Properties

Label 6017.2.a.f.1.2
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 1.2
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74533 q^{2} -1.76027 q^{3} +5.53683 q^{4} -2.91942 q^{5} +4.83253 q^{6} +1.39362 q^{7} -9.70977 q^{8} +0.0985659 q^{9} +O(q^{10})\) \(q-2.74533 q^{2} -1.76027 q^{3} +5.53683 q^{4} -2.91942 q^{5} +4.83253 q^{6} +1.39362 q^{7} -9.70977 q^{8} +0.0985659 q^{9} +8.01478 q^{10} -1.00000 q^{11} -9.74634 q^{12} +4.17660 q^{13} -3.82595 q^{14} +5.13898 q^{15} +15.5828 q^{16} -4.04082 q^{17} -0.270596 q^{18} +4.18485 q^{19} -16.1644 q^{20} -2.45316 q^{21} +2.74533 q^{22} +0.233100 q^{23} +17.0919 q^{24} +3.52303 q^{25} -11.4661 q^{26} +5.10732 q^{27} +7.71625 q^{28} +6.60665 q^{29} -14.1082 q^{30} -10.0639 q^{31} -23.3605 q^{32} +1.76027 q^{33} +11.0934 q^{34} -4.06857 q^{35} +0.545743 q^{36} +0.0900760 q^{37} -11.4888 q^{38} -7.35196 q^{39} +28.3469 q^{40} +5.18704 q^{41} +6.73472 q^{42} +10.6096 q^{43} -5.53683 q^{44} -0.287756 q^{45} -0.639936 q^{46} +10.2834 q^{47} -27.4301 q^{48} -5.05782 q^{49} -9.67187 q^{50} +7.11296 q^{51} +23.1251 q^{52} +2.66520 q^{53} -14.0213 q^{54} +2.91942 q^{55} -13.5317 q^{56} -7.36649 q^{57} -18.1374 q^{58} +7.50326 q^{59} +28.4537 q^{60} -2.25827 q^{61} +27.6288 q^{62} +0.137364 q^{63} +32.9666 q^{64} -12.1933 q^{65} -4.83253 q^{66} -8.19712 q^{67} -22.3734 q^{68} -0.410320 q^{69} +11.1696 q^{70} -14.1572 q^{71} -0.957052 q^{72} +10.4395 q^{73} -0.247288 q^{74} -6.20150 q^{75} +23.1708 q^{76} -1.39362 q^{77} +20.1836 q^{78} -7.55634 q^{79} -45.4929 q^{80} -9.28598 q^{81} -14.2401 q^{82} -0.344433 q^{83} -13.5827 q^{84} +11.7969 q^{85} -29.1267 q^{86} -11.6295 q^{87} +9.70977 q^{88} +0.821841 q^{89} +0.789984 q^{90} +5.82060 q^{91} +1.29063 q^{92} +17.7153 q^{93} -28.2314 q^{94} -12.2174 q^{95} +41.1209 q^{96} +1.35371 q^{97} +13.8854 q^{98} -0.0985659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74533 −1.94124 −0.970620 0.240616i \(-0.922651\pi\)
−0.970620 + 0.240616i \(0.922651\pi\)
\(3\) −1.76027 −1.01629 −0.508147 0.861270i \(-0.669670\pi\)
−0.508147 + 0.861270i \(0.669670\pi\)
\(4\) 5.53683 2.76842
\(5\) −2.91942 −1.30561 −0.652803 0.757528i \(-0.726407\pi\)
−0.652803 + 0.757528i \(0.726407\pi\)
\(6\) 4.83253 1.97287
\(7\) 1.39362 0.526740 0.263370 0.964695i \(-0.415166\pi\)
0.263370 + 0.964695i \(0.415166\pi\)
\(8\) −9.70977 −3.43292
\(9\) 0.0985659 0.0328553
\(10\) 8.01478 2.53449
\(11\) −1.00000 −0.301511
\(12\) −9.74634 −2.81353
\(13\) 4.17660 1.15838 0.579190 0.815192i \(-0.303369\pi\)
0.579190 + 0.815192i \(0.303369\pi\)
\(14\) −3.82595 −1.02253
\(15\) 5.13898 1.32688
\(16\) 15.5828 3.89571
\(17\) −4.04082 −0.980044 −0.490022 0.871710i \(-0.663011\pi\)
−0.490022 + 0.871710i \(0.663011\pi\)
\(18\) −0.270596 −0.0637801
\(19\) 4.18485 0.960071 0.480036 0.877249i \(-0.340624\pi\)
0.480036 + 0.877249i \(0.340624\pi\)
\(20\) −16.1644 −3.61446
\(21\) −2.45316 −0.535323
\(22\) 2.74533 0.585306
\(23\) 0.233100 0.0486047 0.0243023 0.999705i \(-0.492264\pi\)
0.0243023 + 0.999705i \(0.492264\pi\)
\(24\) 17.0919 3.48886
\(25\) 3.52303 0.704606
\(26\) −11.4661 −2.24870
\(27\) 5.10732 0.982904
\(28\) 7.71625 1.45823
\(29\) 6.60665 1.22682 0.613412 0.789763i \(-0.289796\pi\)
0.613412 + 0.789763i \(0.289796\pi\)
\(30\) −14.1082 −2.57579
\(31\) −10.0639 −1.80753 −0.903766 0.428026i \(-0.859209\pi\)
−0.903766 + 0.428026i \(0.859209\pi\)
\(32\) −23.3605 −4.12959
\(33\) 1.76027 0.306424
\(34\) 11.0934 1.90250
\(35\) −4.06857 −0.687714
\(36\) 0.545743 0.0909572
\(37\) 0.0900760 0.0148084 0.00740420 0.999973i \(-0.497643\pi\)
0.00740420 + 0.999973i \(0.497643\pi\)
\(38\) −11.4888 −1.86373
\(39\) −7.35196 −1.17726
\(40\) 28.3469 4.48204
\(41\) 5.18704 0.810080 0.405040 0.914299i \(-0.367258\pi\)
0.405040 + 0.914299i \(0.367258\pi\)
\(42\) 6.73472 1.03919
\(43\) 10.6096 1.61794 0.808971 0.587848i \(-0.200025\pi\)
0.808971 + 0.587848i \(0.200025\pi\)
\(44\) −5.53683 −0.834709
\(45\) −0.287756 −0.0428961
\(46\) −0.639936 −0.0943534
\(47\) 10.2834 1.49999 0.749995 0.661443i \(-0.230056\pi\)
0.749995 + 0.661443i \(0.230056\pi\)
\(48\) −27.4301 −3.95919
\(49\) −5.05782 −0.722545
\(50\) −9.67187 −1.36781
\(51\) 7.11296 0.996013
\(52\) 23.1251 3.20688
\(53\) 2.66520 0.366094 0.183047 0.983104i \(-0.441404\pi\)
0.183047 + 0.983104i \(0.441404\pi\)
\(54\) −14.0213 −1.90805
\(55\) 2.91942 0.393655
\(56\) −13.5317 −1.80826
\(57\) −7.36649 −0.975716
\(58\) −18.1374 −2.38156
\(59\) 7.50326 0.976842 0.488421 0.872608i \(-0.337573\pi\)
0.488421 + 0.872608i \(0.337573\pi\)
\(60\) 28.4537 3.67336
\(61\) −2.25827 −0.289141 −0.144571 0.989494i \(-0.546180\pi\)
−0.144571 + 0.989494i \(0.546180\pi\)
\(62\) 27.6288 3.50886
\(63\) 0.137364 0.0173062
\(64\) 32.9666 4.12082
\(65\) −12.1933 −1.51239
\(66\) −4.83253 −0.594844
\(67\) −8.19712 −1.00144 −0.500719 0.865610i \(-0.666931\pi\)
−0.500719 + 0.865610i \(0.666931\pi\)
\(68\) −22.3734 −2.71317
\(69\) −0.410320 −0.0493967
\(70\) 11.1696 1.33502
\(71\) −14.1572 −1.68015 −0.840075 0.542470i \(-0.817489\pi\)
−0.840075 + 0.542470i \(0.817489\pi\)
\(72\) −0.957052 −0.112790
\(73\) 10.4395 1.22185 0.610926 0.791687i \(-0.290797\pi\)
0.610926 + 0.791687i \(0.290797\pi\)
\(74\) −0.247288 −0.0287467
\(75\) −6.20150 −0.716087
\(76\) 23.1708 2.65788
\(77\) −1.39362 −0.158818
\(78\) 20.1836 2.28534
\(79\) −7.55634 −0.850155 −0.425078 0.905157i \(-0.639753\pi\)
−0.425078 + 0.905157i \(0.639753\pi\)
\(80\) −45.4929 −5.08626
\(81\) −9.28598 −1.03178
\(82\) −14.2401 −1.57256
\(83\) −0.344433 −0.0378064 −0.0189032 0.999821i \(-0.506017\pi\)
−0.0189032 + 0.999821i \(0.506017\pi\)
\(84\) −13.5827 −1.48200
\(85\) 11.7969 1.27955
\(86\) −29.1267 −3.14082
\(87\) −11.6295 −1.24682
\(88\) 9.70977 1.03506
\(89\) 0.821841 0.0871149 0.0435575 0.999051i \(-0.486131\pi\)
0.0435575 + 0.999051i \(0.486131\pi\)
\(90\) 0.789984 0.0832716
\(91\) 5.82060 0.610165
\(92\) 1.29063 0.134558
\(93\) 17.7153 1.83699
\(94\) −28.2314 −2.91184
\(95\) −12.2174 −1.25347
\(96\) 41.1209 4.19688
\(97\) 1.35371 0.137449 0.0687243 0.997636i \(-0.478107\pi\)
0.0687243 + 0.997636i \(0.478107\pi\)
\(98\) 13.8854 1.40263
\(99\) −0.0985659 −0.00990625
\(100\) 19.5064 1.95064
\(101\) −14.6047 −1.45322 −0.726609 0.687051i \(-0.758905\pi\)
−0.726609 + 0.687051i \(0.758905\pi\)
\(102\) −19.5274 −1.93350
\(103\) 14.6073 1.43930 0.719651 0.694336i \(-0.244302\pi\)
0.719651 + 0.694336i \(0.244302\pi\)
\(104\) −40.5538 −3.97663
\(105\) 7.16180 0.698920
\(106\) −7.31686 −0.710677
\(107\) 9.63702 0.931646 0.465823 0.884878i \(-0.345758\pi\)
0.465823 + 0.884878i \(0.345758\pi\)
\(108\) 28.2784 2.72109
\(109\) 9.25588 0.886553 0.443276 0.896385i \(-0.353816\pi\)
0.443276 + 0.896385i \(0.353816\pi\)
\(110\) −8.01478 −0.764179
\(111\) −0.158558 −0.0150497
\(112\) 21.7166 2.05202
\(113\) 3.96690 0.373175 0.186587 0.982438i \(-0.440257\pi\)
0.186587 + 0.982438i \(0.440257\pi\)
\(114\) 20.2234 1.89410
\(115\) −0.680517 −0.0634585
\(116\) 36.5799 3.39636
\(117\) 0.411671 0.0380590
\(118\) −20.5989 −1.89629
\(119\) −5.63138 −0.516228
\(120\) −49.8983 −4.55507
\(121\) 1.00000 0.0909091
\(122\) 6.19968 0.561293
\(123\) −9.13061 −0.823280
\(124\) −55.7222 −5.00400
\(125\) 4.31191 0.385669
\(126\) −0.377108 −0.0335955
\(127\) 6.06002 0.537739 0.268870 0.963177i \(-0.413350\pi\)
0.268870 + 0.963177i \(0.413350\pi\)
\(128\) −43.7831 −3.86991
\(129\) −18.6757 −1.64431
\(130\) 33.4745 2.93591
\(131\) −6.79270 −0.593481 −0.296741 0.954958i \(-0.595900\pi\)
−0.296741 + 0.954958i \(0.595900\pi\)
\(132\) 9.74634 0.848310
\(133\) 5.83210 0.505708
\(134\) 22.5038 1.94403
\(135\) −14.9104 −1.28329
\(136\) 39.2355 3.36441
\(137\) −8.44497 −0.721503 −0.360751 0.932662i \(-0.617480\pi\)
−0.360751 + 0.932662i \(0.617480\pi\)
\(138\) 1.12646 0.0958908
\(139\) −6.39878 −0.542737 −0.271369 0.962475i \(-0.587476\pi\)
−0.271369 + 0.962475i \(0.587476\pi\)
\(140\) −22.5270 −1.90388
\(141\) −18.1016 −1.52443
\(142\) 38.8662 3.26158
\(143\) −4.17660 −0.349265
\(144\) 1.53594 0.127995
\(145\) −19.2876 −1.60175
\(146\) −28.6599 −2.37191
\(147\) 8.90315 0.734319
\(148\) 0.498735 0.0409958
\(149\) 18.1623 1.48792 0.743959 0.668225i \(-0.232946\pi\)
0.743959 + 0.668225i \(0.232946\pi\)
\(150\) 17.0251 1.39010
\(151\) 0.662890 0.0539452 0.0269726 0.999636i \(-0.491413\pi\)
0.0269726 + 0.999636i \(0.491413\pi\)
\(152\) −40.6340 −3.29585
\(153\) −0.398288 −0.0321996
\(154\) 3.82595 0.308304
\(155\) 29.3808 2.35992
\(156\) −40.7066 −3.25914
\(157\) −9.77593 −0.780204 −0.390102 0.920772i \(-0.627560\pi\)
−0.390102 + 0.920772i \(0.627560\pi\)
\(158\) 20.7446 1.65036
\(159\) −4.69149 −0.372059
\(160\) 68.1992 5.39162
\(161\) 0.324853 0.0256020
\(162\) 25.4931 2.00293
\(163\) 1.01986 0.0798812 0.0399406 0.999202i \(-0.487283\pi\)
0.0399406 + 0.999202i \(0.487283\pi\)
\(164\) 28.7198 2.24264
\(165\) −5.13898 −0.400069
\(166\) 0.945582 0.0733914
\(167\) −1.92166 −0.148703 −0.0743513 0.997232i \(-0.523689\pi\)
−0.0743513 + 0.997232i \(0.523689\pi\)
\(168\) 23.8196 1.83772
\(169\) 4.44399 0.341846
\(170\) −32.3863 −2.48392
\(171\) 0.412484 0.0315434
\(172\) 58.7433 4.47914
\(173\) −0.598043 −0.0454684 −0.0227342 0.999742i \(-0.507237\pi\)
−0.0227342 + 0.999742i \(0.507237\pi\)
\(174\) 31.9269 2.42037
\(175\) 4.90977 0.371144
\(176\) −15.5828 −1.17460
\(177\) −13.2078 −0.992759
\(178\) −2.25622 −0.169111
\(179\) 11.0169 0.823439 0.411719 0.911311i \(-0.364928\pi\)
0.411719 + 0.911311i \(0.364928\pi\)
\(180\) −1.59325 −0.118754
\(181\) −6.65971 −0.495012 −0.247506 0.968886i \(-0.579611\pi\)
−0.247506 + 0.968886i \(0.579611\pi\)
\(182\) −15.9795 −1.18448
\(183\) 3.97517 0.293853
\(184\) −2.26334 −0.166856
\(185\) −0.262970 −0.0193339
\(186\) −48.6342 −3.56603
\(187\) 4.04082 0.295494
\(188\) 56.9376 4.15260
\(189\) 7.11767 0.517735
\(190\) 33.5407 2.43330
\(191\) −24.1186 −1.74516 −0.872581 0.488470i \(-0.837555\pi\)
−0.872581 + 0.488470i \(0.837555\pi\)
\(192\) −58.0302 −4.18797
\(193\) −2.73543 −0.196900 −0.0984502 0.995142i \(-0.531389\pi\)
−0.0984502 + 0.995142i \(0.531389\pi\)
\(194\) −3.71638 −0.266821
\(195\) 21.4635 1.53703
\(196\) −28.0043 −2.00031
\(197\) 4.14743 0.295492 0.147746 0.989025i \(-0.452798\pi\)
0.147746 + 0.989025i \(0.452798\pi\)
\(198\) 0.270596 0.0192304
\(199\) 2.20216 0.156107 0.0780536 0.996949i \(-0.475129\pi\)
0.0780536 + 0.996949i \(0.475129\pi\)
\(200\) −34.2078 −2.41886
\(201\) 14.4292 1.01776
\(202\) 40.0946 2.82105
\(203\) 9.20717 0.646217
\(204\) 39.3833 2.75738
\(205\) −15.1432 −1.05764
\(206\) −40.1019 −2.79403
\(207\) 0.0229757 0.00159692
\(208\) 65.0833 4.51272
\(209\) −4.18485 −0.289472
\(210\) −19.6615 −1.35677
\(211\) −3.00306 −0.206739 −0.103370 0.994643i \(-0.532962\pi\)
−0.103370 + 0.994643i \(0.532962\pi\)
\(212\) 14.7568 1.01350
\(213\) 24.9206 1.70753
\(214\) −26.4568 −1.80855
\(215\) −30.9738 −2.11239
\(216\) −49.5909 −3.37423
\(217\) −14.0253 −0.952099
\(218\) −25.4104 −1.72101
\(219\) −18.3764 −1.24176
\(220\) 16.1644 1.08980
\(221\) −16.8769 −1.13526
\(222\) 0.435295 0.0292151
\(223\) −16.2916 −1.09097 −0.545485 0.838121i \(-0.683654\pi\)
−0.545485 + 0.838121i \(0.683654\pi\)
\(224\) −32.5557 −2.17522
\(225\) 0.347251 0.0231500
\(226\) −10.8904 −0.724422
\(227\) −16.4083 −1.08905 −0.544527 0.838743i \(-0.683291\pi\)
−0.544527 + 0.838743i \(0.683291\pi\)
\(228\) −40.7870 −2.70119
\(229\) 23.3002 1.53972 0.769862 0.638211i \(-0.220325\pi\)
0.769862 + 0.638211i \(0.220325\pi\)
\(230\) 1.86824 0.123188
\(231\) 2.45316 0.161406
\(232\) −64.1490 −4.21159
\(233\) 1.59536 0.104515 0.0522577 0.998634i \(-0.483358\pi\)
0.0522577 + 0.998634i \(0.483358\pi\)
\(234\) −1.13017 −0.0738816
\(235\) −30.0216 −1.95840
\(236\) 41.5443 2.70430
\(237\) 13.3012 0.864008
\(238\) 15.4600 1.00212
\(239\) −2.96461 −0.191765 −0.0958824 0.995393i \(-0.530567\pi\)
−0.0958824 + 0.995393i \(0.530567\pi\)
\(240\) 80.0800 5.16914
\(241\) −29.0139 −1.86895 −0.934473 0.356033i \(-0.884129\pi\)
−0.934473 + 0.356033i \(0.884129\pi\)
\(242\) −2.74533 −0.176476
\(243\) 1.02392 0.0656843
\(244\) −12.5036 −0.800463
\(245\) 14.7659 0.943359
\(246\) 25.0665 1.59818
\(247\) 17.4785 1.11213
\(248\) 97.7183 6.20512
\(249\) 0.606296 0.0384225
\(250\) −11.8376 −0.748676
\(251\) −28.6112 −1.80592 −0.902961 0.429723i \(-0.858611\pi\)
−0.902961 + 0.429723i \(0.858611\pi\)
\(252\) 0.760559 0.0479107
\(253\) −0.233100 −0.0146549
\(254\) −16.6367 −1.04388
\(255\) −20.7657 −1.30040
\(256\) 54.2658 3.39161
\(257\) −20.4485 −1.27555 −0.637773 0.770225i \(-0.720144\pi\)
−0.637773 + 0.770225i \(0.720144\pi\)
\(258\) 51.2710 3.19199
\(259\) 0.125532 0.00780017
\(260\) −67.5120 −4.18692
\(261\) 0.651191 0.0403077
\(262\) 18.6482 1.15209
\(263\) −0.931131 −0.0574160 −0.0287080 0.999588i \(-0.509139\pi\)
−0.0287080 + 0.999588i \(0.509139\pi\)
\(264\) −17.0919 −1.05193
\(265\) −7.78086 −0.477974
\(266\) −16.0110 −0.981700
\(267\) −1.44667 −0.0885345
\(268\) −45.3861 −2.77240
\(269\) −16.5950 −1.01181 −0.505907 0.862588i \(-0.668842\pi\)
−0.505907 + 0.862588i \(0.668842\pi\)
\(270\) 40.9340 2.49117
\(271\) 13.7921 0.837813 0.418907 0.908029i \(-0.362413\pi\)
0.418907 + 0.908029i \(0.362413\pi\)
\(272\) −62.9675 −3.81797
\(273\) −10.2459 −0.620107
\(274\) 23.1842 1.40061
\(275\) −3.52303 −0.212447
\(276\) −2.27187 −0.136751
\(277\) 1.31718 0.0791414 0.0395707 0.999217i \(-0.487401\pi\)
0.0395707 + 0.999217i \(0.487401\pi\)
\(278\) 17.5667 1.05358
\(279\) −0.991959 −0.0593871
\(280\) 39.5049 2.36087
\(281\) −0.103367 −0.00616633 −0.00308317 0.999995i \(-0.500981\pi\)
−0.00308317 + 0.999995i \(0.500981\pi\)
\(282\) 49.6950 2.95929
\(283\) −22.1311 −1.31556 −0.657780 0.753210i \(-0.728504\pi\)
−0.657780 + 0.753210i \(0.728504\pi\)
\(284\) −78.3860 −4.65136
\(285\) 21.5059 1.27390
\(286\) 11.4661 0.678007
\(287\) 7.22877 0.426701
\(288\) −2.30255 −0.135679
\(289\) −0.671742 −0.0395143
\(290\) 52.9508 3.10938
\(291\) −2.38290 −0.139688
\(292\) 57.8018 3.38260
\(293\) 24.0575 1.40545 0.702726 0.711461i \(-0.251966\pi\)
0.702726 + 0.711461i \(0.251966\pi\)
\(294\) −24.4421 −1.42549
\(295\) −21.9052 −1.27537
\(296\) −0.874617 −0.0508361
\(297\) −5.10732 −0.296357
\(298\) −49.8616 −2.88841
\(299\) 0.973565 0.0563027
\(300\) −34.3366 −1.98243
\(301\) 14.7857 0.852234
\(302\) −1.81985 −0.104721
\(303\) 25.7082 1.47690
\(304\) 65.2119 3.74016
\(305\) 6.59283 0.377504
\(306\) 1.09343 0.0625073
\(307\) −4.83792 −0.276115 −0.138057 0.990424i \(-0.544086\pi\)
−0.138057 + 0.990424i \(0.544086\pi\)
\(308\) −7.71625 −0.439674
\(309\) −25.7129 −1.46276
\(310\) −80.6600 −4.58118
\(311\) 23.4273 1.32844 0.664220 0.747538i \(-0.268764\pi\)
0.664220 + 0.747538i \(0.268764\pi\)
\(312\) 71.3859 4.04143
\(313\) 21.9358 1.23988 0.619941 0.784648i \(-0.287156\pi\)
0.619941 + 0.784648i \(0.287156\pi\)
\(314\) 26.8381 1.51456
\(315\) −0.401023 −0.0225951
\(316\) −41.8382 −2.35358
\(317\) 15.1930 0.853324 0.426662 0.904411i \(-0.359689\pi\)
0.426662 + 0.904411i \(0.359689\pi\)
\(318\) 12.8797 0.722257
\(319\) −6.60665 −0.369901
\(320\) −96.2433 −5.38017
\(321\) −16.9638 −0.946827
\(322\) −0.891828 −0.0496996
\(323\) −16.9103 −0.940912
\(324\) −51.4149 −2.85638
\(325\) 14.7143 0.816201
\(326\) −2.79984 −0.155069
\(327\) −16.2929 −0.900999
\(328\) −50.3650 −2.78094
\(329\) 14.3312 0.790104
\(330\) 14.1082 0.776631
\(331\) 23.1349 1.27161 0.635804 0.771850i \(-0.280668\pi\)
0.635804 + 0.771850i \(0.280668\pi\)
\(332\) −1.90707 −0.104664
\(333\) 0.00887842 0.000486534 0
\(334\) 5.27559 0.288667
\(335\) 23.9309 1.30748
\(336\) −38.2272 −2.08546
\(337\) −18.8948 −1.02927 −0.514634 0.857410i \(-0.672072\pi\)
−0.514634 + 0.857410i \(0.672072\pi\)
\(338\) −12.2002 −0.663605
\(339\) −6.98283 −0.379255
\(340\) 65.3173 3.54233
\(341\) 10.0639 0.544992
\(342\) −1.13240 −0.0612334
\(343\) −16.8040 −0.907333
\(344\) −103.016 −5.55427
\(345\) 1.19790 0.0644926
\(346\) 1.64182 0.0882650
\(347\) −8.54255 −0.458588 −0.229294 0.973357i \(-0.573642\pi\)
−0.229294 + 0.973357i \(0.573642\pi\)
\(348\) −64.3907 −3.45170
\(349\) −32.2973 −1.72883 −0.864417 0.502775i \(-0.832313\pi\)
−0.864417 + 0.502775i \(0.832313\pi\)
\(350\) −13.4789 −0.720479
\(351\) 21.3312 1.13858
\(352\) 23.3605 1.24512
\(353\) −11.2333 −0.597887 −0.298943 0.954271i \(-0.596634\pi\)
−0.298943 + 0.954271i \(0.596634\pi\)
\(354\) 36.2598 1.92718
\(355\) 41.3308 2.19361
\(356\) 4.55039 0.241170
\(357\) 9.91278 0.524640
\(358\) −30.2449 −1.59849
\(359\) 27.8100 1.46776 0.733878 0.679282i \(-0.237708\pi\)
0.733878 + 0.679282i \(0.237708\pi\)
\(360\) 2.79404 0.147259
\(361\) −1.48700 −0.0782630
\(362\) 18.2831 0.960938
\(363\) −1.76027 −0.0923904
\(364\) 32.2277 1.68919
\(365\) −30.4774 −1.59526
\(366\) −10.9131 −0.570439
\(367\) 13.4579 0.702499 0.351250 0.936282i \(-0.385757\pi\)
0.351250 + 0.936282i \(0.385757\pi\)
\(368\) 3.63236 0.189350
\(369\) 0.511266 0.0266154
\(370\) 0.721939 0.0375318
\(371\) 3.71429 0.192836
\(372\) 98.0864 5.08554
\(373\) 0.687232 0.0355835 0.0177918 0.999842i \(-0.494336\pi\)
0.0177918 + 0.999842i \(0.494336\pi\)
\(374\) −11.0934 −0.573626
\(375\) −7.59014 −0.391953
\(376\) −99.8496 −5.14935
\(377\) 27.5933 1.42113
\(378\) −19.5404 −1.00505
\(379\) −23.8203 −1.22357 −0.611785 0.791024i \(-0.709548\pi\)
−0.611785 + 0.791024i \(0.709548\pi\)
\(380\) −67.6454 −3.47014
\(381\) −10.6673 −0.546502
\(382\) 66.2135 3.38778
\(383\) 0.114211 0.00583593 0.00291797 0.999996i \(-0.499071\pi\)
0.00291797 + 0.999996i \(0.499071\pi\)
\(384\) 77.0702 3.93297
\(385\) 4.06857 0.207354
\(386\) 7.50965 0.382231
\(387\) 1.04574 0.0531580
\(388\) 7.49528 0.380515
\(389\) −20.2010 −1.02423 −0.512115 0.858917i \(-0.671138\pi\)
−0.512115 + 0.858917i \(0.671138\pi\)
\(390\) −58.9243 −2.98375
\(391\) −0.941915 −0.0476347
\(392\) 49.1102 2.48044
\(393\) 11.9570 0.603152
\(394\) −11.3861 −0.573621
\(395\) 22.0602 1.10997
\(396\) −0.545743 −0.0274246
\(397\) −2.84104 −0.142588 −0.0712938 0.997455i \(-0.522713\pi\)
−0.0712938 + 0.997455i \(0.522713\pi\)
\(398\) −6.04566 −0.303042
\(399\) −10.2661 −0.513948
\(400\) 54.8988 2.74494
\(401\) 30.2521 1.51072 0.755359 0.655311i \(-0.227462\pi\)
0.755359 + 0.655311i \(0.227462\pi\)
\(402\) −39.6128 −1.97571
\(403\) −42.0330 −2.09381
\(404\) −80.8635 −4.02311
\(405\) 27.1097 1.34709
\(406\) −25.2767 −1.25446
\(407\) −0.0900760 −0.00446490
\(408\) −69.0652 −3.41924
\(409\) 31.3126 1.54831 0.774155 0.632997i \(-0.218175\pi\)
0.774155 + 0.632997i \(0.218175\pi\)
\(410\) 41.5730 2.05314
\(411\) 14.8655 0.733259
\(412\) 80.8783 3.98459
\(413\) 10.4567 0.514541
\(414\) −0.0630758 −0.00310001
\(415\) 1.00555 0.0493603
\(416\) −97.5675 −4.78364
\(417\) 11.2636 0.551581
\(418\) 11.4888 0.561936
\(419\) 31.7629 1.55172 0.775859 0.630906i \(-0.217317\pi\)
0.775859 + 0.630906i \(0.217317\pi\)
\(420\) 39.6537 1.93490
\(421\) 7.42962 0.362097 0.181049 0.983474i \(-0.442051\pi\)
0.181049 + 0.983474i \(0.442051\pi\)
\(422\) 8.24438 0.401330
\(423\) 1.01359 0.0492827
\(424\) −25.8785 −1.25677
\(425\) −14.2359 −0.690544
\(426\) −68.4151 −3.31472
\(427\) −3.14717 −0.152302
\(428\) 53.3586 2.57918
\(429\) 7.35196 0.354956
\(430\) 85.0332 4.10067
\(431\) −16.9035 −0.814214 −0.407107 0.913381i \(-0.633462\pi\)
−0.407107 + 0.913381i \(0.633462\pi\)
\(432\) 79.5866 3.82911
\(433\) −0.933000 −0.0448371 −0.0224186 0.999749i \(-0.507137\pi\)
−0.0224186 + 0.999749i \(0.507137\pi\)
\(434\) 38.5040 1.84825
\(435\) 33.9515 1.62785
\(436\) 51.2483 2.45435
\(437\) 0.975488 0.0466639
\(438\) 50.4493 2.41056
\(439\) −11.4733 −0.547592 −0.273796 0.961788i \(-0.588279\pi\)
−0.273796 + 0.961788i \(0.588279\pi\)
\(440\) −28.3469 −1.35139
\(441\) −0.498529 −0.0237395
\(442\) 46.3327 2.20382
\(443\) 4.79990 0.228050 0.114025 0.993478i \(-0.463626\pi\)
0.114025 + 0.993478i \(0.463626\pi\)
\(444\) −0.877911 −0.0416638
\(445\) −2.39930 −0.113738
\(446\) 44.7259 2.11783
\(447\) −31.9707 −1.51216
\(448\) 45.9429 2.17060
\(449\) 13.3768 0.631290 0.315645 0.948877i \(-0.397779\pi\)
0.315645 + 0.948877i \(0.397779\pi\)
\(450\) −0.953317 −0.0449398
\(451\) −5.18704 −0.244248
\(452\) 21.9641 1.03310
\(453\) −1.16687 −0.0548243
\(454\) 45.0461 2.11412
\(455\) −16.9928 −0.796635
\(456\) 71.5269 3.34955
\(457\) 32.8355 1.53598 0.767991 0.640461i \(-0.221257\pi\)
0.767991 + 0.640461i \(0.221257\pi\)
\(458\) −63.9668 −2.98897
\(459\) −20.6378 −0.963289
\(460\) −3.76791 −0.175680
\(461\) 11.1740 0.520427 0.260213 0.965551i \(-0.416207\pi\)
0.260213 + 0.965551i \(0.416207\pi\)
\(462\) −6.73472 −0.313328
\(463\) −35.5155 −1.65054 −0.825272 0.564735i \(-0.808978\pi\)
−0.825272 + 0.564735i \(0.808978\pi\)
\(464\) 102.950 4.77935
\(465\) −51.7183 −2.39838
\(466\) −4.37978 −0.202889
\(467\) −25.7390 −1.19106 −0.595530 0.803333i \(-0.703058\pi\)
−0.595530 + 0.803333i \(0.703058\pi\)
\(468\) 2.27935 0.105363
\(469\) −11.4237 −0.527497
\(470\) 82.4193 3.80172
\(471\) 17.2083 0.792917
\(472\) −72.8549 −3.35342
\(473\) −10.6096 −0.487828
\(474\) −36.5163 −1.67725
\(475\) 14.7434 0.676472
\(476\) −31.1800 −1.42913
\(477\) 0.262698 0.0120281
\(478\) 8.13884 0.372262
\(479\) 35.0553 1.60172 0.800858 0.598854i \(-0.204377\pi\)
0.800858 + 0.598854i \(0.204377\pi\)
\(480\) −120.049 −5.47947
\(481\) 0.376211 0.0171538
\(482\) 79.6526 3.62808
\(483\) −0.571830 −0.0260192
\(484\) 5.53683 0.251674
\(485\) −3.95206 −0.179454
\(486\) −2.81099 −0.127509
\(487\) 21.2177 0.961464 0.480732 0.876867i \(-0.340371\pi\)
0.480732 + 0.876867i \(0.340371\pi\)
\(488\) 21.9272 0.992599
\(489\) −1.79522 −0.0811829
\(490\) −40.5373 −1.83129
\(491\) −14.9938 −0.676662 −0.338331 0.941027i \(-0.609862\pi\)
−0.338331 + 0.941027i \(0.609862\pi\)
\(492\) −50.5547 −2.27918
\(493\) −26.6963 −1.20234
\(494\) −47.9841 −2.15891
\(495\) 0.287756 0.0129337
\(496\) −156.824 −7.04162
\(497\) −19.7298 −0.885002
\(498\) −1.66448 −0.0745873
\(499\) 11.5706 0.517969 0.258985 0.965881i \(-0.416612\pi\)
0.258985 + 0.965881i \(0.416612\pi\)
\(500\) 23.8743 1.06769
\(501\) 3.38265 0.151126
\(502\) 78.5471 3.50573
\(503\) 7.10798 0.316929 0.158465 0.987365i \(-0.449346\pi\)
0.158465 + 0.987365i \(0.449346\pi\)
\(504\) −1.33377 −0.0594108
\(505\) 42.6372 1.89733
\(506\) 0.639936 0.0284486
\(507\) −7.82265 −0.347416
\(508\) 33.5533 1.48869
\(509\) −15.1023 −0.669399 −0.334700 0.942325i \(-0.608635\pi\)
−0.334700 + 0.942325i \(0.608635\pi\)
\(510\) 57.0088 2.52439
\(511\) 14.5487 0.643598
\(512\) −61.4114 −2.71403
\(513\) 21.3734 0.943658
\(514\) 56.1380 2.47614
\(515\) −42.6450 −1.87916
\(516\) −103.404 −4.55212
\(517\) −10.2834 −0.452264
\(518\) −0.344626 −0.0151420
\(519\) 1.05272 0.0462093
\(520\) 118.394 5.19191
\(521\) 26.4312 1.15797 0.578987 0.815337i \(-0.303448\pi\)
0.578987 + 0.815337i \(0.303448\pi\)
\(522\) −1.78773 −0.0782469
\(523\) 2.91773 0.127584 0.0637918 0.997963i \(-0.479681\pi\)
0.0637918 + 0.997963i \(0.479681\pi\)
\(524\) −37.6100 −1.64300
\(525\) −8.64254 −0.377191
\(526\) 2.55626 0.111458
\(527\) 40.6665 1.77146
\(528\) 27.4301 1.19374
\(529\) −22.9457 −0.997638
\(530\) 21.3610 0.927863
\(531\) 0.739566 0.0320944
\(532\) 32.2914 1.40001
\(533\) 21.6642 0.938381
\(534\) 3.97157 0.171867
\(535\) −28.1345 −1.21636
\(536\) 79.5921 3.43786
\(537\) −19.3927 −0.836857
\(538\) 45.5586 1.96417
\(539\) 5.05782 0.217856
\(540\) −82.5565 −3.55267
\(541\) −17.4476 −0.750132 −0.375066 0.926998i \(-0.622380\pi\)
−0.375066 + 0.926998i \(0.622380\pi\)
\(542\) −37.8640 −1.62640
\(543\) 11.7229 0.503078
\(544\) 94.3957 4.04718
\(545\) −27.0218 −1.15749
\(546\) 28.1282 1.20378
\(547\) 1.00000 0.0427569
\(548\) −46.7584 −1.99742
\(549\) −0.222588 −0.00949983
\(550\) 9.67187 0.412410
\(551\) 27.6479 1.17784
\(552\) 3.98411 0.169575
\(553\) −10.5307 −0.447810
\(554\) −3.61608 −0.153632
\(555\) 0.462899 0.0196490
\(556\) −35.4290 −1.50252
\(557\) −40.0753 −1.69804 −0.849022 0.528358i \(-0.822808\pi\)
−0.849022 + 0.528358i \(0.822808\pi\)
\(558\) 2.72325 0.115285
\(559\) 44.3119 1.87419
\(560\) −63.3999 −2.67913
\(561\) −7.11296 −0.300309
\(562\) 0.283775 0.0119703
\(563\) 36.6473 1.54450 0.772249 0.635320i \(-0.219132\pi\)
0.772249 + 0.635320i \(0.219132\pi\)
\(564\) −100.226 −4.22026
\(565\) −11.5811 −0.487219
\(566\) 60.7573 2.55382
\(567\) −12.9411 −0.543477
\(568\) 137.463 5.76782
\(569\) 7.94421 0.333038 0.166519 0.986038i \(-0.446747\pi\)
0.166519 + 0.986038i \(0.446747\pi\)
\(570\) −59.0408 −2.47295
\(571\) −28.5304 −1.19396 −0.596981 0.802256i \(-0.703633\pi\)
−0.596981 + 0.802256i \(0.703633\pi\)
\(572\) −23.1251 −0.966911
\(573\) 42.4554 1.77360
\(574\) −19.8454 −0.828329
\(575\) 0.821217 0.0342471
\(576\) 3.24938 0.135391
\(577\) 3.12857 0.130244 0.0651221 0.997877i \(-0.479256\pi\)
0.0651221 + 0.997877i \(0.479256\pi\)
\(578\) 1.84415 0.0767067
\(579\) 4.81510 0.200109
\(580\) −106.792 −4.43431
\(581\) −0.480009 −0.0199141
\(582\) 6.54186 0.271169
\(583\) −2.66520 −0.110381
\(584\) −101.365 −4.19452
\(585\) −1.20184 −0.0496900
\(586\) −66.0456 −2.72832
\(587\) 24.8519 1.02575 0.512873 0.858464i \(-0.328581\pi\)
0.512873 + 0.858464i \(0.328581\pi\)
\(588\) 49.2952 2.03290
\(589\) −42.1160 −1.73536
\(590\) 60.1370 2.47580
\(591\) −7.30061 −0.300307
\(592\) 1.40364 0.0576892
\(593\) 14.8903 0.611471 0.305736 0.952116i \(-0.401098\pi\)
0.305736 + 0.952116i \(0.401098\pi\)
\(594\) 14.0213 0.575300
\(595\) 16.4404 0.673990
\(596\) 100.562 4.11917
\(597\) −3.87641 −0.158651
\(598\) −2.67276 −0.109297
\(599\) 20.4039 0.833680 0.416840 0.908980i \(-0.363137\pi\)
0.416840 + 0.908980i \(0.363137\pi\)
\(600\) 60.2151 2.45827
\(601\) −35.8147 −1.46091 −0.730457 0.682959i \(-0.760693\pi\)
−0.730457 + 0.682959i \(0.760693\pi\)
\(602\) −40.5916 −1.65439
\(603\) −0.807957 −0.0329025
\(604\) 3.67031 0.149343
\(605\) −2.91942 −0.118691
\(606\) −70.5775 −2.86701
\(607\) 5.20724 0.211355 0.105678 0.994400i \(-0.466299\pi\)
0.105678 + 0.994400i \(0.466299\pi\)
\(608\) −97.7603 −3.96470
\(609\) −16.2072 −0.656747
\(610\) −18.0995 −0.732827
\(611\) 42.9497 1.73756
\(612\) −2.20525 −0.0891420
\(613\) 43.1599 1.74321 0.871607 0.490206i \(-0.163078\pi\)
0.871607 + 0.490206i \(0.163078\pi\)
\(614\) 13.2817 0.536005
\(615\) 26.6561 1.07488
\(616\) 13.5317 0.545210
\(617\) 30.2381 1.21734 0.608671 0.793423i \(-0.291703\pi\)
0.608671 + 0.793423i \(0.291703\pi\)
\(618\) 70.5904 2.83956
\(619\) 26.6695 1.07194 0.535970 0.844237i \(-0.319946\pi\)
0.535970 + 0.844237i \(0.319946\pi\)
\(620\) 162.677 6.53325
\(621\) 1.19052 0.0477737
\(622\) −64.3156 −2.57882
\(623\) 1.14534 0.0458869
\(624\) −114.564 −4.58625
\(625\) −30.2034 −1.20814
\(626\) −60.2209 −2.40691
\(627\) 7.36649 0.294189
\(628\) −54.1277 −2.15993
\(629\) −0.363981 −0.0145129
\(630\) 1.10094 0.0438625
\(631\) 15.2518 0.607164 0.303582 0.952805i \(-0.401817\pi\)
0.303582 + 0.952805i \(0.401817\pi\)
\(632\) 73.3703 2.91852
\(633\) 5.28621 0.210108
\(634\) −41.7098 −1.65651
\(635\) −17.6917 −0.702075
\(636\) −25.9760 −1.03002
\(637\) −21.1245 −0.836983
\(638\) 18.1374 0.718068
\(639\) −1.39542 −0.0552019
\(640\) 127.821 5.05258
\(641\) 46.1642 1.82338 0.911689 0.410881i \(-0.134779\pi\)
0.911689 + 0.410881i \(0.134779\pi\)
\(642\) 46.5712 1.83802
\(643\) −21.0821 −0.831396 −0.415698 0.909503i \(-0.636463\pi\)
−0.415698 + 0.909503i \(0.636463\pi\)
\(644\) 1.79866 0.0708770
\(645\) 54.5223 2.14682
\(646\) 46.4242 1.82654
\(647\) 46.6933 1.83570 0.917852 0.396924i \(-0.129922\pi\)
0.917852 + 0.396924i \(0.129922\pi\)
\(648\) 90.1647 3.54201
\(649\) −7.50326 −0.294529
\(650\) −40.3955 −1.58444
\(651\) 24.6884 0.967613
\(652\) 5.64677 0.221144
\(653\) 21.8463 0.854911 0.427456 0.904036i \(-0.359410\pi\)
0.427456 + 0.904036i \(0.359410\pi\)
\(654\) 44.7294 1.74906
\(655\) 19.8308 0.774852
\(656\) 80.8288 3.15584
\(657\) 1.02898 0.0401444
\(658\) −39.3439 −1.53378
\(659\) 19.3462 0.753620 0.376810 0.926291i \(-0.377021\pi\)
0.376810 + 0.926291i \(0.377021\pi\)
\(660\) −28.4537 −1.10756
\(661\) 3.66906 0.142710 0.0713550 0.997451i \(-0.477268\pi\)
0.0713550 + 0.997451i \(0.477268\pi\)
\(662\) −63.5129 −2.46850
\(663\) 29.7080 1.15376
\(664\) 3.34436 0.129786
\(665\) −17.0264 −0.660255
\(666\) −0.0243742 −0.000944481 0
\(667\) 1.54001 0.0596294
\(668\) −10.6399 −0.411671
\(669\) 28.6778 1.10875
\(670\) −65.6981 −2.53814
\(671\) 2.25827 0.0871794
\(672\) 57.3070 2.21066
\(673\) 36.4040 1.40327 0.701636 0.712536i \(-0.252453\pi\)
0.701636 + 0.712536i \(0.252453\pi\)
\(674\) 51.8725 1.99806
\(675\) 17.9932 0.692560
\(676\) 24.6056 0.946371
\(677\) 18.5883 0.714407 0.357203 0.934027i \(-0.383730\pi\)
0.357203 + 0.934027i \(0.383730\pi\)
\(678\) 19.1702 0.736226
\(679\) 1.88656 0.0723996
\(680\) −114.545 −4.39260
\(681\) 28.8830 1.10680
\(682\) −27.6288 −1.05796
\(683\) −6.28731 −0.240577 −0.120289 0.992739i \(-0.538382\pi\)
−0.120289 + 0.992739i \(0.538382\pi\)
\(684\) 2.28385 0.0873254
\(685\) 24.6544 0.941998
\(686\) 46.1326 1.76135
\(687\) −41.0148 −1.56481
\(688\) 165.327 6.30303
\(689\) 11.1315 0.424076
\(690\) −3.28862 −0.125196
\(691\) 31.4679 1.19710 0.598548 0.801087i \(-0.295745\pi\)
0.598548 + 0.801087i \(0.295745\pi\)
\(692\) −3.31126 −0.125875
\(693\) −0.137364 −0.00521801
\(694\) 23.4521 0.890230
\(695\) 18.6807 0.708601
\(696\) 112.920 4.28022
\(697\) −20.9599 −0.793913
\(698\) 88.6667 3.35609
\(699\) −2.80827 −0.106218
\(700\) 27.1846 1.02748
\(701\) −44.8385 −1.69353 −0.846763 0.531971i \(-0.821452\pi\)
−0.846763 + 0.531971i \(0.821452\pi\)
\(702\) −58.5613 −2.21025
\(703\) 0.376955 0.0142171
\(704\) −32.9666 −1.24247
\(705\) 52.8463 1.99031
\(706\) 30.8390 1.16064
\(707\) −20.3534 −0.765467
\(708\) −73.1294 −2.74837
\(709\) −16.7550 −0.629246 −0.314623 0.949217i \(-0.601878\pi\)
−0.314623 + 0.949217i \(0.601878\pi\)
\(710\) −113.467 −4.25833
\(711\) −0.744798 −0.0279321
\(712\) −7.97988 −0.299059
\(713\) −2.34590 −0.0878545
\(714\) −27.2138 −1.01845
\(715\) 12.1933 0.456002
\(716\) 60.9985 2.27962
\(717\) 5.21853 0.194890
\(718\) −76.3476 −2.84927
\(719\) 15.1433 0.564751 0.282375 0.959304i \(-0.408878\pi\)
0.282375 + 0.959304i \(0.408878\pi\)
\(720\) −4.48405 −0.167111
\(721\) 20.3571 0.758138
\(722\) 4.08230 0.151927
\(723\) 51.0723 1.89940
\(724\) −36.8737 −1.37040
\(725\) 23.2754 0.864427
\(726\) 4.83253 0.179352
\(727\) 32.3389 1.19938 0.599691 0.800232i \(-0.295290\pi\)
0.599691 + 0.800232i \(0.295290\pi\)
\(728\) −56.5167 −2.09465
\(729\) 26.0556 0.965021
\(730\) 83.6704 3.09678
\(731\) −42.8713 −1.58565
\(732\) 22.0098 0.813507
\(733\) −4.80015 −0.177298 −0.0886488 0.996063i \(-0.528255\pi\)
−0.0886488 + 0.996063i \(0.528255\pi\)
\(734\) −36.9465 −1.36372
\(735\) −25.9920 −0.958731
\(736\) −5.44533 −0.200717
\(737\) 8.19712 0.301945
\(738\) −1.40359 −0.0516669
\(739\) −18.2578 −0.671625 −0.335813 0.941929i \(-0.609011\pi\)
−0.335813 + 0.941929i \(0.609011\pi\)
\(740\) −1.45602 −0.0535243
\(741\) −30.7669 −1.13025
\(742\) −10.1969 −0.374341
\(743\) 23.7385 0.870880 0.435440 0.900218i \(-0.356593\pi\)
0.435440 + 0.900218i \(0.356593\pi\)
\(744\) −172.011 −6.30623
\(745\) −53.0236 −1.94263
\(746\) −1.88668 −0.0690762
\(747\) −0.0339493 −0.00124214
\(748\) 22.3734 0.818051
\(749\) 13.4304 0.490735
\(750\) 20.8374 0.760875
\(751\) −19.0061 −0.693542 −0.346771 0.937950i \(-0.612722\pi\)
−0.346771 + 0.937950i \(0.612722\pi\)
\(752\) 160.245 5.84353
\(753\) 50.3635 1.83535
\(754\) −75.7528 −2.75875
\(755\) −1.93526 −0.0704312
\(756\) 39.4094 1.43330
\(757\) 11.4560 0.416375 0.208188 0.978089i \(-0.433244\pi\)
0.208188 + 0.978089i \(0.433244\pi\)
\(758\) 65.3947 2.37524
\(759\) 0.410320 0.0148937
\(760\) 118.628 4.30308
\(761\) 5.45779 0.197845 0.0989224 0.995095i \(-0.468460\pi\)
0.0989224 + 0.995095i \(0.468460\pi\)
\(762\) 29.2852 1.06089
\(763\) 12.8992 0.466982
\(764\) −133.541 −4.83133
\(765\) 1.16277 0.0420400
\(766\) −0.313548 −0.0113290
\(767\) 31.3381 1.13155
\(768\) −95.5228 −3.44688
\(769\) 22.1372 0.798288 0.399144 0.916888i \(-0.369307\pi\)
0.399144 + 0.916888i \(0.369307\pi\)
\(770\) −11.1696 −0.402523
\(771\) 35.9951 1.29633
\(772\) −15.1456 −0.545102
\(773\) 49.7206 1.78833 0.894164 0.447740i \(-0.147771\pi\)
0.894164 + 0.447740i \(0.147771\pi\)
\(774\) −2.87090 −0.103192
\(775\) −35.4555 −1.27360
\(776\) −13.1442 −0.471850
\(777\) −0.220970 −0.00792727
\(778\) 55.4583 1.98828
\(779\) 21.7070 0.777734
\(780\) 118.840 4.25514
\(781\) 14.1572 0.506584
\(782\) 2.58587 0.0924704
\(783\) 33.7423 1.20585
\(784\) −78.8152 −2.81483
\(785\) 28.5401 1.01864
\(786\) −32.8260 −1.17086
\(787\) 48.9531 1.74499 0.872496 0.488622i \(-0.162500\pi\)
0.872496 + 0.488622i \(0.162500\pi\)
\(788\) 22.9636 0.818045
\(789\) 1.63905 0.0583516
\(790\) −60.5624 −2.15471
\(791\) 5.52836 0.196566
\(792\) 0.957052 0.0340074
\(793\) −9.43188 −0.334936
\(794\) 7.79958 0.276797
\(795\) 13.6964 0.485763
\(796\) 12.1930 0.432170
\(797\) 44.3730 1.57177 0.785886 0.618371i \(-0.212207\pi\)
0.785886 + 0.618371i \(0.212207\pi\)
\(798\) 28.1838 0.997697
\(799\) −41.5535 −1.47006
\(800\) −82.2997 −2.90973
\(801\) 0.0810055 0.00286219
\(802\) −83.0520 −2.93267
\(803\) −10.4395 −0.368402
\(804\) 79.8919 2.81757
\(805\) −0.948383 −0.0334261
\(806\) 115.394 4.06459
\(807\) 29.2117 1.02830
\(808\) 141.808 4.98878
\(809\) 17.3397 0.609633 0.304816 0.952411i \(-0.401405\pi\)
0.304816 + 0.952411i \(0.401405\pi\)
\(810\) −74.4251 −2.61503
\(811\) −1.03704 −0.0364154 −0.0182077 0.999834i \(-0.505796\pi\)
−0.0182077 + 0.999834i \(0.505796\pi\)
\(812\) 50.9786 1.78900
\(813\) −24.2780 −0.851465
\(814\) 0.247288 0.00866744
\(815\) −2.97739 −0.104293
\(816\) 110.840 3.88018
\(817\) 44.3994 1.55334
\(818\) −85.9634 −3.00564
\(819\) 0.573713 0.0200472
\(820\) −83.8451 −2.92800
\(821\) 48.7330 1.70079 0.850397 0.526141i \(-0.176362\pi\)
0.850397 + 0.526141i \(0.176362\pi\)
\(822\) −40.8106 −1.42343
\(823\) 20.5954 0.717911 0.358956 0.933355i \(-0.383133\pi\)
0.358956 + 0.933355i \(0.383133\pi\)
\(824\) −141.834 −4.94101
\(825\) 6.20150 0.215908
\(826\) −28.7071 −0.998848
\(827\) −17.0096 −0.591481 −0.295741 0.955268i \(-0.595566\pi\)
−0.295741 + 0.955268i \(0.595566\pi\)
\(828\) 0.127213 0.00442094
\(829\) 21.1487 0.734524 0.367262 0.930117i \(-0.380295\pi\)
0.367262 + 0.930117i \(0.380295\pi\)
\(830\) −2.76055 −0.0958202
\(831\) −2.31859 −0.0804310
\(832\) 137.688 4.77348
\(833\) 20.4378 0.708126
\(834\) −30.9223 −1.07075
\(835\) 5.61014 0.194147
\(836\) −23.1708 −0.801380
\(837\) −51.3996 −1.77663
\(838\) −87.1995 −3.01226
\(839\) −44.5242 −1.53715 −0.768573 0.639762i \(-0.779033\pi\)
−0.768573 + 0.639762i \(0.779033\pi\)
\(840\) −69.5394 −2.39934
\(841\) 14.6478 0.505098
\(842\) −20.3967 −0.702918
\(843\) 0.181954 0.00626681
\(844\) −16.6274 −0.572340
\(845\) −12.9739 −0.446316
\(846\) −2.78265 −0.0956695
\(847\) 1.39362 0.0478854
\(848\) 41.5315 1.42620
\(849\) 38.9569 1.33700
\(850\) 39.0823 1.34051
\(851\) 0.0209967 0.000719757 0
\(852\) 137.981 4.72715
\(853\) −20.2031 −0.691741 −0.345871 0.938282i \(-0.612416\pi\)
−0.345871 + 0.938282i \(0.612416\pi\)
\(854\) 8.64001 0.295655
\(855\) −1.20422 −0.0411833
\(856\) −93.5733 −3.19827
\(857\) −55.0124 −1.87919 −0.939595 0.342289i \(-0.888798\pi\)
−0.939595 + 0.342289i \(0.888798\pi\)
\(858\) −20.1836 −0.689055
\(859\) −17.9952 −0.613987 −0.306993 0.951712i \(-0.599323\pi\)
−0.306993 + 0.951712i \(0.599323\pi\)
\(860\) −171.497 −5.84799
\(861\) −12.7246 −0.433654
\(862\) 46.4057 1.58058
\(863\) −31.0200 −1.05593 −0.527966 0.849266i \(-0.677045\pi\)
−0.527966 + 0.849266i \(0.677045\pi\)
\(864\) −119.310 −4.05899
\(865\) 1.74594 0.0593637
\(866\) 2.56139 0.0870397
\(867\) 1.18245 0.0401581
\(868\) −77.6557 −2.63581
\(869\) 7.55634 0.256331
\(870\) −93.2080 −3.16005
\(871\) −34.2361 −1.16005
\(872\) −89.8725 −3.04347
\(873\) 0.133430 0.00451592
\(874\) −2.67804 −0.0905859
\(875\) 6.00917 0.203147
\(876\) −101.747 −3.43772
\(877\) −22.4479 −0.758012 −0.379006 0.925394i \(-0.623734\pi\)
−0.379006 + 0.925394i \(0.623734\pi\)
\(878\) 31.4980 1.06301
\(879\) −42.3477 −1.42835
\(880\) 45.4929 1.53357
\(881\) 25.3401 0.853730 0.426865 0.904315i \(-0.359618\pi\)
0.426865 + 0.904315i \(0.359618\pi\)
\(882\) 1.36863 0.0460840
\(883\) 19.4402 0.654214 0.327107 0.944987i \(-0.393926\pi\)
0.327107 + 0.944987i \(0.393926\pi\)
\(884\) −93.4446 −3.14288
\(885\) 38.5592 1.29615
\(886\) −13.1773 −0.442700
\(887\) −19.9544 −0.670002 −0.335001 0.942218i \(-0.608737\pi\)
−0.335001 + 0.942218i \(0.608737\pi\)
\(888\) 1.53957 0.0516644
\(889\) 8.44537 0.283249
\(890\) 6.58687 0.220792
\(891\) 9.28598 0.311092
\(892\) −90.2041 −3.02026
\(893\) 43.0346 1.44010
\(894\) 87.7701 2.93547
\(895\) −32.1629 −1.07509
\(896\) −61.0171 −2.03844
\(897\) −1.71374 −0.0572201
\(898\) −36.7237 −1.22549
\(899\) −66.4888 −2.21752
\(900\) 1.92267 0.0640889
\(901\) −10.7696 −0.358788
\(902\) 14.2401 0.474145
\(903\) −26.0269 −0.866121
\(904\) −38.5177 −1.28108
\(905\) 19.4425 0.646291
\(906\) 3.20344 0.106427
\(907\) 21.7942 0.723663 0.361832 0.932243i \(-0.382152\pi\)
0.361832 + 0.932243i \(0.382152\pi\)
\(908\) −90.8498 −3.01496
\(909\) −1.43952 −0.0477459
\(910\) 46.6508 1.54646
\(911\) −43.9366 −1.45569 −0.727843 0.685744i \(-0.759477\pi\)
−0.727843 + 0.685744i \(0.759477\pi\)
\(912\) −114.791 −3.80111
\(913\) 0.344433 0.0113991
\(914\) −90.1444 −2.98171
\(915\) −11.6052 −0.383656
\(916\) 129.010 4.26260
\(917\) −9.46646 −0.312610
\(918\) 56.6575 1.86998
\(919\) 44.0816 1.45412 0.727058 0.686576i \(-0.240887\pi\)
0.727058 + 0.686576i \(0.240887\pi\)
\(920\) 6.60766 0.217848
\(921\) 8.51606 0.280614
\(922\) −30.6764 −1.01027
\(923\) −59.1290 −1.94625
\(924\) 13.5827 0.446839
\(925\) 0.317340 0.0104341
\(926\) 97.5017 3.20410
\(927\) 1.43978 0.0472887
\(928\) −154.335 −5.06628
\(929\) −39.3871 −1.29225 −0.646124 0.763232i \(-0.723611\pi\)
−0.646124 + 0.763232i \(0.723611\pi\)
\(930\) 141.984 4.65583
\(931\) −21.1662 −0.693695
\(932\) 8.83323 0.289342
\(933\) −41.2384 −1.35009
\(934\) 70.6621 2.31214
\(935\) −11.7969 −0.385799
\(936\) −3.99723 −0.130653
\(937\) 46.4279 1.51673 0.758367 0.651828i \(-0.225998\pi\)
0.758367 + 0.651828i \(0.225998\pi\)
\(938\) 31.3618 1.02400
\(939\) −38.6130 −1.26009
\(940\) −166.225 −5.42165
\(941\) 6.78771 0.221273 0.110637 0.993861i \(-0.464711\pi\)
0.110637 + 0.993861i \(0.464711\pi\)
\(942\) −47.2425 −1.53924
\(943\) 1.20910 0.0393736
\(944\) 116.922 3.80549
\(945\) −20.7795 −0.675957
\(946\) 29.1267 0.946991
\(947\) −11.8387 −0.384705 −0.192353 0.981326i \(-0.561612\pi\)
−0.192353 + 0.981326i \(0.561612\pi\)
\(948\) 73.6467 2.39193
\(949\) 43.6017 1.41537
\(950\) −40.4754 −1.31319
\(951\) −26.7438 −0.867229
\(952\) 54.6794 1.77217
\(953\) 7.88246 0.255338 0.127669 0.991817i \(-0.459251\pi\)
0.127669 + 0.991817i \(0.459251\pi\)
\(954\) −0.721193 −0.0233495
\(955\) 70.4124 2.27849
\(956\) −16.4146 −0.530885
\(957\) 11.6295 0.375929
\(958\) −96.2382 −3.10932
\(959\) −11.7691 −0.380044
\(960\) 169.415 5.46784
\(961\) 70.2824 2.26717
\(962\) −1.03282 −0.0332996
\(963\) 0.949882 0.0306095
\(964\) −160.645 −5.17402
\(965\) 7.98587 0.257074
\(966\) 1.56986 0.0505095
\(967\) −41.2742 −1.32729 −0.663644 0.748048i \(-0.730991\pi\)
−0.663644 + 0.748048i \(0.730991\pi\)
\(968\) −9.70977 −0.312084
\(969\) 29.7667 0.956244
\(970\) 10.8497 0.348363
\(971\) 4.74863 0.152391 0.0761954 0.997093i \(-0.475723\pi\)
0.0761954 + 0.997093i \(0.475723\pi\)
\(972\) 5.66926 0.181841
\(973\) −8.91748 −0.285881
\(974\) −58.2495 −1.86643
\(975\) −25.9012 −0.829501
\(976\) −35.1902 −1.12641
\(977\) −55.4754 −1.77481 −0.887407 0.460986i \(-0.847496\pi\)
−0.887407 + 0.460986i \(0.847496\pi\)
\(978\) 4.92848 0.157596
\(979\) −0.821841 −0.0262661
\(980\) 81.7563 2.61161
\(981\) 0.912315 0.0291280
\(982\) 41.1630 1.31356
\(983\) 36.5224 1.16488 0.582442 0.812872i \(-0.302097\pi\)
0.582442 + 0.812872i \(0.302097\pi\)
\(984\) 88.6561 2.82625
\(985\) −12.1081 −0.385796
\(986\) 73.2902 2.33403
\(987\) −25.2268 −0.802979
\(988\) 96.7753 3.07883
\(989\) 2.47309 0.0786395
\(990\) −0.789984 −0.0251073
\(991\) 39.0820 1.24148 0.620740 0.784017i \(-0.286832\pi\)
0.620740 + 0.784017i \(0.286832\pi\)
\(992\) 235.098 7.46437
\(993\) −40.7238 −1.29233
\(994\) 54.1648 1.71800
\(995\) −6.42904 −0.203814
\(996\) 3.35696 0.106369
\(997\) −39.9497 −1.26522 −0.632609 0.774471i \(-0.718016\pi\)
−0.632609 + 0.774471i \(0.718016\pi\)
\(998\) −31.7650 −1.00550
\(999\) 0.460047 0.0145552
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.1.2 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.2 121 1.1 even 1 trivial