Properties

Label 1620.4.a.j.1.5
Level $1620$
Weight $4$
Character 1620.1
Self dual yes
Analytic conductor $95.583$
Analytic rank $1$
Dimension $6$
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] = [1620,4,Mod(1,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1620.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.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: \(95.5830942093\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 151x^{4} - 212x^{3} + 4412x^{2} + 8656x - 19148 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{5} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(5.63924\) of defining polynomial
Character \(\chi\) \(=\) 1620.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} +16.5713 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +16.5713 q^{7} +72.5369 q^{11} -59.8975 q^{13} -15.8529 q^{17} -136.646 q^{19} -163.101 q^{23} +25.0000 q^{25} -11.5985 q^{29} -41.0018 q^{31} +82.8565 q^{35} -242.545 q^{37} -57.8664 q^{41} -264.504 q^{43} -599.889 q^{47} -68.3922 q^{49} -592.285 q^{53} +362.684 q^{55} -288.893 q^{59} +825.380 q^{61} -299.488 q^{65} +810.528 q^{67} +966.126 q^{71} +802.840 q^{73} +1202.03 q^{77} -1162.00 q^{79} -502.375 q^{83} -79.2644 q^{85} -8.76580 q^{89} -992.580 q^{91} -683.229 q^{95} +138.364 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 30 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 30 q^{5} + 12 q^{7} - 84 q^{13} - 12 q^{17} - 114 q^{19} - 30 q^{23} + 150 q^{25} - 168 q^{29} - 324 q^{31} + 60 q^{35} - 492 q^{37} - 312 q^{41} - 156 q^{43} - 462 q^{47} - 588 q^{49} - 1014 q^{53} - 1008 q^{59} + 36 q^{61} - 420 q^{65} + 144 q^{67} - 1212 q^{71} - 900 q^{73} - 672 q^{77} - 936 q^{79} - 288 q^{83} - 60 q^{85} + 120 q^{89} + 2286 q^{91} - 570 q^{95} - 1188 q^{97}+O(q^{100}) \) 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
\(7\) 16.5713 0.894766 0.447383 0.894343i \(-0.352356\pi\)
0.447383 + 0.894343i \(0.352356\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 72.5369 1.98824 0.994122 0.108266i \(-0.0345298\pi\)
0.994122 + 0.108266i \(0.0345298\pi\)
\(12\) 0 0
\(13\) −59.8975 −1.27789 −0.638946 0.769252i \(-0.720629\pi\)
−0.638946 + 0.769252i \(0.720629\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −15.8529 −0.226170 −0.113085 0.993585i \(-0.536073\pi\)
−0.113085 + 0.993585i \(0.536073\pi\)
\(18\) 0 0
\(19\) −136.646 −1.64993 −0.824966 0.565182i \(-0.808806\pi\)
−0.824966 + 0.565182i \(0.808806\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −163.101 −1.47864 −0.739322 0.673352i \(-0.764854\pi\)
−0.739322 + 0.673352i \(0.764854\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −11.5985 −0.0742683 −0.0371342 0.999310i \(-0.511823\pi\)
−0.0371342 + 0.999310i \(0.511823\pi\)
\(30\) 0 0
\(31\) −41.0018 −0.237553 −0.118776 0.992921i \(-0.537897\pi\)
−0.118776 + 0.992921i \(0.537897\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 82.8565 0.400151
\(36\) 0 0
\(37\) −242.545 −1.07768 −0.538841 0.842408i \(-0.681138\pi\)
−0.538841 + 0.842408i \(0.681138\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −57.8664 −0.220420 −0.110210 0.993908i \(-0.535152\pi\)
−0.110210 + 0.993908i \(0.535152\pi\)
\(42\) 0 0
\(43\) −264.504 −0.938059 −0.469029 0.883183i \(-0.655396\pi\)
−0.469029 + 0.883183i \(0.655396\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −599.889 −1.86176 −0.930882 0.365321i \(-0.880959\pi\)
−0.930882 + 0.365321i \(0.880959\pi\)
\(48\) 0 0
\(49\) −68.3922 −0.199394
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −592.285 −1.53503 −0.767516 0.641030i \(-0.778507\pi\)
−0.767516 + 0.641030i \(0.778507\pi\)
\(54\) 0 0
\(55\) 362.684 0.889170
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −288.893 −0.637468 −0.318734 0.947844i \(-0.603258\pi\)
−0.318734 + 0.947844i \(0.603258\pi\)
\(60\) 0 0
\(61\) 825.380 1.73244 0.866222 0.499660i \(-0.166542\pi\)
0.866222 + 0.499660i \(0.166542\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −299.488 −0.571490
\(66\) 0 0
\(67\) 810.528 1.47794 0.738968 0.673741i \(-0.235313\pi\)
0.738968 + 0.673741i \(0.235313\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 966.126 1.61490 0.807451 0.589935i \(-0.200847\pi\)
0.807451 + 0.589935i \(0.200847\pi\)
\(72\) 0 0
\(73\) 802.840 1.28720 0.643598 0.765364i \(-0.277441\pi\)
0.643598 + 0.765364i \(0.277441\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1202.03 1.77901
\(78\) 0 0
\(79\) −1162.00 −1.65488 −0.827440 0.561554i \(-0.810204\pi\)
−0.827440 + 0.561554i \(0.810204\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −502.375 −0.664371 −0.332186 0.943214i \(-0.607786\pi\)
−0.332186 + 0.943214i \(0.607786\pi\)
\(84\) 0 0
\(85\) −79.2644 −0.101146
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.76580 −0.0104401 −0.00522007 0.999986i \(-0.501662\pi\)
−0.00522007 + 0.999986i \(0.501662\pi\)
\(90\) 0 0
\(91\) −992.580 −1.14341
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −683.229 −0.737872
\(96\) 0 0
\(97\) 138.364 0.144832 0.0724161 0.997375i \(-0.476929\pi\)
0.0724161 + 0.997375i \(0.476929\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1325.78 1.30614 0.653068 0.757299i \(-0.273481\pi\)
0.653068 + 0.757299i \(0.273481\pi\)
\(102\) 0 0
\(103\) 333.544 0.319078 0.159539 0.987192i \(-0.448999\pi\)
0.159539 + 0.987192i \(0.448999\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −584.004 −0.527643 −0.263821 0.964572i \(-0.584983\pi\)
−0.263821 + 0.964572i \(0.584983\pi\)
\(108\) 0 0
\(109\) −1915.42 −1.68315 −0.841577 0.540137i \(-0.818372\pi\)
−0.841577 + 0.540137i \(0.818372\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1237.32 −1.03006 −0.515030 0.857172i \(-0.672219\pi\)
−0.515030 + 0.857172i \(0.672219\pi\)
\(114\) 0 0
\(115\) −815.503 −0.661270
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −262.703 −0.202369
\(120\) 0 0
\(121\) 3930.59 2.95311
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1785.42 −1.24749 −0.623743 0.781629i \(-0.714389\pi\)
−0.623743 + 0.781629i \(0.714389\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −721.812 −0.481413 −0.240706 0.970598i \(-0.577379\pi\)
−0.240706 + 0.970598i \(0.577379\pi\)
\(132\) 0 0
\(133\) −2264.40 −1.47630
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1108.99 0.691585 0.345792 0.938311i \(-0.387610\pi\)
0.345792 + 0.938311i \(0.387610\pi\)
\(138\) 0 0
\(139\) 436.770 0.266520 0.133260 0.991081i \(-0.457455\pi\)
0.133260 + 0.991081i \(0.457455\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4344.78 −2.54076
\(144\) 0 0
\(145\) −57.9923 −0.0332138
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 177.117 0.0973825 0.0486912 0.998814i \(-0.484495\pi\)
0.0486912 + 0.998814i \(0.484495\pi\)
\(150\) 0 0
\(151\) 828.658 0.446591 0.223296 0.974751i \(-0.428318\pi\)
0.223296 + 0.974751i \(0.428318\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −205.009 −0.106237
\(156\) 0 0
\(157\) −866.524 −0.440485 −0.220242 0.975445i \(-0.570685\pi\)
−0.220242 + 0.975445i \(0.570685\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2702.79 −1.32304
\(162\) 0 0
\(163\) 2984.70 1.43423 0.717116 0.696954i \(-0.245462\pi\)
0.717116 + 0.696954i \(0.245462\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1959.44 −0.907940 −0.453970 0.891017i \(-0.649993\pi\)
−0.453970 + 0.891017i \(0.649993\pi\)
\(168\) 0 0
\(169\) 1390.72 0.633007
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −506.945 −0.222788 −0.111394 0.993776i \(-0.535532\pi\)
−0.111394 + 0.993776i \(0.535532\pi\)
\(174\) 0 0
\(175\) 414.282 0.178953
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3122.26 1.30374 0.651869 0.758332i \(-0.273985\pi\)
0.651869 + 0.758332i \(0.273985\pi\)
\(180\) 0 0
\(181\) −2828.38 −1.16150 −0.580751 0.814082i \(-0.697241\pi\)
−0.580751 + 0.814082i \(0.697241\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1212.73 −0.481954
\(186\) 0 0
\(187\) −1149.92 −0.449681
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4078.64 −1.54513 −0.772565 0.634936i \(-0.781027\pi\)
−0.772565 + 0.634936i \(0.781027\pi\)
\(192\) 0 0
\(193\) 3043.12 1.13497 0.567483 0.823385i \(-0.307917\pi\)
0.567483 + 0.823385i \(0.307917\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1338.21 −0.483978 −0.241989 0.970279i \(-0.577800\pi\)
−0.241989 + 0.970279i \(0.577800\pi\)
\(198\) 0 0
\(199\) 453.645 0.161598 0.0807991 0.996730i \(-0.474253\pi\)
0.0807991 + 0.996730i \(0.474253\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −192.202 −0.0664528
\(204\) 0 0
\(205\) −289.332 −0.0985748
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9911.86 −3.28047
\(210\) 0 0
\(211\) 1905.96 0.621856 0.310928 0.950434i \(-0.399360\pi\)
0.310928 + 0.950434i \(0.399360\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1322.52 −0.419513
\(216\) 0 0
\(217\) −679.452 −0.212554
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 949.548 0.289021
\(222\) 0 0
\(223\) 4455.51 1.33795 0.668976 0.743284i \(-0.266733\pi\)
0.668976 + 0.743284i \(0.266733\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −171.235 −0.0500672 −0.0250336 0.999687i \(-0.507969\pi\)
−0.0250336 + 0.999687i \(0.507969\pi\)
\(228\) 0 0
\(229\) 4429.94 1.27834 0.639168 0.769067i \(-0.279279\pi\)
0.639168 + 0.769067i \(0.279279\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 762.810 0.214478 0.107239 0.994233i \(-0.465799\pi\)
0.107239 + 0.994233i \(0.465799\pi\)
\(234\) 0 0
\(235\) −2999.45 −0.832606
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3044.29 −0.823927 −0.411963 0.911200i \(-0.635157\pi\)
−0.411963 + 0.911200i \(0.635157\pi\)
\(240\) 0 0
\(241\) −2018.31 −0.539465 −0.269733 0.962935i \(-0.586935\pi\)
−0.269733 + 0.962935i \(0.586935\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −341.961 −0.0891718
\(246\) 0 0
\(247\) 8184.75 2.10843
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3031.55 −0.762351 −0.381175 0.924503i \(-0.624481\pi\)
−0.381175 + 0.924503i \(0.624481\pi\)
\(252\) 0 0
\(253\) −11830.8 −2.93990
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4754.62 −1.15403 −0.577013 0.816735i \(-0.695782\pi\)
−0.577013 + 0.816735i \(0.695782\pi\)
\(258\) 0 0
\(259\) −4019.29 −0.964272
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3964.86 0.929595 0.464798 0.885417i \(-0.346127\pi\)
0.464798 + 0.885417i \(0.346127\pi\)
\(264\) 0 0
\(265\) −2961.43 −0.686487
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3989.09 −0.904161 −0.452080 0.891977i \(-0.649318\pi\)
−0.452080 + 0.891977i \(0.649318\pi\)
\(270\) 0 0
\(271\) 2684.00 0.601628 0.300814 0.953683i \(-0.402742\pi\)
0.300814 + 0.953683i \(0.402742\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1813.42 0.397649
\(276\) 0 0
\(277\) 53.5212 0.0116093 0.00580465 0.999983i \(-0.498152\pi\)
0.00580465 + 0.999983i \(0.498152\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3638.06 −0.772344 −0.386172 0.922427i \(-0.626203\pi\)
−0.386172 + 0.922427i \(0.626203\pi\)
\(282\) 0 0
\(283\) 7326.03 1.53882 0.769412 0.638752i \(-0.220549\pi\)
0.769412 + 0.638752i \(0.220549\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −958.922 −0.197224
\(288\) 0 0
\(289\) −4661.69 −0.948847
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2522.24 −0.502903 −0.251452 0.967870i \(-0.580908\pi\)
−0.251452 + 0.967870i \(0.580908\pi\)
\(294\) 0 0
\(295\) −1444.46 −0.285084
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 9769.32 1.88955
\(300\) 0 0
\(301\) −4383.18 −0.839343
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4126.90 0.774772
\(306\) 0 0
\(307\) 640.204 0.119017 0.0595087 0.998228i \(-0.481047\pi\)
0.0595087 + 0.998228i \(0.481047\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4874.34 0.888741 0.444371 0.895843i \(-0.353427\pi\)
0.444371 + 0.895843i \(0.353427\pi\)
\(312\) 0 0
\(313\) −5163.98 −0.932541 −0.466270 0.884642i \(-0.654403\pi\)
−0.466270 + 0.884642i \(0.654403\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7310.00 −1.29517 −0.647587 0.761991i \(-0.724222\pi\)
−0.647587 + 0.761991i \(0.724222\pi\)
\(318\) 0 0
\(319\) −841.316 −0.147664
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2166.23 0.373165
\(324\) 0 0
\(325\) −1497.44 −0.255578
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9940.94 −1.66584
\(330\) 0 0
\(331\) −11735.6 −1.94878 −0.974390 0.224865i \(-0.927806\pi\)
−0.974390 + 0.224865i \(0.927806\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4052.64 0.660953
\(336\) 0 0
\(337\) 2251.02 0.363860 0.181930 0.983311i \(-0.441766\pi\)
0.181930 + 0.983311i \(0.441766\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2974.14 −0.472313
\(342\) 0 0
\(343\) −6817.30 −1.07318
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6958.99 −1.07659 −0.538297 0.842755i \(-0.680932\pi\)
−0.538297 + 0.842755i \(0.680932\pi\)
\(348\) 0 0
\(349\) −2924.01 −0.448477 −0.224238 0.974534i \(-0.571989\pi\)
−0.224238 + 0.974534i \(0.571989\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6552.47 0.987968 0.493984 0.869471i \(-0.335540\pi\)
0.493984 + 0.869471i \(0.335540\pi\)
\(354\) 0 0
\(355\) 4830.63 0.722206
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1324.66 0.194743 0.0973717 0.995248i \(-0.468956\pi\)
0.0973717 + 0.995248i \(0.468956\pi\)
\(360\) 0 0
\(361\) 11813.1 1.72228
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4014.20 0.575651
\(366\) 0 0
\(367\) −3256.21 −0.463141 −0.231571 0.972818i \(-0.574386\pi\)
−0.231571 + 0.972818i \(0.574386\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9814.94 −1.37349
\(372\) 0 0
\(373\) −4544.66 −0.630867 −0.315433 0.948948i \(-0.602150\pi\)
−0.315433 + 0.948948i \(0.602150\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 694.720 0.0949069
\(378\) 0 0
\(379\) −2484.30 −0.336701 −0.168351 0.985727i \(-0.553844\pi\)
−0.168351 + 0.985727i \(0.553844\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2828.87 0.377411 0.188705 0.982034i \(-0.439571\pi\)
0.188705 + 0.982034i \(0.439571\pi\)
\(384\) 0 0
\(385\) 6010.15 0.795599
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2590.17 −0.337601 −0.168801 0.985650i \(-0.553989\pi\)
−0.168801 + 0.985650i \(0.553989\pi\)
\(390\) 0 0
\(391\) 2585.61 0.334425
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5810.01 −0.740085
\(396\) 0 0
\(397\) 12207.4 1.54325 0.771625 0.636077i \(-0.219444\pi\)
0.771625 + 0.636077i \(0.219444\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9520.41 −1.18560 −0.592801 0.805349i \(-0.701978\pi\)
−0.592801 + 0.805349i \(0.701978\pi\)
\(402\) 0 0
\(403\) 2455.91 0.303567
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −17593.5 −2.14269
\(408\) 0 0
\(409\) 11246.7 1.35969 0.679846 0.733355i \(-0.262047\pi\)
0.679846 + 0.733355i \(0.262047\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4787.32 −0.570384
\(414\) 0 0
\(415\) −2511.87 −0.297116
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10682.0 1.24546 0.622731 0.782436i \(-0.286023\pi\)
0.622731 + 0.782436i \(0.286023\pi\)
\(420\) 0 0
\(421\) 10824.0 1.25304 0.626518 0.779407i \(-0.284479\pi\)
0.626518 + 0.779407i \(0.284479\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −396.322 −0.0452340
\(426\) 0 0
\(427\) 13677.6 1.55013
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 235.904 0.0263645 0.0131823 0.999913i \(-0.495804\pi\)
0.0131823 + 0.999913i \(0.495804\pi\)
\(432\) 0 0
\(433\) −11895.5 −1.32024 −0.660118 0.751162i \(-0.729494\pi\)
−0.660118 + 0.751162i \(0.729494\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 22287.0 2.43966
\(438\) 0 0
\(439\) 3811.05 0.414331 0.207166 0.978306i \(-0.433576\pi\)
0.207166 + 0.978306i \(0.433576\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8032.23 0.861451 0.430725 0.902483i \(-0.358258\pi\)
0.430725 + 0.902483i \(0.358258\pi\)
\(444\) 0 0
\(445\) −43.8290 −0.00466897
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12271.3 −1.28980 −0.644898 0.764269i \(-0.723100\pi\)
−0.644898 + 0.764269i \(0.723100\pi\)
\(450\) 0 0
\(451\) −4197.45 −0.438249
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4962.90 −0.511350
\(456\) 0 0
\(457\) 9944.00 1.01786 0.508929 0.860809i \(-0.330042\pi\)
0.508929 + 0.860809i \(0.330042\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6749.48 −0.681897 −0.340949 0.940082i \(-0.610748\pi\)
−0.340949 + 0.940082i \(0.610748\pi\)
\(462\) 0 0
\(463\) −9560.15 −0.959607 −0.479804 0.877376i \(-0.659292\pi\)
−0.479804 + 0.877376i \(0.659292\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6517.56 0.645818 0.322909 0.946430i \(-0.395339\pi\)
0.322909 + 0.946430i \(0.395339\pi\)
\(468\) 0 0
\(469\) 13431.5 1.32241
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −19186.3 −1.86509
\(474\) 0 0
\(475\) −3416.15 −0.329986
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4752.73 0.453357 0.226678 0.973970i \(-0.427213\pi\)
0.226678 + 0.973970i \(0.427213\pi\)
\(480\) 0 0
\(481\) 14527.9 1.37716
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 691.820 0.0647710
\(486\) 0 0
\(487\) −8412.56 −0.782771 −0.391386 0.920227i \(-0.628004\pi\)
−0.391386 + 0.920227i \(0.628004\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5570.45 0.511998 0.255999 0.966677i \(-0.417596\pi\)
0.255999 + 0.966677i \(0.417596\pi\)
\(492\) 0 0
\(493\) 183.869 0.0167973
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 16010.0 1.44496
\(498\) 0 0
\(499\) −15824.6 −1.41966 −0.709828 0.704375i \(-0.751227\pi\)
−0.709828 + 0.704375i \(0.751227\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15946.4 1.41354 0.706772 0.707441i \(-0.250151\pi\)
0.706772 + 0.707441i \(0.250151\pi\)
\(504\) 0 0
\(505\) 6628.89 0.584122
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14638.7 1.27475 0.637375 0.770553i \(-0.280020\pi\)
0.637375 + 0.770553i \(0.280020\pi\)
\(510\) 0 0
\(511\) 13304.1 1.15174
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1667.72 0.142696
\(516\) 0 0
\(517\) −43514.1 −3.70164
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13001.4 1.09329 0.546644 0.837365i \(-0.315905\pi\)
0.546644 + 0.837365i \(0.315905\pi\)
\(522\) 0 0
\(523\) −1938.88 −0.162106 −0.0810531 0.996710i \(-0.525828\pi\)
−0.0810531 + 0.996710i \(0.525828\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 649.996 0.0537273
\(528\) 0 0
\(529\) 14434.8 1.18639
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3466.06 0.281673
\(534\) 0 0
\(535\) −2920.02 −0.235969
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4960.96 −0.396444
\(540\) 0 0
\(541\) −7574.14 −0.601918 −0.300959 0.953637i \(-0.597307\pi\)
−0.300959 + 0.953637i \(0.597307\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −9577.09 −0.752729
\(546\) 0 0
\(547\) −3141.87 −0.245588 −0.122794 0.992432i \(-0.539185\pi\)
−0.122794 + 0.992432i \(0.539185\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1584.88 0.122538
\(552\) 0 0
\(553\) −19255.9 −1.48073
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12191.5 −0.927412 −0.463706 0.885989i \(-0.653481\pi\)
−0.463706 + 0.885989i \(0.653481\pi\)
\(558\) 0 0
\(559\) 15843.2 1.19874
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2182.85 0.163403 0.0817016 0.996657i \(-0.473965\pi\)
0.0817016 + 0.996657i \(0.473965\pi\)
\(564\) 0 0
\(565\) −6186.58 −0.460657
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1785.93 0.131582 0.0657911 0.997833i \(-0.479043\pi\)
0.0657911 + 0.997833i \(0.479043\pi\)
\(570\) 0 0
\(571\) 3404.30 0.249502 0.124751 0.992188i \(-0.460187\pi\)
0.124751 + 0.992188i \(0.460187\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4077.51 −0.295729
\(576\) 0 0
\(577\) −4174.78 −0.301210 −0.150605 0.988594i \(-0.548122\pi\)
−0.150605 + 0.988594i \(0.548122\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8325.00 −0.594457
\(582\) 0 0
\(583\) −42962.5 −3.05202
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18616.9 1.30904 0.654518 0.756047i \(-0.272872\pi\)
0.654518 + 0.756047i \(0.272872\pi\)
\(588\) 0 0
\(589\) 5602.72 0.391946
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24181.4 −1.67456 −0.837278 0.546777i \(-0.815855\pi\)
−0.837278 + 0.546777i \(0.815855\pi\)
\(594\) 0 0
\(595\) −1313.51 −0.0905022
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5339.43 −0.364212 −0.182106 0.983279i \(-0.558291\pi\)
−0.182106 + 0.983279i \(0.558291\pi\)
\(600\) 0 0
\(601\) 9165.72 0.622093 0.311046 0.950395i \(-0.399321\pi\)
0.311046 + 0.950395i \(0.399321\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 19653.0 1.32067
\(606\) 0 0
\(607\) 11431.7 0.764413 0.382206 0.924077i \(-0.375164\pi\)
0.382206 + 0.924077i \(0.375164\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 35931.9 2.37913
\(612\) 0 0
\(613\) 29975.6 1.97505 0.987523 0.157477i \(-0.0503361\pi\)
0.987523 + 0.157477i \(0.0503361\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6112.72 0.398847 0.199424 0.979913i \(-0.436093\pi\)
0.199424 + 0.979913i \(0.436093\pi\)
\(618\) 0 0
\(619\) 1387.97 0.0901250 0.0450625 0.998984i \(-0.485651\pi\)
0.0450625 + 0.998984i \(0.485651\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −145.261 −0.00934148
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3845.04 0.243739
\(630\) 0 0
\(631\) 18608.3 1.17399 0.586993 0.809592i \(-0.300312\pi\)
0.586993 + 0.809592i \(0.300312\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8927.12 −0.557893
\(636\) 0 0
\(637\) 4096.53 0.254804
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8039.55 −0.495387 −0.247693 0.968838i \(-0.579673\pi\)
−0.247693 + 0.968838i \(0.579673\pi\)
\(642\) 0 0
\(643\) −26661.4 −1.63518 −0.817592 0.575798i \(-0.804692\pi\)
−0.817592 + 0.575798i \(0.804692\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6303.13 0.383001 0.191501 0.981492i \(-0.438665\pi\)
0.191501 + 0.981492i \(0.438665\pi\)
\(648\) 0 0
\(649\) −20955.4 −1.26744
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22598.3 −1.35427 −0.677136 0.735857i \(-0.736779\pi\)
−0.677136 + 0.735857i \(0.736779\pi\)
\(654\) 0 0
\(655\) −3609.06 −0.215294
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2397.73 0.141733 0.0708667 0.997486i \(-0.477423\pi\)
0.0708667 + 0.997486i \(0.477423\pi\)
\(660\) 0 0
\(661\) −5063.62 −0.297961 −0.148980 0.988840i \(-0.547599\pi\)
−0.148980 + 0.988840i \(0.547599\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11322.0 −0.660223
\(666\) 0 0
\(667\) 1891.72 0.109816
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 59870.5 3.44452
\(672\) 0 0
\(673\) 7281.32 0.417050 0.208525 0.978017i \(-0.433134\pi\)
0.208525 + 0.978017i \(0.433134\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −28964.2 −1.64429 −0.822146 0.569277i \(-0.807223\pi\)
−0.822146 + 0.569277i \(0.807223\pi\)
\(678\) 0 0
\(679\) 2292.87 0.129591
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9158.42 0.513085 0.256543 0.966533i \(-0.417417\pi\)
0.256543 + 0.966533i \(0.417417\pi\)
\(684\) 0 0
\(685\) 5544.93 0.309286
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 35476.4 1.96160
\(690\) 0 0
\(691\) 10028.3 0.552090 0.276045 0.961145i \(-0.410976\pi\)
0.276045 + 0.961145i \(0.410976\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2183.85 0.119192
\(696\) 0 0
\(697\) 917.349 0.0498523
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27626.7 1.48851 0.744256 0.667894i \(-0.232804\pi\)
0.744256 + 0.667894i \(0.232804\pi\)
\(702\) 0 0
\(703\) 33142.8 1.77810
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 21969.9 1.16869
\(708\) 0 0
\(709\) 9703.69 0.514005 0.257003 0.966411i \(-0.417265\pi\)
0.257003 + 0.966411i \(0.417265\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6687.41 0.351256
\(714\) 0 0
\(715\) −21723.9 −1.13626
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32045.4 1.66216 0.831080 0.556153i \(-0.187723\pi\)
0.831080 + 0.556153i \(0.187723\pi\)
\(720\) 0 0
\(721\) 5527.25 0.285500
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −289.962 −0.0148537
\(726\) 0 0
\(727\) −7447.26 −0.379922 −0.189961 0.981792i \(-0.560836\pi\)
−0.189961 + 0.981792i \(0.560836\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4193.15 0.212161
\(732\) 0 0
\(733\) −18144.7 −0.914312 −0.457156 0.889386i \(-0.651132\pi\)
−0.457156 + 0.889386i \(0.651132\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 58793.1 2.93850
\(738\) 0 0
\(739\) 25920.2 1.29024 0.645121 0.764081i \(-0.276807\pi\)
0.645121 + 0.764081i \(0.276807\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9313.10 −0.459844 −0.229922 0.973209i \(-0.573847\pi\)
−0.229922 + 0.973209i \(0.573847\pi\)
\(744\) 0 0
\(745\) 885.585 0.0435508
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9677.69 −0.472116
\(750\) 0 0
\(751\) −4984.29 −0.242183 −0.121091 0.992641i \(-0.538639\pi\)
−0.121091 + 0.992641i \(0.538639\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4143.29 0.199722
\(756\) 0 0
\(757\) −10452.6 −0.501857 −0.250928 0.968006i \(-0.580736\pi\)
−0.250928 + 0.968006i \(0.580736\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9405.94 0.448049 0.224024 0.974584i \(-0.428080\pi\)
0.224024 + 0.974584i \(0.428080\pi\)
\(762\) 0 0
\(763\) −31741.0 −1.50603
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 17304.0 0.814615
\(768\) 0 0
\(769\) −23568.3 −1.10519 −0.552596 0.833449i \(-0.686363\pi\)
−0.552596 + 0.833449i \(0.686363\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3172.70 −0.147625 −0.0738125 0.997272i \(-0.523517\pi\)
−0.0738125 + 0.997272i \(0.523517\pi\)
\(774\) 0 0
\(775\) −1025.04 −0.0475106
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7907.21 0.363678
\(780\) 0 0
\(781\) 70079.7 3.21082
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4332.62 −0.196991
\(786\) 0 0
\(787\) 15442.4 0.699442 0.349721 0.936854i \(-0.386276\pi\)
0.349721 + 0.936854i \(0.386276\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −20503.9 −0.921663
\(792\) 0 0
\(793\) −49438.2 −2.21388
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −9968.55 −0.443042 −0.221521 0.975156i \(-0.571102\pi\)
−0.221521 + 0.975156i \(0.571102\pi\)
\(798\) 0 0
\(799\) 9509.97 0.421075
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 58235.5 2.55926
\(804\) 0 0
\(805\) −13513.9 −0.591681
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −10439.0 −0.453667 −0.226833 0.973934i \(-0.572837\pi\)
−0.226833 + 0.973934i \(0.572837\pi\)
\(810\) 0 0
\(811\) 17472.9 0.756544 0.378272 0.925694i \(-0.376518\pi\)
0.378272 + 0.925694i \(0.376518\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 14923.5 0.641408
\(816\) 0 0
\(817\) 36143.4 1.54773
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −19501.8 −0.829009 −0.414505 0.910047i \(-0.636045\pi\)
−0.414505 + 0.910047i \(0.636045\pi\)
\(822\) 0 0
\(823\) −16592.4 −0.702765 −0.351383 0.936232i \(-0.614288\pi\)
−0.351383 + 0.936232i \(0.614288\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32449.4 −1.36442 −0.682210 0.731156i \(-0.738981\pi\)
−0.682210 + 0.731156i \(0.738981\pi\)
\(828\) 0 0
\(829\) 7197.10 0.301527 0.150763 0.988570i \(-0.451827\pi\)
0.150763 + 0.988570i \(0.451827\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1084.21 0.0450970
\(834\) 0 0
\(835\) −9797.20 −0.406043
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15431.9 0.635005 0.317503 0.948257i \(-0.397156\pi\)
0.317503 + 0.948257i \(0.397156\pi\)
\(840\) 0 0
\(841\) −24254.5 −0.994484
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 6953.58 0.283089
\(846\) 0 0
\(847\) 65135.0 2.64235
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 39559.3 1.59351
\(852\) 0 0
\(853\) 7914.74 0.317697 0.158848 0.987303i \(-0.449222\pi\)
0.158848 + 0.987303i \(0.449222\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −26812.8 −1.06874 −0.534369 0.845252i \(-0.679451\pi\)
−0.534369 + 0.845252i \(0.679451\pi\)
\(858\) 0 0
\(859\) 1618.53 0.0642882 0.0321441 0.999483i \(-0.489766\pi\)
0.0321441 + 0.999483i \(0.489766\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −16678.5 −0.657869 −0.328935 0.944353i \(-0.606690\pi\)
−0.328935 + 0.944353i \(0.606690\pi\)
\(864\) 0 0
\(865\) −2534.72 −0.0996338
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −84288.0 −3.29030
\(870\) 0 0
\(871\) −48548.6 −1.88864
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2071.41 0.0800303
\(876\) 0 0
\(877\) −2128.31 −0.0819475 −0.0409738 0.999160i \(-0.513046\pi\)
−0.0409738 + 0.999160i \(0.513046\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2379.31 −0.0909886 −0.0454943 0.998965i \(-0.514486\pi\)
−0.0454943 + 0.998965i \(0.514486\pi\)
\(882\) 0 0
\(883\) −36926.5 −1.40733 −0.703666 0.710531i \(-0.748455\pi\)
−0.703666 + 0.710531i \(0.748455\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 4781.40 0.180996 0.0904981 0.995897i \(-0.471154\pi\)
0.0904981 + 0.995897i \(0.471154\pi\)
\(888\) 0 0
\(889\) −29586.8 −1.11621
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 81972.4 3.07178
\(894\) 0 0
\(895\) 15611.3 0.583049
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 475.558 0.0176426
\(900\) 0 0
\(901\) 9389.43 0.347178
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14141.9 −0.519439
\(906\) 0 0
\(907\) 48064.8 1.75961 0.879804 0.475337i \(-0.157674\pi\)
0.879804 + 0.475337i \(0.157674\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −25634.4 −0.932280 −0.466140 0.884711i \(-0.654356\pi\)
−0.466140 + 0.884711i \(0.654356\pi\)
\(912\) 0 0
\(913\) −36440.7 −1.32093
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −11961.4 −0.430751
\(918\) 0 0
\(919\) −9651.68 −0.346441 −0.173221 0.984883i \(-0.555417\pi\)
−0.173221 + 0.984883i \(0.555417\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −57868.6 −2.06367
\(924\) 0 0
\(925\) −6063.63 −0.215536
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −333.995 −0.0117955 −0.00589775 0.999983i \(-0.501877\pi\)
−0.00589775 + 0.999983i \(0.501877\pi\)
\(930\) 0 0
\(931\) 9345.51 0.328987
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5749.59 −0.201103
\(936\) 0 0
\(937\) 11567.3 0.403295 0.201648 0.979458i \(-0.435370\pi\)
0.201648 + 0.979458i \(0.435370\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 20261.7 0.701926 0.350963 0.936389i \(-0.385854\pi\)
0.350963 + 0.936389i \(0.385854\pi\)
\(942\) 0 0
\(943\) 9438.04 0.325923
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −27353.4 −0.938614 −0.469307 0.883035i \(-0.655496\pi\)
−0.469307 + 0.883035i \(0.655496\pi\)
\(948\) 0 0
\(949\) −48088.1 −1.64490
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −45432.0 −1.54427 −0.772133 0.635460i \(-0.780810\pi\)
−0.772133 + 0.635460i \(0.780810\pi\)
\(954\) 0 0
\(955\) −20393.2 −0.691003
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18377.3 0.618806
\(960\) 0 0
\(961\) −28109.9 −0.943569
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 15215.6 0.507572
\(966\) 0 0
\(967\) −7134.19 −0.237249 −0.118625 0.992939i \(-0.537849\pi\)
−0.118625 + 0.992939i \(0.537849\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −31719.4 −1.04833 −0.524163 0.851618i \(-0.675622\pi\)
−0.524163 + 0.851618i \(0.675622\pi\)
\(972\) 0 0
\(973\) 7237.84 0.238473
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 17570.3 0.575357 0.287678 0.957727i \(-0.407117\pi\)
0.287678 + 0.957727i \(0.407117\pi\)
\(978\) 0 0
\(979\) −635.843 −0.0207575
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 57987.3 1.88149 0.940746 0.339111i \(-0.110126\pi\)
0.940746 + 0.339111i \(0.110126\pi\)
\(984\) 0 0
\(985\) −6691.07 −0.216442
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 43140.8 1.38705
\(990\) 0 0
\(991\) 20741.2 0.664851 0.332425 0.943130i \(-0.392133\pi\)
0.332425 + 0.943130i \(0.392133\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2268.22 0.0722689
\(996\) 0 0
\(997\) −9921.41 −0.315160 −0.157580 0.987506i \(-0.550369\pi\)
−0.157580 + 0.987506i \(0.550369\pi\)
\(998\) 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 1620.4.a.j.1.5 yes 6
3.2 odd 2 1620.4.a.i.1.5 6
9.2 odd 6 1620.4.i.x.1081.2 12
9.4 even 3 1620.4.i.w.541.2 12
9.5 odd 6 1620.4.i.x.541.2 12
9.7 even 3 1620.4.i.w.1081.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1620.4.a.i.1.5 6 3.2 odd 2
1620.4.a.j.1.5 yes 6 1.1 even 1 trivial
1620.4.i.w.541.2 12 9.4 even 3
1620.4.i.w.1081.2 12 9.7 even 3
1620.4.i.x.541.2 12 9.5 odd 6
1620.4.i.x.1081.2 12 9.2 odd 6