Properties

Label 4003.2.a.c.1.20
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 1.20
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32611 q^{2} +2.50152 q^{3} +3.41079 q^{4} +0.271197 q^{5} -5.81882 q^{6} +2.22103 q^{7} -3.28166 q^{8} +3.25762 q^{9} +O(q^{10})\) \(q-2.32611 q^{2} +2.50152 q^{3} +3.41079 q^{4} +0.271197 q^{5} -5.81882 q^{6} +2.22103 q^{7} -3.28166 q^{8} +3.25762 q^{9} -0.630834 q^{10} +4.90915 q^{11} +8.53218 q^{12} +4.75288 q^{13} -5.16637 q^{14} +0.678405 q^{15} +0.811925 q^{16} -3.39026 q^{17} -7.57760 q^{18} -0.868020 q^{19} +0.924996 q^{20} +5.55597 q^{21} -11.4192 q^{22} -7.92420 q^{23} -8.20916 q^{24} -4.92645 q^{25} -11.0557 q^{26} +0.644453 q^{27} +7.57549 q^{28} +6.56045 q^{29} -1.57805 q^{30} -0.772720 q^{31} +4.67470 q^{32} +12.2804 q^{33} +7.88612 q^{34} +0.602337 q^{35} +11.1111 q^{36} -3.69055 q^{37} +2.01911 q^{38} +11.8894 q^{39} -0.889977 q^{40} +9.67528 q^{41} -12.9238 q^{42} -4.85912 q^{43} +16.7441 q^{44} +0.883457 q^{45} +18.4326 q^{46} +13.0957 q^{47} +2.03105 q^{48} -2.06701 q^{49} +11.4595 q^{50} -8.48082 q^{51} +16.2111 q^{52} +12.3523 q^{53} -1.49907 q^{54} +1.33135 q^{55} -7.28868 q^{56} -2.17137 q^{57} -15.2603 q^{58} +6.25615 q^{59} +2.31390 q^{60} +9.50978 q^{61} +1.79743 q^{62} +7.23529 q^{63} -12.4977 q^{64} +1.28896 q^{65} -28.5655 q^{66} +10.5996 q^{67} -11.5635 q^{68} -19.8226 q^{69} -1.40110 q^{70} -10.1120 q^{71} -10.6904 q^{72} +13.3187 q^{73} +8.58464 q^{74} -12.3236 q^{75} -2.96064 q^{76} +10.9034 q^{77} -27.6561 q^{78} -10.5815 q^{79} +0.220192 q^{80} -8.16076 q^{81} -22.5058 q^{82} +1.26181 q^{83} +18.9503 q^{84} -0.919428 q^{85} +11.3028 q^{86} +16.4111 q^{87} -16.1102 q^{88} +0.0481094 q^{89} -2.05502 q^{90} +10.5563 q^{91} -27.0278 q^{92} -1.93298 q^{93} -30.4621 q^{94} -0.235404 q^{95} +11.6939 q^{96} -4.91163 q^{97} +4.80810 q^{98} +15.9922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32611 −1.64481 −0.822405 0.568903i \(-0.807368\pi\)
−0.822405 + 0.568903i \(0.807368\pi\)
\(3\) 2.50152 1.44426 0.722128 0.691760i \(-0.243164\pi\)
0.722128 + 0.691760i \(0.243164\pi\)
\(4\) 3.41079 1.70540
\(5\) 0.271197 0.121283 0.0606415 0.998160i \(-0.480685\pi\)
0.0606415 + 0.998160i \(0.480685\pi\)
\(6\) −5.81882 −2.37552
\(7\) 2.22103 0.839472 0.419736 0.907646i \(-0.362123\pi\)
0.419736 + 0.907646i \(0.362123\pi\)
\(8\) −3.28166 −1.16024
\(9\) 3.25762 1.08587
\(10\) −0.630834 −0.199487
\(11\) 4.90915 1.48016 0.740082 0.672516i \(-0.234786\pi\)
0.740082 + 0.672516i \(0.234786\pi\)
\(12\) 8.53218 2.46303
\(13\) 4.75288 1.31821 0.659105 0.752051i \(-0.270935\pi\)
0.659105 + 0.752051i \(0.270935\pi\)
\(14\) −5.16637 −1.38077
\(15\) 0.678405 0.175164
\(16\) 0.811925 0.202981
\(17\) −3.39026 −0.822259 −0.411130 0.911577i \(-0.634866\pi\)
−0.411130 + 0.911577i \(0.634866\pi\)
\(18\) −7.57760 −1.78606
\(19\) −0.868020 −0.199137 −0.0995687 0.995031i \(-0.531746\pi\)
−0.0995687 + 0.995031i \(0.531746\pi\)
\(20\) 0.924996 0.206835
\(21\) 5.55597 1.21241
\(22\) −11.4192 −2.43459
\(23\) −7.92420 −1.65231 −0.826155 0.563443i \(-0.809476\pi\)
−0.826155 + 0.563443i \(0.809476\pi\)
\(24\) −8.20916 −1.67569
\(25\) −4.92645 −0.985290
\(26\) −11.0557 −2.16820
\(27\) 0.644453 0.124025
\(28\) 7.57549 1.43163
\(29\) 6.56045 1.21825 0.609123 0.793076i \(-0.291522\pi\)
0.609123 + 0.793076i \(0.291522\pi\)
\(30\) −1.57805 −0.288111
\(31\) −0.772720 −0.138785 −0.0693923 0.997589i \(-0.522106\pi\)
−0.0693923 + 0.997589i \(0.522106\pi\)
\(32\) 4.67470 0.826377
\(33\) 12.2804 2.13774
\(34\) 7.88612 1.35246
\(35\) 0.602337 0.101814
\(36\) 11.1111 1.85185
\(37\) −3.69055 −0.606723 −0.303362 0.952876i \(-0.598109\pi\)
−0.303362 + 0.952876i \(0.598109\pi\)
\(38\) 2.01911 0.327543
\(39\) 11.8894 1.90383
\(40\) −0.889977 −0.140718
\(41\) 9.67528 1.51102 0.755512 0.655134i \(-0.227388\pi\)
0.755512 + 0.655134i \(0.227388\pi\)
\(42\) −12.9238 −1.99419
\(43\) −4.85912 −0.741009 −0.370504 0.928831i \(-0.620815\pi\)
−0.370504 + 0.928831i \(0.620815\pi\)
\(44\) 16.7441 2.52427
\(45\) 0.883457 0.131698
\(46\) 18.4326 2.71773
\(47\) 13.0957 1.91021 0.955104 0.296269i \(-0.0957425\pi\)
0.955104 + 0.296269i \(0.0957425\pi\)
\(48\) 2.03105 0.293157
\(49\) −2.06701 −0.295287
\(50\) 11.4595 1.62061
\(51\) −8.48082 −1.18755
\(52\) 16.2111 2.24807
\(53\) 12.3523 1.69672 0.848361 0.529419i \(-0.177590\pi\)
0.848361 + 0.529419i \(0.177590\pi\)
\(54\) −1.49907 −0.203997
\(55\) 1.33135 0.179519
\(56\) −7.28868 −0.973991
\(57\) −2.17137 −0.287605
\(58\) −15.2603 −2.00378
\(59\) 6.25615 0.814481 0.407241 0.913321i \(-0.366491\pi\)
0.407241 + 0.913321i \(0.366491\pi\)
\(60\) 2.31390 0.298723
\(61\) 9.50978 1.21760 0.608801 0.793323i \(-0.291651\pi\)
0.608801 + 0.793323i \(0.291651\pi\)
\(62\) 1.79743 0.228274
\(63\) 7.23529 0.911561
\(64\) −12.4977 −1.56221
\(65\) 1.28896 0.159876
\(66\) −28.5655 −3.51617
\(67\) 10.5996 1.29494 0.647471 0.762090i \(-0.275827\pi\)
0.647471 + 0.762090i \(0.275827\pi\)
\(68\) −11.5635 −1.40228
\(69\) −19.8226 −2.38636
\(70\) −1.40110 −0.167464
\(71\) −10.1120 −1.20007 −0.600036 0.799973i \(-0.704847\pi\)
−0.600036 + 0.799973i \(0.704847\pi\)
\(72\) −10.6904 −1.25988
\(73\) 13.3187 1.55884 0.779418 0.626504i \(-0.215515\pi\)
0.779418 + 0.626504i \(0.215515\pi\)
\(74\) 8.58464 0.997944
\(75\) −12.3236 −1.42301
\(76\) −2.96064 −0.339608
\(77\) 10.9034 1.24256
\(78\) −27.6561 −3.13144
\(79\) −10.5815 −1.19052 −0.595258 0.803534i \(-0.702950\pi\)
−0.595258 + 0.803534i \(0.702950\pi\)
\(80\) 0.220192 0.0246182
\(81\) −8.16076 −0.906751
\(82\) −22.5058 −2.48535
\(83\) 1.26181 0.138502 0.0692509 0.997599i \(-0.477939\pi\)
0.0692509 + 0.997599i \(0.477939\pi\)
\(84\) 18.9503 2.06764
\(85\) −0.919428 −0.0997260
\(86\) 11.3028 1.21882
\(87\) 16.4111 1.75946
\(88\) −16.1102 −1.71735
\(89\) 0.0481094 0.00509958 0.00254979 0.999997i \(-0.499188\pi\)
0.00254979 + 0.999997i \(0.499188\pi\)
\(90\) −2.05502 −0.216618
\(91\) 10.5563 1.10660
\(92\) −27.0278 −2.81784
\(93\) −1.93298 −0.200440
\(94\) −30.4621 −3.14193
\(95\) −0.235404 −0.0241520
\(96\) 11.6939 1.19350
\(97\) −4.91163 −0.498700 −0.249350 0.968413i \(-0.580217\pi\)
−0.249350 + 0.968413i \(0.580217\pi\)
\(98\) 4.80810 0.485691
\(99\) 15.9922 1.60727
\(100\) −16.8031 −1.68031
\(101\) −0.0247299 −0.00246071 −0.00123036 0.999999i \(-0.500392\pi\)
−0.00123036 + 0.999999i \(0.500392\pi\)
\(102\) 19.7273 1.95330
\(103\) −10.5795 −1.04243 −0.521213 0.853427i \(-0.674520\pi\)
−0.521213 + 0.853427i \(0.674520\pi\)
\(104\) −15.5973 −1.52944
\(105\) 1.50676 0.147045
\(106\) −28.7329 −2.79078
\(107\) −10.0790 −0.974370 −0.487185 0.873299i \(-0.661976\pi\)
−0.487185 + 0.873299i \(0.661976\pi\)
\(108\) 2.19810 0.211512
\(109\) −3.04268 −0.291435 −0.145718 0.989326i \(-0.546549\pi\)
−0.145718 + 0.989326i \(0.546549\pi\)
\(110\) −3.09686 −0.295274
\(111\) −9.23201 −0.876263
\(112\) 1.80331 0.170397
\(113\) 20.1706 1.89749 0.948743 0.316047i \(-0.102356\pi\)
0.948743 + 0.316047i \(0.102356\pi\)
\(114\) 5.05085 0.473056
\(115\) −2.14902 −0.200397
\(116\) 22.3763 2.07759
\(117\) 15.4831 1.43141
\(118\) −14.5525 −1.33967
\(119\) −7.52988 −0.690263
\(120\) −2.22630 −0.203232
\(121\) 13.0998 1.19089
\(122\) −22.1208 −2.00272
\(123\) 24.2029 2.18231
\(124\) −2.63559 −0.236683
\(125\) −2.69202 −0.240782
\(126\) −16.8301 −1.49934
\(127\) 5.48670 0.486866 0.243433 0.969918i \(-0.421726\pi\)
0.243433 + 0.969918i \(0.421726\pi\)
\(128\) 19.7217 1.74317
\(129\) −12.1552 −1.07021
\(130\) −2.99828 −0.262966
\(131\) 6.37401 0.556900 0.278450 0.960451i \(-0.410179\pi\)
0.278450 + 0.960451i \(0.410179\pi\)
\(132\) 41.8858 3.64569
\(133\) −1.92790 −0.167170
\(134\) −24.6557 −2.12993
\(135\) 0.174774 0.0150421
\(136\) 11.1257 0.954020
\(137\) 14.3030 1.22199 0.610994 0.791635i \(-0.290770\pi\)
0.610994 + 0.791635i \(0.290770\pi\)
\(138\) 46.1095 3.92510
\(139\) −0.576912 −0.0489331 −0.0244665 0.999701i \(-0.507789\pi\)
−0.0244665 + 0.999701i \(0.507789\pi\)
\(140\) 2.05445 0.173633
\(141\) 32.7593 2.75883
\(142\) 23.5216 1.97389
\(143\) 23.3326 1.95117
\(144\) 2.64495 0.220412
\(145\) 1.77917 0.147752
\(146\) −30.9808 −2.56399
\(147\) −5.17068 −0.426470
\(148\) −12.5877 −1.03470
\(149\) −15.9403 −1.30588 −0.652940 0.757410i \(-0.726464\pi\)
−0.652940 + 0.757410i \(0.726464\pi\)
\(150\) 28.6662 2.34058
\(151\) −7.37360 −0.600055 −0.300028 0.953931i \(-0.596996\pi\)
−0.300028 + 0.953931i \(0.596996\pi\)
\(152\) 2.84855 0.231048
\(153\) −11.0442 −0.892870
\(154\) −25.3625 −2.04377
\(155\) −0.209559 −0.0168322
\(156\) 40.5524 3.24679
\(157\) −8.69718 −0.694111 −0.347055 0.937845i \(-0.612818\pi\)
−0.347055 + 0.937845i \(0.612818\pi\)
\(158\) 24.6138 1.95817
\(159\) 30.8996 2.45050
\(160\) 1.26776 0.100225
\(161\) −17.5999 −1.38707
\(162\) 18.9828 1.49143
\(163\) −15.8668 −1.24278 −0.621391 0.783500i \(-0.713432\pi\)
−0.621391 + 0.783500i \(0.713432\pi\)
\(164\) 33.0004 2.57690
\(165\) 3.33040 0.259271
\(166\) −2.93511 −0.227809
\(167\) −0.228934 −0.0177155 −0.00885773 0.999961i \(-0.502820\pi\)
−0.00885773 + 0.999961i \(0.502820\pi\)
\(168\) −18.2328 −1.40669
\(169\) 9.58982 0.737679
\(170\) 2.13869 0.164030
\(171\) −2.82768 −0.216238
\(172\) −16.5734 −1.26371
\(173\) 1.11355 0.0846620 0.0423310 0.999104i \(-0.486522\pi\)
0.0423310 + 0.999104i \(0.486522\pi\)
\(174\) −38.1741 −2.89397
\(175\) −10.9418 −0.827123
\(176\) 3.98587 0.300446
\(177\) 15.6499 1.17632
\(178\) −0.111908 −0.00838784
\(179\) −3.83925 −0.286959 −0.143480 0.989653i \(-0.545829\pi\)
−0.143480 + 0.989653i \(0.545829\pi\)
\(180\) 3.01329 0.224597
\(181\) 8.09138 0.601428 0.300714 0.953714i \(-0.402775\pi\)
0.300714 + 0.953714i \(0.402775\pi\)
\(182\) −24.5551 −1.82015
\(183\) 23.7890 1.75853
\(184\) 26.0046 1.91708
\(185\) −1.00087 −0.0735851
\(186\) 4.49632 0.329686
\(187\) −16.6433 −1.21708
\(188\) 44.6668 3.25766
\(189\) 1.43135 0.104116
\(190\) 0.547576 0.0397254
\(191\) −13.0090 −0.941296 −0.470648 0.882321i \(-0.655980\pi\)
−0.470648 + 0.882321i \(0.655980\pi\)
\(192\) −31.2633 −2.25624
\(193\) 5.25224 0.378065 0.189032 0.981971i \(-0.439465\pi\)
0.189032 + 0.981971i \(0.439465\pi\)
\(194\) 11.4250 0.820266
\(195\) 3.22438 0.230902
\(196\) −7.05015 −0.503582
\(197\) 24.1401 1.71991 0.859955 0.510370i \(-0.170492\pi\)
0.859955 + 0.510370i \(0.170492\pi\)
\(198\) −37.1996 −2.64366
\(199\) −20.4144 −1.44714 −0.723569 0.690253i \(-0.757499\pi\)
−0.723569 + 0.690253i \(0.757499\pi\)
\(200\) 16.1670 1.14318
\(201\) 26.5150 1.87023
\(202\) 0.0575244 0.00404741
\(203\) 14.5710 1.02268
\(204\) −28.9263 −2.02525
\(205\) 2.62390 0.183261
\(206\) 24.6090 1.71459
\(207\) −25.8141 −1.79420
\(208\) 3.85898 0.267572
\(209\) −4.26124 −0.294756
\(210\) −3.50489 −0.241861
\(211\) 9.24353 0.636351 0.318175 0.948032i \(-0.396930\pi\)
0.318175 + 0.948032i \(0.396930\pi\)
\(212\) 42.1312 2.89358
\(213\) −25.2954 −1.73321
\(214\) 23.4448 1.60265
\(215\) −1.31778 −0.0898717
\(216\) −2.11488 −0.143899
\(217\) −1.71624 −0.116506
\(218\) 7.07760 0.479356
\(219\) 33.3171 2.25136
\(220\) 4.54095 0.306151
\(221\) −16.1135 −1.08391
\(222\) 21.4747 1.44129
\(223\) 11.2975 0.756537 0.378269 0.925696i \(-0.376520\pi\)
0.378269 + 0.925696i \(0.376520\pi\)
\(224\) 10.3827 0.693720
\(225\) −16.0485 −1.06990
\(226\) −46.9190 −3.12100
\(227\) 2.02413 0.134346 0.0671732 0.997741i \(-0.478602\pi\)
0.0671732 + 0.997741i \(0.478602\pi\)
\(228\) −7.40610 −0.490481
\(229\) 11.9549 0.789999 0.395000 0.918681i \(-0.370745\pi\)
0.395000 + 0.918681i \(0.370745\pi\)
\(230\) 4.99886 0.329615
\(231\) 27.2751 1.79457
\(232\) −21.5292 −1.41346
\(233\) −28.1718 −1.84560 −0.922799 0.385282i \(-0.874104\pi\)
−0.922799 + 0.385282i \(0.874104\pi\)
\(234\) −36.0154 −2.35440
\(235\) 3.55152 0.231676
\(236\) 21.3384 1.38901
\(237\) −26.4700 −1.71941
\(238\) 17.5153 1.13535
\(239\) −4.49543 −0.290785 −0.145393 0.989374i \(-0.546444\pi\)
−0.145393 + 0.989374i \(0.546444\pi\)
\(240\) 0.550815 0.0355549
\(241\) 15.3477 0.988631 0.494315 0.869283i \(-0.335419\pi\)
0.494315 + 0.869283i \(0.335419\pi\)
\(242\) −30.4715 −1.95878
\(243\) −22.3477 −1.43361
\(244\) 32.4359 2.07650
\(245\) −0.560567 −0.0358133
\(246\) −56.2987 −3.58948
\(247\) −4.12559 −0.262505
\(248\) 2.53581 0.161024
\(249\) 3.15645 0.200032
\(250\) 6.26194 0.396040
\(251\) 14.2360 0.898570 0.449285 0.893388i \(-0.351679\pi\)
0.449285 + 0.893388i \(0.351679\pi\)
\(252\) 24.6781 1.55457
\(253\) −38.9011 −2.44569
\(254\) −12.7627 −0.800801
\(255\) −2.29997 −0.144030
\(256\) −20.8794 −1.30496
\(257\) −19.4820 −1.21525 −0.607627 0.794223i \(-0.707878\pi\)
−0.607627 + 0.794223i \(0.707878\pi\)
\(258\) 28.2744 1.76028
\(259\) −8.19684 −0.509327
\(260\) 4.39639 0.272653
\(261\) 21.3715 1.32286
\(262\) −14.8267 −0.915994
\(263\) −13.5147 −0.833353 −0.416676 0.909055i \(-0.636805\pi\)
−0.416676 + 0.909055i \(0.636805\pi\)
\(264\) −40.3000 −2.48029
\(265\) 3.34991 0.205783
\(266\) 4.48451 0.274963
\(267\) 0.120347 0.00736510
\(268\) 36.1529 2.20839
\(269\) 20.2994 1.23767 0.618837 0.785519i \(-0.287604\pi\)
0.618837 + 0.785519i \(0.287604\pi\)
\(270\) −0.406543 −0.0247414
\(271\) −2.42275 −0.147171 −0.0735857 0.997289i \(-0.523444\pi\)
−0.0735857 + 0.997289i \(0.523444\pi\)
\(272\) −2.75264 −0.166903
\(273\) 26.4068 1.59821
\(274\) −33.2704 −2.00994
\(275\) −24.1847 −1.45839
\(276\) −67.6107 −4.06969
\(277\) 8.18806 0.491973 0.245986 0.969273i \(-0.420888\pi\)
0.245986 + 0.969273i \(0.420888\pi\)
\(278\) 1.34196 0.0804855
\(279\) −2.51723 −0.150703
\(280\) −1.97667 −0.118128
\(281\) 20.4467 1.21975 0.609875 0.792498i \(-0.291220\pi\)
0.609875 + 0.792498i \(0.291220\pi\)
\(282\) −76.2018 −4.53775
\(283\) −22.1221 −1.31503 −0.657513 0.753444i \(-0.728391\pi\)
−0.657513 + 0.753444i \(0.728391\pi\)
\(284\) −34.4899 −2.04660
\(285\) −0.588869 −0.0348816
\(286\) −54.2742 −3.20930
\(287\) 21.4891 1.26846
\(288\) 15.2284 0.897342
\(289\) −5.50613 −0.323890
\(290\) −4.13856 −0.243024
\(291\) −12.2866 −0.720250
\(292\) 45.4273 2.65843
\(293\) −22.8363 −1.33411 −0.667054 0.745009i \(-0.732445\pi\)
−0.667054 + 0.745009i \(0.732445\pi\)
\(294\) 12.0276 0.701462
\(295\) 1.69665 0.0987827
\(296\) 12.1111 0.703946
\(297\) 3.16372 0.183577
\(298\) 37.0789 2.14792
\(299\) −37.6627 −2.17809
\(300\) −42.0334 −2.42680
\(301\) −10.7923 −0.622056
\(302\) 17.1518 0.986976
\(303\) −0.0618624 −0.00355390
\(304\) −0.704767 −0.0404212
\(305\) 2.57902 0.147674
\(306\) 25.6900 1.46860
\(307\) 12.3684 0.705901 0.352951 0.935642i \(-0.385178\pi\)
0.352951 + 0.935642i \(0.385178\pi\)
\(308\) 37.1892 2.11905
\(309\) −26.4648 −1.50553
\(310\) 0.487458 0.0276857
\(311\) −11.1417 −0.631788 −0.315894 0.948794i \(-0.602304\pi\)
−0.315894 + 0.948794i \(0.602304\pi\)
\(312\) −39.0171 −2.20891
\(313\) −5.13903 −0.290475 −0.145238 0.989397i \(-0.546395\pi\)
−0.145238 + 0.989397i \(0.546395\pi\)
\(314\) 20.2306 1.14168
\(315\) 1.96219 0.110557
\(316\) −36.0915 −2.03030
\(317\) 15.8677 0.891217 0.445609 0.895228i \(-0.352987\pi\)
0.445609 + 0.895228i \(0.352987\pi\)
\(318\) −71.8760 −4.03060
\(319\) 32.2062 1.80320
\(320\) −3.38934 −0.189470
\(321\) −25.2128 −1.40724
\(322\) 40.9394 2.28146
\(323\) 2.94281 0.163743
\(324\) −27.8347 −1.54637
\(325\) −23.4148 −1.29882
\(326\) 36.9079 2.04414
\(327\) −7.61133 −0.420907
\(328\) −31.7510 −1.75316
\(329\) 29.0861 1.60357
\(330\) −7.74687 −0.426451
\(331\) 35.3509 1.94306 0.971530 0.236918i \(-0.0761374\pi\)
0.971530 + 0.236918i \(0.0761374\pi\)
\(332\) 4.30378 0.236200
\(333\) −12.0224 −0.658825
\(334\) 0.532526 0.0291386
\(335\) 2.87457 0.157054
\(336\) 4.51103 0.246097
\(337\) 0.272100 0.0148222 0.00741111 0.999973i \(-0.497641\pi\)
0.00741111 + 0.999973i \(0.497641\pi\)
\(338\) −22.3070 −1.21334
\(339\) 50.4572 2.74046
\(340\) −3.13598 −0.170072
\(341\) −3.79340 −0.205424
\(342\) 6.57750 0.355671
\(343\) −20.1381 −1.08736
\(344\) 15.9460 0.859750
\(345\) −5.37582 −0.289424
\(346\) −2.59025 −0.139253
\(347\) −21.4339 −1.15063 −0.575316 0.817931i \(-0.695121\pi\)
−0.575316 + 0.817931i \(0.695121\pi\)
\(348\) 55.9750 3.00057
\(349\) 15.8190 0.846771 0.423386 0.905950i \(-0.360842\pi\)
0.423386 + 0.905950i \(0.360842\pi\)
\(350\) 25.4519 1.36046
\(351\) 3.06300 0.163491
\(352\) 22.9488 1.22317
\(353\) 6.05735 0.322400 0.161200 0.986922i \(-0.448464\pi\)
0.161200 + 0.986922i \(0.448464\pi\)
\(354\) −36.4034 −1.93482
\(355\) −2.74234 −0.145548
\(356\) 0.164091 0.00869681
\(357\) −18.8362 −0.996917
\(358\) 8.93052 0.471993
\(359\) −10.3774 −0.547697 −0.273848 0.961773i \(-0.588297\pi\)
−0.273848 + 0.961773i \(0.588297\pi\)
\(360\) −2.89921 −0.152802
\(361\) −18.2465 −0.960344
\(362\) −18.8215 −0.989234
\(363\) 32.7694 1.71995
\(364\) 36.0053 1.88719
\(365\) 3.61199 0.189060
\(366\) −55.3357 −2.89245
\(367\) 30.7027 1.60267 0.801335 0.598216i \(-0.204124\pi\)
0.801335 + 0.598216i \(0.204124\pi\)
\(368\) −6.43386 −0.335388
\(369\) 31.5184 1.64078
\(370\) 2.32813 0.121034
\(371\) 27.4349 1.42435
\(372\) −6.59299 −0.341830
\(373\) −29.1844 −1.51111 −0.755557 0.655083i \(-0.772634\pi\)
−0.755557 + 0.655083i \(0.772634\pi\)
\(374\) 38.7142 2.00186
\(375\) −6.73416 −0.347751
\(376\) −42.9758 −2.21631
\(377\) 31.1810 1.60590
\(378\) −3.32948 −0.171250
\(379\) −22.3543 −1.14827 −0.574133 0.818762i \(-0.694661\pi\)
−0.574133 + 0.818762i \(0.694661\pi\)
\(380\) −0.802915 −0.0411887
\(381\) 13.7251 0.703158
\(382\) 30.2603 1.54825
\(383\) 35.6178 1.81998 0.909991 0.414627i \(-0.136088\pi\)
0.909991 + 0.414627i \(0.136088\pi\)
\(384\) 49.3343 2.51758
\(385\) 2.95696 0.150701
\(386\) −12.2173 −0.621844
\(387\) −15.8292 −0.804642
\(388\) −16.7525 −0.850481
\(389\) −0.784297 −0.0397654 −0.0198827 0.999802i \(-0.506329\pi\)
−0.0198827 + 0.999802i \(0.506329\pi\)
\(390\) −7.50026 −0.379790
\(391\) 26.8651 1.35863
\(392\) 6.78323 0.342605
\(393\) 15.9447 0.804306
\(394\) −56.1525 −2.82892
\(395\) −2.86968 −0.144389
\(396\) 54.5460 2.74104
\(397\) −21.4992 −1.07902 −0.539508 0.841981i \(-0.681390\pi\)
−0.539508 + 0.841981i \(0.681390\pi\)
\(398\) 47.4861 2.38026
\(399\) −4.82269 −0.241436
\(400\) −3.99991 −0.199996
\(401\) −27.2862 −1.36261 −0.681303 0.732002i \(-0.738586\pi\)
−0.681303 + 0.732002i \(0.738586\pi\)
\(402\) −61.6770 −3.07617
\(403\) −3.67264 −0.182947
\(404\) −0.0843485 −0.00419649
\(405\) −2.21317 −0.109973
\(406\) −33.8937 −1.68212
\(407\) −18.1175 −0.898050
\(408\) 27.8312 1.37785
\(409\) −17.6447 −0.872473 −0.436237 0.899832i \(-0.643689\pi\)
−0.436237 + 0.899832i \(0.643689\pi\)
\(410\) −6.10349 −0.301430
\(411\) 35.7793 1.76486
\(412\) −36.0844 −1.77775
\(413\) 13.8951 0.683734
\(414\) 60.0464 2.95112
\(415\) 0.342199 0.0167979
\(416\) 22.2182 1.08934
\(417\) −1.44316 −0.0706719
\(418\) 9.91212 0.484818
\(419\) 12.5452 0.612876 0.306438 0.951891i \(-0.400863\pi\)
0.306438 + 0.951891i \(0.400863\pi\)
\(420\) 5.13925 0.250770
\(421\) 40.4126 1.96959 0.984794 0.173725i \(-0.0555803\pi\)
0.984794 + 0.173725i \(0.0555803\pi\)
\(422\) −21.5015 −1.04668
\(423\) 42.6610 2.07425
\(424\) −40.5361 −1.96861
\(425\) 16.7020 0.810164
\(426\) 58.8399 2.85080
\(427\) 21.1215 1.02214
\(428\) −34.3773 −1.66169
\(429\) 58.3670 2.81799
\(430\) 3.06530 0.147822
\(431\) 28.2987 1.36310 0.681551 0.731771i \(-0.261306\pi\)
0.681551 + 0.731771i \(0.261306\pi\)
\(432\) 0.523248 0.0251748
\(433\) 14.1155 0.678346 0.339173 0.940724i \(-0.389853\pi\)
0.339173 + 0.940724i \(0.389853\pi\)
\(434\) 3.99216 0.191630
\(435\) 4.45065 0.213392
\(436\) −10.3779 −0.497013
\(437\) 6.87836 0.329037
\(438\) −77.4992 −3.70305
\(439\) −34.1947 −1.63202 −0.816012 0.578035i \(-0.803820\pi\)
−0.816012 + 0.578035i \(0.803820\pi\)
\(440\) −4.36903 −0.208285
\(441\) −6.73354 −0.320645
\(442\) 37.4818 1.78283
\(443\) −29.5320 −1.40311 −0.701553 0.712617i \(-0.747510\pi\)
−0.701553 + 0.712617i \(0.747510\pi\)
\(444\) −31.4885 −1.49438
\(445\) 0.0130471 0.000618492 0
\(446\) −26.2793 −1.24436
\(447\) −39.8750 −1.88602
\(448\) −27.7578 −1.31143
\(449\) −7.90501 −0.373060 −0.186530 0.982449i \(-0.559724\pi\)
−0.186530 + 0.982449i \(0.559724\pi\)
\(450\) 37.3307 1.75978
\(451\) 47.4974 2.23657
\(452\) 68.7976 3.23597
\(453\) −18.4452 −0.866633
\(454\) −4.70836 −0.220974
\(455\) 2.86283 0.134212
\(456\) 7.12571 0.333692
\(457\) 9.83855 0.460228 0.230114 0.973164i \(-0.426090\pi\)
0.230114 + 0.973164i \(0.426090\pi\)
\(458\) −27.8083 −1.29940
\(459\) −2.18486 −0.101981
\(460\) −7.32986 −0.341756
\(461\) −29.8511 −1.39030 −0.695152 0.718862i \(-0.744663\pi\)
−0.695152 + 0.718862i \(0.744663\pi\)
\(462\) −63.4449 −2.95172
\(463\) −38.9046 −1.80805 −0.904025 0.427480i \(-0.859402\pi\)
−0.904025 + 0.427480i \(0.859402\pi\)
\(464\) 5.32660 0.247281
\(465\) −0.524217 −0.0243100
\(466\) 65.5308 3.03566
\(467\) 10.3800 0.480330 0.240165 0.970732i \(-0.422798\pi\)
0.240165 + 0.970732i \(0.422798\pi\)
\(468\) 52.8096 2.44112
\(469\) 23.5420 1.08707
\(470\) −8.26123 −0.381062
\(471\) −21.7562 −1.00247
\(472\) −20.5306 −0.944996
\(473\) −23.8541 −1.09681
\(474\) 61.5721 2.82810
\(475\) 4.27626 0.196208
\(476\) −25.6829 −1.17717
\(477\) 40.2392 1.84243
\(478\) 10.4569 0.478286
\(479\) 11.3549 0.518817 0.259408 0.965768i \(-0.416472\pi\)
0.259408 + 0.965768i \(0.416472\pi\)
\(480\) 3.17134 0.144751
\(481\) −17.5407 −0.799789
\(482\) −35.7004 −1.62611
\(483\) −44.0266 −2.00328
\(484\) 44.6806 2.03094
\(485\) −1.33202 −0.0604838
\(486\) 51.9832 2.35801
\(487\) 10.6873 0.484287 0.242143 0.970240i \(-0.422150\pi\)
0.242143 + 0.970240i \(0.422150\pi\)
\(488\) −31.2079 −1.41272
\(489\) −39.6912 −1.79490
\(490\) 1.30394 0.0589060
\(491\) 16.0231 0.723112 0.361556 0.932350i \(-0.382246\pi\)
0.361556 + 0.932350i \(0.382246\pi\)
\(492\) 82.5512 3.72170
\(493\) −22.2416 −1.00171
\(494\) 9.59658 0.431770
\(495\) 4.33703 0.194935
\(496\) −0.627391 −0.0281707
\(497\) −22.4591 −1.00743
\(498\) −7.34226 −0.329014
\(499\) −14.3257 −0.641306 −0.320653 0.947197i \(-0.603902\pi\)
−0.320653 + 0.947197i \(0.603902\pi\)
\(500\) −9.18193 −0.410629
\(501\) −0.572685 −0.0255857
\(502\) −33.1146 −1.47798
\(503\) 31.9707 1.42550 0.712751 0.701417i \(-0.247449\pi\)
0.712751 + 0.701417i \(0.247449\pi\)
\(504\) −23.7438 −1.05763
\(505\) −0.00670666 −0.000298443 0
\(506\) 90.4883 4.02270
\(507\) 23.9892 1.06540
\(508\) 18.7140 0.830299
\(509\) −0.711031 −0.0315159 −0.0157579 0.999876i \(-0.505016\pi\)
−0.0157579 + 0.999876i \(0.505016\pi\)
\(510\) 5.34999 0.236902
\(511\) 29.5813 1.30860
\(512\) 9.12444 0.403247
\(513\) −0.559398 −0.0246980
\(514\) 45.3173 1.99886
\(515\) −2.86912 −0.126428
\(516\) −41.4589 −1.82513
\(517\) 64.2889 2.82742
\(518\) 19.0668 0.837745
\(519\) 2.78558 0.122274
\(520\) −4.22995 −0.185495
\(521\) −28.8712 −1.26487 −0.632435 0.774613i \(-0.717945\pi\)
−0.632435 + 0.774613i \(0.717945\pi\)
\(522\) −49.7124 −2.17585
\(523\) −27.9348 −1.22150 −0.610751 0.791823i \(-0.709132\pi\)
−0.610751 + 0.791823i \(0.709132\pi\)
\(524\) 21.7404 0.949735
\(525\) −27.3712 −1.19458
\(526\) 31.4367 1.37071
\(527\) 2.61972 0.114117
\(528\) 9.97074 0.433921
\(529\) 39.7930 1.73013
\(530\) −7.79226 −0.338474
\(531\) 20.3802 0.884425
\(532\) −6.57567 −0.285091
\(533\) 45.9854 1.99185
\(534\) −0.279940 −0.0121142
\(535\) −2.73338 −0.118174
\(536\) −34.7842 −1.50245
\(537\) −9.60398 −0.414442
\(538\) −47.2186 −2.03574
\(539\) −10.1473 −0.437074
\(540\) 0.596117 0.0256528
\(541\) −23.0677 −0.991757 −0.495879 0.868392i \(-0.665154\pi\)
−0.495879 + 0.868392i \(0.665154\pi\)
\(542\) 5.63558 0.242069
\(543\) 20.2408 0.868615
\(544\) −15.8484 −0.679496
\(545\) −0.825164 −0.0353461
\(546\) −61.4252 −2.62876
\(547\) 10.4165 0.445377 0.222688 0.974890i \(-0.428517\pi\)
0.222688 + 0.974890i \(0.428517\pi\)
\(548\) 48.7846 2.08397
\(549\) 30.9793 1.32216
\(550\) 56.2563 2.39878
\(551\) −5.69460 −0.242598
\(552\) 65.0510 2.76876
\(553\) −23.5020 −0.999405
\(554\) −19.0463 −0.809201
\(555\) −2.50369 −0.106276
\(556\) −1.96773 −0.0834503
\(557\) −17.6256 −0.746819 −0.373410 0.927667i \(-0.621811\pi\)
−0.373410 + 0.927667i \(0.621811\pi\)
\(558\) 5.85536 0.247877
\(559\) −23.0948 −0.976805
\(560\) 0.489053 0.0206663
\(561\) −41.6336 −1.75777
\(562\) −47.5614 −2.00626
\(563\) 15.4735 0.652128 0.326064 0.945348i \(-0.394277\pi\)
0.326064 + 0.945348i \(0.394277\pi\)
\(564\) 111.735 4.70490
\(565\) 5.47019 0.230133
\(566\) 51.4586 2.16297
\(567\) −18.1253 −0.761192
\(568\) 33.1841 1.39238
\(569\) −19.2204 −0.805763 −0.402881 0.915252i \(-0.631991\pi\)
−0.402881 + 0.915252i \(0.631991\pi\)
\(570\) 1.36978 0.0573736
\(571\) −5.21232 −0.218129 −0.109064 0.994035i \(-0.534785\pi\)
−0.109064 + 0.994035i \(0.534785\pi\)
\(572\) 79.5826 3.32752
\(573\) −32.5423 −1.35947
\(574\) −49.9861 −2.08638
\(575\) 39.0382 1.62801
\(576\) −40.7129 −1.69637
\(577\) −38.7555 −1.61341 −0.806707 0.590952i \(-0.798752\pi\)
−0.806707 + 0.590952i \(0.798752\pi\)
\(578\) 12.8079 0.532737
\(579\) 13.1386 0.546022
\(580\) 6.06839 0.251976
\(581\) 2.80252 0.116268
\(582\) 28.5799 1.18467
\(583\) 60.6394 2.51143
\(584\) −43.7075 −1.80863
\(585\) 4.19896 0.173606
\(586\) 53.1197 2.19435
\(587\) 3.06646 0.126566 0.0632832 0.997996i \(-0.479843\pi\)
0.0632832 + 0.997996i \(0.479843\pi\)
\(588\) −17.6361 −0.727301
\(589\) 0.670736 0.0276372
\(590\) −3.94659 −0.162479
\(591\) 60.3870 2.48399
\(592\) −2.99645 −0.123153
\(593\) −6.84348 −0.281028 −0.140514 0.990079i \(-0.544876\pi\)
−0.140514 + 0.990079i \(0.544876\pi\)
\(594\) −7.35916 −0.301950
\(595\) −2.04208 −0.0837171
\(596\) −54.3690 −2.22704
\(597\) −51.0671 −2.09004
\(598\) 87.6077 3.58255
\(599\) −37.0353 −1.51322 −0.756610 0.653866i \(-0.773146\pi\)
−0.756610 + 0.653866i \(0.773146\pi\)
\(600\) 40.4420 1.65104
\(601\) 38.9440 1.58856 0.794280 0.607552i \(-0.207848\pi\)
0.794280 + 0.607552i \(0.207848\pi\)
\(602\) 25.1040 1.02316
\(603\) 34.5294 1.40614
\(604\) −25.1498 −1.02333
\(605\) 3.55262 0.144434
\(606\) 0.143899 0.00584549
\(607\) 1.58674 0.0644040 0.0322020 0.999481i \(-0.489748\pi\)
0.0322020 + 0.999481i \(0.489748\pi\)
\(608\) −4.05773 −0.164563
\(609\) 36.4497 1.47701
\(610\) −5.99909 −0.242896
\(611\) 62.2424 2.51806
\(612\) −37.6695 −1.52270
\(613\) −3.52832 −0.142507 −0.0712537 0.997458i \(-0.522700\pi\)
−0.0712537 + 0.997458i \(0.522700\pi\)
\(614\) −28.7703 −1.16107
\(615\) 6.56376 0.264676
\(616\) −35.7812 −1.44167
\(617\) 35.4685 1.42791 0.713955 0.700192i \(-0.246902\pi\)
0.713955 + 0.700192i \(0.246902\pi\)
\(618\) 61.5600 2.47631
\(619\) 39.6901 1.59528 0.797640 0.603133i \(-0.206081\pi\)
0.797640 + 0.603133i \(0.206081\pi\)
\(620\) −0.714763 −0.0287056
\(621\) −5.10677 −0.204928
\(622\) 25.9169 1.03917
\(623\) 0.106852 0.00428095
\(624\) 9.65333 0.386443
\(625\) 23.9022 0.956088
\(626\) 11.9540 0.477776
\(627\) −10.6596 −0.425703
\(628\) −29.6643 −1.18373
\(629\) 12.5119 0.498884
\(630\) −4.56427 −0.181845
\(631\) 12.0235 0.478646 0.239323 0.970940i \(-0.423074\pi\)
0.239323 + 0.970940i \(0.423074\pi\)
\(632\) 34.7251 1.38129
\(633\) 23.1229 0.919053
\(634\) −36.9100 −1.46588
\(635\) 1.48797 0.0590485
\(636\) 105.392 4.17907
\(637\) −9.82424 −0.389251
\(638\) −74.9153 −2.96593
\(639\) −32.9411 −1.30313
\(640\) 5.34846 0.211416
\(641\) −19.0504 −0.752445 −0.376223 0.926529i \(-0.622777\pi\)
−0.376223 + 0.926529i \(0.622777\pi\)
\(642\) 58.6477 2.31464
\(643\) −30.9846 −1.22191 −0.610956 0.791665i \(-0.709215\pi\)
−0.610956 + 0.791665i \(0.709215\pi\)
\(644\) −60.0297 −2.36550
\(645\) −3.29645 −0.129798
\(646\) −6.84531 −0.269325
\(647\) 19.0168 0.747627 0.373814 0.927504i \(-0.378050\pi\)
0.373814 + 0.927504i \(0.378050\pi\)
\(648\) 26.7809 1.05205
\(649\) 30.7124 1.20557
\(650\) 54.4655 2.13631
\(651\) −4.29321 −0.168264
\(652\) −54.1183 −2.11944
\(653\) 28.3896 1.11097 0.555486 0.831526i \(-0.312532\pi\)
0.555486 + 0.831526i \(0.312532\pi\)
\(654\) 17.7048 0.692312
\(655\) 1.72861 0.0675424
\(656\) 7.85560 0.306710
\(657\) 43.3873 1.69270
\(658\) −67.6574 −2.63756
\(659\) −34.2699 −1.33497 −0.667483 0.744625i \(-0.732628\pi\)
−0.667483 + 0.744625i \(0.732628\pi\)
\(660\) 11.3593 0.442160
\(661\) 3.09710 0.120463 0.0602316 0.998184i \(-0.480816\pi\)
0.0602316 + 0.998184i \(0.480816\pi\)
\(662\) −82.2300 −3.19596
\(663\) −40.3083 −1.56544
\(664\) −4.14084 −0.160696
\(665\) −0.522841 −0.0202749
\(666\) 27.9655 1.08364
\(667\) −51.9863 −2.01292
\(668\) −0.780847 −0.0302119
\(669\) 28.2610 1.09263
\(670\) −6.68656 −0.258324
\(671\) 46.6850 1.80225
\(672\) 25.9725 1.00191
\(673\) 26.6957 1.02904 0.514522 0.857477i \(-0.327969\pi\)
0.514522 + 0.857477i \(0.327969\pi\)
\(674\) −0.632935 −0.0243797
\(675\) −3.17487 −0.122201
\(676\) 32.7089 1.25803
\(677\) 2.19321 0.0842917 0.0421459 0.999111i \(-0.486581\pi\)
0.0421459 + 0.999111i \(0.486581\pi\)
\(678\) −117.369 −4.50753
\(679\) −10.9089 −0.418645
\(680\) 3.01725 0.115706
\(681\) 5.06342 0.194031
\(682\) 8.82387 0.337883
\(683\) 20.0502 0.767200 0.383600 0.923499i \(-0.374684\pi\)
0.383600 + 0.923499i \(0.374684\pi\)
\(684\) −9.64464 −0.368772
\(685\) 3.87893 0.148206
\(686\) 46.8435 1.78849
\(687\) 29.9054 1.14096
\(688\) −3.94524 −0.150411
\(689\) 58.7090 2.23664
\(690\) 12.5048 0.476048
\(691\) 16.5811 0.630774 0.315387 0.948963i \(-0.397866\pi\)
0.315387 + 0.948963i \(0.397866\pi\)
\(692\) 3.79811 0.144382
\(693\) 35.5191 1.34926
\(694\) 49.8576 1.89257
\(695\) −0.156457 −0.00593474
\(696\) −53.8558 −2.04140
\(697\) −32.8017 −1.24245
\(698\) −36.7967 −1.39278
\(699\) −70.4725 −2.66552
\(700\) −37.3203 −1.41057
\(701\) −30.3337 −1.14569 −0.572844 0.819664i \(-0.694160\pi\)
−0.572844 + 0.819664i \(0.694160\pi\)
\(702\) −7.12489 −0.268912
\(703\) 3.20347 0.120821
\(704\) −61.3532 −2.31233
\(705\) 8.88422 0.334599
\(706\) −14.0901 −0.530287
\(707\) −0.0549259 −0.00206570
\(708\) 53.3786 2.00609
\(709\) −48.3777 −1.81686 −0.908431 0.418035i \(-0.862719\pi\)
−0.908431 + 0.418035i \(0.862719\pi\)
\(710\) 6.37899 0.239399
\(711\) −34.4707 −1.29275
\(712\) −0.157879 −0.00591675
\(713\) 6.12319 0.229315
\(714\) 43.8151 1.63974
\(715\) 6.32772 0.236643
\(716\) −13.0949 −0.489379
\(717\) −11.2454 −0.419968
\(718\) 24.1389 0.900856
\(719\) −24.6084 −0.917738 −0.458869 0.888504i \(-0.651745\pi\)
−0.458869 + 0.888504i \(0.651745\pi\)
\(720\) 0.717302 0.0267322
\(721\) −23.4973 −0.875087
\(722\) 42.4435 1.57958
\(723\) 38.3926 1.42784
\(724\) 27.5980 1.02567
\(725\) −32.3197 −1.20033
\(726\) −76.2252 −2.82898
\(727\) −11.0507 −0.409847 −0.204924 0.978778i \(-0.565695\pi\)
−0.204924 + 0.978778i \(0.565695\pi\)
\(728\) −34.6422 −1.28393
\(729\) −31.4210 −1.16374
\(730\) −8.40189 −0.310968
\(731\) 16.4737 0.609301
\(732\) 81.1392 2.99899
\(733\) −11.4154 −0.421639 −0.210819 0.977525i \(-0.567613\pi\)
−0.210819 + 0.977525i \(0.567613\pi\)
\(734\) −71.4180 −2.63609
\(735\) −1.40227 −0.0517236
\(736\) −37.0432 −1.36543
\(737\) 52.0348 1.91673
\(738\) −73.3154 −2.69878
\(739\) −42.8950 −1.57792 −0.788959 0.614446i \(-0.789379\pi\)
−0.788959 + 0.614446i \(0.789379\pi\)
\(740\) −3.41375 −0.125492
\(741\) −10.3203 −0.379124
\(742\) −63.8167 −2.34278
\(743\) −21.8038 −0.799905 −0.399953 0.916536i \(-0.630973\pi\)
−0.399953 + 0.916536i \(0.630973\pi\)
\(744\) 6.34338 0.232560
\(745\) −4.32296 −0.158381
\(746\) 67.8863 2.48549
\(747\) 4.11051 0.150396
\(748\) −56.7669 −2.07560
\(749\) −22.3857 −0.817956
\(750\) 15.6644 0.571983
\(751\) −6.10080 −0.222621 −0.111311 0.993786i \(-0.535505\pi\)
−0.111311 + 0.993786i \(0.535505\pi\)
\(752\) 10.6328 0.387737
\(753\) 35.6118 1.29777
\(754\) −72.5305 −2.64140
\(755\) −1.99970 −0.0727764
\(756\) 4.88204 0.177558
\(757\) −34.2410 −1.24451 −0.622255 0.782815i \(-0.713783\pi\)
−0.622255 + 0.782815i \(0.713783\pi\)
\(758\) 51.9987 1.88868
\(759\) −97.3120 −3.53220
\(760\) 0.772517 0.0280221
\(761\) −18.5644 −0.672957 −0.336479 0.941691i \(-0.609236\pi\)
−0.336479 + 0.941691i \(0.609236\pi\)
\(762\) −31.9261 −1.15656
\(763\) −6.75788 −0.244652
\(764\) −44.3709 −1.60528
\(765\) −2.99515 −0.108290
\(766\) −82.8509 −2.99352
\(767\) 29.7347 1.07366
\(768\) −52.2303 −1.88470
\(769\) 24.7904 0.893966 0.446983 0.894542i \(-0.352498\pi\)
0.446983 + 0.894542i \(0.352498\pi\)
\(770\) −6.87823 −0.247874
\(771\) −48.7347 −1.75514
\(772\) 17.9143 0.644750
\(773\) −38.7959 −1.39539 −0.697696 0.716394i \(-0.745791\pi\)
−0.697696 + 0.716394i \(0.745791\pi\)
\(774\) 36.8204 1.32348
\(775\) 3.80677 0.136743
\(776\) 16.1183 0.578613
\(777\) −20.5046 −0.735598
\(778\) 1.82436 0.0654065
\(779\) −8.39833 −0.300901
\(780\) 10.9977 0.393780
\(781\) −49.6413 −1.77631
\(782\) −62.4912 −2.23468
\(783\) 4.22790 0.151093
\(784\) −1.67826 −0.0599378
\(785\) −2.35865 −0.0841838
\(786\) −37.0892 −1.32293
\(787\) 0.957677 0.0341375 0.0170687 0.999854i \(-0.494567\pi\)
0.0170687 + 0.999854i \(0.494567\pi\)
\(788\) 82.3368 2.93313
\(789\) −33.8074 −1.20357
\(790\) 6.67520 0.237493
\(791\) 44.7995 1.59289
\(792\) −52.4809 −1.86483
\(793\) 45.1988 1.60506
\(794\) 50.0096 1.77477
\(795\) 8.37988 0.297204
\(796\) −69.6292 −2.46794
\(797\) 46.0174 1.63002 0.815009 0.579448i \(-0.196732\pi\)
0.815009 + 0.579448i \(0.196732\pi\)
\(798\) 11.2181 0.397117
\(799\) −44.3980 −1.57069
\(800\) −23.0297 −0.814222
\(801\) 0.156722 0.00553751
\(802\) 63.4706 2.24123
\(803\) 65.3835 2.30733
\(804\) 90.4374 3.18948
\(805\) −4.77304 −0.168228
\(806\) 8.54297 0.300913
\(807\) 50.7794 1.78752
\(808\) 0.0811551 0.00285503
\(809\) −24.4160 −0.858420 −0.429210 0.903205i \(-0.641208\pi\)
−0.429210 + 0.903205i \(0.641208\pi\)
\(810\) 5.14808 0.180885
\(811\) −34.1686 −1.19982 −0.599911 0.800066i \(-0.704798\pi\)
−0.599911 + 0.800066i \(0.704798\pi\)
\(812\) 49.6986 1.74408
\(813\) −6.06056 −0.212553
\(814\) 42.1433 1.47712
\(815\) −4.30302 −0.150728
\(816\) −6.88579 −0.241051
\(817\) 4.21781 0.147562
\(818\) 41.0435 1.43505
\(819\) 34.3884 1.20163
\(820\) 8.94960 0.312534
\(821\) −25.3672 −0.885320 −0.442660 0.896690i \(-0.645965\pi\)
−0.442660 + 0.896690i \(0.645965\pi\)
\(822\) −83.2266 −2.90286
\(823\) 37.5985 1.31060 0.655301 0.755368i \(-0.272542\pi\)
0.655301 + 0.755368i \(0.272542\pi\)
\(824\) 34.7182 1.20947
\(825\) −60.4986 −2.10629
\(826\) −32.3216 −1.12461
\(827\) −12.1826 −0.423629 −0.211815 0.977310i \(-0.567937\pi\)
−0.211815 + 0.977310i \(0.567937\pi\)
\(828\) −88.0464 −3.05983
\(829\) −28.0127 −0.972923 −0.486461 0.873702i \(-0.661713\pi\)
−0.486461 + 0.873702i \(0.661713\pi\)
\(830\) −0.795993 −0.0276293
\(831\) 20.4826 0.710534
\(832\) −59.4001 −2.05933
\(833\) 7.00771 0.242803
\(834\) 3.35695 0.116242
\(835\) −0.0620862 −0.00214858
\(836\) −14.5342 −0.502676
\(837\) −0.497982 −0.0172128
\(838\) −29.1816 −1.00806
\(839\) 10.1670 0.351002 0.175501 0.984479i \(-0.443845\pi\)
0.175501 + 0.984479i \(0.443845\pi\)
\(840\) −4.94468 −0.170608
\(841\) 14.0395 0.484121
\(842\) −94.0042 −3.23960
\(843\) 51.1480 1.76163
\(844\) 31.5278 1.08523
\(845\) 2.60073 0.0894678
\(846\) −99.2342 −3.41174
\(847\) 29.0950 0.999717
\(848\) 10.0292 0.344403
\(849\) −55.3391 −1.89923
\(850\) −38.8506 −1.33257
\(851\) 29.2447 1.00249
\(852\) −86.2773 −2.95581
\(853\) 7.02855 0.240653 0.120326 0.992734i \(-0.461606\pi\)
0.120326 + 0.992734i \(0.461606\pi\)
\(854\) −49.1311 −1.68123
\(855\) −0.766858 −0.0262260
\(856\) 33.0758 1.13051
\(857\) 17.7230 0.605407 0.302703 0.953085i \(-0.402111\pi\)
0.302703 + 0.953085i \(0.402111\pi\)
\(858\) −135.768 −4.63505
\(859\) −29.5077 −1.00679 −0.503395 0.864057i \(-0.667916\pi\)
−0.503395 + 0.864057i \(0.667916\pi\)
\(860\) −4.49467 −0.153267
\(861\) 53.7555 1.83198
\(862\) −65.8260 −2.24204
\(863\) 53.6261 1.82545 0.912727 0.408571i \(-0.133973\pi\)
0.912727 + 0.408571i \(0.133973\pi\)
\(864\) 3.01262 0.102491
\(865\) 0.301993 0.0102681
\(866\) −32.8341 −1.11575
\(867\) −13.7737 −0.467780
\(868\) −5.85373 −0.198688
\(869\) −51.9464 −1.76216
\(870\) −10.3527 −0.350989
\(871\) 50.3784 1.70701
\(872\) 9.98503 0.338136
\(873\) −16.0002 −0.541526
\(874\) −15.9998 −0.541202
\(875\) −5.97907 −0.202130
\(876\) 113.638 3.83946
\(877\) −39.7822 −1.34335 −0.671674 0.740847i \(-0.734425\pi\)
−0.671674 + 0.740847i \(0.734425\pi\)
\(878\) 79.5407 2.68437
\(879\) −57.1255 −1.92679
\(880\) 1.08095 0.0364390
\(881\) 41.0685 1.38363 0.691816 0.722074i \(-0.256811\pi\)
0.691816 + 0.722074i \(0.256811\pi\)
\(882\) 15.6630 0.527400
\(883\) −14.0568 −0.473048 −0.236524 0.971626i \(-0.576008\pi\)
−0.236524 + 0.971626i \(0.576008\pi\)
\(884\) −54.9598 −1.84850
\(885\) 4.24421 0.142667
\(886\) 68.6947 2.30784
\(887\) 53.7433 1.80452 0.902261 0.431190i \(-0.141906\pi\)
0.902261 + 0.431190i \(0.141906\pi\)
\(888\) 30.2963 1.01668
\(889\) 12.1861 0.408710
\(890\) −0.0303490 −0.00101730
\(891\) −40.0624 −1.34214
\(892\) 38.5335 1.29020
\(893\) −11.3674 −0.380394
\(894\) 92.7537 3.10215
\(895\) −1.04119 −0.0348032
\(896\) 43.8025 1.46334
\(897\) −94.2142 −3.14572
\(898\) 18.3879 0.613613
\(899\) −5.06939 −0.169074
\(900\) −54.7382 −1.82461
\(901\) −41.8776 −1.39514
\(902\) −110.484 −3.67872
\(903\) −26.9971 −0.898408
\(904\) −66.1930 −2.20155
\(905\) 2.19436 0.0729429
\(906\) 42.9057 1.42545
\(907\) −44.3918 −1.47401 −0.737003 0.675889i \(-0.763760\pi\)
−0.737003 + 0.675889i \(0.763760\pi\)
\(908\) 6.90390 0.229114
\(909\) −0.0805606 −0.00267203
\(910\) −6.65927 −0.220753
\(911\) 28.4411 0.942297 0.471149 0.882054i \(-0.343840\pi\)
0.471149 + 0.882054i \(0.343840\pi\)
\(912\) −1.76299 −0.0583785
\(913\) 6.19442 0.205005
\(914\) −22.8856 −0.756987
\(915\) 6.45149 0.213280
\(916\) 40.7755 1.34726
\(917\) 14.1569 0.467502
\(918\) 5.08224 0.167739
\(919\) 2.36681 0.0780738 0.0390369 0.999238i \(-0.487571\pi\)
0.0390369 + 0.999238i \(0.487571\pi\)
\(920\) 7.05235 0.232509
\(921\) 30.9398 1.01950
\(922\) 69.4370 2.28679
\(923\) −48.0610 −1.58195
\(924\) 93.0297 3.06045
\(925\) 18.1813 0.597798
\(926\) 90.4964 2.97390
\(927\) −34.4639 −1.13194
\(928\) 30.6681 1.00673
\(929\) −10.9903 −0.360580 −0.180290 0.983613i \(-0.557704\pi\)
−0.180290 + 0.983613i \(0.557704\pi\)
\(930\) 1.21939 0.0399853
\(931\) 1.79421 0.0588027
\(932\) −96.0883 −3.14748
\(933\) −27.8713 −0.912464
\(934\) −24.1451 −0.790051
\(935\) −4.51361 −0.147611
\(936\) −50.8102 −1.66078
\(937\) 13.6099 0.444617 0.222308 0.974976i \(-0.428641\pi\)
0.222308 + 0.974976i \(0.428641\pi\)
\(938\) −54.7612 −1.78802
\(939\) −12.8554 −0.419521
\(940\) 12.1135 0.395099
\(941\) 36.7911 1.19935 0.599677 0.800242i \(-0.295296\pi\)
0.599677 + 0.800242i \(0.295296\pi\)
\(942\) 50.6074 1.64888
\(943\) −76.6688 −2.49668
\(944\) 5.07953 0.165325
\(945\) 0.388178 0.0126274
\(946\) 55.4874 1.80405
\(947\) −18.9667 −0.616334 −0.308167 0.951332i \(-0.599716\pi\)
−0.308167 + 0.951332i \(0.599716\pi\)
\(948\) −90.2837 −2.93228
\(949\) 63.3021 2.05487
\(950\) −9.94705 −0.322725
\(951\) 39.6934 1.28715
\(952\) 24.7105 0.800873
\(953\) 37.2818 1.20768 0.603838 0.797107i \(-0.293637\pi\)
0.603838 + 0.797107i \(0.293637\pi\)
\(954\) −93.6009 −3.03044
\(955\) −3.52799 −0.114163
\(956\) −15.3330 −0.495904
\(957\) 80.5647 2.60429
\(958\) −26.4127 −0.853354
\(959\) 31.7674 1.02582
\(960\) −8.47852 −0.273643
\(961\) −30.4029 −0.980739
\(962\) 40.8017 1.31550
\(963\) −32.8335 −1.05804
\(964\) 52.3478 1.68601
\(965\) 1.42439 0.0458528
\(966\) 102.411 3.29501
\(967\) −13.5739 −0.436508 −0.218254 0.975892i \(-0.570036\pi\)
−0.218254 + 0.975892i \(0.570036\pi\)
\(968\) −42.9890 −1.38172
\(969\) 7.36152 0.236486
\(970\) 3.09842 0.0994843
\(971\) −22.7808 −0.731072 −0.365536 0.930797i \(-0.619114\pi\)
−0.365536 + 0.930797i \(0.619114\pi\)
\(972\) −76.2234 −2.44487
\(973\) −1.28134 −0.0410779
\(974\) −24.8598 −0.796559
\(975\) −58.5727 −1.87583
\(976\) 7.72123 0.247151
\(977\) −33.0961 −1.05884 −0.529420 0.848360i \(-0.677590\pi\)
−0.529420 + 0.848360i \(0.677590\pi\)
\(978\) 92.3261 2.95226
\(979\) 0.236176 0.00754822
\(980\) −1.91198 −0.0610759
\(981\) −9.91189 −0.316462
\(982\) −37.2715 −1.18938
\(983\) 32.3224 1.03092 0.515462 0.856913i \(-0.327620\pi\)
0.515462 + 0.856913i \(0.327620\pi\)
\(984\) −79.4259 −2.53201
\(985\) 6.54671 0.208596
\(986\) 51.7365 1.64763
\(987\) 72.7595 2.31596
\(988\) −14.0715 −0.447675
\(989\) 38.5046 1.22438
\(990\) −10.0884 −0.320631
\(991\) 2.33683 0.0742318 0.0371159 0.999311i \(-0.488183\pi\)
0.0371159 + 0.999311i \(0.488183\pi\)
\(992\) −3.61223 −0.114688
\(993\) 88.4310 2.80627
\(994\) 52.2423 1.65702
\(995\) −5.53632 −0.175513
\(996\) 10.7660 0.341134
\(997\) 13.3112 0.421568 0.210784 0.977533i \(-0.432398\pi\)
0.210784 + 0.977533i \(0.432398\pi\)
\(998\) 33.3232 1.05483
\(999\) −2.37839 −0.0752489
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.1.20 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.20 179 1.1 even 1 trivial