Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
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 | 161.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.c.491.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.866025 | − | 1.50000i | −0.500000 | − | 0.866025i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 2.59808 | − | 4.50000i | 0.783349 | − | 1.35680i | −0.146631 | − | 0.989191i | \(-0.546843\pi\) |
0.929980 | − | 0.367610i | \(-0.119824\pi\) | |||||||
\(12\) | 0.866025 | + | 1.50000i | 0.250000 | + | 0.433013i | ||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | −0.866025 | + | 0.500000i | −0.231455 | + | 0.133631i | ||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.73205 | + | 3.00000i | 0.420084 | + | 0.727607i | 0.995947 | − | 0.0899392i | \(-0.0286673\pi\) |
−0.575863 | + | 0.817546i | \(0.695334\pi\) | |||||||
\(18\) | −2.59808 | − | 1.50000i | −0.612372 | − | 0.353553i | ||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 0.866025 | − | 1.50000i | 0.188982 | − | 0.327327i | ||||
\(22\) | 4.50000 | + | 2.59808i | 0.959403 | + | 0.553912i | ||||
\(23\) | 6.92820 | 1.44463 | 0.722315 | − | 0.691564i | \(-0.243078\pi\) | ||||
0.722315 | + | 0.691564i | \(0.243078\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.73205 | − | 3.00000i | 0.339683 | − | 0.588348i | ||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 1.73205 | 0.316228 | ||||||||
\(31\) | −5.50000 | + | 0.866025i | −0.987829 | + | 0.155543i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −9.00000 | −1.56670 | ||||||||
\(34\) | −3.00000 | + | 1.73205i | −0.514496 | + | 0.297044i | ||||
\(35\) | 1.00000i | 0.169031i | ||||||||
\(36\) | 1.50000 | − | 2.59808i | 0.250000 | − | 0.433013i | ||||
\(37\) | 6.00000 | − | 3.46410i | 0.986394 | − | 0.569495i | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 3.46410 | − | 2.00000i | 0.561951 | − | 0.324443i | ||||
\(39\) | 6.00000i | 0.960769i | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −5.19615 | − | 3.00000i | −0.811503 | − | 0.468521i | 0.0359748 | − | 0.999353i | \(-0.488546\pi\) |
−0.847477 | + | 0.530831i | \(0.821880\pi\) | |||||||
\(42\) | 1.50000 | + | 0.866025i | 0.231455 | + | 0.133631i | ||||
\(43\) | 3.00000 | − | 1.73205i | 0.457496 | − | 0.264135i | −0.253495 | − | 0.967337i | \(-0.581580\pi\) |
0.710991 | + | 0.703201i | \(0.248247\pi\) | |||||||
\(44\) | −2.59808 | + | 4.50000i | −0.391675 | + | 0.678401i | ||||
\(45\) | −2.59808 | + | 1.50000i | −0.387298 | + | 0.223607i | ||||
\(46\) | 6.92820i | 1.02151i | ||||||||
\(47\) | − | 12.0000i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(48\) | −0.866025 | − | 1.50000i | −0.125000 | − | 0.216506i | ||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | 6.06218 | − | 10.5000i | 0.832704 | − | 1.44229i | −0.0631819 | − | 0.998002i | \(-0.520125\pi\) |
0.895886 | − | 0.444284i | \(-0.146542\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 4.50000 | − | 2.59808i | 0.606780 | − | 0.350325i | ||||
\(56\) | 0.866025 | − | 0.500000i | 0.115728 | − | 0.0668153i | ||||
\(57\) | −3.46410 | + | 6.00000i | −0.458831 | + | 0.794719i | ||||
\(58\) | − | 1.73205i | − | 0.227429i | ||||||
\(59\) | 12.9904 | − | 7.50000i | 1.69120 | − | 0.976417i | 0.737655 | − | 0.675178i | \(-0.235933\pi\) |
0.953549 | − | 0.301239i | \(-0.0974001\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | −0.866025 | − | 5.50000i | −0.109985 | − | 0.698501i | ||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.73205 | − | 3.00000i | −0.214834 | − | 0.372104i | ||||
\(66\) | − | 9.00000i | − | 1.10782i | ||||||
\(67\) | 1.00000 | − | 1.73205i | 0.122169 | − | 0.211604i | −0.798454 | − | 0.602056i | \(-0.794348\pi\) |
0.920623 | + | 0.390453i | \(0.127682\pi\) | |||||||
\(68\) | −1.73205 | − | 3.00000i | −0.210042 | − | 0.363803i | ||||
\(69\) | −6.00000 | − | 10.3923i | −0.722315 | − | 1.25109i | ||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 10.3923 | + | 6.00000i | 1.23334 | + | 0.712069i | 0.967725 | − | 0.252010i | \(-0.0810916\pi\) |
0.265615 | + | 0.964079i | \(0.414425\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 6.00000 | + | 3.46410i | 0.702247 | + | 0.405442i | 0.808184 | − | 0.588930i | \(-0.200451\pi\) |
−0.105937 | + | 0.994373i | \(0.533784\pi\) | |||||||
\(74\) | 3.46410 | + | 6.00000i | 0.402694 | + | 0.697486i | ||||
\(75\) | 0.866025 | − | 1.50000i | 0.100000 | − | 0.173205i | ||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | 5.19615 | 0.592157 | ||||||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | −9.00000 | + | 5.19615i | −1.01258 | + | 0.584613i | −0.911946 | − | 0.410311i | \(-0.865420\pi\) |
−0.100633 | + | 0.994924i | \(0.532087\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −2.59808 | + | 4.50000i | −0.285176 | + | 0.493939i | −0.972652 | − | 0.232268i | \(-0.925385\pi\) |
0.687476 | + | 0.726207i | \(0.258719\pi\) | |||||||
\(84\) | −0.866025 | + | 1.50000i | −0.0944911 | + | 0.163663i | ||||
\(85\) | 3.46410i | 0.375735i | ||||||||
\(86\) | 1.73205 | + | 3.00000i | 0.186772 | + | 0.323498i | ||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | −4.50000 | − | 2.59808i | −0.479702 | − | 0.276956i | ||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | −1.50000 | − | 2.59808i | −0.158114 | − | 0.273861i | ||||
\(91\) | − | 3.46410i | − | 0.363137i | ||||||
\(92\) | −6.92820 | −0.722315 | ||||||||
\(93\) | 6.06218 | + | 7.50000i | 0.628619 | + | 0.777714i | ||||
\(94\) | 12.0000 | 1.23771 | ||||||||
\(95\) | − | 4.00000i | − | 0.410391i | ||||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 5.19615 | + | 3.00000i | 0.524891 | + | 0.303046i | ||||
\(99\) | 7.79423 | + | 13.5000i | 0.783349 | + | 1.35680i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | − | 15.0000i | − | 1.49256i | −0.665635 | − | 0.746278i | \(-0.731839\pi\) | ||
0.665635 | − | 0.746278i | \(-0.268161\pi\) | |||||||
\(102\) | 5.19615 | + | 3.00000i | 0.514496 | + | 0.297044i | ||||
\(103\) | −3.50000 | + | 6.06218i | −0.344865 | + | 0.597324i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | −1.73205 | + | 3.00000i | −0.169842 | + | 0.294174i | ||||
\(105\) | 1.50000 | − | 0.866025i | 0.146385 | − | 0.0845154i | ||||
\(106\) | 10.5000 | + | 6.06218i | 1.01985 | + | 0.588811i | ||||
\(107\) | −2.59808 | + | 1.50000i | −0.251166 | + | 0.145010i | −0.620298 | − | 0.784366i | \(-0.712988\pi\) |
0.369132 | + | 0.929377i | \(0.379655\pi\) | |||||||
\(108\) | −5.19615 | −0.500000 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 2.59808 | + | 4.50000i | 0.247717 | + | 0.429058i | ||||
\(111\) | −10.3923 | − | 6.00000i | −0.986394 | − | 0.569495i | ||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | −6.00000 | − | 3.46410i | −0.561951 | − | 0.324443i | ||||
\(115\) | 6.00000 | + | 3.46410i | 0.559503 | + | 0.323029i | ||||
\(116\) | 1.73205 | 0.160817 | ||||||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | 7.50000 | + | 12.9904i | 0.690431 | + | 1.19586i | ||||
\(119\) | −1.73205 | + | 3.00000i | −0.158777 | + | 0.275010i | ||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | −8.00000 | − | 13.8564i | −0.727273 | − | 1.25967i | ||||
\(122\) | −3.46410 | −0.313625 | ||||||||
\(123\) | 10.3923i | 0.937043i | ||||||||
\(124\) | 5.50000 | − | 0.866025i | 0.493915 | − | 0.0777714i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | − | 3.00000i | − | 0.267261i | ||||||
\(127\) | 10.5000 | − | 6.06218i | 0.931724 | − | 0.537931i | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) |
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −5.19615 | − | 3.00000i | −0.457496 | − | 0.264135i | ||||
\(130\) | 3.00000 | − | 1.73205i | 0.263117 | − | 0.151911i | ||||
\(131\) | −10.3923 | + | 6.00000i | −0.907980 | + | 0.524222i | −0.879781 | − | 0.475380i | \(-0.842311\pi\) |
−0.0281993 | + | 0.999602i | \(0.508977\pi\) | |||||||
\(132\) | 9.00000 | 0.783349 | ||||||||
\(133\) | 2.00000 | − | 3.46410i | 0.173422 | − | 0.300376i | ||||
\(134\) | 1.73205 | + | 1.00000i | 0.149626 | + | 0.0863868i | ||||
\(135\) | 4.50000 | + | 2.59808i | 0.387298 | + | 0.223607i | ||||
\(136\) | 3.00000 | − | 1.73205i | 0.257248 | − | 0.148522i | ||||
\(137\) | −6.92820 | + | 12.0000i | −0.591916 | + | 1.02523i | 0.402058 | + | 0.915614i | \(0.368295\pi\) |
−0.993974 | + | 0.109615i | \(0.965038\pi\) | |||||||
\(138\) | 10.3923 | − | 6.00000i | 0.884652 | − | 0.510754i | ||||
\(139\) | 20.7846i | 1.76293i | 0.472252 | + | 0.881464i | \(0.343441\pi\) | ||||
−0.472252 | + | 0.881464i | \(0.656559\pi\) | |||||||
\(140\) | − | 1.00000i | − | 0.0845154i | ||||||
\(141\) | −18.0000 | + | 10.3923i | −1.51587 | + | 0.875190i | ||||
\(142\) | −6.00000 | + | 10.3923i | −0.503509 | + | 0.872103i | ||||
\(143\) | −15.5885 | + | 9.00000i | −1.30357 | + | 0.752618i | ||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | −1.50000 | − | 0.866025i | −0.124568 | − | 0.0719195i | ||||
\(146\) | −3.46410 | + | 6.00000i | −0.286691 | + | 0.496564i | ||||
\(147\) | −10.3923 | −0.857143 | ||||||||
\(148\) | −6.00000 | + | 3.46410i | −0.493197 | + | 0.284747i | ||||
\(149\) | −12.9904 | + | 7.50000i | −1.06421 | + | 0.614424i | −0.926595 | − | 0.376061i | \(-0.877278\pi\) |
−0.137619 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(150\) | 1.50000 | + | 0.866025i | 0.122474 | + | 0.0707107i | ||||
\(151\) | 8.66025i | 0.704761i | 0.935857 | + | 0.352381i | \(0.114628\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | −3.46410 | + | 2.00000i | −0.280976 | + | 0.162221i | ||||
\(153\) | −10.3923 | −0.840168 | ||||||||
\(154\) | 5.19615i | 0.418718i | ||||||||
\(155\) | −5.19615 | − | 2.00000i | −0.417365 | − | 0.160644i | ||||
\(156\) | − | 6.00000i | − | 0.480384i | ||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | −5.19615 | − | 9.00000i | −0.413384 | − | 0.716002i | ||||
\(159\) | −21.0000 | −1.66541 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 3.46410 | + | 6.00000i | 0.273009 | + | 0.472866i | ||||
\(162\) | 7.79423 | − | 4.50000i | 0.612372 | − | 0.353553i | ||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 5.19615 | + | 3.00000i | 0.405751 | + | 0.234261i | ||||
\(165\) | −7.79423 | − | 4.50000i | −0.606780 | − | 0.350325i | ||||
\(166\) | −4.50000 | − | 2.59808i | −0.349268 | − | 0.201650i | ||||
\(167\) | 5.19615 | + | 9.00000i | 0.402090 | + | 0.696441i | 0.993978 | − | 0.109580i | \(-0.0349504\pi\) |
−0.591888 | + | 0.806020i | \(0.701617\pi\) | |||||||
\(168\) | −1.50000 | − | 0.866025i | −0.115728 | − | 0.0668153i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | −3.46410 | −0.265684 | ||||||||
\(171\) | 12.0000 | 0.917663 | ||||||||
\(172\) | −3.00000 | + | 1.73205i | −0.228748 | + | 0.132068i | ||||
\(173\) | 2.59808 | + | 1.50000i | 0.197528 | + | 0.114043i | 0.595502 | − | 0.803354i | \(-0.296953\pi\) |
−0.397974 | + | 0.917397i | \(0.630287\pi\) | |||||||
\(174\) | −2.59808 | + | 1.50000i | −0.196960 | + | 0.113715i | ||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 2.59808 | − | 4.50000i | 0.195837 | − | 0.339200i | ||||
\(177\) | −22.5000 | − | 12.9904i | −1.69120 | − | 0.976417i | ||||
\(178\) | − | 10.3923i | − | 0.778936i | ||||||
\(179\) | −7.79423 | − | 13.5000i | −0.582568 | − | 1.00904i | −0.995174 | − | 0.0981277i | \(-0.968715\pi\) |
0.412606 | − | 0.910910i | \(-0.364619\pi\) | |||||||
\(180\) | 2.59808 | − | 1.50000i | 0.193649 | − | 0.111803i | ||||
\(181\) | 3.00000 | + | 1.73205i | 0.222988 | + | 0.128742i | 0.607333 | − | 0.794447i | \(-0.292239\pi\) |
−0.384345 | + | 0.923190i | \(0.625573\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | 5.19615 | − | 3.00000i | 0.384111 | − | 0.221766i | ||||
\(184\) | − | 6.92820i | − | 0.510754i | ||||||
\(185\) | 6.92820 | 0.509372 | ||||||||
\(186\) | −7.50000 | + | 6.06218i | −0.549927 | + | 0.444500i | ||||
\(187\) | 18.0000 | 1.31629 | ||||||||
\(188\) | 12.0000i | 0.875190i | ||||||||
\(189\) | 2.59808 | + | 4.50000i | 0.188982 | + | 0.327327i | ||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 10.3923 | + | 6.00000i | 0.751961 | + | 0.434145i | 0.826402 | − | 0.563081i | \(-0.190384\pi\) |
−0.0744412 | + | 0.997225i | \(0.523717\pi\) | |||||||
\(192\) | 0.866025 | + | 1.50000i | 0.0625000 | + | 0.108253i | ||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | − | 1.00000i | − | 0.0717958i | ||||||
\(195\) | −3.00000 | + | 5.19615i | −0.214834 | + | 0.372104i | ||||
\(196\) | −3.00000 | + | 5.19615i | −0.214286 | + | 0.371154i | ||||
\(197\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(198\) | −13.5000 | + | 7.79423i | −0.959403 | + | 0.553912i | ||||
\(199\) | −10.5000 | − | 6.06218i | −0.744325 | − | 0.429736i | 0.0793146 | − | 0.996850i | \(-0.474727\pi\) |
−0.823640 | + | 0.567113i | \(0.808060\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | −3.46410 | −0.244339 | ||||||||
\(202\) | 15.0000 | 1.05540 | ||||||||
\(203\) | −0.866025 | − | 1.50000i | −0.0607831 | − | 0.105279i | ||||
\(204\) | −3.00000 | + | 5.19615i | −0.210042 | + | 0.363803i | ||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −6.06218 | − | 3.50000i | −0.422372 | − | 0.243857i | ||||
\(207\) | −10.3923 | + | 18.0000i | −0.722315 | + | 1.25109i | ||||
\(208\) | −3.00000 | − | 1.73205i | −0.208013 | − | 0.120096i | ||||
\(209\) | −20.7846 | −1.43770 | ||||||||
\(210\) | 0.866025 | + | 1.50000i | 0.0597614 | + | 0.103510i | ||||
\(211\) | 5.00000 | + | 8.66025i | 0.344214 | + | 0.596196i | 0.985211 | − | 0.171347i | \(-0.0548120\pi\) |
−0.640996 | + | 0.767544i | \(0.721479\pi\) | |||||||
\(212\) | −6.06218 | + | 10.5000i | −0.416352 | + | 0.721143i | ||||
\(213\) | − | 20.7846i | − | 1.42414i | ||||||
\(214\) | −1.50000 | − | 2.59808i | −0.102538 | − | 0.177601i | ||||
\(215\) | 3.46410 | 0.236250 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | −3.50000 | − | 4.33013i | −0.237595 | − | 0.293948i | ||||
\(218\) | − | 4.00000i | − | 0.270914i | ||||||
\(219\) | − | 12.0000i | − | 0.810885i | ||||||
\(220\) | −4.50000 | + | 2.59808i | −0.303390 | + | 0.175162i | ||||
\(221\) | − | 12.0000i | − | 0.807207i | ||||||
\(222\) | 6.00000 | − | 10.3923i | 0.402694 | − | 0.697486i | ||||
\(223\) | 13.5000 | − | 7.79423i | 0.904027 | − | 0.521940i | 0.0255224 | − | 0.999674i | \(-0.491875\pi\) |
0.878504 | + | 0.477734i | \(0.158542\pi\) | |||||||
\(224\) | −0.866025 | + | 0.500000i | −0.0578638 | + | 0.0334077i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9904 | + | 7.50000i | 0.862202 | + | 0.497792i | 0.864749 | − | 0.502204i | \(-0.167477\pi\) |
−0.00254715 | + | 0.999997i | \(0.500811\pi\) | |||||||
\(228\) | 3.46410 | − | 6.00000i | 0.229416 | − | 0.397360i | ||||
\(229\) | −24.0000 | + | 13.8564i | −1.58596 | + | 0.915657i | −0.592002 | + | 0.805936i | \(0.701662\pi\) |
−0.993962 | + | 0.109721i | \(0.965004\pi\) | |||||||
\(230\) | −3.46410 | + | 6.00000i | −0.228416 | + | 0.395628i | ||||
\(231\) | −4.50000 | − | 7.79423i | −0.296078 | − | 0.512823i | ||||
\(232\) | 1.73205i | 0.113715i | ||||||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | 5.19615 | + | 9.00000i | 0.339683 | + | 0.588348i | ||||
\(235\) | 6.00000 | − | 10.3923i | 0.391397 | − | 0.677919i | ||||
\(236\) | −12.9904 | + | 7.50000i | −0.845602 | + | 0.488208i | ||||
\(237\) | 15.5885 | + | 9.00000i | 1.01258 | + | 0.584613i | ||||
\(238\) | −3.00000 | − | 1.73205i | −0.194461 | − | 0.112272i | ||||
\(239\) | 13.8564 | − | 24.0000i | 0.896296 | − | 1.55243i | 0.0641045 | − | 0.997943i | \(-0.479581\pi\) |
0.832192 | − | 0.554488i | \(-0.187086\pi\) | |||||||
\(240\) | − | 1.73205i | − | 0.111803i | ||||||
\(241\) | −13.5000 | + | 7.79423i | −0.869611 | + | 0.502070i | −0.867219 | − | 0.497927i | \(-0.834095\pi\) |
−0.00239235 | + | 0.999997i | \(0.500762\pi\) | |||||||
\(242\) | 13.8564 | − | 8.00000i | 0.890724 | − | 0.514259i | ||||
\(243\) | −7.79423 | + | 13.5000i | −0.500000 | + | 0.866025i | ||||
\(244\) | − | 3.46410i | − | 0.221766i | ||||||
\(245\) | 5.19615 | − | 3.00000i | 0.331970 | − | 0.191663i | ||||
\(246\) | −10.3923 | −0.662589 | ||||||||
\(247\) | 13.8564i | 0.881662i | ||||||||
\(248\) | 0.866025 | + | 5.50000i | 0.0549927 | + | 0.349250i | ||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 5.19615 | + | 9.00000i | 0.327978 | + | 0.568075i | 0.982111 | − | 0.188305i | \(-0.0602994\pi\) |
−0.654132 | + | 0.756380i | \(0.726966\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | 18.0000 | − | 31.1769i | 1.13165 | − | 1.96008i | ||||
\(254\) | 6.06218 | + | 10.5000i | 0.380375 | + | 0.658829i | ||||
\(255\) | 5.19615 | − | 3.00000i | 0.325396 | − | 0.187867i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.7846 | − | 12.0000i | −1.29651 | − | 0.748539i | −0.316709 | − | 0.948523i | \(-0.602578\pi\) |
−0.979799 | + | 0.199983i | \(0.935911\pi\) | |||||||
\(258\) | 3.00000 | − | 5.19615i | 0.186772 | − | 0.323498i | ||||
\(259\) | 6.00000 | + | 3.46410i | 0.372822 | + | 0.215249i | ||||
\(260\) | 1.73205 | + | 3.00000i | 0.107417 | + | 0.186052i | ||||
\(261\) | 2.59808 | − | 4.50000i | 0.160817 | − | 0.278543i | ||||
\(262\) | −6.00000 | − | 10.3923i | −0.370681 | − | 0.642039i | ||||
\(263\) | −3.46410 | −0.213606 | −0.106803 | − | 0.994280i | \(-0.534061\pi\) | ||||
−0.106803 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(264\) | 9.00000i | 0.553912i | ||||||||
\(265\) | 10.5000 | − | 6.06218i | 0.645010 | − | 0.372397i | ||||
\(266\) | 3.46410 | + | 2.00000i | 0.212398 | + | 0.122628i | ||||
\(267\) | 9.00000 | + | 15.5885i | 0.550791 | + | 0.953998i | ||||
\(268\) | −1.00000 | + | 1.73205i | −0.0610847 | + | 0.105802i | ||||
\(269\) | 13.8564 | − | 24.0000i | 0.844840 | − | 1.46331i | −0.0409201 | − | 0.999162i | \(-0.513029\pi\) |
0.885760 | − | 0.464143i | \(-0.153638\pi\) | |||||||
\(270\) | −2.59808 | + | 4.50000i | −0.158114 | + | 0.273861i | ||||
\(271\) | − | 12.1244i | − | 0.736502i | −0.929726 | − | 0.368251i | \(-0.879957\pi\) | ||
0.929726 | − | 0.368251i | \(-0.120043\pi\) | |||||||
\(272\) | 1.73205 | + | 3.00000i | 0.105021 | + | 0.181902i | ||||
\(273\) | −5.19615 | + | 3.00000i | −0.314485 | + | 0.181568i | ||||
\(274\) | −12.0000 | − | 6.92820i | −0.724947 | − | 0.418548i | ||||
\(275\) | 5.19615 | 0.313340 | ||||||||
\(276\) | 6.00000 | + | 10.3923i | 0.361158 | + | 0.625543i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | −20.7846 | −1.24658 | ||||||||
\(279\) | 6.00000 | − | 15.5885i | 0.359211 | − | 0.933257i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 12.0000i | 0.715860i | 0.933748 | + | 0.357930i | \(0.116517\pi\) | ||||
−0.933748 | + | 0.357930i | \(0.883483\pi\) | |||||||
\(282\) | −10.3923 | − | 18.0000i | −0.618853 | − | 1.07188i | ||||
\(283\) | −22.0000 | −1.30776 | −0.653882 | − | 0.756596i | \(-0.726861\pi\) | ||||
−0.653882 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(284\) | −10.3923 | − | 6.00000i | −0.616670 | − | 0.356034i | ||||
\(285\) | −6.00000 | + | 3.46410i | −0.355409 | + | 0.205196i | ||||
\(286\) | −9.00000 | − | 15.5885i | −0.532181 | − | 0.921765i | ||||
\(287\) | − | 6.00000i | − | 0.354169i | ||||||
\(288\) | −2.59808 | − | 1.50000i | −0.153093 | − | 0.0883883i | ||||
\(289\) | 2.50000 | − | 4.33013i | 0.147059 | − | 0.254713i | ||||
\(290\) | 0.866025 | − | 1.50000i | 0.0508548 | − | 0.0880830i | ||||
\(291\) | 0.866025 | + | 1.50000i | 0.0507673 | + | 0.0879316i | ||||
\(292\) | −6.00000 | − | 3.46410i | −0.351123 | − | 0.202721i | ||||
\(293\) | −7.79423 | + | 4.50000i | −0.455344 | + | 0.262893i | −0.710084 | − | 0.704117i | \(-0.751343\pi\) |
0.254741 | + | 0.967009i | \(0.418010\pi\) | |||||||
\(294\) | − | 10.3923i | − | 0.606092i | ||||||
\(295\) | 15.0000 | 0.873334 | ||||||||
\(296\) | −3.46410 | − | 6.00000i | −0.201347 | − | 0.348743i | ||||
\(297\) | 13.5000 | − | 23.3827i | 0.783349 | − | 1.35680i | ||||
\(298\) | −7.50000 | − | 12.9904i | −0.434463 | − | 0.752513i | ||||
\(299\) | −20.7846 | − | 12.0000i | −1.20201 | − | 0.693978i | ||||
\(300\) | −0.866025 | + | 1.50000i | −0.0500000 | + | 0.0866025i | ||||
\(301\) | 3.00000 | + | 1.73205i | 0.172917 | + | 0.0998337i | ||||
\(302\) | −8.66025 | −0.498342 | ||||||||
\(303\) | −22.5000 | + | 12.9904i | −1.29259 | + | 0.746278i | ||||
\(304\) | −2.00000 | − | 3.46410i | −0.114708 | − | 0.198680i | ||||
\(305\) | −1.73205 | + | 3.00000i | −0.0991769 | + | 0.171780i | ||||
\(306\) | − | 10.3923i | − | 0.594089i | ||||||
\(307\) | 7.00000 | + | 12.1244i | 0.399511 | + | 0.691974i | 0.993666 | − | 0.112377i | \(-0.0358466\pi\) |
−0.594154 | + | 0.804351i | \(0.702513\pi\) | |||||||
\(308\) | −5.19615 | −0.296078 | ||||||||
\(309\) | 12.1244 | 0.689730 | ||||||||
\(310\) | 2.00000 | − | 5.19615i | 0.113592 | − | 0.295122i | ||||
\(311\) | 30.0000i | 1.70114i | 0.525859 | + | 0.850572i | \(0.323744\pi\) | ||||
−0.525859 | + | 0.850572i | \(0.676256\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | −22.5000 | + | 12.9904i | −1.27178 | + | 0.734260i | −0.975322 | − | 0.220788i | \(-0.929137\pi\) |
−0.296453 | + | 0.955047i | \(0.595804\pi\) | |||||||
\(314\) | 10.0000i | 0.564333i | ||||||||
\(315\) | −2.59808 | − | 1.50000i | −0.146385 | − | 0.0845154i | ||||
\(316\) | 9.00000 | − | 5.19615i | 0.506290 | − | 0.292306i | ||||
\(317\) | −2.59808 | + | 1.50000i | −0.145922 | + | 0.0842484i | −0.571184 | − | 0.820822i | \(-0.693516\pi\) |
0.425261 | + | 0.905071i | \(0.360182\pi\) | |||||||
\(318\) | − | 21.0000i | − | 1.17762i | ||||||
\(319\) | −4.50000 | + | 7.79423i | −0.251952 | + | 0.436393i | ||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | 4.50000 | + | 2.59808i | 0.251166 | + | 0.145010i | ||||
\(322\) | −6.00000 | + | 3.46410i | −0.334367 | + | 0.193047i | ||||
\(323\) | 6.92820 | − | 12.0000i | 0.385496 | − | 0.667698i | ||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | − | 3.46410i | − | 0.192154i | ||||||
\(326\) | 8.00000i | 0.443079i | ||||||||
\(327\) | 3.46410 | + | 6.00000i | 0.191565 | + | 0.331801i | ||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | 10.3923 | − | 6.00000i | 0.572946 | − | 0.330791i | ||||
\(330\) | 4.50000 | − | 7.79423i | 0.247717 | − | 0.429058i | ||||
\(331\) | −15.0000 | − | 8.66025i | −0.824475 | − | 0.476011i | 0.0274825 | − | 0.999622i | \(-0.491251\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 2.59808 | − | 4.50000i | 0.142588 | − | 0.246970i | ||||
\(333\) | 20.7846i | 1.13899i | ||||||||
\(334\) | −9.00000 | + | 5.19615i | −0.492458 | + | 0.284321i | ||||
\(335\) | 1.73205 | − | 1.00000i | 0.0946320 | − | 0.0546358i | ||||
\(336\) | 0.866025 | − | 1.50000i | 0.0472456 | − | 0.0818317i | ||||
\(337\) | − | 12.1244i | − | 0.660456i | −0.943901 | − | 0.330228i | \(-0.892874\pi\) | ||
0.943901 | − | 0.330228i | \(-0.107126\pi\) | |||||||
\(338\) | 0.866025 | − | 0.500000i | 0.0471056 | − | 0.0271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 3.46410i | − | 0.187867i | ||||||
\(341\) | −10.3923 | + | 27.0000i | −0.562775 | + | 1.46213i | ||||
\(342\) | 12.0000i | 0.648886i | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −1.73205 | − | 3.00000i | −0.0933859 | − | 0.161749i | ||||
\(345\) | − | 12.0000i | − | 0.646058i | ||||||
\(346\) | −1.50000 | + | 2.59808i | −0.0806405 | + | 0.139673i | ||||
\(347\) | −9.52628 | − | 16.5000i | −0.511397 | − | 0.885766i | −0.999913 | − | 0.0132111i | \(-0.995795\pi\) |
0.488515 | − | 0.872555i | \(-0.337539\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | −8.00000 | −0.428230 | −0.214115 | − | 0.976808i | \(-0.568687\pi\) | ||||
−0.214115 | + | 0.976808i | \(0.568687\pi\) | |||||||
\(350\) | −0.866025 | − | 0.500000i | −0.0462910 | − | 0.0267261i | ||||
\(351\) | −15.5885 | − | 9.00000i | −0.832050 | − | 0.480384i | ||||
\(352\) | 4.50000 | + | 2.59808i | 0.239851 | + | 0.138478i | ||||
\(353\) | 17.3205 | + | 30.0000i | 0.921878 | + | 1.59674i | 0.796507 | + | 0.604629i | \(0.206679\pi\) |
0.125370 | + | 0.992110i | \(0.459988\pi\) | |||||||
\(354\) | 12.9904 | − | 22.5000i | 0.690431 | − | 1.19586i | ||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | 6.00000 | 0.317554 | ||||||||
\(358\) | 13.5000 | − | 7.79423i | 0.713497 | − | 0.411938i | ||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 1.50000 | + | 2.59808i | 0.0790569 | + | 0.136931i | ||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | −1.73205 | + | 3.00000i | −0.0910346 | + | 0.157676i | ||||
\(363\) | −13.8564 | + | 24.0000i | −0.727273 | + | 1.25967i | ||||
\(364\) | 3.46410i | 0.181568i | ||||||||
\(365\) | 3.46410 | + | 6.00000i | 0.181319 | + | 0.314054i | ||||
\(366\) | 3.00000 | + | 5.19615i | 0.156813 | + | 0.271607i | ||||
\(367\) | 9.00000 | + | 5.19615i | 0.469796 | + | 0.271237i | 0.716154 | − | 0.697942i | \(-0.245901\pi\) |
−0.246358 | + | 0.969179i | \(0.579234\pi\) | |||||||
\(368\) | 6.92820 | 0.361158 | ||||||||
\(369\) | 15.5885 | − | 9.00000i | 0.811503 | − | 0.468521i | ||||
\(370\) | 6.92820i | 0.360180i | ||||||||
\(371\) | 12.1244 | 0.629465 | ||||||||
\(372\) | −6.06218 | − | 7.50000i | −0.314309 | − | 0.388857i | ||||
\(373\) | −28.0000 | −1.44979 | −0.724893 | − | 0.688862i | \(-0.758111\pi\) | ||||
−0.724893 | + | 0.688862i | \(0.758111\pi\) | |||||||
\(374\) | 18.0000i | 0.930758i | ||||||||
\(375\) | 1.50000 | − | 0.866025i | 0.0774597 | − | 0.0447214i | ||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 5.19615 | + | 3.00000i | 0.267615 | + | 0.154508i | ||||
\(378\) | −4.50000 | + | 2.59808i | −0.231455 | + | 0.133631i | ||||
\(379\) | −7.00000 | − | 12.1244i | −0.359566 | − | 0.622786i | 0.628322 | − | 0.777953i | \(-0.283742\pi\) |
−0.987888 | + | 0.155167i | \(0.950409\pi\) | |||||||
\(380\) | 4.00000i | 0.205196i | ||||||||
\(381\) | −18.1865 | − | 10.5000i | −0.931724 | − | 0.537931i | ||||
\(382\) | −6.00000 | + | 10.3923i | −0.306987 | + | 0.531717i | ||||
\(383\) | 5.19615 | − | 9.00000i | 0.265511 | − | 0.459879i | −0.702186 | − | 0.711993i | \(-0.747793\pi\) |
0.967697 | + | 0.252115i | \(0.0811260\pi\) | |||||||
\(384\) | −1.50000 | + | 0.866025i | −0.0765466 | + | 0.0441942i | ||||
\(385\) | 4.50000 | + | 2.59808i | 0.229341 | + | 0.132410i | ||||
\(386\) | −9.52628 | + | 5.50000i | −0.484875 | + | 0.279943i | ||||
\(387\) | 10.3923i | 0.528271i | ||||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | 13.8564 | + | 24.0000i | 0.702548 | + | 1.21685i | 0.967569 | + | 0.252606i | \(0.0812876\pi\) |
−0.265022 | + | 0.964242i | \(0.585379\pi\) | |||||||
\(390\) | −5.19615 | − | 3.00000i | −0.263117 | − | 0.151911i | ||||
\(391\) | 12.0000 | + | 20.7846i | 0.606866 | + | 1.05112i | ||||
\(392\) | −5.19615 | − | 3.00000i | −0.262445 | − | 0.151523i | ||||
\(393\) | 18.0000 | + | 10.3923i | 0.907980 | + | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3923 | −0.522894 | ||||||||
\(396\) | −7.79423 | − | 13.5000i | −0.391675 | − | 0.678401i | ||||
\(397\) | 14.0000 | + | 24.2487i | 0.702640 | + | 1.21701i | 0.967537 | + | 0.252731i | \(0.0813288\pi\) |
−0.264897 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(398\) | 6.06218 | − | 10.5000i | 0.303870 | − | 0.526317i | ||||
\(399\) | −6.92820 | −0.346844 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 6.92820 | 0.345978 | 0.172989 | − | 0.984924i | \(-0.444657\pi\) | ||||
0.172989 | + | 0.984924i | \(0.444657\pi\) | |||||||
\(402\) | − | 3.46410i | − | 0.172774i | ||||||
\(403\) | 18.0000 | + | 6.92820i | 0.896644 | + | 0.345118i | ||||
\(404\) | 15.0000i | 0.746278i | ||||||||
\(405\) | − | 9.00000i | − | 0.447214i | ||||||
\(406\) | 1.50000 | − | 0.866025i | 0.0744438 | − | 0.0429801i | ||||
\(407\) | − | 36.0000i | − | 1.78445i | ||||||
\(408\) | −5.19615 | − | 3.00000i | −0.257248 | − | 0.148522i | ||||
\(409\) | −10.5000 | + | 6.06218i | −0.519192 | + | 0.299755i | −0.736604 | − | 0.676324i | \(-0.763572\pi\) |
0.217412 | + | 0.976080i | \(0.430238\pi\) | |||||||
\(410\) | 5.19615 | − | 3.00000i | 0.256620 | − | 0.148159i | ||||
\(411\) | 24.0000 | 1.18383 | ||||||||
\(412\) | 3.50000 | − | 6.06218i | 0.172433 | − | 0.298662i | ||||
\(413\) | 12.9904 | + | 7.50000i | 0.639215 | + | 0.369051i | ||||
\(414\) | −18.0000 | − | 10.3923i | −0.884652 | − | 0.510754i | ||||
\(415\) | −4.50000 | + | 2.59808i | −0.220896 | + | 0.127535i | ||||
\(416\) | 1.73205 | − | 3.00000i | 0.0849208 | − | 0.147087i | ||||
\(417\) | 31.1769 | − | 18.0000i | 1.52674 | − | 0.881464i | ||||
\(418\) | − | 20.7846i | − | 1.01661i | ||||||
\(419\) | − | 33.0000i | − | 1.61216i | −0.591810 | − | 0.806078i | \(-0.701586\pi\) | ||
0.591810 | − | 0.806078i | \(-0.298414\pi\) | |||||||
\(420\) | −1.50000 | + | 0.866025i | −0.0731925 | + | 0.0422577i | ||||
\(421\) | 10.0000 | − | 17.3205i | 0.487370 | − | 0.844150i | −0.512524 | − | 0.858673i | \(-0.671290\pi\) |
0.999895 | + | 0.0145228i | \(0.00462290\pi\) | |||||||
\(422\) | −8.66025 | + | 5.00000i | −0.421575 | + | 0.243396i | ||||
\(423\) | 31.1769 | + | 18.0000i | 1.51587 | + | 0.875190i | ||||
\(424\) | −10.5000 | − | 6.06218i | −0.509925 | − | 0.294405i | ||||
\(425\) | −1.73205 | + | 3.00000i | −0.0840168 | + | 0.145521i | ||||
\(426\) | 20.7846 | 1.00702 | ||||||||
\(427\) | −3.00000 | + | 1.73205i | −0.145180 | + | 0.0838198i | ||||
\(428\) | 2.59808 | − | 1.50000i | 0.125583 | − | 0.0725052i | ||||
\(429\) | 27.0000 | + | 15.5885i | 1.30357 | + | 0.752618i | ||||
\(430\) | 3.46410i | 0.167054i | ||||||||
\(431\) | 25.9808 | − | 15.0000i | 1.25145 | − | 0.722525i | 0.280052 | − | 0.959985i | \(-0.409648\pi\) |
0.971397 | + | 0.237460i | \(0.0763149\pi\) | |||||||
\(432\) | 5.19615 | 0.250000 | ||||||||
\(433\) | 27.7128i | 1.33179i | 0.746044 | + | 0.665896i | \(0.231951\pi\) | ||||
−0.746044 | + | 0.665896i | \(0.768049\pi\) | |||||||
\(434\) | 4.33013 | − | 3.50000i | 0.207853 | − | 0.168005i | ||||
\(435\) | 3.00000i | 0.143839i | ||||||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | −13.8564 | − | 24.0000i | −0.662842 | − | 1.14808i | ||||
\(438\) | 12.0000 | 0.573382 | ||||||||
\(439\) | 8.50000 | − | 14.7224i | 0.405683 | − | 0.702663i | −0.588718 | − | 0.808339i | \(-0.700367\pi\) |
0.994401 | + | 0.105675i | \(0.0337004\pi\) | |||||||
\(440\) | −2.59808 | − | 4.50000i | −0.123858 | − | 0.214529i | ||||
\(441\) | 9.00000 | + | 15.5885i | 0.428571 | + | 0.742307i | ||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | 10.3923 | + | 6.00000i | 0.493753 | + | 0.285069i | 0.726130 | − | 0.687557i | \(-0.241317\pi\) |
−0.232377 | + | 0.972626i | \(0.574650\pi\) | |||||||
\(444\) | 10.3923 | + | 6.00000i | 0.493197 | + | 0.284747i | ||||
\(445\) | −9.00000 | − | 5.19615i | −0.426641 | − | 0.246321i | ||||
\(446\) | 7.79423 | + | 13.5000i | 0.369067 | + | 0.639244i | ||||
\(447\) | 22.5000 | + | 12.9904i | 1.06421 | + | 0.614424i | ||||
\(448\) | −0.500000 | − | 0.866025i | −0.0236228 | − | 0.0409159i | ||||
\(449\) | −6.92820 | −0.326962 | −0.163481 | − | 0.986546i | \(-0.552272\pi\) | ||||
−0.163481 | + | 0.986546i | \(0.552272\pi\) | |||||||
\(450\) | − | 3.00000i | − | 0.141421i | ||||||
\(451\) | −27.0000 | + | 15.5885i | −1.27138 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.9904 | − | 7.50000i | 0.610341 | − | 0.352381i | ||||
\(454\) | −7.50000 | + | 12.9904i | −0.351992 | + | 0.609669i | ||||
\(455\) | 1.73205 | − | 3.00000i | 0.0811998 | − | 0.140642i | ||||
\(456\) | 6.00000 | + | 3.46410i | 0.280976 | + | 0.162221i | ||||
\(457\) | − | 6.92820i | − | 0.324088i | −0.986784 | − | 0.162044i | \(-0.948191\pi\) | ||
0.986784 | − | 0.162044i | \(-0.0518086\pi\) | |||||||
\(458\) | −13.8564 | − | 24.0000i | −0.647467 | − | 1.12145i | ||||
\(459\) | 9.00000 | + | 15.5885i | 0.420084 | + | 0.727607i | ||||
\(460\) | −6.00000 | − | 3.46410i | −0.279751 | − | 0.161515i | ||||
\(461\) | 39.8372 | 1.85540 | 0.927701 | − | 0.373324i | \(-0.121782\pi\) | ||||
0.927701 | + | 0.373324i | \(0.121782\pi\) | |||||||
\(462\) | 7.79423 | − | 4.50000i | 0.362620 | − | 0.209359i | ||||
\(463\) | 12.1244i | 0.563467i | 0.959493 | + | 0.281733i | \(0.0909093\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(464\) | −1.73205 | −0.0804084 | ||||||||
\(465\) | 1.50000 | + | 9.52628i | 0.0695608 | + | 0.441771i | ||||
\(466\) | −18.0000 | −0.833834 | ||||||||
\(467\) | − | 27.0000i | − | 1.24941i | −0.780860 | − | 0.624705i | \(-0.785219\pi\) | ||
0.780860 | − | 0.624705i | \(-0.214781\pi\) | |||||||
\(468\) | −9.00000 | + | 5.19615i | −0.416025 | + | 0.240192i | ||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | 10.3923 | + | 6.00000i | 0.479361 | + | 0.276759i | ||||
\(471\) | −8.66025 | − | 15.0000i | −0.399043 | − | 0.691164i | ||||
\(472\) | −7.50000 | − | 12.9904i | −0.345215 | − | 0.597931i | ||||
\(473\) | − | 18.0000i | − | 0.827641i | ||||||
\(474\) | −9.00000 | + | 15.5885i | −0.413384 | + | 0.716002i | ||||
\(475\) | 2.00000 | − | 3.46410i | 0.0917663 | − | 0.158944i | ||||
\(476\) | 1.73205 | − | 3.00000i | 0.0793884 | − | 0.137505i | ||||
\(477\) | 18.1865 | + | 31.5000i | 0.832704 | + | 1.44229i | ||||
\(478\) | 24.0000 | + | 13.8564i | 1.09773 | + | 0.633777i | ||||
\(479\) | 10.3923 | − | 6.00000i | 0.474837 | − | 0.274147i | −0.243426 | − | 0.969920i | \(-0.578271\pi\) |
0.718262 | + | 0.695773i | \(0.244938\pi\) | |||||||
\(480\) | 1.73205 | 0.0790569 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | −7.79423 | − | 13.5000i | −0.355017 | − | 0.614908i | ||||
\(483\) | 6.00000 | − | 10.3923i | 0.273009 | − | 0.472866i | ||||
\(484\) | 8.00000 | + | 13.8564i | 0.363636 | + | 0.629837i | ||||
\(485\) | −0.866025 | − | 0.500000i | −0.0393242 | − | 0.0227038i | ||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 31.5000 | + | 18.1865i | 1.42740 | + | 0.824110i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
0.430486 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(488\) | 3.46410 | 0.156813 | ||||||||
\(489\) | −6.92820 | − | 12.0000i | −0.313304 | − | 0.542659i | ||||
\(490\) | 3.00000 | + | 5.19615i | 0.135526 | + | 0.234738i | ||||
\(491\) | −18.1865 | + | 31.5000i | −0.820747 | + | 1.42158i | 0.0843802 | + | 0.996434i | \(0.473109\pi\) |
−0.905127 | + | 0.425141i | \(0.860224\pi\) | |||||||
\(492\) | − | 10.3923i | − | 0.468521i | ||||||
\(493\) | −3.00000 | − | 5.19615i | −0.135113 | − | 0.234023i | ||||
\(494\) | −13.8564 | −0.623429 | ||||||||
\(495\) | 15.5885i | 0.700649i | ||||||||
\(496\) | −5.50000 | + | 0.866025i | −0.246957 | + | 0.0388857i | ||||
\(497\) | 12.0000i | 0.538274i | ||||||||
\(498\) | 9.00000i | 0.403300i | ||||||||
\(499\) | −21.0000 | + | 12.1244i | −0.940089 | + | 0.542761i | −0.889988 | − | 0.455983i | \(-0.849288\pi\) |
−0.0501009 | + | 0.998744i | \(0.515954\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | ||||
\(502\) | −9.00000 | + | 5.19615i | −0.401690 | + | 0.231916i | ||||
\(503\) | −31.1769 | + | 18.0000i | −1.39011 | + | 0.802580i | −0.993327 | − | 0.115332i | \(-0.963207\pi\) |
−0.396783 | + | 0.917912i | \(0.629873\pi\) | |||||||
\(504\) | 3.00000i | 0.133631i | ||||||||
\(505\) | 7.50000 | − | 12.9904i | 0.333746 | − | 0.578064i | ||||
\(506\) | 31.1769 | + | 18.0000i | 1.38598 | + | 0.800198i | ||||
\(507\) | −0.866025 | + | 1.50000i | −0.0384615 | + | 0.0666173i | ||||
\(508\) | −10.5000 | + | 6.06218i | −0.465862 | + | 0.268966i | ||||
\(509\) | 12.9904 | − | 22.5000i | 0.575789 | − | 0.997295i | −0.420167 | − | 0.907447i | \(-0.638028\pi\) |
0.995955 | − | 0.0898481i | \(-0.0286382\pi\) | |||||||
\(510\) | 3.00000 | + | 5.19615i | 0.132842 | + | 0.230089i | ||||
\(511\) | 6.92820i | 0.306486i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −10.3923 | − | 18.0000i | −0.458831 | − | 0.794719i | ||||
\(514\) | 12.0000 | − | 20.7846i | 0.529297 | − | 0.916770i | ||||
\(515\) | −6.06218 | + | 3.50000i | −0.267131 | + | 0.154228i | ||||
\(516\) | 5.19615 | + | 3.00000i | 0.228748 | + | 0.132068i | ||||
\(517\) | −54.0000 | − | 31.1769i | −2.37492 | − | 1.37116i | ||||
\(518\) | −3.46410 | + | 6.00000i | −0.152204 | + | 0.263625i | ||||
\(519\) | − | 5.19615i | − | 0.228086i | ||||||
\(520\) | −3.00000 | + | 1.73205i | −0.131559 | + | 0.0759555i | ||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 4.50000 | + | 2.59808i | 0.196960 | + | 0.113715i | ||||
\(523\) | 17.3205i | 0.757373i | 0.925525 | + | 0.378686i | \(0.123624\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(524\) | 10.3923 | − | 6.00000i | 0.453990 | − | 0.262111i | ||||
\(525\) | 1.73205 | 0.0755929 | ||||||||
\(526\) | − | 3.46410i | − | 0.151042i | ||||||
\(527\) | −12.1244 | − | 15.0000i | −0.528145 | − | 0.653410i | ||||
\(528\) | −9.00000 | −0.391675 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 6.06218 | + | 10.5000i | 0.263324 | + | 0.456091i | ||||
\(531\) | 45.0000i | 1.95283i | ||||||||
\(532\) | −2.00000 | + | 3.46410i | −0.0867110 | + | 0.150188i | ||||
\(533\) | 10.3923 | + | 18.0000i | 0.450141 | + | 0.779667i | ||||
\(534\) | −15.5885 | + | 9.00000i | −0.674579 | + | 0.389468i | ||||
\(535\) | −3.00000 | −0.129701 | ||||||||
\(536\) | −1.73205 | − | 1.00000i | −0.0748132 | − | 0.0431934i | ||||
\(537\) | −13.5000 | + | 23.3827i | −0.582568 | + | 1.00904i | ||||
\(538\) | 24.0000 | + | 13.8564i | 1.03471 | + | 0.597392i | ||||
\(539\) | −15.5885 | − | 27.0000i | −0.671442 | − | 1.16297i | ||||
\(540\) | −4.50000 | − | 2.59808i | −0.193649 | − | 0.111803i | ||||
\(541\) | 4.00000 | + | 6.92820i | 0.171973 | + | 0.297867i | 0.939110 | − | 0.343617i | \(-0.111652\pi\) |
−0.767136 | + | 0.641484i | \(0.778319\pi\) | |||||||
\(542\) | 12.1244 | 0.520786 | ||||||||
\(543\) | − | 6.00000i | − | 0.257485i | ||||||
\(544\) | −3.00000 | + | 1.73205i | −0.128624 | + | 0.0742611i | ||||
\(545\) | −3.46410 | − | 2.00000i | −0.148386 | − | 0.0856706i | ||||
\(546\) | −3.00000 | − | 5.19615i | −0.128388 | − | 0.222375i | ||||
\(547\) | 13.0000 | − | 22.5167i | 0.555840 | − | 0.962743i | −0.441998 | − | 0.897016i | \(-0.645730\pi\) |
0.997838 | − | 0.0657267i | \(-0.0209366\pi\) | |||||||
\(548\) | 6.92820 | − | 12.0000i | 0.295958 | − | 0.512615i | ||||
\(549\) | −9.00000 | − | 5.19615i | −0.384111 | − | 0.221766i | ||||
\(550\) | 5.19615i | 0.221565i | ||||||||
\(551\) | 3.46410 | + | 6.00000i | 0.147576 | + | 0.255609i | ||||
\(552\) | −10.3923 | + | 6.00000i | −0.442326 | + | 0.255377i | ||||
\(553\) | −9.00000 | − | 5.19615i | −0.382719 | − | 0.220963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00000 | − | 10.3923i | −0.254686 | − | 0.441129i | ||||
\(556\) | − | 20.7846i | − | 0.881464i | ||||||
\(557\) | 5.19615 | 0.220168 | 0.110084 | − | 0.993922i | \(-0.464888\pi\) | ||||
0.110084 | + | 0.993922i | \(0.464888\pi\) | |||||||
\(558\) | 15.5885 | + | 6.00000i | 0.659912 | + | 0.254000i | ||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 1.00000i | 0.0422577i | ||||||||
\(561\) | −15.5885 | − | 27.0000i | −0.658145 | − | 1.13994i | ||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | −28.5788 | − | 16.5000i | −1.20445 | − | 0.695392i | −0.242912 | − | 0.970048i | \(-0.578103\pi\) |
−0.961542 | + | 0.274656i | \(0.911436\pi\) | |||||||
\(564\) | 18.0000 | − | 10.3923i | 0.757937 | − | 0.437595i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 22.0000i | − | 0.924729i | ||||||
\(567\) | 4.50000 | − | 7.79423i | 0.188982 | − | 0.327327i | ||||
\(568\) | 6.00000 | − | 10.3923i | 0.251754 | − | 0.436051i | ||||
\(569\) | 20.7846 | − | 36.0000i | 0.871336 | − | 1.50920i | 0.0107211 | − | 0.999943i | \(-0.496587\pi\) |
0.860615 | − | 0.509256i | \(-0.170079\pi\) | |||||||
\(570\) | −3.46410 | − | 6.00000i | −0.145095 | − | 0.251312i | ||||
\(571\) | 36.0000 | + | 20.7846i | 1.50655 | + | 0.869809i | 0.999971 | + | 0.00761713i | \(0.00242463\pi\) |
0.506582 | + | 0.862192i | \(0.330909\pi\) | |||||||
\(572\) | 15.5885 | − | 9.00000i | 0.651786 | − | 0.376309i | ||||
\(573\) | − | 20.7846i | − | 0.868290i | ||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | 3.46410 | + | 6.00000i | 0.144463 | + | 0.250217i | ||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | 1.00000 | + | 1.73205i | 0.0416305 | + | 0.0721062i | 0.886090 | − | 0.463513i | \(-0.153411\pi\) |
−0.844459 | + | 0.535620i | \(0.820078\pi\) | |||||||
\(578\) | 4.33013 | + | 2.50000i | 0.180110 | + | 0.103986i | ||||
\(579\) | 9.52628 | − | 16.5000i | 0.395899 | − | 0.685717i | ||||
\(580\) | 1.50000 | + | 0.866025i | 0.0622841 | + | 0.0359597i | ||||
\(581\) | −5.19615 | −0.215573 | ||||||||
\(582\) | −1.50000 | + | 0.866025i | −0.0621770 | + | 0.0358979i | ||||
\(583\) | −31.5000 | − | 54.5596i | −1.30460 | − | 2.25963i | ||||
\(584\) | 3.46410 | − | 6.00000i | 0.143346 | − | 0.248282i | ||||
\(585\) | 10.3923 | 0.429669 | ||||||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | 25.9808 | 1.07234 | 0.536170 | − | 0.844110i | \(-0.319870\pi\) | ||||
0.536170 | + | 0.844110i | \(0.319870\pi\) | |||||||
\(588\) | 10.3923 | 0.428571 | ||||||||
\(589\) | 14.0000 | + | 17.3205i | 0.576860 | + | 0.713679i | ||||
\(590\) | 15.0000i | 0.617540i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | − | 3.46410i | 0.246598 | − | 0.142374i | ||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | 23.3827 | + | 13.5000i | 0.959403 | + | 0.553912i | ||||
\(595\) | −3.00000 | + | 1.73205i | −0.122988 | + | 0.0710072i | ||||
\(596\) | 12.9904 | − | 7.50000i | 0.532107 | − | 0.307212i | ||||
\(597\) | 21.0000i | 0.859473i | ||||||||
\(598\) | 12.0000 | − | 20.7846i | 0.490716 | − | 0.849946i | ||||
\(599\) | 5.19615 | + | 3.00000i | 0.212309 | + | 0.122577i | 0.602384 | − | 0.798206i | \(-0.294218\pi\) |
−0.390075 | + | 0.920783i | \(0.627551\pi\) | |||||||
\(600\) | −1.50000 | − | 0.866025i | −0.0612372 | − | 0.0353553i | ||||
\(601\) | −12.0000 | + | 6.92820i | −0.489490 | + | 0.282607i | −0.724363 | − | 0.689419i | \(-0.757866\pi\) |
0.234873 | + | 0.972026i | \(0.424533\pi\) | |||||||
\(602\) | −1.73205 | + | 3.00000i | −0.0705931 | + | 0.122271i | ||||
\(603\) | 3.00000 | + | 5.19615i | 0.122169 | + | 0.211604i | ||||
\(604\) | − | 8.66025i | − | 0.352381i | ||||||
\(605\) | − | 16.0000i | − | 0.650493i | ||||||
\(606\) | −12.9904 | − | 22.5000i | −0.527698 | − | 0.914000i | ||||
\(607\) | 16.0000 | − | 27.7128i | 0.649420 | − | 1.12483i | −0.333842 | − | 0.942629i | \(-0.608345\pi\) |
0.983262 | − | 0.182199i | \(-0.0583216\pi\) | |||||||
\(608\) | 3.46410 | − | 2.00000i | 0.140488 | − | 0.0811107i | ||||
\(609\) | −1.50000 | + | 2.59808i | −0.0607831 | + | 0.105279i | ||||
\(610\) | −3.00000 | − | 1.73205i | −0.121466 | − | 0.0701287i | ||||
\(611\) | −20.7846 | + | 36.0000i | −0.840855 | + | 1.45640i | ||||
\(612\) | 10.3923 | 0.420084 | ||||||||
\(613\) | 3.00000 | − | 1.73205i | 0.121169 | − | 0.0699569i | −0.438191 | − | 0.898882i | \(-0.644380\pi\) |
0.559359 | + | 0.828925i | \(0.311047\pi\) | |||||||
\(614\) | −12.1244 | + | 7.00000i | −0.489299 | + | 0.282497i | ||||
\(615\) | −5.19615 | + | 9.00000i | −0.209529 | + | 0.362915i | ||||
\(616\) | − | 5.19615i | − | 0.209359i | ||||||
\(617\) | −36.3731 | + | 21.0000i | −1.46432 | + | 0.845428i | −0.999207 | − | 0.0398207i | \(-0.987321\pi\) |
−0.465118 | + | 0.885249i | \(0.653988\pi\) | |||||||
\(618\) | 12.1244i | 0.487713i | ||||||||
\(619\) | 20.7846i | 0.835404i | 0.908584 | + | 0.417702i | \(0.137164\pi\) | ||||
−0.908584 | + | 0.417702i | \(0.862836\pi\) | |||||||
\(620\) | 5.19615 | + | 2.00000i | 0.208683 | + | 0.0803219i | ||||
\(621\) | 36.0000 | 1.44463 | ||||||||
\(622\) | −30.0000 | −1.20289 | ||||||||
\(623\) | −5.19615 | − | 9.00000i | −0.208179 | − | 0.360577i | ||||
\(624\) | 6.00000i | 0.240192i | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −12.9904 | − | 22.5000i | −0.519200 | − | 0.899281i | ||||
\(627\) | 18.0000 | + | 31.1769i | 0.718851 | + | 1.24509i | ||||
\(628\) | −10.0000 | −0.399043 | ||||||||
\(629\) | 20.7846 | + | 12.0000i | 0.828737 | + | 0.478471i | ||||
\(630\) | 1.50000 | − | 2.59808i | 0.0597614 | − | 0.103510i | ||||
\(631\) | 10.5000 | + | 6.06218i | 0.417998 | + | 0.241331i | 0.694221 | − | 0.719762i | \(-0.255749\pi\) |
−0.276222 | + | 0.961094i | \(0.589083\pi\) | |||||||
\(632\) | 5.19615 | + | 9.00000i | 0.206692 | + | 0.358001i | ||||
\(633\) | 8.66025 | − | 15.0000i | 0.344214 | − | 0.596196i | ||||
\(634\) | −1.50000 | − | 2.59808i | −0.0595726 | − | 0.103183i | ||||
\(635\) | 12.1244 | 0.481140 | ||||||||
\(636\) | 21.0000 | 0.832704 | ||||||||
\(637\) | −18.0000 | + | 10.3923i | −0.713186 | + | 0.411758i | ||||
\(638\) | −7.79423 | − | 4.50000i | −0.308576 | − | 0.178157i | ||||
\(639\) | −31.1769 | + | 18.0000i | −1.23334 | + | 0.712069i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 1.73205 | − | 3.00000i | 0.0684119 | − | 0.118493i | −0.829790 | − | 0.558075i | \(-0.811540\pi\) |
0.898202 | + | 0.439582i | \(0.144873\pi\) | |||||||
\(642\) | −2.59808 | + | 4.50000i | −0.102538 | + | 0.177601i | ||||
\(643\) | 3.46410i | 0.136611i | 0.997664 | + | 0.0683054i | \(0.0217592\pi\) | ||||
−0.997664 | + | 0.0683054i | \(0.978241\pi\) | |||||||
\(644\) | −3.46410 | − | 6.00000i | −0.136505 | − | 0.236433i | ||||
\(645\) | −3.00000 | − | 5.19615i | −0.118125 | − | 0.204598i | ||||
\(646\) | 12.0000 | + | 6.92820i | 0.472134 | + | 0.272587i | ||||
\(647\) | −17.3205 | −0.680939 | −0.340470 | − | 0.940255i | \(-0.610586\pi\) | ||||
−0.340470 | + | 0.940255i | \(0.610586\pi\) | |||||||
\(648\) | −7.79423 | + | 4.50000i | −0.306186 | + | 0.176777i | ||||
\(649\) | − | 77.9423i | − | 3.05950i | ||||||
\(650\) | 3.46410 | 0.135873 | ||||||||
\(651\) | −3.46410 | + | 9.00000i | −0.135769 | + | 0.352738i | ||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | − | 9.00000i | − | 0.352197i | −0.984373 | − | 0.176099i | \(-0.943652\pi\) | ||
0.984373 | − | 0.176099i | \(-0.0563478\pi\) | |||||||
\(654\) | −6.00000 | + | 3.46410i | −0.234619 | + | 0.135457i | ||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | −5.19615 | − | 3.00000i | −0.202876 | − | 0.117130i | ||||
\(657\) | −18.0000 | + | 10.3923i | −0.702247 | + | 0.405442i | ||||
\(658\) | 6.00000 | + | 10.3923i | 0.233904 | + | 0.405134i | ||||
\(659\) | 21.0000i | 0.818044i | 0.912525 | + | 0.409022i | \(0.134130\pi\) | ||||
−0.912525 | + | 0.409022i | \(0.865870\pi\) | |||||||
\(660\) | 7.79423 | + | 4.50000i | 0.303390 | + | 0.175162i | ||||
\(661\) | 2.00000 | − | 3.46410i | 0.0777910 | − | 0.134738i | −0.824506 | − | 0.565854i | \(-0.808547\pi\) |
0.902297 | + | 0.431116i | \(0.141880\pi\) | |||||||
\(662\) | 8.66025 | − | 15.0000i | 0.336590 | − | 0.582992i | ||||
\(663\) | −18.0000 | + | 10.3923i | −0.699062 | + | 0.403604i | ||||
\(664\) | 4.50000 | + | 2.59808i | 0.174634 | + | 0.100825i | ||||
\(665\) | 3.46410 | − | 2.00000i | 0.134332 | − | 0.0775567i | ||||
\(666\) | −20.7846 | −0.805387 | ||||||||
\(667\) | −12.0000 | −0.464642 | ||||||||
\(668\) | −5.19615 | − | 9.00000i | −0.201045 | − | 0.348220i | ||||
\(669\) | −23.3827 | − | 13.5000i | −0.904027 | − | 0.521940i | ||||
\(670\) | 1.00000 | + | 1.73205i | 0.0386334 | + | 0.0669150i | ||||
\(671\) | 15.5885 | + | 9.00000i | 0.601786 | + | 0.347441i | ||||
\(672\) | 1.50000 | + | 0.866025i | 0.0578638 | + | 0.0334077i | ||||
\(673\) | 4.50000 | + | 2.59808i | 0.173462 | + | 0.100148i | 0.584217 | − | 0.811597i | \(-0.301402\pi\) |
−0.410755 | + | 0.911746i | \(0.634735\pi\) | |||||||
\(674\) | 12.1244 | 0.467013 | ||||||||
\(675\) | 2.59808 | + | 4.50000i | 0.100000 | + | 0.173205i | ||||
\(676\) | 0.500000 | + | 0.866025i | 0.0192308 | + | 0.0333087i | ||||
\(677\) | 16.4545 | − | 28.5000i | 0.632397 | − | 1.09534i | −0.354663 | − | 0.934994i | \(-0.615404\pi\) |
0.987060 | − | 0.160350i | \(-0.0512622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.500000 | − | 0.866025i | −0.0191882 | − | 0.0332350i | ||||
\(680\) | 3.46410 | 0.132842 | ||||||||
\(681\) | − | 25.9808i | − | 0.995585i | ||||||
\(682\) | −27.0000 | − | 10.3923i | −1.03388 | − | 0.397942i | ||||
\(683\) | − | 9.00000i | − | 0.344375i | −0.985064 | − | 0.172188i | \(-0.944916\pi\) | ||
0.985064 | − | 0.172188i | \(-0.0550836\pi\) | |||||||
\(684\) | −12.0000 | −0.458831 | ||||||||
\(685\) | −12.0000 | + | 6.92820i | −0.458496 | + | 0.264713i | ||||
\(686\) | 13.0000i | 0.496342i | ||||||||
\(687\) | 41.5692 | + | 24.0000i | 1.58596 | + | 0.915657i | ||||
\(688\) | 3.00000 | − | 1.73205i | 0.114374 | − | 0.0660338i | ||||
\(689\) | −36.3731 | + | 21.0000i | −1.38570 | + | 0.800036i | ||||
\(690\) | 12.0000 | 0.456832 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | −2.59808 | − | 1.50000i | −0.0987640 | − | 0.0570214i | ||||
\(693\) | −7.79423 | + | 13.5000i | −0.296078 | + | 0.512823i | ||||
\(694\) | 16.5000 | − | 9.52628i | 0.626331 | − | 0.361613i | ||||
\(695\) | −10.3923 | + | 18.0000i | −0.394203 | + | 0.682779i | ||||
\(696\) | 2.59808 | − | 1.50000i | 0.0984798 | − | 0.0568574i | ||||
\(697\) | − | 20.7846i | − | 0.787273i | ||||||
\(698\) | − | 8.00000i | − | 0.302804i | ||||||
\(699\) | 27.0000 | − | 15.5885i | 1.02123 | − | 0.589610i | ||||
\(700\) | 0.500000 | − | 0.866025i | 0.0188982 | − | 0.0327327i | ||||
\(701\) | −12.9904 | + | 7.50000i | −0.490640 | + | 0.283271i | −0.724840 | − | 0.688917i | \(-0.758086\pi\) |
0.234200 | + | 0.972188i | \(0.424753\pi\) | |||||||
\(702\) | 9.00000 | − | 15.5885i | 0.339683 | − | 0.588348i | ||||
\(703\) | −24.0000 | − | 13.8564i | −0.905177 | − | 0.522604i | ||||
\(704\) | −2.59808 | + | 4.50000i | −0.0979187 | + | 0.169600i | ||||
\(705\) | −20.7846 | −0.782794 | ||||||||
\(706\) | −30.0000 | + | 17.3205i | −1.12906 | + | 0.651866i | ||||
\(707\) | 12.9904 | − | 7.50000i | 0.488554 | − | 0.282067i | ||||
\(708\) | 22.5000 | + | 12.9904i | 0.845602 | + | 0.488208i | ||||
\(709\) | 24.2487i | 0.910679i | 0.890318 | + | 0.455340i | \(0.150482\pi\) | ||||
−0.890318 | + | 0.455340i | \(0.849518\pi\) | |||||||
\(710\) | −10.3923 | + | 6.00000i | −0.390016 | + | 0.225176i | ||||
\(711\) | − | 31.1769i | − | 1.16923i | ||||||
\(712\) | 10.3923i | 0.389468i | ||||||||
\(713\) | −38.1051 | + | 6.00000i | −1.42705 | + | 0.224702i | ||||
\(714\) | 6.00000i | 0.224544i | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 7.79423 | + | 13.5000i | 0.291284 | + | 0.504519i | ||||
\(717\) | −48.0000 | −1.79259 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.46410 | + | 6.00000i | 0.129189 | + | 0.223762i | 0.923363 | − | 0.383929i | \(-0.125429\pi\) |
−0.794173 | + | 0.607691i | \(0.792096\pi\) | |||||||
\(720\) | −2.59808 | + | 1.50000i | −0.0968246 | + | 0.0559017i | ||||
\(721\) | −7.00000 | −0.260694 | ||||||||
\(722\) | 2.59808 | + | 1.50000i | 0.0966904 | + | 0.0558242i | ||||
\(723\) | 23.3827 | + | 13.5000i | 0.869611 | + | 0.502070i | ||||
\(724\) | −3.00000 | − | 1.73205i | −0.111494 | − | 0.0643712i | ||||
\(725\) | −0.866025 | − | 1.50000i | −0.0321634 | − | 0.0557086i | ||||
\(726\) | −24.0000 | − | 13.8564i | −0.890724 | − | 0.514259i | ||||
\(727\) | −17.5000 | − | 30.3109i | −0.649039 | − | 1.12417i | −0.983353 | − | 0.181707i | \(-0.941838\pi\) |
0.334314 | − | 0.942462i | \(-0.391496\pi\) | |||||||
\(728\) | −3.46410 | −0.128388 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −6.00000 | + | 3.46410i | −0.222070 | + | 0.128212i | ||||
\(731\) | 10.3923 | + | 6.00000i | 0.384373 | + | 0.221918i | ||||
\(732\) | −5.19615 | + | 3.00000i | −0.192055 | + | 0.110883i | ||||
\(733\) | 7.00000 | − | 12.1244i | 0.258551 | − | 0.447823i | −0.707303 | − | 0.706910i | \(-0.750088\pi\) |
0.965854 | + | 0.259087i | \(0.0834217\pi\) | |||||||
\(734\) | −5.19615 | + | 9.00000i | −0.191793 | + | 0.332196i | ||||
\(735\) | −9.00000 | − | 5.19615i | −0.331970 | − | 0.191663i | ||||
\(736\) | 6.92820i | 0.255377i | ||||||||
\(737\) | −5.19615 | − | 9.00000i | −0.191403 | − | 0.331519i | ||||
\(738\) | 9.00000 | + | 15.5885i | 0.331295 | + | 0.573819i | ||||
\(739\) | −3.00000 | − | 1.73205i | −0.110357 | − | 0.0637145i | 0.443806 | − | 0.896123i | \(-0.353628\pi\) |
−0.554162 | + | 0.832409i | \(0.686961\pi\) | |||||||
\(740\) | −6.92820 | −0.254686 | ||||||||
\(741\) | 20.7846 | − | 12.0000i | 0.763542 | − | 0.440831i | ||||
\(742\) | 12.1244i | 0.445099i | ||||||||
\(743\) | 20.7846 | 0.762513 | 0.381257 | − | 0.924469i | \(-0.375491\pi\) | ||||
0.381257 | + | 0.924469i | \(0.375491\pi\) | |||||||
\(744\) | 7.50000 | − | 6.06218i | 0.274963 | − | 0.222250i | ||||
\(745\) | −15.0000 | −0.549557 | ||||||||
\(746\) | − | 28.0000i | − | 1.02515i | ||||||
\(747\) | −7.79423 | − | 13.5000i | −0.285176 | − | 0.493939i | ||||
\(748\) | −18.0000 | −0.658145 | ||||||||
\(749\) | −2.59808 | − | 1.50000i | −0.0949316 | − | 0.0548088i | ||||
\(750\) | 0.866025 | + | 1.50000i | 0.0316228 | + | 0.0547723i | ||||
\(751\) | −15.5000 | − | 26.8468i | −0.565603 | − | 0.979653i | −0.996993 | − | 0.0774878i | \(-0.975310\pi\) |
0.431390 | − | 0.902165i | \(-0.358023\pi\) | |||||||
\(752\) | − | 12.0000i | − | 0.437595i | ||||||
\(753\) | 9.00000 | − | 15.5885i | 0.327978 | − | 0.568075i | ||||
\(754\) | −3.00000 | + | 5.19615i | −0.109254 | + | 0.189233i | ||||
\(755\) | −4.33013 | + | 7.50000i | −0.157589 | + | 0.272953i | ||||
\(756\) | −2.59808 | − | 4.50000i | −0.0944911 | − | 0.163663i | ||||
\(757\) | −3.00000 | − | 1.73205i | −0.109037 | − | 0.0629525i | 0.444490 | − | 0.895784i | \(-0.353385\pi\) |
−0.553527 | + | 0.832831i | \(0.686718\pi\) | |||||||
\(758\) | 12.1244 | − | 7.00000i | 0.440376 | − | 0.254251i | ||||
\(759\) | −62.3538 | −2.26330 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 10.5000 | − | 18.1865i | 0.380375 | − | 0.658829i | ||||
\(763\) | −2.00000 | − | 3.46410i | −0.0724049 | − | 0.125409i | ||||
\(764\) | −10.3923 | − | 6.00000i | −0.375980 | − | 0.217072i | ||||
\(765\) | −9.00000 | − | 5.19615i | −0.325396 | − | 0.187867i | ||||
\(766\) | 9.00000 | + | 5.19615i | 0.325183 | + | 0.187745i | ||||
\(767\) | −51.9615 | −1.87622 | ||||||||
\(768\) | −0.866025 | − | 1.50000i | −0.0312500 | − | 0.0541266i | ||||
\(769\) | 11.5000 | + | 19.9186i | 0.414701 | + | 0.718283i | 0.995397 | − | 0.0958377i | \(-0.0305530\pi\) |
−0.580696 | + | 0.814120i | \(0.697220\pi\) | |||||||
\(770\) | −2.59808 | + | 4.50000i | −0.0936282 | + | 0.162169i | ||||
\(771\) | 41.5692i | 1.49708i | ||||||||
\(772\) | −5.50000 | − | 9.52628i | −0.197949 | − | 0.342858i | ||||
\(773\) | 27.7128 | 0.996761 | 0.498380 | − | 0.866959i | \(-0.333928\pi\) | ||||
0.498380 | + | 0.866959i | \(0.333928\pi\) | |||||||
\(774\) | −10.3923 | −0.373544 | ||||||||
\(775\) | −3.50000 | − | 4.33013i | −0.125724 | − | 0.155543i | ||||
\(776\) | 1.00000i | 0.0358979i | ||||||||
\(777\) | − | 12.0000i | − | 0.430498i | ||||||
\(778\) | −24.0000 | + | 13.8564i | −0.860442 | + | 0.496776i | ||||
\(779\) | 24.0000i | 0.859889i | ||||||||
\(780\) | 3.00000 | − | 5.19615i | 0.107417 | − | 0.186052i | ||||
\(781\) | 54.0000 | − | 31.1769i | 1.93227 | − | 1.11560i | ||||
\(782\) | −20.7846 | + | 12.0000i | −0.743256 | + | 0.429119i | ||||
\(783\) | −9.00000 | −0.321634 | ||||||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | 8.66025 | + | 5.00000i | 0.309098 | + | 0.178458i | ||||
\(786\) | −10.3923 | + | 18.0000i | −0.370681 | + | 0.642039i | ||||
\(787\) | −9.00000 | + | 5.19615i | −0.320815 | + | 0.185223i | −0.651756 | − | 0.758429i | \(-0.725967\pi\) |
0.330941 | + | 0.943652i | \(0.392634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00000 | + | 5.19615i | 0.106803 | + | 0.184988i | ||||
\(790\) | − | 10.3923i | − | 0.369742i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.5000 | − | 7.79423i | 0.479702 | − | 0.276956i | ||||
\(793\) | 6.00000 | − | 10.3923i | 0.213066 | − | 0.369042i | ||||
\(794\) | −24.2487 | + | 14.0000i | −0.860555 | + | 0.496841i | ||||
\(795\) | −18.1865 | − | 10.5000i | −0.645010 | − | 0.372397i | ||||
\(796\) | 10.5000 | + | 6.06218i | 0.372163 | + | 0.214868i | ||||
\(797\) | −19.9186 | + | 34.5000i | −0.705552 | + | 1.22205i | 0.260939 | + | 0.965355i | \(0.415968\pi\) |
−0.966492 | + | 0.256697i | \(0.917366\pi\) | |||||||
\(798\) | − | 6.92820i | − | 0.245256i | ||||||
\(799\) | 36.0000 | − | 20.7846i | 1.27359 | − | 0.735307i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 15.5885 | − | 27.0000i | 0.550791 | − | 0.953998i | ||||
\(802\) | 6.92820i | 0.244643i | ||||||||
\(803\) | 31.1769 | − | 18.0000i | 1.10021 | − | 0.635206i | ||||
\(804\) | 3.46410 | 0.122169 | ||||||||
\(805\) | 6.92820i | 0.244187i | ||||||||
\(806\) | −6.92820 | + | 18.0000i | −0.244036 | + | 0.634023i | ||||
\(807\) | −48.0000 | −1.68968 | ||||||||
\(808\) | −15.0000 | −0.527698 | ||||||||
\(809\) | 13.8564 | + | 24.0000i | 0.487165 | + | 0.843795i | 0.999891 | − | 0.0147574i | \(-0.00469758\pi\) |
−0.512726 | + | 0.858552i | \(0.671364\pi\) | |||||||
\(810\) | 9.00000 | 0.316228 | ||||||||
\(811\) | −20.0000 | + | 34.6410i | −0.702295 | + | 1.21641i | 0.265364 | + | 0.964148i | \(0.414508\pi\) |
−0.967659 | + | 0.252262i | \(0.918825\pi\) | |||||||
\(812\) | 0.866025 | + | 1.50000i | 0.0303915 | + | 0.0526397i | ||||
\(813\) | −18.1865 | + | 10.5000i | −0.637830 | + | 0.368251i | ||||
\(814\) | 36.0000 | 1.26180 | ||||||||
\(815\) | 6.92820 | + | 4.00000i | 0.242684 | + | 0.140114i | ||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | −12.0000 | − | 6.92820i | −0.419827 | − | 0.242387i | ||||
\(818\) | −6.06218 | − | 10.5000i | −0.211959 | − | 0.367124i | ||||
\(819\) | 9.00000 | + | 5.19615i | 0.314485 | + | 0.181568i | ||||
\(820\) | 3.00000 | + | 5.19615i | 0.104765 | + | 0.181458i | ||||
\(821\) | −12.1244 | −0.423143 | −0.211571 | − | 0.977363i | \(-0.567858\pi\) | ||||
−0.211571 | + | 0.977363i | \(0.567858\pi\) | |||||||
\(822\) | 24.0000i | 0.837096i | ||||||||
\(823\) | 1.50000 | − | 0.866025i | 0.0522867 | − | 0.0301877i | −0.473629 | − | 0.880725i | \(-0.657056\pi\) |
0.525915 | + | 0.850537i | \(0.323723\pi\) | |||||||
\(824\) | 6.06218 | + | 3.50000i | 0.211186 | + | 0.121928i | ||||
\(825\) | −4.50000 | − | 7.79423i | −0.156670 | − | 0.271360i | ||||
\(826\) | −7.50000 | + | 12.9904i | −0.260958 | + | 0.451993i | ||||
\(827\) | 19.0526 | − | 33.0000i | 0.662522 | − | 1.14752i | −0.317428 | − | 0.948282i | \(-0.602819\pi\) |
0.979951 | − | 0.199240i | \(-0.0638474\pi\) | |||||||
\(828\) | 10.3923 | − | 18.0000i | 0.361158 | − | 0.625543i | ||||
\(829\) | − | 3.46410i | − | 0.120313i | −0.998189 | − | 0.0601566i | \(-0.980840\pi\) | ||
0.998189 | − | 0.0601566i | \(-0.0191600\pi\) | |||||||
\(830\) | −2.59808 | − | 4.50000i | −0.0901805 | − | 0.156197i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000 | + | 1.73205i | 0.104006 | + | 0.0600481i | ||||
\(833\) | 20.7846 | 0.720144 | ||||||||
\(834\) | 18.0000 | + | 31.1769i | 0.623289 | + | 1.07957i | ||||
\(835\) | 10.3923i | 0.359641i | ||||||||
\(836\) | 20.7846 | 0.718851 | ||||||||
\(837\) | −28.5788 | + | 4.50000i | −0.987829 | + | 0.155543i | ||||
\(838\) | 33.0000 | 1.13997 | ||||||||
\(839\) | − | 12.0000i | − | 0.414286i | −0.978311 | − | 0.207143i | \(-0.933583\pi\) | ||
0.978311 | − | 0.207143i | \(-0.0664165\pi\) | |||||||
\(840\) | −0.866025 | − | 1.50000i | −0.0298807 | − | 0.0517549i | ||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | 17.3205 | + | 10.0000i | 0.596904 | + | 0.344623i | ||||
\(843\) | 18.0000 | − | 10.3923i | 0.619953 | − | 0.357930i | ||||
\(844\) | −5.00000 | − | 8.66025i | −0.172107 | − | 0.298098i | ||||
\(845\) | − | 1.00000i | − | 0.0344010i | ||||||
\(846\) | −18.0000 | + | 31.1769i | −0.618853 | + | 1.07188i | ||||
\(847\) | 8.00000 | − | 13.8564i | 0.274883 | − | 0.476112i | ||||
\(848\) | 6.06218 | − | 10.5000i | 0.208176 | − | 0.360571i | ||||
\(849\) | 19.0526 | + | 33.0000i | 0.653882 | + | 1.13256i | ||||
\(850\) | −3.00000 | − | 1.73205i | −0.102899 | − | 0.0594089i | ||||
\(851\) | 41.5692 | − | 24.0000i | 1.42497 | − | 0.822709i | ||||
\(852\) | 20.7846i | 0.712069i | ||||||||
\(853\) | −2.00000 | −0.0684787 | −0.0342393 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342393 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(854\) | −1.73205 | − | 3.00000i | −0.0592696 | − | 0.102658i | ||||
\(855\) | 10.3923 | + | 6.00000i | 0.355409 | + | 0.205196i | ||||
\(856\) | 1.50000 | + | 2.59808i | 0.0512689 | + | 0.0888004i | ||||
\(857\) | 25.9808 | + | 15.0000i | 0.887486 | + | 0.512390i | 0.873119 | − | 0.487507i | \(-0.162093\pi\) |
0.0143666 | + | 0.999897i | \(0.495427\pi\) | |||||||
\(858\) | −15.5885 | + | 27.0000i | −0.532181 | + | 0.921765i | ||||
\(859\) | −3.00000 | − | 1.73205i | −0.102359 | − | 0.0590968i | 0.447947 | − | 0.894060i | \(-0.352155\pi\) |
−0.550305 | + | 0.834963i | \(0.685489\pi\) | |||||||
\(860\) | −3.46410 | −0.118125 | ||||||||
\(861\) | −9.00000 | + | 5.19615i | −0.306719 | + | 0.177084i | ||||
\(862\) | 15.0000 | + | 25.9808i | 0.510902 | + | 0.884908i | ||||
\(863\) | 6.92820 | − | 12.0000i | 0.235839 | − | 0.408485i | −0.723677 | − | 0.690138i | \(-0.757550\pi\) |
0.959516 | + | 0.281654i | \(0.0908829\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | 1.50000 | + | 2.59808i | 0.0510015 | + | 0.0883372i | ||||
\(866\) | −27.7128 | −0.941720 | ||||||||
\(867\) | −8.66025 | −0.294118 | ||||||||
\(868\) | 3.50000 | + | 4.33013i | 0.118798 | + | 0.146974i | ||||
\(869\) | 54.0000i | 1.83182i | ||||||||
\(870\) | −3.00000 | −0.101710 | ||||||||
\(871\) | −6.00000 | + | 3.46410i | −0.203302 | + | 0.117377i | ||||
\(872\) | 4.00000i | 0.135457i | ||||||||
\(873\) | 1.50000 | − | 2.59808i | 0.0507673 | − | 0.0879316i | ||||
\(874\) | 24.0000 | − | 13.8564i | 0.811812 | − | 0.468700i | ||||
\(875\) | −0.866025 | + | 0.500000i | −0.0292770 | + | 0.0169031i | ||||
\(876\) | 12.0000i | 0.405442i | ||||||||
\(877\) | −17.0000 | + | 29.4449i | −0.574049 | + | 0.994282i | 0.422095 | + | 0.906552i | \(0.361295\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | 14.7224 | + | 8.50000i | 0.496858 | + | 0.286861i | ||||
\(879\) | 13.5000 | + | 7.79423i | 0.455344 | + | 0.262893i | ||||
\(880\) | 4.50000 | − | 2.59808i | 0.151695 | − | 0.0875811i | ||||
\(881\) | 3.46410 | − | 6.00000i | 0.116709 | − | 0.202145i | −0.801753 | − | 0.597656i | \(-0.796099\pi\) |
0.918461 | + | 0.395511i | \(0.129432\pi\) | |||||||
\(882\) | −15.5885 | + | 9.00000i | −0.524891 | + | 0.303046i | ||||
\(883\) | 20.7846i | 0.699458i | 0.936851 | + | 0.349729i | \(0.113726\pi\) | ||||
−0.936851 | + | 0.349729i | \(0.886274\pi\) | |||||||
\(884\) | 12.0000i | 0.403604i | ||||||||
\(885\) | −12.9904 | − | 22.5000i | −0.436667 | − | 0.756329i | ||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | −20.7846 | + | 12.0000i | −0.697879 | + | 0.402921i | −0.806557 | − | 0.591156i | \(-0.798672\pi\) |
0.108678 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(888\) | −6.00000 | + | 10.3923i | −0.201347 | + | 0.348743i | ||||
\(889\) | 10.5000 | + | 6.06218i | 0.352159 | + | 0.203319i | ||||
\(890\) | 5.19615 | − | 9.00000i | 0.174175 | − | 0.301681i | ||||
\(891\) | −46.7654 | −1.56670 | ||||||||
\(892\) | −13.5000 | + | 7.79423i | −0.452013 | + | 0.260970i | ||||
\(893\) | −41.5692 | + | 24.0000i | −1.39106 | + | 0.803129i | ||||
\(894\) | −12.9904 | + | 22.5000i | −0.434463 | + | 0.752513i | ||||
\(895\) | − | 15.5885i | − | 0.521065i | ||||||
\(896\) | 0.866025 | − | 0.500000i | 0.0289319 | − | 0.0167038i | ||||
\(897\) | 41.5692i | 1.38796i | ||||||||
\(898\) | − | 6.92820i | − | 0.231197i | ||||||
\(899\) | 9.52628 | − | 1.50000i | 0.317719 | − | 0.0500278i | ||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | 42.0000 | 1.39922 | ||||||||
\(902\) | −15.5885 | − | 27.0000i | −0.519039 | − | 0.899002i | ||||
\(903\) | − | 6.00000i | − | 0.199667i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.73205 | + | 3.00000i | 0.0575753 | + | 0.0997234i | ||||
\(906\) | 7.50000 | + | 12.9904i | 0.249171 | + | 0.431577i | ||||
\(907\) | 16.0000 | 0.531271 | 0.265636 | − | 0.964073i | \(-0.414418\pi\) | ||||
0.265636 | + | 0.964073i | \(0.414418\pi\) | |||||||
\(908\) | −12.9904 | − | 7.50000i | −0.431101 | − | 0.248896i | ||||
\(909\) | 38.9711 | + | 22.5000i | 1.29259 | + | 0.746278i | ||||
\(910\) | 3.00000 | + | 1.73205i | 0.0994490 | + | 0.0574169i | ||||
\(911\) | −8.66025 | − | 15.0000i | −0.286927 | − | 0.496972i | 0.686148 | − | 0.727462i | \(-0.259300\pi\) |
−0.973075 | + | 0.230490i | \(0.925967\pi\) | |||||||
\(912\) | −3.46410 | + | 6.00000i | −0.114708 | + | 0.198680i | ||||
\(913\) | 13.5000 | + | 23.3827i | 0.446785 | + | 0.773854i | ||||
\(914\) | 6.92820 | 0.229165 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 24.0000 | − | 13.8564i | 0.792982 | − | 0.457829i | ||||
\(917\) | −10.3923 | − | 6.00000i | −0.343184 | − | 0.198137i | ||||
\(918\) | −15.5885 | + | 9.00000i | −0.514496 | + | 0.297044i | ||||
\(919\) | 8.50000 | − | 14.7224i | 0.280389 | − | 0.485648i | −0.691091 | − | 0.722767i | \(-0.742870\pi\) |
0.971481 | + | 0.237119i | \(0.0762032\pi\) | |||||||
\(920\) | 3.46410 | − | 6.00000i | 0.114208 | − | 0.197814i | ||||
\(921\) | 12.1244 | − | 21.0000i | 0.399511 | − | 0.691974i | ||||
\(922\) | 39.8372i | 1.31197i | ||||||||
\(923\) | −20.7846 | − | 36.0000i | −0.684134 | − | 1.18495i | ||||
\(924\) | 4.50000 | + | 7.79423i | 0.148039 | + | 0.256411i | ||||
\(925\) | 6.00000 | + | 3.46410i | 0.197279 | + | 0.113899i | ||||
\(926\) | −12.1244 | −0.398431 | ||||||||
\(927\) | −10.5000 | − | 18.1865i | −0.344865 | − | 0.597324i | ||||
\(928\) | − | 1.73205i | − | 0.0568574i | ||||||
\(929\) | −45.0333 | −1.47750 | −0.738748 | − | 0.673982i | \(-0.764582\pi\) | ||||
−0.738748 | + | 0.673982i | \(0.764582\pi\) | |||||||
\(930\) | −9.52628 | + | 1.50000i | −0.312379 | + | 0.0491869i | ||||
\(931\) | −24.0000 | −0.786568 | ||||||||
\(932\) | − | 18.0000i | − | 0.589610i | ||||||
\(933\) | 45.0000 | − | 25.9808i | 1.47323 | − | 0.850572i | ||||
\(934\) | 27.0000 | 0.883467 | ||||||||
\(935\) | 15.5885 | + | 9.00000i | 0.509797 | + | 0.294331i | ||||
\(936\) | −5.19615 | − | 9.00000i | −0.169842 | − | 0.294174i | ||||
\(937\) | −5.00000 | − | 8.66025i | −0.163343 | − | 0.282918i | 0.772723 | − | 0.634744i | \(-0.218894\pi\) |
−0.936066 | + | 0.351826i | \(0.885561\pi\) | |||||||
\(938\) | 2.00000i | 0.0653023i | ||||||||
\(939\) | 38.9711 | + | 22.5000i | 1.27178 | + | 0.734260i | ||||
\(940\) | −6.00000 | + | 10.3923i | −0.195698 | + | 0.338960i | ||||
\(941\) | 6.06218 | − | 10.5000i | 0.197621 | − | 0.342290i | −0.750135 | − | 0.661284i | \(-0.770012\pi\) |
0.947757 | + | 0.318994i | \(0.103345\pi\) | |||||||
\(942\) | 15.0000 | − | 8.66025i | 0.488726 | − | 0.282166i | ||||
\(943\) | −36.0000 | − | 20.7846i | −1.17232 | − | 0.676840i | ||||
\(944\) | 12.9904 | − | 7.50000i | 0.422801 | − | 0.244104i | ||||
\(945\) | 5.19615i | 0.169031i | ||||||||
\(946\) | 18.0000 | 0.585230 | ||||||||
\(947\) | 12.1244 | + | 21.0000i | 0.393989 | + | 0.682408i | 0.992972 | − | 0.118354i | \(-0.0377616\pi\) |
−0.598983 | + | 0.800762i | \(0.704428\pi\) | |||||||
\(948\) | −15.5885 | − | 9.00000i | −0.506290 | − | 0.292306i | ||||
\(949\) | −12.0000 | − | 20.7846i | −0.389536 | − | 0.674697i | ||||
\(950\) | 3.46410 | + | 2.00000i | 0.112390 | + | 0.0648886i | ||||
\(951\) | 4.50000 | + | 2.59808i | 0.145922 | + | 0.0842484i | ||||
\(952\) | 3.00000 | + | 1.73205i | 0.0972306 | + | 0.0561361i | ||||
\(953\) | 10.3923 | 0.336640 | 0.168320 | − | 0.985732i | \(-0.446166\pi\) | ||||
0.168320 | + | 0.985732i | \(0.446166\pi\) | |||||||
\(954\) | −31.5000 | + | 18.1865i | −1.01985 | + | 0.588811i | ||||
\(955\) | 6.00000 | + | 10.3923i | 0.194155 | + | 0.336287i | ||||
\(956\) | −13.8564 | + | 24.0000i | −0.448148 | + | 0.776215i | ||||
\(957\) | 15.5885 | 0.503903 | ||||||||
\(958\) | 6.00000 | + | 10.3923i | 0.193851 | + | 0.335760i | ||||
\(959\) | −13.8564 | −0.447447 | ||||||||
\(960\) | 1.73205i | 0.0559017i | ||||||||
\(961\) | 29.5000 | − | 9.52628i | 0.951613 | − | 0.307299i | ||||
\(962\) | − | 24.0000i | − | 0.773791i | ||||||
\(963\) | − | 9.00000i | − | 0.290021i | ||||||
\(964\) | 13.5000 | − | 7.79423i | 0.434806 | − | 0.251035i | ||||
\(965\) | 11.0000i | 0.354103i | ||||||||
\(966\) | 10.3923 | + | 6.00000i | 0.334367 | + | 0.193047i | ||||
\(967\) | −27.0000 | + | 15.5885i | −0.868261 | + | 0.501291i | −0.866770 | − | 0.498708i | \(-0.833808\pi\) |
−0.00149135 | + | 0.999999i | \(0.500475\pi\) | |||||||
\(968\) | −13.8564 | + | 8.00000i | −0.445362 | + | 0.257130i | ||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | 0.500000 | − | 0.866025i | 0.0160540 | − | 0.0278064i | ||||
\(971\) | 23.3827 | + | 13.5000i | 0.750386 | + | 0.433236i | 0.825833 | − | 0.563914i | \(-0.190705\pi\) |
−0.0754473 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(972\) | 7.79423 | − | 13.5000i | 0.250000 | − | 0.433013i | ||||
\(973\) | −18.0000 | + | 10.3923i | −0.577054 | + | 0.333162i | ||||
\(974\) | −18.1865 | + | 31.5000i | −0.582734 | + | 1.00933i | ||||
\(975\) | −5.19615 | + | 3.00000i | −0.166410 | + | 0.0960769i | ||||
\(976\) | 3.46410i | 0.110883i | ||||||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | 12.0000 | − | 6.92820i | 0.383718 | − | 0.221540i | ||||
\(979\) | −27.0000 | + | 46.7654i | −0.862924 | + | 1.49463i | ||||
\(980\) | −5.19615 | + | 3.00000i | −0.165985 | + | 0.0958315i | ||||
\(981\) | 6.00000 | − | 10.3923i | 0.191565 | − | 0.331801i | ||||
\(982\) | −31.5000 | − | 18.1865i | −1.00521 | − | 0.580356i | ||||
\(983\) | −8.66025 | + | 15.0000i | −0.276219 | + | 0.478426i | −0.970442 | − | 0.241334i | \(-0.922415\pi\) |
0.694223 | + | 0.719760i | \(0.255748\pi\) | |||||||
\(984\) | 10.3923 | 0.331295 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.19615 | − | 3.00000i | 0.165479 | − | 0.0955395i | ||||
\(987\) | −18.0000 | − | 10.3923i | −0.572946 | − | 0.330791i | ||||
\(988\) | − | 13.8564i | − | 0.440831i | ||||||
\(989\) | 20.7846 | − | 12.0000i | 0.660912 | − | 0.381578i | ||||
\(990\) | −15.5885 | −0.495434 | ||||||||
\(991\) | − | 24.2487i | − | 0.770286i | −0.922857 | − | 0.385143i | \(-0.874152\pi\) | ||
0.922857 | − | 0.385143i | \(-0.125848\pi\) | |||||||
\(992\) | −0.866025 | − | 5.50000i | −0.0274963 | − | 0.174625i | ||||
\(993\) | 30.0000i | 0.952021i | ||||||||
\(994\) | −12.0000 | −0.380617 | ||||||||
\(995\) | −6.06218 | − | 10.5000i | −0.192184 | − | 0.332872i | ||||
\(996\) | −9.00000 | −0.285176 | ||||||||
\(997\) | −1.00000 | + | 1.73205i | −0.0316703 | + | 0.0548546i | −0.881426 | − | 0.472322i | \(-0.843416\pi\) |
0.849756 | + | 0.527176i | \(0.176749\pi\) | |||||||
\(998\) | −12.1244 | − | 21.0000i | −0.383790 | − | 0.664743i | ||||
\(999\) | 31.1769 | − | 18.0000i | 0.986394 | − | 0.569495i |
(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 | 930.2.o.c.161.2 | yes | 4 | |
3.2 | odd | 2 | inner | 930.2.o.c.161.1 | ✓ | 4 | |
31.26 | odd | 6 | inner | 930.2.o.c.491.2 | yes | 4 | |
93.26 | even | 6 | inner | 930.2.o.c.491.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.c.161.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
930.2.o.c.161.2 | yes | 4 | 1.1 | even | 1 | trivial | |
930.2.o.c.491.1 | yes | 4 | 93.26 | even | 6 | inner | |
930.2.o.c.491.2 | yes | 4 | 31.26 | odd | 6 | inner |