Properties

Label 289.4.a.b.1.2
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.0515519917\)
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 \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} -3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} -19.2573 q^{8} -17.0483 q^{9} +O(q^{10})\) \(q+1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} -3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} -19.2573 q^{8} -17.0483 q^{9} -4.12682 q^{10} -27.6161 q^{11} +19.3918 q^{12} +58.1117 q^{13} +10.8088 q^{14} +9.56391 q^{15} +22.9632 q^{16} -23.2065 q^{18} +89.1688 q^{19} +18.6361 q^{20} -25.0493 q^{21} -37.5916 q^{22} +115.269 q^{23} +60.7497 q^{24} -115.809 q^{25} +79.1029 q^{26} +138.956 q^{27} -48.8108 q^{28} +128.558 q^{29} +13.0186 q^{30} -273.460 q^{31} +185.316 q^{32} +87.1187 q^{33} -24.0732 q^{35} +104.797 q^{36} +132.351 q^{37} +121.379 q^{38} -183.321 q^{39} +58.3825 q^{40} +470.559 q^{41} -34.0977 q^{42} +352.642 q^{43} +169.758 q^{44} +51.6854 q^{45} +156.907 q^{46} +152.598 q^{47} -72.4403 q^{48} -279.949 q^{49} -157.641 q^{50} -357.217 q^{52} +527.614 q^{53} +189.150 q^{54} +83.7239 q^{55} -152.912 q^{56} -281.295 q^{57} +174.995 q^{58} -292.020 q^{59} -58.7901 q^{60} +53.8962 q^{61} -372.239 q^{62} -135.372 q^{63} +68.5514 q^{64} -176.178 q^{65} +118.588 q^{66} +52.9572 q^{67} -363.632 q^{69} -32.7690 q^{70} -788.400 q^{71} +328.304 q^{72} -295.780 q^{73} +180.159 q^{74} +365.334 q^{75} -548.127 q^{76} -219.285 q^{77} -249.541 q^{78} +720.325 q^{79} -69.6175 q^{80} +21.9487 q^{81} +640.535 q^{82} -116.051 q^{83} +153.980 q^{84} +480.024 q^{86} -405.552 q^{87} +531.812 q^{88} -813.329 q^{89} +70.3553 q^{90} +461.435 q^{91} -708.569 q^{92} +862.664 q^{93} +207.720 q^{94} -270.334 q^{95} -584.605 q^{96} -794.693 q^{97} -381.072 q^{98} +470.808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 22 q^{7} - 39 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 22 q^{7} - 39 q^{8} + 59 q^{9} + 56 q^{10} + 28 q^{11} - 22 q^{12} + 30 q^{13} - 92 q^{14} + 108 q^{15} + 137 q^{16} - 103 q^{18} + 80 q^{19} + 168 q^{20} - 192 q^{21} - 286 q^{22} - 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} + 20 q^{27} - 476 q^{28} + 456 q^{29} + 400 q^{30} - 230 q^{31} - 71 q^{32} - 332 q^{33} - 332 q^{35} + 1313 q^{36} - 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} + 556 q^{43} + 1122 q^{44} + 384 q^{45} + 704 q^{46} + 640 q^{47} - 774 q^{48} - 269 q^{49} + 547 q^{50} - 774 q^{52} + 302 q^{53} + 1100 q^{54} + 76 q^{55} - 684 q^{56} + 720 q^{57} + 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 2468 q^{66} + 1008 q^{67} + 576 q^{69} - 1504 q^{70} + 402 q^{71} - 927 q^{72} - 838 q^{73} - 836 q^{74} + 1548 q^{75} - 908 q^{76} - 504 q^{77} - 1308 q^{78} + 594 q^{79} + 40 q^{80} - 505 q^{81} - 358 q^{82} - 2396 q^{83} - 2040 q^{84} - 1264 q^{86} + 1428 q^{87} - 1838 q^{88} - 170 q^{89} + 2008 q^{90} + 1016 q^{91} - 4896 q^{92} + 632 q^{93} - 2016 q^{94} + 472 q^{95} - 678 q^{96} + 270 q^{97} + 2857 q^{98} + 2920 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36122 0.481264 0.240632 0.970616i \(-0.422645\pi\)
0.240632 + 0.970616i \(0.422645\pi\)
\(3\) −3.15463 −0.607109 −0.303555 0.952814i \(-0.598173\pi\)
−0.303555 + 0.952814i \(0.598173\pi\)
\(4\) −6.14708 −0.768385
\(5\) −3.03171 −0.271164 −0.135582 0.990766i \(-0.543290\pi\)
−0.135582 + 0.990766i \(0.543290\pi\)
\(6\) −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
\(11\) −27.6161 −0.756961 −0.378481 0.925609i \(-0.623553\pi\)
−0.378481 + 0.925609i \(0.623553\pi\)
\(12\) 19.3918 0.466493
\(13\) 58.1117 1.23979 0.619896 0.784684i \(-0.287175\pi\)
0.619896 + 0.784684i \(0.287175\pi\)
\(14\) 10.8088 0.206340
\(15\) 9.56391 0.164626
\(16\) 22.9632 0.358799
\(17\) 0 0
\(18\) −23.2065 −0.303879
\(19\) 89.1688 1.07667 0.538335 0.842731i \(-0.319054\pi\)
0.538335 + 0.842731i \(0.319054\pi\)
\(20\) 18.6361 0.208358
\(21\) −25.0493 −0.260296
\(22\) −37.5916 −0.364298
\(23\) 115.269 1.04501 0.522507 0.852635i \(-0.324997\pi\)
0.522507 + 0.852635i \(0.324997\pi\)
\(24\) 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 \(-0.791051\pi\)
−0.792174 + 0.610295i \(0.791051\pi\)
\(32\) 185.316 1.02374
\(33\) 87.1187 0.459558
\(34\) 0 0
\(35\) −24.0732 −0.116260
\(36\) 104.797 0.485172
\(37\) 132.351 0.588063 0.294031 0.955796i \(-0.405003\pi\)
0.294031 + 0.955796i \(0.405003\pi\)
\(38\) 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 \(-0.284969\pi\)
0.625318 + 0.780370i \(0.284969\pi\)
\(44\) 169.758 0.581637
\(45\) 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
\(51\) 0 0
\(52\) −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
\(55\) 83.7239 0.205261
\(56\) −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
\(66\) 118.588 0.221169
\(67\) 52.9572 0.0965635 0.0482817 0.998834i \(-0.484625\pi\)
0.0482817 + 0.998834i \(0.484625\pi\)
\(68\) 0 0
\(69\) −363.632 −0.634437
\(70\) −32.7690 −0.0559520
\(71\) −788.400 −1.31783 −0.658915 0.752218i \(-0.728984\pi\)
−0.658915 + 0.752218i \(0.728984\pi\)
\(72\) 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
\(77\) −219.285 −0.324544
\(78\) −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 \(-0.524450\pi\)
−0.0767363 + 0.997051i \(0.524450\pi\)
\(84\) 153.980 0.200007
\(85\) 0 0
\(86\) 480.024 0.601887
\(87\) −405.552 −0.499767
\(88\) 531.812 0.644220
\(89\) −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 \(-0.636541\pi\)
−0.415922 + 0.909400i \(0.636541\pi\)
\(98\) −381.072 −0.392797
\(99\) 470.808 0.477959
\(100\) 711.885 0.711885
\(101\) 265.513 0.261579 0.130790 0.991410i \(-0.458249\pi\)
0.130790 + 0.991410i \(0.458249\pi\)
\(102\) 0 0
\(103\) 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 \(0.793680\pi\)
\(110\) 113.967 0.0987846
\(111\) −417.518 −0.357018
\(112\) 182.339 0.153834
\(113\) 707.339 0.588857 0.294429 0.955673i \(-0.404871\pi\)
0.294429 + 0.955673i \(0.404871\pi\)
\(114\) −382.904 −0.314581
\(115\) −349.463 −0.283370
\(116\) −790.253 −0.632527
\(117\) −990.706 −0.782827
\(118\) −397.503 −0.310112
\(119\) 0 0
\(120\) −184.175 −0.140107
\(121\) −568.350 −0.427010
\(122\) 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 \(-0.123938\pi\)
0.925151 + 0.379600i \(0.123938\pi\)
\(128\) −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 \(0.270567\pi\)
\(132\) −535.525 −0.353117
\(133\) 708.044 0.461618
\(134\) 72.0865 0.0464726
\(135\) −421.274 −0.268574
\(136\) 0 0
\(137\) 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
\(143\) −1604.82 −0.938474
\(144\) −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 \(-0.525055\pi\)
−0.0786316 + 0.996904i \(0.525055\pi\)
\(150\) 497.300 0.270696
\(151\) −669.626 −0.360883 −0.180442 0.983586i \(-0.557753\pi\)
−0.180442 + 0.983586i \(0.557753\pi\)
\(152\) −1717.15 −0.916311
\(153\) 0 0
\(154\) −298.496 −0.156191
\(155\) 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 \(-0.448024\pi\)
0.162562 + 0.986698i \(0.448024\pi\)
\(164\) −2892.56 −1.37726
\(165\) −264.118 −0.124616
\(166\) −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
\(170\) 0 0
\(171\) −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
\(176\) −634.153 −0.271597
\(177\) 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 \(-0.249403\pi\)
0.708432 + 0.705779i \(0.249403\pi\)
\(182\) 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 \(0.579280\pi\)
\(198\) 640.874 0.230025
\(199\) −3737.46 −1.33137 −0.665683 0.746235i \(-0.731860\pi\)
−0.665683 + 0.746235i \(0.731860\pi\)
\(200\) 2230.16 0.788482
\(201\) −167.060 −0.0586246
\(202\) 361.422 0.125889
\(203\) 1020.81 0.352940
\(204\) 0 0
\(205\) −1426.60 −0.486038
\(206\) 712.064 0.240834
\(207\) −1965.15 −0.659841
\(208\) 1334.43 0.444836
\(209\) −2462.50 −0.814997
\(210\) 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
\(220\) −514.657 −0.157719
\(221\) 0 0
\(222\) −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
\(231\) 691.764 0.197034
\(232\) −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
\(238\) 0 0
\(239\) 334.305 0.0904786 0.0452393 0.998976i \(-0.485595\pi\)
0.0452393 + 0.998976i \(0.485595\pi\)
\(240\) 219.618 0.0590677
\(241\) 1918.45 0.512773 0.256386 0.966574i \(-0.417468\pi\)
0.256386 + 0.966574i \(0.417468\pi\)
\(242\) −773.651 −0.205505
\(243\) −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
\(253\) −3183.29 −0.791035
\(254\) 3604.76 0.890484
\(255\) 0 0
\(256\) −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 \(-0.347420\pi\)
0.461198 + 0.887297i \(0.347420\pi\)
\(264\) −1677.67 −0.391112
\(265\) −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 \(-0.626849\pi\)
−0.388044 + 0.921641i \(0.626849\pi\)
\(270\) −573.447 −0.129255
\(271\) 549.034 0.123068 0.0615340 0.998105i \(-0.480401\pi\)
0.0615340 + 0.998105i \(0.480401\pi\)
\(272\) 0 0
\(273\) −1455.66 −0.322712
\(274\) 4276.85 0.942970
\(275\) 3198.19 0.701302
\(276\) 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 \(-0.567635\pi\)
−0.210887 + 0.977510i \(0.567635\pi\)
\(282\) −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
\(286\) −2184.51 −0.451654
\(287\) 3736.47 0.768490
\(288\) −3159.33 −0.646407
\(289\) 0 0
\(290\) −530.534 −0.107428
\(291\) 2506.96 0.505020
\(292\) 1818.18 0.364387
\(293\) −7202.22 −1.43603 −0.718017 0.696025i \(-0.754950\pi\)
−0.718017 + 0.696025i \(0.754950\pi\)
\(294\) 1202.14 0.238471
\(295\) 885.318 0.174729
\(296\) −2548.72 −0.500477
\(297\) −3837.43 −0.749731
\(298\) −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
\(306\) 0 0
\(307\) 2425.71 0.450953 0.225477 0.974249i \(-0.427606\pi\)
0.225477 + 0.974249i \(0.427606\pi\)
\(308\) 1347.96 0.249375
\(309\) −1650.21 −0.303809
\(310\) 1128.52 0.206760
\(311\) 9544.94 1.74033 0.870167 0.492757i \(-0.164011\pi\)
0.870167 + 0.492757i \(0.164011\pi\)
\(312\) 3530.27 0.640584
\(313\) −588.379 −0.106253 −0.0531264 0.998588i \(-0.516919\pi\)
−0.0531264 + 0.998588i \(0.516919\pi\)
\(314\) 981.180 0.176341
\(315\) 410.407 0.0734090
\(316\) −4427.89 −0.788255
\(317\) −7653.31 −1.35600 −0.678001 0.735061i \(-0.737154\pi\)
−0.678001 + 0.735061i \(0.737154\pi\)
\(318\) −2265.65 −0.399533
\(319\) −3550.26 −0.623124
\(320\) −207.828 −0.0363060
\(321\) −3110.59 −0.540860
\(322\) 1245.92 0.215628
\(323\) 0 0
\(324\) −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
\(330\) −359.523 −0.0599730
\(331\) 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
\(340\) 0 0
\(341\) 7551.89 1.19929
\(342\) −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 \(-0.463410\pi\)
0.114697 + 0.993401i \(0.463410\pi\)
\(350\) −1251.75 −0.191168
\(351\) 8074.98 1.22795
\(352\) −5117.72 −0.774930
\(353\) 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
\(357\) 0 0
\(358\) −1393.56 −0.205732
\(359\) −4943.42 −0.726751 −0.363376 0.931643i \(-0.618376\pi\)
−0.363376 + 0.931643i \(0.618376\pi\)
\(360\) −995.322 −0.145717
\(361\) 1092.08 0.159218
\(362\) 4696.50 0.681886
\(363\) 1792.94 0.259242
\(364\) −2836.48 −0.408439
\(365\) 896.717 0.128593
\(366\) −231.439 −0.0330533
\(367\) 14.8871 0.00211743 0.00105872 0.999999i \(-0.499663\pi\)
0.00105872 + 0.999999i \(0.499663\pi\)
\(368\) 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 \(-0.457384\pi\)
0.133483 + 0.991051i \(0.457384\pi\)
\(374\) 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 \(-0.274740\pi\)
0.650069 + 0.759875i \(0.274740\pi\)
\(380\) 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
\(385\) 664.809 0.0880046
\(386\) 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
\(391\) 0 0
\(392\) 5391.06 0.694616
\(393\) −6243.27 −0.801352
\(394\) −1855.55 −0.237262
\(395\) −2183.81 −0.278176
\(396\) −2894.09 −0.367256
\(397\) −10604.5 −1.34061 −0.670307 0.742084i \(-0.733838\pi\)
−0.670307 + 0.742084i \(0.733838\pi\)
\(398\) −5087.51 −0.640739
\(399\) −2233.62 −0.280252
\(400\) −2659.33 −0.332417
\(401\) −13785.4 −1.71674 −0.858368 0.513035i \(-0.828521\pi\)
−0.858368 + 0.513035i \(0.828521\pi\)
\(402\) −227.406 −0.0282139
\(403\) −15891.2 −1.96426
\(404\) −1632.13 −0.200993
\(405\) −66.5420 −0.00816419
\(406\) 1389.55 0.169857
\(407\) −3655.01 −0.445141
\(408\) 0 0
\(409\) −9505.94 −1.14924 −0.574619 0.818421i \(-0.694850\pi\)
−0.574619 + 0.818421i \(0.694850\pi\)
\(410\) −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
\(418\) −3352.00 −0.392229
\(419\) −9680.86 −1.12874 −0.564369 0.825523i \(-0.690880\pi\)
−0.564369 + 0.825523i \(0.690880\pi\)
\(420\) −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
\(425\) 0 0
\(426\) 3385.51 0.385043
\(427\) 427.962 0.0485025
\(428\) −6061.25 −0.684537
\(429\) 5062.61 0.569756
\(430\) −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 \(0.455824\pi\)
\(440\) −1612.30 −0.174689
\(441\) 4772.65 0.515349
\(442\) 0 0
\(443\) 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 \(-0.654089\pi\)
−0.465399 + 0.885101i \(0.654089\pi\)
\(450\) 2687.52 0.281535
\(451\) −12995.0 −1.35679
\(452\) −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 \(-0.619334\pi\)
−0.366178 + 0.930545i \(0.619334\pi\)
\(458\) −5331.82 −0.543973
\(459\) 0 0
\(460\) 2148.17 0.217737
\(461\) −7263.06 −0.733784 −0.366892 0.930264i \(-0.619578\pi\)
−0.366892 + 0.930264i \(0.619578\pi\)
\(462\) 941.645 0.0948253
\(463\) 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
\(473\) −9738.60 −0.946683
\(474\) −3093.19 −0.299736
\(475\) −10326.5 −0.997502
\(476\) 0 0
\(477\) −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
\(484\) 3493.69 0.328108
\(485\) 2409.27 0.225566
\(486\) −5201.30 −0.485465
\(487\) 1129.88 0.105133 0.0525663 0.998617i \(-0.483260\pi\)
0.0525663 + 0.998617i \(0.483260\pi\)
\(488\) −1037.90 −0.0962774
\(489\) −2134.42 −0.197386
\(490\) 1155.30 0.106512
\(491\) 18774.9 1.72566 0.862832 0.505491i \(-0.168689\pi\)
0.862832 + 0.505491i \(0.168689\pi\)
\(492\) 9124.97 0.836149
\(493\) 0 0
\(494\) 7053.51 0.642414
\(495\) −1427.35 −0.129605
\(496\) −6279.49 −0.568463
\(497\) −6260.28 −0.565014
\(498\) 498.339 0.0448416
\(499\) −17329.1 −1.55462 −0.777310 0.629118i \(-0.783416\pi\)
−0.777310 + 0.629118i \(0.783416\pi\)
\(500\) −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
\(506\) −4333.16 −0.380697
\(507\) −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 \(0.327680\pi\)
\(510\) 0 0
\(511\) −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
\(517\) −4214.16 −0.358489
\(518\) 1430.55 0.121341
\(519\) −559.359 −0.0473086
\(520\) 3392.71 0.286115
\(521\) −7686.37 −0.646346 −0.323173 0.946340i \(-0.604750\pi\)
−0.323173 + 0.946340i \(0.604750\pi\)
\(522\) −2983.37 −0.250151
\(523\) 11476.4 0.959518 0.479759 0.877400i \(-0.340724\pi\)
0.479759 + 0.877400i \(0.340724\pi\)
\(524\) −12165.6 −1.01423
\(525\) 2900.93 0.241156
\(526\) 5355.25 0.443916
\(527\) 0 0
\(528\) 2000.52 0.164889
\(529\) 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
\(539\) 7731.09 0.617814
\(540\) 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
\(544\) 0 0
\(545\) 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
\(550\) 4353.44 0.337512
\(551\) 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 \(-0.559447\pi\)
−0.185675 + 0.982611i \(0.559447\pi\)
\(558\) 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 \(-0.413163\pi\)
0.269435 + 0.963019i \(0.413163\pi\)
\(564\) 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 \(-0.843916\pi\)
−0.882167 + 0.470937i \(0.843916\pi\)
\(570\) 1160.85 0.0853032
\(571\) −1593.15 −0.116763 −0.0583813 0.998294i \(-0.518594\pi\)
−0.0583813 + 0.998294i \(0.518594\pi\)
\(572\) 9864.95 0.721109
\(573\) 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 \(0.345436\pi\)
\(578\) 0 0
\(579\) −11195.2 −0.803549
\(580\) 2395.82 0.171519
\(581\) −921.499 −0.0658007
\(582\) 3412.53 0.243048
\(583\) −14570.6 −1.03508
\(584\) 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 \(-0.451794\pi\)
0.150865 + 0.988554i \(0.451794\pi\)
\(594\) −5223.59 −0.360819
\(595\) 0 0
\(596\) 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
\(605\) 1723.07 0.115790
\(606\) −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
\(612\) 0 0
\(613\) −17706.9 −1.16668 −0.583339 0.812228i \(-0.698254\pi\)
−0.583339 + 0.812228i \(0.698254\pi\)
\(614\) 3301.93 0.217028
\(615\) 4500.39 0.295078
\(616\) 4222.84 0.276207
\(617\) 6183.89 0.403491 0.201746 0.979438i \(-0.435339\pi\)
0.201746 + 0.979438i \(0.435339\pi\)
\(618\) −2246.30 −0.146213
\(619\) 1247.51 0.0810046 0.0405023 0.999179i \(-0.487104\pi\)
0.0405023 + 0.999179i \(0.487104\pi\)
\(620\) −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
\(627\) 7768.27 0.494792
\(628\) −4430.87 −0.281546
\(629\) 0 0
\(630\) 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
\(638\) −4832.69 −0.299887
\(639\) 13440.9 0.832102
\(640\) 4211.70 0.260128
\(641\) 21286.8 1.31167 0.655834 0.754905i \(-0.272317\pi\)
0.655834 + 0.754905i \(0.272317\pi\)
\(642\) −4234.20 −0.260297
\(643\) 1789.41 0.109747 0.0548736 0.998493i \(-0.482524\pi\)
0.0548736 + 0.998493i \(0.482524\pi\)
\(644\) −5626.38 −0.344271
\(645\) 3372.64 0.205888
\(646\) 0 0
\(647\) −4378.61 −0.266060 −0.133030 0.991112i \(-0.542471\pi\)
−0.133030 + 0.991112i \(0.542471\pi\)
\(648\) −422.672 −0.0256237
\(649\) 8064.45 0.487762
\(650\) −9160.81 −0.552795
\(651\) 6849.97 0.412399
\(652\) −4159.11 −0.249821
\(653\) 7665.15 0.459358 0.229679 0.973266i \(-0.426232\pi\)
0.229679 + 0.973266i \(0.426232\pi\)
\(654\) 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 \(-0.544458\pi\)
−0.139214 + 0.990262i \(0.544458\pi\)
\(660\) 1623.55 0.0957527
\(661\) −31266.6 −1.83983 −0.919916 0.392116i \(-0.871743\pi\)
−0.919916 + 0.392116i \(0.871743\pi\)
\(662\) 1024.00 0.0601192
\(663\) 0 0
\(664\) 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
\(671\) −1488.40 −0.0856322
\(672\) −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
\(680\) 0 0
\(681\) −6786.45 −0.381875
\(682\) 10279.8 0.577175
\(683\) −1720.10 −0.0963660 −0.0481830 0.998839i \(-0.515343\pi\)
−0.0481830 + 0.998839i \(0.515343\pi\)
\(684\) 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 \(-0.347192\pi\)
0.461832 + 0.886967i \(0.347192\pi\)
\(692\) −1089.96 −0.0598758
\(693\) 3738.44 0.204923
\(694\) −5421.88 −0.296559
\(695\) 4450.77 0.242917
\(696\) 7809.84 0.425332
\(697\) 0 0
\(698\) 2035.86 0.110399
\(699\) −16381.2 −0.886400
\(700\) 5652.71 0.305218
\(701\) 23981.1 1.29209 0.646043 0.763301i \(-0.276423\pi\)
0.646043 + 0.763301i \(0.276423\pi\)
\(702\) 10991.8 0.590969
\(703\) 11801.6 0.633150
\(704\) −1893.12 −0.101349
\(705\) 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 \(-0.434547\pi\)
0.204181 + 0.978933i \(0.434547\pi\)
\(710\) 3253.59 0.171979
\(711\) −12280.3 −0.647747
\(712\) 15662.5 0.824407
\(713\) −31521.5 −1.65567
\(714\) 0 0
\(715\) 4865.34 0.254480
\(716\) 6293.13 0.328471
\(717\) −1054.61 −0.0549304
\(718\) −6729.09 −0.349760
\(719\) 11976.5 0.621209 0.310605 0.950539i \(-0.399468\pi\)
0.310605 + 0.950539i \(0.399468\pi\)
\(720\) 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
\(726\) 2440.58 0.124764
\(727\) −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
\(731\) 0 0
\(732\) 1045.14 0.0527727
\(733\) −23569.5 −1.18767 −0.593833 0.804588i \(-0.702386\pi\)
−0.593833 + 0.804588i \(0.702386\pi\)
\(734\) 20.2646 0.00101905
\(735\) −2677.41 −0.134364
\(736\) 21361.3 1.06982
\(737\) −1462.47 −0.0730948
\(738\) −10920.0 −0.544678
\(739\) 10149.1 0.505199 0.252599 0.967571i \(-0.418715\pi\)
0.252599 + 0.967571i \(0.418715\pi\)
\(740\) 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 \(-0.493695\pi\)
0.0198056 + 0.999804i \(0.493695\pi\)
\(752\) 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
\(759\) 10042.1 0.480244
\(760\) 5205.90 0.248471
\(761\) −11028.2 −0.525324 −0.262662 0.964888i \(-0.584600\pi\)
−0.262662 + 0.964888i \(0.584600\pi\)
\(762\) −11371.7 −0.540621
\(763\) −14407.1 −0.683582
\(764\) 3017.56 0.142895
\(765\) 0 0
\(766\) −12365.0 −0.583246
\(767\) −16969.8 −0.798882
\(768\) 7695.55 0.361574
\(769\) −18921.2 −0.887277 −0.443639 0.896206i \(-0.646313\pi\)
−0.443639 + 0.896206i \(0.646313\pi\)
\(770\) 904.952 0.0423535
\(771\) −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
\(781\) 21772.5 0.997545
\(782\) 0 0
\(783\) 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
\(792\) −9066.49 −0.406772
\(793\) 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
\(799\) 0 0
\(800\) −21461.3 −0.948463
\(801\) 13865.9 0.611644
\(802\) −18765.0 −0.826204
\(803\) 8168.28 0.358969
\(804\) 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
\(814\) −4975.28 −0.214230
\(815\) −2051.25 −0.0881621
\(816\) 0 0
\(817\) 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 \(-0.709935\pi\)
−0.612745 + 0.790281i \(0.709935\pi\)
\(824\) −10073.6 −0.425887
\(825\) −10089.1 −0.425767
\(826\) −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
\(833\) 0 0
\(834\) 6304.13 0.261744
\(835\) −8596.93 −0.356298
\(836\) 15137.1 0.626231
\(837\) −37998.9 −1.56922
\(838\) −13177.8 −0.543221
\(839\) 87.9839 0.00362043 0.00181022 0.999998i \(-0.499424\pi\)
0.00181022 + 0.999998i \(0.499424\pi\)
\(840\) −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
\(847\) −4512.98 −0.183079
\(848\) 12115.7 0.490630
\(849\) 2377.63 0.0961133
\(850\) 0 0
\(851\) 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 \(0.621733\pi\)
\(858\) 6891.34 0.274203
\(859\) −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
\(867\) 0 0
\(868\) 13347.8 0.521950
\(869\) −19892.6 −0.776536
\(870\) 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
\(880\) 1922.57 0.0736473
\(881\) 35073.2 1.34125 0.670627 0.741795i \(-0.266025\pi\)
0.670627 + 0.741795i \(0.266025\pi\)
\(882\) 6496.63 0.248019
\(883\) −48775.7 −1.85893 −0.929463 0.368915i \(-0.879729\pi\)
−0.929463 + 0.368915i \(0.879729\pi\)
\(884\) 0 0
\(885\) −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
\(891\) −606.137 −0.0227905
\(892\) −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
\(901\) 0 0
\(902\) −17689.1 −0.652974
\(903\) −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 \(-0.431447\pi\)
0.213705 + 0.976898i \(0.431447\pi\)
\(908\) −13224.0 −0.483319
\(909\) −4526.54 −0.165166
\(910\) −1904.26 −0.0693689
\(911\) −18552.9 −0.674738 −0.337369 0.941372i \(-0.609537\pi\)
−0.337369 + 0.941372i \(0.609537\pi\)
\(912\) −6459.41 −0.234531
\(913\) 3204.87 0.116173
\(914\) −9739.24 −0.352457
\(915\) 515.459 0.0186235
\(916\) 24077.7 0.868504
\(917\) 15714.9 0.565922
\(918\) 0 0
\(919\) 33956.8 1.21886 0.609429 0.792841i \(-0.291399\pi\)
0.609429 + 0.792841i \(0.291399\pi\)
\(920\) 6729.71 0.241165
\(921\) −7652.23 −0.273778
\(922\) −9886.63 −0.353144
\(923\) −45815.3 −1.63383
\(924\) −4252.33 −0.151398
\(925\) −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 \(-0.362585\pi\)
0.418416 + 0.908256i \(0.362585\pi\)
\(930\) −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 \(-0.455516\pi\)
0.139297 + 0.990251i \(0.455516\pi\)
\(938\) 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
\(946\) −13256.4 −0.455605
\(947\) 1174.62 0.0403064 0.0201532 0.999797i \(-0.493585\pi\)
0.0201532 + 0.999797i \(0.493585\pi\)
\(948\) 13968.4 0.478557
\(949\) −17188.3 −0.587939
\(950\) −14056.7 −0.480063
\(951\) 24143.4 0.823241
\(952\) 0 0
\(953\) −33546.9 −1.14029 −0.570143 0.821546i \(-0.693112\pi\)
−0.570143 + 0.821546i \(0.693112\pi\)
\(954\) −12244.1 −0.415531
\(955\) 1488.25 0.0504277
\(956\) −2055.00 −0.0695224
\(957\) 11199.8 0.378304
\(958\) 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 \(-0.364896\pi\)
0.411813 + 0.911269i \(0.364896\pi\)
\(968\) 10944.9 0.363411
\(969\) 0 0
\(970\) 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
\(979\) 22461.0 0.733254
\(980\) −5217.16 −0.170057
\(981\) 30932.2 1.00672
\(982\) 25556.8 0.830500
\(983\) 11311.9 0.367032 0.183516 0.983017i \(-0.441252\pi\)
0.183516 + 0.983017i \(0.441252\pi\)
\(984\) 28586.3 0.926116
\(985\) 4132.66 0.133683
\(986\) 0 0
\(987\) −3822.47 −0.123273
\(988\) −31852.6 −1.02568
\(989\) 40648.8 1.30693
\(990\) −1942.94 −0.0623744
\(991\) 29405.5 0.942580 0.471290 0.881978i \(-0.343788\pi\)
0.471290 + 0.881978i \(0.343788\pi\)
\(992\) −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 289.4.a.b.1.2 3
17.4 even 4 289.4.b.b.288.4 6
17.13 even 4 289.4.b.b.288.3 6
17.16 even 2 17.4.a.b.1.2 3
51.50 odd 2 153.4.a.g.1.2 3
68.67 odd 2 272.4.a.h.1.2 3
85.33 odd 4 425.4.b.f.324.3 6
85.67 odd 4 425.4.b.f.324.4 6
85.84 even 2 425.4.a.g.1.2 3
119.118 odd 2 833.4.a.d.1.2 3
136.67 odd 2 1088.4.a.x.1.2 3
136.101 even 2 1088.4.a.v.1.2 3
187.186 odd 2 2057.4.a.e.1.2 3
204.203 even 2 2448.4.a.bi.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.b.1.2 3 17.16 even 2
153.4.a.g.1.2 3 51.50 odd 2
272.4.a.h.1.2 3 68.67 odd 2
289.4.a.b.1.2 3 1.1 even 1 trivial
289.4.b.b.288.3 6 17.13 even 4
289.4.b.b.288.4 6 17.4 even 4
425.4.a.g.1.2 3 85.84 even 2
425.4.b.f.324.3 6 85.33 odd 4
425.4.b.f.324.4 6 85.67 odd 4
833.4.a.d.1.2 3 119.118 odd 2
1088.4.a.v.1.2 3 136.101 even 2
1088.4.a.x.1.2 3 136.67 odd 2
2057.4.a.e.1.2 3 187.186 odd 2
2448.4.a.bi.1.1 3 204.203 even 2