Properties

Label 1440.4.a.bj.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
Analytic rank $1$
Dimension $3$
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] = [1440,4,Mod(1,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, 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("1440.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1440.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: \(84.9627504083\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.16773.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 17x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.14660\) of defining polynomial
Character \(\chi\) \(=\) 1440.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -22.5864 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -22.5864 q^{7} +6.39560 q^{11} +78.5364 q^{13} -56.1548 q^{17} -82.9180 q^{19} -10.2548 q^{23} +25.0000 q^{25} +135.836 q^{29} -44.2188 q^{31} -112.932 q^{35} +128.628 q^{37} -174.218 q^{41} +270.455 q^{43} -596.964 q^{47} +167.146 q^{49} -0.289677 q^{53} +31.9780 q^{55} +655.760 q^{59} +48.7433 q^{61} +392.682 q^{65} -358.755 q^{67} -97.3007 q^{71} -617.219 q^{73} -144.454 q^{77} -448.728 q^{79} +723.684 q^{83} -280.774 q^{85} +112.835 q^{89} -1773.86 q^{91} -414.590 q^{95} -396.743 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 15 q^{5} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 15 q^{5} - 14 q^{7} - 22 q^{11} + 8 q^{13} + 34 q^{17} + 4 q^{19} - 176 q^{23} + 75 q^{25} - 98 q^{29} - 88 q^{31} - 70 q^{35} + 284 q^{37} + 8 q^{41} - 504 q^{43} - 280 q^{47} - 409 q^{49} + 150 q^{53} - 110 q^{55} - 350 q^{59} + 350 q^{61} + 40 q^{65} - 804 q^{67} - 500 q^{71} - 486 q^{73} - 788 q^{77} - 1592 q^{79} + 684 q^{83} + 170 q^{85} + 668 q^{89} - 1920 q^{91} + 20 q^{95} - 1394 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −22.5864 −1.21955 −0.609776 0.792574i \(-0.708740\pi\)
−0.609776 + 0.792574i \(0.708740\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.39560 0.175304 0.0876521 0.996151i \(-0.472064\pi\)
0.0876521 + 0.996151i \(0.472064\pi\)
\(12\) 0 0
\(13\) 78.5364 1.67555 0.837773 0.546019i \(-0.183858\pi\)
0.837773 + 0.546019i \(0.183858\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −56.1548 −0.801150 −0.400575 0.916264i \(-0.631190\pi\)
−0.400575 + 0.916264i \(0.631190\pi\)
\(18\) 0 0
\(19\) −82.9180 −1.00119 −0.500597 0.865680i \(-0.666886\pi\)
−0.500597 + 0.865680i \(0.666886\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −10.2548 −0.0929681 −0.0464841 0.998919i \(-0.514802\pi\)
−0.0464841 + 0.998919i \(0.514802\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 135.836 0.869797 0.434899 0.900479i \(-0.356784\pi\)
0.434899 + 0.900479i \(0.356784\pi\)
\(30\) 0 0
\(31\) −44.2188 −0.256191 −0.128096 0.991762i \(-0.540886\pi\)
−0.128096 + 0.991762i \(0.540886\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −112.932 −0.545400
\(36\) 0 0
\(37\) 128.628 0.571524 0.285762 0.958301i \(-0.407753\pi\)
0.285762 + 0.958301i \(0.407753\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −174.218 −0.663615 −0.331808 0.943347i \(-0.607659\pi\)
−0.331808 + 0.943347i \(0.607659\pi\)
\(42\) 0 0
\(43\) 270.455 0.959164 0.479582 0.877497i \(-0.340788\pi\)
0.479582 + 0.877497i \(0.340788\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −596.964 −1.85268 −0.926342 0.376684i \(-0.877064\pi\)
−0.926342 + 0.376684i \(0.877064\pi\)
\(48\) 0 0
\(49\) 167.146 0.487305
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.289677 −0.000750759 0 −0.000375379 1.00000i \(-0.500119\pi\)
−0.000375379 1.00000i \(0.500119\pi\)
\(54\) 0 0
\(55\) 31.9780 0.0783984
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 655.760 1.44699 0.723497 0.690327i \(-0.242533\pi\)
0.723497 + 0.690327i \(0.242533\pi\)
\(60\) 0 0
\(61\) 48.7433 0.102310 0.0511552 0.998691i \(-0.483710\pi\)
0.0511552 + 0.998691i \(0.483710\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 392.682 0.749327
\(66\) 0 0
\(67\) −358.755 −0.654163 −0.327082 0.944996i \(-0.606065\pi\)
−0.327082 + 0.944996i \(0.606065\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −97.3007 −0.162640 −0.0813202 0.996688i \(-0.525914\pi\)
−0.0813202 + 0.996688i \(0.525914\pi\)
\(72\) 0 0
\(73\) −617.219 −0.989589 −0.494794 0.869010i \(-0.664757\pi\)
−0.494794 + 0.869010i \(0.664757\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −144.454 −0.213792
\(78\) 0 0
\(79\) −448.728 −0.639062 −0.319531 0.947576i \(-0.603525\pi\)
−0.319531 + 0.947576i \(0.603525\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 723.684 0.957044 0.478522 0.878076i \(-0.341173\pi\)
0.478522 + 0.878076i \(0.341173\pi\)
\(84\) 0 0
\(85\) −280.774 −0.358285
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 112.835 0.134388 0.0671939 0.997740i \(-0.478595\pi\)
0.0671939 + 0.997740i \(0.478595\pi\)
\(90\) 0 0
\(91\) −1773.86 −2.04341
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −414.590 −0.447748
\(96\) 0 0
\(97\) −396.743 −0.415290 −0.207645 0.978204i \(-0.566580\pi\)
−0.207645 + 0.978204i \(0.566580\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1816.33 −1.78942 −0.894712 0.446643i \(-0.852619\pi\)
−0.894712 + 0.446643i \(0.852619\pi\)
\(102\) 0 0
\(103\) −1467.15 −1.40352 −0.701759 0.712414i \(-0.747602\pi\)
−0.701759 + 0.712414i \(0.747602\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1216.78 −1.09935 −0.549674 0.835379i \(-0.685248\pi\)
−0.549674 + 0.835379i \(0.685248\pi\)
\(108\) 0 0
\(109\) −1210.40 −1.06363 −0.531813 0.846862i \(-0.678489\pi\)
−0.531813 + 0.846862i \(0.678489\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2382.43 1.98336 0.991682 0.128712i \(-0.0410842\pi\)
0.991682 + 0.128712i \(0.0410842\pi\)
\(114\) 0 0
\(115\) −51.2738 −0.0415766
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1268.34 0.977043
\(120\) 0 0
\(121\) −1290.10 −0.969268
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1855.59 −1.29651 −0.648255 0.761423i \(-0.724501\pi\)
−0.648255 + 0.761423i \(0.724501\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 289.842 0.193310 0.0966550 0.995318i \(-0.469186\pi\)
0.0966550 + 0.995318i \(0.469186\pi\)
\(132\) 0 0
\(133\) 1872.82 1.22101
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1193.52 −0.744303 −0.372152 0.928172i \(-0.621380\pi\)
−0.372152 + 0.928172i \(0.621380\pi\)
\(138\) 0 0
\(139\) −709.062 −0.432675 −0.216338 0.976319i \(-0.569411\pi\)
−0.216338 + 0.976319i \(0.569411\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 502.288 0.293730
\(144\) 0 0
\(145\) 679.180 0.388985
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1658.38 −0.911809 −0.455905 0.890029i \(-0.650684\pi\)
−0.455905 + 0.890029i \(0.650684\pi\)
\(150\) 0 0
\(151\) 1180.56 0.636242 0.318121 0.948050i \(-0.396948\pi\)
0.318121 + 0.948050i \(0.396948\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −221.094 −0.114572
\(156\) 0 0
\(157\) 683.954 0.347678 0.173839 0.984774i \(-0.444383\pi\)
0.173839 + 0.984774i \(0.444383\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 231.618 0.113379
\(162\) 0 0
\(163\) −2452.67 −1.17858 −0.589288 0.807923i \(-0.700592\pi\)
−0.589288 + 0.807923i \(0.700592\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2855.65 1.32321 0.661606 0.749851i \(-0.269875\pi\)
0.661606 + 0.749851i \(0.269875\pi\)
\(168\) 0 0
\(169\) 3970.97 1.80745
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3596.35 1.58049 0.790247 0.612789i \(-0.209952\pi\)
0.790247 + 0.612789i \(0.209952\pi\)
\(174\) 0 0
\(175\) −564.660 −0.243910
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1281.58 −0.535139 −0.267570 0.963539i \(-0.586221\pi\)
−0.267570 + 0.963539i \(0.586221\pi\)
\(180\) 0 0
\(181\) 2385.39 0.979583 0.489791 0.871840i \(-0.337073\pi\)
0.489791 + 0.871840i \(0.337073\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 643.142 0.255593
\(186\) 0 0
\(187\) −359.144 −0.140445
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −929.171 −0.352002 −0.176001 0.984390i \(-0.556316\pi\)
−0.176001 + 0.984390i \(0.556316\pi\)
\(192\) 0 0
\(193\) −2126.98 −0.793282 −0.396641 0.917974i \(-0.629824\pi\)
−0.396641 + 0.917974i \(0.629824\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1655.73 −0.598811 −0.299406 0.954126i \(-0.596788\pi\)
−0.299406 + 0.954126i \(0.596788\pi\)
\(198\) 0 0
\(199\) −5009.24 −1.78440 −0.892201 0.451639i \(-0.850840\pi\)
−0.892201 + 0.451639i \(0.850840\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3068.05 −1.06076
\(204\) 0 0
\(205\) −871.088 −0.296778
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −530.311 −0.175514
\(210\) 0 0
\(211\) −4958.57 −1.61783 −0.808915 0.587925i \(-0.799945\pi\)
−0.808915 + 0.587925i \(0.799945\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1352.28 0.428951
\(216\) 0 0
\(217\) 998.743 0.312438
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4410.20 −1.34236
\(222\) 0 0
\(223\) −4155.51 −1.24786 −0.623931 0.781479i \(-0.714465\pi\)
−0.623931 + 0.781479i \(0.714465\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5168.08 1.51109 0.755545 0.655096i \(-0.227372\pi\)
0.755545 + 0.655096i \(0.227372\pi\)
\(228\) 0 0
\(229\) −4391.41 −1.26722 −0.633608 0.773654i \(-0.718427\pi\)
−0.633608 + 0.773654i \(0.718427\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2756.05 0.774913 0.387456 0.921888i \(-0.373354\pi\)
0.387456 + 0.921888i \(0.373354\pi\)
\(234\) 0 0
\(235\) −2984.82 −0.828545
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4742.41 −1.28352 −0.641759 0.766906i \(-0.721795\pi\)
−0.641759 + 0.766906i \(0.721795\pi\)
\(240\) 0 0
\(241\) 1389.76 0.371461 0.185730 0.982601i \(-0.440535\pi\)
0.185730 + 0.982601i \(0.440535\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 835.729 0.217930
\(246\) 0 0
\(247\) −6512.09 −1.67755
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5966.89 −1.50051 −0.750253 0.661151i \(-0.770068\pi\)
−0.750253 + 0.661151i \(0.770068\pi\)
\(252\) 0 0
\(253\) −65.5854 −0.0162977
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4707.74 1.14265 0.571324 0.820725i \(-0.306430\pi\)
0.571324 + 0.820725i \(0.306430\pi\)
\(258\) 0 0
\(259\) −2905.25 −0.697002
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1137.88 −0.266787 −0.133393 0.991063i \(-0.542587\pi\)
−0.133393 + 0.991063i \(0.542587\pi\)
\(264\) 0 0
\(265\) −1.44839 −0.000335749 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2700.80 −0.612158 −0.306079 0.952006i \(-0.599017\pi\)
−0.306079 + 0.952006i \(0.599017\pi\)
\(270\) 0 0
\(271\) −521.725 −0.116947 −0.0584734 0.998289i \(-0.518623\pi\)
−0.0584734 + 0.998289i \(0.518623\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 159.890 0.0350608
\(276\) 0 0
\(277\) −2017.18 −0.437548 −0.218774 0.975776i \(-0.570206\pi\)
−0.218774 + 0.975776i \(0.570206\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3532.33 0.749898 0.374949 0.927045i \(-0.377660\pi\)
0.374949 + 0.927045i \(0.377660\pi\)
\(282\) 0 0
\(283\) −1839.14 −0.386309 −0.193155 0.981168i \(-0.561872\pi\)
−0.193155 + 0.981168i \(0.561872\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3934.95 0.809313
\(288\) 0 0
\(289\) −1759.64 −0.358159
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8569.30 −1.70861 −0.854307 0.519769i \(-0.826018\pi\)
−0.854307 + 0.519769i \(0.826018\pi\)
\(294\) 0 0
\(295\) 3278.80 0.647116
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −805.373 −0.155772
\(300\) 0 0
\(301\) −6108.61 −1.16975
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 243.716 0.0457546
\(306\) 0 0
\(307\) 4574.84 0.850488 0.425244 0.905079i \(-0.360188\pi\)
0.425244 + 0.905079i \(0.360188\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2963.60 −0.540355 −0.270177 0.962811i \(-0.587082\pi\)
−0.270177 + 0.962811i \(0.587082\pi\)
\(312\) 0 0
\(313\) 2131.23 0.384869 0.192435 0.981310i \(-0.438362\pi\)
0.192435 + 0.981310i \(0.438362\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8492.05 −1.50461 −0.752305 0.658815i \(-0.771058\pi\)
−0.752305 + 0.658815i \(0.771058\pi\)
\(318\) 0 0
\(319\) 868.753 0.152479
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4656.25 0.802107
\(324\) 0 0
\(325\) 1963.41 0.335109
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13483.3 2.25944
\(330\) 0 0
\(331\) −6073.88 −1.00861 −0.504306 0.863525i \(-0.668252\pi\)
−0.504306 + 0.863525i \(0.668252\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1793.78 −0.292551
\(336\) 0 0
\(337\) −6616.84 −1.06956 −0.534781 0.844991i \(-0.679606\pi\)
−0.534781 + 0.844991i \(0.679606\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −282.806 −0.0449114
\(342\) 0 0
\(343\) 3971.92 0.625257
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6346.58 0.981850 0.490925 0.871202i \(-0.336659\pi\)
0.490925 + 0.871202i \(0.336659\pi\)
\(348\) 0 0
\(349\) 4000.58 0.613599 0.306799 0.951774i \(-0.400742\pi\)
0.306799 + 0.951774i \(0.400742\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −952.711 −0.143648 −0.0718239 0.997417i \(-0.522882\pi\)
−0.0718239 + 0.997417i \(0.522882\pi\)
\(354\) 0 0
\(355\) −486.504 −0.0727350
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3226.49 0.474339 0.237169 0.971468i \(-0.423780\pi\)
0.237169 + 0.971468i \(0.423780\pi\)
\(360\) 0 0
\(361\) 16.4016 0.00239125
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3086.09 −0.442557
\(366\) 0 0
\(367\) −9864.26 −1.40303 −0.701513 0.712657i \(-0.747492\pi\)
−0.701513 + 0.712657i \(0.747492\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.54276 0.000915589 0
\(372\) 0 0
\(373\) −4388.19 −0.609147 −0.304573 0.952489i \(-0.598514\pi\)
−0.304573 + 0.952489i \(0.598514\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10668.1 1.45738
\(378\) 0 0
\(379\) 4973.16 0.674022 0.337011 0.941501i \(-0.390584\pi\)
0.337011 + 0.941501i \(0.390584\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4210.82 −0.561783 −0.280892 0.959739i \(-0.590630\pi\)
−0.280892 + 0.959739i \(0.590630\pi\)
\(384\) 0 0
\(385\) −722.268 −0.0956109
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1520.60 −0.198194 −0.0990972 0.995078i \(-0.531595\pi\)
−0.0990972 + 0.995078i \(0.531595\pi\)
\(390\) 0 0
\(391\) 575.855 0.0744814
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2243.64 −0.285797
\(396\) 0 0
\(397\) 8353.74 1.05608 0.528038 0.849221i \(-0.322928\pi\)
0.528038 + 0.849221i \(0.322928\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3496.50 0.435429 0.217714 0.976012i \(-0.430140\pi\)
0.217714 + 0.976012i \(0.430140\pi\)
\(402\) 0 0
\(403\) −3472.78 −0.429260
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 822.655 0.100190
\(408\) 0 0
\(409\) −1233.74 −0.149155 −0.0745777 0.997215i \(-0.523761\pi\)
−0.0745777 + 0.997215i \(0.523761\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14811.3 −1.76468
\(414\) 0 0
\(415\) 3618.42 0.428003
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13879.9 1.61832 0.809159 0.587590i \(-0.199923\pi\)
0.809159 + 0.587590i \(0.199923\pi\)
\(420\) 0 0
\(421\) 9607.40 1.11220 0.556100 0.831116i \(-0.312297\pi\)
0.556100 + 0.831116i \(0.312297\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1403.87 −0.160230
\(426\) 0 0
\(427\) −1100.94 −0.124773
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13349.8 −1.49196 −0.745981 0.665968i \(-0.768019\pi\)
−0.745981 + 0.665968i \(0.768019\pi\)
\(432\) 0 0
\(433\) 7546.88 0.837598 0.418799 0.908079i \(-0.362451\pi\)
0.418799 + 0.908079i \(0.362451\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 850.305 0.0930792
\(438\) 0 0
\(439\) −9884.96 −1.07468 −0.537339 0.843367i \(-0.680570\pi\)
−0.537339 + 0.843367i \(0.680570\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4358.12 0.467405 0.233703 0.972308i \(-0.424916\pi\)
0.233703 + 0.972308i \(0.424916\pi\)
\(444\) 0 0
\(445\) 564.176 0.0601000
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4821.91 −0.506816 −0.253408 0.967360i \(-0.581551\pi\)
−0.253408 + 0.967360i \(0.581551\pi\)
\(450\) 0 0
\(451\) −1114.23 −0.116335
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8869.28 −0.913842
\(456\) 0 0
\(457\) 7952.00 0.813958 0.406979 0.913438i \(-0.366582\pi\)
0.406979 + 0.913438i \(0.366582\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14851.4 1.50043 0.750215 0.661194i \(-0.229950\pi\)
0.750215 + 0.661194i \(0.229950\pi\)
\(462\) 0 0
\(463\) 6129.34 0.615237 0.307618 0.951510i \(-0.400468\pi\)
0.307618 + 0.951510i \(0.400468\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8441.69 −0.836477 −0.418238 0.908337i \(-0.637352\pi\)
−0.418238 + 0.908337i \(0.637352\pi\)
\(468\) 0 0
\(469\) 8102.99 0.797785
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1729.72 0.168145
\(474\) 0 0
\(475\) −2072.95 −0.200239
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18616.3 1.77579 0.887894 0.460049i \(-0.152168\pi\)
0.887894 + 0.460049i \(0.152168\pi\)
\(480\) 0 0
\(481\) 10102.0 0.957614
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1983.72 −0.185724
\(486\) 0 0
\(487\) 16711.5 1.55497 0.777484 0.628903i \(-0.216496\pi\)
0.777484 + 0.628903i \(0.216496\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2982.33 −0.274115 −0.137058 0.990563i \(-0.543765\pi\)
−0.137058 + 0.990563i \(0.543765\pi\)
\(492\) 0 0
\(493\) −7627.85 −0.696838
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2197.67 0.198348
\(498\) 0 0
\(499\) 10128.7 0.908662 0.454331 0.890833i \(-0.349878\pi\)
0.454331 + 0.890833i \(0.349878\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 20086.0 1.78050 0.890249 0.455475i \(-0.150530\pi\)
0.890249 + 0.455475i \(0.150530\pi\)
\(504\) 0 0
\(505\) −9081.67 −0.800255
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14570.7 −1.26883 −0.634416 0.772992i \(-0.718759\pi\)
−0.634416 + 0.772992i \(0.718759\pi\)
\(510\) 0 0
\(511\) 13940.7 1.20685
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7335.74 −0.627672
\(516\) 0 0
\(517\) −3817.94 −0.324783
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16023.8 1.34743 0.673717 0.738989i \(-0.264697\pi\)
0.673717 + 0.738989i \(0.264697\pi\)
\(522\) 0 0
\(523\) 18506.3 1.54727 0.773636 0.633631i \(-0.218436\pi\)
0.773636 + 0.633631i \(0.218436\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2483.10 0.205247
\(528\) 0 0
\(529\) −12061.8 −0.991357
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13682.4 −1.11192
\(534\) 0 0
\(535\) −6083.88 −0.491643
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1069.00 0.0854266
\(540\) 0 0
\(541\) −20604.1 −1.63741 −0.818704 0.574216i \(-0.805307\pi\)
−0.818704 + 0.574216i \(0.805307\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6051.99 −0.475668
\(546\) 0 0
\(547\) 18362.0 1.43529 0.717646 0.696408i \(-0.245220\pi\)
0.717646 + 0.696408i \(0.245220\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11263.3 −0.870837
\(552\) 0 0
\(553\) 10135.2 0.779369
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6329.02 0.481452 0.240726 0.970593i \(-0.422614\pi\)
0.240726 + 0.970593i \(0.422614\pi\)
\(558\) 0 0
\(559\) 21240.6 1.60712
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9929.10 −0.743271 −0.371635 0.928379i \(-0.621203\pi\)
−0.371635 + 0.928379i \(0.621203\pi\)
\(564\) 0 0
\(565\) 11912.1 0.886987
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12881.6 0.949074 0.474537 0.880236i \(-0.342615\pi\)
0.474537 + 0.880236i \(0.342615\pi\)
\(570\) 0 0
\(571\) 16052.6 1.17650 0.588251 0.808679i \(-0.299817\pi\)
0.588251 + 0.808679i \(0.299817\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −256.369 −0.0185936
\(576\) 0 0
\(577\) −21368.2 −1.54172 −0.770858 0.637007i \(-0.780172\pi\)
−0.770858 + 0.637007i \(0.780172\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16345.4 −1.16716
\(582\) 0 0
\(583\) −1.85266 −0.000131611 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13913.6 0.978321 0.489160 0.872194i \(-0.337303\pi\)
0.489160 + 0.872194i \(0.337303\pi\)
\(588\) 0 0
\(589\) 3666.53 0.256497
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5244.77 0.363199 0.181600 0.983373i \(-0.441873\pi\)
0.181600 + 0.983373i \(0.441873\pi\)
\(594\) 0 0
\(595\) 6341.68 0.436947
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3140.90 0.214246 0.107123 0.994246i \(-0.465836\pi\)
0.107123 + 0.994246i \(0.465836\pi\)
\(600\) 0 0
\(601\) −22736.7 −1.54317 −0.771587 0.636124i \(-0.780537\pi\)
−0.771587 + 0.636124i \(0.780537\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6450.48 −0.433470
\(606\) 0 0
\(607\) −27.5200 −0.00184020 −0.000920102 1.00000i \(-0.500293\pi\)
−0.000920102 1.00000i \(0.500293\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −46883.4 −3.10425
\(612\) 0 0
\(613\) −10729.4 −0.706944 −0.353472 0.935445i \(-0.614999\pi\)
−0.353472 + 0.935445i \(0.614999\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9914.94 0.646937 0.323469 0.946239i \(-0.395151\pi\)
0.323469 + 0.946239i \(0.395151\pi\)
\(618\) 0 0
\(619\) −6432.47 −0.417678 −0.208839 0.977950i \(-0.566969\pi\)
−0.208839 + 0.977950i \(0.566969\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2548.54 −0.163893
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7223.10 −0.457876
\(630\) 0 0
\(631\) 19656.6 1.24012 0.620061 0.784554i \(-0.287108\pi\)
0.620061 + 0.784554i \(0.287108\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9277.94 −0.579817
\(636\) 0 0
\(637\) 13127.0 0.816502
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16342.0 1.00698 0.503488 0.864002i \(-0.332050\pi\)
0.503488 + 0.864002i \(0.332050\pi\)
\(642\) 0 0
\(643\) −3375.38 −0.207017 −0.103508 0.994629i \(-0.533007\pi\)
−0.103508 + 0.994629i \(0.533007\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13862.2 0.842319 0.421160 0.906986i \(-0.361623\pi\)
0.421160 + 0.906986i \(0.361623\pi\)
\(648\) 0 0
\(649\) 4193.98 0.253664
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14818.2 0.888025 0.444013 0.896021i \(-0.353555\pi\)
0.444013 + 0.896021i \(0.353555\pi\)
\(654\) 0 0
\(655\) 1449.21 0.0864509
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4730.05 −0.279600 −0.139800 0.990180i \(-0.544646\pi\)
−0.139800 + 0.990180i \(0.544646\pi\)
\(660\) 0 0
\(661\) 10646.7 0.626486 0.313243 0.949673i \(-0.398585\pi\)
0.313243 + 0.949673i \(0.398585\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9364.10 0.546052
\(666\) 0 0
\(667\) −1392.97 −0.0808635
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 311.742 0.0179354
\(672\) 0 0
\(673\) −4179.96 −0.239414 −0.119707 0.992809i \(-0.538196\pi\)
−0.119707 + 0.992809i \(0.538196\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31610.0 −1.79449 −0.897245 0.441534i \(-0.854435\pi\)
−0.897245 + 0.441534i \(0.854435\pi\)
\(678\) 0 0
\(679\) 8961.00 0.506468
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12901.6 0.722790 0.361395 0.932413i \(-0.382301\pi\)
0.361395 + 0.932413i \(0.382301\pi\)
\(684\) 0 0
\(685\) −5967.61 −0.332862
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −22.7502 −0.00125793
\(690\) 0 0
\(691\) 5650.46 0.311076 0.155538 0.987830i \(-0.450289\pi\)
0.155538 + 0.987830i \(0.450289\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3545.31 −0.193498
\(696\) 0 0
\(697\) 9783.16 0.531655
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −17485.6 −0.942112 −0.471056 0.882103i \(-0.656127\pi\)
−0.471056 + 0.882103i \(0.656127\pi\)
\(702\) 0 0
\(703\) −10665.6 −0.572207
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 41024.4 2.18230
\(708\) 0 0
\(709\) −21485.3 −1.13808 −0.569039 0.822310i \(-0.692685\pi\)
−0.569039 + 0.822310i \(0.692685\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 453.453 0.0238176
\(714\) 0 0
\(715\) 2511.44 0.131360
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3342.83 0.173389 0.0866944 0.996235i \(-0.472370\pi\)
0.0866944 + 0.996235i \(0.472370\pi\)
\(720\) 0 0
\(721\) 33137.6 1.71166
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3395.90 0.173959
\(726\) 0 0
\(727\) 29934.3 1.52710 0.763549 0.645750i \(-0.223455\pi\)
0.763549 + 0.645750i \(0.223455\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15187.4 −0.768434
\(732\) 0 0
\(733\) 8732.45 0.440028 0.220014 0.975497i \(-0.429390\pi\)
0.220014 + 0.975497i \(0.429390\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2294.45 −0.114677
\(738\) 0 0
\(739\) 25004.3 1.24465 0.622327 0.782758i \(-0.286188\pi\)
0.622327 + 0.782758i \(0.286188\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29841.4 −1.47345 −0.736727 0.676190i \(-0.763630\pi\)
−0.736727 + 0.676190i \(0.763630\pi\)
\(744\) 0 0
\(745\) −8291.89 −0.407773
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 27482.6 1.34071
\(750\) 0 0
\(751\) −16131.9 −0.783836 −0.391918 0.920000i \(-0.628188\pi\)
−0.391918 + 0.920000i \(0.628188\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5902.80 0.284536
\(756\) 0 0
\(757\) 9728.98 0.467115 0.233557 0.972343i \(-0.424963\pi\)
0.233557 + 0.972343i \(0.424963\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12912.5 −0.615082 −0.307541 0.951535i \(-0.599506\pi\)
−0.307541 + 0.951535i \(0.599506\pi\)
\(762\) 0 0
\(763\) 27338.6 1.29715
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 51501.0 2.42450
\(768\) 0 0
\(769\) 32798.5 1.53803 0.769014 0.639232i \(-0.220747\pi\)
0.769014 + 0.639232i \(0.220747\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3174.82 −0.147724 −0.0738618 0.997268i \(-0.523532\pi\)
−0.0738618 + 0.997268i \(0.523532\pi\)
\(774\) 0 0
\(775\) −1105.47 −0.0512382
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 14445.8 0.664408
\(780\) 0 0
\(781\) −622.297 −0.0285115
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3419.77 0.155487
\(786\) 0 0
\(787\) −18315.6 −0.829582 −0.414791 0.909917i \(-0.636145\pi\)
−0.414791 + 0.909917i \(0.636145\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −53810.5 −2.41881
\(792\) 0 0
\(793\) 3828.12 0.171426
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 32597.9 1.44878 0.724389 0.689391i \(-0.242122\pi\)
0.724389 + 0.689391i \(0.242122\pi\)
\(798\) 0 0
\(799\) 33522.4 1.48428
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3947.48 −0.173479
\(804\) 0 0
\(805\) 1158.09 0.0507048
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −11753.1 −0.510774 −0.255387 0.966839i \(-0.582203\pi\)
−0.255387 + 0.966839i \(0.582203\pi\)
\(810\) 0 0
\(811\) 35501.2 1.53713 0.768567 0.639769i \(-0.220970\pi\)
0.768567 + 0.639769i \(0.220970\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −12263.4 −0.527076
\(816\) 0 0
\(817\) −22425.6 −0.960310
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −25528.6 −1.08520 −0.542602 0.839990i \(-0.682561\pi\)
−0.542602 + 0.839990i \(0.682561\pi\)
\(822\) 0 0
\(823\) 30522.5 1.29277 0.646384 0.763013i \(-0.276281\pi\)
0.646384 + 0.763013i \(0.276281\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 43126.4 1.81336 0.906682 0.421814i \(-0.138606\pi\)
0.906682 + 0.421814i \(0.138606\pi\)
\(828\) 0 0
\(829\) −19469.8 −0.815699 −0.407849 0.913049i \(-0.633721\pi\)
−0.407849 + 0.913049i \(0.633721\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −9386.04 −0.390404
\(834\) 0 0
\(835\) 14278.2 0.591759
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −21999.5 −0.905252 −0.452626 0.891700i \(-0.649513\pi\)
−0.452626 + 0.891700i \(0.649513\pi\)
\(840\) 0 0
\(841\) −5937.56 −0.243452
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 19854.9 0.808317
\(846\) 0 0
\(847\) 29138.6 1.18207
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1319.05 −0.0531335
\(852\) 0 0
\(853\) −4233.65 −0.169938 −0.0849691 0.996384i \(-0.527079\pi\)
−0.0849691 + 0.996384i \(0.527079\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −26604.8 −1.06045 −0.530223 0.847858i \(-0.677892\pi\)
−0.530223 + 0.847858i \(0.677892\pi\)
\(858\) 0 0
\(859\) −32033.5 −1.27237 −0.636187 0.771535i \(-0.719489\pi\)
−0.636187 + 0.771535i \(0.719489\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 34015.1 1.34170 0.670851 0.741592i \(-0.265929\pi\)
0.670851 + 0.741592i \(0.265929\pi\)
\(864\) 0 0
\(865\) 17981.7 0.706818
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2869.89 −0.112030
\(870\) 0 0
\(871\) −28175.4 −1.09608
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2823.30 −0.109080
\(876\) 0 0
\(877\) 34479.6 1.32759 0.663793 0.747916i \(-0.268946\pi\)
0.663793 + 0.747916i \(0.268946\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −33877.5 −1.29553 −0.647765 0.761841i \(-0.724296\pi\)
−0.647765 + 0.761841i \(0.724296\pi\)
\(882\) 0 0
\(883\) 3423.93 0.130492 0.0652460 0.997869i \(-0.479217\pi\)
0.0652460 + 0.997869i \(0.479217\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 38158.8 1.44447 0.722237 0.691646i \(-0.243114\pi\)
0.722237 + 0.691646i \(0.243114\pi\)
\(888\) 0 0
\(889\) 41911.0 1.58116
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 49499.1 1.85490
\(894\) 0 0
\(895\) −6407.91 −0.239322
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6006.51 −0.222834
\(900\) 0 0
\(901\) 16.2668 0.000601470 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 11926.9 0.438083
\(906\) 0 0
\(907\) −5349.09 −0.195826 −0.0979128 0.995195i \(-0.531217\pi\)
−0.0979128 + 0.995195i \(0.531217\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −53491.9 −1.94541 −0.972703 0.232054i \(-0.925455\pi\)
−0.972703 + 0.232054i \(0.925455\pi\)
\(912\) 0 0
\(913\) 4628.39 0.167774
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −6546.49 −0.235752
\(918\) 0 0
\(919\) −30116.2 −1.08100 −0.540502 0.841343i \(-0.681766\pi\)
−0.540502 + 0.841343i \(0.681766\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −7641.65 −0.272511
\(924\) 0 0
\(925\) 3215.71 0.114305
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3791.12 −0.133889 −0.0669444 0.997757i \(-0.521325\pi\)
−0.0669444 + 0.997757i \(0.521325\pi\)
\(930\) 0 0
\(931\) −13859.4 −0.487888
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1795.72 −0.0628088
\(936\) 0 0
\(937\) −38027.5 −1.32583 −0.662916 0.748693i \(-0.730682\pi\)
−0.662916 + 0.748693i \(0.730682\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 25378.5 0.879187 0.439594 0.898197i \(-0.355122\pi\)
0.439594 + 0.898197i \(0.355122\pi\)
\(942\) 0 0
\(943\) 1786.56 0.0616951
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18643.7 0.639744 0.319872 0.947461i \(-0.396360\pi\)
0.319872 + 0.947461i \(0.396360\pi\)
\(948\) 0 0
\(949\) −48474.1 −1.65810
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 38558.2 1.31062 0.655311 0.755360i \(-0.272538\pi\)
0.655311 + 0.755360i \(0.272538\pi\)
\(954\) 0 0
\(955\) −4645.85 −0.157420
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 26957.4 0.907716
\(960\) 0 0
\(961\) −27835.7 −0.934366
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −10634.9 −0.354767
\(966\) 0 0
\(967\) −33635.3 −1.11855 −0.559275 0.828982i \(-0.688920\pi\)
−0.559275 + 0.828982i \(0.688920\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −37902.0 −1.25266 −0.626329 0.779559i \(-0.715443\pi\)
−0.626329 + 0.779559i \(0.715443\pi\)
\(972\) 0 0
\(973\) 16015.2 0.527670
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −50034.8 −1.63844 −0.819219 0.573481i \(-0.805593\pi\)
−0.819219 + 0.573481i \(0.805593\pi\)
\(978\) 0 0
\(979\) 721.649 0.0235587
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3864.79 0.125400 0.0626998 0.998032i \(-0.480029\pi\)
0.0626998 + 0.998032i \(0.480029\pi\)
\(984\) 0 0
\(985\) −8278.64 −0.267796
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2773.46 −0.0891717
\(990\) 0 0
\(991\) −33515.9 −1.07434 −0.537168 0.843476i \(-0.680506\pi\)
−0.537168 + 0.843476i \(0.680506\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −25046.2 −0.798009
\(996\) 0 0
\(997\) −21937.2 −0.696848 −0.348424 0.937337i \(-0.613283\pi\)
−0.348424 + 0.937337i \(0.613283\pi\)
\(998\) 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 1440.4.a.bj.1.1 yes 3
3.2 odd 2 1440.4.a.bh.1.1 3
4.3 odd 2 1440.4.a.bk.1.3 yes 3
12.11 even 2 1440.4.a.bi.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1440.4.a.bh.1.1 3 3.2 odd 2
1440.4.a.bi.1.3 yes 3 12.11 even 2
1440.4.a.bj.1.1 yes 3 1.1 even 1 trivial
1440.4.a.bk.1.3 yes 3 4.3 odd 2