Properties

Label 5054.2.a.x.1.2
Level $5054$
Weight $2$
Character 5054.1
Self dual yes
Analytic conductor $40.356$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.3563931816\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.151572.1
Defining polynomial: \( x^{4} - x^{3} - 10x^{2} + 8x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 266)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.352271\) of defining polynomial
Character \(\chi\) \(=\) 5054.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.352271 q^{3} +1.00000 q^{4} +4.32518 q^{5} -0.352271 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.87591 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.352271 q^{3} +1.00000 q^{4} +4.32518 q^{5} -0.352271 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.87591 q^{9} +4.32518 q^{10} +2.35227 q^{11} -0.352271 q^{12} +0.801544 q^{13} +1.00000 q^{14} -1.52363 q^{15} +1.00000 q^{16} +6.22818 q^{17} -2.87591 q^{18} +4.32518 q^{20} -0.352271 q^{21} +2.35227 q^{22} -1.77445 q^{23} -0.352271 q^{24} +13.7072 q^{25} +0.801544 q^{26} +2.06991 q^{27} +1.00000 q^{28} -5.83126 q^{29} -1.52363 q^{30} +5.12672 q^{31} +1.00000 q^{32} -0.828636 q^{33} +6.22818 q^{34} +4.32518 q^{35} -2.87591 q^{36} -10.6504 q^{37} -0.282361 q^{39} +4.32518 q^{40} +3.64773 q^{41} -0.352271 q^{42} +0.873277 q^{43} +2.35227 q^{44} -12.4388 q^{45} -1.77445 q^{46} -5.83126 q^{47} -0.352271 q^{48} +1.00000 q^{49} +13.7072 q^{50} -2.19400 q^{51} +0.801544 q^{52} -1.12672 q^{53} +2.06991 q^{54} +10.1740 q^{55} +1.00000 q^{56} -5.83126 q^{58} +14.2011 q^{59} -1.52363 q^{60} -2.72209 q^{61} +5.12672 q^{62} -2.87591 q^{63} +1.00000 q^{64} +3.46682 q^{65} -0.828636 q^{66} -4.58045 q^{67} +6.22818 q^{68} +0.625088 q^{69} +4.32518 q^{70} -14.0026 q^{71} -2.87591 q^{72} -9.23080 q^{73} -10.6504 q^{74} -4.82864 q^{75} +2.35227 q^{77} -0.282361 q^{78} +7.04727 q^{79} +4.32518 q^{80} +7.89855 q^{81} +3.64773 q^{82} +15.5560 q^{83} -0.352271 q^{84} +26.9380 q^{85} +0.873277 q^{86} +2.05418 q^{87} +2.35227 q^{88} -7.29546 q^{89} -12.4388 q^{90} +0.801544 q^{91} -1.77445 q^{92} -1.80600 q^{93} -5.83126 q^{94} -0.352271 q^{96} -3.05681 q^{97} +1.00000 q^{98} -6.76491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} + q^{12} + 5 q^{13} + 4 q^{14} + 12 q^{15} + 4 q^{16} + 2 q^{17} + 9 q^{18} + q^{20} + q^{21} + 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} + q^{27} + 4 q^{28} - 4 q^{29} + 12 q^{30} + 6 q^{31} + 4 q^{32} - 19 q^{33} + 2 q^{34} + q^{35} + 9 q^{36} - 10 q^{37} - 6 q^{39} + q^{40} + 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} + 5 q^{46} - 4 q^{47} + q^{48} + 4 q^{49} + 15 q^{50} - 22 q^{51} + 5 q^{52} + 10 q^{53} + q^{54} - 10 q^{55} + 4 q^{56} - 4 q^{58} + 20 q^{59} + 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} + 3 q^{65} - 19 q^{66} + 7 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 10 q^{74} - 35 q^{75} + 7 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} + q^{84} + 10 q^{85} + 18 q^{86} + 36 q^{87} + 7 q^{88} - 34 q^{89} - 19 q^{90} + 5 q^{91} + 5 q^{92} + 6 q^{93} - 4 q^{94} + q^{96} - 5 q^{97} + 4 q^{98} + 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −0.352271 −0.203384 −0.101692 0.994816i \(-0.532426\pi\)
−0.101692 + 0.994816i \(0.532426\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.32518 1.93428 0.967139 0.254247i \(-0.0818276\pi\)
0.967139 + 0.254247i \(0.0818276\pi\)
\(6\) −0.352271 −0.143814
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) −2.87591 −0.958635
\(10\) 4.32518 1.36774
\(11\) 2.35227 0.709236 0.354618 0.935011i \(-0.384611\pi\)
0.354618 + 0.935011i \(0.384611\pi\)
\(12\) −0.352271 −0.101692
\(13\) 0.801544 0.222308 0.111154 0.993803i \(-0.464545\pi\)
0.111154 + 0.993803i \(0.464545\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.52363 −0.393401
\(16\) 1.00000 0.250000
\(17\) 6.22818 1.51055 0.755277 0.655405i \(-0.227502\pi\)
0.755277 + 0.655405i \(0.227502\pi\)
\(18\) −2.87591 −0.677857
\(19\) 0 0
\(20\) 4.32518 0.967139
\(21\) −0.352271 −0.0768718
\(22\) 2.35227 0.501506
\(23\) −1.77445 −0.369999 −0.184999 0.982739i \(-0.559228\pi\)
−0.184999 + 0.982739i \(0.559228\pi\)
\(24\) −0.352271 −0.0719070
\(25\) 13.7072 2.74143
\(26\) 0.801544 0.157196
\(27\) 2.06991 0.398354
\(28\) 1.00000 0.188982
\(29\) −5.83126 −1.08284 −0.541419 0.840753i \(-0.682113\pi\)
−0.541419 + 0.840753i \(0.682113\pi\)
\(30\) −1.52363 −0.278176
\(31\) 5.12672 0.920787 0.460393 0.887715i \(-0.347708\pi\)
0.460393 + 0.887715i \(0.347708\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.828636 −0.144247
\(34\) 6.22818 1.06812
\(35\) 4.32518 0.731089
\(36\) −2.87591 −0.479318
\(37\) −10.6504 −1.75091 −0.875454 0.483302i \(-0.839437\pi\)
−0.875454 + 0.483302i \(0.839437\pi\)
\(38\) 0 0
\(39\) −0.282361 −0.0452139
\(40\) 4.32518 0.683871
\(41\) 3.64773 0.569680 0.284840 0.958575i \(-0.408060\pi\)
0.284840 + 0.958575i \(0.408060\pi\)
\(42\) −0.352271 −0.0543566
\(43\) 0.873277 0.133174 0.0665868 0.997781i \(-0.478789\pi\)
0.0665868 + 0.997781i \(0.478789\pi\)
\(44\) 2.35227 0.354618
\(45\) −12.4388 −1.85427
\(46\) −1.77445 −0.261629
\(47\) −5.83126 −0.850577 −0.425289 0.905058i \(-0.639827\pi\)
−0.425289 + 0.905058i \(0.639827\pi\)
\(48\) −0.352271 −0.0508459
\(49\) 1.00000 0.142857
\(50\) 13.7072 1.93849
\(51\) −2.19400 −0.307222
\(52\) 0.801544 0.111154
\(53\) −1.12672 −0.154767 −0.0773836 0.997001i \(-0.524657\pi\)
−0.0773836 + 0.997001i \(0.524657\pi\)
\(54\) 2.06991 0.281679
\(55\) 10.1740 1.37186
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −5.83126 −0.765683
\(59\) 14.2011 1.84882 0.924412 0.381396i \(-0.124557\pi\)
0.924412 + 0.381396i \(0.124557\pi\)
\(60\) −1.52363 −0.196700
\(61\) −2.72209 −0.348528 −0.174264 0.984699i \(-0.555755\pi\)
−0.174264 + 0.984699i \(0.555755\pi\)
\(62\) 5.12672 0.651094
\(63\) −2.87591 −0.362330
\(64\) 1.00000 0.125000
\(65\) 3.46682 0.430006
\(66\) −0.828636 −0.101998
\(67\) −4.58045 −0.559591 −0.279795 0.960060i \(-0.590267\pi\)
−0.279795 + 0.960060i \(0.590267\pi\)
\(68\) 6.22818 0.755277
\(69\) 0.625088 0.0752517
\(70\) 4.32518 0.516958
\(71\) −14.0026 −1.66181 −0.830903 0.556417i \(-0.812176\pi\)
−0.830903 + 0.556417i \(0.812176\pi\)
\(72\) −2.87591 −0.338929
\(73\) −9.23080 −1.08038 −0.540192 0.841542i \(-0.681648\pi\)
−0.540192 + 0.841542i \(0.681648\pi\)
\(74\) −10.6504 −1.23808
\(75\) −4.82864 −0.557563
\(76\) 0 0
\(77\) 2.35227 0.268066
\(78\) −0.282361 −0.0319710
\(79\) 7.04727 0.792880 0.396440 0.918061i \(-0.370246\pi\)
0.396440 + 0.918061i \(0.370246\pi\)
\(80\) 4.32518 0.483570
\(81\) 7.89855 0.877616
\(82\) 3.64773 0.402824
\(83\) 15.5560 1.70749 0.853745 0.520691i \(-0.174325\pi\)
0.853745 + 0.520691i \(0.174325\pi\)
\(84\) −0.352271 −0.0384359
\(85\) 26.9380 2.92183
\(86\) 0.873277 0.0941679
\(87\) 2.05418 0.220232
\(88\) 2.35227 0.250753
\(89\) −7.29546 −0.773317 −0.386659 0.922223i \(-0.626371\pi\)
−0.386659 + 0.922223i \(0.626371\pi\)
\(90\) −12.4388 −1.31117
\(91\) 0.801544 0.0840247
\(92\) −1.77445 −0.184999
\(93\) −1.80600 −0.187273
\(94\) −5.83126 −0.601449
\(95\) 0 0
\(96\) −0.352271 −0.0359535
\(97\) −3.05681 −0.310372 −0.155186 0.987885i \(-0.549598\pi\)
−0.155186 + 0.987885i \(0.549598\pi\)
\(98\) 1.00000 0.101015
\(99\) −6.76491 −0.679899
\(100\) 13.7072 1.37072
\(101\) 1.52363 0.151607 0.0758036 0.997123i \(-0.475848\pi\)
0.0758036 + 0.997123i \(0.475848\pi\)
\(102\) −2.19400 −0.217239
\(103\) 11.5236 1.13546 0.567729 0.823216i \(-0.307822\pi\)
0.567729 + 0.823216i \(0.307822\pi\)
\(104\) 0.801544 0.0785979
\(105\) −1.52363 −0.148691
\(106\) −1.12672 −0.109437
\(107\) −16.0053 −1.54729 −0.773643 0.633621i \(-0.781568\pi\)
−0.773643 + 0.633621i \(0.781568\pi\)
\(108\) 2.06991 0.199177
\(109\) 7.24035 0.693500 0.346750 0.937958i \(-0.387285\pi\)
0.346750 + 0.937958i \(0.387285\pi\)
\(110\) 10.1740 0.970052
\(111\) 3.75181 0.356106
\(112\) 1.00000 0.0944911
\(113\) −1.47637 −0.138885 −0.0694424 0.997586i \(-0.522122\pi\)
−0.0694424 + 0.997586i \(0.522122\pi\)
\(114\) 0 0
\(115\) −7.67482 −0.715681
\(116\) −5.83126 −0.541419
\(117\) −2.30517 −0.213113
\(118\) 14.2011 1.30732
\(119\) 6.22818 0.570936
\(120\) −1.52363 −0.139088
\(121\) −5.46682 −0.496984
\(122\) −2.72209 −0.246446
\(123\) −1.28499 −0.115864
\(124\) 5.12672 0.460393
\(125\) 37.6601 3.36842
\(126\) −2.87591 −0.256206
\(127\) 6.23080 0.552894 0.276447 0.961029i \(-0.410843\pi\)
0.276447 + 0.961029i \(0.410843\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.307630 −0.0270853
\(130\) 3.46682 0.304060
\(131\) −3.66528 −0.320237 −0.160118 0.987098i \(-0.551188\pi\)
−0.160118 + 0.987098i \(0.551188\pi\)
\(132\) −0.828636 −0.0721235
\(133\) 0 0
\(134\) −4.58045 −0.395690
\(135\) 8.95273 0.770528
\(136\) 6.22818 0.534062
\(137\) 3.39691 0.290218 0.145109 0.989416i \(-0.453647\pi\)
0.145109 + 0.989416i \(0.453647\pi\)
\(138\) 0.625088 0.0532110
\(139\) −5.19663 −0.440773 −0.220386 0.975413i \(-0.570732\pi\)
−0.220386 + 0.975413i \(0.570732\pi\)
\(140\) 4.32518 0.365544
\(141\) 2.05418 0.172994
\(142\) −14.0026 −1.17507
\(143\) 1.88545 0.157669
\(144\) −2.87591 −0.239659
\(145\) −25.2213 −2.09451
\(146\) −9.23080 −0.763947
\(147\) −0.352271 −0.0290548
\(148\) −10.6504 −0.875454
\(149\) 14.6504 1.20020 0.600102 0.799923i \(-0.295127\pi\)
0.600102 + 0.799923i \(0.295127\pi\)
\(150\) −4.82864 −0.394257
\(151\) −5.46682 −0.444884 −0.222442 0.974946i \(-0.571403\pi\)
−0.222442 + 0.974946i \(0.571403\pi\)
\(152\) 0 0
\(153\) −17.9116 −1.44807
\(154\) 2.35227 0.189551
\(155\) 22.1740 1.78106
\(156\) −0.282361 −0.0226069
\(157\) −3.45190 −0.275492 −0.137746 0.990468i \(-0.543986\pi\)
−0.137746 + 0.990468i \(0.543986\pi\)
\(158\) 7.04727 0.560651
\(159\) 0.396912 0.0314771
\(160\) 4.32518 0.341935
\(161\) −1.77445 −0.139846
\(162\) 7.89855 0.620568
\(163\) 8.65990 0.678296 0.339148 0.940733i \(-0.389861\pi\)
0.339148 + 0.940733i \(0.389861\pi\)
\(164\) 3.64773 0.284840
\(165\) −3.58400 −0.279014
\(166\) 15.5560 1.20738
\(167\) 6.05944 0.468894 0.234447 0.972129i \(-0.424672\pi\)
0.234447 + 0.972129i \(0.424672\pi\)
\(168\) −0.352271 −0.0271783
\(169\) −12.3575 −0.950579
\(170\) 26.9380 2.06605
\(171\) 0 0
\(172\) 0.873277 0.0665868
\(173\) −15.6259 −1.18801 −0.594007 0.804460i \(-0.702455\pi\)
−0.594007 + 0.804460i \(0.702455\pi\)
\(174\) 2.05418 0.155727
\(175\) 13.7072 1.03616
\(176\) 2.35227 0.177309
\(177\) −5.00263 −0.376021
\(178\) −7.29546 −0.546818
\(179\) −11.3995 −0.852042 −0.426021 0.904713i \(-0.640085\pi\)
−0.426021 + 0.904713i \(0.640085\pi\)
\(180\) −12.4388 −0.927134
\(181\) −3.27791 −0.243645 −0.121823 0.992552i \(-0.538874\pi\)
−0.121823 + 0.992552i \(0.538874\pi\)
\(182\) 0.801544 0.0594144
\(183\) 0.958913 0.0708849
\(184\) −1.77445 −0.130814
\(185\) −46.0647 −3.38674
\(186\) −1.80600 −0.132422
\(187\) 14.6504 1.07134
\(188\) −5.83126 −0.425289
\(189\) 2.06991 0.150564
\(190\) 0 0
\(191\) −3.23865 −0.234340 −0.117170 0.993112i \(-0.537382\pi\)
−0.117170 + 0.993112i \(0.537382\pi\)
\(192\) −0.352271 −0.0254230
\(193\) −12.0568 −0.867868 −0.433934 0.900945i \(-0.642875\pi\)
−0.433934 + 0.900945i \(0.642875\pi\)
\(194\) −3.05681 −0.219466
\(195\) −1.22126 −0.0874563
\(196\) 1.00000 0.0714286
\(197\) −20.9380 −1.49177 −0.745884 0.666075i \(-0.767973\pi\)
−0.745884 + 0.666075i \(0.767973\pi\)
\(198\) −6.76491 −0.480761
\(199\) 9.12672 0.646976 0.323488 0.946232i \(-0.395144\pi\)
0.323488 + 0.946232i \(0.395144\pi\)
\(200\) 13.7072 0.969243
\(201\) 1.61356 0.113812
\(202\) 1.52363 0.107203
\(203\) −5.83126 −0.409275
\(204\) −2.19400 −0.153611
\(205\) 15.7771 1.10192
\(206\) 11.5236 0.802890
\(207\) 5.10316 0.354694
\(208\) 0.801544 0.0555771
\(209\) 0 0
\(210\) −1.52363 −0.105141
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −1.12672 −0.0773836
\(213\) 4.93272 0.337984
\(214\) −16.0053 −1.09410
\(215\) 3.77708 0.257595
\(216\) 2.06991 0.140840
\(217\) 5.12672 0.348025
\(218\) 7.24035 0.490378
\(219\) 3.25174 0.219732
\(220\) 10.1740 0.685930
\(221\) 4.99216 0.335809
\(222\) 3.75181 0.251805
\(223\) 12.2534 0.820551 0.410276 0.911962i \(-0.365432\pi\)
0.410276 + 0.911962i \(0.365432\pi\)
\(224\) 1.00000 0.0668153
\(225\) −39.4205 −2.62803
\(226\) −1.47637 −0.0982064
\(227\) 23.3531 1.55000 0.774999 0.631962i \(-0.217750\pi\)
0.774999 + 0.631962i \(0.217750\pi\)
\(228\) 0 0
\(229\) −25.8830 −1.71040 −0.855198 0.518302i \(-0.826564\pi\)
−0.855198 + 0.518302i \(0.826564\pi\)
\(230\) −7.67482 −0.506063
\(231\) −0.828636 −0.0545203
\(232\) −5.83126 −0.382841
\(233\) −2.60309 −0.170534 −0.0852670 0.996358i \(-0.527174\pi\)
−0.0852670 + 0.996358i \(0.527174\pi\)
\(234\) −2.30517 −0.150693
\(235\) −25.2213 −1.64525
\(236\) 14.2011 0.924412
\(237\) −2.48255 −0.161259
\(238\) 6.22818 0.403713
\(239\) −23.2781 −1.50573 −0.752867 0.658173i \(-0.771330\pi\)
−0.752867 + 0.658173i \(0.771330\pi\)
\(240\) −1.52363 −0.0983502
\(241\) 8.94319 0.576081 0.288041 0.957618i \(-0.406996\pi\)
0.288041 + 0.957618i \(0.406996\pi\)
\(242\) −5.46682 −0.351421
\(243\) −8.99216 −0.576847
\(244\) −2.72209 −0.174264
\(245\) 4.32518 0.276326
\(246\) −1.28499 −0.0819279
\(247\) 0 0
\(248\) 5.12672 0.325547
\(249\) −5.47992 −0.347276
\(250\) 37.6601 2.38183
\(251\) 27.3872 1.72867 0.864334 0.502918i \(-0.167740\pi\)
0.864334 + 0.502918i \(0.167740\pi\)
\(252\) −2.87591 −0.181165
\(253\) −4.17399 −0.262417
\(254\) 6.23080 0.390955
\(255\) −9.48946 −0.594253
\(256\) 1.00000 0.0625000
\(257\) −8.49209 −0.529722 −0.264861 0.964287i \(-0.585326\pi\)
−0.264861 + 0.964287i \(0.585326\pi\)
\(258\) −0.307630 −0.0191522
\(259\) −10.6504 −0.661781
\(260\) 3.46682 0.215003
\(261\) 16.7702 1.03805
\(262\) −3.66528 −0.226442
\(263\) −5.74918 −0.354510 −0.177255 0.984165i \(-0.556722\pi\)
−0.177255 + 0.984165i \(0.556722\pi\)
\(264\) −0.828636 −0.0509990
\(265\) −4.87328 −0.299363
\(266\) 0 0
\(267\) 2.56998 0.157280
\(268\) −4.58045 −0.279795
\(269\) 8.42218 0.513509 0.256755 0.966477i \(-0.417347\pi\)
0.256755 + 0.966477i \(0.417347\pi\)
\(270\) 8.95273 0.544846
\(271\) 20.7298 1.25925 0.629623 0.776901i \(-0.283209\pi\)
0.629623 + 0.776901i \(0.283209\pi\)
\(272\) 6.22818 0.377639
\(273\) −0.282361 −0.0170892
\(274\) 3.39691 0.205215
\(275\) 32.2430 1.94432
\(276\) 0.625088 0.0376259
\(277\) 17.4442 1.04812 0.524060 0.851682i \(-0.324417\pi\)
0.524060 + 0.851682i \(0.324417\pi\)
\(278\) −5.19663 −0.311673
\(279\) −14.7440 −0.882698
\(280\) 4.32518 0.258479
\(281\) −2.12409 −0.126713 −0.0633564 0.997991i \(-0.520180\pi\)
−0.0633564 + 0.997991i \(0.520180\pi\)
\(282\) 2.05418 0.122325
\(283\) −27.6696 −1.64479 −0.822394 0.568919i \(-0.807362\pi\)
−0.822394 + 0.568919i \(0.807362\pi\)
\(284\) −14.0026 −0.830903
\(285\) 0 0
\(286\) 1.88545 0.111489
\(287\) 3.64773 0.215319
\(288\) −2.87591 −0.169464
\(289\) 21.7902 1.28178
\(290\) −25.2213 −1.48104
\(291\) 1.07683 0.0631247
\(292\) −9.23080 −0.540192
\(293\) 13.2326 0.773058 0.386529 0.922277i \(-0.373674\pi\)
0.386529 + 0.922277i \(0.373674\pi\)
\(294\) −0.352271 −0.0205449
\(295\) 61.4222 3.57614
\(296\) −10.6504 −0.619039
\(297\) 4.86899 0.282527
\(298\) 14.6504 0.848672
\(299\) −1.42230 −0.0822538
\(300\) −4.82864 −0.278781
\(301\) 0.873277 0.0503349
\(302\) −5.46682 −0.314580
\(303\) −0.536732 −0.0308344
\(304\) 0 0
\(305\) −11.7735 −0.674150
\(306\) −17.9116 −1.02394
\(307\) −24.9398 −1.42339 −0.711695 0.702489i \(-0.752072\pi\)
−0.711695 + 0.702489i \(0.752072\pi\)
\(308\) 2.35227 0.134033
\(309\) −4.05944 −0.230934
\(310\) 22.1740 1.25940
\(311\) 15.9458 0.904204 0.452102 0.891966i \(-0.350674\pi\)
0.452102 + 0.891966i \(0.350674\pi\)
\(312\) −0.282361 −0.0159855
\(313\) −12.7203 −0.718992 −0.359496 0.933147i \(-0.617051\pi\)
−0.359496 + 0.933147i \(0.617051\pi\)
\(314\) −3.45190 −0.194802
\(315\) −12.4388 −0.700847
\(316\) 7.04727 0.396440
\(317\) 32.9091 1.84836 0.924178 0.381961i \(-0.124751\pi\)
0.924178 + 0.381961i \(0.124751\pi\)
\(318\) 0.396912 0.0222577
\(319\) −13.7167 −0.767989
\(320\) 4.32518 0.241785
\(321\) 5.63819 0.314693
\(322\) −1.77445 −0.0988863
\(323\) 0 0
\(324\) 7.89855 0.438808
\(325\) 10.9869 0.609444
\(326\) 8.65990 0.479628
\(327\) −2.55056 −0.141046
\(328\) 3.64773 0.201412
\(329\) −5.83126 −0.321488
\(330\) −3.58400 −0.197293
\(331\) 19.0079 1.04477 0.522384 0.852710i \(-0.325043\pi\)
0.522384 + 0.852710i \(0.325043\pi\)
\(332\) 15.5560 0.853745
\(333\) 30.6294 1.67848
\(334\) 6.05944 0.331558
\(335\) −19.8113 −1.08240
\(336\) −0.352271 −0.0192180
\(337\) −28.1914 −1.53568 −0.767842 0.640639i \(-0.778670\pi\)
−0.767842 + 0.640639i \(0.778670\pi\)
\(338\) −12.3575 −0.672161
\(339\) 0.520081 0.0282469
\(340\) 26.9380 1.46092
\(341\) 12.0594 0.653055
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.873277 0.0470840
\(345\) 2.70362 0.145558
\(346\) −15.6259 −0.840053
\(347\) 22.7292 1.22017 0.610083 0.792338i \(-0.291136\pi\)
0.610083 + 0.792338i \(0.291136\pi\)
\(348\) 2.05418 0.110116
\(349\) −4.72981 −0.253181 −0.126590 0.991955i \(-0.540403\pi\)
−0.126590 + 0.991955i \(0.540403\pi\)
\(350\) 13.7072 0.732679
\(351\) 1.65912 0.0885575
\(352\) 2.35227 0.125376
\(353\) −5.76135 −0.306646 −0.153323 0.988176i \(-0.548997\pi\)
−0.153323 + 0.988176i \(0.548997\pi\)
\(354\) −5.00263 −0.265887
\(355\) −60.5639 −3.21440
\(356\) −7.29546 −0.386659
\(357\) −2.19400 −0.116119
\(358\) −11.3995 −0.602484
\(359\) −19.9511 −1.05298 −0.526489 0.850182i \(-0.676492\pi\)
−0.526489 + 0.850182i \(0.676492\pi\)
\(360\) −12.4388 −0.655583
\(361\) 0 0
\(362\) −3.27791 −0.172283
\(363\) 1.92580 0.101078
\(364\) 0.801544 0.0420123
\(365\) −39.9249 −2.08976
\(366\) 0.958913 0.0501232
\(367\) −1.24035 −0.0647456 −0.0323728 0.999476i \(-0.510306\pi\)
−0.0323728 + 0.999476i \(0.510306\pi\)
\(368\) −1.77445 −0.0924997
\(369\) −10.4905 −0.546115
\(370\) −46.0647 −2.39479
\(371\) −1.12672 −0.0584965
\(372\) −1.80600 −0.0936365
\(373\) −24.8733 −1.28789 −0.643945 0.765072i \(-0.722703\pi\)
−0.643945 + 0.765072i \(0.722703\pi\)
\(374\) 14.6504 0.757552
\(375\) −13.2665 −0.685081
\(376\) −5.83126 −0.300725
\(377\) −4.67402 −0.240724
\(378\) 2.06991 0.106465
\(379\) −32.4274 −1.66569 −0.832843 0.553510i \(-0.813288\pi\)
−0.832843 + 0.553510i \(0.813288\pi\)
\(380\) 0 0
\(381\) −2.19493 −0.112450
\(382\) −3.23865 −0.165704
\(383\) 14.5105 0.741454 0.370727 0.928742i \(-0.379109\pi\)
0.370727 + 0.928742i \(0.379109\pi\)
\(384\) −0.352271 −0.0179767
\(385\) 10.1740 0.518515
\(386\) −12.0568 −0.613676
\(387\) −2.51146 −0.127665
\(388\) −3.05681 −0.155186
\(389\) 25.5236 1.29410 0.647050 0.762448i \(-0.276003\pi\)
0.647050 + 0.762448i \(0.276003\pi\)
\(390\) −1.22126 −0.0618409
\(391\) −11.0516 −0.558903
\(392\) 1.00000 0.0505076
\(393\) 1.29117 0.0651309
\(394\) −20.9380 −1.05484
\(395\) 30.4807 1.53365
\(396\) −6.76491 −0.339949
\(397\) 11.6373 0.584057 0.292029 0.956410i \(-0.405670\pi\)
0.292029 + 0.956410i \(0.405670\pi\)
\(398\) 9.12672 0.457481
\(399\) 0 0
\(400\) 13.7072 0.685358
\(401\) 25.1740 1.25713 0.628565 0.777757i \(-0.283643\pi\)
0.628565 + 0.777757i \(0.283643\pi\)
\(402\) 1.61356 0.0804770
\(403\) 4.10929 0.204699
\(404\) 1.52363 0.0758036
\(405\) 34.1626 1.69755
\(406\) −5.83126 −0.289401
\(407\) −25.0525 −1.24181
\(408\) −2.19400 −0.108619
\(409\) −31.6277 −1.56389 −0.781945 0.623347i \(-0.785772\pi\)
−0.781945 + 0.623347i \(0.785772\pi\)
\(410\) 15.7771 0.779174
\(411\) −1.19663 −0.0590256
\(412\) 11.5236 0.567729
\(413\) 14.2011 0.698790
\(414\) 5.10316 0.250806
\(415\) 67.2824 3.30276
\(416\) 0.801544 0.0392989
\(417\) 1.83062 0.0896460
\(418\) 0 0
\(419\) −19.9205 −0.973182 −0.486591 0.873630i \(-0.661760\pi\)
−0.486591 + 0.873630i \(0.661760\pi\)
\(420\) −1.52363 −0.0743457
\(421\) −14.4274 −0.703150 −0.351575 0.936160i \(-0.614354\pi\)
−0.351575 + 0.936160i \(0.614354\pi\)
\(422\) 4.00000 0.194717
\(423\) 16.7702 0.815393
\(424\) −1.12672 −0.0547185
\(425\) 85.3707 4.14109
\(426\) 4.93272 0.238991
\(427\) −2.72209 −0.131731
\(428\) −16.0053 −0.773643
\(429\) −0.664189 −0.0320673
\(430\) 3.77708 0.182147
\(431\) 14.6504 0.705683 0.352841 0.935683i \(-0.385216\pi\)
0.352841 + 0.935683i \(0.385216\pi\)
\(432\) 2.06991 0.0995886
\(433\) 18.0043 0.865233 0.432616 0.901578i \(-0.357590\pi\)
0.432616 + 0.901578i \(0.357590\pi\)
\(434\) 5.12672 0.246091
\(435\) 8.88472 0.425989
\(436\) 7.24035 0.346750
\(437\) 0 0
\(438\) 3.25174 0.155374
\(439\) 21.6336 1.03252 0.516258 0.856433i \(-0.327325\pi\)
0.516258 + 0.856433i \(0.327325\pi\)
\(440\) 10.1740 0.485026
\(441\) −2.87591 −0.136948
\(442\) 4.99216 0.237453
\(443\) −3.45465 −0.164135 −0.0820677 0.996627i \(-0.526152\pi\)
−0.0820677 + 0.996627i \(0.526152\pi\)
\(444\) 3.75181 0.178053
\(445\) −31.5542 −1.49581
\(446\) 12.2534 0.580217
\(447\) −5.16089 −0.244102
\(448\) 1.00000 0.0472456
\(449\) 19.5069 0.920587 0.460294 0.887767i \(-0.347744\pi\)
0.460294 + 0.887767i \(0.347744\pi\)
\(450\) −39.4205 −1.85830
\(451\) 8.58045 0.404037
\(452\) −1.47637 −0.0694424
\(453\) 1.92580 0.0904821
\(454\) 23.3531 1.09601
\(455\) 3.46682 0.162527
\(456\) 0 0
\(457\) −13.2876 −0.621568 −0.310784 0.950480i \(-0.600592\pi\)
−0.310784 + 0.950480i \(0.600592\pi\)
\(458\) −25.8830 −1.20943
\(459\) 12.8918 0.601736
\(460\) −7.67482 −0.357840
\(461\) 16.1915 0.754115 0.377058 0.926190i \(-0.376936\pi\)
0.377058 + 0.926190i \(0.376936\pi\)
\(462\) −0.828636 −0.0385517
\(463\) 21.5010 0.999236 0.499618 0.866246i \(-0.333474\pi\)
0.499618 + 0.866246i \(0.333474\pi\)
\(464\) −5.83126 −0.270710
\(465\) −7.81125 −0.362238
\(466\) −2.60309 −0.120586
\(467\) −7.95536 −0.368130 −0.184065 0.982914i \(-0.558926\pi\)
−0.184065 + 0.982914i \(0.558926\pi\)
\(468\) −2.30517 −0.106556
\(469\) −4.58045 −0.211505
\(470\) −25.2213 −1.16337
\(471\) 1.21600 0.0560305
\(472\) 14.2011 0.653658
\(473\) 2.05418 0.0944515
\(474\) −2.48255 −0.114027
\(475\) 0 0
\(476\) 6.22818 0.285468
\(477\) 3.24035 0.148365
\(478\) −23.2781 −1.06471
\(479\) −26.6356 −1.21701 −0.608506 0.793549i \(-0.708231\pi\)
−0.608506 + 0.793549i \(0.708231\pi\)
\(480\) −1.52363 −0.0695441
\(481\) −8.53673 −0.389241
\(482\) 8.94319 0.407351
\(483\) 0.625088 0.0284425
\(484\) −5.46682 −0.248492
\(485\) −13.2213 −0.600347
\(486\) −8.99216 −0.407893
\(487\) −5.34964 −0.242415 −0.121208 0.992627i \(-0.538677\pi\)
−0.121208 + 0.992627i \(0.538677\pi\)
\(488\) −2.72209 −0.123223
\(489\) −3.05063 −0.137954
\(490\) 4.32518 0.195392
\(491\) 0.456352 0.0205949 0.0102974 0.999947i \(-0.496722\pi\)
0.0102974 + 0.999947i \(0.496722\pi\)
\(492\) −1.28499 −0.0579318
\(493\) −36.3181 −1.63569
\(494\) 0 0
\(495\) −29.2594 −1.31511
\(496\) 5.12672 0.230197
\(497\) −14.0026 −0.628104
\(498\) −5.47992 −0.245561
\(499\) −5.99046 −0.268170 −0.134085 0.990970i \(-0.542809\pi\)
−0.134085 + 0.990970i \(0.542809\pi\)
\(500\) 37.6601 1.68421
\(501\) −2.13456 −0.0953653
\(502\) 27.3872 1.22235
\(503\) 28.2929 1.26152 0.630758 0.775979i \(-0.282744\pi\)
0.630758 + 0.775979i \(0.282744\pi\)
\(504\) −2.87591 −0.128103
\(505\) 6.58999 0.293251
\(506\) −4.17399 −0.185557
\(507\) 4.35320 0.193332
\(508\) 6.23080 0.276447
\(509\) −19.0990 −0.846548 −0.423274 0.906002i \(-0.639119\pi\)
−0.423274 + 0.906002i \(0.639119\pi\)
\(510\) −9.48946 −0.420200
\(511\) −9.23080 −0.408347
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −8.49209 −0.374570
\(515\) 49.8418 2.19629
\(516\) −0.307630 −0.0135427
\(517\) −13.7167 −0.603260
\(518\) −10.6504 −0.467950
\(519\) 5.50455 0.241623
\(520\) 3.46682 0.152030
\(521\) −24.1294 −1.05713 −0.528563 0.848894i \(-0.677269\pi\)
−0.528563 + 0.848894i \(0.677269\pi\)
\(522\) 16.7702 0.734010
\(523\) 11.9205 0.521249 0.260625 0.965440i \(-0.416072\pi\)
0.260625 + 0.965440i \(0.416072\pi\)
\(524\) −3.66528 −0.160118
\(525\) −4.82864 −0.210739
\(526\) −5.74918 −0.250676
\(527\) 31.9301 1.39090
\(528\) −0.828636 −0.0360618
\(529\) −19.8513 −0.863101
\(530\) −4.87328 −0.211682
\(531\) −40.8410 −1.77235
\(532\) 0 0
\(533\) 2.92382 0.126645
\(534\) 2.56998 0.111214
\(535\) −69.2256 −2.99288
\(536\) −4.58045 −0.197845
\(537\) 4.01573 0.173291
\(538\) 8.42218 0.363106
\(539\) 2.35227 0.101319
\(540\) 8.95273 0.385264
\(541\) 11.8411 0.509088 0.254544 0.967061i \(-0.418075\pi\)
0.254544 + 0.967061i \(0.418075\pi\)
\(542\) 20.7298 0.890422
\(543\) 1.15471 0.0495534
\(544\) 6.22818 0.267031
\(545\) 31.3158 1.34142
\(546\) −0.282361 −0.0120839
\(547\) −35.4747 −1.51679 −0.758394 0.651796i \(-0.774016\pi\)
−0.758394 + 0.651796i \(0.774016\pi\)
\(548\) 3.39691 0.145109
\(549\) 7.82847 0.334111
\(550\) 32.2430 1.37485
\(551\) 0 0
\(552\) 0.625088 0.0266055
\(553\) 7.04727 0.299680
\(554\) 17.4442 0.741132
\(555\) 16.2273 0.688808
\(556\) −5.19663 −0.220386
\(557\) 11.6976 0.495644 0.247822 0.968806i \(-0.420285\pi\)
0.247822 + 0.968806i \(0.420285\pi\)
\(558\) −14.7440 −0.624162
\(559\) 0.699970 0.0296056
\(560\) 4.32518 0.182772
\(561\) −5.16089 −0.217893
\(562\) −2.12409 −0.0895995
\(563\) 12.2562 0.516537 0.258268 0.966073i \(-0.416848\pi\)
0.258268 + 0.966073i \(0.416848\pi\)
\(564\) 2.05418 0.0864968
\(565\) −6.38554 −0.268642
\(566\) −27.6696 −1.16304
\(567\) 7.89855 0.331708
\(568\) −14.0026 −0.587537
\(569\) −5.80862 −0.243510 −0.121755 0.992560i \(-0.538852\pi\)
−0.121755 + 0.992560i \(0.538852\pi\)
\(570\) 0 0
\(571\) 37.2308 1.55806 0.779030 0.626986i \(-0.215712\pi\)
0.779030 + 0.626986i \(0.215712\pi\)
\(572\) 1.88545 0.0788346
\(573\) 1.14088 0.0476610
\(574\) 3.64773 0.152253
\(575\) −24.3227 −1.01433
\(576\) −2.87591 −0.119829
\(577\) −17.3444 −0.722058 −0.361029 0.932555i \(-0.617574\pi\)
−0.361029 + 0.932555i \(0.617574\pi\)
\(578\) 21.7902 0.906352
\(579\) 4.24726 0.176510
\(580\) −25.2213 −1.04726
\(581\) 15.5560 0.645371
\(582\) 1.07683 0.0446359
\(583\) −2.65036 −0.109767
\(584\) −9.23080 −0.381973
\(585\) −9.97025 −0.412219
\(586\) 13.2326 0.546635
\(587\) −33.7561 −1.39327 −0.696633 0.717428i \(-0.745319\pi\)
−0.696633 + 0.717428i \(0.745319\pi\)
\(588\) −0.352271 −0.0145274
\(589\) 0 0
\(590\) 61.4222 2.52871
\(591\) 7.37584 0.303401
\(592\) −10.6504 −0.437727
\(593\) −15.5079 −0.636833 −0.318417 0.947951i \(-0.603151\pi\)
−0.318417 + 0.947951i \(0.603151\pi\)
\(594\) 4.86899 0.199777
\(595\) 26.9380 1.10435
\(596\) 14.6504 0.600102
\(597\) −3.21508 −0.131584
\(598\) −1.42230 −0.0581622
\(599\) −38.1215 −1.55760 −0.778801 0.627271i \(-0.784172\pi\)
−0.778801 + 0.627271i \(0.784172\pi\)
\(600\) −4.82864 −0.197128
\(601\) −13.4799 −0.549857 −0.274929 0.961465i \(-0.588654\pi\)
−0.274929 + 0.961465i \(0.588654\pi\)
\(602\) 0.873277 0.0355921
\(603\) 13.1729 0.536443
\(604\) −5.46682 −0.222442
\(605\) −23.6450 −0.961305
\(606\) −0.536732 −0.0218032
\(607\) 6.25345 0.253820 0.126910 0.991914i \(-0.459494\pi\)
0.126910 + 0.991914i \(0.459494\pi\)
\(608\) 0 0
\(609\) 2.05418 0.0832398
\(610\) −11.7735 −0.476696
\(611\) −4.67402 −0.189090
\(612\) −17.9116 −0.724035
\(613\) 5.51999 0.222950 0.111475 0.993767i \(-0.464442\pi\)
0.111475 + 0.993767i \(0.464442\pi\)
\(614\) −24.9398 −1.00649
\(615\) −5.55781 −0.224112
\(616\) 2.35227 0.0947757
\(617\) 22.7823 0.917182 0.458591 0.888647i \(-0.348354\pi\)
0.458591 + 0.888647i \(0.348354\pi\)
\(618\) −4.05944 −0.163295
\(619\) −10.6879 −0.429584 −0.214792 0.976660i \(-0.568907\pi\)
−0.214792 + 0.976660i \(0.568907\pi\)
\(620\) 22.1740 0.890529
\(621\) −3.67296 −0.147391
\(622\) 15.9458 0.639369
\(623\) −7.29546 −0.292286
\(624\) −0.282361 −0.0113035
\(625\) 94.3507 3.77403
\(626\) −12.7203 −0.508404
\(627\) 0 0
\(628\) −3.45190 −0.137746
\(629\) −66.3323 −2.64484
\(630\) −12.4388 −0.495574
\(631\) −20.5069 −0.816366 −0.408183 0.912900i \(-0.633838\pi\)
−0.408183 + 0.912900i \(0.633838\pi\)
\(632\) 7.04727 0.280325
\(633\) −1.40908 −0.0560060
\(634\) 32.9091 1.30699
\(635\) 26.9493 1.06945
\(636\) 0.396912 0.0157386
\(637\) 0.801544 0.0317583
\(638\) −13.7167 −0.543050
\(639\) 40.2702 1.59307
\(640\) 4.32518 0.170968
\(641\) −22.3016 −0.880862 −0.440431 0.897787i \(-0.645174\pi\)
−0.440431 + 0.897787i \(0.645174\pi\)
\(642\) 5.63819 0.222521
\(643\) −2.79200 −0.110106 −0.0550529 0.998483i \(-0.517533\pi\)
−0.0550529 + 0.998483i \(0.517533\pi\)
\(644\) −1.77445 −0.0699232
\(645\) −1.33056 −0.0523906
\(646\) 0 0
\(647\) −5.69144 −0.223754 −0.111877 0.993722i \(-0.535686\pi\)
−0.111877 + 0.993722i \(0.535686\pi\)
\(648\) 7.89855 0.310284
\(649\) 33.4048 1.31125
\(650\) 10.9869 0.430942
\(651\) −1.80600 −0.0707825
\(652\) 8.65990 0.339148
\(653\) 0.485267 0.0189900 0.00949499 0.999955i \(-0.496978\pi\)
0.00949499 + 0.999955i \(0.496978\pi\)
\(654\) −2.55056 −0.0997349
\(655\) −15.8530 −0.619427
\(656\) 3.64773 0.142420
\(657\) 26.5469 1.03569
\(658\) −5.83126 −0.227326
\(659\) 17.8023 0.693481 0.346741 0.937961i \(-0.387288\pi\)
0.346741 + 0.937961i \(0.387288\pi\)
\(660\) −3.58400 −0.139507
\(661\) −19.8793 −0.773217 −0.386608 0.922244i \(-0.626353\pi\)
−0.386608 + 0.922244i \(0.626353\pi\)
\(662\) 19.0079 0.738762
\(663\) −1.75859 −0.0682981
\(664\) 15.5560 0.603689
\(665\) 0 0
\(666\) 30.6294 1.18687
\(667\) 10.3473 0.400649
\(668\) 6.05944 0.234447
\(669\) −4.31653 −0.166887
\(670\) −19.8113 −0.765375
\(671\) −6.40309 −0.247189
\(672\) −0.352271 −0.0135891
\(673\) 23.8339 0.918729 0.459365 0.888248i \(-0.348077\pi\)
0.459365 + 0.888248i \(0.348077\pi\)
\(674\) −28.1914 −1.08589
\(675\) 28.3726 1.09206
\(676\) −12.3575 −0.475289
\(677\) 24.7893 0.952728 0.476364 0.879248i \(-0.341954\pi\)
0.476364 + 0.879248i \(0.341954\pi\)
\(678\) 0.520081 0.0199736
\(679\) −3.05681 −0.117310
\(680\) 26.9380 1.03302
\(681\) −8.22661 −0.315244
\(682\) 12.0594 0.461780
\(683\) 39.3592 1.50604 0.753020 0.657998i \(-0.228597\pi\)
0.753020 + 0.657998i \(0.228597\pi\)
\(684\) 0 0
\(685\) 14.6922 0.561362
\(686\) 1.00000 0.0381802
\(687\) 9.11782 0.347867
\(688\) 0.873277 0.0332934
\(689\) −0.903118 −0.0344061
\(690\) 2.70362 0.102925
\(691\) 27.8226 1.05842 0.529211 0.848490i \(-0.322488\pi\)
0.529211 + 0.848490i \(0.322488\pi\)
\(692\) −15.6259 −0.594007
\(693\) −6.76491 −0.256978
\(694\) 22.7292 0.862787
\(695\) −22.4764 −0.852577
\(696\) 2.05418 0.0778637
\(697\) 22.7187 0.860532
\(698\) −4.72981 −0.179026
\(699\) 0.916992 0.0346838
\(700\) 13.7072 0.518082
\(701\) −37.5332 −1.41761 −0.708805 0.705404i \(-0.750765\pi\)
−0.708805 + 0.705404i \(0.750765\pi\)
\(702\) 1.65912 0.0626196
\(703\) 0 0
\(704\) 2.35227 0.0886545
\(705\) 8.88472 0.334618
\(706\) −5.76135 −0.216831
\(707\) 1.52363 0.0573022
\(708\) −5.00263 −0.188010
\(709\) 11.3802 0.427391 0.213696 0.976900i \(-0.431450\pi\)
0.213696 + 0.976900i \(0.431450\pi\)
\(710\) −60.5639 −2.27292
\(711\) −20.2673 −0.760082
\(712\) −7.29546 −0.273409
\(713\) −9.09712 −0.340690
\(714\) −2.19400 −0.0821086
\(715\) 8.15490 0.304976
\(716\) −11.3995 −0.426021
\(717\) 8.20019 0.306242
\(718\) −19.9511 −0.744567
\(719\) −40.3218 −1.50375 −0.751874 0.659306i \(-0.770850\pi\)
−0.751874 + 0.659306i \(0.770850\pi\)
\(720\) −12.4388 −0.463567
\(721\) 11.5236 0.429163
\(722\) 0 0
\(723\) −3.15042 −0.117166
\(724\) −3.27791 −0.121823
\(725\) −79.9301 −2.96853
\(726\) 1.92580 0.0714732
\(727\) 1.55781 0.0577758 0.0288879 0.999583i \(-0.490803\pi\)
0.0288879 + 0.999583i \(0.490803\pi\)
\(728\) 0.801544 0.0297072
\(729\) −20.5280 −0.760295
\(730\) −39.9249 −1.47769
\(731\) 5.43892 0.201166
\(732\) 0.958913 0.0354424
\(733\) −22.7825 −0.841489 −0.420745 0.907179i \(-0.638231\pi\)
−0.420745 + 0.907179i \(0.638231\pi\)
\(734\) −1.24035 −0.0457821
\(735\) −1.52363 −0.0562001
\(736\) −1.77445 −0.0654072
\(737\) −10.7745 −0.396882
\(738\) −10.4905 −0.386162
\(739\) −2.64081 −0.0971439 −0.0485719 0.998820i \(-0.515467\pi\)
−0.0485719 + 0.998820i \(0.515467\pi\)
\(740\) −46.0647 −1.69337
\(741\) 0 0
\(742\) −1.12672 −0.0413633
\(743\) 18.7955 0.689541 0.344770 0.938687i \(-0.387957\pi\)
0.344770 + 0.938687i \(0.387957\pi\)
\(744\) −1.80600 −0.0662110
\(745\) 63.3654 2.32153
\(746\) −24.8733 −0.910675
\(747\) −44.7375 −1.63686
\(748\) 14.6504 0.535670
\(749\) −16.0053 −0.584819
\(750\) −13.2665 −0.484426
\(751\) 42.6889 1.55774 0.778869 0.627186i \(-0.215794\pi\)
0.778869 + 0.627186i \(0.215794\pi\)
\(752\) −5.83126 −0.212644
\(753\) −9.64773 −0.351583
\(754\) −4.67402 −0.170218
\(755\) −23.6450 −0.860529
\(756\) 2.06991 0.0752819
\(757\) 43.8374 1.59330 0.796650 0.604441i \(-0.206604\pi\)
0.796650 + 0.604441i \(0.206604\pi\)
\(758\) −32.4274 −1.17782
\(759\) 1.47038 0.0533713
\(760\) 0 0
\(761\) 5.22462 0.189392 0.0946962 0.995506i \(-0.469812\pi\)
0.0946962 + 0.995506i \(0.469812\pi\)
\(762\) −2.19493 −0.0795140
\(763\) 7.24035 0.262118
\(764\) −3.23865 −0.117170
\(765\) −77.4711 −2.80097
\(766\) 14.5105 0.524287
\(767\) 11.3828 0.411009
\(768\) −0.352271 −0.0127115
\(769\) −32.9678 −1.18885 −0.594425 0.804151i \(-0.702620\pi\)
−0.594425 + 0.804151i \(0.702620\pi\)
\(770\) 10.1740 0.366645
\(771\) 2.99152 0.107737
\(772\) −12.0568 −0.433934
\(773\) −43.6906 −1.57144 −0.785721 0.618582i \(-0.787708\pi\)
−0.785721 + 0.618582i \(0.787708\pi\)
\(774\) −2.51146 −0.0902727
\(775\) 70.2729 2.52428
\(776\) −3.05681 −0.109733
\(777\) 3.75181 0.134595
\(778\) 25.5236 0.915067
\(779\) 0 0
\(780\) −1.22126 −0.0437281
\(781\) −32.9380 −1.17861
\(782\) −11.0516 −0.395204
\(783\) −12.0702 −0.431354
\(784\) 1.00000 0.0357143
\(785\) −14.9301 −0.532878
\(786\) 1.29117 0.0460545
\(787\) −26.7431 −0.953288 −0.476644 0.879097i \(-0.658147\pi\)
−0.476644 + 0.879097i \(0.658147\pi\)
\(788\) −20.9380 −0.745884
\(789\) 2.02527 0.0721015
\(790\) 30.4807 1.08445
\(791\) −1.47637 −0.0524935
\(792\) −6.76491 −0.240381
\(793\) −2.18188 −0.0774807
\(794\) 11.6373 0.412991
\(795\) 1.71671 0.0608856
\(796\) 9.12672 0.323488
\(797\) −7.16861 −0.253925 −0.126963 0.991907i \(-0.540523\pi\)
−0.126963 + 0.991907i \(0.540523\pi\)
\(798\) 0 0
\(799\) −36.3181 −1.28484
\(800\) 13.7072 0.484622
\(801\) 20.9810 0.741329
\(802\) 25.1740 0.888925
\(803\) −21.7134 −0.766248
\(804\) 1.61356 0.0569058
\(805\) −7.67482 −0.270502
\(806\) 4.10929 0.144744
\(807\) −2.96689 −0.104439
\(808\) 1.52363 0.0536013
\(809\) 1.58109 0.0555881 0.0277941 0.999614i \(-0.491152\pi\)
0.0277941 + 0.999614i \(0.491152\pi\)
\(810\) 34.1626 1.20035
\(811\) −1.41001 −0.0495121 −0.0247561 0.999694i \(-0.507881\pi\)
−0.0247561 + 0.999694i \(0.507881\pi\)
\(812\) −5.83126 −0.204637
\(813\) −7.30251 −0.256110
\(814\) −25.0525 −0.878091
\(815\) 37.4556 1.31201
\(816\) −2.19400 −0.0768055
\(817\) 0 0
\(818\) −31.6277 −1.10584
\(819\) −2.30517 −0.0805490
\(820\) 15.7771 0.550960
\(821\) −33.2114 −1.15909 −0.579543 0.814941i \(-0.696769\pi\)
−0.579543 + 0.814941i \(0.696769\pi\)
\(822\) −1.19663 −0.0417374
\(823\) −47.1198 −1.64249 −0.821247 0.570572i \(-0.806721\pi\)
−0.821247 + 0.570572i \(0.806721\pi\)
\(824\) 11.5236 0.401445
\(825\) −11.3583 −0.395444
\(826\) 14.2011 0.494119
\(827\) −16.1284 −0.560840 −0.280420 0.959877i \(-0.590474\pi\)
−0.280420 + 0.959877i \(0.590474\pi\)
\(828\) 5.10316 0.177347
\(829\) −46.9266 −1.62983 −0.814914 0.579582i \(-0.803216\pi\)
−0.814914 + 0.579582i \(0.803216\pi\)
\(830\) 67.2824 2.33541
\(831\) −6.14508 −0.213170
\(832\) 0.801544 0.0277885
\(833\) 6.22818 0.215794
\(834\) 1.83062 0.0633893
\(835\) 26.2082 0.906971
\(836\) 0 0
\(837\) 10.6119 0.366799
\(838\) −19.9205 −0.688144
\(839\) 8.19400 0.282888 0.141444 0.989946i \(-0.454825\pi\)
0.141444 + 0.989946i \(0.454825\pi\)
\(840\) −1.52363 −0.0525704
\(841\) 5.00365 0.172540
\(842\) −14.4274 −0.497202
\(843\) 0.748257 0.0257713
\(844\) 4.00000 0.137686
\(845\) −53.4485 −1.83868
\(846\) 16.7702 0.576570
\(847\) −5.46682 −0.187842
\(848\) −1.12672 −0.0386918
\(849\) 9.74720 0.334523
\(850\) 85.3707 2.92819
\(851\) 18.8985 0.647834
\(852\) 4.93272 0.168992
\(853\) −16.7791 −0.574504 −0.287252 0.957855i \(-0.592742\pi\)
−0.287252 + 0.957855i \(0.592742\pi\)
\(854\) −2.72209 −0.0931480
\(855\) 0 0
\(856\) −16.0053 −0.547048
\(857\) 9.47899 0.323796 0.161898 0.986807i \(-0.448238\pi\)
0.161898 + 0.986807i \(0.448238\pi\)
\(858\) −0.664189 −0.0226750
\(859\) −5.59354 −0.190849 −0.0954246 0.995437i \(-0.530421\pi\)
−0.0954246 + 0.995437i \(0.530421\pi\)
\(860\) 3.77708 0.128797
\(861\) −1.28499 −0.0437923
\(862\) 14.6504 0.498993
\(863\) 46.1241 1.57008 0.785042 0.619443i \(-0.212641\pi\)
0.785042 + 0.619443i \(0.212641\pi\)
\(864\) 2.06991 0.0704198
\(865\) −67.5848 −2.29795
\(866\) 18.0043 0.611812
\(867\) −7.67604 −0.260692
\(868\) 5.12672 0.174012
\(869\) 16.5771 0.562339
\(870\) 8.88472 0.301220
\(871\) −3.67143 −0.124402
\(872\) 7.24035 0.245189
\(873\) 8.79110 0.297534
\(874\) 0 0
\(875\) 37.6601 1.27314
\(876\) 3.25174 0.109866
\(877\) −16.7982 −0.567233 −0.283617 0.958938i \(-0.591534\pi\)
−0.283617 + 0.958938i \(0.591534\pi\)
\(878\) 21.6336 0.730099
\(879\) −4.66147 −0.157227
\(880\) 10.1740 0.342965
\(881\) −29.9153 −1.00787 −0.503937 0.863741i \(-0.668115\pi\)
−0.503937 + 0.863741i \(0.668115\pi\)
\(882\) −2.87591 −0.0968368
\(883\) −26.9284 −0.906214 −0.453107 0.891456i \(-0.649684\pi\)
−0.453107 + 0.891456i \(0.649684\pi\)
\(884\) 4.99216 0.167904
\(885\) −21.6373 −0.727329
\(886\) −3.45465 −0.116061
\(887\) −24.6907 −0.829033 −0.414516 0.910042i \(-0.636049\pi\)
−0.414516 + 0.910042i \(0.636049\pi\)
\(888\) 3.75181 0.125903
\(889\) 6.23080 0.208974
\(890\) −31.5542 −1.05770
\(891\) 18.5795 0.622437
\(892\) 12.2534 0.410276
\(893\) 0 0
\(894\) −5.16089 −0.172606
\(895\) −49.3050 −1.64809
\(896\) 1.00000 0.0334077
\(897\) 0.501035 0.0167291
\(898\) 19.5069 0.650953
\(899\) −29.8953 −0.997063
\(900\) −39.4205 −1.31402
\(901\) −7.01743 −0.233784
\(902\) 8.58045 0.285698
\(903\) −0.307630 −0.0102373
\(904\) −1.47637 −0.0491032
\(905\) −14.1775 −0.471278
\(906\) 1.92580 0.0639805
\(907\) 36.1383 1.19995 0.599975 0.800018i \(-0.295177\pi\)
0.599975 + 0.800018i \(0.295177\pi\)
\(908\) 23.3531 0.774999
\(909\) −4.38183 −0.145336
\(910\) 3.46682 0.114924
\(911\) 41.0210 1.35909 0.679543 0.733636i \(-0.262178\pi\)
0.679543 + 0.733636i \(0.262178\pi\)
\(912\) 0 0
\(913\) 36.5919 1.21101
\(914\) −13.2876 −0.439515
\(915\) 4.14747 0.137111
\(916\) −25.8830 −0.855198
\(917\) −3.66528 −0.121038
\(918\) 12.8918 0.425492
\(919\) −19.4521 −0.641664 −0.320832 0.947136i \(-0.603963\pi\)
−0.320832 + 0.947136i \(0.603963\pi\)
\(920\) −7.67482 −0.253031
\(921\) 8.78556 0.289494
\(922\) 16.1915 0.533240
\(923\) −11.2237 −0.369433
\(924\) −0.828636 −0.0272601
\(925\) −145.986 −4.80000
\(926\) 21.5010 0.706566
\(927\) −33.1409 −1.08849
\(928\) −5.83126 −0.191421
\(929\) 8.86009 0.290690 0.145345 0.989381i \(-0.453571\pi\)
0.145345 + 0.989381i \(0.453571\pi\)
\(930\) −7.81125 −0.256141
\(931\) 0 0
\(932\) −2.60309 −0.0852670
\(933\) −5.61725 −0.183900
\(934\) −7.95536 −0.260307
\(935\) 63.3654 2.07227
\(936\) −2.30517 −0.0753467
\(937\) −35.7413 −1.16762 −0.583809 0.811891i \(-0.698438\pi\)
−0.583809 + 0.811891i \(0.698438\pi\)
\(938\) −4.58045 −0.149557
\(939\) 4.48098 0.146231
\(940\) −25.2213 −0.822627
\(941\) −40.6128 −1.32394 −0.661970 0.749531i \(-0.730279\pi\)
−0.661970 + 0.749531i \(0.730279\pi\)
\(942\) 1.21600 0.0396196
\(943\) −6.47272 −0.210781
\(944\) 14.2011 0.462206
\(945\) 8.95273 0.291232
\(946\) 2.05418 0.0667873
\(947\) −41.3845 −1.34482 −0.672408 0.740181i \(-0.734740\pi\)
−0.672408 + 0.740181i \(0.734740\pi\)
\(948\) −2.48255 −0.0806294
\(949\) −7.39890 −0.240178
\(950\) 0 0
\(951\) −11.5929 −0.375926
\(952\) 6.22818 0.201856
\(953\) 5.45100 0.176575 0.0882877 0.996095i \(-0.471861\pi\)
0.0882877 + 0.996095i \(0.471861\pi\)
\(954\) 3.24035 0.104910
\(955\) −14.0077 −0.453279
\(956\) −23.2781 −0.752867
\(957\) 4.83200 0.156196
\(958\) −26.6356 −0.860557
\(959\) 3.39691 0.109692
\(960\) −1.52363 −0.0491751
\(961\) −4.71671 −0.152152
\(962\) −8.53673 −0.275235
\(963\) 46.0296 1.48328
\(964\) 8.94319 0.288041
\(965\) −52.1479 −1.67870
\(966\) 0.625088 0.0201119
\(967\) 1.62573 0.0522799 0.0261400 0.999658i \(-0.491678\pi\)
0.0261400 + 0.999658i \(0.491678\pi\)
\(968\) −5.46682 −0.175710
\(969\) 0 0
\(970\) −13.2213 −0.424509
\(971\) −35.1634 −1.12845 −0.564224 0.825622i \(-0.690824\pi\)
−0.564224 + 0.825622i \(0.690824\pi\)
\(972\) −8.99216 −0.288424
\(973\) −5.19663 −0.166596
\(974\) −5.34964 −0.171414
\(975\) −3.87037 −0.123951
\(976\) −2.72209 −0.0871320
\(977\) 37.2289 1.19106 0.595528 0.803334i \(-0.296943\pi\)
0.595528 + 0.803334i \(0.296943\pi\)
\(978\) −3.05063 −0.0975484
\(979\) −17.1609 −0.548465
\(980\) 4.32518 0.138163
\(981\) −20.8226 −0.664813
\(982\) 0.456352 0.0145628
\(983\) 1.29546 0.0413187 0.0206594 0.999787i \(-0.493423\pi\)
0.0206594 + 0.999787i \(0.493423\pi\)
\(984\) −1.28499 −0.0409639
\(985\) −90.5605 −2.88550
\(986\) −36.3181 −1.15661
\(987\) 2.05418 0.0653854
\(988\) 0 0
\(989\) −1.54959 −0.0492740
\(990\) −29.2594 −0.929926
\(991\) −13.7843 −0.437872 −0.218936 0.975739i \(-0.570259\pi\)
−0.218936 + 0.975739i \(0.570259\pi\)
\(992\) 5.12672 0.162774
\(993\) −6.69592 −0.212489
\(994\) −14.0026 −0.444136
\(995\) 39.4747 1.25143
\(996\) −5.47992 −0.173638
\(997\) −0.857580 −0.0271598 −0.0135799 0.999908i \(-0.504323\pi\)
−0.0135799 + 0.999908i \(0.504323\pi\)
\(998\) −5.99046 −0.189625
\(999\) −22.0453 −0.697482
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 5054.2.a.x.1.2 4
19.8 odd 6 266.2.f.d.197.2 8
19.12 odd 6 266.2.f.d.239.2 yes 8
19.18 odd 2 5054.2.a.w.1.3 4
57.8 even 6 2394.2.o.v.1261.4 8
57.50 even 6 2394.2.o.v.505.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
266.2.f.d.197.2 8 19.8 odd 6
266.2.f.d.239.2 yes 8 19.12 odd 6
2394.2.o.v.505.4 8 57.50 even 6
2394.2.o.v.1261.4 8 57.8 even 6
5054.2.a.w.1.3 4 19.18 odd 2
5054.2.a.x.1.2 4 1.1 even 1 trivial