Properties

Label 2340.2.c.d.181.6
Level $2340$
Weight $2$
Character 2340.181
Analytic conductor $18.685$
Analytic rank $0$
Dimension $6$
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] = [2340,2,Mod(181,2340)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2340, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2340.181");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.c (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: \(18.6849940730\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.9144576.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 12x^{4} + 36x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.6
Root \(-2.60168i\) of defining polynomial
Character \(\chi\) \(=\) 2340.181
Dual form 2340.2.c.d.181.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{5} +2.76873i q^{7} +O(q^{10})\) \(q+1.00000i q^{5} +2.76873i q^{7} -2.16706i q^{11} +(-0.167055 - 3.60168i) q^{13} -5.03630i q^{19} +4.93579 q^{23} -1.00000 q^{25} +4.43462 q^{29} +3.37041i q^{31} -2.76873 q^{35} -3.97209i q^{37} -1.66589i q^{41} +9.80504 q^{43} -11.6380i q^{47} -0.665890 q^{49} +12.7408 q^{53} +2.16706 q^{55} +8.16706i q^{59} -10.3062 q^{61} +(3.60168 - 0.167055i) q^{65} +7.10284i q^{67} +16.1112i q^{71} +15.9721i q^{73} +6.00000 q^{77} +11.9442 q^{79} -3.97209i q^{83} +7.94419i q^{89} +(9.97209 - 0.462531i) q^{91} +5.03630 q^{95} -0.462531i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 12 q^{23} - 6 q^{25} + 12 q^{29} + 12 q^{43} - 6 q^{49} + 12 q^{53} + 12 q^{55} - 12 q^{61} + 6 q^{65} + 36 q^{77} - 24 q^{79} + 12 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times\).

\(n\) \(937\) \(1081\) \(1171\) \(2081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 2.76873i 1.04648i 0.852184 + 0.523242i \(0.175277\pi\)
−0.852184 + 0.523242i \(0.824723\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.16706i 0.653392i −0.945130 0.326696i \(-0.894065\pi\)
0.945130 0.326696i \(-0.105935\pi\)
\(12\) 0 0
\(13\) −0.167055 3.60168i −0.0463328 0.998926i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 5.03630i 1.15541i −0.816247 0.577704i \(-0.803949\pi\)
0.816247 0.577704i \(-0.196051\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.93579 1.02918 0.514592 0.857435i \(-0.327944\pi\)
0.514592 + 0.857435i \(0.327944\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.43462 0.823489 0.411744 0.911299i \(-0.364920\pi\)
0.411744 + 0.911299i \(0.364920\pi\)
\(30\) 0 0
\(31\) 3.37041i 0.605344i 0.953095 + 0.302672i \(0.0978787\pi\)
−0.953095 + 0.302672i \(0.902121\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.76873 −0.468002
\(36\) 0 0
\(37\) 3.97209i 0.653008i −0.945196 0.326504i \(-0.894129\pi\)
0.945196 0.326504i \(-0.105871\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.66589i 0.260168i −0.991503 0.130084i \(-0.958475\pi\)
0.991503 0.130084i \(-0.0415247\pi\)
\(42\) 0 0
\(43\) 9.80504 1.49525 0.747627 0.664119i \(-0.231193\pi\)
0.747627 + 0.664119i \(0.231193\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.6380i 1.69757i −0.528735 0.848787i \(-0.677333\pi\)
0.528735 0.848787i \(-0.322667\pi\)
\(48\) 0 0
\(49\) −0.665890 −0.0951271
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 12.7408 1.75009 0.875044 0.484044i \(-0.160833\pi\)
0.875044 + 0.484044i \(0.160833\pi\)
\(54\) 0 0
\(55\) 2.16706 0.292206
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.16706i 1.06326i 0.846977 + 0.531630i \(0.178420\pi\)
−0.846977 + 0.531630i \(0.821580\pi\)
\(60\) 0 0
\(61\) −10.3062 −1.31957 −0.659787 0.751453i \(-0.729354\pi\)
−0.659787 + 0.751453i \(0.729354\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.60168 0.167055i 0.446733 0.0207206i
\(66\) 0 0
\(67\) 7.10284i 0.867751i 0.900973 + 0.433875i \(0.142854\pi\)
−0.900973 + 0.433875i \(0.857146\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 16.1112i 1.91205i 0.293281 + 0.956026i \(0.405253\pi\)
−0.293281 + 0.956026i \(0.594747\pi\)
\(72\) 0 0
\(73\) 15.9721i 1.86939i 0.355448 + 0.934696i \(0.384328\pi\)
−0.355448 + 0.934696i \(0.615672\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 11.9442 1.34383 0.671913 0.740630i \(-0.265473\pi\)
0.671913 + 0.740630i \(0.265473\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.97209i 0.435994i −0.975949 0.217997i \(-0.930048\pi\)
0.975949 0.217997i \(-0.0699523\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.94419i 0.842082i 0.907042 + 0.421041i \(0.138335\pi\)
−0.907042 + 0.421041i \(0.861665\pi\)
\(90\) 0 0
\(91\) 9.97209 0.462531i 1.04536 0.0484865i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.03630 0.516714
\(96\) 0 0
\(97\) 0.462531i 0.0469629i −0.999724 0.0234815i \(-0.992525\pi\)
0.999724 0.0234815i \(-0.00747507\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12.7408 −1.26776 −0.633880 0.773432i \(-0.718539\pi\)
−0.633880 + 0.773432i \(0.718539\pi\)
\(102\) 0 0
\(103\) −4.13915 −0.407842 −0.203921 0.978987i \(-0.565369\pi\)
−0.203921 + 0.978987i \(0.565369\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.06421 −0.682923 −0.341462 0.939896i \(-0.610922\pi\)
−0.341462 + 0.939896i \(0.610922\pi\)
\(108\) 0 0
\(109\) 14.8692i 1.42422i −0.702070 0.712108i \(-0.747741\pi\)
0.702070 0.712108i \(-0.252259\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.13075 −0.294516 −0.147258 0.989098i \(-0.547045\pi\)
−0.147258 + 0.989098i \(0.547045\pi\)
\(114\) 0 0
\(115\) 4.93579i 0.460265i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 6.30387 0.573079
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 16.1391 1.43212 0.716059 0.698040i \(-0.245944\pi\)
0.716059 + 0.698040i \(0.245944\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.86925 0.774910 0.387455 0.921889i \(-0.373354\pi\)
0.387455 + 0.921889i \(0.373354\pi\)
\(132\) 0 0
\(133\) 13.9442 1.20911
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.66589i 0.142327i 0.997465 + 0.0711633i \(0.0226711\pi\)
−0.997465 + 0.0711633i \(0.977329\pi\)
\(138\) 0 0
\(139\) 19.2760 1.63497 0.817483 0.575953i \(-0.195369\pi\)
0.817483 + 0.575953i \(0.195369\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.80504 + 0.362018i −0.652690 + 0.0302734i
\(144\) 0 0
\(145\) 4.43462i 0.368275i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.9442i 1.14235i −0.820828 0.571176i \(-0.806487\pi\)
0.820828 0.571176i \(-0.193513\pi\)
\(150\) 0 0
\(151\) 6.96370i 0.566698i 0.959017 + 0.283349i \(0.0914454\pi\)
−0.959017 + 0.283349i \(0.908555\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.37041 −0.270718
\(156\) 0 0
\(157\) 12.3341 0.984369 0.492185 0.870491i \(-0.336199\pi\)
0.492185 + 0.870491i \(0.336199\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 13.6659i 1.07702i
\(162\) 0 0
\(163\) 20.5072i 1.60625i −0.595810 0.803125i \(-0.703169\pi\)
0.595810 0.803125i \(-0.296831\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.3039i 1.49378i −0.664948 0.746889i \(-0.731547\pi\)
0.664948 0.746889i \(-0.268453\pi\)
\(168\) 0 0
\(169\) −12.9442 + 1.20336i −0.995707 + 0.0925660i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.61007 −0.730640 −0.365320 0.930882i \(-0.619041\pi\)
−0.365320 + 0.930882i \(0.619041\pi\)
\(174\) 0 0
\(175\) 2.76873i 0.209297i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.87158 0.737836 0.368918 0.929462i \(-0.379728\pi\)
0.368918 + 0.929462i \(0.379728\pi\)
\(180\) 0 0
\(181\) −1.97209 −0.146584 −0.0732922 0.997311i \(-0.523351\pi\)
−0.0732922 + 0.997311i \(0.523351\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.97209 0.292034
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.73850 0.415223 0.207611 0.978211i \(-0.433431\pi\)
0.207611 + 0.978211i \(0.433431\pi\)
\(192\) 0 0
\(193\) 4.07261i 0.293153i −0.989199 0.146576i \(-0.953175\pi\)
0.989199 0.146576i \(-0.0468254\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.6101i 1.53965i −0.638253 0.769827i \(-0.720342\pi\)
0.638253 0.769827i \(-0.279658\pi\)
\(198\) 0 0
\(199\) −11.6101 −0.823016 −0.411508 0.911406i \(-0.634998\pi\)
−0.411508 + 0.911406i \(0.634998\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.2783i 0.861767i
\(204\) 0 0
\(205\) 1.66589 0.116351
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −10.9139 −0.754933
\(210\) 0 0
\(211\) 16.2783 1.12064 0.560322 0.828275i \(-0.310677\pi\)
0.560322 + 0.828275i \(0.310677\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.80504i 0.668698i
\(216\) 0 0
\(217\) −9.33178 −0.633482
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 11.4370i 0.765875i −0.923774 0.382938i \(-0.874912\pi\)
0.923774 0.382938i \(-0.125088\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.9721i 1.06011i −0.847965 0.530053i \(-0.822172\pi\)
0.847965 0.530053i \(-0.177828\pi\)
\(228\) 0 0
\(229\) 2.12842i 0.140650i 0.997524 + 0.0703250i \(0.0224036\pi\)
−0.997524 + 0.0703250i \(0.977596\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.86925 0.187971 0.0939853 0.995574i \(-0.470039\pi\)
0.0939853 + 0.995574i \(0.470039\pi\)
\(234\) 0 0
\(235\) 11.6380 0.759178
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3.16939i 0.205011i 0.994732 + 0.102505i \(0.0326859\pi\)
−0.994732 + 0.102505i \(0.967314\pi\)
\(240\) 0 0
\(241\) 4.79664i 0.308979i 0.987994 + 0.154489i \(0.0493733\pi\)
−0.987994 + 0.154489i \(0.950627\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.665890i 0.0425421i
\(246\) 0 0
\(247\) −18.1391 + 0.841340i −1.15417 + 0.0535332i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.00233 −0.0632666 −0.0316333 0.999500i \(-0.510071\pi\)
−0.0316333 + 0.999500i \(0.510071\pi\)
\(252\) 0 0
\(253\) 10.6961i 0.672460i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.4817 1.21523 0.607616 0.794231i \(-0.292126\pi\)
0.607616 + 0.794231i \(0.292126\pi\)
\(258\) 0 0
\(259\) 10.9977 0.683362
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.19496 0.258672 0.129336 0.991601i \(-0.458715\pi\)
0.129336 + 0.991601i \(0.458715\pi\)
\(264\) 0 0
\(265\) 12.7408i 0.782663i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −30.4793 −1.85836 −0.929179 0.369631i \(-0.879484\pi\)
−0.929179 + 0.369631i \(0.879484\pi\)
\(270\) 0 0
\(271\) 4.83528i 0.293722i −0.989157 0.146861i \(-0.953083\pi\)
0.989157 0.146861i \(-0.0469170\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.16706i 0.130678i
\(276\) 0 0
\(277\) 3.00233 0.180393 0.0901963 0.995924i \(-0.471251\pi\)
0.0901963 + 0.995924i \(0.471251\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 21.6101i 1.28915i 0.764542 + 0.644574i \(0.222965\pi\)
−0.764542 + 0.644574i \(0.777035\pi\)
\(282\) 0 0
\(283\) 2.47326 0.147020 0.0735100 0.997294i \(-0.476580\pi\)
0.0735100 + 0.997294i \(0.476580\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.61241 0.272262
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 23.9163i 1.39720i 0.715511 + 0.698602i \(0.246194\pi\)
−0.715511 + 0.698602i \(0.753806\pi\)
\(294\) 0 0
\(295\) −8.16706 −0.475504
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.824549 17.7771i −0.0476849 1.02808i
\(300\) 0 0
\(301\) 27.1475i 1.56476i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 10.3062i 0.590131i
\(306\) 0 0
\(307\) 13.5654i 0.774217i 0.922034 + 0.387108i \(0.126526\pi\)
−0.922034 + 0.387108i \(0.873474\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.12842 0.120692 0.0603458 0.998178i \(-0.480780\pi\)
0.0603458 + 0.998178i \(0.480780\pi\)
\(312\) 0 0
\(313\) −22.6077 −1.27787 −0.638933 0.769263i \(-0.720624\pi\)
−0.638933 + 0.769263i \(0.720624\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.6357i 0.597358i 0.954354 + 0.298679i \(0.0965459\pi\)
−0.954354 + 0.298679i \(0.903454\pi\)
\(318\) 0 0
\(319\) 9.61007i 0.538061i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.167055 + 3.60168i 0.00926655 + 0.199785i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 32.2225 1.77648
\(330\) 0 0
\(331\) 1.16472i 0.0640190i −0.999488 0.0320095i \(-0.989809\pi\)
0.999488 0.0320095i \(-0.0101907\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.10284 −0.388070
\(336\) 0 0
\(337\) −20.0000 −1.08947 −0.544735 0.838608i \(-0.683370\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.30387 0.395527
\(342\) 0 0
\(343\) 17.5375i 0.946934i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.67429 −0.250929 −0.125464 0.992098i \(-0.540042\pi\)
−0.125464 + 0.992098i \(0.540042\pi\)
\(348\) 0 0
\(349\) 4.33411i 0.232000i −0.993249 0.116000i \(-0.962993\pi\)
0.993249 0.116000i \(-0.0370072\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 21.3085i 1.13414i −0.823670 0.567069i \(-0.808077\pi\)
0.823670 0.567069i \(-0.191923\pi\)
\(354\) 0 0
\(355\) −16.1112 −0.855096
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.7795i 0.674474i −0.941420 0.337237i \(-0.890508\pi\)
0.941420 0.337237i \(-0.109492\pi\)
\(360\) 0 0
\(361\) −6.36435 −0.334966
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15.9721 −0.836018
\(366\) 0 0
\(367\) 12.1950 0.636572 0.318286 0.947995i \(-0.396893\pi\)
0.318286 + 0.947995i \(0.396893\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 35.2760i 1.83144i
\(372\) 0 0
\(373\) −28.2225 −1.46130 −0.730652 0.682750i \(-0.760784\pi\)
−0.730652 + 0.682750i \(0.760784\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.740827 15.9721i −0.0381545 0.822605i
\(378\) 0 0
\(379\) 23.3146i 1.19759i 0.800902 + 0.598795i \(0.204354\pi\)
−0.800902 + 0.598795i \(0.795646\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.02791i 0.410207i −0.978740 0.205103i \(-0.934247\pi\)
0.978740 0.205103i \(-0.0657531\pi\)
\(384\) 0 0
\(385\) 6.00000i 0.305788i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −23.7385 −1.20359 −0.601795 0.798651i \(-0.705547\pi\)
−0.601795 + 0.798651i \(0.705547\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.9442i 0.600977i
\(396\) 0 0
\(397\) 3.04703i 0.152926i −0.997072 0.0764630i \(-0.975637\pi\)
0.997072 0.0764630i \(-0.0243627\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 31.2201i 1.55906i 0.626365 + 0.779530i \(0.284542\pi\)
−0.626365 + 0.779530i \(0.715458\pi\)
\(402\) 0 0
\(403\) 12.1391 0.563045i 0.604694 0.0280473i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.60774 −0.426670
\(408\) 0 0
\(409\) 33.4090i 1.65197i −0.563691 0.825986i \(-0.690619\pi\)
0.563691 0.825986i \(-0.309381\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −22.6124 −1.11268
\(414\) 0 0
\(415\) 3.97209 0.194982
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 30.7408 1.50179 0.750894 0.660423i \(-0.229623\pi\)
0.750894 + 0.660423i \(0.229623\pi\)
\(420\) 0 0
\(421\) 19.2806i 0.939680i −0.882752 0.469840i \(-0.844312\pi\)
0.882752 0.469840i \(-0.155688\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 28.5351i 1.38091i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.44535i 0.117788i −0.998264 0.0588942i \(-0.981243\pi\)
0.998264 0.0588942i \(-0.0187575\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 24.8581i 1.18913i
\(438\) 0 0
\(439\) −11.6659 −0.556783 −0.278391 0.960468i \(-0.589801\pi\)
−0.278391 + 0.960468i \(0.589801\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −20.8074 −0.988588 −0.494294 0.869295i \(-0.664573\pi\)
−0.494294 + 0.869295i \(0.664573\pi\)
\(444\) 0 0
\(445\) −7.94419 −0.376590
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 30.2783i 1.42892i −0.699676 0.714461i \(-0.746672\pi\)
0.699676 0.714461i \(-0.253328\pi\)
\(450\) 0 0
\(451\) −3.61007 −0.169992
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.462531 + 9.97209i 0.0216838 + 0.467499i
\(456\) 0 0
\(457\) 22.6124i 1.05776i −0.848695 0.528882i \(-0.822611\pi\)
0.848695 0.528882i \(-0.177389\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.9419i 0.882210i 0.897455 + 0.441105i \(0.145413\pi\)
−0.897455 + 0.441105i \(0.854587\pi\)
\(462\) 0 0
\(463\) 11.6380i 0.540863i 0.962739 + 0.270431i \(0.0871663\pi\)
−0.962739 + 0.270431i \(0.912834\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.0642 1.15983 0.579917 0.814676i \(-0.303085\pi\)
0.579917 + 0.814676i \(0.303085\pi\)
\(468\) 0 0
\(469\) −19.6659 −0.908086
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 21.2481i 0.976987i
\(474\) 0 0
\(475\) 5.03630i 0.231081i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18.4407i 0.842577i 0.906927 + 0.421288i \(0.138422\pi\)
−0.906927 + 0.421288i \(0.861578\pi\)
\(480\) 0 0
\(481\) −14.3062 + 0.663559i −0.652307 + 0.0302557i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.462531 0.0210025
\(486\) 0 0
\(487\) 25.1196i 1.13828i −0.822241 0.569140i \(-0.807276\pi\)
0.822241 0.569140i \(-0.192724\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.73850 0.258975 0.129487 0.991581i \(-0.458667\pi\)
0.129487 + 0.991581i \(0.458667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −44.6077 −2.00093
\(498\) 0 0
\(499\) 33.3704i 1.49386i 0.664900 + 0.746932i \(0.268474\pi\)
−0.664900 + 0.746932i \(0.731526\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12.6789 0.565326 0.282663 0.959219i \(-0.408782\pi\)
0.282663 + 0.959219i \(0.408782\pi\)
\(504\) 0 0
\(505\) 12.7408i 0.566959i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.6147i 0.780759i 0.920654 + 0.390380i \(0.127656\pi\)
−0.920654 + 0.390380i \(0.872344\pi\)
\(510\) 0 0
\(511\) −44.2225 −1.95629
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.13915i 0.182393i
\(516\) 0 0
\(517\) −25.2201 −1.10918
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16.4346 0.720014 0.360007 0.932950i \(-0.382774\pi\)
0.360007 + 0.932950i \(0.382774\pi\)
\(522\) 0 0
\(523\) −20.4733 −0.895233 −0.447617 0.894226i \(-0.647727\pi\)
−0.447617 + 0.894226i \(0.647727\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.36202 0.0592182
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.00000 + 0.278295i −0.259889 + 0.0120543i
\(534\) 0 0
\(535\) 7.06421i 0.305412i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.44302i 0.0621553i
\(540\) 0 0
\(541\) 41.2928i 1.77531i 0.460505 + 0.887657i \(0.347668\pi\)
−0.460505 + 0.887657i \(0.652332\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14.8692 0.636929
\(546\) 0 0
\(547\) −10.4174 −0.445418 −0.222709 0.974885i \(-0.571490\pi\)
−0.222709 + 0.974885i \(0.571490\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 22.3341i 0.951465i
\(552\) 0 0
\(553\) 33.0703i 1.40629i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 20.5845i 0.872193i −0.899900 0.436097i \(-0.856361\pi\)
0.899900 0.436097i \(-0.143639\pi\)
\(558\) 0 0
\(559\) −1.63798 35.3146i −0.0692793 1.49365i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.6766 0.997850 0.498925 0.866645i \(-0.333728\pi\)
0.498925 + 0.866645i \(0.333728\pi\)
\(564\) 0 0
\(565\) 3.13075i 0.131712i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.43695 −0.227929 −0.113965 0.993485i \(-0.536355\pi\)
−0.113965 + 0.993485i \(0.536355\pi\)
\(570\) 0 0
\(571\) 15.2760 0.639279 0.319640 0.947539i \(-0.396438\pi\)
0.319640 + 0.947539i \(0.396438\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.93579 −0.205837
\(576\) 0 0
\(577\) 1.76640i 0.0735363i 0.999324 + 0.0367682i \(0.0117063\pi\)
−0.999324 + 0.0367682i \(0.988294\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10.9977 0.456260
\(582\) 0 0
\(583\) 27.6101i 1.14349i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.9139i 0.945760i −0.881127 0.472880i \(-0.843214\pi\)
0.881127 0.472880i \(-0.156786\pi\)
\(588\) 0 0
\(589\) 16.9744 0.699419
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.72404i 0.276123i 0.990424 + 0.138062i \(0.0440872\pi\)
−0.990424 + 0.138062i \(0.955913\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.8669 0.811740 0.405870 0.913931i \(-0.366969\pi\)
0.405870 + 0.913931i \(0.366969\pi\)
\(600\) 0 0
\(601\) −33.2201 −1.35508 −0.677539 0.735487i \(-0.736954\pi\)
−0.677539 + 0.735487i \(0.736954\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.30387i 0.256289i
\(606\) 0 0
\(607\) 14.4174 0.585186 0.292593 0.956237i \(-0.405482\pi\)
0.292593 + 0.956237i \(0.405482\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −41.9163 + 1.94419i −1.69575 + 0.0786533i
\(612\) 0 0
\(613\) 11.3364i 0.457875i −0.973441 0.228937i \(-0.926475\pi\)
0.973441 0.228937i \(-0.0735251\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.8907i 1.40465i 0.711858 + 0.702323i \(0.247854\pi\)
−0.711858 + 0.702323i \(0.752146\pi\)
\(618\) 0 0
\(619\) 32.6464i 1.31217i 0.754688 + 0.656084i \(0.227788\pi\)
−0.754688 + 0.656084i \(0.772212\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21.9953 −0.881225
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 47.3146i 1.88356i 0.336224 + 0.941782i \(0.390850\pi\)
−0.336224 + 0.941782i \(0.609150\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 16.1391i 0.640463i
\(636\) 0 0
\(637\) 0.111240 + 2.39832i 0.00440750 + 0.0950249i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −43.4817 −1.71742 −0.858711 0.512460i \(-0.828734\pi\)
−0.858711 + 0.512460i \(0.828734\pi\)
\(642\) 0 0
\(643\) 20.3062i 0.800798i −0.916341 0.400399i \(-0.868871\pi\)
0.916341 0.400399i \(-0.131129\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.8027 −1.21098 −0.605490 0.795853i \(-0.707023\pi\)
−0.605490 + 0.795853i \(0.707023\pi\)
\(648\) 0 0
\(649\) 17.6985 0.694725
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.61007 −0.141273 −0.0706366 0.997502i \(-0.522503\pi\)
−0.0706366 + 0.997502i \(0.522503\pi\)
\(654\) 0 0
\(655\) 8.86925i 0.346550i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.74083 0.262585 0.131293 0.991344i \(-0.458087\pi\)
0.131293 + 0.991344i \(0.458087\pi\)
\(660\) 0 0
\(661\) 26.6682i 1.03727i −0.854995 0.518637i \(-0.826440\pi\)
0.854995 0.518637i \(-0.173560\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 13.9442i 0.540732i
\(666\) 0 0
\(667\) 21.8884 0.847521
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 22.3341i 0.862199i
\(672\) 0 0
\(673\) −8.61241 −0.331984 −0.165992 0.986127i \(-0.553083\pi\)
−0.165992 + 0.986127i \(0.553083\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.12842 −0.312401 −0.156200 0.987725i \(-0.549925\pi\)
−0.156200 + 0.987725i \(0.549925\pi\)
\(678\) 0 0
\(679\) 1.28063 0.0491459
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8.02791i 0.307179i 0.988135 + 0.153590i \(0.0490834\pi\)
−0.988135 + 0.153590i \(0.950917\pi\)
\(684\) 0 0
\(685\) −1.66589 −0.0636504
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.12842 45.8884i −0.0810864 1.74821i
\(690\) 0 0
\(691\) 22.1112i 0.841151i 0.907257 + 0.420576i \(0.138172\pi\)
−0.907257 + 0.420576i \(0.861828\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 19.2760i 0.731179i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.47932 0.244721 0.122360 0.992486i \(-0.460954\pi\)
0.122360 + 0.992486i \(0.460954\pi\)
\(702\) 0 0
\(703\) −20.0047 −0.754490
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 35.2760i 1.32669i
\(708\) 0 0
\(709\) 2.85246i 0.107126i 0.998564 + 0.0535631i \(0.0170578\pi\)
−0.998564 + 0.0535631i \(0.982942\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 16.6357i 0.623010i
\(714\) 0 0
\(715\) −0.362018 7.80504i −0.0135387 0.291892i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −42.0941 −1.56984 −0.784922 0.619595i \(-0.787297\pi\)
−0.784922 + 0.619595i \(0.787297\pi\)
\(720\) 0 0
\(721\) 11.4602i 0.426800i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.43462 −0.164698
\(726\) 0 0
\(727\) −32.8027 −1.21659 −0.608293 0.793713i \(-0.708145\pi\)
−0.608293 + 0.793713i \(0.708145\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 2.38993i 0.0882739i 0.999025 + 0.0441370i \(0.0140538\pi\)
−0.999025 + 0.0441370i \(0.985946\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.3923 0.566981
\(738\) 0 0
\(739\) 41.4988i 1.52656i −0.646068 0.763280i \(-0.723588\pi\)
0.646068 0.763280i \(-0.276412\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 39.8046i 1.46029i −0.683292 0.730145i \(-0.739452\pi\)
0.683292 0.730145i \(-0.260548\pi\)
\(744\) 0 0
\(745\) 13.9442 0.510875
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 19.5589i 0.714667i
\(750\) 0 0
\(751\) 15.6659 0.571656 0.285828 0.958281i \(-0.407731\pi\)
0.285828 + 0.958281i \(0.407731\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6.96370 −0.253435
\(756\) 0 0
\(757\) 32.2736 1.17301 0.586503 0.809947i \(-0.300504\pi\)
0.586503 + 0.809947i \(0.300504\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.2806i 0.481422i 0.970597 + 0.240711i \(0.0773807\pi\)
−0.970597 + 0.240711i \(0.922619\pi\)
\(762\) 0 0
\(763\) 41.1690 1.49042
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 29.4151 1.36435i 1.06212 0.0492638i
\(768\) 0 0
\(769\) 12.2010i 0.439980i −0.975502 0.219990i \(-0.929397\pi\)
0.975502 0.219990i \(-0.0706025\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 27.9721i 1.00609i −0.864261 0.503043i \(-0.832214\pi\)
0.864261 0.503043i \(-0.167786\pi\)
\(774\) 0 0
\(775\) 3.37041i 0.121069i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.38993 −0.300600
\(780\) 0 0
\(781\) 34.9139 1.24932
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 12.3341i 0.440223i
\(786\) 0 0
\(787\) 10.2336i 0.364788i 0.983225 + 0.182394i \(0.0583847\pi\)
−0.983225 + 0.182394i \(0.941615\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.66822i 0.308206i
\(792\) 0 0
\(793\) 1.72170 + 37.1196i 0.0611395 + 1.31816i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.3532 0.827214 0.413607 0.910456i \(-0.364269\pi\)
0.413607 + 0.910456i \(0.364269\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 34.6124 1.22145
\(804\) 0 0
\(805\) −13.6659 −0.481659
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −37.1364 −1.30565 −0.652824 0.757510i \(-0.726416\pi\)
−0.652824 + 0.757510i \(0.726416\pi\)
\(810\) 0 0
\(811\) 20.6296i 0.724403i 0.932100 + 0.362201i \(0.117975\pi\)
−0.932100 + 0.362201i \(0.882025\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 20.5072 0.718337
\(816\) 0 0
\(817\) 49.3811i 1.72763i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 20.6077i 0.719215i 0.933104 + 0.359608i \(0.117089\pi\)
−0.933104 + 0.359608i \(0.882911\pi\)
\(822\) 0 0
\(823\) 39.8050 1.38752 0.693758 0.720208i \(-0.255954\pi\)
0.693758 + 0.720208i \(0.255954\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 55.8605i 1.94246i 0.238146 + 0.971229i \(0.423460\pi\)
−0.238146 + 0.971229i \(0.576540\pi\)
\(828\) 0 0
\(829\) −33.5822 −1.16636 −0.583178 0.812344i \(-0.698191\pi\)
−0.583178 + 0.812344i \(0.698191\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 19.3039 0.668038
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26.4454i 0.912995i 0.889725 + 0.456497i \(0.150896\pi\)
−0.889725 + 0.456497i \(0.849104\pi\)
\(840\) 0 0
\(841\) −9.33411 −0.321866
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.20336 12.9442i −0.0413968 0.445294i
\(846\) 0 0
\(847\) 17.4537i 0.599718i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 19.6054i 0.672065i
\(852\) 0 0
\(853\) 35.7153i 1.22287i 0.791296 + 0.611433i \(0.209407\pi\)
−0.791296 + 0.611433i \(0.790593\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −22.0894 −0.754559 −0.377280 0.926099i \(-0.623140\pi\)
−0.377280 + 0.926099i \(0.623140\pi\)
\(858\) 0 0
\(859\) −39.2201 −1.33817 −0.669087 0.743184i \(-0.733315\pi\)
−0.669087 + 0.743184i \(0.733315\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 28.9744i 0.986301i −0.869944 0.493150i \(-0.835845\pi\)
0.869944 0.493150i \(-0.164155\pi\)
\(864\) 0 0
\(865\) 9.61007i 0.326752i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 25.8837i 0.878045i
\(870\) 0 0
\(871\) 25.5822 1.18657i 0.866819 0.0402053i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.76873 0.0936003
\(876\) 0 0
\(877\) 30.9251i 1.04427i −0.852864 0.522133i \(-0.825137\pi\)
0.852864 0.522133i \(-0.174863\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −41.2695 −1.39041 −0.695203 0.718814i \(-0.744685\pi\)
−0.695203 + 0.718814i \(0.744685\pi\)
\(882\) 0 0
\(883\) 15.1973 0.511430 0.255715 0.966752i \(-0.417689\pi\)
0.255715 + 0.966752i \(0.417689\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12.4174 0.416937 0.208468 0.978029i \(-0.433152\pi\)
0.208468 + 0.978029i \(0.433152\pi\)
\(888\) 0 0
\(889\) 44.6850i 1.49869i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −58.6124 −1.96139
\(894\) 0 0
\(895\) 9.87158i 0.329970i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 14.9465i 0.498494i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.97209i 0.0655546i
\(906\) 0 0
\(907\) −11.4709 −0.380886 −0.190443 0.981698i \(-0.560992\pi\)
−0.190443 + 0.981698i \(0.560992\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −54.5734 −1.80810 −0.904048 0.427430i \(-0.859419\pi\)
−0.904048 + 0.427430i \(0.859419\pi\)
\(912\) 0 0
\(913\) −8.60774 −0.284875
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 24.5566i 0.810930i
\(918\) 0 0
\(919\) 9.05815 0.298801 0.149400 0.988777i \(-0.452266\pi\)
0.149400 + 0.988777i \(0.452266\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 58.0275 2.69147i 1.91000 0.0885907i
\(924\) 0 0
\(925\) 3.97209i 0.130602i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 50.2225i 1.64775i −0.566774 0.823873i \(-0.691809\pi\)
0.566774 0.823873i \(-0.308191\pi\)
\(930\) 0 0
\(931\) 3.35362i 0.109911i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5.38759 0.176005 0.0880025 0.996120i \(-0.471952\pi\)
0.0880025 + 0.996120i \(0.471952\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 58.8302i 1.91781i 0.283726 + 0.958905i \(0.408429\pi\)
−0.283726 + 0.958905i \(0.591571\pi\)
\(942\) 0 0
\(943\) 8.22248i 0.267761i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.6403i 0.410755i 0.978683 + 0.205377i \(0.0658422\pi\)
−0.978683 + 0.205377i \(0.934158\pi\)
\(948\) 0 0
\(949\) 57.5264 2.66822i 1.86738 0.0866141i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 32.6077 1.05627 0.528134 0.849161i \(-0.322892\pi\)
0.528134 + 0.849161i \(0.322892\pi\)
\(954\) 0 0
\(955\) 5.73850i 0.185693i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.61241 −0.148942
\(960\) 0 0
\(961\) 19.6403 0.633558
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4.07261 0.131102
\(966\) 0 0
\(967\) 20.5845i 0.661953i −0.943639 0.330976i \(-0.892622\pi\)
0.943639 0.330976i \(-0.107378\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 60.8349 1.95228 0.976142 0.217132i \(-0.0696703\pi\)
0.976142 + 0.217132i \(0.0696703\pi\)
\(972\) 0 0
\(973\) 53.3700i 1.71096i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7.30387i 0.233672i 0.993151 + 0.116836i \(0.0372751\pi\)
−0.993151 + 0.116836i \(0.962725\pi\)
\(978\) 0 0
\(979\) 17.2155 0.550209
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 40.2504i 1.28379i 0.766793 + 0.641894i \(0.221851\pi\)
−0.766793 + 0.641894i \(0.778149\pi\)
\(984\) 0 0
\(985\) 21.6101 0.688554
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 48.3956 1.53889
\(990\) 0 0
\(991\) −50.2271 −1.59552 −0.797759 0.602977i \(-0.793981\pi\)
−0.797759 + 0.602977i \(0.793981\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 11.6101i 0.368064i
\(996\) 0 0
\(997\) 0.273633 0.00866606 0.00433303 0.999991i \(-0.498621\pi\)
0.00433303 + 0.999991i \(0.498621\pi\)
\(998\) 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 2340.2.c.d.181.6 6
3.2 odd 2 260.2.f.a.181.5 6
12.11 even 2 1040.2.k.c.961.1 6
13.12 even 2 inner 2340.2.c.d.181.1 6
15.2 even 4 1300.2.d.c.649.1 6
15.8 even 4 1300.2.d.d.649.6 6
15.14 odd 2 1300.2.f.e.701.1 6
39.5 even 4 3380.2.a.m.1.3 3
39.8 even 4 3380.2.a.n.1.3 3
39.38 odd 2 260.2.f.a.181.6 yes 6
156.155 even 2 1040.2.k.c.961.2 6
195.38 even 4 1300.2.d.c.649.6 6
195.77 even 4 1300.2.d.d.649.1 6
195.194 odd 2 1300.2.f.e.701.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.f.a.181.5 6 3.2 odd 2
260.2.f.a.181.6 yes 6 39.38 odd 2
1040.2.k.c.961.1 6 12.11 even 2
1040.2.k.c.961.2 6 156.155 even 2
1300.2.d.c.649.1 6 15.2 even 4
1300.2.d.c.649.6 6 195.38 even 4
1300.2.d.d.649.1 6 195.77 even 4
1300.2.d.d.649.6 6 15.8 even 4
1300.2.f.e.701.1 6 15.14 odd 2
1300.2.f.e.701.2 6 195.194 odd 2
2340.2.c.d.181.1 6 13.12 even 2 inner
2340.2.c.d.181.6 6 1.1 even 1 trivial
3380.2.a.m.1.3 3 39.5 even 4
3380.2.a.n.1.3 3 39.8 even 4