Properties

Label 4029.2.a.l.1.11
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.34067 q^{2} -1.00000 q^{3} -0.202611 q^{4} +1.16053 q^{5} +1.34067 q^{6} -4.05917 q^{7} +2.95297 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.34067 q^{2} -1.00000 q^{3} -0.202611 q^{4} +1.16053 q^{5} +1.34067 q^{6} -4.05917 q^{7} +2.95297 q^{8} +1.00000 q^{9} -1.55588 q^{10} +0.687421 q^{11} +0.202611 q^{12} -5.30961 q^{13} +5.44200 q^{14} -1.16053 q^{15} -3.55373 q^{16} -1.00000 q^{17} -1.34067 q^{18} +7.04145 q^{19} -0.235136 q^{20} +4.05917 q^{21} -0.921603 q^{22} +3.83710 q^{23} -2.95297 q^{24} -3.65317 q^{25} +7.11842 q^{26} -1.00000 q^{27} +0.822434 q^{28} +5.25655 q^{29} +1.55588 q^{30} -6.46598 q^{31} -1.14157 q^{32} -0.687421 q^{33} +1.34067 q^{34} -4.71078 q^{35} -0.202611 q^{36} -10.3188 q^{37} -9.44024 q^{38} +5.30961 q^{39} +3.42700 q^{40} +7.73454 q^{41} -5.44200 q^{42} -11.8132 q^{43} -0.139279 q^{44} +1.16053 q^{45} -5.14428 q^{46} -7.75967 q^{47} +3.55373 q^{48} +9.47688 q^{49} +4.89769 q^{50} +1.00000 q^{51} +1.07579 q^{52} +11.5622 q^{53} +1.34067 q^{54} +0.797771 q^{55} -11.9866 q^{56} -7.04145 q^{57} -7.04729 q^{58} -3.00997 q^{59} +0.235136 q^{60} -11.8368 q^{61} +8.66873 q^{62} -4.05917 q^{63} +8.63792 q^{64} -6.16195 q^{65} +0.921603 q^{66} +11.4342 q^{67} +0.202611 q^{68} -3.83710 q^{69} +6.31559 q^{70} +4.29205 q^{71} +2.95297 q^{72} -2.60512 q^{73} +13.8341 q^{74} +3.65317 q^{75} -1.42668 q^{76} -2.79036 q^{77} -7.11842 q^{78} +1.00000 q^{79} -4.12420 q^{80} +1.00000 q^{81} -10.3694 q^{82} -5.07294 q^{83} -0.822434 q^{84} -1.16053 q^{85} +15.8376 q^{86} -5.25655 q^{87} +2.02993 q^{88} -6.92093 q^{89} -1.55588 q^{90} +21.5526 q^{91} -0.777440 q^{92} +6.46598 q^{93} +10.4031 q^{94} +8.17180 q^{95} +1.14157 q^{96} -7.18674 q^{97} -12.7053 q^{98} +0.687421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34067 −0.947995 −0.473997 0.880526i \(-0.657189\pi\)
−0.473997 + 0.880526i \(0.657189\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.202611 −0.101306
\(5\) 1.16053 0.519004 0.259502 0.965743i \(-0.416442\pi\)
0.259502 + 0.965743i \(0.416442\pi\)
\(6\) 1.34067 0.547325
\(7\) −4.05917 −1.53422 −0.767111 0.641514i \(-0.778307\pi\)
−0.767111 + 0.641514i \(0.778307\pi\)
\(8\) 2.95297 1.04403
\(9\) 1.00000 0.333333
\(10\) −1.55588 −0.492013
\(11\) 0.687421 0.207265 0.103633 0.994616i \(-0.466953\pi\)
0.103633 + 0.994616i \(0.466953\pi\)
\(12\) 0.202611 0.0584888
\(13\) −5.30961 −1.47262 −0.736310 0.676644i \(-0.763434\pi\)
−0.736310 + 0.676644i \(0.763434\pi\)
\(14\) 5.44200 1.45444
\(15\) −1.16053 −0.299647
\(16\) −3.55373 −0.888432
\(17\) −1.00000 −0.242536
\(18\) −1.34067 −0.315998
\(19\) 7.04145 1.61542 0.807710 0.589580i \(-0.200707\pi\)
0.807710 + 0.589580i \(0.200707\pi\)
\(20\) −0.235136 −0.0525780
\(21\) 4.05917 0.885784
\(22\) −0.921603 −0.196486
\(23\) 3.83710 0.800091 0.400045 0.916495i \(-0.368994\pi\)
0.400045 + 0.916495i \(0.368994\pi\)
\(24\) −2.95297 −0.602772
\(25\) −3.65317 −0.730635
\(26\) 7.11842 1.39604
\(27\) −1.00000 −0.192450
\(28\) 0.822434 0.155425
\(29\) 5.25655 0.976118 0.488059 0.872811i \(-0.337705\pi\)
0.488059 + 0.872811i \(0.337705\pi\)
\(30\) 1.55588 0.284064
\(31\) −6.46598 −1.16132 −0.580662 0.814145i \(-0.697206\pi\)
−0.580662 + 0.814145i \(0.697206\pi\)
\(32\) −1.14157 −0.201804
\(33\) −0.687421 −0.119665
\(34\) 1.34067 0.229923
\(35\) −4.71078 −0.796268
\(36\) −0.202611 −0.0337685
\(37\) −10.3188 −1.69640 −0.848200 0.529677i \(-0.822313\pi\)
−0.848200 + 0.529677i \(0.822313\pi\)
\(38\) −9.44024 −1.53141
\(39\) 5.30961 0.850218
\(40\) 3.42700 0.541857
\(41\) 7.73454 1.20793 0.603966 0.797010i \(-0.293586\pi\)
0.603966 + 0.797010i \(0.293586\pi\)
\(42\) −5.44200 −0.839719
\(43\) −11.8132 −1.80150 −0.900749 0.434340i \(-0.856982\pi\)
−0.900749 + 0.434340i \(0.856982\pi\)
\(44\) −0.139279 −0.0209971
\(45\) 1.16053 0.173001
\(46\) −5.14428 −0.758482
\(47\) −7.75967 −1.13186 −0.565932 0.824452i \(-0.691484\pi\)
−0.565932 + 0.824452i \(0.691484\pi\)
\(48\) 3.55373 0.512936
\(49\) 9.47688 1.35384
\(50\) 4.89769 0.692638
\(51\) 1.00000 0.140028
\(52\) 1.07579 0.149185
\(53\) 11.5622 1.58819 0.794093 0.607796i \(-0.207946\pi\)
0.794093 + 0.607796i \(0.207946\pi\)
\(54\) 1.34067 0.182442
\(55\) 0.797771 0.107571
\(56\) −11.9866 −1.60178
\(57\) −7.04145 −0.932663
\(58\) −7.04729 −0.925355
\(59\) −3.00997 −0.391865 −0.195933 0.980617i \(-0.562773\pi\)
−0.195933 + 0.980617i \(0.562773\pi\)
\(60\) 0.235136 0.0303559
\(61\) −11.8368 −1.51555 −0.757774 0.652517i \(-0.773713\pi\)
−0.757774 + 0.652517i \(0.773713\pi\)
\(62\) 8.66873 1.10093
\(63\) −4.05917 −0.511408
\(64\) 8.63792 1.07974
\(65\) −6.16195 −0.764296
\(66\) 0.921603 0.113441
\(67\) 11.4342 1.39690 0.698452 0.715656i \(-0.253872\pi\)
0.698452 + 0.715656i \(0.253872\pi\)
\(68\) 0.202611 0.0245702
\(69\) −3.83710 −0.461933
\(70\) 6.31559 0.754858
\(71\) 4.29205 0.509373 0.254686 0.967024i \(-0.418028\pi\)
0.254686 + 0.967024i \(0.418028\pi\)
\(72\) 2.95297 0.348011
\(73\) −2.60512 −0.304907 −0.152453 0.988311i \(-0.548717\pi\)
−0.152453 + 0.988311i \(0.548717\pi\)
\(74\) 13.8341 1.60818
\(75\) 3.65317 0.421832
\(76\) −1.42668 −0.163651
\(77\) −2.79036 −0.317991
\(78\) −7.11842 −0.806002
\(79\) 1.00000 0.112509
\(80\) −4.12420 −0.461100
\(81\) 1.00000 0.111111
\(82\) −10.3694 −1.14511
\(83\) −5.07294 −0.556828 −0.278414 0.960461i \(-0.589809\pi\)
−0.278414 + 0.960461i \(0.589809\pi\)
\(84\) −0.822434 −0.0897349
\(85\) −1.16053 −0.125877
\(86\) 15.8376 1.70781
\(87\) −5.25655 −0.563562
\(88\) 2.02993 0.216392
\(89\) −6.92093 −0.733617 −0.366809 0.930296i \(-0.619550\pi\)
−0.366809 + 0.930296i \(0.619550\pi\)
\(90\) −1.55588 −0.164004
\(91\) 21.5526 2.25933
\(92\) −0.777440 −0.0810537
\(93\) 6.46598 0.670491
\(94\) 10.4031 1.07300
\(95\) 8.17180 0.838409
\(96\) 1.14157 0.116511
\(97\) −7.18674 −0.729703 −0.364851 0.931066i \(-0.618880\pi\)
−0.364851 + 0.931066i \(0.618880\pi\)
\(98\) −12.7053 −1.28343
\(99\) 0.687421 0.0690884
\(100\) 0.740174 0.0740174
\(101\) 14.3632 1.42919 0.714596 0.699537i \(-0.246611\pi\)
0.714596 + 0.699537i \(0.246611\pi\)
\(102\) −1.34067 −0.132746
\(103\) 16.2362 1.59980 0.799899 0.600135i \(-0.204886\pi\)
0.799899 + 0.600135i \(0.204886\pi\)
\(104\) −15.6791 −1.53746
\(105\) 4.71078 0.459725
\(106\) −15.5010 −1.50559
\(107\) −17.7659 −1.71750 −0.858749 0.512396i \(-0.828758\pi\)
−0.858749 + 0.512396i \(0.828758\pi\)
\(108\) 0.202611 0.0194963
\(109\) −12.2214 −1.17060 −0.585299 0.810817i \(-0.699023\pi\)
−0.585299 + 0.810817i \(0.699023\pi\)
\(110\) −1.06955 −0.101977
\(111\) 10.3188 0.979417
\(112\) 14.4252 1.36305
\(113\) 11.5125 1.08300 0.541502 0.840700i \(-0.317856\pi\)
0.541502 + 0.840700i \(0.317856\pi\)
\(114\) 9.44024 0.884160
\(115\) 4.45307 0.415250
\(116\) −1.06504 −0.0988862
\(117\) −5.30961 −0.490873
\(118\) 4.03537 0.371486
\(119\) 4.05917 0.372104
\(120\) −3.42700 −0.312841
\(121\) −10.5275 −0.957041
\(122\) 15.8692 1.43673
\(123\) −7.73454 −0.697400
\(124\) 1.31008 0.117649
\(125\) −10.0423 −0.898206
\(126\) 5.44200 0.484812
\(127\) 3.35833 0.298004 0.149002 0.988837i \(-0.452394\pi\)
0.149002 + 0.988837i \(0.452394\pi\)
\(128\) −9.29743 −0.821785
\(129\) 11.8132 1.04010
\(130\) 8.26113 0.724549
\(131\) 14.5046 1.26727 0.633635 0.773632i \(-0.281562\pi\)
0.633635 + 0.773632i \(0.281562\pi\)
\(132\) 0.139279 0.0121227
\(133\) −28.5825 −2.47841
\(134\) −15.3294 −1.32426
\(135\) −1.16053 −0.0998824
\(136\) −2.95297 −0.253215
\(137\) −16.8949 −1.44343 −0.721716 0.692190i \(-0.756646\pi\)
−0.721716 + 0.692190i \(0.756646\pi\)
\(138\) 5.14428 0.437910
\(139\) 12.1040 1.02665 0.513326 0.858194i \(-0.328413\pi\)
0.513326 + 0.858194i \(0.328413\pi\)
\(140\) 0.954458 0.0806664
\(141\) 7.75967 0.653482
\(142\) −5.75421 −0.482883
\(143\) −3.64993 −0.305223
\(144\) −3.55373 −0.296144
\(145\) 6.10038 0.506609
\(146\) 3.49260 0.289050
\(147\) −9.47688 −0.781640
\(148\) 2.09070 0.171855
\(149\) −3.03517 −0.248651 −0.124326 0.992241i \(-0.539677\pi\)
−0.124326 + 0.992241i \(0.539677\pi\)
\(150\) −4.89769 −0.399895
\(151\) −11.8078 −0.960903 −0.480452 0.877021i \(-0.659527\pi\)
−0.480452 + 0.877021i \(0.659527\pi\)
\(152\) 20.7932 1.68655
\(153\) −1.00000 −0.0808452
\(154\) 3.74094 0.301454
\(155\) −7.50395 −0.602732
\(156\) −1.07579 −0.0861318
\(157\) −8.10733 −0.647036 −0.323518 0.946222i \(-0.604866\pi\)
−0.323518 + 0.946222i \(0.604866\pi\)
\(158\) −1.34067 −0.106658
\(159\) −11.5622 −0.916940
\(160\) −1.32483 −0.104737
\(161\) −15.5755 −1.22752
\(162\) −1.34067 −0.105333
\(163\) −6.17262 −0.483477 −0.241739 0.970341i \(-0.577718\pi\)
−0.241739 + 0.970341i \(0.577718\pi\)
\(164\) −1.56710 −0.122370
\(165\) −0.797771 −0.0621064
\(166\) 6.80113 0.527870
\(167\) −20.3368 −1.57371 −0.786854 0.617139i \(-0.788292\pi\)
−0.786854 + 0.617139i \(0.788292\pi\)
\(168\) 11.9866 0.924787
\(169\) 15.1919 1.16861
\(170\) 1.55588 0.119331
\(171\) 7.04145 0.538473
\(172\) 2.39349 0.182502
\(173\) 16.1657 1.22906 0.614528 0.788895i \(-0.289347\pi\)
0.614528 + 0.788895i \(0.289347\pi\)
\(174\) 7.04729 0.534254
\(175\) 14.8289 1.12096
\(176\) −2.44291 −0.184141
\(177\) 3.00997 0.226243
\(178\) 9.27866 0.695465
\(179\) 3.23273 0.241625 0.120813 0.992675i \(-0.461450\pi\)
0.120813 + 0.992675i \(0.461450\pi\)
\(180\) −0.235136 −0.0175260
\(181\) −10.3861 −0.771996 −0.385998 0.922500i \(-0.626143\pi\)
−0.385998 + 0.922500i \(0.626143\pi\)
\(182\) −28.8949 −2.14183
\(183\) 11.8368 0.875002
\(184\) 11.3308 0.835321
\(185\) −11.9753 −0.880438
\(186\) −8.66873 −0.635622
\(187\) −0.687421 −0.0502692
\(188\) 1.57220 0.114664
\(189\) 4.05917 0.295261
\(190\) −10.9557 −0.794808
\(191\) 13.0022 0.940803 0.470401 0.882453i \(-0.344109\pi\)
0.470401 + 0.882453i \(0.344109\pi\)
\(192\) −8.63792 −0.623388
\(193\) 3.38016 0.243309 0.121655 0.992572i \(-0.461180\pi\)
0.121655 + 0.992572i \(0.461180\pi\)
\(194\) 9.63503 0.691755
\(195\) 6.16195 0.441266
\(196\) −1.92012 −0.137152
\(197\) −3.49753 −0.249189 −0.124594 0.992208i \(-0.539763\pi\)
−0.124594 + 0.992208i \(0.539763\pi\)
\(198\) −0.921603 −0.0654954
\(199\) 11.2955 0.800715 0.400357 0.916359i \(-0.368886\pi\)
0.400357 + 0.916359i \(0.368886\pi\)
\(200\) −10.7877 −0.762806
\(201\) −11.4342 −0.806503
\(202\) −19.2563 −1.35487
\(203\) −21.3373 −1.49758
\(204\) −0.202611 −0.0141856
\(205\) 8.97615 0.626922
\(206\) −21.7673 −1.51660
\(207\) 3.83710 0.266697
\(208\) 18.8689 1.30832
\(209\) 4.84044 0.334820
\(210\) −6.31559 −0.435817
\(211\) 18.1639 1.25046 0.625228 0.780442i \(-0.285006\pi\)
0.625228 + 0.780442i \(0.285006\pi\)
\(212\) −2.34262 −0.160892
\(213\) −4.29205 −0.294086
\(214\) 23.8182 1.62818
\(215\) −13.7096 −0.934985
\(216\) −2.95297 −0.200924
\(217\) 26.2465 1.78173
\(218\) 16.3848 1.10972
\(219\) 2.60512 0.176038
\(220\) −0.161637 −0.0108976
\(221\) 5.30961 0.357163
\(222\) −13.8341 −0.928482
\(223\) 4.09022 0.273901 0.136951 0.990578i \(-0.456270\pi\)
0.136951 + 0.990578i \(0.456270\pi\)
\(224\) 4.63384 0.309612
\(225\) −3.65317 −0.243545
\(226\) −15.4344 −1.02668
\(227\) 24.9126 1.65351 0.826755 0.562562i \(-0.190184\pi\)
0.826755 + 0.562562i \(0.190184\pi\)
\(228\) 1.42668 0.0944840
\(229\) 27.3467 1.80712 0.903560 0.428461i \(-0.140944\pi\)
0.903560 + 0.428461i \(0.140944\pi\)
\(230\) −5.97008 −0.393655
\(231\) 2.79036 0.183592
\(232\) 15.5224 1.01910
\(233\) 12.8636 0.842723 0.421361 0.906893i \(-0.361552\pi\)
0.421361 + 0.906893i \(0.361552\pi\)
\(234\) 7.11842 0.465345
\(235\) −9.00532 −0.587442
\(236\) 0.609854 0.0396981
\(237\) −1.00000 −0.0649570
\(238\) −5.44200 −0.352752
\(239\) 9.75104 0.630742 0.315371 0.948968i \(-0.397871\pi\)
0.315371 + 0.948968i \(0.397871\pi\)
\(240\) 4.12420 0.266216
\(241\) −3.15488 −0.203224 −0.101612 0.994824i \(-0.532400\pi\)
−0.101612 + 0.994824i \(0.532400\pi\)
\(242\) 14.1138 0.907270
\(243\) −1.00000 −0.0641500
\(244\) 2.39827 0.153534
\(245\) 10.9982 0.702648
\(246\) 10.3694 0.661132
\(247\) −37.3873 −2.37890
\(248\) −19.0938 −1.21246
\(249\) 5.07294 0.321485
\(250\) 13.4633 0.851495
\(251\) 6.60429 0.416859 0.208430 0.978037i \(-0.433165\pi\)
0.208430 + 0.978037i \(0.433165\pi\)
\(252\) 0.822434 0.0518085
\(253\) 2.63770 0.165831
\(254\) −4.50241 −0.282506
\(255\) 1.16053 0.0726751
\(256\) −4.81108 −0.300692
\(257\) −13.9554 −0.870514 −0.435257 0.900306i \(-0.643343\pi\)
−0.435257 + 0.900306i \(0.643343\pi\)
\(258\) −15.8376 −0.986005
\(259\) 41.8858 2.60265
\(260\) 1.24848 0.0774275
\(261\) 5.25655 0.325373
\(262\) −19.4458 −1.20137
\(263\) 25.7056 1.58508 0.792538 0.609823i \(-0.208759\pi\)
0.792538 + 0.609823i \(0.208759\pi\)
\(264\) −2.02993 −0.124934
\(265\) 13.4182 0.824275
\(266\) 38.3196 2.34952
\(267\) 6.92093 0.423554
\(268\) −2.31669 −0.141514
\(269\) 15.0361 0.916767 0.458383 0.888755i \(-0.348429\pi\)
0.458383 + 0.888755i \(0.348429\pi\)
\(270\) 1.55588 0.0946880
\(271\) 11.8915 0.722357 0.361178 0.932497i \(-0.382375\pi\)
0.361178 + 0.932497i \(0.382375\pi\)
\(272\) 3.55373 0.215476
\(273\) −21.5526 −1.30442
\(274\) 22.6505 1.36837
\(275\) −2.51127 −0.151435
\(276\) 0.777440 0.0467964
\(277\) 30.7994 1.85056 0.925278 0.379289i \(-0.123831\pi\)
0.925278 + 0.379289i \(0.123831\pi\)
\(278\) −16.2275 −0.973261
\(279\) −6.46598 −0.387108
\(280\) −13.9108 −0.831329
\(281\) 9.74076 0.581085 0.290543 0.956862i \(-0.406164\pi\)
0.290543 + 0.956862i \(0.406164\pi\)
\(282\) −10.4031 −0.619498
\(283\) 26.2209 1.55867 0.779335 0.626607i \(-0.215557\pi\)
0.779335 + 0.626607i \(0.215557\pi\)
\(284\) −0.869617 −0.0516023
\(285\) −8.17180 −0.484056
\(286\) 4.89335 0.289350
\(287\) −31.3958 −1.85324
\(288\) −1.14157 −0.0672678
\(289\) 1.00000 0.0588235
\(290\) −8.17858 −0.480263
\(291\) 7.18674 0.421294
\(292\) 0.527827 0.0308888
\(293\) −25.6696 −1.49963 −0.749816 0.661647i \(-0.769858\pi\)
−0.749816 + 0.661647i \(0.769858\pi\)
\(294\) 12.7053 0.740990
\(295\) −3.49316 −0.203380
\(296\) −30.4711 −1.77110
\(297\) −0.687421 −0.0398882
\(298\) 4.06916 0.235720
\(299\) −20.3735 −1.17823
\(300\) −0.740174 −0.0427340
\(301\) 47.9519 2.76390
\(302\) 15.8303 0.910931
\(303\) −14.3632 −0.825144
\(304\) −25.0234 −1.43519
\(305\) −13.7370 −0.786576
\(306\) 1.34067 0.0766408
\(307\) 15.0301 0.857811 0.428906 0.903349i \(-0.358899\pi\)
0.428906 + 0.903349i \(0.358899\pi\)
\(308\) 0.565358 0.0322143
\(309\) −16.2362 −0.923644
\(310\) 10.0603 0.571387
\(311\) −23.4034 −1.32709 −0.663543 0.748138i \(-0.730948\pi\)
−0.663543 + 0.748138i \(0.730948\pi\)
\(312\) 15.6791 0.887655
\(313\) −5.99411 −0.338807 −0.169404 0.985547i \(-0.554184\pi\)
−0.169404 + 0.985547i \(0.554184\pi\)
\(314\) 10.8692 0.613387
\(315\) −4.71078 −0.265423
\(316\) −0.202611 −0.0113978
\(317\) 2.48476 0.139558 0.0697789 0.997562i \(-0.477771\pi\)
0.0697789 + 0.997562i \(0.477771\pi\)
\(318\) 15.5010 0.869254
\(319\) 3.61346 0.202315
\(320\) 10.0246 0.560390
\(321\) 17.7659 0.991598
\(322\) 20.8815 1.16368
\(323\) −7.04145 −0.391797
\(324\) −0.202611 −0.0112562
\(325\) 19.3969 1.07595
\(326\) 8.27544 0.458334
\(327\) 12.2214 0.675845
\(328\) 22.8399 1.26112
\(329\) 31.4978 1.73653
\(330\) 1.06955 0.0588766
\(331\) −13.2932 −0.730660 −0.365330 0.930878i \(-0.619044\pi\)
−0.365330 + 0.930878i \(0.619044\pi\)
\(332\) 1.02783 0.0564098
\(333\) −10.3188 −0.565466
\(334\) 27.2649 1.49187
\(335\) 13.2697 0.724999
\(336\) −14.4252 −0.786958
\(337\) −16.1094 −0.877535 −0.438768 0.898601i \(-0.644585\pi\)
−0.438768 + 0.898601i \(0.644585\pi\)
\(338\) −20.3673 −1.10784
\(339\) −11.5125 −0.625273
\(340\) 0.235136 0.0127520
\(341\) −4.44485 −0.240702
\(342\) −9.44024 −0.510470
\(343\) −10.0541 −0.542869
\(344\) −34.8840 −1.88082
\(345\) −4.45307 −0.239745
\(346\) −21.6728 −1.16514
\(347\) 8.63515 0.463559 0.231780 0.972768i \(-0.425545\pi\)
0.231780 + 0.972768i \(0.425545\pi\)
\(348\) 1.06504 0.0570920
\(349\) −19.7336 −1.05631 −0.528157 0.849147i \(-0.677117\pi\)
−0.528157 + 0.849147i \(0.677117\pi\)
\(350\) −19.8806 −1.06266
\(351\) 5.30961 0.283406
\(352\) −0.784741 −0.0418268
\(353\) 20.0675 1.06809 0.534043 0.845457i \(-0.320672\pi\)
0.534043 + 0.845457i \(0.320672\pi\)
\(354\) −4.03537 −0.214478
\(355\) 4.98105 0.264366
\(356\) 1.40226 0.0743195
\(357\) −4.05917 −0.214834
\(358\) −4.33401 −0.229060
\(359\) 0.383076 0.0202180 0.0101090 0.999949i \(-0.496782\pi\)
0.0101090 + 0.999949i \(0.496782\pi\)
\(360\) 3.42700 0.180619
\(361\) 30.5820 1.60958
\(362\) 13.9244 0.731848
\(363\) 10.5275 0.552548
\(364\) −4.36680 −0.228883
\(365\) −3.02332 −0.158248
\(366\) −15.8692 −0.829498
\(367\) 29.8216 1.55667 0.778337 0.627846i \(-0.216063\pi\)
0.778337 + 0.627846i \(0.216063\pi\)
\(368\) −13.6360 −0.710826
\(369\) 7.73454 0.402644
\(370\) 16.0548 0.834651
\(371\) −46.9328 −2.43663
\(372\) −1.31008 −0.0679245
\(373\) −3.20080 −0.165731 −0.0828655 0.996561i \(-0.526407\pi\)
−0.0828655 + 0.996561i \(0.526407\pi\)
\(374\) 0.921603 0.0476549
\(375\) 10.0423 0.518580
\(376\) −22.9141 −1.18170
\(377\) −27.9102 −1.43745
\(378\) −5.44200 −0.279906
\(379\) −7.99675 −0.410765 −0.205383 0.978682i \(-0.565844\pi\)
−0.205383 + 0.978682i \(0.565844\pi\)
\(380\) −1.65570 −0.0849356
\(381\) −3.35833 −0.172053
\(382\) −17.4316 −0.891876
\(383\) 35.3913 1.80841 0.904205 0.427099i \(-0.140464\pi\)
0.904205 + 0.427099i \(0.140464\pi\)
\(384\) 9.29743 0.474458
\(385\) −3.23829 −0.165039
\(386\) −4.53167 −0.230656
\(387\) −11.8132 −0.600499
\(388\) 1.45611 0.0739230
\(389\) 7.34691 0.372503 0.186252 0.982502i \(-0.440366\pi\)
0.186252 + 0.982502i \(0.440366\pi\)
\(390\) −8.26113 −0.418318
\(391\) −3.83710 −0.194051
\(392\) 27.9849 1.41345
\(393\) −14.5046 −0.731658
\(394\) 4.68903 0.236230
\(395\) 1.16053 0.0583925
\(396\) −0.139279 −0.00699904
\(397\) 3.24085 0.162653 0.0813267 0.996687i \(-0.474084\pi\)
0.0813267 + 0.996687i \(0.474084\pi\)
\(398\) −15.1435 −0.759073
\(399\) 28.5825 1.43091
\(400\) 12.9824 0.649119
\(401\) 12.8012 0.639263 0.319632 0.947542i \(-0.396441\pi\)
0.319632 + 0.947542i \(0.396441\pi\)
\(402\) 15.3294 0.764561
\(403\) 34.3318 1.71019
\(404\) −2.91015 −0.144785
\(405\) 1.16053 0.0576671
\(406\) 28.6062 1.41970
\(407\) −7.09335 −0.351605
\(408\) 2.95297 0.146194
\(409\) 27.0191 1.33601 0.668004 0.744158i \(-0.267149\pi\)
0.668004 + 0.744158i \(0.267149\pi\)
\(410\) −12.0340 −0.594319
\(411\) 16.8949 0.833365
\(412\) −3.28963 −0.162069
\(413\) 12.2180 0.601208
\(414\) −5.14428 −0.252827
\(415\) −5.88729 −0.288996
\(416\) 6.06130 0.297180
\(417\) −12.1040 −0.592738
\(418\) −6.48942 −0.317408
\(419\) 11.2668 0.550420 0.275210 0.961384i \(-0.411253\pi\)
0.275210 + 0.961384i \(0.411253\pi\)
\(420\) −0.954458 −0.0465728
\(421\) −18.5205 −0.902633 −0.451317 0.892364i \(-0.649046\pi\)
−0.451317 + 0.892364i \(0.649046\pi\)
\(422\) −24.3518 −1.18543
\(423\) −7.75967 −0.377288
\(424\) 34.1427 1.65812
\(425\) 3.65317 0.177205
\(426\) 5.75421 0.278792
\(427\) 48.0477 2.32519
\(428\) 3.59958 0.173992
\(429\) 3.64993 0.176221
\(430\) 18.3800 0.886361
\(431\) 3.19388 0.153844 0.0769219 0.997037i \(-0.475491\pi\)
0.0769219 + 0.997037i \(0.475491\pi\)
\(432\) 3.55373 0.170979
\(433\) 28.2453 1.35738 0.678692 0.734423i \(-0.262547\pi\)
0.678692 + 0.734423i \(0.262547\pi\)
\(434\) −35.1879 −1.68907
\(435\) −6.10038 −0.292491
\(436\) 2.47619 0.118588
\(437\) 27.0188 1.29248
\(438\) −3.49260 −0.166883
\(439\) −18.6279 −0.889061 −0.444530 0.895764i \(-0.646629\pi\)
−0.444530 + 0.895764i \(0.646629\pi\)
\(440\) 2.35579 0.112308
\(441\) 9.47688 0.451280
\(442\) −7.11842 −0.338589
\(443\) −19.3894 −0.921220 −0.460610 0.887603i \(-0.652369\pi\)
−0.460610 + 0.887603i \(0.652369\pi\)
\(444\) −2.09070 −0.0992204
\(445\) −8.03194 −0.380750
\(446\) −5.48362 −0.259657
\(447\) 3.03517 0.143559
\(448\) −35.0628 −1.65656
\(449\) −4.85756 −0.229243 −0.114621 0.993409i \(-0.536565\pi\)
−0.114621 + 0.993409i \(0.536565\pi\)
\(450\) 4.89769 0.230879
\(451\) 5.31688 0.250362
\(452\) −2.33256 −0.109714
\(453\) 11.8078 0.554778
\(454\) −33.3996 −1.56752
\(455\) 25.0124 1.17260
\(456\) −20.7932 −0.973730
\(457\) 40.2164 1.88124 0.940622 0.339457i \(-0.110243\pi\)
0.940622 + 0.339457i \(0.110243\pi\)
\(458\) −36.6628 −1.71314
\(459\) 1.00000 0.0466760
\(460\) −0.902241 −0.0420672
\(461\) −7.02805 −0.327329 −0.163665 0.986516i \(-0.552331\pi\)
−0.163665 + 0.986516i \(0.552331\pi\)
\(462\) −3.74094 −0.174044
\(463\) −3.27707 −0.152298 −0.0761492 0.997096i \(-0.524263\pi\)
−0.0761492 + 0.997096i \(0.524263\pi\)
\(464\) −18.6804 −0.867214
\(465\) 7.50395 0.347987
\(466\) −17.2458 −0.798897
\(467\) 25.2454 1.16822 0.584108 0.811676i \(-0.301444\pi\)
0.584108 + 0.811676i \(0.301444\pi\)
\(468\) 1.07579 0.0497282
\(469\) −46.4132 −2.14316
\(470\) 12.0731 0.556892
\(471\) 8.10733 0.373566
\(472\) −8.88836 −0.409120
\(473\) −8.12065 −0.373388
\(474\) 1.34067 0.0615789
\(475\) −25.7236 −1.18028
\(476\) −0.822434 −0.0376962
\(477\) 11.5622 0.529395
\(478\) −13.0729 −0.597941
\(479\) 29.0095 1.32548 0.662740 0.748850i \(-0.269394\pi\)
0.662740 + 0.748850i \(0.269394\pi\)
\(480\) 1.32483 0.0604698
\(481\) 54.7888 2.49815
\(482\) 4.22964 0.192655
\(483\) 15.5755 0.708708
\(484\) 2.13298 0.0969536
\(485\) −8.34042 −0.378719
\(486\) 1.34067 0.0608139
\(487\) 27.0840 1.22729 0.613647 0.789581i \(-0.289702\pi\)
0.613647 + 0.789581i \(0.289702\pi\)
\(488\) −34.9537 −1.58228
\(489\) 6.17262 0.279136
\(490\) −14.7449 −0.666107
\(491\) 31.1323 1.40498 0.702491 0.711693i \(-0.252071\pi\)
0.702491 + 0.711693i \(0.252071\pi\)
\(492\) 1.56710 0.0706505
\(493\) −5.25655 −0.236743
\(494\) 50.1240 2.25518
\(495\) 0.797771 0.0358572
\(496\) 22.9783 1.03176
\(497\) −17.4222 −0.781491
\(498\) −6.80113 −0.304766
\(499\) −38.9804 −1.74500 −0.872501 0.488613i \(-0.837503\pi\)
−0.872501 + 0.488613i \(0.837503\pi\)
\(500\) 2.03467 0.0909934
\(501\) 20.3368 0.908581
\(502\) −8.85416 −0.395181
\(503\) −5.89255 −0.262736 −0.131368 0.991334i \(-0.541937\pi\)
−0.131368 + 0.991334i \(0.541937\pi\)
\(504\) −11.9866 −0.533926
\(505\) 16.6689 0.741756
\(506\) −3.53628 −0.157207
\(507\) −15.1919 −0.674697
\(508\) −0.680436 −0.0301895
\(509\) −8.30520 −0.368122 −0.184061 0.982915i \(-0.558924\pi\)
−0.184061 + 0.982915i \(0.558924\pi\)
\(510\) −1.55588 −0.0688956
\(511\) 10.5746 0.467795
\(512\) 25.0449 1.10684
\(513\) −7.04145 −0.310888
\(514\) 18.7096 0.825243
\(515\) 18.8425 0.830302
\(516\) −2.39349 −0.105367
\(517\) −5.33416 −0.234596
\(518\) −56.1549 −2.46730
\(519\) −16.1657 −0.709596
\(520\) −18.1960 −0.797949
\(521\) −36.7470 −1.60992 −0.804958 0.593332i \(-0.797812\pi\)
−0.804958 + 0.593332i \(0.797812\pi\)
\(522\) −7.04729 −0.308452
\(523\) −32.8646 −1.43707 −0.718534 0.695492i \(-0.755186\pi\)
−0.718534 + 0.695492i \(0.755186\pi\)
\(524\) −2.93879 −0.128382
\(525\) −14.8289 −0.647185
\(526\) −34.4627 −1.50264
\(527\) 6.46598 0.281662
\(528\) 2.44291 0.106314
\(529\) −8.27665 −0.359854
\(530\) −17.9894 −0.781408
\(531\) −3.00997 −0.130622
\(532\) 5.79113 0.251077
\(533\) −41.0674 −1.77883
\(534\) −9.27866 −0.401527
\(535\) −20.6179 −0.891389
\(536\) 33.7647 1.45841
\(537\) −3.23273 −0.139502
\(538\) −20.1584 −0.869090
\(539\) 6.51460 0.280604
\(540\) 0.235136 0.0101186
\(541\) −1.61268 −0.0693346 −0.0346673 0.999399i \(-0.511037\pi\)
−0.0346673 + 0.999399i \(0.511037\pi\)
\(542\) −15.9425 −0.684790
\(543\) 10.3861 0.445712
\(544\) 1.14157 0.0489445
\(545\) −14.1833 −0.607545
\(546\) 28.8949 1.23659
\(547\) −29.1427 −1.24605 −0.623025 0.782202i \(-0.714097\pi\)
−0.623025 + 0.782202i \(0.714097\pi\)
\(548\) 3.42310 0.146228
\(549\) −11.8368 −0.505183
\(550\) 3.36677 0.143560
\(551\) 37.0138 1.57684
\(552\) −11.3308 −0.482273
\(553\) −4.05917 −0.172614
\(554\) −41.2917 −1.75432
\(555\) 11.9753 0.508321
\(556\) −2.45242 −0.104006
\(557\) 25.6246 1.08575 0.542874 0.839814i \(-0.317336\pi\)
0.542874 + 0.839814i \(0.317336\pi\)
\(558\) 8.66873 0.366976
\(559\) 62.7235 2.65292
\(560\) 16.7408 0.707430
\(561\) 0.687421 0.0290229
\(562\) −13.0591 −0.550866
\(563\) 18.2169 0.767749 0.383874 0.923385i \(-0.374590\pi\)
0.383874 + 0.923385i \(0.374590\pi\)
\(564\) −1.57220 −0.0662014
\(565\) 13.3606 0.562083
\(566\) −35.1535 −1.47761
\(567\) −4.05917 −0.170469
\(568\) 12.6743 0.531801
\(569\) 14.7930 0.620154 0.310077 0.950711i \(-0.399645\pi\)
0.310077 + 0.950711i \(0.399645\pi\)
\(570\) 10.9557 0.458883
\(571\) −0.378441 −0.0158372 −0.00791862 0.999969i \(-0.502521\pi\)
−0.00791862 + 0.999969i \(0.502521\pi\)
\(572\) 0.739518 0.0309208
\(573\) −13.0022 −0.543173
\(574\) 42.0914 1.75686
\(575\) −14.0176 −0.584574
\(576\) 8.63792 0.359913
\(577\) 14.4007 0.599509 0.299754 0.954016i \(-0.403095\pi\)
0.299754 + 0.954016i \(0.403095\pi\)
\(578\) −1.34067 −0.0557644
\(579\) −3.38016 −0.140475
\(580\) −1.23601 −0.0513223
\(581\) 20.5919 0.854298
\(582\) −9.63503 −0.399385
\(583\) 7.94808 0.329176
\(584\) −7.69285 −0.318332
\(585\) −6.16195 −0.254765
\(586\) 34.4143 1.42164
\(587\) 23.9942 0.990347 0.495173 0.868794i \(-0.335105\pi\)
0.495173 + 0.868794i \(0.335105\pi\)
\(588\) 1.92012 0.0791845
\(589\) −45.5299 −1.87603
\(590\) 4.68316 0.192803
\(591\) 3.49753 0.143869
\(592\) 36.6702 1.50713
\(593\) −24.4590 −1.00441 −0.502205 0.864748i \(-0.667478\pi\)
−0.502205 + 0.864748i \(0.667478\pi\)
\(594\) 0.921603 0.0378138
\(595\) 4.71078 0.193123
\(596\) 0.614960 0.0251897
\(597\) −11.2955 −0.462293
\(598\) 27.3141 1.11696
\(599\) 43.5632 1.77995 0.889973 0.456013i \(-0.150723\pi\)
0.889973 + 0.456013i \(0.150723\pi\)
\(600\) 10.7877 0.440406
\(601\) 16.2585 0.663197 0.331598 0.943421i \(-0.392412\pi\)
0.331598 + 0.943421i \(0.392412\pi\)
\(602\) −64.2875 −2.62016
\(603\) 11.4342 0.465635
\(604\) 2.39239 0.0973449
\(605\) −12.2174 −0.496708
\(606\) 19.2563 0.782233
\(607\) −17.9372 −0.728047 −0.364023 0.931390i \(-0.618597\pi\)
−0.364023 + 0.931390i \(0.618597\pi\)
\(608\) −8.03833 −0.325997
\(609\) 21.3373 0.864629
\(610\) 18.4167 0.745670
\(611\) 41.2008 1.66681
\(612\) 0.202611 0.00819007
\(613\) −33.0964 −1.33675 −0.668374 0.743825i \(-0.733010\pi\)
−0.668374 + 0.743825i \(0.733010\pi\)
\(614\) −20.1503 −0.813201
\(615\) −8.97615 −0.361953
\(616\) −8.23984 −0.331993
\(617\) 38.5578 1.55228 0.776140 0.630561i \(-0.217175\pi\)
0.776140 + 0.630561i \(0.217175\pi\)
\(618\) 21.7673 0.875610
\(619\) 26.6029 1.06926 0.534631 0.845086i \(-0.320451\pi\)
0.534631 + 0.845086i \(0.320451\pi\)
\(620\) 1.52038 0.0610601
\(621\) −3.83710 −0.153978
\(622\) 31.3762 1.25807
\(623\) 28.0932 1.12553
\(624\) −18.8689 −0.755360
\(625\) 6.61155 0.264462
\(626\) 8.03611 0.321187
\(627\) −4.84044 −0.193309
\(628\) 1.64264 0.0655483
\(629\) 10.3188 0.411437
\(630\) 6.31559 0.251619
\(631\) −36.5603 −1.45544 −0.727720 0.685874i \(-0.759420\pi\)
−0.727720 + 0.685874i \(0.759420\pi\)
\(632\) 2.95297 0.117463
\(633\) −18.1639 −0.721951
\(634\) −3.33123 −0.132300
\(635\) 3.89744 0.154665
\(636\) 2.34262 0.0928911
\(637\) −50.3185 −1.99369
\(638\) −4.84445 −0.191794
\(639\) 4.29205 0.169791
\(640\) −10.7899 −0.426510
\(641\) 29.8352 1.17842 0.589210 0.807980i \(-0.299439\pi\)
0.589210 + 0.807980i \(0.299439\pi\)
\(642\) −23.8182 −0.940030
\(643\) 15.3169 0.604040 0.302020 0.953302i \(-0.402339\pi\)
0.302020 + 0.953302i \(0.402339\pi\)
\(644\) 3.15576 0.124354
\(645\) 13.7096 0.539814
\(646\) 9.44024 0.371421
\(647\) 29.3369 1.15335 0.576676 0.816973i \(-0.304349\pi\)
0.576676 + 0.816973i \(0.304349\pi\)
\(648\) 2.95297 0.116004
\(649\) −2.06912 −0.0812200
\(650\) −26.0048 −1.01999
\(651\) −26.2465 −1.02868
\(652\) 1.25064 0.0489790
\(653\) −3.36570 −0.131710 −0.0658550 0.997829i \(-0.520977\pi\)
−0.0658550 + 0.997829i \(0.520977\pi\)
\(654\) −16.3848 −0.640698
\(655\) 16.8330 0.657718
\(656\) −27.4864 −1.07317
\(657\) −2.60512 −0.101636
\(658\) −42.2281 −1.64622
\(659\) −18.9760 −0.739199 −0.369599 0.929191i \(-0.620505\pi\)
−0.369599 + 0.929191i \(0.620505\pi\)
\(660\) 0.161637 0.00629173
\(661\) −20.1214 −0.782632 −0.391316 0.920256i \(-0.627980\pi\)
−0.391316 + 0.920256i \(0.627980\pi\)
\(662\) 17.8218 0.692662
\(663\) −5.30961 −0.206208
\(664\) −14.9802 −0.581346
\(665\) −33.1708 −1.28631
\(666\) 13.8341 0.536059
\(667\) 20.1699 0.780983
\(668\) 4.12046 0.159426
\(669\) −4.09022 −0.158137
\(670\) −17.7902 −0.687296
\(671\) −8.13687 −0.314120
\(672\) −4.63384 −0.178754
\(673\) −24.6487 −0.950138 −0.475069 0.879949i \(-0.657577\pi\)
−0.475069 + 0.879949i \(0.657577\pi\)
\(674\) 21.5974 0.831899
\(675\) 3.65317 0.140611
\(676\) −3.07806 −0.118387
\(677\) −9.69623 −0.372656 −0.186328 0.982488i \(-0.559659\pi\)
−0.186328 + 0.982488i \(0.559659\pi\)
\(678\) 15.4344 0.592755
\(679\) 29.1722 1.11953
\(680\) −3.42700 −0.131420
\(681\) −24.9126 −0.954654
\(682\) 5.95906 0.228184
\(683\) 26.7129 1.02214 0.511070 0.859539i \(-0.329249\pi\)
0.511070 + 0.859539i \(0.329249\pi\)
\(684\) −1.42668 −0.0545504
\(685\) −19.6070 −0.749147
\(686\) 13.4792 0.514637
\(687\) −27.3467 −1.04334
\(688\) 41.9809 1.60051
\(689\) −61.3906 −2.33879
\(690\) 5.97008 0.227277
\(691\) −33.3456 −1.26853 −0.634263 0.773117i \(-0.718696\pi\)
−0.634263 + 0.773117i \(0.718696\pi\)
\(692\) −3.27535 −0.124510
\(693\) −2.79036 −0.105997
\(694\) −11.5769 −0.439452
\(695\) 14.0471 0.532837
\(696\) −15.5224 −0.588377
\(697\) −7.73454 −0.292967
\(698\) 26.4561 1.00138
\(699\) −12.8636 −0.486546
\(700\) −3.00449 −0.113559
\(701\) −13.9025 −0.525091 −0.262546 0.964920i \(-0.584562\pi\)
−0.262546 + 0.964920i \(0.584562\pi\)
\(702\) −7.11842 −0.268667
\(703\) −72.6593 −2.74040
\(704\) 5.93789 0.223793
\(705\) 9.00532 0.339160
\(706\) −26.9039 −1.01254
\(707\) −58.3027 −2.19270
\(708\) −0.609854 −0.0229197
\(709\) −42.8187 −1.60809 −0.804045 0.594568i \(-0.797323\pi\)
−0.804045 + 0.594568i \(0.797323\pi\)
\(710\) −6.67793 −0.250618
\(711\) 1.00000 0.0375029
\(712\) −20.4373 −0.765920
\(713\) −24.8106 −0.929165
\(714\) 5.44200 0.203662
\(715\) −4.23585 −0.158412
\(716\) −0.654987 −0.0244780
\(717\) −9.75104 −0.364159
\(718\) −0.513578 −0.0191666
\(719\) 13.6744 0.509970 0.254985 0.966945i \(-0.417929\pi\)
0.254985 + 0.966945i \(0.417929\pi\)
\(720\) −4.12420 −0.153700
\(721\) −65.9054 −2.45445
\(722\) −41.0003 −1.52587
\(723\) 3.15488 0.117331
\(724\) 2.10435 0.0782075
\(725\) −19.2031 −0.713185
\(726\) −14.1138 −0.523813
\(727\) 30.0101 1.11301 0.556506 0.830843i \(-0.312142\pi\)
0.556506 + 0.830843i \(0.312142\pi\)
\(728\) 63.6442 2.35881
\(729\) 1.00000 0.0370370
\(730\) 4.05327 0.150018
\(731\) 11.8132 0.436927
\(732\) −2.39827 −0.0886426
\(733\) −15.6798 −0.579145 −0.289573 0.957156i \(-0.593513\pi\)
−0.289573 + 0.957156i \(0.593513\pi\)
\(734\) −39.9808 −1.47572
\(735\) −10.9982 −0.405674
\(736\) −4.38033 −0.161461
\(737\) 7.86008 0.289530
\(738\) −10.3694 −0.381705
\(739\) 18.9572 0.697353 0.348676 0.937243i \(-0.386631\pi\)
0.348676 + 0.937243i \(0.386631\pi\)
\(740\) 2.42632 0.0891933
\(741\) 37.3873 1.37346
\(742\) 62.9213 2.30991
\(743\) −35.7120 −1.31015 −0.655074 0.755565i \(-0.727362\pi\)
−0.655074 + 0.755565i \(0.727362\pi\)
\(744\) 19.0938 0.700014
\(745\) −3.52240 −0.129051
\(746\) 4.29121 0.157112
\(747\) −5.07294 −0.185609
\(748\) 0.139279 0.00509255
\(749\) 72.1150 2.63503
\(750\) −13.4633 −0.491611
\(751\) −16.8921 −0.616402 −0.308201 0.951321i \(-0.599727\pi\)
−0.308201 + 0.951321i \(0.599727\pi\)
\(752\) 27.5757 1.00558
\(753\) −6.60429 −0.240674
\(754\) 37.4183 1.36270
\(755\) −13.7033 −0.498713
\(756\) −0.822434 −0.0299116
\(757\) −7.57701 −0.275391 −0.137696 0.990475i \(-0.543970\pi\)
−0.137696 + 0.990475i \(0.543970\pi\)
\(758\) 10.7210 0.389403
\(759\) −2.63770 −0.0957426
\(760\) 24.1311 0.875326
\(761\) −0.126198 −0.00457466 −0.00228733 0.999997i \(-0.500728\pi\)
−0.00228733 + 0.999997i \(0.500728\pi\)
\(762\) 4.50241 0.163105
\(763\) 49.6088 1.79596
\(764\) −2.63438 −0.0953086
\(765\) −1.16053 −0.0419590
\(766\) −47.4479 −1.71436
\(767\) 15.9818 0.577069
\(768\) 4.81108 0.173605
\(769\) −12.5225 −0.451572 −0.225786 0.974177i \(-0.572495\pi\)
−0.225786 + 0.974177i \(0.572495\pi\)
\(770\) 4.34147 0.156456
\(771\) 13.9554 0.502592
\(772\) −0.684858 −0.0246486
\(773\) −21.5135 −0.773786 −0.386893 0.922125i \(-0.626452\pi\)
−0.386893 + 0.922125i \(0.626452\pi\)
\(774\) 15.8376 0.569270
\(775\) 23.6213 0.848504
\(776\) −21.2222 −0.761833
\(777\) −41.8858 −1.50264
\(778\) −9.84976 −0.353131
\(779\) 54.4624 1.95132
\(780\) −1.24848 −0.0447028
\(781\) 2.95044 0.105575
\(782\) 5.14428 0.183959
\(783\) −5.25655 −0.187854
\(784\) −33.6782 −1.20279
\(785\) −9.40879 −0.335814
\(786\) 19.4458 0.693609
\(787\) 38.3753 1.36793 0.683966 0.729514i \(-0.260254\pi\)
0.683966 + 0.729514i \(0.260254\pi\)
\(788\) 0.708639 0.0252442
\(789\) −25.7056 −0.915144
\(790\) −1.55588 −0.0553558
\(791\) −46.7312 −1.66157
\(792\) 2.02993 0.0721305
\(793\) 62.8488 2.23183
\(794\) −4.34490 −0.154195
\(795\) −13.4182 −0.475895
\(796\) −2.28859 −0.0811169
\(797\) 4.11999 0.145938 0.0729688 0.997334i \(-0.476753\pi\)
0.0729688 + 0.997334i \(0.476753\pi\)
\(798\) −38.3196 −1.35650
\(799\) 7.75967 0.274517
\(800\) 4.17036 0.147445
\(801\) −6.92093 −0.244539
\(802\) −17.1622 −0.606018
\(803\) −1.79082 −0.0631965
\(804\) 2.31669 0.0817033
\(805\) −18.0758 −0.637087
\(806\) −46.0275 −1.62125
\(807\) −15.0361 −0.529296
\(808\) 42.4141 1.49212
\(809\) 23.4514 0.824506 0.412253 0.911069i \(-0.364742\pi\)
0.412253 + 0.911069i \(0.364742\pi\)
\(810\) −1.55588 −0.0546681
\(811\) 40.7618 1.43134 0.715670 0.698439i \(-0.246121\pi\)
0.715670 + 0.698439i \(0.246121\pi\)
\(812\) 4.32317 0.151713
\(813\) −11.8915 −0.417053
\(814\) 9.50983 0.333319
\(815\) −7.16351 −0.250927
\(816\) −3.55373 −0.124405
\(817\) −83.1822 −2.91018
\(818\) −36.2236 −1.26653
\(819\) 21.5526 0.753109
\(820\) −1.81867 −0.0635107
\(821\) 1.43536 0.0500944 0.0250472 0.999686i \(-0.492026\pi\)
0.0250472 + 0.999686i \(0.492026\pi\)
\(822\) −22.6505 −0.790026
\(823\) 16.6844 0.581581 0.290790 0.956787i \(-0.406082\pi\)
0.290790 + 0.956787i \(0.406082\pi\)
\(824\) 47.9449 1.67024
\(825\) 2.51127 0.0874311
\(826\) −16.3803 −0.569943
\(827\) 40.9466 1.42385 0.711926 0.702255i \(-0.247823\pi\)
0.711926 + 0.702255i \(0.247823\pi\)
\(828\) −0.777440 −0.0270179
\(829\) −27.7083 −0.962349 −0.481174 0.876625i \(-0.659790\pi\)
−0.481174 + 0.876625i \(0.659790\pi\)
\(830\) 7.89290 0.273967
\(831\) −30.7994 −1.06842
\(832\) −45.8640 −1.59005
\(833\) −9.47688 −0.328354
\(834\) 16.2275 0.561912
\(835\) −23.6014 −0.816761
\(836\) −0.980727 −0.0339192
\(837\) 6.46598 0.223497
\(838\) −15.1051 −0.521796
\(839\) −29.8701 −1.03123 −0.515616 0.856820i \(-0.672437\pi\)
−0.515616 + 0.856820i \(0.672437\pi\)
\(840\) 13.9108 0.479968
\(841\) −1.36864 −0.0471945
\(842\) 24.8298 0.855692
\(843\) −9.74076 −0.335490
\(844\) −3.68021 −0.126678
\(845\) 17.6307 0.606513
\(846\) 10.4031 0.357667
\(847\) 42.7327 1.46831
\(848\) −41.0888 −1.41099
\(849\) −26.2209 −0.899899
\(850\) −4.89769 −0.167989
\(851\) −39.5943 −1.35727
\(852\) 0.869617 0.0297926
\(853\) −0.862347 −0.0295262 −0.0147631 0.999891i \(-0.504699\pi\)
−0.0147631 + 0.999891i \(0.504699\pi\)
\(854\) −64.4159 −2.20427
\(855\) 8.17180 0.279470
\(856\) −52.4623 −1.79312
\(857\) 40.0791 1.36908 0.684539 0.728977i \(-0.260004\pi\)
0.684539 + 0.728977i \(0.260004\pi\)
\(858\) −4.89335 −0.167056
\(859\) 14.4423 0.492764 0.246382 0.969173i \(-0.420758\pi\)
0.246382 + 0.969173i \(0.420758\pi\)
\(860\) 2.77771 0.0947192
\(861\) 31.3958 1.06997
\(862\) −4.28193 −0.145843
\(863\) 44.0445 1.49929 0.749646 0.661840i \(-0.230224\pi\)
0.749646 + 0.661840i \(0.230224\pi\)
\(864\) 1.14157 0.0388371
\(865\) 18.7608 0.637885
\(866\) −37.8676 −1.28679
\(867\) −1.00000 −0.0339618
\(868\) −5.31784 −0.180499
\(869\) 0.687421 0.0233192
\(870\) 8.17858 0.277280
\(871\) −60.7109 −2.05711
\(872\) −36.0894 −1.22214
\(873\) −7.18674 −0.243234
\(874\) −36.2232 −1.22527
\(875\) 40.7632 1.37805
\(876\) −0.527827 −0.0178336
\(877\) −19.0013 −0.641630 −0.320815 0.947142i \(-0.603957\pi\)
−0.320815 + 0.947142i \(0.603957\pi\)
\(878\) 24.9738 0.842825
\(879\) 25.6696 0.865813
\(880\) −2.83506 −0.0955699
\(881\) −35.1472 −1.18414 −0.592070 0.805886i \(-0.701689\pi\)
−0.592070 + 0.805886i \(0.701689\pi\)
\(882\) −12.7053 −0.427811
\(883\) −7.42449 −0.249854 −0.124927 0.992166i \(-0.539870\pi\)
−0.124927 + 0.992166i \(0.539870\pi\)
\(884\) −1.07579 −0.0361826
\(885\) 3.49316 0.117421
\(886\) 25.9948 0.873312
\(887\) −49.0405 −1.64662 −0.823309 0.567593i \(-0.807875\pi\)
−0.823309 + 0.567593i \(0.807875\pi\)
\(888\) 30.4711 1.02254
\(889\) −13.6320 −0.457204
\(890\) 10.7682 0.360949
\(891\) 0.687421 0.0230295
\(892\) −0.828724 −0.0277477
\(893\) −54.6393 −1.82844
\(894\) −4.06916 −0.136093
\(895\) 3.75167 0.125405
\(896\) 37.7399 1.26080
\(897\) 20.3735 0.680251
\(898\) 6.51238 0.217321
\(899\) −33.9888 −1.13359
\(900\) 0.740174 0.0246725
\(901\) −11.5622 −0.385192
\(902\) −7.12817 −0.237342
\(903\) −47.9519 −1.59574
\(904\) 33.9960 1.13069
\(905\) −12.0534 −0.400669
\(906\) −15.8303 −0.525926
\(907\) −27.6460 −0.917970 −0.458985 0.888444i \(-0.651787\pi\)
−0.458985 + 0.888444i \(0.651787\pi\)
\(908\) −5.04758 −0.167510
\(909\) 14.3632 0.476397
\(910\) −33.5333 −1.11162
\(911\) −33.8793 −1.12247 −0.561236 0.827656i \(-0.689674\pi\)
−0.561236 + 0.827656i \(0.689674\pi\)
\(912\) 25.0234 0.828607
\(913\) −3.48725 −0.115411
\(914\) −53.9168 −1.78341
\(915\) 13.7370 0.454130
\(916\) −5.54075 −0.183071
\(917\) −58.8765 −1.94427
\(918\) −1.34067 −0.0442486
\(919\) 0.763246 0.0251772 0.0125886 0.999921i \(-0.495993\pi\)
0.0125886 + 0.999921i \(0.495993\pi\)
\(920\) 13.1498 0.433535
\(921\) −15.0301 −0.495258
\(922\) 9.42228 0.310306
\(923\) −22.7891 −0.750112
\(924\) −0.565358 −0.0185989
\(925\) 37.6964 1.23945
\(926\) 4.39346 0.144378
\(927\) 16.2362 0.533266
\(928\) −6.00074 −0.196984
\(929\) −36.2828 −1.19040 −0.595199 0.803578i \(-0.702927\pi\)
−0.595199 + 0.803578i \(0.702927\pi\)
\(930\) −10.0603 −0.329890
\(931\) 66.7310 2.18702
\(932\) −2.60631 −0.0853725
\(933\) 23.4034 0.766193
\(934\) −33.8456 −1.10746
\(935\) −0.797771 −0.0260899
\(936\) −15.6791 −0.512488
\(937\) 20.3153 0.663672 0.331836 0.943337i \(-0.392332\pi\)
0.331836 + 0.943337i \(0.392332\pi\)
\(938\) 62.2247 2.03171
\(939\) 5.99411 0.195610
\(940\) 1.82458 0.0595112
\(941\) 2.62083 0.0854366 0.0427183 0.999087i \(-0.486398\pi\)
0.0427183 + 0.999087i \(0.486398\pi\)
\(942\) −10.8692 −0.354139
\(943\) 29.6782 0.966456
\(944\) 10.6966 0.348145
\(945\) 4.71078 0.153242
\(946\) 10.8871 0.353970
\(947\) −27.0615 −0.879381 −0.439690 0.898149i \(-0.644912\pi\)
−0.439690 + 0.898149i \(0.644912\pi\)
\(948\) 0.202611 0.00658051
\(949\) 13.8322 0.449012
\(950\) 34.4868 1.11890
\(951\) −2.48476 −0.0805737
\(952\) 11.9866 0.388488
\(953\) −45.7337 −1.48146 −0.740730 0.671803i \(-0.765520\pi\)
−0.740730 + 0.671803i \(0.765520\pi\)
\(954\) −15.5010 −0.501864
\(955\) 15.0894 0.488280
\(956\) −1.97567 −0.0638977
\(957\) −3.61346 −0.116807
\(958\) −38.8921 −1.25655
\(959\) 68.5794 2.21455
\(960\) −10.0246 −0.323541
\(961\) 10.8089 0.348674
\(962\) −73.4535 −2.36824
\(963\) −17.7659 −0.572500
\(964\) 0.639214 0.0205877
\(965\) 3.92277 0.126279
\(966\) −20.8815 −0.671851
\(967\) 52.2890 1.68150 0.840751 0.541423i \(-0.182114\pi\)
0.840751 + 0.541423i \(0.182114\pi\)
\(968\) −31.0872 −0.999182
\(969\) 7.04145 0.226204
\(970\) 11.1817 0.359023
\(971\) 43.9402 1.41011 0.705055 0.709153i \(-0.250922\pi\)
0.705055 + 0.709153i \(0.250922\pi\)
\(972\) 0.202611 0.00649876
\(973\) −49.1324 −1.57511
\(974\) −36.3106 −1.16347
\(975\) −19.3969 −0.621199
\(976\) 42.0648 1.34646
\(977\) 1.90620 0.0609848 0.0304924 0.999535i \(-0.490292\pi\)
0.0304924 + 0.999535i \(0.490292\pi\)
\(978\) −8.27544 −0.264619
\(979\) −4.75759 −0.152053
\(980\) −2.22836 −0.0711822
\(981\) −12.2214 −0.390199
\(982\) −41.7381 −1.33192
\(983\) 5.52324 0.176164 0.0880819 0.996113i \(-0.471926\pi\)
0.0880819 + 0.996113i \(0.471926\pi\)
\(984\) −22.8399 −0.728108
\(985\) −4.05898 −0.129330
\(986\) 7.04729 0.224431
\(987\) −31.4978 −1.00259
\(988\) 7.57509 0.240996
\(989\) −45.3285 −1.44136
\(990\) −1.06955 −0.0339924
\(991\) −0.489112 −0.0155372 −0.00776858 0.999970i \(-0.502473\pi\)
−0.00776858 + 0.999970i \(0.502473\pi\)
\(992\) 7.38139 0.234359
\(993\) 13.2932 0.421847
\(994\) 23.3573 0.740850
\(995\) 13.1087 0.415574
\(996\) −1.02783 −0.0325682
\(997\) −29.4566 −0.932900 −0.466450 0.884547i \(-0.654467\pi\)
−0.466450 + 0.884547i \(0.654467\pi\)
\(998\) 52.2597 1.65425
\(999\) 10.3188 0.326472
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 4029.2.a.l.1.11 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.11 32 1.1 even 1 trivial