Properties

Label 1152.4.a.r.1.1
Level $1152$
Weight $4$
Character 1152.1
Self dual yes
Analytic conductor $67.970$
Analytic rank $0$
Dimension $2$
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] = [1152,4,Mod(1,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, 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("1152.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1152.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: \(67.9702003266\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 128)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 1152.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-15.8564 q^{5} +17.8564 q^{7} +O(q^{10})\) \(q-15.8564 q^{5} +17.8564 q^{7} +52.9282 q^{11} +8.43078 q^{13} -129.138 q^{17} -50.4974 q^{19} +128.708 q^{23} +126.426 q^{25} -111.282 q^{29} +302.851 q^{31} -283.138 q^{35} -182.995 q^{37} +94.5744 q^{41} -184.641 q^{43} +296.841 q^{47} -24.1487 q^{49} +102.995 q^{53} -839.251 q^{55} -93.3693 q^{59} -338.974 q^{61} -133.682 q^{65} -489.041 q^{67} -86.9845 q^{71} -154.267 q^{73} +945.108 q^{77} +449.415 q^{79} +383.933 q^{83} +2047.67 q^{85} +517.672 q^{89} +150.543 q^{91} +800.708 q^{95} +1739.39 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{5} + 8 q^{7} + 92 q^{11} + 100 q^{13} - 92 q^{17} - 4 q^{19} + 8 q^{23} + 142 q^{25} - 84 q^{29} + 384 q^{31} - 400 q^{35} - 172 q^{37} + 300 q^{41} - 300 q^{43} - 16 q^{47} - 270 q^{49} + 12 q^{53} - 376 q^{55} - 644 q^{59} + 292 q^{61} + 952 q^{65} + 172 q^{67} + 408 q^{71} + 412 q^{73} + 560 q^{77} + 400 q^{79} + 948 q^{83} + 2488 q^{85} - 572 q^{89} - 752 q^{91} + 1352 q^{95} + 2204 q^{97}+O(q^{100}) \) 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
\(5\) −15.8564 −1.41824 −0.709120 0.705088i \(-0.750908\pi\)
−0.709120 + 0.705088i \(0.750908\pi\)
\(6\) 0 0
\(7\) 17.8564 0.964155 0.482078 0.876128i \(-0.339882\pi\)
0.482078 + 0.876128i \(0.339882\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 52.9282 1.45077 0.725384 0.688344i \(-0.241662\pi\)
0.725384 + 0.688344i \(0.241662\pi\)
\(12\) 0 0
\(13\) 8.43078 0.179868 0.0899338 0.995948i \(-0.471334\pi\)
0.0899338 + 0.995948i \(0.471334\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −129.138 −1.84239 −0.921196 0.389098i \(-0.872787\pi\)
−0.921196 + 0.389098i \(0.872787\pi\)
\(18\) 0 0
\(19\) −50.4974 −0.609732 −0.304866 0.952395i \(-0.598612\pi\)
−0.304866 + 0.952395i \(0.598612\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 128.708 1.16684 0.583422 0.812169i \(-0.301713\pi\)
0.583422 + 0.812169i \(0.301713\pi\)
\(24\) 0 0
\(25\) 126.426 1.01141
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −111.282 −0.712571 −0.356285 0.934377i \(-0.615957\pi\)
−0.356285 + 0.934377i \(0.615957\pi\)
\(30\) 0 0
\(31\) 302.851 1.75464 0.877318 0.479910i \(-0.159331\pi\)
0.877318 + 0.479910i \(0.159331\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −283.138 −1.36740
\(36\) 0 0
\(37\) −182.995 −0.813086 −0.406543 0.913632i \(-0.633266\pi\)
−0.406543 + 0.913632i \(0.633266\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 94.5744 0.360245 0.180122 0.983644i \(-0.442351\pi\)
0.180122 + 0.983644i \(0.442351\pi\)
\(42\) 0 0
\(43\) −184.641 −0.654825 −0.327413 0.944881i \(-0.606177\pi\)
−0.327413 + 0.944881i \(0.606177\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 296.841 0.921249 0.460624 0.887595i \(-0.347625\pi\)
0.460624 + 0.887595i \(0.347625\pi\)
\(48\) 0 0
\(49\) −24.1487 −0.0704045
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 102.995 0.266933 0.133466 0.991053i \(-0.457389\pi\)
0.133466 + 0.991053i \(0.457389\pi\)
\(54\) 0 0
\(55\) −839.251 −2.05754
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −93.3693 −0.206028 −0.103014 0.994680i \(-0.532849\pi\)
−0.103014 + 0.994680i \(0.532849\pi\)
\(60\) 0 0
\(61\) −338.974 −0.711495 −0.355748 0.934582i \(-0.615774\pi\)
−0.355748 + 0.934582i \(0.615774\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −133.682 −0.255095
\(66\) 0 0
\(67\) −489.041 −0.891729 −0.445865 0.895100i \(-0.647104\pi\)
−0.445865 + 0.895100i \(0.647104\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −86.9845 −0.145397 −0.0726983 0.997354i \(-0.523161\pi\)
−0.0726983 + 0.997354i \(0.523161\pi\)
\(72\) 0 0
\(73\) −154.267 −0.247336 −0.123668 0.992324i \(-0.539466\pi\)
−0.123668 + 0.992324i \(0.539466\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 945.108 1.39877
\(78\) 0 0
\(79\) 449.415 0.640040 0.320020 0.947411i \(-0.396310\pi\)
0.320020 + 0.947411i \(0.396310\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 383.933 0.507737 0.253868 0.967239i \(-0.418297\pi\)
0.253868 + 0.967239i \(0.418297\pi\)
\(84\) 0 0
\(85\) 2047.67 2.61295
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 517.672 0.616551 0.308276 0.951297i \(-0.400248\pi\)
0.308276 + 0.951297i \(0.400248\pi\)
\(90\) 0 0
\(91\) 150.543 0.173420
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 800.708 0.864746
\(96\) 0 0
\(97\) 1739.39 1.82071 0.910355 0.413829i \(-0.135809\pi\)
0.910355 + 0.413829i \(0.135809\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1158.99 1.14182 0.570912 0.821011i \(-0.306590\pi\)
0.570912 + 0.821011i \(0.306590\pi\)
\(102\) 0 0
\(103\) 1635.01 1.56410 0.782048 0.623218i \(-0.214175\pi\)
0.782048 + 0.623218i \(0.214175\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 282.589 0.255317 0.127659 0.991818i \(-0.459254\pi\)
0.127659 + 0.991818i \(0.459254\pi\)
\(108\) 0 0
\(109\) 1004.98 0.883120 0.441560 0.897232i \(-0.354425\pi\)
0.441560 + 0.897232i \(0.354425\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 567.108 0.472115 0.236057 0.971739i \(-0.424145\pi\)
0.236057 + 0.971739i \(0.424145\pi\)
\(114\) 0 0
\(115\) −2040.84 −1.65486
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2305.95 −1.77635
\(120\) 0 0
\(121\) 1470.39 1.10473
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −22.6053 −0.0161750
\(126\) 0 0
\(127\) 496.616 0.346988 0.173494 0.984835i \(-0.444494\pi\)
0.173494 + 0.984835i \(0.444494\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1658.72 1.10628 0.553142 0.833087i \(-0.313429\pi\)
0.553142 + 0.833087i \(0.313429\pi\)
\(132\) 0 0
\(133\) −901.703 −0.587876
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 432.872 0.269947 0.134974 0.990849i \(-0.456905\pi\)
0.134974 + 0.990849i \(0.456905\pi\)
\(138\) 0 0
\(139\) 146.148 0.0891809 0.0445904 0.999005i \(-0.485802\pi\)
0.0445904 + 0.999005i \(0.485802\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 446.226 0.260946
\(144\) 0 0
\(145\) 1764.53 1.01060
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3556.29 −1.95532 −0.977659 0.210198i \(-0.932589\pi\)
−0.977659 + 0.210198i \(0.932589\pi\)
\(150\) 0 0
\(151\) 1320.32 0.711562 0.355781 0.934569i \(-0.384215\pi\)
0.355781 + 0.934569i \(0.384215\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4802.13 −2.48849
\(156\) 0 0
\(157\) 2040.43 1.03722 0.518612 0.855010i \(-0.326449\pi\)
0.518612 + 0.855010i \(0.326449\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2298.26 1.12502
\(162\) 0 0
\(163\) 2392.21 1.14952 0.574762 0.818321i \(-0.305095\pi\)
0.574762 + 0.818321i \(0.305095\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2068.34 0.958400 0.479200 0.877706i \(-0.340927\pi\)
0.479200 + 0.877706i \(0.340927\pi\)
\(168\) 0 0
\(169\) −2125.92 −0.967648
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2441.87 1.07313 0.536566 0.843859i \(-0.319721\pi\)
0.536566 + 0.843859i \(0.319721\pi\)
\(174\) 0 0
\(175\) 2257.51 0.975152
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2430.84 −1.01502 −0.507512 0.861645i \(-0.669435\pi\)
−0.507512 + 0.861645i \(0.669435\pi\)
\(180\) 0 0
\(181\) 1928.96 0.792148 0.396074 0.918219i \(-0.370372\pi\)
0.396074 + 0.918219i \(0.370372\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2901.64 1.15315
\(186\) 0 0
\(187\) −6835.07 −2.67288
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4087.34 1.54843 0.774214 0.632924i \(-0.218145\pi\)
0.774214 + 0.632924i \(0.218145\pi\)
\(192\) 0 0
\(193\) −1156.52 −0.431339 −0.215669 0.976466i \(-0.569193\pi\)
−0.215669 + 0.976466i \(0.569193\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2658.44 0.961452 0.480726 0.876871i \(-0.340373\pi\)
0.480726 + 0.876871i \(0.340373\pi\)
\(198\) 0 0
\(199\) 742.369 0.264448 0.132224 0.991220i \(-0.457788\pi\)
0.132224 + 0.991220i \(0.457788\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1987.10 −0.687029
\(204\) 0 0
\(205\) −1499.61 −0.510914
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2672.74 −0.884580
\(210\) 0 0
\(211\) 3838.30 1.25232 0.626160 0.779694i \(-0.284626\pi\)
0.626160 + 0.779694i \(0.284626\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2927.74 0.928700
\(216\) 0 0
\(217\) 5407.84 1.69174
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1088.74 −0.331387
\(222\) 0 0
\(223\) 3418.34 1.02650 0.513249 0.858240i \(-0.328442\pi\)
0.513249 + 0.858240i \(0.328442\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 515.729 0.150793 0.0753967 0.997154i \(-0.475978\pi\)
0.0753967 + 0.997154i \(0.475978\pi\)
\(228\) 0 0
\(229\) 1595.26 0.460340 0.230170 0.973150i \(-0.426072\pi\)
0.230170 + 0.973150i \(0.426072\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5251.27 −1.47649 −0.738245 0.674533i \(-0.764345\pi\)
−0.738245 + 0.674533i \(0.764345\pi\)
\(234\) 0 0
\(235\) −4706.83 −1.30655
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2029.27 −0.549216 −0.274608 0.961556i \(-0.588548\pi\)
−0.274608 + 0.961556i \(0.588548\pi\)
\(240\) 0 0
\(241\) −4615.72 −1.23371 −0.616856 0.787076i \(-0.711594\pi\)
−0.616856 + 0.787076i \(0.711594\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 382.912 0.0998505
\(246\) 0 0
\(247\) −425.733 −0.109671
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2702.52 −0.679607 −0.339804 0.940496i \(-0.610361\pi\)
−0.339804 + 0.940496i \(0.610361\pi\)
\(252\) 0 0
\(253\) 6812.27 1.69282
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −991.785 −0.240723 −0.120362 0.992730i \(-0.538405\pi\)
−0.120362 + 0.992730i \(0.538405\pi\)
\(258\) 0 0
\(259\) −3267.63 −0.783941
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7430.74 −1.74220 −0.871101 0.491105i \(-0.836593\pi\)
−0.871101 + 0.491105i \(0.836593\pi\)
\(264\) 0 0
\(265\) −1633.13 −0.378575
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3281.50 −0.743778 −0.371889 0.928277i \(-0.621290\pi\)
−0.371889 + 0.928277i \(0.621290\pi\)
\(270\) 0 0
\(271\) 221.518 0.0496542 0.0248271 0.999692i \(-0.492096\pi\)
0.0248271 + 0.999692i \(0.492096\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6691.48 1.46731
\(276\) 0 0
\(277\) 1106.28 0.239963 0.119982 0.992776i \(-0.461716\pi\)
0.119982 + 0.992776i \(0.461716\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2372.52 0.503676 0.251838 0.967769i \(-0.418965\pi\)
0.251838 + 0.967769i \(0.418965\pi\)
\(282\) 0 0
\(283\) −2549.89 −0.535602 −0.267801 0.963474i \(-0.586297\pi\)
−0.267801 + 0.963474i \(0.586297\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1688.76 0.347332
\(288\) 0 0
\(289\) 11763.7 2.39441
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −130.319 −0.0259840 −0.0129920 0.999916i \(-0.504136\pi\)
−0.0129920 + 0.999916i \(0.504136\pi\)
\(294\) 0 0
\(295\) 1480.50 0.292197
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1085.11 0.209877
\(300\) 0 0
\(301\) −3297.03 −0.631353
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5374.91 1.00907
\(306\) 0 0
\(307\) 62.1182 0.0115481 0.00577406 0.999983i \(-0.498162\pi\)
0.00577406 + 0.999983i \(0.498162\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −593.837 −0.108275 −0.0541373 0.998533i \(-0.517241\pi\)
−0.0541373 + 0.998533i \(0.517241\pi\)
\(312\) 0 0
\(313\) 3669.69 0.662694 0.331347 0.943509i \(-0.392497\pi\)
0.331347 + 0.943509i \(0.392497\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −374.339 −0.0663249 −0.0331625 0.999450i \(-0.510558\pi\)
−0.0331625 + 0.999450i \(0.510558\pi\)
\(318\) 0 0
\(319\) −5889.96 −1.03378
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6521.16 1.12337
\(324\) 0 0
\(325\) 1065.87 0.181919
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5300.51 0.888227
\(330\) 0 0
\(331\) 5871.13 0.974945 0.487472 0.873138i \(-0.337919\pi\)
0.487472 + 0.873138i \(0.337919\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7754.43 1.26469
\(336\) 0 0
\(337\) 1047.83 0.169373 0.0846865 0.996408i \(-0.473011\pi\)
0.0846865 + 0.996408i \(0.473011\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16029.4 2.54557
\(342\) 0 0
\(343\) −6555.96 −1.03204
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3921.88 −0.606737 −0.303368 0.952873i \(-0.598111\pi\)
−0.303368 + 0.952873i \(0.598111\pi\)
\(348\) 0 0
\(349\) −11604.9 −1.77993 −0.889966 0.456027i \(-0.849272\pi\)
−0.889966 + 0.456027i \(0.849272\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1530.22 0.230724 0.115362 0.993324i \(-0.463197\pi\)
0.115362 + 0.993324i \(0.463197\pi\)
\(354\) 0 0
\(355\) 1379.26 0.206207
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10764.0 −1.58246 −0.791231 0.611518i \(-0.790559\pi\)
−0.791231 + 0.611518i \(0.790559\pi\)
\(360\) 0 0
\(361\) −4309.01 −0.628227
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2446.11 0.350782
\(366\) 0 0
\(367\) 10713.0 1.52374 0.761869 0.647731i \(-0.224282\pi\)
0.761869 + 0.647731i \(0.224282\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1839.12 0.257365
\(372\) 0 0
\(373\) −9186.32 −1.27520 −0.637600 0.770368i \(-0.720073\pi\)
−0.637600 + 0.770368i \(0.720073\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −938.194 −0.128168
\(378\) 0 0
\(379\) 14201.0 1.92468 0.962342 0.271842i \(-0.0876327\pi\)
0.962342 + 0.271842i \(0.0876327\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9691.24 1.29295 0.646474 0.762936i \(-0.276243\pi\)
0.646474 + 0.762936i \(0.276243\pi\)
\(384\) 0 0
\(385\) −14986.0 −1.98379
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6358.79 −0.828801 −0.414400 0.910095i \(-0.636009\pi\)
−0.414400 + 0.910095i \(0.636009\pi\)
\(390\) 0 0
\(391\) −16621.1 −2.14978
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7126.11 −0.907731
\(396\) 0 0
\(397\) 13034.2 1.64778 0.823888 0.566752i \(-0.191800\pi\)
0.823888 + 0.566752i \(0.191800\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6705.06 −0.834999 −0.417499 0.908677i \(-0.637093\pi\)
−0.417499 + 0.908677i \(0.637093\pi\)
\(402\) 0 0
\(403\) 2553.27 0.315602
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9685.59 −1.17960
\(408\) 0 0
\(409\) 10967.8 1.32598 0.662988 0.748630i \(-0.269288\pi\)
0.662988 + 0.748630i \(0.269288\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1667.24 −0.198643
\(414\) 0 0
\(415\) −6087.80 −0.720093
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13686.0 1.59571 0.797856 0.602849i \(-0.205968\pi\)
0.797856 + 0.602849i \(0.205968\pi\)
\(420\) 0 0
\(421\) −8552.92 −0.990128 −0.495064 0.868857i \(-0.664855\pi\)
−0.495064 + 0.868857i \(0.664855\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −16326.4 −1.86340
\(426\) 0 0
\(427\) −6052.86 −0.685992
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12187.6 1.36208 0.681039 0.732247i \(-0.261528\pi\)
0.681039 + 0.732247i \(0.261528\pi\)
\(432\) 0 0
\(433\) −8906.35 −0.988480 −0.494240 0.869326i \(-0.664554\pi\)
−0.494240 + 0.869326i \(0.664554\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6499.41 −0.711462
\(438\) 0 0
\(439\) 4655.21 0.506107 0.253054 0.967452i \(-0.418565\pi\)
0.253054 + 0.967452i \(0.418565\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10008.8 1.07343 0.536716 0.843763i \(-0.319665\pi\)
0.536716 + 0.843763i \(0.319665\pi\)
\(444\) 0 0
\(445\) −8208.41 −0.874418
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3373.71 0.354600 0.177300 0.984157i \(-0.443264\pi\)
0.177300 + 0.984157i \(0.443264\pi\)
\(450\) 0 0
\(451\) 5005.65 0.522632
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2387.08 −0.245952
\(456\) 0 0
\(457\) −13600.4 −1.39212 −0.696060 0.717984i \(-0.745065\pi\)
−0.696060 + 0.717984i \(0.745065\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3559.45 0.359609 0.179805 0.983702i \(-0.442453\pi\)
0.179805 + 0.983702i \(0.442453\pi\)
\(462\) 0 0
\(463\) 8019.14 0.804926 0.402463 0.915436i \(-0.368154\pi\)
0.402463 + 0.915436i \(0.368154\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2066.14 −0.204731 −0.102365 0.994747i \(-0.532641\pi\)
−0.102365 + 0.994747i \(0.532641\pi\)
\(468\) 0 0
\(469\) −8732.51 −0.859765
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9772.72 −0.950000
\(474\) 0 0
\(475\) −6384.17 −0.616686
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3679.26 −0.350960 −0.175480 0.984483i \(-0.556148\pi\)
−0.175480 + 0.984483i \(0.556148\pi\)
\(480\) 0 0
\(481\) −1542.79 −0.146248
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −27580.5 −2.58220
\(486\) 0 0
\(487\) −10884.4 −1.01277 −0.506386 0.862307i \(-0.669019\pi\)
−0.506386 + 0.862307i \(0.669019\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14548.9 −1.33723 −0.668616 0.743608i \(-0.733113\pi\)
−0.668616 + 0.743608i \(0.733113\pi\)
\(492\) 0 0
\(493\) 14370.8 1.31284
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1553.23 −0.140185
\(498\) 0 0
\(499\) −8461.92 −0.759134 −0.379567 0.925164i \(-0.623927\pi\)
−0.379567 + 0.925164i \(0.623927\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −983.702 −0.0871990 −0.0435995 0.999049i \(-0.513883\pi\)
−0.0435995 + 0.999049i \(0.513883\pi\)
\(504\) 0 0
\(505\) −18377.5 −1.61938
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14472.5 −1.26028 −0.630140 0.776481i \(-0.717003\pi\)
−0.630140 + 0.776481i \(0.717003\pi\)
\(510\) 0 0
\(511\) −2754.65 −0.238470
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −25925.3 −2.21826
\(516\) 0 0
\(517\) 15711.3 1.33652
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10761.8 0.904959 0.452480 0.891775i \(-0.350540\pi\)
0.452480 + 0.891775i \(0.350540\pi\)
\(522\) 0 0
\(523\) 1516.67 0.126806 0.0634029 0.997988i \(-0.479805\pi\)
0.0634029 + 0.997988i \(0.479805\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −39109.7 −3.23273
\(528\) 0 0
\(529\) 4398.66 0.361524
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 797.336 0.0647963
\(534\) 0 0
\(535\) −4480.85 −0.362101
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1278.15 −0.102141
\(540\) 0 0
\(541\) −22541.9 −1.79141 −0.895704 0.444652i \(-0.853327\pi\)
−0.895704 + 0.444652i \(0.853327\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −15935.4 −1.25248
\(546\) 0 0
\(547\) 10202.0 0.797448 0.398724 0.917071i \(-0.369453\pi\)
0.398724 + 0.917071i \(0.369453\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5619.46 0.434477
\(552\) 0 0
\(553\) 8024.94 0.617098
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7139.06 0.543073 0.271536 0.962428i \(-0.412468\pi\)
0.271536 + 0.962428i \(0.412468\pi\)
\(558\) 0 0
\(559\) −1556.67 −0.117782
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19558.0 1.46407 0.732034 0.681268i \(-0.238571\pi\)
0.732034 + 0.681268i \(0.238571\pi\)
\(564\) 0 0
\(565\) −8992.29 −0.669572
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5835.86 0.429969 0.214984 0.976617i \(-0.431030\pi\)
0.214984 + 0.976617i \(0.431030\pi\)
\(570\) 0 0
\(571\) 9820.65 0.719757 0.359879 0.932999i \(-0.382818\pi\)
0.359879 + 0.932999i \(0.382818\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16271.9 1.18015
\(576\) 0 0
\(577\) 451.231 0.0325563 0.0162782 0.999868i \(-0.494818\pi\)
0.0162782 + 0.999868i \(0.494818\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6855.67 0.489537
\(582\) 0 0
\(583\) 5451.33 0.387257
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24775.7 1.74208 0.871042 0.491209i \(-0.163445\pi\)
0.871042 + 0.491209i \(0.163445\pi\)
\(588\) 0 0
\(589\) −15293.2 −1.06986
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4207.64 0.291378 0.145689 0.989330i \(-0.453460\pi\)
0.145689 + 0.989330i \(0.453460\pi\)
\(594\) 0 0
\(595\) 36564.1 2.51929
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1916.32 0.130715 0.0653577 0.997862i \(-0.479181\pi\)
0.0653577 + 0.997862i \(0.479181\pi\)
\(600\) 0 0
\(601\) −19361.1 −1.31407 −0.657034 0.753861i \(-0.728189\pi\)
−0.657034 + 0.753861i \(0.728189\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −23315.2 −1.56677
\(606\) 0 0
\(607\) −6097.02 −0.407694 −0.203847 0.979003i \(-0.565345\pi\)
−0.203847 + 0.979003i \(0.565345\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2502.60 0.165703
\(612\) 0 0
\(613\) −13837.7 −0.911743 −0.455872 0.890046i \(-0.650672\pi\)
−0.455872 + 0.890046i \(0.650672\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11959.1 −0.780318 −0.390159 0.920747i \(-0.627580\pi\)
−0.390159 + 0.920747i \(0.627580\pi\)
\(618\) 0 0
\(619\) 8385.02 0.544463 0.272231 0.962232i \(-0.412238\pi\)
0.272231 + 0.962232i \(0.412238\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9243.75 0.594451
\(624\) 0 0
\(625\) −15444.8 −0.988465
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 23631.7 1.49802
\(630\) 0 0
\(631\) −13592.1 −0.857513 −0.428757 0.903420i \(-0.641048\pi\)
−0.428757 + 0.903420i \(0.641048\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7874.54 −0.492113
\(636\) 0 0
\(637\) −203.593 −0.0126635
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 18123.4 1.11674 0.558371 0.829591i \(-0.311427\pi\)
0.558371 + 0.829591i \(0.311427\pi\)
\(642\) 0 0
\(643\) 25042.1 1.53587 0.767935 0.640528i \(-0.221284\pi\)
0.767935 + 0.640528i \(0.221284\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6022.08 −0.365923 −0.182962 0.983120i \(-0.558568\pi\)
−0.182962 + 0.983120i \(0.558568\pi\)
\(648\) 0 0
\(649\) −4941.87 −0.298899
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14093.8 0.844617 0.422308 0.906452i \(-0.361220\pi\)
0.422308 + 0.906452i \(0.361220\pi\)
\(654\) 0 0
\(655\) −26301.4 −1.56898
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17240.7 1.01912 0.509562 0.860434i \(-0.329807\pi\)
0.509562 + 0.860434i \(0.329807\pi\)
\(660\) 0 0
\(661\) 20209.5 1.18920 0.594598 0.804023i \(-0.297311\pi\)
0.594598 + 0.804023i \(0.297311\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 14297.8 0.833749
\(666\) 0 0
\(667\) −14322.8 −0.831459
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −17941.3 −1.03221
\(672\) 0 0
\(673\) 6838.55 0.391689 0.195845 0.980635i \(-0.437255\pi\)
0.195845 + 0.980635i \(0.437255\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 187.425 0.0106401 0.00532003 0.999986i \(-0.498307\pi\)
0.00532003 + 0.999986i \(0.498307\pi\)
\(678\) 0 0
\(679\) 31059.3 1.75545
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −23476.0 −1.31520 −0.657601 0.753367i \(-0.728429\pi\)
−0.657601 + 0.753367i \(0.728429\pi\)
\(684\) 0 0
\(685\) −6863.79 −0.382850
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 868.327 0.0480125
\(690\) 0 0
\(691\) −6309.92 −0.347382 −0.173691 0.984800i \(-0.555569\pi\)
−0.173691 + 0.984800i \(0.555569\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2317.39 −0.126480
\(696\) 0 0
\(697\) −12213.2 −0.663712
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 24920.4 1.34270 0.671348 0.741142i \(-0.265716\pi\)
0.671348 + 0.741142i \(0.265716\pi\)
\(702\) 0 0
\(703\) 9240.77 0.495764
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 20695.5 1.10090
\(708\) 0 0
\(709\) 14478.9 0.766949 0.383474 0.923551i \(-0.374727\pi\)
0.383474 + 0.923551i \(0.374727\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 38979.3 2.04738
\(714\) 0 0
\(715\) −7075.54 −0.370084
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6411.30 0.332547 0.166273 0.986080i \(-0.446827\pi\)
0.166273 + 0.986080i \(0.446827\pi\)
\(720\) 0 0
\(721\) 29195.3 1.50803
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −14068.9 −0.720698
\(726\) 0 0
\(727\) −20626.3 −1.05225 −0.526126 0.850407i \(-0.676356\pi\)
−0.526126 + 0.850407i \(0.676356\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 23844.3 1.20645
\(732\) 0 0
\(733\) 5732.29 0.288850 0.144425 0.989516i \(-0.453867\pi\)
0.144425 + 0.989516i \(0.453867\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −25884.1 −1.29369
\(738\) 0 0
\(739\) −36336.0 −1.80872 −0.904359 0.426773i \(-0.859650\pi\)
−0.904359 + 0.426773i \(0.859650\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4363.83 −0.215469 −0.107734 0.994180i \(-0.534360\pi\)
−0.107734 + 0.994180i \(0.534360\pi\)
\(744\) 0 0
\(745\) 56389.9 2.77311
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5046.03 0.246166
\(750\) 0 0
\(751\) −16162.7 −0.785334 −0.392667 0.919681i \(-0.628448\pi\)
−0.392667 + 0.919681i \(0.628448\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20935.5 −1.00917
\(756\) 0 0
\(757\) 4411.92 0.211828 0.105914 0.994375i \(-0.466223\pi\)
0.105914 + 0.994375i \(0.466223\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −28281.8 −1.34719 −0.673597 0.739099i \(-0.735251\pi\)
−0.673597 + 0.739099i \(0.735251\pi\)
\(762\) 0 0
\(763\) 17945.4 0.851465
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −787.176 −0.0370577
\(768\) 0 0
\(769\) −15016.8 −0.704186 −0.352093 0.935965i \(-0.614530\pi\)
−0.352093 + 0.935965i \(0.614530\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8674.11 −0.403604 −0.201802 0.979426i \(-0.564680\pi\)
−0.201802 + 0.979426i \(0.564680\pi\)
\(774\) 0 0
\(775\) 38288.2 1.77465
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4775.76 −0.219653
\(780\) 0 0
\(781\) −4603.94 −0.210937
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −32353.9 −1.47103
\(786\) 0 0
\(787\) −23660.2 −1.07166 −0.535829 0.844327i \(-0.680001\pi\)
−0.535829 + 0.844327i \(0.680001\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10126.5 0.455192
\(792\) 0 0
\(793\) −2857.82 −0.127975
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −35432.5 −1.57476 −0.787380 0.616468i \(-0.788563\pi\)
−0.787380 + 0.616468i \(0.788563\pi\)
\(798\) 0 0
\(799\) −38333.6 −1.69730
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8165.05 −0.358827
\(804\) 0 0
\(805\) −36442.1 −1.59555
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 14005.5 0.608664 0.304332 0.952566i \(-0.401567\pi\)
0.304332 + 0.952566i \(0.401567\pi\)
\(810\) 0 0
\(811\) −22580.8 −0.977706 −0.488853 0.872366i \(-0.662584\pi\)
−0.488853 + 0.872366i \(0.662584\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −37931.8 −1.63030
\(816\) 0 0
\(817\) 9323.90 0.399268
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −21308.9 −0.905827 −0.452914 0.891554i \(-0.649615\pi\)
−0.452914 + 0.891554i \(0.649615\pi\)
\(822\) 0 0
\(823\) 13571.4 0.574810 0.287405 0.957809i \(-0.407207\pi\)
0.287405 + 0.957809i \(0.407207\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 19295.2 0.811318 0.405659 0.914025i \(-0.367042\pi\)
0.405659 + 0.914025i \(0.367042\pi\)
\(828\) 0 0
\(829\) 28752.7 1.20461 0.602306 0.798265i \(-0.294249\pi\)
0.602306 + 0.798265i \(0.294249\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3118.53 0.129713
\(834\) 0 0
\(835\) −32796.4 −1.35924
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 566.927 0.0233284 0.0116642 0.999932i \(-0.496287\pi\)
0.0116642 + 0.999932i \(0.496287\pi\)
\(840\) 0 0
\(841\) −12005.3 −0.492243
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 33709.5 1.37236
\(846\) 0 0
\(847\) 26256.0 1.06513
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −23552.8 −0.948744
\(852\) 0 0
\(853\) 34698.1 1.39278 0.696389 0.717665i \(-0.254789\pi\)
0.696389 + 0.717665i \(0.254789\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −37362.0 −1.48922 −0.744610 0.667500i \(-0.767364\pi\)
−0.744610 + 0.667500i \(0.767364\pi\)
\(858\) 0 0
\(859\) 29572.2 1.17461 0.587305 0.809366i \(-0.300189\pi\)
0.587305 + 0.809366i \(0.300189\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11636.5 0.458994 0.229497 0.973309i \(-0.426292\pi\)
0.229497 + 0.973309i \(0.426292\pi\)
\(864\) 0 0
\(865\) −38719.2 −1.52196
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 23786.7 0.928550
\(870\) 0 0
\(871\) −4123.00 −0.160393
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −403.649 −0.0155952
\(876\) 0 0
\(877\) 19878.2 0.765380 0.382690 0.923877i \(-0.374998\pi\)
0.382690 + 0.923877i \(0.374998\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 36460.3 1.39430 0.697150 0.716926i \(-0.254451\pi\)
0.697150 + 0.716926i \(0.254451\pi\)
\(882\) 0 0
\(883\) −28119.9 −1.07170 −0.535849 0.844314i \(-0.680009\pi\)
−0.535849 + 0.844314i \(0.680009\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 41888.4 1.58565 0.792826 0.609448i \(-0.208609\pi\)
0.792826 + 0.609448i \(0.208609\pi\)
\(888\) 0 0
\(889\) 8867.77 0.334551
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −14989.7 −0.561715
\(894\) 0 0
\(895\) 38544.3 1.43955
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −33701.9 −1.25030
\(900\) 0 0
\(901\) −13300.6 −0.491795
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −30586.4 −1.12346
\(906\) 0 0
\(907\) 12575.3 0.460371 0.230185 0.973147i \(-0.426067\pi\)
0.230185 + 0.973147i \(0.426067\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 39814.7 1.44799 0.723995 0.689805i \(-0.242304\pi\)
0.723995 + 0.689805i \(0.242304\pi\)
\(912\) 0 0
\(913\) 20320.9 0.736609
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 29618.8 1.06663
\(918\) 0 0
\(919\) 8987.93 0.322616 0.161308 0.986904i \(-0.448429\pi\)
0.161308 + 0.986904i \(0.448429\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −733.348 −0.0261521
\(924\) 0 0
\(925\) −23135.2 −0.822359
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −234.252 −0.00827293 −0.00413647 0.999991i \(-0.501317\pi\)
−0.00413647 + 0.999991i \(0.501317\pi\)
\(930\) 0 0
\(931\) 1219.45 0.0429279
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 108380. 3.79079
\(936\) 0 0
\(937\) 17624.6 0.614483 0.307241 0.951632i \(-0.400594\pi\)
0.307241 + 0.951632i \(0.400594\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 30532.1 1.05772 0.528861 0.848708i \(-0.322619\pi\)
0.528861 + 0.848708i \(0.322619\pi\)
\(942\) 0 0
\(943\) 12172.4 0.420349
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −42092.8 −1.44438 −0.722192 0.691692i \(-0.756865\pi\)
−0.722192 + 0.691692i \(0.756865\pi\)
\(948\) 0 0
\(949\) −1300.59 −0.0444877
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 48641.0 1.65334 0.826672 0.562683i \(-0.190231\pi\)
0.826672 + 0.562683i \(0.190231\pi\)
\(954\) 0 0
\(955\) −64810.6 −2.19604
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 7729.54 0.260271
\(960\) 0 0
\(961\) 61927.9 2.07874
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 18338.3 0.611742
\(966\) 0 0
\(967\) −53000.5 −1.76254 −0.881272 0.472609i \(-0.843312\pi\)
−0.881272 + 0.472609i \(0.843312\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 26286.3 0.868761 0.434381 0.900729i \(-0.356967\pi\)
0.434381 + 0.900729i \(0.356967\pi\)
\(972\) 0 0
\(973\) 2609.68 0.0859842
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30508.0 0.999014 0.499507 0.866310i \(-0.333514\pi\)
0.499507 + 0.866310i \(0.333514\pi\)
\(978\) 0 0
\(979\) 27399.4 0.894473
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −37044.3 −1.20196 −0.600982 0.799263i \(-0.705224\pi\)
−0.600982 + 0.799263i \(0.705224\pi\)
\(984\) 0 0
\(985\) −42153.3 −1.36357
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −23764.7 −0.764079
\(990\) 0 0
\(991\) 47803.5 1.53232 0.766160 0.642650i \(-0.222165\pi\)
0.766160 + 0.642650i \(0.222165\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −11771.3 −0.375051
\(996\) 0 0
\(997\) −13478.1 −0.428140 −0.214070 0.976818i \(-0.568672\pi\)
−0.214070 + 0.976818i \(0.568672\pi\)
\(998\) 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 1152.4.a.r.1.1 2
3.2 odd 2 128.4.a.f.1.2 yes 2
4.3 odd 2 1152.4.a.q.1.1 2
8.3 odd 2 1152.4.a.s.1.2 2
8.5 even 2 1152.4.a.t.1.2 2
12.11 even 2 128.4.a.h.1.1 yes 2
24.5 odd 2 128.4.a.g.1.1 yes 2
24.11 even 2 128.4.a.e.1.2 2
48.5 odd 4 256.4.b.h.129.2 4
48.11 even 4 256.4.b.i.129.3 4
48.29 odd 4 256.4.b.h.129.3 4
48.35 even 4 256.4.b.i.129.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.a.e.1.2 2 24.11 even 2
128.4.a.f.1.2 yes 2 3.2 odd 2
128.4.a.g.1.1 yes 2 24.5 odd 2
128.4.a.h.1.1 yes 2 12.11 even 2
256.4.b.h.129.2 4 48.5 odd 4
256.4.b.h.129.3 4 48.29 odd 4
256.4.b.i.129.2 4 48.35 even 4
256.4.b.i.129.3 4 48.11 even 4
1152.4.a.q.1.1 2 4.3 odd 2
1152.4.a.r.1.1 2 1.1 even 1 trivial
1152.4.a.s.1.2 2 8.3 odd 2
1152.4.a.t.1.2 2 8.5 even 2