Properties

Label 4003.2.a.c.1.12
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46969 q^{2} +0.639879 q^{3} +4.09938 q^{4} -1.75762 q^{5} -1.58030 q^{6} -0.0776251 q^{7} -5.18482 q^{8} -2.59056 q^{9} +O(q^{10})\) \(q-2.46969 q^{2} +0.639879 q^{3} +4.09938 q^{4} -1.75762 q^{5} -1.58030 q^{6} -0.0776251 q^{7} -5.18482 q^{8} -2.59056 q^{9} +4.34079 q^{10} -0.622748 q^{11} +2.62311 q^{12} -2.61937 q^{13} +0.191710 q^{14} -1.12467 q^{15} +4.60616 q^{16} -0.276397 q^{17} +6.39787 q^{18} -6.23326 q^{19} -7.20516 q^{20} -0.0496707 q^{21} +1.53800 q^{22} -1.37220 q^{23} -3.31766 q^{24} -1.91076 q^{25} +6.46904 q^{26} -3.57728 q^{27} -0.318215 q^{28} -1.18130 q^{29} +2.77758 q^{30} +0.419170 q^{31} -1.00615 q^{32} -0.398483 q^{33} +0.682615 q^{34} +0.136436 q^{35} -10.6197 q^{36} -9.00901 q^{37} +15.3942 q^{38} -1.67608 q^{39} +9.11296 q^{40} +6.47523 q^{41} +0.122671 q^{42} +3.50454 q^{43} -2.55288 q^{44} +4.55322 q^{45} +3.38891 q^{46} -0.474996 q^{47} +2.94738 q^{48} -6.99397 q^{49} +4.71900 q^{50} -0.176860 q^{51} -10.7378 q^{52} -3.44910 q^{53} +8.83477 q^{54} +1.09456 q^{55} +0.402473 q^{56} -3.98853 q^{57} +2.91744 q^{58} +3.79175 q^{59} -4.61043 q^{60} -1.11631 q^{61} -1.03522 q^{62} +0.201092 q^{63} -6.72744 q^{64} +4.60387 q^{65} +0.984131 q^{66} -13.0788 q^{67} -1.13306 q^{68} -0.878041 q^{69} -0.336954 q^{70} -0.468661 q^{71} +13.4316 q^{72} +8.13902 q^{73} +22.2495 q^{74} -1.22266 q^{75} -25.5525 q^{76} +0.0483409 q^{77} +4.13940 q^{78} +6.79858 q^{79} -8.09589 q^{80} +5.48264 q^{81} -15.9918 q^{82} +15.1662 q^{83} -0.203619 q^{84} +0.485801 q^{85} -8.65515 q^{86} -0.755887 q^{87} +3.22884 q^{88} -8.61138 q^{89} -11.2450 q^{90} +0.203329 q^{91} -5.62516 q^{92} +0.268218 q^{93} +1.17309 q^{94} +10.9557 q^{95} -0.643812 q^{96} +11.3026 q^{97} +17.2730 q^{98} +1.61326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46969 −1.74634 −0.873168 0.487419i \(-0.837938\pi\)
−0.873168 + 0.487419i \(0.837938\pi\)
\(3\) 0.639879 0.369434 0.184717 0.982792i \(-0.440863\pi\)
0.184717 + 0.982792i \(0.440863\pi\)
\(4\) 4.09938 2.04969
\(5\) −1.75762 −0.786033 −0.393016 0.919532i \(-0.628568\pi\)
−0.393016 + 0.919532i \(0.628568\pi\)
\(6\) −1.58030 −0.645156
\(7\) −0.0776251 −0.0293395 −0.0146698 0.999892i \(-0.504670\pi\)
−0.0146698 + 0.999892i \(0.504670\pi\)
\(8\) −5.18482 −1.83311
\(9\) −2.59056 −0.863518
\(10\) 4.34079 1.37268
\(11\) −0.622748 −0.187766 −0.0938828 0.995583i \(-0.529928\pi\)
−0.0938828 + 0.995583i \(0.529928\pi\)
\(12\) 2.62311 0.757226
\(13\) −2.61937 −0.726483 −0.363241 0.931695i \(-0.618330\pi\)
−0.363241 + 0.931695i \(0.618330\pi\)
\(14\) 0.191710 0.0512367
\(15\) −1.12467 −0.290387
\(16\) 4.60616 1.15154
\(17\) −0.276397 −0.0670361 −0.0335180 0.999438i \(-0.510671\pi\)
−0.0335180 + 0.999438i \(0.510671\pi\)
\(18\) 6.39787 1.50799
\(19\) −6.23326 −1.43001 −0.715003 0.699121i \(-0.753575\pi\)
−0.715003 + 0.699121i \(0.753575\pi\)
\(20\) −7.20516 −1.61112
\(21\) −0.0496707 −0.0108390
\(22\) 1.53800 0.327902
\(23\) −1.37220 −0.286123 −0.143062 0.989714i \(-0.545695\pi\)
−0.143062 + 0.989714i \(0.545695\pi\)
\(24\) −3.31766 −0.677214
\(25\) −1.91076 −0.382153
\(26\) 6.46904 1.26868
\(27\) −3.57728 −0.688447
\(28\) −0.318215 −0.0601370
\(29\) −1.18130 −0.219361 −0.109681 0.993967i \(-0.534983\pi\)
−0.109681 + 0.993967i \(0.534983\pi\)
\(30\) 2.77758 0.507114
\(31\) 0.419170 0.0752852 0.0376426 0.999291i \(-0.488015\pi\)
0.0376426 + 0.999291i \(0.488015\pi\)
\(32\) −1.00615 −0.177863
\(33\) −0.398483 −0.0693670
\(34\) 0.682615 0.117068
\(35\) 0.136436 0.0230618
\(36\) −10.6197 −1.76995
\(37\) −9.00901 −1.48107 −0.740536 0.672017i \(-0.765428\pi\)
−0.740536 + 0.672017i \(0.765428\pi\)
\(38\) 15.3942 2.49727
\(39\) −1.67608 −0.268388
\(40\) 9.11296 1.44089
\(41\) 6.47523 1.01126 0.505630 0.862750i \(-0.331260\pi\)
0.505630 + 0.862750i \(0.331260\pi\)
\(42\) 0.122671 0.0189286
\(43\) 3.50454 0.534438 0.267219 0.963636i \(-0.413895\pi\)
0.267219 + 0.963636i \(0.413895\pi\)
\(44\) −2.55288 −0.384861
\(45\) 4.55322 0.678754
\(46\) 3.38891 0.499667
\(47\) −0.474996 −0.0692853 −0.0346427 0.999400i \(-0.511029\pi\)
−0.0346427 + 0.999400i \(0.511029\pi\)
\(48\) 2.94738 0.425418
\(49\) −6.99397 −0.999139
\(50\) 4.71900 0.667367
\(51\) −0.176860 −0.0247654
\(52\) −10.7378 −1.48906
\(53\) −3.44910 −0.473770 −0.236885 0.971538i \(-0.576127\pi\)
−0.236885 + 0.971538i \(0.576127\pi\)
\(54\) 8.83477 1.20226
\(55\) 1.09456 0.147590
\(56\) 0.402473 0.0537827
\(57\) −3.98853 −0.528293
\(58\) 2.91744 0.383079
\(59\) 3.79175 0.493643 0.246822 0.969061i \(-0.420614\pi\)
0.246822 + 0.969061i \(0.420614\pi\)
\(60\) −4.61043 −0.595204
\(61\) −1.11631 −0.142929 −0.0714644 0.997443i \(-0.522767\pi\)
−0.0714644 + 0.997443i \(0.522767\pi\)
\(62\) −1.03522 −0.131473
\(63\) 0.201092 0.0253352
\(64\) −6.72744 −0.840930
\(65\) 4.60387 0.571039
\(66\) 0.984131 0.121138
\(67\) −13.0788 −1.59783 −0.798917 0.601442i \(-0.794593\pi\)
−0.798917 + 0.601442i \(0.794593\pi\)
\(68\) −1.13306 −0.137403
\(69\) −0.878041 −0.105704
\(70\) −0.336954 −0.0402737
\(71\) −0.468661 −0.0556198 −0.0278099 0.999613i \(-0.508853\pi\)
−0.0278099 + 0.999613i \(0.508853\pi\)
\(72\) 13.4316 1.58293
\(73\) 8.13902 0.952601 0.476300 0.879283i \(-0.341978\pi\)
0.476300 + 0.879283i \(0.341978\pi\)
\(74\) 22.2495 2.58645
\(75\) −1.22266 −0.141180
\(76\) −25.5525 −2.93107
\(77\) 0.0483409 0.00550896
\(78\) 4.13940 0.468695
\(79\) 6.79858 0.764900 0.382450 0.923976i \(-0.375080\pi\)
0.382450 + 0.923976i \(0.375080\pi\)
\(80\) −8.09589 −0.905148
\(81\) 5.48264 0.609182
\(82\) −15.9918 −1.76600
\(83\) 15.1662 1.66471 0.832355 0.554243i \(-0.186992\pi\)
0.832355 + 0.554243i \(0.186992\pi\)
\(84\) −0.203619 −0.0222166
\(85\) 0.485801 0.0526925
\(86\) −8.65515 −0.933308
\(87\) −0.755887 −0.0810396
\(88\) 3.22884 0.344195
\(89\) −8.61138 −0.912804 −0.456402 0.889774i \(-0.650862\pi\)
−0.456402 + 0.889774i \(0.650862\pi\)
\(90\) −11.2450 −1.18533
\(91\) 0.203329 0.0213147
\(92\) −5.62516 −0.586464
\(93\) 0.268218 0.0278129
\(94\) 1.17309 0.120995
\(95\) 10.9557 1.12403
\(96\) −0.643812 −0.0657088
\(97\) 11.3026 1.14760 0.573802 0.818994i \(-0.305468\pi\)
0.573802 + 0.818994i \(0.305468\pi\)
\(98\) 17.2730 1.74483
\(99\) 1.61326 0.162139
\(100\) −7.83295 −0.783295
\(101\) 5.36680 0.534017 0.267008 0.963694i \(-0.413965\pi\)
0.267008 + 0.963694i \(0.413965\pi\)
\(102\) 0.436791 0.0432487
\(103\) −1.01634 −0.100143 −0.0500715 0.998746i \(-0.515945\pi\)
−0.0500715 + 0.998746i \(0.515945\pi\)
\(104\) 13.5810 1.33172
\(105\) 0.0873023 0.00851983
\(106\) 8.51821 0.827362
\(107\) −10.2687 −0.992713 −0.496356 0.868119i \(-0.665329\pi\)
−0.496356 + 0.868119i \(0.665329\pi\)
\(108\) −14.6646 −1.41110
\(109\) −17.3745 −1.66418 −0.832088 0.554644i \(-0.812855\pi\)
−0.832088 + 0.554644i \(0.812855\pi\)
\(110\) −2.70322 −0.257742
\(111\) −5.76467 −0.547158
\(112\) −0.357554 −0.0337856
\(113\) −10.1745 −0.957134 −0.478567 0.878051i \(-0.658844\pi\)
−0.478567 + 0.878051i \(0.658844\pi\)
\(114\) 9.85044 0.922578
\(115\) 2.41181 0.224902
\(116\) −4.84259 −0.449623
\(117\) 6.78563 0.627331
\(118\) −9.36445 −0.862067
\(119\) 0.0214553 0.00196681
\(120\) 5.83119 0.532312
\(121\) −10.6122 −0.964744
\(122\) 2.75694 0.249602
\(123\) 4.14336 0.373594
\(124\) 1.71834 0.154311
\(125\) 12.1465 1.08642
\(126\) −0.496636 −0.0442438
\(127\) 11.3092 1.00353 0.501764 0.865005i \(-0.332685\pi\)
0.501764 + 0.865005i \(0.332685\pi\)
\(128\) 18.6270 1.64641
\(129\) 2.24248 0.197440
\(130\) −11.3701 −0.997226
\(131\) 8.92797 0.780041 0.390020 0.920806i \(-0.372468\pi\)
0.390020 + 0.920806i \(0.372468\pi\)
\(132\) −1.63353 −0.142181
\(133\) 0.483857 0.0419557
\(134\) 32.3007 2.79035
\(135\) 6.28750 0.541142
\(136\) 1.43307 0.122885
\(137\) 13.5105 1.15428 0.577141 0.816644i \(-0.304168\pi\)
0.577141 + 0.816644i \(0.304168\pi\)
\(138\) 2.16849 0.184594
\(139\) 3.35825 0.284843 0.142421 0.989806i \(-0.454511\pi\)
0.142421 + 0.989806i \(0.454511\pi\)
\(140\) 0.559302 0.0472696
\(141\) −0.303940 −0.0255964
\(142\) 1.15745 0.0971308
\(143\) 1.63121 0.136409
\(144\) −11.9325 −0.994376
\(145\) 2.07627 0.172425
\(146\) −20.1009 −1.66356
\(147\) −4.47530 −0.369116
\(148\) −36.9313 −3.03574
\(149\) 19.6756 1.61189 0.805943 0.591993i \(-0.201659\pi\)
0.805943 + 0.591993i \(0.201659\pi\)
\(150\) 3.01959 0.246548
\(151\) 4.69726 0.382258 0.191129 0.981565i \(-0.438785\pi\)
0.191129 + 0.981565i \(0.438785\pi\)
\(152\) 32.3183 2.62136
\(153\) 0.716021 0.0578869
\(154\) −0.119387 −0.00962049
\(155\) −0.736743 −0.0591767
\(156\) −6.87089 −0.550111
\(157\) 6.31085 0.503661 0.251831 0.967771i \(-0.418967\pi\)
0.251831 + 0.967771i \(0.418967\pi\)
\(158\) −16.7904 −1.33577
\(159\) −2.20701 −0.175027
\(160\) 1.76843 0.139806
\(161\) 0.106517 0.00839472
\(162\) −13.5404 −1.06384
\(163\) 6.75346 0.528972 0.264486 0.964390i \(-0.414798\pi\)
0.264486 + 0.964390i \(0.414798\pi\)
\(164\) 26.5444 2.07277
\(165\) 0.700383 0.0545247
\(166\) −37.4559 −2.90714
\(167\) −6.35223 −0.491550 −0.245775 0.969327i \(-0.579042\pi\)
−0.245775 + 0.969327i \(0.579042\pi\)
\(168\) 0.257534 0.0198691
\(169\) −6.13889 −0.472223
\(170\) −1.19978 −0.0920189
\(171\) 16.1476 1.23484
\(172\) 14.3665 1.09543
\(173\) 8.61162 0.654730 0.327365 0.944898i \(-0.393839\pi\)
0.327365 + 0.944898i \(0.393839\pi\)
\(174\) 1.86681 0.141522
\(175\) 0.148323 0.0112122
\(176\) −2.86848 −0.216220
\(177\) 2.42626 0.182369
\(178\) 21.2675 1.59406
\(179\) 15.9192 1.18985 0.594927 0.803780i \(-0.297181\pi\)
0.594927 + 0.803780i \(0.297181\pi\)
\(180\) 18.6654 1.39123
\(181\) 17.1541 1.27506 0.637528 0.770427i \(-0.279957\pi\)
0.637528 + 0.770427i \(0.279957\pi\)
\(182\) −0.502160 −0.0372226
\(183\) −0.714303 −0.0528028
\(184\) 7.11461 0.524496
\(185\) 15.8344 1.16417
\(186\) −0.662417 −0.0485707
\(187\) 0.172126 0.0125871
\(188\) −1.94719 −0.142013
\(189\) 0.277687 0.0201987
\(190\) −27.0572 −1.96294
\(191\) −23.4411 −1.69614 −0.848071 0.529883i \(-0.822236\pi\)
−0.848071 + 0.529883i \(0.822236\pi\)
\(192\) −4.30475 −0.310668
\(193\) −8.90737 −0.641166 −0.320583 0.947220i \(-0.603879\pi\)
−0.320583 + 0.947220i \(0.603879\pi\)
\(194\) −27.9139 −2.00410
\(195\) 2.94592 0.210961
\(196\) −28.6710 −2.04793
\(197\) −16.5719 −1.18070 −0.590348 0.807149i \(-0.701010\pi\)
−0.590348 + 0.807149i \(0.701010\pi\)
\(198\) −3.98426 −0.283149
\(199\) −22.9296 −1.62544 −0.812720 0.582655i \(-0.802014\pi\)
−0.812720 + 0.582655i \(0.802014\pi\)
\(200\) 9.90697 0.700529
\(201\) −8.36886 −0.590294
\(202\) −13.2544 −0.932573
\(203\) 0.0916983 0.00643596
\(204\) −0.725018 −0.0507614
\(205\) −11.3810 −0.794884
\(206\) 2.51005 0.174883
\(207\) 3.55476 0.247073
\(208\) −12.0652 −0.836574
\(209\) 3.88175 0.268506
\(210\) −0.215610 −0.0148785
\(211\) −25.5205 −1.75690 −0.878451 0.477833i \(-0.841422\pi\)
−0.878451 + 0.477833i \(0.841422\pi\)
\(212\) −14.1392 −0.971082
\(213\) −0.299886 −0.0205478
\(214\) 25.3605 1.73361
\(215\) −6.15967 −0.420086
\(216\) 18.5476 1.26200
\(217\) −0.0325382 −0.00220883
\(218\) 42.9097 2.90621
\(219\) 5.20799 0.351923
\(220\) 4.48700 0.302514
\(221\) 0.723986 0.0487005
\(222\) 14.2370 0.955522
\(223\) −14.1307 −0.946261 −0.473130 0.880992i \(-0.656876\pi\)
−0.473130 + 0.880992i \(0.656876\pi\)
\(224\) 0.0781023 0.00521843
\(225\) 4.94994 0.329996
\(226\) 25.1278 1.67148
\(227\) −20.0704 −1.33212 −0.666060 0.745898i \(-0.732020\pi\)
−0.666060 + 0.745898i \(0.732020\pi\)
\(228\) −16.3505 −1.08284
\(229\) 8.76531 0.579228 0.289614 0.957143i \(-0.406473\pi\)
0.289614 + 0.957143i \(0.406473\pi\)
\(230\) −5.95642 −0.392755
\(231\) 0.0309323 0.00203520
\(232\) 6.12482 0.402114
\(233\) −13.5172 −0.885544 −0.442772 0.896634i \(-0.646005\pi\)
−0.442772 + 0.896634i \(0.646005\pi\)
\(234\) −16.7584 −1.09553
\(235\) 0.834864 0.0544605
\(236\) 15.5438 1.01182
\(237\) 4.35027 0.282580
\(238\) −0.0529881 −0.00343471
\(239\) 4.80739 0.310964 0.155482 0.987839i \(-0.450307\pi\)
0.155482 + 0.987839i \(0.450307\pi\)
\(240\) −5.18039 −0.334392
\(241\) −23.9040 −1.53979 −0.769895 0.638170i \(-0.779692\pi\)
−0.769895 + 0.638170i \(0.779692\pi\)
\(242\) 26.2088 1.68477
\(243\) 14.2401 0.913500
\(244\) −4.57618 −0.292960
\(245\) 12.2928 0.785356
\(246\) −10.2328 −0.652421
\(247\) 16.3272 1.03888
\(248\) −2.17332 −0.138006
\(249\) 9.70455 0.615001
\(250\) −29.9981 −1.89725
\(251\) 22.8838 1.44441 0.722205 0.691679i \(-0.243129\pi\)
0.722205 + 0.691679i \(0.243129\pi\)
\(252\) 0.824353 0.0519294
\(253\) 0.854534 0.0537241
\(254\) −27.9302 −1.75250
\(255\) 0.310854 0.0194664
\(256\) −32.5481 −2.03426
\(257\) −22.6514 −1.41295 −0.706477 0.707736i \(-0.749717\pi\)
−0.706477 + 0.707736i \(0.749717\pi\)
\(258\) −5.53824 −0.344796
\(259\) 0.699325 0.0434539
\(260\) 18.8730 1.17045
\(261\) 3.06022 0.189423
\(262\) −22.0494 −1.36221
\(263\) 27.3715 1.68780 0.843900 0.536501i \(-0.180254\pi\)
0.843900 + 0.536501i \(0.180254\pi\)
\(264\) 2.06607 0.127158
\(265\) 6.06221 0.372399
\(266\) −1.19498 −0.0732688
\(267\) −5.51024 −0.337221
\(268\) −53.6151 −3.27506
\(269\) 19.5875 1.19427 0.597136 0.802140i \(-0.296305\pi\)
0.597136 + 0.802140i \(0.296305\pi\)
\(270\) −15.5282 −0.945016
\(271\) −10.0696 −0.611687 −0.305844 0.952082i \(-0.598939\pi\)
−0.305844 + 0.952082i \(0.598939\pi\)
\(272\) −1.27313 −0.0771947
\(273\) 0.130106 0.00787437
\(274\) −33.3669 −2.01577
\(275\) 1.18992 0.0717552
\(276\) −3.59942 −0.216660
\(277\) 30.5292 1.83432 0.917160 0.398520i \(-0.130476\pi\)
0.917160 + 0.398520i \(0.130476\pi\)
\(278\) −8.29384 −0.497432
\(279\) −1.08588 −0.0650102
\(280\) −0.707395 −0.0422749
\(281\) −16.3866 −0.977541 −0.488770 0.872412i \(-0.662554\pi\)
−0.488770 + 0.872412i \(0.662554\pi\)
\(282\) 0.750638 0.0446998
\(283\) 31.9209 1.89750 0.948750 0.316029i \(-0.102350\pi\)
0.948750 + 0.316029i \(0.102350\pi\)
\(284\) −1.92122 −0.114003
\(285\) 7.01032 0.415256
\(286\) −4.02858 −0.238215
\(287\) −0.502640 −0.0296699
\(288\) 2.60648 0.153588
\(289\) −16.9236 −0.995506
\(290\) −5.12776 −0.301112
\(291\) 7.23228 0.423964
\(292\) 33.3649 1.95254
\(293\) −2.56430 −0.149808 −0.0749041 0.997191i \(-0.523865\pi\)
−0.0749041 + 0.997191i \(0.523865\pi\)
\(294\) 11.0526 0.644601
\(295\) −6.66446 −0.388020
\(296\) 46.7101 2.71497
\(297\) 2.22774 0.129267
\(298\) −48.5926 −2.81490
\(299\) 3.59430 0.207864
\(300\) −5.01214 −0.289376
\(301\) −0.272041 −0.0156802
\(302\) −11.6008 −0.667550
\(303\) 3.43410 0.197284
\(304\) −28.7114 −1.64671
\(305\) 1.96205 0.112347
\(306\) −1.76835 −0.101090
\(307\) 5.29605 0.302261 0.151131 0.988514i \(-0.451709\pi\)
0.151131 + 0.988514i \(0.451709\pi\)
\(308\) 0.198168 0.0112917
\(309\) −0.650334 −0.0369962
\(310\) 1.81953 0.103342
\(311\) 28.2574 1.60233 0.801165 0.598444i \(-0.204214\pi\)
0.801165 + 0.598444i \(0.204214\pi\)
\(312\) 8.69018 0.491984
\(313\) 17.9679 1.01561 0.507804 0.861473i \(-0.330457\pi\)
0.507804 + 0.861473i \(0.330457\pi\)
\(314\) −15.5859 −0.879561
\(315\) −0.353444 −0.0199143
\(316\) 27.8700 1.56781
\(317\) −4.80103 −0.269652 −0.134826 0.990869i \(-0.543048\pi\)
−0.134826 + 0.990869i \(0.543048\pi\)
\(318\) 5.45062 0.305656
\(319\) 0.735651 0.0411885
\(320\) 11.8243 0.660999
\(321\) −6.57072 −0.366742
\(322\) −0.263064 −0.0146600
\(323\) 1.72285 0.0958620
\(324\) 22.4754 1.24864
\(325\) 5.00500 0.277627
\(326\) −16.6790 −0.923762
\(327\) −11.1176 −0.614803
\(328\) −33.5729 −1.85375
\(329\) 0.0368716 0.00203280
\(330\) −1.72973 −0.0952185
\(331\) 20.4770 1.12552 0.562758 0.826622i \(-0.309740\pi\)
0.562758 + 0.826622i \(0.309740\pi\)
\(332\) 62.1721 3.41214
\(333\) 23.3383 1.27893
\(334\) 15.6880 0.858412
\(335\) 22.9876 1.25595
\(336\) −0.228791 −0.0124816
\(337\) 0.331751 0.0180716 0.00903582 0.999959i \(-0.497124\pi\)
0.00903582 + 0.999959i \(0.497124\pi\)
\(338\) 15.1612 0.824660
\(339\) −6.51043 −0.353598
\(340\) 1.99148 0.108003
\(341\) −0.261038 −0.0141360
\(342\) −39.8796 −2.15644
\(343\) 1.08628 0.0586538
\(344\) −18.1704 −0.979685
\(345\) 1.54326 0.0830865
\(346\) −21.2681 −1.14338
\(347\) 10.1908 0.547069 0.273535 0.961862i \(-0.411807\pi\)
0.273535 + 0.961862i \(0.411807\pi\)
\(348\) −3.09867 −0.166106
\(349\) −27.5442 −1.47441 −0.737205 0.675670i \(-0.763855\pi\)
−0.737205 + 0.675670i \(0.763855\pi\)
\(350\) −0.366313 −0.0195802
\(351\) 9.37022 0.500145
\(352\) 0.626576 0.0333966
\(353\) −37.0364 −1.97125 −0.985623 0.168959i \(-0.945959\pi\)
−0.985623 + 0.168959i \(0.945959\pi\)
\(354\) −5.99211 −0.318477
\(355\) 0.823728 0.0437190
\(356\) −35.3013 −1.87097
\(357\) 0.0137288 0.000726606 0
\(358\) −39.3154 −2.07788
\(359\) −23.0040 −1.21410 −0.607052 0.794662i \(-0.707648\pi\)
−0.607052 + 0.794662i \(0.707648\pi\)
\(360\) −23.6076 −1.24423
\(361\) 19.8535 1.04492
\(362\) −42.3654 −2.22668
\(363\) −6.79051 −0.356409
\(364\) 0.833523 0.0436885
\(365\) −14.3053 −0.748775
\(366\) 1.76411 0.0922114
\(367\) 17.5877 0.918070 0.459035 0.888418i \(-0.348195\pi\)
0.459035 + 0.888418i \(0.348195\pi\)
\(368\) −6.32056 −0.329482
\(369\) −16.7744 −0.873242
\(370\) −39.1062 −2.03303
\(371\) 0.267737 0.0139002
\(372\) 1.09953 0.0570079
\(373\) 0.537812 0.0278468 0.0139234 0.999903i \(-0.495568\pi\)
0.0139234 + 0.999903i \(0.495568\pi\)
\(374\) −0.425097 −0.0219813
\(375\) 7.77229 0.401360
\(376\) 2.46277 0.127008
\(377\) 3.09426 0.159362
\(378\) −0.685800 −0.0352738
\(379\) −23.8711 −1.22618 −0.613089 0.790014i \(-0.710073\pi\)
−0.613089 + 0.790014i \(0.710073\pi\)
\(380\) 44.9116 2.30392
\(381\) 7.23650 0.370737
\(382\) 57.8924 2.96203
\(383\) 0.749125 0.0382785 0.0191392 0.999817i \(-0.493907\pi\)
0.0191392 + 0.999817i \(0.493907\pi\)
\(384\) 11.9190 0.608240
\(385\) −0.0849650 −0.00433022
\(386\) 21.9985 1.11969
\(387\) −9.07872 −0.461497
\(388\) 46.3336 2.35223
\(389\) −30.6065 −1.55181 −0.775906 0.630849i \(-0.782707\pi\)
−0.775906 + 0.630849i \(0.782707\pi\)
\(390\) −7.27550 −0.368409
\(391\) 0.379271 0.0191806
\(392\) 36.2625 1.83153
\(393\) 5.71282 0.288174
\(394\) 40.9274 2.06189
\(395\) −11.9493 −0.601236
\(396\) 6.61338 0.332335
\(397\) 30.0655 1.50895 0.754473 0.656331i \(-0.227893\pi\)
0.754473 + 0.656331i \(0.227893\pi\)
\(398\) 56.6292 2.83856
\(399\) 0.309610 0.0154999
\(400\) −8.80128 −0.440064
\(401\) 16.2471 0.811342 0.405671 0.914019i \(-0.367038\pi\)
0.405671 + 0.914019i \(0.367038\pi\)
\(402\) 20.6685 1.03085
\(403\) −1.09796 −0.0546934
\(404\) 22.0006 1.09457
\(405\) −9.63641 −0.478837
\(406\) −0.226467 −0.0112394
\(407\) 5.61034 0.278094
\(408\) 0.916990 0.0453978
\(409\) 12.9372 0.639702 0.319851 0.947468i \(-0.396367\pi\)
0.319851 + 0.947468i \(0.396367\pi\)
\(410\) 28.1076 1.38813
\(411\) 8.64510 0.426432
\(412\) −4.16636 −0.205262
\(413\) −0.294335 −0.0144833
\(414\) −8.77915 −0.431472
\(415\) −26.6565 −1.30852
\(416\) 2.63547 0.129215
\(417\) 2.14887 0.105231
\(418\) −9.58673 −0.468902
\(419\) 38.5722 1.88438 0.942189 0.335082i \(-0.108764\pi\)
0.942189 + 0.335082i \(0.108764\pi\)
\(420\) 0.357885 0.0174630
\(421\) 22.7141 1.10702 0.553508 0.832844i \(-0.313289\pi\)
0.553508 + 0.832844i \(0.313289\pi\)
\(422\) 63.0277 3.06814
\(423\) 1.23050 0.0598291
\(424\) 17.8830 0.868474
\(425\) 0.528129 0.0256180
\(426\) 0.740626 0.0358834
\(427\) 0.0866537 0.00419347
\(428\) −42.0953 −2.03475
\(429\) 1.04378 0.0503940
\(430\) 15.2125 0.733611
\(431\) 12.4009 0.597329 0.298664 0.954358i \(-0.403459\pi\)
0.298664 + 0.954358i \(0.403459\pi\)
\(432\) −16.4775 −0.792774
\(433\) 29.2259 1.40451 0.702255 0.711926i \(-0.252177\pi\)
0.702255 + 0.711926i \(0.252177\pi\)
\(434\) 0.0803592 0.00385737
\(435\) 1.32856 0.0636997
\(436\) −71.2247 −3.41104
\(437\) 8.55326 0.409158
\(438\) −12.8621 −0.614576
\(439\) −5.71773 −0.272892 −0.136446 0.990647i \(-0.543568\pi\)
−0.136446 + 0.990647i \(0.543568\pi\)
\(440\) −5.67508 −0.270549
\(441\) 18.1183 0.862775
\(442\) −1.78802 −0.0850475
\(443\) 21.7892 1.03523 0.517617 0.855612i \(-0.326819\pi\)
0.517617 + 0.855612i \(0.326819\pi\)
\(444\) −23.6316 −1.12151
\(445\) 15.1356 0.717494
\(446\) 34.8985 1.65249
\(447\) 12.5900 0.595486
\(448\) 0.522219 0.0246725
\(449\) 12.7188 0.600238 0.300119 0.953902i \(-0.402974\pi\)
0.300119 + 0.953902i \(0.402974\pi\)
\(450\) −12.2248 −0.576284
\(451\) −4.03244 −0.189880
\(452\) −41.7091 −1.96183
\(453\) 3.00568 0.141219
\(454\) 49.5677 2.32633
\(455\) −0.357376 −0.0167540
\(456\) 20.6798 0.968421
\(457\) −15.7316 −0.735894 −0.367947 0.929847i \(-0.619939\pi\)
−0.367947 + 0.929847i \(0.619939\pi\)
\(458\) −21.6476 −1.01153
\(459\) 0.988748 0.0461508
\(460\) 9.88691 0.460980
\(461\) −5.35434 −0.249376 −0.124688 0.992196i \(-0.539793\pi\)
−0.124688 + 0.992196i \(0.539793\pi\)
\(462\) −0.0763933 −0.00355414
\(463\) −0.396006 −0.0184040 −0.00920199 0.999958i \(-0.502929\pi\)
−0.00920199 + 0.999958i \(0.502929\pi\)
\(464\) −5.44124 −0.252603
\(465\) −0.471426 −0.0218619
\(466\) 33.3834 1.54646
\(467\) 39.0548 1.80724 0.903620 0.428336i \(-0.140900\pi\)
0.903620 + 0.428336i \(0.140900\pi\)
\(468\) 27.8169 1.28583
\(469\) 1.01525 0.0468797
\(470\) −2.06186 −0.0951064
\(471\) 4.03818 0.186070
\(472\) −19.6595 −0.904904
\(473\) −2.18245 −0.100349
\(474\) −10.7438 −0.493480
\(475\) 11.9103 0.546481
\(476\) 0.0879536 0.00403134
\(477\) 8.93508 0.409109
\(478\) −11.8728 −0.543048
\(479\) −8.11202 −0.370648 −0.185324 0.982677i \(-0.559333\pi\)
−0.185324 + 0.982677i \(0.559333\pi\)
\(480\) 1.13158 0.0516492
\(481\) 23.5979 1.07597
\(482\) 59.0355 2.68899
\(483\) 0.0681580 0.00310130
\(484\) −43.5034 −1.97743
\(485\) −19.8657 −0.902054
\(486\) −35.1686 −1.59528
\(487\) 28.2477 1.28003 0.640013 0.768364i \(-0.278929\pi\)
0.640013 + 0.768364i \(0.278929\pi\)
\(488\) 5.78787 0.262005
\(489\) 4.32139 0.195420
\(490\) −30.3593 −1.37150
\(491\) −5.36976 −0.242334 −0.121167 0.992632i \(-0.538664\pi\)
−0.121167 + 0.992632i \(0.538664\pi\)
\(492\) 16.9852 0.765752
\(493\) 0.326507 0.0147051
\(494\) −40.3232 −1.81423
\(495\) −2.83551 −0.127447
\(496\) 1.93077 0.0866939
\(497\) 0.0363798 0.00163186
\(498\) −23.9672 −1.07400
\(499\) −0.247100 −0.0110617 −0.00553086 0.999985i \(-0.501761\pi\)
−0.00553086 + 0.999985i \(0.501761\pi\)
\(500\) 49.7932 2.22682
\(501\) −4.06465 −0.181595
\(502\) −56.5159 −2.52243
\(503\) −19.1889 −0.855589 −0.427794 0.903876i \(-0.640709\pi\)
−0.427794 + 0.903876i \(0.640709\pi\)
\(504\) −1.04263 −0.0464423
\(505\) −9.43281 −0.419755
\(506\) −2.11044 −0.0938203
\(507\) −3.92815 −0.174455
\(508\) 46.3606 2.05692
\(509\) 28.5030 1.26337 0.631687 0.775224i \(-0.282363\pi\)
0.631687 + 0.775224i \(0.282363\pi\)
\(510\) −0.767713 −0.0339949
\(511\) −0.631793 −0.0279489
\(512\) 43.1298 1.90608
\(513\) 22.2981 0.984484
\(514\) 55.9419 2.46749
\(515\) 1.78634 0.0787156
\(516\) 9.19279 0.404690
\(517\) 0.295803 0.0130094
\(518\) −1.72712 −0.0758852
\(519\) 5.51039 0.241879
\(520\) −23.8702 −1.04678
\(521\) 40.7952 1.78727 0.893634 0.448796i \(-0.148147\pi\)
0.893634 + 0.448796i \(0.148147\pi\)
\(522\) −7.55779 −0.330796
\(523\) 22.2202 0.971620 0.485810 0.874064i \(-0.338525\pi\)
0.485810 + 0.874064i \(0.338525\pi\)
\(524\) 36.5992 1.59884
\(525\) 0.0949089 0.00414216
\(526\) −67.5992 −2.94747
\(527\) −0.115857 −0.00504683
\(528\) −1.83548 −0.0798789
\(529\) −21.1171 −0.918134
\(530\) −14.9718 −0.650334
\(531\) −9.82273 −0.426270
\(532\) 1.98351 0.0859963
\(533\) −16.9610 −0.734663
\(534\) 13.6086 0.588901
\(535\) 18.0485 0.780305
\(536\) 67.8114 2.92901
\(537\) 10.1863 0.439573
\(538\) −48.3751 −2.08560
\(539\) 4.35548 0.187604
\(540\) 25.7749 1.10917
\(541\) −39.4200 −1.69480 −0.847399 0.530957i \(-0.821832\pi\)
−0.847399 + 0.530957i \(0.821832\pi\)
\(542\) 24.8689 1.06821
\(543\) 10.9766 0.471049
\(544\) 0.278096 0.0119233
\(545\) 30.5378 1.30810
\(546\) −0.321322 −0.0137513
\(547\) −28.0759 −1.20044 −0.600218 0.799836i \(-0.704920\pi\)
−0.600218 + 0.799836i \(0.704920\pi\)
\(548\) 55.3848 2.36592
\(549\) 2.89186 0.123422
\(550\) −2.93875 −0.125309
\(551\) 7.36333 0.313688
\(552\) 4.55249 0.193767
\(553\) −0.527741 −0.0224418
\(554\) −75.3976 −3.20334
\(555\) 10.1321 0.430084
\(556\) 13.7667 0.583840
\(557\) 7.46987 0.316508 0.158254 0.987398i \(-0.449413\pi\)
0.158254 + 0.987398i \(0.449413\pi\)
\(558\) 2.68180 0.113530
\(559\) −9.17970 −0.388260
\(560\) 0.628444 0.0265566
\(561\) 0.110139 0.00465009
\(562\) 40.4698 1.70712
\(563\) 8.17106 0.344369 0.172184 0.985065i \(-0.444917\pi\)
0.172184 + 0.985065i \(0.444917\pi\)
\(564\) −1.24597 −0.0524646
\(565\) 17.8829 0.752339
\(566\) −78.8348 −3.31367
\(567\) −0.425591 −0.0178731
\(568\) 2.42992 0.101957
\(569\) −24.5159 −1.02776 −0.513879 0.857862i \(-0.671792\pi\)
−0.513879 + 0.857862i \(0.671792\pi\)
\(570\) −17.3133 −0.725176
\(571\) 0.765742 0.0320453 0.0160227 0.999872i \(-0.494900\pi\)
0.0160227 + 0.999872i \(0.494900\pi\)
\(572\) 6.68694 0.279595
\(573\) −14.9995 −0.626613
\(574\) 1.24137 0.0518136
\(575\) 2.62195 0.109343
\(576\) 17.4278 0.726159
\(577\) 30.7583 1.28049 0.640243 0.768172i \(-0.278834\pi\)
0.640243 + 0.768172i \(0.278834\pi\)
\(578\) 41.7961 1.73849
\(579\) −5.69964 −0.236869
\(580\) 8.51144 0.353418
\(581\) −1.17728 −0.0488418
\(582\) −17.8615 −0.740383
\(583\) 2.14792 0.0889578
\(584\) −42.1994 −1.74622
\(585\) −11.9266 −0.493103
\(586\) 6.33304 0.261615
\(587\) −18.1973 −0.751083 −0.375541 0.926806i \(-0.622543\pi\)
−0.375541 + 0.926806i \(0.622543\pi\)
\(588\) −18.3459 −0.756574
\(589\) −2.61280 −0.107658
\(590\) 16.4592 0.677613
\(591\) −10.6040 −0.436190
\(592\) −41.4969 −1.70551
\(593\) −27.7814 −1.14084 −0.570422 0.821352i \(-0.693220\pi\)
−0.570422 + 0.821352i \(0.693220\pi\)
\(594\) −5.50184 −0.225743
\(595\) −0.0377104 −0.00154597
\(596\) 80.6577 3.30387
\(597\) −14.6722 −0.600493
\(598\) −8.87681 −0.363000
\(599\) 8.64097 0.353060 0.176530 0.984295i \(-0.443513\pi\)
0.176530 + 0.984295i \(0.443513\pi\)
\(600\) 6.33926 0.258799
\(601\) 5.81863 0.237347 0.118673 0.992933i \(-0.462136\pi\)
0.118673 + 0.992933i \(0.462136\pi\)
\(602\) 0.671857 0.0273828
\(603\) 33.8814 1.37976
\(604\) 19.2559 0.783510
\(605\) 18.6522 0.758320
\(606\) −8.48118 −0.344524
\(607\) 37.7277 1.53132 0.765660 0.643246i \(-0.222413\pi\)
0.765660 + 0.643246i \(0.222413\pi\)
\(608\) 6.27157 0.254346
\(609\) 0.0586758 0.00237766
\(610\) −4.84566 −0.196195
\(611\) 1.24419 0.0503346
\(612\) 2.93524 0.118650
\(613\) 32.7466 1.32262 0.661311 0.750112i \(-0.270001\pi\)
0.661311 + 0.750112i \(0.270001\pi\)
\(614\) −13.0796 −0.527850
\(615\) −7.28246 −0.293657
\(616\) −0.250639 −0.0100985
\(617\) 4.70353 0.189357 0.0946784 0.995508i \(-0.469818\pi\)
0.0946784 + 0.995508i \(0.469818\pi\)
\(618\) 1.60613 0.0646079
\(619\) −14.1488 −0.568687 −0.284344 0.958722i \(-0.591776\pi\)
−0.284344 + 0.958722i \(0.591776\pi\)
\(620\) −3.02019 −0.121294
\(621\) 4.90873 0.196981
\(622\) −69.7871 −2.79821
\(623\) 0.668459 0.0267813
\(624\) −7.72029 −0.309059
\(625\) −11.7952 −0.471806
\(626\) −44.3753 −1.77359
\(627\) 2.48385 0.0991953
\(628\) 25.8706 1.03235
\(629\) 2.49006 0.0992852
\(630\) 0.872898 0.0347771
\(631\) 27.8998 1.11068 0.555338 0.831625i \(-0.312589\pi\)
0.555338 + 0.831625i \(0.312589\pi\)
\(632\) −35.2494 −1.40215
\(633\) −16.3300 −0.649059
\(634\) 11.8571 0.470904
\(635\) −19.8773 −0.788805
\(636\) −9.04735 −0.358751
\(637\) 18.3198 0.725857
\(638\) −1.81683 −0.0719290
\(639\) 1.21409 0.0480287
\(640\) −32.7392 −1.29413
\(641\) 31.6041 1.24829 0.624144 0.781309i \(-0.285448\pi\)
0.624144 + 0.781309i \(0.285448\pi\)
\(642\) 16.2277 0.640455
\(643\) −3.52386 −0.138967 −0.0694837 0.997583i \(-0.522135\pi\)
−0.0694837 + 0.997583i \(0.522135\pi\)
\(644\) 0.436654 0.0172066
\(645\) −3.94144 −0.155194
\(646\) −4.25491 −0.167407
\(647\) −4.82955 −0.189869 −0.0949346 0.995484i \(-0.530264\pi\)
−0.0949346 + 0.995484i \(0.530264\pi\)
\(648\) −28.4265 −1.11670
\(649\) −2.36130 −0.0926893
\(650\) −12.3608 −0.484831
\(651\) −0.0208205 −0.000816019 0
\(652\) 27.6850 1.08423
\(653\) 29.6467 1.16016 0.580082 0.814558i \(-0.303020\pi\)
0.580082 + 0.814558i \(0.303020\pi\)
\(654\) 27.4570 1.07365
\(655\) −15.6920 −0.613137
\(656\) 29.8259 1.16451
\(657\) −21.0846 −0.822588
\(658\) −0.0910616 −0.00354995
\(659\) 39.9981 1.55810 0.779052 0.626959i \(-0.215701\pi\)
0.779052 + 0.626959i \(0.215701\pi\)
\(660\) 2.87114 0.111759
\(661\) −15.1275 −0.588392 −0.294196 0.955745i \(-0.595052\pi\)
−0.294196 + 0.955745i \(0.595052\pi\)
\(662\) −50.5718 −1.96553
\(663\) 0.463263 0.0179916
\(664\) −78.6342 −3.05160
\(665\) −0.850438 −0.0329786
\(666\) −57.6385 −2.23345
\(667\) 1.62097 0.0627644
\(668\) −26.0402 −1.00753
\(669\) −9.04193 −0.349581
\(670\) −56.7724 −2.19331
\(671\) 0.695180 0.0268371
\(672\) 0.0499760 0.00192787
\(673\) −4.50642 −0.173710 −0.0868550 0.996221i \(-0.527682\pi\)
−0.0868550 + 0.996221i \(0.527682\pi\)
\(674\) −0.819323 −0.0315591
\(675\) 6.83533 0.263092
\(676\) −25.1657 −0.967910
\(677\) 0.251554 0.00966799 0.00483400 0.999988i \(-0.498461\pi\)
0.00483400 + 0.999988i \(0.498461\pi\)
\(678\) 16.0788 0.617501
\(679\) −0.877364 −0.0336701
\(680\) −2.51879 −0.0965913
\(681\) −12.8426 −0.492130
\(682\) 0.644683 0.0246862
\(683\) −19.7567 −0.755969 −0.377984 0.925812i \(-0.623383\pi\)
−0.377984 + 0.925812i \(0.623383\pi\)
\(684\) 66.1951 2.53103
\(685\) −23.7464 −0.907304
\(686\) −2.68279 −0.102429
\(687\) 5.60874 0.213987
\(688\) 16.1425 0.615427
\(689\) 9.03447 0.344186
\(690\) −3.81139 −0.145097
\(691\) 38.9366 1.48122 0.740609 0.671936i \(-0.234537\pi\)
0.740609 + 0.671936i \(0.234537\pi\)
\(692\) 35.3023 1.34199
\(693\) −0.125230 −0.00475709
\(694\) −25.1681 −0.955367
\(695\) −5.90253 −0.223896
\(696\) 3.91914 0.148555
\(697\) −1.78973 −0.0677909
\(698\) 68.0258 2.57481
\(699\) −8.64939 −0.327150
\(700\) 0.608033 0.0229815
\(701\) −7.69697 −0.290710 −0.145355 0.989380i \(-0.546432\pi\)
−0.145355 + 0.989380i \(0.546432\pi\)
\(702\) −23.1416 −0.873422
\(703\) 56.1554 2.11794
\(704\) 4.18950 0.157898
\(705\) 0.534212 0.0201196
\(706\) 91.4684 3.44246
\(707\) −0.416599 −0.0156678
\(708\) 9.94615 0.373799
\(709\) −48.2786 −1.81314 −0.906571 0.422053i \(-0.861310\pi\)
−0.906571 + 0.422053i \(0.861310\pi\)
\(710\) −2.03436 −0.0763480
\(711\) −17.6121 −0.660505
\(712\) 44.6485 1.67327
\(713\) −0.575185 −0.0215409
\(714\) −0.0339059 −0.00126890
\(715\) −2.86705 −0.107222
\(716\) 65.2587 2.43883
\(717\) 3.07615 0.114881
\(718\) 56.8128 2.12024
\(719\) −27.2538 −1.01639 −0.508197 0.861241i \(-0.669688\pi\)
−0.508197 + 0.861241i \(0.669688\pi\)
\(720\) 20.9728 0.781612
\(721\) 0.0788935 0.00293815
\(722\) −49.0320 −1.82478
\(723\) −15.2956 −0.568851
\(724\) 70.3212 2.61347
\(725\) 2.25718 0.0838296
\(726\) 16.7705 0.622411
\(727\) 19.3640 0.718169 0.359085 0.933305i \(-0.383089\pi\)
0.359085 + 0.933305i \(0.383089\pi\)
\(728\) −1.05422 −0.0390722
\(729\) −7.33602 −0.271704
\(730\) 35.3298 1.30761
\(731\) −0.968645 −0.0358266
\(732\) −2.92820 −0.108229
\(733\) −32.4867 −1.19992 −0.599962 0.800029i \(-0.704817\pi\)
−0.599962 + 0.800029i \(0.704817\pi\)
\(734\) −43.4362 −1.60326
\(735\) 7.86588 0.290137
\(736\) 1.38063 0.0508908
\(737\) 8.14482 0.300018
\(738\) 41.4277 1.52497
\(739\) 41.9311 1.54246 0.771230 0.636557i \(-0.219642\pi\)
0.771230 + 0.636557i \(0.219642\pi\)
\(740\) 64.9113 2.38619
\(741\) 10.4474 0.383796
\(742\) −0.661227 −0.0242744
\(743\) 19.5219 0.716189 0.358095 0.933685i \(-0.383427\pi\)
0.358095 + 0.933685i \(0.383427\pi\)
\(744\) −1.39066 −0.0509842
\(745\) −34.5822 −1.26700
\(746\) −1.32823 −0.0486300
\(747\) −39.2890 −1.43751
\(748\) 0.705608 0.0257996
\(749\) 0.797109 0.0291257
\(750\) −19.1952 −0.700909
\(751\) −29.2466 −1.06722 −0.533612 0.845729i \(-0.679166\pi\)
−0.533612 + 0.845729i \(0.679166\pi\)
\(752\) −2.18791 −0.0797848
\(753\) 14.6428 0.533614
\(754\) −7.64186 −0.278300
\(755\) −8.25601 −0.300467
\(756\) 1.13834 0.0414011
\(757\) −5.96924 −0.216956 −0.108478 0.994099i \(-0.534598\pi\)
−0.108478 + 0.994099i \(0.534598\pi\)
\(758\) 58.9544 2.14132
\(759\) 0.546798 0.0198475
\(760\) −56.8034 −2.06048
\(761\) −51.0740 −1.85143 −0.925716 0.378218i \(-0.876537\pi\)
−0.925716 + 0.378218i \(0.876537\pi\)
\(762\) −17.8719 −0.647432
\(763\) 1.34870 0.0488261
\(764\) −96.0942 −3.47656
\(765\) −1.25849 −0.0455010
\(766\) −1.85011 −0.0668471
\(767\) −9.93199 −0.358623
\(768\) −20.8268 −0.751524
\(769\) −6.24105 −0.225058 −0.112529 0.993648i \(-0.535895\pi\)
−0.112529 + 0.993648i \(0.535895\pi\)
\(770\) 0.209838 0.00756202
\(771\) −14.4941 −0.521993
\(772\) −36.5147 −1.31419
\(773\) −12.3269 −0.443369 −0.221684 0.975118i \(-0.571155\pi\)
−0.221684 + 0.975118i \(0.571155\pi\)
\(774\) 22.4216 0.805929
\(775\) −0.800936 −0.0287705
\(776\) −58.6019 −2.10369
\(777\) 0.447483 0.0160534
\(778\) 75.5887 2.70999
\(779\) −40.3617 −1.44611
\(780\) 12.0764 0.432405
\(781\) 0.291858 0.0104435
\(782\) −0.936683 −0.0334957
\(783\) 4.22583 0.151019
\(784\) −32.2154 −1.15055
\(785\) −11.0921 −0.395894
\(786\) −14.1089 −0.503248
\(787\) −8.75601 −0.312118 −0.156059 0.987748i \(-0.549879\pi\)
−0.156059 + 0.987748i \(0.549879\pi\)
\(788\) −67.9344 −2.42006
\(789\) 17.5144 0.623531
\(790\) 29.5112 1.04996
\(791\) 0.789795 0.0280819
\(792\) −8.36449 −0.297219
\(793\) 2.92403 0.103835
\(794\) −74.2526 −2.63513
\(795\) 3.87908 0.137577
\(796\) −93.9973 −3.33165
\(797\) 26.6158 0.942781 0.471390 0.881925i \(-0.343752\pi\)
0.471390 + 0.881925i \(0.343752\pi\)
\(798\) −0.764641 −0.0270680
\(799\) 0.131287 0.00464461
\(800\) 1.92251 0.0679710
\(801\) 22.3083 0.788223
\(802\) −40.1254 −1.41688
\(803\) −5.06856 −0.178866
\(804\) −34.3072 −1.20992
\(805\) −0.187217 −0.00659852
\(806\) 2.71163 0.0955131
\(807\) 12.5336 0.441205
\(808\) −27.8259 −0.978913
\(809\) 21.1454 0.743433 0.371717 0.928346i \(-0.378769\pi\)
0.371717 + 0.928346i \(0.378769\pi\)
\(810\) 23.7990 0.836211
\(811\) −56.2823 −1.97634 −0.988169 0.153372i \(-0.950987\pi\)
−0.988169 + 0.153372i \(0.950987\pi\)
\(812\) 0.375906 0.0131917
\(813\) −6.44335 −0.225978
\(814\) −13.8558 −0.485646
\(815\) −11.8700 −0.415789
\(816\) −0.814647 −0.0285183
\(817\) −21.8447 −0.764250
\(818\) −31.9508 −1.11713
\(819\) −0.526735 −0.0184056
\(820\) −46.6551 −1.62927
\(821\) 7.43052 0.259327 0.129663 0.991558i \(-0.458610\pi\)
0.129663 + 0.991558i \(0.458610\pi\)
\(822\) −21.3507 −0.744693
\(823\) 51.3661 1.79051 0.895255 0.445553i \(-0.146993\pi\)
0.895255 + 0.445553i \(0.146993\pi\)
\(824\) 5.26954 0.183573
\(825\) 0.761407 0.0265088
\(826\) 0.726916 0.0252927
\(827\) 1.33372 0.0463779 0.0231890 0.999731i \(-0.492618\pi\)
0.0231890 + 0.999731i \(0.492618\pi\)
\(828\) 14.5723 0.506422
\(829\) 43.1032 1.49704 0.748519 0.663114i \(-0.230765\pi\)
0.748519 + 0.663114i \(0.230765\pi\)
\(830\) 65.8334 2.28511
\(831\) 19.5350 0.677660
\(832\) 17.6217 0.610922
\(833\) 1.93311 0.0669784
\(834\) −5.30705 −0.183768
\(835\) 11.1648 0.386374
\(836\) 15.9128 0.550354
\(837\) −1.49949 −0.0518299
\(838\) −95.2616 −3.29076
\(839\) −16.4811 −0.568990 −0.284495 0.958677i \(-0.591826\pi\)
−0.284495 + 0.958677i \(0.591826\pi\)
\(840\) −0.452647 −0.0156178
\(841\) −27.6045 −0.951881
\(842\) −56.0968 −1.93322
\(843\) −10.4854 −0.361137
\(844\) −104.618 −3.60110
\(845\) 10.7899 0.371182
\(846\) −3.03897 −0.104482
\(847\) 0.823772 0.0283051
\(848\) −15.8871 −0.545565
\(849\) 20.4255 0.701001
\(850\) −1.30432 −0.0447377
\(851\) 12.3621 0.423769
\(852\) −1.22935 −0.0421167
\(853\) −32.0353 −1.09687 −0.548434 0.836194i \(-0.684776\pi\)
−0.548434 + 0.836194i \(0.684776\pi\)
\(854\) −0.214008 −0.00732320
\(855\) −28.3814 −0.970622
\(856\) 53.2414 1.81975
\(857\) 53.7988 1.83773 0.918867 0.394568i \(-0.129106\pi\)
0.918867 + 0.394568i \(0.129106\pi\)
\(858\) −2.57780 −0.0880048
\(859\) −36.2488 −1.23679 −0.618396 0.785866i \(-0.712217\pi\)
−0.618396 + 0.785866i \(0.712217\pi\)
\(860\) −25.2508 −0.861045
\(861\) −0.321629 −0.0109611
\(862\) −30.6263 −1.04314
\(863\) 23.8972 0.813472 0.406736 0.913546i \(-0.366667\pi\)
0.406736 + 0.913546i \(0.366667\pi\)
\(864\) 3.59927 0.122450
\(865\) −15.1360 −0.514639
\(866\) −72.1791 −2.45275
\(867\) −10.8291 −0.367774
\(868\) −0.133386 −0.00452743
\(869\) −4.23380 −0.143622
\(870\) −3.28114 −0.111241
\(871\) 34.2583 1.16080
\(872\) 90.0837 3.05062
\(873\) −29.2800 −0.990977
\(874\) −21.1239 −0.714528
\(875\) −0.942874 −0.0318750
\(876\) 21.3495 0.721333
\(877\) −12.9459 −0.437153 −0.218576 0.975820i \(-0.570141\pi\)
−0.218576 + 0.975820i \(0.570141\pi\)
\(878\) 14.1210 0.476562
\(879\) −1.64084 −0.0553443
\(880\) 5.04170 0.169956
\(881\) −16.4095 −0.552851 −0.276426 0.961035i \(-0.589150\pi\)
−0.276426 + 0.961035i \(0.589150\pi\)
\(882\) −44.7466 −1.50670
\(883\) 34.4101 1.15799 0.578995 0.815331i \(-0.303445\pi\)
0.578995 + 0.815331i \(0.303445\pi\)
\(884\) 2.96789 0.0998210
\(885\) −4.26444 −0.143348
\(886\) −53.8125 −1.80787
\(887\) −14.4982 −0.486801 −0.243401 0.969926i \(-0.578263\pi\)
−0.243401 + 0.969926i \(0.578263\pi\)
\(888\) 29.8888 1.00300
\(889\) −0.877876 −0.0294430
\(890\) −37.3802 −1.25299
\(891\) −3.41431 −0.114384
\(892\) −57.9271 −1.93954
\(893\) 2.96077 0.0990785
\(894\) −31.0934 −1.03992
\(895\) −27.9799 −0.935264
\(896\) −1.44592 −0.0483049
\(897\) 2.29991 0.0767919
\(898\) −31.4115 −1.04822
\(899\) −0.495165 −0.0165147
\(900\) 20.2917 0.676389
\(901\) 0.953320 0.0317597
\(902\) 9.95888 0.331594
\(903\) −0.174073 −0.00579279
\(904\) 52.7529 1.75453
\(905\) −30.1505 −1.00224
\(906\) −7.42310 −0.246616
\(907\) −1.14545 −0.0380340 −0.0190170 0.999819i \(-0.506054\pi\)
−0.0190170 + 0.999819i \(0.506054\pi\)
\(908\) −82.2762 −2.73043
\(909\) −13.9030 −0.461133
\(910\) 0.882608 0.0292582
\(911\) −42.1429 −1.39626 −0.698128 0.715973i \(-0.745983\pi\)
−0.698128 + 0.715973i \(0.745983\pi\)
\(912\) −18.3718 −0.608351
\(913\) −9.44474 −0.312575
\(914\) 38.8523 1.28512
\(915\) 1.25547 0.0415047
\(916\) 35.9324 1.18724
\(917\) −0.693035 −0.0228860
\(918\) −2.44190 −0.0805948
\(919\) −6.72125 −0.221714 −0.110857 0.993836i \(-0.535359\pi\)
−0.110857 + 0.993836i \(0.535359\pi\)
\(920\) −12.5048 −0.412271
\(921\) 3.38883 0.111666
\(922\) 13.2236 0.435495
\(923\) 1.22760 0.0404068
\(924\) 0.126803 0.00417152
\(925\) 17.2141 0.565996
\(926\) 0.978014 0.0321395
\(927\) 2.63289 0.0864753
\(928\) 1.18856 0.0390163
\(929\) −55.5226 −1.82164 −0.910818 0.412808i \(-0.864548\pi\)
−0.910818 + 0.412808i \(0.864548\pi\)
\(930\) 1.16428 0.0381782
\(931\) 43.5952 1.42878
\(932\) −55.4123 −1.81509
\(933\) 18.0813 0.591955
\(934\) −96.4533 −3.15605
\(935\) −0.302532 −0.00989385
\(936\) −35.1823 −1.14997
\(937\) 1.39422 0.0455471 0.0227735 0.999741i \(-0.492750\pi\)
0.0227735 + 0.999741i \(0.492750\pi\)
\(938\) −2.50734 −0.0818677
\(939\) 11.4973 0.375200
\(940\) 3.42242 0.111627
\(941\) −10.6883 −0.348428 −0.174214 0.984708i \(-0.555739\pi\)
−0.174214 + 0.984708i \(0.555739\pi\)
\(942\) −9.97307 −0.324940
\(943\) −8.88530 −0.289345
\(944\) 17.4654 0.568450
\(945\) −0.488068 −0.0158769
\(946\) 5.38998 0.175243
\(947\) −15.8304 −0.514418 −0.257209 0.966356i \(-0.582803\pi\)
−0.257209 + 0.966356i \(0.582803\pi\)
\(948\) 17.8334 0.579202
\(949\) −21.3191 −0.692048
\(950\) −29.4147 −0.954340
\(951\) −3.07207 −0.0996188
\(952\) −0.111242 −0.00360538
\(953\) −30.8070 −0.997937 −0.498968 0.866620i \(-0.666288\pi\)
−0.498968 + 0.866620i \(0.666288\pi\)
\(954\) −22.0669 −0.714442
\(955\) 41.2007 1.33322
\(956\) 19.7073 0.637380
\(957\) 0.470727 0.0152164
\(958\) 20.0342 0.647276
\(959\) −1.04876 −0.0338661
\(960\) 7.56612 0.244195
\(961\) −30.8243 −0.994332
\(962\) −58.2796 −1.87901
\(963\) 26.6016 0.857226
\(964\) −97.9915 −3.15609
\(965\) 15.6558 0.503978
\(966\) −0.168329 −0.00541591
\(967\) −3.16907 −0.101911 −0.0509553 0.998701i \(-0.516227\pi\)
−0.0509553 + 0.998701i \(0.516227\pi\)
\(968\) 55.0223 1.76848
\(969\) 1.10242 0.0354147
\(970\) 49.0621 1.57529
\(971\) −30.1645 −0.968024 −0.484012 0.875061i \(-0.660821\pi\)
−0.484012 + 0.875061i \(0.660821\pi\)
\(972\) 58.3754 1.87239
\(973\) −0.260684 −0.00835716
\(974\) −69.7631 −2.23535
\(975\) 3.20259 0.102565
\(976\) −5.14190 −0.164588
\(977\) −6.80390 −0.217676 −0.108838 0.994060i \(-0.534713\pi\)
−0.108838 + 0.994060i \(0.534713\pi\)
\(978\) −10.6725 −0.341269
\(979\) 5.36272 0.171393
\(980\) 50.3927 1.60974
\(981\) 45.0096 1.43705
\(982\) 13.2617 0.423197
\(983\) −11.5281 −0.367690 −0.183845 0.982955i \(-0.558854\pi\)
−0.183845 + 0.982955i \(0.558854\pi\)
\(984\) −21.4826 −0.684840
\(985\) 29.1271 0.928066
\(986\) −0.806371 −0.0256801
\(987\) 0.0235934 0.000750985 0
\(988\) 66.9314 2.12937
\(989\) −4.80893 −0.152915
\(990\) 7.00283 0.222565
\(991\) −42.4652 −1.34895 −0.674476 0.738297i \(-0.735630\pi\)
−0.674476 + 0.738297i \(0.735630\pi\)
\(992\) −0.421747 −0.0133905
\(993\) 13.1028 0.415804
\(994\) −0.0898470 −0.00284977
\(995\) 40.3017 1.27765
\(996\) 39.7826 1.26056
\(997\) −45.0388 −1.42639 −0.713197 0.700964i \(-0.752753\pi\)
−0.713197 + 0.700964i \(0.752753\pi\)
\(998\) 0.610261 0.0193175
\(999\) 32.2277 1.01964
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 4003.2.a.c.1.12 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.12 179 1.1 even 1 trivial