Properties

Label 7920.2.a.cf.1.1
Level $7920$
Weight $2$
Character 7920.1
Self dual yes
Analytic conductor $63.242$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7920,2,Mod(1,7920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7920, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7920.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(63.2415184009\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3960)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 7920.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} +0.585786 q^{7} -1.00000 q^{11} +1.41421 q^{13} -4.24264 q^{17} +1.17157 q^{19} +2.82843 q^{23} +1.00000 q^{25} -7.65685 q^{29} +4.82843 q^{31} +0.585786 q^{35} -3.65685 q^{37} +3.65685 q^{41} +9.07107 q^{43} -4.48528 q^{47} -6.65685 q^{49} +6.48528 q^{53} -1.00000 q^{55} +8.82843 q^{59} +8.82843 q^{61} +1.41421 q^{65} -8.48528 q^{67} +10.4853 q^{71} +7.07107 q^{73} -0.585786 q^{77} -0.485281 q^{79} +10.2426 q^{83} -4.24264 q^{85} -2.00000 q^{89} +0.828427 q^{91} +1.17157 q^{95} +8.82843 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} + 4 q^{7} - 2 q^{11} + 8 q^{19} + 2 q^{25} - 4 q^{29} + 4 q^{31} + 4 q^{35} + 4 q^{37} - 4 q^{41} + 4 q^{43} + 8 q^{47} - 2 q^{49} - 4 q^{53} - 2 q^{55} + 12 q^{59} + 12 q^{61} + 4 q^{71}+ \cdots + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.585786 0.221406 0.110703 0.993854i \(-0.464690\pi\)
0.110703 + 0.993854i \(0.464690\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 1.41421 0.392232 0.196116 0.980581i \(-0.437167\pi\)
0.196116 + 0.980581i \(0.437167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.24264 −1.02899 −0.514496 0.857493i \(-0.672021\pi\)
−0.514496 + 0.857493i \(0.672021\pi\)
\(18\) 0 0
\(19\) 1.17157 0.268777 0.134389 0.990929i \(-0.457093\pi\)
0.134389 + 0.990929i \(0.457093\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.82843 0.589768 0.294884 0.955533i \(-0.404719\pi\)
0.294884 + 0.955533i \(0.404719\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.65685 −1.42184 −0.710921 0.703272i \(-0.751722\pi\)
−0.710921 + 0.703272i \(0.751722\pi\)
\(30\) 0 0
\(31\) 4.82843 0.867211 0.433606 0.901103i \(-0.357241\pi\)
0.433606 + 0.901103i \(0.357241\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.585786 0.0990160
\(36\) 0 0
\(37\) −3.65685 −0.601183 −0.300592 0.953753i \(-0.597184\pi\)
−0.300592 + 0.953753i \(0.597184\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.65685 0.571105 0.285552 0.958363i \(-0.407823\pi\)
0.285552 + 0.958363i \(0.407823\pi\)
\(42\) 0 0
\(43\) 9.07107 1.38332 0.691662 0.722221i \(-0.256879\pi\)
0.691662 + 0.722221i \(0.256879\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.48528 −0.654246 −0.327123 0.944982i \(-0.606079\pi\)
−0.327123 + 0.944982i \(0.606079\pi\)
\(48\) 0 0
\(49\) −6.65685 −0.950979
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.48528 0.890822 0.445411 0.895326i \(-0.353058\pi\)
0.445411 + 0.895326i \(0.353058\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.82843 1.14936 0.574682 0.818377i \(-0.305126\pi\)
0.574682 + 0.818377i \(0.305126\pi\)
\(60\) 0 0
\(61\) 8.82843 1.13036 0.565182 0.824966i \(-0.308806\pi\)
0.565182 + 0.824966i \(0.308806\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.41421 0.175412
\(66\) 0 0
\(67\) −8.48528 −1.03664 −0.518321 0.855186i \(-0.673443\pi\)
−0.518321 + 0.855186i \(0.673443\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.4853 1.24437 0.622187 0.782869i \(-0.286244\pi\)
0.622187 + 0.782869i \(0.286244\pi\)
\(72\) 0 0
\(73\) 7.07107 0.827606 0.413803 0.910366i \(-0.364200\pi\)
0.413803 + 0.910366i \(0.364200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.585786 −0.0667566
\(78\) 0 0
\(79\) −0.485281 −0.0545984 −0.0272992 0.999627i \(-0.508691\pi\)
−0.0272992 + 0.999627i \(0.508691\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.2426 1.12428 0.562138 0.827043i \(-0.309979\pi\)
0.562138 + 0.827043i \(0.309979\pi\)
\(84\) 0 0
\(85\) −4.24264 −0.460179
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 0.828427 0.0868428
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.17157 0.120201
\(96\) 0 0
\(97\) 8.82843 0.896391 0.448195 0.893936i \(-0.352067\pi\)
0.448195 + 0.893936i \(0.352067\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.4853 −1.83935 −0.919677 0.392675i \(-0.871550\pi\)
−0.919677 + 0.392675i \(0.871550\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.58579 0.443325 0.221662 0.975123i \(-0.428852\pi\)
0.221662 + 0.975123i \(0.428852\pi\)
\(108\) 0 0
\(109\) 9.31371 0.892091 0.446046 0.895010i \(-0.352832\pi\)
0.446046 + 0.895010i \(0.352832\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.65685 −0.720296 −0.360148 0.932895i \(-0.617274\pi\)
−0.360148 + 0.932895i \(0.617274\pi\)
\(114\) 0 0
\(115\) 2.82843 0.263752
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.48528 −0.227825
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 9.55635 0.847989 0.423994 0.905665i \(-0.360628\pi\)
0.423994 + 0.905665i \(0.360628\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.17157 0.102361 0.0511804 0.998689i \(-0.483702\pi\)
0.0511804 + 0.998689i \(0.483702\pi\)
\(132\) 0 0
\(133\) 0.686292 0.0595090
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.31371 0.453981 0.226990 0.973897i \(-0.427111\pi\)
0.226990 + 0.973897i \(0.427111\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.41421 −0.118262
\(144\) 0 0
\(145\) −7.65685 −0.635867
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.48528 0.203602 0.101801 0.994805i \(-0.467539\pi\)
0.101801 + 0.994805i \(0.467539\pi\)
\(150\) 0 0
\(151\) −10.1421 −0.825355 −0.412678 0.910877i \(-0.635406\pi\)
−0.412678 + 0.910877i \(0.635406\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.82843 0.387829
\(156\) 0 0
\(157\) 5.51472 0.440122 0.220061 0.975486i \(-0.429374\pi\)
0.220061 + 0.975486i \(0.429374\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.65685 0.130578
\(162\) 0 0
\(163\) −11.3137 −0.886158 −0.443079 0.896483i \(-0.646114\pi\)
−0.443079 + 0.896483i \(0.646114\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.7279 1.44921 0.724605 0.689164i \(-0.242022\pi\)
0.724605 + 0.689164i \(0.242022\pi\)
\(168\) 0 0
\(169\) −11.0000 −0.846154
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −21.8995 −1.66499 −0.832494 0.554034i \(-0.813088\pi\)
−0.832494 + 0.554034i \(0.813088\pi\)
\(174\) 0 0
\(175\) 0.585786 0.0442813
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 17.6569 1.31974 0.659868 0.751382i \(-0.270612\pi\)
0.659868 + 0.751382i \(0.270612\pi\)
\(180\) 0 0
\(181\) 23.3137 1.73289 0.866447 0.499269i \(-0.166398\pi\)
0.866447 + 0.499269i \(0.166398\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.65685 −0.268857
\(186\) 0 0
\(187\) 4.24264 0.310253
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.31371 −0.239772 −0.119886 0.992788i \(-0.538253\pi\)
−0.119886 + 0.992788i \(0.538253\pi\)
\(192\) 0 0
\(193\) 17.8995 1.28843 0.644217 0.764843i \(-0.277183\pi\)
0.644217 + 0.764843i \(0.277183\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.24264 −0.587264 −0.293632 0.955919i \(-0.594864\pi\)
−0.293632 + 0.955919i \(0.594864\pi\)
\(198\) 0 0
\(199\) 16.9706 1.20301 0.601506 0.798869i \(-0.294568\pi\)
0.601506 + 0.798869i \(0.294568\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.48528 −0.314805
\(204\) 0 0
\(205\) 3.65685 0.255406
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.17157 −0.0810394
\(210\) 0 0
\(211\) 20.4853 1.41026 0.705132 0.709076i \(-0.250888\pi\)
0.705132 + 0.709076i \(0.250888\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.07107 0.618642
\(216\) 0 0
\(217\) 2.82843 0.192006
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) −14.8284 −0.992985 −0.496492 0.868041i \(-0.665379\pi\)
−0.496492 + 0.868041i \(0.665379\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.07107 −0.0710893 −0.0355446 0.999368i \(-0.511317\pi\)
−0.0355446 + 0.999368i \(0.511317\pi\)
\(228\) 0 0
\(229\) −9.31371 −0.615467 −0.307734 0.951473i \(-0.599571\pi\)
−0.307734 + 0.951473i \(0.599571\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.72792 0.571785 0.285893 0.958262i \(-0.407710\pi\)
0.285893 + 0.958262i \(0.407710\pi\)
\(234\) 0 0
\(235\) −4.48528 −0.292587
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.1421 −1.17352 −0.586759 0.809762i \(-0.699596\pi\)
−0.586759 + 0.809762i \(0.699596\pi\)
\(240\) 0 0
\(241\) −12.1421 −0.782144 −0.391072 0.920360i \(-0.627896\pi\)
−0.391072 + 0.920360i \(0.627896\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.65685 −0.425291
\(246\) 0 0
\(247\) 1.65685 0.105423
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.51472 −0.600564 −0.300282 0.953851i \(-0.597081\pi\)
−0.300282 + 0.953851i \(0.597081\pi\)
\(252\) 0 0
\(253\) −2.82843 −0.177822
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.79899 −0.611244 −0.305622 0.952153i \(-0.598864\pi\)
−0.305622 + 0.952153i \(0.598864\pi\)
\(258\) 0 0
\(259\) −2.14214 −0.133106
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.7279 1.15481 0.577407 0.816457i \(-0.304065\pi\)
0.577407 + 0.816457i \(0.304065\pi\)
\(264\) 0 0
\(265\) 6.48528 0.398388
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.65685 −0.101020 −0.0505101 0.998724i \(-0.516085\pi\)
−0.0505101 + 0.998724i \(0.516085\pi\)
\(270\) 0 0
\(271\) 12.4853 0.758427 0.379213 0.925309i \(-0.376195\pi\)
0.379213 + 0.925309i \(0.376195\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 −0.0603023
\(276\) 0 0
\(277\) 14.5858 0.876375 0.438187 0.898884i \(-0.355621\pi\)
0.438187 + 0.898884i \(0.355621\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.68629 −0.398871 −0.199435 0.979911i \(-0.563911\pi\)
−0.199435 + 0.979911i \(0.563911\pi\)
\(282\) 0 0
\(283\) 10.2426 0.608862 0.304431 0.952534i \(-0.401534\pi\)
0.304431 + 0.952534i \(0.401534\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.14214 0.126446
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.41421 0.549984 0.274992 0.961446i \(-0.411325\pi\)
0.274992 + 0.961446i \(0.411325\pi\)
\(294\) 0 0
\(295\) 8.82843 0.514011
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.00000 0.231326
\(300\) 0 0
\(301\) 5.31371 0.306277
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.82843 0.505514
\(306\) 0 0
\(307\) 10.2426 0.584578 0.292289 0.956330i \(-0.405583\pi\)
0.292289 + 0.956330i \(0.405583\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.828427 −0.0469758 −0.0234879 0.999724i \(-0.507477\pi\)
−0.0234879 + 0.999724i \(0.507477\pi\)
\(312\) 0 0
\(313\) 18.0000 1.01742 0.508710 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.0000 −1.46031 −0.730153 0.683284i \(-0.760551\pi\)
−0.730153 + 0.683284i \(0.760551\pi\)
\(318\) 0 0
\(319\) 7.65685 0.428702
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.97056 −0.276570
\(324\) 0 0
\(325\) 1.41421 0.0784465
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.62742 −0.144854
\(330\) 0 0
\(331\) −14.4853 −0.796183 −0.398092 0.917346i \(-0.630327\pi\)
−0.398092 + 0.917346i \(0.630327\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.48528 −0.463600
\(336\) 0 0
\(337\) 18.8701 1.02792 0.513959 0.857815i \(-0.328178\pi\)
0.513959 + 0.857815i \(0.328178\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.82843 −0.261474
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.2426 −0.979316 −0.489658 0.871915i \(-0.662878\pi\)
−0.489658 + 0.871915i \(0.662878\pi\)
\(348\) 0 0
\(349\) −11.1716 −0.598001 −0.299000 0.954253i \(-0.596653\pi\)
−0.299000 + 0.954253i \(0.596653\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.4853 0.558075 0.279038 0.960280i \(-0.409985\pi\)
0.279038 + 0.960280i \(0.409985\pi\)
\(354\) 0 0
\(355\) 10.4853 0.556501
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.48528 0.447836 0.223918 0.974608i \(-0.428115\pi\)
0.223918 + 0.974608i \(0.428115\pi\)
\(360\) 0 0
\(361\) −17.6274 −0.927759
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.07107 0.370117
\(366\) 0 0
\(367\) 21.1716 1.10515 0.552574 0.833464i \(-0.313646\pi\)
0.552574 + 0.833464i \(0.313646\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.79899 0.197234
\(372\) 0 0
\(373\) 15.7574 0.815885 0.407943 0.913008i \(-0.366246\pi\)
0.407943 + 0.913008i \(0.366246\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.8284 −0.557692
\(378\) 0 0
\(379\) −7.31371 −0.375680 −0.187840 0.982200i \(-0.560149\pi\)
−0.187840 + 0.982200i \(0.560149\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.970563 0.0495934 0.0247967 0.999693i \(-0.492106\pi\)
0.0247967 + 0.999693i \(0.492106\pi\)
\(384\) 0 0
\(385\) −0.585786 −0.0298544
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.31371 0.168012 0.0840058 0.996465i \(-0.473229\pi\)
0.0840058 + 0.996465i \(0.473229\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.485281 −0.0244172
\(396\) 0 0
\(397\) 18.4853 0.927750 0.463875 0.885901i \(-0.346459\pi\)
0.463875 + 0.885901i \(0.346459\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.31371 −0.465104 −0.232552 0.972584i \(-0.574708\pi\)
−0.232552 + 0.972584i \(0.574708\pi\)
\(402\) 0 0
\(403\) 6.82843 0.340148
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.65685 0.181264
\(408\) 0 0
\(409\) 6.97056 0.344672 0.172336 0.985038i \(-0.444868\pi\)
0.172336 + 0.985038i \(0.444868\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.17157 0.254476
\(414\) 0 0
\(415\) 10.2426 0.502791
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −26.6274 −1.30083 −0.650417 0.759577i \(-0.725406\pi\)
−0.650417 + 0.759577i \(0.725406\pi\)
\(420\) 0 0
\(421\) 33.6569 1.64033 0.820167 0.572124i \(-0.193880\pi\)
0.820167 + 0.572124i \(0.193880\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.24264 −0.205798
\(426\) 0 0
\(427\) 5.17157 0.250270
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.97056 −0.432097 −0.216048 0.976383i \(-0.569317\pi\)
−0.216048 + 0.976383i \(0.569317\pi\)
\(432\) 0 0
\(433\) −15.1716 −0.729099 −0.364550 0.931184i \(-0.618777\pi\)
−0.364550 + 0.931184i \(0.618777\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.31371 0.158516
\(438\) 0 0
\(439\) 39.3137 1.87634 0.938170 0.346174i \(-0.112519\pi\)
0.938170 + 0.346174i \(0.112519\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 0 0
\(445\) −2.00000 −0.0948091
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −15.6569 −0.738893 −0.369446 0.929252i \(-0.620453\pi\)
−0.369446 + 0.929252i \(0.620453\pi\)
\(450\) 0 0
\(451\) −3.65685 −0.172195
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.828427 0.0388373
\(456\) 0 0
\(457\) −33.6985 −1.57635 −0.788174 0.615452i \(-0.788973\pi\)
−0.788174 + 0.615452i \(0.788973\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.4558 0.533552 0.266776 0.963759i \(-0.414042\pi\)
0.266776 + 0.963759i \(0.414042\pi\)
\(462\) 0 0
\(463\) −3.51472 −0.163343 −0.0816714 0.996659i \(-0.526026\pi\)
−0.0816714 + 0.996659i \(0.526026\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.82843 0.130884 0.0654420 0.997856i \(-0.479154\pi\)
0.0654420 + 0.997856i \(0.479154\pi\)
\(468\) 0 0
\(469\) −4.97056 −0.229519
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.07107 −0.417088
\(474\) 0 0
\(475\) 1.17157 0.0537555
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 26.1421 1.19446 0.597232 0.802068i \(-0.296267\pi\)
0.597232 + 0.802068i \(0.296267\pi\)
\(480\) 0 0
\(481\) −5.17157 −0.235803
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.82843 0.400878
\(486\) 0 0
\(487\) −27.7990 −1.25969 −0.629846 0.776720i \(-0.716882\pi\)
−0.629846 + 0.776720i \(0.716882\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.02944 −0.317234 −0.158617 0.987340i \(-0.550704\pi\)
−0.158617 + 0.987340i \(0.550704\pi\)
\(492\) 0 0
\(493\) 32.4853 1.46306
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.14214 0.275512
\(498\) 0 0
\(499\) 36.0000 1.61158 0.805791 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.92893 0.130595 0.0652973 0.997866i \(-0.479200\pi\)
0.0652973 + 0.997866i \(0.479200\pi\)
\(504\) 0 0
\(505\) −18.4853 −0.822584
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 35.3137 1.56525 0.782626 0.622492i \(-0.213880\pi\)
0.782626 + 0.622492i \(0.213880\pi\)
\(510\) 0 0
\(511\) 4.14214 0.183237
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 4.48528 0.197262
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −20.6274 −0.903704 −0.451852 0.892093i \(-0.649236\pi\)
−0.451852 + 0.892093i \(0.649236\pi\)
\(522\) 0 0
\(523\) −23.8995 −1.04505 −0.522526 0.852623i \(-0.675010\pi\)
−0.522526 + 0.852623i \(0.675010\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.4853 −0.892353
\(528\) 0 0
\(529\) −15.0000 −0.652174
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.17157 0.224006
\(534\) 0 0
\(535\) 4.58579 0.198261
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.65685 0.286731
\(540\) 0 0
\(541\) 20.3431 0.874620 0.437310 0.899311i \(-0.355931\pi\)
0.437310 + 0.899311i \(0.355931\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.31371 0.398955
\(546\) 0 0
\(547\) 38.7279 1.65589 0.827943 0.560812i \(-0.189511\pi\)
0.827943 + 0.560812i \(0.189511\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8.97056 −0.382159
\(552\) 0 0
\(553\) −0.284271 −0.0120884
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.21320 0.0514051 0.0257025 0.999670i \(-0.491818\pi\)
0.0257025 + 0.999670i \(0.491818\pi\)
\(558\) 0 0
\(559\) 12.8284 0.542585
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.07107 0.382300 0.191150 0.981561i \(-0.438778\pi\)
0.191150 + 0.981561i \(0.438778\pi\)
\(564\) 0 0
\(565\) −7.65685 −0.322126
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −24.1421 −1.01209 −0.506045 0.862507i \(-0.668893\pi\)
−0.506045 + 0.862507i \(0.668893\pi\)
\(570\) 0 0
\(571\) 6.34315 0.265452 0.132726 0.991153i \(-0.457627\pi\)
0.132726 + 0.991153i \(0.457627\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.82843 0.117954
\(576\) 0 0
\(577\) 3.17157 0.132034 0.0660172 0.997818i \(-0.478971\pi\)
0.0660172 + 0.997818i \(0.478971\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.00000 0.248922
\(582\) 0 0
\(583\) −6.48528 −0.268593
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.51472 −0.310166 −0.155083 0.987901i \(-0.549564\pi\)
−0.155083 + 0.987901i \(0.549564\pi\)
\(588\) 0 0
\(589\) 5.65685 0.233087
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 30.5858 1.25601 0.628004 0.778210i \(-0.283872\pi\)
0.628004 + 0.778210i \(0.283872\pi\)
\(594\) 0 0
\(595\) −2.48528 −0.101887
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13.6569 −0.558004 −0.279002 0.960291i \(-0.590004\pi\)
−0.279002 + 0.960291i \(0.590004\pi\)
\(600\) 0 0
\(601\) −8.14214 −0.332125 −0.166062 0.986115i \(-0.553105\pi\)
−0.166062 + 0.986115i \(0.553105\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.00000 0.0406558
\(606\) 0 0
\(607\) −0.384776 −0.0156176 −0.00780879 0.999970i \(-0.502486\pi\)
−0.00780879 + 0.999970i \(0.502486\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.34315 −0.256616
\(612\) 0 0
\(613\) 35.5563 1.43611 0.718054 0.695988i \(-0.245033\pi\)
0.718054 + 0.695988i \(0.245033\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 39.6569 1.59652 0.798262 0.602310i \(-0.205753\pi\)
0.798262 + 0.602310i \(0.205753\pi\)
\(618\) 0 0
\(619\) 35.4558 1.42509 0.712545 0.701626i \(-0.247542\pi\)
0.712545 + 0.701626i \(0.247542\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.17157 −0.0469381
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 15.5147 0.618612
\(630\) 0 0
\(631\) −22.6274 −0.900783 −0.450392 0.892831i \(-0.648716\pi\)
−0.450392 + 0.892831i \(0.648716\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.55635 0.379232
\(636\) 0 0
\(637\) −9.41421 −0.373005
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.68629 −0.106102 −0.0530511 0.998592i \(-0.516895\pi\)
−0.0530511 + 0.998592i \(0.516895\pi\)
\(642\) 0 0
\(643\) −29.6569 −1.16955 −0.584776 0.811195i \(-0.698818\pi\)
−0.584776 + 0.811195i \(0.698818\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −38.6274 −1.51860 −0.759300 0.650740i \(-0.774459\pi\)
−0.759300 + 0.650740i \(0.774459\pi\)
\(648\) 0 0
\(649\) −8.82843 −0.346546
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 33.7990 1.32266 0.661328 0.750097i \(-0.269993\pi\)
0.661328 + 0.750097i \(0.269993\pi\)
\(654\) 0 0
\(655\) 1.17157 0.0457771
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −22.6274 −0.881439 −0.440720 0.897645i \(-0.645277\pi\)
−0.440720 + 0.897645i \(0.645277\pi\)
\(660\) 0 0
\(661\) 28.3431 1.10242 0.551210 0.834366i \(-0.314166\pi\)
0.551210 + 0.834366i \(0.314166\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.686292 0.0266132
\(666\) 0 0
\(667\) −21.6569 −0.838557
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.82843 −0.340818
\(672\) 0 0
\(673\) 6.10051 0.235157 0.117579 0.993064i \(-0.462487\pi\)
0.117579 + 0.993064i \(0.462487\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.10051 0.234461 0.117231 0.993105i \(-0.462598\pi\)
0.117231 + 0.993105i \(0.462598\pi\)
\(678\) 0 0
\(679\) 5.17157 0.198467
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 35.7990 1.36981 0.684905 0.728632i \(-0.259844\pi\)
0.684905 + 0.728632i \(0.259844\pi\)
\(684\) 0 0
\(685\) 5.31371 0.203026
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.17157 0.349409
\(690\) 0 0
\(691\) −17.6569 −0.671698 −0.335849 0.941916i \(-0.609023\pi\)
−0.335849 + 0.941916i \(0.609023\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 16.0000 0.606915
\(696\) 0 0
\(697\) −15.5147 −0.587662
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −26.2843 −0.992743 −0.496372 0.868110i \(-0.665335\pi\)
−0.496372 + 0.868110i \(0.665335\pi\)
\(702\) 0 0
\(703\) −4.28427 −0.161584
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.8284 −0.407245
\(708\) 0 0
\(709\) 35.3137 1.32623 0.663117 0.748516i \(-0.269233\pi\)
0.663117 + 0.748516i \(0.269233\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13.6569 0.511453
\(714\) 0 0
\(715\) −1.41421 −0.0528886
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.65685 0.210965 0.105483 0.994421i \(-0.466361\pi\)
0.105483 + 0.994421i \(0.466361\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.65685 −0.284368
\(726\) 0 0
\(727\) −28.2843 −1.04901 −0.524503 0.851409i \(-0.675749\pi\)
−0.524503 + 0.851409i \(0.675749\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −38.4853 −1.42343
\(732\) 0 0
\(733\) 4.44365 0.164130 0.0820650 0.996627i \(-0.473848\pi\)
0.0820650 + 0.996627i \(0.473848\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.48528 0.312559
\(738\) 0 0
\(739\) 20.2843 0.746169 0.373084 0.927797i \(-0.378300\pi\)
0.373084 + 0.927797i \(0.378300\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −42.5269 −1.56016 −0.780081 0.625679i \(-0.784822\pi\)
−0.780081 + 0.625679i \(0.784822\pi\)
\(744\) 0 0
\(745\) 2.48528 0.0910537
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.68629 0.0981550
\(750\) 0 0
\(751\) −2.34315 −0.0855026 −0.0427513 0.999086i \(-0.513612\pi\)
−0.0427513 + 0.999086i \(0.513612\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10.1421 −0.369110
\(756\) 0 0
\(757\) 5.51472 0.200436 0.100218 0.994966i \(-0.468046\pi\)
0.100218 + 0.994966i \(0.468046\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.828427 −0.0300305 −0.0150152 0.999887i \(-0.504780\pi\)
−0.0150152 + 0.999887i \(0.504780\pi\)
\(762\) 0 0
\(763\) 5.45584 0.197515
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.4853 0.450817
\(768\) 0 0
\(769\) −27.1716 −0.979832 −0.489916 0.871770i \(-0.662973\pi\)
−0.489916 + 0.871770i \(0.662973\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11.8579 0.426498 0.213249 0.976998i \(-0.431595\pi\)
0.213249 + 0.976998i \(0.431595\pi\)
\(774\) 0 0
\(775\) 4.82843 0.173442
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.28427 0.153500
\(780\) 0 0
\(781\) −10.4853 −0.375193
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.51472 0.196829
\(786\) 0 0
\(787\) −23.8995 −0.851925 −0.425962 0.904741i \(-0.640064\pi\)
−0.425962 + 0.904741i \(0.640064\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.48528 −0.159478
\(792\) 0 0
\(793\) 12.4853 0.443365
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16.6274 −0.588973 −0.294487 0.955656i \(-0.595149\pi\)
−0.294487 + 0.955656i \(0.595149\pi\)
\(798\) 0 0
\(799\) 19.0294 0.673213
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7.07107 −0.249533
\(804\) 0 0
\(805\) 1.65685 0.0583964
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −21.0294 −0.739356 −0.369678 0.929160i \(-0.620532\pi\)
−0.369678 + 0.929160i \(0.620532\pi\)
\(810\) 0 0
\(811\) 14.6274 0.513638 0.256819 0.966460i \(-0.417326\pi\)
0.256819 + 0.966460i \(0.417326\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11.3137 −0.396302
\(816\) 0 0
\(817\) 10.6274 0.371806
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −21.3137 −0.743854 −0.371927 0.928262i \(-0.621303\pi\)
−0.371927 + 0.928262i \(0.621303\pi\)
\(822\) 0 0
\(823\) 2.62742 0.0915860 0.0457930 0.998951i \(-0.485419\pi\)
0.0457930 + 0.998951i \(0.485419\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −16.8701 −0.586629 −0.293315 0.956016i \(-0.594758\pi\)
−0.293315 + 0.956016i \(0.594758\pi\)
\(828\) 0 0
\(829\) −38.6274 −1.34159 −0.670793 0.741645i \(-0.734046\pi\)
−0.670793 + 0.741645i \(0.734046\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 28.2426 0.978550
\(834\) 0 0
\(835\) 18.7279 0.648106
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −15.8579 −0.547474 −0.273737 0.961805i \(-0.588260\pi\)
−0.273737 + 0.961805i \(0.588260\pi\)
\(840\) 0 0
\(841\) 29.6274 1.02164
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −11.0000 −0.378412
\(846\) 0 0
\(847\) 0.585786 0.0201279
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −10.3431 −0.354558
\(852\) 0 0
\(853\) 37.4142 1.28104 0.640519 0.767942i \(-0.278719\pi\)
0.640519 + 0.767942i \(0.278719\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 41.8995 1.43126 0.715630 0.698480i \(-0.246140\pi\)
0.715630 + 0.698480i \(0.246140\pi\)
\(858\) 0 0
\(859\) −7.85786 −0.268107 −0.134053 0.990974i \(-0.542799\pi\)
−0.134053 + 0.990974i \(0.542799\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 27.3137 0.929769 0.464885 0.885371i \(-0.346096\pi\)
0.464885 + 0.885371i \(0.346096\pi\)
\(864\) 0 0
\(865\) −21.8995 −0.744605
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.485281 0.0164620
\(870\) 0 0
\(871\) −12.0000 −0.406604
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.585786 0.0198032
\(876\) 0 0
\(877\) −14.3848 −0.485739 −0.242870 0.970059i \(-0.578089\pi\)
−0.242870 + 0.970059i \(0.578089\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.34315 0.0789426 0.0394713 0.999221i \(-0.487433\pi\)
0.0394713 + 0.999221i \(0.487433\pi\)
\(882\) 0 0
\(883\) 16.2843 0.548009 0.274005 0.961728i \(-0.411652\pi\)
0.274005 + 0.961728i \(0.411652\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.10051 −0.137681 −0.0688407 0.997628i \(-0.521930\pi\)
−0.0688407 + 0.997628i \(0.521930\pi\)
\(888\) 0 0
\(889\) 5.59798 0.187750
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.25483 −0.175846
\(894\) 0 0
\(895\) 17.6569 0.590204
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −36.9706 −1.23304
\(900\) 0 0
\(901\) −27.5147 −0.916648
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 23.3137 0.774974
\(906\) 0 0
\(907\) −39.5147 −1.31206 −0.656032 0.754733i \(-0.727767\pi\)
−0.656032 + 0.754733i \(0.727767\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −36.6863 −1.21547 −0.607736 0.794139i \(-0.707922\pi\)
−0.607736 + 0.794139i \(0.707922\pi\)
\(912\) 0 0
\(913\) −10.2426 −0.338982
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.686292 0.0226633
\(918\) 0 0
\(919\) −12.6863 −0.418482 −0.209241 0.977864i \(-0.567099\pi\)
−0.209241 + 0.977864i \(0.567099\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 14.8284 0.488084
\(924\) 0 0
\(925\) −3.65685 −0.120237
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −6.34315 −0.208112 −0.104056 0.994571i \(-0.533182\pi\)
−0.104056 + 0.994571i \(0.533182\pi\)
\(930\) 0 0
\(931\) −7.79899 −0.255602
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.24264 0.138749
\(936\) 0 0
\(937\) 11.0711 0.361676 0.180838 0.983513i \(-0.442119\pi\)
0.180838 + 0.983513i \(0.442119\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 34.4853 1.12419 0.562094 0.827073i \(-0.309996\pi\)
0.562094 + 0.827073i \(0.309996\pi\)
\(942\) 0 0
\(943\) 10.3431 0.336819
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 37.4558 1.21715 0.608576 0.793496i \(-0.291741\pi\)
0.608576 + 0.793496i \(0.291741\pi\)
\(948\) 0 0
\(949\) 10.0000 0.324614
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 21.8995 0.709394 0.354697 0.934981i \(-0.384584\pi\)
0.354697 + 0.934981i \(0.384584\pi\)
\(954\) 0 0
\(955\) −3.31371 −0.107229
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 3.11270 0.100514
\(960\) 0 0
\(961\) −7.68629 −0.247945
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 17.8995 0.576205
\(966\) 0 0
\(967\) 44.8701 1.44292 0.721462 0.692454i \(-0.243471\pi\)
0.721462 + 0.692454i \(0.243471\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −37.9411 −1.21759 −0.608794 0.793328i \(-0.708347\pi\)
−0.608794 + 0.793328i \(0.708347\pi\)
\(972\) 0 0
\(973\) 9.37258 0.300471
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6.28427 0.201052 0.100526 0.994934i \(-0.467947\pi\)
0.100526 + 0.994934i \(0.467947\pi\)
\(978\) 0 0
\(979\) 2.00000 0.0639203
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 56.9706 1.81708 0.908539 0.417799i \(-0.137198\pi\)
0.908539 + 0.417799i \(0.137198\pi\)
\(984\) 0 0
\(985\) −8.24264 −0.262632
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 25.6569 0.815841
\(990\) 0 0
\(991\) 15.4558 0.490971 0.245486 0.969400i \(-0.421053\pi\)
0.245486 + 0.969400i \(0.421053\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 16.9706 0.538003
\(996\) 0 0
\(997\) 0.242641 0.00768451 0.00384225 0.999993i \(-0.498777\pi\)
0.00384225 + 0.999993i \(0.498777\pi\)
\(998\) 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 7920.2.a.cf.1.1 2
3.2 odd 2 7920.2.a.bx.1.1 2
4.3 odd 2 3960.2.a.bb.1.2 yes 2
12.11 even 2 3960.2.a.u.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3960.2.a.u.1.2 2 12.11 even 2
3960.2.a.bb.1.2 yes 2 4.3 odd 2
7920.2.a.bx.1.1 2 3.2 odd 2
7920.2.a.cf.1.1 2 1.1 even 1 trivial