Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 683.4 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.683 |
Dual form | 930.2.j.d.497.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.707107 | + | 0.707107i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.12132 | − | 0.707107i | 0.948683 | − | 0.316228i | ||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 1.44949 | − | 1.44949i | 0.547856 | − | 0.547856i | −0.377964 | − | 0.925820i | \(-0.623376\pi\) |
0.925820 | + | 0.377964i | \(0.123376\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 2.00000 | + | 1.00000i | 0.632456 | + | 0.316228i | ||||
\(11\) | 0.635674i | 0.191663i | 0.995398 | + | 0.0958315i | \(0.0305510\pi\) | ||||
−0.995398 | + | 0.0958315i | \(0.969449\pi\) | |||||||
\(12\) | −1.22474 | + | 1.22474i | −0.353553 | + | 0.353553i | ||||
\(13\) | 0.449490 | + | 0.449490i | 0.124666 | + | 0.124666i | 0.766687 | − | 0.642021i | \(-0.221904\pi\) |
−0.642021 | + | 0.766687i | \(0.721904\pi\) | |||||||
\(14\) | 2.04989 | 0.547856 | ||||||||
\(15\) | 3.46410 | + | 1.73205i | 0.894427 | + | 0.447214i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.14626 | − | 3.14626i | −0.763081 | − | 0.763081i | 0.213797 | − | 0.976878i | \(-0.431417\pi\) |
−0.976878 | + | 0.213797i | \(0.931417\pi\) | |||||||
\(18\) | −2.12132 | + | 2.12132i | −0.500000 | + | 0.500000i | ||||
\(19\) | 4.89898i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0.707107 | + | 2.12132i | 0.158114 | + | 0.474342i | ||||
\(21\) | 3.55051 | 0.774785 | ||||||||
\(22\) | −0.449490 | + | 0.449490i | −0.0958315 | + | 0.0958315i | ||||
\(23\) | 1.73205 | − | 1.73205i | 0.361158 | − | 0.361158i | −0.503081 | − | 0.864239i | \(-0.667800\pi\) |
0.864239 | + | 0.503081i | \(0.167800\pi\) | |||||||
\(24\) | −1.73205 | −0.353553 | ||||||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | 0.635674i | 0.124666i | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.707107 | + | 0.707107i | ||||
\(28\) | 1.44949 | + | 1.44949i | 0.273928 | + | 0.273928i | ||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 1.22474 | + | 3.67423i | 0.223607 | + | 0.670820i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −0.778539 | + | 0.778539i | −0.135526 | + | 0.135526i | ||||
\(34\) | − | 4.44949i | − | 0.763081i | ||||||
\(35\) | 2.04989 | − | 4.09978i | 0.346494 | − | 0.692989i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | −3.46410 | + | 3.46410i | −0.561951 | + | 0.561951i | ||||
\(39\) | 1.10102i | 0.176304i | ||||||||
\(40\) | −1.00000 | + | 2.00000i | −0.158114 | + | 0.316228i | ||||
\(41\) | − | 2.82843i | − | 0.441726i | −0.975305 | − | 0.220863i | \(-0.929113\pi\) | ||
0.975305 | − | 0.220863i | \(-0.0708874\pi\) | |||||||
\(42\) | 2.51059 | + | 2.51059i | 0.387392 | + | 0.387392i | ||||
\(43\) | 2.44949 | + | 2.44949i | 0.373544 | + | 0.373544i | 0.868766 | − | 0.495222i | \(-0.164913\pi\) |
−0.495222 | + | 0.868766i | \(0.664913\pi\) | |||||||
\(44\) | −0.635674 | −0.0958315 | ||||||||
\(45\) | 2.12132 | + | 6.36396i | 0.316228 | + | 0.948683i | ||||
\(46\) | 2.44949 | 0.361158 | ||||||||
\(47\) | −5.65685 | − | 5.65685i | −0.825137 | − | 0.825137i | 0.161703 | − | 0.986840i | \(-0.448301\pi\) |
−0.986840 | + | 0.161703i | \(0.948301\pi\) | |||||||
\(48\) | −1.22474 | − | 1.22474i | −0.176777 | − | 0.176777i | ||||
\(49\) | 2.79796i | 0.399708i | ||||||||
\(50\) | 4.94975 | + | 0.707107i | 0.700000 | + | 0.100000i | ||||
\(51\) | − | 7.70674i | − | 1.07916i | ||||||
\(52\) | −0.449490 | + | 0.449490i | −0.0623330 | + | 0.0623330i | ||||
\(53\) | 4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | −5.19615 | −0.707107 | ||||||||
\(55\) | 0.449490 | + | 1.34847i | 0.0606092 | + | 0.181828i | ||||
\(56\) | 2.04989i | 0.273928i | ||||||||
\(57\) | −6.00000 | + | 6.00000i | −0.794719 | + | 0.794719i | ||||
\(58\) | 2.00000 | + | 2.00000i | 0.262613 | + | 0.262613i | ||||
\(59\) | −3.60697 | −0.469587 | −0.234794 | − | 0.972045i | \(-0.575441\pi\) | ||||
−0.234794 | + | 0.972045i | \(0.575441\pi\) | |||||||
\(60\) | −1.73205 | + | 3.46410i | −0.223607 | + | 0.447214i | ||||
\(61\) | −4.44949 | −0.569699 | −0.284849 | − | 0.958572i | \(-0.591944\pi\) | ||||
−0.284849 | + | 0.958572i | \(0.591944\pi\) | |||||||
\(62\) | −0.707107 | − | 0.707107i | −0.0898027 | − | 0.0898027i | ||||
\(63\) | 4.34847 | + | 4.34847i | 0.547856 | + | 0.547856i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.27135 | + | 0.635674i | 0.157691 | + | 0.0788457i | ||||
\(66\) | −1.10102 | −0.135526 | ||||||||
\(67\) | −8.44949 | + | 8.44949i | −1.03227 | + | 1.03227i | −0.0328078 | + | 0.999462i | \(0.510445\pi\) |
−0.999462 | + | 0.0328078i | \(0.989555\pi\) | |||||||
\(68\) | 3.14626 | − | 3.14626i | 0.381541 | − | 0.381541i | ||||
\(69\) | 4.24264 | 0.510754 | ||||||||
\(70\) | 4.34847 | − | 1.44949i | 0.519741 | − | 0.173247i | ||||
\(71\) | − | 9.12096i | − | 1.08246i | −0.840875 | − | 0.541229i | \(-0.817959\pi\) | ||
0.840875 | − | 0.541229i | \(-0.182041\pi\) | |||||||
\(72\) | −2.12132 | − | 2.12132i | −0.250000 | − | 0.250000i | ||||
\(73\) | −4.89898 | − | 4.89898i | −0.573382 | − | 0.573382i | 0.359690 | − | 0.933072i | \(-0.382883\pi\) |
−0.933072 | + | 0.359690i | \(0.882883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.57321 | + | 1.22474i | 0.989949 | + | 0.141421i | ||||
\(76\) | −4.89898 | −0.561951 | ||||||||
\(77\) | 0.921404 | + | 0.921404i | 0.105004 | + | 0.105004i | ||||
\(78\) | −0.778539 | + | 0.778539i | −0.0881522 | + | 0.0881522i | ||||
\(79\) | − | 8.89898i | − | 1.00121i | −0.865675 | − | 0.500607i | \(-0.833110\pi\) | ||
0.865675 | − | 0.500607i | \(-0.166890\pi\) | |||||||
\(80\) | −2.12132 | + | 0.707107i | −0.237171 | + | 0.0790569i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 2.00000 | − | 2.00000i | 0.220863 | − | 0.220863i | ||||
\(83\) | 0.635674 | − | 0.635674i | 0.0697743 | − | 0.0697743i | −0.671358 | − | 0.741133i | \(-0.734289\pi\) |
0.741133 | + | 0.671358i | \(0.234289\pi\) | |||||||
\(84\) | 3.55051i | 0.387392i | ||||||||
\(85\) | −8.89898 | − | 4.44949i | −0.965230 | − | 0.482615i | ||||
\(86\) | 3.46410i | 0.373544i | ||||||||
\(87\) | 3.46410 | + | 3.46410i | 0.371391 | + | 0.371391i | ||||
\(88\) | −0.449490 | − | 0.449490i | −0.0479158 | − | 0.0479158i | ||||
\(89\) | −18.2419 | −1.93364 | −0.966819 | − | 0.255461i | \(-0.917773\pi\) | ||||
−0.966819 | + | 0.255461i | \(0.917773\pi\) | |||||||
\(90\) | −3.00000 | + | 6.00000i | −0.316228 | + | 0.632456i | ||||
\(91\) | 1.30306 | 0.136598 | ||||||||
\(92\) | 1.73205 | + | 1.73205i | 0.180579 | + | 0.180579i | ||||
\(93\) | −1.22474 | − | 1.22474i | −0.127000 | − | 0.127000i | ||||
\(94\) | − | 8.00000i | − | 0.825137i | ||||||
\(95\) | 3.46410 | + | 10.3923i | 0.355409 | + | 1.06623i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | −3.00000 | + | 3.00000i | −0.304604 | + | 0.304604i | −0.842812 | − | 0.538208i | \(-0.819101\pi\) |
0.538208 | + | 0.842812i | \(0.319101\pi\) | |||||||
\(98\) | −1.97846 | + | 1.97846i | −0.199854 | + | 0.199854i | ||||
\(99\) | −1.90702 | −0.191663 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | 9.89949i | 0.985037i | 0.870302 | + | 0.492518i | \(0.163924\pi\) | ||||
−0.870302 | + | 0.492518i | \(0.836076\pi\) | |||||||
\(102\) | 5.44949 | − | 5.44949i | 0.539580 | − | 0.539580i | ||||
\(103\) | 3.44949 | + | 3.44949i | 0.339888 | + | 0.339888i | 0.856325 | − | 0.516437i | \(-0.172742\pi\) |
−0.516437 | + | 0.856325i | \(0.672742\pi\) | |||||||
\(104\) | −0.635674 | −0.0623330 | ||||||||
\(105\) | 7.53177 | − | 2.51059i | 0.735025 | − | 0.245008i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 0.778539 | + | 0.778539i | 0.0752642 | + | 0.0752642i | 0.743737 | − | 0.668473i | \(-0.233052\pi\) |
−0.668473 | + | 0.743737i | \(0.733052\pi\) | |||||||
\(108\) | −3.67423 | − | 3.67423i | −0.353553 | − | 0.353553i | ||||
\(109\) | − | 6.89898i | − | 0.660802i | −0.943841 | − | 0.330401i | \(-0.892816\pi\) | ||
0.943841 | − | 0.330401i | \(-0.107184\pi\) | |||||||
\(110\) | −0.635674 | + | 1.27135i | −0.0606092 | + | 0.121218i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.44949 | + | 1.44949i | −0.136964 | + | 0.136964i | ||||
\(113\) | 5.51399 | − | 5.51399i | 0.518713 | − | 0.518713i | −0.398469 | − | 0.917182i | \(-0.630458\pi\) |
0.917182 | + | 0.398469i | \(0.130458\pi\) | |||||||
\(114\) | −8.48528 | −0.794719 | ||||||||
\(115\) | 2.44949 | − | 4.89898i | 0.228416 | − | 0.456832i | ||||
\(116\) | 2.82843i | 0.262613i | ||||||||
\(117\) | −1.34847 | + | 1.34847i | −0.124666 | + | 0.124666i | ||||
\(118\) | −2.55051 | − | 2.55051i | −0.234794 | − | 0.234794i | ||||
\(119\) | −9.12096 | −0.836117 | ||||||||
\(120\) | −3.67423 | + | 1.22474i | −0.335410 | + | 0.111803i | ||||
\(121\) | 10.5959 | 0.963265 | ||||||||
\(122\) | −3.14626 | − | 3.14626i | −0.284849 | − | 0.284849i | ||||
\(123\) | 3.46410 | − | 3.46410i | 0.312348 | − | 0.312348i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 6.36396 | − | 9.19239i | 0.569210 | − | 0.822192i | ||||
\(126\) | 6.14966i | 0.547856i | ||||||||
\(127\) | 5.55051 | − | 5.55051i | 0.492528 | − | 0.492528i | −0.416574 | − | 0.909102i | \(-0.636769\pi\) |
0.909102 | + | 0.416574i | \(0.136769\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 6.00000i | 0.528271i | ||||||||
\(130\) | 0.449490 | + | 1.34847i | 0.0394229 | + | 0.118269i | ||||
\(131\) | 10.5352i | 0.920462i | 0.887799 | + | 0.460231i | \(0.152233\pi\) | ||||
−0.887799 | + | 0.460231i | \(0.847767\pi\) | |||||||
\(132\) | −0.778539 | − | 0.778539i | −0.0677631 | − | 0.0677631i | ||||
\(133\) | 7.10102 | + | 7.10102i | 0.615737 | + | 0.615737i | ||||
\(134\) | −11.9494 | −1.03227 | ||||||||
\(135\) | −5.19615 | + | 10.3923i | −0.447214 | + | 0.894427i | ||||
\(136\) | 4.44949 | 0.381541 | ||||||||
\(137\) | −13.5386 | − | 13.5386i | −1.15668 | − | 1.15668i | −0.985185 | − | 0.171493i | \(-0.945141\pi\) |
−0.171493 | − | 0.985185i | \(-0.554859\pi\) | |||||||
\(138\) | 3.00000 | + | 3.00000i | 0.255377 | + | 0.255377i | ||||
\(139\) | − | 13.5505i | − | 1.14934i | −0.818385 | − | 0.574670i | \(-0.805131\pi\) | ||
0.818385 | − | 0.574670i | \(-0.194869\pi\) | |||||||
\(140\) | 4.09978 | + | 2.04989i | 0.346494 | + | 0.173247i | ||||
\(141\) | − | 13.8564i | − | 1.16692i | ||||||
\(142\) | 6.44949 | − | 6.44949i | 0.541229 | − | 0.541229i | ||||
\(143\) | −0.285729 | + | 0.285729i | −0.0238939 | + | 0.0238939i | ||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 6.00000 | − | 2.00000i | 0.498273 | − | 0.166091i | ||||
\(146\) | − | 6.92820i | − | 0.573382i | ||||||
\(147\) | −3.42679 | + | 3.42679i | −0.282637 | + | 0.282637i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.78534 | −0.555877 | −0.277938 | − | 0.960599i | \(-0.589651\pi\) | ||||
−0.277938 | + | 0.960599i | \(0.589651\pi\) | |||||||
\(150\) | 5.19615 | + | 6.92820i | 0.424264 | + | 0.565685i | ||||
\(151\) | 7.10102 | 0.577873 | 0.288936 | − | 0.957348i | \(-0.406698\pi\) | ||||
0.288936 | + | 0.957348i | \(0.406698\pi\) | |||||||
\(152\) | −3.46410 | − | 3.46410i | −0.280976 | − | 0.280976i | ||||
\(153\) | 9.43879 | − | 9.43879i | 0.763081 | − | 0.763081i | ||||
\(154\) | 1.30306i | 0.105004i | ||||||||
\(155\) | −2.12132 | + | 0.707107i | −0.170389 | + | 0.0567962i | ||||
\(156\) | −1.10102 | −0.0881522 | ||||||||
\(157\) | 16.8990 | − | 16.8990i | 1.34869 | − | 1.34869i | 0.461594 | − | 0.887091i | \(-0.347278\pi\) |
0.887091 | − | 0.461594i | \(-0.152722\pi\) | |||||||
\(158\) | 6.29253 | − | 6.29253i | 0.500607 | − | 0.500607i | ||||
\(159\) | 10.3923 | 0.824163 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | − | 5.02118i | − | 0.395724i | ||||||
\(162\) | −6.36396 | − | 6.36396i | −0.500000 | − | 0.500000i | ||||
\(163\) | 17.3485 | + | 17.3485i | 1.35884 | + | 1.35884i | 0.875353 | + | 0.483484i | \(0.160629\pi\) |
0.483484 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(164\) | 2.82843 | 0.220863 | ||||||||
\(165\) | −1.10102 | + | 2.20204i | −0.0857143 | + | 0.171429i | ||||
\(166\) | 0.898979 | 0.0697743 | ||||||||
\(167\) | 12.1244 | + | 12.1244i | 0.938211 | + | 0.938211i | 0.998199 | − | 0.0599883i | \(-0.0191063\pi\) |
−0.0599883 | + | 0.998199i | \(0.519106\pi\) | |||||||
\(168\) | −2.51059 | + | 2.51059i | −0.193696 | + | 0.193696i | ||||
\(169\) | − | 12.5959i | − | 0.968917i | ||||||
\(170\) | −3.14626 | − | 9.43879i | −0.241307 | − | 0.723922i | ||||
\(171\) | −14.6969 | −1.12390 | ||||||||
\(172\) | −2.44949 | + | 2.44949i | −0.186772 | + | 0.186772i | ||||
\(173\) | 0.142865 | − | 0.142865i | 0.0108618 | − | 0.0108618i | −0.701655 | − | 0.712517i | \(-0.747555\pi\) |
0.712517 | + | 0.701655i | \(0.247555\pi\) | |||||||
\(174\) | 4.89898i | 0.371391i | ||||||||
\(175\) | 1.44949 | − | 10.1464i | 0.109571 | − | 0.766998i | ||||
\(176\) | − | 0.635674i | − | 0.0479158i | ||||||
\(177\) | −4.41761 | − | 4.41761i | −0.332048 | − | 0.332048i | ||||
\(178\) | −12.8990 | − | 12.8990i | −0.966819 | − | 0.966819i | ||||
\(179\) | −3.74983 | −0.280276 | −0.140138 | − | 0.990132i | \(-0.544755\pi\) | ||||
−0.140138 | + | 0.990132i | \(0.544755\pi\) | |||||||
\(180\) | −6.36396 | + | 2.12132i | −0.474342 | + | 0.158114i | ||||
\(181\) | −3.55051 | −0.263907 | −0.131954 | − | 0.991256i | \(-0.542125\pi\) | ||||
−0.131954 | + | 0.991256i | \(0.542125\pi\) | |||||||
\(182\) | 0.921404 | + | 0.921404i | 0.0682990 | + | 0.0682990i | ||||
\(183\) | −5.44949 | − | 5.44949i | −0.402838 | − | 0.402838i | ||||
\(184\) | 2.44949i | 0.180579i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 1.73205i | − | 0.127000i | ||||||
\(187\) | 2.00000 | − | 2.00000i | 0.146254 | − | 0.146254i | ||||
\(188\) | 5.65685 | − | 5.65685i | 0.412568 | − | 0.412568i | ||||
\(189\) | 10.6515i | 0.774785i | ||||||||
\(190\) | −4.89898 | + | 9.79796i | −0.355409 | + | 0.710819i | ||||
\(191\) | 21.7060i | 1.57059i | 0.619120 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(192\) | 1.22474 | − | 1.22474i | 0.0883883 | − | 0.0883883i | ||||
\(193\) | −7.00000 | − | 7.00000i | −0.503871 | − | 0.503871i | 0.408768 | − | 0.912639i | \(-0.365959\pi\) |
−0.912639 | + | 0.408768i | \(0.865959\pi\) | |||||||
\(194\) | −4.24264 | −0.304604 | ||||||||
\(195\) | 0.778539 | + | 2.33562i | 0.0557523 | + | 0.167257i | ||||
\(196\) | −2.79796 | −0.199854 | ||||||||
\(197\) | 4.87832 | + | 4.87832i | 0.347566 | + | 0.347566i | 0.859202 | − | 0.511636i | \(-0.170961\pi\) |
−0.511636 | + | 0.859202i | \(0.670961\pi\) | |||||||
\(198\) | −1.34847 | − | 1.34847i | −0.0958315 | − | 0.0958315i | ||||
\(199\) | − | 10.6969i | − | 0.758286i | −0.925338 | − | 0.379143i | \(-0.876219\pi\) | ||
0.925338 | − | 0.379143i | \(-0.123781\pi\) | |||||||
\(200\) | −0.707107 | + | 4.94975i | −0.0500000 | + | 0.350000i | ||||
\(201\) | −20.6969 | −1.45985 | ||||||||
\(202\) | −7.00000 | + | 7.00000i | −0.492518 | + | 0.492518i | ||||
\(203\) | 4.09978 | − | 4.09978i | 0.287748 | − | 0.287748i | ||||
\(204\) | 7.70674 | 0.539580 | ||||||||
\(205\) | −2.00000 | − | 6.00000i | −0.139686 | − | 0.419058i | ||||
\(206\) | 4.87832i | 0.339888i | ||||||||
\(207\) | 5.19615 | + | 5.19615i | 0.361158 | + | 0.361158i | ||||
\(208\) | −0.449490 | − | 0.449490i | −0.0311665 | − | 0.0311665i | ||||
\(209\) | −3.11416 | −0.215411 | ||||||||
\(210\) | 7.10102 | + | 3.55051i | 0.490017 | + | 0.245008i | ||||
\(211\) | −22.6969 | −1.56252 | −0.781261 | − | 0.624205i | \(-0.785423\pi\) | ||||
−0.781261 | + | 0.624205i | \(0.785423\pi\) | |||||||
\(212\) | 4.24264 | + | 4.24264i | 0.291386 | + | 0.291386i | ||||
\(213\) | 11.1708 | − | 11.1708i | 0.765414 | − | 0.765414i | ||||
\(214\) | 1.10102i | 0.0752642i | ||||||||
\(215\) | 6.92820 | + | 3.46410i | 0.472500 | + | 0.236250i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | −1.44949 | + | 1.44949i | −0.0983978 | + | 0.0983978i | ||||
\(218\) | 4.87832 | − | 4.87832i | 0.330401 | − | 0.330401i | ||||
\(219\) | − | 12.0000i | − | 0.810885i | ||||||
\(220\) | −1.34847 | + | 0.449490i | −0.0909138 | + | 0.0303046i | ||||
\(221\) | − | 2.82843i | − | 0.190261i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.44949 | + | 8.44949i | 0.565820 | + | 0.565820i | 0.930955 | − | 0.365135i | \(-0.118977\pi\) |
−0.365135 | + | 0.930955i | \(0.618977\pi\) | |||||||
\(224\) | −2.04989 | −0.136964 | ||||||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | 7.79796 | 0.518713 | ||||||||
\(227\) | 13.3636 | + | 13.3636i | 0.886973 | + | 0.886973i | 0.994231 | − | 0.107258i | \(-0.0342071\pi\) |
−0.107258 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(228\) | −6.00000 | − | 6.00000i | −0.397360 | − | 0.397360i | ||||
\(229\) | − | 11.5505i | − | 0.763279i | −0.924311 | − | 0.381640i | \(-0.875360\pi\) | ||
0.924311 | − | 0.381640i | \(-0.124640\pi\) | |||||||
\(230\) | 5.19615 | − | 1.73205i | 0.342624 | − | 0.114208i | ||||
\(231\) | 2.25697i | 0.148498i | ||||||||
\(232\) | −2.00000 | + | 2.00000i | −0.131306 | + | 0.131306i | ||||
\(233\) | 0.778539 | − | 0.778539i | 0.0510038 | − | 0.0510038i | −0.681145 | − | 0.732149i | \(-0.738518\pi\) |
0.732149 | + | 0.681145i | \(0.238518\pi\) | |||||||
\(234\) | −1.90702 | −0.124666 | ||||||||
\(235\) | −16.0000 | − | 8.00000i | −1.04372 | − | 0.521862i | ||||
\(236\) | − | 3.60697i | − | 0.234794i | ||||||
\(237\) | 10.8990 | − | 10.8990i | 0.707965 | − | 0.707965i | ||||
\(238\) | −6.44949 | − | 6.44949i | −0.418058 | − | 0.418058i | ||||
\(239\) | −6.00680 | −0.388548 | −0.194274 | − | 0.980947i | \(-0.562235\pi\) | ||||
−0.194274 | + | 0.980947i | \(0.562235\pi\) | |||||||
\(240\) | −3.46410 | − | 1.73205i | −0.223607 | − | 0.111803i | ||||
\(241\) | 22.8990 | 1.47505 | 0.737526 | − | 0.675318i | \(-0.235994\pi\) | ||||
0.737526 | + | 0.675318i | \(0.235994\pi\) | |||||||
\(242\) | 7.49245 | + | 7.49245i | 0.481633 | + | 0.481633i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.707107 | − | 0.707107i | ||||
\(244\) | − | 4.44949i | − | 0.284849i | ||||||
\(245\) | 1.97846 | + | 5.93537i | 0.126399 | + | 0.379197i | ||||
\(246\) | 4.89898 | 0.312348 | ||||||||
\(247\) | −2.20204 | + | 2.20204i | −0.140113 | + | 0.140113i | ||||
\(248\) | 0.707107 | − | 0.707107i | 0.0449013 | − | 0.0449013i | ||||
\(249\) | 1.55708 | 0.0986758 | ||||||||
\(250\) | 11.0000 | − | 2.00000i | 0.695701 | − | 0.126491i | ||||
\(251\) | 18.8776i | 1.19154i | 0.803154 | + | 0.595771i | \(0.203154\pi\) | ||||
−0.803154 | + | 0.595771i | \(0.796846\pi\) | |||||||
\(252\) | −4.34847 | + | 4.34847i | −0.273928 | + | 0.273928i | ||||
\(253\) | 1.10102 | + | 1.10102i | 0.0692206 | + | 0.0692206i | ||||
\(254\) | 7.84961 | 0.492528 | ||||||||
\(255\) | −5.44949 | − | 16.3485i | −0.341260 | − | 1.02378i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.3636 | − | 13.3636i | −0.833598 | − | 0.833598i | 0.154409 | − | 0.988007i | \(-0.450653\pi\) |
−0.988007 | + | 0.154409i | \(0.950653\pi\) | |||||||
\(258\) | −4.24264 | + | 4.24264i | −0.264135 | + | 0.264135i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.635674 | + | 1.27135i | −0.0394229 | + | 0.0788457i | ||||
\(261\) | 8.48528i | 0.525226i | ||||||||
\(262\) | −7.44949 | + | 7.44949i | −0.460231 | + | 0.460231i | ||||
\(263\) | 19.9740 | − | 19.9740i | 1.23165 | − | 1.23165i | 0.268316 | − | 0.963331i | \(-0.413533\pi\) |
0.963331 | − | 0.268316i | \(-0.0864673\pi\) | |||||||
\(264\) | − | 1.10102i | − | 0.0677631i | ||||||
\(265\) | 6.00000 | − | 12.0000i | 0.368577 | − | 0.737154i | ||||
\(266\) | 10.0424i | 0.615737i | ||||||||
\(267\) | −22.3417 | − | 22.3417i | −1.36729 | − | 1.36729i | ||||
\(268\) | −8.44949 | − | 8.44949i | −0.516135 | − | 0.516135i | ||||
\(269\) | −5.65685 | −0.344904 | −0.172452 | − | 0.985018i | \(-0.555169\pi\) | ||||
−0.172452 | + | 0.985018i | \(0.555169\pi\) | |||||||
\(270\) | −11.0227 | + | 3.67423i | −0.670820 | + | 0.223607i | ||||
\(271\) | −13.7980 | −0.838166 | −0.419083 | − | 0.907948i | \(-0.637648\pi\) | ||||
−0.419083 | + | 0.907948i | \(0.637648\pi\) | |||||||
\(272\) | 3.14626 | + | 3.14626i | 0.190770 | + | 0.190770i | ||||
\(273\) | 1.59592 | + | 1.59592i | 0.0965893 | + | 0.0965893i | ||||
\(274\) | − | 19.1464i | − | 1.15668i | ||||||
\(275\) | 1.90702 | + | 2.54270i | 0.114998 | + | 0.153330i | ||||
\(276\) | 4.24264i | 0.255377i | ||||||||
\(277\) | −17.3485 | + | 17.3485i | −1.04237 | + | 1.04237i | −0.0433067 | + | 0.999062i | \(0.513789\pi\) |
−0.999062 | + | 0.0433067i | \(0.986211\pi\) | |||||||
\(278\) | 9.58166 | − | 9.58166i | 0.574670 | − | 0.574670i | ||||
\(279\) | − | 3.00000i | − | 0.179605i | ||||||
\(280\) | 1.44949 | + | 4.34847i | 0.0866236 | + | 0.259871i | ||||
\(281\) | 5.65685i | 0.337460i | 0.985662 | + | 0.168730i | \(0.0539665\pi\) | ||||
−0.985662 | + | 0.168730i | \(0.946033\pi\) | |||||||
\(282\) | 9.79796 | − | 9.79796i | 0.583460 | − | 0.583460i | ||||
\(283\) | 6.24745 | + | 6.24745i | 0.371372 | + | 0.371372i | 0.867977 | − | 0.496605i | \(-0.165420\pi\) |
−0.496605 | + | 0.867977i | \(0.665420\pi\) | |||||||
\(284\) | 9.12096 | 0.541229 | ||||||||
\(285\) | −8.48528 | + | 16.9706i | −0.502625 | + | 1.00525i | ||||
\(286\) | −0.404082 | −0.0238939 | ||||||||
\(287\) | −4.09978 | − | 4.09978i | −0.242002 | − | 0.242002i | ||||
\(288\) | 2.12132 | − | 2.12132i | 0.125000 | − | 0.125000i | ||||
\(289\) | 2.79796i | 0.164586i | ||||||||
\(290\) | 5.65685 | + | 2.82843i | 0.332182 | + | 0.166091i | ||||
\(291\) | −7.34847 | −0.430775 | ||||||||
\(292\) | 4.89898 | − | 4.89898i | 0.286691 | − | 0.286691i | ||||
\(293\) | −12.7279 | + | 12.7279i | −0.743573 | + | 0.743573i | −0.973264 | − | 0.229691i | \(-0.926229\pi\) |
0.229691 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(294\) | −4.84621 | −0.282637 | ||||||||
\(295\) | −7.65153 | + | 2.55051i | −0.445489 | + | 0.148496i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.33562 | − | 2.33562i | −0.135526 | − | 0.135526i | ||||
\(298\) | −4.79796 | − | 4.79796i | −0.277938 | − | 0.277938i | ||||
\(299\) | 1.55708 | 0.0900482 | ||||||||
\(300\) | −1.22474 | + | 8.57321i | −0.0707107 | + | 0.494975i | ||||
\(301\) | 7.10102 | 0.409296 | ||||||||
\(302\) | 5.02118 | + | 5.02118i | 0.288936 | + | 0.288936i | ||||
\(303\) | −12.1244 | + | 12.1244i | −0.696526 | + | 0.696526i | ||||
\(304\) | − | 4.89898i | − | 0.280976i | ||||||
\(305\) | −9.43879 | + | 3.14626i | −0.540464 | + | 0.180155i | ||||
\(306\) | 13.3485 | 0.763081 | ||||||||
\(307\) | 3.34847 | − | 3.34847i | 0.191107 | − | 0.191107i | −0.605067 | − | 0.796174i | \(-0.706854\pi\) |
0.796174 | + | 0.605067i | \(0.206854\pi\) | |||||||
\(308\) | −0.921404 | + | 0.921404i | −0.0525018 | + | 0.0525018i | ||||
\(309\) | 8.44949i | 0.480675i | ||||||||
\(310\) | −2.00000 | − | 1.00000i | −0.113592 | − | 0.0567962i | ||||
\(311\) | 26.0915i | 1.47951i | 0.672874 | + | 0.739757i | \(0.265060\pi\) | ||||
−0.672874 | + | 0.739757i | \(0.734940\pi\) | |||||||
\(312\) | −0.778539 | − | 0.778539i | −0.0440761 | − | 0.0440761i | ||||
\(313\) | −14.8990 | − | 14.8990i | −0.842140 | − | 0.842140i | 0.146997 | − | 0.989137i | \(-0.453039\pi\) |
−0.989137 | + | 0.146997i | \(0.953039\pi\) | |||||||
\(314\) | 23.8988 | 1.34869 | ||||||||
\(315\) | 12.2993 | + | 6.14966i | 0.692989 | + | 0.346494i | ||||
\(316\) | 8.89898 | 0.500607 | ||||||||
\(317\) | −11.1708 | − | 11.1708i | −0.627417 | − | 0.627417i | 0.320000 | − | 0.947417i | \(-0.396317\pi\) |
−0.947417 | + | 0.320000i | \(0.896317\pi\) | |||||||
\(318\) | 7.34847 | + | 7.34847i | 0.412082 | + | 0.412082i | ||||
\(319\) | 1.79796i | 0.100666i | ||||||||
\(320\) | −0.707107 | − | 2.12132i | −0.0395285 | − | 0.118585i | ||||
\(321\) | 1.90702i | 0.106440i | ||||||||
\(322\) | 3.55051 | − | 3.55051i | 0.197862 | − | 0.197862i | ||||
\(323\) | 15.4135 | − | 15.4135i | 0.857629 | − | 0.857629i | ||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | 3.14643 | + | 0.449490i | 0.174532 | + | 0.0249332i | ||||
\(326\) | 24.5344i | 1.35884i | ||||||||
\(327\) | 8.44949 | − | 8.44949i | 0.467258 | − | 0.467258i | ||||
\(328\) | 2.00000 | + | 2.00000i | 0.110432 | + | 0.110432i | ||||
\(329\) | −16.3991 | −0.904112 | ||||||||
\(330\) | −2.33562 | + | 0.778539i | −0.128571 | + | 0.0428572i | ||||
\(331\) | −4.24745 | −0.233461 | −0.116730 | − | 0.993164i | \(-0.537241\pi\) | ||||
−0.116730 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(332\) | 0.635674 | + | 0.635674i | 0.0348872 | + | 0.0348872i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.1464i | 0.938211i | ||||||||
\(335\) | −11.9494 | + | 23.8988i | −0.652865 | + | 1.30573i | ||||
\(336\) | −3.55051 | −0.193696 | ||||||||
\(337\) | 4.89898 | − | 4.89898i | 0.266864 | − | 0.266864i | −0.560971 | − | 0.827835i | \(-0.689572\pi\) |
0.827835 | + | 0.560971i | \(0.189572\pi\) | |||||||
\(338\) | 8.90666 | − | 8.90666i | 0.484458 | − | 0.484458i | ||||
\(339\) | 13.5065 | 0.733570 | ||||||||
\(340\) | 4.44949 | − | 8.89898i | 0.241307 | − | 0.482615i | ||||
\(341\) | − | 0.635674i | − | 0.0344237i | ||||||
\(342\) | −10.3923 | − | 10.3923i | −0.561951 | − | 0.561951i | ||||
\(343\) | 14.2020 | + | 14.2020i | 0.766838 | + | 0.766838i | ||||
\(344\) | −3.46410 | −0.186772 | ||||||||
\(345\) | 9.00000 | − | 3.00000i | 0.484544 | − | 0.161515i | ||||
\(346\) | 0.202041 | 0.0108618 | ||||||||
\(347\) | −10.6780 | − | 10.6780i | −0.573227 | − | 0.573227i | 0.359802 | − | 0.933029i | \(-0.382844\pi\) |
−0.933029 | + | 0.359802i | \(0.882844\pi\) | |||||||
\(348\) | −3.46410 | + | 3.46410i | −0.185695 | + | 0.185695i | ||||
\(349\) | 31.3939i | 1.68048i | 0.542218 | + | 0.840238i | \(0.317585\pi\) | ||||
−0.542218 | + | 0.840238i | \(0.682415\pi\) | |||||||
\(350\) | 8.19955 | − | 6.14966i | 0.438285 | − | 0.328713i | ||||
\(351\) | −3.30306 | −0.176304 | ||||||||
\(352\) | 0.449490 | − | 0.449490i | 0.0239579 | − | 0.0239579i | ||||
\(353\) | 10.7101 | − | 10.7101i | 0.570043 | − | 0.570043i | −0.362097 | − | 0.932140i | \(-0.617939\pi\) |
0.932140 | + | 0.362097i | \(0.117939\pi\) | |||||||
\(354\) | − | 6.24745i | − | 0.332048i | ||||||
\(355\) | −6.44949 | − | 19.3485i | −0.342303 | − | 1.02691i | ||||
\(356\) | − | 18.2419i | − | 0.966819i | ||||||
\(357\) | −11.1708 | − | 11.1708i | −0.591224 | − | 0.591224i | ||||
\(358\) | −2.65153 | − | 2.65153i | −0.140138 | − | 0.140138i | ||||
\(359\) | 3.74983 | 0.197908 | 0.0989542 | − | 0.995092i | \(-0.468450\pi\) | ||||
0.0989542 | + | 0.995092i | \(0.468450\pi\) | |||||||
\(360\) | −6.00000 | − | 3.00000i | −0.316228 | − | 0.158114i | ||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | −2.51059 | − | 2.51059i | −0.131954 | − | 0.131954i | ||||
\(363\) | 12.9773 | + | 12.9773i | 0.681131 | + | 0.681131i | ||||
\(364\) | 1.30306i | 0.0682990i | ||||||||
\(365\) | −13.8564 | − | 6.92820i | −0.725277 | − | 0.362639i | ||||
\(366\) | − | 7.70674i | − | 0.402838i | ||||||
\(367\) | 3.55051 | − | 3.55051i | 0.185335 | − | 0.185335i | −0.608341 | − | 0.793676i | \(-0.708165\pi\) |
0.793676 | + | 0.608341i | \(0.208165\pi\) | |||||||
\(368\) | −1.73205 | + | 1.73205i | −0.0902894 | + | 0.0902894i | ||||
\(369\) | 8.48528 | 0.441726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 12.2993i | − | 0.638549i | ||||||
\(372\) | 1.22474 | − | 1.22474i | 0.0635001 | − | 0.0635001i | ||||
\(373\) | −10.0000 | − | 10.0000i | −0.517780 | − | 0.517780i | 0.399119 | − | 0.916899i | \(-0.369316\pi\) |
−0.916899 | + | 0.399119i | \(0.869316\pi\) | |||||||
\(374\) | 2.82843 | 0.146254 | ||||||||
\(375\) | 19.0526 | − | 3.46410i | 0.983870 | − | 0.178885i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 1.27135 | + | 1.27135i | 0.0654778 | + | 0.0654778i | ||||
\(378\) | −7.53177 | + | 7.53177i | −0.387392 | + | 0.387392i | ||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | −10.3923 | + | 3.46410i | −0.533114 | + | 0.177705i | ||||
\(381\) | 13.5959 | 0.696540 | ||||||||
\(382\) | −15.3485 | + | 15.3485i | −0.785296 | + | 0.785296i | ||||
\(383\) | 6.11756 | − | 6.11756i | 0.312593 | − | 0.312593i | −0.533321 | − | 0.845913i | \(-0.679056\pi\) |
0.845913 | + | 0.533321i | \(0.179056\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 2.60612 | + | 1.30306i | 0.132820 | + | 0.0664102i | ||||
\(386\) | − | 9.89949i | − | 0.503871i | ||||||
\(387\) | −7.34847 | + | 7.34847i | −0.373544 | + | 0.373544i | ||||
\(388\) | −3.00000 | − | 3.00000i | −0.152302 | − | 0.152302i | ||||
\(389\) | −21.0703 | −1.06831 | −0.534154 | − | 0.845387i | \(-0.679370\pi\) | ||||
−0.534154 | + | 0.845387i | \(0.679370\pi\) | |||||||
\(390\) | −1.10102 | + | 2.20204i | −0.0557523 | + | 0.111505i | ||||
\(391\) | −10.8990 | −0.551185 | ||||||||
\(392\) | −1.97846 | − | 1.97846i | −0.0999271 | − | 0.0999271i | ||||
\(393\) | −12.9029 | + | 12.9029i | −0.650865 | + | 0.650865i | ||||
\(394\) | 6.89898i | 0.347566i | ||||||||
\(395\) | −6.29253 | − | 18.8776i | −0.316611 | − | 0.949834i | ||||
\(396\) | − | 1.90702i | − | 0.0958315i | ||||||
\(397\) | −16.6969 | + | 16.6969i | −0.837995 | + | 0.837995i | −0.988595 | − | 0.150600i | \(-0.951880\pi\) |
0.150600 | + | 0.988595i | \(0.451880\pi\) | |||||||
\(398\) | 7.56388 | − | 7.56388i | 0.379143 | − | 0.379143i | ||||
\(399\) | 17.3939i | 0.870783i | ||||||||
\(400\) | −4.00000 | + | 3.00000i | −0.200000 | + | 0.150000i | ||||
\(401\) | − | 4.38551i | − | 0.219002i | −0.993987 | − | 0.109501i | \(-0.965075\pi\) | ||
0.993987 | − | 0.109501i | \(-0.0349252\pi\) | |||||||
\(402\) | −14.6349 | − | 14.6349i | −0.729925 | − | 0.729925i | ||||
\(403\) | −0.449490 | − | 0.449490i | −0.0223907 | − | 0.0223907i | ||||
\(404\) | −9.89949 | −0.492518 | ||||||||
\(405\) | −19.0919 | + | 6.36396i | −0.948683 | + | 0.316228i | ||||
\(406\) | 5.79796 | 0.287748 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.44949 | + | 5.44949i | 0.269790 | + | 0.269790i | ||||
\(409\) | 31.3939i | 1.55233i | 0.630532 | + | 0.776164i | \(0.282837\pi\) | ||||
−0.630532 | + | 0.776164i | \(0.717163\pi\) | |||||||
\(410\) | 2.82843 | − | 5.65685i | 0.139686 | − | 0.279372i | ||||
\(411\) | − | 33.1626i | − | 1.63579i | ||||||
\(412\) | −3.44949 | + | 3.44949i | −0.169944 | + | 0.169944i | ||||
\(413\) | −5.22826 | + | 5.22826i | −0.257266 | + | 0.257266i | ||||
\(414\) | 7.34847i | 0.361158i | ||||||||
\(415\) | 0.898979 | − | 1.79796i | 0.0441292 | − | 0.0882583i | ||||
\(416\) | − | 0.635674i | − | 0.0311665i | ||||||
\(417\) | 16.5959 | − | 16.5959i | 0.812706 | − | 0.812706i | ||||
\(418\) | −2.20204 | − | 2.20204i | −0.107705 | − | 0.107705i | ||||
\(419\) | 35.9910 | 1.75828 | 0.879138 | − | 0.476567i | \(-0.158119\pi\) | ||||
0.879138 | + | 0.476567i | \(0.158119\pi\) | |||||||
\(420\) | 2.51059 | + | 7.53177i | 0.122504 | + | 0.367513i | ||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | −16.0492 | − | 16.0492i | −0.781261 | − | 0.781261i | ||||
\(423\) | 16.9706 | − | 16.9706i | 0.825137 | − | 0.825137i | ||||
\(424\) | 6.00000i | 0.291386i | ||||||||
\(425\) | −22.0239 | − | 3.14626i | −1.06831 | − | 0.152616i | ||||
\(426\) | 15.7980 | 0.765414 | ||||||||
\(427\) | −6.44949 | + | 6.44949i | −0.312113 | + | 0.312113i | ||||
\(428\) | −0.778539 | + | 0.778539i | −0.0376321 | + | 0.0376321i | ||||
\(429\) | −0.699891 | −0.0337910 | ||||||||
\(430\) | 2.44949 | + | 7.34847i | 0.118125 | + | 0.354375i | ||||
\(431\) | 27.6486i | 1.33179i | 0.746047 | + | 0.665893i | \(0.231949\pi\) | ||||
−0.746047 | + | 0.665893i | \(0.768051\pi\) | |||||||
\(432\) | 3.67423 | − | 3.67423i | 0.176777 | − | 0.176777i | ||||
\(433\) | 9.79796 | + | 9.79796i | 0.470860 | + | 0.470860i | 0.902193 | − | 0.431333i | \(-0.141957\pi\) |
−0.431333 | + | 0.902193i | \(0.641957\pi\) | |||||||
\(434\) | −2.04989 | −0.0983978 | ||||||||
\(435\) | 9.79796 | + | 4.89898i | 0.469776 | + | 0.234888i | ||||
\(436\) | 6.89898 | 0.330401 | ||||||||
\(437\) | 8.48528 | + | 8.48528i | 0.405906 | + | 0.405906i | ||||
\(438\) | 8.48528 | − | 8.48528i | 0.405442 | − | 0.405442i | ||||
\(439\) | 6.89898i | 0.329270i | 0.986355 | + | 0.164635i | \(0.0526447\pi\) | ||||
−0.986355 | + | 0.164635i | \(0.947355\pi\) | |||||||
\(440\) | −1.27135 | − | 0.635674i | −0.0606092 | − | 0.0303046i | ||||
\(441\) | −8.39388 | −0.399708 | ||||||||
\(442\) | 2.00000 | − | 2.00000i | 0.0951303 | − | 0.0951303i | ||||
\(443\) | −12.0922 | + | 12.0922i | −0.574520 | + | 0.574520i | −0.933388 | − | 0.358868i | \(-0.883163\pi\) |
0.358868 | + | 0.933388i | \(0.383163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.6969 | + | 12.8990i | −1.83441 | + | 0.611470i | ||||
\(446\) | 11.9494i | 0.565820i | ||||||||
\(447\) | −8.31031 | − | 8.31031i | −0.393064 | − | 0.393064i | ||||
\(448\) | −1.44949 | − | 1.44949i | −0.0684820 | − | 0.0684820i | ||||
\(449\) | −10.0424 | −0.473928 | −0.236964 | − | 0.971518i | \(-0.576152\pi\) | ||||
−0.236964 | + | 0.971518i | \(0.576152\pi\) | |||||||
\(450\) | −2.12132 | + | 14.8492i | −0.100000 | + | 0.700000i | ||||
\(451\) | 1.79796 | 0.0846626 | ||||||||
\(452\) | 5.51399 | + | 5.51399i | 0.259356 | + | 0.259356i | ||||
\(453\) | 8.69694 | + | 8.69694i | 0.408618 | + | 0.408618i | ||||
\(454\) | 18.8990i | 0.886973i | ||||||||
\(455\) | 2.76421 | − | 0.921404i | 0.129588 | − | 0.0431961i | ||||
\(456\) | − | 8.48528i | − | 0.397360i | ||||||
\(457\) | 16.8990 | − | 16.8990i | 0.790501 | − | 0.790501i | −0.191075 | − | 0.981576i | \(-0.561197\pi\) |
0.981576 | + | 0.191075i | \(0.0611972\pi\) | |||||||
\(458\) | 8.16744 | − | 8.16744i | 0.381640 | − | 0.381640i | ||||
\(459\) | 23.1202 | 1.07916 | ||||||||
\(460\) | 4.89898 | + | 2.44949i | 0.228416 | + | 0.114208i | ||||
\(461\) | 3.11416i | 0.145041i | 0.997367 | + | 0.0725204i | \(0.0231042\pi\) | ||||
−0.997367 | + | 0.0725204i | \(0.976896\pi\) | |||||||
\(462\) | −1.59592 | + | 1.59592i | −0.0742488 | + | 0.0742488i | ||||
\(463\) | 11.3485 | + | 11.3485i | 0.527408 | + | 0.527408i | 0.919799 | − | 0.392391i | \(-0.128352\pi\) |
−0.392391 | + | 0.919799i | \(0.628352\pi\) | |||||||
\(464\) | −2.82843 | −0.131306 | ||||||||
\(465\) | −3.46410 | − | 1.73205i | −0.160644 | − | 0.0803219i | ||||
\(466\) | 1.10102 | 0.0510038 | ||||||||
\(467\) | 28.4914 | + | 28.4914i | 1.31842 | + | 1.31842i | 0.915025 | + | 0.403398i | \(0.132171\pi\) |
0.403398 | + | 0.915025i | \(0.367829\pi\) | |||||||
\(468\) | −1.34847 | − | 1.34847i | −0.0623330 | − | 0.0623330i | ||||
\(469\) | 24.4949i | 1.13107i | ||||||||
\(470\) | −5.65685 | − | 16.9706i | −0.260931 | − | 0.782794i | ||||
\(471\) | 41.3939 | 1.90733 | ||||||||
\(472\) | 2.55051 | − | 2.55051i | 0.117397 | − | 0.117397i | ||||
\(473\) | −1.55708 | + | 1.55708i | −0.0715945 | + | 0.0715945i | ||||
\(474\) | 15.4135 | 0.707965 | ||||||||
\(475\) | 14.6969 | + | 19.5959i | 0.674342 | + | 0.899122i | ||||
\(476\) | − | 9.12096i | − | 0.418058i | ||||||
\(477\) | 12.7279 | + | 12.7279i | 0.582772 | + | 0.582772i | ||||
\(478\) | −4.24745 | − | 4.24745i | −0.194274 | − | 0.194274i | ||||
\(479\) | −26.0915 | −1.19215 | −0.596076 | − | 0.802928i | \(-0.703274\pi\) | ||||
−0.596076 | + | 0.802928i | \(0.703274\pi\) | |||||||
\(480\) | −1.22474 | − | 3.67423i | −0.0559017 | − | 0.167705i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 16.1920 | + | 16.1920i | 0.737526 | + | 0.737526i | ||||
\(483\) | 6.14966 | − | 6.14966i | 0.279819 | − | 0.279819i | ||||
\(484\) | 10.5959i | 0.481633i | ||||||||
\(485\) | −4.24264 | + | 8.48528i | −0.192648 | + | 0.385297i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | 17.1464 | − | 17.1464i | 0.776979 | − | 0.776979i | −0.202337 | − | 0.979316i | \(-0.564854\pi\) |
0.979316 | + | 0.202337i | \(0.0648537\pi\) | |||||||
\(488\) | 3.14626 | − | 3.14626i | 0.142425 | − | 0.142425i | ||||
\(489\) | 42.4949i | 1.92169i | ||||||||
\(490\) | −2.79796 | + | 5.59592i | −0.126399 | + | 0.252798i | ||||
\(491\) | 18.5919i | 0.839039i | 0.907746 | + | 0.419519i | \(0.137801\pi\) | ||||
−0.907746 | + | 0.419519i | \(0.862199\pi\) | |||||||
\(492\) | 3.46410 | + | 3.46410i | 0.156174 | + | 0.156174i | ||||
\(493\) | −8.89898 | − | 8.89898i | −0.400790 | − | 0.400790i | ||||
\(494\) | −3.11416 | −0.140113 | ||||||||
\(495\) | −4.04541 | + | 1.34847i | −0.181828 | + | 0.0606092i | ||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −13.2207 | − | 13.2207i | −0.593031 | − | 0.593031i | ||||
\(498\) | 1.10102 | + | 1.10102i | 0.0493379 | + | 0.0493379i | ||||
\(499\) | − | 5.55051i | − | 0.248475i | −0.992253 | − | 0.124237i | \(-0.960352\pi\) | ||
0.992253 | − | 0.124237i | \(-0.0396485\pi\) | |||||||
\(500\) | 9.19239 | + | 6.36396i | 0.411096 | + | 0.284605i | ||||
\(501\) | 29.6985i | 1.32683i | ||||||||
\(502\) | −13.3485 | + | 13.3485i | −0.595771 | + | 0.595771i | ||||
\(503\) | −24.2487 | + | 24.2487i | −1.08120 | + | 1.08120i | −0.0847985 | + | 0.996398i | \(0.527025\pi\) |
−0.996398 | + | 0.0847985i | \(0.972975\pi\) | |||||||
\(504\) | −6.14966 | −0.273928 | ||||||||
\(505\) | 7.00000 | + | 21.0000i | 0.311496 | + | 0.934488i | ||||
\(506\) | 1.55708i | 0.0692206i | ||||||||
\(507\) | 15.4268 | − | 15.4268i | 0.685128 | − | 0.685128i | ||||
\(508\) | 5.55051 | + | 5.55051i | 0.246264 | + | 0.246264i | ||||
\(509\) | −17.9562 | −0.795894 | −0.397947 | − | 0.917408i | \(-0.630277\pi\) | ||||
−0.397947 | + | 0.917408i | \(0.630277\pi\) | |||||||
\(510\) | 7.70674 | − | 15.4135i | 0.341260 | − | 0.682521i | ||||
\(511\) | −14.2020 | −0.628261 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −18.0000 | − | 18.0000i | −0.794719 | − | 0.794719i | ||||
\(514\) | − | 18.8990i | − | 0.833598i | ||||||
\(515\) | 9.75663 | + | 4.87832i | 0.429929 | + | 0.214964i | ||||
\(516\) | −6.00000 | −0.264135 | ||||||||
\(517\) | 3.59592 | − | 3.59592i | 0.158148 | − | 0.158148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.349945 | 0.0153609 | ||||||||
\(520\) | −1.34847 | + | 0.449490i | −0.0591343 | + | 0.0197114i | ||||
\(521\) | − | 25.1701i | − | 1.10272i | −0.834267 | − | 0.551361i | \(-0.814109\pi\) | ||
0.834267 | − | 0.551361i | \(-0.185891\pi\) | |||||||
\(522\) | −6.00000 | + | 6.00000i | −0.262613 | + | 0.262613i | ||||
\(523\) | 31.5959 | + | 31.5959i | 1.38159 | + | 1.38159i | 0.841794 | + | 0.539799i | \(0.181500\pi\) |
0.539799 | + | 0.841794i | \(0.318500\pi\) | |||||||
\(524\) | −10.5352 | −0.460231 | ||||||||
\(525\) | 14.2020 | − | 10.6515i | 0.619828 | − | 0.464871i | ||||
\(526\) | 28.2474 | 1.23165 | ||||||||
\(527\) | 3.14626 | + | 3.14626i | 0.137053 | + | 0.137053i | ||||
\(528\) | 0.778539 | − | 0.778539i | 0.0338816 | − | 0.0338816i | ||||
\(529\) | 17.0000i | 0.739130i | ||||||||
\(530\) | 12.7279 | − | 4.24264i | 0.552866 | − | 0.184289i | ||||
\(531\) | − | 10.8209i | − | 0.469587i | ||||||
\(532\) | −7.10102 | + | 7.10102i | −0.307868 | + | 0.307868i | ||||
\(533\) | 1.27135 | − | 1.27135i | 0.0550682 | − | 0.0550682i | ||||
\(534\) | − | 31.5959i | − | 1.36729i | ||||||
\(535\) | 2.20204 | + | 1.10102i | 0.0952025 | + | 0.0476013i | ||||
\(536\) | − | 11.9494i | − | 0.516135i | ||||||
\(537\) | −4.59259 | − | 4.59259i | −0.198185 | − | 0.198185i | ||||
\(538\) | −4.00000 | − | 4.00000i | −0.172452 | − | 0.172452i | ||||
\(539\) | −1.77859 | −0.0766093 | ||||||||
\(540\) | −10.3923 | − | 5.19615i | −0.447214 | − | 0.223607i | ||||
\(541\) | 24.6969 | 1.06180 | 0.530902 | − | 0.847433i | \(-0.321853\pi\) | ||||
0.530902 | + | 0.847433i | \(0.321853\pi\) | |||||||
\(542\) | −9.75663 | − | 9.75663i | −0.419083 | − | 0.419083i | ||||
\(543\) | −4.34847 | − | 4.34847i | −0.186611 | − | 0.186611i | ||||
\(544\) | 4.44949i | 0.190770i | ||||||||
\(545\) | −4.87832 | − | 14.6349i | −0.208964 | − | 0.626892i | ||||
\(546\) | 2.25697i | 0.0965893i | ||||||||
\(547\) | −8.24745 | + | 8.24745i | −0.352635 | + | 0.352635i | −0.861089 | − | 0.508454i | \(-0.830217\pi\) |
0.508454 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(548\) | 13.5386 | − | 13.5386i | 0.578339 | − | 0.578339i | ||||
\(549\) | − | 13.3485i | − | 0.569699i | ||||||
\(550\) | −0.449490 | + | 3.14643i | −0.0191663 | + | 0.134164i | ||||
\(551\) | 13.8564i | 0.590303i | ||||||||
\(552\) | −3.00000 | + | 3.00000i | −0.127688 | + | 0.127688i | ||||
\(553\) | −12.8990 | − | 12.8990i | −0.548520 | − | 0.548520i | ||||
\(554\) | −24.5344 | −1.04237 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.5505 | 0.574670 | ||||||||
\(557\) | 17.7491 | + | 17.7491i | 0.752054 | + | 0.752054i | 0.974862 | − | 0.222809i | \(-0.0715225\pi\) |
−0.222809 | + | 0.974862i | \(0.571523\pi\) | |||||||
\(558\) | 2.12132 | − | 2.12132i | 0.0898027 | − | 0.0898027i | ||||
\(559\) | 2.20204i | 0.0931364i | ||||||||
\(560\) | −2.04989 | + | 4.09978i | −0.0866236 | + | 0.173247i | ||||
\(561\) | 4.89898 | 0.206835 | ||||||||
\(562\) | −4.00000 | + | 4.00000i | −0.168730 | + | 0.168730i | ||||
\(563\) | 8.48528 | − | 8.48528i | 0.357612 | − | 0.357612i | −0.505320 | − | 0.862932i | \(-0.668626\pi\) |
0.862932 | + | 0.505320i | \(0.168626\pi\) | |||||||
\(564\) | 13.8564 | 0.583460 | ||||||||
\(565\) | 7.79796 | − | 15.5959i | 0.328063 | − | 0.656125i | ||||
\(566\) | 8.83523i | 0.371372i | ||||||||
\(567\) | −13.0454 | + | 13.0454i | −0.547856 | + | 0.547856i | ||||
\(568\) | 6.44949 | + | 6.44949i | 0.270615 | + | 0.270615i | ||||
\(569\) | −34.5768 | −1.44953 | −0.724767 | − | 0.688994i | \(-0.758053\pi\) | ||||
−0.724767 | + | 0.688994i | \(0.758053\pi\) | |||||||
\(570\) | −18.0000 | + | 6.00000i | −0.753937 | + | 0.251312i | ||||
\(571\) | −18.9444 | −0.792798 | −0.396399 | − | 0.918078i | \(-0.629740\pi\) | ||||
−0.396399 | + | 0.918078i | \(0.629740\pi\) | |||||||
\(572\) | −0.285729 | − | 0.285729i | −0.0119469 | − | 0.0119469i | ||||
\(573\) | −26.5843 | + | 26.5843i | −1.11058 | + | 1.11058i | ||||
\(574\) | − | 5.79796i | − | 0.242002i | ||||||
\(575\) | 1.73205 | − | 12.1244i | 0.0722315 | − | 0.505621i | ||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | −10.7980 | + | 10.7980i | −0.449525 | + | 0.449525i | −0.895197 | − | 0.445672i | \(-0.852965\pi\) |
0.445672 | + | 0.895197i | \(0.352965\pi\) | |||||||
\(578\) | −1.97846 | + | 1.97846i | −0.0822929 | + | 0.0822929i | ||||
\(579\) | − | 17.1464i | − | 0.712581i | ||||||
\(580\) | 2.00000 | + | 6.00000i | 0.0830455 | + | 0.249136i | ||||
\(581\) | − | 1.84281i | − | 0.0764525i | ||||||
\(582\) | −5.19615 | − | 5.19615i | −0.215387 | − | 0.215387i | ||||
\(583\) | 2.69694 | + | 2.69694i | 0.111696 | + | 0.111696i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | −1.90702 | + | 3.81405i | −0.0788457 | + | 0.157691i | ||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 17.6062 | + | 17.6062i | 0.726687 | + | 0.726687i | 0.969958 | − | 0.243271i | \(-0.0782205\pi\) |
−0.243271 | + | 0.969958i | \(0.578220\pi\) | |||||||
\(588\) | −3.42679 | − | 3.42679i | −0.141318 | − | 0.141318i | ||||
\(589\) | − | 4.89898i | − | 0.201859i | ||||||
\(590\) | −7.21393 | − | 3.60697i | −0.296993 | − | 0.148496i | ||||
\(591\) | 11.9494i | 0.491532i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.5631 | + | 21.5631i | −0.885492 | + | 0.885492i | −0.994086 | − | 0.108594i | \(-0.965365\pi\) |
0.108594 | + | 0.994086i | \(0.465365\pi\) | |||||||
\(594\) | − | 3.30306i | − | 0.135526i | ||||||
\(595\) | −19.3485 | + | 6.44949i | −0.793210 | + | 0.264403i | ||||
\(596\) | − | 6.78534i | − | 0.277938i | ||||||
\(597\) | 13.1010 | − | 13.1010i | 0.536189 | − | 0.536189i | ||||
\(598\) | 1.10102 | + | 1.10102i | 0.0450241 | + | 0.0450241i | ||||
\(599\) | −16.3349 | −0.667425 | −0.333713 | − | 0.942675i | \(-0.608302\pi\) | ||||
−0.333713 | + | 0.942675i | \(0.608302\pi\) | |||||||
\(600\) | −6.92820 | + | 5.19615i | −0.282843 | + | 0.212132i | ||||
\(601\) | −5.10102 | −0.208075 | −0.104037 | − | 0.994573i | \(-0.533176\pi\) | ||||
−0.104037 | + | 0.994573i | \(0.533176\pi\) | |||||||
\(602\) | 5.02118 | + | 5.02118i | 0.204648 | + | 0.204648i | ||||
\(603\) | −25.3485 | − | 25.3485i | −1.03227 | − | 1.03227i | ||||
\(604\) | 7.10102i | 0.288936i | ||||||||
\(605\) | 22.4773 | − | 7.49245i | 0.913834 | − | 0.304611i | ||||
\(606\) | −17.1464 | −0.696526 | ||||||||
\(607\) | −1.44949 | + | 1.44949i | −0.0588330 | + | 0.0588330i | −0.735911 | − | 0.677078i | \(-0.763246\pi\) |
0.677078 | + | 0.735911i | \(0.263246\pi\) | |||||||
\(608\) | 3.46410 | − | 3.46410i | 0.140488 | − | 0.140488i | ||||
\(609\) | 10.0424 | 0.406937 | ||||||||
\(610\) | −8.89898 | − | 4.44949i | −0.360309 | − | 0.180155i | ||||
\(611\) | − | 5.08540i | − | 0.205733i | ||||||
\(612\) | 9.43879 | + | 9.43879i | 0.381541 | + | 0.381541i | ||||
\(613\) | 28.0454 | + | 28.0454i | 1.13274 | + | 1.13274i | 0.989719 | + | 0.143024i | \(0.0456827\pi\) |
0.143024 | + | 0.989719i | \(0.454317\pi\) | |||||||
\(614\) | 4.73545 | 0.191107 | ||||||||
\(615\) | 4.89898 | − | 9.79796i | 0.197546 | − | 0.395092i | ||||
\(616\) | −1.30306 | −0.0525018 | ||||||||
\(617\) | 18.7347 | + | 18.7347i | 0.754231 | + | 0.754231i | 0.975266 | − | 0.221034i | \(-0.0709433\pi\) |
−0.221034 | + | 0.975266i | \(0.570943\pi\) | |||||||
\(618\) | −5.97469 | + | 5.97469i | −0.240337 | + | 0.240337i | ||||
\(619\) | 10.9444i | 0.439892i | 0.975512 | + | 0.219946i | \(0.0705881\pi\) | ||||
−0.975512 | + | 0.219946i | \(0.929412\pi\) | |||||||
\(620\) | −0.707107 | − | 2.12132i | −0.0283981 | − | 0.0851943i | ||||
\(621\) | 12.7279i | 0.510754i | ||||||||
\(622\) | −18.4495 | + | 18.4495i | −0.739757 | + | 0.739757i | ||||
\(623\) | −26.4415 | + | 26.4415i | −1.05935 | + | 1.05935i | ||||
\(624\) | − | 1.10102i | − | 0.0440761i | ||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | − | 21.0703i | − | 0.842140i | ||||||
\(627\) | −3.81405 | − | 3.81405i | −0.152318 | − | 0.152318i | ||||
\(628\) | 16.8990 | + | 16.8990i | 0.674343 | + | 0.674343i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 4.34847 | + | 13.0454i | 0.173247 | + | 0.519741i | ||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | 6.29253 | + | 6.29253i | 0.250303 | + | 0.250303i | ||||
\(633\) | −27.7980 | − | 27.7980i | −1.10487 | − | 1.10487i | ||||
\(634\) | − | 15.7980i | − | 0.627417i | ||||||
\(635\) | 7.84961 | − | 15.6992i | 0.311502 | − | 0.623004i | ||||
\(636\) | 10.3923i | 0.412082i | ||||||||
\(637\) | −1.25765 | + | 1.25765i | −0.0498301 | + | 0.0498301i | ||||
\(638\) | −1.27135 | + | 1.27135i | −0.0503332 | + | 0.0503332i | ||||
\(639\) | 27.3629 | 1.08246 | ||||||||
\(640\) | 1.00000 | − | 2.00000i | 0.0395285 | − | 0.0790569i | ||||
\(641\) | − | 13.2207i | − | 0.522188i | −0.965313 | − | 0.261094i | \(-0.915917\pi\) | ||
0.965313 | − | 0.261094i | \(-0.0840832\pi\) | |||||||
\(642\) | −1.34847 | + | 1.34847i | −0.0532198 | + | 0.0532198i | ||||
\(643\) | −12.0000 | − | 12.0000i | −0.473234 | − | 0.473234i | 0.429726 | − | 0.902959i | \(-0.358610\pi\) |
−0.902959 | + | 0.429726i | \(0.858610\pi\) | |||||||
\(644\) | 5.02118 | 0.197862 | ||||||||
\(645\) | 4.24264 | + | 12.7279i | 0.167054 | + | 0.501161i | ||||
\(646\) | 21.7980 | 0.857629 | ||||||||
\(647\) | −9.93160 | − | 9.93160i | −0.390452 | − | 0.390452i | 0.484397 | − | 0.874848i | \(-0.339039\pi\) |
−0.874848 | + | 0.484397i | \(0.839039\pi\) | |||||||
\(648\) | 6.36396 | − | 6.36396i | 0.250000 | − | 0.250000i | ||||
\(649\) | − | 2.29286i | − | 0.0900025i | ||||||
\(650\) | 1.90702 | + | 2.54270i | 0.0747996 | + | 0.0997328i | ||||
\(651\) | −3.55051 | −0.139155 | ||||||||
\(652\) | −17.3485 | + | 17.3485i | −0.679418 | + | 0.679418i | ||||
\(653\) | 30.8270 | − | 30.8270i | 1.20635 | − | 1.20635i | 0.234153 | − | 0.972200i | \(-0.424768\pi\) |
0.972200 | − | 0.234153i | \(-0.0752316\pi\) | |||||||
\(654\) | 11.9494 | 0.467258 | ||||||||
\(655\) | 7.44949 | + | 22.3485i | 0.291076 | + | 0.873227i | ||||
\(656\) | 2.82843i | 0.110432i | ||||||||
\(657\) | 14.6969 | − | 14.6969i | 0.573382 | − | 0.573382i | ||||
\(658\) | −11.5959 | − | 11.5959i | −0.452056 | − | 0.452056i | ||||
\(659\) | 17.4634 | 0.680276 | 0.340138 | − | 0.940375i | \(-0.389526\pi\) | ||||
0.340138 | + | 0.940375i | \(0.389526\pi\) | |||||||
\(660\) | −2.20204 | − | 1.10102i | −0.0857143 | − | 0.0428572i | ||||
\(661\) | −2.00000 | −0.0777910 | −0.0388955 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388955 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(662\) | −3.00340 | − | 3.00340i | −0.116730 | − | 0.116730i | ||||
\(663\) | 3.46410 | − | 3.46410i | 0.134535 | − | 0.134535i | ||||
\(664\) | 0.898979i | 0.0348872i | ||||||||
\(665\) | 20.0847 | + | 10.0424i | 0.778852 | + | 0.389426i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.89898 | − | 4.89898i | 0.189689 | − | 0.189689i | ||||
\(668\) | −12.1244 | + | 12.1244i | −0.469105 | + | 0.469105i | ||||
\(669\) | 20.6969i | 0.800190i | ||||||||
\(670\) | −25.3485 | + | 8.44949i | −0.979297 | + | 0.326432i | ||||
\(671\) | − | 2.82843i | − | 0.109190i | ||||||
\(672\) | −2.51059 | − | 2.51059i | −0.0968481 | − | 0.0968481i | ||||
\(673\) | 15.7980 | + | 15.7980i | 0.608967 | + | 0.608967i | 0.942676 | − | 0.333709i | \(-0.108300\pi\) |
−0.333709 | + | 0.942676i | \(0.608300\pi\) | |||||||
\(674\) | 6.92820 | 0.266864 | ||||||||
\(675\) | −3.67423 | + | 25.7196i | −0.141421 | + | 0.989949i | ||||
\(676\) | 12.5959 | 0.484458 | ||||||||
\(677\) | −12.7279 | − | 12.7279i | −0.489174 | − | 0.489174i | 0.418872 | − | 0.908045i | \(-0.362426\pi\) |
−0.908045 | + | 0.418872i | \(0.862426\pi\) | |||||||
\(678\) | 9.55051 | + | 9.55051i | 0.366785 | + | 0.366785i | ||||
\(679\) | 8.69694i | 0.333758i | ||||||||
\(680\) | 9.43879 | − | 3.14626i | 0.361961 | − | 0.120654i | ||||
\(681\) | 32.7340i | 1.25437i | ||||||||
\(682\) | 0.449490 | − | 0.449490i | 0.0172119 | − | 0.0172119i | ||||
\(683\) | 9.26382 | − | 9.26382i | 0.354470 | − | 0.354470i | −0.507300 | − | 0.861770i | \(-0.669356\pi\) |
0.861770 | + | 0.507300i | \(0.169356\pi\) | |||||||
\(684\) | − | 14.6969i | − | 0.561951i | ||||||
\(685\) | −38.2929 | − | 19.1464i | −1.46309 | − | 0.731547i | ||||
\(686\) | 20.0847i | 0.766838i | ||||||||
\(687\) | 14.1464 | − | 14.1464i | 0.539720 | − | 0.539720i | ||||
\(688\) | −2.44949 | − | 2.44949i | −0.0933859 | − | 0.0933859i | ||||
\(689\) | 3.81405 | 0.145304 | ||||||||
\(690\) | 8.48528 | + | 4.24264i | 0.323029 | + | 0.161515i | ||||
\(691\) | −28.4949 | −1.08400 | −0.541998 | − | 0.840379i | \(-0.682332\pi\) | ||||
−0.541998 | + | 0.840379i | \(0.682332\pi\) | |||||||
\(692\) | 0.142865 | + | 0.142865i | 0.00543090 | + | 0.00543090i | ||||
\(693\) | −2.76421 | + | 2.76421i | −0.105004 | + | 0.105004i | ||||
\(694\) | − | 15.1010i | − | 0.573227i | ||||||
\(695\) | −9.58166 | − | 28.7450i | −0.363453 | − | 1.09036i | ||||
\(696\) | −4.89898 | −0.185695 | ||||||||
\(697\) | −8.89898 | + | 8.89898i | −0.337073 | + | 0.337073i | ||||
\(698\) | −22.1988 | + | 22.1988i | −0.840238 | + | 0.840238i | ||||
\(699\) | 1.90702 | 0.0721303 | ||||||||
\(700\) | 10.1464 | + | 1.44949i | 0.383499 | + | 0.0547856i | ||||
\(701\) | 1.69994i | 0.0642060i | 0.999485 | + | 0.0321030i | \(0.0102205\pi\) | ||||
−0.999485 | + | 0.0321030i | \(0.989780\pi\) | |||||||
\(702\) | −2.33562 | − | 2.33562i | −0.0881522 | − | 0.0881522i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.635674 | 0.0239579 | ||||||||
\(705\) | −9.79796 | − | 29.3939i | −0.369012 | − | 1.10704i | ||||
\(706\) | 15.1464 | 0.570043 | ||||||||
\(707\) | 14.3492 | + | 14.3492i | 0.539658 | + | 0.539658i | ||||
\(708\) | 4.41761 | − | 4.41761i | 0.166024 | − | 0.166024i | ||||
\(709\) | 32.0454i | 1.20349i | 0.798688 | + | 0.601745i | \(0.205528\pi\) | ||||
−0.798688 | + | 0.601745i | \(0.794472\pi\) | |||||||
\(710\) | 9.12096 | − | 18.2419i | 0.342303 | − | 0.684607i | ||||
\(711\) | 26.6969 | 1.00121 | ||||||||
\(712\) | 12.8990 | − | 12.8990i | 0.483410 | − | 0.483410i | ||||
\(713\) | −1.73205 | + | 1.73205i | −0.0648658 | + | 0.0648658i | ||||
\(714\) | − | 15.7980i | − | 0.591224i | ||||||
\(715\) | −0.404082 | + | 0.808164i | −0.0151118 | + | 0.0302236i | ||||
\(716\) | − | 3.74983i | − | 0.140138i | ||||||
\(717\) | −7.35680 | − | 7.35680i | −0.274745 | − | 0.274745i | ||||
\(718\) | 2.65153 | + | 2.65153i | 0.0989542 | + | 0.0989542i | ||||
\(719\) | 0.921404 | 0.0343626 | 0.0171813 | − | 0.999852i | \(-0.494531\pi\) | ||||
0.0171813 | + | 0.999852i | \(0.494531\pi\) | |||||||
\(720\) | −2.12132 | − | 6.36396i | −0.0790569 | − | 0.237171i | ||||
\(721\) | 10.0000 | 0.372419 | ||||||||
\(722\) | −3.53553 | − | 3.53553i | −0.131579 | − | 0.131579i | ||||
\(723\) | 28.0454 | + | 28.0454i | 1.04302 | + | 1.04302i | ||||
\(724\) | − | 3.55051i | − | 0.131954i | ||||||
\(725\) | 11.3137 | − | 8.48528i | 0.420181 | − | 0.315135i | ||||
\(726\) | 18.3527i | 0.681131i | ||||||||
\(727\) | 20.1464 | − | 20.1464i | 0.747190 | − | 0.747190i | −0.226761 | − | 0.973950i | \(-0.572814\pi\) |
0.973950 | + | 0.226761i | \(0.0728136\pi\) | |||||||
\(728\) | −0.921404 | + | 0.921404i | −0.0341495 | + | 0.0341495i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | −4.89898 | − | 14.6969i | −0.181319 | − | 0.543958i | ||||
\(731\) | − | 15.4135i | − | 0.570088i | ||||||
\(732\) | 5.44949 | − | 5.44949i | 0.201419 | − | 0.201419i | ||||
\(733\) | −27.3939 | − | 27.3939i | −1.01182 | − | 1.01182i | −0.999929 | − | 0.0118866i | \(-0.996216\pi\) |
−0.0118866 | − | 0.999929i | \(-0.503784\pi\) | |||||||
\(734\) | 5.02118 | 0.185335 | ||||||||
\(735\) | −4.84621 | + | 9.69241i | −0.178755 | + | 0.357510i | ||||
\(736\) | −2.44949 | −0.0902894 | ||||||||
\(737\) | −5.37113 | − | 5.37113i | −0.197848 | − | 0.197848i | ||||
\(738\) | 6.00000 | + | 6.00000i | 0.220863 | + | 0.220863i | ||||
\(739\) | − | 42.9444i | − | 1.57973i | −0.613278 | − | 0.789867i | \(-0.710149\pi\) | ||
0.613278 | − | 0.789867i | \(-0.289851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.39388 | −0.198149 | ||||||||
\(742\) | 8.69694 | − | 8.69694i | 0.319275 | − | 0.319275i | ||||
\(743\) | −3.92480 | + | 3.92480i | −0.143987 | + | 0.143987i | −0.775426 | − | 0.631439i | \(-0.782465\pi\) |
0.631439 | + | 0.775426i | \(0.282465\pi\) | |||||||
\(744\) | 1.73205 | 0.0635001 | ||||||||
\(745\) | −14.3939 | + | 4.79796i | −0.527351 | + | 0.175784i | ||||
\(746\) | − | 14.1421i | − | 0.517780i | ||||||
\(747\) | 1.90702 | + | 1.90702i | 0.0697743 | + | 0.0697743i | ||||
\(748\) | 2.00000 | + | 2.00000i | 0.0731272 | + | 0.0731272i | ||||
\(749\) | 2.25697 | 0.0824678 | ||||||||
\(750\) | 15.9217 | + | 11.0227i | 0.581378 | + | 0.402492i | ||||
\(751\) | −32.6969 | −1.19313 | −0.596564 | − | 0.802565i | \(-0.703468\pi\) | ||||
−0.596564 | + | 0.802565i | \(0.703468\pi\) | |||||||
\(752\) | 5.65685 | + | 5.65685i | 0.206284 | + | 0.206284i | ||||
\(753\) | −23.1202 | + | 23.1202i | −0.842548 | + | 0.842548i | ||||
\(754\) | 1.79796i | 0.0654778i | ||||||||
\(755\) | 15.0635 | − | 5.02118i | 0.548218 | − | 0.182739i | ||||
\(756\) | −10.6515 | −0.387392 | ||||||||
\(757\) | 13.3485 | − | 13.3485i | 0.485158 | − | 0.485158i | −0.421616 | − | 0.906774i | \(-0.638537\pi\) |
0.906774 | + | 0.421616i | \(0.138537\pi\) | |||||||
\(758\) | −8.48528 | + | 8.48528i | −0.308199 | + | 0.308199i | ||||
\(759\) | 2.69694i | 0.0978927i | ||||||||
\(760\) | −9.79796 | − | 4.89898i | −0.355409 | − | 0.177705i | ||||
\(761\) | − | 49.0689i | − | 1.77875i | −0.457183 | − | 0.889373i | \(-0.651141\pi\) | ||
0.457183 | − | 0.889373i | \(-0.348859\pi\) | |||||||
\(762\) | 9.61377 | + | 9.61377i | 0.348270 | + | 0.348270i | ||||
\(763\) | −10.0000 | − | 10.0000i | −0.362024 | − | 0.362024i | ||||
\(764\) | −21.7060 | −0.785296 | ||||||||
\(765\) | 13.3485 | − | 26.6969i | 0.482615 | − | 0.965230i | ||||
\(766\) | 8.65153 | 0.312593 | ||||||||
\(767\) | −1.62129 | − | 1.62129i | −0.0585415 | − | 0.0585415i | ||||
\(768\) | 1.22474 | + | 1.22474i | 0.0441942 | + | 0.0441942i | ||||
\(769\) | 27.5959i | 0.995134i | 0.867425 | + | 0.497567i | \(0.165773\pi\) | ||||
−0.867425 | + | 0.497567i | \(0.834227\pi\) | |||||||
\(770\) | 0.921404 | + | 2.76421i | 0.0332051 | + | 0.0996152i | ||||
\(771\) | − | 32.7340i | − | 1.17889i | ||||||
\(772\) | 7.00000 | − | 7.00000i | 0.251936 | − | 0.251936i | ||||
\(773\) | −10.2494 | + | 10.2494i | −0.368647 | + | 0.368647i | −0.866984 | − | 0.498337i | \(-0.833944\pi\) |
0.498337 | + | 0.866984i | \(0.333944\pi\) | |||||||
\(774\) | −10.3923 | −0.373544 | ||||||||
\(775\) | −4.00000 | + | 3.00000i | −0.143684 | + | 0.107763i | ||||
\(776\) | − | 4.24264i | − | 0.152302i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.8990 | − | 14.8990i | −0.534154 | − | 0.534154i | ||||
\(779\) | 13.8564 | 0.496457 | ||||||||
\(780\) | −2.33562 | + | 0.778539i | −0.0836285 | + | 0.0278762i | ||||
\(781\) | 5.79796 | 0.207467 | ||||||||
\(782\) | −7.70674 | − | 7.70674i | −0.275593 | − | 0.275593i | ||||
\(783\) | −10.3923 | + | 10.3923i | −0.371391 | + | 0.371391i | ||||
\(784\) | − | 2.79796i | − | 0.0999271i | ||||||
\(785\) | 23.8988 | − | 47.7975i | 0.852984 | − | 1.70597i | ||||
\(786\) | −18.2474 | −0.650865 | ||||||||
\(787\) | 8.65153 | − | 8.65153i | 0.308394 | − | 0.308394i | −0.535892 | − | 0.844286i | \(-0.680025\pi\) |
0.844286 | + | 0.535892i | \(0.180025\pi\) | |||||||
\(788\) | −4.87832 | + | 4.87832i | −0.173783 | + | 0.173783i | ||||
\(789\) | 48.9260 | 1.74181 | ||||||||
\(790\) | 8.89898 | − | 17.7980i | 0.316611 | − | 0.633223i | ||||
\(791\) | − | 15.9849i | − | 0.568359i | ||||||
\(792\) | 1.34847 | − | 1.34847i | 0.0479158 | − | 0.0479158i | ||||
\(793\) | −2.00000 | − | 2.00000i | −0.0710221 | − | 0.0710221i | ||||
\(794\) | −23.6130 | −0.837995 | ||||||||
\(795\) | 22.0454 | − | 7.34847i | 0.781870 | − | 0.260623i | ||||
\(796\) | 10.6969 | 0.379143 | ||||||||
\(797\) | −16.4778 | − | 16.4778i | −0.583672 | − | 0.583672i | 0.352238 | − | 0.935910i | \(-0.385421\pi\) |
−0.935910 | + | 0.352238i | \(0.885421\pi\) | |||||||
\(798\) | −12.2993 | + | 12.2993i | −0.435392 | + | 0.435392i | ||||
\(799\) | 35.5959i | 1.25929i | ||||||||
\(800\) | −4.94975 | − | 0.707107i | −0.175000 | − | 0.0250000i | ||||
\(801\) | − | 54.7257i | − | 1.93364i | ||||||
\(802\) | 3.10102 | − | 3.10102i | 0.109501 | − | 0.109501i | ||||
\(803\) | 3.11416 | − | 3.11416i | 0.109896 | − | 0.109896i | ||||
\(804\) | − | 20.6969i | − | 0.729925i | ||||||
\(805\) | −3.55051 | − | 10.6515i | −0.125139 | − | 0.375417i | ||||
\(806\) | − | 0.635674i | − | 0.0223907i | ||||||
\(807\) | −6.92820 | − | 6.92820i | −0.243884 | − | 0.243884i | ||||
\(808\) | −7.00000 | − | 7.00000i | −0.246259 | − | 0.246259i | ||||
\(809\) | 34.6410 | 1.21791 | 0.608957 | − | 0.793204i | \(-0.291588\pi\) | ||||
0.608957 | + | 0.793204i | \(0.291588\pi\) | |||||||
\(810\) | −18.0000 | − | 9.00000i | −0.632456 | − | 0.316228i | ||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 4.09978 | + | 4.09978i | 0.143874 | + | 0.143874i | ||||
\(813\) | −16.8990 | − | 16.8990i | −0.592673 | − | 0.592673i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49.0689 | + | 24.5344i | 1.71881 | + | 0.859404i | ||||
\(816\) | 7.70674i | 0.269790i | ||||||||
\(817\) | −12.0000 | + | 12.0000i | −0.419827 | + | 0.419827i | ||||
\(818\) | −22.1988 | + | 22.1988i | −0.776164 | + | 0.776164i | ||||
\(819\) | 3.90918i | 0.136598i | ||||||||
\(820\) | 6.00000 | − | 2.00000i | 0.209529 | − | 0.0698430i | ||||
\(821\) | 45.9547i | 1.60383i | 0.597438 | + | 0.801915i | \(0.296186\pi\) | ||||
−0.597438 | + | 0.801915i | \(0.703814\pi\) | |||||||
\(822\) | 23.4495 | − | 23.4495i | 0.817895 | − | 0.817895i | ||||
\(823\) | −25.1464 | − | 25.1464i | −0.876549 | − | 0.876549i | 0.116626 | − | 0.993176i | \(-0.462792\pi\) |
−0.993176 | + | 0.116626i | \(0.962792\pi\) | |||||||
\(824\) | −4.87832 | −0.169944 | ||||||||
\(825\) | −0.778539 | + | 5.44977i | −0.0271053 | + | 0.189737i | ||||
\(826\) | −7.39388 | −0.257266 | ||||||||
\(827\) | 37.1195 | + | 37.1195i | 1.29077 | + | 1.29077i | 0.934310 | + | 0.356461i | \(0.116017\pi\) |
0.356461 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(828\) | −5.19615 | + | 5.19615i | −0.180579 | + | 0.180579i | ||||
\(829\) | − | 30.6515i | − | 1.06457i | −0.846565 | − | 0.532286i | \(-0.821333\pi\) | ||
0.846565 | − | 0.532286i | \(-0.178667\pi\) | |||||||
\(830\) | 1.90702 | − | 0.635674i | 0.0661938 | − | 0.0220646i | ||||
\(831\) | −42.4949 | −1.47413 | ||||||||
\(832\) | 0.449490 | − | 0.449490i | 0.0155833 | − | 0.0155833i | ||||
\(833\) | 8.80312 | − | 8.80312i | 0.305010 | − | 0.305010i | ||||
\(834\) | 23.4702 | 0.812706 | ||||||||
\(835\) | 34.2929 | + | 17.1464i | 1.18675 | + | 0.593377i | ||||
\(836\) | − | 3.11416i | − | 0.107705i | ||||||
\(837\) | 3.67423 | − | 3.67423i | 0.127000 | − | 0.127000i | ||||
\(838\) | 25.4495 | + | 25.4495i | 0.879138 | + | 0.879138i | ||||
\(839\) | 33.3055 | 1.14983 | 0.574916 | − | 0.818212i | \(-0.305035\pi\) | ||||
0.574916 | + | 0.818212i | \(0.305035\pi\) | |||||||
\(840\) | −3.55051 | + | 7.10102i | −0.122504 | + | 0.245008i | ||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | −1.41421 | − | 1.41421i | −0.0487370 | − | 0.0487370i | ||||
\(843\) | −6.92820 | + | 6.92820i | −0.238620 | + | 0.238620i | ||||
\(844\) | − | 22.6969i | − | 0.781261i | ||||||
\(845\) | −8.90666 | − | 26.7200i | −0.306398 | − | 0.919195i | ||||
\(846\) | 24.0000 | 0.825137 | ||||||||
\(847\) | 15.3587 | − | 15.3587i | 0.527730 | − | 0.527730i | ||||
\(848\) | −4.24264 | + | 4.24264i | −0.145693 | + | 0.145693i | ||||
\(849\) | 15.3031i | 0.525200i | ||||||||
\(850\) | −13.3485 | − | 17.7980i | −0.457849 | − | 0.610465i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 11.1708 | + | 11.1708i | 0.382707 | + | 0.382707i | ||||
\(853\) | 20.0000 | + | 20.0000i | 0.684787 | + | 0.684787i | 0.961075 | − | 0.276288i | \(-0.0891043\pi\) |
−0.276288 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(854\) | −9.12096 | −0.312113 | ||||||||
\(855\) | −31.1769 | + | 10.3923i | −1.06623 | + | 0.355409i | ||||
\(856\) | −1.10102 | −0.0376321 | ||||||||
\(857\) | 11.1708 | + | 11.1708i | 0.381589 | + | 0.381589i | 0.871674 | − | 0.490086i | \(-0.163034\pi\) |
−0.490086 | + | 0.871674i | \(0.663034\pi\) | |||||||
\(858\) | −0.494897 | − | 0.494897i | −0.0168955 | − | 0.0168955i | ||||
\(859\) | − | 39.8434i | − | 1.35944i | −0.733473 | − | 0.679719i | \(-0.762102\pi\) | ||
0.733473 | − | 0.679719i | \(-0.237898\pi\) | |||||||
\(860\) | −3.46410 | + | 6.92820i | −0.118125 | + | 0.236250i | ||||
\(861\) | − | 10.0424i | − | 0.342243i | ||||||
\(862\) | −19.5505 | + | 19.5505i | −0.665893 | + | 0.665893i | ||||
\(863\) | −39.4872 | + | 39.4872i | −1.34416 | + | 1.34416i | −0.452290 | + | 0.891871i | \(0.649393\pi\) |
−0.891871 | + | 0.452290i | \(0.850607\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | 0.202041 | − | 0.404082i | 0.00686960 | − | 0.0137392i | ||||
\(866\) | 13.8564i | 0.470860i | ||||||||
\(867\) | −3.42679 | + | 3.42679i | −0.116380 | + | 0.116380i | ||||
\(868\) | −1.44949 | − | 1.44949i | −0.0491989 | − | 0.0491989i | ||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | 3.46410 | + | 10.3923i | 0.117444 | + | 0.352332i | ||||
\(871\) | −7.59592 | −0.257378 | ||||||||
\(872\) | 4.87832 | + | 4.87832i | 0.165201 | + | 0.165201i | ||||
\(873\) | −9.00000 | − | 9.00000i | −0.304604 | − | 0.304604i | ||||
\(874\) | 12.0000i | 0.405906i | ||||||||
\(875\) | −4.09978 | − | 22.5488i | −0.138598 | − | 0.762288i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 20.8990 | − | 20.8990i | 0.705708 | − | 0.705708i | −0.259921 | − | 0.965630i | \(-0.583697\pi\) |
0.965630 | + | 0.259921i | \(0.0836967\pi\) | |||||||
\(878\) | −4.87832 | + | 4.87832i | −0.164635 | + | 0.164635i | ||||
\(879\) | −31.1769 | −1.05157 | ||||||||
\(880\) | −0.449490 | − | 1.34847i | −0.0151523 | − | 0.0454569i | ||||
\(881\) | 5.02118i | 0.169168i | 0.996416 | + | 0.0845839i | \(0.0269561\pi\) | ||||
−0.996416 | + | 0.0845839i | \(0.973044\pi\) | |||||||
\(882\) | −5.93537 | − | 5.93537i | −0.199854 | − | 0.199854i | ||||
\(883\) | 19.1010 | + | 19.1010i | 0.642801 | + | 0.642801i | 0.951243 | − | 0.308442i | \(-0.0998077\pi\) |
−0.308442 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(884\) | 2.82843 | 0.0951303 | ||||||||
\(885\) | −12.4949 | − | 6.24745i | −0.420011 | − | 0.210006i | ||||
\(886\) | −17.1010 | −0.574520 | ||||||||
\(887\) | 23.8988 | + | 23.8988i | 0.802442 | + | 0.802442i | 0.983477 | − | 0.181035i | \(-0.0579446\pi\) |
−0.181035 | + | 0.983477i | \(0.557945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.0908i | − | 0.539669i | ||||||
\(890\) | −36.4838 | − | 18.2419i | −1.22294 | − | 0.611470i | ||||
\(891\) | − | 5.72107i | − | 0.191663i | ||||||
\(892\) | −8.44949 | + | 8.44949i | −0.282910 | + | 0.282910i | ||||
\(893\) | 27.7128 | − | 27.7128i | 0.927374 | − | 0.927374i | ||||
\(894\) | − | 11.7526i | − | 0.393064i | ||||||
\(895\) | −7.95459 | + | 2.65153i | −0.265893 | + | 0.0886309i | ||||
\(896\) | − | 2.04989i | − | 0.0684820i | ||||||
\(897\) | 1.90702 | + | 1.90702i | 0.0636737 | + | 0.0636737i | ||||
\(898\) | −7.10102 | − | 7.10102i | −0.236964 | − | 0.236964i | ||||
\(899\) | −2.82843 | −0.0943333 | ||||||||
\(900\) | −12.0000 | + | 9.00000i | −0.400000 | + | 0.300000i | ||||
\(901\) | −26.6969 | −0.889404 | ||||||||
\(902\) | 1.27135 | + | 1.27135i | 0.0423313 | + | 0.0423313i | ||||
\(903\) | 8.69694 | + | 8.69694i | 0.289416 | + | 0.289416i | ||||
\(904\) | 7.79796i | 0.259356i | ||||||||
\(905\) | −7.53177 | + | 2.51059i | −0.250364 | + | 0.0834548i | ||||
\(906\) | 12.2993i | 0.408618i | ||||||||
\(907\) | −26.9444 | + | 26.9444i | −0.894674 | + | 0.894674i | −0.994959 | − | 0.100285i | \(-0.968025\pi\) |
0.100285 | + | 0.994959i | \(0.468025\pi\) | |||||||
\(908\) | −13.3636 | + | 13.3636i | −0.443487 | + | 0.443487i | ||||
\(909\) | −29.6985 | −0.985037 | ||||||||
\(910\) | 2.60612 | + | 1.30306i | 0.0863921 | + | 0.0431961i | ||||
\(911\) | − | 22.6274i | − | 0.749680i | −0.927090 | − | 0.374840i | \(-0.877698\pi\) | ||
0.927090 | − | 0.374840i | \(-0.122302\pi\) | |||||||
\(912\) | 6.00000 | − | 6.00000i | 0.198680 | − | 0.198680i | ||||
\(913\) | 0.404082 | + | 0.404082i | 0.0133732 | + | 0.0133732i | ||||
\(914\) | 23.8988 | 0.790501 | ||||||||
\(915\) | −15.4135 | − | 7.70674i | −0.509554 | − | 0.254777i | ||||
\(916\) | 11.5505 | 0.381640 | ||||||||
\(917\) | 15.2706 | + | 15.2706i | 0.504280 | + | 0.504280i | ||||
\(918\) | 16.3485 | + | 16.3485i | 0.539580 | + | 0.539580i | ||||
\(919\) | − | 47.1918i | − | 1.55672i | −0.627821 | − | 0.778358i | \(-0.716053\pi\) | ||
0.627821 | − | 0.778358i | \(-0.283947\pi\) | |||||||
\(920\) | 1.73205 | + | 5.19615i | 0.0571040 | + | 0.171312i | ||||
\(921\) | 8.20204 | 0.270266 | ||||||||
\(922\) | −2.20204 | + | 2.20204i | −0.0725204 | + | 0.0725204i | ||||
\(923\) | 4.09978 | − | 4.09978i | 0.134946 | − | 0.134946i | ||||
\(924\) | −2.25697 | −0.0742488 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.0492i | 0.527408i | ||||||||
\(927\) | −10.3485 | + | 10.3485i | −0.339888 | + | 0.339888i | ||||
\(928\) | −2.00000 | − | 2.00000i | −0.0656532 | − | 0.0656532i | ||||
\(929\) | −20.1489 | −0.661065 | −0.330533 | − | 0.943795i | \(-0.607228\pi\) | ||||
−0.330533 | + | 0.943795i | \(0.607228\pi\) | |||||||
\(930\) | −1.22474 | − | 3.67423i | −0.0401610 | − | 0.120483i | ||||
\(931\) | −13.7071 | −0.449233 | ||||||||
\(932\) | 0.778539 | + | 0.778539i | 0.0255019 | + | 0.0255019i | ||||
\(933\) | −31.9555 | + | 31.9555i | −1.04617 | + | 1.04617i | ||||
\(934\) | 40.2929i | 1.31842i | ||||||||
\(935\) | 2.82843 | − | 5.65685i | 0.0924995 | − | 0.184999i | ||||
\(936\) | − | 1.90702i | − | 0.0623330i | ||||||
\(937\) | 10.5959 | − | 10.5959i | 0.346154 | − | 0.346154i | −0.512521 | − | 0.858675i | \(-0.671288\pi\) |
0.858675 | + | 0.512521i | \(0.171288\pi\) | |||||||
\(938\) | −17.3205 | + | 17.3205i | −0.565535 | + | 0.565535i | ||||
\(939\) | − | 36.4949i | − | 1.19097i | ||||||
\(940\) | 8.00000 | − | 16.0000i | 0.260931 | − | 0.521862i | ||||
\(941\) | − | 50.0545i | − | 1.63173i | −0.578242 | − | 0.815865i | \(-0.696261\pi\) | ||
0.578242 | − | 0.815865i | \(-0.303739\pi\) | |||||||
\(942\) | 29.2699 | + | 29.2699i | 0.953665 | + | 0.953665i | ||||
\(943\) | −4.89898 | − | 4.89898i | −0.159533 | − | 0.159533i | ||||
\(944\) | 3.60697 | 0.117397 | ||||||||
\(945\) | 7.53177 | + | 22.5953i | 0.245008 | + | 0.735025i | ||||
\(946\) | −2.20204 | −0.0715945 | ||||||||
\(947\) | −30.8270 | − | 30.8270i | −1.00174 | − | 1.00174i | −0.999998 | − | 0.00174342i | \(-0.999445\pi\) |
−0.00174342 | − | 0.999998i | \(-0.500555\pi\) | |||||||
\(948\) | 10.8990 | + | 10.8990i | 0.353982 | + | 0.353982i | ||||
\(949\) | − | 4.40408i | − | 0.142963i | ||||||
\(950\) | −3.46410 | + | 24.2487i | −0.112390 | + | 0.786732i | ||||
\(951\) | − | 27.3629i | − | 0.887302i | ||||||
\(952\) | 6.44949 | − | 6.44949i | 0.209029 | − | 0.209029i | ||||
\(953\) | 19.4812 | − | 19.4812i | 0.631056 | − | 0.631056i | −0.317277 | − | 0.948333i | \(-0.602768\pi\) |
0.948333 | + | 0.317277i | \(0.102768\pi\) | |||||||
\(954\) | 18.0000i | 0.582772i | ||||||||
\(955\) | 15.3485 | + | 46.0454i | 0.496665 | + | 1.48999i | ||||
\(956\) | − | 6.00680i | − | 0.194274i | ||||||
\(957\) | −2.20204 | + | 2.20204i | −0.0711819 | + | 0.0711819i | ||||
\(958\) | −18.4495 | − | 18.4495i | −0.596076 | − | 0.596076i | ||||
\(959\) | −39.2480 | −1.26739 | ||||||||
\(960\) | 1.73205 | − | 3.46410i | 0.0559017 | − | 0.111803i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.33562 | + | 2.33562i | −0.0752642 | + | 0.0752642i | ||||
\(964\) | 22.8990i | 0.737526i | ||||||||
\(965\) | −19.7990 | − | 9.89949i | −0.637352 | − | 0.318676i | ||||
\(966\) | 8.69694 | 0.279819 | ||||||||
\(967\) | −25.8434 | + | 25.8434i | −0.831067 | + | 0.831067i | −0.987663 | − | 0.156596i | \(-0.949948\pi\) |
0.156596 | + | 0.987663i | \(0.449948\pi\) | |||||||
\(968\) | −7.49245 | + | 7.49245i | −0.240816 | + | 0.240816i | ||||
\(969\) | 37.7552 | 1.21287 | ||||||||
\(970\) | −9.00000 | + | 3.00000i | −0.288973 | + | 0.0963242i | ||||
\(971\) | − | 18.4490i | − | 0.592056i | −0.955179 | − | 0.296028i | \(-0.904338\pi\) | ||
0.955179 | − | 0.296028i | \(-0.0956622\pi\) | |||||||
\(972\) | 11.0227 | − | 11.0227i | 0.353553 | − | 0.353553i | ||||
\(973\) | −19.6413 | − | 19.6413i | −0.629672 | − | 0.629672i | ||||
\(974\) | 24.2487 | 0.776979 | ||||||||
\(975\) | 3.30306 | + | 4.40408i | 0.105783 | + | 0.141044i | ||||
\(976\) | 4.44949 | 0.142425 | ||||||||
\(977\) | −35.4196 | − | 35.4196i | −1.13317 | − | 1.13317i | −0.989647 | − | 0.143525i | \(-0.954156\pi\) |
−0.143525 | − | 0.989647i | \(-0.545844\pi\) | |||||||
\(978\) | −30.0484 | + | 30.0484i | −0.960843 | + | 0.960843i | ||||
\(979\) | − | 11.5959i | − | 0.370607i | ||||||
\(980\) | −5.93537 | + | 1.97846i | −0.189598 | + | 0.0631995i | ||||
\(981\) | 20.6969 | 0.660802 | ||||||||
\(982\) | −13.1464 | + | 13.1464i | −0.419519 | + | 0.419519i | ||||
\(983\) | −1.73205 | + | 1.73205i | −0.0552438 | + | 0.0552438i | −0.734189 | − | 0.678945i | \(-0.762437\pi\) |
0.678945 | + | 0.734189i | \(0.262437\pi\) | |||||||
\(984\) | 4.89898i | 0.156174i | ||||||||
\(985\) | 13.7980 | + | 6.89898i | 0.439640 | + | 0.219820i | ||||
\(986\) | − | 12.5851i | − | 0.400790i | ||||||
\(987\) | −20.0847 | − | 20.0847i | −0.639304 | − | 0.639304i | ||||
\(988\) | −2.20204 | − | 2.20204i | −0.0700563 | − | 0.0700563i | ||||
\(989\) | 8.48528 | 0.269816 | ||||||||
\(990\) | −3.81405 | − | 1.90702i | −0.121218 | − | 0.0606092i | ||||
\(991\) | 35.1010 | 1.11502 | 0.557510 | − | 0.830170i | \(-0.311757\pi\) | ||||
0.557510 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(992\) | 0.707107 | + | 0.707107i | 0.0224507 | + | 0.0224507i | ||||
\(993\) | −5.20204 | − | 5.20204i | −0.165082 | − | 0.165082i | ||||
\(994\) | − | 18.6969i | − | 0.593031i | ||||||
\(995\) | −7.56388 | − | 22.6916i | −0.239791 | − | 0.719373i | ||||
\(996\) | 1.55708i | 0.0493379i | ||||||||
\(997\) | 3.30306 | − | 3.30306i | 0.104609 | − | 0.104609i | −0.652865 | − | 0.757474i | \(-0.726433\pi\) |
0.757474 | + | 0.652865i | \(0.226433\pi\) | |||||||
\(998\) | 3.92480 | − | 3.92480i | 0.124237 | − | 0.124237i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 930.2.j.d.683.4 | yes | 8 | |
3.2 | odd | 2 | inner | 930.2.j.d.683.2 | yes | 8 | |
5.2 | odd | 4 | inner | 930.2.j.d.497.2 | ✓ | 8 | |
15.2 | even | 4 | inner | 930.2.j.d.497.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.d.497.2 | ✓ | 8 | 5.2 | odd | 4 | inner | |
930.2.j.d.497.4 | yes | 8 | 15.2 | even | 4 | inner | |
930.2.j.d.683.2 | yes | 8 | 3.2 | odd | 2 | inner | |
930.2.j.d.683.4 | yes | 8 | 1.1 | even | 1 | trivial |