Properties

Label 6037.2.a.b.1.17
Level 6037
Weight 2
Character 6037.1
Self dual yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42988 q^{2} +0.381455 q^{3} +3.90430 q^{4} -2.17078 q^{5} -0.926887 q^{6} -2.70764 q^{7} -4.62721 q^{8} -2.85449 q^{9} +O(q^{10})\) \(q-2.42988 q^{2} +0.381455 q^{3} +3.90430 q^{4} -2.17078 q^{5} -0.926887 q^{6} -2.70764 q^{7} -4.62721 q^{8} -2.85449 q^{9} +5.27472 q^{10} +5.11321 q^{11} +1.48931 q^{12} +6.54077 q^{13} +6.57923 q^{14} -0.828053 q^{15} +3.43495 q^{16} -0.0279003 q^{17} +6.93606 q^{18} +7.94119 q^{19} -8.47537 q^{20} -1.03284 q^{21} -12.4245 q^{22} +7.01359 q^{23} -1.76507 q^{24} -0.287719 q^{25} -15.8933 q^{26} -2.23322 q^{27} -10.5714 q^{28} +8.51367 q^{29} +2.01207 q^{30} +3.77239 q^{31} +0.907913 q^{32} +1.95046 q^{33} +0.0677944 q^{34} +5.87769 q^{35} -11.1448 q^{36} -0.838138 q^{37} -19.2961 q^{38} +2.49501 q^{39} +10.0447 q^{40} -8.68434 q^{41} +2.50968 q^{42} +3.58105 q^{43} +19.9635 q^{44} +6.19647 q^{45} -17.0422 q^{46} +7.68087 q^{47} +1.31028 q^{48} +0.331317 q^{49} +0.699122 q^{50} -0.0106427 q^{51} +25.5371 q^{52} +13.0055 q^{53} +5.42645 q^{54} -11.0996 q^{55} +12.5288 q^{56} +3.02920 q^{57} -20.6872 q^{58} +10.0502 q^{59} -3.23297 q^{60} +5.26980 q^{61} -9.16644 q^{62} +7.72894 q^{63} -9.07602 q^{64} -14.1986 q^{65} -4.73937 q^{66} -12.6218 q^{67} -0.108931 q^{68} +2.67537 q^{69} -14.2821 q^{70} -11.1737 q^{71} +13.2083 q^{72} +5.14509 q^{73} +2.03657 q^{74} -0.109752 q^{75} +31.0048 q^{76} -13.8447 q^{77} -6.06256 q^{78} -9.63964 q^{79} -7.45652 q^{80} +7.71160 q^{81} +21.1019 q^{82} +9.70275 q^{83} -4.03252 q^{84} +0.0605655 q^{85} -8.70150 q^{86} +3.24758 q^{87} -23.6599 q^{88} +0.517760 q^{89} -15.0567 q^{90} -17.7101 q^{91} +27.3832 q^{92} +1.43899 q^{93} -18.6636 q^{94} -17.2386 q^{95} +0.346327 q^{96} -6.38286 q^{97} -0.805060 q^{98} -14.5956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42988 −1.71818 −0.859091 0.511823i \(-0.828970\pi\)
−0.859091 + 0.511823i \(0.828970\pi\)
\(3\) 0.381455 0.220233 0.110116 0.993919i \(-0.464878\pi\)
0.110116 + 0.993919i \(0.464878\pi\)
\(4\) 3.90430 1.95215
\(5\) −2.17078 −0.970802 −0.485401 0.874292i \(-0.661326\pi\)
−0.485401 + 0.874292i \(0.661326\pi\)
\(6\) −0.926887 −0.378400
\(7\) −2.70764 −1.02339 −0.511696 0.859167i \(-0.670983\pi\)
−0.511696 + 0.859167i \(0.670983\pi\)
\(8\) −4.62721 −1.63597
\(9\) −2.85449 −0.951497
\(10\) 5.27472 1.66801
\(11\) 5.11321 1.54169 0.770845 0.637022i \(-0.219834\pi\)
0.770845 + 0.637022i \(0.219834\pi\)
\(12\) 1.48931 0.429927
\(13\) 6.54077 1.81408 0.907042 0.421040i \(-0.138335\pi\)
0.907042 + 0.421040i \(0.138335\pi\)
\(14\) 6.57923 1.75837
\(15\) −0.828053 −0.213802
\(16\) 3.43495 0.858738
\(17\) −0.0279003 −0.00676683 −0.00338341 0.999994i \(-0.501077\pi\)
−0.00338341 + 0.999994i \(0.501077\pi\)
\(18\) 6.93606 1.63485
\(19\) 7.94119 1.82183 0.910917 0.412590i \(-0.135376\pi\)
0.910917 + 0.412590i \(0.135376\pi\)
\(20\) −8.47537 −1.89515
\(21\) −1.03284 −0.225385
\(22\) −12.4245 −2.64891
\(23\) 7.01359 1.46244 0.731218 0.682144i \(-0.238952\pi\)
0.731218 + 0.682144i \(0.238952\pi\)
\(24\) −1.76507 −0.360294
\(25\) −0.287719 −0.0575438
\(26\) −15.8933 −3.11693
\(27\) −2.23322 −0.429784
\(28\) −10.5714 −1.99781
\(29\) 8.51367 1.58095 0.790474 0.612495i \(-0.209834\pi\)
0.790474 + 0.612495i \(0.209834\pi\)
\(30\) 2.01207 0.367352
\(31\) 3.77239 0.677541 0.338770 0.940869i \(-0.389989\pi\)
0.338770 + 0.940869i \(0.389989\pi\)
\(32\) 0.907913 0.160498
\(33\) 1.95046 0.339531
\(34\) 0.0677944 0.0116266
\(35\) 5.87769 0.993511
\(36\) −11.1448 −1.85747
\(37\) −0.838138 −0.137789 −0.0688946 0.997624i \(-0.521947\pi\)
−0.0688946 + 0.997624i \(0.521947\pi\)
\(38\) −19.2961 −3.13024
\(39\) 2.49501 0.399521
\(40\) 10.0447 1.58820
\(41\) −8.68434 −1.35627 −0.678133 0.734939i \(-0.737211\pi\)
−0.678133 + 0.734939i \(0.737211\pi\)
\(42\) 2.50968 0.387252
\(43\) 3.58105 0.546104 0.273052 0.961999i \(-0.411967\pi\)
0.273052 + 0.961999i \(0.411967\pi\)
\(44\) 19.9635 3.00961
\(45\) 6.19647 0.923715
\(46\) −17.0422 −2.51273
\(47\) 7.68087 1.12037 0.560185 0.828368i \(-0.310730\pi\)
0.560185 + 0.828368i \(0.310730\pi\)
\(48\) 1.31028 0.189122
\(49\) 0.331317 0.0473311
\(50\) 0.699122 0.0988708
\(51\) −0.0106427 −0.00149028
\(52\) 25.5371 3.54136
\(53\) 13.0055 1.78645 0.893223 0.449613i \(-0.148438\pi\)
0.893223 + 0.449613i \(0.148438\pi\)
\(54\) 5.42645 0.738447
\(55\) −11.0996 −1.49668
\(56\) 12.5288 1.67423
\(57\) 3.02920 0.401228
\(58\) −20.6872 −2.71636
\(59\) 10.0502 1.30843 0.654215 0.756309i \(-0.272999\pi\)
0.654215 + 0.756309i \(0.272999\pi\)
\(60\) −3.23297 −0.417374
\(61\) 5.26980 0.674729 0.337364 0.941374i \(-0.390465\pi\)
0.337364 + 0.941374i \(0.390465\pi\)
\(62\) −9.16644 −1.16414
\(63\) 7.72894 0.973755
\(64\) −9.07602 −1.13450
\(65\) −14.1986 −1.76112
\(66\) −4.73937 −0.583376
\(67\) −12.6218 −1.54200 −0.770999 0.636837i \(-0.780243\pi\)
−0.770999 + 0.636837i \(0.780243\pi\)
\(68\) −0.108931 −0.0132099
\(69\) 2.67537 0.322076
\(70\) −14.2821 −1.70703
\(71\) −11.1737 −1.32607 −0.663036 0.748587i \(-0.730733\pi\)
−0.663036 + 0.748587i \(0.730733\pi\)
\(72\) 13.2083 1.55662
\(73\) 5.14509 0.602187 0.301094 0.953595i \(-0.402648\pi\)
0.301094 + 0.953595i \(0.402648\pi\)
\(74\) 2.03657 0.236747
\(75\) −0.109752 −0.0126730
\(76\) 31.0048 3.55649
\(77\) −13.8447 −1.57775
\(78\) −6.06256 −0.686450
\(79\) −9.63964 −1.08454 −0.542272 0.840203i \(-0.682436\pi\)
−0.542272 + 0.840203i \(0.682436\pi\)
\(80\) −7.45652 −0.833664
\(81\) 7.71160 0.856845
\(82\) 21.1019 2.33031
\(83\) 9.70275 1.06502 0.532508 0.846425i \(-0.321250\pi\)
0.532508 + 0.846425i \(0.321250\pi\)
\(84\) −4.03252 −0.439984
\(85\) 0.0605655 0.00656925
\(86\) −8.70150 −0.938307
\(87\) 3.24758 0.348177
\(88\) −23.6599 −2.52215
\(89\) 0.517760 0.0548824 0.0274412 0.999623i \(-0.491264\pi\)
0.0274412 + 0.999623i \(0.491264\pi\)
\(90\) −15.0567 −1.58711
\(91\) −17.7101 −1.85652
\(92\) 27.3832 2.85489
\(93\) 1.43899 0.149217
\(94\) −18.6636 −1.92500
\(95\) −17.2386 −1.76864
\(96\) 0.346327 0.0353469
\(97\) −6.38286 −0.648081 −0.324041 0.946043i \(-0.605041\pi\)
−0.324041 + 0.946043i \(0.605041\pi\)
\(98\) −0.805060 −0.0813234
\(99\) −14.5956 −1.46691
\(100\) −1.12334 −0.112334
\(101\) −3.42167 −0.340469 −0.170234 0.985404i \(-0.554453\pi\)
−0.170234 + 0.985404i \(0.554453\pi\)
\(102\) 0.0258605 0.00256057
\(103\) 10.9741 1.08131 0.540654 0.841245i \(-0.318177\pi\)
0.540654 + 0.841245i \(0.318177\pi\)
\(104\) −30.2655 −2.96778
\(105\) 2.24207 0.218804
\(106\) −31.6018 −3.06944
\(107\) −1.70405 −0.164737 −0.0823684 0.996602i \(-0.526248\pi\)
−0.0823684 + 0.996602i \(0.526248\pi\)
\(108\) −8.71917 −0.839002
\(109\) −7.63030 −0.730850 −0.365425 0.930841i \(-0.619076\pi\)
−0.365425 + 0.930841i \(0.619076\pi\)
\(110\) 26.9708 2.57156
\(111\) −0.319712 −0.0303457
\(112\) −9.30062 −0.878826
\(113\) −11.9116 −1.12055 −0.560274 0.828307i \(-0.689304\pi\)
−0.560274 + 0.828307i \(0.689304\pi\)
\(114\) −7.36059 −0.689382
\(115\) −15.2250 −1.41973
\(116\) 33.2399 3.08625
\(117\) −18.6706 −1.72610
\(118\) −24.4208 −2.24812
\(119\) 0.0755441 0.00692511
\(120\) 3.83158 0.349774
\(121\) 15.1449 1.37681
\(122\) −12.8050 −1.15931
\(123\) −3.31268 −0.298694
\(124\) 14.7285 1.32266
\(125\) 11.4785 1.02667
\(126\) −18.7804 −1.67309
\(127\) −19.0225 −1.68797 −0.843985 0.536366i \(-0.819797\pi\)
−0.843985 + 0.536366i \(0.819797\pi\)
\(128\) 20.2378 1.78878
\(129\) 1.36601 0.120270
\(130\) 34.5008 3.02592
\(131\) −12.8748 −1.12488 −0.562439 0.826839i \(-0.690137\pi\)
−0.562439 + 0.826839i \(0.690137\pi\)
\(132\) 7.61517 0.662815
\(133\) −21.5019 −1.86445
\(134\) 30.6694 2.64943
\(135\) 4.84783 0.417235
\(136\) 0.129101 0.0110703
\(137\) 7.15901 0.611636 0.305818 0.952090i \(-0.401070\pi\)
0.305818 + 0.952090i \(0.401070\pi\)
\(138\) −6.50081 −0.553386
\(139\) 1.79961 0.152641 0.0763206 0.997083i \(-0.475683\pi\)
0.0763206 + 0.997083i \(0.475683\pi\)
\(140\) 22.9483 1.93948
\(141\) 2.92990 0.246742
\(142\) 27.1507 2.27843
\(143\) 33.4444 2.79676
\(144\) −9.80505 −0.817087
\(145\) −18.4813 −1.53479
\(146\) −12.5019 −1.03467
\(147\) 0.126383 0.0104239
\(148\) −3.27234 −0.268985
\(149\) 3.26256 0.267279 0.133640 0.991030i \(-0.457334\pi\)
0.133640 + 0.991030i \(0.457334\pi\)
\(150\) 0.266683 0.0217746
\(151\) −7.50807 −0.610998 −0.305499 0.952192i \(-0.598823\pi\)
−0.305499 + 0.952192i \(0.598823\pi\)
\(152\) −36.7455 −2.98046
\(153\) 0.0796413 0.00643862
\(154\) 33.6410 2.71087
\(155\) −8.18902 −0.657758
\(156\) 9.74126 0.779925
\(157\) 17.4635 1.39374 0.696870 0.717198i \(-0.254576\pi\)
0.696870 + 0.717198i \(0.254576\pi\)
\(158\) 23.4231 1.86344
\(159\) 4.96102 0.393434
\(160\) −1.97088 −0.155812
\(161\) −18.9903 −1.49664
\(162\) −18.7382 −1.47222
\(163\) −4.63131 −0.362752 −0.181376 0.983414i \(-0.558055\pi\)
−0.181376 + 0.983414i \(0.558055\pi\)
\(164\) −33.9063 −2.64763
\(165\) −4.23401 −0.329617
\(166\) −23.5765 −1.82989
\(167\) −4.60701 −0.356501 −0.178251 0.983985i \(-0.557044\pi\)
−0.178251 + 0.983985i \(0.557044\pi\)
\(168\) 4.77918 0.368721
\(169\) 29.7817 2.29090
\(170\) −0.147167 −0.0112872
\(171\) −22.6681 −1.73347
\(172\) 13.9815 1.06608
\(173\) −3.85338 −0.292967 −0.146483 0.989213i \(-0.546795\pi\)
−0.146483 + 0.989213i \(0.546795\pi\)
\(174\) −7.89121 −0.598231
\(175\) 0.779040 0.0588899
\(176\) 17.5636 1.32391
\(177\) 3.83371 0.288159
\(178\) −1.25809 −0.0942980
\(179\) −10.1651 −0.759778 −0.379889 0.925032i \(-0.624038\pi\)
−0.379889 + 0.925032i \(0.624038\pi\)
\(180\) 24.1929 1.80323
\(181\) 3.73076 0.277305 0.138653 0.990341i \(-0.455723\pi\)
0.138653 + 0.990341i \(0.455723\pi\)
\(182\) 43.0333 3.18984
\(183\) 2.01019 0.148597
\(184\) −32.4534 −2.39249
\(185\) 1.81941 0.133766
\(186\) −3.49658 −0.256382
\(187\) −0.142660 −0.0104324
\(188\) 29.9884 2.18713
\(189\) 6.04676 0.439837
\(190\) 41.8876 3.03884
\(191\) 24.5691 1.77776 0.888880 0.458140i \(-0.151484\pi\)
0.888880 + 0.458140i \(0.151484\pi\)
\(192\) −3.46209 −0.249855
\(193\) −1.32536 −0.0954014 −0.0477007 0.998862i \(-0.515189\pi\)
−0.0477007 + 0.998862i \(0.515189\pi\)
\(194\) 15.5096 1.11352
\(195\) −5.41611 −0.387856
\(196\) 1.29356 0.0923973
\(197\) 27.2035 1.93817 0.969086 0.246724i \(-0.0793541\pi\)
0.969086 + 0.246724i \(0.0793541\pi\)
\(198\) 35.4655 2.52043
\(199\) 10.4326 0.739547 0.369773 0.929122i \(-0.379435\pi\)
0.369773 + 0.929122i \(0.379435\pi\)
\(200\) 1.33134 0.0941398
\(201\) −4.81464 −0.339599
\(202\) 8.31424 0.584988
\(203\) −23.0520 −1.61793
\(204\) −0.0415523 −0.00290924
\(205\) 18.8518 1.31667
\(206\) −26.6656 −1.85788
\(207\) −20.0202 −1.39150
\(208\) 22.4672 1.55782
\(209\) 40.6050 2.80870
\(210\) −5.44796 −0.375945
\(211\) −13.3026 −0.915790 −0.457895 0.889006i \(-0.651396\pi\)
−0.457895 + 0.889006i \(0.651396\pi\)
\(212\) 50.7775 3.48741
\(213\) −4.26225 −0.292045
\(214\) 4.14063 0.283048
\(215\) −7.77366 −0.530159
\(216\) 10.3336 0.703112
\(217\) −10.2143 −0.693390
\(218\) 18.5407 1.25573
\(219\) 1.96262 0.132621
\(220\) −43.3363 −2.92174
\(221\) −0.182490 −0.0122756
\(222\) 0.776860 0.0521394
\(223\) −16.7060 −1.11872 −0.559358 0.828926i \(-0.688952\pi\)
−0.559358 + 0.828926i \(0.688952\pi\)
\(224\) −2.45830 −0.164252
\(225\) 0.821292 0.0547528
\(226\) 28.9437 1.92531
\(227\) 19.5423 1.29707 0.648533 0.761186i \(-0.275383\pi\)
0.648533 + 0.761186i \(0.275383\pi\)
\(228\) 11.8269 0.783256
\(229\) 10.7710 0.711769 0.355884 0.934530i \(-0.384180\pi\)
0.355884 + 0.934530i \(0.384180\pi\)
\(230\) 36.9948 2.43936
\(231\) −5.28114 −0.347473
\(232\) −39.3945 −2.58638
\(233\) 17.3009 1.13342 0.566710 0.823917i \(-0.308216\pi\)
0.566710 + 0.823917i \(0.308216\pi\)
\(234\) 45.3672 2.96575
\(235\) −16.6735 −1.08766
\(236\) 39.2392 2.55425
\(237\) −3.67708 −0.238852
\(238\) −0.183563 −0.0118986
\(239\) 8.99359 0.581747 0.290874 0.956761i \(-0.406054\pi\)
0.290874 + 0.956761i \(0.406054\pi\)
\(240\) −2.84432 −0.183600
\(241\) −0.747944 −0.0481793 −0.0240896 0.999710i \(-0.507669\pi\)
−0.0240896 + 0.999710i \(0.507669\pi\)
\(242\) −36.8003 −2.36561
\(243\) 9.64129 0.618489
\(244\) 20.5749 1.31717
\(245\) −0.719217 −0.0459491
\(246\) 8.04941 0.513211
\(247\) 51.9415 3.30496
\(248\) −17.4556 −1.10843
\(249\) 3.70116 0.234551
\(250\) −27.8913 −1.76400
\(251\) 3.19751 0.201825 0.100913 0.994895i \(-0.467824\pi\)
0.100913 + 0.994895i \(0.467824\pi\)
\(252\) 30.1761 1.90092
\(253\) 35.8620 2.25462
\(254\) 46.2222 2.90024
\(255\) 0.0231030 0.00144676
\(256\) −31.0233 −1.93895
\(257\) 2.11386 0.131859 0.0659293 0.997824i \(-0.478999\pi\)
0.0659293 + 0.997824i \(0.478999\pi\)
\(258\) −3.31923 −0.206646
\(259\) 2.26938 0.141012
\(260\) −55.4355 −3.43796
\(261\) −24.3022 −1.50427
\(262\) 31.2842 1.93275
\(263\) −10.2742 −0.633534 −0.316767 0.948503i \(-0.602597\pi\)
−0.316767 + 0.948503i \(0.602597\pi\)
\(264\) −9.02518 −0.555461
\(265\) −28.2321 −1.73429
\(266\) 52.2469 3.20346
\(267\) 0.197502 0.0120869
\(268\) −49.2793 −3.01021
\(269\) −8.18748 −0.499199 −0.249600 0.968349i \(-0.580299\pi\)
−0.249600 + 0.968349i \(0.580299\pi\)
\(270\) −11.7796 −0.716886
\(271\) −8.44352 −0.512907 −0.256454 0.966557i \(-0.582554\pi\)
−0.256454 + 0.966557i \(0.582554\pi\)
\(272\) −0.0958363 −0.00581093
\(273\) −6.75558 −0.408867
\(274\) −17.3955 −1.05090
\(275\) −1.47117 −0.0887148
\(276\) 10.4454 0.628741
\(277\) −8.86079 −0.532393 −0.266197 0.963919i \(-0.585767\pi\)
−0.266197 + 0.963919i \(0.585767\pi\)
\(278\) −4.37284 −0.262265
\(279\) −10.7683 −0.644678
\(280\) −27.1973 −1.62535
\(281\) −15.8292 −0.944291 −0.472146 0.881521i \(-0.656520\pi\)
−0.472146 + 0.881521i \(0.656520\pi\)
\(282\) −7.11930 −0.423948
\(283\) −2.83901 −0.168761 −0.0843807 0.996434i \(-0.526891\pi\)
−0.0843807 + 0.996434i \(0.526891\pi\)
\(284\) −43.6254 −2.58869
\(285\) −6.57573 −0.389512
\(286\) −81.2656 −4.80534
\(287\) 23.5141 1.38799
\(288\) −2.59163 −0.152713
\(289\) −16.9992 −0.999954
\(290\) 44.9073 2.63704
\(291\) −2.43477 −0.142729
\(292\) 20.0880 1.17556
\(293\) −3.38920 −0.197999 −0.0989997 0.995087i \(-0.531564\pi\)
−0.0989997 + 0.995087i \(0.531564\pi\)
\(294\) −0.307094 −0.0179101
\(295\) −21.8169 −1.27023
\(296\) 3.87824 0.225418
\(297\) −11.4189 −0.662594
\(298\) −7.92761 −0.459234
\(299\) 45.8743 2.65298
\(300\) −0.428504 −0.0247397
\(301\) −9.69619 −0.558879
\(302\) 18.2437 1.04981
\(303\) −1.30521 −0.0749825
\(304\) 27.2776 1.56448
\(305\) −11.4396 −0.655028
\(306\) −0.193518 −0.0110627
\(307\) 20.9825 1.19754 0.598768 0.800923i \(-0.295657\pi\)
0.598768 + 0.800923i \(0.295657\pi\)
\(308\) −54.0540 −3.08001
\(309\) 4.18611 0.238139
\(310\) 19.8983 1.13015
\(311\) −34.0275 −1.92952 −0.964761 0.263129i \(-0.915245\pi\)
−0.964761 + 0.263129i \(0.915245\pi\)
\(312\) −11.5449 −0.653603
\(313\) 20.6352 1.16637 0.583186 0.812339i \(-0.301806\pi\)
0.583186 + 0.812339i \(0.301806\pi\)
\(314\) −42.4342 −2.39470
\(315\) −16.7778 −0.945323
\(316\) −37.6360 −2.11719
\(317\) −7.59523 −0.426591 −0.213295 0.976988i \(-0.568420\pi\)
−0.213295 + 0.976988i \(0.568420\pi\)
\(318\) −12.0547 −0.675992
\(319\) 43.5322 2.43733
\(320\) 19.7020 1.10138
\(321\) −0.650018 −0.0362805
\(322\) 46.1440 2.57151
\(323\) −0.221562 −0.0123280
\(324\) 30.1084 1.67269
\(325\) −1.88191 −0.104389
\(326\) 11.2535 0.623275
\(327\) −2.91061 −0.160957
\(328\) 40.1843 2.21881
\(329\) −20.7970 −1.14658
\(330\) 10.2881 0.566343
\(331\) −6.91192 −0.379913 −0.189957 0.981792i \(-0.560835\pi\)
−0.189957 + 0.981792i \(0.560835\pi\)
\(332\) 37.8824 2.07907
\(333\) 2.39246 0.131106
\(334\) 11.1945 0.612534
\(335\) 27.3991 1.49697
\(336\) −3.54776 −0.193546
\(337\) −6.84462 −0.372850 −0.186425 0.982469i \(-0.559690\pi\)
−0.186425 + 0.982469i \(0.559690\pi\)
\(338\) −72.3659 −3.93619
\(339\) −4.54373 −0.246782
\(340\) 0.236466 0.0128242
\(341\) 19.2890 1.04456
\(342\) 55.0806 2.97842
\(343\) 18.0564 0.974954
\(344\) −16.5703 −0.893408
\(345\) −5.80763 −0.312672
\(346\) 9.36323 0.503370
\(347\) 10.6196 0.570091 0.285045 0.958514i \(-0.407991\pi\)
0.285045 + 0.958514i \(0.407991\pi\)
\(348\) 12.6795 0.679693
\(349\) −0.592091 −0.0316939 −0.0158470 0.999874i \(-0.505044\pi\)
−0.0158470 + 0.999874i \(0.505044\pi\)
\(350\) −1.89297 −0.101184
\(351\) −14.6070 −0.779664
\(352\) 4.64235 0.247438
\(353\) −13.3053 −0.708169 −0.354084 0.935213i \(-0.615207\pi\)
−0.354084 + 0.935213i \(0.615207\pi\)
\(354\) −9.31544 −0.495110
\(355\) 24.2556 1.28735
\(356\) 2.02149 0.107139
\(357\) 0.0288166 0.00152514
\(358\) 24.7000 1.30544
\(359\) −7.21305 −0.380690 −0.190345 0.981717i \(-0.560961\pi\)
−0.190345 + 0.981717i \(0.560961\pi\)
\(360\) −28.6724 −1.51117
\(361\) 44.0625 2.31908
\(362\) −9.06529 −0.476461
\(363\) 5.77710 0.303219
\(364\) −69.1454 −3.62420
\(365\) −11.1688 −0.584604
\(366\) −4.88451 −0.255317
\(367\) −6.54698 −0.341749 −0.170875 0.985293i \(-0.554659\pi\)
−0.170875 + 0.985293i \(0.554659\pi\)
\(368\) 24.0914 1.25585
\(369\) 24.7894 1.29048
\(370\) −4.42095 −0.229834
\(371\) −35.2143 −1.82824
\(372\) 5.61826 0.291293
\(373\) −21.7384 −1.12557 −0.562786 0.826602i \(-0.690271\pi\)
−0.562786 + 0.826602i \(0.690271\pi\)
\(374\) 0.346647 0.0179247
\(375\) 4.37851 0.226105
\(376\) −35.5410 −1.83289
\(377\) 55.6860 2.86797
\(378\) −14.6929 −0.755721
\(379\) −31.4655 −1.61628 −0.808138 0.588994i \(-0.799524\pi\)
−0.808138 + 0.588994i \(0.799524\pi\)
\(380\) −67.3045 −3.45265
\(381\) −7.25620 −0.371747
\(382\) −59.7000 −3.05452
\(383\) 27.5479 1.40763 0.703816 0.710382i \(-0.251478\pi\)
0.703816 + 0.710382i \(0.251478\pi\)
\(384\) 7.71979 0.393949
\(385\) 30.0539 1.53169
\(386\) 3.22046 0.163917
\(387\) −10.2221 −0.519617
\(388\) −24.9206 −1.26515
\(389\) 10.9966 0.557548 0.278774 0.960357i \(-0.410072\pi\)
0.278774 + 0.960357i \(0.410072\pi\)
\(390\) 13.1605 0.666407
\(391\) −0.195682 −0.00989604
\(392\) −1.53308 −0.0774320
\(393\) −4.91116 −0.247735
\(394\) −66.1012 −3.33013
\(395\) 20.9255 1.05288
\(396\) −56.9857 −2.86364
\(397\) −39.5138 −1.98314 −0.991571 0.129561i \(-0.958643\pi\)
−0.991571 + 0.129561i \(0.958643\pi\)
\(398\) −25.3499 −1.27068
\(399\) −8.20199 −0.410613
\(400\) −0.988302 −0.0494151
\(401\) 33.7732 1.68656 0.843278 0.537478i \(-0.180623\pi\)
0.843278 + 0.537478i \(0.180623\pi\)
\(402\) 11.6990 0.583492
\(403\) 24.6743 1.22912
\(404\) −13.3592 −0.664646
\(405\) −16.7402 −0.831827
\(406\) 56.0134 2.77990
\(407\) −4.28558 −0.212428
\(408\) 0.0492461 0.00243804
\(409\) 25.7484 1.27317 0.636587 0.771205i \(-0.280345\pi\)
0.636587 + 0.771205i \(0.280345\pi\)
\(410\) −45.8075 −2.26227
\(411\) 2.73084 0.134702
\(412\) 42.8461 2.11087
\(413\) −27.2124 −1.33904
\(414\) 48.6467 2.39086
\(415\) −21.0625 −1.03392
\(416\) 5.93845 0.291157
\(417\) 0.686471 0.0336166
\(418\) −98.6650 −4.82586
\(419\) −29.0944 −1.42135 −0.710677 0.703518i \(-0.751611\pi\)
−0.710677 + 0.703518i \(0.751611\pi\)
\(420\) 8.75372 0.427138
\(421\) −30.4606 −1.48456 −0.742278 0.670092i \(-0.766255\pi\)
−0.742278 + 0.670092i \(0.766255\pi\)
\(422\) 32.3237 1.57349
\(423\) −21.9250 −1.06603
\(424\) −60.1793 −2.92257
\(425\) 0.00802746 0.000389389 0
\(426\) 10.3567 0.501786
\(427\) −14.2687 −0.690512
\(428\) −6.65312 −0.321591
\(429\) 12.7575 0.615938
\(430\) 18.8890 0.910910
\(431\) −35.1939 −1.69523 −0.847616 0.530610i \(-0.821963\pi\)
−0.847616 + 0.530610i \(0.821963\pi\)
\(432\) −7.67101 −0.369072
\(433\) 37.1689 1.78622 0.893110 0.449837i \(-0.148518\pi\)
0.893110 + 0.449837i \(0.148518\pi\)
\(434\) 24.8194 1.19137
\(435\) −7.04977 −0.338011
\(436\) −29.7910 −1.42673
\(437\) 55.6962 2.66431
\(438\) −4.76892 −0.227868
\(439\) −33.8850 −1.61724 −0.808622 0.588329i \(-0.799786\pi\)
−0.808622 + 0.588329i \(0.799786\pi\)
\(440\) 51.3604 2.44851
\(441\) −0.945743 −0.0450354
\(442\) 0.443428 0.0210917
\(443\) 24.6304 1.17022 0.585112 0.810952i \(-0.301050\pi\)
0.585112 + 0.810952i \(0.301050\pi\)
\(444\) −1.24825 −0.0592393
\(445\) −1.12394 −0.0532800
\(446\) 40.5935 1.92216
\(447\) 1.24452 0.0588637
\(448\) 24.5746 1.16104
\(449\) −31.3391 −1.47898 −0.739491 0.673166i \(-0.764934\pi\)
−0.739491 + 0.673166i \(0.764934\pi\)
\(450\) −1.99564 −0.0940753
\(451\) −44.4049 −2.09094
\(452\) −46.5064 −2.18748
\(453\) −2.86399 −0.134562
\(454\) −47.4853 −2.22860
\(455\) 38.4446 1.80231
\(456\) −14.0168 −0.656395
\(457\) −5.27861 −0.246923 −0.123461 0.992349i \(-0.539400\pi\)
−0.123461 + 0.992349i \(0.539400\pi\)
\(458\) −26.1722 −1.22295
\(459\) 0.0623077 0.00290827
\(460\) −59.4428 −2.77153
\(461\) 1.04519 0.0486793 0.0243397 0.999704i \(-0.492252\pi\)
0.0243397 + 0.999704i \(0.492252\pi\)
\(462\) 12.8325 0.597022
\(463\) 12.7165 0.590985 0.295492 0.955345i \(-0.404516\pi\)
0.295492 + 0.955345i \(0.404516\pi\)
\(464\) 29.2440 1.35762
\(465\) −3.12374 −0.144860
\(466\) −42.0391 −1.94742
\(467\) 42.9765 1.98871 0.994357 0.106083i \(-0.0338309\pi\)
0.994357 + 0.106083i \(0.0338309\pi\)
\(468\) −72.8956 −3.36960
\(469\) 34.1753 1.57807
\(470\) 40.5145 1.86879
\(471\) 6.66153 0.306947
\(472\) −46.5046 −2.14055
\(473\) 18.3106 0.841924
\(474\) 8.93486 0.410392
\(475\) −2.28483 −0.104835
\(476\) 0.294947 0.0135189
\(477\) −37.1242 −1.69980
\(478\) −21.8533 −0.999548
\(479\) 14.7895 0.675750 0.337875 0.941191i \(-0.390292\pi\)
0.337875 + 0.941191i \(0.390292\pi\)
\(480\) −0.751800 −0.0343148
\(481\) −5.48207 −0.249961
\(482\) 1.81741 0.0827808
\(483\) −7.24393 −0.329610
\(484\) 59.1303 2.68774
\(485\) 13.8558 0.629158
\(486\) −23.4272 −1.06268
\(487\) 7.61778 0.345195 0.172597 0.984992i \(-0.444784\pi\)
0.172597 + 0.984992i \(0.444784\pi\)
\(488\) −24.3845 −1.10383
\(489\) −1.76664 −0.0798900
\(490\) 1.74761 0.0789489
\(491\) −3.95144 −0.178326 −0.0891630 0.996017i \(-0.528419\pi\)
−0.0891630 + 0.996017i \(0.528419\pi\)
\(492\) −12.9337 −0.583096
\(493\) −0.237534 −0.0106980
\(494\) −126.211 −5.67852
\(495\) 31.6839 1.42408
\(496\) 12.9580 0.581830
\(497\) 30.2543 1.35709
\(498\) −8.99336 −0.403002
\(499\) 9.77167 0.437440 0.218720 0.975788i \(-0.429812\pi\)
0.218720 + 0.975788i \(0.429812\pi\)
\(500\) 44.8154 2.00420
\(501\) −1.75737 −0.0785133
\(502\) −7.76955 −0.346772
\(503\) 11.9231 0.531625 0.265812 0.964025i \(-0.414360\pi\)
0.265812 + 0.964025i \(0.414360\pi\)
\(504\) −35.7634 −1.59303
\(505\) 7.42769 0.330528
\(506\) −87.1402 −3.87385
\(507\) 11.3604 0.504532
\(508\) −74.2694 −3.29517
\(509\) 12.1535 0.538693 0.269346 0.963043i \(-0.413192\pi\)
0.269346 + 0.963043i \(0.413192\pi\)
\(510\) −0.0561374 −0.00248580
\(511\) −13.9311 −0.616273
\(512\) 34.9071 1.54269
\(513\) −17.7344 −0.782995
\(514\) −5.13641 −0.226557
\(515\) −23.8223 −1.04974
\(516\) 5.33330 0.234785
\(517\) 39.2739 1.72726
\(518\) −5.51431 −0.242285
\(519\) −1.46989 −0.0645209
\(520\) 65.6998 2.88113
\(521\) 37.3354 1.63569 0.817847 0.575435i \(-0.195167\pi\)
0.817847 + 0.575435i \(0.195167\pi\)
\(522\) 59.0513 2.58461
\(523\) 11.8713 0.519095 0.259548 0.965730i \(-0.416427\pi\)
0.259548 + 0.965730i \(0.416427\pi\)
\(524\) −50.2672 −2.19593
\(525\) 0.297168 0.0129695
\(526\) 24.9650 1.08853
\(527\) −0.105251 −0.00458480
\(528\) 6.69973 0.291568
\(529\) 26.1905 1.13872
\(530\) 68.6006 2.97982
\(531\) −28.6883 −1.24497
\(532\) −83.9498 −3.63968
\(533\) −56.8023 −2.46038
\(534\) −0.479905 −0.0207675
\(535\) 3.69912 0.159927
\(536\) 58.4037 2.52266
\(537\) −3.87754 −0.167328
\(538\) 19.8946 0.857715
\(539\) 1.69410 0.0729699
\(540\) 18.9274 0.814505
\(541\) −1.58914 −0.0683225 −0.0341612 0.999416i \(-0.510876\pi\)
−0.0341612 + 0.999416i \(0.510876\pi\)
\(542\) 20.5167 0.881268
\(543\) 1.42312 0.0610718
\(544\) −0.0253311 −0.00108606
\(545\) 16.5637 0.709511
\(546\) 16.4152 0.702507
\(547\) −40.2811 −1.72230 −0.861148 0.508354i \(-0.830254\pi\)
−0.861148 + 0.508354i \(0.830254\pi\)
\(548\) 27.9509 1.19400
\(549\) −15.0426 −0.642003
\(550\) 3.57476 0.152428
\(551\) 67.6086 2.88022
\(552\) −12.3795 −0.526906
\(553\) 26.1007 1.10991
\(554\) 21.5306 0.914749
\(555\) 0.694023 0.0294597
\(556\) 7.02623 0.297979
\(557\) 17.6685 0.748640 0.374320 0.927300i \(-0.377876\pi\)
0.374320 + 0.927300i \(0.377876\pi\)
\(558\) 26.1655 1.10767
\(559\) 23.4228 0.990680
\(560\) 20.1896 0.853166
\(561\) −0.0544184 −0.00229755
\(562\) 38.4630 1.62246
\(563\) −23.4192 −0.987001 −0.493500 0.869746i \(-0.664283\pi\)
−0.493500 + 0.869746i \(0.664283\pi\)
\(564\) 11.4392 0.481678
\(565\) 25.8574 1.08783
\(566\) 6.89843 0.289963
\(567\) −20.8803 −0.876888
\(568\) 51.7030 2.16941
\(569\) 3.60300 0.151045 0.0755227 0.997144i \(-0.475937\pi\)
0.0755227 + 0.997144i \(0.475937\pi\)
\(570\) 15.9782 0.669253
\(571\) 7.82842 0.327609 0.163805 0.986493i \(-0.447623\pi\)
0.163805 + 0.986493i \(0.447623\pi\)
\(572\) 130.577 5.45969
\(573\) 9.37201 0.391521
\(574\) −57.1363 −2.38482
\(575\) −2.01794 −0.0841541
\(576\) 25.9074 1.07948
\(577\) −8.78037 −0.365532 −0.182766 0.983156i \(-0.558505\pi\)
−0.182766 + 0.983156i \(0.558505\pi\)
\(578\) 41.3060 1.71810
\(579\) −0.505564 −0.0210105
\(580\) −72.1565 −2.99614
\(581\) −26.2716 −1.08993
\(582\) 5.91619 0.245234
\(583\) 66.5000 2.75415
\(584\) −23.8074 −0.985158
\(585\) 40.5297 1.67570
\(586\) 8.23534 0.340199
\(587\) 26.3610 1.08803 0.544017 0.839074i \(-0.316903\pi\)
0.544017 + 0.839074i \(0.316903\pi\)
\(588\) 0.493435 0.0203489
\(589\) 29.9572 1.23437
\(590\) 53.0123 2.18248
\(591\) 10.3769 0.426849
\(592\) −2.87897 −0.118325
\(593\) −22.3609 −0.918252 −0.459126 0.888371i \(-0.651837\pi\)
−0.459126 + 0.888371i \(0.651837\pi\)
\(594\) 27.7466 1.13846
\(595\) −0.163989 −0.00672291
\(596\) 12.7380 0.521769
\(597\) 3.97956 0.162872
\(598\) −111.469 −4.55830
\(599\) −9.04870 −0.369720 −0.184860 0.982765i \(-0.559183\pi\)
−0.184860 + 0.982765i \(0.559183\pi\)
\(600\) 0.507845 0.0207327
\(601\) 16.9125 0.689876 0.344938 0.938625i \(-0.387900\pi\)
0.344938 + 0.938625i \(0.387900\pi\)
\(602\) 23.5605 0.960256
\(603\) 36.0288 1.46721
\(604\) −29.3138 −1.19276
\(605\) −32.8763 −1.33661
\(606\) 3.17150 0.128833
\(607\) −33.3170 −1.35230 −0.676148 0.736766i \(-0.736352\pi\)
−0.676148 + 0.736766i \(0.736352\pi\)
\(608\) 7.20990 0.292400
\(609\) −8.79327 −0.356321
\(610\) 27.7967 1.12546
\(611\) 50.2388 2.03245
\(612\) 0.310943 0.0125691
\(613\) 45.4364 1.83516 0.917580 0.397550i \(-0.130140\pi\)
0.917580 + 0.397550i \(0.130140\pi\)
\(614\) −50.9849 −2.05758
\(615\) 7.19110 0.289973
\(616\) 64.0625 2.58115
\(617\) −26.2290 −1.05594 −0.527970 0.849263i \(-0.677047\pi\)
−0.527970 + 0.849263i \(0.677047\pi\)
\(618\) −10.1717 −0.409167
\(619\) −27.5434 −1.10706 −0.553531 0.832828i \(-0.686720\pi\)
−0.553531 + 0.832828i \(0.686720\pi\)
\(620\) −31.9724 −1.28404
\(621\) −15.6629 −0.628531
\(622\) 82.6826 3.31527
\(623\) −1.40191 −0.0561662
\(624\) 8.57023 0.343084
\(625\) −23.4786 −0.939145
\(626\) −50.1410 −2.00404
\(627\) 15.4889 0.618569
\(628\) 68.1828 2.72079
\(629\) 0.0233843 0.000932395 0
\(630\) 40.7680 1.62424
\(631\) 33.7132 1.34210 0.671050 0.741412i \(-0.265844\pi\)
0.671050 + 0.741412i \(0.265844\pi\)
\(632\) 44.6046 1.77428
\(633\) −5.07435 −0.201687
\(634\) 18.4555 0.732960
\(635\) 41.2936 1.63868
\(636\) 19.3693 0.768043
\(637\) 2.16707 0.0858625
\(638\) −105.778 −4.18778
\(639\) 31.8952 1.26175
\(640\) −43.9317 −1.73655
\(641\) −17.4400 −0.688838 −0.344419 0.938816i \(-0.611924\pi\)
−0.344419 + 0.938816i \(0.611924\pi\)
\(642\) 1.57946 0.0623364
\(643\) −13.5358 −0.533798 −0.266899 0.963724i \(-0.585999\pi\)
−0.266899 + 0.963724i \(0.585999\pi\)
\(644\) −74.1438 −2.92167
\(645\) −2.96530 −0.116758
\(646\) 0.538368 0.0211818
\(647\) −2.40965 −0.0947332 −0.0473666 0.998878i \(-0.515083\pi\)
−0.0473666 + 0.998878i \(0.515083\pi\)
\(648\) −35.6832 −1.40177
\(649\) 51.3890 2.01719
\(650\) 4.57280 0.179360
\(651\) −3.89628 −0.152707
\(652\) −18.0820 −0.708147
\(653\) −44.3138 −1.73413 −0.867066 0.498193i \(-0.833997\pi\)
−0.867066 + 0.498193i \(0.833997\pi\)
\(654\) 7.07243 0.276554
\(655\) 27.9484 1.09203
\(656\) −29.8303 −1.16468
\(657\) −14.6866 −0.572979
\(658\) 50.5342 1.97003
\(659\) 16.6422 0.648290 0.324145 0.946007i \(-0.394923\pi\)
0.324145 + 0.946007i \(0.394923\pi\)
\(660\) −16.5308 −0.643462
\(661\) 2.68299 0.104356 0.0521781 0.998638i \(-0.483384\pi\)
0.0521781 + 0.998638i \(0.483384\pi\)
\(662\) 16.7951 0.652760
\(663\) −0.0696116 −0.00270349
\(664\) −44.8967 −1.74233
\(665\) 46.6758 1.81001
\(666\) −5.81338 −0.225264
\(667\) 59.7114 2.31203
\(668\) −17.9872 −0.695944
\(669\) −6.37258 −0.246378
\(670\) −66.5765 −2.57207
\(671\) 26.9456 1.04022
\(672\) −0.937730 −0.0361737
\(673\) 4.65760 0.179537 0.0897686 0.995963i \(-0.471387\pi\)
0.0897686 + 0.995963i \(0.471387\pi\)
\(674\) 16.6316 0.640625
\(675\) 0.642541 0.0247314
\(676\) 116.277 4.47218
\(677\) −24.3519 −0.935919 −0.467959 0.883750i \(-0.655011\pi\)
−0.467959 + 0.883750i \(0.655011\pi\)
\(678\) 11.0407 0.424016
\(679\) 17.2825 0.663241
\(680\) −0.280249 −0.0107471
\(681\) 7.45449 0.285657
\(682\) −46.8699 −1.79474
\(683\) 48.2607 1.84665 0.923323 0.384024i \(-0.125462\pi\)
0.923323 + 0.384024i \(0.125462\pi\)
\(684\) −88.5029 −3.38399
\(685\) −15.5406 −0.593777
\(686\) −43.8748 −1.67515
\(687\) 4.10865 0.156755
\(688\) 12.3007 0.468961
\(689\) 85.0662 3.24077
\(690\) 14.1118 0.537228
\(691\) 31.2586 1.18913 0.594566 0.804047i \(-0.297324\pi\)
0.594566 + 0.804047i \(0.297324\pi\)
\(692\) −15.0447 −0.571915
\(693\) 39.5197 1.50123
\(694\) −25.8043 −0.979520
\(695\) −3.90656 −0.148184
\(696\) −15.0272 −0.569606
\(697\) 0.242296 0.00917762
\(698\) 1.43871 0.0544559
\(699\) 6.59951 0.249617
\(700\) 3.04161 0.114962
\(701\) −41.9224 −1.58339 −0.791693 0.610919i \(-0.790800\pi\)
−0.791693 + 0.610919i \(0.790800\pi\)
\(702\) 35.4932 1.33961
\(703\) −6.65581 −0.251029
\(704\) −46.4076 −1.74905
\(705\) −6.36017 −0.239538
\(706\) 32.3302 1.21676
\(707\) 9.26465 0.348433
\(708\) 14.9680 0.562530
\(709\) 13.4696 0.505863 0.252931 0.967484i \(-0.418605\pi\)
0.252931 + 0.967484i \(0.418605\pi\)
\(710\) −58.9381 −2.21191
\(711\) 27.5163 1.03194
\(712\) −2.39578 −0.0897858
\(713\) 26.4580 0.990859
\(714\) −0.0700208 −0.00262046
\(715\) −72.6003 −2.71510
\(716\) −39.6877 −1.48320
\(717\) 3.43065 0.128120
\(718\) 17.5268 0.654095
\(719\) 26.7882 0.999030 0.499515 0.866305i \(-0.333512\pi\)
0.499515 + 0.866305i \(0.333512\pi\)
\(720\) 21.2846 0.793230
\(721\) −29.7138 −1.10660
\(722\) −107.066 −3.98460
\(723\) −0.285306 −0.0106107
\(724\) 14.5660 0.541342
\(725\) −2.44955 −0.0909738
\(726\) −14.0376 −0.520985
\(727\) −16.9320 −0.627973 −0.313987 0.949427i \(-0.601665\pi\)
−0.313987 + 0.949427i \(0.601665\pi\)
\(728\) 81.9482 3.03720
\(729\) −19.4571 −0.720633
\(730\) 27.1389 1.00446
\(731\) −0.0999124 −0.00369539
\(732\) 7.84838 0.290084
\(733\) −15.2462 −0.563130 −0.281565 0.959542i \(-0.590853\pi\)
−0.281565 + 0.959542i \(0.590853\pi\)
\(734\) 15.9083 0.587188
\(735\) −0.274349 −0.0101195
\(736\) 6.36773 0.234718
\(737\) −64.5379 −2.37728
\(738\) −60.2352 −2.21729
\(739\) −24.7430 −0.910184 −0.455092 0.890444i \(-0.650394\pi\)
−0.455092 + 0.890444i \(0.650394\pi\)
\(740\) 7.10353 0.261131
\(741\) 19.8133 0.727861
\(742\) 85.5664 3.14124
\(743\) 10.6923 0.392261 0.196131 0.980578i \(-0.437162\pi\)
0.196131 + 0.980578i \(0.437162\pi\)
\(744\) −6.65853 −0.244114
\(745\) −7.08229 −0.259475
\(746\) 52.8217 1.93394
\(747\) −27.6964 −1.01336
\(748\) −0.556988 −0.0203655
\(749\) 4.61396 0.168590
\(750\) −10.6392 −0.388490
\(751\) 19.9609 0.728385 0.364192 0.931324i \(-0.381345\pi\)
0.364192 + 0.931324i \(0.381345\pi\)
\(752\) 26.3834 0.962104
\(753\) 1.21970 0.0444485
\(754\) −135.310 −4.92770
\(755\) 16.2984 0.593158
\(756\) 23.6084 0.858628
\(757\) 5.54047 0.201372 0.100686 0.994918i \(-0.467896\pi\)
0.100686 + 0.994918i \(0.467896\pi\)
\(758\) 76.4573 2.77705
\(759\) 13.6797 0.496542
\(760\) 79.7665 2.89343
\(761\) 10.5736 0.383293 0.191646 0.981464i \(-0.438617\pi\)
0.191646 + 0.981464i \(0.438617\pi\)
\(762\) 17.6317 0.638728
\(763\) 20.6601 0.747946
\(764\) 95.9252 3.47045
\(765\) −0.172884 −0.00625062
\(766\) −66.9380 −2.41857
\(767\) 65.7364 2.37360
\(768\) −11.8340 −0.427021
\(769\) −5.21778 −0.188158 −0.0940789 0.995565i \(-0.529991\pi\)
−0.0940789 + 0.995565i \(0.529991\pi\)
\(770\) −73.0272 −2.63172
\(771\) 0.806340 0.0290396
\(772\) −5.17459 −0.186238
\(773\) −18.8714 −0.678756 −0.339378 0.940650i \(-0.610217\pi\)
−0.339378 + 0.940650i \(0.610217\pi\)
\(774\) 24.8384 0.892797
\(775\) −1.08539 −0.0389883
\(776\) 29.5348 1.06024
\(777\) 0.865664 0.0310555
\(778\) −26.7203 −0.957969
\(779\) −68.9640 −2.47089
\(780\) −21.1461 −0.757152
\(781\) −57.1334 −2.04439
\(782\) 0.475482 0.0170032
\(783\) −19.0129 −0.679466
\(784\) 1.13806 0.0406450
\(785\) −37.9094 −1.35305
\(786\) 11.9335 0.425654
\(787\) −9.14067 −0.325830 −0.162915 0.986640i \(-0.552090\pi\)
−0.162915 + 0.986640i \(0.552090\pi\)
\(788\) 106.211 3.78360
\(789\) −3.91914 −0.139525
\(790\) −50.8464 −1.80903
\(791\) 32.2523 1.14676
\(792\) 67.5370 2.39982
\(793\) 34.4686 1.22401
\(794\) 96.0137 3.40740
\(795\) −10.7693 −0.381947
\(796\) 40.7319 1.44371
\(797\) −2.79399 −0.0989680 −0.0494840 0.998775i \(-0.515758\pi\)
−0.0494840 + 0.998775i \(0.515758\pi\)
\(798\) 19.9298 0.705508
\(799\) −0.214299 −0.00758135
\(800\) −0.261224 −0.00923566
\(801\) −1.47794 −0.0522205
\(802\) −82.0648 −2.89781
\(803\) 26.3079 0.928386
\(804\) −18.7978 −0.662947
\(805\) 41.2237 1.45294
\(806\) −59.9556 −2.11185
\(807\) −3.12315 −0.109940
\(808\) 15.8328 0.556996
\(809\) −8.03597 −0.282530 −0.141265 0.989972i \(-0.545117\pi\)
−0.141265 + 0.989972i \(0.545117\pi\)
\(810\) 40.6766 1.42923
\(811\) 16.0818 0.564707 0.282354 0.959310i \(-0.408885\pi\)
0.282354 + 0.959310i \(0.408885\pi\)
\(812\) −90.0017 −3.15844
\(813\) −3.22082 −0.112959
\(814\) 10.4134 0.364990
\(815\) 10.0536 0.352161
\(816\) −0.0365572 −0.00127976
\(817\) 28.4378 0.994911
\(818\) −62.5653 −2.18755
\(819\) 50.5532 1.76647
\(820\) 73.6030 2.57033
\(821\) 22.7981 0.795659 0.397830 0.917459i \(-0.369764\pi\)
0.397830 + 0.917459i \(0.369764\pi\)
\(822\) −6.63560 −0.231443
\(823\) 47.7720 1.66523 0.832613 0.553855i \(-0.186844\pi\)
0.832613 + 0.553855i \(0.186844\pi\)
\(824\) −50.7794 −1.76898
\(825\) −0.561184 −0.0195379
\(826\) 66.1229 2.30071
\(827\) 16.8441 0.585728 0.292864 0.956154i \(-0.405392\pi\)
0.292864 + 0.956154i \(0.405392\pi\)
\(828\) −78.1650 −2.71642
\(829\) −34.0417 −1.18232 −0.591159 0.806555i \(-0.701330\pi\)
−0.591159 + 0.806555i \(0.701330\pi\)
\(830\) 51.1793 1.77646
\(831\) −3.37999 −0.117251
\(832\) −59.3642 −2.05808
\(833\) −0.00924387 −0.000320281 0
\(834\) −1.66804 −0.0577595
\(835\) 10.0008 0.346092
\(836\) 158.534 5.48301
\(837\) −8.42458 −0.291196
\(838\) 70.6958 2.44215
\(839\) −25.2000 −0.870002 −0.435001 0.900430i \(-0.643252\pi\)
−0.435001 + 0.900430i \(0.643252\pi\)
\(840\) −10.3745 −0.357955
\(841\) 43.4826 1.49940
\(842\) 74.0154 2.55074
\(843\) −6.03812 −0.207964
\(844\) −51.9374 −1.78776
\(845\) −64.6495 −2.22401
\(846\) 53.2750 1.83163
\(847\) −41.0070 −1.40902
\(848\) 44.6734 1.53409
\(849\) −1.08295 −0.0371668
\(850\) −0.0195057 −0.000669041 0
\(851\) −5.87836 −0.201508
\(852\) −16.6411 −0.570115
\(853\) 0.607629 0.0208048 0.0104024 0.999946i \(-0.496689\pi\)
0.0104024 + 0.999946i \(0.496689\pi\)
\(854\) 34.6712 1.18643
\(855\) 49.2073 1.68286
\(856\) 7.88500 0.269504
\(857\) 2.78457 0.0951191 0.0475595 0.998868i \(-0.484856\pi\)
0.0475595 + 0.998868i \(0.484856\pi\)
\(858\) −30.9991 −1.05829
\(859\) 4.46737 0.152425 0.0762123 0.997092i \(-0.475717\pi\)
0.0762123 + 0.997092i \(0.475717\pi\)
\(860\) −30.3507 −1.03495
\(861\) 8.96955 0.305682
\(862\) 85.5169 2.91272
\(863\) 47.2136 1.60717 0.803585 0.595190i \(-0.202923\pi\)
0.803585 + 0.595190i \(0.202923\pi\)
\(864\) −2.02757 −0.0689794
\(865\) 8.36483 0.284413
\(866\) −90.3157 −3.06905
\(867\) −6.48443 −0.220223
\(868\) −39.8796 −1.35360
\(869\) −49.2895 −1.67203
\(870\) 17.1301 0.580764
\(871\) −82.5563 −2.79731
\(872\) 35.3070 1.19565
\(873\) 18.2198 0.616647
\(874\) −135.335 −4.57777
\(875\) −31.0796 −1.05068
\(876\) 7.66264 0.258897
\(877\) −54.6348 −1.84489 −0.922443 0.386134i \(-0.873810\pi\)
−0.922443 + 0.386134i \(0.873810\pi\)
\(878\) 82.3364 2.77872
\(879\) −1.29283 −0.0436060
\(880\) −38.1268 −1.28525
\(881\) −10.3240 −0.347825 −0.173912 0.984761i \(-0.555641\pi\)
−0.173912 + 0.984761i \(0.555641\pi\)
\(882\) 2.29804 0.0773790
\(883\) −3.12060 −0.105017 −0.0525083 0.998620i \(-0.516722\pi\)
−0.0525083 + 0.998620i \(0.516722\pi\)
\(884\) −0.712495 −0.0239638
\(885\) −8.32214 −0.279746
\(886\) −59.8488 −2.01066
\(887\) 10.6041 0.356050 0.178025 0.984026i \(-0.443029\pi\)
0.178025 + 0.984026i \(0.443029\pi\)
\(888\) 1.47937 0.0496445
\(889\) 51.5060 1.72746
\(890\) 2.73104 0.0915447
\(891\) 39.4311 1.32099
\(892\) −65.2252 −2.18390
\(893\) 60.9952 2.04113
\(894\) −3.02402 −0.101139
\(895\) 22.0663 0.737594
\(896\) −54.7966 −1.83063
\(897\) 17.4990 0.584274
\(898\) 76.1501 2.54116
\(899\) 32.1169 1.07116
\(900\) 3.20657 0.106886
\(901\) −0.362859 −0.0120886
\(902\) 107.898 3.59262
\(903\) −3.69865 −0.123084
\(904\) 55.1175 1.83318
\(905\) −8.09866 −0.269209
\(906\) 6.95914 0.231202
\(907\) −33.1586 −1.10101 −0.550506 0.834831i \(-0.685565\pi\)
−0.550506 + 0.834831i \(0.685565\pi\)
\(908\) 76.2989 2.53207
\(909\) 9.76713 0.323955
\(910\) −93.4157 −3.09670
\(911\) −11.7842 −0.390427 −0.195213 0.980761i \(-0.562540\pi\)
−0.195213 + 0.980761i \(0.562540\pi\)
\(912\) 10.4052 0.344549
\(913\) 49.6122 1.64192
\(914\) 12.8264 0.424259
\(915\) −4.36368 −0.144259
\(916\) 42.0533 1.38948
\(917\) 34.8604 1.15119
\(918\) −0.151400 −0.00499694
\(919\) 34.9680 1.15349 0.576744 0.816925i \(-0.304323\pi\)
0.576744 + 0.816925i \(0.304323\pi\)
\(920\) 70.4491 2.32264
\(921\) 8.00387 0.263737
\(922\) −2.53968 −0.0836399
\(923\) −73.0846 −2.40561
\(924\) −20.6191 −0.678320
\(925\) 0.241148 0.00792891
\(926\) −30.8995 −1.01542
\(927\) −31.3254 −1.02886
\(928\) 7.72967 0.253739
\(929\) −25.5273 −0.837523 −0.418762 0.908096i \(-0.637536\pi\)
−0.418762 + 0.908096i \(0.637536\pi\)
\(930\) 7.59030 0.248896
\(931\) 2.63105 0.0862293
\(932\) 67.5480 2.21261
\(933\) −12.9799 −0.424944
\(934\) −104.428 −3.41697
\(935\) 0.309684 0.0101277
\(936\) 86.3928 2.82384
\(937\) 52.7905 1.72459 0.862295 0.506407i \(-0.169027\pi\)
0.862295 + 0.506407i \(0.169027\pi\)
\(938\) −83.0417 −2.71141
\(939\) 7.87140 0.256873
\(940\) −65.0982 −2.12327
\(941\) 24.6981 0.805136 0.402568 0.915390i \(-0.368118\pi\)
0.402568 + 0.915390i \(0.368118\pi\)
\(942\) −16.1867 −0.527391
\(943\) −60.9084 −1.98345
\(944\) 34.5221 1.12360
\(945\) −13.1262 −0.426995
\(946\) −44.4926 −1.44658
\(947\) −49.7029 −1.61513 −0.807563 0.589782i \(-0.799214\pi\)
−0.807563 + 0.589782i \(0.799214\pi\)
\(948\) −14.3564 −0.466275
\(949\) 33.6529 1.09242
\(950\) 5.55186 0.180126
\(951\) −2.89723 −0.0939493
\(952\) −0.349558 −0.0113293
\(953\) 2.56181 0.0829853 0.0414926 0.999139i \(-0.486789\pi\)
0.0414926 + 0.999139i \(0.486789\pi\)
\(954\) 90.2072 2.92057
\(955\) −53.3342 −1.72585
\(956\) 35.1137 1.13566
\(957\) 16.6055 0.536781
\(958\) −35.9367 −1.16106
\(959\) −19.3840 −0.625943
\(960\) 7.51543 0.242559
\(961\) −16.7691 −0.540938
\(962\) 13.3208 0.429479
\(963\) 4.86420 0.156747
\(964\) −2.92020 −0.0940532
\(965\) 2.87706 0.0926158
\(966\) 17.6019 0.566330
\(967\) 5.97558 0.192162 0.0960808 0.995374i \(-0.469369\pi\)
0.0960808 + 0.995374i \(0.469369\pi\)
\(968\) −70.0787 −2.25242
\(969\) −0.0845157 −0.00271504
\(970\) −33.6678 −1.08101
\(971\) −38.4435 −1.23371 −0.616855 0.787076i \(-0.711594\pi\)
−0.616855 + 0.787076i \(0.711594\pi\)
\(972\) 37.6425 1.20738
\(973\) −4.87271 −0.156212
\(974\) −18.5103 −0.593107
\(975\) −0.717862 −0.0229900
\(976\) 18.1015 0.579415
\(977\) 24.4448 0.782057 0.391029 0.920379i \(-0.372119\pi\)
0.391029 + 0.920379i \(0.372119\pi\)
\(978\) 4.29271 0.137266
\(979\) 2.64741 0.0846117
\(980\) −2.80804 −0.0896995
\(981\) 21.7806 0.695402
\(982\) 9.60151 0.306396
\(983\) −52.1539 −1.66345 −0.831725 0.555188i \(-0.812646\pi\)
−0.831725 + 0.555188i \(0.812646\pi\)
\(984\) 15.3285 0.488654
\(985\) −59.0529 −1.88158
\(986\) 0.577179 0.0183811
\(987\) −7.93312 −0.252514
\(988\) 202.795 6.45177
\(989\) 25.1160 0.798642
\(990\) −76.9879 −2.44683
\(991\) 17.7836 0.564915 0.282458 0.959280i \(-0.408850\pi\)
0.282458 + 0.959280i \(0.408850\pi\)
\(992\) 3.42500 0.108744
\(993\) −2.63658 −0.0836694
\(994\) −73.5143 −2.33173
\(995\) −22.6468 −0.717953
\(996\) 14.4504 0.457879
\(997\) −41.2168 −1.30535 −0.652674 0.757639i \(-0.726353\pi\)
−0.652674 + 0.757639i \(0.726353\pi\)
\(998\) −23.7439 −0.751601
\(999\) 1.87175 0.0592195
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 6037.2.a.b.1.17 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.17 259 1.1 even 1 trivial