Properties

Label 105.4.a.f.1.1
Level $105$
Weight $4$
Character 105.1
Self dual yes
Analytic conductor $6.195$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{65}) \)
Defining polynomial: \( x^{2} - x - 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.53113\) of defining polynomial
Character \(\chi\) \(=\) 105.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.53113 q^{2} +3.00000 q^{3} +4.46887 q^{4} +5.00000 q^{5} -10.5934 q^{6} -7.00000 q^{7} +12.4689 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-3.53113 q^{2} +3.00000 q^{3} +4.46887 q^{4} +5.00000 q^{5} -10.5934 q^{6} -7.00000 q^{7} +12.4689 q^{8} +9.00000 q^{9} -17.6556 q^{10} -2.93774 q^{11} +13.4066 q^{12} -19.0623 q^{13} +24.7179 q^{14} +15.0000 q^{15} -79.7802 q^{16} +122.498 q^{17} -31.7802 q^{18} +107.436 q^{19} +22.3444 q^{20} -21.0000 q^{21} +10.3735 q^{22} +210.623 q^{23} +37.4066 q^{24} +25.0000 q^{25} +67.3113 q^{26} +27.0000 q^{27} -31.2821 q^{28} +95.4942 q^{29} -52.9669 q^{30} -94.3074 q^{31} +181.963 q^{32} -8.81323 q^{33} -432.556 q^{34} -35.0000 q^{35} +40.2198 q^{36} +97.1206 q^{37} -379.370 q^{38} -57.1868 q^{39} +62.3444 q^{40} -491.113 q^{41} +74.1537 q^{42} -43.0039 q^{43} -13.1284 q^{44} +45.0000 q^{45} -743.735 q^{46} +473.494 q^{47} -239.340 q^{48} +49.0000 q^{49} -88.2782 q^{50} +367.494 q^{51} -85.1868 q^{52} -183.677 q^{53} -95.3405 q^{54} -14.6887 q^{55} -87.2821 q^{56} +322.307 q^{57} -337.202 q^{58} -760.615 q^{59} +67.0331 q^{60} -198.747 q^{61} +333.012 q^{62} -63.0000 q^{63} -4.29373 q^{64} -95.3113 q^{65} +31.1206 q^{66} -309.992 q^{67} +547.428 q^{68} +631.868 q^{69} +123.590 q^{70} +665.693 q^{71} +112.220 q^{72} +621.288 q^{73} -342.945 q^{74} +75.0000 q^{75} +480.117 q^{76} +20.5642 q^{77} +201.934 q^{78} -24.7626 q^{79} -398.901 q^{80} +81.0000 q^{81} +1734.18 q^{82} -406.724 q^{83} -93.8463 q^{84} +612.490 q^{85} +151.852 q^{86} +286.483 q^{87} -36.6303 q^{88} +261.751 q^{89} -158.901 q^{90} +133.436 q^{91} +941.245 q^{92} -282.922 q^{93} -1671.97 q^{94} +537.179 q^{95} +545.889 q^{96} -1004.77 q^{97} -173.025 q^{98} -26.4397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 6 q^{3} + 17 q^{4} + 10 q^{5} + 3 q^{6} - 14 q^{7} + 33 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 6 q^{3} + 17 q^{4} + 10 q^{5} + 3 q^{6} - 14 q^{7} + 33 q^{8} + 18 q^{9} + 5 q^{10} - 22 q^{11} + 51 q^{12} - 22 q^{13} - 7 q^{14} + 30 q^{15} - 87 q^{16} + 116 q^{17} + 9 q^{18} + 102 q^{19} + 85 q^{20} - 42 q^{21} - 76 q^{22} + 260 q^{23} + 99 q^{24} + 50 q^{25} + 54 q^{26} + 54 q^{27} - 119 q^{28} - 196 q^{29} + 15 q^{30} + 150 q^{31} - 15 q^{32} - 66 q^{33} - 462 q^{34} - 70 q^{35} + 153 q^{36} - 96 q^{37} - 404 q^{38} - 66 q^{39} + 165 q^{40} - 176 q^{41} - 21 q^{42} - 344 q^{43} - 252 q^{44} + 90 q^{45} - 520 q^{46} + 560 q^{47} - 261 q^{48} + 98 q^{49} + 25 q^{50} + 348 q^{51} - 122 q^{52} + 326 q^{53} + 27 q^{54} - 110 q^{55} - 231 q^{56} + 306 q^{57} - 1658 q^{58} - 844 q^{59} + 255 q^{60} - 204 q^{61} + 1440 q^{62} - 126 q^{63} - 839 q^{64} - 110 q^{65} - 228 q^{66} - 104 q^{67} + 466 q^{68} + 780 q^{69} - 35 q^{70} + 1670 q^{71} + 297 q^{72} - 386 q^{73} - 1218 q^{74} + 150 q^{75} + 412 q^{76} + 154 q^{77} + 162 q^{78} - 888 q^{79} - 435 q^{80} + 162 q^{81} + 3162 q^{82} + 928 q^{83} - 357 q^{84} + 580 q^{85} - 1212 q^{86} - 588 q^{87} - 428 q^{88} + 588 q^{89} + 45 q^{90} + 154 q^{91} + 1560 q^{92} + 450 q^{93} - 1280 q^{94} + 510 q^{95} - 45 q^{96} + 522 q^{97} + 49 q^{98} - 198 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.53113 −1.24844 −0.624221 0.781248i \(-0.714584\pi\)
−0.624221 + 0.781248i \(0.714584\pi\)
\(3\) 3.00000 0.577350
\(4\) 4.46887 0.558609
\(5\) 5.00000 0.447214
\(6\) −10.5934 −0.720789
\(7\) −7.00000 −0.377964
\(8\) 12.4689 0.551051
\(9\) 9.00000 0.333333
\(10\) −17.6556 −0.558320
\(11\) −2.93774 −0.0805239 −0.0402619 0.999189i \(-0.512819\pi\)
−0.0402619 + 0.999189i \(0.512819\pi\)
\(12\) 13.4066 0.322513
\(13\) −19.0623 −0.406686 −0.203343 0.979108i \(-0.565181\pi\)
−0.203343 + 0.979108i \(0.565181\pi\)
\(14\) 24.7179 0.471867
\(15\) 15.0000 0.258199
\(16\) −79.7802 −1.24656
\(17\) 122.498 1.74766 0.873828 0.486236i \(-0.161630\pi\)
0.873828 + 0.486236i \(0.161630\pi\)
\(18\) −31.7802 −0.416148
\(19\) 107.436 1.29723 0.648617 0.761115i \(-0.275348\pi\)
0.648617 + 0.761115i \(0.275348\pi\)
\(20\) 22.3444 0.249817
\(21\) −21.0000 −0.218218
\(22\) 10.3735 0.100529
\(23\) 210.623 1.90947 0.954736 0.297455i \(-0.0961379\pi\)
0.954736 + 0.297455i \(0.0961379\pi\)
\(24\) 37.4066 0.318150
\(25\) 25.0000 0.200000
\(26\) 67.3113 0.507724
\(27\) 27.0000 0.192450
\(28\) −31.2821 −0.211134
\(29\) 95.4942 0.611477 0.305738 0.952116i \(-0.401097\pi\)
0.305738 + 0.952116i \(0.401097\pi\)
\(30\) −52.9669 −0.322346
\(31\) −94.3074 −0.546391 −0.273195 0.961959i \(-0.588081\pi\)
−0.273195 + 0.961959i \(0.588081\pi\)
\(32\) 181.963 1.00521
\(33\) −8.81323 −0.0464905
\(34\) −432.556 −2.18185
\(35\) −35.0000 −0.169031
\(36\) 40.2198 0.186203
\(37\) 97.1206 0.431528 0.215764 0.976446i \(-0.430776\pi\)
0.215764 + 0.976446i \(0.430776\pi\)
\(38\) −379.370 −1.61952
\(39\) −57.1868 −0.234800
\(40\) 62.3444 0.246438
\(41\) −491.113 −1.87071 −0.935353 0.353716i \(-0.884918\pi\)
−0.935353 + 0.353716i \(0.884918\pi\)
\(42\) 74.1537 0.272433
\(43\) −43.0039 −0.152512 −0.0762562 0.997088i \(-0.524297\pi\)
−0.0762562 + 0.997088i \(0.524297\pi\)
\(44\) −13.1284 −0.0449814
\(45\) 45.0000 0.149071
\(46\) −743.735 −2.38387
\(47\) 473.494 1.46949 0.734747 0.678341i \(-0.237301\pi\)
0.734747 + 0.678341i \(0.237301\pi\)
\(48\) −239.340 −0.719705
\(49\) 49.0000 0.142857
\(50\) −88.2782 −0.249689
\(51\) 367.494 1.00901
\(52\) −85.1868 −0.227178
\(53\) −183.677 −0.476038 −0.238019 0.971261i \(-0.576498\pi\)
−0.238019 + 0.971261i \(0.576498\pi\)
\(54\) −95.3405 −0.240263
\(55\) −14.6887 −0.0360114
\(56\) −87.2821 −0.208278
\(57\) 322.307 0.748959
\(58\) −337.202 −0.763394
\(59\) −760.615 −1.67837 −0.839183 0.543849i \(-0.816966\pi\)
−0.839183 + 0.543849i \(0.816966\pi\)
\(60\) 67.0331 0.144232
\(61\) −198.747 −0.417163 −0.208582 0.978005i \(-0.566885\pi\)
−0.208582 + 0.978005i \(0.566885\pi\)
\(62\) 333.012 0.682137
\(63\) −63.0000 −0.125988
\(64\) −4.29373 −0.00838618
\(65\) −95.3113 −0.181876
\(66\) 31.1206 0.0580407
\(67\) −309.992 −0.565247 −0.282624 0.959231i \(-0.591205\pi\)
−0.282624 + 0.959231i \(0.591205\pi\)
\(68\) 547.428 0.976256
\(69\) 631.868 1.10243
\(70\) 123.590 0.211025
\(71\) 665.693 1.11272 0.556360 0.830941i \(-0.312197\pi\)
0.556360 + 0.830941i \(0.312197\pi\)
\(72\) 112.220 0.183684
\(73\) 621.288 0.996113 0.498057 0.867145i \(-0.334047\pi\)
0.498057 + 0.867145i \(0.334047\pi\)
\(74\) −342.945 −0.538738
\(75\) 75.0000 0.115470
\(76\) 480.117 0.724647
\(77\) 20.5642 0.0304352
\(78\) 201.934 0.293135
\(79\) −24.7626 −0.0352659 −0.0176330 0.999845i \(-0.505613\pi\)
−0.0176330 + 0.999845i \(0.505613\pi\)
\(80\) −398.901 −0.557481
\(81\) 81.0000 0.111111
\(82\) 1734.18 2.33547
\(83\) −406.724 −0.537876 −0.268938 0.963157i \(-0.586673\pi\)
−0.268938 + 0.963157i \(0.586673\pi\)
\(84\) −93.8463 −0.121898
\(85\) 612.490 0.781575
\(86\) 151.852 0.190403
\(87\) 286.483 0.353036
\(88\) −36.6303 −0.0443728
\(89\) 261.751 0.311748 0.155874 0.987777i \(-0.450181\pi\)
0.155874 + 0.987777i \(0.450181\pi\)
\(90\) −158.901 −0.186107
\(91\) 133.436 0.153713
\(92\) 941.245 1.06665
\(93\) −282.922 −0.315459
\(94\) −1671.97 −1.83458
\(95\) 537.179 0.580141
\(96\) 545.889 0.580360
\(97\) −1004.77 −1.05175 −0.525873 0.850563i \(-0.676261\pi\)
−0.525873 + 0.850563i \(0.676261\pi\)
\(98\) −173.025 −0.178349
\(99\) −26.4397 −0.0268413
\(100\) 111.722 0.111722
\(101\) −128.872 −0.126962 −0.0634812 0.997983i \(-0.520220\pi\)
−0.0634812 + 0.997983i \(0.520220\pi\)
\(102\) −1297.67 −1.25969
\(103\) 806.008 0.771051 0.385526 0.922697i \(-0.374020\pi\)
0.385526 + 0.922697i \(0.374020\pi\)
\(104\) −237.685 −0.224105
\(105\) −105.000 −0.0975900
\(106\) 648.587 0.594305
\(107\) −769.712 −0.695429 −0.347714 0.937600i \(-0.613042\pi\)
−0.347714 + 0.937600i \(0.613042\pi\)
\(108\) 120.660 0.107504
\(109\) −780.856 −0.686169 −0.343085 0.939304i \(-0.611472\pi\)
−0.343085 + 0.939304i \(0.611472\pi\)
\(110\) 51.8677 0.0449581
\(111\) 291.362 0.249143
\(112\) 558.461 0.471157
\(113\) −1115.65 −0.928771 −0.464386 0.885633i \(-0.653725\pi\)
−0.464386 + 0.885633i \(0.653725\pi\)
\(114\) −1138.11 −0.935032
\(115\) 1053.11 0.853942
\(116\) 426.751 0.341576
\(117\) −171.560 −0.135562
\(118\) 2685.83 2.09534
\(119\) −857.486 −0.660552
\(120\) 187.033 0.142281
\(121\) −1322.37 −0.993516
\(122\) 701.802 0.520804
\(123\) −1473.34 −1.08005
\(124\) −421.448 −0.305219
\(125\) 125.000 0.0894427
\(126\) 222.461 0.157289
\(127\) −1875.98 −1.31076 −0.655381 0.755299i \(-0.727492\pi\)
−0.655381 + 0.755299i \(0.727492\pi\)
\(128\) −1440.54 −0.994744
\(129\) −129.012 −0.0880530
\(130\) 336.556 0.227061
\(131\) 364.203 0.242905 0.121452 0.992597i \(-0.461245\pi\)
0.121452 + 0.992597i \(0.461245\pi\)
\(132\) −39.3852 −0.0259700
\(133\) −752.051 −0.490309
\(134\) 1094.62 0.705679
\(135\) 135.000 0.0860663
\(136\) 1527.41 0.963048
\(137\) 1603.13 0.999743 0.499872 0.866099i \(-0.333380\pi\)
0.499872 + 0.866099i \(0.333380\pi\)
\(138\) −2231.21 −1.37633
\(139\) 2431.12 1.48349 0.741746 0.670681i \(-0.233998\pi\)
0.741746 + 0.670681i \(0.233998\pi\)
\(140\) −156.410 −0.0944221
\(141\) 1420.48 0.848413
\(142\) −2350.65 −1.38917
\(143\) 56.0000 0.0327479
\(144\) −718.021 −0.415522
\(145\) 477.471 0.273461
\(146\) −2193.85 −1.24359
\(147\) 147.000 0.0824786
\(148\) 434.020 0.241055
\(149\) 2341.57 1.28744 0.643722 0.765260i \(-0.277389\pi\)
0.643722 + 0.765260i \(0.277389\pi\)
\(150\) −264.835 −0.144158
\(151\) −2104.07 −1.13395 −0.566976 0.823734i \(-0.691887\pi\)
−0.566976 + 0.823734i \(0.691887\pi\)
\(152\) 1339.60 0.714843
\(153\) 1102.48 0.582552
\(154\) −72.6148 −0.0379966
\(155\) −471.537 −0.244353
\(156\) −255.560 −0.131162
\(157\) −593.467 −0.301680 −0.150840 0.988558i \(-0.548198\pi\)
−0.150840 + 0.988558i \(0.548198\pi\)
\(158\) 87.4399 0.0440275
\(159\) −551.031 −0.274840
\(160\) 909.815 0.449545
\(161\) −1474.36 −0.721712
\(162\) −286.021 −0.138716
\(163\) 2178.71 1.04693 0.523465 0.852047i \(-0.324639\pi\)
0.523465 + 0.852047i \(0.324639\pi\)
\(164\) −2194.72 −1.04499
\(165\) −44.0661 −0.0207912
\(166\) 1436.19 0.671508
\(167\) 799.502 0.370463 0.185231 0.982695i \(-0.440697\pi\)
0.185231 + 0.982695i \(0.440697\pi\)
\(168\) −261.846 −0.120249
\(169\) −1833.63 −0.834606
\(170\) −2162.78 −0.975752
\(171\) 966.922 0.432412
\(172\) −192.179 −0.0851947
\(173\) −1444.36 −0.634754 −0.317377 0.948299i \(-0.602802\pi\)
−0.317377 + 0.948299i \(0.602802\pi\)
\(174\) −1011.61 −0.440745
\(175\) −175.000 −0.0755929
\(176\) 234.374 0.100378
\(177\) −2281.84 −0.969005
\(178\) −924.276 −0.389199
\(179\) 3343.49 1.39611 0.698056 0.716043i \(-0.254048\pi\)
0.698056 + 0.716043i \(0.254048\pi\)
\(180\) 201.099 0.0832725
\(181\) 2251.81 0.924729 0.462365 0.886690i \(-0.347001\pi\)
0.462365 + 0.886690i \(0.347001\pi\)
\(182\) −471.179 −0.191902
\(183\) −596.241 −0.240849
\(184\) 2626.23 1.05222
\(185\) 485.603 0.192985
\(186\) 999.035 0.393832
\(187\) −359.868 −0.140728
\(188\) 2115.98 0.820873
\(189\) −189.000 −0.0727393
\(190\) −1896.85 −0.724273
\(191\) −1001.93 −0.379565 −0.189782 0.981826i \(-0.560778\pi\)
−0.189782 + 0.981826i \(0.560778\pi\)
\(192\) −12.8812 −0.00484177
\(193\) −4054.97 −1.51235 −0.756173 0.654372i \(-0.772933\pi\)
−0.756173 + 0.654372i \(0.772933\pi\)
\(194\) 3547.99 1.31304
\(195\) −285.934 −0.105006
\(196\) 218.975 0.0798013
\(197\) −5140.23 −1.85902 −0.929508 0.368802i \(-0.879768\pi\)
−0.929508 + 0.368802i \(0.879768\pi\)
\(198\) 93.3619 0.0335098
\(199\) 585.631 0.208614 0.104307 0.994545i \(-0.466737\pi\)
0.104307 + 0.994545i \(0.466737\pi\)
\(200\) 311.722 0.110210
\(201\) −929.977 −0.326346
\(202\) 455.062 0.158505
\(203\) −668.459 −0.231116
\(204\) 1642.28 0.563642
\(205\) −2455.56 −0.836605
\(206\) −2846.12 −0.962614
\(207\) 1895.60 0.636490
\(208\) 1520.79 0.506961
\(209\) −315.619 −0.104458
\(210\) 370.769 0.121836
\(211\) −1055.16 −0.344266 −0.172133 0.985074i \(-0.555066\pi\)
−0.172133 + 0.985074i \(0.555066\pi\)
\(212\) −820.829 −0.265919
\(213\) 1997.08 0.642430
\(214\) 2717.95 0.868203
\(215\) −215.019 −0.0682056
\(216\) 336.660 0.106050
\(217\) 660.152 0.206516
\(218\) 2757.30 0.856643
\(219\) 1863.86 0.575106
\(220\) −65.6420 −0.0201163
\(221\) −2335.09 −0.710747
\(222\) −1028.84 −0.311040
\(223\) 4675.85 1.40412 0.702059 0.712119i \(-0.252264\pi\)
0.702059 + 0.712119i \(0.252264\pi\)
\(224\) −1273.74 −0.379935
\(225\) 225.000 0.0666667
\(226\) 3939.49 1.15952
\(227\) 5443.11 1.59151 0.795754 0.605621i \(-0.207075\pi\)
0.795754 + 0.605621i \(0.207075\pi\)
\(228\) 1440.35 0.418375
\(229\) −536.303 −0.154759 −0.0773797 0.997002i \(-0.524655\pi\)
−0.0773797 + 0.997002i \(0.524655\pi\)
\(230\) −3718.68 −1.06610
\(231\) 61.6926 0.0175717
\(232\) 1190.70 0.336955
\(233\) −183.490 −0.0515916 −0.0257958 0.999667i \(-0.508212\pi\)
−0.0257958 + 0.999667i \(0.508212\pi\)
\(234\) 605.802 0.169241
\(235\) 2367.47 0.657178
\(236\) −3399.09 −0.937550
\(237\) −74.2878 −0.0203608
\(238\) 3027.90 0.824661
\(239\) 643.218 0.174085 0.0870425 0.996205i \(-0.472258\pi\)
0.0870425 + 0.996205i \(0.472258\pi\)
\(240\) −1196.70 −0.321862
\(241\) −5755.61 −1.53839 −0.769194 0.639015i \(-0.779342\pi\)
−0.769194 + 0.639015i \(0.779342\pi\)
\(242\) 4669.46 1.24035
\(243\) 243.000 0.0641500
\(244\) −888.175 −0.233031
\(245\) 245.000 0.0638877
\(246\) 5202.55 1.34838
\(247\) −2047.97 −0.527567
\(248\) −1175.91 −0.301089
\(249\) −1220.17 −0.310543
\(250\) −441.391 −0.111664
\(251\) −5132.27 −1.29062 −0.645311 0.763920i \(-0.723272\pi\)
−0.645311 + 0.763920i \(0.723272\pi\)
\(252\) −281.539 −0.0703781
\(253\) −618.755 −0.153758
\(254\) 6624.34 1.63641
\(255\) 1837.47 0.451243
\(256\) 5121.09 1.25027
\(257\) 5041.74 1.22372 0.611859 0.790967i \(-0.290422\pi\)
0.611859 + 0.790967i \(0.290422\pi\)
\(258\) 455.557 0.109929
\(259\) −679.844 −0.163102
\(260\) −425.934 −0.101597
\(261\) 859.448 0.203826
\(262\) −1286.05 −0.303253
\(263\) 7577.00 1.77649 0.888246 0.459367i \(-0.151924\pi\)
0.888246 + 0.459367i \(0.151924\pi\)
\(264\) −109.891 −0.0256186
\(265\) −918.385 −0.212890
\(266\) 2655.59 0.612122
\(267\) 785.253 0.179988
\(268\) −1385.32 −0.315752
\(269\) 1023.10 0.231893 0.115947 0.993255i \(-0.463010\pi\)
0.115947 + 0.993255i \(0.463010\pi\)
\(270\) −476.702 −0.107449
\(271\) −2251.98 −0.504790 −0.252395 0.967624i \(-0.581218\pi\)
−0.252395 + 0.967624i \(0.581218\pi\)
\(272\) −9772.91 −2.17857
\(273\) 400.307 0.0887462
\(274\) −5660.87 −1.24812
\(275\) −73.4436 −0.0161048
\(276\) 2823.74 0.615829
\(277\) −8630.72 −1.87209 −0.936047 0.351875i \(-0.885544\pi\)
−0.936047 + 0.351875i \(0.885544\pi\)
\(278\) −8584.61 −1.85205
\(279\) −848.767 −0.182130
\(280\) −436.410 −0.0931447
\(281\) −7521.62 −1.59680 −0.798402 0.602124i \(-0.794321\pi\)
−0.798402 + 0.602124i \(0.794321\pi\)
\(282\) −5015.91 −1.05919
\(283\) 14.8169 0.00311226 0.00155613 0.999999i \(-0.499505\pi\)
0.00155613 + 0.999999i \(0.499505\pi\)
\(284\) 2974.89 0.621576
\(285\) 1611.54 0.334945
\(286\) −197.743 −0.0408839
\(287\) 3437.79 0.707060
\(288\) 1637.67 0.335071
\(289\) 10092.8 2.05430
\(290\) −1686.01 −0.341400
\(291\) −3014.32 −0.607226
\(292\) 2776.46 0.556438
\(293\) 6913.39 1.37844 0.689222 0.724550i \(-0.257952\pi\)
0.689222 + 0.724550i \(0.257952\pi\)
\(294\) −519.076 −0.102970
\(295\) −3803.07 −0.750588
\(296\) 1210.98 0.237794
\(297\) −79.3190 −0.0154968
\(298\) −8268.39 −1.60730
\(299\) −4014.94 −0.776555
\(300\) 335.165 0.0645026
\(301\) 301.027 0.0576442
\(302\) 7429.74 1.41567
\(303\) −386.615 −0.0733018
\(304\) −8571.25 −1.61709
\(305\) −993.735 −0.186561
\(306\) −3893.01 −0.727283
\(307\) −7644.12 −1.42108 −0.710542 0.703655i \(-0.751550\pi\)
−0.710542 + 0.703655i \(0.751550\pi\)
\(308\) 91.8987 0.0170014
\(309\) 2418.02 0.445167
\(310\) 1665.06 0.305061
\(311\) 7593.99 1.38462 0.692308 0.721602i \(-0.256594\pi\)
0.692308 + 0.721602i \(0.256594\pi\)
\(312\) −713.055 −0.129387
\(313\) −9127.84 −1.64836 −0.824179 0.566329i \(-0.808363\pi\)
−0.824179 + 0.566329i \(0.808363\pi\)
\(314\) 2095.61 0.376631
\(315\) −315.000 −0.0563436
\(316\) −110.661 −0.0196999
\(317\) −4929.81 −0.873456 −0.436728 0.899593i \(-0.643863\pi\)
−0.436728 + 0.899593i \(0.643863\pi\)
\(318\) 1945.76 0.343122
\(319\) −280.537 −0.0492385
\(320\) −21.4686 −0.00375042
\(321\) −2309.14 −0.401506
\(322\) 5206.15 0.901016
\(323\) 13160.7 2.26712
\(324\) 361.979 0.0620677
\(325\) −476.556 −0.0813372
\(326\) −7693.30 −1.30703
\(327\) −2342.57 −0.396160
\(328\) −6123.62 −1.03086
\(329\) −3314.46 −0.555417
\(330\) 155.603 0.0259566
\(331\) 1221.67 0.202867 0.101433 0.994842i \(-0.467657\pi\)
0.101433 + 0.994842i \(0.467657\pi\)
\(332\) −1817.60 −0.300463
\(333\) 874.086 0.143843
\(334\) −2823.14 −0.462502
\(335\) −1549.96 −0.252786
\(336\) 1675.38 0.272023
\(337\) −8744.83 −1.41354 −0.706768 0.707446i \(-0.749847\pi\)
−0.706768 + 0.707446i \(0.749847\pi\)
\(338\) 6474.79 1.04196
\(339\) −3346.94 −0.536226
\(340\) 2737.14 0.436595
\(341\) 277.051 0.0439975
\(342\) −3414.33 −0.539841
\(343\) −343.000 −0.0539949
\(344\) −536.210 −0.0840421
\(345\) 3159.34 0.493023
\(346\) 5100.21 0.792454
\(347\) 4589.56 0.710031 0.355015 0.934860i \(-0.384476\pi\)
0.355015 + 0.934860i \(0.384476\pi\)
\(348\) 1280.25 0.197209
\(349\) −3989.89 −0.611960 −0.305980 0.952038i \(-0.598984\pi\)
−0.305980 + 0.952038i \(0.598984\pi\)
\(350\) 617.948 0.0943734
\(351\) −514.681 −0.0782668
\(352\) −534.561 −0.0809437
\(353\) 2416.35 0.364333 0.182166 0.983268i \(-0.441689\pi\)
0.182166 + 0.983268i \(0.441689\pi\)
\(354\) 8057.49 1.20975
\(355\) 3328.46 0.497624
\(356\) 1169.73 0.174145
\(357\) −2572.46 −0.381370
\(358\) −11806.3 −1.74297
\(359\) −2756.24 −0.405206 −0.202603 0.979261i \(-0.564940\pi\)
−0.202603 + 0.979261i \(0.564940\pi\)
\(360\) 561.099 0.0821459
\(361\) 4683.45 0.682818
\(362\) −7951.44 −1.15447
\(363\) −3967.11 −0.573607
\(364\) 596.307 0.0858654
\(365\) 3106.44 0.445475
\(366\) 2105.40 0.300687
\(367\) 11112.8 1.58061 0.790307 0.612711i \(-0.209921\pi\)
0.790307 + 0.612711i \(0.209921\pi\)
\(368\) −16803.5 −2.38028
\(369\) −4420.02 −0.623569
\(370\) −1714.73 −0.240931
\(371\) 1285.74 0.179925
\(372\) −1264.34 −0.176218
\(373\) 6091.09 0.845535 0.422768 0.906238i \(-0.361059\pi\)
0.422768 + 0.906238i \(0.361059\pi\)
\(374\) 1270.74 0.175691
\(375\) 375.000 0.0516398
\(376\) 5903.94 0.809767
\(377\) −1820.33 −0.248679
\(378\) 667.383 0.0908108
\(379\) 3984.29 0.539998 0.269999 0.962861i \(-0.412977\pi\)
0.269999 + 0.962861i \(0.412977\pi\)
\(380\) 2400.58 0.324072
\(381\) −5627.95 −0.756768
\(382\) 3537.93 0.473865
\(383\) 318.475 0.0424890 0.0212445 0.999774i \(-0.493237\pi\)
0.0212445 + 0.999774i \(0.493237\pi\)
\(384\) −4321.63 −0.574316
\(385\) 102.821 0.0136110
\(386\) 14318.6 1.88808
\(387\) −387.035 −0.0508374
\(388\) −4490.21 −0.587515
\(389\) 3885.46 0.506429 0.253214 0.967410i \(-0.418512\pi\)
0.253214 + 0.967410i \(0.418512\pi\)
\(390\) 1009.67 0.131094
\(391\) 25800.9 3.33710
\(392\) 610.975 0.0787216
\(393\) 1092.61 0.140241
\(394\) 18150.8 2.32088
\(395\) −123.813 −0.0157714
\(396\) −118.156 −0.0149938
\(397\) 4806.04 0.607578 0.303789 0.952739i \(-0.401748\pi\)
0.303789 + 0.952739i \(0.401748\pi\)
\(398\) −2067.94 −0.260443
\(399\) −2256.15 −0.283080
\(400\) −1994.50 −0.249313
\(401\) 3618.59 0.450633 0.225316 0.974286i \(-0.427658\pi\)
0.225316 + 0.974286i \(0.427658\pi\)
\(402\) 3283.87 0.407424
\(403\) 1797.71 0.222209
\(404\) −575.911 −0.0709223
\(405\) 405.000 0.0496904
\(406\) 2360.42 0.288536
\(407\) −285.315 −0.0347483
\(408\) 4582.24 0.556016
\(409\) −2109.05 −0.254978 −0.127489 0.991840i \(-0.540692\pi\)
−0.127489 + 0.991840i \(0.540692\pi\)
\(410\) 8670.91 1.04445
\(411\) 4809.40 0.577202
\(412\) 3601.94 0.430716
\(413\) 5324.30 0.634363
\(414\) −6693.62 −0.794622
\(415\) −2033.62 −0.240546
\(416\) −3468.63 −0.408806
\(417\) 7293.37 0.856494
\(418\) 1114.49 0.130410
\(419\) −6905.91 −0.805193 −0.402597 0.915377i \(-0.631892\pi\)
−0.402597 + 0.915377i \(0.631892\pi\)
\(420\) −469.231 −0.0545146
\(421\) −9647.54 −1.11685 −0.558423 0.829556i \(-0.688593\pi\)
−0.558423 + 0.829556i \(0.688593\pi\)
\(422\) 3725.91 0.429797
\(423\) 4261.45 0.489831
\(424\) −2290.25 −0.262321
\(425\) 3062.45 0.349531
\(426\) −7051.94 −0.802037
\(427\) 1391.23 0.157673
\(428\) −3439.74 −0.388473
\(429\) 168.000 0.0189070
\(430\) 759.261 0.0851508
\(431\) −13002.7 −1.45318 −0.726589 0.687073i \(-0.758895\pi\)
−0.726589 + 0.687073i \(0.758895\pi\)
\(432\) −2154.06 −0.239902
\(433\) 7356.07 0.816420 0.408210 0.912888i \(-0.366153\pi\)
0.408210 + 0.912888i \(0.366153\pi\)
\(434\) −2331.08 −0.257824
\(435\) 1432.41 0.157883
\(436\) −3489.55 −0.383300
\(437\) 22628.4 2.47703
\(438\) −6581.54 −0.717987
\(439\) 6909.21 0.751159 0.375579 0.926790i \(-0.377444\pi\)
0.375579 + 0.926790i \(0.377444\pi\)
\(440\) −183.152 −0.0198441
\(441\) 441.000 0.0476190
\(442\) 8245.50 0.887327
\(443\) −14812.6 −1.58864 −0.794318 0.607502i \(-0.792172\pi\)
−0.794318 + 0.607502i \(0.792172\pi\)
\(444\) 1302.06 0.139173
\(445\) 1308.75 0.139418
\(446\) −16511.0 −1.75296
\(447\) 7024.72 0.743306
\(448\) 30.0561 0.00316968
\(449\) −10654.5 −1.11986 −0.559932 0.828538i \(-0.689173\pi\)
−0.559932 + 0.828538i \(0.689173\pi\)
\(450\) −794.504 −0.0832295
\(451\) 1442.76 0.150636
\(452\) −4985.68 −0.518820
\(453\) −6312.21 −0.654688
\(454\) −19220.3 −1.98691
\(455\) 667.179 0.0687425
\(456\) 4018.81 0.412715
\(457\) −5855.16 −0.599328 −0.299664 0.954045i \(-0.596875\pi\)
−0.299664 + 0.954045i \(0.596875\pi\)
\(458\) 1893.76 0.193208
\(459\) 3307.45 0.336336
\(460\) 4706.23 0.477019
\(461\) 3204.74 0.323774 0.161887 0.986809i \(-0.448242\pi\)
0.161887 + 0.986809i \(0.448242\pi\)
\(462\) −217.844 −0.0219373
\(463\) 371.658 0.0373054 0.0186527 0.999826i \(-0.494062\pi\)
0.0186527 + 0.999826i \(0.494062\pi\)
\(464\) −7618.54 −0.762245
\(465\) −1414.61 −0.141077
\(466\) 647.927 0.0644091
\(467\) −19752.3 −1.95723 −0.978614 0.205703i \(-0.934052\pi\)
−0.978614 + 0.205703i \(0.934052\pi\)
\(468\) −766.681 −0.0757262
\(469\) 2169.95 0.213643
\(470\) −8359.84 −0.820449
\(471\) −1780.40 −0.174175
\(472\) −9484.01 −0.924866
\(473\) 126.334 0.0122809
\(474\) 262.320 0.0254193
\(475\) 2685.90 0.259447
\(476\) −3832.00 −0.368990
\(477\) −1653.09 −0.158679
\(478\) −2271.28 −0.217335
\(479\) −20762.0 −1.98046 −0.990232 0.139433i \(-0.955472\pi\)
−0.990232 + 0.139433i \(0.955472\pi\)
\(480\) 2729.45 0.259545
\(481\) −1851.34 −0.175496
\(482\) 20323.8 1.92059
\(483\) −4423.07 −0.416681
\(484\) −5909.50 −0.554987
\(485\) −5023.87 −0.470355
\(486\) −858.064 −0.0800876
\(487\) 17647.6 1.64207 0.821035 0.570878i \(-0.193397\pi\)
0.821035 + 0.570878i \(0.193397\pi\)
\(488\) −2478.15 −0.229878
\(489\) 6536.12 0.604445
\(490\) −865.127 −0.0797601
\(491\) −5637.46 −0.518157 −0.259078 0.965856i \(-0.583419\pi\)
−0.259078 + 0.965856i \(0.583419\pi\)
\(492\) −6584.16 −0.603327
\(493\) 11697.9 1.06865
\(494\) 7231.64 0.658638
\(495\) −132.198 −0.0120038
\(496\) 7523.86 0.681112
\(497\) −4659.85 −0.420569
\(498\) 4308.58 0.387695
\(499\) −17474.1 −1.56764 −0.783818 0.620991i \(-0.786730\pi\)
−0.783818 + 0.620991i \(0.786730\pi\)
\(500\) 558.609 0.0499635
\(501\) 2398.51 0.213887
\(502\) 18122.7 1.61127
\(503\) 7444.81 0.659936 0.329968 0.943992i \(-0.392962\pi\)
0.329968 + 0.943992i \(0.392962\pi\)
\(504\) −785.539 −0.0694260
\(505\) −644.358 −0.0567793
\(506\) 2184.90 0.191958
\(507\) −5500.89 −0.481860
\(508\) −8383.53 −0.732203
\(509\) −3384.48 −0.294724 −0.147362 0.989083i \(-0.547078\pi\)
−0.147362 + 0.989083i \(0.547078\pi\)
\(510\) −6488.35 −0.563351
\(511\) −4349.02 −0.376495
\(512\) −6558.89 −0.566142
\(513\) 2900.77 0.249653
\(514\) −17803.0 −1.52774
\(515\) 4030.04 0.344825
\(516\) −576.536 −0.0491872
\(517\) −1391.00 −0.118329
\(518\) 2400.62 0.203624
\(519\) −4333.07 −0.366476
\(520\) −1188.42 −0.100223
\(521\) 2973.12 0.250009 0.125005 0.992156i \(-0.460105\pi\)
0.125005 + 0.992156i \(0.460105\pi\)
\(522\) −3034.82 −0.254465
\(523\) 2689.02 0.224823 0.112412 0.993662i \(-0.464142\pi\)
0.112412 + 0.993662i \(0.464142\pi\)
\(524\) 1627.57 0.135689
\(525\) −525.000 −0.0436436
\(526\) −26755.3 −2.21785
\(527\) −11552.5 −0.954903
\(528\) 703.121 0.0579534
\(529\) 32194.9 2.64608
\(530\) 3242.94 0.265781
\(531\) −6845.53 −0.559455
\(532\) −3360.82 −0.273891
\(533\) 9361.72 0.760790
\(534\) −2772.83 −0.224704
\(535\) −3848.56 −0.311005
\(536\) −3865.25 −0.311480
\(537\) 10030.5 0.806046
\(538\) −3612.69 −0.289506
\(539\) −143.949 −0.0115034
\(540\) 603.298 0.0480774
\(541\) −14429.5 −1.14671 −0.573356 0.819306i \(-0.694359\pi\)
−0.573356 + 0.819306i \(0.694359\pi\)
\(542\) 7952.03 0.630201
\(543\) 6755.44 0.533893
\(544\) 22290.1 1.75677
\(545\) −3904.28 −0.306864
\(546\) −1413.54 −0.110795
\(547\) 13811.2 1.07957 0.539784 0.841804i \(-0.318506\pi\)
0.539784 + 0.841804i \(0.318506\pi\)
\(548\) 7164.19 0.558466
\(549\) −1788.72 −0.139054
\(550\) 259.339 0.0201059
\(551\) 10259.5 0.793229
\(552\) 7878.68 0.607498
\(553\) 173.338 0.0133293
\(554\) 30476.2 2.33720
\(555\) 1456.81 0.111420
\(556\) 10864.4 0.828692
\(557\) −6033.26 −0.458954 −0.229477 0.973314i \(-0.573702\pi\)
−0.229477 + 0.973314i \(0.573702\pi\)
\(558\) 2997.10 0.227379
\(559\) 819.751 0.0620246
\(560\) 2792.31 0.210708
\(561\) −1079.60 −0.0812493
\(562\) 26559.8 1.99352
\(563\) −6958.47 −0.520896 −0.260448 0.965488i \(-0.583870\pi\)
−0.260448 + 0.965488i \(0.583870\pi\)
\(564\) 6347.95 0.473931
\(565\) −5578.23 −0.415359
\(566\) −52.3202 −0.00388548
\(567\) −567.000 −0.0419961
\(568\) 8300.44 0.613166
\(569\) −13396.4 −0.987009 −0.493505 0.869743i \(-0.664284\pi\)
−0.493505 + 0.869743i \(0.664284\pi\)
\(570\) −5690.55 −0.418159
\(571\) −8055.84 −0.590414 −0.295207 0.955433i \(-0.595389\pi\)
−0.295207 + 0.955433i \(0.595389\pi\)
\(572\) 250.257 0.0182933
\(573\) −3005.78 −0.219142
\(574\) −12139.3 −0.882724
\(575\) 5265.56 0.381894
\(576\) −38.6435 −0.00279539
\(577\) −21456.9 −1.54812 −0.774059 0.633114i \(-0.781777\pi\)
−0.774059 + 0.633114i \(0.781777\pi\)
\(578\) −35638.9 −2.56468
\(579\) −12164.9 −0.873153
\(580\) 2133.76 0.152758
\(581\) 2847.07 0.203298
\(582\) 10644.0 0.758087
\(583\) 539.596 0.0383324
\(584\) 7746.76 0.548910
\(585\) −857.802 −0.0606252
\(586\) −24412.1 −1.72091
\(587\) 20156.3 1.41728 0.708638 0.705572i \(-0.249310\pi\)
0.708638 + 0.705572i \(0.249310\pi\)
\(588\) 656.924 0.0460733
\(589\) −10132.0 −0.708797
\(590\) 13429.1 0.937066
\(591\) −15420.7 −1.07330
\(592\) −7748.30 −0.537928
\(593\) 599.307 0.0415018 0.0207509 0.999785i \(-0.493394\pi\)
0.0207509 + 0.999785i \(0.493394\pi\)
\(594\) 280.086 0.0193469
\(595\) −4287.43 −0.295408
\(596\) 10464.2 0.719177
\(597\) 1756.89 0.120444
\(598\) 14177.3 0.969485
\(599\) −5493.05 −0.374691 −0.187346 0.982294i \(-0.559988\pi\)
−0.187346 + 0.982294i \(0.559988\pi\)
\(600\) 935.165 0.0636299
\(601\) 24292.8 1.64879 0.824396 0.566014i \(-0.191515\pi\)
0.824396 + 0.566014i \(0.191515\pi\)
\(602\) −1062.97 −0.0719655
\(603\) −2789.93 −0.188416
\(604\) −9402.82 −0.633436
\(605\) −6611.85 −0.444314
\(606\) 1365.19 0.0915131
\(607\) 3029.50 0.202576 0.101288 0.994857i \(-0.467704\pi\)
0.101288 + 0.994857i \(0.467704\pi\)
\(608\) 19549.3 1.30400
\(609\) −2005.38 −0.133435
\(610\) 3509.01 0.232911
\(611\) −9025.87 −0.597623
\(612\) 4926.85 0.325419
\(613\) −19339.6 −1.27426 −0.637129 0.770757i \(-0.719878\pi\)
−0.637129 + 0.770757i \(0.719878\pi\)
\(614\) 26992.4 1.77414
\(615\) −7366.69 −0.483014
\(616\) 256.412 0.0167713
\(617\) −5743.91 −0.374783 −0.187391 0.982285i \(-0.560003\pi\)
−0.187391 + 0.982285i \(0.560003\pi\)
\(618\) −8538.35 −0.555765
\(619\) −8243.35 −0.535264 −0.267632 0.963521i \(-0.586241\pi\)
−0.267632 + 0.963521i \(0.586241\pi\)
\(620\) −2107.24 −0.136498
\(621\) 5686.81 0.367478
\(622\) −26815.4 −1.72861
\(623\) −1832.26 −0.117830
\(624\) 4562.37 0.292694
\(625\) 625.000 0.0400000
\(626\) 32231.6 2.05788
\(627\) −946.856 −0.0603091
\(628\) −2652.13 −0.168521
\(629\) 11897.1 0.754162
\(630\) 1112.31 0.0703418
\(631\) −4376.56 −0.276114 −0.138057 0.990424i \(-0.544086\pi\)
−0.138057 + 0.990424i \(0.544086\pi\)
\(632\) −308.762 −0.0194334
\(633\) −3165.48 −0.198762
\(634\) 17407.8 1.09046
\(635\) −9379.92 −0.586190
\(636\) −2462.49 −0.153528
\(637\) −934.051 −0.0580980
\(638\) 990.613 0.0614714
\(639\) 5991.23 0.370907
\(640\) −7202.71 −0.444863
\(641\) 11836.6 0.729357 0.364678 0.931133i \(-0.381179\pi\)
0.364678 + 0.931133i \(0.381179\pi\)
\(642\) 8153.86 0.501257
\(643\) 1448.21 0.0888209 0.0444104 0.999013i \(-0.485859\pi\)
0.0444104 + 0.999013i \(0.485859\pi\)
\(644\) −6588.72 −0.403155
\(645\) −645.058 −0.0393785
\(646\) −46472.0 −2.83037
\(647\) −8732.95 −0.530646 −0.265323 0.964160i \(-0.585479\pi\)
−0.265323 + 0.964160i \(0.585479\pi\)
\(648\) 1009.98 0.0612279
\(649\) 2234.49 0.135149
\(650\) 1682.78 0.101545
\(651\) 1980.46 0.119232
\(652\) 9736.37 0.584824
\(653\) −21978.4 −1.31712 −0.658562 0.752527i \(-0.728835\pi\)
−0.658562 + 0.752527i \(0.728835\pi\)
\(654\) 8271.91 0.494583
\(655\) 1821.01 0.108630
\(656\) 39181.1 2.33196
\(657\) 5591.59 0.332038
\(658\) 11703.8 0.693406
\(659\) −27761.7 −1.64103 −0.820516 0.571623i \(-0.806314\pi\)
−0.820516 + 0.571623i \(0.806314\pi\)
\(660\) −196.926 −0.0116141
\(661\) −8573.72 −0.504507 −0.252254 0.967661i \(-0.581172\pi\)
−0.252254 + 0.967661i \(0.581172\pi\)
\(662\) −4313.86 −0.253267
\(663\) −7005.27 −0.410350
\(664\) −5071.39 −0.296398
\(665\) −3760.25 −0.219273
\(666\) −3086.51 −0.179579
\(667\) 20113.2 1.16760
\(668\) 3572.87 0.206944
\(669\) 14027.6 0.810668
\(670\) 5473.11 0.315589
\(671\) 583.868 0.0335916
\(672\) −3821.22 −0.219356
\(673\) 27159.2 1.55559 0.777795 0.628518i \(-0.216338\pi\)
0.777795 + 0.628518i \(0.216338\pi\)
\(674\) 30879.1 1.76472
\(675\) 675.000 0.0384900
\(676\) −8194.26 −0.466219
\(677\) −1392.30 −0.0790404 −0.0395202 0.999219i \(-0.512583\pi\)
−0.0395202 + 0.999219i \(0.512583\pi\)
\(678\) 11818.5 0.669448
\(679\) 7033.42 0.397523
\(680\) 7637.06 0.430688
\(681\) 16329.3 0.918857
\(682\) −978.302 −0.0549283
\(683\) −8675.09 −0.486007 −0.243004 0.970025i \(-0.578133\pi\)
−0.243004 + 0.970025i \(0.578133\pi\)
\(684\) 4321.05 0.241549
\(685\) 8015.66 0.447099
\(686\) 1211.18 0.0674096
\(687\) −1608.91 −0.0893504
\(688\) 3430.86 0.190117
\(689\) 3501.30 0.193598
\(690\) −11156.0 −0.615511
\(691\) −21426.0 −1.17957 −0.589785 0.807561i \(-0.700787\pi\)
−0.589785 + 0.807561i \(0.700787\pi\)
\(692\) −6454.65 −0.354579
\(693\) 185.078 0.0101451
\(694\) −16206.3 −0.886433
\(695\) 12155.6 0.663438
\(696\) 3572.11 0.194541
\(697\) −60160.4 −3.26935
\(698\) 14088.8 0.763997
\(699\) −550.470 −0.0297864
\(700\) −782.052 −0.0422269
\(701\) 24840.5 1.33839 0.669197 0.743085i \(-0.266638\pi\)
0.669197 + 0.743085i \(0.266638\pi\)
\(702\) 1817.40 0.0977116
\(703\) 10434.2 0.559793
\(704\) 12.6139 0.000675288 0
\(705\) 7102.41 0.379422
\(706\) −8532.45 −0.454848
\(707\) 902.101 0.0479873
\(708\) −10197.3 −0.541295
\(709\) 12525.0 0.663450 0.331725 0.943376i \(-0.392369\pi\)
0.331725 + 0.943376i \(0.392369\pi\)
\(710\) −11753.2 −0.621255
\(711\) −222.863 −0.0117553
\(712\) 3263.74 0.171789
\(713\) −19863.3 −1.04332
\(714\) 9083.69 0.476118
\(715\) 280.000 0.0146453
\(716\) 14941.6 0.779881
\(717\) 1929.65 0.100508
\(718\) 9732.66 0.505877
\(719\) 28085.0 1.45674 0.728369 0.685185i \(-0.240279\pi\)
0.728369 + 0.685185i \(0.240279\pi\)
\(720\) −3590.11 −0.185827
\(721\) −5642.05 −0.291430
\(722\) −16537.9 −0.852460
\(723\) −17266.8 −0.888189
\(724\) 10063.1 0.516562
\(725\) 2387.35 0.122295
\(726\) 14008.4 0.716115
\(727\) −14326.2 −0.730851 −0.365426 0.930841i \(-0.619077\pi\)
−0.365426 + 0.930841i \(0.619077\pi\)
\(728\) 1663.79 0.0847037
\(729\) 729.000 0.0370370
\(730\) −10969.2 −0.556150
\(731\) −5267.89 −0.266539
\(732\) −2664.53 −0.134541
\(733\) 6727.85 0.339016 0.169508 0.985529i \(-0.445782\pi\)
0.169508 + 0.985529i \(0.445782\pi\)
\(734\) −39240.8 −1.97331
\(735\) 735.000 0.0368856
\(736\) 38325.5 1.91943
\(737\) 910.677 0.0455159
\(738\) 15607.6 0.778490
\(739\) −3418.51 −0.170165 −0.0850826 0.996374i \(-0.527115\pi\)
−0.0850826 + 0.996374i \(0.527115\pi\)
\(740\) 2170.10 0.107803
\(741\) −6143.91 −0.304591
\(742\) −4540.11 −0.224626
\(743\) 8095.50 0.399724 0.199862 0.979824i \(-0.435951\pi\)
0.199862 + 0.979824i \(0.435951\pi\)
\(744\) −3527.72 −0.173834
\(745\) 11707.9 0.575762
\(746\) −21508.4 −1.05560
\(747\) −3660.51 −0.179292
\(748\) −1608.20 −0.0786119
\(749\) 5387.99 0.262847
\(750\) −1324.17 −0.0644693
\(751\) 13446.8 0.653371 0.326686 0.945133i \(-0.394068\pi\)
0.326686 + 0.945133i \(0.394068\pi\)
\(752\) −37775.4 −1.83182
\(753\) −15396.8 −0.745141
\(754\) 6427.84 0.310462
\(755\) −10520.4 −0.507119
\(756\) −844.617 −0.0406328
\(757\) −2593.24 −0.124508 −0.0622541 0.998060i \(-0.519829\pi\)
−0.0622541 + 0.998060i \(0.519829\pi\)
\(758\) −14069.0 −0.674156
\(759\) −1856.26 −0.0887722
\(760\) 6698.02 0.319688
\(761\) 27079.4 1.28992 0.644959 0.764217i \(-0.276875\pi\)
0.644959 + 0.764217i \(0.276875\pi\)
\(762\) 19873.0 0.944782
\(763\) 5465.99 0.259348
\(764\) −4477.48 −0.212028
\(765\) 5512.41 0.260525
\(766\) −1124.58 −0.0530451
\(767\) 14499.0 0.682568
\(768\) 15363.3 0.721842
\(769\) 2138.72 0.100292 0.0501458 0.998742i \(-0.484031\pi\)
0.0501458 + 0.998742i \(0.484031\pi\)
\(770\) −363.074 −0.0169926
\(771\) 15125.2 0.706513
\(772\) −18121.1 −0.844810
\(773\) 25864.0 1.20345 0.601724 0.798704i \(-0.294481\pi\)
0.601724 + 0.798704i \(0.294481\pi\)
\(774\) 1366.67 0.0634676
\(775\) −2357.69 −0.109278
\(776\) −12528.4 −0.579566
\(777\) −2039.53 −0.0941671
\(778\) −13720.1 −0.632247
\(779\) −52763.1 −2.42675
\(780\) −1277.80 −0.0586572
\(781\) −1955.63 −0.0896006
\(782\) −91106.2 −4.16618
\(783\) 2578.34 0.117679
\(784\) −3909.23 −0.178081
\(785\) −2967.33 −0.134916
\(786\) −3858.14 −0.175083
\(787\) −32371.3 −1.46621 −0.733107 0.680113i \(-0.761931\pi\)
−0.733107 + 0.680113i \(0.761931\pi\)
\(788\) −22971.0 −1.03846
\(789\) 22731.0 1.02566
\(790\) 437.200 0.0196897
\(791\) 7809.52 0.351043
\(792\) −329.673 −0.0147909
\(793\) 3788.57 0.169654
\(794\) −16970.8 −0.758526
\(795\) −2755.16 −0.122912
\(796\) 2617.11 0.116534
\(797\) 2024.33 0.0899691 0.0449845 0.998988i \(-0.485676\pi\)
0.0449845 + 0.998988i \(0.485676\pi\)
\(798\) 7966.76 0.353409
\(799\) 58002.1 2.56817
\(800\) 4549.08 0.201043
\(801\) 2355.76 0.103916
\(802\) −12777.7 −0.562589
\(803\) −1825.18 −0.0802109
\(804\) −4155.95 −0.182300
\(805\) −7371.79 −0.322760
\(806\) −6347.95 −0.277416
\(807\) 3069.29 0.133884
\(808\) −1606.88 −0.0699628
\(809\) 12391.7 0.538526 0.269263 0.963067i \(-0.413220\pi\)
0.269263 + 0.963067i \(0.413220\pi\)
\(810\) −1430.11 −0.0620356
\(811\) 14654.5 0.634511 0.317256 0.948340i \(-0.397239\pi\)
0.317256 + 0.948340i \(0.397239\pi\)
\(812\) −2987.26 −0.129104
\(813\) −6755.94 −0.291441
\(814\) 1007.49 0.0433813
\(815\) 10893.5 0.468201
\(816\) −29318.7 −1.25780
\(817\) −4620.16 −0.197844
\(818\) 7447.33 0.318325
\(819\) 1200.92 0.0512376
\(820\) −10973.6 −0.467335
\(821\) 23887.9 1.01546 0.507731 0.861516i \(-0.330485\pi\)
0.507731 + 0.861516i \(0.330485\pi\)
\(822\) −16982.6 −0.720604
\(823\) −4008.41 −0.169774 −0.0848871 0.996391i \(-0.527053\pi\)
−0.0848871 + 0.996391i \(0.527053\pi\)
\(824\) 10050.0 0.424889
\(825\) −220.331 −0.00929810
\(826\) −18800.8 −0.791966
\(827\) −45110.4 −1.89679 −0.948394 0.317096i \(-0.897292\pi\)
−0.948394 + 0.317096i \(0.897292\pi\)
\(828\) 8471.21 0.355549
\(829\) 16165.4 0.677260 0.338630 0.940920i \(-0.390036\pi\)
0.338630 + 0.940920i \(0.390036\pi\)
\(830\) 7180.97 0.300307
\(831\) −25892.2 −1.08085
\(832\) 81.8481 0.00341054
\(833\) 6002.41 0.249665
\(834\) −25753.8 −1.06928
\(835\) 3997.51 0.165676
\(836\) −1410.46 −0.0583514
\(837\) −2546.30 −0.105153
\(838\) 24385.7 1.00524
\(839\) −25244.4 −1.03878 −0.519388 0.854538i \(-0.673840\pi\)
−0.519388 + 0.854538i \(0.673840\pi\)
\(840\) −1309.23 −0.0537771
\(841\) −15269.9 −0.626096
\(842\) 34066.7 1.39432
\(843\) −22564.9 −0.921916
\(844\) −4715.37 −0.192310
\(845\) −9168.15 −0.373247
\(846\) −15047.7 −0.611526
\(847\) 9256.59 0.375514
\(848\) 14653.8 0.593412
\(849\) 44.4506 0.00179687
\(850\) −10813.9 −0.436370
\(851\) 20455.8 0.823990
\(852\) 8924.68 0.358867
\(853\) −30168.1 −1.21094 −0.605472 0.795867i \(-0.707016\pi\)
−0.605472 + 0.795867i \(0.707016\pi\)
\(854\) −4912.61 −0.196846
\(855\) 4834.61 0.193380
\(856\) −9597.44 −0.383217
\(857\) −13393.6 −0.533857 −0.266929 0.963716i \(-0.586009\pi\)
−0.266929 + 0.963716i \(0.586009\pi\)
\(858\) −593.230 −0.0236043
\(859\) 19060.4 0.757081 0.378541 0.925585i \(-0.376426\pi\)
0.378541 + 0.925585i \(0.376426\pi\)
\(860\) −960.894 −0.0381002
\(861\) 10313.4 0.408222
\(862\) 45914.3 1.81421
\(863\) −9466.86 −0.373413 −0.186707 0.982416i \(-0.559781\pi\)
−0.186707 + 0.982416i \(0.559781\pi\)
\(864\) 4913.00 0.193453
\(865\) −7221.79 −0.283871
\(866\) −25975.2 −1.01925
\(867\) 30278.3 1.18605
\(868\) 2950.13 0.115362
\(869\) 72.7461 0.00283975
\(870\) −5058.03 −0.197107
\(871\) 5909.15 0.229878
\(872\) −9736.39 −0.378115
\(873\) −9042.97 −0.350582
\(874\) −79903.8 −3.09243
\(875\) −875.000 −0.0338062
\(876\) 8329.37 0.321259
\(877\) 37740.6 1.45315 0.726573 0.687090i \(-0.241112\pi\)
0.726573 + 0.687090i \(0.241112\pi\)
\(878\) −24397.3 −0.937778
\(879\) 20740.2 0.795845
\(880\) 1171.87 0.0448905
\(881\) 25991.5 0.993957 0.496979 0.867763i \(-0.334443\pi\)
0.496979 + 0.867763i \(0.334443\pi\)
\(882\) −1557.23 −0.0594496
\(883\) 39420.3 1.50238 0.751189 0.660087i \(-0.229481\pi\)
0.751189 + 0.660087i \(0.229481\pi\)
\(884\) −10435.2 −0.397030
\(885\) −11409.2 −0.433352
\(886\) 52305.0 1.98332
\(887\) 46005.2 1.74149 0.870745 0.491735i \(-0.163637\pi\)
0.870745 + 0.491735i \(0.163637\pi\)
\(888\) 3632.95 0.137290
\(889\) 13131.9 0.495421
\(890\) −4621.38 −0.174055
\(891\) −237.957 −0.00894710
\(892\) 20895.8 0.784353
\(893\) 50870.2 1.90628
\(894\) −24805.2 −0.927975
\(895\) 16717.5 0.624361
\(896\) 10083.8 0.375978
\(897\) −12044.8 −0.448345
\(898\) 37622.6 1.39809
\(899\) −9005.81 −0.334105
\(900\) 1005.50 0.0372406
\(901\) −22500.1 −0.831950
\(902\) −5094.58 −0.188061
\(903\) 903.081 0.0332809
\(904\) −13910.8 −0.511801
\(905\) 11259.1 0.413551
\(906\) 22289.2 0.817340
\(907\) −2838.97 −0.103932 −0.0519661 0.998649i \(-0.516549\pi\)
−0.0519661 + 0.998649i \(0.516549\pi\)
\(908\) 24324.6 0.889030
\(909\) −1159.84 −0.0423208
\(910\) −2355.90 −0.0858211
\(911\) 39890.9 1.45076 0.725382 0.688347i \(-0.241663\pi\)
0.725382 + 0.688347i \(0.241663\pi\)
\(912\) −25713.7 −0.933626
\(913\) 1194.85 0.0433119
\(914\) 20675.3 0.748226
\(915\) −2981.21 −0.107711
\(916\) −2396.67 −0.0864500
\(917\) −2549.42 −0.0918094
\(918\) −11679.0 −0.419897
\(919\) −646.475 −0.0232048 −0.0116024 0.999933i \(-0.503693\pi\)
−0.0116024 + 0.999933i \(0.503693\pi\)
\(920\) 13131.1 0.470566
\(921\) −22932.4 −0.820463
\(922\) −11316.3 −0.404213
\(923\) −12689.6 −0.452528
\(924\) 275.696 0.00981574
\(925\) 2428.02 0.0863056
\(926\) −1312.37 −0.0465737
\(927\) 7254.07 0.257017
\(928\) 17376.4 0.614665
\(929\) 51188.2 1.80778 0.903892 0.427760i \(-0.140697\pi\)
0.903892 + 0.427760i \(0.140697\pi\)
\(930\) 4995.17 0.176127
\(931\) 5264.35 0.185319
\(932\) −819.993 −0.0288195
\(933\) 22782.0 0.799409
\(934\) 69747.8 2.44349
\(935\) −1799.34 −0.0629355
\(936\) −2139.16 −0.0747017
\(937\) 29786.1 1.03849 0.519247 0.854624i \(-0.326212\pi\)
0.519247 + 0.854624i \(0.326212\pi\)
\(938\) −7662.36 −0.266722
\(939\) −27383.5 −0.951680
\(940\) 10579.9 0.367105
\(941\) −44817.4 −1.55261 −0.776304 0.630358i \(-0.782908\pi\)
−0.776304 + 0.630358i \(0.782908\pi\)
\(942\) 6286.82 0.217448
\(943\) −103439. −3.57206
\(944\) 60682.0 2.09219
\(945\) −945.000 −0.0325300
\(946\) −446.103 −0.0153320
\(947\) 54697.1 1.87689 0.938446 0.345425i \(-0.112265\pi\)
0.938446 + 0.345425i \(0.112265\pi\)
\(948\) −331.983 −0.0113737
\(949\) −11843.2 −0.405105
\(950\) −9484.24 −0.323905
\(951\) −14789.4 −0.504290
\(952\) −10691.9 −0.363998
\(953\) −7577.51 −0.257565 −0.128783 0.991673i \(-0.541107\pi\)
−0.128783 + 0.991673i \(0.541107\pi\)
\(954\) 5837.29 0.198102
\(955\) −5009.63 −0.169746
\(956\) 2874.46 0.0972454
\(957\) −841.612 −0.0284278
\(958\) 73313.4 2.47249
\(959\) −11221.9 −0.377868
\(960\) −64.4059 −0.00216530
\(961\) −20897.1 −0.701457
\(962\) 6537.32 0.219097
\(963\) −6927.41 −0.231810
\(964\) −25721.1 −0.859357
\(965\) −20274.8 −0.676342
\(966\) 15618.4 0.520202
\(967\) 50779.0 1.68867 0.844334 0.535817i \(-0.179996\pi\)
0.844334 + 0.535817i \(0.179996\pi\)
\(968\) −16488.5 −0.547478
\(969\) 39482.0 1.30892
\(970\) 17739.9 0.587212
\(971\) −15313.2 −0.506102 −0.253051 0.967453i \(-0.581434\pi\)
−0.253051 + 0.967453i \(0.581434\pi\)
\(972\) 1085.94 0.0358348
\(973\) −17017.9 −0.560707
\(974\) −62315.9 −2.05003
\(975\) −1429.67 −0.0469601
\(976\) 15856.1 0.520021
\(977\) 46620.4 1.52663 0.763316 0.646025i \(-0.223570\pi\)
0.763316 + 0.646025i \(0.223570\pi\)
\(978\) −23079.9 −0.754615
\(979\) −768.957 −0.0251031
\(980\) 1094.87 0.0356882
\(981\) −7027.70 −0.228723
\(982\) 19906.6 0.646889
\(983\) −2824.37 −0.0916414 −0.0458207 0.998950i \(-0.514590\pi\)
−0.0458207 + 0.998950i \(0.514590\pi\)
\(984\) −18370.9 −0.595165
\(985\) −25701.1 −0.831377
\(986\) −41306.6 −1.33415
\(987\) −9943.38 −0.320670
\(988\) −9152.11 −0.294704
\(989\) −9057.59 −0.291218
\(990\) 466.810 0.0149860
\(991\) 16951.4 0.543370 0.271685 0.962386i \(-0.412419\pi\)
0.271685 + 0.962386i \(0.412419\pi\)
\(992\) −17160.5 −0.549239
\(993\) 3665.00 0.117125
\(994\) 16454.5 0.525056
\(995\) 2928.15 0.0932952
\(996\) −5452.79 −0.173472
\(997\) 23847.8 0.757540 0.378770 0.925491i \(-0.376347\pi\)
0.378770 + 0.925491i \(0.376347\pi\)
\(998\) 61703.4 1.95710
\(999\) 2622.26 0.0830476
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 105.4.a.f.1.1 2
3.2 odd 2 315.4.a.i.1.2 2
4.3 odd 2 1680.4.a.bg.1.1 2
5.2 odd 4 525.4.d.h.274.2 4
5.3 odd 4 525.4.d.h.274.3 4
5.4 even 2 525.4.a.k.1.2 2
7.6 odd 2 735.4.a.p.1.1 2
15.14 odd 2 1575.4.a.w.1.1 2
21.20 even 2 2205.4.a.z.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.f.1.1 2 1.1 even 1 trivial
315.4.a.i.1.2 2 3.2 odd 2
525.4.a.k.1.2 2 5.4 even 2
525.4.d.h.274.2 4 5.2 odd 4
525.4.d.h.274.3 4 5.3 odd 4
735.4.a.p.1.1 2 7.6 odd 2
1575.4.a.w.1.1 2 15.14 odd 2
1680.4.a.bg.1.1 2 4.3 odd 2
2205.4.a.z.1.2 2 21.20 even 2