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 | 729.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.g.323.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | 0.999773 | − | 0.0213149i | \(-0.00678525\pi\) |
−0.821362 | + | 0.570408i | \(0.806785\pi\) | |||||||
\(4\) | −0.618034 | + | 1.90211i | −0.309017 | + | 0.951057i | ||||
\(5\) | −2.42705 | − | 1.76336i | −1.08541 | − | 0.788597i | −0.106792 | − | 0.994281i | \(-0.534058\pi\) |
−0.978618 | + | 0.205685i | \(0.934058\pi\) | |||||||
\(6\) | 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 | \(-0.887167\pi\) |
0.0403050 | + | 0.999187i | \(0.487167\pi\) | |||||||
\(14\) | 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 | \(-0.559367\pi\) |
−0.991864 | + | 0.127304i | \(0.959367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.618034 | − | 1.90211i | −0.141787 | − | 0.436375i | 0.854797 | − | 0.518962i | \(-0.173682\pi\) |
−0.996584 | + | 0.0825877i | \(0.973682\pi\) | |||||||
\(20\) | 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 | −0.617660 | − | 0.786445i | \(-0.711919\pi\) |
0.961958 | − | 0.273196i | \(-0.0880806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04508 | + | 2.93893i | −0.726519 | + | 0.527847i | −0.888460 | − | 0.458954i | \(-0.848224\pi\) |
0.161942 | + | 0.986800i | \(0.448224\pi\) | |||||||
\(32\) | 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 | −0.126805 | − | 0.991928i | \(-0.540472\pi\) |
0.685628 | − | 0.727952i | \(-0.259528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.23607 | − | 2.35114i | −0.518186 | − | 0.376484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.85410 | − | 5.70634i | −0.289562 | − | 0.891180i | −0.984994 | − | 0.172588i | \(-0.944787\pi\) |
0.695432 | − | 0.718592i | \(-0.255213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(48\) | 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 | −0.202178 | − | 0.979349i | \(-0.564802\pi\) |
0.868940 | + | 0.494918i | \(0.164802\pi\) | |||||||
\(54\) | 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 | 0.589717 | + | 0.807610i | \(0.299239\pi\) |
−0.951792 | + | 0.306743i | \(0.900761\pi\) | |||||||
\(60\) | 4.85410 | + | 3.52671i | 0.626662 | + | 0.455296i | ||||
\(61\) | −8.09017 | − | 5.87785i | −1.03584 | − | 0.752582i | −0.0663709 | − | 0.997795i | \(-0.521142\pi\) |
−0.969469 | + | 0.245213i | \(0.921142\pi\) | |||||||
\(62\) | 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 | 0.0648872 | − | 0.997893i | \(-0.479331\pi\) |
−0.929001 | + | 0.370077i | \(0.879331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.618034 | + | 1.90211i | −0.0723354 | + | 0.222625i | −0.980688 | − | 0.195580i | \(-0.937341\pi\) |
0.908352 | + | 0.418206i | \(0.137341\pi\) | |||||||
\(74\) | 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 | \(-0.890177\pi\) |
0.0308541 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(80\) | 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 | \(-0.0711551\pi\) |
0.0904951 | + | 0.995897i | \(0.471155\pi\) | |||||||
\(84\) | 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 | −0.545956 | − | 0.837814i | \(-0.683833\pi\) |
0.628099 | + | 0.778133i | \(0.283833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.00000 | −0.800000 | ||||||||
\(101\) | −9.70820 | + | 7.05342i | −0.966002 | + | 0.701842i | −0.954537 | − | 0.298092i | \(-0.903650\pi\) |
−0.0114654 | + | 0.999934i | \(0.503650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23607 | + | 3.80423i | −0.121793 | + | 0.374842i | −0.993303 | − | 0.115536i | \(-0.963141\pi\) |
0.871510 | + | 0.490378i | \(0.163141\pi\) | |||||||
\(104\) | 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 | \(-0.193662\pi\) |
−0.999802 | + | 0.0199092i | \(0.993662\pi\) | |||||||
\(108\) | −8.09017 | + | 5.87785i | −0.778477 | + | 0.565597i | ||||
\(109\) | −20.0000 | −1.91565 | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 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 | 0.897936 | − | 0.440127i | \(-0.145067\pi\) |
−0.985145 | + | 0.171723i | \(0.945067\pi\) | |||||||
\(114\) | 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 | \(-0.271717\pi\) |
−0.513678 | + | 0.857983i | \(0.671717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.47214 | − | 7.60845i | −0.217659 | − | 0.669887i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 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 | 0.686617 | − | 0.727019i | \(-0.259095\pi\) |
−0.479260 | + | 0.877673i | \(0.659095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.32624 | + | 13.3148i | −0.366947 | + | 1.12935i | 0.581806 | + | 0.813327i | \(0.302346\pi\) |
−0.948753 | + | 0.316018i | \(0.897654\pi\) | |||||||
\(140\) | 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 | \(-0.379041\pi\) |
−0.768589 | + | 0.639743i | \(0.779041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.09017 | + | 9.51057i | 0.251474 | + | 0.773959i | 0.994504 | + | 0.104700i | \(0.0333882\pi\) |
−0.743029 | + | 0.669259i | \(0.766612\pi\) | |||||||
\(152\) | 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 | −0.973384 | − | 0.229181i | \(-0.926395\pi\) |
0.652775 | − | 0.757552i | \(-0.273605\pi\) | |||||||
\(158\) | 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 | −0.999093 | − | 0.0425718i | \(-0.986445\pi\) |
−0.268249 | + | 0.963350i | \(0.586445\pi\) | |||||||
\(164\) | 12.0000 | 0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.85410 | − | 3.52671i | 0.375622 | − | 0.272905i | −0.383917 | − | 0.923368i | \(-0.625425\pi\) |
0.759538 | + | 0.650463i | \(0.225425\pi\) | |||||||
\(168\) | 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 | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(174\) | 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 | −0.960800 | − | 0.277242i | \(-0.910580\pi\) |
0.614345 | − | 0.789038i | \(-0.289420\pi\) | |||||||
\(180\) | 3.70820 | − | 11.4127i | 0.276393 | − | 0.850651i | ||||
\(181\) | 5.66312 | + | 4.11450i | 0.420936 | + | 0.305828i | 0.778014 | − | 0.628246i | \(-0.216227\pi\) |
−0.357078 | + | 0.934075i | \(0.616227\pi\) | |||||||
\(182\) | 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 | −0.0982952 | + | 0.995157i | \(0.531339\pi\) |
−0.505416 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(192\) | 6.47214 | + | 4.70228i | 0.467086 | + | 0.339358i | ||||
\(193\) | 11.3262 | + | 8.22899i | 0.815280 | + | 0.592336i | 0.915357 | − | 0.402644i | \(-0.131909\pi\) |
−0.100076 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(194\) | 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 | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 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 | \(-0.539947\pi\) |
0.904898 | + | 0.425628i | \(0.139947\pi\) | |||||||
\(212\) | 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 | −0.930375 | − | 0.366608i | \(-0.880519\pi\) |
0.537203 | − | 0.843453i | \(-0.319481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.47214 | + | 4.70228i | 0.431476 | + | 0.313485i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.70820 | − | 11.4127i | 0.246122 | − | 0.757486i | −0.749328 | − | 0.662199i | \(-0.769623\pi\) |
0.995450 | − | 0.0952867i | \(-0.0303768\pi\) | |||||||
\(228\) | 1.23607 | + | 3.80423i | 0.0818606 | + | 0.251941i | ||||
\(229\) | −4.04508 | + | 2.93893i | −0.267307 | + | 0.194210i | −0.713362 | − | 0.700796i | \(-0.752828\pi\) |
0.446055 | + | 0.895005i | \(0.352828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.85410 | − | 3.52671i | 0.318003 | − | 0.231043i | −0.417320 | − | 0.908760i | \(-0.637031\pi\) |
0.735323 | + | 0.677717i | \(0.237031\pi\) | |||||||
\(234\) | 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 | 0.996439 | + | 0.0843180i | \(0.0268712\pi\) |
−0.756575 | + | 0.653907i | \(0.773129\pi\) | |||||||
\(240\) | −9.70820 | + | 7.05342i | −0.626662 | + | 0.455296i | ||||
\(241\) | 28.0000 | 1.80364 | 0.901819 | − | 0.432113i | \(-0.142232\pi\) | ||||
0.901819 | + | 0.432113i | \(0.142232\pi\) | |||||||
\(242\) | 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 | −0.333785 | − | 0.942649i | \(-0.608326\pi\) |
0.793367 | + | 0.608743i | \(0.208326\pi\) | |||||||
\(252\) | −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 | −0.992083 | − | 0.125582i | \(-0.959920\pi\) |
0.876428 | + | 0.481534i | \(0.159920\pi\) | |||||||
\(258\) | 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 | \(-0.124115\pi\) | ||||
0.924940 | + | 0.380114i | \(0.124115\pi\) | |||||||
\(264\) | 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 | −0.977621 | − | 0.210373i | \(-0.932532\pi\) |
−0.502178 | − | 0.864764i | \(-0.667468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.94427 | − | 15.2169i | 0.300343 | − | 0.924361i | −0.681031 | − | 0.732255i | \(-0.738468\pi\) |
0.981374 | − | 0.192106i | \(-0.0615319\pi\) | |||||||
\(272\) | 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 | \(-0.622742\pi\) |
0.764994 | + | 0.644038i | \(0.222742\pi\) | |||||||
\(278\) | 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 | \(-0.183483\pi\) |
−0.259272 | + | 0.965804i | \(0.583483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.88854 | − | 30.4338i | −0.587813 | − | 1.80910i | −0.587668 | − | 0.809102i | \(-0.699954\pi\) |
−0.000144882 | − | 1.00000i | \(-0.500046\pi\) | |||||||
\(284\) | 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 | −0.187376 | − | 0.982288i | \(-0.559998\pi\) |
0.728965 | − | 0.684551i | \(-0.240002\pi\) | |||||||
\(294\) | 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 | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3713 | + | 11.1679i | 0.868839 | + | 0.631248i | 0.930275 | − | 0.366863i | \(-0.119568\pi\) |
−0.0614365 | + | 0.998111i | \(0.519568\pi\) | |||||||
\(314\) | 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 | −0.773177 | − | 0.634191i | \(-0.781333\pi\) |
0.364226 | + | 0.931310i | \(0.381333\pi\) | |||||||
\(318\) | 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 | 0.761367 | + | 0.648321i | \(0.224528\pi\) |
−0.997032 | + | 0.0769821i | \(0.975472\pi\) | |||||||
\(338\) | 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 | \(-0.460506\pi\) |
−0.905502 | + | 0.424341i | \(0.860506\pi\) | |||||||
\(348\) | −3.70820 | + | 11.4127i | −0.198781 | + | 0.611784i | ||||
\(349\) | 3.09017 | + | 9.51057i | 0.165413 | + | 0.509089i | 0.999066 | − | 0.0431990i | \(-0.0137549\pi\) |
−0.833653 | + | 0.552288i | \(0.813755\pi\) | |||||||
\(350\) | 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 | 0.540289 | + | 0.841479i | \(0.318315\pi\) |
−0.931712 | + | 0.363197i | \(0.881685\pi\) | |||||||
\(360\) | 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 | −0.715205 | − | 0.698914i | \(-0.753667\pi\) |
0.989425 | − | 0.145046i | \(-0.0463331\pi\) | |||||||
\(368\) | −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 | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 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 | 0.335280 | − | 0.942118i | \(-0.391169\pi\) |
−0.792401 | + | 0.610001i | \(0.791169\pi\) | |||||||
\(380\) | −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 | −0.930081 | − | 0.367355i | \(-0.880263\pi\) |
0.0619651 | + | 0.998078i | \(0.480263\pi\) | |||||||
\(384\) | 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 | −0.262508 | − | 0.964930i | \(-0.584550\pi\) |
0.779545 | − | 0.626346i | \(-0.215450\pi\) | |||||||
\(390\) | 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 | 0.702353 | − | 0.711829i | \(-0.252133\pi\) |
−0.459951 | + | 0.887945i | \(0.652133\pi\) | |||||||
\(402\) | 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 | \(-0.587496\pi\) |
0.831476 | + | 0.555561i | \(0.187496\pi\) | |||||||
\(410\) | 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 | 0.847084 | − | 0.531460i | \(-0.178356\pi\) |
−0.997689 | + | 0.0679432i | \(0.978356\pi\) | |||||||
\(422\) | 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 | \(-0.606674\pi\) |
0.796516 | + | 0.604617i | \(0.206674\pi\) | |||||||
\(432\) | −6.18034 | − | 19.0211i | −0.297352 | − | 0.915155i | ||||
\(433\) | 3.39919 | − | 10.4616i | 0.163354 | − | 0.502753i | −0.835557 | − | 0.549404i | \(-0.814855\pi\) |
0.998911 | + | 0.0466507i | \(0.0148548\pi\) | |||||||
\(434\) | 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 | \(-0.713053\pi\) | ||||
−0.620456 | + | 0.784241i | \(0.713053\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.78115 | + | 8.55951i | 0.132137 | + | 0.406675i | 0.995134 | − | 0.0985344i | \(-0.0314154\pi\) |
−0.862997 | + | 0.505209i | \(0.831415\pi\) | |||||||
\(444\) | −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 | −0.402568 | − | 0.915390i | \(-0.631882\pi\) |
0.746187 | + | 0.665736i | \(0.231882\pi\) | |||||||
\(450\) | 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 | \(-0.240087\pi\) |
−0.426027 | + | 0.904710i | \(0.640087\pi\) | |||||||
\(458\) | 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 | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 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 | 0.270474 | − | 0.962727i | \(-0.412820\pi\) |
−0.832027 | + | 0.554735i | \(0.812820\pi\) | |||||||
\(468\) | −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 | \(-0.388395\pi\) |
−0.787055 | + | 0.616882i | \(0.788395\pi\) | |||||||
\(480\) | 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 | 0.998062 | − | 0.0622352i | \(-0.0198229\pi\) |
−0.844030 | + | 0.536297i | \(0.819823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.1803 | − | 11.7557i | −0.731700 | − | 0.531611i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.27051 | − | 28.5317i | 0.418372 | − | 1.28762i | −0.490827 | − | 0.871257i | \(-0.663305\pi\) |
0.909200 | − | 0.416361i | \(-0.136695\pi\) | |||||||
\(492\) | 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 | −0.974904 | − | 0.222626i | \(-0.928537\pi\) |
0.919570 | + | 0.392926i | \(0.128537\pi\) | |||||||
\(500\) | −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 | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(504\) | 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 | 0.985596 | + | 0.169115i | \(0.0540911\pi\) |
−0.697961 | + | 0.716136i | \(0.745909\pi\) | |||||||
\(510\) | 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 | −0.928693 | − | 0.370849i | \(-0.879067\pi\) |
0.969308 | + | 0.245849i | \(0.0790668\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9443 | − | 9.40456i | −0.566013 | − | 0.411233i | 0.267641 | − | 0.963519i | \(-0.413756\pi\) |
−0.833655 | + | 0.552286i | \(0.813756\pi\) | |||||||
\(524\) | −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 | \(-0.811764\pi\) |
0.273665 | + | 0.961825i | \(0.411764\pi\) | |||||||
\(542\) | 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 | \(-0.154709\pi\) |
−0.989894 | + | 0.141807i | \(0.954709\pi\) | |||||||
\(548\) | −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 | 0.537854 | + | 0.843038i | \(0.319235\pi\) |
−0.930659 | + | 0.365889i | \(0.880765\pi\) | |||||||
\(558\) | 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 | \(-0.425879\pi\) |
0.996697 | + | 0.0812119i | \(0.0258790\pi\) | |||||||
\(564\) | 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 | 0.997357 | + | 0.0726553i | \(0.0231473\pi\) |
−0.764173 | + | 0.645011i | \(0.776853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 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 | 0.386931 | − | 0.922109i | \(-0.373535\pi\) |
−0.757409 | + | 0.652941i | \(0.773535\pi\) | |||||||
\(578\) | 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 | −0.844905 | − | 0.534917i | \(-0.820343\pi\) |
0.997959 | + | 0.0638654i | \(0.0203428\pi\) | |||||||
\(588\) | 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 | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 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 | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.47214 | + | 7.60845i | −0.100841 | + | 0.310355i | −0.988732 | − | 0.149698i | \(-0.952170\pi\) |
0.887891 | + | 0.460053i | \(0.152170\pi\) | |||||||
\(602\) | 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 | \(-0.608298\pi\) |
0.793421 | + | 0.608674i | \(0.208298\pi\) | |||||||
\(608\) | 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 | 0.999890 | + | 0.0148615i | \(0.00473072\pi\) |
−0.800192 | + | 0.599744i | \(0.795269\pi\) | |||||||
\(614\) | 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 | −0.996989 | − | 0.0775461i | \(-0.975291\pi\) |
0.761000 | − | 0.648751i | \(-0.224709\pi\) | |||||||
\(620\) | −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 | −0.860320 | − | 0.509754i | \(-0.829736\pi\) |
0.995640 | + | 0.0932836i | \(0.0297363\pi\) | |||||||
\(632\) | 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 | 0.999910 | − | 0.0134135i | \(-0.00426978\pi\) |
−0.816828 | + | 0.576881i | \(0.804270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.6418 | + | 28.8015i | 1.56332 | + | 1.13582i | 0.933219 | + | 0.359307i | \(0.116987\pi\) |
0.630102 | + | 0.776513i | \(0.283013\pi\) | |||||||
\(644\) | −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 | 0.0774551 | − | 0.996996i | \(-0.475321\pi\) |
0.972134 | + | 0.234424i | \(0.0753206\pi\) | |||||||
\(648\) | 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 | −0.378847 | − | 0.925459i | \(-0.623679\pi\) |
0.850465 | − | 0.526032i | \(-0.176321\pi\) | |||||||
\(654\) | 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 | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 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 | \(-0.881447\pi\) |
0.0582519 | + | 0.998302i | \(0.481447\pi\) | |||||||
\(674\) | 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 | \(-0.412426\pi\) |
−0.831340 | + | 0.555764i | \(0.812426\pi\) | |||||||
\(678\) | 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 | −0.977188 | − | 0.212375i | \(-0.931880\pi\) |
−0.0999876 | + | 0.994989i | \(0.531880\pi\) | |||||||
\(692\) | 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 | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(702\) | 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 | 0.602873 | − | 0.797837i | \(-0.294022\pi\) |
−0.572490 | + | 0.819912i | \(0.694022\pi\) | |||||||
\(710\) | 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 | 0.428076 | + | 0.903743i | \(0.359191\pi\) |
−0.877528 | + | 0.479526i | \(0.840809\pi\) | |||||||
\(720\) | 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 | \(-0.876464\pi\) |
0.971286 | + | 0.237917i | \(0.0764645\pi\) | |||||||
\(734\) | 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 | \(-0.915046\pi\) |
−0.0472504 | + | 0.998883i | \(0.515046\pi\) | |||||||
\(740\) | −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 | \(-0.154894\pi\) |
−0.171602 | + | 0.985166i | \(0.554894\pi\) | |||||||
\(744\) | 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 | −0.959096 | − | 0.283081i | \(-0.908643\pi\) |
0.609534 | − | 0.792760i | \(-0.291357\pi\) | |||||||
\(752\) | 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 | −0.983807 | − | 0.179232i | \(-0.942639\pi\) |
−0.133554 | + | 0.991042i | \(0.542639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.8328 | − | 28.2137i | 1.40769 | − | 1.02275i | 0.414035 | − | 0.910261i | \(-0.364119\pi\) |
0.993653 | − | 0.112485i | \(-0.0358809\pi\) | |||||||
\(762\) | 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 | \(-0.243582\pi\) | ||||
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(770\) | 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 | 0.912160 | − | 0.409834i | \(-0.134413\pi\) |
−0.978847 | + | 0.204591i | \(0.934413\pi\) | |||||||
\(774\) | 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 | 0.987638 | + | 0.156755i | \(0.0501033\pi\) |
0.454280 | + | 0.890859i | \(0.349897\pi\) | |||||||
\(788\) | 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 | 0.846515 | − | 0.532365i | \(-0.178696\pi\) |
−0.244721 | + | 0.969593i | \(0.578696\pi\) | |||||||
\(798\) | 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 | \(-0.123177\pi\) |
−0.0727498 | + | 0.997350i | \(0.523177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.618034 | − | 1.90211i | −0.0217021 | − | 0.0667922i | 0.939619 | − | 0.342223i | \(-0.111180\pi\) |
−0.961321 | + | 0.275430i | \(0.911180\pi\) | |||||||
\(812\) | −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 | 0.805860 | + | 0.592106i | \(0.201703\pi\) |
−0.999986 | + | 0.00535152i | \(0.998297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.6074 | + | 13.5191i | −0.648613 | + | 0.471245i | −0.862798 | − | 0.505548i | \(-0.831290\pi\) |
0.214186 | + | 0.976793i | \(0.431290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.1246 | − | 21.1603i | 1.01276 | − | 0.735815i | 0.0479754 | − | 0.998849i | \(-0.484723\pi\) |
0.964787 | + | 0.263034i | \(0.0847231\pi\) | |||||||
\(828\) | 3.70820 | + | 11.4127i | 0.128869 | + | 0.396618i | ||||
\(829\) | −7.72542 | + | 23.7764i | −0.268315 | + | 0.825789i | 0.722596 | + | 0.691271i | \(0.242949\pi\) |
−0.990911 | + | 0.134518i | \(0.957051\pi\) | |||||||
\(830\) | 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 | 0.838609 | − | 0.544734i | \(-0.183369\pi\) |
−0.998635 | + | 0.0522225i | \(0.983369\pi\) | |||||||
\(840\) | 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 | \(-0.354763\pi\) |
−0.717609 | + | 0.696446i | \(0.754763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.70820 | + | 11.4127i | 0.126818 | + | 0.390305i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0000 | 0.409912 | 0.204956 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204956 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(858\) | 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 | 0.740630 | − | 0.671913i | \(-0.234527\pi\) |
−0.410159 | + | 0.912014i | \(0.634527\pi\) | |||||||
\(864\) | 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 | 0.997796 | + | 0.0663553i | \(0.0211371\pi\) |
−0.768231 | + | 0.640172i | \(0.778863\pi\) | |||||||
\(878\) | 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 | 0.999578 | + | 0.0290628i | \(0.00925227\pi\) |
−0.791593 | + | 0.611049i | \(0.790748\pi\) | |||||||
\(884\) | −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 | −0.456500 | − | 0.889723i | \(-0.650897\pi\) |
0.892283 | − | 0.451477i | \(-0.149103\pi\) | |||||||
\(888\) | 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 | 0.475126 | − | 0.879918i | \(-0.342403\pi\) |
−0.690030 | + | 0.723781i | \(0.742403\pi\) | |||||||
\(908\) | 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 | −0.999731 | − | 0.0232118i | \(-0.992611\pi\) |
−0.286858 | + | 0.957973i | \(0.592611\pi\) | |||||||
\(912\) | −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 | \(-0.385007\pi\) |
−0.780445 | + | 0.625224i | \(0.785007\pi\) | |||||||
\(920\) | 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 | 0.322689 | − | 0.946505i | \(-0.395413\pi\) |
−0.800463 | + | 0.599382i | \(0.795413\pi\) | |||||||
\(930\) | 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 | \(-0.594068\pi\) |
0.819830 | + | 0.572608i | \(0.194068\pi\) | |||||||
\(938\) | 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 | \(-0.205216\pi\) |
−0.324559 | + | 0.945865i | \(0.605216\pi\) | |||||||
\(942\) | 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 | −0.592473 | − | 0.805590i | \(-0.701849\pi\) |
0.952835 | − | 0.303489i | \(-0.0981515\pi\) | |||||||
\(954\) | 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 | \(-0.572272\pi\) | ||||
−0.225105 | + | 0.974335i | \(0.572272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | −0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0517 | − | 37.0912i | −0.386756 | − | 1.19031i | −0.935198 | − | 0.354125i | \(-0.884779\pi\) |
0.548442 | − | 0.836189i | \(-0.315221\pi\) | |||||||
\(972\) | −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 | −0.698134 | − | 0.715967i | \(-0.745986\pi\) |
0.465190 | + | 0.885211i | \(0.345986\pi\) | |||||||
\(978\) | 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 | −0.646075 | − | 0.763274i | \(-0.723591\pi\) |
0.971327 | − | 0.237748i | \(-0.0764092\pi\) | |||||||
\(984\) | 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 | −0.715449 | − | 0.698665i | \(-0.753778\pi\) |
0.989475 | − | 0.144702i | \(-0.0462223\pi\) | |||||||
\(998\) | 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.g.729.1 | 4 | ||
11.2 | odd | 10 | 77.2.a.b.1.1 | ✓ | 1 | ||
11.3 | even | 5 | inner | 847.2.f.g.148.1 | 4 | ||
11.4 | even | 5 | inner | 847.2.f.g.323.1 | 4 | ||
11.5 | even | 5 | inner | 847.2.f.g.372.1 | 4 | ||
11.6 | odd | 10 | 847.2.f.f.372.1 | 4 | |||
11.7 | odd | 10 | 847.2.f.f.323.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.f.148.1 | 4 | |||
11.9 | even | 5 | 847.2.a.c.1.1 | 1 | |||
11.10 | odd | 2 | 847.2.f.f.729.1 | 4 | |||
33.2 | even | 10 | 693.2.a.b.1.1 | 1 | |||
33.20 | odd | 10 | 7623.2.a.i.1.1 | 1 | |||
44.35 | even | 10 | 1232.2.a.d.1.1 | 1 | |||
55.2 | even | 20 | 1925.2.b.g.1849.1 | 2 | |||
55.13 | even | 20 | 1925.2.b.g.1849.2 | 2 | |||
55.24 | odd | 10 | 1925.2.a.f.1.1 | 1 | |||
77.2 | odd | 30 | 539.2.e.d.67.1 | 2 | |||
77.13 | even | 10 | 539.2.a.b.1.1 | 1 | |||
77.20 | odd | 10 | 5929.2.a.d.1.1 | 1 | |||
77.24 | even | 30 | 539.2.e.e.177.1 | 2 | |||
77.46 | odd | 30 | 539.2.e.d.177.1 | 2 | |||
77.68 | even | 30 | 539.2.e.e.67.1 | 2 | |||
88.13 | odd | 10 | 4928.2.a.i.1.1 | 1 | |||
88.35 | even | 10 | 4928.2.a.x.1.1 | 1 | |||
231.167 | odd | 10 | 4851.2.a.k.1.1 | 1 | |||
308.167 | odd | 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 | 11.2 | odd | 10 | ||
539.2.a.b.1.1 | 1 | 77.13 | even | 10 | |||
539.2.e.d.67.1 | 2 | 77.2 | odd | 30 | |||
539.2.e.d.177.1 | 2 | 77.46 | odd | 30 | |||
539.2.e.e.67.1 | 2 | 77.68 | even | 30 | |||
539.2.e.e.177.1 | 2 | 77.24 | even | 30 | |||
693.2.a.b.1.1 | 1 | 33.2 | even | 10 | |||
847.2.a.c.1.1 | 1 | 11.9 | even | 5 | |||
847.2.f.f.148.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.f.323.1 | 4 | 11.7 | odd | 10 | |||
847.2.f.f.372.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.f.729.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.g.148.1 | 4 | 11.3 | even | 5 | inner | ||
847.2.f.g.323.1 | 4 | 11.4 | even | 5 | inner | ||
847.2.f.g.372.1 | 4 | 11.5 | even | 5 | inner | ||
847.2.f.g.729.1 | 4 | 1.1 | even | 1 | trivial | ||
1232.2.a.d.1.1 | 1 | 44.35 | even | 10 | |||
1925.2.a.f.1.1 | 1 | 55.24 | odd | 10 | |||
1925.2.b.g.1849.1 | 2 | 55.2 | even | 20 | |||
1925.2.b.g.1849.2 | 2 | 55.13 | even | 20 | |||
4851.2.a.k.1.1 | 1 | 231.167 | odd | 10 | |||
4928.2.a.i.1.1 | 1 | 88.13 | odd | 10 | |||
4928.2.a.x.1.1 | 1 | 88.35 | even | 10 | |||
5929.2.a.d.1.1 | 1 | 77.20 | odd | 10 | |||
7623.2.a.i.1.1 | 1 | 33.20 | odd | 10 | |||
8624.2.a.s.1.1 | 1 | 308.167 | odd | 10 |