Properties

Label 1368.4.a.d.1.1
Level $1368$
Weight $4$
Character 1368.1
Self dual yes
Analytic conductor $80.715$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1368,4,Mod(1,1368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, 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("1368.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1368.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: \(80.7146128879\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.7057.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 22x + 32 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 152)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.36181\) of defining polynomial
Character \(\chi\) \(=\) 1368.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-18.4427 q^{5} +10.3872 q^{7} +O(q^{10})\) \(q-18.4427 q^{5} +10.3872 q^{7} -50.4519 q^{11} -61.8352 q^{13} -68.1070 q^{17} -19.0000 q^{19} -145.632 q^{23} +215.132 q^{25} -42.6097 q^{29} +91.6582 q^{31} -191.568 q^{35} -400.965 q^{37} +123.355 q^{41} +449.802 q^{43} +453.075 q^{47} -235.105 q^{49} -437.142 q^{53} +930.466 q^{55} +159.352 q^{59} -476.816 q^{61} +1140.41 q^{65} -629.682 q^{67} -471.459 q^{71} -725.055 q^{73} -524.055 q^{77} -1057.66 q^{79} +726.957 q^{83} +1256.07 q^{85} +468.065 q^{89} -642.297 q^{91} +350.410 q^{95} -891.891 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 7 q^{5} + 7 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 7 q^{5} + 7 q^{7} - 103 q^{11} + 32 q^{13} - 11 q^{17} - 57 q^{19} - 316 q^{23} + 162 q^{25} + 138 q^{29} + 420 q^{31} - 333 q^{35} + 102 q^{37} + 370 q^{41} + 431 q^{43} + 199 q^{47} - 802 q^{49} + 308 q^{53} + 85 q^{55} + 188 q^{59} - 609 q^{61} + 1536 q^{65} - 246 q^{67} + 954 q^{71} - 629 q^{73} + 71 q^{77} + 452 q^{79} + 780 q^{83} + 1883 q^{85} + 1356 q^{89} - 670 q^{91} + 133 q^{95} - 548 q^{97}+O(q^{100}) \) 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
\(5\) −18.4427 −1.64956 −0.824781 0.565453i \(-0.808701\pi\)
−0.824781 + 0.565453i \(0.808701\pi\)
\(6\) 0 0
\(7\) 10.3872 0.560858 0.280429 0.959875i \(-0.409523\pi\)
0.280429 + 0.959875i \(0.409523\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −50.4519 −1.38289 −0.691446 0.722428i \(-0.743026\pi\)
−0.691446 + 0.722428i \(0.743026\pi\)
\(12\) 0 0
\(13\) −61.8352 −1.31923 −0.659616 0.751603i \(-0.729281\pi\)
−0.659616 + 0.751603i \(0.729281\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −68.1070 −0.971669 −0.485835 0.874051i \(-0.661484\pi\)
−0.485835 + 0.874051i \(0.661484\pi\)
\(18\) 0 0
\(19\) −19.0000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −145.632 −1.32028 −0.660138 0.751144i \(-0.729502\pi\)
−0.660138 + 0.751144i \(0.729502\pi\)
\(24\) 0 0
\(25\) 215.132 1.72105
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −42.6097 −0.272842 −0.136421 0.990651i \(-0.543560\pi\)
−0.136421 + 0.990651i \(0.543560\pi\)
\(30\) 0 0
\(31\) 91.6582 0.531042 0.265521 0.964105i \(-0.414456\pi\)
0.265521 + 0.964105i \(0.414456\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −191.568 −0.925169
\(36\) 0 0
\(37\) −400.965 −1.78158 −0.890788 0.454419i \(-0.849847\pi\)
−0.890788 + 0.454419i \(0.849847\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 123.355 0.469873 0.234936 0.972011i \(-0.424512\pi\)
0.234936 + 0.972011i \(0.424512\pi\)
\(42\) 0 0
\(43\) 449.802 1.59521 0.797607 0.603178i \(-0.206099\pi\)
0.797607 + 0.603178i \(0.206099\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 453.075 1.40612 0.703062 0.711129i \(-0.251816\pi\)
0.703062 + 0.711129i \(0.251816\pi\)
\(48\) 0 0
\(49\) −235.105 −0.685439
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −437.142 −1.13294 −0.566472 0.824081i \(-0.691692\pi\)
−0.566472 + 0.824081i \(0.691692\pi\)
\(54\) 0 0
\(55\) 930.466 2.28116
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 159.352 0.351624 0.175812 0.984424i \(-0.443745\pi\)
0.175812 + 0.984424i \(0.443745\pi\)
\(60\) 0 0
\(61\) −476.816 −1.00082 −0.500410 0.865789i \(-0.666817\pi\)
−0.500410 + 0.865789i \(0.666817\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1140.41 2.17615
\(66\) 0 0
\(67\) −629.682 −1.14818 −0.574089 0.818793i \(-0.694643\pi\)
−0.574089 + 0.818793i \(0.694643\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −471.459 −0.788056 −0.394028 0.919099i \(-0.628919\pi\)
−0.394028 + 0.919099i \(0.628919\pi\)
\(72\) 0 0
\(73\) −725.055 −1.16248 −0.581241 0.813731i \(-0.697433\pi\)
−0.581241 + 0.813731i \(0.697433\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −524.055 −0.775605
\(78\) 0 0
\(79\) −1057.66 −1.50628 −0.753139 0.657861i \(-0.771461\pi\)
−0.753139 + 0.657861i \(0.771461\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 726.957 0.961373 0.480686 0.876893i \(-0.340388\pi\)
0.480686 + 0.876893i \(0.340388\pi\)
\(84\) 0 0
\(85\) 1256.07 1.60283
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 468.065 0.557469 0.278735 0.960368i \(-0.410085\pi\)
0.278735 + 0.960368i \(0.410085\pi\)
\(90\) 0 0
\(91\) −642.297 −0.739901
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 350.410 0.378435
\(96\) 0 0
\(97\) −891.891 −0.933585 −0.466793 0.884367i \(-0.654591\pi\)
−0.466793 + 0.884367i \(0.654591\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 16.6636 0.0164167 0.00820835 0.999966i \(-0.497387\pi\)
0.00820835 + 0.999966i \(0.497387\pi\)
\(102\) 0 0
\(103\) 1292.68 1.23662 0.618309 0.785935i \(-0.287818\pi\)
0.618309 + 0.785935i \(0.287818\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 176.185 0.159182 0.0795911 0.996828i \(-0.474639\pi\)
0.0795911 + 0.996828i \(0.474639\pi\)
\(108\) 0 0
\(109\) 1378.74 1.21155 0.605776 0.795635i \(-0.292863\pi\)
0.605776 + 0.795635i \(0.292863\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 601.795 0.500992 0.250496 0.968118i \(-0.419406\pi\)
0.250496 + 0.968118i \(0.419406\pi\)
\(114\) 0 0
\(115\) 2685.84 2.17788
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −707.443 −0.544968
\(120\) 0 0
\(121\) 1214.39 0.912389
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1662.26 −1.18942
\(126\) 0 0
\(127\) 1890.38 1.32082 0.660409 0.750906i \(-0.270383\pi\)
0.660409 + 0.750906i \(0.270383\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −331.964 −0.221403 −0.110701 0.993854i \(-0.535310\pi\)
−0.110701 + 0.993854i \(0.535310\pi\)
\(132\) 0 0
\(133\) −197.357 −0.128670
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1956.20 1.21992 0.609962 0.792430i \(-0.291185\pi\)
0.609962 + 0.792430i \(0.291185\pi\)
\(138\) 0 0
\(139\) 547.821 0.334285 0.167142 0.985933i \(-0.446546\pi\)
0.167142 + 0.985933i \(0.446546\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3119.70 1.82435
\(144\) 0 0
\(145\) 785.836 0.450070
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 992.480 0.545686 0.272843 0.962059i \(-0.412036\pi\)
0.272843 + 0.962059i \(0.412036\pi\)
\(150\) 0 0
\(151\) −148.167 −0.0798520 −0.0399260 0.999203i \(-0.512712\pi\)
−0.0399260 + 0.999203i \(0.512712\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1690.42 −0.875987
\(156\) 0 0
\(157\) 2356.36 1.19782 0.598910 0.800817i \(-0.295601\pi\)
0.598910 + 0.800817i \(0.295601\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1512.71 −0.740487
\(162\) 0 0
\(163\) −2974.86 −1.42950 −0.714751 0.699379i \(-0.753460\pi\)
−0.714751 + 0.699379i \(0.753460\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3133.09 1.45177 0.725885 0.687816i \(-0.241430\pi\)
0.725885 + 0.687816i \(0.241430\pi\)
\(168\) 0 0
\(169\) 1626.60 0.740372
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3415.40 −1.50097 −0.750485 0.660887i \(-0.770180\pi\)
−0.750485 + 0.660887i \(0.770180\pi\)
\(174\) 0 0
\(175\) 2234.62 0.965265
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −80.0505 −0.0334260 −0.0167130 0.999860i \(-0.505320\pi\)
−0.0167130 + 0.999860i \(0.505320\pi\)
\(180\) 0 0
\(181\) 3379.91 1.38799 0.693996 0.719978i \(-0.255848\pi\)
0.693996 + 0.719978i \(0.255848\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7394.87 2.93882
\(186\) 0 0
\(187\) 3436.13 1.34371
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3288.78 1.24590 0.622952 0.782260i \(-0.285933\pi\)
0.622952 + 0.782260i \(0.285933\pi\)
\(192\) 0 0
\(193\) 2906.89 1.08416 0.542079 0.840327i \(-0.317637\pi\)
0.542079 + 0.840327i \(0.317637\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.1879 0.00621617 0.00310808 0.999995i \(-0.499011\pi\)
0.00310808 + 0.999995i \(0.499011\pi\)
\(198\) 0 0
\(199\) −613.599 −0.218577 −0.109289 0.994010i \(-0.534857\pi\)
−0.109289 + 0.994010i \(0.534857\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −442.597 −0.153026
\(204\) 0 0
\(205\) −2274.99 −0.775084
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 958.585 0.317257
\(210\) 0 0
\(211\) −3991.85 −1.30242 −0.651209 0.758898i \(-0.725738\pi\)
−0.651209 + 0.758898i \(0.725738\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8295.54 −2.63140
\(216\) 0 0
\(217\) 952.075 0.297839
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4211.41 1.28186
\(222\) 0 0
\(223\) −1051.16 −0.315653 −0.157827 0.987467i \(-0.550449\pi\)
−0.157827 + 0.987467i \(0.550449\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3430.64 −1.00308 −0.501541 0.865134i \(-0.667233\pi\)
−0.501541 + 0.865134i \(0.667233\pi\)
\(228\) 0 0
\(229\) −5907.75 −1.70478 −0.852392 0.522904i \(-0.824849\pi\)
−0.852392 + 0.522904i \(0.824849\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2109.67 0.593171 0.296586 0.955006i \(-0.404152\pi\)
0.296586 + 0.955006i \(0.404152\pi\)
\(234\) 0 0
\(235\) −8355.91 −2.31949
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2898.33 −0.784426 −0.392213 0.919875i \(-0.628290\pi\)
−0.392213 + 0.919875i \(0.628290\pi\)
\(240\) 0 0
\(241\) −734.884 −0.196423 −0.0982117 0.995166i \(-0.531312\pi\)
−0.0982117 + 0.995166i \(0.531312\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4335.97 1.13067
\(246\) 0 0
\(247\) 1174.87 0.302652
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2758.13 −0.693593 −0.346796 0.937940i \(-0.612730\pi\)
−0.346796 + 0.937940i \(0.612730\pi\)
\(252\) 0 0
\(253\) 7347.40 1.82580
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −486.309 −0.118036 −0.0590178 0.998257i \(-0.518797\pi\)
−0.0590178 + 0.998257i \(0.518797\pi\)
\(258\) 0 0
\(259\) −4164.92 −0.999211
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3381.74 −0.792878 −0.396439 0.918061i \(-0.629754\pi\)
−0.396439 + 0.918061i \(0.629754\pi\)
\(264\) 0 0
\(265\) 8062.06 1.86886
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2628.18 0.595699 0.297849 0.954613i \(-0.403731\pi\)
0.297849 + 0.954613i \(0.403731\pi\)
\(270\) 0 0
\(271\) 1104.06 0.247480 0.123740 0.992315i \(-0.460511\pi\)
0.123740 + 0.992315i \(0.460511\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10853.8 −2.38003
\(276\) 0 0
\(277\) −549.699 −0.119235 −0.0596177 0.998221i \(-0.518988\pi\)
−0.0596177 + 0.998221i \(0.518988\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 182.930 0.0388352 0.0194176 0.999811i \(-0.493819\pi\)
0.0194176 + 0.999811i \(0.493819\pi\)
\(282\) 0 0
\(283\) 5218.27 1.09609 0.548046 0.836448i \(-0.315372\pi\)
0.548046 + 0.836448i \(0.315372\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1281.31 0.263532
\(288\) 0 0
\(289\) −274.434 −0.0558587
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6160.17 −1.22826 −0.614131 0.789204i \(-0.710494\pi\)
−0.614131 + 0.789204i \(0.710494\pi\)
\(294\) 0 0
\(295\) −2938.87 −0.580026
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 9005.19 1.74175
\(300\) 0 0
\(301\) 4672.20 0.894687
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8793.75 1.65091
\(306\) 0 0
\(307\) 6620.89 1.23086 0.615430 0.788192i \(-0.288982\pi\)
0.615430 + 0.788192i \(0.288982\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8280.27 −1.50975 −0.754873 0.655870i \(-0.772302\pi\)
−0.754873 + 0.655870i \(0.772302\pi\)
\(312\) 0 0
\(313\) 3338.77 0.602934 0.301467 0.953477i \(-0.402524\pi\)
0.301467 + 0.953477i \(0.402524\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9587.72 −1.69874 −0.849369 0.527800i \(-0.823017\pi\)
−0.849369 + 0.527800i \(0.823017\pi\)
\(318\) 0 0
\(319\) 2149.74 0.377311
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1294.03 0.222916
\(324\) 0 0
\(325\) −13302.7 −2.27047
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4706.19 0.788635
\(330\) 0 0
\(331\) 11195.2 1.85905 0.929526 0.368756i \(-0.120216\pi\)
0.929526 + 0.368756i \(0.120216\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 11613.0 1.89399
\(336\) 0 0
\(337\) 5991.21 0.968432 0.484216 0.874948i \(-0.339105\pi\)
0.484216 + 0.874948i \(0.339105\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4624.33 −0.734374
\(342\) 0 0
\(343\) −6004.91 −0.945291
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6755.35 −1.04509 −0.522545 0.852612i \(-0.675017\pi\)
−0.522545 + 0.852612i \(0.675017\pi\)
\(348\) 0 0
\(349\) −2358.14 −0.361685 −0.180843 0.983512i \(-0.557883\pi\)
−0.180843 + 0.983512i \(0.557883\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5950.00 0.897129 0.448565 0.893750i \(-0.351935\pi\)
0.448565 + 0.893750i \(0.351935\pi\)
\(354\) 0 0
\(355\) 8694.96 1.29995
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1892.90 −0.278283 −0.139141 0.990273i \(-0.544434\pi\)
−0.139141 + 0.990273i \(0.544434\pi\)
\(360\) 0 0
\(361\) 361.000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 13371.9 1.91759
\(366\) 0 0
\(367\) 3643.63 0.518245 0.259122 0.965844i \(-0.416567\pi\)
0.259122 + 0.965844i \(0.416567\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4540.69 −0.635421
\(372\) 0 0
\(373\) 4820.77 0.669195 0.334598 0.942361i \(-0.391400\pi\)
0.334598 + 0.942361i \(0.391400\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2634.78 0.359942
\(378\) 0 0
\(379\) −8138.02 −1.10296 −0.551480 0.834188i \(-0.685937\pi\)
−0.551480 + 0.834188i \(0.685937\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −904.971 −0.120736 −0.0603679 0.998176i \(-0.519227\pi\)
−0.0603679 + 0.998176i \(0.519227\pi\)
\(384\) 0 0
\(385\) 9664.96 1.27941
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8885.27 −1.15810 −0.579050 0.815292i \(-0.696576\pi\)
−0.579050 + 0.815292i \(0.696576\pi\)
\(390\) 0 0
\(391\) 9918.56 1.28287
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 19506.1 2.48470
\(396\) 0 0
\(397\) −981.841 −0.124124 −0.0620619 0.998072i \(-0.519768\pi\)
−0.0620619 + 0.998072i \(0.519768\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15512.7 1.93184 0.965919 0.258845i \(-0.0833420\pi\)
0.965919 + 0.258845i \(0.0833420\pi\)
\(402\) 0 0
\(403\) −5667.71 −0.700568
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 20229.5 2.46373
\(408\) 0 0
\(409\) −13347.9 −1.61371 −0.806857 0.590747i \(-0.798833\pi\)
−0.806857 + 0.590747i \(0.798833\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1655.22 0.197211
\(414\) 0 0
\(415\) −13407.0 −1.58584
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1557.12 −0.181552 −0.0907758 0.995871i \(-0.528935\pi\)
−0.0907758 + 0.995871i \(0.528935\pi\)
\(420\) 0 0
\(421\) 1281.41 0.148342 0.0741710 0.997246i \(-0.476369\pi\)
0.0741710 + 0.997246i \(0.476369\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −14652.0 −1.67229
\(426\) 0 0
\(427\) −4952.79 −0.561317
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9742.61 −1.08883 −0.544414 0.838817i \(-0.683248\pi\)
−0.544414 + 0.838817i \(0.683248\pi\)
\(432\) 0 0
\(433\) −5262.21 −0.584031 −0.292016 0.956414i \(-0.594326\pi\)
−0.292016 + 0.956414i \(0.594326\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2767.01 0.302892
\(438\) 0 0
\(439\) −15015.7 −1.63249 −0.816243 0.577708i \(-0.803947\pi\)
−0.816243 + 0.577708i \(0.803947\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4296.96 0.460846 0.230423 0.973091i \(-0.425989\pi\)
0.230423 + 0.973091i \(0.425989\pi\)
\(444\) 0 0
\(445\) −8632.36 −0.919580
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6749.23 −0.709389 −0.354695 0.934982i \(-0.615415\pi\)
−0.354695 + 0.934982i \(0.615415\pi\)
\(450\) 0 0
\(451\) −6223.48 −0.649783
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11845.7 1.22051
\(456\) 0 0
\(457\) 11399.9 1.16689 0.583443 0.812154i \(-0.301705\pi\)
0.583443 + 0.812154i \(0.301705\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5799.27 0.585898 0.292949 0.956128i \(-0.405363\pi\)
0.292949 + 0.956128i \(0.405363\pi\)
\(462\) 0 0
\(463\) 620.160 0.0622490 0.0311245 0.999516i \(-0.490091\pi\)
0.0311245 + 0.999516i \(0.490091\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9426.16 −0.934027 −0.467014 0.884250i \(-0.654670\pi\)
−0.467014 + 0.884250i \(0.654670\pi\)
\(468\) 0 0
\(469\) −6540.65 −0.643964
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −22693.3 −2.20601
\(474\) 0 0
\(475\) −4087.50 −0.394836
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15813.6 −1.50844 −0.754218 0.656625i \(-0.771984\pi\)
−0.754218 + 0.656625i \(0.771984\pi\)
\(480\) 0 0
\(481\) 24793.8 2.35031
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16448.8 1.54001
\(486\) 0 0
\(487\) −6832.36 −0.635736 −0.317868 0.948135i \(-0.602967\pi\)
−0.317868 + 0.948135i \(0.602967\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15084.5 1.38646 0.693232 0.720714i \(-0.256186\pi\)
0.693232 + 0.720714i \(0.256186\pi\)
\(492\) 0 0
\(493\) 2902.02 0.265112
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4897.16 −0.441987
\(498\) 0 0
\(499\) 21771.2 1.95313 0.976564 0.215226i \(-0.0690490\pi\)
0.976564 + 0.215226i \(0.0690490\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21300.9 −1.88819 −0.944097 0.329668i \(-0.893063\pi\)
−0.944097 + 0.329668i \(0.893063\pi\)
\(504\) 0 0
\(505\) −307.320 −0.0270803
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15897.9 1.38440 0.692202 0.721704i \(-0.256641\pi\)
0.692202 + 0.721704i \(0.256641\pi\)
\(510\) 0 0
\(511\) −7531.31 −0.651987
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −23840.5 −2.03988
\(516\) 0 0
\(517\) −22858.5 −1.94452
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13864.6 1.16587 0.582937 0.812517i \(-0.301903\pi\)
0.582937 + 0.812517i \(0.301903\pi\)
\(522\) 0 0
\(523\) −20503.0 −1.71421 −0.857106 0.515141i \(-0.827740\pi\)
−0.857106 + 0.515141i \(0.827740\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6242.57 −0.515997
\(528\) 0 0
\(529\) 9041.66 0.743130
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7627.67 −0.619871
\(534\) 0 0
\(535\) −3249.33 −0.262581
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 11861.5 0.947887
\(540\) 0 0
\(541\) −15933.8 −1.26626 −0.633131 0.774045i \(-0.718231\pi\)
−0.633131 + 0.774045i \(0.718231\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −25427.6 −1.99853
\(546\) 0 0
\(547\) 20542.0 1.60569 0.802847 0.596185i \(-0.203318\pi\)
0.802847 + 0.596185i \(0.203318\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 809.584 0.0625943
\(552\) 0 0
\(553\) −10986.2 −0.844808
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12338.5 −0.938599 −0.469299 0.883039i \(-0.655493\pi\)
−0.469299 + 0.883039i \(0.655493\pi\)
\(558\) 0 0
\(559\) −27813.6 −2.10446
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7611.22 −0.569759 −0.284880 0.958563i \(-0.591954\pi\)
−0.284880 + 0.958563i \(0.591954\pi\)
\(564\) 0 0
\(565\) −11098.7 −0.826417
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9237.35 −0.680579 −0.340290 0.940321i \(-0.610525\pi\)
−0.340290 + 0.940321i \(0.610525\pi\)
\(570\) 0 0
\(571\) 7061.48 0.517537 0.258769 0.965939i \(-0.416683\pi\)
0.258769 + 0.965939i \(0.416683\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −31330.0 −2.27226
\(576\) 0 0
\(577\) −12167.1 −0.877856 −0.438928 0.898522i \(-0.644642\pi\)
−0.438928 + 0.898522i \(0.644642\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7551.07 0.539193
\(582\) 0 0
\(583\) 22054.6 1.56674
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11396.4 0.801327 0.400663 0.916225i \(-0.368780\pi\)
0.400663 + 0.916225i \(0.368780\pi\)
\(588\) 0 0
\(589\) −1741.51 −0.121829
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10401.1 0.720276 0.360138 0.932899i \(-0.382730\pi\)
0.360138 + 0.932899i \(0.382730\pi\)
\(594\) 0 0
\(595\) 13047.1 0.898958
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2296.79 −0.156668 −0.0783340 0.996927i \(-0.524960\pi\)
−0.0783340 + 0.996927i \(0.524960\pi\)
\(600\) 0 0
\(601\) −7376.50 −0.500655 −0.250328 0.968161i \(-0.580538\pi\)
−0.250328 + 0.968161i \(0.580538\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −22396.6 −1.50504
\(606\) 0 0
\(607\) −11793.0 −0.788570 −0.394285 0.918988i \(-0.629008\pi\)
−0.394285 + 0.918988i \(0.629008\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −28016.0 −1.85500
\(612\) 0 0
\(613\) 20918.1 1.37826 0.689131 0.724637i \(-0.257992\pi\)
0.689131 + 0.724637i \(0.257992\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3951.13 0.257806 0.128903 0.991657i \(-0.458854\pi\)
0.128903 + 0.991657i \(0.458854\pi\)
\(618\) 0 0
\(619\) −22159.8 −1.43890 −0.719450 0.694544i \(-0.755606\pi\)
−0.719450 + 0.694544i \(0.755606\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4861.90 0.312661
\(624\) 0 0
\(625\) 3765.14 0.240969
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 27308.6 1.73110
\(630\) 0 0
\(631\) 11645.2 0.734687 0.367344 0.930085i \(-0.380267\pi\)
0.367344 + 0.930085i \(0.380267\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −34863.6 −2.17877
\(636\) 0 0
\(637\) 14537.8 0.904252
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21970.1 1.35377 0.676885 0.736089i \(-0.263329\pi\)
0.676885 + 0.736089i \(0.263329\pi\)
\(642\) 0 0
\(643\) −14047.2 −0.861537 −0.430769 0.902462i \(-0.641757\pi\)
−0.430769 + 0.902462i \(0.641757\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20700.0 −1.25780 −0.628902 0.777485i \(-0.716495\pi\)
−0.628902 + 0.777485i \(0.716495\pi\)
\(648\) 0 0
\(649\) −8039.59 −0.486258
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17197.8 −1.03063 −0.515315 0.857001i \(-0.672325\pi\)
−0.515315 + 0.857001i \(0.672325\pi\)
\(654\) 0 0
\(655\) 6122.29 0.365218
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 23084.0 1.36453 0.682264 0.731106i \(-0.260995\pi\)
0.682264 + 0.731106i \(0.260995\pi\)
\(660\) 0 0
\(661\) −9283.22 −0.546256 −0.273128 0.961978i \(-0.588058\pi\)
−0.273128 + 0.961978i \(0.588058\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3639.79 0.212248
\(666\) 0 0
\(667\) 6205.33 0.360227
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 24056.2 1.38402
\(672\) 0 0
\(673\) 11565.0 0.662403 0.331202 0.943560i \(-0.392546\pi\)
0.331202 + 0.943560i \(0.392546\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8808.39 −0.500050 −0.250025 0.968239i \(-0.580439\pi\)
−0.250025 + 0.968239i \(0.580439\pi\)
\(678\) 0 0
\(679\) −9264.27 −0.523608
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16282.3 −0.912186 −0.456093 0.889932i \(-0.650752\pi\)
−0.456093 + 0.889932i \(0.650752\pi\)
\(684\) 0 0
\(685\) −36077.6 −2.01234
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 27030.8 1.49462
\(690\) 0 0
\(691\) −21900.4 −1.20569 −0.602845 0.797859i \(-0.705966\pi\)
−0.602845 + 0.797859i \(0.705966\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10103.3 −0.551423
\(696\) 0 0
\(697\) −8401.33 −0.456561
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12286.6 0.661994 0.330997 0.943632i \(-0.392615\pi\)
0.330997 + 0.943632i \(0.392615\pi\)
\(702\) 0 0
\(703\) 7618.34 0.408722
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 173.088 0.00920743
\(708\) 0 0
\(709\) −12918.9 −0.684315 −0.342158 0.939643i \(-0.611158\pi\)
−0.342158 + 0.939643i \(0.611158\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −13348.4 −0.701122
\(714\) 0 0
\(715\) −57535.6 −3.00938
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 15819.9 0.820558 0.410279 0.911960i \(-0.365431\pi\)
0.410279 + 0.911960i \(0.365431\pi\)
\(720\) 0 0
\(721\) 13427.4 0.693567
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9166.69 −0.469576
\(726\) 0 0
\(727\) 1793.81 0.0915112 0.0457556 0.998953i \(-0.485430\pi\)
0.0457556 + 0.998953i \(0.485430\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −30634.7 −1.55002
\(732\) 0 0
\(733\) 10370.0 0.522541 0.261271 0.965266i \(-0.415858\pi\)
0.261271 + 0.965266i \(0.415858\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31768.6 1.58780
\(738\) 0 0
\(739\) 29414.1 1.46416 0.732081 0.681218i \(-0.238549\pi\)
0.732081 + 0.681218i \(0.238549\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14932.0 0.737286 0.368643 0.929571i \(-0.379823\pi\)
0.368643 + 0.929571i \(0.379823\pi\)
\(744\) 0 0
\(745\) −18304.0 −0.900142
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1830.08 0.0892785
\(750\) 0 0
\(751\) 21916.9 1.06492 0.532462 0.846454i \(-0.321267\pi\)
0.532462 + 0.846454i \(0.321267\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2732.59 0.131721
\(756\) 0 0
\(757\) −26973.4 −1.29506 −0.647532 0.762038i \(-0.724199\pi\)
−0.647532 + 0.762038i \(0.724199\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16145.3 0.769076 0.384538 0.923109i \(-0.374361\pi\)
0.384538 + 0.923109i \(0.374361\pi\)
\(762\) 0 0
\(763\) 14321.3 0.679508
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9853.55 −0.463874
\(768\) 0 0
\(769\) −23777.1 −1.11499 −0.557494 0.830181i \(-0.688237\pi\)
−0.557494 + 0.830181i \(0.688237\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −27962.2 −1.30107 −0.650537 0.759475i \(-0.725456\pi\)
−0.650537 + 0.759475i \(0.725456\pi\)
\(774\) 0 0
\(775\) 19718.6 0.913951
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2343.74 −0.107796
\(780\) 0 0
\(781\) 23786.0 1.08980
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −43457.5 −1.97588
\(786\) 0 0
\(787\) 19000.4 0.860600 0.430300 0.902686i \(-0.358408\pi\)
0.430300 + 0.902686i \(0.358408\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6250.98 0.280985
\(792\) 0 0
\(793\) 29484.0 1.32031
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 19991.0 0.888480 0.444240 0.895908i \(-0.353474\pi\)
0.444240 + 0.895908i \(0.353474\pi\)
\(798\) 0 0
\(799\) −30857.6 −1.36629
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 36580.3 1.60759
\(804\) 0 0
\(805\) 27898.4 1.22148
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 40779.8 1.77224 0.886120 0.463455i \(-0.153391\pi\)
0.886120 + 0.463455i \(0.153391\pi\)
\(810\) 0 0
\(811\) −23160.4 −1.00280 −0.501400 0.865216i \(-0.667181\pi\)
−0.501400 + 0.865216i \(0.667181\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 54864.3 2.35805
\(816\) 0 0
\(817\) −8546.24 −0.365967
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29453.3 −1.25204 −0.626021 0.779806i \(-0.715318\pi\)
−0.626021 + 0.779806i \(0.715318\pi\)
\(822\) 0 0
\(823\) −43227.2 −1.83087 −0.915435 0.402465i \(-0.868153\pi\)
−0.915435 + 0.402465i \(0.868153\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 34232.7 1.43940 0.719702 0.694283i \(-0.244278\pi\)
0.719702 + 0.694283i \(0.244278\pi\)
\(828\) 0 0
\(829\) 32410.2 1.35785 0.678923 0.734209i \(-0.262447\pi\)
0.678923 + 0.734209i \(0.262447\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 16012.3 0.666020
\(834\) 0 0
\(835\) −57782.5 −2.39478
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 6363.50 0.261851 0.130925 0.991392i \(-0.458205\pi\)
0.130925 + 0.991392i \(0.458205\pi\)
\(840\) 0 0
\(841\) −22573.4 −0.925557
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −29998.8 −1.22129
\(846\) 0 0
\(847\) 12614.1 0.511720
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 58393.4 2.35217
\(852\) 0 0
\(853\) 22798.2 0.915117 0.457558 0.889180i \(-0.348724\pi\)
0.457558 + 0.889180i \(0.348724\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −26426.8 −1.05335 −0.526675 0.850067i \(-0.676562\pi\)
−0.526675 + 0.850067i \(0.676562\pi\)
\(858\) 0 0
\(859\) 22484.5 0.893087 0.446544 0.894762i \(-0.352655\pi\)
0.446544 + 0.894762i \(0.352655\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22062.6 0.870242 0.435121 0.900372i \(-0.356706\pi\)
0.435121 + 0.900372i \(0.356706\pi\)
\(864\) 0 0
\(865\) 62989.0 2.47594
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 53360.9 2.08302
\(870\) 0 0
\(871\) 38936.5 1.51471
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −17266.3 −0.667095
\(876\) 0 0
\(877\) 17.2794 0.000665316 0 0.000332658 1.00000i \(-0.499894\pi\)
0.000332658 1.00000i \(0.499894\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −19338.2 −0.739524 −0.369762 0.929126i \(-0.620561\pi\)
−0.369762 + 0.929126i \(0.620561\pi\)
\(882\) 0 0
\(883\) 35899.9 1.36821 0.684105 0.729384i \(-0.260193\pi\)
0.684105 + 0.729384i \(0.260193\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −51076.9 −1.93348 −0.966738 0.255767i \(-0.917672\pi\)
−0.966738 + 0.255767i \(0.917672\pi\)
\(888\) 0 0
\(889\) 19635.8 0.740791
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −8608.43 −0.322587
\(894\) 0 0
\(895\) 1476.34 0.0551383
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3905.53 −0.144891
\(900\) 0 0
\(901\) 29772.4 1.10085
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −62334.5 −2.28958
\(906\) 0 0
\(907\) 18999.5 0.695555 0.347778 0.937577i \(-0.386936\pi\)
0.347778 + 0.937577i \(0.386936\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −17147.0 −0.623605 −0.311802 0.950147i \(-0.600933\pi\)
−0.311802 + 0.950147i \(0.600933\pi\)
\(912\) 0 0
\(913\) −36676.3 −1.32947
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3448.18 −0.124176
\(918\) 0 0
\(919\) −10013.4 −0.359425 −0.179712 0.983719i \(-0.557517\pi\)
−0.179712 + 0.983719i \(0.557517\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 29152.8 1.03963
\(924\) 0 0
\(925\) −86260.3 −3.06619
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 22893.7 0.808524 0.404262 0.914643i \(-0.367528\pi\)
0.404262 + 0.914643i \(0.367528\pi\)
\(930\) 0 0
\(931\) 4467.00 0.157250
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −63371.3 −2.21654
\(936\) 0 0
\(937\) 1003.65 0.0349922 0.0174961 0.999847i \(-0.494431\pi\)
0.0174961 + 0.999847i \(0.494431\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14679.7 −0.508550 −0.254275 0.967132i \(-0.581837\pi\)
−0.254275 + 0.967132i \(0.581837\pi\)
\(942\) 0 0
\(943\) −17964.4 −0.620362
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −38570.8 −1.32353 −0.661765 0.749711i \(-0.730192\pi\)
−0.661765 + 0.749711i \(0.730192\pi\)
\(948\) 0 0
\(949\) 44833.9 1.53358
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2208.75 −0.0750770 −0.0375385 0.999295i \(-0.511952\pi\)
−0.0375385 + 0.999295i \(0.511952\pi\)
\(954\) 0 0
\(955\) −60653.8 −2.05520
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 20319.5 0.684204
\(960\) 0 0
\(961\) −21389.8 −0.717994
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −53610.8 −1.78839
\(966\) 0 0
\(967\) 5440.71 0.180932 0.0904661 0.995900i \(-0.471164\pi\)
0.0904661 + 0.995900i \(0.471164\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −25018.4 −0.826857 −0.413428 0.910537i \(-0.635669\pi\)
−0.413428 + 0.910537i \(0.635669\pi\)
\(972\) 0 0
\(973\) 5690.34 0.187486
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 45055.8 1.47540 0.737698 0.675131i \(-0.235913\pi\)
0.737698 + 0.675131i \(0.235913\pi\)
\(978\) 0 0
\(979\) −23614.7 −0.770920
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 13675.5 0.443725 0.221862 0.975078i \(-0.428786\pi\)
0.221862 + 0.975078i \(0.428786\pi\)
\(984\) 0 0
\(985\) −316.990 −0.0102539
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −65505.5 −2.10612
\(990\) 0 0
\(991\) 23018.0 0.737832 0.368916 0.929463i \(-0.379729\pi\)
0.368916 + 0.929463i \(0.379729\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 11316.4 0.360557
\(996\) 0 0
\(997\) −16189.1 −0.514256 −0.257128 0.966377i \(-0.582776\pi\)
−0.257128 + 0.966377i \(0.582776\pi\)
\(998\) 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 1368.4.a.d.1.1 3
3.2 odd 2 152.4.a.c.1.2 3
12.11 even 2 304.4.a.g.1.2 3
24.5 odd 2 1216.4.a.r.1.2 3
24.11 even 2 1216.4.a.w.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.4.a.c.1.2 3 3.2 odd 2
304.4.a.g.1.2 3 12.11 even 2
1216.4.a.r.1.2 3 24.5 odd 2
1216.4.a.w.1.2 3 24.11 even 2
1368.4.a.d.1.1 3 1.1 even 1 trivial