Properties

Label 1152.2.w.b.143.5
Level $1152$
Weight $2$
Character 1152.143
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,2,Mod(143,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not 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: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 143.5
Character \(\chi\) \(=\) 1152.143
Dual form 1152.2.w.b.1007.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.352978 - 0.852163i) q^{5} +(3.43393 - 3.43393i) q^{7} +O(q^{10})\) \(q+(0.352978 - 0.852163i) q^{5} +(3.43393 - 3.43393i) q^{7} +(1.44650 - 3.49216i) q^{11} +(-0.258636 + 0.107131i) q^{13} -5.30575 q^{17} +(-2.72546 - 6.57983i) q^{19} +(-2.23882 + 2.23882i) q^{23} +(2.93394 + 2.93394i) q^{25} +(-3.16953 + 1.31286i) q^{29} +3.46749i q^{31} +(-1.71417 - 4.13837i) q^{35} +(1.27512 + 0.528171i) q^{37} +(5.28251 + 5.28251i) q^{41} +(-2.46955 - 1.02292i) q^{43} +0.423698i q^{47} -16.5838i q^{49} +(-12.5563 - 5.20097i) q^{53} +(-2.46531 - 2.46531i) q^{55} +(5.24194 + 2.17128i) q^{59} +(0.0138304 + 0.0333895i) q^{61} +0.258215i q^{65} +(9.82224 - 4.06850i) q^{67} +(-4.64969 - 4.64969i) q^{71} +(3.96752 - 3.96752i) q^{73} +(-7.02466 - 16.9590i) q^{77} +12.7319 q^{79} +(0.867335 - 0.359262i) q^{83} +(-1.87281 + 4.52137i) q^{85} +(4.82033 - 4.82033i) q^{89} +(-0.520260 + 1.25602i) q^{91} -6.56912 q^{95} +8.78058 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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
\(5\) 0.352978 0.852163i 0.157856 0.381099i −0.825087 0.565005i \(-0.808874\pi\)
0.982944 + 0.183906i \(0.0588742\pi\)
\(6\) 0 0
\(7\) 3.43393 3.43393i 1.29790 1.29790i 0.368130 0.929774i \(-0.379998\pi\)
0.929774 0.368130i \(-0.120002\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.44650 3.49216i 0.436136 1.05293i −0.541135 0.840936i \(-0.682005\pi\)
0.977272 0.211991i \(-0.0679947\pi\)
\(12\) 0 0
\(13\) −0.258636 + 0.107131i −0.0717328 + 0.0297127i −0.418261 0.908327i \(-0.637360\pi\)
0.346529 + 0.938039i \(0.387360\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.30575 −1.28683 −0.643417 0.765516i \(-0.722484\pi\)
−0.643417 + 0.765516i \(0.722484\pi\)
\(18\) 0 0
\(19\) −2.72546 6.57983i −0.625263 1.50952i −0.845447 0.534059i \(-0.820666\pi\)
0.220185 0.975458i \(-0.429334\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.23882 + 2.23882i −0.466825 + 0.466825i −0.900884 0.434059i \(-0.857081\pi\)
0.434059 + 0.900884i \(0.357081\pi\)
\(24\) 0 0
\(25\) 2.93394 + 2.93394i 0.586789 + 0.586789i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.16953 + 1.31286i −0.588568 + 0.243793i −0.657034 0.753861i \(-0.728189\pi\)
0.0684666 + 0.997653i \(0.478189\pi\)
\(30\) 0 0
\(31\) 3.46749i 0.622779i 0.950282 + 0.311390i \(0.100794\pi\)
−0.950282 + 0.311390i \(0.899206\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.71417 4.13837i −0.289748 0.699513i
\(36\) 0 0
\(37\) 1.27512 + 0.528171i 0.209628 + 0.0868308i 0.485027 0.874499i \(-0.338810\pi\)
−0.275399 + 0.961330i \(0.588810\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.28251 + 5.28251i 0.824989 + 0.824989i 0.986819 0.161830i \(-0.0517396\pi\)
−0.161830 + 0.986819i \(0.551740\pi\)
\(42\) 0 0
\(43\) −2.46955 1.02292i −0.376603 0.155994i 0.186349 0.982484i \(-0.440334\pi\)
−0.562952 + 0.826489i \(0.690334\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.423698i 0.0618027i 0.999522 + 0.0309013i \(0.00983776\pi\)
−0.999522 + 0.0309013i \(0.990162\pi\)
\(48\) 0 0
\(49\) 16.5838i 2.36911i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.5563 5.20097i −1.72474 0.714409i −0.999669 0.0257295i \(-0.991809\pi\)
−0.725066 0.688679i \(-0.758191\pi\)
\(54\) 0 0
\(55\) −2.46531 2.46531i −0.332422 0.332422i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.24194 + 2.17128i 0.682442 + 0.282677i 0.696847 0.717220i \(-0.254586\pi\)
−0.0144054 + 0.999896i \(0.504586\pi\)
\(60\) 0 0
\(61\) 0.0138304 + 0.0333895i 0.00177080 + 0.00427509i 0.924762 0.380545i \(-0.124264\pi\)
−0.922992 + 0.384820i \(0.874264\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.258215i 0.0320276i
\(66\) 0 0
\(67\) 9.82224 4.06850i 1.19998 0.497047i 0.308986 0.951067i \(-0.400010\pi\)
0.890992 + 0.454020i \(0.150010\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.64969 4.64969i −0.551817 0.551817i 0.375148 0.926965i \(-0.377592\pi\)
−0.926965 + 0.375148i \(0.877592\pi\)
\(72\) 0 0
\(73\) 3.96752 3.96752i 0.464363 0.464363i −0.435720 0.900082i \(-0.643506\pi\)
0.900082 + 0.435720i \(0.143506\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.02466 16.9590i −0.800534 1.93266i
\(78\) 0 0
\(79\) 12.7319 1.43245 0.716224 0.697870i \(-0.245869\pi\)
0.716224 + 0.697870i \(0.245869\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.867335 0.359262i 0.0952024 0.0394341i −0.334574 0.942369i \(-0.608592\pi\)
0.429776 + 0.902935i \(0.358592\pi\)
\(84\) 0 0
\(85\) −1.87281 + 4.52137i −0.203135 + 0.490411i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.82033 4.82033i 0.510954 0.510954i −0.403865 0.914819i \(-0.632333\pi\)
0.914819 + 0.403865i \(0.132333\pi\)
\(90\) 0 0
\(91\) −0.520260 + 1.25602i −0.0545381 + 0.131667i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.56912 −0.673977
\(96\) 0 0
\(97\) 8.78058 0.891532 0.445766 0.895149i \(-0.352931\pi\)
0.445766 + 0.895149i \(0.352931\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.37141 + 10.5535i −0.434972 + 1.05011i 0.542691 + 0.839933i \(0.317406\pi\)
−0.977662 + 0.210182i \(0.932594\pi\)
\(102\) 0 0
\(103\) −2.54327 + 2.54327i −0.250596 + 0.250596i −0.821215 0.570619i \(-0.806703\pi\)
0.570619 + 0.821215i \(0.306703\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.34953 3.25806i 0.130464 0.314968i −0.845126 0.534567i \(-0.820475\pi\)
0.975590 + 0.219599i \(0.0704748\pi\)
\(108\) 0 0
\(109\) 11.5904 4.80089i 1.11016 0.459842i 0.249165 0.968461i \(-0.419844\pi\)
0.860992 + 0.508619i \(0.169844\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.5004 1.55223 0.776115 0.630591i \(-0.217188\pi\)
0.776115 + 0.630591i \(0.217188\pi\)
\(114\) 0 0
\(115\) 1.11758 + 2.69809i 0.104215 + 0.251598i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −18.2196 + 18.2196i −1.67019 + 1.67019i
\(120\) 0 0
\(121\) −2.32465 2.32465i −0.211332 0.211332i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 7.79663 3.22947i 0.697352 0.288853i
\(126\) 0 0
\(127\) 9.43014i 0.836790i 0.908265 + 0.418395i \(0.137407\pi\)
−0.908265 + 0.418395i \(0.862593\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.19791 14.9631i −0.541514 1.30733i −0.923654 0.383227i \(-0.874813\pi\)
0.382140 0.924104i \(-0.375187\pi\)
\(132\) 0 0
\(133\) −31.9537 13.2357i −2.77074 1.14768i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.01737 + 5.01737i 0.428663 + 0.428663i 0.888173 0.459510i \(-0.151975\pi\)
−0.459510 + 0.888173i \(0.651975\pi\)
\(138\) 0 0
\(139\) −19.0610 7.89534i −1.61674 0.669674i −0.623083 0.782156i \(-0.714120\pi\)
−0.993654 + 0.112482i \(0.964120\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.05816i 0.0884881i
\(144\) 0 0
\(145\) 3.16437i 0.262787i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 20.8124 + 8.62076i 1.70502 + 0.706240i 0.999996 0.00294754i \(-0.000938232\pi\)
0.705019 + 0.709188i \(0.250938\pi\)
\(150\) 0 0
\(151\) −4.68070 4.68070i −0.380910 0.380910i 0.490520 0.871430i \(-0.336807\pi\)
−0.871430 + 0.490520i \(0.836807\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.95487 + 1.22395i 0.237341 + 0.0983097i
\(156\) 0 0
\(157\) 6.17384 + 14.9050i 0.492726 + 1.18955i 0.953327 + 0.301939i \(0.0976340\pi\)
−0.460601 + 0.887607i \(0.652366\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.3759i 1.21179i
\(162\) 0 0
\(163\) 2.13457 0.884169i 0.167193 0.0692534i −0.297517 0.954716i \(-0.596159\pi\)
0.464710 + 0.885463i \(0.346159\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.2052 + 14.2052i 1.09923 + 1.09923i 0.994500 + 0.104733i \(0.0333990\pi\)
0.104733 + 0.994500i \(0.466601\pi\)
\(168\) 0 0
\(169\) −9.13697 + 9.13697i −0.702844 + 0.702844i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4.53353 10.9449i −0.344678 0.832127i −0.997230 0.0743825i \(-0.976301\pi\)
0.652552 0.757744i \(-0.273699\pi\)
\(174\) 0 0
\(175\) 20.1499 1.52319
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.00945 3.73184i 0.673398 0.278931i −0.0196661 0.999807i \(-0.506260\pi\)
0.693064 + 0.720876i \(0.256260\pi\)
\(180\) 0 0
\(181\) −5.75935 + 13.9043i −0.428089 + 1.03350i 0.551804 + 0.833974i \(0.313940\pi\)
−0.979893 + 0.199524i \(0.936060\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.900176 0.900176i 0.0661823 0.0661823i
\(186\) 0 0
\(187\) −7.67477 + 18.5285i −0.561235 + 1.35494i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.18207 0.447319 0.223660 0.974667i \(-0.428200\pi\)
0.223660 + 0.974667i \(0.428200\pi\)
\(192\) 0 0
\(193\) −11.2515 −0.809899 −0.404949 0.914339i \(-0.632711\pi\)
−0.404949 + 0.914339i \(0.632711\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.59303 6.26014i 0.184746 0.446016i −0.804187 0.594376i \(-0.797399\pi\)
0.988934 + 0.148359i \(0.0473992\pi\)
\(198\) 0 0
\(199\) −8.67622 + 8.67622i −0.615041 + 0.615041i −0.944255 0.329214i \(-0.893216\pi\)
0.329214 + 0.944255i \(0.393216\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.37568 + 15.3922i −0.447485 + 1.08032i
\(204\) 0 0
\(205\) 6.36616 2.63695i 0.444632 0.184173i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −26.9202 −1.86211
\(210\) 0 0
\(211\) −3.18497 7.68919i −0.219262 0.529345i 0.775525 0.631317i \(-0.217485\pi\)
−0.994787 + 0.101971i \(0.967485\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.74339 + 1.74339i −0.118898 + 0.118898i
\(216\) 0 0
\(217\) 11.9071 + 11.9071i 0.808308 + 0.808308i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.37226 0.568409i 0.0923082 0.0382353i
\(222\) 0 0
\(223\) 12.9728i 0.868722i 0.900739 + 0.434361i \(0.143026\pi\)
−0.900739 + 0.434361i \(0.856974\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.79613 9.16468i −0.251958 0.608281i 0.746404 0.665493i \(-0.231779\pi\)
−0.998362 + 0.0572122i \(0.981779\pi\)
\(228\) 0 0
\(229\) 4.91823 + 2.03720i 0.325006 + 0.134622i 0.539220 0.842165i \(-0.318719\pi\)
−0.214214 + 0.976787i \(0.568719\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.8493 + 10.8493i 0.710759 + 0.710759i 0.966694 0.255935i \(-0.0823834\pi\)
−0.255935 + 0.966694i \(0.582383\pi\)
\(234\) 0 0
\(235\) 0.361060 + 0.149556i 0.0235529 + 0.00975594i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.69444i 0.497712i −0.968540 0.248856i \(-0.919945\pi\)
0.968540 0.248856i \(-0.0800546\pi\)
\(240\) 0 0
\(241\) 14.5669i 0.938338i −0.883108 0.469169i \(-0.844553\pi\)
0.883108 0.469169i \(-0.155447\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −14.1321 5.85370i −0.902866 0.373979i
\(246\) 0 0
\(247\) 1.40980 + 1.40980i 0.0897037 + 0.0897037i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14.1528 + 5.86227i 0.893315 + 0.370023i 0.781646 0.623722i \(-0.214380\pi\)
0.111669 + 0.993745i \(0.464380\pi\)
\(252\) 0 0
\(253\) 4.57986 + 11.0568i 0.287933 + 0.695132i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.4990i 1.21632i −0.793816 0.608159i \(-0.791908\pi\)
0.793816 0.608159i \(-0.208092\pi\)
\(258\) 0 0
\(259\) 6.19237 2.56496i 0.384775 0.159379i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.65433 9.65433i −0.595312 0.595312i 0.343750 0.939061i \(-0.388303\pi\)
−0.939061 + 0.343750i \(0.888303\pi\)
\(264\) 0 0
\(265\) −8.86416 + 8.86416i −0.544521 + 0.544521i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.95451 + 19.2039i 0.484995 + 1.17088i 0.957209 + 0.289397i \(0.0934549\pi\)
−0.472214 + 0.881484i \(0.656545\pi\)
\(270\) 0 0
\(271\) −19.1213 −1.16154 −0.580770 0.814068i \(-0.697248\pi\)
−0.580770 + 0.814068i \(0.697248\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 14.4898 6.00186i 0.873765 0.361926i
\(276\) 0 0
\(277\) −0.609964 + 1.47258i −0.0366492 + 0.0884789i −0.941144 0.338005i \(-0.890248\pi\)
0.904495 + 0.426484i \(0.140248\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.76628 8.76628i 0.522953 0.522953i −0.395509 0.918462i \(-0.629432\pi\)
0.918462 + 0.395509i \(0.129432\pi\)
\(282\) 0 0
\(283\) −7.64026 + 18.4452i −0.454166 + 1.09645i 0.516557 + 0.856253i \(0.327213\pi\)
−0.970723 + 0.240201i \(0.922787\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 36.2795 2.14151
\(288\) 0 0
\(289\) 11.1510 0.655942
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8.73727 + 21.0936i −0.510437 + 1.23230i 0.433194 + 0.901301i \(0.357387\pi\)
−0.943630 + 0.331002i \(0.892613\pi\)
\(294\) 0 0
\(295\) 3.70057 3.70057i 0.215456 0.215456i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.339193 0.818885i 0.0196160 0.0473573i
\(300\) 0 0
\(301\) −11.9929 + 4.96763i −0.691260 + 0.286329i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.0333351 0.00190876
\(306\) 0 0
\(307\) −2.29860 5.54931i −0.131188 0.316716i 0.844613 0.535378i \(-0.179831\pi\)
−0.975801 + 0.218662i \(0.929831\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.3351 12.3351i 0.699460 0.699460i −0.264834 0.964294i \(-0.585317\pi\)
0.964294 + 0.264834i \(0.0853171\pi\)
\(312\) 0 0
\(313\) 9.07712 + 9.07712i 0.513069 + 0.513069i 0.915465 0.402397i \(-0.131823\pi\)
−0.402397 + 0.915465i \(0.631823\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.7317 + 6.10208i −0.827416 + 0.342727i −0.755879 0.654711i \(-0.772790\pi\)
−0.0715366 + 0.997438i \(0.522790\pi\)
\(318\) 0 0
\(319\) 12.9676i 0.726045i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 14.4606 + 34.9110i 0.804609 + 1.94250i
\(324\) 0 0
\(325\) −1.07314 0.444509i −0.0595271 0.0246569i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.45495 + 1.45495i 0.0802139 + 0.0802139i
\(330\) 0 0
\(331\) 20.7207 + 8.58281i 1.13892 + 0.471754i 0.870802 0.491633i \(-0.163600\pi\)
0.268113 + 0.963387i \(0.413600\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.80624i 0.535772i
\(336\) 0 0
\(337\) 12.9981i 0.708052i −0.935236 0.354026i \(-0.884812\pi\)
0.935236 0.354026i \(-0.115188\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 12.1090 + 5.01573i 0.655741 + 0.271617i
\(342\) 0 0
\(343\) −32.9100 32.9100i −1.77697 1.77697i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 24.4093 + 10.1107i 1.31036 + 0.542769i 0.924990 0.379992i \(-0.124073\pi\)
0.385372 + 0.922762i \(0.374073\pi\)
\(348\) 0 0
\(349\) −3.82444 9.23301i −0.204717 0.494231i 0.787859 0.615856i \(-0.211190\pi\)
−0.992576 + 0.121624i \(0.961190\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.4035i 1.29887i 0.760418 + 0.649434i \(0.224994\pi\)
−0.760418 + 0.649434i \(0.775006\pi\)
\(354\) 0 0
\(355\) −5.60353 + 2.32106i −0.297405 + 0.123189i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.52733 6.52733i −0.344500 0.344500i 0.513556 0.858056i \(-0.328328\pi\)
−0.858056 + 0.513556i \(0.828328\pi\)
\(360\) 0 0
\(361\) −22.4311 + 22.4311i −1.18058 + 1.18058i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.98053 4.78142i −0.103666 0.250271i
\(366\) 0 0
\(367\) −19.4291 −1.01419 −0.507096 0.861889i \(-0.669281\pi\)
−0.507096 + 0.861889i \(0.669281\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −60.9771 + 25.2576i −3.16577 + 1.31131i
\(372\) 0 0
\(373\) −4.15808 + 10.0385i −0.215297 + 0.519773i −0.994222 0.107344i \(-0.965765\pi\)
0.778925 + 0.627117i \(0.215765\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.679109 0.679109i 0.0349759 0.0349759i
\(378\) 0 0
\(379\) −1.96668 + 4.74798i −0.101021 + 0.243887i −0.966307 0.257392i \(-0.917137\pi\)
0.865286 + 0.501279i \(0.167137\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6.30106 0.321969 0.160985 0.986957i \(-0.448533\pi\)
0.160985 + 0.986957i \(0.448533\pi\)
\(384\) 0 0
\(385\) −16.9314 −0.862905
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.331782 + 0.800993i −0.0168220 + 0.0406119i −0.932067 0.362285i \(-0.881997\pi\)
0.915245 + 0.402897i \(0.131997\pi\)
\(390\) 0 0
\(391\) 11.8786 11.8786i 0.600727 0.600727i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.49407 10.8496i 0.226121 0.545905i
\(396\) 0 0
\(397\) 11.2798 4.67225i 0.566118 0.234494i −0.0812209 0.996696i \(-0.525882\pi\)
0.647339 + 0.762202i \(0.275882\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.7890 −0.538777 −0.269388 0.963032i \(-0.586822\pi\)
−0.269388 + 0.963032i \(0.586822\pi\)
\(402\) 0 0
\(403\) −0.371474 0.896819i −0.0185045 0.0446737i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.68892 3.68892i 0.182853 0.182853i
\(408\) 0 0
\(409\) −0.0980818 0.0980818i −0.00484983 0.00484983i 0.704678 0.709528i \(-0.251092\pi\)
−0.709528 + 0.704678i \(0.751092\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 25.4565 10.5444i 1.25263 0.518857i
\(414\) 0 0
\(415\) 0.865923i 0.0425065i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −11.5665 27.9241i −0.565063 1.36418i −0.905673 0.423977i \(-0.860634\pi\)
0.340610 0.940205i \(-0.389366\pi\)
\(420\) 0 0
\(421\) 18.0670 + 7.48361i 0.880533 + 0.364729i 0.776703 0.629867i \(-0.216890\pi\)
0.103829 + 0.994595i \(0.466890\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −15.5668 15.5668i −0.755100 0.755100i
\(426\) 0 0
\(427\) 0.162150 + 0.0671647i 0.00784698 + 0.00325033i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.6345i 0.512245i 0.966644 + 0.256123i \(0.0824451\pi\)
−0.966644 + 0.256123i \(0.917555\pi\)
\(432\) 0 0
\(433\) 11.8688i 0.570377i 0.958471 + 0.285189i \(0.0920562\pi\)
−0.958471 + 0.285189i \(0.907944\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 20.8328 + 8.62924i 0.996569 + 0.412793i
\(438\) 0 0
\(439\) 11.2613 + 11.2613i 0.537471 + 0.537471i 0.922785 0.385314i \(-0.125907\pi\)
−0.385314 + 0.922785i \(0.625907\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −17.1370 7.09839i −0.814204 0.337255i −0.0635743 0.997977i \(-0.520250\pi\)
−0.750630 + 0.660723i \(0.770250\pi\)
\(444\) 0 0
\(445\) −2.40624 5.80918i −0.114067 0.275381i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 38.4537i 1.81474i −0.420331 0.907371i \(-0.638086\pi\)
0.420331 0.907371i \(-0.361914\pi\)
\(450\) 0 0
\(451\) 26.0885 10.8062i 1.22846 0.508845i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.886693 + 0.886693i 0.0415688 + 0.0415688i
\(456\) 0 0
\(457\) −11.6258 + 11.6258i −0.543833 + 0.543833i −0.924650 0.380817i \(-0.875643\pi\)
0.380817 + 0.924650i \(0.375643\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.95672 + 4.72395i 0.0911337 + 0.220016i 0.962874 0.269953i \(-0.0870081\pi\)
−0.871740 + 0.489969i \(0.837008\pi\)
\(462\) 0 0
\(463\) 24.2082 1.12505 0.562524 0.826781i \(-0.309830\pi\)
0.562524 + 0.826781i \(0.309830\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.35140 2.21662i 0.247633 0.102573i −0.255415 0.966832i \(-0.582212\pi\)
0.503048 + 0.864259i \(0.332212\pi\)
\(468\) 0 0
\(469\) 19.7579 47.6999i 0.912336 2.20257i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7.14442 + 7.14442i −0.328501 + 0.328501i
\(474\) 0 0
\(475\) 11.3085 27.3012i 0.518871 1.25267i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −26.4282 −1.20754 −0.603768 0.797160i \(-0.706335\pi\)
−0.603768 + 0.797160i \(0.706335\pi\)
\(480\) 0 0
\(481\) −0.386375 −0.0176172
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.09935 7.48249i 0.140734 0.339762i
\(486\) 0 0
\(487\) 9.32733 9.32733i 0.422662 0.422662i −0.463457 0.886119i \(-0.653391\pi\)
0.886119 + 0.463457i \(0.153391\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.97593 + 7.18453i −0.134302 + 0.324233i −0.976696 0.214629i \(-0.931146\pi\)
0.842394 + 0.538862i \(0.181146\pi\)
\(492\) 0 0
\(493\) 16.8168 6.96573i 0.757389 0.313721i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −31.9334 −1.43241
\(498\) 0 0
\(499\) 10.3839 + 25.0689i 0.464846 + 1.12224i 0.966384 + 0.257103i \(0.0827679\pi\)
−0.501538 + 0.865136i \(0.667232\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.53224 + 3.53224i −0.157495 + 0.157495i −0.781456 0.623961i \(-0.785522\pi\)
0.623961 + 0.781456i \(0.285522\pi\)
\(504\) 0 0
\(505\) 7.45031 + 7.45031i 0.331535 + 0.331535i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19.0074 7.87311i 0.842487 0.348969i 0.0806532 0.996742i \(-0.474299\pi\)
0.761834 + 0.647773i \(0.224299\pi\)
\(510\) 0 0
\(511\) 27.2484i 1.20540i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.26957 + 3.06500i 0.0559437 + 0.135060i
\(516\) 0 0
\(517\) 1.47962 + 0.612879i 0.0650736 + 0.0269544i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.5687 12.5687i −0.550643 0.550643i 0.375984 0.926626i \(-0.377305\pi\)
−0.926626 + 0.375984i \(0.877305\pi\)
\(522\) 0 0
\(523\) −9.66162 4.00197i −0.422473 0.174994i 0.161310 0.986904i \(-0.448428\pi\)
−0.583783 + 0.811910i \(0.698428\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.3976i 0.801414i
\(528\) 0 0
\(529\) 12.9754i 0.564148i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.93217 0.800329i −0.0836914 0.0346661i
\(534\) 0 0
\(535\) −2.30004 2.30004i −0.0994395 0.0994395i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −57.9132 23.9884i −2.49450 1.03326i
\(540\) 0 0
\(541\) −14.6046 35.2587i −0.627901 1.51589i −0.842225 0.539125i \(-0.818755\pi\)
0.214324 0.976763i \(-0.431245\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 11.5715i 0.495669i
\(546\) 0 0
\(547\) 9.22367 3.82057i 0.394376 0.163356i −0.176677 0.984269i \(-0.556535\pi\)
0.571053 + 0.820913i \(0.306535\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 17.2769 + 17.2769i 0.736019 + 0.736019i
\(552\) 0 0
\(553\) 43.7204 43.7204i 1.85918 1.85918i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.65349 + 20.8914i 0.366660 + 0.885196i 0.994293 + 0.106686i \(0.0340241\pi\)
−0.627632 + 0.778510i \(0.715976\pi\)
\(558\) 0 0
\(559\) 0.748302 0.0316498
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.53958 1.46614i 0.149175 0.0617905i −0.306847 0.951759i \(-0.599274\pi\)
0.456022 + 0.889969i \(0.349274\pi\)
\(564\) 0 0
\(565\) 5.82428 14.0611i 0.245029 0.591553i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.855711 0.855711i 0.0358733 0.0358733i −0.688943 0.724816i \(-0.741925\pi\)
0.724816 + 0.688943i \(0.241925\pi\)
\(570\) 0 0
\(571\) −4.33854 + 10.4742i −0.181562 + 0.438330i −0.988289 0.152595i \(-0.951237\pi\)
0.806726 + 0.590925i \(0.201237\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −13.1371 −0.547856
\(576\) 0 0
\(577\) −2.91000 −0.121145 −0.0605724 0.998164i \(-0.519293\pi\)
−0.0605724 + 0.998164i \(0.519293\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.74469 4.21205i 0.0723819 0.174745i
\(582\) 0 0
\(583\) −36.3253 + 36.3253i −1.50444 + 1.50444i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.1052 + 43.7099i −0.747283 + 1.80410i −0.173996 + 0.984746i \(0.555668\pi\)
−0.573287 + 0.819355i \(0.694332\pi\)
\(588\) 0 0
\(589\) 22.8155 9.45049i 0.940096 0.389401i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 30.7464 1.26260 0.631301 0.775538i \(-0.282521\pi\)
0.631301 + 0.775538i \(0.282521\pi\)
\(594\) 0 0
\(595\) 9.09496 + 21.9572i 0.372857 + 0.900157i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.3435 19.3435i 0.790354 0.790354i −0.191198 0.981552i \(-0.561237\pi\)
0.981552 + 0.191198i \(0.0612371\pi\)
\(600\) 0 0
\(601\) −28.4893 28.4893i −1.16210 1.16210i −0.984015 0.178087i \(-0.943009\pi\)
−0.178087 0.984015i \(-0.556991\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.80153 + 1.16043i −0.113899 + 0.0471783i
\(606\) 0 0
\(607\) 31.5078i 1.27886i −0.768848 0.639432i \(-0.779170\pi\)
0.768848 0.639432i \(-0.220830\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.0453910 0.109584i −0.00183632 0.00443328i
\(612\) 0 0
\(613\) −40.5414 16.7928i −1.63745 0.678254i −0.641413 0.767196i \(-0.721651\pi\)
−0.996037 + 0.0889418i \(0.971651\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.1405 14.1405i −0.569276 0.569276i 0.362650 0.931926i \(-0.381872\pi\)
−0.931926 + 0.362650i \(0.881872\pi\)
\(618\) 0 0
\(619\) 17.7763 + 7.36320i 0.714491 + 0.295952i 0.710162 0.704039i \(-0.248622\pi\)
0.00432943 + 0.999991i \(0.498622\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 33.1054i 1.32634i
\(624\) 0 0
\(625\) 12.9622i 0.518487i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.76546 2.80235i −0.269757 0.111737i
\(630\) 0 0
\(631\) 14.1654 + 14.1654i 0.563915 + 0.563915i 0.930417 0.366502i \(-0.119445\pi\)
−0.366502 + 0.930417i \(0.619445\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 8.03602 + 3.32863i 0.318900 + 0.132093i
\(636\) 0 0
\(637\) 1.77663 + 4.28917i 0.0703927 + 0.169943i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.51722i 0.138922i 0.997585 + 0.0694610i \(0.0221279\pi\)
−0.997585 + 0.0694610i \(0.977872\pi\)
\(642\) 0 0
\(643\) −28.4159 + 11.7702i −1.12061 + 0.464173i −0.864580 0.502496i \(-0.832415\pi\)
−0.256032 + 0.966668i \(0.582415\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.2793 22.2793i −0.875889 0.875889i 0.117217 0.993106i \(-0.462603\pi\)
−0.993106 + 0.117217i \(0.962603\pi\)
\(648\) 0 0
\(649\) 15.1649 15.1649i 0.595275 0.595275i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.57865 3.81119i −0.0617772 0.149143i 0.889976 0.456007i \(-0.150721\pi\)
−0.951754 + 0.306863i \(0.900721\pi\)
\(654\) 0 0
\(655\) −14.9387 −0.583704
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.2385 5.48357i 0.515699 0.213610i −0.109627 0.993973i \(-0.534966\pi\)
0.625327 + 0.780363i \(0.284966\pi\)
\(660\) 0 0
\(661\) −9.61142 + 23.2040i −0.373841 + 0.902532i 0.619251 + 0.785193i \(0.287436\pi\)
−0.993092 + 0.117339i \(0.962564\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −22.5579 + 22.5579i −0.874758 + 0.874758i
\(666\) 0 0
\(667\) 4.15674 10.0353i 0.160950 0.388567i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.136607 0.00527366
\(672\) 0 0
\(673\) −12.4509 −0.479947 −0.239974 0.970779i \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.84859 + 16.5340i −0.263213 + 0.635451i −0.999134 0.0416159i \(-0.986749\pi\)
0.735921 + 0.677067i \(0.236749\pi\)
\(678\) 0 0
\(679\) 30.1519 30.1519i 1.15712 1.15712i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.54777 + 23.0504i −0.365335 + 0.881997i 0.629166 + 0.777271i \(0.283397\pi\)
−0.994501 + 0.104726i \(0.966603\pi\)
\(684\) 0 0
\(685\) 6.04663 2.50460i 0.231030 0.0956958i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.80469 0.144947
\(690\) 0 0
\(691\) 0.714680 + 1.72539i 0.0271877 + 0.0656369i 0.936890 0.349623i \(-0.113690\pi\)
−0.909703 + 0.415260i \(0.863690\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −13.4562 + 13.4562i −0.510424 + 0.510424i
\(696\) 0 0
\(697\) −28.0277 28.0277i −1.06162 1.06162i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23.2566 + 9.63319i −0.878388 + 0.363840i −0.775872 0.630891i \(-0.782690\pi\)
−0.102517 + 0.994731i \(0.532690\pi\)
\(702\) 0 0
\(703\) 9.82957i 0.370729i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 21.2289 + 51.2512i 0.798396 + 1.92750i
\(708\) 0 0
\(709\) 37.2006 + 15.4090i 1.39710 + 0.578698i 0.948997 0.315285i \(-0.102100\pi\)
0.448102 + 0.893982i \(0.352100\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.76307 7.76307i −0.290729 0.290729i
\(714\) 0 0
\(715\) 0.901729 + 0.373508i 0.0337227 + 0.0139684i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.2965i 0.383996i 0.981395 + 0.191998i \(0.0614968\pi\)
−0.981395 + 0.191998i \(0.938503\pi\)
\(720\) 0 0
\(721\) 17.4669i 0.650500i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −13.1511 5.44737i −0.488420 0.202310i
\(726\) 0 0
\(727\) −13.6565 13.6565i −0.506493 0.506493i 0.406955 0.913448i \(-0.366591\pi\)
−0.913448 + 0.406955i \(0.866591\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 13.1028 + 5.42737i 0.484626 + 0.200739i
\(732\) 0 0
\(733\) 12.2351 + 29.5382i 0.451915 + 1.09102i 0.971593 + 0.236657i \(0.0760517\pi\)
−0.519678 + 0.854362i \(0.673948\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 40.1859i 1.48027i
\(738\) 0 0
\(739\) 5.26176 2.17949i 0.193557 0.0801739i −0.283800 0.958884i \(-0.591595\pi\)
0.477356 + 0.878710i \(0.341595\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 17.0314 + 17.0314i 0.624823 + 0.624823i 0.946761 0.321938i \(-0.104334\pi\)
−0.321938 + 0.946761i \(0.604334\pi\)
\(744\) 0 0
\(745\) 14.6926 14.6926i 0.538295 0.538295i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.55375 15.8221i −0.239469 0.578129i
\(750\) 0 0
\(751\) −5.21219 −0.190196 −0.0950978 0.995468i \(-0.530316\pi\)
−0.0950978 + 0.995468i \(0.530316\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.64090 + 2.33654i −0.205293 + 0.0850353i
\(756\) 0 0
\(757\) 5.99669 14.4773i 0.217953 0.526186i −0.776650 0.629932i \(-0.783083\pi\)
0.994604 + 0.103746i \(0.0330828\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16.7870 16.7870i 0.608528 0.608528i −0.334033 0.942561i \(-0.608410\pi\)
0.942561 + 0.334033i \(0.108410\pi\)
\(762\) 0 0
\(763\) 23.3146 56.2865i 0.844046 2.03771i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.58837 −0.0573526
\(768\) 0 0
\(769\) 33.1933 1.19698 0.598491 0.801129i \(-0.295767\pi\)
0.598491 + 0.801129i \(0.295767\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.41657 13.0767i 0.194820 0.470338i −0.796038 0.605247i \(-0.793074\pi\)
0.990858 + 0.134909i \(0.0430743\pi\)
\(774\) 0 0
\(775\) −10.1734 + 10.1734i −0.365440 + 0.365440i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.3608 49.1552i 0.729500 1.76117i
\(780\) 0 0
\(781\) −22.9632 + 9.51169i −0.821689 + 0.340355i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14.8807 0.531115
\(786\) 0 0
\(787\) −18.2278 44.0057i −0.649750 1.56864i −0.813136 0.582073i \(-0.802242\pi\)
0.163387 0.986562i \(-0.447758\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 56.6614 56.6614i 2.01465 2.01465i
\(792\) 0 0
\(793\) −0.00715408 0.00715408i −0.000254049 0.000254049i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.3377 + 13.8089i −1.18088 + 0.489138i −0.884776 0.466017i \(-0.845689\pi\)
−0.296107 + 0.955155i \(0.595689\pi\)
\(798\) 0 0
\(799\) 2.24803i 0.0795298i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8.11619 19.5942i −0.286414 0.691465i
\(804\) 0 0
\(805\) 13.1028 + 5.42734i 0.461812 + 0.191289i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −13.3585 13.3585i −0.469661 0.469661i 0.432144 0.901805i \(-0.357757\pi\)
−0.901805 + 0.432144i \(0.857757\pi\)
\(810\) 0 0
\(811\) 24.9118 + 10.3188i 0.874772 + 0.362343i 0.774467 0.632614i \(-0.218018\pi\)
0.100305 + 0.994957i \(0.468018\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.13110i 0.0746490i
\(816\) 0 0
\(817\) 19.0372i 0.666026i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 39.1686 + 16.2242i 1.36699 + 0.566228i 0.940972 0.338485i \(-0.109914\pi\)
0.426023 + 0.904712i \(0.359914\pi\)
\(822\) 0 0
\(823\) 26.6538 + 26.6538i 0.929095 + 0.929095i 0.997647 0.0685527i \(-0.0218381\pi\)
−0.0685527 + 0.997647i \(0.521838\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −25.4095 10.5250i −0.883576 0.365989i −0.105693 0.994399i \(-0.533706\pi\)
−0.777883 + 0.628410i \(0.783706\pi\)
\(828\) 0 0
\(829\) −5.57539 13.4602i −0.193641 0.467491i 0.797001 0.603979i \(-0.206419\pi\)
−0.990642 + 0.136487i \(0.956419\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 87.9894i 3.04865i
\(834\) 0 0
\(835\) 17.1193 7.09105i 0.592438 0.245396i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −20.3694 20.3694i −0.703231 0.703231i 0.261872 0.965103i \(-0.415660\pi\)
−0.965103 + 0.261872i \(0.915660\pi\)
\(840\) 0 0
\(841\) −12.1838 + 12.1838i −0.420130 + 0.420130i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4.56105 + 11.0113i 0.156905 + 0.378802i
\(846\) 0 0
\(847\) −15.9654 −0.548577
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.03723 + 1.67228i −0.138395 + 0.0573249i
\(852\) 0 0
\(853\) 2.58123 6.23163i 0.0883795 0.213367i −0.873510 0.486807i \(-0.838161\pi\)
0.961889 + 0.273440i \(0.0881615\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −11.2096 + 11.2096i −0.382911 + 0.382911i −0.872150 0.489239i \(-0.837275\pi\)
0.489239 + 0.872150i \(0.337275\pi\)
\(858\) 0 0
\(859\) 2.70400 6.52804i 0.0922594 0.222734i −0.871013 0.491260i \(-0.836537\pi\)
0.963272 + 0.268526i \(0.0865365\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −17.1544 −0.583943 −0.291972 0.956427i \(-0.594311\pi\)
−0.291972 + 0.956427i \(0.594311\pi\)
\(864\) 0 0
\(865\) −10.9271 −0.371532
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 18.4167 44.4618i 0.624743 1.50826i
\(870\) 0 0
\(871\) −2.10453 + 2.10453i −0.0713091 + 0.0713091i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 15.6833 37.8629i 0.530193 1.28000i
\(876\) 0 0
\(877\) −46.9641 + 19.4532i −1.58586 + 0.656886i −0.989329 0.145700i \(-0.953456\pi\)
−0.596535 + 0.802587i \(0.703456\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 24.1442 0.813438 0.406719 0.913553i \(-0.366673\pi\)
0.406719 + 0.913553i \(0.366673\pi\)
\(882\) 0 0
\(883\) 16.3495 + 39.4712i 0.550205 + 1.32831i 0.917325 + 0.398140i \(0.130344\pi\)
−0.367120 + 0.930174i \(0.619656\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22.4225 + 22.4225i −0.752872 + 0.752872i −0.975014 0.222142i \(-0.928695\pi\)
0.222142 + 0.975014i \(0.428695\pi\)
\(888\) 0 0
\(889\) 32.3825 + 32.3825i 1.08607 + 1.08607i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.78786 1.15477i 0.0932922 0.0386429i
\(894\) 0 0
\(895\) 8.99478i 0.300662i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.55234 10.9903i −0.151829 0.366548i
\(900\) 0 0
\(901\) 66.6204 + 27.5951i 2.21945 + 0.919325i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 9.81581 + 9.81581i 0.326289 + 0.326289i
\(906\) 0 0
\(907\) −16.7879 6.95376i −0.557431 0.230896i 0.0861382 0.996283i \(-0.472547\pi\)
−0.643570 + 0.765388i \(0.722547\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 51.4718i 1.70534i 0.522451 + 0.852669i \(0.325018\pi\)
−0.522451 + 0.852669i \(0.674982\pi\)
\(912\) 0 0
\(913\) 3.54855i 0.117440i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −72.6654 30.0990i −2.39962 0.993957i
\(918\) 0 0
\(919\) 24.8706 + 24.8706i 0.820407 + 0.820407i 0.986166 0.165760i \(-0.0530076\pi\)
−0.165760 + 0.986166i \(0.553008\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.70070 + 0.704454i 0.0559793 + 0.0231874i
\(924\) 0 0
\(925\) 2.19150 + 5.29075i 0.0720561 + 0.173959i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 10.4466i 0.342740i −0.985207 0.171370i \(-0.945181\pi\)
0.985207 0.171370i \(-0.0548194\pi\)
\(930\) 0 0
\(931\) −109.118 + 45.1984i −3.57621 + 1.48132i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 13.0803 + 13.0803i 0.427772 + 0.427772i
\(936\) 0 0
\(937\) −32.5899 + 32.5899i −1.06466 + 1.06466i −0.0669050 + 0.997759i \(0.521312\pi\)
−0.997759 + 0.0669050i \(0.978688\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 20.8677 + 50.3791i 0.680268 + 1.64231i 0.763520 + 0.645785i \(0.223470\pi\)
−0.0832512 + 0.996529i \(0.526530\pi\)
\(942\) 0 0
\(943\) −23.6531 −0.770251
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.61124 1.49582i 0.117349 0.0486077i −0.323236 0.946318i \(-0.604771\pi\)
0.440586 + 0.897711i \(0.354771\pi\)
\(948\) 0 0
\(949\) −0.601101 + 1.45119i −0.0195126 + 0.0471075i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −29.6527 + 29.6527i −0.960544 + 0.960544i −0.999251 0.0387065i \(-0.987676\pi\)
0.0387065 + 0.999251i \(0.487676\pi\)
\(954\) 0 0
\(955\) 2.18213 5.26814i 0.0706122 0.170473i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 34.4586 1.11273
\(960\) 0 0
\(961\) 18.9765 0.612146
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.97152 + 9.58810i −0.127848 + 0.308652i
\(966\) 0 0
\(967\) 15.0414 15.0414i 0.483697 0.483697i −0.422613 0.906310i \(-0.638887\pi\)
0.906310 + 0.422613i \(0.138887\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0.522995 1.26262i 0.0167837 0.0405195i −0.915266 0.402851i \(-0.868019\pi\)
0.932049 + 0.362332i \(0.118019\pi\)
\(972\) 0 0
\(973\) −92.5664 + 38.3423i −2.96754 + 1.22920i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.54082 −0.209259 −0.104630 0.994511i \(-0.533366\pi\)
−0.104630 + 0.994511i \(0.533366\pi\)
\(978\) 0 0
\(979\) −9.86076 23.8060i −0.315151 0.760843i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −11.2187 + 11.2187i −0.357820 + 0.357820i −0.863009 0.505189i \(-0.831423\pi\)
0.505189 + 0.863009i \(0.331423\pi\)
\(984\) 0 0
\(985\) −4.41938 4.41938i −0.140813 0.140813i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7.81900 3.23874i 0.248630 0.102986i
\(990\) 0 0
\(991\) 18.7152i 0.594507i −0.954799 0.297254i \(-0.903929\pi\)
0.954799 0.297254i \(-0.0960707\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.33105 + 10.4561i 0.137303 + 0.331480i
\(996\) 0 0
\(997\) −5.03956 2.08745i −0.159604 0.0661103i 0.301451 0.953482i \(-0.402529\pi\)
−0.461055 + 0.887371i \(0.652529\pi\)
\(998\) 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 1152.2.w.b.143.5 32
3.2 odd 2 1152.2.w.a.143.4 32
4.3 odd 2 288.2.w.a.251.3 yes 32
12.11 even 2 288.2.w.b.251.6 yes 32
32.13 even 8 288.2.w.b.179.6 yes 32
32.19 odd 8 1152.2.w.a.1007.4 32
96.77 odd 8 288.2.w.a.179.3 32
96.83 even 8 inner 1152.2.w.b.1007.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.w.a.179.3 32 96.77 odd 8
288.2.w.a.251.3 yes 32 4.3 odd 2
288.2.w.b.179.6 yes 32 32.13 even 8
288.2.w.b.251.6 yes 32 12.11 even 2
1152.2.w.a.143.4 32 3.2 odd 2
1152.2.w.a.1007.4 32 32.19 odd 8
1152.2.w.b.143.5 32 1.1 even 1 trivial
1152.2.w.b.1007.5 32 96.83 even 8 inner