Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(49,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.x (of order \(6\), degree \(2\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.5 | ||
Root | \(1.75374 + 1.62986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.49 |
Dual form | 390.2.x.b.199.5 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.40066 | + | 1.74303i | 0.626394 | + | 0.779507i | ||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −0.763837 | + | 1.32301i | −0.288703 | + | 0.500049i | −0.973501 | − | 0.228685i | \(-0.926557\pi\) |
0.684797 | + | 0.728734i | \(0.259891\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.809179 | + | 2.08452i | −0.255885 | + | 0.659184i | ||||
\(11\) | −1.14057 | + | 0.658509i | −0.343895 | + | 0.198548i | −0.661993 | − | 0.749510i | \(-0.730289\pi\) |
0.318098 | + | 0.948058i | \(0.396956\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.41225 | + | 2.67975i | 0.669037 | + | 0.743229i | ||||
\(14\) | −1.52767 | −0.408288 | ||||||||
\(15\) | 2.08452 | + | 0.809179i | 0.538221 | + | 0.208929i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.35904 | + | 0.784645i | 0.329617 | + | 0.190304i | 0.655671 | − | 0.755047i | \(-0.272386\pi\) |
−0.326054 | + | 0.945351i | \(0.605719\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.18063 | − | 2.41369i | −0.959103 | − | 0.553738i | −0.0632058 | − | 0.998001i | \(-0.520132\pi\) |
−0.895897 | + | 0.444262i | \(0.853466\pi\) | |||||||
\(20\) | −2.20984 | + | 0.341491i | −0.494135 | + | 0.0763597i | ||||
\(21\) | 1.52767i | 0.333366i | ||||||||
\(22\) | −1.14057 | − | 0.658509i | −0.243171 | − | 0.140395i | ||||
\(23\) | 7.31172 | − | 4.22143i | 1.52460 | − | 0.880228i | 0.525025 | − | 0.851087i | \(-0.324056\pi\) |
0.999575 | − | 0.0291412i | \(-0.00927724\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | −1.07631 | + | 4.88278i | −0.215262 | + | 0.976556i | ||||
\(26\) | −1.11461 | + | 3.42894i | −0.218593 | + | 0.672471i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.763837 | − | 1.32301i | −0.144352 | − | 0.250025i | ||||
\(29\) | −2.21438 | − | 3.83543i | −0.411201 | − | 0.712221i | 0.583821 | − | 0.811883i | \(-0.301557\pi\) |
−0.995021 | + | 0.0996620i | \(0.968224\pi\) | |||||||
\(30\) | 0.341491 | + | 2.20984i | 0.0623475 | + | 0.403459i | ||||
\(31\) | − | 1.62745i | − | 0.292299i | −0.989263 | − | 0.146149i | \(-0.953312\pi\) | ||
0.989263 | − | 0.146149i | \(-0.0466880\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.658509 | + | 1.14057i | −0.114632 | + | 0.198548i | ||||
\(34\) | 1.56929i | 0.269131i | ||||||||
\(35\) | −3.37591 | + | 0.521687i | −0.570634 | + | 0.0881813i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 1.40148 | + | 2.42743i | 0.230402 | + | 0.399067i | 0.957926 | − | 0.287014i | \(-0.0926627\pi\) |
−0.727525 | + | 0.686081i | \(0.759329\pi\) | |||||||
\(38\) | − | 4.82738i | − | 0.783104i | ||||||
\(39\) | 3.42894 | + | 1.11461i | 0.549070 | + | 0.178480i | ||||
\(40\) | −1.40066 | − | 1.74303i | −0.221464 | − | 0.275597i | ||||
\(41\) | 1.35904 | − | 0.784645i | 0.212247 | − | 0.122541i | −0.390108 | − | 0.920769i | \(-0.627562\pi\) |
0.602355 | + | 0.798228i | \(0.294229\pi\) | |||||||
\(42\) | −1.32301 | + | 0.763837i | −0.204144 | + | 0.117863i | ||||
\(43\) | 4.58006 | + | 2.64430i | 0.698452 | + | 0.403252i | 0.806771 | − | 0.590865i | \(-0.201213\pi\) |
−0.108318 | + | 0.994116i | \(0.534547\pi\) | |||||||
\(44\) | − | 1.31702i | − | 0.198548i | ||||||
\(45\) | 2.20984 | − | 0.341491i | 0.329423 | − | 0.0509065i | ||||
\(46\) | 7.31172 | + | 4.22143i | 1.07805 | + | 0.622415i | ||||
\(47\) | −4.94552 | −0.721378 | −0.360689 | − | 0.932686i | \(-0.617458\pi\) | ||||
−0.360689 | + | 0.932686i | \(0.617458\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 2.33310 | + | 4.04106i | 0.333301 | + | 0.577294i | ||||
\(50\) | −4.76677 | + | 1.50928i | −0.674123 | + | 0.213444i | ||||
\(51\) | 1.56929 | 0.219744 | ||||||||
\(52\) | −3.52686 | + | 0.749192i | −0.489087 | + | 0.103894i | ||||
\(53\) | − | 13.9161i | − | 1.91152i | −0.294148 | − | 0.955760i | \(-0.595036\pi\) | ||
0.294148 | − | 0.955760i | \(-0.404964\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −2.74535 | − | 1.06570i | −0.370183 | − | 0.143699i | ||||
\(56\) | 0.763837 | − | 1.32301i | 0.102072 | − | 0.176794i | ||||
\(57\) | −4.82738 | −0.639402 | ||||||||
\(58\) | 2.21438 | − | 3.83543i | 0.290763 | − | 0.503616i | ||||
\(59\) | −9.07005 | − | 5.23660i | −1.18082 | − | 0.681747i | −0.224616 | − | 0.974447i | \(-0.572113\pi\) |
−0.956204 | + | 0.292700i | \(0.905446\pi\) | |||||||
\(60\) | −1.74303 | + | 1.40066i | −0.225024 | + | 0.180824i | ||||
\(61\) | 2.49134 | − | 4.31513i | 0.318984 | − | 0.552496i | −0.661293 | − | 0.750128i | \(-0.729992\pi\) |
0.980276 | + | 0.197632i | \(0.0633252\pi\) | |||||||
\(62\) | 1.40941 | − | 0.813725i | 0.178996 | − | 0.103343i | ||||
\(63\) | 0.763837 | + | 1.32301i | 0.0962345 | + | 0.166683i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.29215 | + | 7.95804i | −0.160272 | + | 0.987073i | ||||
\(66\) | −1.31702 | −0.162114 | ||||||||
\(67\) | −1.38628 | − | 2.40112i | −0.169362 | − | 0.293343i | 0.768834 | − | 0.639448i | \(-0.220837\pi\) |
−0.938196 | + | 0.346105i | \(0.887504\pi\) | |||||||
\(68\) | −1.35904 | + | 0.784645i | −0.164808 | + | 0.0951521i | ||||
\(69\) | 4.22143 | − | 7.31172i | 0.508200 | − | 0.880228i | ||||
\(70\) | −2.13975 | − | 2.66278i | −0.255749 | − | 0.318264i | ||||
\(71\) | −12.8513 | − | 7.41968i | −1.52516 | − | 0.880554i | −0.999555 | − | 0.0298269i | \(-0.990504\pi\) |
−0.525608 | − | 0.850727i | \(-0.676162\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −5.98944 | −0.701011 | −0.350505 | − | 0.936561i | \(-0.613990\pi\) | ||||
−0.350505 | + | 0.936561i | \(0.613990\pi\) | |||||||
\(74\) | −1.40148 | + | 2.42743i | −0.162919 | + | 0.282183i | ||||
\(75\) | 1.50928 | + | 4.76677i | 0.174277 | + | 0.550419i | ||||
\(76\) | 4.18063 | − | 2.41369i | 0.479551 | − | 0.276869i | ||||
\(77\) | − | 2.01198i | − | 0.229286i | ||||||
\(78\) | 0.749192 | + | 3.52686i | 0.0848293 | + | 0.399338i | ||||
\(79\) | 4.87632 | 0.548629 | 0.274315 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274315 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(80\) | 0.809179 | − | 2.08452i | 0.0904690 | − | 0.233057i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.35904 | + | 0.784645i | 0.150081 | + | 0.0866495i | ||||
\(83\) | 6.39020 | 0.701416 | 0.350708 | − | 0.936485i | \(-0.385941\pi\) | ||||
0.350708 | + | 0.936485i | \(0.385941\pi\) | |||||||
\(84\) | −1.32301 | − | 0.763837i | −0.144352 | − | 0.0833415i | ||||
\(85\) | 0.535898 | + | 3.46788i | 0.0581263 | + | 0.376144i | ||||
\(86\) | 5.28860i | 0.570284i | ||||||||
\(87\) | −3.83543 | − | 2.21438i | −0.411201 | − | 0.237407i | ||||
\(88\) | 1.14057 | − | 0.658509i | 0.121585 | − | 0.0701973i | ||||
\(89\) | 15.9738 | − | 9.22251i | 1.69322 | − | 0.977584i | 0.741338 | − | 0.671131i | \(-0.234191\pi\) |
0.951886 | − | 0.306452i | \(-0.0991419\pi\) | |||||||
\(90\) | 1.40066 | + | 1.74303i | 0.147642 | + | 0.183732i | ||||
\(91\) | −5.38789 | + | 1.14452i | −0.564804 | + | 0.119978i | ||||
\(92\) | 8.44285i | 0.880228i | ||||||||
\(93\) | −0.813725 | − | 1.40941i | −0.0843794 | − | 0.146149i | ||||
\(94\) | −2.47276 | − | 4.28295i | −0.255046 | − | 0.441752i | ||||
\(95\) | −1.64851 | − | 10.6677i | −0.169133 | − | 1.09449i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −0.963028 | + | 1.66801i | −0.0977807 | + | 0.169361i | −0.910766 | − | 0.412923i | \(-0.864508\pi\) |
0.812985 | + | 0.582285i | \(0.197841\pi\) | |||||||
\(98\) | −2.33310 | + | 4.04106i | −0.235679 | + | 0.408208i | ||||
\(99\) | 1.31702i | 0.132365i | ||||||||
\(100\) | −3.69046 | − | 3.37350i | −0.369046 | − | 0.337350i | ||||
\(101\) | 1.21929 | + | 2.11188i | 0.121324 | + | 0.210140i | 0.920290 | − | 0.391237i | \(-0.127953\pi\) |
−0.798966 | + | 0.601376i | \(0.794619\pi\) | |||||||
\(102\) | 0.784645 | + | 1.35904i | 0.0776914 | + | 0.134565i | ||||
\(103\) | − | 12.4300i | − | 1.22477i | −0.790561 | − | 0.612383i | \(-0.790211\pi\) | ||
0.790561 | − | 0.612383i | \(-0.209789\pi\) | |||||||
\(104\) | −2.41225 | − | 2.67975i | −0.236540 | − | 0.262771i | ||||
\(105\) | −2.66278 | + | 2.13975i | −0.259861 | + | 0.208818i | ||||
\(106\) | 12.0517 | − | 6.95804i | 1.17056 | − | 0.675824i | ||||
\(107\) | 9.07302 | − | 5.23831i | 0.877122 | − | 0.506407i | 0.00741349 | − | 0.999973i | \(-0.497640\pi\) |
0.869708 | + | 0.493566i | \(0.164307\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 17.1799i | 1.64553i | 0.568379 | + | 0.822767i | \(0.307571\pi\) | ||||
−0.568379 | + | 0.822767i | \(0.692429\pi\) | |||||||
\(110\) | −0.449750 | − | 2.91040i | −0.0428820 | − | 0.277495i | ||||
\(111\) | 2.42743 | + | 1.40148i | 0.230402 | + | 0.133022i | ||||
\(112\) | 1.52767 | 0.144352 | ||||||||
\(113\) | −2.25151 | − | 1.29991i | −0.211805 | − | 0.122285i | 0.390345 | − | 0.920669i | \(-0.372356\pi\) |
−0.602150 | + | 0.798383i | \(0.705689\pi\) | |||||||
\(114\) | −2.41369 | − | 4.18063i | −0.226063 | − | 0.391552i | ||||
\(115\) | 17.5993 | + | 6.83178i | 1.64114 | + | 0.637067i | ||||
\(116\) | 4.42877 | 0.411201 | ||||||||
\(117\) | 3.52686 | − | 0.749192i | 0.326058 | − | 0.0692628i | ||||
\(118\) | − | 10.4732i | − | 0.964136i | ||||||
\(119\) | −2.07618 | + | 1.19868i | −0.190323 | + | 0.109883i | ||||
\(120\) | −2.08452 | − | 0.809179i | −0.190290 | − | 0.0738676i | ||||
\(121\) | −4.63273 | + | 8.02413i | −0.421157 | + | 0.729466i | ||||
\(122\) | 4.98268 | 0.451111 | ||||||||
\(123\) | 0.784645 | − | 1.35904i | 0.0707490 | − | 0.122541i | ||||
\(124\) | 1.40941 | + | 0.813725i | 0.126569 | + | 0.0730747i | ||||
\(125\) | −10.0184 | + | 4.96307i | −0.896071 | + | 0.443911i | ||||
\(126\) | −0.763837 | + | 1.32301i | −0.0680481 | + | 0.117863i | ||||
\(127\) | −7.01552 | + | 4.05041i | −0.622527 | + | 0.359416i | −0.777852 | − | 0.628447i | \(-0.783691\pi\) |
0.155325 | + | 0.987863i | \(0.450357\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.28860 | 0.465635 | ||||||||
\(130\) | −7.53794 | + | 2.85998i | −0.661121 | + | 0.250837i | ||||
\(131\) | −2.32506 | −0.203141 | −0.101571 | − | 0.994828i | \(-0.532387\pi\) | ||||
−0.101571 | + | 0.994828i | \(0.532387\pi\) | |||||||
\(132\) | −0.658509 | − | 1.14057i | −0.0573158 | − | 0.0992740i | ||||
\(133\) | 6.38665 | − | 3.68733i | 0.553792 | − | 0.319732i | ||||
\(134\) | 1.38628 | − | 2.40112i | 0.119757 | − | 0.207425i | ||||
\(135\) | 1.74303 | − | 1.40066i | 0.150016 | − | 0.120550i | ||||
\(136\) | −1.35904 | − | 0.784645i | −0.116537 | − | 0.0672827i | ||||
\(137\) | −6.14192 | + | 10.6381i | −0.524740 | + | 0.908876i | 0.474845 | + | 0.880069i | \(0.342504\pi\) |
−0.999585 | + | 0.0288066i | \(0.990829\pi\) | |||||||
\(138\) | 8.44285 | 0.718703 | ||||||||
\(139\) | −3.32861 | + | 5.76531i | −0.282329 | + | 0.489008i | −0.971958 | − | 0.235155i | \(-0.924440\pi\) |
0.689629 | + | 0.724163i | \(0.257774\pi\) | |||||||
\(140\) | 1.23616 | − | 3.18447i | 0.104475 | − | 0.269137i | ||||
\(141\) | −4.28295 | + | 2.47276i | −0.360689 | + | 0.208244i | ||||
\(142\) | − | 14.8394i | − | 1.24529i | ||||||
\(143\) | −4.51598 | − | 1.46796i | −0.377645 | − | 0.122757i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 3.58367 | − | 9.23186i | 0.297607 | − | 0.766664i | ||||
\(146\) | −2.99472 | − | 5.18700i | −0.247845 | − | 0.429280i | ||||
\(147\) | 4.04106 | + | 2.33310i | 0.333301 | + | 0.192431i | ||||
\(148\) | −2.80296 | −0.230402 | ||||||||
\(149\) | −2.60768 | − | 1.50554i | −0.213629 | − | 0.123339i | 0.389368 | − | 0.921082i | \(-0.372694\pi\) |
−0.602997 | + | 0.797744i | \(0.706027\pi\) | |||||||
\(150\) | −3.37350 | + | 3.69046i | −0.275445 | + | 0.301325i | ||||
\(151\) | − | 12.0149i | − | 0.977759i | −0.872351 | − | 0.488880i | \(-0.837406\pi\) | ||
0.872351 | − | 0.488880i | \(-0.162594\pi\) | |||||||
\(152\) | 4.18063 | + | 2.41369i | 0.339094 | + | 0.195776i | ||||
\(153\) | 1.35904 | − | 0.784645i | 0.109872 | − | 0.0634348i | ||||
\(154\) | 1.74242 | − | 1.00599i | 0.140408 | − | 0.0810648i | ||||
\(155\) | 2.83670 | − | 2.27950i | 0.227849 | − | 0.183094i | ||||
\(156\) | −2.67975 | + | 2.41225i | −0.214552 | + | 0.193134i | ||||
\(157\) | 3.01556i | 0.240668i | 0.992733 | + | 0.120334i | \(0.0383965\pi\) | ||||
−0.992733 | + | 0.120334i | \(0.961604\pi\) | |||||||
\(158\) | 2.43816 | + | 4.22302i | 0.193970 | + | 0.335965i | ||||
\(159\) | −6.95804 | − | 12.0517i | −0.551808 | − | 0.955760i | ||||
\(160\) | 2.20984 | − | 0.341491i | 0.174703 | − | 0.0269972i | ||||
\(161\) | 12.8979i | 1.01650i | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 4.95812 | − | 8.58772i | 0.388350 | − | 0.672642i | −0.603878 | − | 0.797077i | \(-0.706379\pi\) |
0.992228 | + | 0.124435i | \(0.0397119\pi\) | |||||||
\(164\) | 1.56929i | 0.122541i | ||||||||
\(165\) | −2.91040 | + | 0.449750i | −0.226574 | + | 0.0350130i | ||||
\(166\) | 3.19510 | + | 5.53408i | 0.247988 | + | 0.429528i | ||||
\(167\) | 6.49472 | + | 11.2492i | 0.502576 | + | 0.870488i | 0.999996 | + | 0.00297754i | \(0.000947782\pi\) |
−0.497419 | + | 0.867510i | \(0.665719\pi\) | |||||||
\(168\) | − | 1.52767i | − | 0.117863i | ||||||
\(169\) | −1.36213 | + | 12.9284i | −0.104779 | + | 0.994496i | ||||
\(170\) | −2.73532 | + | 2.19804i | −0.209789 | + | 0.168582i | ||||
\(171\) | −4.18063 | + | 2.41369i | −0.319701 | + | 0.184579i | ||||
\(172\) | −4.58006 | + | 2.64430i | −0.349226 | + | 0.201626i | ||||
\(173\) | −3.35755 | − | 1.93848i | −0.255270 | − | 0.147380i | 0.366905 | − | 0.930258i | \(-0.380417\pi\) |
−0.622175 | + | 0.782878i | \(0.713751\pi\) | |||||||
\(174\) | − | 4.42877i | − | 0.335744i | ||||||
\(175\) | −5.63782 | − | 5.15361i | −0.426179 | − | 0.389577i | ||||
\(176\) | 1.14057 | + | 0.658509i | 0.0859738 | + | 0.0496370i | ||||
\(177\) | −10.4732 | −0.787213 | ||||||||
\(178\) | 15.9738 | + | 9.22251i | 1.19729 | + | 0.691256i | ||||
\(179\) | 7.05325 | + | 12.2166i | 0.527185 | + | 0.913111i | 0.999498 | + | 0.0316802i | \(0.0100858\pi\) |
−0.472313 | + | 0.881431i | \(0.656581\pi\) | |||||||
\(180\) | −0.809179 | + | 2.08452i | −0.0603126 | + | 0.155371i | ||||
\(181\) | −26.1472 | −1.94351 | −0.971753 | − | 0.236001i | \(-0.924163\pi\) | ||||
−0.971753 | + | 0.236001i | \(0.924163\pi\) | |||||||
\(182\) | −3.68513 | − | 4.09379i | −0.273160 | − | 0.303452i | ||||
\(183\) | − | 4.98268i | − | 0.368331i | ||||||
\(184\) | −7.31172 | + | 4.22143i | −0.539027 | + | 0.311208i | ||||
\(185\) | −2.26809 | + | 5.84282i | −0.166754 | + | 0.429573i | ||||
\(186\) | 0.813725 | − | 1.40941i | 0.0596652 | − | 0.103343i | ||||
\(187\) | −2.06678 | −0.151138 | ||||||||
\(188\) | 2.47276 | − | 4.28295i | 0.180345 | − | 0.312366i | ||||
\(189\) | 1.32301 | + | 0.763837i | 0.0962345 | + | 0.0555610i | ||||
\(190\) | 8.41426 | − | 6.76151i | 0.610435 | − | 0.490531i | ||||
\(191\) | −9.42713 | + | 16.3283i | −0.682123 | + | 1.18147i | 0.292208 | + | 0.956355i | \(0.405610\pi\) |
−0.974332 | + | 0.225117i | \(0.927723\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 8.94600 | + | 15.4949i | 0.643947 | + | 1.11535i | 0.984544 | + | 0.175140i | \(0.0560378\pi\) |
−0.340596 | + | 0.940210i | \(0.610629\pi\) | |||||||
\(194\) | −1.92606 | −0.138283 | ||||||||
\(195\) | 2.85998 | + | 7.53794i | 0.204808 | + | 0.539803i | ||||
\(196\) | −4.66621 | −0.333301 | ||||||||
\(197\) | −0.312928 | − | 0.542008i | −0.0222952 | − | 0.0386165i | 0.854663 | − | 0.519184i | \(-0.173764\pi\) |
−0.876958 | + | 0.480567i | \(0.840431\pi\) | |||||||
\(198\) | −1.14057 | + | 0.658509i | −0.0810568 | + | 0.0467982i | ||||
\(199\) | −8.84057 | + | 15.3123i | −0.626691 | + | 1.08546i | 0.361520 | + | 0.932364i | \(0.382258\pi\) |
−0.988211 | + | 0.153097i | \(0.951075\pi\) | |||||||
\(200\) | 1.07631 | − | 4.88278i | 0.0761065 | − | 0.345265i | ||||
\(201\) | −2.40112 | − | 1.38628i | −0.169362 | − | 0.0977810i | ||||
\(202\) | −1.21929 | + | 2.11188i | −0.0857891 | + | 0.148591i | ||||
\(203\) | 6.76572 | 0.474860 | ||||||||
\(204\) | −0.784645 | + | 1.35904i | −0.0549361 | + | 0.0951521i | ||||
\(205\) | 3.27122 | + | 1.26984i | 0.228472 | + | 0.0886892i | ||||
\(206\) | 10.7647 | − | 6.21501i | 0.750013 | − | 0.433020i | ||||
\(207\) | − | 8.44285i | − | 0.586819i | ||||||
\(208\) | 1.11461 | − | 3.42894i | 0.0772842 | − | 0.237754i | ||||
\(209\) | 6.35774 | 0.439774 | ||||||||
\(210\) | −3.18447 | − | 1.23616i | −0.219749 | − | 0.0853033i | ||||
\(211\) | −8.62227 | − | 14.9342i | −0.593581 | − | 1.02811i | −0.993745 | − | 0.111669i | \(-0.964380\pi\) |
0.400164 | − | 0.916443i | \(-0.368953\pi\) | |||||||
\(212\) | 12.0517 | + | 6.95804i | 0.827712 | + | 0.477880i | ||||
\(213\) | −14.8394 | −1.01678 | ||||||||
\(214\) | 9.07302 | + | 5.23831i | 0.620219 | + | 0.358083i | ||||
\(215\) | 1.80601 | + | 11.6869i | 0.123169 | + | 0.797043i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 2.15313 | + | 1.24311i | 0.146164 | + | 0.0843877i | ||||
\(218\) | −14.8782 | + | 8.58994i | −1.00768 | + | 0.581784i | ||||
\(219\) | −5.18700 | + | 2.99472i | −0.350505 | + | 0.202364i | ||||
\(220\) | 2.29560 | − | 1.84469i | 0.154769 | − | 0.124369i | ||||
\(221\) | 1.17570 | + | 5.53466i | 0.0790861 | + | 0.372301i | ||||
\(222\) | 2.80296i | 0.188122i | ||||||||
\(223\) | 2.44858 | + | 4.24107i | 0.163969 | + | 0.284003i | 0.936289 | − | 0.351231i | \(-0.114237\pi\) |
−0.772320 | + | 0.635234i | \(0.780904\pi\) | |||||||
\(224\) | 0.763837 | + | 1.32301i | 0.0510360 | + | 0.0883970i | ||||
\(225\) | 3.69046 | + | 3.37350i | 0.246031 | + | 0.224900i | ||||
\(226\) | − | 2.59982i | − | 0.172938i | ||||||
\(227\) | −5.07567 | + | 8.79132i | −0.336884 | + | 0.583500i | −0.983845 | − | 0.179023i | \(-0.942706\pi\) |
0.646961 | + | 0.762523i | \(0.276040\pi\) | |||||||
\(228\) | 2.41369 | − | 4.18063i | 0.159850 | − | 0.276869i | ||||
\(229\) | 15.3959i | 1.01739i | 0.860947 | + | 0.508694i | \(0.169871\pi\) | ||||
−0.860947 | + | 0.508694i | \(0.830129\pi\) | |||||||
\(230\) | 2.88316 | + | 18.6573i | 0.190110 | + | 1.23023i | ||||
\(231\) | −1.00599 | − | 1.74242i | −0.0661891 | − | 0.114643i | ||||
\(232\) | 2.21438 | + | 3.83543i | 0.145381 | + | 0.251808i | ||||
\(233\) | 9.91624i | 0.649634i | 0.945777 | + | 0.324817i | \(0.105303\pi\) | ||||
−0.945777 | + | 0.324817i | \(0.894697\pi\) | |||||||
\(234\) | 2.41225 | + | 2.67975i | 0.157694 | + | 0.175181i | ||||
\(235\) | −6.92699 | − | 8.62019i | −0.451867 | − | 0.562319i | ||||
\(236\) | 9.07005 | − | 5.23660i | 0.590410 | − | 0.340873i | ||||
\(237\) | 4.22302 | − | 2.43816i | 0.274315 | − | 0.158376i | ||||
\(238\) | −2.07618 | − | 1.19868i | −0.134579 | − | 0.0776990i | ||||
\(239\) | 9.46167i | 0.612024i | 0.952028 | + | 0.306012i | \(0.0989948\pi\) | ||||
−0.952028 | + | 0.306012i | \(0.901005\pi\) | |||||||
\(240\) | −0.341491 | − | 2.20984i | −0.0220432 | − | 0.142644i | ||||
\(241\) | 11.3482 | + | 6.55189i | 0.731002 | + | 0.422044i | 0.818789 | − | 0.574095i | \(-0.194646\pi\) |
−0.0877865 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(242\) | −9.26546 | −0.595607 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 2.49134 | + | 4.31513i | 0.159492 | + | 0.276248i | ||||
\(245\) | −3.77580 | + | 9.72681i | −0.241227 | + | 0.621423i | ||||
\(246\) | 1.56929 | 0.100054 | ||||||||
\(247\) | −3.61663 | − | 17.0255i | −0.230121 | − | 1.08330i | ||||
\(248\) | 1.62745i | 0.103343i | ||||||||
\(249\) | 5.53408 | − | 3.19510i | 0.350708 | − | 0.202481i | ||||
\(250\) | −9.30734 | − | 6.19463i | −0.588648 | − | 0.391783i | ||||
\(251\) | 11.5822 | − | 20.0610i | 0.731062 | − | 1.26624i | −0.225367 | − | 0.974274i | \(-0.572358\pi\) |
0.956430 | − | 0.291963i | \(-0.0943085\pi\) | |||||||
\(252\) | −1.52767 | −0.0962345 | ||||||||
\(253\) | −5.55969 | + | 9.62967i | −0.349535 | + | 0.605412i | ||||
\(254\) | −7.01552 | − | 4.05041i | −0.440193 | − | 0.254146i | ||||
\(255\) | 2.19804 | + | 2.73532i | 0.137647 | + | 0.171292i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.32895 | + | 1.92197i | −0.207654 | + | 0.119889i | −0.600221 | − | 0.799834i | \(-0.704921\pi\) |
0.392566 | + | 0.919724i | \(0.371587\pi\) | |||||||
\(258\) | 2.64430 | + | 4.58006i | 0.164627 | + | 0.285142i | ||||
\(259\) | −4.28201 | −0.266071 | ||||||||
\(260\) | −6.24579 | − | 5.09805i | −0.387347 | − | 0.316168i | ||||
\(261\) | −4.42877 | −0.274134 | ||||||||
\(262\) | −1.16253 | − | 2.01356i | −0.0718213 | − | 0.124398i | ||||
\(263\) | 26.5060 | − | 15.3032i | 1.63443 | − | 0.943638i | 0.651726 | − | 0.758455i | \(-0.274045\pi\) |
0.982704 | − | 0.185184i | \(-0.0592880\pi\) | |||||||
\(264\) | 0.658509 | − | 1.14057i | 0.0405284 | − | 0.0701973i | ||||
\(265\) | 24.2561 | − | 19.4917i | 1.49004 | − | 1.19736i | ||||
\(266\) | 6.38665 | + | 3.68733i | 0.391590 | + | 0.226085i | ||||
\(267\) | 9.22251 | − | 15.9738i | 0.564408 | − | 0.977584i | ||||
\(268\) | 2.77257 | 0.169362 | ||||||||
\(269\) | 9.04370 | − | 15.6641i | 0.551404 | − | 0.955060i | −0.446769 | − | 0.894649i | \(-0.647426\pi\) |
0.998174 | − | 0.0604109i | \(-0.0192411\pi\) | |||||||
\(270\) | 2.08452 | + | 0.809179i | 0.126860 | + | 0.0492451i | ||||
\(271\) | 12.2869 | − | 7.09382i | 0.746373 | − | 0.430919i | −0.0780089 | − | 0.996953i | \(-0.524856\pi\) |
0.824382 | + | 0.566034i | \(0.191523\pi\) | |||||||
\(272\) | − | 1.56929i | − | 0.0951521i | ||||||
\(273\) | −4.09379 | + | 3.68513i | −0.247767 | + | 0.223034i | ||||
\(274\) | −12.2838 | −0.742094 | ||||||||
\(275\) | −1.98775 | − | 6.27792i | −0.119866 | − | 0.378573i | ||||
\(276\) | 4.22143 | + | 7.31172i | 0.254100 | + | 0.440114i | ||||
\(277\) | 14.5855 | + | 8.42097i | 0.876360 | + | 0.505967i | 0.869457 | − | 0.494009i | \(-0.164469\pi\) |
0.00690380 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(278\) | −6.65721 | −0.399273 | ||||||||
\(279\) | −1.40941 | − | 0.813725i | −0.0843794 | − | 0.0487165i | ||||
\(280\) | 3.37591 | − | 0.521687i | 0.201749 | − | 0.0311768i | ||||
\(281\) | − | 8.61535i | − | 0.513949i | −0.966418 | − | 0.256974i | \(-0.917274\pi\) | ||
0.966418 | − | 0.256974i | \(-0.0827256\pi\) | |||||||
\(282\) | −4.28295 | − | 2.47276i | −0.255046 | − | 0.147251i | ||||
\(283\) | −23.9192 | + | 13.8098i | −1.42185 | + | 0.820905i | −0.996457 | − | 0.0841040i | \(-0.973197\pi\) |
−0.425392 | + | 0.905009i | \(0.639864\pi\) | |||||||
\(284\) | 12.8513 | − | 7.41968i | 0.762582 | − | 0.440277i | ||||
\(285\) | −6.76151 | − | 8.41426i | −0.400517 | − | 0.498418i | ||||
\(286\) | −0.986699 | − | 4.64493i | −0.0583447 | − | 0.274661i | ||||
\(287\) | 2.39736i | 0.141512i | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −7.26867 | − | 12.5897i | −0.427569 | − | 0.740570i | ||||
\(290\) | 9.78686 | − | 1.51239i | 0.574704 | − | 0.0888103i | ||||
\(291\) | 1.92606i | 0.112907i | ||||||||
\(292\) | 2.99472 | − | 5.18700i | 0.175253 | − | 0.303546i | ||||
\(293\) | −15.1250 | + | 26.1973i | −0.883614 | + | 1.53046i | −0.0363205 | + | 0.999340i | \(0.511564\pi\) |
−0.847294 | + | 0.531125i | \(0.821770\pi\) | |||||||
\(294\) | 4.66621i | 0.272139i | ||||||||
\(295\) | −3.57650 | − | 23.1441i | −0.208232 | − | 1.34750i | ||||
\(296\) | −1.40148 | − | 2.42743i | −0.0814593 | − | 0.141092i | ||||
\(297\) | 0.658509 | + | 1.14057i | 0.0382106 | + | 0.0661826i | ||||
\(298\) | − | 3.01108i | − | 0.174427i | ||||||
\(299\) | 28.9501 | + | 9.41048i | 1.67422 | + | 0.544222i | ||||
\(300\) | −4.88278 | − | 1.07631i | −0.281908 | − | 0.0621407i | ||||
\(301\) | −6.99684 | + | 4.03963i | −0.403291 | + | 0.232840i | ||||
\(302\) | 10.4052 | − | 6.00745i | 0.598753 | − | 0.345690i | ||||
\(303\) | 2.11188 | + | 1.21929i | 0.121324 | + | 0.0700465i | ||||
\(304\) | 4.82738i | 0.276869i | ||||||||
\(305\) | 11.0109 | − | 1.70154i | 0.630484 | − | 0.0974300i | ||||
\(306\) | 1.35904 | + | 0.784645i | 0.0776914 | + | 0.0448552i | ||||
\(307\) | −14.1392 | −0.806966 | −0.403483 | − | 0.914987i | \(-0.632201\pi\) | ||||
−0.403483 | + | 0.914987i | \(0.632201\pi\) | |||||||
\(308\) | 1.74242 | + | 1.00599i | 0.0992837 | + | 0.0573215i | ||||
\(309\) | −6.21501 | − | 10.7647i | −0.353559 | − | 0.612383i | ||||
\(310\) | 3.39246 | + | 1.31690i | 0.192679 | + | 0.0747948i | ||||
\(311\) | −9.97427 | −0.565589 | −0.282794 | − | 0.959181i | \(-0.591261\pi\) | ||||
−0.282794 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(312\) | −3.42894 | − | 1.11461i | −0.194126 | − | 0.0631023i | ||||
\(313\) | 3.08460i | 0.174352i | 0.996193 | + | 0.0871760i | \(0.0277843\pi\) | ||||
−0.996193 | + | 0.0871760i | \(0.972216\pi\) | |||||||
\(314\) | −2.61155 | + | 1.50778i | −0.147378 | + | 0.0850888i | ||||
\(315\) | −1.23616 | + | 3.18447i | −0.0696499 | + | 0.179425i | ||||
\(316\) | −2.43816 | + | 4.22302i | −0.137157 | + | 0.237563i | ||||
\(317\) | 14.2980 | 0.803054 | 0.401527 | − | 0.915847i | \(-0.368480\pi\) | ||||
0.401527 | + | 0.915847i | \(0.368480\pi\) | |||||||
\(318\) | 6.95804 | − | 12.0517i | 0.390187 | − | 0.675824i | ||||
\(319\) | 5.05132 | + | 2.91638i | 0.282820 | + | 0.163286i | ||||
\(320\) | 1.40066 | + | 1.74303i | 0.0782992 | + | 0.0974384i | ||||
\(321\) | 5.23831 | − | 9.07302i | 0.292374 | − | 0.506407i | ||||
\(322\) | −11.1699 | + | 6.44897i | −0.622476 | + | 0.359387i | ||||
\(323\) | −3.78778 | − | 6.56062i | −0.210757 | − | 0.365043i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −15.6810 | + | 8.89424i | −0.869823 | + | 0.493363i | ||||
\(326\) | 9.91624 | 0.549210 | ||||||||
\(327\) | 8.58994 | + | 14.8782i | 0.475025 | + | 0.822767i | ||||
\(328\) | −1.35904 | + | 0.784645i | −0.0750407 | + | 0.0433248i | ||||
\(329\) | 3.77757 | − | 6.54295i | 0.208264 | − | 0.360724i | ||||
\(330\) | −1.84469 | − | 2.29560i | −0.101547 | − | 0.126369i | ||||
\(331\) | −9.89017 | − | 5.71009i | −0.543613 | − | 0.313855i | 0.202929 | − | 0.979193i | \(-0.434954\pi\) |
−0.746542 | + | 0.665338i | \(0.768287\pi\) | |||||||
\(332\) | −3.19510 | + | 5.53408i | −0.175354 | + | 0.303722i | ||||
\(333\) | 2.80296 | 0.153601 | ||||||||
\(334\) | −6.49472 | + | 11.2492i | −0.355375 | + | 0.615528i | ||||
\(335\) | 2.24351 | − | 5.77948i | 0.122576 | − | 0.315767i | ||||
\(336\) | 1.32301 | − | 0.763837i | 0.0721759 | − | 0.0416708i | ||||
\(337\) | − | 5.53208i | − | 0.301352i | −0.988583 | − | 0.150676i | \(-0.951855\pi\) | ||
0.988583 | − | 0.150676i | \(-0.0481450\pi\) | |||||||
\(338\) | −11.8774 | + | 5.28458i | −0.646047 | + | 0.287443i | ||||
\(339\) | −2.59982 | −0.141203 | ||||||||
\(340\) | −3.27122 | − | 1.26984i | −0.177407 | − | 0.0688665i | ||||
\(341\) | 1.07169 | + | 1.85622i | 0.0580353 | + | 0.100520i | ||||
\(342\) | −4.18063 | − | 2.41369i | −0.226063 | − | 0.130517i | ||||
\(343\) | −17.8222 | −0.962307 | ||||||||
\(344\) | −4.58006 | − | 2.64430i | −0.246940 | − | 0.142571i | ||||
\(345\) | 18.6573 | − | 2.88316i | 1.00448 | − | 0.155224i | ||||
\(346\) | − | 3.87696i | − | 0.208427i | ||||||
\(347\) | −2.44226 | − | 1.41004i | −0.131107 | − | 0.0756949i | 0.433012 | − | 0.901388i | \(-0.357451\pi\) |
−0.564119 | + | 0.825693i | \(0.690784\pi\) | |||||||
\(348\) | 3.83543 | − | 2.21438i | 0.205600 | − | 0.118703i | ||||
\(349\) | 23.0704 | − | 13.3197i | 1.23493 | − | 0.712986i | 0.266875 | − | 0.963731i | \(-0.414009\pi\) |
0.968053 | + | 0.250745i | \(0.0806757\pi\) | |||||||
\(350\) | 1.64425 | − | 7.45930i | 0.0878889 | − | 0.398717i | ||||
\(351\) | 2.67975 | − | 2.41225i | 0.143035 | − | 0.128756i | ||||
\(352\) | 1.31702i | 0.0701973i | ||||||||
\(353\) | 6.61308 | + | 11.4542i | 0.351979 | + | 0.609645i | 0.986596 | − | 0.163182i | \(-0.0521757\pi\) |
−0.634617 | + | 0.772826i | \(0.718842\pi\) | |||||||
\(354\) | −5.23660 | − | 9.07005i | −0.278322 | − | 0.482068i | ||||
\(355\) | −5.06751 | − | 32.7926i | −0.268955 | − | 1.74045i | ||||
\(356\) | 18.4450i | 0.977584i | ||||||||
\(357\) | −1.19868 | + | 2.07618i | −0.0634410 | + | 0.109883i | ||||
\(358\) | −7.05325 | + | 12.2166i | −0.372776 | + | 0.645667i | ||||
\(359\) | − | 12.3827i | − | 0.653532i | −0.945105 | − | 0.326766i | \(-0.894041\pi\) | ||
0.945105 | − | 0.326766i | \(-0.105959\pi\) | |||||||
\(360\) | −2.20984 | + | 0.341491i | −0.116469 | + | 0.0179982i | ||||
\(361\) | 2.15178 | + | 3.72700i | 0.113252 | + | 0.196158i | ||||
\(362\) | −13.0736 | − | 22.6441i | −0.687133 | − | 1.19015i | ||||
\(363\) | 9.26546i | 0.486311i | ||||||||
\(364\) | 1.70276 | − | 5.23831i | 0.0892489 | − | 0.274562i | ||||
\(365\) | −8.38916 | − | 10.4398i | −0.439109 | − | 0.546443i | ||||
\(366\) | 4.31513 | − | 2.49134i | 0.225556 | − | 0.130225i | ||||
\(367\) | 6.14226 | − | 3.54624i | 0.320623 | − | 0.185112i | −0.331047 | − | 0.943614i | \(-0.607402\pi\) |
0.651670 | + | 0.758502i | \(0.274069\pi\) | |||||||
\(368\) | −7.31172 | − | 4.22143i | −0.381150 | − | 0.220057i | ||||
\(369\) | − | 1.56929i | − | 0.0816939i | ||||||
\(370\) | −6.19408 | + | 0.957185i | −0.322015 | + | 0.0497617i | ||||
\(371\) | 18.4110 | + | 10.6296i | 0.955854 | + | 0.551862i | ||||
\(372\) | 1.62745 | 0.0843794 | ||||||||
\(373\) | −32.0259 | − | 18.4902i | −1.65824 | − | 0.957384i | −0.973528 | − | 0.228568i | \(-0.926596\pi\) |
−0.684709 | − | 0.728816i | \(-0.740071\pi\) | |||||||
\(374\) | −1.03339 | − | 1.78989i | −0.0534354 | − | 0.0925528i | ||||
\(375\) | −6.19463 | + | 9.30734i | −0.319890 | + | 0.480629i | ||||
\(376\) | 4.94552 | 0.255046 | ||||||||
\(377\) | 4.93634 | − | 15.1860i | 0.254235 | − | 0.782118i | ||||
\(378\) | 1.52767i | 0.0785751i | ||||||||
\(379\) | −29.6252 | + | 17.1041i | −1.52174 | + | 0.878580i | −0.522075 | + | 0.852900i | \(0.674842\pi\) |
−0.999670 | + | 0.0256802i | \(0.991825\pi\) | |||||||
\(380\) | 10.0628 | + | 3.90621i | 0.516209 | + | 0.200384i | ||||
\(381\) | −4.05041 | + | 7.01552i | −0.207509 | + | 0.359416i | ||||
\(382\) | −18.8543 | −0.964668 | ||||||||
\(383\) | −13.0170 | + | 22.5461i | −0.665137 | + | 1.15205i | 0.314111 | + | 0.949386i | \(0.398294\pi\) |
−0.979248 | + | 0.202665i | \(0.935040\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 3.50693 | − | 2.81809i | 0.178730 | − | 0.143623i | ||||
\(386\) | −8.94600 | + | 15.4949i | −0.455340 | + | 0.788671i | ||||
\(387\) | 4.58006 | − | 2.64430i | 0.232817 | − | 0.134417i | ||||
\(388\) | −0.963028 | − | 1.66801i | −0.0488904 | − | 0.0846806i | ||||
\(389\) | −6.23568 | −0.316162 | −0.158081 | − | 0.987426i | \(-0.550531\pi\) | ||||
−0.158081 | + | 0.987426i | \(0.550531\pi\) | |||||||
\(390\) | −5.09805 | + | 6.24579i | −0.258150 | + | 0.316268i | ||||
\(391\) | 13.2493 | 0.670045 | ||||||||
\(392\) | −2.33310 | − | 4.04106i | −0.117840 | − | 0.204104i | ||||
\(393\) | −2.01356 | + | 1.16253i | −0.101571 | + | 0.0586419i | ||||
\(394\) | 0.312928 | − | 0.542008i | 0.0157651 | − | 0.0273060i | ||||
\(395\) | 6.83007 | + | 8.49958i | 0.343658 | + | 0.427660i | ||||
\(396\) | −1.14057 | − | 0.658509i | −0.0573158 | − | 0.0330913i | ||||
\(397\) | 18.3498 | − | 31.7827i | 0.920948 | − | 1.59513i | 0.122997 | − | 0.992407i | \(-0.460750\pi\) |
0.797951 | − | 0.602722i | \(-0.205917\pi\) | |||||||
\(398\) | −17.6811 | −0.886275 | ||||||||
\(399\) | 3.68733 | − | 6.38665i | 0.184597 | − | 0.319732i | ||||
\(400\) | 4.76677 | − | 1.50928i | 0.238338 | − | 0.0754640i | ||||
\(401\) | 24.5044 | − | 14.1476i | 1.22369 | − | 0.706498i | 0.257987 | − | 0.966148i | \(-0.416941\pi\) |
0.965703 | + | 0.259651i | \(0.0836074\pi\) | |||||||
\(402\) | − | 2.77257i | − | 0.138283i | ||||||
\(403\) | 4.36116 | − | 3.92581i | 0.217245 | − | 0.195559i | ||||
\(404\) | −2.43859 | −0.121324 | ||||||||
\(405\) | 0.809179 | − | 2.08452i | 0.0402084 | − | 0.103581i | ||||
\(406\) | 3.38286 | + | 5.85928i | 0.167888 | + | 0.290791i | ||||
\(407\) | −3.19697 | − | 1.84577i | −0.158468 | − | 0.0914915i | ||||
\(408\) | −1.56929 | −0.0776914 | ||||||||
\(409\) | 13.2744 | + | 7.66400i | 0.656379 | + | 0.378961i | 0.790896 | − | 0.611951i | \(-0.209615\pi\) |
−0.134517 | + | 0.990911i | \(0.542948\pi\) | |||||||
\(410\) | 0.535898 | + | 3.46788i | 0.0264661 | + | 0.171266i | ||||
\(411\) | 12.2838i | 0.605917i | ||||||||
\(412\) | 10.7647 | + | 6.21501i | 0.530339 | + | 0.306191i | ||||
\(413\) | 13.8561 | − | 7.99982i | 0.681814 | − | 0.393645i | ||||
\(414\) | 7.31172 | − | 4.22143i | 0.359352 | − | 0.207472i | ||||
\(415\) | 8.95050 | + | 11.1383i | 0.439363 | + | 0.546758i | ||||
\(416\) | 3.52686 | − | 0.749192i | 0.172918 | − | 0.0367322i | ||||
\(417\) | 6.65721i | 0.326005i | ||||||||
\(418\) | 3.17887 | + | 5.50597i | 0.155484 | + | 0.269306i | ||||
\(419\) | −13.4692 | − | 23.3293i | −0.658013 | − | 1.13971i | −0.981129 | − | 0.193353i | \(-0.938064\pi\) |
0.323116 | − | 0.946359i | \(-0.395270\pi\) | |||||||
\(420\) | −0.521687 | − | 3.37591i | −0.0254557 | − | 0.164728i | ||||
\(421\) | − | 38.5359i | − | 1.87812i | −0.343747 | − | 0.939062i | \(-0.611696\pi\) | ||
0.343747 | − | 0.939062i | \(-0.388304\pi\) | |||||||
\(422\) | 8.62227 | − | 14.9342i | 0.419725 | − | 0.726986i | ||||
\(423\) | −2.47276 | + | 4.28295i | −0.120230 | + | 0.208244i | ||||
\(424\) | 13.9161i | 0.675824i | ||||||||
\(425\) | −5.29400 | + | 5.79140i | −0.256797 | + | 0.280924i | ||||
\(426\) | −7.41968 | − | 12.8513i | −0.359484 | − | 0.622645i | ||||
\(427\) | 3.80596 | + | 6.59212i | 0.184183 | + | 0.319015i | ||||
\(428\) | 10.4766i | 0.506407i | ||||||||
\(429\) | −4.64493 | + | 0.986699i | −0.224259 | + | 0.0476383i | ||||
\(430\) | −9.21818 | + | 7.40752i | −0.444540 | + | 0.357222i | ||||
\(431\) | 2.48744 | − | 1.43612i | 0.119816 | − | 0.0691756i | −0.438894 | − | 0.898539i | \(-0.644630\pi\) |
0.558710 | + | 0.829363i | \(0.311296\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 11.2344 | + | 6.48619i | 0.539891 | + | 0.311706i | 0.745035 | − | 0.667026i | \(-0.232433\pi\) |
−0.205144 | + | 0.978732i | \(0.565766\pi\) | |||||||
\(434\) | 2.48622i | 0.119342i | ||||||||
\(435\) | −1.51239 | − | 9.78686i | −0.0725133 | − | 0.469244i | ||||
\(436\) | −14.8782 | − | 8.58994i | −0.712537 | − | 0.411383i | ||||
\(437\) | −40.7568 | −1.94966 | ||||||||
\(438\) | −5.18700 | − | 2.99472i | −0.247845 | − | 0.143093i | ||||
\(439\) | −1.02411 | − | 1.77380i | −0.0488779 | − | 0.0846590i | 0.840551 | − | 0.541732i | \(-0.182231\pi\) |
−0.889429 | + | 0.457073i | \(0.848898\pi\) | |||||||
\(440\) | 2.74535 | + | 1.06570i | 0.130880 | + | 0.0508054i | ||||
\(441\) | 4.66621 | 0.222200 | ||||||||
\(442\) | −4.20530 | + | 3.78551i | −0.200026 | + | 0.180059i | ||||
\(443\) | − | 25.7082i | − | 1.22143i | −0.791849 | − | 0.610717i | \(-0.790881\pi\) | ||
0.791849 | − | 0.610717i | \(-0.209119\pi\) | |||||||
\(444\) | −2.42743 | + | 1.40148i | −0.115201 | + | 0.0665112i | ||||
\(445\) | 38.4490 | + | 14.9253i | 1.82266 | + | 0.707528i | ||||
\(446\) | −2.44858 | + | 4.24107i | −0.115944 | + | 0.200820i | ||||
\(447\) | −3.01108 | −0.142419 | ||||||||
\(448\) | −0.763837 | + | 1.32301i | −0.0360879 | + | 0.0625061i | ||||
\(449\) | −16.0756 | − | 9.28127i | −0.758656 | − | 0.438010i | 0.0701571 | − | 0.997536i | \(-0.477650\pi\) |
−0.828813 | + | 0.559526i | \(0.810983\pi\) | |||||||
\(450\) | −1.07631 | + | 4.88278i | −0.0507377 | + | 0.230177i | ||||
\(451\) | −1.03339 | + | 1.78989i | −0.0486605 | + | 0.0842824i | ||||
\(452\) | 2.25151 | − | 1.29991i | 0.105902 | − | 0.0611427i | ||||
\(453\) | −6.00745 | − | 10.4052i | −0.282255 | − | 0.488880i | ||||
\(454\) | −10.1513 | −0.476426 | ||||||||
\(455\) | −9.54153 | − | 7.78817i | −0.447314 | − | 0.365115i | ||||
\(456\) | 4.82738 | 0.226063 | ||||||||
\(457\) | 12.3213 | + | 21.3412i | 0.576368 | + | 0.998299i | 0.995891 | + | 0.0905546i | \(0.0288640\pi\) |
−0.419523 | + | 0.907745i | \(0.637803\pi\) | |||||||
\(458\) | −13.3332 | + | 7.69794i | −0.623020 | + | 0.359701i | ||||
\(459\) | 0.784645 | − | 1.35904i | 0.0366241 | − | 0.0634348i | ||||
\(460\) | −14.7161 | + | 11.8256i | −0.686144 | + | 0.551369i | ||||
\(461\) | −27.5693 | − | 15.9171i | −1.28403 | − | 0.741334i | −0.306446 | − | 0.951888i | \(-0.599140\pi\) |
−0.977582 | + | 0.210554i | \(0.932473\pi\) | |||||||
\(462\) | 1.00599 | − | 1.74242i | 0.0468028 | − | 0.0810648i | ||||
\(463\) | −3.18319 | −0.147936 | −0.0739678 | − | 0.997261i | \(-0.523566\pi\) | ||||
−0.0739678 | + | 0.997261i | \(0.523566\pi\) | |||||||
\(464\) | −2.21438 | + | 3.83543i | −0.102800 | + | 0.178055i | ||||
\(465\) | 1.31690 | − | 3.39246i | 0.0610697 | − | 0.157321i | ||||
\(466\) | −8.58772 | + | 4.95812i | −0.397818 | + | 0.229680i | ||||
\(467\) | 21.6747i | 1.00298i | 0.865162 | + | 0.501492i | \(0.167215\pi\) | ||||
−0.865162 | + | 0.501492i | \(0.832785\pi\) | |||||||
\(468\) | −1.11461 | + | 3.42894i | −0.0515228 | + | 0.158503i | ||||
\(469\) | 4.23559 | 0.195581 | ||||||||
\(470\) | 4.00181 | − | 10.3090i | 0.184590 | − | 0.475521i | ||||
\(471\) | 1.50778 | + | 2.61155i | 0.0694747 | + | 0.120334i | ||||
\(472\) | 9.07005 | + | 5.23660i | 0.417483 | + | 0.241034i | ||||
\(473\) | −6.96517 | −0.320259 | ||||||||
\(474\) | 4.22302 | + | 2.43816i | 0.193970 | + | 0.111988i | ||||
\(475\) | 16.2852 | − | 17.8152i | 0.747215 | − | 0.817419i | ||||
\(476\) | − | 2.39736i | − | 0.109883i | ||||||
\(477\) | −12.0517 | − | 6.95804i | −0.551808 | − | 0.318587i | ||||
\(478\) | −8.19404 | + | 4.73083i | −0.374787 | + | 0.216383i | ||||
\(479\) | −25.3765 | + | 14.6511i | −1.15948 | + | 0.669426i | −0.951179 | − | 0.308639i | \(-0.900127\pi\) |
−0.208300 | + | 0.978065i | \(0.566793\pi\) | |||||||
\(480\) | 1.74303 | − | 1.40066i | 0.0795581 | − | 0.0639310i | ||||
\(481\) | −3.12420 | + | 9.61118i | −0.142451 | + | 0.438232i | ||||
\(482\) | 13.1038i | 0.596861i | ||||||||
\(483\) | 6.44897 | + | 11.1699i | 0.293438 | + | 0.508250i | ||||
\(484\) | −4.63273 | − | 8.02413i | −0.210579 | − | 0.364733i | ||||
\(485\) | −4.25627 | + | 0.657731i | −0.193267 | + | 0.0298660i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 21.2643 | − | 36.8309i | 0.963579 | − | 1.66897i | 0.250194 | − | 0.968196i | \(-0.419506\pi\) |
0.713385 | − | 0.700772i | \(-0.247161\pi\) | |||||||
\(488\) | −2.49134 | + | 4.31513i | −0.112778 | + | 0.195337i | ||||
\(489\) | − | 9.91624i | − | 0.448428i | ||||||
\(490\) | −10.3116 | + | 1.59347i | −0.465829 | + | 0.0719856i | ||||
\(491\) | 6.32521 | + | 10.9556i | 0.285453 | + | 0.494418i | 0.972719 | − | 0.231987i | \(-0.0745228\pi\) |
−0.687266 | + | 0.726406i | \(0.741189\pi\) | |||||||
\(492\) | 0.784645 | + | 1.35904i | 0.0353745 | + | 0.0612705i | ||||
\(493\) | − | 6.95002i | − | 0.313013i | ||||||
\(494\) | 12.9362 | − | 11.6448i | 0.582026 | − | 0.523925i | ||||
\(495\) | −2.29560 | + | 1.84469i | −0.103180 | + | 0.0829128i | ||||
\(496\) | −1.40941 | + | 0.813725i | −0.0632845 | + | 0.0365373i | ||||
\(497\) | 19.6325 | − | 11.3349i | 0.880640 | − | 0.508438i | ||||
\(498\) | 5.53408 | + | 3.19510i | 0.247988 | + | 0.143176i | ||||
\(499\) | − | 4.54007i | − | 0.203242i | −0.994823 | − | 0.101621i | \(-0.967597\pi\) | ||
0.994823 | − | 0.101621i | \(-0.0324028\pi\) | |||||||
\(500\) | 0.711042 | − | 11.1577i | 0.0317988 | − | 0.498988i | ||||
\(501\) | 11.2492 | + | 6.49472i | 0.502576 | + | 0.290163i | ||||
\(502\) | 23.1644 | 1.03388 | ||||||||
\(503\) | 17.2476 | + | 9.95791i | 0.769033 | + | 0.444001i | 0.832529 | − | 0.553981i | \(-0.186892\pi\) |
−0.0634967 | + | 0.997982i | \(0.520225\pi\) | |||||||
\(504\) | −0.763837 | − | 1.32301i | −0.0340240 | − | 0.0589313i | ||||
\(505\) | −1.97325 | + | 5.08328i | −0.0878086 | + | 0.226203i | ||||
\(506\) | −11.1194 | −0.494317 | ||||||||
\(507\) | 5.28458 | + | 11.8774i | 0.234697 | + | 0.527495i | ||||
\(508\) | − | 8.10083i | − | 0.359416i | ||||||
\(509\) | −9.09532 | + | 5.25118i | −0.403143 | + | 0.232755i | −0.687839 | − | 0.725863i | \(-0.741441\pi\) |
0.284696 | + | 0.958618i | \(0.408107\pi\) | |||||||
\(510\) | −1.26984 | + | 3.27122i | −0.0562293 | + | 0.144852i | ||||
\(511\) | 4.57496 | − | 7.92406i | 0.202384 | − | 0.350540i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.41369 | + | 4.18063i | −0.106567 | + | 0.184579i | ||||
\(514\) | −3.32895 | − | 1.92197i | −0.146834 | − | 0.0847746i | ||||
\(515\) | 21.6659 | − | 17.4102i | 0.954713 | − | 0.767185i | ||||
\(516\) | −2.64430 | + | 4.58006i | −0.116409 | + | 0.201626i | ||||
\(517\) | 5.64072 | − | 3.25667i | 0.248078 | − | 0.143228i | ||||
\(518\) | −2.14100 | − | 3.70833i | −0.0940703 | − | 0.162934i | ||||
\(519\) | −3.87696 | −0.170180 | ||||||||
\(520\) | 1.29215 | − | 7.95804i | 0.0566646 | − | 0.348983i | ||||
\(521\) | −24.5221 | −1.07433 | −0.537166 | − | 0.843477i | \(-0.680505\pi\) | ||||
−0.537166 | + | 0.843477i | \(0.680505\pi\) | |||||||
\(522\) | −2.21438 | − | 3.83543i | −0.0969210 | − | 0.167872i | ||||
\(523\) | −21.6924 | + | 12.5241i | −0.948541 | + | 0.547641i | −0.892627 | − | 0.450795i | \(-0.851141\pi\) |
−0.0559138 | + | 0.998436i | \(0.517807\pi\) | |||||||
\(524\) | 1.16253 | − | 2.01356i | 0.0507853 | − | 0.0879628i | ||||
\(525\) | −7.45930 | − | 1.64425i | −0.325551 | − | 0.0717610i | ||||
\(526\) | 26.5060 | + | 15.3032i | 1.15572 | + | 0.667253i | ||||
\(527\) | 1.27697 | − | 2.21178i | 0.0556257 | − | 0.0963466i | ||||
\(528\) | 1.31702 | 0.0573158 | ||||||||
\(529\) | 24.1409 | − | 41.8132i | 1.04960 | − | 1.81797i | ||||
\(530\) | 29.0084 | + | 11.2606i | 1.26004 | + | 0.489129i | ||||
\(531\) | −9.07005 | + | 5.23660i | −0.393607 | + | 0.227249i | ||||
\(532\) | 7.37466i | 0.319732i | ||||||||
\(533\) | 5.38100 | + | 1.74914i | 0.233077 | + | 0.0757638i | ||||
\(534\) | 18.4450 | 0.798194 | ||||||||
\(535\) | 21.8387 | + | 8.47746i | 0.944171 | + | 0.366513i | ||||
\(536\) | 1.38628 | + | 2.40112i | 0.0598784 | + | 0.103712i | ||||
\(537\) | 12.2166 | + | 7.05325i | 0.527185 | + | 0.304370i | ||||
\(538\) | 18.0874 | 0.779803 | ||||||||
\(539\) | −5.32214 | − | 3.07274i | −0.229241 | − | 0.132352i | ||||
\(540\) | 0.341491 | + | 2.20984i | 0.0146954 | + | 0.0950963i | ||||
\(541\) | 20.6859i | 0.889356i | 0.895690 | + | 0.444678i | \(0.146682\pi\) | ||||
−0.895690 | + | 0.444678i | \(0.853318\pi\) | |||||||
\(542\) | 12.2869 | + | 7.09382i | 0.527765 | + | 0.304705i | ||||
\(543\) | −22.6441 | + | 13.0736i | −0.971753 | + | 0.561042i | ||||
\(544\) | 1.35904 | − | 0.784645i | 0.0582686 | − | 0.0336414i | ||||
\(545\) | −29.9450 | + | 24.0631i | −1.28270 | + | 1.03075i | ||||
\(546\) | −5.23831 | − | 1.70276i | −0.224179 | − | 0.0728714i | ||||
\(547\) | 40.5960i | 1.73576i | 0.496773 | + | 0.867880i | \(0.334518\pi\) | ||||
−0.496773 | + | 0.867880i | \(0.665482\pi\) | |||||||
\(548\) | −6.14192 | − | 10.6381i | −0.262370 | − | 0.454438i | ||||
\(549\) | −2.49134 | − | 4.31513i | −0.106328 | − | 0.184165i | ||||
\(550\) | 4.44296 | − | 4.86040i | 0.189449 | − | 0.207248i | ||||
\(551\) | 21.3793i | 0.910790i | ||||||||
\(552\) | −4.22143 | + | 7.31172i | −0.179676 | + | 0.311208i | ||||
\(553\) | −3.72472 | + | 6.45140i | −0.158391 | + | 0.274342i | ||||
\(554\) | 16.8419i | 0.715545i | ||||||||
\(555\) | 0.957185 | + | 6.19408i | 0.0406302 | + | 0.262924i | ||||
\(556\) | −3.32861 | − | 5.76531i | −0.141164 | − | 0.244504i | ||||
\(557\) | −20.6032 | − | 35.6858i | −0.872985 | − | 1.51205i | −0.858894 | − | 0.512153i | \(-0.828848\pi\) |
−0.0140907 | − | 0.999901i | \(-0.504485\pi\) | |||||||
\(558\) | − | 1.62745i | − | 0.0688955i | ||||||
\(559\) | 3.96217 | + | 18.6521i | 0.167582 | + | 0.788900i | ||||
\(560\) | 2.13975 | + | 2.66278i | 0.0904210 | + | 0.112523i | ||||
\(561\) | −1.78989 | + | 1.03339i | −0.0755690 | + | 0.0436298i | ||||
\(562\) | 7.46112 | − | 4.30768i | 0.314728 | − | 0.181708i | ||||
\(563\) | 13.0933 | + | 7.55940i | 0.551815 | + | 0.318591i | 0.749854 | − | 0.661603i | \(-0.230124\pi\) |
−0.198038 | + | 0.980194i | \(0.563457\pi\) | |||||||
\(564\) | − | 4.94552i | − | 0.208244i | ||||||
\(565\) | −0.887817 | − | 5.74519i | −0.0373507 | − | 0.241702i | ||||
\(566\) | −23.9192 | − | 13.8098i | −1.00540 | − | 0.580468i | ||||
\(567\) | 1.52767 | 0.0641563 | ||||||||
\(568\) | 12.8513 | + | 7.41968i | 0.539227 | + | 0.311323i | ||||
\(569\) | −13.2995 | − | 23.0353i | −0.557542 | − | 0.965692i | −0.997701 | − | 0.0677716i | \(-0.978411\pi\) |
0.440159 | − | 0.897920i | \(-0.354922\pi\) | |||||||
\(570\) | 3.90621 | − | 10.0628i | 0.163613 | − | 0.421483i | ||||
\(571\) | 31.8452 | 1.33268 | 0.666340 | − | 0.745648i | \(-0.267860\pi\) | ||||
0.666340 | + | 0.745648i | \(0.267860\pi\) | |||||||
\(572\) | 3.52928 | − | 3.17697i | 0.147567 | − | 0.132836i | ||||
\(573\) | 18.8543i | 0.787648i | ||||||||
\(574\) | −2.07618 | + | 1.19868i | −0.0866580 | + | 0.0500320i | ||||
\(575\) | 12.7426 | + | 40.2451i | 0.531404 | + | 1.67834i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 1.20258 | 0.0500639 | 0.0250319 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250319 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(578\) | 7.26867 | − | 12.5897i | 0.302337 | − | 0.523662i | ||||
\(579\) | 15.4949 | + | 8.94600i | 0.643947 | + | 0.371783i | ||||
\(580\) | 6.20319 | + | 7.71948i | 0.257574 | + | 0.320534i | ||||
\(581\) | −4.88108 | + | 8.45427i | −0.202501 | + | 0.350742i | ||||
\(582\) | −1.66801 | + | 0.963028i | −0.0691414 | + | 0.0399188i | ||||
\(583\) | 9.16386 | + | 15.8723i | 0.379528 | + | 0.657362i | ||||
\(584\) | 5.98944 | 0.247845 | ||||||||
\(585\) | 6.24579 | + | 5.09805i | 0.258231 | + | 0.210779i | ||||
\(586\) | −30.2501 | −1.24962 | ||||||||
\(587\) | 9.53243 | + | 16.5107i | 0.393446 | + | 0.681468i | 0.992901 | − | 0.118940i | \(-0.0379496\pi\) |
−0.599456 | + | 0.800408i | \(0.704616\pi\) | |||||||
\(588\) | −4.04106 | + | 2.33310i | −0.166650 | + | 0.0962156i | ||||
\(589\) | −3.92816 | + | 6.80377i | −0.161857 | + | 0.280344i | ||||
\(590\) | 18.2551 | − | 14.6694i | 0.751550 | − | 0.603929i | ||||
\(591\) | −0.542008 | − | 0.312928i | −0.0222952 | − | 0.0128722i | ||||
\(592\) | 1.40148 | − | 2.42743i | 0.0576004 | − | 0.0997668i | ||||
\(593\) | 11.8496 | 0.486606 | 0.243303 | − | 0.969950i | \(-0.421769\pi\) | ||||
0.243303 | + | 0.969950i | \(0.421769\pi\) | |||||||
\(594\) | −0.658509 | + | 1.14057i | −0.0270189 | + | 0.0467982i | ||||
\(595\) | −4.99736 | − | 1.93990i | −0.204872 | − | 0.0795280i | ||||
\(596\) | 2.60768 | − | 1.50554i | 0.106815 | − | 0.0616694i | ||||
\(597\) | 17.6811i | 0.723641i | ||||||||
\(598\) | 6.32532 | + | 29.7767i | 0.258661 | + | 1.21766i | ||||
\(599\) | 13.1277 | 0.536382 | 0.268191 | − | 0.963366i | \(-0.413574\pi\) | ||||
0.268191 | + | 0.963366i | \(0.413574\pi\) | |||||||
\(600\) | −1.50928 | − | 4.76677i | −0.0616161 | − | 0.194602i | ||||
\(601\) | 17.8125 | + | 30.8522i | 0.726589 | + | 1.25849i | 0.958317 | + | 0.285708i | \(0.0922288\pi\) |
−0.231728 | + | 0.972781i | \(0.574438\pi\) | |||||||
\(602\) | −6.99684 | − | 4.03963i | −0.285170 | − | 0.164643i | ||||
\(603\) | −2.77257 | −0.112908 | ||||||||
\(604\) | 10.4052 | + | 6.00745i | 0.423382 | + | 0.244440i | ||||
\(605\) | −20.4752 | + | 3.16407i | −0.832434 | + | 0.128638i | ||||
\(606\) | 2.43859i | 0.0990608i | ||||||||
\(607\) | 4.20075 | + | 2.42530i | 0.170503 | + | 0.0984400i | 0.582823 | − | 0.812599i | \(-0.301948\pi\) |
−0.412320 | + | 0.911039i | \(0.635281\pi\) | |||||||
\(608\) | −4.18063 | + | 2.41369i | −0.169547 | + | 0.0978880i | ||||
\(609\) | 5.85928 | − | 3.38286i | 0.237430 | − | 0.137080i | ||||
\(610\) | 6.97904 | + | 8.68497i | 0.282573 | + | 0.351644i | ||||
\(611\) | −11.9298 | − | 13.2528i | −0.482629 | − | 0.536149i | ||||
\(612\) | 1.56929i | 0.0634348i | ||||||||
\(613\) | −11.7172 | − | 20.2948i | −0.473253 | − | 0.819698i | 0.526279 | − | 0.850312i | \(-0.323587\pi\) |
−0.999531 | + | 0.0306146i | \(0.990254\pi\) | |||||||
\(614\) | −7.06959 | − | 12.2449i | −0.285306 | − | 0.494164i | ||||
\(615\) | 3.46788 | − | 0.535898i | 0.139838 | − | 0.0216095i | ||||
\(616\) | 2.01198i | 0.0810648i | ||||||||
\(617\) | 7.01830 | − | 12.1560i | 0.282546 | − | 0.489384i | −0.689465 | − | 0.724319i | \(-0.742154\pi\) |
0.972011 | + | 0.234935i | \(0.0754877\pi\) | |||||||
\(618\) | 6.21501 | − | 10.7647i | 0.250004 | − | 0.433020i | ||||
\(619\) | 16.1470i | 0.649002i | 0.945885 | + | 0.324501i | \(0.105196\pi\) | ||||
−0.945885 | + | 0.324501i | \(0.894804\pi\) | |||||||
\(620\) | 0.555760 | + | 3.59640i | 0.0223199 | + | 0.144435i | ||||
\(621\) | −4.22143 | − | 7.31172i | −0.169400 | − | 0.293409i | ||||
\(622\) | −4.98713 | − | 8.63797i | −0.199966 | − | 0.346351i | ||||
\(623\) | 28.1780i | 1.12893i | ||||||||
\(624\) | −0.749192 | − | 3.52686i | −0.0299917 | − | 0.141187i | ||||
\(625\) | −22.6831 | − | 10.5108i | −0.907325 | − | 0.420431i | ||||
\(626\) | −2.67134 | + | 1.54230i | −0.106768 | + | 0.0616428i | ||||
\(627\) | 5.50597 | − | 3.17887i | 0.219887 | − | 0.126952i | ||||
\(628\) | −2.61155 | − | 1.50778i | −0.104212 | − | 0.0601669i | ||||
\(629\) | 4.39865i | 0.175386i | ||||||||
\(630\) | −3.37591 | + | 0.521687i | −0.134500 | + | 0.0207845i | ||||
\(631\) | 16.3611 | + | 9.44608i | 0.651325 | + | 0.376043i | 0.788964 | − | 0.614440i | \(-0.210618\pi\) |
−0.137639 | + | 0.990483i | \(0.543951\pi\) | |||||||
\(632\) | −4.87632 | −0.193970 | ||||||||
\(633\) | −14.9342 | − | 8.62227i | −0.593581 | − | 0.342704i | ||||
\(634\) | 7.14899 | + | 12.3824i | 0.283922 | + | 0.491768i | ||||
\(635\) | −16.8863 | − | 6.55502i | −0.670114 | − | 0.260128i | ||||
\(636\) | 13.9161 | 0.551808 | ||||||||
\(637\) | −5.20100 | + | 16.0002i | −0.206071 | + | 0.633950i | ||||
\(638\) | 5.83277i | 0.230921i | ||||||||
\(639\) | −12.8513 | + | 7.41968i | −0.508388 | + | 0.293518i | ||||
\(640\) | −0.809179 | + | 2.08452i | −0.0319856 | + | 0.0823979i | ||||
\(641\) | 3.57648 | − | 6.19465i | 0.141262 | − | 0.244674i | −0.786710 | − | 0.617323i | \(-0.788217\pi\) |
0.927972 | + | 0.372649i | \(0.121551\pi\) | |||||||
\(642\) | 10.4766 | 0.413479 | ||||||||
\(643\) | −19.9623 | + | 34.5756i | −0.787235 | + | 1.36353i | 0.140420 | + | 0.990092i | \(0.455155\pi\) |
−0.927655 | + | 0.373438i | \(0.878179\pi\) | |||||||
\(644\) | −11.1699 | − | 6.44897i | −0.440157 | − | 0.254125i | ||||
\(645\) | 7.40752 | + | 9.21818i | 0.291671 | + | 0.362966i | ||||
\(646\) | 3.78778 | − | 6.56062i | 0.149028 | − | 0.258124i | ||||
\(647\) | −12.0656 | + | 6.96608i | −0.474348 | + | 0.273865i | −0.718058 | − | 0.695983i | \(-0.754969\pi\) |
0.243710 | + | 0.969848i | \(0.421635\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 13.7934 | 0.541438 | ||||||||
\(650\) | −15.5431 | − | 9.13299i | −0.609651 | − | 0.358225i | ||||
\(651\) | 2.48622 | 0.0974425 | ||||||||
\(652\) | 4.95812 | + | 8.58772i | 0.194175 | + | 0.336321i | ||||
\(653\) | 25.7670 | − | 14.8766i | 1.00834 | − | 0.582165i | 0.0976340 | − | 0.995222i | \(-0.468873\pi\) |
0.910705 | + | 0.413058i | \(0.135539\pi\) | |||||||
\(654\) | −8.58994 | + | 14.8782i | −0.335893 | + | 0.581784i | ||||
\(655\) | −3.25662 | − | 4.05265i | −0.127246 | − | 0.158350i | ||||
\(656\) | −1.35904 | − | 0.784645i | −0.0530618 | − | 0.0306352i | ||||
\(657\) | −2.99472 | + | 5.18700i | −0.116835 | + | 0.202364i | ||||
\(658\) | 7.55515 | 0.294530 | ||||||||
\(659\) | −14.6318 | + | 25.3431i | −0.569975 | + | 0.987226i | 0.426593 | + | 0.904444i | \(0.359714\pi\) |
−0.996568 | + | 0.0827819i | \(0.973620\pi\) | |||||||
\(660\) | 1.06570 | − | 2.74535i | 0.0414824 | − | 0.106863i | ||||
\(661\) | −30.0903 | + | 17.3726i | −1.17038 | + | 0.675717i | −0.953769 | − | 0.300541i | \(-0.902833\pi\) |
−0.216608 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(662\) | − | 11.4202i | − | 0.443858i | ||||||
\(663\) | 3.78551 | + | 4.20530i | 0.147017 | + | 0.163320i | ||||
\(664\) | −6.39020 | −0.247988 | ||||||||
\(665\) | 15.3726 | + | 5.96742i | 0.596125 | + | 0.231407i | ||||
\(666\) | 1.40148 | + | 2.42743i | 0.0543062 | + | 0.0940611i | ||||
\(667\) | −32.3819 | − | 18.6957i | −1.25383 | − | 0.723901i | ||||
\(668\) | −12.9894 | −0.502576 | ||||||||
\(669\) | 4.24107 | + | 2.44858i | 0.163969 | + | 0.0946676i | ||||
\(670\) | 6.12693 | − | 0.946808i | 0.236704 | − | 0.0365784i | ||||
\(671\) | 6.56228i | 0.253334i | ||||||||
\(672\) | 1.32301 | + | 0.763837i | 0.0510360 | + | 0.0294657i | ||||
\(673\) | 28.1953 | − | 16.2786i | 1.08685 | − | 0.627492i | 0.154113 | − | 0.988053i | \(-0.450748\pi\) |
0.932736 | + | 0.360561i | \(0.117415\pi\) | |||||||
\(674\) | 4.79092 | − | 2.76604i | 0.184539 | − | 0.106544i | ||||
\(675\) | 4.88278 | + | 1.07631i | 0.187938 | + | 0.0414272i | ||||
\(676\) | −10.5153 | − | 7.64386i | −0.404434 | − | 0.293995i | ||||
\(677\) | − | 32.2002i | − | 1.23756i | −0.785566 | − | 0.618778i | \(-0.787628\pi\) | ||
0.785566 | − | 0.618778i | \(-0.212372\pi\) | |||||||
\(678\) | −1.29991 | − | 2.25151i | −0.0499228 | − | 0.0864689i | ||||
\(679\) | −1.47119 | − | 2.54818i | −0.0564593 | − | 0.0977903i | ||||
\(680\) | −0.535898 | − | 3.46788i | −0.0205508 | − | 0.132987i | ||||
\(681\) | 10.1513i | 0.389000i | ||||||||
\(682\) | −1.07169 | + | 1.85622i | −0.0410372 | + | 0.0710784i | ||||
\(683\) | −3.19280 | + | 5.53009i | −0.122169 | + | 0.211603i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(684\) | − | 4.82738i | − | 0.184579i | ||||||
\(685\) | −27.1453 | + | 4.19482i | −1.03717 | + | 0.160276i | ||||
\(686\) | −8.91109 | − | 15.4345i | −0.340227 | − | 0.589290i | ||||
\(687\) | 7.69794 | + | 13.3332i | 0.293695 | + | 0.508694i | ||||
\(688\) | − | 5.28860i | − | 0.201626i | ||||||
\(689\) | 37.2916 | − | 33.5690i | 1.42070 | − | 1.27888i | ||||
\(690\) | 11.8256 | + | 14.7161i | 0.450191 | + | 0.560234i | ||||
\(691\) | 13.6788 | − | 7.89748i | 0.520368 | − | 0.300434i | −0.216717 | − | 0.976234i | \(-0.569535\pi\) |
0.737085 | + | 0.675800i | \(0.236202\pi\) | |||||||
\(692\) | 3.35755 | − | 1.93848i | 0.127635 | − | 0.0736900i | ||||
\(693\) | −1.74242 | − | 1.00599i | −0.0661891 | − | 0.0382143i | ||||
\(694\) | − | 2.82008i | − | 0.107049i | ||||||
\(695\) | −14.7114 | + | 2.27338i | −0.558034 | + | 0.0862342i | ||||
\(696\) | 3.83543 | + | 2.21438i | 0.145381 | + | 0.0839360i | ||||
\(697\) | 2.46267 | 0.0932803 | ||||||||
\(698\) | 23.0704 | + | 13.3197i | 0.873226 | + | 0.504157i | ||||
\(699\) | 4.95812 | + | 8.58772i | 0.187533 | + | 0.324817i | ||||
\(700\) | 7.28207 | − | 2.30569i | 0.275236 | − | 0.0871469i | ||||
\(701\) | −43.7481 | −1.65234 | −0.826171 | − | 0.563420i | \(-0.809485\pi\) | ||||
−0.826171 | + | 0.563420i | \(0.809485\pi\) | |||||||
\(702\) | 3.42894 | + | 1.11461i | 0.129417 | + | 0.0420682i | ||||
\(703\) | − | 13.5309i | − | 0.510329i | ||||||
\(704\) | −1.14057 | + | 0.658509i | −0.0429869 | + | 0.0248185i | ||||
\(705\) | −10.3090 | − | 4.00181i | −0.388261 | − | 0.150717i | ||||
\(706\) | −6.61308 | + | 11.4542i | −0.248886 | + | 0.431084i | ||||
\(707\) | −3.72537 | −0.140107 | ||||||||
\(708\) | 5.23660 | − | 9.07005i | 0.196803 | − | 0.340873i | ||||
\(709\) | −30.0167 | − | 17.3302i | −1.12730 | − | 0.650848i | −0.184046 | − | 0.982918i | \(-0.558920\pi\) |
−0.943255 | + | 0.332070i | \(0.892253\pi\) | |||||||
\(710\) | 25.8654 | − | 20.7849i | 0.970713 | − | 0.780042i | ||||
\(711\) | 2.43816 | − | 4.22302i | 0.0914382 | − | 0.158376i | ||||
\(712\) | −15.9738 | + | 9.22251i | −0.598645 | + | 0.345628i | ||||
\(713\) | −6.87016 | − | 11.8995i | −0.257290 | − | 0.445639i | ||||
\(714\) | −2.39736 | −0.0897191 | ||||||||
\(715\) | −3.76665 | − | 9.92760i | −0.140865 | − | 0.371271i | ||||
\(716\) | −14.1065 | −0.527185 | ||||||||
\(717\) | 4.73083 | + | 8.19404i | 0.176676 | + | 0.306012i | ||||
\(718\) | 10.7237 | − | 6.19133i | 0.400205 | − | 0.231058i | ||||
\(719\) | −21.9251 | + | 37.9755i | −0.817670 | + | 1.41625i | 0.0897253 | + | 0.995967i | \(0.471401\pi\) |
−0.907395 | + | 0.420279i | \(0.861932\pi\) | |||||||
\(720\) | −1.40066 | − | 1.74303i | −0.0521995 | − | 0.0649589i | ||||
\(721\) | 16.4450 | + | 9.49451i | 0.612443 | + | 0.353594i | ||||
\(722\) | −2.15178 | + | 3.72700i | −0.0800811 | + | 0.138704i | ||||
\(723\) | 13.1038 | 0.487335 | ||||||||
\(724\) | 13.0736 | − | 22.6441i | 0.485876 | − | 0.841563i | ||||
\(725\) | 21.1109 | − | 6.68425i | 0.784040 | − | 0.248247i | ||||
\(726\) | −8.02413 | + | 4.63273i | −0.297803 | + | 0.171937i | ||||
\(727\) | − | 17.2599i | − | 0.640136i | −0.947395 | − | 0.320068i | \(-0.896294\pi\) | ||
0.947395 | − | 0.320068i | \(-0.103706\pi\) | |||||||
\(728\) | 5.38789 | − | 1.14452i | 0.199688 | − | 0.0424188i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.84653 | − | 12.4851i | 0.179378 | − | 0.462095i | ||||
\(731\) | 4.14967 | + | 7.18744i | 0.153481 | + | 0.265837i | ||||
\(732\) | 4.31513 | + | 2.49134i | 0.159492 | + | 0.0920826i | ||||
\(733\) | 0.304799 | 0.0112580 | 0.00562900 | − | 0.999984i | \(-0.498208\pi\) | ||||
0.00562900 | + | 0.999984i | \(0.498208\pi\) | |||||||
\(734\) | 6.14226 | + | 3.54624i | 0.226715 | + | 0.130894i | ||||
\(735\) | 1.59347 | + | 10.3116i | 0.0587760 | + | 0.380348i | ||||
\(736\) | − | 8.44285i | − | 0.311208i | ||||||
\(737\) | 3.16231 | + | 1.82576i | 0.116485 | + | 0.0672528i | ||||
\(738\) | 1.35904 | − | 0.784645i | 0.0500271 | − | 0.0288832i | ||||
\(739\) | 3.14941 | − | 1.81831i | 0.115853 | − | 0.0668877i | −0.440954 | − | 0.897530i | \(-0.645360\pi\) |
0.556807 | + | 0.830642i | \(0.312026\pi\) | |||||||
\(740\) | −3.92599 | − | 4.88564i | −0.144322 | − | 0.179600i | ||||
\(741\) | −11.6448 | − | 12.9362i | −0.427783 | − | 0.475222i | ||||
\(742\) | 21.2592i | 0.780451i | ||||||||
\(743\) | −15.1150 | − | 26.1800i | −0.554517 | − | 0.960451i | −0.997941 | − | 0.0641394i | \(-0.979570\pi\) |
0.443424 | − | 0.896312i | \(-0.353764\pi\) | |||||||
\(744\) | 0.813725 | + | 1.40941i | 0.0298326 | + | 0.0516716i | ||||
\(745\) | −1.02826 | − | 6.65401i | −0.0376725 | − | 0.243784i | ||||
\(746\) | − | 36.9803i | − | 1.35395i | ||||||
\(747\) | 3.19510 | − | 5.53408i | 0.116903 | − | 0.202481i | ||||
\(748\) | 1.03339 | − | 1.78989i | 0.0377845 | − | 0.0654447i | ||||
\(749\) | 16.0049i | 0.584805i | ||||||||
\(750\) | −11.1577 | − | 0.711042i | −0.407422 | − | 0.0259636i | ||||
\(751\) | −0.00159080 | − | 0.00275535i | −5.80493e−5 | − | 0.000100544i | 0.865996 | − | 0.500050i | \(-0.166685\pi\) |
−0.866054 | + | 0.499950i | \(0.833352\pi\) | |||||||
\(752\) | 2.47276 | + | 4.28295i | 0.0901723 | + | 0.156183i | ||||
\(753\) | − | 23.1644i | − | 0.844158i | ||||||
\(754\) | 15.6196 | − | 3.31800i | 0.568833 | − | 0.120834i | ||||
\(755\) | 20.9423 | − | 16.8288i | 0.762170 | − | 0.612462i | ||||
\(756\) | −1.32301 | + | 0.763837i | −0.0481172 | + | 0.0277805i | ||||
\(757\) | −36.4328 | + | 21.0345i | −1.32417 | + | 0.764512i | −0.984392 | − | 0.175992i | \(-0.943687\pi\) |
−0.339782 | + | 0.940504i | \(0.610353\pi\) | |||||||
\(758\) | −29.6252 | − | 17.1041i | −1.07604 | − | 0.621250i | ||||
\(759\) | 11.1194i | 0.403608i | ||||||||
\(760\) | 1.64851 | + | 10.6677i | 0.0597976 | + | 0.386959i | ||||
\(761\) | 21.1489 | + | 12.2103i | 0.766646 | + | 0.442623i | 0.831677 | − | 0.555260i | \(-0.187381\pi\) |
−0.0650310 | + | 0.997883i | \(0.520715\pi\) | |||||||
\(762\) | −8.10083 | −0.293462 | ||||||||
\(763\) | −22.7291 | − | 13.1226i | −0.822847 | − | 0.475071i | ||||
\(764\) | −9.42713 | − | 16.3283i | −0.341062 | − | 0.590736i | ||||
\(765\) | 3.27122 | + | 1.26984i | 0.118271 | + | 0.0459110i | ||||
\(766\) | −26.0340 | −0.940646 | ||||||||
\(767\) | −7.84643 | − | 36.9374i | −0.283318 | − | 1.33373i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −28.1198 | + | 16.2350i | −1.01403 | + | 0.585449i | −0.912368 | − | 0.409370i | \(-0.865748\pi\) |
−0.101659 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(770\) | 4.19401 | + | 1.62805i | 0.151141 | + | 0.0586708i | ||||
\(771\) | −1.92197 | + | 3.32895i | −0.0692182 | + | 0.119889i | ||||
\(772\) | −17.8920 | −0.643947 | ||||||||
\(773\) | 4.13819 | − | 7.16756i | 0.148840 | − | 0.257799i | −0.781959 | − | 0.623330i | \(-0.785779\pi\) |
0.930799 | + | 0.365531i | \(0.119113\pi\) | |||||||
\(774\) | 4.58006 | + | 2.64430i | 0.164627 | + | 0.0950473i | ||||
\(775\) | 7.94649 | + | 1.75164i | 0.285446 | + | 0.0629208i | ||||
\(776\) | 0.963028 | − | 1.66801i | 0.0345707 | − | 0.0598782i | ||||
\(777\) | −3.70833 | + | 2.14100i | −0.133035 | + | 0.0768081i | ||||
\(778\) | −3.11784 | − | 5.40026i | −0.111780 | − | 0.193609i | ||||
\(779\) | −7.57555 | −0.271422 | ||||||||
\(780\) | −7.95804 | − | 1.29215i | −0.284943 | − | 0.0462664i | ||||
\(781\) | 19.5437 | 0.699328 | ||||||||
\(782\) | 6.62464 | + | 11.4742i | 0.236897 | + | 0.410317i | ||||
\(783\) | −3.83543 | + | 2.21438i | −0.137067 | + | 0.0791356i | ||||
\(784\) | 2.33310 | − | 4.04106i | 0.0833252 | − | 0.144323i | ||||
\(785\) | −5.25620 | + | 4.22376i | −0.187602 | + | 0.150753i | ||||
\(786\) | −2.01356 | − | 1.16253i | −0.0718213 | − | 0.0414661i | ||||
\(787\) | 1.61500 | − | 2.79726i | 0.0575685 | − | 0.0997115i | −0.835805 | − | 0.549027i | \(-0.814999\pi\) |
0.893373 | + | 0.449315i | \(0.148332\pi\) | |||||||
\(788\) | 0.625857 | 0.0222952 | ||||||||
\(789\) | 15.3032 | − | 26.5060i | 0.544810 | − | 0.943638i | ||||
\(790\) | −3.94582 | + | 10.1648i | −0.140386 | + | 0.361647i | ||||
\(791\) | 3.43958 | − | 1.98584i | 0.122297 | − | 0.0706085i | ||||
\(792\) | − | 1.31702i | − | 0.0467982i | ||||||
\(793\) | 17.5732 | − | 3.73299i | 0.624043 | − | 0.132562i | ||||
\(794\) | 36.6995 | 1.30242 | ||||||||
\(795\) | 11.2606 | − | 29.0084i | 0.399372 | − | 1.02882i | ||||
\(796\) | −8.84057 | − | 15.3123i | −0.313346 | − | 0.542731i | ||||
\(797\) | −35.1612 | − | 20.3003i | −1.24547 | − | 0.719075i | −0.275271 | − | 0.961367i | \(-0.588768\pi\) |
−0.970203 | + | 0.242292i | \(0.922101\pi\) | |||||||
\(798\) | 7.37466 | 0.261060 | ||||||||
\(799\) | −6.72118 | − | 3.88048i | −0.237778 | − | 0.137281i | ||||
\(800\) | 3.69046 | + | 3.37350i | 0.130477 | + | 0.119271i | ||||
\(801\) | − | 18.4450i | − | 0.651722i | ||||||
\(802\) | 24.5044 | + | 14.1476i | 0.865279 | + | 0.499569i | ||||
\(803\) | 6.83138 | − | 3.94410i | 0.241074 | − | 0.139184i | ||||
\(804\) | 2.40112 | − | 1.38628i | 0.0846808 | − | 0.0488905i | ||||
\(805\) | −22.4815 | + | 18.0656i | −0.792368 | + | 0.636729i | ||||
\(806\) | 5.58043 | + | 1.81397i | 0.196562 | + | 0.0638944i | ||||
\(807\) | − | 18.0874i | − | 0.636707i | ||||||
\(808\) | −1.21929 | − | 2.11188i | −0.0428946 | − | 0.0742956i | ||||
\(809\) | 0.000840236 | 0.00145533i | 2.95411e−5 | 5.11667e-5i | 0.866040 | − | 0.499974i | \(-0.166657\pi\) | ||
−0.866011 | + | 0.500026i | \(0.833324\pi\) | |||||||
\(810\) | 2.20984 | − | 0.341491i | 0.0776458 | − | 0.0119988i | ||||
\(811\) | − | 34.9476i | − | 1.22718i | −0.789626 | − | 0.613588i | \(-0.789726\pi\) | ||
0.789626 | − | 0.613588i | \(-0.210274\pi\) | |||||||
\(812\) | −3.38286 | + | 5.85928i | −0.118715 | + | 0.205621i | ||||
\(813\) | 7.09382 | − | 12.2869i | 0.248791 | − | 0.430919i | ||||
\(814\) | − | 3.69154i | − | 0.129389i | ||||||
\(815\) | 21.9133 | − | 3.38631i | 0.767589 | − | 0.118617i | ||||
\(816\) | −0.784645 | − | 1.35904i | −0.0274681 | − | 0.0475761i | ||||
\(817\) | −12.7650 | − | 22.1097i | −0.446592 | − | 0.773519i | ||||
\(818\) | 15.3280i | 0.535931i | ||||||||
\(819\) | −1.70276 | + | 5.23831i | −0.0594992 | + | 0.183041i | ||||
\(820\) | −2.73532 | + | 2.19804i | −0.0955215 | + | 0.0767589i | ||||
\(821\) | 22.0044 | − | 12.7042i | 0.767957 | − | 0.443380i | −0.0641882 | − | 0.997938i | \(-0.520446\pi\) |
0.832145 | + | 0.554557i | \(0.187112\pi\) | |||||||
\(822\) | −10.6381 | + | 6.14192i | −0.371047 | + | 0.214224i | ||||
\(823\) | −18.9040 | − | 10.9142i | −0.658952 | − | 0.380446i | 0.132926 | − | 0.991126i | \(-0.457563\pi\) |
−0.791878 | + | 0.610680i | \(0.790896\pi\) | |||||||
\(824\) | 12.4300i | 0.433020i | ||||||||
\(825\) | −4.86040 | − | 4.44296i | −0.169217 | − | 0.154684i | ||||
\(826\) | 13.8561 | + | 7.99982i | 0.482115 | + | 0.278349i | ||||
\(827\) | −18.9366 | −0.658492 | −0.329246 | − | 0.944244i | \(-0.606794\pi\) | ||||
−0.329246 | + | 0.944244i | \(0.606794\pi\) | |||||||
\(828\) | 7.31172 | + | 4.22143i | 0.254100 | + | 0.146705i | ||||
\(829\) | −0.304309 | − | 0.527078i | −0.0105691 | − | 0.0183062i | 0.860692 | − | 0.509125i | \(-0.170031\pi\) |
−0.871262 | + | 0.490819i | \(0.836698\pi\) | |||||||
\(830\) | −5.17082 | + | 13.3205i | −0.179482 | + | 0.462362i | ||||
\(831\) | 16.8419 | 0.584240 | ||||||||
\(832\) | 2.41225 | + | 2.67975i | 0.0836296 | + | 0.0929036i | ||||
\(833\) | 7.32263i | 0.253714i | ||||||||
\(834\) | −5.76531 | + | 3.32861i | −0.199637 | + | 0.115260i | ||||
\(835\) | −10.5108 | + | 27.0768i | −0.363741 | + | 0.937030i | ||||
\(836\) | −3.17887 | + | 5.50597i | −0.109944 | + | 0.190428i | ||||
\(837\) | −1.62745 | −0.0562529 | ||||||||
\(838\) | 13.4692 | − | 23.3293i | 0.465286 | − | 0.805898i | ||||
\(839\) | −23.3215 | − | 13.4647i | −0.805148 | − | 0.464853i | 0.0401198 | − | 0.999195i | \(-0.487226\pi\) |
−0.845268 | + | 0.534342i | \(0.820559\pi\) | |||||||
\(840\) | 2.66278 | − | 2.13975i | 0.0918748 | − | 0.0738284i | ||||
\(841\) | 4.69300 | − | 8.12852i | 0.161828 | − | 0.280294i | ||||
\(842\) | 33.3731 | − | 19.2679i | 1.15011 | − | 0.664017i | ||||
\(843\) | −4.30768 | − | 7.46112i | −0.148364 | − | 0.256974i | ||||
\(844\) | 17.2445 | 0.593581 | ||||||||
\(845\) | −24.4425 | + | 15.7341i | −0.840849 | + | 0.541270i | ||||
\(846\) | −4.94552 | −0.170030 | ||||||||
\(847\) | −7.07731 | − | 12.2583i | −0.243179 | − | 0.421199i | ||||
\(848\) | −12.0517 | + | 6.95804i | −0.413856 | + | 0.238940i | ||||
\(849\) | −13.8098 | + | 23.9192i | −0.473950 | + | 0.820905i | ||||
\(850\) | −7.66250 | − | 1.68904i | −0.262822 | − | 0.0579336i | ||||
\(851\) | 20.4944 | + | 11.8325i | 0.702541 | + | 0.405612i | ||||
\(852\) | 7.41968 | − | 12.8513i | 0.254194 | − | 0.440277i | ||||
\(853\) | 41.3790 | 1.41679 | 0.708394 | − | 0.705817i | \(-0.249420\pi\) | ||||
0.708394 | + | 0.705817i | \(0.249420\pi\) | |||||||
\(854\) | −3.80596 | + | 6.59212i | −0.130237 | + | 0.225578i | ||||
\(855\) | −10.0628 | − | 3.90621i | −0.344139 | − | 0.133590i | ||||
\(856\) | −9.07302 | + | 5.23831i | −0.310109 | + | 0.179042i | ||||
\(857\) | 30.6051i | 1.04545i | 0.852501 | + | 0.522726i | \(0.175085\pi\) | ||||
−0.852501 | + | 0.522726i | \(0.824915\pi\) | |||||||
\(858\) | −3.17697 | − | 3.52928i | −0.108460 | − | 0.120488i | ||||
\(859\) | 30.9385 | 1.05561 | 0.527803 | − | 0.849367i | \(-0.323016\pi\) | ||||
0.527803 | + | 0.849367i | \(0.323016\pi\) | |||||||
\(860\) | −11.0242 | − | 4.27942i | −0.375922 | − | 0.145927i | ||||
\(861\) | 1.19868 | + | 2.07618i | 0.0408510 | + | 0.0707560i | ||||
\(862\) | 2.48744 | + | 1.43612i | 0.0847225 | + | 0.0489145i | ||||
\(863\) | 15.1133 | 0.514464 | 0.257232 | − | 0.966350i | \(-0.417190\pi\) | ||||
0.257232 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | −1.32395 | − | 8.56746i | −0.0450156 | − | 0.291302i | ||||
\(866\) | 12.9724i | 0.440819i | ||||||||
\(867\) | −12.5897 | − | 7.26867i | −0.427569 | − | 0.246857i | ||||
\(868\) | −2.15313 | + | 1.24311i | −0.0730819 | + | 0.0421938i | ||||
\(869\) | −5.56179 | + | 3.21110i | −0.188671 | + | 0.108929i | ||||
\(870\) | 7.71948 | − | 6.20319i | 0.261715 | − | 0.210308i | ||||
\(871\) | 3.09033 | − | 9.50698i | 0.104712 | − | 0.322132i | ||||
\(872\) | − | 17.1799i | − | 0.581784i | ||||||
\(873\) | 0.963028 | + | 1.66801i | 0.0325936 | + | 0.0564537i | ||||
\(874\) | −20.3784 | − | 35.2964i | −0.689310 | − | 1.19392i | ||||
\(875\) | 1.08624 | − | 17.0453i | 0.0367216 | − | 0.576238i | ||||
\(876\) | − | 5.98944i | − | 0.202364i | ||||||
\(877\) | 5.54757 | − | 9.60868i | 0.187328 | − | 0.324462i | −0.757030 | − | 0.653380i | \(-0.773351\pi\) |
0.944359 | + | 0.328918i | \(0.106684\pi\) | |||||||
\(878\) | 1.02411 | − | 1.77380i | 0.0345619 | − | 0.0598629i | ||||
\(879\) | 30.2501i | 1.02031i | ||||||||
\(880\) | 0.449750 | + | 2.91040i | 0.0151611 | + | 0.0981094i | ||||
\(881\) | 22.3598 | + | 38.7283i | 0.753321 | + | 1.30479i | 0.946205 | + | 0.323568i | \(0.104883\pi\) |
−0.192884 | + | 0.981222i | \(0.561784\pi\) | |||||||
\(882\) | 2.33310 | + | 4.04106i | 0.0785597 | + | 0.136069i | ||||
\(883\) | 10.9779i | 0.369435i | 0.982792 | + | 0.184718i | \(0.0591371\pi\) | ||||
−0.982792 | + | 0.184718i | \(0.940863\pi\) | |||||||
\(884\) | −5.38100 | − | 1.74914i | −0.180983 | − | 0.0588301i | ||||
\(885\) | −14.6694 | − | 18.2551i | −0.493106 | − | 0.613638i | ||||
\(886\) | 22.2640 | − | 12.8541i | 0.747973 | − | 0.431842i | ||||
\(887\) | −33.2555 | + | 19.2001i | −1.11661 | + | 0.644675i | −0.940533 | − | 0.339702i | \(-0.889674\pi\) |
−0.176076 | + | 0.984377i | \(0.556341\pi\) | |||||||
\(888\) | −2.42743 | − | 1.40148i | −0.0814593 | − | 0.0470305i | ||||
\(889\) | − | 12.3754i | − | 0.415059i | ||||||
\(890\) | 6.29881 | + | 40.7605i | 0.211136 | + | 1.36629i | ||||
\(891\) | 1.14057 | + | 0.658509i | 0.0382106 | + | 0.0220609i | ||||
\(892\) | −4.89716 | −0.163969 | ||||||||
\(893\) | 20.6754 | + | 11.9369i | 0.691876 | + | 0.399455i | ||||
\(894\) | −1.50554 | − | 2.60768i | −0.0503529 | − | 0.0872137i | ||||
\(895\) | −11.4147 | + | 29.4053i | −0.381551 | + | 0.982911i | ||||
\(896\) | −1.52767 | −0.0510360 | ||||||||
\(897\) | 29.7767 | − | 6.32532i | 0.994216 | − | 0.211196i | ||||
\(898\) | − | 18.5625i | − | 0.619440i | ||||||
\(899\) | −6.24197 | + | 3.60380i | −0.208181 | + | 0.120193i | ||||
\(900\) | −4.76677 | + | 1.50928i | −0.158892 | + | 0.0503093i | ||||
\(901\) | 10.9192 | − | 18.9126i | 0.363770 | − | 0.630069i | ||||
\(902\) | −2.06678 | −0.0688163 | ||||||||
\(903\) | −4.03963 | + | 6.99684i | −0.134430 | + | 0.232840i | ||||
\(904\) | 2.25151 | + | 1.29991i | 0.0748842 | + | 0.0432344i | ||||
\(905\) | −36.6233 | − | 45.5754i | −1.21740 | − | 1.51498i | ||||
\(906\) | 6.00745 | − | 10.4052i | 0.199584 | − | 0.345690i | ||||
\(907\) | −34.3953 | + | 19.8581i | −1.14208 | + | 0.659378i | −0.946944 | − | 0.321399i | \(-0.895847\pi\) |
−0.195133 | + | 0.980777i | \(0.562514\pi\) | |||||||
\(908\) | −5.07567 | − | 8.79132i | −0.168442 | − | 0.291750i | ||||
\(909\) | 2.43859 | 0.0808828 | ||||||||
\(910\) | 1.97399 | − | 12.1573i | 0.0654370 | − | 0.403010i | ||||
\(911\) | 17.9575 | 0.594959 | 0.297479 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297479 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(912\) | 2.41369 | + | 4.18063i | 0.0799252 | + | 0.138435i | ||||
\(913\) | −7.28848 | + | 4.20801i | −0.241213 | + | 0.139265i | ||||
\(914\) | −12.3213 | + | 21.3412i | −0.407554 | + | 0.705904i | ||||
\(915\) | 8.68497 | − | 6.97904i | 0.287116 | − | 0.230720i | ||||
\(916\) | −13.3332 | − | 7.69794i | −0.440542 | − | 0.254347i | ||||
\(917\) | 1.77597 | − | 3.07607i | 0.0586476 | − | 0.101581i | ||||
\(918\) | 1.56929 | 0.0517943 | ||||||||
\(919\) | 10.0149 | − | 17.3463i | 0.330361 | − | 0.572203i | −0.652221 | − | 0.758029i | \(-0.726163\pi\) |
0.982583 | + | 0.185826i | \(0.0594961\pi\) | |||||||
\(920\) | −17.5993 | − | 6.83178i | −0.580232 | − | 0.225237i | ||||
\(921\) | −12.2449 | + | 7.06959i | −0.403483 | + | 0.232951i | ||||
\(922\) | − | 31.8342i | − | 1.04840i | ||||||
\(923\) | −11.1175 | − | 52.3363i | −0.365938 | − | 1.72267i | ||||
\(924\) | 2.01198 | 0.0661891 | ||||||||
\(925\) | −13.3610 | + | 4.23045i | −0.439308 | + | 0.139096i | ||||
\(926\) | −1.59160 | − | 2.75673i | −0.0523031 | − | 0.0905916i | ||||
\(927\) | −10.7647 | − | 6.21501i | −0.353559 | − | 0.204128i | ||||
\(928\) | −4.42877 | −0.145381 | ||||||||
\(929\) | 35.1451 | + | 20.2910i | 1.15307 | + | 0.665727i | 0.949634 | − | 0.313361i | \(-0.101455\pi\) |
0.203439 | + | 0.979088i | \(0.434788\pi\) | |||||||
\(930\) | 3.59640 | − | 0.555760i | 0.117931 | − | 0.0182241i | ||||
\(931\) | − | 22.5255i | − | 0.738245i | ||||||
\(932\) | −8.58772 | − | 4.95812i | −0.281300 | − | 0.162409i | ||||
\(933\) | −8.63797 | + | 4.98713i | −0.282794 | + | 0.163271i | ||||
\(934\) | −18.7708 | + | 10.8373i | −0.614200 | + | 0.354609i | ||||
\(935\) | −2.89486 | − | 3.60246i | −0.0946719 | − | 0.117813i | ||||
\(936\) | −3.52686 | + | 0.749192i | −0.115279 | + | 0.0244881i | ||||
\(937\) | 47.1112i | 1.53905i | 0.638614 | + | 0.769527i | \(0.279508\pi\) | ||||
−0.638614 | + | 0.769527i | \(0.720492\pi\) | |||||||
\(938\) | 2.11779 | + | 3.66812i | 0.0691484 | + | 0.119769i | ||||
\(939\) | 1.54230 | + | 2.67134i | 0.0503311 | + | 0.0871760i | ||||
\(940\) | 10.9288 | − | 1.68885i | 0.356458 | − | 0.0550842i | ||||
\(941\) | − | 4.35101i | − | 0.141839i | −0.997482 | − | 0.0709195i | \(-0.977407\pi\) | ||
0.997482 | − | 0.0709195i | \(-0.0225933\pi\) | |||||||
\(942\) | −1.50778 | + | 2.61155i | −0.0491261 | + | 0.0850888i | ||||
\(943\) | 6.62464 | − | 11.4742i | 0.215728 | − | 0.373652i | ||||
\(944\) | 10.4732i | 0.340873i | ||||||||
\(945\) | 0.521687 | + | 3.37591i | 0.0169705 | + | 0.109818i | ||||
\(946\) | −3.48259 | − | 6.03202i | −0.113229 | − | 0.196118i | ||||
\(947\) | 17.4580 | + | 30.2381i | 0.567307 | + | 0.982605i | 0.996831 | + | 0.0795494i | \(0.0253481\pi\) |
−0.429524 | + | 0.903056i | \(0.641319\pi\) | |||||||
\(948\) | 4.87632i | 0.158376i | ||||||||
\(949\) | −14.4480 | − | 16.0502i | −0.469002 | − | 0.521011i | ||||
\(950\) | 23.5710 | + | 5.19575i | 0.764745 | + | 0.168572i | ||||
\(951\) | 12.3824 | − | 7.14899i | 0.401527 | − | 0.231822i | ||||
\(952\) | 2.07618 | − | 1.19868i | 0.0672893 | − | 0.0388495i | ||||
\(953\) | 8.39700 | + | 4.84801i | 0.272005 | + | 0.157042i | 0.629799 | − | 0.776758i | \(-0.283137\pi\) |
−0.357793 | + | 0.933801i | \(0.616471\pi\) | |||||||
\(954\) | − | 13.9161i | − | 0.450550i | ||||||
\(955\) | −41.6649 | + | 6.43856i | −1.34824 | + | 0.208347i | ||||
\(956\) | −8.19404 | − | 4.73083i | −0.265014 | − | 0.153006i | ||||
\(957\) | 5.83277 | 0.188547 | ||||||||
\(958\) | −25.3765 | − | 14.6511i | −0.819876 | − | 0.473356i | ||||
\(959\) | −9.38286 | − | 16.2516i | −0.302988 | − | 0.524791i | ||||
\(960\) | 2.08452 | + | 0.809179i | 0.0672776 | + | 0.0261161i | ||||
\(961\) | 28.3514 | 0.914561 | ||||||||
\(962\) | −9.88562 | + | 2.09995i | −0.318725 | + | 0.0677052i | ||||
\(963\) | − | 10.4766i | − | 0.337604i | ||||||
\(964\) | −11.3482 | + | 6.55189i | −0.365501 | + | 0.211022i | ||||
\(965\) | −14.4778 | + | 37.2963i | −0.466058 | + | 1.20061i | ||||
\(966\) | −6.44897 | + | 11.1699i | −0.207492 | + | 0.359387i | ||||
\(967\) | 36.1715 | 1.16320 | 0.581599 | − | 0.813476i | \(-0.302427\pi\) | ||||
0.581599 | + | 0.813476i | \(0.302427\pi\) | |||||||
\(968\) | 4.63273 | − | 8.02413i | 0.148902 | − | 0.257905i | ||||
\(969\) | −6.56062 | − | 3.78778i | −0.210757 | − | 0.121681i | ||||
\(970\) | −2.69775 | − | 3.35718i | −0.0866195 | − | 0.107792i | ||||
\(971\) | 0.194688 | − | 0.337209i | 0.00624783 | − | 0.0108216i | −0.862885 | − | 0.505401i | \(-0.831345\pi\) |
0.869132 | + | 0.494579i | \(0.164678\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −5.08503 | − | 8.80753i | −0.163019 | − | 0.282356i | ||||
\(974\) | 42.5287 | 1.36271 | ||||||||
\(975\) | −9.13299 | + | 15.5431i | −0.292490 | + | 0.497778i | ||||
\(976\) | −4.98268 | −0.159492 | ||||||||
\(977\) | −2.70086 | − | 4.67802i | −0.0864080 | − | 0.149663i | 0.819582 | − | 0.572961i | \(-0.194206\pi\) |
−0.905990 | + | 0.423298i | \(0.860872\pi\) | |||||||
\(978\) | 8.58772 | − | 4.95812i | 0.274605 | − | 0.158543i | ||||
\(979\) | −12.1462 | + | 21.0378i | −0.388194 | + | 0.672372i | ||||
\(980\) | −6.53577 | − | 8.13334i | −0.208777 | − | 0.259810i | ||||
\(981\) | 14.8782 | + | 8.58994i | 0.475025 | + | 0.274256i | ||||
\(982\) | −6.32521 | + | 10.9556i | −0.201845 | + | 0.349607i | ||||
\(983\) | 43.6819 | 1.39324 | 0.696618 | − | 0.717442i | \(-0.254687\pi\) | ||||
0.696618 | + | 0.717442i | \(0.254687\pi\) | |||||||
\(984\) | −0.784645 | + | 1.35904i | −0.0250136 | + | 0.0433248i | ||||
\(985\) | 0.506430 | − | 1.30461i | 0.0161362 | − | 0.0415684i | ||||
\(986\) | 6.01889 | − | 3.47501i | 0.191681 | − | 0.110667i | ||||
\(987\) | − | 7.55515i | − | 0.240483i | ||||||
\(988\) | 16.5528 | + | 5.38064i | 0.526615 | + | 0.171181i | ||||
\(989\) | 44.6508 | 1.41981 | ||||||||
\(990\) | −2.74535 | − | 1.06570i | −0.0872530 | − | 0.0338703i | ||||
\(991\) | 27.9427 | + | 48.3981i | 0.887628 | + | 1.53742i | 0.842671 | + | 0.538428i | \(0.180982\pi\) |
0.0449569 | + | 0.998989i | \(0.485685\pi\) | |||||||
\(992\) | −1.40941 | − | 0.813725i | −0.0447489 | − | 0.0258358i | ||||
\(993\) | −11.4202 | −0.362409 | ||||||||
\(994\) | 19.6325 | + | 11.3349i | 0.622706 | + | 0.359520i | ||||
\(995\) | −39.0725 | + | 6.03795i | −1.23868 | + | 0.191416i | ||||
\(996\) | 6.39020i | 0.202481i | ||||||||
\(997\) | 30.9866 | + | 17.8901i | 0.981357 | + | 0.566587i | 0.902680 | − | 0.430314i | \(-0.141597\pi\) |
0.0786773 | + | 0.996900i | \(0.474930\pi\) | |||||||
\(998\) | 3.93182 | − | 2.27004i | 0.124460 | − | 0.0718567i | ||||
\(999\) | 2.42743 | − | 1.40148i | 0.0768005 | − | 0.0443408i |
(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 | 390.2.x.b.49.5 | yes | 12 | |
3.2 | odd | 2 | 1170.2.bj.c.829.2 | 12 | |||
5.2 | odd | 4 | 1950.2.bc.i.751.1 | 12 | |||
5.3 | odd | 4 | 1950.2.bc.j.751.6 | 12 | |||
5.4 | even | 2 | 390.2.x.a.49.2 | ✓ | 12 | ||
13.4 | even | 6 | 390.2.x.a.199.2 | yes | 12 | ||
15.14 | odd | 2 | 1170.2.bj.d.829.5 | 12 | |||
39.17 | odd | 6 | 1170.2.bj.d.199.5 | 12 | |||
65.4 | even | 6 | inner | 390.2.x.b.199.5 | yes | 12 | |
65.17 | odd | 12 | 1950.2.bc.i.901.1 | 12 | |||
65.43 | odd | 12 | 1950.2.bc.j.901.6 | 12 | |||
195.134 | odd | 6 | 1170.2.bj.c.199.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.x.a.49.2 | ✓ | 12 | 5.4 | even | 2 | ||
390.2.x.a.199.2 | yes | 12 | 13.4 | even | 6 | ||
390.2.x.b.49.5 | yes | 12 | 1.1 | even | 1 | trivial | |
390.2.x.b.199.5 | yes | 12 | 65.4 | even | 6 | inner | |
1170.2.bj.c.199.2 | 12 | 195.134 | odd | 6 | |||
1170.2.bj.c.829.2 | 12 | 3.2 | odd | 2 | |||
1170.2.bj.d.199.5 | 12 | 39.17 | odd | 6 | |||
1170.2.bj.d.829.5 | 12 | 15.14 | odd | 2 | |||
1950.2.bc.i.751.1 | 12 | 5.2 | odd | 4 | |||
1950.2.bc.i.901.1 | 12 | 65.17 | odd | 12 | |||
1950.2.bc.j.751.6 | 12 | 5.3 | odd | 4 | |||
1950.2.bc.j.901.6 | 12 | 65.43 | odd | 12 |