Properties

Label 6001.2.a.d.1.13
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 1.13
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.26922 q^{2} -1.02425 q^{3} +3.14937 q^{4} -0.261054 q^{5} +2.32424 q^{6} +2.61024 q^{7} -2.60816 q^{8} -1.95092 q^{9} +O(q^{10})\) \(q-2.26922 q^{2} -1.02425 q^{3} +3.14937 q^{4} -0.261054 q^{5} +2.32424 q^{6} +2.61024 q^{7} -2.60816 q^{8} -1.95092 q^{9} +0.592389 q^{10} -3.66108 q^{11} -3.22572 q^{12} +0.188101 q^{13} -5.92322 q^{14} +0.267383 q^{15} -0.380228 q^{16} +1.00000 q^{17} +4.42707 q^{18} -5.72965 q^{19} -0.822154 q^{20} -2.67353 q^{21} +8.30781 q^{22} +6.42867 q^{23} +2.67140 q^{24} -4.93185 q^{25} -0.426843 q^{26} +5.07096 q^{27} +8.22061 q^{28} +1.16519 q^{29} -0.606752 q^{30} -0.117894 q^{31} +6.07915 q^{32} +3.74985 q^{33} -2.26922 q^{34} -0.681414 q^{35} -6.14416 q^{36} -9.59028 q^{37} +13.0018 q^{38} -0.192662 q^{39} +0.680872 q^{40} -9.94171 q^{41} +6.06683 q^{42} -4.91368 q^{43} -11.5301 q^{44} +0.509295 q^{45} -14.5881 q^{46} -1.43177 q^{47} +0.389447 q^{48} -0.186635 q^{49} +11.1915 q^{50} -1.02425 q^{51} +0.592399 q^{52} +4.56654 q^{53} -11.5071 q^{54} +0.955740 q^{55} -6.80794 q^{56} +5.86857 q^{57} -2.64407 q^{58} -12.1482 q^{59} +0.842088 q^{60} -0.202236 q^{61} +0.267527 q^{62} -5.09237 q^{63} -13.0345 q^{64} -0.0491045 q^{65} -8.50924 q^{66} +6.24354 q^{67} +3.14937 q^{68} -6.58454 q^{69} +1.54628 q^{70} -1.38354 q^{71} +5.08832 q^{72} +12.2273 q^{73} +21.7625 q^{74} +5.05143 q^{75} -18.0448 q^{76} -9.55631 q^{77} +0.437192 q^{78} +5.85241 q^{79} +0.0992600 q^{80} +0.658851 q^{81} +22.5599 q^{82} -0.703528 q^{83} -8.41992 q^{84} -0.261054 q^{85} +11.1502 q^{86} -1.19344 q^{87} +9.54870 q^{88} -0.554775 q^{89} -1.15570 q^{90} +0.490990 q^{91} +20.2462 q^{92} +0.120752 q^{93} +3.24901 q^{94} +1.49575 q^{95} -6.22655 q^{96} +15.8374 q^{97} +0.423516 q^{98} +7.14248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26922 −1.60458 −0.802291 0.596933i \(-0.796386\pi\)
−0.802291 + 0.596933i \(0.796386\pi\)
\(3\) −1.02425 −0.591349 −0.295674 0.955289i \(-0.595544\pi\)
−0.295674 + 0.955289i \(0.595544\pi\)
\(4\) 3.14937 1.57468
\(5\) −0.261054 −0.116747 −0.0583734 0.998295i \(-0.518591\pi\)
−0.0583734 + 0.998295i \(0.518591\pi\)
\(6\) 2.32424 0.948867
\(7\) 2.61024 0.986579 0.493289 0.869865i \(-0.335794\pi\)
0.493289 + 0.869865i \(0.335794\pi\)
\(8\) −2.60816 −0.922125
\(9\) −1.95092 −0.650307
\(10\) 0.592389 0.187330
\(11\) −3.66108 −1.10386 −0.551929 0.833891i \(-0.686108\pi\)
−0.551929 + 0.833891i \(0.686108\pi\)
\(12\) −3.22572 −0.931187
\(13\) 0.188101 0.0521699 0.0260849 0.999660i \(-0.491696\pi\)
0.0260849 + 0.999660i \(0.491696\pi\)
\(14\) −5.92322 −1.58305
\(15\) 0.267383 0.0690381
\(16\) −0.380228 −0.0950570
\(17\) 1.00000 0.242536
\(18\) 4.42707 1.04347
\(19\) −5.72965 −1.31447 −0.657236 0.753685i \(-0.728275\pi\)
−0.657236 + 0.753685i \(0.728275\pi\)
\(20\) −0.822154 −0.183839
\(21\) −2.67353 −0.583412
\(22\) 8.30781 1.77123
\(23\) 6.42867 1.34047 0.670235 0.742149i \(-0.266193\pi\)
0.670235 + 0.742149i \(0.266193\pi\)
\(24\) 2.67140 0.545298
\(25\) −4.93185 −0.986370
\(26\) −0.426843 −0.0837108
\(27\) 5.07096 0.975907
\(28\) 8.22061 1.55355
\(29\) 1.16519 0.216370 0.108185 0.994131i \(-0.465496\pi\)
0.108185 + 0.994131i \(0.465496\pi\)
\(30\) −0.606752 −0.110777
\(31\) −0.117894 −0.0211743 −0.0105872 0.999944i \(-0.503370\pi\)
−0.0105872 + 0.999944i \(0.503370\pi\)
\(32\) 6.07915 1.07465
\(33\) 3.74985 0.652765
\(34\) −2.26922 −0.389168
\(35\) −0.681414 −0.115180
\(36\) −6.14416 −1.02403
\(37\) −9.59028 −1.57663 −0.788316 0.615270i \(-0.789047\pi\)
−0.788316 + 0.615270i \(0.789047\pi\)
\(38\) 13.0018 2.10918
\(39\) −0.192662 −0.0308506
\(40\) 0.680872 0.107655
\(41\) −9.94171 −1.55263 −0.776317 0.630343i \(-0.782914\pi\)
−0.776317 + 0.630343i \(0.782914\pi\)
\(42\) 6.06683 0.936132
\(43\) −4.91368 −0.749329 −0.374664 0.927160i \(-0.622242\pi\)
−0.374664 + 0.927160i \(0.622242\pi\)
\(44\) −11.5301 −1.73823
\(45\) 0.509295 0.0759213
\(46\) −14.5881 −2.15089
\(47\) −1.43177 −0.208846 −0.104423 0.994533i \(-0.533300\pi\)
−0.104423 + 0.994533i \(0.533300\pi\)
\(48\) 0.389447 0.0562118
\(49\) −0.186635 −0.0266621
\(50\) 11.1915 1.58271
\(51\) −1.02425 −0.143423
\(52\) 0.592399 0.0821510
\(53\) 4.56654 0.627263 0.313631 0.949545i \(-0.398454\pi\)
0.313631 + 0.949545i \(0.398454\pi\)
\(54\) −11.5071 −1.56592
\(55\) 0.955740 0.128872
\(56\) −6.80794 −0.909749
\(57\) 5.86857 0.777312
\(58\) −2.64407 −0.347184
\(59\) −12.1482 −1.58156 −0.790781 0.612099i \(-0.790326\pi\)
−0.790781 + 0.612099i \(0.790326\pi\)
\(60\) 0.842088 0.108713
\(61\) −0.202236 −0.0258937 −0.0129469 0.999916i \(-0.504121\pi\)
−0.0129469 + 0.999916i \(0.504121\pi\)
\(62\) 0.267527 0.0339759
\(63\) −5.09237 −0.641579
\(64\) −13.0345 −1.62931
\(65\) −0.0491045 −0.00609067
\(66\) −8.50924 −1.04741
\(67\) 6.24354 0.762770 0.381385 0.924416i \(-0.375447\pi\)
0.381385 + 0.924416i \(0.375447\pi\)
\(68\) 3.14937 0.381917
\(69\) −6.58454 −0.792685
\(70\) 1.54628 0.184816
\(71\) −1.38354 −0.164196 −0.0820980 0.996624i \(-0.526162\pi\)
−0.0820980 + 0.996624i \(0.526162\pi\)
\(72\) 5.08832 0.599664
\(73\) 12.2273 1.43110 0.715551 0.698561i \(-0.246176\pi\)
0.715551 + 0.698561i \(0.246176\pi\)
\(74\) 21.7625 2.52984
\(75\) 5.05143 0.583289
\(76\) −18.0448 −2.06988
\(77\) −9.55631 −1.08904
\(78\) 0.437192 0.0495023
\(79\) 5.85241 0.658447 0.329224 0.944252i \(-0.393213\pi\)
0.329224 + 0.944252i \(0.393213\pi\)
\(80\) 0.0992600 0.0110976
\(81\) 0.658851 0.0732056
\(82\) 22.5599 2.49133
\(83\) −0.703528 −0.0772222 −0.0386111 0.999254i \(-0.512293\pi\)
−0.0386111 + 0.999254i \(0.512293\pi\)
\(84\) −8.41992 −0.918689
\(85\) −0.261054 −0.0283153
\(86\) 11.1502 1.20236
\(87\) −1.19344 −0.127950
\(88\) 9.54870 1.01790
\(89\) −0.554775 −0.0588060 −0.0294030 0.999568i \(-0.509361\pi\)
−0.0294030 + 0.999568i \(0.509361\pi\)
\(90\) −1.15570 −0.121822
\(91\) 0.490990 0.0514697
\(92\) 20.2462 2.11081
\(93\) 0.120752 0.0125214
\(94\) 3.24901 0.335110
\(95\) 1.49575 0.153461
\(96\) −6.22655 −0.635494
\(97\) 15.8374 1.60805 0.804024 0.594597i \(-0.202688\pi\)
0.804024 + 0.594597i \(0.202688\pi\)
\(98\) 0.423516 0.0427816
\(99\) 7.14248 0.717846
\(100\) −15.5322 −1.55322
\(101\) 17.7617 1.76735 0.883677 0.468096i \(-0.155060\pi\)
0.883677 + 0.468096i \(0.155060\pi\)
\(102\) 2.32424 0.230134
\(103\) 0.311787 0.0307213 0.0153606 0.999882i \(-0.495110\pi\)
0.0153606 + 0.999882i \(0.495110\pi\)
\(104\) −0.490599 −0.0481072
\(105\) 0.697935 0.0681115
\(106\) −10.3625 −1.00649
\(107\) −3.38784 −0.327515 −0.163757 0.986501i \(-0.552361\pi\)
−0.163757 + 0.986501i \(0.552361\pi\)
\(108\) 15.9703 1.53674
\(109\) −15.5189 −1.48644 −0.743222 0.669045i \(-0.766703\pi\)
−0.743222 + 0.669045i \(0.766703\pi\)
\(110\) −2.16878 −0.206786
\(111\) 9.82281 0.932340
\(112\) −0.992487 −0.0937812
\(113\) 19.4650 1.83112 0.915559 0.402184i \(-0.131749\pi\)
0.915559 + 0.402184i \(0.131749\pi\)
\(114\) −13.3171 −1.24726
\(115\) −1.67823 −0.156496
\(116\) 3.66961 0.340714
\(117\) −0.366970 −0.0339264
\(118\) 27.5670 2.53775
\(119\) 2.61024 0.239281
\(120\) −0.697380 −0.0636618
\(121\) 2.40352 0.218502
\(122\) 0.458919 0.0415486
\(123\) 10.1828 0.918148
\(124\) −0.371290 −0.0333428
\(125\) 2.59275 0.231902
\(126\) 11.5557 1.02947
\(127\) −0.0941906 −0.00835807 −0.00417903 0.999991i \(-0.501330\pi\)
−0.00417903 + 0.999991i \(0.501330\pi\)
\(128\) 17.4198 1.53971
\(129\) 5.03281 0.443115
\(130\) 0.111429 0.00977298
\(131\) −16.8285 −1.47031 −0.735157 0.677897i \(-0.762892\pi\)
−0.735157 + 0.677897i \(0.762892\pi\)
\(132\) 11.8096 1.02790
\(133\) −14.9558 −1.29683
\(134\) −14.1680 −1.22393
\(135\) −1.32379 −0.113934
\(136\) −2.60816 −0.223648
\(137\) 1.15254 0.0984678 0.0492339 0.998787i \(-0.484322\pi\)
0.0492339 + 0.998787i \(0.484322\pi\)
\(138\) 14.9418 1.27193
\(139\) −18.6215 −1.57946 −0.789729 0.613456i \(-0.789779\pi\)
−0.789729 + 0.613456i \(0.789779\pi\)
\(140\) −2.14602 −0.181372
\(141\) 1.46649 0.123501
\(142\) 3.13956 0.263466
\(143\) −0.688654 −0.0575881
\(144\) 0.741795 0.0618162
\(145\) −0.304177 −0.0252605
\(146\) −27.7465 −2.29632
\(147\) 0.191160 0.0157666
\(148\) −30.2033 −2.48270
\(149\) 21.1182 1.73007 0.865034 0.501714i \(-0.167297\pi\)
0.865034 + 0.501714i \(0.167297\pi\)
\(150\) −11.4628 −0.935934
\(151\) 17.4481 1.41991 0.709955 0.704247i \(-0.248715\pi\)
0.709955 + 0.704247i \(0.248715\pi\)
\(152\) 14.9439 1.21211
\(153\) −1.95092 −0.157723
\(154\) 21.6854 1.74746
\(155\) 0.0307766 0.00247204
\(156\) −0.606763 −0.0485799
\(157\) 4.95563 0.395503 0.197751 0.980252i \(-0.436636\pi\)
0.197751 + 0.980252i \(0.436636\pi\)
\(158\) −13.2804 −1.05653
\(159\) −4.67726 −0.370931
\(160\) −1.58699 −0.125462
\(161\) 16.7804 1.32248
\(162\) −1.49508 −0.117464
\(163\) −17.9737 −1.40781 −0.703903 0.710297i \(-0.748561\pi\)
−0.703903 + 0.710297i \(0.748561\pi\)
\(164\) −31.3101 −2.44491
\(165\) −0.978913 −0.0762082
\(166\) 1.59646 0.123909
\(167\) 21.8559 1.69126 0.845629 0.533771i \(-0.179226\pi\)
0.845629 + 0.533771i \(0.179226\pi\)
\(168\) 6.97301 0.537979
\(169\) −12.9646 −0.997278
\(170\) 0.592389 0.0454342
\(171\) 11.1781 0.854810
\(172\) −15.4750 −1.17996
\(173\) −19.3743 −1.47300 −0.736501 0.676437i \(-0.763523\pi\)
−0.736501 + 0.676437i \(0.763523\pi\)
\(174\) 2.70818 0.205307
\(175\) −12.8733 −0.973132
\(176\) 1.39205 0.104929
\(177\) 12.4428 0.935255
\(178\) 1.25891 0.0943590
\(179\) −2.08339 −0.155720 −0.0778599 0.996964i \(-0.524809\pi\)
−0.0778599 + 0.996964i \(0.524809\pi\)
\(180\) 1.60396 0.119552
\(181\) −11.2681 −0.837552 −0.418776 0.908090i \(-0.637541\pi\)
−0.418776 + 0.908090i \(0.637541\pi\)
\(182\) −1.11416 −0.0825873
\(183\) 0.207140 0.0153122
\(184\) −16.7670 −1.23608
\(185\) 2.50358 0.184067
\(186\) −0.274013 −0.0200916
\(187\) −3.66108 −0.267725
\(188\) −4.50918 −0.328866
\(189\) 13.2364 0.962809
\(190\) −3.39418 −0.246240
\(191\) −13.3234 −0.964047 −0.482024 0.876158i \(-0.660098\pi\)
−0.482024 + 0.876158i \(0.660098\pi\)
\(192\) 13.3505 0.963491
\(193\) −19.6130 −1.41177 −0.705886 0.708326i \(-0.749451\pi\)
−0.705886 + 0.708326i \(0.749451\pi\)
\(194\) −35.9387 −2.58025
\(195\) 0.0502951 0.00360171
\(196\) −0.587782 −0.0419844
\(197\) 6.48871 0.462302 0.231151 0.972918i \(-0.425751\pi\)
0.231151 + 0.972918i \(0.425751\pi\)
\(198\) −16.2079 −1.15184
\(199\) 7.68122 0.544507 0.272253 0.962226i \(-0.412231\pi\)
0.272253 + 0.962226i \(0.412231\pi\)
\(200\) 12.8631 0.909557
\(201\) −6.39492 −0.451063
\(202\) −40.3052 −2.83587
\(203\) 3.04143 0.213466
\(204\) −3.22572 −0.225846
\(205\) 2.59532 0.181265
\(206\) −0.707514 −0.0492948
\(207\) −12.5418 −0.871717
\(208\) −0.0715213 −0.00495911
\(209\) 20.9767 1.45099
\(210\) −1.58377 −0.109291
\(211\) −6.63914 −0.457057 −0.228529 0.973537i \(-0.573391\pi\)
−0.228529 + 0.973537i \(0.573391\pi\)
\(212\) 14.3817 0.987740
\(213\) 1.41708 0.0970971
\(214\) 7.68775 0.525524
\(215\) 1.28273 0.0874818
\(216\) −13.2259 −0.899908
\(217\) −0.307731 −0.0208901
\(218\) 35.2159 2.38512
\(219\) −12.5238 −0.846280
\(220\) 3.00997 0.202932
\(221\) 0.188101 0.0126531
\(222\) −22.2901 −1.49602
\(223\) 13.7318 0.919548 0.459774 0.888036i \(-0.347930\pi\)
0.459774 + 0.888036i \(0.347930\pi\)
\(224\) 15.8681 1.06023
\(225\) 9.62165 0.641443
\(226\) −44.1705 −2.93818
\(227\) 4.70353 0.312185 0.156092 0.987742i \(-0.450110\pi\)
0.156092 + 0.987742i \(0.450110\pi\)
\(228\) 18.4823 1.22402
\(229\) −10.3658 −0.684992 −0.342496 0.939519i \(-0.611272\pi\)
−0.342496 + 0.939519i \(0.611272\pi\)
\(230\) 3.80827 0.251110
\(231\) 9.78801 0.644004
\(232\) −3.03900 −0.199520
\(233\) 21.0575 1.37952 0.689762 0.724036i \(-0.257715\pi\)
0.689762 + 0.724036i \(0.257715\pi\)
\(234\) 0.832737 0.0544377
\(235\) 0.373770 0.0243821
\(236\) −38.2592 −2.49046
\(237\) −5.99430 −0.389372
\(238\) −5.92322 −0.383945
\(239\) −18.5434 −1.19947 −0.599736 0.800198i \(-0.704728\pi\)
−0.599736 + 0.800198i \(0.704728\pi\)
\(240\) −0.101667 −0.00656255
\(241\) −18.0872 −1.16510 −0.582549 0.812795i \(-0.697945\pi\)
−0.582549 + 0.812795i \(0.697945\pi\)
\(242\) −5.45412 −0.350604
\(243\) −15.8877 −1.01920
\(244\) −0.636916 −0.0407744
\(245\) 0.0487218 0.00311272
\(246\) −23.1069 −1.47324
\(247\) −1.07775 −0.0685759
\(248\) 0.307486 0.0195254
\(249\) 0.720586 0.0456653
\(250\) −5.88352 −0.372106
\(251\) 28.6791 1.81021 0.905105 0.425188i \(-0.139792\pi\)
0.905105 + 0.425188i \(0.139792\pi\)
\(252\) −16.0377 −1.01028
\(253\) −23.5359 −1.47969
\(254\) 0.213739 0.0134112
\(255\) 0.267383 0.0167442
\(256\) −13.4605 −0.841280
\(257\) −26.6483 −1.66227 −0.831136 0.556069i \(-0.812309\pi\)
−0.831136 + 0.556069i \(0.812309\pi\)
\(258\) −11.4206 −0.711014
\(259\) −25.0330 −1.55547
\(260\) −0.154648 −0.00959087
\(261\) −2.27319 −0.140707
\(262\) 38.1876 2.35924
\(263\) 20.5527 1.26733 0.633665 0.773607i \(-0.281550\pi\)
0.633665 + 0.773607i \(0.281550\pi\)
\(264\) −9.78022 −0.601931
\(265\) −1.19211 −0.0732310
\(266\) 33.9380 2.08087
\(267\) 0.568226 0.0347749
\(268\) 19.6632 1.20112
\(269\) 12.2097 0.744440 0.372220 0.928145i \(-0.378597\pi\)
0.372220 + 0.928145i \(0.378597\pi\)
\(270\) 3.00398 0.182816
\(271\) −0.590600 −0.0358764 −0.0179382 0.999839i \(-0.505710\pi\)
−0.0179382 + 0.999839i \(0.505710\pi\)
\(272\) −0.380228 −0.0230547
\(273\) −0.502894 −0.0304365
\(274\) −2.61536 −0.158000
\(275\) 18.0559 1.08881
\(276\) −20.7371 −1.24823
\(277\) −16.5574 −0.994836 −0.497418 0.867511i \(-0.665718\pi\)
−0.497418 + 0.867511i \(0.665718\pi\)
\(278\) 42.2564 2.53437
\(279\) 0.230001 0.0137698
\(280\) 1.77724 0.106210
\(281\) 2.94326 0.175580 0.0877900 0.996139i \(-0.472020\pi\)
0.0877900 + 0.996139i \(0.472020\pi\)
\(282\) −3.32779 −0.198167
\(283\) −10.1128 −0.601144 −0.300572 0.953759i \(-0.597178\pi\)
−0.300572 + 0.953759i \(0.597178\pi\)
\(284\) −4.35727 −0.258557
\(285\) −1.53201 −0.0907487
\(286\) 1.56271 0.0924048
\(287\) −25.9503 −1.53180
\(288\) −11.8599 −0.698854
\(289\) 1.00000 0.0588235
\(290\) 0.690245 0.0405326
\(291\) −16.2214 −0.950917
\(292\) 38.5084 2.25353
\(293\) 21.2925 1.24392 0.621960 0.783049i \(-0.286337\pi\)
0.621960 + 0.783049i \(0.286337\pi\)
\(294\) −0.433785 −0.0252988
\(295\) 3.17134 0.184642
\(296\) 25.0130 1.45385
\(297\) −18.5652 −1.07726
\(298\) −47.9218 −2.77603
\(299\) 1.20924 0.0699321
\(300\) 15.9088 0.918495
\(301\) −12.8259 −0.739272
\(302\) −39.5937 −2.27836
\(303\) −18.1923 −1.04512
\(304\) 2.17857 0.124950
\(305\) 0.0527946 0.00302301
\(306\) 4.42707 0.253079
\(307\) 16.9868 0.969488 0.484744 0.874656i \(-0.338913\pi\)
0.484744 + 0.874656i \(0.338913\pi\)
\(308\) −30.0963 −1.71490
\(309\) −0.319347 −0.0181670
\(310\) −0.0698389 −0.00396658
\(311\) 9.42445 0.534411 0.267206 0.963640i \(-0.413900\pi\)
0.267206 + 0.963640i \(0.413900\pi\)
\(312\) 0.502494 0.0284481
\(313\) 19.1318 1.08139 0.540697 0.841217i \(-0.318161\pi\)
0.540697 + 0.841217i \(0.318161\pi\)
\(314\) −11.2454 −0.634616
\(315\) 1.32938 0.0749023
\(316\) 18.4314 1.03685
\(317\) 15.3104 0.859917 0.429958 0.902849i \(-0.358528\pi\)
0.429958 + 0.902849i \(0.358528\pi\)
\(318\) 10.6137 0.595189
\(319\) −4.26585 −0.238842
\(320\) 3.40270 0.190217
\(321\) 3.46998 0.193675
\(322\) −38.0784 −2.12203
\(323\) −5.72965 −0.318806
\(324\) 2.07496 0.115276
\(325\) −0.927687 −0.0514588
\(326\) 40.7862 2.25894
\(327\) 15.8952 0.879007
\(328\) 25.9296 1.43172
\(329\) −3.73728 −0.206043
\(330\) 2.22137 0.122282
\(331\) 17.2604 0.948715 0.474358 0.880332i \(-0.342680\pi\)
0.474358 + 0.880332i \(0.342680\pi\)
\(332\) −2.21567 −0.121601
\(333\) 18.7099 1.02529
\(334\) −49.5958 −2.71376
\(335\) −1.62990 −0.0890510
\(336\) 1.01655 0.0554574
\(337\) 20.1821 1.09939 0.549694 0.835366i \(-0.314744\pi\)
0.549694 + 0.835366i \(0.314744\pi\)
\(338\) 29.4196 1.60021
\(339\) −19.9370 −1.08283
\(340\) −0.822154 −0.0445876
\(341\) 0.431618 0.0233734
\(342\) −25.3656 −1.37161
\(343\) −18.7589 −1.01288
\(344\) 12.8157 0.690975
\(345\) 1.71892 0.0925435
\(346\) 43.9646 2.36355
\(347\) −0.631746 −0.0339139 −0.0169569 0.999856i \(-0.505398\pi\)
−0.0169569 + 0.999856i \(0.505398\pi\)
\(348\) −3.75858 −0.201481
\(349\) 4.79300 0.256564 0.128282 0.991738i \(-0.459054\pi\)
0.128282 + 0.991738i \(0.459054\pi\)
\(350\) 29.2124 1.56147
\(351\) 0.953853 0.0509129
\(352\) −22.2563 −1.18626
\(353\) −1.00000 −0.0532246
\(354\) −28.2354 −1.50069
\(355\) 0.361178 0.0191694
\(356\) −1.74719 −0.0926008
\(357\) −2.67353 −0.141498
\(358\) 4.72767 0.249865
\(359\) 20.7339 1.09429 0.547147 0.837037i \(-0.315714\pi\)
0.547147 + 0.837037i \(0.315714\pi\)
\(360\) −1.32833 −0.0700089
\(361\) 13.8289 0.727838
\(362\) 25.5698 1.34392
\(363\) −2.46180 −0.129211
\(364\) 1.54631 0.0810484
\(365\) −3.19199 −0.167077
\(366\) −0.470046 −0.0245697
\(367\) −13.9016 −0.725659 −0.362830 0.931856i \(-0.618189\pi\)
−0.362830 + 0.931856i \(0.618189\pi\)
\(368\) −2.44436 −0.127421
\(369\) 19.3955 1.00969
\(370\) −5.68118 −0.295350
\(371\) 11.9198 0.618844
\(372\) 0.380292 0.0197172
\(373\) −11.9271 −0.617559 −0.308780 0.951134i \(-0.599921\pi\)
−0.308780 + 0.951134i \(0.599921\pi\)
\(374\) 8.30781 0.429586
\(375\) −2.65561 −0.137135
\(376\) 3.73430 0.192582
\(377\) 0.219173 0.0112880
\(378\) −30.0364 −1.54491
\(379\) 1.73456 0.0890985 0.0445493 0.999007i \(-0.485815\pi\)
0.0445493 + 0.999007i \(0.485815\pi\)
\(380\) 4.71066 0.241652
\(381\) 0.0964744 0.00494253
\(382\) 30.2337 1.54689
\(383\) 11.5744 0.591426 0.295713 0.955277i \(-0.404443\pi\)
0.295713 + 0.955277i \(0.404443\pi\)
\(384\) −17.8422 −0.910505
\(385\) 2.49471 0.127142
\(386\) 44.5061 2.26530
\(387\) 9.58619 0.487294
\(388\) 49.8779 2.53217
\(389\) −12.8440 −0.651218 −0.325609 0.945504i \(-0.605569\pi\)
−0.325609 + 0.945504i \(0.605569\pi\)
\(390\) −0.114131 −0.00577924
\(391\) 6.42867 0.325112
\(392\) 0.486775 0.0245858
\(393\) 17.2365 0.869468
\(394\) −14.7243 −0.741801
\(395\) −1.52779 −0.0768716
\(396\) 22.4943 1.13038
\(397\) 27.9607 1.40331 0.701653 0.712519i \(-0.252446\pi\)
0.701653 + 0.712519i \(0.252446\pi\)
\(398\) −17.4304 −0.873706
\(399\) 15.3184 0.766879
\(400\) 1.87523 0.0937614
\(401\) −18.9111 −0.944378 −0.472189 0.881497i \(-0.656536\pi\)
−0.472189 + 0.881497i \(0.656536\pi\)
\(402\) 14.5115 0.723768
\(403\) −0.0221759 −0.00110466
\(404\) 55.9381 2.78302
\(405\) −0.171996 −0.00854653
\(406\) −6.90167 −0.342524
\(407\) 35.1108 1.74038
\(408\) 2.67140 0.132254
\(409\) 2.30224 0.113838 0.0569192 0.998379i \(-0.481872\pi\)
0.0569192 + 0.998379i \(0.481872\pi\)
\(410\) −5.88936 −0.290855
\(411\) −1.18048 −0.0582288
\(412\) 0.981932 0.0483763
\(413\) −31.7098 −1.56034
\(414\) 28.4602 1.39874
\(415\) 0.183659 0.00901545
\(416\) 1.14350 0.0560645
\(417\) 19.0730 0.934010
\(418\) −47.6008 −2.32823
\(419\) −18.5387 −0.905673 −0.452836 0.891594i \(-0.649588\pi\)
−0.452836 + 0.891594i \(0.649588\pi\)
\(420\) 2.19805 0.107254
\(421\) −26.9735 −1.31461 −0.657305 0.753625i \(-0.728303\pi\)
−0.657305 + 0.753625i \(0.728303\pi\)
\(422\) 15.0657 0.733386
\(423\) 2.79328 0.135814
\(424\) −11.9103 −0.578415
\(425\) −4.93185 −0.239230
\(426\) −3.21568 −0.155800
\(427\) −0.527886 −0.0255462
\(428\) −10.6695 −0.515732
\(429\) 0.705351 0.0340547
\(430\) −2.91081 −0.140372
\(431\) 14.7579 0.710863 0.355432 0.934702i \(-0.384334\pi\)
0.355432 + 0.934702i \(0.384334\pi\)
\(432\) −1.92812 −0.0927668
\(433\) −27.6514 −1.32884 −0.664422 0.747358i \(-0.731322\pi\)
−0.664422 + 0.747358i \(0.731322\pi\)
\(434\) 0.698310 0.0335199
\(435\) 0.311552 0.0149378
\(436\) −48.8748 −2.34068
\(437\) −36.8340 −1.76201
\(438\) 28.4193 1.35793
\(439\) −18.1898 −0.868152 −0.434076 0.900876i \(-0.642925\pi\)
−0.434076 + 0.900876i \(0.642925\pi\)
\(440\) −2.49273 −0.118836
\(441\) 0.364110 0.0173386
\(442\) −0.426843 −0.0203029
\(443\) −6.68715 −0.317716 −0.158858 0.987301i \(-0.550781\pi\)
−0.158858 + 0.987301i \(0.550781\pi\)
\(444\) 30.9356 1.46814
\(445\) 0.144826 0.00686542
\(446\) −31.1604 −1.47549
\(447\) −21.6302 −1.02307
\(448\) −34.0232 −1.60744
\(449\) 21.3978 1.00983 0.504913 0.863170i \(-0.331525\pi\)
0.504913 + 0.863170i \(0.331525\pi\)
\(450\) −21.8336 −1.02925
\(451\) 36.3974 1.71389
\(452\) 61.3025 2.88343
\(453\) −17.8712 −0.839662
\(454\) −10.6734 −0.500926
\(455\) −0.128175 −0.00600892
\(456\) −15.3062 −0.716779
\(457\) −31.5753 −1.47703 −0.738516 0.674236i \(-0.764473\pi\)
−0.738516 + 0.674236i \(0.764473\pi\)
\(458\) 23.5223 1.09913
\(459\) 5.07096 0.236692
\(460\) −5.28536 −0.246431
\(461\) 24.3344 1.13337 0.566683 0.823936i \(-0.308226\pi\)
0.566683 + 0.823936i \(0.308226\pi\)
\(462\) −22.2112 −1.03336
\(463\) 1.95408 0.0908138 0.0454069 0.998969i \(-0.485542\pi\)
0.0454069 + 0.998969i \(0.485542\pi\)
\(464\) −0.443037 −0.0205675
\(465\) −0.0315228 −0.00146183
\(466\) −47.7842 −2.21356
\(467\) 2.50298 0.115824 0.0579120 0.998322i \(-0.481556\pi\)
0.0579120 + 0.998322i \(0.481556\pi\)
\(468\) −1.15572 −0.0534233
\(469\) 16.2972 0.752533
\(470\) −0.848167 −0.0391230
\(471\) −5.07579 −0.233880
\(472\) 31.6845 1.45840
\(473\) 17.9894 0.827152
\(474\) 13.6024 0.624779
\(475\) 28.2578 1.29656
\(476\) 8.22061 0.376791
\(477\) −8.90896 −0.407913
\(478\) 42.0791 1.92465
\(479\) 11.5276 0.526709 0.263355 0.964699i \(-0.415171\pi\)
0.263355 + 0.964699i \(0.415171\pi\)
\(480\) 1.62546 0.0741919
\(481\) −1.80394 −0.0822527
\(482\) 41.0439 1.86950
\(483\) −17.1872 −0.782046
\(484\) 7.56957 0.344071
\(485\) −4.13443 −0.187735
\(486\) 36.0527 1.63538
\(487\) −4.63325 −0.209952 −0.104976 0.994475i \(-0.533477\pi\)
−0.104976 + 0.994475i \(0.533477\pi\)
\(488\) 0.527466 0.0238773
\(489\) 18.4094 0.832504
\(490\) −0.110561 −0.00499462
\(491\) −15.5822 −0.703213 −0.351607 0.936148i \(-0.614364\pi\)
−0.351607 + 0.936148i \(0.614364\pi\)
\(492\) 32.0692 1.44579
\(493\) 1.16519 0.0524775
\(494\) 2.44566 0.110036
\(495\) −1.86457 −0.0838063
\(496\) 0.0448265 0.00201277
\(497\) −3.61137 −0.161992
\(498\) −1.63517 −0.0732737
\(499\) 39.7840 1.78098 0.890489 0.455005i \(-0.150363\pi\)
0.890489 + 0.455005i \(0.150363\pi\)
\(500\) 8.16551 0.365173
\(501\) −22.3858 −1.00012
\(502\) −65.0793 −2.90463
\(503\) 5.04201 0.224812 0.112406 0.993662i \(-0.464144\pi\)
0.112406 + 0.993662i \(0.464144\pi\)
\(504\) 13.2818 0.591616
\(505\) −4.63676 −0.206333
\(506\) 53.4081 2.37428
\(507\) 13.2790 0.589739
\(508\) −0.296641 −0.0131613
\(509\) 34.3319 1.52173 0.760867 0.648908i \(-0.224774\pi\)
0.760867 + 0.648908i \(0.224774\pi\)
\(510\) −0.606752 −0.0268674
\(511\) 31.9163 1.41189
\(512\) −4.29486 −0.189808
\(513\) −29.0548 −1.28280
\(514\) 60.4708 2.66725
\(515\) −0.0813932 −0.00358661
\(516\) 15.8502 0.697765
\(517\) 5.24184 0.230536
\(518\) 56.8053 2.49588
\(519\) 19.8441 0.871057
\(520\) 0.128073 0.00561636
\(521\) −3.98150 −0.174433 −0.0872163 0.996189i \(-0.527797\pi\)
−0.0872163 + 0.996189i \(0.527797\pi\)
\(522\) 5.15837 0.225776
\(523\) 33.0765 1.44633 0.723167 0.690673i \(-0.242686\pi\)
0.723167 + 0.690673i \(0.242686\pi\)
\(524\) −52.9991 −2.31528
\(525\) 13.1855 0.575460
\(526\) −46.6385 −2.03354
\(527\) −0.117894 −0.00513553
\(528\) −1.42580 −0.0620499
\(529\) 18.3278 0.796860
\(530\) 2.70517 0.117505
\(531\) 23.7002 1.02850
\(532\) −47.1012 −2.04210
\(533\) −1.87005 −0.0810007
\(534\) −1.28943 −0.0557991
\(535\) 0.884408 0.0382363
\(536\) −16.2842 −0.703370
\(537\) 2.13390 0.0920847
\(538\) −27.7066 −1.19451
\(539\) 0.683286 0.0294312
\(540\) −4.16911 −0.179410
\(541\) 5.55000 0.238613 0.119307 0.992857i \(-0.461933\pi\)
0.119307 + 0.992857i \(0.461933\pi\)
\(542\) 1.34020 0.0575666
\(543\) 11.5413 0.495285
\(544\) 6.07915 0.260641
\(545\) 4.05128 0.173538
\(546\) 1.14118 0.0488379
\(547\) −14.6764 −0.627518 −0.313759 0.949503i \(-0.601588\pi\)
−0.313759 + 0.949503i \(0.601588\pi\)
\(548\) 3.62976 0.155056
\(549\) 0.394547 0.0168389
\(550\) −40.9729 −1.74709
\(551\) −6.67613 −0.284413
\(552\) 17.1736 0.730955
\(553\) 15.2762 0.649610
\(554\) 37.5723 1.59630
\(555\) −2.56428 −0.108848
\(556\) −58.6460 −2.48715
\(557\) 24.9861 1.05869 0.529347 0.848406i \(-0.322437\pi\)
0.529347 + 0.848406i \(0.322437\pi\)
\(558\) −0.521923 −0.0220948
\(559\) −0.924268 −0.0390924
\(560\) 0.259093 0.0109487
\(561\) 3.74985 0.158319
\(562\) −6.67890 −0.281733
\(563\) −32.6496 −1.37602 −0.688009 0.725702i \(-0.741515\pi\)
−0.688009 + 0.725702i \(0.741515\pi\)
\(564\) 4.61851 0.194474
\(565\) −5.08143 −0.213777
\(566\) 22.9482 0.964584
\(567\) 1.71976 0.0722231
\(568\) 3.60850 0.151409
\(569\) 6.26413 0.262606 0.131303 0.991342i \(-0.458084\pi\)
0.131303 + 0.991342i \(0.458084\pi\)
\(570\) 3.47648 0.145614
\(571\) 22.8138 0.954727 0.477364 0.878706i \(-0.341592\pi\)
0.477364 + 0.878706i \(0.341592\pi\)
\(572\) −2.16882 −0.0906830
\(573\) 13.6464 0.570088
\(574\) 58.8869 2.45789
\(575\) −31.7052 −1.32220
\(576\) 25.4292 1.05955
\(577\) −5.90062 −0.245646 −0.122823 0.992429i \(-0.539195\pi\)
−0.122823 + 0.992429i \(0.539195\pi\)
\(578\) −2.26922 −0.0943872
\(579\) 20.0885 0.834849
\(580\) −0.957965 −0.0397773
\(581\) −1.83638 −0.0761858
\(582\) 36.8100 1.52582
\(583\) −16.7185 −0.692409
\(584\) −31.8909 −1.31966
\(585\) 0.0957990 0.00396080
\(586\) −48.3174 −1.99597
\(587\) 24.2350 1.00029 0.500143 0.865943i \(-0.333281\pi\)
0.500143 + 0.865943i \(0.333281\pi\)
\(588\) 0.602033 0.0248274
\(589\) 0.675489 0.0278331
\(590\) −7.19647 −0.296274
\(591\) −6.64604 −0.273381
\(592\) 3.64649 0.149870
\(593\) 42.2853 1.73645 0.868224 0.496173i \(-0.165262\pi\)
0.868224 + 0.496173i \(0.165262\pi\)
\(594\) 42.1285 1.72856
\(595\) −0.681414 −0.0279352
\(596\) 66.5088 2.72431
\(597\) −7.86745 −0.321993
\(598\) −2.74403 −0.112212
\(599\) 19.9022 0.813182 0.406591 0.913610i \(-0.366717\pi\)
0.406591 + 0.913610i \(0.366717\pi\)
\(600\) −13.1750 −0.537865
\(601\) −25.9737 −1.05949 −0.529744 0.848158i \(-0.677712\pi\)
−0.529744 + 0.848158i \(0.677712\pi\)
\(602\) 29.1048 1.18622
\(603\) −12.1807 −0.496035
\(604\) 54.9506 2.23591
\(605\) −0.627449 −0.0255094
\(606\) 41.2825 1.67699
\(607\) 28.2669 1.14732 0.573658 0.819095i \(-0.305524\pi\)
0.573658 + 0.819095i \(0.305524\pi\)
\(608\) −34.8314 −1.41260
\(609\) −3.11517 −0.126233
\(610\) −0.119803 −0.00485067
\(611\) −0.269318 −0.0108955
\(612\) −6.14416 −0.248363
\(613\) 47.1794 1.90556 0.952778 0.303668i \(-0.0982113\pi\)
0.952778 + 0.303668i \(0.0982113\pi\)
\(614\) −38.5468 −1.55562
\(615\) −2.65825 −0.107191
\(616\) 24.9244 1.00423
\(617\) −15.6247 −0.629027 −0.314514 0.949253i \(-0.601841\pi\)
−0.314514 + 0.949253i \(0.601841\pi\)
\(618\) 0.724668 0.0291504
\(619\) 1.98743 0.0798816 0.0399408 0.999202i \(-0.487283\pi\)
0.0399408 + 0.999202i \(0.487283\pi\)
\(620\) 0.0969267 0.00389267
\(621\) 32.5995 1.30817
\(622\) −21.3862 −0.857507
\(623\) −1.44810 −0.0580168
\(624\) 0.0732554 0.00293256
\(625\) 23.9824 0.959296
\(626\) −43.4143 −1.73518
\(627\) −21.4853 −0.858041
\(628\) 15.6071 0.622791
\(629\) −9.59028 −0.382390
\(630\) −3.01667 −0.120187
\(631\) 13.8012 0.549416 0.274708 0.961528i \(-0.411419\pi\)
0.274708 + 0.961528i \(0.411419\pi\)
\(632\) −15.2640 −0.607171
\(633\) 6.80011 0.270280
\(634\) −34.7427 −1.37981
\(635\) 0.0245888 0.000975778 0
\(636\) −14.7304 −0.584099
\(637\) −0.0351063 −0.00139096
\(638\) 9.68016 0.383241
\(639\) 2.69918 0.106778
\(640\) −4.54751 −0.179756
\(641\) 48.9494 1.93338 0.966692 0.255942i \(-0.0823857\pi\)
0.966692 + 0.255942i \(0.0823857\pi\)
\(642\) −7.87415 −0.310768
\(643\) −30.2371 −1.19243 −0.596217 0.802823i \(-0.703330\pi\)
−0.596217 + 0.802823i \(0.703330\pi\)
\(644\) 52.8476 2.08249
\(645\) −1.31384 −0.0517322
\(646\) 13.0018 0.511551
\(647\) −31.5786 −1.24148 −0.620741 0.784016i \(-0.713168\pi\)
−0.620741 + 0.784016i \(0.713168\pi\)
\(648\) −1.71839 −0.0675048
\(649\) 44.4756 1.74582
\(650\) 2.10513 0.0825699
\(651\) 0.315192 0.0123534
\(652\) −56.6056 −2.21685
\(653\) 21.4932 0.841096 0.420548 0.907270i \(-0.361838\pi\)
0.420548 + 0.907270i \(0.361838\pi\)
\(654\) −36.0697 −1.41044
\(655\) 4.39315 0.171655
\(656\) 3.78012 0.147589
\(657\) −23.8546 −0.930655
\(658\) 8.48071 0.330612
\(659\) 1.65772 0.0645755 0.0322877 0.999479i \(-0.489721\pi\)
0.0322877 + 0.999479i \(0.489721\pi\)
\(660\) −3.08295 −0.120004
\(661\) 39.5301 1.53754 0.768770 0.639525i \(-0.220869\pi\)
0.768770 + 0.639525i \(0.220869\pi\)
\(662\) −39.1676 −1.52229
\(663\) −0.192662 −0.00748237
\(664\) 1.83492 0.0712086
\(665\) 3.90426 0.151401
\(666\) −42.4569 −1.64517
\(667\) 7.49061 0.290038
\(668\) 68.8321 2.66319
\(669\) −14.0647 −0.543773
\(670\) 3.69861 0.142890
\(671\) 0.740404 0.0285830
\(672\) −16.2528 −0.626965
\(673\) 7.60349 0.293093 0.146547 0.989204i \(-0.453184\pi\)
0.146547 + 0.989204i \(0.453184\pi\)
\(674\) −45.7976 −1.76406
\(675\) −25.0092 −0.962605
\(676\) −40.8303 −1.57040
\(677\) −46.9268 −1.80354 −0.901771 0.432215i \(-0.857732\pi\)
−0.901771 + 0.432215i \(0.857732\pi\)
\(678\) 45.2415 1.73749
\(679\) 41.3396 1.58647
\(680\) 0.680872 0.0261102
\(681\) −4.81758 −0.184610
\(682\) −0.979437 −0.0375046
\(683\) 47.5297 1.81867 0.909337 0.416061i \(-0.136590\pi\)
0.909337 + 0.416061i \(0.136590\pi\)
\(684\) 35.2039 1.34606
\(685\) −0.300874 −0.0114958
\(686\) 42.5680 1.62525
\(687\) 10.6171 0.405069
\(688\) 1.86832 0.0712290
\(689\) 0.858972 0.0327242
\(690\) −3.90061 −0.148494
\(691\) 34.1189 1.29794 0.648972 0.760813i \(-0.275199\pi\)
0.648972 + 0.760813i \(0.275199\pi\)
\(692\) −61.0168 −2.31951
\(693\) 18.6436 0.708212
\(694\) 1.43357 0.0544176
\(695\) 4.86122 0.184397
\(696\) 3.11269 0.117986
\(697\) −9.94171 −0.376569
\(698\) −10.8764 −0.411677
\(699\) −21.5681 −0.815780
\(700\) −40.5428 −1.53237
\(701\) −42.7264 −1.61375 −0.806876 0.590720i \(-0.798844\pi\)
−0.806876 + 0.590720i \(0.798844\pi\)
\(702\) −2.16450 −0.0816940
\(703\) 54.9490 2.07244
\(704\) 47.7203 1.79853
\(705\) −0.382832 −0.0144183
\(706\) 2.26922 0.0854033
\(707\) 46.3623 1.74363
\(708\) 39.1868 1.47273
\(709\) −52.2315 −1.96159 −0.980797 0.195033i \(-0.937519\pi\)
−0.980797 + 0.195033i \(0.937519\pi\)
\(710\) −0.819594 −0.0307588
\(711\) −11.4176 −0.428193
\(712\) 1.44694 0.0542265
\(713\) −0.757899 −0.0283835
\(714\) 6.06683 0.227045
\(715\) 0.179776 0.00672323
\(716\) −6.56135 −0.245209
\(717\) 18.9930 0.709306
\(718\) −47.0498 −1.75588
\(719\) 27.3320 1.01931 0.509655 0.860379i \(-0.329773\pi\)
0.509655 + 0.860379i \(0.329773\pi\)
\(720\) −0.193648 −0.00721685
\(721\) 0.813840 0.0303090
\(722\) −31.3809 −1.16788
\(723\) 18.5257 0.688980
\(724\) −35.4874 −1.31888
\(725\) −5.74654 −0.213421
\(726\) 5.58636 0.207329
\(727\) −28.9801 −1.07481 −0.537407 0.843323i \(-0.680596\pi\)
−0.537407 + 0.843323i \(0.680596\pi\)
\(728\) −1.28058 −0.0474615
\(729\) 14.2964 0.529495
\(730\) 7.24334 0.268088
\(731\) −4.91368 −0.181739
\(732\) 0.652359 0.0241119
\(733\) 30.3523 1.12109 0.560545 0.828124i \(-0.310592\pi\)
0.560545 + 0.828124i \(0.310592\pi\)
\(734\) 31.5459 1.16438
\(735\) −0.0499031 −0.00184070
\(736\) 39.0808 1.44054
\(737\) −22.8581 −0.841990
\(738\) −44.0126 −1.62013
\(739\) 45.1340 1.66028 0.830141 0.557553i \(-0.188260\pi\)
0.830141 + 0.557553i \(0.188260\pi\)
\(740\) 7.88469 0.289847
\(741\) 1.10389 0.0405522
\(742\) −27.0486 −0.992986
\(743\) −45.1424 −1.65611 −0.828057 0.560644i \(-0.810554\pi\)
−0.828057 + 0.560644i \(0.810554\pi\)
\(744\) −0.314941 −0.0115463
\(745\) −5.51298 −0.201980
\(746\) 27.0651 0.990925
\(747\) 1.37253 0.0502181
\(748\) −11.5301 −0.421582
\(749\) −8.84308 −0.323119
\(750\) 6.02617 0.220045
\(751\) −27.6825 −1.01015 −0.505074 0.863076i \(-0.668535\pi\)
−0.505074 + 0.863076i \(0.668535\pi\)
\(752\) 0.544400 0.0198522
\(753\) −29.3745 −1.07047
\(754\) −0.497353 −0.0181125
\(755\) −4.55491 −0.165770
\(756\) 41.6864 1.51612
\(757\) 10.7888 0.392125 0.196063 0.980591i \(-0.437184\pi\)
0.196063 + 0.980591i \(0.437184\pi\)
\(758\) −3.93611 −0.142966
\(759\) 24.1065 0.875012
\(760\) −3.90116 −0.141510
\(761\) −20.6249 −0.747652 −0.373826 0.927499i \(-0.621954\pi\)
−0.373826 + 0.927499i \(0.621954\pi\)
\(762\) −0.218922 −0.00793070
\(763\) −40.5082 −1.46649
\(764\) −41.9603 −1.51807
\(765\) 0.509295 0.0184136
\(766\) −26.2649 −0.948991
\(767\) −2.28509 −0.0825099
\(768\) 13.7868 0.497490
\(769\) 49.3078 1.77808 0.889042 0.457825i \(-0.151371\pi\)
0.889042 + 0.457825i \(0.151371\pi\)
\(770\) −5.66105 −0.204010
\(771\) 27.2944 0.982983
\(772\) −61.7684 −2.22309
\(773\) −32.3239 −1.16261 −0.581305 0.813686i \(-0.697458\pi\)
−0.581305 + 0.813686i \(0.697458\pi\)
\(774\) −21.7532 −0.781902
\(775\) 0.581434 0.0208857
\(776\) −41.3067 −1.48282
\(777\) 25.6399 0.919827
\(778\) 29.1460 1.04493
\(779\) 56.9625 2.04089
\(780\) 0.158398 0.00567155
\(781\) 5.06525 0.181249
\(782\) −14.5881 −0.521668
\(783\) 5.90863 0.211157
\(784\) 0.0709639 0.00253442
\(785\) −1.29369 −0.0461737
\(786\) −39.1135 −1.39513
\(787\) 26.9077 0.959157 0.479578 0.877499i \(-0.340790\pi\)
0.479578 + 0.877499i \(0.340790\pi\)
\(788\) 20.4353 0.727978
\(789\) −21.0510 −0.749434
\(790\) 3.46690 0.123347
\(791\) 50.8085 1.80654
\(792\) −18.6288 −0.661944
\(793\) −0.0380409 −0.00135087
\(794\) −63.4489 −2.25172
\(795\) 1.22102 0.0433050
\(796\) 24.1910 0.857426
\(797\) −14.6233 −0.517982 −0.258991 0.965880i \(-0.583390\pi\)
−0.258991 + 0.965880i \(0.583390\pi\)
\(798\) −34.7608 −1.23052
\(799\) −1.43177 −0.0506525
\(800\) −29.9815 −1.06000
\(801\) 1.08232 0.0382419
\(802\) 42.9136 1.51533
\(803\) −44.7653 −1.57973
\(804\) −20.1400 −0.710281
\(805\) −4.38058 −0.154395
\(806\) 0.0503221 0.00177252
\(807\) −12.5058 −0.440223
\(808\) −46.3254 −1.62972
\(809\) 29.4584 1.03570 0.517850 0.855471i \(-0.326732\pi\)
0.517850 + 0.855471i \(0.326732\pi\)
\(810\) 0.390296 0.0137136
\(811\) 39.7001 1.39406 0.697030 0.717042i \(-0.254504\pi\)
0.697030 + 0.717042i \(0.254504\pi\)
\(812\) 9.57856 0.336142
\(813\) 0.604920 0.0212155
\(814\) −79.6742 −2.79258
\(815\) 4.69209 0.164357
\(816\) 0.389447 0.0136334
\(817\) 28.1537 0.984972
\(818\) −5.22429 −0.182663
\(819\) −0.957882 −0.0334711
\(820\) 8.17361 0.285435
\(821\) −11.5370 −0.402643 −0.201322 0.979525i \(-0.564524\pi\)
−0.201322 + 0.979525i \(0.564524\pi\)
\(822\) 2.67877 0.0934329
\(823\) 22.6789 0.790538 0.395269 0.918565i \(-0.370651\pi\)
0.395269 + 0.918565i \(0.370651\pi\)
\(824\) −0.813192 −0.0283289
\(825\) −18.4937 −0.643868
\(826\) 71.9565 2.50369
\(827\) 9.07701 0.315638 0.157819 0.987468i \(-0.449554\pi\)
0.157819 + 0.987468i \(0.449554\pi\)
\(828\) −39.4988 −1.37268
\(829\) −25.1705 −0.874209 −0.437104 0.899411i \(-0.643996\pi\)
−0.437104 + 0.899411i \(0.643996\pi\)
\(830\) −0.416762 −0.0144660
\(831\) 16.9588 0.588295
\(832\) −2.45180 −0.0850009
\(833\) −0.186635 −0.00646652
\(834\) −43.2809 −1.49870
\(835\) −5.70556 −0.197449
\(836\) 66.0634 2.28485
\(837\) −0.597834 −0.0206642
\(838\) 42.0683 1.45323
\(839\) 8.59556 0.296752 0.148376 0.988931i \(-0.452595\pi\)
0.148376 + 0.988931i \(0.452595\pi\)
\(840\) −1.82033 −0.0628074
\(841\) −27.6423 −0.953184
\(842\) 61.2089 2.10940
\(843\) −3.01462 −0.103829
\(844\) −20.9091 −0.719720
\(845\) 3.38446 0.116429
\(846\) −6.33856 −0.217924
\(847\) 6.27377 0.215569
\(848\) −1.73633 −0.0596257
\(849\) 10.3580 0.355486
\(850\) 11.1915 0.383864
\(851\) −61.6527 −2.11343
\(852\) 4.46292 0.152897
\(853\) −27.9160 −0.955825 −0.477912 0.878407i \(-0.658606\pi\)
−0.477912 + 0.878407i \(0.658606\pi\)
\(854\) 1.19789 0.0409910
\(855\) −2.91809 −0.0997964
\(856\) 8.83604 0.302010
\(857\) 57.5848 1.96706 0.983529 0.180750i \(-0.0578524\pi\)
0.983529 + 0.180750i \(0.0578524\pi\)
\(858\) −1.60060 −0.0546435
\(859\) 32.9890 1.12557 0.562785 0.826603i \(-0.309730\pi\)
0.562785 + 0.826603i \(0.309730\pi\)
\(860\) 4.03980 0.137756
\(861\) 26.5794 0.905825
\(862\) −33.4890 −1.14064
\(863\) 4.84337 0.164870 0.0824351 0.996596i \(-0.473730\pi\)
0.0824351 + 0.996596i \(0.473730\pi\)
\(864\) 30.8271 1.04876
\(865\) 5.05774 0.171968
\(866\) 62.7472 2.13224
\(867\) −1.02425 −0.0347852
\(868\) −0.969157 −0.0328953
\(869\) −21.4261 −0.726832
\(870\) −0.706981 −0.0239689
\(871\) 1.17442 0.0397936
\(872\) 40.4759 1.37069
\(873\) −30.8976 −1.04572
\(874\) 83.5846 2.82729
\(875\) 6.76770 0.228790
\(876\) −39.4420 −1.33262
\(877\) −31.4974 −1.06359 −0.531796 0.846872i \(-0.678483\pi\)
−0.531796 + 0.846872i \(0.678483\pi\)
\(878\) 41.2767 1.39302
\(879\) −21.8087 −0.735590
\(880\) −0.363399 −0.0122502
\(881\) −31.1249 −1.04862 −0.524312 0.851526i \(-0.675678\pi\)
−0.524312 + 0.851526i \(0.675678\pi\)
\(882\) −0.826246 −0.0278212
\(883\) 48.8828 1.64504 0.822519 0.568737i \(-0.192568\pi\)
0.822519 + 0.568737i \(0.192568\pi\)
\(884\) 0.592399 0.0199245
\(885\) −3.24823 −0.109188
\(886\) 15.1746 0.509802
\(887\) −1.91025 −0.0641400 −0.0320700 0.999486i \(-0.510210\pi\)
−0.0320700 + 0.999486i \(0.510210\pi\)
\(888\) −25.6195 −0.859734
\(889\) −0.245860 −0.00824589
\(890\) −0.328643 −0.0110161
\(891\) −2.41211 −0.0808086
\(892\) 43.2464 1.44800
\(893\) 8.20356 0.274522
\(894\) 49.0837 1.64160
\(895\) 0.543877 0.0181798
\(896\) 45.4700 1.51904
\(897\) −1.23856 −0.0413543
\(898\) −48.5564 −1.62035
\(899\) −0.137368 −0.00458149
\(900\) 30.3021 1.01007
\(901\) 4.56654 0.152134
\(902\) −82.5938 −2.75007
\(903\) 13.1369 0.437167
\(904\) −50.7680 −1.68852
\(905\) 2.94158 0.0977816
\(906\) 40.5537 1.34731
\(907\) 51.2411 1.70143 0.850716 0.525625i \(-0.176169\pi\)
0.850716 + 0.525625i \(0.176169\pi\)
\(908\) 14.8131 0.491592
\(909\) −34.6517 −1.14932
\(910\) 0.290857 0.00964181
\(911\) −25.6317 −0.849216 −0.424608 0.905377i \(-0.639588\pi\)
−0.424608 + 0.905377i \(0.639588\pi\)
\(912\) −2.23140 −0.0738889
\(913\) 2.57567 0.0852424
\(914\) 71.6514 2.37002
\(915\) −0.0540747 −0.00178765
\(916\) −32.6457 −1.07865
\(917\) −43.9265 −1.45058
\(918\) −11.5071 −0.379792
\(919\) −34.5643 −1.14017 −0.570085 0.821586i \(-0.693090\pi\)
−0.570085 + 0.821586i \(0.693090\pi\)
\(920\) 4.37710 0.144309
\(921\) −17.3987 −0.573305
\(922\) −55.2202 −1.81858
\(923\) −0.260245 −0.00856608
\(924\) 30.8260 1.01410
\(925\) 47.2978 1.55514
\(926\) −4.43424 −0.145718
\(927\) −0.608272 −0.0199783
\(928\) 7.08336 0.232523
\(929\) −27.3989 −0.898930 −0.449465 0.893298i \(-0.648385\pi\)
−0.449465 + 0.893298i \(0.648385\pi\)
\(930\) 0.0715322 0.00234563
\(931\) 1.06935 0.0350467
\(932\) 66.3178 2.17231
\(933\) −9.65295 −0.316023
\(934\) −5.67981 −0.185849
\(935\) 0.955740 0.0312560
\(936\) 0.957119 0.0312844
\(937\) −6.44316 −0.210489 −0.105244 0.994446i \(-0.533562\pi\)
−0.105244 + 0.994446i \(0.533562\pi\)
\(938\) −36.9819 −1.20750
\(939\) −19.5957 −0.639481
\(940\) 1.17714 0.0383940
\(941\) −35.7110 −1.16414 −0.582072 0.813137i \(-0.697758\pi\)
−0.582072 + 0.813137i \(0.697758\pi\)
\(942\) 11.5181 0.375280
\(943\) −63.9119 −2.08126
\(944\) 4.61909 0.150339
\(945\) −3.45542 −0.112405
\(946\) −40.8219 −1.32723
\(947\) −10.0170 −0.325507 −0.162754 0.986667i \(-0.552038\pi\)
−0.162754 + 0.986667i \(0.552038\pi\)
\(948\) −18.8782 −0.613137
\(949\) 2.29998 0.0746604
\(950\) −64.1232 −2.08043
\(951\) −15.6816 −0.508511
\(952\) −6.80794 −0.220647
\(953\) 52.7523 1.70881 0.854407 0.519605i \(-0.173921\pi\)
0.854407 + 0.519605i \(0.173921\pi\)
\(954\) 20.2164 0.654530
\(955\) 3.47812 0.112549
\(956\) −58.3999 −1.88879
\(957\) 4.36928 0.141239
\(958\) −26.1587 −0.845148
\(959\) 3.00840 0.0971463
\(960\) −3.48520 −0.112484
\(961\) −30.9861 −0.999552
\(962\) 4.09355 0.131981
\(963\) 6.60940 0.212985
\(964\) −56.9632 −1.83466
\(965\) 5.12004 0.164820
\(966\) 39.0016 1.25486
\(967\) −21.9876 −0.707072 −0.353536 0.935421i \(-0.615021\pi\)
−0.353536 + 0.935421i \(0.615021\pi\)
\(968\) −6.26878 −0.201486
\(969\) 5.86857 0.188526
\(970\) 9.38193 0.301235
\(971\) 9.93393 0.318795 0.159398 0.987214i \(-0.449045\pi\)
0.159398 + 0.987214i \(0.449045\pi\)
\(972\) −50.0362 −1.60491
\(973\) −48.6067 −1.55826
\(974\) 10.5139 0.336886
\(975\) 0.950179 0.0304301
\(976\) 0.0768960 0.00246138
\(977\) 19.4550 0.622421 0.311211 0.950341i \(-0.399266\pi\)
0.311211 + 0.950341i \(0.399266\pi\)
\(978\) −41.7751 −1.33582
\(979\) 2.03108 0.0649135
\(980\) 0.153443 0.00490155
\(981\) 30.2762 0.966645
\(982\) 35.3594 1.12836
\(983\) 42.8746 1.36749 0.683744 0.729722i \(-0.260350\pi\)
0.683744 + 0.729722i \(0.260350\pi\)
\(984\) −26.5583 −0.846647
\(985\) −1.69390 −0.0539723
\(986\) −2.64407 −0.0842044
\(987\) 3.82789 0.121843
\(988\) −3.39424 −0.107985
\(989\) −31.5884 −1.00445
\(990\) 4.23113 0.134474
\(991\) −2.67623 −0.0850133 −0.0425066 0.999096i \(-0.513534\pi\)
−0.0425066 + 0.999096i \(0.513534\pi\)
\(992\) −0.716693 −0.0227550
\(993\) −17.6789 −0.561021
\(994\) 8.19501 0.259930
\(995\) −2.00521 −0.0635695
\(996\) 2.26939 0.0719083
\(997\) 31.6978 1.00388 0.501939 0.864903i \(-0.332620\pi\)
0.501939 + 0.864903i \(0.332620\pi\)
\(998\) −90.2788 −2.85772
\(999\) −48.6319 −1.53865
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.1.13 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.13 121 1.1 even 1 trivial