Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
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([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.5 | ||
Root | \(0.0477388 + 0.0477388i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.253 |
Dual form | 370.2.h.e.117.5 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.0477388 | − | 0.0477388i | 0.0275620 | − | 0.0275620i | −0.693191 | − | 0.720753i | \(-0.743796\pi\) |
0.720753 | + | 0.693191i | \(0.243796\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.531109 | − | 2.17208i | 0.237519 | − | 0.971383i | ||||
\(6\) | −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 | \(0.983413\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.99544i | 0.998481i | ||||||||
\(10\) | −0.531109 | + | 2.17208i | −0.167951 | + | 0.686871i | ||||
\(11\) | 4.24241i | 1.27913i | 0.768735 | + | 0.639567i | \(0.220886\pi\) | ||||
−0.768735 | + | 0.639567i | \(0.779114\pi\) | |||||||
\(12\) | 0.0477388 | − | 0.0477388i | 0.0137810 | − | 0.0137810i | ||||
\(13\) | 3.32010 | 0.920831 | 0.460416 | − | 0.887703i | \(-0.347700\pi\) | ||||
0.460416 | + | 0.887703i | \(0.347700\pi\) | |||||||
\(14\) | 2.77997 | − | 2.77997i | 0.742978 | − | 0.742978i | ||||
\(15\) | −0.0783380 | − | 0.129047i | −0.0202268 | − | 0.0333198i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.64900i | − | 0.885013i | −0.896765 | − | 0.442507i | \(-0.854089\pi\) | ||
0.896765 | − | 0.442507i | \(-0.145911\pi\) | |||||||
\(18\) | − | 2.99544i | − | 0.706032i | ||||||
\(19\) | 4.65117 | + | 4.65117i | 1.06705 | + | 1.06705i | 0.997584 | + | 0.0694677i | \(0.0221301\pi\) |
0.0694677 | + | 0.997584i | \(0.477870\pi\) | |||||||
\(20\) | 0.531109 | − | 2.17208i | 0.118760 | − | 0.485691i | ||||
\(21\) | 0.265425i | 0.0579205i | ||||||||
\(22\) | − | 4.24241i | − | 0.904484i | ||||||
\(23\) | 3.99058 | 0.832094 | 0.416047 | − | 0.909343i | \(-0.363415\pi\) | ||||
0.416047 | + | 0.909343i | \(0.363415\pi\) | |||||||
\(24\) | −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 | \(-0.695098\pi\) |
0.817973 | + | 0.575256i | \(0.195098\pi\) | |||||||
\(30\) | 0.0783380 | + | 0.129047i | 0.0143025 | + | 0.0235607i | ||||
\(31\) | 3.96252 | + | 3.96252i | 0.711689 | + | 0.711689i | 0.966888 | − | 0.255199i | \(-0.0821411\pi\) |
−0.255199 | + | 0.966888i | \(0.582141\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.202528 | + | 0.202528i | 0.0352555 | + | 0.0352555i | ||||
\(34\) | 3.64900i | 0.625799i | ||||||||
\(35\) | 4.56184 | + | 7.51477i | 0.771092 | + | 1.27023i | ||||
\(36\) | 2.99544i | 0.499240i | ||||||||
\(37\) | −3.91278 | + | 4.65727i | −0.643258 | + | 0.765650i | ||||
\(38\) | −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 | \(0.0676785\pi\) | ||||
−0.977482 | + | 0.211020i | \(0.932321\pi\) | |||||||
\(42\) | − | 0.265425i | − | 0.0409560i | ||||||
\(43\) | −6.95570 | −1.06073 | −0.530367 | − | 0.847768i | \(-0.677946\pi\) | ||||
−0.530367 | + | 0.847768i | \(0.677946\pi\) | |||||||
\(44\) | 4.24241i | 0.639567i | ||||||||
\(45\) | 6.50633 | + | 1.59091i | 0.969907 | + | 0.237158i | ||||
\(46\) | −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 | ||||||
\(50\) | 4.43585 | + | 2.30722i | 0.627324 | + | 0.326290i | ||||
\(51\) | −0.174199 | − | 0.174199i | −0.0243928 | − | 0.0243928i | ||||
\(52\) | 3.32010 | 0.460416 | ||||||||
\(53\) | 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 | ||||
\(55\) | 9.21484 | + | 2.25318i | 1.24253 | + | 0.303819i | ||||
\(56\) | 2.77997 | − | 2.77997i | 0.371489 | − | 0.371489i | ||||
\(57\) | 0.444083 | 0.0588202 | ||||||||
\(58\) | −1.30707 | + | 1.30707i | −0.171627 | + | 0.171627i | ||||
\(59\) | −8.04404 | − | 8.04404i | −1.04725 | − | 1.04725i | −0.998827 | − | 0.0484179i | \(-0.984582\pi\) |
−0.0484179 | − | 0.998827i | \(-0.515418\pi\) | |||||||
\(60\) | −0.0783380 | − | 0.129047i | −0.0101134 | − | 0.0166599i | ||||
\(61\) | 1.55262 | + | 1.55262i | 0.198793 | + | 0.198793i | 0.799482 | − | 0.600690i | \(-0.205107\pi\) |
−0.600690 | + | 0.799482i | \(0.705107\pi\) | |||||||
\(62\) | −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 | 0.390348 | − | 0.920668i | \(-0.372355\pi\) |
−0.920668 | + | 0.390348i | \(0.872355\pi\) | |||||||
\(68\) | − | 3.64900i | − | 0.442507i | ||||||
\(69\) | 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 | \(0.393222\pi\) | |||||||
\(72\) | − | 2.99544i | − | 0.353016i | ||||||
\(73\) | −11.1383 | + | 11.1383i | −1.30364 | + | 1.30364i | −0.377712 | + | 0.925923i | \(0.623289\pi\) |
−0.925923 | + | 0.377712i | \(0.876711\pi\) | |||||||
\(74\) | 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 | \(-0.331332\pi\) |
−0.862864 | + | 0.505436i | \(0.831332\pi\) | |||||||
\(80\) | 0.531109 | − | 2.17208i | 0.0593798 | − | 0.242846i | ||||
\(81\) | −8.95900 | −0.995444 | ||||||||
\(82\) | − | 2.70237i | − | 0.298427i | ||||||
\(83\) | 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 | ||||||||
\(87\) | − | 0.124796i | − | 0.0133795i | ||||||
\(88\) | − | 4.24241i | − | 0.452242i | ||||||
\(89\) | 7.75651 | − | 7.75651i | 0.822188 | − | 0.822188i | −0.164233 | − | 0.986422i | \(-0.552515\pi\) |
0.986422 | + | 0.164233i | \(0.0525149\pi\) | |||||||
\(90\) | −6.50633 | − | 1.59091i | −0.685828 | − | 0.167696i | ||||
\(91\) | −9.22978 | + | 9.22978i | −0.967544 | + | 0.967544i | ||||
\(92\) | 3.99058 | 0.416047 | ||||||||
\(93\) | 0.378332 | 0.0392312 | ||||||||
\(94\) | −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 | ||||
\(97\) | − | 10.0451i | − | 1.01992i | −0.860197 | − | 0.509962i | \(-0.829660\pi\) | ||
0.860197 | − | 0.509962i | \(-0.170340\pi\) | |||||||
\(98\) | 8.45644i | 0.854230i | ||||||||
\(99\) | −12.7079 | −1.27719 | ||||||||
\(100\) | −4.43585 | − | 2.30722i | −0.443585 | − | 0.230722i | ||||
\(101\) | − | 1.51442i | − | 0.150691i | −0.997157 | − | 0.0753454i | \(-0.975994\pi\) | ||
0.997157 | − | 0.0753454i | \(-0.0240059\pi\) | |||||||
\(102\) | 0.174199 | + | 0.174199i | 0.0172483 | + | 0.0172483i | ||||
\(103\) | − | 3.88757i | − | 0.383054i | −0.981487 | − | 0.191527i | \(-0.938656\pi\) | ||
0.981487 | − | 0.191527i | \(-0.0613439\pi\) | |||||||
\(104\) | −3.32010 | −0.325563 | ||||||||
\(105\) | 0.576524 | + | 0.140969i | 0.0562629 | + | 0.0137572i | ||||
\(106\) | −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 | \(-0.212682\pi\) |
−0.619542 | + | 0.784964i | \(0.712682\pi\) | |||||||
\(110\) | −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 | ||||
\(113\) | − | 4.23008i | − | 0.397933i | −0.980006 | − | 0.198966i | \(-0.936242\pi\) | ||
0.980006 | − | 0.198966i | \(-0.0637585\pi\) | |||||||
\(114\) | −0.444083 | −0.0415922 | ||||||||
\(115\) | 2.11943 | − | 8.66786i | 0.197638 | − | 0.808282i | ||||
\(116\) | 1.30707 | − | 1.30707i | 0.121358 | − | 0.121358i | ||||
\(117\) | 9.94518i | 0.919432i | ||||||||
\(118\) | 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 | ||||
\(125\) | −7.36738 | + | 8.40962i | −0.658958 | + | 0.752179i | ||||
\(126\) | 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 | \(0.236346\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.332057 | + | 0.332057i | −0.0292360 | + | 0.0292360i | ||||
\(130\) | −1.76334 | + | 7.21153i | −0.154655 | + | 0.632493i | ||||
\(131\) | −3.35210 | − | 3.35210i | −0.292875 | − | 0.292875i | 0.545340 | − | 0.838215i | \(-0.316400\pi\) |
−0.838215 | + | 0.545340i | \(0.816400\pi\) | |||||||
\(132\) | 0.202528 | + | 0.202528i | 0.0176278 | + | 0.0176278i | ||||
\(133\) | −25.8602 | −2.24237 | ||||||||
\(134\) | 4.34085 | + | 4.34085i | 0.374993 | + | 0.374993i | ||||
\(135\) | 0.773694 | − | 0.469671i | 0.0665890 | − | 0.0404228i | ||||
\(136\) | 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 | \(-0.226868\pi\) | ||||
0.756582 | + | 0.653899i | \(0.226868\pi\) | |||||||
\(140\) | 4.56184 | + | 7.51477i | 0.385546 | + | 0.635114i | ||||
\(141\) | − | 0.128130i | − | 0.0107905i | ||||||
\(142\) | −5.54775 | −0.465557 | ||||||||
\(143\) | 14.0852i | 1.17787i | ||||||||
\(144\) | 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 | ||||
\(148\) | −3.91278 | + | 4.65727i | −0.321629 | + | 0.382825i | ||||
\(149\) | − | 17.7144i | − | 1.45122i | −0.688106 | − | 0.725610i | \(-0.741558\pi\) | ||
0.688106 | − | 0.725610i | \(-0.258442\pi\) | |||||||
\(150\) | 0.321906 | − | 0.101618i | 0.0262835 | − | 0.00829709i | ||||
\(151\) | 5.53031i | 0.450050i | 0.974353 | + | 0.225025i | \(0.0722464\pi\) | ||||
−0.974353 | + | 0.225025i | \(0.927754\pi\) | |||||||
\(152\) | −4.65117 | − | 4.65117i | −0.377260 | − | 0.377260i | ||||
\(153\) | 10.9304 | 0.883669 | ||||||||
\(154\) | 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 | ||||
\(162\) | 8.95900 | 0.703885 | ||||||||
\(163\) | − | 21.7952i | − | 1.70713i | −0.520985 | − | 0.853566i | \(-0.674435\pi\) | ||
0.520985 | − | 0.853566i | \(-0.325565\pi\) | |||||||
\(164\) | 2.70237i | 0.211020i | ||||||||
\(165\) | 0.547470 | − | 0.332342i | 0.0426205 | − | 0.0258728i | ||||
\(166\) | −7.08119 | − | 7.08119i | −0.549607 | − | 0.549607i | ||||
\(167\) | 11.1575i | 0.863394i | 0.902019 | + | 0.431697i | \(0.142085\pi\) | ||||
−0.902019 | + | 0.431697i | \(0.857915\pi\) | |||||||
\(168\) | − | 0.265425i | − | 0.0204780i | ||||||
\(169\) | −1.97691 | −0.152070 | ||||||||
\(170\) | 7.92592 | + | 1.93802i | 0.607890 | + | 0.148639i | ||||
\(171\) | −13.9323 | + | 13.9323i | −1.06543 | + | 1.06543i | ||||
\(172\) | −6.95570 | −0.530367 | ||||||||
\(173\) | 14.4965 | − | 14.4965i | 1.10215 | − | 1.10215i | 0.107994 | − | 0.994152i | \(-0.465557\pi\) |
0.994152 | − | 0.107994i | \(-0.0344428\pi\) | |||||||
\(174\) | 0.124796i | 0.00946076i | ||||||||
\(175\) | 18.7455 | − | 5.91752i | 1.41703 | − | 0.447322i | ||||
\(176\) | 4.24241i | 0.319783i | ||||||||
\(177\) | −0.768026 | −0.0577284 | ||||||||
\(178\) | −7.75651 | + | 7.75651i | −0.581375 | + | 0.581375i | ||||
\(179\) | −12.6119 | + | 12.6119i | −0.942658 | + | 0.942658i | −0.998443 | − | 0.0557848i | \(-0.982234\pi\) |
0.0557848 | + | 0.998443i | \(0.482234\pi\) | |||||||
\(180\) | 6.50633 | + | 1.59091i | 0.484954 | + | 0.118579i | ||||
\(181\) | 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 | ||||
\(183\) | 0.148241 | 0.0109583 | ||||||||
\(184\) | −3.99058 | −0.294190 | ||||||||
\(185\) | 8.03783 | + | 10.9724i | 0.590953 | + | 0.806706i | ||||
\(186\) | −0.378332 | −0.0277406 | ||||||||
\(187\) | 15.4806 | 1.13205 | ||||||||
\(188\) | 1.34199 | − | 1.34199i | 0.0978746 | − | 0.0978746i | ||||
\(189\) | −1.59134 | −0.115753 | ||||||||
\(190\) | −12.5730 | + | 7.63243i | −0.912140 | + | 0.553715i | ||||
\(191\) | 10.0822 | − | 10.0822i | 0.729521 | − | 0.729521i | −0.241003 | − | 0.970524i | \(-0.577476\pi\) |
0.970524 | + | 0.241003i | \(0.0774763\pi\) | |||||||
\(192\) | 0.0477388 | − | 0.0477388i | 0.00344525 | − | 0.00344525i | ||||
\(193\) | 7.58052 | 0.545658 | 0.272829 | − | 0.962063i | \(-0.412041\pi\) | ||||
0.272829 | + | 0.962063i | \(0.412041\pi\) | |||||||
\(194\) | 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 | \(0.925915\pi\) | |||||||
\(198\) | 12.7079 | 0.903110 | ||||||||
\(199\) | 0.576031 | − | 0.576031i | 0.0408338 | − | 0.0408338i | −0.686395 | − | 0.727229i | \(-0.740808\pi\) |
0.727229 | + | 0.686395i | \(0.240808\pi\) | |||||||
\(200\) | 4.43585 | + | 2.30722i | 0.313662 | + | 0.163145i | ||||
\(201\) | −0.414455 | −0.0292334 | ||||||||
\(202\) | 1.51442i | 0.106554i | ||||||||
\(203\) | 7.26722i | 0.510059i | ||||||||
\(204\) | −0.174199 | − | 0.174199i | −0.0121964 | − | 0.0121964i | ||||
\(205\) | 5.86977 | + | 1.43525i | 0.409962 | + | 0.100243i | ||||
\(206\) | 3.88757i | 0.270860i | ||||||||
\(207\) | 11.9536i | 0.830830i | ||||||||
\(208\) | 3.32010 | 0.230208 | ||||||||
\(209\) | −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 | ||||
\(217\) | −22.0313 | −1.49559 | ||||||||
\(218\) | −1.72705 | − | 1.72705i | −0.116971 | − | 0.116971i | ||||
\(219\) | 1.06346i | 0.0718617i | ||||||||
\(220\) | 9.21484 | + | 2.25318i | 0.621264 | + | 0.151909i | ||||
\(221\) | − | 12.1151i | − | 0.814948i | ||||||
\(222\) | −0.0355407 | − | 0.409124i | −0.00238534 | − | 0.0274586i | ||||
\(223\) | 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 | ||||||||
\(227\) | 17.0093i | 1.12895i | 0.825450 | + | 0.564475i | \(0.190921\pi\) | ||||
−0.825450 | + | 0.564475i | \(0.809079\pi\) | |||||||
\(228\) | 0.444083 | 0.0294101 | ||||||||
\(229\) | 8.49131i | 0.561121i | 0.959836 | + | 0.280561i | \(0.0905204\pi\) | ||||
−0.959836 | + | 0.280561i | \(0.909480\pi\) | |||||||
\(230\) | −2.11943 | + | 8.66786i | −0.139751 | + | 0.571542i | ||||
\(231\) | −1.12604 | −0.0740880 | ||||||||
\(232\) | −1.30707 | + | 1.30707i | −0.0858133 | + | 0.0858133i | ||||
\(233\) | 11.1205 | − | 11.1205i | 0.728530 | − | 0.728530i | −0.241797 | − | 0.970327i | \(-0.577737\pi\) |
0.970327 | + | 0.241797i | \(0.0777367\pi\) | |||||||
\(234\) | − | 9.94518i | − | 0.650137i | ||||||
\(235\) | −2.20216 | − | 3.62765i | −0.143653 | − | 0.236642i | ||||
\(236\) | −8.04404 | − | 8.04404i | −0.523623 | − | 0.523623i | ||||
\(237\) | −0.303322 | −0.0197029 | ||||||||
\(238\) | −10.1441 | − | 10.1441i | −0.657545 | − | 0.657545i | ||||
\(239\) | −14.6371 | − | 14.6371i | −0.946797 | − | 0.946797i | 0.0518580 | − | 0.998654i | \(-0.483486\pi\) |
−0.998654 | + | 0.0518580i | \(0.983486\pi\) | |||||||
\(240\) | −0.0783380 | − | 0.129047i | −0.00505669 | − | 0.00832995i | ||||
\(241\) | 10.5430 | − | 10.5430i | 0.679137 | − | 0.679137i | −0.280668 | − | 0.959805i | \(-0.590556\pi\) |
0.959805 | + | 0.280668i | \(0.0905560\pi\) | |||||||
\(242\) | 6.99802 | 0.449850 | ||||||||
\(243\) | −1.28634 | + | 1.28634i | −0.0825187 | + | 0.0825187i | ||||
\(244\) | 1.55262 | + | 1.55262i | 0.0993963 | + | 0.0993963i | ||||
\(245\) | −18.3681 | − | 4.49129i | −1.17349 | − | 0.286938i | ||||
\(246\) | −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 | −0.999679 | − | 0.0253206i | \(-0.991939\pi\) |
−0.0253206 | − | 0.999679i | \(-0.508061\pi\) | |||||||
\(252\) | −8.32723 | − | 8.32723i | −0.524566 | − | 0.524566i | ||||
\(253\) | 16.9297i | 1.06436i | ||||||||
\(254\) | −0.683408 | + | 0.683408i | −0.0428808 | + | 0.0428808i | ||||
\(255\) | −0.470893 | + | 0.285856i | −0.0294885 | + | 0.0179010i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 5.00407i | − | 0.312145i | −0.987746 | − | 0.156073i | \(-0.950117\pi\) | ||
0.987746 | − | 0.156073i | \(-0.0498834\pi\) | |||||||
\(258\) | 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 | −0.977436 | − | 0.211233i | \(-0.932252\pi\) |
0.211233 | + | 0.977436i | \(0.432252\pi\) | |||||||
\(264\) | −0.202528 | − | 0.202528i | −0.0124647 | − | 0.0124647i | ||||
\(265\) | 14.5263 | − | 8.81821i | 0.892345 | − | 0.541698i | ||||
\(266\) | 25.8602 | 1.58559 | ||||||||
\(267\) | − | 0.740574i | − | 0.0453224i | ||||||
\(268\) | −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 | \(0.313647\pi\) | |||||||
\(272\) | − | 3.64900i | − | 0.221253i | ||||||
\(273\) | 0.881238i | 0.0533350i | ||||||||
\(274\) | −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 | ||||
\(277\) | 23.4453 | 1.40869 | 0.704346 | − | 0.709857i | \(-0.251241\pi\) | ||||
0.704346 | + | 0.709857i | \(0.251241\pi\) | |||||||
\(278\) | −17.8399 | −1.06997 | ||||||||
\(279\) | −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 | −0.601054 | − | 0.799208i | \(-0.705253\pi\) |
0.799208 | + | 0.601054i | \(0.205253\pi\) | |||||||
\(282\) | 0.128130i | 0.00763003i | ||||||||
\(283\) | 12.1785i | 0.723935i | 0.932191 | + | 0.361968i | \(0.117895\pi\) | ||||
−0.932191 | + | 0.361968i | \(0.882105\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | − | 2.99544i | − | 0.176508i | ||||||
\(289\) | 3.68477 | 0.216751 | ||||||||
\(290\) | 2.14486 | + | 3.53325i | 0.125951 | + | 0.207480i | ||||
\(291\) | −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 | ||||
\(298\) | 17.7144i | 1.02617i | ||||||||
\(299\) | 13.2492 | 0.766219 | ||||||||
\(300\) | −0.321906 | + | 0.101618i | −0.0185853 | + | 0.00586693i | ||||
\(301\) | 19.3366 | − | 19.3366i | 1.11454 | − | 1.11454i | ||||
\(302\) | − | 5.53031i | − | 0.318233i | ||||||
\(303\) | −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 | 0.996950 | − | 0.0780426i | \(-0.0248670\pi\) |
−0.0780426 | + | 0.996950i | \(0.524867\pi\) | |||||||
\(308\) | −11.7938 | − | 11.7938i | −0.672012 | − | 0.672012i | ||||
\(309\) | −0.185588 | − | 0.185588i | −0.0105577 | − | 0.0105577i | ||||
\(310\) | −10.7114 | + | 6.50237i | −0.608368 | + | 0.369310i | ||||
\(311\) | −18.5878 | − | 18.5878i | −1.05402 | − | 1.05402i | −0.998455 | − | 0.0555639i | \(-0.982304\pi\) |
−0.0555639 | − | 0.998455i | \(-0.517696\pi\) | |||||||
\(312\) | −0.158498 | + | 0.158498i | −0.00897318 | + | 0.00897318i | ||||
\(313\) | −21.7608 | −1.22999 | −0.614995 | − | 0.788531i | \(-0.710842\pi\) | ||||
−0.614995 | + | 0.788531i | \(0.710842\pi\) | |||||||
\(314\) | 3.47940 | − | 3.47940i | 0.196354 | − | 0.196354i | ||||
\(315\) | −22.5101 | + | 13.6647i | −1.26830 | + | 0.769921i | ||||
\(316\) | −3.17689 | − | 3.17689i | −0.178714 | − | 0.178714i | ||||
\(317\) | −22.3061 | − | 22.3061i | −1.25284 | − | 1.25284i | −0.954443 | − | 0.298392i | \(-0.903550\pi\) |
−0.298392 | − | 0.954443i | \(-0.596450\pi\) | |||||||
\(318\) | −0.513076 | −0.0287719 | ||||||||
\(319\) | 5.54512 | + | 5.54512i | 0.310467 | + | 0.310467i | ||||
\(320\) | 0.531109 | − | 2.17208i | 0.0296899 | − | 0.121423i | ||||
\(321\) | − | 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 | ||||||||
\(325\) | −14.7275 | − | 7.66021i | −0.816933 | − | 0.424912i | ||||
\(326\) | 21.7952i | 1.20712i | ||||||||
\(327\) | 0.164895 | 0.00911871 | ||||||||
\(328\) | − | 2.70237i | − | 0.149214i | ||||||
\(329\) | 7.46137i | 0.411359i | ||||||||
\(330\) | −0.547470 | + | 0.332342i | −0.0301372 | + | 0.0182948i | ||||
\(331\) | 23.9871 | − | 23.9871i | 1.31845 | − | 1.31845i | 0.403447 | − | 0.915003i | \(-0.367812\pi\) |
0.915003 | − | 0.403447i | \(-0.132188\pi\) | |||||||
\(332\) | 7.08119 | + | 7.08119i | 0.388631 | + | 0.388631i | ||||
\(333\) | −13.9506 | − | 11.7205i | −0.764486 | − | 0.642280i | ||||
\(334\) | − | 11.1575i | − | 0.610512i | ||||||
\(335\) | −11.7341 | + | 7.12321i | −0.641105 | + | 0.389183i | ||||
\(336\) | 0.265425i | 0.0144801i | ||||||||
\(337\) | 17.5570 | + | 17.5570i | 0.956390 | + | 0.956390i | 0.999088 | − | 0.0426980i | \(-0.0135953\pi\) |
−0.0426980 | + | 0.999088i | \(0.513595\pi\) | |||||||
\(338\) | 1.97691 | 0.107530 | ||||||||
\(339\) | −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 | ||||
\(347\) | 11.0678 | 0.594151 | 0.297075 | − | 0.954854i | \(-0.403989\pi\) | ||||
0.297075 | + | 0.954854i | \(0.403989\pi\) | |||||||
\(348\) | − | 0.124796i | − | 0.00668977i | ||||||
\(349\) | − | 31.6855i | − | 1.69609i | −0.529926 | − | 0.848044i | \(-0.677780\pi\) | ||
0.529926 | − | 0.848044i | \(-0.322220\pi\) | |||||||
\(350\) | −18.7455 | + | 5.91752i | −1.00199 | + | 0.316305i | ||||
\(351\) | 0.950265 | + | 0.950265i | 0.0507214 | + | 0.0507214i | ||||
\(352\) | − | 4.24241i | − | 0.226121i | ||||||
\(353\) | − | 15.6047i | − | 0.830555i | −0.909695 | − | 0.415278i | \(-0.863684\pi\) | ||
0.909695 | − | 0.415278i | \(-0.136316\pi\) | |||||||
\(354\) | 0.768026 | 0.0408201 | ||||||||
\(355\) | 2.94646 | − | 12.0501i | 0.156382 | − | 0.639555i | ||||
\(356\) | 7.75651 | − | 7.75651i | 0.411094 | − | 0.411094i | ||||
\(357\) | 0.968537 | 0.0512604 | ||||||||
\(358\) | 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 | ||||||||
\(362\) | −12.8145 | −0.673515 | ||||||||
\(363\) | −0.334077 | + | 0.334077i | −0.0175345 | + | 0.0175345i | ||||
\(364\) | −9.22978 | + | 9.22978i | −0.483772 | + | 0.483772i | ||||
\(365\) | 18.2775 | + | 30.1088i | 0.956691 | + | 1.57597i | ||||
\(366\) | −0.148241 | −0.00774866 | ||||||||
\(367\) | −4.61443 | + | 4.61443i | −0.240871 | + | 0.240871i | −0.817211 | − | 0.576339i | \(-0.804481\pi\) |
0.576339 | + | 0.817211i | \(0.304481\pi\) | |||||||
\(368\) | 3.99058 | 0.208024 | ||||||||
\(369\) | −8.09481 | −0.421399 | ||||||||
\(370\) | −8.03783 | − | 10.9724i | −0.417867 | − | 0.570427i | ||||
\(371\) | −29.8779 | −1.55118 | ||||||||
\(372\) | 0.378332 | 0.0196156 | ||||||||
\(373\) | 15.3464 | − | 15.3464i | 0.794607 | − | 0.794607i | −0.187632 | − | 0.982239i | \(-0.560081\pi\) |
0.982239 | + | 0.187632i | \(0.0600813\pi\) | |||||||
\(374\) | −15.4806 | −0.800481 | ||||||||
\(375\) | 0.0497555 | + | 0.753176i | 0.00256937 | + | 0.0388938i | ||||
\(376\) | −1.34199 | + | 1.34199i | −0.0692078 | + | 0.0692078i | ||||
\(377\) | 4.33961 | − | 4.33961i | 0.223501 | − | 0.223501i | ||||
\(378\) | 1.59134 | 0.0818497 | ||||||||
\(379\) | − | 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 | ||||
\(383\) | 0.480522 | 0.0245535 | 0.0122768 | − | 0.999925i | \(-0.496092\pi\) | ||||
0.0122768 | + | 0.999925i | \(0.496092\pi\) | |||||||
\(384\) | −0.0477388 | + | 0.0477388i | −0.00243616 | + | 0.00243616i | ||||
\(385\) | −31.8807 | + | 19.3532i | −1.62479 | + | 0.986330i | ||||
\(386\) | −7.58052 | −0.385838 | ||||||||
\(387\) | − | 20.8354i | − | 1.05912i | ||||||
\(388\) | − | 10.0451i | − | 0.509962i | ||||||
\(389\) | −11.0293 | − | 11.0293i | −0.559208 | − | 0.559208i | 0.369874 | − | 0.929082i | \(-0.379401\pi\) |
−0.929082 | + | 0.369874i | \(0.879401\pi\) | |||||||
\(390\) | 0.260090 | + | 0.428450i | 0.0131702 | + | 0.0216954i | ||||
\(391\) | − | 14.5617i | − | 0.736415i | ||||||
\(392\) | 8.45644i | 0.427115i | ||||||||
\(393\) | −0.320051 | −0.0161444 | ||||||||
\(394\) | 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 | 0.998032 | − | 0.0627054i | \(-0.0199729\pi\) |
−0.0627054 | + | 0.998032i | \(0.519973\pi\) | |||||||
\(398\) | −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 | 0.981874 | + | 0.189535i | \(0.0606980\pi\) |
0.189535 | + | 0.981874i | \(0.439302\pi\) | |||||||
\(402\) | 0.414455 | 0.0206711 | ||||||||
\(403\) | 13.1560 | + | 13.1560i | 0.655346 | + | 0.655346i | ||||
\(404\) | − | 1.51442i | − | 0.0753454i | ||||||
\(405\) | −4.75820 | + | 19.4596i | −0.236437 | + | 0.966958i | ||||
\(406\) | − | 7.26722i | − | 0.360666i | ||||||
\(407\) | −19.7580 | − | 16.5996i | −0.979369 | − | 0.822813i | ||||
\(408\) | 0.174199 | + | 0.174199i | 0.00862415 | + | 0.00862415i | ||||
\(409\) | −20.5642 | + | 20.5642i | −1.01684 | + | 1.01684i | −0.0169803 | + | 0.999856i | \(0.505405\pi\) |
−0.999856 | + | 0.0169803i | \(0.994595\pi\) | |||||||
\(410\) | −5.86977 | − | 1.43525i | −0.289887 | − | 0.0708822i | ||||
\(411\) | − | 1.47447i | − | 0.0727303i | ||||||
\(412\) | − | 3.88757i | − | 0.191527i | ||||||
\(413\) | 44.7244 | 2.20074 | ||||||||
\(414\) | − | 11.9536i | − | 0.587486i | ||||||
\(415\) | 19.1418 | − | 11.6200i | 0.939633 | − | 0.570404i | ||||
\(416\) | −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 | \(-0.376671\pi\) | |||||||
\(420\) | 0.576524 | + | 0.140969i | 0.0281315 | + | 0.00687861i | ||||
\(421\) | 24.4985 | + | 24.4985i | 1.19398 | + | 1.19398i | 0.975939 | + | 0.218043i | \(0.0699674\pi\) |
0.218043 | + | 0.975939i | \(0.430033\pi\) | |||||||
\(422\) | 21.1449 | 1.02932 | ||||||||
\(423\) | 4.01985 | + | 4.01985i | 0.195452 | + | 0.195452i | ||||
\(424\) | −5.37378 | − | 5.37378i | −0.260974 | − | 0.260974i | ||||
\(425\) | −8.41905 | + | 16.1864i | −0.408384 | + | 0.785157i | ||||
\(426\) | −0.264843 | + | 0.264843i | −0.0128317 | + | 0.0128317i | ||||
\(427\) | −8.63247 | −0.417754 | ||||||||
\(428\) | 0.736249 | − | 0.736249i | 0.0355879 | − | 0.0355879i | ||||
\(429\) | 0.672413 | + | 0.672413i | 0.0324644 | + | 0.0324644i | ||||
\(430\) | 3.69423 | − | 15.1083i | 0.178152 | − | 0.728588i | ||||
\(431\) | 15.3753 | + | 15.3753i | 0.740601 | + | 0.740601i | 0.972694 | − | 0.232092i | \(-0.0745571\pi\) |
−0.232092 | + | 0.972694i | \(0.574557\pi\) | |||||||
\(432\) | 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 | ||||
\(438\) | − | 1.06346i | − | 0.0508139i | ||||||
\(439\) | −17.5768 | + | 17.5768i | −0.838896 | + | 0.838896i | −0.988714 | − | 0.149817i | \(-0.952131\pi\) |
0.149817 | + | 0.988714i | \(0.452131\pi\) | |||||||
\(440\) | −9.21484 | − | 2.25318i | −0.439300 | − | 0.107416i | ||||
\(441\) | 25.3308 | 1.20623 | ||||||||
\(442\) | 12.1151i | 0.576255i | ||||||||
\(443\) | −14.2624 | + | 14.2624i | −0.677629 | + | 0.677629i | −0.959463 | − | 0.281834i | \(-0.909057\pi\) |
0.281834 | + | 0.959463i | \(0.409057\pi\) | |||||||
\(444\) | 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 | \(-0.0501709\pi\) |
−0.156965 | + | 0.987604i | \(0.550171\pi\) | |||||||
\(450\) | −6.91114 | + | 13.2873i | −0.325794 | + | 0.626370i | ||||
\(451\) | −11.4646 | −0.539846 | ||||||||
\(452\) | − | 4.23008i | − | 0.198966i | ||||||
\(453\) | 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 | ||||||||
\(457\) | 8.32533i | 0.389443i | 0.980859 | + | 0.194721i | \(0.0623802\pi\) | ||||
−0.980859 | + | 0.194721i | \(0.937620\pi\) | |||||||
\(458\) | − | 8.49131i | − | 0.396773i | ||||||
\(459\) | 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 | −0.701792 | − | 0.712382i | \(-0.747616\pi\) |
0.712382 | + | 0.701792i | \(0.247616\pi\) | |||||||
\(462\) | 1.12604 | 0.0523881 | ||||||||
\(463\) | 0.781658 | 0.0363267 | 0.0181634 | − | 0.999835i | \(-0.494218\pi\) | ||||
0.0181634 | + | 0.999835i | \(0.494218\pi\) | |||||||
\(464\) | 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 | ||||
\(467\) | 2.66280i | 0.123220i | 0.998100 | + | 0.0616098i | \(0.0196235\pi\) | ||||
−0.998100 | + | 0.0616098i | \(0.980377\pi\) | |||||||
\(468\) | 9.94518i | 0.459716i | ||||||||
\(469\) | 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 | ||||
\(473\) | − | 29.5089i | − | 1.35682i | ||||||
\(474\) | 0.303322 | 0.0139320 | ||||||||
\(475\) | −9.90061 | − | 31.3632i | −0.454271 | − | 1.43904i | ||||
\(476\) | 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 | \(-0.0720075\pi\) |
−0.224294 | + | 0.974522i | \(0.572007\pi\) | |||||||
\(480\) | 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 | ||||
\(483\) | 1.05920i | 0.0481953i | ||||||||
\(484\) | −6.99802 | −0.318092 | ||||||||
\(485\) | −21.8187 | − | 5.33503i | −0.990736 | − | 0.242251i | ||||
\(486\) | 1.28634 | − | 1.28634i | 0.0583495 | − | 0.0583495i | ||||
\(487\) | − | 9.02775i | − | 0.409087i | −0.978858 | − | 0.204543i | \(-0.934429\pi\) | ||
0.978858 | − | 0.204543i | \(-0.0655709\pi\) | |||||||
\(488\) | −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 | ||||
\(495\) | −6.74927 | + | 27.6025i | −0.303357 | + | 1.24064i | ||||
\(496\) | 3.96252 | + | 3.96252i | 0.177922 | + | 0.177922i | ||||
\(497\) | −15.4226 | + | 15.4226i | −0.691796 | + | 0.691796i | ||||
\(498\) | −0.676095 | −0.0302966 | ||||||||
\(499\) | −11.5866 | + | 11.5866i | −0.518686 | + | 0.518686i | −0.917174 | − | 0.398487i | \(-0.869535\pi\) |
0.398487 | + | 0.917174i | \(0.369535\pi\) | |||||||
\(500\) | −7.36738 | + | 8.40962i | −0.329479 | + | 0.376090i | ||||
\(501\) | 0.532647 | + | 0.532647i | 0.0237969 | + | 0.0237969i | ||||
\(502\) | 16.2391 | + | 16.2391i | 0.724784 | + | 0.724784i | ||||
\(503\) | 19.3861 | 0.864382 | 0.432191 | − | 0.901782i | \(-0.357741\pi\) | ||||
0.432191 | + | 0.901782i | \(0.357741\pi\) | |||||||
\(504\) | 8.32723 | + | 8.32723i | 0.370924 | + | 0.370924i | ||||
\(505\) | −3.28945 | − | 0.804324i | −0.146378 | − | 0.0357919i | ||||
\(506\) | − | 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 | \(-0.445434\pi\) | ||||
0.170585 | + | 0.985343i | \(0.445434\pi\) | |||||||
\(510\) | 0.470893 | − | 0.285856i | 0.0208515 | − | 0.0126579i | ||||
\(511\) | − | 61.9280i | − | 2.73953i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.66247i | 0.117551i | ||||||||
\(514\) | 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 | ||||
\(518\) | 2.06964 | + | 23.8245i | 0.0909346 | + | 1.04679i | ||||
\(519\) | − | 1.38409i | − | 0.0607548i | ||||||
\(520\) | −1.76334 | + | 7.21153i | −0.0773274 | + | 0.316246i | ||||
\(521\) | 15.1959i | 0.665746i | 0.942972 | + | 0.332873i | \(0.108018\pi\) | ||||
−0.942972 | + | 0.332873i | \(0.891982\pi\) | |||||||
\(522\) | −3.91525 | − | 3.91525i | −0.171366 | − | 0.171366i | ||||
\(523\) | 8.67427 | 0.379299 | 0.189650 | − | 0.981852i | \(-0.439265\pi\) | ||||
0.189650 | + | 0.981852i | \(0.439265\pi\) | |||||||
\(524\) | −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 | ||||
\(532\) | −25.8602 | −1.12118 | ||||||||
\(533\) | 8.97216i | 0.388628i | ||||||||
\(534\) | 0.740574i | 0.0320478i | ||||||||
\(535\) | −1.20816 | − | 1.99022i | −0.0522334 | − | 0.0860446i | ||||
\(536\) | 4.34085 | + | 4.34085i | 0.187496 | + | 0.187496i | ||||
\(537\) | 1.20416i | 0.0519631i | ||||||||
\(538\) | 22.6019i | 0.974436i | ||||||||
\(539\) | 35.8757 | 1.54527 | ||||||||
\(540\) | 0.773694 | − | 0.469671i | 0.0332945 | − | 0.0202114i | ||||
\(541\) | 19.2216 | − | 19.2216i | 0.826402 | − | 0.826402i | −0.160615 | − | 0.987017i | \(-0.551348\pi\) |
0.987017 | + | 0.160615i | \(0.0513477\pi\) | |||||||
\(542\) | −18.1930 | −0.781454 | ||||||||
\(543\) | 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 | ||||||
\(547\) | 0.0420593 | 0.00179833 | 0.000899163 | − | 1.00000i | \(-0.499714\pi\) | ||||
0.000899163 | 1.00000i | \(0.499714\pi\) | ||||||||
\(548\) | 15.4431 | − | 15.4431i | 0.659697 | − | 0.659697i | ||||
\(549\) | −4.65078 | + | 4.65078i | −0.198491 | + | 0.198491i | ||||
\(550\) | −9.78816 | + | 18.8187i | −0.417369 | + | 0.802431i | ||||
\(551\) | 12.1588 | 0.517983 | ||||||||
\(552\) | −0.190506 | + | 0.190506i | −0.00810847 | + | 0.00810847i | ||||
\(553\) | 17.6633 | 0.751120 | ||||||||
\(554\) | −23.4453 | −0.996095 | ||||||||
\(555\) | 0.907526 | + | 0.140092i | 0.0385223 | + | 0.00594659i | ||||
\(556\) | 17.8399 | 0.756582 | ||||||||
\(557\) | −12.8111 | −0.542823 | −0.271412 | − | 0.962463i | \(-0.587491\pi\) | ||||
−0.271412 | + | 0.962463i | \(0.587491\pi\) | |||||||
\(558\) | 11.8695 | − | 11.8695i | 0.502476 | − | 0.502476i | ||||
\(559\) | −23.0937 | −0.976758 | ||||||||
\(560\) | 4.56184 | + | 7.51477i | 0.192773 | + | 0.317557i | ||||
\(561\) | 0.739024 | − | 0.739024i | 0.0312016 | − | 0.0312016i | ||||
\(562\) | −3.32166 | + | 3.32166i | −0.140116 | + | 0.140116i | ||||
\(563\) | −29.4317 | −1.24040 | −0.620200 | − | 0.784444i | \(-0.712949\pi\) | ||||
−0.620200 | + | 0.784444i | \(0.712949\pi\) | |||||||
\(564\) | − | 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 | ||||
\(568\) | −5.54775 | −0.232778 | ||||||||
\(569\) | 1.25554 | − | 1.25554i | 0.0526351 | − | 0.0526351i | −0.680299 | − | 0.732934i | \(-0.738150\pi\) |
0.732934 | + | 0.680299i | \(0.238150\pi\) | |||||||
\(570\) | −0.235856 | + | 0.964583i | −0.00987894 | + | 0.0404019i | ||||
\(571\) | −40.9624 | −1.71422 | −0.857111 | − | 0.515132i | \(-0.827743\pi\) | ||||
−0.857111 | + | 0.515132i | \(0.827743\pi\) | |||||||
\(572\) | 14.0852i | 0.588933i | ||||||||
\(573\) | − | 0.962624i | − | 0.0402142i | ||||||
\(574\) | 7.51251 | + | 7.51251i | 0.313566 | + | 0.313566i | ||||
\(575\) | −17.7016 | − | 9.20715i | −0.738209 | − | 0.383965i | ||||
\(576\) | 2.99544i | 0.124810i | ||||||||
\(577\) | 7.71924i | 0.321356i | 0.987007 | + | 0.160678i | \(0.0513681\pi\) | ||||
−0.987007 | + | 0.160678i | \(0.948632\pi\) | |||||||
\(578\) | −3.68477 | −0.153266 | ||||||||
\(579\) | 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 | ||||
\(587\) | −5.39311 | −0.222597 | −0.111299 | − | 0.993787i | \(-0.535501\pi\) | ||||
−0.111299 | + | 0.993787i | \(0.535501\pi\) | |||||||
\(588\) | −0.403701 | − | 0.403701i | −0.0166483 | − | 0.0166483i | ||||
\(589\) | 36.8607i | 1.51882i | ||||||||
\(590\) | 21.7445 | − | 13.2000i | 0.895209 | − | 0.543437i | ||||
\(591\) | 1.61305i | 0.0663521i | ||||||||
\(592\) | −3.91278 | + | 4.65727i | −0.160814 | + | 0.191412i | ||||
\(593\) | −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 | ||||||
\(597\) | − | 0.0549981i | − | 0.00225092i | ||||||
\(598\) | −13.2492 | −0.541798 | ||||||||
\(599\) | − | 19.3788i | − | 0.791798i | −0.918294 | − | 0.395899i | \(-0.870433\pi\) | ||
0.918294 | − | 0.395899i | \(-0.129567\pi\) | |||||||
\(600\) | 0.321906 | − | 0.101618i | 0.0131418 | − | 0.00414855i | ||||
\(601\) | −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 | ||||||||
\(605\) | −3.71671 | + | 15.2002i | −0.151106 | + | 0.617978i | ||||
\(606\) | 0.0722968 | + | 0.0722968i | 0.00293686 | + | 0.00293686i | ||||
\(607\) | 29.8434 | 1.21131 | 0.605653 | − | 0.795729i | \(-0.292912\pi\) | ||||
0.605653 | + | 0.795729i | \(0.292912\pi\) | |||||||
\(608\) | −4.65117 | − | 4.65117i | −0.188630 | − | 0.188630i | ||||
\(609\) | 0.346929 | + | 0.346929i | 0.0140583 | + | 0.0140583i | ||||
\(610\) | −4.19702 | + | 2.54780i | −0.169932 | + | 0.103158i | ||||
\(611\) | 4.45554 | − | 4.45554i | 0.180252 | − | 0.180252i | ||||
\(612\) | 10.9304 | 0.441834 | ||||||||
\(613\) | 7.97850 | − | 7.97850i | 0.322248 | − | 0.322248i | −0.527381 | − | 0.849629i | \(-0.676826\pi\) |
0.849629 | + | 0.527381i | \(0.176826\pi\) | |||||||
\(614\) | −16.1006 | − | 16.1006i | −0.649766 | − | 0.649766i | ||||
\(615\) | 0.348733 | − | 0.211699i | 0.0140623 | − | 0.00853651i | ||||
\(616\) | 11.7938 | + | 11.7938i | 0.475184 | + | 0.475184i | ||||
\(617\) | 21.2579 | + | 21.2579i | 0.855812 | + | 0.855812i | 0.990842 | − | 0.135030i | \(-0.0431130\pi\) |
−0.135030 | + | 0.990842i | \(0.543113\pi\) | |||||||
\(618\) | 0.185588 | + | 0.185588i | 0.00746545 | + | 0.00746545i | ||||
\(619\) | −7.54167 | −0.303125 | −0.151563 | − | 0.988448i | \(-0.548431\pi\) | ||||
−0.151563 | + | 0.988448i | \(0.548431\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 43.1257i | 1.72779i | ||||||||
\(624\) | 0.158498 | − | 0.158498i | 0.00634500 | − | 0.00634500i | ||||
\(625\) | 14.3535 | + | 20.4689i | 0.574139 | + | 0.818758i | ||||
\(626\) | 21.7608 | 0.869735 | ||||||||
\(627\) | 1.88398i | 0.0752390i | ||||||||
\(628\) | −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 | 0.997247 | − | 0.0741448i | \(-0.0236227\pi\) |
−0.0741448 | + | 0.997247i | \(0.523623\pi\) | |||||||
\(632\) | 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 | ||||
\(635\) | −1.12145 | − | 1.84738i | −0.0445034 | − | 0.0733110i | ||||
\(636\) | 0.513076 | 0.0203448 | ||||||||
\(637\) | − | 28.0763i | − | 1.11242i | ||||||
\(638\) | −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 | \(0.577475\pi\) | |||||||
\(642\) | 0.0702953i | 0.00277433i | ||||||||
\(643\) | − | 26.4268i | − | 1.04217i | −0.853505 | − | 0.521085i | \(-0.825528\pi\) | ||
0.853505 | − | 0.521085i | \(-0.174472\pi\) | |||||||
\(644\) | −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 | ||||
\(647\) | −23.6177 | −0.928509 | −0.464255 | − | 0.885702i | \(-0.653678\pi\) | ||||
−0.464255 | + | 0.885702i | \(0.653678\pi\) | |||||||
\(648\) | 8.95900 | 0.351943 | ||||||||
\(649\) | 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 | ||||
\(652\) | − | 21.7952i | − | 0.853566i | ||||||
\(653\) | − | 11.5143i | − | 0.450588i | −0.974291 | − | 0.225294i | \(-0.927666\pi\) | ||
0.974291 | − | 0.225294i | \(-0.0723342\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | − | 7.46137i | − | 0.290875i | ||||||
\(659\) | −45.6299 | −1.77749 | −0.888744 | − | 0.458404i | \(-0.848421\pi\) | ||||
−0.888744 | + | 0.458404i | \(0.848421\pi\) | |||||||
\(660\) | 0.547470 | − | 0.332342i | 0.0213102 | − | 0.0129364i | ||||
\(661\) | −8.90268 | − | 8.90268i | −0.346274 | − | 0.346274i | 0.512446 | − | 0.858720i | \(-0.328740\pi\) |
−0.858720 | + | 0.512446i | \(0.828740\pi\) | |||||||
\(662\) | −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 | ||||
\(668\) | 11.1575i | 0.431697i | ||||||||
\(669\) | 1.33975 | 0.0517976 | ||||||||
\(670\) | 11.7341 | − | 7.12321i | 0.453329 | − | 0.275194i | ||||
\(671\) | −6.58685 | + | 6.58685i | −0.254282 | + | 0.254282i | ||||
\(672\) | − | 0.265425i | − | 0.0102390i | ||||||
\(673\) | −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 | 0.844273 | − | 0.535914i | \(-0.180033\pi\) |
−0.535914 | + | 0.844273i | \(0.680033\pi\) | |||||||
\(678\) | 0.201939 | + | 0.201939i | 0.00775543 | + | 0.00775543i | ||||
\(679\) | 27.9250 | + | 27.9250i | 1.07166 | + | 1.07166i | ||||
\(680\) | 7.92592 | + | 1.93802i | 0.303945 | + | 0.0743196i | ||||
\(681\) | 0.812006 | + | 0.812006i | 0.0311161 | + | 0.0311161i | ||||
\(682\) | 16.8106 | − | 16.8106i | 0.643712 | − | 0.643712i | ||||
\(683\) | −14.7249 | −0.563434 | −0.281717 | − | 0.959498i | \(-0.590904\pi\) | ||||
−0.281717 | + | 0.959498i | \(0.590904\pi\) | |||||||
\(684\) | −13.9323 | + | 13.9323i | −0.532715 | + | 0.532715i | ||||
\(685\) | −25.3417 | − | 41.7456i | −0.968255 | − | 1.59502i | ||||
\(686\) | −4.04887 | − | 4.04887i | −0.154586 | − | 0.154586i | ||||
\(687\) | 0.405365 | + | 0.405365i | 0.0154656 | + | 0.0154656i | ||||
\(688\) | −6.95570 | −0.265184 | ||||||||
\(689\) | 17.8415 | + | 17.8415i | 0.679707 | + | 0.679707i | ||||
\(690\) | 0.312614 | + | 0.514973i | 0.0119010 | + | 0.0196047i | ||||
\(691\) | − | 7.03274i | − | 0.267538i | −0.991013 | − | 0.133769i | \(-0.957292\pi\) | ||
0.991013 | − | 0.133769i | \(-0.0427080\pi\) | |||||||
\(692\) | 14.4965 | − | 14.4965i | 0.551073 | − | 0.551073i | ||||
\(693\) | 35.3275 | − | 35.3275i | 1.34198 | − | 1.34198i | ||||
\(694\) | −11.0678 | −0.420128 | ||||||||
\(695\) | 9.47495 | − | 38.7497i | 0.359405 | − | 1.46986i | ||||
\(696\) | 0.124796i | 0.00473038i | ||||||||
\(697\) | 9.86097 | 0.373511 | ||||||||
\(698\) | 31.6855i | 1.19931i | ||||||||
\(699\) | − | 1.06176i | − | 0.0401595i | ||||||
\(700\) | 18.7455 | − | 5.91752i | 0.708514 | − | 0.223661i | ||||
\(701\) | −18.7062 | + | 18.7062i | −0.706523 | + | 0.706523i | −0.965802 | − | 0.259279i | \(-0.916515\pi\) |
0.259279 | + | 0.965802i | \(0.416515\pi\) | |||||||
\(702\) | −0.950265 | − | 0.950265i | −0.0358654 | − | 0.0358654i | ||||
\(703\) | −39.8608 | + | 3.46271i | −1.50338 | + | 0.130599i | ||||
\(704\) | 4.24241i | 0.159892i | ||||||||
\(705\) | −0.278308 | − | 0.0680510i | −0.0104817 | − | 0.00256295i | ||||
\(706\) | 15.6047i | 0.587291i | ||||||||
\(707\) | 4.21005 | + | 4.21005i | 0.158335 | + | 0.158335i | ||||
\(708\) | −0.768026 | −0.0288642 | ||||||||
\(709\) | 24.5474 | + | 24.5474i | 0.921895 | + | 0.921895i | 0.997163 | − | 0.0752682i | \(-0.0239813\pi\) |
−0.0752682 | + | 0.997163i | \(0.523981\pi\) | |||||||
\(710\) | −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 | ||||
\(717\) | −1.39752 | −0.0521913 | ||||||||
\(718\) | − | 34.4499i | − | 1.28566i | ||||||
\(719\) | − | 12.2897i | − | 0.458329i | −0.973388 | − | 0.229164i | \(-0.926401\pi\) | ||
0.973388 | − | 0.229164i | \(-0.0735993\pi\) | |||||||
\(720\) | 6.50633 | + | 1.59091i | 0.242477 | + | 0.0592895i | ||||
\(721\) | 10.8073 | + | 10.8073i | 0.402486 | + | 0.402486i | ||||
\(722\) | − | 24.2668i | − | 0.903116i | ||||||
\(723\) | − | 1.00663i | − | 0.0374368i | ||||||
\(724\) | 12.8145 | 0.476247 | ||||||||
\(725\) | −8.81366 | + | 2.78226i | −0.327331 | + | 0.103331i | ||||
\(726\) | 0.334077 | − | 0.334077i | 0.0123988 | − | 0.0123988i | ||||
\(727\) | 12.2686 | 0.455016 | 0.227508 | − | 0.973776i | \(-0.426942\pi\) | ||||
0.227508 | + | 0.973776i | \(0.426942\pi\) | |||||||
\(728\) | 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 | ||||||||
\(732\) | 0.148241 | 0.00547913 | ||||||||
\(733\) | −26.4738 | + | 26.4738i | −0.977831 | + | 0.977831i | −0.999760 | − | 0.0219285i | \(-0.993019\pi\) |
0.0219285 | + | 0.999760i | \(0.493019\pi\) | |||||||
\(734\) | 4.61443 | − | 4.61443i | 0.170322 | − | 0.170322i | ||||
\(735\) | −1.09128 | + | 0.662461i | −0.0402524 | + | 0.0244352i | ||||
\(736\) | −3.99058 | −0.147095 | ||||||||
\(737\) | 18.4157 | − | 18.4157i | 0.678350 | − | 0.678350i | ||||
\(738\) | 8.09481 | 0.297974 | ||||||||
\(739\) | −23.9200 | −0.879912 | −0.439956 | − | 0.898019i | \(-0.645006\pi\) | ||||
−0.439956 | + | 0.898019i | \(0.645006\pi\) | |||||||
\(740\) | 8.03783 | + | 10.9724i | 0.295477 | + | 0.403353i | ||||
\(741\) | 1.47440 | 0.0541635 | ||||||||
\(742\) | 29.8779 | 1.09685 | ||||||||
\(743\) | −8.98938 | + | 8.98938i | −0.329788 | + | 0.329788i | −0.852506 | − | 0.522718i | \(-0.824918\pi\) |
0.522718 | + | 0.852506i | \(0.324918\pi\) | |||||||
\(744\) | −0.378332 | −0.0138703 | ||||||||
\(745\) | −38.4771 | − | 9.40827i | −1.40969 | − | 0.344692i | ||||
\(746\) | −15.3464 | + | 15.3464i | −0.561872 | + | 0.561872i | ||||
\(747\) | −21.2113 | + | 21.2113i | −0.776080 | + | 0.776080i | ||||
\(748\) | 15.4806 | 0.566025 | ||||||||
\(749\) | 4.09349i | 0.149573i | ||||||||
\(750\) | −0.0497555 | − | 0.753176i | −0.00181682 | − | 0.0275021i | ||||
\(751\) | − | 34.7552i | − | 1.26824i | −0.773236 | − | 0.634118i | \(-0.781363\pi\) | ||
0.773236 | − | 0.634118i | \(-0.218637\pi\) | |||||||
\(752\) | 1.34199 | − | 1.34199i | 0.0489373 | − | 0.0489373i | ||||
\(753\) | −1.55047 | −0.0565022 | ||||||||
\(754\) | −4.33961 | + | 4.33961i | −0.158039 | + | 0.158039i | ||||
\(755\) | 12.0123 | + | 2.93719i | 0.437171 | + | 0.106895i | ||||
\(756\) | −1.59134 | −0.0578765 | ||||||||
\(757\) | − | 2.66868i | − | 0.0969950i | −0.998823 | − | 0.0484975i | \(-0.984557\pi\) | ||
0.998823 | − | 0.0484975i | \(-0.0154433\pi\) | |||||||
\(758\) | 23.4892i | 0.853164i | ||||||||
\(759\) | 0.808204 | + | 0.808204i | 0.0293359 | + | 0.0293359i | ||||
\(760\) | −12.5730 | + | 7.63243i | −0.456070 | + | 0.276857i | ||||
\(761\) | − | 50.1338i | − | 1.81735i | −0.417507 | − | 0.908674i | \(-0.637096\pi\) | ||
0.417507 | − | 0.908674i | \(-0.362904\pi\) | |||||||
\(762\) | 0.0652502i | 0.00236376i | ||||||||
\(763\) | −9.60230 | −0.347626 | ||||||||
\(764\) | 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 | 0.321974 | − | 0.946748i | \(-0.395654\pi\) |
0.946748 | − | 0.321974i | \(-0.104346\pi\) | |||||||
\(770\) | 31.8807 | − | 19.3532i | 1.14890 | − | 0.697441i | ||||
\(771\) | −0.238888 | − | 0.238888i | −0.00860335 | − | 0.00860335i | ||||
\(772\) | 7.58052 | 0.272829 | ||||||||
\(773\) | −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 | ||||||||
\(775\) | −8.43473 | − | 26.7195i | −0.302984 | − | 0.959793i | ||||
\(776\) | 10.0451i | 0.360597i | ||||||||
\(777\) | −1.23615 | − | 1.03855i | −0.0443468 | − | 0.0372578i | ||||
\(778\) | 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 | ||||||||
\(782\) | 14.5617i | 0.520724i | ||||||||
\(783\) | 0.748207 | 0.0267387 | ||||||||
\(784\) | − | 8.45644i | − | 0.302016i | ||||||
\(785\) | 5.70959 | + | 9.40547i | 0.203784 | + | 0.335696i | ||||
\(786\) | 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 | ||||||||
\(790\) | 8.58772 | − | 5.21318i | 0.305537 | − | 0.185476i | ||||
\(791\) | 11.7595 | + | 11.7595i | 0.418120 | + | 0.418120i | ||||
\(792\) | 12.7079 | 0.451555 | ||||||||
\(793\) | 5.15486 | + | 5.15486i | 0.183054 | + | 0.183054i | ||||
\(794\) | −18.6363 | − | 18.6363i | −0.661376 | − | 0.661376i | ||||
\(795\) | 0.272499 | − | 1.11444i | 0.00966455 | − | 0.0395252i | ||||
\(796\) | 0.576031 | − | 0.576031i | 0.0204169 | − | 0.0204169i | ||||
\(797\) | −41.1330 | −1.45700 | −0.728502 | − | 0.685043i | \(-0.759783\pi\) | ||||
−0.728502 | + | 0.685043i | \(0.759783\pi\) | |||||||
\(798\) | 1.23454 | − | 1.23454i | 0.0437021 | − | 0.0437021i | ||||
\(799\) | −4.89692 | − | 4.89692i | −0.173241 | − | 0.173241i | ||||
\(800\) | 4.43585 | + | 2.30722i | 0.156831 | + | 0.0815725i | ||||
\(801\) | 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 | ||||
\(808\) | 1.51442i | 0.0532772i | ||||||||
\(809\) | 25.8572 | − | 25.8572i | 0.909092 | − | 0.909092i | −0.0871071 | − | 0.996199i | \(-0.527762\pi\) |
0.996199 | + | 0.0871071i | \(0.0277622\pi\) | |||||||
\(810\) | 4.75820 | − | 19.4596i | 0.167186 | − | 0.683742i | ||||
\(811\) | −26.4820 | −0.929907 | −0.464954 | − | 0.885335i | \(-0.653929\pi\) | ||||
−0.464954 | + | 0.885335i | \(0.653929\pi\) | |||||||
\(812\) | 7.26722i | 0.255030i | ||||||||
\(813\) | 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 | ||||
\(820\) | 5.86977 | + | 1.43525i | 0.204981 | + | 0.0501213i | ||||
\(821\) | 31.1573 | 1.08740 | 0.543699 | − | 0.839280i | \(-0.317023\pi\) | ||||
0.543699 | + | 0.839280i | \(0.317023\pi\) | |||||||
\(822\) | 1.47447i | 0.0514281i | ||||||||
\(823\) | 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 | ||||||||
\(827\) | − | 23.8982i | − | 0.831021i | −0.909588 | − | 0.415510i | \(-0.863603\pi\) | ||
0.909588 | − | 0.415510i | \(-0.136397\pi\) | |||||||
\(828\) | 11.9536i | 0.415415i | ||||||||
\(829\) | −7.39911 | + | 7.39911i | −0.256982 | + | 0.256982i | −0.823825 | − | 0.566844i | \(-0.808164\pi\) |
0.566844 | + | 0.823825i | \(0.308164\pi\) | |||||||
\(830\) | −19.1418 | + | 11.6200i | −0.664421 | + | 0.403337i | ||||
\(831\) | 1.11925 | − | 1.11925i | 0.0388264 | − | 0.0388264i | ||||
\(832\) | 3.32010 | 0.115104 | ||||||||
\(833\) | −30.8576 | −1.06915 | ||||||||
\(834\) | −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 | ||||
\(837\) | 2.26827i | 0.0784028i | ||||||||
\(838\) | 37.9044i | 1.30939i | ||||||||
\(839\) | −22.2697 | −0.768834 | −0.384417 | − | 0.923160i | \(-0.625598\pi\) | ||||
−0.384417 | + | 0.923160i | \(0.625598\pi\) | |||||||
\(840\) | −0.576524 | − | 0.140969i | −0.0198920 | − | 0.00486391i | ||||
\(841\) | 25.5831i | 0.882177i | ||||||||
\(842\) | −24.4985 | − | 24.4985i | −0.844273 | − | 0.844273i | ||||
\(843\) | − | 0.317145i | − | 0.0109230i | ||||||
\(844\) | −21.1449 | −0.727838 | ||||||||
\(845\) | −1.04995 | + | 4.29399i | −0.0361194 | + | 0.147718i | ||||
\(846\) | −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 | ||||
\(853\) | 30.0733i | 1.02969i | 0.857283 | + | 0.514845i | \(0.172150\pi\) | ||||
−0.857283 | + | 0.514845i | \(0.827850\pi\) | |||||||
\(854\) | 8.63247 | 0.295397 | ||||||||
\(855\) | 22.8625 | + | 37.6616i | 0.781881 | + | 1.28800i | ||||
\(856\) | −0.736249 | + | 0.736249i | −0.0251645 | + | 0.0251645i | ||||
\(857\) | − | 19.5685i | − | 0.668446i | −0.942494 | − | 0.334223i | \(-0.891526\pi\) | ||
0.942494 | − | 0.334223i | \(-0.108474\pi\) | |||||||
\(858\) | −0.672413 | − | 0.672413i | −0.0229558 | − | 0.0229558i | ||||
\(859\) | −12.9463 | − | 12.9463i | −0.441723 | − | 0.441723i | 0.450868 | − | 0.892591i | \(-0.351115\pi\) |
−0.892591 | + | 0.450868i | \(0.851115\pi\) | |||||||
\(860\) | −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 | ||||
\(865\) | −23.7883 | − | 39.1867i | −0.808825 | − | 1.33239i | ||||
\(866\) | 16.4923 | + | 16.4923i | 0.560432 | + | 0.560432i | ||||
\(867\) | 0.175907 | − | 0.175907i | 0.00597410 | − | 0.00597410i | ||||
\(868\) | −22.0313 | −0.747793 | ||||||||
\(869\) | 13.4777 | − | 13.4777i | 0.457198 | − | 0.457198i | ||||
\(870\) | 0.271067 | + | 0.0662802i | 0.00919002 | + | 0.00224711i | ||||
\(871\) | −14.4121 | − | 14.4121i | −0.488335 | − | 0.488335i | ||||
\(872\) | −1.72705 | − | 1.72705i | −0.0584853 | − | 0.0584853i | ||||
\(873\) | 30.0895 | 1.01837 | ||||||||
\(874\) | −18.5609 | − | 18.5609i | −0.627832 | − | 0.627832i | ||||
\(875\) | −2.89741 | − | 43.8596i | −0.0979502 | − | 1.48272i | ||||
\(876\) | 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 | ||||||||
\(880\) | 9.21484 | + | 2.25318i | 0.310632 | + | 0.0759547i | ||||
\(881\) | 41.3883i | 1.39441i | 0.716873 | + | 0.697204i | \(0.245573\pi\) | ||||
−0.716873 | + | 0.697204i | \(0.754427\pi\) | |||||||
\(882\) | −25.3308 | −0.852932 | ||||||||
\(883\) | − | 16.0092i | − | 0.538751i | −0.963035 | − | 0.269376i | \(-0.913183\pi\) | ||
0.963035 | − | 0.269376i | \(-0.0868173\pi\) | |||||||
\(884\) | − | 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 | 0.688992 | − | 0.724769i | \(-0.258054\pi\) |
−0.724769 | + | 0.688992i | \(0.758054\pi\) | |||||||
\(888\) | −0.0355407 | − | 0.409124i | −0.00119267 | − | 0.0137293i | ||||
\(889\) | 3.79970i | 0.127438i | ||||||||
\(890\) | 12.7282 | + | 20.9673i | 0.426650 | + | 0.702825i | ||||
\(891\) | − | 38.0077i | − | 1.27331i | ||||||
\(892\) | 14.0320 | + | 14.0320i | 0.469828 | + | 0.469828i | ||||
\(893\) | 12.4836 | 0.417749 | ||||||||
\(894\) | 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 | ||||
\(902\) | 11.4646 | 0.381728 | ||||||||
\(903\) | − | 1.84622i | − | 0.0614382i | ||||||
\(904\) | 4.23008i | 0.140691i | ||||||||
\(905\) | 6.80589 | − | 27.8341i | 0.226235 | − | 0.925236i | ||||
\(906\) | −0.264010 | − | 0.264010i | −0.00877116 | − | 0.00877116i | ||||
\(907\) | 0.646631i | 0.0214710i | 0.999942 | + | 0.0107355i | \(0.00341728\pi\) | ||||
−0.999942 | + | 0.0107355i | \(0.996583\pi\) | |||||||
\(908\) | 17.0093i | 0.564475i | ||||||||
\(909\) | 4.53637 | 0.150462 | ||||||||
\(910\) | −15.1458 | − | 24.9498i | −0.502078 | − | 0.827079i | ||||
\(911\) | 8.55384 | − | 8.55384i | 0.283401 | − | 0.283401i | −0.551063 | − | 0.834464i | \(-0.685777\pi\) |
0.834464 | + | 0.551063i | \(0.185777\pi\) | |||||||
\(912\) | 0.444083 | 0.0147051 | ||||||||
\(913\) | −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 | ||||||||
\(917\) | 18.6375 | 0.615464 | ||||||||
\(918\) | −1.04440 | + | 1.04440i | −0.0344704 | + | 0.0344704i | ||||
\(919\) | 2.27110 | − | 2.27110i | 0.0749167 | − | 0.0749167i | −0.668656 | − | 0.743572i | \(-0.733130\pi\) |
0.743572 | + | 0.668656i | \(0.233130\pi\) | |||||||
\(920\) | −2.11943 | + | 8.66786i | −0.0698757 | + | 0.285771i | ||||
\(921\) | 1.53724 | 0.0506539 | ||||||||
\(922\) | −0.227378 | + | 0.227378i | −0.00748828 | + | 0.00748828i | ||||
\(923\) | 18.4191 | 0.606272 | ||||||||
\(924\) | −1.12604 | −0.0370440 | ||||||||
\(925\) | 28.1018 | − | 11.6313i | 0.923983 | − | 0.382434i | ||||
\(926\) | −0.781658 | −0.0256869 | ||||||||
\(927\) | 11.6450 | 0.382472 | ||||||||
\(928\) | −1.30707 | + | 1.30707i | −0.0429067 | + | 0.0429067i | ||||
\(929\) | 7.69649 | 0.252514 | 0.126257 | − | 0.991998i | \(-0.459704\pi\) | ||||
0.126257 | + | 0.991998i | \(0.459704\pi\) | |||||||
\(930\) | −0.200935 | + | 0.821767i | −0.00658893 | + | 0.0269468i | ||||
\(931\) | 39.3324 | − | 39.3324i | 1.28907 | − | 1.28907i | ||||
\(932\) | 11.1205 | − | 11.1205i | 0.364265 | − | 0.364265i | ||||
\(933\) | −1.77472 | −0.0581018 | ||||||||
\(934\) | − | 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 | \(0.229429\pi\) | |||||||
\(938\) | −24.1349 | −0.788032 | ||||||||
\(939\) | −1.03883 | + | 1.03883i | −0.0339010 | + | 0.0339010i | ||||
\(940\) | −2.20216 | − | 3.62765i | −0.0718266 | − | 0.118321i | ||||
\(941\) | −1.41774 | −0.0462169 | −0.0231085 | − | 0.999733i | \(-0.507356\pi\) | ||||
−0.0231085 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(942\) | − | 0.332205i | − | 0.0108238i | ||||||
\(943\) | 10.7841i | 0.351177i | ||||||||
\(944\) | −8.04404 | − | 8.04404i | −0.261811 | − | 0.261811i | ||||
\(945\) | −0.845174 | + | 3.45651i | −0.0274935 | + | 0.112440i | ||||
\(946\) | 29.5089i | 0.959418i | ||||||||
\(947\) | − | 20.5099i | − | 0.666483i | −0.942841 | − | 0.333242i | \(-0.891858\pi\) | ||
0.942841 | − | 0.333242i | \(-0.108142\pi\) | |||||||
\(948\) | −0.303322 | −0.00985144 | ||||||||
\(949\) | −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 | −0.779798 | − | 0.626031i | \(-0.784678\pi\) |
0.626031 | + | 0.779798i | \(0.284678\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 0.529435 | 0.0171142 | ||||||||
\(958\) | −16.4195 | − | 16.4195i | −0.530491 | − | 0.530491i | ||||
\(959\) | 85.8627i | 2.77265i | ||||||||
\(960\) | −0.0783380 | − | 0.129047i | −0.00252835 | − | 0.00416497i | ||||
\(961\) | 0.403092i | 0.0130030i | ||||||||
\(962\) | 12.9909 | − | 15.4626i | 0.418842 | − | 0.498535i | ||||
\(963\) | 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 | ||||||
\(967\) | − | 51.7273i | − | 1.66344i | −0.555197 | − | 0.831719i | \(-0.687357\pi\) | ||
0.555197 | − | 0.831719i | \(-0.312643\pi\) | |||||||
\(968\) | 6.99802 | 0.224925 | ||||||||
\(969\) | − | 1.62046i | − | 0.0520567i | ||||||
\(970\) | 21.8187 | + | 5.33503i | 0.700556 | + | 0.171297i | ||||
\(971\) | −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 | ||||||||
\(975\) | −1.06876 | + | 0.337383i | −0.0342278 | + | 0.0108049i | ||||
\(976\) | 1.55262 | + | 1.55262i | 0.0496982 | + | 0.0496982i | ||||
\(977\) | −21.5483 | −0.689390 | −0.344695 | − | 0.938715i | \(-0.612018\pi\) | ||||
−0.344695 | + | 0.938715i | \(0.612018\pi\) | |||||||
\(978\) | 1.04048 | + | 1.04048i | 0.0332708 | + | 0.0332708i | ||||
\(979\) | 32.9063 | + | 32.9063i | 1.05169 | + | 1.05169i | ||||
\(980\) | −18.3681 | − | 4.49129i | −0.586746 | − | 0.143469i | ||||
\(981\) | −5.17328 | + | 5.17328i | −0.165170 | + | 0.165170i | ||||
\(982\) | 2.91238 | 0.0929378 | ||||||||
\(983\) | 9.09050 | − | 9.09050i | 0.289942 | − | 0.289942i | −0.547115 | − | 0.837057i | \(-0.684274\pi\) |
0.837057 | + | 0.547115i | \(0.184274\pi\) | |||||||
\(984\) | −0.129008 | − | 0.129008i | −0.00411263 | − | 0.00411263i | ||||
\(985\) | 27.7234 | + | 45.6691i | 0.883342 | + | 1.45514i | ||||
\(986\) | 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 | 0.874766 | − | 0.484546i | \(-0.161015\pi\) |
−0.484546 | + | 0.874766i | \(0.661015\pi\) | |||||||
\(992\) | −3.96252 | − | 3.96252i | −0.125810 | − | 0.125810i | ||||
\(993\) | − | 2.29023i | − | 0.0726783i | ||||||
\(994\) | 15.4226 | − | 15.4226i | 0.489174 | − | 0.489174i | ||||
\(995\) | −0.945250 | − | 1.55712i | −0.0299664 | − | 0.0493640i | ||||
\(996\) | 0.676095 | 0.0214229 | ||||||||
\(997\) | 49.7309i | 1.57499i | 0.616318 | + | 0.787497i | \(0.288623\pi\) | ||||
−0.616318 | + | 0.787497i | \(0.711377\pi\) | |||||||
\(998\) | 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.h.e.253.5 | yes | 20 | |
5.2 | odd | 4 | 370.2.g.e.327.6 | yes | 20 | ||
37.6 | odd | 4 | 370.2.g.e.43.6 | ✓ | 20 | ||
185.117 | even | 4 | inner | 370.2.h.e.117.5 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.6 | ✓ | 20 | 37.6 | odd | 4 | ||
370.2.g.e.327.6 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.117.5 | yes | 20 | 185.117 | even | 4 | inner | |
370.2.h.e.253.5 | yes | 20 | 1.1 | even | 1 | trivial |