Properties

Label 2900.2.a.g.1.2
Level $2900$
Weight $2$
Character 2900.1
Self dual yes
Analytic conductor $23.157$
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] = [2900,2,Mod(1,2900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2900, 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("2900.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2900.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: \(23.1566165862\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 580)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.08613\) of defining polynomial
Character \(\chi\) \(=\) 2900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.35194 q^{3} +0.648061 q^{7} -1.17226 q^{9} +O(q^{10})\) \(q-1.35194 q^{3} +0.648061 q^{7} -1.17226 q^{9} +3.35194 q^{11} -4.17226 q^{13} -4.82032 q^{17} +6.82032 q^{19} -0.876139 q^{21} -5.52420 q^{23} +5.64064 q^{27} -1.00000 q^{29} -2.82032 q^{31} -4.53162 q^{33} +10.2281 q^{37} +5.64064 q^{39} +8.17226 q^{41} +5.69646 q^{43} +2.64806 q^{47} -6.58002 q^{49} +6.51678 q^{51} +2.87614 q^{53} -9.22066 q^{57} -13.2207 q^{59} -1.12386 q^{61} -0.759696 q^{63} -1.52420 q^{67} +7.46838 q^{69} -8.87614 q^{71} -9.69646 q^{73} +2.17226 q^{77} +8.99258 q^{79} -4.10902 q^{81} -1.94418 q^{83} +1.35194 q^{87} +17.0484 q^{89} -2.70388 q^{91} +3.81290 q^{93} +13.3519 q^{97} -3.92935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} + 4 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} + 4 q^{7} + 11 q^{9} + 8 q^{11} + 2 q^{13} - 2 q^{17} + 8 q^{19} + 16 q^{21} - 8 q^{27} - 3 q^{29} + 4 q^{31} - 24 q^{33} + 10 q^{37} - 8 q^{39} + 10 q^{41} - 14 q^{43} + 10 q^{47} + 3 q^{49} - 24 q^{51} - 10 q^{53} + 20 q^{57} + 8 q^{59} - 22 q^{61} + 8 q^{63} + 12 q^{67} + 12 q^{69} - 8 q^{71} + 2 q^{73} - 8 q^{77} + 23 q^{81} - 12 q^{83} + 2 q^{87} + 18 q^{89} - 4 q^{91} - 28 q^{93} + 38 q^{97} + 36 q^{99}+O(q^{100}) \) 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
\(3\) −1.35194 −0.780542 −0.390271 0.920700i \(-0.627619\pi\)
−0.390271 + 0.920700i \(0.627619\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.648061 0.244944 0.122472 0.992472i \(-0.460918\pi\)
0.122472 + 0.992472i \(0.460918\pi\)
\(8\) 0 0
\(9\) −1.17226 −0.390753
\(10\) 0 0
\(11\) 3.35194 1.01065 0.505324 0.862930i \(-0.331373\pi\)
0.505324 + 0.862930i \(0.331373\pi\)
\(12\) 0 0
\(13\) −4.17226 −1.15718 −0.578588 0.815620i \(-0.696396\pi\)
−0.578588 + 0.815620i \(0.696396\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.82032 −1.16910 −0.584550 0.811358i \(-0.698729\pi\)
−0.584550 + 0.811358i \(0.698729\pi\)
\(18\) 0 0
\(19\) 6.82032 1.56469 0.782344 0.622846i \(-0.214024\pi\)
0.782344 + 0.622846i \(0.214024\pi\)
\(20\) 0 0
\(21\) −0.876139 −0.191189
\(22\) 0 0
\(23\) −5.52420 −1.15188 −0.575938 0.817494i \(-0.695363\pi\)
−0.575938 + 0.817494i \(0.695363\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.64064 1.08554
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −2.82032 −0.506545 −0.253272 0.967395i \(-0.581507\pi\)
−0.253272 + 0.967395i \(0.581507\pi\)
\(32\) 0 0
\(33\) −4.53162 −0.788853
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.2281 1.68149 0.840743 0.541435i \(-0.182119\pi\)
0.840743 + 0.541435i \(0.182119\pi\)
\(38\) 0 0
\(39\) 5.64064 0.903226
\(40\) 0 0
\(41\) 8.17226 1.27629 0.638146 0.769915i \(-0.279701\pi\)
0.638146 + 0.769915i \(0.279701\pi\)
\(42\) 0 0
\(43\) 5.69646 0.868702 0.434351 0.900744i \(-0.356978\pi\)
0.434351 + 0.900744i \(0.356978\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.64806 0.386259 0.193130 0.981173i \(-0.438136\pi\)
0.193130 + 0.981173i \(0.438136\pi\)
\(48\) 0 0
\(49\) −6.58002 −0.940002
\(50\) 0 0
\(51\) 6.51678 0.912532
\(52\) 0 0
\(53\) 2.87614 0.395068 0.197534 0.980296i \(-0.436707\pi\)
0.197534 + 0.980296i \(0.436707\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9.22066 −1.22131
\(58\) 0 0
\(59\) −13.2207 −1.72118 −0.860592 0.509296i \(-0.829906\pi\)
−0.860592 + 0.509296i \(0.829906\pi\)
\(60\) 0 0
\(61\) −1.12386 −0.143896 −0.0719478 0.997408i \(-0.522922\pi\)
−0.0719478 + 0.997408i \(0.522922\pi\)
\(62\) 0 0
\(63\) −0.759696 −0.0957127
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.52420 −0.186211 −0.0931053 0.995656i \(-0.529679\pi\)
−0.0931053 + 0.995656i \(0.529679\pi\)
\(68\) 0 0
\(69\) 7.46838 0.899088
\(70\) 0 0
\(71\) −8.87614 −1.05340 −0.526702 0.850050i \(-0.676572\pi\)
−0.526702 + 0.850050i \(0.676572\pi\)
\(72\) 0 0
\(73\) −9.69646 −1.13488 −0.567442 0.823413i \(-0.692067\pi\)
−0.567442 + 0.823413i \(0.692067\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.17226 0.247552
\(78\) 0 0
\(79\) 8.99258 1.01174 0.505872 0.862608i \(-0.331171\pi\)
0.505872 + 0.862608i \(0.331171\pi\)
\(80\) 0 0
\(81\) −4.10902 −0.456558
\(82\) 0 0
\(83\) −1.94418 −0.213402 −0.106701 0.994291i \(-0.534029\pi\)
−0.106701 + 0.994291i \(0.534029\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.35194 0.144943
\(88\) 0 0
\(89\) 17.0484 1.80713 0.903563 0.428455i \(-0.140942\pi\)
0.903563 + 0.428455i \(0.140942\pi\)
\(90\) 0 0
\(91\) −2.70388 −0.283443
\(92\) 0 0
\(93\) 3.81290 0.395380
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.3519 1.35568 0.677842 0.735208i \(-0.262915\pi\)
0.677842 + 0.735208i \(0.262915\pi\)
\(98\) 0 0
\(99\) −3.92935 −0.394914
\(100\) 0 0
\(101\) 18.4562 1.83646 0.918228 0.396052i \(-0.129620\pi\)
0.918228 + 0.396052i \(0.129620\pi\)
\(102\) 0 0
\(103\) 14.8203 1.46029 0.730145 0.683292i \(-0.239453\pi\)
0.730145 + 0.683292i \(0.239453\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.35194 0.324044 0.162022 0.986787i \(-0.448198\pi\)
0.162022 + 0.986787i \(0.448198\pi\)
\(108\) 0 0
\(109\) 2.76450 0.264791 0.132396 0.991197i \(-0.457733\pi\)
0.132396 + 0.991197i \(0.457733\pi\)
\(110\) 0 0
\(111\) −13.8277 −1.31247
\(112\) 0 0
\(113\) −7.94418 −0.747326 −0.373663 0.927565i \(-0.621898\pi\)
−0.373663 + 0.927565i \(0.621898\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.89098 0.452171
\(118\) 0 0
\(119\) −3.12386 −0.286364
\(120\) 0 0
\(121\) 0.235496 0.0214088
\(122\) 0 0
\(123\) −11.0484 −0.996201
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 17.6965 1.57031 0.785153 0.619301i \(-0.212584\pi\)
0.785153 + 0.619301i \(0.212584\pi\)
\(128\) 0 0
\(129\) −7.70127 −0.678059
\(130\) 0 0
\(131\) 5.52420 0.482652 0.241326 0.970444i \(-0.422418\pi\)
0.241326 + 0.970444i \(0.422418\pi\)
\(132\) 0 0
\(133\) 4.41998 0.383261
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.86872 0.330527 0.165264 0.986249i \(-0.447153\pi\)
0.165264 + 0.986249i \(0.447153\pi\)
\(138\) 0 0
\(139\) 5.64064 0.478433 0.239217 0.970966i \(-0.423109\pi\)
0.239217 + 0.970966i \(0.423109\pi\)
\(140\) 0 0
\(141\) −3.58002 −0.301492
\(142\) 0 0
\(143\) −13.9852 −1.16950
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 8.89578 0.733712
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −17.2207 −1.40140 −0.700699 0.713457i \(-0.747128\pi\)
−0.700699 + 0.713457i \(0.747128\pi\)
\(152\) 0 0
\(153\) 5.65067 0.456830
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.69646 0.454627 0.227314 0.973822i \(-0.427006\pi\)
0.227314 + 0.973822i \(0.427006\pi\)
\(158\) 0 0
\(159\) −3.88836 −0.308367
\(160\) 0 0
\(161\) −3.58002 −0.282145
\(162\) 0 0
\(163\) −16.4003 −1.28457 −0.642287 0.766464i \(-0.722014\pi\)
−0.642287 + 0.766464i \(0.722014\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.2765 1.80119 0.900594 0.434661i \(-0.143132\pi\)
0.900594 + 0.434661i \(0.143132\pi\)
\(168\) 0 0
\(169\) 4.40776 0.339058
\(170\) 0 0
\(171\) −7.99519 −0.611408
\(172\) 0 0
\(173\) 13.9245 1.05866 0.529332 0.848415i \(-0.322443\pi\)
0.529332 + 0.848415i \(0.322443\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.8735 1.34346
\(178\) 0 0
\(179\) −4.34452 −0.324725 −0.162362 0.986731i \(-0.551911\pi\)
−0.162362 + 0.986731i \(0.551911\pi\)
\(180\) 0 0
\(181\) 20.5168 1.52500 0.762500 0.646988i \(-0.223972\pi\)
0.762500 + 0.646988i \(0.223972\pi\)
\(182\) 0 0
\(183\) 1.51939 0.112317
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −16.1574 −1.18155
\(188\) 0 0
\(189\) 3.65548 0.265897
\(190\) 0 0
\(191\) −9.10422 −0.658758 −0.329379 0.944198i \(-0.606839\pi\)
−0.329379 + 0.944198i \(0.606839\pi\)
\(192\) 0 0
\(193\) 25.1648 1.81140 0.905702 0.423914i \(-0.139344\pi\)
0.905702 + 0.423914i \(0.139344\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.703878 0.0501493 0.0250746 0.999686i \(-0.492018\pi\)
0.0250746 + 0.999686i \(0.492018\pi\)
\(198\) 0 0
\(199\) −5.22066 −0.370083 −0.185041 0.982731i \(-0.559242\pi\)
−0.185041 + 0.982731i \(0.559242\pi\)
\(200\) 0 0
\(201\) 2.06063 0.145345
\(202\) 0 0
\(203\) −0.648061 −0.0454850
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.47580 0.450099
\(208\) 0 0
\(209\) 22.8613 1.58135
\(210\) 0 0
\(211\) −13.1042 −0.902131 −0.451066 0.892491i \(-0.648956\pi\)
−0.451066 + 0.892491i \(0.648956\pi\)
\(212\) 0 0
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.82774 −0.124075
\(218\) 0 0
\(219\) 13.1090 0.885826
\(220\) 0 0
\(221\) 20.1116 1.35285
\(222\) 0 0
\(223\) 20.5726 1.37764 0.688822 0.724931i \(-0.258128\pi\)
0.688822 + 0.724931i \(0.258128\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.41256 0.624734 0.312367 0.949962i \(-0.398878\pi\)
0.312367 + 0.949962i \(0.398878\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) −2.93676 −0.193225
\(232\) 0 0
\(233\) −10.3445 −0.677692 −0.338846 0.940842i \(-0.610037\pi\)
−0.338846 + 0.940842i \(0.610037\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −12.1574 −0.789710
\(238\) 0 0
\(239\) 20.8761 1.35037 0.675183 0.737651i \(-0.264065\pi\)
0.675183 + 0.737651i \(0.264065\pi\)
\(240\) 0 0
\(241\) 21.1600 1.36304 0.681519 0.731801i \(-0.261320\pi\)
0.681519 + 0.731801i \(0.261320\pi\)
\(242\) 0 0
\(243\) −11.3668 −0.729179
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −28.4562 −1.81062
\(248\) 0 0
\(249\) 2.62842 0.166569
\(250\) 0 0
\(251\) −8.64806 −0.545861 −0.272930 0.962034i \(-0.587993\pi\)
−0.272930 + 0.962034i \(0.587993\pi\)
\(252\) 0 0
\(253\) −18.5168 −1.16414
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −27.4535 −1.71251 −0.856253 0.516557i \(-0.827213\pi\)
−0.856253 + 0.516557i \(0.827213\pi\)
\(258\) 0 0
\(259\) 6.62842 0.411870
\(260\) 0 0
\(261\) 1.17226 0.0725611
\(262\) 0 0
\(263\) 11.3371 0.699076 0.349538 0.936922i \(-0.386339\pi\)
0.349538 + 0.936922i \(0.386339\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −23.0484 −1.41054
\(268\) 0 0
\(269\) −20.1723 −1.22992 −0.614962 0.788557i \(-0.710829\pi\)
−0.614962 + 0.788557i \(0.710829\pi\)
\(270\) 0 0
\(271\) −10.7449 −0.652704 −0.326352 0.945248i \(-0.605819\pi\)
−0.326352 + 0.945248i \(0.605819\pi\)
\(272\) 0 0
\(273\) 3.65548 0.221240
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.6284 0.758768 0.379384 0.925239i \(-0.376136\pi\)
0.379384 + 0.925239i \(0.376136\pi\)
\(278\) 0 0
\(279\) 3.30615 0.197934
\(280\) 0 0
\(281\) 6.76450 0.403536 0.201768 0.979433i \(-0.435331\pi\)
0.201768 + 0.979433i \(0.435331\pi\)
\(282\) 0 0
\(283\) −1.06804 −0.0634886 −0.0317443 0.999496i \(-0.510106\pi\)
−0.0317443 + 0.999496i \(0.510106\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.29612 0.312620
\(288\) 0 0
\(289\) 6.23550 0.366794
\(290\) 0 0
\(291\) −18.0510 −1.05817
\(292\) 0 0
\(293\) −5.46357 −0.319185 −0.159593 0.987183i \(-0.551018\pi\)
−0.159593 + 0.987183i \(0.551018\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 18.9071 1.09710
\(298\) 0 0
\(299\) 23.0484 1.33292
\(300\) 0 0
\(301\) 3.69165 0.212783
\(302\) 0 0
\(303\) −24.9516 −1.43343
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −6.30354 −0.359762 −0.179881 0.983688i \(-0.557571\pi\)
−0.179881 + 0.983688i \(0.557571\pi\)
\(308\) 0 0
\(309\) −20.0362 −1.13982
\(310\) 0 0
\(311\) 24.6842 1.39971 0.699857 0.714283i \(-0.253247\pi\)
0.699857 + 0.714283i \(0.253247\pi\)
\(312\) 0 0
\(313\) 24.1723 1.36630 0.683148 0.730280i \(-0.260610\pi\)
0.683148 + 0.730280i \(0.260610\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.42740 −0.0801708 −0.0400854 0.999196i \(-0.512763\pi\)
−0.0400854 + 0.999196i \(0.512763\pi\)
\(318\) 0 0
\(319\) −3.35194 −0.187673
\(320\) 0 0
\(321\) −4.53162 −0.252930
\(322\) 0 0
\(323\) −32.8761 −1.82928
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3.73744 −0.206681
\(328\) 0 0
\(329\) 1.71610 0.0946119
\(330\) 0 0
\(331\) 34.2132 1.88053 0.940265 0.340444i \(-0.110577\pi\)
0.940265 + 0.340444i \(0.110577\pi\)
\(332\) 0 0
\(333\) −11.9900 −0.657046
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −4.40034 −0.239702 −0.119851 0.992792i \(-0.538242\pi\)
−0.119851 + 0.992792i \(0.538242\pi\)
\(338\) 0 0
\(339\) 10.7401 0.583320
\(340\) 0 0
\(341\) −9.45355 −0.511938
\(342\) 0 0
\(343\) −8.80068 −0.475192
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.9926 −0.697478 −0.348739 0.937220i \(-0.613390\pi\)
−0.348739 + 0.937220i \(0.613390\pi\)
\(348\) 0 0
\(349\) −20.0968 −1.07576 −0.537878 0.843022i \(-0.680774\pi\)
−0.537878 + 0.843022i \(0.680774\pi\)
\(350\) 0 0
\(351\) −23.5342 −1.25616
\(352\) 0 0
\(353\) 17.8129 0.948085 0.474043 0.880502i \(-0.342794\pi\)
0.474043 + 0.880502i \(0.342794\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 4.22327 0.223519
\(358\) 0 0
\(359\) 5.52420 0.291556 0.145778 0.989317i \(-0.453431\pi\)
0.145778 + 0.989317i \(0.453431\pi\)
\(360\) 0 0
\(361\) 27.5168 1.44825
\(362\) 0 0
\(363\) −0.318377 −0.0167104
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 20.0558 1.04691 0.523453 0.852055i \(-0.324644\pi\)
0.523453 + 0.852055i \(0.324644\pi\)
\(368\) 0 0
\(369\) −9.58002 −0.498716
\(370\) 0 0
\(371\) 1.86391 0.0967695
\(372\) 0 0
\(373\) 1.88836 0.0977758 0.0488879 0.998804i \(-0.484432\pi\)
0.0488879 + 0.998804i \(0.484432\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.17226 0.214882
\(378\) 0 0
\(379\) −15.0894 −0.775089 −0.387545 0.921851i \(-0.626677\pi\)
−0.387545 + 0.921851i \(0.626677\pi\)
\(380\) 0 0
\(381\) −23.9245 −1.22569
\(382\) 0 0
\(383\) −17.3371 −0.885885 −0.442942 0.896550i \(-0.646065\pi\)
−0.442942 + 0.896550i \(0.646065\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.67773 −0.339448
\(388\) 0 0
\(389\) −0.890976 −0.0451743 −0.0225871 0.999745i \(-0.507190\pi\)
−0.0225871 + 0.999745i \(0.507190\pi\)
\(390\) 0 0
\(391\) 26.6284 1.34666
\(392\) 0 0
\(393\) −7.46838 −0.376730
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −5.39292 −0.270663 −0.135331 0.990800i \(-0.543210\pi\)
−0.135331 + 0.990800i \(0.543210\pi\)
\(398\) 0 0
\(399\) −5.97555 −0.299152
\(400\) 0 0
\(401\) 5.23550 0.261448 0.130724 0.991419i \(-0.458270\pi\)
0.130724 + 0.991419i \(0.458270\pi\)
\(402\) 0 0
\(403\) 11.7671 0.586162
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 34.2839 1.69939
\(408\) 0 0
\(409\) −16.0606 −0.794147 −0.397073 0.917787i \(-0.629974\pi\)
−0.397073 + 0.917787i \(0.629974\pi\)
\(410\) 0 0
\(411\) −5.23027 −0.257990
\(412\) 0 0
\(413\) −8.56779 −0.421593
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.62581 −0.373437
\(418\) 0 0
\(419\) −19.9245 −0.973377 −0.486689 0.873575i \(-0.661795\pi\)
−0.486689 + 0.873575i \(0.661795\pi\)
\(420\) 0 0
\(421\) −15.5652 −0.758600 −0.379300 0.925274i \(-0.623835\pi\)
−0.379300 + 0.925274i \(0.623835\pi\)
\(422\) 0 0
\(423\) −3.10422 −0.150932
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.728330 −0.0352464
\(428\) 0 0
\(429\) 18.9071 0.912843
\(430\) 0 0
\(431\) −13.4078 −0.645829 −0.322914 0.946428i \(-0.604663\pi\)
−0.322914 + 0.946428i \(0.604663\pi\)
\(432\) 0 0
\(433\) 34.6842 1.66682 0.833409 0.552657i \(-0.186386\pi\)
0.833409 + 0.552657i \(0.186386\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −37.6768 −1.80233
\(438\) 0 0
\(439\) −15.2355 −0.727151 −0.363575 0.931565i \(-0.618444\pi\)
−0.363575 + 0.931565i \(0.618444\pi\)
\(440\) 0 0
\(441\) 7.71349 0.367309
\(442\) 0 0
\(443\) −5.00742 −0.237910 −0.118955 0.992900i \(-0.537954\pi\)
−0.118955 + 0.992900i \(0.537954\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −24.3349 −1.15100
\(448\) 0 0
\(449\) −17.8129 −0.840643 −0.420321 0.907375i \(-0.638083\pi\)
−0.420321 + 0.907375i \(0.638083\pi\)
\(450\) 0 0
\(451\) 27.3929 1.28988
\(452\) 0 0
\(453\) 23.2813 1.09385
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −24.4051 −1.14162 −0.570812 0.821081i \(-0.693372\pi\)
−0.570812 + 0.821081i \(0.693372\pi\)
\(458\) 0 0
\(459\) −27.1897 −1.26911
\(460\) 0 0
\(461\) −7.98516 −0.371906 −0.185953 0.982559i \(-0.559537\pi\)
−0.185953 + 0.982559i \(0.559537\pi\)
\(462\) 0 0
\(463\) −11.6210 −0.540074 −0.270037 0.962850i \(-0.587036\pi\)
−0.270037 + 0.962850i \(0.587036\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.24030 −0.0573944 −0.0286972 0.999588i \(-0.509136\pi\)
−0.0286972 + 0.999588i \(0.509136\pi\)
\(468\) 0 0
\(469\) −0.987774 −0.0456112
\(470\) 0 0
\(471\) −7.70127 −0.354856
\(472\) 0 0
\(473\) 19.0942 0.877952
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.37158 −0.154374
\(478\) 0 0
\(479\) 19.6965 0.899954 0.449977 0.893040i \(-0.351432\pi\)
0.449977 + 0.893040i \(0.351432\pi\)
\(480\) 0 0
\(481\) −42.6742 −1.94578
\(482\) 0 0
\(483\) 4.83997 0.220226
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 15.0894 0.683765 0.341883 0.939743i \(-0.388936\pi\)
0.341883 + 0.939743i \(0.388936\pi\)
\(488\) 0 0
\(489\) 22.1723 1.00266
\(490\) 0 0
\(491\) −12.2281 −0.551845 −0.275923 0.961180i \(-0.588983\pi\)
−0.275923 + 0.961180i \(0.588983\pi\)
\(492\) 0 0
\(493\) 4.82032 0.217096
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.75228 −0.258025
\(498\) 0 0
\(499\) −5.52901 −0.247512 −0.123756 0.992313i \(-0.539494\pi\)
−0.123756 + 0.992313i \(0.539494\pi\)
\(500\) 0 0
\(501\) −31.4684 −1.40590
\(502\) 0 0
\(503\) −24.2887 −1.08298 −0.541490 0.840707i \(-0.682140\pi\)
−0.541490 + 0.840707i \(0.682140\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −5.95902 −0.264649
\(508\) 0 0
\(509\) −9.58002 −0.424627 −0.212313 0.977202i \(-0.568100\pi\)
−0.212313 + 0.977202i \(0.568100\pi\)
\(510\) 0 0
\(511\) −6.28390 −0.277983
\(512\) 0 0
\(513\) 38.4710 1.69854
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.87614 0.390372
\(518\) 0 0
\(519\) −18.8251 −0.826331
\(520\) 0 0
\(521\) −21.5800 −0.945438 −0.472719 0.881213i \(-0.656727\pi\)
−0.472719 + 0.881213i \(0.656727\pi\)
\(522\) 0 0
\(523\) 42.2132 1.84586 0.922928 0.384972i \(-0.125789\pi\)
0.922928 + 0.384972i \(0.125789\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13.5949 0.592201
\(528\) 0 0
\(529\) 7.51678 0.326817
\(530\) 0 0
\(531\) 15.4981 0.672558
\(532\) 0 0
\(533\) −34.0968 −1.47690
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 5.87353 0.253461
\(538\) 0 0
\(539\) −22.0558 −0.950011
\(540\) 0 0
\(541\) 36.5530 1.57153 0.785767 0.618522i \(-0.212268\pi\)
0.785767 + 0.618522i \(0.212268\pi\)
\(542\) 0 0
\(543\) −27.7374 −1.19033
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −26.6236 −1.13834 −0.569172 0.822219i \(-0.692736\pi\)
−0.569172 + 0.822219i \(0.692736\pi\)
\(548\) 0 0
\(549\) 1.31746 0.0562277
\(550\) 0 0
\(551\) −6.82032 −0.290555
\(552\) 0 0
\(553\) 5.82774 0.247821
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22.2233 −0.941630 −0.470815 0.882232i \(-0.656040\pi\)
−0.470815 + 0.882232i \(0.656040\pi\)
\(558\) 0 0
\(559\) −23.7671 −1.00524
\(560\) 0 0
\(561\) 21.8439 0.922248
\(562\) 0 0
\(563\) −1.11905 −0.0471625 −0.0235812 0.999722i \(-0.507507\pi\)
−0.0235812 + 0.999722i \(0.507507\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.66290 −0.111831
\(568\) 0 0
\(569\) −10.5316 −0.441508 −0.220754 0.975329i \(-0.570852\pi\)
−0.220754 + 0.975329i \(0.570852\pi\)
\(570\) 0 0
\(571\) −1.18449 −0.0495692 −0.0247846 0.999693i \(-0.507890\pi\)
−0.0247846 + 0.999693i \(0.507890\pi\)
\(572\) 0 0
\(573\) 12.3083 0.514189
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.8687 −0.494101 −0.247051 0.969003i \(-0.579461\pi\)
−0.247051 + 0.969003i \(0.579461\pi\)
\(578\) 0 0
\(579\) −34.0213 −1.41388
\(580\) 0 0
\(581\) −1.25995 −0.0522715
\(582\) 0 0
\(583\) 9.64064 0.399275
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −32.4610 −1.33981 −0.669904 0.742448i \(-0.733665\pi\)
−0.669904 + 0.742448i \(0.733665\pi\)
\(588\) 0 0
\(589\) −19.2355 −0.792585
\(590\) 0 0
\(591\) −0.951601 −0.0391436
\(592\) 0 0
\(593\) −9.12386 −0.374672 −0.187336 0.982296i \(-0.559985\pi\)
−0.187336 + 0.982296i \(0.559985\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.05801 0.288865
\(598\) 0 0
\(599\) −30.2887 −1.23756 −0.618781 0.785563i \(-0.712373\pi\)
−0.618781 + 0.785563i \(0.712373\pi\)
\(600\) 0 0
\(601\) 20.5168 0.836897 0.418448 0.908241i \(-0.362574\pi\)
0.418448 + 0.908241i \(0.362574\pi\)
\(602\) 0 0
\(603\) 1.78676 0.0727624
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.9293 0.565375 0.282687 0.959212i \(-0.408774\pi\)
0.282687 + 0.959212i \(0.408774\pi\)
\(608\) 0 0
\(609\) 0.876139 0.0355029
\(610\) 0 0
\(611\) −11.0484 −0.446970
\(612\) 0 0
\(613\) −19.7523 −0.797787 −0.398893 0.916997i \(-0.630606\pi\)
−0.398893 + 0.916997i \(0.630606\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.2010 1.49766 0.748828 0.662764i \(-0.230617\pi\)
0.748828 + 0.662764i \(0.230617\pi\)
\(618\) 0 0
\(619\) 7.46357 0.299986 0.149993 0.988687i \(-0.452075\pi\)
0.149993 + 0.988687i \(0.452075\pi\)
\(620\) 0 0
\(621\) −31.1600 −1.25041
\(622\) 0 0
\(623\) 11.0484 0.442645
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −30.9071 −1.23431
\(628\) 0 0
\(629\) −49.3026 −1.96582
\(630\) 0 0
\(631\) 44.4562 1.76977 0.884886 0.465808i \(-0.154236\pi\)
0.884886 + 0.465808i \(0.154236\pi\)
\(632\) 0 0
\(633\) 17.7161 0.704152
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 27.4535 1.08775
\(638\) 0 0
\(639\) 10.4051 0.411621
\(640\) 0 0
\(641\) −40.7401 −1.60914 −0.804568 0.593861i \(-0.797603\pi\)
−0.804568 + 0.593861i \(0.797603\pi\)
\(642\) 0 0
\(643\) −20.3493 −0.802499 −0.401250 0.915969i \(-0.631424\pi\)
−0.401250 + 0.915969i \(0.631424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −41.7933 −1.64306 −0.821531 0.570163i \(-0.806880\pi\)
−0.821531 + 0.570163i \(0.806880\pi\)
\(648\) 0 0
\(649\) −44.3148 −1.73951
\(650\) 0 0
\(651\) 2.47099 0.0968458
\(652\) 0 0
\(653\) −23.7933 −0.931102 −0.465551 0.885021i \(-0.654144\pi\)
−0.465551 + 0.885021i \(0.654144\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11.3668 0.443460
\(658\) 0 0
\(659\) 7.50936 0.292523 0.146262 0.989246i \(-0.453276\pi\)
0.146262 + 0.989246i \(0.453276\pi\)
\(660\) 0 0
\(661\) 45.9245 1.78626 0.893129 0.449801i \(-0.148505\pi\)
0.893129 + 0.449801i \(0.148505\pi\)
\(662\) 0 0
\(663\) −27.1897 −1.05596
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.52420 0.213898
\(668\) 0 0
\(669\) −27.8129 −1.07531
\(670\) 0 0
\(671\) −3.76711 −0.145428
\(672\) 0 0
\(673\) −7.29612 −0.281245 −0.140622 0.990063i \(-0.544910\pi\)
−0.140622 + 0.990063i \(0.544910\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −36.2494 −1.39318 −0.696589 0.717470i \(-0.745300\pi\)
−0.696589 + 0.717470i \(0.745300\pi\)
\(678\) 0 0
\(679\) 8.65287 0.332067
\(680\) 0 0
\(681\) −12.7252 −0.487631
\(682\) 0 0
\(683\) 5.40295 0.206738 0.103369 0.994643i \(-0.467038\pi\)
0.103369 + 0.994643i \(0.467038\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.70388 −0.103159
\(688\) 0 0
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −36.0458 −1.37125 −0.685623 0.727957i \(-0.740470\pi\)
−0.685623 + 0.727957i \(0.740470\pi\)
\(692\) 0 0
\(693\) −2.54645 −0.0967318
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −39.3929 −1.49211
\(698\) 0 0
\(699\) 13.9852 0.528967
\(700\) 0 0
\(701\) 3.33229 0.125859 0.0629295 0.998018i \(-0.479956\pi\)
0.0629295 + 0.998018i \(0.479956\pi\)
\(702\) 0 0
\(703\) 69.7588 2.63100
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.9607 0.449829
\(708\) 0 0
\(709\) 7.48322 0.281038 0.140519 0.990078i \(-0.455123\pi\)
0.140519 + 0.990078i \(0.455123\pi\)
\(710\) 0 0
\(711\) −10.5416 −0.395343
\(712\) 0 0
\(713\) 15.5800 0.583476
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −28.2233 −1.05402
\(718\) 0 0
\(719\) −39.6620 −1.47914 −0.739571 0.673078i \(-0.764972\pi\)
−0.739571 + 0.673078i \(0.764972\pi\)
\(720\) 0 0
\(721\) 9.60447 0.357689
\(722\) 0 0
\(723\) −28.6071 −1.06391
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 8.05582 0.298774 0.149387 0.988779i \(-0.452270\pi\)
0.149387 + 0.988779i \(0.452270\pi\)
\(728\) 0 0
\(729\) 27.6943 1.02571
\(730\) 0 0
\(731\) −27.4588 −1.01560
\(732\) 0 0
\(733\) 28.9320 1.06863 0.534313 0.845287i \(-0.320570\pi\)
0.534313 + 0.845287i \(0.320570\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.10902 −0.188193
\(738\) 0 0
\(739\) 36.0772 1.32712 0.663560 0.748123i \(-0.269045\pi\)
0.663560 + 0.748123i \(0.269045\pi\)
\(740\) 0 0
\(741\) 38.4710 1.41327
\(742\) 0 0
\(743\) 40.9681 1.50297 0.751487 0.659747i \(-0.229337\pi\)
0.751487 + 0.659747i \(0.229337\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.27909 0.0833875
\(748\) 0 0
\(749\) 2.17226 0.0793727
\(750\) 0 0
\(751\) 23.2861 0.849722 0.424861 0.905259i \(-0.360323\pi\)
0.424861 + 0.905259i \(0.360323\pi\)
\(752\) 0 0
\(753\) 11.6917 0.426067
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −27.3275 −0.993234 −0.496617 0.867970i \(-0.665425\pi\)
−0.496617 + 0.867970i \(0.665425\pi\)
\(758\) 0 0
\(759\) 25.0336 0.908661
\(760\) 0 0
\(761\) 44.5626 1.61539 0.807696 0.589599i \(-0.200714\pi\)
0.807696 + 0.589599i \(0.200714\pi\)
\(762\) 0 0
\(763\) 1.79157 0.0648591
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 55.1600 1.99171
\(768\) 0 0
\(769\) 51.6110 1.86114 0.930570 0.366115i \(-0.119312\pi\)
0.930570 + 0.366115i \(0.119312\pi\)
\(770\) 0 0
\(771\) 37.1155 1.33668
\(772\) 0 0
\(773\) 19.6358 0.706252 0.353126 0.935576i \(-0.385119\pi\)
0.353126 + 0.935576i \(0.385119\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −8.96122 −0.321482
\(778\) 0 0
\(779\) 55.7374 1.99700
\(780\) 0 0
\(781\) −29.7523 −1.06462
\(782\) 0 0
\(783\) −5.64064 −0.201580
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −37.3371 −1.33092 −0.665462 0.746432i \(-0.731765\pi\)
−0.665462 + 0.746432i \(0.731765\pi\)
\(788\) 0 0
\(789\) −15.3271 −0.545658
\(790\) 0 0
\(791\) −5.14831 −0.183053
\(792\) 0 0
\(793\) 4.68904 0.166513
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.2159 0.397286 0.198643 0.980072i \(-0.436347\pi\)
0.198643 + 0.980072i \(0.436347\pi\)
\(798\) 0 0
\(799\) −12.7645 −0.451576
\(800\) 0 0
\(801\) −19.9852 −0.706141
\(802\) 0 0
\(803\) −32.5019 −1.14697
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 27.2717 0.960008
\(808\) 0 0
\(809\) 11.1749 0.392888 0.196444 0.980515i \(-0.437061\pi\)
0.196444 + 0.980515i \(0.437061\pi\)
\(810\) 0 0
\(811\) 17.6406 0.619447 0.309723 0.950827i \(-0.399764\pi\)
0.309723 + 0.950827i \(0.399764\pi\)
\(812\) 0 0
\(813\) 14.5264 0.509463
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 38.8517 1.35925
\(818\) 0 0
\(819\) 3.16965 0.110757
\(820\) 0 0
\(821\) 24.2477 0.846251 0.423126 0.906071i \(-0.360933\pi\)
0.423126 + 0.906071i \(0.360933\pi\)
\(822\) 0 0
\(823\) −16.9777 −0.591807 −0.295903 0.955218i \(-0.595621\pi\)
−0.295903 + 0.955218i \(0.595621\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5.58482 0.194203 0.0971017 0.995274i \(-0.469043\pi\)
0.0971017 + 0.995274i \(0.469043\pi\)
\(828\) 0 0
\(829\) 18.6136 0.646476 0.323238 0.946318i \(-0.395229\pi\)
0.323238 + 0.946318i \(0.395229\pi\)
\(830\) 0 0
\(831\) −17.0729 −0.592251
\(832\) 0 0
\(833\) 31.7178 1.09896
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −15.9084 −0.549876
\(838\) 0 0
\(839\) −15.9293 −0.549942 −0.274971 0.961453i \(-0.588668\pi\)
−0.274971 + 0.961453i \(0.588668\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −9.14520 −0.314977
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.152616 0.00524395
\(848\) 0 0
\(849\) 1.44393 0.0495555
\(850\) 0 0
\(851\) −56.5019 −1.93686
\(852\) 0 0
\(853\) 27.0288 0.925447 0.462723 0.886503i \(-0.346872\pi\)
0.462723 + 0.886503i \(0.346872\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −30.2691 −1.03397 −0.516986 0.855994i \(-0.672946\pi\)
−0.516986 + 0.855994i \(0.672946\pi\)
\(858\) 0 0
\(859\) −41.4487 −1.41421 −0.707106 0.707107i \(-0.750000\pi\)
−0.707106 + 0.707107i \(0.750000\pi\)
\(860\) 0 0
\(861\) −7.16003 −0.244013
\(862\) 0 0
\(863\) −42.2494 −1.43819 −0.719093 0.694913i \(-0.755443\pi\)
−0.719093 + 0.694913i \(0.755443\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8.43001 −0.286298
\(868\) 0 0
\(869\) 30.1426 1.02252
\(870\) 0 0
\(871\) 6.35936 0.215479
\(872\) 0 0
\(873\) −15.6519 −0.529738
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37.8129 −1.27685 −0.638426 0.769684i \(-0.720414\pi\)
−0.638426 + 0.769684i \(0.720414\pi\)
\(878\) 0 0
\(879\) 7.38642 0.249138
\(880\) 0 0
\(881\) −5.35675 −0.180473 −0.0902367 0.995920i \(-0.528762\pi\)
−0.0902367 + 0.995920i \(0.528762\pi\)
\(882\) 0 0
\(883\) −8.53643 −0.287274 −0.143637 0.989630i \(-0.545880\pi\)
−0.143637 + 0.989630i \(0.545880\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 22.7597 0.764196 0.382098 0.924122i \(-0.375202\pi\)
0.382098 + 0.924122i \(0.375202\pi\)
\(888\) 0 0
\(889\) 11.4684 0.384637
\(890\) 0 0
\(891\) −13.7732 −0.461420
\(892\) 0 0
\(893\) 18.0606 0.604376
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −31.1600 −1.04040
\(898\) 0 0
\(899\) 2.82032 0.0940630
\(900\) 0 0
\(901\) −13.8639 −0.461874
\(902\) 0 0
\(903\) −4.99089 −0.166086
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −3.94418 −0.130964 −0.0654822 0.997854i \(-0.520859\pi\)
−0.0654822 + 0.997854i \(0.520859\pi\)
\(908\) 0 0
\(909\) −21.6354 −0.717602
\(910\) 0 0
\(911\) −40.6546 −1.34695 −0.673473 0.739212i \(-0.735198\pi\)
−0.673473 + 0.739212i \(0.735198\pi\)
\(912\) 0 0
\(913\) −6.51678 −0.215674
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.58002 0.118223
\(918\) 0 0
\(919\) 27.3471 0.902099 0.451049 0.892499i \(-0.351050\pi\)
0.451049 + 0.892499i \(0.351050\pi\)
\(920\) 0 0
\(921\) 8.52200 0.280810
\(922\) 0 0
\(923\) 37.0336 1.21897
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −17.3733 −0.570613
\(928\) 0 0
\(929\) 20.9368 0.686913 0.343456 0.939169i \(-0.388402\pi\)
0.343456 + 0.939169i \(0.388402\pi\)
\(930\) 0 0
\(931\) −44.8778 −1.47081
\(932\) 0 0
\(933\) −33.3716 −1.09254
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −36.4051 −1.18930 −0.594652 0.803983i \(-0.702710\pi\)
−0.594652 + 0.803983i \(0.702710\pi\)
\(938\) 0 0
\(939\) −32.6794 −1.06645
\(940\) 0 0
\(941\) 28.0968 0.915929 0.457965 0.888970i \(-0.348579\pi\)
0.457965 + 0.888970i \(0.348579\pi\)
\(942\) 0 0
\(943\) −45.1452 −1.47013
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 10.8809 0.353583 0.176792 0.984248i \(-0.443428\pi\)
0.176792 + 0.984248i \(0.443428\pi\)
\(948\) 0 0
\(949\) 40.4562 1.31326
\(950\) 0 0
\(951\) 1.92976 0.0625767
\(952\) 0 0
\(953\) −38.8103 −1.25719 −0.628594 0.777733i \(-0.716369\pi\)
−0.628594 + 0.777733i \(0.716369\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 4.53162 0.146486
\(958\) 0 0
\(959\) 2.50717 0.0809606
\(960\) 0 0
\(961\) −23.0458 −0.743413
\(962\) 0 0
\(963\) −3.92935 −0.126621
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −47.1862 −1.51741 −0.758703 0.651437i \(-0.774166\pi\)
−0.758703 + 0.651437i \(0.774166\pi\)
\(968\) 0 0
\(969\) 44.4465 1.42783
\(970\) 0 0
\(971\) 40.0772 1.28614 0.643069 0.765809i \(-0.277661\pi\)
0.643069 + 0.765809i \(0.277661\pi\)
\(972\) 0 0
\(973\) 3.65548 0.117189
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.29873 −0.0735430 −0.0367715 0.999324i \(-0.511707\pi\)
−0.0367715 + 0.999324i \(0.511707\pi\)
\(978\) 0 0
\(979\) 57.1452 1.82637
\(980\) 0 0
\(981\) −3.24072 −0.103468
\(982\) 0 0
\(983\) 8.89578 0.283731 0.141866 0.989886i \(-0.454690\pi\)
0.141866 + 0.989886i \(0.454690\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2.32007 −0.0738486
\(988\) 0 0
\(989\) −31.4684 −1.00064
\(990\) 0 0
\(991\) 37.5652 1.19330 0.596649 0.802503i \(-0.296499\pi\)
0.596649 + 0.802503i \(0.296499\pi\)
\(992\) 0 0
\(993\) −46.2542 −1.46783
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 25.8081 0.817351 0.408675 0.912680i \(-0.365991\pi\)
0.408675 + 0.912680i \(0.365991\pi\)
\(998\) 0 0
\(999\) 57.6929 1.82532
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 2900.2.a.g.1.2 3
5.2 odd 4 2900.2.c.f.349.4 6
5.3 odd 4 2900.2.c.f.349.3 6
5.4 even 2 580.2.a.c.1.2 3
15.14 odd 2 5220.2.a.x.1.2 3
20.19 odd 2 2320.2.a.m.1.2 3
40.19 odd 2 9280.2.a.bw.1.2 3
40.29 even 2 9280.2.a.bk.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.2.a.c.1.2 3 5.4 even 2
2320.2.a.m.1.2 3 20.19 odd 2
2900.2.a.g.1.2 3 1.1 even 1 trivial
2900.2.c.f.349.3 6 5.3 odd 4
2900.2.c.f.349.4 6 5.2 odd 4
5220.2.a.x.1.2 3 15.14 odd 2
9280.2.a.bk.1.2 3 40.29 even 2
9280.2.a.bw.1.2 3 40.19 odd 2