Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (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: | \(4.83094932229\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 366.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.366 |
Dual form | 605.2.g.c.81.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | −0.263792 | − | 0.964580i | \(-0.584973\pi\) |
0.835853 | + | 0.548953i | \(0.184973\pi\) | |||||||
\(3\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(4\) | −0.309017 | + | 0.951057i | −0.154508 | + | 0.475528i | ||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(8\) | 0.927051 | + | 2.85317i | 0.327762 | + | 1.00875i | ||||
\(9\) | 2.42705 | − | 1.76336i | 0.809017 | − | 0.587785i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.61803 | − | 1.17557i | 0.448762 | − | 0.326045i | −0.340345 | − | 0.940301i | \(-0.610544\pi\) |
0.789107 | + | 0.614256i | \(0.210544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.809017 | + | 0.587785i | 0.202254 | + | 0.146946i | ||||
\(17\) | 4.85410 | + | 3.52671i | 1.17729 | + | 0.855353i | 0.991864 | − | 0.127304i | \(-0.0406325\pi\) |
0.185429 | + | 0.982658i | \(0.440633\pi\) | |||||||
\(18\) | 0.927051 | − | 2.85317i | 0.218508 | − | 0.672499i | ||||
\(19\) | 1.23607 | + | 3.80423i | 0.283573 | + | 0.872749i | 0.986823 | + | 0.161806i | \(0.0517318\pi\) |
−0.703249 | + | 0.710943i | \(0.748268\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0.618034 | − | 1.90211i | 0.121206 | − | 0.373035i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.85410 | + | 5.70634i | −0.344298 | + | 1.05964i | 0.617660 | + | 0.786445i | \(0.288081\pi\) |
−0.961958 | + | 0.273196i | \(0.911919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | − | 4.70228i | 1.16243 | − | 0.844555i | 0.172347 | − | 0.985036i | \(-0.444865\pi\) |
0.990083 | + | 0.140482i | \(0.0448651\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.927051 | + | 2.85317i | 0.154508 | + | 0.475528i | ||||
\(37\) | −0.618034 | + | 1.90211i | −0.101604 | + | 0.312705i | −0.988918 | − | 0.148460i | \(-0.952568\pi\) |
0.887314 | + | 0.461165i | \(0.152568\pi\) | |||||||
\(38\) | 3.23607 | + | 2.35114i | 0.524960 | + | 0.381405i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.927051 | − | 2.85317i | 0.146580 | − | 0.451126i | ||||
\(41\) | −0.618034 | − | 1.90211i | −0.0965207 | − | 0.297060i | 0.891126 | − | 0.453755i | \(-0.149916\pi\) |
−0.987647 | + | 0.156695i | \(0.949916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 3.23607 | − | 2.35114i | 0.477132 | − | 0.346657i | ||||
\(47\) | −3.70820 | − | 11.4127i | −0.540897 | − | 1.66471i | −0.730550 | − | 0.682859i | \(-0.760736\pi\) |
0.189653 | − | 0.981851i | \(-0.439264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.66312 | + | 4.11450i | 0.809017 | + | 0.587785i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.618034 | + | 1.90211i | 0.0857059 | + | 0.263776i | ||||
\(53\) | 1.61803 | − | 1.17557i | 0.222254 | − | 0.161477i | −0.471087 | − | 0.882087i | \(-0.656138\pi\) |
0.693341 | + | 0.720610i | \(0.256138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.85410 | + | 5.70634i | 0.243456 | + | 0.749279i | ||||
\(59\) | 1.23607 | − | 3.80423i | 0.160922 | − | 0.495268i | −0.837790 | − | 0.545992i | \(-0.816153\pi\) |
0.998713 | + | 0.0507240i | \(0.0161529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.09017 | − | 5.87785i | −1.03584 | − | 0.752582i | −0.0663709 | − | 0.997795i | \(-0.521142\pi\) |
−0.969469 | + | 0.245213i | \(0.921142\pi\) | |||||||
\(62\) | 2.47214 | − | 7.60845i | 0.313962 | − | 0.966274i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.66312 | + | 4.11450i | −0.707890 | + | 0.514312i | ||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.0000 | −1.95471 | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −4.85410 | + | 3.52671i | −0.588646 | + | 0.427677i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.47214 | − | 4.70228i | −0.768101 | − | 0.558058i | 0.133283 | − | 0.991078i | \(-0.457448\pi\) |
−0.901384 | + | 0.433020i | \(0.857448\pi\) | |||||||
\(72\) | 7.28115 | + | 5.29007i | 0.858092 | + | 0.623440i | ||||
\(73\) | −4.32624 | + | 13.3148i | −0.506348 | + | 1.55838i | 0.292145 | + | 0.956374i | \(0.405631\pi\) |
−0.798493 | + | 0.602004i | \(0.794369\pi\) | |||||||
\(74\) | 0.618034 | + | 1.90211i | 0.0718450 | + | 0.221116i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.47214 | − | 4.70228i | 0.728172 | − | 0.529048i | −0.160813 | − | 0.986985i | \(-0.551411\pi\) |
0.888985 | + | 0.457937i | \(0.151411\pi\) | |||||||
\(80\) | −0.309017 | − | 0.951057i | −0.0345492 | − | 0.106331i | ||||
\(81\) | 2.78115 | − | 8.55951i | 0.309017 | − | 0.951057i | ||||
\(82\) | −1.61803 | − | 1.17557i | −0.178682 | − | 0.129820i | ||||
\(83\) | −3.23607 | − | 2.35114i | −0.355205 | − | 0.258071i | 0.395845 | − | 0.918318i | \(-0.370452\pi\) |
−0.751049 | + | 0.660246i | \(0.770452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.85410 | − | 5.70634i | −0.201106 | − | 0.618939i | ||||
\(86\) | −3.23607 | + | 2.35114i | −0.348954 | + | 0.253530i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −2.42705 | + | 1.76336i | −0.255834 | + | 0.185874i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.23607 | + | 3.80423i | −0.128869 | + | 0.396618i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.70820 | − | 7.05342i | −1.00132 | − | 0.727505i | ||||
\(95\) | 1.23607 | − | 3.80423i | 0.126818 | − | 0.390305i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.09017 | + | 5.87785i | −0.821432 | + | 0.596806i | −0.917122 | − | 0.398606i | \(-0.869494\pi\) |
0.0956901 | + | 0.995411i | \(0.469494\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −8.09017 | + | 5.87785i | −0.805002 | + | 0.584868i | −0.912377 | − | 0.409350i | \(-0.865755\pi\) |
0.107375 | + | 0.994219i | \(0.465755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23607 | + | 3.80423i | −0.121793 | + | 0.374842i | −0.993303 | − | 0.115536i | \(-0.963141\pi\) |
0.871510 | + | 0.490378i | \(0.163141\pi\) | |||||||
\(104\) | 4.85410 | + | 3.52671i | 0.475984 | + | 0.345823i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.618034 | − | 1.90211i | 0.0600288 | − | 0.184750i | ||||
\(107\) | −3.70820 | − | 11.4127i | −0.358486 | − | 1.10331i | −0.953961 | − | 0.299932i | \(-0.903036\pi\) |
0.595475 | − | 0.803374i | \(-0.296964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000 | 1.72409 | 0.862044 | − | 0.506834i | \(-0.169184\pi\) | ||||
0.862044 | + | 0.506834i | \(0.169184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.85410 | − | 5.70634i | −0.174419 | − | 0.536807i | 0.825187 | − | 0.564859i | \(-0.191070\pi\) |
−0.999606 | + | 0.0280521i | \(0.991070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.23607 | − | 2.35114i | −0.301765 | − | 0.219245i | ||||
\(116\) | −4.85410 | − | 3.52671i | −0.450692 | − | 0.327447i | ||||
\(117\) | 1.85410 | − | 5.70634i | 0.171412 | − | 0.527551i | ||||
\(118\) | −1.23607 | − | 3.80423i | −0.113789 | − | 0.350207i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.47214 | + | 7.60845i | 0.222004 | + | 0.683259i | ||||
\(125\) | 0.309017 | − | 0.951057i | 0.0276393 | − | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9443 | + | 9.40456i | 1.14862 | + | 0.834520i | 0.988297 | − | 0.152545i | \(-0.0487468\pi\) |
0.160322 | + | 0.987065i | \(0.448747\pi\) | |||||||
\(128\) | 0.927051 | − | 2.85317i | 0.0819405 | − | 0.252187i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.61803 | + | 1.17557i | −0.141911 | + | 0.103104i | ||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.9443 | + | 9.40456i | −1.11821 | + | 0.812431i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.56231 | + | 17.1190i | −0.476964 | + | 1.46794i | ||||
\(137\) | −14.5623 | − | 10.5801i | −1.24414 | − | 0.903922i | −0.246275 | − | 0.969200i | \(-0.579207\pi\) |
−0.997867 | + | 0.0652782i | \(0.979207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.70820 | + | 11.4127i | −0.314526 | + | 0.968011i | 0.661423 | + | 0.750013i | \(0.269953\pi\) |
−0.975949 | + | 0.217998i | \(0.930047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 4.85410 | − | 3.52671i | 0.403111 | − | 0.292877i | ||||
\(146\) | 4.32624 | + | 13.3148i | 0.358042 | + | 1.10194i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.61803 | − | 1.17557i | −0.133002 | − | 0.0966313i | ||||
\(149\) | −8.09017 | − | 5.87785i | −0.662773 | − | 0.481532i | 0.204826 | − | 0.978798i | \(-0.434337\pi\) |
−0.867598 | + | 0.497266i | \(0.834337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.47214 | − | 7.60845i | −0.201180 | − | 0.619167i | −0.999849 | − | 0.0173966i | \(-0.994462\pi\) |
0.798669 | − | 0.601770i | \(-0.205538\pi\) | |||||||
\(152\) | −9.70820 | + | 7.05342i | −0.787439 | + | 0.572108i | ||||
\(153\) | 18.0000 | 1.45521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.618034 | − | 1.90211i | −0.0493245 | − | 0.151805i | 0.923361 | − | 0.383934i | \(-0.125431\pi\) |
−0.972685 | + | 0.232129i | \(0.925431\pi\) | |||||||
\(158\) | 2.47214 | − | 7.60845i | 0.196673 | − | 0.605296i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.04508 | + | 2.93893i | 0.319792 | + | 0.232343i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.78115 | − | 8.55951i | −0.218508 | − | 0.672499i | ||||
\(163\) | −12.9443 | + | 9.40456i | −1.01387 | + | 0.736622i | −0.965018 | − | 0.262184i | \(-0.915557\pi\) |
−0.0488556 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | −6.47214 | + | 4.70228i | −0.500829 | + | 0.363874i | −0.809334 | − | 0.587349i | \(-0.800171\pi\) |
0.308505 | + | 0.951223i | \(0.400171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.78115 | + | 8.55951i | −0.213935 | + | 0.658424i | ||||
\(170\) | −4.85410 | − | 3.52671i | −0.372293 | − | 0.270486i | ||||
\(171\) | 9.70820 | + | 7.05342i | 0.742405 | + | 0.539389i | ||||
\(172\) | 1.23607 | − | 3.80423i | 0.0942493 | − | 0.290070i | ||||
\(173\) | 1.85410 | + | 5.70634i | 0.140965 | + | 0.433845i | 0.996470 | − | 0.0839492i | \(-0.0267533\pi\) |
−0.855505 | + | 0.517794i | \(0.826753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.09017 | − | 5.87785i | 0.606384 | − | 0.440564i | ||||
\(179\) | 1.23607 | + | 3.80423i | 0.0923881 | + | 0.284341i | 0.986564 | − | 0.163374i | \(-0.0522378\pi\) |
−0.894176 | + | 0.447715i | \(0.852238\pi\) | |||||||
\(180\) | 0.927051 | − | 2.85317i | 0.0690983 | − | 0.212663i | ||||
\(181\) | 8.09017 | + | 5.87785i | 0.601338 | + | 0.436897i | 0.846353 | − | 0.532622i | \(-0.178793\pi\) |
−0.245016 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.70820 | + | 11.4127i | 0.273372 | + | 0.841354i | ||||
\(185\) | 1.61803 | − | 1.17557i | 0.118960 | − | 0.0864297i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.23607 | − | 3.80423i | −0.0896738 | − | 0.275988i | ||||
\(191\) | 2.47214 | − | 7.60845i | 0.178877 | − | 0.550528i | −0.820912 | − | 0.571055i | \(-0.806534\pi\) |
0.999789 | + | 0.0205267i | \(0.00653431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.0344 | − | 15.2824i | −1.51409 | − | 1.10005i | −0.964321 | − | 0.264737i | \(-0.914715\pi\) |
−0.549772 | − | 0.835315i | \(-0.685285\pi\) | |||||||
\(194\) | −3.09017 | + | 9.51057i | −0.221861 | + | 0.682819i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.66312 | + | 4.11450i | −0.404508 | + | 0.293893i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −2.42705 | + | 1.76336i | −0.171618 | + | 0.124688i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.09017 | + | 9.51057i | −0.217424 | + | 0.669161i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.618034 | + | 1.90211i | −0.0431654 | + | 0.132849i | ||||
\(206\) | 1.23607 | + | 3.80423i | 0.0861209 | + | 0.265053i | ||||
\(207\) | 9.70820 | − | 7.05342i | 0.674767 | − | 0.490247i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.23607 | − | 2.35114i | 0.222780 | − | 0.161859i | −0.470797 | − | 0.882242i | \(-0.656034\pi\) |
0.693577 | + | 0.720382i | \(0.256034\pi\) | |||||||
\(212\) | 0.618034 | + | 1.90211i | 0.0424467 | + | 0.130638i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.70820 | − | 7.05342i | −0.663639 | − | 0.482162i | ||||
\(215\) | 3.23607 | + | 2.35114i | 0.220698 | + | 0.160346i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.5623 | − | 10.5801i | 0.986284 | − | 0.716577i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.23607 | − | 3.80423i | −0.0827732 | − | 0.254750i | 0.901102 | − | 0.433608i | \(-0.142760\pi\) |
−0.983875 | + | 0.178858i | \(0.942760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.42705 | + | 1.76336i | 0.161803 | + | 0.117557i | ||||
\(226\) | −4.85410 | − | 3.52671i | −0.322890 | − | 0.234593i | ||||
\(227\) | 6.18034 | − | 19.0211i | 0.410204 | − | 1.26248i | −0.506268 | − | 0.862376i | \(-0.668975\pi\) |
0.916471 | − | 0.400100i | \(-0.131025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.09017 | − | 5.87785i | 0.534613 | − | 0.388419i | −0.287467 | − | 0.957790i | \(-0.592813\pi\) |
0.822081 | + | 0.569371i | \(0.192813\pi\) | |||||||
\(230\) | −4.00000 | −0.263752 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.0000 | −1.18176 | ||||||||
\(233\) | 4.85410 | − | 3.52671i | 0.318003 | − | 0.231043i | −0.417320 | − | 0.908760i | \(-0.637031\pi\) |
0.735323 | + | 0.677717i | \(0.237031\pi\) | |||||||
\(234\) | −1.85410 | − | 5.70634i | −0.121206 | − | 0.373035i | ||||
\(235\) | −3.70820 | + | 11.4127i | −0.241897 | + | 0.744481i | ||||
\(236\) | 3.23607 | + | 2.35114i | 0.210650 | + | 0.153046i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.47214 | − | 7.60845i | −0.159909 | − | 0.492150i | 0.838716 | − | 0.544569i | \(-0.183307\pi\) |
−0.998625 | + | 0.0524192i | \(0.983307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.09017 | − | 5.87785i | 0.517920 | − | 0.376291i | ||||
\(245\) | −2.16312 | − | 6.65740i | −0.138197 | − | 0.425325i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.47214 | + | 4.70228i | 0.411812 | + | 0.299199i | ||||
\(248\) | 19.4164 | + | 14.1068i | 1.23294 | + | 0.895786i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.309017 | − | 0.951057i | −0.0195440 | − | 0.0601501i | ||||
\(251\) | −9.70820 | + | 7.05342i | −0.612776 | + | 0.445208i | −0.850391 | − | 0.526151i | \(-0.823635\pi\) |
0.237614 | + | 0.971360i | \(0.423635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.25329 | − | 16.1680i | −0.328331 | − | 1.01050i | ||||
\(257\) | 5.56231 | − | 17.1190i | 0.346967 | − | 1.06785i | −0.613555 | − | 0.789652i | \(-0.710261\pi\) |
0.960522 | − | 0.278203i | \(-0.0897388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.618034 | − | 1.90211i | 0.0383288 | − | 0.117964i | ||||
\(261\) | 5.56231 | + | 17.1190i | 0.344298 | + | 1.05964i | ||||
\(262\) | 9.70820 | − | 7.05342i | 0.599775 | − | 0.435762i | ||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | −0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.94427 | − | 15.2169i | 0.302019 | − | 0.929520i | ||||
\(269\) | 14.5623 | + | 10.5801i | 0.887879 | + | 0.645082i | 0.935324 | − | 0.353792i | \(-0.115108\pi\) |
−0.0474448 | + | 0.998874i | \(0.515108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(272\) | 1.85410 | + | 5.70634i | 0.112421 | + | 0.345998i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.09017 | − | 5.87785i | 0.486091 | − | 0.353166i | −0.317588 | − | 0.948229i | \(-0.602873\pi\) |
0.803679 | + | 0.595063i | \(0.202873\pi\) | |||||||
\(278\) | 3.70820 | + | 11.4127i | 0.222403 | + | 0.684487i | ||||
\(279\) | 7.41641 | − | 22.8254i | 0.444009 | − | 1.36652i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5623 | + | 10.5801i | 0.868714 | + | 0.631158i | 0.930242 | − | 0.366947i | \(-0.119597\pi\) |
−0.0615273 | + | 0.998105i | \(0.519597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23607 | − | 3.80423i | −0.0734766 | − | 0.226138i | 0.907573 | − | 0.419894i | \(-0.137933\pi\) |
−0.981050 | + | 0.193756i | \(0.937933\pi\) | |||||||
\(284\) | 6.47214 | − | 4.70228i | 0.384051 | − | 0.279029i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12.1353 | + | 8.81678i | −0.715077 | + | 0.519534i | ||||
\(289\) | 5.87132 | + | 18.0701i | 0.345372 | + | 1.06295i | ||||
\(290\) | 1.85410 | − | 5.70634i | 0.108877 | − | 0.335088i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.3262 | − | 8.22899i | −0.662818 | − | 0.481565i | ||||
\(293\) | −3.09017 | + | 9.51057i | −0.180530 | + | 0.555613i | −0.999843 | − | 0.0177332i | \(-0.994355\pi\) |
0.819313 | + | 0.573346i | \(0.194355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.23607 | + | 2.35114i | −0.188411 | + | 0.136889i | ||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | 6.47214 | − | 4.70228i | 0.374293 | − | 0.271940i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.47214 | − | 4.70228i | −0.372430 | − | 0.270586i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.23607 | + | 3.80423i | −0.0708934 | + | 0.218187i | ||||
\(305\) | 3.09017 | + | 9.51057i | 0.176943 | + | 0.544573i | ||||
\(306\) | 14.5623 | − | 10.5801i | 0.832472 | − | 0.604826i | ||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.47214 | + | 4.70228i | −0.367593 | + | 0.267072i | ||||
\(311\) | −7.41641 | − | 22.8254i | −0.420546 | − | 1.29431i | −0.907195 | − | 0.420710i | \(-0.861781\pi\) |
0.486649 | − | 0.873597i | \(-0.338219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7984 | + | 12.9313i | 1.00602 | + | 0.730919i | 0.963371 | − | 0.268171i | \(-0.0864192\pi\) |
0.0426523 | + | 0.999090i | \(0.486419\pi\) | |||||||
\(314\) | −1.61803 | − | 1.17557i | −0.0913109 | − | 0.0663413i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.47214 | + | 7.60845i | 0.139069 | + | 0.428009i | ||||
\(317\) | 14.5623 | − | 10.5801i | 0.817901 | − | 0.594240i | −0.0982098 | − | 0.995166i | \(-0.531312\pi\) |
0.916110 | + | 0.400926i | \(0.131312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.00000 | 0.391312 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.41641 | + | 22.8254i | −0.412660 | + | 1.27004i | ||||
\(324\) | 7.28115 | + | 5.29007i | 0.404508 | + | 0.293893i | ||||
\(325\) | 1.61803 | + | 1.17557i | 0.0897524 | + | 0.0652089i | ||||
\(326\) | −4.94427 | + | 15.2169i | −0.273838 | + | 0.842786i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.85410 | − | 3.52671i | 0.268023 | − | 0.194730i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 3.23607 | − | 2.35114i | 0.177602 | − | 0.129036i | ||||
\(333\) | 1.85410 | + | 5.70634i | 0.101604 | + | 0.312705i | ||||
\(334\) | −2.47214 | + | 7.60845i | −0.135269 | + | 0.416316i | ||||
\(335\) | 12.9443 | + | 9.40456i | 0.707221 | + | 0.513826i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.85410 | + | 5.70634i | −0.100999 | + | 0.310844i | −0.988771 | − | 0.149441i | \(-0.952253\pi\) |
0.887771 | + | 0.460285i | \(0.152253\pi\) | |||||||
\(338\) | 2.78115 | + | 8.55951i | 0.151275 | + | 0.465576i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.70820 | − | 11.4127i | −0.199933 | − | 0.615330i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.85410 | + | 3.52671i | 0.260958 | + | 0.189597i | ||||
\(347\) | −3.23607 | − | 2.35114i | −0.173721 | − | 0.126216i | 0.497527 | − | 0.867448i | \(-0.334242\pi\) |
−0.671248 | + | 0.741233i | \(0.734242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.47214 | + | 7.60845i | 0.131207 | + | 0.403815i | ||||
\(356\) | −3.09017 | + | 9.51057i | −0.163779 | + | 0.504059i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.23607 | + | 2.35114i | 0.171032 | + | 0.124262i | ||||
\(359\) | 9.88854 | − | 30.4338i | 0.521897 | − | 1.60623i | −0.248473 | − | 0.968639i | \(-0.579929\pi\) |
0.770371 | − | 0.637596i | \(-0.220071\pi\) | |||||||
\(360\) | −2.78115 | − | 8.55951i | −0.146580 | − | 0.451126i | ||||
\(361\) | 2.42705 | − | 1.76336i | 0.127740 | − | 0.0928082i | ||||
\(362\) | 10.0000 | 0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.3262 | − | 8.22899i | 0.592842 | − | 0.430725i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.23607 | − | 3.80423i | 0.0645222 | − | 0.198579i | −0.913598 | − | 0.406618i | \(-0.866708\pi\) |
0.978121 | + | 0.208039i | \(0.0667081\pi\) | |||||||
\(368\) | 3.23607 | + | 2.35114i | 0.168692 | + | 0.122562i | ||||
\(369\) | −4.85410 | − | 3.52671i | −0.252694 | − | 0.183593i | ||||
\(370\) | 0.618034 | − | 1.90211i | 0.0321301 | − | 0.0988861i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0000 | −0.932005 | −0.466002 | − | 0.884783i | \(-0.654306\pi\) | ||||
−0.466002 | + | 0.884783i | \(0.654306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29.1246 | − | 21.1603i | 1.50199 | − | 1.09126i | ||||
\(377\) | 3.70820 | + | 11.4127i | 0.190982 | + | 0.587783i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1803 | − | 11.7557i | −0.831128 | − | 0.603850i | 0.0887501 | − | 0.996054i | \(-0.471713\pi\) |
−0.919878 | + | 0.392204i | \(0.871713\pi\) | |||||||
\(380\) | 3.23607 | + | 2.35114i | 0.166007 | + | 0.120611i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.47214 | − | 7.60845i | −0.126485 | − | 0.389282i | ||||
\(383\) | 9.70820 | − | 7.05342i | 0.496066 | − | 0.360413i | −0.311446 | − | 0.950264i | \(-0.600813\pi\) |
0.807512 | + | 0.589851i | \(0.200813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.0000 | −1.32337 | ||||||||
\(387\) | −9.70820 | + | 7.05342i | −0.493496 | + | 0.358546i | ||||
\(388\) | −3.09017 | − | 9.51057i | −0.156880 | − | 0.482826i | ||||
\(389\) | 1.85410 | − | 5.70634i | 0.0940067 | − | 0.289323i | −0.892987 | − | 0.450083i | \(-0.851394\pi\) |
0.986994 | + | 0.160760i | \(0.0513945\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4164 | + | 14.1068i | 0.981930 | + | 0.713414i | ||||
\(392\) | −6.48936 | + | 19.9722i | −0.327762 | + | 1.00875i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.61803 | + | 1.17557i | −0.0815154 | + | 0.0592244i | ||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.0000 | 1.50566 | 0.752828 | − | 0.658217i | \(-0.228689\pi\) | ||||
0.752828 | + | 0.658217i | \(0.228689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.309017 | + | 0.951057i | −0.0154508 | + | 0.0475528i | ||||
\(401\) | −1.61803 | − | 1.17557i | −0.0808008 | − | 0.0587052i | 0.546652 | − | 0.837360i | \(-0.315902\pi\) |
−0.627452 | + | 0.778655i | \(0.715902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.94427 | − | 15.2169i | 0.246292 | − | 0.758008i | ||||
\(404\) | −3.09017 | − | 9.51057i | −0.153742 | − | 0.473168i | ||||
\(405\) | −7.28115 | + | 5.29007i | −0.361803 | + | 0.262866i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.85410 | + | 3.52671i | −0.240020 | + | 0.174385i | −0.701292 | − | 0.712874i | \(-0.747393\pi\) |
0.461272 | + | 0.887259i | \(0.347393\pi\) | |||||||
\(410\) | 0.618034 | + | 1.90211i | 0.0305225 | + | 0.0939387i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.23607 | − | 2.35114i | −0.159430 | − | 0.115832i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.70820 | − | 11.4127i | 0.182248 | − | 0.560903i | ||||
\(415\) | 1.23607 | + | 3.80423i | 0.0606762 | + | 0.186742i | ||||
\(416\) | −8.09017 | + | 5.87785i | −0.396653 | + | 0.288185i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.85410 | + | 5.70634i | 0.0903634 | + | 0.278110i | 0.986018 | − | 0.166641i | \(-0.0532921\pi\) |
−0.895654 | + | 0.444751i | \(0.853292\pi\) | |||||||
\(422\) | 1.23607 | − | 3.80423i | 0.0601708 | − | 0.185187i | ||||
\(423\) | −29.1246 | − | 21.1603i | −1.41609 | − | 1.02885i | ||||
\(424\) | 4.85410 | + | 3.52671i | 0.235736 | + | 0.171272i | ||||
\(425\) | −1.85410 | + | 5.70634i | −0.0899372 | + | 0.276798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −19.4164 | + | 14.1068i | −0.935255 | + | 0.679503i | −0.947274 | − | 0.320425i | \(-0.896174\pi\) |
0.0120185 | + | 0.999928i | \(0.496174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.79837 | + | 20.9232i | −0.326709 | + | 1.00551i | 0.643954 | + | 0.765064i | \(0.277293\pi\) |
−0.970663 | + | 0.240443i | \(0.922707\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.56231 | + | 17.1190i | −0.266386 | + | 0.819852i | ||||
\(437\) | 4.94427 | + | 15.2169i | 0.236517 | + | 0.727923i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 9.70820 | − | 7.05342i | 0.461772 | − | 0.335497i | ||||
\(443\) | 2.47214 | + | 7.60845i | 0.117455 | + | 0.361488i | 0.992451 | − | 0.122641i | \(-0.0391364\pi\) |
−0.874996 | + | 0.484129i | \(0.839136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.09017 | − | 5.87785i | −0.383511 | − | 0.278637i | ||||
\(446\) | −3.23607 | − | 2.35114i | −0.153232 | − | 0.111330i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.61803 | + | 1.17557i | −0.0763597 | + | 0.0554786i | −0.625310 | − | 0.780376i | \(-0.715028\pi\) |
0.548950 | + | 0.835855i | \(0.315028\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.18034 | − | 19.0211i | −0.290058 | − | 0.892706i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.0344 | − | 15.2824i | −0.983950 | − | 0.714881i | −0.0253618 | − | 0.999678i | \(-0.508074\pi\) |
−0.958588 | + | 0.284797i | \(0.908074\pi\) | |||||||
\(458\) | 3.09017 | − | 9.51057i | 0.144394 | − | 0.444400i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.23607 | − | 2.35114i | 0.150882 | − | 0.109623i | ||||
\(461\) | 34.0000 | 1.58354 | 0.791769 | − | 0.610821i | \(-0.209160\pi\) | ||||
0.791769 | + | 0.610821i | \(0.209160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.0000 | −1.67306 | −0.836531 | − | 0.547920i | \(-0.815420\pi\) | ||||
−0.836531 | + | 0.547920i | \(0.815420\pi\) | |||||||
\(464\) | −4.85410 | + | 3.52671i | −0.225346 | + | 0.163723i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.85410 | − | 5.70634i | 0.0858896 | − | 0.264341i | ||||
\(467\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(468\) | 4.85410 | + | 3.52671i | 0.224381 | + | 0.163022i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.70820 | + | 11.4127i | 0.171047 | + | 0.526428i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.23607 | + | 2.35114i | −0.148481 | + | 0.107878i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.85410 | − | 5.70634i | 0.0848935 | − | 0.261275i | ||||
\(478\) | −6.47214 | − | 4.70228i | −0.296029 | − | 0.215077i | ||||
\(479\) | 19.4164 | + | 14.1068i | 0.887158 | + | 0.644558i | 0.935136 | − | 0.354290i | \(-0.115277\pi\) |
−0.0479772 | + | 0.998848i | \(0.515277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23607 | + | 3.80423i | 0.0563598 | + | 0.173458i | ||||
\(482\) | −8.09017 | + | 5.87785i | −0.368497 | + | 0.267729i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0000 | 0.454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.65248 | + | 26.6296i | 0.392081 | + | 1.20670i | 0.931212 | + | 0.364479i | \(0.118753\pi\) |
−0.539130 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(488\) | 9.27051 | − | 28.5317i | 0.419656 | − | 1.29157i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.66312 | − | 4.11450i | −0.255834 | − | 0.185874i | ||||
\(491\) | 8.65248 | − | 26.6296i | 0.390481 | − | 1.20178i | −0.541945 | − | 0.840414i | \(-0.682312\pi\) |
0.932426 | − | 0.361362i | \(-0.117688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.1246 | + | 21.1603i | −1.31171 | + | 0.953011i | ||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1246 | + | 34.2380i | −0.498006 | + | 1.53270i | 0.314213 | + | 0.949352i | \(0.398259\pi\) |
−0.812219 | + | 0.583352i | \(0.801741\pi\) | |||||||
\(500\) | 0.809017 | + | 0.587785i | 0.0361803 | + | 0.0262866i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.70820 | + | 11.4127i | −0.165505 | + | 0.509373i | ||||
\(503\) | 4.94427 | + | 15.2169i | 0.220454 | + | 0.678488i | 0.998721 | + | 0.0505549i | \(0.0160990\pi\) |
−0.778267 | + | 0.627933i | \(0.783901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.9443 | + | 9.40456i | −0.574309 | + | 0.417260i | ||||
\(509\) | 4.32624 | + | 13.3148i | 0.191757 | + | 0.590168i | 0.999999 | + | 0.00131729i | \(0.000419307\pi\) |
−0.808242 | + | 0.588850i | \(0.799581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.89919 | − | 6.46564i | −0.393292 | − | 0.285744i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.56231 | − | 17.1190i | −0.245343 | − | 0.755087i | ||||
\(515\) | 3.23607 | − | 2.35114i | 0.142598 | − | 0.103604i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.85410 | − | 5.70634i | −0.0813077 | − | 0.250240i | ||||
\(521\) | −1.85410 | + | 5.70634i | −0.0812297 | + | 0.249999i | −0.983421 | − | 0.181337i | \(-0.941958\pi\) |
0.902191 | + | 0.431336i | \(0.141958\pi\) | |||||||
\(522\) | 14.5623 | + | 10.5801i | 0.637375 | + | 0.463080i | ||||
\(523\) | −16.1803 | − | 11.7557i | −0.707517 | − | 0.514041i | 0.174855 | − | 0.984594i | \(-0.444054\pi\) |
−0.882372 | + | 0.470553i | \(0.844054\pi\) | |||||||
\(524\) | −3.70820 | + | 11.4127i | −0.161994 | + | 0.498565i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.4164 | + | 14.1068i | −0.846596 | + | 0.615088i | ||||
\(527\) | 48.0000 | 2.09091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −1.61803 | + | 1.17557i | −0.0702829 | + | 0.0510635i | ||||
\(531\) | −3.70820 | − | 11.4127i | −0.160922 | − | 0.495268i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.23607 | − | 2.35114i | −0.140170 | − | 0.101839i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.70820 | + | 11.4127i | −0.160320 | + | 0.493413i | ||||
\(536\) | −14.8328 | − | 45.6507i | −0.640680 | − | 1.97181i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.5066 | + | 19.9847i | −1.18260 | + | 0.859209i | −0.992463 | − | 0.122548i | \(-0.960893\pi\) |
−0.190138 | + | 0.981757i | \(0.560893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −24.2705 | − | 17.6336i | −1.04059 | − | 0.756033i | ||||
\(545\) | −14.5623 | − | 10.5801i | −0.623781 | − | 0.453203i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.70820 | − | 11.4127i | −0.158551 | − | 0.487971i | 0.839952 | − | 0.542661i | \(-0.182583\pi\) |
−0.998503 | + | 0.0546898i | \(0.982583\pi\) | |||||||
\(548\) | 14.5623 | − | 10.5801i | 0.622071 | − | 0.451961i | ||||
\(549\) | −30.0000 | −1.28037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0000 | −1.02243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.09017 | − | 9.51057i | 0.131289 | − | 0.404065i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.70820 | − | 7.05342i | −0.411720 | − | 0.299132i | ||||
\(557\) | −3.09017 | + | 9.51057i | −0.130935 | + | 0.402976i | −0.994936 | − | 0.100515i | \(-0.967951\pi\) |
0.864001 | + | 0.503490i | \(0.167951\pi\) | |||||||
\(558\) | −7.41641 | − | 22.8254i | −0.313962 | − | 0.966274i | ||||
\(559\) | −6.47214 | + | 4.70228i | −0.273742 | + | 0.198885i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | 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 | ||||||||
\(565\) | −1.85410 | + | 5.70634i | −0.0780027 | + | 0.240067i | ||||
\(566\) | −3.23607 | − | 2.35114i | −0.136022 | − | 0.0988258i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.41641 | − | 22.8254i | 0.311186 | − | 0.957731i | ||||
\(569\) | −8.03444 | − | 24.7275i | −0.336821 | − | 1.03663i | −0.965818 | − | 0.259221i | \(-0.916534\pi\) |
0.628997 | − | 0.777408i | \(-0.283466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0000 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.23607 | + | 3.80423i | 0.0515476 | + | 0.158647i | ||||
\(576\) | −6.48936 | + | 19.9722i | −0.270390 | + | 0.832174i | ||||
\(577\) | 17.7984 | + | 12.9313i | 0.740956 | + | 0.538336i | 0.893010 | − | 0.450036i | \(-0.148589\pi\) |
−0.152054 | + | 0.988372i | \(0.548589\pi\) | |||||||
\(578\) | 15.3713 | + | 11.1679i | 0.639363 | + | 0.464524i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.85410 | + | 5.70634i | 0.0769874 | + | 0.236943i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −42.0000 | −1.73797 | ||||||||
\(585\) | −4.85410 | + | 3.52671i | −0.200692 | + | 0.145812i | ||||
\(586\) | 3.09017 | + | 9.51057i | 0.127654 | + | 0.392878i | ||||
\(587\) | −7.41641 | + | 22.8254i | −0.306108 | + | 0.942103i | 0.673154 | + | 0.739503i | \(0.264939\pi\) |
−0.979261 | + | 0.202601i | \(0.935061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.8885 | + | 18.8091i | 1.06672 | + | 0.775017i | ||||
\(590\) | −1.23607 | + | 3.80423i | −0.0508881 | + | 0.156618i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.61803 | + | 1.17557i | −0.0665008 | + | 0.0483157i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.09017 | − | 5.87785i | 0.331386 | − | 0.240766i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.47214 | − | 7.60845i | 0.101093 | − | 0.311133i | ||||
\(599\) | −19.4164 | − | 14.1068i | −0.793333 | − | 0.576390i | 0.115618 | − | 0.993294i | \(-0.463115\pi\) |
−0.908951 | + | 0.416904i | \(0.863115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.618034 | + | 1.90211i | −0.0252101 | + | 0.0775888i | −0.962870 | − | 0.269965i | \(-0.912988\pi\) |
0.937660 | + | 0.347554i | \(0.112988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.8328 | + | 28.2137i | −1.58139 | + | 1.14895i | ||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8885 | + | 18.8091i | −1.05078 | + | 0.763439i | −0.972361 | − | 0.233481i | \(-0.924988\pi\) |
−0.0784223 | + | 0.996920i | \(0.524988\pi\) | |||||||
\(608\) | −6.18034 | − | 19.0211i | −0.250646 | − | 0.771409i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.09017 | + | 5.87785i | 0.327561 | + | 0.237987i | ||||
\(611\) | −19.4164 | − | 14.1068i | −0.785504 | − | 0.570702i | ||||
\(612\) | −5.56231 | + | 17.1190i | −0.224843 | + | 0.691995i | ||||
\(613\) | −10.5066 | − | 32.3359i | −0.424357 | − | 1.30604i | −0.903609 | − | 0.428358i | \(-0.859092\pi\) |
0.479252 | − | 0.877677i | \(-0.340908\pi\) | |||||||
\(614\) | −16.1803 | + | 11.7557i | −0.652985 | + | 0.474422i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.18034 | − | 19.0211i | −0.248409 | − | 0.764524i | −0.995057 | − | 0.0993047i | \(-0.968338\pi\) |
0.746648 | − | 0.665219i | \(-0.231662\pi\) | |||||||
\(620\) | 2.47214 | − | 7.60845i | 0.0992834 | − | 0.305563i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.4164 | − | 14.1068i | −0.778527 | − | 0.565633i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 22.0000 | 0.879297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | −9.70820 | + | 7.05342i | −0.387091 | + | 0.281238i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3607 | − | 38.0423i | 0.492071 | − | 1.51444i | −0.329401 | − | 0.944190i | \(-0.606847\pi\) |
0.821472 | − | 0.570248i | \(-0.193153\pi\) | |||||||
\(632\) | 19.4164 | + | 14.1068i | 0.772343 | + | 0.561140i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.56231 | − | 17.1190i | 0.220907 | − | 0.679883i | ||||
\(635\) | −4.94427 | − | 15.2169i | −0.196207 | − | 0.603864i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0000 | 0.554700 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.0000 | −0.949425 | ||||||||
\(640\) | −2.42705 | + | 1.76336i | −0.0959376 | + | 0.0697028i | ||||
\(641\) | 10.5066 | + | 32.3359i | 0.414985 | + | 1.27719i | 0.912264 | + | 0.409602i | \(0.134332\pi\) |
−0.497280 | + | 0.867590i | \(0.665668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.9443 | + | 9.40456i | 0.510472 | + | 0.370880i | 0.813003 | − | 0.582260i | \(-0.197831\pi\) |
−0.302530 | + | 0.953140i | \(0.597831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.41641 | + | 22.8254i | 0.291795 | + | 0.898052i | ||||
\(647\) | −16.1803 | + | 11.7557i | −0.636115 | + | 0.462164i | −0.858513 | − | 0.512791i | \(-0.828611\pi\) |
0.222398 | + | 0.974956i | \(0.428611\pi\) | |||||||
\(648\) | 27.0000 | 1.06066 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.94427 | − | 15.2169i | −0.193633 | − | 0.595940i | ||||
\(653\) | −3.09017 | + | 9.51057i | −0.120928 | + | 0.372177i | −0.993137 | − | 0.116955i | \(-0.962687\pi\) |
0.872209 | + | 0.489133i | \(0.162687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.70820 | − | 7.05342i | −0.379331 | − | 0.275600i | ||||
\(656\) | 0.618034 | − | 1.90211i | 0.0241302 | − | 0.0742650i | ||||
\(657\) | 12.9787 | + | 39.9444i | 0.506348 | + | 1.55838i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 3.23607 | − | 2.35114i | 0.125773 | − | 0.0913797i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.70820 | − | 11.4127i | 0.143906 | − | 0.442898i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.85410 | + | 3.52671i | 0.188093 | + | 0.136657i | ||||
\(667\) | −7.41641 | + | 22.8254i | −0.287164 | + | 0.883801i | ||||
\(668\) | −2.47214 | − | 7.60845i | −0.0956498 | − | 0.294380i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.0000 | 0.618134 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0344 | + | 15.2824i | −0.810818 | + | 0.589094i | −0.914068 | − | 0.405562i | \(-0.867076\pi\) |
0.103250 | + | 0.994655i | \(0.467076\pi\) | |||||||
\(674\) | 1.85410 | + | 5.70634i | 0.0714173 | + | 0.219800i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.28115 | − | 5.29007i | −0.280044 | − | 0.203464i | ||||
\(677\) | −30.7426 | − | 22.3358i | −1.18154 | − | 0.858436i | −0.189192 | − | 0.981940i | \(-0.560587\pi\) |
−0.992344 | + | 0.123504i | \(0.960587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.5623 | − | 10.5801i | 0.558439 | − | 0.405730i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0000 | −0.612223 | −0.306111 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306111 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(684\) | −9.70820 | + | 7.05342i | −0.371202 | + | 0.269694i | ||||
\(685\) | 5.56231 | + | 17.1190i | 0.212525 | + | 0.654084i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.23607 | − | 2.35114i | −0.123374 | − | 0.0896364i | ||||
\(689\) | 1.23607 | − | 3.80423i | 0.0470904 | − | 0.144929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6525 | − | 16.4580i | 0.861741 | − | 0.626091i | −0.0666172 | − | 0.997779i | \(-0.521221\pi\) |
0.928358 | + | 0.371687i | \(0.121221\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 9.70820 | − | 7.05342i | 0.368253 | − | 0.267552i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.70820 | − | 11.4127i | 0.140458 | − | 0.432286i | ||||
\(698\) | 8.09017 | + | 5.87785i | 0.306217 | + | 0.222480i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.79837 | − | 20.9232i | −0.256771 | − | 0.790260i | −0.993476 | − | 0.114045i | \(-0.963619\pi\) |
0.736705 | − | 0.676215i | \(-0.236381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5623 | − | 10.5801i | 0.548060 | − | 0.398189i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.09017 | + | 5.87785i | 0.303833 | + | 0.220747i | 0.729246 | − | 0.684252i | \(-0.239871\pi\) |
−0.425413 | + | 0.904999i | \(0.639871\pi\) | |||||||
\(710\) | 6.47214 | + | 4.70228i | 0.242895 | + | 0.176473i | ||||
\(711\) | 7.41641 | − | 22.8254i | 0.278137 | − | 0.856018i | ||||
\(712\) | 9.27051 | + | 28.5317i | 0.347427 | + | 1.06927i | ||||
\(713\) | 25.8885 | − | 18.8091i | 0.969534 | − | 0.704407i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.88854 | − | 30.4338i | −0.369037 | − | 1.13578i | ||||
\(719\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(720\) | −2.42705 | − | 1.76336i | −0.0904508 | − | 0.0657164i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.927051 | − | 2.85317i | 0.0345013 | − | 0.106184i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.09017 | + | 5.87785i | −0.300669 | + | 0.218449i | ||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.0000 | 1.92857 | 0.964287 | − | 0.264861i | \(-0.0853260\pi\) | ||||
0.964287 | + | 0.264861i | \(0.0853260\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.34346 | − | 25.6785i | −0.309017 | − | 0.951057i | ||||
\(730\) | 4.32624 | − | 13.3148i | 0.160121 | − | 0.492803i | ||||
\(731\) | −19.4164 | − | 14.1068i | −0.718142 | − | 0.521761i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.9787 | + | 39.9444i | −0.479380 | + | 1.47538i | 0.360579 | + | 0.932729i | \(0.382579\pi\) |
−0.839959 | + | 0.542650i | \(0.817421\pi\) | |||||||
\(734\) | −1.23607 | − | 3.80423i | −0.0456241 | − | 0.140417i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.0000 | −0.737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | 3.23607 | − | 2.35114i | 0.119041 | − | 0.0864881i | −0.526672 | − | 0.850069i | \(-0.676560\pi\) |
0.645713 | + | 0.763580i | \(0.276560\pi\) | |||||||
\(740\) | 0.618034 | + | 1.90211i | 0.0227194 | + | 0.0699231i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.3607 | + | 23.5114i | 1.18720 | + | 0.862550i | 0.992965 | − | 0.118405i | \(-0.0377783\pi\) |
0.194233 | + | 0.980955i | \(0.437778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.09017 | + | 9.51057i | 0.113215 | + | 0.348440i | ||||
\(746\) | −14.5623 | + | 10.5801i | −0.533164 | + | 0.387366i | ||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.94427 | + | 15.2169i | 0.180419 | + | 0.555273i | 0.999839 | − | 0.0179203i | \(-0.00570452\pi\) |
−0.819420 | + | 0.573193i | \(0.805705\pi\) | |||||||
\(752\) | 3.70820 | − | 11.4127i | 0.135224 | − | 0.416178i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.70820 | + | 7.05342i | 0.353552 | + | 0.256871i | ||||
\(755\) | −2.47214 | + | 7.60845i | −0.0899702 | + | 0.276900i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.85410 | + | 3.52671i | −0.176425 | + | 0.128181i | −0.672493 | − | 0.740103i | \(-0.734777\pi\) |
0.496068 | + | 0.868284i | \(0.334777\pi\) | |||||||
\(758\) | −20.0000 | −0.726433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 8.09017 | − | 5.87785i | 0.293268 | − | 0.213072i | −0.431416 | − | 0.902153i | \(-0.641986\pi\) |
0.724684 | + | 0.689081i | \(0.241986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.47214 | + | 4.70228i | 0.234154 | + | 0.170123i | ||||
\(765\) | −14.5623 | − | 10.5801i | −0.526501 | − | 0.382526i | ||||
\(766\) | 3.70820 | − | 11.4127i | 0.133983 | − | 0.412357i | ||||
\(767\) | −2.47214 | − | 7.60845i | −0.0892637 | − | 0.274725i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.0344 | − | 15.2824i | 0.757046 | − | 0.550026i | ||||
\(773\) | 4.32624 | + | 13.3148i | 0.155604 | + | 0.478900i | 0.998222 | − | 0.0596126i | \(-0.0189865\pi\) |
−0.842618 | + | 0.538512i | \(0.818987\pi\) | |||||||
\(774\) | −3.70820 | + | 11.4127i | −0.133289 | + | 0.410220i | ||||
\(775\) | 6.47214 | + | 4.70228i | 0.232486 | + | 0.168911i | ||||
\(776\) | −24.2705 | − | 17.6336i | −0.871261 | − | 0.633008i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.85410 | − | 5.70634i | −0.0664728 | − | 0.204582i | ||||
\(779\) | 6.47214 | − | 4.70228i | 0.231888 | − | 0.168477i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 24.0000 | 0.858238 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.16312 | + | 6.65740i | 0.0772542 | + | 0.237764i | ||||
\(785\) | −0.618034 | + | 1.90211i | −0.0220586 | + | 0.0678893i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.0689 | + | 30.5648i | 1.49959 | + | 1.08952i | 0.970543 | + | 0.240929i | \(0.0774519\pi\) |
0.529051 | + | 0.848590i | \(0.322548\pi\) | |||||||
\(788\) | 0.618034 | − | 1.90211i | 0.0220165 | − | 0.0677600i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.47214 | + | 4.70228i | −0.230268 | + | 0.167300i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 24.2705 | − | 17.6336i | 0.861328 | − | 0.625792i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.61803 | + | 1.17557i | 0.0573137 | + | 0.0416408i | 0.616073 | − | 0.787689i | \(-0.288723\pi\) |
−0.558760 | + | 0.829330i | \(0.688723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.2492 | − | 68.4761i | 0.787121 | − | 2.42251i | ||||
\(800\) | −1.54508 | − | 4.75528i | −0.0546270 | − | 0.168125i | ||||
\(801\) | 24.2705 | − | 17.6336i | 0.857556 | − | 0.623051i | ||||
\(802\) | −2.00000 | −0.0706225 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.94427 | − | 15.2169i | −0.174155 | − | 0.535993i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −24.2705 | − | 17.6336i | −0.853834 | − | 0.620346i | ||||
\(809\) | 14.5623 | + | 10.5801i | 0.511983 | + | 0.371978i | 0.813575 | − | 0.581459i | \(-0.197518\pi\) |
−0.301592 | + | 0.953437i | \(0.597518\pi\) | |||||||
\(810\) | −2.78115 | + | 8.55951i | −0.0977198 | + | 0.300750i | ||||
\(811\) | 3.70820 | + | 11.4127i | 0.130213 | + | 0.400753i | 0.994815 | − | 0.101704i | \(-0.0324294\pi\) |
−0.864602 | + | 0.502457i | \(0.832429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0000 | 0.560456 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.94427 | − | 15.2169i | −0.172978 | − | 0.532372i | ||||
\(818\) | −1.85410 | + | 5.70634i | −0.0648272 | + | 0.199517i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.61803 | − | 1.17557i | −0.0565042 | − | 0.0410527i | ||||
\(821\) | 5.56231 | − | 17.1190i | 0.194126 | − | 0.597458i | −0.805860 | − | 0.592106i | \(-0.798297\pi\) |
0.999986 | − | 0.00535152i | \(-0.00170345\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.1246 | − | 21.1603i | 1.01522 | − | 0.737601i | 0.0499226 | − | 0.998753i | \(-0.484103\pi\) |
0.965298 | + | 0.261152i | \(0.0841025\pi\) | |||||||
\(824\) | −12.0000 | −0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.70820 | − | 7.05342i | 0.337587 | − | 0.245272i | −0.406056 | − | 0.913848i | \(-0.633096\pi\) |
0.743643 | + | 0.668577i | \(0.233096\pi\) | |||||||
\(828\) | 3.70820 | + | 11.4127i | 0.128869 | + | 0.396618i | ||||
\(829\) | −0.618034 | + | 1.90211i | −0.0214652 | + | 0.0660631i | −0.961215 | − | 0.275799i | \(-0.911058\pi\) |
0.939750 | + | 0.341862i | \(0.111058\pi\) | |||||||
\(830\) | 3.23607 | + | 2.35114i | 0.112326 | + | 0.0816093i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.32624 | + | 13.3148i | −0.149985 | + | 0.461607i | ||||
\(833\) | 12.9787 | + | 39.9444i | 0.449686 | + | 1.38399i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.6525 | + | 16.4580i | −0.782517 | + | 0.568532i | ||||
\(839\) | −9.88854 | − | 30.4338i | −0.341390 | − | 1.05069i | −0.963488 | − | 0.267752i | \(-0.913719\pi\) |
0.622097 | − | 0.782940i | \(-0.286281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.66312 | − | 4.11450i | −0.195280 | − | 0.141879i | ||||
\(842\) | 4.85410 | + | 3.52671i | 0.167283 | + | 0.121539i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.23607 | + | 3.80423i | 0.0425472 | + | 0.130947i | ||||
\(845\) | 7.28115 | − | 5.29007i | 0.250479 | − | 0.181984i | ||||
\(846\) | −36.0000 | −1.23771 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.85410 | + | 5.70634i | 0.0635952 | + | 0.195726i | ||||
\(851\) | −2.47214 | + | 7.60845i | −0.0847437 | + | 0.260814i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.61803 | + | 1.17557i | 0.0554004 | + | 0.0402508i | 0.615141 | − | 0.788417i | \(-0.289099\pi\) |
−0.559740 | + | 0.828668i | \(0.689099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.70820 | − | 11.4127i | −0.126818 | − | 0.390305i | ||||
\(856\) | 29.1246 | − | 21.1603i | 0.995459 | − | 0.723243i | ||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0000 | 0.955348 | 0.477674 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477674 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(860\) | −3.23607 | + | 2.35114i | −0.110349 | + | 0.0801732i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.41641 | + | 22.8254i | −0.252604 | + | 0.777435i | ||||
\(863\) | −3.23607 | − | 2.35114i | −0.110157 | − | 0.0800338i | 0.531343 | − | 0.847157i | \(-0.321688\pi\) |
−0.641500 | + | 0.767123i | \(0.721688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.85410 | − | 5.70634i | 0.0630414 | − | 0.194021i | ||||
\(866\) | 6.79837 | + | 20.9232i | 0.231018 | + | 0.711001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.8885 | + | 18.8091i | −0.877200 | + | 0.637323i | ||||
\(872\) | 16.6869 | + | 51.3571i | 0.565090 | + | 1.73917i | ||||
\(873\) | −9.27051 | + | 28.5317i | −0.313759 | + | 0.965652i | ||||
\(874\) | 12.9443 | + | 9.40456i | 0.437847 | + | 0.318114i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.79837 | + | 20.9232i | 0.229565 | + | 0.706528i | 0.997796 | + | 0.0663553i | \(0.0211371\pi\) |
−0.768231 | + | 0.640172i | \(0.778863\pi\) | |||||||
\(878\) | 6.47214 | − | 4.70228i | 0.218424 | − | 0.158694i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 16.9894 | − | 12.3435i | 0.572061 | − | 0.415627i | ||||
\(883\) | −4.94427 | − | 15.2169i | −0.166388 | − | 0.512090i | 0.832748 | − | 0.553652i | \(-0.186766\pi\) |
−0.999136 | + | 0.0415628i | \(0.986766\pi\) | |||||||
\(884\) | −3.70820 | + | 11.4127i | −0.124720 | + | 0.383850i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.47214 | + | 4.70228i | 0.217436 | + | 0.157976i | ||||
\(887\) | −17.3050 | + | 53.2592i | −0.581043 | + | 1.78827i | 0.0335664 | + | 0.999436i | \(0.489313\pi\) |
−0.614610 | + | 0.788831i | \(0.710687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10.0000 | −0.335201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.00000 | 0.133930 | ||||||||
\(893\) | 38.8328 | − | 28.2137i | 1.29949 | − | 0.944135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.23607 | − | 3.80423i | 0.0413172 | − | 0.127161i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.618034 | + | 1.90211i | −0.0206241 | + | 0.0634743i | ||||
\(899\) | 14.8328 | + | 45.6507i | 0.494702 | + | 1.52254i | ||||
\(900\) | −2.42705 | + | 1.76336i | −0.0809017 | + | 0.0587785i | ||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.5623 | − | 10.5801i | 0.484335 | − | 0.351890i | ||||
\(905\) | −3.09017 | − | 9.51057i | −0.102721 | − | 0.316142i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.3607 | + | 23.5114i | 1.07452 | + | 0.780684i | 0.976719 | − | 0.214523i | \(-0.0688195\pi\) |
0.0977997 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(908\) | 16.1803 | + | 11.7557i | 0.536963 | + | 0.390127i | ||||
\(909\) | −9.27051 | + | 28.5317i | −0.307483 | + | 0.946337i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.47214 | + | 4.70228i | −0.214431 | + | 0.155794i | −0.689816 | − | 0.723984i | \(-0.742309\pi\) |
0.475385 | + | 0.879778i | \(0.342309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.0000 | −0.860004 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.09017 | + | 9.51057i | 0.102102 | + | 0.314238i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.4164 | + | 14.1068i | 0.640488 | + | 0.465342i | 0.860018 | − | 0.510264i | \(-0.170452\pi\) |
−0.219530 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(920\) | 3.70820 | − | 11.4127i | 0.122256 | − | 0.376265i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.5066 | − | 19.9847i | 0.905881 | − | 0.658161i | ||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | −29.1246 | + | 21.1603i | −0.957094 | + | 0.695370i | ||||
\(927\) | 3.70820 | + | 11.4127i | 0.121793 | + | 0.374842i | ||||
\(928\) | 9.27051 | − | 28.5317i | 0.304319 | − | 0.936599i | ||||
\(929\) | 11.3262 | + | 8.22899i | 0.371602 | + | 0.269985i | 0.757875 | − | 0.652400i | \(-0.226238\pi\) |
−0.386273 | + | 0.922384i | \(0.626238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.65248 | + | 26.6296i | −0.283573 | + | 0.872749i | ||||
\(932\) | 1.85410 | + | 5.70634i | 0.0607331 | + | 0.186917i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 18.0000 | 0.588348 | ||||||||
\(937\) | 4.85410 | − | 3.52671i | 0.158577 | − | 0.115213i | −0.505667 | − | 0.862729i | \(-0.668754\pi\) |
0.664244 | + | 0.747516i | \(0.268754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.70820 | − | 7.05342i | −0.316647 | − | 0.230057i | ||||
\(941\) | −1.61803 | − | 1.17557i | −0.0527464 | − | 0.0383225i | 0.561100 | − | 0.827748i | \(-0.310378\pi\) |
−0.613846 | + | 0.789426i | \(0.710378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.47214 | − | 7.60845i | −0.0805038 | − | 0.247765i | ||||
\(944\) | 3.23607 | − | 2.35114i | 0.105325 | − | 0.0765231i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.65248 | + | 26.6296i | 0.280871 | + | 0.864433i | ||||
\(950\) | −1.23607 | + | 3.80423i | −0.0401033 | + | 0.123425i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.9787 | − | 39.9444i | 0.420422 | − | 1.29393i | −0.486889 | − | 0.873464i | \(-0.661868\pi\) |
0.907311 | − | 0.420461i | \(-0.138132\pi\) | |||||||
\(954\) | −1.85410 | − | 5.70634i | −0.0600288 | − | 0.184750i | ||||
\(955\) | −6.47214 | + | 4.70228i | −0.209433 | + | 0.152162i | ||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.0000 | 0.775405 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1976 | − | 31.3849i | 0.328954 | − | 1.01242i | ||||
\(962\) | 3.23607 | + | 2.35114i | 0.104335 | + | 0.0758038i | ||||
\(963\) | −29.1246 | − | 21.1603i | −0.938527 | − | 0.681880i | ||||
\(964\) | 3.09017 | − | 9.51057i | 0.0995277 | − | 0.306315i | ||||
\(965\) | 8.03444 | + | 24.7275i | 0.258638 | + | 0.796005i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.09017 | − | 5.87785i | 0.259760 | − | 0.188726i | ||||
\(971\) | 11.1246 | + | 34.2380i | 0.357006 | + | 1.09875i | 0.954837 | + | 0.297129i | \(0.0960292\pi\) |
−0.597832 | + | 0.801622i | \(0.703971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.6525 | + | 16.4580i | 0.725832 | + | 0.527348i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.09017 | − | 9.51057i | −0.0989139 | − | 0.304426i | ||||
\(977\) | −8.09017 | + | 5.87785i | −0.258827 | + | 0.188049i | −0.709630 | − | 0.704575i | \(-0.751138\pi\) |
0.450803 | + | 0.892624i | \(0.351138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7.00000 | 0.223607 | ||||||||
\(981\) | 43.6869 | − | 31.7404i | 1.39482 | − | 1.01339i | ||||
\(982\) | −8.65248 | − | 26.6296i | −0.276112 | − | 0.849784i | ||||
\(983\) | −1.23607 | + | 3.80423i | −0.0394244 | + | 0.121336i | −0.968832 | − | 0.247720i | \(-0.920319\pi\) |
0.929407 | + | 0.369056i | \(0.120319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.61803 | + | 1.17557i | 0.0515548 | + | 0.0374568i | ||||
\(986\) | −11.1246 | + | 34.2380i | −0.354280 | + | 1.09036i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.47214 | + | 4.70228i | −0.205906 | + | 0.149600i | ||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | −32.3607 | + | 23.5114i | −1.02745 | + | 0.746488i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2148 | − | 43.7486i | 0.450187 | − | 1.38553i | −0.426508 | − | 0.904484i | \(-0.640256\pi\) |
0.876694 | − | 0.481048i | \(-0.159744\pi\) | |||||||
\(998\) | 11.1246 | + | 34.2380i | 0.352143 | + | 1.08379i | ||||
\(999\) | 0 | 0 |
(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 | 605.2.g.c.366.1 | 4 | ||
11.2 | odd | 10 | 55.2.a.a.1.1 | ✓ | 1 | ||
11.3 | even | 5 | inner | 605.2.g.c.511.1 | 4 | ||
11.4 | even | 5 | inner | 605.2.g.c.81.1 | 4 | ||
11.5 | even | 5 | inner | 605.2.g.c.251.1 | 4 | ||
11.6 | odd | 10 | 605.2.g.a.251.1 | 4 | |||
11.7 | odd | 10 | 605.2.g.a.81.1 | 4 | |||
11.8 | odd | 10 | 605.2.g.a.511.1 | 4 | |||
11.9 | even | 5 | 605.2.a.b.1.1 | 1 | |||
11.10 | odd | 2 | 605.2.g.a.366.1 | 4 | |||
33.2 | even | 10 | 495.2.a.a.1.1 | 1 | |||
33.20 | odd | 10 | 5445.2.a.i.1.1 | 1 | |||
44.31 | odd | 10 | 9680.2.a.r.1.1 | 1 | |||
44.35 | even | 10 | 880.2.a.h.1.1 | 1 | |||
55.2 | even | 20 | 275.2.b.b.199.2 | 2 | |||
55.9 | even | 10 | 3025.2.a.f.1.1 | 1 | |||
55.13 | even | 20 | 275.2.b.b.199.1 | 2 | |||
55.24 | odd | 10 | 275.2.a.a.1.1 | 1 | |||
77.13 | even | 10 | 2695.2.a.c.1.1 | 1 | |||
88.13 | odd | 10 | 3520.2.a.p.1.1 | 1 | |||
88.35 | even | 10 | 3520.2.a.n.1.1 | 1 | |||
132.35 | odd | 10 | 7920.2.a.i.1.1 | 1 | |||
143.90 | odd | 10 | 9295.2.a.b.1.1 | 1 | |||
165.2 | odd | 20 | 2475.2.c.f.199.1 | 2 | |||
165.68 | odd | 20 | 2475.2.c.f.199.2 | 2 | |||
165.134 | even | 10 | 2475.2.a.i.1.1 | 1 | |||
220.79 | even | 10 | 4400.2.a.p.1.1 | 1 | |||
220.123 | odd | 20 | 4400.2.b.n.4049.2 | 2 | |||
220.167 | odd | 20 | 4400.2.b.n.4049.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.a.1.1 | ✓ | 1 | 11.2 | odd | 10 | ||
275.2.a.a.1.1 | 1 | 55.24 | odd | 10 | |||
275.2.b.b.199.1 | 2 | 55.13 | even | 20 | |||
275.2.b.b.199.2 | 2 | 55.2 | even | 20 | |||
495.2.a.a.1.1 | 1 | 33.2 | even | 10 | |||
605.2.a.b.1.1 | 1 | 11.9 | even | 5 | |||
605.2.g.a.81.1 | 4 | 11.7 | odd | 10 | |||
605.2.g.a.251.1 | 4 | 11.6 | odd | 10 | |||
605.2.g.a.366.1 | 4 | 11.10 | odd | 2 | |||
605.2.g.a.511.1 | 4 | 11.8 | odd | 10 | |||
605.2.g.c.81.1 | 4 | 11.4 | even | 5 | inner | ||
605.2.g.c.251.1 | 4 | 11.5 | even | 5 | inner | ||
605.2.g.c.366.1 | 4 | 1.1 | even | 1 | trivial | ||
605.2.g.c.511.1 | 4 | 11.3 | even | 5 | inner | ||
880.2.a.h.1.1 | 1 | 44.35 | even | 10 | |||
2475.2.a.i.1.1 | 1 | 165.134 | even | 10 | |||
2475.2.c.f.199.1 | 2 | 165.2 | odd | 20 | |||
2475.2.c.f.199.2 | 2 | 165.68 | odd | 20 | |||
2695.2.a.c.1.1 | 1 | 77.13 | even | 10 | |||
3025.2.a.f.1.1 | 1 | 55.9 | even | 10 | |||
3520.2.a.n.1.1 | 1 | 88.35 | even | 10 | |||
3520.2.a.p.1.1 | 1 | 88.13 | odd | 10 | |||
4400.2.a.p.1.1 | 1 | 220.79 | even | 10 | |||
4400.2.b.n.4049.1 | 2 | 220.167 | odd | 20 | |||
4400.2.b.n.4049.2 | 2 | 220.123 | odd | 20 | |||
5445.2.a.i.1.1 | 1 | 33.20 | odd | 10 | |||
7920.2.a.i.1.1 | 1 | 132.35 | odd | 10 | |||
9295.2.a.b.1.1 | 1 | 143.90 | odd | 10 | |||
9680.2.a.r.1.1 | 1 | 44.31 | odd | 10 |