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Properties

Label 1008.4.a.m.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+4.00000 q^{5} +7.00000 q^{7} +62.0000 q^{11} -62.0000 q^{13} -84.0000 q^{17} -100.000 q^{19} -42.0000 q^{23} -109.000 q^{25} +10.0000 q^{29} +48.0000 q^{31} +28.0000 q^{35} -246.000 q^{37} +248.000 q^{41} -68.0000 q^{43} +324.000 q^{47} +49.0000 q^{49} -258.000 q^{53} +248.000 q^{55} +120.000 q^{59} +622.000 q^{61} -248.000 q^{65} -904.000 q^{67} -678.000 q^{71} -642.000 q^{73} +434.000 q^{77} -740.000 q^{79} +468.000 q^{83} -336.000 q^{85} -200.000 q^{89} -434.000 q^{91} -400.000 q^{95} -1266.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) 4.00000 0.357771 0.178885 − 0.983870i \(-0.442751\pi\)
0.178885 + 0.983870i \(0.442751\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 62.0000 1.69943 0.849714 − 0.527244i \(-0.176775\pi\)
0.849714 + 0.527244i \(0.176775\pi\)
\(12\) 0 0
\(13\) −62.0000 −1.32275 −0.661373 − 0.750057i \(-0.730026\pi\)
−0.661373 + 0.750057i \(0.730026\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −84.0000 −1.19841 −0.599206 − 0.800595i \(-0.704517\pi\)
−0.599206 + 0.800595i \(0.704517\pi\)
\(18\) 0 0
\(19\) −100.000 −1.20745 −0.603726 − 0.797192i \(-0.706318\pi\)
−0.603726 + 0.797192i \(0.706318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −42.0000 −0.380765 −0.190383 − 0.981710i \(-0.560973\pi\)
−0.190383 + 0.981710i \(0.560973\pi\)
\(24\) 0 0
\(25\) −109.000 −0.872000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 10.0000 0.0640329 0.0320164 − 0.999487i \(-0.489807\pi\)
0.0320164 + 0.999487i \(0.489807\pi\)
\(30\) 0 0
\(31\) 48.0000 0.278099 0.139049 − 0.990285i \(-0.455595\pi\)
0.139049 + 0.990285i \(0.455595\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 28.0000 0.135225
\(36\) 0 0
\(37\) −246.000 −1.09303 −0.546516 − 0.837449i \(-0.684046\pi\)
−0.546516 + 0.837449i \(0.684046\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 248.000 0.944661 0.472330 − 0.881422i \(-0.343413\pi\)
0.472330 + 0.881422i \(0.343413\pi\)
\(42\) 0 0
\(43\) −68.0000 −0.241161 −0.120580 − 0.992704i \(-0.538476\pi\)
−0.120580 + 0.992704i \(0.538476\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 324.000 1.00554 0.502769 − 0.864421i \(-0.332315\pi\)
0.502769 + 0.864421i \(0.332315\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −258.000 −0.668661 −0.334330 − 0.942456i \(-0.608510\pi\)
−0.334330 + 0.942456i \(0.608510\pi\)
\(54\) 0 0
\(55\) 248.000 0.608006
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 120.000 0.264791 0.132396 − 0.991197i \(-0.457733\pi\)
0.132396 + 0.991197i \(0.457733\pi\)
\(60\) 0 0
\(61\) 622.000 1.30556 0.652778 − 0.757549i \(-0.273603\pi\)
0.652778 + 0.757549i \(0.273603\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −248.000 −0.473240
\(66\) 0 0
\(67\) −904.000 −1.64838 −0.824188 − 0.566316i \(-0.808368\pi\)
−0.824188 + 0.566316i \(0.808368\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −678.000 −1.13329 −0.566646 − 0.823961i \(-0.691759\pi\)
−0.566646 + 0.823961i \(0.691759\pi\)
\(72\) 0 0
\(73\) −642.000 −1.02932 −0.514660 − 0.857394i \(-0.672082\pi\)
−0.514660 + 0.857394i \(0.672082\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 434.000 0.642323
\(78\) 0 0
\(79\) −740.000 −1.05388 −0.526940 − 0.849903i \(-0.676661\pi\)
−0.526940 + 0.849903i \(0.676661\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 468.000 0.618912 0.309456 − 0.950914i \(-0.399853\pi\)
0.309456 + 0.950914i \(0.399853\pi\)
\(84\) 0 0
\(85\) −336.000 −0.428757
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −200.000 −0.238202 −0.119101 − 0.992882i \(-0.538001\pi\)
−0.119101 + 0.992882i \(0.538001\pi\)
\(90\) 0 0
\(91\) −434.000 −0.499951
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −400.000 −0.431991
\(96\) 0 0
\(97\) −1266.00 −1.32518 −0.662592 − 0.748981i \(-0.730544\pi\)
−0.662592 + 0.748981i \(0.730544\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −232.000 −0.228563 −0.114281 − 0.993448i \(-0.536457\pi\)
−0.114281 + 0.993448i \(0.536457\pi\)
\(102\) 0 0
\(103\) 1792.00 1.71428 0.857141 − 0.515082i \(-0.172239\pi\)
0.857141 + 0.515082i \(0.172239\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1906.00 −1.72206 −0.861028 − 0.508558i \(-0.830179\pi\)
−0.861028 + 0.508558i \(0.830179\pi\)
\(108\) 0 0
\(109\) −90.0000 −0.0790866 −0.0395433 − 0.999218i \(-0.512590\pi\)
−0.0395433 + 0.999218i \(0.512590\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −458.000 −0.381283 −0.190642 − 0.981660i \(-0.561057\pi\)
−0.190642 + 0.981660i \(0.561057\pi\)
\(114\) 0 0
\(115\) −168.000 −0.136227
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −588.000 −0.452957
\(120\) 0 0
\(121\) 2513.00 1.88805
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −936.000 −0.669747
\(126\) 0 0
\(127\) −804.000 −0.561760 −0.280880 − 0.959743i \(-0.590626\pi\)
−0.280880 + 0.959743i \(0.590626\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 812.000 0.541563 0.270782 − 0.962641i \(-0.412718\pi\)
0.270782 + 0.962641i \(0.412718\pi\)
\(132\) 0 0
\(133\) −700.000 −0.456374
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −414.000 −0.258178 −0.129089 − 0.991633i \(-0.541205\pi\)
−0.129089 + 0.991633i \(0.541205\pi\)
\(138\) 0 0
\(139\) 1620.00 0.988537 0.494268 − 0.869309i \(-0.335436\pi\)
0.494268 + 0.869309i \(0.335436\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3844.00 −2.24791
\(144\) 0 0
\(145\) 40.0000 0.0229091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2370.00 −1.30307 −0.651537 − 0.758617i \(-0.725875\pi\)
−0.651537 + 0.758617i \(0.725875\pi\)
\(150\) 0 0
\(151\) 568.000 0.306114 0.153057 − 0.988217i \(-0.451088\pi\)
0.153057 + 0.988217i \(0.451088\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 192.000 0.0994956
\(156\) 0 0
\(157\) −266.000 −0.135217 −0.0676086 − 0.997712i \(-0.521537\pi\)
−0.0676086 + 0.997712i \(0.521537\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −294.000 −0.143916
\(162\) 0 0
\(163\) 272.000 0.130704 0.0653518 − 0.997862i \(-0.479183\pi\)
0.0653518 + 0.997862i \(0.479183\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1876.00 −0.869277 −0.434638 − 0.900605i \(-0.643124\pi\)
−0.434638 + 0.900605i \(0.643124\pi\)
\(168\) 0 0
\(169\) 1647.00 0.749659
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 152.000 0.0667997 0.0333998 − 0.999442i \(-0.489367\pi\)
0.0333998 + 0.999442i \(0.489367\pi\)
\(174\) 0 0
\(175\) −763.000 −0.329585
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 610.000 0.254713 0.127356 − 0.991857i \(-0.459351\pi\)
0.127356 + 0.991857i \(0.459351\pi\)
\(180\) 0 0
\(181\) 1042.00 0.427907 0.213954 − 0.976844i \(-0.431366\pi\)
0.213954 + 0.976844i \(0.431366\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −984.000 −0.391055
\(186\) 0 0
\(187\) −5208.00 −2.03661
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2038.00 −0.772065 −0.386033 − 0.922485i \(-0.626155\pi\)
−0.386033 + 0.922485i \(0.626155\pi\)
\(192\) 0 0
\(193\) −2602.00 −0.970446 −0.485223 − 0.874390i \(-0.661262\pi\)
−0.485223 + 0.874390i \(0.661262\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2354.00 −0.851348 −0.425674 − 0.904877i \(-0.639963\pi\)
−0.425674 + 0.904877i \(0.639963\pi\)
\(198\) 0 0
\(199\) −1680.00 −0.598452 −0.299226 − 0.954182i \(-0.596729\pi\)
−0.299226 + 0.954182i \(0.596729\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 70.0000 0.0242022
\(204\) 0 0
\(205\) 992.000 0.337972
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6200.00 −2.05198
\(210\) 0 0
\(211\) 668.000 0.217948 0.108974 − 0.994045i \(-0.465243\pi\)
0.108974 + 0.994045i \(0.465243\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −272.000 −0.0862802
\(216\) 0 0
\(217\) 336.000 0.105111
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5208.00 1.58519
\(222\) 0 0
\(223\) 1832.00 0.550134 0.275067 − 0.961425i \(-0.411300\pi\)
0.275067 + 0.961425i \(0.411300\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4944.00 1.44557 0.722786 − 0.691072i \(-0.242861\pi\)
0.722786 + 0.691072i \(0.242861\pi\)
\(228\) 0 0
\(229\) −5470.00 −1.57846 −0.789231 − 0.614096i \(-0.789521\pi\)
−0.789231 + 0.614096i \(0.789521\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2802.00 0.787833 0.393917 − 0.919146i \(-0.371120\pi\)
0.393917 + 0.919146i \(0.371120\pi\)
\(234\) 0 0
\(235\) 1296.00 0.359752
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1170.00 −0.316657 −0.158328 − 0.987386i \(-0.550610\pi\)
−0.158328 + 0.987386i \(0.550610\pi\)
\(240\) 0 0
\(241\) −2338.00 −0.624912 −0.312456 − 0.949932i \(-0.601152\pi\)
−0.312456 + 0.949932i \(0.601152\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 196.000 0.0511101
\(246\) 0 0
\(247\) 6200.00 1.59715
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2792.00 0.702109 0.351055 − 0.936355i \(-0.385823\pi\)
0.351055 + 0.936355i \(0.385823\pi\)
\(252\) 0 0
\(253\) −2604.00 −0.647083
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7024.00 −1.70484 −0.852422 − 0.522854i \(-0.824867\pi\)
−0.852422 + 0.522854i \(0.824867\pi\)
\(258\) 0 0
\(259\) −1722.00 −0.413127
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2438.00 0.571610 0.285805 − 0.958288i \(-0.407739\pi\)
0.285805 + 0.958288i \(0.407739\pi\)
\(264\) 0 0
\(265\) −1032.00 −0.239227
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6780.00 1.53674 0.768372 − 0.640004i \(-0.221067\pi\)
0.768372 + 0.640004i \(0.221067\pi\)
\(270\) 0 0
\(271\) 1928.00 0.432168 0.216084 − 0.976375i \(-0.430671\pi\)
0.216084 + 0.976375i \(0.430671\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6758.00 −1.48190
\(276\) 0 0
\(277\) 5554.00 1.20472 0.602360 − 0.798224i \(-0.294227\pi\)
0.602360 + 0.798224i \(0.294227\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1942.00 −0.412278 −0.206139 − 0.978523i \(-0.566090\pi\)
−0.206139 + 0.978523i \(0.566090\pi\)
\(282\) 0 0
\(283\) −4828.00 −1.01412 −0.507058 − 0.861912i \(-0.669267\pi\)
−0.507058 + 0.861912i \(0.669267\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1736.00 0.357048
\(288\) 0 0
\(289\) 2143.00 0.436190
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6152.00 1.22663 0.613317 − 0.789837i \(-0.289835\pi\)
0.613317 + 0.789837i \(0.289835\pi\)
\(294\) 0 0
\(295\) 480.000 0.0947345
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2604.00 0.503656
\(300\) 0 0
\(301\) −476.000 −0.0911501
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2488.00 0.467090
\(306\) 0 0
\(307\) −5884.00 −1.09387 −0.546934 − 0.837176i \(-0.684205\pi\)
−0.546934 + 0.837176i \(0.684205\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9132.00 1.66504 0.832521 − 0.553993i \(-0.186897\pi\)
0.832521 + 0.553993i \(0.186897\pi\)
\(312\) 0 0
\(313\) −9382.00 −1.69426 −0.847128 − 0.531389i \(-0.821670\pi\)
−0.847128 + 0.531389i \(0.821670\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3114.00 −0.551734 −0.275867 − 0.961196i \(-0.588965\pi\)
−0.275867 + 0.961196i \(0.588965\pi\)
\(318\) 0 0
\(319\) 620.000 0.108819
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8400.00 1.44702
\(324\) 0 0
\(325\) 6758.00 1.15344
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2268.00 0.380057
\(330\) 0 0
\(331\) −1532.00 −0.254400 −0.127200 − 0.991877i \(-0.540599\pi\)
−0.127200 + 0.991877i \(0.540599\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3616.00 −0.589741
\(336\) 0 0
\(337\) −4166.00 −0.673402 −0.336701 − 0.941612i \(-0.609311\pi\)
−0.336701 + 0.941612i \(0.609311\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2976.00 0.472608
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11366.0 −1.75838 −0.879191 − 0.476469i \(-0.841917\pi\)
−0.879191 + 0.476469i \(0.841917\pi\)
\(348\) 0 0
\(349\) 9310.00 1.42795 0.713973 − 0.700174i \(-0.246894\pi\)
0.713973 + 0.700174i \(0.246894\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8572.00 1.29247 0.646234 − 0.763139i \(-0.276343\pi\)
0.646234 + 0.763139i \(0.276343\pi\)
\(354\) 0 0
\(355\) −2712.00 −0.405459
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4790.00 −0.704196 −0.352098 − 0.935963i \(-0.614532\pi\)
−0.352098 + 0.935963i \(0.614532\pi\)
\(360\) 0 0
\(361\) 3141.00 0.457938
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2568.00 −0.368261
\(366\) 0 0
\(367\) −5424.00 −0.771473 −0.385736 − 0.922609i \(-0.626053\pi\)
−0.385736 + 0.922609i \(0.626053\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1806.00 −0.252730
\(372\) 0 0
\(373\) 1838.00 0.255142 0.127571 − 0.991829i \(-0.459282\pi\)
0.127571 + 0.991829i \(0.459282\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −620.000 −0.0846993
\(378\) 0 0
\(379\) 4260.00 0.577365 0.288683 − 0.957425i \(-0.406783\pi\)
0.288683 + 0.957425i \(0.406783\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9048.00 1.20713 0.603566 − 0.797313i \(-0.293746\pi\)
0.603566 + 0.797313i \(0.293746\pi\)
\(384\) 0 0
\(385\) 1736.00 0.229805
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11490.0 1.49760 0.748800 − 0.662796i \(-0.230631\pi\)
0.748800 + 0.662796i \(0.230631\pi\)
\(390\) 0 0
\(391\) 3528.00 0.456314
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2960.00 −0.377048
\(396\) 0 0
\(397\) −1866.00 −0.235899 −0.117949 − 0.993020i \(-0.537632\pi\)
−0.117949 + 0.993020i \(0.537632\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13662.0 −1.70137 −0.850683 − 0.525679i \(-0.823811\pi\)
−0.850683 + 0.525679i \(0.823811\pi\)
\(402\) 0 0
\(403\) −2976.00 −0.367854
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15252.0 −1.85753
\(408\) 0 0
\(409\) −13210.0 −1.59705 −0.798524 − 0.601963i \(-0.794385\pi\)
−0.798524 + 0.601963i \(0.794385\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 840.000 0.100082
\(414\) 0 0
\(415\) 1872.00 0.221429
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6960.00 0.811499 0.405750 − 0.913984i \(-0.367010\pi\)
0.405750 + 0.913984i \(0.367010\pi\)
\(420\) 0 0
\(421\) 8162.00 0.944873 0.472437 − 0.881365i \(-0.343375\pi\)
0.472437 + 0.881365i \(0.343375\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9156.00 1.04501
\(426\) 0 0
\(427\) 4354.00 0.493454
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16602.0 1.85543 0.927715 − 0.373290i \(-0.121770\pi\)
0.927715 + 0.373290i \(0.121770\pi\)
\(432\) 0 0
\(433\) 7738.00 0.858810 0.429405 − 0.903112i \(-0.358723\pi\)
0.429405 + 0.903112i \(0.358723\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4200.00 0.459756
\(438\) 0 0
\(439\) 840.000 0.0913235 0.0456617 − 0.998957i \(-0.485460\pi\)
0.0456617 + 0.998957i \(0.485460\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6618.00 0.709776 0.354888 − 0.934909i \(-0.384519\pi\)
0.354888 + 0.934909i \(0.384519\pi\)
\(444\) 0 0
\(445\) −800.000 −0.0852217
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3090.00 −0.324780 −0.162390 − 0.986727i \(-0.551920\pi\)
−0.162390 + 0.986727i \(0.551920\pi\)
\(450\) 0 0
\(451\) 15376.0 1.60538
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1736.00 −0.178868
\(456\) 0 0
\(457\) 5914.00 0.605351 0.302675 − 0.953094i \(-0.402120\pi\)
0.302675 + 0.953094i \(0.402120\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15968.0 1.61324 0.806620 − 0.591070i \(-0.201294\pi\)
0.806620 + 0.591070i \(0.201294\pi\)
\(462\) 0 0
\(463\) 1172.00 0.117640 0.0588202 − 0.998269i \(-0.481266\pi\)
0.0588202 + 0.998269i \(0.481266\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5304.00 0.525567 0.262784 − 0.964855i \(-0.415359\pi\)
0.262784 + 0.964855i \(0.415359\pi\)
\(468\) 0 0
\(469\) −6328.00 −0.623027
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4216.00 −0.409835
\(474\) 0 0
\(475\) 10900.0 1.05290
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5740.00 0.547531 0.273765 − 0.961796i \(-0.411731\pi\)
0.273765 + 0.961796i \(0.411731\pi\)
\(480\) 0 0
\(481\) 15252.0 1.44580
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5064.00 −0.474112
\(486\) 0 0
\(487\) −8944.00 −0.832220 −0.416110 − 0.909314i \(-0.636607\pi\)
−0.416110 + 0.909314i \(0.636607\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5558.00 −0.510853 −0.255427 − 0.966828i \(-0.582216\pi\)
−0.255427 + 0.966828i \(0.582216\pi\)
\(492\) 0 0
\(493\) −840.000 −0.0767377
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4746.00 −0.428344
\(498\) 0 0
\(499\) 19820.0 1.77809 0.889043 − 0.457823i \(-0.151371\pi\)
0.889043 + 0.457823i \(0.151371\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1848.00 0.163814 0.0819068 − 0.996640i \(-0.473899\pi\)
0.0819068 + 0.996640i \(0.473899\pi\)
\(504\) 0 0
\(505\) −928.000 −0.0817732
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −340.000 −0.0296075 −0.0148038 − 0.999890i \(-0.504712\pi\)
−0.0148038 + 0.999890i \(0.504712\pi\)
\(510\) 0 0
\(511\) −4494.00 −0.389047
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7168.00 0.613320
\(516\) 0 0
\(517\) 20088.0 1.70884
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10212.0 −0.858725 −0.429363 − 0.903132i \(-0.641262\pi\)
−0.429363 + 0.903132i \(0.641262\pi\)
\(522\) 0 0
\(523\) 9332.00 0.780229 0.390115 − 0.920766i \(-0.372435\pi\)
0.390115 + 0.920766i \(0.372435\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4032.00 −0.333276
\(528\) 0 0
\(529\) −10403.0 −0.855018
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −15376.0 −1.24955
\(534\) 0 0
\(535\) −7624.00 −0.616101
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3038.00 0.242775
\(540\) 0 0
\(541\) −8998.00 −0.715073 −0.357536 − 0.933899i \(-0.616383\pi\)
−0.357536 + 0.933899i \(0.616383\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −360.000 −0.0282949
\(546\) 0 0
\(547\) 3416.00 0.267016 0.133508 − 0.991048i \(-0.457376\pi\)
0.133508 + 0.991048i \(0.457376\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1000.00 −0.0773166
\(552\) 0 0
\(553\) −5180.00 −0.398329
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 526.000 0.0400132 0.0200066 − 0.999800i \(-0.493631\pi\)
0.0200066 + 0.999800i \(0.493631\pi\)
\(558\) 0 0
\(559\) 4216.00 0.318994
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6712.00 −0.502446 −0.251223 − 0.967929i \(-0.580833\pi\)
−0.251223 + 0.967929i \(0.580833\pi\)
\(564\) 0 0
\(565\) −1832.00 −0.136412
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4190.00 −0.308706 −0.154353 − 0.988016i \(-0.549329\pi\)
−0.154353 + 0.988016i \(0.549329\pi\)
\(570\) 0 0
\(571\) −3032.00 −0.222216 −0.111108 − 0.993808i \(-0.535440\pi\)
−0.111108 + 0.993808i \(0.535440\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4578.00 0.332027
\(576\) 0 0
\(577\) 5434.00 0.392063 0.196032 − 0.980598i \(-0.437195\pi\)
0.196032 + 0.980598i \(0.437195\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3276.00 0.233927
\(582\) 0 0
\(583\) −15996.0 −1.13634
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 464.000 0.0326258 0.0163129 − 0.999867i \(-0.494807\pi\)
0.0163129 + 0.999867i \(0.494807\pi\)
\(588\) 0 0
\(589\) −4800.00 −0.335790
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11748.0 −0.813546 −0.406773 − 0.913529i \(-0.633346\pi\)
−0.406773 + 0.913529i \(0.633346\pi\)
\(594\) 0 0
\(595\) −2352.00 −0.162055
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7650.00 0.521821 0.260910 − 0.965363i \(-0.415977\pi\)
0.260910 + 0.965363i \(0.415977\pi\)
\(600\) 0 0
\(601\) −22878.0 −1.55277 −0.776384 − 0.630261i \(-0.782948\pi\)
−0.776384 + 0.630261i \(0.782948\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10052.0 0.675491
\(606\) 0 0
\(607\) −704.000 −0.0470749 −0.0235375 − 0.999723i \(-0.507493\pi\)
−0.0235375 + 0.999723i \(0.507493\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20088.0 −1.33007
\(612\) 0 0
\(613\) 24958.0 1.64444 0.822222 − 0.569167i \(-0.192734\pi\)
0.822222 + 0.569167i \(0.192734\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8826.00 0.575886 0.287943 − 0.957648i \(-0.407029\pi\)
0.287943 + 0.957648i \(0.407029\pi\)
\(618\) 0 0
\(619\) −21220.0 −1.37787 −0.688937 − 0.724821i \(-0.741922\pi\)
−0.688937 + 0.724821i \(0.741922\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1400.00 −0.0900318
\(624\) 0 0
\(625\) 9881.00 0.632384
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20664.0 1.30990
\(630\) 0 0
\(631\) 3268.00 0.206176 0.103088 − 0.994672i \(-0.467128\pi\)
0.103088 + 0.994672i \(0.467128\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3216.00 −0.200981
\(636\) 0 0
\(637\) −3038.00 −0.188964
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −13062.0 −0.804864 −0.402432 − 0.915450i \(-0.631835\pi\)
−0.402432 + 0.915450i \(0.631835\pi\)
\(642\) 0 0
\(643\) 28012.0 1.71802 0.859009 − 0.511961i \(-0.171081\pi\)
0.859009 + 0.511961i \(0.171081\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3844.00 0.233575 0.116788 − 0.993157i \(-0.462740\pi\)
0.116788 + 0.993157i \(0.462740\pi\)
\(648\) 0 0
\(649\) 7440.00 0.449993
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 28482.0 1.70687 0.853436 − 0.521198i \(-0.174515\pi\)
0.853436 + 0.521198i \(0.174515\pi\)
\(654\) 0 0
\(655\) 3248.00 0.193756
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9330.00 −0.551510 −0.275755 − 0.961228i \(-0.588928\pi\)
−0.275755 + 0.961228i \(0.588928\pi\)
\(660\) 0 0
\(661\) 8782.00 0.516763 0.258381 − 0.966043i \(-0.416811\pi\)
0.258381 + 0.966043i \(0.416811\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2800.00 −0.163277
\(666\) 0 0
\(667\) −420.000 −0.0243815
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 38564.0 2.21870
\(672\) 0 0
\(673\) −10562.0 −0.604956 −0.302478 − 0.953156i \(-0.597814\pi\)
−0.302478 + 0.953156i \(0.597814\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 26016.0 1.47692 0.738461 − 0.674296i \(-0.235553\pi\)
0.738461 + 0.674296i \(0.235553\pi\)
\(678\) 0 0
\(679\) −8862.00 −0.500872
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8898.00 0.498496 0.249248 − 0.968440i \(-0.419817\pi\)
0.249248 + 0.968440i \(0.419817\pi\)
\(684\) 0 0
\(685\) −1656.00 −0.0923686
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 15996.0 0.884469
\(690\) 0 0
\(691\) −30572.0 −1.68309 −0.841544 − 0.540189i \(-0.818353\pi\)
−0.841544 + 0.540189i \(0.818353\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6480.00 0.353670
\(696\) 0 0
\(697\) −20832.0 −1.13209
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30618.0 1.64968 0.824840 − 0.565366i \(-0.191265\pi\)
0.824840 + 0.565366i \(0.191265\pi\)
\(702\) 0 0
\(703\) 24600.0 1.31978
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1624.00 −0.0863887
\(708\) 0 0
\(709\) −8130.00 −0.430647 −0.215323 − 0.976543i \(-0.569081\pi\)
−0.215323 + 0.976543i \(0.569081\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2016.00 −0.105890
\(714\) 0 0
\(715\) −15376.0 −0.804237
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −27840.0 −1.44403 −0.722014 − 0.691878i \(-0.756784\pi\)
−0.722014 + 0.691878i \(0.756784\pi\)
\(720\) 0 0
\(721\) 12544.0 0.647938
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1090.00 −0.0558367
\(726\) 0 0
\(727\) −14624.0 −0.746044 −0.373022 − 0.927822i \(-0.621678\pi\)
−0.373022 + 0.927822i \(0.621678\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5712.00 0.289010
\(732\) 0 0
\(733\) −20862.0 −1.05124 −0.525618 − 0.850721i \(-0.676166\pi\)
−0.525618 + 0.850721i \(0.676166\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −56048.0 −2.80130
\(738\) 0 0
\(739\) 13920.0 0.692903 0.346452 − 0.938068i \(-0.387386\pi\)
0.346452 + 0.938068i \(0.387386\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 25578.0 1.26294 0.631471 − 0.775400i \(-0.282452\pi\)
0.631471 + 0.775400i \(0.282452\pi\)
\(744\) 0 0
\(745\) −9480.00 −0.466202
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13342.0 −0.650876
\(750\) 0 0
\(751\) −33472.0 −1.62638 −0.813189 − 0.581999i \(-0.802271\pi\)
−0.813189 + 0.581999i \(0.802271\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2272.00 0.109519
\(756\) 0 0
\(757\) 25934.0 1.24516 0.622581 − 0.782556i \(-0.286084\pi\)
0.622581 + 0.782556i \(0.286084\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26952.0 −1.28385 −0.641925 − 0.766768i \(-0.721864\pi\)
−0.641925 + 0.766768i \(0.721864\pi\)
\(762\) 0 0
\(763\) −630.000 −0.0298919
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7440.00 −0.350251
\(768\) 0 0
\(769\) 23450.0 1.09965 0.549824 − 0.835281i \(-0.314695\pi\)
0.549824 + 0.835281i \(0.314695\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −39568.0 −1.84109 −0.920545 − 0.390637i \(-0.872255\pi\)
−0.920545 + 0.390637i \(0.872255\pi\)
\(774\) 0 0
\(775\) −5232.00 −0.242502
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24800.0 −1.14063
\(780\) 0 0
\(781\) −42036.0 −1.92595
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1064.00 −0.0483768
\(786\) 0 0
\(787\) 12356.0 0.559649 0.279825 − 0.960051i \(-0.409724\pi\)
0.279825 + 0.960051i \(0.409724\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3206.00 −0.144112
\(792\) 0 0
\(793\) −38564.0 −1.72692
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21736.0 0.966033 0.483017 − 0.875611i \(-0.339541\pi\)
0.483017 + 0.875611i \(0.339541\pi\)
\(798\) 0 0
\(799\) −27216.0 −1.20505
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −39804.0 −1.74926
\(804\) 0 0
\(805\) −1176.00 −0.0514889
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 38310.0 1.66490 0.832452 − 0.554097i \(-0.186936\pi\)
0.832452 + 0.554097i \(0.186936\pi\)
\(810\) 0 0
\(811\) −2132.00 −0.0923115 −0.0461558 − 0.998934i \(-0.514697\pi\)
−0.0461558 + 0.998934i \(0.514697\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1088.00 0.0467619
\(816\) 0 0
\(817\) 6800.00 0.291190
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −5002.00 −0.212632 −0.106316 − 0.994332i \(-0.533906\pi\)
−0.106316 + 0.994332i \(0.533906\pi\)
\(822\) 0 0
\(823\) 3612.00 0.152985 0.0764923 − 0.997070i \(-0.475628\pi\)
0.0764923 + 0.997070i \(0.475628\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −27666.0 −1.16329 −0.581645 − 0.813443i \(-0.697591\pi\)
−0.581645 + 0.813443i \(0.697591\pi\)
\(828\) 0 0
\(829\) 12890.0 0.540034 0.270017 − 0.962856i \(-0.412971\pi\)
0.270017 + 0.962856i \(0.412971\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −4116.00 −0.171202
\(834\) 0 0
\(835\) −7504.00 −0.311002
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −9340.00 −0.384330 −0.192165 − 0.981363i \(-0.561551\pi\)
−0.192165 + 0.981363i \(0.561551\pi\)
\(840\) 0 0
\(841\) −24289.0 −0.995900
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 6588.00 0.268206
\(846\) 0 0
\(847\) 17591.0 0.713617
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 10332.0 0.416188
\(852\) 0 0
\(853\) −33082.0 −1.32791 −0.663954 − 0.747773i \(-0.731123\pi\)
−0.663954 + 0.747773i \(0.731123\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −7544.00 −0.300698 −0.150349 − 0.988633i \(-0.548040\pi\)
−0.150349 + 0.988633i \(0.548040\pi\)
\(858\) 0 0
\(859\) −8180.00 −0.324910 −0.162455 − 0.986716i \(-0.551941\pi\)
−0.162455 + 0.986716i \(0.551941\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10518.0 0.414875 0.207437 − 0.978248i \(-0.433488\pi\)
0.207437 + 0.978248i \(0.433488\pi\)
\(864\) 0 0
\(865\) 608.000 0.0238990
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −45880.0 −1.79099
\(870\) 0 0
\(871\) 56048.0 2.18038
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6552.00 −0.253141
\(876\) 0 0
\(877\) 14134.0 0.544209 0.272104 − 0.962268i \(-0.412280\pi\)
0.272104 + 0.962268i \(0.412280\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −6492.00 −0.248265 −0.124132 − 0.992266i \(-0.539615\pi\)
−0.124132 + 0.992266i \(0.539615\pi\)
\(882\) 0 0
\(883\) −38228.0 −1.45694 −0.728468 − 0.685080i \(-0.759767\pi\)
−0.728468 + 0.685080i \(0.759767\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −43076.0 −1.63061 −0.815305 − 0.579032i \(-0.803431\pi\)
−0.815305 + 0.579032i \(0.803431\pi\)
\(888\) 0 0
\(889\) −5628.00 −0.212325
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −32400.0 −1.21414
\(894\) 0 0
\(895\) 2440.00 0.0911287
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 480.000 0.0178074
\(900\) 0 0
\(901\) 21672.0 0.801331
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4168.00 0.153093
\(906\) 0 0
\(907\) 32236.0 1.18013 0.590065 − 0.807355i \(-0.299102\pi\)
0.590065 + 0.807355i \(0.299102\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −46518.0 −1.69178 −0.845889 − 0.533359i \(-0.820930\pi\)
−0.845889 + 0.533359i \(0.820930\pi\)
\(912\) 0 0
\(913\) 29016.0 1.05180
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5684.00 0.204692
\(918\) 0 0
\(919\) −17840.0 −0.640356 −0.320178 − 0.947357i \(-0.603743\pi\)
−0.320178 + 0.947357i \(0.603743\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 42036.0 1.49906
\(924\) 0 0
\(925\) 26814.0 0.953123
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −7000.00 −0.247215 −0.123607 − 0.992331i \(-0.539446\pi\)
−0.123607 + 0.992331i \(0.539446\pi\)
\(930\) 0 0
\(931\) −4900.00 −0.172493
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −20832.0 −0.728641
\(936\) 0 0
\(937\) 36114.0 1.25912 0.629559 − 0.776953i \(-0.283236\pi\)
0.629559 + 0.776953i \(0.283236\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4748.00 0.164485 0.0822425 − 0.996612i \(-0.473792\pi\)
0.0822425 + 0.996612i \(0.473792\pi\)
\(942\) 0 0
\(943\) −10416.0 −0.359694
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 42694.0 1.46501 0.732507 − 0.680759i \(-0.238350\pi\)
0.732507 + 0.680759i \(0.238350\pi\)
\(948\) 0 0
\(949\) 39804.0 1.36153
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 16742.0 0.569073 0.284537 − 0.958665i \(-0.408160\pi\)
0.284537 + 0.958665i \(0.408160\pi\)
\(954\) 0 0
\(955\) −8152.00 −0.276223
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2898.00 −0.0975822
\(960\) 0 0
\(961\) −27487.0 −0.922661
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −10408.0 −0.347197
\(966\) 0 0
\(967\) 9956.00 0.331089 0.165545 − 0.986202i \(-0.447062\pi\)
0.165545 + 0.986202i \(0.447062\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −26388.0 −0.872123 −0.436061 − 0.899917i \(-0.643627\pi\)
−0.436061 + 0.899917i \(0.643627\pi\)
\(972\) 0 0
\(973\) 11340.0 0.373632
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 786.000 0.0257383 0.0128692 − 0.999917i \(-0.495904\pi\)
0.0128692 + 0.999917i \(0.495904\pi\)
\(978\) 0 0
\(979\) −12400.0 −0.404807
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 51888.0 1.68359 0.841796 − 0.539796i \(-0.181499\pi\)
0.841796 + 0.539796i \(0.181499\pi\)
\(984\) 0 0
\(985\) −9416.00 −0.304588
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2856.00 0.0918256
\(990\) 0 0
\(991\) 51928.0 1.66453 0.832264 − 0.554379i \(-0.187044\pi\)
0.832264 + 0.554379i \(0.187044\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −6720.00 −0.214109
\(996\) 0 0
\(997\) −386.000 −0.0122615 −0.00613076 − 0.999981i \(-0.501951\pi\)
−0.00613076 + 0.999981i \(0.501951\pi\)
\(998\) 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 1008.4.a.m.1.1 1
3.2 odd 2 336.4.a.h.1.1 1
4.3 odd 2 63.4.a.a.1.1 1
12.11 even 2 21.4.a.b.1.1 ✓ 1
20.19 odd 2 1575.4.a.k.1.1 1
21.20 even 2 2352.4.a.l.1.1 1
24.5 odd 2 1344.4.a.i.1.1 1
24.11 even 2 1344.4.a.w.1.1 1
28.3 even 6 441.4.e.n.226.1 2
28.11 odd 6 441.4.e.m.226.1 2
28.19 even 6 441.4.e.n.361.1 2
28.23 odd 6 441.4.e.m.361.1 2
28.27 even 2 441.4.a.b.1.1 1
60.23 odd 4 525.4.d.b.274.1 2
60.47 odd 4 525.4.d.b.274.2 2
60.59 even 2 525.4.a.b.1.1 1
84.11 even 6 147.4.e.c.79.1 2
84.23 even 6 147.4.e.c.67.1 2
84.47 odd 6 147.4.e.b.67.1 2
84.59 odd 6 147.4.e.b.79.1 2
84.83 odd 2 147.4.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.b.1.1 ✓ 1 12.11 even 2
63.4.a.a.1.1 1 4.3 odd 2
147.4.a.g.1.1 1 84.83 odd 2
147.4.e.b.67.1 2 84.47 odd 6
147.4.e.b.79.1 2 84.59 odd 6
147.4.e.c.67.1 2 84.23 even 6
147.4.e.c.79.1 2 84.11 even 6
336.4.a.h.1.1 1 3.2 odd 2
441.4.a.b.1.1 1 28.27 even 2
441.4.e.m.226.1 2 28.11 odd 6
441.4.e.m.361.1 2 28.23 odd 6
441.4.e.n.226.1 2 28.3 even 6
441.4.e.n.361.1 2 28.19 even 6
525.4.a.b.1.1 1 60.59 even 2
525.4.d.b.274.1 2 60.23 odd 4
525.4.d.b.274.2 2 60.47 odd 4
1008.4.a.m.1.1 1 1.1 even 1 trivial
1344.4.a.i.1.1 1 24.5 odd 2
1344.4.a.w.1.1 1 24.11 even 2
1575.4.a.k.1.1 1 20.19 odd 2
2352.4.a.l.1.1 1 21.20 even 2