Properties

Label 2016.3.g.b.1135.7
Level $2016$
Weight $3$
Character 2016.1135
Analytic conductor $54.932$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2016,3,Mod(1135,2016)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2016, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2016.1135");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2016.g (of order \(2\), degree \(1\), not 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: \(54.9320212950\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.292213762624.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1135.7
Root \(-1.67467 + 1.09337i\) of defining polynomial
Character \(\chi\) \(=\) 2016.1135
Dual form 2016.3.g.b.1135.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.73252i q^{5} -2.64575i q^{7} +O(q^{10})\) \(q+5.73252i q^{5} -2.64575i q^{7} -1.40065 q^{11} +19.0821i q^{13} +32.2699 q^{17} -12.5675 q^{19} -15.8893i q^{23} -7.86180 q^{25} -3.29194i q^{29} +22.6705i q^{31} +15.1668 q^{35} +54.1537i q^{37} +7.59607 q^{41} +20.8478 q^{43} -21.6384i q^{47} -7.00000 q^{49} +0.356667i q^{53} -8.02924i q^{55} +26.8583 q^{59} -86.2287i q^{61} -109.389 q^{65} -114.523 q^{67} +104.792i q^{71} -24.3974 q^{73} +3.70576i q^{77} +117.128i q^{79} +79.2706 q^{83} +184.988i q^{85} -2.66078 q^{89} +50.4865 q^{91} -72.0433i q^{95} -52.0930 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 32 q^{11} + 80 q^{17} - 56 q^{19} - 16 q^{25} + 56 q^{35} - 128 q^{41} - 56 q^{49} + 104 q^{59} + 72 q^{65} - 304 q^{67} - 112 q^{73} + 72 q^{83} + 512 q^{89} + 56 q^{91} + 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1765\) \(1793\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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
\(5\) 5.73252i 1.14650i 0.819379 + 0.573252i \(0.194318\pi\)
−0.819379 + 0.573252i \(0.805682\pi\)
\(6\) 0 0
\(7\) − 2.64575i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.40065 −0.127332 −0.0636658 0.997971i \(-0.520279\pi\)
−0.0636658 + 0.997971i \(0.520279\pi\)
\(12\) 0 0
\(13\) 19.0821i 1.46785i 0.679228 + 0.733927i \(0.262315\pi\)
−0.679228 + 0.733927i \(0.737685\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 32.2699 1.89823 0.949114 0.314932i \(-0.101982\pi\)
0.949114 + 0.314932i \(0.101982\pi\)
\(18\) 0 0
\(19\) −12.5675 −0.661446 −0.330723 0.943728i \(-0.607293\pi\)
−0.330723 + 0.943728i \(0.607293\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 15.8893i − 0.690839i −0.938448 0.345419i \(-0.887737\pi\)
0.938448 0.345419i \(-0.112263\pi\)
\(24\) 0 0
\(25\) −7.86180 −0.314472
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 3.29194i − 0.113515i −0.998388 0.0567576i \(-0.981924\pi\)
0.998388 0.0567576i \(-0.0180762\pi\)
\(30\) 0 0
\(31\) 22.6705i 0.731306i 0.930751 + 0.365653i \(0.119154\pi\)
−0.930751 + 0.365653i \(0.880846\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 15.1668 0.433338
\(36\) 0 0
\(37\) 54.1537i 1.46361i 0.681512 + 0.731807i \(0.261323\pi\)
−0.681512 + 0.731807i \(0.738677\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.59607 0.185270 0.0926350 0.995700i \(-0.470471\pi\)
0.0926350 + 0.995700i \(0.470471\pi\)
\(42\) 0 0
\(43\) 20.8478 0.484833 0.242417 0.970172i \(-0.422060\pi\)
0.242417 + 0.970172i \(0.422060\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 21.6384i − 0.460392i −0.973144 0.230196i \(-0.926063\pi\)
0.973144 0.230196i \(-0.0739367\pi\)
\(48\) 0 0
\(49\) −7.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.356667i 0.00672957i 0.999994 + 0.00336479i \(0.00107105\pi\)
−0.999994 + 0.00336479i \(0.998929\pi\)
\(54\) 0 0
\(55\) − 8.02924i − 0.145986i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 26.8583 0.455226 0.227613 0.973752i \(-0.426908\pi\)
0.227613 + 0.973752i \(0.426908\pi\)
\(60\) 0 0
\(61\) − 86.2287i − 1.41359i −0.707420 0.706793i \(-0.750141\pi\)
0.707420 0.706793i \(-0.249859\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −109.389 −1.68290
\(66\) 0 0
\(67\) −114.523 −1.70929 −0.854646 0.519211i \(-0.826226\pi\)
−0.854646 + 0.519211i \(0.826226\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 104.792i 1.47594i 0.674834 + 0.737969i \(0.264215\pi\)
−0.674834 + 0.737969i \(0.735785\pi\)
\(72\) 0 0
\(73\) −24.3974 −0.334211 −0.167106 0.985939i \(-0.553442\pi\)
−0.167106 + 0.985939i \(0.553442\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.70576i 0.0481268i
\(78\) 0 0
\(79\) 117.128i 1.48263i 0.671157 + 0.741315i \(0.265798\pi\)
−0.671157 + 0.741315i \(0.734202\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 79.2706 0.955067 0.477534 0.878614i \(-0.341531\pi\)
0.477534 + 0.878614i \(0.341531\pi\)
\(84\) 0 0
\(85\) 184.988i 2.17633i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.66078 −0.0298964 −0.0149482 0.999888i \(-0.504758\pi\)
−0.0149482 + 0.999888i \(0.504758\pi\)
\(90\) 0 0
\(91\) 50.4865 0.554797
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) − 72.0433i − 0.758350i
\(96\) 0 0
\(97\) −52.0930 −0.537042 −0.268521 0.963274i \(-0.586535\pi\)
−0.268521 + 0.963274i \(0.586535\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 91.4742i 0.905685i 0.891591 + 0.452842i \(0.149590\pi\)
−0.891591 + 0.452842i \(0.850410\pi\)
\(102\) 0 0
\(103\) 39.7891i 0.386302i 0.981169 + 0.193151i \(0.0618708\pi\)
−0.981169 + 0.193151i \(0.938129\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 82.6631 0.772552 0.386276 0.922383i \(-0.373761\pi\)
0.386276 + 0.922383i \(0.373761\pi\)
\(108\) 0 0
\(109\) 29.4719i 0.270384i 0.990819 + 0.135192i \(0.0431652\pi\)
−0.990819 + 0.135192i \(0.956835\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −159.133 −1.40826 −0.704130 0.710071i \(-0.748663\pi\)
−0.704130 + 0.710071i \(0.748663\pi\)
\(114\) 0 0
\(115\) 91.0857 0.792049
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) − 85.3781i − 0.717463i
\(120\) 0 0
\(121\) −119.038 −0.983787
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 98.2451i 0.785961i
\(126\) 0 0
\(127\) 16.0834i 0.126641i 0.997993 + 0.0633205i \(0.0201690\pi\)
−0.997993 + 0.0633205i \(0.979831\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −118.136 −0.901799 −0.450899 0.892575i \(-0.648897\pi\)
−0.450899 + 0.892575i \(0.648897\pi\)
\(132\) 0 0
\(133\) 33.2504i 0.250003i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.1708 0.139933 0.0699664 0.997549i \(-0.477711\pi\)
0.0699664 + 0.997549i \(0.477711\pi\)
\(138\) 0 0
\(139\) −104.954 −0.755062 −0.377531 0.925997i \(-0.623227\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 26.7273i − 0.186904i
\(144\) 0 0
\(145\) 18.8711 0.130146
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 82.3906i − 0.552957i −0.961020 0.276478i \(-0.910833\pi\)
0.961020 0.276478i \(-0.0891674\pi\)
\(150\) 0 0
\(151\) − 57.7395i − 0.382381i −0.981553 0.191190i \(-0.938765\pi\)
0.981553 0.191190i \(-0.0612347\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −129.959 −0.838445
\(156\) 0 0
\(157\) − 3.72975i − 0.0237564i −0.999929 0.0118782i \(-0.996219\pi\)
0.999929 0.0118782i \(-0.00378104\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −42.0391 −0.261112
\(162\) 0 0
\(163\) −77.7069 −0.476729 −0.238365 0.971176i \(-0.576611\pi\)
−0.238365 + 0.971176i \(0.576611\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 62.0837i − 0.371759i −0.982573 0.185879i \(-0.940487\pi\)
0.982573 0.185879i \(-0.0595133\pi\)
\(168\) 0 0
\(169\) −195.127 −1.15459
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 195.614i − 1.13072i −0.824846 0.565358i \(-0.808738\pi\)
0.824846 0.565358i \(-0.191262\pi\)
\(174\) 0 0
\(175\) 20.8004i 0.118859i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 72.2099 0.403407 0.201704 0.979447i \(-0.435352\pi\)
0.201704 + 0.979447i \(0.435352\pi\)
\(180\) 0 0
\(181\) 140.980i 0.778895i 0.921049 + 0.389448i \(0.127334\pi\)
−0.921049 + 0.389448i \(0.872666\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −310.437 −1.67804
\(186\) 0 0
\(187\) −45.1987 −0.241704
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 284.473i 1.48939i 0.667407 + 0.744693i \(0.267404\pi\)
−0.667407 + 0.744693i \(0.732596\pi\)
\(192\) 0 0
\(193\) −123.850 −0.641710 −0.320855 0.947128i \(-0.603970\pi\)
−0.320855 + 0.947128i \(0.603970\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 108.098i 0.548721i 0.961627 + 0.274361i \(0.0884662\pi\)
−0.961627 + 0.274361i \(0.911534\pi\)
\(198\) 0 0
\(199\) 331.854i 1.66761i 0.552060 + 0.833804i \(0.313842\pi\)
−0.552060 + 0.833804i \(0.686158\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.70966 −0.0429047
\(204\) 0 0
\(205\) 43.5446i 0.212413i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 17.6026 0.0842229
\(210\) 0 0
\(211\) −26.3950 −0.125095 −0.0625475 0.998042i \(-0.519922\pi\)
−0.0625475 + 0.998042i \(0.519922\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 119.511i 0.555864i
\(216\) 0 0
\(217\) 59.9804 0.276408
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 615.777i 2.78632i
\(222\) 0 0
\(223\) − 161.183i − 0.722796i −0.932412 0.361398i \(-0.882300\pi\)
0.932412 0.361398i \(-0.117700\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −171.279 −0.754533 −0.377266 0.926105i \(-0.623136\pi\)
−0.377266 + 0.926105i \(0.623136\pi\)
\(228\) 0 0
\(229\) − 229.251i − 1.00110i −0.865709 0.500548i \(-0.833132\pi\)
0.865709 0.500548i \(-0.166868\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 270.154 1.15946 0.579730 0.814808i \(-0.303158\pi\)
0.579730 + 0.814808i \(0.303158\pi\)
\(234\) 0 0
\(235\) 124.043 0.527841
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 157.155i 0.657551i 0.944408 + 0.328776i \(0.106636\pi\)
−0.944408 + 0.328776i \(0.893364\pi\)
\(240\) 0 0
\(241\) −97.7124 −0.405445 −0.202723 0.979236i \(-0.564979\pi\)
−0.202723 + 0.979236i \(0.564979\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 40.1276i − 0.163786i
\(246\) 0 0
\(247\) − 239.814i − 0.970906i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −313.145 −1.24759 −0.623796 0.781587i \(-0.714410\pi\)
−0.623796 + 0.781587i \(0.714410\pi\)
\(252\) 0 0
\(253\) 22.2553i 0.0879655i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 348.855 1.35741 0.678707 0.734409i \(-0.262541\pi\)
0.678707 + 0.734409i \(0.262541\pi\)
\(258\) 0 0
\(259\) 143.277 0.553194
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 384.364i 1.46146i 0.682667 + 0.730729i \(0.260820\pi\)
−0.682667 + 0.730729i \(0.739180\pi\)
\(264\) 0 0
\(265\) −2.04460 −0.00771548
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 37.7613i − 0.140376i −0.997534 0.0701882i \(-0.977640\pi\)
0.997534 0.0701882i \(-0.0223600\pi\)
\(270\) 0 0
\(271\) 308.730i 1.13922i 0.821914 + 0.569612i \(0.192907\pi\)
−0.821914 + 0.569612i \(0.807093\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.0116 0.0400422
\(276\) 0 0
\(277\) 244.210i 0.881623i 0.897600 + 0.440812i \(0.145309\pi\)
−0.897600 + 0.440812i \(0.854691\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −266.569 −0.948646 −0.474323 0.880351i \(-0.657307\pi\)
−0.474323 + 0.880351i \(0.657307\pi\)
\(282\) 0 0
\(283\) −165.605 −0.585177 −0.292589 0.956238i \(-0.594517\pi\)
−0.292589 + 0.956238i \(0.594517\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 20.0973i − 0.0700255i
\(288\) 0 0
\(289\) 752.346 2.60327
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 34.3652i − 0.117288i −0.998279 0.0586438i \(-0.981322\pi\)
0.998279 0.0586438i \(-0.0186776\pi\)
\(294\) 0 0
\(295\) 153.966i 0.521918i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 303.201 1.01405
\(300\) 0 0
\(301\) − 55.1582i − 0.183250i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 494.308 1.62068
\(306\) 0 0
\(307\) 222.934 0.726170 0.363085 0.931756i \(-0.381724\pi\)
0.363085 + 0.931756i \(0.381724\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 419.934i 1.35027i 0.737694 + 0.675135i \(0.235915\pi\)
−0.737694 + 0.675135i \(0.764085\pi\)
\(312\) 0 0
\(313\) −293.869 −0.938878 −0.469439 0.882965i \(-0.655544\pi\)
−0.469439 + 0.882965i \(0.655544\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 423.461i − 1.33584i −0.744234 0.667919i \(-0.767185\pi\)
0.744234 0.667919i \(-0.232815\pi\)
\(318\) 0 0
\(319\) 4.61085i 0.0144541i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −405.551 −1.25558
\(324\) 0 0
\(325\) − 150.020i − 0.461599i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −57.2499 −0.174012
\(330\) 0 0
\(331\) 126.666 0.382678 0.191339 0.981524i \(-0.438717\pi\)
0.191339 + 0.981524i \(0.438717\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 656.503i − 1.95971i
\(336\) 0 0
\(337\) 302.404 0.897341 0.448671 0.893697i \(-0.351898\pi\)
0.448671 + 0.893697i \(0.351898\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 31.7533i − 0.0931183i
\(342\) 0 0
\(343\) 18.5203i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 320.532 0.923724 0.461862 0.886952i \(-0.347182\pi\)
0.461862 + 0.886952i \(0.347182\pi\)
\(348\) 0 0
\(349\) 380.678i 1.09077i 0.838186 + 0.545385i \(0.183616\pi\)
−0.838186 + 0.545385i \(0.816384\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 364.369 1.03221 0.516104 0.856526i \(-0.327382\pi\)
0.516104 + 0.856526i \(0.327382\pi\)
\(354\) 0 0
\(355\) −600.720 −1.69217
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 111.995i 0.311965i 0.987760 + 0.155982i \(0.0498543\pi\)
−0.987760 + 0.155982i \(0.950146\pi\)
\(360\) 0 0
\(361\) −203.059 −0.562489
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 139.859i − 0.383174i
\(366\) 0 0
\(367\) 439.042i 1.19630i 0.801384 + 0.598150i \(0.204097\pi\)
−0.801384 + 0.598150i \(0.795903\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.943653 0.00254354
\(372\) 0 0
\(373\) − 254.996i − 0.683637i −0.939766 0.341818i \(-0.888957\pi\)
0.939766 0.341818i \(-0.111043\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 62.8172 0.166624
\(378\) 0 0
\(379\) −603.048 −1.59116 −0.795578 0.605852i \(-0.792833\pi\)
−0.795578 + 0.605852i \(0.792833\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 73.3855i − 0.191607i −0.995400 0.0958035i \(-0.969458\pi\)
0.995400 0.0958035i \(-0.0305420\pi\)
\(384\) 0 0
\(385\) −21.2434 −0.0551776
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 340.800i 0.876092i 0.898953 + 0.438046i \(0.144329\pi\)
−0.898953 + 0.438046i \(0.855671\pi\)
\(390\) 0 0
\(391\) − 512.745i − 1.31137i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −671.438 −1.69984
\(396\) 0 0
\(397\) 111.540i 0.280957i 0.990084 + 0.140478i \(0.0448640\pi\)
−0.990084 + 0.140478i \(0.955136\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −340.535 −0.849215 −0.424607 0.905378i \(-0.639588\pi\)
−0.424607 + 0.905378i \(0.639588\pi\)
\(402\) 0 0
\(403\) −432.600 −1.07345
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 75.8502i − 0.186364i
\(408\) 0 0
\(409\) 666.959 1.63071 0.815354 0.578963i \(-0.196543\pi\)
0.815354 + 0.578963i \(0.196543\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 71.0604i − 0.172059i
\(414\) 0 0
\(415\) 454.420i 1.09499i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −200.191 −0.477783 −0.238891 0.971046i \(-0.576784\pi\)
−0.238891 + 0.971046i \(0.576784\pi\)
\(420\) 0 0
\(421\) 15.9136i 0.0377996i 0.999821 + 0.0188998i \(0.00601636\pi\)
−0.999821 + 0.0188998i \(0.993984\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −253.699 −0.596940
\(426\) 0 0
\(427\) −228.140 −0.534285
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 628.013i − 1.45711i −0.684989 0.728553i \(-0.740193\pi\)
0.684989 0.728553i \(-0.259807\pi\)
\(432\) 0 0
\(433\) 789.232 1.82271 0.911353 0.411625i \(-0.135039\pi\)
0.911353 + 0.411625i \(0.135039\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 199.688i 0.456952i
\(438\) 0 0
\(439\) − 665.570i − 1.51610i −0.652194 0.758052i \(-0.726151\pi\)
0.652194 0.758052i \(-0.273849\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 507.152 1.14481 0.572406 0.819970i \(-0.306010\pi\)
0.572406 + 0.819970i \(0.306010\pi\)
\(444\) 0 0
\(445\) − 15.2530i − 0.0342764i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 279.029 0.621446 0.310723 0.950501i \(-0.399429\pi\)
0.310723 + 0.950501i \(0.399429\pi\)
\(450\) 0 0
\(451\) −10.6394 −0.0235907
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 289.415i 0.636077i
\(456\) 0 0
\(457\) −720.881 −1.57742 −0.788710 0.614765i \(-0.789251\pi\)
−0.788710 + 0.614765i \(0.789251\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 483.262i − 1.04829i −0.851629 0.524145i \(-0.824385\pi\)
0.851629 0.524145i \(-0.175615\pi\)
\(462\) 0 0
\(463\) 39.6326i 0.0855995i 0.999084 + 0.0427997i \(0.0136277\pi\)
−0.999084 + 0.0427997i \(0.986372\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.7868 0.0380874 0.0190437 0.999819i \(-0.493938\pi\)
0.0190437 + 0.999819i \(0.493938\pi\)
\(468\) 0 0
\(469\) 302.998i 0.646052i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −29.2005 −0.0617346
\(474\) 0 0
\(475\) 98.8029 0.208006
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) − 668.616i − 1.39586i −0.716166 0.697930i \(-0.754105\pi\)
0.716166 0.697930i \(-0.245895\pi\)
\(480\) 0 0
\(481\) −1033.37 −2.14837
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 298.624i − 0.615720i
\(486\) 0 0
\(487\) − 418.484i − 0.859311i −0.902993 0.429656i \(-0.858635\pi\)
0.902993 0.429656i \(-0.141365\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 381.031 0.776030 0.388015 0.921653i \(-0.373161\pi\)
0.388015 + 0.921653i \(0.373161\pi\)
\(492\) 0 0
\(493\) − 106.231i − 0.215478i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 277.253 0.557852
\(498\) 0 0
\(499\) 438.392 0.878541 0.439271 0.898355i \(-0.355237\pi\)
0.439271 + 0.898355i \(0.355237\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 754.754i − 1.50050i −0.661151 0.750252i \(-0.729932\pi\)
0.661151 0.750252i \(-0.270068\pi\)
\(504\) 0 0
\(505\) −524.378 −1.03837
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 494.029i − 0.970588i −0.874351 0.485294i \(-0.838713\pi\)
0.874351 0.485294i \(-0.161287\pi\)
\(510\) 0 0
\(511\) 64.5495i 0.126320i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −228.092 −0.442897
\(516\) 0 0
\(517\) 30.3078i 0.0586224i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 32.8747 0.0630993 0.0315496 0.999502i \(-0.489956\pi\)
0.0315496 + 0.999502i \(0.489956\pi\)
\(522\) 0 0
\(523\) 28.2755 0.0540640 0.0270320 0.999635i \(-0.491394\pi\)
0.0270320 + 0.999635i \(0.491394\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 731.574i 1.38819i
\(528\) 0 0
\(529\) 276.531 0.522742
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 144.949i 0.271949i
\(534\) 0 0
\(535\) 473.868i 0.885735i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.80453 0.0181902
\(540\) 0 0
\(541\) − 1071.59i − 1.98077i −0.138352 0.990383i \(-0.544180\pi\)
0.138352 0.990383i \(-0.455820\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −168.948 −0.309997
\(546\) 0 0
\(547\) 986.888 1.80418 0.902091 0.431545i \(-0.142032\pi\)
0.902091 + 0.431545i \(0.142032\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 41.3714i 0.0750842i
\(552\) 0 0
\(553\) 309.891 0.560382
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 483.550i − 0.868133i −0.900881 0.434067i \(-0.857078\pi\)
0.900881 0.434067i \(-0.142922\pi\)
\(558\) 0 0
\(559\) 397.821i 0.711665i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 520.893 0.925210 0.462605 0.886564i \(-0.346915\pi\)
0.462605 + 0.886564i \(0.346915\pi\)
\(564\) 0 0
\(565\) − 912.236i − 1.61458i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 732.959 1.28815 0.644077 0.764961i \(-0.277242\pi\)
0.644077 + 0.764961i \(0.277242\pi\)
\(570\) 0 0
\(571\) 999.584 1.75058 0.875292 0.483595i \(-0.160669\pi\)
0.875292 + 0.483595i \(0.160669\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 124.918i 0.217249i
\(576\) 0 0
\(577\) 465.859 0.807381 0.403690 0.914896i \(-0.367727\pi\)
0.403690 + 0.914896i \(0.367727\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 209.730i − 0.360981i
\(582\) 0 0
\(583\) − 0.499565i 0 0.000856887i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −574.851 −0.979303 −0.489651 0.871918i \(-0.662876\pi\)
−0.489651 + 0.871918i \(0.662876\pi\)
\(588\) 0 0
\(589\) − 284.911i − 0.483719i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −943.055 −1.59031 −0.795156 0.606405i \(-0.792611\pi\)
−0.795156 + 0.606405i \(0.792611\pi\)
\(594\) 0 0
\(595\) 489.432 0.822574
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 9.26699i − 0.0154708i −0.999970 0.00773538i \(-0.997538\pi\)
0.999970 0.00773538i \(-0.00246227\pi\)
\(600\) 0 0
\(601\) 57.7003 0.0960072 0.0480036 0.998847i \(-0.484714\pi\)
0.0480036 + 0.998847i \(0.484714\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 682.389i − 1.12792i
\(606\) 0 0
\(607\) − 1024.68i − 1.68810i −0.536264 0.844050i \(-0.680165\pi\)
0.536264 0.844050i \(-0.319835\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 412.906 0.675788
\(612\) 0 0
\(613\) 404.818i 0.660389i 0.943913 + 0.330195i \(0.107114\pi\)
−0.943913 + 0.330195i \(0.892886\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −894.209 −1.44928 −0.724642 0.689125i \(-0.757995\pi\)
−0.724642 + 0.689125i \(0.757995\pi\)
\(618\) 0 0
\(619\) 779.388 1.25911 0.629554 0.776957i \(-0.283238\pi\)
0.629554 + 0.776957i \(0.283238\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.03977i 0.0112998i
\(624\) 0 0
\(625\) −759.737 −1.21558
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1747.53i 2.77827i
\(630\) 0 0
\(631\) − 780.191i − 1.23644i −0.786007 0.618218i \(-0.787855\pi\)
0.786007 0.618218i \(-0.212145\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −92.1985 −0.145194
\(636\) 0 0
\(637\) − 133.575i − 0.209693i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.3139 0.0363712 0.0181856 0.999835i \(-0.494211\pi\)
0.0181856 + 0.999835i \(0.494211\pi\)
\(642\) 0 0
\(643\) −530.706 −0.825360 −0.412680 0.910876i \(-0.635407\pi\)
−0.412680 + 0.910876i \(0.635407\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 213.435i 0.329883i 0.986303 + 0.164942i \(0.0527436\pi\)
−0.986303 + 0.164942i \(0.947256\pi\)
\(648\) 0 0
\(649\) −37.6190 −0.0579646
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 274.874i 0.420941i 0.977600 + 0.210470i \(0.0674995\pi\)
−0.977600 + 0.210470i \(0.932500\pi\)
\(654\) 0 0
\(655\) − 677.215i − 1.03392i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1234.48 1.87327 0.936633 0.350313i \(-0.113925\pi\)
0.936633 + 0.350313i \(0.113925\pi\)
\(660\) 0 0
\(661\) 582.733i 0.881593i 0.897607 + 0.440797i \(0.145304\pi\)
−0.897607 + 0.440797i \(0.854696\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −190.609 −0.286630
\(666\) 0 0
\(667\) −52.3066 −0.0784207
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 120.776i 0.179994i
\(672\) 0 0
\(673\) −399.145 −0.593083 −0.296542 0.955020i \(-0.595833\pi\)
−0.296542 + 0.955020i \(0.595833\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 754.467i 1.11443i 0.830369 + 0.557214i \(0.188130\pi\)
−0.830369 + 0.557214i \(0.811870\pi\)
\(678\) 0 0
\(679\) 137.825i 0.202983i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 288.264 0.422055 0.211028 0.977480i \(-0.432319\pi\)
0.211028 + 0.977480i \(0.432319\pi\)
\(684\) 0 0
\(685\) 109.897i 0.160433i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.80596 −0.00987803
\(690\) 0 0
\(691\) 156.692 0.226761 0.113380 0.993552i \(-0.463832\pi\)
0.113380 + 0.993552i \(0.463832\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 601.649i − 0.865682i
\(696\) 0 0
\(697\) 245.124 0.351685
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 1126.50i − 1.60700i −0.595307 0.803498i \(-0.702970\pi\)
0.595307 0.803498i \(-0.297030\pi\)
\(702\) 0 0
\(703\) − 680.575i − 0.968102i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 242.018 0.342317
\(708\) 0 0
\(709\) 1096.17i 1.54608i 0.634356 + 0.773041i \(0.281266\pi\)
−0.634356 + 0.773041i \(0.718734\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 360.218 0.505214
\(714\) 0 0
\(715\) 153.215 0.214286
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 605.362i − 0.841949i −0.907072 0.420975i \(-0.861688\pi\)
0.907072 0.420975i \(-0.138312\pi\)
\(720\) 0 0
\(721\) 105.272 0.146009
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 25.8806i 0.0356974i
\(726\) 0 0
\(727\) − 443.659i − 0.610260i −0.952311 0.305130i \(-0.901300\pi\)
0.952311 0.305130i \(-0.0986999\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 672.757 0.920325
\(732\) 0 0
\(733\) − 750.026i − 1.02323i −0.859216 0.511614i \(-0.829048\pi\)
0.859216 0.511614i \(-0.170952\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 160.406 0.217647
\(738\) 0 0
\(739\) −619.293 −0.838015 −0.419007 0.907983i \(-0.637622\pi\)
−0.419007 + 0.907983i \(0.637622\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 30.5255i 0.0410842i 0.999789 + 0.0205421i \(0.00653921\pi\)
−0.999789 + 0.0205421i \(0.993461\pi\)
\(744\) 0 0
\(745\) 472.306 0.633967
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 218.706i − 0.291997i
\(750\) 0 0
\(751\) 968.214i 1.28923i 0.764506 + 0.644616i \(0.222983\pi\)
−0.764506 + 0.644616i \(0.777017\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 330.993 0.438401
\(756\) 0 0
\(757\) − 1171.15i − 1.54710i −0.633736 0.773550i \(-0.718479\pi\)
0.633736 0.773550i \(-0.281521\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −235.996 −0.310113 −0.155057 0.987906i \(-0.549556\pi\)
−0.155057 + 0.987906i \(0.549556\pi\)
\(762\) 0 0
\(763\) 77.9753 0.102196
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 512.513i 0.668205i
\(768\) 0 0
\(769\) −124.257 −0.161582 −0.0807912 0.996731i \(-0.525745\pi\)
−0.0807912 + 0.996731i \(0.525745\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 178.223i − 0.230560i −0.993333 0.115280i \(-0.963224\pi\)
0.993333 0.115280i \(-0.0367765\pi\)
\(774\) 0 0
\(775\) − 178.231i − 0.229975i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −95.4634 −0.122546
\(780\) 0 0
\(781\) − 146.776i − 0.187933i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 21.3809 0.0272368
\(786\) 0 0
\(787\) 1107.90 1.40775 0.703873 0.710326i \(-0.251453\pi\)
0.703873 + 0.710326i \(0.251453\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 421.028i 0.532273i
\(792\) 0 0
\(793\) 1645.43 2.07494
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1094.69i 1.37351i 0.726889 + 0.686755i \(0.240966\pi\)
−0.726889 + 0.686755i \(0.759034\pi\)
\(798\) 0 0
\(799\) − 698.269i − 0.873929i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 34.1722 0.0425556
\(804\) 0 0
\(805\) − 240.990i − 0.299367i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1386.75 1.71416 0.857079 0.515185i \(-0.172277\pi\)
0.857079 + 0.515185i \(0.172277\pi\)
\(810\) 0 0
\(811\) 312.204 0.384962 0.192481 0.981301i \(-0.438347\pi\)
0.192481 + 0.981301i \(0.438347\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 445.456i − 0.546572i
\(816\) 0 0
\(817\) −262.005 −0.320691
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1092.89i 1.33117i 0.746324 + 0.665583i \(0.231817\pi\)
−0.746324 + 0.665583i \(0.768183\pi\)
\(822\) 0 0
\(823\) 907.162i 1.10226i 0.834419 + 0.551131i \(0.185804\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −607.144 −0.734152 −0.367076 0.930191i \(-0.619641\pi\)
−0.367076 + 0.930191i \(0.619641\pi\)
\(828\) 0 0
\(829\) − 427.969i − 0.516247i −0.966112 0.258124i \(-0.916896\pi\)
0.966112 0.258124i \(-0.0831042\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −225.889 −0.271176
\(834\) 0 0
\(835\) 355.896 0.426223
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 1133.09i − 1.35053i −0.737575 0.675265i \(-0.764029\pi\)
0.737575 0.675265i \(-0.235971\pi\)
\(840\) 0 0
\(841\) 830.163 0.987114
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 1118.57i − 1.32375i
\(846\) 0 0
\(847\) 314.945i 0.371836i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 860.464 1.01112
\(852\) 0 0
\(853\) − 169.502i − 0.198712i −0.995052 0.0993562i \(-0.968322\pi\)
0.995052 0.0993562i \(-0.0316783\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 234.079 0.273138 0.136569 0.990631i \(-0.456393\pi\)
0.136569 + 0.990631i \(0.456393\pi\)
\(858\) 0 0
\(859\) −894.342 −1.04114 −0.520571 0.853818i \(-0.674281\pi\)
−0.520571 + 0.853818i \(0.674281\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 778.580i 0.902178i 0.892479 + 0.451089i \(0.148964\pi\)
−0.892479 + 0.451089i \(0.851036\pi\)
\(864\) 0 0
\(865\) 1121.36 1.29637
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 164.055i − 0.188786i
\(870\) 0 0
\(871\) − 2185.33i − 2.50899i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 259.932 0.297065
\(876\) 0 0
\(877\) 17.2780i 0.0197013i 0.999951 + 0.00985064i \(0.00313561\pi\)
−0.999951 + 0.00985064i \(0.996864\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −770.918 −0.875049 −0.437524 0.899207i \(-0.644145\pi\)
−0.437524 + 0.899207i \(0.644145\pi\)
\(882\) 0 0
\(883\) −776.362 −0.879232 −0.439616 0.898186i \(-0.644886\pi\)
−0.439616 + 0.898186i \(0.644886\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1630.80i 1.83856i 0.393603 + 0.919280i \(0.371228\pi\)
−0.393603 + 0.919280i \(0.628772\pi\)
\(888\) 0 0
\(889\) 42.5527 0.0478658
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 271.940i 0.304524i
\(894\) 0 0
\(895\) 413.945i 0.462508i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 74.6299 0.0830144
\(900\) 0 0
\(901\) 11.5096i 0.0127743i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −808.171 −0.893007
\(906\) 0 0
\(907\) 953.863 1.05167 0.525834 0.850587i \(-0.323753\pi\)
0.525834 + 0.850587i \(0.323753\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 1681.15i − 1.84539i −0.385534 0.922694i \(-0.625983\pi\)
0.385534 0.922694i \(-0.374017\pi\)
\(912\) 0 0
\(913\) −111.030 −0.121610
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 312.557i 0.340848i
\(918\) 0 0
\(919\) 504.991i 0.549500i 0.961516 + 0.274750i \(0.0885952\pi\)
−0.961516 + 0.274750i \(0.911405\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1999.64 −2.16646
\(924\) 0 0
\(925\) − 425.746i − 0.460266i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −983.851 −1.05904 −0.529521 0.848297i \(-0.677628\pi\)
−0.529521 + 0.848297i \(0.677628\pi\)
\(930\) 0 0
\(931\) 87.9723 0.0944923
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 259.103i − 0.277115i
\(936\) 0 0
\(937\) −389.648 −0.415846 −0.207923 0.978145i \(-0.566670\pi\)
−0.207923 + 0.978145i \(0.566670\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 875.465i 0.930356i 0.885217 + 0.465178i \(0.154010\pi\)
−0.885217 + 0.465178i \(0.845990\pi\)
\(942\) 0 0
\(943\) − 120.696i − 0.127992i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1251.29 −1.32132 −0.660661 0.750685i \(-0.729724\pi\)
−0.660661 + 0.750685i \(0.729724\pi\)
\(948\) 0 0
\(949\) − 465.554i − 0.490573i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 882.129 0.925633 0.462817 0.886454i \(-0.346839\pi\)
0.462817 + 0.886454i \(0.346839\pi\)
\(954\) 0 0
\(955\) −1630.75 −1.70759
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) − 50.7211i − 0.0528896i
\(960\) 0 0
\(961\) 447.049 0.465192
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 709.973i − 0.735724i
\(966\) 0 0
\(967\) 1410.24i 1.45836i 0.684320 + 0.729182i \(0.260099\pi\)
−0.684320 + 0.729182i \(0.739901\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 678.550 0.698815 0.349408 0.936971i \(-0.386383\pi\)
0.349408 + 0.936971i \(0.386383\pi\)
\(972\) 0 0
\(973\) 277.681i 0.285387i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −111.815 −0.114447 −0.0572235 0.998361i \(-0.518225\pi\)
−0.0572235 + 0.998361i \(0.518225\pi\)
\(978\) 0 0
\(979\) 3.72682 0.00380676
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 202.226i 0.205723i 0.994696 + 0.102862i \(0.0327999\pi\)
−0.994696 + 0.102862i \(0.967200\pi\)
\(984\) 0 0
\(985\) −619.675 −0.629111
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 331.257i − 0.334942i
\(990\) 0 0
\(991\) 189.064i 0.190781i 0.995440 + 0.0953907i \(0.0304100\pi\)
−0.995440 + 0.0953907i \(0.969590\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1902.36 −1.91192
\(996\) 0 0
\(997\) 1632.91i 1.63783i 0.573917 + 0.818914i \(0.305423\pi\)
−0.573917 + 0.818914i \(0.694577\pi\)
\(998\) 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 2016.3.g.b.1135.7 8
3.2 odd 2 224.3.g.b.15.1 8
4.3 odd 2 504.3.g.b.379.7 8
8.3 odd 2 inner 2016.3.g.b.1135.2 8
8.5 even 2 504.3.g.b.379.8 8
12.11 even 2 56.3.g.b.43.2 yes 8
21.20 even 2 1568.3.g.m.687.8 8
24.5 odd 2 56.3.g.b.43.1 8
24.11 even 2 224.3.g.b.15.2 8
48.5 odd 4 1792.3.d.j.1023.14 16
48.11 even 4 1792.3.d.j.1023.4 16
48.29 odd 4 1792.3.d.j.1023.3 16
48.35 even 4 1792.3.d.j.1023.13 16
84.11 even 6 392.3.k.o.275.5 16
84.23 even 6 392.3.k.o.67.7 16
84.47 odd 6 392.3.k.n.67.7 16
84.59 odd 6 392.3.k.n.275.5 16
84.83 odd 2 392.3.g.m.99.2 8
168.5 even 6 392.3.k.n.67.5 16
168.53 odd 6 392.3.k.o.275.7 16
168.83 odd 2 1568.3.g.m.687.7 8
168.101 even 6 392.3.k.n.275.7 16
168.125 even 2 392.3.g.m.99.1 8
168.149 odd 6 392.3.k.o.67.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.g.b.43.1 8 24.5 odd 2
56.3.g.b.43.2 yes 8 12.11 even 2
224.3.g.b.15.1 8 3.2 odd 2
224.3.g.b.15.2 8 24.11 even 2
392.3.g.m.99.1 8 168.125 even 2
392.3.g.m.99.2 8 84.83 odd 2
392.3.k.n.67.5 16 168.5 even 6
392.3.k.n.67.7 16 84.47 odd 6
392.3.k.n.275.5 16 84.59 odd 6
392.3.k.n.275.7 16 168.101 even 6
392.3.k.o.67.5 16 168.149 odd 6
392.3.k.o.67.7 16 84.23 even 6
392.3.k.o.275.5 16 84.11 even 6
392.3.k.o.275.7 16 168.53 odd 6
504.3.g.b.379.7 8 4.3 odd 2
504.3.g.b.379.8 8 8.5 even 2
1568.3.g.m.687.7 8 168.83 odd 2
1568.3.g.m.687.8 8 21.20 even 2
1792.3.d.j.1023.3 16 48.29 odd 4
1792.3.d.j.1023.4 16 48.11 even 4
1792.3.d.j.1023.13 16 48.35 even 4
1792.3.d.j.1023.14 16 48.5 odd 4
2016.3.g.b.1135.2 8 8.3 odd 2 inner
2016.3.g.b.1135.7 8 1.1 even 1 trivial