Properties

Label 6017.2.a.f.1.11
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
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 1.11
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.47328 q^{2} -1.34586 q^{3} +4.11710 q^{4} +2.94670 q^{5} +3.32869 q^{6} -2.85130 q^{7} -5.23618 q^{8} -1.18866 q^{9} +O(q^{10})\) \(q-2.47328 q^{2} -1.34586 q^{3} +4.11710 q^{4} +2.94670 q^{5} +3.32869 q^{6} -2.85130 q^{7} -5.23618 q^{8} -1.18866 q^{9} -7.28801 q^{10} -1.00000 q^{11} -5.54105 q^{12} -1.72879 q^{13} +7.05206 q^{14} -3.96585 q^{15} +4.71631 q^{16} -6.02426 q^{17} +2.93988 q^{18} -4.89251 q^{19} +12.1319 q^{20} +3.83746 q^{21} +2.47328 q^{22} +3.06664 q^{23} +7.04717 q^{24} +3.68306 q^{25} +4.27577 q^{26} +5.63735 q^{27} -11.7391 q^{28} -9.51723 q^{29} +9.80866 q^{30} -2.12362 q^{31} -1.19240 q^{32} +1.34586 q^{33} +14.8997 q^{34} -8.40194 q^{35} -4.89382 q^{36} -2.03716 q^{37} +12.1005 q^{38} +2.32671 q^{39} -15.4295 q^{40} -2.59459 q^{41} -9.49109 q^{42} -10.3932 q^{43} -4.11710 q^{44} -3.50262 q^{45} -7.58466 q^{46} -4.16877 q^{47} -6.34750 q^{48} +1.12992 q^{49} -9.10923 q^{50} +8.10782 q^{51} -7.11759 q^{52} +10.0709 q^{53} -13.9427 q^{54} -2.94670 q^{55} +14.9299 q^{56} +6.58464 q^{57} +23.5388 q^{58} +4.62139 q^{59} -16.3278 q^{60} -14.6861 q^{61} +5.25230 q^{62} +3.38922 q^{63} -6.48349 q^{64} -5.09422 q^{65} -3.32869 q^{66} -7.80053 q^{67} -24.8025 q^{68} -4.12728 q^{69} +20.7803 q^{70} -16.5584 q^{71} +6.22402 q^{72} +10.1702 q^{73} +5.03845 q^{74} -4.95689 q^{75} -20.1429 q^{76} +2.85130 q^{77} -5.75459 q^{78} +8.61927 q^{79} +13.8976 q^{80} -4.02112 q^{81} +6.41714 q^{82} -8.70178 q^{83} +15.7992 q^{84} -17.7517 q^{85} +25.7053 q^{86} +12.8089 q^{87} +5.23618 q^{88} +7.51142 q^{89} +8.66295 q^{90} +4.92929 q^{91} +12.6257 q^{92} +2.85810 q^{93} +10.3105 q^{94} -14.4168 q^{95} +1.60481 q^{96} -3.08062 q^{97} -2.79461 q^{98} +1.18866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47328 −1.74887 −0.874436 0.485142i \(-0.838768\pi\)
−0.874436 + 0.485142i \(0.838768\pi\)
\(3\) −1.34586 −0.777033 −0.388517 0.921442i \(-0.627012\pi\)
−0.388517 + 0.921442i \(0.627012\pi\)
\(4\) 4.11710 2.05855
\(5\) 2.94670 1.31781 0.658903 0.752228i \(-0.271021\pi\)
0.658903 + 0.752228i \(0.271021\pi\)
\(6\) 3.32869 1.35893
\(7\) −2.85130 −1.07769 −0.538845 0.842405i \(-0.681139\pi\)
−0.538845 + 0.842405i \(0.681139\pi\)
\(8\) −5.23618 −1.85127
\(9\) −1.18866 −0.396219
\(10\) −7.28801 −2.30467
\(11\) −1.00000 −0.301511
\(12\) −5.54105 −1.59956
\(13\) −1.72879 −0.479479 −0.239740 0.970837i \(-0.577062\pi\)
−0.239740 + 0.970837i \(0.577062\pi\)
\(14\) 7.05206 1.88474
\(15\) −3.96585 −1.02398
\(16\) 4.71631 1.17908
\(17\) −6.02426 −1.46110 −0.730549 0.682861i \(-0.760736\pi\)
−0.730549 + 0.682861i \(0.760736\pi\)
\(18\) 2.93988 0.692936
\(19\) −4.89251 −1.12242 −0.561209 0.827674i \(-0.689664\pi\)
−0.561209 + 0.827674i \(0.689664\pi\)
\(20\) 12.1319 2.71277
\(21\) 3.83746 0.837402
\(22\) 2.47328 0.527304
\(23\) 3.06664 0.639439 0.319720 0.947512i \(-0.396411\pi\)
0.319720 + 0.947512i \(0.396411\pi\)
\(24\) 7.04717 1.43850
\(25\) 3.68306 0.736612
\(26\) 4.27577 0.838547
\(27\) 5.63735 1.08491
\(28\) −11.7391 −2.21848
\(29\) −9.51723 −1.76731 −0.883653 0.468143i \(-0.844923\pi\)
−0.883653 + 0.468143i \(0.844923\pi\)
\(30\) 9.80866 1.79081
\(31\) −2.12362 −0.381413 −0.190707 0.981647i \(-0.561078\pi\)
−0.190707 + 0.981647i \(0.561078\pi\)
\(32\) −1.19240 −0.210789
\(33\) 1.34586 0.234284
\(34\) 14.8997 2.55527
\(35\) −8.40194 −1.42019
\(36\) −4.89382 −0.815637
\(37\) −2.03716 −0.334906 −0.167453 0.985880i \(-0.553554\pi\)
−0.167453 + 0.985880i \(0.553554\pi\)
\(38\) 12.1005 1.96296
\(39\) 2.32671 0.372571
\(40\) −15.4295 −2.43961
\(41\) −2.59459 −0.405207 −0.202603 0.979261i \(-0.564940\pi\)
−0.202603 + 0.979261i \(0.564940\pi\)
\(42\) −9.49109 −1.46451
\(43\) −10.3932 −1.58495 −0.792476 0.609904i \(-0.791208\pi\)
−0.792476 + 0.609904i \(0.791208\pi\)
\(44\) −4.11710 −0.620676
\(45\) −3.50262 −0.522140
\(46\) −7.58466 −1.11830
\(47\) −4.16877 −0.608078 −0.304039 0.952660i \(-0.598335\pi\)
−0.304039 + 0.952660i \(0.598335\pi\)
\(48\) −6.34750 −0.916183
\(49\) 1.12992 0.161417
\(50\) −9.10923 −1.28824
\(51\) 8.10782 1.13532
\(52\) −7.11759 −0.987032
\(53\) 10.0709 1.38335 0.691675 0.722209i \(-0.256873\pi\)
0.691675 + 0.722209i \(0.256873\pi\)
\(54\) −13.9427 −1.89737
\(55\) −2.94670 −0.397333
\(56\) 14.9299 1.99509
\(57\) 6.58464 0.872156
\(58\) 23.5388 3.09079
\(59\) 4.62139 0.601653 0.300827 0.953679i \(-0.402737\pi\)
0.300827 + 0.953679i \(0.402737\pi\)
\(60\) −16.3278 −2.10791
\(61\) −14.6861 −1.88037 −0.940183 0.340670i \(-0.889346\pi\)
−0.940183 + 0.340670i \(0.889346\pi\)
\(62\) 5.25230 0.667043
\(63\) 3.38922 0.427002
\(64\) −6.48349 −0.810436
\(65\) −5.09422 −0.631861
\(66\) −3.32869 −0.409733
\(67\) −7.80053 −0.952987 −0.476493 0.879178i \(-0.658092\pi\)
−0.476493 + 0.879178i \(0.658092\pi\)
\(68\) −24.8025 −3.00774
\(69\) −4.12728 −0.496866
\(70\) 20.7803 2.48372
\(71\) −16.5584 −1.96512 −0.982560 0.185946i \(-0.940465\pi\)
−0.982560 + 0.185946i \(0.940465\pi\)
\(72\) 6.22402 0.733508
\(73\) 10.1702 1.19033 0.595164 0.803605i \(-0.297087\pi\)
0.595164 + 0.803605i \(0.297087\pi\)
\(74\) 5.03845 0.585708
\(75\) −4.95689 −0.572372
\(76\) −20.1429 −2.31055
\(77\) 2.85130 0.324936
\(78\) −5.75459 −0.651579
\(79\) 8.61927 0.969744 0.484872 0.874585i \(-0.338866\pi\)
0.484872 + 0.874585i \(0.338866\pi\)
\(80\) 13.8976 1.55380
\(81\) −4.02112 −0.446791
\(82\) 6.41714 0.708655
\(83\) −8.70178 −0.955144 −0.477572 0.878593i \(-0.658483\pi\)
−0.477572 + 0.878593i \(0.658483\pi\)
\(84\) 15.7992 1.72383
\(85\) −17.7517 −1.92544
\(86\) 25.7053 2.77188
\(87\) 12.8089 1.37326
\(88\) 5.23618 0.558178
\(89\) 7.51142 0.796208 0.398104 0.917340i \(-0.369668\pi\)
0.398104 + 0.917340i \(0.369668\pi\)
\(90\) 8.66295 0.913156
\(91\) 4.92929 0.516730
\(92\) 12.6257 1.31632
\(93\) 2.85810 0.296371
\(94\) 10.3105 1.06345
\(95\) −14.4168 −1.47913
\(96\) 1.60481 0.163790
\(97\) −3.08062 −0.312790 −0.156395 0.987695i \(-0.549987\pi\)
−0.156395 + 0.987695i \(0.549987\pi\)
\(98\) −2.79461 −0.282298
\(99\) 1.18866 0.119465
\(100\) 15.1635 1.51635
\(101\) −9.37227 −0.932576 −0.466288 0.884633i \(-0.654409\pi\)
−0.466288 + 0.884633i \(0.654409\pi\)
\(102\) −20.0529 −1.98553
\(103\) 4.16480 0.410370 0.205185 0.978723i \(-0.434220\pi\)
0.205185 + 0.978723i \(0.434220\pi\)
\(104\) 9.05223 0.887645
\(105\) 11.3078 1.10353
\(106\) −24.9082 −2.41930
\(107\) 9.72118 0.939782 0.469891 0.882724i \(-0.344293\pi\)
0.469891 + 0.882724i \(0.344293\pi\)
\(108\) 23.2095 2.23334
\(109\) −2.01684 −0.193178 −0.0965891 0.995324i \(-0.530793\pi\)
−0.0965891 + 0.995324i \(0.530793\pi\)
\(110\) 7.28801 0.694885
\(111\) 2.74173 0.260233
\(112\) −13.4476 −1.27068
\(113\) −0.484566 −0.0455842 −0.0227921 0.999740i \(-0.507256\pi\)
−0.0227921 + 0.999740i \(0.507256\pi\)
\(114\) −16.2856 −1.52529
\(115\) 9.03649 0.842657
\(116\) −39.1834 −3.63809
\(117\) 2.05494 0.189979
\(118\) −11.4300 −1.05221
\(119\) 17.1770 1.57461
\(120\) 20.7659 1.89566
\(121\) 1.00000 0.0909091
\(122\) 36.3229 3.28852
\(123\) 3.49196 0.314859
\(124\) −8.74315 −0.785158
\(125\) −3.88063 −0.347094
\(126\) −8.38248 −0.746771
\(127\) 19.5778 1.73725 0.868624 0.495472i \(-0.165005\pi\)
0.868624 + 0.495472i \(0.165005\pi\)
\(128\) 18.4203 1.62814
\(129\) 13.9878 1.23156
\(130\) 12.5994 1.10504
\(131\) 16.6115 1.45135 0.725677 0.688036i \(-0.241527\pi\)
0.725677 + 0.688036i \(0.241527\pi\)
\(132\) 5.54105 0.482286
\(133\) 13.9500 1.20962
\(134\) 19.2929 1.66665
\(135\) 16.6116 1.42970
\(136\) 31.5441 2.70488
\(137\) 3.70035 0.316142 0.158071 0.987428i \(-0.449472\pi\)
0.158071 + 0.987428i \(0.449472\pi\)
\(138\) 10.2079 0.868954
\(139\) 12.1430 1.02996 0.514978 0.857203i \(-0.327800\pi\)
0.514978 + 0.857203i \(0.327800\pi\)
\(140\) −34.5916 −2.92353
\(141\) 5.61059 0.472497
\(142\) 40.9535 3.43674
\(143\) 1.72879 0.144568
\(144\) −5.60608 −0.467174
\(145\) −28.0445 −2.32897
\(146\) −25.1536 −2.08173
\(147\) −1.52072 −0.125427
\(148\) −8.38718 −0.689422
\(149\) −9.58037 −0.784854 −0.392427 0.919783i \(-0.628365\pi\)
−0.392427 + 0.919783i \(0.628365\pi\)
\(150\) 12.2598 1.00101
\(151\) 6.00145 0.488391 0.244196 0.969726i \(-0.421476\pi\)
0.244196 + 0.969726i \(0.421476\pi\)
\(152\) 25.6180 2.07790
\(153\) 7.16078 0.578915
\(154\) −7.05206 −0.568271
\(155\) −6.25768 −0.502629
\(156\) 9.57929 0.766957
\(157\) 2.85994 0.228248 0.114124 0.993467i \(-0.463594\pi\)
0.114124 + 0.993467i \(0.463594\pi\)
\(158\) −21.3179 −1.69596
\(159\) −13.5541 −1.07491
\(160\) −3.51365 −0.277779
\(161\) −8.74392 −0.689118
\(162\) 9.94534 0.781380
\(163\) 4.96638 0.388997 0.194498 0.980903i \(-0.437692\pi\)
0.194498 + 0.980903i \(0.437692\pi\)
\(164\) −10.6822 −0.834139
\(165\) 3.96585 0.308741
\(166\) 21.5219 1.67042
\(167\) 24.2458 1.87619 0.938097 0.346372i \(-0.112587\pi\)
0.938097 + 0.346372i \(0.112587\pi\)
\(168\) −20.0936 −1.55025
\(169\) −10.0113 −0.770100
\(170\) 43.9049 3.36735
\(171\) 5.81552 0.444724
\(172\) −42.7899 −3.26270
\(173\) −14.9495 −1.13659 −0.568295 0.822825i \(-0.692397\pi\)
−0.568295 + 0.822825i \(0.692397\pi\)
\(174\) −31.6799 −2.40165
\(175\) −10.5015 −0.793840
\(176\) −4.71631 −0.355506
\(177\) −6.21975 −0.467505
\(178\) −18.5778 −1.39247
\(179\) −19.8200 −1.48141 −0.740707 0.671828i \(-0.765509\pi\)
−0.740707 + 0.671828i \(0.765509\pi\)
\(180\) −14.4206 −1.07485
\(181\) −22.3787 −1.66340 −0.831698 0.555229i \(-0.812631\pi\)
−0.831698 + 0.555229i \(0.812631\pi\)
\(182\) −12.1915 −0.903695
\(183\) 19.7655 1.46111
\(184\) −16.0575 −1.18377
\(185\) −6.00290 −0.441342
\(186\) −7.06886 −0.518314
\(187\) 6.02426 0.440537
\(188\) −17.1633 −1.25176
\(189\) −16.0738 −1.16920
\(190\) 35.6567 2.58681
\(191\) 24.5052 1.77313 0.886567 0.462600i \(-0.153083\pi\)
0.886567 + 0.462600i \(0.153083\pi\)
\(192\) 8.72588 0.629736
\(193\) −11.3225 −0.815009 −0.407504 0.913203i \(-0.633601\pi\)
−0.407504 + 0.913203i \(0.633601\pi\)
\(194\) 7.61923 0.547029
\(195\) 6.85612 0.490977
\(196\) 4.65200 0.332286
\(197\) 12.6698 0.902686 0.451343 0.892351i \(-0.350945\pi\)
0.451343 + 0.892351i \(0.350945\pi\)
\(198\) −2.93988 −0.208928
\(199\) 5.92740 0.420182 0.210091 0.977682i \(-0.432624\pi\)
0.210091 + 0.977682i \(0.432624\pi\)
\(200\) −19.2852 −1.36367
\(201\) 10.4984 0.740502
\(202\) 23.1802 1.63095
\(203\) 27.1365 1.90461
\(204\) 33.3807 2.33712
\(205\) −7.64549 −0.533984
\(206\) −10.3007 −0.717684
\(207\) −3.64519 −0.253358
\(208\) −8.15350 −0.565344
\(209\) 4.89251 0.338422
\(210\) −27.9674 −1.92994
\(211\) −2.85902 −0.196823 −0.0984116 0.995146i \(-0.531376\pi\)
−0.0984116 + 0.995146i \(0.531376\pi\)
\(212\) 41.4631 2.84769
\(213\) 22.2853 1.52696
\(214\) −24.0432 −1.64356
\(215\) −30.6257 −2.08866
\(216\) −29.5182 −2.00846
\(217\) 6.05508 0.411045
\(218\) 4.98820 0.337844
\(219\) −13.6876 −0.924924
\(220\) −12.1319 −0.817931
\(221\) 10.4147 0.700566
\(222\) −6.78106 −0.455115
\(223\) −11.6398 −0.779460 −0.389730 0.920929i \(-0.627432\pi\)
−0.389730 + 0.920929i \(0.627432\pi\)
\(224\) 3.39990 0.227165
\(225\) −4.37790 −0.291860
\(226\) 1.19847 0.0797208
\(227\) −9.44804 −0.627088 −0.313544 0.949574i \(-0.601516\pi\)
−0.313544 + 0.949574i \(0.601516\pi\)
\(228\) 27.1096 1.79538
\(229\) 10.0854 0.666459 0.333230 0.942846i \(-0.391862\pi\)
0.333230 + 0.942846i \(0.391862\pi\)
\(230\) −22.3497 −1.47370
\(231\) −3.83746 −0.252486
\(232\) 49.8339 3.27176
\(233\) −25.7384 −1.68618 −0.843091 0.537772i \(-0.819266\pi\)
−0.843091 + 0.537772i \(0.819266\pi\)
\(234\) −5.08243 −0.332249
\(235\) −12.2841 −0.801329
\(236\) 19.0267 1.23853
\(237\) −11.6003 −0.753524
\(238\) −42.4834 −2.75379
\(239\) 1.51678 0.0981123 0.0490561 0.998796i \(-0.484379\pi\)
0.0490561 + 0.998796i \(0.484379\pi\)
\(240\) −18.7042 −1.20735
\(241\) 11.0955 0.714723 0.357361 0.933966i \(-0.383676\pi\)
0.357361 + 0.933966i \(0.383676\pi\)
\(242\) −2.47328 −0.158988
\(243\) −11.5002 −0.737737
\(244\) −60.4643 −3.87083
\(245\) 3.32954 0.212717
\(246\) −8.63658 −0.550648
\(247\) 8.45810 0.538176
\(248\) 11.1196 0.706098
\(249\) 11.7114 0.742179
\(250\) 9.59787 0.607022
\(251\) −26.1803 −1.65248 −0.826242 0.563316i \(-0.809525\pi\)
−0.826242 + 0.563316i \(0.809525\pi\)
\(252\) 13.9538 0.879005
\(253\) −3.06664 −0.192798
\(254\) −48.4213 −3.03822
\(255\) 23.8913 1.49613
\(256\) −32.5915 −2.03697
\(257\) −9.94390 −0.620284 −0.310142 0.950690i \(-0.600377\pi\)
−0.310142 + 0.950690i \(0.600377\pi\)
\(258\) −34.5958 −2.15384
\(259\) 5.80855 0.360926
\(260\) −20.9734 −1.30072
\(261\) 11.3127 0.700241
\(262\) −41.0849 −2.53823
\(263\) 11.8030 0.727805 0.363903 0.931437i \(-0.381444\pi\)
0.363903 + 0.931437i \(0.381444\pi\)
\(264\) −7.04717 −0.433723
\(265\) 29.6761 1.82299
\(266\) −34.5023 −2.11547
\(267\) −10.1093 −0.618680
\(268\) −32.1156 −1.96177
\(269\) −12.3852 −0.755138 −0.377569 0.925982i \(-0.623240\pi\)
−0.377569 + 0.925982i \(0.623240\pi\)
\(270\) −41.0851 −2.50036
\(271\) 20.1293 1.22277 0.611383 0.791335i \(-0.290614\pi\)
0.611383 + 0.791335i \(0.290614\pi\)
\(272\) −28.4123 −1.72275
\(273\) −6.63414 −0.401517
\(274\) −9.15199 −0.552892
\(275\) −3.68306 −0.222097
\(276\) −16.9924 −1.02282
\(277\) −8.40085 −0.504758 −0.252379 0.967628i \(-0.581213\pi\)
−0.252379 + 0.967628i \(0.581213\pi\)
\(278\) −30.0330 −1.80126
\(279\) 2.52426 0.151123
\(280\) 43.9940 2.62915
\(281\) −11.0582 −0.659675 −0.329838 0.944038i \(-0.606994\pi\)
−0.329838 + 0.944038i \(0.606994\pi\)
\(282\) −13.8765 −0.826336
\(283\) −22.2760 −1.32417 −0.662087 0.749427i \(-0.730329\pi\)
−0.662087 + 0.749427i \(0.730329\pi\)
\(284\) −68.1726 −4.04530
\(285\) 19.4030 1.14933
\(286\) −4.27577 −0.252832
\(287\) 7.39796 0.436688
\(288\) 1.41736 0.0835186
\(289\) 19.2917 1.13481
\(290\) 69.3617 4.07306
\(291\) 4.14609 0.243048
\(292\) 41.8716 2.45035
\(293\) 27.4214 1.60198 0.800989 0.598680i \(-0.204308\pi\)
0.800989 + 0.598680i \(0.204308\pi\)
\(294\) 3.76115 0.219355
\(295\) 13.6179 0.792862
\(296\) 10.6669 0.620001
\(297\) −5.63735 −0.327112
\(298\) 23.6949 1.37261
\(299\) −5.30157 −0.306598
\(300\) −20.4080 −1.17826
\(301\) 29.6342 1.70809
\(302\) −14.8433 −0.854134
\(303\) 12.6138 0.724642
\(304\) −23.0746 −1.32342
\(305\) −43.2757 −2.47796
\(306\) −17.7106 −1.01245
\(307\) 20.9564 1.19605 0.598023 0.801479i \(-0.295953\pi\)
0.598023 + 0.801479i \(0.295953\pi\)
\(308\) 11.7391 0.668897
\(309\) −5.60524 −0.318871
\(310\) 15.4770 0.879033
\(311\) −11.5550 −0.655227 −0.327613 0.944812i \(-0.606244\pi\)
−0.327613 + 0.944812i \(0.606244\pi\)
\(312\) −12.1831 −0.689729
\(313\) 30.0546 1.69879 0.849394 0.527759i \(-0.176968\pi\)
0.849394 + 0.527759i \(0.176968\pi\)
\(314\) −7.07342 −0.399176
\(315\) 9.98703 0.562705
\(316\) 35.4864 1.99627
\(317\) −11.0222 −0.619066 −0.309533 0.950889i \(-0.600173\pi\)
−0.309533 + 0.950889i \(0.600173\pi\)
\(318\) 33.5230 1.87988
\(319\) 9.51723 0.532863
\(320\) −19.1049 −1.06800
\(321\) −13.0834 −0.730242
\(322\) 21.6261 1.20518
\(323\) 29.4737 1.63996
\(324\) −16.5554 −0.919742
\(325\) −6.36723 −0.353190
\(326\) −12.2832 −0.680305
\(327\) 2.71439 0.150106
\(328\) 13.5857 0.750146
\(329\) 11.8864 0.655320
\(330\) −9.80866 −0.539949
\(331\) −31.0083 −1.70437 −0.852186 0.523239i \(-0.824723\pi\)
−0.852186 + 0.523239i \(0.824723\pi\)
\(332\) −35.8261 −1.96621
\(333\) 2.42148 0.132696
\(334\) −59.9665 −3.28122
\(335\) −22.9859 −1.25585
\(336\) 18.0987 0.987362
\(337\) 19.4136 1.05753 0.528764 0.848769i \(-0.322656\pi\)
0.528764 + 0.848769i \(0.322656\pi\)
\(338\) 24.7607 1.34680
\(339\) 0.652159 0.0354204
\(340\) −73.0855 −3.96362
\(341\) 2.12362 0.115000
\(342\) −14.3834 −0.777764
\(343\) 16.7374 0.903733
\(344\) 54.4207 2.93417
\(345\) −12.1619 −0.654772
\(346\) 36.9742 1.98775
\(347\) 23.0518 1.23749 0.618744 0.785593i \(-0.287642\pi\)
0.618744 + 0.785593i \(0.287642\pi\)
\(348\) 52.7354 2.82692
\(349\) −14.5280 −0.777664 −0.388832 0.921309i \(-0.627121\pi\)
−0.388832 + 0.921309i \(0.627121\pi\)
\(350\) 25.9732 1.38832
\(351\) −9.74578 −0.520191
\(352\) 1.19240 0.0635552
\(353\) −17.6495 −0.939390 −0.469695 0.882829i \(-0.655636\pi\)
−0.469695 + 0.882829i \(0.655636\pi\)
\(354\) 15.3832 0.817606
\(355\) −48.7927 −2.58965
\(356\) 30.9252 1.63903
\(357\) −23.1178 −1.22353
\(358\) 49.0203 2.59080
\(359\) −18.5507 −0.979068 −0.489534 0.871984i \(-0.662833\pi\)
−0.489534 + 0.871984i \(0.662833\pi\)
\(360\) 18.3403 0.966621
\(361\) 4.93663 0.259822
\(362\) 55.3487 2.90906
\(363\) −1.34586 −0.0706394
\(364\) 20.2944 1.06372
\(365\) 29.9684 1.56862
\(366\) −48.8855 −2.55529
\(367\) −14.7257 −0.768677 −0.384339 0.923192i \(-0.625570\pi\)
−0.384339 + 0.923192i \(0.625570\pi\)
\(368\) 14.4633 0.753949
\(369\) 3.08408 0.160551
\(370\) 14.8468 0.771850
\(371\) −28.7153 −1.49082
\(372\) 11.7671 0.610094
\(373\) −6.08274 −0.314952 −0.157476 0.987523i \(-0.550336\pi\)
−0.157476 + 0.987523i \(0.550336\pi\)
\(374\) −14.8997 −0.770443
\(375\) 5.22279 0.269703
\(376\) 21.8284 1.12572
\(377\) 16.4533 0.847387
\(378\) 39.7549 2.04477
\(379\) 16.3669 0.840710 0.420355 0.907360i \(-0.361906\pi\)
0.420355 + 0.907360i \(0.361906\pi\)
\(380\) −59.3553 −3.04486
\(381\) −26.3490 −1.34990
\(382\) −60.6082 −3.10098
\(383\) −13.3470 −0.681998 −0.340999 0.940064i \(-0.610765\pi\)
−0.340999 + 0.940064i \(0.610765\pi\)
\(384\) −24.7911 −1.26512
\(385\) 8.40194 0.428203
\(386\) 28.0036 1.42535
\(387\) 12.3540 0.627988
\(388\) −12.6832 −0.643893
\(389\) 35.5734 1.80364 0.901822 0.432107i \(-0.142230\pi\)
0.901822 + 0.432107i \(0.142230\pi\)
\(390\) −16.9571 −0.858655
\(391\) −18.4742 −0.934283
\(392\) −5.91646 −0.298827
\(393\) −22.3568 −1.12775
\(394\) −31.3359 −1.57868
\(395\) 25.3984 1.27793
\(396\) 4.89382 0.245924
\(397\) −4.96886 −0.249380 −0.124690 0.992196i \(-0.539794\pi\)
−0.124690 + 0.992196i \(0.539794\pi\)
\(398\) −14.6601 −0.734844
\(399\) −18.7748 −0.939915
\(400\) 17.3705 0.868524
\(401\) −22.3891 −1.11806 −0.559029 0.829148i \(-0.688826\pi\)
−0.559029 + 0.829148i \(0.688826\pi\)
\(402\) −25.9655 −1.29504
\(403\) 3.67128 0.182880
\(404\) −38.5866 −1.91975
\(405\) −11.8490 −0.588784
\(406\) −67.1161 −3.33092
\(407\) 2.03716 0.100978
\(408\) −42.4540 −2.10178
\(409\) 20.7219 1.02463 0.512316 0.858797i \(-0.328788\pi\)
0.512316 + 0.858797i \(0.328788\pi\)
\(410\) 18.9094 0.933869
\(411\) −4.98016 −0.245653
\(412\) 17.1469 0.844767
\(413\) −13.1770 −0.648396
\(414\) 9.01556 0.443091
\(415\) −25.6416 −1.25869
\(416\) 2.06141 0.101069
\(417\) −16.3428 −0.800311
\(418\) −12.1005 −0.591856
\(419\) −13.9473 −0.681373 −0.340686 0.940177i \(-0.610659\pi\)
−0.340686 + 0.940177i \(0.610659\pi\)
\(420\) 46.5555 2.27168
\(421\) −25.1352 −1.22501 −0.612506 0.790466i \(-0.709839\pi\)
−0.612506 + 0.790466i \(0.709839\pi\)
\(422\) 7.07116 0.344219
\(423\) 4.95524 0.240932
\(424\) −52.7332 −2.56095
\(425\) −22.1877 −1.07626
\(426\) −55.1177 −2.67046
\(427\) 41.8746 2.02645
\(428\) 40.0231 1.93459
\(429\) −2.32671 −0.112334
\(430\) 75.7459 3.65279
\(431\) 21.1769 1.02006 0.510028 0.860158i \(-0.329635\pi\)
0.510028 + 0.860158i \(0.329635\pi\)
\(432\) 26.5875 1.27919
\(433\) 23.1733 1.11364 0.556819 0.830634i \(-0.312022\pi\)
0.556819 + 0.830634i \(0.312022\pi\)
\(434\) −14.9759 −0.718866
\(435\) 37.7440 1.80968
\(436\) −8.30353 −0.397667
\(437\) −15.0036 −0.717718
\(438\) 33.8533 1.61757
\(439\) −12.2394 −0.584152 −0.292076 0.956395i \(-0.594346\pi\)
−0.292076 + 0.956395i \(0.594346\pi\)
\(440\) 15.4295 0.735571
\(441\) −1.34309 −0.0639566
\(442\) −25.7583 −1.22520
\(443\) 9.69077 0.460423 0.230211 0.973141i \(-0.426058\pi\)
0.230211 + 0.973141i \(0.426058\pi\)
\(444\) 11.2880 0.535704
\(445\) 22.1339 1.04925
\(446\) 28.7885 1.36318
\(447\) 12.8938 0.609858
\(448\) 18.4864 0.873400
\(449\) −21.6836 −1.02331 −0.511657 0.859190i \(-0.670968\pi\)
−0.511657 + 0.859190i \(0.670968\pi\)
\(450\) 10.8278 0.510425
\(451\) 2.59459 0.122174
\(452\) −1.99501 −0.0938373
\(453\) −8.07712 −0.379496
\(454\) 23.3676 1.09670
\(455\) 14.5252 0.680950
\(456\) −34.4783 −1.61459
\(457\) 6.22311 0.291105 0.145552 0.989351i \(-0.453504\pi\)
0.145552 + 0.989351i \(0.453504\pi\)
\(458\) −24.9439 −1.16555
\(459\) −33.9609 −1.58516
\(460\) 37.2041 1.73465
\(461\) 12.0412 0.560813 0.280406 0.959881i \(-0.409531\pi\)
0.280406 + 0.959881i \(0.409531\pi\)
\(462\) 9.49109 0.441566
\(463\) 25.3485 1.17805 0.589023 0.808116i \(-0.299513\pi\)
0.589023 + 0.808116i \(0.299513\pi\)
\(464\) −44.8863 −2.08379
\(465\) 8.42196 0.390559
\(466\) 63.6583 2.94891
\(467\) −38.0466 −1.76059 −0.880293 0.474430i \(-0.842654\pi\)
−0.880293 + 0.474430i \(0.842654\pi\)
\(468\) 8.46038 0.391081
\(469\) 22.2417 1.02702
\(470\) 30.3821 1.40142
\(471\) −3.84908 −0.177356
\(472\) −24.1984 −1.11382
\(473\) 10.3932 0.477881
\(474\) 28.6909 1.31782
\(475\) −18.0194 −0.826787
\(476\) 70.7193 3.24142
\(477\) −11.9709 −0.548110
\(478\) −3.75142 −0.171586
\(479\) −19.3242 −0.882945 −0.441472 0.897275i \(-0.645544\pi\)
−0.441472 + 0.897275i \(0.645544\pi\)
\(480\) 4.72889 0.215843
\(481\) 3.52181 0.160581
\(482\) −27.4422 −1.24996
\(483\) 11.7681 0.535467
\(484\) 4.11710 0.187141
\(485\) −9.07768 −0.412196
\(486\) 28.4431 1.29021
\(487\) 36.9264 1.67330 0.836648 0.547741i \(-0.184512\pi\)
0.836648 + 0.547741i \(0.184512\pi\)
\(488\) 76.8992 3.48106
\(489\) −6.68405 −0.302263
\(490\) −8.23488 −0.372014
\(491\) −1.06706 −0.0481558 −0.0240779 0.999710i \(-0.507665\pi\)
−0.0240779 + 0.999710i \(0.507665\pi\)
\(492\) 14.3767 0.648153
\(493\) 57.3343 2.58221
\(494\) −20.9192 −0.941201
\(495\) 3.50262 0.157431
\(496\) −10.0157 −0.449716
\(497\) 47.2130 2.11779
\(498\) −28.9655 −1.29798
\(499\) 21.8418 0.977775 0.488888 0.872347i \(-0.337403\pi\)
0.488888 + 0.872347i \(0.337403\pi\)
\(500\) −15.9769 −0.714510
\(501\) −32.6314 −1.45787
\(502\) 64.7510 2.88998
\(503\) −38.3443 −1.70969 −0.854843 0.518887i \(-0.826347\pi\)
−0.854843 + 0.518887i \(0.826347\pi\)
\(504\) −17.7466 −0.790495
\(505\) −27.6173 −1.22895
\(506\) 7.58466 0.337179
\(507\) 13.4738 0.598393
\(508\) 80.6037 3.57621
\(509\) −9.43955 −0.418401 −0.209200 0.977873i \(-0.567086\pi\)
−0.209200 + 0.977873i \(0.567086\pi\)
\(510\) −59.0899 −2.61654
\(511\) −28.9982 −1.28280
\(512\) 43.7672 1.93425
\(513\) −27.5808 −1.21772
\(514\) 24.5940 1.08480
\(515\) 12.2724 0.540788
\(516\) 57.5893 2.53523
\(517\) 4.16877 0.183342
\(518\) −14.3661 −0.631212
\(519\) 20.1199 0.883168
\(520\) 26.6742 1.16974
\(521\) 27.6098 1.20961 0.604803 0.796375i \(-0.293252\pi\)
0.604803 + 0.796375i \(0.293252\pi\)
\(522\) −27.9795 −1.22463
\(523\) 3.62718 0.158605 0.0793027 0.996851i \(-0.474731\pi\)
0.0793027 + 0.996851i \(0.474731\pi\)
\(524\) 68.3912 2.98768
\(525\) 14.1336 0.616840
\(526\) −29.1921 −1.27284
\(527\) 12.7932 0.557282
\(528\) 6.34750 0.276240
\(529\) −13.5957 −0.591118
\(530\) −73.3971 −3.18817
\(531\) −5.49325 −0.238387
\(532\) 57.4336 2.49006
\(533\) 4.48549 0.194288
\(534\) 25.0032 1.08199
\(535\) 28.6454 1.23845
\(536\) 40.8450 1.76423
\(537\) 26.6749 1.15111
\(538\) 30.6320 1.32064
\(539\) −1.12992 −0.0486691
\(540\) 68.3916 2.94311
\(541\) 0.119301 0.00512916 0.00256458 0.999997i \(-0.499184\pi\)
0.00256458 + 0.999997i \(0.499184\pi\)
\(542\) −49.7852 −2.13846
\(543\) 30.1186 1.29251
\(544\) 7.18333 0.307983
\(545\) −5.94303 −0.254571
\(546\) 16.4081 0.702201
\(547\) 1.00000 0.0427569
\(548\) 15.2347 0.650795
\(549\) 17.4568 0.745037
\(550\) 9.10923 0.388419
\(551\) 46.5631 1.98366
\(552\) 21.6111 0.919831
\(553\) −24.5762 −1.04508
\(554\) 20.7776 0.882757
\(555\) 8.07906 0.342937
\(556\) 49.9940 2.12022
\(557\) −17.7576 −0.752415 −0.376208 0.926535i \(-0.622772\pi\)
−0.376208 + 0.926535i \(0.622772\pi\)
\(558\) −6.24318 −0.264295
\(559\) 17.9677 0.759951
\(560\) −39.6262 −1.67451
\(561\) −8.10782 −0.342312
\(562\) 27.3499 1.15369
\(563\) 10.3785 0.437402 0.218701 0.975792i \(-0.429818\pi\)
0.218701 + 0.975792i \(0.429818\pi\)
\(564\) 23.0994 0.972658
\(565\) −1.42787 −0.0600711
\(566\) 55.0948 2.31581
\(567\) 11.4654 0.481503
\(568\) 86.7027 3.63796
\(569\) −4.73917 −0.198676 −0.0993381 0.995054i \(-0.531673\pi\)
−0.0993381 + 0.995054i \(0.531673\pi\)
\(570\) −47.9889 −2.01003
\(571\) −4.72994 −0.197942 −0.0989709 0.995090i \(-0.531555\pi\)
−0.0989709 + 0.995090i \(0.531555\pi\)
\(572\) 7.11759 0.297601
\(573\) −32.9806 −1.37778
\(574\) −18.2972 −0.763710
\(575\) 11.2946 0.471019
\(576\) 7.70665 0.321110
\(577\) −19.7444 −0.821971 −0.410986 0.911642i \(-0.634815\pi\)
−0.410986 + 0.911642i \(0.634815\pi\)
\(578\) −47.7137 −1.98463
\(579\) 15.2385 0.633289
\(580\) −115.462 −4.79429
\(581\) 24.8114 1.02935
\(582\) −10.2544 −0.425060
\(583\) −10.0709 −0.417096
\(584\) −53.2527 −2.20361
\(585\) 6.05529 0.250355
\(586\) −67.8208 −2.80165
\(587\) 20.7071 0.854675 0.427338 0.904092i \(-0.359452\pi\)
0.427338 + 0.904092i \(0.359452\pi\)
\(588\) −6.26094 −0.258197
\(589\) 10.3898 0.428105
\(590\) −33.6807 −1.38661
\(591\) −17.0518 −0.701417
\(592\) −9.60787 −0.394881
\(593\) −13.2597 −0.544510 −0.272255 0.962225i \(-0.587769\pi\)
−0.272255 + 0.962225i \(0.587769\pi\)
\(594\) 13.9427 0.572077
\(595\) 50.6155 2.07503
\(596\) −39.4433 −1.61566
\(597\) −7.97745 −0.326495
\(598\) 13.1123 0.536200
\(599\) −8.90443 −0.363825 −0.181913 0.983315i \(-0.558229\pi\)
−0.181913 + 0.983315i \(0.558229\pi\)
\(600\) 25.9551 1.05961
\(601\) 23.6532 0.964836 0.482418 0.875941i \(-0.339759\pi\)
0.482418 + 0.875941i \(0.339759\pi\)
\(602\) −73.2936 −2.98722
\(603\) 9.27216 0.377592
\(604\) 24.7086 1.00538
\(605\) 2.94670 0.119801
\(606\) −31.1974 −1.26731
\(607\) 44.2974 1.79797 0.898987 0.437975i \(-0.144304\pi\)
0.898987 + 0.437975i \(0.144304\pi\)
\(608\) 5.83383 0.236593
\(609\) −36.5220 −1.47994
\(610\) 107.033 4.33363
\(611\) 7.20692 0.291561
\(612\) 29.4817 1.19173
\(613\) −11.5228 −0.465400 −0.232700 0.972549i \(-0.574756\pi\)
−0.232700 + 0.972549i \(0.574756\pi\)
\(614\) −51.8310 −2.09173
\(615\) 10.2898 0.414923
\(616\) −14.9299 −0.601544
\(617\) 12.4727 0.502132 0.251066 0.967970i \(-0.419219\pi\)
0.251066 + 0.967970i \(0.419219\pi\)
\(618\) 13.8633 0.557665
\(619\) 12.3058 0.494614 0.247307 0.968937i \(-0.420454\pi\)
0.247307 + 0.968937i \(0.420454\pi\)
\(620\) −25.7635 −1.03469
\(621\) 17.2877 0.693733
\(622\) 28.5788 1.14591
\(623\) −21.4173 −0.858066
\(624\) 10.9735 0.439291
\(625\) −29.8504 −1.19401
\(626\) −74.3334 −2.97096
\(627\) −6.58464 −0.262965
\(628\) 11.7746 0.469860
\(629\) 12.2724 0.489331
\(630\) −24.7007 −0.984099
\(631\) 24.5884 0.978850 0.489425 0.872045i \(-0.337207\pi\)
0.489425 + 0.872045i \(0.337207\pi\)
\(632\) −45.1320 −1.79526
\(633\) 3.84785 0.152938
\(634\) 27.2608 1.08267
\(635\) 57.6899 2.28936
\(636\) −55.8035 −2.21275
\(637\) −1.95339 −0.0773962
\(638\) −23.5388 −0.931908
\(639\) 19.6823 0.778618
\(640\) 54.2791 2.14557
\(641\) 17.2955 0.683131 0.341566 0.939858i \(-0.389043\pi\)
0.341566 + 0.939858i \(0.389043\pi\)
\(642\) 32.3588 1.27710
\(643\) 13.1943 0.520334 0.260167 0.965564i \(-0.416222\pi\)
0.260167 + 0.965564i \(0.416222\pi\)
\(644\) −35.9996 −1.41858
\(645\) 41.2180 1.62296
\(646\) −72.8967 −2.86808
\(647\) 40.6351 1.59753 0.798765 0.601643i \(-0.205487\pi\)
0.798765 + 0.601643i \(0.205487\pi\)
\(648\) 21.0553 0.827130
\(649\) −4.62139 −0.181405
\(650\) 15.7479 0.617684
\(651\) −8.14929 −0.319396
\(652\) 20.4471 0.800769
\(653\) −26.3499 −1.03115 −0.515575 0.856844i \(-0.672422\pi\)
−0.515575 + 0.856844i \(0.672422\pi\)
\(654\) −6.71343 −0.262516
\(655\) 48.9492 1.91260
\(656\) −12.2369 −0.477771
\(657\) −12.0888 −0.471631
\(658\) −29.3984 −1.14607
\(659\) 38.5793 1.50283 0.751417 0.659827i \(-0.229371\pi\)
0.751417 + 0.659827i \(0.229371\pi\)
\(660\) 16.3278 0.635559
\(661\) 12.3498 0.480351 0.240176 0.970729i \(-0.422795\pi\)
0.240176 + 0.970729i \(0.422795\pi\)
\(662\) 76.6922 2.98073
\(663\) −14.0167 −0.544363
\(664\) 45.5640 1.76823
\(665\) 41.1066 1.59404
\(666\) −5.98899 −0.232069
\(667\) −29.1860 −1.13008
\(668\) 99.8223 3.86224
\(669\) 15.6656 0.605667
\(670\) 56.8504 2.19632
\(671\) 14.6861 0.566952
\(672\) −4.57579 −0.176515
\(673\) −41.2498 −1.59006 −0.795031 0.606568i \(-0.792546\pi\)
−0.795031 + 0.606568i \(0.792546\pi\)
\(674\) −48.0153 −1.84948
\(675\) 20.7627 0.799157
\(676\) −41.2175 −1.58529
\(677\) 20.4798 0.787104 0.393552 0.919302i \(-0.371246\pi\)
0.393552 + 0.919302i \(0.371246\pi\)
\(678\) −1.61297 −0.0619457
\(679\) 8.78378 0.337090
\(680\) 92.9511 3.56451
\(681\) 12.7157 0.487269
\(682\) −5.25230 −0.201121
\(683\) −48.8368 −1.86869 −0.934344 0.356371i \(-0.884014\pi\)
−0.934344 + 0.356371i \(0.884014\pi\)
\(684\) 23.9431 0.915486
\(685\) 10.9038 0.416614
\(686\) −41.3961 −1.58051
\(687\) −13.5735 −0.517861
\(688\) −49.0177 −1.86878
\(689\) −17.4105 −0.663287
\(690\) 30.0796 1.14511
\(691\) 1.68571 0.0641275 0.0320637 0.999486i \(-0.489792\pi\)
0.0320637 + 0.999486i \(0.489792\pi\)
\(692\) −61.5486 −2.33973
\(693\) −3.38922 −0.128746
\(694\) −57.0136 −2.16421
\(695\) 35.7819 1.35728
\(696\) −67.0695 −2.54226
\(697\) 15.6305 0.592047
\(698\) 35.9317 1.36003
\(699\) 34.6404 1.31022
\(700\) −43.2358 −1.63416
\(701\) −45.6853 −1.72551 −0.862756 0.505621i \(-0.831263\pi\)
−0.862756 + 0.505621i \(0.831263\pi\)
\(702\) 24.1040 0.909748
\(703\) 9.96680 0.375905
\(704\) 6.48349 0.244356
\(705\) 16.5327 0.622659
\(706\) 43.6522 1.64287
\(707\) 26.7232 1.00503
\(708\) −25.6073 −0.962382
\(709\) −30.4771 −1.14459 −0.572296 0.820047i \(-0.693947\pi\)
−0.572296 + 0.820047i \(0.693947\pi\)
\(710\) 120.678 4.52896
\(711\) −10.2454 −0.384231
\(712\) −39.3311 −1.47400
\(713\) −6.51238 −0.243891
\(714\) 57.1768 2.13979
\(715\) 5.09422 0.190513
\(716\) −81.6008 −3.04957
\(717\) −2.04137 −0.0762365
\(718\) 45.8810 1.71226
\(719\) −35.6273 −1.32867 −0.664337 0.747433i \(-0.731286\pi\)
−0.664337 + 0.747433i \(0.731286\pi\)
\(720\) −16.5195 −0.615644
\(721\) −11.8751 −0.442252
\(722\) −12.2096 −0.454396
\(723\) −14.9330 −0.555364
\(724\) −92.1353 −3.42418
\(725\) −35.0526 −1.30182
\(726\) 3.32869 0.123539
\(727\) −14.8843 −0.552028 −0.276014 0.961154i \(-0.589014\pi\)
−0.276014 + 0.961154i \(0.589014\pi\)
\(728\) −25.8106 −0.956606
\(729\) 27.5410 1.02004
\(730\) −74.1203 −2.74331
\(731\) 62.6115 2.31577
\(732\) 81.3765 3.00776
\(733\) 36.0575 1.33181 0.665907 0.746035i \(-0.268045\pi\)
0.665907 + 0.746035i \(0.268045\pi\)
\(734\) 36.4208 1.34432
\(735\) −4.48110 −0.165288
\(736\) −3.65667 −0.134787
\(737\) 7.80053 0.287336
\(738\) −7.62778 −0.280783
\(739\) −24.3289 −0.894954 −0.447477 0.894295i \(-0.647677\pi\)
−0.447477 + 0.894295i \(0.647677\pi\)
\(740\) −24.7145 −0.908524
\(741\) −11.3834 −0.418181
\(742\) 71.0208 2.60726
\(743\) −24.1041 −0.884293 −0.442146 0.896943i \(-0.645783\pi\)
−0.442146 + 0.896943i \(0.645783\pi\)
\(744\) −14.9655 −0.548662
\(745\) −28.2305 −1.03429
\(746\) 15.0443 0.550811
\(747\) 10.3434 0.378447
\(748\) 24.8025 0.906868
\(749\) −27.7180 −1.01279
\(750\) −12.9174 −0.471677
\(751\) 47.9202 1.74863 0.874317 0.485355i \(-0.161310\pi\)
0.874317 + 0.485355i \(0.161310\pi\)
\(752\) −19.6612 −0.716972
\(753\) 35.2350 1.28403
\(754\) −40.6935 −1.48197
\(755\) 17.6845 0.643605
\(756\) −66.1774 −2.40685
\(757\) 39.8742 1.44925 0.724625 0.689143i \(-0.242013\pi\)
0.724625 + 0.689143i \(0.242013\pi\)
\(758\) −40.4798 −1.47029
\(759\) 4.12728 0.149811
\(760\) 75.4887 2.73826
\(761\) −16.5601 −0.600303 −0.300151 0.953892i \(-0.597037\pi\)
−0.300151 + 0.953892i \(0.597037\pi\)
\(762\) 65.1683 2.36080
\(763\) 5.75062 0.208186
\(764\) 100.890 3.65009
\(765\) 21.1007 0.762897
\(766\) 33.0107 1.19273
\(767\) −7.98940 −0.288480
\(768\) 43.8636 1.58279
\(769\) 12.8474 0.463288 0.231644 0.972801i \(-0.425590\pi\)
0.231644 + 0.972801i \(0.425590\pi\)
\(770\) −20.7803 −0.748871
\(771\) 13.3831 0.481981
\(772\) −46.6157 −1.67774
\(773\) 3.37971 0.121560 0.0607798 0.998151i \(-0.480641\pi\)
0.0607798 + 0.998151i \(0.480641\pi\)
\(774\) −30.5548 −1.09827
\(775\) −7.82142 −0.280954
\(776\) 16.1307 0.579057
\(777\) −7.81750 −0.280451
\(778\) −87.9830 −3.15434
\(779\) 12.6940 0.454811
\(780\) 28.2273 1.01070
\(781\) 16.5584 0.592506
\(782\) 45.6919 1.63394
\(783\) −53.6520 −1.91737
\(784\) 5.32906 0.190324
\(785\) 8.42739 0.300786
\(786\) 55.2945 1.97229
\(787\) −46.3437 −1.65198 −0.825988 0.563688i \(-0.809382\pi\)
−0.825988 + 0.563688i \(0.809382\pi\)
\(788\) 52.1628 1.85822
\(789\) −15.8852 −0.565529
\(790\) −62.8174 −2.23494
\(791\) 1.38164 0.0491256
\(792\) −6.22402 −0.221161
\(793\) 25.3892 0.901597
\(794\) 12.2894 0.436133
\(795\) −39.9399 −1.41652
\(796\) 24.4037 0.864966
\(797\) −31.2883 −1.10829 −0.554145 0.832420i \(-0.686955\pi\)
−0.554145 + 0.832420i \(0.686955\pi\)
\(798\) 46.4352 1.64379
\(799\) 25.1138 0.888461
\(800\) −4.39169 −0.155270
\(801\) −8.92850 −0.315473
\(802\) 55.3745 1.95534
\(803\) −10.1702 −0.358897
\(804\) 43.2231 1.52436
\(805\) −25.7657 −0.908123
\(806\) −9.08011 −0.319833
\(807\) 16.6687 0.586767
\(808\) 49.0749 1.72645
\(809\) −2.21503 −0.0778761 −0.0389381 0.999242i \(-0.512398\pi\)
−0.0389381 + 0.999242i \(0.512398\pi\)
\(810\) 29.3060 1.02971
\(811\) −21.2640 −0.746681 −0.373340 0.927694i \(-0.621788\pi\)
−0.373340 + 0.927694i \(0.621788\pi\)
\(812\) 111.724 3.92073
\(813\) −27.0912 −0.950129
\(814\) −5.03845 −0.176598
\(815\) 14.6344 0.512622
\(816\) 38.2390 1.33863
\(817\) 50.8489 1.77898
\(818\) −51.2510 −1.79195
\(819\) −5.85924 −0.204739
\(820\) −31.4772 −1.09923
\(821\) 30.7599 1.07353 0.536764 0.843733i \(-0.319647\pi\)
0.536764 + 0.843733i \(0.319647\pi\)
\(822\) 12.3173 0.429615
\(823\) 18.3193 0.638570 0.319285 0.947659i \(-0.396557\pi\)
0.319285 + 0.947659i \(0.396557\pi\)
\(824\) −21.8076 −0.759705
\(825\) 4.95689 0.172577
\(826\) 32.5903 1.13396
\(827\) −20.2249 −0.703288 −0.351644 0.936134i \(-0.614377\pi\)
−0.351644 + 0.936134i \(0.614377\pi\)
\(828\) −15.0076 −0.521550
\(829\) 12.8392 0.445923 0.222962 0.974827i \(-0.428428\pi\)
0.222962 + 0.974827i \(0.428428\pi\)
\(830\) 63.4187 2.20129
\(831\) 11.3064 0.392214
\(832\) 11.2086 0.388587
\(833\) −6.80694 −0.235846
\(834\) 40.4203 1.39964
\(835\) 71.4451 2.47246
\(836\) 20.1429 0.696658
\(837\) −11.9716 −0.413799
\(838\) 34.4957 1.19163
\(839\) −0.367383 −0.0126835 −0.00634173 0.999980i \(-0.502019\pi\)
−0.00634173 + 0.999980i \(0.502019\pi\)
\(840\) −59.2099 −2.04293
\(841\) 61.5777 2.12337
\(842\) 62.1662 2.14239
\(843\) 14.8828 0.512590
\(844\) −11.7709 −0.405171
\(845\) −29.5003 −1.01484
\(846\) −12.2557 −0.421359
\(847\) −2.85130 −0.0979719
\(848\) 47.4977 1.63108
\(849\) 29.9805 1.02893
\(850\) 54.8764 1.88224
\(851\) −6.24723 −0.214152
\(852\) 91.7508 3.14333
\(853\) 48.0920 1.64664 0.823319 0.567578i \(-0.192120\pi\)
0.823319 + 0.567578i \(0.192120\pi\)
\(854\) −103.567 −3.54400
\(855\) 17.1366 0.586059
\(856\) −50.9018 −1.73979
\(857\) 16.9505 0.579019 0.289510 0.957175i \(-0.406508\pi\)
0.289510 + 0.957175i \(0.406508\pi\)
\(858\) 5.75459 0.196459
\(859\) 36.1630 1.23387 0.616933 0.787016i \(-0.288375\pi\)
0.616933 + 0.787016i \(0.288375\pi\)
\(860\) −126.089 −4.29961
\(861\) −9.95662 −0.339321
\(862\) −52.3764 −1.78395
\(863\) −34.4936 −1.17418 −0.587089 0.809523i \(-0.699726\pi\)
−0.587089 + 0.809523i \(0.699726\pi\)
\(864\) −6.72199 −0.228687
\(865\) −44.0517 −1.49780
\(866\) −57.3140 −1.94761
\(867\) −25.9639 −0.881782
\(868\) 24.9294 0.846158
\(869\) −8.61927 −0.292389
\(870\) −93.3513 −3.16490
\(871\) 13.4855 0.456937
\(872\) 10.5605 0.357625
\(873\) 3.66180 0.123933
\(874\) 37.1080 1.25520
\(875\) 11.0648 0.374060
\(876\) −56.3533 −1.90400
\(877\) −13.7788 −0.465277 −0.232639 0.972563i \(-0.574736\pi\)
−0.232639 + 0.972563i \(0.574736\pi\)
\(878\) 30.2713 1.02161
\(879\) −36.9054 −1.24479
\(880\) −13.8976 −0.468487
\(881\) 48.3733 1.62974 0.814868 0.579646i \(-0.196809\pi\)
0.814868 + 0.579646i \(0.196809\pi\)
\(882\) 3.32183 0.111852
\(883\) 12.5634 0.422793 0.211396 0.977400i \(-0.432199\pi\)
0.211396 + 0.977400i \(0.432199\pi\)
\(884\) 42.8782 1.44215
\(885\) −18.3277 −0.616081
\(886\) −23.9680 −0.805220
\(887\) −30.5742 −1.02658 −0.513291 0.858215i \(-0.671574\pi\)
−0.513291 + 0.858215i \(0.671574\pi\)
\(888\) −14.3562 −0.481762
\(889\) −55.8222 −1.87222
\(890\) −54.7433 −1.83500
\(891\) 4.02112 0.134713
\(892\) −47.9223 −1.60456
\(893\) 20.3957 0.682518
\(894\) −31.8901 −1.06656
\(895\) −58.4036 −1.95222
\(896\) −52.5217 −1.75463
\(897\) 7.13518 0.238237
\(898\) 53.6296 1.78964
\(899\) 20.2110 0.674074
\(900\) −18.0243 −0.600808
\(901\) −60.6699 −2.02121
\(902\) −6.41714 −0.213667
\(903\) −39.8835 −1.32724
\(904\) 2.53727 0.0843885
\(905\) −65.9434 −2.19203
\(906\) 19.9770 0.663690
\(907\) 48.3468 1.60533 0.802665 0.596430i \(-0.203415\pi\)
0.802665 + 0.596430i \(0.203415\pi\)
\(908\) −38.8985 −1.29089
\(909\) 11.1404 0.369504
\(910\) −35.9248 −1.19089
\(911\) −28.2675 −0.936544 −0.468272 0.883584i \(-0.655123\pi\)
−0.468272 + 0.883584i \(0.655123\pi\)
\(912\) 31.0552 1.02834
\(913\) 8.70178 0.287987
\(914\) −15.3915 −0.509105
\(915\) 58.2430 1.92546
\(916\) 41.5224 1.37194
\(917\) −47.3644 −1.56411
\(918\) 83.9946 2.77224
\(919\) −35.0627 −1.15661 −0.578306 0.815820i \(-0.696286\pi\)
−0.578306 + 0.815820i \(0.696286\pi\)
\(920\) −47.3166 −1.55998
\(921\) −28.2044 −0.929368
\(922\) −29.7811 −0.980789
\(923\) 28.6259 0.942234
\(924\) −15.7992 −0.519755
\(925\) −7.50297 −0.246696
\(926\) −62.6940 −2.06025
\(927\) −4.95052 −0.162597
\(928\) 11.3484 0.372528
\(929\) −10.7945 −0.354155 −0.177078 0.984197i \(-0.556664\pi\)
−0.177078 + 0.984197i \(0.556664\pi\)
\(930\) −20.8298 −0.683038
\(931\) −5.52815 −0.181178
\(932\) −105.968 −3.47109
\(933\) 15.5515 0.509133
\(934\) 94.0998 3.07904
\(935\) 17.7517 0.580543
\(936\) −10.7600 −0.351702
\(937\) 23.2088 0.758199 0.379099 0.925356i \(-0.376234\pi\)
0.379099 + 0.925356i \(0.376234\pi\)
\(938\) −55.0098 −1.79613
\(939\) −40.4494 −1.32001
\(940\) −50.5750 −1.64958
\(941\) −43.4382 −1.41604 −0.708022 0.706190i \(-0.750412\pi\)
−0.708022 + 0.706190i \(0.750412\pi\)
\(942\) 9.51984 0.310173
\(943\) −7.95668 −0.259105
\(944\) 21.7959 0.709397
\(945\) −47.3647 −1.54077
\(946\) −25.7053 −0.835752
\(947\) 5.09549 0.165581 0.0827905 0.996567i \(-0.473617\pi\)
0.0827905 + 0.996567i \(0.473617\pi\)
\(948\) −47.7598 −1.55117
\(949\) −17.5820 −0.570737
\(950\) 44.5670 1.44594
\(951\) 14.8343 0.481035
\(952\) −89.9417 −2.91503
\(953\) 25.1708 0.815363 0.407682 0.913124i \(-0.366337\pi\)
0.407682 + 0.913124i \(0.366337\pi\)
\(954\) 29.6073 0.958573
\(955\) 72.2096 2.33665
\(956\) 6.24473 0.201969
\(957\) −12.8089 −0.414052
\(958\) 47.7941 1.54416
\(959\) −10.5508 −0.340704
\(960\) 25.7126 0.829870
\(961\) −26.4902 −0.854524
\(962\) −8.71041 −0.280835
\(963\) −11.5552 −0.372360
\(964\) 45.6812 1.47129
\(965\) −33.3639 −1.07402
\(966\) −29.1058 −0.936463
\(967\) 56.1142 1.80451 0.902256 0.431200i \(-0.141910\pi\)
0.902256 + 0.431200i \(0.141910\pi\)
\(968\) −5.23618 −0.168297
\(969\) −39.6675 −1.27431
\(970\) 22.4516 0.720878
\(971\) 51.7528 1.66083 0.830413 0.557149i \(-0.188105\pi\)
0.830413 + 0.557149i \(0.188105\pi\)
\(972\) −47.3474 −1.51867
\(973\) −34.6234 −1.10997
\(974\) −91.3293 −2.92638
\(975\) 8.56941 0.274441
\(976\) −69.2644 −2.21710
\(977\) −22.7312 −0.727235 −0.363618 0.931548i \(-0.618458\pi\)
−0.363618 + 0.931548i \(0.618458\pi\)
\(978\) 16.5315 0.528620
\(979\) −7.51142 −0.240066
\(980\) 13.7081 0.437888
\(981\) 2.39733 0.0765409
\(982\) 2.63914 0.0842184
\(983\) −7.96890 −0.254169 −0.127084 0.991892i \(-0.540562\pi\)
−0.127084 + 0.991892i \(0.540562\pi\)
\(984\) −18.2845 −0.582889
\(985\) 37.3341 1.18956
\(986\) −141.804 −4.51595
\(987\) −15.9975 −0.509205
\(988\) 34.8229 1.10786
\(989\) −31.8723 −1.01348
\(990\) −8.66295 −0.275327
\(991\) −41.3921 −1.31486 −0.657431 0.753514i \(-0.728357\pi\)
−0.657431 + 0.753514i \(0.728357\pi\)
\(992\) 2.53221 0.0803976
\(993\) 41.7329 1.32435
\(994\) −116.771 −3.70374
\(995\) 17.4663 0.553718
\(996\) 48.2170 1.52781
\(997\) 37.9007 1.20033 0.600163 0.799878i \(-0.295102\pi\)
0.600163 + 0.799878i \(0.295102\pi\)
\(998\) −54.0209 −1.71000
\(999\) −11.4842 −0.363343
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 6017.2.a.f.1.11 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.11 121 1.1 even 1 trivial