Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(43,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.g (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.6 | ||
Root | \(0.0477388 - 0.0477388i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.43 |
Dual form | 370.2.g.e.327.6 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.0477388 | + | 0.0477388i | −0.0275620 | + | 0.0275620i | −0.720753 | − | 0.693191i | \(-0.756204\pi\) |
0.693191 | + | 0.720753i | \(0.256204\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.17208 | + | 0.531109i | 0.971383 | + | 0.237519i | ||||
\(6\) | −0.0477388 | − | 0.0477388i | −0.0194893 | − | 0.0194893i | ||||
\(7\) | −2.77997 | + | 2.77997i | −1.05073 | + | 1.05073i | −0.0520865 | + | 0.998643i | \(0.516587\pi\) |
−0.998643 | + | 0.0520865i | \(0.983413\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.99544i | 0.998481i | ||||||||
\(10\) | −0.531109 | + | 2.17208i | −0.167951 | + | 0.686871i | ||||
\(11\) | − | 4.24241i | − | 1.27913i | −0.768735 | − | 0.639567i | \(-0.779114\pi\) | ||
0.768735 | − | 0.639567i | \(-0.220886\pi\) | |||||||
\(12\) | 0.0477388 | − | 0.0477388i | 0.0137810 | − | 0.0137810i | ||||
\(13\) | 3.32010i | 0.920831i | 0.887703 | + | 0.460416i | \(0.152300\pi\) | ||||
−0.887703 | + | 0.460416i | \(0.847700\pi\) | |||||||
\(14\) | −2.77997 | − | 2.77997i | −0.742978 | − | 0.742978i | ||||
\(15\) | −0.129047 | + | 0.0783380i | −0.0333198 | + | 0.0202268i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.64900 | 0.885013 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(18\) | −2.99544 | −0.706032 | ||||||||
\(19\) | −4.65117 | + | 4.65117i | −1.06705 | + | 1.06705i | −0.0694677 | + | 0.997584i | \(0.522130\pi\) |
−0.997584 | + | 0.0694677i | \(0.977870\pi\) | |||||||
\(20\) | −2.17208 | − | 0.531109i | −0.485691 | − | 0.118760i | ||||
\(21\) | − | 0.265425i | − | 0.0579205i | ||||||
\(22\) | 4.24241 | 0.904484 | ||||||||
\(23\) | 3.99058i | 0.832094i | 0.909343 | + | 0.416047i | \(0.136585\pi\) | ||||
−0.909343 | + | 0.416047i | \(0.863415\pi\) | |||||||
\(24\) | 0.0477388 | + | 0.0477388i | 0.00974465 | + | 0.00974465i | ||||
\(25\) | 4.43585 | + | 2.30722i | 0.887169 | + | 0.461444i | ||||
\(26\) | −3.32010 | −0.651126 | ||||||||
\(27\) | −0.286215 | − | 0.286215i | −0.0550822 | − | 0.0550822i | ||||
\(28\) | 2.77997 | − | 2.77997i | 0.525365 | − | 0.525365i | ||||
\(29\) | −1.30707 | − | 1.30707i | −0.242717 | − | 0.242717i | 0.575256 | − | 0.817973i | \(-0.304902\pi\) |
−0.817973 | + | 0.575256i | \(0.804902\pi\) | |||||||
\(30\) | −0.0783380 | − | 0.129047i | −0.0143025 | − | 0.0235607i | ||||
\(31\) | 3.96252 | − | 3.96252i | 0.711689 | − | 0.711689i | −0.255199 | − | 0.966888i | \(-0.582141\pi\) |
0.966888 | + | 0.255199i | \(0.0821411\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.202528 | + | 0.202528i | 0.0352555 | + | 0.0352555i | ||||
\(34\) | 3.64900i | 0.625799i | ||||||||
\(35\) | −7.51477 | + | 4.56184i | −1.27023 | + | 0.771092i | ||||
\(36\) | − | 2.99544i | − | 0.499240i | ||||||
\(37\) | −4.65727 | + | 3.91278i | −0.765650 | + | 0.643258i | ||||
\(38\) | −4.65117 | − | 4.65117i | −0.754520 | − | 0.754520i | ||||
\(39\) | −0.158498 | − | 0.158498i | −0.0253800 | − | 0.0253800i | ||||
\(40\) | 0.531109 | − | 2.17208i | 0.0839757 | − | 0.343436i | ||||
\(41\) | − | 2.70237i | − | 0.422040i | −0.977482 | − | 0.211020i | \(-0.932321\pi\) | ||
0.977482 | − | 0.211020i | \(-0.0676785\pi\) | |||||||
\(42\) | 0.265425 | 0.0409560 | ||||||||
\(43\) | − | 6.95570i | − | 1.06073i | −0.847768 | − | 0.530367i | \(-0.822054\pi\) | ||
0.847768 | − | 0.530367i | \(-0.177946\pi\) | |||||||
\(44\) | 4.24241i | 0.639567i | ||||||||
\(45\) | −1.59091 | + | 6.50633i | −0.237158 | + | 0.969907i | ||||
\(46\) | −3.99058 | −0.588380 | ||||||||
\(47\) | 1.34199 | − | 1.34199i | 0.195749 | − | 0.195749i | −0.602426 | − | 0.798175i | \(-0.705799\pi\) |
0.798175 | + | 0.602426i | \(0.205799\pi\) | |||||||
\(48\) | −0.0477388 | + | 0.0477388i | −0.00689051 | + | 0.00689051i | ||||
\(49\) | − | 8.45644i | − | 1.20806i | ||||||
\(50\) | −2.30722 | + | 4.43585i | −0.326290 | + | 0.627324i | ||||
\(51\) | −0.174199 | + | 0.174199i | −0.0243928 | + | 0.0243928i | ||||
\(52\) | − | 3.32010i | − | 0.460416i | ||||||
\(53\) | 5.37378 | + | 5.37378i | 0.738145 | + | 0.738145i | 0.972219 | − | 0.234074i | \(-0.0752057\pi\) |
−0.234074 | + | 0.972219i | \(0.575206\pi\) | |||||||
\(54\) | 0.286215 | − | 0.286215i | 0.0389490 | − | 0.0389490i | ||||
\(55\) | 2.25318 | − | 9.21484i | 0.303819 | − | 1.24253i | ||||
\(56\) | 2.77997 | + | 2.77997i | 0.371489 | + | 0.371489i | ||||
\(57\) | − | 0.444083i | − | 0.0588202i | ||||||
\(58\) | 1.30707 | − | 1.30707i | 0.171627 | − | 0.171627i | ||||
\(59\) | 8.04404 | − | 8.04404i | 1.04725 | − | 1.04725i | 0.0484179 | − | 0.998827i | \(-0.484582\pi\) |
0.998827 | − | 0.0484179i | \(-0.0154179\pi\) | |||||||
\(60\) | 0.129047 | − | 0.0783380i | 0.0166599 | − | 0.0101134i | ||||
\(61\) | 1.55262 | − | 1.55262i | 0.198793 | − | 0.198793i | −0.600690 | − | 0.799482i | \(-0.705107\pi\) |
0.799482 | + | 0.600690i | \(0.205107\pi\) | |||||||
\(62\) | 3.96252 | + | 3.96252i | 0.503240 | + | 0.503240i | ||||
\(63\) | −8.32723 | − | 8.32723i | −1.04913 | − | 1.04913i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.76334 | + | 7.21153i | −0.218715 | + | 0.894480i | ||||
\(66\) | −0.202528 | + | 0.202528i | −0.0249294 | + | 0.0249294i | ||||
\(67\) | 4.34085 | + | 4.34085i | 0.530320 | + | 0.530320i | 0.920668 | − | 0.390348i | \(-0.127645\pi\) |
−0.390348 | + | 0.920668i | \(0.627645\pi\) | |||||||
\(68\) | −3.64900 | −0.442507 | ||||||||
\(69\) | −0.190506 | − | 0.190506i | −0.0229342 | − | 0.0229342i | ||||
\(70\) | −4.56184 | − | 7.51477i | −0.545244 | − | 0.898187i | ||||
\(71\) | 5.54775 | 0.658397 | 0.329198 | − | 0.944261i | \(-0.393222\pi\) | ||||
0.329198 | + | 0.944261i | \(0.393222\pi\) | |||||||
\(72\) | 2.99544 | 0.353016 | ||||||||
\(73\) | 11.1383 | − | 11.1383i | 1.30364 | − | 1.30364i | 0.377712 | − | 0.925923i | \(-0.376711\pi\) |
0.925923 | − | 0.377712i | \(-0.123289\pi\) | |||||||
\(74\) | −3.91278 | − | 4.65727i | −0.454852 | − | 0.541396i | ||||
\(75\) | −0.321906 | + | 0.101618i | −0.0371705 | + | 0.0117339i | ||||
\(76\) | 4.65117 | − | 4.65117i | 0.533526 | − | 0.533526i | ||||
\(77\) | 11.7938 | + | 11.7938i | 1.34402 | + | 1.34402i | ||||
\(78\) | 0.158498 | − | 0.158498i | 0.0179464 | − | 0.0179464i | ||||
\(79\) | 3.17689 | − | 3.17689i | 0.357428 | − | 0.357428i | −0.505436 | − | 0.862864i | \(-0.668668\pi\) |
0.862864 | + | 0.505436i | \(0.168668\pi\) | |||||||
\(80\) | 2.17208 | + | 0.531109i | 0.242846 | + | 0.0593798i | ||||
\(81\) | −8.95900 | −0.995444 | ||||||||
\(82\) | 2.70237 | 0.298427 | ||||||||
\(83\) | 7.08119 | + | 7.08119i | 0.777261 | + | 0.777261i | 0.979364 | − | 0.202103i | \(-0.0647775\pi\) |
−0.202103 | + | 0.979364i | \(0.564778\pi\) | |||||||
\(84\) | 0.265425i | 0.0289602i | ||||||||
\(85\) | 7.92592 | + | 1.93802i | 0.859687 | + | 0.210208i | ||||
\(86\) | 6.95570 | 0.750053 | ||||||||
\(87\) | 0.124796 | 0.0133795 | ||||||||
\(88\) | −4.24241 | −0.452242 | ||||||||
\(89\) | −7.75651 | − | 7.75651i | −0.822188 | − | 0.822188i | 0.164233 | − | 0.986422i | \(-0.447485\pi\) |
−0.986422 | + | 0.164233i | \(0.947485\pi\) | |||||||
\(90\) | −6.50633 | − | 1.59091i | −0.685828 | − | 0.167696i | ||||
\(91\) | −9.22978 | − | 9.22978i | −0.967544 | − | 0.967544i | ||||
\(92\) | − | 3.99058i | − | 0.416047i | ||||||
\(93\) | 0.378332i | 0.0392312i | ||||||||
\(94\) | 1.34199 | + | 1.34199i | 0.138416 | + | 0.138416i | ||||
\(95\) | −12.5730 | + | 7.63243i | −1.28996 | + | 0.783071i | ||||
\(96\) | −0.0477388 | − | 0.0477388i | −0.00487233 | − | 0.00487233i | ||||
\(97\) | 10.0451 | 1.01992 | 0.509962 | − | 0.860197i | \(-0.329660\pi\) | ||||
0.509962 | + | 0.860197i | \(0.329660\pi\) | |||||||
\(98\) | 8.45644 | 0.854230 | ||||||||
\(99\) | 12.7079 | 1.27719 | ||||||||
\(100\) | −4.43585 | − | 2.30722i | −0.443585 | − | 0.230722i | ||||
\(101\) | 1.51442i | 0.150691i | 0.997157 | + | 0.0753454i | \(0.0240059\pi\) | ||||
−0.997157 | + | 0.0753454i | \(0.975994\pi\) | |||||||
\(102\) | −0.174199 | − | 0.174199i | −0.0172483 | − | 0.0172483i | ||||
\(103\) | −3.88757 | −0.383054 | −0.191527 | − | 0.981487i | \(-0.561344\pi\) | ||||
−0.191527 | + | 0.981487i | \(0.561344\pi\) | |||||||
\(104\) | 3.32010 | 0.325563 | ||||||||
\(105\) | 0.140969 | − | 0.576524i | 0.0137572 | − | 0.0562629i | ||||
\(106\) | −5.37378 | + | 5.37378i | −0.521948 | + | 0.521948i | ||||
\(107\) | 0.736249 | − | 0.736249i | 0.0711758 | − | 0.0711758i | −0.670623 | − | 0.741799i | \(-0.733973\pi\) |
0.741799 | + | 0.670623i | \(0.233973\pi\) | |||||||
\(108\) | 0.286215 | + | 0.286215i | 0.0275411 | + | 0.0275411i | ||||
\(109\) | −1.72705 | + | 1.72705i | −0.165422 | + | 0.165422i | −0.784964 | − | 0.619542i | \(-0.787318\pi\) |
0.619542 | + | 0.784964i | \(0.287318\pi\) | |||||||
\(110\) | 9.21484 | + | 2.25318i | 0.878600 | + | 0.214832i | ||||
\(111\) | 0.0355407 | − | 0.409124i | 0.00337337 | − | 0.0388324i | ||||
\(112\) | −2.77997 | + | 2.77997i | −0.262682 | + | 0.262682i | ||||
\(113\) | −4.23008 | −0.397933 | −0.198966 | − | 0.980006i | \(-0.563758\pi\) | ||||
−0.198966 | + | 0.980006i | \(0.563758\pi\) | |||||||
\(114\) | 0.444083 | 0.0415922 | ||||||||
\(115\) | −2.11943 | + | 8.66786i | −0.197638 | + | 0.808282i | ||||
\(116\) | 1.30707 | + | 1.30707i | 0.121358 | + | 0.121358i | ||||
\(117\) | −9.94518 | −0.919432 | ||||||||
\(118\) | 8.04404 | + | 8.04404i | 0.740514 | + | 0.740514i | ||||
\(119\) | −10.1441 | + | 10.1441i | −0.929909 | + | 0.929909i | ||||
\(120\) | 0.0783380 | + | 0.129047i | 0.00715125 | + | 0.0117803i | ||||
\(121\) | −6.99802 | −0.636183 | ||||||||
\(122\) | 1.55262 | + | 1.55262i | 0.140568 | + | 0.140568i | ||||
\(123\) | 0.129008 | + | 0.129008i | 0.0116323 | + | 0.0116323i | ||||
\(124\) | −3.96252 | + | 3.96252i | −0.355845 | + | 0.355845i | ||||
\(125\) | 8.40962 | + | 7.36738i | 0.752179 | + | 0.658958i | ||||
\(126\) | 8.32723 | − | 8.32723i | 0.741849 | − | 0.741849i | ||||
\(127\) | 0.683408 | − | 0.683408i | 0.0606426 | − | 0.0606426i | −0.676135 | − | 0.736778i | \(-0.736346\pi\) |
0.736778 | + | 0.676135i | \(0.236346\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0.332057 | + | 0.332057i | 0.0292360 | + | 0.0292360i | ||||
\(130\) | −7.21153 | − | 1.76334i | −0.632493 | − | 0.154655i | ||||
\(131\) | −3.35210 | + | 3.35210i | −0.292875 | + | 0.292875i | −0.838215 | − | 0.545340i | \(-0.816400\pi\) |
0.545340 | + | 0.838215i | \(0.316400\pi\) | |||||||
\(132\) | −0.202528 | − | 0.202528i | −0.0176278 | − | 0.0176278i | ||||
\(133\) | − | 25.8602i | − | 2.24237i | ||||||
\(134\) | −4.34085 | + | 4.34085i | −0.374993 | + | 0.374993i | ||||
\(135\) | −0.469671 | − | 0.773694i | −0.0404228 | − | 0.0665890i | ||||
\(136\) | − | 3.64900i | − | 0.312900i | ||||||
\(137\) | 15.4431 | − | 15.4431i | 1.31939 | − | 1.31939i | 0.405138 | − | 0.914256i | \(-0.367223\pi\) |
0.914256 | − | 0.405138i | \(-0.132777\pi\) | |||||||
\(138\) | 0.190506 | − | 0.190506i | 0.0162169 | − | 0.0162169i | ||||
\(139\) | −17.8399 | −1.51316 | −0.756582 | − | 0.653899i | \(-0.773132\pi\) | ||||
−0.756582 | + | 0.653899i | \(0.773132\pi\) | |||||||
\(140\) | 7.51477 | − | 4.56184i | 0.635114 | − | 0.385546i | ||||
\(141\) | 0.128130i | 0.0107905i | ||||||||
\(142\) | 5.54775i | 0.465557i | ||||||||
\(143\) | 14.0852 | 1.17787 | ||||||||
\(144\) | 2.99544i | 0.249620i | ||||||||
\(145\) | −2.14486 | − | 3.53325i | −0.178121 | − | 0.293421i | ||||
\(146\) | 11.1383 | + | 11.1383i | 0.921809 | + | 0.921809i | ||||
\(147\) | 0.403701 | + | 0.403701i | 0.0332967 | + | 0.0332967i | ||||
\(148\) | 4.65727 | − | 3.91278i | 0.382825 | − | 0.321629i | ||||
\(149\) | − | 17.7144i | − | 1.45122i | −0.688106 | − | 0.725610i | \(-0.741558\pi\) | ||
0.688106 | − | 0.725610i | \(-0.258442\pi\) | |||||||
\(150\) | −0.101618 | − | 0.321906i | −0.00829709 | − | 0.0262835i | ||||
\(151\) | − | 5.53031i | − | 0.450050i | −0.974353 | − | 0.225025i | \(-0.927754\pi\) | ||
0.974353 | − | 0.225025i | \(-0.0722464\pi\) | |||||||
\(152\) | 4.65117 | + | 4.65117i | 0.377260 | + | 0.377260i | ||||
\(153\) | 10.9304i | 0.883669i | ||||||||
\(154\) | −11.7938 | + | 11.7938i | −0.950368 | + | 0.950368i | ||||
\(155\) | 10.7114 | − | 6.50237i | 0.860362 | − | 0.522283i | ||||
\(156\) | 0.158498 | + | 0.158498i | 0.0126900 | + | 0.0126900i | ||||
\(157\) | −3.47940 | + | 3.47940i | −0.277687 | + | 0.277687i | −0.832185 | − | 0.554498i | \(-0.812910\pi\) |
0.554498 | + | 0.832185i | \(0.312910\pi\) | |||||||
\(158\) | 3.17689 | + | 3.17689i | 0.252740 | + | 0.252740i | ||||
\(159\) | −0.513076 | −0.0406896 | ||||||||
\(160\) | −0.531109 | + | 2.17208i | −0.0419878 | + | 0.171718i | ||||
\(161\) | −11.0937 | − | 11.0937i | −0.874306 | − | 0.874306i | ||||
\(162\) | − | 8.95900i | − | 0.703885i | ||||||
\(163\) | −21.7952 | −1.70713 | −0.853566 | − | 0.520985i | \(-0.825565\pi\) | ||||
−0.853566 | + | 0.520985i | \(0.825565\pi\) | |||||||
\(164\) | 2.70237i | 0.211020i | ||||||||
\(165\) | 0.332342 | + | 0.547470i | 0.0258728 | + | 0.0426205i | ||||
\(166\) | −7.08119 | + | 7.08119i | −0.549607 | + | 0.549607i | ||||
\(167\) | −11.1575 | −0.863394 | −0.431697 | − | 0.902019i | \(-0.642085\pi\) | ||||
−0.431697 | + | 0.902019i | \(0.642085\pi\) | |||||||
\(168\) | −0.265425 | −0.0204780 | ||||||||
\(169\) | 1.97691 | 0.152070 | ||||||||
\(170\) | −1.93802 | + | 7.92592i | −0.148639 | + | 0.607890i | ||||
\(171\) | −13.9323 | − | 13.9323i | −1.06543 | − | 1.06543i | ||||
\(172\) | 6.95570i | 0.530367i | ||||||||
\(173\) | −14.4965 | + | 14.4965i | −1.10215 | + | 1.10215i | −0.107994 | + | 0.994152i | \(0.534443\pi\) |
−0.994152 | + | 0.107994i | \(0.965557\pi\) | |||||||
\(174\) | 0.124796i | 0.00946076i | ||||||||
\(175\) | −18.7455 | + | 5.91752i | −1.41703 | + | 0.447322i | ||||
\(176\) | − | 4.24241i | − | 0.319783i | ||||||
\(177\) | 0.768026i | 0.0577284i | ||||||||
\(178\) | 7.75651 | − | 7.75651i | 0.581375 | − | 0.581375i | ||||
\(179\) | 12.6119 | + | 12.6119i | 0.942658 | + | 0.942658i | 0.998443 | − | 0.0557848i | \(-0.0177661\pi\) |
−0.0557848 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(180\) | 1.59091 | − | 6.50633i | 0.118579 | − | 0.484954i | ||||
\(181\) | 12.8145 | 0.952494 | 0.476247 | − | 0.879312i | \(-0.341997\pi\) | ||||
0.476247 | + | 0.879312i | \(0.341997\pi\) | |||||||
\(182\) | 9.22978 | − | 9.22978i | 0.684157 | − | 0.684157i | ||||
\(183\) | 0.148241i | 0.0109583i | ||||||||
\(184\) | 3.99058 | 0.294190 | ||||||||
\(185\) | −12.1941 | + | 6.02536i | −0.896525 | + | 0.442993i | ||||
\(186\) | −0.378332 | −0.0277406 | ||||||||
\(187\) | − | 15.4806i | − | 1.13205i | ||||||
\(188\) | −1.34199 | + | 1.34199i | −0.0978746 | + | 0.0978746i | ||||
\(189\) | 1.59134 | 0.115753 | ||||||||
\(190\) | −7.63243 | − | 12.5730i | −0.553715 | − | 0.912140i | ||||
\(191\) | 10.0822 | + | 10.0822i | 0.729521 | + | 0.729521i | 0.970524 | − | 0.241003i | \(-0.0774763\pi\) |
−0.241003 | + | 0.970524i | \(0.577476\pi\) | |||||||
\(192\) | 0.0477388 | − | 0.0477388i | 0.00344525 | − | 0.00344525i | ||||
\(193\) | 7.58052i | 0.545658i | 0.962063 | + | 0.272829i | \(0.0879593\pi\) | ||||
−0.962063 | + | 0.272829i | \(0.912041\pi\) | |||||||
\(194\) | 10.0451i | 0.721195i | ||||||||
\(195\) | −0.260090 | − | 0.428450i | −0.0186255 | − | 0.0306819i | ||||
\(196\) | 8.45644i | 0.604032i | ||||||||
\(197\) | −16.8945 | + | 16.8945i | −1.20369 | + | 1.20369i | −0.230649 | + | 0.973037i | \(0.574085\pi\) |
−0.973037 | + | 0.230649i | \(0.925915\pi\) | |||||||
\(198\) | 12.7079i | 0.903110i | ||||||||
\(199\) | −0.576031 | − | 0.576031i | −0.0408338 | − | 0.0408338i | 0.686395 | − | 0.727229i | \(-0.259192\pi\) |
−0.727229 | + | 0.686395i | \(0.759192\pi\) | |||||||
\(200\) | 2.30722 | − | 4.43585i | 0.163145 | − | 0.313662i | ||||
\(201\) | −0.414455 | −0.0292334 | ||||||||
\(202\) | −1.51442 | −0.106554 | ||||||||
\(203\) | 7.26722 | 0.510059 | ||||||||
\(204\) | 0.174199 | − | 0.174199i | 0.0121964 | − | 0.0121964i | ||||
\(205\) | 1.43525 | − | 5.86977i | 0.100243 | − | 0.409962i | ||||
\(206\) | − | 3.88757i | − | 0.270860i | ||||||
\(207\) | −11.9536 | −0.830830 | ||||||||
\(208\) | 3.32010i | 0.230208i | ||||||||
\(209\) | 19.7322 | + | 19.7322i | 1.36490 | + | 1.36490i | ||||
\(210\) | 0.576524 | + | 0.140969i | 0.0397839 | + | 0.00972782i | ||||
\(211\) | −21.1449 | −1.45568 | −0.727838 | − | 0.685749i | \(-0.759475\pi\) | ||||
−0.727838 | + | 0.685749i | \(0.759475\pi\) | |||||||
\(212\) | −5.37378 | − | 5.37378i | −0.369073 | − | 0.369073i | ||||
\(213\) | −0.264843 | + | 0.264843i | −0.0181467 | + | 0.0181467i | ||||
\(214\) | 0.736249 | + | 0.736249i | 0.0503289 | + | 0.0503289i | ||||
\(215\) | 3.69423 | − | 15.1083i | 0.251945 | − | 1.03038i | ||||
\(216\) | −0.286215 | + | 0.286215i | −0.0194745 | + | 0.0194745i | ||||
\(217\) | 22.0313i | 1.49559i | ||||||||
\(218\) | −1.72705 | − | 1.72705i | −0.116971 | − | 0.116971i | ||||
\(219\) | 1.06346i | 0.0718617i | ||||||||
\(220\) | −2.25318 | + | 9.21484i | −0.151909 | + | 0.621264i | ||||
\(221\) | 12.1151i | 0.814948i | ||||||||
\(222\) | 0.409124 | + | 0.0355407i | 0.0274586 | + | 0.00238534i | ||||
\(223\) | 14.0320 | + | 14.0320i | 0.939655 | + | 0.939655i | 0.998280 | − | 0.0586249i | \(-0.0186716\pi\) |
−0.0586249 | + | 0.998280i | \(0.518672\pi\) | |||||||
\(224\) | −2.77997 | − | 2.77997i | −0.185744 | − | 0.185744i | ||||
\(225\) | −6.91114 | + | 13.2873i | −0.460743 | + | 0.885822i | ||||
\(226\) | − | 4.23008i | − | 0.281381i | ||||||
\(227\) | −17.0093 | −1.12895 | −0.564475 | − | 0.825450i | \(-0.690921\pi\) | ||||
−0.564475 | + | 0.825450i | \(0.690921\pi\) | |||||||
\(228\) | 0.444083i | 0.0294101i | ||||||||
\(229\) | 8.49131i | 0.561121i | 0.959836 | + | 0.280561i | \(0.0905204\pi\) | ||||
−0.959836 | + | 0.280561i | \(0.909480\pi\) | |||||||
\(230\) | −8.66786 | − | 2.11943i | −0.571542 | − | 0.139751i | ||||
\(231\) | −1.12604 | −0.0740880 | ||||||||
\(232\) | −1.30707 | + | 1.30707i | −0.0858133 | + | 0.0858133i | ||||
\(233\) | −11.1205 | + | 11.1205i | −0.728530 | + | 0.728530i | −0.970327 | − | 0.241797i | \(-0.922263\pi\) |
0.241797 | + | 0.970327i | \(0.422263\pi\) | |||||||
\(234\) | − | 9.94518i | − | 0.650137i | ||||||
\(235\) | 3.62765 | − | 2.20216i | 0.236642 | − | 0.143653i | ||||
\(236\) | −8.04404 | + | 8.04404i | −0.523623 | + | 0.523623i | ||||
\(237\) | 0.303322i | 0.0197029i | ||||||||
\(238\) | −10.1441 | − | 10.1441i | −0.657545 | − | 0.657545i | ||||
\(239\) | 14.6371 | − | 14.6371i | 0.946797 | − | 0.946797i | −0.0518580 | − | 0.998654i | \(-0.516514\pi\) |
0.998654 | + | 0.0518580i | \(0.0165143\pi\) | |||||||
\(240\) | −0.129047 | + | 0.0783380i | −0.00832995 | + | 0.00505669i | ||||
\(241\) | 10.5430 | + | 10.5430i | 0.679137 | + | 0.679137i | 0.959805 | − | 0.280668i | \(-0.0905560\pi\) |
−0.280668 | + | 0.959805i | \(0.590556\pi\) | |||||||
\(242\) | − | 6.99802i | − | 0.449850i | ||||||
\(243\) | 1.28634 | − | 1.28634i | 0.0825187 | − | 0.0825187i | ||||
\(244\) | −1.55262 | + | 1.55262i | −0.0993963 | + | 0.0993963i | ||||
\(245\) | 4.49129 | − | 18.3681i | 0.286938 | − | 1.17349i | ||||
\(246\) | −0.129008 | + | 0.129008i | −0.00822526 | + | 0.00822526i | ||||
\(247\) | −15.4424 | − | 15.4424i | −0.982575 | − | 0.982575i | ||||
\(248\) | −3.96252 | − | 3.96252i | −0.251620 | − | 0.251620i | ||||
\(249\) | −0.676095 | −0.0428458 | ||||||||
\(250\) | −7.36738 | + | 8.40962i | −0.465954 | + | 0.531871i | ||||
\(251\) | −16.2391 | + | 16.2391i | −1.02500 | + | 1.02500i | −0.0253206 | + | 0.999679i | \(0.508061\pi\) |
−0.999679 | + | 0.0253206i | \(0.991939\pi\) | |||||||
\(252\) | 8.32723 | + | 8.32723i | 0.524566 | + | 0.524566i | ||||
\(253\) | 16.9297 | 1.06436 | ||||||||
\(254\) | 0.683408 | + | 0.683408i | 0.0428808 | + | 0.0428808i | ||||
\(255\) | −0.470893 | + | 0.285856i | −0.0294885 | + | 0.0179010i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.00407 | 0.312145 | 0.156073 | − | 0.987746i | \(-0.450117\pi\) | ||||
0.156073 | + | 0.987746i | \(0.450117\pi\) | |||||||
\(258\) | −0.332057 | + | 0.332057i | −0.0206730 | + | 0.0206730i | ||||
\(259\) | 2.06964 | − | 23.8245i | 0.128601 | − | 1.48038i | ||||
\(260\) | 1.76334 | − | 7.21153i | 0.109357 | − | 0.447240i | ||||
\(261\) | 3.91525 | − | 3.91525i | 0.242348 | − | 0.242348i | ||||
\(262\) | −3.35210 | − | 3.35210i | −0.207094 | − | 0.207094i | ||||
\(263\) | 12.4257 | − | 12.4257i | 0.766203 | − | 0.766203i | −0.211233 | − | 0.977436i | \(-0.567748\pi\) |
0.977436 | + | 0.211233i | \(0.0677477\pi\) | |||||||
\(264\) | 0.202528 | − | 0.202528i | 0.0124647 | − | 0.0124647i | ||||
\(265\) | 8.81821 | + | 14.5263i | 0.541698 | + | 0.892345i | ||||
\(266\) | 25.8602 | 1.58559 | ||||||||
\(267\) | 0.740574 | 0.0453224 | ||||||||
\(268\) | −4.34085 | − | 4.34085i | −0.265160 | − | 0.265160i | ||||
\(269\) | − | 22.6019i | − | 1.37806i | −0.724732 | − | 0.689030i | \(-0.758037\pi\) | ||
0.724732 | − | 0.689030i | \(-0.241963\pi\) | |||||||
\(270\) | 0.773694 | − | 0.469671i | 0.0470855 | − | 0.0285833i | ||||
\(271\) | 18.1930 | 1.10514 | 0.552572 | − | 0.833465i | \(-0.313647\pi\) | ||||
0.552572 | + | 0.833465i | \(0.313647\pi\) | |||||||
\(272\) | 3.64900 | 0.221253 | ||||||||
\(273\) | 0.881238 | 0.0533350 | ||||||||
\(274\) | 15.4431 | + | 15.4431i | 0.932952 | + | 0.932952i | ||||
\(275\) | 9.78816 | − | 18.8187i | 0.590248 | − | 1.13481i | ||||
\(276\) | 0.190506 | + | 0.190506i | 0.0114671 | + | 0.0114671i | ||||
\(277\) | − | 23.4453i | − | 1.40869i | −0.709857 | − | 0.704346i | \(-0.751241\pi\) | ||
0.709857 | − | 0.704346i | \(-0.248759\pi\) | |||||||
\(278\) | − | 17.8399i | − | 1.06997i | ||||||
\(279\) | 11.8695 | + | 11.8695i | 0.710608 | + | 0.710608i | ||||
\(280\) | 4.56184 | + | 7.51477i | 0.272622 | + | 0.449094i | ||||
\(281\) | 3.32166 | + | 3.32166i | 0.198154 | + | 0.198154i | 0.799208 | − | 0.601054i | \(-0.205253\pi\) |
−0.601054 | + | 0.799208i | \(0.705253\pi\) | |||||||
\(282\) | −0.128130 | −0.00763003 | ||||||||
\(283\) | 12.1785 | 0.723935 | 0.361968 | − | 0.932191i | \(-0.382105\pi\) | ||||
0.361968 | + | 0.932191i | \(0.382105\pi\) | |||||||
\(284\) | −5.54775 | −0.329198 | ||||||||
\(285\) | 0.235856 | − | 0.964583i | 0.0139709 | − | 0.0571370i | ||||
\(286\) | 14.0852i | 0.832877i | ||||||||
\(287\) | 7.51251 | + | 7.51251i | 0.443450 | + | 0.443450i | ||||
\(288\) | −2.99544 | −0.176508 | ||||||||
\(289\) | −3.68477 | −0.216751 | ||||||||
\(290\) | 3.53325 | − | 2.14486i | 0.207480 | − | 0.125951i | ||||
\(291\) | −0.479541 | + | 0.479541i | −0.0281112 | + | 0.0281112i | ||||
\(292\) | −11.1383 | + | 11.1383i | −0.651818 | + | 0.651818i | ||||
\(293\) | 1.06493 | + | 1.06493i | 0.0622140 | + | 0.0622140i | 0.737529 | − | 0.675315i | \(-0.235992\pi\) |
−0.675315 | + | 0.737529i | \(0.735992\pi\) | |||||||
\(294\) | −0.403701 | + | 0.403701i | −0.0235443 | + | 0.0235443i | ||||
\(295\) | 21.7445 | − | 13.2000i | 1.26602 | − | 0.768535i | ||||
\(296\) | 3.91278 | + | 4.65727i | 0.227426 | + | 0.270698i | ||||
\(297\) | −1.21424 | + | 1.21424i | −0.0704575 | + | 0.0704575i | ||||
\(298\) | 17.7144 | 1.02617 | ||||||||
\(299\) | −13.2492 | −0.766219 | ||||||||
\(300\) | 0.321906 | − | 0.101618i | 0.0185853 | − | 0.00586693i | ||||
\(301\) | 19.3366 | + | 19.3366i | 1.11454 | + | 1.11454i | ||||
\(302\) | 5.53031 | 0.318233 | ||||||||
\(303\) | −0.0722968 | − | 0.0722968i | −0.00415334 | − | 0.00415334i | ||||
\(304\) | −4.65117 | + | 4.65117i | −0.266763 | + | 0.266763i | ||||
\(305\) | 4.19702 | − | 2.54780i | 0.240321 | − | 0.145887i | ||||
\(306\) | −10.9304 | −0.624848 | ||||||||
\(307\) | −16.1006 | − | 16.1006i | −0.918907 | − | 0.918907i | 0.0780426 | − | 0.996950i | \(-0.475133\pi\) |
−0.996950 | + | 0.0780426i | \(0.975133\pi\) | |||||||
\(308\) | −11.7938 | − | 11.7938i | −0.672012 | − | 0.672012i | ||||
\(309\) | 0.185588 | − | 0.185588i | 0.0105577 | − | 0.0105577i | ||||
\(310\) | 6.50237 | + | 10.7114i | 0.369310 | + | 0.608368i | ||||
\(311\) | −18.5878 | + | 18.5878i | −1.05402 | + | 1.05402i | −0.0555639 | + | 0.998455i | \(0.517696\pi\) |
−0.998455 | + | 0.0555639i | \(0.982304\pi\) | |||||||
\(312\) | −0.158498 | + | 0.158498i | −0.00897318 | + | 0.00897318i | ||||
\(313\) | − | 21.7608i | − | 1.22999i | −0.788531 | − | 0.614995i | \(-0.789158\pi\) | ||
0.788531 | − | 0.614995i | \(-0.210842\pi\) | |||||||
\(314\) | −3.47940 | − | 3.47940i | −0.196354 | − | 0.196354i | ||||
\(315\) | −13.6647 | − | 22.5101i | −0.769921 | − | 1.26830i | ||||
\(316\) | −3.17689 | + | 3.17689i | −0.178714 | + | 0.178714i | ||||
\(317\) | 22.3061 | + | 22.3061i | 1.25284 | + | 1.25284i | 0.954443 | + | 0.298392i | \(0.0964504\pi\) |
0.298392 | + | 0.954443i | \(0.403550\pi\) | |||||||
\(318\) | − | 0.513076i | − | 0.0287719i | ||||||
\(319\) | −5.54512 | + | 5.54512i | −0.310467 | + | 0.310467i | ||||
\(320\) | −2.17208 | − | 0.531109i | −0.121423 | − | 0.0296899i | ||||
\(321\) | 0.0702953i | 0.00392350i | ||||||||
\(322\) | 11.0937 | − | 11.0937i | 0.618228 | − | 0.618228i | ||||
\(323\) | −16.9721 | + | 16.9721i | −0.944355 | + | 0.944355i | ||||
\(324\) | 8.95900 | 0.497722 | ||||||||
\(325\) | −7.66021 | + | 14.7275i | −0.424912 | + | 0.816933i | ||||
\(326\) | − | 21.7952i | − | 1.20712i | ||||||
\(327\) | − | 0.164895i | − | 0.00911871i | ||||||
\(328\) | −2.70237 | −0.149214 | ||||||||
\(329\) | 7.46137i | 0.411359i | ||||||||
\(330\) | −0.547470 | + | 0.332342i | −0.0301372 | + | 0.0182948i | ||||
\(331\) | 23.9871 | + | 23.9871i | 1.31845 | + | 1.31845i | 0.915003 | + | 0.403447i | \(0.132188\pi\) |
0.403447 | + | 0.915003i | \(0.367812\pi\) | |||||||
\(332\) | −7.08119 | − | 7.08119i | −0.388631 | − | 0.388631i | ||||
\(333\) | −11.7205 | − | 13.9506i | −0.642280 | − | 0.764486i | ||||
\(334\) | − | 11.1575i | − | 0.610512i | ||||||
\(335\) | 7.12321 | + | 11.7341i | 0.389183 | + | 0.641105i | ||||
\(336\) | − | 0.265425i | − | 0.0144801i | ||||||
\(337\) | −17.5570 | − | 17.5570i | −0.956390 | − | 0.956390i | 0.0426980 | − | 0.999088i | \(-0.486405\pi\) |
−0.999088 | + | 0.0426980i | \(0.986405\pi\) | |||||||
\(338\) | 1.97691i | 0.107530i | ||||||||
\(339\) | 0.201939 | − | 0.201939i | 0.0109678 | − | 0.0109678i | ||||
\(340\) | −7.92592 | − | 1.93802i | −0.429843 | − | 0.105104i | ||||
\(341\) | −16.8106 | − | 16.8106i | −0.910346 | − | 0.910346i | ||||
\(342\) | 13.9323 | − | 13.9323i | 0.753373 | − | 0.753373i | ||||
\(343\) | 4.04887 | + | 4.04887i | 0.218618 | + | 0.218618i | ||||
\(344\) | −6.95570 | −0.375026 | ||||||||
\(345\) | −0.312614 | − | 0.514973i | −0.0168306 | − | 0.0277252i | ||||
\(346\) | −14.4965 | − | 14.4965i | −0.779335 | − | 0.779335i | ||||
\(347\) | − | 11.0678i | − | 0.594151i | −0.954854 | − | 0.297075i | \(-0.903989\pi\) | ||
0.954854 | − | 0.297075i | \(-0.0960112\pi\) | |||||||
\(348\) | −0.124796 | −0.00668977 | ||||||||
\(349\) | − | 31.6855i | − | 1.69609i | −0.529926 | − | 0.848044i | \(-0.677780\pi\) | ||
0.529926 | − | 0.848044i | \(-0.322220\pi\) | |||||||
\(350\) | −5.91752 | − | 18.7455i | −0.316305 | − | 1.00199i | ||||
\(351\) | 0.950265 | − | 0.950265i | 0.0507214 | − | 0.0507214i | ||||
\(352\) | 4.24241 | 0.226121 | ||||||||
\(353\) | −15.6047 | −0.830555 | −0.415278 | − | 0.909695i | \(-0.636316\pi\) | ||||
−0.415278 | + | 0.909695i | \(0.636316\pi\) | |||||||
\(354\) | −0.768026 | −0.0408201 | ||||||||
\(355\) | 12.0501 | + | 2.94646i | 0.639555 | + | 0.156382i | ||||
\(356\) | 7.75651 | + | 7.75651i | 0.411094 | + | 0.411094i | ||||
\(357\) | − | 0.968537i | − | 0.0512604i | ||||||
\(358\) | −12.6119 | + | 12.6119i | −0.666560 | + | 0.666560i | ||||
\(359\) | 34.4499i | 1.81820i | 0.416580 | + | 0.909099i | \(0.363229\pi\) | ||||
−0.416580 | + | 0.909099i | \(0.636771\pi\) | |||||||
\(360\) | 6.50633 | + | 1.59091i | 0.342914 | + | 0.0838481i | ||||
\(361\) | − | 24.2668i | − | 1.27720i | ||||||
\(362\) | 12.8145i | 0.673515i | ||||||||
\(363\) | 0.334077 | − | 0.334077i | 0.0175345 | − | 0.0175345i | ||||
\(364\) | 9.22978 | + | 9.22978i | 0.483772 | + | 0.483772i | ||||
\(365\) | 30.1088 | − | 18.2775i | 1.57597 | − | 0.956691i | ||||
\(366\) | −0.148241 | −0.00774866 | ||||||||
\(367\) | −4.61443 | + | 4.61443i | −0.240871 | + | 0.240871i | −0.817211 | − | 0.576339i | \(-0.804481\pi\) |
0.576339 | + | 0.817211i | \(0.304481\pi\) | |||||||
\(368\) | 3.99058i | 0.208024i | ||||||||
\(369\) | 8.09481 | 0.421399 | ||||||||
\(370\) | −6.02536 | − | 12.1941i | −0.313243 | − | 0.633939i | ||||
\(371\) | −29.8779 | −1.55118 | ||||||||
\(372\) | − | 0.378332i | − | 0.0196156i | ||||||
\(373\) | −15.3464 | + | 15.3464i | −0.794607 | + | 0.794607i | −0.982239 | − | 0.187632i | \(-0.939919\pi\) |
0.187632 | + | 0.982239i | \(0.439919\pi\) | |||||||
\(374\) | 15.4806 | 0.800481 | ||||||||
\(375\) | −0.753176 | + | 0.0497555i | −0.0388938 | + | 0.00256937i | ||||
\(376\) | −1.34199 | − | 1.34199i | −0.0692078 | − | 0.0692078i | ||||
\(377\) | 4.33961 | − | 4.33961i | 0.223501 | − | 0.223501i | ||||
\(378\) | 1.59134i | 0.0818497i | ||||||||
\(379\) | − | 23.4892i | − | 1.20656i | −0.797531 | − | 0.603278i | \(-0.793861\pi\) | ||
0.797531 | − | 0.603278i | \(-0.206139\pi\) | |||||||
\(380\) | 12.5730 | − | 7.63243i | 0.644981 | − | 0.391535i | ||||
\(381\) | 0.0652502i | 0.00334287i | ||||||||
\(382\) | −10.0822 | + | 10.0822i | −0.515850 | + | 0.515850i | ||||
\(383\) | 0.480522i | 0.0245535i | 0.999925 | + | 0.0122768i | \(0.00390791\pi\) | ||||
−0.999925 | + | 0.0122768i | \(0.996092\pi\) | |||||||
\(384\) | 0.0477388 | + | 0.0477388i | 0.00243616 | + | 0.00243616i | ||||
\(385\) | 19.3532 | + | 31.8807i | 0.986330 | + | 1.62479i | ||||
\(386\) | −7.58052 | −0.385838 | ||||||||
\(387\) | 20.8354 | 1.05912 | ||||||||
\(388\) | −10.0451 | −0.509962 | ||||||||
\(389\) | 11.0293 | − | 11.0293i | 0.559208 | − | 0.559208i | −0.369874 | − | 0.929082i | \(-0.620599\pi\) |
0.929082 | + | 0.369874i | \(0.120599\pi\) | |||||||
\(390\) | 0.428450 | − | 0.260090i | 0.0216954 | − | 0.0131702i | ||||
\(391\) | 14.5617i | 0.736415i | ||||||||
\(392\) | −8.45644 | −0.427115 | ||||||||
\(393\) | − | 0.320051i | − | 0.0161444i | ||||||
\(394\) | −16.8945 | − | 16.8945i | −0.851134 | − | 0.851134i | ||||
\(395\) | 8.58772 | − | 5.21318i | 0.432095 | − | 0.262303i | ||||
\(396\) | −12.7079 | −0.638595 | ||||||||
\(397\) | −18.6363 | − | 18.6363i | −0.935327 | − | 0.935327i | 0.0627054 | − | 0.998032i | \(-0.480027\pi\) |
−0.998032 | + | 0.0627054i | \(0.980027\pi\) | |||||||
\(398\) | 0.576031 | − | 0.576031i | 0.0288738 | − | 0.0288738i | ||||
\(399\) | 1.23454 | + | 1.23454i | 0.0618041 | + | 0.0618041i | ||||
\(400\) | 4.43585 | + | 2.30722i | 0.221792 | + | 0.115361i | ||||
\(401\) | 23.4574 | − | 23.4574i | 1.17141 | − | 1.17141i | 0.189535 | − | 0.981874i | \(-0.439302\pi\) |
0.981874 | − | 0.189535i | \(-0.0606980\pi\) | |||||||
\(402\) | − | 0.414455i | − | 0.0206711i | ||||||
\(403\) | 13.1560 | + | 13.1560i | 0.655346 | + | 0.655346i | ||||
\(404\) | − | 1.51442i | − | 0.0753454i | ||||||
\(405\) | −19.4596 | − | 4.75820i | −0.966958 | − | 0.236437i | ||||
\(406\) | 7.26722i | 0.360666i | ||||||||
\(407\) | 16.5996 | + | 19.7580i | 0.822813 | + | 0.979369i | ||||
\(408\) | 0.174199 | + | 0.174199i | 0.00862415 | + | 0.00862415i | ||||
\(409\) | 20.5642 | + | 20.5642i | 1.01684 | + | 1.01684i | 0.999856 | + | 0.0169803i | \(0.00540527\pi\) |
0.0169803 | + | 0.999856i | \(0.494595\pi\) | |||||||
\(410\) | 5.86977 | + | 1.43525i | 0.289887 | + | 0.0708822i | ||||
\(411\) | 1.47447i | 0.0727303i | ||||||||
\(412\) | 3.88757 | 0.191527 | ||||||||
\(413\) | 44.7244i | 2.20074i | ||||||||
\(414\) | − | 11.9536i | − | 0.587486i | ||||||
\(415\) | 11.6200 | + | 19.1418i | 0.570404 | + | 0.939633i | ||||
\(416\) | −3.32010 | −0.162782 | ||||||||
\(417\) | 0.851658 | − | 0.851658i | 0.0417059 | − | 0.0417059i | ||||
\(418\) | −19.7322 | + | 19.7322i | −0.965132 | + | 0.965132i | ||||
\(419\) | − | 37.9044i | − | 1.85175i | −0.377827 | − | 0.925876i | \(-0.623329\pi\) | ||
0.377827 | − | 0.925876i | \(-0.376671\pi\) | |||||||
\(420\) | −0.140969 | + | 0.576524i | −0.00687861 | + | 0.0281315i | ||||
\(421\) | 24.4985 | − | 24.4985i | 1.19398 | − | 1.19398i | 0.218043 | − | 0.975939i | \(-0.430033\pi\) |
0.975939 | − | 0.218043i | \(-0.0699674\pi\) | |||||||
\(422\) | − | 21.1449i | − | 1.02932i | ||||||
\(423\) | 4.01985 | + | 4.01985i | 0.195452 | + | 0.195452i | ||||
\(424\) | 5.37378 | − | 5.37378i | 0.260974 | − | 0.260974i | ||||
\(425\) | 16.1864 | + | 8.41905i | 0.785157 | + | 0.408384i | ||||
\(426\) | −0.264843 | − | 0.264843i | −0.0128317 | − | 0.0128317i | ||||
\(427\) | 8.63247i | 0.417754i | ||||||||
\(428\) | −0.736249 | + | 0.736249i | −0.0355879 | + | 0.0355879i | ||||
\(429\) | −0.672413 | + | 0.672413i | −0.0324644 | + | 0.0324644i | ||||
\(430\) | 15.1083 | + | 3.69423i | 0.728588 | + | 0.178152i | ||||
\(431\) | 15.3753 | − | 15.3753i | 0.740601 | − | 0.740601i | −0.232092 | − | 0.972694i | \(-0.574557\pi\) |
0.972694 | + | 0.232092i | \(0.0745571\pi\) | |||||||
\(432\) | −0.286215 | − | 0.286215i | −0.0137705 | − | 0.0137705i | ||||
\(433\) | −16.4923 | − | 16.4923i | −0.792570 | − | 0.792570i | 0.189341 | − | 0.981911i | \(-0.439365\pi\) |
−0.981911 | + | 0.189341i | \(0.939365\pi\) | |||||||
\(434\) | −22.0313 | −1.05754 | ||||||||
\(435\) | 0.271067 | + | 0.0662802i | 0.0129966 | + | 0.00317789i | ||||
\(436\) | 1.72705 | − | 1.72705i | 0.0827108 | − | 0.0827108i | ||||
\(437\) | −18.5609 | − | 18.5609i | −0.887888 | − | 0.887888i | ||||
\(438\) | −1.06346 | −0.0508139 | ||||||||
\(439\) | 17.5768 | + | 17.5768i | 0.838896 | + | 0.838896i | 0.988714 | − | 0.149817i | \(-0.0478686\pi\) |
−0.149817 | + | 0.988714i | \(0.547869\pi\) | |||||||
\(440\) | −9.21484 | − | 2.25318i | −0.439300 | − | 0.107416i | ||||
\(441\) | 25.3308 | 1.20623 | ||||||||
\(442\) | −12.1151 | −0.576255 | ||||||||
\(443\) | 14.2624 | − | 14.2624i | 0.677629 | − | 0.677629i | −0.281834 | − | 0.959463i | \(-0.590943\pi\) |
0.959463 | + | 0.281834i | \(0.0909427\pi\) | |||||||
\(444\) | −0.0355407 | + | 0.409124i | −0.00168669 | + | 0.0194162i | ||||
\(445\) | −12.7282 | − | 20.9673i | −0.603374 | − | 0.993945i | ||||
\(446\) | −14.0320 | + | 14.0320i | −0.664437 | + | 0.664437i | ||||
\(447\) | 0.845665 | + | 0.845665i | 0.0399986 | + | 0.0399986i | ||||
\(448\) | 2.77997 | − | 2.77997i | 0.131341 | − | 0.131341i | ||||
\(449\) | −17.6009 | + | 17.6009i | −0.830639 | + | 0.830639i | −0.987604 | − | 0.156965i | \(-0.949829\pi\) |
0.156965 | + | 0.987604i | \(0.449829\pi\) | |||||||
\(450\) | −13.2873 | − | 6.91114i | −0.626370 | − | 0.325794i | ||||
\(451\) | −11.4646 | −0.539846 | ||||||||
\(452\) | 4.23008 | 0.198966 | ||||||||
\(453\) | 0.264010 | + | 0.264010i | 0.0124043 | + | 0.0124043i | ||||
\(454\) | − | 17.0093i | − | 0.798288i | ||||||
\(455\) | −15.1458 | − | 24.9498i | −0.710046 | − | 1.16967i | ||||
\(456\) | −0.444083 | −0.0207961 | ||||||||
\(457\) | −8.32533 | −0.389443 | −0.194721 | − | 0.980859i | \(-0.562380\pi\) | ||||
−0.194721 | + | 0.980859i | \(0.562380\pi\) | |||||||
\(458\) | −8.49131 | −0.396773 | ||||||||
\(459\) | −1.04440 | − | 1.04440i | −0.0487485 | − | 0.0487485i | ||||
\(460\) | 2.11943 | − | 8.66786i | 0.0988191 | − | 0.404141i | ||||
\(461\) | 0.227378 | + | 0.227378i | 0.0105900 | + | 0.0105900i | 0.712382 | − | 0.701792i | \(-0.247616\pi\) |
−0.701792 | + | 0.712382i | \(0.747616\pi\) | |||||||
\(462\) | − | 1.12604i | − | 0.0523881i | ||||||
\(463\) | 0.781658i | 0.0363267i | 0.999835 | + | 0.0181634i | \(0.00578189\pi\) | ||||
−0.999835 | + | 0.0181634i | \(0.994218\pi\) | |||||||
\(464\) | −1.30707 | − | 1.30707i | −0.0606792 | − | 0.0606792i | ||||
\(465\) | −0.200935 | + | 0.821767i | −0.00931816 | + | 0.0381085i | ||||
\(466\) | −11.1205 | − | 11.1205i | −0.515149 | − | 0.515149i | ||||
\(467\) | −2.66280 | −0.123220 | −0.0616098 | − | 0.998100i | \(-0.519623\pi\) | ||||
−0.0616098 | + | 0.998100i | \(0.519623\pi\) | |||||||
\(468\) | 9.94518 | 0.459716 | ||||||||
\(469\) | −24.1349 | −1.11444 | ||||||||
\(470\) | 2.20216 | + | 3.62765i | 0.101578 | + | 0.167331i | ||||
\(471\) | − | 0.332205i | − | 0.0153072i | ||||||
\(472\) | −8.04404 | − | 8.04404i | −0.370257 | − | 0.370257i | ||||
\(473\) | −29.5089 | −1.35682 | ||||||||
\(474\) | −0.303322 | −0.0139320 | ||||||||
\(475\) | −31.3632 | + | 9.90061i | −1.43904 | + | 0.454271i | ||||
\(476\) | 10.1441 | − | 10.1441i | 0.464955 | − | 0.464955i | ||||
\(477\) | −16.0968 | + | 16.0968i | −0.737024 | + | 0.737024i | ||||
\(478\) | 14.6371 | + | 14.6371i | 0.669486 | + | 0.669486i | ||||
\(479\) | −16.4195 | + | 16.4195i | −0.750228 | + | 0.750228i | −0.974522 | − | 0.224294i | \(-0.927993\pi\) |
0.224294 | + | 0.974522i | \(0.427993\pi\) | |||||||
\(480\) | −0.0783380 | − | 0.129047i | −0.00357562 | − | 0.00589016i | ||||
\(481\) | −12.9909 | − | 15.4626i | −0.592332 | − | 0.705034i | ||||
\(482\) | −10.5430 | + | 10.5430i | −0.480222 | + | 0.480222i | ||||
\(483\) | 1.05920 | 0.0481953 | ||||||||
\(484\) | 6.99802 | 0.318092 | ||||||||
\(485\) | 21.8187 | + | 5.33503i | 0.990736 | + | 0.242251i | ||||
\(486\) | 1.28634 | + | 1.28634i | 0.0583495 | + | 0.0583495i | ||||
\(487\) | 9.02775 | 0.409087 | 0.204543 | − | 0.978858i | \(-0.434429\pi\) | ||||
0.204543 | + | 0.978858i | \(0.434429\pi\) | |||||||
\(488\) | −1.55262 | − | 1.55262i | −0.0702838 | − | 0.0702838i | ||||
\(489\) | 1.04048 | − | 1.04048i | 0.0470520 | − | 0.0470520i | ||||
\(490\) | 18.3681 | + | 4.49129i | 0.829784 | + | 0.202896i | ||||
\(491\) | −2.91238 | −0.131434 | −0.0657169 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657169 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(492\) | −0.129008 | − | 0.129008i | −0.00581614 | − | 0.00581614i | ||||
\(493\) | −4.76950 | − | 4.76950i | −0.214808 | − | 0.214808i | ||||
\(494\) | 15.4424 | − | 15.4424i | 0.694785 | − | 0.694785i | ||||
\(495\) | 27.6025 | + | 6.74927i | 1.24064 | + | 0.303357i | ||||
\(496\) | 3.96252 | − | 3.96252i | 0.177922 | − | 0.177922i | ||||
\(497\) | −15.4226 | + | 15.4226i | −0.691796 | + | 0.691796i | ||||
\(498\) | − | 0.676095i | − | 0.0302966i | ||||||
\(499\) | 11.5866 | + | 11.5866i | 0.518686 | + | 0.518686i | 0.917174 | − | 0.398487i | \(-0.130465\pi\) |
−0.398487 | + | 0.917174i | \(0.630465\pi\) | |||||||
\(500\) | −8.40962 | − | 7.36738i | −0.376090 | − | 0.329479i | ||||
\(501\) | 0.532647 | − | 0.532647i | 0.0237969 | − | 0.0237969i | ||||
\(502\) | −16.2391 | − | 16.2391i | −0.724784 | − | 0.724784i | ||||
\(503\) | 19.3861i | 0.864382i | 0.901782 | + | 0.432191i | \(0.142259\pi\) | ||||
−0.901782 | + | 0.432191i | \(0.857741\pi\) | |||||||
\(504\) | −8.32723 | + | 8.32723i | −0.370924 | + | 0.370924i | ||||
\(505\) | −0.804324 | + | 3.28945i | −0.0357919 | + | 0.146378i | ||||
\(506\) | 16.9297i | 0.752616i | ||||||||
\(507\) | −0.0943752 | + | 0.0943752i | −0.00419135 | + | 0.00419135i | ||||
\(508\) | −0.683408 | + | 0.683408i | −0.0303213 | + | 0.0303213i | ||||
\(509\) | −7.69714 | −0.341170 | −0.170585 | − | 0.985343i | \(-0.554566\pi\) | ||||
−0.170585 | + | 0.985343i | \(0.554566\pi\) | |||||||
\(510\) | −0.285856 | − | 0.470893i | −0.0126579 | − | 0.0208515i | ||||
\(511\) | 61.9280i | 2.73953i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.66247 | 0.117551 | ||||||||
\(514\) | 5.00407i | 0.220720i | ||||||||
\(515\) | −8.44410 | − | 2.06472i | −0.372092 | − | 0.0909825i | ||||
\(516\) | −0.332057 | − | 0.332057i | −0.0146180 | − | 0.0146180i | ||||
\(517\) | −5.69326 | − | 5.69326i | −0.250389 | − | 0.250389i | ||||
\(518\) | 23.8245 | + | 2.06964i | 1.04679 | + | 0.0909346i | ||||
\(519\) | − | 1.38409i | − | 0.0607548i | ||||||
\(520\) | 7.21153 | + | 1.76334i | 0.316246 | + | 0.0773274i | ||||
\(521\) | − | 15.1959i | − | 0.665746i | −0.942972 | − | 0.332873i | \(-0.891982\pi\) | ||
0.942972 | − | 0.332873i | \(-0.108018\pi\) | |||||||
\(522\) | 3.91525 | + | 3.91525i | 0.171366 | + | 0.171366i | ||||
\(523\) | 8.67427i | 0.379299i | 0.981852 | + | 0.189650i | \(0.0607352\pi\) | ||||
−0.981852 | + | 0.189650i | \(0.939265\pi\) | |||||||
\(524\) | 3.35210 | − | 3.35210i | 0.146437 | − | 0.146437i | ||||
\(525\) | 0.612393 | − | 1.17738i | 0.0267270 | − | 0.0513853i | ||||
\(526\) | 12.4257 | + | 12.4257i | 0.541788 | + | 0.541788i | ||||
\(527\) | 14.4592 | − | 14.4592i | 0.629855 | − | 0.629855i | ||||
\(528\) | 0.202528 | + | 0.202528i | 0.00881388 | + | 0.00881388i | ||||
\(529\) | 7.07523 | 0.307619 | ||||||||
\(530\) | −14.5263 | + | 8.81821i | −0.630983 | + | 0.383038i | ||||
\(531\) | 24.0955 | + | 24.0955i | 1.04565 | + | 1.04565i | ||||
\(532\) | 25.8602i | 1.12118i | ||||||||
\(533\) | 8.97216 | 0.388628 | ||||||||
\(534\) | 0.740574i | 0.0320478i | ||||||||
\(535\) | 1.99022 | − | 1.20816i | 0.0860446 | − | 0.0522334i | ||||
\(536\) | 4.34085 | − | 4.34085i | 0.187496 | − | 0.187496i | ||||
\(537\) | −1.20416 | −0.0519631 | ||||||||
\(538\) | 22.6019 | 0.974436 | ||||||||
\(539\) | −35.8757 | −1.54527 | ||||||||
\(540\) | 0.469671 | + | 0.773694i | 0.0202114 | + | 0.0332945i | ||||
\(541\) | 19.2216 | + | 19.2216i | 0.826402 | + | 0.826402i | 0.987017 | − | 0.160615i | \(-0.0513477\pi\) |
−0.160615 | + | 0.987017i | \(0.551348\pi\) | |||||||
\(542\) | 18.1930i | 0.781454i | ||||||||
\(543\) | −0.611749 | + | 0.611749i | −0.0262527 | + | 0.0262527i | ||||
\(544\) | 3.64900i | 0.156450i | ||||||||
\(545\) | −4.66854 | + | 2.83404i | −0.199978 | + | 0.121397i | ||||
\(546\) | 0.881238i | 0.0377135i | ||||||||
\(547\) | − | 0.0420593i | − | 0.00179833i | −1.00000 | 0.000899163i | \(-0.999714\pi\) | |||
1.00000 | 0.000899163i | \(-0.000286213\pi\) | ||||||||
\(548\) | −15.4431 | + | 15.4431i | −0.659697 | + | 0.659697i | ||||
\(549\) | 4.65078 | + | 4.65078i | 0.198491 | + | 0.198491i | ||||
\(550\) | 18.8187 | + | 9.78816i | 0.802431 | + | 0.417369i | ||||
\(551\) | 12.1588 | 0.517983 | ||||||||
\(552\) | −0.190506 | + | 0.190506i | −0.00810847 | + | 0.00810847i | ||||
\(553\) | 17.6633i | 0.751120i | ||||||||
\(554\) | 23.4453 | 0.996095 | ||||||||
\(555\) | 0.294487 | − | 0.869774i | 0.0125003 | − | 0.0369198i | ||||
\(556\) | 17.8399 | 0.756582 | ||||||||
\(557\) | 12.8111i | 0.542823i | 0.962463 | + | 0.271412i | \(0.0874905\pi\) | ||||
−0.962463 | + | 0.271412i | \(0.912509\pi\) | |||||||
\(558\) | −11.8695 | + | 11.8695i | −0.502476 | + | 0.502476i | ||||
\(559\) | 23.0937 | 0.976758 | ||||||||
\(560\) | −7.51477 | + | 4.56184i | −0.317557 | + | 0.192773i | ||||
\(561\) | 0.739024 | + | 0.739024i | 0.0312016 | + | 0.0312016i | ||||
\(562\) | −3.32166 | + | 3.32166i | −0.140116 | + | 0.140116i | ||||
\(563\) | − | 29.4317i | − | 1.24040i | −0.784444 | − | 0.620200i | \(-0.787051\pi\) | ||
0.784444 | − | 0.620200i | \(-0.212949\pi\) | |||||||
\(564\) | − | 0.128130i | − | 0.00539525i | ||||||
\(565\) | −9.18807 | − | 2.24663i | −0.386545 | − | 0.0945166i | ||||
\(566\) | 12.1785i | 0.511900i | ||||||||
\(567\) | 24.9057 | − | 24.9057i | 1.04594 | − | 1.04594i | ||||
\(568\) | − | 5.54775i | − | 0.232778i | ||||||
\(569\) | −1.25554 | − | 1.25554i | −0.0526351 | − | 0.0526351i | 0.680299 | − | 0.732934i | \(-0.261850\pi\) |
−0.732934 | + | 0.680299i | \(0.761850\pi\) | |||||||
\(570\) | 0.964583 | + | 0.235856i | 0.0404019 | + | 0.00987894i | ||||
\(571\) | −40.9624 | −1.71422 | −0.857111 | − | 0.515132i | \(-0.827743\pi\) | ||||
−0.857111 | + | 0.515132i | \(0.827743\pi\) | |||||||
\(572\) | −14.0852 | −0.588933 | ||||||||
\(573\) | −0.962624 | −0.0402142 | ||||||||
\(574\) | −7.51251 | + | 7.51251i | −0.313566 | + | 0.313566i | ||||
\(575\) | −9.20715 | + | 17.7016i | −0.383965 | + | 0.738209i | ||||
\(576\) | − | 2.99544i | − | 0.124810i | ||||||
\(577\) | −7.71924 | −0.321356 | −0.160678 | − | 0.987007i | \(-0.551368\pi\) | ||||
−0.160678 | + | 0.987007i | \(0.551368\pi\) | |||||||
\(578\) | − | 3.68477i | − | 0.153266i | ||||||
\(579\) | −0.361885 | − | 0.361885i | −0.0150394 | − | 0.0150394i | ||||
\(580\) | 2.14486 | + | 3.53325i | 0.0890605 | + | 0.146710i | ||||
\(581\) | −39.3710 | −1.63338 | ||||||||
\(582\) | −0.479541 | − | 0.479541i | −0.0198776 | − | 0.0198776i | ||||
\(583\) | 22.7978 | − | 22.7978i | 0.944187 | − | 0.944187i | ||||
\(584\) | −11.1383 | − | 11.1383i | −0.460905 | − | 0.460905i | ||||
\(585\) | −21.6017 | − | 5.28197i | −0.893121 | − | 0.218383i | ||||
\(586\) | −1.06493 | + | 1.06493i | −0.0439919 | + | 0.0439919i | ||||
\(587\) | 5.39311i | 0.222597i | 0.993787 | + | 0.111299i | \(0.0355010\pi\) | ||||
−0.993787 | + | 0.111299i | \(0.964499\pi\) | |||||||
\(588\) | −0.403701 | − | 0.403701i | −0.0166483 | − | 0.0166483i | ||||
\(589\) | 36.8607i | 1.51882i | ||||||||
\(590\) | 13.2000 | + | 21.7445i | 0.543437 | + | 0.895209i | ||||
\(591\) | − | 1.61305i | − | 0.0663521i | ||||||
\(592\) | −4.65727 | + | 3.91278i | −0.191412 | + | 0.160814i | ||||
\(593\) | −10.4329 | − | 10.4329i | −0.428427 | − | 0.428427i | 0.459665 | − | 0.888092i | \(-0.347969\pi\) |
−0.888092 | + | 0.459665i | \(0.847969\pi\) | |||||||
\(594\) | −1.21424 | − | 1.21424i | −0.0498210 | − | 0.0498210i | ||||
\(595\) | −27.4214 | + | 16.6462i | −1.12417 | + | 0.682427i | ||||
\(596\) | 17.7144i | 0.725610i | ||||||||
\(597\) | 0.0549981 | 0.00225092 | ||||||||
\(598\) | − | 13.2492i | − | 0.541798i | ||||||
\(599\) | − | 19.3788i | − | 0.791798i | −0.918294 | − | 0.395899i | \(-0.870433\pi\) | ||
0.918294 | − | 0.395899i | \(-0.129567\pi\) | |||||||
\(600\) | 0.101618 | + | 0.321906i | 0.00414855 | + | 0.0131418i | ||||
\(601\) | −4.17046 | −0.170117 | −0.0850583 | − | 0.996376i | \(-0.527108\pi\) | ||||
−0.0850583 | + | 0.996376i | \(0.527108\pi\) | |||||||
\(602\) | −19.3366 | + | 19.3366i | −0.788102 | + | 0.788102i | ||||
\(603\) | −13.0028 | + | 13.0028i | −0.529514 | + | 0.529514i | ||||
\(604\) | 5.53031i | 0.225025i | ||||||||
\(605\) | −15.2002 | − | 3.71671i | −0.617978 | − | 0.151106i | ||||
\(606\) | 0.0722968 | − | 0.0722968i | 0.00293686 | − | 0.00293686i | ||||
\(607\) | − | 29.8434i | − | 1.21131i | −0.795729 | − | 0.605653i | \(-0.792912\pi\) | ||
0.795729 | − | 0.605653i | \(-0.207088\pi\) | |||||||
\(608\) | −4.65117 | − | 4.65117i | −0.188630 | − | 0.188630i | ||||
\(609\) | −0.346929 | + | 0.346929i | −0.0140583 | + | 0.0140583i | ||||
\(610\) | 2.54780 | + | 4.19702i | 0.103158 | + | 0.169932i | ||||
\(611\) | 4.45554 | + | 4.45554i | 0.180252 | + | 0.180252i | ||||
\(612\) | − | 10.9304i | − | 0.441834i | ||||||
\(613\) | −7.97850 | + | 7.97850i | −0.322248 | + | 0.322248i | −0.849629 | − | 0.527381i | \(-0.823174\pi\) |
0.527381 | + | 0.849629i | \(0.323174\pi\) | |||||||
\(614\) | 16.1006 | − | 16.1006i | 0.649766 | − | 0.649766i | ||||
\(615\) | 0.211699 | + | 0.348733i | 0.00853651 | + | 0.0140623i | ||||
\(616\) | 11.7938 | − | 11.7938i | 0.475184 | − | 0.475184i | ||||
\(617\) | −21.2579 | − | 21.2579i | −0.855812 | − | 0.855812i | 0.135030 | − | 0.990842i | \(-0.456887\pi\) |
−0.990842 | + | 0.135030i | \(0.956887\pi\) | |||||||
\(618\) | 0.185588 | + | 0.185588i | 0.00746545 | + | 0.00746545i | ||||
\(619\) | 7.54167 | 0.303125 | 0.151563 | − | 0.988448i | \(-0.451569\pi\) | ||||
0.151563 | + | 0.988448i | \(0.451569\pi\) | |||||||
\(620\) | −10.7114 | + | 6.50237i | −0.430181 | + | 0.261141i | ||||
\(621\) | 1.14217 | − | 1.14217i | 0.0458336 | − | 0.0458336i | ||||
\(622\) | −18.5878 | − | 18.5878i | −0.745304 | − | 0.745304i | ||||
\(623\) | 43.1257 | 1.72779 | ||||||||
\(624\) | −0.158498 | − | 0.158498i | −0.00634500 | − | 0.00634500i | ||||
\(625\) | 14.3535 | + | 20.4689i | 0.574139 | + | 0.818758i | ||||
\(626\) | 21.7608 | 0.869735 | ||||||||
\(627\) | −1.88398 | −0.0752390 | ||||||||
\(628\) | 3.47940 | − | 3.47940i | 0.138843 | − | 0.138843i | ||||
\(629\) | −16.9944 | + | 14.2778i | −0.677610 | + | 0.569292i | ||||
\(630\) | 22.5101 | − | 13.6647i | 0.896822 | − | 0.544416i | ||||
\(631\) | 23.1881 | − | 23.1881i | 0.923103 | − | 0.923103i | −0.0741448 | − | 0.997247i | \(-0.523623\pi\) |
0.997247 | + | 0.0741448i | \(0.0236227\pi\) | |||||||
\(632\) | −3.17689 | − | 3.17689i | −0.126370 | − | 0.126370i | ||||
\(633\) | 1.00943 | − | 1.00943i | 0.0401214 | − | 0.0401214i | ||||
\(634\) | −22.3061 | + | 22.3061i | −0.885889 | + | 0.885889i | ||||
\(635\) | 1.84738 | − | 1.12145i | 0.0733110 | − | 0.0445034i | ||||
\(636\) | 0.513076 | 0.0203448 | ||||||||
\(637\) | 28.0763 | 1.11242 | ||||||||
\(638\) | −5.54512 | − | 5.54512i | −0.219533 | − | 0.219533i | ||||
\(639\) | 16.6180i | 0.657396i | ||||||||
\(640\) | 0.531109 | − | 2.17208i | 0.0209939 | − | 0.0858589i | ||||
\(641\) | −12.2032 | −0.481999 | −0.240999 | − | 0.970525i | \(-0.577475\pi\) | ||||
−0.240999 | + | 0.970525i | \(0.577475\pi\) | |||||||
\(642\) | −0.0702953 | −0.00277433 | ||||||||
\(643\) | −26.4268 | −1.04217 | −0.521085 | − | 0.853505i | \(-0.674472\pi\) | ||||
−0.521085 | + | 0.853505i | \(0.674472\pi\) | |||||||
\(644\) | 11.0937 | + | 11.0937i | 0.437153 | + | 0.437153i | ||||
\(645\) | 0.544896 | + | 0.897613i | 0.0214552 | + | 0.0353435i | ||||
\(646\) | −16.9721 | − | 16.9721i | −0.667760 | − | 0.667760i | ||||
\(647\) | 23.6177i | 0.928509i | 0.885702 | + | 0.464255i | \(0.153678\pi\) | ||||
−0.885702 | + | 0.464255i | \(0.846322\pi\) | |||||||
\(648\) | 8.95900i | 0.351943i | ||||||||
\(649\) | −34.1261 | − | 34.1261i | −1.33957 | − | 1.33957i | ||||
\(650\) | −14.7275 | − | 7.66021i | −0.577659 | − | 0.300458i | ||||
\(651\) | −1.05175 | − | 1.05175i | −0.0412214 | − | 0.0412214i | ||||
\(652\) | 21.7952 | 0.853566 | ||||||||
\(653\) | −11.5143 | −0.450588 | −0.225294 | − | 0.974291i | \(-0.572334\pi\) | ||||
−0.225294 | + | 0.974291i | \(0.572334\pi\) | |||||||
\(654\) | 0.164895 | 0.00644790 | ||||||||
\(655\) | −9.06136 | + | 5.50070i | −0.354057 | + | 0.214930i | ||||
\(656\) | − | 2.70237i | − | 0.105510i | ||||||
\(657\) | 33.3640 | + | 33.3640i | 1.30165 | + | 1.30165i | ||||
\(658\) | −7.46137 | −0.290875 | ||||||||
\(659\) | 45.6299 | 1.77749 | 0.888744 | − | 0.458404i | \(-0.151579\pi\) | ||||
0.888744 | + | 0.458404i | \(0.151579\pi\) | |||||||
\(660\) | −0.332342 | − | 0.547470i | −0.0129364 | − | 0.0213102i | ||||
\(661\) | −8.90268 | + | 8.90268i | −0.346274 | + | 0.346274i | −0.858720 | − | 0.512446i | \(-0.828740\pi\) |
0.512446 | + | 0.858720i | \(0.328740\pi\) | |||||||
\(662\) | −23.9871 | + | 23.9871i | −0.932285 | + | 0.932285i | ||||
\(663\) | −0.578360 | − | 0.578360i | −0.0224616 | − | 0.0224616i | ||||
\(664\) | 7.08119 | − | 7.08119i | 0.274803 | − | 0.274803i | ||||
\(665\) | 13.7346 | − | 56.1704i | 0.532604 | − | 2.17819i | ||||
\(666\) | 13.9506 | − | 11.7205i | 0.540574 | − | 0.454161i | ||||
\(667\) | 5.21597 | − | 5.21597i | 0.201963 | − | 0.201963i | ||||
\(668\) | 11.1575 | 0.431697 | ||||||||
\(669\) | −1.33975 | −0.0517976 | ||||||||
\(670\) | −11.7341 | + | 7.12321i | −0.453329 | + | 0.275194i | ||||
\(671\) | −6.58685 | − | 6.58685i | −0.254282 | − | 0.254282i | ||||
\(672\) | 0.265425 | 0.0102390 | ||||||||
\(673\) | −25.0377 | − | 25.0377i | −0.965134 | − | 0.965134i | 0.0342781 | − | 0.999412i | \(-0.489087\pi\) |
−0.999412 | + | 0.0342781i | \(0.989087\pi\) | |||||||
\(674\) | 17.5570 | − | 17.5570i | 0.676270 | − | 0.676270i | ||||
\(675\) | −0.609246 | − | 1.92997i | −0.0234499 | − | 0.0742846i | ||||
\(676\) | −1.97691 | −0.0760348 | ||||||||
\(677\) | −8.02326 | − | 8.02326i | −0.308359 | − | 0.308359i | 0.535914 | − | 0.844273i | \(-0.319967\pi\) |
−0.844273 | + | 0.535914i | \(0.819967\pi\) | |||||||
\(678\) | 0.201939 | + | 0.201939i | 0.00775543 | + | 0.00775543i | ||||
\(679\) | −27.9250 | + | 27.9250i | −1.07166 | + | 1.07166i | ||||
\(680\) | 1.93802 | − | 7.92592i | 0.0743196 | − | 0.303945i | ||||
\(681\) | 0.812006 | − | 0.812006i | 0.0311161 | − | 0.0311161i | ||||
\(682\) | 16.8106 | − | 16.8106i | 0.643712 | − | 0.643712i | ||||
\(683\) | − | 14.7249i | − | 0.563434i | −0.959498 | − | 0.281717i | \(-0.909096\pi\) | ||
0.959498 | − | 0.281717i | \(-0.0909039\pi\) | |||||||
\(684\) | 13.9323 | + | 13.9323i | 0.532715 | + | 0.532715i | ||||
\(685\) | 41.7456 | − | 25.3417i | 1.59502 | − | 0.968255i | ||||
\(686\) | −4.04887 | + | 4.04887i | −0.154586 | + | 0.154586i | ||||
\(687\) | −0.405365 | − | 0.405365i | −0.0154656 | − | 0.0154656i | ||||
\(688\) | − | 6.95570i | − | 0.265184i | ||||||
\(689\) | −17.8415 | + | 17.8415i | −0.679707 | + | 0.679707i | ||||
\(690\) | 0.514973 | − | 0.312614i | 0.0196047 | − | 0.0119010i | ||||
\(691\) | 7.03274i | 0.267538i | 0.991013 | + | 0.133769i | \(0.0427080\pi\) | ||||
−0.991013 | + | 0.133769i | \(0.957292\pi\) | |||||||
\(692\) | 14.4965 | − | 14.4965i | 0.551073 | − | 0.551073i | ||||
\(693\) | −35.3275 | + | 35.3275i | −1.34198 | + | 1.34198i | ||||
\(694\) | 11.0678 | 0.420128 | ||||||||
\(695\) | −38.7497 | − | 9.47495i | −1.46986 | − | 0.359405i | ||||
\(696\) | − | 0.124796i | − | 0.00473038i | ||||||
\(697\) | − | 9.86097i | − | 0.373511i | ||||||
\(698\) | 31.6855 | 1.19931 | ||||||||
\(699\) | − | 1.06176i | − | 0.0401595i | ||||||
\(700\) | 18.7455 | − | 5.91752i | 0.708514 | − | 0.223661i | ||||
\(701\) | −18.7062 | − | 18.7062i | −0.706523 | − | 0.706523i | 0.259279 | − | 0.965802i | \(-0.416515\pi\) |
−0.965802 | + | 0.259279i | \(0.916515\pi\) | |||||||
\(702\) | 0.950265 | + | 0.950265i | 0.0358654 | + | 0.0358654i | ||||
\(703\) | 3.46271 | − | 39.8608i | 0.130599 | − | 1.50338i | ||||
\(704\) | 4.24241i | 0.159892i | ||||||||
\(705\) | −0.0680510 | + | 0.278308i | −0.00256295 | + | 0.0104817i | ||||
\(706\) | − | 15.6047i | − | 0.587291i | ||||||
\(707\) | −4.21005 | − | 4.21005i | −0.158335 | − | 0.158335i | ||||
\(708\) | − | 0.768026i | − | 0.0288642i | ||||||
\(709\) | −24.5474 | + | 24.5474i | −0.921895 | + | 0.921895i | −0.997163 | − | 0.0752682i | \(-0.976019\pi\) |
0.0752682 | + | 0.997163i | \(0.476019\pi\) | |||||||
\(710\) | −2.94646 | + | 12.0501i | −0.110579 | + | 0.452234i | ||||
\(711\) | 9.51618 | + | 9.51618i | 0.356885 | + | 0.356885i | ||||
\(712\) | −7.75651 | + | 7.75651i | −0.290688 | + | 0.290688i | ||||
\(713\) | 15.8128 | + | 15.8128i | 0.592193 | + | 0.592193i | ||||
\(714\) | 0.968537 | 0.0362466 | ||||||||
\(715\) | 30.5942 | + | 7.48079i | 1.14416 | + | 0.279766i | ||||
\(716\) | −12.6119 | − | 12.6119i | −0.471329 | − | 0.471329i | ||||
\(717\) | 1.39752i | 0.0521913i | ||||||||
\(718\) | −34.4499 | −1.28566 | ||||||||
\(719\) | − | 12.2897i | − | 0.458329i | −0.973388 | − | 0.229164i | \(-0.926401\pi\) | ||
0.973388 | − | 0.229164i | \(-0.0735993\pi\) | |||||||
\(720\) | −1.59091 | + | 6.50633i | −0.0592895 | + | 0.242477i | ||||
\(721\) | 10.8073 | − | 10.8073i | 0.402486 | − | 0.402486i | ||||
\(722\) | 24.2668 | 0.903116 | ||||||||
\(723\) | −1.00663 | −0.0374368 | ||||||||
\(724\) | −12.8145 | −0.476247 | ||||||||
\(725\) | −2.78226 | − | 8.81366i | −0.103331 | − | 0.327331i | ||||
\(726\) | 0.334077 | + | 0.334077i | 0.0123988 | + | 0.0123988i | ||||
\(727\) | − | 12.2686i | − | 0.455016i | −0.973776 | − | 0.227508i | \(-0.926942\pi\) | ||
0.973776 | − | 0.227508i | \(-0.0730579\pi\) | |||||||
\(728\) | −9.22978 | + | 9.22978i | −0.342079 | + | 0.342079i | ||||
\(729\) | − | 26.7542i | − | 0.990896i | ||||||
\(730\) | 18.2775 | + | 30.1088i | 0.676482 | + | 1.11438i | ||||
\(731\) | − | 25.3814i | − | 0.938765i | ||||||
\(732\) | − | 0.148241i | − | 0.00547913i | ||||||
\(733\) | 26.4738 | − | 26.4738i | 0.977831 | − | 0.977831i | −0.0219285 | − | 0.999760i | \(-0.506981\pi\) |
0.999760 | + | 0.0219285i | \(0.00698063\pi\) | |||||||
\(734\) | −4.61443 | − | 4.61443i | −0.170322 | − | 0.170322i | ||||
\(735\) | 0.662461 | + | 1.09128i | 0.0244352 | + | 0.0402524i | ||||
\(736\) | −3.99058 | −0.147095 | ||||||||
\(737\) | 18.4157 | − | 18.4157i | 0.678350 | − | 0.678350i | ||||
\(738\) | 8.09481i | 0.297974i | ||||||||
\(739\) | 23.9200 | 0.879912 | 0.439956 | − | 0.898019i | \(-0.354994\pi\) | ||||
0.439956 | + | 0.898019i | \(0.354994\pi\) | |||||||
\(740\) | 12.1941 | − | 6.02536i | 0.448263 | − | 0.221497i | ||||
\(741\) | 1.47440 | 0.0541635 | ||||||||
\(742\) | − | 29.8779i | − | 1.09685i | ||||||
\(743\) | 8.98938 | − | 8.98938i | 0.329788 | − | 0.329788i | −0.522718 | − | 0.852506i | \(-0.675082\pi\) |
0.852506 | + | 0.522718i | \(0.175082\pi\) | |||||||
\(744\) | 0.378332 | 0.0138703 | ||||||||
\(745\) | 9.40827 | − | 38.4771i | 0.344692 | − | 1.40969i | ||||
\(746\) | −15.3464 | − | 15.3464i | −0.561872 | − | 0.561872i | ||||
\(747\) | −21.2113 | + | 21.2113i | −0.776080 | + | 0.776080i | ||||
\(748\) | 15.4806i | 0.566025i | ||||||||
\(749\) | 4.09349i | 0.149573i | ||||||||
\(750\) | −0.0497555 | − | 0.753176i | −0.00181682 | − | 0.0275021i | ||||
\(751\) | 34.7552i | 1.26824i | 0.773236 | + | 0.634118i | \(0.218637\pi\) | ||||
−0.773236 | + | 0.634118i | \(0.781363\pi\) | |||||||
\(752\) | 1.34199 | − | 1.34199i | 0.0489373 | − | 0.0489373i | ||||
\(753\) | − | 1.55047i | − | 0.0565022i | ||||||
\(754\) | 4.33961 | + | 4.33961i | 0.158039 | + | 0.158039i | ||||
\(755\) | 2.93719 | − | 12.0123i | 0.106895 | − | 0.437171i | ||||
\(756\) | −1.59134 | −0.0578765 | ||||||||
\(757\) | 2.66868 | 0.0969950 | 0.0484975 | − | 0.998823i | \(-0.484557\pi\) | ||||
0.0484975 | + | 0.998823i | \(0.484557\pi\) | |||||||
\(758\) | 23.4892 | 0.853164 | ||||||||
\(759\) | −0.808204 | + | 0.808204i | −0.0293359 | + | 0.0293359i | ||||
\(760\) | 7.63243 | + | 12.5730i | 0.276857 | + | 0.456070i | ||||
\(761\) | 50.1338i | 1.81735i | 0.417507 | + | 0.908674i | \(0.362904\pi\) | ||||
−0.417507 | + | 0.908674i | \(0.637096\pi\) | |||||||
\(762\) | −0.0652502 | −0.00236376 | ||||||||
\(763\) | − | 9.60230i | − | 0.347626i | ||||||
\(764\) | −10.0822 | − | 10.0822i | −0.364761 | − | 0.364761i | ||||
\(765\) | −5.80522 | + | 23.7416i | −0.209888 | + | 0.858381i | ||||
\(766\) | −0.480522 | −0.0173620 | ||||||||
\(767\) | 26.7071 | + | 26.7071i | 0.964336 | + | 0.964336i | ||||
\(768\) | −0.0477388 | + | 0.0477388i | −0.00172263 | + | 0.00172263i | ||||
\(769\) | −35.1828 | − | 35.1828i | −1.26872 | − | 1.26872i | −0.946748 | − | 0.321974i | \(-0.895654\pi\) |
−0.321974 | − | 0.946748i | \(-0.604346\pi\) | |||||||
\(770\) | −31.8807 | + | 19.3532i | −1.14890 | + | 0.697441i | ||||
\(771\) | −0.238888 | + | 0.238888i | −0.00860335 | + | 0.00860335i | ||||
\(772\) | − | 7.58052i | − | 0.272829i | ||||||
\(773\) | −5.35033 | − | 5.35033i | −0.192438 | − | 0.192438i | 0.604311 | − | 0.796749i | \(-0.293449\pi\) |
−0.796749 | + | 0.604311i | \(0.793449\pi\) | |||||||
\(774\) | 20.8354i | 0.748913i | ||||||||
\(775\) | 26.7195 | − | 8.43473i | 0.959793 | − | 0.302984i | ||||
\(776\) | − | 10.0451i | − | 0.360597i | ||||||
\(777\) | 1.03855 | + | 1.23615i | 0.0372578 | + | 0.0443468i | ||||
\(778\) | 11.0293 | + | 11.0293i | 0.395420 | + | 0.395420i | ||||
\(779\) | 12.5692 | + | 12.5692i | 0.450339 | + | 0.450339i | ||||
\(780\) | 0.260090 | + | 0.428450i | 0.00931273 | + | 0.0153410i | ||||
\(781\) | − | 23.5358i | − | 0.842177i | ||||||
\(782\) | −14.5617 | −0.520724 | ||||||||
\(783\) | 0.748207i | 0.0267387i | ||||||||
\(784\) | − | 8.45644i | − | 0.302016i | ||||||
\(785\) | −9.40547 | + | 5.70959i | −0.335696 | + | 0.203784i | ||||
\(786\) | 0.320051 | 0.0114158 | ||||||||
\(787\) | −34.2308 | + | 34.2308i | −1.22020 | + | 1.22020i | −0.252637 | + | 0.967561i | \(0.581298\pi\) |
−0.967561 | + | 0.252637i | \(0.918702\pi\) | |||||||
\(788\) | 16.8945 | − | 16.8945i | 0.601843 | − | 0.601843i | ||||
\(789\) | 1.18638i | 0.0422362i | ||||||||
\(790\) | 5.21318 | + | 8.58772i | 0.185476 | + | 0.305537i | ||||
\(791\) | 11.7595 | − | 11.7595i | 0.418120 | − | 0.418120i | ||||
\(792\) | − | 12.7079i | − | 0.451555i | ||||||
\(793\) | 5.15486 | + | 5.15486i | 0.183054 | + | 0.183054i | ||||
\(794\) | 18.6363 | − | 18.6363i | 0.661376 | − | 0.661376i | ||||
\(795\) | −1.11444 | − | 0.272499i | −0.0395252 | − | 0.00966455i | ||||
\(796\) | 0.576031 | + | 0.576031i | 0.0204169 | + | 0.0204169i | ||||
\(797\) | 41.1330i | 1.45700i | 0.685043 | + | 0.728502i | \(0.259783\pi\) | ||||
−0.685043 | + | 0.728502i | \(0.740217\pi\) | |||||||
\(798\) | −1.23454 | + | 1.23454i | −0.0437021 | + | 0.0437021i | ||||
\(799\) | 4.89692 | − | 4.89692i | 0.173241 | − | 0.173241i | ||||
\(800\) | −2.30722 | + | 4.43585i | −0.0815725 | + | 0.156831i | ||||
\(801\) | 23.2342 | − | 23.2342i | 0.820939 | − | 0.820939i | ||||
\(802\) | 23.4574 | + | 23.4574i | 0.828311 | + | 0.828311i | ||||
\(803\) | −47.2530 | − | 47.2530i | −1.66752 | − | 1.66752i | ||||
\(804\) | 0.414455 | 0.0146167 | ||||||||
\(805\) | −18.2044 | − | 29.9883i | −0.641621 | − | 1.05695i | ||||
\(806\) | −13.1560 | + | 13.1560i | −0.463399 | + | 0.463399i | ||||
\(807\) | 1.07899 | + | 1.07899i | 0.0379822 | + | 0.0379822i | ||||
\(808\) | 1.51442 | 0.0532772 | ||||||||
\(809\) | −25.8572 | − | 25.8572i | −0.909092 | − | 0.909092i | 0.0871071 | − | 0.996199i | \(-0.472238\pi\) |
−0.996199 | + | 0.0871071i | \(0.972238\pi\) | |||||||
\(810\) | 4.75820 | − | 19.4596i | 0.167186 | − | 0.683742i | ||||
\(811\) | −26.4820 | −0.929907 | −0.464954 | − | 0.885335i | \(-0.653929\pi\) | ||||
−0.464954 | + | 0.885335i | \(0.653929\pi\) | |||||||
\(812\) | −7.26722 | −0.255030 | ||||||||
\(813\) | −0.868510 | + | 0.868510i | −0.0304600 | + | 0.0304600i | ||||
\(814\) | −19.7580 | + | 16.5996i | −0.692518 | + | 0.581816i | ||||
\(815\) | −47.3409 | − | 11.5756i | −1.65828 | − | 0.405476i | ||||
\(816\) | −0.174199 | + | 0.174199i | −0.00609819 | + | 0.00609819i | ||||
\(817\) | 32.3522 | + | 32.3522i | 1.13186 | + | 1.13186i | ||||
\(818\) | −20.5642 | + | 20.5642i | −0.719012 | + | 0.719012i | ||||
\(819\) | 27.6473 | − | 27.6473i | 0.966074 | − | 0.966074i | ||||
\(820\) | −1.43525 | + | 5.86977i | −0.0501213 | + | 0.204981i | ||||
\(821\) | 31.1573 | 1.08740 | 0.543699 | − | 0.839280i | \(-0.317023\pi\) | ||||
0.543699 | + | 0.839280i | \(0.317023\pi\) | |||||||
\(822\) | −1.47447 | −0.0514281 | ||||||||
\(823\) | 26.4495 | + | 26.4495i | 0.921971 | + | 0.921971i | 0.997169 | − | 0.0751977i | \(-0.0239588\pi\) |
−0.0751977 | + | 0.997169i | \(0.523959\pi\) | |||||||
\(824\) | 3.88757i | 0.135430i | ||||||||
\(825\) | 0.431106 | + | 1.36566i | 0.0150092 | + | 0.0475461i | ||||
\(826\) | −44.7244 | −1.55616 | ||||||||
\(827\) | 23.8982 | 0.831021 | 0.415510 | − | 0.909588i | \(-0.363603\pi\) | ||||
0.415510 | + | 0.909588i | \(0.363603\pi\) | |||||||
\(828\) | 11.9536 | 0.415415 | ||||||||
\(829\) | 7.39911 | + | 7.39911i | 0.256982 | + | 0.256982i | 0.823825 | − | 0.566844i | \(-0.191836\pi\) |
−0.566844 | + | 0.823825i | \(0.691836\pi\) | |||||||
\(830\) | −19.1418 | + | 11.6200i | −0.664421 | + | 0.403337i | ||||
\(831\) | 1.11925 | + | 1.11925i | 0.0388264 | + | 0.0388264i | ||||
\(832\) | − | 3.32010i | − | 0.115104i | ||||||
\(833\) | − | 30.8576i | − | 1.06915i | ||||||
\(834\) | 0.851658 | + | 0.851658i | 0.0294905 | + | 0.0294905i | ||||
\(835\) | −24.2350 | − | 5.92585i | −0.838687 | − | 0.205073i | ||||
\(836\) | −19.7322 | − | 19.7322i | −0.682451 | − | 0.682451i | ||||
\(837\) | −2.26827 | −0.0784028 | ||||||||
\(838\) | 37.9044 | 1.30939 | ||||||||
\(839\) | 22.2697 | 0.768834 | 0.384417 | − | 0.923160i | \(-0.374402\pi\) | ||||
0.384417 | + | 0.923160i | \(0.374402\pi\) | |||||||
\(840\) | −0.576524 | − | 0.140969i | −0.0198920 | − | 0.00486391i | ||||
\(841\) | − | 25.5831i | − | 0.882177i | ||||||
\(842\) | 24.4985 | + | 24.4985i | 0.844273 | + | 0.844273i | ||||
\(843\) | −0.317145 | −0.0109230 | ||||||||
\(844\) | 21.1449 | 0.727838 | ||||||||
\(845\) | 4.29399 | + | 1.04995i | 0.147718 | + | 0.0361194i | ||||
\(846\) | −4.01985 | + | 4.01985i | −0.138205 | + | 0.138205i | ||||
\(847\) | 19.4543 | − | 19.4543i | 0.668456 | − | 0.668456i | ||||
\(848\) | 5.37378 | + | 5.37378i | 0.184536 | + | 0.184536i | ||||
\(849\) | −0.581386 | + | 0.581386i | −0.0199531 | + | 0.0199531i | ||||
\(850\) | −8.41905 | + | 16.1864i | −0.288771 | + | 0.555190i | ||||
\(851\) | −15.6143 | − | 18.5852i | −0.535251 | − | 0.637093i | ||||
\(852\) | 0.264843 | − | 0.264843i | 0.00907337 | − | 0.00907337i | ||||
\(853\) | 30.0733 | 1.02969 | 0.514845 | − | 0.857283i | \(-0.327850\pi\) | ||||
0.514845 | + | 0.857283i | \(0.327850\pi\) | |||||||
\(854\) | −8.63247 | −0.295397 | ||||||||
\(855\) | −22.8625 | − | 37.6616i | −0.781881 | − | 1.28800i | ||||
\(856\) | −0.736249 | − | 0.736249i | −0.0251645 | − | 0.0251645i | ||||
\(857\) | 19.5685 | 0.668446 | 0.334223 | − | 0.942494i | \(-0.391526\pi\) | ||||
0.334223 | + | 0.942494i | \(0.391526\pi\) | |||||||
\(858\) | −0.672413 | − | 0.672413i | −0.0229558 | − | 0.0229558i | ||||
\(859\) | 12.9463 | − | 12.9463i | 0.441723 | − | 0.441723i | −0.450868 | − | 0.892591i | \(-0.648885\pi\) |
0.892591 | + | 0.450868i | \(0.148885\pi\) | |||||||
\(860\) | −3.69423 | + | 15.1083i | −0.125972 | + | 0.515190i | ||||
\(861\) | −0.717277 | −0.0244447 | ||||||||
\(862\) | 15.3753 | + | 15.3753i | 0.523684 | + | 0.523684i | ||||
\(863\) | 0.279402 | + | 0.279402i | 0.00951094 | + | 0.00951094i | 0.711846 | − | 0.702335i | \(-0.247859\pi\) |
−0.702335 | + | 0.711846i | \(0.747859\pi\) | |||||||
\(864\) | 0.286215 | − | 0.286215i | 0.00973725 | − | 0.00973725i | ||||
\(865\) | −39.1867 | + | 23.7883i | −1.33239 | + | 0.808825i | ||||
\(866\) | 16.4923 | − | 16.4923i | 0.560432 | − | 0.560432i | ||||
\(867\) | 0.175907 | − | 0.175907i | 0.00597410 | − | 0.00597410i | ||||
\(868\) | − | 22.0313i | − | 0.747793i | ||||||
\(869\) | −13.4777 | − | 13.4777i | −0.457198 | − | 0.457198i | ||||
\(870\) | −0.0662802 | + | 0.271067i | −0.00224711 | + | 0.00919002i | ||||
\(871\) | −14.4121 | + | 14.4121i | −0.488335 | + | 0.488335i | ||||
\(872\) | 1.72705 | + | 1.72705i | 0.0584853 | + | 0.0584853i | ||||
\(873\) | 30.0895i | 1.01837i | ||||||||
\(874\) | 18.5609 | − | 18.5609i | 0.627832 | − | 0.627832i | ||||
\(875\) | −43.8596 | + | 2.89741i | −1.48272 | + | 0.0979502i | ||||
\(876\) | − | 1.06346i | − | 0.0359308i | ||||||
\(877\) | 29.4697 | − | 29.4697i | 0.995121 | − | 0.995121i | −0.00486751 | − | 0.999988i | \(-0.501549\pi\) |
0.999988 | + | 0.00486751i | \(0.00154938\pi\) | |||||||
\(878\) | −17.5768 | + | 17.5768i | −0.593189 | + | 0.593189i | ||||
\(879\) | −0.101677 | −0.00342949 | ||||||||
\(880\) | 2.25318 | − | 9.21484i | 0.0759547 | − | 0.310632i | ||||
\(881\) | − | 41.3883i | − | 1.39441i | −0.716873 | − | 0.697204i | \(-0.754427\pi\) | ||
0.716873 | − | 0.697204i | \(-0.245573\pi\) | |||||||
\(882\) | 25.3308i | 0.852932i | ||||||||
\(883\) | −16.0092 | −0.538751 | −0.269376 | − | 0.963035i | \(-0.586817\pi\) | ||||
−0.269376 | + | 0.963035i | \(0.586817\pi\) | |||||||
\(884\) | − | 12.1151i | − | 0.407474i | ||||||
\(885\) | −0.407906 | + | 1.66821i | −0.0137116 | + | 0.0560764i | ||||
\(886\) | 14.2624 | + | 14.2624i | 0.479156 | + | 0.479156i | ||||
\(887\) | 1.06556 | + | 1.06556i | 0.0357779 | + | 0.0357779i | 0.724769 | − | 0.688992i | \(-0.241946\pi\) |
−0.688992 | + | 0.724769i | \(0.741946\pi\) | |||||||
\(888\) | −0.409124 | − | 0.0355407i | −0.0137293 | − | 0.00119267i | ||||
\(889\) | 3.79970i | 0.127438i | ||||||||
\(890\) | 20.9673 | − | 12.7282i | 0.702825 | − | 0.426650i | ||||
\(891\) | 38.0077i | 1.27331i | ||||||||
\(892\) | −14.0320 | − | 14.0320i | −0.469828 | − | 0.469828i | ||||
\(893\) | 12.4836i | 0.417749i | ||||||||
\(894\) | −0.845665 | + | 0.845665i | −0.0282833 | + | 0.0282833i | ||||
\(895\) | 20.6958 | + | 34.0923i | 0.691783 | + | 1.13958i | ||||
\(896\) | 2.77997 | + | 2.77997i | 0.0928722 | + | 0.0928722i | ||||
\(897\) | 0.632499 | − | 0.632499i | 0.0211185 | − | 0.0211185i | ||||
\(898\) | −17.6009 | − | 17.6009i | −0.587351 | − | 0.587351i | ||||
\(899\) | −10.3586 | −0.345478 | ||||||||
\(900\) | 6.91114 | − | 13.2873i | 0.230371 | − | 0.442911i | ||||
\(901\) | 19.6089 | + | 19.6089i | 0.653269 | + | 0.653269i | ||||
\(902\) | − | 11.4646i | − | 0.381728i | ||||||
\(903\) | −1.84622 | −0.0614382 | ||||||||
\(904\) | 4.23008i | 0.140691i | ||||||||
\(905\) | 27.8341 | + | 6.80589i | 0.925236 | + | 0.226235i | ||||
\(906\) | −0.264010 | + | 0.264010i | −0.00877116 | + | 0.00877116i | ||||
\(907\) | −0.646631 | −0.0214710 | −0.0107355 | − | 0.999942i | \(-0.503417\pi\) | ||||
−0.0107355 | + | 0.999942i | \(0.503417\pi\) | |||||||
\(908\) | 17.0093 | 0.564475 | ||||||||
\(909\) | −4.53637 | −0.150462 | ||||||||
\(910\) | 24.9498 | − | 15.1458i | 0.827079 | − | 0.502078i | ||||
\(911\) | 8.55384 | + | 8.55384i | 0.283401 | + | 0.283401i | 0.834464 | − | 0.551063i | \(-0.185777\pi\) |
−0.551063 | + | 0.834464i | \(0.685777\pi\) | |||||||
\(912\) | − | 0.444083i | − | 0.0147051i | ||||||
\(913\) | 30.0413 | − | 30.0413i | 0.994221 | − | 0.994221i | ||||
\(914\) | − | 8.32533i | − | 0.275377i | ||||||
\(915\) | −0.0787319 | + | 0.321990i | −0.00260280 | + | 0.0106447i | ||||
\(916\) | − | 8.49131i | − | 0.280561i | ||||||
\(917\) | − | 18.6375i | − | 0.615464i | ||||||
\(918\) | 1.04440 | − | 1.04440i | 0.0344704 | − | 0.0344704i | ||||
\(919\) | −2.27110 | − | 2.27110i | −0.0749167 | − | 0.0749167i | 0.668656 | − | 0.743572i | \(-0.266870\pi\) |
−0.743572 | + | 0.668656i | \(0.766870\pi\) | |||||||
\(920\) | 8.66786 | + | 2.11943i | 0.285771 | + | 0.0698757i | ||||
\(921\) | 1.53724 | 0.0506539 | ||||||||
\(922\) | −0.227378 | + | 0.227378i | −0.00748828 | + | 0.00748828i | ||||
\(923\) | 18.4191i | 0.606272i | ||||||||
\(924\) | 1.12604 | 0.0370440 | ||||||||
\(925\) | −29.6866 | + | 6.61118i | −0.976088 | + | 0.217374i | ||||
\(926\) | −0.781658 | −0.0256869 | ||||||||
\(927\) | − | 11.6450i | − | 0.382472i | ||||||
\(928\) | 1.30707 | − | 1.30707i | 0.0429067 | − | 0.0429067i | ||||
\(929\) | −7.69649 | −0.252514 | −0.126257 | − | 0.991998i | \(-0.540296\pi\) | ||||
−0.126257 | + | 0.991998i | \(0.540296\pi\) | |||||||
\(930\) | −0.821767 | − | 0.200935i | −0.0269468 | − | 0.00658893i | ||||
\(931\) | 39.3324 | + | 39.3324i | 1.28907 | + | 1.28907i | ||||
\(932\) | 11.1205 | − | 11.1205i | 0.364265 | − | 0.364265i | ||||
\(933\) | − | 1.77472i | − | 0.0581018i | ||||||
\(934\) | − | 2.66280i | − | 0.0871295i | ||||||
\(935\) | 8.22186 | − | 33.6250i | 0.268884 | − | 1.09965i | ||||
\(936\) | 9.94518i | 0.325068i | ||||||||
\(937\) | 2.79563 | − | 2.79563i | 0.0913291 | − | 0.0913291i | −0.659966 | − | 0.751295i | \(-0.729429\pi\) |
0.751295 | + | 0.659966i | \(0.229429\pi\) | |||||||
\(938\) | − | 24.1349i | − | 0.788032i | ||||||
\(939\) | 1.03883 | + | 1.03883i | 0.0339010 | + | 0.0339010i | ||||
\(940\) | −3.62765 | + | 2.20216i | −0.118321 | + | 0.0718266i | ||||
\(941\) | −1.41774 | −0.0462169 | −0.0231085 | − | 0.999733i | \(-0.507356\pi\) | ||||
−0.0231085 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(942\) | 0.332205 | 0.0108238 | ||||||||
\(943\) | 10.7841 | 0.351177 | ||||||||
\(944\) | 8.04404 | − | 8.04404i | 0.261811 | − | 0.261811i | ||||
\(945\) | 3.45651 | + | 0.845174i | 0.112440 | + | 0.0274935i | ||||
\(946\) | − | 29.5089i | − | 0.959418i | ||||||
\(947\) | 20.5099 | 0.666483 | 0.333242 | − | 0.942841i | \(-0.391858\pi\) | ||||
0.333242 | + | 0.942841i | \(0.391858\pi\) | |||||||
\(948\) | − | 0.303322i | − | 0.00985144i | ||||||
\(949\) | 36.9802 | + | 36.9802i | 1.20043 | + | 1.20043i | ||||
\(950\) | −9.90061 | − | 31.3632i | −0.321218 | − | 1.01756i | ||||
\(951\) | −2.12974 | −0.0690614 | ||||||||
\(952\) | 10.1441 | + | 10.1441i | 0.328773 | + | 0.328773i | ||||
\(953\) | 4.74691 | − | 4.74691i | 0.153768 | − | 0.153768i | −0.626031 | − | 0.779798i | \(-0.715322\pi\) |
0.779798 | + | 0.626031i | \(0.215322\pi\) | |||||||
\(954\) | −16.0968 | − | 16.0968i | −0.521155 | − | 0.521155i | ||||
\(955\) | 16.5446 | + | 27.2540i | 0.535369 | + | 0.881920i | ||||
\(956\) | −14.6371 | + | 14.6371i | −0.473398 | + | 0.473398i | ||||
\(957\) | − | 0.529435i | − | 0.0171142i | ||||||
\(958\) | −16.4195 | − | 16.4195i | −0.530491 | − | 0.530491i | ||||
\(959\) | 85.8627i | 2.77265i | ||||||||
\(960\) | 0.129047 | − | 0.0783380i | 0.00416497 | − | 0.00252835i | ||||
\(961\) | − | 0.403092i | − | 0.0130030i | ||||||
\(962\) | 15.4626 | − | 12.9909i | 0.498535 | − | 0.418842i | ||||
\(963\) | 2.20539 | + | 2.20539i | 0.0710677 | + | 0.0710677i | ||||
\(964\) | −10.5430 | − | 10.5430i | −0.339569 | − | 0.339569i | ||||
\(965\) | −4.02608 | + | 16.4655i | −0.129604 | + | 0.530042i | ||||
\(966\) | 1.05920i | 0.0340792i | ||||||||
\(967\) | 51.7273 | 1.66344 | 0.831719 | − | 0.555197i | \(-0.187357\pi\) | ||||
0.831719 | + | 0.555197i | \(0.187357\pi\) | |||||||
\(968\) | 6.99802i | 0.224925i | ||||||||
\(969\) | − | 1.62046i | − | 0.0520567i | ||||||
\(970\) | −5.33503 | + | 21.8187i | −0.171297 | + | 0.700556i | ||||
\(971\) | −20.2722 | −0.650566 | −0.325283 | − | 0.945617i | \(-0.605460\pi\) | ||||
−0.325283 | + | 0.945617i | \(0.605460\pi\) | |||||||
\(972\) | −1.28634 | + | 1.28634i | −0.0412593 | + | 0.0412593i | ||||
\(973\) | 49.5945 | − | 49.5945i | 1.58993 | − | 1.58993i | ||||
\(974\) | 9.02775i | 0.289268i | ||||||||
\(975\) | −0.337383 | − | 1.06876i | −0.0108049 | − | 0.0342278i | ||||
\(976\) | 1.55262 | − | 1.55262i | 0.0496982 | − | 0.0496982i | ||||
\(977\) | 21.5483i | 0.689390i | 0.938715 | + | 0.344695i | \(0.112018\pi\) | ||||
−0.938715 | + | 0.344695i | \(0.887982\pi\) | |||||||
\(978\) | 1.04048 | + | 1.04048i | 0.0332708 | + | 0.0332708i | ||||
\(979\) | −32.9063 | + | 32.9063i | −1.05169 | + | 1.05169i | ||||
\(980\) | −4.49129 | + | 18.3681i | −0.143469 | + | 0.586746i | ||||
\(981\) | −5.17328 | − | 5.17328i | −0.165170 | − | 0.165170i | ||||
\(982\) | − | 2.91238i | − | 0.0929378i | ||||||
\(983\) | −9.09050 | + | 9.09050i | −0.289942 | + | 0.289942i | −0.837057 | − | 0.547115i | \(-0.815726\pi\) |
0.547115 | + | 0.837057i | \(0.315726\pi\) | |||||||
\(984\) | 0.129008 | − | 0.129008i | 0.00411263 | − | 0.00411263i | ||||
\(985\) | −45.6691 | + | 27.7234i | −1.45514 | + | 0.883342i | ||||
\(986\) | 4.76950 | − | 4.76950i | 0.151892 | − | 0.151892i | ||||
\(987\) | −0.356197 | − | 0.356197i | −0.0113379 | − | 0.0113379i | ||||
\(988\) | 15.4424 | + | 15.4424i | 0.491287 | + | 0.491287i | ||||
\(989\) | 27.7573 | 0.882632 | ||||||||
\(990\) | −6.74927 | + | 27.6025i | −0.214506 | + | 0.877266i | ||||
\(991\) | 12.2842 | − | 12.2842i | 0.390219 | − | 0.390219i | −0.484546 | − | 0.874766i | \(-0.661015\pi\) |
0.874766 | + | 0.484546i | \(0.161015\pi\) | |||||||
\(992\) | 3.96252 | + | 3.96252i | 0.125810 | + | 0.125810i | ||||
\(993\) | −2.29023 | −0.0726783 | ||||||||
\(994\) | −15.4226 | − | 15.4226i | −0.489174 | − | 0.489174i | ||||
\(995\) | −0.945250 | − | 1.55712i | −0.0299664 | − | 0.0493640i | ||||
\(996\) | 0.676095 | 0.0214229 | ||||||||
\(997\) | −49.7309 | −1.57499 | −0.787497 | − | 0.616318i | \(-0.788623\pi\) | ||||
−0.787497 | + | 0.616318i | \(0.788623\pi\) | |||||||
\(998\) | −11.5866 | + | 11.5866i | −0.366767 | + | 0.366767i | ||||
\(999\) | 2.45288 | + | 0.213082i | 0.0776057 | + | 0.00674162i |
(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 | 370.2.g.e.43.6 | ✓ | 20 | |
5.2 | odd | 4 | 370.2.h.e.117.5 | yes | 20 | ||
37.31 | odd | 4 | 370.2.h.e.253.5 | yes | 20 | ||
185.142 | even | 4 | inner | 370.2.g.e.327.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
370.2.g.e.327.6 | yes | 20 | 185.142 | even | 4 | inner | |
370.2.h.e.117.5 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.253.5 | yes | 20 | 37.31 | odd | 4 |