Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(295,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.f (of order \(3\), 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: | \(5.08647060876\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 393.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.393 |
Dual form | 637.2.f.a.295.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | 0.633316 | − | 0.773893i | \(-0.281693\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(3\) | −1.50000 | − | 2.59808i | −0.866025 | − | 1.50000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | −1.50000 | + | 2.59808i | −0.612372 | + | 1.06066i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | −3.00000 | + | 5.19615i | −1.00000 | + | 1.73205i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | −3.00000 | −0.866025 | ||||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.50000 | + | 7.79423i | 1.16190 | + | 2.01246i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 6.00000 | 1.41421 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 4.50000 | + | 7.79423i | 0.918559 | + | 1.59099i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | −3.50000 | + | 0.866025i | −0.686406 | + | 0.169842i | ||||
\(27\) | 9.00000 | 1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.50000 | − | 6.06218i | −0.649934 | − | 1.12572i | −0.983138 | − | 0.182864i | \(-0.941463\pi\) |
0.333205 | − | 0.942855i | \(-0.391870\pi\) | |||||||
\(30\) | 4.50000 | − | 7.79423i | 0.821584 | − | 1.42302i | ||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | −2.50000 | + | 4.33013i | −0.441942 | + | 0.765466i | ||||
\(33\) | 4.50000 | − | 7.79423i | 0.783349 | − | 1.35680i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −10.5000 | + | 2.59808i | −1.68135 | + | 0.416025i | ||||
\(40\) | 9.00000 | 1.42302 | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | − | 6.06218i | 0.533745 | − | 0.924473i | −0.465478 | − | 0.885059i | \(-0.654118\pi\) |
0.999223 | − | 0.0394140i | \(-0.0125491\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 9.00000 | − | 15.5885i | 1.34164 | − | 2.32379i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | −0.0729325 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729325 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(48\) | 1.50000 | − | 2.59808i | 0.216506 | − | 0.375000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | −2.50000 | − | 2.59808i | −0.346688 | − | 0.360288i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | −4.50000 | − | 7.79423i | −0.606780 | − | 1.05097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | −3.50000 | + | 6.06218i | −0.459573 | + | 0.796003i | ||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 9.00000 | 1.16190 | ||||||||
\(61\) | −6.50000 | + | 11.2583i | −0.832240 | + | 1.44148i | 0.0640184 | + | 0.997949i | \(0.479608\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 1.50000 | + | 2.59808i | 0.190500 | + | 0.329956i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −3.00000 | + | 10.3923i | −0.372104 | + | 1.28901i | ||||
\(66\) | −9.00000 | −1.10782 | ||||||||
\(67\) | 1.50000 | + | 2.59808i | 0.183254 | + | 0.317406i | 0.942987 | − | 0.332830i | \(-0.108004\pi\) |
−0.759733 | + | 0.650236i | \(0.774670\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.50000 | + | 11.2583i | −0.771408 | + | 1.33612i | 0.165383 | + | 0.986229i | \(0.447114\pi\) |
−0.936791 | + | 0.349889i | \(0.886219\pi\) | |||||||
\(72\) | 9.00000 | − | 15.5885i | 1.06066 | − | 1.83712i | ||||
\(73\) | 13.0000 | 1.52153 | 0.760767 | − | 0.649025i | \(-0.224823\pi\) | ||||
0.760767 | + | 0.649025i | \(0.224823\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | −6.00000 | − | 10.3923i | −0.692820 | − | 1.20000i | ||||
\(76\) | 0.500000 | + | 0.866025i | 0.0573539 | + | 0.0993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.50000 | + | 7.79423i | 0.849208 | + | 0.882523i | ||||
\(79\) | −3.00000 | −0.337526 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | − | 5.19615i | 0.325396 | − | 0.563602i | ||||
\(86\) | −7.00000 | −0.754829 | ||||||||
\(87\) | −10.5000 | + | 18.1865i | −1.12572 | + | 1.94980i | ||||
\(88\) | −4.50000 | − | 7.79423i | −0.479702 | − | 0.830868i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | −18.0000 | −1.89737 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.50000 | + | 7.79423i | 0.466628 | + | 0.808224i | ||||
\(94\) | 0.500000 | + | 0.866025i | 0.0515711 | + | 0.0893237i | ||||
\(95\) | 1.50000 | − | 2.59808i | 0.153897 | − | 0.266557i | ||||
\(96\) | 15.0000 | 1.53093 | ||||||||
\(97\) | −2.50000 | + | 4.33013i | −0.253837 | + | 0.439658i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.0000 | −1.80907 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −2.50000 | − | 4.33013i | −0.248759 | − | 0.430864i | 0.714423 | − | 0.699715i | \(-0.246689\pi\) |
−0.963182 | + | 0.268851i | \(0.913356\pi\) | |||||||
\(102\) | −3.00000 | − | 5.19615i | −0.297044 | − | 0.514496i | ||||
\(103\) | −5.00000 | −0.492665 | −0.246332 | − | 0.969185i | \(-0.579225\pi\) | ||||
−0.246332 | + | 0.969185i | \(0.579225\pi\) | |||||||
\(104\) | −3.00000 | + | 10.3923i | −0.294174 | + | 1.01905i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.50000 | − | 2.59808i | −0.145693 | − | 0.252347i | ||||
\(107\) | −4.00000 | − | 6.92820i | −0.386695 | − | 0.669775i | 0.605308 | − | 0.795991i | \(-0.293050\pi\) |
−0.992003 | + | 0.126217i | \(0.959717\pi\) | |||||||
\(108\) | 4.50000 | − | 7.79423i | 0.433013 | − | 0.750000i | ||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | −4.50000 | + | 7.79423i | −0.429058 | + | 0.743151i | ||||
\(111\) | −3.00000 | + | 5.19615i | −0.284747 | + | 0.493197i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.50000 | + | 12.9904i | −0.705541 | + | 1.22203i | 0.260955 | + | 0.965351i | \(0.415962\pi\) |
−0.966496 | + | 0.256681i | \(0.917371\pi\) | |||||||
\(114\) | −1.50000 | − | 2.59808i | −0.140488 | − | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.00000 | −0.649934 | ||||||||
\(117\) | 15.0000 | + | 15.5885i | 1.38675 | + | 1.44115i | ||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −13.5000 | − | 23.3827i | −1.23238 | − | 2.13454i | ||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 13.0000 | 1.17696 | ||||||||
\(123\) | 4.50000 | − | 7.79423i | 0.405751 | − | 0.702782i | ||||
\(124\) | −1.50000 | + | 2.59808i | −0.134704 | + | 0.233314i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.50000 | − | 9.52628i | −0.488046 | − | 0.845321i | 0.511859 | − | 0.859069i | \(-0.328957\pi\) |
−0.999905 | + | 0.0137486i | \(0.995624\pi\) | |||||||
\(128\) | 1.50000 | + | 2.59808i | 0.132583 | + | 0.229640i | ||||
\(129\) | −21.0000 | −1.84895 | ||||||||
\(130\) | 10.5000 | − | 2.59808i | 0.920911 | − | 0.227866i | ||||
\(131\) | −5.00000 | −0.436852 | −0.218426 | − | 0.975854i | \(-0.570092\pi\) | ||||
−0.218426 | + | 0.975854i | \(0.570092\pi\) | |||||||
\(132\) | −4.50000 | − | 7.79423i | −0.391675 | − | 0.678401i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.50000 | − | 2.59808i | 0.129580 | − | 0.224440i | ||||
\(135\) | −27.0000 | −2.32379 | ||||||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | −5.00000 | + | 8.66025i | −0.427179 | + | 0.739895i | −0.996621 | − | 0.0821359i | \(-0.973826\pi\) |
0.569442 | + | 0.822031i | \(0.307159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.50000 | + | 12.9904i | −0.636142 | + | 1.10183i | 0.350130 | + | 0.936701i | \(0.386137\pi\) |
−0.986272 | + | 0.165129i | \(0.947196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.50000 | + | 2.59808i | 0.126323 | + | 0.218797i | ||||
\(142\) | 13.0000 | 1.09094 | ||||||||
\(143\) | 10.5000 | − | 2.59808i | 0.878054 | − | 0.217262i | ||||
\(144\) | −6.00000 | −0.500000 | ||||||||
\(145\) | 10.5000 | + | 18.1865i | 0.871978 | + | 1.51031i | ||||
\(146\) | −6.50000 | − | 11.2583i | −0.537944 | − | 0.931746i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −7.50000 | + | 12.9904i | −0.614424 | + | 1.06421i | 0.376061 | + | 0.926595i | \(0.377278\pi\) |
−0.990485 | + | 0.137619i | \(0.956055\pi\) | |||||||
\(150\) | −6.00000 | + | 10.3923i | −0.489898 | + | 0.848528i | ||||
\(151\) | −21.0000 | −1.70896 | −0.854478 | − | 0.519488i | \(-0.826123\pi\) | ||||
−0.854478 | + | 0.519488i | \(0.826123\pi\) | |||||||
\(152\) | 1.50000 | − | 2.59808i | 0.121666 | − | 0.210732i | ||||
\(153\) | −6.00000 | − | 10.3923i | −0.485071 | − | 0.840168i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00000 | 0.722897 | ||||||||
\(156\) | −3.00000 | + | 10.3923i | −0.240192 | + | 0.832050i | ||||
\(157\) | −19.0000 | −1.51637 | −0.758183 | − | 0.652042i | \(-0.773912\pi\) | ||||
−0.758183 | + | 0.652042i | \(0.773912\pi\) | |||||||
\(158\) | 1.50000 | + | 2.59808i | 0.119334 | + | 0.206692i | ||||
\(159\) | −4.50000 | − | 7.79423i | −0.356873 | − | 0.618123i | ||||
\(160\) | 7.50000 | − | 12.9904i | 0.592927 | − | 1.02698i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | −13.5000 | + | 23.3827i | −1.05097 | + | 1.82034i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.50000 | − | 11.2583i | −0.502985 | − | 0.871196i | −0.999994 | − | 0.00345033i | \(-0.998902\pi\) |
0.497009 | − | 0.867745i | \(-0.334432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | −6.00000 | −0.460179 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | −3.50000 | − | 6.06218i | −0.266872 | − | 0.462237i | ||||
\(173\) | 9.50000 | − | 16.4545i | 0.722272 | − | 1.25101i | −0.237816 | − | 0.971310i | \(-0.576431\pi\) |
0.960087 | − | 0.279701i | \(-0.0902353\pi\) | |||||||
\(174\) | 21.0000 | 1.59201 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −8.50000 | − | 14.7224i | −0.635320 | − | 1.10041i | −0.986447 | − | 0.164079i | \(-0.947535\pi\) |
0.351127 | − | 0.936328i | \(-0.385798\pi\) | |||||||
\(180\) | −9.00000 | − | 15.5885i | −0.670820 | − | 1.16190i | ||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 39.0000 | 2.88296 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 4.50000 | − | 7.79423i | 0.329956 | − | 0.571501i | ||||
\(187\) | −6.00000 | −0.438763 | ||||||||
\(188\) | −0.500000 | + | 0.866025i | −0.0364662 | + | 0.0631614i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.00000 | −0.217643 | ||||||||
\(191\) | 8.50000 | − | 14.7224i | 0.615038 | − | 1.06528i | −0.375339 | − | 0.926887i | \(-0.622474\pi\) |
0.990378 | − | 0.138390i | \(-0.0441928\pi\) | |||||||
\(192\) | −10.5000 | − | 18.1865i | −0.757772 | − | 1.31250i | ||||
\(193\) | −3.50000 | − | 6.06218i | −0.251936 | − | 0.436365i | 0.712123 | − | 0.702055i | \(-0.247734\pi\) |
−0.964059 | + | 0.265689i | \(0.914400\pi\) | |||||||
\(194\) | 5.00000 | 0.358979 | ||||||||
\(195\) | 31.5000 | − | 7.79423i | 2.25576 | − | 0.558156i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.500000 | + | 0.866025i | 0.0356235 | + | 0.0617018i | 0.883287 | − | 0.468832i | \(-0.155325\pi\) |
−0.847664 | + | 0.530534i | \(0.821992\pi\) | |||||||
\(198\) | 9.00000 | + | 15.5885i | 0.639602 | + | 1.10782i | ||||
\(199\) | −10.0000 | + | 17.3205i | −0.708881 | + | 1.22782i | 0.256391 | + | 0.966573i | \(0.417466\pi\) |
−0.965272 | + | 0.261245i | \(0.915867\pi\) | |||||||
\(200\) | −12.0000 | −0.848528 | ||||||||
\(201\) | 4.50000 | − | 7.79423i | 0.317406 | − | 0.549762i | ||||
\(202\) | −2.50000 | + | 4.33013i | −0.175899 | + | 0.304667i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.00000 | − | 5.19615i | 0.210042 | − | 0.363803i | ||||
\(205\) | −4.50000 | − | 7.79423i | −0.314294 | − | 0.544373i | ||||
\(206\) | 2.50000 | + | 4.33013i | 0.174183 | + | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.50000 | − | 0.866025i | 0.242681 | − | 0.0600481i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.50000 | − | 6.06218i | −0.240950 | − | 0.417338i | 0.720035 | − | 0.693938i | \(-0.244126\pi\) |
−0.960985 | + | 0.276600i | \(0.910792\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | 39.0000 | 2.67224 | ||||||||
\(214\) | −4.00000 | + | 6.92820i | −0.273434 | + | 0.473602i | ||||
\(215\) | −10.5000 | + | 18.1865i | −0.716094 | + | 1.24031i | ||||
\(216\) | −27.0000 | −1.83712 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.50000 | − | 6.06218i | −0.237050 | − | 0.410582i | ||||
\(219\) | −19.5000 | − | 33.7750i | −1.31769 | − | 2.28230i | ||||
\(220\) | −9.00000 | −0.606780 | ||||||||
\(221\) | 5.00000 | + | 5.19615i | 0.336336 | + | 0.349531i | ||||
\(222\) | 6.00000 | 0.402694 | ||||||||
\(223\) | −4.50000 | − | 7.79423i | −0.301342 | − | 0.521940i | 0.675098 | − | 0.737728i | \(-0.264101\pi\) |
−0.976440 | + | 0.215788i | \(0.930768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | + | 20.7846i | −0.800000 | + | 1.38564i | ||||
\(226\) | 15.0000 | 0.997785 | ||||||||
\(227\) | −2.00000 | + | 3.46410i | −0.132745 | + | 0.229920i | −0.924734 | − | 0.380615i | \(-0.875712\pi\) |
0.791989 | + | 0.610535i | \(0.209046\pi\) | |||||||
\(228\) | 1.50000 | − | 2.59808i | 0.0993399 | − | 0.172062i | ||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.5000 | + | 18.1865i | 0.689359 | + | 1.19400i | ||||
\(233\) | −21.0000 | −1.37576 | −0.687878 | − | 0.725826i | \(-0.741458\pi\) | ||||
−0.687878 | + | 0.725826i | \(0.741458\pi\) | |||||||
\(234\) | 6.00000 | − | 20.7846i | 0.392232 | − | 1.35873i | ||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 2.00000 | + | 3.46410i | 0.130189 | + | 0.225494i | ||||
\(237\) | 4.50000 | + | 7.79423i | 0.292306 | + | 0.506290i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | −4.50000 | + | 7.79423i | −0.290474 | + | 0.503115i | ||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.50000 | + | 11.2583i | 0.416120 | + | 0.720741i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 2.50000 | + | 2.59808i | 0.159071 | + | 0.165312i | ||||
\(248\) | 9.00000 | 0.571501 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.50000 | − | 2.59808i | −0.0948683 | − | 0.164317i | ||||
\(251\) | −11.5000 | + | 19.9186i | −0.725874 | + | 1.25725i | 0.232740 | + | 0.972539i | \(0.425231\pi\) |
−0.958613 | + | 0.284711i | \(0.908102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.50000 | + | 9.52628i | −0.345101 | + | 0.597732i | ||||
\(255\) | −18.0000 | −1.12720 | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | −1.00000 | − | 1.73205i | −0.0623783 | − | 0.108042i | 0.833150 | − | 0.553047i | \(-0.186535\pi\) |
−0.895528 | + | 0.445005i | \(0.853202\pi\) | |||||||
\(258\) | 10.5000 | + | 18.1865i | 0.653701 | + | 1.13224i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.50000 | + | 7.79423i | 0.465130 | + | 0.483378i | ||||
\(261\) | 42.0000 | 2.59973 | ||||||||
\(262\) | 2.50000 | + | 4.33013i | 0.154451 | + | 0.267516i | ||||
\(263\) | 13.5000 | + | 23.3827i | 0.832446 | + | 1.44184i | 0.896093 | + | 0.443866i | \(0.146393\pi\) |
−0.0636476 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(264\) | −13.5000 | + | 23.3827i | −0.830868 | + | 1.43910i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00000 | − | 15.5885i | 0.550791 | − | 0.953998i | ||||
\(268\) | 3.00000 | 0.183254 | ||||||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | 13.5000 | + | 23.3827i | 0.821584 | + | 1.42302i | ||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 6.00000 | + | 10.3923i | 0.361814 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0000 | + | 19.0526i | −0.660926 | + | 1.14476i | 0.319447 | + | 0.947604i | \(0.396503\pi\) |
−0.980373 | + | 0.197153i | \(0.936830\pi\) | |||||||
\(278\) | 15.0000 | 0.899640 | ||||||||
\(279\) | 9.00000 | − | 15.5885i | 0.538816 | − | 0.933257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 1.50000 | − | 2.59808i | 0.0893237 | − | 0.154713i | ||||
\(283\) | 0.500000 | + | 0.866025i | 0.0297219 | + | 0.0514799i | 0.880504 | − | 0.474039i | \(-0.157204\pi\) |
−0.850782 | + | 0.525519i | \(0.823871\pi\) | |||||||
\(284\) | 6.50000 | + | 11.2583i | 0.385704 | + | 0.668059i | ||||
\(285\) | −9.00000 | −0.533114 | ||||||||
\(286\) | −7.50000 | − | 7.79423i | −0.443484 | − | 0.460882i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −15.0000 | − | 25.9808i | −0.883883 | − | 1.53093i | ||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 10.5000 | − | 18.1865i | 0.616581 | − | 1.06795i | ||||
\(291\) | 15.0000 | 0.879316 | ||||||||
\(292\) | 6.50000 | − | 11.2583i | 0.380384 | − | 0.658844i | ||||
\(293\) | 5.50000 | − | 9.52628i | 0.321313 | − | 0.556531i | −0.659446 | − | 0.751752i | \(-0.729209\pi\) |
0.980759 | + | 0.195221i | \(0.0625424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 10.3923i | 0.349334 | − | 0.605063i | ||||
\(296\) | 3.00000 | + | 5.19615i | 0.174371 | + | 0.302020i | ||||
\(297\) | 13.5000 | + | 23.3827i | 0.783349 | + | 1.35680i | ||||
\(298\) | 15.0000 | 0.868927 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.0000 | −0.692820 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.5000 | + | 18.1865i | 0.604207 | + | 1.04652i | ||||
\(303\) | −7.50000 | + | 12.9904i | −0.430864 | + | 0.746278i | ||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 19.5000 | − | 33.7750i | 1.11657 | − | 1.93395i | ||||
\(306\) | −6.00000 | + | 10.3923i | −0.342997 | + | 0.594089i | ||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.50000 | + | 12.9904i | 0.426660 | + | 0.738997i | ||||
\(310\) | −4.50000 | − | 7.79423i | −0.255583 | − | 0.442682i | ||||
\(311\) | 9.00000 | 0.510343 | 0.255172 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255172 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(312\) | 31.5000 | − | 7.79423i | 1.78334 | − | 0.441261i | ||||
\(313\) | −19.0000 | −1.07394 | −0.536972 | − | 0.843600i | \(-0.680432\pi\) | ||||
−0.536972 | + | 0.843600i | \(0.680432\pi\) | |||||||
\(314\) | 9.50000 | + | 16.4545i | 0.536116 | + | 0.928580i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.50000 | + | 2.59808i | −0.0843816 | + | 0.146153i | ||||
\(317\) | −9.00000 | −0.505490 | −0.252745 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252745 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(318\) | −4.50000 | + | 7.79423i | −0.252347 | + | 0.437079i | ||||
\(319\) | 10.5000 | − | 18.1865i | 0.587887 | − | 1.01825i | ||||
\(320\) | −21.0000 | −1.17394 | ||||||||
\(321\) | −12.0000 | + | 20.7846i | −0.669775 | + | 1.16008i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00000 | − | 1.73205i | −0.0556415 | − | 0.0963739i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 4.00000 | − | 13.8564i | 0.221880 | − | 0.768615i | ||||
\(326\) | −1.00000 | −0.0553849 | ||||||||
\(327\) | −10.5000 | − | 18.1865i | −0.580651 | − | 1.00572i | ||||
\(328\) | −4.50000 | − | 7.79423i | −0.248471 | − | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 27.0000 | 1.48630 | ||||||||
\(331\) | 14.5000 | − | 25.1147i | 0.796992 | − | 1.38043i | −0.124574 | − | 0.992210i | \(-0.539757\pi\) |
0.921567 | − | 0.388221i | \(-0.126910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | −6.50000 | + | 11.2583i | −0.355664 | + | 0.616028i | ||||
\(335\) | −4.50000 | − | 7.79423i | −0.245861 | − | 0.425844i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | −0.500000 | + | 12.9904i | −0.0271964 | + | 0.706584i | ||||
\(339\) | 45.0000 | 2.44406 | ||||||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | −4.50000 | − | 7.79423i | −0.243689 | − | 0.422081i | ||||
\(342\) | −3.00000 | + | 5.19615i | −0.162221 | + | 0.280976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.5000 | + | 18.1865i | −0.566122 | + | 0.980552i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.0000 | −1.02145 | ||||||||
\(347\) | 4.00000 | − | 6.92820i | 0.214731 | − | 0.371925i | −0.738458 | − | 0.674299i | \(-0.764446\pi\) |
0.953189 | + | 0.302374i | \(0.0977791\pi\) | |||||||
\(348\) | 10.5000 | + | 18.1865i | 0.562859 | + | 0.974901i | ||||
\(349\) | 11.5000 | + | 19.9186i | 0.615581 | + | 1.06622i | 0.990282 | + | 0.139072i | \(0.0444119\pi\) |
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | − | 31.1769i | 0.480384 | − | 1.66410i | ||||
\(352\) | −15.0000 | −0.799503 | ||||||||
\(353\) | −12.5000 | − | 21.6506i | −0.665308 | − | 1.15235i | −0.979202 | − | 0.202889i | \(-0.934967\pi\) |
0.313894 | − | 0.949458i | \(-0.398366\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | 19.5000 | − | 33.7750i | 1.03495 | − | 1.79259i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.50000 | + | 14.7224i | −0.449239 | + | 0.778105i | ||||
\(359\) | 17.0000 | 0.897226 | 0.448613 | − | 0.893726i | \(-0.351918\pi\) | ||||
0.448613 | + | 0.893726i | \(0.351918\pi\) | |||||||
\(360\) | −27.0000 | + | 46.7654i | −1.42302 | + | 2.46475i | ||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −11.0000 | − | 19.0526i | −0.578147 | − | 1.00138i | ||||
\(363\) | −6.00000 | −0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.0000 | −2.04135 | ||||||||
\(366\) | −19.5000 | − | 33.7750i | −1.01928 | − | 1.76545i | ||||
\(367\) | −15.5000 | − | 26.8468i | −0.809093 | − | 1.40139i | −0.913493 | − | 0.406855i | \(-0.866625\pi\) |
0.104399 | − | 0.994535i | \(-0.466708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 3.00000 | − | 5.19615i | 0.155963 | − | 0.270135i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.00000 | 0.466628 | ||||||||
\(373\) | 4.50000 | − | 7.79423i | 0.233001 | − | 0.403570i | −0.725689 | − | 0.688023i | \(-0.758479\pi\) |
0.958690 | + | 0.284453i | \(0.0918121\pi\) | |||||||
\(374\) | 3.00000 | + | 5.19615i | 0.155126 | + | 0.268687i | ||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −24.5000 | + | 6.06218i | −1.26181 | + | 0.312218i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.5000 | + | 28.5788i | 0.847548 | + | 1.46800i | 0.883390 | + | 0.468639i | \(0.155255\pi\) |
−0.0358418 | + | 0.999357i | \(0.511411\pi\) | |||||||
\(380\) | −1.50000 | − | 2.59808i | −0.0769484 | − | 0.133278i | ||||
\(381\) | −16.5000 | + | 28.5788i | −0.845321 | + | 1.46414i | ||||
\(382\) | −17.0000 | −0.869796 | ||||||||
\(383\) | −10.5000 | + | 18.1865i | −0.536525 | + | 0.929288i | 0.462563 | + | 0.886586i | \(0.346930\pi\) |
−0.999088 | + | 0.0427020i | \(0.986403\pi\) | |||||||
\(384\) | 4.50000 | − | 7.79423i | 0.229640 | − | 0.397748i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.50000 | + | 6.06218i | −0.178145 | + | 0.308557i | ||||
\(387\) | 21.0000 | + | 36.3731i | 1.06749 | + | 1.84895i | ||||
\(388\) | 2.50000 | + | 4.33013i | 0.126918 | + | 0.219829i | ||||
\(389\) | −33.0000 | −1.67317 | −0.836583 | − | 0.547840i | \(-0.815450\pi\) | ||||
−0.836583 | + | 0.547840i | \(0.815450\pi\) | |||||||
\(390\) | −22.5000 | − | 23.3827i | −1.13933 | − | 1.18403i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50000 | + | 12.9904i | 0.378325 | + | 0.655278i | ||||
\(394\) | 0.500000 | − | 0.866025i | 0.0251896 | − | 0.0436297i | ||||
\(395\) | 9.00000 | 0.452839 | ||||||||
\(396\) | −9.00000 | + | 15.5885i | −0.452267 | + | 0.783349i | ||||
\(397\) | −0.500000 | + | 0.866025i | −0.0250943 | + | 0.0434646i | −0.878300 | − | 0.478110i | \(-0.841322\pi\) |
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | 20.0000 | 1.00251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | 1.00000 | + | 1.73205i | 0.0499376 | + | 0.0864945i | 0.889914 | − | 0.456129i | \(-0.150764\pi\) |
−0.839976 | + | 0.542623i | \(0.817431\pi\) | |||||||
\(402\) | −9.00000 | −0.448879 | ||||||||
\(403\) | −3.00000 | + | 10.3923i | −0.149441 | + | 0.517678i | ||||
\(404\) | −5.00000 | −0.248759 | ||||||||
\(405\) | 13.5000 | + | 23.3827i | 0.670820 | + | 1.16190i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000 | − | 5.19615i | 0.148704 | − | 0.257564i | ||||
\(408\) | −18.0000 | −0.891133 | ||||||||
\(409\) | 7.00000 | − | 12.1244i | 0.346128 | − | 0.599511i | −0.639430 | − | 0.768849i | \(-0.720830\pi\) |
0.985558 | + | 0.169338i | \(0.0541630\pi\) | |||||||
\(410\) | −4.50000 | + | 7.79423i | −0.222239 | + | 0.384930i | ||||
\(411\) | 30.0000 | 1.47979 | ||||||||
\(412\) | −2.50000 | + | 4.33013i | −0.123166 | + | 0.213330i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.5000 | + | 12.9904i | 0.612863 | + | 0.636906i | ||||
\(417\) | 45.0000 | 2.20366 | ||||||||
\(418\) | 1.50000 | + | 2.59808i | 0.0733674 | + | 0.127076i | ||||
\(419\) | −12.5000 | − | 21.6506i | −0.610665 | − | 1.05770i | −0.991129 | − | 0.132907i | \(-0.957569\pi\) |
0.380464 | − | 0.924796i | \(-0.375764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | −3.50000 | + | 6.06218i | −0.170377 | + | 0.295102i | ||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | −9.00000 | −0.437079 | ||||||||
\(425\) | −4.00000 | + | 6.92820i | −0.194029 | + | 0.336067i | ||||
\(426\) | −19.5000 | − | 33.7750i | −0.944778 | − | 1.63640i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | −22.5000 | − | 23.3827i | −1.08631 | − | 1.12893i | ||||
\(430\) | 21.0000 | 1.01271 | ||||||||
\(431\) | −4.50000 | − | 7.79423i | −0.216757 | − | 0.375435i | 0.737057 | − | 0.675830i | \(-0.236215\pi\) |
−0.953815 | + | 0.300395i | \(0.902881\pi\) | |||||||
\(432\) | 4.50000 | + | 7.79423i | 0.216506 | + | 0.375000i | ||||
\(433\) | 13.5000 | − | 23.3827i | 0.648769 | − | 1.12370i | −0.334649 | − | 0.942343i | \(-0.608618\pi\) |
0.983417 | − | 0.181357i | \(-0.0580490\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.5000 | − | 54.5596i | 1.51031 | − | 2.61593i | ||||
\(436\) | 3.50000 | − | 6.06218i | 0.167620 | − | 0.290326i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −19.5000 | + | 33.7750i | −0.931746 | + | 1.61383i | ||||
\(439\) | −8.00000 | − | 13.8564i | −0.381819 | − | 0.661330i | 0.609503 | − | 0.792784i | \(-0.291369\pi\) |
−0.991322 | + | 0.131453i | \(0.958036\pi\) | |||||||
\(440\) | 13.5000 | + | 23.3827i | 0.643587 | + | 1.11473i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | − | 6.92820i | 0.0951303 | − | 0.329541i | ||||
\(443\) | −11.0000 | −0.522626 | −0.261313 | − | 0.965254i | \(-0.584155\pi\) | ||||
−0.261313 | + | 0.965254i | \(0.584155\pi\) | |||||||
\(444\) | 3.00000 | + | 5.19615i | 0.142374 | + | 0.246598i | ||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | −4.50000 | + | 7.79423i | −0.213081 | + | 0.369067i | ||||
\(447\) | 45.0000 | 2.12843 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.50000 | + | 12.9904i | −0.353947 | + | 0.613054i | −0.986937 | − | 0.161106i | \(-0.948494\pi\) |
0.632990 | + | 0.774160i | \(0.281827\pi\) | |||||||
\(450\) | 24.0000 | 1.13137 | ||||||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | 7.50000 | + | 12.9904i | 0.352770 | + | 0.611016i | ||||
\(453\) | 31.5000 | + | 54.5596i | 1.48000 | + | 2.56343i | ||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.00000 | −0.421464 | ||||||||
\(457\) | 9.00000 | + | 15.5885i | 0.421002 | + | 0.729197i | 0.996038 | − | 0.0889312i | \(-0.0283451\pi\) |
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(458\) | −6.50000 | − | 11.2583i | −0.303725 | − | 0.526067i | ||||
\(459\) | −9.00000 | + | 15.5885i | −0.420084 | + | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5000 | − | 30.3109i | 0.815056 | − | 1.41172i | −0.0942312 | − | 0.995550i | \(-0.530039\pi\) |
0.909288 | − | 0.416169i | \(-0.136627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 3.50000 | − | 6.06218i | 0.162483 | − | 0.281430i | ||||
\(465\) | −13.5000 | − | 23.3827i | −0.626048 | − | 1.08435i | ||||
\(466\) | 10.5000 | + | 18.1865i | 0.486403 | + | 0.842475i | ||||
\(467\) | 7.00000 | 0.323921 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(468\) | 21.0000 | − | 5.19615i | 0.970725 | − | 0.240192i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.50000 | − | 2.59808i | −0.0691898 | − | 0.119840i | ||||
\(471\) | 28.5000 | + | 49.3634i | 1.31321 | + | 2.27455i | ||||
\(472\) | 6.00000 | − | 10.3923i | 0.276172 | − | 0.478345i | ||||
\(473\) | 21.0000 | 0.965581 | ||||||||
\(474\) | 4.50000 | − | 7.79423i | 0.206692 | − | 0.358001i | ||||
\(475\) | −2.00000 | + | 3.46410i | −0.0917663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | + | 15.5885i | −0.412082 | + | 0.713746i | ||||
\(478\) | 2.00000 | + | 3.46410i | 0.0914779 | + | 0.158444i | ||||
\(479\) | −17.5000 | − | 30.3109i | −0.799595 | − | 1.38494i | −0.919880 | − | 0.392200i | \(-0.871714\pi\) |
0.120284 | − | 0.992739i | \(-0.461619\pi\) | |||||||
\(480\) | −45.0000 | −2.05396 | ||||||||
\(481\) | −7.00000 | + | 1.73205i | −0.319173 | + | 0.0789747i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | 7.50000 | − | 12.9904i | 0.340557 | − | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | + | 13.8564i | −0.362515 | + | 0.627894i | −0.988374 | − | 0.152042i | \(-0.951415\pi\) |
0.625859 | + | 0.779936i | \(0.284748\pi\) | |||||||
\(488\) | 19.5000 | − | 33.7750i | 0.882724 | − | 1.52892i | ||||
\(489\) | −3.00000 | −0.135665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | − | 12.9904i | −0.338470 | − | 0.586248i | 0.645675 | − | 0.763612i | \(-0.276576\pi\) |
−0.984145 | + | 0.177365i | \(0.943243\pi\) | |||||||
\(492\) | −4.50000 | − | 7.79423i | −0.202876 | − | 0.351391i | ||||
\(493\) | 14.0000 | 0.630528 | ||||||||
\(494\) | 1.00000 | − | 3.46410i | 0.0449921 | − | 0.155857i | ||||
\(495\) | 54.0000 | 2.42712 | ||||||||
\(496\) | −1.50000 | − | 2.59808i | −0.0673520 | − | 0.116657i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.0000 | −1.38775 | −0.693875 | − | 0.720095i | \(-0.744098\pi\) | ||||
−0.693875 | + | 0.720095i | \(0.744098\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | −19.5000 | + | 33.7750i | −0.871196 | + | 1.50896i | ||||
\(502\) | 23.0000 | 1.02654 | ||||||||
\(503\) | −15.5000 | + | 26.8468i | −0.691111 | + | 1.19704i | 0.280363 | + | 0.959894i | \(0.409545\pi\) |
−0.971474 | + | 0.237145i | \(0.923788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.50000 | + | 12.9904i | 0.333746 | + | 0.578064i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.50000 | + | 38.9711i | −0.0666173 | + | 1.73077i | ||||
\(508\) | −11.0000 | −0.488046 | ||||||||
\(509\) | −17.0000 | − | 29.4449i | −0.753512 | − | 1.30512i | −0.946111 | − | 0.323843i | \(-0.895025\pi\) |
0.192599 | − | 0.981278i | \(-0.438308\pi\) | |||||||
\(510\) | 9.00000 | + | 15.5885i | 0.398527 | + | 0.690268i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | −4.50000 | + | 7.79423i | −0.198680 | + | 0.344124i | ||||
\(514\) | −1.00000 | + | 1.73205i | −0.0441081 | + | 0.0763975i | ||||
\(515\) | 15.0000 | 0.660979 | ||||||||
\(516\) | −10.5000 | + | 18.1865i | −0.462237 | + | 0.800617i | ||||
\(517\) | −1.50000 | − | 2.59808i | −0.0659699 | − | 0.114263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −57.0000 | −2.50202 | ||||||||
\(520\) | 9.00000 | − | 31.1769i | 0.394676 | − | 1.36720i | ||||
\(521\) | 17.0000 | 0.744784 | 0.372392 | − | 0.928076i | \(-0.378538\pi\) | ||||
0.372392 | + | 0.928076i | \(0.378538\pi\) | |||||||
\(522\) | −21.0000 | − | 36.3731i | −0.919145 | − | 1.59201i | ||||
\(523\) | 2.00000 | + | 3.46410i | 0.0874539 | + | 0.151475i | 0.906434 | − | 0.422347i | \(-0.138794\pi\) |
−0.818980 | + | 0.573822i | \(0.805460\pi\) | |||||||
\(524\) | −2.50000 | + | 4.33013i | −0.109213 | + | 0.189162i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5000 | − | 23.3827i | 0.588628 | − | 1.01953i | ||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 9.00000 | 0.391675 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | −12.0000 | − | 20.7846i | −0.520756 | − | 0.901975i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5000 | − | 2.59808i | 0.454805 | − | 0.112535i | ||||
\(534\) | −18.0000 | −0.778936 | ||||||||
\(535\) | 12.0000 | + | 20.7846i | 0.518805 | + | 0.898597i | ||||
\(536\) | −4.50000 | − | 7.79423i | −0.194370 | − | 0.336659i | ||||
\(537\) | −25.5000 | + | 44.1673i | −1.10041 | + | 1.90596i | ||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.5000 | + | 23.3827i | −0.580948 | + | 1.00623i | ||||
\(541\) | −37.0000 | −1.59075 | −0.795377 | − | 0.606115i | \(-0.792727\pi\) | ||||
−0.795377 | + | 0.606115i | \(0.792727\pi\) | |||||||
\(542\) | −8.00000 | + | 13.8564i | −0.343629 | + | 0.595184i | ||||
\(543\) | −33.0000 | − | 57.1577i | −1.41617 | − | 2.45287i | ||||
\(544\) | −5.00000 | − | 8.66025i | −0.214373 | − | 0.371305i | ||||
\(545\) | −21.0000 | −0.899541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 5.00000 | + | 8.66025i | 0.213589 | + | 0.369948i | ||||
\(549\) | −39.0000 | − | 67.5500i | −1.66448 | − | 2.88296i | ||||
\(550\) | 6.00000 | − | 10.3923i | 0.255841 | − | 0.443129i | ||||
\(551\) | 7.00000 | 0.298210 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | 9.00000 | − | 15.5885i | 0.382029 | − | 0.661693i | ||||
\(556\) | 7.50000 | + | 12.9904i | 0.318071 | + | 0.550915i | ||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | −18.0000 | −0.762001 | ||||||||
\(559\) | −17.5000 | − | 18.1865i | −0.740171 | − | 0.769208i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | + | 15.5885i | 0.379980 | + | 0.658145i | ||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | 2.00000 | − | 3.46410i | 0.0842900 | − | 0.145994i | −0.820798 | − | 0.571218i | \(-0.806471\pi\) |
0.905088 | + | 0.425223i | \(0.139804\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | 22.5000 | − | 38.9711i | 0.946582 | − | 1.63953i | ||||
\(566\) | 0.500000 | − | 0.866025i | 0.0210166 | − | 0.0364018i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.5000 | − | 33.7750i | 0.818202 | − | 1.41717i | ||||
\(569\) | −5.00000 | − | 8.66025i | −0.209611 | − | 0.363057i | 0.741981 | − | 0.670421i | \(-0.233886\pi\) |
−0.951592 | + | 0.307364i | \(0.900553\pi\) | |||||||
\(570\) | 4.50000 | + | 7.79423i | 0.188484 | + | 0.326464i | ||||
\(571\) | 43.0000 | 1.79949 | 0.899747 | − | 0.436412i | \(-0.143751\pi\) | ||||
0.899747 | + | 0.436412i | \(0.143751\pi\) | |||||||
\(572\) | 3.00000 | − | 10.3923i | 0.125436 | − | 0.434524i | ||||
\(573\) | −51.0000 | −2.13056 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −21.0000 | + | 36.3731i | −0.875000 | + | 1.51554i | ||||
\(577\) | 1.00000 | 0.0416305 | 0.0208153 | − | 0.999783i | \(-0.493374\pi\) | ||||
0.0208153 | + | 0.999783i | \(0.493374\pi\) | |||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | −10.5000 | + | 18.1865i | −0.436365 | + | 0.755807i | ||||
\(580\) | 21.0000 | 0.871978 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.50000 | − | 12.9904i | −0.310885 | − | 0.538469i | ||||
\(583\) | 4.50000 | + | 7.79423i | 0.186371 | + | 0.322804i | ||||
\(584\) | −39.0000 | −1.61383 | ||||||||
\(585\) | −45.0000 | − | 46.7654i | −1.86052 | − | 1.93351i | ||||
\(586\) | −11.0000 | −0.454406 | ||||||||
\(587\) | −16.5000 | − | 28.5788i | −0.681028 | − | 1.17957i | −0.974668 | − | 0.223659i | \(-0.928200\pi\) |
0.293640 | − | 0.955916i | \(-0.405133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50000 | − | 2.59808i | 0.0618064 | − | 0.107052i | ||||
\(590\) | −12.0000 | −0.494032 | ||||||||
\(591\) | 1.50000 | − | 2.59808i | 0.0617018 | − | 0.106871i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | −27.0000 | −1.10876 | −0.554379 | − | 0.832265i | \(-0.687044\pi\) | ||||
−0.554379 | + | 0.832265i | \(0.687044\pi\) | |||||||
\(594\) | 13.5000 | − | 23.3827i | 0.553912 | − | 0.959403i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.50000 | + | 12.9904i | 0.307212 | + | 0.532107i | ||||
\(597\) | 60.0000 | 2.45564 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.0000 | −1.02147 | −0.510736 | − | 0.859738i | \(-0.670627\pi\) | ||||
−0.510736 | + | 0.859738i | \(0.670627\pi\) | |||||||
\(600\) | 18.0000 | + | 31.1769i | 0.734847 | + | 1.27279i | ||||
\(601\) | 17.5000 | + | 30.3109i | 0.713840 | + | 1.23641i | 0.963405 | + | 0.268049i | \(0.0863789\pi\) |
−0.249565 | + | 0.968358i | \(0.580288\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.0000 | −0.733017 | ||||||||
\(604\) | −10.5000 | + | 18.1865i | −0.427239 | + | 0.740000i | ||||
\(605\) | −3.00000 | + | 5.19615i | −0.121967 | + | 0.211254i | ||||
\(606\) | 15.0000 | 0.609333 | ||||||||
\(607\) | 5.50000 | − | 9.52628i | 0.223238 | − | 0.386660i | −0.732551 | − | 0.680712i | \(-0.761671\pi\) |
0.955789 | + | 0.294052i | \(0.0950039\pi\) | |||||||
\(608\) | −2.50000 | − | 4.33013i | −0.101388 | − | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.0000 | −1.57906 | ||||||||
\(611\) | −1.00000 | + | 3.46410i | −0.0404557 | + | 0.140143i | ||||
\(612\) | −12.0000 | −0.485071 | ||||||||
\(613\) | 12.5000 | + | 21.6506i | 0.504870 | + | 0.874461i | 0.999984 | + | 0.00563283i | \(0.00179300\pi\) |
−0.495114 | + | 0.868828i | \(0.664874\pi\) | |||||||
\(614\) | 6.00000 | + | 10.3923i | 0.242140 | + | 0.419399i | ||||
\(615\) | −13.5000 | + | 23.3827i | −0.544373 | + | 0.942881i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5000 | − | 28.5788i | 0.664265 | − | 1.15054i | −0.315219 | − | 0.949019i | \(-0.602078\pi\) |
0.979484 | − | 0.201522i | \(-0.0645887\pi\) | |||||||
\(618\) | 7.50000 | − | 12.9904i | 0.301694 | − | 0.522550i | ||||
\(619\) | −11.0000 | −0.442127 | −0.221064 | − | 0.975259i | \(-0.570953\pi\) | ||||
−0.221064 | + | 0.975259i | \(0.570953\pi\) | |||||||
\(620\) | 4.50000 | − | 7.79423i | 0.180724 | − | 0.313024i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.50000 | − | 7.79423i | −0.180434 | − | 0.312520i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.50000 | − | 7.79423i | −0.300240 | − | 0.312019i | ||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 9.50000 | + | 16.4545i | 0.379696 | + | 0.657653i | ||||
\(627\) | 4.50000 | + | 7.79423i | 0.179713 | + | 0.311272i | ||||
\(628\) | −9.50000 | + | 16.4545i | −0.379091 | + | 0.656605i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5000 | + | 21.6506i | −0.497617 | + | 0.861898i | −0.999996 | − | 0.00274930i | \(-0.999125\pi\) |
0.502379 | + | 0.864647i | \(0.332458\pi\) | |||||||
\(632\) | 9.00000 | 0.358001 | ||||||||
\(633\) | −10.5000 | + | 18.1865i | −0.417338 | + | 0.722850i | ||||
\(634\) | 4.50000 | + | 7.79423i | 0.178718 | + | 0.309548i | ||||
\(635\) | 16.5000 | + | 28.5788i | 0.654783 | + | 1.13412i | ||||
\(636\) | −9.00000 | −0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21.0000 | −0.831398 | ||||||||
\(639\) | −39.0000 | − | 67.5500i | −1.54282 | − | 2.67224i | ||||
\(640\) | −4.50000 | − | 7.79423i | −0.177878 | − | 0.308094i | ||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 24.0000 | 0.947204 | ||||||||
\(643\) | −9.50000 | + | 16.4545i | −0.374643 | + | 0.648901i | −0.990274 | − | 0.139134i | \(-0.955568\pi\) |
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 63.0000 | 2.48062 | ||||||||
\(646\) | −1.00000 | + | 1.73205i | −0.0393445 | + | 0.0681466i | ||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | 13.5000 | + | 23.3827i | 0.530330 | + | 0.918559i | ||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | −14.0000 | + | 3.46410i | −0.549125 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.500000 | − | 0.866025i | −0.0195815 | − | 0.0339162i | ||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | −10.5000 | + | 18.1865i | −0.410582 | + | 0.711150i | ||||
\(655\) | 15.0000 | 0.586098 | ||||||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | −39.0000 | + | 67.5500i | −1.52153 | + | 2.63538i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5000 | + | 25.1147i | −0.564840 | + | 0.978331i | 0.432225 | + | 0.901766i | \(0.357729\pi\) |
−0.997065 | + | 0.0765653i | \(0.975605\pi\) | |||||||
\(660\) | 13.5000 | + | 23.3827i | 0.525487 | + | 0.910170i | ||||
\(661\) | −4.50000 | − | 7.79423i | −0.175030 | − | 0.303160i | 0.765142 | − | 0.643862i | \(-0.222669\pi\) |
−0.940172 | + | 0.340701i | \(0.889335\pi\) | |||||||
\(662\) | −29.0000 | −1.12712 | ||||||||
\(663\) | 6.00000 | − | 20.7846i | 0.233021 | − | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.00000 | − | 10.3923i | −0.232495 | − | 0.402694i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −13.0000 | −0.502985 | ||||||||
\(669\) | −13.5000 | + | 23.3827i | −0.521940 | + | 0.904027i | ||||
\(670\) | −4.50000 | + | 7.79423i | −0.173850 | + | 0.301117i | ||||
\(671\) | −39.0000 | −1.50558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.5000 | + | 35.5070i | 0.790217 | + | 1.36870i | 0.925832 | + | 0.377934i | \(0.123365\pi\) |
−0.135615 | + | 0.990762i | \(0.543301\pi\) | |||||||
\(674\) | −7.00000 | − | 12.1244i | −0.269630 | − | 0.467013i | ||||
\(675\) | 36.0000 | 1.38564 | ||||||||
\(676\) | −11.5000 | + | 6.06218i | −0.442308 | + | 0.233161i | ||||
\(677\) | −7.00000 | −0.269032 | −0.134516 | − | 0.990911i | \(-0.542948\pi\) | ||||
−0.134516 | + | 0.990911i | \(0.542948\pi\) | |||||||
\(678\) | −22.5000 | − | 38.9711i | −0.864107 | − | 1.49668i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.00000 | + | 15.5885i | −0.345134 | + | 0.597790i | ||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | −4.50000 | + | 7.79423i | −0.172314 | + | 0.298456i | ||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | 15.0000 | − | 25.9808i | 0.573121 | − | 0.992674i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.5000 | − | 33.7750i | −0.743971 | − | 1.28860i | ||||
\(688\) | 7.00000 | 0.266872 | ||||||||
\(689\) | 3.00000 | − | 10.3923i | 0.114291 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.00000 | − | 3.46410i | −0.0760836 | − | 0.131781i | 0.825473 | − | 0.564441i | \(-0.190908\pi\) |
−0.901557 | + | 0.432660i | \(0.857575\pi\) | |||||||
\(692\) | −9.50000 | − | 16.4545i | −0.361136 | − | 0.625506i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | −0.303676 | ||||||||
\(695\) | 22.5000 | − | 38.9711i | 0.853474 | − | 1.47826i | ||||
\(696\) | 31.5000 | − | 54.5596i | 1.19400 | − | 2.06808i | ||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | 11.5000 | − | 19.9186i | 0.435281 | − | 0.753930i | ||||
\(699\) | 31.5000 | + | 54.5596i | 1.19144 | + | 2.06363i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | −31.5000 | + | 7.79423i | −1.18889 | + | 0.294174i | ||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 10.5000 | + | 18.1865i | 0.395734 | + | 0.685431i | ||||
\(705\) | −4.50000 | − | 7.79423i | −0.169480 | − | 0.293548i | ||||
\(706\) | −12.5000 | + | 21.6506i | −0.470444 | + | 0.814832i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.00000 | − | 10.3923i | 0.225494 | − | 0.390567i | ||||
\(709\) | −5.50000 | + | 9.52628i | −0.206557 | + | 0.357767i | −0.950628 | − | 0.310334i | \(-0.899559\pi\) |
0.744071 | + | 0.668101i | \(0.232892\pi\) | |||||||
\(710\) | −39.0000 | −1.46364 | ||||||||
\(711\) | 9.00000 | − | 15.5885i | 0.337526 | − | 0.584613i | ||||
\(712\) | −9.00000 | − | 15.5885i | −0.337289 | − | 0.584202i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.5000 | + | 7.79423i | −1.17803 | + | 0.291488i | ||||
\(716\) | −17.0000 | −0.635320 | ||||||||
\(717\) | 6.00000 | + | 10.3923i | 0.224074 | + | 0.388108i | ||||
\(718\) | −8.50000 | − | 14.7224i | −0.317217 | − | 0.549436i | ||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 18.0000 | 0.670820 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.00000 | − | 15.5885i | 0.334945 | − | 0.580142i | ||||
\(723\) | 78.0000 | 2.90085 | ||||||||
\(724\) | 11.0000 | − | 19.0526i | 0.408812 | − | 0.708083i | ||||
\(725\) | −14.0000 | − | 24.2487i | −0.519947 | − | 0.900575i | ||||
\(726\) | 3.00000 | + | 5.19615i | 0.111340 | + | 0.192847i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 19.5000 | + | 33.7750i | 0.721727 | + | 1.25007i | ||||
\(731\) | 7.00000 | + | 12.1244i | 0.258904 | + | 0.448435i | ||||
\(732\) | 19.5000 | − | 33.7750i | 0.720741 | − | 1.24836i | ||||
\(733\) | 9.00000 | 0.332423 | 0.166211 | − | 0.986090i | \(-0.446847\pi\) | ||||
0.166211 | + | 0.986090i | \(0.446847\pi\) | |||||||
\(734\) | −15.5000 | + | 26.8468i | −0.572115 | + | 0.990933i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | + | 7.79423i | −0.165760 | + | 0.287104i | ||||
\(738\) | 9.00000 | + | 15.5885i | 0.331295 | + | 0.573819i | ||||
\(739\) | −0.500000 | − | 0.866025i | −0.0183928 | − | 0.0318573i | 0.856683 | − | 0.515844i | \(-0.172522\pi\) |
−0.875075 | + | 0.483987i | \(0.839188\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 3.00000 | − | 10.3923i | 0.110208 | − | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.5000 | − | 44.1673i | −0.935504 | − | 1.62034i | −0.773732 | − | 0.633513i | \(-0.781612\pi\) |
−0.161772 | − | 0.986828i | \(-0.551721\pi\) | |||||||
\(744\) | −13.5000 | − | 23.3827i | −0.494934 | − | 0.857251i | ||||
\(745\) | 22.5000 | − | 38.9711i | 0.824336 | − | 1.42779i | ||||
\(746\) | −9.00000 | −0.329513 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.00000 | + | 5.19615i | −0.109691 | + | 0.189990i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.50000 | + | 7.79423i | −0.164317 | + | 0.284605i | ||||
\(751\) | −14.0000 | − | 24.2487i | −0.510867 | − | 0.884848i | −0.999921 | − | 0.0125942i | \(-0.995991\pi\) |
0.489053 | − | 0.872254i | \(-0.337342\pi\) | |||||||
\(752\) | −0.500000 | − | 0.866025i | −0.0182331 | − | 0.0315807i | ||||
\(753\) | 69.0000 | 2.51450 | ||||||||
\(754\) | 17.5000 | + | 18.1865i | 0.637312 | + | 0.662314i | ||||
\(755\) | 63.0000 | 2.29280 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.50000 | − | 2.59808i | −0.0545184 | − | 0.0944287i | 0.837478 | − | 0.546471i | \(-0.184029\pi\) |
−0.891997 | + | 0.452042i | \(0.850696\pi\) | |||||||
\(758\) | 16.5000 | − | 28.5788i | 0.599307 | − | 1.03803i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.50000 | + | 7.79423i | −0.163232 | + | 0.282726i | ||||
\(761\) | −4.50000 | + | 7.79423i | −0.163125 | + | 0.282541i | −0.935988 | − | 0.352032i | \(-0.885491\pi\) |
0.772863 | + | 0.634573i | \(0.218824\pi\) | |||||||
\(762\) | 33.0000 | 1.19546 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.50000 | − | 14.7224i | −0.307519 | − | 0.532639i | ||||
\(765\) | 18.0000 | + | 31.1769i | 0.650791 | + | 1.12720i | ||||
\(766\) | 21.0000 | 0.758761 | ||||||||
\(767\) | 10.0000 | + | 10.3923i | 0.361079 | + | 0.375244i | ||||
\(768\) | −51.0000 | −1.84030 | ||||||||
\(769\) | 9.50000 | + | 16.4545i | 0.342579 | + | 0.593364i | 0.984911 | − | 0.173063i | \(-0.0553663\pi\) |
−0.642332 | + | 0.766426i | \(0.722033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00000 | + | 5.19615i | −0.108042 | + | 0.187135i | ||||
\(772\) | −7.00000 | −0.251936 | ||||||||
\(773\) | −3.00000 | + | 5.19615i | −0.107903 | + | 0.186893i | −0.914920 | − | 0.403634i | \(-0.867747\pi\) |
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | 21.0000 | − | 36.3731i | 0.754829 | − | 1.30740i | ||||
\(775\) | −12.0000 | −0.431053 | ||||||||
\(776\) | 7.50000 | − | 12.9904i | 0.269234 | − | 0.466328i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.5000 | + | 28.5788i | 0.591554 | + | 1.02460i | ||||
\(779\) | −3.00000 | −0.107486 | ||||||||
\(780\) | 9.00000 | − | 31.1769i | 0.322252 | − | 1.11631i | ||||
\(781\) | −39.0000 | −1.39553 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.5000 | − | 54.5596i | −1.12572 | − | 1.94980i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57.0000 | 2.03442 | ||||||||
\(786\) | 7.50000 | − | 12.9904i | 0.267516 | − | 0.463352i | ||||
\(787\) | −10.0000 | + | 17.3205i | −0.356462 | + | 0.617409i | −0.987367 | − | 0.158450i | \(-0.949350\pi\) |
0.630905 | + | 0.775860i | \(0.282684\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 40.5000 | − | 70.1481i | 1.44184 | − | 2.49734i | ||||
\(790\) | −4.50000 | − | 7.79423i | −0.160103 | − | 0.277306i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 54.0000 | 1.91881 | ||||||||
\(793\) | 32.5000 | + | 33.7750i | 1.15411 | + | 1.19939i | ||||
\(794\) | 1.00000 | 0.0354887 | ||||||||
\(795\) | 13.5000 | + | 23.3827i | 0.478796 | + | 0.829298i | ||||
\(796\) | 10.0000 | + | 17.3205i | 0.354441 | + | 0.613909i | ||||
\(797\) | 1.50000 | − | 2.59808i | 0.0531327 | − | 0.0920286i | −0.838236 | − | 0.545308i | \(-0.816413\pi\) |
0.891368 | + | 0.453279i | \(0.149746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.00000 | − | 1.73205i | 0.0353775 | − | 0.0612756i | ||||
\(800\) | −10.0000 | + | 17.3205i | −0.353553 | + | 0.612372i | ||||
\(801\) | −36.0000 | −1.27200 | ||||||||
\(802\) | 1.00000 | − | 1.73205i | 0.0353112 | − | 0.0611608i | ||||
\(803\) | 19.5000 | + | 33.7750i | 0.688140 | + | 1.19189i | ||||
\(804\) | −4.50000 | − | 7.79423i | −0.158703 | − | 0.274881i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.5000 | − | 2.59808i | 0.369847 | − | 0.0915133i | ||||
\(807\) | −54.0000 | −1.90089 | ||||||||
\(808\) | 7.50000 | + | 12.9904i | 0.263849 | + | 0.457000i | ||||
\(809\) | −5.50000 | − | 9.52628i | −0.193370 | − | 0.334926i | 0.752995 | − | 0.658026i | \(-0.228608\pi\) |
−0.946365 | + | 0.323100i | \(0.895275\pi\) | |||||||
\(810\) | 13.5000 | − | 23.3827i | 0.474342 | − | 0.821584i | ||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0000 | + | 41.5692i | −0.841717 | + | 1.45790i | ||||
\(814\) | −6.00000 | −0.210300 | ||||||||
\(815\) | −1.50000 | + | 2.59808i | −0.0525427 | + | 0.0910066i | ||||
\(816\) | 3.00000 | + | 5.19615i | 0.105021 | + | 0.181902i | ||||
\(817\) | 3.50000 | + | 6.06218i | 0.122449 | + | 0.212089i | ||||
\(818\) | −14.0000 | −0.489499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 27.0000 | + | 46.7654i | 0.942306 | + | 1.63212i | 0.761056 | + | 0.648686i | \(0.224681\pi\) |
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(822\) | −15.0000 | − | 25.9808i | −0.523185 | − | 0.906183i | ||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | 15.0000 | 0.522550 | ||||||||
\(825\) | 18.0000 | − | 31.1769i | 0.626680 | − | 1.08544i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.00000 | 0.139094 | 0.0695468 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695468 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | + | 9.52628i | 0.191023 | + | 0.330861i | 0.945589 | − | 0.325362i | \(-0.105486\pi\) |
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 66.0000 | 2.28951 | ||||||||
\(832\) | 7.00000 | − | 24.2487i | 0.242681 | − | 0.840673i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −22.5000 | − | 38.9711i | −0.779111 | − | 1.34946i | ||||
\(835\) | 19.5000 | + | 33.7750i | 0.674825 | + | 1.16883i | ||||
\(836\) | −1.50000 | + | 2.59808i | −0.0518786 | + | 0.0898563i | ||||
\(837\) | −27.0000 | −0.933257 | ||||||||
\(838\) | −12.5000 | + | 21.6506i | −0.431805 | + | 0.747909i | ||||
\(839\) | 18.5000 | − | 32.0429i | 0.638691 | − | 1.10625i | −0.347029 | − | 0.937854i | \(-0.612810\pi\) |
0.985720 | − | 0.168391i | \(-0.0538571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | + | 17.3205i | −0.344828 | + | 0.597259i | ||||
\(842\) | −9.00000 | − | 15.5885i | −0.310160 | − | 0.537214i | ||||
\(843\) | 27.0000 | + | 46.7654i | 0.929929 | + | 1.61068i | ||||
\(844\) | −7.00000 | −0.240950 | ||||||||
\(845\) | 33.0000 | + | 20.7846i | 1.13523 | + | 0.715012i | ||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.50000 | + | 2.59808i | 0.0515102 | + | 0.0892183i | ||||
\(849\) | 1.50000 | − | 2.59808i | 0.0514799 | − | 0.0891657i | ||||
\(850\) | 8.00000 | 0.274398 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 19.5000 | − | 33.7750i | 0.668059 | − | 1.15711i | ||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.00000 | + | 15.5885i | 0.307794 | + | 0.533114i | ||||
\(856\) | 12.0000 | + | 20.7846i | 0.410152 | + | 0.710403i | ||||
\(857\) | 33.0000 | 1.12726 | 0.563629 | − | 0.826028i | \(-0.309405\pi\) | ||||
0.563629 | + | 0.826028i | \(0.309405\pi\) | |||||||
\(858\) | −9.00000 | + | 31.1769i | −0.307255 | + | 1.06436i | ||||
\(859\) | −25.0000 | −0.852989 | −0.426494 | − | 0.904490i | \(-0.640252\pi\) | ||||
−0.426494 | + | 0.904490i | \(0.640252\pi\) | |||||||
\(860\) | 10.5000 | + | 18.1865i | 0.358047 | + | 0.620156i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.50000 | + | 7.79423i | −0.153271 | + | 0.265472i | ||||
\(863\) | 37.0000 | 1.25949 | 0.629747 | − | 0.776800i | \(-0.283158\pi\) | ||||
0.629747 | + | 0.776800i | \(0.283158\pi\) | |||||||
\(864\) | −22.5000 | + | 38.9711i | −0.765466 | + | 1.32583i | ||||
\(865\) | −28.5000 | + | 49.3634i | −0.969029 | + | 1.67841i | ||||
\(866\) | −27.0000 | −0.917497 | ||||||||
\(867\) | 19.5000 | − | 33.7750i | 0.662255 | − | 1.14706i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.50000 | − | 7.79423i | −0.152652 | − | 0.264401i | ||||
\(870\) | −63.0000 | −2.13590 | ||||||||
\(871\) | 10.5000 | − | 2.59808i | 0.355779 | − | 0.0880325i | ||||
\(872\) | −21.0000 | −0.711150 | ||||||||
\(873\) | −15.0000 | − | 25.9808i | −0.507673 | − | 0.879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −39.0000 | −1.31769 | ||||||||
\(877\) | 22.5000 | − | 38.9711i | 0.759771 | − | 1.31596i | −0.183196 | − | 0.983076i | \(-0.558644\pi\) |
0.942967 | − | 0.332886i | \(-0.108022\pi\) | |||||||
\(878\) | −8.00000 | + | 13.8564i | −0.269987 | + | 0.467631i | ||||
\(879\) | −33.0000 | −1.11306 | ||||||||
\(880\) | 4.50000 | − | 7.79423i | 0.151695 | − | 0.262743i | ||||
\(881\) | 7.50000 | + | 12.9904i | 0.252681 | + | 0.437657i | 0.964263 | − | 0.264946i | \(-0.0853542\pi\) |
−0.711582 | + | 0.702603i | \(0.752021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 7.00000 | − | 1.73205i | 0.235435 | − | 0.0582552i | ||||
\(885\) | −36.0000 | −1.21013 | ||||||||
\(886\) | 5.50000 | + | 9.52628i | 0.184776 | + | 0.320042i | ||||
\(887\) | 12.0000 | + | 20.7846i | 0.402921 | + | 0.697879i | 0.994077 | − | 0.108678i | \(-0.0346618\pi\) |
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(888\) | 9.00000 | − | 15.5885i | 0.302020 | − | 0.523114i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.00000 | + | 15.5885i | −0.301681 | + | 0.522526i | ||||
\(891\) | 13.5000 | − | 23.3827i | 0.452267 | − | 0.783349i | ||||
\(892\) | −9.00000 | −0.301342 | ||||||||
\(893\) | 0.500000 | − | 0.866025i | 0.0167319 | − | 0.0289804i | ||||
\(894\) | −22.5000 | − | 38.9711i | −0.752513 | − | 1.30339i | ||||
\(895\) | 25.5000 | + | 44.1673i | 0.852371 | + | 1.47635i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0000 | 0.500556 | ||||||||
\(899\) | 10.5000 | + | 18.1865i | 0.350195 | + | 0.606555i | ||||
\(900\) | 12.0000 | + | 20.7846i | 0.400000 | + | 0.692820i | ||||
\(901\) | −3.00000 | + | 5.19615i | −0.0999445 | + | 0.173109i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.5000 | − | 38.9711i | 0.748339 | − | 1.29616i | ||||
\(905\) | −66.0000 | −2.19391 | ||||||||
\(906\) | 31.5000 | − | 54.5596i | 1.04652 | − | 1.81262i | ||||
\(907\) | 23.5000 | + | 40.7032i | 0.780305 | + | 1.35153i | 0.931764 | + | 0.363064i | \(0.118269\pi\) |
−0.151460 | + | 0.988463i | \(0.548397\pi\) | |||||||
\(908\) | 2.00000 | + | 3.46410i | 0.0663723 | + | 0.114960i | ||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 1.50000 | + | 2.59808i | 0.0496700 | + | 0.0860309i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.00000 | − | 15.5885i | 0.297694 | − | 0.515620i | ||||
\(915\) | −117.000 | −3.86790 | ||||||||
\(916\) | 6.50000 | − | 11.2583i | 0.214766 | − | 0.371986i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 18.0000 | 0.594089 | ||||||||
\(919\) | 12.5000 | − | 21.6506i | 0.412337 | − | 0.714189i | −0.582808 | − | 0.812610i | \(-0.698046\pi\) |
0.995145 | + | 0.0984214i | \(0.0313793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.0000 | + | 31.1769i | 0.593120 | + | 1.02731i | ||||
\(922\) | −35.0000 | −1.15266 | ||||||||
\(923\) | 32.5000 | + | 33.7750i | 1.06975 | + | 1.11172i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | − | 6.92820i | −0.131519 | − | 0.227798i | ||||
\(926\) | 4.00000 | + | 6.92820i | 0.131448 | + | 0.227675i | ||||
\(927\) | 15.0000 | − | 25.9808i | 0.492665 | − | 0.853320i | ||||
\(928\) | 35.0000 | 1.14893 | ||||||||
\(929\) | −6.50000 | + | 11.2583i | −0.213258 | + | 0.369374i | −0.952732 | − | 0.303811i | \(-0.901741\pi\) |
0.739474 | + | 0.673185i | \(0.235074\pi\) | |||||||
\(930\) | −13.5000 | + | 23.3827i | −0.442682 | + | 0.766748i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.5000 | + | 18.1865i | −0.343939 | + | 0.595720i | ||||
\(933\) | −13.5000 | − | 23.3827i | −0.441970 | − | 0.765515i | ||||
\(934\) | −3.50000 | − | 6.06218i | −0.114523 | − | 0.198361i | ||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | −45.0000 | − | 46.7654i | −1.47087 | − | 1.52857i | ||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.5000 | + | 49.3634i | 0.930062 | + | 1.61092i | ||||
\(940\) | 1.50000 | − | 2.59808i | 0.0489246 | − | 0.0847399i | ||||
\(941\) | 17.0000 | 0.554184 | 0.277092 | − | 0.960843i | \(-0.410629\pi\) | ||||
0.277092 | + | 0.960843i | \(0.410629\pi\) | |||||||
\(942\) | 28.5000 | − | 49.3634i | 0.928580 | − | 1.60835i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.5000 | − | 18.1865i | −0.341384 | − | 0.591295i | ||||
\(947\) | 6.00000 | + | 10.3923i | 0.194974 | + | 0.337705i | 0.946892 | − | 0.321552i | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | 9.00000 | 0.292306 | ||||||||
\(949\) | 13.0000 | − | 45.0333i | 0.421998 | − | 1.46184i | ||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | 13.5000 | + | 23.3827i | 0.437767 | + | 0.758236i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.5000 | − | 28.5788i | 0.534487 | − | 0.925759i | −0.464701 | − | 0.885468i | \(-0.653838\pi\) |
0.999188 | − | 0.0402915i | \(-0.0128286\pi\) | |||||||
\(954\) | 18.0000 | 0.582772 | ||||||||
\(955\) | −25.5000 | + | 44.1673i | −0.825161 | + | 1.42922i | ||||
\(956\) | −2.00000 | + | 3.46410i | −0.0646846 | + | 0.112037i | ||||
\(957\) | −63.0000 | −2.03650 | ||||||||
\(958\) | −17.5000 | + | 30.3109i | −0.565399 | + | 0.979300i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 31.5000 | + | 54.5596i | 1.01666 | + | 1.76090i | ||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 5.00000 | + | 5.19615i | 0.161206 | + | 0.167531i | ||||
\(963\) | 48.0000 | 1.54678 | ||||||||
\(964\) | 13.0000 | + | 22.5167i | 0.418702 | + | 0.725213i | ||||
\(965\) | 10.5000 | + | 18.1865i | 0.338007 | + | 0.585445i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | −3.00000 | + | 5.19615i | −0.0964237 | + | 0.167011i | ||||
\(969\) | −3.00000 | + | 5.19615i | −0.0963739 | + | 0.166924i | ||||
\(970\) | −15.0000 | −0.481621 | ||||||||
\(971\) | −0.500000 | + | 0.866025i | −0.0160458 | + | 0.0277921i | −0.873937 | − | 0.486040i | \(-0.838441\pi\) |
0.857891 | + | 0.513832i | \(0.171774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | −42.0000 | + | 10.3923i | −1.34508 | + | 0.332820i | ||||
\(976\) | −13.0000 | −0.416120 | ||||||||
\(977\) | 2.50000 | + | 4.33013i | 0.0799821 | + | 0.138533i | 0.903242 | − | 0.429132i | \(-0.141180\pi\) |
−0.823260 | + | 0.567665i | \(0.807847\pi\) | |||||||
\(978\) | 1.50000 | + | 2.59808i | 0.0479647 | + | 0.0830773i | ||||
\(979\) | −9.00000 | + | 15.5885i | −0.287641 | + | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.0000 | + | 36.3731i | −0.670478 | + | 1.16130i | ||||
\(982\) | −7.50000 | + | 12.9904i | −0.239335 | + | 0.414540i | ||||
\(983\) | −47.0000 | −1.49907 | −0.749534 | − | 0.661966i | \(-0.769722\pi\) | ||||
−0.749534 | + | 0.661966i | \(0.769722\pi\) | |||||||
\(984\) | −13.5000 | + | 23.3827i | −0.430364 | + | 0.745413i | ||||
\(985\) | −1.50000 | − | 2.59808i | −0.0477940 | − | 0.0827816i | ||||
\(986\) | −7.00000 | − | 12.1244i | −0.222925 | − | 0.386118i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.50000 | − | 0.866025i | 0.111350 | − | 0.0275519i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −27.0000 | − | 46.7654i | −0.858116 | − | 1.48630i | ||||
\(991\) | −6.50000 | − | 11.2583i | −0.206479 | − | 0.357633i | 0.744124 | − | 0.668042i | \(-0.232867\pi\) |
−0.950603 | + | 0.310409i | \(0.899534\pi\) | |||||||
\(992\) | 7.50000 | − | 12.9904i | 0.238125 | − | 0.412445i | ||||
\(993\) | −87.0000 | −2.76086 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.0000 | − | 51.9615i | 0.951064 | − | 1.64729i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.00000 | − | 1.73205i | 0.0316703 | − | 0.0548546i | −0.849756 | − | 0.527176i | \(-0.823251\pi\) |
0.881426 | + | 0.472322i | \(0.156584\pi\) | |||||||
\(998\) | 15.5000 | + | 26.8468i | 0.490644 | + | 0.849820i | ||||
\(999\) | −9.00000 | − | 15.5885i | −0.284747 | − | 0.493197i |
(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 | 637.2.f.a.393.1 | 2 | ||
7.2 | even | 3 | 637.2.g.a.263.1 | 2 | |||
7.3 | odd | 6 | 91.2.h.a.16.1 | yes | 2 | ||
7.4 | even | 3 | 637.2.h.a.471.1 | 2 | |||
7.5 | odd | 6 | 91.2.g.a.81.1 | yes | 2 | ||
7.6 | odd | 2 | 637.2.f.b.393.1 | 2 | |||
13.3 | even | 3 | 8281.2.a.j.1.1 | 1 | |||
13.9 | even | 3 | inner | 637.2.f.a.295.1 | 2 | ||
13.10 | even | 6 | 8281.2.a.g.1.1 | 1 | |||
21.5 | even | 6 | 819.2.n.c.172.1 | 2 | |||
21.17 | even | 6 | 819.2.s.a.289.1 | 2 | |||
91.3 | odd | 6 | 1183.2.e.a.170.1 | 2 | |||
91.9 | even | 3 | 637.2.h.a.165.1 | 2 | |||
91.10 | odd | 6 | 1183.2.e.c.170.1 | 2 | |||
91.48 | odd | 6 | 637.2.f.b.295.1 | 2 | |||
91.55 | odd | 6 | 8281.2.a.i.1.1 | 1 | |||
91.61 | odd | 6 | 91.2.h.a.74.1 | yes | 2 | ||
91.62 | odd | 6 | 8281.2.a.c.1.1 | 1 | |||
91.68 | odd | 6 | 1183.2.e.a.508.1 | 2 | |||
91.74 | even | 3 | 637.2.g.a.373.1 | 2 | |||
91.75 | odd | 6 | 1183.2.e.c.508.1 | 2 | |||
91.87 | odd | 6 | 91.2.g.a.9.1 | ✓ | 2 | ||
273.152 | even | 6 | 819.2.s.a.802.1 | 2 | |||
273.269 | even | 6 | 819.2.n.c.100.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.a.9.1 | ✓ | 2 | 91.87 | odd | 6 | ||
91.2.g.a.81.1 | yes | 2 | 7.5 | odd | 6 | ||
91.2.h.a.16.1 | yes | 2 | 7.3 | odd | 6 | ||
91.2.h.a.74.1 | yes | 2 | 91.61 | odd | 6 | ||
637.2.f.a.295.1 | 2 | 13.9 | even | 3 | inner | ||
637.2.f.a.393.1 | 2 | 1.1 | even | 1 | trivial | ||
637.2.f.b.295.1 | 2 | 91.48 | odd | 6 | |||
637.2.f.b.393.1 | 2 | 7.6 | odd | 2 | |||
637.2.g.a.263.1 | 2 | 7.2 | even | 3 | |||
637.2.g.a.373.1 | 2 | 91.74 | even | 3 | |||
637.2.h.a.165.1 | 2 | 91.9 | even | 3 | |||
637.2.h.a.471.1 | 2 | 7.4 | even | 3 | |||
819.2.n.c.100.1 | 2 | 273.269 | even | 6 | |||
819.2.n.c.172.1 | 2 | 21.5 | even | 6 | |||
819.2.s.a.289.1 | 2 | 21.17 | even | 6 | |||
819.2.s.a.802.1 | 2 | 273.152 | even | 6 | |||
1183.2.e.a.170.1 | 2 | 91.3 | odd | 6 | |||
1183.2.e.a.508.1 | 2 | 91.68 | odd | 6 | |||
1183.2.e.c.170.1 | 2 | 91.10 | odd | 6 | |||
1183.2.e.c.508.1 | 2 | 91.75 | odd | 6 | |||
8281.2.a.c.1.1 | 1 | 91.62 | odd | 6 | |||
8281.2.a.g.1.1 | 1 | 13.10 | even | 6 | |||
8281.2.a.i.1.1 | 1 | 91.55 | odd | 6 | |||
8281.2.a.j.1.1 | 1 | 13.3 | even | 3 |