Properties

Label 6037.2.a.b.1.2
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 1.2
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66503 q^{2} +2.65532 q^{3} +5.10237 q^{4} -0.476820 q^{5} -7.07650 q^{6} -1.66384 q^{7} -8.26789 q^{8} +4.05073 q^{9} +O(q^{10})\) \(q-2.66503 q^{2} +2.65532 q^{3} +5.10237 q^{4} -0.476820 q^{5} -7.07650 q^{6} -1.66384 q^{7} -8.26789 q^{8} +4.05073 q^{9} +1.27074 q^{10} -0.629601 q^{11} +13.5484 q^{12} -2.17206 q^{13} +4.43418 q^{14} -1.26611 q^{15} +11.8294 q^{16} +1.89267 q^{17} -10.7953 q^{18} +4.87194 q^{19} -2.43291 q^{20} -4.41804 q^{21} +1.67790 q^{22} -2.42543 q^{23} -21.9539 q^{24} -4.77264 q^{25} +5.78859 q^{26} +2.79004 q^{27} -8.48953 q^{28} +2.79052 q^{29} +3.37422 q^{30} -9.28173 q^{31} -14.9899 q^{32} -1.67179 q^{33} -5.04400 q^{34} +0.793353 q^{35} +20.6683 q^{36} +10.4951 q^{37} -12.9839 q^{38} -5.76751 q^{39} +3.94229 q^{40} +10.1975 q^{41} +11.7742 q^{42} -3.90292 q^{43} -3.21246 q^{44} -1.93147 q^{45} +6.46383 q^{46} -2.47028 q^{47} +31.4109 q^{48} -4.23163 q^{49} +12.7192 q^{50} +5.02564 q^{51} -11.0826 q^{52} +5.57028 q^{53} -7.43552 q^{54} +0.300206 q^{55} +13.7565 q^{56} +12.9366 q^{57} -7.43681 q^{58} +6.84689 q^{59} -6.46016 q^{60} +3.24232 q^{61} +24.7361 q^{62} -6.73978 q^{63} +16.2897 q^{64} +1.03568 q^{65} +4.45537 q^{66} +2.16066 q^{67} +9.65707 q^{68} -6.44029 q^{69} -2.11431 q^{70} +8.34707 q^{71} -33.4910 q^{72} +8.10565 q^{73} -27.9698 q^{74} -12.6729 q^{75} +24.8584 q^{76} +1.04756 q^{77} +15.3706 q^{78} -15.2822 q^{79} -5.64049 q^{80} -4.74376 q^{81} -27.1767 q^{82} +9.31489 q^{83} -22.5424 q^{84} -0.902460 q^{85} +10.4014 q^{86} +7.40973 q^{87} +5.20547 q^{88} +1.68083 q^{89} +5.14742 q^{90} +3.61396 q^{91} -12.3754 q^{92} -24.6460 q^{93} +6.58336 q^{94} -2.32304 q^{95} -39.8030 q^{96} +8.74411 q^{97} +11.2774 q^{98} -2.55035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66503 −1.88446 −0.942229 0.334969i \(-0.891274\pi\)
−0.942229 + 0.334969i \(0.891274\pi\)
\(3\) 2.65532 1.53305 0.766525 0.642214i \(-0.221984\pi\)
0.766525 + 0.642214i \(0.221984\pi\)
\(4\) 5.10237 2.55118
\(5\) −0.476820 −0.213240 −0.106620 0.994300i \(-0.534003\pi\)
−0.106620 + 0.994300i \(0.534003\pi\)
\(6\) −7.07650 −2.88897
\(7\) −1.66384 −0.628873 −0.314437 0.949278i \(-0.601816\pi\)
−0.314437 + 0.949278i \(0.601816\pi\)
\(8\) −8.26789 −2.92314
\(9\) 4.05073 1.35024
\(10\) 1.27074 0.401842
\(11\) −0.629601 −0.189832 −0.0949159 0.995485i \(-0.530258\pi\)
−0.0949159 + 0.995485i \(0.530258\pi\)
\(12\) 13.5484 3.91109
\(13\) −2.17206 −0.602420 −0.301210 0.953558i \(-0.597391\pi\)
−0.301210 + 0.953558i \(0.597391\pi\)
\(14\) 4.43418 1.18509
\(15\) −1.26611 −0.326908
\(16\) 11.8294 2.95735
\(17\) 1.89267 0.459039 0.229519 0.973304i \(-0.426285\pi\)
0.229519 + 0.973304i \(0.426285\pi\)
\(18\) −10.7953 −2.54448
\(19\) 4.87194 1.11770 0.558850 0.829269i \(-0.311243\pi\)
0.558850 + 0.829269i \(0.311243\pi\)
\(20\) −2.43291 −0.544015
\(21\) −4.41804 −0.964094
\(22\) 1.67790 0.357730
\(23\) −2.42543 −0.505736 −0.252868 0.967501i \(-0.581374\pi\)
−0.252868 + 0.967501i \(0.581374\pi\)
\(24\) −21.9539 −4.48132
\(25\) −4.77264 −0.954529
\(26\) 5.78859 1.13524
\(27\) 2.79004 0.536943
\(28\) −8.48953 −1.60437
\(29\) 2.79052 0.518187 0.259093 0.965852i \(-0.416576\pi\)
0.259093 + 0.965852i \(0.416576\pi\)
\(30\) 3.37422 0.616045
\(31\) −9.28173 −1.66705 −0.833524 0.552483i \(-0.813680\pi\)
−0.833524 + 0.552483i \(0.813680\pi\)
\(32\) −14.9899 −2.64987
\(33\) −1.67179 −0.291022
\(34\) −5.04400 −0.865039
\(35\) 0.793353 0.134101
\(36\) 20.6683 3.44472
\(37\) 10.4951 1.72539 0.862694 0.505727i \(-0.168776\pi\)
0.862694 + 0.505727i \(0.168776\pi\)
\(38\) −12.9839 −2.10626
\(39\) −5.76751 −0.923540
\(40\) 3.94229 0.623331
\(41\) 10.1975 1.59259 0.796293 0.604912i \(-0.206792\pi\)
0.796293 + 0.604912i \(0.206792\pi\)
\(42\) 11.7742 1.81680
\(43\) −3.90292 −0.595190 −0.297595 0.954692i \(-0.596184\pi\)
−0.297595 + 0.954692i \(0.596184\pi\)
\(44\) −3.21246 −0.484296
\(45\) −1.93147 −0.287927
\(46\) 6.46383 0.953039
\(47\) −2.47028 −0.360327 −0.180164 0.983637i \(-0.557663\pi\)
−0.180164 + 0.983637i \(0.557663\pi\)
\(48\) 31.4109 4.53377
\(49\) −4.23163 −0.604519
\(50\) 12.7192 1.79877
\(51\) 5.02564 0.703730
\(52\) −11.0826 −1.53688
\(53\) 5.57028 0.765136 0.382568 0.923927i \(-0.375040\pi\)
0.382568 + 0.923927i \(0.375040\pi\)
\(54\) −7.43552 −1.01185
\(55\) 0.300206 0.0404798
\(56\) 13.7565 1.83828
\(57\) 12.9366 1.71349
\(58\) −7.43681 −0.976501
\(59\) 6.84689 0.891389 0.445694 0.895185i \(-0.352957\pi\)
0.445694 + 0.895185i \(0.352957\pi\)
\(60\) −6.46016 −0.834003
\(61\) 3.24232 0.415137 0.207568 0.978220i \(-0.433445\pi\)
0.207568 + 0.978220i \(0.433445\pi\)
\(62\) 24.7361 3.14148
\(63\) −6.73978 −0.849133
\(64\) 16.2897 2.03621
\(65\) 1.03568 0.128460
\(66\) 4.45537 0.548419
\(67\) 2.16066 0.263966 0.131983 0.991252i \(-0.457866\pi\)
0.131983 + 0.991252i \(0.457866\pi\)
\(68\) 9.65707 1.17109
\(69\) −6.44029 −0.775320
\(70\) −2.11431 −0.252708
\(71\) 8.34707 0.990615 0.495307 0.868718i \(-0.335055\pi\)
0.495307 + 0.868718i \(0.335055\pi\)
\(72\) −33.4910 −3.94695
\(73\) 8.10565 0.948695 0.474347 0.880338i \(-0.342684\pi\)
0.474347 + 0.880338i \(0.342684\pi\)
\(74\) −27.9698 −3.25142
\(75\) −12.6729 −1.46334
\(76\) 24.8584 2.85146
\(77\) 1.04756 0.119380
\(78\) 15.3706 1.74037
\(79\) −15.2822 −1.71939 −0.859694 0.510810i \(-0.829345\pi\)
−0.859694 + 0.510810i \(0.829345\pi\)
\(80\) −5.64049 −0.630627
\(81\) −4.74376 −0.527084
\(82\) −27.1767 −3.00116
\(83\) 9.31489 1.02244 0.511221 0.859449i \(-0.329193\pi\)
0.511221 + 0.859449i \(0.329193\pi\)
\(84\) −22.5424 −2.45958
\(85\) −0.902460 −0.0978856
\(86\) 10.4014 1.12161
\(87\) 7.40973 0.794406
\(88\) 5.20547 0.554905
\(89\) 1.68083 0.178168 0.0890840 0.996024i \(-0.471606\pi\)
0.0890840 + 0.996024i \(0.471606\pi\)
\(90\) 5.14742 0.542586
\(91\) 3.61396 0.378846
\(92\) −12.3754 −1.29023
\(93\) −24.6460 −2.55567
\(94\) 6.58336 0.679022
\(95\) −2.32304 −0.238339
\(96\) −39.8030 −4.06238
\(97\) 8.74411 0.887830 0.443915 0.896069i \(-0.353589\pi\)
0.443915 + 0.896069i \(0.353589\pi\)
\(98\) 11.2774 1.13919
\(99\) −2.55035 −0.256319
\(100\) −24.3518 −2.43518
\(101\) −9.12625 −0.908096 −0.454048 0.890977i \(-0.650020\pi\)
−0.454048 + 0.890977i \(0.650020\pi\)
\(102\) −13.3935 −1.32615
\(103\) 7.27485 0.716812 0.358406 0.933566i \(-0.383320\pi\)
0.358406 + 0.933566i \(0.383320\pi\)
\(104\) 17.9583 1.76096
\(105\) 2.10661 0.205584
\(106\) −14.8449 −1.44187
\(107\) 17.6960 1.71073 0.855366 0.518024i \(-0.173332\pi\)
0.855366 + 0.518024i \(0.173332\pi\)
\(108\) 14.2358 1.36984
\(109\) −0.528860 −0.0506556 −0.0253278 0.999679i \(-0.508063\pi\)
−0.0253278 + 0.999679i \(0.508063\pi\)
\(110\) −0.800058 −0.0762825
\(111\) 27.8679 2.64511
\(112\) −19.6823 −1.85980
\(113\) −8.84180 −0.831767 −0.415883 0.909418i \(-0.636528\pi\)
−0.415883 + 0.909418i \(0.636528\pi\)
\(114\) −34.4763 −3.22900
\(115\) 1.15649 0.107843
\(116\) 14.2383 1.32199
\(117\) −8.79842 −0.813414
\(118\) −18.2471 −1.67979
\(119\) −3.14910 −0.288677
\(120\) 10.4681 0.955598
\(121\) −10.6036 −0.963964
\(122\) −8.64088 −0.782308
\(123\) 27.0777 2.44151
\(124\) −47.3588 −4.25295
\(125\) 4.65979 0.416784
\(126\) 17.9617 1.60015
\(127\) 12.4634 1.10594 0.552972 0.833200i \(-0.313494\pi\)
0.552972 + 0.833200i \(0.313494\pi\)
\(128\) −13.4326 −1.18729
\(129\) −10.3635 −0.912456
\(130\) −2.76011 −0.242078
\(131\) 3.61022 0.315427 0.157713 0.987485i \(-0.449588\pi\)
0.157713 + 0.987485i \(0.449588\pi\)
\(132\) −8.53010 −0.742450
\(133\) −8.10614 −0.702892
\(134\) −5.75820 −0.497433
\(135\) −1.33034 −0.114498
\(136\) −15.6483 −1.34183
\(137\) −9.65300 −0.824712 −0.412356 0.911023i \(-0.635294\pi\)
−0.412356 + 0.911023i \(0.635294\pi\)
\(138\) 17.1635 1.46106
\(139\) −2.95693 −0.250804 −0.125402 0.992106i \(-0.540022\pi\)
−0.125402 + 0.992106i \(0.540022\pi\)
\(140\) 4.04798 0.342116
\(141\) −6.55939 −0.552400
\(142\) −22.2452 −1.86677
\(143\) 1.36753 0.114359
\(144\) 47.9178 3.99315
\(145\) −1.33057 −0.110498
\(146\) −21.6018 −1.78778
\(147\) −11.2363 −0.926758
\(148\) 53.5499 4.40178
\(149\) −7.73243 −0.633465 −0.316733 0.948515i \(-0.602586\pi\)
−0.316733 + 0.948515i \(0.602586\pi\)
\(150\) 33.7736 2.75760
\(151\) 0.790890 0.0643617 0.0321808 0.999482i \(-0.489755\pi\)
0.0321808 + 0.999482i \(0.489755\pi\)
\(152\) −40.2807 −3.26720
\(153\) 7.66668 0.619815
\(154\) −2.79177 −0.224967
\(155\) 4.42571 0.355482
\(156\) −29.4279 −2.35612
\(157\) 11.8652 0.946944 0.473472 0.880809i \(-0.343000\pi\)
0.473472 + 0.880809i \(0.343000\pi\)
\(158\) 40.7276 3.24011
\(159\) 14.7909 1.17299
\(160\) 7.14748 0.565058
\(161\) 4.03553 0.318044
\(162\) 12.6422 0.993268
\(163\) −1.90792 −0.149440 −0.0747200 0.997205i \(-0.523806\pi\)
−0.0747200 + 0.997205i \(0.523806\pi\)
\(164\) 52.0315 4.06298
\(165\) 0.797144 0.0620576
\(166\) −24.8244 −1.92675
\(167\) 0.838151 0.0648581 0.0324291 0.999474i \(-0.489676\pi\)
0.0324291 + 0.999474i \(0.489676\pi\)
\(168\) 36.5278 2.81818
\(169\) −8.28217 −0.637090
\(170\) 2.40508 0.184461
\(171\) 19.7349 1.50917
\(172\) −19.9141 −1.51844
\(173\) 19.0906 1.45143 0.725716 0.687994i \(-0.241509\pi\)
0.725716 + 0.687994i \(0.241509\pi\)
\(174\) −19.7471 −1.49703
\(175\) 7.94092 0.600277
\(176\) −7.44781 −0.561400
\(177\) 18.1807 1.36654
\(178\) −4.47947 −0.335750
\(179\) 16.5224 1.23494 0.617472 0.786593i \(-0.288157\pi\)
0.617472 + 0.786593i \(0.288157\pi\)
\(180\) −9.85507 −0.734553
\(181\) −3.25226 −0.241739 −0.120869 0.992668i \(-0.538568\pi\)
−0.120869 + 0.992668i \(0.538568\pi\)
\(182\) −9.63129 −0.713919
\(183\) 8.60941 0.636426
\(184\) 20.0532 1.47834
\(185\) −5.00428 −0.367922
\(186\) 65.6822 4.81605
\(187\) −1.19162 −0.0871402
\(188\) −12.6043 −0.919261
\(189\) −4.64218 −0.337669
\(190\) 6.19096 0.449139
\(191\) 17.8176 1.28924 0.644619 0.764504i \(-0.277016\pi\)
0.644619 + 0.764504i \(0.277016\pi\)
\(192\) 43.2544 3.12161
\(193\) 11.4990 0.827713 0.413857 0.910342i \(-0.364181\pi\)
0.413857 + 0.910342i \(0.364181\pi\)
\(194\) −23.3033 −1.67308
\(195\) 2.75006 0.196936
\(196\) −21.5913 −1.54224
\(197\) 1.99176 0.141907 0.0709534 0.997480i \(-0.477396\pi\)
0.0709534 + 0.997480i \(0.477396\pi\)
\(198\) 6.79674 0.483023
\(199\) 9.41249 0.667234 0.333617 0.942709i \(-0.391731\pi\)
0.333617 + 0.942709i \(0.391731\pi\)
\(200\) 39.4597 2.79022
\(201\) 5.73723 0.404673
\(202\) 24.3217 1.71127
\(203\) −4.64298 −0.325874
\(204\) 25.6426 1.79534
\(205\) −4.86238 −0.339603
\(206\) −19.3877 −1.35080
\(207\) −9.82476 −0.682868
\(208\) −25.6941 −1.78157
\(209\) −3.06738 −0.212175
\(210\) −5.61416 −0.387414
\(211\) −10.8751 −0.748673 −0.374337 0.927293i \(-0.622130\pi\)
−0.374337 + 0.927293i \(0.622130\pi\)
\(212\) 28.4216 1.95200
\(213\) 22.1642 1.51866
\(214\) −47.1602 −3.22380
\(215\) 1.86099 0.126918
\(216\) −23.0677 −1.56956
\(217\) 15.4433 1.04836
\(218\) 1.40943 0.0954584
\(219\) 21.5231 1.45440
\(220\) 1.53176 0.103271
\(221\) −4.11098 −0.276534
\(222\) −74.2687 −4.98459
\(223\) 17.2972 1.15831 0.579154 0.815218i \(-0.303383\pi\)
0.579154 + 0.815218i \(0.303383\pi\)
\(224\) 24.9408 1.66643
\(225\) −19.3327 −1.28885
\(226\) 23.5636 1.56743
\(227\) 26.8714 1.78352 0.891759 0.452512i \(-0.149472\pi\)
0.891759 + 0.452512i \(0.149472\pi\)
\(228\) 66.0072 4.37143
\(229\) −20.1702 −1.33288 −0.666441 0.745558i \(-0.732183\pi\)
−0.666441 + 0.745558i \(0.732183\pi\)
\(230\) −3.08208 −0.203226
\(231\) 2.78160 0.183016
\(232\) −23.0717 −1.51473
\(233\) 16.7885 1.09985 0.549925 0.835214i \(-0.314656\pi\)
0.549925 + 0.835214i \(0.314656\pi\)
\(234\) 23.4480 1.53285
\(235\) 1.17788 0.0768363
\(236\) 34.9353 2.27410
\(237\) −40.5793 −2.63591
\(238\) 8.39242 0.544000
\(239\) 1.79676 0.116223 0.0581113 0.998310i \(-0.481492\pi\)
0.0581113 + 0.998310i \(0.481492\pi\)
\(240\) −14.9773 −0.966782
\(241\) 17.4288 1.12269 0.561343 0.827583i \(-0.310285\pi\)
0.561343 + 0.827583i \(0.310285\pi\)
\(242\) 28.2589 1.81655
\(243\) −20.9663 −1.34499
\(244\) 16.5435 1.05909
\(245\) 2.01772 0.128908
\(246\) −72.1628 −4.60093
\(247\) −10.5821 −0.673325
\(248\) 76.7403 4.87302
\(249\) 24.7340 1.56746
\(250\) −12.4185 −0.785412
\(251\) 16.6108 1.04846 0.524232 0.851576i \(-0.324352\pi\)
0.524232 + 0.851576i \(0.324352\pi\)
\(252\) −34.3888 −2.16629
\(253\) 1.52705 0.0960049
\(254\) −33.2152 −2.08411
\(255\) −2.39632 −0.150064
\(256\) 3.21895 0.201184
\(257\) 13.4851 0.841180 0.420590 0.907251i \(-0.361823\pi\)
0.420590 + 0.907251i \(0.361823\pi\)
\(258\) 27.6190 1.71948
\(259\) −17.4622 −1.08505
\(260\) 5.28441 0.327725
\(261\) 11.3037 0.699679
\(262\) −9.62134 −0.594408
\(263\) −20.9271 −1.29042 −0.645211 0.764004i \(-0.723231\pi\)
−0.645211 + 0.764004i \(0.723231\pi\)
\(264\) 13.8222 0.850698
\(265\) −2.65602 −0.163158
\(266\) 21.6031 1.32457
\(267\) 4.46316 0.273141
\(268\) 11.0245 0.673426
\(269\) 4.57948 0.279216 0.139608 0.990207i \(-0.455416\pi\)
0.139608 + 0.990207i \(0.455416\pi\)
\(270\) 3.54540 0.215766
\(271\) 0.282769 0.0171770 0.00858849 0.999963i \(-0.497266\pi\)
0.00858849 + 0.999963i \(0.497266\pi\)
\(272\) 22.3891 1.35754
\(273\) 9.59622 0.580790
\(274\) 25.7255 1.55413
\(275\) 3.00486 0.181200
\(276\) −32.8607 −1.97798
\(277\) −20.2951 −1.21941 −0.609707 0.792627i \(-0.708713\pi\)
−0.609707 + 0.792627i \(0.708713\pi\)
\(278\) 7.88030 0.472629
\(279\) −37.5978 −2.25092
\(280\) −6.55935 −0.391996
\(281\) 3.24315 0.193470 0.0967351 0.995310i \(-0.469160\pi\)
0.0967351 + 0.995310i \(0.469160\pi\)
\(282\) 17.4809 1.04098
\(283\) 27.9086 1.65899 0.829496 0.558512i \(-0.188628\pi\)
0.829496 + 0.558512i \(0.188628\pi\)
\(284\) 42.5898 2.52724
\(285\) −6.16842 −0.365385
\(286\) −3.64450 −0.215504
\(287\) −16.9671 −1.00153
\(288\) −60.7201 −3.57797
\(289\) −13.4178 −0.789283
\(290\) 3.54602 0.208229
\(291\) 23.2184 1.36109
\(292\) 41.3580 2.42029
\(293\) 21.7248 1.26918 0.634588 0.772850i \(-0.281170\pi\)
0.634588 + 0.772850i \(0.281170\pi\)
\(294\) 29.9451 1.74644
\(295\) −3.26473 −0.190080
\(296\) −86.7725 −5.04355
\(297\) −1.75661 −0.101929
\(298\) 20.6071 1.19374
\(299\) 5.26816 0.304666
\(300\) −64.6618 −3.73325
\(301\) 6.49384 0.374299
\(302\) −2.10774 −0.121287
\(303\) −24.2331 −1.39216
\(304\) 57.6322 3.30543
\(305\) −1.54600 −0.0885239
\(306\) −20.4319 −1.16801
\(307\) 22.3117 1.27340 0.636698 0.771113i \(-0.280300\pi\)
0.636698 + 0.771113i \(0.280300\pi\)
\(308\) 5.34502 0.304561
\(309\) 19.3171 1.09891
\(310\) −11.7946 −0.669891
\(311\) 5.81204 0.329571 0.164785 0.986329i \(-0.447307\pi\)
0.164785 + 0.986329i \(0.447307\pi\)
\(312\) 47.6851 2.69964
\(313\) 13.8227 0.781304 0.390652 0.920538i \(-0.372250\pi\)
0.390652 + 0.920538i \(0.372250\pi\)
\(314\) −31.6210 −1.78448
\(315\) 3.21366 0.181069
\(316\) −77.9756 −4.38647
\(317\) −29.6147 −1.66333 −0.831665 0.555278i \(-0.812612\pi\)
−0.831665 + 0.555278i \(0.812612\pi\)
\(318\) −39.4181 −2.21046
\(319\) −1.75691 −0.0983683
\(320\) −7.76725 −0.434202
\(321\) 46.9885 2.62264
\(322\) −10.7548 −0.599341
\(323\) 9.22096 0.513068
\(324\) −24.2044 −1.34469
\(325\) 10.3664 0.575027
\(326\) 5.08466 0.281613
\(327\) −1.40429 −0.0776576
\(328\) −84.3120 −4.65535
\(329\) 4.11016 0.226600
\(330\) −2.12441 −0.116945
\(331\) −18.2723 −1.00433 −0.502167 0.864771i \(-0.667464\pi\)
−0.502167 + 0.864771i \(0.667464\pi\)
\(332\) 47.5280 2.60844
\(333\) 42.5129 2.32969
\(334\) −2.23370 −0.122222
\(335\) −1.03024 −0.0562882
\(336\) −52.2627 −2.85117
\(337\) 1.67030 0.0909871 0.0454935 0.998965i \(-0.485514\pi\)
0.0454935 + 0.998965i \(0.485514\pi\)
\(338\) 22.0722 1.20057
\(339\) −23.4778 −1.27514
\(340\) −4.60468 −0.249724
\(341\) 5.84379 0.316459
\(342\) −52.5942 −2.84397
\(343\) 18.6877 1.00904
\(344\) 32.2689 1.73982
\(345\) 3.07086 0.165329
\(346\) −50.8770 −2.73516
\(347\) −22.2192 −1.19279 −0.596393 0.802692i \(-0.703400\pi\)
−0.596393 + 0.802692i \(0.703400\pi\)
\(348\) 37.8071 2.02668
\(349\) 2.55806 0.136930 0.0684648 0.997654i \(-0.478190\pi\)
0.0684648 + 0.997654i \(0.478190\pi\)
\(350\) −21.1628 −1.13120
\(351\) −6.06011 −0.323465
\(352\) 9.43766 0.503029
\(353\) −9.84088 −0.523777 −0.261888 0.965098i \(-0.584345\pi\)
−0.261888 + 0.965098i \(0.584345\pi\)
\(354\) −48.4520 −2.57520
\(355\) −3.98005 −0.211239
\(356\) 8.57623 0.454539
\(357\) −8.36186 −0.442557
\(358\) −44.0327 −2.32720
\(359\) −12.2530 −0.646687 −0.323344 0.946282i \(-0.604807\pi\)
−0.323344 + 0.946282i \(0.604807\pi\)
\(360\) 15.9692 0.841649
\(361\) 4.73584 0.249255
\(362\) 8.66736 0.455546
\(363\) −28.1560 −1.47781
\(364\) 18.4397 0.966505
\(365\) −3.86493 −0.202300
\(366\) −22.9443 −1.19932
\(367\) −4.70231 −0.245459 −0.122729 0.992440i \(-0.539165\pi\)
−0.122729 + 0.992440i \(0.539165\pi\)
\(368\) −28.6914 −1.49564
\(369\) 41.3074 2.15038
\(370\) 13.3365 0.693334
\(371\) −9.26806 −0.481174
\(372\) −125.753 −6.51998
\(373\) −1.64294 −0.0850684 −0.0425342 0.999095i \(-0.513543\pi\)
−0.0425342 + 0.999095i \(0.513543\pi\)
\(374\) 3.17571 0.164212
\(375\) 12.3732 0.638951
\(376\) 20.4240 1.05329
\(377\) −6.06117 −0.312166
\(378\) 12.3715 0.636323
\(379\) −1.45615 −0.0747976 −0.0373988 0.999300i \(-0.511907\pi\)
−0.0373988 + 0.999300i \(0.511907\pi\)
\(380\) −11.8530 −0.608046
\(381\) 33.0942 1.69547
\(382\) −47.4845 −2.42952
\(383\) 27.8637 1.42377 0.711884 0.702297i \(-0.247842\pi\)
0.711884 + 0.702297i \(0.247842\pi\)
\(384\) −35.6680 −1.82017
\(385\) −0.499496 −0.0254567
\(386\) −30.6450 −1.55979
\(387\) −15.8097 −0.803651
\(388\) 44.6156 2.26502
\(389\) −15.2793 −0.774692 −0.387346 0.921934i \(-0.626608\pi\)
−0.387346 + 0.921934i \(0.626608\pi\)
\(390\) −7.32899 −0.371118
\(391\) −4.59052 −0.232153
\(392\) 34.9866 1.76709
\(393\) 9.58630 0.483565
\(394\) −5.30809 −0.267418
\(395\) 7.28688 0.366643
\(396\) −13.0128 −0.653918
\(397\) −1.50186 −0.0753764 −0.0376882 0.999290i \(-0.511999\pi\)
−0.0376882 + 0.999290i \(0.511999\pi\)
\(398\) −25.0845 −1.25737
\(399\) −21.5244 −1.07757
\(400\) −56.4575 −2.82288
\(401\) 17.6776 0.882775 0.441387 0.897317i \(-0.354486\pi\)
0.441387 + 0.897317i \(0.354486\pi\)
\(402\) −15.2899 −0.762590
\(403\) 20.1604 1.00426
\(404\) −46.5655 −2.31672
\(405\) 2.26192 0.112396
\(406\) 12.3737 0.614095
\(407\) −6.60774 −0.327533
\(408\) −41.5514 −2.05710
\(409\) 14.2535 0.704790 0.352395 0.935851i \(-0.385367\pi\)
0.352395 + 0.935851i \(0.385367\pi\)
\(410\) 12.9584 0.639968
\(411\) −25.6318 −1.26432
\(412\) 37.1189 1.82872
\(413\) −11.3921 −0.560571
\(414\) 26.1832 1.28684
\(415\) −4.44153 −0.218026
\(416\) 32.5589 1.59633
\(417\) −7.85161 −0.384495
\(418\) 8.17465 0.399835
\(419\) −25.1630 −1.22929 −0.614647 0.788802i \(-0.710701\pi\)
−0.614647 + 0.788802i \(0.710701\pi\)
\(420\) 10.7487 0.524482
\(421\) −37.2496 −1.81543 −0.907716 0.419584i \(-0.862176\pi\)
−0.907716 + 0.419584i \(0.862176\pi\)
\(422\) 28.9825 1.41084
\(423\) −10.0064 −0.486530
\(424\) −46.0544 −2.23660
\(425\) −9.03302 −0.438166
\(426\) −59.0681 −2.86186
\(427\) −5.39471 −0.261068
\(428\) 90.2912 4.36439
\(429\) 3.63123 0.175317
\(430\) −4.95958 −0.239172
\(431\) 26.7250 1.28730 0.643649 0.765321i \(-0.277420\pi\)
0.643649 + 0.765321i \(0.277420\pi\)
\(432\) 33.0045 1.58793
\(433\) −23.7427 −1.14100 −0.570501 0.821297i \(-0.693251\pi\)
−0.570501 + 0.821297i \(0.693251\pi\)
\(434\) −41.1569 −1.97559
\(435\) −3.53310 −0.169399
\(436\) −2.69844 −0.129232
\(437\) −11.8165 −0.565262
\(438\) −57.3597 −2.74075
\(439\) 31.2161 1.48986 0.744931 0.667141i \(-0.232482\pi\)
0.744931 + 0.667141i \(0.232482\pi\)
\(440\) −2.48207 −0.118328
\(441\) −17.1412 −0.816248
\(442\) 10.9559 0.521117
\(443\) −18.8952 −0.897739 −0.448870 0.893597i \(-0.648173\pi\)
−0.448870 + 0.893597i \(0.648173\pi\)
\(444\) 142.192 6.74815
\(445\) −0.801455 −0.0379926
\(446\) −46.0976 −2.18278
\(447\) −20.5321 −0.971135
\(448\) −27.1035 −1.28052
\(449\) 13.2907 0.627226 0.313613 0.949551i \(-0.398461\pi\)
0.313613 + 0.949551i \(0.398461\pi\)
\(450\) 51.5222 2.42878
\(451\) −6.42037 −0.302323
\(452\) −45.1141 −2.12199
\(453\) 2.10007 0.0986697
\(454\) −71.6130 −3.36096
\(455\) −1.72321 −0.0807852
\(456\) −106.958 −5.00878
\(457\) 37.8519 1.77064 0.885318 0.464987i \(-0.153941\pi\)
0.885318 + 0.464987i \(0.153941\pi\)
\(458\) 53.7540 2.51176
\(459\) 5.28061 0.246478
\(460\) 5.90084 0.275128
\(461\) −10.5862 −0.493050 −0.246525 0.969136i \(-0.579289\pi\)
−0.246525 + 0.969136i \(0.579289\pi\)
\(462\) −7.41304 −0.344886
\(463\) −0.691953 −0.0321578 −0.0160789 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(464\) 33.0102 1.53246
\(465\) 11.7517 0.544972
\(466\) −44.7417 −2.07262
\(467\) 22.9608 1.06250 0.531251 0.847215i \(-0.321722\pi\)
0.531251 + 0.847215i \(0.321722\pi\)
\(468\) −44.8928 −2.07517
\(469\) −3.59499 −0.166001
\(470\) −3.13908 −0.144795
\(471\) 31.5059 1.45171
\(472\) −56.6093 −2.60565
\(473\) 2.45728 0.112986
\(474\) 108.145 4.96726
\(475\) −23.2520 −1.06688
\(476\) −16.0678 −0.736468
\(477\) 22.5637 1.03312
\(478\) −4.78840 −0.219017
\(479\) 24.8439 1.13515 0.567573 0.823323i \(-0.307882\pi\)
0.567573 + 0.823323i \(0.307882\pi\)
\(480\) 18.9789 0.866263
\(481\) −22.7960 −1.03941
\(482\) −46.4481 −2.11565
\(483\) 10.7156 0.487578
\(484\) −54.1035 −2.45925
\(485\) −4.16936 −0.189321
\(486\) 55.8758 2.53458
\(487\) −23.1251 −1.04790 −0.523949 0.851750i \(-0.675542\pi\)
−0.523949 + 0.851750i \(0.675542\pi\)
\(488\) −26.8072 −1.21350
\(489\) −5.06615 −0.229099
\(490\) −5.37729 −0.242921
\(491\) −41.0083 −1.85068 −0.925339 0.379142i \(-0.876219\pi\)
−0.925339 + 0.379142i \(0.876219\pi\)
\(492\) 138.160 6.22875
\(493\) 5.28152 0.237868
\(494\) 28.2017 1.26885
\(495\) 1.21606 0.0546576
\(496\) −109.797 −4.93005
\(497\) −13.8882 −0.622971
\(498\) −65.9169 −2.95381
\(499\) 2.53732 0.113586 0.0567931 0.998386i \(-0.481912\pi\)
0.0567931 + 0.998386i \(0.481912\pi\)
\(500\) 23.7759 1.06329
\(501\) 2.22556 0.0994308
\(502\) −44.2682 −1.97579
\(503\) −20.3136 −0.905736 −0.452868 0.891577i \(-0.649599\pi\)
−0.452868 + 0.891577i \(0.649599\pi\)
\(504\) 55.7237 2.48213
\(505\) 4.35158 0.193643
\(506\) −4.06963 −0.180917
\(507\) −21.9918 −0.976692
\(508\) 63.5926 2.82147
\(509\) −1.84315 −0.0816963 −0.0408481 0.999165i \(-0.513006\pi\)
−0.0408481 + 0.999165i \(0.513006\pi\)
\(510\) 6.38626 0.282788
\(511\) −13.4865 −0.596609
\(512\) 18.2867 0.808165
\(513\) 13.5929 0.600141
\(514\) −35.9383 −1.58517
\(515\) −3.46879 −0.152853
\(516\) −52.8784 −2.32784
\(517\) 1.55529 0.0684016
\(518\) 46.5373 2.04473
\(519\) 50.6917 2.22512
\(520\) −8.56288 −0.375507
\(521\) −2.10028 −0.0920150 −0.0460075 0.998941i \(-0.514650\pi\)
−0.0460075 + 0.998941i \(0.514650\pi\)
\(522\) −30.1245 −1.31852
\(523\) −23.1459 −1.01210 −0.506051 0.862504i \(-0.668895\pi\)
−0.506051 + 0.862504i \(0.668895\pi\)
\(524\) 18.4207 0.804711
\(525\) 21.0857 0.920256
\(526\) 55.7713 2.43175
\(527\) −17.5672 −0.765240
\(528\) −19.7763 −0.860654
\(529\) −17.1173 −0.744231
\(530\) 7.07836 0.307464
\(531\) 27.7349 1.20359
\(532\) −41.3605 −1.79321
\(533\) −22.1496 −0.959405
\(534\) −11.8944 −0.514722
\(535\) −8.43778 −0.364797
\(536\) −17.8641 −0.771610
\(537\) 43.8724 1.89323
\(538\) −12.2044 −0.526171
\(539\) 2.66424 0.114757
\(540\) −6.78790 −0.292105
\(541\) 30.8543 1.32653 0.663264 0.748385i \(-0.269171\pi\)
0.663264 + 0.748385i \(0.269171\pi\)
\(542\) −0.753586 −0.0323693
\(543\) −8.63579 −0.370597
\(544\) −28.3709 −1.21639
\(545\) 0.252171 0.0108018
\(546\) −25.5742 −1.09447
\(547\) 39.4572 1.68707 0.843535 0.537074i \(-0.180471\pi\)
0.843535 + 0.537074i \(0.180471\pi\)
\(548\) −49.2532 −2.10399
\(549\) 13.1338 0.560536
\(550\) −8.00803 −0.341464
\(551\) 13.5953 0.579177
\(552\) 53.2476 2.26637
\(553\) 25.4272 1.08128
\(554\) 54.0869 2.29793
\(555\) −13.2880 −0.564043
\(556\) −15.0874 −0.639846
\(557\) −5.56036 −0.235600 −0.117800 0.993037i \(-0.537584\pi\)
−0.117800 + 0.993037i \(0.537584\pi\)
\(558\) 100.199 4.24177
\(559\) 8.47736 0.358554
\(560\) 9.38489 0.396584
\(561\) −3.16415 −0.133590
\(562\) −8.64308 −0.364586
\(563\) 19.1706 0.807945 0.403972 0.914771i \(-0.367629\pi\)
0.403972 + 0.914771i \(0.367629\pi\)
\(564\) −33.4684 −1.40927
\(565\) 4.21595 0.177366
\(566\) −74.3771 −3.12630
\(567\) 7.89286 0.331469
\(568\) −69.0126 −2.89571
\(569\) 11.1814 0.468750 0.234375 0.972146i \(-0.424696\pi\)
0.234375 + 0.972146i \(0.424696\pi\)
\(570\) 16.4390 0.688554
\(571\) 10.6580 0.446023 0.223011 0.974816i \(-0.428411\pi\)
0.223011 + 0.974816i \(0.428411\pi\)
\(572\) 6.97763 0.291749
\(573\) 47.3116 1.97647
\(574\) 45.2177 1.88735
\(575\) 11.5757 0.482740
\(576\) 65.9852 2.74938
\(577\) 41.6013 1.73189 0.865943 0.500143i \(-0.166719\pi\)
0.865943 + 0.500143i \(0.166719\pi\)
\(578\) 35.7588 1.48737
\(579\) 30.5334 1.26893
\(580\) −6.78908 −0.281901
\(581\) −15.4985 −0.642987
\(582\) −61.8777 −2.56491
\(583\) −3.50705 −0.145247
\(584\) −67.0166 −2.77317
\(585\) 4.19526 0.173453
\(586\) −57.8972 −2.39171
\(587\) 33.6324 1.38816 0.694080 0.719898i \(-0.255812\pi\)
0.694080 + 0.719898i \(0.255812\pi\)
\(588\) −57.3319 −2.36433
\(589\) −45.2201 −1.86326
\(590\) 8.70060 0.358198
\(591\) 5.28876 0.217550
\(592\) 124.151 5.10258
\(593\) −23.1396 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(594\) 4.68141 0.192081
\(595\) 1.50155 0.0615576
\(596\) −39.4537 −1.61609
\(597\) 24.9932 1.02290
\(598\) −14.0398 −0.574130
\(599\) −15.6251 −0.638424 −0.319212 0.947683i \(-0.603418\pi\)
−0.319212 + 0.947683i \(0.603418\pi\)
\(600\) 104.778 4.27755
\(601\) 21.1450 0.862522 0.431261 0.902227i \(-0.358069\pi\)
0.431261 + 0.902227i \(0.358069\pi\)
\(602\) −17.3063 −0.705350
\(603\) 8.75224 0.356419
\(604\) 4.03541 0.164198
\(605\) 5.05601 0.205556
\(606\) 64.5819 2.62346
\(607\) −30.9275 −1.25531 −0.627655 0.778492i \(-0.715985\pi\)
−0.627655 + 0.778492i \(0.715985\pi\)
\(608\) −73.0300 −2.96176
\(609\) −12.3286 −0.499581
\(610\) 4.12014 0.166820
\(611\) 5.36559 0.217068
\(612\) 39.1182 1.58126
\(613\) −20.1976 −0.815773 −0.407886 0.913033i \(-0.633734\pi\)
−0.407886 + 0.913033i \(0.633734\pi\)
\(614\) −59.4612 −2.39966
\(615\) −12.9112 −0.520629
\(616\) −8.66108 −0.348965
\(617\) 10.3812 0.417932 0.208966 0.977923i \(-0.432990\pi\)
0.208966 + 0.977923i \(0.432990\pi\)
\(618\) −51.4805 −2.07085
\(619\) 17.0984 0.687244 0.343622 0.939108i \(-0.388346\pi\)
0.343622 + 0.939108i \(0.388346\pi\)
\(620\) 22.5816 0.906899
\(621\) −6.76703 −0.271551
\(622\) −15.4893 −0.621062
\(623\) −2.79664 −0.112045
\(624\) −68.2262 −2.73123
\(625\) 21.6413 0.865653
\(626\) −36.8378 −1.47234
\(627\) −8.14488 −0.325275
\(628\) 60.5405 2.41583
\(629\) 19.8638 0.792020
\(630\) −8.56449 −0.341217
\(631\) −35.3022 −1.40536 −0.702679 0.711507i \(-0.748013\pi\)
−0.702679 + 0.711507i \(0.748013\pi\)
\(632\) 126.352 5.02601
\(633\) −28.8769 −1.14775
\(634\) 78.9241 3.13447
\(635\) −5.94278 −0.235832
\(636\) 75.4684 2.99252
\(637\) 9.19134 0.364174
\(638\) 4.68222 0.185371
\(639\) 33.8118 1.33757
\(640\) 6.40494 0.253178
\(641\) −11.2592 −0.444712 −0.222356 0.974966i \(-0.571375\pi\)
−0.222356 + 0.974966i \(0.571375\pi\)
\(642\) −125.225 −4.94226
\(643\) −36.5342 −1.44077 −0.720385 0.693575i \(-0.756035\pi\)
−0.720385 + 0.693575i \(0.756035\pi\)
\(644\) 20.5907 0.811389
\(645\) 4.94152 0.194572
\(646\) −24.5741 −0.966855
\(647\) −33.4960 −1.31686 −0.658432 0.752640i \(-0.728780\pi\)
−0.658432 + 0.752640i \(0.728780\pi\)
\(648\) 39.2209 1.54074
\(649\) −4.31081 −0.169214
\(650\) −27.6269 −1.08361
\(651\) 41.0070 1.60719
\(652\) −9.73492 −0.381249
\(653\) 32.2965 1.26386 0.631930 0.775026i \(-0.282263\pi\)
0.631930 + 0.775026i \(0.282263\pi\)
\(654\) 3.74248 0.146343
\(655\) −1.72143 −0.0672617
\(656\) 120.631 4.70984
\(657\) 32.8338 1.28097
\(658\) −10.9537 −0.427019
\(659\) 17.0705 0.664973 0.332487 0.943108i \(-0.392112\pi\)
0.332487 + 0.943108i \(0.392112\pi\)
\(660\) 4.06732 0.158320
\(661\) −12.0076 −0.467041 −0.233521 0.972352i \(-0.575025\pi\)
−0.233521 + 0.972352i \(0.575025\pi\)
\(662\) 48.6961 1.89263
\(663\) −10.9160 −0.423941
\(664\) −77.0145 −2.98874
\(665\) 3.86517 0.149885
\(666\) −113.298 −4.39021
\(667\) −6.76820 −0.262066
\(668\) 4.27656 0.165465
\(669\) 45.9297 1.77575
\(670\) 2.74562 0.106073
\(671\) −2.04137 −0.0788062
\(672\) 66.2260 2.55472
\(673\) 50.2827 1.93826 0.969129 0.246555i \(-0.0792987\pi\)
0.969129 + 0.246555i \(0.0792987\pi\)
\(674\) −4.45140 −0.171461
\(675\) −13.3158 −0.512527
\(676\) −42.2587 −1.62533
\(677\) −18.2257 −0.700472 −0.350236 0.936661i \(-0.613899\pi\)
−0.350236 + 0.936661i \(0.613899\pi\)
\(678\) 62.5691 2.40295
\(679\) −14.5488 −0.558332
\(680\) 7.46144 0.286133
\(681\) 71.3522 2.73422
\(682\) −15.5739 −0.596354
\(683\) −0.621821 −0.0237933 −0.0118967 0.999929i \(-0.503787\pi\)
−0.0118967 + 0.999929i \(0.503787\pi\)
\(684\) 100.695 3.85017
\(685\) 4.60274 0.175862
\(686\) −49.8031 −1.90149
\(687\) −53.5583 −2.04338
\(688\) −46.1692 −1.76018
\(689\) −12.0989 −0.460933
\(690\) −8.18391 −0.311556
\(691\) 35.9372 1.36711 0.683557 0.729897i \(-0.260432\pi\)
0.683557 + 0.729897i \(0.260432\pi\)
\(692\) 97.4073 3.70287
\(693\) 4.24337 0.161192
\(694\) 59.2146 2.24776
\(695\) 1.40992 0.0534815
\(696\) −61.2628 −2.32216
\(697\) 19.3005 0.731058
\(698\) −6.81728 −0.258038
\(699\) 44.5788 1.68612
\(700\) 40.5175 1.53142
\(701\) 19.0812 0.720687 0.360344 0.932820i \(-0.382659\pi\)
0.360344 + 0.932820i \(0.382659\pi\)
\(702\) 16.1504 0.609556
\(703\) 51.1316 1.92847
\(704\) −10.2560 −0.386538
\(705\) 3.12765 0.117794
\(706\) 26.2262 0.987036
\(707\) 15.1846 0.571077
\(708\) 92.7646 3.48631
\(709\) −37.0067 −1.38982 −0.694908 0.719099i \(-0.744555\pi\)
−0.694908 + 0.719099i \(0.744555\pi\)
\(710\) 10.6069 0.398071
\(711\) −61.9043 −2.32159
\(712\) −13.8969 −0.520810
\(713\) 22.5122 0.843087
\(714\) 22.2846 0.833980
\(715\) −0.652065 −0.0243858
\(716\) 84.3035 3.15057
\(717\) 4.77097 0.178175
\(718\) 32.6545 1.21865
\(719\) 32.7839 1.22263 0.611316 0.791387i \(-0.290640\pi\)
0.611316 + 0.791387i \(0.290640\pi\)
\(720\) −22.8481 −0.851500
\(721\) −12.1042 −0.450784
\(722\) −12.6211 −0.469710
\(723\) 46.2790 1.72113
\(724\) −16.5942 −0.616719
\(725\) −13.3182 −0.494624
\(726\) 75.0364 2.78486
\(727\) 38.7643 1.43769 0.718844 0.695172i \(-0.244672\pi\)
0.718844 + 0.695172i \(0.244672\pi\)
\(728\) −29.8798 −1.10742
\(729\) −41.4410 −1.53485
\(730\) 10.3002 0.381226
\(731\) −7.38692 −0.273215
\(732\) 43.9284 1.62364
\(733\) −31.7198 −1.17160 −0.585799 0.810456i \(-0.699219\pi\)
−0.585799 + 0.810456i \(0.699219\pi\)
\(734\) 12.5318 0.462557
\(735\) 5.35771 0.197622
\(736\) 36.3569 1.34013
\(737\) −1.36035 −0.0501092
\(738\) −110.085 −4.05230
\(739\) 15.4728 0.569177 0.284588 0.958650i \(-0.408143\pi\)
0.284588 + 0.958650i \(0.408143\pi\)
\(740\) −25.5337 −0.938636
\(741\) −28.0990 −1.03224
\(742\) 24.6996 0.906751
\(743\) 31.9261 1.17126 0.585628 0.810580i \(-0.300848\pi\)
0.585628 + 0.810580i \(0.300848\pi\)
\(744\) 203.770 7.47058
\(745\) 3.68698 0.135080
\(746\) 4.37849 0.160308
\(747\) 37.7322 1.38055
\(748\) −6.08010 −0.222311
\(749\) −29.4433 −1.07583
\(750\) −32.9750 −1.20408
\(751\) 10.0729 0.367564 0.183782 0.982967i \(-0.441166\pi\)
0.183782 + 0.982967i \(0.441166\pi\)
\(752\) −29.2220 −1.06561
\(753\) 44.1070 1.60735
\(754\) 16.1532 0.588264
\(755\) −0.377112 −0.0137245
\(756\) −23.6861 −0.861455
\(757\) −54.2042 −1.97009 −0.985043 0.172306i \(-0.944878\pi\)
−0.985043 + 0.172306i \(0.944878\pi\)
\(758\) 3.88069 0.140953
\(759\) 4.05481 0.147180
\(760\) 19.2066 0.696698
\(761\) −17.6664 −0.640406 −0.320203 0.947349i \(-0.603751\pi\)
−0.320203 + 0.947349i \(0.603751\pi\)
\(762\) −88.1970 −3.19504
\(763\) 0.879939 0.0318559
\(764\) 90.9121 3.28908
\(765\) −3.65563 −0.132169
\(766\) −74.2575 −2.68303
\(767\) −14.8718 −0.536991
\(768\) 8.54734 0.308426
\(769\) 26.3359 0.949697 0.474848 0.880068i \(-0.342503\pi\)
0.474848 + 0.880068i \(0.342503\pi\)
\(770\) 1.33117 0.0479720
\(771\) 35.8074 1.28957
\(772\) 58.6719 2.11165
\(773\) −24.2415 −0.871907 −0.435953 0.899969i \(-0.643589\pi\)
−0.435953 + 0.899969i \(0.643589\pi\)
\(774\) 42.1332 1.51445
\(775\) 44.2984 1.59125
\(776\) −72.2953 −2.59525
\(777\) −46.3678 −1.66344
\(778\) 40.7198 1.45988
\(779\) 49.6818 1.78003
\(780\) 14.0318 0.502420
\(781\) −5.25532 −0.188050
\(782\) 12.2339 0.437482
\(783\) 7.78565 0.278236
\(784\) −50.0577 −1.78777
\(785\) −5.65755 −0.201927
\(786\) −25.5478 −0.911258
\(787\) 4.69371 0.167313 0.0836564 0.996495i \(-0.473340\pi\)
0.0836564 + 0.996495i \(0.473340\pi\)
\(788\) 10.1627 0.362030
\(789\) −55.5683 −1.97828
\(790\) −19.4197 −0.690923
\(791\) 14.7114 0.523076
\(792\) 21.0860 0.749258
\(793\) −7.04251 −0.250087
\(794\) 4.00251 0.142044
\(795\) −7.05258 −0.250129
\(796\) 48.0260 1.70223
\(797\) −45.1053 −1.59771 −0.798855 0.601524i \(-0.794561\pi\)
−0.798855 + 0.601524i \(0.794561\pi\)
\(798\) 57.3632 2.03063
\(799\) −4.67541 −0.165404
\(800\) 71.5415 2.52937
\(801\) 6.80861 0.240570
\(802\) −47.1112 −1.66355
\(803\) −5.10333 −0.180093
\(804\) 29.2735 1.03240
\(805\) −1.92422 −0.0678198
\(806\) −53.7281 −1.89249
\(807\) 12.1600 0.428052
\(808\) 75.4548 2.65449
\(809\) −6.74598 −0.237176 −0.118588 0.992944i \(-0.537837\pi\)
−0.118588 + 0.992944i \(0.537837\pi\)
\(810\) −6.02807 −0.211805
\(811\) −11.5613 −0.405971 −0.202986 0.979182i \(-0.565064\pi\)
−0.202986 + 0.979182i \(0.565064\pi\)
\(812\) −23.6902 −0.831363
\(813\) 0.750842 0.0263332
\(814\) 17.6098 0.617223
\(815\) 0.909735 0.0318666
\(816\) 59.4503 2.08118
\(817\) −19.0148 −0.665244
\(818\) −37.9860 −1.32815
\(819\) 14.6392 0.511534
\(820\) −24.8096 −0.866390
\(821\) 18.2734 0.637745 0.318873 0.947798i \(-0.396696\pi\)
0.318873 + 0.947798i \(0.396696\pi\)
\(822\) 68.3095 2.38257
\(823\) 20.7578 0.723572 0.361786 0.932261i \(-0.382167\pi\)
0.361786 + 0.932261i \(0.382167\pi\)
\(824\) −60.1476 −2.09534
\(825\) 7.97887 0.277789
\(826\) 30.3604 1.05637
\(827\) 17.3850 0.604536 0.302268 0.953223i \(-0.402256\pi\)
0.302268 + 0.953223i \(0.402256\pi\)
\(828\) −50.1295 −1.74212
\(829\) 4.50263 0.156383 0.0781914 0.996938i \(-0.475085\pi\)
0.0781914 + 0.996938i \(0.475085\pi\)
\(830\) 11.8368 0.410861
\(831\) −53.8900 −1.86942
\(832\) −35.3821 −1.22665
\(833\) −8.00906 −0.277497
\(834\) 20.9247 0.724565
\(835\) −0.399647 −0.0138304
\(836\) −15.6509 −0.541298
\(837\) −25.8964 −0.895110
\(838\) 67.0601 2.31655
\(839\) 10.6023 0.366033 0.183016 0.983110i \(-0.441414\pi\)
0.183016 + 0.983110i \(0.441414\pi\)
\(840\) −17.4172 −0.600950
\(841\) −21.2130 −0.731483
\(842\) 99.2711 3.42111
\(843\) 8.61161 0.296599
\(844\) −55.4888 −1.91000
\(845\) 3.94910 0.135853
\(846\) 26.6674 0.916846
\(847\) 17.6427 0.606211
\(848\) 65.8931 2.26278
\(849\) 74.1063 2.54332
\(850\) 24.0732 0.825705
\(851\) −25.4551 −0.872591
\(852\) 113.090 3.87439
\(853\) −3.31605 −0.113539 −0.0567697 0.998387i \(-0.518080\pi\)
−0.0567697 + 0.998387i \(0.518080\pi\)
\(854\) 14.3771 0.491973
\(855\) −9.41001 −0.321816
\(856\) −146.308 −5.00071
\(857\) −10.7568 −0.367444 −0.183722 0.982978i \(-0.558815\pi\)
−0.183722 + 0.982978i \(0.558815\pi\)
\(858\) −9.67732 −0.330378
\(859\) −39.5786 −1.35041 −0.675203 0.737632i \(-0.735944\pi\)
−0.675203 + 0.737632i \(0.735944\pi\)
\(860\) 9.49545 0.323792
\(861\) −45.0530 −1.53540
\(862\) −71.2229 −2.42586
\(863\) 35.1070 1.19506 0.597528 0.801848i \(-0.296150\pi\)
0.597528 + 0.801848i \(0.296150\pi\)
\(864\) −41.8224 −1.42283
\(865\) −9.10278 −0.309504
\(866\) 63.2749 2.15017
\(867\) −35.6286 −1.21001
\(868\) 78.7976 2.67456
\(869\) 9.62172 0.326394
\(870\) 9.41582 0.319226
\(871\) −4.69306 −0.159018
\(872\) 4.37256 0.148073
\(873\) 35.4201 1.19879
\(874\) 31.4914 1.06521
\(875\) −7.75315 −0.262104
\(876\) 109.819 3.71043
\(877\) −52.0002 −1.75592 −0.877961 0.478732i \(-0.841096\pi\)
−0.877961 + 0.478732i \(0.841096\pi\)
\(878\) −83.1917 −2.80758
\(879\) 57.6863 1.94571
\(880\) 3.55126 0.119713
\(881\) 12.3669 0.416650 0.208325 0.978060i \(-0.433199\pi\)
0.208325 + 0.978060i \(0.433199\pi\)
\(882\) 45.6818 1.53819
\(883\) −37.4088 −1.25891 −0.629453 0.777039i \(-0.716721\pi\)
−0.629453 + 0.777039i \(0.716721\pi\)
\(884\) −20.9757 −0.705489
\(885\) −8.66891 −0.291402
\(886\) 50.3563 1.69175
\(887\) −37.4655 −1.25797 −0.628984 0.777418i \(-0.716529\pi\)
−0.628984 + 0.777418i \(0.716529\pi\)
\(888\) −230.409 −7.73201
\(889\) −20.7371 −0.695499
\(890\) 2.13590 0.0715955
\(891\) 2.98667 0.100057
\(892\) 88.2568 2.95506
\(893\) −12.0351 −0.402738
\(894\) 54.7186 1.83006
\(895\) −7.87822 −0.263340
\(896\) 22.3498 0.746654
\(897\) 13.9887 0.467068
\(898\) −35.4200 −1.18198
\(899\) −25.9009 −0.863842
\(900\) −98.6425 −3.28808
\(901\) 10.5427 0.351227
\(902\) 17.1105 0.569716
\(903\) 17.2432 0.573819
\(904\) 73.1030 2.43137
\(905\) 1.55074 0.0515484
\(906\) −5.59673 −0.185939
\(907\) 32.8195 1.08976 0.544878 0.838516i \(-0.316576\pi\)
0.544878 + 0.838516i \(0.316576\pi\)
\(908\) 137.108 4.55008
\(909\) −36.9680 −1.22615
\(910\) 4.59239 0.152236
\(911\) −1.29703 −0.0429726 −0.0214863 0.999769i \(-0.506840\pi\)
−0.0214863 + 0.999769i \(0.506840\pi\)
\(912\) 153.032 5.06740
\(913\) −5.86467 −0.194092
\(914\) −100.876 −3.33669
\(915\) −4.10514 −0.135712
\(916\) −102.916 −3.40043
\(917\) −6.00684 −0.198363
\(918\) −14.0730 −0.464477
\(919\) −6.23139 −0.205555 −0.102777 0.994704i \(-0.532773\pi\)
−0.102777 + 0.994704i \(0.532773\pi\)
\(920\) −9.56174 −0.315241
\(921\) 59.2447 1.95218
\(922\) 28.2126 0.929132
\(923\) −18.1303 −0.596766
\(924\) 14.1927 0.466907
\(925\) −50.0895 −1.64693
\(926\) 1.84407 0.0606000
\(927\) 29.4685 0.967872
\(928\) −41.8296 −1.37313
\(929\) 19.6391 0.644337 0.322169 0.946682i \(-0.395588\pi\)
0.322169 + 0.946682i \(0.395588\pi\)
\(930\) −31.3186 −1.02698
\(931\) −20.6163 −0.675671
\(932\) 85.6609 2.80592
\(933\) 15.4328 0.505249
\(934\) −61.1913 −2.00224
\(935\) 0.568190 0.0185818
\(936\) 72.7444 2.37772
\(937\) 9.54113 0.311695 0.155848 0.987781i \(-0.450189\pi\)
0.155848 + 0.987781i \(0.450189\pi\)
\(938\) 9.58074 0.312822
\(939\) 36.7037 1.19778
\(940\) 6.00997 0.196024
\(941\) −7.75937 −0.252948 −0.126474 0.991970i \(-0.540366\pi\)
−0.126474 + 0.991970i \(0.540366\pi\)
\(942\) −83.9640 −2.73569
\(943\) −24.7333 −0.805428
\(944\) 80.9946 2.63615
\(945\) 2.21348 0.0720046
\(946\) −6.54872 −0.212917
\(947\) −26.9880 −0.876991 −0.438496 0.898733i \(-0.644489\pi\)
−0.438496 + 0.898733i \(0.644489\pi\)
\(948\) −207.050 −6.72468
\(949\) −17.6059 −0.571513
\(950\) 61.9673 2.01049
\(951\) −78.6367 −2.54997
\(952\) 26.0364 0.843844
\(953\) 35.8155 1.16018 0.580090 0.814553i \(-0.303017\pi\)
0.580090 + 0.814553i \(0.303017\pi\)
\(954\) −60.1329 −1.94687
\(955\) −8.49580 −0.274918
\(956\) 9.16771 0.296505
\(957\) −4.66517 −0.150804
\(958\) −66.2096 −2.13914
\(959\) 16.0611 0.518639
\(960\) −20.6245 −0.665654
\(961\) 55.1506 1.77905
\(962\) 60.7519 1.95872
\(963\) 71.6816 2.30991
\(964\) 88.9280 2.86418
\(965\) −5.48293 −0.176502
\(966\) −28.5574 −0.918820
\(967\) −6.75120 −0.217104 −0.108552 0.994091i \(-0.534621\pi\)
−0.108552 + 0.994091i \(0.534621\pi\)
\(968\) 87.6694 2.81780
\(969\) 24.4846 0.786559
\(970\) 11.1115 0.356768
\(971\) 9.20648 0.295450 0.147725 0.989028i \(-0.452805\pi\)
0.147725 + 0.989028i \(0.452805\pi\)
\(972\) −106.978 −3.43131
\(973\) 4.91987 0.157724
\(974\) 61.6290 1.97472
\(975\) 27.5263 0.881546
\(976\) 38.3548 1.22771
\(977\) 30.8382 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(978\) 13.5014 0.431728
\(979\) −1.05826 −0.0338220
\(980\) 10.2952 0.328867
\(981\) −2.14227 −0.0683975
\(982\) 109.288 3.48752
\(983\) 55.7554 1.77832 0.889160 0.457596i \(-0.151290\pi\)
0.889160 + 0.457596i \(0.151290\pi\)
\(984\) −223.875 −7.13689
\(985\) −0.949710 −0.0302603
\(986\) −14.0754 −0.448252
\(987\) 10.9138 0.347390
\(988\) −53.9939 −1.71778
\(989\) 9.46624 0.301009
\(990\) −3.24082 −0.103000
\(991\) −50.9029 −1.61698 −0.808492 0.588508i \(-0.799716\pi\)
−0.808492 + 0.588508i \(0.799716\pi\)
\(992\) 139.132 4.41746
\(993\) −48.5187 −1.53970
\(994\) 37.0124 1.17396
\(995\) −4.48806 −0.142281
\(996\) 126.202 3.99887
\(997\) 25.3506 0.802863 0.401431 0.915889i \(-0.368513\pi\)
0.401431 + 0.915889i \(0.368513\pi\)
\(998\) −6.76203 −0.214048
\(999\) 29.2818 0.926434
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.1.2 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.2 259 1.1 even 1 trivial