Properties

Label 3600.2.h.h.1151.3
Level $3600$
Weight $2$
Character 3600.1151
Analytic conductor $28.746$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3600,2,Mod(1151,3600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3600.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.h (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.7461447277\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1151.3
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 3600.1151
Dual form 3600.2.h.h.1151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.73205i q^{7} +O(q^{10})\) \(q+1.73205i q^{7} -2.44949 q^{11} +1.00000 q^{13} -4.24264i q^{17} -1.73205i q^{19} -2.44949 q^{23} +4.24264i q^{29} +5.19615i q^{31} -4.00000 q^{37} +5.19615i q^{43} -12.2474 q^{47} +4.00000 q^{49} +12.2474 q^{59} -7.00000 q^{61} +8.66025i q^{67} -9.79796 q^{71} -8.00000 q^{73} -4.24264i q^{77} -6.92820i q^{79} -7.34847 q^{83} +1.73205i q^{91} -11.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{13} - 16 q^{37} + 16 q^{49} - 28 q^{61} - 32 q^{73} - 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(2801\) \(3151\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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
\(5\) 0 0
\(6\) 0 0
\(7\) 1.73205i 0.654654i 0.944911 + 0.327327i \(0.106148\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.44949 −0.738549 −0.369274 0.929320i \(-0.620394\pi\)
−0.369274 + 0.929320i \(0.620394\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 4.24264i − 1.02899i −0.857493 0.514496i \(-0.827979\pi\)
0.857493 0.514496i \(-0.172021\pi\)
\(18\) 0 0
\(19\) − 1.73205i − 0.397360i −0.980064 0.198680i \(-0.936335\pi\)
0.980064 0.198680i \(-0.0636654\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.44949 −0.510754 −0.255377 0.966842i \(-0.582200\pi\)
−0.255377 + 0.966842i \(0.582200\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.24264i 0.787839i 0.919145 + 0.393919i \(0.128881\pi\)
−0.919145 + 0.393919i \(0.871119\pi\)
\(30\) 0 0
\(31\) 5.19615i 0.933257i 0.884454 + 0.466628i \(0.154531\pi\)
−0.884454 + 0.466628i \(0.845469\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.19615i 0.792406i 0.918163 + 0.396203i \(0.129672\pi\)
−0.918163 + 0.396203i \(0.870328\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.2474 −1.78647 −0.893237 0.449586i \(-0.851571\pi\)
−0.893237 + 0.449586i \(0.851571\pi\)
\(48\) 0 0
\(49\) 4.00000 0.571429
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.2474 1.59448 0.797241 0.603661i \(-0.206292\pi\)
0.797241 + 0.603661i \(0.206292\pi\)
\(60\) 0 0
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 8.66025i 1.05802i 0.848616 + 0.529009i \(0.177436\pi\)
−0.848616 + 0.529009i \(0.822564\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.79796 −1.16280 −0.581402 0.813617i \(-0.697496\pi\)
−0.581402 + 0.813617i \(0.697496\pi\)
\(72\) 0 0
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 4.24264i − 0.483494i
\(78\) 0 0
\(79\) − 6.92820i − 0.779484i −0.920924 0.389742i \(-0.872564\pi\)
0.920924 0.389742i \(-0.127436\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.34847 −0.806599 −0.403300 0.915068i \(-0.632137\pi\)
−0.403300 + 0.915068i \(0.632137\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1.73205i 0.181568i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −11.0000 −1.11688 −0.558440 0.829545i \(-0.688600\pi\)
−0.558440 + 0.829545i \(0.688600\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 16.9706i − 1.68863i −0.535844 0.844317i \(-0.680006\pi\)
0.535844 0.844317i \(-0.319994\pi\)
\(102\) 0 0
\(103\) − 3.46410i − 0.341328i −0.985329 0.170664i \(-0.945409\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −19.5959 −1.89441 −0.947204 0.320630i \(-0.896105\pi\)
−0.947204 + 0.320630i \(0.896105\pi\)
\(108\) 0 0
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 16.9706i − 1.59646i −0.602355 0.798228i \(-0.705771\pi\)
0.602355 0.798228i \(-0.294229\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.34847 0.673633
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 20.7846i 1.84434i 0.386790 + 0.922168i \(0.373584\pi\)
−0.386790 + 0.922168i \(0.626416\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.79796 −0.856052 −0.428026 0.903767i \(-0.640791\pi\)
−0.428026 + 0.903767i \(0.640791\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 12.7279i − 1.08742i −0.839273 0.543710i \(-0.817019\pi\)
0.839273 0.543710i \(-0.182981\pi\)
\(138\) 0 0
\(139\) − 13.8564i − 1.17529i −0.809121 0.587643i \(-0.800056\pi\)
0.809121 0.587643i \(-0.199944\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.44949 −0.204837
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 12.7279i 1.04271i 0.853339 + 0.521356i \(0.174574\pi\)
−0.853339 + 0.521356i \(0.825426\pi\)
\(150\) 0 0
\(151\) 8.66025i 0.704761i 0.935857 + 0.352381i \(0.114628\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 4.24264i − 0.334367i
\(162\) 0 0
\(163\) 12.1244i 0.949653i 0.880079 + 0.474826i \(0.157489\pi\)
−0.880079 + 0.474826i \(0.842511\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.5959 −1.51638 −0.758189 0.652035i \(-0.773915\pi\)
−0.758189 + 0.652035i \(0.773915\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.7279i 0.967686i 0.875155 + 0.483843i \(0.160759\pi\)
−0.875155 + 0.483843i \(0.839241\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.2474 0.915417 0.457709 0.889102i \(-0.348670\pi\)
0.457709 + 0.889102i \(0.348670\pi\)
\(180\) 0 0
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 10.3923i 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.34847 −0.531717 −0.265858 0.964012i \(-0.585655\pi\)
−0.265858 + 0.964012i \(0.585655\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 12.7279i − 0.906827i −0.891300 0.453413i \(-0.850206\pi\)
0.891300 0.453413i \(-0.149794\pi\)
\(198\) 0 0
\(199\) 1.73205i 0.122782i 0.998114 + 0.0613909i \(0.0195536\pi\)
−0.998114 + 0.0613909i \(0.980446\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.34847 −0.515761
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.24264i 0.293470i
\(210\) 0 0
\(211\) 22.5167i 1.55011i 0.631893 + 0.775055i \(0.282278\pi\)
−0.631893 + 0.775055i \(0.717722\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −9.00000 −0.610960
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 4.24264i − 0.285391i
\(222\) 0 0
\(223\) 15.5885i 1.04388i 0.852982 + 0.521940i \(0.174792\pi\)
−0.852982 + 0.521940i \(0.825208\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.79796 −0.650313 −0.325157 0.945660i \(-0.605417\pi\)
−0.325157 + 0.945660i \(0.605417\pi\)
\(228\) 0 0
\(229\) 25.0000 1.65205 0.826023 0.563636i \(-0.190598\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 16.9706i − 1.11178i −0.831256 0.555889i \(-0.812378\pi\)
0.831256 0.555889i \(-0.187622\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.79796 0.633777 0.316889 0.948463i \(-0.397362\pi\)
0.316889 + 0.948463i \(0.397362\pi\)
\(240\) 0 0
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 1.73205i − 0.110208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.79796 −0.618442 −0.309221 0.950990i \(-0.600068\pi\)
−0.309221 + 0.950990i \(0.600068\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 16.9706i − 1.05859i −0.848436 0.529297i \(-0.822456\pi\)
0.848436 0.529297i \(-0.177544\pi\)
\(258\) 0 0
\(259\) − 6.92820i − 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.79796 −0.604168 −0.302084 0.953281i \(-0.597682\pi\)
−0.302084 + 0.953281i \(0.597682\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.7279i 0.776035i 0.921652 + 0.388018i \(0.126840\pi\)
−0.921652 + 0.388018i \(0.873160\pi\)
\(270\) 0 0
\(271\) − 6.92820i − 0.420858i −0.977609 0.210429i \(-0.932514\pi\)
0.977609 0.210429i \(-0.0674861\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −17.0000 −1.02143 −0.510716 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 21.2132i 1.26547i 0.774367 + 0.632737i \(0.218068\pi\)
−0.774367 + 0.632737i \(0.781932\pi\)
\(282\) 0 0
\(283\) − 25.9808i − 1.54440i −0.635382 0.772198i \(-0.719157\pi\)
0.635382 0.772198i \(-0.280843\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.2132i 1.23929i 0.784883 + 0.619644i \(0.212723\pi\)
−0.784883 + 0.619644i \(0.787277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.44949 −0.141658
\(300\) 0 0
\(301\) −9.00000 −0.518751
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 5.19615i 0.296560i 0.988945 + 0.148280i \(0.0473737\pi\)
−0.988945 + 0.148280i \(0.952626\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −17.1464 −0.972285 −0.486142 0.873880i \(-0.661596\pi\)
−0.486142 + 0.873880i \(0.661596\pi\)
\(312\) 0 0
\(313\) −13.0000 −0.734803 −0.367402 0.930062i \(-0.619753\pi\)
−0.367402 + 0.930062i \(0.619753\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.9706i 0.953162i 0.879131 + 0.476581i \(0.158124\pi\)
−0.879131 + 0.476581i \(0.841876\pi\)
\(318\) 0 0
\(319\) − 10.3923i − 0.581857i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7.34847 −0.408880
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 21.2132i − 1.16952i
\(330\) 0 0
\(331\) − 13.8564i − 0.761617i −0.924654 0.380808i \(-0.875646\pi\)
0.924654 0.380808i \(-0.124354\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.0000 −0.599208 −0.299604 0.954064i \(-0.596855\pi\)
−0.299604 + 0.954064i \(0.596855\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 12.7279i − 0.689256i
\(342\) 0 0
\(343\) 19.0526i 1.02874i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.34847 −0.394486 −0.197243 0.980355i \(-0.563199\pi\)
−0.197243 + 0.980355i \(0.563199\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 21.2132i − 1.12906i −0.825411 0.564532i \(-0.809057\pi\)
0.825411 0.564532i \(-0.190943\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.79796 0.517116 0.258558 0.965996i \(-0.416753\pi\)
0.258558 + 0.965996i \(0.416753\pi\)
\(360\) 0 0
\(361\) 16.0000 0.842105
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.73205i 0.0904123i 0.998978 + 0.0452062i \(0.0143945\pi\)
−0.998978 + 0.0452062i \(0.985606\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 29.0000 1.50156 0.750782 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.24264i 0.218507i
\(378\) 0 0
\(379\) 19.0526i 0.978664i 0.872098 + 0.489332i \(0.162759\pi\)
−0.872098 + 0.489332i \(0.837241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.79796 0.500652 0.250326 0.968162i \(-0.419462\pi\)
0.250326 + 0.968162i \(0.419462\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.9706i 0.860442i 0.902724 + 0.430221i \(0.141564\pi\)
−0.902724 + 0.430221i \(0.858436\pi\)
\(390\) 0 0
\(391\) 10.3923i 0.525561i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 17.0000 0.853206 0.426603 0.904439i \(-0.359710\pi\)
0.426603 + 0.904439i \(0.359710\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 5.19615i 0.258839i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.79796 0.485667
\(408\) 0 0
\(409\) 1.00000 0.0494468 0.0247234 0.999694i \(-0.492129\pi\)
0.0247234 + 0.999694i \(0.492129\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 21.2132i 1.04383i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −29.3939 −1.43598 −0.717992 0.696051i \(-0.754939\pi\)
−0.717992 + 0.696051i \(0.754939\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 12.1244i − 0.586739i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 31.8434 1.53384 0.766921 0.641742i \(-0.221788\pi\)
0.766921 + 0.641742i \(0.221788\pi\)
\(432\) 0 0
\(433\) −37.0000 −1.77811 −0.889053 0.457804i \(-0.848636\pi\)
−0.889053 + 0.457804i \(0.848636\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.24264i 0.202953i
\(438\) 0 0
\(439\) 5.19615i 0.247999i 0.992282 + 0.123999i \(0.0395721\pi\)
−0.992282 + 0.123999i \(0.960428\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.5959 0.931030 0.465515 0.885040i \(-0.345869\pi\)
0.465515 + 0.885040i \(0.345869\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 16.9706i − 0.800890i −0.916321 0.400445i \(-0.868855\pi\)
0.916321 0.400445i \(-0.131145\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 16.9706i − 0.790398i −0.918596 0.395199i \(-0.870676\pi\)
0.918596 0.395199i \(-0.129324\pi\)
\(462\) 0 0
\(463\) − 34.6410i − 1.60990i −0.593340 0.804952i \(-0.702191\pi\)
0.593340 0.804952i \(-0.297809\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.2474 0.566744 0.283372 0.959010i \(-0.408547\pi\)
0.283372 + 0.959010i \(0.408547\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 12.7279i − 0.585230i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7.34847 0.335760 0.167880 0.985807i \(-0.446308\pi\)
0.167880 + 0.985807i \(0.446308\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 8.66025i − 0.392434i −0.980561 0.196217i \(-0.937134\pi\)
0.980561 0.196217i \(-0.0628656\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 29.3939 1.32653 0.663264 0.748386i \(-0.269171\pi\)
0.663264 + 0.748386i \(0.269171\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 16.9706i − 0.761234i
\(498\) 0 0
\(499\) − 5.19615i − 0.232612i −0.993213 0.116306i \(-0.962895\pi\)
0.993213 0.116306i \(-0.0371053\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.24264i 0.188052i 0.995570 + 0.0940259i \(0.0299736\pi\)
−0.995570 + 0.0940259i \(0.970026\pi\)
\(510\) 0 0
\(511\) − 13.8564i − 0.612971i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 30.0000 1.31940
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 21.2132i 0.929367i 0.885477 + 0.464684i \(0.153832\pi\)
−0.885477 + 0.464684i \(0.846168\pi\)
\(522\) 0 0
\(523\) 19.0526i 0.833110i 0.909110 + 0.416555i \(0.136763\pi\)
−0.909110 + 0.416555i \(0.863237\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.0454 0.960313
\(528\) 0 0
\(529\) −17.0000 −0.739130
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.79796 −0.422028
\(540\) 0 0
\(541\) 13.0000 0.558914 0.279457 0.960158i \(-0.409846\pi\)
0.279457 + 0.960158i \(0.409846\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 3.46410i − 0.148114i −0.997254 0.0740571i \(-0.976405\pi\)
0.997254 0.0740571i \(-0.0235947\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.34847 0.313055
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 46.6690i 1.97743i 0.149805 + 0.988716i \(0.452135\pi\)
−0.149805 + 0.988716i \(0.547865\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 17.1464 0.722636 0.361318 0.932443i \(-0.382327\pi\)
0.361318 + 0.932443i \(0.382327\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 38.1838i − 1.60075i −0.599502 0.800373i \(-0.704635\pi\)
0.599502 0.800373i \(-0.295365\pi\)
\(570\) 0 0
\(571\) − 1.73205i − 0.0724841i −0.999343 0.0362420i \(-0.988461\pi\)
0.999343 0.0362420i \(-0.0115387\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −13.0000 −0.541197 −0.270599 0.962692i \(-0.587222\pi\)
−0.270599 + 0.962692i \(0.587222\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 12.7279i − 0.528043i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 29.3939 1.21322 0.606608 0.795001i \(-0.292530\pi\)
0.606608 + 0.795001i \(0.292530\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 16.9706i − 0.696897i −0.937328 0.348449i \(-0.886709\pi\)
0.937328 0.348449i \(-0.113291\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −29.3939 −1.20100 −0.600501 0.799624i \(-0.705032\pi\)
−0.600501 + 0.799624i \(0.705032\pi\)
\(600\) 0 0
\(601\) 41.0000 1.67242 0.836212 0.548406i \(-0.184765\pi\)
0.836212 + 0.548406i \(0.184765\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 34.6410i − 1.40604i −0.711172 0.703018i \(-0.751835\pi\)
0.711172 0.703018i \(-0.248165\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.2474 −0.495479
\(612\) 0 0
\(613\) −4.00000 −0.161558 −0.0807792 0.996732i \(-0.525741\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 33.9411i 1.36642i 0.730223 + 0.683209i \(0.239416\pi\)
−0.730223 + 0.683209i \(0.760584\pi\)
\(618\) 0 0
\(619\) 29.4449i 1.18349i 0.806126 + 0.591744i \(0.201561\pi\)
−0.806126 + 0.591744i \(0.798439\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.9706i 0.676661i
\(630\) 0 0
\(631\) − 43.3013i − 1.72380i −0.507081 0.861898i \(-0.669276\pi\)
0.507081 0.861898i \(-0.330724\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 33.9411i 1.34059i 0.742093 + 0.670297i \(0.233833\pi\)
−0.742093 + 0.670297i \(0.766167\pi\)
\(642\) 0 0
\(643\) − 41.5692i − 1.63933i −0.572843 0.819665i \(-0.694160\pi\)
0.572843 0.819665i \(-0.305840\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 39.1918 1.54079 0.770395 0.637567i \(-0.220059\pi\)
0.770395 + 0.637567i \(0.220059\pi\)
\(648\) 0 0
\(649\) −30.0000 −1.17760
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 46.6690i 1.82630i 0.407623 + 0.913150i \(0.366358\pi\)
−0.407623 + 0.913150i \(0.633642\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 10.3923i − 0.402392i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.1464 0.661931
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.24264i 0.163058i 0.996671 + 0.0815290i \(0.0259803\pi\)
−0.996671 + 0.0815290i \(0.974020\pi\)
\(678\) 0 0
\(679\) − 19.0526i − 0.731170i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.79796 0.374908 0.187454 0.982273i \(-0.439976\pi\)
0.187454 + 0.982273i \(0.439976\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) − 31.1769i − 1.18603i −0.805193 0.593013i \(-0.797938\pi\)
0.805193 0.593013i \(-0.202062\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.7279i 0.480727i 0.970683 + 0.240363i \(0.0772666\pi\)
−0.970683 + 0.240363i \(0.922733\pi\)
\(702\) 0 0
\(703\) 6.92820i 0.261302i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 29.3939 1.10547
\(708\) 0 0
\(709\) 43.0000 1.61490 0.807449 0.589937i \(-0.200847\pi\)
0.807449 + 0.589937i \(0.200847\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 12.7279i − 0.476664i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −41.6413 −1.55296 −0.776480 0.630142i \(-0.782997\pi\)
−0.776480 + 0.630142i \(0.782997\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 25.9808i − 0.963573i −0.876289 0.481787i \(-0.839988\pi\)
0.876289 0.481787i \(-0.160012\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 22.0454 0.815379
\(732\) 0 0
\(733\) 52.0000 1.92066 0.960332 0.278859i \(-0.0899564\pi\)
0.960332 + 0.278859i \(0.0899564\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 21.2132i − 0.781398i
\(738\) 0 0
\(739\) 41.5692i 1.52915i 0.644536 + 0.764574i \(0.277051\pi\)
−0.644536 + 0.764574i \(0.722949\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.79796 −0.359452 −0.179726 0.983717i \(-0.557521\pi\)
−0.179726 + 0.983717i \(0.557521\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 33.9411i − 1.24018i
\(750\) 0 0
\(751\) 34.6410i 1.26407i 0.774940 + 0.632034i \(0.217780\pi\)
−0.774940 + 0.632034i \(0.782220\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5.00000 −0.181728 −0.0908640 0.995863i \(-0.528963\pi\)
−0.0908640 + 0.995863i \(0.528963\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.9411i 1.23036i 0.788385 + 0.615182i \(0.210918\pi\)
−0.788385 + 0.615182i \(0.789082\pi\)
\(762\) 0 0
\(763\) 12.1244i 0.438931i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.2474 0.442230
\(768\) 0 0
\(769\) −7.00000 −0.252426 −0.126213 0.992003i \(-0.540282\pi\)
−0.126213 + 0.992003i \(0.540282\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 50.9117i 1.83117i 0.402129 + 0.915583i \(0.368270\pi\)
−0.402129 + 0.915583i \(0.631730\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 53.6936i − 1.91397i −0.290139 0.956985i \(-0.593701\pi\)
0.290139 0.956985i \(-0.406299\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 29.3939 1.04513
\(792\) 0 0
\(793\) −7.00000 −0.248577
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 33.9411i 1.20226i 0.799153 + 0.601128i \(0.205282\pi\)
−0.799153 + 0.601128i \(0.794718\pi\)
\(798\) 0 0
\(799\) 51.9615i 1.83827i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 19.5959 0.691525
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 16.9706i − 0.596653i −0.954464 0.298327i \(-0.903572\pi\)
0.954464 0.298327i \(-0.0964285\pi\)
\(810\) 0 0
\(811\) − 5.19615i − 0.182462i −0.995830 0.0912308i \(-0.970920\pi\)
0.995830 0.0912308i \(-0.0290801\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 9.00000 0.314870
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.24264i 0.148069i 0.997256 + 0.0740346i \(0.0235875\pi\)
−0.997256 + 0.0740346i \(0.976412\pi\)
\(822\) 0 0
\(823\) − 43.3013i − 1.50939i −0.656077 0.754694i \(-0.727785\pi\)
0.656077 0.754694i \(-0.272215\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 19.5959 0.681417 0.340708 0.940169i \(-0.389333\pi\)
0.340708 + 0.940169i \(0.389333\pi\)
\(828\) 0 0
\(829\) −14.0000 −0.486240 −0.243120 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 16.9706i − 0.587995i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −26.9444 −0.930224 −0.465112 0.885252i \(-0.653986\pi\)
−0.465112 + 0.885252i \(0.653986\pi\)
\(840\) 0 0
\(841\) 11.0000 0.379310
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 8.66025i − 0.297570i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9.79796 0.335870
\(852\) 0 0
\(853\) −25.0000 −0.855984 −0.427992 0.903783i \(-0.640779\pi\)
−0.427992 + 0.903783i \(0.640779\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 33.9411i 1.15941i 0.814828 + 0.579703i \(0.196832\pi\)
−0.814828 + 0.579703i \(0.803168\pi\)
\(858\) 0 0
\(859\) − 45.0333i − 1.53652i −0.640140 0.768259i \(-0.721124\pi\)
0.640140 0.768259i \(-0.278876\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 29.3939 1.00058 0.500290 0.865858i \(-0.333227\pi\)
0.500290 + 0.865858i \(0.333227\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 16.9706i 0.575687i
\(870\) 0 0
\(871\) 8.66025i 0.293442i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 53.0000 1.78968 0.894841 0.446384i \(-0.147289\pi\)
0.894841 + 0.446384i \(0.147289\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 16.9706i 0.571753i 0.958267 + 0.285876i \(0.0922847\pi\)
−0.958267 + 0.285876i \(0.907715\pi\)
\(882\) 0 0
\(883\) 43.3013i 1.45720i 0.684937 + 0.728602i \(0.259830\pi\)
−0.684937 + 0.728602i \(0.740170\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 26.9444 0.904704 0.452352 0.891839i \(-0.350585\pi\)
0.452352 + 0.891839i \(0.350585\pi\)
\(888\) 0 0
\(889\) −36.0000 −1.20740
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 21.2132i 0.709873i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −22.0454 −0.735256
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 13.8564i 0.460094i 0.973179 + 0.230047i \(0.0738881\pi\)
−0.973179 + 0.230047i \(0.926112\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12.2474 −0.405776 −0.202888 0.979202i \(-0.565033\pi\)
−0.202888 + 0.979202i \(0.565033\pi\)
\(912\) 0 0
\(913\) 18.0000 0.595713
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 16.9706i − 0.560417i
\(918\) 0 0
\(919\) 36.3731i 1.19984i 0.800061 + 0.599918i \(0.204800\pi\)
−0.800061 + 0.599918i \(0.795200\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −9.79796 −0.322504
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.24264i 0.139197i 0.997575 + 0.0695983i \(0.0221717\pi\)
−0.997575 + 0.0695983i \(0.977828\pi\)
\(930\) 0 0
\(931\) − 6.92820i − 0.227063i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5.00000 0.163343 0.0816714 0.996659i \(-0.473974\pi\)
0.0816714 + 0.996659i \(0.473974\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.24264i 0.138306i 0.997606 + 0.0691531i \(0.0220297\pi\)
−0.997606 + 0.0691531i \(0.977970\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.7423 1.19397 0.596983 0.802254i \(-0.296366\pi\)
0.596983 + 0.802254i \(0.296366\pi\)
\(948\) 0 0
\(949\) −8.00000 −0.259691
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 16.9706i − 0.549730i −0.961483 0.274865i \(-0.911367\pi\)
0.961483 0.274865i \(-0.0886332\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22.0454 0.711883
\(960\) 0 0
\(961\) 4.00000 0.129032
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 6.92820i − 0.222796i −0.993776 0.111398i \(-0.964467\pi\)
0.993776 0.111398i \(-0.0355328\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12.2474 0.393039 0.196520 0.980500i \(-0.437036\pi\)
0.196520 + 0.980500i \(0.437036\pi\)
\(972\) 0 0
\(973\) 24.0000 0.769405
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 21.2132i − 0.678671i −0.940666 0.339335i \(-0.889798\pi\)
0.940666 0.339335i \(-0.110202\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 39.1918 1.25003 0.625013 0.780615i \(-0.285094\pi\)
0.625013 + 0.780615i \(0.285094\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 12.7279i − 0.404724i
\(990\) 0 0
\(991\) − 60.6218i − 1.92571i −0.270011 0.962857i \(-0.587027\pi\)
0.270011 0.962857i \(-0.412973\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −4.00000 −0.126681 −0.0633406 0.997992i \(-0.520175\pi\)
−0.0633406 + 0.997992i \(0.520175\pi\)
\(998\) 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 3600.2.h.h.1151.3 yes 4
3.2 odd 2 inner 3600.2.h.h.1151.4 yes 4
4.3 odd 2 inner 3600.2.h.h.1151.2 yes 4
5.2 odd 4 3600.2.o.b.3599.1 8
5.3 odd 4 3600.2.o.b.3599.6 8
5.4 even 2 3600.2.h.e.1151.1 4
12.11 even 2 inner 3600.2.h.h.1151.1 yes 4
15.2 even 4 3600.2.o.b.3599.3 8
15.8 even 4 3600.2.o.b.3599.8 8
15.14 odd 2 3600.2.h.e.1151.2 yes 4
20.3 even 4 3600.2.o.b.3599.4 8
20.7 even 4 3600.2.o.b.3599.7 8
20.19 odd 2 3600.2.h.e.1151.4 yes 4
60.23 odd 4 3600.2.o.b.3599.2 8
60.47 odd 4 3600.2.o.b.3599.5 8
60.59 even 2 3600.2.h.e.1151.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3600.2.h.e.1151.1 4 5.4 even 2
3600.2.h.e.1151.2 yes 4 15.14 odd 2
3600.2.h.e.1151.3 yes 4 60.59 even 2
3600.2.h.e.1151.4 yes 4 20.19 odd 2
3600.2.h.h.1151.1 yes 4 12.11 even 2 inner
3600.2.h.h.1151.2 yes 4 4.3 odd 2 inner
3600.2.h.h.1151.3 yes 4 1.1 even 1 trivial
3600.2.h.h.1151.4 yes 4 3.2 odd 2 inner
3600.2.o.b.3599.1 8 5.2 odd 4
3600.2.o.b.3599.2 8 60.23 odd 4
3600.2.o.b.3599.3 8 15.2 even 4
3600.2.o.b.3599.4 8 20.3 even 4
3600.2.o.b.3599.5 8 60.47 odd 4
3600.2.o.b.3599.6 8 5.3 odd 4
3600.2.o.b.3599.7 8 20.7 even 4
3600.2.o.b.3599.8 8 15.8 even 4