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Properties

Label 2400.4.a.c.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)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} -12.0000 q^{7} +9.00000 q^{9} +60.0000 q^{11} +42.0000 q^{13} -10.0000 q^{17} +132.000 q^{19} +36.0000 q^{21} +48.0000 q^{23} -27.0000 q^{27} +226.000 q^{29} -252.000 q^{31} -180.000 q^{33} +362.000 q^{37} -126.000 q^{39} -94.0000 q^{41} +228.000 q^{43} +408.000 q^{47} -199.000 q^{49} +30.0000 q^{51} -346.000 q^{53} -396.000 q^{57} -300.000 q^{59} -466.000 q^{61} -108.000 q^{63} -204.000 q^{67} -144.000 q^{69} +1056.00 q^{71} -330.000 q^{73} -720.000 q^{77} +612.000 q^{79} +81.0000 q^{81} -564.000 q^{83} -678.000 q^{87} -1510.00 q^{89} -504.000 q^{91} +756.000 q^{93} -594.000 q^{97} +540.000 q^{99} +O(q^{100})\)

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
\(7\) −12.0000 −0.647939 −0.323970 − 0.946068i \(-0.605018\pi\)
−0.323970 + 0.946068i \(0.605018\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 60.0000 1.64461 0.822304 − 0.569049i \(-0.192689\pi\)
0.822304 + 0.569049i \(0.192689\pi\)
\(12\) 0 0
\(13\) 42.0000 0.896054 0.448027 − 0.894020i \(-0.352127\pi\)
0.448027 + 0.894020i \(0.352127\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −10.0000 −0.142668 −0.0713340 − 0.997452i \(-0.522726\pi\)
−0.0713340 + 0.997452i \(0.522726\pi\)
\(18\) 0 0
\(19\) 132.000 1.59384 0.796918 − 0.604088i \(-0.206462\pi\)
0.796918 + 0.604088i \(0.206462\pi\)
\(20\) 0 0
\(21\) 36.0000 0.374088
\(22\) 0 0
\(23\) 48.0000 0.435161 0.217580 − 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 226.000 1.44714 0.723571 − 0.690249i \(-0.242499\pi\)
0.723571 + 0.690249i \(0.242499\pi\)
\(30\) 0 0
\(31\) −252.000 −1.46002 −0.730009 − 0.683438i \(-0.760484\pi\)
−0.730009 + 0.683438i \(0.760484\pi\)
\(32\) 0 0
\(33\) −180.000 −0.949514
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 362.000 1.60844 0.804222 − 0.594329i \(-0.202582\pi\)
0.804222 + 0.594329i \(0.202582\pi\)
\(38\) 0 0
\(39\) −126.000 −0.517337
\(40\) 0 0
\(41\) −94.0000 −0.358057 −0.179028 − 0.983844i \(-0.557295\pi\)
−0.179028 + 0.983844i \(0.557295\pi\)
\(42\) 0 0
\(43\) 228.000 0.808597 0.404299 − 0.914627i \(-0.367516\pi\)
0.404299 + 0.914627i \(0.367516\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 408.000 1.26623 0.633116 − 0.774057i \(-0.281776\pi\)
0.633116 + 0.774057i \(0.281776\pi\)
\(48\) 0 0
\(49\) −199.000 −0.580175
\(50\) 0 0
\(51\) 30.0000 0.0823694
\(52\) 0 0
\(53\) −346.000 −0.896731 −0.448366 − 0.893850i \(-0.647994\pi\)
−0.448366 + 0.893850i \(0.647994\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −396.000 −0.920201
\(58\) 0 0
\(59\) −300.000 −0.661978 −0.330989 − 0.943635i \(-0.607382\pi\)
−0.330989 + 0.943635i \(0.607382\pi\)
\(60\) 0 0
\(61\) −466.000 −0.978118 −0.489059 − 0.872251i \(-0.662660\pi\)
−0.489059 + 0.872251i \(0.662660\pi\)
\(62\) 0 0
\(63\) −108.000 −0.215980
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −204.000 −0.371979 −0.185989 − 0.982552i \(-0.559549\pi\)
−0.185989 + 0.982552i \(0.559549\pi\)
\(68\) 0 0
\(69\) −144.000 −0.251240
\(70\) 0 0
\(71\) 1056.00 1.76513 0.882564 − 0.470192i \(-0.155815\pi\)
0.882564 + 0.470192i \(0.155815\pi\)
\(72\) 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
\(77\) −720.000 −1.06561
\(78\) 0 0
\(79\) 612.000 0.871587 0.435794 − 0.900047i \(-0.356468\pi\)
0.435794 + 0.900047i \(0.356468\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −564.000 −0.745868 −0.372934 − 0.927858i \(-0.621648\pi\)
−0.372934 + 0.927858i \(0.621648\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −678.000 −0.835508
\(88\) 0 0
\(89\) −1510.00 −1.79842 −0.899212 − 0.437514i \(-0.855859\pi\)
−0.899212 + 0.437514i \(0.855859\pi\)
\(90\) 0 0
\(91\) −504.000 −0.580589
\(92\) 0 0
\(93\) 756.000 0.842941
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −594.000 −0.621769 −0.310884 − 0.950448i \(-0.600625\pi\)
−0.310884 + 0.950448i \(0.600625\pi\)
\(98\) 0 0
\(99\) 540.000 0.548202
\(100\) 0 0
\(101\) 554.000 0.545793 0.272896 − 0.962043i \(-0.412018\pi\)
0.272896 + 0.962043i \(0.412018\pi\)
\(102\) 0 0
\(103\) −1284.00 −1.22831 −0.614157 − 0.789184i \(-0.710504\pi\)
−0.614157 + 0.789184i \(0.710504\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1356.00 1.22514 0.612568 − 0.790418i \(-0.290137\pi\)
0.612568 + 0.790418i \(0.290137\pi\)
\(108\) 0 0
\(109\) 390.000 0.342708 0.171354 − 0.985209i \(-0.445186\pi\)
0.171354 + 0.985209i \(0.445186\pi\)
\(110\) 0 0
\(111\) −1086.00 −0.928636
\(112\) 0 0
\(113\) 766.000 0.637692 0.318846 − 0.947807i \(-0.396705\pi\)
0.318846 + 0.947807i \(0.396705\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 378.000 0.298685
\(118\) 0 0
\(119\) 120.000 0.0924402
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) 282.000 0.206724
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2388.00 1.66851 0.834255 − 0.551379i \(-0.185898\pi\)
0.834255 + 0.551379i \(0.185898\pi\)
\(128\) 0 0
\(129\) −684.000 −0.466844
\(130\) 0 0
\(131\) 396.000 0.264112 0.132056 − 0.991242i \(-0.457842\pi\)
0.132056 + 0.991242i \(0.457842\pi\)
\(132\) 0 0
\(133\) −1584.00 −1.03271
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 110.000 0.0685981 0.0342990 − 0.999412i \(-0.489080\pi\)
0.0342990 + 0.999412i \(0.489080\pi\)
\(138\) 0 0
\(139\) −732.000 −0.446672 −0.223336 − 0.974742i \(-0.571695\pi\)
−0.223336 + 0.974742i \(0.571695\pi\)
\(140\) 0 0
\(141\) −1224.00 −0.731060
\(142\) 0 0
\(143\) 2520.00 1.47366
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 597.000 0.334964
\(148\) 0 0
\(149\) −1934.00 −1.06335 −0.531676 − 0.846948i \(-0.678438\pi\)
−0.531676 + 0.846948i \(0.678438\pi\)
\(150\) 0 0
\(151\) −1092.00 −0.588515 −0.294257 − 0.955726i \(-0.595072\pi\)
−0.294257 + 0.955726i \(0.595072\pi\)
\(152\) 0 0
\(153\) −90.0000 −0.0475560
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 578.000 0.293818 0.146909 − 0.989150i \(-0.453068\pi\)
0.146909 + 0.989150i \(0.453068\pi\)
\(158\) 0 0
\(159\) 1038.00 0.517728
\(160\) 0 0
\(161\) −576.000 −0.281958
\(162\) 0 0
\(163\) −2532.00 −1.21670 −0.608348 − 0.793670i \(-0.708168\pi\)
−0.608348 + 0.793670i \(0.708168\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 648.000 0.300262 0.150131 − 0.988666i \(-0.452030\pi\)
0.150131 + 0.988666i \(0.452030\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) 0 0
\(171\) 1188.00 0.531279
\(172\) 0 0
\(173\) −3338.00 −1.46696 −0.733478 − 0.679713i \(-0.762104\pi\)
−0.733478 + 0.679713i \(0.762104\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 900.000 0.382193
\(178\) 0 0
\(179\) 3804.00 1.58840 0.794202 − 0.607654i \(-0.207889\pi\)
0.794202 + 0.607654i \(0.207889\pi\)
\(180\) 0 0
\(181\) 1854.00 0.761363 0.380682 − 0.924706i \(-0.375689\pi\)
0.380682 + 0.924706i \(0.375689\pi\)
\(182\) 0 0
\(183\) 1398.00 0.564717
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −600.000 −0.234633
\(188\) 0 0
\(189\) 324.000 0.124696
\(190\) 0 0
\(191\) 1344.00 0.509154 0.254577 − 0.967052i \(-0.418064\pi\)
0.254577 + 0.967052i \(0.418064\pi\)
\(192\) 0 0
\(193\) 1262.00 0.470677 0.235339 − 0.971913i \(-0.424380\pi\)
0.235339 + 0.971913i \(0.424380\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4294.00 1.55297 0.776484 − 0.630137i \(-0.217001\pi\)
0.776484 + 0.630137i \(0.217001\pi\)
\(198\) 0 0
\(199\) 4308.00 1.53460 0.767302 − 0.641286i \(-0.221599\pi\)
0.767302 + 0.641286i \(0.221599\pi\)
\(200\) 0 0
\(201\) 612.000 0.214762
\(202\) 0 0
\(203\) −2712.00 −0.937661
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 432.000 0.145054
\(208\) 0 0
\(209\) 7920.00 2.62123
\(210\) 0 0
\(211\) 1212.00 0.395438 0.197719 − 0.980259i \(-0.436647\pi\)
0.197719 + 0.980259i \(0.436647\pi\)
\(212\) 0 0
\(213\) −3168.00 −1.01910
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3024.00 0.946002
\(218\) 0 0
\(219\) 990.000 0.305470
\(220\) 0 0
\(221\) −420.000 −0.127838
\(222\) 0 0
\(223\) −2172.00 −0.652233 −0.326116 − 0.945330i \(-0.605740\pi\)
−0.326116 + 0.945330i \(0.605740\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3948.00 1.15435 0.577176 − 0.816620i \(-0.304155\pi\)
0.577176 + 0.816620i \(0.304155\pi\)
\(228\) 0 0
\(229\) −3522.00 −1.01633 −0.508167 − 0.861259i \(-0.669677\pi\)
−0.508167 + 0.861259i \(0.669677\pi\)
\(230\) 0 0
\(231\) 2160.00 0.615228
\(232\) 0 0
\(233\) 2774.00 0.779960 0.389980 − 0.920823i \(-0.372482\pi\)
0.389980 + 0.920823i \(0.372482\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1836.00 −0.503211
\(238\) 0 0
\(239\) 2784.00 0.753481 0.376741 − 0.926319i \(-0.377045\pi\)
0.376741 + 0.926319i \(0.377045\pi\)
\(240\) 0 0
\(241\) −4686.00 −1.25250 −0.626249 − 0.779623i \(-0.715410\pi\)
−0.626249 + 0.779623i \(0.715410\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5544.00 1.42816
\(248\) 0 0
\(249\) 1692.00 0.430627
\(250\) 0 0
\(251\) −2484.00 −0.624656 −0.312328 − 0.949974i \(-0.601109\pi\)
−0.312328 + 0.949974i \(0.601109\pi\)
\(252\) 0 0
\(253\) 2880.00 0.715668
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6658.00 −1.61601 −0.808005 − 0.589175i \(-0.799453\pi\)
−0.808005 + 0.589175i \(0.799453\pi\)
\(258\) 0 0
\(259\) −4344.00 −1.04217
\(260\) 0 0
\(261\) 2034.00 0.482381
\(262\) 0 0
\(263\) −2904.00 −0.680868 −0.340434 − 0.940268i \(-0.610574\pi\)
−0.340434 + 0.940268i \(0.610574\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 4530.00 1.03832
\(268\) 0 0
\(269\) −1006.00 −0.228018 −0.114009 − 0.993480i \(-0.536369\pi\)
−0.114009 + 0.993480i \(0.536369\pi\)
\(270\) 0 0
\(271\) 876.000 0.196359 0.0981794 − 0.995169i \(-0.468698\pi\)
0.0981794 + 0.995169i \(0.468698\pi\)
\(272\) 0 0
\(273\) 1512.00 0.335203
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2718.00 −0.589562 −0.294781 − 0.955565i \(-0.595247\pi\)
−0.294781 + 0.955565i \(0.595247\pi\)
\(278\) 0 0
\(279\) −2268.00 −0.486672
\(280\) 0 0
\(281\) 5354.00 1.13663 0.568315 − 0.822811i \(-0.307596\pi\)
0.568315 + 0.822811i \(0.307596\pi\)
\(282\) 0 0
\(283\) 780.000 0.163838 0.0819191 − 0.996639i \(-0.473895\pi\)
0.0819191 + 0.996639i \(0.473895\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1128.00 0.231999
\(288\) 0 0
\(289\) −4813.00 −0.979646
\(290\) 0 0
\(291\) 1782.00 0.358978
\(292\) 0 0
\(293\) 3350.00 0.667949 0.333975 − 0.942582i \(-0.391610\pi\)
0.333975 + 0.942582i \(0.391610\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1620.00 −0.316505
\(298\) 0 0
\(299\) 2016.00 0.389927
\(300\) 0 0
\(301\) −2736.00 −0.523922
\(302\) 0 0
\(303\) −1662.00 −0.315114
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9636.00 1.79139 0.895693 − 0.444673i \(-0.146680\pi\)
0.895693 + 0.444673i \(0.146680\pi\)
\(308\) 0 0
\(309\) 3852.00 0.709167
\(310\) 0 0
\(311\) −7560.00 −1.37842 −0.689209 − 0.724562i \(-0.742042\pi\)
−0.689209 + 0.724562i \(0.742042\pi\)
\(312\) 0 0
\(313\) 3526.00 0.636745 0.318373 − 0.947966i \(-0.396864\pi\)
0.318373 + 0.947966i \(0.396864\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7634.00 −1.35258 −0.676290 − 0.736635i \(-0.736414\pi\)
−0.676290 + 0.736635i \(0.736414\pi\)
\(318\) 0 0
\(319\) 13560.0 2.37998
\(320\) 0 0
\(321\) −4068.00 −0.707332
\(322\) 0 0
\(323\) −1320.00 −0.227389
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1170.00 −0.197863
\(328\) 0 0
\(329\) −4896.00 −0.820441
\(330\) 0 0
\(331\) 7572.00 1.25739 0.628693 − 0.777654i \(-0.283590\pi\)
0.628693 + 0.777654i \(0.283590\pi\)
\(332\) 0 0
\(333\) 3258.00 0.536148
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −162.000 −0.0261861 −0.0130930 − 0.999914i \(-0.504168\pi\)
−0.0130930 + 0.999914i \(0.504168\pi\)
\(338\) 0 0
\(339\) −2298.00 −0.368172
\(340\) 0 0
\(341\) −15120.0 −2.40116
\(342\) 0 0
\(343\) 6504.00 1.02386
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6636.00 −1.02663 −0.513313 − 0.858202i \(-0.671582\pi\)
−0.513313 + 0.858202i \(0.671582\pi\)
\(348\) 0 0
\(349\) 4430.00 0.679463 0.339731 − 0.940523i \(-0.389664\pi\)
0.339731 + 0.940523i \(0.389664\pi\)
\(350\) 0 0
\(351\) −1134.00 −0.172446
\(352\) 0 0
\(353\) −8402.00 −1.26684 −0.633418 − 0.773810i \(-0.718349\pi\)
−0.633418 + 0.773810i \(0.718349\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −360.000 −0.0533704
\(358\) 0 0
\(359\) 11520.0 1.69360 0.846800 − 0.531912i \(-0.178526\pi\)
0.846800 + 0.531912i \(0.178526\pi\)
\(360\) 0 0
\(361\) 10565.0 1.54031
\(362\) 0 0
\(363\) −6807.00 −0.984228
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 7404.00 1.05309 0.526547 − 0.850146i \(-0.323486\pi\)
0.526547 + 0.850146i \(0.323486\pi\)
\(368\) 0 0
\(369\) −846.000 −0.119352
\(370\) 0 0
\(371\) 4152.00 0.581027
\(372\) 0 0
\(373\) −1910.00 −0.265137 −0.132568 − 0.991174i \(-0.542322\pi\)
−0.132568 + 0.991174i \(0.542322\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9492.00 1.29672
\(378\) 0 0
\(379\) 10332.0 1.40031 0.700157 − 0.713989i \(-0.253113\pi\)
0.700157 + 0.713989i \(0.253113\pi\)
\(380\) 0 0
\(381\) −7164.00 −0.963315
\(382\) 0 0
\(383\) −6624.00 −0.883735 −0.441868 − 0.897080i \(-0.645684\pi\)
−0.441868 + 0.897080i \(0.645684\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2052.00 0.269532
\(388\) 0 0
\(389\) 10210.0 1.33076 0.665382 − 0.746503i \(-0.268268\pi\)
0.665382 + 0.746503i \(0.268268\pi\)
\(390\) 0 0
\(391\) −480.000 −0.0620835
\(392\) 0 0
\(393\) −1188.00 −0.152485
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4066.00 0.514022 0.257011 − 0.966408i \(-0.417262\pi\)
0.257011 + 0.966408i \(0.417262\pi\)
\(398\) 0 0
\(399\) 4752.00 0.596234
\(400\) 0 0
\(401\) −5510.00 −0.686175 −0.343088 − 0.939303i \(-0.611473\pi\)
−0.343088 + 0.939303i \(0.611473\pi\)
\(402\) 0 0
\(403\) −10584.0 −1.30825
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 21720.0 2.64526
\(408\) 0 0
\(409\) 15450.0 1.86786 0.933928 − 0.357460i \(-0.116357\pi\)
0.933928 + 0.357460i \(0.116357\pi\)
\(410\) 0 0
\(411\) −330.000 −0.0396051
\(412\) 0 0
\(413\) 3600.00 0.428921
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2196.00 0.257886
\(418\) 0 0
\(419\) −3084.00 −0.359578 −0.179789 − 0.983705i \(-0.557542\pi\)
−0.179789 + 0.983705i \(0.557542\pi\)
\(420\) 0 0
\(421\) 10446.0 1.20928 0.604640 − 0.796499i \(-0.293317\pi\)
0.604640 + 0.796499i \(0.293317\pi\)
\(422\) 0 0
\(423\) 3672.00 0.422077
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5592.00 0.633761
\(428\) 0 0
\(429\) −7560.00 −0.850816
\(430\) 0 0
\(431\) −2184.00 −0.244083 −0.122041 − 0.992525i \(-0.538944\pi\)
−0.122041 + 0.992525i \(0.538944\pi\)
\(432\) 0 0
\(433\) 110.000 0.0122085 0.00610423 − 0.999981i \(-0.498057\pi\)
0.00610423 + 0.999981i \(0.498057\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6336.00 0.693574
\(438\) 0 0
\(439\) −2412.00 −0.262229 −0.131114 − 0.991367i \(-0.541856\pi\)
−0.131114 + 0.991367i \(0.541856\pi\)
\(440\) 0 0
\(441\) −1791.00 −0.193392
\(442\) 0 0
\(443\) −6540.00 −0.701410 −0.350705 − 0.936486i \(-0.614058\pi\)
−0.350705 + 0.936486i \(0.614058\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5802.00 0.613927
\(448\) 0 0
\(449\) −9670.00 −1.01638 −0.508191 − 0.861244i \(-0.669686\pi\)
−0.508191 + 0.861244i \(0.669686\pi\)
\(450\) 0 0
\(451\) −5640.00 −0.588863
\(452\) 0 0
\(453\) 3276.00 0.339779
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6774.00 0.693379 0.346690 − 0.937980i \(-0.387306\pi\)
0.346690 + 0.937980i \(0.387306\pi\)
\(458\) 0 0
\(459\) 270.000 0.0274565
\(460\) 0 0
\(461\) 14602.0 1.47523 0.737617 − 0.675219i \(-0.235951\pi\)
0.737617 + 0.675219i \(0.235951\pi\)
\(462\) 0 0
\(463\) 13620.0 1.36712 0.683558 − 0.729896i \(-0.260431\pi\)
0.683558 + 0.729896i \(0.260431\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8508.00 0.843048 0.421524 − 0.906817i \(-0.361495\pi\)
0.421524 + 0.906817i \(0.361495\pi\)
\(468\) 0 0
\(469\) 2448.00 0.241019
\(470\) 0 0
\(471\) −1734.00 −0.169636
\(472\) 0 0
\(473\) 13680.0 1.32982
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3114.00 −0.298910
\(478\) 0 0
\(479\) 6312.00 0.602093 0.301047 − 0.953609i \(-0.402664\pi\)
0.301047 + 0.953609i \(0.402664\pi\)
\(480\) 0 0
\(481\) 15204.0 1.44125
\(482\) 0 0
\(483\) 1728.00 0.162788
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −10572.0 −0.983702 −0.491851 − 0.870679i \(-0.663680\pi\)
−0.491851 + 0.870679i \(0.663680\pi\)
\(488\) 0 0
\(489\) 7596.00 0.702460
\(490\) 0 0
\(491\) −4332.00 −0.398168 −0.199084 − 0.979982i \(-0.563797\pi\)
−0.199084 + 0.979982i \(0.563797\pi\)
\(492\) 0 0
\(493\) −2260.00 −0.206461
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −12672.0 −1.14370
\(498\) 0 0
\(499\) −3684.00 −0.330498 −0.165249 − 0.986252i \(-0.552843\pi\)
−0.165249 + 0.986252i \(0.552843\pi\)
\(500\) 0 0
\(501\) −1944.00 −0.173356
\(502\) 0 0
\(503\) 11184.0 0.991391 0.495696 − 0.868496i \(-0.334913\pi\)
0.495696 + 0.868496i \(0.334913\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1299.00 0.113788
\(508\) 0 0
\(509\) 12946.0 1.12735 0.563675 − 0.825997i \(-0.309387\pi\)
0.563675 + 0.825997i \(0.309387\pi\)
\(510\) 0 0
\(511\) 3960.00 0.342818
\(512\) 0 0
\(513\) −3564.00 −0.306734
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 24480.0 2.08245
\(518\) 0 0
\(519\) 10014.0 0.846948
\(520\) 0 0
\(521\) −17150.0 −1.44214 −0.721070 − 0.692862i \(-0.756349\pi\)
−0.721070 + 0.692862i \(0.756349\pi\)
\(522\) 0 0
\(523\) −7884.00 −0.659165 −0.329582 − 0.944127i \(-0.606908\pi\)
−0.329582 + 0.944127i \(0.606908\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2520.00 0.208298
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) −2700.00 −0.220659
\(532\) 0 0
\(533\) −3948.00 −0.320838
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −11412.0 −0.917065
\(538\) 0 0
\(539\) −11940.0 −0.954160
\(540\) 0 0
\(541\) 5910.00 0.469669 0.234834 − 0.972035i \(-0.424545\pi\)
0.234834 + 0.972035i \(0.424545\pi\)
\(542\) 0 0
\(543\) −5562.00 −0.439573
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 972.000 0.0759775 0.0379888 − 0.999278i \(-0.487905\pi\)
0.0379888 + 0.999278i \(0.487905\pi\)
\(548\) 0 0
\(549\) −4194.00 −0.326039
\(550\) 0 0
\(551\) 29832.0 2.30651
\(552\) 0 0
\(553\) −7344.00 −0.564735
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2458.00 −0.186982 −0.0934908 − 0.995620i \(-0.529803\pi\)
−0.0934908 + 0.995620i \(0.529803\pi\)
\(558\) 0 0
\(559\) 9576.00 0.724547
\(560\) 0 0
\(561\) 1800.00 0.135465
\(562\) 0 0
\(563\) −11316.0 −0.847092 −0.423546 − 0.905875i \(-0.639215\pi\)
−0.423546 + 0.905875i \(0.639215\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −972.000 −0.0719932
\(568\) 0 0
\(569\) 1810.00 0.133355 0.0666776 − 0.997775i \(-0.478760\pi\)
0.0666776 + 0.997775i \(0.478760\pi\)
\(570\) 0 0
\(571\) 10500.0 0.769547 0.384773 − 0.923011i \(-0.374280\pi\)
0.384773 + 0.923011i \(0.374280\pi\)
\(572\) 0 0
\(573\) −4032.00 −0.293960
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19438.0 1.40245 0.701226 − 0.712939i \(-0.252637\pi\)
0.701226 + 0.712939i \(0.252637\pi\)
\(578\) 0 0
\(579\) −3786.00 −0.271746
\(580\) 0 0
\(581\) 6768.00 0.483277
\(582\) 0 0
\(583\) −20760.0 −1.47477
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15084.0 1.06062 0.530309 − 0.847804i \(-0.322076\pi\)
0.530309 + 0.847804i \(0.322076\pi\)
\(588\) 0 0
\(589\) −33264.0 −2.32703
\(590\) 0 0
\(591\) −12882.0 −0.896607
\(592\) 0 0
\(593\) −5794.00 −0.401233 −0.200616 − 0.979670i \(-0.564294\pi\)
−0.200616 + 0.979670i \(0.564294\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −12924.0 −0.886004
\(598\) 0 0
\(599\) 25152.0 1.71566 0.857832 − 0.513930i \(-0.171811\pi\)
0.857832 + 0.513930i \(0.171811\pi\)
\(600\) 0 0
\(601\) −11846.0 −0.804007 −0.402004 − 0.915638i \(-0.631686\pi\)
−0.402004 + 0.915638i \(0.631686\pi\)
\(602\) 0 0
\(603\) −1836.00 −0.123993
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −8940.00 −0.597798 −0.298899 − 0.954285i \(-0.596619\pi\)
−0.298899 + 0.954285i \(0.596619\pi\)
\(608\) 0 0
\(609\) 8136.00 0.541359
\(610\) 0 0
\(611\) 17136.0 1.13461
\(612\) 0 0
\(613\) 4570.00 0.301110 0.150555 − 0.988602i \(-0.451894\pi\)
0.150555 + 0.988602i \(0.451894\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17786.0 −1.16051 −0.580257 − 0.814433i \(-0.697048\pi\)
−0.580257 + 0.814433i \(0.697048\pi\)
\(618\) 0 0
\(619\) −15804.0 −1.02620 −0.513099 − 0.858330i \(-0.671503\pi\)
−0.513099 + 0.858330i \(0.671503\pi\)
\(620\) 0 0
\(621\) −1296.00 −0.0837467
\(622\) 0 0
\(623\) 18120.0 1.16527
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −23760.0 −1.51337
\(628\) 0 0
\(629\) −3620.00 −0.229474
\(630\) 0 0
\(631\) −18468.0 −1.16513 −0.582567 − 0.812783i \(-0.697952\pi\)
−0.582567 + 0.812783i \(0.697952\pi\)
\(632\) 0 0
\(633\) −3636.00 −0.228307
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −8358.00 −0.519868
\(638\) 0 0
\(639\) 9504.00 0.588376
\(640\) 0 0
\(641\) −7814.00 −0.481489 −0.240744 − 0.970589i \(-0.577392\pi\)
−0.240744 + 0.970589i \(0.577392\pi\)
\(642\) 0 0
\(643\) −5364.00 −0.328982 −0.164491 − 0.986379i \(-0.552598\pi\)
−0.164491 + 0.986379i \(0.552598\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3936.00 0.239166 0.119583 − 0.992824i \(-0.461844\pi\)
0.119583 + 0.992824i \(0.461844\pi\)
\(648\) 0 0
\(649\) −18000.0 −1.08869
\(650\) 0 0
\(651\) −9072.00 −0.546175
\(652\) 0 0
\(653\) −7610.00 −0.456053 −0.228026 − 0.973655i \(-0.573227\pi\)
−0.228026 + 0.973655i \(0.573227\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2970.00 −0.176363
\(658\) 0 0
\(659\) −13620.0 −0.805098 −0.402549 − 0.915398i \(-0.631876\pi\)
−0.402549 + 0.915398i \(0.631876\pi\)
\(660\) 0 0
\(661\) 8710.00 0.512526 0.256263 − 0.966607i \(-0.417509\pi\)
0.256263 + 0.966607i \(0.417509\pi\)
\(662\) 0 0
\(663\) 1260.00 0.0738075
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10848.0 0.629739
\(668\) 0 0
\(669\) 6516.00 0.376567
\(670\) 0 0
\(671\) −27960.0 −1.60862
\(672\) 0 0
\(673\) 12094.0 0.692703 0.346352 − 0.938105i \(-0.387420\pi\)
0.346352 + 0.938105i \(0.387420\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16466.0 −0.934771 −0.467385 − 0.884054i \(-0.654804\pi\)
−0.467385 + 0.884054i \(0.654804\pi\)
\(678\) 0 0
\(679\) 7128.00 0.402868
\(680\) 0 0
\(681\) −11844.0 −0.666466
\(682\) 0 0
\(683\) −16428.0 −0.920351 −0.460176 − 0.887828i \(-0.652214\pi\)
−0.460176 + 0.887828i \(0.652214\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 10566.0 0.586780
\(688\) 0 0
\(689\) −14532.0 −0.803520
\(690\) 0 0
\(691\) 13332.0 0.733970 0.366985 − 0.930227i \(-0.380390\pi\)
0.366985 + 0.930227i \(0.380390\pi\)
\(692\) 0 0
\(693\) −6480.00 −0.355202
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 940.000 0.0510833
\(698\) 0 0
\(699\) −8322.00 −0.450310
\(700\) 0 0
\(701\) −19118.0 −1.03007 −0.515033 − 0.857170i \(-0.672221\pi\)
−0.515033 + 0.857170i \(0.672221\pi\)
\(702\) 0 0
\(703\) 47784.0 2.56360
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6648.00 −0.353640
\(708\) 0 0
\(709\) 798.000 0.0422701 0.0211351 − 0.999777i \(-0.493272\pi\)
0.0211351 + 0.999777i \(0.493272\pi\)
\(710\) 0 0
\(711\) 5508.00 0.290529
\(712\) 0 0
\(713\) −12096.0 −0.635342
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8352.00 −0.435023
\(718\) 0 0
\(719\) −8856.00 −0.459351 −0.229675 − 0.973267i \(-0.573766\pi\)
−0.229675 + 0.973267i \(0.573766\pi\)
\(720\) 0 0
\(721\) 15408.0 0.795872
\(722\) 0 0
\(723\) 14058.0 0.723130
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 13764.0 0.702171 0.351086 − 0.936343i \(-0.385813\pi\)
0.351086 + 0.936343i \(0.385813\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −2280.00 −0.115361
\(732\) 0 0
\(733\) 20538.0 1.03491 0.517455 − 0.855711i \(-0.326880\pi\)
0.517455 + 0.855711i \(0.326880\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12240.0 −0.611759
\(738\) 0 0
\(739\) 15900.0 0.791463 0.395731 − 0.918366i \(-0.370491\pi\)
0.395731 + 0.918366i \(0.370491\pi\)
\(740\) 0 0
\(741\) −16632.0 −0.824550
\(742\) 0 0
\(743\) 20856.0 1.02979 0.514894 − 0.857254i \(-0.327831\pi\)
0.514894 + 0.857254i \(0.327831\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5076.00 −0.248623
\(748\) 0 0
\(749\) −16272.0 −0.793813
\(750\) 0 0
\(751\) −10332.0 −0.502024 −0.251012 − 0.967984i \(-0.580763\pi\)
−0.251012 + 0.967984i \(0.580763\pi\)
\(752\) 0 0
\(753\) 7452.00 0.360645
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −13806.0 −0.662863 −0.331432 − 0.943479i \(-0.607532\pi\)
−0.331432 + 0.943479i \(0.607532\pi\)
\(758\) 0 0
\(759\) −8640.00 −0.413191
\(760\) 0 0
\(761\) 15554.0 0.740909 0.370455 − 0.928851i \(-0.379202\pi\)
0.370455 + 0.928851i \(0.379202\pi\)
\(762\) 0 0
\(763\) −4680.00 −0.222054
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12600.0 −0.593168
\(768\) 0 0
\(769\) 13106.0 0.614583 0.307292 − 0.951615i \(-0.400577\pi\)
0.307292 + 0.951615i \(0.400577\pi\)
\(770\) 0 0
\(771\) 19974.0 0.933004
\(772\) 0 0
\(773\) −18874.0 −0.878203 −0.439101 − 0.898438i \(-0.644703\pi\)
−0.439101 + 0.898438i \(0.644703\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 13032.0 0.601699
\(778\) 0 0
\(779\) −12408.0 −0.570684
\(780\) 0 0
\(781\) 63360.0 2.90294
\(782\) 0 0
\(783\) −6102.00 −0.278503
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −15444.0 −0.699516 −0.349758 − 0.936840i \(-0.613736\pi\)
−0.349758 + 0.936840i \(0.613736\pi\)
\(788\) 0 0
\(789\) 8712.00 0.393099
\(790\) 0 0
\(791\) −9192.00 −0.413186
\(792\) 0 0
\(793\) −19572.0 −0.876447
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 39286.0 1.74602 0.873012 − 0.487698i \(-0.162163\pi\)
0.873012 + 0.487698i \(0.162163\pi\)
\(798\) 0 0
\(799\) −4080.00 −0.180651
\(800\) 0 0
\(801\) −13590.0 −0.599474
\(802\) 0 0
\(803\) −19800.0 −0.870145
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 3018.00 0.131646
\(808\) 0 0
\(809\) 20018.0 0.869957 0.434979 − 0.900441i \(-0.356756\pi\)
0.434979 + 0.900441i \(0.356756\pi\)
\(810\) 0 0
\(811\) −8388.00 −0.363184 −0.181592 − 0.983374i \(-0.558125\pi\)
−0.181592 + 0.983374i \(0.558125\pi\)
\(812\) 0 0
\(813\) −2628.00 −0.113368
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 30096.0 1.28877
\(818\) 0 0
\(819\) −4536.00 −0.193530
\(820\) 0 0
\(821\) −37942.0 −1.61289 −0.806446 − 0.591307i \(-0.798612\pi\)
−0.806446 + 0.591307i \(0.798612\pi\)
\(822\) 0 0
\(823\) −11628.0 −0.492499 −0.246249 − 0.969206i \(-0.579198\pi\)
−0.246249 + 0.969206i \(0.579198\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32388.0 −1.36184 −0.680920 − 0.732358i \(-0.738420\pi\)
−0.680920 + 0.732358i \(0.738420\pi\)
\(828\) 0 0
\(829\) 9846.00 0.412504 0.206252 − 0.978499i \(-0.433873\pi\)
0.206252 + 0.978499i \(0.433873\pi\)
\(830\) 0 0
\(831\) 8154.00 0.340384
\(832\) 0 0
\(833\) 1990.00 0.0827724
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 6804.00 0.280980
\(838\) 0 0
\(839\) 16848.0 0.693275 0.346637 − 0.937999i \(-0.387323\pi\)
0.346637 + 0.937999i \(0.387323\pi\)
\(840\) 0 0
\(841\) 26687.0 1.09422
\(842\) 0 0
\(843\) −16062.0 −0.656233
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −27228.0 −1.10456
\(848\) 0 0
\(849\) −2340.00 −0.0945920
\(850\) 0 0
\(851\) 17376.0 0.699931
\(852\) 0 0
\(853\) −18214.0 −0.731108 −0.365554 − 0.930790i \(-0.619121\pi\)
−0.365554 + 0.930790i \(0.619121\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2446.00 0.0974956 0.0487478 − 0.998811i \(-0.484477\pi\)
0.0487478 + 0.998811i \(0.484477\pi\)
\(858\) 0 0
\(859\) −26244.0 −1.04241 −0.521207 − 0.853430i \(-0.674518\pi\)
−0.521207 + 0.853430i \(0.674518\pi\)
\(860\) 0 0
\(861\) −3384.00 −0.133945
\(862\) 0 0
\(863\) −25248.0 −0.995889 −0.497944 − 0.867209i \(-0.665912\pi\)
−0.497944 + 0.867209i \(0.665912\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 14439.0 0.565599
\(868\) 0 0
\(869\) 36720.0 1.43342
\(870\) 0 0
\(871\) −8568.00 −0.333313
\(872\) 0 0
\(873\) −5346.00 −0.207256
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 34.0000 0.00130912 0.000654560 − 1.00000i \(-0.499792\pi\)
0.000654560 1.00000i \(0.499792\pi\)
\(878\) 0 0
\(879\) −10050.0 −0.385641
\(880\) 0 0
\(881\) −19022.0 −0.727432 −0.363716 − 0.931510i \(-0.618492\pi\)
−0.363716 + 0.931510i \(0.618492\pi\)
\(882\) 0 0
\(883\) −12852.0 −0.489812 −0.244906 − 0.969547i \(-0.578757\pi\)
−0.244906 + 0.969547i \(0.578757\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40104.0 −1.51811 −0.759053 − 0.651028i \(-0.774338\pi\)
−0.759053 + 0.651028i \(0.774338\pi\)
\(888\) 0 0
\(889\) −28656.0 −1.08109
\(890\) 0 0
\(891\) 4860.00 0.182734
\(892\) 0 0
\(893\) 53856.0 2.01817
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −6048.00 −0.225125
\(898\) 0 0
\(899\) −56952.0 −2.11285
\(900\) 0 0
\(901\) 3460.00 0.127935
\(902\) 0 0
\(903\) 8208.00 0.302486
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −42540.0 −1.55735 −0.778676 − 0.627427i \(-0.784108\pi\)
−0.778676 + 0.627427i \(0.784108\pi\)
\(908\) 0 0
\(909\) 4986.00 0.181931
\(910\) 0 0
\(911\) −18528.0 −0.673831 −0.336915 − 0.941535i \(-0.609384\pi\)
−0.336915 + 0.941535i \(0.609384\pi\)
\(912\) 0 0
\(913\) −33840.0 −1.22666
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4752.00 −0.171129
\(918\) 0 0
\(919\) 15756.0 0.565552 0.282776 − 0.959186i \(-0.408745\pi\)
0.282776 + 0.959186i \(0.408745\pi\)
\(920\) 0 0
\(921\) −28908.0 −1.03426
\(922\) 0 0
\(923\) 44352.0 1.58165
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −11556.0 −0.409438
\(928\) 0 0
\(929\) −15542.0 −0.548887 −0.274444 − 0.961603i \(-0.588494\pi\)
−0.274444 + 0.961603i \(0.588494\pi\)
\(930\) 0 0
\(931\) −26268.0 −0.924703
\(932\) 0 0
\(933\) 22680.0 0.795831
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 29702.0 1.03556 0.517781 − 0.855513i \(-0.326758\pi\)
0.517781 + 0.855513i \(0.326758\pi\)
\(938\) 0 0
\(939\) −10578.0 −0.367625
\(940\) 0 0
\(941\) 2890.00 0.100118 0.0500591 − 0.998746i \(-0.484059\pi\)
0.0500591 + 0.998746i \(0.484059\pi\)
\(942\) 0 0
\(943\) −4512.00 −0.155812
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9180.00 −0.315005 −0.157503 − 0.987519i \(-0.550344\pi\)
−0.157503 + 0.987519i \(0.550344\pi\)
\(948\) 0 0
\(949\) −13860.0 −0.474093
\(950\) 0 0
\(951\) 22902.0 0.780913
\(952\) 0 0
\(953\) −37906.0 −1.28845 −0.644227 − 0.764835i \(-0.722821\pi\)
−0.644227 + 0.764835i \(0.722821\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −40680.0 −1.37408
\(958\) 0 0
\(959\) −1320.00 −0.0444474
\(960\) 0 0
\(961\) 33713.0 1.13165
\(962\) 0 0
\(963\) 12204.0 0.408378
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 41916.0 1.39393 0.696964 − 0.717106i \(-0.254534\pi\)
0.696964 + 0.717106i \(0.254534\pi\)
\(968\) 0 0
\(969\) 3960.00 0.131283
\(970\) 0 0
\(971\) −7764.00 −0.256600 −0.128300 − 0.991735i \(-0.540952\pi\)
−0.128300 + 0.991735i \(0.540952\pi\)
\(972\) 0 0
\(973\) 8784.00 0.289416
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32666.0 −1.06968 −0.534840 − 0.844953i \(-0.679628\pi\)
−0.534840 + 0.844953i \(0.679628\pi\)
\(978\) 0 0
\(979\) −90600.0 −2.95770
\(980\) 0 0
\(981\) 3510.00 0.114236
\(982\) 0 0
\(983\) 53016.0 1.72019 0.860096 − 0.510133i \(-0.170404\pi\)
0.860096 + 0.510133i \(0.170404\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 14688.0 0.473682
\(988\) 0 0
\(989\) 10944.0 0.351870
\(990\) 0 0
\(991\) 17844.0 0.571981 0.285991 − 0.958232i \(-0.407677\pi\)
0.285991 + 0.958232i \(0.407677\pi\)
\(992\) 0 0
\(993\) −22716.0 −0.725952
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 55834.0 1.77360 0.886801 − 0.462152i \(-0.152923\pi\)
0.886801 + 0.462152i \(0.152923\pi\)
\(998\) 0 0
\(999\) −9774.00 −0.309545
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.c.1.1 1
4.3 odd 2 2400.4.a.t.1.1 1
5.4 even 2 96.4.a.e.1.1 yes 1
15.14 odd 2 288.4.a.f.1.1 1
20.19 odd 2 96.4.a.b.1.1 ✓ 1
40.19 odd 2 192.4.a.j.1.1 1
40.29 even 2 192.4.a.d.1.1 1
60.59 even 2 288.4.a.e.1.1 1
80.19 odd 4 768.4.d.m.385.1 2
80.29 even 4 768.4.d.d.385.2 2
80.59 odd 4 768.4.d.m.385.2 2
80.69 even 4 768.4.d.d.385.1 2
120.29 odd 2 576.4.a.o.1.1 1
120.59 even 2 576.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.4.a.b.1.1 ✓ 1 20.19 odd 2
96.4.a.e.1.1 yes 1 5.4 even 2
192.4.a.d.1.1 1 40.29 even 2
192.4.a.j.1.1 1 40.19 odd 2
288.4.a.e.1.1 1 60.59 even 2
288.4.a.f.1.1 1 15.14 odd 2
576.4.a.n.1.1 1 120.59 even 2
576.4.a.o.1.1 1 120.29 odd 2
768.4.d.d.385.1 2 80.69 even 4
768.4.d.d.385.2 2 80.29 even 4
768.4.d.m.385.1 2 80.19 odd 4
768.4.d.m.385.2 2 80.59 odd 4
2400.4.a.c.1.1 1 1.1 even 1 trivial
2400.4.a.t.1.1 1 4.3 odd 2