Properties

Label 9576.2.a.cn.1.5
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $1$
Dimension $5$
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] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.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: \(76.4647449756\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.401584.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 7x^{3} + 8x^{2} + 12x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 3192)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.86937\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.93275 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+2.93275 q^{5} +1.00000 q^{7} -5.73874 q^{11} +2.54964 q^{13} +2.34470 q^{17} +1.00000 q^{19} +2.32679 q^{23} +3.60104 q^{25} -6.47147 q^{29} -9.87850 q^{31} +2.93275 q^{35} -3.68734 q^{37} -10.6536 q^{41} -4.08836 q^{43} -4.29330 q^{47} +1.00000 q^{49} -6.47147 q^{53} -16.8303 q^{55} -7.07744 q^{59} -2.00000 q^{61} +7.47747 q^{65} +2.95067 q^{67} -8.98415 q^{71} +7.86551 q^{73} -5.73874 q^{77} -2.32679 q^{79} +3.29537 q^{83} +6.87643 q^{85} +11.7529 q^{89} +2.54964 q^{91} +2.93275 q^{95} -1.46335 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{5} + 5 q^{7} - 6 q^{11} - 6 q^{17} + 5 q^{19} - 10 q^{23} + 7 q^{25} - 4 q^{29} - 4 q^{31} - 2 q^{35} + 6 q^{37} - 10 q^{41} + 4 q^{43} - 2 q^{47} + 5 q^{49} - 4 q^{53} + 8 q^{55} - 12 q^{59} - 10 q^{61} - 8 q^{65} + 2 q^{67} - 30 q^{71} + 6 q^{73} - 6 q^{77} + 10 q^{79} - 14 q^{83} - 10 q^{89} - 2 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 2.93275 1.31157 0.655784 0.754949i \(-0.272338\pi\)
0.655784 + 0.754949i \(0.272338\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.73874 −1.73029 −0.865147 0.501518i \(-0.832775\pi\)
−0.865147 + 0.501518i \(0.832775\pi\)
\(12\) 0 0
\(13\) 2.54964 0.707144 0.353572 0.935407i \(-0.384967\pi\)
0.353572 + 0.935407i \(0.384967\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.34470 0.568674 0.284337 0.958724i \(-0.408227\pi\)
0.284337 + 0.958724i \(0.408227\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.32679 0.485169 0.242584 0.970130i \(-0.422005\pi\)
0.242584 + 0.970130i \(0.422005\pi\)
\(24\) 0 0
\(25\) 3.60104 0.720208
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.47147 −1.20172 −0.600861 0.799353i \(-0.705176\pi\)
−0.600861 + 0.799353i \(0.705176\pi\)
\(30\) 0 0
\(31\) −9.87850 −1.77423 −0.887115 0.461548i \(-0.847294\pi\)
−0.887115 + 0.461548i \(0.847294\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.93275 0.495726
\(36\) 0 0
\(37\) −3.68734 −0.606195 −0.303097 0.952960i \(-0.598021\pi\)
−0.303097 + 0.952960i \(0.598021\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.6536 −1.66381 −0.831905 0.554919i \(-0.812749\pi\)
−0.831905 + 0.554919i \(0.812749\pi\)
\(42\) 0 0
\(43\) −4.08836 −0.623469 −0.311735 0.950169i \(-0.600910\pi\)
−0.311735 + 0.950169i \(0.600910\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.29330 −0.626242 −0.313121 0.949713i \(-0.601375\pi\)
−0.313121 + 0.949713i \(0.601375\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.47147 −0.888925 −0.444462 0.895797i \(-0.646605\pi\)
−0.444462 + 0.895797i \(0.646605\pi\)
\(54\) 0 0
\(55\) −16.8303 −2.26940
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.07744 −0.921404 −0.460702 0.887555i \(-0.652402\pi\)
−0.460702 + 0.887555i \(0.652402\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.47747 0.927466
\(66\) 0 0
\(67\) 2.95067 0.360481 0.180241 0.983623i \(-0.442312\pi\)
0.180241 + 0.983623i \(0.442312\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.98415 −1.06622 −0.533111 0.846045i \(-0.678977\pi\)
−0.533111 + 0.846045i \(0.678977\pi\)
\(72\) 0 0
\(73\) 7.86551 0.920588 0.460294 0.887767i \(-0.347744\pi\)
0.460294 + 0.887767i \(0.347744\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.73874 −0.653990
\(78\) 0 0
\(79\) −2.32679 −0.261784 −0.130892 0.991397i \(-0.541784\pi\)
−0.130892 + 0.991397i \(0.541784\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.29537 0.361714 0.180857 0.983509i \(-0.442113\pi\)
0.180857 + 0.983509i \(0.442113\pi\)
\(84\) 0 0
\(85\) 6.87643 0.745854
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 11.7529 1.24580 0.622900 0.782301i \(-0.285954\pi\)
0.622900 + 0.782301i \(0.285954\pi\)
\(90\) 0 0
\(91\) 2.54964 0.267275
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.93275 0.300894
\(96\) 0 0
\(97\) −1.46335 −0.148580 −0.0742902 0.997237i \(-0.523669\pi\)
−0.0742902 + 0.997237i \(0.523669\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.9011 1.28370 0.641852 0.766829i \(-0.278166\pi\)
0.641852 + 0.766829i \(0.278166\pi\)
\(102\) 0 0
\(103\) −3.41195 −0.336189 −0.168095 0.985771i \(-0.553761\pi\)
−0.168095 + 0.985771i \(0.553761\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.8715 −1.63103 −0.815515 0.578736i \(-0.803546\pi\)
−0.815515 + 0.578736i \(0.803546\pi\)
\(108\) 0 0
\(109\) 2.47541 0.237101 0.118551 0.992948i \(-0.462175\pi\)
0.118551 + 0.992948i \(0.462175\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15.1250 −1.42284 −0.711422 0.702765i \(-0.751949\pi\)
−0.711422 + 0.702765i \(0.751949\pi\)
\(114\) 0 0
\(115\) 6.82390 0.636332
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.34470 0.214938
\(120\) 0 0
\(121\) 21.9331 1.99392
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.10280 −0.366965
\(126\) 0 0
\(127\) 13.2916 1.17944 0.589719 0.807609i \(-0.299239\pi\)
0.589719 + 0.807609i \(0.299239\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.39404 −0.471279 −0.235640 0.971841i \(-0.575718\pi\)
−0.235640 + 0.971841i \(0.575718\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.07744 −0.775538 −0.387769 0.921757i \(-0.626754\pi\)
−0.387769 + 0.921757i \(0.626754\pi\)
\(138\) 0 0
\(139\) 7.51330 0.637270 0.318635 0.947878i \(-0.396776\pi\)
0.318635 + 0.947878i \(0.396776\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −14.6317 −1.22357
\(144\) 0 0
\(145\) −18.9792 −1.57614
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.200018 −0.0163861 −0.00819307 0.999966i \(-0.502608\pi\)
−0.00819307 + 0.999966i \(0.502608\pi\)
\(150\) 0 0
\(151\) −19.2697 −1.56815 −0.784074 0.620667i \(-0.786862\pi\)
−0.784074 + 0.620667i \(0.786862\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −28.9712 −2.32702
\(156\) 0 0
\(157\) 17.6542 1.40896 0.704479 0.709725i \(-0.251181\pi\)
0.704479 + 0.709725i \(0.251181\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.32679 0.183377
\(162\) 0 0
\(163\) −11.5658 −0.905906 −0.452953 0.891534i \(-0.649629\pi\)
−0.452953 + 0.891534i \(0.649629\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −24.4204 −1.88971 −0.944854 0.327491i \(-0.893797\pi\)
−0.944854 + 0.327491i \(0.893797\pi\)
\(168\) 0 0
\(169\) −6.49932 −0.499948
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 20.5549 1.56276 0.781380 0.624055i \(-0.214516\pi\)
0.781380 + 0.624055i \(0.214516\pi\)
\(174\) 0 0
\(175\) 3.60104 0.272213
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.59612 0.194043 0.0970215 0.995282i \(-0.469068\pi\)
0.0970215 + 0.995282i \(0.469068\pi\)
\(180\) 0 0
\(181\) 17.7056 1.31605 0.658023 0.752998i \(-0.271393\pi\)
0.658023 + 0.752998i \(0.271393\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −10.8141 −0.795065
\(186\) 0 0
\(187\) −13.4556 −0.983973
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.69506 −0.556795 −0.278398 0.960466i \(-0.589803\pi\)
−0.278398 + 0.960466i \(0.589803\pi\)
\(192\) 0 0
\(193\) 24.1092 1.73542 0.867709 0.497072i \(-0.165592\pi\)
0.867709 + 0.497072i \(0.165592\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.3450 −1.30703 −0.653515 0.756913i \(-0.726706\pi\)
−0.653515 + 0.756913i \(0.726706\pi\)
\(198\) 0 0
\(199\) 17.4198 1.23486 0.617428 0.786627i \(-0.288175\pi\)
0.617428 + 0.786627i \(0.288175\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.47147 −0.454208
\(204\) 0 0
\(205\) −31.2443 −2.18220
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.73874 −0.396957
\(210\) 0 0
\(211\) 14.0951 0.970345 0.485173 0.874418i \(-0.338757\pi\)
0.485173 + 0.874418i \(0.338757\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.9902 −0.817722
\(216\) 0 0
\(217\) −9.87850 −0.670596
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.97815 0.402134
\(222\) 0 0
\(223\) −1.95532 −0.130938 −0.0654688 0.997855i \(-0.520854\pi\)
−0.0654688 + 0.997855i \(0.520854\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.512681 −0.0340278 −0.0170139 0.999855i \(-0.505416\pi\)
−0.0170139 + 0.999855i \(0.505416\pi\)
\(228\) 0 0
\(229\) −22.1409 −1.46311 −0.731556 0.681782i \(-0.761205\pi\)
−0.731556 + 0.681782i \(0.761205\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.2402 −0.998417 −0.499209 0.866482i \(-0.666376\pi\)
−0.499209 + 0.866482i \(0.666376\pi\)
\(234\) 0 0
\(235\) −12.5912 −0.821359
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 21.3176 1.37892 0.689459 0.724325i \(-0.257848\pi\)
0.689459 + 0.724325i \(0.257848\pi\)
\(240\) 0 0
\(241\) −21.0459 −1.35568 −0.677842 0.735207i \(-0.737085\pi\)
−0.677842 + 0.735207i \(0.737085\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.93275 0.187367
\(246\) 0 0
\(247\) 2.54964 0.162230
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.3271 0.651843 0.325921 0.945397i \(-0.394326\pi\)
0.325921 + 0.945397i \(0.394326\pi\)
\(252\) 0 0
\(253\) −13.3528 −0.839485
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.8661 1.42635 0.713175 0.700986i \(-0.247257\pi\)
0.713175 + 0.700986i \(0.247257\pi\)
\(258\) 0 0
\(259\) −3.68734 −0.229120
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.45777 0.0898899 0.0449449 0.998989i \(-0.485689\pi\)
0.0449449 + 0.998989i \(0.485689\pi\)
\(264\) 0 0
\(265\) −18.9792 −1.16588
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 26.7177 1.62900 0.814502 0.580161i \(-0.197010\pi\)
0.814502 + 0.580161i \(0.197010\pi\)
\(270\) 0 0
\(271\) 9.70916 0.589790 0.294895 0.955530i \(-0.404715\pi\)
0.294895 + 0.955530i \(0.404715\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −20.6654 −1.24617
\(276\) 0 0
\(277\) −18.2552 −1.09685 −0.548425 0.836199i \(-0.684773\pi\)
−0.548425 + 0.836199i \(0.684773\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −20.1117 −1.19976 −0.599881 0.800089i \(-0.704786\pi\)
−0.599881 + 0.800089i \(0.704786\pi\)
\(282\) 0 0
\(283\) 15.4416 0.917911 0.458955 0.888459i \(-0.348224\pi\)
0.458955 + 0.888459i \(0.348224\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10.6536 −0.628861
\(288\) 0 0
\(289\) −11.5024 −0.676610
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 31.0382 1.81327 0.906635 0.421917i \(-0.138643\pi\)
0.906635 + 0.421917i \(0.138643\pi\)
\(294\) 0 0
\(295\) −20.7564 −1.20848
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.93248 0.343084
\(300\) 0 0
\(301\) −4.08836 −0.235649
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.86551 −0.335858
\(306\) 0 0
\(307\) −19.9222 −1.13702 −0.568509 0.822677i \(-0.692480\pi\)
−0.568509 + 0.822677i \(0.692480\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 21.8800 1.24070 0.620350 0.784325i \(-0.286991\pi\)
0.620350 + 0.784325i \(0.286991\pi\)
\(312\) 0 0
\(313\) 13.0577 0.738067 0.369034 0.929416i \(-0.379689\pi\)
0.369034 + 0.929416i \(0.379689\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.05746 0.452552 0.226276 0.974063i \(-0.427345\pi\)
0.226276 + 0.974063i \(0.427345\pi\)
\(318\) 0 0
\(319\) 37.1381 2.07933
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.34470 0.130463
\(324\) 0 0
\(325\) 9.18137 0.509291
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.29330 −0.236697
\(330\) 0 0
\(331\) −13.0776 −0.718809 −0.359405 0.933182i \(-0.617020\pi\)
−0.359405 + 0.933182i \(0.617020\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.65358 0.472795
\(336\) 0 0
\(337\) −23.9966 −1.30718 −0.653588 0.756851i \(-0.726737\pi\)
−0.653588 + 0.756851i \(0.726737\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 56.6901 3.06994
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −32.1373 −1.72522 −0.862610 0.505869i \(-0.831172\pi\)
−0.862610 + 0.505869i \(0.831172\pi\)
\(348\) 0 0
\(349\) −13.8795 −0.742952 −0.371476 0.928443i \(-0.621148\pi\)
−0.371476 + 0.928443i \(0.621148\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.24190 −0.332223 −0.166111 0.986107i \(-0.553121\pi\)
−0.166111 + 0.986107i \(0.553121\pi\)
\(354\) 0 0
\(355\) −26.3483 −1.39842
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.5964 −0.717590 −0.358795 0.933416i \(-0.616812\pi\)
−0.358795 + 0.933416i \(0.616812\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 23.0676 1.20741
\(366\) 0 0
\(367\) 22.6958 1.18471 0.592356 0.805677i \(-0.298198\pi\)
0.592356 + 0.805677i \(0.298198\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.47147 −0.335982
\(372\) 0 0
\(373\) −1.23523 −0.0639576 −0.0319788 0.999489i \(-0.510181\pi\)
−0.0319788 + 0.999489i \(0.510181\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16.4999 −0.849790
\(378\) 0 0
\(379\) 13.2064 0.678365 0.339183 0.940721i \(-0.389850\pi\)
0.339183 + 0.940721i \(0.389850\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −18.1450 −0.927168 −0.463584 0.886053i \(-0.653437\pi\)
−0.463584 + 0.886053i \(0.653437\pi\)
\(384\) 0 0
\(385\) −16.8303 −0.857751
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 27.4085 1.38967 0.694833 0.719171i \(-0.255478\pi\)
0.694833 + 0.719171i \(0.255478\pi\)
\(390\) 0 0
\(391\) 5.45562 0.275903
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.82390 −0.343347
\(396\) 0 0
\(397\) −17.8972 −0.898235 −0.449117 0.893473i \(-0.648262\pi\)
−0.449117 + 0.893473i \(0.648262\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −25.9749 −1.29713 −0.648563 0.761161i \(-0.724630\pi\)
−0.648563 + 0.761161i \(0.724630\pi\)
\(402\) 0 0
\(403\) −25.1866 −1.25464
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 21.1607 1.04889
\(408\) 0 0
\(409\) 23.9223 1.18288 0.591441 0.806348i \(-0.298559\pi\)
0.591441 + 0.806348i \(0.298559\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.07744 −0.348258
\(414\) 0 0
\(415\) 9.66450 0.474412
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 36.2925 1.77301 0.886503 0.462722i \(-0.153127\pi\)
0.886503 + 0.462722i \(0.153127\pi\)
\(420\) 0 0
\(421\) −7.93103 −0.386535 −0.193267 0.981146i \(-0.561908\pi\)
−0.193267 + 0.981146i \(0.561908\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.44337 0.409564
\(426\) 0 0
\(427\) −2.00000 −0.0967868
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −22.3012 −1.07421 −0.537104 0.843516i \(-0.680482\pi\)
−0.537104 + 0.843516i \(0.680482\pi\)
\(432\) 0 0
\(433\) −3.27960 −0.157607 −0.0788037 0.996890i \(-0.525110\pi\)
−0.0788037 + 0.996890i \(0.525110\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.32679 0.111305
\(438\) 0 0
\(439\) −4.94540 −0.236031 −0.118016 0.993012i \(-0.537653\pi\)
−0.118016 + 0.993012i \(0.537653\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.3809 0.540724 0.270362 0.962759i \(-0.412857\pi\)
0.270362 + 0.962759i \(0.412857\pi\)
\(444\) 0 0
\(445\) 34.4682 1.63395
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 25.8363 1.21929 0.609645 0.792674i \(-0.291312\pi\)
0.609645 + 0.792674i \(0.291312\pi\)
\(450\) 0 0
\(451\) 61.1381 2.87888
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 7.47747 0.350549
\(456\) 0 0
\(457\) 7.47701 0.349760 0.174880 0.984590i \(-0.444046\pi\)
0.174880 + 0.984590i \(0.444046\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19.7174 −0.918330 −0.459165 0.888351i \(-0.651851\pi\)
−0.459165 + 0.888351i \(0.651851\pi\)
\(462\) 0 0
\(463\) 10.9112 0.507089 0.253544 0.967324i \(-0.418404\pi\)
0.253544 + 0.967324i \(0.418404\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 23.9693 1.10917 0.554584 0.832128i \(-0.312877\pi\)
0.554584 + 0.832128i \(0.312877\pi\)
\(468\) 0 0
\(469\) 2.95067 0.136249
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 23.4620 1.07879
\(474\) 0 0
\(475\) 3.60104 0.165227
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 28.8806 1.31959 0.659794 0.751447i \(-0.270644\pi\)
0.659794 + 0.751447i \(0.270644\pi\)
\(480\) 0 0
\(481\) −9.40139 −0.428667
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.29164 −0.194873
\(486\) 0 0
\(487\) −32.0028 −1.45019 −0.725093 0.688651i \(-0.758203\pi\)
−0.725093 + 0.688651i \(0.758203\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18.9050 0.853170 0.426585 0.904447i \(-0.359716\pi\)
0.426585 + 0.904447i \(0.359716\pi\)
\(492\) 0 0
\(493\) −15.1737 −0.683388
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.98415 −0.402994
\(498\) 0 0
\(499\) −18.5809 −0.831795 −0.415897 0.909412i \(-0.636532\pi\)
−0.415897 + 0.909412i \(0.636532\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −37.0878 −1.65366 −0.826831 0.562450i \(-0.809859\pi\)
−0.826831 + 0.562450i \(0.809859\pi\)
\(504\) 0 0
\(505\) 37.8356 1.68366
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 28.7881 1.27601 0.638004 0.770033i \(-0.279760\pi\)
0.638004 + 0.770033i \(0.279760\pi\)
\(510\) 0 0
\(511\) 7.86551 0.347950
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10.0064 −0.440935
\(516\) 0 0
\(517\) 24.6381 1.08358
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.1197 0.662405 0.331202 0.943560i \(-0.392546\pi\)
0.331202 + 0.943560i \(0.392546\pi\)
\(522\) 0 0
\(523\) 2.72009 0.118941 0.0594706 0.998230i \(-0.481059\pi\)
0.0594706 + 0.998230i \(0.481059\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.1621 −1.00896
\(528\) 0 0
\(529\) −17.5861 −0.764611
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −27.1628 −1.17655
\(534\) 0 0
\(535\) −49.4800 −2.13921
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.73874 −0.247185
\(540\) 0 0
\(541\) 27.6606 1.18922 0.594611 0.804014i \(-0.297306\pi\)
0.594611 + 0.804014i \(0.297306\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.25976 0.310974
\(546\) 0 0
\(547\) −21.6619 −0.926197 −0.463098 0.886307i \(-0.653262\pi\)
−0.463098 + 0.886307i \(0.653262\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.47147 −0.275694
\(552\) 0 0
\(553\) −2.32679 −0.0989451
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.2006 0.813557 0.406779 0.913527i \(-0.366652\pi\)
0.406779 + 0.913527i \(0.366652\pi\)
\(558\) 0 0
\(559\) −10.4239 −0.440882
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −29.4429 −1.24087 −0.620435 0.784258i \(-0.713044\pi\)
−0.620435 + 0.784258i \(0.713044\pi\)
\(564\) 0 0
\(565\) −44.3580 −1.86616
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.2954 0.557371 0.278685 0.960382i \(-0.410101\pi\)
0.278685 + 0.960382i \(0.410101\pi\)
\(570\) 0 0
\(571\) −2.34704 −0.0982206 −0.0491103 0.998793i \(-0.515639\pi\)
−0.0491103 + 0.998793i \(0.515639\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.37886 0.349423
\(576\) 0 0
\(577\) −6.17672 −0.257140 −0.128570 0.991700i \(-0.541039\pi\)
−0.128570 + 0.991700i \(0.541039\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.29537 0.136715
\(582\) 0 0
\(583\) 37.1381 1.53810
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −39.9953 −1.65078 −0.825391 0.564561i \(-0.809046\pi\)
−0.825391 + 0.564561i \(0.809046\pi\)
\(588\) 0 0
\(589\) −9.87850 −0.407036
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11.9130 −0.489207 −0.244604 0.969623i \(-0.578658\pi\)
−0.244604 + 0.969623i \(0.578658\pi\)
\(594\) 0 0
\(595\) 6.87643 0.281906
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.21793 0.335776 0.167888 0.985806i \(-0.446305\pi\)
0.167888 + 0.985806i \(0.446305\pi\)
\(600\) 0 0
\(601\) −28.8380 −1.17633 −0.588164 0.808742i \(-0.700149\pi\)
−0.588164 + 0.808742i \(0.700149\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 64.3244 2.61516
\(606\) 0 0
\(607\) −1.77960 −0.0722318 −0.0361159 0.999348i \(-0.511499\pi\)
−0.0361159 + 0.999348i \(0.511499\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.9464 −0.442843
\(612\) 0 0
\(613\) −6.09623 −0.246225 −0.123112 0.992393i \(-0.539288\pi\)
−0.123112 + 0.992393i \(0.539288\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.4740 0.421666 0.210833 0.977522i \(-0.432382\pi\)
0.210833 + 0.977522i \(0.432382\pi\)
\(618\) 0 0
\(619\) 25.0428 1.00656 0.503278 0.864124i \(-0.332127\pi\)
0.503278 + 0.864124i \(0.332127\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.7529 0.470868
\(624\) 0 0
\(625\) −30.0377 −1.20151
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.64571 −0.344727
\(630\) 0 0
\(631\) −10.9174 −0.434616 −0.217308 0.976103i \(-0.569728\pi\)
−0.217308 + 0.976103i \(0.569728\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 38.9809 1.54691
\(636\) 0 0
\(637\) 2.54964 0.101021
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −15.0870 −0.595899 −0.297949 0.954582i \(-0.596303\pi\)
−0.297949 + 0.954582i \(0.596303\pi\)
\(642\) 0 0
\(643\) −39.6029 −1.56179 −0.780893 0.624664i \(-0.785236\pi\)
−0.780893 + 0.624664i \(0.785236\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.6834 −0.459323 −0.229661 0.973271i \(-0.573762\pi\)
−0.229661 + 0.973271i \(0.573762\pi\)
\(648\) 0 0
\(649\) 40.6155 1.59430
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16.3127 0.638364 0.319182 0.947693i \(-0.396592\pi\)
0.319182 + 0.947693i \(0.396592\pi\)
\(654\) 0 0
\(655\) −15.8194 −0.618114
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −38.8573 −1.51367 −0.756833 0.653609i \(-0.773254\pi\)
−0.756833 + 0.653609i \(0.773254\pi\)
\(660\) 0 0
\(661\) −3.17497 −0.123492 −0.0617460 0.998092i \(-0.519667\pi\)
−0.0617460 + 0.998092i \(0.519667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.93275 0.113727
\(666\) 0 0
\(667\) −15.0577 −0.583038
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 11.4775 0.443083
\(672\) 0 0
\(673\) 12.9444 0.498970 0.249485 0.968379i \(-0.419739\pi\)
0.249485 + 0.968379i \(0.419739\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −46.3085 −1.77978 −0.889889 0.456176i \(-0.849219\pi\)
−0.889889 + 0.456176i \(0.849219\pi\)
\(678\) 0 0
\(679\) −1.46335 −0.0561581
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.2482 0.774774 0.387387 0.921917i \(-0.373378\pi\)
0.387387 + 0.921917i \(0.373378\pi\)
\(684\) 0 0
\(685\) −26.6219 −1.01717
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16.4999 −0.628598
\(690\) 0 0
\(691\) −0.445709 −0.0169556 −0.00847778 0.999964i \(-0.502699\pi\)
−0.00847778 + 0.999964i \(0.502699\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 22.0347 0.835822
\(696\) 0 0
\(697\) −24.9795 −0.946164
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −0.220398 −0.00832432 −0.00416216 0.999991i \(-0.501325\pi\)
−0.00416216 + 0.999991i \(0.501325\pi\)
\(702\) 0 0
\(703\) −3.68734 −0.139071
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.9011 0.485194
\(708\) 0 0
\(709\) −33.2765 −1.24972 −0.624862 0.780735i \(-0.714845\pi\)
−0.624862 + 0.780735i \(0.714845\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −22.9852 −0.860801
\(714\) 0 0
\(715\) −42.9112 −1.60479
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 25.2060 0.940026 0.470013 0.882660i \(-0.344249\pi\)
0.470013 + 0.882660i \(0.344249\pi\)
\(720\) 0 0
\(721\) −3.41195 −0.127068
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −23.3040 −0.865490
\(726\) 0 0
\(727\) 0.202702 0.00751781 0.00375891 0.999993i \(-0.498803\pi\)
0.00375891 + 0.999993i \(0.498803\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −9.58599 −0.354551
\(732\) 0 0
\(733\) 17.0647 0.630299 0.315149 0.949042i \(-0.397945\pi\)
0.315149 + 0.949042i \(0.397945\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.9331 −0.623739
\(738\) 0 0
\(739\) −0.0167085 −0.000614633 0 −0.000307316 1.00000i \(-0.500098\pi\)
−0.000307316 1.00000i \(0.500098\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.12849 0.114773 0.0573866 0.998352i \(-0.481723\pi\)
0.0573866 + 0.998352i \(0.481723\pi\)
\(744\) 0 0
\(745\) −0.586604 −0.0214915
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16.8715 −0.616471
\(750\) 0 0
\(751\) 21.2459 0.775274 0.387637 0.921812i \(-0.373291\pi\)
0.387637 + 0.921812i \(0.373291\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −56.5134 −2.05673
\(756\) 0 0
\(757\) −16.6879 −0.606533 −0.303267 0.952906i \(-0.598077\pi\)
−0.303267 + 0.952906i \(0.598077\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20.0440 −0.726595 −0.363298 0.931673i \(-0.618349\pi\)
−0.363298 + 0.931673i \(0.618349\pi\)
\(762\) 0 0
\(763\) 2.47541 0.0896158
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18.0449 −0.651565
\(768\) 0 0
\(769\) −15.4537 −0.557273 −0.278636 0.960397i \(-0.589882\pi\)
−0.278636 + 0.960397i \(0.589882\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.39591 −0.158110 −0.0790549 0.996870i \(-0.525190\pi\)
−0.0790549 + 0.996870i \(0.525190\pi\)
\(774\) 0 0
\(775\) −35.5729 −1.27782
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.6536 −0.381704
\(780\) 0 0
\(781\) 51.5577 1.84488
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 51.7754 1.84794
\(786\) 0 0
\(787\) 26.6744 0.950840 0.475420 0.879759i \(-0.342296\pi\)
0.475420 + 0.879759i \(0.342296\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.1250 −0.537785
\(792\) 0 0
\(793\) −5.09929 −0.181081
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.2641 −0.363572 −0.181786 0.983338i \(-0.558188\pi\)
−0.181786 + 0.983338i \(0.558188\pi\)
\(798\) 0 0
\(799\) −10.0665 −0.356128
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −45.1381 −1.59289
\(804\) 0 0
\(805\) 6.82390 0.240511
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8.44158 −0.296790 −0.148395 0.988928i \(-0.547411\pi\)
−0.148395 + 0.988928i \(0.547411\pi\)
\(810\) 0 0
\(811\) −34.1040 −1.19755 −0.598777 0.800916i \(-0.704347\pi\)
−0.598777 + 0.800916i \(0.704347\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −33.9197 −1.18816
\(816\) 0 0
\(817\) −4.08836 −0.143034
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −25.9352 −0.905143 −0.452572 0.891728i \(-0.649493\pi\)
−0.452572 + 0.891728i \(0.649493\pi\)
\(822\) 0 0
\(823\) −11.9116 −0.415214 −0.207607 0.978212i \(-0.566567\pi\)
−0.207607 + 0.978212i \(0.566567\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 41.2404 1.43407 0.717035 0.697038i \(-0.245499\pi\)
0.717035 + 0.697038i \(0.245499\pi\)
\(828\) 0 0
\(829\) −45.6796 −1.58652 −0.793259 0.608884i \(-0.791617\pi\)
−0.793259 + 0.608884i \(0.791617\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.34470 0.0812391
\(834\) 0 0
\(835\) −71.6191 −2.47848
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −13.0536 −0.450661 −0.225330 0.974282i \(-0.572346\pi\)
−0.225330 + 0.974282i \(0.572346\pi\)
\(840\) 0 0
\(841\) 12.8799 0.444136
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −19.0609 −0.655715
\(846\) 0 0
\(847\) 21.9331 0.753630
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −8.57965 −0.294107
\(852\) 0 0
\(853\) −7.82451 −0.267906 −0.133953 0.990988i \(-0.542767\pi\)
−0.133953 + 0.990988i \(0.542767\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0.423860 0.0144788 0.00723939 0.999974i \(-0.497696\pi\)
0.00723939 + 0.999974i \(0.497696\pi\)
\(858\) 0 0
\(859\) −21.8297 −0.744819 −0.372410 0.928068i \(-0.621468\pi\)
−0.372410 + 0.928068i \(0.621468\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 35.2885 1.20123 0.600617 0.799537i \(-0.294922\pi\)
0.600617 + 0.799537i \(0.294922\pi\)
\(864\) 0 0
\(865\) 60.2825 2.04967
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 13.3528 0.452964
\(870\) 0 0
\(871\) 7.52315 0.254912
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.10280 −0.138700
\(876\) 0 0
\(877\) 43.8267 1.47992 0.739960 0.672650i \(-0.234844\pi\)
0.739960 + 0.672650i \(0.234844\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 44.7975 1.50927 0.754633 0.656147i \(-0.227815\pi\)
0.754633 + 0.656147i \(0.227815\pi\)
\(882\) 0 0
\(883\) 57.0176 1.91879 0.959397 0.282060i \(-0.0910178\pi\)
0.959397 + 0.282060i \(0.0910178\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −16.5669 −0.556262 −0.278131 0.960543i \(-0.589715\pi\)
−0.278131 + 0.960543i \(0.589715\pi\)
\(888\) 0 0
\(889\) 13.2916 0.445785
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −4.29330 −0.143670
\(894\) 0 0
\(895\) 7.61378 0.254500
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 63.9284 2.13213
\(900\) 0 0
\(901\) −15.1737 −0.505508
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 51.9261 1.72608
\(906\) 0 0
\(907\) −33.4212 −1.10973 −0.554866 0.831940i \(-0.687231\pi\)
−0.554866 + 0.831940i \(0.687231\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.98292 0.0988284 0.0494142 0.998778i \(-0.484265\pi\)
0.0494142 + 0.998778i \(0.484265\pi\)
\(912\) 0 0
\(913\) −18.9112 −0.625871
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5.39404 −0.178127
\(918\) 0 0
\(919\) 2.91125 0.0960332 0.0480166 0.998847i \(-0.484710\pi\)
0.0480166 + 0.998847i \(0.484710\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −22.9064 −0.753973
\(924\) 0 0
\(925\) −13.2783 −0.436586
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −38.2708 −1.25563 −0.627813 0.778364i \(-0.716050\pi\)
−0.627813 + 0.778364i \(0.716050\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −39.4620 −1.29055
\(936\) 0 0
\(937\) 7.33313 0.239563 0.119782 0.992800i \(-0.461781\pi\)
0.119782 + 0.992800i \(0.461781\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 22.5846 0.736238 0.368119 0.929779i \(-0.380002\pi\)
0.368119 + 0.929779i \(0.380002\pi\)
\(942\) 0 0
\(943\) −24.7886 −0.807228
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 43.6943 1.41987 0.709937 0.704265i \(-0.248723\pi\)
0.709937 + 0.704265i \(0.248723\pi\)
\(948\) 0 0
\(949\) 20.0542 0.650988
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 13.9131 0.450690 0.225345 0.974279i \(-0.427649\pi\)
0.225345 + 0.974279i \(0.427649\pi\)
\(954\) 0 0
\(955\) −22.5677 −0.730274
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −9.07744 −0.293126
\(960\) 0 0
\(961\) 66.5847 2.14789
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 70.7063 2.27612
\(966\) 0 0
\(967\) −51.4995 −1.65611 −0.828057 0.560644i \(-0.810554\pi\)
−0.828057 + 0.560644i \(0.810554\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −17.0536 −0.547276 −0.273638 0.961833i \(-0.588227\pi\)
−0.273638 + 0.961833i \(0.588227\pi\)
\(972\) 0 0
\(973\) 7.51330 0.240865
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −45.1469 −1.44438 −0.722189 0.691696i \(-0.756864\pi\)
−0.722189 + 0.691696i \(0.756864\pi\)
\(978\) 0 0
\(979\) −67.4466 −2.15560
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 22.9655 0.732485 0.366243 0.930519i \(-0.380644\pi\)
0.366243 + 0.930519i \(0.380644\pi\)
\(984\) 0 0
\(985\) −53.8015 −1.71426
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.51275 −0.302488
\(990\) 0 0
\(991\) −11.2776 −0.358245 −0.179122 0.983827i \(-0.557326\pi\)
−0.179122 + 0.983827i \(0.557326\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 51.0880 1.61960
\(996\) 0 0
\(997\) −5.65420 −0.179070 −0.0895351 0.995984i \(-0.528538\pi\)
−0.0895351 + 0.995984i \(0.528538\pi\)
\(998\) 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 9576.2.a.cn.1.5 5
3.2 odd 2 3192.2.a.bb.1.1 5
12.11 even 2 6384.2.a.cd.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3192.2.a.bb.1.1 5 3.2 odd 2
6384.2.a.cd.1.1 5 12.11 even 2
9576.2.a.cn.1.5 5 1.1 even 1 trivial