Properties

Label 648.4.a.d.1.1
Level $648$
Weight $4$
Character 648.1
Self dual yes
Analytic conductor $38.233$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{129}) \)
Defining polynomial: \(x^{2} - x - 32\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(6.17891\) of defining polynomial
Character \(\chi\) \(=\) 648.1

$q$-expansion

\(f(q)\) \(=\) \(q-13.3578 q^{5} -14.3578 q^{7} +O(q^{10})\) \(q-13.3578 q^{5} -14.3578 q^{7} -39.0735 q^{11} -76.7891 q^{13} +62.4313 q^{17} -39.7891 q^{19} +128.505 q^{23} +53.4313 q^{25} -64.9360 q^{29} -9.13747 q^{31} +191.789 q^{35} +319.505 q^{37} -17.5782 q^{41} -450.945 q^{43} +581.597 q^{47} -136.853 q^{49} -329.450 q^{53} +521.936 q^{55} +241.853 q^{59} +497.524 q^{61} +1025.73 q^{65} -578.064 q^{67} +660.927 q^{71} +696.559 q^{73} +561.009 q^{77} +730.268 q^{79} -1090.48 q^{83} -833.945 q^{85} +317.588 q^{89} +1102.52 q^{91} +531.495 q^{95} -1485.65 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{5} - 6q^{7} + O(q^{10}) \) \( 2q - 4q^{5} - 6q^{7} - 10q^{11} - 40q^{13} + 34q^{17} + 34q^{19} + 98q^{23} + 16q^{25} + 120q^{29} - 200q^{31} + 270q^{35} + 480q^{37} + 192q^{41} - 334q^{43} + 300q^{47} - 410q^{49} + 68q^{53} + 794q^{55} + 620q^{59} + 200q^{61} + 1370q^{65} - 1406q^{67} + 1390q^{71} + 1802q^{73} + 804q^{77} - 334q^{79} - 500q^{83} - 1100q^{85} + 90q^{89} + 1410q^{91} + 1222q^{95} - 200q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −13.3578 −1.19476 −0.597380 0.801959i \(-0.703791\pi\)
−0.597380 + 0.801959i \(0.703791\pi\)
\(6\) 0 0
\(7\) −14.3578 −0.775249 −0.387625 0.921817i \(-0.626704\pi\)
−0.387625 + 0.921817i \(0.626704\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −39.0735 −1.07101 −0.535504 0.844533i \(-0.679878\pi\)
−0.535504 + 0.844533i \(0.679878\pi\)
\(12\) 0 0
\(13\) −76.7891 −1.63827 −0.819133 0.573604i \(-0.805545\pi\)
−0.819133 + 0.573604i \(0.805545\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 62.4313 0.890694 0.445347 0.895358i \(-0.353080\pi\)
0.445347 + 0.895358i \(0.353080\pi\)
\(18\) 0 0
\(19\) −39.7891 −0.480434 −0.240217 0.970719i \(-0.577219\pi\)
−0.240217 + 0.970719i \(0.577219\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 128.505 1.16500 0.582502 0.812829i \(-0.302074\pi\)
0.582502 + 0.812829i \(0.302074\pi\)
\(24\) 0 0
\(25\) 53.4313 0.427450
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −64.9360 −0.415804 −0.207902 0.978150i \(-0.566663\pi\)
−0.207902 + 0.978150i \(0.566663\pi\)
\(30\) 0 0
\(31\) −9.13747 −0.0529399 −0.0264700 0.999650i \(-0.508427\pi\)
−0.0264700 + 0.999650i \(0.508427\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 191.789 0.926236
\(36\) 0 0
\(37\) 319.505 1.41963 0.709814 0.704389i \(-0.248779\pi\)
0.709814 + 0.704389i \(0.248779\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −17.5782 −0.0669573 −0.0334786 0.999439i \(-0.510659\pi\)
−0.0334786 + 0.999439i \(0.510659\pi\)
\(42\) 0 0
\(43\) −450.945 −1.59927 −0.799634 0.600488i \(-0.794973\pi\)
−0.799634 + 0.600488i \(0.794973\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 581.597 1.80499 0.902496 0.430698i \(-0.141732\pi\)
0.902496 + 0.430698i \(0.141732\pi\)
\(48\) 0 0
\(49\) −136.853 −0.398989
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −329.450 −0.853839 −0.426919 0.904290i \(-0.640401\pi\)
−0.426919 + 0.904290i \(0.640401\pi\)
\(54\) 0 0
\(55\) 521.936 1.27960
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 241.853 0.533671 0.266836 0.963742i \(-0.414022\pi\)
0.266836 + 0.963742i \(0.414022\pi\)
\(60\) 0 0
\(61\) 497.524 1.04428 0.522142 0.852858i \(-0.325133\pi\)
0.522142 + 0.852858i \(0.325133\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1025.73 1.95733
\(66\) 0 0
\(67\) −578.064 −1.05406 −0.527028 0.849848i \(-0.676694\pi\)
−0.527028 + 0.849848i \(0.676694\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 660.927 1.10475 0.552377 0.833594i \(-0.313721\pi\)
0.552377 + 0.833594i \(0.313721\pi\)
\(72\) 0 0
\(73\) 696.559 1.11680 0.558398 0.829573i \(-0.311416\pi\)
0.558398 + 0.829573i \(0.311416\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 561.009 0.830298
\(78\) 0 0
\(79\) 730.268 1.04002 0.520010 0.854160i \(-0.325928\pi\)
0.520010 + 0.854160i \(0.325928\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1090.48 −1.44212 −0.721058 0.692875i \(-0.756344\pi\)
−0.721058 + 0.692875i \(0.756344\pi\)
\(84\) 0 0
\(85\) −833.945 −1.06417
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 317.588 0.378250 0.189125 0.981953i \(-0.439435\pi\)
0.189125 + 0.981953i \(0.439435\pi\)
\(90\) 0 0
\(91\) 1102.52 1.27006
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 531.495 0.574003
\(96\) 0 0
\(97\) −1485.65 −1.55511 −0.777553 0.628817i \(-0.783539\pi\)
−0.777553 + 0.628817i \(0.783539\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1003.27 0.988402 0.494201 0.869348i \(-0.335461\pi\)
0.494201 + 0.869348i \(0.335461\pi\)
\(102\) 0 0
\(103\) −1717.60 −1.64311 −0.821553 0.570133i \(-0.806892\pi\)
−0.821553 + 0.570133i \(0.806892\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1006.27 0.909161 0.454581 0.890706i \(-0.349789\pi\)
0.454581 + 0.890706i \(0.349789\pi\)
\(108\) 0 0
\(109\) 1724.94 1.51577 0.757885 0.652388i \(-0.226233\pi\)
0.757885 + 0.652388i \(0.226233\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 627.019 0.521991 0.260995 0.965340i \(-0.415949\pi\)
0.260995 + 0.965340i \(0.415949\pi\)
\(114\) 0 0
\(115\) −1716.54 −1.39190
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −896.377 −0.690510
\(120\) 0 0
\(121\) 195.735 0.147058
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 956.002 0.684059
\(126\) 0 0
\(127\) −1990.05 −1.39046 −0.695230 0.718788i \(-0.744697\pi\)
−0.695230 + 0.718788i \(0.744697\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −156.414 −0.104321 −0.0521603 0.998639i \(-0.516611\pi\)
−0.0521603 + 0.998639i \(0.516611\pi\)
\(132\) 0 0
\(133\) 571.284 0.372456
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2119.31 1.32164 0.660822 0.750543i \(-0.270208\pi\)
0.660822 + 0.750543i \(0.270208\pi\)
\(138\) 0 0
\(139\) −2686.77 −1.63949 −0.819745 0.572729i \(-0.805885\pi\)
−0.819745 + 0.572729i \(0.805885\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3000.41 1.75460
\(144\) 0 0
\(145\) 867.403 0.496785
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1551.56 0.853080 0.426540 0.904469i \(-0.359732\pi\)
0.426540 + 0.904469i \(0.359732\pi\)
\(150\) 0 0
\(151\) −18.1092 −0.00975962 −0.00487981 0.999988i \(-0.501553\pi\)
−0.00487981 + 0.999988i \(0.501553\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 122.057 0.0632505
\(156\) 0 0
\(157\) 3741.51 1.90194 0.950971 0.309280i \(-0.100088\pi\)
0.950971 + 0.309280i \(0.100088\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1845.05 −0.903168
\(162\) 0 0
\(163\) 2608.90 1.25365 0.626826 0.779160i \(-0.284354\pi\)
0.626826 + 0.779160i \(0.284354\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1562.89 0.724193 0.362097 0.932141i \(-0.382061\pi\)
0.362097 + 0.932141i \(0.382061\pi\)
\(168\) 0 0
\(169\) 3699.56 1.68392
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1502.77 0.660425 0.330212 0.943907i \(-0.392880\pi\)
0.330212 + 0.943907i \(0.392880\pi\)
\(174\) 0 0
\(175\) −767.156 −0.331380
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4126.50 −1.72307 −0.861534 0.507700i \(-0.830496\pi\)
−0.861534 + 0.507700i \(0.830496\pi\)
\(180\) 0 0
\(181\) 1582.33 0.649800 0.324900 0.945748i \(-0.394669\pi\)
0.324900 + 0.945748i \(0.394669\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4267.89 −1.69611
\(186\) 0 0
\(187\) −2439.40 −0.953941
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2575.88 −0.975833 −0.487916 0.872890i \(-0.662243\pi\)
−0.487916 + 0.872890i \(0.662243\pi\)
\(192\) 0 0
\(193\) −1395.30 −0.520392 −0.260196 0.965556i \(-0.583787\pi\)
−0.260196 + 0.965556i \(0.583787\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5047.62 −1.82552 −0.912761 0.408494i \(-0.866054\pi\)
−0.912761 + 0.408494i \(0.866054\pi\)
\(198\) 0 0
\(199\) −2441.47 −0.869704 −0.434852 0.900502i \(-0.643199\pi\)
−0.434852 + 0.900502i \(0.643199\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 932.339 0.322352
\(204\) 0 0
\(205\) 234.806 0.0799978
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1554.70 0.514548
\(210\) 0 0
\(211\) 4266.16 1.39192 0.695959 0.718081i \(-0.254979\pi\)
0.695959 + 0.718081i \(0.254979\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6023.65 1.91074
\(216\) 0 0
\(217\) 131.194 0.0410416
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4794.04 −1.45919
\(222\) 0 0
\(223\) 1751.15 0.525855 0.262927 0.964816i \(-0.415312\pi\)
0.262927 + 0.964816i \(0.415312\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2200.05 −0.643269 −0.321635 0.946864i \(-0.604232\pi\)
−0.321635 + 0.946864i \(0.604232\pi\)
\(228\) 0 0
\(229\) −1191.29 −0.343767 −0.171884 0.985117i \(-0.554985\pi\)
−0.171884 + 0.985117i \(0.554985\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2644.52 −0.743555 −0.371778 0.928322i \(-0.621252\pi\)
−0.371778 + 0.928322i \(0.621252\pi\)
\(234\) 0 0
\(235\) −7768.87 −2.15653
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1437.52 −0.389061 −0.194530 0.980896i \(-0.562318\pi\)
−0.194530 + 0.980896i \(0.562318\pi\)
\(240\) 0 0
\(241\) 3267.08 0.873240 0.436620 0.899646i \(-0.356175\pi\)
0.436620 + 0.899646i \(0.356175\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1828.06 0.476695
\(246\) 0 0
\(247\) 3055.37 0.787078
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1871.89 0.470727 0.235364 0.971907i \(-0.424372\pi\)
0.235364 + 0.971907i \(0.424372\pi\)
\(252\) 0 0
\(253\) −5021.12 −1.24773
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4690.82 1.13854 0.569271 0.822150i \(-0.307225\pi\)
0.569271 + 0.822150i \(0.307225\pi\)
\(258\) 0 0
\(259\) −4587.39 −1.10057
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4593.38 −1.07696 −0.538479 0.842639i \(-0.681001\pi\)
−0.538479 + 0.842639i \(0.681001\pi\)
\(264\) 0 0
\(265\) 4400.73 1.02013
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −83.0074 −0.0188143 −0.00940716 0.999956i \(-0.502994\pi\)
−0.00940716 + 0.999956i \(0.502994\pi\)
\(270\) 0 0
\(271\) −3464.08 −0.776487 −0.388244 0.921557i \(-0.626918\pi\)
−0.388244 + 0.921557i \(0.626918\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2087.74 −0.457803
\(276\) 0 0
\(277\) −1270.70 −0.275628 −0.137814 0.990458i \(-0.544008\pi\)
−0.137814 + 0.990458i \(0.544008\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7651.80 −1.62444 −0.812221 0.583350i \(-0.801742\pi\)
−0.812221 + 0.583350i \(0.801742\pi\)
\(282\) 0 0
\(283\) −7.45013 −0.00156489 −0.000782446 1.00000i \(-0.500249\pi\)
−0.000782446 1.00000i \(0.500249\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 252.384 0.0519086
\(288\) 0 0
\(289\) −1015.34 −0.206663
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2814.02 0.561082 0.280541 0.959842i \(-0.409486\pi\)
0.280541 + 0.959842i \(0.409486\pi\)
\(294\) 0 0
\(295\) −3230.63 −0.637609
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9867.76 −1.90859
\(300\) 0 0
\(301\) 6474.59 1.23983
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6645.83 −1.24767
\(306\) 0 0
\(307\) −5096.55 −0.947477 −0.473739 0.880666i \(-0.657096\pi\)
−0.473739 + 0.880666i \(0.657096\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7784.81 −1.41941 −0.709705 0.704499i \(-0.751172\pi\)
−0.709705 + 0.704499i \(0.751172\pi\)
\(312\) 0 0
\(313\) −246.469 −0.0445088 −0.0222544 0.999752i \(-0.507084\pi\)
−0.0222544 + 0.999752i \(0.507084\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 59.3201 0.0105102 0.00525512 0.999986i \(-0.498327\pi\)
0.00525512 + 0.999986i \(0.498327\pi\)
\(318\) 0 0
\(319\) 2537.27 0.445329
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2484.08 −0.427920
\(324\) 0 0
\(325\) −4102.94 −0.700277
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8350.46 −1.39932
\(330\) 0 0
\(331\) 4409.10 0.732163 0.366082 0.930583i \(-0.380699\pi\)
0.366082 + 0.930583i \(0.380699\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7721.67 1.25934
\(336\) 0 0
\(337\) 6032.30 0.975075 0.487537 0.873102i \(-0.337895\pi\)
0.487537 + 0.873102i \(0.337895\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 357.032 0.0566991
\(342\) 0 0
\(343\) 6889.64 1.08456
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6240.78 0.965484 0.482742 0.875763i \(-0.339641\pi\)
0.482742 + 0.875763i \(0.339641\pi\)
\(348\) 0 0
\(349\) 5634.61 0.864223 0.432111 0.901820i \(-0.357769\pi\)
0.432111 + 0.901820i \(0.357769\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3441.32 0.518875 0.259437 0.965760i \(-0.416463\pi\)
0.259437 + 0.965760i \(0.416463\pi\)
\(354\) 0 0
\(355\) −8828.54 −1.31992
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7808.79 −1.14800 −0.574000 0.818855i \(-0.694609\pi\)
−0.574000 + 0.818855i \(0.694609\pi\)
\(360\) 0 0
\(361\) −5275.83 −0.769183
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −9304.51 −1.33430
\(366\) 0 0
\(367\) 13608.1 1.93553 0.967763 0.251862i \(-0.0810429\pi\)
0.967763 + 0.251862i \(0.0810429\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4730.18 0.661938
\(372\) 0 0
\(373\) −3748.17 −0.520303 −0.260151 0.965568i \(-0.583772\pi\)
−0.260151 + 0.965568i \(0.583772\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4986.37 0.681197
\(378\) 0 0
\(379\) −10210.3 −1.38382 −0.691909 0.721985i \(-0.743230\pi\)
−0.691909 + 0.721985i \(0.743230\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6129.49 −0.817761 −0.408880 0.912588i \(-0.634081\pi\)
−0.408880 + 0.912588i \(0.634081\pi\)
\(384\) 0 0
\(385\) −7493.86 −0.992007
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4865.97 0.634227 0.317114 0.948388i \(-0.397286\pi\)
0.317114 + 0.948388i \(0.397286\pi\)
\(390\) 0 0
\(391\) 8022.71 1.03766
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9754.78 −1.24257
\(396\) 0 0
\(397\) −438.311 −0.0554110 −0.0277055 0.999616i \(-0.508820\pi\)
−0.0277055 + 0.999616i \(0.508820\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11753.7 1.46371 0.731857 0.681458i \(-0.238654\pi\)
0.731857 + 0.681458i \(0.238654\pi\)
\(402\) 0 0
\(403\) 701.658 0.0867297
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −12484.2 −1.52043
\(408\) 0 0
\(409\) 11246.5 1.35967 0.679833 0.733367i \(-0.262052\pi\)
0.679833 + 0.733367i \(0.262052\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3472.48 −0.413728
\(414\) 0 0
\(415\) 14566.4 1.72298
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12316.4 1.43602 0.718012 0.696031i \(-0.245052\pi\)
0.718012 + 0.696031i \(0.245052\pi\)
\(420\) 0 0
\(421\) −4702.60 −0.544396 −0.272198 0.962241i \(-0.587751\pi\)
−0.272198 + 0.962241i \(0.587751\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3335.78 0.380727
\(426\) 0 0
\(427\) −7143.35 −0.809581
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2204.89 0.246417 0.123208 0.992381i \(-0.460682\pi\)
0.123208 + 0.992381i \(0.460682\pi\)
\(432\) 0 0
\(433\) 9426.46 1.04620 0.523102 0.852270i \(-0.324775\pi\)
0.523102 + 0.852270i \(0.324775\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5113.08 −0.559707
\(438\) 0 0
\(439\) −7684.59 −0.835457 −0.417728 0.908572i \(-0.637174\pi\)
−0.417728 + 0.908572i \(0.637174\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12394.3 1.32928 0.664640 0.747164i \(-0.268585\pi\)
0.664640 + 0.747164i \(0.268585\pi\)
\(444\) 0 0
\(445\) −4242.28 −0.451917
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14568.7 1.53127 0.765635 0.643275i \(-0.222425\pi\)
0.765635 + 0.643275i \(0.222425\pi\)
\(450\) 0 0
\(451\) 686.840 0.0717118
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −14727.3 −1.51742
\(456\) 0 0
\(457\) −646.047 −0.0661287 −0.0330643 0.999453i \(-0.510527\pi\)
−0.0330643 + 0.999453i \(0.510527\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19001.0 −1.91966 −0.959831 0.280579i \(-0.909473\pi\)
−0.959831 + 0.280579i \(0.909473\pi\)
\(462\) 0 0
\(463\) 13665.7 1.37171 0.685853 0.727740i \(-0.259429\pi\)
0.685853 + 0.727740i \(0.259429\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3762.83 −0.372855 −0.186427 0.982469i \(-0.559691\pi\)
−0.186427 + 0.982469i \(0.559691\pi\)
\(468\) 0 0
\(469\) 8299.74 0.817156
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 17620.0 1.71283
\(474\) 0 0
\(475\) −2125.98 −0.205361
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6763.87 0.645197 0.322598 0.946536i \(-0.395444\pi\)
0.322598 + 0.946536i \(0.395444\pi\)
\(480\) 0 0
\(481\) −24534.5 −2.32573
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 19845.1 1.85798
\(486\) 0 0
\(487\) −1447.72 −0.134708 −0.0673538 0.997729i \(-0.521456\pi\)
−0.0673538 + 0.997729i \(0.521456\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7838.28 0.720441 0.360220 0.932867i \(-0.382701\pi\)
0.360220 + 0.932867i \(0.382701\pi\)
\(492\) 0 0
\(493\) −4054.04 −0.370354
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9489.46 −0.856460
\(498\) 0 0
\(499\) −4245.34 −0.380857 −0.190428 0.981701i \(-0.560988\pi\)
−0.190428 + 0.981701i \(0.560988\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17914.9 1.58804 0.794021 0.607891i \(-0.207984\pi\)
0.794021 + 0.607891i \(0.207984\pi\)
\(504\) 0 0
\(505\) −13401.4 −1.18090
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14520.3 1.26444 0.632220 0.774789i \(-0.282144\pi\)
0.632220 + 0.774789i \(0.282144\pi\)
\(510\) 0 0
\(511\) −10001.1 −0.865795
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 22943.3 1.96312
\(516\) 0 0
\(517\) −22725.0 −1.93316
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3372.49 −0.283592 −0.141796 0.989896i \(-0.545288\pi\)
−0.141796 + 0.989896i \(0.545288\pi\)
\(522\) 0 0
\(523\) 4339.40 0.362808 0.181404 0.983409i \(-0.441936\pi\)
0.181404 + 0.983409i \(0.441936\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −570.464 −0.0471533
\(528\) 0 0
\(529\) 4346.46 0.357234
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1349.81 0.109694
\(534\) 0 0
\(535\) −13441.6 −1.08623
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5347.32 0.427320
\(540\) 0 0
\(541\) −3831.98 −0.304528 −0.152264 0.988340i \(-0.548656\pi\)
−0.152264 + 0.988340i \(0.548656\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −23041.4 −1.81098
\(546\) 0 0
\(547\) 13402.7 1.04764 0.523818 0.851830i \(-0.324507\pi\)
0.523818 + 0.851830i \(0.324507\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2583.74 0.199766
\(552\) 0 0
\(553\) −10485.0 −0.806274
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14810.0 −1.12661 −0.563304 0.826249i \(-0.690470\pi\)
−0.563304 + 0.826249i \(0.690470\pi\)
\(558\) 0 0
\(559\) 34627.7 2.62003
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12233.2 0.915753 0.457877 0.889016i \(-0.348610\pi\)
0.457877 + 0.889016i \(0.348610\pi\)
\(564\) 0 0
\(565\) −8375.60 −0.623654
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9711.68 −0.715527 −0.357763 0.933812i \(-0.616461\pi\)
−0.357763 + 0.933812i \(0.616461\pi\)
\(570\) 0 0
\(571\) 8529.61 0.625137 0.312568 0.949895i \(-0.398811\pi\)
0.312568 + 0.949895i \(0.398811\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6866.17 0.497981
\(576\) 0 0
\(577\) 15314.0 1.10491 0.552453 0.833544i \(-0.313692\pi\)
0.552453 + 0.833544i \(0.313692\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 15656.9 1.11800
\(582\) 0 0
\(583\) 12872.8 0.914468
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19675.1 1.38343 0.691717 0.722168i \(-0.256854\pi\)
0.691717 + 0.722168i \(0.256854\pi\)
\(588\) 0 0
\(589\) 363.571 0.0254341
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15635.9 1.08278 0.541391 0.840771i \(-0.317898\pi\)
0.541391 + 0.840771i \(0.317898\pi\)
\(594\) 0 0
\(595\) 11973.6 0.824994
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −485.189 −0.0330956 −0.0165478 0.999863i \(-0.505268\pi\)
−0.0165478 + 0.999863i \(0.505268\pi\)
\(600\) 0 0
\(601\) −14796.2 −1.00425 −0.502123 0.864796i \(-0.667447\pi\)
−0.502123 + 0.864796i \(0.667447\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2614.59 −0.175699
\(606\) 0 0
\(607\) 3547.98 0.237245 0.118623 0.992939i \(-0.462152\pi\)
0.118623 + 0.992939i \(0.462152\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −44660.3 −2.95706
\(612\) 0 0
\(613\) 20450.9 1.34748 0.673740 0.738968i \(-0.264687\pi\)
0.673740 + 0.738968i \(0.264687\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15305.2 −0.998646 −0.499323 0.866416i \(-0.666418\pi\)
−0.499323 + 0.866416i \(0.666418\pi\)
\(618\) 0 0
\(619\) −4151.19 −0.269548 −0.134774 0.990876i \(-0.543031\pi\)
−0.134774 + 0.990876i \(0.543031\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4559.86 −0.293238
\(624\) 0 0
\(625\) −19449.0 −1.24474
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 19947.1 1.26446
\(630\) 0 0
\(631\) 25954.4 1.63745 0.818724 0.574187i \(-0.194682\pi\)
0.818724 + 0.574187i \(0.194682\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 26582.7 1.66126
\(636\) 0 0
\(637\) 10508.8 0.653650
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 17261.3 1.06362 0.531811 0.846863i \(-0.321512\pi\)
0.531811 + 0.846863i \(0.321512\pi\)
\(642\) 0 0
\(643\) 2860.36 0.175430 0.0877152 0.996146i \(-0.472043\pi\)
0.0877152 + 0.996146i \(0.472043\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28384.9 1.72477 0.862384 0.506255i \(-0.168971\pi\)
0.862384 + 0.506255i \(0.168971\pi\)
\(648\) 0 0
\(649\) −9450.04 −0.571566
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11036.4 0.661393 0.330696 0.943737i \(-0.392716\pi\)
0.330696 + 0.943737i \(0.392716\pi\)
\(654\) 0 0
\(655\) 2089.36 0.124638
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21294.9 1.25877 0.629387 0.777092i \(-0.283306\pi\)
0.629387 + 0.777092i \(0.283306\pi\)
\(660\) 0 0
\(661\) 12324.7 0.725229 0.362615 0.931939i \(-0.381884\pi\)
0.362615 + 0.931939i \(0.381884\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7631.11 −0.444995
\(666\) 0 0
\(667\) −8344.58 −0.484413
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −19440.0 −1.11844
\(672\) 0 0
\(673\) 3050.94 0.174748 0.0873738 0.996176i \(-0.472153\pi\)
0.0873738 + 0.996176i \(0.472153\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1685.47 0.0956835 0.0478418 0.998855i \(-0.484766\pi\)
0.0478418 + 0.998855i \(0.484766\pi\)
\(678\) 0 0
\(679\) 21330.7 1.20559
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −34715.5 −1.94488 −0.972440 0.233155i \(-0.925095\pi\)
−0.972440 + 0.233155i \(0.925095\pi\)
\(684\) 0 0
\(685\) −28309.4 −1.57905
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 25298.2 1.39882
\(690\) 0 0
\(691\) −8295.37 −0.456687 −0.228343 0.973581i \(-0.573331\pi\)
−0.228343 + 0.973581i \(0.573331\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 35889.4 1.95880
\(696\) 0 0
\(697\) −1097.43 −0.0596385
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 23420.5 1.26188 0.630942 0.775830i \(-0.282669\pi\)
0.630942 + 0.775830i \(0.282669\pi\)
\(702\) 0 0
\(703\) −12712.8 −0.682037
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −14404.7 −0.766258
\(708\) 0 0
\(709\) −5282.67 −0.279823 −0.139912 0.990164i \(-0.544682\pi\)
−0.139912 + 0.990164i \(0.544682\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1174.21 −0.0616752
\(714\) 0 0
\(715\) −40079.0 −2.09632
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 714.975 0.0370849 0.0185425 0.999828i \(-0.494097\pi\)
0.0185425 + 0.999828i \(0.494097\pi\)
\(720\) 0 0
\(721\) 24660.9 1.27382
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3469.61 −0.177735
\(726\) 0 0
\(727\) 25795.5 1.31596 0.657979 0.753036i \(-0.271412\pi\)
0.657979 + 0.753036i \(0.271412\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −28153.1 −1.42446
\(732\) 0 0
\(733\) 3631.55 0.182994 0.0914969 0.995805i \(-0.470835\pi\)
0.0914969 + 0.995805i \(0.470835\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22587.0 1.12890
\(738\) 0 0
\(739\) −24758.3 −1.23241 −0.616203 0.787588i \(-0.711330\pi\)
−0.616203 + 0.787588i \(0.711330\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8845.33 −0.436748 −0.218374 0.975865i \(-0.570075\pi\)
−0.218374 + 0.975865i \(0.570075\pi\)
\(744\) 0 0
\(745\) −20725.5 −1.01922
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14447.9 −0.704827
\(750\) 0 0
\(751\) 1660.40 0.0806775 0.0403387 0.999186i \(-0.487156\pi\)
0.0403387 + 0.999186i \(0.487156\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 241.899 0.0116604
\(756\) 0 0
\(757\) 19937.2 0.957239 0.478619 0.878022i \(-0.341137\pi\)
0.478619 + 0.878022i \(0.341137\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8443.74 −0.402215 −0.201107 0.979569i \(-0.564454\pi\)
−0.201107 + 0.979569i \(0.564454\pi\)
\(762\) 0 0
\(763\) −24766.3 −1.17510
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18571.7 −0.874295
\(768\) 0 0
\(769\) 17107.9 0.802243 0.401122 0.916025i \(-0.368620\pi\)
0.401122 + 0.916025i \(0.368620\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9821.05 0.456971 0.228486 0.973547i \(-0.426623\pi\)
0.228486 + 0.973547i \(0.426623\pi\)
\(774\) 0 0
\(775\) −488.226 −0.0226292
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 699.419 0.0321685
\(780\) 0 0
\(781\) −25824.7 −1.18320
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −49978.4 −2.27236
\(786\) 0 0
\(787\) −5245.57 −0.237591 −0.118796 0.992919i \(-0.537903\pi\)
−0.118796 + 0.992919i \(0.537903\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9002.62 −0.404673
\(792\) 0 0
\(793\) −38204.4 −1.71082
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9218.52 0.409707 0.204854 0.978793i \(-0.434328\pi\)
0.204854 + 0.978793i \(0.434328\pi\)
\(798\) 0 0
\(799\) 36309.8 1.60770
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −27217.0 −1.19610
\(804\) 0 0
\(805\) 24645.8 1.07907
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −16397.4 −0.712611 −0.356305 0.934370i \(-0.615964\pi\)
−0.356305 + 0.934370i \(0.615964\pi\)
\(810\) 0 0
\(811\) 8468.88 0.366686 0.183343 0.983049i \(-0.441308\pi\)
0.183343 + 0.983049i \(0.441308\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −34849.3 −1.49781
\(816\) 0 0
\(817\) 17942.7 0.768342
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5233.46 0.222471 0.111236 0.993794i \(-0.464519\pi\)
0.111236 + 0.993794i \(0.464519\pi\)
\(822\) 0 0
\(823\) −3124.68 −0.132344 −0.0661722 0.997808i \(-0.521079\pi\)
−0.0661722 + 0.997808i \(0.521079\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11037.6 −0.464103 −0.232052 0.972703i \(-0.574544\pi\)
−0.232052 + 0.972703i \(0.574544\pi\)
\(828\) 0 0
\(829\) −23941.9 −1.00306 −0.501529 0.865141i \(-0.667229\pi\)
−0.501529 + 0.865141i \(0.667229\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −8543.91 −0.355377
\(834\) 0 0
\(835\) −20876.8 −0.865237
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −21259.4 −0.874798 −0.437399 0.899268i \(-0.644100\pi\)
−0.437399 + 0.899268i \(0.644100\pi\)
\(840\) 0 0
\(841\) −20172.3 −0.827107
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −49418.1 −2.01187
\(846\) 0 0
\(847\) −2810.32 −0.114007
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 41057.9 1.65387
\(852\) 0 0
\(853\) 8828.74 0.354385 0.177192 0.984176i \(-0.443299\pi\)
0.177192 + 0.984176i \(0.443299\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 38014.8 1.51524 0.757621 0.652695i \(-0.226362\pi\)
0.757621 + 0.652695i \(0.226362\pi\)
\(858\) 0 0
\(859\) 4917.61 0.195328 0.0976640 0.995219i \(-0.468863\pi\)
0.0976640 + 0.995219i \(0.468863\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 20474.1 0.807585 0.403792 0.914851i \(-0.367692\pi\)
0.403792 + 0.914851i \(0.367692\pi\)
\(864\) 0 0
\(865\) −20073.7 −0.789049
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −28534.1 −1.11387
\(870\) 0 0
\(871\) 44389.0 1.72682
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −13726.1 −0.530316
\(876\) 0 0
\(877\) 14280.7 0.549858 0.274929 0.961464i \(-0.411346\pi\)
0.274929 + 0.961464i \(0.411346\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −12505.2 −0.478217 −0.239109 0.970993i \(-0.576855\pi\)
−0.239109 + 0.970993i \(0.576855\pi\)
\(882\) 0 0
\(883\) −34255.9 −1.30555 −0.652776 0.757551i \(-0.726396\pi\)
−0.652776 + 0.757551i \(0.726396\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24372.4 0.922600 0.461300 0.887244i \(-0.347383\pi\)
0.461300 + 0.887244i \(0.347383\pi\)
\(888\) 0 0
\(889\) 28572.8 1.07795
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −23141.2 −0.867179
\(894\) 0 0
\(895\) 55121.0 2.05865
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 593.350 0.0220126
\(900\) 0 0
\(901\) −20568.0 −0.760510
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −21136.5 −0.776355
\(906\) 0 0
\(907\) −42836.1 −1.56819 −0.784095 0.620641i \(-0.786873\pi\)
−0.784095 + 0.620641i \(0.786873\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 36145.3 1.31454 0.657271 0.753655i \(-0.271711\pi\)
0.657271 + 0.753655i \(0.271711\pi\)
\(912\) 0 0
\(913\) 42608.8 1.54452
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2245.77 0.0808744
\(918\) 0 0
\(919\) −23283.2 −0.835738 −0.417869 0.908507i \(-0.637223\pi\)
−0.417869 + 0.908507i \(0.637223\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −50751.9 −1.80988
\(924\) 0 0
\(925\) 17071.5 0.606820
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 39190.5 1.38407 0.692033 0.721866i \(-0.256715\pi\)
0.692033 + 0.721866i \(0.256715\pi\)
\(930\) 0 0
\(931\) 5445.26 0.191688
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 32585.1 1.13973
\(936\) 0 0
\(937\) −36892.8 −1.28627 −0.643135 0.765753i \(-0.722366\pi\)
−0.643135 + 0.765753i \(0.722366\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −26605.8 −0.921705 −0.460853 0.887477i \(-0.652456\pi\)
−0.460853 + 0.887477i \(0.652456\pi\)
\(942\) 0 0
\(943\) −2258.88 −0.0780055
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12841.3 −0.440641 −0.220321 0.975427i \(-0.570710\pi\)
−0.220321 + 0.975427i \(0.570710\pi\)
\(948\) 0 0
\(949\) −53488.2 −1.82961
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −33977.5 −1.15492 −0.577460 0.816419i \(-0.695956\pi\)
−0.577460 + 0.816419i \(0.695956\pi\)
\(954\) 0 0
\(955\) 34408.1 1.16589
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −30428.7 −1.02460
\(960\) 0 0
\(961\) −29707.5 −0.997197
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 18638.1 0.621744
\(966\) 0 0
\(967\) 49342.9 1.64091 0.820455 0.571712i \(-0.193720\pi\)
0.820455 + 0.571712i \(0.193720\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −43375.7 −1.43356 −0.716782 0.697297i \(-0.754386\pi\)
−0.716782 + 0.697297i \(0.754386\pi\)
\(972\) 0 0
\(973\) 38576.2 1.27101
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 39694.6 1.29984 0.649919 0.760004i \(-0.274803\pi\)
0.649919 + 0.760004i \(0.274803\pi\)
\(978\) 0 0
\(979\) −12409.2 −0.405108
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −9058.89 −0.293931 −0.146965 0.989142i \(-0.546951\pi\)
−0.146965 + 0.989142i \(0.546951\pi\)
\(984\) 0 0
\(985\) 67425.2 2.18106
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −57948.6 −1.86315
\(990\) 0 0
\(991\) −33006.3 −1.05800 −0.529001 0.848621i \(-0.677433\pi\)
−0.529001 + 0.848621i \(0.677433\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 32612.7 1.03909
\(996\) 0 0
\(997\) 44324.4 1.40799 0.703996 0.710204i \(-0.251397\pi\)
0.703996 + 0.710204i \(0.251397\pi\)
\(998\) 0 0
\(999\) 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 648.4.a.d.1.1 2
3.2 odd 2 648.4.a.e.1.2 yes 2
4.3 odd 2 1296.4.a.n.1.1 2
9.2 odd 6 648.4.i.p.433.1 4
9.4 even 3 648.4.i.q.217.2 4
9.5 odd 6 648.4.i.p.217.1 4
9.7 even 3 648.4.i.q.433.2 4
12.11 even 2 1296.4.a.p.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.4.a.d.1.1 2 1.1 even 1 trivial
648.4.a.e.1.2 yes 2 3.2 odd 2
648.4.i.p.217.1 4 9.5 odd 6
648.4.i.p.433.1 4 9.2 odd 6
648.4.i.q.217.2 4 9.4 even 3
648.4.i.q.433.2 4 9.7 even 3
1296.4.a.n.1.1 2 4.3 odd 2
1296.4.a.p.1.2 2 12.11 even 2