Properties

Label 4900.2.a.bd.1.1
Level $4900$
Weight $2$
Character 4900.1
Self dual yes
Analytic conductor $39.127$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4900,2,Mod(1,4900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4900.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.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: \(39.1266969904\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 700)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.91223\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.56885 q^{3} +3.59899 q^{9} +O(q^{10})\) \(q-2.56885 q^{3} +3.59899 q^{9} -1.56885 q^{11} +5.56885 q^{13} +7.16784 q^{17} -3.16784 q^{19} -5.73669 q^{23} -1.53871 q^{27} +1.96986 q^{29} -0.969861 q^{31} +4.03014 q^{33} +6.70655 q^{37} -14.3055 q^{39} +8.87439 q^{41} +4.59899 q^{43} +0.401012 q^{47} -18.4131 q^{51} -9.53871 q^{53} +8.13770 q^{57} +4.56885 q^{59} -15.3055 q^{61} -0.862301 q^{67} +14.7367 q^{69} -12.1377 q^{71} +4.00000 q^{73} -12.8744 q^{79} -6.84425 q^{81} +17.1076 q^{83} -5.06028 q^{87} +5.59899 q^{89} +2.49143 q^{93} +0.233174 q^{97} -5.64627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{3} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{3} + 8 q^{9} + 4 q^{11} + 8 q^{13} + 10 q^{17} + 2 q^{19} + 3 q^{23} + 10 q^{27} + 3 q^{31} + 18 q^{33} - 6 q^{37} - 14 q^{39} - 11 q^{41} + 11 q^{43} + 4 q^{47} - 3 q^{51} - 14 q^{53} + 7 q^{57} + 5 q^{59} - 17 q^{61} - 20 q^{67} + 24 q^{69} - 19 q^{71} + 12 q^{73} - q^{79} + 23 q^{81} + 28 q^{83} - 27 q^{87} + 14 q^{89} + 28 q^{93} + 15 q^{97} + 21 q^{99}+O(q^{100}) \) 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
\(3\) −2.56885 −1.48313 −0.741563 0.670883i \(-0.765915\pi\)
−0.741563 + 0.670883i \(0.765915\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.59899 1.19966
\(10\) 0 0
\(11\) −1.56885 −0.473026 −0.236513 0.971628i \(-0.576005\pi\)
−0.236513 + 0.971628i \(0.576005\pi\)
\(12\) 0 0
\(13\) 5.56885 1.54452 0.772260 0.635306i \(-0.219126\pi\)
0.772260 + 0.635306i \(0.219126\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.16784 1.73846 0.869228 0.494411i \(-0.164616\pi\)
0.869228 + 0.494411i \(0.164616\pi\)
\(18\) 0 0
\(19\) −3.16784 −0.726752 −0.363376 0.931643i \(-0.618376\pi\)
−0.363376 + 0.931643i \(0.618376\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.73669 −1.19618 −0.598091 0.801428i \(-0.704074\pi\)
−0.598091 + 0.801428i \(0.704074\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.53871 −0.296125
\(28\) 0 0
\(29\) 1.96986 0.365794 0.182897 0.983132i \(-0.441453\pi\)
0.182897 + 0.983132i \(0.441453\pi\)
\(30\) 0 0
\(31\) −0.969861 −0.174192 −0.0870961 0.996200i \(-0.527759\pi\)
−0.0870961 + 0.996200i \(0.527759\pi\)
\(32\) 0 0
\(33\) 4.03014 0.701557
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.70655 1.10255 0.551275 0.834324i \(-0.314142\pi\)
0.551275 + 0.834324i \(0.314142\pi\)
\(38\) 0 0
\(39\) −14.3055 −2.29072
\(40\) 0 0
\(41\) 8.87439 1.38595 0.692973 0.720963i \(-0.256300\pi\)
0.692973 + 0.720963i \(0.256300\pi\)
\(42\) 0 0
\(43\) 4.59899 0.701339 0.350670 0.936499i \(-0.385954\pi\)
0.350670 + 0.936499i \(0.385954\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.401012 0.0584936 0.0292468 0.999572i \(-0.490689\pi\)
0.0292468 + 0.999572i \(0.490689\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −18.4131 −2.57835
\(52\) 0 0
\(53\) −9.53871 −1.31024 −0.655121 0.755524i \(-0.727383\pi\)
−0.655121 + 0.755524i \(0.727383\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.13770 1.07786
\(58\) 0 0
\(59\) 4.56885 0.594814 0.297407 0.954751i \(-0.403878\pi\)
0.297407 + 0.954751i \(0.403878\pi\)
\(60\) 0 0
\(61\) −15.3055 −1.95967 −0.979837 0.199800i \(-0.935971\pi\)
−0.979837 + 0.199800i \(0.935971\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −0.862301 −0.105347 −0.0526734 0.998612i \(-0.516774\pi\)
−0.0526734 + 0.998612i \(0.516774\pi\)
\(68\) 0 0
\(69\) 14.7367 1.77409
\(70\) 0 0
\(71\) −12.1377 −1.44048 −0.720240 0.693725i \(-0.755968\pi\)
−0.720240 + 0.693725i \(0.755968\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −12.8744 −1.44848 −0.724241 0.689547i \(-0.757810\pi\)
−0.724241 + 0.689547i \(0.757810\pi\)
\(80\) 0 0
\(81\) −6.84425 −0.760472
\(82\) 0 0
\(83\) 17.1076 1.87780 0.938899 0.344192i \(-0.111847\pi\)
0.938899 + 0.344192i \(0.111847\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.06028 −0.542519
\(88\) 0 0
\(89\) 5.59899 0.593492 0.296746 0.954957i \(-0.404099\pi\)
0.296746 + 0.954957i \(0.404099\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.49143 0.258349
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.233174 0.0236752 0.0118376 0.999930i \(-0.496232\pi\)
0.0118376 + 0.999930i \(0.496232\pi\)
\(98\) 0 0
\(99\) −5.64627 −0.567472
\(100\) 0 0
\(101\) −12.5035 −1.24415 −0.622073 0.782959i \(-0.713709\pi\)
−0.622073 + 0.782959i \(0.713709\pi\)
\(102\) 0 0
\(103\) 3.37087 0.332142 0.166071 0.986114i \(-0.446892\pi\)
0.166071 + 0.986114i \(0.446892\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.7367 1.71467 0.857335 0.514759i \(-0.172118\pi\)
0.857335 + 0.514759i \(0.172118\pi\)
\(108\) 0 0
\(109\) 5.90453 0.565551 0.282775 0.959186i \(-0.408745\pi\)
0.282775 + 0.959186i \(0.408745\pi\)
\(110\) 0 0
\(111\) −17.2281 −1.63522
\(112\) 0 0
\(113\) −15.6412 −1.47140 −0.735701 0.677307i \(-0.763147\pi\)
−0.735701 + 0.677307i \(0.763147\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 20.0422 1.85290
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.53871 −0.776246
\(122\) 0 0
\(123\) −22.7970 −2.05553
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −12.8744 −1.14242 −0.571209 0.820805i \(-0.693525\pi\)
−0.571209 + 0.820805i \(0.693525\pi\)
\(128\) 0 0
\(129\) −11.8141 −1.04017
\(130\) 0 0
\(131\) 0.228115 0.0199305 0.00996526 0.999950i \(-0.496828\pi\)
0.00996526 + 0.999950i \(0.496828\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.67641 0.826712 0.413356 0.910570i \(-0.364357\pi\)
0.413356 + 0.910570i \(0.364357\pi\)
\(138\) 0 0
\(139\) 12.3709 1.04928 0.524642 0.851323i \(-0.324199\pi\)
0.524642 + 0.851323i \(0.324199\pi\)
\(140\) 0 0
\(141\) −1.03014 −0.0867533
\(142\) 0 0
\(143\) −8.73669 −0.730599
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.9096 0.975671 0.487836 0.872936i \(-0.337787\pi\)
0.487836 + 0.872936i \(0.337787\pi\)
\(150\) 0 0
\(151\) 9.96986 0.811336 0.405668 0.914021i \(-0.367039\pi\)
0.405668 + 0.914021i \(0.367039\pi\)
\(152\) 0 0
\(153\) 25.7970 2.08556
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.0422 −0.961074 −0.480537 0.876974i \(-0.659558\pi\)
−0.480537 + 0.876974i \(0.659558\pi\)
\(158\) 0 0
\(159\) 24.5035 1.94326
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 16.7367 1.31092 0.655459 0.755231i \(-0.272475\pi\)
0.655459 + 0.755231i \(0.272475\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.76683 −0.523633 −0.261816 0.965118i \(-0.584321\pi\)
−0.261816 + 0.965118i \(0.584321\pi\)
\(168\) 0 0
\(169\) 18.0121 1.38555
\(170\) 0 0
\(171\) −11.4010 −0.871857
\(172\) 0 0
\(173\) 4.69446 0.356913 0.178457 0.983948i \(-0.442890\pi\)
0.178457 + 0.983948i \(0.442890\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −11.7367 −0.882183
\(178\) 0 0
\(179\) 11.4734 0.857560 0.428780 0.903409i \(-0.358943\pi\)
0.428780 + 0.903409i \(0.358943\pi\)
\(180\) 0 0
\(181\) −0.832162 −0.0618541 −0.0309271 0.999522i \(-0.509846\pi\)
−0.0309271 + 0.999522i \(0.509846\pi\)
\(182\) 0 0
\(183\) 39.3176 2.90644
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −11.2453 −0.822335
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.93972 0.502141 0.251070 0.967969i \(-0.419217\pi\)
0.251070 + 0.967969i \(0.419217\pi\)
\(192\) 0 0
\(193\) −19.6764 −1.41634 −0.708169 0.706042i \(-0.750479\pi\)
−0.708169 + 0.706042i \(0.750479\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.0422 1.14296 0.571481 0.820616i \(-0.306369\pi\)
0.571481 + 0.820616i \(0.306369\pi\)
\(198\) 0 0
\(199\) 10.6764 0.756831 0.378415 0.925636i \(-0.376469\pi\)
0.378415 + 0.925636i \(0.376469\pi\)
\(200\) 0 0
\(201\) 2.21512 0.156243
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −20.6463 −1.43502
\(208\) 0 0
\(209\) 4.96986 0.343772
\(210\) 0 0
\(211\) 11.3658 0.782455 0.391227 0.920294i \(-0.372051\pi\)
0.391227 + 0.920294i \(0.372051\pi\)
\(212\) 0 0
\(213\) 31.1799 2.13641
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −10.2754 −0.694347
\(220\) 0 0
\(221\) 39.9166 2.68508
\(222\) 0 0
\(223\) −6.04222 −0.404617 −0.202309 0.979322i \(-0.564844\pi\)
−0.202309 + 0.979322i \(0.564844\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 21.6412 1.43638 0.718189 0.695848i \(-0.244971\pi\)
0.718189 + 0.695848i \(0.244971\pi\)
\(228\) 0 0
\(229\) 5.43115 0.358901 0.179450 0.983767i \(-0.442568\pi\)
0.179450 + 0.983767i \(0.442568\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.93972 0.454636 0.227318 0.973821i \(-0.427004\pi\)
0.227318 + 0.973821i \(0.427004\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 33.0724 2.14828
\(238\) 0 0
\(239\) 1.69446 0.109606 0.0548028 0.998497i \(-0.482547\pi\)
0.0548028 + 0.998497i \(0.482547\pi\)
\(240\) 0 0
\(241\) 14.9347 0.962026 0.481013 0.876713i \(-0.340269\pi\)
0.481013 + 0.876713i \(0.340269\pi\)
\(242\) 0 0
\(243\) 22.1980 1.42400
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −17.6412 −1.12248
\(248\) 0 0
\(249\) −43.9468 −2.78501
\(250\) 0 0
\(251\) −8.90958 −0.562368 −0.281184 0.959654i \(-0.590727\pi\)
−0.281184 + 0.959654i \(0.590727\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 9.66432 0.602844 0.301422 0.953491i \(-0.402539\pi\)
0.301422 + 0.953491i \(0.402539\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 7.08951 0.438830
\(262\) 0 0
\(263\) 6.10250 0.376296 0.188148 0.982141i \(-0.439751\pi\)
0.188148 + 0.982141i \(0.439751\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −14.3830 −0.880223
\(268\) 0 0
\(269\) −22.5337 −1.37390 −0.686951 0.726704i \(-0.741051\pi\)
−0.686951 + 0.726704i \(0.741051\pi\)
\(270\) 0 0
\(271\) −4.46129 −0.271004 −0.135502 0.990777i \(-0.543265\pi\)
−0.135502 + 0.990777i \(0.543265\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −6.50857 −0.391062 −0.195531 0.980698i \(-0.562643\pi\)
−0.195531 + 0.980698i \(0.562643\pi\)
\(278\) 0 0
\(279\) −3.49052 −0.208972
\(280\) 0 0
\(281\) −11.1980 −0.668015 −0.334008 0.942570i \(-0.608401\pi\)
−0.334008 + 0.942570i \(0.608401\pi\)
\(282\) 0 0
\(283\) −7.64627 −0.454524 −0.227262 0.973834i \(-0.572977\pi\)
−0.227262 + 0.973834i \(0.572977\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 34.3779 2.02223
\(290\) 0 0
\(291\) −0.598988 −0.0351133
\(292\) 0 0
\(293\) 6.12561 0.357862 0.178931 0.983862i \(-0.442736\pi\)
0.178931 + 0.983862i \(0.442736\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.41401 0.140075
\(298\) 0 0
\(299\) −31.9468 −1.84753
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 32.1196 1.84523
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 26.4080 1.50719 0.753593 0.657341i \(-0.228319\pi\)
0.753593 + 0.657341i \(0.228319\pi\)
\(308\) 0 0
\(309\) −8.65927 −0.492608
\(310\) 0 0
\(311\) 19.3528 1.09740 0.548699 0.836020i \(-0.315123\pi\)
0.548699 + 0.836020i \(0.315123\pi\)
\(312\) 0 0
\(313\) 8.70655 0.492123 0.246062 0.969254i \(-0.420863\pi\)
0.246062 + 0.969254i \(0.420863\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −15.2754 −0.857952 −0.428976 0.903316i \(-0.641125\pi\)
−0.428976 + 0.903316i \(0.641125\pi\)
\(318\) 0 0
\(319\) −3.09042 −0.173030
\(320\) 0 0
\(321\) −45.5629 −2.54307
\(322\) 0 0
\(323\) −22.7065 −1.26343
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −15.1678 −0.838783
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 16.7488 0.920596 0.460298 0.887765i \(-0.347743\pi\)
0.460298 + 0.887765i \(0.347743\pi\)
\(332\) 0 0
\(333\) 24.1368 1.32269
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 31.2453 1.70204 0.851019 0.525135i \(-0.175985\pi\)
0.851019 + 0.525135i \(0.175985\pi\)
\(338\) 0 0
\(339\) 40.1799 2.18227
\(340\) 0 0
\(341\) 1.52157 0.0823974
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.1025 −0.649696 −0.324848 0.945766i \(-0.605313\pi\)
−0.324848 + 0.945766i \(0.605313\pi\)
\(348\) 0 0
\(349\) 3.87439 0.207391 0.103696 0.994609i \(-0.466933\pi\)
0.103696 + 0.994609i \(0.466933\pi\)
\(350\) 0 0
\(351\) −8.56885 −0.457371
\(352\) 0 0
\(353\) −2.56379 −0.136457 −0.0682284 0.997670i \(-0.521735\pi\)
−0.0682284 + 0.997670i \(0.521735\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.8392 1.09985 0.549925 0.835214i \(-0.314656\pi\)
0.549925 + 0.835214i \(0.314656\pi\)
\(360\) 0 0
\(361\) −8.96480 −0.471832
\(362\) 0 0
\(363\) 21.9347 1.15127
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −15.8322 −0.826432 −0.413216 0.910633i \(-0.635595\pi\)
−0.413216 + 0.910633i \(0.635595\pi\)
\(368\) 0 0
\(369\) 31.9388 1.66267
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −22.5035 −1.16519 −0.582594 0.812763i \(-0.697962\pi\)
−0.582594 + 0.812763i \(0.697962\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.9699 0.564977
\(378\) 0 0
\(379\) −7.36581 −0.378356 −0.189178 0.981943i \(-0.560582\pi\)
−0.189178 + 0.981943i \(0.560582\pi\)
\(380\) 0 0
\(381\) 33.0724 1.69435
\(382\) 0 0
\(383\) 33.6533 1.71960 0.859802 0.510628i \(-0.170587\pi\)
0.859802 + 0.510628i \(0.170587\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.5517 0.841370
\(388\) 0 0
\(389\) 17.4855 0.886548 0.443274 0.896386i \(-0.353817\pi\)
0.443274 + 0.896386i \(0.353817\pi\)
\(390\) 0 0
\(391\) −41.1196 −2.07951
\(392\) 0 0
\(393\) −0.585994 −0.0295595
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7.59899 −0.381382 −0.190691 0.981650i \(-0.561073\pi\)
−0.190691 + 0.981650i \(0.561073\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.8442 0.541536 0.270768 0.962645i \(-0.412722\pi\)
0.270768 + 0.962645i \(0.412722\pi\)
\(402\) 0 0
\(403\) −5.40101 −0.269044
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.5216 −0.521535
\(408\) 0 0
\(409\) 16.8693 0.834135 0.417067 0.908876i \(-0.363058\pi\)
0.417067 + 0.908876i \(0.363058\pi\)
\(410\) 0 0
\(411\) −24.8572 −1.22612
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −31.7789 −1.55622
\(418\) 0 0
\(419\) 4.03014 0.196885 0.0984426 0.995143i \(-0.468614\pi\)
0.0984426 + 0.995143i \(0.468614\pi\)
\(420\) 0 0
\(421\) 25.1196 1.22426 0.612128 0.790758i \(-0.290314\pi\)
0.612128 + 0.790758i \(0.290314\pi\)
\(422\) 0 0
\(423\) 1.44324 0.0701726
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 22.4432 1.08357
\(430\) 0 0
\(431\) 30.2402 1.45662 0.728310 0.685248i \(-0.240306\pi\)
0.728310 + 0.685248i \(0.240306\pi\)
\(432\) 0 0
\(433\) −22.9769 −1.10420 −0.552099 0.833778i \(-0.686173\pi\)
−0.552099 + 0.833778i \(0.686173\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.1729 0.869328
\(438\) 0 0
\(439\) −11.9518 −0.570429 −0.285214 0.958464i \(-0.592065\pi\)
−0.285214 + 0.958464i \(0.592065\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.1076 0.670270 0.335135 0.942170i \(-0.391218\pi\)
0.335135 + 0.942170i \(0.391218\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −30.5939 −1.44704
\(448\) 0 0
\(449\) 37.9468 1.79082 0.895409 0.445245i \(-0.146883\pi\)
0.895409 + 0.445245i \(0.146883\pi\)
\(450\) 0 0
\(451\) −13.9226 −0.655589
\(452\) 0 0
\(453\) −25.6111 −1.20331
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 18.5457 0.867533 0.433767 0.901025i \(-0.357184\pi\)
0.433767 + 0.901025i \(0.357184\pi\)
\(458\) 0 0
\(459\) −11.0292 −0.514800
\(460\) 0 0
\(461\) 23.2453 1.08264 0.541320 0.840817i \(-0.317925\pi\)
0.541320 + 0.840817i \(0.317925\pi\)
\(462\) 0 0
\(463\) −7.59393 −0.352920 −0.176460 0.984308i \(-0.556465\pi\)
−0.176460 + 0.984308i \(0.556465\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.1678 1.30345 0.651726 0.758454i \(-0.274045\pi\)
0.651726 + 0.758454i \(0.274045\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 30.9347 1.42539
\(472\) 0 0
\(473\) −7.21512 −0.331752
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −34.3297 −1.57185
\(478\) 0 0
\(479\) 34.1799 1.56172 0.780860 0.624706i \(-0.214781\pi\)
0.780860 + 0.624706i \(0.214781\pi\)
\(480\) 0 0
\(481\) 37.3478 1.70291
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 11.5035 0.521274 0.260637 0.965437i \(-0.416067\pi\)
0.260637 + 0.965437i \(0.416067\pi\)
\(488\) 0 0
\(489\) −42.9940 −1.94426
\(490\) 0 0
\(491\) −25.5337 −1.15232 −0.576159 0.817338i \(-0.695449\pi\)
−0.576159 + 0.817338i \(0.695449\pi\)
\(492\) 0 0
\(493\) 14.1196 0.635917
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −11.3960 −0.510153 −0.255076 0.966921i \(-0.582101\pi\)
−0.255076 + 0.966921i \(0.582101\pi\)
\(500\) 0 0
\(501\) 17.3830 0.776613
\(502\) 0 0
\(503\) −2.49649 −0.111313 −0.0556564 0.998450i \(-0.517725\pi\)
−0.0556564 + 0.998450i \(0.517725\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −46.2703 −2.05494
\(508\) 0 0
\(509\) −11.5438 −0.511669 −0.255834 0.966721i \(-0.582350\pi\)
−0.255834 + 0.966721i \(0.582350\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 4.87439 0.215209
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −0.629127 −0.0276690
\(518\) 0 0
\(519\) −12.0594 −0.529348
\(520\) 0 0
\(521\) −23.7488 −1.04045 −0.520226 0.854028i \(-0.674152\pi\)
−0.520226 + 0.854028i \(0.674152\pi\)
\(522\) 0 0
\(523\) 16.1377 0.705652 0.352826 0.935689i \(-0.385221\pi\)
0.352826 + 0.935689i \(0.385221\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.95181 −0.302826
\(528\) 0 0
\(529\) 9.90958 0.430851
\(530\) 0 0
\(531\) 16.4432 0.713576
\(532\) 0 0
\(533\) 49.4201 2.14062
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −29.4734 −1.27187
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.53871 −0.0661543 −0.0330772 0.999453i \(-0.510531\pi\)
−0.0330772 + 0.999453i \(0.510531\pi\)
\(542\) 0 0
\(543\) 2.13770 0.0917375
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14.3779 0.614755 0.307377 0.951588i \(-0.400549\pi\)
0.307377 + 0.951588i \(0.400549\pi\)
\(548\) 0 0
\(549\) −55.0844 −2.35095
\(550\) 0 0
\(551\) −6.24020 −0.265842
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.9347 0.717545 0.358772 0.933425i \(-0.383195\pi\)
0.358772 + 0.933425i \(0.383195\pi\)
\(558\) 0 0
\(559\) 25.6111 1.08323
\(560\) 0 0
\(561\) 28.8874 1.21963
\(562\) 0 0
\(563\) 0.664324 0.0279979 0.0139990 0.999902i \(-0.495544\pi\)
0.0139990 + 0.999902i \(0.495544\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.0372 −1.72037 −0.860184 0.509984i \(-0.829651\pi\)
−0.860184 + 0.509984i \(0.829651\pi\)
\(570\) 0 0
\(571\) −28.6291 −1.19809 −0.599046 0.800715i \(-0.704453\pi\)
−0.599046 + 0.800715i \(0.704453\pi\)
\(572\) 0 0
\(573\) −17.8271 −0.744738
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 31.4604 1.30971 0.654856 0.755753i \(-0.272729\pi\)
0.654856 + 0.755753i \(0.272729\pi\)
\(578\) 0 0
\(579\) 50.5457 2.10061
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 14.9648 0.619779
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.53871 −0.393705 −0.196852 0.980433i \(-0.563072\pi\)
−0.196852 + 0.980433i \(0.563072\pi\)
\(588\) 0 0
\(589\) 3.07236 0.126595
\(590\) 0 0
\(591\) −41.2101 −1.69516
\(592\) 0 0
\(593\) 9.93972 0.408175 0.204088 0.978953i \(-0.434577\pi\)
0.204088 + 0.978953i \(0.434577\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −27.4261 −1.12248
\(598\) 0 0
\(599\) 9.41310 0.384609 0.192304 0.981335i \(-0.438404\pi\)
0.192304 + 0.981335i \(0.438404\pi\)
\(600\) 0 0
\(601\) 3.00506 0.122579 0.0612894 0.998120i \(-0.480479\pi\)
0.0612894 + 0.998120i \(0.480479\pi\)
\(602\) 0 0
\(603\) −3.10341 −0.126381
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −18.8322 −0.764374 −0.382187 0.924085i \(-0.624829\pi\)
−0.382187 + 0.924085i \(0.624829\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.23317 0.0903445
\(612\) 0 0
\(613\) −15.8392 −0.639739 −0.319869 0.947462i \(-0.603639\pi\)
−0.319869 + 0.947462i \(0.603639\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.778912 0.0313578 0.0156789 0.999877i \(-0.495009\pi\)
0.0156789 + 0.999877i \(0.495009\pi\)
\(618\) 0 0
\(619\) −9.94675 −0.399794 −0.199897 0.979817i \(-0.564061\pi\)
−0.199897 + 0.979817i \(0.564061\pi\)
\(620\) 0 0
\(621\) 8.82710 0.354219
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −12.7668 −0.509858
\(628\) 0 0
\(629\) 48.0715 1.91673
\(630\) 0 0
\(631\) −12.5638 −0.500157 −0.250078 0.968226i \(-0.580456\pi\)
−0.250078 + 0.968226i \(0.580456\pi\)
\(632\) 0 0
\(633\) −29.1971 −1.16048
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −43.6834 −1.72809
\(640\) 0 0
\(641\) −11.5207 −0.455039 −0.227519 0.973774i \(-0.573061\pi\)
−0.227519 + 0.973774i \(0.573061\pi\)
\(642\) 0 0
\(643\) −9.74175 −0.384177 −0.192088 0.981378i \(-0.561526\pi\)
−0.192088 + 0.981378i \(0.561526\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.7538 −1.01249 −0.506244 0.862390i \(-0.668966\pi\)
−0.506244 + 0.862390i \(0.668966\pi\)
\(648\) 0 0
\(649\) −7.16784 −0.281362
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 15.1929 0.594545 0.297272 0.954793i \(-0.403923\pi\)
0.297272 + 0.954793i \(0.403923\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.3960 0.561640
\(658\) 0 0
\(659\) −14.6894 −0.572218 −0.286109 0.958197i \(-0.592362\pi\)
−0.286109 + 0.958197i \(0.592362\pi\)
\(660\) 0 0
\(661\) −4.33568 −0.168638 −0.0843191 0.996439i \(-0.526872\pi\)
−0.0843191 + 0.996439i \(0.526872\pi\)
\(662\) 0 0
\(663\) −102.540 −3.98231
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −11.3005 −0.437556
\(668\) 0 0
\(669\) 15.5216 0.600098
\(670\) 0 0
\(671\) 24.0121 0.926976
\(672\) 0 0
\(673\) −34.1971 −1.31820 −0.659100 0.752055i \(-0.729063\pi\)
−0.659100 + 0.752055i \(0.729063\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.0904 0.695271 0.347636 0.937630i \(-0.386985\pi\)
0.347636 + 0.937630i \(0.386985\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −55.5930 −2.13033
\(682\) 0 0
\(683\) 24.1256 0.923141 0.461570 0.887104i \(-0.347286\pi\)
0.461570 + 0.887104i \(0.347286\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −13.9518 −0.532295
\(688\) 0 0
\(689\) −53.1196 −2.02370
\(690\) 0 0
\(691\) −17.4483 −0.663764 −0.331882 0.943321i \(-0.607684\pi\)
−0.331882 + 0.943321i \(0.607684\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 63.6102 2.40941
\(698\) 0 0
\(699\) −17.8271 −0.674283
\(700\) 0 0
\(701\) 20.7015 0.781885 0.390942 0.920415i \(-0.372149\pi\)
0.390942 + 0.920415i \(0.372149\pi\)
\(702\) 0 0
\(703\) −21.2453 −0.801280
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7.09547 0.266476 0.133238 0.991084i \(-0.457463\pi\)
0.133238 + 0.991084i \(0.457463\pi\)
\(710\) 0 0
\(711\) −46.3348 −1.73769
\(712\) 0 0
\(713\) 5.56379 0.208366
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −4.35282 −0.162559
\(718\) 0 0
\(719\) −52.4432 −1.95580 −0.977901 0.209067i \(-0.932957\pi\)
−0.977901 + 0.209067i \(0.932957\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −38.3649 −1.42681
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −29.9045 −1.10910 −0.554549 0.832151i \(-0.687109\pi\)
−0.554549 + 0.832151i \(0.687109\pi\)
\(728\) 0 0
\(729\) −36.4905 −1.35150
\(730\) 0 0
\(731\) 32.9648 1.21925
\(732\) 0 0
\(733\) 5.58094 0.206137 0.103068 0.994674i \(-0.467134\pi\)
0.103068 + 0.994674i \(0.467134\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.35282 0.0498318
\(738\) 0 0
\(739\) 40.7488 1.49897 0.749484 0.662023i \(-0.230302\pi\)
0.749484 + 0.662023i \(0.230302\pi\)
\(740\) 0 0
\(741\) 45.3176 1.66478
\(742\) 0 0
\(743\) −50.5327 −1.85387 −0.926933 0.375226i \(-0.877565\pi\)
−0.926933 + 0.375226i \(0.877565\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 61.5699 2.25273
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −30.7136 −1.12075 −0.560377 0.828238i \(-0.689344\pi\)
−0.560377 + 0.828238i \(0.689344\pi\)
\(752\) 0 0
\(753\) 22.8874 0.834063
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 20.7116 0.752776 0.376388 0.926462i \(-0.377166\pi\)
0.376388 + 0.926462i \(0.377166\pi\)
\(758\) 0 0
\(759\) −23.1196 −0.839190
\(760\) 0 0
\(761\) 34.3528 1.24529 0.622644 0.782505i \(-0.286058\pi\)
0.622644 + 0.782505i \(0.286058\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 25.4432 0.918702
\(768\) 0 0
\(769\) −46.8392 −1.68906 −0.844532 0.535505i \(-0.820121\pi\)
−0.844532 + 0.535505i \(0.820121\pi\)
\(770\) 0 0
\(771\) −24.8262 −0.894094
\(772\) 0 0
\(773\) 33.3306 1.19882 0.599409 0.800443i \(-0.295402\pi\)
0.599409 + 0.800443i \(0.295402\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −28.1126 −1.00724
\(780\) 0 0
\(781\) 19.0422 0.681384
\(782\) 0 0
\(783\) −3.03105 −0.108321
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 8.40804 0.299714 0.149857 0.988708i \(-0.452119\pi\)
0.149857 + 0.988708i \(0.452119\pi\)
\(788\) 0 0
\(789\) −15.6764 −0.558095
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −85.2342 −3.02676
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.2935 0.577144 0.288572 0.957458i \(-0.406820\pi\)
0.288572 + 0.957458i \(0.406820\pi\)
\(798\) 0 0
\(799\) 2.87439 0.101688
\(800\) 0 0
\(801\) 20.1507 0.711990
\(802\) 0 0
\(803\) −6.27540 −0.221454
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 57.8856 2.03767
\(808\) 0 0
\(809\) −15.5035 −0.545075 −0.272537 0.962145i \(-0.587863\pi\)
−0.272537 + 0.962145i \(0.587863\pi\)
\(810\) 0 0
\(811\) 36.6232 1.28601 0.643007 0.765861i \(-0.277687\pi\)
0.643007 + 0.765861i \(0.277687\pi\)
\(812\) 0 0
\(813\) 11.4604 0.401933
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −14.5688 −0.509700
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −43.3297 −1.51222 −0.756109 0.654446i \(-0.772902\pi\)
−0.756109 + 0.654446i \(0.772902\pi\)
\(822\) 0 0
\(823\) −41.0543 −1.43106 −0.715532 0.698580i \(-0.753815\pi\)
−0.715532 + 0.698580i \(0.753815\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −30.0473 −1.04485 −0.522423 0.852686i \(-0.674972\pi\)
−0.522423 + 0.852686i \(0.674972\pi\)
\(828\) 0 0
\(829\) 42.0292 1.45974 0.729868 0.683588i \(-0.239582\pi\)
0.729868 + 0.683588i \(0.239582\pi\)
\(830\) 0 0
\(831\) 16.7195 0.579995
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.49234 0.0515827
\(838\) 0 0
\(839\) −3.38893 −0.116999 −0.0584994 0.998287i \(-0.518632\pi\)
−0.0584994 + 0.998287i \(0.518632\pi\)
\(840\) 0 0
\(841\) −25.1196 −0.866195
\(842\) 0 0
\(843\) 28.7659 0.990751
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 19.6421 0.674116
\(850\) 0 0
\(851\) −38.4734 −1.31885
\(852\) 0 0
\(853\) 25.1267 0.860321 0.430160 0.902752i \(-0.358457\pi\)
0.430160 + 0.902752i \(0.358457\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 47.7367 1.63065 0.815327 0.579001i \(-0.196557\pi\)
0.815327 + 0.579001i \(0.196557\pi\)
\(858\) 0 0
\(859\) 41.0422 1.40034 0.700171 0.713975i \(-0.253107\pi\)
0.700171 + 0.713975i \(0.253107\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −31.1326 −1.05977 −0.529884 0.848070i \(-0.677764\pi\)
−0.529884 + 0.848070i \(0.677764\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −88.3117 −2.99922
\(868\) 0 0
\(869\) 20.1980 0.685169
\(870\) 0 0
\(871\) −4.80202 −0.162710
\(872\) 0 0
\(873\) 0.839190 0.0284023
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −7.93972 −0.268105 −0.134053 0.990974i \(-0.542799\pi\)
−0.134053 + 0.990974i \(0.542799\pi\)
\(878\) 0 0
\(879\) −15.7358 −0.530755
\(880\) 0 0
\(881\) 29.3709 0.989530 0.494765 0.869027i \(-0.335254\pi\)
0.494765 + 0.869027i \(0.335254\pi\)
\(882\) 0 0
\(883\) 26.9718 0.907674 0.453837 0.891085i \(-0.350055\pi\)
0.453837 + 0.891085i \(0.350055\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23.4855 −0.788565 −0.394282 0.918989i \(-0.629007\pi\)
−0.394282 + 0.918989i \(0.629007\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 10.7376 0.359723
\(892\) 0 0
\(893\) −1.27034 −0.0425103
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 82.0664 2.74012
\(898\) 0 0
\(899\) −1.91049 −0.0637185
\(900\) 0 0
\(901\) −68.3719 −2.27780
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −9.58690 −0.318328 −0.159164 0.987252i \(-0.550880\pi\)
−0.159164 + 0.987252i \(0.550880\pi\)
\(908\) 0 0
\(909\) −45.0000 −1.49256
\(910\) 0 0
\(911\) −3.78994 −0.125566 −0.0627831 0.998027i \(-0.519998\pi\)
−0.0627831 + 0.998027i \(0.519998\pi\)
\(912\) 0 0
\(913\) −26.8392 −0.888248
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 23.3900 0.771564 0.385782 0.922590i \(-0.373932\pi\)
0.385782 + 0.922590i \(0.373932\pi\)
\(920\) 0 0
\(921\) −67.8383 −2.23535
\(922\) 0 0
\(923\) −67.5930 −2.22485
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 12.1317 0.398458
\(928\) 0 0
\(929\) −50.2573 −1.64889 −0.824445 0.565942i \(-0.808513\pi\)
−0.824445 + 0.565942i \(0.808513\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −49.7145 −1.62758
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.43621 −0.0795875 −0.0397937 0.999208i \(-0.512670\pi\)
−0.0397937 + 0.999208i \(0.512670\pi\)
\(938\) 0 0
\(939\) −22.3658 −0.729881
\(940\) 0 0
\(941\) 23.9648 0.781230 0.390615 0.920554i \(-0.372262\pi\)
0.390615 + 0.920554i \(0.372262\pi\)
\(942\) 0 0
\(943\) −50.9096 −1.65784
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 51.1619 1.66254 0.831269 0.555871i \(-0.187615\pi\)
0.831269 + 0.555871i \(0.187615\pi\)
\(948\) 0 0
\(949\) 22.2754 0.723090
\(950\) 0 0
\(951\) 39.2402 1.27245
\(952\) 0 0
\(953\) −33.3306 −1.07968 −0.539842 0.841766i \(-0.681516\pi\)
−0.539842 + 0.841766i \(0.681516\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 7.93881 0.256625
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.0594 −0.969657
\(962\) 0 0
\(963\) 63.8341 2.05703
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 31.8392 1.02388 0.511940 0.859021i \(-0.328927\pi\)
0.511940 + 0.859021i \(0.328927\pi\)
\(968\) 0 0
\(969\) 58.3297 1.87382
\(970\) 0 0
\(971\) −1.94675 −0.0624742 −0.0312371 0.999512i \(-0.509945\pi\)
−0.0312371 + 0.999512i \(0.509945\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 50.1196 1.60347 0.801735 0.597680i \(-0.203911\pi\)
0.801735 + 0.597680i \(0.203911\pi\)
\(978\) 0 0
\(979\) −8.78397 −0.280737
\(980\) 0 0
\(981\) 21.2503 0.678470
\(982\) 0 0
\(983\) −47.9217 −1.52846 −0.764232 0.644941i \(-0.776882\pi\)
−0.764232 + 0.644941i \(0.776882\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −26.3830 −0.838929
\(990\) 0 0
\(991\) 8.86933 0.281743 0.140872 0.990028i \(-0.455009\pi\)
0.140872 + 0.990028i \(0.455009\pi\)
\(992\) 0 0
\(993\) −43.0251 −1.36536
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 12.2101 0.386697 0.193348 0.981130i \(-0.438065\pi\)
0.193348 + 0.981130i \(0.438065\pi\)
\(998\) 0 0
\(999\) −10.3194 −0.326493
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 4900.2.a.bd.1.1 3
5.2 odd 4 4900.2.e.s.2549.5 6
5.3 odd 4 4900.2.e.s.2549.2 6
5.4 even 2 4900.2.a.bb.1.3 3
7.3 odd 6 700.2.i.e.401.1 yes 6
7.5 odd 6 700.2.i.e.501.1 yes 6
7.6 odd 2 4900.2.a.ba.1.3 3
35.3 even 12 700.2.r.d.149.5 12
35.12 even 12 700.2.r.d.249.5 12
35.13 even 4 4900.2.e.t.2549.5 6
35.17 even 12 700.2.r.d.149.2 12
35.19 odd 6 700.2.i.d.501.3 yes 6
35.24 odd 6 700.2.i.d.401.3 6
35.27 even 4 4900.2.e.t.2549.2 6
35.33 even 12 700.2.r.d.249.2 12
35.34 odd 2 4900.2.a.bc.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.i.d.401.3 6 35.24 odd 6
700.2.i.d.501.3 yes 6 35.19 odd 6
700.2.i.e.401.1 yes 6 7.3 odd 6
700.2.i.e.501.1 yes 6 7.5 odd 6
700.2.r.d.149.2 12 35.17 even 12
700.2.r.d.149.5 12 35.3 even 12
700.2.r.d.249.2 12 35.33 even 12
700.2.r.d.249.5 12 35.12 even 12
4900.2.a.ba.1.3 3 7.6 odd 2
4900.2.a.bb.1.3 3 5.4 even 2
4900.2.a.bc.1.1 3 35.34 odd 2
4900.2.a.bd.1.1 3 1.1 even 1 trivial
4900.2.e.s.2549.2 6 5.3 odd 4
4900.2.e.s.2549.5 6 5.2 odd 4
4900.2.e.t.2549.2 6 35.27 even 4
4900.2.e.t.2549.5 6 35.13 even 4