Properties

Label 7056.2.h.l.4607.7
Level $7056$
Weight $2$
Character 7056.4607
Analytic conductor $56.342$
Analytic rank $0$
Dimension $8$
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] = [7056,2,Mod(4607,7056)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7056, 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("7056.4607");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.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: \(56.3424436662\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4607.7
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 7056.4607
Dual form 7056.2.h.l.4607.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.73205i q^{5} +O(q^{10})\) \(q+2.73205i q^{5} -4.24264 q^{11} +6.31319 q^{13} +0.732051i q^{17} -6.69213i q^{19} +9.14162 q^{23} -2.46410 q^{25} +2.44949i q^{29} -1.79315i q^{31} -3.46410 q^{37} -4.19615i q^{41} -9.46410i q^{43} +3.46410 q^{47} +1.41421i q^{53} -11.5911i q^{55} -10.3923 q^{59} +8.10634 q^{61} +17.2480i q^{65} -12.9282i q^{67} -4.24264 q^{71} -8.10634 q^{73} +8.53590i q^{79} -2.53590 q^{83} -2.00000 q^{85} -9.66025i q^{89} +18.2832 q^{95} -4.52004 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{25} - 48 q^{83} - 16 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7056\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1765\) \(4609\) \(6175\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\)

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
\(5\) 2.73205i 1.22181i 0.791704 + 0.610905i \(0.209194\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.24264 −1.27920 −0.639602 0.768706i \(-0.720901\pi\)
−0.639602 + 0.768706i \(0.720901\pi\)
\(12\) 0 0
\(13\) 6.31319 1.75096 0.875482 0.483250i \(-0.160544\pi\)
0.875482 + 0.483250i \(0.160544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.732051i 0.177548i 0.996052 + 0.0887742i \(0.0282950\pi\)
−0.996052 + 0.0887742i \(0.971705\pi\)
\(18\) 0 0
\(19\) − 6.69213i − 1.53528i −0.640881 0.767640i \(-0.721431\pi\)
0.640881 0.767640i \(-0.278569\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 9.14162 1.90616 0.953080 0.302719i \(-0.0978944\pi\)
0.953080 + 0.302719i \(0.0978944\pi\)
\(24\) 0 0
\(25\) −2.46410 −0.492820
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.44949i 0.454859i 0.973795 + 0.227429i \(0.0730321\pi\)
−0.973795 + 0.227429i \(0.926968\pi\)
\(30\) 0 0
\(31\) − 1.79315i − 0.322059i −0.986950 0.161030i \(-0.948519\pi\)
0.986950 0.161030i \(-0.0514815\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.46410 −0.569495 −0.284747 0.958603i \(-0.591910\pi\)
−0.284747 + 0.958603i \(0.591910\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 4.19615i − 0.655329i −0.944794 0.327664i \(-0.893738\pi\)
0.944794 0.327664i \(-0.106262\pi\)
\(42\) 0 0
\(43\) − 9.46410i − 1.44326i −0.692278 0.721631i \(-0.743393\pi\)
0.692278 0.721631i \(-0.256607\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.46410 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.41421i 0.194257i 0.995272 + 0.0971286i \(0.0309658\pi\)
−0.995272 + 0.0971286i \(0.969034\pi\)
\(54\) 0 0
\(55\) − 11.5911i − 1.56294i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.3923 −1.35296 −0.676481 0.736460i \(-0.736496\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(60\) 0 0
\(61\) 8.10634 1.03791 0.518955 0.854801i \(-0.326321\pi\)
0.518955 + 0.854801i \(0.326321\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 17.2480i 2.13935i
\(66\) 0 0
\(67\) − 12.9282i − 1.57943i −0.613473 0.789716i \(-0.710228\pi\)
0.613473 0.789716i \(-0.289772\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.24264 −0.503509 −0.251754 0.967791i \(-0.581008\pi\)
−0.251754 + 0.967791i \(0.581008\pi\)
\(72\) 0 0
\(73\) −8.10634 −0.948776 −0.474388 0.880316i \(-0.657331\pi\)
−0.474388 + 0.880316i \(0.657331\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 8.53590i 0.960364i 0.877169 + 0.480182i \(0.159429\pi\)
−0.877169 + 0.480182i \(0.840571\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −2.53590 −0.278351 −0.139176 0.990268i \(-0.544445\pi\)
−0.139176 + 0.990268i \(0.544445\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 9.66025i − 1.02398i −0.858990 0.511992i \(-0.828908\pi\)
0.858990 0.511992i \(-0.171092\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 18.2832 1.87582
\(96\) 0 0
\(97\) −4.52004 −0.458941 −0.229470 0.973316i \(-0.573699\pi\)
−0.229470 + 0.973316i \(0.573699\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 18.1962i − 1.81058i −0.424789 0.905292i \(-0.639652\pi\)
0.424789 0.905292i \(-0.360348\pi\)
\(102\) 0 0
\(103\) − 3.10583i − 0.306026i −0.988224 0.153013i \(-0.951102\pi\)
0.988224 0.153013i \(-0.0488977\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.4543 1.01066 0.505328 0.862928i \(-0.331372\pi\)
0.505328 + 0.862928i \(0.331372\pi\)
\(108\) 0 0
\(109\) 19.8564 1.90190 0.950949 0.309346i \(-0.100110\pi\)
0.950949 + 0.309346i \(0.100110\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 13.2827i − 1.24953i −0.780811 0.624767i \(-0.785194\pi\)
0.780811 0.624767i \(-0.214806\pi\)
\(114\) 0 0
\(115\) 24.9754i 2.32897i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 6.00000i 0.532414i 0.963916 + 0.266207i \(0.0857705\pi\)
−0.963916 + 0.266207i \(0.914230\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.07180 −0.443125 −0.221562 0.975146i \(-0.571116\pi\)
−0.221562 + 0.975146i \(0.571116\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.03579i 0.515672i 0.966189 + 0.257836i \(0.0830095\pi\)
−0.966189 + 0.257836i \(0.916990\pi\)
\(138\) 0 0
\(139\) − 13.3843i − 1.13524i −0.823291 0.567619i \(-0.807865\pi\)
0.823291 0.567619i \(-0.192135\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −26.7846 −2.23984
\(144\) 0 0
\(145\) −6.69213 −0.555751
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 13.2827i − 1.08816i −0.839032 0.544082i \(-0.816878\pi\)
0.839032 0.544082i \(-0.183122\pi\)
\(150\) 0 0
\(151\) − 4.39230i − 0.357441i −0.983900 0.178720i \(-0.942804\pi\)
0.983900 0.178720i \(-0.0571957\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.89898 0.393496
\(156\) 0 0
\(157\) 6.59059 0.525987 0.262993 0.964798i \(-0.415290\pi\)
0.262993 + 0.964798i \(0.415290\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) − 19.8564i − 1.55527i −0.628714 0.777637i \(-0.716418\pi\)
0.628714 0.777637i \(-0.283582\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.3923 0.804181 0.402090 0.915600i \(-0.368284\pi\)
0.402090 + 0.915600i \(0.368284\pi\)
\(168\) 0 0
\(169\) 26.8564 2.06588
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 20.7321i 1.57623i 0.615529 + 0.788114i \(0.288942\pi\)
−0.615529 + 0.788114i \(0.711058\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.9396 1.41561 0.707805 0.706408i \(-0.249685\pi\)
0.707805 + 0.706408i \(0.249685\pi\)
\(180\) 0 0
\(181\) 7.07107 0.525588 0.262794 0.964852i \(-0.415356\pi\)
0.262794 + 0.964852i \(0.415356\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 9.46410i − 0.695815i
\(186\) 0 0
\(187\) − 3.10583i − 0.227121i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 23.8386 1.72490 0.862449 0.506144i \(-0.168930\pi\)
0.862449 + 0.506144i \(0.168930\pi\)
\(192\) 0 0
\(193\) 4.00000 0.287926 0.143963 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.2827i 0.946355i 0.880967 + 0.473177i \(0.156893\pi\)
−0.880967 + 0.473177i \(0.843107\pi\)
\(198\) 0 0
\(199\) 11.1106i 0.787612i 0.919194 + 0.393806i \(0.128842\pi\)
−0.919194 + 0.393806i \(0.871158\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 11.4641 0.800688
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 28.3923i 1.96394i
\(210\) 0 0
\(211\) 12.0000i 0.826114i 0.910705 + 0.413057i \(0.135539\pi\)
−0.910705 + 0.413057i \(0.864461\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 25.8564 1.76339
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.62158i 0.310881i
\(222\) 0 0
\(223\) 21.8695i 1.46449i 0.681040 + 0.732246i \(0.261528\pi\)
−0.681040 + 0.732246i \(0.738472\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.32051 −0.353135 −0.176567 0.984289i \(-0.556499\pi\)
−0.176567 + 0.984289i \(0.556499\pi\)
\(228\) 0 0
\(229\) 20.4553 1.35173 0.675863 0.737027i \(-0.263771\pi\)
0.675863 + 0.737027i \(0.263771\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.4201i 1.27225i 0.771586 + 0.636125i \(0.219464\pi\)
−0.771586 + 0.636125i \(0.780536\pi\)
\(234\) 0 0
\(235\) 9.46410i 0.617370i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 17.6269 1.14019 0.570095 0.821579i \(-0.306906\pi\)
0.570095 + 0.821579i \(0.306906\pi\)
\(240\) 0 0
\(241\) −23.5612 −1.51771 −0.758854 0.651261i \(-0.774240\pi\)
−0.758854 + 0.651261i \(0.774240\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 42.2487i − 2.68822i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 19.8564 1.25333 0.626663 0.779291i \(-0.284420\pi\)
0.626663 + 0.779291i \(0.284420\pi\)
\(252\) 0 0
\(253\) −38.7846 −2.43837
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.0526i 0.876575i 0.898835 + 0.438287i \(0.144415\pi\)
−0.898835 + 0.438287i \(0.855585\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −16.3142 −1.00598 −0.502989 0.864293i \(-0.667766\pi\)
−0.502989 + 0.864293i \(0.667766\pi\)
\(264\) 0 0
\(265\) −3.86370 −0.237345
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 10.3397i − 0.630425i −0.949021 0.315213i \(-0.897924\pi\)
0.949021 0.315213i \(-0.102076\pi\)
\(270\) 0 0
\(271\) − 6.69213i − 0.406518i −0.979125 0.203259i \(-0.934847\pi\)
0.979125 0.203259i \(-0.0651533\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.4543 0.630418
\(276\) 0 0
\(277\) −18.7846 −1.12866 −0.564329 0.825550i \(-0.690865\pi\)
−0.564329 + 0.825550i \(0.690865\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 29.2180i 1.74300i 0.490395 + 0.871500i \(0.336852\pi\)
−0.490395 + 0.871500i \(0.663148\pi\)
\(282\) 0 0
\(283\) − 0.480473i − 0.0285612i −0.999898 0.0142806i \(-0.995454\pi\)
0.999898 0.0142806i \(-0.00454581\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 16.4641 0.968477
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 20.0526i − 1.17148i −0.810498 0.585741i \(-0.800803\pi\)
0.810498 0.585741i \(-0.199197\pi\)
\(294\) 0 0
\(295\) − 28.3923i − 1.65306i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 57.7128 3.33762
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 22.1469i 1.26813i
\(306\) 0 0
\(307\) − 4.41851i − 0.252177i −0.992019 0.126089i \(-0.959758\pi\)
0.992019 0.126089i \(-0.0402424\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.2487 −1.37502 −0.687509 0.726176i \(-0.741296\pi\)
−0.687509 + 0.726176i \(0.741296\pi\)
\(312\) 0 0
\(313\) −6.31319 −0.356843 −0.178421 0.983954i \(-0.557099\pi\)
−0.178421 + 0.983954i \(0.557099\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.7680i 1.22261i 0.791394 + 0.611307i \(0.209356\pi\)
−0.791394 + 0.611307i \(0.790644\pi\)
\(318\) 0 0
\(319\) − 10.3923i − 0.581857i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.89898 0.272587
\(324\) 0 0
\(325\) −15.5563 −0.862911
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) − 32.7846i − 1.80201i −0.433814 0.901003i \(-0.642832\pi\)
0.433814 0.901003i \(-0.357168\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 35.3205 1.92977
\(336\) 0 0
\(337\) 1.60770 0.0875767 0.0437884 0.999041i \(-0.486057\pi\)
0.0437884 + 0.999041i \(0.486057\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.60770i 0.411980i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.8386 1.27972 0.639860 0.768491i \(-0.278992\pi\)
0.639860 + 0.768491i \(0.278992\pi\)
\(348\) 0 0
\(349\) −6.79367 −0.363657 −0.181828 0.983330i \(-0.558202\pi\)
−0.181828 + 0.983330i \(0.558202\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 26.9808i 1.43604i 0.696022 + 0.718021i \(0.254952\pi\)
−0.696022 + 0.718021i \(0.745048\pi\)
\(354\) 0 0
\(355\) − 11.5911i − 0.615192i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11.4152 −0.602474 −0.301237 0.953549i \(-0.597399\pi\)
−0.301237 + 0.953549i \(0.597399\pi\)
\(360\) 0 0
\(361\) −25.7846 −1.35708
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 22.1469i − 1.15922i
\(366\) 0 0
\(367\) 26.7685i 1.39731i 0.715461 + 0.698653i \(0.246217\pi\)
−0.715461 + 0.698653i \(0.753783\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 30.7846 1.59397 0.796983 0.604001i \(-0.206428\pi\)
0.796983 + 0.604001i \(0.206428\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.4641i 0.796442i
\(378\) 0 0
\(379\) 13.8564i 0.711756i 0.934532 + 0.355878i \(0.115818\pi\)
−0.934532 + 0.355878i \(0.884182\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −17.0718 −0.872328 −0.436164 0.899867i \(-0.643663\pi\)
−0.436164 + 0.899867i \(0.643663\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 15.8338i − 0.802803i −0.915902 0.401402i \(-0.868523\pi\)
0.915902 0.401402i \(-0.131477\pi\)
\(390\) 0 0
\(391\) 6.69213i 0.338436i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −23.3205 −1.17338
\(396\) 0 0
\(397\) −11.4896 −0.576645 −0.288323 0.957533i \(-0.593098\pi\)
−0.288323 + 0.957533i \(0.593098\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.72311i 0.235861i 0.993022 + 0.117931i \(0.0376260\pi\)
−0.993022 + 0.117931i \(0.962374\pi\)
\(402\) 0 0
\(403\) − 11.3205i − 0.563915i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14.6969 0.728500
\(408\) 0 0
\(409\) −9.41902 −0.465741 −0.232870 0.972508i \(-0.574812\pi\)
−0.232870 + 0.972508i \(0.574812\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) − 6.92820i − 0.340092i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.9282 1.21782 0.608911 0.793238i \(-0.291607\pi\)
0.608911 + 0.793238i \(0.291607\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 1.80385i − 0.0874995i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.4249 1.32101 0.660505 0.750822i \(-0.270342\pi\)
0.660505 + 0.750822i \(0.270342\pi\)
\(432\) 0 0
\(433\) 31.7690 1.52672 0.763361 0.645972i \(-0.223548\pi\)
0.763361 + 0.645972i \(0.223548\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 61.1769i − 2.92649i
\(438\) 0 0
\(439\) − 6.21166i − 0.296466i −0.988952 0.148233i \(-0.952641\pi\)
0.988952 0.148233i \(-0.0473586\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 32.3238 1.53575 0.767876 0.640599i \(-0.221314\pi\)
0.767876 + 0.640599i \(0.221314\pi\)
\(444\) 0 0
\(445\) 26.3923 1.25112
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.89949i 0.467186i 0.972334 + 0.233593i \(0.0750483\pi\)
−0.972334 + 0.233593i \(0.924952\pi\)
\(450\) 0 0
\(451\) 17.8028i 0.838300i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.78461 −0.223815 −0.111907 0.993719i \(-0.535696\pi\)
−0.111907 + 0.993719i \(0.535696\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 22.1962i − 1.03378i −0.856052 0.516889i \(-0.827090\pi\)
0.856052 0.516889i \(-0.172910\pi\)
\(462\) 0 0
\(463\) 18.0000i 0.836531i 0.908325 + 0.418265i \(0.137362\pi\)
−0.908325 + 0.418265i \(0.862638\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −24.9282 −1.15354 −0.576770 0.816907i \(-0.695687\pi\)
−0.576770 + 0.816907i \(0.695687\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 40.1528i 1.84623i
\(474\) 0 0
\(475\) 16.4901i 0.756617i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.85641 −0.358968 −0.179484 0.983761i \(-0.557443\pi\)
−0.179484 + 0.983761i \(0.557443\pi\)
\(480\) 0 0
\(481\) −21.8695 −0.997165
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 12.3490i − 0.560739i
\(486\) 0 0
\(487\) − 7.60770i − 0.344738i −0.985032 0.172369i \(-0.944858\pi\)
0.985032 0.172369i \(-0.0551421\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −17.6269 −0.795491 −0.397745 0.917496i \(-0.630207\pi\)
−0.397745 + 0.917496i \(0.630207\pi\)
\(492\) 0 0
\(493\) −1.79315 −0.0807595
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 26.5359i 1.18791i 0.804498 + 0.593955i \(0.202434\pi\)
−0.804498 + 0.593955i \(0.797566\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −33.4641 −1.49209 −0.746045 0.665895i \(-0.768050\pi\)
−0.746045 + 0.665895i \(0.768050\pi\)
\(504\) 0 0
\(505\) 49.7128 2.21219
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 23.8038i 1.05509i 0.849528 + 0.527543i \(0.176887\pi\)
−0.849528 + 0.527543i \(0.823113\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.48528 0.373906
\(516\) 0 0
\(517\) −14.6969 −0.646371
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 14.5885i − 0.639132i −0.947564 0.319566i \(-0.896463\pi\)
0.947564 0.319566i \(-0.103537\pi\)
\(522\) 0 0
\(523\) 30.3548i 1.32732i 0.748033 + 0.663662i \(0.230999\pi\)
−0.748033 + 0.663662i \(0.769001\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.31268 0.0571811
\(528\) 0 0
\(529\) 60.5692 2.63344
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 26.4911i − 1.14746i
\(534\) 0 0
\(535\) 28.5617i 1.23483i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −14.0000 −0.601907 −0.300954 0.953639i \(-0.597305\pi\)
−0.300954 + 0.953639i \(0.597305\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 54.2487i 2.32376i
\(546\) 0 0
\(547\) − 5.32051i − 0.227488i −0.993510 0.113744i \(-0.963716\pi\)
0.993510 0.113744i \(-0.0362844\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 16.3923 0.698336
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.07107i 0.299611i 0.988716 + 0.149805i \(0.0478647\pi\)
−0.988716 + 0.149805i \(0.952135\pi\)
\(558\) 0 0
\(559\) − 59.7487i − 2.52710i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −41.3205 −1.74145 −0.870726 0.491769i \(-0.836351\pi\)
−0.870726 + 0.491769i \(0.836351\pi\)
\(564\) 0 0
\(565\) 36.2891 1.52669
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 18.4591i − 0.773846i −0.922112 0.386923i \(-0.873538\pi\)
0.922112 0.386923i \(-0.126462\pi\)
\(570\) 0 0
\(571\) − 17.3205i − 0.724841i −0.932015 0.362420i \(-0.881950\pi\)
0.932015 0.362420i \(-0.118050\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −22.5259 −0.939394
\(576\) 0 0
\(577\) 17.4238 0.725364 0.362682 0.931913i \(-0.381861\pi\)
0.362682 + 0.931913i \(0.381861\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) − 6.00000i − 0.248495i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.5359 −0.847607 −0.423804 0.905754i \(-0.639305\pi\)
−0.423804 + 0.905754i \(0.639305\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 37.1244i − 1.52451i −0.647274 0.762257i \(-0.724091\pi\)
0.647274 0.762257i \(-0.275909\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 31.0112 1.26708 0.633541 0.773709i \(-0.281601\pi\)
0.633541 + 0.773709i \(0.281601\pi\)
\(600\) 0 0
\(601\) −6.31319 −0.257521 −0.128760 0.991676i \(-0.541100\pi\)
−0.128760 + 0.991676i \(0.541100\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 19.1244i 0.777516i
\(606\) 0 0
\(607\) − 16.9706i − 0.688814i −0.938820 0.344407i \(-0.888080\pi\)
0.938820 0.344407i \(-0.111920\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 21.8695 0.884747
\(612\) 0 0
\(613\) −19.6077 −0.791947 −0.395974 0.918262i \(-0.629593\pi\)
−0.395974 + 0.918262i \(0.629593\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 31.4916i 1.26781i 0.773413 + 0.633903i \(0.218548\pi\)
−0.773413 + 0.633903i \(0.781452\pi\)
\(618\) 0 0
\(619\) − 35.2538i − 1.41697i −0.705726 0.708485i \(-0.749379\pi\)
0.705726 0.708485i \(-0.250621\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −31.2487 −1.24995
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 2.53590i − 0.101113i
\(630\) 0 0
\(631\) 7.85641i 0.312759i 0.987697 + 0.156379i \(0.0499822\pi\)
−0.987697 + 0.156379i \(0.950018\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −16.3923 −0.650509
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 43.9149i − 1.73454i −0.497841 0.867268i \(-0.665874\pi\)
0.497841 0.867268i \(-0.334126\pi\)
\(642\) 0 0
\(643\) 3.10583i 0.122482i 0.998123 + 0.0612410i \(0.0195058\pi\)
−0.998123 + 0.0612410i \(0.980494\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.4641 0.607957 0.303978 0.952679i \(-0.401685\pi\)
0.303978 + 0.952679i \(0.401685\pi\)
\(648\) 0 0
\(649\) 44.0908 1.73072
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 22.0454i 0.862703i 0.902184 + 0.431352i \(0.141963\pi\)
−0.902184 + 0.431352i \(0.858037\pi\)
\(654\) 0 0
\(655\) − 13.8564i − 0.541415i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.7995 0.966052 0.483026 0.875606i \(-0.339538\pi\)
0.483026 + 0.875606i \(0.339538\pi\)
\(660\) 0 0
\(661\) −11.6926 −0.454791 −0.227396 0.973802i \(-0.573021\pi\)
−0.227396 + 0.973802i \(0.573021\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 22.3923i 0.867034i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −34.3923 −1.32770
\(672\) 0 0
\(673\) −7.85641 −0.302842 −0.151421 0.988469i \(-0.548385\pi\)
−0.151421 + 0.988469i \(0.548385\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.80385i 0.0693275i 0.999399 + 0.0346637i \(0.0110360\pi\)
−0.999399 + 0.0346637i \(0.988964\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −22.5259 −0.861929 −0.430964 0.902369i \(-0.641827\pi\)
−0.430964 + 0.902369i \(0.641827\pi\)
\(684\) 0 0
\(685\) −16.4901 −0.630054
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.92820i 0.340137i
\(690\) 0 0
\(691\) − 31.6675i − 1.20469i −0.798236 0.602344i \(-0.794233\pi\)
0.798236 0.602344i \(-0.205767\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 36.5665 1.38705
\(696\) 0 0
\(697\) 3.07180 0.116353
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 29.2180i − 1.10355i −0.833993 0.551775i \(-0.813951\pi\)
0.833993 0.551775i \(-0.186049\pi\)
\(702\) 0 0
\(703\) 23.1822i 0.874334i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −11.0718 −0.415810 −0.207905 0.978149i \(-0.566664\pi\)
−0.207905 + 0.978149i \(0.566664\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 16.3923i − 0.613897i
\(714\) 0 0
\(715\) − 73.1769i − 2.73666i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.92820 0.258378 0.129189 0.991620i \(-0.458763\pi\)
0.129189 + 0.991620i \(0.458763\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 6.03579i − 0.224164i
\(726\) 0 0
\(727\) − 44.2196i − 1.64001i −0.572354 0.820006i \(-0.693970\pi\)
0.572354 0.820006i \(-0.306030\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.92820 0.256249
\(732\) 0 0
\(733\) 24.0416 0.887998 0.443999 0.896027i \(-0.353559\pi\)
0.443999 + 0.896027i \(0.353559\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 54.8497i 2.02042i
\(738\) 0 0
\(739\) 33.7128i 1.24015i 0.784544 + 0.620073i \(0.212897\pi\)
−0.784544 + 0.620073i \(0.787103\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −22.5259 −0.826394 −0.413197 0.910642i \(-0.635588\pi\)
−0.413197 + 0.910642i \(0.635588\pi\)
\(744\) 0 0
\(745\) 36.2891 1.32953
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 6.92820i 0.252814i 0.991978 + 0.126407i \(0.0403445\pi\)
−0.991978 + 0.126407i \(0.959656\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) 2.78461 0.101208 0.0506042 0.998719i \(-0.483885\pi\)
0.0506042 + 0.998719i \(0.483885\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 50.0526i − 1.81440i −0.420695 0.907202i \(-0.638214\pi\)
0.420695 0.907202i \(-0.361786\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −65.6086 −2.36899
\(768\) 0 0
\(769\) 29.4954 1.06363 0.531816 0.846860i \(-0.321510\pi\)
0.531816 + 0.846860i \(0.321510\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 15.2679i − 0.549150i −0.961566 0.274575i \(-0.911463\pi\)
0.961566 0.274575i \(-0.0885372\pi\)
\(774\) 0 0
\(775\) 4.41851i 0.158717i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −28.0812 −1.00611
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 18.0058i 0.642656i
\(786\) 0 0
\(787\) − 24.4949i − 0.873149i −0.899668 0.436574i \(-0.856192\pi\)
0.899668 0.436574i \(-0.143808\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 51.1769 1.81735
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 32.7321i − 1.15943i −0.814820 0.579714i \(-0.803164\pi\)
0.814820 0.579714i \(-0.196836\pi\)
\(798\) 0 0
\(799\) 2.53590i 0.0897136i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 34.3923 1.21368
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 7.62587i − 0.268111i −0.990974 0.134056i \(-0.957200\pi\)
0.990974 0.134056i \(-0.0428001\pi\)
\(810\) 0 0
\(811\) − 34.2929i − 1.20419i −0.798426 0.602093i \(-0.794334\pi\)
0.798426 0.602093i \(-0.205666\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 54.2487 1.90025
\(816\) 0 0
\(817\) −63.3350 −2.21581
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 3.68784i − 0.128706i −0.997927 0.0643532i \(-0.979502\pi\)
0.997927 0.0643532i \(-0.0204984\pi\)
\(822\) 0 0
\(823\) 8.53590i 0.297543i 0.988872 + 0.148771i \(0.0475318\pi\)
−0.988872 + 0.148771i \(0.952468\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 15.3533 0.533886 0.266943 0.963712i \(-0.413986\pi\)
0.266943 + 0.963712i \(0.413986\pi\)
\(828\) 0 0
\(829\) −36.4649 −1.26648 −0.633240 0.773956i \(-0.718275\pi\)
−0.633240 + 0.773956i \(0.718275\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 28.3923i 0.982556i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 35.0718 1.21081 0.605406 0.795916i \(-0.293011\pi\)
0.605406 + 0.795916i \(0.293011\pi\)
\(840\) 0 0
\(841\) 23.0000 0.793103
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 73.3731i 2.52411i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −31.6675 −1.08555
\(852\) 0 0
\(853\) 7.90327 0.270603 0.135301 0.990804i \(-0.456800\pi\)
0.135301 + 0.990804i \(0.456800\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 9.94744i 0.339798i 0.985461 + 0.169899i \(0.0543442\pi\)
−0.985461 + 0.169899i \(0.945656\pi\)
\(858\) 0 0
\(859\) − 34.7733i − 1.18645i −0.805036 0.593225i \(-0.797854\pi\)
0.805036 0.593225i \(-0.202146\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10.1026 0.343895 0.171948 0.985106i \(-0.444994\pi\)
0.171948 + 0.985106i \(0.444994\pi\)
\(864\) 0 0
\(865\) −56.6410 −1.92585
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 36.2147i − 1.22850i
\(870\) 0 0
\(871\) − 81.6182i − 2.76553i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −44.1051 −1.48932 −0.744662 0.667442i \(-0.767389\pi\)
−0.744662 + 0.667442i \(0.767389\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 35.7654i − 1.20497i −0.798132 0.602483i \(-0.794178\pi\)
0.798132 0.602483i \(-0.205822\pi\)
\(882\) 0 0
\(883\) 25.1769i 0.847271i 0.905833 + 0.423635i \(0.139246\pi\)
−0.905833 + 0.423635i \(0.860754\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −19.1769 −0.643898 −0.321949 0.946757i \(-0.604338\pi\)
−0.321949 + 0.946757i \(0.604338\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 23.1822i − 0.775763i
\(894\) 0 0
\(895\) 51.7439i 1.72961i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 4.39230 0.146492
\(900\) 0 0
\(901\) −1.03528 −0.0344901
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19.3185i 0.642169i
\(906\) 0 0
\(907\) − 35.3205i − 1.17280i −0.810022 0.586399i \(-0.800545\pi\)
0.810022 0.586399i \(-0.199455\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9.14162 0.302875 0.151438 0.988467i \(-0.451610\pi\)
0.151438 + 0.988467i \(0.451610\pi\)
\(912\) 0 0
\(913\) 10.7589 0.356068
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 49.1769i 1.62220i 0.584910 + 0.811098i \(0.301130\pi\)
−0.584910 + 0.811098i \(0.698870\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −26.7846 −0.881626
\(924\) 0 0
\(925\) 8.53590 0.280659
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 10.4449i 0.342685i 0.985212 + 0.171342i \(0.0548104\pi\)
−0.985212 + 0.171342i \(0.945190\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 8.48528 0.277498
\(936\) 0 0
\(937\) 52.1228 1.70278 0.851389 0.524534i \(-0.175761\pi\)
0.851389 + 0.524534i \(0.175761\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 43.9090i 1.43139i 0.698412 + 0.715696i \(0.253890\pi\)
−0.698412 + 0.715696i \(0.746110\pi\)
\(942\) 0 0
\(943\) − 38.3596i − 1.24916i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.24264 0.137867 0.0689336 0.997621i \(-0.478040\pi\)
0.0689336 + 0.997621i \(0.478040\pi\)
\(948\) 0 0
\(949\) −51.1769 −1.66127
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.34469i 0.302704i 0.988480 + 0.151352i \(0.0483627\pi\)
−0.988480 + 0.151352i \(0.951637\pi\)
\(954\) 0 0
\(955\) 65.1282i 2.10750i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 27.7846 0.896278
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10.9282i 0.351791i
\(966\) 0 0
\(967\) − 24.9282i − 0.801637i −0.916157 0.400818i \(-0.868726\pi\)
0.916157 0.400818i \(-0.131274\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −47.3205 −1.51859 −0.759294 0.650748i \(-0.774455\pi\)
−0.759294 + 0.650748i \(0.774455\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 3.41044i − 0.109110i −0.998511 0.0545548i \(-0.982626\pi\)
0.998511 0.0545548i \(-0.0173739\pi\)
\(978\) 0 0
\(979\) 40.9850i 1.30989i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −0.679492 −0.0216724 −0.0108362 0.999941i \(-0.503449\pi\)
−0.0108362 + 0.999941i \(0.503449\pi\)
\(984\) 0 0
\(985\) −36.2891 −1.15627
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 86.5172i − 2.75109i
\(990\) 0 0
\(991\) 32.1051i 1.01985i 0.860218 + 0.509926i \(0.170327\pi\)
−0.860218 + 0.509926i \(0.829673\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −30.3548 −0.962313
\(996\) 0 0
\(997\) 23.5612 0.746189 0.373095 0.927793i \(-0.378297\pi\)
0.373095 + 0.927793i \(0.378297\pi\)
\(998\) 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 7056.2.h.l.4607.7 yes 8
3.2 odd 2 7056.2.h.m.4607.2 yes 8
4.3 odd 2 7056.2.h.m.4607.8 yes 8
7.6 odd 2 7056.2.h.m.4607.1 yes 8
12.11 even 2 inner 7056.2.h.l.4607.1 8
21.20 even 2 inner 7056.2.h.l.4607.8 yes 8
28.27 even 2 inner 7056.2.h.l.4607.2 yes 8
84.83 odd 2 7056.2.h.m.4607.7 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7056.2.h.l.4607.1 8 12.11 even 2 inner
7056.2.h.l.4607.2 yes 8 28.27 even 2 inner
7056.2.h.l.4607.7 yes 8 1.1 even 1 trivial
7056.2.h.l.4607.8 yes 8 21.20 even 2 inner
7056.2.h.m.4607.1 yes 8 7.6 odd 2
7056.2.h.m.4607.2 yes 8 3.2 odd 2
7056.2.h.m.4607.7 yes 8 84.83 odd 2
7056.2.h.m.4607.8 yes 8 4.3 odd 2