Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(25,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.l (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 403.129 |
Dual form | 403.2.l.b.25.1 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.73205i | − | 1.22474i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||
0.790569 | − | 0.612372i | \(-0.209785\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | 1.50000 | + | 0.866025i | 0.566947 | + | 0.327327i | 0.755929 | − | 0.654654i | \(-0.227186\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | 4.50000 | − | 2.59808i | 1.35680 | − | 0.783349i | 0.367610 | − | 0.929980i | \(-0.380176\pi\) |
0.989191 | + | 0.146631i | \(0.0468429\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | 1.50000 | − | 2.59808i | 0.400892 | − | 0.694365i | ||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 3.00000 | − | 1.73205i | 0.707107 | − | 0.408248i | ||||
\(19\) | −4.50000 | − | 2.59808i | −1.03237 | − | 0.596040i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −1.50000 | + | 0.866025i | −0.335410 | + | 0.193649i | ||||
\(21\) | 1.50000 | − | 0.866025i | 0.327327 | − | 0.188982i | ||||
\(22\) | −4.50000 | − | 7.79423i | −0.959403 | − | 1.66174i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 6.00000 | + | 1.73205i | 1.17670 | + | 0.339683i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −1.50000 | − | 0.866025i | −0.283473 | − | 0.163663i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | −3.00000 | −0.547723 | ||||||||
\(31\) | −2.00000 | + | 5.19615i | −0.359211 | + | 0.933257i | ||||
\(32\) | 5.19615i | 0.918559i | ||||||||
\(33\) | − | 5.19615i | − | 0.904534i | ||||||
\(34\) | 4.50000 | + | 2.59808i | 0.771744 | + | 0.445566i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | −1.00000 | − | 1.73205i | −0.166667 | − | 0.288675i | ||||
\(37\) | −4.50000 | − | 2.59808i | −0.739795 | − | 0.427121i | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | −4.50000 | + | 7.79423i | −0.729996 | + | 1.26439i | ||||
\(39\) | 2.50000 | + | 2.59808i | 0.400320 | + | 0.416025i | ||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | −4.50000 | + | 2.59808i | −0.702782 | + | 0.405751i | −0.808383 | − | 0.588657i | \(-0.799657\pi\) |
0.105601 | + | 0.994409i | \(0.466323\pi\) | |||||||
\(42\) | −1.50000 | − | 2.59808i | −0.231455 | − | 0.400892i | ||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | −4.50000 | + | 2.59808i | −0.678401 | + | 0.391675i | ||||
\(45\) | 3.00000 | + | 1.73205i | 0.447214 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410i | 0.505291i | 0.967559 | + | 0.252646i | \(0.0813007\pi\) | ||||
−0.967559 | + | 0.252646i | \(0.918699\pi\) | |||||||
\(48\) | −2.50000 | + | 4.33013i | −0.360844 | + | 0.625000i | ||||
\(49\) | −2.00000 | − | 3.46410i | −0.285714 | − | 0.494872i | ||||
\(50\) | 3.00000 | + | 1.73205i | 0.424264 | + | 0.244949i | ||||
\(51\) | 1.50000 | + | 2.59808i | 0.210042 | + | 0.363803i | ||||
\(52\) | 1.00000 | − | 3.46410i | 0.138675 | − | 0.480384i | ||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | − | 8.66025i | − | 1.17851i | ||||||
\(55\) | 4.50000 | − | 7.79423i | 0.606780 | − | 1.05097i | ||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | −4.50000 | + | 2.59808i | −0.596040 | + | 0.344124i | ||||
\(58\) | 10.3923i | 1.36458i | ||||||||
\(59\) | 1.50000 | + | 0.866025i | 0.195283 | + | 0.112747i | 0.594454 | − | 0.804130i | \(-0.297368\pi\) |
−0.399170 | + | 0.916877i | \(0.630702\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 9.00000 | + | 3.46410i | 1.14300 | + | 0.439941i | ||||
\(63\) | 3.46410i | 0.436436i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.50000 | + | 6.06218i | 0.186052 | + | 0.751921i | ||||
\(66\) | −9.00000 | −1.10782 | ||||||||
\(67\) | −7.50000 | + | 4.33013i | −0.916271 | + | 0.529009i | −0.882443 | − | 0.470418i | \(-0.844103\pi\) |
−0.0338274 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 5.19615i | − | 0.621059i | ||||||
\(71\) | −7.50000 | + | 4.33013i | −0.890086 | + | 0.513892i | −0.873971 | − | 0.485979i | \(-0.838463\pi\) |
−0.0161155 | + | 0.999870i | \(0.505130\pi\) | |||||||
\(72\) | 3.00000 | − | 1.73205i | 0.353553 | − | 0.204124i | ||||
\(73\) | 7.50000 | − | 4.33013i | 0.877809 | − | 0.506803i | 0.00787336 | − | 0.999969i | \(-0.497494\pi\) |
0.869935 | + | 0.493166i | \(0.164160\pi\) | |||||||
\(74\) | −4.50000 | + | 7.79423i | −0.523114 | + | 0.906061i | ||||
\(75\) | 1.00000 | + | 1.73205i | 0.115470 | + | 0.200000i | ||||
\(76\) | 4.50000 | + | 2.59808i | 0.516185 | + | 0.298020i | ||||
\(77\) | 9.00000 | 1.02565 | ||||||||
\(78\) | 4.50000 | − | 4.33013i | 0.509525 | − | 0.490290i | ||||
\(79\) | 2.50000 | − | 4.33013i | 0.281272 | − | 0.487177i | −0.690426 | − | 0.723403i | \(-0.742577\pi\) |
0.971698 | + | 0.236225i | \(0.0759104\pi\) | |||||||
\(80\) | −7.50000 | + | 4.33013i | −0.838525 | + | 0.484123i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.50000 | + | 7.79423i | 0.496942 | + | 0.860729i | ||||
\(83\) | 10.5000 | − | 6.06218i | 1.15252 | − | 0.665410i | 0.203024 | − | 0.979174i | \(-0.434923\pi\) |
0.949501 | + | 0.313763i | \(0.101590\pi\) | |||||||
\(84\) | −1.50000 | + | 0.866025i | −0.163663 | + | 0.0944911i | ||||
\(85\) | 5.19615i | 0.563602i | ||||||||
\(86\) | −1.50000 | − | 0.866025i | −0.161749 | − | 0.0933859i | ||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | −4.50000 | − | 7.79423i | −0.479702 | − | 0.830868i | ||||
\(89\) | − | 6.92820i | − | 0.734388i | −0.930144 | − | 0.367194i | \(-0.880318\pi\) | ||
0.930144 | − | 0.367194i | \(-0.119682\pi\) | |||||||
\(90\) | 3.00000 | − | 5.19615i | 0.316228 | − | 0.547723i | ||||
\(91\) | −4.50000 | + | 4.33013i | −0.471728 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50000 | + | 4.33013i | 0.362933 | + | 0.449013i | ||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −9.00000 | −0.923381 | ||||||||
\(96\) | 4.50000 | + | 2.59808i | 0.459279 | + | 0.265165i | ||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | −6.00000 | + | 3.46410i | −0.606092 | + | 0.349927i | ||||
\(99\) | 9.00000 | + | 5.19615i | 0.904534 | + | 0.522233i | ||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | 18.0000 | 1.79107 | 0.895533 | − | 0.444994i | \(-0.146794\pi\) | ||||
0.895533 | + | 0.444994i | \(0.146794\pi\) | |||||||
\(102\) | 4.50000 | − | 2.59808i | 0.445566 | − | 0.257248i | ||||
\(103\) | 9.50000 | + | 16.4545i | 0.936063 | + | 1.62131i | 0.772728 | + | 0.634738i | \(0.218892\pi\) |
0.163335 | + | 0.986571i | \(0.447775\pi\) | |||||||
\(104\) | 6.00000 | + | 1.73205i | 0.588348 | + | 0.169842i | ||||
\(105\) | 1.50000 | − | 2.59808i | 0.146385 | − | 0.253546i | ||||
\(106\) | −4.50000 | + | 2.59808i | −0.437079 | + | 0.252347i | ||||
\(107\) | 4.50000 | − | 7.79423i | 0.435031 | − | 0.753497i | −0.562267 | − | 0.826956i | \(-0.690071\pi\) |
0.997298 | + | 0.0734594i | \(0.0234039\pi\) | |||||||
\(108\) | −5.00000 | −0.481125 | ||||||||
\(109\) | − | 13.8564i | − | 1.32720i | −0.748086 | − | 0.663602i | \(-0.769027\pi\) | ||
0.748086 | − | 0.663602i | \(-0.230973\pi\) | |||||||
\(110\) | −13.5000 | − | 7.79423i | −1.28717 | − | 0.743151i | ||||
\(111\) | −4.50000 | + | 2.59808i | −0.427121 | + | 0.246598i | ||||
\(112\) | −7.50000 | − | 4.33013i | −0.708683 | − | 0.409159i | ||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 4.50000 | + | 7.79423i | 0.421464 | + | 0.729996i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | −7.00000 | + | 1.73205i | −0.647150 | + | 0.160128i | ||||
\(118\) | 1.50000 | − | 2.59808i | 0.138086 | − | 0.239172i | ||||
\(119\) | −4.50000 | + | 2.59808i | −0.412514 | + | 0.238165i | ||||
\(120\) | −3.00000 | −0.273861 | ||||||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | − | 17.3205i | − | 1.56813i | ||||||
\(123\) | 5.19615i | 0.468521i | ||||||||
\(124\) | 2.00000 | − | 5.19615i | 0.179605 | − | 0.466628i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 6.00000 | 0.534522 | ||||||||
\(127\) | −3.50000 | + | 6.06218i | −0.310575 | + | 0.537931i | −0.978487 | − | 0.206309i | \(-0.933855\pi\) |
0.667912 | + | 0.744240i | \(0.267188\pi\) | |||||||
\(128\) | 12.1244i | 1.07165i | ||||||||
\(129\) | −0.500000 | − | 0.866025i | −0.0440225 | − | 0.0762493i | ||||
\(130\) | 10.5000 | − | 2.59808i | 0.920911 | − | 0.227866i | ||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | 5.19615i | 0.452267i | ||||||||
\(133\) | −4.50000 | − | 7.79423i | −0.390199 | − | 0.675845i | ||||
\(134\) | 7.50000 | + | 12.9904i | 0.647901 | + | 1.12220i | ||||
\(135\) | 7.50000 | − | 4.33013i | 0.645497 | − | 0.372678i | ||||
\(136\) | 4.50000 | + | 2.59808i | 0.385872 | + | 0.222783i | ||||
\(137\) | −4.50000 | + | 2.59808i | −0.384461 | + | 0.221969i | −0.679757 | − | 0.733437i | \(-0.737915\pi\) |
0.295296 | + | 0.955406i | \(0.404582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 3.00000 | + | 1.73205i | 0.252646 | + | 0.145865i | ||||
\(142\) | 7.50000 | + | 12.9904i | 0.629386 | + | 1.09013i | ||||
\(143\) | 4.50000 | + | 18.1865i | 0.376309 | + | 1.52083i | ||||
\(144\) | −5.00000 | − | 8.66025i | −0.416667 | − | 0.721688i | ||||
\(145\) | −9.00000 | + | 5.19615i | −0.747409 | + | 0.431517i | ||||
\(146\) | −7.50000 | − | 12.9904i | −0.620704 | − | 1.07509i | ||||
\(147\) | −4.00000 | −0.329914 | ||||||||
\(148\) | 4.50000 | + | 2.59808i | 0.369898 | + | 0.213561i | ||||
\(149\) | −16.5000 | − | 9.52628i | −1.35173 | − | 0.780423i | −0.363241 | − | 0.931695i | \(-0.618330\pi\) |
−0.988492 | + | 0.151272i | \(0.951663\pi\) | |||||||
\(150\) | 3.00000 | − | 1.73205i | 0.244949 | − | 0.141421i | ||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | −4.50000 | + | 7.79423i | −0.364998 | + | 0.632195i | ||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | − | 15.5885i | − | 1.25615i | ||||||
\(155\) | 1.50000 | + | 9.52628i | 0.120483 | + | 0.765169i | ||||
\(156\) | −2.50000 | − | 2.59808i | −0.200160 | − | 0.208013i | ||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | −7.50000 | − | 4.33013i | −0.596668 | − | 0.344486i | ||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | 4.50000 | + | 7.79423i | 0.355756 | + | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.50000 | + | 0.866025i | 0.117851 | + | 0.0680414i | ||||
\(163\) | 10.3923i | 0.813988i | 0.913431 | + | 0.406994i | \(0.133423\pi\) | ||||
−0.913431 | + | 0.406994i | \(0.866577\pi\) | |||||||
\(164\) | 4.50000 | − | 2.59808i | 0.351391 | − | 0.202876i | ||||
\(165\) | −4.50000 | − | 7.79423i | −0.350325 | − | 0.606780i | ||||
\(166\) | −10.5000 | − | 18.1865i | −0.814958 | − | 1.41155i | ||||
\(167\) | 7.50000 | + | 4.33013i | 0.580367 | + | 0.335075i | 0.761279 | − | 0.648424i | \(-0.224572\pi\) |
−0.180912 | + | 0.983499i | \(0.557905\pi\) | |||||||
\(168\) | −1.50000 | − | 2.59808i | −0.115728 | − | 0.200446i | ||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | − | 10.3923i | − | 0.794719i | ||||||
\(172\) | −0.500000 | + | 0.866025i | −0.0381246 | + | 0.0660338i | ||||
\(173\) | 4.50000 | + | 7.79423i | 0.342129 | + | 0.592584i | 0.984828 | − | 0.173534i | \(-0.0555188\pi\) |
−0.642699 | + | 0.766119i | \(0.722185\pi\) | |||||||
\(174\) | 9.00000 | + | 5.19615i | 0.682288 | + | 0.393919i | ||||
\(175\) | −3.00000 | + | 1.73205i | −0.226779 | + | 0.130931i | ||||
\(176\) | −22.5000 | + | 12.9904i | −1.69600 | + | 0.979187i | ||||
\(177\) | 1.50000 | − | 0.866025i | 0.112747 | − | 0.0650945i | ||||
\(178\) | −12.0000 | −0.899438 | ||||||||
\(179\) | −1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | \(-0.869096\pi\) |
0.804508 | + | 0.593942i | \(0.202429\pi\) | |||||||
\(180\) | −3.00000 | − | 1.73205i | −0.223607 | − | 0.129099i | ||||
\(181\) | −11.5000 | − | 19.9186i | −0.854788 | − | 1.48054i | −0.876841 | − | 0.480780i | \(-0.840354\pi\) |
0.0220530 | − | 0.999757i | \(-0.492980\pi\) | |||||||
\(182\) | 7.50000 | + | 7.79423i | 0.555937 | + | 0.577747i | ||||
\(183\) | 5.00000 | − | 8.66025i | 0.369611 | − | 0.640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.00000 | −0.661693 | ||||||||
\(186\) | 7.50000 | − | 6.06218i | 0.549927 | − | 0.444500i | ||||
\(187\) | 15.5885i | 1.13994i | ||||||||
\(188\) | − | 3.46410i | − | 0.252646i | ||||||
\(189\) | 7.50000 | + | 4.33013i | 0.545545 | + | 0.314970i | ||||
\(190\) | 15.5885i | 1.13091i | ||||||||
\(191\) | 7.50000 | + | 12.9904i | 0.542681 | + | 0.939951i | 0.998749 | + | 0.0500060i | \(0.0159241\pi\) |
−0.456068 | + | 0.889945i | \(0.650743\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 19.5000 | + | 11.2583i | 1.40364 | + | 0.810392i | 0.994764 | − | 0.102197i | \(-0.0325873\pi\) |
0.408877 | + | 0.912590i | \(0.365921\pi\) | |||||||
\(194\) | −12.0000 | −0.861550 | ||||||||
\(195\) | 6.00000 | + | 1.73205i | 0.429669 | + | 0.124035i | ||||
\(196\) | 2.00000 | + | 3.46410i | 0.142857 | + | 0.247436i | ||||
\(197\) | 7.50000 | − | 4.33013i | 0.534353 | − | 0.308509i | −0.208434 | − | 0.978036i | \(-0.566837\pi\) |
0.742787 | + | 0.669528i | \(0.233503\pi\) | |||||||
\(198\) | 9.00000 | − | 15.5885i | 0.639602 | − | 1.10782i | ||||
\(199\) | −12.5000 | − | 21.6506i | −0.886102 | − | 1.53477i | −0.844446 | − | 0.535641i | \(-0.820070\pi\) |
−0.0416556 | − | 0.999132i | \(-0.513263\pi\) | |||||||
\(200\) | 3.00000 | + | 1.73205i | 0.212132 | + | 0.122474i | ||||
\(201\) | 8.66025i | 0.610847i | ||||||||
\(202\) | − | 31.1769i | − | 2.19360i | ||||||
\(203\) | −9.00000 | − | 5.19615i | −0.631676 | − | 0.364698i | ||||
\(204\) | −1.50000 | − | 2.59808i | −0.105021 | − | 0.181902i | ||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | 28.5000 | − | 16.4545i | 1.98569 | − | 1.14644i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00000 | − | 17.3205i | 0.346688 | − | 1.20096i | ||||
\(209\) | −27.0000 | −1.86763 | ||||||||
\(210\) | −4.50000 | − | 2.59808i | −0.310530 | − | 0.179284i | ||||
\(211\) | 2.50000 | − | 4.33013i | 0.172107 | − | 0.298098i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) |
0.939156 | + | 0.343490i | \(0.111609\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | 8.66025i | 0.593391i | ||||||||
\(214\) | −13.5000 | − | 7.79423i | −0.922841 | − | 0.532803i | ||||
\(215\) | − | 1.73205i | − | 0.118125i | ||||||
\(216\) | − | 8.66025i | − | 0.589256i | ||||||
\(217\) | −7.50000 | + | 6.06218i | −0.509133 | + | 0.411527i | ||||
\(218\) | −24.0000 | −1.62549 | ||||||||
\(219\) | − | 8.66025i | − | 0.585206i | ||||||
\(220\) | −4.50000 | + | 7.79423i | −0.303390 | + | 0.525487i | ||||
\(221\) | −7.50000 | − | 7.79423i | −0.504505 | − | 0.524297i | ||||
\(222\) | 4.50000 | + | 7.79423i | 0.302020 | + | 0.523114i | ||||
\(223\) | 1.50000 | + | 0.866025i | 0.100447 | + | 0.0579934i | 0.549382 | − | 0.835571i | \(-0.314863\pi\) |
−0.448935 | + | 0.893565i | \(0.648196\pi\) | |||||||
\(224\) | −4.50000 | + | 7.79423i | −0.300669 | + | 0.520774i | ||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 13.5000 | − | 7.79423i | 0.898007 | − | 0.518464i | ||||
\(227\) | −7.50000 | + | 4.33013i | −0.497792 | + | 0.287401i | −0.727801 | − | 0.685788i | \(-0.759458\pi\) |
0.230009 | + | 0.973189i | \(0.426124\pi\) | |||||||
\(228\) | 4.50000 | − | 2.59808i | 0.298020 | − | 0.172062i | ||||
\(229\) | 1.50000 | + | 0.866025i | 0.0991228 | + | 0.0572286i | 0.548742 | − | 0.835992i | \(-0.315107\pi\) |
−0.449619 | + | 0.893220i | \(0.648440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.50000 | − | 7.79423i | 0.296078 | − | 0.512823i | ||||
\(232\) | 10.3923i | 0.682288i | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 3.00000 | + | 12.1244i | 0.196116 | + | 0.792594i | ||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | −1.50000 | − | 0.866025i | −0.0976417 | − | 0.0563735i | ||||
\(237\) | −2.50000 | − | 4.33013i | −0.162392 | − | 0.281272i | ||||
\(238\) | 4.50000 | + | 7.79423i | 0.291692 | + | 0.505225i | ||||
\(239\) | −13.5000 | + | 7.79423i | −0.873242 | + | 0.504167i | −0.868424 | − | 0.495822i | \(-0.834867\pi\) |
−0.00481804 | + | 0.999988i | \(0.501534\pi\) | |||||||
\(240\) | 8.66025i | 0.559017i | ||||||||
\(241\) | 1.50000 | + | 0.866025i | 0.0966235 | + | 0.0557856i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | −24.0000 | − | 13.8564i | −1.54278 | − | 0.890724i | ||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | −6.00000 | − | 3.46410i | −0.383326 | − | 0.221313i | ||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 13.5000 | − | 12.9904i | 0.858984 | − | 0.826558i | ||||
\(248\) | 9.00000 | + | 3.46410i | 0.571501 | + | 0.219971i | ||||
\(249\) | − | 12.1244i | − | 0.768350i | ||||||
\(250\) | 21.0000 | 1.32816 | ||||||||
\(251\) | 10.5000 | − | 18.1865i | 0.662754 | − | 1.14792i | −0.317135 | − | 0.948380i | \(-0.602721\pi\) |
0.979889 | − | 0.199543i | \(-0.0639459\pi\) | |||||||
\(252\) | − | 3.46410i | − | 0.218218i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.5000 | + | 6.06218i | 0.658829 | + | 0.380375i | ||||
\(255\) | 4.50000 | + | 2.59808i | 0.281801 | + | 0.162698i | ||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | −1.50000 | + | 0.866025i | −0.0933859 | + | 0.0539164i | ||||
\(259\) | −4.50000 | − | 7.79423i | −0.279616 | − | 0.484310i | ||||
\(260\) | −1.50000 | − | 6.06218i | −0.0930261 | − | 0.375960i | ||||
\(261\) | −6.00000 | − | 10.3923i | −0.371391 | − | 0.643268i | ||||
\(262\) | −13.5000 | − | 7.79423i | −0.834033 | − | 0.481529i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −9.00000 | −0.553912 | ||||||||
\(265\) | −4.50000 | − | 2.59808i | −0.276433 | − | 0.159599i | ||||
\(266\) | −13.5000 | + | 7.79423i | −0.827738 | + | 0.477895i | ||||
\(267\) | −6.00000 | − | 3.46410i | −0.367194 | − | 0.212000i | ||||
\(268\) | 7.50000 | − | 4.33013i | 0.458135 | − | 0.264505i | ||||
\(269\) | 10.5000 | + | 18.1865i | 0.640196 | + | 1.10885i | 0.985389 | + | 0.170321i | \(0.0544803\pi\) |
−0.345192 | + | 0.938532i | \(0.612186\pi\) | |||||||
\(270\) | −7.50000 | − | 12.9904i | −0.456435 | − | 0.790569i | ||||
\(271\) | − | 10.3923i | − | 0.631288i | −0.948878 | − | 0.315644i | \(-0.897780\pi\) | ||
0.948878 | − | 0.315644i | \(-0.102220\pi\) | |||||||
\(272\) | 7.50000 | − | 12.9904i | 0.454754 | − | 0.787658i | ||||
\(273\) | 1.50000 | + | 6.06218i | 0.0907841 | + | 0.366900i | ||||
\(274\) | 4.50000 | + | 7.79423i | 0.271855 | + | 0.470867i | ||||
\(275\) | 10.3923i | 0.626680i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | 6.92820i | 0.415526i | ||||||||
\(279\) | −11.0000 | + | 1.73205i | −0.658553 | + | 0.103695i | ||||
\(280\) | − | 5.19615i | − | 0.310530i | ||||||
\(281\) | − | 13.8564i | − | 0.826604i | −0.910594 | − | 0.413302i | \(-0.864375\pi\) | ||
0.910594 | − | 0.413302i | \(-0.135625\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 7.50000 | − | 4.33013i | 0.445043 | − | 0.256946i | ||||
\(285\) | −4.50000 | + | 7.79423i | −0.266557 | + | 0.461690i | ||||
\(286\) | 31.5000 | − | 7.79423i | 1.86263 | − | 0.460882i | ||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | −9.00000 | + | 5.19615i | −0.530330 | + | 0.306186i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 9.00000 | + | 15.5885i | 0.528498 | + | 0.915386i | ||||
\(291\) | −6.00000 | − | 3.46410i | −0.351726 | − | 0.203069i | ||||
\(292\) | −7.50000 | + | 4.33013i | −0.438904 | + | 0.253402i | ||||
\(293\) | −22.5000 | − | 12.9904i | −1.31446 | − | 0.758906i | −0.331632 | − | 0.943409i | \(-0.607599\pi\) |
−0.982832 | + | 0.184503i | \(0.940933\pi\) | |||||||
\(294\) | 6.92820i | 0.404061i | ||||||||
\(295\) | 3.00000 | 0.174667 | ||||||||
\(296\) | −4.50000 | + | 7.79423i | −0.261557 | + | 0.453030i | ||||
\(297\) | 22.5000 | − | 12.9904i | 1.30558 | − | 0.753778i | ||||
\(298\) | −16.5000 | + | 28.5788i | −0.955819 | + | 1.65553i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | − | 1.73205i | −0.0577350 | − | 0.100000i | ||||
\(301\) | 1.50000 | − | 0.866025i | 0.0864586 | − | 0.0499169i | ||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | 9.00000 | − | 15.5885i | 0.517036 | − | 0.895533i | ||||
\(304\) | 22.5000 | + | 12.9904i | 1.29046 | + | 0.745049i | ||||
\(305\) | 15.0000 | − | 8.66025i | 0.858898 | − | 0.495885i | ||||
\(306\) | 10.3923i | 0.594089i | ||||||||
\(307\) | 1.50000 | + | 0.866025i | 0.0856095 | + | 0.0494267i | 0.542194 | − | 0.840254i | \(-0.317594\pi\) |
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −9.00000 | −0.512823 | ||||||||
\(309\) | 19.0000 | 1.08087 | ||||||||
\(310\) | 16.5000 | − | 2.59808i | 0.937137 | − | 0.147561i | ||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 4.50000 | − | 4.33013i | 0.254762 | − | 0.245145i | ||||
\(313\) | −9.50000 | + | 16.4545i | −0.536972 | + | 0.930062i | 0.462093 | + | 0.886831i | \(0.347098\pi\) |
−0.999065 | + | 0.0432311i | \(0.986235\pi\) | |||||||
\(314\) | 38.1051i | 2.15040i | ||||||||
\(315\) | 3.00000 | + | 5.19615i | 0.169031 | + | 0.292770i | ||||
\(316\) | −2.50000 | + | 4.33013i | −0.140636 | + | 0.243589i | ||||
\(317\) | 13.5000 | + | 7.79423i | 0.758236 | + | 0.437767i | 0.828662 | − | 0.559749i | \(-0.189103\pi\) |
−0.0704263 | + | 0.997517i | \(0.522436\pi\) | |||||||
\(318\) | 5.19615i | 0.291386i | ||||||||
\(319\) | −27.0000 | + | 15.5885i | −1.51171 | + | 0.872786i | ||||
\(320\) | −1.50000 | + | 0.866025i | −0.0838525 | + | 0.0484123i | ||||
\(321\) | −4.50000 | − | 7.79423i | −0.251166 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5000 | − | 7.79423i | 0.751160 | − | 0.433682i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −5.00000 | − | 5.19615i | −0.277350 | − | 0.288231i | ||||
\(326\) | 18.0000 | 0.996928 | ||||||||
\(327\) | −12.0000 | − | 6.92820i | −0.663602 | − | 0.383131i | ||||
\(328\) | 4.50000 | + | 7.79423i | 0.248471 | + | 0.430364i | ||||
\(329\) | −3.00000 | + | 5.19615i | −0.165395 | + | 0.286473i | ||||
\(330\) | −13.5000 | + | 7.79423i | −0.743151 | + | 0.429058i | ||||
\(331\) | 10.5000 | − | 6.06218i | 0.577132 | − | 0.333207i | −0.182861 | − | 0.983139i | \(-0.558536\pi\) |
0.759993 | + | 0.649931i | \(0.225202\pi\) | |||||||
\(332\) | −10.5000 | + | 6.06218i | −0.576262 | + | 0.332705i | ||||
\(333\) | − | 10.3923i | − | 0.569495i | ||||||
\(334\) | 7.50000 | − | 12.9904i | 0.410382 | − | 0.710802i | ||||
\(335\) | −7.50000 | + | 12.9904i | −0.409769 | + | 0.709740i | ||||
\(336\) | −7.50000 | + | 4.33013i | −0.409159 | + | 0.236228i | ||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | −12.0000 | + | 19.0526i | −0.652714 | + | 1.03632i | ||||
\(339\) | 9.00000 | 0.488813 | ||||||||
\(340\) | − | 5.19615i | − | 0.281801i | ||||||
\(341\) | 4.50000 | + | 28.5788i | 0.243689 | + | 1.54763i | ||||
\(342\) | −18.0000 | −0.973329 | ||||||||
\(343\) | − | 19.0526i | − | 1.02874i | ||||||
\(344\) | −1.50000 | − | 0.866025i | −0.0808746 | − | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.5000 | − | 7.79423i | 0.725764 | − | 0.419020i | ||||
\(347\) | 16.5000 | − | 28.5788i | 0.885766 | − | 1.53419i | 0.0409337 | − | 0.999162i | \(-0.486967\pi\) |
0.844833 | − | 0.535031i | \(-0.179700\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 3.00000 | + | 5.19615i | 0.160357 | + | 0.277746i | ||||
\(351\) | −5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | ||||
\(352\) | 13.5000 | + | 23.3827i | 0.719552 | + | 1.24630i | ||||
\(353\) | 25.5000 | + | 14.7224i | 1.35723 | + | 0.783596i | 0.989249 | − | 0.146238i | \(-0.0467166\pi\) |
0.367979 | + | 0.929834i | \(0.380050\pi\) | |||||||
\(354\) | −1.50000 | − | 2.59808i | −0.0797241 | − | 0.138086i | ||||
\(355\) | −7.50000 | + | 12.9904i | −0.398059 | + | 0.689458i | ||||
\(356\) | 6.92820i | 0.367194i | ||||||||
\(357\) | 5.19615i | 0.275010i | ||||||||
\(358\) | 4.50000 | + | 2.59808i | 0.237832 | + | 0.137313i | ||||
\(359\) | −7.50000 | + | 4.33013i | −0.395835 | + | 0.228535i | −0.684685 | − | 0.728839i | \(-0.740060\pi\) |
0.288850 | + | 0.957374i | \(0.406727\pi\) | |||||||
\(360\) | 3.00000 | − | 5.19615i | 0.158114 | − | 0.273861i | ||||
\(361\) | 4.00000 | + | 6.92820i | 0.210526 | + | 0.364642i | ||||
\(362\) | −34.5000 | + | 19.9186i | −1.81328 | + | 1.04690i | ||||
\(363\) | −8.00000 | − | 13.8564i | −0.419891 | − | 0.727273i | ||||
\(364\) | 4.50000 | − | 4.33013i | 0.235864 | − | 0.226960i | ||||
\(365\) | 7.50000 | − | 12.9904i | 0.392568 | − | 0.679948i | ||||
\(366\) | −15.0000 | − | 8.66025i | −0.784063 | − | 0.452679i | ||||
\(367\) | 15.5000 | + | 26.8468i | 0.809093 | + | 1.40139i | 0.913493 | + | 0.406855i | \(0.133375\pi\) |
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | − | 5.19615i | −0.468521 | − | 0.270501i | ||||
\(370\) | 15.5885i | 0.810405i | ||||||||
\(371\) | − | 5.19615i | − | 0.269771i | ||||||
\(372\) | −3.50000 | − | 4.33013i | −0.181467 | − | 0.224507i | ||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | 27.0000 | 1.39614 | ||||||||
\(375\) | 10.5000 | + | 6.06218i | 0.542218 | + | 0.313050i | ||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 6.00000 | − | 20.7846i | 0.309016 | − | 1.07046i | ||||
\(378\) | 7.50000 | − | 12.9904i | 0.385758 | − | 0.668153i | ||||
\(379\) | −10.5000 | − | 6.06218i | −0.539349 | − | 0.311393i | 0.205466 | − | 0.978664i | \(-0.434129\pi\) |
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 9.00000 | 0.461690 | ||||||||
\(381\) | 3.50000 | + | 6.06218i | 0.179310 | + | 0.310575i | ||||
\(382\) | 22.5000 | − | 12.9904i | 1.15120 | − | 0.664646i | ||||
\(383\) | 22.5000 | − | 12.9904i | 1.14970 | − | 0.663777i | 0.200883 | − | 0.979615i | \(-0.435619\pi\) |
0.948813 | + | 0.315838i | \(0.102286\pi\) | |||||||
\(384\) | 10.5000 | + | 6.06218i | 0.535826 | + | 0.309359i | ||||
\(385\) | 13.5000 | − | 7.79423i | 0.688024 | − | 0.397231i | ||||
\(386\) | 19.5000 | − | 33.7750i | 0.992524 | − | 1.71910i | ||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | 6.92820i | 0.351726i | ||||||||
\(389\) | 16.5000 | − | 28.5788i | 0.836583 | − | 1.44900i | −0.0561516 | − | 0.998422i | \(-0.517883\pi\) |
0.892735 | − | 0.450582i | \(-0.148784\pi\) | |||||||
\(390\) | 3.00000 | − | 10.3923i | 0.151911 | − | 0.526235i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.00000 | + | 3.46410i | −0.303046 | + | 0.174964i | ||||
\(393\) | −4.50000 | − | 7.79423i | −0.226995 | − | 0.393167i | ||||
\(394\) | −7.50000 | − | 12.9904i | −0.377845 | − | 0.654446i | ||||
\(395\) | − | 8.66025i | − | 0.435745i | ||||||
\(396\) | −9.00000 | − | 5.19615i | −0.452267 | − | 0.261116i | ||||
\(397\) | 13.5000 | + | 7.79423i | 0.677546 | + | 0.391181i | 0.798930 | − | 0.601424i | \(-0.205400\pi\) |
−0.121384 | + | 0.992606i | \(0.538733\pi\) | |||||||
\(398\) | −37.5000 | + | 21.6506i | −1.87971 | + | 1.08525i | ||||
\(399\) | −9.00000 | −0.450564 | ||||||||
\(400\) | 5.00000 | − | 8.66025i | 0.250000 | − | 0.433013i | ||||
\(401\) | − | 6.92820i | − | 0.345978i | −0.984924 | − | 0.172989i | \(-0.944657\pi\) | ||
0.984924 | − | 0.172989i | \(-0.0553425\pi\) | |||||||
\(402\) | 15.0000 | 0.748132 | ||||||||
\(403\) | −16.0000 | − | 12.1244i | −0.797017 | − | 0.603957i | ||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | 1.73205i | 0.0860663i | ||||||||
\(406\) | −9.00000 | + | 15.5885i | −0.446663 | + | 0.773642i | ||||
\(407\) | −27.0000 | −1.33834 | ||||||||
\(408\) | 4.50000 | − | 2.59808i | 0.222783 | − | 0.128624i | ||||
\(409\) | −22.5000 | − | 12.9904i | −1.11255 | − | 0.642333i | −0.173064 | − | 0.984911i | \(-0.555367\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 13.5000 | + | 7.79423i | 0.666717 | + | 0.384930i | ||||
\(411\) | 5.19615i | 0.256307i | ||||||||
\(412\) | −9.50000 | − | 16.4545i | −0.468031 | − | 0.810654i | ||||
\(413\) | 1.50000 | + | 2.59808i | 0.0738102 | + | 0.127843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5000 | − | 18.1865i | 0.515425 | − | 0.892742i | ||||
\(416\) | −18.0000 | − | 5.19615i | −0.882523 | − | 0.254762i | ||||
\(417\) | −2.00000 | + | 3.46410i | −0.0979404 | + | 0.169638i | ||||
\(418\) | 46.7654i | 2.28737i | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | −1.50000 | + | 2.59808i | −0.0731925 | + | 0.126773i | ||||
\(421\) | −28.5000 | + | 16.4545i | −1.38901 | + | 0.801942i | −0.993203 | − | 0.116394i | \(-0.962867\pi\) |
−0.395802 | + | 0.918336i | \(0.629533\pi\) | |||||||
\(422\) | −7.50000 | − | 4.33013i | −0.365094 | − | 0.210787i | ||||
\(423\) | −6.00000 | + | 3.46410i | −0.291730 | + | 0.168430i | ||||
\(424\) | −4.50000 | + | 2.59808i | −0.218539 | + | 0.126174i | ||||
\(425\) | −3.00000 | − | 5.19615i | −0.145521 | − | 0.252050i | ||||
\(426\) | 15.0000 | 0.726752 | ||||||||
\(427\) | 15.0000 | + | 8.66025i | 0.725901 | + | 0.419099i | ||||
\(428\) | −4.50000 | + | 7.79423i | −0.217516 | + | 0.376748i | ||||
\(429\) | 18.0000 | + | 5.19615i | 0.869048 | + | 0.250873i | ||||
\(430\) | −3.00000 | −0.144673 | ||||||||
\(431\) | 19.5000 | + | 11.2583i | 0.939282 | + | 0.542295i | 0.889735 | − | 0.456477i | \(-0.150889\pi\) |
0.0495468 | + | 0.998772i | \(0.484222\pi\) | |||||||
\(432\) | −25.0000 | −1.20281 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 10.5000 | + | 12.9904i | 0.504016 | + | 0.623558i | ||||
\(435\) | 10.3923i | 0.498273i | ||||||||
\(436\) | 13.8564i | 0.663602i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −15.0000 | −0.716728 | ||||||||
\(439\) | 9.50000 | + | 16.4545i | 0.453410 | + | 0.785330i | 0.998595 | − | 0.0529862i | \(-0.0168739\pi\) |
−0.545185 | + | 0.838316i | \(0.683541\pi\) | |||||||
\(440\) | −13.5000 | − | 7.79423i | −0.643587 | − | 0.371575i | ||||
\(441\) | 4.00000 | − | 6.92820i | 0.190476 | − | 0.329914i | ||||
\(442\) | −13.5000 | + | 12.9904i | −0.642130 | + | 0.617889i | ||||
\(443\) | 7.50000 | + | 12.9904i | 0.356336 | + | 0.617192i | 0.987346 | − | 0.158583i | \(-0.0506926\pi\) |
−0.631010 | + | 0.775775i | \(0.717359\pi\) | |||||||
\(444\) | 4.50000 | − | 2.59808i | 0.213561 | − | 0.123299i | ||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 1.50000 | − | 2.59808i | 0.0710271 | − | 0.123022i | ||||
\(447\) | −16.5000 | + | 9.52628i | −0.780423 | + | 0.450578i | ||||
\(448\) | −1.50000 | − | 0.866025i | −0.0708683 | − | 0.0409159i | ||||
\(449\) | − | 13.8564i | − | 0.653924i | −0.945037 | − | 0.326962i | \(-0.893975\pi\) | ||
0.945037 | − | 0.326962i | \(-0.106025\pi\) | |||||||
\(450\) | 6.92820i | 0.326599i | ||||||||
\(451\) | −13.5000 | + | 23.3827i | −0.635690 | + | 1.10105i | ||||
\(452\) | −4.50000 | − | 7.79423i | −0.211662 | − | 0.366610i | ||||
\(453\) | −3.00000 | − | 1.73205i | −0.140952 | − | 0.0813788i | ||||
\(454\) | 7.50000 | + | 12.9904i | 0.351992 | + | 0.609669i | ||||
\(455\) | −3.00000 | + | 10.3923i | −0.140642 | + | 0.487199i | ||||
\(456\) | 4.50000 | + | 7.79423i | 0.210732 | + | 0.364998i | ||||
\(457\) | − | 6.92820i | − | 0.324088i | −0.986784 | − | 0.162044i | \(-0.948191\pi\) | ||
0.986784 | − | 0.162044i | \(-0.0518086\pi\) | |||||||
\(458\) | 1.50000 | − | 2.59808i | 0.0700904 | − | 0.121400i | ||||
\(459\) | −7.50000 | + | 12.9904i | −0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564i | 0.645357i | 0.946509 | + | 0.322679i | \(0.104583\pi\) | ||||
−0.946509 | + | 0.322679i | \(0.895417\pi\) | |||||||
\(462\) | −13.5000 | − | 7.79423i | −0.628077 | − | 0.362620i | ||||
\(463\) | 17.3205i | 0.804952i | 0.915430 | + | 0.402476i | \(0.131850\pi\) | ||||
−0.915430 | + | 0.402476i | \(0.868150\pi\) | |||||||
\(464\) | 30.0000 | 1.39272 | ||||||||
\(465\) | 9.00000 | + | 3.46410i | 0.417365 | + | 0.160644i | ||||
\(466\) | 31.1769i | 1.44424i | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 7.00000 | − | 1.73205i | 0.323575 | − | 0.0800641i | ||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | 9.00000 | − | 5.19615i | 0.415139 | − | 0.239681i | ||||
\(471\) | −11.0000 | + | 19.0526i | −0.506853 | + | 0.877896i | ||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | − | 5.19615i | − | 0.238919i | ||||||
\(474\) | −7.50000 | + | 4.33013i | −0.344486 | + | 0.198889i | ||||
\(475\) | 9.00000 | − | 5.19615i | 0.412948 | − | 0.238416i | ||||
\(476\) | 4.50000 | − | 2.59808i | 0.206257 | − | 0.119083i | ||||
\(477\) | 3.00000 | − | 5.19615i | 0.137361 | − | 0.237915i | ||||
\(478\) | 13.5000 | + | 23.3827i | 0.617476 | + | 1.06950i | ||||
\(479\) | 1.50000 | + | 0.866025i | 0.0685367 | + | 0.0395697i | 0.533877 | − | 0.845562i | \(-0.320735\pi\) |
−0.465340 | + | 0.885132i | \(0.654068\pi\) | |||||||
\(480\) | 9.00000 | 0.410792 | ||||||||
\(481\) | 13.5000 | − | 12.9904i | 0.615547 | − | 0.592310i | ||||
\(482\) | 1.50000 | − | 2.59808i | 0.0683231 | − | 0.118339i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | + | 13.8564i | −0.363636 | + | 0.629837i | ||||
\(485\) | −6.00000 | − | 10.3923i | −0.272446 | − | 0.471890i | ||||
\(486\) | 24.0000 | − | 13.8564i | 1.08866 | − | 0.628539i | ||||
\(487\) | −19.5000 | + | 11.2583i | −0.883629 | + | 0.510164i | −0.871853 | − | 0.489767i | \(-0.837082\pi\) |
−0.0117760 | + | 0.999931i | \(0.503749\pi\) | |||||||
\(488\) | − | 17.3205i | − | 0.784063i | ||||||
\(489\) | 9.00000 | + | 5.19615i | 0.406994 | + | 0.234978i | ||||
\(490\) | −6.00000 | + | 10.3923i | −0.271052 | + | 0.469476i | ||||
\(491\) | −4.50000 | − | 7.79423i | −0.203082 | − | 0.351749i | 0.746438 | − | 0.665455i | \(-0.231763\pi\) |
−0.949520 | + | 0.313707i | \(0.898429\pi\) | |||||||
\(492\) | − | 5.19615i | − | 0.234261i | ||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | −22.5000 | − | 23.3827i | −1.01232 | − | 1.05204i | ||||
\(495\) | 18.0000 | 0.809040 | ||||||||
\(496\) | 10.0000 | − | 25.9808i | 0.449013 | − | 1.16657i | ||||
\(497\) | −15.0000 | −0.672842 | ||||||||
\(498\) | −21.0000 | −0.941033 | ||||||||
\(499\) | 31.5000 | + | 18.1865i | 1.41013 | + | 0.814141i | 0.995400 | − | 0.0958020i | \(-0.0305416\pi\) |
0.414733 | + | 0.909943i | \(0.363875\pi\) | |||||||
\(500\) | − | 12.1244i | − | 0.542218i | ||||||
\(501\) | 7.50000 | − | 4.33013i | 0.335075 | − | 0.193456i | ||||
\(502\) | −31.5000 | − | 18.1865i | −1.40591 | − | 0.811705i | ||||
\(503\) | 10.5000 | − | 18.1865i | 0.468172 | − | 0.810897i | −0.531167 | − | 0.847267i | \(-0.678246\pi\) |
0.999338 | + | 0.0363700i | \(0.0115795\pi\) | |||||||
\(504\) | 6.00000 | 0.267261 | ||||||||
\(505\) | 27.0000 | − | 15.5885i | 1.20148 | − | 0.693677i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.5000 | + | 6.06218i | −0.510733 | + | 0.269231i | ||||
\(508\) | 3.50000 | − | 6.06218i | 0.155287 | − | 0.268966i | ||||
\(509\) | 7.50000 | − | 4.33013i | 0.332432 | − | 0.191930i | −0.324489 | − | 0.945890i | \(-0.605192\pi\) |
0.656920 | + | 0.753960i | \(0.271859\pi\) | |||||||
\(510\) | 4.50000 | − | 7.79423i | 0.199263 | − | 0.345134i | ||||
\(511\) | 15.0000 | 0.663561 | ||||||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | −22.5000 | − | 12.9904i | −0.993399 | − | 0.573539i | ||||
\(514\) | −22.5000 | + | 12.9904i | −0.992432 | + | 0.572981i | ||||
\(515\) | 28.5000 | + | 16.4545i | 1.25586 | + | 0.725071i | ||||
\(516\) | 0.500000 | + | 0.866025i | 0.0220113 | + | 0.0381246i | ||||
\(517\) | 9.00000 | + | 15.5885i | 0.395820 | + | 0.685580i | ||||
\(518\) | −13.5000 | + | 7.79423i | −0.593156 | + | 0.342459i | ||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 10.5000 | − | 2.59808i | 0.460455 | − | 0.113933i | ||||
\(521\) | 10.5000 | − | 18.1865i | 0.460013 | − | 0.796766i | −0.538948 | − | 0.842339i | \(-0.681178\pi\) |
0.998961 | + | 0.0455727i | \(0.0145113\pi\) | |||||||
\(522\) | −18.0000 | + | 10.3923i | −0.787839 | + | 0.454859i | ||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | −4.50000 | + | 7.79423i | −0.196583 | + | 0.340492i | ||||
\(525\) | 3.46410i | 0.151186i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.5000 | − | 12.9904i | −0.457387 | − | 0.565870i | ||||
\(528\) | 25.9808i | 1.13067i | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −4.50000 | + | 7.79423i | −0.195468 | + | 0.338560i | ||||
\(531\) | 3.46410i | 0.150329i | ||||||||
\(532\) | 4.50000 | + | 7.79423i | 0.195100 | + | 0.337923i | ||||
\(533\) | −4.50000 | − | 18.1865i | −0.194917 | − | 0.787746i | ||||
\(534\) | −6.00000 | + | 10.3923i | −0.259645 | + | 0.449719i | ||||
\(535\) | − | 15.5885i | − | 0.673948i | ||||||
\(536\) | 7.50000 | + | 12.9904i | 0.323951 | + | 0.561099i | ||||
\(537\) | 1.50000 | + | 2.59808i | 0.0647298 | + | 0.112115i | ||||
\(538\) | 31.5000 | − | 18.1865i | 1.35806 | − | 0.784077i | ||||
\(539\) | −18.0000 | − | 10.3923i | −0.775315 | − | 0.447628i | ||||
\(540\) | −7.50000 | + | 4.33013i | −0.322749 | + | 0.186339i | ||||
\(541\) | 7.50000 | + | 4.33013i | 0.322450 | + | 0.186167i | 0.652484 | − | 0.757802i | \(-0.273727\pi\) |
−0.330034 | + | 0.943969i | \(0.607060\pi\) | |||||||
\(542\) | −18.0000 | −0.773166 | ||||||||
\(543\) | −23.0000 | −0.987024 | ||||||||
\(544\) | −13.5000 | − | 7.79423i | −0.578808 | − | 0.334175i | ||||
\(545\) | −12.0000 | − | 20.7846i | −0.514024 | − | 0.890315i | ||||
\(546\) | 10.5000 | − | 2.59808i | 0.449359 | − | 0.111187i | ||||
\(547\) | 9.50000 | + | 16.4545i | 0.406191 | + | 0.703543i | 0.994459 | − | 0.105123i | \(-0.0335235\pi\) |
−0.588269 | + | 0.808666i | \(0.700190\pi\) | |||||||
\(548\) | 4.50000 | − | 2.59808i | 0.192230 | − | 0.110984i | ||||
\(549\) | 10.0000 | + | 17.3205i | 0.426790 | + | 0.739221i | ||||
\(550\) | 18.0000 | 0.767523 | ||||||||
\(551\) | 27.0000 | + | 15.5885i | 1.15024 | + | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | − | 4.33013i | 0.318932 | − | 0.184136i | ||||
\(554\) | − | 45.0333i | − | 1.91328i | ||||||
\(555\) | −4.50000 | + | 7.79423i | −0.191014 | + | 0.330847i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 3.00000 | + | 19.0526i | 0.127000 | + | 0.806559i | ||||
\(559\) | 2.50000 | + | 2.59808i | 0.105739 | + | 0.109887i | ||||
\(560\) | −15.0000 | −0.633866 | ||||||||
\(561\) | 13.5000 | + | 7.79423i | 0.569970 | + | 0.329073i | ||||
\(562\) | −24.0000 | −1.01238 | ||||||||
\(563\) | 1.50000 | + | 2.59808i | 0.0632175 | + | 0.109496i | 0.895902 | − | 0.444252i | \(-0.146530\pi\) |
−0.832684 | + | 0.553748i | \(0.813197\pi\) | |||||||
\(564\) | −3.00000 | − | 1.73205i | −0.126323 | − | 0.0729325i | ||||
\(565\) | 13.5000 | + | 7.79423i | 0.567949 | + | 0.327906i | ||||
\(566\) | − | 6.92820i | − | 0.291214i | ||||||
\(567\) | −1.50000 | + | 0.866025i | −0.0629941 | + | 0.0363696i | ||||
\(568\) | 7.50000 | + | 12.9904i | 0.314693 | + | 0.545064i | ||||
\(569\) | 10.5000 | + | 18.1865i | 0.440183 | + | 0.762419i | 0.997703 | − | 0.0677445i | \(-0.0215803\pi\) |
−0.557520 | + | 0.830164i | \(0.688247\pi\) | |||||||
\(570\) | 13.5000 | + | 7.79423i | 0.565453 | + | 0.326464i | ||||
\(571\) | −18.5000 | − | 32.0429i | −0.774201 | − | 1.34096i | −0.935243 | − | 0.354008i | \(-0.884819\pi\) |
0.161042 | − | 0.986948i | \(-0.448515\pi\) | |||||||
\(572\) | −4.50000 | − | 18.1865i | −0.188154 | − | 0.760417i | ||||
\(573\) | 15.0000 | 0.626634 | ||||||||
\(574\) | 15.5885i | 0.650650i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | − | 1.73205i | −0.0416667 | − | 0.0721688i | ||||
\(577\) | −34.5000 | − | 19.9186i | −1.43625 | − | 0.829222i | −0.438667 | − | 0.898650i | \(-0.644549\pi\) |
−0.997587 | + | 0.0694283i | \(0.977883\pi\) | |||||||
\(578\) | 12.0000 | − | 6.92820i | 0.499134 | − | 0.288175i | ||||
\(579\) | 19.5000 | − | 11.2583i | 0.810392 | − | 0.467880i | ||||
\(580\) | 9.00000 | − | 5.19615i | 0.373705 | − | 0.215758i | ||||
\(581\) | 21.0000 | 0.871227 | ||||||||
\(582\) | −6.00000 | + | 10.3923i | −0.248708 | + | 0.430775i | ||||
\(583\) | −13.5000 | − | 7.79423i | −0.559113 | − | 0.322804i | ||||
\(584\) | −7.50000 | − | 12.9904i | −0.310352 | − | 0.537546i | ||||
\(585\) | −9.00000 | + | 8.66025i | −0.372104 | + | 0.358057i | ||||
\(586\) | −22.5000 | + | 38.9711i | −0.929466 | + | 1.60988i | ||||
\(587\) | − | 10.3923i | − | 0.428936i | −0.976731 | − | 0.214468i | \(-0.931198\pi\) | ||
0.976731 | − | 0.214468i | \(-0.0688018\pi\) | |||||||
\(588\) | 4.00000 | 0.164957 | ||||||||
\(589\) | 22.5000 | − | 18.1865i | 0.927096 | − | 0.749363i | ||||
\(590\) | − | 5.19615i | − | 0.213922i | ||||||
\(591\) | − | 8.66025i | − | 0.356235i | ||||||
\(592\) | 22.5000 | + | 12.9904i | 0.924744 | + | 0.533901i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −22.5000 | − | 38.9711i | −0.923186 | − | 1.59901i | ||||
\(595\) | −4.50000 | + | 7.79423i | −0.184482 | + | 0.319532i | ||||
\(596\) | 16.5000 | + | 9.52628i | 0.675866 | + | 0.390212i | ||||
\(597\) | −25.0000 | −1.02318 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.5000 | − | 28.5788i | −0.674172 | − | 1.16770i | −0.976710 | − | 0.214563i | \(-0.931167\pi\) |
0.302539 | − | 0.953137i | \(-0.402166\pi\) | |||||||
\(600\) | 3.00000 | − | 1.73205i | 0.122474 | − | 0.0707107i | ||||
\(601\) | 14.5000 | − | 25.1147i | 0.591467 | − | 1.02445i | −0.402568 | − | 0.915390i | \(-0.631882\pi\) |
0.994035 | − | 0.109061i | \(-0.0347845\pi\) | |||||||
\(602\) | −1.50000 | − | 2.59808i | −0.0611354 | − | 0.105890i | ||||
\(603\) | −15.0000 | − | 8.66025i | −0.610847 | − | 0.352673i | ||||
\(604\) | 3.46410i | 0.140952i | ||||||||
\(605\) | − | 27.7128i | − | 1.12669i | ||||||
\(606\) | −27.0000 | − | 15.5885i | −1.09680 | − | 0.633238i | ||||
\(607\) | 3.50000 | + | 6.06218i | 0.142061 | + | 0.246056i | 0.928272 | − | 0.371901i | \(-0.121294\pi\) |
−0.786212 | + | 0.617957i | \(0.787961\pi\) | |||||||
\(608\) | 13.5000 | − | 23.3827i | 0.547497 | − | 0.948293i | ||||
\(609\) | −9.00000 | + | 5.19615i | −0.364698 | + | 0.210559i | ||||
\(610\) | −15.0000 | − | 25.9808i | −0.607332 | − | 1.05193i | ||||
\(611\) | −12.0000 | − | 3.46410i | −0.485468 | − | 0.140143i | ||||
\(612\) | 6.00000 | 0.242536 | ||||||||
\(613\) | −40.5000 | − | 23.3827i | −1.63578 | − | 0.944418i | −0.982264 | − | 0.187505i | \(-0.939960\pi\) |
−0.653516 | − | 0.756913i | \(-0.726707\pi\) | |||||||
\(614\) | 1.50000 | − | 2.59808i | 0.0605351 | − | 0.104850i | ||||
\(615\) | 4.50000 | + | 7.79423i | 0.181458 | + | 0.314294i | ||||
\(616\) | − | 15.5885i | − | 0.628077i | ||||||
\(617\) | −10.5000 | − | 6.06218i | −0.422714 | − | 0.244054i | 0.273524 | − | 0.961865i | \(-0.411811\pi\) |
−0.696238 | + | 0.717811i | \(0.745144\pi\) | |||||||
\(618\) | − | 32.9090i | − | 1.32379i | ||||||
\(619\) | − | 10.3923i | − | 0.417702i | −0.977947 | − | 0.208851i | \(-0.933028\pi\) | ||
0.977947 | − | 0.208851i | \(-0.0669724\pi\) | |||||||
\(620\) | −1.50000 | − | 9.52628i | −0.0602414 | − | 0.382585i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 41.5692i | − | 1.66677i | ||||||
\(623\) | 6.00000 | − | 10.3923i | 0.240385 | − | 0.416359i | ||||
\(624\) | −12.5000 | − | 12.9904i | −0.500400 | − | 0.520031i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 28.5000 | + | 16.4545i | 1.13909 | + | 0.657653i | ||||
\(627\) | −13.5000 | + | 23.3827i | −0.539138 | + | 0.933815i | ||||
\(628\) | 22.0000 | 0.877896 | ||||||||
\(629\) | 13.5000 | − | 7.79423i | 0.538280 | − | 0.310776i | ||||
\(630\) | 9.00000 | − | 5.19615i | 0.358569 | − | 0.207020i | ||||
\(631\) | −19.5000 | + | 11.2583i | −0.776283 | + | 0.448187i | −0.835111 | − | 0.550081i | \(-0.814597\pi\) |
0.0588285 | + | 0.998268i | \(0.481263\pi\) | |||||||
\(632\) | −7.50000 | − | 4.33013i | −0.298334 | − | 0.172243i | ||||
\(633\) | −2.50000 | − | 4.33013i | −0.0993661 | − | 0.172107i | ||||
\(634\) | 13.5000 | − | 23.3827i | 0.536153 | − | 0.928645i | ||||
\(635\) | 12.1244i | 0.481140i | ||||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 14.0000 | − | 3.46410i | 0.554700 | − | 0.137253i | ||||
\(638\) | 27.0000 | + | 46.7654i | 1.06894 | + | 1.85146i | ||||
\(639\) | −15.0000 | − | 8.66025i | −0.593391 | − | 0.342594i | ||||
\(640\) | 10.5000 | + | 18.1865i | 0.415049 | + | 0.718886i | ||||
\(641\) | −7.50000 | − | 12.9904i | −0.296232 | − | 0.513089i | 0.679039 | − | 0.734103i | \(-0.262397\pi\) |
−0.975271 | + | 0.221013i | \(0.929064\pi\) | |||||||
\(642\) | −13.5000 | + | 7.79423i | −0.532803 | + | 0.307614i | ||||
\(643\) | − | 17.3205i | − | 0.683054i | −0.939872 | − | 0.341527i | \(-0.889056\pi\) | ||
0.939872 | − | 0.341527i | \(-0.110944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.50000 | − | 0.866025i | −0.0590624 | − | 0.0340997i | ||||
\(646\) | −13.5000 | − | 23.3827i | −0.531150 | − | 0.919979i | ||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 1.50000 | + | 0.866025i | 0.0589256 | + | 0.0340207i | ||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | −9.00000 | + | 8.66025i | −0.353009 | + | 0.339683i | ||||
\(651\) | 1.50000 | + | 9.52628i | 0.0587896 | + | 0.373364i | ||||
\(652\) | − | 10.3923i | − | 0.406994i | ||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | −12.0000 | + | 20.7846i | −0.469237 | + | 0.812743i | ||||
\(655\) | − | 15.5885i | − | 0.609091i | ||||||
\(656\) | 22.5000 | − | 12.9904i | 0.878477 | − | 0.507189i | ||||
\(657\) | 15.0000 | + | 8.66025i | 0.585206 | + | 0.337869i | ||||
\(658\) | 9.00000 | + | 5.19615i | 0.350857 | + | 0.202567i | ||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 4.50000 | + | 7.79423i | 0.175162 | + | 0.303390i | ||||
\(661\) | −4.50000 | + | 2.59808i | −0.175030 | + | 0.101053i | −0.584955 | − | 0.811065i | \(-0.698888\pi\) |
0.409926 | + | 0.912119i | \(0.365555\pi\) | |||||||
\(662\) | −10.5000 | − | 18.1865i | −0.408094 | − | 0.706840i | ||||
\(663\) | −10.5000 | + | 2.59808i | −0.407786 | + | 0.100901i | ||||
\(664\) | −10.5000 | − | 18.1865i | −0.407479 | − | 0.705774i | ||||
\(665\) | −13.5000 | − | 7.79423i | −0.523508 | − | 0.302247i | ||||
\(666\) | −18.0000 | −0.697486 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −7.50000 | − | 4.33013i | −0.290184 | − | 0.167538i | ||||
\(669\) | 1.50000 | − | 0.866025i | 0.0579934 | − | 0.0334825i | ||||
\(670\) | 22.5000 | + | 12.9904i | 0.869251 | + | 0.501862i | ||||
\(671\) | 45.0000 | − | 25.9808i | 1.73721 | − | 1.00298i | ||||
\(672\) | 4.50000 | + | 7.79423i | 0.173591 | + | 0.300669i | ||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | 24.2487i | 0.934025i | ||||||||
\(675\) | −5.00000 | + | 8.66025i | −0.192450 | + | 0.333333i | ||||
\(676\) | 11.0000 | + | 6.92820i | 0.423077 | + | 0.266469i | ||||
\(677\) | 4.50000 | + | 7.79423i | 0.172949 | + | 0.299557i | 0.939450 | − | 0.342687i | \(-0.111337\pi\) |
−0.766501 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(678\) | − | 15.5885i | − | 0.598671i | ||||||
\(679\) | 6.00000 | − | 10.3923i | 0.230259 | − | 0.398820i | ||||
\(680\) | 9.00000 | 0.345134 | ||||||||
\(681\) | 8.66025i | 0.331862i | ||||||||
\(682\) | 49.5000 | − | 7.79423i | 1.89545 | − | 0.298456i | ||||
\(683\) | 38.1051i | 1.45805i | 0.684486 | + | 0.729026i | \(0.260027\pi\) | ||||
−0.684486 | + | 0.729026i | \(0.739973\pi\) | |||||||
\(684\) | 10.3923i | 0.397360i | ||||||||
\(685\) | −4.50000 | + | 7.79423i | −0.171936 | + | 0.297802i | ||||
\(686\) | −33.0000 | −1.25995 | ||||||||
\(687\) | 1.50000 | − | 0.866025i | 0.0572286 | − | 0.0330409i | ||||
\(688\) | −2.50000 | + | 4.33013i | −0.0953116 | + | 0.165085i | ||||
\(689\) | 10.5000 | − | 2.59808i | 0.400018 | − | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.50000 | − | 2.59808i | 0.171188 | − | 0.0988355i | −0.411958 | − | 0.911203i | \(-0.635155\pi\) |
0.583146 | + | 0.812367i | \(0.301822\pi\) | |||||||
\(692\) | −4.50000 | − | 7.79423i | −0.171064 | − | 0.296292i | ||||
\(693\) | 9.00000 | + | 15.5885i | 0.341882 | + | 0.592157i | ||||
\(694\) | −49.5000 | − | 28.5788i | −1.87899 | − | 1.08484i | ||||
\(695\) | −6.00000 | + | 3.46410i | −0.227593 | + | 0.131401i | ||||
\(696\) | 9.00000 | + | 5.19615i | 0.341144 | + | 0.196960i | ||||
\(697\) | − | 15.5885i | − | 0.590455i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.00000 | + | 15.5885i | −0.340411 | + | 0.589610i | ||||
\(700\) | 3.00000 | − | 1.73205i | 0.113389 | − | 0.0654654i | ||||
\(701\) | 4.50000 | − | 7.79423i | 0.169963 | − | 0.294384i | −0.768444 | − | 0.639917i | \(-0.778969\pi\) |
0.938406 | + | 0.345533i | \(0.112302\pi\) | |||||||
\(702\) | 30.0000 | + | 8.66025i | 1.13228 | + | 0.326860i | ||||
\(703\) | 13.5000 | + | 23.3827i | 0.509162 | + | 0.881895i | ||||
\(704\) | −4.50000 | + | 2.59808i | −0.169600 | + | 0.0979187i | ||||
\(705\) | 6.00000 | 0.225973 | ||||||||
\(706\) | 25.5000 | − | 44.1673i | 0.959705 | − | 1.66226i | ||||
\(707\) | 27.0000 | + | 15.5885i | 1.01544 | + | 0.586264i | ||||
\(708\) | −1.50000 | + | 0.866025i | −0.0563735 | + | 0.0325472i | ||||
\(709\) | 48.4974i | 1.82136i | 0.413114 | + | 0.910679i | \(0.364441\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 22.5000 | + | 12.9904i | 0.844410 | + | 0.487520i | ||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | −12.0000 | −0.449719 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 9.00000 | 0.336817 | ||||||||
\(715\) | 22.5000 | + | 23.3827i | 0.841452 | + | 0.874463i | ||||
\(716\) | 1.50000 | − | 2.59808i | 0.0560576 | − | 0.0970947i | ||||
\(717\) | 15.5885i | 0.582162i | ||||||||
\(718\) | 7.50000 | + | 12.9904i | 0.279898 | + | 0.484797i | ||||
\(719\) | 4.50000 | − | 7.79423i | 0.167822 | − | 0.290676i | −0.769832 | − | 0.638247i | \(-0.779660\pi\) |
0.937654 | + | 0.347571i | \(0.112993\pi\) | |||||||
\(720\) | −15.0000 | − | 8.66025i | −0.559017 | − | 0.322749i | ||||
\(721\) | 32.9090i | 1.22559i | ||||||||
\(722\) | 12.0000 | − | 6.92820i | 0.446594 | − | 0.257841i | ||||
\(723\) | 1.50000 | − | 0.866025i | 0.0557856 | − | 0.0322078i | ||||
\(724\) | 11.5000 | + | 19.9186i | 0.427394 | + | 0.740268i | ||||
\(725\) | 6.00000 | − | 10.3923i | 0.222834 | − | 0.385961i | ||||
\(726\) | −24.0000 | + | 13.8564i | −0.890724 | + | 0.514259i | ||||
\(727\) | 2.50000 | − | 4.33013i | 0.0927199 | − | 0.160596i | −0.815935 | − | 0.578144i | \(-0.803777\pi\) |
0.908655 | + | 0.417548i | \(0.137111\pi\) | |||||||
\(728\) | 7.50000 | + | 7.79423i | 0.277968 | + | 0.288873i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −22.5000 | − | 12.9904i | −0.832762 | − | 0.480796i | ||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | −5.00000 | + | 8.66025i | −0.184805 | + | 0.320092i | ||||
\(733\) | −10.5000 | + | 6.06218i | −0.387826 | + | 0.223912i | −0.681218 | − | 0.732081i | \(-0.738549\pi\) |
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(734\) | 46.5000 | − | 26.8468i | 1.71635 | − | 0.990933i | ||||
\(735\) | −6.00000 | + | 3.46410i | −0.221313 | + | 0.127775i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5000 | + | 38.9711i | −0.828798 | + | 1.43552i | ||||
\(738\) | −9.00000 | + | 15.5885i | −0.331295 | + | 0.573819i | ||||
\(739\) | −19.5000 | + | 11.2583i | −0.717319 | + | 0.414144i | −0.813765 | − | 0.581194i | \(-0.802586\pi\) |
0.0964461 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(740\) | 9.00000 | 0.330847 | ||||||||
\(741\) | −4.50000 | − | 18.1865i | −0.165312 | − | 0.668099i | ||||
\(742\) | −9.00000 | −0.330400 | ||||||||
\(743\) | 17.3205i | 0.635428i | 0.948187 | + | 0.317714i | \(0.102915\pi\) | ||||
−0.948187 | + | 0.317714i | \(0.897085\pi\) | |||||||
\(744\) | 7.50000 | − | 6.06218i | 0.274963 | − | 0.222250i | ||||
\(745\) | −33.0000 | −1.20903 | ||||||||
\(746\) | 45.0333i | 1.64879i | ||||||||
\(747\) | 21.0000 | + | 12.1244i | 0.768350 | + | 0.443607i | ||||
\(748\) | − | 15.5885i | − | 0.569970i | ||||||
\(749\) | 13.5000 | − | 7.79423i | 0.493279 | − | 0.284795i | ||||
\(750\) | 10.5000 | − | 18.1865i | 0.383406 | − | 0.664078i | ||||
\(751\) | −23.5000 | + | 40.7032i | −0.857527 | + | 1.48528i | 0.0167534 | + | 0.999860i | \(0.494667\pi\) |
−0.874281 | + | 0.485421i | \(0.838666\pi\) | |||||||
\(752\) | − | 17.3205i | − | 0.631614i | ||||||
\(753\) | −10.5000 | − | 18.1865i | −0.382641 | − | 0.662754i | ||||
\(754\) | −36.0000 | − | 10.3923i | −1.31104 | − | 0.378465i | ||||
\(755\) | −3.00000 | − | 5.19615i | −0.109181 | − | 0.189107i | ||||
\(756\) | −7.50000 | − | 4.33013i | −0.272772 | − | 0.157485i | ||||
\(757\) | 8.50000 | + | 14.7224i | 0.308938 | + | 0.535096i | 0.978130 | − | 0.207993i | \(-0.0666932\pi\) |
−0.669193 | + | 0.743089i | \(0.733360\pi\) | |||||||
\(758\) | −10.5000 | + | 18.1865i | −0.381377 | + | 0.660565i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.5885i | 0.565453i | ||||||||
\(761\) | 7.50000 | + | 4.33013i | 0.271875 | + | 0.156967i | 0.629739 | − | 0.776807i | \(-0.283162\pi\) |
−0.357865 | + | 0.933774i | \(0.616495\pi\) | |||||||
\(762\) | 10.5000 | − | 6.06218i | 0.380375 | − | 0.219610i | ||||
\(763\) | 12.0000 | − | 20.7846i | 0.434429 | − | 0.752453i | ||||
\(764\) | −7.50000 | − | 12.9904i | −0.271340 | − | 0.469975i | ||||
\(765\) | −9.00000 | + | 5.19615i | −0.325396 | + | 0.187867i | ||||
\(766\) | −22.5000 | − | 38.9711i | −0.812958 | − | 1.40808i | ||||
\(767\) | −4.50000 | + | 4.33013i | −0.162486 | + | 0.156352i | ||||
\(768\) | 9.50000 | − | 16.4545i | 0.342802 | − | 0.593750i | ||||
\(769\) | 43.5000 | + | 25.1147i | 1.56865 | + | 0.905661i | 0.996327 | + | 0.0856325i | \(0.0272911\pi\) |
0.572323 | + | 0.820028i | \(0.306042\pi\) | |||||||
\(770\) | −13.5000 | − | 23.3827i | −0.486506 | − | 0.842654i | ||||
\(771\) | −15.0000 | −0.540212 | ||||||||
\(772\) | −19.5000 | − | 11.2583i | −0.701820 | − | 0.405196i | ||||
\(773\) | 34.6410i | 1.24595i | 0.782241 | + | 0.622975i | \(0.214076\pi\) | ||||
−0.782241 | + | 0.622975i | \(0.785924\pi\) | |||||||
\(774\) | − | 3.46410i | − | 0.124515i | ||||||
\(775\) | −7.00000 | − | 8.66025i | −0.251447 | − | 0.311086i | ||||
\(776\) | −12.0000 | −0.430775 | ||||||||
\(777\) | −9.00000 | −0.322873 | ||||||||
\(778\) | −49.5000 | − | 28.5788i | −1.77466 | − | 1.02460i | ||||
\(779\) | 27.0000 | 0.967375 | ||||||||
\(780\) | −6.00000 | − | 1.73205i | −0.214834 | − | 0.0620174i | ||||
\(781\) | −22.5000 | + | 38.9711i | −0.805113 | + | 1.39450i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.0000 | −1.07211 | ||||||||
\(784\) | 10.0000 | + | 17.3205i | 0.357143 | + | 0.618590i | ||||
\(785\) | −33.0000 | + | 19.0526i | −1.17782 | + | 0.680015i | ||||
\(786\) | −13.5000 | + | 7.79423i | −0.481529 | + | 0.278011i | ||||
\(787\) | −22.5000 | − | 12.9904i | −0.802038 | − | 0.463057i | 0.0421450 | − | 0.999112i | \(-0.486581\pi\) |
−0.844183 | + | 0.536054i | \(0.819914\pi\) | |||||||
\(788\) | −7.50000 | + | 4.33013i | −0.267176 | + | 0.154254i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.0000 | −0.533676 | ||||||||
\(791\) | 15.5885i | 0.554262i | ||||||||
\(792\) | 9.00000 | − | 15.5885i | 0.319801 | − | 0.553912i | ||||
\(793\) | −10.0000 | + | 34.6410i | −0.355110 | + | 1.23014i | ||||
\(794\) | 13.5000 | − | 23.3827i | 0.479097 | − | 0.829820i | ||||
\(795\) | −4.50000 | + | 2.59808i | −0.159599 | + | 0.0921443i | ||||
\(796\) | 12.5000 | + | 21.6506i | 0.443051 | + | 0.767386i | ||||
\(797\) | −1.50000 | − | 2.59808i | −0.0531327 | − | 0.0920286i | 0.838236 | − | 0.545308i | \(-0.183587\pi\) |
−0.891368 | + | 0.453279i | \(0.850254\pi\) | |||||||
\(798\) | 15.5885i | 0.551825i | ||||||||
\(799\) | −9.00000 | − | 5.19615i | −0.318397 | − | 0.183827i | ||||
\(800\) | −9.00000 | − | 5.19615i | −0.318198 | − | 0.183712i | ||||
\(801\) | 12.0000 | − | 6.92820i | 0.423999 | − | 0.244796i | ||||
\(802\) | −12.0000 | −0.423735 | ||||||||
\(803\) | 22.5000 | − | 38.9711i | 0.794008 | − | 1.37526i | ||||
\(804\) | − | 8.66025i | − | 0.305424i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.0000 | + | 27.7128i | −0.739693 | + | 0.976142i | ||||
\(807\) | 21.0000 | 0.739235 | ||||||||
\(808\) | − | 31.1769i | − | 1.09680i | ||||||
\(809\) | −7.50000 | + | 12.9904i | −0.263686 | + | 0.456717i | −0.967219 | − | 0.253946i | \(-0.918272\pi\) |
0.703533 | + | 0.710663i | \(0.251605\pi\) | |||||||
\(810\) | 3.00000 | 0.105409 | ||||||||
\(811\) | −43.5000 | + | 25.1147i | −1.52749 | + | 0.881898i | −0.528025 | + | 0.849229i | \(0.677067\pi\) |
−0.999466 | + | 0.0326691i | \(0.989599\pi\) | |||||||
\(812\) | 9.00000 | + | 5.19615i | 0.315838 | + | 0.182349i | ||||
\(813\) | −9.00000 | − | 5.19615i | −0.315644 | − | 0.182237i | ||||
\(814\) | 46.7654i | 1.63913i | ||||||||
\(815\) | 9.00000 | + | 15.5885i | 0.315256 | + | 0.546040i | ||||
\(816\) | −7.50000 | − | 12.9904i | −0.262553 | − | 0.454754i | ||||
\(817\) | −4.50000 | + | 2.59808i | −0.157435 | + | 0.0908952i | ||||
\(818\) | −22.5000 | + | 38.9711i | −0.786694 | + | 1.36259i | ||||
\(819\) | −12.0000 | − | 3.46410i | −0.419314 | − | 0.121046i | ||||
\(820\) | 4.50000 | − | 7.79423i | 0.157147 | − | 0.272186i | ||||
\(821\) | 41.5692i | 1.45078i | 0.688340 | + | 0.725388i | \(0.258340\pi\) | ||||
−0.688340 | + | 0.725388i | \(0.741660\pi\) | |||||||
\(822\) | 9.00000 | 0.313911 | ||||||||
\(823\) | 24.5000 | − | 42.4352i | 0.854016 | − | 1.47920i | −0.0235383 | − | 0.999723i | \(-0.507493\pi\) |
0.877555 | − | 0.479477i | \(-0.159174\pi\) | |||||||
\(824\) | 28.5000 | − | 16.4545i | 0.992845 | − | 0.573219i | ||||
\(825\) | 9.00000 | + | 5.19615i | 0.313340 | + | 0.180907i | ||||
\(826\) | 4.50000 | − | 2.59808i | 0.156575 | − | 0.0903986i | ||||
\(827\) | 4.50000 | − | 2.59808i | 0.156480 | − | 0.0903440i | −0.419715 | − | 0.907656i | \(-0.637870\pi\) |
0.576195 | + | 0.817312i | \(0.304537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | −31.5000 | − | 18.1865i | −1.09338 | − | 0.631264i | ||||
\(831\) | 13.0000 | − | 22.5167i | 0.450965 | − | 0.781094i | ||||
\(832\) | 1.00000 | − | 3.46410i | 0.0346688 | − | 0.120096i | ||||
\(833\) | 12.0000 | 0.415775 | ||||||||
\(834\) | 6.00000 | + | 3.46410i | 0.207763 | + | 0.119952i | ||||
\(835\) | 15.0000 | 0.519096 | ||||||||
\(836\) | 27.0000 | 0.933815 | ||||||||
\(837\) | −10.0000 | + | 25.9808i | −0.345651 | + | 0.898027i | ||||
\(838\) | − | 20.7846i | − | 0.717992i | ||||||
\(839\) | 17.3205i | 0.597970i | 0.954258 | + | 0.298985i | \(0.0966481\pi\) | ||||
−0.954258 | + | 0.298985i | \(0.903352\pi\) | |||||||
\(840\) | −4.50000 | − | 2.59808i | −0.155265 | − | 0.0896421i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 28.5000 | + | 49.3634i | 0.982175 | + | 1.70118i | ||||
\(843\) | −12.0000 | − | 6.92820i | −0.413302 | − | 0.238620i | ||||
\(844\) | −2.50000 | + | 4.33013i | −0.0860535 | + | 0.149049i | ||||
\(845\) | −22.5000 | − | 0.866025i | −0.774024 | − | 0.0297922i | ||||
\(846\) | 6.00000 | + | 10.3923i | 0.206284 | + | 0.357295i | ||||
\(847\) | 24.0000 | − | 13.8564i | 0.824650 | − | 0.476112i | ||||
\(848\) | 7.50000 | + | 12.9904i | 0.257551 | + | 0.446092i | ||||
\(849\) | 2.00000 | − | 3.46410i | 0.0686398 | − | 0.118888i | ||||
\(850\) | −9.00000 | + | 5.19615i | −0.308697 | + | 0.178227i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − | 8.66025i | − | 0.296695i | ||||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | 15.0000 | − | 25.9808i | 0.513289 | − | 0.889043i | ||||
\(855\) | −9.00000 | − | 15.5885i | −0.307794 | − | 0.533114i | ||||
\(856\) | −13.5000 | − | 7.79423i | −0.461421 | − | 0.266401i | ||||
\(857\) | 10.5000 | + | 18.1865i | 0.358673 | + | 0.621240i | 0.987739 | − | 0.156112i | \(-0.0498959\pi\) |
−0.629066 | + | 0.777352i | \(0.716563\pi\) | |||||||
\(858\) | 9.00000 | − | 31.1769i | 0.307255 | − | 1.06436i | ||||
\(859\) | 5.50000 | + | 9.52628i | 0.187658 | + | 0.325032i | 0.944469 | − | 0.328601i | \(-0.106577\pi\) |
−0.756811 | + | 0.653633i | \(0.773244\pi\) | |||||||
\(860\) | 1.73205i | 0.0590624i | ||||||||
\(861\) | −4.50000 | + | 7.79423i | −0.153360 | + | 0.265627i | ||||
\(862\) | 19.5000 | − | 33.7750i | 0.664173 | − | 1.15038i | ||||
\(863\) | 10.5000 | − | 6.06218i | 0.357424 | − | 0.206359i | −0.310526 | − | 0.950565i | \(-0.600505\pi\) |
0.667950 | + | 0.744206i | \(0.267172\pi\) | |||||||
\(864\) | 25.9808i | 0.883883i | ||||||||
\(865\) | 13.5000 | + | 7.79423i | 0.459014 | + | 0.265012i | ||||
\(866\) | 45.0333i | 1.53029i | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 7.50000 | − | 6.06218i | 0.254567 | − | 0.205764i | ||||
\(869\) | − | 25.9808i | − | 0.881337i | ||||||
\(870\) | 18.0000 | 0.610257 | ||||||||
\(871\) | −7.50000 | − | 30.3109i | −0.254128 | − | 1.02705i | ||||
\(872\) | −24.0000 | −0.812743 | ||||||||
\(873\) | 12.0000 | − | 6.92820i | 0.406138 | − | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5000 | + | 18.1865i | −0.354965 | + | 0.614817i | ||||
\(876\) | 8.66025i | 0.292603i | ||||||||
\(877\) | −16.5000 | + | 9.52628i | −0.557165 | + | 0.321680i | −0.752007 | − | 0.659155i | \(-0.770914\pi\) |
0.194842 | + | 0.980835i | \(0.437581\pi\) | |||||||
\(878\) | 28.5000 | − | 16.4545i | 0.961828 | − | 0.555312i | ||||
\(879\) | −22.5000 | + | 12.9904i | −0.758906 | + | 0.438155i | ||||
\(880\) | −22.5000 | + | 38.9711i | −0.758475 | + | 1.31372i | ||||
\(881\) | −7.50000 | − | 12.9904i | −0.252681 | − | 0.437657i | 0.711582 | − | 0.702603i | \(-0.247979\pi\) |
−0.964263 | + | 0.264946i | \(0.914646\pi\) | |||||||
\(882\) | −12.0000 | − | 6.92820i | −0.404061 | − | 0.233285i | ||||
\(883\) | −56.0000 | −1.88455 | −0.942275 | − | 0.334840i | \(-0.891318\pi\) | ||||
−0.942275 | + | 0.334840i | \(0.891318\pi\) | |||||||
\(884\) | 7.50000 | + | 7.79423i | 0.252252 | + | 0.262148i | ||||
\(885\) | 1.50000 | − | 2.59808i | 0.0504219 | − | 0.0873334i | ||||
\(886\) | 22.5000 | − | 12.9904i | 0.755902 | − | 0.436420i | ||||
\(887\) | −13.5000 | + | 23.3827i | −0.453286 | + | 0.785114i | −0.998588 | − | 0.0531258i | \(-0.983082\pi\) |
0.545302 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(888\) | 4.50000 | + | 7.79423i | 0.151010 | + | 0.261557i | ||||
\(889\) | −10.5000 | + | 6.06218i | −0.352159 | + | 0.203319i | ||||
\(890\) | −18.0000 | + | 10.3923i | −0.603361 | + | 0.348351i | ||||
\(891\) | 5.19615i | 0.174078i | ||||||||
\(892\) | −1.50000 | − | 0.866025i | −0.0502237 | − | 0.0289967i | ||||
\(893\) | 9.00000 | − | 15.5885i | 0.301174 | − | 0.521648i | ||||
\(894\) | 16.5000 | + | 28.5788i | 0.551843 | + | 0.955819i | ||||
\(895\) | 5.19615i | 0.173688i | ||||||||
\(896\) | −10.5000 | + | 18.1865i | −0.350780 | + | 0.607569i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.0000 | −0.800890 | ||||||||
\(899\) | 12.0000 | − | 31.1769i | 0.400222 | − | 1.03981i | ||||
\(900\) | 4.00000 | 0.133333 | ||||||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 40.5000 | + | 23.3827i | 1.34850 | + | 0.778558i | ||||
\(903\) | − | 1.73205i | − | 0.0576390i | ||||||
\(904\) | 13.5000 | − | 7.79423i | 0.449003 | − | 0.259232i | ||||
\(905\) | −34.5000 | − | 19.9186i | −1.14682 | − | 0.662116i | ||||
\(906\) | −3.00000 | + | 5.19615i | −0.0996683 | + | 0.172631i | ||||
\(907\) | 28.0000 | 0.929725 | 0.464862 | − | 0.885383i | \(-0.346104\pi\) | ||||
0.464862 | + | 0.885383i | \(0.346104\pi\) | |||||||
\(908\) | 7.50000 | − | 4.33013i | 0.248896 | − | 0.143700i | ||||
\(909\) | 18.0000 | + | 31.1769i | 0.597022 | + | 1.03407i | ||||
\(910\) | 18.0000 | + | 5.19615i | 0.596694 | + | 0.172251i | ||||
\(911\) | 10.5000 | − | 18.1865i | 0.347881 | − | 0.602547i | −0.637992 | − | 0.770043i | \(-0.720235\pi\) |
0.985873 | + | 0.167496i | \(0.0535682\pi\) | |||||||
\(912\) | 22.5000 | − | 12.9904i | 0.745049 | − | 0.430155i | ||||
\(913\) | 31.5000 | − | 54.5596i | 1.04250 | − | 1.80566i | ||||
\(914\) | −12.0000 | −0.396925 | ||||||||
\(915\) | − | 17.3205i | − | 0.572598i | ||||||
\(916\) | −1.50000 | − | 0.866025i | −0.0495614 | − | 0.0286143i | ||||
\(917\) | 13.5000 | − | 7.79423i | 0.445809 | − | 0.257388i | ||||
\(918\) | 22.5000 | + | 12.9904i | 0.742611 | + | 0.428746i | ||||
\(919\) | 5.50000 | + | 9.52628i | 0.181428 | + | 0.314243i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50000 | − | 0.866025i | 0.0494267 | − | 0.0285365i | ||||
\(922\) | 24.0000 | 0.790398 | ||||||||
\(923\) | −7.50000 | − | 30.3109i | −0.246866 | − | 0.997695i | ||||
\(924\) | −4.50000 | + | 7.79423i | −0.148039 | + | 0.256411i | ||||
\(925\) | 9.00000 | − | 5.19615i | 0.295918 | − | 0.170848i | ||||
\(926\) | 30.0000 | 0.985861 | ||||||||
\(927\) | −19.0000 | + | 32.9090i | −0.624042 | + | 1.08087i | ||||
\(928\) | − | 31.1769i | − | 1.02343i | ||||||
\(929\) | − | 20.7846i | − | 0.681921i | −0.940078 | − | 0.340960i | \(-0.889248\pi\) | ||
0.940078 | − | 0.340960i | \(-0.110752\pi\) | |||||||
\(930\) | 6.00000 | − | 15.5885i | 0.196748 | − | 0.511166i | ||||
\(931\) | 20.7846i | 0.681188i | ||||||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | 12.0000 | − | 20.7846i | 0.392862 | − | 0.680458i | ||||
\(934\) | 62.3538i | 2.04028i | ||||||||
\(935\) | 13.5000 | + | 23.3827i | 0.441497 | + | 0.764696i | ||||
\(936\) | 3.00000 | + | 12.1244i | 0.0980581 | + | 0.396297i | ||||
\(937\) | −3.50000 | + | 6.06218i | −0.114340 | + | 0.198043i | −0.917516 | − | 0.397699i | \(-0.869809\pi\) |
0.803176 | + | 0.595742i | \(0.203142\pi\) | |||||||
\(938\) | 25.9808i | 0.848302i | ||||||||
\(939\) | 9.50000 | + | 16.4545i | 0.310021 | + | 0.536972i | ||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | −22.5000 | + | 12.9904i | −0.733479 | + | 0.423474i | −0.819694 | − | 0.572802i | \(-0.805856\pi\) |
0.0862145 | + | 0.996277i | \(0.472523\pi\) | |||||||
\(942\) | 33.0000 | + | 19.0526i | 1.07520 | + | 0.620766i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.50000 | − | 4.33013i | −0.244104 | − | 0.140934i | ||||
\(945\) | 15.0000 | 0.487950 | ||||||||
\(946\) | −9.00000 | −0.292615 | ||||||||
\(947\) | 37.5000 | + | 21.6506i | 1.21859 | + | 0.703551i | 0.964615 | − | 0.263661i | \(-0.0849300\pi\) |
0.253971 | + | 0.967212i | \(0.418263\pi\) | |||||||
\(948\) | 2.50000 | + | 4.33013i | 0.0811962 | + | 0.140636i | ||||
\(949\) | 7.50000 | + | 30.3109i | 0.243460 | + | 0.983933i | ||||
\(950\) | −9.00000 | − | 15.5885i | −0.291999 | − | 0.505756i | ||||
\(951\) | 13.5000 | − | 7.79423i | 0.437767 | − | 0.252745i | ||||
\(952\) | 4.50000 | + | 7.79423i | 0.145846 | + | 0.252612i | ||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | −9.00000 | − | 5.19615i | −0.291386 | − | 0.168232i | ||||
\(955\) | 22.5000 | + | 12.9904i | 0.728083 | + | 0.420359i | ||||
\(956\) | 13.5000 | − | 7.79423i | 0.436621 | − | 0.252083i | ||||
\(957\) | 31.1769i | 1.00781i | ||||||||
\(958\) | 1.50000 | − | 2.59808i | 0.0484628 | − | 0.0839400i | ||||
\(959\) | −9.00000 | −0.290625 | ||||||||
\(960\) | 1.73205i | 0.0559017i | ||||||||
\(961\) | −23.0000 | − | 20.7846i | −0.741935 | − | 0.670471i | ||||
\(962\) | −22.5000 | − | 23.3827i | −0.725429 | − | 0.753888i | ||||
\(963\) | 18.0000 | 0.580042 | ||||||||
\(964\) | −1.50000 | − | 0.866025i | −0.0483117 | − | 0.0278928i | ||||
\(965\) | 39.0000 | 1.25545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.5000 | + | 21.6506i | 1.20592 | + | 0.696237i | 0.961865 | − | 0.273524i | \(-0.0881894\pi\) |
0.244054 | + | 0.969762i | \(0.421523\pi\) | |||||||
\(968\) | −24.0000 | − | 13.8564i | −0.771389 | − | 0.445362i | ||||
\(969\) | − | 15.5885i | − | 0.500773i | ||||||
\(970\) | −18.0000 | + | 10.3923i | −0.577945 | + | 0.333677i | ||||
\(971\) | 13.5000 | + | 23.3827i | 0.433236 | + | 0.750386i | 0.997150 | − | 0.0754473i | \(-0.0240385\pi\) |
−0.563914 | + | 0.825833i | \(0.690705\pi\) | |||||||
\(972\) | −8.00000 | − | 13.8564i | −0.256600 | − | 0.444444i | ||||
\(973\) | −6.00000 | − | 3.46410i | −0.192351 | − | 0.111054i | ||||
\(974\) | 19.5000 | + | 33.7750i | 0.624820 | + | 1.08222i | ||||
\(975\) | −7.00000 | + | 1.73205i | −0.224179 | + | 0.0554700i | ||||
\(976\) | −50.0000 | −1.60046 | ||||||||
\(977\) | − | 34.6410i | − | 1.10826i | −0.832429 | − | 0.554132i | \(-0.813050\pi\) | ||
0.832429 | − | 0.554132i | \(-0.186950\pi\) | |||||||
\(978\) | 9.00000 | − | 15.5885i | 0.287788 | − | 0.498464i | ||||
\(979\) | −18.0000 | − | 31.1769i | −0.575282 | − | 0.996419i | ||||
\(980\) | 6.00000 | + | 3.46410i | 0.191663 | + | 0.110657i | ||||
\(981\) | 24.0000 | − | 13.8564i | 0.766261 | − | 0.442401i | ||||
\(982\) | −13.5000 | + | 7.79423i | −0.430802 | + | 0.248724i | ||||
\(983\) | 40.5000 | − | 23.3827i | 1.29175 | − | 0.745792i | 0.312785 | − | 0.949824i | \(-0.398738\pi\) |
0.978964 | + | 0.204032i | \(0.0654047\pi\) | |||||||
\(984\) | 9.00000 | 0.286910 | ||||||||
\(985\) | 7.50000 | − | 12.9904i | 0.238970 | − | 0.413908i | ||||
\(986\) | −27.0000 | − | 15.5885i | −0.859855 | − | 0.496438i | ||||
\(987\) | 3.00000 | + | 5.19615i | 0.0954911 | + | 0.165395i | ||||
\(988\) | −13.5000 | + | 12.9904i | −0.429492 | + | 0.413279i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | − | 31.1769i | − | 0.990867i | ||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | −27.0000 | − | 10.3923i | −0.857251 | − | 0.329956i | ||||
\(993\) | − | 12.1244i | − | 0.384755i | ||||||
\(994\) | 25.9808i | 0.824060i | ||||||||
\(995\) | −37.5000 | − | 21.6506i | −1.18883 | − | 0.686371i | ||||
\(996\) | 12.1244i | 0.384175i | ||||||||
\(997\) | 12.5000 | + | 21.6506i | 0.395879 | + | 0.685682i | 0.993213 | − | 0.116310i | \(-0.0371066\pi\) |
−0.597334 | + | 0.801993i | \(0.703773\pi\) | |||||||
\(998\) | 31.5000 | − | 54.5596i | 0.997115 | − | 1.72705i | ||||
\(999\) | −22.5000 | − | 12.9904i | −0.711868 | − | 0.410997i |
(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 | 403.2.l.b.129.1 | yes | 2 | |
13.12 | even | 2 | 403.2.l.a.129.1 | yes | 2 | ||
31.25 | even | 3 | 403.2.l.a.25.1 | ✓ | 2 | ||
403.25 | even | 6 | inner | 403.2.l.b.25.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.l.a.25.1 | ✓ | 2 | 31.25 | even | 3 | ||
403.2.l.a.129.1 | yes | 2 | 13.12 | even | 2 | ||
403.2.l.b.25.1 | yes | 2 | 403.25 | even | 6 | inner | |
403.2.l.b.129.1 | yes | 2 | 1.1 | even | 1 | trivial |