Properties

Label 7200.2.h.m.1151.11
Level $7200$
Weight $2$
Character 7200.1151
Analytic conductor $57.492$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7200,2,Mod(1151,7200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7200.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.h (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(57.4922894553\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.426337261060096.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: no (minimal twist has level 1440)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1151.11
Root \(-1.35818 - 0.394157i\) of defining polynomial
Character \(\chi\) \(=\) 7200.1151
Dual form 7200.2.h.m.1151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.50466i q^{7} +O(q^{10})\) \(q+3.50466i q^{7} -1.92804 q^{11} +5.50466 q^{13} -4.44252i q^{17} -7.00933i q^{19} +1.10027 q^{23} +5.47017i q^{29} -8.28267i q^{31} -0.778008 q^{37} -2.44186i q^{41} -9.55602i q^{43} -11.7135 q^{47} -5.28267 q^{49} +11.5268i q^{53} -9.78543 q^{59} -3.45331 q^{61} -5.45331i q^{67} -4.25583 q^{71} +7.27334 q^{73} -6.75712i q^{77} +2.82936i q^{79} +4.25583 q^{83} -0.386566i q^{89} +19.2920i q^{91} -9.29200 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 24 q^{13} + 16 q^{37} + 4 q^{49} - 8 q^{61} + 104 q^{73} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7200\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(6401\) \(6751\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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
\(5\) 0 0
\(6\) 0 0
\(7\) 3.50466i 1.32464i 0.749222 + 0.662319i \(0.230428\pi\)
−0.749222 + 0.662319i \(0.769572\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.92804 −0.581325 −0.290663 0.956826i \(-0.593876\pi\)
−0.290663 + 0.956826i \(0.593876\pi\)
\(12\) 0 0
\(13\) 5.50466 1.52672 0.763360 0.645974i \(-0.223548\pi\)
0.763360 + 0.645974i \(0.223548\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 4.44252i − 1.07747i −0.842475 0.538735i \(-0.818903\pi\)
0.842475 0.538735i \(-0.181097\pi\)
\(18\) 0 0
\(19\) − 7.00933i − 1.60805i −0.594595 0.804025i \(-0.702688\pi\)
0.594595 0.804025i \(-0.297312\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.10027 0.229422 0.114711 0.993399i \(-0.463406\pi\)
0.114711 + 0.993399i \(0.463406\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.47017i 1.01578i 0.861421 + 0.507892i \(0.169575\pi\)
−0.861421 + 0.507892i \(0.830425\pi\)
\(30\) 0 0
\(31\) − 8.28267i − 1.48761i −0.668396 0.743806i \(-0.733019\pi\)
0.668396 0.743806i \(-0.266981\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.778008 −0.127904 −0.0639519 0.997953i \(-0.520370\pi\)
−0.0639519 + 0.997953i \(0.520370\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 2.44186i − 0.381355i −0.981653 0.190677i \(-0.938932\pi\)
0.981653 0.190677i \(-0.0610684\pi\)
\(42\) 0 0
\(43\) − 9.55602i − 1.45728i −0.684898 0.728639i \(-0.740153\pi\)
0.684898 0.728639i \(-0.259847\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.7135 −1.70858 −0.854292 0.519793i \(-0.826009\pi\)
−0.854292 + 0.519793i \(0.826009\pi\)
\(48\) 0 0
\(49\) −5.28267 −0.754667
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.5268i 1.58333i 0.610959 + 0.791663i \(0.290784\pi\)
−0.610959 + 0.791663i \(0.709216\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.78543 −1.27395 −0.636977 0.770883i \(-0.719815\pi\)
−0.636977 + 0.770883i \(0.719815\pi\)
\(60\) 0 0
\(61\) −3.45331 −0.442151 −0.221076 0.975257i \(-0.570957\pi\)
−0.221076 + 0.975257i \(0.570957\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 5.45331i − 0.666228i −0.942887 0.333114i \(-0.891901\pi\)
0.942887 0.333114i \(-0.108099\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.25583 −0.505075 −0.252537 0.967587i \(-0.581265\pi\)
−0.252537 + 0.967587i \(0.581265\pi\)
\(72\) 0 0
\(73\) 7.27334 0.851280 0.425640 0.904892i \(-0.360049\pi\)
0.425640 + 0.904892i \(0.360049\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 6.75712i − 0.770046i
\(78\) 0 0
\(79\) 2.82936i 0.318328i 0.987252 + 0.159164i \(0.0508798\pi\)
−0.987252 + 0.159164i \(0.949120\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.25583 0.467138 0.233569 0.972340i \(-0.424959\pi\)
0.233569 + 0.972340i \(0.424959\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 0.386566i − 0.0409759i −0.999790 0.0204880i \(-0.993478\pi\)
0.999790 0.0204880i \(-0.00652198\pi\)
\(90\) 0 0
\(91\) 19.2920i 2.02235i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.29200 −0.943460 −0.471730 0.881743i \(-0.656370\pi\)
−0.471730 + 0.881743i \(0.656370\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.27095i 0.723486i 0.932278 + 0.361743i \(0.117818\pi\)
−0.932278 + 0.361743i \(0.882182\pi\)
\(102\) 0 0
\(103\) − 16.9580i − 1.67092i −0.549552 0.835460i \(-0.685202\pi\)
0.549552 0.835460i \(-0.314798\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.91269 −0.958296 −0.479148 0.877734i \(-0.659054\pi\)
−0.479148 + 0.877734i \(0.659054\pi\)
\(108\) 0 0
\(109\) −8.28267 −0.793336 −0.396668 0.917962i \(-0.629834\pi\)
−0.396668 + 0.917962i \(0.629834\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 17.8115i − 1.67557i −0.546002 0.837784i \(-0.683851\pi\)
0.546002 0.837784i \(-0.316149\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 15.5695 1.42726
\(120\) 0 0
\(121\) −7.28267 −0.662061
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.957977i 0.0850067i 0.999096 + 0.0425034i \(0.0135333\pi\)
−0.999096 + 0.0425034i \(0.986467\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.38441 0.732549 0.366275 0.930507i \(-0.380633\pi\)
0.366275 + 0.930507i \(0.380633\pi\)
\(132\) 0 0
\(133\) 24.5653 2.13009
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 11.1270i − 0.950646i −0.879811 0.475323i \(-0.842331\pi\)
0.879811 0.475323i \(-0.157669\pi\)
\(138\) 0 0
\(139\) 1.17064i 0.0992924i 0.998767 + 0.0496462i \(0.0158094\pi\)
−0.998767 + 0.0496462i \(0.984191\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −10.6132 −0.887520
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 11.5268i − 0.944311i −0.881515 0.472155i \(-0.843476\pi\)
0.881515 0.472155i \(-0.156524\pi\)
\(150\) 0 0
\(151\) − 10.8294i − 0.881281i −0.897684 0.440640i \(-0.854751\pi\)
0.897684 0.440640i \(-0.145249\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 10.3340 0.824745 0.412372 0.911015i \(-0.364700\pi\)
0.412372 + 0.911015i \(0.364700\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.85607i 0.303901i
\(162\) 0 0
\(163\) − 8.99067i − 0.704204i −0.935962 0.352102i \(-0.885467\pi\)
0.935962 0.352102i \(-0.114533\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.0683 1.01125 0.505626 0.862753i \(-0.331262\pi\)
0.505626 + 0.862753i \(0.331262\pi\)
\(168\) 0 0
\(169\) 17.3013 1.33087
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 19.6123i − 1.49110i −0.666452 0.745548i \(-0.732188\pi\)
0.666452 0.745548i \(-0.267812\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.58489 −0.566921 −0.283461 0.958984i \(-0.591483\pi\)
−0.283461 + 0.958984i \(0.591483\pi\)
\(180\) 0 0
\(181\) −2.82936 −0.210305 −0.105152 0.994456i \(-0.533533\pi\)
−0.105152 + 0.994456i \(0.533533\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.56534i 0.626360i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.1698 1.09765 0.548823 0.835938i \(-0.315076\pi\)
0.548823 + 0.835938i \(0.315076\pi\)
\(192\) 0 0
\(193\) −0.565344 −0.0406944 −0.0203472 0.999793i \(-0.506477\pi\)
−0.0203472 + 0.999793i \(0.506477\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.37122i 0.596424i 0.954500 + 0.298212i \(0.0963903\pi\)
−0.954500 + 0.298212i \(0.903610\pi\)
\(198\) 0 0
\(199\) 19.7546i 1.40037i 0.713962 + 0.700185i \(0.246899\pi\)
−0.713962 + 0.700185i \(0.753101\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −19.1711 −1.34555
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.5142i 0.934800i
\(210\) 0 0
\(211\) 14.8294i 1.02090i 0.859909 + 0.510448i \(0.170520\pi\)
−0.859909 + 0.510448i \(0.829480\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 29.0280 1.97055
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 24.4546i − 1.64499i
\(222\) 0 0
\(223\) − 19.5047i − 1.30613i −0.757302 0.653064i \(-0.773483\pi\)
0.757302 0.653064i \(-0.226517\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.45637 0.428524 0.214262 0.976776i \(-0.431265\pi\)
0.214262 + 0.976776i \(0.431265\pi\)
\(228\) 0 0
\(229\) 24.8480 1.64200 0.821002 0.570926i \(-0.193416\pi\)
0.821002 + 0.570926i \(0.193416\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 8.04408i − 0.526985i −0.964661 0.263493i \(-0.915126\pi\)
0.964661 0.263493i \(-0.0848745\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 19.5709 1.26593 0.632967 0.774179i \(-0.281837\pi\)
0.632967 + 0.774179i \(0.281837\pi\)
\(240\) 0 0
\(241\) 25.1307 1.61881 0.809405 0.587251i \(-0.199790\pi\)
0.809405 + 0.587251i \(0.199790\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 38.5840i − 2.45504i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −26.7560 −1.68882 −0.844412 0.535695i \(-0.820050\pi\)
−0.844412 + 0.535695i \(0.820050\pi\)
\(252\) 0 0
\(253\) −2.12136 −0.133369
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.69835i 0.542588i 0.962496 + 0.271294i \(0.0874516\pi\)
−0.962496 + 0.271294i \(0.912548\pi\)
\(258\) 0 0
\(259\) − 2.72666i − 0.169426i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.0708 −1.11430 −0.557148 0.830413i \(-0.688104\pi\)
−0.557148 + 0.830413i \(0.688104\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 9.95413i − 0.606914i −0.952845 0.303457i \(-0.901859\pi\)
0.952845 0.303457i \(-0.0981409\pi\)
\(270\) 0 0
\(271\) − 27.1893i − 1.65163i −0.563939 0.825816i \(-0.690715\pi\)
0.563939 0.825816i \(-0.309285\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.40196 0.564909 0.282455 0.959281i \(-0.408851\pi\)
0.282455 + 0.959281i \(0.408851\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.52612i 0.568281i 0.958783 + 0.284140i \(0.0917082\pi\)
−0.958783 + 0.284140i \(0.908292\pi\)
\(282\) 0 0
\(283\) 14.5840i 0.866929i 0.901171 + 0.433464i \(0.142709\pi\)
−0.901171 + 0.433464i \(0.857291\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.55790 0.505157
\(288\) 0 0
\(289\) −2.73599 −0.160940
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 21.8855i − 1.27856i −0.768973 0.639281i \(-0.779232\pi\)
0.768973 0.639281i \(-0.220768\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.05661 0.350263
\(300\) 0 0
\(301\) 33.4906 1.93037
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 25.1307i − 1.43428i −0.696927 0.717142i \(-0.745450\pi\)
0.696927 0.717142i \(-0.254550\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 22.8819 1.29752 0.648758 0.760995i \(-0.275289\pi\)
0.648758 + 0.760995i \(0.275289\pi\)
\(312\) 0 0
\(313\) 32.5653 1.84070 0.920351 0.391093i \(-0.127903\pi\)
0.920351 + 0.391093i \(0.127903\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 1.91484i − 0.107548i −0.998553 0.0537742i \(-0.982875\pi\)
0.998553 0.0537742i \(-0.0171251\pi\)
\(318\) 0 0
\(319\) − 10.5467i − 0.590501i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −31.1391 −1.73262
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 41.0518i − 2.26326i
\(330\) 0 0
\(331\) 6.44398i 0.354193i 0.984193 + 0.177097i \(0.0566705\pi\)
−0.984193 + 0.177097i \(0.943329\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.93206 0.486560 0.243280 0.969956i \(-0.421777\pi\)
0.243280 + 0.969956i \(0.421777\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.9693i 0.864786i
\(342\) 0 0
\(343\) 6.01866i 0.324977i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −23.2817 −1.24983 −0.624913 0.780694i \(-0.714866\pi\)
−0.624913 + 0.780694i \(0.714866\pi\)
\(348\) 0 0
\(349\) −17.1120 −0.915986 −0.457993 0.888956i \(-0.651432\pi\)
−0.457993 + 0.888956i \(0.651432\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 14.7286i − 0.783923i −0.919982 0.391962i \(-0.871797\pi\)
0.919982 0.391962i \(-0.128203\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.2251 −1.06744 −0.533721 0.845661i \(-0.679207\pi\)
−0.533721 + 0.845661i \(0.679207\pi\)
\(360\) 0 0
\(361\) −30.1307 −1.58583
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 12.0700i 0.630049i 0.949083 + 0.315025i \(0.102013\pi\)
−0.949083 + 0.315025i \(0.897987\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −40.3975 −2.09733
\(372\) 0 0
\(373\) −12.8153 −0.663552 −0.331776 0.943358i \(-0.607648\pi\)
−0.331776 + 0.943358i \(0.607648\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 30.1114i 1.55082i
\(378\) 0 0
\(379\) 17.7360i 0.911036i 0.890226 + 0.455518i \(0.150546\pi\)
−0.890226 + 0.455518i \(0.849454\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −25.0825 −1.28165 −0.640827 0.767685i \(-0.721408\pi\)
−0.640827 + 0.767685i \(0.721408\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 23.4684i 1.18989i 0.803765 + 0.594947i \(0.202827\pi\)
−0.803765 + 0.594947i \(0.797173\pi\)
\(390\) 0 0
\(391\) − 4.88797i − 0.247195i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2.69396 −0.135206 −0.0676031 0.997712i \(-0.521535\pi\)
−0.0676031 + 0.997712i \(0.521535\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 32.3252i − 1.61424i −0.590386 0.807121i \(-0.701025\pi\)
0.590386 0.807121i \(-0.298975\pi\)
\(402\) 0 0
\(403\) − 45.5933i − 2.27117i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.50003 0.0743536
\(408\) 0 0
\(409\) −20.6426 −1.02071 −0.510356 0.859963i \(-0.670486\pi\)
−0.510356 + 0.859963i \(0.670486\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 34.2946i − 1.68753i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −23.1544 −1.13117 −0.565584 0.824691i \(-0.691349\pi\)
−0.565584 + 0.824691i \(0.691349\pi\)
\(420\) 0 0
\(421\) −28.3200 −1.38023 −0.690116 0.723699i \(-0.742440\pi\)
−0.690116 + 0.723699i \(0.742440\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 12.1027i − 0.585691i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 26.6287 1.28266 0.641331 0.767265i \(-0.278383\pi\)
0.641331 + 0.767265i \(0.278383\pi\)
\(432\) 0 0
\(433\) 23.3693 1.12306 0.561528 0.827458i \(-0.310214\pi\)
0.561528 + 0.827458i \(0.310214\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 7.71215i − 0.368922i
\(438\) 0 0
\(439\) − 28.3200i − 1.35164i −0.737067 0.675820i \(-0.763790\pi\)
0.737067 0.675820i \(-0.236210\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −23.2817 −1.10615 −0.553073 0.833133i \(-0.686545\pi\)
−0.553073 + 0.833133i \(0.686545\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 29.3251i 1.38394i 0.721927 + 0.691969i \(0.243256\pi\)
−0.721927 + 0.691969i \(0.756744\pi\)
\(450\) 0 0
\(451\) 4.70800i 0.221691i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.9507 −0.886477 −0.443239 0.896404i \(-0.646171\pi\)
−0.443239 + 0.896404i \(0.646171\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 10.3539i 0.482229i 0.970497 + 0.241114i \(0.0775129\pi\)
−0.970497 + 0.241114i \(0.922487\pi\)
\(462\) 0 0
\(463\) 3.07934i 0.143109i 0.997437 + 0.0715545i \(0.0227960\pi\)
−0.997437 + 0.0715545i \(0.977204\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 40.9065 1.89293 0.946464 0.322809i \(-0.104627\pi\)
0.946464 + 0.322809i \(0.104627\pi\)
\(468\) 0 0
\(469\) 19.1120 0.882512
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 18.4244i 0.847153i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16.3691 −0.747921 −0.373961 0.927445i \(-0.622001\pi\)
−0.373961 + 0.927445i \(0.622001\pi\)
\(480\) 0 0
\(481\) −4.28267 −0.195273
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 0.957977i − 0.0434101i −0.999764 0.0217050i \(-0.993091\pi\)
0.999764 0.0217050i \(-0.00690947\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.8395 0.489178 0.244589 0.969627i \(-0.421347\pi\)
0.244589 + 0.969627i \(0.421347\pi\)
\(492\) 0 0
\(493\) 24.3013 1.09448
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 14.9153i − 0.669041i
\(498\) 0 0
\(499\) 31.5747i 1.41348i 0.707475 + 0.706738i \(0.249834\pi\)
−0.707475 + 0.706738i \(0.750166\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15.8241 0.705560 0.352780 0.935706i \(-0.385236\pi\)
0.352780 + 0.935706i \(0.385236\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10.1258i 0.448816i 0.974495 + 0.224408i \(0.0720449\pi\)
−0.974495 + 0.224408i \(0.927955\pi\)
\(510\) 0 0
\(511\) 25.4906i 1.12764i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 22.5840 0.993243
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 33.3528i 1.46121i 0.682799 + 0.730607i \(0.260763\pi\)
−0.682799 + 0.730607i \(0.739237\pi\)
\(522\) 0 0
\(523\) − 25.9160i − 1.13323i −0.823984 0.566613i \(-0.808254\pi\)
0.823984 0.566613i \(-0.191746\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −36.7959 −1.60286
\(528\) 0 0
\(529\) −21.7894 −0.947366
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 13.4416i − 0.582221i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.1852 0.438707
\(540\) 0 0
\(541\) 3.39470 0.145950 0.0729749 0.997334i \(-0.476751\pi\)
0.0729749 + 0.997334i \(0.476751\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.57467i 0.323870i 0.986801 + 0.161935i \(0.0517734\pi\)
−0.986801 + 0.161935i \(0.948227\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 38.3422 1.63343
\(552\) 0 0
\(553\) −9.91595 −0.421669
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 1.38596i − 0.0587252i −0.999569 0.0293626i \(-0.990652\pi\)
0.999569 0.0293626i \(-0.00934774\pi\)
\(558\) 0 0
\(559\) − 52.6027i − 2.22486i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 31.7934 1.33993 0.669965 0.742393i \(-0.266309\pi\)
0.669965 + 0.742393i \(0.266309\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 11.3005i − 0.473742i −0.971541 0.236871i \(-0.923878\pi\)
0.971541 0.236871i \(-0.0761219\pi\)
\(570\) 0 0
\(571\) − 13.5933i − 0.568863i −0.958696 0.284432i \(-0.908195\pi\)
0.958696 0.284432i \(-0.0918049\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 43.0466 1.79206 0.896028 0.443998i \(-0.146440\pi\)
0.896028 + 0.443998i \(0.146440\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 14.9153i 0.618790i
\(582\) 0 0
\(583\) − 22.2241i − 0.920427i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.80210 −0.239478 −0.119739 0.992805i \(-0.538206\pi\)
−0.119739 + 0.992805i \(0.538206\pi\)
\(588\) 0 0
\(589\) −58.0560 −2.39215
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.9015i 0.652995i 0.945198 + 0.326498i \(0.105869\pi\)
−0.945198 + 0.326498i \(0.894131\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 39.2510 1.60375 0.801876 0.597490i \(-0.203835\pi\)
0.801876 + 0.597490i \(0.203835\pi\)
\(600\) 0 0
\(601\) −7.73599 −0.315557 −0.157779 0.987474i \(-0.550433\pi\)
−0.157779 + 0.987474i \(0.550433\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.60737i 0.308774i 0.988010 + 0.154387i \(0.0493402\pi\)
−0.988010 + 0.154387i \(0.950660\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −64.4787 −2.60853
\(612\) 0 0
\(613\) 0.418069 0.0168856 0.00844282 0.999964i \(-0.497313\pi\)
0.00844282 + 0.999964i \(0.497313\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 44.3214i − 1.78431i −0.451727 0.892156i \(-0.649192\pi\)
0.451727 0.892156i \(-0.350808\pi\)
\(618\) 0 0
\(619\) − 4.07727i − 0.163879i −0.996637 0.0819396i \(-0.973889\pi\)
0.996637 0.0819396i \(-0.0261115\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.35478 0.0542783
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.45632i 0.137812i
\(630\) 0 0
\(631\) − 7.71733i − 0.307222i −0.988131 0.153611i \(-0.950910\pi\)
0.988131 0.153611i \(-0.0490903\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −29.0793 −1.15217
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.18866i 0.244438i 0.992503 + 0.122219i \(0.0390010\pi\)
−0.992503 + 0.122219i \(0.960999\pi\)
\(642\) 0 0
\(643\) 26.1214i 1.03013i 0.857152 + 0.515063i \(0.172231\pi\)
−0.857152 + 0.515063i \(0.827769\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.20180 0.125876 0.0629379 0.998017i \(-0.479953\pi\)
0.0629379 + 0.998017i \(0.479953\pi\)
\(648\) 0 0
\(649\) 18.8667 0.740582
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.4568i 0.761403i 0.924698 + 0.380702i \(0.124317\pi\)
−0.924698 + 0.380702i \(0.875683\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.32780 0.0906781 0.0453390 0.998972i \(-0.485563\pi\)
0.0453390 + 0.998972i \(0.485563\pi\)
\(660\) 0 0
\(661\) −38.0373 −1.47948 −0.739740 0.672893i \(-0.765052\pi\)
−0.739740 + 0.672893i \(0.765052\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.01866i 0.233043i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.65812 0.257034
\(672\) 0 0
\(673\) 34.6867 1.33707 0.668537 0.743679i \(-0.266921\pi\)
0.668537 + 0.743679i \(0.266921\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 45.1672i − 1.73591i −0.496639 0.867957i \(-0.665433\pi\)
0.496639 0.867957i \(-0.334567\pi\)
\(678\) 0 0
\(679\) − 32.5653i − 1.24974i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 44.7986 1.71417 0.857085 0.515175i \(-0.172273\pi\)
0.857085 + 0.515175i \(0.172273\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 63.4511i 2.41729i
\(690\) 0 0
\(691\) 6.80392i 0.258833i 0.991590 + 0.129417i \(0.0413105\pi\)
−0.991590 + 0.129417i \(0.958690\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −10.8480 −0.410898
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 29.5250i − 1.11514i −0.830129 0.557572i \(-0.811733\pi\)
0.830129 0.557572i \(-0.188267\pi\)
\(702\) 0 0
\(703\) 5.45331i 0.205676i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −25.4822 −0.958358
\(708\) 0 0
\(709\) 27.1893 1.02112 0.510558 0.859843i \(-0.329439\pi\)
0.510558 + 0.859843i \(0.329439\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 9.11317i − 0.341291i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.1145 −0.600971 −0.300486 0.953786i \(-0.597149\pi\)
−0.300486 + 0.953786i \(0.597149\pi\)
\(720\) 0 0
\(721\) 59.4320 2.21336
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 31.1820i 1.15648i 0.815867 + 0.578239i \(0.196260\pi\)
−0.815867 + 0.578239i \(0.803740\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −42.4528 −1.57017
\(732\) 0 0
\(733\) 4.41129 0.162935 0.0814674 0.996676i \(-0.474039\pi\)
0.0814674 + 0.996676i \(0.474039\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.5142i 0.387295i
\(738\) 0 0
\(739\) 17.5560i 0.645808i 0.946432 + 0.322904i \(0.104659\pi\)
−0.946432 + 0.322904i \(0.895341\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.65817 0.354324 0.177162 0.984182i \(-0.443308\pi\)
0.177162 + 0.984182i \(0.443308\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 34.7406i − 1.26940i
\(750\) 0 0
\(751\) − 12.6053i − 0.459974i −0.973194 0.229987i \(-0.926132\pi\)
0.973194 0.229987i \(-0.0738683\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −36.0887 −1.31166 −0.655832 0.754906i \(-0.727682\pi\)
−0.655832 + 0.754906i \(0.727682\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 16.8385i − 0.610396i −0.952289 0.305198i \(-0.901277\pi\)
0.952289 0.305198i \(-0.0987226\pi\)
\(762\) 0 0
\(763\) − 29.0280i − 1.05088i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −53.8655 −1.94497
\(768\) 0 0
\(769\) 54.3200 1.95883 0.979414 0.201860i \(-0.0646986\pi\)
0.979414 + 0.201860i \(0.0646986\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.17068i 0.221944i 0.993824 + 0.110972i \(0.0353964\pi\)
−0.993824 + 0.110972i \(0.964604\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −17.1158 −0.613237
\(780\) 0 0
\(781\) 8.20541 0.293612
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 2.12136i − 0.0756183i −0.999285 0.0378092i \(-0.987962\pi\)
0.999285 0.0378092i \(-0.0120379\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 62.4234 2.21952
\(792\) 0 0
\(793\) −19.0093 −0.675041
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.92522i 0.280726i 0.990100 + 0.140363i \(0.0448269\pi\)
−0.990100 + 0.140363i \(0.955173\pi\)
\(798\) 0 0
\(799\) 52.0373i 1.84095i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −14.0233 −0.494871
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 29.2158i − 1.02717i −0.858037 0.513587i \(-0.828316\pi\)
0.858037 0.513587i \(-0.171684\pi\)
\(810\) 0 0
\(811\) − 10.3013i − 0.361729i −0.983508 0.180864i \(-0.942111\pi\)
0.983508 0.180864i \(-0.0578895\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −66.9813 −2.34338
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 11.1270i − 0.388336i −0.980968 0.194168i \(-0.937799\pi\)
0.980968 0.194168i \(-0.0622006\pi\)
\(822\) 0 0
\(823\) − 35.6447i − 1.24250i −0.783614 0.621248i \(-0.786626\pi\)
0.783614 0.621248i \(-0.213374\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.11317 0.316896 0.158448 0.987367i \(-0.449351\pi\)
0.158448 + 0.987367i \(0.449351\pi\)
\(828\) 0 0
\(829\) −10.2640 −0.356484 −0.178242 0.983987i \(-0.557041\pi\)
−0.178242 + 0.983987i \(0.557041\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 23.4684i 0.813131i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −31.5388 −1.08884 −0.544421 0.838812i \(-0.683251\pi\)
−0.544421 + 0.838812i \(0.683251\pi\)
\(840\) 0 0
\(841\) −0.922733 −0.0318184
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 25.5233i − 0.876992i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −0.856018 −0.0293439
\(852\) 0 0
\(853\) 15.3620 0.525985 0.262993 0.964798i \(-0.415291\pi\)
0.262993 + 0.964798i \(0.415291\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.4105i 0.560572i 0.959917 + 0.280286i \(0.0904293\pi\)
−0.959917 + 0.280286i \(0.909571\pi\)
\(858\) 0 0
\(859\) 14.8294i 0.505971i 0.967470 + 0.252986i \(0.0814125\pi\)
−0.967470 + 0.252986i \(0.918587\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 24.3820 0.829972 0.414986 0.909828i \(-0.363787\pi\)
0.414986 + 0.909828i \(0.363787\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 5.45511i − 0.185052i
\(870\) 0 0
\(871\) − 30.0187i − 1.01714i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 19.6846 0.664703 0.332351 0.943156i \(-0.392158\pi\)
0.332351 + 0.943156i \(0.392158\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 15.7280i − 0.529889i −0.964264 0.264945i \(-0.914646\pi\)
0.964264 0.264945i \(-0.0853536\pi\)
\(882\) 0 0
\(883\) 8.99067i 0.302560i 0.988491 + 0.151280i \(0.0483395\pi\)
−0.988491 + 0.151280i \(0.951660\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.66717 0.291015 0.145508 0.989357i \(-0.453518\pi\)
0.145508 + 0.989357i \(0.453518\pi\)
\(888\) 0 0
\(889\) −3.35739 −0.112603
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 82.1035i 2.74749i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 45.3076 1.51109
\(900\) 0 0
\(901\) 51.2080 1.70598
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 39.5747i 1.31406i 0.753866 + 0.657028i \(0.228187\pi\)
−0.753866 + 0.657028i \(0.771813\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.60156 0.119325 0.0596625 0.998219i \(-0.480998\pi\)
0.0596625 + 0.998219i \(0.480998\pi\)
\(912\) 0 0
\(913\) −8.20541 −0.271559
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 29.3845i 0.970363i
\(918\) 0 0
\(919\) − 15.7173i − 0.518467i −0.965815 0.259233i \(-0.916530\pi\)
0.965815 0.259233i \(-0.0834699\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −23.4269 −0.771107
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 44.6929i − 1.46633i −0.680053 0.733163i \(-0.738043\pi\)
0.680053 0.733163i \(-0.261957\pi\)
\(930\) 0 0
\(931\) 37.0280i 1.21354i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −17.9813 −0.587425 −0.293712 0.955894i \(-0.594891\pi\)
−0.293712 + 0.955894i \(0.594891\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 13.3276i − 0.434466i −0.976120 0.217233i \(-0.930297\pi\)
0.976120 0.217233i \(-0.0697032\pi\)
\(942\) 0 0
\(943\) − 2.68670i − 0.0874911i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −43.8538 −1.42506 −0.712529 0.701643i \(-0.752450\pi\)
−0.712529 + 0.701643i \(0.752450\pi\)
\(948\) 0 0
\(949\) 40.0373 1.29967
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 20.4382i − 0.662058i −0.943621 0.331029i \(-0.892604\pi\)
0.943621 0.331029i \(-0.107396\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 38.9965 1.25926
\(960\) 0 0
\(961\) −37.6027 −1.21299
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 14.6167i − 0.470041i −0.971990 0.235021i \(-0.924484\pi\)
0.971990 0.235021i \(-0.0755158\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −50.4374 −1.61861 −0.809307 0.587385i \(-0.800157\pi\)
−0.809307 + 0.587385i \(0.800157\pi\)
\(972\) 0 0
\(973\) −4.10270 −0.131527
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 17.0744i − 0.546257i −0.961978 0.273129i \(-0.911942\pi\)
0.961978 0.273129i \(-0.0880585\pi\)
\(978\) 0 0
\(979\) 0.745314i 0.0238203i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −13.7688 −0.439155 −0.219578 0.975595i \(-0.570468\pi\)
−0.219578 + 0.975595i \(0.570468\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 10.5142i − 0.334332i
\(990\) 0 0
\(991\) 14.0959i 0.447772i 0.974615 + 0.223886i \(0.0718743\pi\)
−0.974615 + 0.223886i \(0.928126\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 32.7126 1.03602 0.518010 0.855375i \(-0.326673\pi\)
0.518010 + 0.855375i \(0.326673\pi\)
\(998\) 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 7200.2.h.m.1151.11 12
3.2 odd 2 inner 7200.2.h.m.1151.12 12
4.3 odd 2 inner 7200.2.h.m.1151.2 12
5.2 odd 4 1440.2.o.a.1439.6 yes 12
5.3 odd 4 1440.2.o.b.1439.8 yes 12
5.4 even 2 7200.2.h.l.1151.1 12
12.11 even 2 inner 7200.2.h.m.1151.1 12
15.2 even 4 1440.2.o.a.1439.7 yes 12
15.8 even 4 1440.2.o.b.1439.5 yes 12
15.14 odd 2 7200.2.h.l.1151.2 12
20.3 even 4 1440.2.o.a.1439.8 yes 12
20.7 even 4 1440.2.o.b.1439.6 yes 12
20.19 odd 2 7200.2.h.l.1151.12 12
40.3 even 4 2880.2.o.f.2879.5 12
40.13 odd 4 2880.2.o.e.2879.5 12
40.27 even 4 2880.2.o.e.2879.7 12
40.37 odd 4 2880.2.o.f.2879.7 12
60.23 odd 4 1440.2.o.a.1439.5 12
60.47 odd 4 1440.2.o.b.1439.7 yes 12
60.59 even 2 7200.2.h.l.1151.11 12
120.53 even 4 2880.2.o.e.2879.8 12
120.77 even 4 2880.2.o.f.2879.6 12
120.83 odd 4 2880.2.o.f.2879.8 12
120.107 odd 4 2880.2.o.e.2879.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1440.2.o.a.1439.5 12 60.23 odd 4
1440.2.o.a.1439.6 yes 12 5.2 odd 4
1440.2.o.a.1439.7 yes 12 15.2 even 4
1440.2.o.a.1439.8 yes 12 20.3 even 4
1440.2.o.b.1439.5 yes 12 15.8 even 4
1440.2.o.b.1439.6 yes 12 20.7 even 4
1440.2.o.b.1439.7 yes 12 60.47 odd 4
1440.2.o.b.1439.8 yes 12 5.3 odd 4
2880.2.o.e.2879.5 12 40.13 odd 4
2880.2.o.e.2879.6 12 120.107 odd 4
2880.2.o.e.2879.7 12 40.27 even 4
2880.2.o.e.2879.8 12 120.53 even 4
2880.2.o.f.2879.5 12 40.3 even 4
2880.2.o.f.2879.6 12 120.77 even 4
2880.2.o.f.2879.7 12 40.37 odd 4
2880.2.o.f.2879.8 12 120.83 odd 4
7200.2.h.l.1151.1 12 5.4 even 2
7200.2.h.l.1151.2 12 15.14 odd 2
7200.2.h.l.1151.11 12 60.59 even 2
7200.2.h.l.1151.12 12 20.19 odd 2
7200.2.h.m.1151.1 12 12.11 even 2 inner
7200.2.h.m.1151.2 12 4.3 odd 2 inner
7200.2.h.m.1151.11 12 1.1 even 1 trivial
7200.2.h.m.1151.12 12 3.2 odd 2 inner