Properties

Label 4034.2.a.d.1.5
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.59634 q^{3} +1.00000 q^{4} -2.79905 q^{5} -2.59634 q^{6} +1.81461 q^{7} +1.00000 q^{8} +3.74100 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.59634 q^{3} +1.00000 q^{4} -2.79905 q^{5} -2.59634 q^{6} +1.81461 q^{7} +1.00000 q^{8} +3.74100 q^{9} -2.79905 q^{10} +3.73633 q^{11} -2.59634 q^{12} -2.30742 q^{13} +1.81461 q^{14} +7.26729 q^{15} +1.00000 q^{16} +5.01126 q^{17} +3.74100 q^{18} +8.09803 q^{19} -2.79905 q^{20} -4.71134 q^{21} +3.73633 q^{22} -7.38910 q^{23} -2.59634 q^{24} +2.83467 q^{25} -2.30742 q^{26} -1.92388 q^{27} +1.81461 q^{28} -6.39213 q^{29} +7.26729 q^{30} -7.51818 q^{31} +1.00000 q^{32} -9.70078 q^{33} +5.01126 q^{34} -5.07917 q^{35} +3.74100 q^{36} +0.201937 q^{37} +8.09803 q^{38} +5.99084 q^{39} -2.79905 q^{40} +4.54257 q^{41} -4.71134 q^{42} +5.72003 q^{43} +3.73633 q^{44} -10.4712 q^{45} -7.38910 q^{46} -6.67146 q^{47} -2.59634 q^{48} -3.70721 q^{49} +2.83467 q^{50} -13.0109 q^{51} -2.30742 q^{52} -8.13695 q^{53} -1.92388 q^{54} -10.4582 q^{55} +1.81461 q^{56} -21.0253 q^{57} -6.39213 q^{58} +12.9865 q^{59} +7.26729 q^{60} +5.99606 q^{61} -7.51818 q^{62} +6.78843 q^{63} +1.00000 q^{64} +6.45857 q^{65} -9.70078 q^{66} -11.1756 q^{67} +5.01126 q^{68} +19.1846 q^{69} -5.07917 q^{70} +10.8218 q^{71} +3.74100 q^{72} +2.14894 q^{73} +0.201937 q^{74} -7.35978 q^{75} +8.09803 q^{76} +6.77995 q^{77} +5.99084 q^{78} +12.4748 q^{79} -2.79905 q^{80} -6.22794 q^{81} +4.54257 q^{82} +8.15019 q^{83} -4.71134 q^{84} -14.0268 q^{85} +5.72003 q^{86} +16.5962 q^{87} +3.73633 q^{88} +1.40180 q^{89} -10.4712 q^{90} -4.18705 q^{91} -7.38910 q^{92} +19.5198 q^{93} -6.67146 q^{94} -22.6668 q^{95} -2.59634 q^{96} -0.714395 q^{97} -3.70721 q^{98} +13.9776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.59634 −1.49900 −0.749500 0.662005i \(-0.769706\pi\)
−0.749500 + 0.662005i \(0.769706\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.79905 −1.25177 −0.625886 0.779914i \(-0.715263\pi\)
−0.625886 + 0.779914i \(0.715263\pi\)
\(6\) −2.59634 −1.05995
\(7\) 1.81461 0.685856 0.342928 0.939362i \(-0.388581\pi\)
0.342928 + 0.939362i \(0.388581\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.74100 1.24700
\(10\) −2.79905 −0.885137
\(11\) 3.73633 1.12654 0.563272 0.826271i \(-0.309542\pi\)
0.563272 + 0.826271i \(0.309542\pi\)
\(12\) −2.59634 −0.749500
\(13\) −2.30742 −0.639962 −0.319981 0.947424i \(-0.603676\pi\)
−0.319981 + 0.947424i \(0.603676\pi\)
\(14\) 1.81461 0.484974
\(15\) 7.26729 1.87641
\(16\) 1.00000 0.250000
\(17\) 5.01126 1.21541 0.607704 0.794163i \(-0.292091\pi\)
0.607704 + 0.794163i \(0.292091\pi\)
\(18\) 3.74100 0.881761
\(19\) 8.09803 1.85781 0.928907 0.370312i \(-0.120749\pi\)
0.928907 + 0.370312i \(0.120749\pi\)
\(20\) −2.79905 −0.625886
\(21\) −4.71134 −1.02810
\(22\) 3.73633 0.796587
\(23\) −7.38910 −1.54073 −0.770367 0.637601i \(-0.779927\pi\)
−0.770367 + 0.637601i \(0.779927\pi\)
\(24\) −2.59634 −0.529976
\(25\) 2.83467 0.566935
\(26\) −2.30742 −0.452521
\(27\) −1.92388 −0.370251
\(28\) 1.81461 0.342928
\(29\) −6.39213 −1.18699 −0.593494 0.804838i \(-0.702252\pi\)
−0.593494 + 0.804838i \(0.702252\pi\)
\(30\) 7.26729 1.32682
\(31\) −7.51818 −1.35030 −0.675152 0.737678i \(-0.735922\pi\)
−0.675152 + 0.737678i \(0.735922\pi\)
\(32\) 1.00000 0.176777
\(33\) −9.70078 −1.68869
\(34\) 5.01126 0.859424
\(35\) −5.07917 −0.858536
\(36\) 3.74100 0.623499
\(37\) 0.201937 0.0331982 0.0165991 0.999862i \(-0.494716\pi\)
0.0165991 + 0.999862i \(0.494716\pi\)
\(38\) 8.09803 1.31367
\(39\) 5.99084 0.959302
\(40\) −2.79905 −0.442568
\(41\) 4.54257 0.709431 0.354715 0.934974i \(-0.384578\pi\)
0.354715 + 0.934974i \(0.384578\pi\)
\(42\) −4.71134 −0.726975
\(43\) 5.72003 0.872297 0.436148 0.899875i \(-0.356342\pi\)
0.436148 + 0.899875i \(0.356342\pi\)
\(44\) 3.73633 0.563272
\(45\) −10.4712 −1.56096
\(46\) −7.38910 −1.08946
\(47\) −6.67146 −0.973132 −0.486566 0.873644i \(-0.661751\pi\)
−0.486566 + 0.873644i \(0.661751\pi\)
\(48\) −2.59634 −0.374750
\(49\) −3.70721 −0.529601
\(50\) 2.83467 0.400883
\(51\) −13.0109 −1.82190
\(52\) −2.30742 −0.319981
\(53\) −8.13695 −1.11770 −0.558848 0.829270i \(-0.688756\pi\)
−0.558848 + 0.829270i \(0.688756\pi\)
\(54\) −1.92388 −0.261807
\(55\) −10.4582 −1.41018
\(56\) 1.81461 0.242487
\(57\) −21.0253 −2.78486
\(58\) −6.39213 −0.839328
\(59\) 12.9865 1.69070 0.845351 0.534211i \(-0.179391\pi\)
0.845351 + 0.534211i \(0.179391\pi\)
\(60\) 7.26729 0.938203
\(61\) 5.99606 0.767717 0.383858 0.923392i \(-0.374595\pi\)
0.383858 + 0.923392i \(0.374595\pi\)
\(62\) −7.51818 −0.954809
\(63\) 6.78843 0.855262
\(64\) 1.00000 0.125000
\(65\) 6.45857 0.801087
\(66\) −9.70078 −1.19408
\(67\) −11.1756 −1.36532 −0.682659 0.730737i \(-0.739177\pi\)
−0.682659 + 0.730737i \(0.739177\pi\)
\(68\) 5.01126 0.607704
\(69\) 19.1846 2.30956
\(70\) −5.07917 −0.607077
\(71\) 10.8218 1.28431 0.642153 0.766576i \(-0.278041\pi\)
0.642153 + 0.766576i \(0.278041\pi\)
\(72\) 3.74100 0.440881
\(73\) 2.14894 0.251514 0.125757 0.992061i \(-0.459864\pi\)
0.125757 + 0.992061i \(0.459864\pi\)
\(74\) 0.201937 0.0234747
\(75\) −7.35978 −0.849835
\(76\) 8.09803 0.928907
\(77\) 6.77995 0.772648
\(78\) 5.99084 0.678329
\(79\) 12.4748 1.40353 0.701765 0.712409i \(-0.252396\pi\)
0.701765 + 0.712409i \(0.252396\pi\)
\(80\) −2.79905 −0.312943
\(81\) −6.22794 −0.691993
\(82\) 4.54257 0.501643
\(83\) 8.15019 0.894599 0.447300 0.894384i \(-0.352386\pi\)
0.447300 + 0.894384i \(0.352386\pi\)
\(84\) −4.71134 −0.514049
\(85\) −14.0268 −1.52142
\(86\) 5.72003 0.616807
\(87\) 16.5962 1.77930
\(88\) 3.73633 0.398294
\(89\) 1.40180 0.148591 0.0742955 0.997236i \(-0.476329\pi\)
0.0742955 + 0.997236i \(0.476329\pi\)
\(90\) −10.4712 −1.10376
\(91\) −4.18705 −0.438922
\(92\) −7.38910 −0.770367
\(93\) 19.5198 2.02411
\(94\) −6.67146 −0.688108
\(95\) −22.6668 −2.32556
\(96\) −2.59634 −0.264988
\(97\) −0.714395 −0.0725358 −0.0362679 0.999342i \(-0.511547\pi\)
−0.0362679 + 0.999342i \(0.511547\pi\)
\(98\) −3.70721 −0.374485
\(99\) 13.9776 1.40480
\(100\) 2.83467 0.283467
\(101\) −5.60599 −0.557817 −0.278908 0.960318i \(-0.589973\pi\)
−0.278908 + 0.960318i \(0.589973\pi\)
\(102\) −13.0109 −1.28828
\(103\) 18.3479 1.80787 0.903936 0.427668i \(-0.140665\pi\)
0.903936 + 0.427668i \(0.140665\pi\)
\(104\) −2.30742 −0.226261
\(105\) 13.1873 1.28694
\(106\) −8.13695 −0.790330
\(107\) −8.61101 −0.832457 −0.416229 0.909260i \(-0.636648\pi\)
−0.416229 + 0.909260i \(0.636648\pi\)
\(108\) −1.92388 −0.185125
\(109\) 16.1371 1.54565 0.772827 0.634617i \(-0.218842\pi\)
0.772827 + 0.634617i \(0.218842\pi\)
\(110\) −10.4582 −0.997146
\(111\) −0.524297 −0.0497640
\(112\) 1.81461 0.171464
\(113\) −3.25029 −0.305762 −0.152881 0.988245i \(-0.548855\pi\)
−0.152881 + 0.988245i \(0.548855\pi\)
\(114\) −21.0253 −1.96920
\(115\) 20.6825 1.92865
\(116\) −6.39213 −0.593494
\(117\) −8.63203 −0.798032
\(118\) 12.9865 1.19551
\(119\) 9.09345 0.833596
\(120\) 7.26729 0.663410
\(121\) 2.96012 0.269102
\(122\) 5.99606 0.542858
\(123\) −11.7941 −1.06344
\(124\) −7.51818 −0.675152
\(125\) 6.06085 0.542099
\(126\) 6.78843 0.604761
\(127\) 3.05914 0.271455 0.135728 0.990746i \(-0.456663\pi\)
0.135728 + 0.990746i \(0.456663\pi\)
\(128\) 1.00000 0.0883883
\(129\) −14.8512 −1.30757
\(130\) 6.45857 0.566454
\(131\) 10.0018 0.873861 0.436931 0.899495i \(-0.356066\pi\)
0.436931 + 0.899495i \(0.356066\pi\)
\(132\) −9.70078 −0.844345
\(133\) 14.6947 1.27419
\(134\) −11.1756 −0.965426
\(135\) 5.38503 0.463470
\(136\) 5.01126 0.429712
\(137\) 8.84414 0.755606 0.377803 0.925886i \(-0.376680\pi\)
0.377803 + 0.925886i \(0.376680\pi\)
\(138\) 19.1846 1.63310
\(139\) 2.97770 0.252566 0.126283 0.991994i \(-0.459695\pi\)
0.126283 + 0.991994i \(0.459695\pi\)
\(140\) −5.07917 −0.429268
\(141\) 17.3214 1.45872
\(142\) 10.8218 0.908142
\(143\) −8.62125 −0.720945
\(144\) 3.74100 0.311750
\(145\) 17.8919 1.48584
\(146\) 2.14894 0.177847
\(147\) 9.62518 0.793872
\(148\) 0.201937 0.0165991
\(149\) −18.6279 −1.52606 −0.763029 0.646365i \(-0.776289\pi\)
−0.763029 + 0.646365i \(0.776289\pi\)
\(150\) −7.35978 −0.600924
\(151\) −9.68586 −0.788224 −0.394112 0.919062i \(-0.628948\pi\)
−0.394112 + 0.919062i \(0.628948\pi\)
\(152\) 8.09803 0.656837
\(153\) 18.7471 1.51561
\(154\) 6.77995 0.546344
\(155\) 21.0437 1.69027
\(156\) 5.99084 0.479651
\(157\) 11.0835 0.884558 0.442279 0.896877i \(-0.354170\pi\)
0.442279 + 0.896877i \(0.354170\pi\)
\(158\) 12.4748 0.992445
\(159\) 21.1263 1.67542
\(160\) −2.79905 −0.221284
\(161\) −13.4083 −1.05672
\(162\) −6.22794 −0.489313
\(163\) 17.7999 1.39420 0.697099 0.716975i \(-0.254474\pi\)
0.697099 + 0.716975i \(0.254474\pi\)
\(164\) 4.54257 0.354715
\(165\) 27.1530 2.11385
\(166\) 8.15019 0.632577
\(167\) −15.4874 −1.19845 −0.599227 0.800579i \(-0.704525\pi\)
−0.599227 + 0.800579i \(0.704525\pi\)
\(168\) −4.71134 −0.363488
\(169\) −7.67584 −0.590449
\(170\) −14.0268 −1.07580
\(171\) 30.2947 2.31669
\(172\) 5.72003 0.436148
\(173\) 11.8491 0.900873 0.450436 0.892809i \(-0.351268\pi\)
0.450436 + 0.892809i \(0.351268\pi\)
\(174\) 16.5962 1.25815
\(175\) 5.14381 0.388836
\(176\) 3.73633 0.281636
\(177\) −33.7175 −2.53436
\(178\) 1.40180 0.105070
\(179\) 18.8961 1.41236 0.706181 0.708031i \(-0.250416\pi\)
0.706181 + 0.708031i \(0.250416\pi\)
\(180\) −10.4712 −0.780479
\(181\) 19.7139 1.46532 0.732661 0.680593i \(-0.238278\pi\)
0.732661 + 0.680593i \(0.238278\pi\)
\(182\) −4.18705 −0.310365
\(183\) −15.5678 −1.15081
\(184\) −7.38910 −0.544732
\(185\) −0.565230 −0.0415566
\(186\) 19.5198 1.43126
\(187\) 18.7237 1.36921
\(188\) −6.67146 −0.486566
\(189\) −3.49108 −0.253939
\(190\) −22.6668 −1.64442
\(191\) 2.81685 0.203820 0.101910 0.994794i \(-0.467505\pi\)
0.101910 + 0.994794i \(0.467505\pi\)
\(192\) −2.59634 −0.187375
\(193\) 2.38607 0.171753 0.0858767 0.996306i \(-0.472631\pi\)
0.0858767 + 0.996306i \(0.472631\pi\)
\(194\) −0.714395 −0.0512906
\(195\) −16.7687 −1.20083
\(196\) −3.70721 −0.264801
\(197\) 2.28133 0.162538 0.0812689 0.996692i \(-0.474103\pi\)
0.0812689 + 0.996692i \(0.474103\pi\)
\(198\) 13.9776 0.993343
\(199\) 5.50846 0.390484 0.195242 0.980755i \(-0.437451\pi\)
0.195242 + 0.980755i \(0.437451\pi\)
\(200\) 2.83467 0.200442
\(201\) 29.0157 2.04661
\(202\) −5.60599 −0.394436
\(203\) −11.5992 −0.814104
\(204\) −13.0109 −0.910948
\(205\) −12.7149 −0.888046
\(206\) 18.3479 1.27836
\(207\) −27.6426 −1.92129
\(208\) −2.30742 −0.159990
\(209\) 30.2569 2.09291
\(210\) 13.1873 0.910008
\(211\) −11.7839 −0.811240 −0.405620 0.914042i \(-0.632944\pi\)
−0.405620 + 0.914042i \(0.632944\pi\)
\(212\) −8.13695 −0.558848
\(213\) −28.0970 −1.92517
\(214\) −8.61101 −0.588636
\(215\) −16.0107 −1.09192
\(216\) −1.92388 −0.130903
\(217\) −13.6425 −0.926115
\(218\) 16.1371 1.09294
\(219\) −5.57937 −0.377019
\(220\) −10.4582 −0.705089
\(221\) −11.5631 −0.777815
\(222\) −0.524297 −0.0351885
\(223\) −25.7948 −1.72735 −0.863673 0.504052i \(-0.831842\pi\)
−0.863673 + 0.504052i \(0.831842\pi\)
\(224\) 1.81461 0.121243
\(225\) 10.6045 0.706967
\(226\) −3.25029 −0.216206
\(227\) −5.89354 −0.391168 −0.195584 0.980687i \(-0.562660\pi\)
−0.195584 + 0.980687i \(0.562660\pi\)
\(228\) −21.0253 −1.39243
\(229\) 9.92639 0.655955 0.327977 0.944686i \(-0.393633\pi\)
0.327977 + 0.944686i \(0.393633\pi\)
\(230\) 20.6825 1.36376
\(231\) −17.6031 −1.15820
\(232\) −6.39213 −0.419664
\(233\) 4.76540 0.312192 0.156096 0.987742i \(-0.450109\pi\)
0.156096 + 0.987742i \(0.450109\pi\)
\(234\) −8.63203 −0.564293
\(235\) 18.6737 1.21814
\(236\) 12.9865 0.845351
\(237\) −32.3890 −2.10389
\(238\) 9.09345 0.589441
\(239\) −20.1082 −1.30069 −0.650347 0.759637i \(-0.725376\pi\)
−0.650347 + 0.759637i \(0.725376\pi\)
\(240\) 7.26729 0.469102
\(241\) 26.0099 1.67545 0.837723 0.546095i \(-0.183886\pi\)
0.837723 + 0.546095i \(0.183886\pi\)
\(242\) 2.96012 0.190284
\(243\) 21.9415 1.40755
\(244\) 5.99606 0.383858
\(245\) 10.3767 0.662940
\(246\) −11.7941 −0.751963
\(247\) −18.6855 −1.18893
\(248\) −7.51818 −0.477405
\(249\) −21.1607 −1.34100
\(250\) 6.06085 0.383322
\(251\) −0.843188 −0.0532216 −0.0266108 0.999646i \(-0.508471\pi\)
−0.0266108 + 0.999646i \(0.508471\pi\)
\(252\) 6.78843 0.427631
\(253\) −27.6081 −1.73571
\(254\) 3.05914 0.191948
\(255\) 36.4183 2.28060
\(256\) 1.00000 0.0625000
\(257\) −6.69460 −0.417598 −0.208799 0.977959i \(-0.566955\pi\)
−0.208799 + 0.977959i \(0.566955\pi\)
\(258\) −14.8512 −0.924593
\(259\) 0.366435 0.0227692
\(260\) 6.45857 0.400543
\(261\) −23.9129 −1.48017
\(262\) 10.0018 0.617913
\(263\) 1.56168 0.0962971 0.0481486 0.998840i \(-0.484668\pi\)
0.0481486 + 0.998840i \(0.484668\pi\)
\(264\) −9.70078 −0.597042
\(265\) 22.7757 1.39910
\(266\) 14.6947 0.900991
\(267\) −3.63956 −0.222738
\(268\) −11.1756 −0.682659
\(269\) 20.3991 1.24376 0.621878 0.783114i \(-0.286370\pi\)
0.621878 + 0.783114i \(0.286370\pi\)
\(270\) 5.38503 0.327723
\(271\) −8.75555 −0.531862 −0.265931 0.963992i \(-0.585679\pi\)
−0.265931 + 0.963992i \(0.585679\pi\)
\(272\) 5.01126 0.303852
\(273\) 10.8710 0.657943
\(274\) 8.84414 0.534294
\(275\) 10.5913 0.638677
\(276\) 19.1846 1.15478
\(277\) −4.81514 −0.289314 −0.144657 0.989482i \(-0.546208\pi\)
−0.144657 + 0.989482i \(0.546208\pi\)
\(278\) 2.97770 0.178591
\(279\) −28.1255 −1.68383
\(280\) −5.07917 −0.303538
\(281\) −9.86698 −0.588614 −0.294307 0.955711i \(-0.595089\pi\)
−0.294307 + 0.955711i \(0.595089\pi\)
\(282\) 17.3214 1.03147
\(283\) 15.5724 0.925683 0.462842 0.886441i \(-0.346830\pi\)
0.462842 + 0.886441i \(0.346830\pi\)
\(284\) 10.8218 0.642153
\(285\) 58.8507 3.48602
\(286\) −8.62125 −0.509785
\(287\) 8.24298 0.486567
\(288\) 3.74100 0.220440
\(289\) 8.11270 0.477218
\(290\) 17.8919 1.05065
\(291\) 1.85481 0.108731
\(292\) 2.14894 0.125757
\(293\) 6.10995 0.356947 0.178474 0.983945i \(-0.442884\pi\)
0.178474 + 0.983945i \(0.442884\pi\)
\(294\) 9.62518 0.561352
\(295\) −36.3499 −2.11638
\(296\) 0.201937 0.0117373
\(297\) −7.18824 −0.417104
\(298\) −18.6279 −1.07909
\(299\) 17.0497 0.986011
\(300\) −7.35978 −0.424917
\(301\) 10.3796 0.598270
\(302\) −9.68586 −0.557358
\(303\) 14.5551 0.836167
\(304\) 8.09803 0.464454
\(305\) −16.7833 −0.961007
\(306\) 18.7471 1.07170
\(307\) 3.61652 0.206406 0.103203 0.994660i \(-0.467091\pi\)
0.103203 + 0.994660i \(0.467091\pi\)
\(308\) 6.77995 0.386324
\(309\) −47.6374 −2.71000
\(310\) 21.0437 1.19520
\(311\) 30.0397 1.70340 0.851698 0.524033i \(-0.175573\pi\)
0.851698 + 0.524033i \(0.175573\pi\)
\(312\) 5.99084 0.339165
\(313\) −4.83636 −0.273367 −0.136684 0.990615i \(-0.543644\pi\)
−0.136684 + 0.990615i \(0.543644\pi\)
\(314\) 11.0835 0.625477
\(315\) −19.0011 −1.07059
\(316\) 12.4748 0.701765
\(317\) 5.25987 0.295424 0.147712 0.989030i \(-0.452809\pi\)
0.147712 + 0.989030i \(0.452809\pi\)
\(318\) 21.1263 1.18470
\(319\) −23.8831 −1.33720
\(320\) −2.79905 −0.156472
\(321\) 22.3571 1.24785
\(322\) −13.4083 −0.747215
\(323\) 40.5813 2.25800
\(324\) −6.22794 −0.345996
\(325\) −6.54077 −0.362817
\(326\) 17.7999 0.985847
\(327\) −41.8975 −2.31693
\(328\) 4.54257 0.250822
\(329\) −12.1061 −0.667429
\(330\) 27.1530 1.49472
\(331\) 7.85381 0.431685 0.215842 0.976428i \(-0.430750\pi\)
0.215842 + 0.976428i \(0.430750\pi\)
\(332\) 8.15019 0.447300
\(333\) 0.755444 0.0413981
\(334\) −15.4874 −0.847435
\(335\) 31.2811 1.70907
\(336\) −4.71134 −0.257025
\(337\) 35.5945 1.93896 0.969478 0.245179i \(-0.0788468\pi\)
0.969478 + 0.245179i \(0.0788468\pi\)
\(338\) −7.67584 −0.417510
\(339\) 8.43888 0.458337
\(340\) −14.0268 −0.760708
\(341\) −28.0904 −1.52118
\(342\) 30.2947 1.63815
\(343\) −19.4294 −1.04909
\(344\) 5.72003 0.308404
\(345\) −53.6987 −2.89104
\(346\) 11.8491 0.637013
\(347\) −3.55494 −0.190839 −0.0954195 0.995437i \(-0.530419\pi\)
−0.0954195 + 0.995437i \(0.530419\pi\)
\(348\) 16.5962 0.889648
\(349\) −14.5467 −0.778669 −0.389334 0.921096i \(-0.627295\pi\)
−0.389334 + 0.921096i \(0.627295\pi\)
\(350\) 5.14381 0.274948
\(351\) 4.43919 0.236946
\(352\) 3.73633 0.199147
\(353\) 15.8453 0.843360 0.421680 0.906745i \(-0.361441\pi\)
0.421680 + 0.906745i \(0.361441\pi\)
\(354\) −33.7175 −1.79206
\(355\) −30.2906 −1.60766
\(356\) 1.40180 0.0742955
\(357\) −23.6097 −1.24956
\(358\) 18.8961 0.998691
\(359\) −10.6745 −0.563380 −0.281690 0.959505i \(-0.590895\pi\)
−0.281690 + 0.959505i \(0.590895\pi\)
\(360\) −10.4712 −0.551882
\(361\) 46.5780 2.45148
\(362\) 19.7139 1.03614
\(363\) −7.68550 −0.403384
\(364\) −4.18705 −0.219461
\(365\) −6.01498 −0.314838
\(366\) −15.5678 −0.813743
\(367\) 18.2218 0.951169 0.475584 0.879670i \(-0.342237\pi\)
0.475584 + 0.879670i \(0.342237\pi\)
\(368\) −7.38910 −0.385183
\(369\) 16.9937 0.884659
\(370\) −0.565230 −0.0293849
\(371\) −14.7653 −0.766578
\(372\) 19.5198 1.01205
\(373\) 10.5185 0.544625 0.272312 0.962209i \(-0.412212\pi\)
0.272312 + 0.962209i \(0.412212\pi\)
\(374\) 18.7237 0.968179
\(375\) −15.7361 −0.812606
\(376\) −6.67146 −0.344054
\(377\) 14.7493 0.759627
\(378\) −3.49108 −0.179562
\(379\) 21.7891 1.11923 0.559614 0.828753i \(-0.310949\pi\)
0.559614 + 0.828753i \(0.310949\pi\)
\(380\) −22.6668 −1.16278
\(381\) −7.94258 −0.406911
\(382\) 2.81685 0.144123
\(383\) −20.7204 −1.05876 −0.529381 0.848384i \(-0.677576\pi\)
−0.529381 + 0.848384i \(0.677576\pi\)
\(384\) −2.59634 −0.132494
\(385\) −18.9774 −0.967179
\(386\) 2.38607 0.121448
\(387\) 21.3986 1.08775
\(388\) −0.714395 −0.0362679
\(389\) 11.3569 0.575816 0.287908 0.957658i \(-0.407040\pi\)
0.287908 + 0.957658i \(0.407040\pi\)
\(390\) −16.7687 −0.849114
\(391\) −37.0287 −1.87262
\(392\) −3.70721 −0.187242
\(393\) −25.9681 −1.30992
\(394\) 2.28133 0.114932
\(395\) −34.9177 −1.75690
\(396\) 13.9776 0.702400
\(397\) −11.6878 −0.586593 −0.293296 0.956022i \(-0.594752\pi\)
−0.293296 + 0.956022i \(0.594752\pi\)
\(398\) 5.50846 0.276114
\(399\) −38.1525 −1.91002
\(400\) 2.83467 0.141734
\(401\) 30.2649 1.51135 0.755677 0.654944i \(-0.227308\pi\)
0.755677 + 0.654944i \(0.227308\pi\)
\(402\) 29.0157 1.44717
\(403\) 17.3476 0.864143
\(404\) −5.60599 −0.278908
\(405\) 17.4323 0.866218
\(406\) −11.5992 −0.575658
\(407\) 0.754501 0.0373992
\(408\) −13.0109 −0.644138
\(409\) −19.3460 −0.956597 −0.478299 0.878197i \(-0.658746\pi\)
−0.478299 + 0.878197i \(0.658746\pi\)
\(410\) −12.7149 −0.627943
\(411\) −22.9624 −1.13265
\(412\) 18.3479 0.903936
\(413\) 23.5654 1.15958
\(414\) −27.6426 −1.35856
\(415\) −22.8128 −1.11983
\(416\) −2.30742 −0.113130
\(417\) −7.73114 −0.378596
\(418\) 30.2569 1.47991
\(419\) −0.160620 −0.00784679 −0.00392339 0.999992i \(-0.501249\pi\)
−0.00392339 + 0.999992i \(0.501249\pi\)
\(420\) 13.1873 0.643472
\(421\) 23.3447 1.13775 0.568876 0.822423i \(-0.307378\pi\)
0.568876 + 0.822423i \(0.307378\pi\)
\(422\) −11.7839 −0.573633
\(423\) −24.9579 −1.21349
\(424\) −8.13695 −0.395165
\(425\) 14.2053 0.689057
\(426\) −28.0970 −1.36130
\(427\) 10.8805 0.526543
\(428\) −8.61101 −0.416229
\(429\) 22.3837 1.08070
\(430\) −16.0107 −0.772102
\(431\) −18.3971 −0.886157 −0.443079 0.896483i \(-0.646114\pi\)
−0.443079 + 0.896483i \(0.646114\pi\)
\(432\) −1.92388 −0.0925627
\(433\) 35.9253 1.72646 0.863229 0.504813i \(-0.168438\pi\)
0.863229 + 0.504813i \(0.168438\pi\)
\(434\) −13.6425 −0.654862
\(435\) −46.4535 −2.22727
\(436\) 16.1371 0.772827
\(437\) −59.8371 −2.86240
\(438\) −5.57937 −0.266593
\(439\) 6.02526 0.287570 0.143785 0.989609i \(-0.454073\pi\)
0.143785 + 0.989609i \(0.454073\pi\)
\(440\) −10.4582 −0.498573
\(441\) −13.8687 −0.660412
\(442\) −11.5631 −0.549998
\(443\) −25.0509 −1.19020 −0.595101 0.803651i \(-0.702888\pi\)
−0.595101 + 0.803651i \(0.702888\pi\)
\(444\) −0.524297 −0.0248820
\(445\) −3.92372 −0.186002
\(446\) −25.7948 −1.22142
\(447\) 48.3644 2.28756
\(448\) 1.81461 0.0857320
\(449\) 17.5393 0.827731 0.413866 0.910338i \(-0.364178\pi\)
0.413866 + 0.910338i \(0.364178\pi\)
\(450\) 10.6045 0.499901
\(451\) 16.9725 0.799205
\(452\) −3.25029 −0.152881
\(453\) 25.1478 1.18155
\(454\) −5.89354 −0.276598
\(455\) 11.7197 0.549430
\(456\) −21.0253 −0.984598
\(457\) 7.55158 0.353248 0.176624 0.984278i \(-0.443482\pi\)
0.176624 + 0.984278i \(0.443482\pi\)
\(458\) 9.92639 0.463830
\(459\) −9.64106 −0.450006
\(460\) 20.6825 0.964324
\(461\) 23.5472 1.09670 0.548351 0.836248i \(-0.315256\pi\)
0.548351 + 0.836248i \(0.315256\pi\)
\(462\) −17.6031 −0.818970
\(463\) 22.0830 1.02628 0.513142 0.858303i \(-0.328481\pi\)
0.513142 + 0.858303i \(0.328481\pi\)
\(464\) −6.39213 −0.296747
\(465\) −54.6368 −2.53372
\(466\) 4.76540 0.220753
\(467\) −17.9243 −0.829437 −0.414719 0.909950i \(-0.636120\pi\)
−0.414719 + 0.909950i \(0.636120\pi\)
\(468\) −8.63203 −0.399016
\(469\) −20.2793 −0.936412
\(470\) 18.6737 0.861355
\(471\) −28.7765 −1.32595
\(472\) 12.9865 0.597754
\(473\) 21.3719 0.982681
\(474\) −32.3890 −1.48767
\(475\) 22.9553 1.05326
\(476\) 9.09345 0.416798
\(477\) −30.4403 −1.39376
\(478\) −20.1082 −0.919730
\(479\) 1.78123 0.0813865 0.0406933 0.999172i \(-0.487043\pi\)
0.0406933 + 0.999172i \(0.487043\pi\)
\(480\) 7.26729 0.331705
\(481\) −0.465952 −0.0212456
\(482\) 26.0099 1.18472
\(483\) 34.8125 1.58403
\(484\) 2.96012 0.134551
\(485\) 1.99963 0.0907984
\(486\) 21.9415 0.995287
\(487\) −7.91140 −0.358500 −0.179250 0.983804i \(-0.557367\pi\)
−0.179250 + 0.983804i \(0.557367\pi\)
\(488\) 5.99606 0.271429
\(489\) −46.2147 −2.08990
\(490\) 10.3767 0.468770
\(491\) −16.6083 −0.749520 −0.374760 0.927122i \(-0.622275\pi\)
−0.374760 + 0.927122i \(0.622275\pi\)
\(492\) −11.7941 −0.531718
\(493\) −32.0326 −1.44268
\(494\) −18.6855 −0.840701
\(495\) −39.1239 −1.75849
\(496\) −7.51818 −0.337576
\(497\) 19.6372 0.880850
\(498\) −21.1607 −0.948233
\(499\) −15.9285 −0.713056 −0.356528 0.934285i \(-0.616040\pi\)
−0.356528 + 0.934285i \(0.616040\pi\)
\(500\) 6.06085 0.271050
\(501\) 40.2107 1.79648
\(502\) −0.843188 −0.0376333
\(503\) 10.2612 0.457522 0.228761 0.973483i \(-0.426533\pi\)
0.228761 + 0.973483i \(0.426533\pi\)
\(504\) 6.78843 0.302381
\(505\) 15.6914 0.698260
\(506\) −27.6081 −1.22733
\(507\) 19.9291 0.885082
\(508\) 3.05914 0.135728
\(509\) 2.45716 0.108912 0.0544559 0.998516i \(-0.482658\pi\)
0.0544559 + 0.998516i \(0.482658\pi\)
\(510\) 36.4183 1.61263
\(511\) 3.89947 0.172502
\(512\) 1.00000 0.0441942
\(513\) −15.5796 −0.687858
\(514\) −6.69460 −0.295286
\(515\) −51.3567 −2.26304
\(516\) −14.8512 −0.653786
\(517\) −24.9267 −1.09628
\(518\) 0.366435 0.0161002
\(519\) −30.7644 −1.35041
\(520\) 6.45857 0.283227
\(521\) −3.29420 −0.144322 −0.0721608 0.997393i \(-0.522989\pi\)
−0.0721608 + 0.997393i \(0.522989\pi\)
\(522\) −23.9129 −1.04664
\(523\) −3.01703 −0.131926 −0.0659628 0.997822i \(-0.521012\pi\)
−0.0659628 + 0.997822i \(0.521012\pi\)
\(524\) 10.0018 0.436931
\(525\) −13.3551 −0.582864
\(526\) 1.56168 0.0680924
\(527\) −37.6755 −1.64117
\(528\) −9.70078 −0.422172
\(529\) 31.5988 1.37386
\(530\) 22.7757 0.989313
\(531\) 48.5826 2.10830
\(532\) 14.6947 0.637097
\(533\) −10.4816 −0.454008
\(534\) −3.63956 −0.157499
\(535\) 24.1026 1.04205
\(536\) −11.1756 −0.482713
\(537\) −49.0608 −2.11713
\(538\) 20.3991 0.879469
\(539\) −13.8513 −0.596619
\(540\) 5.38503 0.231735
\(541\) 31.2687 1.34434 0.672172 0.740395i \(-0.265361\pi\)
0.672172 + 0.740395i \(0.265361\pi\)
\(542\) −8.75555 −0.376083
\(543\) −51.1841 −2.19652
\(544\) 5.01126 0.214856
\(545\) −45.1685 −1.93481
\(546\) 10.8710 0.465236
\(547\) 13.6270 0.582650 0.291325 0.956624i \(-0.405904\pi\)
0.291325 + 0.956624i \(0.405904\pi\)
\(548\) 8.84414 0.377803
\(549\) 22.4312 0.957342
\(550\) 10.5913 0.451613
\(551\) −51.7636 −2.20521
\(552\) 19.1846 0.816552
\(553\) 22.6369 0.962620
\(554\) −4.81514 −0.204576
\(555\) 1.46753 0.0622933
\(556\) 2.97770 0.126283
\(557\) 22.0573 0.934599 0.467299 0.884099i \(-0.345227\pi\)
0.467299 + 0.884099i \(0.345227\pi\)
\(558\) −28.1255 −1.19065
\(559\) −13.1985 −0.558237
\(560\) −5.07917 −0.214634
\(561\) −48.6131 −2.05245
\(562\) −9.86698 −0.416213
\(563\) 10.3023 0.434191 0.217095 0.976150i \(-0.430342\pi\)
0.217095 + 0.976150i \(0.430342\pi\)
\(564\) 17.3214 0.729362
\(565\) 9.09773 0.382744
\(566\) 15.5724 0.654557
\(567\) −11.3012 −0.474608
\(568\) 10.8218 0.454071
\(569\) 32.0750 1.34465 0.672326 0.740255i \(-0.265295\pi\)
0.672326 + 0.740255i \(0.265295\pi\)
\(570\) 58.8507 2.46499
\(571\) −33.4574 −1.40015 −0.700075 0.714070i \(-0.746850\pi\)
−0.700075 + 0.714070i \(0.746850\pi\)
\(572\) −8.62125 −0.360473
\(573\) −7.31350 −0.305526
\(574\) 8.24298 0.344055
\(575\) −20.9457 −0.873495
\(576\) 3.74100 0.155875
\(577\) −28.4013 −1.18236 −0.591182 0.806538i \(-0.701338\pi\)
−0.591182 + 0.806538i \(0.701338\pi\)
\(578\) 8.11270 0.337444
\(579\) −6.19507 −0.257458
\(580\) 17.8919 0.742920
\(581\) 14.7894 0.613567
\(582\) 1.85481 0.0768845
\(583\) −30.4023 −1.25913
\(584\) 2.14894 0.0889236
\(585\) 24.1615 0.998954
\(586\) 6.10995 0.252400
\(587\) −17.2172 −0.710628 −0.355314 0.934747i \(-0.615626\pi\)
−0.355314 + 0.934747i \(0.615626\pi\)
\(588\) 9.62518 0.396936
\(589\) −60.8824 −2.50862
\(590\) −36.3499 −1.49650
\(591\) −5.92310 −0.243644
\(592\) 0.201937 0.00829955
\(593\) −17.8587 −0.733370 −0.366685 0.930345i \(-0.619507\pi\)
−0.366685 + 0.930345i \(0.619507\pi\)
\(594\) −7.18824 −0.294937
\(595\) −25.4530 −1.04347
\(596\) −18.6279 −0.763029
\(597\) −14.3018 −0.585335
\(598\) 17.0497 0.697215
\(599\) −18.4898 −0.755471 −0.377736 0.925913i \(-0.623297\pi\)
−0.377736 + 0.925913i \(0.623297\pi\)
\(600\) −7.35978 −0.300462
\(601\) −42.8072 −1.74614 −0.873071 0.487593i \(-0.837875\pi\)
−0.873071 + 0.487593i \(0.837875\pi\)
\(602\) 10.3796 0.423041
\(603\) −41.8079 −1.70255
\(604\) −9.68586 −0.394112
\(605\) −8.28553 −0.336855
\(606\) 14.5551 0.591259
\(607\) −1.14822 −0.0466050 −0.0233025 0.999728i \(-0.507418\pi\)
−0.0233025 + 0.999728i \(0.507418\pi\)
\(608\) 8.09803 0.328418
\(609\) 30.1155 1.22034
\(610\) −16.7833 −0.679534
\(611\) 15.3938 0.622767
\(612\) 18.7471 0.757806
\(613\) 2.43867 0.0984968 0.0492484 0.998787i \(-0.484317\pi\)
0.0492484 + 0.998787i \(0.484317\pi\)
\(614\) 3.61652 0.145951
\(615\) 33.0122 1.33118
\(616\) 6.77995 0.273172
\(617\) −46.9897 −1.89173 −0.945867 0.324555i \(-0.894785\pi\)
−0.945867 + 0.324555i \(0.894785\pi\)
\(618\) −47.6374 −1.91626
\(619\) 41.2650 1.65858 0.829291 0.558817i \(-0.188745\pi\)
0.829291 + 0.558817i \(0.188745\pi\)
\(620\) 21.0437 0.845137
\(621\) 14.2157 0.570458
\(622\) 30.0397 1.20448
\(623\) 2.54372 0.101912
\(624\) 5.99084 0.239826
\(625\) −31.1380 −1.24552
\(626\) −4.83636 −0.193300
\(627\) −78.5572 −3.13727
\(628\) 11.0835 0.442279
\(629\) 1.01196 0.0403494
\(630\) −19.0011 −0.757024
\(631\) −34.1921 −1.36116 −0.680582 0.732671i \(-0.738273\pi\)
−0.680582 + 0.732671i \(0.738273\pi\)
\(632\) 12.4748 0.496223
\(633\) 30.5952 1.21605
\(634\) 5.25987 0.208896
\(635\) −8.56269 −0.339800
\(636\) 21.1263 0.837712
\(637\) 8.55407 0.338925
\(638\) −23.8831 −0.945540
\(639\) 40.4842 1.60153
\(640\) −2.79905 −0.110642
\(641\) −48.9695 −1.93418 −0.967090 0.254436i \(-0.918110\pi\)
−0.967090 + 0.254436i \(0.918110\pi\)
\(642\) 22.3571 0.882365
\(643\) 6.23411 0.245849 0.122925 0.992416i \(-0.460773\pi\)
0.122925 + 0.992416i \(0.460773\pi\)
\(644\) −13.4083 −0.528361
\(645\) 41.5691 1.63678
\(646\) 40.5813 1.59665
\(647\) −41.3964 −1.62746 −0.813731 0.581242i \(-0.802567\pi\)
−0.813731 + 0.581242i \(0.802567\pi\)
\(648\) −6.22794 −0.244656
\(649\) 48.5219 1.90465
\(650\) −6.54077 −0.256550
\(651\) 35.4207 1.38825
\(652\) 17.7999 0.697099
\(653\) 41.3329 1.61748 0.808741 0.588166i \(-0.200150\pi\)
0.808741 + 0.588166i \(0.200150\pi\)
\(654\) −41.8975 −1.63832
\(655\) −27.9955 −1.09388
\(656\) 4.54257 0.177358
\(657\) 8.03916 0.313637
\(658\) −12.1061 −0.471943
\(659\) −17.8082 −0.693707 −0.346854 0.937919i \(-0.612750\pi\)
−0.346854 + 0.937919i \(0.612750\pi\)
\(660\) 27.1530 1.05693
\(661\) 36.8165 1.43200 0.715999 0.698101i \(-0.245972\pi\)
0.715999 + 0.698101i \(0.245972\pi\)
\(662\) 7.85381 0.305247
\(663\) 30.0216 1.16594
\(664\) 8.15019 0.316289
\(665\) −41.1312 −1.59500
\(666\) 0.755444 0.0292729
\(667\) 47.2321 1.82883
\(668\) −15.4874 −0.599227
\(669\) 66.9721 2.58929
\(670\) 31.2811 1.20849
\(671\) 22.4032 0.864867
\(672\) −4.71134 −0.181744
\(673\) 25.2726 0.974188 0.487094 0.873350i \(-0.338057\pi\)
0.487094 + 0.873350i \(0.338057\pi\)
\(674\) 35.5945 1.37105
\(675\) −5.45357 −0.209908
\(676\) −7.67584 −0.295224
\(677\) −28.0981 −1.07990 −0.539949 0.841698i \(-0.681556\pi\)
−0.539949 + 0.841698i \(0.681556\pi\)
\(678\) 8.43888 0.324093
\(679\) −1.29634 −0.0497491
\(680\) −14.0268 −0.537901
\(681\) 15.3016 0.586360
\(682\) −28.0904 −1.07564
\(683\) 17.1968 0.658017 0.329008 0.944327i \(-0.393286\pi\)
0.329008 + 0.944327i \(0.393286\pi\)
\(684\) 30.2947 1.15835
\(685\) −24.7552 −0.945846
\(686\) −19.4294 −0.741816
\(687\) −25.7723 −0.983275
\(688\) 5.72003 0.218074
\(689\) 18.7753 0.715282
\(690\) −53.6987 −2.04428
\(691\) −8.36409 −0.318185 −0.159092 0.987264i \(-0.550857\pi\)
−0.159092 + 0.987264i \(0.550857\pi\)
\(692\) 11.8491 0.450436
\(693\) 25.3638 0.963490
\(694\) −3.55494 −0.134944
\(695\) −8.33474 −0.316155
\(696\) 16.5962 0.629076
\(697\) 22.7640 0.862248
\(698\) −14.5467 −0.550602
\(699\) −12.3726 −0.467976
\(700\) 5.14381 0.194418
\(701\) −37.4475 −1.41437 −0.707187 0.707027i \(-0.750036\pi\)
−0.707187 + 0.707027i \(0.750036\pi\)
\(702\) 4.43919 0.167546
\(703\) 1.63529 0.0616761
\(704\) 3.73633 0.140818
\(705\) −48.4834 −1.82599
\(706\) 15.8453 0.596345
\(707\) −10.1727 −0.382582
\(708\) −33.7175 −1.26718
\(709\) 40.2774 1.51265 0.756324 0.654197i \(-0.226993\pi\)
0.756324 + 0.654197i \(0.226993\pi\)
\(710\) −30.2906 −1.13679
\(711\) 46.6683 1.75020
\(712\) 1.40180 0.0525348
\(713\) 55.5526 2.08046
\(714\) −23.6097 −0.883572
\(715\) 24.1313 0.902460
\(716\) 18.8961 0.706181
\(717\) 52.2079 1.94974
\(718\) −10.6745 −0.398370
\(719\) −12.2314 −0.456155 −0.228077 0.973643i \(-0.573244\pi\)
−0.228077 + 0.973643i \(0.573244\pi\)
\(720\) −10.4712 −0.390240
\(721\) 33.2942 1.23994
\(722\) 46.5780 1.73346
\(723\) −67.5307 −2.51149
\(724\) 19.7139 0.732661
\(725\) −18.1196 −0.672945
\(726\) −7.68550 −0.285236
\(727\) 19.4032 0.719624 0.359812 0.933025i \(-0.382841\pi\)
0.359812 + 0.933025i \(0.382841\pi\)
\(728\) −4.18705 −0.155182
\(729\) −38.2838 −1.41792
\(730\) −6.01498 −0.222624
\(731\) 28.6646 1.06020
\(732\) −15.5678 −0.575403
\(733\) −3.14593 −0.116198 −0.0580988 0.998311i \(-0.518504\pi\)
−0.0580988 + 0.998311i \(0.518504\pi\)
\(734\) 18.2218 0.672578
\(735\) −26.9414 −0.993747
\(736\) −7.38910 −0.272366
\(737\) −41.7557 −1.53809
\(738\) 16.9937 0.625548
\(739\) −6.45304 −0.237379 −0.118690 0.992931i \(-0.537869\pi\)
−0.118690 + 0.992931i \(0.537869\pi\)
\(740\) −0.565230 −0.0207783
\(741\) 48.5140 1.78221
\(742\) −14.7653 −0.542053
\(743\) 37.2173 1.36537 0.682685 0.730713i \(-0.260812\pi\)
0.682685 + 0.730713i \(0.260812\pi\)
\(744\) 19.5198 0.715629
\(745\) 52.1404 1.91028
\(746\) 10.5185 0.385108
\(747\) 30.4898 1.11556
\(748\) 18.7237 0.684606
\(749\) −15.6256 −0.570946
\(750\) −15.7361 −0.574600
\(751\) −28.7137 −1.04778 −0.523888 0.851787i \(-0.675519\pi\)
−0.523888 + 0.851787i \(0.675519\pi\)
\(752\) −6.67146 −0.243283
\(753\) 2.18921 0.0797791
\(754\) 14.7493 0.537138
\(755\) 27.1112 0.986677
\(756\) −3.49108 −0.126969
\(757\) 5.54213 0.201432 0.100716 0.994915i \(-0.467887\pi\)
0.100716 + 0.994915i \(0.467887\pi\)
\(758\) 21.7891 0.791414
\(759\) 71.6800 2.60182
\(760\) −22.6668 −0.822210
\(761\) 42.3560 1.53540 0.767702 0.640807i \(-0.221400\pi\)
0.767702 + 0.640807i \(0.221400\pi\)
\(762\) −7.94258 −0.287729
\(763\) 29.2825 1.06010
\(764\) 2.81685 0.101910
\(765\) −52.4740 −1.89720
\(766\) −20.7204 −0.748658
\(767\) −29.9653 −1.08199
\(768\) −2.59634 −0.0936875
\(769\) 15.1038 0.544657 0.272328 0.962204i \(-0.412206\pi\)
0.272328 + 0.962204i \(0.412206\pi\)
\(770\) −18.9774 −0.683899
\(771\) 17.3815 0.625979
\(772\) 2.38607 0.0858767
\(773\) 0.217543 0.00782449 0.00391225 0.999992i \(-0.498755\pi\)
0.00391225 + 0.999992i \(0.498755\pi\)
\(774\) 21.3986 0.769158
\(775\) −21.3116 −0.765534
\(776\) −0.714395 −0.0256453
\(777\) −0.951392 −0.0341310
\(778\) 11.3569 0.407163
\(779\) 36.7859 1.31799
\(780\) −16.7687 −0.600414
\(781\) 40.4336 1.44683
\(782\) −37.0287 −1.32414
\(783\) 12.2977 0.439484
\(784\) −3.70721 −0.132400
\(785\) −31.0232 −1.10727
\(786\) −25.9681 −0.926251
\(787\) −46.9844 −1.67481 −0.837407 0.546580i \(-0.815930\pi\)
−0.837407 + 0.546580i \(0.815930\pi\)
\(788\) 2.28133 0.0812689
\(789\) −4.05465 −0.144349
\(790\) −34.9177 −1.24232
\(791\) −5.89800 −0.209709
\(792\) 13.9776 0.496672
\(793\) −13.8354 −0.491309
\(794\) −11.6878 −0.414784
\(795\) −59.1335 −2.09725
\(796\) 5.50846 0.195242
\(797\) 32.9004 1.16539 0.582696 0.812690i \(-0.301998\pi\)
0.582696 + 0.812690i \(0.301998\pi\)
\(798\) −38.1525 −1.35059
\(799\) −33.4324 −1.18275
\(800\) 2.83467 0.100221
\(801\) 5.24414 0.185293
\(802\) 30.2649 1.06869
\(803\) 8.02912 0.283342
\(804\) 29.0157 1.02331
\(805\) 37.5305 1.32278
\(806\) 17.3476 0.611042
\(807\) −52.9631 −1.86439
\(808\) −5.60599 −0.197218
\(809\) 36.9609 1.29948 0.649738 0.760158i \(-0.274878\pi\)
0.649738 + 0.760158i \(0.274878\pi\)
\(810\) 17.4323 0.612509
\(811\) 19.8919 0.698499 0.349249 0.937030i \(-0.386437\pi\)
0.349249 + 0.937030i \(0.386437\pi\)
\(812\) −11.5992 −0.407052
\(813\) 22.7324 0.797260
\(814\) 0.754501 0.0264452
\(815\) −49.8229 −1.74522
\(816\) −13.0109 −0.455474
\(817\) 46.3210 1.62057
\(818\) −19.3460 −0.676416
\(819\) −15.6637 −0.547335
\(820\) −12.7149 −0.444023
\(821\) 22.9557 0.801160 0.400580 0.916262i \(-0.368809\pi\)
0.400580 + 0.916262i \(0.368809\pi\)
\(822\) −22.9624 −0.800906
\(823\) −5.46848 −0.190619 −0.0953095 0.995448i \(-0.530384\pi\)
−0.0953095 + 0.995448i \(0.530384\pi\)
\(824\) 18.3479 0.639179
\(825\) −27.4985 −0.957376
\(826\) 23.5654 0.819946
\(827\) −46.7998 −1.62739 −0.813695 0.581292i \(-0.802547\pi\)
−0.813695 + 0.581292i \(0.802547\pi\)
\(828\) −27.6426 −0.960647
\(829\) −25.0318 −0.869389 −0.434695 0.900578i \(-0.643144\pi\)
−0.434695 + 0.900578i \(0.643144\pi\)
\(830\) −22.8128 −0.791843
\(831\) 12.5018 0.433681
\(832\) −2.30742 −0.0799952
\(833\) −18.5778 −0.643682
\(834\) −7.73114 −0.267707
\(835\) 43.3501 1.50019
\(836\) 30.2569 1.04646
\(837\) 14.4641 0.499951
\(838\) −0.160620 −0.00554852
\(839\) 4.01981 0.138779 0.0693897 0.997590i \(-0.477895\pi\)
0.0693897 + 0.997590i \(0.477895\pi\)
\(840\) 13.1873 0.455004
\(841\) 11.8593 0.408942
\(842\) 23.3447 0.804512
\(843\) 25.6181 0.882333
\(844\) −11.7839 −0.405620
\(845\) 21.4850 0.739108
\(846\) −24.9579 −0.858070
\(847\) 5.37146 0.184565
\(848\) −8.13695 −0.279424
\(849\) −40.4313 −1.38760
\(850\) 14.2053 0.487237
\(851\) −1.49213 −0.0511496
\(852\) −28.0970 −0.962587
\(853\) 2.39122 0.0818739 0.0409370 0.999162i \(-0.486966\pi\)
0.0409370 + 0.999162i \(0.486966\pi\)
\(854\) 10.8805 0.372322
\(855\) −84.7963 −2.89997
\(856\) −8.61101 −0.294318
\(857\) −36.6836 −1.25309 −0.626545 0.779386i \(-0.715531\pi\)
−0.626545 + 0.779386i \(0.715531\pi\)
\(858\) 22.3837 0.764168
\(859\) 31.0239 1.05852 0.529261 0.848459i \(-0.322469\pi\)
0.529261 + 0.848459i \(0.322469\pi\)
\(860\) −16.0107 −0.545959
\(861\) −21.4016 −0.729364
\(862\) −18.3971 −0.626608
\(863\) 14.1474 0.481582 0.240791 0.970577i \(-0.422593\pi\)
0.240791 + 0.970577i \(0.422593\pi\)
\(864\) −1.92388 −0.0654517
\(865\) −33.1663 −1.12769
\(866\) 35.9253 1.22079
\(867\) −21.0634 −0.715349
\(868\) −13.6425 −0.463057
\(869\) 46.6101 1.58114
\(870\) −46.4535 −1.57492
\(871\) 25.7868 0.873751
\(872\) 16.1371 0.546471
\(873\) −2.67255 −0.0904521
\(874\) −59.8371 −2.02402
\(875\) 10.9981 0.371802
\(876\) −5.57937 −0.188510
\(877\) 23.2864 0.786326 0.393163 0.919469i \(-0.371381\pi\)
0.393163 + 0.919469i \(0.371381\pi\)
\(878\) 6.02526 0.203343
\(879\) −15.8635 −0.535064
\(880\) −10.4582 −0.352544
\(881\) −40.3612 −1.35980 −0.679902 0.733303i \(-0.737978\pi\)
−0.679902 + 0.733303i \(0.737978\pi\)
\(882\) −13.8687 −0.466982
\(883\) −33.0022 −1.11061 −0.555307 0.831645i \(-0.687399\pi\)
−0.555307 + 0.831645i \(0.687399\pi\)
\(884\) −11.5631 −0.388908
\(885\) 94.3769 3.17245
\(886\) −25.0509 −0.841600
\(887\) −30.9691 −1.03984 −0.519921 0.854215i \(-0.674039\pi\)
−0.519921 + 0.854215i \(0.674039\pi\)
\(888\) −0.524297 −0.0175942
\(889\) 5.55114 0.186179
\(890\) −3.92372 −0.131523
\(891\) −23.2696 −0.779561
\(892\) −25.7948 −0.863673
\(893\) −54.0257 −1.80790
\(894\) 48.3644 1.61755
\(895\) −52.8912 −1.76796
\(896\) 1.81461 0.0606217
\(897\) −44.2669 −1.47803
\(898\) 17.5393 0.585295
\(899\) 48.0572 1.60280
\(900\) 10.6045 0.353483
\(901\) −40.7763 −1.35846
\(902\) 16.9725 0.565123
\(903\) −26.9490 −0.896807
\(904\) −3.25029 −0.108103
\(905\) −55.1802 −1.83425
\(906\) 25.1478 0.835480
\(907\) 20.5672 0.682922 0.341461 0.939896i \(-0.389078\pi\)
0.341461 + 0.939896i \(0.389078\pi\)
\(908\) −5.89354 −0.195584
\(909\) −20.9720 −0.695597
\(910\) 11.7197 0.388506
\(911\) 38.0326 1.26008 0.630039 0.776564i \(-0.283039\pi\)
0.630039 + 0.776564i \(0.283039\pi\)
\(912\) −21.0253 −0.696216
\(913\) 30.4518 1.00781
\(914\) 7.55158 0.249784
\(915\) 43.5751 1.44055
\(916\) 9.92639 0.327977
\(917\) 18.1493 0.599343
\(918\) −9.64106 −0.318202
\(919\) 49.7426 1.64086 0.820428 0.571749i \(-0.193735\pi\)
0.820428 + 0.571749i \(0.193735\pi\)
\(920\) 20.6825 0.681880
\(921\) −9.38972 −0.309402
\(922\) 23.5472 0.775485
\(923\) −24.9703 −0.821907
\(924\) −17.6031 −0.579099
\(925\) 0.572424 0.0188212
\(926\) 22.0830 0.725693
\(927\) 68.6394 2.25441
\(928\) −6.39213 −0.209832
\(929\) −20.5080 −0.672847 −0.336424 0.941711i \(-0.609217\pi\)
−0.336424 + 0.941711i \(0.609217\pi\)
\(930\) −54.6368 −1.79161
\(931\) −30.0211 −0.983901
\(932\) 4.76540 0.156096
\(933\) −77.9934 −2.55339
\(934\) −17.9243 −0.586501
\(935\) −52.4085 −1.71394
\(936\) −8.63203 −0.282147
\(937\) −40.5348 −1.32421 −0.662107 0.749409i \(-0.730338\pi\)
−0.662107 + 0.749409i \(0.730338\pi\)
\(938\) −20.2793 −0.662143
\(939\) 12.5568 0.409777
\(940\) 18.6737 0.609070
\(941\) −40.1789 −1.30980 −0.654898 0.755718i \(-0.727288\pi\)
−0.654898 + 0.755718i \(0.727288\pi\)
\(942\) −28.7765 −0.937590
\(943\) −33.5655 −1.09304
\(944\) 12.9865 0.422676
\(945\) 9.77171 0.317874
\(946\) 21.3719 0.694861
\(947\) 48.5772 1.57855 0.789273 0.614042i \(-0.210458\pi\)
0.789273 + 0.614042i \(0.210458\pi\)
\(948\) −32.3890 −1.05194
\(949\) −4.95849 −0.160959
\(950\) 22.9553 0.744767
\(951\) −13.6564 −0.442840
\(952\) 9.09345 0.294721
\(953\) −21.1309 −0.684498 −0.342249 0.939609i \(-0.611189\pi\)
−0.342249 + 0.939609i \(0.611189\pi\)
\(954\) −30.4403 −0.985540
\(955\) −7.88450 −0.255136
\(956\) −20.1082 −0.650347
\(957\) 62.0086 2.00445
\(958\) 1.78123 0.0575490
\(959\) 16.0486 0.518237
\(960\) 7.26729 0.234551
\(961\) 25.5230 0.823322
\(962\) −0.465952 −0.0150229
\(963\) −32.2137 −1.03807
\(964\) 26.0099 0.837723
\(965\) −6.67874 −0.214996
\(966\) 34.8125 1.12008
\(967\) −23.8068 −0.765574 −0.382787 0.923837i \(-0.625036\pi\)
−0.382787 + 0.923837i \(0.625036\pi\)
\(968\) 2.96012 0.0951420
\(969\) −105.363 −3.38475
\(970\) 1.99963 0.0642041
\(971\) −31.5328 −1.01194 −0.505968 0.862553i \(-0.668864\pi\)
−0.505968 + 0.862553i \(0.668864\pi\)
\(972\) 21.9415 0.703774
\(973\) 5.40336 0.173224
\(974\) −7.91140 −0.253498
\(975\) 16.9821 0.543862
\(976\) 5.99606 0.191929
\(977\) −61.2465 −1.95945 −0.979725 0.200348i \(-0.935793\pi\)
−0.979725 + 0.200348i \(0.935793\pi\)
\(978\) −46.2147 −1.47778
\(979\) 5.23760 0.167394
\(980\) 10.3767 0.331470
\(981\) 60.3688 1.92743
\(982\) −16.6083 −0.529991
\(983\) 27.9383 0.891094 0.445547 0.895259i \(-0.353009\pi\)
0.445547 + 0.895259i \(0.353009\pi\)
\(984\) −11.7941 −0.375981
\(985\) −6.38554 −0.203460
\(986\) −32.0326 −1.02013
\(987\) 31.4315 1.00048
\(988\) −18.6855 −0.594465
\(989\) −42.2659 −1.34398
\(990\) −39.1239 −1.24344
\(991\) 16.1529 0.513114 0.256557 0.966529i \(-0.417412\pi\)
0.256557 + 0.966529i \(0.417412\pi\)
\(992\) −7.51818 −0.238702
\(993\) −20.3912 −0.647095
\(994\) 19.6372 0.622855
\(995\) −15.4184 −0.488797
\(996\) −21.1607 −0.670502
\(997\) 61.0563 1.93367 0.966837 0.255395i \(-0.0822054\pi\)
0.966837 + 0.255395i \(0.0822054\pi\)
\(998\) −15.9285 −0.504207
\(999\) −0.388502 −0.0122917
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 4034.2.a.d.1.5 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.5 52 1.1 even 1 trivial