Properties

Label 6001.2.a.d.1.18
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.15009 q^{2} -0.229401 q^{3} +2.62287 q^{4} +4.13461 q^{5} +0.493233 q^{6} -0.301576 q^{7} -1.33923 q^{8} -2.94737 q^{9} +O(q^{10})\) \(q-2.15009 q^{2} -0.229401 q^{3} +2.62287 q^{4} +4.13461 q^{5} +0.493233 q^{6} -0.301576 q^{7} -1.33923 q^{8} -2.94737 q^{9} -8.88976 q^{10} -5.38017 q^{11} -0.601690 q^{12} -0.811082 q^{13} +0.648415 q^{14} -0.948485 q^{15} -2.36629 q^{16} +1.00000 q^{17} +6.33711 q^{18} +2.69071 q^{19} +10.8445 q^{20} +0.0691820 q^{21} +11.5678 q^{22} -0.617925 q^{23} +0.307221 q^{24} +12.0950 q^{25} +1.74390 q^{26} +1.36434 q^{27} -0.790996 q^{28} +3.32277 q^{29} +2.03932 q^{30} +0.966316 q^{31} +7.76618 q^{32} +1.23422 q^{33} -2.15009 q^{34} -1.24690 q^{35} -7.73059 q^{36} -8.98970 q^{37} -5.78525 q^{38} +0.186063 q^{39} -5.53718 q^{40} -1.11131 q^{41} -0.148747 q^{42} +10.4631 q^{43} -14.1115 q^{44} -12.1862 q^{45} +1.32859 q^{46} +0.820515 q^{47} +0.542830 q^{48} -6.90905 q^{49} -26.0052 q^{50} -0.229401 q^{51} -2.12736 q^{52} +2.60253 q^{53} -2.93344 q^{54} -22.2449 q^{55} +0.403879 q^{56} -0.617252 q^{57} -7.14423 q^{58} +2.03633 q^{59} -2.48775 q^{60} -4.11570 q^{61} -2.07766 q^{62} +0.888858 q^{63} -11.9654 q^{64} -3.35350 q^{65} -2.65367 q^{66} +7.84579 q^{67} +2.62287 q^{68} +0.141753 q^{69} +2.68094 q^{70} -6.52799 q^{71} +3.94721 q^{72} -13.3574 q^{73} +19.3286 q^{74} -2.77460 q^{75} +7.05738 q^{76} +1.62253 q^{77} -0.400052 q^{78} +4.58165 q^{79} -9.78367 q^{80} +8.52914 q^{81} +2.38941 q^{82} +15.6604 q^{83} +0.181456 q^{84} +4.13461 q^{85} -22.4965 q^{86} -0.762247 q^{87} +7.20527 q^{88} -10.5903 q^{89} +26.2015 q^{90} +0.244603 q^{91} -1.62074 q^{92} -0.221674 q^{93} -1.76418 q^{94} +11.1250 q^{95} -1.78157 q^{96} +14.2851 q^{97} +14.8551 q^{98} +15.8574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15009 −1.52034 −0.760170 0.649724i \(-0.774885\pi\)
−0.760170 + 0.649724i \(0.774885\pi\)
\(3\) −0.229401 −0.132445 −0.0662225 0.997805i \(-0.521095\pi\)
−0.0662225 + 0.997805i \(0.521095\pi\)
\(4\) 2.62287 1.31144
\(5\) 4.13461 1.84905 0.924526 0.381119i \(-0.124461\pi\)
0.924526 + 0.381119i \(0.124461\pi\)
\(6\) 0.493233 0.201361
\(7\) −0.301576 −0.113985 −0.0569926 0.998375i \(-0.518151\pi\)
−0.0569926 + 0.998375i \(0.518151\pi\)
\(8\) −1.33923 −0.473489
\(9\) −2.94737 −0.982458
\(10\) −8.88976 −2.81119
\(11\) −5.38017 −1.62218 −0.811090 0.584921i \(-0.801126\pi\)
−0.811090 + 0.584921i \(0.801126\pi\)
\(12\) −0.601690 −0.173693
\(13\) −0.811082 −0.224954 −0.112477 0.993654i \(-0.535878\pi\)
−0.112477 + 0.993654i \(0.535878\pi\)
\(14\) 0.648415 0.173296
\(15\) −0.948485 −0.244898
\(16\) −2.36629 −0.591572
\(17\) 1.00000 0.242536
\(18\) 6.33711 1.49367
\(19\) 2.69071 0.617291 0.308645 0.951177i \(-0.400124\pi\)
0.308645 + 0.951177i \(0.400124\pi\)
\(20\) 10.8445 2.42491
\(21\) 0.0691820 0.0150968
\(22\) 11.5678 2.46627
\(23\) −0.617925 −0.128846 −0.0644231 0.997923i \(-0.520521\pi\)
−0.0644231 + 0.997923i \(0.520521\pi\)
\(24\) 0.307221 0.0627112
\(25\) 12.0950 2.41899
\(26\) 1.74390 0.342006
\(27\) 1.36434 0.262567
\(28\) −0.790996 −0.149484
\(29\) 3.32277 0.617022 0.308511 0.951221i \(-0.400169\pi\)
0.308511 + 0.951221i \(0.400169\pi\)
\(30\) 2.03932 0.372328
\(31\) 0.966316 0.173555 0.0867777 0.996228i \(-0.472343\pi\)
0.0867777 + 0.996228i \(0.472343\pi\)
\(32\) 7.76618 1.37288
\(33\) 1.23422 0.214850
\(34\) −2.15009 −0.368737
\(35\) −1.24690 −0.210764
\(36\) −7.73059 −1.28843
\(37\) −8.98970 −1.47790 −0.738949 0.673761i \(-0.764678\pi\)
−0.738949 + 0.673761i \(0.764678\pi\)
\(38\) −5.78525 −0.938492
\(39\) 0.186063 0.0297940
\(40\) −5.53718 −0.875505
\(41\) −1.11131 −0.173557 −0.0867787 0.996228i \(-0.527657\pi\)
−0.0867787 + 0.996228i \(0.527657\pi\)
\(42\) −0.148747 −0.0229522
\(43\) 10.4631 1.59560 0.797802 0.602920i \(-0.205996\pi\)
0.797802 + 0.602920i \(0.205996\pi\)
\(44\) −14.1115 −2.12739
\(45\) −12.1862 −1.81662
\(46\) 1.32859 0.195890
\(47\) 0.820515 0.119684 0.0598422 0.998208i \(-0.480940\pi\)
0.0598422 + 0.998208i \(0.480940\pi\)
\(48\) 0.542830 0.0783507
\(49\) −6.90905 −0.987007
\(50\) −26.0052 −3.67770
\(51\) −0.229401 −0.0321226
\(52\) −2.12736 −0.295012
\(53\) 2.60253 0.357485 0.178743 0.983896i \(-0.442797\pi\)
0.178743 + 0.983896i \(0.442797\pi\)
\(54\) −2.93344 −0.399191
\(55\) −22.2449 −2.99950
\(56\) 0.403879 0.0539706
\(57\) −0.617252 −0.0817570
\(58\) −7.14423 −0.938084
\(59\) 2.03633 0.265108 0.132554 0.991176i \(-0.457682\pi\)
0.132554 + 0.991176i \(0.457682\pi\)
\(60\) −2.48775 −0.321168
\(61\) −4.11570 −0.526961 −0.263481 0.964665i \(-0.584871\pi\)
−0.263481 + 0.964665i \(0.584871\pi\)
\(62\) −2.07766 −0.263863
\(63\) 0.888858 0.111986
\(64\) −11.9654 −1.49567
\(65\) −3.35350 −0.415951
\(66\) −2.65367 −0.326645
\(67\) 7.84579 0.958515 0.479258 0.877674i \(-0.340906\pi\)
0.479258 + 0.877674i \(0.340906\pi\)
\(68\) 2.62287 0.318070
\(69\) 0.141753 0.0170650
\(70\) 2.68094 0.320434
\(71\) −6.52799 −0.774730 −0.387365 0.921926i \(-0.626615\pi\)
−0.387365 + 0.921926i \(0.626615\pi\)
\(72\) 3.94721 0.465183
\(73\) −13.3574 −1.56336 −0.781681 0.623679i \(-0.785637\pi\)
−0.781681 + 0.623679i \(0.785637\pi\)
\(74\) 19.3286 2.24691
\(75\) −2.77460 −0.320384
\(76\) 7.05738 0.809537
\(77\) 1.62253 0.184904
\(78\) −0.400052 −0.0452970
\(79\) 4.58165 0.515476 0.257738 0.966215i \(-0.417023\pi\)
0.257738 + 0.966215i \(0.417023\pi\)
\(80\) −9.78367 −1.09385
\(81\) 8.52914 0.947683
\(82\) 2.38941 0.263866
\(83\) 15.6604 1.71896 0.859478 0.511173i \(-0.170789\pi\)
0.859478 + 0.511173i \(0.170789\pi\)
\(84\) 0.181456 0.0197984
\(85\) 4.13461 0.448461
\(86\) −22.4965 −2.42586
\(87\) −0.762247 −0.0817215
\(88\) 7.20527 0.768084
\(89\) −10.5903 −1.12257 −0.561286 0.827622i \(-0.689693\pi\)
−0.561286 + 0.827622i \(0.689693\pi\)
\(90\) 26.2015 2.76188
\(91\) 0.244603 0.0256414
\(92\) −1.62074 −0.168974
\(93\) −0.221674 −0.0229865
\(94\) −1.76418 −0.181961
\(95\) 11.1250 1.14140
\(96\) −1.78157 −0.181831
\(97\) 14.2851 1.45043 0.725214 0.688523i \(-0.241741\pi\)
0.725214 + 0.688523i \(0.241741\pi\)
\(98\) 14.8551 1.50059
\(99\) 15.8574 1.59373
\(100\) 31.7236 3.17236
\(101\) −0.129727 −0.0129083 −0.00645415 0.999979i \(-0.502054\pi\)
−0.00645415 + 0.999979i \(0.502054\pi\)
\(102\) 0.493233 0.0488373
\(103\) −1.68298 −0.165829 −0.0829146 0.996557i \(-0.526423\pi\)
−0.0829146 + 0.996557i \(0.526423\pi\)
\(104\) 1.08622 0.106513
\(105\) 0.286040 0.0279147
\(106\) −5.59567 −0.543499
\(107\) −1.12537 −0.108794 −0.0543969 0.998519i \(-0.517324\pi\)
−0.0543969 + 0.998519i \(0.517324\pi\)
\(108\) 3.57848 0.344339
\(109\) 11.7229 1.12285 0.561424 0.827528i \(-0.310254\pi\)
0.561424 + 0.827528i \(0.310254\pi\)
\(110\) 47.8284 4.56026
\(111\) 2.06225 0.195740
\(112\) 0.713616 0.0674304
\(113\) −8.81705 −0.829439 −0.414719 0.909949i \(-0.636120\pi\)
−0.414719 + 0.909949i \(0.636120\pi\)
\(114\) 1.32715 0.124299
\(115\) −2.55488 −0.238243
\(116\) 8.71519 0.809185
\(117\) 2.39056 0.221008
\(118\) −4.37829 −0.403054
\(119\) −0.301576 −0.0276455
\(120\) 1.27024 0.115956
\(121\) 17.9462 1.63147
\(122\) 8.84911 0.801161
\(123\) 0.254936 0.0229868
\(124\) 2.53452 0.227607
\(125\) 29.3349 2.62379
\(126\) −1.91112 −0.170256
\(127\) −6.39058 −0.567072 −0.283536 0.958962i \(-0.591508\pi\)
−0.283536 + 0.958962i \(0.591508\pi\)
\(128\) 10.1942 0.901052
\(129\) −2.40024 −0.211330
\(130\) 7.21032 0.632387
\(131\) 4.62743 0.404300 0.202150 0.979355i \(-0.435207\pi\)
0.202150 + 0.979355i \(0.435207\pi\)
\(132\) 3.23719 0.281762
\(133\) −0.811453 −0.0703619
\(134\) −16.8691 −1.45727
\(135\) 5.64099 0.485499
\(136\) −1.33923 −0.114838
\(137\) −0.514658 −0.0439702 −0.0219851 0.999758i \(-0.506999\pi\)
−0.0219851 + 0.999758i \(0.506999\pi\)
\(138\) −0.304781 −0.0259447
\(139\) −3.65059 −0.309639 −0.154819 0.987943i \(-0.549480\pi\)
−0.154819 + 0.987943i \(0.549480\pi\)
\(140\) −3.27046 −0.276404
\(141\) −0.188227 −0.0158516
\(142\) 14.0357 1.17785
\(143\) 4.36375 0.364916
\(144\) 6.97434 0.581195
\(145\) 13.7383 1.14091
\(146\) 28.7195 2.37684
\(147\) 1.58495 0.130724
\(148\) −23.5788 −1.93817
\(149\) 1.45346 0.119072 0.0595359 0.998226i \(-0.481038\pi\)
0.0595359 + 0.998226i \(0.481038\pi\)
\(150\) 5.96564 0.487092
\(151\) −12.5756 −1.02339 −0.511694 0.859168i \(-0.670982\pi\)
−0.511694 + 0.859168i \(0.670982\pi\)
\(152\) −3.60347 −0.292280
\(153\) −2.94737 −0.238281
\(154\) −3.48858 −0.281118
\(155\) 3.99534 0.320913
\(156\) 0.488020 0.0390729
\(157\) 17.8395 1.42375 0.711874 0.702307i \(-0.247847\pi\)
0.711874 + 0.702307i \(0.247847\pi\)
\(158\) −9.85094 −0.783699
\(159\) −0.597024 −0.0473471
\(160\) 32.1101 2.53853
\(161\) 0.186351 0.0146866
\(162\) −18.3384 −1.44080
\(163\) 22.2011 1.73892 0.869462 0.494001i \(-0.164466\pi\)
0.869462 + 0.494001i \(0.164466\pi\)
\(164\) −2.91482 −0.227609
\(165\) 5.10300 0.397268
\(166\) −33.6713 −2.61340
\(167\) −3.68696 −0.285305 −0.142653 0.989773i \(-0.545563\pi\)
−0.142653 + 0.989773i \(0.545563\pi\)
\(168\) −0.0926505 −0.00714814
\(169\) −12.3421 −0.949396
\(170\) −8.88976 −0.681814
\(171\) −7.93052 −0.606462
\(172\) 27.4433 2.09253
\(173\) 13.1657 1.00097 0.500483 0.865746i \(-0.333156\pi\)
0.500483 + 0.865746i \(0.333156\pi\)
\(174\) 1.63890 0.124245
\(175\) −3.64756 −0.275729
\(176\) 12.7310 0.959637
\(177\) −0.467137 −0.0351122
\(178\) 22.7701 1.70669
\(179\) 11.5441 0.862846 0.431423 0.902150i \(-0.358012\pi\)
0.431423 + 0.902150i \(0.358012\pi\)
\(180\) −31.9629 −2.38238
\(181\) 16.8525 1.25264 0.626318 0.779568i \(-0.284561\pi\)
0.626318 + 0.779568i \(0.284561\pi\)
\(182\) −0.525918 −0.0389836
\(183\) 0.944147 0.0697934
\(184\) 0.827542 0.0610072
\(185\) −37.1689 −2.73271
\(186\) 0.476619 0.0349474
\(187\) −5.38017 −0.393437
\(188\) 2.15211 0.156958
\(189\) −0.411452 −0.0299287
\(190\) −23.9197 −1.73532
\(191\) −2.24328 −0.162318 −0.0811589 0.996701i \(-0.525862\pi\)
−0.0811589 + 0.996701i \(0.525862\pi\)
\(192\) 2.74488 0.198094
\(193\) 16.3118 1.17415 0.587076 0.809532i \(-0.300279\pi\)
0.587076 + 0.809532i \(0.300279\pi\)
\(194\) −30.7141 −2.20515
\(195\) 0.769299 0.0550906
\(196\) −18.1216 −1.29440
\(197\) 2.46129 0.175359 0.0876797 0.996149i \(-0.472055\pi\)
0.0876797 + 0.996149i \(0.472055\pi\)
\(198\) −34.0947 −2.42301
\(199\) 6.22025 0.440942 0.220471 0.975394i \(-0.429241\pi\)
0.220471 + 0.975394i \(0.429241\pi\)
\(200\) −16.1979 −1.14537
\(201\) −1.79983 −0.126951
\(202\) 0.278924 0.0196250
\(203\) −1.00207 −0.0703314
\(204\) −0.601690 −0.0421268
\(205\) −4.59483 −0.320917
\(206\) 3.61856 0.252117
\(207\) 1.82126 0.126586
\(208\) 1.91925 0.133076
\(209\) −14.4764 −1.00136
\(210\) −0.615012 −0.0424398
\(211\) −6.37786 −0.439070 −0.219535 0.975605i \(-0.570454\pi\)
−0.219535 + 0.975605i \(0.570454\pi\)
\(212\) 6.82611 0.468819
\(213\) 1.49753 0.102609
\(214\) 2.41965 0.165404
\(215\) 43.2607 2.95035
\(216\) −1.82716 −0.124322
\(217\) −0.291418 −0.0197827
\(218\) −25.2052 −1.70711
\(219\) 3.06420 0.207059
\(220\) −58.3454 −3.93365
\(221\) −0.811082 −0.0545593
\(222\) −4.43402 −0.297592
\(223\) −13.6750 −0.915745 −0.457872 0.889018i \(-0.651388\pi\)
−0.457872 + 0.889018i \(0.651388\pi\)
\(224\) −2.34210 −0.156488
\(225\) −35.6484 −2.37656
\(226\) 18.9574 1.26103
\(227\) 23.9413 1.58904 0.794520 0.607238i \(-0.207723\pi\)
0.794520 + 0.607238i \(0.207723\pi\)
\(228\) −1.61897 −0.107219
\(229\) −8.26655 −0.546269 −0.273134 0.961976i \(-0.588060\pi\)
−0.273134 + 0.961976i \(0.588060\pi\)
\(230\) 5.49320 0.362211
\(231\) −0.372211 −0.0244897
\(232\) −4.44994 −0.292153
\(233\) −25.1323 −1.64647 −0.823236 0.567699i \(-0.807834\pi\)
−0.823236 + 0.567699i \(0.807834\pi\)
\(234\) −5.13992 −0.336007
\(235\) 3.39251 0.221303
\(236\) 5.34103 0.347672
\(237\) −1.05104 −0.0682722
\(238\) 0.648415 0.0420305
\(239\) 3.37894 0.218565 0.109283 0.994011i \(-0.465145\pi\)
0.109283 + 0.994011i \(0.465145\pi\)
\(240\) 2.24439 0.144875
\(241\) −9.81730 −0.632388 −0.316194 0.948695i \(-0.602405\pi\)
−0.316194 + 0.948695i \(0.602405\pi\)
\(242\) −38.5858 −2.48039
\(243\) −6.04961 −0.388082
\(244\) −10.7950 −0.691076
\(245\) −28.5662 −1.82503
\(246\) −0.548134 −0.0349478
\(247\) −2.18238 −0.138862
\(248\) −1.29412 −0.0821765
\(249\) −3.59252 −0.227667
\(250\) −63.0726 −3.98906
\(251\) 3.97725 0.251041 0.125521 0.992091i \(-0.459940\pi\)
0.125521 + 0.992091i \(0.459940\pi\)
\(252\) 2.33136 0.146862
\(253\) 3.32454 0.209012
\(254\) 13.7403 0.862143
\(255\) −0.948485 −0.0593964
\(256\) 2.01226 0.125766
\(257\) −4.30378 −0.268462 −0.134231 0.990950i \(-0.542856\pi\)
−0.134231 + 0.990950i \(0.542856\pi\)
\(258\) 5.16073 0.321293
\(259\) 2.71108 0.168458
\(260\) −8.79581 −0.545493
\(261\) −9.79344 −0.606199
\(262\) −9.94936 −0.614674
\(263\) 22.7049 1.40004 0.700021 0.714122i \(-0.253174\pi\)
0.700021 + 0.714122i \(0.253174\pi\)
\(264\) −1.65290 −0.101729
\(265\) 10.7604 0.661009
\(266\) 1.74470 0.106974
\(267\) 2.42944 0.148679
\(268\) 20.5785 1.25703
\(269\) 32.1863 1.96243 0.981217 0.192909i \(-0.0617923\pi\)
0.981217 + 0.192909i \(0.0617923\pi\)
\(270\) −12.1286 −0.738125
\(271\) 11.5747 0.703113 0.351556 0.936167i \(-0.385653\pi\)
0.351556 + 0.936167i \(0.385653\pi\)
\(272\) −2.36629 −0.143477
\(273\) −0.0561123 −0.00339607
\(274\) 1.10656 0.0668497
\(275\) −65.0729 −3.92405
\(276\) 0.371800 0.0223797
\(277\) 26.9904 1.62170 0.810849 0.585255i \(-0.199006\pi\)
0.810849 + 0.585255i \(0.199006\pi\)
\(278\) 7.84908 0.470757
\(279\) −2.84810 −0.170511
\(280\) 1.66988 0.0997946
\(281\) −3.78428 −0.225751 −0.112875 0.993609i \(-0.536006\pi\)
−0.112875 + 0.993609i \(0.536006\pi\)
\(282\) 0.404705 0.0240998
\(283\) −15.4707 −0.919639 −0.459820 0.888012i \(-0.652086\pi\)
−0.459820 + 0.888012i \(0.652086\pi\)
\(284\) −17.1221 −1.01601
\(285\) −2.55209 −0.151173
\(286\) −9.38245 −0.554796
\(287\) 0.335145 0.0197830
\(288\) −22.8898 −1.34880
\(289\) 1.00000 0.0588235
\(290\) −29.5386 −1.73457
\(291\) −3.27702 −0.192102
\(292\) −35.0347 −2.05025
\(293\) −1.81795 −0.106206 −0.0531030 0.998589i \(-0.516911\pi\)
−0.0531030 + 0.998589i \(0.516911\pi\)
\(294\) −3.40777 −0.198745
\(295\) 8.41943 0.490198
\(296\) 12.0393 0.699768
\(297\) −7.34035 −0.425931
\(298\) −3.12506 −0.181030
\(299\) 0.501188 0.0289844
\(300\) −7.27743 −0.420163
\(301\) −3.15541 −0.181875
\(302\) 27.0386 1.55590
\(303\) 0.0297595 0.00170964
\(304\) −6.36699 −0.365172
\(305\) −17.0168 −0.974379
\(306\) 6.33711 0.362269
\(307\) 21.6248 1.23419 0.617095 0.786889i \(-0.288309\pi\)
0.617095 + 0.786889i \(0.288309\pi\)
\(308\) 4.25569 0.242490
\(309\) 0.386079 0.0219632
\(310\) −8.59032 −0.487897
\(311\) 14.3243 0.812258 0.406129 0.913816i \(-0.366878\pi\)
0.406129 + 0.913816i \(0.366878\pi\)
\(312\) −0.249181 −0.0141071
\(313\) −20.7723 −1.17412 −0.587060 0.809543i \(-0.699715\pi\)
−0.587060 + 0.809543i \(0.699715\pi\)
\(314\) −38.3565 −2.16458
\(315\) 3.67508 0.207067
\(316\) 12.0171 0.676013
\(317\) 0.451826 0.0253771 0.0126885 0.999919i \(-0.495961\pi\)
0.0126885 + 0.999919i \(0.495961\pi\)
\(318\) 1.28365 0.0719837
\(319\) −17.8770 −1.00092
\(320\) −49.4721 −2.76558
\(321\) 0.258162 0.0144092
\(322\) −0.400672 −0.0223286
\(323\) 2.69071 0.149715
\(324\) 22.3709 1.24283
\(325\) −9.81001 −0.544162
\(326\) −47.7343 −2.64376
\(327\) −2.68924 −0.148716
\(328\) 1.48830 0.0821774
\(329\) −0.247448 −0.0136422
\(330\) −10.9719 −0.603983
\(331\) 9.14018 0.502390 0.251195 0.967937i \(-0.419177\pi\)
0.251195 + 0.967937i \(0.419177\pi\)
\(332\) 41.0753 2.25430
\(333\) 26.4960 1.45197
\(334\) 7.92728 0.433761
\(335\) 32.4392 1.77235
\(336\) −0.163705 −0.00893082
\(337\) −3.98478 −0.217065 −0.108532 0.994093i \(-0.534615\pi\)
−0.108532 + 0.994093i \(0.534615\pi\)
\(338\) 26.5367 1.44341
\(339\) 2.02264 0.109855
\(340\) 10.8445 0.588128
\(341\) −5.19894 −0.281538
\(342\) 17.0513 0.922029
\(343\) 4.19464 0.226489
\(344\) −14.0124 −0.755500
\(345\) 0.586092 0.0315541
\(346\) −28.3073 −1.52181
\(347\) 2.12266 0.113950 0.0569752 0.998376i \(-0.481854\pi\)
0.0569752 + 0.998376i \(0.481854\pi\)
\(348\) −1.99928 −0.107172
\(349\) −0.870292 −0.0465857 −0.0232928 0.999729i \(-0.507415\pi\)
−0.0232928 + 0.999729i \(0.507415\pi\)
\(350\) 7.84256 0.419203
\(351\) −1.10659 −0.0590653
\(352\) −41.7833 −2.22706
\(353\) −1.00000 −0.0532246
\(354\) 1.00439 0.0533825
\(355\) −26.9907 −1.43252
\(356\) −27.7771 −1.47218
\(357\) 0.0691820 0.00366150
\(358\) −24.8208 −1.31182
\(359\) 7.58794 0.400476 0.200238 0.979747i \(-0.435828\pi\)
0.200238 + 0.979747i \(0.435828\pi\)
\(360\) 16.3201 0.860147
\(361\) −11.7601 −0.618952
\(362\) −36.2343 −1.90443
\(363\) −4.11688 −0.216080
\(364\) 0.641563 0.0336270
\(365\) −55.2275 −2.89074
\(366\) −2.03000 −0.106110
\(367\) 24.6479 1.28661 0.643306 0.765609i \(-0.277562\pi\)
0.643306 + 0.765609i \(0.277562\pi\)
\(368\) 1.46219 0.0762218
\(369\) 3.27544 0.170513
\(370\) 79.9163 4.15465
\(371\) −0.784862 −0.0407480
\(372\) −0.581423 −0.0301454
\(373\) −17.6264 −0.912660 −0.456330 0.889811i \(-0.650836\pi\)
−0.456330 + 0.889811i \(0.650836\pi\)
\(374\) 11.5678 0.598158
\(375\) −6.72947 −0.347508
\(376\) −1.09886 −0.0566692
\(377\) −2.69504 −0.138801
\(378\) 0.884656 0.0455018
\(379\) 34.3812 1.76604 0.883022 0.469332i \(-0.155505\pi\)
0.883022 + 0.469332i \(0.155505\pi\)
\(380\) 29.1795 1.49688
\(381\) 1.46601 0.0751059
\(382\) 4.82324 0.246778
\(383\) 21.1338 1.07989 0.539945 0.841701i \(-0.318445\pi\)
0.539945 + 0.841701i \(0.318445\pi\)
\(384\) −2.33857 −0.119340
\(385\) 6.70852 0.341898
\(386\) −35.0719 −1.78511
\(387\) −30.8386 −1.56761
\(388\) 37.4679 1.90214
\(389\) 29.2647 1.48378 0.741889 0.670523i \(-0.233930\pi\)
0.741889 + 0.670523i \(0.233930\pi\)
\(390\) −1.65406 −0.0837565
\(391\) −0.617925 −0.0312498
\(392\) 9.25279 0.467337
\(393\) −1.06154 −0.0535475
\(394\) −5.29198 −0.266606
\(395\) 18.9433 0.953142
\(396\) 41.5918 2.09007
\(397\) −1.66864 −0.0837466 −0.0418733 0.999123i \(-0.513333\pi\)
−0.0418733 + 0.999123i \(0.513333\pi\)
\(398\) −13.3741 −0.670382
\(399\) 0.186149 0.00931909
\(400\) −28.6202 −1.43101
\(401\) 17.4592 0.871871 0.435935 0.899978i \(-0.356418\pi\)
0.435935 + 0.899978i \(0.356418\pi\)
\(402\) 3.86980 0.193008
\(403\) −0.783761 −0.0390419
\(404\) −0.340257 −0.0169284
\(405\) 35.2647 1.75231
\(406\) 2.15453 0.106928
\(407\) 48.3661 2.39742
\(408\) 0.307221 0.0152097
\(409\) 18.2463 0.902223 0.451111 0.892468i \(-0.351028\pi\)
0.451111 + 0.892468i \(0.351028\pi\)
\(410\) 9.87927 0.487903
\(411\) 0.118063 0.00582364
\(412\) −4.41425 −0.217474
\(413\) −0.614109 −0.0302183
\(414\) −3.91586 −0.192454
\(415\) 64.7497 3.17844
\(416\) −6.29901 −0.308834
\(417\) 0.837450 0.0410101
\(418\) 31.1256 1.52240
\(419\) 2.20273 0.107610 0.0538052 0.998551i \(-0.482865\pi\)
0.0538052 + 0.998551i \(0.482865\pi\)
\(420\) 0.750247 0.0366083
\(421\) −34.0908 −1.66148 −0.830741 0.556659i \(-0.812083\pi\)
−0.830741 + 0.556659i \(0.812083\pi\)
\(422\) 13.7129 0.667536
\(423\) −2.41837 −0.117585
\(424\) −3.48538 −0.169265
\(425\) 12.0950 0.586692
\(426\) −3.21982 −0.156001
\(427\) 1.24120 0.0600658
\(428\) −2.95171 −0.142676
\(429\) −1.00105 −0.0483312
\(430\) −93.0142 −4.48554
\(431\) 20.9210 1.00773 0.503864 0.863783i \(-0.331911\pi\)
0.503864 + 0.863783i \(0.331911\pi\)
\(432\) −3.22841 −0.155327
\(433\) −8.72148 −0.419128 −0.209564 0.977795i \(-0.567204\pi\)
−0.209564 + 0.977795i \(0.567204\pi\)
\(434\) 0.626574 0.0300765
\(435\) −3.15159 −0.151107
\(436\) 30.7476 1.47254
\(437\) −1.66265 −0.0795356
\(438\) −6.58829 −0.314801
\(439\) 23.8512 1.13835 0.569177 0.822215i \(-0.307262\pi\)
0.569177 + 0.822215i \(0.307262\pi\)
\(440\) 29.7909 1.42023
\(441\) 20.3636 0.969694
\(442\) 1.74390 0.0829487
\(443\) 14.3820 0.683308 0.341654 0.939826i \(-0.389013\pi\)
0.341654 + 0.939826i \(0.389013\pi\)
\(444\) 5.40902 0.256701
\(445\) −43.7868 −2.07569
\(446\) 29.4024 1.39224
\(447\) −0.333425 −0.0157705
\(448\) 3.60848 0.170484
\(449\) −22.7746 −1.07480 −0.537401 0.843327i \(-0.680594\pi\)
−0.537401 + 0.843327i \(0.680594\pi\)
\(450\) 76.6472 3.61318
\(451\) 5.97903 0.281541
\(452\) −23.1260 −1.08776
\(453\) 2.88486 0.135543
\(454\) −51.4759 −2.41588
\(455\) 1.01134 0.0474122
\(456\) 0.826641 0.0387110
\(457\) −18.4668 −0.863842 −0.431921 0.901911i \(-0.642164\pi\)
−0.431921 + 0.901911i \(0.642164\pi\)
\(458\) 17.7738 0.830515
\(459\) 1.36434 0.0636818
\(460\) −6.70111 −0.312441
\(461\) −0.536864 −0.0250043 −0.0125021 0.999922i \(-0.503980\pi\)
−0.0125021 + 0.999922i \(0.503980\pi\)
\(462\) 0.800285 0.0372326
\(463\) −15.4089 −0.716113 −0.358056 0.933700i \(-0.616560\pi\)
−0.358056 + 0.933700i \(0.616560\pi\)
\(464\) −7.86262 −0.365013
\(465\) −0.916536 −0.0425033
\(466\) 54.0367 2.50320
\(467\) 5.12605 0.237205 0.118603 0.992942i \(-0.462159\pi\)
0.118603 + 0.992942i \(0.462159\pi\)
\(468\) 6.27014 0.289837
\(469\) −2.36610 −0.109257
\(470\) −7.29418 −0.336456
\(471\) −4.09241 −0.188568
\(472\) −2.72711 −0.125525
\(473\) −56.2930 −2.58836
\(474\) 2.25982 0.103797
\(475\) 32.5440 1.49322
\(476\) −0.790996 −0.0362552
\(477\) −7.67064 −0.351214
\(478\) −7.26501 −0.332294
\(479\) 23.8786 1.09104 0.545521 0.838097i \(-0.316332\pi\)
0.545521 + 0.838097i \(0.316332\pi\)
\(480\) −7.36610 −0.336215
\(481\) 7.29139 0.332459
\(482\) 21.1081 0.961445
\(483\) −0.0427493 −0.00194516
\(484\) 47.0705 2.13957
\(485\) 59.0631 2.68192
\(486\) 13.0072 0.590018
\(487\) −4.70024 −0.212988 −0.106494 0.994313i \(-0.533962\pi\)
−0.106494 + 0.994313i \(0.533962\pi\)
\(488\) 5.51186 0.249510
\(489\) −5.09296 −0.230312
\(490\) 61.4198 2.77466
\(491\) −5.06414 −0.228542 −0.114271 0.993450i \(-0.536453\pi\)
−0.114271 + 0.993450i \(0.536453\pi\)
\(492\) 0.668664 0.0301457
\(493\) 3.32277 0.149650
\(494\) 4.69231 0.211117
\(495\) 65.5640 2.94688
\(496\) −2.28658 −0.102671
\(497\) 1.96869 0.0883077
\(498\) 7.72424 0.346131
\(499\) 6.79190 0.304047 0.152024 0.988377i \(-0.451421\pi\)
0.152024 + 0.988377i \(0.451421\pi\)
\(500\) 76.9417 3.44094
\(501\) 0.845793 0.0377873
\(502\) −8.55142 −0.381669
\(503\) −6.54044 −0.291624 −0.145812 0.989312i \(-0.546579\pi\)
−0.145812 + 0.989312i \(0.546579\pi\)
\(504\) −1.19038 −0.0530239
\(505\) −0.536370 −0.0238681
\(506\) −7.14804 −0.317769
\(507\) 2.83131 0.125743
\(508\) −16.7617 −0.743679
\(509\) −5.05869 −0.224223 −0.112111 0.993696i \(-0.535761\pi\)
−0.112111 + 0.993696i \(0.535761\pi\)
\(510\) 2.03932 0.0903028
\(511\) 4.02826 0.178200
\(512\) −24.7150 −1.09226
\(513\) 3.67103 0.162080
\(514\) 9.25349 0.408154
\(515\) −6.95847 −0.306627
\(516\) −6.29553 −0.277145
\(517\) −4.41451 −0.194150
\(518\) −5.82906 −0.256114
\(519\) −3.02022 −0.132573
\(520\) 4.49111 0.196948
\(521\) 9.14209 0.400522 0.200261 0.979743i \(-0.435821\pi\)
0.200261 + 0.979743i \(0.435821\pi\)
\(522\) 21.0567 0.921628
\(523\) −6.35760 −0.277998 −0.138999 0.990292i \(-0.544389\pi\)
−0.138999 + 0.990292i \(0.544389\pi\)
\(524\) 12.1371 0.530214
\(525\) 0.836755 0.0365190
\(526\) −48.8174 −2.12854
\(527\) 0.966316 0.0420934
\(528\) −2.92051 −0.127099
\(529\) −22.6182 −0.983399
\(530\) −23.1359 −1.00496
\(531\) −6.00183 −0.260457
\(532\) −2.12834 −0.0922752
\(533\) 0.901363 0.0390424
\(534\) −5.22350 −0.226043
\(535\) −4.65297 −0.201165
\(536\) −10.5073 −0.453846
\(537\) −2.64823 −0.114280
\(538\) −69.2033 −2.98357
\(539\) 37.1718 1.60110
\(540\) 14.7956 0.636701
\(541\) −20.2912 −0.872386 −0.436193 0.899853i \(-0.643674\pi\)
−0.436193 + 0.899853i \(0.643674\pi\)
\(542\) −24.8866 −1.06897
\(543\) −3.86598 −0.165905
\(544\) 7.76618 0.332972
\(545\) 48.4695 2.07620
\(546\) 0.120646 0.00516318
\(547\) 17.1379 0.732765 0.366382 0.930464i \(-0.380596\pi\)
0.366382 + 0.930464i \(0.380596\pi\)
\(548\) −1.34988 −0.0576641
\(549\) 12.1305 0.517718
\(550\) 139.912 5.96589
\(551\) 8.94059 0.380882
\(552\) −0.189839 −0.00808010
\(553\) −1.38172 −0.0587566
\(554\) −58.0318 −2.46553
\(555\) 8.52660 0.361934
\(556\) −9.57502 −0.406071
\(557\) −19.9773 −0.846466 −0.423233 0.906021i \(-0.639105\pi\)
−0.423233 + 0.906021i \(0.639105\pi\)
\(558\) 6.12365 0.259235
\(559\) −8.48641 −0.358937
\(560\) 2.95052 0.124682
\(561\) 1.23422 0.0521087
\(562\) 8.13652 0.343218
\(563\) −2.45152 −0.103319 −0.0516596 0.998665i \(-0.516451\pi\)
−0.0516596 + 0.998665i \(0.516451\pi\)
\(564\) −0.493696 −0.0207884
\(565\) −36.4551 −1.53368
\(566\) 33.2634 1.39816
\(567\) −2.57219 −0.108022
\(568\) 8.74247 0.366826
\(569\) 15.5542 0.652066 0.326033 0.945358i \(-0.394288\pi\)
0.326033 + 0.945358i \(0.394288\pi\)
\(570\) 5.48722 0.229834
\(571\) −13.8110 −0.577973 −0.288987 0.957333i \(-0.593318\pi\)
−0.288987 + 0.957333i \(0.593318\pi\)
\(572\) 11.4456 0.478563
\(573\) 0.514611 0.0214982
\(574\) −0.720590 −0.0300768
\(575\) −7.47378 −0.311678
\(576\) 35.2665 1.46944
\(577\) 39.5938 1.64831 0.824155 0.566364i \(-0.191650\pi\)
0.824155 + 0.566364i \(0.191650\pi\)
\(578\) −2.15009 −0.0894318
\(579\) −3.74196 −0.155510
\(580\) 36.0339 1.49623
\(581\) −4.72281 −0.195935
\(582\) 7.04587 0.292061
\(583\) −14.0020 −0.579906
\(584\) 17.8886 0.740234
\(585\) 9.88404 0.408655
\(586\) 3.90876 0.161469
\(587\) −0.959496 −0.0396026 −0.0198013 0.999804i \(-0.506303\pi\)
−0.0198013 + 0.999804i \(0.506303\pi\)
\(588\) 4.15711 0.171436
\(589\) 2.60007 0.107134
\(590\) −18.1025 −0.745268
\(591\) −0.564623 −0.0232255
\(592\) 21.2722 0.874283
\(593\) 26.1010 1.07184 0.535919 0.844269i \(-0.319965\pi\)
0.535919 + 0.844269i \(0.319965\pi\)
\(594\) 15.7824 0.647560
\(595\) −1.24690 −0.0511179
\(596\) 3.81223 0.156155
\(597\) −1.42693 −0.0584005
\(598\) −1.07760 −0.0440662
\(599\) −14.4510 −0.590451 −0.295225 0.955428i \(-0.595395\pi\)
−0.295225 + 0.955428i \(0.595395\pi\)
\(600\) 3.71583 0.151698
\(601\) 5.26976 0.214958 0.107479 0.994207i \(-0.465722\pi\)
0.107479 + 0.994207i \(0.465722\pi\)
\(602\) 6.78441 0.276512
\(603\) −23.1245 −0.941701
\(604\) −32.9842 −1.34211
\(605\) 74.2004 3.01667
\(606\) −0.0639856 −0.00259924
\(607\) −40.8569 −1.65833 −0.829165 0.559003i \(-0.811184\pi\)
−0.829165 + 0.559003i \(0.811184\pi\)
\(608\) 20.8965 0.847465
\(609\) 0.229876 0.00931503
\(610\) 36.5876 1.48139
\(611\) −0.665505 −0.0269235
\(612\) −7.73059 −0.312490
\(613\) 24.2455 0.979266 0.489633 0.871929i \(-0.337131\pi\)
0.489633 + 0.871929i \(0.337131\pi\)
\(614\) −46.4951 −1.87639
\(615\) 1.05406 0.0425038
\(616\) −2.17294 −0.0875502
\(617\) 38.2547 1.54008 0.770038 0.637998i \(-0.220237\pi\)
0.770038 + 0.637998i \(0.220237\pi\)
\(618\) −0.830102 −0.0333916
\(619\) 36.3278 1.46014 0.730069 0.683373i \(-0.239488\pi\)
0.730069 + 0.683373i \(0.239488\pi\)
\(620\) 10.4793 0.420857
\(621\) −0.843057 −0.0338307
\(622\) −30.7985 −1.23491
\(623\) 3.19379 0.127957
\(624\) −0.440279 −0.0176253
\(625\) 60.8135 2.43254
\(626\) 44.6622 1.78506
\(627\) 3.32092 0.132625
\(628\) 46.7908 1.86715
\(629\) −8.98970 −0.358443
\(630\) −7.90174 −0.314813
\(631\) 32.8933 1.30946 0.654730 0.755863i \(-0.272782\pi\)
0.654730 + 0.755863i \(0.272782\pi\)
\(632\) −6.13587 −0.244072
\(633\) 1.46309 0.0581526
\(634\) −0.971465 −0.0385818
\(635\) −26.4225 −1.04855
\(636\) −1.56592 −0.0620927
\(637\) 5.60381 0.222031
\(638\) 38.4372 1.52174
\(639\) 19.2404 0.761140
\(640\) 42.1492 1.66609
\(641\) 4.42099 0.174618 0.0873092 0.996181i \(-0.472173\pi\)
0.0873092 + 0.996181i \(0.472173\pi\)
\(642\) −0.555070 −0.0219069
\(643\) 9.24488 0.364582 0.182291 0.983245i \(-0.441649\pi\)
0.182291 + 0.983245i \(0.441649\pi\)
\(644\) 0.488776 0.0192605
\(645\) −9.92406 −0.390760
\(646\) −5.78525 −0.227618
\(647\) −13.7024 −0.538695 −0.269348 0.963043i \(-0.586808\pi\)
−0.269348 + 0.963043i \(0.586808\pi\)
\(648\) −11.4225 −0.448717
\(649\) −10.9558 −0.430053
\(650\) 21.0924 0.827311
\(651\) 0.0668517 0.00262012
\(652\) 58.2306 2.28049
\(653\) −1.20069 −0.0469867 −0.0234934 0.999724i \(-0.507479\pi\)
−0.0234934 + 0.999724i \(0.507479\pi\)
\(654\) 5.78211 0.226098
\(655\) 19.1326 0.747572
\(656\) 2.62968 0.102672
\(657\) 39.3692 1.53594
\(658\) 0.532034 0.0207409
\(659\) −46.2575 −1.80194 −0.900968 0.433885i \(-0.857142\pi\)
−0.900968 + 0.433885i \(0.857142\pi\)
\(660\) 13.3845 0.520992
\(661\) 4.40115 0.171185 0.0855924 0.996330i \(-0.472722\pi\)
0.0855924 + 0.996330i \(0.472722\pi\)
\(662\) −19.6522 −0.763804
\(663\) 0.186063 0.00722610
\(664\) −20.9729 −0.813906
\(665\) −3.35504 −0.130103
\(666\) −56.9687 −2.20749
\(667\) −2.05322 −0.0795010
\(668\) −9.67042 −0.374160
\(669\) 3.13706 0.121286
\(670\) −69.7472 −2.69457
\(671\) 22.1431 0.854827
\(672\) 0.537280 0.0207260
\(673\) −31.7196 −1.22270 −0.611351 0.791359i \(-0.709374\pi\)
−0.611351 + 0.791359i \(0.709374\pi\)
\(674\) 8.56763 0.330013
\(675\) 16.5016 0.635147
\(676\) −32.3719 −1.24507
\(677\) 8.31310 0.319498 0.159749 0.987158i \(-0.448931\pi\)
0.159749 + 0.987158i \(0.448931\pi\)
\(678\) −4.34886 −0.167017
\(679\) −4.30804 −0.165327
\(680\) −5.53718 −0.212341
\(681\) −5.49217 −0.210460
\(682\) 11.1782 0.428034
\(683\) −5.74035 −0.219648 −0.109824 0.993951i \(-0.535029\pi\)
−0.109824 + 0.993951i \(0.535029\pi\)
\(684\) −20.8007 −0.795336
\(685\) −2.12791 −0.0813032
\(686\) −9.01884 −0.344341
\(687\) 1.89636 0.0723506
\(688\) −24.7586 −0.943914
\(689\) −2.11087 −0.0804176
\(690\) −1.26015 −0.0479731
\(691\) 7.93203 0.301749 0.150874 0.988553i \(-0.451791\pi\)
0.150874 + 0.988553i \(0.451791\pi\)
\(692\) 34.5318 1.31270
\(693\) −4.78221 −0.181661
\(694\) −4.56391 −0.173244
\(695\) −15.0937 −0.572538
\(696\) 1.02082 0.0386942
\(697\) −1.11131 −0.0420938
\(698\) 1.87120 0.0708261
\(699\) 5.76539 0.218067
\(700\) −9.56707 −0.361601
\(701\) −13.3653 −0.504802 −0.252401 0.967623i \(-0.581220\pi\)
−0.252401 + 0.967623i \(0.581220\pi\)
\(702\) 2.37926 0.0897994
\(703\) −24.1887 −0.912292
\(704\) 64.3757 2.42625
\(705\) −0.778246 −0.0293104
\(706\) 2.15009 0.0809196
\(707\) 0.0391226 0.00147136
\(708\) −1.22524 −0.0460474
\(709\) −34.6063 −1.29967 −0.649834 0.760077i \(-0.725161\pi\)
−0.649834 + 0.760077i \(0.725161\pi\)
\(710\) 58.0323 2.17791
\(711\) −13.5038 −0.506433
\(712\) 14.1829 0.531525
\(713\) −0.597111 −0.0223620
\(714\) −0.148747 −0.00556673
\(715\) 18.0424 0.674748
\(716\) 30.2787 1.13157
\(717\) −0.775134 −0.0289479
\(718\) −16.3147 −0.608860
\(719\) 43.0421 1.60520 0.802600 0.596518i \(-0.203450\pi\)
0.802600 + 0.596518i \(0.203450\pi\)
\(720\) 28.8361 1.07466
\(721\) 0.507548 0.0189021
\(722\) 25.2852 0.941019
\(723\) 2.25210 0.0837566
\(724\) 44.2019 1.64275
\(725\) 40.1888 1.49257
\(726\) 8.85164 0.328515
\(727\) −48.6651 −1.80489 −0.902445 0.430805i \(-0.858230\pi\)
−0.902445 + 0.430805i \(0.858230\pi\)
\(728\) −0.327579 −0.0121409
\(729\) −24.1996 −0.896283
\(730\) 118.744 4.39490
\(731\) 10.4631 0.386991
\(732\) 2.47638 0.0915295
\(733\) 13.4449 0.496599 0.248300 0.968683i \(-0.420128\pi\)
0.248300 + 0.968683i \(0.420128\pi\)
\(734\) −52.9952 −1.95609
\(735\) 6.55313 0.241716
\(736\) −4.79891 −0.176890
\(737\) −42.2116 −1.55489
\(738\) −7.04249 −0.259238
\(739\) 21.7163 0.798848 0.399424 0.916766i \(-0.369210\pi\)
0.399424 + 0.916766i \(0.369210\pi\)
\(740\) −97.4892 −3.58377
\(741\) 0.500642 0.0183915
\(742\) 1.68752 0.0619508
\(743\) −0.570392 −0.0209257 −0.0104628 0.999945i \(-0.503330\pi\)
−0.0104628 + 0.999945i \(0.503330\pi\)
\(744\) 0.296872 0.0108839
\(745\) 6.00947 0.220170
\(746\) 37.8983 1.38755
\(747\) −46.1572 −1.68880
\(748\) −14.1115 −0.515967
\(749\) 0.339385 0.0124009
\(750\) 14.4689 0.528331
\(751\) 30.7825 1.12327 0.561634 0.827386i \(-0.310173\pi\)
0.561634 + 0.827386i \(0.310173\pi\)
\(752\) −1.94158 −0.0708020
\(753\) −0.912386 −0.0332492
\(754\) 5.79456 0.211025
\(755\) −51.9952 −1.89230
\(756\) −1.07918 −0.0392496
\(757\) −25.4668 −0.925607 −0.462804 0.886461i \(-0.653156\pi\)
−0.462804 + 0.886461i \(0.653156\pi\)
\(758\) −73.9225 −2.68499
\(759\) −0.762654 −0.0276826
\(760\) −14.8989 −0.540441
\(761\) 43.4037 1.57338 0.786692 0.617346i \(-0.211792\pi\)
0.786692 + 0.617346i \(0.211792\pi\)
\(762\) −3.15205 −0.114187
\(763\) −3.53534 −0.127988
\(764\) −5.88383 −0.212869
\(765\) −12.1862 −0.440594
\(766\) −45.4396 −1.64180
\(767\) −1.65163 −0.0596369
\(768\) −0.461614 −0.0166571
\(769\) −46.0252 −1.65971 −0.829855 0.557980i \(-0.811577\pi\)
−0.829855 + 0.557980i \(0.811577\pi\)
\(770\) −14.4239 −0.519802
\(771\) 0.987293 0.0355565
\(772\) 42.7839 1.53982
\(773\) −15.5301 −0.558577 −0.279289 0.960207i \(-0.590099\pi\)
−0.279289 + 0.960207i \(0.590099\pi\)
\(774\) 66.3056 2.38331
\(775\) 11.6876 0.419830
\(776\) −19.1310 −0.686761
\(777\) −0.621926 −0.0223115
\(778\) −62.9216 −2.25585
\(779\) −2.99021 −0.107135
\(780\) 2.01777 0.0722478
\(781\) 35.1217 1.25675
\(782\) 1.32859 0.0475103
\(783\) 4.53337 0.162009
\(784\) 16.3488 0.583886
\(785\) 73.7594 2.63258
\(786\) 2.28240 0.0814105
\(787\) −36.4713 −1.30006 −0.650030 0.759908i \(-0.725244\pi\)
−0.650030 + 0.759908i \(0.725244\pi\)
\(788\) 6.45564 0.229973
\(789\) −5.20853 −0.185428
\(790\) −40.7298 −1.44910
\(791\) 2.65901 0.0945437
\(792\) −21.2366 −0.754611
\(793\) 3.33817 0.118542
\(794\) 3.58772 0.127323
\(795\) −2.46846 −0.0875473
\(796\) 16.3149 0.578267
\(797\) 25.7477 0.912030 0.456015 0.889972i \(-0.349276\pi\)
0.456015 + 0.889972i \(0.349276\pi\)
\(798\) −0.400236 −0.0141682
\(799\) 0.820515 0.0290277
\(800\) 93.9317 3.32099
\(801\) 31.2137 1.10288
\(802\) −37.5388 −1.32554
\(803\) 71.8648 2.53605
\(804\) −4.72074 −0.166487
\(805\) 0.770490 0.0271562
\(806\) 1.68515 0.0593570
\(807\) −7.38358 −0.259914
\(808\) 0.173734 0.00611194
\(809\) 18.1042 0.636508 0.318254 0.948005i \(-0.396903\pi\)
0.318254 + 0.948005i \(0.396903\pi\)
\(810\) −75.8221 −2.66412
\(811\) −5.98045 −0.210002 −0.105001 0.994472i \(-0.533485\pi\)
−0.105001 + 0.994472i \(0.533485\pi\)
\(812\) −2.62829 −0.0922351
\(813\) −2.65525 −0.0931238
\(814\) −103.991 −3.64489
\(815\) 91.7928 3.21536
\(816\) 0.542830 0.0190028
\(817\) 28.1531 0.984951
\(818\) −39.2312 −1.37169
\(819\) −0.720937 −0.0251916
\(820\) −12.0516 −0.420861
\(821\) 28.4921 0.994381 0.497190 0.867641i \(-0.334365\pi\)
0.497190 + 0.867641i \(0.334365\pi\)
\(822\) −0.253846 −0.00885391
\(823\) −21.9940 −0.766663 −0.383332 0.923611i \(-0.625223\pi\)
−0.383332 + 0.923611i \(0.625223\pi\)
\(824\) 2.25390 0.0785182
\(825\) 14.9278 0.519720
\(826\) 1.32039 0.0459422
\(827\) 44.2680 1.53935 0.769674 0.638437i \(-0.220419\pi\)
0.769674 + 0.638437i \(0.220419\pi\)
\(828\) 4.77692 0.166009
\(829\) −47.1078 −1.63612 −0.818061 0.575131i \(-0.804951\pi\)
−0.818061 + 0.575131i \(0.804951\pi\)
\(830\) −139.217 −4.83231
\(831\) −6.19165 −0.214786
\(832\) 9.70490 0.336457
\(833\) −6.90905 −0.239384
\(834\) −1.80059 −0.0623493
\(835\) −15.2441 −0.527544
\(836\) −37.9699 −1.31322
\(837\) 1.31838 0.0455699
\(838\) −4.73606 −0.163604
\(839\) 21.6850 0.748650 0.374325 0.927298i \(-0.377874\pi\)
0.374325 + 0.927298i \(0.377874\pi\)
\(840\) −0.383073 −0.0132173
\(841\) −17.9592 −0.619284
\(842\) 73.2981 2.52602
\(843\) 0.868118 0.0298996
\(844\) −16.7283 −0.575812
\(845\) −51.0299 −1.75548
\(846\) 5.19970 0.178769
\(847\) −5.41214 −0.185963
\(848\) −6.15834 −0.211478
\(849\) 3.54901 0.121802
\(850\) −26.0052 −0.891972
\(851\) 5.55496 0.190422
\(852\) 3.92783 0.134565
\(853\) 7.73647 0.264892 0.132446 0.991190i \(-0.457717\pi\)
0.132446 + 0.991190i \(0.457717\pi\)
\(854\) −2.66868 −0.0913204
\(855\) −32.7896 −1.12138
\(856\) 1.50713 0.0515126
\(857\) −45.9407 −1.56930 −0.784651 0.619937i \(-0.787158\pi\)
−0.784651 + 0.619937i \(0.787158\pi\)
\(858\) 2.15235 0.0734799
\(859\) 53.0718 1.81079 0.905393 0.424575i \(-0.139577\pi\)
0.905393 + 0.424575i \(0.139577\pi\)
\(860\) 113.467 3.86920
\(861\) −0.0768826 −0.00262015
\(862\) −44.9819 −1.53209
\(863\) −4.51306 −0.153626 −0.0768132 0.997045i \(-0.524475\pi\)
−0.0768132 + 0.997045i \(0.524475\pi\)
\(864\) 10.5957 0.360472
\(865\) 54.4348 1.85084
\(866\) 18.7519 0.637217
\(867\) −0.229401 −0.00779088
\(868\) −0.764352 −0.0259438
\(869\) −24.6500 −0.836195
\(870\) 6.77620 0.229735
\(871\) −6.36358 −0.215622
\(872\) −15.6996 −0.531655
\(873\) −42.1035 −1.42499
\(874\) 3.57485 0.120921
\(875\) −8.84672 −0.299074
\(876\) 8.03700 0.271545
\(877\) −17.0271 −0.574963 −0.287482 0.957786i \(-0.592818\pi\)
−0.287482 + 0.957786i \(0.592818\pi\)
\(878\) −51.2821 −1.73069
\(879\) 0.417041 0.0140664
\(880\) 52.6378 1.77442
\(881\) −1.95238 −0.0657772 −0.0328886 0.999459i \(-0.510471\pi\)
−0.0328886 + 0.999459i \(0.510471\pi\)
\(882\) −43.7834 −1.47426
\(883\) −4.32658 −0.145601 −0.0728005 0.997347i \(-0.523194\pi\)
−0.0728005 + 0.997347i \(0.523194\pi\)
\(884\) −2.12736 −0.0715510
\(885\) −1.93143 −0.0649242
\(886\) −30.9225 −1.03886
\(887\) 14.3260 0.481020 0.240510 0.970647i \(-0.422685\pi\)
0.240510 + 0.970647i \(0.422685\pi\)
\(888\) −2.76182 −0.0926807
\(889\) 1.92725 0.0646378
\(890\) 94.1454 3.15576
\(891\) −45.8882 −1.53731
\(892\) −35.8677 −1.20094
\(893\) 2.20777 0.0738801
\(894\) 0.716892 0.0239765
\(895\) 47.7303 1.59545
\(896\) −3.07434 −0.102707
\(897\) −0.114973 −0.00383884
\(898\) 48.9674 1.63406
\(899\) 3.21084 0.107088
\(900\) −93.5012 −3.11671
\(901\) 2.60253 0.0867029
\(902\) −12.8554 −0.428039
\(903\) 0.723856 0.0240884
\(904\) 11.8080 0.392730
\(905\) 69.6784 2.31619
\(906\) −6.20270 −0.206071
\(907\) 42.5403 1.41253 0.706263 0.707950i \(-0.250380\pi\)
0.706263 + 0.707950i \(0.250380\pi\)
\(908\) 62.7950 2.08392
\(909\) 0.382354 0.0126819
\(910\) −2.17446 −0.0720828
\(911\) 11.1759 0.370275 0.185137 0.982713i \(-0.440727\pi\)
0.185137 + 0.982713i \(0.440727\pi\)
\(912\) 1.46060 0.0483652
\(913\) −84.2557 −2.78846
\(914\) 39.7053 1.31333
\(915\) 3.90368 0.129052
\(916\) −21.6821 −0.716396
\(917\) −1.39552 −0.0460842
\(918\) −2.93344 −0.0968180
\(919\) −26.2890 −0.867195 −0.433597 0.901107i \(-0.642756\pi\)
−0.433597 + 0.901107i \(0.642756\pi\)
\(920\) 3.42156 0.112806
\(921\) −4.96075 −0.163462
\(922\) 1.15430 0.0380150
\(923\) 5.29474 0.174278
\(924\) −0.976261 −0.0321166
\(925\) −108.730 −3.57503
\(926\) 33.1305 1.08874
\(927\) 4.96038 0.162920
\(928\) 25.8052 0.847097
\(929\) −17.6695 −0.579717 −0.289859 0.957070i \(-0.593608\pi\)
−0.289859 + 0.957070i \(0.593608\pi\)
\(930\) 1.97063 0.0646195
\(931\) −18.5902 −0.609270
\(932\) −65.9188 −2.15924
\(933\) −3.28602 −0.107579
\(934\) −11.0215 −0.360633
\(935\) −22.2449 −0.727485
\(936\) −3.20151 −0.104645
\(937\) −38.7895 −1.26720 −0.633599 0.773662i \(-0.718423\pi\)
−0.633599 + 0.773662i \(0.718423\pi\)
\(938\) 5.08733 0.166107
\(939\) 4.76520 0.155506
\(940\) 8.89811 0.290224
\(941\) 57.4282 1.87211 0.936053 0.351860i \(-0.114451\pi\)
0.936053 + 0.351860i \(0.114451\pi\)
\(942\) 8.79903 0.286688
\(943\) 0.686706 0.0223622
\(944\) −4.81854 −0.156830
\(945\) −1.70119 −0.0553397
\(946\) 121.035 3.93518
\(947\) 33.1693 1.07786 0.538928 0.842352i \(-0.318829\pi\)
0.538928 + 0.842352i \(0.318829\pi\)
\(948\) −2.75673 −0.0895346
\(949\) 10.8339 0.351684
\(950\) −69.9725 −2.27021
\(951\) −0.103650 −0.00336107
\(952\) 0.403879 0.0130898
\(953\) 48.3080 1.56485 0.782425 0.622745i \(-0.213983\pi\)
0.782425 + 0.622745i \(0.213983\pi\)
\(954\) 16.4925 0.533965
\(955\) −9.27507 −0.300134
\(956\) 8.86253 0.286635
\(957\) 4.10102 0.132567
\(958\) −51.3411 −1.65876
\(959\) 0.155209 0.00501195
\(960\) 11.3490 0.366287
\(961\) −30.0662 −0.969879
\(962\) −15.6771 −0.505450
\(963\) 3.31689 0.106885
\(964\) −25.7495 −0.829336
\(965\) 67.4430 2.17107
\(966\) 0.0919147 0.00295731
\(967\) −42.4442 −1.36491 −0.682457 0.730925i \(-0.739089\pi\)
−0.682457 + 0.730925i \(0.739089\pi\)
\(968\) −24.0340 −0.772483
\(969\) −0.617252 −0.0198290
\(970\) −126.991 −4.07743
\(971\) 3.37345 0.108259 0.0541296 0.998534i \(-0.482762\pi\)
0.0541296 + 0.998534i \(0.482762\pi\)
\(972\) −15.8673 −0.508945
\(973\) 1.10093 0.0352942
\(974\) 10.1059 0.323814
\(975\) 2.25043 0.0720715
\(976\) 9.73893 0.311736
\(977\) −19.6089 −0.627343 −0.313672 0.949532i \(-0.601559\pi\)
−0.313672 + 0.949532i \(0.601559\pi\)
\(978\) 10.9503 0.350152
\(979\) 56.9777 1.82101
\(980\) −74.9255 −2.39341
\(981\) −34.5517 −1.10315
\(982\) 10.8883 0.347461
\(983\) −51.1722 −1.63214 −0.816070 0.577953i \(-0.803852\pi\)
−0.816070 + 0.577953i \(0.803852\pi\)
\(984\) −0.341417 −0.0108840
\(985\) 10.1765 0.324249
\(986\) −7.14423 −0.227519
\(987\) 0.0567649 0.00180685
\(988\) −5.72411 −0.182108
\(989\) −6.46539 −0.205587
\(990\) −140.968 −4.48026
\(991\) 15.7705 0.500965 0.250483 0.968121i \(-0.419411\pi\)
0.250483 + 0.968121i \(0.419411\pi\)
\(992\) 7.50458 0.238271
\(993\) −2.09677 −0.0665390
\(994\) −4.23285 −0.134258
\(995\) 25.7183 0.815324
\(996\) −9.42273 −0.298571
\(997\) −49.5269 −1.56853 −0.784266 0.620425i \(-0.786960\pi\)
−0.784266 + 0.620425i \(0.786960\pi\)
\(998\) −14.6032 −0.462255
\(999\) −12.2650 −0.388047
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 6001.2.a.d.1.18 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.18 121 1.1 even 1 trivial