Properties

Label 507.4.a.i.1.1
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.9139683729\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \( x^{4} - 2x^{3} - 25x^{2} + 24x + 78 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(5.33039\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.33039 q^{2} -3.00000 q^{3} +20.4131 q^{4} +16.4131 q^{5} +15.9912 q^{6} -9.67968 q^{7} -66.1667 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.33039 q^{2} -3.00000 q^{3} +20.4131 q^{4} +16.4131 q^{5} +15.9912 q^{6} -9.67968 q^{7} -66.1667 q^{8} +9.00000 q^{9} -87.4882 q^{10} -27.5882 q^{11} -61.2393 q^{12} +51.5965 q^{14} -49.2393 q^{15} +189.390 q^{16} +107.928 q^{17} -47.9735 q^{18} +2.24723 q^{19} +335.042 q^{20} +29.0391 q^{21} +147.056 q^{22} +41.8090 q^{23} +198.500 q^{24} +144.390 q^{25} -27.0000 q^{27} -197.592 q^{28} +61.6213 q^{29} +262.465 q^{30} -191.932 q^{31} -480.187 q^{32} +82.7645 q^{33} -575.300 q^{34} -158.874 q^{35} +183.718 q^{36} -98.4236 q^{37} -11.9786 q^{38} -1086.00 q^{40} +30.7452 q^{41} -154.790 q^{42} +238.325 q^{43} -563.160 q^{44} +147.718 q^{45} -222.858 q^{46} +511.482 q^{47} -568.169 q^{48} -249.304 q^{49} -769.653 q^{50} -323.785 q^{51} +492.825 q^{53} +143.921 q^{54} -452.807 q^{55} +640.472 q^{56} -6.74170 q^{57} -328.466 q^{58} -484.179 q^{59} -1005.13 q^{60} -444.021 q^{61} +1023.07 q^{62} -87.1172 q^{63} +1044.47 q^{64} -441.167 q^{66} -190.114 q^{67} +2203.15 q^{68} -125.427 q^{69} +846.858 q^{70} -484.785 q^{71} -595.500 q^{72} +957.780 q^{73} +524.636 q^{74} -433.169 q^{75} +45.8729 q^{76} +267.045 q^{77} -375.216 q^{79} +3108.47 q^{80} +81.0000 q^{81} -163.884 q^{82} +715.765 q^{83} +592.777 q^{84} +1771.43 q^{85} -1270.37 q^{86} -184.864 q^{87} +1825.42 q^{88} +1038.15 q^{89} -787.394 q^{90} +853.451 q^{92} +575.796 q^{93} -2726.40 q^{94} +36.8840 q^{95} +1440.56 q^{96} -65.5636 q^{97} +1328.89 q^{98} -248.293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 12 q^{3} + 22 q^{4} + 6 q^{5} + 6 q^{6} + 14 q^{7} - 54 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 12 q^{3} + 22 q^{4} + 6 q^{5} + 6 q^{6} + 14 q^{7} - 54 q^{8} + 36 q^{9} - 62 q^{10} - 40 q^{11} - 66 q^{12} + 40 q^{14} - 18 q^{15} + 122 q^{16} + 98 q^{17} - 18 q^{18} - 124 q^{19} + 466 q^{20} - 42 q^{21} + 220 q^{22} + 104 q^{23} + 162 q^{24} - 58 q^{25} - 108 q^{27} + 144 q^{28} + 194 q^{29} + 186 q^{30} - 26 q^{31} - 654 q^{32} + 120 q^{33} - 1062 q^{34} + 88 q^{35} + 198 q^{36} - 102 q^{37} + 332 q^{38} - 998 q^{40} + 1054 q^{41} - 120 q^{42} + 450 q^{43} + 44 q^{44} + 54 q^{45} + 172 q^{46} + 96 q^{47} - 366 q^{48} + 1070 q^{49} - 996 q^{50} - 294 q^{51} + 262 q^{53} + 54 q^{54} + 204 q^{55} + 2164 q^{56} + 372 q^{57} - 722 q^{58} - 308 q^{59} - 1398 q^{60} - 928 q^{61} + 2780 q^{62} + 126 q^{63} + 1026 q^{64} - 660 q^{66} + 1134 q^{67} + 1786 q^{68} - 312 q^{69} + 2324 q^{70} - 1064 q^{71} - 486 q^{72} - 952 q^{73} + 1158 q^{74} + 174 q^{75} + 1708 q^{76} + 2508 q^{77} - 746 q^{79} + 2922 q^{80} + 324 q^{81} + 1734 q^{82} + 404 q^{83} - 432 q^{84} + 1394 q^{85} - 3168 q^{86} - 582 q^{87} + 3060 q^{88} - 1620 q^{89} - 558 q^{90} + 332 q^{92} + 78 q^{93} - 772 q^{94} + 2204 q^{95} + 1962 q^{96} - 2166 q^{97} + 1906 q^{98} - 360 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.33039 −1.88458 −0.942289 0.334800i \(-0.891331\pi\)
−0.942289 + 0.334800i \(0.891331\pi\)
\(3\) −3.00000 −0.577350
\(4\) 20.4131 2.55164
\(5\) 16.4131 1.46803 0.734016 0.679132i \(-0.237644\pi\)
0.734016 + 0.679132i \(0.237644\pi\)
\(6\) 15.9912 1.08806
\(7\) −9.67968 −0.522654 −0.261327 0.965250i \(-0.584160\pi\)
−0.261327 + 0.965250i \(0.584160\pi\)
\(8\) −66.1667 −2.92418
\(9\) 9.00000 0.333333
\(10\) −87.4882 −2.76662
\(11\) −27.5882 −0.756195 −0.378098 0.925766i \(-0.623422\pi\)
−0.378098 + 0.925766i \(0.623422\pi\)
\(12\) −61.2393 −1.47319
\(13\) 0 0
\(14\) 51.5965 0.984982
\(15\) −49.2393 −0.847568
\(16\) 189.390 2.95921
\(17\) 107.928 1.53979 0.769895 0.638171i \(-0.220309\pi\)
0.769895 + 0.638171i \(0.220309\pi\)
\(18\) −47.9735 −0.628193
\(19\) 2.24723 0.0271342 0.0135671 0.999908i \(-0.495681\pi\)
0.0135671 + 0.999908i \(0.495681\pi\)
\(20\) 335.042 3.74588
\(21\) 29.0391 0.301754
\(22\) 147.056 1.42511
\(23\) 41.8090 0.379034 0.189517 0.981877i \(-0.439308\pi\)
0.189517 + 0.981877i \(0.439308\pi\)
\(24\) 198.500 1.68828
\(25\) 144.390 1.15512
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) −197.592 −1.33362
\(29\) 61.6213 0.394579 0.197289 0.980345i \(-0.436786\pi\)
0.197289 + 0.980345i \(0.436786\pi\)
\(30\) 262.465 1.59731
\(31\) −191.932 −1.11200 −0.556000 0.831182i \(-0.687665\pi\)
−0.556000 + 0.831182i \(0.687665\pi\)
\(32\) −480.187 −2.65269
\(33\) 82.7645 0.436589
\(34\) −575.300 −2.90185
\(35\) −158.874 −0.767272
\(36\) 183.718 0.850545
\(37\) −98.4236 −0.437317 −0.218659 0.975801i \(-0.570168\pi\)
−0.218659 + 0.975801i \(0.570168\pi\)
\(38\) −11.9786 −0.0511366
\(39\) 0 0
\(40\) −1086.00 −4.29279
\(41\) 30.7452 0.117112 0.0585561 0.998284i \(-0.481350\pi\)
0.0585561 + 0.998284i \(0.481350\pi\)
\(42\) −154.790 −0.568680
\(43\) 238.325 0.845216 0.422608 0.906313i \(-0.361115\pi\)
0.422608 + 0.906313i \(0.361115\pi\)
\(44\) −563.160 −1.92953
\(45\) 147.718 0.489344
\(46\) −222.858 −0.714319
\(47\) 511.482 1.58739 0.793695 0.608316i \(-0.208155\pi\)
0.793695 + 0.608316i \(0.208155\pi\)
\(48\) −568.169 −1.70850
\(49\) −249.304 −0.726833
\(50\) −769.653 −2.17691
\(51\) −323.785 −0.888998
\(52\) 0 0
\(53\) 492.825 1.27726 0.638630 0.769514i \(-0.279502\pi\)
0.638630 + 0.769514i \(0.279502\pi\)
\(54\) 143.921 0.362687
\(55\) −452.807 −1.11012
\(56\) 640.472 1.52833
\(57\) −6.74170 −0.0156660
\(58\) −328.466 −0.743615
\(59\) −484.179 −1.06838 −0.534192 0.845363i \(-0.679384\pi\)
−0.534192 + 0.845363i \(0.679384\pi\)
\(60\) −1005.13 −2.16269
\(61\) −444.021 −0.931985 −0.465993 0.884789i \(-0.654303\pi\)
−0.465993 + 0.884789i \(0.654303\pi\)
\(62\) 1023.07 2.09565
\(63\) −87.1172 −0.174218
\(64\) 1044.47 2.03998
\(65\) 0 0
\(66\) −441.167 −0.822787
\(67\) −190.114 −0.346658 −0.173329 0.984864i \(-0.555452\pi\)
−0.173329 + 0.984864i \(0.555452\pi\)
\(68\) 2203.15 3.92898
\(69\) −125.427 −0.218835
\(70\) 846.858 1.44598
\(71\) −484.785 −0.810329 −0.405164 0.914244i \(-0.632786\pi\)
−0.405164 + 0.914244i \(0.632786\pi\)
\(72\) −595.500 −0.974727
\(73\) 957.780 1.53561 0.767806 0.640683i \(-0.221349\pi\)
0.767806 + 0.640683i \(0.221349\pi\)
\(74\) 524.636 0.824159
\(75\) −433.169 −0.666907
\(76\) 45.8729 0.0692367
\(77\) 267.045 0.395228
\(78\) 0 0
\(79\) −375.216 −0.534368 −0.267184 0.963646i \(-0.586093\pi\)
−0.267184 + 0.963646i \(0.586093\pi\)
\(80\) 3108.47 4.34422
\(81\) 81.0000 0.111111
\(82\) −163.884 −0.220707
\(83\) 715.765 0.946571 0.473286 0.880909i \(-0.343068\pi\)
0.473286 + 0.880909i \(0.343068\pi\)
\(84\) 592.777 0.769967
\(85\) 1771.43 2.26046
\(86\) −1270.37 −1.59288
\(87\) −184.864 −0.227810
\(88\) 1825.42 2.21125
\(89\) 1038.15 1.23645 0.618224 0.786002i \(-0.287852\pi\)
0.618224 + 0.786002i \(0.287852\pi\)
\(90\) −787.394 −0.922207
\(91\) 0 0
\(92\) 853.451 0.967157
\(93\) 575.796 0.642013
\(94\) −2726.40 −2.99156
\(95\) 36.8840 0.0398339
\(96\) 1440.56 1.53153
\(97\) −65.5636 −0.0686286 −0.0343143 0.999411i \(-0.510925\pi\)
−0.0343143 + 0.999411i \(0.510925\pi\)
\(98\) 1328.89 1.36977
\(99\) −248.293 −0.252065
\(100\) 2947.44 2.94744
\(101\) 531.798 0.523920 0.261960 0.965079i \(-0.415631\pi\)
0.261960 + 0.965079i \(0.415631\pi\)
\(102\) 1725.90 1.67539
\(103\) −735.984 −0.704064 −0.352032 0.935988i \(-0.614509\pi\)
−0.352032 + 0.935988i \(0.614509\pi\)
\(104\) 0 0
\(105\) 476.621 0.442985
\(106\) −2626.95 −2.40710
\(107\) −783.265 −0.707673 −0.353837 0.935307i \(-0.615123\pi\)
−0.353837 + 0.935307i \(0.615123\pi\)
\(108\) −551.153 −0.491063
\(109\) 532.339 0.467788 0.233894 0.972262i \(-0.424853\pi\)
0.233894 + 0.972262i \(0.424853\pi\)
\(110\) 2413.64 2.09210
\(111\) 295.271 0.252485
\(112\) −1833.23 −1.54664
\(113\) −180.589 −0.150340 −0.0751699 0.997171i \(-0.523950\pi\)
−0.0751699 + 0.997171i \(0.523950\pi\)
\(114\) 35.9359 0.0295237
\(115\) 686.215 0.556434
\(116\) 1257.88 1.00682
\(117\) 0 0
\(118\) 2580.86 2.01346
\(119\) −1044.71 −0.804777
\(120\) 3258.00 2.47844
\(121\) −569.893 −0.428169
\(122\) 2366.81 1.75640
\(123\) −92.2357 −0.0676147
\(124\) −3917.92 −2.83742
\(125\) 318.242 0.227716
\(126\) 464.369 0.328327
\(127\) 1431.63 1.00029 0.500146 0.865941i \(-0.333280\pi\)
0.500146 + 0.865941i \(0.333280\pi\)
\(128\) −1725.94 −1.19182
\(129\) −714.976 −0.487986
\(130\) 0 0
\(131\) 2067.32 1.37880 0.689400 0.724381i \(-0.257874\pi\)
0.689400 + 0.724381i \(0.257874\pi\)
\(132\) 1689.48 1.11402
\(133\) −21.7525 −0.0141818
\(134\) 1013.38 0.653304
\(135\) −443.153 −0.282523
\(136\) −7141.25 −4.50262
\(137\) 387.512 0.241660 0.120830 0.992673i \(-0.461444\pi\)
0.120830 + 0.992673i \(0.461444\pi\)
\(138\) 668.575 0.412412
\(139\) 752.568 0.459223 0.229611 0.973282i \(-0.426254\pi\)
0.229611 + 0.973282i \(0.426254\pi\)
\(140\) −3243.10 −1.95780
\(141\) −1534.45 −0.916480
\(142\) 2584.09 1.52713
\(143\) 0 0
\(144\) 1704.51 0.986404
\(145\) 1011.40 0.579254
\(146\) −5105.34 −2.89398
\(147\) 747.911 0.419637
\(148\) −2009.13 −1.11587
\(149\) 2636.72 1.44972 0.724862 0.688895i \(-0.241904\pi\)
0.724862 + 0.688895i \(0.241904\pi\)
\(150\) 2308.96 1.25684
\(151\) 3332.42 1.79595 0.897975 0.440046i \(-0.145038\pi\)
0.897975 + 0.440046i \(0.145038\pi\)
\(152\) −148.692 −0.0793454
\(153\) 971.354 0.513263
\(154\) −1423.45 −0.744839
\(155\) −3150.20 −1.63245
\(156\) 0 0
\(157\) −1625.26 −0.826179 −0.413089 0.910690i \(-0.635550\pi\)
−0.413089 + 0.910690i \(0.635550\pi\)
\(158\) 2000.05 1.00706
\(159\) −1478.48 −0.737426
\(160\) −7881.36 −3.89423
\(161\) −404.698 −0.198104
\(162\) −431.762 −0.209398
\(163\) 1835.37 0.881944 0.440972 0.897521i \(-0.354634\pi\)
0.440972 + 0.897521i \(0.354634\pi\)
\(164\) 627.605 0.298828
\(165\) 1358.42 0.640927
\(166\) −3815.31 −1.78389
\(167\) −1945.00 −0.901248 −0.450624 0.892714i \(-0.648798\pi\)
−0.450624 + 0.892714i \(0.648798\pi\)
\(168\) −1921.42 −0.882384
\(169\) 0 0
\(170\) −9442.44 −4.26001
\(171\) 20.2251 0.00904474
\(172\) 4864.96 2.15668
\(173\) 2531.63 1.11258 0.556289 0.830989i \(-0.312225\pi\)
0.556289 + 0.830989i \(0.312225\pi\)
\(174\) 985.397 0.429326
\(175\) −1397.65 −0.603726
\(176\) −5224.91 −2.23774
\(177\) 1452.54 0.616832
\(178\) −5533.76 −2.33018
\(179\) 4263.01 1.78007 0.890035 0.455892i \(-0.150680\pi\)
0.890035 + 0.455892i \(0.150680\pi\)
\(180\) 3015.38 1.24863
\(181\) 3944.61 1.61989 0.809946 0.586504i \(-0.199496\pi\)
0.809946 + 0.586504i \(0.199496\pi\)
\(182\) 0 0
\(183\) 1332.06 0.538082
\(184\) −2766.36 −1.10836
\(185\) −1615.43 −0.641995
\(186\) −3069.22 −1.20992
\(187\) −2977.54 −1.16438
\(188\) 10440.9 4.05044
\(189\) 261.351 0.100585
\(190\) −196.606 −0.0750701
\(191\) −214.109 −0.0811119 −0.0405559 0.999177i \(-0.512913\pi\)
−0.0405559 + 0.999177i \(0.512913\pi\)
\(192\) −3133.42 −1.17779
\(193\) 1207.19 0.450234 0.225117 0.974332i \(-0.427724\pi\)
0.225117 + 0.974332i \(0.427724\pi\)
\(194\) 349.480 0.129336
\(195\) 0 0
\(196\) −5089.06 −1.85461
\(197\) 927.631 0.335487 0.167744 0.985831i \(-0.446352\pi\)
0.167744 + 0.985831i \(0.446352\pi\)
\(198\) 1323.50 0.475036
\(199\) 478.951 0.170613 0.0853064 0.996355i \(-0.472813\pi\)
0.0853064 + 0.996355i \(0.472813\pi\)
\(200\) −9553.77 −3.37777
\(201\) 570.341 0.200143
\(202\) −2834.69 −0.987368
\(203\) −596.474 −0.206228
\(204\) −6609.44 −2.26840
\(205\) 504.624 0.171924
\(206\) 3923.08 1.32686
\(207\) 376.281 0.126345
\(208\) 0 0
\(209\) −61.9970 −0.0205188
\(210\) −2540.58 −0.834840
\(211\) −1450.95 −0.473402 −0.236701 0.971583i \(-0.576066\pi\)
−0.236701 + 0.971583i \(0.576066\pi\)
\(212\) 10060.1 3.25910
\(213\) 1454.35 0.467843
\(214\) 4175.11 1.33367
\(215\) 3911.66 1.24080
\(216\) 1786.50 0.562759
\(217\) 1857.84 0.581191
\(218\) −2837.58 −0.881583
\(219\) −2873.34 −0.886586
\(220\) −9243.19 −2.83262
\(221\) 0 0
\(222\) −1573.91 −0.475828
\(223\) 2059.79 0.618536 0.309268 0.950975i \(-0.399916\pi\)
0.309268 + 0.950975i \(0.399916\pi\)
\(224\) 4648.06 1.38644
\(225\) 1299.51 0.385039
\(226\) 962.612 0.283327
\(227\) −4482.46 −1.31062 −0.655311 0.755359i \(-0.727463\pi\)
−0.655311 + 0.755359i \(0.727463\pi\)
\(228\) −137.619 −0.0399738
\(229\) 1630.39 0.470477 0.235239 0.971938i \(-0.424413\pi\)
0.235239 + 0.971938i \(0.424413\pi\)
\(230\) −3657.80 −1.04864
\(231\) −801.134 −0.228185
\(232\) −4077.27 −1.15382
\(233\) −1903.69 −0.535258 −0.267629 0.963522i \(-0.586240\pi\)
−0.267629 + 0.963522i \(0.586240\pi\)
\(234\) 0 0
\(235\) 8395.00 2.33034
\(236\) −9883.58 −2.72613
\(237\) 1125.65 0.308517
\(238\) 5568.72 1.51667
\(239\) −3763.79 −1.01866 −0.509328 0.860572i \(-0.670106\pi\)
−0.509328 + 0.860572i \(0.670106\pi\)
\(240\) −9325.40 −2.50813
\(241\) 3614.74 0.966166 0.483083 0.875575i \(-0.339517\pi\)
0.483083 + 0.875575i \(0.339517\pi\)
\(242\) 3037.75 0.806918
\(243\) −243.000 −0.0641500
\(244\) −9063.85 −2.37809
\(245\) −4091.84 −1.06701
\(246\) 491.652 0.127425
\(247\) 0 0
\(248\) 12699.5 3.25169
\(249\) −2147.30 −0.546503
\(250\) −1696.36 −0.429148
\(251\) −5729.77 −1.44088 −0.720438 0.693520i \(-0.756059\pi\)
−0.720438 + 0.693520i \(0.756059\pi\)
\(252\) −1778.33 −0.444541
\(253\) −1153.43 −0.286624
\(254\) −7631.18 −1.88513
\(255\) −5314.30 −1.30508
\(256\) 844.191 0.206101
\(257\) −5525.79 −1.34120 −0.670602 0.741818i \(-0.733964\pi\)
−0.670602 + 0.741818i \(0.733964\pi\)
\(258\) 3811.10 0.919647
\(259\) 952.709 0.228565
\(260\) 0 0
\(261\) 554.591 0.131526
\(262\) −11019.6 −2.59846
\(263\) 5223.21 1.22463 0.612313 0.790615i \(-0.290239\pi\)
0.612313 + 0.790615i \(0.290239\pi\)
\(264\) −5476.25 −1.27667
\(265\) 8088.78 1.87506
\(266\) 115.949 0.0267267
\(267\) −3114.46 −0.713864
\(268\) −3880.81 −0.884545
\(269\) 7203.88 1.63282 0.816410 0.577473i \(-0.195961\pi\)
0.816410 + 0.577473i \(0.195961\pi\)
\(270\) 2362.18 0.532436
\(271\) 8577.69 1.92272 0.961360 0.275293i \(-0.0887750\pi\)
0.961360 + 0.275293i \(0.0887750\pi\)
\(272\) 20440.5 4.55656
\(273\) 0 0
\(274\) −2065.59 −0.455427
\(275\) −3983.44 −0.873493
\(276\) −2560.35 −0.558388
\(277\) 7169.19 1.55507 0.777536 0.628838i \(-0.216469\pi\)
0.777536 + 0.628838i \(0.216469\pi\)
\(278\) −4011.48 −0.865442
\(279\) −1727.39 −0.370667
\(280\) 10512.1 2.24364
\(281\) −849.157 −0.180272 −0.0901360 0.995929i \(-0.528730\pi\)
−0.0901360 + 0.995929i \(0.528730\pi\)
\(282\) 8179.20 1.72718
\(283\) 1115.37 0.234283 0.117141 0.993115i \(-0.462627\pi\)
0.117141 + 0.993115i \(0.462627\pi\)
\(284\) −9895.95 −2.06766
\(285\) −110.652 −0.0229981
\(286\) 0 0
\(287\) −297.604 −0.0612091
\(288\) −4321.69 −0.884229
\(289\) 6735.49 1.37095
\(290\) −5391.14 −1.09165
\(291\) 196.691 0.0396227
\(292\) 19551.2 3.91832
\(293\) 1863.53 0.371565 0.185782 0.982591i \(-0.440518\pi\)
0.185782 + 0.982591i \(0.440518\pi\)
\(294\) −3986.66 −0.790839
\(295\) −7946.87 −1.56842
\(296\) 6512.36 1.27879
\(297\) 744.880 0.145530
\(298\) −14054.8 −2.73212
\(299\) 0 0
\(300\) −8842.31 −1.70170
\(301\) −2306.91 −0.441755
\(302\) −17763.1 −3.38461
\(303\) −1595.39 −0.302485
\(304\) 425.602 0.0802959
\(305\) −7287.76 −1.36818
\(306\) −5177.70 −0.967285
\(307\) 6387.50 1.18747 0.593736 0.804660i \(-0.297652\pi\)
0.593736 + 0.804660i \(0.297652\pi\)
\(308\) 5451.21 1.00848
\(309\) 2207.95 0.406492
\(310\) 16791.8 3.07648
\(311\) −3492.59 −0.636806 −0.318403 0.947955i \(-0.603147\pi\)
−0.318403 + 0.947955i \(0.603147\pi\)
\(312\) 0 0
\(313\) −5912.01 −1.06762 −0.533812 0.845603i \(-0.679241\pi\)
−0.533812 + 0.845603i \(0.679241\pi\)
\(314\) 8663.29 1.55700
\(315\) −1429.86 −0.255757
\(316\) −7659.31 −1.36351
\(317\) 1677.54 0.297224 0.148612 0.988896i \(-0.452519\pi\)
0.148612 + 0.988896i \(0.452519\pi\)
\(318\) 7880.86 1.38974
\(319\) −1700.02 −0.298378
\(320\) 17143.0 2.99476
\(321\) 2349.79 0.408575
\(322\) 2157.20 0.373342
\(323\) 242.540 0.0417810
\(324\) 1653.46 0.283515
\(325\) 0 0
\(326\) −9783.22 −1.66209
\(327\) −1597.02 −0.270077
\(328\) −2034.31 −0.342457
\(329\) −4950.98 −0.829655
\(330\) −7240.92 −1.20788
\(331\) −2010.31 −0.333827 −0.166913 0.985972i \(-0.553380\pi\)
−0.166913 + 0.985972i \(0.553380\pi\)
\(332\) 14611.0 2.41531
\(333\) −885.812 −0.145772
\(334\) 10367.6 1.69847
\(335\) −3120.35 −0.508905
\(336\) 5499.69 0.892955
\(337\) 7139.24 1.15400 0.577002 0.816743i \(-0.304222\pi\)
0.577002 + 0.816743i \(0.304222\pi\)
\(338\) 0 0
\(339\) 541.768 0.0867988
\(340\) 36160.5 5.76787
\(341\) 5295.05 0.840889
\(342\) −107.808 −0.0170455
\(343\) 5733.31 0.902536
\(344\) −15769.2 −2.47156
\(345\) −2058.64 −0.321257
\(346\) −13494.6 −2.09674
\(347\) 1.13990 0.000176349 0 8.81743e−5 1.00000i \(-0.499972\pi\)
8.81743e−5 1.00000i \(0.499972\pi\)
\(348\) −3773.64 −0.581289
\(349\) −12199.1 −1.87107 −0.935535 0.353235i \(-0.885082\pi\)
−0.935535 + 0.353235i \(0.885082\pi\)
\(350\) 7450.00 1.13777
\(351\) 0 0
\(352\) 13247.5 2.00595
\(353\) 10892.3 1.64232 0.821160 0.570698i \(-0.193327\pi\)
0.821160 + 0.570698i \(0.193327\pi\)
\(354\) −7742.59 −1.16247
\(355\) −7956.81 −1.18959
\(356\) 21191.9 3.15497
\(357\) 3134.13 0.464638
\(358\) −22723.5 −3.35468
\(359\) 3525.78 0.518339 0.259169 0.965832i \(-0.416551\pi\)
0.259169 + 0.965832i \(0.416551\pi\)
\(360\) −9773.99 −1.43093
\(361\) −6853.95 −0.999264
\(362\) −21026.3 −3.05281
\(363\) 1709.68 0.247204
\(364\) 0 0
\(365\) 15720.1 2.25433
\(366\) −7100.42 −1.01406
\(367\) 2383.75 0.339049 0.169525 0.985526i \(-0.445777\pi\)
0.169525 + 0.985526i \(0.445777\pi\)
\(368\) 7918.19 1.12164
\(369\) 276.707 0.0390374
\(370\) 8610.90 1.20989
\(371\) −4770.39 −0.667564
\(372\) 11753.8 1.63818
\(373\) −13282.2 −1.84377 −0.921885 0.387463i \(-0.873352\pi\)
−0.921885 + 0.387463i \(0.873352\pi\)
\(374\) 15871.5 2.19437
\(375\) −954.727 −0.131472
\(376\) −33843.1 −4.64181
\(377\) 0 0
\(378\) −1393.11 −0.189560
\(379\) 4436.73 0.601318 0.300659 0.953732i \(-0.402793\pi\)
0.300659 + 0.953732i \(0.402793\pi\)
\(380\) 752.917 0.101642
\(381\) −4294.90 −0.577519
\(382\) 1141.28 0.152862
\(383\) 810.412 0.108120 0.0540602 0.998538i \(-0.482784\pi\)
0.0540602 + 0.998538i \(0.482784\pi\)
\(384\) 5177.83 0.688100
\(385\) 4383.03 0.580207
\(386\) −6434.78 −0.848501
\(387\) 2144.93 0.281739
\(388\) −1338.35 −0.175115
\(389\) 3463.79 0.451469 0.225734 0.974189i \(-0.427522\pi\)
0.225734 + 0.974189i \(0.427522\pi\)
\(390\) 0 0
\(391\) 4512.37 0.583633
\(392\) 16495.6 2.12539
\(393\) −6201.96 −0.796050
\(394\) −4944.64 −0.632252
\(395\) −6158.45 −0.784469
\(396\) −5068.44 −0.643178
\(397\) −425.405 −0.0537796 −0.0268898 0.999638i \(-0.508560\pi\)
−0.0268898 + 0.999638i \(0.508560\pi\)
\(398\) −2553.00 −0.321533
\(399\) 65.2575 0.00818787
\(400\) 27345.9 3.41823
\(401\) 1186.85 0.147801 0.0739007 0.997266i \(-0.476455\pi\)
0.0739007 + 0.997266i \(0.476455\pi\)
\(402\) −3040.14 −0.377185
\(403\) 0 0
\(404\) 10855.6 1.33685
\(405\) 1329.46 0.163115
\(406\) 3179.44 0.388653
\(407\) 2715.33 0.330697
\(408\) 21423.7 2.59959
\(409\) −8007.42 −0.968071 −0.484036 0.875048i \(-0.660830\pi\)
−0.484036 + 0.875048i \(0.660830\pi\)
\(410\) −2689.84 −0.324005
\(411\) −1162.54 −0.139522
\(412\) −15023.7 −1.79652
\(413\) 4686.70 0.558395
\(414\) −2005.73 −0.238106
\(415\) 11747.9 1.38960
\(416\) 0 0
\(417\) −2257.70 −0.265132
\(418\) 330.468 0.0386692
\(419\) 6832.46 0.796629 0.398314 0.917249i \(-0.369595\pi\)
0.398314 + 0.917249i \(0.369595\pi\)
\(420\) 9729.30 1.13034
\(421\) −10739.6 −1.24326 −0.621632 0.783309i \(-0.713530\pi\)
−0.621632 + 0.783309i \(0.713530\pi\)
\(422\) 7734.16 0.892163
\(423\) 4603.34 0.529130
\(424\) −32608.6 −3.73494
\(425\) 15583.7 1.77864
\(426\) −7752.28 −0.881688
\(427\) 4297.99 0.487106
\(428\) −15988.9 −1.80573
\(429\) 0 0
\(430\) −20850.7 −2.33839
\(431\) −5214.45 −0.582763 −0.291382 0.956607i \(-0.594115\pi\)
−0.291382 + 0.956607i \(0.594115\pi\)
\(432\) −5113.52 −0.569501
\(433\) 8642.24 0.959168 0.479584 0.877496i \(-0.340788\pi\)
0.479584 + 0.877496i \(0.340788\pi\)
\(434\) −9903.02 −1.09530
\(435\) −3034.19 −0.334432
\(436\) 10866.7 1.19362
\(437\) 93.9545 0.0102848
\(438\) 15316.0 1.67084
\(439\) −13026.2 −1.41619 −0.708097 0.706116i \(-0.750446\pi\)
−0.708097 + 0.706116i \(0.750446\pi\)
\(440\) 29960.7 3.24619
\(441\) −2243.73 −0.242278
\(442\) 0 0
\(443\) −11533.0 −1.23690 −0.618450 0.785824i \(-0.712239\pi\)
−0.618450 + 0.785824i \(0.712239\pi\)
\(444\) 6027.39 0.644250
\(445\) 17039.3 1.81515
\(446\) −10979.5 −1.16568
\(447\) −7910.17 −0.836998
\(448\) −10110.2 −1.06621
\(449\) −9882.75 −1.03874 −0.519372 0.854548i \(-0.673834\pi\)
−0.519372 + 0.854548i \(0.673834\pi\)
\(450\) −6926.88 −0.725636
\(451\) −848.204 −0.0885596
\(452\) −3686.38 −0.383613
\(453\) −9997.26 −1.03689
\(454\) 23893.3 2.46997
\(455\) 0 0
\(456\) 446.075 0.0458101
\(457\) 15628.1 1.59967 0.799836 0.600218i \(-0.204920\pi\)
0.799836 + 0.600218i \(0.204920\pi\)
\(458\) −8690.63 −0.886652
\(459\) −2914.06 −0.296333
\(460\) 14007.8 1.41982
\(461\) 7747.46 0.782723 0.391361 0.920237i \(-0.372004\pi\)
0.391361 + 0.920237i \(0.372004\pi\)
\(462\) 4270.36 0.430033
\(463\) 333.422 0.0334675 0.0167337 0.999860i \(-0.494673\pi\)
0.0167337 + 0.999860i \(0.494673\pi\)
\(464\) 11670.4 1.16764
\(465\) 9450.59 0.942496
\(466\) 10147.4 1.00874
\(467\) 8198.33 0.812363 0.406182 0.913792i \(-0.366860\pi\)
0.406182 + 0.913792i \(0.366860\pi\)
\(468\) 0 0
\(469\) 1840.24 0.181182
\(470\) −44748.7 −4.39171
\(471\) 4875.79 0.476995
\(472\) 32036.5 3.12415
\(473\) −6574.96 −0.639148
\(474\) −6000.14 −0.581425
\(475\) 324.477 0.0313432
\(476\) −21325.8 −2.05350
\(477\) 4435.43 0.425753
\(478\) 20062.5 1.91974
\(479\) 6435.88 0.613910 0.306955 0.951724i \(-0.400690\pi\)
0.306955 + 0.951724i \(0.400690\pi\)
\(480\) 23644.1 2.24833
\(481\) 0 0
\(482\) −19268.0 −1.82082
\(483\) 1214.09 0.114375
\(484\) −11633.3 −1.09253
\(485\) −1076.10 −0.100749
\(486\) 1295.29 0.120896
\(487\) −8095.37 −0.753257 −0.376629 0.926364i \(-0.622917\pi\)
−0.376629 + 0.926364i \(0.622917\pi\)
\(488\) 29379.4 2.72529
\(489\) −5506.10 −0.509191
\(490\) 21811.1 2.01087
\(491\) 5116.46 0.470270 0.235135 0.971963i \(-0.424447\pi\)
0.235135 + 0.971963i \(0.424447\pi\)
\(492\) −1882.82 −0.172528
\(493\) 6650.67 0.607568
\(494\) 0 0
\(495\) −4075.26 −0.370039
\(496\) −36349.9 −3.29064
\(497\) 4692.56 0.423521
\(498\) 11445.9 1.02993
\(499\) 18050.7 1.61936 0.809682 0.586870i \(-0.199640\pi\)
0.809682 + 0.586870i \(0.199640\pi\)
\(500\) 6496.31 0.581047
\(501\) 5834.99 0.520336
\(502\) 30541.9 2.71544
\(503\) 10531.1 0.933512 0.466756 0.884386i \(-0.345423\pi\)
0.466756 + 0.884386i \(0.345423\pi\)
\(504\) 5764.25 0.509445
\(505\) 8728.45 0.769131
\(506\) 6148.25 0.540165
\(507\) 0 0
\(508\) 29224.1 2.55238
\(509\) 1963.31 0.170967 0.0854834 0.996340i \(-0.472757\pi\)
0.0854834 + 0.996340i \(0.472757\pi\)
\(510\) 28327.3 2.45952
\(511\) −9271.00 −0.802593
\(512\) 9307.69 0.803409
\(513\) −60.6753 −0.00522198
\(514\) 29454.6 2.52760
\(515\) −12079.8 −1.03359
\(516\) −14594.9 −1.24516
\(517\) −14110.9 −1.20038
\(518\) −5078.31 −0.430750
\(519\) −7594.89 −0.642348
\(520\) 0 0
\(521\) −7044.93 −0.592407 −0.296203 0.955125i \(-0.595721\pi\)
−0.296203 + 0.955125i \(0.595721\pi\)
\(522\) −2956.19 −0.247872
\(523\) −3213.29 −0.268657 −0.134328 0.990937i \(-0.542888\pi\)
−0.134328 + 0.990937i \(0.542888\pi\)
\(524\) 42200.4 3.51819
\(525\) 4192.94 0.348561
\(526\) −27841.7 −2.30790
\(527\) −20714.9 −1.71225
\(528\) 15674.7 1.29196
\(529\) −10419.0 −0.856333
\(530\) −43116.4 −3.53369
\(531\) −4357.61 −0.356128
\(532\) −444.036 −0.0361868
\(533\) 0 0
\(534\) 16601.3 1.34533
\(535\) −12855.8 −1.03889
\(536\) 12579.2 1.01369
\(537\) −12789.0 −1.02772
\(538\) −38399.5 −3.07718
\(539\) 6877.83 0.549627
\(540\) −9046.13 −0.720895
\(541\) −11251.4 −0.894150 −0.447075 0.894497i \(-0.647534\pi\)
−0.447075 + 0.894497i \(0.647534\pi\)
\(542\) −45722.4 −3.62352
\(543\) −11833.8 −0.935245
\(544\) −51825.8 −4.08458
\(545\) 8737.33 0.686727
\(546\) 0 0
\(547\) 1533.54 0.119871 0.0599353 0.998202i \(-0.480911\pi\)
0.0599353 + 0.998202i \(0.480911\pi\)
\(548\) 7910.31 0.616628
\(549\) −3996.19 −0.310662
\(550\) 21233.3 1.64617
\(551\) 138.477 0.0107066
\(552\) 8299.08 0.639914
\(553\) 3631.97 0.279289
\(554\) −38214.6 −2.93066
\(555\) 4846.30 0.370656
\(556\) 15362.2 1.17177
\(557\) −16845.7 −1.28146 −0.640731 0.767766i \(-0.721369\pi\)
−0.640731 + 0.767766i \(0.721369\pi\)
\(558\) 9207.65 0.698550
\(559\) 0 0
\(560\) −30089.0 −2.27052
\(561\) 8932.62 0.672256
\(562\) 4526.34 0.339737
\(563\) −20820.1 −1.55855 −0.779273 0.626685i \(-0.784411\pi\)
−0.779273 + 0.626685i \(0.784411\pi\)
\(564\) −31322.8 −2.33852
\(565\) −2964.03 −0.220704
\(566\) −5945.37 −0.441524
\(567\) −784.054 −0.0580726
\(568\) 32076.6 2.36955
\(569\) 23636.6 1.74147 0.870735 0.491752i \(-0.163643\pi\)
0.870735 + 0.491752i \(0.163643\pi\)
\(570\) 589.819 0.0433417
\(571\) −26955.1 −1.97554 −0.987771 0.155913i \(-0.950168\pi\)
−0.987771 + 0.155913i \(0.950168\pi\)
\(572\) 0 0
\(573\) 642.326 0.0468300
\(574\) 1586.35 0.115353
\(575\) 6036.78 0.437828
\(576\) 9400.25 0.679995
\(577\) −23499.8 −1.69551 −0.847755 0.530388i \(-0.822046\pi\)
−0.847755 + 0.530388i \(0.822046\pi\)
\(578\) −35902.8 −2.58367
\(579\) −3621.56 −0.259943
\(580\) 20645.7 1.47805
\(581\) −6928.38 −0.494729
\(582\) −1048.44 −0.0746721
\(583\) −13596.1 −0.965857
\(584\) −63373.1 −4.49040
\(585\) 0 0
\(586\) −9933.33 −0.700243
\(587\) −4637.50 −0.326082 −0.163041 0.986619i \(-0.552130\pi\)
−0.163041 + 0.986619i \(0.552130\pi\)
\(588\) 15267.2 1.07076
\(589\) −431.316 −0.0301733
\(590\) 42359.9 2.95582
\(591\) −2782.89 −0.193694
\(592\) −18640.4 −1.29411
\(593\) −12633.5 −0.874869 −0.437434 0.899250i \(-0.644113\pi\)
−0.437434 + 0.899250i \(0.644113\pi\)
\(594\) −3970.51 −0.274262
\(595\) −17146.9 −1.18144
\(596\) 53823.7 3.69917
\(597\) −1436.85 −0.0985033
\(598\) 0 0
\(599\) −18757.1 −1.27946 −0.639730 0.768600i \(-0.720954\pi\)
−0.639730 + 0.768600i \(0.720954\pi\)
\(600\) 28661.3 1.95016
\(601\) −3632.98 −0.246576 −0.123288 0.992371i \(-0.539344\pi\)
−0.123288 + 0.992371i \(0.539344\pi\)
\(602\) 12296.8 0.832522
\(603\) −1711.02 −0.115553
\(604\) 68025.0 4.58261
\(605\) −9353.71 −0.628566
\(606\) 8504.08 0.570057
\(607\) −12700.0 −0.849219 −0.424610 0.905377i \(-0.639589\pi\)
−0.424610 + 0.905377i \(0.639589\pi\)
\(608\) −1079.09 −0.0719786
\(609\) 1789.42 0.119066
\(610\) 38846.6 2.57845
\(611\) 0 0
\(612\) 19828.3 1.30966
\(613\) −21640.1 −1.42584 −0.712918 0.701248i \(-0.752627\pi\)
−0.712918 + 0.701248i \(0.752627\pi\)
\(614\) −34047.9 −2.23788
\(615\) −1513.87 −0.0992605
\(616\) −17669.5 −1.15572
\(617\) 16541.7 1.07933 0.539663 0.841881i \(-0.318552\pi\)
0.539663 + 0.841881i \(0.318552\pi\)
\(618\) −11769.2 −0.766066
\(619\) 21138.9 1.37261 0.686303 0.727316i \(-0.259233\pi\)
0.686303 + 0.727316i \(0.259233\pi\)
\(620\) −64305.2 −4.16542
\(621\) −1128.84 −0.0729451
\(622\) 18616.9 1.20011
\(623\) −10049.0 −0.646235
\(624\) 0 0
\(625\) −12825.4 −0.820823
\(626\) 31513.3 2.01202
\(627\) 185.991 0.0118465
\(628\) −33176.6 −2.10811
\(629\) −10622.7 −0.673377
\(630\) 7621.73 0.481995
\(631\) −5489.80 −0.346348 −0.173174 0.984891i \(-0.555402\pi\)
−0.173174 + 0.984891i \(0.555402\pi\)
\(632\) 24826.8 1.56259
\(633\) 4352.86 0.273319
\(634\) −8941.94 −0.560141
\(635\) 23497.5 1.46846
\(636\) −30180.3 −1.88164
\(637\) 0 0
\(638\) 9061.76 0.562318
\(639\) −4363.06 −0.270110
\(640\) −28328.1 −1.74963
\(641\) 4297.04 0.264778 0.132389 0.991198i \(-0.457735\pi\)
0.132389 + 0.991198i \(0.457735\pi\)
\(642\) −12525.3 −0.769993
\(643\) −25696.9 −1.57603 −0.788016 0.615655i \(-0.788892\pi\)
−0.788016 + 0.615655i \(0.788892\pi\)
\(644\) −8261.14 −0.505488
\(645\) −11735.0 −0.716378
\(646\) −1292.83 −0.0787396
\(647\) 2174.98 0.132160 0.0660798 0.997814i \(-0.478951\pi\)
0.0660798 + 0.997814i \(0.478951\pi\)
\(648\) −5359.50 −0.324909
\(649\) 13357.6 0.807907
\(650\) 0 0
\(651\) −5573.52 −0.335551
\(652\) 37465.5 2.25040
\(653\) −15454.5 −0.926160 −0.463080 0.886316i \(-0.653256\pi\)
−0.463080 + 0.886316i \(0.653256\pi\)
\(654\) 8512.73 0.508982
\(655\) 33931.1 2.02412
\(656\) 5822.82 0.346560
\(657\) 8620.02 0.511870
\(658\) 26390.7 1.56355
\(659\) −3148.77 −0.186129 −0.0930643 0.995660i \(-0.529666\pi\)
−0.0930643 + 0.995660i \(0.529666\pi\)
\(660\) 27729.6 1.63541
\(661\) 2099.70 0.123553 0.0617767 0.998090i \(-0.480323\pi\)
0.0617767 + 0.998090i \(0.480323\pi\)
\(662\) 10715.7 0.629122
\(663\) 0 0
\(664\) −47359.8 −2.76795
\(665\) −357.026 −0.0208193
\(666\) 4721.73 0.274720
\(667\) 2576.32 0.149559
\(668\) −39703.4 −2.29966
\(669\) −6179.36 −0.357112
\(670\) 16632.7 0.959071
\(671\) 12249.7 0.704763
\(672\) −13944.2 −0.800460
\(673\) 30970.8 1.77390 0.886950 0.461865i \(-0.152819\pi\)
0.886950 + 0.461865i \(0.152819\pi\)
\(674\) −38055.0 −2.17481
\(675\) −3898.52 −0.222302
\(676\) 0 0
\(677\) 14640.6 0.831141 0.415570 0.909561i \(-0.363582\pi\)
0.415570 + 0.909561i \(0.363582\pi\)
\(678\) −2887.83 −0.163579
\(679\) 634.635 0.0358690
\(680\) −117210. −6.60999
\(681\) 13447.4 0.756688
\(682\) −28224.7 −1.58472
\(683\) 6685.83 0.374563 0.187281 0.982306i \(-0.440032\pi\)
0.187281 + 0.982306i \(0.440032\pi\)
\(684\) 412.856 0.0230789
\(685\) 6360.27 0.354764
\(686\) −30560.8 −1.70090
\(687\) −4891.18 −0.271630
\(688\) 45136.3 2.50117
\(689\) 0 0
\(690\) 10973.4 0.605434
\(691\) 30194.1 1.66228 0.831141 0.556062i \(-0.187688\pi\)
0.831141 + 0.556062i \(0.187688\pi\)
\(692\) 51678.4 2.83890
\(693\) 2403.40 0.131743
\(694\) −6.07611 −0.000332343 0
\(695\) 12352.0 0.674154
\(696\) 12231.8 0.666158
\(697\) 3318.28 0.180328
\(698\) 65026.0 3.52618
\(699\) 5711.08 0.309031
\(700\) −28530.3 −1.54049
\(701\) −30300.9 −1.63260 −0.816298 0.577631i \(-0.803977\pi\)
−0.816298 + 0.577631i \(0.803977\pi\)
\(702\) 0 0
\(703\) −221.181 −0.0118663
\(704\) −28815.1 −1.54263
\(705\) −25185.0 −1.34542
\(706\) −58060.3 −3.09508
\(707\) −5147.64 −0.273829
\(708\) 29650.8 1.57393
\(709\) −26123.2 −1.38375 −0.691875 0.722017i \(-0.743215\pi\)
−0.691875 + 0.722017i \(0.743215\pi\)
\(710\) 42412.9 2.24187
\(711\) −3376.94 −0.178123
\(712\) −68691.1 −3.61560
\(713\) −8024.48 −0.421486
\(714\) −16706.2 −0.875647
\(715\) 0 0
\(716\) 87021.3 4.54209
\(717\) 11291.4 0.588122
\(718\) −18793.8 −0.976850
\(719\) 19325.7 1.00240 0.501200 0.865331i \(-0.332892\pi\)
0.501200 + 0.865331i \(0.332892\pi\)
\(720\) 27976.2 1.44807
\(721\) 7124.09 0.367982
\(722\) 36534.2 1.88319
\(723\) −10844.2 −0.557816
\(724\) 80521.7 4.13338
\(725\) 8897.47 0.455784
\(726\) −9113.26 −0.465875
\(727\) 26065.8 1.32975 0.664875 0.746954i \(-0.268485\pi\)
0.664875 + 0.746954i \(0.268485\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −83794.4 −4.24845
\(731\) 25722.0 1.30145
\(732\) 27191.5 1.37299
\(733\) −1055.45 −0.0531843 −0.0265921 0.999646i \(-0.508466\pi\)
−0.0265921 + 0.999646i \(0.508466\pi\)
\(734\) −12706.4 −0.638965
\(735\) 12275.5 0.616041
\(736\) −20076.2 −1.00546
\(737\) 5244.89 0.262141
\(738\) −1474.96 −0.0735690
\(739\) −9410.40 −0.468426 −0.234213 0.972185i \(-0.575251\pi\)
−0.234213 + 0.972185i \(0.575251\pi\)
\(740\) −32976.0 −1.63814
\(741\) 0 0
\(742\) 25428.1 1.25808
\(743\) 7523.70 0.371491 0.185746 0.982598i \(-0.440530\pi\)
0.185746 + 0.982598i \(0.440530\pi\)
\(744\) −38098.5 −1.87736
\(745\) 43276.8 2.12824
\(746\) 70799.4 3.47473
\(747\) 6441.89 0.315524
\(748\) −60780.8 −2.97108
\(749\) 7581.76 0.369868
\(750\) 5089.07 0.247769
\(751\) −12984.1 −0.630886 −0.315443 0.948945i \(-0.602153\pi\)
−0.315443 + 0.948945i \(0.602153\pi\)
\(752\) 96869.3 4.69742
\(753\) 17189.3 0.831890
\(754\) 0 0
\(755\) 54695.3 2.63651
\(756\) 5334.99 0.256656
\(757\) −27934.6 −1.34122 −0.670609 0.741811i \(-0.733967\pi\)
−0.670609 + 0.741811i \(0.733967\pi\)
\(758\) −23649.5 −1.13323
\(759\) 3460.30 0.165482
\(760\) −2440.49 −0.116482
\(761\) 15519.3 0.739255 0.369627 0.929180i \(-0.379485\pi\)
0.369627 + 0.929180i \(0.379485\pi\)
\(762\) 22893.5 1.08838
\(763\) −5152.88 −0.244491
\(764\) −4370.62 −0.206968
\(765\) 15942.9 0.753487
\(766\) −4319.82 −0.203761
\(767\) 0 0
\(768\) −2532.57 −0.118993
\(769\) −12885.2 −0.604228 −0.302114 0.953272i \(-0.597692\pi\)
−0.302114 + 0.953272i \(0.597692\pi\)
\(770\) −23363.3 −1.09345
\(771\) 16577.4 0.774344
\(772\) 24642.4 1.14883
\(773\) −5892.04 −0.274155 −0.137078 0.990560i \(-0.543771\pi\)
−0.137078 + 0.990560i \(0.543771\pi\)
\(774\) −11433.3 −0.530958
\(775\) −27713.0 −1.28449
\(776\) 4338.12 0.200682
\(777\) −2858.13 −0.131962
\(778\) −18463.4 −0.850828
\(779\) 69.0916 0.00317775
\(780\) 0 0
\(781\) 13374.3 0.612766
\(782\) −24052.7 −1.09990
\(783\) −1663.77 −0.0759367
\(784\) −47215.5 −2.15085
\(785\) −26675.6 −1.21286
\(786\) 33058.9 1.50022
\(787\) 21020.4 0.952091 0.476045 0.879421i \(-0.342070\pi\)
0.476045 + 0.879421i \(0.342070\pi\)
\(788\) 18935.8 0.856042
\(789\) −15669.6 −0.707038
\(790\) 32827.0 1.47839
\(791\) 1748.05 0.0785757
\(792\) 16428.7 0.737084
\(793\) 0 0
\(794\) 2267.58 0.101352
\(795\) −24266.4 −1.08256
\(796\) 9776.87 0.435342
\(797\) 31355.6 1.39356 0.696782 0.717283i \(-0.254614\pi\)
0.696782 + 0.717283i \(0.254614\pi\)
\(798\) −347.848 −0.0154307
\(799\) 55203.3 2.44425
\(800\) −69334.0 −3.06416
\(801\) 9343.37 0.412150
\(802\) −6326.37 −0.278543
\(803\) −26423.4 −1.16122
\(804\) 11642.4 0.510692
\(805\) −6642.34 −0.290822
\(806\) 0 0
\(807\) −21611.7 −0.942709
\(808\) −35187.3 −1.53204
\(809\) −18132.5 −0.788017 −0.394009 0.919107i \(-0.628912\pi\)
−0.394009 + 0.919107i \(0.628912\pi\)
\(810\) −7086.55 −0.307402
\(811\) 24755.3 1.07186 0.535928 0.844263i \(-0.319962\pi\)
0.535928 + 0.844263i \(0.319962\pi\)
\(812\) −12175.9 −0.526219
\(813\) −25733.1 −1.11008
\(814\) −14473.8 −0.623225
\(815\) 30124.0 1.29472
\(816\) −61321.4 −2.63073
\(817\) 535.572 0.0229343
\(818\) 42682.7 1.82441
\(819\) 0 0
\(820\) 10300.9 0.438688
\(821\) −4082.65 −0.173551 −0.0867755 0.996228i \(-0.527656\pi\)
−0.0867755 + 0.996228i \(0.527656\pi\)
\(822\) 6196.77 0.262941
\(823\) −34327.0 −1.45391 −0.726954 0.686687i \(-0.759065\pi\)
−0.726954 + 0.686687i \(0.759065\pi\)
\(824\) 48697.6 2.05881
\(825\) 11950.3 0.504312
\(826\) −24981.9 −1.05234
\(827\) −3228.87 −0.135767 −0.0678833 0.997693i \(-0.521625\pi\)
−0.0678833 + 0.997693i \(0.521625\pi\)
\(828\) 7681.06 0.322386
\(829\) −10452.4 −0.437908 −0.218954 0.975735i \(-0.570265\pi\)
−0.218954 + 0.975735i \(0.570265\pi\)
\(830\) −62621.0 −2.61880
\(831\) −21507.6 −0.897821
\(832\) 0 0
\(833\) −26906.9 −1.11917
\(834\) 12034.5 0.499663
\(835\) −31923.4 −1.32306
\(836\) −1265.55 −0.0523564
\(837\) 5182.16 0.214004
\(838\) −36419.7 −1.50131
\(839\) 28289.0 1.16406 0.582028 0.813169i \(-0.302259\pi\)
0.582028 + 0.813169i \(0.302259\pi\)
\(840\) −31536.4 −1.29537
\(841\) −20591.8 −0.844308
\(842\) 57246.1 2.34303
\(843\) 2547.47 0.104080
\(844\) −29618.5 −1.20795
\(845\) 0 0
\(846\) −24537.6 −0.997187
\(847\) 5516.39 0.223784
\(848\) 93335.9 3.77968
\(849\) −3346.12 −0.135263
\(850\) −83067.2 −3.35198
\(851\) −4114.99 −0.165758
\(852\) 29687.8 1.19377
\(853\) 26631.8 1.06900 0.534498 0.845170i \(-0.320501\pi\)
0.534498 + 0.845170i \(0.320501\pi\)
\(854\) −22910.0 −0.917989
\(855\) 331.956 0.0132780
\(856\) 51826.0 2.06936
\(857\) 11796.7 0.470209 0.235104 0.971970i \(-0.424457\pi\)
0.235104 + 0.971970i \(0.424457\pi\)
\(858\) 0 0
\(859\) −22672.8 −0.900567 −0.450283 0.892886i \(-0.648677\pi\)
−0.450283 + 0.892886i \(0.648677\pi\)
\(860\) 79849.0 3.16608
\(861\) 892.812 0.0353391
\(862\) 27795.0 1.09826
\(863\) −21421.1 −0.844940 −0.422470 0.906377i \(-0.638837\pi\)
−0.422470 + 0.906377i \(0.638837\pi\)
\(864\) 12965.1 0.510510
\(865\) 41551.9 1.63330
\(866\) −46066.6 −1.80763
\(867\) −20206.5 −0.791520
\(868\) 37924.3 1.48299
\(869\) 10351.5 0.404086
\(870\) 16173.4 0.630264
\(871\) 0 0
\(872\) −35223.1 −1.36790
\(873\) −590.072 −0.0228762
\(874\) −500.814 −0.0193825
\(875\) −3080.48 −0.119016
\(876\) −58653.7 −2.26224
\(877\) 5155.20 0.198493 0.0992466 0.995063i \(-0.468357\pi\)
0.0992466 + 0.995063i \(0.468357\pi\)
\(878\) 69435.0 2.66893
\(879\) −5590.58 −0.214523
\(880\) −85756.9 −3.28507
\(881\) 23692.2 0.906027 0.453013 0.891504i \(-0.350349\pi\)
0.453013 + 0.891504i \(0.350349\pi\)
\(882\) 11960.0 0.456591
\(883\) −14591.5 −0.556108 −0.278054 0.960565i \(-0.589689\pi\)
−0.278054 + 0.960565i \(0.589689\pi\)
\(884\) 0 0
\(885\) 23840.6 0.905529
\(886\) 61475.2 2.33104
\(887\) −9722.26 −0.368029 −0.184014 0.982924i \(-0.558909\pi\)
−0.184014 + 0.982924i \(0.558909\pi\)
\(888\) −19537.1 −0.738312
\(889\) −13857.8 −0.522806
\(890\) −90826.1 −3.42078
\(891\) −2234.64 −0.0840217
\(892\) 42046.6 1.57828
\(893\) 1149.42 0.0430726
\(894\) 42164.3 1.57739
\(895\) 69969.2 2.61320
\(896\) 16706.6 0.622911
\(897\) 0 0
\(898\) 52678.9 1.95759
\(899\) −11827.1 −0.438771
\(900\) 26526.9 0.982479
\(901\) 53189.7 1.96671
\(902\) 4521.26 0.166898
\(903\) 6920.74 0.255048
\(904\) 11949.0 0.439621
\(905\) 64743.2 2.37805
\(906\) 53289.3 1.95411
\(907\) 11799.0 0.431951 0.215975 0.976399i \(-0.430707\pi\)
0.215975 + 0.976399i \(0.430707\pi\)
\(908\) −91500.9 −3.34423
\(909\) 4786.18 0.174640
\(910\) 0 0
\(911\) −43012.4 −1.56429 −0.782143 0.623099i \(-0.785873\pi\)
−0.782143 + 0.623099i \(0.785873\pi\)
\(912\) −1276.81 −0.0463589
\(913\) −19746.6 −0.715793
\(914\) −83303.8 −3.01471
\(915\) 21863.3 0.789921
\(916\) 33281.3 1.20049
\(917\) −20011.0 −0.720635
\(918\) 15533.1 0.558462
\(919\) −4951.41 −0.177728 −0.0888639 0.996044i \(-0.528324\pi\)
−0.0888639 + 0.996044i \(0.528324\pi\)
\(920\) −45404.5 −1.62711
\(921\) −19162.5 −0.685587
\(922\) −41297.0 −1.47510
\(923\) 0 0
\(924\) −16353.6 −0.582245
\(925\) −14211.3 −0.505152
\(926\) −1777.27 −0.0630721
\(927\) −6623.85 −0.234688
\(928\) −29589.8 −1.04669
\(929\) 8934.86 0.315547 0.157774 0.987475i \(-0.449568\pi\)
0.157774 + 0.987475i \(0.449568\pi\)
\(930\) −50375.4 −1.77621
\(931\) −560.243 −0.0197221
\(932\) −38860.2 −1.36578
\(933\) 10477.8 0.367660
\(934\) −43700.3 −1.53096
\(935\) −48870.6 −1.70935
\(936\) 0 0
\(937\) −13182.8 −0.459620 −0.229810 0.973235i \(-0.573811\pi\)
−0.229810 + 0.973235i \(0.573811\pi\)
\(938\) −9809.20 −0.341452
\(939\) 17736.0 0.616393
\(940\) 171368. 5.94618
\(941\) 21693.7 0.751536 0.375768 0.926714i \(-0.377379\pi\)
0.375768 + 0.926714i \(0.377379\pi\)
\(942\) −25989.9 −0.898934
\(943\) 1285.43 0.0443895
\(944\) −91698.4 −3.16158
\(945\) 4289.59 0.147662
\(946\) 35047.1 1.20452
\(947\) 49790.0 1.70851 0.854254 0.519856i \(-0.174014\pi\)
0.854254 + 0.519856i \(0.174014\pi\)
\(948\) 22977.9 0.787224
\(949\) 0 0
\(950\) −1729.59 −0.0590687
\(951\) −5032.61 −0.171602
\(952\) 69125.0 2.35331
\(953\) 4217.93 0.143371 0.0716853 0.997427i \(-0.477162\pi\)
0.0716853 + 0.997427i \(0.477162\pi\)
\(954\) −23642.6 −0.802365
\(955\) −3514.19 −0.119075
\(956\) −76830.5 −2.59924
\(957\) 5100.05 0.172269
\(958\) −34305.8 −1.15696
\(959\) −3750.99 −0.126304
\(960\) −51429.0 −1.72903
\(961\) 7046.87 0.236544
\(962\) 0 0
\(963\) −7049.38 −0.235891
\(964\) 73788.1 2.46530
\(965\) 19813.7 0.660958
\(966\) −6471.60 −0.215549
\(967\) 40927.9 1.36107 0.680534 0.732717i \(-0.261748\pi\)
0.680534 + 0.732717i \(0.261748\pi\)
\(968\) 37707.9 1.25204
\(969\) −727.619 −0.0241223
\(970\) 5736.04 0.189869
\(971\) −17114.8 −0.565645 −0.282822 0.959172i \(-0.591271\pi\)
−0.282822 + 0.959172i \(0.591271\pi\)
\(972\) −4960.38 −0.163688
\(973\) −7284.62 −0.240015
\(974\) 43151.5 1.41957
\(975\) 0 0
\(976\) −84093.0 −2.75794
\(977\) 118.470 0.00387940 0.00193970 0.999998i \(-0.499383\pi\)
0.00193970 + 0.999998i \(0.499383\pi\)
\(978\) 29349.7 0.959610
\(979\) −28640.7 −0.934996
\(980\) −83527.2 −2.72263
\(981\) 4791.05 0.155929
\(982\) −27272.8 −0.886261
\(983\) −26002.8 −0.843705 −0.421852 0.906665i \(-0.638620\pi\)
−0.421852 + 0.906665i \(0.638620\pi\)
\(984\) 6102.93 0.197718
\(985\) 15225.3 0.492506
\(986\) −35450.7 −1.14501
\(987\) 14853.0 0.479002
\(988\) 0 0
\(989\) 9964.14 0.320365
\(990\) 21722.8 0.697368
\(991\) −16062.0 −0.514860 −0.257430 0.966297i \(-0.582876\pi\)
−0.257430 + 0.966297i \(0.582876\pi\)
\(992\) 92163.3 2.94979
\(993\) 6030.93 0.192735
\(994\) −25013.2 −0.798159
\(995\) 7861.07 0.250465
\(996\) −43832.9 −1.39448
\(997\) 1361.54 0.0432503 0.0216251 0.999766i \(-0.493116\pi\)
0.0216251 + 0.999766i \(0.493116\pi\)
\(998\) −96217.5 −3.05182
\(999\) 2657.44 0.0841617
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 507.4.a.i.1.1 4
3.2 odd 2 1521.4.a.bb.1.4 4
13.4 even 6 39.4.e.c.16.1 8
13.5 odd 4 507.4.b.h.337.8 8
13.8 odd 4 507.4.b.h.337.1 8
13.10 even 6 39.4.e.c.22.1 yes 8
13.12 even 2 507.4.a.m.1.4 4
39.17 odd 6 117.4.g.e.55.4 8
39.23 odd 6 117.4.g.e.100.4 8
39.38 odd 2 1521.4.a.v.1.1 4
52.23 odd 6 624.4.q.i.529.1 8
52.43 odd 6 624.4.q.i.289.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.c.16.1 8 13.4 even 6
39.4.e.c.22.1 yes 8 13.10 even 6
117.4.g.e.55.4 8 39.17 odd 6
117.4.g.e.100.4 8 39.23 odd 6
507.4.a.i.1.1 4 1.1 even 1 trivial
507.4.a.m.1.4 4 13.12 even 2
507.4.b.h.337.1 8 13.8 odd 4
507.4.b.h.337.8 8 13.5 odd 4
624.4.q.i.289.1 8 52.43 odd 6
624.4.q.i.529.1 8 52.23 odd 6
1521.4.a.v.1.1 4 39.38 odd 2
1521.4.a.bb.1.4 4 3.2 odd 2