Properties

Label 4029.2.a.k.1.20
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
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: \(31\)
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 \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.959467 q^{2} +1.00000 q^{3} -1.07942 q^{4} -3.93035 q^{5} +0.959467 q^{6} -0.0159719 q^{7} -2.95460 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.959467 q^{2} +1.00000 q^{3} -1.07942 q^{4} -3.93035 q^{5} +0.959467 q^{6} -0.0159719 q^{7} -2.95460 q^{8} +1.00000 q^{9} -3.77104 q^{10} -0.0651658 q^{11} -1.07942 q^{12} -1.13960 q^{13} -0.0153245 q^{14} -3.93035 q^{15} -0.675997 q^{16} +1.00000 q^{17} +0.959467 q^{18} -6.81607 q^{19} +4.24251 q^{20} -0.0159719 q^{21} -0.0625244 q^{22} -3.11319 q^{23} -2.95460 q^{24} +10.4477 q^{25} -1.09341 q^{26} +1.00000 q^{27} +0.0172404 q^{28} +0.147476 q^{29} -3.77104 q^{30} -3.00436 q^{31} +5.26061 q^{32} -0.0651658 q^{33} +0.959467 q^{34} +0.0627751 q^{35} -1.07942 q^{36} +0.619732 q^{37} -6.53980 q^{38} -1.13960 q^{39} +11.6126 q^{40} +6.70124 q^{41} -0.0153245 q^{42} +0.482967 q^{43} +0.0703415 q^{44} -3.93035 q^{45} -2.98700 q^{46} -1.80113 q^{47} -0.675997 q^{48} -6.99974 q^{49} +10.0242 q^{50} +1.00000 q^{51} +1.23011 q^{52} +2.47166 q^{53} +0.959467 q^{54} +0.256125 q^{55} +0.0471906 q^{56} -6.81607 q^{57} +0.141499 q^{58} -0.178477 q^{59} +4.24251 q^{60} +2.91148 q^{61} -2.88259 q^{62} -0.0159719 q^{63} +6.39938 q^{64} +4.47904 q^{65} -0.0625244 q^{66} +14.4005 q^{67} -1.07942 q^{68} -3.11319 q^{69} +0.0602306 q^{70} +7.32560 q^{71} -2.95460 q^{72} +4.12876 q^{73} +0.594612 q^{74} +10.4477 q^{75} +7.35743 q^{76} +0.00104082 q^{77} -1.09341 q^{78} +1.00000 q^{79} +2.65691 q^{80} +1.00000 q^{81} +6.42962 q^{82} +10.0814 q^{83} +0.0172404 q^{84} -3.93035 q^{85} +0.463390 q^{86} +0.147476 q^{87} +0.192539 q^{88} +3.56683 q^{89} -3.77104 q^{90} +0.0182016 q^{91} +3.36045 q^{92} -3.00436 q^{93} -1.72812 q^{94} +26.7896 q^{95} +5.26061 q^{96} -0.920142 q^{97} -6.71602 q^{98} -0.0651658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.959467 0.678445 0.339223 0.940706i \(-0.389836\pi\)
0.339223 + 0.940706i \(0.389836\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.07942 −0.539712
\(5\) −3.93035 −1.75771 −0.878853 0.477092i \(-0.841691\pi\)
−0.878853 + 0.477092i \(0.841691\pi\)
\(6\) 0.959467 0.391701
\(7\) −0.0159719 −0.00603680 −0.00301840 0.999995i \(-0.500961\pi\)
−0.00301840 + 0.999995i \(0.500961\pi\)
\(8\) −2.95460 −1.04461
\(9\) 1.00000 0.333333
\(10\) −3.77104 −1.19251
\(11\) −0.0651658 −0.0196482 −0.00982412 0.999952i \(-0.503127\pi\)
−0.00982412 + 0.999952i \(0.503127\pi\)
\(12\) −1.07942 −0.311603
\(13\) −1.13960 −0.316069 −0.158034 0.987434i \(-0.550516\pi\)
−0.158034 + 0.987434i \(0.550516\pi\)
\(14\) −0.0153245 −0.00409564
\(15\) −3.93035 −1.01481
\(16\) −0.675997 −0.168999
\(17\) 1.00000 0.242536
\(18\) 0.959467 0.226148
\(19\) −6.81607 −1.56371 −0.781857 0.623457i \(-0.785728\pi\)
−0.781857 + 0.623457i \(0.785728\pi\)
\(20\) 4.24251 0.948655
\(21\) −0.0159719 −0.00348535
\(22\) −0.0625244 −0.0133303
\(23\) −3.11319 −0.649144 −0.324572 0.945861i \(-0.605220\pi\)
−0.324572 + 0.945861i \(0.605220\pi\)
\(24\) −2.95460 −0.603106
\(25\) 10.4477 2.08953
\(26\) −1.09341 −0.214435
\(27\) 1.00000 0.192450
\(28\) 0.0172404 0.00325813
\(29\) 0.147476 0.0273857 0.0136928 0.999906i \(-0.495641\pi\)
0.0136928 + 0.999906i \(0.495641\pi\)
\(30\) −3.77104 −0.688495
\(31\) −3.00436 −0.539599 −0.269800 0.962916i \(-0.586957\pi\)
−0.269800 + 0.962916i \(0.586957\pi\)
\(32\) 5.26061 0.929954
\(33\) −0.0651658 −0.0113439
\(34\) 0.959467 0.164547
\(35\) 0.0627751 0.0106109
\(36\) −1.07942 −0.179904
\(37\) 0.619732 0.101883 0.0509416 0.998702i \(-0.483778\pi\)
0.0509416 + 0.998702i \(0.483778\pi\)
\(38\) −6.53980 −1.06090
\(39\) −1.13960 −0.182482
\(40\) 11.6126 1.83612
\(41\) 6.70124 1.04656 0.523279 0.852161i \(-0.324709\pi\)
0.523279 + 0.852161i \(0.324709\pi\)
\(42\) −0.0153245 −0.00236462
\(43\) 0.482967 0.0736517 0.0368259 0.999322i \(-0.488275\pi\)
0.0368259 + 0.999322i \(0.488275\pi\)
\(44\) 0.0703415 0.0106044
\(45\) −3.93035 −0.585902
\(46\) −2.98700 −0.440409
\(47\) −1.80113 −0.262721 −0.131361 0.991335i \(-0.541935\pi\)
−0.131361 + 0.991335i \(0.541935\pi\)
\(48\) −0.675997 −0.0975718
\(49\) −6.99974 −0.999964
\(50\) 10.0242 1.41763
\(51\) 1.00000 0.140028
\(52\) 1.23011 0.170586
\(53\) 2.47166 0.339509 0.169754 0.985486i \(-0.445703\pi\)
0.169754 + 0.985486i \(0.445703\pi\)
\(54\) 0.959467 0.130567
\(55\) 0.256125 0.0345358
\(56\) 0.0471906 0.00630611
\(57\) −6.81607 −0.902811
\(58\) 0.141499 0.0185797
\(59\) −0.178477 −0.0232358 −0.0116179 0.999933i \(-0.503698\pi\)
−0.0116179 + 0.999933i \(0.503698\pi\)
\(60\) 4.24251 0.547706
\(61\) 2.91148 0.372777 0.186388 0.982476i \(-0.440322\pi\)
0.186388 + 0.982476i \(0.440322\pi\)
\(62\) −2.88259 −0.366089
\(63\) −0.0159719 −0.00201227
\(64\) 6.39938 0.799922
\(65\) 4.47904 0.555556
\(66\) −0.0625244 −0.00769622
\(67\) 14.4005 1.75930 0.879650 0.475622i \(-0.157777\pi\)
0.879650 + 0.475622i \(0.157777\pi\)
\(68\) −1.07942 −0.130899
\(69\) −3.11319 −0.374784
\(70\) 0.0602306 0.00719893
\(71\) 7.32560 0.869389 0.434695 0.900578i \(-0.356856\pi\)
0.434695 + 0.900578i \(0.356856\pi\)
\(72\) −2.95460 −0.348203
\(73\) 4.12876 0.483234 0.241617 0.970372i \(-0.422322\pi\)
0.241617 + 0.970372i \(0.422322\pi\)
\(74\) 0.594612 0.0691222
\(75\) 10.4477 1.20639
\(76\) 7.35743 0.843955
\(77\) 0.00104082 0.000118612 0
\(78\) −1.09341 −0.123804
\(79\) 1.00000 0.112509
\(80\) 2.65691 0.297051
\(81\) 1.00000 0.111111
\(82\) 6.42962 0.710033
\(83\) 10.0814 1.10657 0.553287 0.832991i \(-0.313373\pi\)
0.553287 + 0.832991i \(0.313373\pi\)
\(84\) 0.0172404 0.00188108
\(85\) −3.93035 −0.426306
\(86\) 0.463390 0.0499687
\(87\) 0.147476 0.0158111
\(88\) 0.192539 0.0205247
\(89\) 3.56683 0.378084 0.189042 0.981969i \(-0.439462\pi\)
0.189042 + 0.981969i \(0.439462\pi\)
\(90\) −3.77104 −0.397503
\(91\) 0.0182016 0.00190804
\(92\) 3.36045 0.350351
\(93\) −3.00436 −0.311538
\(94\) −1.72812 −0.178242
\(95\) 26.7896 2.74855
\(96\) 5.26061 0.536909
\(97\) −0.920142 −0.0934263 −0.0467131 0.998908i \(-0.514875\pi\)
−0.0467131 + 0.998908i \(0.514875\pi\)
\(98\) −6.71602 −0.678421
\(99\) −0.0651658 −0.00654941
\(100\) −11.2775 −1.12775
\(101\) 8.15477 0.811430 0.405715 0.914000i \(-0.367023\pi\)
0.405715 + 0.914000i \(0.367023\pi\)
\(102\) 0.959467 0.0950014
\(103\) 3.69861 0.364435 0.182218 0.983258i \(-0.441672\pi\)
0.182218 + 0.983258i \(0.441672\pi\)
\(104\) 3.36707 0.330169
\(105\) 0.0627751 0.00612622
\(106\) 2.37148 0.230338
\(107\) −10.5464 −1.01955 −0.509777 0.860307i \(-0.670272\pi\)
−0.509777 + 0.860307i \(0.670272\pi\)
\(108\) −1.07942 −0.103868
\(109\) −12.0152 −1.15084 −0.575421 0.817857i \(-0.695162\pi\)
−0.575421 + 0.817857i \(0.695162\pi\)
\(110\) 0.245743 0.0234307
\(111\) 0.619732 0.0588223
\(112\) 0.0107969 0.00102021
\(113\) 12.3319 1.16009 0.580045 0.814585i \(-0.303035\pi\)
0.580045 + 0.814585i \(0.303035\pi\)
\(114\) −6.53980 −0.612508
\(115\) 12.2359 1.14101
\(116\) −0.159189 −0.0147804
\(117\) −1.13960 −0.105356
\(118\) −0.171243 −0.0157642
\(119\) −0.0159719 −0.00146414
\(120\) 11.6126 1.06008
\(121\) −10.9958 −0.999614
\(122\) 2.79347 0.252909
\(123\) 6.70124 0.604231
\(124\) 3.24298 0.291228
\(125\) −21.4112 −1.91508
\(126\) −0.0153245 −0.00136521
\(127\) 12.0038 1.06517 0.532583 0.846378i \(-0.321221\pi\)
0.532583 + 0.846378i \(0.321221\pi\)
\(128\) −4.38124 −0.387250
\(129\) 0.482967 0.0425228
\(130\) 4.29749 0.376915
\(131\) 16.6459 1.45436 0.727181 0.686446i \(-0.240830\pi\)
0.727181 + 0.686446i \(0.240830\pi\)
\(132\) 0.0703415 0.00612244
\(133\) 0.108865 0.00943984
\(134\) 13.8168 1.19359
\(135\) −3.93035 −0.338271
\(136\) −2.95460 −0.253355
\(137\) −10.2100 −0.872298 −0.436149 0.899874i \(-0.643658\pi\)
−0.436149 + 0.899874i \(0.643658\pi\)
\(138\) −2.98700 −0.254270
\(139\) 6.65275 0.564279 0.282140 0.959373i \(-0.408956\pi\)
0.282140 + 0.959373i \(0.408956\pi\)
\(140\) −0.0677609 −0.00572684
\(141\) −1.80113 −0.151682
\(142\) 7.02867 0.589833
\(143\) 0.0742631 0.00621019
\(144\) −0.675997 −0.0563331
\(145\) −0.579634 −0.0481360
\(146\) 3.96140 0.327848
\(147\) −6.99974 −0.577329
\(148\) −0.668953 −0.0549876
\(149\) 3.47475 0.284663 0.142332 0.989819i \(-0.454540\pi\)
0.142332 + 0.989819i \(0.454540\pi\)
\(150\) 10.0242 0.818471
\(151\) −4.73716 −0.385505 −0.192752 0.981247i \(-0.561741\pi\)
−0.192752 + 0.981247i \(0.561741\pi\)
\(152\) 20.1388 1.63347
\(153\) 1.00000 0.0808452
\(154\) 0.000998632 0 8.04721e−5 0
\(155\) 11.8082 0.948457
\(156\) 1.23011 0.0984879
\(157\) 0.886583 0.0707570 0.0353785 0.999374i \(-0.488736\pi\)
0.0353785 + 0.999374i \(0.488736\pi\)
\(158\) 0.959467 0.0763311
\(159\) 2.47166 0.196015
\(160\) −20.6761 −1.63459
\(161\) 0.0497234 0.00391876
\(162\) 0.959467 0.0753828
\(163\) −3.22247 −0.252403 −0.126202 0.992005i \(-0.540279\pi\)
−0.126202 + 0.992005i \(0.540279\pi\)
\(164\) −7.23348 −0.564840
\(165\) 0.256125 0.0199393
\(166\) 9.67274 0.750750
\(167\) 13.3747 1.03496 0.517481 0.855695i \(-0.326870\pi\)
0.517481 + 0.855695i \(0.326870\pi\)
\(168\) 0.0471906 0.00364083
\(169\) −11.7013 −0.900101
\(170\) −3.77104 −0.289226
\(171\) −6.81607 −0.521238
\(172\) −0.521326 −0.0397507
\(173\) 15.8197 1.20275 0.601374 0.798967i \(-0.294620\pi\)
0.601374 + 0.798967i \(0.294620\pi\)
\(174\) 0.141499 0.0107270
\(175\) −0.166869 −0.0126141
\(176\) 0.0440519 0.00332054
\(177\) −0.178477 −0.0134152
\(178\) 3.42226 0.256509
\(179\) 11.7407 0.877539 0.438769 0.898600i \(-0.355415\pi\)
0.438769 + 0.898600i \(0.355415\pi\)
\(180\) 4.24251 0.316218
\(181\) 12.5486 0.932728 0.466364 0.884593i \(-0.345564\pi\)
0.466364 + 0.884593i \(0.345564\pi\)
\(182\) 0.0174638 0.00129450
\(183\) 2.91148 0.215223
\(184\) 9.19824 0.678103
\(185\) −2.43576 −0.179081
\(186\) −2.88259 −0.211361
\(187\) −0.0651658 −0.00476540
\(188\) 1.94418 0.141794
\(189\) −0.0159719 −0.00116178
\(190\) 25.7037 1.86474
\(191\) −7.42412 −0.537190 −0.268595 0.963253i \(-0.586559\pi\)
−0.268595 + 0.963253i \(0.586559\pi\)
\(192\) 6.39938 0.461835
\(193\) −16.8962 −1.21621 −0.608107 0.793855i \(-0.708071\pi\)
−0.608107 + 0.793855i \(0.708071\pi\)
\(194\) −0.882845 −0.0633846
\(195\) 4.47904 0.320751
\(196\) 7.55569 0.539692
\(197\) 6.58428 0.469110 0.234555 0.972103i \(-0.424637\pi\)
0.234555 + 0.972103i \(0.424637\pi\)
\(198\) −0.0625244 −0.00444342
\(199\) −24.6876 −1.75006 −0.875029 0.484071i \(-0.839158\pi\)
−0.875029 + 0.484071i \(0.839158\pi\)
\(200\) −30.8687 −2.18275
\(201\) 14.4005 1.01573
\(202\) 7.82423 0.550511
\(203\) −0.00235547 −0.000165322 0
\(204\) −1.07942 −0.0755748
\(205\) −26.3382 −1.83954
\(206\) 3.54870 0.247249
\(207\) −3.11319 −0.216381
\(208\) 0.770368 0.0534154
\(209\) 0.444175 0.0307242
\(210\) 0.0602306 0.00415631
\(211\) 0.866183 0.0596305 0.0298153 0.999555i \(-0.490508\pi\)
0.0298153 + 0.999555i \(0.490508\pi\)
\(212\) −2.66797 −0.183237
\(213\) 7.32560 0.501942
\(214\) −10.1189 −0.691712
\(215\) −1.89823 −0.129458
\(216\) −2.95460 −0.201035
\(217\) 0.0479853 0.00325745
\(218\) −11.5281 −0.780784
\(219\) 4.12876 0.278995
\(220\) −0.276467 −0.0186394
\(221\) −1.13960 −0.0766579
\(222\) 0.594612 0.0399077
\(223\) 8.48759 0.568371 0.284185 0.958769i \(-0.408277\pi\)
0.284185 + 0.958769i \(0.408277\pi\)
\(224\) −0.0840218 −0.00561395
\(225\) 10.4477 0.696511
\(226\) 11.8321 0.787057
\(227\) 7.23551 0.480238 0.240119 0.970743i \(-0.422814\pi\)
0.240119 + 0.970743i \(0.422814\pi\)
\(228\) 7.35743 0.487258
\(229\) 8.20090 0.541931 0.270965 0.962589i \(-0.412657\pi\)
0.270965 + 0.962589i \(0.412657\pi\)
\(230\) 11.7400 0.774110
\(231\) 0.00104082 6.84809e−5 0
\(232\) −0.435734 −0.0286074
\(233\) −3.88340 −0.254410 −0.127205 0.991876i \(-0.540601\pi\)
−0.127205 + 0.991876i \(0.540601\pi\)
\(234\) −1.09341 −0.0714785
\(235\) 7.07906 0.461787
\(236\) 0.192653 0.0125406
\(237\) 1.00000 0.0649570
\(238\) −0.0153245 −0.000993339 0
\(239\) −6.99870 −0.452708 −0.226354 0.974045i \(-0.572681\pi\)
−0.226354 + 0.974045i \(0.572681\pi\)
\(240\) 2.65691 0.171503
\(241\) −8.91752 −0.574428 −0.287214 0.957866i \(-0.592729\pi\)
−0.287214 + 0.957866i \(0.592729\pi\)
\(242\) −10.5501 −0.678183
\(243\) 1.00000 0.0641500
\(244\) −3.14272 −0.201192
\(245\) 27.5115 1.75764
\(246\) 6.42962 0.409937
\(247\) 7.76761 0.494241
\(248\) 8.87670 0.563671
\(249\) 10.0814 0.638881
\(250\) −20.5434 −1.29928
\(251\) 25.1611 1.58816 0.794078 0.607815i \(-0.207954\pi\)
0.794078 + 0.607815i \(0.207954\pi\)
\(252\) 0.0172404 0.00108604
\(253\) 0.202873 0.0127545
\(254\) 11.5173 0.722657
\(255\) −3.93035 −0.246128
\(256\) −17.0024 −1.06265
\(257\) −6.43201 −0.401218 −0.200609 0.979671i \(-0.564292\pi\)
−0.200609 + 0.979671i \(0.564292\pi\)
\(258\) 0.463390 0.0288494
\(259\) −0.00989828 −0.000615049 0
\(260\) −4.83478 −0.299840
\(261\) 0.147476 0.00912856
\(262\) 15.9712 0.986705
\(263\) −19.2936 −1.18969 −0.594846 0.803840i \(-0.702787\pi\)
−0.594846 + 0.803840i \(0.702787\pi\)
\(264\) 0.192539 0.0118500
\(265\) −9.71449 −0.596757
\(266\) 0.104453 0.00640441
\(267\) 3.56683 0.218287
\(268\) −15.5442 −0.949515
\(269\) −24.7396 −1.50840 −0.754201 0.656643i \(-0.771976\pi\)
−0.754201 + 0.656643i \(0.771976\pi\)
\(270\) −3.77104 −0.229498
\(271\) −22.1634 −1.34633 −0.673166 0.739491i \(-0.735066\pi\)
−0.673166 + 0.739491i \(0.735066\pi\)
\(272\) −0.675997 −0.0409883
\(273\) 0.0182016 0.00110161
\(274\) −9.79614 −0.591807
\(275\) −0.680831 −0.0410556
\(276\) 3.36045 0.202275
\(277\) −19.4586 −1.16916 −0.584578 0.811337i \(-0.698740\pi\)
−0.584578 + 0.811337i \(0.698740\pi\)
\(278\) 6.38309 0.382832
\(279\) −3.00436 −0.179866
\(280\) −0.185476 −0.0110843
\(281\) 25.1970 1.50313 0.751565 0.659659i \(-0.229299\pi\)
0.751565 + 0.659659i \(0.229299\pi\)
\(282\) −1.72812 −0.102908
\(283\) 23.7291 1.41055 0.705274 0.708935i \(-0.250824\pi\)
0.705274 + 0.708935i \(0.250824\pi\)
\(284\) −7.90743 −0.469220
\(285\) 26.7896 1.58688
\(286\) 0.0712530 0.00421328
\(287\) −0.107031 −0.00631786
\(288\) 5.26061 0.309985
\(289\) 1.00000 0.0588235
\(290\) −0.556139 −0.0326576
\(291\) −0.920142 −0.0539397
\(292\) −4.45668 −0.260807
\(293\) 22.4175 1.30964 0.654822 0.755783i \(-0.272744\pi\)
0.654822 + 0.755783i \(0.272744\pi\)
\(294\) −6.71602 −0.391686
\(295\) 0.701479 0.0408417
\(296\) −1.83106 −0.106428
\(297\) −0.0651658 −0.00378130
\(298\) 3.33391 0.193128
\(299\) 3.54779 0.205174
\(300\) −11.2775 −0.651104
\(301\) −0.00771388 −0.000444621 0
\(302\) −4.54515 −0.261544
\(303\) 8.15477 0.468479
\(304\) 4.60765 0.264267
\(305\) −11.4431 −0.655233
\(306\) 0.959467 0.0548491
\(307\) 7.21037 0.411518 0.205759 0.978603i \(-0.434034\pi\)
0.205759 + 0.978603i \(0.434034\pi\)
\(308\) −0.00112349 −6.40166e−5 0
\(309\) 3.69861 0.210407
\(310\) 11.3296 0.643477
\(311\) 29.7883 1.68914 0.844570 0.535445i \(-0.179856\pi\)
0.844570 + 0.535445i \(0.179856\pi\)
\(312\) 3.36707 0.190623
\(313\) 20.1310 1.13787 0.568935 0.822383i \(-0.307356\pi\)
0.568935 + 0.822383i \(0.307356\pi\)
\(314\) 0.850646 0.0480048
\(315\) 0.0627751 0.00353698
\(316\) −1.07942 −0.0607223
\(317\) 13.3012 0.747067 0.373534 0.927617i \(-0.378146\pi\)
0.373534 + 0.927617i \(0.378146\pi\)
\(318\) 2.37148 0.132986
\(319\) −0.00961042 −0.000538080 0
\(320\) −25.1518 −1.40603
\(321\) −10.5464 −0.588640
\(322\) 0.0477080 0.00265866
\(323\) −6.81607 −0.379257
\(324\) −1.07942 −0.0599680
\(325\) −11.9062 −0.660436
\(326\) −3.09185 −0.171242
\(327\) −12.0152 −0.664439
\(328\) −19.7995 −1.09325
\(329\) 0.0287674 0.00158600
\(330\) 0.245743 0.0135277
\(331\) −14.5188 −0.798028 −0.399014 0.916945i \(-0.630648\pi\)
−0.399014 + 0.916945i \(0.630648\pi\)
\(332\) −10.8821 −0.597231
\(333\) 0.619732 0.0339611
\(334\) 12.8325 0.702165
\(335\) −56.5990 −3.09233
\(336\) 0.0107969 0.000589021 0
\(337\) 1.09532 0.0596660 0.0298330 0.999555i \(-0.490502\pi\)
0.0298330 + 0.999555i \(0.490502\pi\)
\(338\) −11.2270 −0.610669
\(339\) 12.3319 0.669778
\(340\) 4.24251 0.230083
\(341\) 0.195782 0.0106022
\(342\) −6.53980 −0.353632
\(343\) 0.223602 0.0120734
\(344\) −1.42698 −0.0769374
\(345\) 12.2359 0.658760
\(346\) 15.1785 0.815999
\(347\) −14.3275 −0.769140 −0.384570 0.923096i \(-0.625650\pi\)
−0.384570 + 0.923096i \(0.625650\pi\)
\(348\) −0.159189 −0.00853345
\(349\) −18.4260 −0.986321 −0.493160 0.869938i \(-0.664158\pi\)
−0.493160 + 0.869938i \(0.664158\pi\)
\(350\) −0.160105 −0.00855797
\(351\) −1.13960 −0.0608275
\(352\) −0.342812 −0.0182719
\(353\) −5.62999 −0.299654 −0.149827 0.988712i \(-0.547872\pi\)
−0.149827 + 0.988712i \(0.547872\pi\)
\(354\) −0.171243 −0.00910147
\(355\) −28.7922 −1.52813
\(356\) −3.85012 −0.204056
\(357\) −0.0159719 −0.000845321 0
\(358\) 11.2648 0.595362
\(359\) −29.6945 −1.56722 −0.783609 0.621254i \(-0.786623\pi\)
−0.783609 + 0.621254i \(0.786623\pi\)
\(360\) 11.6126 0.612040
\(361\) 27.4589 1.44520
\(362\) 12.0399 0.632805
\(363\) −10.9958 −0.577127
\(364\) −0.0196472 −0.00102979
\(365\) −16.2275 −0.849384
\(366\) 2.79347 0.146017
\(367\) 14.1238 0.737257 0.368628 0.929577i \(-0.379828\pi\)
0.368628 + 0.929577i \(0.379828\pi\)
\(368\) 2.10451 0.109705
\(369\) 6.70124 0.348853
\(370\) −2.33703 −0.121497
\(371\) −0.0394770 −0.00204955
\(372\) 3.24298 0.168141
\(373\) 26.1016 1.35149 0.675744 0.737137i \(-0.263823\pi\)
0.675744 + 0.737137i \(0.263823\pi\)
\(374\) −0.0625244 −0.00323306
\(375\) −21.4112 −1.10567
\(376\) 5.32162 0.274441
\(377\) −0.168064 −0.00865575
\(378\) −0.0153245 −0.000788206 0
\(379\) 21.4221 1.10038 0.550191 0.835039i \(-0.314555\pi\)
0.550191 + 0.835039i \(0.314555\pi\)
\(380\) −28.9173 −1.48343
\(381\) 12.0038 0.614974
\(382\) −7.12319 −0.364454
\(383\) −28.5364 −1.45814 −0.729071 0.684438i \(-0.760048\pi\)
−0.729071 + 0.684438i \(0.760048\pi\)
\(384\) −4.38124 −0.223579
\(385\) −0.00409079 −0.000208486 0
\(386\) −16.2113 −0.825135
\(387\) 0.482967 0.0245506
\(388\) 0.993223 0.0504233
\(389\) −14.3090 −0.725495 −0.362747 0.931887i \(-0.618161\pi\)
−0.362747 + 0.931887i \(0.618161\pi\)
\(390\) 4.29749 0.217612
\(391\) −3.11319 −0.157441
\(392\) 20.6815 1.04457
\(393\) 16.6459 0.839676
\(394\) 6.31740 0.318266
\(395\) −3.93035 −0.197757
\(396\) 0.0703415 0.00353479
\(397\) −13.6764 −0.686399 −0.343200 0.939263i \(-0.611511\pi\)
−0.343200 + 0.939263i \(0.611511\pi\)
\(398\) −23.6869 −1.18732
\(399\) 0.108865 0.00545009
\(400\) −7.06259 −0.353130
\(401\) −2.74041 −0.136849 −0.0684246 0.997656i \(-0.521797\pi\)
−0.0684246 + 0.997656i \(0.521797\pi\)
\(402\) 13.8168 0.689119
\(403\) 3.42378 0.170551
\(404\) −8.80245 −0.437938
\(405\) −3.93035 −0.195301
\(406\) −0.00226000 −0.000112162 0
\(407\) −0.0403853 −0.00200183
\(408\) −2.95460 −0.146275
\(409\) 13.0519 0.645377 0.322688 0.946505i \(-0.395413\pi\)
0.322688 + 0.946505i \(0.395413\pi\)
\(410\) −25.2707 −1.24803
\(411\) −10.2100 −0.503622
\(412\) −3.99237 −0.196690
\(413\) 0.00285062 0.000140270 0
\(414\) −2.98700 −0.146803
\(415\) −39.6233 −1.94503
\(416\) −5.99500 −0.293929
\(417\) 6.65275 0.325787
\(418\) 0.426171 0.0208447
\(419\) 23.1403 1.13048 0.565239 0.824927i \(-0.308784\pi\)
0.565239 + 0.824927i \(0.308784\pi\)
\(420\) −0.0677609 −0.00330639
\(421\) −7.23885 −0.352800 −0.176400 0.984319i \(-0.556445\pi\)
−0.176400 + 0.984319i \(0.556445\pi\)
\(422\) 0.831074 0.0404560
\(423\) −1.80113 −0.0875738
\(424\) −7.30278 −0.354654
\(425\) 10.4477 0.506786
\(426\) 7.02867 0.340540
\(427\) −0.0465018 −0.00225038
\(428\) 11.3840 0.550265
\(429\) 0.0742631 0.00358546
\(430\) −1.82129 −0.0878303
\(431\) −29.6728 −1.42929 −0.714644 0.699489i \(-0.753411\pi\)
−0.714644 + 0.699489i \(0.753411\pi\)
\(432\) −0.675997 −0.0325239
\(433\) 22.2900 1.07119 0.535596 0.844475i \(-0.320087\pi\)
0.535596 + 0.844475i \(0.320087\pi\)
\(434\) 0.0460403 0.00221000
\(435\) −0.579634 −0.0277913
\(436\) 12.9694 0.621123
\(437\) 21.2197 1.01508
\(438\) 3.96140 0.189283
\(439\) −10.0081 −0.477661 −0.238831 0.971061i \(-0.576764\pi\)
−0.238831 + 0.971061i \(0.576764\pi\)
\(440\) −0.756747 −0.0360765
\(441\) −6.99974 −0.333321
\(442\) −1.09341 −0.0520082
\(443\) −29.7876 −1.41525 −0.707625 0.706588i \(-0.750233\pi\)
−0.707625 + 0.706588i \(0.750233\pi\)
\(444\) −0.668953 −0.0317471
\(445\) −14.0189 −0.664560
\(446\) 8.14356 0.385609
\(447\) 3.47475 0.164350
\(448\) −0.102210 −0.00482897
\(449\) 0.598430 0.0282416 0.0141208 0.999900i \(-0.495505\pi\)
0.0141208 + 0.999900i \(0.495505\pi\)
\(450\) 10.0242 0.472545
\(451\) −0.436692 −0.0205630
\(452\) −13.3114 −0.626114
\(453\) −4.73716 −0.222571
\(454\) 6.94223 0.325815
\(455\) −0.0715386 −0.00335378
\(456\) 20.1388 0.943086
\(457\) −31.3201 −1.46509 −0.732547 0.680717i \(-0.761668\pi\)
−0.732547 + 0.680717i \(0.761668\pi\)
\(458\) 7.86849 0.367671
\(459\) 1.00000 0.0466760
\(460\) −13.2077 −0.615814
\(461\) −21.3776 −0.995654 −0.497827 0.867276i \(-0.665868\pi\)
−0.497827 + 0.867276i \(0.665868\pi\)
\(462\) 0.000998632 0 4.64606e−5 0
\(463\) 22.3273 1.03764 0.518818 0.854885i \(-0.326372\pi\)
0.518818 + 0.854885i \(0.326372\pi\)
\(464\) −0.0996936 −0.00462816
\(465\) 11.8082 0.547592
\(466\) −3.72600 −0.172603
\(467\) 25.7610 1.19208 0.596039 0.802956i \(-0.296740\pi\)
0.596039 + 0.802956i \(0.296740\pi\)
\(468\) 1.23011 0.0568620
\(469\) −0.230003 −0.0106205
\(470\) 6.79212 0.313297
\(471\) 0.886583 0.0408516
\(472\) 0.527330 0.0242723
\(473\) −0.0314729 −0.00144713
\(474\) 0.959467 0.0440698
\(475\) −71.2121 −3.26743
\(476\) 0.0172404 0.000790213 0
\(477\) 2.47166 0.113170
\(478\) −6.71502 −0.307138
\(479\) 17.4209 0.795979 0.397990 0.917390i \(-0.369708\pi\)
0.397990 + 0.917390i \(0.369708\pi\)
\(480\) −20.6761 −0.943729
\(481\) −0.706247 −0.0322021
\(482\) −8.55606 −0.389718
\(483\) 0.0497234 0.00226249
\(484\) 11.8691 0.539503
\(485\) 3.61648 0.164216
\(486\) 0.959467 0.0435223
\(487\) 1.10880 0.0502444 0.0251222 0.999684i \(-0.492003\pi\)
0.0251222 + 0.999684i \(0.492003\pi\)
\(488\) −8.60228 −0.389407
\(489\) −3.22247 −0.145725
\(490\) 26.3963 1.19246
\(491\) 36.3792 1.64177 0.820884 0.571094i \(-0.193481\pi\)
0.820884 + 0.571094i \(0.193481\pi\)
\(492\) −7.23348 −0.326110
\(493\) 0.147476 0.00664200
\(494\) 7.45277 0.335316
\(495\) 0.256125 0.0115119
\(496\) 2.03094 0.0911919
\(497\) −0.117004 −0.00524833
\(498\) 9.67274 0.433446
\(499\) 5.10789 0.228661 0.114330 0.993443i \(-0.463528\pi\)
0.114330 + 0.993443i \(0.463528\pi\)
\(500\) 23.1118 1.03359
\(501\) 13.3747 0.597536
\(502\) 24.1413 1.07748
\(503\) −17.2101 −0.767359 −0.383680 0.923466i \(-0.625343\pi\)
−0.383680 + 0.923466i \(0.625343\pi\)
\(504\) 0.0471906 0.00210204
\(505\) −32.0511 −1.42626
\(506\) 0.194650 0.00865326
\(507\) −11.7013 −0.519673
\(508\) −12.9572 −0.574883
\(509\) −7.65504 −0.339304 −0.169652 0.985504i \(-0.554264\pi\)
−0.169652 + 0.985504i \(0.554264\pi\)
\(510\) −3.77104 −0.166985
\(511\) −0.0659440 −0.00291719
\(512\) −7.55077 −0.333700
\(513\) −6.81607 −0.300937
\(514\) −6.17130 −0.272204
\(515\) −14.5368 −0.640570
\(516\) −0.521326 −0.0229501
\(517\) 0.117372 0.00516201
\(518\) −0.00949707 −0.000417277 0
\(519\) 15.8197 0.694407
\(520\) −13.2338 −0.580340
\(521\) 13.8703 0.607668 0.303834 0.952725i \(-0.401733\pi\)
0.303834 + 0.952725i \(0.401733\pi\)
\(522\) 0.141499 0.00619323
\(523\) −14.7109 −0.643264 −0.321632 0.946865i \(-0.604231\pi\)
−0.321632 + 0.946865i \(0.604231\pi\)
\(524\) −17.9680 −0.784936
\(525\) −0.166869 −0.00728275
\(526\) −18.5115 −0.807141
\(527\) −3.00436 −0.130872
\(528\) 0.0440519 0.00191711
\(529\) −13.3081 −0.578612
\(530\) −9.32073 −0.404867
\(531\) −0.178477 −0.00774526
\(532\) −0.117512 −0.00509479
\(533\) −7.63675 −0.330784
\(534\) 3.42226 0.148096
\(535\) 41.4509 1.79208
\(536\) −42.5477 −1.83778
\(537\) 11.7407 0.506647
\(538\) −23.7369 −1.02337
\(539\) 0.456144 0.0196475
\(540\) 4.24251 0.182569
\(541\) −30.8850 −1.32785 −0.663926 0.747799i \(-0.731111\pi\)
−0.663926 + 0.747799i \(0.731111\pi\)
\(542\) −21.2651 −0.913413
\(543\) 12.5486 0.538511
\(544\) 5.26061 0.225547
\(545\) 47.2238 2.02284
\(546\) 0.0174638 0.000747382 0
\(547\) −8.19687 −0.350473 −0.175236 0.984526i \(-0.556069\pi\)
−0.175236 + 0.984526i \(0.556069\pi\)
\(548\) 11.0209 0.470790
\(549\) 2.91148 0.124259
\(550\) −0.653234 −0.0278540
\(551\) −1.00521 −0.0428234
\(552\) 9.19824 0.391503
\(553\) −0.0159719 −0.000679193 0
\(554\) −18.6699 −0.793209
\(555\) −2.43576 −0.103392
\(556\) −7.18114 −0.304548
\(557\) 30.7603 1.30335 0.651677 0.758497i \(-0.274066\pi\)
0.651677 + 0.758497i \(0.274066\pi\)
\(558\) −2.88259 −0.122030
\(559\) −0.550390 −0.0232790
\(560\) −0.0424358 −0.00179324
\(561\) −0.0651658 −0.00275130
\(562\) 24.1757 1.01979
\(563\) −36.1210 −1.52232 −0.761159 0.648566i \(-0.775369\pi\)
−0.761159 + 0.648566i \(0.775369\pi\)
\(564\) 1.94418 0.0818647
\(565\) −48.4688 −2.03910
\(566\) 22.7673 0.956980
\(567\) −0.0159719 −0.000670756 0
\(568\) −21.6443 −0.908173
\(569\) 8.53839 0.357948 0.178974 0.983854i \(-0.442722\pi\)
0.178974 + 0.983854i \(0.442722\pi\)
\(570\) 25.7037 1.07661
\(571\) 23.0989 0.966659 0.483329 0.875439i \(-0.339427\pi\)
0.483329 + 0.875439i \(0.339427\pi\)
\(572\) −0.0801613 −0.00335171
\(573\) −7.42412 −0.310147
\(574\) −0.102693 −0.00428633
\(575\) −32.5255 −1.35641
\(576\) 6.39938 0.266641
\(577\) −9.68378 −0.403141 −0.201571 0.979474i \(-0.564605\pi\)
−0.201571 + 0.979474i \(0.564605\pi\)
\(578\) 0.959467 0.0399086
\(579\) −16.8962 −0.702181
\(580\) 0.625671 0.0259796
\(581\) −0.161018 −0.00668017
\(582\) −0.882845 −0.0365951
\(583\) −0.161068 −0.00667074
\(584\) −12.1988 −0.504792
\(585\) 4.47904 0.185185
\(586\) 21.5088 0.888522
\(587\) 10.9296 0.451113 0.225557 0.974230i \(-0.427580\pi\)
0.225557 + 0.974230i \(0.427580\pi\)
\(588\) 7.55569 0.311591
\(589\) 20.4780 0.843780
\(590\) 0.673045 0.0277088
\(591\) 6.58428 0.270841
\(592\) −0.418937 −0.0172182
\(593\) −9.83762 −0.403983 −0.201991 0.979387i \(-0.564741\pi\)
−0.201991 + 0.979387i \(0.564741\pi\)
\(594\) −0.0625244 −0.00256541
\(595\) 0.0627751 0.00257353
\(596\) −3.75073 −0.153636
\(597\) −24.6876 −1.01040
\(598\) 3.40399 0.139200
\(599\) 3.57030 0.145878 0.0729392 0.997336i \(-0.476762\pi\)
0.0729392 + 0.997336i \(0.476762\pi\)
\(600\) −30.8687 −1.26021
\(601\) 10.4946 0.428083 0.214041 0.976825i \(-0.431337\pi\)
0.214041 + 0.976825i \(0.431337\pi\)
\(602\) −0.00740121 −0.000301651 0
\(603\) 14.4005 0.586433
\(604\) 5.11340 0.208061
\(605\) 43.2172 1.75703
\(606\) 7.82423 0.317838
\(607\) −24.7558 −1.00481 −0.502403 0.864634i \(-0.667551\pi\)
−0.502403 + 0.864634i \(0.667551\pi\)
\(608\) −35.8567 −1.45418
\(609\) −0.00235547 −9.54486e−5 0
\(610\) −10.9793 −0.444540
\(611\) 2.05257 0.0830380
\(612\) −1.07942 −0.0436331
\(613\) −0.389380 −0.0157269 −0.00786346 0.999969i \(-0.502503\pi\)
−0.00786346 + 0.999969i \(0.502503\pi\)
\(614\) 6.91811 0.279192
\(615\) −26.3382 −1.06206
\(616\) −0.00307521 −0.000123904 0
\(617\) 31.5848 1.27156 0.635779 0.771871i \(-0.280679\pi\)
0.635779 + 0.771871i \(0.280679\pi\)
\(618\) 3.54870 0.142749
\(619\) −5.87315 −0.236062 −0.118031 0.993010i \(-0.537658\pi\)
−0.118031 + 0.993010i \(0.537658\pi\)
\(620\) −12.7461 −0.511894
\(621\) −3.11319 −0.124928
\(622\) 28.5809 1.14599
\(623\) −0.0569690 −0.00228242
\(624\) 0.770368 0.0308394
\(625\) 31.9154 1.27661
\(626\) 19.3150 0.771982
\(627\) 0.444175 0.0177386
\(628\) −0.956998 −0.0381884
\(629\) 0.619732 0.0247103
\(630\) 0.0602306 0.00239964
\(631\) −36.9771 −1.47203 −0.736017 0.676963i \(-0.763295\pi\)
−0.736017 + 0.676963i \(0.763295\pi\)
\(632\) −2.95460 −0.117528
\(633\) 0.866183 0.0344277
\(634\) 12.7620 0.506844
\(635\) −47.1792 −1.87225
\(636\) −2.66797 −0.105792
\(637\) 7.97692 0.316057
\(638\) −0.00922087 −0.000365058 0
\(639\) 7.32560 0.289796
\(640\) 17.2198 0.680672
\(641\) 11.8230 0.466980 0.233490 0.972359i \(-0.424985\pi\)
0.233490 + 0.972359i \(0.424985\pi\)
\(642\) −10.1189 −0.399360
\(643\) 7.95713 0.313798 0.156899 0.987615i \(-0.449850\pi\)
0.156899 + 0.987615i \(0.449850\pi\)
\(644\) −0.0536727 −0.00211500
\(645\) −1.89823 −0.0747427
\(646\) −6.53980 −0.257305
\(647\) −44.7463 −1.75916 −0.879580 0.475751i \(-0.842176\pi\)
−0.879580 + 0.475751i \(0.842176\pi\)
\(648\) −2.95460 −0.116068
\(649\) 0.0116306 0.000456542 0
\(650\) −11.4236 −0.448070
\(651\) 0.0479853 0.00188069
\(652\) 3.47841 0.136225
\(653\) 3.73814 0.146285 0.0731423 0.997322i \(-0.476697\pi\)
0.0731423 + 0.997322i \(0.476697\pi\)
\(654\) −11.5281 −0.450786
\(655\) −65.4244 −2.55634
\(656\) −4.53002 −0.176868
\(657\) 4.12876 0.161078
\(658\) 0.0276013 0.00107601
\(659\) 12.7381 0.496207 0.248104 0.968733i \(-0.420193\pi\)
0.248104 + 0.968733i \(0.420193\pi\)
\(660\) −0.276467 −0.0107615
\(661\) −29.0859 −1.13131 −0.565655 0.824642i \(-0.691377\pi\)
−0.565655 + 0.824642i \(0.691377\pi\)
\(662\) −13.9303 −0.541418
\(663\) −1.13960 −0.0442585
\(664\) −29.7865 −1.15594
\(665\) −0.427880 −0.0165925
\(666\) 0.594612 0.0230407
\(667\) −0.459121 −0.0177773
\(668\) −14.4369 −0.558581
\(669\) 8.48759 0.328149
\(670\) −54.3048 −2.09798
\(671\) −0.189729 −0.00732441
\(672\) −0.0840218 −0.00324121
\(673\) 6.07420 0.234143 0.117072 0.993123i \(-0.462649\pi\)
0.117072 + 0.993123i \(0.462649\pi\)
\(674\) 1.05093 0.0404801
\(675\) 10.4477 0.402131
\(676\) 12.6307 0.485795
\(677\) 42.3898 1.62917 0.814586 0.580043i \(-0.196964\pi\)
0.814586 + 0.580043i \(0.196964\pi\)
\(678\) 11.8321 0.454408
\(679\) 0.0146964 0.000563996 0
\(680\) 11.6126 0.445324
\(681\) 7.23551 0.277265
\(682\) 0.187846 0.00719300
\(683\) 37.5410 1.43647 0.718234 0.695801i \(-0.244951\pi\)
0.718234 + 0.695801i \(0.244951\pi\)
\(684\) 7.35743 0.281318
\(685\) 40.1288 1.53324
\(686\) 0.214539 0.00819113
\(687\) 8.20090 0.312884
\(688\) −0.326484 −0.0124471
\(689\) −2.81671 −0.107308
\(690\) 11.7400 0.446933
\(691\) 22.6172 0.860400 0.430200 0.902734i \(-0.358443\pi\)
0.430200 + 0.902734i \(0.358443\pi\)
\(692\) −17.0761 −0.649138
\(693\) 0.00104082 3.95375e−5 0
\(694\) −13.7468 −0.521820
\(695\) −26.1477 −0.991837
\(696\) −0.435734 −0.0165165
\(697\) 6.70124 0.253828
\(698\) −17.6791 −0.669165
\(699\) −3.88340 −0.146884
\(700\) 0.180122 0.00680798
\(701\) 25.4839 0.962512 0.481256 0.876580i \(-0.340181\pi\)
0.481256 + 0.876580i \(0.340181\pi\)
\(702\) −1.09341 −0.0412681
\(703\) −4.22414 −0.159316
\(704\) −0.417021 −0.0157171
\(705\) 7.07906 0.266613
\(706\) −5.40179 −0.203299
\(707\) −0.130247 −0.00489844
\(708\) 0.192653 0.00724033
\(709\) 8.91381 0.334765 0.167383 0.985892i \(-0.446468\pi\)
0.167383 + 0.985892i \(0.446468\pi\)
\(710\) −27.6252 −1.03675
\(711\) 1.00000 0.0375029
\(712\) −10.5386 −0.394950
\(713\) 9.35314 0.350278
\(714\) −0.0153245 −0.000573504 0
\(715\) −0.291880 −0.0109157
\(716\) −12.6732 −0.473618
\(717\) −6.99870 −0.261371
\(718\) −28.4909 −1.06327
\(719\) 48.7025 1.81630 0.908148 0.418648i \(-0.137496\pi\)
0.908148 + 0.418648i \(0.137496\pi\)
\(720\) 2.65691 0.0990170
\(721\) −0.0590738 −0.00220002
\(722\) 26.3459 0.980492
\(723\) −8.91752 −0.331646
\(724\) −13.5452 −0.503404
\(725\) 1.54078 0.0572233
\(726\) −10.5501 −0.391549
\(727\) 38.5277 1.42891 0.714456 0.699680i \(-0.246674\pi\)
0.714456 + 0.699680i \(0.246674\pi\)
\(728\) −0.0537785 −0.00199316
\(729\) 1.00000 0.0370370
\(730\) −15.5697 −0.576261
\(731\) 0.482967 0.0178632
\(732\) −3.14272 −0.116158
\(733\) 27.5212 1.01652 0.508260 0.861204i \(-0.330289\pi\)
0.508260 + 0.861204i \(0.330289\pi\)
\(734\) 13.5513 0.500188
\(735\) 27.5115 1.01478
\(736\) −16.3773 −0.603674
\(737\) −0.938419 −0.0345671
\(738\) 6.42962 0.236678
\(739\) 34.8732 1.28283 0.641416 0.767194i \(-0.278347\pi\)
0.641416 + 0.767194i \(0.278347\pi\)
\(740\) 2.62922 0.0966521
\(741\) 7.76761 0.285350
\(742\) −0.0378769 −0.00139051
\(743\) 1.40984 0.0517219 0.0258610 0.999666i \(-0.491767\pi\)
0.0258610 + 0.999666i \(0.491767\pi\)
\(744\) 8.87670 0.325436
\(745\) −13.6570 −0.500354
\(746\) 25.0436 0.916910
\(747\) 10.0814 0.368858
\(748\) 0.0703415 0.00257194
\(749\) 0.168445 0.00615485
\(750\) −20.5434 −0.750138
\(751\) 40.3381 1.47196 0.735979 0.677005i \(-0.236722\pi\)
0.735979 + 0.677005i \(0.236722\pi\)
\(752\) 1.21756 0.0443997
\(753\) 25.1611 0.916923
\(754\) −0.161252 −0.00587246
\(755\) 18.6187 0.677604
\(756\) 0.0172404 0.000627028 0
\(757\) −2.61955 −0.0952090 −0.0476045 0.998866i \(-0.515159\pi\)
−0.0476045 + 0.998866i \(0.515159\pi\)
\(758\) 20.5538 0.746549
\(759\) 0.202873 0.00736384
\(760\) −79.1526 −2.87117
\(761\) 15.4011 0.558289 0.279144 0.960249i \(-0.409949\pi\)
0.279144 + 0.960249i \(0.409949\pi\)
\(762\) 11.5173 0.417226
\(763\) 0.191904 0.00694741
\(764\) 8.01377 0.289928
\(765\) −3.93035 −0.142102
\(766\) −27.3797 −0.989270
\(767\) 0.203393 0.00734410
\(768\) −17.0024 −0.613521
\(769\) 15.2773 0.550913 0.275457 0.961314i \(-0.411171\pi\)
0.275457 + 0.961314i \(0.411171\pi\)
\(770\) −0.00392498 −0.000141446 0
\(771\) −6.43201 −0.231643
\(772\) 18.2381 0.656405
\(773\) 23.9573 0.861684 0.430842 0.902427i \(-0.358217\pi\)
0.430842 + 0.902427i \(0.358217\pi\)
\(774\) 0.463390 0.0166562
\(775\) −31.3886 −1.12751
\(776\) 2.71866 0.0975940
\(777\) −0.00989828 −0.000355099 0
\(778\) −13.7290 −0.492209
\(779\) −45.6762 −1.63652
\(780\) −4.83478 −0.173113
\(781\) −0.477379 −0.0170820
\(782\) −2.98700 −0.106815
\(783\) 0.147476 0.00527037
\(784\) 4.73181 0.168993
\(785\) −3.48458 −0.124370
\(786\) 15.9712 0.569674
\(787\) 27.8730 0.993567 0.496783 0.867875i \(-0.334514\pi\)
0.496783 + 0.867875i \(0.334514\pi\)
\(788\) −7.10723 −0.253184
\(789\) −19.2936 −0.686869
\(790\) −3.77104 −0.134168
\(791\) −0.196964 −0.00700323
\(792\) 0.192539 0.00684158
\(793\) −3.31793 −0.117823
\(794\) −13.1221 −0.465684
\(795\) −9.71449 −0.344538
\(796\) 26.6484 0.944527
\(797\) 19.4277 0.688163 0.344082 0.938940i \(-0.388190\pi\)
0.344082 + 0.938940i \(0.388190\pi\)
\(798\) 0.104453 0.00369759
\(799\) −1.80113 −0.0637193
\(800\) 54.9611 1.94317
\(801\) 3.56683 0.126028
\(802\) −2.62933 −0.0928448
\(803\) −0.269054 −0.00949470
\(804\) −15.5442 −0.548202
\(805\) −0.195431 −0.00688802
\(806\) 3.28500 0.115709
\(807\) −24.7396 −0.870877
\(808\) −24.0941 −0.847628
\(809\) −14.9533 −0.525731 −0.262866 0.964832i \(-0.584668\pi\)
−0.262866 + 0.964832i \(0.584668\pi\)
\(810\) −3.77104 −0.132501
\(811\) 44.0460 1.54666 0.773332 0.634001i \(-0.218589\pi\)
0.773332 + 0.634001i \(0.218589\pi\)
\(812\) 0.00254255 8.92262e−5 0
\(813\) −22.1634 −0.777305
\(814\) −0.0387484 −0.00135813
\(815\) 12.6654 0.443651
\(816\) −0.675997 −0.0236646
\(817\) −3.29194 −0.115170
\(818\) 12.5229 0.437853
\(819\) 0.0182016 0.000636015 0
\(820\) 28.4301 0.992823
\(821\) 34.6371 1.20884 0.604421 0.796665i \(-0.293405\pi\)
0.604421 + 0.796665i \(0.293405\pi\)
\(822\) −9.79614 −0.341680
\(823\) 23.1865 0.808231 0.404116 0.914708i \(-0.367579\pi\)
0.404116 + 0.914708i \(0.367579\pi\)
\(824\) −10.9279 −0.380693
\(825\) −0.680831 −0.0237035
\(826\) 0.00273507 9.51654e−5 0
\(827\) 9.59765 0.333743 0.166871 0.985979i \(-0.446634\pi\)
0.166871 + 0.985979i \(0.446634\pi\)
\(828\) 3.36045 0.116784
\(829\) 34.6244 1.20255 0.601277 0.799040i \(-0.294659\pi\)
0.601277 + 0.799040i \(0.294659\pi\)
\(830\) −38.0173 −1.31960
\(831\) −19.4586 −0.675013
\(832\) −7.29274 −0.252830
\(833\) −6.99974 −0.242527
\(834\) 6.38309 0.221028
\(835\) −52.5671 −1.81916
\(836\) −0.479453 −0.0165822
\(837\) −3.00436 −0.103846
\(838\) 22.2024 0.766968
\(839\) −7.76267 −0.267997 −0.133999 0.990982i \(-0.542782\pi\)
−0.133999 + 0.990982i \(0.542782\pi\)
\(840\) −0.185476 −0.00639951
\(841\) −28.9783 −0.999250
\(842\) −6.94543 −0.239355
\(843\) 25.1970 0.867832
\(844\) −0.934979 −0.0321833
\(845\) 45.9903 1.58211
\(846\) −1.72812 −0.0594140
\(847\) 0.175623 0.00603447
\(848\) −1.67084 −0.0573767
\(849\) 23.7291 0.814380
\(850\) 10.0242 0.343827
\(851\) −1.92934 −0.0661369
\(852\) −7.90743 −0.270904
\(853\) −33.4815 −1.14638 −0.573192 0.819421i \(-0.694295\pi\)
−0.573192 + 0.819421i \(0.694295\pi\)
\(854\) −0.0446169 −0.00152676
\(855\) 26.7896 0.916184
\(856\) 31.1603 1.06504
\(857\) 20.5662 0.702527 0.351263 0.936277i \(-0.385752\pi\)
0.351263 + 0.936277i \(0.385752\pi\)
\(858\) 0.0712530 0.00243254
\(859\) 33.3077 1.13644 0.568221 0.822876i \(-0.307632\pi\)
0.568221 + 0.822876i \(0.307632\pi\)
\(860\) 2.04899 0.0698701
\(861\) −0.107031 −0.00364762
\(862\) −28.4700 −0.969693
\(863\) −21.8597 −0.744111 −0.372056 0.928210i \(-0.621347\pi\)
−0.372056 + 0.928210i \(0.621347\pi\)
\(864\) 5.26061 0.178970
\(865\) −62.1769 −2.11408
\(866\) 21.3866 0.726745
\(867\) 1.00000 0.0339618
\(868\) −0.0517965 −0.00175809
\(869\) −0.0651658 −0.00221060
\(870\) −0.556139 −0.0188549
\(871\) −16.4108 −0.556059
\(872\) 35.5000 1.20218
\(873\) −0.920142 −0.0311421
\(874\) 20.3596 0.688674
\(875\) 0.341978 0.0115610
\(876\) −4.45668 −0.150577
\(877\) 9.72757 0.328477 0.164238 0.986421i \(-0.447483\pi\)
0.164238 + 0.986421i \(0.447483\pi\)
\(878\) −9.60245 −0.324067
\(879\) 22.4175 0.756123
\(880\) −0.173139 −0.00583653
\(881\) 42.8279 1.44291 0.721455 0.692461i \(-0.243474\pi\)
0.721455 + 0.692461i \(0.243474\pi\)
\(882\) −6.71602 −0.226140
\(883\) −2.78237 −0.0936341 −0.0468171 0.998903i \(-0.514908\pi\)
−0.0468171 + 0.998903i \(0.514908\pi\)
\(884\) 1.23011 0.0413732
\(885\) 0.701479 0.0235799
\(886\) −28.5802 −0.960170
\(887\) 31.6063 1.06124 0.530618 0.847611i \(-0.321960\pi\)
0.530618 + 0.847611i \(0.321960\pi\)
\(888\) −1.83106 −0.0614464
\(889\) −0.191723 −0.00643020
\(890\) −13.4507 −0.450868
\(891\) −0.0651658 −0.00218314
\(892\) −9.16170 −0.306757
\(893\) 12.2766 0.410821
\(894\) 3.33391 0.111503
\(895\) −46.1449 −1.54246
\(896\) 0.0699766 0.00233775
\(897\) 3.54779 0.118457
\(898\) 0.574173 0.0191604
\(899\) −0.443072 −0.0147773
\(900\) −11.2775 −0.375915
\(901\) 2.47166 0.0823429
\(902\) −0.418991 −0.0139509
\(903\) −0.00771388 −0.000256702 0
\(904\) −36.4359 −1.21184
\(905\) −49.3203 −1.63946
\(906\) −4.54515 −0.151002
\(907\) −42.8161 −1.42168 −0.710842 0.703352i \(-0.751686\pi\)
−0.710842 + 0.703352i \(0.751686\pi\)
\(908\) −7.81018 −0.259190
\(909\) 8.15477 0.270477
\(910\) −0.0686389 −0.00227536
\(911\) 33.8733 1.12227 0.561136 0.827723i \(-0.310364\pi\)
0.561136 + 0.827723i \(0.310364\pi\)
\(912\) 4.60765 0.152574
\(913\) −0.656961 −0.0217422
\(914\) −30.0506 −0.993986
\(915\) −11.4431 −0.378299
\(916\) −8.85225 −0.292487
\(917\) −0.265867 −0.00877969
\(918\) 0.959467 0.0316671
\(919\) −29.2074 −0.963464 −0.481732 0.876319i \(-0.659992\pi\)
−0.481732 + 0.876319i \(0.659992\pi\)
\(920\) −36.1523 −1.19191
\(921\) 7.21037 0.237590
\(922\) −20.5111 −0.675497
\(923\) −8.34827 −0.274787
\(924\) −0.00112349 −3.69600e−5 0
\(925\) 6.47475 0.212888
\(926\) 21.4223 0.703979
\(927\) 3.69861 0.121478
\(928\) 0.775816 0.0254674
\(929\) 33.9710 1.11455 0.557277 0.830327i \(-0.311846\pi\)
0.557277 + 0.830327i \(0.311846\pi\)
\(930\) 11.3296 0.371511
\(931\) 47.7108 1.56366
\(932\) 4.19184 0.137308
\(933\) 29.7883 0.975226
\(934\) 24.7168 0.808759
\(935\) 0.256125 0.00837617
\(936\) 3.36707 0.110056
\(937\) −6.02058 −0.196684 −0.0983418 0.995153i \(-0.531354\pi\)
−0.0983418 + 0.995153i \(0.531354\pi\)
\(938\) −0.220680 −0.00720546
\(939\) 20.1310 0.656949
\(940\) −7.64130 −0.249232
\(941\) −21.1006 −0.687860 −0.343930 0.938995i \(-0.611758\pi\)
−0.343930 + 0.938995i \(0.611758\pi\)
\(942\) 0.850646 0.0277156
\(943\) −20.8622 −0.679367
\(944\) 0.120650 0.00392683
\(945\) 0.0627751 0.00204207
\(946\) −0.0301972 −0.000981796 0
\(947\) 23.6547 0.768675 0.384338 0.923193i \(-0.374430\pi\)
0.384338 + 0.923193i \(0.374430\pi\)
\(948\) −1.07942 −0.0350581
\(949\) −4.70514 −0.152735
\(950\) −68.3256 −2.21678
\(951\) 13.3012 0.431319
\(952\) 0.0471906 0.00152946
\(953\) 24.4904 0.793323 0.396661 0.917965i \(-0.370169\pi\)
0.396661 + 0.917965i \(0.370169\pi\)
\(954\) 2.37148 0.0767794
\(955\) 29.1794 0.944223
\(956\) 7.55456 0.244332
\(957\) −0.00961042 −0.000310661 0
\(958\) 16.7147 0.540028
\(959\) 0.163073 0.00526589
\(960\) −25.1518 −0.811771
\(961\) −21.9738 −0.708832
\(962\) −0.677621 −0.0218474
\(963\) −10.5464 −0.339851
\(964\) 9.62578 0.310025
\(965\) 66.4079 2.13775
\(966\) 0.0477080 0.00153498
\(967\) −9.73216 −0.312965 −0.156483 0.987681i \(-0.550015\pi\)
−0.156483 + 0.987681i \(0.550015\pi\)
\(968\) 32.4881 1.04421
\(969\) −6.81607 −0.218964
\(970\) 3.46989 0.111412
\(971\) 5.94716 0.190854 0.0954268 0.995436i \(-0.469578\pi\)
0.0954268 + 0.995436i \(0.469578\pi\)
\(972\) −1.07942 −0.0346225
\(973\) −0.106257 −0.00340644
\(974\) 1.06385 0.0340881
\(975\) −11.9062 −0.381303
\(976\) −1.96815 −0.0629990
\(977\) 3.55776 0.113823 0.0569114 0.998379i \(-0.481875\pi\)
0.0569114 + 0.998379i \(0.481875\pi\)
\(978\) −3.09185 −0.0988666
\(979\) −0.232436 −0.00742867
\(980\) −29.6965 −0.948621
\(981\) −12.0152 −0.383614
\(982\) 34.9046 1.11385
\(983\) −0.0183782 −0.000586173 0 −0.000293087 1.00000i \(-0.500093\pi\)
−0.000293087 1.00000i \(0.500093\pi\)
\(984\) −19.7995 −0.631186
\(985\) −25.8785 −0.824559
\(986\) 0.141499 0.00450623
\(987\) 0.0287674 0.000915675 0
\(988\) −8.38455 −0.266748
\(989\) −1.50357 −0.0478106
\(990\) 0.245743 0.00781022
\(991\) −49.7820 −1.58138 −0.790689 0.612218i \(-0.790278\pi\)
−0.790689 + 0.612218i \(0.790278\pi\)
\(992\) −15.8048 −0.501802
\(993\) −14.5188 −0.460742
\(994\) −0.112261 −0.00356070
\(995\) 97.0309 3.07609
\(996\) −10.8821 −0.344812
\(997\) 13.7478 0.435398 0.217699 0.976016i \(-0.430145\pi\)
0.217699 + 0.976016i \(0.430145\pi\)
\(998\) 4.90085 0.155134
\(999\) 0.619732 0.0196074
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.k.1.20 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.20 31 1.1 even 1 trivial