Properties

Label 6017.2.a.f.1.16
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 1.16
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.27604 q^{2} +3.24984 q^{3} +3.18035 q^{4} -3.77187 q^{5} -7.39676 q^{6} +3.04189 q^{7} -2.68652 q^{8} +7.56146 q^{9} +O(q^{10})\) \(q-2.27604 q^{2} +3.24984 q^{3} +3.18035 q^{4} -3.77187 q^{5} -7.39676 q^{6} +3.04189 q^{7} -2.68652 q^{8} +7.56146 q^{9} +8.58492 q^{10} -1.00000 q^{11} +10.3356 q^{12} +2.98790 q^{13} -6.92346 q^{14} -12.2580 q^{15} -0.246085 q^{16} +3.51504 q^{17} -17.2102 q^{18} +7.12894 q^{19} -11.9959 q^{20} +9.88567 q^{21} +2.27604 q^{22} -5.25842 q^{23} -8.73075 q^{24} +9.22700 q^{25} -6.80058 q^{26} +14.8240 q^{27} +9.67428 q^{28} +7.47443 q^{29} +27.8996 q^{30} +9.02332 q^{31} +5.93313 q^{32} -3.24984 q^{33} -8.00036 q^{34} -11.4736 q^{35} +24.0481 q^{36} +0.681731 q^{37} -16.2257 q^{38} +9.71020 q^{39} +10.1332 q^{40} -0.935542 q^{41} -22.5002 q^{42} -9.56394 q^{43} -3.18035 q^{44} -28.5209 q^{45} +11.9684 q^{46} +4.58453 q^{47} -0.799736 q^{48} +2.25312 q^{49} -21.0010 q^{50} +11.4233 q^{51} +9.50256 q^{52} +7.60591 q^{53} -33.7400 q^{54} +3.77187 q^{55} -8.17209 q^{56} +23.1679 q^{57} -17.0121 q^{58} -9.87880 q^{59} -38.9846 q^{60} -10.0123 q^{61} -20.5374 q^{62} +23.0012 q^{63} -13.0119 q^{64} -11.2700 q^{65} +7.39676 q^{66} -11.2585 q^{67} +11.1790 q^{68} -17.0890 q^{69} +26.1144 q^{70} +2.25394 q^{71} -20.3140 q^{72} +9.49343 q^{73} -1.55164 q^{74} +29.9863 q^{75} +22.6725 q^{76} -3.04189 q^{77} -22.1008 q^{78} -9.21869 q^{79} +0.928200 q^{80} +25.4913 q^{81} +2.12933 q^{82} -0.475185 q^{83} +31.4399 q^{84} -13.2583 q^{85} +21.7679 q^{86} +24.2907 q^{87} +2.68652 q^{88} +3.26265 q^{89} +64.9145 q^{90} +9.08888 q^{91} -16.7236 q^{92} +29.3244 q^{93} -10.4346 q^{94} -26.8894 q^{95} +19.2817 q^{96} +6.72640 q^{97} -5.12818 q^{98} -7.56146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27604 −1.60940 −0.804701 0.593681i \(-0.797674\pi\)
−0.804701 + 0.593681i \(0.797674\pi\)
\(3\) 3.24984 1.87630 0.938148 0.346234i \(-0.112540\pi\)
0.938148 + 0.346234i \(0.112540\pi\)
\(4\) 3.18035 1.59017
\(5\) −3.77187 −1.68683 −0.843416 0.537261i \(-0.819459\pi\)
−0.843416 + 0.537261i \(0.819459\pi\)
\(6\) −7.39676 −3.01971
\(7\) 3.04189 1.14973 0.574864 0.818249i \(-0.305055\pi\)
0.574864 + 0.818249i \(0.305055\pi\)
\(8\) −2.68652 −0.949827
\(9\) 7.56146 2.52049
\(10\) 8.58492 2.71479
\(11\) −1.00000 −0.301511
\(12\) 10.3356 2.98364
\(13\) 2.98790 0.828695 0.414347 0.910119i \(-0.364010\pi\)
0.414347 + 0.910119i \(0.364010\pi\)
\(14\) −6.92346 −1.85037
\(15\) −12.2580 −3.16500
\(16\) −0.246085 −0.0615212
\(17\) 3.51504 0.852522 0.426261 0.904600i \(-0.359831\pi\)
0.426261 + 0.904600i \(0.359831\pi\)
\(18\) −17.2102 −4.05648
\(19\) 7.12894 1.63549 0.817746 0.575580i \(-0.195224\pi\)
0.817746 + 0.575580i \(0.195224\pi\)
\(20\) −11.9959 −2.68236
\(21\) 9.88567 2.15723
\(22\) 2.27604 0.485253
\(23\) −5.25842 −1.09646 −0.548228 0.836329i \(-0.684697\pi\)
−0.548228 + 0.836329i \(0.684697\pi\)
\(24\) −8.73075 −1.78216
\(25\) 9.22700 1.84540
\(26\) −6.80058 −1.33370
\(27\) 14.8240 2.85289
\(28\) 9.67428 1.82827
\(29\) 7.47443 1.38797 0.693984 0.719991i \(-0.255854\pi\)
0.693984 + 0.719991i \(0.255854\pi\)
\(30\) 27.8996 5.09375
\(31\) 9.02332 1.62064 0.810318 0.585990i \(-0.199294\pi\)
0.810318 + 0.585990i \(0.199294\pi\)
\(32\) 5.93313 1.04884
\(33\) −3.24984 −0.565725
\(34\) −8.00036 −1.37205
\(35\) −11.4736 −1.93940
\(36\) 24.0481 4.00801
\(37\) 0.681731 0.112076 0.0560379 0.998429i \(-0.482153\pi\)
0.0560379 + 0.998429i \(0.482153\pi\)
\(38\) −16.2257 −2.63216
\(39\) 9.71020 1.55488
\(40\) 10.1332 1.60220
\(41\) −0.935542 −0.146107 −0.0730536 0.997328i \(-0.523274\pi\)
−0.0730536 + 0.997328i \(0.523274\pi\)
\(42\) −22.5002 −3.47185
\(43\) −9.56394 −1.45849 −0.729243 0.684254i \(-0.760128\pi\)
−0.729243 + 0.684254i \(0.760128\pi\)
\(44\) −3.18035 −0.479455
\(45\) −28.5209 −4.25164
\(46\) 11.9684 1.76464
\(47\) 4.58453 0.668723 0.334362 0.942445i \(-0.391479\pi\)
0.334362 + 0.942445i \(0.391479\pi\)
\(48\) −0.799736 −0.115432
\(49\) 2.25312 0.321874
\(50\) −21.0010 −2.96999
\(51\) 11.4233 1.59958
\(52\) 9.50256 1.31777
\(53\) 7.60591 1.04475 0.522376 0.852715i \(-0.325046\pi\)
0.522376 + 0.852715i \(0.325046\pi\)
\(54\) −33.7400 −4.59144
\(55\) 3.77187 0.508599
\(56\) −8.17209 −1.09204
\(57\) 23.1679 3.06867
\(58\) −17.0121 −2.23380
\(59\) −9.87880 −1.28611 −0.643055 0.765820i \(-0.722333\pi\)
−0.643055 + 0.765820i \(0.722333\pi\)
\(60\) −38.9846 −5.03289
\(61\) −10.0123 −1.28194 −0.640970 0.767566i \(-0.721468\pi\)
−0.640970 + 0.767566i \(0.721468\pi\)
\(62\) −20.5374 −2.60826
\(63\) 23.0012 2.89787
\(64\) −13.0119 −1.62648
\(65\) −11.2700 −1.39787
\(66\) 7.39676 0.910478
\(67\) −11.2585 −1.37545 −0.687723 0.725973i \(-0.741390\pi\)
−0.687723 + 0.725973i \(0.741390\pi\)
\(68\) 11.1790 1.35566
\(69\) −17.0890 −2.05728
\(70\) 26.1144 3.12127
\(71\) 2.25394 0.267493 0.133746 0.991016i \(-0.457299\pi\)
0.133746 + 0.991016i \(0.457299\pi\)
\(72\) −20.3140 −2.39403
\(73\) 9.49343 1.11112 0.555561 0.831476i \(-0.312504\pi\)
0.555561 + 0.831476i \(0.312504\pi\)
\(74\) −1.55164 −0.180375
\(75\) 29.9863 3.46252
\(76\) 22.6725 2.60071
\(77\) −3.04189 −0.346656
\(78\) −22.1008 −2.50242
\(79\) −9.21869 −1.03718 −0.518592 0.855022i \(-0.673544\pi\)
−0.518592 + 0.855022i \(0.673544\pi\)
\(80\) 0.928200 0.103776
\(81\) 25.4913 2.83237
\(82\) 2.12933 0.235145
\(83\) −0.475185 −0.0521584 −0.0260792 0.999660i \(-0.508302\pi\)
−0.0260792 + 0.999660i \(0.508302\pi\)
\(84\) 31.4399 3.43037
\(85\) −13.2583 −1.43806
\(86\) 21.7679 2.34729
\(87\) 24.2907 2.60424
\(88\) 2.68652 0.286383
\(89\) 3.26265 0.345840 0.172920 0.984936i \(-0.444680\pi\)
0.172920 + 0.984936i \(0.444680\pi\)
\(90\) 64.9145 6.84259
\(91\) 9.08888 0.952773
\(92\) −16.7236 −1.74355
\(93\) 29.3244 3.04079
\(94\) −10.4346 −1.07624
\(95\) −26.8894 −2.75880
\(96\) 19.2817 1.96793
\(97\) 6.72640 0.682963 0.341481 0.939889i \(-0.389071\pi\)
0.341481 + 0.939889i \(0.389071\pi\)
\(98\) −5.12818 −0.518024
\(99\) −7.56146 −0.759956
\(100\) 29.3451 2.93451
\(101\) 4.62667 0.460371 0.230185 0.973147i \(-0.426067\pi\)
0.230185 + 0.973147i \(0.426067\pi\)
\(102\) −25.9999 −2.57437
\(103\) 8.26742 0.814613 0.407306 0.913292i \(-0.366468\pi\)
0.407306 + 0.913292i \(0.366468\pi\)
\(104\) −8.02704 −0.787116
\(105\) −37.2875 −3.63888
\(106\) −17.3113 −1.68142
\(107\) −18.8968 −1.82683 −0.913413 0.407034i \(-0.866563\pi\)
−0.913413 + 0.407034i \(0.866563\pi\)
\(108\) 47.1456 4.53658
\(109\) 10.1632 0.973458 0.486729 0.873553i \(-0.338190\pi\)
0.486729 + 0.873553i \(0.338190\pi\)
\(110\) −8.58492 −0.818540
\(111\) 2.21552 0.210287
\(112\) −0.748564 −0.0707326
\(113\) −3.90886 −0.367715 −0.183858 0.982953i \(-0.558859\pi\)
−0.183858 + 0.982953i \(0.558859\pi\)
\(114\) −52.7311 −4.93872
\(115\) 19.8341 1.84954
\(116\) 23.7713 2.20711
\(117\) 22.5929 2.08871
\(118\) 22.4845 2.06987
\(119\) 10.6924 0.980168
\(120\) 32.9312 3.00620
\(121\) 1.00000 0.0909091
\(122\) 22.7883 2.06316
\(123\) −3.04036 −0.274140
\(124\) 28.6973 2.57709
\(125\) −15.9437 −1.42605
\(126\) −52.3515 −4.66384
\(127\) 6.46613 0.573776 0.286888 0.957964i \(-0.407379\pi\)
0.286888 + 0.957964i \(0.407379\pi\)
\(128\) 17.7492 1.56882
\(129\) −31.0813 −2.73655
\(130\) 25.6509 2.24973
\(131\) −14.1995 −1.24061 −0.620306 0.784360i \(-0.712992\pi\)
−0.620306 + 0.784360i \(0.712992\pi\)
\(132\) −10.3356 −0.899600
\(133\) 21.6855 1.88037
\(134\) 25.6248 2.21364
\(135\) −55.9143 −4.81234
\(136\) −9.44320 −0.809748
\(137\) −11.2452 −0.960745 −0.480372 0.877065i \(-0.659499\pi\)
−0.480372 + 0.877065i \(0.659499\pi\)
\(138\) 38.8952 3.31098
\(139\) −4.63778 −0.393371 −0.196685 0.980467i \(-0.563018\pi\)
−0.196685 + 0.980467i \(0.563018\pi\)
\(140\) −36.4901 −3.08398
\(141\) 14.8990 1.25472
\(142\) −5.13004 −0.430504
\(143\) −2.98790 −0.249861
\(144\) −1.86076 −0.155063
\(145\) −28.1926 −2.34127
\(146\) −21.6074 −1.78824
\(147\) 7.32227 0.603931
\(148\) 2.16814 0.178220
\(149\) −20.7381 −1.69893 −0.849466 0.527643i \(-0.823076\pi\)
−0.849466 + 0.527643i \(0.823076\pi\)
\(150\) −68.2499 −5.57258
\(151\) −9.08633 −0.739435 −0.369717 0.929144i \(-0.620545\pi\)
−0.369717 + 0.929144i \(0.620545\pi\)
\(152\) −19.1520 −1.55343
\(153\) 26.5788 2.14877
\(154\) 6.92346 0.557909
\(155\) −34.0348 −2.73374
\(156\) 30.8818 2.47252
\(157\) 15.1617 1.21004 0.605018 0.796212i \(-0.293166\pi\)
0.605018 + 0.796212i \(0.293166\pi\)
\(158\) 20.9821 1.66925
\(159\) 24.7180 1.96026
\(160\) −22.3790 −1.76921
\(161\) −15.9955 −1.26063
\(162\) −58.0192 −4.55842
\(163\) 7.15503 0.560425 0.280213 0.959938i \(-0.409595\pi\)
0.280213 + 0.959938i \(0.409595\pi\)
\(164\) −2.97535 −0.232336
\(165\) 12.2580 0.954282
\(166\) 1.08154 0.0839438
\(167\) −7.40941 −0.573357 −0.286679 0.958027i \(-0.592551\pi\)
−0.286679 + 0.958027i \(0.592551\pi\)
\(168\) −26.5580 −2.04899
\(169\) −4.07245 −0.313265
\(170\) 30.1763 2.31442
\(171\) 53.9052 4.12223
\(172\) −30.4166 −2.31925
\(173\) −15.8450 −1.20468 −0.602338 0.798241i \(-0.705764\pi\)
−0.602338 + 0.798241i \(0.705764\pi\)
\(174\) −55.2866 −4.19127
\(175\) 28.0676 2.12171
\(176\) 0.246085 0.0185493
\(177\) −32.1045 −2.41312
\(178\) −7.42592 −0.556596
\(179\) 8.53816 0.638172 0.319086 0.947726i \(-0.396624\pi\)
0.319086 + 0.947726i \(0.396624\pi\)
\(180\) −90.7062 −6.76084
\(181\) 14.5160 1.07896 0.539482 0.841997i \(-0.318620\pi\)
0.539482 + 0.841997i \(0.318620\pi\)
\(182\) −20.6866 −1.53339
\(183\) −32.5383 −2.40530
\(184\) 14.1268 1.04144
\(185\) −2.57140 −0.189053
\(186\) −66.7434 −4.89386
\(187\) −3.51504 −0.257045
\(188\) 14.5804 1.06339
\(189\) 45.0931 3.28004
\(190\) 61.2014 4.44001
\(191\) 20.9815 1.51817 0.759085 0.650992i \(-0.225647\pi\)
0.759085 + 0.650992i \(0.225647\pi\)
\(192\) −42.2865 −3.05176
\(193\) 20.1039 1.44711 0.723556 0.690266i \(-0.242506\pi\)
0.723556 + 0.690266i \(0.242506\pi\)
\(194\) −15.3095 −1.09916
\(195\) −36.6256 −2.62282
\(196\) 7.16570 0.511835
\(197\) −1.81650 −0.129420 −0.0647100 0.997904i \(-0.520612\pi\)
−0.0647100 + 0.997904i \(0.520612\pi\)
\(198\) 17.2102 1.22307
\(199\) −8.13487 −0.576666 −0.288333 0.957530i \(-0.593101\pi\)
−0.288333 + 0.957530i \(0.593101\pi\)
\(200\) −24.7885 −1.75281
\(201\) −36.5884 −2.58074
\(202\) −10.5305 −0.740921
\(203\) 22.7364 1.59578
\(204\) 36.3301 2.54362
\(205\) 3.52874 0.246458
\(206\) −18.8170 −1.31104
\(207\) −39.7613 −2.76360
\(208\) −0.735277 −0.0509823
\(209\) −7.12894 −0.493119
\(210\) 84.8677 5.85642
\(211\) 15.3362 1.05579 0.527895 0.849309i \(-0.322981\pi\)
0.527895 + 0.849309i \(0.322981\pi\)
\(212\) 24.1894 1.66134
\(213\) 7.32493 0.501896
\(214\) 43.0099 2.94010
\(215\) 36.0739 2.46022
\(216\) −39.8250 −2.70975
\(217\) 27.4480 1.86329
\(218\) −23.1318 −1.56668
\(219\) 30.8521 2.08479
\(220\) 11.9959 0.808760
\(221\) 10.5026 0.706480
\(222\) −5.04260 −0.338437
\(223\) 8.49225 0.568683 0.284341 0.958723i \(-0.408225\pi\)
0.284341 + 0.958723i \(0.408225\pi\)
\(224\) 18.0479 1.20588
\(225\) 69.7696 4.65131
\(226\) 8.89672 0.591801
\(227\) 23.1166 1.53430 0.767152 0.641466i \(-0.221673\pi\)
0.767152 + 0.641466i \(0.221673\pi\)
\(228\) 73.6820 4.87971
\(229\) −11.5117 −0.760712 −0.380356 0.924840i \(-0.624198\pi\)
−0.380356 + 0.924840i \(0.624198\pi\)
\(230\) −45.1431 −2.97665
\(231\) −9.88567 −0.650429
\(232\) −20.0802 −1.31833
\(233\) 19.9675 1.30812 0.654058 0.756445i \(-0.273065\pi\)
0.654058 + 0.756445i \(0.273065\pi\)
\(234\) −51.4223 −3.36158
\(235\) −17.2923 −1.12802
\(236\) −31.4180 −2.04514
\(237\) −29.9593 −1.94606
\(238\) −24.3362 −1.57748
\(239\) 27.2265 1.76113 0.880567 0.473922i \(-0.157162\pi\)
0.880567 + 0.473922i \(0.157162\pi\)
\(240\) 3.01650 0.194714
\(241\) −23.7118 −1.52741 −0.763705 0.645566i \(-0.776622\pi\)
−0.763705 + 0.645566i \(0.776622\pi\)
\(242\) −2.27604 −0.146309
\(243\) 38.3707 2.46148
\(244\) −31.8425 −2.03851
\(245\) −8.49846 −0.542947
\(246\) 6.91998 0.441202
\(247\) 21.3006 1.35532
\(248\) −24.2413 −1.53932
\(249\) −1.54428 −0.0978645
\(250\) 36.2885 2.29508
\(251\) −5.03470 −0.317788 −0.158894 0.987296i \(-0.550793\pi\)
−0.158894 + 0.987296i \(0.550793\pi\)
\(252\) 73.1517 4.60812
\(253\) 5.25842 0.330594
\(254\) −14.7172 −0.923437
\(255\) −43.0873 −2.69823
\(256\) −14.3742 −0.898386
\(257\) −4.97421 −0.310283 −0.155141 0.987892i \(-0.549583\pi\)
−0.155141 + 0.987892i \(0.549583\pi\)
\(258\) 70.7421 4.40421
\(259\) 2.07375 0.128857
\(260\) −35.8424 −2.22285
\(261\) 56.5177 3.49836
\(262\) 32.3185 1.99664
\(263\) −10.5629 −0.651336 −0.325668 0.945484i \(-0.605589\pi\)
−0.325668 + 0.945484i \(0.605589\pi\)
\(264\) 8.73075 0.537340
\(265\) −28.6885 −1.76232
\(266\) −49.3570 −3.02627
\(267\) 10.6031 0.648899
\(268\) −35.8060 −2.18720
\(269\) −11.6840 −0.712385 −0.356193 0.934413i \(-0.615925\pi\)
−0.356193 + 0.934413i \(0.615925\pi\)
\(270\) 127.263 7.74498
\(271\) 1.96384 0.119295 0.0596474 0.998220i \(-0.481002\pi\)
0.0596474 + 0.998220i \(0.481002\pi\)
\(272\) −0.864998 −0.0524482
\(273\) 29.5374 1.78768
\(274\) 25.5946 1.54622
\(275\) −9.22700 −0.556409
\(276\) −54.3490 −3.27143
\(277\) −5.44910 −0.327405 −0.163702 0.986510i \(-0.552344\pi\)
−0.163702 + 0.986510i \(0.552344\pi\)
\(278\) 10.5558 0.633092
\(279\) 68.2295 4.08479
\(280\) 30.8241 1.84209
\(281\) −21.4948 −1.28227 −0.641135 0.767428i \(-0.721536\pi\)
−0.641135 + 0.767428i \(0.721536\pi\)
\(282\) −33.9107 −2.01935
\(283\) −22.5192 −1.33863 −0.669314 0.742979i \(-0.733412\pi\)
−0.669314 + 0.742979i \(0.733412\pi\)
\(284\) 7.16830 0.425360
\(285\) −87.3864 −5.17632
\(286\) 6.80058 0.402126
\(287\) −2.84582 −0.167983
\(288\) 44.8631 2.64359
\(289\) −4.64450 −0.273206
\(290\) 64.1674 3.76804
\(291\) 21.8597 1.28144
\(292\) 30.1924 1.76688
\(293\) −3.91791 −0.228887 −0.114443 0.993430i \(-0.536508\pi\)
−0.114443 + 0.993430i \(0.536508\pi\)
\(294\) −16.6658 −0.971967
\(295\) 37.2615 2.16945
\(296\) −1.83148 −0.106453
\(297\) −14.8240 −0.860177
\(298\) 47.2007 2.73426
\(299\) −15.7116 −0.908627
\(300\) 95.3668 5.50600
\(301\) −29.0925 −1.67686
\(302\) 20.6808 1.19005
\(303\) 15.0359 0.863792
\(304\) −1.75432 −0.100617
\(305\) 37.7650 2.16242
\(306\) −60.4944 −3.45824
\(307\) 23.5018 1.34132 0.670661 0.741764i \(-0.266011\pi\)
0.670661 + 0.741764i \(0.266011\pi\)
\(308\) −9.67428 −0.551243
\(309\) 26.8678 1.52845
\(310\) 77.4645 4.39969
\(311\) 26.0769 1.47869 0.739343 0.673329i \(-0.235136\pi\)
0.739343 + 0.673329i \(0.235136\pi\)
\(312\) −26.0866 −1.47686
\(313\) −6.22687 −0.351963 −0.175982 0.984393i \(-0.556310\pi\)
−0.175982 + 0.984393i \(0.556310\pi\)
\(314\) −34.5086 −1.94743
\(315\) −86.7574 −4.88823
\(316\) −29.3186 −1.64930
\(317\) −10.4612 −0.587561 −0.293780 0.955873i \(-0.594913\pi\)
−0.293780 + 0.955873i \(0.594913\pi\)
\(318\) −56.2590 −3.15485
\(319\) −7.47443 −0.418488
\(320\) 49.0790 2.74360
\(321\) −61.4117 −3.42767
\(322\) 36.4065 2.02885
\(323\) 25.0585 1.39429
\(324\) 81.0713 4.50396
\(325\) 27.5694 1.52927
\(326\) −16.2851 −0.901949
\(327\) 33.0288 1.82650
\(328\) 2.51335 0.138776
\(329\) 13.9457 0.768850
\(330\) −27.8996 −1.53582
\(331\) 28.3672 1.55920 0.779601 0.626277i \(-0.215422\pi\)
0.779601 + 0.626277i \(0.215422\pi\)
\(332\) −1.51125 −0.0829409
\(333\) 5.15488 0.282486
\(334\) 16.8641 0.922762
\(335\) 42.4656 2.32015
\(336\) −2.43271 −0.132715
\(337\) −34.8851 −1.90031 −0.950157 0.311773i \(-0.899077\pi\)
−0.950157 + 0.311773i \(0.899077\pi\)
\(338\) 9.26904 0.504169
\(339\) −12.7032 −0.689942
\(340\) −42.1659 −2.28677
\(341\) −9.02332 −0.488640
\(342\) −122.690 −6.63433
\(343\) −14.4395 −0.779660
\(344\) 25.6937 1.38531
\(345\) 64.4575 3.47028
\(346\) 36.0639 1.93881
\(347\) 22.5867 1.21252 0.606258 0.795268i \(-0.292670\pi\)
0.606258 + 0.795268i \(0.292670\pi\)
\(348\) 77.2529 4.14119
\(349\) 10.3139 0.552092 0.276046 0.961144i \(-0.410976\pi\)
0.276046 + 0.961144i \(0.410976\pi\)
\(350\) −63.8828 −3.41468
\(351\) 44.2927 2.36417
\(352\) −5.93313 −0.316237
\(353\) −1.70135 −0.0905536 −0.0452768 0.998974i \(-0.514417\pi\)
−0.0452768 + 0.998974i \(0.514417\pi\)
\(354\) 73.0711 3.88369
\(355\) −8.50155 −0.451215
\(356\) 10.3764 0.549946
\(357\) 34.7485 1.83909
\(358\) −19.4332 −1.02707
\(359\) 24.4321 1.28948 0.644740 0.764402i \(-0.276966\pi\)
0.644740 + 0.764402i \(0.276966\pi\)
\(360\) 76.6217 4.03832
\(361\) 31.8218 1.67483
\(362\) −33.0389 −1.73649
\(363\) 3.24984 0.170572
\(364\) 28.9058 1.51508
\(365\) −35.8080 −1.87427
\(366\) 74.0584 3.87109
\(367\) −13.1690 −0.687418 −0.343709 0.939076i \(-0.611683\pi\)
−0.343709 + 0.939076i \(0.611683\pi\)
\(368\) 1.29402 0.0674553
\(369\) −7.07407 −0.368261
\(370\) 5.85260 0.304262
\(371\) 23.1364 1.20118
\(372\) 93.2617 4.83539
\(373\) −13.4012 −0.693888 −0.346944 0.937886i \(-0.612781\pi\)
−0.346944 + 0.937886i \(0.612781\pi\)
\(374\) 8.00036 0.413689
\(375\) −51.8145 −2.67569
\(376\) −12.3164 −0.635171
\(377\) 22.3329 1.15020
\(378\) −102.634 −5.27890
\(379\) −15.2800 −0.784879 −0.392440 0.919778i \(-0.628369\pi\)
−0.392440 + 0.919778i \(0.628369\pi\)
\(380\) −85.5177 −4.38697
\(381\) 21.0139 1.07657
\(382\) −47.7547 −2.44334
\(383\) 14.2949 0.730438 0.365219 0.930922i \(-0.380994\pi\)
0.365219 + 0.930922i \(0.380994\pi\)
\(384\) 57.6821 2.94358
\(385\) 11.4736 0.584750
\(386\) −45.7573 −2.32898
\(387\) −72.3174 −3.67610
\(388\) 21.3923 1.08603
\(389\) 16.6277 0.843059 0.421530 0.906815i \(-0.361493\pi\)
0.421530 + 0.906815i \(0.361493\pi\)
\(390\) 83.3613 4.22116
\(391\) −18.4835 −0.934753
\(392\) −6.05303 −0.305724
\(393\) −46.1460 −2.32776
\(394\) 4.13442 0.208289
\(395\) 34.7717 1.74955
\(396\) −24.0481 −1.20846
\(397\) −8.38998 −0.421081 −0.210541 0.977585i \(-0.567522\pi\)
−0.210541 + 0.977585i \(0.567522\pi\)
\(398\) 18.5153 0.928087
\(399\) 70.4743 3.52813
\(400\) −2.27063 −0.113531
\(401\) 16.9050 0.844198 0.422099 0.906550i \(-0.361293\pi\)
0.422099 + 0.906550i \(0.361293\pi\)
\(402\) 83.2765 4.15345
\(403\) 26.9608 1.34301
\(404\) 14.7144 0.732069
\(405\) −96.1500 −4.77773
\(406\) −51.7490 −2.56826
\(407\) −0.681731 −0.0337921
\(408\) −30.6889 −1.51933
\(409\) 18.3070 0.905223 0.452611 0.891708i \(-0.350493\pi\)
0.452611 + 0.891708i \(0.350493\pi\)
\(410\) −8.03155 −0.396650
\(411\) −36.5452 −1.80264
\(412\) 26.2933 1.29538
\(413\) −30.0503 −1.47868
\(414\) 90.4983 4.44775
\(415\) 1.79234 0.0879824
\(416\) 17.7276 0.869167
\(417\) −15.0720 −0.738081
\(418\) 16.2257 0.793627
\(419\) −33.9243 −1.65731 −0.828656 0.559759i \(-0.810894\pi\)
−0.828656 + 0.559759i \(0.810894\pi\)
\(420\) −118.587 −5.78646
\(421\) −8.38174 −0.408501 −0.204251 0.978919i \(-0.565476\pi\)
−0.204251 + 0.978919i \(0.565476\pi\)
\(422\) −34.9059 −1.69919
\(423\) 34.6658 1.68551
\(424\) −20.4334 −0.992333
\(425\) 32.4333 1.57324
\(426\) −16.6718 −0.807752
\(427\) −30.4563 −1.47388
\(428\) −60.0985 −2.90497
\(429\) −9.71020 −0.468813
\(430\) −82.1056 −3.95948
\(431\) 6.50995 0.313573 0.156787 0.987632i \(-0.449886\pi\)
0.156787 + 0.987632i \(0.449886\pi\)
\(432\) −3.64797 −0.175513
\(433\) −25.8359 −1.24159 −0.620796 0.783972i \(-0.713190\pi\)
−0.620796 + 0.783972i \(0.713190\pi\)
\(434\) −62.4727 −2.99878
\(435\) −91.6214 −4.39291
\(436\) 32.3225 1.54797
\(437\) −37.4869 −1.79324
\(438\) −70.2206 −3.35527
\(439\) −3.85518 −0.183998 −0.0919988 0.995759i \(-0.529326\pi\)
−0.0919988 + 0.995759i \(0.529326\pi\)
\(440\) −10.1332 −0.483081
\(441\) 17.0369 0.811279
\(442\) −23.9043 −1.13701
\(443\) 9.37232 0.445292 0.222646 0.974899i \(-0.428531\pi\)
0.222646 + 0.974899i \(0.428531\pi\)
\(444\) 7.04611 0.334394
\(445\) −12.3063 −0.583374
\(446\) −19.3287 −0.915239
\(447\) −67.3955 −3.18770
\(448\) −39.5807 −1.87001
\(449\) −14.1776 −0.669083 −0.334542 0.942381i \(-0.608581\pi\)
−0.334542 + 0.942381i \(0.608581\pi\)
\(450\) −158.798 −7.48582
\(451\) 0.935542 0.0440529
\(452\) −12.4315 −0.584731
\(453\) −29.5291 −1.38740
\(454\) −52.6143 −2.46931
\(455\) −34.2821 −1.60717
\(456\) −62.2410 −2.91470
\(457\) 11.3475 0.530813 0.265407 0.964137i \(-0.414494\pi\)
0.265407 + 0.964137i \(0.414494\pi\)
\(458\) 26.2010 1.22429
\(459\) 52.1070 2.43215
\(460\) 63.0792 2.94108
\(461\) 10.8250 0.504172 0.252086 0.967705i \(-0.418883\pi\)
0.252086 + 0.967705i \(0.418883\pi\)
\(462\) 22.5002 1.04680
\(463\) −33.9987 −1.58005 −0.790027 0.613072i \(-0.789933\pi\)
−0.790027 + 0.613072i \(0.789933\pi\)
\(464\) −1.83934 −0.0853894
\(465\) −110.608 −5.12931
\(466\) −45.4468 −2.10528
\(467\) −1.10202 −0.0509952 −0.0254976 0.999675i \(-0.508117\pi\)
−0.0254976 + 0.999675i \(0.508117\pi\)
\(468\) 71.8533 3.32142
\(469\) −34.2472 −1.58139
\(470\) 39.3579 1.81544
\(471\) 49.2731 2.27039
\(472\) 26.5395 1.22158
\(473\) 9.56394 0.439750
\(474\) 68.1884 3.13200
\(475\) 65.7787 3.01814
\(476\) 34.0055 1.55864
\(477\) 57.5118 2.63328
\(478\) −61.9685 −2.83437
\(479\) 11.3866 0.520266 0.260133 0.965573i \(-0.416234\pi\)
0.260133 + 0.965573i \(0.416234\pi\)
\(480\) −72.7281 −3.31957
\(481\) 2.03694 0.0928766
\(482\) 53.9689 2.45822
\(483\) −51.9830 −2.36531
\(484\) 3.18035 0.144561
\(485\) −25.3711 −1.15204
\(486\) −87.3331 −3.96151
\(487\) 22.1526 1.00383 0.501915 0.864917i \(-0.332629\pi\)
0.501915 + 0.864917i \(0.332629\pi\)
\(488\) 26.8981 1.21762
\(489\) 23.2527 1.05152
\(490\) 19.3428 0.873820
\(491\) −41.6473 −1.87951 −0.939757 0.341842i \(-0.888949\pi\)
−0.939757 + 0.341842i \(0.888949\pi\)
\(492\) −9.66941 −0.435931
\(493\) 26.2729 1.18327
\(494\) −48.4809 −2.18126
\(495\) 28.5209 1.28192
\(496\) −2.22050 −0.0997035
\(497\) 6.85623 0.307544
\(498\) 3.51483 0.157503
\(499\) 12.5987 0.563993 0.281997 0.959415i \(-0.409003\pi\)
0.281997 + 0.959415i \(0.409003\pi\)
\(500\) −50.7065 −2.26766
\(501\) −24.0794 −1.07579
\(502\) 11.4592 0.511448
\(503\) 20.6064 0.918794 0.459397 0.888231i \(-0.348065\pi\)
0.459397 + 0.888231i \(0.348065\pi\)
\(504\) −61.7930 −2.75248
\(505\) −17.4512 −0.776568
\(506\) −11.9684 −0.532058
\(507\) −13.2348 −0.587778
\(508\) 20.5645 0.912404
\(509\) 37.2689 1.65192 0.825958 0.563732i \(-0.190635\pi\)
0.825958 + 0.563732i \(0.190635\pi\)
\(510\) 98.0682 4.34253
\(511\) 28.8780 1.27749
\(512\) −2.78227 −0.122960
\(513\) 105.680 4.66587
\(514\) 11.3215 0.499370
\(515\) −31.1836 −1.37411
\(516\) −98.8492 −4.35160
\(517\) −4.58453 −0.201628
\(518\) −4.71994 −0.207382
\(519\) −51.4938 −2.26033
\(520\) 30.2770 1.32773
\(521\) 28.3204 1.24074 0.620370 0.784310i \(-0.286983\pi\)
0.620370 + 0.784310i \(0.286983\pi\)
\(522\) −128.636 −5.63026
\(523\) −19.9093 −0.870574 −0.435287 0.900292i \(-0.643353\pi\)
−0.435287 + 0.900292i \(0.643353\pi\)
\(524\) −45.1592 −1.97279
\(525\) 91.2151 3.98095
\(526\) 24.0415 1.04826
\(527\) 31.7173 1.38163
\(528\) 0.799736 0.0348041
\(529\) 4.65094 0.202215
\(530\) 65.2961 2.83628
\(531\) −74.6982 −3.24163
\(532\) 68.9674 2.99011
\(533\) −2.79531 −0.121078
\(534\) −24.1330 −1.04434
\(535\) 71.2764 3.08155
\(536\) 30.2462 1.30643
\(537\) 27.7476 1.19740
\(538\) 26.5932 1.14651
\(539\) −2.25312 −0.0970486
\(540\) −177.827 −7.65245
\(541\) −2.13346 −0.0917245 −0.0458623 0.998948i \(-0.514604\pi\)
−0.0458623 + 0.998948i \(0.514604\pi\)
\(542\) −4.46977 −0.191993
\(543\) 47.1746 2.02446
\(544\) 20.8552 0.894158
\(545\) −38.3343 −1.64206
\(546\) −67.2282 −2.87710
\(547\) 1.00000 0.0427569
\(548\) −35.7637 −1.52775
\(549\) −75.7074 −3.23111
\(550\) 21.0010 0.895486
\(551\) 53.2848 2.27001
\(552\) 45.9099 1.95405
\(553\) −28.0423 −1.19248
\(554\) 12.4024 0.526926
\(555\) −8.35664 −0.354719
\(556\) −14.7497 −0.625528
\(557\) −9.12473 −0.386627 −0.193314 0.981137i \(-0.561923\pi\)
−0.193314 + 0.981137i \(0.561923\pi\)
\(558\) −155.293 −6.57408
\(559\) −28.5761 −1.20864
\(560\) 2.82349 0.119314
\(561\) −11.4233 −0.482293
\(562\) 48.9229 2.06369
\(563\) −14.8233 −0.624727 −0.312364 0.949963i \(-0.601121\pi\)
−0.312364 + 0.949963i \(0.601121\pi\)
\(564\) 47.3840 1.99523
\(565\) 14.7437 0.620273
\(566\) 51.2546 2.15439
\(567\) 77.5419 3.25645
\(568\) −6.05523 −0.254072
\(569\) −7.51895 −0.315211 −0.157605 0.987502i \(-0.550377\pi\)
−0.157605 + 0.987502i \(0.550377\pi\)
\(570\) 198.895 8.33078
\(571\) 14.6097 0.611396 0.305698 0.952129i \(-0.401110\pi\)
0.305698 + 0.952129i \(0.401110\pi\)
\(572\) −9.50256 −0.397322
\(573\) 68.1866 2.84854
\(574\) 6.47719 0.270353
\(575\) −48.5194 −2.02340
\(576\) −98.3887 −4.09953
\(577\) −30.3530 −1.26361 −0.631807 0.775126i \(-0.717686\pi\)
−0.631807 + 0.775126i \(0.717686\pi\)
\(578\) 10.5711 0.439698
\(579\) 65.3345 2.71521
\(580\) −89.6622 −3.72302
\(581\) −1.44546 −0.0599679
\(582\) −49.7536 −2.06235
\(583\) −7.60591 −0.315004
\(584\) −25.5042 −1.05537
\(585\) −85.2175 −3.52331
\(586\) 8.91732 0.368371
\(587\) 14.0828 0.581257 0.290629 0.956836i \(-0.406136\pi\)
0.290629 + 0.956836i \(0.406136\pi\)
\(588\) 23.2874 0.960355
\(589\) 64.3267 2.65054
\(590\) −84.8087 −3.49152
\(591\) −5.90333 −0.242830
\(592\) −0.167764 −0.00689504
\(593\) 17.8641 0.733592 0.366796 0.930301i \(-0.380455\pi\)
0.366796 + 0.930301i \(0.380455\pi\)
\(594\) 33.7400 1.38437
\(595\) −40.3302 −1.65338
\(596\) −65.9544 −2.70160
\(597\) −26.4370 −1.08200
\(598\) 35.7603 1.46235
\(599\) 42.0396 1.71769 0.858845 0.512235i \(-0.171182\pi\)
0.858845 + 0.512235i \(0.171182\pi\)
\(600\) −80.5586 −3.28879
\(601\) −14.1540 −0.577355 −0.288677 0.957426i \(-0.593215\pi\)
−0.288677 + 0.957426i \(0.593215\pi\)
\(602\) 66.2156 2.69875
\(603\) −85.1308 −3.46679
\(604\) −28.8977 −1.17583
\(605\) −3.77187 −0.153348
\(606\) −34.2223 −1.39019
\(607\) −37.4173 −1.51872 −0.759361 0.650670i \(-0.774488\pi\)
−0.759361 + 0.650670i \(0.774488\pi\)
\(608\) 42.2969 1.71537
\(609\) 73.8898 2.99417
\(610\) −85.9546 −3.48020
\(611\) 13.6981 0.554167
\(612\) 84.5299 3.41692
\(613\) 39.5547 1.59760 0.798800 0.601597i \(-0.205468\pi\)
0.798800 + 0.601597i \(0.205468\pi\)
\(614\) −53.4911 −2.15872
\(615\) 11.4678 0.462428
\(616\) 8.17209 0.329263
\(617\) 9.17894 0.369530 0.184765 0.982783i \(-0.440848\pi\)
0.184765 + 0.982783i \(0.440848\pi\)
\(618\) −61.1521 −2.45990
\(619\) −7.80282 −0.313622 −0.156811 0.987629i \(-0.550121\pi\)
−0.156811 + 0.987629i \(0.550121\pi\)
\(620\) −108.242 −4.34712
\(621\) −77.9509 −3.12806
\(622\) −59.3521 −2.37980
\(623\) 9.92464 0.397622
\(624\) −2.38953 −0.0956579
\(625\) 14.0026 0.560102
\(626\) 14.1726 0.566450
\(627\) −23.1679 −0.925238
\(628\) 48.2195 1.92417
\(629\) 2.39631 0.0955471
\(630\) 197.463 7.86712
\(631\) 4.78125 0.190339 0.0951694 0.995461i \(-0.469661\pi\)
0.0951694 + 0.995461i \(0.469661\pi\)
\(632\) 24.7662 0.985145
\(633\) 49.8403 1.98098
\(634\) 23.8101 0.945621
\(635\) −24.3894 −0.967864
\(636\) 78.6118 3.11716
\(637\) 6.73209 0.266735
\(638\) 17.0121 0.673515
\(639\) 17.0430 0.674213
\(640\) −66.9477 −2.64634
\(641\) 9.53337 0.376546 0.188273 0.982117i \(-0.439711\pi\)
0.188273 + 0.982117i \(0.439711\pi\)
\(642\) 139.775 5.51649
\(643\) 22.6393 0.892808 0.446404 0.894832i \(-0.352704\pi\)
0.446404 + 0.894832i \(0.352704\pi\)
\(644\) −50.8714 −2.00461
\(645\) 117.235 4.61610
\(646\) −57.0341 −2.24398
\(647\) −0.925536 −0.0363866 −0.0181933 0.999834i \(-0.505791\pi\)
−0.0181933 + 0.999834i \(0.505791\pi\)
\(648\) −68.4829 −2.69026
\(649\) 9.87880 0.387777
\(650\) −62.7489 −2.46122
\(651\) 89.2016 3.49609
\(652\) 22.7555 0.891174
\(653\) 1.98127 0.0775332 0.0387666 0.999248i \(-0.487657\pi\)
0.0387666 + 0.999248i \(0.487657\pi\)
\(654\) −75.1747 −2.93956
\(655\) 53.5585 2.09271
\(656\) 0.230223 0.00898869
\(657\) 71.7842 2.80057
\(658\) −31.7409 −1.23739
\(659\) −29.8531 −1.16291 −0.581456 0.813578i \(-0.697517\pi\)
−0.581456 + 0.813578i \(0.697517\pi\)
\(660\) 38.9846 1.51747
\(661\) −32.7152 −1.27247 −0.636236 0.771494i \(-0.719510\pi\)
−0.636236 + 0.771494i \(0.719510\pi\)
\(662\) −64.5648 −2.50938
\(663\) 34.1317 1.32557
\(664\) 1.27659 0.0495414
\(665\) −81.7948 −3.17187
\(666\) −11.7327 −0.454633
\(667\) −39.3037 −1.52184
\(668\) −23.5645 −0.911738
\(669\) 27.5984 1.06702
\(670\) −96.6534 −3.73405
\(671\) 10.0123 0.386520
\(672\) 58.6529 2.26259
\(673\) 33.4371 1.28890 0.644452 0.764645i \(-0.277085\pi\)
0.644452 + 0.764645i \(0.277085\pi\)
\(674\) 79.3998 3.05837
\(675\) 136.781 5.26472
\(676\) −12.9518 −0.498146
\(677\) 10.3875 0.399223 0.199611 0.979875i \(-0.436032\pi\)
0.199611 + 0.979875i \(0.436032\pi\)
\(678\) 28.9129 1.11039
\(679\) 20.4610 0.785221
\(680\) 35.6185 1.36591
\(681\) 75.1253 2.87881
\(682\) 20.5374 0.786419
\(683\) −40.3605 −1.54435 −0.772176 0.635409i \(-0.780832\pi\)
−0.772176 + 0.635409i \(0.780832\pi\)
\(684\) 171.437 6.55507
\(685\) 42.4155 1.62061
\(686\) 32.8649 1.25479
\(687\) −37.4110 −1.42732
\(688\) 2.35354 0.0897279
\(689\) 22.7257 0.865780
\(690\) −146.708 −5.58507
\(691\) −7.98448 −0.303744 −0.151872 0.988400i \(-0.548530\pi\)
−0.151872 + 0.988400i \(0.548530\pi\)
\(692\) −50.3927 −1.91564
\(693\) −23.0012 −0.873742
\(694\) −51.4081 −1.95143
\(695\) 17.4931 0.663551
\(696\) −65.2574 −2.47358
\(697\) −3.28847 −0.124560
\(698\) −23.4749 −0.888538
\(699\) 64.8912 2.45441
\(700\) 89.2646 3.37388
\(701\) −12.8568 −0.485593 −0.242797 0.970077i \(-0.578065\pi\)
−0.242797 + 0.970077i \(0.578065\pi\)
\(702\) −100.812 −3.80490
\(703\) 4.86002 0.183299
\(704\) 13.0119 0.490403
\(705\) −56.1971 −2.11651
\(706\) 3.87233 0.145737
\(707\) 14.0738 0.529301
\(708\) −102.104 −3.83729
\(709\) 39.9096 1.49883 0.749417 0.662098i \(-0.230334\pi\)
0.749417 + 0.662098i \(0.230334\pi\)
\(710\) 19.3499 0.726187
\(711\) −69.7068 −2.61421
\(712\) −8.76516 −0.328488
\(713\) −47.4484 −1.77696
\(714\) −79.0889 −2.95983
\(715\) 11.2700 0.421473
\(716\) 27.1543 1.01480
\(717\) 88.4817 3.30441
\(718\) −55.6085 −2.07529
\(719\) 7.35621 0.274340 0.137170 0.990548i \(-0.456199\pi\)
0.137170 + 0.990548i \(0.456199\pi\)
\(720\) 7.01855 0.261566
\(721\) 25.1486 0.936583
\(722\) −72.4276 −2.69548
\(723\) −77.0595 −2.86587
\(724\) 46.1659 1.71574
\(725\) 68.9666 2.56136
\(726\) −7.39676 −0.274519
\(727\) 14.9947 0.556124 0.278062 0.960563i \(-0.410308\pi\)
0.278062 + 0.960563i \(0.410308\pi\)
\(728\) −24.4174 −0.904969
\(729\) 48.2246 1.78610
\(730\) 81.5003 3.01646
\(731\) −33.6176 −1.24339
\(732\) −103.483 −3.82484
\(733\) −48.3623 −1.78630 −0.893152 0.449756i \(-0.851511\pi\)
−0.893152 + 0.449756i \(0.851511\pi\)
\(734\) 29.9732 1.10633
\(735\) −27.6187 −1.01873
\(736\) −31.1989 −1.15001
\(737\) 11.2585 0.414712
\(738\) 16.1008 0.592680
\(739\) −15.8412 −0.582727 −0.291363 0.956612i \(-0.594109\pi\)
−0.291363 + 0.956612i \(0.594109\pi\)
\(740\) −8.17794 −0.300627
\(741\) 69.2235 2.54299
\(742\) −52.6592 −1.93318
\(743\) 33.3692 1.22420 0.612098 0.790782i \(-0.290326\pi\)
0.612098 + 0.790782i \(0.290326\pi\)
\(744\) −78.7803 −2.88823
\(745\) 78.2214 2.86581
\(746\) 30.5016 1.11674
\(747\) −3.59310 −0.131465
\(748\) −11.1790 −0.408746
\(749\) −57.4822 −2.10035
\(750\) 117.932 4.30626
\(751\) 45.6382 1.66536 0.832681 0.553753i \(-0.186805\pi\)
0.832681 + 0.553753i \(0.186805\pi\)
\(752\) −1.12818 −0.0411407
\(753\) −16.3620 −0.596264
\(754\) −50.8305 −1.85114
\(755\) 34.2724 1.24730
\(756\) 143.412 5.21584
\(757\) −6.19470 −0.225150 −0.112575 0.993643i \(-0.535910\pi\)
−0.112575 + 0.993643i \(0.535910\pi\)
\(758\) 34.7778 1.26319
\(759\) 17.0890 0.620292
\(760\) 72.2389 2.62038
\(761\) 6.56982 0.238156 0.119078 0.992885i \(-0.462006\pi\)
0.119078 + 0.992885i \(0.462006\pi\)
\(762\) −47.8284 −1.73264
\(763\) 30.9154 1.11921
\(764\) 66.7285 2.41415
\(765\) −100.252 −3.62461
\(766\) −32.5358 −1.17557
\(767\) −29.5169 −1.06579
\(768\) −46.7138 −1.68564
\(769\) 26.8517 0.968297 0.484148 0.874986i \(-0.339130\pi\)
0.484148 + 0.874986i \(0.339130\pi\)
\(770\) −26.1144 −0.941098
\(771\) −16.1654 −0.582183
\(772\) 63.9375 2.30116
\(773\) 52.1783 1.87672 0.938362 0.345653i \(-0.112343\pi\)
0.938362 + 0.345653i \(0.112343\pi\)
\(774\) 164.597 5.91632
\(775\) 83.2582 2.99072
\(776\) −18.0706 −0.648696
\(777\) 6.73936 0.241773
\(778\) −37.8453 −1.35682
\(779\) −6.66942 −0.238957
\(780\) −116.482 −4.17073
\(781\) −2.25394 −0.0806522
\(782\) 42.0692 1.50439
\(783\) 110.801 3.95971
\(784\) −0.554458 −0.0198021
\(785\) −57.1880 −2.04113
\(786\) 105.030 3.74630
\(787\) −1.69894 −0.0605608 −0.0302804 0.999541i \(-0.509640\pi\)
−0.0302804 + 0.999541i \(0.509640\pi\)
\(788\) −5.77709 −0.205800
\(789\) −34.3277 −1.22210
\(790\) −79.1417 −2.81574
\(791\) −11.8904 −0.422772
\(792\) 20.3140 0.721826
\(793\) −29.9157 −1.06234
\(794\) 19.0959 0.677689
\(795\) −93.2330 −3.30663
\(796\) −25.8717 −0.916999
\(797\) −38.4456 −1.36181 −0.680906 0.732371i \(-0.738414\pi\)
−0.680906 + 0.732371i \(0.738414\pi\)
\(798\) −160.402 −5.67818
\(799\) 16.1148 0.570101
\(800\) 54.7450 1.93553
\(801\) 24.6704 0.871686
\(802\) −38.4765 −1.35865
\(803\) −9.49343 −0.335016
\(804\) −116.364 −4.10383
\(805\) 60.3331 2.12646
\(806\) −61.3638 −2.16145
\(807\) −37.9711 −1.33665
\(808\) −12.4296 −0.437272
\(809\) 17.1890 0.604334 0.302167 0.953255i \(-0.402290\pi\)
0.302167 + 0.953255i \(0.402290\pi\)
\(810\) 218.841 7.68929
\(811\) 0.878136 0.0308355 0.0154178 0.999881i \(-0.495092\pi\)
0.0154178 + 0.999881i \(0.495092\pi\)
\(812\) 72.3098 2.53758
\(813\) 6.38216 0.223832
\(814\) 1.55164 0.0543851
\(815\) −26.9878 −0.945343
\(816\) −2.81110 −0.0984083
\(817\) −68.1807 −2.38534
\(818\) −41.6674 −1.45687
\(819\) 68.7252 2.40145
\(820\) 11.2226 0.391911
\(821\) −39.5022 −1.37864 −0.689318 0.724459i \(-0.742090\pi\)
−0.689318 + 0.724459i \(0.742090\pi\)
\(822\) 83.1783 2.90118
\(823\) −35.8622 −1.25008 −0.625039 0.780594i \(-0.714917\pi\)
−0.625039 + 0.780594i \(0.714917\pi\)
\(824\) −22.2105 −0.773741
\(825\) −29.9863 −1.04399
\(826\) 68.3955 2.37978
\(827\) 6.55235 0.227848 0.113924 0.993489i \(-0.463658\pi\)
0.113924 + 0.993489i \(0.463658\pi\)
\(828\) −126.455 −4.39461
\(829\) 9.57063 0.332402 0.166201 0.986092i \(-0.446850\pi\)
0.166201 + 0.986092i \(0.446850\pi\)
\(830\) −4.07943 −0.141599
\(831\) −17.7087 −0.614308
\(832\) −38.8781 −1.34786
\(833\) 7.91979 0.274405
\(834\) 34.3045 1.18787
\(835\) 27.9473 0.967157
\(836\) −22.6725 −0.784145
\(837\) 133.762 4.62349
\(838\) 77.2130 2.66728
\(839\) −28.6415 −0.988816 −0.494408 0.869230i \(-0.664615\pi\)
−0.494408 + 0.869230i \(0.664615\pi\)
\(840\) 100.173 3.45631
\(841\) 26.8672 0.926454
\(842\) 19.0772 0.657443
\(843\) −69.8545 −2.40592
\(844\) 48.7746 1.67889
\(845\) 15.3607 0.528425
\(846\) −78.9006 −2.71266
\(847\) 3.04189 0.104521
\(848\) −1.87170 −0.0642744
\(849\) −73.1839 −2.51166
\(850\) −73.8193 −2.53198
\(851\) −3.58482 −0.122886
\(852\) 23.2958 0.798102
\(853\) −8.82426 −0.302137 −0.151068 0.988523i \(-0.548271\pi\)
−0.151068 + 0.988523i \(0.548271\pi\)
\(854\) 69.3196 2.37207
\(855\) −203.323 −6.95352
\(856\) 50.7666 1.73517
\(857\) −48.1708 −1.64548 −0.822742 0.568415i \(-0.807557\pi\)
−0.822742 + 0.568415i \(0.807557\pi\)
\(858\) 22.1008 0.754508
\(859\) −14.0331 −0.478802 −0.239401 0.970921i \(-0.576951\pi\)
−0.239401 + 0.970921i \(0.576951\pi\)
\(860\) 114.728 3.91218
\(861\) −9.24846 −0.315187
\(862\) −14.8169 −0.504666
\(863\) 42.2100 1.43684 0.718422 0.695607i \(-0.244865\pi\)
0.718422 + 0.695607i \(0.244865\pi\)
\(864\) 87.9529 2.99222
\(865\) 59.7654 2.03208
\(866\) 58.8034 1.99822
\(867\) −15.0939 −0.512616
\(868\) 87.2941 2.96296
\(869\) 9.21869 0.312723
\(870\) 208.534 7.06996
\(871\) −33.6393 −1.13982
\(872\) −27.3036 −0.924616
\(873\) 50.8615 1.72140
\(874\) 85.3217 2.88605
\(875\) −48.4990 −1.63957
\(876\) 98.1205 3.31518
\(877\) 41.0906 1.38753 0.693765 0.720201i \(-0.255951\pi\)
0.693765 + 0.720201i \(0.255951\pi\)
\(878\) 8.77453 0.296126
\(879\) −12.7326 −0.429460
\(880\) −0.928200 −0.0312896
\(881\) −37.7361 −1.27136 −0.635681 0.771952i \(-0.719281\pi\)
−0.635681 + 0.771952i \(0.719281\pi\)
\(882\) −38.7765 −1.30567
\(883\) −23.3877 −0.787060 −0.393530 0.919312i \(-0.628746\pi\)
−0.393530 + 0.919312i \(0.628746\pi\)
\(884\) 33.4019 1.12343
\(885\) 121.094 4.07053
\(886\) −21.3318 −0.716654
\(887\) −34.8749 −1.17098 −0.585492 0.810678i \(-0.699099\pi\)
−0.585492 + 0.810678i \(0.699099\pi\)
\(888\) −5.95202 −0.199737
\(889\) 19.6693 0.659687
\(890\) 28.0096 0.938884
\(891\) −25.4913 −0.853992
\(892\) 27.0083 0.904305
\(893\) 32.6829 1.09369
\(894\) 153.395 5.13029
\(895\) −32.2048 −1.07649
\(896\) 53.9912 1.80372
\(897\) −51.0603 −1.70485
\(898\) 32.2688 1.07682
\(899\) 67.4442 2.24939
\(900\) 221.892 7.39639
\(901\) 26.7350 0.890674
\(902\) −2.12933 −0.0708989
\(903\) −94.5459 −3.14629
\(904\) 10.5012 0.349266
\(905\) −54.7524 −1.82003
\(906\) 67.2094 2.23288
\(907\) −49.5133 −1.64406 −0.822032 0.569441i \(-0.807160\pi\)
−0.822032 + 0.569441i \(0.807160\pi\)
\(908\) 73.5189 2.43981
\(909\) 34.9844 1.16036
\(910\) 78.0273 2.58658
\(911\) 15.3013 0.506956 0.253478 0.967341i \(-0.418425\pi\)
0.253478 + 0.967341i \(0.418425\pi\)
\(912\) −5.70127 −0.188788
\(913\) 0.475185 0.0157263
\(914\) −25.8273 −0.854292
\(915\) 122.730 4.05734
\(916\) −36.6111 −1.20966
\(917\) −43.1933 −1.42637
\(918\) −118.598 −3.91430
\(919\) −0.254958 −0.00841028 −0.00420514 0.999991i \(-0.501339\pi\)
−0.00420514 + 0.999991i \(0.501339\pi\)
\(920\) −53.2845 −1.75674
\(921\) 76.3772 2.51672
\(922\) −24.6382 −0.811416
\(923\) 6.73454 0.221670
\(924\) −31.4399 −1.03430
\(925\) 6.29033 0.206825
\(926\) 77.3823 2.54294
\(927\) 62.5138 2.05322
\(928\) 44.3468 1.45575
\(929\) −60.6273 −1.98912 −0.994559 0.104174i \(-0.966780\pi\)
−0.994559 + 0.104174i \(0.966780\pi\)
\(930\) 251.747 8.25512
\(931\) 16.0623 0.526422
\(932\) 63.5036 2.08013
\(933\) 84.7459 2.77445
\(934\) 2.50823 0.0820718
\(935\) 13.2583 0.433592
\(936\) −60.6962 −1.98392
\(937\) 1.17209 0.0382905 0.0191453 0.999817i \(-0.493905\pi\)
0.0191453 + 0.999817i \(0.493905\pi\)
\(938\) 77.9479 2.54509
\(939\) −20.2363 −0.660387
\(940\) −54.9954 −1.79375
\(941\) −0.992503 −0.0323547 −0.0161773 0.999869i \(-0.505150\pi\)
−0.0161773 + 0.999869i \(0.505150\pi\)
\(942\) −112.148 −3.65396
\(943\) 4.91947 0.160200
\(944\) 2.43102 0.0791231
\(945\) −170.085 −5.53288
\(946\) −21.7679 −0.707735
\(947\) 39.9828 1.29926 0.649632 0.760248i \(-0.274923\pi\)
0.649632 + 0.760248i \(0.274923\pi\)
\(948\) −95.2809 −3.09458
\(949\) 28.3654 0.920781
\(950\) −149.715 −4.85739
\(951\) −33.9973 −1.10244
\(952\) −28.7252 −0.930990
\(953\) −53.2406 −1.72463 −0.862317 0.506369i \(-0.830987\pi\)
−0.862317 + 0.506369i \(0.830987\pi\)
\(954\) −130.899 −4.23801
\(955\) −79.1396 −2.56090
\(956\) 86.5896 2.80051
\(957\) −24.2907 −0.785207
\(958\) −25.9163 −0.837317
\(959\) −34.2068 −1.10460
\(960\) 159.499 5.14781
\(961\) 50.4204 1.62646
\(962\) −4.63616 −0.149476
\(963\) −142.888 −4.60449
\(964\) −75.4117 −2.42885
\(965\) −75.8294 −2.44103
\(966\) 118.315 3.80673
\(967\) 25.2119 0.810758 0.405379 0.914149i \(-0.367139\pi\)
0.405379 + 0.914149i \(0.367139\pi\)
\(968\) −2.68652 −0.0863479
\(969\) 81.4361 2.61611
\(970\) 57.7456 1.85410
\(971\) −10.7166 −0.343913 −0.171956 0.985105i \(-0.555009\pi\)
−0.171956 + 0.985105i \(0.555009\pi\)
\(972\) 122.032 3.91418
\(973\) −14.1076 −0.452270
\(974\) −50.4202 −1.61557
\(975\) 89.5961 2.86937
\(976\) 2.46387 0.0788665
\(977\) 43.9578 1.40633 0.703167 0.711025i \(-0.251769\pi\)
0.703167 + 0.711025i \(0.251769\pi\)
\(978\) −52.9240 −1.69232
\(979\) −3.26265 −0.104275
\(980\) −27.0281 −0.863380
\(981\) 76.8487 2.45359
\(982\) 94.7907 3.02489
\(983\) −6.36589 −0.203040 −0.101520 0.994833i \(-0.532371\pi\)
−0.101520 + 0.994833i \(0.532371\pi\)
\(984\) 8.16798 0.260386
\(985\) 6.85159 0.218310
\(986\) −59.7982 −1.90436
\(987\) 45.3212 1.44259
\(988\) 67.7432 2.15520
\(989\) 50.2912 1.59917
\(990\) −64.9145 −2.06312
\(991\) −19.6080 −0.622869 −0.311435 0.950268i \(-0.600809\pi\)
−0.311435 + 0.950268i \(0.600809\pi\)
\(992\) 53.5365 1.69979
\(993\) 92.1888 2.92552
\(994\) −15.6050 −0.494962
\(995\) 30.6837 0.972738
\(996\) −4.91134 −0.155622
\(997\) −50.9270 −1.61288 −0.806438 0.591319i \(-0.798607\pi\)
−0.806438 + 0.591319i \(0.798607\pi\)
\(998\) −28.6750 −0.907692
\(999\) 10.1060 0.319739
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.1.16 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.16 121 1.1 even 1 trivial