Properties

Label 4006.2.a.g.1.17
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.779235 q^{3} +1.00000 q^{4} -0.867411 q^{5} +0.779235 q^{6} -3.45139 q^{7} -1.00000 q^{8} -2.39279 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.779235 q^{3} +1.00000 q^{4} -0.867411 q^{5} +0.779235 q^{6} -3.45139 q^{7} -1.00000 q^{8} -2.39279 q^{9} +0.867411 q^{10} +3.23634 q^{11} -0.779235 q^{12} +0.0959992 q^{13} +3.45139 q^{14} +0.675917 q^{15} +1.00000 q^{16} +5.34635 q^{17} +2.39279 q^{18} +1.96760 q^{19} -0.867411 q^{20} +2.68944 q^{21} -3.23634 q^{22} -4.56800 q^{23} +0.779235 q^{24} -4.24760 q^{25} -0.0959992 q^{26} +4.20225 q^{27} -3.45139 q^{28} -4.12205 q^{29} -0.675917 q^{30} +0.192159 q^{31} -1.00000 q^{32} -2.52187 q^{33} -5.34635 q^{34} +2.99377 q^{35} -2.39279 q^{36} +3.45176 q^{37} -1.96760 q^{38} -0.0748059 q^{39} +0.867411 q^{40} +6.89417 q^{41} -2.68944 q^{42} -3.27590 q^{43} +3.23634 q^{44} +2.07553 q^{45} +4.56800 q^{46} +11.3951 q^{47} -0.779235 q^{48} +4.91210 q^{49} +4.24760 q^{50} -4.16606 q^{51} +0.0959992 q^{52} -1.21545 q^{53} -4.20225 q^{54} -2.80724 q^{55} +3.45139 q^{56} -1.53323 q^{57} +4.12205 q^{58} +0.581098 q^{59} +0.675917 q^{60} -3.01819 q^{61} -0.192159 q^{62} +8.25846 q^{63} +1.00000 q^{64} -0.0832707 q^{65} +2.52187 q^{66} +9.49351 q^{67} +5.34635 q^{68} +3.55955 q^{69} -2.99377 q^{70} -14.4713 q^{71} +2.39279 q^{72} +11.7161 q^{73} -3.45176 q^{74} +3.30988 q^{75} +1.96760 q^{76} -11.1699 q^{77} +0.0748059 q^{78} +2.62921 q^{79} -0.867411 q^{80} +3.90384 q^{81} -6.89417 q^{82} +7.45027 q^{83} +2.68944 q^{84} -4.63748 q^{85} +3.27590 q^{86} +3.21205 q^{87} -3.23634 q^{88} +7.41702 q^{89} -2.07553 q^{90} -0.331331 q^{91} -4.56800 q^{92} -0.149737 q^{93} -11.3951 q^{94} -1.70672 q^{95} +0.779235 q^{96} -2.66158 q^{97} -4.91210 q^{98} -7.74389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.779235 −0.449891 −0.224946 0.974371i \(-0.572220\pi\)
−0.224946 + 0.974371i \(0.572220\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.867411 −0.387918 −0.193959 0.981010i \(-0.562133\pi\)
−0.193959 + 0.981010i \(0.562133\pi\)
\(6\) 0.779235 0.318121
\(7\) −3.45139 −1.30450 −0.652252 0.758003i \(-0.726175\pi\)
−0.652252 + 0.758003i \(0.726175\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.39279 −0.797598
\(10\) 0.867411 0.274299
\(11\) 3.23634 0.975793 0.487897 0.872901i \(-0.337764\pi\)
0.487897 + 0.872901i \(0.337764\pi\)
\(12\) −0.779235 −0.224946
\(13\) 0.0959992 0.0266254 0.0133127 0.999911i \(-0.495762\pi\)
0.0133127 + 0.999911i \(0.495762\pi\)
\(14\) 3.45139 0.922423
\(15\) 0.675917 0.174521
\(16\) 1.00000 0.250000
\(17\) 5.34635 1.29668 0.648340 0.761351i \(-0.275463\pi\)
0.648340 + 0.761351i \(0.275463\pi\)
\(18\) 2.39279 0.563987
\(19\) 1.96760 0.451400 0.225700 0.974197i \(-0.427533\pi\)
0.225700 + 0.974197i \(0.427533\pi\)
\(20\) −0.867411 −0.193959
\(21\) 2.68944 0.586885
\(22\) −3.23634 −0.689990
\(23\) −4.56800 −0.952495 −0.476247 0.879311i \(-0.658003\pi\)
−0.476247 + 0.879311i \(0.658003\pi\)
\(24\) 0.779235 0.159061
\(25\) −4.24760 −0.849520
\(26\) −0.0959992 −0.0188270
\(27\) 4.20225 0.808724
\(28\) −3.45139 −0.652252
\(29\) −4.12205 −0.765446 −0.382723 0.923863i \(-0.625014\pi\)
−0.382723 + 0.923863i \(0.625014\pi\)
\(30\) −0.675917 −0.123405
\(31\) 0.192159 0.0345128 0.0172564 0.999851i \(-0.494507\pi\)
0.0172564 + 0.999851i \(0.494507\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.52187 −0.439001
\(34\) −5.34635 −0.916892
\(35\) 2.99377 0.506040
\(36\) −2.39279 −0.398799
\(37\) 3.45176 0.567466 0.283733 0.958903i \(-0.408427\pi\)
0.283733 + 0.958903i \(0.408427\pi\)
\(38\) −1.96760 −0.319188
\(39\) −0.0748059 −0.0119785
\(40\) 0.867411 0.137150
\(41\) 6.89417 1.07669 0.538344 0.842725i \(-0.319050\pi\)
0.538344 + 0.842725i \(0.319050\pi\)
\(42\) −2.68944 −0.414990
\(43\) −3.27590 −0.499570 −0.249785 0.968301i \(-0.580360\pi\)
−0.249785 + 0.968301i \(0.580360\pi\)
\(44\) 3.23634 0.487897
\(45\) 2.07553 0.309402
\(46\) 4.56800 0.673515
\(47\) 11.3951 1.66215 0.831074 0.556161i \(-0.187726\pi\)
0.831074 + 0.556161i \(0.187726\pi\)
\(48\) −0.779235 −0.112473
\(49\) 4.91210 0.701729
\(50\) 4.24760 0.600701
\(51\) −4.16606 −0.583365
\(52\) 0.0959992 0.0133127
\(53\) −1.21545 −0.166955 −0.0834775 0.996510i \(-0.526603\pi\)
−0.0834775 + 0.996510i \(0.526603\pi\)
\(54\) −4.20225 −0.571854
\(55\) −2.80724 −0.378528
\(56\) 3.45139 0.461212
\(57\) −1.53323 −0.203081
\(58\) 4.12205 0.541252
\(59\) 0.581098 0.0756525 0.0378263 0.999284i \(-0.487957\pi\)
0.0378263 + 0.999284i \(0.487957\pi\)
\(60\) 0.675917 0.0872605
\(61\) −3.01819 −0.386440 −0.193220 0.981155i \(-0.561893\pi\)
−0.193220 + 0.981155i \(0.561893\pi\)
\(62\) −0.192159 −0.0244042
\(63\) 8.25846 1.04047
\(64\) 1.00000 0.125000
\(65\) −0.0832707 −0.0103285
\(66\) 2.52187 0.310421
\(67\) 9.49351 1.15982 0.579908 0.814682i \(-0.303088\pi\)
0.579908 + 0.814682i \(0.303088\pi\)
\(68\) 5.34635 0.648340
\(69\) 3.55955 0.428519
\(70\) −2.99377 −0.357824
\(71\) −14.4713 −1.71743 −0.858715 0.512453i \(-0.828737\pi\)
−0.858715 + 0.512453i \(0.828737\pi\)
\(72\) 2.39279 0.281993
\(73\) 11.7161 1.37127 0.685634 0.727946i \(-0.259525\pi\)
0.685634 + 0.727946i \(0.259525\pi\)
\(74\) −3.45176 −0.401259
\(75\) 3.30988 0.382192
\(76\) 1.96760 0.225700
\(77\) −11.1699 −1.27293
\(78\) 0.0748059 0.00847010
\(79\) 2.62921 0.295810 0.147905 0.989002i \(-0.452747\pi\)
0.147905 + 0.989002i \(0.452747\pi\)
\(80\) −0.867411 −0.0969795
\(81\) 3.90384 0.433760
\(82\) −6.89417 −0.761334
\(83\) 7.45027 0.817773 0.408887 0.912585i \(-0.365917\pi\)
0.408887 + 0.912585i \(0.365917\pi\)
\(84\) 2.68944 0.293442
\(85\) −4.63748 −0.503006
\(86\) 3.27590 0.353250
\(87\) 3.21205 0.344368
\(88\) −3.23634 −0.344995
\(89\) 7.41702 0.786202 0.393101 0.919495i \(-0.371402\pi\)
0.393101 + 0.919495i \(0.371402\pi\)
\(90\) −2.07553 −0.218781
\(91\) −0.331331 −0.0347329
\(92\) −4.56800 −0.476247
\(93\) −0.149737 −0.0155270
\(94\) −11.3951 −1.17532
\(95\) −1.70672 −0.175106
\(96\) 0.779235 0.0795303
\(97\) −2.66158 −0.270243 −0.135121 0.990829i \(-0.543142\pi\)
−0.135121 + 0.990829i \(0.543142\pi\)
\(98\) −4.91210 −0.496197
\(99\) −7.74389 −0.778290
\(100\) −4.24760 −0.424760
\(101\) 1.05027 0.104506 0.0522530 0.998634i \(-0.483360\pi\)
0.0522530 + 0.998634i \(0.483360\pi\)
\(102\) 4.16606 0.412502
\(103\) −12.3758 −1.21943 −0.609714 0.792622i \(-0.708716\pi\)
−0.609714 + 0.792622i \(0.708716\pi\)
\(104\) −0.0959992 −0.00941349
\(105\) −2.33285 −0.227663
\(106\) 1.21545 0.118055
\(107\) 5.13993 0.496896 0.248448 0.968645i \(-0.420080\pi\)
0.248448 + 0.968645i \(0.420080\pi\)
\(108\) 4.20225 0.404362
\(109\) −18.7459 −1.79553 −0.897766 0.440472i \(-0.854811\pi\)
−0.897766 + 0.440472i \(0.854811\pi\)
\(110\) 2.80724 0.267659
\(111\) −2.68973 −0.255298
\(112\) −3.45139 −0.326126
\(113\) −4.47243 −0.420731 −0.210365 0.977623i \(-0.567465\pi\)
−0.210365 + 0.977623i \(0.567465\pi\)
\(114\) 1.53323 0.143600
\(115\) 3.96234 0.369490
\(116\) −4.12205 −0.382723
\(117\) −0.229706 −0.0212363
\(118\) −0.581098 −0.0534944
\(119\) −18.4523 −1.69152
\(120\) −0.675917 −0.0617025
\(121\) −0.526105 −0.0478277
\(122\) 3.01819 0.273254
\(123\) −5.37218 −0.484393
\(124\) 0.192159 0.0172564
\(125\) 8.02147 0.717462
\(126\) −8.25846 −0.735723
\(127\) −0.301641 −0.0267663 −0.0133832 0.999910i \(-0.504260\pi\)
−0.0133832 + 0.999910i \(0.504260\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.55270 0.224752
\(130\) 0.0832707 0.00730333
\(131\) 7.50878 0.656045 0.328023 0.944670i \(-0.393618\pi\)
0.328023 + 0.944670i \(0.393618\pi\)
\(132\) −2.52187 −0.219500
\(133\) −6.79097 −0.588852
\(134\) −9.49351 −0.820114
\(135\) −3.64508 −0.313718
\(136\) −5.34635 −0.458446
\(137\) −19.3698 −1.65487 −0.827437 0.561558i \(-0.810202\pi\)
−0.827437 + 0.561558i \(0.810202\pi\)
\(138\) −3.55955 −0.303009
\(139\) −13.4646 −1.14205 −0.571025 0.820933i \(-0.693454\pi\)
−0.571025 + 0.820933i \(0.693454\pi\)
\(140\) 2.99377 0.253020
\(141\) −8.87947 −0.747786
\(142\) 14.4713 1.21441
\(143\) 0.310686 0.0259809
\(144\) −2.39279 −0.199399
\(145\) 3.57551 0.296930
\(146\) −11.7161 −0.969633
\(147\) −3.82768 −0.315702
\(148\) 3.45176 0.283733
\(149\) −11.0624 −0.906263 −0.453132 0.891444i \(-0.649693\pi\)
−0.453132 + 0.891444i \(0.649693\pi\)
\(150\) −3.30988 −0.270250
\(151\) −18.5776 −1.51182 −0.755911 0.654674i \(-0.772806\pi\)
−0.755911 + 0.654674i \(0.772806\pi\)
\(152\) −1.96760 −0.159594
\(153\) −12.7927 −1.03423
\(154\) 11.1699 0.900094
\(155\) −0.166681 −0.0133881
\(156\) −0.0748059 −0.00598927
\(157\) 6.59557 0.526384 0.263192 0.964744i \(-0.415225\pi\)
0.263192 + 0.964744i \(0.415225\pi\)
\(158\) −2.62921 −0.209169
\(159\) 0.947122 0.0751117
\(160\) 0.867411 0.0685748
\(161\) 15.7660 1.24253
\(162\) −3.90384 −0.306715
\(163\) 21.3886 1.67529 0.837643 0.546218i \(-0.183933\pi\)
0.837643 + 0.546218i \(0.183933\pi\)
\(164\) 6.89417 0.538344
\(165\) 2.18750 0.170296
\(166\) −7.45027 −0.578253
\(167\) −2.21303 −0.171249 −0.0856246 0.996327i \(-0.527289\pi\)
−0.0856246 + 0.996327i \(0.527289\pi\)
\(168\) −2.68944 −0.207495
\(169\) −12.9908 −0.999291
\(170\) 4.63748 0.355679
\(171\) −4.70807 −0.360035
\(172\) −3.27590 −0.249785
\(173\) −18.0587 −1.37298 −0.686489 0.727140i \(-0.740849\pi\)
−0.686489 + 0.727140i \(0.740849\pi\)
\(174\) −3.21205 −0.243505
\(175\) 14.6601 1.10820
\(176\) 3.23634 0.243948
\(177\) −0.452812 −0.0340354
\(178\) −7.41702 −0.555929
\(179\) −9.99822 −0.747302 −0.373651 0.927569i \(-0.621894\pi\)
−0.373651 + 0.927569i \(0.621894\pi\)
\(180\) 2.07553 0.154701
\(181\) 10.7591 0.799719 0.399859 0.916577i \(-0.369059\pi\)
0.399859 + 0.916577i \(0.369059\pi\)
\(182\) 0.331331 0.0245599
\(183\) 2.35188 0.173856
\(184\) 4.56800 0.336758
\(185\) −2.99410 −0.220130
\(186\) 0.149737 0.0109793
\(187\) 17.3026 1.26529
\(188\) 11.3951 0.831074
\(189\) −14.5036 −1.05498
\(190\) 1.70672 0.123819
\(191\) −18.8593 −1.36461 −0.682306 0.731067i \(-0.739023\pi\)
−0.682306 + 0.731067i \(0.739023\pi\)
\(192\) −0.779235 −0.0562364
\(193\) −13.3166 −0.958547 −0.479273 0.877666i \(-0.659100\pi\)
−0.479273 + 0.877666i \(0.659100\pi\)
\(194\) 2.66158 0.191090
\(195\) 0.0648874 0.00464669
\(196\) 4.91210 0.350864
\(197\) 13.6777 0.974493 0.487247 0.873264i \(-0.338001\pi\)
0.487247 + 0.873264i \(0.338001\pi\)
\(198\) 7.74389 0.550334
\(199\) 3.84768 0.272755 0.136377 0.990657i \(-0.456454\pi\)
0.136377 + 0.990657i \(0.456454\pi\)
\(200\) 4.24760 0.300351
\(201\) −7.39767 −0.521792
\(202\) −1.05027 −0.0738969
\(203\) 14.2268 0.998527
\(204\) −4.16606 −0.291683
\(205\) −5.98008 −0.417667
\(206\) 12.3758 0.862265
\(207\) 10.9303 0.759708
\(208\) 0.0959992 0.00665635
\(209\) 6.36784 0.440473
\(210\) 2.33285 0.160982
\(211\) 0.276423 0.0190297 0.00951486 0.999955i \(-0.496971\pi\)
0.00951486 + 0.999955i \(0.496971\pi\)
\(212\) −1.21545 −0.0834775
\(213\) 11.2766 0.772657
\(214\) −5.13993 −0.351358
\(215\) 2.84155 0.193792
\(216\) −4.20225 −0.285927
\(217\) −0.663217 −0.0450221
\(218\) 18.7459 1.26963
\(219\) −9.12961 −0.616922
\(220\) −2.80724 −0.189264
\(221\) 0.513245 0.0345246
\(222\) 2.68973 0.180523
\(223\) 4.91884 0.329390 0.164695 0.986345i \(-0.447336\pi\)
0.164695 + 0.986345i \(0.447336\pi\)
\(224\) 3.45139 0.230606
\(225\) 10.1636 0.677575
\(226\) 4.47243 0.297502
\(227\) 12.1843 0.808698 0.404349 0.914605i \(-0.367498\pi\)
0.404349 + 0.914605i \(0.367498\pi\)
\(228\) −1.53323 −0.101540
\(229\) 28.5001 1.88334 0.941669 0.336541i \(-0.109257\pi\)
0.941669 + 0.336541i \(0.109257\pi\)
\(230\) −3.96234 −0.261269
\(231\) 8.70395 0.572678
\(232\) 4.12205 0.270626
\(233\) −16.2015 −1.06140 −0.530698 0.847561i \(-0.678070\pi\)
−0.530698 + 0.847561i \(0.678070\pi\)
\(234\) 0.229706 0.0150164
\(235\) −9.88425 −0.644777
\(236\) 0.581098 0.0378263
\(237\) −2.04878 −0.133082
\(238\) 18.4523 1.19609
\(239\) −12.3676 −0.799997 −0.399998 0.916516i \(-0.630989\pi\)
−0.399998 + 0.916516i \(0.630989\pi\)
\(240\) 0.675917 0.0436302
\(241\) −14.1994 −0.914663 −0.457332 0.889296i \(-0.651195\pi\)
−0.457332 + 0.889296i \(0.651195\pi\)
\(242\) 0.526105 0.0338193
\(243\) −15.6488 −1.00387
\(244\) −3.01819 −0.193220
\(245\) −4.26081 −0.272213
\(246\) 5.37218 0.342518
\(247\) 0.188888 0.0120187
\(248\) −0.192159 −0.0122021
\(249\) −5.80551 −0.367909
\(250\) −8.02147 −0.507322
\(251\) −25.9160 −1.63580 −0.817902 0.575358i \(-0.804863\pi\)
−0.817902 + 0.575358i \(0.804863\pi\)
\(252\) 8.25846 0.520234
\(253\) −14.7836 −0.929438
\(254\) 0.301641 0.0189266
\(255\) 3.61369 0.226298
\(256\) 1.00000 0.0625000
\(257\) 5.04209 0.314517 0.157259 0.987557i \(-0.449734\pi\)
0.157259 + 0.987557i \(0.449734\pi\)
\(258\) −2.55270 −0.158924
\(259\) −11.9134 −0.740262
\(260\) −0.0832707 −0.00516423
\(261\) 9.86322 0.610518
\(262\) −7.50878 −0.463894
\(263\) 22.4472 1.38415 0.692076 0.721825i \(-0.256696\pi\)
0.692076 + 0.721825i \(0.256696\pi\)
\(264\) 2.52187 0.155210
\(265\) 1.05430 0.0647649
\(266\) 6.79097 0.416381
\(267\) −5.77960 −0.353706
\(268\) 9.49351 0.579908
\(269\) −28.9496 −1.76509 −0.882543 0.470231i \(-0.844171\pi\)
−0.882543 + 0.470231i \(0.844171\pi\)
\(270\) 3.64508 0.221832
\(271\) 13.2887 0.807233 0.403617 0.914928i \(-0.367753\pi\)
0.403617 + 0.914928i \(0.367753\pi\)
\(272\) 5.34635 0.324170
\(273\) 0.258184 0.0156260
\(274\) 19.3698 1.17017
\(275\) −13.7467 −0.828956
\(276\) 3.55955 0.214260
\(277\) −22.1313 −1.32974 −0.664870 0.746959i \(-0.731513\pi\)
−0.664870 + 0.746959i \(0.731513\pi\)
\(278\) 13.4646 0.807552
\(279\) −0.459797 −0.0275273
\(280\) −2.99377 −0.178912
\(281\) −1.85417 −0.110611 −0.0553054 0.998469i \(-0.517613\pi\)
−0.0553054 + 0.998469i \(0.517613\pi\)
\(282\) 8.87947 0.528765
\(283\) −7.27477 −0.432440 −0.216220 0.976345i \(-0.569373\pi\)
−0.216220 + 0.976345i \(0.569373\pi\)
\(284\) −14.4713 −0.858715
\(285\) 1.32994 0.0787787
\(286\) −0.310686 −0.0183712
\(287\) −23.7945 −1.40454
\(288\) 2.39279 0.140997
\(289\) 11.5835 0.681381
\(290\) −3.57551 −0.209961
\(291\) 2.07400 0.121580
\(292\) 11.7161 0.685634
\(293\) −10.0667 −0.588104 −0.294052 0.955789i \(-0.595004\pi\)
−0.294052 + 0.955789i \(0.595004\pi\)
\(294\) 3.82768 0.223235
\(295\) −0.504051 −0.0293470
\(296\) −3.45176 −0.200630
\(297\) 13.5999 0.789147
\(298\) 11.0624 0.640825
\(299\) −0.438525 −0.0253605
\(300\) 3.30988 0.191096
\(301\) 11.3064 0.651691
\(302\) 18.5776 1.06902
\(303\) −0.818408 −0.0470163
\(304\) 1.96760 0.112850
\(305\) 2.61801 0.149907
\(306\) 12.7927 0.731311
\(307\) −5.07778 −0.289804 −0.144902 0.989446i \(-0.546287\pi\)
−0.144902 + 0.989446i \(0.546287\pi\)
\(308\) −11.1699 −0.636463
\(309\) 9.64368 0.548610
\(310\) 0.166681 0.00946684
\(311\) −26.8661 −1.52344 −0.761718 0.647909i \(-0.775644\pi\)
−0.761718 + 0.647909i \(0.775644\pi\)
\(312\) 0.0748059 0.00423505
\(313\) 3.90340 0.220633 0.110317 0.993897i \(-0.464814\pi\)
0.110317 + 0.993897i \(0.464814\pi\)
\(314\) −6.59557 −0.372209
\(315\) −7.16348 −0.403616
\(316\) 2.62921 0.147905
\(317\) −11.3372 −0.636762 −0.318381 0.947963i \(-0.603139\pi\)
−0.318381 + 0.947963i \(0.603139\pi\)
\(318\) −0.947122 −0.0531120
\(319\) −13.3404 −0.746917
\(320\) −0.867411 −0.0484897
\(321\) −4.00521 −0.223549
\(322\) −15.7660 −0.878603
\(323\) 10.5195 0.585321
\(324\) 3.90384 0.216880
\(325\) −0.407766 −0.0226188
\(326\) −21.3886 −1.18461
\(327\) 14.6075 0.807795
\(328\) −6.89417 −0.380667
\(329\) −39.3290 −2.16828
\(330\) −2.18750 −0.120418
\(331\) 22.9868 1.26347 0.631733 0.775186i \(-0.282344\pi\)
0.631733 + 0.775186i \(0.282344\pi\)
\(332\) 7.45027 0.408887
\(333\) −8.25935 −0.452610
\(334\) 2.21303 0.121091
\(335\) −8.23477 −0.449914
\(336\) 2.68944 0.146721
\(337\) −23.7930 −1.29609 −0.648045 0.761602i \(-0.724413\pi\)
−0.648045 + 0.761602i \(0.724413\pi\)
\(338\) 12.9908 0.706606
\(339\) 3.48507 0.189283
\(340\) −4.63748 −0.251503
\(341\) 0.621892 0.0336774
\(342\) 4.70807 0.254583
\(343\) 7.20616 0.389096
\(344\) 3.27590 0.176625
\(345\) −3.08759 −0.166230
\(346\) 18.0587 0.970843
\(347\) 8.54376 0.458653 0.229327 0.973350i \(-0.426348\pi\)
0.229327 + 0.973350i \(0.426348\pi\)
\(348\) 3.21205 0.172184
\(349\) −4.21459 −0.225602 −0.112801 0.993618i \(-0.535982\pi\)
−0.112801 + 0.993618i \(0.535982\pi\)
\(350\) −14.6601 −0.783617
\(351\) 0.403413 0.0215326
\(352\) −3.23634 −0.172497
\(353\) −33.4718 −1.78152 −0.890761 0.454472i \(-0.849828\pi\)
−0.890761 + 0.454472i \(0.849828\pi\)
\(354\) 0.452812 0.0240667
\(355\) 12.5526 0.666222
\(356\) 7.41702 0.393101
\(357\) 14.3787 0.761002
\(358\) 9.99822 0.528422
\(359\) −8.74319 −0.461448 −0.230724 0.973019i \(-0.574109\pi\)
−0.230724 + 0.973019i \(0.574109\pi\)
\(360\) −2.07553 −0.109390
\(361\) −15.1285 −0.796238
\(362\) −10.7591 −0.565486
\(363\) 0.409959 0.0215173
\(364\) −0.331331 −0.0173664
\(365\) −10.1627 −0.531939
\(366\) −2.35188 −0.122935
\(367\) 26.4685 1.38164 0.690821 0.723025i \(-0.257249\pi\)
0.690821 + 0.723025i \(0.257249\pi\)
\(368\) −4.56800 −0.238124
\(369\) −16.4963 −0.858765
\(370\) 2.99410 0.155656
\(371\) 4.19500 0.217793
\(372\) −0.149737 −0.00776351
\(373\) −2.69198 −0.139386 −0.0696928 0.997568i \(-0.522202\pi\)
−0.0696928 + 0.997568i \(0.522202\pi\)
\(374\) −17.3026 −0.894697
\(375\) −6.25061 −0.322780
\(376\) −11.3951 −0.587658
\(377\) −0.395714 −0.0203803
\(378\) 14.5036 0.745985
\(379\) 1.93851 0.0995743 0.0497872 0.998760i \(-0.484146\pi\)
0.0497872 + 0.998760i \(0.484146\pi\)
\(380\) −1.70672 −0.0875530
\(381\) 0.235049 0.0120419
\(382\) 18.8593 0.964926
\(383\) −12.7553 −0.651767 −0.325883 0.945410i \(-0.605662\pi\)
−0.325883 + 0.945410i \(0.605662\pi\)
\(384\) 0.779235 0.0397652
\(385\) 9.68887 0.493790
\(386\) 13.3166 0.677795
\(387\) 7.83856 0.398456
\(388\) −2.66158 −0.135121
\(389\) 24.8983 1.26239 0.631196 0.775624i \(-0.282564\pi\)
0.631196 + 0.775624i \(0.282564\pi\)
\(390\) −0.0648874 −0.00328570
\(391\) −24.4222 −1.23508
\(392\) −4.91210 −0.248099
\(393\) −5.85111 −0.295149
\(394\) −13.6777 −0.689071
\(395\) −2.28061 −0.114750
\(396\) −7.74389 −0.389145
\(397\) 4.20895 0.211241 0.105620 0.994407i \(-0.466317\pi\)
0.105620 + 0.994407i \(0.466317\pi\)
\(398\) −3.84768 −0.192867
\(399\) 5.29176 0.264920
\(400\) −4.24760 −0.212380
\(401\) −2.63918 −0.131794 −0.0658972 0.997826i \(-0.520991\pi\)
−0.0658972 + 0.997826i \(0.520991\pi\)
\(402\) 7.39767 0.368962
\(403\) 0.0184471 0.000918917 0
\(404\) 1.05027 0.0522530
\(405\) −3.38623 −0.168263
\(406\) −14.2268 −0.706065
\(407\) 11.1711 0.553730
\(408\) 4.16606 0.206251
\(409\) 5.20799 0.257518 0.128759 0.991676i \(-0.458901\pi\)
0.128759 + 0.991676i \(0.458901\pi\)
\(410\) 5.98008 0.295335
\(411\) 15.0936 0.744514
\(412\) −12.3758 −0.609714
\(413\) −2.00560 −0.0986890
\(414\) −10.9303 −0.537194
\(415\) −6.46244 −0.317229
\(416\) −0.0959992 −0.00470675
\(417\) 10.4921 0.513799
\(418\) −6.36784 −0.311461
\(419\) 0.0975118 0.00476377 0.00238188 0.999997i \(-0.499242\pi\)
0.00238188 + 0.999997i \(0.499242\pi\)
\(420\) −2.33285 −0.113832
\(421\) −17.1483 −0.835756 −0.417878 0.908503i \(-0.637226\pi\)
−0.417878 + 0.908503i \(0.637226\pi\)
\(422\) −0.276423 −0.0134560
\(423\) −27.2662 −1.32573
\(424\) 1.21545 0.0590275
\(425\) −22.7092 −1.10156
\(426\) −11.2766 −0.546351
\(427\) 10.4170 0.504112
\(428\) 5.13993 0.248448
\(429\) −0.242097 −0.0116886
\(430\) −2.84155 −0.137032
\(431\) −34.9830 −1.68507 −0.842535 0.538642i \(-0.818938\pi\)
−0.842535 + 0.538642i \(0.818938\pi\)
\(432\) 4.20225 0.202181
\(433\) 30.9613 1.48790 0.743952 0.668233i \(-0.232949\pi\)
0.743952 + 0.668233i \(0.232949\pi\)
\(434\) 0.663217 0.0318354
\(435\) −2.78616 −0.133586
\(436\) −18.7459 −0.897766
\(437\) −8.98803 −0.429956
\(438\) 9.12961 0.436230
\(439\) −3.18963 −0.152233 −0.0761164 0.997099i \(-0.524252\pi\)
−0.0761164 + 0.997099i \(0.524252\pi\)
\(440\) 2.80724 0.133830
\(441\) −11.7536 −0.559697
\(442\) −0.513245 −0.0244126
\(443\) −1.23026 −0.0584512 −0.0292256 0.999573i \(-0.509304\pi\)
−0.0292256 + 0.999573i \(0.509304\pi\)
\(444\) −2.68973 −0.127649
\(445\) −6.43360 −0.304982
\(446\) −4.91884 −0.232914
\(447\) 8.62017 0.407720
\(448\) −3.45139 −0.163063
\(449\) 12.7510 0.601759 0.300879 0.953662i \(-0.402720\pi\)
0.300879 + 0.953662i \(0.402720\pi\)
\(450\) −10.1636 −0.479118
\(451\) 22.3119 1.05063
\(452\) −4.47243 −0.210365
\(453\) 14.4763 0.680156
\(454\) −12.1843 −0.571836
\(455\) 0.287400 0.0134735
\(456\) 1.53323 0.0717999
\(457\) −40.6338 −1.90077 −0.950384 0.311080i \(-0.899309\pi\)
−0.950384 + 0.311080i \(0.899309\pi\)
\(458\) −28.5001 −1.33172
\(459\) 22.4667 1.04866
\(460\) 3.96234 0.184745
\(461\) 11.5464 0.537768 0.268884 0.963173i \(-0.413345\pi\)
0.268884 + 0.963173i \(0.413345\pi\)
\(462\) −8.70395 −0.404945
\(463\) −9.95124 −0.462473 −0.231237 0.972898i \(-0.574277\pi\)
−0.231237 + 0.972898i \(0.574277\pi\)
\(464\) −4.12205 −0.191361
\(465\) 0.129884 0.00602321
\(466\) 16.2015 0.750520
\(467\) −3.65923 −0.169329 −0.0846645 0.996410i \(-0.526982\pi\)
−0.0846645 + 0.996410i \(0.526982\pi\)
\(468\) −0.229706 −0.0106182
\(469\) −32.7658 −1.51298
\(470\) 9.88425 0.455926
\(471\) −5.13949 −0.236815
\(472\) −0.581098 −0.0267472
\(473\) −10.6019 −0.487477
\(474\) 2.04878 0.0941034
\(475\) −8.35760 −0.383473
\(476\) −18.4523 −0.845762
\(477\) 2.90832 0.133163
\(478\) 12.3676 0.565683
\(479\) −2.48553 −0.113567 −0.0567835 0.998387i \(-0.518084\pi\)
−0.0567835 + 0.998387i \(0.518084\pi\)
\(480\) −0.675917 −0.0308512
\(481\) 0.331366 0.0151090
\(482\) 14.1994 0.646765
\(483\) −12.2854 −0.559005
\(484\) −0.526105 −0.0239138
\(485\) 2.30869 0.104832
\(486\) 15.6488 0.709842
\(487\) 4.61836 0.209278 0.104639 0.994510i \(-0.466631\pi\)
0.104639 + 0.994510i \(0.466631\pi\)
\(488\) 3.01819 0.136627
\(489\) −16.6668 −0.753697
\(490\) 4.26081 0.192484
\(491\) 4.91052 0.221609 0.110804 0.993842i \(-0.464657\pi\)
0.110804 + 0.993842i \(0.464657\pi\)
\(492\) −5.37218 −0.242197
\(493\) −22.0379 −0.992539
\(494\) −0.188888 −0.00849849
\(495\) 6.71713 0.301913
\(496\) 0.192159 0.00862820
\(497\) 49.9462 2.24039
\(498\) 5.80551 0.260151
\(499\) −4.25660 −0.190552 −0.0952758 0.995451i \(-0.530373\pi\)
−0.0952758 + 0.995451i \(0.530373\pi\)
\(500\) 8.02147 0.358731
\(501\) 1.72447 0.0770435
\(502\) 25.9160 1.15669
\(503\) −11.9884 −0.534537 −0.267269 0.963622i \(-0.586121\pi\)
−0.267269 + 0.963622i \(0.586121\pi\)
\(504\) −8.25846 −0.367861
\(505\) −0.911017 −0.0405397
\(506\) 14.7836 0.657212
\(507\) 10.1229 0.449572
\(508\) −0.301641 −0.0133832
\(509\) −19.9944 −0.886235 −0.443117 0.896464i \(-0.646128\pi\)
−0.443117 + 0.896464i \(0.646128\pi\)
\(510\) −3.61369 −0.160017
\(511\) −40.4369 −1.78882
\(512\) −1.00000 −0.0441942
\(513\) 8.26837 0.365058
\(514\) −5.04209 −0.222397
\(515\) 10.7349 0.473038
\(516\) 2.55270 0.112376
\(517\) 36.8785 1.62191
\(518\) 11.9134 0.523444
\(519\) 14.0720 0.617691
\(520\) 0.0832707 0.00365166
\(521\) −15.2285 −0.667173 −0.333587 0.942719i \(-0.608259\pi\)
−0.333587 + 0.942719i \(0.608259\pi\)
\(522\) −9.86322 −0.431701
\(523\) 31.9781 1.39831 0.699153 0.714972i \(-0.253561\pi\)
0.699153 + 0.714972i \(0.253561\pi\)
\(524\) 7.50878 0.328023
\(525\) −11.4237 −0.498570
\(526\) −22.4472 −0.978743
\(527\) 1.02735 0.0447521
\(528\) −2.52187 −0.109750
\(529\) −2.13334 −0.0927537
\(530\) −1.05430 −0.0457957
\(531\) −1.39045 −0.0603403
\(532\) −6.79097 −0.294426
\(533\) 0.661835 0.0286673
\(534\) 5.77960 0.250108
\(535\) −4.45843 −0.192755
\(536\) −9.49351 −0.410057
\(537\) 7.79096 0.336205
\(538\) 28.9496 1.24810
\(539\) 15.8972 0.684742
\(540\) −3.64508 −0.156859
\(541\) 23.3171 1.00248 0.501240 0.865308i \(-0.332877\pi\)
0.501240 + 0.865308i \(0.332877\pi\)
\(542\) −13.2887 −0.570800
\(543\) −8.38388 −0.359787
\(544\) −5.34635 −0.229223
\(545\) 16.2604 0.696519
\(546\) −0.258184 −0.0110493
\(547\) 21.9020 0.936462 0.468231 0.883606i \(-0.344891\pi\)
0.468231 + 0.883606i \(0.344891\pi\)
\(548\) −19.3698 −0.827437
\(549\) 7.22191 0.308224
\(550\) 13.7467 0.586160
\(551\) −8.11057 −0.345522
\(552\) −3.55955 −0.151504
\(553\) −9.07445 −0.385885
\(554\) 22.1313 0.940268
\(555\) 2.33310 0.0990347
\(556\) −13.4646 −0.571025
\(557\) 4.88359 0.206924 0.103462 0.994633i \(-0.467008\pi\)
0.103462 + 0.994633i \(0.467008\pi\)
\(558\) 0.459797 0.0194648
\(559\) −0.314484 −0.0133013
\(560\) 2.99377 0.126510
\(561\) −13.4828 −0.569244
\(562\) 1.85417 0.0782136
\(563\) 20.2065 0.851603 0.425802 0.904817i \(-0.359992\pi\)
0.425802 + 0.904817i \(0.359992\pi\)
\(564\) −8.87947 −0.373893
\(565\) 3.87943 0.163209
\(566\) 7.27477 0.305781
\(567\) −13.4737 −0.565841
\(568\) 14.4713 0.607203
\(569\) 6.24900 0.261972 0.130986 0.991384i \(-0.458186\pi\)
0.130986 + 0.991384i \(0.458186\pi\)
\(570\) −1.32994 −0.0557049
\(571\) −23.9895 −1.00393 −0.501964 0.864888i \(-0.667389\pi\)
−0.501964 + 0.864888i \(0.667389\pi\)
\(572\) 0.310686 0.0129904
\(573\) 14.6958 0.613927
\(574\) 23.7945 0.993163
\(575\) 19.4030 0.809163
\(576\) −2.39279 −0.0996997
\(577\) 19.8350 0.825742 0.412871 0.910790i \(-0.364526\pi\)
0.412871 + 0.910790i \(0.364526\pi\)
\(578\) −11.5835 −0.481809
\(579\) 10.3767 0.431242
\(580\) 3.57551 0.148465
\(581\) −25.7138 −1.06679
\(582\) −2.07400 −0.0859700
\(583\) −3.93361 −0.162914
\(584\) −11.7161 −0.484816
\(585\) 0.199250 0.00823796
\(586\) 10.0667 0.415853
\(587\) 3.89913 0.160934 0.0804671 0.996757i \(-0.474359\pi\)
0.0804671 + 0.996757i \(0.474359\pi\)
\(588\) −3.82768 −0.157851
\(589\) 0.378093 0.0155791
\(590\) 0.504051 0.0207514
\(591\) −10.6581 −0.438416
\(592\) 3.45176 0.141867
\(593\) −13.3065 −0.546431 −0.273215 0.961953i \(-0.588087\pi\)
−0.273215 + 0.961953i \(0.588087\pi\)
\(594\) −13.5999 −0.558011
\(595\) 16.0058 0.656172
\(596\) −11.0624 −0.453132
\(597\) −2.99824 −0.122710
\(598\) 0.438525 0.0179326
\(599\) −1.00310 −0.0409855 −0.0204927 0.999790i \(-0.506523\pi\)
−0.0204927 + 0.999790i \(0.506523\pi\)
\(600\) −3.30988 −0.135125
\(601\) −4.14151 −0.168936 −0.0844679 0.996426i \(-0.526919\pi\)
−0.0844679 + 0.996426i \(0.526919\pi\)
\(602\) −11.3064 −0.460815
\(603\) −22.7160 −0.925067
\(604\) −18.5776 −0.755911
\(605\) 0.456349 0.0185532
\(606\) 0.818408 0.0332456
\(607\) 39.2901 1.59474 0.797368 0.603493i \(-0.206225\pi\)
0.797368 + 0.603493i \(0.206225\pi\)
\(608\) −1.96760 −0.0797969
\(609\) −11.0860 −0.449229
\(610\) −2.61801 −0.106000
\(611\) 1.09392 0.0442553
\(612\) −12.7927 −0.517115
\(613\) −48.6851 −1.96637 −0.983187 0.182601i \(-0.941548\pi\)
−0.983187 + 0.182601i \(0.941548\pi\)
\(614\) 5.07778 0.204923
\(615\) 4.65989 0.187905
\(616\) 11.1699 0.450047
\(617\) 24.2435 0.976008 0.488004 0.872841i \(-0.337725\pi\)
0.488004 + 0.872841i \(0.337725\pi\)
\(618\) −9.64368 −0.387926
\(619\) 28.7387 1.15511 0.577553 0.816353i \(-0.304008\pi\)
0.577553 + 0.816353i \(0.304008\pi\)
\(620\) −0.166681 −0.00669407
\(621\) −19.1959 −0.770305
\(622\) 26.8661 1.07723
\(623\) −25.5990 −1.02560
\(624\) −0.0748059 −0.00299463
\(625\) 14.2801 0.571204
\(626\) −3.90340 −0.156011
\(627\) −4.96204 −0.198165
\(628\) 6.59557 0.263192
\(629\) 18.4543 0.735822
\(630\) 7.16348 0.285400
\(631\) 17.5171 0.697346 0.348673 0.937244i \(-0.386632\pi\)
0.348673 + 0.937244i \(0.386632\pi\)
\(632\) −2.62921 −0.104585
\(633\) −0.215398 −0.00856131
\(634\) 11.3372 0.450259
\(635\) 0.261647 0.0103831
\(636\) 0.947122 0.0375558
\(637\) 0.471558 0.0186838
\(638\) 13.3404 0.528150
\(639\) 34.6269 1.36982
\(640\) 0.867411 0.0342874
\(641\) −8.63427 −0.341033 −0.170517 0.985355i \(-0.554544\pi\)
−0.170517 + 0.985355i \(0.554544\pi\)
\(642\) 4.00521 0.158073
\(643\) −6.19646 −0.244365 −0.122182 0.992508i \(-0.538989\pi\)
−0.122182 + 0.992508i \(0.538989\pi\)
\(644\) 15.7660 0.621266
\(645\) −2.21424 −0.0871855
\(646\) −10.5195 −0.413884
\(647\) −35.5876 −1.39909 −0.699547 0.714587i \(-0.746615\pi\)
−0.699547 + 0.714587i \(0.746615\pi\)
\(648\) −3.90384 −0.153357
\(649\) 1.88063 0.0738212
\(650\) 0.407766 0.0159939
\(651\) 0.516801 0.0202550
\(652\) 21.3886 0.837643
\(653\) −17.7723 −0.695483 −0.347742 0.937590i \(-0.613051\pi\)
−0.347742 + 0.937590i \(0.613051\pi\)
\(654\) −14.6075 −0.571197
\(655\) −6.51320 −0.254492
\(656\) 6.89417 0.269172
\(657\) −28.0343 −1.09372
\(658\) 39.3290 1.53320
\(659\) −14.5964 −0.568595 −0.284297 0.958736i \(-0.591760\pi\)
−0.284297 + 0.958736i \(0.591760\pi\)
\(660\) 2.18750 0.0851482
\(661\) 7.25358 0.282132 0.141066 0.990000i \(-0.454947\pi\)
0.141066 + 0.990000i \(0.454947\pi\)
\(662\) −22.9868 −0.893406
\(663\) −0.399939 −0.0155323
\(664\) −7.45027 −0.289127
\(665\) 5.89056 0.228426
\(666\) 8.25935 0.320043
\(667\) 18.8296 0.729083
\(668\) −2.21303 −0.0856246
\(669\) −3.83293 −0.148190
\(670\) 8.23477 0.318137
\(671\) −9.76790 −0.377086
\(672\) −2.68944 −0.103748
\(673\) −34.9431 −1.34696 −0.673480 0.739206i \(-0.735201\pi\)
−0.673480 + 0.739206i \(0.735201\pi\)
\(674\) 23.7930 0.916473
\(675\) −17.8495 −0.687027
\(676\) −12.9908 −0.499646
\(677\) −30.6635 −1.17849 −0.589246 0.807953i \(-0.700575\pi\)
−0.589246 + 0.807953i \(0.700575\pi\)
\(678\) −3.48507 −0.133843
\(679\) 9.18616 0.352533
\(680\) 4.63748 0.177839
\(681\) −9.49441 −0.363826
\(682\) −0.621892 −0.0238135
\(683\) −2.35310 −0.0900390 −0.0450195 0.998986i \(-0.514335\pi\)
−0.0450195 + 0.998986i \(0.514335\pi\)
\(684\) −4.70807 −0.180018
\(685\) 16.8016 0.641956
\(686\) −7.20616 −0.275132
\(687\) −22.2082 −0.847297
\(688\) −3.27590 −0.124893
\(689\) −0.116682 −0.00444524
\(690\) 3.08759 0.117543
\(691\) −50.4834 −1.92048 −0.960240 0.279176i \(-0.909939\pi\)
−0.960240 + 0.279176i \(0.909939\pi\)
\(692\) −18.0587 −0.686489
\(693\) 26.7272 1.01528
\(694\) −8.54376 −0.324317
\(695\) 11.6793 0.443022
\(696\) −3.21205 −0.121752
\(697\) 36.8587 1.39612
\(698\) 4.21459 0.159525
\(699\) 12.6248 0.477513
\(700\) 14.6601 0.554101
\(701\) −44.6603 −1.68680 −0.843399 0.537288i \(-0.819449\pi\)
−0.843399 + 0.537288i \(0.819449\pi\)
\(702\) −0.403413 −0.0152258
\(703\) 6.79170 0.256154
\(704\) 3.23634 0.121974
\(705\) 7.70215 0.290080
\(706\) 33.4718 1.25973
\(707\) −3.62490 −0.136328
\(708\) −0.452812 −0.0170177
\(709\) 13.0371 0.489617 0.244809 0.969571i \(-0.421275\pi\)
0.244809 + 0.969571i \(0.421275\pi\)
\(710\) −12.5526 −0.471090
\(711\) −6.29117 −0.235937
\(712\) −7.41702 −0.277964
\(713\) −0.877784 −0.0328733
\(714\) −14.3787 −0.538110
\(715\) −0.269492 −0.0100784
\(716\) −9.99822 −0.373651
\(717\) 9.63730 0.359912
\(718\) 8.74319 0.326293
\(719\) 33.9522 1.26620 0.633102 0.774069i \(-0.281781\pi\)
0.633102 + 0.774069i \(0.281781\pi\)
\(720\) 2.07553 0.0773506
\(721\) 42.7139 1.59075
\(722\) 15.1285 0.563026
\(723\) 11.0647 0.411499
\(724\) 10.7591 0.399859
\(725\) 17.5088 0.650261
\(726\) −0.409959 −0.0152150
\(727\) 7.56181 0.280452 0.140226 0.990120i \(-0.455217\pi\)
0.140226 + 0.990120i \(0.455217\pi\)
\(728\) 0.331331 0.0122799
\(729\) 0.482546 0.0178721
\(730\) 10.1627 0.376138
\(731\) −17.5141 −0.647783
\(732\) 2.35188 0.0869281
\(733\) 38.3444 1.41628 0.708141 0.706071i \(-0.249534\pi\)
0.708141 + 0.706071i \(0.249534\pi\)
\(734\) −26.4685 −0.976969
\(735\) 3.32017 0.122466
\(736\) 4.56800 0.168379
\(737\) 30.7242 1.13174
\(738\) 16.4963 0.607238
\(739\) 46.2671 1.70196 0.850981 0.525196i \(-0.176008\pi\)
0.850981 + 0.525196i \(0.176008\pi\)
\(740\) −2.99410 −0.110065
\(741\) −0.147188 −0.00540710
\(742\) −4.19500 −0.154003
\(743\) 18.5448 0.680342 0.340171 0.940364i \(-0.389515\pi\)
0.340171 + 0.940364i \(0.389515\pi\)
\(744\) 0.149737 0.00548963
\(745\) 9.59560 0.351556
\(746\) 2.69198 0.0985606
\(747\) −17.8270 −0.652254
\(748\) 17.3026 0.632646
\(749\) −17.7399 −0.648202
\(750\) 6.25061 0.228240
\(751\) 10.4620 0.381762 0.190881 0.981613i \(-0.438866\pi\)
0.190881 + 0.981613i \(0.438866\pi\)
\(752\) 11.3951 0.415537
\(753\) 20.1946 0.735934
\(754\) 0.395714 0.0144110
\(755\) 16.1144 0.586463
\(756\) −14.5036 −0.527491
\(757\) 46.4642 1.68877 0.844385 0.535736i \(-0.179966\pi\)
0.844385 + 0.535736i \(0.179966\pi\)
\(758\) −1.93851 −0.0704097
\(759\) 11.5199 0.418146
\(760\) 1.70672 0.0619093
\(761\) 29.9129 1.08434 0.542171 0.840268i \(-0.317602\pi\)
0.542171 + 0.840268i \(0.317602\pi\)
\(762\) −0.235049 −0.00851493
\(763\) 64.6995 2.34228
\(764\) −18.8593 −0.682306
\(765\) 11.0965 0.401196
\(766\) 12.7553 0.460869
\(767\) 0.0557849 0.00201428
\(768\) −0.779235 −0.0281182
\(769\) 15.2809 0.551043 0.275522 0.961295i \(-0.411149\pi\)
0.275522 + 0.961295i \(0.411149\pi\)
\(770\) −9.68887 −0.349163
\(771\) −3.92898 −0.141499
\(772\) −13.3166 −0.479273
\(773\) −46.5211 −1.67325 −0.836624 0.547778i \(-0.815474\pi\)
−0.836624 + 0.547778i \(0.815474\pi\)
\(774\) −7.83856 −0.281751
\(775\) −0.816215 −0.0293193
\(776\) 2.66158 0.0955452
\(777\) 9.28332 0.333037
\(778\) −24.8983 −0.892646
\(779\) 13.5650 0.486017
\(780\) 0.0648874 0.00232334
\(781\) −46.8341 −1.67586
\(782\) 24.4222 0.873334
\(783\) −17.3219 −0.619034
\(784\) 4.91210 0.175432
\(785\) −5.72106 −0.204194
\(786\) 5.85111 0.208702
\(787\) 29.4127 1.04845 0.524225 0.851580i \(-0.324355\pi\)
0.524225 + 0.851580i \(0.324355\pi\)
\(788\) 13.6777 0.487247
\(789\) −17.4916 −0.622718
\(790\) 2.28061 0.0811404
\(791\) 15.4361 0.548845
\(792\) 7.74389 0.275167
\(793\) −0.289744 −0.0102891
\(794\) −4.20895 −0.149370
\(795\) −0.821544 −0.0291372
\(796\) 3.84768 0.136377
\(797\) −49.4209 −1.75058 −0.875289 0.483600i \(-0.839329\pi\)
−0.875289 + 0.483600i \(0.839329\pi\)
\(798\) −5.29176 −0.187326
\(799\) 60.9223 2.15528
\(800\) 4.24760 0.150175
\(801\) −17.7474 −0.627073
\(802\) 2.63918 0.0931927
\(803\) 37.9173 1.33807
\(804\) −7.39767 −0.260896
\(805\) −13.6756 −0.482001
\(806\) −0.0184471 −0.000649772 0
\(807\) 22.5585 0.794097
\(808\) −1.05027 −0.0369484
\(809\) 1.58840 0.0558450 0.0279225 0.999610i \(-0.491111\pi\)
0.0279225 + 0.999610i \(0.491111\pi\)
\(810\) 3.38623 0.118980
\(811\) 21.0118 0.737824 0.368912 0.929464i \(-0.379730\pi\)
0.368912 + 0.929464i \(0.379730\pi\)
\(812\) 14.2268 0.499263
\(813\) −10.3550 −0.363167
\(814\) −11.1711 −0.391546
\(815\) −18.5527 −0.649873
\(816\) −4.16606 −0.145841
\(817\) −6.44568 −0.225506
\(818\) −5.20799 −0.182093
\(819\) 0.792806 0.0277029
\(820\) −5.98008 −0.208833
\(821\) −35.1367 −1.22628 −0.613140 0.789974i \(-0.710094\pi\)
−0.613140 + 0.789974i \(0.710094\pi\)
\(822\) −15.0936 −0.526451
\(823\) −2.54877 −0.0888445 −0.0444222 0.999013i \(-0.514145\pi\)
−0.0444222 + 0.999013i \(0.514145\pi\)
\(824\) 12.3758 0.431133
\(825\) 10.7119 0.372940
\(826\) 2.00560 0.0697836
\(827\) 11.7412 0.408282 0.204141 0.978941i \(-0.434560\pi\)
0.204141 + 0.978941i \(0.434560\pi\)
\(828\) 10.9303 0.379854
\(829\) 17.3405 0.602261 0.301130 0.953583i \(-0.402636\pi\)
0.301130 + 0.953583i \(0.402636\pi\)
\(830\) 6.46244 0.224315
\(831\) 17.2455 0.598238
\(832\) 0.0959992 0.00332817
\(833\) 26.2618 0.909918
\(834\) −10.4921 −0.363311
\(835\) 1.91960 0.0664306
\(836\) 6.36784 0.220236
\(837\) 0.807501 0.0279113
\(838\) −0.0975118 −0.00336849
\(839\) 4.44264 0.153377 0.0766886 0.997055i \(-0.475565\pi\)
0.0766886 + 0.997055i \(0.475565\pi\)
\(840\) 2.33285 0.0804911
\(841\) −12.0087 −0.414093
\(842\) 17.1483 0.590969
\(843\) 1.44484 0.0497628
\(844\) 0.276423 0.00951486
\(845\) 11.2683 0.387643
\(846\) 27.2662 0.937430
\(847\) 1.81579 0.0623914
\(848\) −1.21545 −0.0417388
\(849\) 5.66875 0.194551
\(850\) 22.7092 0.778918
\(851\) −15.7677 −0.540509
\(852\) 11.2766 0.386329
\(853\) −4.20687 −0.144041 −0.0720203 0.997403i \(-0.522945\pi\)
−0.0720203 + 0.997403i \(0.522945\pi\)
\(854\) −10.4170 −0.356461
\(855\) 4.08383 0.139664
\(856\) −5.13993 −0.175679
\(857\) −9.04752 −0.309058 −0.154529 0.987988i \(-0.549386\pi\)
−0.154529 + 0.987988i \(0.549386\pi\)
\(858\) 0.242097 0.00826507
\(859\) 4.53254 0.154648 0.0773241 0.997006i \(-0.475362\pi\)
0.0773241 + 0.997006i \(0.475362\pi\)
\(860\) 2.84155 0.0968961
\(861\) 18.5415 0.631892
\(862\) 34.9830 1.19152
\(863\) −15.9516 −0.542998 −0.271499 0.962439i \(-0.587519\pi\)
−0.271499 + 0.962439i \(0.587519\pi\)
\(864\) −4.20225 −0.142964
\(865\) 15.6643 0.532603
\(866\) −30.9613 −1.05211
\(867\) −9.02624 −0.306547
\(868\) −0.663217 −0.0225110
\(869\) 8.50903 0.288649
\(870\) 2.78616 0.0944598
\(871\) 0.911369 0.0308806
\(872\) 18.7459 0.634817
\(873\) 6.36862 0.215545
\(874\) 8.98803 0.304025
\(875\) −27.6852 −0.935931
\(876\) −9.12961 −0.308461
\(877\) 19.3910 0.654786 0.327393 0.944888i \(-0.393830\pi\)
0.327393 + 0.944888i \(0.393830\pi\)
\(878\) 3.18963 0.107645
\(879\) 7.84434 0.264583
\(880\) −2.80724 −0.0946319
\(881\) −9.25692 −0.311873 −0.155937 0.987767i \(-0.549840\pi\)
−0.155937 + 0.987767i \(0.549840\pi\)
\(882\) 11.7536 0.395766
\(883\) −1.20086 −0.0404122 −0.0202061 0.999796i \(-0.506432\pi\)
−0.0202061 + 0.999796i \(0.506432\pi\)
\(884\) 0.513245 0.0172623
\(885\) 0.392774 0.0132029
\(886\) 1.23026 0.0413313
\(887\) −33.8199 −1.13556 −0.567781 0.823180i \(-0.692198\pi\)
−0.567781 + 0.823180i \(0.692198\pi\)
\(888\) 2.68973 0.0902615
\(889\) 1.04108 0.0349167
\(890\) 6.43360 0.215655
\(891\) 12.6341 0.423260
\(892\) 4.91884 0.164695
\(893\) 22.4211 0.750293
\(894\) −8.62017 −0.288302
\(895\) 8.67256 0.289892
\(896\) 3.45139 0.115303
\(897\) 0.341714 0.0114095
\(898\) −12.7510 −0.425508
\(899\) −0.792090 −0.0264177
\(900\) 10.1636 0.338787
\(901\) −6.49823 −0.216487
\(902\) −22.3119 −0.742905
\(903\) −8.81036 −0.293190
\(904\) 4.47243 0.148751
\(905\) −9.33257 −0.310225
\(906\) −14.4763 −0.480943
\(907\) 24.3191 0.807503 0.403752 0.914869i \(-0.367706\pi\)
0.403752 + 0.914869i \(0.367706\pi\)
\(908\) 12.1843 0.404349
\(909\) −2.51308 −0.0833537
\(910\) −0.287400 −0.00952721
\(911\) 31.3793 1.03964 0.519821 0.854275i \(-0.325999\pi\)
0.519821 + 0.854275i \(0.325999\pi\)
\(912\) −1.53323 −0.0507702
\(913\) 24.1116 0.797978
\(914\) 40.6338 1.34405
\(915\) −2.04005 −0.0674419
\(916\) 28.5001 0.941669
\(917\) −25.9157 −0.855813
\(918\) −22.4667 −0.741512
\(919\) 10.1822 0.335879 0.167940 0.985797i \(-0.446289\pi\)
0.167940 + 0.985797i \(0.446289\pi\)
\(920\) −3.96234 −0.130634
\(921\) 3.95679 0.130381
\(922\) −11.5464 −0.380259
\(923\) −1.38924 −0.0457273
\(924\) 8.70395 0.286339
\(925\) −14.6617 −0.482074
\(926\) 9.95124 0.327018
\(927\) 29.6128 0.972613
\(928\) 4.12205 0.135313
\(929\) 18.3399 0.601714 0.300857 0.953669i \(-0.402727\pi\)
0.300857 + 0.953669i \(0.402727\pi\)
\(930\) −0.129884 −0.00425905
\(931\) 9.66507 0.316760
\(932\) −16.2015 −0.530698
\(933\) 20.9350 0.685380
\(934\) 3.65923 0.119734
\(935\) −15.0085 −0.490829
\(936\) 0.229706 0.00750818
\(937\) 31.0179 1.01331 0.506656 0.862148i \(-0.330881\pi\)
0.506656 + 0.862148i \(0.330881\pi\)
\(938\) 32.7658 1.06984
\(939\) −3.04166 −0.0992609
\(940\) −9.88425 −0.322389
\(941\) 13.9596 0.455069 0.227534 0.973770i \(-0.426934\pi\)
0.227534 + 0.973770i \(0.426934\pi\)
\(942\) 5.13949 0.167454
\(943\) −31.4926 −1.02554
\(944\) 0.581098 0.0189131
\(945\) 12.5806 0.409247
\(946\) 10.6019 0.344699
\(947\) −29.8175 −0.968940 −0.484470 0.874808i \(-0.660988\pi\)
−0.484470 + 0.874808i \(0.660988\pi\)
\(948\) −2.04878 −0.0665411
\(949\) 1.12474 0.0365105
\(950\) 8.35760 0.271156
\(951\) 8.83436 0.286474
\(952\) 18.4523 0.598044
\(953\) −25.2102 −0.816637 −0.408318 0.912840i \(-0.633885\pi\)
−0.408318 + 0.912840i \(0.633885\pi\)
\(954\) −2.90832 −0.0941605
\(955\) 16.3588 0.529357
\(956\) −12.3676 −0.399998
\(957\) 10.3953 0.336031
\(958\) 2.48553 0.0803040
\(959\) 66.8528 2.15879
\(960\) 0.675917 0.0218151
\(961\) −30.9631 −0.998809
\(962\) −0.331366 −0.0106837
\(963\) −12.2988 −0.396323
\(964\) −14.1994 −0.457332
\(965\) 11.5509 0.371837
\(966\) 12.2854 0.395276
\(967\) 15.8056 0.508272 0.254136 0.967168i \(-0.418209\pi\)
0.254136 + 0.967168i \(0.418209\pi\)
\(968\) 0.526105 0.0169096
\(969\) −8.19717 −0.263331
\(970\) −2.30869 −0.0741274
\(971\) −2.83347 −0.0909303 −0.0454652 0.998966i \(-0.514477\pi\)
−0.0454652 + 0.998966i \(0.514477\pi\)
\(972\) −15.6488 −0.501934
\(973\) 46.4715 1.48981
\(974\) −4.61836 −0.147982
\(975\) 0.317745 0.0101760
\(976\) −3.01819 −0.0966100
\(977\) 26.5337 0.848889 0.424445 0.905454i \(-0.360469\pi\)
0.424445 + 0.905454i \(0.360469\pi\)
\(978\) 16.6668 0.532944
\(979\) 24.0040 0.767171
\(980\) −4.26081 −0.136107
\(981\) 44.8551 1.43211
\(982\) −4.91052 −0.156701
\(983\) 53.5794 1.70892 0.854459 0.519519i \(-0.173889\pi\)
0.854459 + 0.519519i \(0.173889\pi\)
\(984\) 5.37218 0.171259
\(985\) −11.8642 −0.378023
\(986\) 22.0379 0.701831
\(987\) 30.6465 0.975490
\(988\) 0.188888 0.00600934
\(989\) 14.9643 0.475838
\(990\) −6.71713 −0.213485
\(991\) −55.4201 −1.76048 −0.880239 0.474531i \(-0.842618\pi\)
−0.880239 + 0.474531i \(0.842618\pi\)
\(992\) −0.192159 −0.00610106
\(993\) −17.9121 −0.568423
\(994\) −49.9462 −1.58420
\(995\) −3.33752 −0.105806
\(996\) −5.80551 −0.183955
\(997\) −60.1035 −1.90350 −0.951748 0.306879i \(-0.900715\pi\)
−0.951748 + 0.306879i \(0.900715\pi\)
\(998\) 4.25660 0.134740
\(999\) 14.5052 0.458923
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 4006.2.a.g.1.17 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.17 40 1.1 even 1 trivial