) 54.5225 2.13855
\(651\) 0.801462 0.0314118
\(652\) 84.7896 3.32062
\(653\) −37.2591 −1.45806 −0.729031 0.684480i \(-0.760029\pi\)
−0.729031 + 0.684480i \(0.760029\pi\)
\(654\) −31.2246 −1.22098
\(655\) 0.0909327 0.00355303
\(656\) −25.9167 −1.01188
\(657\) 16.7834 0.654784
\(658\) −0.142657 −0.00556135
\(659\) −27.8300 −1.08410 −0.542052 0.840345i \(-0.682352\pi\)
−0.542052 + 0.840345i \(0.682352\pi\)
\(660\) 0.115397 0.00449181
\(661\) 22.0184 0.856417 0.428208 0.903680i \(-0.359145\pi\)
0.428208 + 0.903680i \(0.359145\pi\)
\(662\) −84.2851 −3.27583
\(663\) 22.6873 0.881100
\(664\) −19.8938 −0.772028
\(665\) −0.00458555 −0.000177820 0
\(666\) 20.0492 0.776891
\(667\) 7.12566 0.275906
\(668\) −105.672 −4.08857
\(669\) −13.6921 −0.529368
\(670\) 0.184362 0.00712252
\(671\) −49.4596 −1.90937
\(672\) −0.676432 −0.0260939
\(673\) 12.9910 0.500765 0.250383 0.968147i \(-0.419444\pi\)
0.250383 + 0.968147i \(0.419444\pi\)
\(674\) −24.0642 −0.926919
\(675\) −23.6968 −0.912090
\(676\) 23.9161 0.919849
\(677\) 19.2858 0.741214 0.370607 0.928790i \(-0.379150\pi\)
0.370607 + 0.928790i \(0.379150\pi\)
\(678\) 12.6321 0.485134
\(679\) 1.16345 0.0446490
\(680\) −0.182139 −0.00698470
\(681\) −14.8569 −0.569316
\(682\) −94.2052 −3.60731
\(683\) 3.84053 0.146954 0.0734769 0.997297i \(-0.476590\pi\)
0.0734769 + 0.997297i \(0.476590\pi\)
\(684\) 67.2557 2.57159
\(685\) −0.0682168 −0.00260643
\(686\) −4.70575 −0.179667
\(687\) 4.25835 0.162466
\(688\) 11.0967 0.423057
\(689\) −2.99037 −0.113924
\(690\) −0.0747657 −0.00284628
\(691\) −4.53712 −0.172600 −0.0863001 0.996269i \(-0.527504\pi\)
−0.0863001 + 0.996269i \(0.527504\pi\)
\(692\) 95.0476 3.61317
\(693\) 1.59622 0.0606352
\(694\) −75.2058 −2.85477
\(695\) −0.0335263 −0.00127172
\(696\) 6.48522 0.245822
\(697\) 20.8603 0.790142
\(698\) 56.6608 2.14464
\(699\) 9.40841 0.355859
\(700\) 2.96453 0.112049
\(701\) 16.3276 0.616686 0.308343 0.951275i \(-0.400226\pi\)
0.308343 + 0.951275i \(0.400226\pi\)
\(702\) −51.6808 −1.95057
\(703\) −25.4146 −0.958529
\(704\) −0.782659 −0.0294976
\(705\) −0.00194431 −7.32271e−5 0
\(706\) −82.5642 −3.10735
\(707\) −0.475972 −0.0179008
\(708\) −1.76427 −0.0663054
\(709\) 1.04251 0.0391523 0.0195761 0.999808i \(-0.493768\pi\)
0.0195761 + 0.999808i \(0.493768\pi\)
\(710\) 0.145196 0.00544911
\(711\) −19.1875 −0.719586
\(712\) −59.2888 −2.22194
\(713\) 42.2184 1.58109
\(714\) 1.78339 0.0667416
\(715\) −0.119750 −0.00447840
\(716\) −95.2763 −3.56064
\(717\) −19.7117 −0.736145
\(718\) −28.4376 −1.06128
\(719\) 21.2837 0.793749 0.396875 0.917873i \(-0.370095\pi\)
0.396875 + 0.917873i \(0.370095\pi\)
\(720\) 0.0769659 0.00286835
\(721\) 0.206289 0.00768259
\(722\) −74.8601 −2.78600
\(723\) 4.38498 0.163079
\(724\) −66.1520 −2.45852
\(725\) −5.56716 −0.206759
\(726\) 47.8543 1.77604
\(727\) 10.6453 0.394813 0.197406 0.980322i \(-0.436748\pi\)
0.197406 + 0.980322i \(0.436748\pi\)
\(728\) 3.58368 0.132820
\(729\) 8.53455 0.316094
\(730\) −0.0989756 −0.00366325
\(731\) −8.93170 −0.330351
\(732\) 36.3951 1.34520
\(733\) 49.2118 1.81768 0.908840 0.417145i \(-0.136969\pi\)
0.908840 + 0.417145i \(0.136969\pi\)
\(734\) −11.2394 −0.414855
\(735\) −0.0320280 −0.00118137
\(736\) −35.6322 −1.31342
\(737\) 81.3499 2.99656
\(738\) −19.8629 −0.731164
\(739\) 11.3132 0.416164 0.208082 0.978111i \(-0.433278\pi\)
0.208082 + 0.978111i \(0.433278\pi\)
\(740\) −0.0817828 −0.00300640
\(741\) 27.3835 1.00596
\(742\) −0.235065 −0.00862952
\(743\) 30.3159 1.11218 0.556091 0.831122i \(-0.312301\pi\)
0.556091 + 0.831122i \(0.312301\pi\)
\(744\) 38.4239 1.40869
\(745\) −0.0439434 −0.00160996
\(746\) 76.5748 2.80360
\(747\) −6.76636 −0.247568
\(748\) −144.996 −5.30157
\(749\) −1.26857 −0.0463525
\(750\) 0.116827 0.00426591
\(751\) 33.8317 1.23454 0.617269 0.786752i \(-0.288239\pi\)
0.617269 + 0.786752i \(0.288239\pi\)
\(752\) −3.03519 −0.110682
\(753\) 8.44076 0.307598
\(754\) −12.1415 −0.442169
\(755\) −0.0177224 −0.000644983 0
\(756\) −2.81002 −0.102200
\(757\) −32.9599 −1.19795 −0.598975 0.800768i \(-0.704425\pi\)
−0.598975 + 0.800768i \(0.704425\pi\)
\(758\) −5.19257 −0.188603
\(759\) −32.9905 −1.19748
\(760\) −0.219842 −0.00797449
\(761\) 37.8923 1.37359 0.686797 0.726849i \(-0.259016\pi\)
0.686797 + 0.726849i \(0.259016\pi\)
\(762\) −38.8586 −1.40770
\(763\) 1.76181 0.0637819
\(764\) −37.5593 −1.35885
\(765\) −0.0619498 −0.00223980
\(766\) −27.9993 −1.01165
\(767\) 1.83083 0.0661073
\(768\) 26.6535 0.961774
\(769\) −13.6451 −0.492057 −0.246028 0.969263i \(-0.579126\pi\)
−0.246028 + 0.969263i \(0.579126\pi\)
\(770\) −0.00941324 −0.000339230 0
\(771\) −17.7256 −0.638372
\(772\) 22.6828 0.816372
\(773\) 16.3568 0.588312 0.294156 0.955757i \(-0.404961\pi\)
0.294156 + 0.955757i \(0.404961\pi\)
\(774\) 8.50464 0.305693
\(775\) −32.9845 −1.18484
\(776\) 55.7783 2.00232
\(777\) 0.443852 0.0159231
\(778\) −84.1719 −3.01771
\(779\) 25.1784 0.902111
\(780\) 0.0881188 0.00315516
\(781\) 64.0679 2.29253
\(782\) 93.9429 3.35939
\(783\) 5.27701 0.188585
\(784\) −49.9976 −1.78563
\(785\) 0.0477949 0.00170587
\(786\) −42.6856 −1.52255
\(787\) 43.2127 1.54037 0.770183 0.637823i \(-0.220165\pi\)
0.770183 + 0.637823i \(0.220165\pi\)
\(788\) −44.8943 −1.59929
\(789\) −8.52772 −0.303595
\(790\) 0.113153 0.00402579
\(791\) −0.712753 −0.0253426
\(792\) 76.5262 2.71924
\(793\) −37.7681 −1.34118
\(794\) 77.5778 2.75313
\(795\) −0.00320377 −0.000113626 0
\(796\) −5.13910 −0.182150
\(797\) −41.2363 −1.46067 −0.730333 0.683091i \(-0.760635\pi\)
−0.730333 + 0.683091i \(0.760635\pi\)
\(798\) 2.15255 0.0761994
\(799\) 2.44302 0.0864280
\(800\) 27.8389 0.984253
\(801\) −20.1656 −0.712516
\(802\) 24.4156 0.862143
\(803\) −43.6731 −1.54119
\(804\) −59.8618 −2.11116
\(805\) 0.00421857 0.000148685 0
\(806\) −71.9366 −2.53386
\(807\) −15.2976 −0.538500
\(808\) −22.8192 −0.802775
\(809\) 8.31538 0.292353 0.146177 0.989259i \(-0.453303\pi\)
0.146177 + 0.989259i \(0.453303\pi\)
\(810\) 0.0267630 0.000940356 0
\(811\) 25.4116 0.892321 0.446160 0.894953i \(-0.352791\pi\)
0.446160 + 0.894953i \(0.352791\pi\)
\(812\) −0.660168 −0.0231673
\(813\) 6.82993 0.239536
\(814\) −52.1712 −1.82860
\(815\) −0.0942673 −0.00330204
\(816\) 37.9436 1.32829
\(817\) −10.7806 −0.377164
\(818\) −22.3639 −0.781937
\(819\) 1.21890 0.0425917
\(820\) 0.0810229 0.00282944
\(821\) −0.188389 −0.00657482 −0.00328741 0.999995i \(-0.501046\pi\)
−0.00328741 + 0.999995i \(0.501046\pi\)
\(822\) 32.0223 1.11691
\(823\) 2.93960 0.102468 0.0512340 0.998687i \(-0.483685\pi\)
0.0512340 + 0.998687i \(0.483685\pi\)
\(824\) 9.88994 0.344533
\(825\) 25.7749 0.897368
\(826\) 0.143917 0.00500750
\(827\) 5.22540 0.181705 0.0908526 0.995864i \(-0.471041\pi\)
0.0908526 + 0.995864i \(0.471041\pi\)
\(828\) −61.8733 −2.15025
\(829\) 12.2304 0.424779 0.212389 0.977185i \(-0.431875\pi\)
0.212389 + 0.977185i \(0.431875\pi\)
\(830\) 0.0399027 0.00138504
\(831\) −22.6030 −0.784088
\(832\) −0.597651 −0.0207198
\(833\) 40.2431 1.39434
\(834\) 15.7379 0.544959
\(835\) 0.117484 0.00406569
\(836\) −175.010 −6.05284
\(837\) 31.2654 1.08069
\(838\) −12.7856 −0.441670
\(839\) −34.6254 −1.19540 −0.597700 0.801720i \(-0.703919\pi\)
−0.597700 + 0.801720i \(0.703919\pi\)
\(840\) 0.00383942 0.000132472 0
\(841\) −27.7603 −0.957250
\(842\) 18.2235 0.628022
\(843\) −3.16908 −0.109149
\(844\) −93.5039 −3.21854
\(845\) −0.0265894 −0.000914703 0
\(846\) −2.32621 −0.0799769
\(847\) −2.70013 −0.0927774
\(848\) −5.00128 −0.171745
\(849\) 12.1198 0.415949
\(850\) −73.3961 −2.51747
\(851\) 23.3807 0.801479
\(852\) −47.1448 −1.61515
\(853\) −41.2028 −1.41076 −0.705379 0.708830i \(-0.749223\pi\)
−0.705379 + 0.708830i \(0.749223\pi\)
\(854\) −2.96885 −0.101592
\(855\) −0.0747735 −0.00255720
\(856\) −60.8181 −2.07872
\(857\) −42.5430 −1.45324 −0.726620 0.687040i \(-0.758910\pi\)
−0.726620 + 0.687040i \(0.758910\pi\)
\(858\) 56.2131 1.91908
\(859\) −11.8359 −0.403835 −0.201917 0.979403i \(-0.564717\pi\)
−0.201917 + 0.979403i \(0.564717\pi\)
\(860\) −0.0346913 −0.00118296
\(861\) −0.439728 −0.0149859
\(862\) −38.7477 −1.31975
\(863\) −23.3851 −0.796037 −0.398019 0.917377i \(-0.630302\pi\)
−0.398019 + 0.917377i \(0.630302\pi\)
\(864\) −26.3880 −0.897737
\(865\) −0.105672 −0.00359295
\(866\) −96.0620 −3.26432
\(867\) −14.9102 −0.506378
\(868\) −3.91139 −0.132761
\(869\) 49.9288 1.69372
\(870\) −0.0130080 −0.000441012 0
\(871\) 62.1200 2.10486
\(872\) 84.4652 2.86035
\(873\) 18.9715 0.642090
\(874\) 113.389 3.83544
\(875\) −0.00659182 −0.000222844 0
\(876\) 32.1371 1.08581
\(877\) 3.34805 0.113056 0.0565278 0.998401i \(-0.481997\pi\)
0.0565278 + 0.998401i \(0.481997\pi\)
\(878\) 16.6903 0.563270
\(879\) −13.1420 −0.443267
\(880\) −0.200277 −0.00675135
\(881\) −20.3096 −0.684248 −0.342124 0.939655i \(-0.611146\pi\)
−0.342124 + 0.939655i \(0.611146\pi\)
\(882\) −38.3189 −1.29026
\(883\) −53.3092 −1.79400 −0.896999 0.442033i \(-0.854257\pi\)
−0.896999 + 0.442033i \(0.854257\pi\)
\(884\) −110.721 −3.72395
\(885\) 0.00196148 6.59344e−5 0
\(886\) −95.3556 −3.20354
\(887\) 28.4212 0.954290 0.477145 0.878825i \(-0.341672\pi\)
0.477145 + 0.878825i \(0.341672\pi\)
\(888\) 21.2793 0.714085
\(889\) 2.19255 0.0735358
\(890\) 0.118921 0.00398624
\(891\) 11.8092 0.395623
\(892\) 66.8218 2.23736
\(893\) 2.94873 0.0986755
\(894\) 20.6279 0.689900
\(895\) 0.105926 0.00354072
\(896\) −1.51838 −0.0507254
\(897\) −25.1920 −0.841138
\(898\) −1.51874 −0.0506809
\(899\) 7.34528 0.244979
\(900\) 48.3406 1.61135
\(901\) 4.02553 0.134110
\(902\) 51.6864 1.72097
\(903\) 0.188277 0.00626546
\(904\) −34.1710 −1.13651
\(905\) 0.0735464 0.00244477
\(906\) 8.31924 0.276388
\(907\) −25.8031 −0.856778 −0.428389 0.903594i \(-0.640919\pi\)
−0.428389 + 0.903594i \(0.640919\pi\)
\(908\) 72.5062 2.40620
\(909\) −7.76135 −0.257428
\(910\) −0.00718810 −0.000238283 0
\(911\) 4.69496 0.155551 0.0777755 0.996971i \(-0.475218\pi\)
0.0777755 + 0.996971i \(0.475218\pi\)
\(912\) 45.7979 1.51652
\(913\) 17.6071 0.582710
\(914\) −92.7050 −3.06641
\(915\) −0.0404633 −0.00133768
\(916\) −20.7821 −0.686660
\(917\) 2.40849 0.0795352
\(918\) 69.5708 2.29618
\(919\) 0.415191 0.0136959 0.00684794 0.999977i \(-0.497820\pi\)
0.00684794 + 0.999977i \(0.497820\pi\)
\(920\) 0.202248 0.00666791
\(921\) 9.27622 0.305662
\(922\) 92.8123 3.05661
\(923\) 48.9233 1.61033
\(924\) 3.05645 0.100550
\(925\) −18.2669 −0.600613
\(926\) −96.8091 −3.18134
\(927\) 3.36381 0.110482
\(928\) −6.19940 −0.203505
\(929\) 27.8702 0.914392 0.457196 0.889366i \(-0.348854\pi\)
0.457196 + 0.889366i \(0.348854\pi\)
\(930\) −0.0770702 −0.00252723
\(931\) 48.5734 1.59193
\(932\) −45.9160 −1.50403
\(933\) 12.3104 0.403026
\(934\) −32.8943 −1.07633
\(935\) 0.161203 0.00527191
\(936\) 58.4366 1.91006
\(937\) 5.72390 0.186992 0.0934959 0.995620i \(-0.470196\pi\)
0.0934959 + 0.995620i \(0.470196\pi\)
\(938\) 4.88309 0.159439
\(939\) −12.9697 −0.423252
\(940\) 0.00948887 0.000309493 0
\(941\) 14.9870 0.488561 0.244281 0.969705i \(-0.421448\pi\)
0.244281 + 0.969705i \(0.421448\pi\)
\(942\) −22.4359 −0.731001
\(943\) −23.1634 −0.754305
\(944\) 3.06199 0.0996592
\(945\) 0.00312413 0.000101628 0
\(946\) −22.1304 −0.719521
\(947\) 17.2751 0.561366 0.280683 0.959801i \(-0.409439\pi\)
0.280683 + 0.959801i \(0.409439\pi\)
\(948\) −36.7404 −1.19327
\(949\) −33.3495 −1.08257
\(950\) −88.5891 −2.87421
\(951\) −13.9717 −0.453064
\(952\) −4.82421 −0.156354
\(953\) −21.2276 −0.687631 −0.343815 0.939037i \(-0.611719\pi\)
−0.343815 + 0.939037i \(0.611719\pi\)
\(954\) −3.83305 −0.124100
\(955\) 0.0417577 0.00135125
\(956\) 96.1991 3.11130
\(957\) −5.73979 −0.185541
\(958\) −55.3652 −1.78877
\(959\) −1.80682 −0.0583454
\(960\) −0.000640301 0 −2.06656e−5 0
\(961\) 12.5196 0.403859
\(962\) −39.8387 −1.28445
\(963\) −20.6857 −0.666588
\(964\) −21.4001 −0.689251
\(965\) −0.0252183 −0.000811804 0
\(966\) −1.98028 −0.0637145
\(967\) 17.7383 0.570426 0.285213 0.958464i \(-0.407936\pi\)
0.285213 + 0.958464i \(0.407936\pi\)
\(968\) −129.450 −4.16068
\(969\) −36.8627 −1.18420
\(970\) −0.111879 −0.00359223
\(971\) −56.1507 −1.80196 −0.900980 0.433860i \(-0.857151\pi\)
−0.900980 + 0.433860i \(0.857151\pi\)
\(972\) −72.4892 −2.32509
\(973\) −0.887993 −0.0284677
\(974\) −86.1838 −2.76151
\(975\) 19.6821 0.630333
\(976\) −63.1657 −2.02188
\(977\) −17.3861 −0.556230 −0.278115 0.960548i \(-0.589710\pi\)
−0.278115 + 0.960548i \(0.589710\pi\)
\(978\) 44.2509 1.41499
\(979\) 52.4740 1.67708
\(980\) 0.156307 0.00499303
\(981\) 28.7287 0.917236
\(982\) 6.38101 0.203626
\(983\) 42.6594 1.36062 0.680311 0.732924i \(-0.261845\pi\)
0.680311 + 0.732924i \(0.261845\pi\)
\(984\) −21.0816 −0.672055
\(985\) 0.0499126 0.00159035
\(986\) 16.3445 0.520514
\(987\) −0.0514980 −0.00163920
\(988\) −133.640 −4.25166
\(989\) 9.91781 0.315368
\(990\) −0.153495 −0.00487840
\(991\) 3.73568 0.118668 0.0593340 0.998238i \(-0.481102\pi\)
0.0593340 + 0.998238i \(0.481102\pi\)
\(992\) −36.7305 −1.16619
\(993\) −30.4262 −0.965547
\(994\) 3.84573 0.121979
\(995\) 0.00571354 0.000181131 0
\(996\) −12.9563 −0.410536
\(997\) 43.5670 1.37978 0.689890 0.723914i \(-0.257659\pi\)
0.689890 + 0.723914i \(0.257659\pi\)
\(998\) −48.1432 −1.52395
\(999\) 17.3149 0.547819
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.1.10 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.10 179 1.1 even 1 trivial