Properties

Label 833.4.a.d.1.2
Level $833$
Weight $4$
Character 833.1
Self dual yes
Analytic conductor $49.149$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 833.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.1485910348\)
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 \(\chi\) \(=\) 833.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} -3.03171 q^{5} -4.29415 q^{6} -19.2573 q^{8} -17.0483 q^{9} +O(q^{10})\) \(q+1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} -3.03171 q^{5} -4.29415 q^{6} -19.2573 q^{8} -17.0483 q^{9} -4.12682 q^{10} +27.6161 q^{11} +19.3918 q^{12} -58.1117 q^{13} +9.56391 q^{15} +22.9632 q^{16} +17.0000 q^{17} -23.2065 q^{18} -89.1688 q^{19} +18.6361 q^{20} +37.5916 q^{22} -115.269 q^{23} +60.7497 q^{24} -115.809 q^{25} -79.1029 q^{26} +138.956 q^{27} -128.558 q^{29} +13.0186 q^{30} -273.460 q^{31} +185.316 q^{32} -87.1187 q^{33} +23.1408 q^{34} +104.797 q^{36} -132.351 q^{37} -121.379 q^{38} +183.321 q^{39} +58.3825 q^{40} +470.559 q^{41} +352.642 q^{43} -169.758 q^{44} +51.6854 q^{45} -156.907 q^{46} -152.598 q^{47} -72.4403 q^{48} -157.641 q^{50} -53.6287 q^{51} +357.217 q^{52} +527.614 q^{53} +189.150 q^{54} -83.7239 q^{55} +281.295 q^{57} -174.995 q^{58} +292.020 q^{59} -58.7901 q^{60} +53.8962 q^{61} -372.239 q^{62} +68.5514 q^{64} +176.178 q^{65} -118.588 q^{66} +52.9572 q^{67} -104.500 q^{68} +363.632 q^{69} +788.400 q^{71} +328.304 q^{72} -295.780 q^{73} -180.159 q^{74} +365.334 q^{75} +548.127 q^{76} +249.541 q^{78} -720.325 q^{79} -69.6175 q^{80} +21.9487 q^{81} +640.535 q^{82} +116.051 q^{83} -51.5390 q^{85} +480.024 q^{86} +405.552 q^{87} -531.812 q^{88} +813.329 q^{89} +70.3553 q^{90} +708.569 q^{92} +862.664 q^{93} -207.720 q^{94} +270.334 q^{95} -584.605 q^{96} -794.693 q^{97} -470.808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 39 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 39 q^{8} + 59 q^{9} + 56 q^{10} - 28 q^{11} - 22 q^{12} - 30 q^{13} + 108 q^{15} + 137 q^{16} + 51 q^{17} - 103 q^{18} - 80 q^{19} + 168 q^{20} + 286 q^{22} + 142 q^{23} + 666 q^{24} - 223 q^{25} - 26 q^{26} + 20 q^{27} - 456 q^{29} + 400 q^{30} - 230 q^{31} - 71 q^{32} + 332 q^{33} + 17 q^{34} + 1313 q^{36} + 356 q^{37} - 724 q^{38} + 268 q^{39} + 424 q^{40} + 294 q^{41} + 556 q^{43} - 1122 q^{44} + 384 q^{45} - 704 q^{46} - 640 q^{47} - 774 q^{48} + 547 q^{50} - 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} - 76 q^{55} - 720 q^{57} - 1304 q^{58} - 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 919 q^{64} + 408 q^{65} - 2468 q^{66} + 1008 q^{67} + 425 q^{68} - 576 q^{69} - 402 q^{71} - 927 q^{72} - 838 q^{73} + 836 q^{74} + 1548 q^{75} + 908 q^{76} + 1308 q^{78} - 594 q^{79} + 40 q^{80} - 505 q^{81} - 358 q^{82} + 2396 q^{83} + 136 q^{85} - 1264 q^{86} - 1428 q^{87} + 1838 q^{88} + 170 q^{89} + 2008 q^{90} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} - 472 q^{95} - 678 q^{96} + 270 q^{97} - 2920 q^{99}+O(q^{100}) \) 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
\(7\) 0 0
\(8\) −19.2573 −0.851061
\(9\) −17.0483 −0.631419
\(10\) −4.12682 −0.130502
\(11\) 27.6161 0.756961 0.378481 0.925609i \(-0.376447\pi\)
0.378481 + 0.925609i \(0.376447\pi\)
\(12\) 19.3918 0.466493
\(13\) −58.1117 −1.23979 −0.619896 0.784684i \(-0.712825\pi\)
−0.619896 + 0.784684i \(0.712825\pi\)
\(14\) 0 0
\(15\) 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
\(21\) 0 0
\(22\) 37.5916 0.364298
\(23\) −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
\(28\) 0 0
\(29\) −128.558 −0.823191 −0.411596 0.911367i \(-0.635028\pi\)
−0.411596 + 0.911367i \(0.635028\pi\)
\(30\) 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
\(34\) 23.1408 0.116724
\(35\) 0 0
\(36\) 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 \(0.146312\pi\)
\(42\) 0 0
\(43\) 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 \(-0.576097\pi\)
−0.236795 + 0.971560i \(0.576097\pi\)
\(48\) −72.4403 −0.217830
\(49\) 0 0
\(50\) −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
\(55\) −83.7239 −0.205261
\(56\) 0 0
\(57\) 281.295 0.653656
\(58\) −174.995 −0.396173
\(59\) 292.020 0.644368 0.322184 0.946677i \(-0.395583\pi\)
0.322184 + 0.946677i \(0.395583\pi\)
\(60\) −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
\(63\) 0 0
\(64\) 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 \(0.484625\pi\)
\(68\) −104.500 −0.186361
\(69\) 363.632 0.634437
\(70\) 0 0
\(71\) 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 \(-0.671440\pi\)
−0.512930 + 0.858430i \(0.671440\pi\)
\(80\) −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 \(0.475550\pi\)
\(84\) 0 0
\(85\) −51.5390 −0.0657669
\(86\) 480.024 0.601887
\(87\) 405.552 0.499767
\(88\) −531.812 −0.644220
\(89\) 813.329 0.968682 0.484341 0.874879i \(-0.339059\pi\)
0.484341 + 0.874879i \(0.339059\pi\)
\(90\) 70.3553 0.0824011
\(91\) 0 0
\(92\) 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 \(0.636541\pi\)
\(98\) 0 0
\(99\) −470.808 −0.477959
\(100\) 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 \(-0.580500\pi\)
−0.250210 + 0.968192i \(0.580500\pi\)
\(104\) 1119.07 1.05514
\(105\) 0 0
\(106\) 718.199 0.658091
\(107\) −986.039 −0.890878 −0.445439 0.895312i \(-0.646952\pi\)
−0.445439 + 0.895312i \(0.646952\pi\)
\(108\) −854.174 −0.761046
\(109\) 1814.39 1.59438 0.797188 0.603732i \(-0.206320\pi\)
0.797188 + 0.603732i \(0.206320\pi\)
\(110\) −113.967 −0.0987846
\(111\) 417.518 0.357018
\(112\) 0 0
\(113\) −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
\(119\) 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
\(126\) 0 0
\(127\) 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
\(133\) 0 0
\(134\) 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 \(0.647833\pi\)
\(140\) 0 0
\(141\) 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
\(147\) 0 0
\(148\) 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
\(153\) −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 \(-0.558648\pi\)
−0.183206 + 0.983074i \(0.558648\pi\)
\(158\) −980.522 −0.493710
\(159\) −1664.43 −0.830174
\(160\) −561.825 −0.277601
\(161\) 0 0
\(162\) 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
\(165\) 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 \(0.271834\pi\)
\(168\) 0 0
\(169\) 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
\(175\) 0 0
\(176\) 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 \(0.249403\pi\)
\(182\) 0 0
\(183\) −170.023 −0.0686800
\(184\) 2219.78 0.889370
\(185\) 401.248 0.159461
\(186\) 1174.28 0.462915
\(187\) 469.474 0.183590
\(188\) 938.031 0.363899
\(189\) 0 0
\(190\) 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 \(-0.730200\pi\)
−0.661783 + 0.749696i \(0.730200\pi\)
\(194\) −1081.75 −0.400337
\(195\) −555.775 −0.204102
\(196\) 0 0
\(197\) 1363.15 0.492996 0.246498 0.969143i \(-0.420720\pi\)
0.246498 + 0.969143i \(0.420720\pi\)
\(198\) −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
\(203\) 0 0
\(204\) 329.660 0.113141
\(205\) −1426.60 −0.486038
\(206\) −712.064 −0.240834
\(207\) 1965.15 0.659841
\(208\) −1334.43 −0.444836
\(209\) −2462.50 −0.814997
\(210\) 0 0
\(211\) −5266.12 −1.71817 −0.859087 0.511829i \(-0.828968\pi\)
−0.859087 + 0.511829i \(0.828968\pi\)
\(212\) −3243.28 −1.05071
\(213\) −2487.11 −0.800066
\(214\) −1342.22 −0.428748
\(215\) −1069.11 −0.339128
\(216\) −2675.92 −0.842932
\(217\) 0 0
\(218\) 2469.78 0.767316
\(219\) 933.075 0.287906
\(220\) 514.657 0.157719
\(221\) −987.899 −0.300694
\(222\) 568.334 0.171820
\(223\) −704.546 −0.211569 −0.105785 0.994389i \(-0.533735\pi\)
−0.105785 + 0.994389i \(0.533735\pi\)
\(224\) 0 0
\(225\) 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 \(-0.308819\pi\)
0.565149 + 0.824989i \(0.308819\pi\)
\(230\) 475.696 0.136376
\(231\) 0 0
\(232\) 2475.67 0.700586
\(233\) −5192.74 −1.46003 −0.730017 0.683429i \(-0.760488\pi\)
−0.730017 + 0.683429i \(0.760488\pi\)
\(234\) 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
\(245\) 0 0
\(246\) −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 \(-0.918785\pi\)
−0.967627 + 0.252385i \(0.918785\pi\)
\(252\) 0 0
\(253\) −3183.29 −0.791035
\(254\) 3604.76 0.890484
\(255\) 162.587 0.0399277
\(256\) −2439.44 −0.595567
\(257\) −5335.10 −1.29492 −0.647460 0.762099i \(-0.724169\pi\)
−0.647460 + 0.762099i \(0.724169\pi\)
\(258\) −1514.30 −0.365411
\(259\) 0 0
\(260\) −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
\(266\) 0 0
\(267\) −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 \(-0.519599\pi\)
−0.0615340 + 0.998105i \(0.519599\pi\)
\(272\) 390.374 0.0870216
\(273\) 0 0
\(274\) 4276.85 0.942970
\(275\) −3198.19 −0.701302
\(276\) −2235.27 −0.487492
\(277\) 5203.65 1.12873 0.564363 0.825527i \(-0.309122\pi\)
0.564363 + 0.825527i \(0.309122\pi\)
\(278\) −1998.37 −0.431131
\(279\) 4662.02 1.00039
\(280\) 0 0
\(281\) −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
\(287\) 0 0
\(288\) −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 \(0.245050\pi\)
\(294\) 0 0
\(295\) −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
\(301\) 0 0
\(302\) −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 \(-0.164011\pi\)
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
\(315\) 0 0
\(316\) 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
\(319\) −3550.26 −0.623124
\(320\) −207.828 −0.0363060
\(321\) 3110.59 0.540860
\(322\) 0 0
\(323\) −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
\(329\) 0 0
\(330\) 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
\(336\) 0 0
\(337\) −1968.57 −0.318204 −0.159102 0.987262i \(-0.550860\pi\)
−0.159102 + 0.987262i \(0.550860\pi\)
\(338\) 1606.20 0.258479
\(339\) 2231.39 0.357501
\(340\) 316.814 0.0505343
\(341\) −7551.89 −1.19929
\(342\) 2069.30 0.327178
\(343\) 0 0
\(344\) −6790.93 −1.06437
\(345\) −1102.43 −0.172037
\(346\) 241.363 0.0375022
\(347\) 3983.10 0.616207 0.308104 0.951353i \(-0.400306\pi\)
0.308104 + 0.951353i \(0.400306\pi\)
\(348\) −2492.96 −0.384013
\(349\) −1495.61 −0.229393 −0.114697 0.993401i \(-0.536590\pi\)
−0.114697 + 0.993401i \(0.536590\pi\)
\(350\) 0 0
\(351\) −8074.98 −1.22795
\(352\) 5117.72 0.774930
\(353\) −6482.49 −0.977417 −0.488708 0.872447i \(-0.662532\pi\)
−0.488708 + 0.872447i \(0.662532\pi\)
\(354\) −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
\(364\) 0 0
\(365\) 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
\(371\) 0 0
\(372\) −5302.86 −0.739088
\(373\) 1923.18 0.266966 0.133483 0.991051i \(-0.457384\pi\)
0.133483 + 0.991051i \(0.457384\pi\)
\(374\) 639.058 0.0883554
\(375\) −2303.07 −0.317147
\(376\) 2938.63 0.403053
\(377\) 7470.70 1.02059
\(378\) 0 0
\(379\) −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 \(-0.292793\pi\)
0.605951 + 0.795502i \(0.292793\pi\)
\(384\) 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
\(392\) 0 0
\(393\) −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
\(399\) 0 0
\(400\) −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
\(406\) 0 0
\(407\) −3655.01 −0.445141
\(408\) 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
\(413\) 0 0
\(414\) 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 \(0.690880\pi\)
\(420\) 0 0
\(421\) −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
\(427\) 0 0
\(428\) 6061.25 0.684537
\(429\) 5062.61 0.569756
\(430\) −1455.29 −0.163210
\(431\) 2970.58 0.331990 0.165995 0.986127i \(-0.446916\pi\)
0.165995 + 0.986127i \(0.446916\pi\)
\(432\) 3190.87 0.355372
\(433\) −6131.50 −0.680510 −0.340255 0.940333i \(-0.610513\pi\)
−0.340255 + 0.940333i \(0.610513\pi\)
\(434\) 0 0
\(435\) −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
\(441\) 0 0
\(442\) −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
\(448\) 0 0
\(449\) 8855.74 0.930798 0.465399 0.885101i \(-0.345911\pi\)
0.465399 + 0.885101i \(0.345911\pi\)
\(450\) 2687.52 0.281535
\(451\) 12995.0 1.35679
\(452\) 4348.07 0.452469
\(453\) 2112.42 0.219095
\(454\) 2928.35 0.302718
\(455\) 0 0
\(456\) −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
\(459\) 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 \(-0.523409\pi\)
−0.0734753 + 0.997297i \(0.523409\pi\)
\(468\) −6089.94 −0.601512
\(469\) 0 0
\(470\) 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
\(483\) 0 0
\(484\) 3493.69 0.328108
\(485\) 2409.27 0.225566
\(486\) −5201.30 −0.485465
\(487\) −1129.88 −0.105133 −0.0525663 0.998617i \(-0.516740\pi\)
−0.0525663 + 0.998617i \(0.516740\pi\)
\(488\) −1037.90 −0.0962774
\(489\) 2134.42 0.197386
\(490\) 0 0
\(491\) 18774.9 1.72566 0.862832 0.505491i \(-0.168689\pi\)
0.862832 + 0.505491i \(0.168689\pi\)
\(492\) 9124.97 0.836149
\(493\) −2185.48 −0.199653
\(494\) 7053.51 0.642414
\(495\) 1427.35 0.129605
\(496\) −6279.49 −0.568463
\(497\) 0 0
\(498\) −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 \(0.125288\pi\)
\(504\) 0 0
\(505\) 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 \(-0.672320\pi\)
−0.515301 + 0.857009i \(0.672320\pi\)
\(510\) 221.316 0.0192158
\(511\) 0 0
\(512\) 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
\(518\) 0 0
\(519\) −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 \(-0.659276\pi\)
−0.479759 + 0.877400i \(0.659276\pi\)
\(524\) −12165.6 −1.01423
\(525\) 0 0
\(526\) 5355.25 0.443916
\(527\) −4648.81 −0.384261
\(528\) −2000.52 −0.164889
\(529\) 1120.01 0.0920535
\(530\) −2177.37 −0.178451
\(531\) −4978.44 −0.406866
\(532\) 0 0
\(533\) −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 \(-0.506912\pi\)
−0.0217145 + 0.999764i \(0.506912\pi\)
\(542\) −747.357 −0.0592283
\(543\) −10884.1 −0.860191
\(544\) 3150.38 0.248293
\(545\) −5500.69 −0.432337
\(546\) 0 0
\(547\) 8397.33 0.656388 0.328194 0.944610i \(-0.393560\pi\)
0.328194 + 0.944610i \(0.393560\pi\)
\(548\) −19313.6 −1.50554
\(549\) −918.839 −0.0714301
\(550\) −4353.44 −0.337512
\(551\) 11463.3 0.886305
\(552\) −7002.58 −0.539945
\(553\) 0 0
\(554\) 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
\(560\) 0 0
\(561\) −1481.02 −0.111459
\(562\) −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
\(567\) 0 0
\(568\) −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 \(-0.481406\pi\)
0.0583813 + 0.998294i \(0.481406\pi\)
\(572\) 9864.95 0.721109
\(573\) 1548.59 0.112903
\(574\) 0 0
\(575\) 13349.2 0.968174
\(576\) −1168.69 −0.0845403
\(577\) −12937.4 −0.933435 −0.466717 0.884406i \(-0.654564\pi\)
−0.466717 + 0.884406i \(0.654564\pi\)
\(578\) 393.393 0.0283097
\(579\) 11195.2 0.803549
\(580\) −2395.82 −0.171519
\(581\) 0 0
\(582\) 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 \(-0.350176\pi\)
0.453499 + 0.891257i \(0.350176\pi\)
\(588\) 0 0
\(589\) 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 \(0.548206\pi\)
\(594\) 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 \(0.527378\pi\)
\(602\) 0 0
\(603\) −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
\(609\) 0 0
\(610\) −222.420 −0.0147632
\(611\) 8867.73 0.587152
\(612\) 1781.55 0.117672
\(613\) −17706.9 −1.16668 −0.583339 0.812228i \(-0.698254\pi\)
−0.583339 + 0.812228i \(0.698254\pi\)
\(614\) −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 \(-0.487104\pi\)
0.0405023 + 0.999179i \(0.487104\pi\)
\(620\) −5096.23 −0.330112
\(621\) −16017.4 −1.03503
\(622\) 12992.8 0.837561
\(623\) 0 0
\(624\) 4209.63 0.270064
\(625\) 12262.8 0.784817
\(626\) −800.914 −0.0511357
\(627\) 7768.27 0.494792
\(628\) 4430.87 0.281546
\(629\) −2249.96 −0.142626
\(630\) 0 0
\(631\) 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
\(637\) 0 0
\(638\) −4832.69 −0.299887
\(639\) −13440.9 −0.832102
\(640\) 4211.70 0.260128
\(641\) −21286.8 −1.31167 −0.655834 0.754905i \(-0.727683\pi\)
−0.655834 + 0.754905i \(0.727683\pi\)
\(642\) 4234.20 0.260297
\(643\) 1789.41 0.109747 0.0548736 0.998493i \(-0.482524\pi\)
0.0548736 + 0.998493i \(0.482524\pi\)
\(644\) 0 0
\(645\) 3372.64 0.205888
\(646\) −2063.43 −0.125673
\(647\) 4378.61 0.266060 0.133030 0.991112i \(-0.457529\pi\)
0.133030 + 0.991112i \(0.457529\pi\)
\(648\) −422.672 −0.0256237
\(649\) 8064.45 0.487762
\(650\) 9160.81 0.552795
\(651\) 0 0
\(652\) 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
\(658\) 0 0
\(659\) −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 \(-0.128257\pi\)
0.919916 + 0.392116i \(0.128257\pi\)
\(662\) 1024.00 0.0601192
\(663\) 3116.46 0.182554
\(664\) −2234.82 −0.130614
\(665\) 0 0
\(666\) 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
\(672\) 0 0
\(673\) 11723.0 0.671454 0.335727 0.941959i \(-0.391018\pi\)
0.335727 + 0.941959i \(0.391018\pi\)
\(674\) −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
\(679\) 0 0
\(680\) 992.502 0.0559716
\(681\) −6786.45 −0.381875
\(682\) −10279.8 −0.577175
\(683\) 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
\(686\) 0 0
\(687\) −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
\(693\) 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
\(700\) 0 0
\(701\) 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
\(707\) 0 0
\(708\) 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
\(714\) 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
\(721\) 0 0
\(722\) 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 \(-0.342675\pi\)
0.474372 + 0.880324i \(0.342675\pi\)
\(728\) 0 0
\(729\) 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
\(735\) 0 0
\(736\) −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
\(742\) 0 0
\(743\) 27758.0 1.37058 0.685291 0.728269i \(-0.259675\pi\)
0.685291 + 0.728269i \(0.259675\pi\)
\(744\) −16612.6 −0.818611
\(745\) 867.148 0.0426441
\(746\) 2617.87 0.128481
\(747\) −1978.47 −0.0969054
\(748\) −2885.89 −0.141068
\(749\) 0 0
\(750\) −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
\(756\) 0 0
\(757\) −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 \(-0.415400\pi\)
0.262662 + 0.964888i \(0.415400\pi\)
\(762\) −11371.7 −0.540621
\(763\) 0 0
\(764\) 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 \(-0.857177\pi\)
−0.901016 + 0.433786i \(0.857177\pi\)
\(774\) −8183.59 −0.380043
\(775\) 31669.0 1.46785
\(776\) 15303.6 0.707949
\(777\) 0 0
\(778\) −1556.93 −0.0717465
\(779\) −41959.2 −1.92984
\(780\) 3416.39 0.156829
\(781\) 21772.5 0.997545
\(782\) −2667.42 −0.121978
\(783\) −17863.9 −0.815329
\(784\) 0 0
\(785\) 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
\(791\) 0 0
\(792\) 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 \(-0.385266\pi\)
0.352693 + 0.935739i \(0.385266\pi\)
\(798\) 0 0
\(799\) −2594.17 −0.114862
\(800\) −21461.3 −0.948463
\(801\) −13865.9 −0.611644
\(802\) 18765.0 0.826204
\(803\) −8168.28 −0.358969
\(804\) 1026.93 0.0450462
\(805\) 0 0
\(806\) 21631.4 0.945329
\(807\) 10801.6 0.471170
\(808\) 5113.06 0.222620
\(809\) 39667.1 1.72388 0.861942 0.507007i \(-0.169248\pi\)
0.861942 + 0.507007i \(0.169248\pi\)
\(810\) −90.5783 −0.00392913
\(811\) −8003.87 −0.346552 −0.173276 0.984873i \(-0.555435\pi\)
−0.173276 + 0.984873i \(0.555435\pi\)
\(812\) 0 0
\(813\) 1732.00 0.0747157
\(814\) −4975.28 −0.214230
\(815\) 2051.25 0.0881621
\(816\) −1231.48 −0.0528316
\(817\) −31444.7 −1.34652
\(818\) 12939.7 0.553088
\(819\) 0 0
\(820\) 8769.40 0.373464
\(821\) −13279.1 −0.564489 −0.282244 0.959343i \(-0.591079\pi\)
−0.282244 + 0.959343i \(0.591079\pi\)
\(822\) −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
\(825\) 10089.1 0.425767
\(826\) 0 0
\(827\) −13679.6 −0.575193 −0.287597 0.957752i \(-0.592856\pi\)
−0.287597 + 0.957752i \(0.592856\pi\)
\(828\) −12079.9 −0.507012
\(829\) −16514.5 −0.691886 −0.345943 0.938256i \(-0.612441\pi\)
−0.345943 + 0.938256i \(0.612441\pi\)
\(830\) −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 \(0.499424\pi\)
\(840\) 0 0
\(841\) −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 \(0.552385\pi\)
\(854\) 0 0
\(855\) −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 \(-0.126593\pi\)
0.921953 + 0.387301i \(0.126593\pi\)
\(860\) 6571.88 0.260580
\(861\) 0 0
\(862\) 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
\(868\) 0 0
\(869\) −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
\(875\) 0 0
\(876\) −5735.69 −0.221222
\(877\) 39163.0 1.50791 0.753957 0.656924i \(-0.228143\pi\)
0.753957 + 0.656924i \(0.228143\pi\)
\(878\) 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 \(0.266025\pi\)
\(882\) 0 0
\(883\) −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
\(889\) 0 0
\(890\) −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
\(896\) 0 0
\(897\) −21131.3 −0.786570
\(898\) 12054.6 0.447960
\(899\) 35155.3 1.30422
\(900\) −12136.4 −0.449498
\(901\) 8969.43 0.331648
\(902\) 17689.1 0.652974
\(903\) 0 0
\(904\) 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
\(910\) 0 0
\(911\) 18552.9 0.674738 0.337369 0.941372i \(-0.390463\pi\)
0.337369 + 0.941372i \(0.390463\pi\)
\(912\) 6459.41 0.234531
\(913\) 3204.87 0.116173
\(914\) −9739.24 −0.352457
\(915\) 515.459 0.0186235
\(916\) −24077.7 −0.868504
\(917\) 0 0
\(918\) 3215.55 0.115609
\(919\) 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
\(924\) 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 \(-0.362585\pi\)
0.418416 + 0.908256i \(0.362585\pi\)
\(930\) −3560.06 −0.125526
\(931\) 0 0
\(932\) 31920.2 1.12187
\(933\) −30110.8 −1.05657
\(934\) −2018.72 −0.0707221
\(935\) −1423.31 −0.0497830
\(936\) −19078.3 −0.666234
\(937\) −7990.62 −0.278593 −0.139297 0.990251i \(-0.544484\pi\)
−0.139297 + 0.990251i \(0.544484\pi\)
\(938\) 0 0
\(939\) 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
\(945\) 0 0
\(946\) 13256.4 0.455605
\(947\) −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
\(952\) 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
\(959\) 0 0
\(960\) 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
\(966\) 0 0
\(967\) 24766.8 0.823625 0.411813 0.911269i \(-0.364896\pi\)
0.411813 + 0.911269i \(0.364896\pi\)
\(968\) 10944.9 0.363411
\(969\) 4782.01 0.158535
\(970\) 3279.56 0.108557
\(971\) −42324.3 −1.39882 −0.699409 0.714721i \(-0.746553\pi\)
−0.699409 + 0.714721i \(0.746553\pi\)
\(972\) 23488.3 0.775091
\(973\) 0 0
\(974\) −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
\(980\) 0 0
\(981\) −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
\(986\) −2974.92 −0.0960860
\(987\) 0 0
\(988\) −31852.6 −1.02568
\(989\) −40648.8 −1.30693
\(990\) 1942.94 0.0623744
\(991\) −29405.5 −0.942580 −0.471290 0.881978i \(-0.656212\pi\)
−0.471290 + 0.881978i \(0.656212\pi\)
\(992\) −50676.5 −1.62196
\(993\) −2373.12 −0.0758397
\(994\) 0 0
\(995\) 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 833.4.a.d.1.2 3
7.6 odd 2 17.4.a.b.1.2 3
21.20 even 2 153.4.a.g.1.2 3
28.27 even 2 272.4.a.h.1.2 3
35.13 even 4 425.4.b.f.324.3 6
35.27 even 4 425.4.b.f.324.4 6
35.34 odd 2 425.4.a.g.1.2 3
56.13 odd 2 1088.4.a.v.1.2 3
56.27 even 2 1088.4.a.x.1.2 3
77.76 even 2 2057.4.a.e.1.2 3
84.83 odd 2 2448.4.a.bi.1.1 3
119.13 odd 4 289.4.b.b.288.4 6
119.55 odd 4 289.4.b.b.288.3 6
119.118 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 7.6 odd 2
153.4.a.g.1.2 3 21.20 even 2
272.4.a.h.1.2 3 28.27 even 2
289.4.a.b.1.2 3 119.118 odd 2
289.4.b.b.288.3 6 119.55 odd 4
289.4.b.b.288.4 6 119.13 odd 4
425.4.a.g.1.2 3 35.34 odd 2
425.4.b.f.324.3 6 35.13 even 4
425.4.b.f.324.4 6 35.27 even 4
833.4.a.d.1.2 3 1.1 even 1 trivial
1088.4.a.v.1.2 3 56.13 odd 2
1088.4.a.x.1.2 3 56.27 even 2
2057.4.a.e.1.2 3 77.76 even 2
2448.4.a.bi.1.1 3 84.83 odd 2