Properties

Label 1440.4.a.y.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{89}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 22 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 480)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.21699\) 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)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -12.8680 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -12.8680 q^{7} -49.7359 q^{11} -52.6039 q^{13} -84.6039 q^{17} -26.6039 q^{19} -136.340 q^{23} +25.0000 q^{25} -6.00000 q^{29} +47.1320 q^{31} +64.3398 q^{35} +344.227 q^{37} +43.2078 q^{41} +252.000 q^{43} -306.076 q^{47} -177.416 q^{49} +455.208 q^{53} +248.680 q^{55} -708.151 q^{59} -652.039 q^{61} +263.019 q^{65} +704.528 q^{67} +531.775 q^{71} +57.6233 q^{73} +640.000 q^{77} +429.699 q^{79} -227.697 q^{83} +423.019 q^{85} -1032.87 q^{89} +676.905 q^{91} +133.019 q^{95} -152.416 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 10 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 10 q^{5} + 12 q^{7} - 24 q^{11} + 8 q^{13} - 56 q^{17} + 60 q^{19} - 84 q^{23} + 50 q^{25} - 12 q^{29} + 132 q^{31} - 60 q^{35} - 104 q^{37} - 140 q^{41} + 504 q^{43} - 348 q^{47} + 98 q^{49} + 684 q^{53} + 120 q^{55} - 888 q^{59} - 172 q^{61} - 40 q^{65} + 1560 q^{67} - 144 q^{71} - 564 q^{73} + 1280 q^{77} - 84 q^{79} - 1512 q^{83} + 280 q^{85} - 28 q^{89} + 2184 q^{91} - 300 q^{95} + 148 q^{97}+O(q^{100}) \) 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
\(7\) −12.8680 −0.694805 −0.347402 0.937716i \(-0.612936\pi\)
−0.347402 + 0.937716i \(0.612936\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −49.7359 −1.36327 −0.681634 0.731693i \(-0.738730\pi\)
−0.681634 + 0.731693i \(0.738730\pi\)
\(12\) 0 0
\(13\) −52.6039 −1.12228 −0.561142 0.827720i \(-0.689638\pi\)
−0.561142 + 0.827720i \(0.689638\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −84.6039 −1.20703 −0.603513 0.797353i \(-0.706233\pi\)
−0.603513 + 0.797353i \(0.706233\pi\)
\(18\) 0 0
\(19\) −26.6039 −0.321229 −0.160614 0.987017i \(-0.551348\pi\)
−0.160614 + 0.987017i \(0.551348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −136.340 −1.23604 −0.618018 0.786164i \(-0.712064\pi\)
−0.618018 + 0.786164i \(0.712064\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −0.0384197 −0.0192099 0.999815i \(-0.506115\pi\)
−0.0192099 + 0.999815i \(0.506115\pi\)
\(30\) 0 0
\(31\) 47.1320 0.273070 0.136535 0.990635i \(-0.456403\pi\)
0.136535 + 0.990635i \(0.456403\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 64.3398 0.310726
\(36\) 0 0
\(37\) 344.227 1.52948 0.764738 0.644341i \(-0.222868\pi\)
0.764738 + 0.644341i \(0.222868\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 43.2078 0.164583 0.0822917 0.996608i \(-0.473776\pi\)
0.0822917 + 0.996608i \(0.473776\pi\)
\(42\) 0 0
\(43\) 252.000 0.893713 0.446856 0.894606i \(-0.352544\pi\)
0.446856 + 0.894606i \(0.352544\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −306.076 −0.949909 −0.474955 0.880010i \(-0.657536\pi\)
−0.474955 + 0.880010i \(0.657536\pi\)
\(48\) 0 0
\(49\) −177.416 −0.517246
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 455.208 1.17977 0.589883 0.807489i \(-0.299174\pi\)
0.589883 + 0.807489i \(0.299174\pi\)
\(54\) 0 0
\(55\) 248.680 0.609672
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −708.151 −1.56260 −0.781301 0.624155i \(-0.785443\pi\)
−0.781301 + 0.624155i \(0.785443\pi\)
\(60\) 0 0
\(61\) −652.039 −1.36861 −0.684303 0.729197i \(-0.739894\pi\)
−0.684303 + 0.729197i \(0.739894\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 263.019 0.501901
\(66\) 0 0
\(67\) 704.528 1.28465 0.642327 0.766431i \(-0.277969\pi\)
0.642327 + 0.766431i \(0.277969\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 531.775 0.888874 0.444437 0.895810i \(-0.353404\pi\)
0.444437 + 0.895810i \(0.353404\pi\)
\(72\) 0 0
\(73\) 57.6233 0.0923877 0.0461938 0.998932i \(-0.485291\pi\)
0.0461938 + 0.998932i \(0.485291\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 640.000 0.947205
\(78\) 0 0
\(79\) 429.699 0.611961 0.305981 0.952038i \(-0.401016\pi\)
0.305981 + 0.952038i \(0.401016\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −227.697 −0.301120 −0.150560 0.988601i \(-0.548108\pi\)
−0.150560 + 0.988601i \(0.548108\pi\)
\(84\) 0 0
\(85\) 423.019 0.539799
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1032.87 −1.23016 −0.615079 0.788466i \(-0.710876\pi\)
−0.615079 + 0.788466i \(0.710876\pi\)
\(90\) 0 0
\(91\) 676.905 0.779768
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 133.019 0.143658
\(96\) 0 0
\(97\) −152.416 −0.159541 −0.0797704 0.996813i \(-0.525419\pi\)
−0.0797704 + 0.996813i \(0.525419\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 290.753 0.286446 0.143223 0.989690i \(-0.454253\pi\)
0.143223 + 0.989690i \(0.454253\pi\)
\(102\) 0 0
\(103\) −5.62132 −0.00537753 −0.00268876 0.999996i \(-0.500856\pi\)
−0.00268876 + 0.999996i \(0.500856\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2170.57 −1.96109 −0.980545 0.196294i \(-0.937109\pi\)
−0.980545 + 0.196294i \(0.937109\pi\)
\(108\) 0 0
\(109\) 1411.58 1.24042 0.620208 0.784438i \(-0.287048\pi\)
0.620208 + 0.784438i \(0.287048\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1557.81 1.29687 0.648436 0.761269i \(-0.275423\pi\)
0.648436 + 0.761269i \(0.275423\pi\)
\(114\) 0 0
\(115\) 681.699 0.552772
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1088.68 0.838648
\(120\) 0 0
\(121\) 1142.66 0.858499
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1920.19 −1.34165 −0.670825 0.741616i \(-0.734060\pi\)
−0.670825 + 0.741616i \(0.734060\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −600.303 −0.400372 −0.200186 0.979758i \(-0.564155\pi\)
−0.200186 + 0.979758i \(0.564155\pi\)
\(132\) 0 0
\(133\) 342.338 0.223191
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1953.51 1.21825 0.609124 0.793075i \(-0.291521\pi\)
0.609124 + 0.793075i \(0.291521\pi\)
\(138\) 0 0
\(139\) −2261.25 −1.37983 −0.689916 0.723890i \(-0.742352\pi\)
−0.689916 + 0.723890i \(0.742352\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2616.30 1.52997
\(144\) 0 0
\(145\) 30.0000 0.0171818
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2938.16 1.61546 0.807728 0.589555i \(-0.200697\pi\)
0.807728 + 0.589555i \(0.200697\pi\)
\(150\) 0 0
\(151\) −1053.40 −0.567710 −0.283855 0.958867i \(-0.591613\pi\)
−0.283855 + 0.958867i \(0.591613\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −235.660 −0.122121
\(156\) 0 0
\(157\) 2789.43 1.41797 0.708985 0.705224i \(-0.249154\pi\)
0.708985 + 0.705224i \(0.249154\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1754.42 0.858803
\(162\) 0 0
\(163\) 2170.35 1.04291 0.521456 0.853278i \(-0.325389\pi\)
0.521456 + 0.853278i \(0.325389\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3175.74 −1.47153 −0.735767 0.677234i \(-0.763178\pi\)
−0.735767 + 0.677234i \(0.763178\pi\)
\(168\) 0 0
\(169\) 570.169 0.259522
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −947.740 −0.416505 −0.208252 0.978075i \(-0.566778\pi\)
−0.208252 + 0.978075i \(0.566778\pi\)
\(174\) 0 0
\(175\) −321.699 −0.138961
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3003.47 1.25413 0.627067 0.778965i \(-0.284255\pi\)
0.627067 + 0.778965i \(0.284255\pi\)
\(180\) 0 0
\(181\) 1502.91 0.617184 0.308592 0.951194i \(-0.400142\pi\)
0.308592 + 0.951194i \(0.400142\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1721.14 −0.684002
\(186\) 0 0
\(187\) 4207.85 1.64550
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3144.00 1.19106 0.595528 0.803334i \(-0.296943\pi\)
0.595528 + 0.803334i \(0.296943\pi\)
\(192\) 0 0
\(193\) −3100.87 −1.15651 −0.578253 0.815858i \(-0.696265\pi\)
−0.578253 + 0.815858i \(0.696265\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2563.13 0.926982 0.463491 0.886102i \(-0.346597\pi\)
0.463491 + 0.886102i \(0.346597\pi\)
\(198\) 0 0
\(199\) −2929.17 −1.04343 −0.521717 0.853119i \(-0.674708\pi\)
−0.521717 + 0.853119i \(0.674708\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 77.2078 0.0266942
\(204\) 0 0
\(205\) −216.039 −0.0736039
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1323.17 0.437921
\(210\) 0 0
\(211\) −3876.80 −1.26488 −0.632440 0.774609i \(-0.717947\pi\)
−0.632440 + 0.774609i \(0.717947\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1260.00 −0.399680
\(216\) 0 0
\(217\) −606.493 −0.189730
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4450.49 1.35463
\(222\) 0 0
\(223\) −4268.94 −1.28193 −0.640963 0.767572i \(-0.721465\pi\)
−0.640963 + 0.767572i \(0.721465\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4191.03 1.22541 0.612706 0.790311i \(-0.290081\pi\)
0.612706 + 0.790311i \(0.290081\pi\)
\(228\) 0 0
\(229\) 2036.12 0.587556 0.293778 0.955874i \(-0.405087\pi\)
0.293778 + 0.955874i \(0.405087\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4544.76 1.27784 0.638921 0.769273i \(-0.279381\pi\)
0.638921 + 0.769273i \(0.279381\pi\)
\(234\) 0 0
\(235\) 1530.38 0.424812
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2068.00 0.559697 0.279848 0.960044i \(-0.409716\pi\)
0.279848 + 0.960044i \(0.409716\pi\)
\(240\) 0 0
\(241\) −1901.25 −0.508175 −0.254087 0.967181i \(-0.581775\pi\)
−0.254087 + 0.967181i \(0.581775\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 887.078 0.231320
\(246\) 0 0
\(247\) 1399.47 0.360510
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3794.42 −0.954191 −0.477095 0.878852i \(-0.658310\pi\)
−0.477095 + 0.878852i \(0.658310\pi\)
\(252\) 0 0
\(253\) 6780.99 1.68505
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3103.33 −0.753231 −0.376616 0.926370i \(-0.622912\pi\)
−0.376616 + 0.926370i \(0.622912\pi\)
\(258\) 0 0
\(259\) −4429.50 −1.06269
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4110.83 0.963821 0.481910 0.876221i \(-0.339943\pi\)
0.481910 + 0.876221i \(0.339943\pi\)
\(264\) 0 0
\(265\) −2276.04 −0.527607
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4272.34 0.968361 0.484180 0.874968i \(-0.339118\pi\)
0.484180 + 0.874968i \(0.339118\pi\)
\(270\) 0 0
\(271\) −4396.64 −0.985524 −0.492762 0.870164i \(-0.664013\pi\)
−0.492762 + 0.870164i \(0.664013\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1243.40 −0.272654
\(276\) 0 0
\(277\) −3068.54 −0.665598 −0.332799 0.942998i \(-0.607993\pi\)
−0.332799 + 0.942998i \(0.607993\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2672.71 −0.567405 −0.283702 0.958912i \(-0.591563\pi\)
−0.283702 + 0.958912i \(0.591563\pi\)
\(282\) 0 0
\(283\) −6135.64 −1.28878 −0.644392 0.764696i \(-0.722889\pi\)
−0.644392 + 0.764696i \(0.722889\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −555.996 −0.114353
\(288\) 0 0
\(289\) 2244.82 0.456914
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −40.7922 −0.00813347 −0.00406674 0.999992i \(-0.501294\pi\)
−0.00406674 + 0.999992i \(0.501294\pi\)
\(294\) 0 0
\(295\) 3540.76 0.698816
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7172.00 1.38718
\(300\) 0 0
\(301\) −3242.73 −0.620956
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3260.19 0.612060
\(306\) 0 0
\(307\) 7126.80 1.32491 0.662456 0.749101i \(-0.269514\pi\)
0.662456 + 0.749101i \(0.269514\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1704.52 −0.310787 −0.155393 0.987853i \(-0.549665\pi\)
−0.155393 + 0.987853i \(0.549665\pi\)
\(312\) 0 0
\(313\) 5343.52 0.964963 0.482482 0.875906i \(-0.339735\pi\)
0.482482 + 0.875906i \(0.339735\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5644.19 1.00003 0.500015 0.866017i \(-0.333328\pi\)
0.500015 + 0.866017i \(0.333328\pi\)
\(318\) 0 0
\(319\) 298.416 0.0523764
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2250.79 0.387732
\(324\) 0 0
\(325\) −1315.10 −0.224457
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3938.57 0.660001
\(330\) 0 0
\(331\) 2361.55 0.392152 0.196076 0.980589i \(-0.437180\pi\)
0.196076 + 0.980589i \(0.437180\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3522.64 −0.574515
\(336\) 0 0
\(337\) 5117.10 0.827141 0.413570 0.910472i \(-0.364282\pi\)
0.413570 + 0.910472i \(0.364282\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2344.16 −0.372267
\(342\) 0 0
\(343\) 6696.69 1.05419
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6087.39 −0.941753 −0.470876 0.882199i \(-0.656062\pi\)
−0.470876 + 0.882199i \(0.656062\pi\)
\(348\) 0 0
\(349\) 7827.52 1.20057 0.600283 0.799788i \(-0.295055\pi\)
0.600283 + 0.799788i \(0.295055\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2515.47 −0.379278 −0.189639 0.981854i \(-0.560732\pi\)
−0.189639 + 0.981854i \(0.560732\pi\)
\(354\) 0 0
\(355\) −2658.87 −0.397517
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −915.914 −0.134652 −0.0673261 0.997731i \(-0.521447\pi\)
−0.0673261 + 0.997731i \(0.521447\pi\)
\(360\) 0 0
\(361\) −6151.23 −0.896812
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −288.117 −0.0413170
\(366\) 0 0
\(367\) 12237.6 1.74060 0.870298 0.492525i \(-0.163926\pi\)
0.870298 + 0.492525i \(0.163926\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5857.60 −0.819707
\(372\) 0 0
\(373\) 3825.20 0.530996 0.265498 0.964111i \(-0.414464\pi\)
0.265498 + 0.964111i \(0.414464\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 315.623 0.0431178
\(378\) 0 0
\(379\) −8197.63 −1.11104 −0.555519 0.831504i \(-0.687481\pi\)
−0.555519 + 0.831504i \(0.687481\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −452.196 −0.0603294 −0.0301647 0.999545i \(-0.509603\pi\)
−0.0301647 + 0.999545i \(0.509603\pi\)
\(384\) 0 0
\(385\) −3200.00 −0.423603
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6816.13 −0.888410 −0.444205 0.895925i \(-0.646514\pi\)
−0.444205 + 0.895925i \(0.646514\pi\)
\(390\) 0 0
\(391\) 11534.9 1.49193
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2148.50 −0.273677
\(396\) 0 0
\(397\) 13380.3 1.69153 0.845766 0.533554i \(-0.179144\pi\)
0.845766 + 0.533554i \(0.179144\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6130.00 −0.763386 −0.381693 0.924289i \(-0.624659\pi\)
−0.381693 + 0.924289i \(0.624659\pi\)
\(402\) 0 0
\(403\) −2479.33 −0.306462
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −17120.5 −2.08509
\(408\) 0 0
\(409\) −15003.5 −1.81387 −0.906935 0.421270i \(-0.861584\pi\)
−0.906935 + 0.421270i \(0.861584\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9112.47 1.08570
\(414\) 0 0
\(415\) 1138.49 0.134665
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16300.7 1.90057 0.950287 0.311375i \(-0.100790\pi\)
0.950287 + 0.311375i \(0.100790\pi\)
\(420\) 0 0
\(421\) 7663.91 0.887211 0.443606 0.896222i \(-0.353699\pi\)
0.443606 + 0.896222i \(0.353699\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2115.10 −0.241405
\(426\) 0 0
\(427\) 8390.41 0.950914
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3702.20 0.413755 0.206878 0.978367i \(-0.433670\pi\)
0.206878 + 0.978367i \(0.433670\pi\)
\(432\) 0 0
\(433\) −10275.8 −1.14047 −0.570237 0.821481i \(-0.693148\pi\)
−0.570237 + 0.821481i \(0.693148\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3627.17 0.397050
\(438\) 0 0
\(439\) 14178.6 1.54148 0.770738 0.637152i \(-0.219888\pi\)
0.770738 + 0.637152i \(0.219888\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13395.6 −1.43666 −0.718332 0.695700i \(-0.755094\pi\)
−0.718332 + 0.695700i \(0.755094\pi\)
\(444\) 0 0
\(445\) 5164.35 0.550143
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9490.39 0.997504 0.498752 0.866745i \(-0.333792\pi\)
0.498752 + 0.866745i \(0.333792\pi\)
\(450\) 0 0
\(451\) −2148.98 −0.224371
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3384.52 −0.348723
\(456\) 0 0
\(457\) 587.064 0.0600913 0.0300456 0.999549i \(-0.490435\pi\)
0.0300456 + 0.999549i \(0.490435\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2800.42 −0.282925 −0.141462 0.989944i \(-0.545180\pi\)
−0.141462 + 0.989944i \(0.545180\pi\)
\(462\) 0 0
\(463\) −19745.6 −1.98198 −0.990988 0.133952i \(-0.957233\pi\)
−0.990988 + 0.133952i \(0.957233\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13552.0 −1.34285 −0.671427 0.741071i \(-0.734318\pi\)
−0.671427 + 0.741071i \(0.734318\pi\)
\(468\) 0 0
\(469\) −9065.84 −0.892584
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −12533.5 −1.21837
\(474\) 0 0
\(475\) −665.097 −0.0642458
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14131.9 −1.34803 −0.674014 0.738719i \(-0.735431\pi\)
−0.674014 + 0.738719i \(0.735431\pi\)
\(480\) 0 0
\(481\) −18107.7 −1.71651
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 762.078 0.0713488
\(486\) 0 0
\(487\) 7958.52 0.740524 0.370262 0.928927i \(-0.379268\pi\)
0.370262 + 0.928927i \(0.379268\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10984.3 1.00960 0.504799 0.863237i \(-0.331567\pi\)
0.504799 + 0.863237i \(0.331567\pi\)
\(492\) 0 0
\(493\) 507.623 0.0463736
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6842.86 −0.617594
\(498\) 0 0
\(499\) −17710.3 −1.58882 −0.794411 0.607381i \(-0.792220\pi\)
−0.794411 + 0.607381i \(0.792220\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2279.89 0.202098 0.101049 0.994881i \(-0.467780\pi\)
0.101049 + 0.994881i \(0.467780\pi\)
\(504\) 0 0
\(505\) −1453.77 −0.128103
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3254.99 0.283447 0.141724 0.989906i \(-0.454736\pi\)
0.141724 + 0.989906i \(0.454736\pi\)
\(510\) 0 0
\(511\) −741.495 −0.0641914
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 28.1066 0.00240490
\(516\) 0 0
\(517\) 15223.0 1.29498
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −21591.2 −1.81560 −0.907799 0.419406i \(-0.862238\pi\)
−0.907799 + 0.419406i \(0.862238\pi\)
\(522\) 0 0
\(523\) 16868.8 1.41037 0.705185 0.709024i \(-0.250864\pi\)
0.705185 + 0.709024i \(0.250864\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3987.55 −0.329603
\(528\) 0 0
\(529\) 6421.54 0.527784
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2272.90 −0.184709
\(534\) 0 0
\(535\) 10852.8 0.877026
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8823.93 0.705145
\(540\) 0 0
\(541\) −4366.23 −0.346985 −0.173493 0.984835i \(-0.555505\pi\)
−0.173493 + 0.984835i \(0.555505\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7057.92 −0.554731
\(546\) 0 0
\(547\) −16579.7 −1.29597 −0.647987 0.761652i \(-0.724389\pi\)
−0.647987 + 0.761652i \(0.724389\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 159.623 0.0123415
\(552\) 0 0
\(553\) −5529.35 −0.425193
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5971.66 0.454268 0.227134 0.973863i \(-0.427064\pi\)
0.227134 + 0.973863i \(0.427064\pi\)
\(558\) 0 0
\(559\) −13256.2 −1.00300
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15561.2 1.16488 0.582441 0.812873i \(-0.302098\pi\)
0.582441 + 0.812873i \(0.302098\pi\)
\(564\) 0 0
\(565\) −7789.06 −0.579979
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11871.6 −0.874662 −0.437331 0.899301i \(-0.644076\pi\)
−0.437331 + 0.899301i \(0.644076\pi\)
\(570\) 0 0
\(571\) 18660.0 1.36759 0.683797 0.729672i \(-0.260327\pi\)
0.683797 + 0.729672i \(0.260327\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3408.50 −0.247207
\(576\) 0 0
\(577\) −7549.12 −0.544669 −0.272334 0.962203i \(-0.587796\pi\)
−0.272334 + 0.962203i \(0.587796\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2930.00 0.209220
\(582\) 0 0
\(583\) −22640.2 −1.60834
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4513.39 0.317355 0.158678 0.987330i \(-0.449277\pi\)
0.158678 + 0.987330i \(0.449277\pi\)
\(588\) 0 0
\(589\) −1253.90 −0.0877179
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8335.46 −0.577228 −0.288614 0.957445i \(-0.593194\pi\)
−0.288614 + 0.957445i \(0.593194\pi\)
\(594\) 0 0
\(595\) −5443.40 −0.375055
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −10806.9 −0.737162 −0.368581 0.929596i \(-0.620156\pi\)
−0.368581 + 0.929596i \(0.620156\pi\)
\(600\) 0 0
\(601\) −25653.1 −1.74112 −0.870559 0.492063i \(-0.836243\pi\)
−0.870559 + 0.492063i \(0.836243\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5713.31 −0.383932
\(606\) 0 0
\(607\) 8879.17 0.593730 0.296865 0.954919i \(-0.404059\pi\)
0.296865 + 0.954919i \(0.404059\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16100.8 1.06607
\(612\) 0 0
\(613\) 3846.28 0.253425 0.126713 0.991939i \(-0.459557\pi\)
0.126713 + 0.991939i \(0.459557\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15821.2 1.03231 0.516156 0.856495i \(-0.327363\pi\)
0.516156 + 0.856495i \(0.327363\pi\)
\(618\) 0 0
\(619\) 11518.7 0.747942 0.373971 0.927440i \(-0.377996\pi\)
0.373971 + 0.927440i \(0.377996\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 13290.9 0.854719
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −29123.0 −1.84612
\(630\) 0 0
\(631\) −9053.33 −0.571169 −0.285584 0.958354i \(-0.592188\pi\)
−0.285584 + 0.958354i \(0.592188\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9600.96 0.600004
\(636\) 0 0
\(637\) 9332.75 0.580498
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1700.77 −0.104799 −0.0523996 0.998626i \(-0.516687\pi\)
−0.0523996 + 0.998626i \(0.516687\pi\)
\(642\) 0 0
\(643\) 17275.1 1.05951 0.529755 0.848151i \(-0.322284\pi\)
0.529755 + 0.848151i \(0.322284\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11182.2 0.679468 0.339734 0.940522i \(-0.389663\pi\)
0.339734 + 0.940522i \(0.389663\pi\)
\(648\) 0 0
\(649\) 35220.6 2.13024
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −20720.5 −1.24174 −0.620869 0.783915i \(-0.713220\pi\)
−0.620869 + 0.783915i \(0.713220\pi\)
\(654\) 0 0
\(655\) 3001.51 0.179052
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8745.26 0.516945 0.258473 0.966019i \(-0.416781\pi\)
0.258473 + 0.966019i \(0.416781\pi\)
\(660\) 0 0
\(661\) −25921.8 −1.52533 −0.762663 0.646796i \(-0.776108\pi\)
−0.762663 + 0.646796i \(0.776108\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1711.69 −0.0998142
\(666\) 0 0
\(667\) 818.039 0.0474881
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 32429.8 1.86578
\(672\) 0 0
\(673\) −12111.4 −0.693702 −0.346851 0.937920i \(-0.612749\pi\)
−0.346851 + 0.937920i \(0.612749\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4961.50 −0.281663 −0.140832 0.990034i \(-0.544978\pi\)
−0.140832 + 0.990034i \(0.544978\pi\)
\(678\) 0 0
\(679\) 1961.28 0.110850
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24838.1 −1.39151 −0.695755 0.718279i \(-0.744930\pi\)
−0.695755 + 0.718279i \(0.744930\pi\)
\(684\) 0 0
\(685\) −9767.56 −0.544817
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −23945.7 −1.32403
\(690\) 0 0
\(691\) −6857.65 −0.377536 −0.188768 0.982022i \(-0.560449\pi\)
−0.188768 + 0.982022i \(0.560449\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 11306.2 0.617079
\(696\) 0 0
\(697\) −3655.55 −0.198657
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −32760.0 −1.76509 −0.882545 0.470228i \(-0.844172\pi\)
−0.882545 + 0.470228i \(0.844172\pi\)
\(702\) 0 0
\(703\) −9157.78 −0.491312
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3741.40 −0.199024
\(708\) 0 0
\(709\) 8678.69 0.459711 0.229855 0.973225i \(-0.426175\pi\)
0.229855 + 0.973225i \(0.426175\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6425.97 −0.337524
\(714\) 0 0
\(715\) −13081.5 −0.684225
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 8160.85 0.423294 0.211647 0.977346i \(-0.432117\pi\)
0.211647 + 0.977346i \(0.432117\pi\)
\(720\) 0 0
\(721\) 72.3349 0.00373633
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −150.000 −0.00768395
\(726\) 0 0
\(727\) −23907.3 −1.21963 −0.609816 0.792543i \(-0.708757\pi\)
−0.609816 + 0.792543i \(0.708757\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −21320.2 −1.07874
\(732\) 0 0
\(733\) −28946.6 −1.45862 −0.729309 0.684185i \(-0.760158\pi\)
−0.729309 + 0.684185i \(0.760158\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −35040.4 −1.75133
\(738\) 0 0
\(739\) −39038.5 −1.94324 −0.971620 0.236547i \(-0.923984\pi\)
−0.971620 + 0.236547i \(0.923984\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4175.77 −0.206183 −0.103092 0.994672i \(-0.532874\pi\)
−0.103092 + 0.994672i \(0.532874\pi\)
\(744\) 0 0
\(745\) −14690.8 −0.722454
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 27930.8 1.36257
\(750\) 0 0
\(751\) −22219.1 −1.07961 −0.539805 0.841790i \(-0.681502\pi\)
−0.539805 + 0.841790i \(0.681502\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5266.98 0.253887
\(756\) 0 0
\(757\) 22514.1 1.08096 0.540482 0.841355i \(-0.318242\pi\)
0.540482 + 0.841355i \(0.318242\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 26354.3 1.25538 0.627689 0.778465i \(-0.284001\pi\)
0.627689 + 0.778465i \(0.284001\pi\)
\(762\) 0 0
\(763\) −18164.2 −0.861846
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 37251.5 1.75368
\(768\) 0 0
\(769\) −26226.3 −1.22983 −0.614917 0.788591i \(-0.710811\pi\)
−0.614917 + 0.788591i \(0.710811\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 28023.6 1.30393 0.651965 0.758249i \(-0.273945\pi\)
0.651965 + 0.758249i \(0.273945\pi\)
\(774\) 0 0
\(775\) 1178.30 0.0546140
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1149.49 −0.0528690
\(780\) 0 0
\(781\) −26448.3 −1.21177
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −13947.2 −0.634135
\(786\) 0 0
\(787\) −16361.2 −0.741061 −0.370530 0.928820i \(-0.620824\pi\)
−0.370530 + 0.928820i \(0.620824\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −20045.9 −0.901073
\(792\) 0 0
\(793\) 34299.8 1.53597
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20999.9 0.933319 0.466660 0.884437i \(-0.345457\pi\)
0.466660 + 0.884437i \(0.345457\pi\)
\(798\) 0 0
\(799\) 25895.2 1.14657
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2865.95 −0.125949
\(804\) 0 0
\(805\) −8772.08 −0.384068
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 29390.4 1.27727 0.638635 0.769510i \(-0.279499\pi\)
0.638635 + 0.769510i \(0.279499\pi\)
\(810\) 0 0
\(811\) 17296.9 0.748924 0.374462 0.927242i \(-0.377827\pi\)
0.374462 + 0.927242i \(0.377827\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −10851.7 −0.466404
\(816\) 0 0
\(817\) −6704.18 −0.287086
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −19989.1 −0.849725 −0.424862 0.905258i \(-0.639678\pi\)
−0.424862 + 0.905258i \(0.639678\pi\)
\(822\) 0 0
\(823\) 20226.7 0.856694 0.428347 0.903614i \(-0.359096\pi\)
0.428347 + 0.903614i \(0.359096\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −24124.7 −1.01439 −0.507193 0.861833i \(-0.669317\pi\)
−0.507193 + 0.861833i \(0.669317\pi\)
\(828\) 0 0
\(829\) 43594.3 1.82641 0.913204 0.407503i \(-0.133600\pi\)
0.913204 + 0.407503i \(0.133600\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 15010.0 0.624330
\(834\) 0 0
\(835\) 15878.7 0.658090
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −29937.7 −1.23190 −0.615949 0.787786i \(-0.711227\pi\)
−0.615949 + 0.787786i \(0.711227\pi\)
\(840\) 0 0
\(841\) −24353.0 −0.998524
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2850.84 −0.116062
\(846\) 0 0
\(847\) −14703.7 −0.596489
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −46931.9 −1.89049
\(852\) 0 0
\(853\) −2147.83 −0.0862136 −0.0431068 0.999070i \(-0.513726\pi\)
−0.0431068 + 0.999070i \(0.513726\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −15771.5 −0.628638 −0.314319 0.949317i \(-0.601776\pi\)
−0.314319 + 0.949317i \(0.601776\pi\)
\(858\) 0 0
\(859\) 29364.8 1.16637 0.583187 0.812338i \(-0.301806\pi\)
0.583187 + 0.812338i \(0.301806\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 44989.3 1.77457 0.887285 0.461221i \(-0.152588\pi\)
0.887285 + 0.461221i \(0.152588\pi\)
\(864\) 0 0
\(865\) 4738.70 0.186267
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −21371.5 −0.834267
\(870\) 0 0
\(871\) −37060.9 −1.44175
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1608.50 0.0621452
\(876\) 0 0
\(877\) 36547.6 1.40721 0.703606 0.710590i \(-0.251572\pi\)
0.703606 + 0.710590i \(0.251572\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −21146.4 −0.808672 −0.404336 0.914610i \(-0.632497\pi\)
−0.404336 + 0.914610i \(0.632497\pi\)
\(882\) 0 0
\(883\) 39103.3 1.49030 0.745148 0.666899i \(-0.232379\pi\)
0.745148 + 0.666899i \(0.232379\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32169.3 1.21775 0.608873 0.793268i \(-0.291622\pi\)
0.608873 + 0.793268i \(0.291622\pi\)
\(888\) 0 0
\(889\) 24709.0 0.932184
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8142.80 0.305138
\(894\) 0 0
\(895\) −15017.4 −0.560866
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −282.792 −0.0104913
\(900\) 0 0
\(901\) −38512.3 −1.42401
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7514.54 −0.276013
\(906\) 0 0
\(907\) 10810.4 0.395759 0.197880 0.980226i \(-0.436595\pi\)
0.197880 + 0.980226i \(0.436595\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −244.183 −0.00888053 −0.00444026 0.999990i \(-0.501413\pi\)
−0.00444026 + 0.999990i \(0.501413\pi\)
\(912\) 0 0
\(913\) 11324.7 0.410508
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 7724.68 0.278180
\(918\) 0 0
\(919\) 34164.1 1.22630 0.613151 0.789966i \(-0.289902\pi\)
0.613151 + 0.789966i \(0.289902\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −27973.4 −0.997569
\(924\) 0 0
\(925\) 8605.68 0.305895
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 35758.6 1.26287 0.631433 0.775431i \(-0.282467\pi\)
0.631433 + 0.775431i \(0.282467\pi\)
\(930\) 0 0
\(931\) 4719.94 0.166155
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −21039.3 −0.735890
\(936\) 0 0
\(937\) 40301.0 1.40510 0.702549 0.711635i \(-0.252045\pi\)
0.702549 + 0.711635i \(0.252045\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −48866.6 −1.69289 −0.846443 0.532480i \(-0.821260\pi\)
−0.846443 + 0.532480i \(0.821260\pi\)
\(942\) 0 0
\(943\) −5890.94 −0.203431
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 42669.4 1.46417 0.732084 0.681214i \(-0.238548\pi\)
0.732084 + 0.681214i \(0.238548\pi\)
\(948\) 0 0
\(949\) −3031.21 −0.103685
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 42523.5 1.44541 0.722703 0.691158i \(-0.242899\pi\)
0.722703 + 0.691158i \(0.242899\pi\)
\(954\) 0 0
\(955\) −15720.0 −0.532657
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −25137.7 −0.846444
\(960\) 0 0
\(961\) −27569.6 −0.925433
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 15504.3 0.517205
\(966\) 0 0
\(967\) −13205.1 −0.439138 −0.219569 0.975597i \(-0.570465\pi\)
−0.219569 + 0.975597i \(0.570465\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3545.55 0.117180 0.0585901 0.998282i \(-0.481339\pi\)
0.0585901 + 0.998282i \(0.481339\pi\)
\(972\) 0 0
\(973\) 29097.7 0.958713
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 13070.8 0.428015 0.214008 0.976832i \(-0.431348\pi\)
0.214008 + 0.976832i \(0.431348\pi\)
\(978\) 0 0
\(979\) 51370.7 1.67703
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 12342.3 0.400467 0.200234 0.979748i \(-0.435830\pi\)
0.200234 + 0.979748i \(0.435830\pi\)
\(984\) 0 0
\(985\) −12815.7 −0.414559
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −34357.6 −1.10466
\(990\) 0 0
\(991\) 35095.4 1.12497 0.562484 0.826808i \(-0.309846\pi\)
0.562484 + 0.826808i \(0.309846\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14645.9 0.466638
\(996\) 0 0
\(997\) −46486.0 −1.47666 −0.738328 0.674442i \(-0.764384\pi\)
−0.738328 + 0.674442i \(0.764384\pi\)
\(998\) 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.y.1.1 2
3.2 odd 2 480.4.a.r.1.1 yes 2
4.3 odd 2 1440.4.a.s.1.2 2
12.11 even 2 480.4.a.o.1.2 2
15.14 odd 2 2400.4.a.y.1.2 2
24.5 odd 2 960.4.a.bk.1.1 2
24.11 even 2 960.4.a.bn.1.2 2
60.59 even 2 2400.4.a.bb.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.4.a.o.1.2 2 12.11 even 2
480.4.a.r.1.1 yes 2 3.2 odd 2
960.4.a.bk.1.1 2 24.5 odd 2
960.4.a.bn.1.2 2 24.11 even 2
1440.4.a.s.1.2 2 4.3 odd 2
1440.4.a.y.1.1 2 1.1 even 1 trivial
2400.4.a.y.1.2 2 15.14 odd 2
2400.4.a.bb.1.1 2 60.59 even 2