Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(751,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 841.8 | ||
Root | \(3.78749i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.841 |
Dual form | 1110.2.x.d.751.8 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 1.89374 | + | 3.28006i | 0.715768 | + | 1.23975i | 0.962663 | + | 0.270704i | \(0.0872565\pi\) |
−0.246895 | + | 0.969042i | \(0.579410\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.84038 | −1.15792 | −0.578960 | − | 0.815356i | \(-0.696541\pi\) | ||||
−0.578960 | + | 0.815356i | \(0.696541\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 5.82335 | − | 3.36212i | 1.61511 | − | 0.932483i | 0.626947 | − | 0.779062i | \(-0.284304\pi\) |
0.988161 | − | 0.153421i | \(-0.0490290\pi\) | |||||||
\(14\) | 3.78749i | 1.01225i | ||||||||
\(15\) | −0.866025 | − | 0.500000i | −0.223607 | − | 0.129099i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.14609 | + | 2.39374i | 1.00557 | + | 0.580568i | 0.909893 | − | 0.414844i | \(-0.136164\pi\) |
0.0956811 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −4.79142 | + | 2.76633i | −1.09923 | + | 0.634639i | −0.936018 | − | 0.351952i | \(-0.885518\pi\) |
−0.163210 | + | 0.986591i | \(0.552185\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | 1.89374 | − | 3.28006i | 0.413249 | − | 0.715768i | ||||
\(22\) | −3.32587 | − | 1.92019i | −0.709078 | − | 0.409386i | ||||
\(23\) | 8.45628i | 1.76326i | 0.471945 | + | 0.881628i | \(0.343552\pi\) | ||||
−0.471945 | + | 0.881628i | \(0.656448\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 6.72423 | 1.31873 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.89374 | + | 3.28006i | −0.357884 | + | 0.619873i | ||||
\(29\) | 1.86387i | 0.346111i | 0.984912 | + | 0.173056i | \(0.0553640\pi\) | ||||
−0.984912 | + | 0.173056i | \(0.944636\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | − | 8.49606i | − | 1.52594i | −0.646436 | − | 0.762968i | \(-0.723741\pi\) | ||
0.646436 | − | 0.762968i | \(-0.276259\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 1.92019 | + | 3.32587i | 0.334263 | + | 0.578960i | ||||
\(34\) | 2.39374 | + | 4.14609i | 0.410524 | + | 0.711048i | ||||
\(35\) | 3.28006 | + | 1.89374i | 0.554432 | + | 0.320101i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.29396 | − | 5.63363i | 0.377125 | − | 0.926162i | ||||
\(38\) | −5.53266 | −0.897516 | ||||||||
\(39\) | −5.82335 | − | 3.36212i | −0.932483 | − | 0.538369i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 4.99616 | + | 8.65360i | 0.780269 | + | 1.35147i | 0.931785 | + | 0.363011i | \(0.118251\pi\) |
−0.151516 | + | 0.988455i | \(0.548416\pi\) | |||||||
\(42\) | 3.28006 | − | 1.89374i | 0.506124 | − | 0.292211i | ||||
\(43\) | 0.0397760i | 0.00606579i | 0.999995 | + | 0.00303289i | \(0.000965402\pi\) | ||||
−0.999995 | + | 0.00303289i | \(0.999035\pi\) | |||||||
\(44\) | −1.92019 | − | 3.32587i | −0.289480 | − | 0.501394i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | −4.22814 | + | 7.32335i | −0.623405 | + | 1.07977i | ||||
\(47\) | 1.04092 | 0.151834 | 0.0759169 | − | 0.997114i | \(-0.475812\pi\) | ||||
0.0759169 | + | 0.997114i | \(0.475812\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.67253 | + | 6.36102i | −0.524648 | + | 0.908717i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | − | 4.78749i | − | 0.670382i | ||||||
\(52\) | 5.82335 | + | 3.36212i | 0.807554 | + | 0.466241i | ||||
\(53\) | −1.60374 | + | 2.77776i | −0.220291 | + | 0.381555i | −0.954896 | − | 0.296940i | \(-0.904034\pi\) |
0.734606 | + | 0.678494i | \(0.237367\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | −3.32587 | + | 1.92019i | −0.448460 | + | 0.258919i | ||||
\(56\) | −3.28006 | + | 1.89374i | −0.438317 | + | 0.253062i | ||||
\(57\) | 4.79142 | + | 2.76633i | 0.634639 | + | 0.366409i | ||||
\(58\) | −0.931933 | + | 1.61416i | −0.122369 | + | 0.211949i | ||||
\(59\) | 1.56278 | + | 0.902271i | 0.203456 | + | 0.117466i | 0.598267 | − | 0.801297i | \(-0.295856\pi\) |
−0.394810 | + | 0.918763i | \(0.629190\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | 11.4759 | − | 6.62563i | 1.46934 | − | 0.848325i | 0.469932 | − | 0.882702i | \(-0.344278\pi\) |
0.999409 | + | 0.0343779i | \(0.0109450\pi\) | |||||||
\(62\) | 4.24803 | − | 7.35780i | 0.539500 | − | 0.934442i | ||||
\(63\) | −3.78749 | −0.477179 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.36212 | − | 5.82335i | 0.417019 | − | 0.722298i | ||||
\(66\) | 3.84038i | 0.472719i | ||||||||
\(67\) | 4.58744 | + | 7.94568i | 0.560445 | + | 0.970719i | 0.997458 | + | 0.0712634i | \(0.0227031\pi\) |
−0.437013 | + | 0.899455i | \(0.643964\pi\) | |||||||
\(68\) | 4.78749i | 0.580568i | ||||||||
\(69\) | 7.32335 | − | 4.22814i | 0.881628 | − | 0.509008i | ||||
\(70\) | 1.89374 | + | 3.28006i | 0.226346 | + | 0.392042i | ||||
\(71\) | −0.928191 | − | 1.60767i | −0.110156 | − | 0.190796i | 0.805677 | − | 0.592355i | \(-0.201802\pi\) |
−0.915833 | + | 0.401559i | \(0.868468\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −11.8343 | −1.38510 | −0.692550 | − | 0.721370i | \(-0.743513\pi\) | ||||
−0.692550 | + | 0.721370i | \(0.743513\pi\) | |||||||
\(74\) | 4.80344 | − | 3.73188i | 0.558389 | − | 0.433822i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −4.79142 | − | 2.76633i | −0.549614 | − | 0.317320i | ||||
\(77\) | −7.27270 | − | 12.5967i | −0.828802 | − | 1.43553i | ||||
\(78\) | −3.36212 | − | 5.82335i | −0.380685 | − | 0.659365i | ||||
\(79\) | −3.13047 | + | 1.80738i | −0.352205 | + | 0.203346i | −0.665656 | − | 0.746259i | \(-0.731848\pi\) |
0.313451 | + | 0.949604i | \(0.398515\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 9.99232i | 1.10347i | ||||||||
\(83\) | 6.79367 | − | 11.7670i | 0.745702 | − | 1.29159i | −0.204164 | − | 0.978937i | \(-0.565448\pi\) |
0.949866 | − | 0.312657i | \(-0.101219\pi\) | |||||||
\(84\) | 3.78749 | 0.413249 | ||||||||
\(85\) | 4.78749 | 0.519276 | ||||||||
\(86\) | −0.0198880 | + | 0.0344471i | −0.00214458 | + | 0.00371452i | ||||
\(87\) | 1.61416 | − | 0.931933i | 0.173056 | − | 0.0999137i | ||||
\(88\) | − | 3.84038i | − | 0.409386i | ||||||
\(89\) | 14.8116 | + | 8.55149i | 1.57003 | + | 0.906457i | 0.996164 | + | 0.0875067i | \(0.0278899\pi\) |
0.573865 | + | 0.818950i | \(0.305443\pi\) | |||||||
\(90\) | −0.500000 | + | 0.866025i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | 22.0559 | + | 12.7340i | 2.31209 | + | 1.33488i | ||||
\(92\) | −7.32335 | + | 4.22814i | −0.763512 | + | 0.440814i | ||||
\(93\) | −7.35780 | + | 4.24803i | −0.762968 | + | 0.440500i | ||||
\(94\) | 0.901463 | + | 0.520460i | 0.0929789 | + | 0.0536814i | ||||
\(95\) | −2.76633 | + | 4.79142i | −0.283819 | + | 0.491590i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | − | 6.15065i | − | 0.624504i | −0.949999 | − | 0.312252i | \(-0.898917\pi\) | ||
0.949999 | − | 0.312252i | \(-0.101083\pi\) | |||||||
\(98\) | −6.36102 | + | 3.67253i | −0.642560 | + | 0.370982i | ||||
\(99\) | 1.92019 | − | 3.32587i | 0.192987 | − | 0.334263i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.96357 | −0.891909 | −0.445954 | − | 0.895056i | \(-0.647136\pi\) | ||||
−0.445954 | + | 0.895056i | \(0.647136\pi\) | |||||||
\(102\) | 2.39374 | − | 4.14609i | 0.237016 | − | 0.410524i | ||||
\(103\) | − | 14.7060i | − | 1.44903i | −0.689260 | − | 0.724514i | \(-0.742064\pi\) | ||
0.689260 | − | 0.724514i | \(-0.257936\pi\) | |||||||
\(104\) | 3.36212 | + | 5.82335i | 0.329683 | + | 0.571027i | ||||
\(105\) | − | 3.78749i | − | 0.369621i | ||||||
\(106\) | −2.77776 | + | 1.60374i | −0.269800 | + | 0.155769i | ||||
\(107\) | −1.95561 | − | 3.38721i | −0.189056 | − | 0.327454i | 0.755880 | − | 0.654710i | \(-0.227209\pi\) |
−0.944936 | + | 0.327256i | \(0.893876\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 3.31422 | + | 1.91346i | 0.317444 | + | 0.183277i | 0.650253 | − | 0.759718i | \(-0.274663\pi\) |
−0.332809 | + | 0.942994i | \(0.607996\pi\) | |||||||
\(110\) | −3.84038 | −0.366166 | ||||||||
\(111\) | −6.02584 | + | 0.830184i | −0.571948 | + | 0.0787976i | ||||
\(112\) | −3.78749 | −0.357884 | ||||||||
\(113\) | −14.1231 | − | 8.15399i | −1.32859 | − | 0.767062i | −0.343509 | − | 0.939149i | \(-0.611616\pi\) |
−0.985082 | + | 0.172087i | \(0.944949\pi\) | |||||||
\(114\) | 2.76633 | + | 4.79142i | 0.259090 | + | 0.448758i | ||||
\(115\) | 4.22814 | + | 7.32335i | 0.394276 | + | 0.682906i | ||||
\(116\) | −1.61416 | + | 0.931933i | −0.149871 | + | 0.0865278i | ||||
\(117\) | 6.72423i | 0.621655i | ||||||||
\(118\) | 0.902271 | + | 1.56278i | 0.0830607 | + | 0.143865i | ||||
\(119\) | 18.1326i | 1.66221i | ||||||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | 3.74855 | 0.340777 | ||||||||
\(122\) | 13.2513 | 1.19971 | ||||||||
\(123\) | 4.99616 | − | 8.65360i | 0.450488 | − | 0.780269i | ||||
\(124\) | 7.35780 | − | 4.24803i | 0.660750 | − | 0.381484i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −3.28006 | − | 1.89374i | −0.292211 | − | 0.168708i | ||||
\(127\) | −5.63891 | + | 9.76689i | −0.500373 | + | 0.866671i | 0.499627 | + | 0.866241i | \(0.333470\pi\) |
−1.00000 | 0.000430450i | \(0.999863\pi\) | ||||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0.0344471 | − | 0.0198880i | 0.00303289 | − | 0.00175104i | ||||
\(130\) | 5.82335 | − | 3.36212i | 0.510742 | − | 0.294877i | ||||
\(131\) | 7.20809 | + | 4.16159i | 0.629774 | + | 0.363600i | 0.780664 | − | 0.624950i | \(-0.214881\pi\) |
−0.150891 | + | 0.988550i | \(0.548214\pi\) | |||||||
\(132\) | −1.92019 | + | 3.32587i | −0.167131 | + | 0.289480i | ||||
\(133\) | −18.1475 | − | 10.4774i | −1.57358 | − | 0.908509i | ||||
\(134\) | 9.17488i | 0.792589i | ||||||||
\(135\) | 0.866025 | − | 0.500000i | 0.0745356 | − | 0.0430331i | ||||
\(136\) | −2.39374 | + | 4.14609i | −0.205262 | + | 0.355524i | ||||
\(137\) | −15.6219 | −1.33467 | −0.667334 | − | 0.744759i | \(-0.732565\pi\) | ||||
−0.667334 | + | 0.744759i | \(0.732565\pi\) | |||||||
\(138\) | 8.45628 | 0.719846 | ||||||||
\(139\) | −1.46820 | + | 2.54301i | −0.124531 | + | 0.215695i | −0.921550 | − | 0.388260i | \(-0.873076\pi\) |
0.797018 | + | 0.603955i | \(0.206409\pi\) | |||||||
\(140\) | 3.78749i | 0.320101i | ||||||||
\(141\) | −0.520460 | − | 0.901463i | −0.0438307 | − | 0.0759169i | ||||
\(142\) | − | 1.85638i | − | 0.155784i | ||||||
\(143\) | −22.3639 | + | 12.9118i | −1.87016 | + | 1.07974i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0.931933 | + | 1.61416i | 0.0773928 | + | 0.134048i | ||||
\(146\) | −10.2488 | − | 5.91715i | −0.848197 | − | 0.489707i | ||||
\(147\) | 7.34507 | 0.605811 | ||||||||
\(148\) | 6.02584 | − | 0.830184i | 0.495321 | − | 0.0682407i | ||||
\(149\) | −16.2875 | −1.33433 | −0.667163 | − | 0.744912i | \(-0.732492\pi\) | ||||
−0.667163 | + | 0.744912i | \(0.732492\pi\) | |||||||
\(150\) | −0.866025 | − | 0.500000i | −0.0707107 | − | 0.0408248i | ||||
\(151\) | −10.1392 | − | 17.5616i | −0.825117 | − | 1.42914i | −0.901830 | − | 0.432091i | \(-0.857776\pi\) |
0.0767136 | − | 0.997053i | \(-0.475557\pi\) | |||||||
\(152\) | −2.76633 | − | 4.79142i | −0.224379 | − | 0.388636i | ||||
\(153\) | −4.14609 | + | 2.39374i | −0.335191 | + | 0.193523i | ||||
\(154\) | − | 14.5454i | − | 1.17210i | ||||||
\(155\) | −4.24803 | − | 7.35780i | −0.341210 | − | 0.590993i | ||||
\(156\) | − | 6.72423i | − | 0.538369i | ||||||
\(157\) | 3.39853 | − | 5.88642i | 0.271232 | − | 0.469788i | −0.697945 | − | 0.716151i | \(-0.745902\pi\) |
0.969178 | + | 0.246363i | \(0.0792356\pi\) | |||||||
\(158\) | −3.61475 | −0.287574 | ||||||||
\(159\) | 3.20748 | 0.254370 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | −27.7371 | + | 16.0140i | −2.18599 | + | 1.26208i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −7.74406 | − | 4.47104i | −0.606562 | − | 0.350199i | 0.165057 | − | 0.986284i | \(-0.447219\pi\) |
−0.771619 | + | 0.636085i | \(0.780553\pi\) | |||||||
\(164\) | −4.99616 | + | 8.65360i | −0.390134 | + | 0.675733i | ||||
\(165\) | 3.32587 | + | 1.92019i | 0.258919 | + | 0.149487i | ||||
\(166\) | 11.7670 | − | 6.79367i | 0.913295 | − | 0.527291i | ||||
\(167\) | 2.72208 | − | 1.57160i | 0.210641 | − | 0.121614i | −0.390968 | − | 0.920404i | \(-0.627860\pi\) |
0.601609 | + | 0.798790i | \(0.294526\pi\) | |||||||
\(168\) | 3.28006 | + | 1.89374i | 0.253062 | + | 0.146106i | ||||
\(169\) | 16.1076 | − | 27.8992i | 1.23905 | − | 2.14610i | ||||
\(170\) | 4.14609 | + | 2.39374i | 0.317990 | + | 0.183592i | ||||
\(171\) | − | 5.53266i | − | 0.423093i | ||||||
\(172\) | −0.0344471 | + | 0.0198880i | −0.00262656 | + | 0.00151645i | ||||
\(173\) | −0.362029 | + | 0.627052i | −0.0275245 | + | 0.0476739i | −0.879460 | − | 0.475974i | \(-0.842096\pi\) |
0.851935 | + | 0.523648i | \(0.175429\pi\) | |||||||
\(174\) | 1.86387 | 0.141299 | ||||||||
\(175\) | 3.78749 | 0.286307 | ||||||||
\(176\) | 1.92019 | − | 3.32587i | 0.144740 | − | 0.250697i | ||||
\(177\) | − | 1.80454i | − | 0.135638i | ||||||
\(178\) | 8.55149 | + | 14.8116i | 0.640962 | + | 1.11018i | ||||
\(179\) | − | 20.9563i | − | 1.56635i | −0.621801 | − | 0.783175i | \(-0.713599\pi\) | ||
0.621801 | − | 0.783175i | \(-0.286401\pi\) | |||||||
\(180\) | −0.866025 | + | 0.500000i | −0.0645497 | + | 0.0372678i | ||||
\(181\) | −7.72795 | − | 13.3852i | −0.574414 | − | 0.994914i | −0.996105 | − | 0.0881744i | \(-0.971897\pi\) |
0.421691 | − | 0.906740i | \(-0.361437\pi\) | |||||||
\(182\) | 12.7340 | + | 22.0559i | 0.943905 | + | 1.63489i | ||||
\(183\) | −11.4759 | − | 6.62563i | −0.848325 | − | 0.489780i | ||||
\(184\) | −8.45628 | −0.623405 | ||||||||
\(185\) | −0.830184 | − | 6.02584i | −0.0610363 | − | 0.443029i | ||||
\(186\) | −8.49606 | −0.622961 | ||||||||
\(187\) | −15.9226 | − | 9.19290i | −1.16437 | − | 0.672251i | ||||
\(188\) | 0.520460 | + | 0.901463i | 0.0379585 | + | 0.0657460i | ||||
\(189\) | 1.89374 | + | 3.28006i | 0.137750 | + | 0.238589i | ||||
\(190\) | −4.79142 | + | 2.76633i | −0.347606 | + | 0.200691i | ||||
\(191\) | − | 3.03855i | − | 0.219862i | −0.993939 | − | 0.109931i | \(-0.964937\pi\) | ||
0.993939 | − | 0.109931i | \(-0.0350630\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 14.3431i | 1.03244i | 0.856456 | + | 0.516220i | \(0.172661\pi\) | ||||
−0.856456 | + | 0.516220i | \(0.827339\pi\) | |||||||
\(194\) | 3.07533 | − | 5.32662i | 0.220796 | − | 0.382429i | ||||
\(195\) | −6.72423 | −0.481532 | ||||||||
\(196\) | −7.34507 | −0.524648 | ||||||||
\(197\) | −0.401713 | + | 0.695787i | −0.0286209 | + | 0.0495728i | −0.879981 | − | 0.475009i | \(-0.842445\pi\) |
0.851360 | + | 0.524582i | \(0.175778\pi\) | |||||||
\(198\) | 3.32587 | − | 1.92019i | 0.236359 | − | 0.136462i | ||||
\(199\) | − | 4.01820i | − | 0.284842i | −0.989806 | − | 0.142421i | \(-0.954511\pi\) | ||
0.989806 | − | 0.142421i | \(-0.0454888\pi\) | |||||||
\(200\) | 0.866025 | + | 0.500000i | 0.0612372 | + | 0.0353553i | ||||
\(201\) | 4.58744 | − | 7.94568i | 0.323573 | − | 0.560445i | ||||
\(202\) | −7.76268 | − | 4.48179i | −0.546180 | − | 0.315337i | ||||
\(203\) | −6.11359 | + | 3.52969i | −0.429090 | + | 0.247735i | ||||
\(204\) | 4.14609 | − | 2.39374i | 0.290284 | − | 0.167596i | ||||
\(205\) | 8.65360 | + | 4.99616i | 0.604394 | + | 0.348947i | ||||
\(206\) | 7.35302 | − | 12.7358i | 0.512309 | − | 0.887345i | ||||
\(207\) | −7.32335 | − | 4.22814i | −0.509008 | − | 0.293876i | ||||
\(208\) | 6.72423i | 0.466241i | ||||||||
\(209\) | 18.4009 | − | 10.6238i | 1.27282 | − | 0.734861i | ||||
\(210\) | 1.89374 | − | 3.28006i | 0.130681 | − | 0.226346i | ||||
\(211\) | −9.46215 | −0.651401 | −0.325701 | − | 0.945473i | \(-0.605600\pi\) | ||||
−0.325701 | + | 0.945473i | \(0.605600\pi\) | |||||||
\(212\) | −3.20748 | −0.220291 | ||||||||
\(213\) | −0.928191 | + | 1.60767i | −0.0635986 | + | 0.110156i | ||||
\(214\) | − | 3.91122i | − | 0.267365i | ||||||
\(215\) | 0.0198880 | + | 0.0344471i | 0.00135635 | + | 0.00234927i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 27.8676 | − | 16.0894i | 1.89178 | − | 1.09222i | ||||
\(218\) | 1.91346 | + | 3.31422i | 0.129596 | + | 0.224467i | ||||
\(219\) | 5.91715 | + | 10.2488i | 0.399844 | + | 0.692550i | ||||
\(220\) | −3.32587 | − | 1.92019i | −0.224230 | − | 0.129459i | ||||
\(221\) | 32.1922 | 2.16548 | ||||||||
\(222\) | −5.63363 | − | 2.29396i | −0.378104 | − | 0.153961i | ||||
\(223\) | 11.8558 | 0.793923 | 0.396961 | − | 0.917835i | \(-0.370065\pi\) | ||||
0.396961 | + | 0.917835i | \(0.370065\pi\) | |||||||
\(224\) | −3.28006 | − | 1.89374i | −0.219158 | − | 0.126531i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | −8.15399 | − | 14.1231i | −0.542395 | − | 0.939456i | ||||
\(227\) | 10.7982 | − | 6.23432i | 0.716699 | − | 0.413786i | −0.0968375 | − | 0.995300i | \(-0.530873\pi\) |
0.813537 | + | 0.581514i | \(0.197539\pi\) | |||||||
\(228\) | 5.53266i | 0.366409i | ||||||||
\(229\) | −5.00593 | − | 8.67053i | −0.330801 | − | 0.572965i | 0.651868 | − | 0.758332i | \(-0.273986\pi\) |
−0.982669 | + | 0.185368i | \(0.940652\pi\) | |||||||
\(230\) | 8.45628i | 0.557591i | ||||||||
\(231\) | −7.27270 | + | 12.5967i | −0.478509 | + | 0.828802i | ||||
\(232\) | −1.86387 | −0.122369 | ||||||||
\(233\) | 9.91106 | 0.649295 | 0.324648 | − | 0.945835i | \(-0.394754\pi\) | ||||
0.324648 | + | 0.945835i | \(0.394754\pi\) | |||||||
\(234\) | −3.36212 | + | 5.82335i | −0.219788 | + | 0.380685i | ||||
\(235\) | 0.901463 | − | 0.520460i | 0.0588050 | − | 0.0339511i | ||||
\(236\) | 1.80454i | 0.117466i | ||||||||
\(237\) | 3.13047 | + | 1.80738i | 0.203346 | + | 0.117402i | ||||
\(238\) | −9.06628 | + | 15.7033i | −0.587680 | + | 1.01789i | ||||
\(239\) | −13.5328 | − | 7.81314i | −0.875361 | − | 0.505390i | −0.00623501 | − | 0.999981i | \(-0.501985\pi\) |
−0.869126 | + | 0.494591i | \(0.835318\pi\) | |||||||
\(240\) | 0.866025 | − | 0.500000i | 0.0559017 | − | 0.0322749i | ||||
\(241\) | −11.0815 | + | 6.39792i | −0.713824 | + | 0.412127i | −0.812475 | − | 0.582996i | \(-0.801880\pi\) |
0.0986513 | + | 0.995122i | \(0.468547\pi\) | |||||||
\(242\) | 3.24634 | + | 1.87427i | 0.208682 | + | 0.120483i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 11.4759 | + | 6.62563i | 0.734671 | + | 0.424162i | ||||
\(245\) | 7.34507i | 0.469259i | ||||||||
\(246\) | 8.65360 | − | 4.99616i | 0.551733 | − | 0.318543i | ||||
\(247\) | −18.6014 | + | 32.2186i | −1.18358 | + | 2.05002i | ||||
\(248\) | 8.49606 | 0.539500 | ||||||||
\(249\) | −13.5873 | −0.861063 | ||||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 9.23928i | 0.583178i | 0.956544 | + | 0.291589i | \(0.0941840\pi\) | ||||
−0.956544 | + | 0.291589i | \(0.905816\pi\) | |||||||
\(252\) | −1.89374 | − | 3.28006i | −0.119295 | − | 0.206624i | ||||
\(253\) | − | 32.4754i | − | 2.04171i | ||||||
\(254\) | −9.76689 | + | 5.63891i | −0.612829 | + | 0.353817i | ||||
\(255\) | −2.39374 | − | 4.14609i | −0.149902 | − | 0.259638i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.4372 | − | 6.02592i | −0.651055 | − | 0.375887i | 0.137805 | − | 0.990459i | \(-0.455995\pi\) |
−0.788860 | + | 0.614573i | \(0.789328\pi\) | |||||||
\(258\) | 0.0397760 | 0.00247635 | ||||||||
\(259\) | 22.8228 | − | 3.14431i | 1.41814 | − | 0.195378i | ||||
\(260\) | 6.72423 | 0.417019 | ||||||||
\(261\) | −1.61416 | − | 0.931933i | −0.0999137 | − | 0.0576852i | ||||
\(262\) | 4.16159 | + | 7.20809i | 0.257104 | + | 0.445317i | ||||
\(263\) | −3.65537 | − | 6.33128i | −0.225400 | − | 0.390404i | 0.731040 | − | 0.682335i | \(-0.239035\pi\) |
−0.956439 | + | 0.291931i | \(0.905702\pi\) | |||||||
\(264\) | −3.32587 | + | 1.92019i | −0.204693 | + | 0.118180i | ||||
\(265\) | 3.20748i | 0.197034i | ||||||||
\(266\) | −10.4774 | − | 18.1475i | −0.642413 | − | 1.11269i | ||||
\(267\) | − | 17.1030i | − | 1.04669i | ||||||
\(268\) | −4.58744 | + | 7.94568i | −0.280222 | + | 0.485359i | ||||
\(269\) | −15.1627 | −0.924484 | −0.462242 | − | 0.886754i | \(-0.652955\pi\) | ||||
−0.462242 | + | 0.886754i | \(0.652955\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −5.39620 | + | 9.34650i | −0.327796 | + | 0.567759i | −0.982074 | − | 0.188495i | \(-0.939639\pi\) |
0.654278 | + | 0.756254i | \(0.272973\pi\) | |||||||
\(272\) | −4.14609 | + | 2.39374i | −0.251393 | + | 0.145142i | ||||
\(273\) | − | 25.4679i | − | 1.54139i | ||||||
\(274\) | −13.5290 | − | 7.81094i | −0.817314 | − | 0.471876i | ||||
\(275\) | −1.92019 | + | 3.32587i | −0.115792 | + | 0.200558i | ||||
\(276\) | 7.32335 | + | 4.22814i | 0.440814 | + | 0.254504i | ||||
\(277\) | 6.93540 | − | 4.00416i | 0.416708 | − | 0.240587i | −0.276960 | − | 0.960882i | \(-0.589327\pi\) |
0.693668 | + | 0.720295i | \(0.255994\pi\) | |||||||
\(278\) | −2.54301 | + | 1.46820i | −0.152519 | + | 0.0880571i | ||||
\(279\) | 7.35780 | + | 4.24803i | 0.440500 | + | 0.254323i | ||||
\(280\) | −1.89374 | + | 3.28006i | −0.113173 | + | 0.196021i | ||||
\(281\) | 21.6964 | + | 12.5264i | 1.29430 | + | 0.747262i | 0.979413 | − | 0.201868i | \(-0.0647011\pi\) |
0.314884 | + | 0.949130i | \(0.398034\pi\) | |||||||
\(282\) | − | 1.04092i | − | 0.0619859i | ||||||
\(283\) | 3.42387 | − | 1.97677i | 0.203528 | − | 0.117507i | −0.394772 | − | 0.918779i | \(-0.629176\pi\) |
0.598300 | + | 0.801272i | \(0.295843\pi\) | |||||||
\(284\) | 0.928191 | − | 1.60767i | 0.0550780 | − | 0.0953979i | ||||
\(285\) | 5.53266 | 0.327726 | ||||||||
\(286\) | −25.8236 | −1.52698 | ||||||||
\(287\) | −18.9229 | + | 32.7754i | −1.11698 | + | 1.93467i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 2.96002 | + | 5.12691i | 0.174119 | + | 0.301583i | ||||
\(290\) | 1.86387i | 0.109450i | ||||||||
\(291\) | −5.32662 | + | 3.07533i | −0.312252 | + | 0.180279i | ||||
\(292\) | −5.91715 | − | 10.2488i | −0.346275 | − | 0.599766i | ||||
\(293\) | −6.27495 | − | 10.8685i | −0.366586 | − | 0.634946i | 0.622443 | − | 0.782665i | \(-0.286140\pi\) |
−0.989029 | + | 0.147719i | \(0.952807\pi\) | |||||||
\(294\) | 6.36102 | + | 3.67253i | 0.370982 | + | 0.214187i | ||||
\(295\) | 1.80454 | 0.105064 | ||||||||
\(296\) | 5.63363 | + | 2.29396i | 0.327448 | + | 0.133334i | ||||
\(297\) | −3.84038 | −0.222842 | ||||||||
\(298\) | −14.1054 | − | 8.14376i | −0.817105 | − | 0.471756i | ||||
\(299\) | 28.4310 | + | 49.2439i | 1.64421 | + | 2.84785i | ||||
\(300\) | −0.500000 | − | 0.866025i | −0.0288675 | − | 0.0500000i | ||||
\(301\) | −0.130468 | + | 0.0753256i | −0.00752004 | + | 0.00434170i | ||||
\(302\) | − | 20.2784i | − | 1.16689i | ||||||
\(303\) | 4.48179 | + | 7.76268i | 0.257472 | + | 0.445954i | ||||
\(304\) | − | 5.53266i | − | 0.317320i | ||||||
\(305\) | 6.62563 | − | 11.4759i | 0.379382 | − | 0.657109i | ||||
\(306\) | −4.78749 | −0.273682 | ||||||||
\(307\) | −2.35294 | −0.134289 | −0.0671446 | − | 0.997743i | \(-0.521389\pi\) | ||||
−0.0671446 | + | 0.997743i | \(0.521389\pi\) | |||||||
\(308\) | 7.27270 | − | 12.5967i | 0.414401 | − | 0.717763i | ||||
\(309\) | −12.7358 | + | 7.35302i | −0.724514 | + | 0.418298i | ||||
\(310\) | − | 8.49606i | − | 0.482544i | ||||||
\(311\) | −19.5888 | − | 11.3096i | −1.11078 | − | 0.641309i | −0.171748 | − | 0.985141i | \(-0.554942\pi\) |
−0.939031 | + | 0.343832i | \(0.888275\pi\) | |||||||
\(312\) | 3.36212 | − | 5.82335i | 0.190342 | − | 0.329683i | ||||
\(313\) | 13.5051 | + | 7.79719i | 0.763355 | + | 0.440723i | 0.830499 | − | 0.557020i | \(-0.188055\pi\) |
−0.0671443 | + | 0.997743i | \(0.521389\pi\) | |||||||
\(314\) | 5.88642 | − | 3.39853i | 0.332190 | − | 0.191790i | ||||
\(315\) | −3.28006 | + | 1.89374i | −0.184811 | + | 0.106700i | ||||
\(316\) | −3.13047 | − | 1.80738i | −0.176103 | − | 0.101673i | ||||
\(317\) | 12.3149 | − | 21.3299i | 0.691671 | − | 1.19801i | −0.279619 | − | 0.960111i | \(-0.590208\pi\) |
0.971290 | − | 0.237898i | \(-0.0764585\pi\) | |||||||
\(318\) | 2.77776 | + | 1.60374i | 0.155769 | + | 0.0899333i | ||||
\(319\) | − | 7.15796i | − | 0.400769i | ||||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −1.95561 | + | 3.38721i | −0.109151 | + | 0.189056i | ||||
\(322\) | −32.0281 | −1.78485 | ||||||||
\(323\) | −26.4875 | −1.47381 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | − | 6.72423i | − | 0.372993i | ||||||
\(326\) | −4.47104 | − | 7.74406i | −0.247628 | − | 0.428904i | ||||
\(327\) | − | 3.82693i | − | 0.211630i | ||||||
\(328\) | −8.65360 | + | 4.99616i | −0.477815 | + | 0.275867i | ||||
\(329\) | 1.97124 | + | 3.41428i | 0.108678 | + | 0.188235i | ||||
\(330\) | 1.92019 | + | 3.32587i | 0.105703 | + | 0.183083i | ||||
\(331\) | 7.39622 | + | 4.27021i | 0.406533 | + | 0.234712i | 0.689299 | − | 0.724477i | \(-0.257919\pi\) |
−0.282766 | + | 0.959189i | \(0.591252\pi\) | |||||||
\(332\) | 13.5873 | 0.745702 | ||||||||
\(333\) | 3.73188 | + | 4.80344i | 0.204506 | + | 0.263227i | ||||
\(334\) | 3.14319 | 0.171988 | ||||||||
\(335\) | 7.94568 | + | 4.58744i | 0.434119 | + | 0.250638i | ||||
\(336\) | 1.89374 | + | 3.28006i | 0.103312 | + | 0.178942i | ||||
\(337\) | 6.00674 | + | 10.4040i | 0.327208 | + | 0.566741i | 0.981957 | − | 0.189106i | \(-0.0605589\pi\) |
−0.654749 | + | 0.755847i | \(0.727226\pi\) | |||||||
\(338\) | 27.8992 | − | 16.1076i | 1.51752 | − | 0.876140i | ||||
\(339\) | 16.3080i | 0.885727i | ||||||||
\(340\) | 2.39374 | + | 4.14609i | 0.129819 | + | 0.224853i | ||||
\(341\) | 32.6281i | 1.76691i | ||||||||
\(342\) | 2.76633 | − | 4.79142i | 0.149586 | − | 0.259090i | ||||
\(343\) | −1.30694 | −0.0705683 | ||||||||
\(344\) | −0.0397760 | −0.00214458 | ||||||||
\(345\) | 4.22814 | − | 7.32335i | 0.227635 | − | 0.394276i | ||||
\(346\) | −0.627052 | + | 0.362029i | −0.0337105 | + | 0.0194628i | ||||
\(347\) | 5.81798i | 0.312325i | 0.987731 | + | 0.156163i | \(0.0499124\pi\) | ||||
−0.987731 | + | 0.156163i | \(0.950088\pi\) | |||||||
\(348\) | 1.61416 | + | 0.931933i | 0.0865278 | + | 0.0499569i | ||||
\(349\) | 14.8951 | − | 25.7991i | 0.797318 | − | 1.38099i | −0.124039 | − | 0.992277i | \(-0.539585\pi\) |
0.921357 | − | 0.388717i | \(-0.127082\pi\) | |||||||
\(350\) | 3.28006 | + | 1.89374i | 0.175327 | + | 0.101225i | ||||
\(351\) | 5.82335 | − | 3.36212i | 0.310828 | − | 0.179456i | ||||
\(352\) | 3.32587 | − | 1.92019i | 0.177269 | − | 0.102347i | ||||
\(353\) | −13.6952 | − | 7.90695i | −0.728924 | − | 0.420845i | 0.0891041 | − | 0.996022i | \(-0.471600\pi\) |
−0.818029 | + | 0.575178i | \(0.804933\pi\) | |||||||
\(354\) | 0.902271 | − | 1.56278i | 0.0479551 | − | 0.0830607i | ||||
\(355\) | −1.60767 | − | 0.928191i | −0.0853265 | − | 0.0492633i | ||||
\(356\) | 17.1030i | 0.906457i | ||||||||
\(357\) | 15.7033 | − | 9.06628i | 0.831104 | − | 0.479838i | ||||
\(358\) | 10.4782 | − | 18.1487i | 0.553788 | − | 0.959190i | ||||
\(359\) | 20.8727 | 1.10162 | 0.550809 | − | 0.834631i | \(-0.314319\pi\) | ||||
0.550809 | + | 0.834631i | \(0.314319\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 5.80516 | − | 10.0548i | 0.305534 | − | 0.529201i | ||||
\(362\) | − | 15.4559i | − | 0.812344i | ||||||
\(363\) | −1.87427 | − | 3.24634i | −0.0983739 | − | 0.170389i | ||||
\(364\) | 25.4679i | 1.33488i | ||||||||
\(365\) | −10.2488 | + | 5.91715i | −0.536447 | + | 0.309718i | ||||
\(366\) | −6.62563 | − | 11.4759i | −0.346327 | − | 0.599856i | ||||
\(367\) | 12.5188 | + | 21.6833i | 0.653478 | + | 1.13186i | 0.982273 | + | 0.187456i | \(0.0600242\pi\) |
−0.328795 | + | 0.944401i | \(0.606643\pi\) | |||||||
\(368\) | −7.32335 | − | 4.22814i | −0.381756 | − | 0.220407i | ||||
\(369\) | −9.99232 | −0.520179 | ||||||||
\(370\) | 2.29396 | − | 5.63363i | 0.119257 | − | 0.292878i | ||||
\(371\) | −12.1483 | −0.630708 | ||||||||
\(372\) | −7.35780 | − | 4.24803i | −0.381484 | − | 0.220250i | ||||
\(373\) | 8.34468 | + | 14.4534i | 0.432071 | + | 0.748369i | 0.997052 | − | 0.0767350i | \(-0.0244495\pi\) |
−0.564980 | + | 0.825104i | \(0.691116\pi\) | |||||||
\(374\) | −9.19290 | − | 15.9226i | −0.475353 | − | 0.823336i | ||||
\(375\) | −0.866025 | + | 0.500000i | −0.0447214 | + | 0.0258199i | ||||
\(376\) | 1.04092i | 0.0536814i | ||||||||
\(377\) | 6.26653 | + | 10.8540i | 0.322743 | + | 0.559007i | ||||
\(378\) | 3.78749i | 0.194807i | ||||||||
\(379\) | 12.4760 | − | 21.6091i | 0.640849 | − | 1.10998i | −0.344394 | − | 0.938825i | \(-0.611916\pi\) |
0.985244 | − | 0.171158i | \(-0.0547509\pi\) | |||||||
\(380\) | −5.53266 | −0.283819 | ||||||||
\(381\) | 11.2778 | 0.577781 | ||||||||
\(382\) | 1.51928 | − | 2.63146i | 0.0777329 | − | 0.134637i | ||||
\(383\) | −8.07527 | + | 4.66226i | −0.412627 | + | 0.238230i | −0.691918 | − | 0.721976i | \(-0.743234\pi\) |
0.279291 | + | 0.960207i | \(0.409901\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −12.5967 | − | 7.27270i | −0.641987 | − | 0.370651i | ||||
\(386\) | −7.17156 | + | 12.4215i | −0.365023 | + | 0.632238i | ||||
\(387\) | −0.0344471 | − | 0.0198880i | −0.00175104 | − | 0.00101096i | ||||
\(388\) | 5.32662 | − | 3.07533i | 0.270418 | − | 0.156126i | ||||
\(389\) | 18.8460 | − | 10.8808i | 0.955532 | − | 0.551677i | 0.0607371 | − | 0.998154i | \(-0.480655\pi\) |
0.894795 | + | 0.446477i | \(0.147322\pi\) | |||||||
\(390\) | −5.82335 | − | 3.36212i | −0.294877 | − | 0.170247i | ||||
\(391\) | −20.2422 | + | 35.0605i | −1.02369 | + | 1.77308i | ||||
\(392\) | −6.36102 | − | 3.67253i | −0.321280 | − | 0.185491i | ||||
\(393\) | − | 8.32318i | − | 0.419849i | ||||||
\(394\) | −0.695787 | + | 0.401713i | −0.0350533 | + | 0.0202380i | ||||
\(395\) | −1.80738 | + | 3.13047i | −0.0909390 | + | 0.157511i | ||||
\(396\) | 3.84038 | 0.192987 | ||||||||
\(397\) | −4.30813 | −0.216219 | −0.108109 | − | 0.994139i | \(-0.534480\pi\) | ||||
−0.108109 | + | 0.994139i | \(0.534480\pi\) | |||||||
\(398\) | 2.00910 | − | 3.47986i | 0.100707 | − | 0.174430i | ||||
\(399\) | 20.9549i | 1.04906i | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 15.7601i | 0.787021i | 0.919320 | + | 0.393510i | \(0.128739\pi\) | ||||
−0.919320 | + | 0.393510i | \(0.871261\pi\) | |||||||
\(402\) | 7.94568 | − | 4.58744i | 0.396294 | − | 0.228801i | ||||
\(403\) | −28.5647 | − | 49.4755i | −1.42291 | − | 2.46455i | ||||
\(404\) | −4.48179 | − | 7.76268i | −0.222977 | − | 0.386208i | ||||
\(405\) | −0.866025 | − | 0.500000i | −0.0430331 | − | 0.0248452i | ||||
\(406\) | −7.05937 | −0.350351 | ||||||||
\(407\) | −8.80969 | + | 21.6353i | −0.436680 | + | 1.07242i | ||||
\(408\) | 4.78749 | 0.237016 | ||||||||
\(409\) | 25.1445 | + | 14.5172i | 1.24331 | + | 0.717828i | 0.969768 | − | 0.244030i | \(-0.0784697\pi\) |
0.273547 | + | 0.961859i | \(0.411803\pi\) | |||||||
\(410\) | 4.99616 | + | 8.65360i | 0.246743 | + | 0.427371i | ||||
\(411\) | 7.81094 | + | 13.5290i | 0.385285 | + | 0.667334i | ||||
\(412\) | 12.7358 | − | 7.35302i | 0.627448 | − | 0.362257i | ||||
\(413\) | 6.83468i | 0.336313i | ||||||||
\(414\) | −4.22814 | − | 7.32335i | −0.207802 | − | 0.359923i | ||||
\(415\) | − | 13.5873i | − | 0.666976i | ||||||
\(416\) | −3.36212 | + | 5.82335i | −0.164841 | + | 0.285513i | ||||
\(417\) | 2.93641 | 0.143797 | ||||||||
\(418\) | 21.2475 | 1.03925 | ||||||||
\(419\) | −14.1287 | + | 24.4716i | −0.690230 | + | 1.19551i | 0.281532 | + | 0.959552i | \(0.409157\pi\) |
−0.971762 | + | 0.235962i | \(0.924176\pi\) | |||||||
\(420\) | 3.28006 | − | 1.89374i | 0.160051 | − | 0.0924053i | ||||
\(421\) | − | 3.46274i | − | 0.168763i | −0.996434 | − | 0.0843817i | \(-0.973108\pi\) | ||
0.996434 | − | 0.0843817i | \(-0.0268915\pi\) | |||||||
\(422\) | −8.19446 | − | 4.73108i | −0.398900 | − | 0.230305i | ||||
\(423\) | −0.520460 | + | 0.901463i | −0.0253056 | + | 0.0438307i | ||||
\(424\) | −2.77776 | − | 1.60374i | −0.134900 | − | 0.0778845i | ||||
\(425\) | 4.14609 | − | 2.39374i | 0.201115 | − | 0.116114i | ||||
\(426\) | −1.60767 | + | 0.928191i | −0.0778921 | + | 0.0449710i | ||||
\(427\) | 43.4649 | + | 25.0945i | 2.10341 | + | 1.21441i | ||||
\(428\) | 1.95561 | − | 3.38721i | 0.0945279 | − | 0.163727i | ||||
\(429\) | 22.3639 | + | 12.9118i | 1.07974 | + | 0.623388i | ||||
\(430\) | 0.0397760i | 0.00191817i | ||||||||
\(431\) | 1.54704 | − | 0.893186i | 0.0745185 | − | 0.0430233i | −0.462278 | − | 0.886735i | \(-0.652968\pi\) |
0.536796 | + | 0.843712i | \(0.319634\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −33.6257 | −1.61595 | −0.807974 | − | 0.589218i | \(-0.799436\pi\) | ||||
−0.807974 | + | 0.589218i | \(0.799436\pi\) | |||||||
\(434\) | 32.1787 | 1.54463 | ||||||||
\(435\) | 0.931933 | − | 1.61416i | 0.0446828 | − | 0.0773928i | ||||
\(436\) | 3.82693i | 0.183277i | ||||||||
\(437\) | −23.3929 | − | 40.5176i | −1.11903 | − | 1.93822i | ||||
\(438\) | 11.8343i | 0.565465i | ||||||||
\(439\) | 10.2005 | − | 5.88926i | 0.486843 | − | 0.281079i | −0.236421 | − | 0.971651i | \(-0.575974\pi\) |
0.723264 | + | 0.690572i | \(0.242641\pi\) | |||||||
\(440\) | −1.92019 | − | 3.32587i | −0.0915416 | − | 0.158555i | ||||
\(441\) | −3.67253 | − | 6.36102i | −0.174883 | − | 0.302906i | ||||
\(442\) | 27.8792 | + | 16.0961i | 1.32608 | + | 0.765613i | ||||
\(443\) | −26.7397 | −1.27044 | −0.635220 | − | 0.772331i | \(-0.719091\pi\) | ||||
−0.635220 | + | 0.772331i | \(0.719091\pi\) | |||||||
\(444\) | −3.73188 | − | 4.80344i | −0.177107 | − | 0.227961i | ||||
\(445\) | 17.1030 | 0.810759 | ||||||||
\(446\) | 10.2674 | + | 5.92790i | 0.486176 | + | 0.280694i | ||||
\(447\) | 8.14376 | + | 14.1054i | 0.385187 | + | 0.667163i | ||||
\(448\) | −1.89374 | − | 3.28006i | −0.0894710 | − | 0.154968i | ||||
\(449\) | 12.1655 | − | 7.02375i | 0.574125 | − | 0.331471i | −0.184670 | − | 0.982801i | \(-0.559122\pi\) |
0.758795 | + | 0.651329i | \(0.225788\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −19.1872 | − | 33.2331i | −0.903488 | − | 1.56489i | ||||
\(452\) | − | 16.3080i | − | 0.767062i | ||||||
\(453\) | −10.1392 | + | 17.5616i | −0.476381 | + | 0.825117i | ||||
\(454\) | 12.4686 | 0.585182 | ||||||||
\(455\) | 25.4679 | 1.19396 | ||||||||
\(456\) | −2.76633 | + | 4.79142i | −0.129545 | + | 0.224379i | ||||
\(457\) | 10.5277 | − | 6.07816i | 0.492464 | − | 0.284324i | −0.233132 | − | 0.972445i | \(-0.574897\pi\) |
0.725596 | + | 0.688121i | \(0.241564\pi\) | |||||||
\(458\) | − | 10.0119i | − | 0.467824i | ||||||
\(459\) | 4.14609 | + | 2.39374i | 0.193523 | + | 0.111730i | ||||
\(460\) | −4.22814 | + | 7.32335i | −0.197138 | + | 0.341453i | ||||
\(461\) | 28.6410 | + | 16.5359i | 1.33395 | + | 0.770154i | 0.985902 | − | 0.167324i | \(-0.0535127\pi\) |
0.348044 | + | 0.937478i | \(0.386846\pi\) | |||||||
\(462\) | −12.5967 | + | 7.27270i | −0.586051 | + | 0.338357i | ||||
\(463\) | 32.8685 | − | 18.9767i | 1.52753 | − | 0.881920i | 0.528066 | − | 0.849203i | \(-0.322917\pi\) |
0.999465 | − | 0.0327173i | \(-0.0104161\pi\) | |||||||
\(464\) | −1.61416 | − | 0.931933i | −0.0749353 | − | 0.0432639i | ||||
\(465\) | −4.24803 | + | 7.35780i | −0.196998 | + | 0.341210i | ||||
\(466\) | 8.58323 | + | 4.95553i | 0.397610 | + | 0.229561i | ||||
\(467\) | − | 13.0633i | − | 0.604500i | −0.953229 | − | 0.302250i | \(-0.902262\pi\) | ||
0.953229 | − | 0.302250i | \(-0.0977377\pi\) | |||||||
\(468\) | −5.82335 | + | 3.36212i | −0.269185 | + | 0.155414i | ||||
\(469\) | −17.3749 | + | 30.0942i | −0.802297 | + | 1.38962i | ||||
\(470\) | 1.04092 | 0.0480141 | ||||||||
\(471\) | −6.79706 | −0.313192 | ||||||||
\(472\) | −0.902271 | + | 1.56278i | −0.0415304 | + | 0.0719327i | ||||
\(473\) | − | 0.152755i | − | 0.00702369i | ||||||
\(474\) | 1.80738 | + | 3.13047i | 0.0830155 | + | 0.143787i | ||||
\(475\) | 5.53266i | 0.253856i | ||||||||
\(476\) | −15.7033 | + | 9.06628i | −0.719758 | + | 0.415552i | ||||
\(477\) | −1.60374 | − | 2.77776i | −0.0734302 | − | 0.127185i | ||||
\(478\) | −7.81314 | − | 13.5328i | −0.357365 | − | 0.618974i | ||||
\(479\) | −3.55432 | − | 2.05209i | −0.162401 | − | 0.0937623i | 0.416597 | − | 0.909091i | \(-0.363223\pi\) |
−0.578998 | + | 0.815329i | \(0.696556\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −5.58235 | − | 40.5192i | −0.254533 | − | 1.84751i | ||||
\(482\) | −12.7958 | −0.582835 | ||||||||
\(483\) | 27.7371 | + | 16.0140i | 1.26208 | + | 0.728664i | ||||
\(484\) | 1.87427 | + | 3.24634i | 0.0851943 | + | 0.147561i | ||||
\(485\) | −3.07533 | − | 5.32662i | −0.139643 | − | 0.241869i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 32.1531i | 1.45699i | 0.685049 | + | 0.728497i | \(0.259781\pi\) | ||||
−0.685049 | + | 0.728497i | \(0.740219\pi\) | |||||||
\(488\) | 6.62563 | + | 11.4759i | 0.299928 | + | 0.519491i | ||||
\(489\) | 8.94207i | 0.404375i | ||||||||
\(490\) | −3.67253 | + | 6.36102i | −0.165908 | + | 0.287361i | ||||
\(491\) | 31.3238 | 1.41362 | 0.706812 | − | 0.707402i | \(-0.250133\pi\) | ||||
0.706812 | + | 0.707402i | \(0.250133\pi\) | |||||||
\(492\) | 9.99232 | 0.450488 | ||||||||
\(493\) | −4.46162 | + | 7.72775i | −0.200941 | + | 0.348040i | ||||
\(494\) | −32.2186 | + | 18.6014i | −1.44958 | + | 0.836918i | ||||
\(495\) | − | 3.84038i | − | 0.172612i | ||||||
\(496\) | 7.35780 | + | 4.24803i | 0.330375 | + | 0.190742i | ||||
\(497\) | 3.51551 | − | 6.08905i | 0.157692 | − | 0.273131i | ||||
\(498\) | −11.7670 | − | 6.79367i | −0.527291 | − | 0.304432i | ||||
\(499\) | −24.8514 | + | 14.3480i | −1.11250 | + | 0.642303i | −0.939476 | − | 0.342615i | \(-0.888687\pi\) |
−0.173025 | + | 0.984917i | \(0.555354\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | −2.72208 | − | 1.57160i | −0.121614 | − | 0.0702137i | ||||
\(502\) | −4.61964 | + | 8.00145i | −0.206185 | + | 0.357122i | ||||
\(503\) | −17.4569 | − | 10.0787i | −0.778364 | − | 0.449389i | 0.0574859 | − | 0.998346i | \(-0.481692\pi\) |
−0.835850 | + | 0.548957i | \(0.815025\pi\) | |||||||
\(504\) | − | 3.78749i | − | 0.168708i | ||||||
\(505\) | −7.76268 | + | 4.48179i | −0.345435 | + | 0.199437i | ||||
\(506\) | 16.2377 | − | 28.1245i | 0.721853 | − | 1.25029i | ||||
\(507\) | −32.2153 | −1.43073 | ||||||||
\(508\) | −11.2778 | −0.500373 | ||||||||
\(509\) | −16.5772 | + | 28.7126i | −0.734772 | + | 1.27266i | 0.220052 | + | 0.975488i | \(0.429377\pi\) |
−0.954823 | + | 0.297174i | \(0.903956\pi\) | |||||||
\(510\) | − | 4.78749i | − | 0.211994i | ||||||
\(511\) | −22.4111 | − | 38.8172i | −0.991410 | − | 1.71717i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −4.79142 | + | 2.76633i | −0.211546 | + | 0.122136i | ||||
\(514\) | −6.02592 | − | 10.4372i | −0.265792 | − | 0.460365i | ||||
\(515\) | −7.35302 | − | 12.7358i | −0.324013 | − | 0.561206i | ||||
\(516\) | 0.0344471 | + | 0.0198880i | 0.00151645 | + | 0.000875521i | ||||
\(517\) | −3.99753 | −0.175811 | ||||||||
\(518\) | 21.3373 | + | 8.68835i | 0.937507 | + | 0.381744i | ||||
\(519\) | 0.724057 | 0.0317826 | ||||||||
\(520\) | 5.82335 | + | 3.36212i | 0.255371 | + | 0.147438i | ||||
\(521\) | −12.7108 | − | 22.0158i | −0.556870 | − | 0.964528i | −0.997755 | − | 0.0669640i | \(-0.978669\pi\) |
0.440885 | − | 0.897564i | \(-0.354665\pi\) | |||||||
\(522\) | −0.931933 | − | 1.61416i | −0.0407896 | − | 0.0706497i | ||||
\(523\) | 15.7552 | − | 9.09627i | 0.688927 | − | 0.397752i | −0.114283 | − | 0.993448i | \(-0.536457\pi\) |
0.803210 | + | 0.595696i | \(0.203124\pi\) | |||||||
\(524\) | 8.32318i | 0.363600i | ||||||||
\(525\) | −1.89374 | − | 3.28006i | −0.0826498 | − | 0.143154i | ||||
\(526\) | − | 7.31074i | − | 0.318763i | ||||||
\(527\) | 20.3374 | − | 35.2254i | 0.885910 | − | 1.53444i | ||||
\(528\) | −3.84038 | −0.167131 | ||||||||
\(529\) | −48.5087 | −2.10907 | ||||||||
\(530\) | −1.60374 | + | 2.77776i | −0.0696620 | + | 0.120658i | ||||
\(531\) | −1.56278 | + | 0.902271i | −0.0678188 | + | 0.0391552i | ||||
\(532\) | − | 20.9549i | − | 0.908509i | ||||||
\(533\) | 58.1888 | + | 33.5953i | 2.52044 | + | 1.45517i | ||||
\(534\) | 8.55149 | − | 14.8116i | 0.370059 | − | 0.640962i | ||||
\(535\) | −3.38721 | − | 1.95561i | −0.146442 | − | 0.0845483i | ||||
\(536\) | −7.94568 | + | 4.58744i | −0.343201 | + | 0.198147i | ||||
\(537\) | −18.1487 | + | 10.4782i | −0.783175 | + | 0.452166i | ||||
\(538\) | −13.1312 | − | 7.58133i | −0.566128 | − | 0.326854i | ||||
\(539\) | 14.1039 | − | 24.4287i | 0.607500 | − | 1.05222i | ||||
\(540\) | 0.866025 | + | 0.500000i | 0.0372678 | + | 0.0215166i | ||||
\(541\) | 32.6823i | 1.40512i | 0.711624 | + | 0.702560i | \(0.247960\pi\) | ||||
−0.711624 | + | 0.702560i | \(0.752040\pi\) | |||||||
\(542\) | −9.34650 | + | 5.39620i | −0.401466 | + | 0.231787i | ||||
\(543\) | −7.72795 | + | 13.3852i | −0.331638 | + | 0.574414i | ||||
\(544\) | −4.78749 | −0.205262 | ||||||||
\(545\) | 3.82693 | 0.163928 | ||||||||
\(546\) | 12.7340 | − | 22.0559i | 0.544964 | − | 0.943905i | ||||
\(547\) | 21.1126i | 0.902711i | 0.892344 | + | 0.451355i | \(0.149059\pi\) | ||||
−0.892344 | + | 0.451355i | \(0.850941\pi\) | |||||||
\(548\) | −7.81094 | − | 13.5290i | −0.333667 | − | 0.577928i | ||||
\(549\) | 13.2513i | 0.565550i | ||||||||
\(550\) | −3.32587 | + | 1.92019i | −0.141816 | + | 0.0818773i | ||||
\(551\) | −5.15607 | − | 8.93057i | −0.219656 | − | 0.380455i | ||||
\(552\) | 4.22814 | + | 7.32335i | 0.179962 | + | 0.311703i | ||||
\(553\) | −11.8566 | − | 6.84542i | −0.504194 | − | 0.291097i | ||||
\(554\) | 8.00832 | 0.340241 | ||||||||
\(555\) | −4.80344 | + | 3.73188i | −0.203895 | + | 0.158410i | ||||
\(556\) | −2.93641 | −0.124531 | ||||||||
\(557\) | −14.5555 | − | 8.40363i | −0.616737 | − | 0.356073i | 0.158860 | − | 0.987301i | \(-0.449218\pi\) |
−0.775598 | + | 0.631228i | \(0.782551\pi\) | |||||||
\(558\) | 4.24803 | + | 7.35780i | 0.179833 | + | 0.311481i | ||||
\(559\) | 0.133732 | + | 0.231630i | 0.00565624 | + | 0.00979690i | ||||
\(560\) | −3.28006 | + | 1.89374i | −0.138608 | + | 0.0800253i | ||||
\(561\) | 18.3858i | 0.776249i | ||||||||
\(562\) | 12.5264 | + | 21.6964i | 0.528394 | + | 0.915206i | ||||
\(563\) | − | 5.35688i | − | 0.225766i | −0.993608 | − | 0.112883i | \(-0.963992\pi\) | ||
0.993608 | − | 0.112883i | \(-0.0360085\pi\) | |||||||
\(564\) | 0.520460 | − | 0.901463i | 0.0219153 | − | 0.0379585i | ||||
\(565\) | −16.3080 | −0.686082 | ||||||||
\(566\) | 3.95355 | 0.166180 | ||||||||
\(567\) | 1.89374 | − | 3.28006i | 0.0795298 | − | 0.137750i | ||||
\(568\) | 1.60767 | − | 0.928191i | 0.0674565 | − | 0.0389460i | ||||
\(569\) | − | 8.95342i | − | 0.375347i | −0.982231 | − | 0.187673i | \(-0.939905\pi\) | ||
0.982231 | − | 0.187673i | \(-0.0600947\pi\) | |||||||
\(570\) | 4.79142 | + | 2.76633i | 0.200691 | + | 0.115869i | ||||
\(571\) | −18.6922 | + | 32.3758i | −0.782242 | + | 1.35488i | 0.148390 | + | 0.988929i | \(0.452591\pi\) |
−0.930633 | + | 0.365955i | \(0.880743\pi\) | |||||||
\(572\) | −22.3639 | − | 12.9118i | −0.935082 | − | 0.539870i | ||||
\(573\) | −2.63146 | + | 1.51928i | −0.109931 | + | 0.0634686i | ||||
\(574\) | −32.7754 | + | 18.9229i | −1.36802 | + | 0.789826i | ||||
\(575\) | 7.32335 | + | 4.22814i | 0.305405 | + | 0.176326i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 3.18442 | + | 1.83852i | 0.132569 | + | 0.0765387i | 0.564818 | − | 0.825216i | \(-0.308946\pi\) |
−0.432249 | + | 0.901754i | \(0.642280\pi\) | |||||||
\(578\) | 5.92005i | 0.246241i | ||||||||
\(579\) | 12.4215 | − | 7.17156i | 0.516220 | − | 0.298040i | ||||
\(580\) | −0.931933 | + | 1.61416i | −0.0386964 | + | 0.0670242i | ||||
\(581\) | 51.4619 | 2.13500 | ||||||||
\(582\) | −6.15065 | −0.254953 | ||||||||
\(583\) | 6.15898 | − | 10.6677i | 0.255079 | − | 0.441809i | ||||
\(584\) | − | 11.8343i | − | 0.489707i | ||||||
\(585\) | 3.36212 | + | 5.82335i | 0.139006 | + | 0.240766i | ||||
\(586\) | − | 12.5499i | − | 0.518431i | ||||||
\(587\) | −33.6978 | + | 19.4555i | −1.39086 | + | 0.803013i | −0.993410 | − | 0.114612i | \(-0.963438\pi\) |
−0.397448 | + | 0.917625i | \(0.630104\pi\) | |||||||
\(588\) | 3.67253 | + | 6.36102i | 0.151453 | + | 0.262324i | ||||
\(589\) | 23.5029 | + | 40.7082i | 0.968420 | + | 1.67735i | ||||
\(590\) | 1.56278 | + | 0.902271i | 0.0643386 | + | 0.0371459i | ||||
\(591\) | 0.803426 | 0.0330485 | ||||||||
\(592\) | 3.73188 | + | 4.80344i | 0.153379 | + | 0.197420i | ||||
\(593\) | 2.91438 | 0.119679 | 0.0598397 | − | 0.998208i | \(-0.480941\pi\) | ||||
0.0598397 | + | 0.998208i | \(0.480941\pi\) | |||||||
\(594\) | −3.32587 | − | 1.92019i | −0.136462 | − | 0.0787864i | ||||
\(595\) | 9.06628 | + | 15.7033i | 0.371681 | + | 0.643771i | ||||
\(596\) | −8.14376 | − | 14.1054i | −0.333582 | − | 0.577780i | ||||
\(597\) | −3.47986 | + | 2.00910i | −0.142421 | + | 0.0822269i | ||||
\(598\) | 56.8620i | 2.32526i | ||||||||
\(599\) | −1.93950 | − | 3.35931i | −0.0792458 | − | 0.137258i | 0.823679 | − | 0.567056i | \(-0.191918\pi\) |
−0.902925 | + | 0.429799i | \(0.858585\pi\) | |||||||
\(600\) | − | 1.00000i | − | 0.0408248i | ||||||
\(601\) | −20.7686 | + | 35.9723i | −0.847170 | + | 1.46734i | 0.0365530 | + | 0.999332i | \(0.488362\pi\) |
−0.883723 | + | 0.468010i | \(0.844971\pi\) | |||||||
\(602\) | −0.150651 | −0.00614009 | ||||||||
\(603\) | −9.17488 | −0.373630 | ||||||||
\(604\) | 10.1392 | − | 17.5616i | 0.412558 | − | 0.714572i | ||||
\(605\) | 3.24634 | − | 1.87427i | 0.131982 | − | 0.0762001i | ||||
\(606\) | 8.96357i | 0.364120i | ||||||||
\(607\) | −10.3055 | − | 5.94986i | −0.418286 | − | 0.241497i | 0.276058 | − | 0.961141i | \(-0.410972\pi\) |
−0.694344 | + | 0.719644i | \(0.744305\pi\) | |||||||
\(608\) | 2.76633 | − | 4.79142i | 0.112189 | − | 0.194318i | ||||
\(609\) | 6.11359 | + | 3.52969i | 0.247735 | + | 0.143030i | ||||
\(610\) | 11.4759 | − | 6.62563i | 0.464646 | − | 0.268264i | ||||
\(611\) | 6.06165 | − | 3.49969i | 0.245228 | − | 0.141582i | ||||
\(612\) | −4.14609 | − | 2.39374i | −0.167596 | − | 0.0967614i | ||||
\(613\) | −4.99067 | + | 8.64409i | −0.201571 | + | 0.349132i | −0.949035 | − | 0.315171i | \(-0.897938\pi\) |
0.747464 | + | 0.664303i | \(0.231271\pi\) | |||||||
\(614\) | −2.03770 | − | 1.17647i | −0.0822350 | − | 0.0474784i | ||||
\(615\) | − | 9.99232i | − | 0.402929i | ||||||
\(616\) | 12.5967 | − | 7.27270i | 0.507535 | − | 0.293026i | ||||
\(617\) | −9.78398 | + | 16.9464i | −0.393888 | + | 0.682234i | −0.992959 | − | 0.118462i | \(-0.962204\pi\) |
0.599070 | + | 0.800696i | \(0.295537\pi\) | |||||||
\(618\) | −14.7060 | −0.591563 | ||||||||
\(619\) | 27.2882 | 1.09680 | 0.548402 | − | 0.836215i | \(-0.315236\pi\) | ||||
0.548402 | + | 0.836215i | \(0.315236\pi\) | |||||||
\(620\) | 4.24803 | − | 7.35780i | 0.170605 | − | 0.295496i | ||||
\(621\) | 8.45628i | 0.339339i | ||||||||
\(622\) | −11.3096 | − | 19.5888i | −0.453474 | − | 0.785439i | ||||
\(623\) | 64.7774i | 2.59525i | ||||||||
\(624\) | 5.82335 | − | 3.36212i | 0.233121 | − | 0.134592i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 7.79719 | + | 13.5051i | 0.311638 | + | 0.539773i | ||||
\(627\) | −18.4009 | − | 10.6238i | −0.734861 | − | 0.424272i | ||||
\(628\) | 6.79706 | 0.271232 | ||||||||
\(629\) | 22.9964 | − | 17.8663i | 0.916927 | − | 0.712378i | ||||
\(630\) | −3.78749 | −0.150897 | ||||||||
\(631\) | 17.1937 | + | 9.92680i | 0.684471 | + | 0.395180i | 0.801538 | − | 0.597945i | \(-0.204016\pi\) |
−0.117066 | + | 0.993124i | \(0.537349\pi\) | |||||||
\(632\) | −1.80738 | − | 3.13047i | −0.0718936 | − | 0.124523i | ||||
\(633\) | 4.73108 | + | 8.19446i | 0.188043 | + | 0.325701i | ||||
\(634\) | 21.3299 | − | 12.3149i | 0.847120 | − | 0.489085i | ||||
\(635\) | 11.2778i | 0.447547i | ||||||||
\(636\) | 1.60374 | + | 2.77776i | 0.0635924 | + | 0.110145i | ||||
\(637\) | 49.3899i | 1.95690i | ||||||||
\(638\) | 3.57898 | − | 6.19898i | 0.141693 | − | 0.245420i | ||||
\(639\) | 1.85638 | 0.0734374 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.37909 | − | 7.58480i | 0.172964 | − | 0.299582i | −0.766491 | − | 0.642255i | \(-0.777999\pi\) |
0.939455 | + | 0.342673i | \(0.111332\pi\) | |||||||
\(642\) | −3.38721 | + | 1.95561i | −0.133683 | + | 0.0771817i | ||||
\(643\) | − | 23.7722i | − | 0.937485i | −0.883335 | − | 0.468742i | \(-0.844707\pi\) | ||
0.883335 | − | 0.468742i | \(-0.155293\pi\) | |||||||
\(644\) | −27.7371 | − | 16.0140i | −1.09300 | − | 0.631041i | ||||
\(645\) | 0.0198880 | − | 0.0344471i | 0.000783090 | − | 0.00135635i | ||||
\(646\) | −22.9389 | − | 13.2438i | −0.902518 | − | 0.521069i | ||||
\(647\) | 14.1817 | − | 8.18780i | 0.557539 | − | 0.321896i | −0.194618 | − | 0.980879i | \(-0.562347\pi\) |
0.752157 | + | 0.658984i | \(0.229013\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −6.00167 | − | 3.46507i | −0.235586 | − | 0.136016i | ||||
\(650\) | 3.36212 | − | 5.82335i | 0.131873 | − | 0.228411i | ||||
\(651\) | −27.8676 | − | 16.0894i | −1.09222 | − | 0.630592i | ||||
\(652\) | − | 8.94207i | − | 0.350199i | ||||||
\(653\) | 19.1663 | − | 11.0657i | 0.750034 | − | 0.433032i | −0.0756720 | − | 0.997133i | \(-0.524110\pi\) |
0.825706 | + | 0.564100i | \(0.190777\pi\) | |||||||
\(654\) | 1.91346 | − | 3.31422i | 0.0748223 | − | 0.129596i | ||||
\(655\) | 8.32318 | 0.325214 | ||||||||
\(656\) | −9.99232 | −0.390134 | ||||||||
\(657\) | 5.91715 | − | 10.2488i | 0.230850 | − | 0.399844i | ||||
\(658\) | 3.94247i | 0.153694i | ||||||||
\(659\) | −1.48559 | − | 2.57312i | −0.0578705 | − | 0.100235i | 0.835639 | − | 0.549279i | \(-0.185098\pi\) |
−0.893509 | + | 0.449045i | \(0.851764\pi\) | |||||||
\(660\) | 3.84038i | 0.149487i | ||||||||
\(661\) | −7.65152 | + | 4.41761i | −0.297609 | + | 0.171825i | −0.641368 | − | 0.767233i | \(-0.721633\pi\) |
0.343759 | + | 0.939058i | \(0.388300\pi\) | |||||||
\(662\) | 4.27021 | + | 7.39622i | 0.165966 | + | 0.287462i | ||||
\(663\) | −16.0961 | − | 27.8792i | −0.625120 | − | 1.08274i | ||||
\(664\) | 11.7670 | + | 6.79367i | 0.456647 | + | 0.263645i | ||||
\(665\) | −20.9549 | −0.812595 | ||||||||
\(666\) | 0.830184 | + | 6.02584i | 0.0321690 | + | 0.233497i | ||||
\(667\) | −15.7614 | −0.610283 | ||||||||
\(668\) | 2.72208 | + | 1.57160i | 0.105321 | + | 0.0608069i | ||||
\(669\) | −5.92790 | − | 10.2674i | −0.229186 | − | 0.396961i | ||||
\(670\) | 4.58744 | + | 7.94568i | 0.177228 | + | 0.306968i | ||||
\(671\) | −44.0719 | + | 25.4449i | −1.70138 | + | 0.982291i | ||||
\(672\) | 3.78749i | 0.146106i | ||||||||
\(673\) | 13.7552 | + | 23.8248i | 0.530226 | + | 0.918378i | 0.999378 | + | 0.0352608i | \(0.0112262\pi\) |
−0.469152 | + | 0.883117i | \(0.655440\pi\) | |||||||
\(674\) | 12.0135i | 0.462742i | ||||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 32.2153 | 1.23905 | ||||||||
\(677\) | −6.30629 | −0.242370 | −0.121185 | − | 0.992630i | \(-0.538669\pi\) | ||||
−0.121185 | + | 0.992630i | \(0.538669\pi\) | |||||||
\(678\) | −8.15399 | + | 14.1231i | −0.313152 | + | 0.542395i | ||||
\(679\) | 20.1745 | − | 11.6478i | 0.774227 | − | 0.447000i | ||||
\(680\) | 4.78749i | 0.183592i | ||||||||
\(681\) | −10.7982 | − | 6.23432i | −0.413786 | − | 0.238900i | ||||
\(682\) | −16.3141 | + | 28.2568i | −0.624698 | + | 1.08201i | ||||
\(683\) | −32.6161 | − | 18.8309i | −1.24802 | − | 0.720544i | −0.277305 | − | 0.960782i | \(-0.589441\pi\) |
−0.970714 | + | 0.240238i | \(0.922774\pi\) | |||||||
\(684\) | 4.79142 | − | 2.76633i | 0.183205 | − | 0.105773i | ||||
\(685\) | −13.5290 | + | 7.81094i | −0.516915 | + | 0.298441i | ||||
\(686\) | −1.13185 | − | 0.653472i | −0.0432141 | − | 0.0249497i | ||||
\(687\) | −5.00593 | + | 8.67053i | −0.190988 | + | 0.330801i | ||||
\(688\) | −0.0344471 | − | 0.0198880i | −0.00131328 | − | 0.000758223i | ||||
\(689\) | 21.5678i | 0.821669i | ||||||||
\(690\) | 7.32335 | − | 4.22814i | 0.278795 | − | 0.160963i | ||||
\(691\) | 10.7311 | − | 18.5868i | 0.408230 | − | 0.707075i | −0.586461 | − | 0.809977i | \(-0.699479\pi\) |
0.994692 | + | 0.102902i | \(0.0328128\pi\) | |||||||
\(692\) | −0.724057 | −0.0275245 | ||||||||
\(693\) | 14.5454 | 0.552534 | ||||||||
\(694\) | −2.90899 | + | 5.03851i | −0.110424 | + | 0.191259i | ||||
\(695\) | 2.93641i | 0.111384i | ||||||||
\(696\) | 0.931933 | + | 1.61416i | 0.0353248 | + | 0.0611844i | ||||
\(697\) | 47.8381i | 1.81200i | ||||||||
\(698\) | 25.7991 | − | 14.8951i | 0.976511 | − | 0.563789i | ||||
\(699\) | −4.95553 | − | 8.58323i | −0.187435 | − | 0.324648i | ||||
\(700\) | 1.89374 | + | 3.28006i | 0.0715768 | + | 0.123975i | ||||
\(701\) | 36.0348 | + | 20.8047i | 1.36102 | + | 0.785783i | 0.989759 | − | 0.142747i | \(-0.0455934\pi\) |
0.371257 | + | 0.928530i | \(0.378927\pi\) | |||||||
\(702\) | 6.72423 | 0.253790 | ||||||||
\(703\) | 4.59312 | + | 33.3389i | 0.173233 | + | 1.25740i | ||||
\(704\) | 3.84038 | 0.144740 | ||||||||
\(705\) | −0.901463 | − | 0.520460i | −0.0339511 | − | 0.0196017i | ||||
\(706\) | −7.90695 | − | 13.6952i | −0.297582 | − | 0.515427i | ||||
\(707\) | −16.9747 | − | 29.4011i | −0.638400 | − | 1.10574i | ||||
\(708\) | 1.56278 | − | 0.902271i | 0.0587328 | − | 0.0339094i | ||||
\(709\) | − | 40.2595i | − | 1.51198i | −0.654584 | − | 0.755989i | \(-0.727156\pi\) | ||
0.654584 | − | 0.755989i | \(-0.272844\pi\) | |||||||
\(710\) | −0.928191 | − | 1.60767i | −0.0348344 | − | 0.0603349i | ||||
\(711\) | − | 3.61475i | − | 0.135564i | ||||||
\(712\) | −8.55149 | + | 14.8116i | −0.320481 | + | 0.555089i | ||||
\(713\) | 71.8450 | 2.69062 | ||||||||
\(714\) | 18.1326 | 0.678594 | ||||||||
\(715\) | −12.9118 | + | 22.3639i | −0.482874 | + | 0.836363i | ||||
\(716\) | 18.1487 | − | 10.4782i | 0.678249 | − | 0.391587i | ||||
\(717\) | 15.6263i | 0.583574i | ||||||||
\(718\) | 18.0763 | + | 10.4363i | 0.674601 | + | 0.389481i | ||||
\(719\) | 16.2180 | − | 28.0903i | 0.604828 | − | 1.04759i | −0.387251 | − | 0.921974i | \(-0.626575\pi\) |
0.992079 | − | 0.125618i | \(-0.0400914\pi\) | |||||||
\(720\) | −0.866025 | − | 0.500000i | −0.0322749 | − | 0.0186339i | ||||
\(721\) | 48.2367 | − | 27.8495i | 1.79643 | − | 1.03717i | ||||
\(722\) | 10.0548 | − | 5.80516i | 0.374202 | − | 0.216046i | ||||
\(723\) | 11.0815 | + | 6.39792i | 0.412127 | + | 0.237941i | ||||
\(724\) | 7.72795 | − | 13.3852i | 0.287207 | − | 0.497457i | ||||
\(725\) | 1.61416 | + | 0.931933i | 0.0599482 | + | 0.0346111i | ||||
\(726\) | − | 3.74855i | − | 0.139122i | ||||||
\(727\) | −5.34178 | + | 3.08408i | −0.198116 | + | 0.114382i | −0.595776 | − | 0.803150i | \(-0.703155\pi\) |
0.397661 | + | 0.917533i | \(0.369822\pi\) | |||||||
\(728\) | −12.7340 | + | 22.0559i | −0.471952 | + | 0.817446i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.8343 | −0.438007 | ||||||||
\(731\) | −0.0952136 | + | 0.164915i | −0.00352160 | + | 0.00609960i | ||||
\(732\) | − | 13.2513i | − | 0.489780i | ||||||
\(733\) | −5.59909 | − | 9.69791i | −0.206807 | − | 0.358201i | 0.743900 | − | 0.668291i | \(-0.232974\pi\) |
−0.950707 | + | 0.310091i | \(0.899641\pi\) | |||||||
\(734\) | 25.0377i | 0.924158i | ||||||||
\(735\) | 6.36102 | − | 3.67253i | 0.234630 | − | 0.135463i | ||||
\(736\) | −4.22814 | − | 7.32335i | −0.155851 | − | 0.269942i | ||||
\(737\) | −17.6175 | − | 30.5144i | −0.648950 | − | 1.12401i | ||||
\(738\) | −8.65360 | − | 4.99616i | −0.318543 | − | 0.183911i | ||||
\(739\) | 47.1766 | 1.73542 | 0.867709 | − | 0.497073i | \(-0.165592\pi\) | ||||
0.867709 | + | 0.497073i | \(0.165592\pi\) | |||||||
\(740\) | 4.80344 | − | 3.73188i | 0.176578 | − | 0.137187i | ||||
\(741\) | 37.2029 | 1.36668 | ||||||||
\(742\) | −10.5207 | − | 6.07415i | −0.386228 | − | 0.222989i | ||||
\(743\) | 7.62157 | + | 13.2009i | 0.279608 | + | 0.484296i | 0.971287 | − | 0.237909i | \(-0.0764621\pi\) |
−0.691679 | + | 0.722205i | \(0.743129\pi\) | |||||||
\(744\) | −4.24803 | − | 7.35780i | −0.155740 | − | 0.269750i | ||||
\(745\) | −14.1054 | + | 8.14376i | −0.516782 | + | 0.298364i | ||||
\(746\) | 16.6894i | 0.611041i | ||||||||
\(747\) | 6.79367 | + | 11.7670i | 0.248567 | + | 0.430531i | ||||
\(748\) | − | 18.3858i | − | 0.672251i | ||||||
\(749\) | 7.40684 | − | 12.8290i | 0.270640 | − | 0.468762i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 43.2557 | 1.57842 | 0.789212 | − | 0.614120i | \(-0.210489\pi\) | ||||
0.789212 | + | 0.614120i | \(0.210489\pi\) | |||||||
\(752\) | −0.520460 | + | 0.901463i | −0.0189792 | + | 0.0328730i | ||||
\(753\) | 8.00145 | − | 4.61964i | 0.291589 | − | 0.168349i | ||||
\(754\) | 12.5331i | 0.456427i | ||||||||
\(755\) | −17.5616 | − | 10.1392i | −0.639133 | − | 0.369003i | ||||
\(756\) | −1.89374 | + | 3.28006i | −0.0688748 | + | 0.119295i | ||||
\(757\) | −9.03971 | − | 5.21908i | −0.328554 | − | 0.189691i | 0.326645 | − | 0.945147i | \(-0.394082\pi\) |
−0.655199 | + | 0.755456i | \(0.727415\pi\) | |||||||
\(758\) | 21.6091 | − | 12.4760i | 0.784877 | − | 0.453149i | ||||
\(759\) | −28.1245 | + | 16.2377i | −1.02085 | + | 0.589391i | ||||
\(760\) | −4.79142 | − | 2.76633i | −0.173803 | − | 0.100345i | ||||
\(761\) | −25.3188 | + | 43.8534i | −0.917805 | + | 1.58969i | −0.115064 | + | 0.993358i | \(0.536707\pi\) |
−0.802742 | + | 0.596327i | \(0.796626\pi\) | |||||||
\(762\) | 9.76689 | + | 5.63891i | 0.353817 | + | 0.204276i | ||||
\(763\) | 14.4944i | 0.524734i | ||||||||
\(764\) | 2.63146 | − | 1.51928i | 0.0952030 | − | 0.0549655i | ||||
\(765\) | −2.39374 | + | 4.14609i | −0.0865460 | + | 0.149902i | ||||
\(766\) | −9.32452 | −0.336909 | ||||||||
\(767\) | 12.1341 | 0.438139 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | − | 49.0740i | − | 1.76965i | −0.465920 | − | 0.884827i | \(-0.654276\pi\) | ||
0.465920 | − | 0.884827i | \(-0.345724\pi\) | |||||||
\(770\) | −7.27270 | − | 12.5967i | −0.262090 | − | 0.453953i | ||||
\(771\) | 12.0518i | 0.434036i | ||||||||
\(772\) | −12.4215 | + | 7.17156i | −0.447060 | + | 0.258110i | ||||
\(773\) | −16.7780 | − | 29.0604i | −0.603464 | − | 1.04523i | −0.992292 | − | 0.123920i | \(-0.960453\pi\) |
0.388828 | − | 0.921310i | \(-0.372880\pi\) | |||||||
\(774\) | −0.0198880 | − | 0.0344471i | −0.000714860 | − | 0.00123817i | ||||
\(775\) | −7.35780 | − | 4.24803i | −0.264300 | − | 0.152594i | ||||
\(776\) | 6.15065 | 0.220796 | ||||||||
\(777\) | −14.1345 | − | 18.1930i | −0.507071 | − | 0.652670i | ||||
\(778\) | 21.7615 | 0.780189 | ||||||||
\(779\) | −47.8774 | − | 27.6420i | −1.71539 | − | 0.990379i | ||||
\(780\) | −3.36212 | − | 5.82335i | −0.120383 | − | 0.208510i | ||||
\(781\) | 3.56461 | + | 6.17409i | 0.127552 | + | 0.220926i | ||||
\(782\) | −35.0605 | + | 20.2422i | −1.25376 | + | 0.723859i | ||||
\(783\) | 1.86387i | 0.0666091i | ||||||||
\(784\) | −3.67253 | − | 6.36102i | −0.131162 | − | 0.227179i | ||||
\(785\) | − | 6.79706i | − | 0.242597i | ||||||
\(786\) | 4.16159 | − | 7.20809i | 0.148439 | − | 0.257104i | ||||
\(787\) | 33.2665 | 1.18582 | 0.592912 | − | 0.805267i | \(-0.297978\pi\) | ||||
0.592912 | + | 0.805267i | \(0.297978\pi\) | |||||||
\(788\) | −0.803426 | −0.0286209 | ||||||||
\(789\) | −3.65537 | + | 6.33128i | −0.130135 | + | 0.225400i | ||||
\(790\) | −3.13047 | + | 1.80738i | −0.111377 | + | 0.0643036i | ||||
\(791\) | − | 61.7663i | − | 2.19616i | ||||||
\(792\) | 3.32587 | + | 1.92019i | 0.118180 | + | 0.0682310i | ||||
\(793\) | 44.5522 | − | 77.1667i | 1.58210 | − | 2.74027i | ||||
\(794\) | −3.73095 | − | 2.15406i | −0.132406 | − | 0.0764448i | ||||
\(795\) | 2.77776 | − | 1.60374i | 0.0985170 | − | 0.0568788i | ||||
\(796\) | 3.47986 | − | 2.00910i | 0.123340 | − | 0.0712106i | ||||
\(797\) | 25.4158 | + | 14.6738i | 0.900275 | + | 0.519774i | 0.877289 | − | 0.479962i | \(-0.159349\pi\) |
0.0229858 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(798\) | −10.4774 | + | 18.1475i | −0.370897 | + | 0.642413i | ||||
\(799\) | 4.31575 | + | 2.49170i | 0.152680 | + | 0.0881499i | ||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | −14.8116 | + | 8.55149i | −0.523343 | + | 0.302152i | ||||
\(802\) | −7.88004 | + | 13.6486i | −0.278254 | + | 0.481950i | ||||
\(803\) | 45.4482 | 1.60383 | ||||||||
\(804\) | 9.17488 | 0.323573 | ||||||||
\(805\) | −16.0140 | + | 27.7371i | −0.564421 | + | 0.977605i | ||||
\(806\) | − | 57.1294i | − | 2.01230i | ||||||
\(807\) | 7.58133 | + | 13.1312i | 0.266875 | + | 0.462242i | ||||
\(808\) | − | 8.96357i | − | 0.315337i | ||||||
\(809\) | −17.2300 | + | 9.94776i | −0.605775 | + | 0.349745i | −0.771310 | − | 0.636459i | \(-0.780398\pi\) |
0.165535 | + | 0.986204i | \(0.447065\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 12.9034 | + | 22.3493i | 0.453098 | + | 0.784789i | 0.998577 | − | 0.0533355i | \(-0.0169853\pi\) |
−0.545478 | + | 0.838125i | \(0.683652\pi\) | |||||||
\(812\) | −6.11359 | − | 3.52969i | −0.214545 | − | 0.123868i | ||||
\(813\) | 10.7924 | 0.378506 | ||||||||
\(814\) | −18.4471 | + | 14.3319i | −0.646569 | + | 0.502331i | ||||
\(815\) | −8.94207 | −0.313227 | ||||||||
\(816\) | 4.14609 | + | 2.39374i | 0.145142 | + | 0.0837978i | ||||
\(817\) | −0.110034 | − | 0.190584i | −0.00384959 | − | 0.00666768i | ||||
\(818\) | 14.5172 | + | 25.1445i | 0.507581 | + | 0.879156i | ||||
\(819\) | −22.0559 | + | 12.7340i | −0.770695 | + | 0.444961i | ||||
\(820\) | 9.99232i | 0.348947i | ||||||||
\(821\) | 1.17515 | + | 2.03542i | 0.0410129 | + | 0.0710365i | 0.885803 | − | 0.464061i | \(-0.153608\pi\) |
−0.844790 | + | 0.535098i | \(0.820275\pi\) | |||||||
\(822\) | 15.6219i | 0.544876i | ||||||||
\(823\) | 5.13012 | − | 8.88563i | 0.178825 | − | 0.309734i | −0.762653 | − | 0.646807i | \(-0.776104\pi\) |
0.941478 | + | 0.337074i | \(0.109437\pi\) | |||||||
\(824\) | 14.7060 | 0.512309 | ||||||||
\(825\) | 3.84038 | 0.133705 | ||||||||
\(826\) | −3.41734 | + | 5.91901i | −0.118904 | + | 0.205949i | ||||
\(827\) | 19.6335 | − | 11.3354i | 0.682724 | − | 0.394171i | −0.118157 | − | 0.992995i | \(-0.537699\pi\) |
0.800881 | + | 0.598824i | \(0.204365\pi\) | |||||||
\(828\) | − | 8.45628i | − | 0.293876i | ||||||
\(829\) | −13.9690 | − | 8.06501i | −0.485164 | − | 0.280109i | 0.237402 | − | 0.971411i | \(-0.423704\pi\) |
−0.722566 | + | 0.691302i | \(0.757037\pi\) | |||||||
\(830\) | 6.79367 | − | 11.7670i | 0.235812 | − | 0.408438i | ||||
\(831\) | −6.93540 | − | 4.00416i | −0.240587 | − | 0.138903i | ||||
\(832\) | −5.82335 | + | 3.36212i | −0.201888 | + | 0.116560i | ||||
\(833\) | −30.4533 | + | 17.5822i | −1.05514 | + | 0.609188i | ||||
\(834\) | 2.54301 | + | 1.46820i | 0.0880571 | + | 0.0508398i | ||||
\(835\) | 1.57160 | − | 2.72208i | 0.0543873 | − | 0.0942016i | ||||
\(836\) | 18.4009 | + | 10.6238i | 0.636409 | + | 0.367431i | ||||
\(837\) | − | 8.49606i | − | 0.293667i | ||||||
\(838\) | −24.4716 | + | 14.1287i | −0.845356 | + | 0.488066i | ||||
\(839\) | 6.02505 | − | 10.4357i | 0.208008 | − | 0.360280i | −0.743079 | − | 0.669204i | \(-0.766635\pi\) |
0.951087 | + | 0.308923i | \(0.0999687\pi\) | |||||||
\(840\) | 3.78749 | 0.130681 | ||||||||
\(841\) | 25.5260 | 0.880207 | ||||||||
\(842\) | 1.73137 | − | 2.99882i | 0.0596669 | − | 0.103346i | ||||
\(843\) | − | 25.0528i | − | 0.862864i | ||||||
\(844\) | −4.73108 | − | 8.19446i | −0.162850 | − | 0.282065i | ||||
\(845\) | − | 32.2153i | − | 1.10824i | ||||||
\(846\) | −0.901463 | + | 0.520460i | −0.0309930 | + | 0.0178938i | ||||
\(847\) | 7.09879 | + | 12.2955i | 0.243917 | + | 0.422477i | ||||
\(848\) | −1.60374 | − | 2.77776i | −0.0550727 | − | 0.0953886i | ||||
\(849\) | −3.42387 | − | 1.97677i | −0.117507 | − | 0.0678427i | ||||
\(850\) | 4.78749 | 0.164209 | ||||||||
\(851\) | 47.6395 | + | 19.3984i | 1.63306 | + | 0.664968i | ||||
\(852\) | −1.85638 | −0.0635986 | ||||||||
\(853\) | −23.5276 | − | 13.5837i | −0.805571 | − | 0.465097i | 0.0398445 | − | 0.999206i | \(-0.487314\pi\) |
−0.845415 | + | 0.534109i | \(0.820647\pi\) | |||||||
\(854\) | 25.0945 | + | 43.4649i | 0.858716 | + | 1.48734i | ||||
\(855\) | −2.76633 | − | 4.79142i | −0.0946065 | − | 0.163863i | ||||
\(856\) | 3.38721 | − | 1.95561i | 0.115773 | − | 0.0668413i | ||||
\(857\) | − | 26.7290i | − | 0.913046i | −0.889712 | − | 0.456523i | \(-0.849095\pi\) | ||
0.889712 | − | 0.456523i | \(-0.150905\pi\) | |||||||
\(858\) | 12.9118 | + | 22.3639i | 0.440802 | + | 0.763491i | ||||
\(859\) | 35.7523i | 1.21985i | 0.792458 | + | 0.609926i | \(0.208801\pi\) | ||||
−0.792458 | + | 0.609926i | \(0.791199\pi\) | |||||||
\(860\) | −0.0198880 | + | 0.0344471i | −0.000678176 | + | 0.00117463i | ||||
\(861\) | 37.8458 | 1.28978 | ||||||||
\(862\) | 1.78637 | 0.0608441 | ||||||||
\(863\) | 14.4391 | − | 25.0092i | 0.491512 | − | 0.851324i | −0.508440 | − | 0.861097i | \(-0.669778\pi\) |
0.999952 | + | 0.00977353i | \(0.00311106\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0.724057i | 0.0246187i | ||||||||
\(866\) | −29.1207 | − | 16.8128i | −0.989562 | − | 0.571324i | ||||
\(867\) | 2.96002 | − | 5.12691i | 0.100528 | − | 0.174119i | ||||
\(868\) | 27.8676 | + | 16.0894i | 0.945888 | + | 0.546108i | ||||
\(869\) | 12.0222 | − | 6.94102i | 0.407825 | − | 0.235458i | ||||
\(870\) | 1.61416 | − | 0.931933i | 0.0547250 | − | 0.0315955i | ||||
\(871\) | 53.4285 | + | 30.8470i | 1.81036 | + | 1.04521i | ||||
\(872\) | −1.91346 | + | 3.31422i | −0.0647981 | + | 0.112234i | ||||
\(873\) | 5.32662 | + | 3.07533i | 0.180279 | + | 0.104084i | ||||
\(874\) | − | 46.7857i | − | 1.58255i | ||||||
\(875\) | 3.28006 | − | 1.89374i | 0.110886 | − | 0.0640202i | ||||
\(876\) | −5.91715 | + | 10.2488i | −0.199922 | + | 0.346275i | ||||
\(877\) | 23.8280 | 0.804613 | 0.402307 | − | 0.915505i | \(-0.368209\pi\) | ||||
0.402307 | + | 0.915505i | \(0.368209\pi\) | |||||||
\(878\) | 11.7785 | 0.397506 | ||||||||
\(879\) | −6.27495 | + | 10.8685i | −0.211649 | + | 0.366586i | ||||
\(880\) | − | 3.84038i | − | 0.129459i | ||||||
\(881\) | −21.2103 | − | 36.7374i | −0.714594 | − | 1.23771i | −0.963116 | − | 0.269087i | \(-0.913278\pi\) |
0.248522 | − | 0.968626i | \(-0.420055\pi\) | |||||||
\(882\) | − | 7.34507i | − | 0.247321i | ||||||
\(883\) | 5.82032 | − | 3.36036i | 0.195869 | − | 0.113085i | −0.398858 | − | 0.917013i | \(-0.630593\pi\) |
0.594727 | + | 0.803927i | \(0.297260\pi\) | |||||||
\(884\) | 16.0961 | + | 27.8792i | 0.541370 | + | 0.937680i | ||||
\(885\) | −0.902271 | − | 1.56278i | −0.0303295 | − | 0.0525322i | ||||
\(886\) | −23.1572 | − | 13.3698i | −0.777983 | − | 0.449168i | ||||
\(887\) | 3.85496 | 0.129437 | 0.0647184 | − | 0.997904i | \(-0.479385\pi\) | ||||
0.0647184 | + | 0.997904i | \(0.479385\pi\) | |||||||
\(888\) | −0.830184 | − | 6.02584i | −0.0278591 | − | 0.202214i | ||||
\(889\) | −42.7146 | −1.43260 | ||||||||
\(890\) | 14.8116 | + | 8.55149i | 0.496487 | + | 0.286647i | ||||
\(891\) | 1.92019 | + | 3.32587i | 0.0643288 | + | 0.111421i | ||||
\(892\) | 5.92790 | + | 10.2674i | 0.198481 | + | 0.343779i | ||||
\(893\) | −4.98749 | + | 2.87953i | −0.166900 | + | 0.0963597i | ||||
\(894\) | 16.2875i | 0.544736i | ||||||||
\(895\) | −10.4782 | − | 18.1487i | −0.350247 | − | 0.606645i | ||||
\(896\) | − | 3.78749i | − | 0.126531i | ||||||
\(897\) | 28.4310 | − | 49.2439i | 0.949283 | − | 1.64421i | ||||
\(898\) | 14.0475 | 0.468771 | ||||||||
\(899\) | 15.8355 | 0.528144 | ||||||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −13.2985 | + | 7.67789i | −0.443037 | + | 0.255787i | ||||
\(902\) | − | 38.3743i | − | 1.27773i | ||||||
\(903\) | 0.130468 | + | 0.0753256i | 0.00434170 | + | 0.00250668i | ||||
\(904\) | 8.15399 | − | 14.1231i | 0.271198 | − | 0.469728i | ||||
\(905\) | −13.3852 | − | 7.72795i | −0.444939 | − | 0.256886i | ||||
\(906\) | −17.5616 | + | 10.1392i | −0.583446 | + | 0.336852i | ||||
\(907\) | −16.1579 | + | 9.32878i | −0.536515 | + | 0.309757i | −0.743665 | − | 0.668552i | \(-0.766914\pi\) |
0.207150 | + | 0.978309i | \(0.433581\pi\) | |||||||
\(908\) | 10.7982 | + | 6.23432i | 0.358350 | + | 0.206893i | ||||
\(909\) | 4.48179 | − | 7.76268i | 0.148651 | − | 0.257472i | ||||
\(910\) | 22.0559 | + | 12.7340i | 0.731146 | + | 0.422127i | ||||
\(911\) | 6.79087i | 0.224992i | 0.993652 | + | 0.112496i | \(0.0358845\pi\) | ||||
−0.993652 | + | 0.112496i | \(0.964116\pi\) | |||||||
\(912\) | −4.79142 | + | 2.76633i | −0.158660 | + | 0.0916023i | ||||
\(913\) | −26.0903 | + | 45.1897i | −0.863463 | + | 1.49556i | ||||
\(914\) | 12.1563 | 0.402095 | ||||||||
\(915\) | −13.2513 | −0.438073 | ||||||||
\(916\) | 5.00593 | − | 8.67053i | 0.165401 | − | 0.286482i | ||||
\(917\) | 31.5240i | 1.04101i | ||||||||
\(918\) | 2.39374 | + | 4.14609i | 0.0790053 | + | 0.136841i | ||||
\(919\) | − | 15.0052i | − | 0.494976i | −0.968891 | − | 0.247488i | \(-0.920395\pi\) | ||
0.968891 | − | 0.247488i | \(-0.0796051\pi\) | |||||||
\(920\) | −7.32335 | + | 4.22814i | −0.241444 | + | 0.139398i | ||||
\(921\) | 1.17647 | + | 2.03770i | 0.0387660 | + | 0.0671446i | ||||
\(922\) | 16.5359 | + | 28.6410i | 0.544581 | + | 0.943242i | ||||
\(923\) | −10.8104 | − | 6.24137i | −0.355828 | − | 0.205437i | ||||
\(924\) | −14.5454 | −0.478509 | ||||||||
\(925\) | −3.73188 | − | 4.80344i | −0.122704 | − | 0.157936i | ||||
\(926\) | 37.9533 | 1.24722 | ||||||||
\(927\) | 12.7358 | + | 7.35302i | 0.418298 | + | 0.241505i | ||||
\(928\) | −0.931933 | − | 1.61416i | −0.0305922 | − | 0.0529872i | ||||
\(929\) | −4.02128 | − | 6.96506i | −0.131934 | − | 0.228516i | 0.792488 | − | 0.609887i | \(-0.208785\pi\) |
−0.924422 | + | 0.381371i | \(0.875452\pi\) | |||||||
\(930\) | −7.35780 | + | 4.24803i | −0.241272 | + | 0.139298i | ||||
\(931\) | − | 40.6378i | − | 1.33185i | ||||||
\(932\) | 4.95553 | + | 8.58323i | 0.162324 | + | 0.281153i | ||||
\(933\) | 22.6192i | 0.740519i | ||||||||
\(934\) | 6.53167 | − | 11.3132i | 0.213723 | − | 0.370179i | ||||
\(935\) | −18.3858 | −0.601280 | ||||||||
\(936\) | −6.72423 | −0.219788 | ||||||||
\(937\) | −11.6870 | + | 20.2425i | −0.381799 | + | 0.661295i | −0.991319 | − | 0.131475i | \(-0.958029\pi\) |
0.609521 | + | 0.792770i | \(0.291362\pi\) | |||||||
\(938\) | −30.0942 | + | 17.3749i | −0.982609 | + | 0.567310i | ||||
\(939\) | − | 15.5944i | − | 0.508903i | ||||||
\(940\) | 0.901463 | + | 0.520460i | 0.0294025 | + | 0.0169755i | ||||
\(941\) | −8.10702 | + | 14.0418i | −0.264281 | + | 0.457749i | −0.967375 | − | 0.253348i | \(-0.918468\pi\) |
0.703094 | + | 0.711097i | \(0.251801\pi\) | |||||||
\(942\) | −5.88642 | − | 3.39853i | −0.191790 | − | 0.110730i | ||||
\(943\) | −73.1773 | + | 42.2489i | −2.38298 | + | 1.37581i | ||||
\(944\) | −1.56278 | + | 0.902271i | −0.0508641 | + | 0.0293664i | ||||
\(945\) | 3.28006 | + | 1.89374i | 0.106700 | + | 0.0616035i | ||||
\(946\) | 0.0763776 | − | 0.132290i | 0.00248325 | − | 0.00430112i | ||||
\(947\) | 13.9750 | + | 8.06844i | 0.454125 | + | 0.262189i | 0.709571 | − | 0.704634i | \(-0.248889\pi\) |
−0.255446 | + | 0.966823i | \(0.582222\pi\) | |||||||
\(948\) | 3.61475i | 0.117402i | ||||||||
\(949\) | −68.9153 | + | 39.7883i | −2.23709 | + | 1.29158i | ||||
\(950\) | −2.76633 | + | 4.79142i | −0.0897516 | + | 0.155454i | ||||
\(951\) | −24.6297 | −0.798673 | ||||||||
\(952\) | −18.1326 | −0.587680 | ||||||||
\(953\) | 5.18120 | − | 8.97411i | 0.167836 | − | 0.290700i | −0.769823 | − | 0.638257i | \(-0.779656\pi\) |
0.937659 | + | 0.347558i | \(0.112989\pi\) | |||||||
\(954\) | − | 3.20748i | − | 0.103846i | ||||||
\(955\) | −1.51928 | − | 2.63146i | −0.0491626 | − | 0.0851521i | ||||
\(956\) | − | 15.6263i | − | 0.505390i | ||||||
\(957\) | −6.19898 | + | 3.57898i | −0.200384 | + | 0.115692i | ||||
\(958\) | −2.05209 | − | 3.55432i | −0.0663000 | − | 0.114835i | ||||
\(959\) | −29.5839 | − | 51.2408i | −0.955313 | − | 1.65465i | ||||
\(960\) | 0.866025 | + | 0.500000i | 0.0279508 | + | 0.0161374i | ||||
\(961\) | −41.1830 | −1.32848 | ||||||||
\(962\) | 15.4251 | − | 37.8818i | 0.497326 | − | 1.22136i | ||||
\(963\) | 3.91122 | 0.126037 | ||||||||
\(964\) | −11.0815 | − | 6.39792i | −0.356912 | − | 0.206063i | ||||
\(965\) | 7.17156 | + | 12.4215i | 0.230861 | + | 0.399862i | ||||
\(966\) | 16.0140 | + | 27.7371i | 0.515243 | + | 0.892427i | ||||
\(967\) | −16.2667 | + | 9.39158i | −0.523102 | + | 0.302013i | −0.738203 | − | 0.674579i | \(-0.764325\pi\) |
0.215101 | + | 0.976592i | \(0.430992\pi\) | |||||||
\(968\) | 3.74855i | 0.120483i | ||||||||
\(969\) | 13.2438 | + | 22.9389i | 0.425451 | + | 0.736903i | ||||
\(970\) | − | 6.15065i | − | 0.197486i | ||||||
\(971\) | 1.43963 | − | 2.49352i | 0.0462000 | − | 0.0800207i | −0.842001 | − | 0.539476i | \(-0.818622\pi\) |
0.888201 | + | 0.459456i | \(0.151956\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −11.1216 | −0.356543 | ||||||||
\(974\) | −16.0765 | + | 27.8454i | −0.515125 | + | 0.892223i | ||||
\(975\) | −5.82335 | + | 3.36212i | −0.186497 | + | 0.107674i | ||||
\(976\) | 13.2513i | 0.424162i | ||||||||
\(977\) | 14.3874 | + | 8.30659i | 0.460295 | + | 0.265751i | 0.712168 | − | 0.702009i | \(-0.247713\pi\) |
−0.251873 | + | 0.967760i | \(0.581047\pi\) | |||||||
\(978\) | −4.47104 | + | 7.74406i | −0.142968 | + | 0.247628i | ||||
\(979\) | −56.8823 | − | 32.8410i | −1.81797 | − | 1.04960i | ||||
\(980\) | −6.36102 | + | 3.67253i | −0.203195 | + | 0.117315i | ||||
\(981\) | −3.31422 | + | 1.91346i | −0.105815 | + | 0.0610922i | ||||
\(982\) | 27.1272 | + | 15.6619i | 0.865664 | + | 0.499791i | ||||
\(983\) | −15.1275 | + | 26.2015i | −0.482491 | + | 0.835699i | −0.999798 | − | 0.0201012i | \(-0.993601\pi\) |
0.517307 | + | 0.855800i | \(0.326934\pi\) | |||||||
\(984\) | 8.65360 | + | 4.99616i | 0.275867 | + | 0.159272i | ||||
\(985\) | 0.803426i | 0.0255993i | ||||||||
\(986\) | −7.72775 | + | 4.46162i | −0.246102 | + | 0.142087i | ||||
\(987\) | 1.97124 | − | 3.41428i | 0.0627452 | − | 0.108678i | ||||
\(988\) | −37.2029 | −1.18358 | ||||||||
\(989\) | −0.336357 | −0.0106955 | ||||||||
\(990\) | 1.92019 | − | 3.32587i | 0.0610277 | − | 0.105703i | ||||
\(991\) | 61.6071i | 1.95701i | 0.206214 | + | 0.978507i | \(0.433886\pi\) | ||||
−0.206214 | + | 0.978507i | \(0.566114\pi\) | |||||||
\(992\) | 4.24803 | + | 7.35780i | 0.134875 | + | 0.233610i | ||||
\(993\) | − | 8.54041i | − | 0.271022i | ||||||
\(994\) | 6.08905 | − | 3.51551i | 0.193133 | − | 0.111505i | ||||
\(995\) | −2.00910 | − | 3.47986i | −0.0636927 | − | 0.110319i | ||||
\(996\) | −6.79367 | − | 11.7670i | −0.215266 | − | 0.372851i | ||||
\(997\) | −28.7258 | − | 16.5848i | −0.909755 | − | 0.525247i | −0.0294024 | − | 0.999568i | \(-0.509360\pi\) |
−0.880352 | + | 0.474321i | \(0.842694\pi\) | |||||||
\(998\) | −28.6959 | −0.908353 | ||||||||
\(999\) | 2.29396 | − | 5.63363i | 0.0725777 | − | 0.178240i |
(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 | 1110.2.x.d.841.8 | yes | 16 | |
37.11 | even | 6 | inner | 1110.2.x.d.751.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.x.d.751.8 | ✓ | 16 | 37.11 | even | 6 | inner | |
1110.2.x.d.841.8 | yes | 16 | 1.1 | even | 1 | trivial |