Properties

Label 1521.4.a.bm.1.11
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(89.7419051187\)
Analytic rank: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} - 37096332 x^{4} + 27824160 x^{2} - 6889792 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 7\cdot 13^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(1.15064\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.15064 q^{2} -6.67603 q^{4} +21.2034 q^{5} -31.2668 q^{7} -16.8868 q^{8} +O(q^{10})\) \(q+1.15064 q^{2} -6.67603 q^{4} +21.2034 q^{5} -31.2668 q^{7} -16.8868 q^{8} +24.3975 q^{10} +17.3811 q^{11} -35.9768 q^{14} +33.9775 q^{16} +89.1071 q^{17} -80.6466 q^{19} -141.555 q^{20} +19.9994 q^{22} -149.683 q^{23} +324.586 q^{25} +208.738 q^{28} +6.30162 q^{29} +78.3099 q^{31} +174.191 q^{32} +102.530 q^{34} -662.964 q^{35} +39.2975 q^{37} -92.7953 q^{38} -358.059 q^{40} +330.647 q^{41} -198.803 q^{43} -116.037 q^{44} -172.231 q^{46} -246.612 q^{47} +634.613 q^{49} +373.482 q^{50} -600.345 q^{53} +368.540 q^{55} +527.997 q^{56} +7.25090 q^{58} -709.534 q^{59} -472.354 q^{61} +90.1066 q^{62} -71.3895 q^{64} -331.545 q^{67} -594.881 q^{68} -762.833 q^{70} -472.765 q^{71} +651.016 q^{73} +45.2173 q^{74} +538.399 q^{76} -543.452 q^{77} +240.920 q^{79} +720.441 q^{80} +380.456 q^{82} +538.031 q^{83} +1889.38 q^{85} -228.751 q^{86} -293.512 q^{88} -673.484 q^{89} +999.288 q^{92} -283.762 q^{94} -1709.99 q^{95} -468.827 q^{97} +730.211 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 56 q^{4} - 94 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 56 q^{4} - 94 q^{7} + 156 q^{10} + 88 q^{16} - 448 q^{19} - 256 q^{22} - 16 q^{25} - 1300 q^{28} - 818 q^{31} - 900 q^{34} - 524 q^{37} + 800 q^{40} + 752 q^{43} - 1650 q^{46} + 2948 q^{49} - 464 q^{55} - 1626 q^{58} - 1784 q^{61} - 4274 q^{64} - 2872 q^{67} - 5772 q^{70} - 3078 q^{73} - 5726 q^{76} + 3326 q^{79} - 1038 q^{82} - 2340 q^{85} + 780 q^{88} + 1220 q^{94} - 4630 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.15064 0.406813 0.203406 0.979094i \(-0.434799\pi\)
0.203406 + 0.979094i \(0.434799\pi\)
\(3\) 0 0
\(4\) −6.67603 −0.834503
\(5\) 21.2034 1.89649 0.948247 0.317534i \(-0.102855\pi\)
0.948247 + 0.317534i \(0.102855\pi\)
\(6\) 0 0
\(7\) −31.2668 −1.68825 −0.844124 0.536148i \(-0.819879\pi\)
−0.844124 + 0.536148i \(0.819879\pi\)
\(8\) −16.8868 −0.746300
\(9\) 0 0
\(10\) 24.3975 0.771518
\(11\) 17.3811 0.476419 0.238209 0.971214i \(-0.423440\pi\)
0.238209 + 0.971214i \(0.423440\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −35.9768 −0.686801
\(15\) 0 0
\(16\) 33.9775 0.530899
\(17\) 89.1071 1.27127 0.635637 0.771988i \(-0.280738\pi\)
0.635637 + 0.771988i \(0.280738\pi\)
\(18\) 0 0
\(19\) −80.6466 −0.973769 −0.486884 0.873466i \(-0.661867\pi\)
−0.486884 + 0.873466i \(0.661867\pi\)
\(20\) −141.555 −1.58263
\(21\) 0 0
\(22\) 19.9994 0.193813
\(23\) −149.683 −1.35700 −0.678502 0.734599i \(-0.737370\pi\)
−0.678502 + 0.734599i \(0.737370\pi\)
\(24\) 0 0
\(25\) 324.586 2.59669
\(26\) 0 0
\(27\) 0 0
\(28\) 208.738 1.40885
\(29\) 6.30162 0.0403511 0.0201755 0.999796i \(-0.493577\pi\)
0.0201755 + 0.999796i \(0.493577\pi\)
\(30\) 0 0
\(31\) 78.3099 0.453706 0.226853 0.973929i \(-0.427156\pi\)
0.226853 + 0.973929i \(0.427156\pi\)
\(32\) 174.191 0.962276
\(33\) 0 0
\(34\) 102.530 0.517170
\(35\) −662.964 −3.20175
\(36\) 0 0
\(37\) 39.2975 0.174607 0.0873037 0.996182i \(-0.472175\pi\)
0.0873037 + 0.996182i \(0.472175\pi\)
\(38\) −92.7953 −0.396142
\(39\) 0 0
\(40\) −358.059 −1.41535
\(41\) 330.647 1.25947 0.629737 0.776809i \(-0.283163\pi\)
0.629737 + 0.776809i \(0.283163\pi\)
\(42\) 0 0
\(43\) −198.803 −0.705052 −0.352526 0.935802i \(-0.614677\pi\)
−0.352526 + 0.935802i \(0.614677\pi\)
\(44\) −116.037 −0.397573
\(45\) 0 0
\(46\) −172.231 −0.552046
\(47\) −246.612 −0.765364 −0.382682 0.923880i \(-0.625000\pi\)
−0.382682 + 0.923880i \(0.625000\pi\)
\(48\) 0 0
\(49\) 634.613 1.85018
\(50\) 373.482 1.05637
\(51\) 0 0
\(52\) 0 0
\(53\) −600.345 −1.55592 −0.777960 0.628314i \(-0.783745\pi\)
−0.777960 + 0.628314i \(0.783745\pi\)
\(54\) 0 0
\(55\) 368.540 0.903525
\(56\) 527.997 1.25994
\(57\) 0 0
\(58\) 7.25090 0.0164153
\(59\) −709.534 −1.56565 −0.782826 0.622240i \(-0.786223\pi\)
−0.782826 + 0.622240i \(0.786223\pi\)
\(60\) 0 0
\(61\) −472.354 −0.991455 −0.495727 0.868478i \(-0.665098\pi\)
−0.495727 + 0.868478i \(0.665098\pi\)
\(62\) 90.1066 0.184573
\(63\) 0 0
\(64\) −71.3895 −0.139433
\(65\) 0 0
\(66\) 0 0
\(67\) −331.545 −0.604547 −0.302273 0.953221i \(-0.597746\pi\)
−0.302273 + 0.953221i \(0.597746\pi\)
\(68\) −594.881 −1.06088
\(69\) 0 0
\(70\) −762.833 −1.30251
\(71\) −472.765 −0.790238 −0.395119 0.918630i \(-0.629297\pi\)
−0.395119 + 0.918630i \(0.629297\pi\)
\(72\) 0 0
\(73\) 651.016 1.04378 0.521888 0.853014i \(-0.325228\pi\)
0.521888 + 0.853014i \(0.325228\pi\)
\(74\) 45.2173 0.0710325
\(75\) 0 0
\(76\) 538.399 0.812613
\(77\) −543.452 −0.804313
\(78\) 0 0
\(79\) 240.920 0.343109 0.171555 0.985175i \(-0.445121\pi\)
0.171555 + 0.985175i \(0.445121\pi\)
\(80\) 720.441 1.00685
\(81\) 0 0
\(82\) 380.456 0.512370
\(83\) 538.031 0.711524 0.355762 0.934577i \(-0.384221\pi\)
0.355762 + 0.934577i \(0.384221\pi\)
\(84\) 0 0
\(85\) 1889.38 2.41096
\(86\) −228.751 −0.286824
\(87\) 0 0
\(88\) −293.512 −0.355551
\(89\) −673.484 −0.802126 −0.401063 0.916050i \(-0.631359\pi\)
−0.401063 + 0.916050i \(0.631359\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 999.288 1.13242
\(93\) 0 0
\(94\) −283.762 −0.311360
\(95\) −1709.99 −1.84675
\(96\) 0 0
\(97\) −468.827 −0.490744 −0.245372 0.969429i \(-0.578910\pi\)
−0.245372 + 0.969429i \(0.578910\pi\)
\(98\) 730.211 0.752678
\(99\) 0 0
\(100\) −2166.94 −2.16694
\(101\) −305.731 −0.301201 −0.150601 0.988595i \(-0.548121\pi\)
−0.150601 + 0.988595i \(0.548121\pi\)
\(102\) 0 0
\(103\) −1560.85 −1.49315 −0.746576 0.665300i \(-0.768304\pi\)
−0.746576 + 0.665300i \(0.768304\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −690.781 −0.632968
\(107\) −707.803 −0.639494 −0.319747 0.947503i \(-0.603598\pi\)
−0.319747 + 0.947503i \(0.603598\pi\)
\(108\) 0 0
\(109\) −1714.25 −1.50638 −0.753192 0.657801i \(-0.771487\pi\)
−0.753192 + 0.657801i \(0.771487\pi\)
\(110\) 424.057 0.367566
\(111\) 0 0
\(112\) −1062.37 −0.896289
\(113\) 1263.51 1.05187 0.525935 0.850525i \(-0.323715\pi\)
0.525935 + 0.850525i \(0.323715\pi\)
\(114\) 0 0
\(115\) −3173.80 −2.57355
\(116\) −42.0698 −0.0336731
\(117\) 0 0
\(118\) −816.419 −0.636928
\(119\) −2786.09 −2.14623
\(120\) 0 0
\(121\) −1028.90 −0.773025
\(122\) −543.510 −0.403337
\(123\) 0 0
\(124\) −522.799 −0.378619
\(125\) 4231.91 3.02811
\(126\) 0 0
\(127\) 893.935 0.624598 0.312299 0.949984i \(-0.398901\pi\)
0.312299 + 0.949984i \(0.398901\pi\)
\(128\) −1475.67 −1.01900
\(129\) 0 0
\(130\) 0 0
\(131\) −9.87226 −0.00658430 −0.00329215 0.999995i \(-0.501048\pi\)
−0.00329215 + 0.999995i \(0.501048\pi\)
\(132\) 0 0
\(133\) 2521.56 1.64396
\(134\) −381.489 −0.245937
\(135\) 0 0
\(136\) −1504.74 −0.948751
\(137\) 1486.59 0.927063 0.463532 0.886080i \(-0.346582\pi\)
0.463532 + 0.886080i \(0.346582\pi\)
\(138\) 0 0
\(139\) 530.179 0.323520 0.161760 0.986830i \(-0.448283\pi\)
0.161760 + 0.986830i \(0.448283\pi\)
\(140\) 4425.96 2.67187
\(141\) 0 0
\(142\) −543.983 −0.321479
\(143\) 0 0
\(144\) 0 0
\(145\) 133.616 0.0765255
\(146\) 749.086 0.424622
\(147\) 0 0
\(148\) −262.351 −0.145710
\(149\) −1796.65 −0.987832 −0.493916 0.869510i \(-0.664435\pi\)
−0.493916 + 0.869510i \(0.664435\pi\)
\(150\) 0 0
\(151\) −1818.69 −0.980150 −0.490075 0.871680i \(-0.663031\pi\)
−0.490075 + 0.871680i \(0.663031\pi\)
\(152\) 1361.87 0.726723
\(153\) 0 0
\(154\) −625.318 −0.327205
\(155\) 1660.44 0.860450
\(156\) 0 0
\(157\) −875.076 −0.444832 −0.222416 0.974952i \(-0.571394\pi\)
−0.222416 + 0.974952i \(0.571394\pi\)
\(158\) 277.213 0.139581
\(159\) 0 0
\(160\) 3693.44 1.82495
\(161\) 4680.11 2.29096
\(162\) 0 0
\(163\) 1777.39 0.854083 0.427042 0.904232i \(-0.359556\pi\)
0.427042 + 0.904232i \(0.359556\pi\)
\(164\) −2207.41 −1.05103
\(165\) 0 0
\(166\) 619.080 0.289457
\(167\) −2526.37 −1.17064 −0.585319 0.810803i \(-0.699031\pi\)
−0.585319 + 0.810803i \(0.699031\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 2173.99 0.980810
\(171\) 0 0
\(172\) 1327.22 0.588368
\(173\) −204.999 −0.0900913 −0.0450457 0.998985i \(-0.514343\pi\)
−0.0450457 + 0.998985i \(0.514343\pi\)
\(174\) 0 0
\(175\) −10148.8 −4.38385
\(176\) 590.568 0.252930
\(177\) 0 0
\(178\) −774.939 −0.326315
\(179\) −1768.15 −0.738311 −0.369156 0.929368i \(-0.620353\pi\)
−0.369156 + 0.929368i \(0.620353\pi\)
\(180\) 0 0
\(181\) 2542.64 1.04416 0.522079 0.852897i \(-0.325157\pi\)
0.522079 + 0.852897i \(0.325157\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2527.67 1.01273
\(185\) 833.243 0.331142
\(186\) 0 0
\(187\) 1548.78 0.605659
\(188\) 1646.39 0.638699
\(189\) 0 0
\(190\) −1967.58 −0.751280
\(191\) 40.7190 0.0154258 0.00771289 0.999970i \(-0.497545\pi\)
0.00771289 + 0.999970i \(0.497545\pi\)
\(192\) 0 0
\(193\) −2774.70 −1.03486 −0.517428 0.855727i \(-0.673110\pi\)
−0.517428 + 0.855727i \(0.673110\pi\)
\(194\) −539.451 −0.199641
\(195\) 0 0
\(196\) −4236.69 −1.54398
\(197\) −1171.74 −0.423770 −0.211885 0.977295i \(-0.567960\pi\)
−0.211885 + 0.977295i \(0.567960\pi\)
\(198\) 0 0
\(199\) 1940.97 0.691417 0.345708 0.938342i \(-0.387639\pi\)
0.345708 + 0.938342i \(0.387639\pi\)
\(200\) −5481.23 −1.93791
\(201\) 0 0
\(202\) −351.786 −0.122533
\(203\) −197.031 −0.0681226
\(204\) 0 0
\(205\) 7010.86 2.38858
\(206\) −1795.97 −0.607434
\(207\) 0 0
\(208\) 0 0
\(209\) −1401.73 −0.463922
\(210\) 0 0
\(211\) 1659.92 0.541580 0.270790 0.962638i \(-0.412715\pi\)
0.270790 + 0.962638i \(0.412715\pi\)
\(212\) 4007.92 1.29842
\(213\) 0 0
\(214\) −814.427 −0.260155
\(215\) −4215.32 −1.33713
\(216\) 0 0
\(217\) −2448.50 −0.765968
\(218\) −1972.49 −0.612816
\(219\) 0 0
\(220\) −2460.38 −0.753995
\(221\) 0 0
\(222\) 0 0
\(223\) −4619.40 −1.38716 −0.693582 0.720378i \(-0.743969\pi\)
−0.693582 + 0.720378i \(0.743969\pi\)
\(224\) −5446.38 −1.62456
\(225\) 0 0
\(226\) 1453.85 0.427914
\(227\) 1220.49 0.356859 0.178429 0.983953i \(-0.442898\pi\)
0.178429 + 0.983953i \(0.442898\pi\)
\(228\) 0 0
\(229\) −3911.47 −1.12872 −0.564361 0.825528i \(-0.690878\pi\)
−0.564361 + 0.825528i \(0.690878\pi\)
\(230\) −3651.90 −1.04695
\(231\) 0 0
\(232\) −106.414 −0.0301140
\(233\) −4235.15 −1.19079 −0.595395 0.803433i \(-0.703004\pi\)
−0.595395 + 0.803433i \(0.703004\pi\)
\(234\) 0 0
\(235\) −5229.03 −1.45151
\(236\) 4736.87 1.30654
\(237\) 0 0
\(238\) −3205.79 −0.873112
\(239\) 772.395 0.209046 0.104523 0.994522i \(-0.466668\pi\)
0.104523 + 0.994522i \(0.466668\pi\)
\(240\) 0 0
\(241\) 1319.51 0.352684 0.176342 0.984329i \(-0.443574\pi\)
0.176342 + 0.984329i \(0.443574\pi\)
\(242\) −1183.89 −0.314477
\(243\) 0 0
\(244\) 3153.45 0.827372
\(245\) 13456.0 3.50886
\(246\) 0 0
\(247\) 0 0
\(248\) −1322.41 −0.338600
\(249\) 0 0
\(250\) 4869.41 1.23187
\(251\) −2422.90 −0.609292 −0.304646 0.952466i \(-0.598538\pi\)
−0.304646 + 0.952466i \(0.598538\pi\)
\(252\) 0 0
\(253\) −2601.66 −0.646502
\(254\) 1028.60 0.254094
\(255\) 0 0
\(256\) −1126.85 −0.275109
\(257\) −3778.25 −0.917047 −0.458523 0.888682i \(-0.651621\pi\)
−0.458523 + 0.888682i \(0.651621\pi\)
\(258\) 0 0
\(259\) −1228.71 −0.294781
\(260\) 0 0
\(261\) 0 0
\(262\) −11.3594 −0.00267858
\(263\) 7343.43 1.72173 0.860866 0.508832i \(-0.169923\pi\)
0.860866 + 0.508832i \(0.169923\pi\)
\(264\) 0 0
\(265\) −12729.4 −2.95079
\(266\) 2901.41 0.668786
\(267\) 0 0
\(268\) 2213.40 0.504496
\(269\) −7812.34 −1.77073 −0.885365 0.464896i \(-0.846092\pi\)
−0.885365 + 0.464896i \(0.846092\pi\)
\(270\) 0 0
\(271\) −5592.09 −1.25349 −0.626745 0.779225i \(-0.715613\pi\)
−0.626745 + 0.779225i \(0.715613\pi\)
\(272\) 3027.64 0.674918
\(273\) 0 0
\(274\) 1710.53 0.377141
\(275\) 5641.67 1.23711
\(276\) 0 0
\(277\) 3897.19 0.845342 0.422671 0.906283i \(-0.361093\pi\)
0.422671 + 0.906283i \(0.361093\pi\)
\(278\) 610.046 0.131612
\(279\) 0 0
\(280\) 11195.4 2.38947
\(281\) −5921.18 −1.25704 −0.628519 0.777794i \(-0.716339\pi\)
−0.628519 + 0.777794i \(0.716339\pi\)
\(282\) 0 0
\(283\) −4936.47 −1.03690 −0.518450 0.855108i \(-0.673491\pi\)
−0.518450 + 0.855108i \(0.673491\pi\)
\(284\) 3156.19 0.659456
\(285\) 0 0
\(286\) 0 0
\(287\) −10338.3 −2.12630
\(288\) 0 0
\(289\) 3027.07 0.616136
\(290\) 153.744 0.0311316
\(291\) 0 0
\(292\) −4346.20 −0.871035
\(293\) −5575.98 −1.11178 −0.555891 0.831255i \(-0.687623\pi\)
−0.555891 + 0.831255i \(0.687623\pi\)
\(294\) 0 0
\(295\) −15044.6 −2.96925
\(296\) −663.611 −0.130309
\(297\) 0 0
\(298\) −2067.29 −0.401863
\(299\) 0 0
\(300\) 0 0
\(301\) 6215.95 1.19030
\(302\) −2092.66 −0.398738
\(303\) 0 0
\(304\) −2740.17 −0.516973
\(305\) −10015.5 −1.88029
\(306\) 0 0
\(307\) 10168.3 1.89035 0.945175 0.326564i \(-0.105891\pi\)
0.945175 + 0.326564i \(0.105891\pi\)
\(308\) 3628.10 0.671202
\(309\) 0 0
\(310\) 1910.57 0.350042
\(311\) 4680.41 0.853382 0.426691 0.904397i \(-0.359679\pi\)
0.426691 + 0.904397i \(0.359679\pi\)
\(312\) 0 0
\(313\) 2990.32 0.540009 0.270004 0.962859i \(-0.412975\pi\)
0.270004 + 0.962859i \(0.412975\pi\)
\(314\) −1006.90 −0.180963
\(315\) 0 0
\(316\) −1608.39 −0.286326
\(317\) −9081.93 −1.60912 −0.804561 0.593870i \(-0.797599\pi\)
−0.804561 + 0.593870i \(0.797599\pi\)
\(318\) 0 0
\(319\) 109.529 0.0192240
\(320\) −1513.70 −0.264433
\(321\) 0 0
\(322\) 5385.12 0.931991
\(323\) −7186.19 −1.23793
\(324\) 0 0
\(325\) 0 0
\(326\) 2045.13 0.347452
\(327\) 0 0
\(328\) −5583.58 −0.939945
\(329\) 7710.78 1.29213
\(330\) 0 0
\(331\) 5290.27 0.878488 0.439244 0.898368i \(-0.355246\pi\)
0.439244 + 0.898368i \(0.355246\pi\)
\(332\) −3591.91 −0.593769
\(333\) 0 0
\(334\) −2906.95 −0.476231
\(335\) −7029.89 −1.14652
\(336\) 0 0
\(337\) −3313.51 −0.535603 −0.267802 0.963474i \(-0.586297\pi\)
−0.267802 + 0.963474i \(0.586297\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −12613.5 −2.01196
\(341\) 1361.11 0.216154
\(342\) 0 0
\(343\) −9117.79 −1.43532
\(344\) 3357.16 0.526180
\(345\) 0 0
\(346\) −235.880 −0.0366503
\(347\) 4218.65 0.652649 0.326324 0.945258i \(-0.394190\pi\)
0.326324 + 0.945258i \(0.394190\pi\)
\(348\) 0 0
\(349\) −6552.91 −1.00507 −0.502535 0.864557i \(-0.667599\pi\)
−0.502535 + 0.864557i \(0.667599\pi\)
\(350\) −11677.6 −1.78341
\(351\) 0 0
\(352\) 3027.63 0.458447
\(353\) −3864.50 −0.582681 −0.291341 0.956619i \(-0.594101\pi\)
−0.291341 + 0.956619i \(0.594101\pi\)
\(354\) 0 0
\(355\) −10024.2 −1.49868
\(356\) 4496.20 0.669377
\(357\) 0 0
\(358\) −2034.51 −0.300355
\(359\) −588.511 −0.0865192 −0.0432596 0.999064i \(-0.513774\pi\)
−0.0432596 + 0.999064i \(0.513774\pi\)
\(360\) 0 0
\(361\) −355.122 −0.0517746
\(362\) 2925.66 0.424777
\(363\) 0 0
\(364\) 0 0
\(365\) 13803.8 1.97952
\(366\) 0 0
\(367\) 11082.7 1.57633 0.788167 0.615462i \(-0.211030\pi\)
0.788167 + 0.615462i \(0.211030\pi\)
\(368\) −5085.86 −0.720432
\(369\) 0 0
\(370\) 958.763 0.134713
\(371\) 18770.9 2.62678
\(372\) 0 0
\(373\) −4106.52 −0.570048 −0.285024 0.958520i \(-0.592001\pi\)
−0.285024 + 0.958520i \(0.592001\pi\)
\(374\) 1782.09 0.246390
\(375\) 0 0
\(376\) 4164.50 0.571191
\(377\) 0 0
\(378\) 0 0
\(379\) 6169.89 0.836216 0.418108 0.908397i \(-0.362693\pi\)
0.418108 + 0.908397i \(0.362693\pi\)
\(380\) 11415.9 1.54112
\(381\) 0 0
\(382\) 46.8530 0.00627541
\(383\) 9133.11 1.21849 0.609243 0.792984i \(-0.291473\pi\)
0.609243 + 0.792984i \(0.291473\pi\)
\(384\) 0 0
\(385\) −11523.1 −1.52538
\(386\) −3192.68 −0.420992
\(387\) 0 0
\(388\) 3129.90 0.409527
\(389\) 12369.3 1.61221 0.806104 0.591774i \(-0.201572\pi\)
0.806104 + 0.591774i \(0.201572\pi\)
\(390\) 0 0
\(391\) −13337.8 −1.72512
\(392\) −10716.6 −1.38079
\(393\) 0 0
\(394\) −1348.25 −0.172395
\(395\) 5108.34 0.650705
\(396\) 0 0
\(397\) −2520.20 −0.318603 −0.159301 0.987230i \(-0.550924\pi\)
−0.159301 + 0.987230i \(0.550924\pi\)
\(398\) 2233.36 0.281277
\(399\) 0 0
\(400\) 11028.6 1.37858
\(401\) −4400.92 −0.548059 −0.274029 0.961721i \(-0.588357\pi\)
−0.274029 + 0.961721i \(0.588357\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 2041.07 0.251353
\(405\) 0 0
\(406\) −226.712 −0.0277132
\(407\) 683.035 0.0831862
\(408\) 0 0
\(409\) −6482.35 −0.783696 −0.391848 0.920030i \(-0.628164\pi\)
−0.391848 + 0.920030i \(0.628164\pi\)
\(410\) 8066.98 0.971707
\(411\) 0 0
\(412\) 10420.2 1.24604
\(413\) 22184.9 2.64321
\(414\) 0 0
\(415\) 11408.1 1.34940
\(416\) 0 0
\(417\) 0 0
\(418\) −1612.89 −0.188729
\(419\) −6293.72 −0.733815 −0.366908 0.930257i \(-0.619583\pi\)
−0.366908 + 0.930257i \(0.619583\pi\)
\(420\) 0 0
\(421\) 8376.89 0.969749 0.484875 0.874584i \(-0.338865\pi\)
0.484875 + 0.874584i \(0.338865\pi\)
\(422\) 1909.97 0.220322
\(423\) 0 0
\(424\) 10137.9 1.16118
\(425\) 28922.9 3.30110
\(426\) 0 0
\(427\) 14769.0 1.67382
\(428\) 4725.31 0.533660
\(429\) 0 0
\(430\) −4850.32 −0.543961
\(431\) −3392.05 −0.379094 −0.189547 0.981872i \(-0.560702\pi\)
−0.189547 + 0.981872i \(0.560702\pi\)
\(432\) 0 0
\(433\) 13767.3 1.52798 0.763991 0.645227i \(-0.223237\pi\)
0.763991 + 0.645227i \(0.223237\pi\)
\(434\) −2817.34 −0.311606
\(435\) 0 0
\(436\) 11444.4 1.25708
\(437\) 12071.4 1.32141
\(438\) 0 0
\(439\) −6355.98 −0.691013 −0.345506 0.938416i \(-0.612293\pi\)
−0.345506 + 0.938416i \(0.612293\pi\)
\(440\) −6223.47 −0.674301
\(441\) 0 0
\(442\) 0 0
\(443\) 20.2187 0.00216844 0.00108422 0.999999i \(-0.499655\pi\)
0.00108422 + 0.999999i \(0.499655\pi\)
\(444\) 0 0
\(445\) −14280.2 −1.52123
\(446\) −5315.26 −0.564316
\(447\) 0 0
\(448\) 2232.12 0.235397
\(449\) −10039.8 −1.05525 −0.527626 0.849477i \(-0.676918\pi\)
−0.527626 + 0.849477i \(0.676918\pi\)
\(450\) 0 0
\(451\) 5747.02 0.600037
\(452\) −8435.25 −0.877789
\(453\) 0 0
\(454\) 1404.35 0.145175
\(455\) 0 0
\(456\) 0 0
\(457\) 14931.2 1.52834 0.764168 0.645017i \(-0.223150\pi\)
0.764168 + 0.645017i \(0.223150\pi\)
\(458\) −4500.70 −0.459179
\(459\) 0 0
\(460\) 21188.3 2.14763
\(461\) 952.278 0.0962083 0.0481041 0.998842i \(-0.484682\pi\)
0.0481041 + 0.998842i \(0.484682\pi\)
\(462\) 0 0
\(463\) 666.672 0.0669176 0.0334588 0.999440i \(-0.489348\pi\)
0.0334588 + 0.999440i \(0.489348\pi\)
\(464\) 214.113 0.0214223
\(465\) 0 0
\(466\) −4873.14 −0.484428
\(467\) 13525.2 1.34020 0.670098 0.742273i \(-0.266252\pi\)
0.670098 + 0.742273i \(0.266252\pi\)
\(468\) 0 0
\(469\) 10366.3 1.02062
\(470\) −6016.74 −0.590492
\(471\) 0 0
\(472\) 11981.8 1.16845
\(473\) −3455.43 −0.335900
\(474\) 0 0
\(475\) −26176.8 −2.52857
\(476\) 18600.0 1.79103
\(477\) 0 0
\(478\) 888.749 0.0850427
\(479\) −5120.03 −0.488393 −0.244196 0.969726i \(-0.578524\pi\)
−0.244196 + 0.969726i \(0.578524\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1518.28 0.143476
\(483\) 0 0
\(484\) 6868.94 0.645092
\(485\) −9940.74 −0.930692
\(486\) 0 0
\(487\) −9776.37 −0.909671 −0.454835 0.890575i \(-0.650302\pi\)
−0.454835 + 0.890575i \(0.650302\pi\)
\(488\) 7976.56 0.739922
\(489\) 0 0
\(490\) 15483.0 1.42745
\(491\) 10423.9 0.958097 0.479048 0.877788i \(-0.340982\pi\)
0.479048 + 0.877788i \(0.340982\pi\)
\(492\) 0 0
\(493\) 561.519 0.0512972
\(494\) 0 0
\(495\) 0 0
\(496\) 2660.78 0.240872
\(497\) 14781.8 1.33412
\(498\) 0 0
\(499\) 10785.0 0.967544 0.483772 0.875194i \(-0.339266\pi\)
0.483772 + 0.875194i \(0.339266\pi\)
\(500\) −28252.3 −2.52697
\(501\) 0 0
\(502\) −2787.89 −0.247868
\(503\) −2135.13 −0.189266 −0.0946330 0.995512i \(-0.530168\pi\)
−0.0946330 + 0.995512i \(0.530168\pi\)
\(504\) 0 0
\(505\) −6482.54 −0.571226
\(506\) −2993.58 −0.263005
\(507\) 0 0
\(508\) −5967.93 −0.521229
\(509\) 13658.8 1.18942 0.594711 0.803939i \(-0.297266\pi\)
0.594711 + 0.803939i \(0.297266\pi\)
\(510\) 0 0
\(511\) −20355.2 −1.76215
\(512\) 10508.7 0.907081
\(513\) 0 0
\(514\) −4347.41 −0.373066
\(515\) −33095.3 −2.83175
\(516\) 0 0
\(517\) −4286.40 −0.364634
\(518\) −1413.80 −0.119921
\(519\) 0 0
\(520\) 0 0
\(521\) 14644.5 1.23146 0.615728 0.787958i \(-0.288862\pi\)
0.615728 + 0.787958i \(0.288862\pi\)
\(522\) 0 0
\(523\) −810.895 −0.0677973 −0.0338986 0.999425i \(-0.510792\pi\)
−0.0338986 + 0.999425i \(0.510792\pi\)
\(524\) 65.9075 0.00549462
\(525\) 0 0
\(526\) 8449.65 0.700422
\(527\) 6977.97 0.576784
\(528\) 0 0
\(529\) 10238.0 0.841458
\(530\) −14646.9 −1.20042
\(531\) 0 0
\(532\) −16834.0 −1.37189
\(533\) 0 0
\(534\) 0 0
\(535\) −15007.9 −1.21280
\(536\) 5598.74 0.451173
\(537\) 0 0
\(538\) −8989.19 −0.720356
\(539\) 11030.3 0.881462
\(540\) 0 0
\(541\) −23330.4 −1.85407 −0.927036 0.374971i \(-0.877653\pi\)
−0.927036 + 0.374971i \(0.877653\pi\)
\(542\) −6434.49 −0.509935
\(543\) 0 0
\(544\) 15521.6 1.22332
\(545\) −36348.1 −2.85685
\(546\) 0 0
\(547\) 24537.6 1.91801 0.959005 0.283390i \(-0.0914589\pi\)
0.959005 + 0.283390i \(0.0914589\pi\)
\(548\) −9924.49 −0.773637
\(549\) 0 0
\(550\) 6491.54 0.503273
\(551\) −508.204 −0.0392926
\(552\) 0 0
\(553\) −7532.81 −0.579254
\(554\) 4484.27 0.343896
\(555\) 0 0
\(556\) −3539.49 −0.269978
\(557\) 4219.10 0.320950 0.160475 0.987040i \(-0.448697\pi\)
0.160475 + 0.987040i \(0.448697\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −22525.9 −1.69981
\(561\) 0 0
\(562\) −6813.15 −0.511379
\(563\) 981.849 0.0734991 0.0367496 0.999325i \(-0.488300\pi\)
0.0367496 + 0.999325i \(0.488300\pi\)
\(564\) 0 0
\(565\) 26790.8 1.99486
\(566\) −5680.11 −0.421825
\(567\) 0 0
\(568\) 7983.50 0.589754
\(569\) −2021.40 −0.148930 −0.0744652 0.997224i \(-0.523725\pi\)
−0.0744652 + 0.997224i \(0.523725\pi\)
\(570\) 0 0
\(571\) 11994.8 0.879099 0.439549 0.898218i \(-0.355138\pi\)
0.439549 + 0.898218i \(0.355138\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −11895.6 −0.865008
\(575\) −48585.0 −3.52371
\(576\) 0 0
\(577\) −176.997 −0.0127703 −0.00638516 0.999980i \(-0.502032\pi\)
−0.00638516 + 0.999980i \(0.502032\pi\)
\(578\) 3483.08 0.250652
\(579\) 0 0
\(580\) −892.024 −0.0638608
\(581\) −16822.5 −1.20123
\(582\) 0 0
\(583\) −10434.7 −0.741269
\(584\) −10993.6 −0.778970
\(585\) 0 0
\(586\) −6415.95 −0.452288
\(587\) 10885.6 0.765413 0.382707 0.923870i \(-0.374992\pi\)
0.382707 + 0.923870i \(0.374992\pi\)
\(588\) 0 0
\(589\) −6315.43 −0.441804
\(590\) −17310.9 −1.20793
\(591\) 0 0
\(592\) 1335.23 0.0926989
\(593\) 6043.37 0.418502 0.209251 0.977862i \(-0.432897\pi\)
0.209251 + 0.977862i \(0.432897\pi\)
\(594\) 0 0
\(595\) −59074.8 −4.07030
\(596\) 11994.5 0.824349
\(597\) 0 0
\(598\) 0 0
\(599\) −23893.3 −1.62981 −0.814904 0.579596i \(-0.803211\pi\)
−0.814904 + 0.579596i \(0.803211\pi\)
\(600\) 0 0
\(601\) −25840.1 −1.75381 −0.876905 0.480665i \(-0.840395\pi\)
−0.876905 + 0.480665i \(0.840395\pi\)
\(602\) 7152.32 0.484231
\(603\) 0 0
\(604\) 12141.6 0.817939
\(605\) −21816.1 −1.46604
\(606\) 0 0
\(607\) −395.714 −0.0264605 −0.0132303 0.999912i \(-0.504211\pi\)
−0.0132303 + 0.999912i \(0.504211\pi\)
\(608\) −14047.9 −0.937034
\(609\) 0 0
\(610\) −11524.3 −0.764925
\(611\) 0 0
\(612\) 0 0
\(613\) 20523.7 1.35228 0.676139 0.736774i \(-0.263652\pi\)
0.676139 + 0.736774i \(0.263652\pi\)
\(614\) 11700.1 0.769019
\(615\) 0 0
\(616\) 9177.19 0.600259
\(617\) −2398.68 −0.156511 −0.0782556 0.996933i \(-0.524935\pi\)
−0.0782556 + 0.996933i \(0.524935\pi\)
\(618\) 0 0
\(619\) 17708.2 1.14984 0.574922 0.818208i \(-0.305032\pi\)
0.574922 + 0.818208i \(0.305032\pi\)
\(620\) −11085.1 −0.718048
\(621\) 0 0
\(622\) 5385.47 0.347167
\(623\) 21057.7 1.35419
\(624\) 0 0
\(625\) 49157.8 3.14610
\(626\) 3440.78 0.219682
\(627\) 0 0
\(628\) 5842.03 0.371214
\(629\) 3501.69 0.221974
\(630\) 0 0
\(631\) 18170.1 1.14634 0.573170 0.819437i \(-0.305713\pi\)
0.573170 + 0.819437i \(0.305713\pi\)
\(632\) −4068.38 −0.256062
\(633\) 0 0
\(634\) −10450.0 −0.654612
\(635\) 18954.5 1.18455
\(636\) 0 0
\(637\) 0 0
\(638\) 126.029 0.00782058
\(639\) 0 0
\(640\) −31289.2 −1.93253
\(641\) 30492.4 1.87891 0.939453 0.342678i \(-0.111334\pi\)
0.939453 + 0.342678i \(0.111334\pi\)
\(642\) 0 0
\(643\) 22280.9 1.36652 0.683260 0.730175i \(-0.260562\pi\)
0.683260 + 0.730175i \(0.260562\pi\)
\(644\) −31244.5 −1.91181
\(645\) 0 0
\(646\) −8268.72 −0.503604
\(647\) 16844.4 1.02353 0.511763 0.859127i \(-0.328992\pi\)
0.511763 + 0.859127i \(0.328992\pi\)
\(648\) 0 0
\(649\) −12332.5 −0.745906
\(650\) 0 0
\(651\) 0 0
\(652\) −11865.9 −0.712735
\(653\) 5880.96 0.352435 0.176217 0.984351i \(-0.443614\pi\)
0.176217 + 0.984351i \(0.443614\pi\)
\(654\) 0 0
\(655\) −209.326 −0.0124871
\(656\) 11234.6 0.668653
\(657\) 0 0
\(658\) 8872.34 0.525653
\(659\) −29655.1 −1.75296 −0.876479 0.481441i \(-0.840114\pi\)
−0.876479 + 0.481441i \(0.840114\pi\)
\(660\) 0 0
\(661\) −18713.4 −1.10116 −0.550581 0.834782i \(-0.685594\pi\)
−0.550581 + 0.834782i \(0.685594\pi\)
\(662\) 6087.20 0.357380
\(663\) 0 0
\(664\) −9085.63 −0.531010
\(665\) 53465.8 3.11777
\(666\) 0 0
\(667\) −943.245 −0.0547565
\(668\) 16866.1 0.976901
\(669\) 0 0
\(670\) −8088.87 −0.466419
\(671\) −8210.05 −0.472348
\(672\) 0 0
\(673\) 7932.59 0.454352 0.227176 0.973854i \(-0.427051\pi\)
0.227176 + 0.973854i \(0.427051\pi\)
\(674\) −3812.66 −0.217890
\(675\) 0 0
\(676\) 0 0
\(677\) 14742.2 0.836910 0.418455 0.908238i \(-0.362572\pi\)
0.418455 + 0.908238i \(0.362572\pi\)
\(678\) 0 0
\(679\) 14658.7 0.828497
\(680\) −31905.6 −1.79930
\(681\) 0 0
\(682\) 1566.15 0.0879342
\(683\) −3081.46 −0.172634 −0.0863169 0.996268i \(-0.527510\pi\)
−0.0863169 + 0.996268i \(0.527510\pi\)
\(684\) 0 0
\(685\) 31520.8 1.75817
\(686\) −10491.3 −0.583906
\(687\) 0 0
\(688\) −6754.85 −0.374312
\(689\) 0 0
\(690\) 0 0
\(691\) −11563.5 −0.636607 −0.318303 0.947989i \(-0.603113\pi\)
−0.318303 + 0.947989i \(0.603113\pi\)
\(692\) 1368.58 0.0751815
\(693\) 0 0
\(694\) 4854.15 0.265506
\(695\) 11241.6 0.613553
\(696\) 0 0
\(697\) 29463.0 1.60114
\(698\) −7540.04 −0.408875
\(699\) 0 0
\(700\) 67753.4 3.65834
\(701\) 3283.53 0.176914 0.0884572 0.996080i \(-0.471806\pi\)
0.0884572 + 0.996080i \(0.471806\pi\)
\(702\) 0 0
\(703\) −3169.21 −0.170027
\(704\) −1240.83 −0.0664283
\(705\) 0 0
\(706\) −4446.65 −0.237042
\(707\) 9559.22 0.508503
\(708\) 0 0
\(709\) −22397.5 −1.18640 −0.593198 0.805056i \(-0.702135\pi\)
−0.593198 + 0.805056i \(0.702135\pi\)
\(710\) −11534.3 −0.609683
\(711\) 0 0
\(712\) 11373.0 0.598626
\(713\) −11721.7 −0.615680
\(714\) 0 0
\(715\) 0 0
\(716\) 11804.2 0.616123
\(717\) 0 0
\(718\) −677.164 −0.0351971
\(719\) 21475.6 1.11392 0.556958 0.830540i \(-0.311968\pi\)
0.556958 + 0.830540i \(0.311968\pi\)
\(720\) 0 0
\(721\) 48802.6 2.52081
\(722\) −408.617 −0.0210626
\(723\) 0 0
\(724\) −16974.7 −0.871353
\(725\) 2045.42 0.104779
\(726\) 0 0
\(727\) −2541.54 −0.129657 −0.0648285 0.997896i \(-0.520650\pi\)
−0.0648285 + 0.997896i \(0.520650\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 15883.2 0.805293
\(731\) −17714.8 −0.896314
\(732\) 0 0
\(733\) 1921.91 0.0968447 0.0484224 0.998827i \(-0.484581\pi\)
0.0484224 + 0.998827i \(0.484581\pi\)
\(734\) 12752.3 0.641273
\(735\) 0 0
\(736\) −26073.4 −1.30581
\(737\) −5762.62 −0.288017
\(738\) 0 0
\(739\) 3501.37 0.174290 0.0871448 0.996196i \(-0.472226\pi\)
0.0871448 + 0.996196i \(0.472226\pi\)
\(740\) −5562.75 −0.276339
\(741\) 0 0
\(742\) 21598.5 1.06861
\(743\) −38056.5 −1.87908 −0.939541 0.342437i \(-0.888748\pi\)
−0.939541 + 0.342437i \(0.888748\pi\)
\(744\) 0 0
\(745\) −38095.1 −1.87342
\(746\) −4725.13 −0.231903
\(747\) 0 0
\(748\) −10339.7 −0.505424
\(749\) 22130.7 1.07963
\(750\) 0 0
\(751\) −9334.53 −0.453557 −0.226779 0.973946i \(-0.572819\pi\)
−0.226779 + 0.973946i \(0.572819\pi\)
\(752\) −8379.28 −0.406331
\(753\) 0 0
\(754\) 0 0
\(755\) −38562.4 −1.85885
\(756\) 0 0
\(757\) 12334.1 0.592193 0.296097 0.955158i \(-0.404315\pi\)
0.296097 + 0.955158i \(0.404315\pi\)
\(758\) 7099.32 0.340183
\(759\) 0 0
\(760\) 28876.2 1.37823
\(761\) −16234.5 −0.773326 −0.386663 0.922221i \(-0.626372\pi\)
−0.386663 + 0.922221i \(0.626372\pi\)
\(762\) 0 0
\(763\) 53599.2 2.54315
\(764\) −271.841 −0.0128729
\(765\) 0 0
\(766\) 10508.9 0.495696
\(767\) 0 0
\(768\) 0 0
\(769\) 2020.55 0.0947501 0.0473750 0.998877i \(-0.484914\pi\)
0.0473750 + 0.998877i \(0.484914\pi\)
\(770\) −13258.9 −0.620542
\(771\) 0 0
\(772\) 18523.9 0.863590
\(773\) −31025.1 −1.44359 −0.721795 0.692106i \(-0.756683\pi\)
−0.721795 + 0.692106i \(0.756683\pi\)
\(774\) 0 0
\(775\) 25418.3 1.17813
\(776\) 7917.00 0.366242
\(777\) 0 0
\(778\) 14232.6 0.655867
\(779\) −26665.6 −1.22644
\(780\) 0 0
\(781\) −8217.19 −0.376484
\(782\) −15347.0 −0.701802
\(783\) 0 0
\(784\) 21562.6 0.982260
\(785\) −18554.6 −0.843621
\(786\) 0 0
\(787\) −31464.9 −1.42516 −0.712581 0.701590i \(-0.752474\pi\)
−0.712581 + 0.701590i \(0.752474\pi\)
\(788\) 7822.54 0.353638
\(789\) 0 0
\(790\) 5877.86 0.264715
\(791\) −39506.0 −1.77582
\(792\) 0 0
\(793\) 0 0
\(794\) −2899.85 −0.129612
\(795\) 0 0
\(796\) −12958.0 −0.576989
\(797\) 15051.4 0.668945 0.334473 0.942405i \(-0.391442\pi\)
0.334473 + 0.942405i \(0.391442\pi\)
\(798\) 0 0
\(799\) −21974.9 −0.972987
\(800\) 56539.8 2.49873
\(801\) 0 0
\(802\) −5063.88 −0.222957
\(803\) 11315.4 0.497275
\(804\) 0 0
\(805\) 99234.4 4.34479
\(806\) 0 0
\(807\) 0 0
\(808\) 5162.82 0.224786
\(809\) 36468.2 1.58486 0.792432 0.609960i \(-0.208815\pi\)
0.792432 + 0.609960i \(0.208815\pi\)
\(810\) 0 0
\(811\) 21761.0 0.942210 0.471105 0.882077i \(-0.343855\pi\)
0.471105 + 0.882077i \(0.343855\pi\)
\(812\) 1315.39 0.0568486
\(813\) 0 0
\(814\) 785.928 0.0338412
\(815\) 37686.7 1.61976
\(816\) 0 0
\(817\) 16032.8 0.686558
\(818\) −7458.86 −0.318818
\(819\) 0 0
\(820\) −46804.7 −1.99328
\(821\) −43320.0 −1.84151 −0.920754 0.390144i \(-0.872425\pi\)
−0.920754 + 0.390144i \(0.872425\pi\)
\(822\) 0 0
\(823\) 5819.88 0.246498 0.123249 0.992376i \(-0.460669\pi\)
0.123249 + 0.992376i \(0.460669\pi\)
\(824\) 26357.7 1.11434
\(825\) 0 0
\(826\) 25526.8 1.07529
\(827\) −9099.01 −0.382592 −0.191296 0.981532i \(-0.561269\pi\)
−0.191296 + 0.981532i \(0.561269\pi\)
\(828\) 0 0
\(829\) 6582.90 0.275794 0.137897 0.990447i \(-0.455966\pi\)
0.137897 + 0.990447i \(0.455966\pi\)
\(830\) 13126.6 0.548954
\(831\) 0 0
\(832\) 0 0
\(833\) 56548.5 2.35209
\(834\) 0 0
\(835\) −53567.8 −2.22011
\(836\) 9357.98 0.387144
\(837\) 0 0
\(838\) −7241.82 −0.298526
\(839\) 28867.9 1.18788 0.593939 0.804510i \(-0.297572\pi\)
0.593939 + 0.804510i \(0.297572\pi\)
\(840\) 0 0
\(841\) −24349.3 −0.998372
\(842\) 9638.78 0.394506
\(843\) 0 0
\(844\) −11081.6 −0.451950
\(845\) 0 0
\(846\) 0 0
\(847\) 32170.3 1.30506
\(848\) −20398.2 −0.826036
\(849\) 0 0
\(850\) 33279.9 1.34293
\(851\) −5882.17 −0.236943
\(852\) 0 0
\(853\) 17014.4 0.682958 0.341479 0.939889i \(-0.389072\pi\)
0.341479 + 0.939889i \(0.389072\pi\)
\(854\) 16993.8 0.680932
\(855\) 0 0
\(856\) 11952.5 0.477254
\(857\) 6261.29 0.249570 0.124785 0.992184i \(-0.460176\pi\)
0.124785 + 0.992184i \(0.460176\pi\)
\(858\) 0 0
\(859\) 29513.0 1.17226 0.586129 0.810218i \(-0.300651\pi\)
0.586129 + 0.810218i \(0.300651\pi\)
\(860\) 28141.6 1.11584
\(861\) 0 0
\(862\) −3903.03 −0.154220
\(863\) 7073.47 0.279008 0.139504 0.990222i \(-0.455449\pi\)
0.139504 + 0.990222i \(0.455449\pi\)
\(864\) 0 0
\(865\) −4346.69 −0.170858
\(866\) 15841.3 0.621603
\(867\) 0 0
\(868\) 16346.2 0.639203
\(869\) 4187.47 0.163464
\(870\) 0 0
\(871\) 0 0
\(872\) 28948.3 1.12421
\(873\) 0 0
\(874\) 13889.9 0.537565
\(875\) −132318. −5.11220
\(876\) 0 0
\(877\) −12567.8 −0.483906 −0.241953 0.970288i \(-0.577788\pi\)
−0.241953 + 0.970288i \(0.577788\pi\)
\(878\) −7313.45 −0.281113
\(879\) 0 0
\(880\) 12522.1 0.479681
\(881\) 4722.06 0.180579 0.0902895 0.995916i \(-0.471221\pi\)
0.0902895 + 0.995916i \(0.471221\pi\)
\(882\) 0 0
\(883\) 20943.3 0.798185 0.399093 0.916911i \(-0.369325\pi\)
0.399093 + 0.916911i \(0.369325\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 23.2645 0.000882151 0
\(887\) 36524.2 1.38260 0.691298 0.722570i \(-0.257039\pi\)
0.691298 + 0.722570i \(0.257039\pi\)
\(888\) 0 0
\(889\) −27950.5 −1.05448
\(890\) −16431.4 −0.618855
\(891\) 0 0
\(892\) 30839.2 1.15759
\(893\) 19888.5 0.745288
\(894\) 0 0
\(895\) −37490.9 −1.40020
\(896\) 46139.4 1.72032
\(897\) 0 0
\(898\) −11552.2 −0.429290
\(899\) 493.479 0.0183075
\(900\) 0 0
\(901\) −53495.0 −1.97800
\(902\) 6612.76 0.244103
\(903\) 0 0
\(904\) −21336.7 −0.785010
\(905\) 53912.6 1.98024
\(906\) 0 0
\(907\) −19686.4 −0.720701 −0.360351 0.932817i \(-0.617343\pi\)
−0.360351 + 0.932817i \(0.617343\pi\)
\(908\) −8148.04 −0.297800
\(909\) 0 0
\(910\) 0 0
\(911\) −22339.4 −0.812444 −0.406222 0.913774i \(-0.633154\pi\)
−0.406222 + 0.913774i \(0.633154\pi\)
\(912\) 0 0
\(913\) 9351.58 0.338984
\(914\) 17180.4 0.621747
\(915\) 0 0
\(916\) 26113.1 0.941923
\(917\) 308.674 0.0111159
\(918\) 0 0
\(919\) 34118.9 1.22468 0.612338 0.790596i \(-0.290229\pi\)
0.612338 + 0.790596i \(0.290229\pi\)
\(920\) 53595.4 1.92064
\(921\) 0 0
\(922\) 1095.73 0.0391388
\(923\) 0 0
\(924\) 0 0
\(925\) 12755.4 0.453401
\(926\) 767.100 0.0272230
\(927\) 0 0
\(928\) 1097.68 0.0388289
\(929\) −19596.3 −0.692071 −0.346035 0.938221i \(-0.612472\pi\)
−0.346035 + 0.938221i \(0.612472\pi\)
\(930\) 0 0
\(931\) −51179.4 −1.80165
\(932\) 28274.0 0.993718
\(933\) 0 0
\(934\) 15562.6 0.545209
\(935\) 32839.5 1.14863
\(936\) 0 0
\(937\) 52085.3 1.81596 0.907978 0.419017i \(-0.137625\pi\)
0.907978 + 0.419017i \(0.137625\pi\)
\(938\) 11927.9 0.415203
\(939\) 0 0
\(940\) 34909.2 1.21129
\(941\) 1090.90 0.0377921 0.0188960 0.999821i \(-0.493985\pi\)
0.0188960 + 0.999821i \(0.493985\pi\)
\(942\) 0 0
\(943\) −49492.3 −1.70911
\(944\) −24108.2 −0.831203
\(945\) 0 0
\(946\) −3975.96 −0.136649
\(947\) −25306.1 −0.868361 −0.434181 0.900826i \(-0.642962\pi\)
−0.434181 + 0.900826i \(0.642962\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −30120.0 −1.02866
\(951\) 0 0
\(952\) 47048.3 1.60173
\(953\) 5321.09 0.180868 0.0904339 0.995902i \(-0.471175\pi\)
0.0904339 + 0.995902i \(0.471175\pi\)
\(954\) 0 0
\(955\) 863.383 0.0292549
\(956\) −5156.53 −0.174450
\(957\) 0 0
\(958\) −5891.31 −0.198684
\(959\) −46480.8 −1.56511
\(960\) 0 0
\(961\) −23658.6 −0.794151
\(962\) 0 0
\(963\) 0 0
\(964\) −8809.06 −0.294316
\(965\) −58833.1 −1.96260
\(966\) 0 0
\(967\) −33045.4 −1.09893 −0.549466 0.835516i \(-0.685169\pi\)
−0.549466 + 0.835516i \(0.685169\pi\)
\(968\) 17374.8 0.576908
\(969\) 0 0
\(970\) −11438.2 −0.378618
\(971\) 53559.8 1.77015 0.885076 0.465447i \(-0.154106\pi\)
0.885076 + 0.465447i \(0.154106\pi\)
\(972\) 0 0
\(973\) −16577.0 −0.546181
\(974\) −11249.1 −0.370066
\(975\) 0 0
\(976\) −16049.4 −0.526362
\(977\) −31189.3 −1.02132 −0.510662 0.859782i \(-0.670600\pi\)
−0.510662 + 0.859782i \(0.670600\pi\)
\(978\) 0 0
\(979\) −11705.9 −0.382148
\(980\) −89832.4 −2.92815
\(981\) 0 0
\(982\) 11994.2 0.389766
\(983\) 6235.44 0.202319 0.101160 0.994870i \(-0.467745\pi\)
0.101160 + 0.994870i \(0.467745\pi\)
\(984\) 0 0
\(985\) −24844.8 −0.803677
\(986\) 646.106 0.0208684
\(987\) 0 0
\(988\) 0 0
\(989\) 29757.5 0.956758
\(990\) 0 0
\(991\) 24157.5 0.774357 0.387178 0.922005i \(-0.373450\pi\)
0.387178 + 0.922005i \(0.373450\pi\)
\(992\) 13640.8 0.436590
\(993\) 0 0
\(994\) 17008.6 0.542736
\(995\) 41155.3 1.31127
\(996\) 0 0
\(997\) −35679.6 −1.13339 −0.566693 0.823929i \(-0.691777\pi\)
−0.566693 + 0.823929i \(0.691777\pi\)
\(998\) 12409.7 0.393609
\(999\) 0 0
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 1521.4.a.bm.1.11 yes 18
3.2 odd 2 inner 1521.4.a.bm.1.8 18
13.12 even 2 1521.4.a.bn.1.8 yes 18
39.38 odd 2 1521.4.a.bn.1.11 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1521.4.a.bm.1.8 18 3.2 odd 2 inner
1521.4.a.bm.1.11 yes 18 1.1 even 1 trivial
1521.4.a.bn.1.8 yes 18 13.12 even 2
1521.4.a.bn.1.11 yes 18 39.38 odd 2