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Properties

Label 2400.4.a.e.1.1
Level $2400$
Weight $4$
Character 2400.1
Self dual yes
Analytic conductor $141.605$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2400,4,Mod(1,2400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2400, 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("2400.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2400.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: \(141.604584014\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 96)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2400.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} -4.00000 q^{7} +9.00000 q^{9} -20.0000 q^{11} -70.0000 q^{13} -90.0000 q^{17} -140.000 q^{19} +12.0000 q^{21} -192.000 q^{23} -27.0000 q^{27} -134.000 q^{29} -100.000 q^{31} +60.0000 q^{33} +170.000 q^{37} +210.000 q^{39} -110.000 q^{41} +532.000 q^{43} -56.0000 q^{47} -327.000 q^{49} +270.000 q^{51} +430.000 q^{53} +420.000 q^{57} +20.0000 q^{59} +270.000 q^{61} -36.0000 q^{63} -524.000 q^{67} +576.000 q^{69} +80.0000 q^{71} -330.000 q^{73} +80.0000 q^{77} -1060.00 q^{79} +81.0000 q^{81} -1188.00 q^{83} +402.000 q^{87} +1274.00 q^{89} +280.000 q^{91} +300.000 q^{93} +590.000 q^{97} -180.000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.00000 −0.215980 −0.107990 − 0.994152i \(-0.534441\pi\)
−0.107990 + 0.994152i \(0.534441\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −20.0000 −0.548202 −0.274101 − 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 0 0
\(13\) −70.0000 −1.49342 −0.746712 − 0.665148i \(-0.768369\pi\)
−0.746712 + 0.665148i \(0.768369\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −90.0000 −1.28401 −0.642006 − 0.766700i \(-0.721898\pi\)
−0.642006 + 0.766700i \(0.721898\pi\)
\(18\) 0 0
\(19\) −140.000 −1.69043 −0.845216 − 0.534425i \(-0.820528\pi\)
−0.845216 + 0.534425i \(0.820528\pi\)
\(20\) 0 0
\(21\) 12.0000 0.124696
\(22\) 0 0
\(23\) −192.000 −1.74064 −0.870321 − 0.492485i \(-0.836089\pi\)
−0.870321 + 0.492485i \(0.836089\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −134.000 −0.858041 −0.429020 − 0.903295i \(-0.641141\pi\)
−0.429020 + 0.903295i \(0.641141\pi\)
\(30\) 0 0
\(31\) −100.000 −0.579372 −0.289686 − 0.957122i \(-0.593551\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(32\) 0 0
\(33\) 60.0000 0.316505
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 170.000 0.755347 0.377673 − 0.925939i \(-0.376724\pi\)
0.377673 + 0.925939i \(0.376724\pi\)
\(38\) 0 0
\(39\) 210.000 0.862229
\(40\) 0 0
\(41\) −110.000 −0.419003 −0.209501 − 0.977808i \(-0.567184\pi\)
−0.209501 + 0.977808i \(0.567184\pi\)
\(42\) 0 0
\(43\) 532.000 1.88673 0.943363 − 0.331762i \(-0.107643\pi\)
0.943363 + 0.331762i \(0.107643\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −56.0000 −0.173797 −0.0868983 − 0.996217i \(-0.527696\pi\)
−0.0868983 + 0.996217i \(0.527696\pi\)
\(48\) 0 0
\(49\) −327.000 −0.953353
\(50\) 0 0
\(51\) 270.000 0.741325
\(52\) 0 0
\(53\) 430.000 1.11443 0.557217 − 0.830367i \(-0.311869\pi\)
0.557217 + 0.830367i \(0.311869\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 420.000 0.975971
\(58\) 0 0
\(59\) 20.0000 0.0441318 0.0220659 − 0.999757i \(-0.492976\pi\)
0.0220659 + 0.999757i \(0.492976\pi\)
\(60\) 0 0
\(61\) 270.000 0.566721 0.283360 − 0.959014i \(-0.408551\pi\)
0.283360 + 0.959014i \(0.408551\pi\)
\(62\) 0 0
\(63\) −36.0000 −0.0719932
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −524.000 −0.955474 −0.477737 − 0.878503i \(-0.658543\pi\)
−0.477737 + 0.878503i \(0.658543\pi\)
\(68\) 0 0
\(69\) 576.000 1.00496
\(70\) 0 0
\(71\) 80.0000 0.133722 0.0668609 − 0.997762i \(-0.478702\pi\)
0.0668609 + 0.997762i \(0.478702\pi\)
\(72\) 0 0
\(73\) −330.000 −0.529090 −0.264545 − 0.964373i \(-0.585222\pi\)
−0.264545 + 0.964373i \(0.585222\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 80.0000 0.118401
\(78\) 0 0
\(79\) −1060.00 −1.50961 −0.754806 − 0.655948i \(-0.772269\pi\)
−0.754806 + 0.655948i \(0.772269\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −1188.00 −1.57108 −0.785542 − 0.618809i \(-0.787616\pi\)
−0.785542 + 0.618809i \(0.787616\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 402.000 0.495390
\(88\) 0 0
\(89\) 1274.00 1.51735 0.758673 − 0.651472i \(-0.225848\pi\)
0.758673 + 0.651472i \(0.225848\pi\)
\(90\) 0 0
\(91\) 280.000 0.322549
\(92\) 0 0
\(93\) 300.000 0.334501
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 590.000 0.617582 0.308791 − 0.951130i \(-0.400076\pi\)
0.308791 + 0.951130i \(0.400076\pi\)
\(98\) 0 0
\(99\) −180.000 −0.182734
\(100\) 0 0
\(101\) −798.000 −0.786178 −0.393089 − 0.919500i \(-0.628594\pi\)
−0.393089 + 0.919500i \(0.628594\pi\)
\(102\) 0 0
\(103\) −1548.00 −1.48086 −0.740432 − 0.672131i \(-0.765379\pi\)
−0.740432 + 0.672131i \(0.765379\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1324.00 1.19622 0.598112 − 0.801413i \(-0.295918\pi\)
0.598112 + 0.801413i \(0.295918\pi\)
\(108\) 0 0
\(109\) 470.000 0.413008 0.206504 − 0.978446i \(-0.433791\pi\)
0.206504 + 0.978446i \(0.433791\pi\)
\(110\) 0 0
\(111\) −510.000 −0.436100
\(112\) 0 0
\(113\) −610.000 −0.507823 −0.253911 − 0.967227i \(-0.581717\pi\)
−0.253911 + 0.967227i \(0.581717\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −630.000 −0.497808
\(118\) 0 0
\(119\) 360.000 0.277321
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) 330.000 0.241911
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −884.000 −0.617656 −0.308828 − 0.951118i \(-0.599937\pi\)
−0.308828 + 0.951118i \(0.599937\pi\)
\(128\) 0 0
\(129\) −1596.00 −1.08930
\(130\) 0 0
\(131\) −500.000 −0.333475 −0.166737 − 0.986001i \(-0.553323\pi\)
−0.166737 + 0.986001i \(0.553323\pi\)
\(132\) 0 0
\(133\) 560.000 0.365099
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1950.00 1.21606 0.608028 − 0.793915i \(-0.291961\pi\)
0.608028 + 0.793915i \(0.291961\pi\)
\(138\) 0 0
\(139\) −220.000 −0.134246 −0.0671229 − 0.997745i \(-0.521382\pi\)
−0.0671229 + 0.997745i \(0.521382\pi\)
\(140\) 0 0
\(141\) 168.000 0.100342
\(142\) 0 0
\(143\) 1400.00 0.818698
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 981.000 0.550418
\(148\) 0 0
\(149\) −390.000 −0.214430 −0.107215 − 0.994236i \(-0.534193\pi\)
−0.107215 + 0.994236i \(0.534193\pi\)
\(150\) 0 0
\(151\) 2100.00 1.13176 0.565879 − 0.824488i \(-0.308537\pi\)
0.565879 + 0.824488i \(0.308537\pi\)
\(152\) 0 0
\(153\) −810.000 −0.428004
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2050.00 1.04209 0.521044 − 0.853530i \(-0.325543\pi\)
0.521044 + 0.853530i \(0.325543\pi\)
\(158\) 0 0
\(159\) −1290.00 −0.643419
\(160\) 0 0
\(161\) 768.000 0.375943
\(162\) 0 0
\(163\) 332.000 0.159535 0.0797676 − 0.996813i \(-0.474582\pi\)
0.0797676 + 0.996813i \(0.474582\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2744.00 −1.27148 −0.635740 − 0.771903i \(-0.719305\pi\)
−0.635740 + 0.771903i \(0.719305\pi\)
\(168\) 0 0
\(169\) 2703.00 1.23031
\(170\) 0 0
\(171\) −1260.00 −0.563477
\(172\) 0 0
\(173\) −3570.00 −1.56891 −0.784457 − 0.620183i \(-0.787058\pi\)
−0.784457 + 0.620183i \(0.787058\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −60.0000 −0.0254795
\(178\) 0 0
\(179\) −1380.00 −0.576235 −0.288117 − 0.957595i \(-0.593029\pi\)
−0.288117 + 0.957595i \(0.593029\pi\)
\(180\) 0 0
\(181\) 1358.00 0.557676 0.278838 − 0.960338i \(-0.410051\pi\)
0.278838 + 0.960338i \(0.410051\pi\)
\(182\) 0 0
\(183\) −810.000 −0.327196
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1800.00 0.703899
\(188\) 0 0
\(189\) 108.000 0.0415653
\(190\) 0 0
\(191\) 3840.00 1.45473 0.727363 − 0.686253i \(-0.240746\pi\)
0.727363 + 0.686253i \(0.240746\pi\)
\(192\) 0 0
\(193\) −3090.00 −1.15245 −0.576226 − 0.817291i \(-0.695475\pi\)
−0.576226 + 0.817291i \(0.695475\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1070.00 0.386976 0.193488 − 0.981103i \(-0.438020\pi\)
0.193488 + 0.981103i \(0.438020\pi\)
\(198\) 0 0
\(199\) 380.000 0.135364 0.0676821 − 0.997707i \(-0.478440\pi\)
0.0676821 + 0.997707i \(0.478440\pi\)
\(200\) 0 0
\(201\) 1572.00 0.551643
\(202\) 0 0
\(203\) 536.000 0.185319
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1728.00 −0.580214
\(208\) 0 0
\(209\) 2800.00 0.926699
\(210\) 0 0
\(211\) −2180.00 −0.711267 −0.355634 − 0.934625i \(-0.615735\pi\)
−0.355634 + 0.934625i \(0.615735\pi\)
\(212\) 0 0
\(213\) −240.000 −0.0772044
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 400.000 0.125133
\(218\) 0 0
\(219\) 990.000 0.305470
\(220\) 0 0
\(221\) 6300.00 1.91757
\(222\) 0 0
\(223\) 668.000 0.200595 0.100297 − 0.994958i \(-0.468021\pi\)
0.100297 + 0.994958i \(0.468021\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4836.00 −1.41399 −0.706997 − 0.707217i \(-0.749951\pi\)
−0.706997 + 0.707217i \(0.749951\pi\)
\(228\) 0 0
\(229\) 4334.00 1.25065 0.625325 − 0.780365i \(-0.284966\pi\)
0.625325 + 0.780365i \(0.284966\pi\)
\(230\) 0 0
\(231\) −240.000 −0.0683586
\(232\) 0 0
\(233\) 2550.00 0.716979 0.358489 − 0.933534i \(-0.383292\pi\)
0.358489 + 0.933534i \(0.383292\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 3180.00 0.871575
\(238\) 0 0
\(239\) −1920.00 −0.519642 −0.259821 − 0.965657i \(-0.583664\pi\)
−0.259821 + 0.965657i \(0.583664\pi\)
\(240\) 0 0
\(241\) −1070.00 −0.285995 −0.142997 − 0.989723i \(-0.545674\pi\)
−0.142997 + 0.989723i \(0.545674\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 9800.00 2.52453
\(248\) 0 0
\(249\) 3564.00 0.907066
\(250\) 0 0
\(251\) 1020.00 0.256501 0.128251 − 0.991742i \(-0.459064\pi\)
0.128251 + 0.991742i \(0.459064\pi\)
\(252\) 0 0
\(253\) 3840.00 0.954224
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5630.00 1.36650 0.683249 − 0.730186i \(-0.260567\pi\)
0.683249 + 0.730186i \(0.260567\pi\)
\(258\) 0 0
\(259\) −680.000 −0.163140
\(260\) 0 0
\(261\) −1206.00 −0.286014
\(262\) 0 0
\(263\) −7128.00 −1.67122 −0.835611 − 0.549322i \(-0.814886\pi\)
−0.835611 + 0.549322i \(0.814886\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3822.00 −0.876040
\(268\) 0 0
\(269\) 4650.00 1.05396 0.526980 − 0.849877i \(-0.323324\pi\)
0.526980 + 0.849877i \(0.323324\pi\)
\(270\) 0 0
\(271\) −3180.00 −0.712809 −0.356405 − 0.934332i \(-0.615997\pi\)
−0.356405 + 0.934332i \(0.615997\pi\)
\(272\) 0 0
\(273\) −840.000 −0.186224
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 5330.00 1.15613 0.578066 − 0.815990i \(-0.303808\pi\)
0.578066 + 0.815990i \(0.303808\pi\)
\(278\) 0 0
\(279\) −900.000 −0.193124
\(280\) 0 0
\(281\) −7830.00 −1.66227 −0.831136 − 0.556069i \(-0.812309\pi\)
−0.831136 + 0.556069i \(0.812309\pi\)
\(282\) 0 0
\(283\) 268.000 0.0562931 0.0281465 − 0.999604i \(-0.491039\pi\)
0.0281465 + 0.999604i \(0.491039\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 440.000 0.0904961
\(288\) 0 0
\(289\) 3187.00 0.648687
\(290\) 0 0
\(291\) −1770.00 −0.356561
\(292\) 0 0
\(293\) 1950.00 0.388806 0.194403 − 0.980922i \(-0.437723\pi\)
0.194403 + 0.980922i \(0.437723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 540.000 0.105502
\(298\) 0 0
\(299\) 13440.0 2.59952
\(300\) 0 0
\(301\) −2128.00 −0.407495
\(302\) 0 0
\(303\) 2394.00 0.453900
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2916.00 0.542101 0.271050 − 0.962565i \(-0.412629\pi\)
0.271050 + 0.962565i \(0.412629\pi\)
\(308\) 0 0
\(309\) 4644.00 0.854977
\(310\) 0 0
\(311\) −9000.00 −1.64097 −0.820487 − 0.571665i \(-0.806298\pi\)
−0.820487 + 0.571665i \(0.806298\pi\)
\(312\) 0 0
\(313\) −8890.00 −1.60541 −0.802704 − 0.596378i \(-0.796606\pi\)
−0.802704 + 0.596378i \(0.796606\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1290.00 −0.228560 −0.114280 − 0.993449i \(-0.536456\pi\)
−0.114280 + 0.993449i \(0.536456\pi\)
\(318\) 0 0
\(319\) 2680.00 0.470380
\(320\) 0 0
\(321\) −3972.00 −0.690640
\(322\) 0 0
\(323\) 12600.0 2.17053
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1410.00 −0.238450
\(328\) 0 0
\(329\) 224.000 0.0375365
\(330\) 0 0
\(331\) 5300.00 0.880104 0.440052 − 0.897972i \(-0.354960\pi\)
0.440052 + 0.897972i \(0.354960\pi\)
\(332\) 0 0
\(333\) 1530.00 0.251782
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 9310.00 1.50489 0.752445 − 0.658655i \(-0.228874\pi\)
0.752445 + 0.658655i \(0.228874\pi\)
\(338\) 0 0
\(339\) 1830.00 0.293192
\(340\) 0 0
\(341\) 2000.00 0.317613
\(342\) 0 0
\(343\) 2680.00 0.421885
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2596.00 0.401616 0.200808 − 0.979631i \(-0.435643\pi\)
0.200808 + 0.979631i \(0.435643\pi\)
\(348\) 0 0
\(349\) 814.000 0.124849 0.0624247 − 0.998050i \(-0.480117\pi\)
0.0624247 + 0.998050i \(0.480117\pi\)
\(350\) 0 0
\(351\) 1890.00 0.287410
\(352\) 0 0
\(353\) −7730.00 −1.16551 −0.582757 − 0.812647i \(-0.698026\pi\)
−0.582757 + 0.812647i \(0.698026\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1080.00 −0.160111
\(358\) 0 0
\(359\) −5840.00 −0.858561 −0.429281 − 0.903171i \(-0.641233\pi\)
−0.429281 + 0.903171i \(0.641233\pi\)
\(360\) 0 0
\(361\) 12741.0 1.85756
\(362\) 0 0
\(363\) 2793.00 0.403842
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −6636.00 −0.943859 −0.471930 − 0.881636i \(-0.656442\pi\)
−0.471930 + 0.881636i \(0.656442\pi\)
\(368\) 0 0
\(369\) −990.000 −0.139668
\(370\) 0 0
\(371\) −1720.00 −0.240695
\(372\) 0 0
\(373\) −12950.0 −1.79766 −0.898828 − 0.438302i \(-0.855580\pi\)
−0.898828 + 0.438302i \(0.855580\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9380.00 1.28142
\(378\) 0 0
\(379\) 6220.00 0.843008 0.421504 − 0.906827i \(-0.361502\pi\)
0.421504 + 0.906827i \(0.361502\pi\)
\(380\) 0 0
\(381\) 2652.00 0.356604
\(382\) 0 0
\(383\) −8672.00 −1.15697 −0.578484 − 0.815694i \(-0.696355\pi\)
−0.578484 + 0.815694i \(0.696355\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4788.00 0.628909
\(388\) 0 0
\(389\) 7530.00 0.981455 0.490728 − 0.871313i \(-0.336731\pi\)
0.490728 + 0.871313i \(0.336731\pi\)
\(390\) 0 0
\(391\) 17280.0 2.23501
\(392\) 0 0
\(393\) 1500.00 0.192532
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3650.00 0.461431 0.230716 − 0.973021i \(-0.425893\pi\)
0.230716 + 0.973021i \(0.425893\pi\)
\(398\) 0 0
\(399\) −1680.00 −0.210790
\(400\) 0 0
\(401\) 11498.0 1.43188 0.715939 − 0.698163i \(-0.245999\pi\)
0.715939 + 0.698163i \(0.245999\pi\)
\(402\) 0 0
\(403\) 7000.00 0.865248
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3400.00 −0.414083
\(408\) 0 0
\(409\) −3590.00 −0.434020 −0.217010 − 0.976169i \(-0.569630\pi\)
−0.217010 + 0.976169i \(0.569630\pi\)
\(410\) 0 0
\(411\) −5850.00 −0.702091
\(412\) 0 0
\(413\) −80.0000 −0.00953158
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 660.000 0.0775068
\(418\) 0 0
\(419\) −380.000 −0.0443060 −0.0221530 − 0.999755i \(-0.507052\pi\)
−0.0221530 + 0.999755i \(0.507052\pi\)
\(420\) 0 0
\(421\) −5410.00 −0.626288 −0.313144 − 0.949706i \(-0.601382\pi\)
−0.313144 + 0.949706i \(0.601382\pi\)
\(422\) 0 0
\(423\) −504.000 −0.0579322
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1080.00 −0.122400
\(428\) 0 0
\(429\) −4200.00 −0.472676
\(430\) 0 0
\(431\) −8280.00 −0.925368 −0.462684 − 0.886523i \(-0.653114\pi\)
−0.462684 + 0.886523i \(0.653114\pi\)
\(432\) 0 0
\(433\) 12590.0 1.39731 0.698657 − 0.715457i \(-0.253781\pi\)
0.698657 + 0.715457i \(0.253781\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 26880.0 2.94244
\(438\) 0 0
\(439\) −15140.0 −1.64600 −0.822999 − 0.568043i \(-0.807701\pi\)
−0.822999 + 0.568043i \(0.807701\pi\)
\(440\) 0 0
\(441\) −2943.00 −0.317784
\(442\) 0 0
\(443\) −5628.00 −0.603599 −0.301799 − 0.953371i \(-0.597587\pi\)
−0.301799 + 0.953371i \(0.597587\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1170.00 0.123801
\(448\) 0 0
\(449\) 5450.00 0.572832 0.286416 − 0.958105i \(-0.407536\pi\)
0.286416 + 0.958105i \(0.407536\pi\)
\(450\) 0 0
\(451\) 2200.00 0.229698
\(452\) 0 0
\(453\) −6300.00 −0.653421
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2710.00 0.277393 0.138696 − 0.990335i \(-0.455709\pi\)
0.138696 + 0.990335i \(0.455709\pi\)
\(458\) 0 0
\(459\) 2430.00 0.247108
\(460\) 0 0
\(461\) −11982.0 −1.21054 −0.605268 − 0.796022i \(-0.706934\pi\)
−0.605268 + 0.796022i \(0.706934\pi\)
\(462\) 0 0
\(463\) −6068.00 −0.609080 −0.304540 − 0.952500i \(-0.598503\pi\)
−0.304540 + 0.952500i \(0.598503\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5036.00 0.499011 0.249506 − 0.968373i \(-0.419732\pi\)
0.249506 + 0.968373i \(0.419732\pi\)
\(468\) 0 0
\(469\) 2096.00 0.206363
\(470\) 0 0
\(471\) −6150.00 −0.601650
\(472\) 0 0
\(473\) −10640.0 −1.03431
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3870.00 0.371478
\(478\) 0 0
\(479\) 4440.00 0.423526 0.211763 − 0.977321i \(-0.432080\pi\)
0.211763 + 0.977321i \(0.432080\pi\)
\(480\) 0 0
\(481\) −11900.0 −1.12805
\(482\) 0 0
\(483\) −2304.00 −0.217051
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4996.00 −0.464867 −0.232434 − 0.972612i \(-0.574669\pi\)
−0.232434 + 0.972612i \(0.574669\pi\)
\(488\) 0 0
\(489\) −996.000 −0.0921077
\(490\) 0 0
\(491\) −10700.0 −0.983471 −0.491735 − 0.870745i \(-0.663637\pi\)
−0.491735 + 0.870745i \(0.663637\pi\)
\(492\) 0 0
\(493\) 12060.0 1.10173
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −320.000 −0.0288812
\(498\) 0 0
\(499\) 13980.0 1.25417 0.627085 − 0.778951i \(-0.284248\pi\)
0.627085 + 0.778951i \(0.284248\pi\)
\(500\) 0 0
\(501\) 8232.00 0.734089
\(502\) 0 0
\(503\) 13632.0 1.20839 0.604196 − 0.796836i \(-0.293495\pi\)
0.604196 + 0.796836i \(0.293495\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −8109.00 −0.710322
\(508\) 0 0
\(509\) 4746.00 0.413286 0.206643 − 0.978416i \(-0.433746\pi\)
0.206643 + 0.978416i \(0.433746\pi\)
\(510\) 0 0
\(511\) 1320.00 0.114273
\(512\) 0 0
\(513\) 3780.00 0.325324
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1120.00 0.0952757
\(518\) 0 0
\(519\) 10710.0 0.905813
\(520\) 0 0
\(521\) −5838.00 −0.490916 −0.245458 − 0.969407i \(-0.578938\pi\)
−0.245458 + 0.969407i \(0.578938\pi\)
\(522\) 0 0
\(523\) 8388.00 0.701303 0.350652 − 0.936506i \(-0.385960\pi\)
0.350652 + 0.936506i \(0.385960\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9000.00 0.743921
\(528\) 0 0
\(529\) 24697.0 2.02983
\(530\) 0 0
\(531\) 180.000 0.0147106
\(532\) 0 0
\(533\) 7700.00 0.625749
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4140.00 0.332689
\(538\) 0 0
\(539\) 6540.00 0.522630
\(540\) 0 0
\(541\) 7078.00 0.562490 0.281245 − 0.959636i \(-0.409253\pi\)
0.281245 + 0.959636i \(0.409253\pi\)
\(542\) 0 0
\(543\) −4074.00 −0.321974
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8604.00 0.672542 0.336271 − 0.941765i \(-0.390834\pi\)
0.336271 + 0.941765i \(0.390834\pi\)
\(548\) 0 0
\(549\) 2430.00 0.188907
\(550\) 0 0
\(551\) 18760.0 1.45046
\(552\) 0 0
\(553\) 4240.00 0.326045
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18850.0 −1.43393 −0.716966 − 0.697108i \(-0.754470\pi\)
−0.716966 + 0.697108i \(0.754470\pi\)
\(558\) 0 0
\(559\) −37240.0 −2.81768
\(560\) 0 0
\(561\) −5400.00 −0.406396
\(562\) 0 0
\(563\) −5412.00 −0.405131 −0.202565 − 0.979269i \(-0.564928\pi\)
−0.202565 + 0.979269i \(0.564928\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −324.000 −0.0239977
\(568\) 0 0
\(569\) 13570.0 0.999796 0.499898 − 0.866084i \(-0.333371\pi\)
0.499898 + 0.866084i \(0.333371\pi\)
\(570\) 0 0
\(571\) −860.000 −0.0630296 −0.0315148 − 0.999503i \(-0.510033\pi\)
−0.0315148 + 0.999503i \(0.510033\pi\)
\(572\) 0 0
\(573\) −11520.0 −0.839886
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −5010.00 −0.361471 −0.180736 − 0.983532i \(-0.557848\pi\)
−0.180736 + 0.983532i \(0.557848\pi\)
\(578\) 0 0
\(579\) 9270.00 0.665368
\(580\) 0 0
\(581\) 4752.00 0.339322
\(582\) 0 0
\(583\) −8600.00 −0.610936
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16116.0 −1.13318 −0.566592 − 0.823999i \(-0.691738\pi\)
−0.566592 + 0.823999i \(0.691738\pi\)
\(588\) 0 0
\(589\) 14000.0 0.979389
\(590\) 0 0
\(591\) −3210.00 −0.223421
\(592\) 0 0
\(593\) −7170.00 −0.496520 −0.248260 − 0.968693i \(-0.579859\pi\)
−0.248260 + 0.968693i \(0.579859\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1140.00 −0.0781526
\(598\) 0 0
\(599\) −9520.00 −0.649377 −0.324688 − 0.945821i \(-0.605259\pi\)
−0.324688 + 0.945821i \(0.605259\pi\)
\(600\) 0 0
\(601\) 6010.00 0.407909 0.203954 − 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) −4716.00 −0.318491
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 24844.0 1.66126 0.830632 − 0.556822i \(-0.187980\pi\)
0.830632 + 0.556822i \(0.187980\pi\)
\(608\) 0 0
\(609\) −1608.00 −0.106994
\(610\) 0 0
\(611\) 3920.00 0.259552
\(612\) 0 0
\(613\) −9990.00 −0.658226 −0.329113 − 0.944291i \(-0.606750\pi\)
−0.329113 + 0.944291i \(0.606750\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −570.000 −0.0371918 −0.0185959 − 0.999827i \(-0.505920\pi\)
−0.0185959 + 0.999827i \(0.505920\pi\)
\(618\) 0 0
\(619\) −8700.00 −0.564915 −0.282458 − 0.959280i \(-0.591150\pi\)
−0.282458 + 0.959280i \(0.591150\pi\)
\(620\) 0 0
\(621\) 5184.00 0.334987
\(622\) 0 0
\(623\) −5096.00 −0.327716
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −8400.00 −0.535030
\(628\) 0 0
\(629\) −15300.0 −0.969874
\(630\) 0 0
\(631\) 16340.0 1.03088 0.515440 − 0.856926i \(-0.327629\pi\)
0.515440 + 0.856926i \(0.327629\pi\)
\(632\) 0 0
\(633\) 6540.00 0.410650
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 22890.0 1.42376
\(638\) 0 0
\(639\) 720.000 0.0445740
\(640\) 0 0
\(641\) 11210.0 0.690746 0.345373 − 0.938465i \(-0.387752\pi\)
0.345373 + 0.938465i \(0.387752\pi\)
\(642\) 0 0
\(643\) 12828.0 0.786760 0.393380 − 0.919376i \(-0.371306\pi\)
0.393380 + 0.919376i \(0.371306\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24336.0 −1.47874 −0.739372 − 0.673298i \(-0.764877\pi\)
−0.739372 + 0.673298i \(0.764877\pi\)
\(648\) 0 0
\(649\) −400.000 −0.0241932
\(650\) 0 0
\(651\) −1200.00 −0.0722453
\(652\) 0 0
\(653\) −770.000 −0.0461446 −0.0230723 − 0.999734i \(-0.507345\pi\)
−0.0230723 + 0.999734i \(0.507345\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2970.00 −0.176363
\(658\) 0 0
\(659\) 4140.00 0.244722 0.122361 − 0.992486i \(-0.460954\pi\)
0.122361 + 0.992486i \(0.460954\pi\)
\(660\) 0 0
\(661\) 8390.00 0.493696 0.246848 − 0.969054i \(-0.420605\pi\)
0.246848 + 0.969054i \(0.420605\pi\)
\(662\) 0 0
\(663\) −18900.0 −1.10711
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25728.0 1.49354
\(668\) 0 0
\(669\) −2004.00 −0.115813
\(670\) 0 0
\(671\) −5400.00 −0.310678
\(672\) 0 0
\(673\) −1730.00 −0.0990886 −0.0495443 − 0.998772i \(-0.515777\pi\)
−0.0495443 + 0.998772i \(0.515777\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23930.0 −1.35850 −0.679250 − 0.733907i \(-0.737695\pi\)
−0.679250 + 0.733907i \(0.737695\pi\)
\(678\) 0 0
\(679\) −2360.00 −0.133385
\(680\) 0 0
\(681\) 14508.0 0.816370
\(682\) 0 0
\(683\) 29892.0 1.67465 0.837325 − 0.546706i \(-0.184118\pi\)
0.837325 + 0.546706i \(0.184118\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −13002.0 −0.722063
\(688\) 0 0
\(689\) −30100.0 −1.66432
\(690\) 0 0
\(691\) 21220.0 1.16823 0.584115 − 0.811671i \(-0.301442\pi\)
0.584115 + 0.811671i \(0.301442\pi\)
\(692\) 0 0
\(693\) 720.000 0.0394669
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9900.00 0.538005
\(698\) 0 0
\(699\) −7650.00 −0.413948
\(700\) 0 0
\(701\) −21750.0 −1.17188 −0.585939 − 0.810355i \(-0.699274\pi\)
−0.585939 + 0.810355i \(0.699274\pi\)
\(702\) 0 0
\(703\) −23800.0 −1.27686
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3192.00 0.169798
\(708\) 0 0
\(709\) −21554.0 −1.14172 −0.570859 − 0.821048i \(-0.693390\pi\)
−0.570859 + 0.821048i \(0.693390\pi\)
\(710\) 0 0
\(711\) −9540.00 −0.503204
\(712\) 0 0
\(713\) 19200.0 1.00848
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 5760.00 0.300016
\(718\) 0 0
\(719\) −13000.0 −0.674295 −0.337148 − 0.941452i \(-0.609462\pi\)
−0.337148 + 0.941452i \(0.609462\pi\)
\(720\) 0 0
\(721\) 6192.00 0.319837
\(722\) 0 0
\(723\) 3210.00 0.165119
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3276.00 0.167125 0.0835627 − 0.996503i \(-0.473370\pi\)
0.0835627 + 0.996503i \(0.473370\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −47880.0 −2.42258
\(732\) 0 0
\(733\) −21110.0 −1.06373 −0.531866 − 0.846828i \(-0.678509\pi\)
−0.531866 + 0.846828i \(0.678509\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10480.0 0.523793
\(738\) 0 0
\(739\) 17980.0 0.895000 0.447500 − 0.894284i \(-0.352314\pi\)
0.447500 + 0.894284i \(0.352314\pi\)
\(740\) 0 0
\(741\) −29400.0 −1.45754
\(742\) 0 0
\(743\) −33192.0 −1.63889 −0.819446 − 0.573157i \(-0.805719\pi\)
−0.819446 + 0.573157i \(0.805719\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −10692.0 −0.523695
\(748\) 0 0
\(749\) −5296.00 −0.258360
\(750\) 0 0
\(751\) 23900.0 1.16128 0.580641 − 0.814159i \(-0.302802\pi\)
0.580641 + 0.814159i \(0.302802\pi\)
\(752\) 0 0
\(753\) −3060.00 −0.148091
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1950.00 −0.0936248 −0.0468124 − 0.998904i \(-0.514906\pi\)
−0.0468124 + 0.998904i \(0.514906\pi\)
\(758\) 0 0
\(759\) −11520.0 −0.550922
\(760\) 0 0
\(761\) 8082.00 0.384983 0.192492 − 0.981299i \(-0.438343\pi\)
0.192492 + 0.981299i \(0.438343\pi\)
\(762\) 0 0
\(763\) −1880.00 −0.0892013
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1400.00 −0.0659075
\(768\) 0 0
\(769\) −36494.0 −1.71132 −0.855661 − 0.517536i \(-0.826849\pi\)
−0.855661 + 0.517536i \(0.826849\pi\)
\(770\) 0 0
\(771\) −16890.0 −0.788947
\(772\) 0 0
\(773\) −28050.0 −1.30516 −0.652580 − 0.757720i \(-0.726313\pi\)
−0.652580 + 0.757720i \(0.726313\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2040.00 0.0941887
\(778\) 0 0
\(779\) 15400.0 0.708296
\(780\) 0 0
\(781\) −1600.00 −0.0733067
\(782\) 0 0
\(783\) 3618.00 0.165130
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 23004.0 1.04194 0.520968 − 0.853576i \(-0.325571\pi\)
0.520968 + 0.853576i \(0.325571\pi\)
\(788\) 0 0
\(789\) 21384.0 0.964880
\(790\) 0 0
\(791\) 2440.00 0.109679
\(792\) 0 0
\(793\) −18900.0 −0.846354
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19410.0 −0.862657 −0.431328 − 0.902195i \(-0.641955\pi\)
−0.431328 + 0.902195i \(0.641955\pi\)
\(798\) 0 0
\(799\) 5040.00 0.223157
\(800\) 0 0
\(801\) 11466.0 0.505782
\(802\) 0 0
\(803\) 6600.00 0.290048
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −13950.0 −0.608505
\(808\) 0 0
\(809\) 34946.0 1.51871 0.759355 − 0.650677i \(-0.225515\pi\)
0.759355 + 0.650677i \(0.225515\pi\)
\(810\) 0 0
\(811\) 28300.0 1.22534 0.612668 − 0.790340i \(-0.290096\pi\)
0.612668 + 0.790340i \(0.290096\pi\)
\(812\) 0 0
\(813\) 9540.00 0.411540
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −74480.0 −3.18938
\(818\) 0 0
\(819\) 2520.00 0.107516
\(820\) 0 0
\(821\) 16930.0 0.719685 0.359842 − 0.933013i \(-0.382830\pi\)
0.359842 + 0.933013i \(0.382830\pi\)
\(822\) 0 0
\(823\) −24772.0 −1.04921 −0.524604 − 0.851347i \(-0.675786\pi\)
−0.524604 + 0.851347i \(0.675786\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −12004.0 −0.504740 −0.252370 − 0.967631i \(-0.581210\pi\)
−0.252370 + 0.967631i \(0.581210\pi\)
\(828\) 0 0
\(829\) −22330.0 −0.935528 −0.467764 − 0.883853i \(-0.654940\pi\)
−0.467764 + 0.883853i \(0.654940\pi\)
\(830\) 0 0
\(831\) −15990.0 −0.667493
\(832\) 0 0
\(833\) 29430.0 1.22412
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2700.00 0.111500
\(838\) 0 0
\(839\) −45280.0 −1.86322 −0.931609 − 0.363463i \(-0.881594\pi\)
−0.931609 + 0.363463i \(0.881594\pi\)
\(840\) 0 0
\(841\) −6433.00 −0.263766
\(842\) 0 0
\(843\) 23490.0 0.959714
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 3724.00 0.151072
\(848\) 0 0
\(849\) −804.000 −0.0325008
\(850\) 0 0
\(851\) −32640.0 −1.31479
\(852\) 0 0
\(853\) 26970.0 1.08257 0.541287 − 0.840838i \(-0.317937\pi\)
0.541287 + 0.840838i \(0.317937\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 12190.0 0.485884 0.242942 − 0.970041i \(-0.421888\pi\)
0.242942 + 0.970041i \(0.421888\pi\)
\(858\) 0 0
\(859\) 9260.00 0.367808 0.183904 − 0.982944i \(-0.441126\pi\)
0.183904 + 0.982944i \(0.441126\pi\)
\(860\) 0 0
\(861\) −1320.00 −0.0522479
\(862\) 0 0
\(863\) −4832.00 −0.190595 −0.0952973 − 0.995449i \(-0.530380\pi\)
−0.0952973 + 0.995449i \(0.530380\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −9561.00 −0.374520
\(868\) 0 0
\(869\) 21200.0 0.827573
\(870\) 0 0
\(871\) 36680.0 1.42693
\(872\) 0 0
\(873\) 5310.00 0.205861
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37630.0 −1.44889 −0.724444 − 0.689334i \(-0.757903\pi\)
−0.724444 + 0.689334i \(0.757903\pi\)
\(878\) 0 0
\(879\) −5850.00 −0.224477
\(880\) 0 0
\(881\) −15630.0 −0.597716 −0.298858 − 0.954298i \(-0.596606\pi\)
−0.298858 + 0.954298i \(0.596606\pi\)
\(882\) 0 0
\(883\) 12988.0 0.494995 0.247498 − 0.968888i \(-0.420392\pi\)
0.247498 + 0.968888i \(0.420392\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5976.00 0.226217 0.113108 − 0.993583i \(-0.463919\pi\)
0.113108 + 0.993583i \(0.463919\pi\)
\(888\) 0 0
\(889\) 3536.00 0.133401
\(890\) 0 0
\(891\) −1620.00 −0.0609114
\(892\) 0 0
\(893\) 7840.00 0.293791
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −40320.0 −1.50083
\(898\) 0 0
\(899\) 13400.0 0.497125
\(900\) 0 0
\(901\) −38700.0 −1.43095
\(902\) 0 0
\(903\) 6384.00 0.235267
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −15004.0 −0.549283 −0.274641 − 0.961547i \(-0.588559\pi\)
−0.274641 + 0.961547i \(0.588559\pi\)
\(908\) 0 0
\(909\) −7182.00 −0.262059
\(910\) 0 0
\(911\) −21120.0 −0.768097 −0.384049 − 0.923313i \(-0.625471\pi\)
−0.384049 + 0.923313i \(0.625471\pi\)
\(912\) 0 0
\(913\) 23760.0 0.861272
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2000.00 0.0720238
\(918\) 0 0
\(919\) −25500.0 −0.915307 −0.457654 − 0.889131i \(-0.651310\pi\)
−0.457654 + 0.889131i \(0.651310\pi\)
\(920\) 0 0
\(921\) −8748.00 −0.312982
\(922\) 0 0
\(923\) −5600.00 −0.199703
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −13932.0 −0.493621
\(928\) 0 0
\(929\) −390.000 −0.0137734 −0.00688670 − 0.999976i \(-0.502192\pi\)
−0.00688670 + 0.999976i \(0.502192\pi\)
\(930\) 0 0
\(931\) 45780.0 1.61158
\(932\) 0 0
\(933\) 27000.0 0.947417
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −890.000 −0.0310299 −0.0155150 − 0.999880i \(-0.504939\pi\)
−0.0155150 + 0.999880i \(0.504939\pi\)
\(938\) 0 0
\(939\) 26670.0 0.926882
\(940\) 0 0
\(941\) −3022.00 −0.104691 −0.0523456 − 0.998629i \(-0.516670\pi\)
−0.0523456 + 0.998629i \(0.516670\pi\)
\(942\) 0 0
\(943\) 21120.0 0.729334
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2916.00 0.100060 0.0500302 − 0.998748i \(-0.484068\pi\)
0.0500302 + 0.998748i \(0.484068\pi\)
\(948\) 0 0
\(949\) 23100.0 0.790156
\(950\) 0 0
\(951\) 3870.00 0.131959
\(952\) 0 0
\(953\) 12990.0 0.441540 0.220770 − 0.975326i \(-0.429143\pi\)
0.220770 + 0.975326i \(0.429143\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −8040.00 −0.271574
\(958\) 0 0
\(959\) −7800.00 −0.262644
\(960\) 0 0
\(961\) −19791.0 −0.664328
\(962\) 0 0
\(963\) 11916.0 0.398741
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 41844.0 1.39153 0.695766 − 0.718268i \(-0.255065\pi\)
0.695766 + 0.718268i \(0.255065\pi\)
\(968\) 0 0
\(969\) −37800.0 −1.25316
\(970\) 0 0
\(971\) 43900.0 1.45089 0.725447 − 0.688278i \(-0.241633\pi\)
0.725447 + 0.688278i \(0.241633\pi\)
\(972\) 0 0
\(973\) 880.000 0.0289944
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 8630.00 0.282598 0.141299 − 0.989967i \(-0.454872\pi\)
0.141299 + 0.989967i \(0.454872\pi\)
\(978\) 0 0
\(979\) −25480.0 −0.831812
\(980\) 0 0
\(981\) 4230.00 0.137669
\(982\) 0 0
\(983\) −168.000 −0.00545104 −0.00272552 − 0.999996i \(-0.500868\pi\)
−0.00272552 + 0.999996i \(0.500868\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −672.000 −0.0216717
\(988\) 0 0
\(989\) −102144. −3.28412
\(990\) 0 0
\(991\) 25580.0 0.819955 0.409978 − 0.912096i \(-0.365537\pi\)
0.409978 + 0.912096i \(0.365537\pi\)
\(992\) 0 0
\(993\) −15900.0 −0.508128
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 47610.0 1.51236 0.756180 − 0.654363i \(-0.227063\pi\)
0.756180 + 0.654363i \(0.227063\pi\)
\(998\) 0 0
\(999\) −4590.00 −0.145367
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 2400.4.a.e.1.1 1
4.3 odd 2 2400.4.a.r.1.1 1
5.4 even 2 96.4.a.f.1.1 yes 1
15.14 odd 2 288.4.a.c.1.1 1
20.19 odd 2 96.4.a.c.1.1 ✓ 1
40.19 odd 2 192.4.a.h.1.1 1
40.29 even 2 192.4.a.b.1.1 1
60.59 even 2 288.4.a.b.1.1 1
80.19 odd 4 768.4.d.i.385.1 2
80.29 even 4 768.4.d.h.385.2 2
80.59 odd 4 768.4.d.i.385.2 2
80.69 even 4 768.4.d.h.385.1 2
120.29 odd 2 576.4.a.t.1.1 1
120.59 even 2 576.4.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.4.a.c.1.1 ✓ 1 20.19 odd 2
96.4.a.f.1.1 yes 1 5.4 even 2
192.4.a.b.1.1 1 40.29 even 2
192.4.a.h.1.1 1 40.19 odd 2
288.4.a.b.1.1 1 60.59 even 2
288.4.a.c.1.1 1 15.14 odd 2
576.4.a.s.1.1 1 120.59 even 2
576.4.a.t.1.1 1 120.29 odd 2
768.4.d.h.385.1 2 80.69 even 4
768.4.d.h.385.2 2 80.29 even 4
768.4.d.i.385.1 2 80.19 odd 4
768.4.d.i.385.2 2 80.59 odd 4
2400.4.a.e.1.1 1 1.1 even 1 trivial
2400.4.a.r.1.1 1 4.3 odd 2