Properties

Label 2057.4.a.e.1.2
Level $2057$
Weight $4$
Character 2057.1
Self dual yes
Analytic conductor $121.367$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(121.366928882\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2636.1
Defining polynomial: \( x^{3} - 14x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.87707\) of defining polynomial
Character \(\chi\) \(=\) 2057.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +O(q^{10})\) \(q-1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} -4.12682 q^{10} -19.3918 q^{12} -58.1117 q^{13} -10.8088 q^{14} +9.56391 q^{15} +22.9632 q^{16} +17.0000 q^{17} +23.2065 q^{18} -89.1688 q^{19} -18.6361 q^{20} +25.0493 q^{21} -115.269 q^{23} +60.7497 q^{24} -115.809 q^{25} +79.1029 q^{26} -138.956 q^{27} -48.8108 q^{28} +128.558 q^{29} -13.0186 q^{30} +273.460 q^{31} -185.316 q^{32} -23.1408 q^{34} +24.0732 q^{35} +104.797 q^{36} -132.351 q^{37} +121.379 q^{38} -183.321 q^{39} +58.3825 q^{40} +470.559 q^{41} -34.0977 q^{42} -352.642 q^{43} -51.6854 q^{45} +156.907 q^{46} +152.598 q^{47} +72.4403 q^{48} -279.949 q^{49} +157.641 q^{50} +53.6287 q^{51} +357.217 q^{52} +527.614 q^{53} +189.150 q^{54} +152.912 q^{56} -281.295 q^{57} -174.995 q^{58} -292.020 q^{59} -58.7901 q^{60} +53.8962 q^{61} -372.239 q^{62} -135.372 q^{63} +68.5514 q^{64} -176.178 q^{65} +52.9572 q^{67} -104.500 q^{68} -363.632 q^{69} -32.7690 q^{70} +788.400 q^{71} -328.304 q^{72} -295.780 q^{73} +180.159 q^{74} -365.334 q^{75} +548.127 q^{76} +249.541 q^{78} +720.325 q^{79} +69.6175 q^{80} +21.9487 q^{81} -640.535 q^{82} +116.051 q^{83} -153.980 q^{84} +51.5390 q^{85} +480.024 q^{86} +405.552 q^{87} -813.329 q^{89} +70.3553 q^{90} -461.435 q^{91} +708.569 q^{92} +862.664 q^{93} -207.720 q^{94} -270.334 q^{95} -584.605 q^{96} +794.693 q^{97} +381.072 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} + 56 q^{10} + 22 q^{12} - 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} + 51 q^{17} + 103 q^{18} - 80 q^{19} - 168 q^{20} + 192 q^{21} + 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} - 476 q^{28} + 456 q^{29} - 400 q^{30} + 230 q^{31} + 71 q^{32} - 17 q^{34} + 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} - 556 q^{43} - 384 q^{45} + 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} - 547 q^{50} + 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} + 684 q^{56} + 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 1008 q^{67} + 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} + 927 q^{72} - 838 q^{73} - 836 q^{74} - 1548 q^{75} + 908 q^{76} + 1308 q^{78} + 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} + 2396 q^{83} + 2040 q^{84} - 136 q^{85} - 1264 q^{86} - 1428 q^{87} - 170 q^{89} + 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} + 472 q^{95} - 678 q^{96} - 270 q^{97} - 2857 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36122 −0.481264 −0.240632 0.970616i \(-0.577355\pi\)
−0.240632 + 0.970616i \(0.577355\pi\)
\(3\) 3.15463 0.607109 0.303555 0.952814i \(-0.401827\pi\)
0.303555 + 0.952814i \(0.401827\pi\)
\(4\) −6.14708 −0.768385
\(5\) 3.03171 0.271164 0.135582 0.990766i \(-0.456710\pi\)
0.135582 + 0.990766i \(0.456710\pi\)
\(6\) −4.29415 −0.292180
\(7\) 7.94049 0.428746 0.214373 0.976752i \(-0.431229\pi\)
0.214373 + 0.976752i \(0.431229\pi\)
\(8\) 19.2573 0.851061
\(9\) −17.0483 −0.631419
\(10\) −4.12682 −0.130502
\(11\) 0 0
\(12\) −19.3918 −0.466493
\(13\) −58.1117 −1.23979 −0.619896 0.784684i \(-0.712825\pi\)
−0.619896 + 0.784684i \(0.712825\pi\)
\(14\) −10.8088 −0.206340
\(15\) 9.56391 0.164626
\(16\) 22.9632 0.358799
\(17\) 17.0000 0.242536
\(18\) 23.2065 0.303879
\(19\) −89.1688 −1.07667 −0.538335 0.842731i \(-0.680946\pi\)
−0.538335 + 0.842731i \(0.680946\pi\)
\(20\) −18.6361 −0.208358
\(21\) 25.0493 0.260296
\(22\) 0 0
\(23\) −115.269 −1.04501 −0.522507 0.852635i \(-0.675003\pi\)
−0.522507 + 0.852635i \(0.675003\pi\)
\(24\) 60.7497 0.516687
\(25\) −115.809 −0.926470
\(26\) 79.1029 0.596668
\(27\) −138.956 −0.990449
\(28\) −48.8108 −0.329442
\(29\) 128.558 0.823191 0.411596 0.911367i \(-0.364972\pi\)
0.411596 + 0.911367i \(0.364972\pi\)
\(30\) −13.0186 −0.0792287
\(31\) 273.460 1.58435 0.792174 0.610295i \(-0.208949\pi\)
0.792174 + 0.610295i \(0.208949\pi\)
\(32\) −185.316 −1.02374
\(33\) 0 0
\(34\) −23.1408 −0.116724
\(35\) 24.0732 0.116260
\(36\) 104.797 0.485172
\(37\) −132.351 −0.588063 −0.294031 0.955796i \(-0.594997\pi\)
−0.294031 + 0.955796i \(0.594997\pi\)
\(38\) 121.379 0.518163
\(39\) −183.321 −0.752689
\(40\) 58.3825 0.230777
\(41\) 470.559 1.79241 0.896207 0.443636i \(-0.146312\pi\)
0.896207 + 0.443636i \(0.146312\pi\)
\(42\) −34.0977 −0.125271
\(43\) −352.642 −1.25064 −0.625318 0.780370i \(-0.715031\pi\)
−0.625318 + 0.780370i \(0.715031\pi\)
\(44\) 0 0
\(45\) −51.6854 −0.171218
\(46\) 156.907 0.502928
\(47\) 152.598 0.473589 0.236795 0.971560i \(-0.423903\pi\)
0.236795 + 0.971560i \(0.423903\pi\)
\(48\) 72.4403 0.217830
\(49\) −279.949 −0.816177
\(50\) 157.641 0.445877
\(51\) 53.6287 0.147246
\(52\) 357.217 0.952637
\(53\) 527.614 1.36742 0.683711 0.729753i \(-0.260365\pi\)
0.683711 + 0.729753i \(0.260365\pi\)
\(54\) 189.150 0.476668
\(55\) 0 0
\(56\) 152.912 0.364889
\(57\) −281.295 −0.653656
\(58\) −174.995 −0.396173
\(59\) −292.020 −0.644368 −0.322184 0.946677i \(-0.604417\pi\)
−0.322184 + 0.946677i \(0.604417\pi\)
\(60\) −58.7901 −0.126496
\(61\) 53.8962 0.113126 0.0565632 0.998399i \(-0.481986\pi\)
0.0565632 + 0.998399i \(0.481986\pi\)
\(62\) −372.239 −0.762490
\(63\) −135.372 −0.270718
\(64\) 68.5514 0.133889
\(65\) −176.178 −0.336187
\(66\) 0 0
\(67\) 52.9572 0.0965635 0.0482817 0.998834i \(-0.484625\pi\)
0.0482817 + 0.998834i \(0.484625\pi\)
\(68\) −104.500 −0.186361
\(69\) −363.632 −0.634437
\(70\) −32.7690 −0.0559520
\(71\) 788.400 1.31783 0.658915 0.752218i \(-0.271016\pi\)
0.658915 + 0.752218i \(0.271016\pi\)
\(72\) −328.304 −0.537375
\(73\) −295.780 −0.474224 −0.237112 0.971482i \(-0.576201\pi\)
−0.237112 + 0.971482i \(0.576201\pi\)
\(74\) 180.159 0.283014
\(75\) −365.334 −0.562468
\(76\) 548.127 0.827296
\(77\) 0 0
\(78\) 249.541 0.362242
\(79\) 720.325 1.02586 0.512930 0.858430i \(-0.328560\pi\)
0.512930 + 0.858430i \(0.328560\pi\)
\(80\) 69.6175 0.0972934
\(81\) 21.9487 0.0301079
\(82\) −640.535 −0.862625
\(83\) 116.051 0.153473 0.0767363 0.997051i \(-0.475550\pi\)
0.0767363 + 0.997051i \(0.475550\pi\)
\(84\) −153.980 −0.200007
\(85\) 51.5390 0.0657669
\(86\) 480.024 0.601887
\(87\) 405.552 0.499767
\(88\) 0 0
\(89\) −813.329 −0.968682 −0.484341 0.874879i \(-0.660941\pi\)
−0.484341 + 0.874879i \(0.660941\pi\)
\(90\) 70.3553 0.0824011
\(91\) −461.435 −0.531556
\(92\) 708.569 0.802972
\(93\) 862.664 0.961872
\(94\) −207.720 −0.227922
\(95\) −270.334 −0.291954
\(96\) −584.605 −0.621521
\(97\) 794.693 0.831844 0.415922 0.909400i \(-0.363459\pi\)
0.415922 + 0.909400i \(0.363459\pi\)
\(98\) 381.072 0.392797
\(99\) 0 0
\(100\) 711.885 0.711885
\(101\) −265.513 −0.261579 −0.130790 0.991410i \(-0.541751\pi\)
−0.130790 + 0.991410i \(0.541751\pi\)
\(102\) −73.0006 −0.0708641
\(103\) 523.107 0.500420 0.250210 0.968192i \(-0.419500\pi\)
0.250210 + 0.968192i \(0.419500\pi\)
\(104\) −1119.07 −1.05514
\(105\) 75.9421 0.0705828
\(106\) −718.199 −0.658091
\(107\) 986.039 0.890878 0.445439 0.895312i \(-0.353048\pi\)
0.445439 + 0.895312i \(0.353048\pi\)
\(108\) 854.174 0.761046
\(109\) −1814.39 −1.59438 −0.797188 0.603732i \(-0.793680\pi\)
−0.797188 + 0.603732i \(0.793680\pi\)
\(110\) 0 0
\(111\) −417.518 −0.357018
\(112\) 182.339 0.153834
\(113\) −707.339 −0.588857 −0.294429 0.955673i \(-0.595129\pi\)
−0.294429 + 0.955673i \(0.595129\pi\)
\(114\) 382.904 0.314581
\(115\) −349.463 −0.283370
\(116\) −790.253 −0.632527
\(117\) 990.706 0.782827
\(118\) 397.503 0.310112
\(119\) 134.988 0.103986
\(120\) 184.175 0.140107
\(121\) 0 0
\(122\) −73.3647 −0.0544437
\(123\) 1484.44 1.08819
\(124\) −1680.98 −1.21739
\(125\) −730.061 −0.522389
\(126\) 184.271 0.130287
\(127\) −2648.18 −1.85030 −0.925151 0.379600i \(-0.876062\pi\)
−0.925151 + 0.379600i \(0.876062\pi\)
\(128\) 1389.22 0.959302
\(129\) −1112.46 −0.759273
\(130\) 239.817 0.161795
\(131\) 1979.08 1.31995 0.659974 0.751289i \(-0.270567\pi\)
0.659974 + 0.751289i \(0.270567\pi\)
\(132\) 0 0
\(133\) −708.044 −0.461618
\(134\) −72.0865 −0.0464726
\(135\) −421.274 −0.268574
\(136\) 327.374 0.206413
\(137\) 3141.92 1.95936 0.979679 0.200570i \(-0.0642794\pi\)
0.979679 + 0.200570i \(0.0642794\pi\)
\(138\) 494.984 0.305332
\(139\) −1468.07 −0.895830 −0.447915 0.894076i \(-0.647833\pi\)
−0.447915 + 0.894076i \(0.647833\pi\)
\(140\) −147.980 −0.0893327
\(141\) 481.390 0.287520
\(142\) −1073.19 −0.634224
\(143\) 0 0
\(144\) −391.483 −0.226553
\(145\) 389.749 0.223220
\(146\) 402.621 0.228227
\(147\) −883.135 −0.495508
\(148\) 813.570 0.451858
\(149\) 286.027 0.157263 0.0786316 0.996904i \(-0.474945\pi\)
0.0786316 + 0.996904i \(0.474945\pi\)
\(150\) 497.300 0.270696
\(151\) 669.626 0.360883 0.180442 0.983586i \(-0.442247\pi\)
0.180442 + 0.983586i \(0.442247\pi\)
\(152\) −1717.15 −0.916311
\(153\) −289.821 −0.153141
\(154\) 0 0
\(155\) 829.049 0.429618
\(156\) 1126.89 0.578354
\(157\) 720.809 0.366413 0.183206 0.983074i \(-0.441352\pi\)
0.183206 + 0.983074i \(0.441352\pi\)
\(158\) −980.522 −0.493710
\(159\) 1664.43 0.830174
\(160\) −561.825 −0.277601
\(161\) −915.294 −0.448045
\(162\) −29.8770 −0.0144899
\(163\) −676.599 −0.325125 −0.162562 0.986698i \(-0.551976\pi\)
−0.162562 + 0.986698i \(0.551976\pi\)
\(164\) −2892.56 −1.37726
\(165\) 0 0
\(166\) −157.971 −0.0738609
\(167\) 2835.67 1.31396 0.656979 0.753909i \(-0.271834\pi\)
0.656979 + 0.753909i \(0.271834\pi\)
\(168\) 482.382 0.221527
\(169\) 1179.97 0.537083
\(170\) −70.1560 −0.0316513
\(171\) 1520.18 0.679829
\(172\) 2167.72 0.960970
\(173\) 177.314 0.0779243 0.0389621 0.999241i \(-0.487595\pi\)
0.0389621 + 0.999241i \(0.487595\pi\)
\(174\) −552.046 −0.240520
\(175\) −919.578 −0.397220
\(176\) 0 0
\(177\) −921.214 −0.391202
\(178\) 1107.12 0.466192
\(179\) −1023.76 −0.427483 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(180\) 317.714 0.131561
\(181\) −3450.21 −1.41686 −0.708432 0.705779i \(-0.750597\pi\)
−0.708432 + 0.705779i \(0.750597\pi\)
\(182\) 628.116 0.255819
\(183\) 170.023 0.0686800
\(184\) −2219.78 −0.889370
\(185\) −401.248 −0.159461
\(186\) −1174.28 −0.462915
\(187\) 0 0
\(188\) −938.031 −0.363899
\(189\) −1103.38 −0.424651
\(190\) 367.984 0.140507
\(191\) −490.894 −0.185968 −0.0929839 0.995668i \(-0.529640\pi\)
−0.0929839 + 0.995668i \(0.529640\pi\)
\(192\) 216.254 0.0812855
\(193\) 3548.80 1.32357 0.661783 0.749696i \(-0.269800\pi\)
0.661783 + 0.749696i \(0.269800\pi\)
\(194\) −1081.75 −0.400337
\(195\) −555.775 −0.204102
\(196\) 1720.87 0.627138
\(197\) −1363.15 −0.492996 −0.246498 0.969143i \(-0.579280\pi\)
−0.246498 + 0.969143i \(0.579280\pi\)
\(198\) 0 0
\(199\) 3737.46 1.33137 0.665683 0.746235i \(-0.268140\pi\)
0.665683 + 0.746235i \(0.268140\pi\)
\(200\) −2230.16 −0.788482
\(201\) 167.060 0.0586246
\(202\) 361.422 0.125889
\(203\) 1020.81 0.352940
\(204\) −329.660 −0.113141
\(205\) 1426.60 0.486038
\(206\) −712.064 −0.240834
\(207\) 1965.15 0.659841
\(208\) −1334.43 −0.444836
\(209\) 0 0
\(210\) −103.374 −0.0339690
\(211\) 5266.12 1.71817 0.859087 0.511829i \(-0.171032\pi\)
0.859087 + 0.511829i \(0.171032\pi\)
\(212\) −3243.28 −1.05071
\(213\) 2487.11 0.800066
\(214\) −1342.22 −0.428748
\(215\) −1069.11 −0.339128
\(216\) −2675.92 −0.842932
\(217\) 2171.40 0.679283
\(218\) 2469.78 0.767316
\(219\) −933.075 −0.287906
\(220\) 0 0
\(221\) −987.899 −0.300694
\(222\) 568.334 0.171820
\(223\) 704.546 0.211569 0.105785 0.994389i \(-0.466265\pi\)
0.105785 + 0.994389i \(0.466265\pi\)
\(224\) −1471.50 −0.438923
\(225\) 1974.34 0.584990
\(226\) 962.845 0.283396
\(227\) 2151.26 0.629006 0.314503 0.949256i \(-0.398162\pi\)
0.314503 + 0.949256i \(0.398162\pi\)
\(228\) 1729.14 0.502259
\(229\) −3916.94 −1.13030 −0.565149 0.824989i \(-0.691181\pi\)
−0.565149 + 0.824989i \(0.691181\pi\)
\(230\) 475.696 0.136376
\(231\) 0 0
\(232\) 2475.67 0.700586
\(233\) 5192.74 1.46003 0.730017 0.683429i \(-0.239512\pi\)
0.730017 + 0.683429i \(0.239512\pi\)
\(234\) −1348.57 −0.376747
\(235\) 462.632 0.128420
\(236\) 1795.07 0.495123
\(237\) 2272.36 0.622809
\(238\) −183.749 −0.0500448
\(239\) −334.305 −0.0904786 −0.0452393 0.998976i \(-0.514405\pi\)
−0.0452393 + 0.998976i \(0.514405\pi\)
\(240\) 219.618 0.0590677
\(241\) 1918.45 0.512773 0.256386 0.966574i \(-0.417468\pi\)
0.256386 + 0.966574i \(0.417468\pi\)
\(242\) 0 0
\(243\) 3821.06 1.00873
\(244\) −331.304 −0.0869245
\(245\) −848.722 −0.221318
\(246\) −2020.65 −0.523708
\(247\) 5181.75 1.33485
\(248\) 5266.09 1.34838
\(249\) 366.097 0.0931746
\(250\) 993.775 0.251407
\(251\) 7695.71 1.93525 0.967627 0.252385i \(-0.0812148\pi\)
0.967627 + 0.252385i \(0.0812148\pi\)
\(252\) 832.141 0.208016
\(253\) 0 0
\(254\) 3604.76 0.890484
\(255\) 162.587 0.0399277
\(256\) −2439.44 −0.595567
\(257\) 5335.10 1.29492 0.647460 0.762099i \(-0.275831\pi\)
0.647460 + 0.762099i \(0.275831\pi\)
\(258\) 1514.30 0.365411
\(259\) −1050.93 −0.252130
\(260\) 1082.98 0.258321
\(261\) −2191.69 −0.519778
\(262\) −2693.97 −0.635244
\(263\) −3934.15 −0.922396 −0.461198 0.887297i \(-0.652580\pi\)
−0.461198 + 0.887297i \(0.652580\pi\)
\(264\) 0 0
\(265\) 1599.57 0.370795
\(266\) 963.804 0.222160
\(267\) −2565.75 −0.588095
\(268\) −325.532 −0.0741979
\(269\) 3424.04 0.776088 0.388044 0.921641i \(-0.373151\pi\)
0.388044 + 0.921641i \(0.373151\pi\)
\(270\) 573.447 0.129255
\(271\) −549.034 −0.123068 −0.0615340 0.998105i \(-0.519599\pi\)
−0.0615340 + 0.998105i \(0.519599\pi\)
\(272\) 390.374 0.0870216
\(273\) −1455.66 −0.322712
\(274\) −4276.85 −0.942970
\(275\) 0 0
\(276\) 2235.27 0.487492
\(277\) −5203.65 −1.12873 −0.564363 0.825527i \(-0.690878\pi\)
−0.564363 + 0.825527i \(0.690878\pi\)
\(278\) 1998.37 0.431131
\(279\) −4662.02 −1.00039
\(280\) 463.585 0.0989447
\(281\) 1986.73 0.421774 0.210887 0.977510i \(-0.432365\pi\)
0.210887 + 0.977510i \(0.432365\pi\)
\(282\) −655.279 −0.138373
\(283\) −753.696 −0.158313 −0.0791565 0.996862i \(-0.525223\pi\)
−0.0791565 + 0.996862i \(0.525223\pi\)
\(284\) −4846.36 −1.01260
\(285\) −852.803 −0.177248
\(286\) 0 0
\(287\) 3736.47 0.768490
\(288\) 3159.33 0.646407
\(289\) 289.000 0.0588235
\(290\) −530.534 −0.107428
\(291\) 2506.96 0.505020
\(292\) 1818.18 0.364387
\(293\) 7202.22 1.43603 0.718017 0.696025i \(-0.245050\pi\)
0.718017 + 0.696025i \(0.245050\pi\)
\(294\) 1202.14 0.238471
\(295\) −885.318 −0.174729
\(296\) −2548.72 −0.500477
\(297\) 0 0
\(298\) −389.345 −0.0756852
\(299\) 6698.50 1.29560
\(300\) 2245.74 0.432192
\(301\) −2800.15 −0.536205
\(302\) −911.509 −0.173680
\(303\) −837.595 −0.158807
\(304\) −2047.60 −0.386308
\(305\) 163.398 0.0306758
\(306\) 394.511 0.0737016
\(307\) −2425.71 −0.450953 −0.225477 0.974249i \(-0.572394\pi\)
−0.225477 + 0.974249i \(0.572394\pi\)
\(308\) 0 0
\(309\) 1650.21 0.303809
\(310\) −1128.52 −0.206760
\(311\) −9544.94 −1.74033 −0.870167 0.492757i \(-0.835989\pi\)
−0.870167 + 0.492757i \(0.835989\pi\)
\(312\) −3530.27 −0.640584
\(313\) 588.379 0.106253 0.0531264 0.998588i \(-0.483081\pi\)
0.0531264 + 0.998588i \(0.483081\pi\)
\(314\) −981.180 −0.176341
\(315\) −410.407 −0.0734090
\(316\) −4427.89 −0.788255
\(317\) 7653.31 1.35600 0.678001 0.735061i \(-0.262846\pi\)
0.678001 + 0.735061i \(0.262846\pi\)
\(318\) −2265.65 −0.399533
\(319\) 0 0
\(320\) 207.828 0.0363060
\(321\) 3110.59 0.540860
\(322\) 1245.92 0.215628
\(323\) −1515.87 −0.261131
\(324\) −134.920 −0.0231345
\(325\) 6729.85 1.14863
\(326\) 921.001 0.156471
\(327\) −5723.73 −0.967960
\(328\) 9061.70 1.52545
\(329\) 1211.70 0.203050
\(330\) 0 0
\(331\) 752.266 0.124919 0.0624597 0.998047i \(-0.480106\pi\)
0.0624597 + 0.998047i \(0.480106\pi\)
\(332\) −713.373 −0.117926
\(333\) 2256.36 0.371314
\(334\) −3859.98 −0.632361
\(335\) 160.551 0.0261845
\(336\) 575.211 0.0933939
\(337\) 1968.57 0.318204 0.159102 0.987262i \(-0.449140\pi\)
0.159102 + 0.987262i \(0.449140\pi\)
\(338\) −1606.20 −0.258479
\(339\) −2231.39 −0.357501
\(340\) −316.814 −0.0505343
\(341\) 0 0
\(342\) −2069.30 −0.327178
\(343\) −4946.52 −0.778678
\(344\) −6790.93 −1.06437
\(345\) −1102.43 −0.172037
\(346\) −241.363 −0.0375022
\(347\) −3983.10 −0.616207 −0.308104 0.951353i \(-0.599694\pi\)
−0.308104 + 0.951353i \(0.599694\pi\)
\(348\) −2492.96 −0.384013
\(349\) −1495.61 −0.229393 −0.114697 0.993401i \(-0.536590\pi\)
−0.114697 + 0.993401i \(0.536590\pi\)
\(350\) 1251.75 0.191168
\(351\) 8074.98 1.22795
\(352\) 0 0
\(353\) 6482.49 0.977417 0.488708 0.872447i \(-0.337468\pi\)
0.488708 + 0.872447i \(0.337468\pi\)
\(354\) 1253.98 0.188272
\(355\) 2390.20 0.357348
\(356\) 4999.59 0.744320
\(357\) 425.838 0.0631309
\(358\) 1393.56 0.205732
\(359\) 4943.42 0.726751 0.363376 0.931643i \(-0.381624\pi\)
0.363376 + 0.931643i \(0.381624\pi\)
\(360\) −995.322 −0.145717
\(361\) 1092.08 0.159218
\(362\) 4696.50 0.681886
\(363\) 0 0
\(364\) 2836.48 0.408439
\(365\) −896.717 −0.128593
\(366\) −231.439 −0.0330533
\(367\) −14.8871 −0.00211743 −0.00105872 0.999999i \(-0.500337\pi\)
−0.00105872 + 0.999999i \(0.500337\pi\)
\(368\) −2646.95 −0.374950
\(369\) −8022.23 −1.13176
\(370\) 546.188 0.0767431
\(371\) 4189.51 0.586276
\(372\) −5302.86 −0.739088
\(373\) −1923.18 −0.266966 −0.133483 0.991051i \(-0.542616\pi\)
−0.133483 + 0.991051i \(0.542616\pi\)
\(374\) 0 0
\(375\) −2303.07 −0.317147
\(376\) 2938.63 0.403053
\(377\) −7470.70 −1.02059
\(378\) 1501.94 0.204369
\(379\) −9592.87 −1.30014 −0.650069 0.759875i \(-0.725260\pi\)
−0.650069 + 0.759875i \(0.725260\pi\)
\(380\) 1661.76 0.224333
\(381\) −8354.04 −1.12333
\(382\) 668.215 0.0894996
\(383\) −9083.77 −1.21190 −0.605951 0.795502i \(-0.707207\pi\)
−0.605951 + 0.795502i \(0.707207\pi\)
\(384\) 4382.47 0.582401
\(385\) 0 0
\(386\) −4830.70 −0.636985
\(387\) 6011.95 0.789675
\(388\) −4885.04 −0.639176
\(389\) −1143.78 −0.149079 −0.0745396 0.997218i \(-0.523749\pi\)
−0.0745396 + 0.997218i \(0.523749\pi\)
\(390\) 756.533 0.0982271
\(391\) −1959.58 −0.253453
\(392\) −5391.06 −0.694616
\(393\) 6243.27 0.801352
\(394\) 1855.55 0.237262
\(395\) 2183.81 0.278176
\(396\) 0 0
\(397\) 10604.5 1.34061 0.670307 0.742084i \(-0.266162\pi\)
0.670307 + 0.742084i \(0.266162\pi\)
\(398\) −5087.51 −0.640739
\(399\) −2233.62 −0.280252
\(400\) −2659.33 −0.332417
\(401\) 13785.4 1.71674 0.858368 0.513035i \(-0.171479\pi\)
0.858368 + 0.513035i \(0.171479\pi\)
\(402\) −227.406 −0.0282139
\(403\) −15891.2 −1.96426
\(404\) 1632.13 0.200993
\(405\) 66.5420 0.00816419
\(406\) −1389.55 −0.169857
\(407\) 0 0
\(408\) 1032.74 0.125315
\(409\) 9505.94 1.14924 0.574619 0.818421i \(-0.305150\pi\)
0.574619 + 0.818421i \(0.305150\pi\)
\(410\) −1941.91 −0.233913
\(411\) 9911.59 1.18954
\(412\) −3215.58 −0.384515
\(413\) −2318.78 −0.276270
\(414\) −2675.00 −0.317558
\(415\) 351.832 0.0416162
\(416\) 10769.1 1.26922
\(417\) −4631.23 −0.543866
\(418\) 0 0
\(419\) 9680.86 1.12874 0.564369 0.825523i \(-0.309120\pi\)
0.564369 + 0.825523i \(0.309120\pi\)
\(420\) −466.822 −0.0542347
\(421\) −12360.3 −1.43089 −0.715444 0.698671i \(-0.753775\pi\)
−0.715444 + 0.698671i \(0.753775\pi\)
\(422\) −7168.36 −0.826897
\(423\) −2601.54 −0.299033
\(424\) 10160.4 1.16376
\(425\) −1968.75 −0.224702
\(426\) −3385.51 −0.385043
\(427\) 427.962 0.0485025
\(428\) −6061.25 −0.684537
\(429\) 0 0
\(430\) 1455.29 0.163210
\(431\) −2970.58 −0.331990 −0.165995 0.986127i \(-0.553084\pi\)
−0.165995 + 0.986127i \(0.553084\pi\)
\(432\) −3190.87 −0.355372
\(433\) 6131.50 0.680510 0.340255 0.940333i \(-0.389487\pi\)
0.340255 + 0.940333i \(0.389487\pi\)
\(434\) −2955.76 −0.326915
\(435\) 1229.51 0.135519
\(436\) 11153.2 1.22509
\(437\) 10278.4 1.12513
\(438\) 1270.12 0.138559
\(439\) 2544.91 0.276679 0.138339 0.990385i \(-0.455824\pi\)
0.138339 + 0.990385i \(0.455824\pi\)
\(440\) 0 0
\(441\) 4772.65 0.515349
\(442\) 1344.75 0.144713
\(443\) 8529.82 0.914817 0.457408 0.889257i \(-0.348778\pi\)
0.457408 + 0.889257i \(0.348778\pi\)
\(444\) 2566.51 0.274327
\(445\) −2465.77 −0.262672
\(446\) −959.043 −0.101821
\(447\) 902.308 0.0954759
\(448\) 544.331 0.0574046
\(449\) 8855.74 0.930798 0.465399 0.885101i \(-0.345911\pi\)
0.465399 + 0.885101i \(0.345911\pi\)
\(450\) −2687.52 −0.281535
\(451\) 0 0
\(452\) 4348.07 0.452469
\(453\) 2112.42 0.219095
\(454\) −2928.35 −0.302718
\(455\) −1398.94 −0.144139
\(456\) −5416.98 −0.556301
\(457\) 7154.78 0.732356 0.366178 0.930545i \(-0.380666\pi\)
0.366178 + 0.930545i \(0.380666\pi\)
\(458\) 5331.82 0.543973
\(459\) −2362.25 −0.240219
\(460\) 2148.17 0.217737
\(461\) 7263.06 0.733784 0.366892 0.930264i \(-0.380422\pi\)
0.366892 + 0.930264i \(0.380422\pi\)
\(462\) 0 0
\(463\) 352.898 0.0354224 0.0177112 0.999843i \(-0.494362\pi\)
0.0177112 + 0.999843i \(0.494362\pi\)
\(464\) 2952.09 0.295360
\(465\) 2615.34 0.260825
\(466\) −7068.47 −0.702662
\(467\) 1483.02 0.146951 0.0734753 0.997297i \(-0.476591\pi\)
0.0734753 + 0.997297i \(0.476591\pi\)
\(468\) −6089.94 −0.601512
\(469\) 420.506 0.0414012
\(470\) −629.745 −0.0618042
\(471\) 2273.89 0.222452
\(472\) −5623.51 −0.548396
\(473\) 0 0
\(474\) −3093.19 −0.299736
\(475\) 10326.5 0.997502
\(476\) −829.783 −0.0799014
\(477\) −8994.92 −0.863415
\(478\) 455.063 0.0435441
\(479\) 9990.10 0.952942 0.476471 0.879190i \(-0.341916\pi\)
0.476471 + 0.879190i \(0.341916\pi\)
\(480\) −1772.35 −0.168534
\(481\) 7691.13 0.729075
\(482\) −2611.44 −0.246779
\(483\) −2887.42 −0.272012
\(484\) 0 0
\(485\) 2409.27 0.225566
\(486\) −5201.30 −0.485465
\(487\) −1129.88 −0.105133 −0.0525663 0.998617i \(-0.516740\pi\)
−0.0525663 + 0.998617i \(0.516740\pi\)
\(488\) 1037.90 0.0962774
\(489\) −2134.42 −0.197386
\(490\) 1155.30 0.106512
\(491\) −18774.9 −1.72566 −0.862832 0.505491i \(-0.831311\pi\)
−0.862832 + 0.505491i \(0.831311\pi\)
\(492\) −9124.97 −0.836149
\(493\) 2185.48 0.199653
\(494\) −7053.51 −0.642414
\(495\) 0 0
\(496\) 6279.49 0.568463
\(497\) 6260.28 0.565014
\(498\) −498.339 −0.0448416
\(499\) 17329.1 1.55462 0.777310 0.629118i \(-0.216584\pi\)
0.777310 + 0.629118i \(0.216584\pi\)
\(500\) 4487.74 0.401396
\(501\) 8945.50 0.797716
\(502\) −10475.6 −0.931369
\(503\) 20837.0 1.84707 0.923533 0.383518i \(-0.125288\pi\)
0.923533 + 0.383518i \(0.125288\pi\)
\(504\) −2606.90 −0.230398
\(505\) −804.957 −0.0709309
\(506\) 0 0
\(507\) 3722.37 0.326068
\(508\) 16278.6 1.42174
\(509\) 11835.0 1.03060 0.515301 0.857009i \(-0.327680\pi\)
0.515301 + 0.857009i \(0.327680\pi\)
\(510\) −221.316 −0.0192158
\(511\) −2348.63 −0.203322
\(512\) −7793.12 −0.672676
\(513\) 12390.6 1.06639
\(514\) −7262.26 −0.623199
\(515\) 1585.91 0.135696
\(516\) 6838.35 0.583414
\(517\) 0 0
\(518\) 1430.55 0.121341
\(519\) 559.359 0.0473086
\(520\) −3392.71 −0.286115
\(521\) 7686.37 0.646346 0.323173 0.946340i \(-0.395250\pi\)
0.323173 + 0.946340i \(0.395250\pi\)
\(522\) 2983.37 0.250151
\(523\) −11476.4 −0.959518 −0.479759 0.877400i \(-0.659276\pi\)
−0.479759 + 0.877400i \(0.659276\pi\)
\(524\) −12165.6 −1.01423
\(525\) −2900.93 −0.241156
\(526\) 5355.25 0.443916
\(527\) 4648.81 0.384261
\(528\) 0 0
\(529\) 1120.01 0.0920535
\(530\) −2177.37 −0.178451
\(531\) 4978.44 0.406866
\(532\) 4352.40 0.354700
\(533\) −27345.0 −2.22222
\(534\) 3492.56 0.283029
\(535\) 2989.38 0.241574
\(536\) 1019.81 0.0821814
\(537\) −3229.59 −0.259529
\(538\) −4660.88 −0.373504
\(539\) 0 0
\(540\) 2589.60 0.206368
\(541\) 546.481 0.0434289 0.0217145 0.999764i \(-0.493088\pi\)
0.0217145 + 0.999764i \(0.493088\pi\)
\(542\) 747.357 0.0592283
\(543\) −10884.1 −0.860191
\(544\) −3150.38 −0.248293
\(545\) −5500.69 −0.432337
\(546\) 1981.47 0.155310
\(547\) −8397.33 −0.656388 −0.328194 0.944610i \(-0.606440\pi\)
−0.328194 + 0.944610i \(0.606440\pi\)
\(548\) −19313.6 −1.50554
\(549\) −918.839 −0.0714301
\(550\) 0 0
\(551\) −11463.3 −0.886305
\(552\) −7002.58 −0.539945
\(553\) 5719.73 0.439833
\(554\) 7083.32 0.543215
\(555\) −1265.79 −0.0968105
\(556\) 9024.36 0.688342
\(557\) 4881.65 0.371350 0.185675 0.982611i \(-0.440553\pi\)
0.185675 + 0.982611i \(0.440553\pi\)
\(558\) 6346.04 0.481451
\(559\) 20492.6 1.55053
\(560\) 552.797 0.0417142
\(561\) 0 0
\(562\) −2704.38 −0.202985
\(563\) −7198.57 −0.538870 −0.269435 0.963019i \(-0.586837\pi\)
−0.269435 + 0.963019i \(0.586837\pi\)
\(564\) −2959.14 −0.220926
\(565\) −2144.44 −0.159677
\(566\) 1025.95 0.0761904
\(567\) 174.283 0.0129087
\(568\) 15182.5 1.12155
\(569\) 23946.9 1.76433 0.882167 0.470937i \(-0.156084\pi\)
0.882167 + 0.470937i \(0.156084\pi\)
\(570\) 1160.85 0.0853032
\(571\) −1593.15 −0.116763 −0.0583813 0.998294i \(-0.518594\pi\)
−0.0583813 + 0.998294i \(0.518594\pi\)
\(572\) 0 0
\(573\) −1548.59 −0.112903
\(574\) −5086.16 −0.369847
\(575\) 13349.2 0.968174
\(576\) −1168.69 −0.0845403
\(577\) 12937.4 0.933435 0.466717 0.884406i \(-0.345436\pi\)
0.466717 + 0.884406i \(0.345436\pi\)
\(578\) −393.393 −0.0283097
\(579\) 11195.2 0.803549
\(580\) −2395.82 −0.171519
\(581\) 921.499 0.0658007
\(582\) −3412.53 −0.243048
\(583\) 0 0
\(584\) −5695.92 −0.403594
\(585\) 3003.53 0.212275
\(586\) −9803.82 −0.691112
\(587\) −12899.2 −0.906998 −0.453499 0.891257i \(-0.649824\pi\)
−0.453499 + 0.891257i \(0.649824\pi\)
\(588\) 5428.70 0.380741
\(589\) −24384.1 −1.70582
\(590\) 1205.11 0.0840911
\(591\) −4300.23 −0.299302
\(592\) −3039.19 −0.210997
\(593\) −4357.13 −0.301730 −0.150865 0.988554i \(-0.548206\pi\)
−0.150865 + 0.988554i \(0.548206\pi\)
\(594\) 0 0
\(595\) 409.245 0.0281973
\(596\) −1758.23 −0.120839
\(597\) 11790.3 0.808284
\(598\) −9118.14 −0.623526
\(599\) 13726.8 0.936328 0.468164 0.883642i \(-0.344916\pi\)
0.468164 + 0.883642i \(0.344916\pi\)
\(600\) −7035.35 −0.478695
\(601\) −2531.41 −0.171811 −0.0859056 0.996303i \(-0.527378\pi\)
−0.0859056 + 0.996303i \(0.527378\pi\)
\(602\) 3811.62 0.258057
\(603\) −902.830 −0.0609720
\(604\) −4116.24 −0.277297
\(605\) 0 0
\(606\) 1140.15 0.0764283
\(607\) −185.004 −0.0123708 −0.00618540 0.999981i \(-0.501969\pi\)
−0.00618540 + 0.999981i \(0.501969\pi\)
\(608\) 16524.4 1.10223
\(609\) 3220.28 0.214273
\(610\) −222.420 −0.0147632
\(611\) −8867.73 −0.587152
\(612\) 1781.55 0.117672
\(613\) 17706.9 1.16668 0.583339 0.812228i \(-0.301746\pi\)
0.583339 + 0.812228i \(0.301746\pi\)
\(614\) 3301.93 0.217028
\(615\) 4500.39 0.295078
\(616\) 0 0
\(617\) −6183.89 −0.403491 −0.201746 0.979438i \(-0.564661\pi\)
−0.201746 + 0.979438i \(0.564661\pi\)
\(618\) −2246.30 −0.146213
\(619\) −1247.51 −0.0810046 −0.0405023 0.999179i \(-0.512896\pi\)
−0.0405023 + 0.999179i \(0.512896\pi\)
\(620\) −5096.23 −0.330112
\(621\) 16017.4 1.03503
\(622\) 12992.8 0.837561
\(623\) −6458.23 −0.415318
\(624\) −4209.63 −0.270064
\(625\) 12262.8 0.784817
\(626\) −800.914 −0.0511357
\(627\) 0 0
\(628\) −4430.87 −0.281546
\(629\) −2249.96 −0.142626
\(630\) 558.655 0.0353292
\(631\) 24053.3 1.51750 0.758752 0.651379i \(-0.225809\pi\)
0.758752 + 0.651379i \(0.225809\pi\)
\(632\) 13871.5 0.873069
\(633\) 16612.7 1.04312
\(634\) −10417.8 −0.652596
\(635\) −8028.51 −0.501735
\(636\) −10231.4 −0.637893
\(637\) 16268.3 1.01189
\(638\) 0 0
\(639\) −13440.9 −0.832102
\(640\) 4211.70 0.260128
\(641\) −21286.8 −1.31167 −0.655834 0.754905i \(-0.727683\pi\)
−0.655834 + 0.754905i \(0.727683\pi\)
\(642\) −4234.20 −0.260297
\(643\) −1789.41 −0.109747 −0.0548736 0.998493i \(-0.517476\pi\)
−0.0548736 + 0.998493i \(0.517476\pi\)
\(644\) 5626.38 0.344271
\(645\) −3372.64 −0.205888
\(646\) 2063.43 0.125673
\(647\) −4378.61 −0.266060 −0.133030 0.991112i \(-0.542471\pi\)
−0.133030 + 0.991112i \(0.542471\pi\)
\(648\) 422.672 0.0256237
\(649\) 0 0
\(650\) −9160.81 −0.552795
\(651\) 6849.97 0.412399
\(652\) 4159.11 0.249821
\(653\) −7665.15 −0.459358 −0.229679 0.973266i \(-0.573768\pi\)
−0.229679 + 0.973266i \(0.573768\pi\)
\(654\) 7791.26 0.465845
\(655\) 5999.99 0.357922
\(656\) 10805.5 0.643117
\(657\) 5042.54 0.299434
\(658\) −1649.39 −0.0977205
\(659\) 4710.22 0.278428 0.139214 0.990262i \(-0.455542\pi\)
0.139214 + 0.990262i \(0.455542\pi\)
\(660\) 0 0
\(661\) −31266.6 −1.83983 −0.919916 0.392116i \(-0.871743\pi\)
−0.919916 + 0.392116i \(0.871743\pi\)
\(662\) −1024.00 −0.0601192
\(663\) −3116.46 −0.182554
\(664\) 2234.82 0.130614
\(665\) −2146.58 −0.125174
\(666\) −3071.40 −0.178700
\(667\) −14818.7 −0.860246
\(668\) −17431.1 −1.00962
\(669\) 2222.58 0.128446
\(670\) −218.545 −0.0126017
\(671\) 0 0
\(672\) −4642.05 −0.266474
\(673\) −11723.0 −0.671454 −0.335727 0.941959i \(-0.608982\pi\)
−0.335727 + 0.941959i \(0.608982\pi\)
\(674\) −2679.65 −0.153140
\(675\) 16092.3 0.917621
\(676\) −7253.37 −0.412686
\(677\) 289.531 0.0164366 0.00821829 0.999966i \(-0.497384\pi\)
0.00821829 + 0.999966i \(0.497384\pi\)
\(678\) 3037.42 0.172052
\(679\) 6310.25 0.356650
\(680\) 992.502 0.0559716
\(681\) 6786.45 0.381875
\(682\) 0 0
\(683\) 1720.10 0.0963660 0.0481830 0.998839i \(-0.484657\pi\)
0.0481830 + 0.998839i \(0.484657\pi\)
\(684\) −9344.64 −0.522370
\(685\) 9525.37 0.531308
\(686\) 6733.30 0.374750
\(687\) −12356.5 −0.686215
\(688\) −8097.77 −0.448728
\(689\) −30660.5 −1.69532
\(690\) 1500.65 0.0827951
\(691\) −16777.7 −0.923665 −0.461832 0.886967i \(-0.652808\pi\)
−0.461832 + 0.886967i \(0.652808\pi\)
\(692\) −1089.96 −0.0598758
\(693\) 0 0
\(694\) 5421.88 0.296559
\(695\) −4450.77 −0.242917
\(696\) 7809.84 0.425332
\(697\) 7999.50 0.434724
\(698\) 2035.86 0.110399
\(699\) 16381.2 0.886400
\(700\) 5652.71 0.305218
\(701\) −23981.1 −1.29209 −0.646043 0.763301i \(-0.723577\pi\)
−0.646043 + 0.763301i \(0.723577\pi\)
\(702\) −10991.8 −0.590969
\(703\) 11801.6 0.633150
\(704\) 0 0
\(705\) 1459.43 0.0779652
\(706\) −8824.10 −0.470396
\(707\) −2108.30 −0.112151
\(708\) 5662.78 0.300593
\(709\) −7709.28 −0.408361 −0.204181 0.978933i \(-0.565453\pi\)
−0.204181 + 0.978933i \(0.565453\pi\)
\(710\) −3253.59 −0.171979
\(711\) −12280.3 −0.647747
\(712\) −15662.5 −0.824407
\(713\) −31521.5 −1.65567
\(714\) −579.660 −0.0303827
\(715\) 0 0
\(716\) 6293.13 0.328471
\(717\) −1054.61 −0.0549304
\(718\) −6729.09 −0.349760
\(719\) −11976.5 −0.621209 −0.310605 0.950539i \(-0.600532\pi\)
−0.310605 + 0.950539i \(0.600532\pi\)
\(720\) −1186.86 −0.0614329
\(721\) 4153.72 0.214553
\(722\) −1486.56 −0.0766260
\(723\) 6052.00 0.311309
\(724\) 21208.7 1.08870
\(725\) −14888.1 −0.762662
\(726\) 0 0
\(727\) −18597.3 −0.948745 −0.474372 0.880324i \(-0.657325\pi\)
−0.474372 + 0.880324i \(0.657325\pi\)
\(728\) −8886.00 −0.452386
\(729\) 11461.4 0.582300
\(730\) 1220.63 0.0618870
\(731\) −5994.91 −0.303324
\(732\) −1045.14 −0.0527727
\(733\) 23569.5 1.18767 0.593833 0.804588i \(-0.297614\pi\)
0.593833 + 0.804588i \(0.297614\pi\)
\(734\) 20.2646 0.00101905
\(735\) −2677.41 −0.134364
\(736\) 21361.3 1.06982
\(737\) 0 0
\(738\) 10920.0 0.544678
\(739\) −10149.1 −0.505199 −0.252599 0.967571i \(-0.581285\pi\)
−0.252599 + 0.967571i \(0.581285\pi\)
\(740\) 2466.50 0.122528
\(741\) 16346.5 0.810397
\(742\) −5702.85 −0.282154
\(743\) −27758.0 −1.37058 −0.685291 0.728269i \(-0.740325\pi\)
−0.685291 + 0.728269i \(0.740325\pi\)
\(744\) 16612.6 0.818611
\(745\) 867.148 0.0426441
\(746\) 2617.87 0.128481
\(747\) −1978.47 −0.0969054
\(748\) 0 0
\(749\) 7829.63 0.381960
\(750\) 3134.99 0.152632
\(751\) −815.225 −0.0396112 −0.0198056 0.999804i \(-0.506305\pi\)
−0.0198056 + 0.999804i \(0.506305\pi\)
\(752\) 3504.13 0.169924
\(753\) 24277.1 1.17491
\(754\) 10169.3 0.491172
\(755\) 2030.11 0.0978585
\(756\) 6782.56 0.326295
\(757\) −13239.4 −0.635659 −0.317829 0.948148i \(-0.602954\pi\)
−0.317829 + 0.948148i \(0.602954\pi\)
\(758\) 13058.0 0.625710
\(759\) 0 0
\(760\) −5205.90 −0.248471
\(761\) 11028.2 0.525324 0.262662 0.964888i \(-0.415400\pi\)
0.262662 + 0.964888i \(0.415400\pi\)
\(762\) 11371.7 0.540621
\(763\) −14407.1 −0.683582
\(764\) 3017.56 0.142895
\(765\) −878.652 −0.0415265
\(766\) 12365.0 0.583246
\(767\) 16969.8 0.798882
\(768\) −7695.55 −0.361574
\(769\) 18921.2 0.887277 0.443639 0.896206i \(-0.353687\pi\)
0.443639 + 0.896206i \(0.353687\pi\)
\(770\) 0 0
\(771\) 16830.3 0.786158
\(772\) −21814.7 −1.01701
\(773\) 38728.6 1.80203 0.901016 0.433786i \(-0.142823\pi\)
0.901016 + 0.433786i \(0.142823\pi\)
\(774\) −8183.59 −0.380043
\(775\) −31669.0 −1.46785
\(776\) 15303.6 0.707949
\(777\) −3315.29 −0.153070
\(778\) 1556.93 0.0717465
\(779\) −41959.2 −1.92984
\(780\) 3416.39 0.156829
\(781\) 0 0
\(782\) 2667.42 0.121978
\(783\) −17863.9 −0.815329
\(784\) −6428.50 −0.292844
\(785\) 2185.28 0.0993579
\(786\) −8498.47 −0.385662
\(787\) 20587.3 0.932477 0.466239 0.884659i \(-0.345609\pi\)
0.466239 + 0.884659i \(0.345609\pi\)
\(788\) 8379.37 0.378811
\(789\) −12410.8 −0.559995
\(790\) −2972.66 −0.133876
\(791\) −5616.62 −0.252470
\(792\) 0 0
\(793\) −3132.00 −0.140253
\(794\) −14435.0 −0.645190
\(795\) 5046.05 0.225113
\(796\) −22974.5 −1.02300
\(797\) −15871.4 −0.705385 −0.352693 0.935739i \(-0.614734\pi\)
−0.352693 + 0.935739i \(0.614734\pi\)
\(798\) 3040.45 0.134876
\(799\) 2594.17 0.114862
\(800\) 21461.3 0.948463
\(801\) 13865.9 0.611644
\(802\) −18765.0 −0.826204
\(803\) 0 0
\(804\) −1026.93 −0.0450462
\(805\) −2774.90 −0.121494
\(806\) 21631.4 0.945329
\(807\) 10801.6 0.471170
\(808\) −5113.06 −0.222620
\(809\) −39667.1 −1.72388 −0.861942 0.507007i \(-0.830752\pi\)
−0.861942 + 0.507007i \(0.830752\pi\)
\(810\) −90.5783 −0.00392913
\(811\) −8003.87 −0.346552 −0.173276 0.984873i \(-0.555435\pi\)
−0.173276 + 0.984873i \(0.555435\pi\)
\(812\) −6275.00 −0.271194
\(813\) −1732.00 −0.0747157
\(814\) 0 0
\(815\) −2051.25 −0.0881621
\(816\) 1231.48 0.0528316
\(817\) 31444.7 1.34652
\(818\) −12939.7 −0.553088
\(819\) 7866.69 0.335634
\(820\) −8769.40 −0.373464
\(821\) 13279.1 0.564489 0.282244 0.959343i \(-0.408921\pi\)
0.282244 + 0.959343i \(0.408921\pi\)
\(822\) −13491.9 −0.572486
\(823\) 28934.0 1.22549 0.612745 0.790281i \(-0.290065\pi\)
0.612745 + 0.790281i \(0.290065\pi\)
\(824\) 10073.6 0.425887
\(825\) 0 0
\(826\) 3156.37 0.132959
\(827\) 13679.6 0.575193 0.287597 0.957752i \(-0.407144\pi\)
0.287597 + 0.957752i \(0.407144\pi\)
\(828\) −12079.9 −0.507012
\(829\) 16514.5 0.691886 0.345943 0.938256i \(-0.387559\pi\)
0.345943 + 0.938256i \(0.387559\pi\)
\(830\) −478.921 −0.0200284
\(831\) −16415.6 −0.685260
\(832\) −3983.64 −0.165995
\(833\) −4759.13 −0.197952
\(834\) 6304.13 0.261744
\(835\) 8596.93 0.356298
\(836\) 0 0
\(837\) −37998.9 −1.56922
\(838\) −13177.8 −0.543221
\(839\) −87.9839 −0.00362043 −0.00181022 0.999998i \(-0.500576\pi\)
−0.00181022 + 0.999998i \(0.500576\pi\)
\(840\) 1462.44 0.0600702
\(841\) −7861.94 −0.322356
\(842\) 16825.1 0.688635
\(843\) 6267.41 0.256063
\(844\) −32371.3 −1.32022
\(845\) 3577.33 0.145638
\(846\) 3541.27 0.143914
\(847\) 0 0
\(848\) 12115.7 0.490630
\(849\) −2377.63 −0.0961133
\(850\) 2679.90 0.108141
\(851\) 15256.0 0.614534
\(852\) −15288.5 −0.614758
\(853\) −8162.96 −0.327660 −0.163830 0.986489i \(-0.552385\pi\)
−0.163830 + 0.986489i \(0.552385\pi\)
\(854\) −582.551 −0.0233425
\(855\) 4608.73 0.184345
\(856\) 18988.4 0.758191
\(857\) −18724.9 −0.746361 −0.373181 0.927759i \(-0.621733\pi\)
−0.373181 + 0.927759i \(0.621733\pi\)
\(858\) 0 0
\(859\) −46422.5 −1.84391 −0.921953 0.387301i \(-0.873407\pi\)
−0.921953 + 0.387301i \(0.873407\pi\)
\(860\) 6571.88 0.260580
\(861\) 11787.2 0.466557
\(862\) 4043.61 0.159775
\(863\) 29112.3 1.14831 0.574157 0.818746i \(-0.305330\pi\)
0.574157 + 0.818746i \(0.305330\pi\)
\(864\) 25750.8 1.01396
\(865\) 537.563 0.0211303
\(866\) −8346.33 −0.327505
\(867\) 911.688 0.0357123
\(868\) −13347.8 −0.521950
\(869\) 0 0
\(870\) −1673.64 −0.0652204
\(871\) −3077.43 −0.119719
\(872\) −34940.2 −1.35691
\(873\) −13548.2 −0.525241
\(874\) −13991.2 −0.541487
\(875\) −5797.04 −0.223972
\(876\) 5735.69 0.221222
\(877\) −39163.0 −1.50791 −0.753957 0.656924i \(-0.771857\pi\)
−0.753957 + 0.656924i \(0.771857\pi\)
\(878\) −3464.19 −0.133156
\(879\) 22720.3 0.871830
\(880\) 0 0
\(881\) −35073.2 −1.34125 −0.670627 0.741795i \(-0.733975\pi\)
−0.670627 + 0.741795i \(0.733975\pi\)
\(882\) −6496.63 −0.248019
\(883\) −48775.7 −1.85893 −0.929463 0.368915i \(-0.879729\pi\)
−0.929463 + 0.368915i \(0.879729\pi\)
\(884\) 6072.69 0.231048
\(885\) −2792.85 −0.106080
\(886\) −11611.0 −0.440269
\(887\) −13296.0 −0.503309 −0.251654 0.967817i \(-0.580975\pi\)
−0.251654 + 0.967817i \(0.580975\pi\)
\(888\) −8040.27 −0.303844
\(889\) −21027.9 −0.793309
\(890\) 3356.46 0.126415
\(891\) 0 0
\(892\) −4330.90 −0.162566
\(893\) −13607.0 −0.509899
\(894\) −1228.24 −0.0459492
\(895\) −3103.74 −0.115918
\(896\) 11031.1 0.411297
\(897\) 21131.3 0.786570
\(898\) −12054.6 −0.447960
\(899\) 35155.3 1.30422
\(900\) −12136.4 −0.449498
\(901\) 8969.43 0.331648
\(902\) 0 0
\(903\) −8833.44 −0.325535
\(904\) −13621.4 −0.501153
\(905\) −10460.0 −0.384202
\(906\) −2875.47 −0.105443
\(907\) −11675.0 −0.427410 −0.213705 0.976898i \(-0.568553\pi\)
−0.213705 + 0.976898i \(0.568553\pi\)
\(908\) −13224.0 −0.483319
\(909\) 4526.54 0.165166
\(910\) 1904.26 0.0693689
\(911\) 18552.9 0.674738 0.337369 0.941372i \(-0.390463\pi\)
0.337369 + 0.941372i \(0.390463\pi\)
\(912\) −6459.41 −0.234531
\(913\) 0 0
\(914\) −9739.24 −0.352457
\(915\) 515.459 0.0186235
\(916\) 24077.7 0.868504
\(917\) 15714.9 0.565922
\(918\) 3215.55 0.115609
\(919\) −33956.8 −1.21886 −0.609429 0.792841i \(-0.708601\pi\)
−0.609429 + 0.792841i \(0.708601\pi\)
\(920\) −6729.71 −0.241165
\(921\) −7652.23 −0.273778
\(922\) −9886.63 −0.353144
\(923\) −45815.3 −1.63383
\(924\) 0 0
\(925\) 15327.4 0.544823
\(926\) −480.372 −0.0170475
\(927\) −8918.08 −0.315974
\(928\) −23823.8 −0.842732
\(929\) −23695.3 −0.836832 −0.418416 0.908256i \(-0.637415\pi\)
−0.418416 + 0.908256i \(0.637415\pi\)
\(930\) −3560.06 −0.125526
\(931\) 24962.7 0.878753
\(932\) −31920.2 −1.12187
\(933\) −30110.8 −1.05657
\(934\) −2018.72 −0.0707221
\(935\) 0 0
\(936\) 19078.3 0.666234
\(937\) −7990.62 −0.278593 −0.139297 0.990251i \(-0.544484\pi\)
−0.139297 + 0.990251i \(0.544484\pi\)
\(938\) −572.402 −0.0199249
\(939\) 1856.12 0.0645071
\(940\) −2843.83 −0.0986762
\(941\) −24385.9 −0.844799 −0.422400 0.906410i \(-0.638812\pi\)
−0.422400 + 0.906410i \(0.638812\pi\)
\(942\) −3095.26 −0.107058
\(943\) −54241.0 −1.87310
\(944\) −6705.69 −0.231199
\(945\) −3345.12 −0.115150
\(946\) 0 0
\(947\) −1174.62 −0.0403064 −0.0201532 0.999797i \(-0.506415\pi\)
−0.0201532 + 0.999797i \(0.506415\pi\)
\(948\) −13968.4 −0.478557
\(949\) 17188.3 0.587939
\(950\) −14056.7 −0.480063
\(951\) 24143.4 0.823241
\(952\) 2599.51 0.0884985
\(953\) 33546.9 1.14029 0.570143 0.821546i \(-0.306888\pi\)
0.570143 + 0.821546i \(0.306888\pi\)
\(954\) 12244.1 0.415531
\(955\) −1488.25 −0.0504277
\(956\) 2055.00 0.0695224
\(957\) 0 0
\(958\) −13598.7 −0.458617
\(959\) 24948.4 0.840067
\(960\) 655.620 0.0220417
\(961\) 44989.1 1.51016
\(962\) −10469.3 −0.350878
\(963\) −16810.3 −0.562517
\(964\) −11792.9 −0.394007
\(965\) 10758.9 0.358903
\(966\) 3930.41 0.130910
\(967\) −24766.8 −0.823625 −0.411813 0.911269i \(-0.635104\pi\)
−0.411813 + 0.911269i \(0.635104\pi\)
\(968\) 0 0
\(969\) −4782.01 −0.158535
\(970\) −3279.56 −0.108557
\(971\) 42324.3 1.39882 0.699409 0.714721i \(-0.253447\pi\)
0.699409 + 0.714721i \(0.253447\pi\)
\(972\) −23488.3 −0.775091
\(973\) −11657.2 −0.384083
\(974\) 1538.01 0.0505966
\(975\) 21230.2 0.697344
\(976\) 1237.63 0.0405896
\(977\) −11320.4 −0.370698 −0.185349 0.982673i \(-0.559342\pi\)
−0.185349 + 0.982673i \(0.559342\pi\)
\(978\) 2905.42 0.0949949
\(979\) 0 0
\(980\) 5217.16 0.170057
\(981\) 30932.2 1.00672
\(982\) 25556.8 0.830500
\(983\) −11311.9 −0.367032 −0.183516 0.983017i \(-0.558748\pi\)
−0.183516 + 0.983017i \(0.558748\pi\)
\(984\) 28586.3 0.926116
\(985\) −4132.66 −0.133683
\(986\) −2974.92 −0.0960860
\(987\) 3822.47 0.123273
\(988\) −31852.6 −1.02568
\(989\) 40648.8 1.30693
\(990\) 0 0
\(991\) −29405.5 −0.942580 −0.471290 0.881978i \(-0.656212\pi\)
−0.471290 + 0.881978i \(0.656212\pi\)
\(992\) −50676.5 −1.62196
\(993\) 2373.12 0.0758397
\(994\) −8521.63 −0.271921
\(995\) 11330.9 0.361018
\(996\) −2250.43 −0.0715939
\(997\) 54905.9 1.74412 0.872060 0.489398i \(-0.162784\pi\)
0.872060 + 0.489398i \(0.162784\pi\)
\(998\) −23588.7 −0.748183
\(999\) 18390.9 0.582446
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 2057.4.a.e.1.2 3
11.10 odd 2 17.4.a.b.1.2 3
33.32 even 2 153.4.a.g.1.2 3
44.43 even 2 272.4.a.h.1.2 3
55.32 even 4 425.4.b.f.324.4 6
55.43 even 4 425.4.b.f.324.3 6
55.54 odd 2 425.4.a.g.1.2 3
77.76 even 2 833.4.a.d.1.2 3
88.21 odd 2 1088.4.a.v.1.2 3
88.43 even 2 1088.4.a.x.1.2 3
132.131 odd 2 2448.4.a.bi.1.1 3
187.21 odd 4 289.4.b.b.288.3 6
187.98 odd 4 289.4.b.b.288.4 6
187.186 odd 2 289.4.a.b.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.b.1.2 3 11.10 odd 2
153.4.a.g.1.2 3 33.32 even 2
272.4.a.h.1.2 3 44.43 even 2
289.4.a.b.1.2 3 187.186 odd 2
289.4.b.b.288.3 6 187.21 odd 4
289.4.b.b.288.4 6 187.98 odd 4
425.4.a.g.1.2 3 55.54 odd 2
425.4.b.f.324.3 6 55.43 even 4
425.4.b.f.324.4 6 55.32 even 4
833.4.a.d.1.2 3 77.76 even 2
1088.4.a.v.1.2 3 88.21 odd 2
1088.4.a.x.1.2 3 88.43 even 2
2057.4.a.e.1.2 3 1.1 even 1 trivial
2448.4.a.bi.1.1 3 132.131 odd 2