Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.f.729.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | −0.821362 | − | 0.570408i | \(-0.806785\pi\) |
0.999773 | + | 0.0213149i | \(0.00678525\pi\) | |||||||
\(4\) | −0.618034 | − | 1.90211i | −0.309017 | − | 0.951057i | ||||
\(5\) | −2.42705 | + | 1.76336i | −1.08541 | + | 0.788597i | −0.978618 | − | 0.205685i | \(-0.934058\pi\) |
−0.106792 | + | 0.994281i | \(0.534058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.61803 | + | 1.17557i | 0.539345 | + | 0.391857i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 3.23607 | + | 2.35114i | 0.897524 | + | 0.652089i | 0.937829 | − | 0.347098i | \(-0.112833\pi\) |
−0.0403050 | + | 0.999187i | \(0.512833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.927051 | + | 2.85317i | 0.239364 | + | 0.736685i | ||||
\(16\) | −3.23607 | + | 2.35114i | −0.809017 | + | 0.587785i | ||||
\(17\) | 4.85410 | − | 3.52671i | 1.17729 | − | 0.855353i | 0.185429 | − | 0.982658i | \(-0.440633\pi\) |
0.991864 | + | 0.127304i | \(0.0406325\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.618034 | − | 1.90211i | 0.141787 | − | 0.436375i | −0.854797 | − | 0.518962i | \(-0.826318\pi\) |
0.996584 | + | 0.0825877i | \(0.0263185\pi\) | |||||||
\(20\) | 4.85410 | + | 3.52671i | 1.08541 | + | 0.788597i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23607 | − | 3.80423i | 0.247214 | − | 0.760845i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.04508 | − | 2.93893i | 0.778477 | − | 0.565597i | ||||
\(28\) | 1.61803 | − | 1.17557i | 0.305780 | − | 0.222162i | ||||
\(29\) | −1.85410 | − | 5.70634i | −0.344298 | − | 1.05964i | −0.961958 | − | 0.273196i | \(-0.911919\pi\) |
0.617660 | − | 0.786445i | \(-0.288081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04508 | − | 2.93893i | −0.726519 | − | 0.527847i | 0.161942 | − | 0.986800i | \(-0.448224\pi\) |
−0.888460 | + | 0.458954i | \(0.848224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.42705 | − | 1.76336i | −0.410246 | − | 0.298062i | ||||
\(36\) | 1.23607 | − | 3.80423i | 0.206011 | − | 0.634038i | ||||
\(37\) | 3.39919 | + | 10.4616i | 0.558823 | + | 1.71988i | 0.685628 | + | 0.727952i | \(0.259528\pi\) |
−0.126805 | + | 0.991928i | \(0.540472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.23607 | − | 2.35114i | 0.518186 | − | 0.376484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.85410 | − | 5.70634i | 0.289562 | − | 0.891180i | −0.695432 | − | 0.718592i | \(-0.744787\pi\) |
0.984994 | − | 0.172588i | \(-0.0552131\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(48\) | 1.23607 | + | 3.80423i | 0.178411 | + | 0.549093i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.85410 | − | 5.70634i | −0.259626 | − | 0.799047i | ||||
\(52\) | 2.47214 | − | 7.60845i | 0.342824 | − | 1.05510i | ||||
\(53\) | 4.85410 | + | 3.52671i | 0.666762 | + | 0.484431i | 0.868940 | − | 0.494918i | \(-0.164802\pi\) |
−0.202178 | + | 0.979349i | \(0.564802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.61803 | − | 1.17557i | −0.214314 | − | 0.155708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.78115 | − | 8.55951i | −0.362075 | − | 1.11435i | −0.951792 | − | 0.306743i | \(-0.900761\pi\) |
0.589717 | − | 0.807610i | \(-0.299239\pi\) | |||||||
\(60\) | 4.85410 | − | 3.52671i | 0.626662 | − | 0.455296i | ||||
\(61\) | 8.09017 | − | 5.87785i | 1.03584 | − | 0.752582i | 0.0663709 | − | 0.997795i | \(-0.478858\pi\) |
0.969469 | + | 0.245213i | \(0.0788579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.618034 | + | 1.90211i | −0.0778650 | + | 0.239644i | ||||
\(64\) | 6.47214 | + | 4.70228i | 0.809017 | + | 0.587785i | ||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | 0.610847 | 0.305424 | − | 0.952217i | \(-0.401202\pi\) | ||||
0.305424 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(68\) | −9.70820 | − | 7.05342i | −1.17729 | − | 0.855353i | ||||
\(69\) | 0.927051 | − | 2.85317i | 0.111604 | − | 0.343481i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.28115 | + | 5.29007i | −0.864114 | + | 0.627815i | −0.929001 | − | 0.370077i | \(-0.879331\pi\) |
0.0648872 | + | 0.997893i | \(0.479331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.618034 | + | 1.90211i | 0.0723354 | + | 0.222625i | 0.980688 | − | 0.195580i | \(-0.0626591\pi\) |
−0.908352 | + | 0.418206i | \(0.862659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.23607 | − | 2.35114i | −0.373669 | − | 0.271486i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.09017 | + | 5.87785i | 0.910215 | + | 0.661310i | 0.941069 | − | 0.338214i | \(-0.109823\pi\) |
−0.0308541 | + | 0.999524i | \(0.509823\pi\) | |||||||
\(80\) | 3.70820 | − | 11.4127i | 0.414590 | − | 1.27598i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.70820 | + | 7.05342i | −1.06561 | + | 0.774214i | −0.975119 | − | 0.221683i | \(-0.928845\pi\) |
−0.0904951 | + | 0.995897i | \(0.528845\pi\) | |||||||
\(84\) | −0.618034 | − | 1.90211i | −0.0674330 | − | 0.207538i | ||||
\(85\) | −5.56231 | + | 17.1190i | −0.603317 | + | 1.85682i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | + | 3.80423i | −0.129575 | + | 0.398791i | ||||
\(92\) | −1.85410 | − | 5.70634i | −0.193303 | − | 0.594927i | ||||
\(93\) | −4.04508 | + | 2.93893i | −0.419456 | + | 0.304752i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.85410 | + | 5.70634i | 0.190227 | + | 0.585458i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.809017 | + | 0.587785i | 0.0821432 | + | 0.0596806i | 0.628099 | − | 0.778133i | \(-0.283833\pi\) |
−0.545956 | + | 0.837814i | \(0.683833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.00000 | −0.800000 | ||||||||
\(101\) | 9.70820 | + | 7.05342i | 0.966002 | + | 0.701842i | 0.954537 | − | 0.298092i | \(-0.0963504\pi\) |
0.0114654 | + | 0.999934i | \(0.496350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23607 | − | 3.80423i | −0.121793 | − | 0.374842i | 0.871510 | − | 0.490378i | \(-0.163141\pi\) |
−0.993303 | + | 0.115536i | \(0.963141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.42705 | + | 1.76336i | −0.236856 | + | 0.172086i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.85410 | − | 5.70634i | 0.179243 | − | 0.551653i | −0.820559 | − | 0.571562i | \(-0.806338\pi\) |
0.999802 | + | 0.0199092i | \(0.00633772\pi\) | |||||||
\(108\) | −8.09017 | − | 5.87785i | −0.778477 | − | 0.565597i | ||||
\(109\) | 20.0000 | 1.91565 | 0.957826 | − | 0.287348i | \(-0.0927736\pi\) | ||||
0.957826 | + | 0.287348i | \(0.0927736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.0000 | 1.04407 | ||||||||
\(112\) | −3.23607 | − | 2.35114i | −0.305780 | − | 0.222162i | ||||
\(113\) | −0.927051 | + | 2.85317i | −0.0872096 | + | 0.268404i | −0.985145 | − | 0.171723i | \(-0.945067\pi\) |
0.897936 | + | 0.440127i | \(0.145067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.28115 | + | 5.29007i | −0.678971 | + | 0.493301i | ||||
\(116\) | −9.70820 | + | 7.05342i | −0.901384 | + | 0.654894i | ||||
\(117\) | 2.47214 | + | 7.60845i | 0.228549 | + | 0.703402i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.85410 | + | 3.52671i | 0.444975 | + | 0.323293i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.85410 | − | 3.52671i | −0.437680 | − | 0.317993i | ||||
\(124\) | −3.09017 | + | 9.51057i | −0.277505 | + | 0.854074i | ||||
\(125\) | −0.927051 | − | 2.85317i | −0.0829180 | − | 0.255195i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.61803 | + | 1.17557i | −0.143577 | + | 0.104315i | −0.657255 | − | 0.753668i | \(-0.728283\pi\) |
0.513678 | + | 0.857983i | \(0.328283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.47214 | − | 7.60845i | 0.217659 | − | 0.669887i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | 0.173422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.63525 | + | 14.2658i | −0.398939 | + | 1.22781i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.42705 | − | 1.76336i | 0.207357 | − | 0.150654i | −0.479260 | − | 0.877673i | \(-0.659095\pi\) |
0.686617 | + | 0.727019i | \(0.259095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.32624 | + | 13.3148i | 0.366947 | + | 1.12935i | 0.948753 | + | 0.316018i | \(0.102346\pi\) |
−0.581806 | + | 0.813327i | \(0.697654\pi\) | |||||||
\(140\) | −1.85410 | + | 5.70634i | −0.156700 | + | 0.482274i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.00000 | −0.666667 | ||||||||
\(145\) | 14.5623 | + | 10.5801i | 1.20933 | + | 0.878632i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.309017 | + | 0.951057i | 0.0254873 | + | 0.0784418i | ||||
\(148\) | 17.7984 | − | 12.9313i | 1.46302 | − | 1.06294i | ||||
\(149\) | 4.85410 | − | 3.52671i | 0.397664 | − | 0.288919i | −0.370925 | − | 0.928663i | \(-0.620959\pi\) |
0.768589 | + | 0.639743i | \(0.220959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.09017 | + | 9.51057i | −0.251474 | + | 0.773959i | 0.743029 | + | 0.669259i | \(0.233388\pi\) |
−0.994504 | + | 0.104700i | \(0.966612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.0000 | 1.20483 | ||||||||
\(156\) | −6.47214 | − | 4.70228i | −0.518186 | − | 0.376484i | ||||
\(157\) | −4.01722 | + | 12.3637i | −0.320609 | + | 0.986733i | 0.652775 | + | 0.757552i | \(0.273605\pi\) |
−0.973384 | + | 0.229181i | \(0.926395\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.85410 | − | 3.52671i | 0.384955 | − | 0.279686i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.927051 | + | 2.85317i | 0.0730619 | + | 0.224861i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1803 | − | 11.7557i | −1.26734 | − | 0.920778i | −0.268249 | − | 0.963350i | \(-0.586445\pi\) |
−0.999093 | + | 0.0425718i | \(0.986445\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.85410 | − | 3.52671i | −0.375622 | − | 0.272905i | 0.383917 | − | 0.923368i | \(-0.374575\pi\) |
−0.759538 | + | 0.650463i | \(0.774575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.927051 | + | 2.85317i | 0.0713116 | + | 0.219475i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.23607 | − | 2.35114i | 0.247468 | − | 0.179796i | ||||
\(172\) | −4.94427 | − | 15.2169i | −0.376997 | − | 1.16028i | ||||
\(173\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.00000 | −0.676481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.63525 | + | 14.2658i | −0.346455 | + | 1.06628i | 0.614345 | + | 0.789038i | \(0.289420\pi\) |
−0.960800 | + | 0.277242i | \(0.910580\pi\) | |||||||
\(180\) | 3.70820 | + | 11.4127i | 0.276393 | + | 0.850651i | ||||
\(181\) | 5.66312 | − | 4.11450i | 0.420936 | − | 0.305828i | −0.357078 | − | 0.934075i | \(-0.616227\pi\) |
0.778014 | + | 0.628246i | \(0.216227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.09017 | − | 9.51057i | −0.228432 | − | 0.703041i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −26.6976 | − | 19.3969i | −1.96284 | − | 1.42609i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.04508 | + | 2.93893i | 0.294237 | + | 0.213775i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.34346 | − | 25.6785i | −0.603711 | − | 1.85803i | −0.505416 | − | 0.862876i | \(-0.668661\pi\) |
−0.0982952 | − | 0.995157i | \(-0.531339\pi\) | |||||||
\(192\) | 6.47214 | − | 4.70228i | 0.467086 | − | 0.339358i | ||||
\(193\) | −11.3262 | + | 8.22899i | −0.815280 | + | 0.592336i | −0.915357 | − | 0.402644i | \(-0.868091\pi\) |
0.100076 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.70820 | + | 11.4127i | −0.265550 | + | 0.817279i | ||||
\(196\) | 1.61803 | + | 1.17557i | 0.115574 | + | 0.0839693i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.54508 | − | 4.75528i | 0.108982 | − | 0.335412i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.85410 | − | 3.52671i | 0.340691 | − | 0.247527i | ||||
\(204\) | −9.70820 | + | 7.05342i | −0.679710 | + | 0.493838i | ||||
\(205\) | 5.56231 | + | 17.1190i | 0.388488 | + | 1.19564i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.85410 | + | 3.52671i | 0.337383 | + | 0.245123i | ||||
\(208\) | −16.0000 | −1.10940 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3262 | − | 8.22899i | −0.779730 | − | 0.566507i | 0.125168 | − | 0.992136i | \(-0.460053\pi\) |
−0.904898 | + | 0.425628i | \(0.860053\pi\) | |||||||
\(212\) | 3.70820 | − | 11.4127i | 0.254680 | − | 0.783826i | ||||
\(213\) | 2.78115 | + | 8.55951i | 0.190561 | + | 0.586488i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.4164 | + | 14.1068i | −1.32419 | + | 0.962079i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.54508 | − | 4.75528i | 0.104887 | − | 0.322810i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.87132 | + | 18.0701i | −0.393173 | + | 1.21006i | 0.537203 | + | 0.843453i | \(0.319481\pi\) |
−0.930375 | + | 0.366608i | \(0.880519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.47214 | − | 4.70228i | 0.431476 | − | 0.313485i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.70820 | − | 11.4127i | −0.246122 | − | 0.757486i | −0.995450 | − | 0.0952867i | \(-0.969623\pi\) |
0.749328 | − | 0.662199i | \(-0.230377\pi\) | |||||||
\(228\) | −1.23607 | + | 3.80423i | −0.0818606 | + | 0.251941i | ||||
\(229\) | −4.04508 | − | 2.93893i | −0.267307 | − | 0.194210i | 0.446055 | − | 0.895005i | \(-0.352828\pi\) |
−0.713362 | + | 0.700796i | \(0.752828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.85410 | − | 3.52671i | −0.318003 | − | 0.231043i | 0.417320 | − | 0.908760i | \(-0.362969\pi\) |
−0.735323 | + | 0.677717i | \(0.762969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.5623 | + | 10.5801i | −0.947925 | + | 0.688708i | ||||
\(237\) | 8.09017 | − | 5.87785i | 0.525513 | − | 0.381808i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.70820 | + | 11.4127i | −0.239864 | + | 0.738225i | 0.756575 | + | 0.653907i | \(0.226871\pi\) |
−0.996439 | + | 0.0843180i | \(0.973129\pi\) | |||||||
\(240\) | −9.70820 | − | 7.05342i | −0.626662 | − | 0.455296i | ||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | −16.1803 | − | 11.7557i | −1.03584 | − | 0.752582i | ||||
\(245\) | 0.927051 | − | 2.85317i | 0.0592271 | − | 0.182282i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.47214 | − | 4.70228i | 0.411812 | − | 0.299199i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.70820 | + | 11.4127i | 0.234998 | + | 0.723249i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.28115 | + | 5.29007i | 0.459582 | + | 0.333906i | 0.793367 | − | 0.608743i | \(-0.208326\pi\) |
−0.333785 | + | 0.942649i | \(0.608326\pi\) | |||||||
\(252\) | 4.00000 | 0.251976 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.5623 | + | 10.5801i | 0.911927 | + | 0.662554i | ||||
\(256\) | 4.94427 | − | 15.2169i | 0.309017 | − | 0.951057i | ||||
\(257\) | −1.85410 | − | 5.70634i | −0.115656 | − | 0.355952i | 0.876428 | − | 0.481534i | \(-0.159920\pi\) |
−0.992083 | + | 0.125582i | \(0.959920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.89919 | + | 6.46564i | −0.552969 | + | 0.401755i | ||||
\(260\) | 7.41641 | + | 22.8254i | 0.459946 | + | 1.41557i | ||||
\(261\) | 3.70820 | − | 11.4127i | 0.229532 | − | 0.706427i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.0000 | −1.84988 | −0.924940 | − | 0.380114i | \(-0.875885\pi\) | ||||
−0.924940 | + | 0.380114i | \(0.875885\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0000 | −1.10573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.927051 | + | 2.85317i | −0.0567346 | + | 0.174611i | ||||
\(268\) | −3.09017 | − | 9.51057i | −0.188762 | − | 0.580950i | ||||
\(269\) | −24.2705 | + | 17.6336i | −1.47980 | + | 1.07514i | −0.502178 | + | 0.864764i | \(0.667468\pi\) |
−0.977621 | + | 0.210373i | \(0.932532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.94427 | − | 15.2169i | −0.300343 | − | 0.924361i | −0.981374 | − | 0.192106i | \(-0.938468\pi\) |
0.681031 | − | 0.732255i | \(-0.261532\pi\) | |||||||
\(272\) | −7.41641 | + | 22.8254i | −0.449686 | + | 1.38399i | ||||
\(273\) | 3.23607 | + | 2.35114i | 0.195856 | + | 0.142298i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | −6.47214 | − | 4.70228i | −0.388873 | − | 0.282533i | 0.376121 | − | 0.926571i | \(-0.377258\pi\) |
−0.764994 | + | 0.644038i | \(0.777258\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.09017 | − | 9.51057i | −0.185004 | − | 0.569383i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.70820 | + | 7.05342i | −0.579143 | + | 0.420772i | −0.838415 | − | 0.545032i | \(-0.816517\pi\) |
0.259272 | + | 0.965804i | \(0.416517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.88854 | − | 30.4338i | 0.587813 | − | 1.80910i | 0.000144882 | − | 1.00000i | \(-0.499954\pi\) |
0.587668 | − | 0.809102i | \(-0.300046\pi\) | |||||||
\(284\) | 14.5623 | + | 10.5801i | 0.864114 | + | 0.627815i | ||||
\(285\) | 6.00000 | 0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.87132 | − | 18.0701i | 0.345372 | − | 1.06295i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.809017 | − | 0.587785i | 0.0474254 | − | 0.0344566i | ||||
\(292\) | 3.23607 | − | 2.35114i | 0.189377 | − | 0.137590i | ||||
\(293\) | −9.27051 | − | 28.5317i | −0.541589 | − | 1.66684i | −0.728965 | − | 0.684551i | \(-0.759998\pi\) |
0.187376 | − | 0.982288i | \(-0.440002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.8435 | + | 15.8702i | 1.27178 | + | 0.923999i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.70820 | + | 7.05342i | 0.561440 | + | 0.407910i | ||||
\(300\) | −2.47214 | + | 7.60845i | −0.142729 | + | 0.439274i | ||||
\(301\) | 2.47214 | + | 7.60845i | 0.142492 | + | 0.438544i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.70820 | − | 7.05342i | 0.557722 | − | 0.405209i | ||||
\(304\) | 2.47214 | + | 7.60845i | 0.141787 | + | 0.436375i | ||||
\(305\) | −9.27051 | + | 28.5317i | −0.530828 | + | 1.63372i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3713 | − | 11.1679i | 0.868839 | − | 0.631248i | −0.0614365 | − | 0.998111i | \(-0.519568\pi\) |
0.930275 | + | 0.366863i | \(0.119568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.85410 | − | 5.70634i | −0.104467 | − | 0.321516i | ||||
\(316\) | 6.18034 | − | 19.0211i | 0.347671 | − | 1.07002i | ||||
\(317\) | −7.28115 | − | 5.29007i | −0.408950 | − | 0.297120i | 0.364226 | − | 0.931310i | \(-0.381333\pi\) |
−0.773177 | + | 0.634191i | \(0.781333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −24.0000 | −1.34164 | ||||||||
\(321\) | −4.85410 | − | 3.52671i | −0.270930 | − | 0.196842i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.70820 | − | 11.4127i | −0.206330 | − | 0.635018i | ||||
\(324\) | 1.61803 | − | 1.17557i | 0.0898908 | − | 0.0653095i | ||||
\(325\) | 12.9443 | − | 9.40456i | 0.718019 | − | 0.521671i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.18034 | − | 19.0211i | 0.341774 | − | 1.05187i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00000 | −0.0549650 | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274825 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(332\) | 19.4164 | + | 14.1068i | 1.06561 | + | 0.774214i | ||||
\(333\) | −6.79837 | + | 20.9232i | −0.372549 | + | 1.14659i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1353 | + | 8.81678i | −0.663020 | + | 0.481712i | ||||
\(336\) | −3.23607 | + | 2.35114i | −0.176542 | + | 0.128265i | ||||
\(337\) | 4.32624 | + | 13.3148i | 0.235665 | + | 0.725303i | 0.997032 | + | 0.0769821i | \(0.0245284\pi\) |
−0.761367 | + | 0.648321i | \(0.775472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.42705 | + | 1.76336i | 0.131819 | + | 0.0957723i | ||||
\(340\) | 36.0000 | 1.95237 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.78115 | + | 8.55951i | 0.149732 | + | 0.460828i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.5623 | − | 10.5801i | 0.781746 | − | 0.567971i | −0.123757 | − | 0.992313i | \(-0.539494\pi\) |
0.905502 | + | 0.424341i | \(0.139494\pi\) | |||||||
\(348\) | 3.70820 | + | 11.4127i | 0.198781 | + | 0.611784i | ||||
\(349\) | −3.09017 | + | 9.51057i | −0.165413 | + | 0.509089i | −0.999066 | − | 0.0431990i | \(-0.986245\pi\) |
0.833653 | + | 0.552288i | \(0.186245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | −0.159674 | −0.0798369 | − | 0.996808i | \(-0.525440\pi\) | ||||
−0.0798369 | + | 0.996808i | \(0.525440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.34346 | − | 25.6785i | 0.442825 | − | 1.36287i | ||||
\(356\) | 1.85410 | + | 5.70634i | 0.0982672 | + | 0.302435i | ||||
\(357\) | 4.85410 | − | 3.52671i | 0.256906 | − | 0.186653i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.41641 | + | 22.8254i | 0.391423 | + | 1.20468i | 0.931712 | + | 0.363197i | \(0.118315\pi\) |
−0.540289 | + | 0.841479i | \(0.681685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1353 | + | 8.81678i | 0.638698 | + | 0.464041i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | 0.419314 | ||||||||
\(365\) | −4.85410 | − | 3.52671i | −0.254075 | − | 0.184597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.25329 | + | 16.1680i | 0.274219 | + | 0.843961i | 0.989425 | + | 0.145046i | \(0.0463331\pi\) |
−0.715205 | + | 0.698914i | \(0.753667\pi\) | |||||||
\(368\) | −9.70820 | + | 7.05342i | −0.506075 | + | 0.367685i | ||||
\(369\) | 9.70820 | − | 7.05342i | 0.505389 | − | 0.367187i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.85410 | + | 5.70634i | −0.0962602 | + | 0.296258i | ||||
\(372\) | 8.09017 | + | 5.87785i | 0.419456 | + | 0.304752i | ||||
\(373\) | −4.00000 | −0.207112 | −0.103556 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103556 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.41641 | − | 22.8254i | 0.381964 | − | 1.17557i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.89919 | + | 6.46564i | −0.457121 | + | 0.332118i | −0.792401 | − | 0.610001i | \(-0.791169\pi\) |
0.335280 | + | 0.942118i | \(0.391169\pi\) | |||||||
\(380\) | 9.70820 | − | 7.05342i | 0.498020 | − | 0.361833i | ||||
\(381\) | 0.618034 | + | 1.90211i | 0.0316628 | + | 0.0974482i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9894 | − | 12.3435i | −0.868116 | − | 0.630723i | 0.0619651 | − | 0.998078i | \(-0.480263\pi\) |
−0.930081 | + | 0.367355i | \(0.880263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.9443 | + | 9.40456i | 0.657994 | + | 0.478061i | ||||
\(388\) | 0.618034 | − | 1.90211i | 0.0313759 | − | 0.0965652i | ||||
\(389\) | 10.1976 | + | 31.3849i | 0.517037 | + | 1.59128i | 0.779545 | + | 0.626346i | \(0.215450\pi\) |
−0.262508 | + | 0.964930i | \(0.584550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5623 | − | 10.5801i | 0.736447 | − | 0.535060i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.85410 | + | 5.70634i | −0.0935271 | + | 0.287847i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.0000 | −1.50946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.618034 | − | 1.90211i | 0.0309404 | − | 0.0952248i | ||||
\(400\) | 4.94427 | + | 15.2169i | 0.247214 | + | 0.760845i | ||||
\(401\) | 4.85410 | − | 3.52671i | 0.242402 | − | 0.176116i | −0.459951 | − | 0.887945i | \(-0.652133\pi\) |
0.702353 | + | 0.711829i | \(0.252133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.18034 | − | 19.0211i | −0.307865 | − | 0.947510i | ||||
\(404\) | 7.41641 | − | 22.8254i | 0.368980 | − | 1.13560i | ||||
\(405\) | −2.42705 | − | 1.76336i | −0.120601 | − | 0.0876219i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.3262 | − | 8.22899i | −0.560046 | − | 0.406898i | 0.271430 | − | 0.962458i | \(-0.412504\pi\) |
−0.831476 | + | 0.555561i | \(0.812504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.927051 | − | 2.85317i | −0.0457281 | − | 0.140736i | ||||
\(412\) | −6.47214 | + | 4.70228i | −0.318859 | + | 0.231665i | ||||
\(413\) | 7.28115 | − | 5.29007i | 0.358282 | − | 0.260307i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.1246 | − | 34.2380i | 0.546086 | − | 1.68068i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0000 | 0.685583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 4.85410 | + | 3.52671i | 0.236856 | + | 0.172086i | ||||
\(421\) | −3.09017 | + | 9.51057i | −0.150606 | + | 0.463517i | −0.997689 | − | 0.0679432i | \(-0.978356\pi\) |
0.847084 | + | 0.531460i | \(0.178356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.41641 | − | 22.8254i | −0.359749 | − | 1.10719i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.09017 | + | 5.87785i | 0.391511 | + | 0.284449i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.70820 | − | 7.05342i | −0.467628 | − | 0.339751i | 0.328888 | − | 0.944369i | \(-0.393326\pi\) |
−0.796516 | + | 0.604617i | \(0.793326\pi\) | |||||||
\(432\) | −6.18034 | + | 19.0211i | −0.297352 | + | 0.915155i | ||||
\(433\) | 3.39919 | + | 10.4616i | 0.163354 | + | 0.502753i | 0.998911 | − | 0.0466507i | \(-0.0148548\pi\) |
−0.835557 | + | 0.549404i | \(0.814855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.5623 | − | 10.5801i | 0.698209 | − | 0.507279i | ||||
\(436\) | −12.3607 | − | 38.0423i | −0.591969 | − | 1.82189i | ||||
\(437\) | 1.85410 | − | 5.70634i | 0.0886937 | − | 0.272971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0000 | 1.24091 | 0.620456 | − | 0.784241i | \(-0.286947\pi\) | ||||
0.620456 | + | 0.784241i | \(0.286947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.78115 | − | 8.55951i | 0.132137 | − | 0.406675i | −0.862997 | − | 0.505209i | \(-0.831415\pi\) |
0.995134 | + | 0.0985344i | \(0.0314154\pi\) | |||||||
\(444\) | −6.79837 | − | 20.9232i | −0.322637 | − | 0.992973i | ||||
\(445\) | 7.28115 | − | 5.29007i | 0.345160 | − | 0.250773i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.85410 | − | 5.70634i | −0.0876960 | − | 0.269901i | ||||
\(448\) | −2.47214 | + | 7.60845i | −0.116797 | + | 0.359466i | ||||
\(449\) | 7.28115 | + | 5.29007i | 0.343619 | + | 0.249654i | 0.746187 | − | 0.665736i | \(-0.231882\pi\) |
−0.402568 | + | 0.915390i | \(0.631882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 8.09017 | + | 5.87785i | 0.380109 | + | 0.276166i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.70820 | − | 11.4127i | −0.173843 | − | 0.535035i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.47214 | + | 4.70228i | −0.302754 | + | 0.219963i | −0.728781 | − | 0.684747i | \(-0.759913\pi\) |
0.426027 | + | 0.904710i | \(0.359913\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.27051 | − | 28.5317i | 0.432710 | − | 1.33175i | ||||
\(460\) | 14.5623 | + | 10.5801i | 0.678971 | + | 0.493301i | ||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00000 | 0.232370 | 0.116185 | − | 0.993228i | \(-0.462933\pi\) | ||||
0.116185 | + | 0.993228i | \(0.462933\pi\) | |||||||
\(464\) | 19.4164 | + | 14.1068i | 0.901384 | + | 0.654894i | ||||
\(465\) | 4.63525 | − | 14.2658i | 0.214955 | − | 0.661563i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.1353 | + | 8.81678i | −0.561553 | + | 0.407992i | −0.832027 | − | 0.554735i | \(-0.812820\pi\) |
0.270474 | + | 0.962727i | \(0.412820\pi\) | |||||||
\(468\) | 12.9443 | − | 9.40456i | 0.598349 | − | 0.434726i | ||||
\(469\) | 1.54508 | + | 4.75528i | 0.0713454 | + | 0.219579i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5172 | + | 7.64121i | 0.484608 | + | 0.352088i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.47214 | − | 4.70228i | −0.296962 | − | 0.215755i | ||||
\(476\) | 3.70820 | − | 11.4127i | 0.169965 | − | 0.523099i | ||||
\(477\) | 3.70820 | + | 11.4127i | 0.169787 | + | 0.522551i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.70820 | − | 7.05342i | 0.443579 | − | 0.322279i | −0.343476 | − | 0.939161i | \(-0.611605\pi\) |
0.787055 | + | 0.616882i | \(0.211605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.5967 | + | 41.8465i | −0.619958 | + | 1.90804i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.00000 | 0.136505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | −0.136223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.39919 | − | 10.4616i | 0.154032 | − | 0.474061i | −0.844030 | − | 0.536297i | \(-0.819823\pi\) |
0.998062 | + | 0.0622352i | \(0.0198229\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.1803 | + | 11.7557i | −0.731700 | + | 0.531611i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.27051 | − | 28.5317i | −0.418372 | − | 1.28762i | −0.909200 | − | 0.416361i | \(-0.863305\pi\) |
0.490827 | − | 0.871257i | \(-0.336695\pi\) | |||||||
\(492\) | −3.70820 | + | 11.4127i | −0.167179 | + | 0.514523i | ||||
\(493\) | −29.1246 | − | 21.1603i | −1.31171 | − | 0.953011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | −7.28115 | − | 5.29007i | −0.326604 | − | 0.237292i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.23607 | − | 3.80423i | −0.0553340 | − | 0.170301i | 0.919570 | − | 0.392926i | \(-0.128537\pi\) |
−0.974904 | + | 0.222626i | \(0.928537\pi\) | |||||||
\(500\) | −4.85410 | + | 3.52671i | −0.217082 | + | 0.157719i | ||||
\(501\) | −4.85410 | + | 3.52671i | −0.216865 | + | 0.157562i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000 | 0.133235 | ||||||||
\(508\) | 3.23607 | + | 2.35114i | 0.143577 | + | 0.104315i | ||||
\(509\) | 6.48936 | − | 19.9722i | 0.287636 | − | 0.885252i | −0.697961 | − | 0.716136i | \(-0.745909\pi\) |
0.985596 | − | 0.169115i | \(-0.0540911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.61803 | + | 1.17557i | −0.0715776 | + | 0.0520042i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.09017 | − | 9.51057i | −0.136434 | − | 0.419902i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.70820 | + | 7.05342i | 0.427795 | + | 0.310811i | ||||
\(516\) | −16.0000 | −0.704361 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.927051 | + | 2.85317i | 0.0406148 | + | 0.125000i | 0.969308 | − | 0.245849i | \(-0.0790668\pi\) |
−0.928693 | + | 0.370849i | \(0.879067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9443 | − | 9.40456i | 0.566013 | − | 0.411233i | −0.267641 | − | 0.963519i | \(-0.586244\pi\) |
0.833655 | + | 0.552286i | \(0.186244\pi\) | |||||||
\(524\) | 3.70820 | + | 11.4127i | 0.161994 | + | 0.498565i | ||||
\(525\) | 1.23607 | − | 3.80423i | 0.0539464 | − | 0.166030i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.0000 | −1.30682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.56231 | − | 17.1190i | 0.241384 | − | 0.742902i | ||||
\(532\) | −1.23607 | − | 3.80423i | −0.0535903 | − | 0.164934i | ||||
\(533\) | 19.4164 | − | 14.1068i | 0.841018 | − | 0.611035i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.56231 | + | 17.1190i | 0.240479 | + | 0.740120i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.1353 | + | 8.81678i | 0.523675 | + | 0.380472i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 30.0000 | 1.29099 | ||||||||
\(541\) | 12.9443 | + | 9.40456i | 0.556518 | + | 0.404334i | 0.830183 | − | 0.557491i | \(-0.188236\pi\) |
−0.273665 | + | 0.961825i | \(0.588236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.16312 | − | 6.65740i | −0.0928283 | − | 0.285696i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −48.5410 | + | 35.2671i | −2.07927 | + | 1.51068i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47214 | − | 7.60845i | 0.105701 | − | 0.325314i | −0.884193 | − | 0.467121i | \(-0.845291\pi\) |
0.989894 | + | 0.141807i | \(0.0452913\pi\) | |||||||
\(548\) | −4.85410 | − | 3.52671i | −0.207357 | − | 0.150654i | ||||
\(549\) | 20.0000 | 0.853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.09017 | + | 9.51057i | −0.131407 | + | 0.404430i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.6976 | + | 19.3969i | −1.13325 | + | 0.823353i | ||||
\(556\) | 22.6525 | − | 16.4580i | 0.960679 | − | 0.697974i | ||||
\(557\) | 9.27051 | + | 28.5317i | 0.392804 | + | 1.20893i | 0.930659 | + | 0.365889i | \(0.119235\pi\) |
−0.537854 | + | 0.843038i | \(0.680765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.8885 | + | 18.8091i | 1.09497 | + | 0.795541i | ||||
\(560\) | 12.0000 | 0.507093 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.1246 | − | 21.1603i | −1.22746 | − | 0.891799i | −0.230759 | − | 0.973011i | \(-0.574121\pi\) |
−0.996697 | + | 0.0812119i | \(0.974121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.78115 | − | 8.55951i | −0.117004 | − | 0.360101i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.809017 | + | 0.587785i | −0.0339755 | + | 0.0246847i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.56231 | + | 17.1190i | −0.233184 | + | 0.717667i | 0.764173 | + | 0.645011i | \(0.223147\pi\) |
−0.997357 | + | 0.0726553i | \(0.976853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.0000 | −1.12794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.70820 | − | 11.4127i | 0.154643 | − | 0.475942i | ||||
\(576\) | 4.94427 | + | 15.2169i | 0.206011 | + | 0.634038i | ||||
\(577\) | −8.89919 | + | 6.46564i | −0.370478 | + | 0.269168i | −0.757409 | − | 0.652941i | \(-0.773535\pi\) |
0.386931 | + | 0.922109i | \(0.373535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.32624 | + | 13.3148i | 0.179792 | + | 0.553344i | ||||
\(580\) | 11.1246 | − | 34.2380i | 0.461924 | − | 1.42166i | ||||
\(581\) | −9.70820 | − | 7.05342i | −0.402764 | − | 0.292625i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.4164 | − | 14.1068i | −0.802770 | − | 0.583246i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.70820 | + | 11.4127i | 0.153054 | + | 0.471052i | 0.997959 | − | 0.0638654i | \(-0.0203428\pi\) |
−0.844905 | + | 0.534917i | \(0.820343\pi\) | |||||||
\(588\) | 1.61803 | − | 1.17557i | 0.0667266 | − | 0.0484797i | ||||
\(589\) | −8.09017 | + | 5.87785i | −0.333350 | + | 0.242193i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.56231 | − | 17.1190i | 0.228803 | − | 0.704182i | ||||
\(592\) | −35.5967 | − | 25.8626i | −1.46302 | − | 1.06294i | ||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0000 | −0.737928 | ||||||||
\(596\) | −9.70820 | − | 7.05342i | −0.397664 | − | 0.288919i | ||||
\(597\) | −4.94427 | + | 15.2169i | −0.202356 | + | 0.622786i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.47214 | + | 7.60845i | 0.100841 | + | 0.310355i | 0.988732 | − | 0.149698i | \(-0.0478302\pi\) |
−0.887891 | + | 0.460053i | \(0.847830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.09017 | + | 5.87785i | 0.329457 | + | 0.239365i | ||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3262 | − | 8.22899i | −0.459718 | − | 0.334005i | 0.333703 | − | 0.942678i | \(-0.391702\pi\) |
−0.793421 | + | 0.608674i | \(0.791702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.85410 | − | 5.70634i | −0.0751320 | − | 0.231233i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.41641 | − | 22.8254i | −0.299791 | − | 0.922660i | ||||
\(613\) | −4.94427 | + | 15.2169i | −0.199697 | + | 0.614605i | 0.800192 | + | 0.599744i | \(0.204731\pi\) |
−0.999890 | + | 0.0148615i | \(0.995269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.0000 | 0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.87132 | + | 18.0701i | −0.235988 | + | 0.726298i | 0.761000 | + | 0.648751i | \(0.224709\pi\) |
−0.996989 | + | 0.0775461i | \(0.975291\pi\) | |||||||
\(620\) | −9.27051 | − | 28.5317i | −0.372313 | − | 1.14586i | ||||
\(621\) | 12.1353 | − | 8.81678i | 0.486971 | − | 0.353805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.927051 | − | 2.85317i | −0.0371415 | − | 0.114310i | ||||
\(624\) | −4.94427 | + | 15.2169i | −0.197929 | + | 0.609164i | ||||
\(625\) | 23.4615 | + | 17.0458i | 0.938460 | + | 0.681831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.0000 | 1.03751 | ||||||||
\(629\) | 53.3951 | + | 38.7938i | 2.12900 | + | 1.54681i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.39919 | + | 10.4616i | 0.135319 | + | 0.416471i | 0.995640 | − | 0.0932836i | \(-0.0297363\pi\) |
−0.860320 | + | 0.509754i | \(0.829736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.3262 | + | 8.22899i | −0.450178 | + | 0.327073i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.85410 | − | 5.70634i | 0.0735778 | − | 0.226449i | ||||
\(636\) | −9.70820 | − | 7.05342i | −0.384955 | − | 0.279686i | ||||
\(637\) | −4.00000 | −0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.0000 | −0.712069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.63525 | − | 14.2658i | 0.183082 | − | 0.563467i | −0.816828 | − | 0.576881i | \(-0.804270\pi\) |
0.999910 | + | 0.0134135i | \(0.00426978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.6418 | − | 28.8015i | 1.56332 | − | 1.13582i | 0.630102 | − | 0.776513i | \(-0.283013\pi\) |
0.933219 | − | 0.359307i | \(-0.116987\pi\) | |||||||
\(644\) | 4.85410 | − | 3.52671i | 0.191278 | − | 0.138972i | ||||
\(645\) | 7.41641 | + | 22.8254i | 0.292021 | + | 0.898748i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.6976 | + | 19.3969i | 1.04959 | + | 0.762571i | 0.972134 | − | 0.234424i | \(-0.0753206\pi\) |
0.0774551 | + | 0.996996i | \(0.475321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.04508 | − | 2.93893i | −0.158539 | − | 0.115186i | ||||
\(652\) | −12.3607 | + | 38.0423i | −0.484082 | + | 1.48985i | ||||
\(653\) | 12.0517 | + | 37.0912i | 0.471618 | + | 1.45149i | 0.850465 | + | 0.526032i | \(0.176321\pi\) |
−0.378847 | + | 0.925459i | \(0.623679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5623 | − | 10.5801i | 0.568996 | − | 0.413400i | ||||
\(656\) | 7.41641 | + | 22.8254i | 0.289562 | + | 0.891180i | ||||
\(657\) | −1.23607 | + | 3.80423i | −0.0482236 | + | 0.148417i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.0000 | 1.16863 | 0.584317 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584317 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.0000 | −1.90588 | −0.952940 | − | 0.303160i | \(-0.901958\pi\) | ||||
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.41641 | − | 22.8254i | 0.288029 | − | 0.886463i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.85410 | + | 3.52671i | −0.188234 | + | 0.136760i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.56231 | − | 17.1190i | −0.215373 | − | 0.662851i | ||||
\(668\) | −3.70820 | + | 11.4127i | −0.143475 | + | 0.441570i | ||||
\(669\) | 15.3713 | + | 11.1679i | 0.594290 | + | 0.431777i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6525 | + | 16.4580i | 0.873189 | + | 0.634409i | 0.931441 | − | 0.363893i | \(-0.118553\pi\) |
−0.0582519 | + | 0.998302i | \(0.518553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.18034 | − | 19.0211i | −0.237881 | − | 0.732124i | ||||
\(676\) | 4.85410 | − | 3.52671i | 0.186696 | − | 0.135643i | ||||
\(677\) | 14.5623 | − | 10.5801i | 0.559675 | − | 0.406628i | −0.271665 | − | 0.962392i | \(-0.587574\pi\) |
0.831340 | + | 0.555764i | \(0.187574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.309017 | + | 0.951057i | −0.0118590 | + | 0.0364982i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | −6.47214 | − | 4.70228i | −0.247468 | − | 0.179796i | ||||
\(685\) | −2.78115 | + | 8.55951i | −0.106262 | + | 0.327042i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.04508 | + | 2.93893i | −0.154330 | + | 0.112127i | ||||
\(688\) | −25.8885 | + | 18.8091i | −0.986991 | + | 0.717091i | ||||
\(689\) | 7.41641 | + | 22.8254i | 0.282543 | + | 0.869577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.3156 | − | 20.5725i | −1.07718 | − | 0.782614i | −0.0999876 | − | 0.994989i | \(-0.531880\pi\) |
−0.977188 | + | 0.212375i | \(0.931880\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.9787 | − | 24.6870i | −1.28889 | − | 0.936431i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1246 | − | 34.2380i | −0.421375 | − | 1.29686i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.85410 | + | 3.52671i | −0.183599 | + | 0.133392i | ||||
\(700\) | −2.47214 | − | 7.60845i | −0.0934380 | − | 0.287572i | ||||
\(701\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.0000 | 0.829746 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.70820 | + | 11.4127i | −0.139461 | + | 0.429218i | ||||
\(708\) | 5.56231 | + | 17.1190i | 0.209044 | + | 0.643372i | ||||
\(709\) | 0.809017 | − | 0.587785i | 0.0303833 | − | 0.0220747i | −0.572490 | − | 0.819912i | \(-0.694022\pi\) |
0.602873 | + | 0.797837i | \(0.294022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.18034 | + | 19.0211i | 0.231781 | + | 0.713348i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.1353 | − | 8.81678i | −0.454469 | − | 0.330191i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30.0000 | 1.12115 | ||||||||
\(717\) | 9.70820 | + | 7.05342i | 0.362560 | + | 0.263415i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0517 | − | 37.0912i | −0.449451 | − | 1.38327i | −0.877528 | − | 0.479526i | \(-0.840809\pi\) |
0.428076 | − | 0.903743i | \(-0.359191\pi\) | |||||||
\(720\) | 19.4164 | − | 14.1068i | 0.723607 | − | 0.525731i | ||||
\(721\) | 3.23607 | − | 2.35114i | 0.120517 | − | 0.0875611i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.65248 | + | 26.6296i | −0.321789 | + | 0.990365i | ||||
\(724\) | −11.3262 | − | 8.22899i | −0.420936 | − | 0.305828i | ||||
\(725\) | −24.0000 | −0.891338 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0000 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.01722 | − | 12.3637i | 0.148786 | − | 0.457916i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.8328 | − | 28.2137i | 1.43628 | − | 1.04352i | ||||
\(732\) | −16.1803 | + | 11.7557i | −0.598043 | + | 0.434503i | ||||
\(733\) | −1.23607 | − | 3.80423i | −0.0456552 | − | 0.140512i | 0.925630 | − | 0.378429i | \(-0.123536\pi\) |
−0.971286 | + | 0.237917i | \(0.923536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.42705 | − | 1.76336i | −0.0895231 | − | 0.0650424i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.5066 | + | 19.9847i | 1.01185 | + | 0.735149i | 0.964595 | − | 0.263734i | \(-0.0849541\pi\) |
0.0472504 | + | 0.998883i | \(0.484954\pi\) | |||||||
\(740\) | −20.3951 | + | 62.7697i | −0.749740 | + | 2.30746i | ||||
\(741\) | −2.47214 | − | 7.60845i | −0.0908162 | − | 0.279503i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4164 | + | 14.1068i | −0.712319 | + | 0.517530i | −0.883921 | − | 0.467636i | \(-0.845106\pi\) |
0.171602 | + | 0.985166i | \(0.445106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.56231 | + | 17.1190i | −0.203787 | + | 0.627192i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.0000 | −0.878114 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | 0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.57953 | + | 29.4828i | −0.349562 | + | 1.07584i | 0.609534 | + | 0.792760i | \(0.291357\pi\) |
−0.959096 | + | 0.283081i | \(0.908643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.28115 | − | 5.29007i | 0.265340 | − | 0.192781i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.27051 | − | 28.5317i | −0.337388 | − | 1.03837i | ||||
\(756\) | 3.09017 | − | 9.51057i | 0.112388 | − | 0.345896i | ||||
\(757\) | −30.7426 | − | 22.3358i | −1.11736 | − | 0.811810i | −0.133554 | − | 0.991042i | \(-0.542639\pi\) |
−0.983807 | + | 0.179232i | \(0.942639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.8328 | − | 28.2137i | −1.40769 | − | 1.02275i | −0.993653 | − | 0.112485i | \(-0.964119\pi\) |
−0.414035 | − | 0.910261i | \(-0.635881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.18034 | + | 19.0211i | 0.223743 | + | 0.688611i | ||||
\(764\) | −43.6869 | + | 31.7404i | −1.58054 | + | 1.14833i | ||||
\(765\) | −29.1246 | + | 21.1603i | −1.05300 | + | 0.765051i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1246 | − | 34.2380i | 0.401686 | − | 1.23626i | ||||
\(768\) | −12.9443 | − | 9.40456i | −0.467086 | − | 0.339358i | ||||
\(769\) | −40.0000 | −1.44244 | −0.721218 | − | 0.692708i | \(-0.756418\pi\) | ||||
−0.721218 | + | 0.692708i | \(0.756418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 22.6525 | + | 16.4580i | 0.815280 | + | 0.592336i | ||||
\(773\) | −1.85410 | + | 5.70634i | −0.0666874 | + | 0.205243i | −0.978847 | − | 0.204591i | \(-0.934413\pi\) |
0.912160 | + | 0.409834i | \(0.134413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.1803 | + | 11.7557i | −0.581215 | + | 0.422277i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.39919 | + | 10.4616i | 0.121945 | + | 0.375309i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.70820 | − | 7.05342i | −0.347833 | − | 0.252715i | ||||
\(780\) | 24.0000 | 0.859338 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.2705 | − | 17.6336i | −0.867357 | − | 0.630172i | ||||
\(784\) | 1.23607 | − | 3.80423i | 0.0441453 | − | 0.135865i | ||||
\(785\) | −12.0517 | − | 37.0912i | −0.430142 | − | 1.32384i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4508 | + | 29.3893i | −1.44192 | + | 1.04761i | −0.454280 | + | 0.890859i | \(0.650103\pi\) |
−0.987638 | + | 0.156755i | \(0.949897\pi\) | |||||||
\(788\) | −11.1246 | − | 34.2380i | −0.396298 | − | 1.21968i | ||||
\(789\) | −9.27051 | + | 28.5317i | −0.330039 | + | 1.01576i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.00000 | −0.106668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000 | 1.42044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.56231 | + | 17.1190i | −0.197275 | + | 0.607149i | ||||
\(796\) | 9.88854 | + | 30.4338i | 0.350490 | + | 1.07870i | ||||
\(797\) | 16.9894 | − | 12.3435i | 0.601794 | − | 0.437229i | −0.244721 | − | 0.969593i | \(-0.578696\pi\) |
0.846515 | + | 0.532365i | \(0.178696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.85410 | − | 3.52671i | −0.171511 | − | 0.124610i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | −7.28115 | − | 5.29007i | −0.256627 | − | 0.186450i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.27051 | + | 28.5317i | 0.326337 | + | 1.00436i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.2705 | + | 17.6336i | −0.853306 | + | 0.619963i | −0.926055 | − | 0.377387i | \(-0.876823\pi\) |
0.0727498 | + | 0.997350i | \(0.476823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.618034 | − | 1.90211i | 0.0217021 | − | 0.0667922i | −0.939619 | − | 0.342223i | \(-0.888820\pi\) |
0.961321 | + | 0.275430i | \(0.0888203\pi\) | |||||||
\(812\) | −9.70820 | − | 7.05342i | −0.340691 | − | 0.247527i | ||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 60.0000 | 2.10171 | ||||||||
\(816\) | 19.4164 | + | 14.1068i | 0.679710 | + | 0.493838i | ||||
\(817\) | 4.94427 | − | 15.2169i | 0.172978 | − | 0.532372i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.47214 | + | 4.70228i | −0.226155 | + | 0.164311i | ||||
\(820\) | 29.1246 | − | 21.1603i | 1.01708 | − | 0.738949i | ||||
\(821\) | 5.56231 | + | 17.1190i | 0.194126 | + | 0.597458i | 0.999986 | + | 0.00535152i | \(0.00170345\pi\) |
−0.805860 | + | 0.592106i | \(0.798297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.6074 | − | 13.5191i | −0.648613 | − | 0.471245i | 0.214186 | − | 0.976793i | \(-0.431290\pi\) |
−0.862798 | + | 0.505548i | \(0.831290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.1246 | − | 21.1603i | −1.01276 | − | 0.735815i | −0.0479754 | − | 0.998849i | \(-0.515277\pi\) |
−0.964787 | + | 0.263034i | \(0.915277\pi\) | |||||||
\(828\) | 3.70820 | − | 11.4127i | 0.128869 | − | 0.396618i | ||||
\(829\) | −7.72542 | − | 23.7764i | −0.268315 | − | 0.825789i | −0.990911 | − | 0.134518i | \(-0.957051\pi\) |
0.722596 | − | 0.691271i | \(-0.242949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.47214 | + | 4.70228i | −0.224516 | + | 0.163120i | ||||
\(832\) | 9.88854 | + | 30.4338i | 0.342824 | + | 1.05510i | ||||
\(833\) | −1.85410 | + | 5.70634i | −0.0642408 | + | 0.197713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | 0.622916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.0000 | −0.864126 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.63525 | + | 14.2658i | −0.160027 | + | 0.492512i | −0.998635 | − | 0.0522225i | \(-0.983369\pi\) |
0.838609 | + | 0.544734i | \(0.183369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.66312 | + | 4.11450i | −0.195280 | + | 0.141879i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.70820 | + | 11.4127i | 0.127717 | + | 0.393074i | ||||
\(844\) | −8.65248 | + | 26.6296i | −0.297831 | + | 0.916628i | ||||
\(845\) | −7.28115 | − | 5.29007i | −0.250479 | − | 0.181984i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.0000 | −0.824163 | ||||||||
\(849\) | −25.8885 | − | 18.8091i | −0.888493 | − | 0.645528i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1976 | + | 31.3849i | 0.349568 | + | 1.07586i | ||||
\(852\) | 14.5623 | − | 10.5801i | 0.498896 | − | 0.362469i | ||||
\(853\) | 8.09017 | − | 5.87785i | 0.277002 | − | 0.201254i | −0.440607 | − | 0.897700i | \(-0.645237\pi\) |
0.717609 | + | 0.696446i | \(0.245237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.70820 | + | 11.4127i | −0.126818 | + | 0.390305i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.0000 | −0.409912 | −0.204956 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204956 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0000 | −0.443554 | −0.221777 | − | 0.975097i | \(-0.571186\pi\) | ||||
−0.221777 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(860\) | 38.8328 | + | 28.2137i | 1.32419 | + | 0.962079i | ||||
\(861\) | 1.85410 | − | 5.70634i | 0.0631876 | − | 0.194472i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.70820 | − | 7.05342i | 0.330471 | − | 0.240101i | −0.410159 | − | 0.912014i | \(-0.634527\pi\) |
0.740630 | + | 0.671913i | \(0.234527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.3713 | − | 11.1679i | −0.522037 | − | 0.379282i | ||||
\(868\) | −10.0000 | −0.339422 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1803 | + | 11.7557i | 0.548250 | + | 0.398327i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.618034 | + | 1.90211i | 0.0209173 | + | 0.0643768i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.42705 | − | 1.76336i | 0.0820493 | − | 0.0596123i | ||||
\(876\) | −1.23607 | − | 3.80423i | −0.0417629 | − | 0.128533i | ||||
\(877\) | −6.79837 | + | 20.9232i | −0.229565 | + | 0.706528i | 0.768231 | + | 0.640172i | \(0.221137\pi\) |
−0.997796 | + | 0.0663553i | \(0.978863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.0000 | −1.01187 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.00000 | −0.303218 | −0.151609 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151609 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.18034 | − | 19.0211i | 0.207985 | − | 0.640112i | −0.791593 | − | 0.611049i | \(-0.790748\pi\) |
0.999578 | − | 0.0290628i | \(-0.00925227\pi\) | |||||||
\(884\) | −14.8328 | − | 45.6507i | −0.498882 | − | 1.53540i | ||||
\(885\) | 21.8435 | − | 15.8702i | 0.734260 | − | 0.533471i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9787 | − | 39.9444i | −0.435783 | − | 1.34120i | −0.892283 | − | 0.451477i | \(-0.850897\pi\) |
0.456500 | − | 0.889723i | \(-0.349103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.61803 | − | 1.17557i | −0.0542671 | − | 0.0394274i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38.0000 | 1.27233 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.9058 | − | 42.7975i | −0.464818 | − | 1.43056i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.70820 | − | 7.05342i | 0.324147 | − | 0.235507i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.27051 | + | 28.5317i | −0.309189 | + | 0.951585i | ||||
\(900\) | −12.9443 | − | 9.40456i | −0.431476 | − | 0.313485i | ||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.48936 | + | 19.9722i | −0.215714 | + | 0.663898i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.47214 | + | 4.70228i | −0.214904 | + | 0.156137i | −0.690030 | − | 0.723781i | \(-0.742403\pi\) |
0.475126 | + | 0.879918i | \(0.342403\pi\) | |||||||
\(908\) | −19.4164 | + | 14.1068i | −0.644356 | + | 0.468152i | ||||
\(909\) | 7.41641 | + | 22.8254i | 0.245987 | + | 0.757069i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.8328 | − | 28.2137i | −1.28659 | − | 0.934761i | −0.286858 | − | 0.957973i | \(-0.592611\pi\) |
−0.999731 | + | 0.0232118i | \(0.992611\pi\) | |||||||
\(912\) | 8.00000 | 0.264906 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.2705 | + | 17.6336i | 0.802358 | + | 0.582947i | ||||
\(916\) | −3.09017 | + | 9.51057i | −0.102102 | + | 0.314238i | ||||
\(917\) | −1.85410 | − | 5.70634i | −0.0612278 | − | 0.188440i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9443 | − | 9.40456i | 0.426992 | − | 0.310228i | −0.353453 | − | 0.935452i | \(-0.614993\pi\) |
0.780445 | + | 0.625224i | \(0.214993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.18034 | − | 19.0211i | 0.203649 | − | 0.626768i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.0000 | −1.18495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.0000 | 1.44671 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.47214 | − | 7.60845i | 0.0811956 | − | 0.249894i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5623 | + | 10.5801i | −0.477774 | + | 0.347123i | −0.800463 | − | 0.599382i | \(-0.795413\pi\) |
0.322689 | + | 0.946505i | \(0.395413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.618034 | + | 1.90211i | 0.0202552 | + | 0.0623392i | ||||
\(932\) | −3.70820 | + | 11.4127i | −0.121466 | + | 0.373835i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1803 | − | 11.7557i | −0.528589 | − | 0.384042i | 0.291241 | − | 0.956650i | \(-0.405932\pi\) |
−0.819830 | + | 0.572608i | \(0.805932\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.87132 | − | 18.0701i | −0.191603 | − | 0.589695i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.5623 | + | 10.5801i | −0.474718 | + | 0.344903i | −0.799277 | − | 0.600963i | \(-0.794784\pi\) |
0.324559 | + | 0.945865i | \(0.394784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.56231 | − | 17.1190i | 0.181134 | − | 0.557472i | ||||
\(944\) | 29.1246 | + | 21.1603i | 0.947925 | + | 0.688708i | ||||
\(945\) | −15.0000 | −0.487950 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.0000 | −0.877382 | −0.438691 | − | 0.898638i | \(-0.644558\pi\) | ||||
−0.438691 | + | 0.898638i | \(0.644558\pi\) | |||||||
\(948\) | −16.1803 | − | 11.7557i | −0.525513 | − | 0.381808i | ||||
\(949\) | −2.47214 | + | 7.60845i | −0.0802489 | + | 0.246981i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.28115 | + | 5.29007i | −0.236108 | + | 0.171542i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.1246 | − | 34.2380i | −0.360362 | − | 1.10908i | −0.952835 | − | 0.303489i | \(-0.901849\pi\) |
0.592473 | − | 0.805590i | \(-0.298151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65.5304 | + | 47.6106i | 2.12051 | + | 1.54064i | ||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.42705 | + | 1.76336i | 0.0783736 | + | 0.0569417i | ||||
\(960\) | −7.41641 | + | 22.8254i | −0.239364 | + | 0.736685i | ||||
\(961\) | −1.85410 | − | 5.70634i | −0.0598097 | − | 0.184075i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.70820 | − | 7.05342i | 0.312842 | − | 0.227293i | ||||
\(964\) | 17.3050 | + | 53.2592i | 0.557355 | + | 1.71536i | ||||
\(965\) | 12.9787 | − | 39.9444i | 0.417800 | − | 1.28585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0000 | 0.450210 | 0.225105 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225105 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | −0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0517 | + | 37.0912i | −0.386756 | + | 1.19031i | 0.548442 | + | 0.836189i | \(0.315221\pi\) |
−0.935198 | + | 0.354125i | \(0.884779\pi\) | |||||||
\(972\) | −9.88854 | − | 30.4338i | −0.317175 | − | 0.976165i | ||||
\(973\) | −11.3262 | + | 8.22899i | −0.363103 | + | 0.263809i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.94427 | − | 15.2169i | −0.158343 | − | 0.487331i | ||||
\(976\) | −12.3607 | + | 38.0423i | −0.395656 | + | 1.21770i | ||||
\(977\) | −7.28115 | − | 5.29007i | −0.232945 | − | 0.169244i | 0.465190 | − | 0.885211i | \(-0.345986\pi\) |
−0.698134 | + | 0.715967i | \(0.745986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 32.3607 | + | 23.5114i | 1.03320 | + | 0.750662i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.1976 | + | 31.3849i | 0.325252 | + | 1.00102i | 0.971327 | + | 0.237748i | \(0.0764092\pi\) |
−0.646075 | + | 0.763274i | \(0.723591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.6869 | + | 31.7404i | −1.39198 | + | 1.01133i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.9443 | − | 9.40456i | −0.411812 | − | 0.299199i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.309017 | + | 0.951057i | −0.00980636 | + | 0.0301809i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.8328 | − | 28.2137i | 1.23108 | − | 0.894434i | ||||
\(996\) | 19.4164 | − | 14.1068i | 0.615232 | − | 0.446993i | ||||
\(997\) | −8.65248 | − | 26.6296i | −0.274027 | − | 0.843367i | −0.989475 | − | 0.144702i | \(-0.953778\pi\) |
0.715449 | − | 0.698665i | \(-0.246222\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.4959 | + | 32.3282i | 1.40779 | + | 1.02282i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 847.2.f.f.323.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.g.148.1 | 4 | |||
11.3 | even | 5 | inner | 847.2.f.f.729.1 | 4 | ||
11.4 | even | 5 | inner | 847.2.f.f.372.1 | 4 | ||
11.5 | even | 5 | 77.2.a.b.1.1 | ✓ | 1 | ||
11.6 | odd | 10 | 847.2.a.c.1.1 | 1 | |||
11.7 | odd | 10 | 847.2.f.g.372.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.g.729.1 | 4 | |||
11.9 | even | 5 | inner | 847.2.f.f.148.1 | 4 | ||
11.10 | odd | 2 | 847.2.f.g.323.1 | 4 | |||
33.5 | odd | 10 | 693.2.a.b.1.1 | 1 | |||
33.17 | even | 10 | 7623.2.a.i.1.1 | 1 | |||
44.27 | odd | 10 | 1232.2.a.d.1.1 | 1 | |||
55.27 | odd | 20 | 1925.2.b.g.1849.1 | 2 | |||
55.38 | odd | 20 | 1925.2.b.g.1849.2 | 2 | |||
55.49 | even | 10 | 1925.2.a.f.1.1 | 1 | |||
77.5 | odd | 30 | 539.2.e.e.67.1 | 2 | |||
77.6 | even | 10 | 5929.2.a.d.1.1 | 1 | |||
77.16 | even | 15 | 539.2.e.d.67.1 | 2 | |||
77.27 | odd | 10 | 539.2.a.b.1.1 | 1 | |||
77.38 | odd | 30 | 539.2.e.e.177.1 | 2 | |||
77.60 | even | 15 | 539.2.e.d.177.1 | 2 | |||
88.5 | even | 10 | 4928.2.a.i.1.1 | 1 | |||
88.27 | odd | 10 | 4928.2.a.x.1.1 | 1 | |||
231.104 | even | 10 | 4851.2.a.k.1.1 | 1 | |||
308.27 | even | 10 | 8624.2.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.b.1.1 | ✓ | 1 | 11.5 | even | 5 | ||
539.2.a.b.1.1 | 1 | 77.27 | odd | 10 | |||
539.2.e.d.67.1 | 2 | 77.16 | even | 15 | |||
539.2.e.d.177.1 | 2 | 77.60 | even | 15 | |||
539.2.e.e.67.1 | 2 | 77.5 | odd | 30 | |||
539.2.e.e.177.1 | 2 | 77.38 | odd | 30 | |||
693.2.a.b.1.1 | 1 | 33.5 | odd | 10 | |||
847.2.a.c.1.1 | 1 | 11.6 | odd | 10 | |||
847.2.f.f.148.1 | 4 | 11.9 | even | 5 | inner | ||
847.2.f.f.323.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.f.372.1 | 4 | 11.4 | even | 5 | inner | ||
847.2.f.f.729.1 | 4 | 11.3 | even | 5 | inner | ||
847.2.f.g.148.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.g.323.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.g.372.1 | 4 | 11.7 | odd | 10 | |||
847.2.f.g.729.1 | 4 | 11.8 | odd | 10 | |||
1232.2.a.d.1.1 | 1 | 44.27 | odd | 10 | |||
1925.2.a.f.1.1 | 1 | 55.49 | even | 10 | |||
1925.2.b.g.1849.1 | 2 | 55.27 | odd | 20 | |||
1925.2.b.g.1849.2 | 2 | 55.38 | odd | 20 | |||
4851.2.a.k.1.1 | 1 | 231.104 | even | 10 | |||
4928.2.a.i.1.1 | 1 | 88.5 | even | 10 | |||
4928.2.a.x.1.1 | 1 | 88.27 | odd | 10 | |||
5929.2.a.d.1.1 | 1 | 77.6 | even | 10 | |||
7623.2.a.i.1.1 | 1 | 33.17 | even | 10 | |||
8624.2.a.s.1.1 | 1 | 308.27 | even | 10 |