Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,2,Mod(5,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("78.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.622833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.58498535041007616.52 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(-0.0980500 - 1.72927i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.5 |
Dual form | 78.2.g.a.47.3 |
$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.29211 | − | 1.15345i | 0.746002 | − | 0.665944i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.82732 | + | 1.82732i | 0.817204 | + | 0.817204i | 0.985702 | − | 0.168498i | \(-0.0538917\pi\) |
−0.168498 | + | 0.985702i | \(0.553892\pi\) | |||||||
\(6\) | −1.72927 | − | 0.0980500i | −0.705973 | − | 0.0400288i | ||||
\(7\) | −2.63122 | − | 2.63122i | −0.994509 | − | 0.994509i | 0.00547608 | − | 0.999985i | \(-0.498257\pi\) |
−0.999985 | + | 0.00547608i | \(0.998257\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0.339111 | − | 2.98077i | 0.113037 | − | 0.993591i | ||||
\(10\) | − | 2.58423i | − | 0.817204i | ||||||
\(11\) | −2.30690 | + | 2.30690i | −0.695556 | + | 0.695556i | −0.963449 | − | 0.267893i | \(-0.913673\pi\) |
0.267893 | + | 0.963449i | \(0.413673\pi\) | |||||||
\(12\) | 1.15345 | + | 1.29211i | 0.332972 | + | 0.373001i | ||||
\(13\) | 1.63122 | + | 3.21545i | 0.452420 | + | 0.891805i | ||||
\(14\) | 3.72111i | 0.994509i | ||||||||
\(15\) | 4.46883 | + | 0.253383i | 1.15385 | + | 0.0654233i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.34775 | −0.326877 | −0.163439 | − | 0.986554i | \(-0.552259\pi\) | ||||
−0.163439 | + | 0.986554i | \(0.552259\pi\) | |||||||
\(18\) | −2.34751 | + | 1.86794i | −0.553314 | + | 0.440277i | ||||
\(19\) | −3.58423 | + | 3.58423i | −0.822278 | + | 0.822278i | −0.986434 | − | 0.164157i | \(-0.947510\pi\) |
0.164157 | + | 0.986434i | \(0.447510\pi\) | |||||||
\(20\) | −1.82732 | + | 1.82732i | −0.408602 | + | 0.408602i | ||||
\(21\) | −6.43482 | − | 0.364855i | −1.40419 | − | 0.0796179i | ||||
\(22\) | 3.26245 | 0.695556 | ||||||||
\(23\) | 3.65465 | 0.762047 | 0.381023 | − | 0.924565i | \(-0.375572\pi\) | ||||
0.381023 | + | 0.924565i | \(0.375572\pi\) | |||||||
\(24\) | 0.0980500 | − | 1.72927i | 0.0200144 | − | 0.352986i | ||||
\(25\) | 1.67822i | 0.335644i | ||||||||
\(26\) | 1.12022 | − | 3.42711i | 0.219693 | − | 0.672112i | ||||
\(27\) | −3.00000 | − | 4.24264i | −0.577350 | − | 0.816497i | ||||
\(28\) | 2.63122 | − | 2.63122i | 0.497254 | − | 0.497254i | ||||
\(29\) | 3.65465i | 0.678651i | 0.940669 | + | 0.339325i | \(0.110199\pi\) | ||||
−0.940669 | + | 0.339325i | \(0.889801\pi\) | |||||||
\(30\) | −2.98077 | − | 3.33911i | −0.544212 | − | 0.609635i | ||||
\(31\) | 0.321779 | − | 0.321779i | 0.0577932 | − | 0.0577932i | −0.677619 | − | 0.735413i | \(-0.736988\pi\) |
0.735413 | + | 0.677619i | \(0.236988\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −0.319883 | + | 5.64166i | −0.0556845 | + | 0.982087i | ||||
\(34\) | 0.953002 | + | 0.953002i | 0.163439 | + | 0.163439i | ||||
\(35\) | − | 9.61619i | − | 1.62543i | ||||||
\(36\) | 2.98077 | + | 0.339111i | 0.496795 | + | 0.0565184i | ||||
\(37\) | 1.95300 | + | 1.95300i | 0.321072 | + | 0.321072i | 0.849178 | − | 0.528107i | \(-0.177098\pi\) |
−0.528107 | + | 0.849178i | \(0.677098\pi\) | |||||||
\(38\) | 5.06886 | 0.822278 | ||||||||
\(39\) | 5.81658 | + | 2.27319i | 0.931398 | + | 0.364002i | ||||
\(40\) | 2.58423 | 0.408602 | ||||||||
\(41\) | −7.89729 | − | 7.89729i | −1.23335 | − | 1.23335i | −0.962670 | − | 0.270680i | \(-0.912752\pi\) |
−0.270680 | − | 0.962670i | \(-0.587248\pi\) | |||||||
\(42\) | 4.29211 | + | 4.80810i | 0.662287 | + | 0.741905i | ||||
\(43\) | − | 9.10912i | − | 1.38913i | −0.719431 | − | 0.694564i | \(-0.755597\pi\) | ||
0.719431 | − | 0.694564i | \(-0.244403\pi\) | |||||||
\(44\) | −2.30690 | − | 2.30690i | −0.347778 | − | 0.347778i | ||||
\(45\) | 6.06650 | − | 4.82717i | 0.904340 | − | 0.719592i | ||||
\(46\) | −2.58423 | − | 2.58423i | −0.381023 | − | 0.381023i | ||||
\(47\) | 4.72222 | − | 4.72222i | 0.688806 | − | 0.688806i | −0.273162 | − | 0.961968i | \(-0.588070\pi\) |
0.961968 | + | 0.273162i | \(0.0880695\pi\) | |||||||
\(48\) | −1.29211 | + | 1.15345i | −0.186500 | + | 0.166486i | ||||
\(49\) | 6.84667i | 0.978096i | ||||||||
\(50\) | 1.18668 | − | 1.18668i | 0.167822 | − | 0.167822i | ||||
\(51\) | −1.74144 | + | 1.55456i | −0.243851 | + | 0.217682i | ||||
\(52\) | −3.21545 | + | 1.63122i | −0.445903 | + | 0.226210i | ||||
\(53\) | 0.216838i | 0.0297851i | 0.999889 | + | 0.0148925i | \(0.00474061\pi\) | ||||
−0.999889 | + | 0.0148925i | \(0.995259\pi\) | |||||||
\(54\) | −0.878680 | + | 5.12132i | −0.119573 | + | 0.696923i | ||||
\(55\) | −8.43090 | −1.13682 | ||||||||
\(56\) | −3.72111 | −0.497254 | ||||||||
\(57\) | −0.497002 | + | 8.76544i | −0.0658295 | + | 1.16101i | ||||
\(58\) | 2.58423 | − | 2.58423i | 0.339325 | − | 0.339325i | ||||
\(59\) | −3.65465 | + | 3.65465i | −0.475794 | + | 0.475794i | −0.903784 | − | 0.427989i | \(-0.859222\pi\) |
0.427989 | + | 0.903784i | \(0.359222\pi\) | |||||||
\(60\) | −0.253383 | + | 4.46883i | −0.0327117 | + | 0.576924i | ||||
\(61\) | 6.52489 | 0.835427 | 0.417713 | − | 0.908579i | \(-0.362832\pi\) | ||||
0.417713 | + | 0.908579i | \(0.362832\pi\) | |||||||
\(62\) | −0.455064 | −0.0577932 | ||||||||
\(63\) | −8.73535 | + | 6.95080i | −1.10055 | + | 0.875719i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −2.89489 | + | 8.85644i | −0.359067 | + | 1.09851i | ||||
\(66\) | 4.21545 | − | 3.76307i | 0.518886 | − | 0.463201i | ||||
\(67\) | 2.26245 | − | 2.26245i | 0.276402 | − | 0.276402i | −0.555269 | − | 0.831671i | \(-0.687385\pi\) |
0.831671 | + | 0.555269i | \(0.187385\pi\) | |||||||
\(68\) | − | 1.34775i | − | 0.163439i | ||||||
\(69\) | 4.72222 | − | 4.21545i | 0.568488 | − | 0.507480i | ||||
\(70\) | −6.79967 | + | 6.79967i | −0.812717 | + | 0.812717i | ||||
\(71\) | 0.108419 | + | 0.108419i | 0.0128670 | + | 0.0128670i | 0.713511 | − | 0.700644i | \(-0.247104\pi\) |
−0.700644 | + | 0.713511i | \(0.747104\pi\) | |||||||
\(72\) | −1.86794 | − | 2.34751i | −0.220138 | − | 0.276657i | ||||
\(73\) | −3.58423 | − | 3.58423i | −0.419502 | − | 0.419502i | 0.465530 | − | 0.885032i | \(-0.345864\pi\) |
−0.885032 | + | 0.465530i | \(0.845864\pi\) | |||||||
\(74\) | − | 2.76196i | − | 0.321072i | ||||||
\(75\) | 1.93574 | + | 2.16845i | 0.223520 | + | 0.250391i | ||||
\(76\) | −3.58423 | − | 3.58423i | −0.411139 | − | 0.411139i | ||||
\(77\) | 12.1399 | 1.38347 | ||||||||
\(78\) | −2.50556 | − | 5.72033i | −0.283698 | − | 0.647700i | ||||
\(79\) | 4.09400 | 0.460611 | 0.230305 | − | 0.973118i | \(-0.426028\pi\) | ||||
0.230305 | + | 0.973118i | \(0.426028\pi\) | |||||||
\(80\) | −1.82732 | − | 1.82732i | −0.204301 | − | 0.204301i | ||||
\(81\) | −8.77001 | − | 2.02162i | −0.974445 | − | 0.224625i | ||||
\(82\) | 11.1685i | 1.23335i | ||||||||
\(83\) | 10.5753 | + | 10.5753i | 1.16079 | + | 1.16079i | 0.984302 | + | 0.176492i | \(0.0564751\pi\) |
0.176492 | + | 0.984302i | \(0.443525\pi\) | |||||||
\(84\) | 0.364855 | − | 6.43482i | 0.0398090 | − | 0.702096i | ||||
\(85\) | −2.46277 | − | 2.46277i | −0.267125 | − | 0.267125i | ||||
\(86\) | −6.44112 | + | 6.44112i | −0.694564 | + | 0.694564i | ||||
\(87\) | 4.21545 | + | 4.72222i | 0.451944 | + | 0.506275i | ||||
\(88\) | 3.26245i | 0.347778i | ||||||||
\(89\) | 8.85644 | − | 8.85644i | 0.938780 | − | 0.938780i | −0.0594508 | − | 0.998231i | \(-0.518935\pi\) |
0.998231 | + | 0.0594508i | \(0.0189349\pi\) | |||||||
\(90\) | −7.70299 | − | 0.876338i | −0.811966 | − | 0.0923742i | ||||
\(91\) | 4.16845 | − | 12.7527i | 0.436972 | − | 1.33684i | ||||
\(92\) | 3.65465i | 0.381023i | ||||||||
\(93\) | 0.0446190 | − | 0.786930i | 0.00462678 | − | 0.0816008i | ||||
\(94\) | −6.67822 | −0.688806 | ||||||||
\(95\) | −13.0991 | −1.34394 | ||||||||
\(96\) | 1.72927 | + | 0.0980500i | 0.176493 | + | 0.0100072i | ||||
\(97\) | 0.168451 | − | 0.168451i | 0.0171036 | − | 0.0171036i | −0.698503 | − | 0.715607i | \(-0.746150\pi\) |
0.715607 | + | 0.698503i | \(0.246150\pi\) | |||||||
\(98\) | 4.84133 | − | 4.84133i | 0.489048 | − | 0.489048i | ||||
\(99\) | 6.09404 | + | 7.65863i | 0.612475 | + | 0.769721i | ||||
\(100\) | −1.67822 | −0.167822 | ||||||||
\(101\) | −17.7129 | −1.76250 | −0.881248 | − | 0.472653i | \(-0.843296\pi\) | ||||
−0.881248 | + | 0.472653i | \(0.843296\pi\) | |||||||
\(102\) | 2.33063 | + | 0.132147i | 0.230766 | + | 0.0130845i | ||||
\(103\) | 7.90600i | 0.779002i | 0.921026 | + | 0.389501i | \(0.127352\pi\) | ||||
−0.921026 | + | 0.389501i | \(0.872648\pi\) | |||||||
\(104\) | 3.42711 | + | 1.12022i | 0.336056 | + | 0.109846i | ||||
\(105\) | −11.0918 | − | 12.4252i | −1.08245 | − | 1.21258i | ||||
\(106\) | 0.153328 | − | 0.153328i | 0.0148925 | − | 0.0148925i | ||||
\(107\) | − | 4.61380i | − | 0.446033i | −0.974815 | − | 0.223016i | \(-0.928410\pi\) | ||
0.974815 | − | 0.223016i | \(-0.0715903\pi\) | |||||||
\(108\) | 4.24264 | − | 3.00000i | 0.408248 | − | 0.288675i | ||||
\(109\) | 9.21545 | − | 9.21545i | 0.882680 | − | 0.882680i | −0.111126 | − | 0.993806i | \(-0.535446\pi\) |
0.993806 | + | 0.111126i | \(0.0354458\pi\) | |||||||
\(110\) | 5.96154 | + | 5.96154i | 0.568411 | + | 0.568411i | ||||
\(111\) | 4.77619 | + | 0.270810i | 0.453336 | + | 0.0257042i | ||||
\(112\) | 2.63122 | + | 2.63122i | 0.248627 | + | 0.248627i | ||||
\(113\) | 3.43781i | 0.323402i | 0.986840 | + | 0.161701i | \(0.0516980\pi\) | ||||
−0.986840 | + | 0.161701i | \(0.948302\pi\) | |||||||
\(114\) | 6.54954 | − | 5.84667i | 0.613421 | − | 0.547591i | ||||
\(115\) | 6.67822 | + | 6.67822i | 0.622747 | + | 0.622747i | ||||
\(116\) | −3.65465 | −0.339325 | ||||||||
\(117\) | 10.1377 | − | 3.77191i | 0.937229 | − | 0.348713i | ||||
\(118\) | 5.16845 | 0.475794 | ||||||||
\(119\) | 3.54623 | + | 3.54623i | 0.325082 | + | 0.325082i | ||||
\(120\) | 3.33911 | − | 2.98077i | 0.304818 | − | 0.272106i | ||||
\(121\) | 0.356442i | 0.0324038i | ||||||||
\(122\) | −4.61380 | − | 4.61380i | −0.417713 | − | 0.417713i | ||||
\(123\) | −19.3133 | − | 1.09507i | −1.74142 | − | 0.0987389i | ||||
\(124\) | 0.321779 | + | 0.321779i | 0.0288966 | + | 0.0288966i | ||||
\(125\) | 6.06996 | − | 6.06996i | 0.542914 | − | 0.542914i | ||||
\(126\) | 11.0918 | + | 1.26187i | 0.988135 | + | 0.112416i | ||||
\(127\) | 11.0745i | 0.982699i | 0.870962 | + | 0.491349i | \(0.163496\pi\) | ||||
−0.870962 | + | 0.491349i | \(0.836504\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −10.5069 | − | 11.7700i | −0.925081 | − | 1.03629i | ||||
\(130\) | 8.30944 | − | 4.21545i | 0.728786 | − | 0.369719i | ||||
\(131\) | 18.1015i | 1.58153i | 0.612118 | + | 0.790767i | \(0.290318\pi\) | ||||
−0.612118 | + | 0.790767i | \(0.709682\pi\) | |||||||
\(132\) | −5.64166 | − | 0.319883i | −0.491044 | − | 0.0278422i | ||||
\(133\) | 18.8618 | 1.63553 | ||||||||
\(134\) | −3.19958 | −0.276402 | ||||||||
\(135\) | 2.27071 | − | 13.2346i | 0.195431 | − | 1.13906i | ||||
\(136\) | −0.953002 | + | 0.953002i | −0.0817193 | + | 0.0817193i | ||||
\(137\) | 0.976593 | − | 0.976593i | 0.0834360 | − | 0.0834360i | −0.664157 | − | 0.747593i | \(-0.731209\pi\) |
0.747593 | + | 0.664157i | \(0.231209\pi\) | |||||||
\(138\) | −6.31988 | − | 0.358338i | −0.537984 | − | 0.0305038i | ||||
\(139\) | −7.10912 | −0.602988 | −0.301494 | − | 0.953468i | \(-0.597485\pi\) | ||||
−0.301494 | + | 0.953468i | \(0.597485\pi\) | |||||||
\(140\) | 9.61619 | 0.812717 | ||||||||
\(141\) | 0.654800 | − | 11.5485i | 0.0551441 | − | 0.972557i | ||||
\(142\) | − | 0.153328i | − | 0.0128670i | ||||||
\(143\) | −11.1808 | − | 3.65465i | −0.934984 | − | 0.305617i | ||||
\(144\) | −0.339111 | + | 2.98077i | −0.0282592 | + | 0.248398i | ||||
\(145\) | −6.67822 | + | 6.67822i | −0.554596 | + | 0.554596i | ||||
\(146\) | 5.06886i | 0.419502i | ||||||||
\(147\) | 7.89729 | + | 8.84667i | 0.651357 | + | 0.729661i | ||||
\(148\) | −1.95300 | + | 1.95300i | −0.160536 | + | 0.160536i | ||||
\(149\) | 8.85644 | + | 8.85644i | 0.725548 | + | 0.725548i | 0.969729 | − | 0.244182i | \(-0.0785194\pi\) |
−0.244182 | + | 0.969729i | \(0.578519\pi\) | |||||||
\(150\) | 0.164550 | − | 2.90210i | 0.0134354 | − | 0.236956i | ||||
\(151\) | −11.7997 | − | 11.7997i | −0.960244 | − | 0.960244i | 0.0389955 | − | 0.999239i | \(-0.487584\pi\) |
−0.999239 | + | 0.0389955i | \(0.987584\pi\) | |||||||
\(152\) | 5.06886i | 0.411139i | ||||||||
\(153\) | −0.457036 | + | 4.01733i | −0.0369492 | + | 0.324782i | ||||
\(154\) | −8.58423 | − | 8.58423i | −0.691737 | − | 0.691737i | ||||
\(155\) | 1.17599 | 0.0944576 | ||||||||
\(156\) | −2.27319 | + | 5.81658i | −0.182001 | + | 0.465699i | ||||
\(157\) | −18.8618 | −1.50534 | −0.752668 | − | 0.658401i | \(-0.771233\pi\) | ||||
−0.752668 | + | 0.658401i | \(0.771233\pi\) | |||||||
\(158\) | −2.89489 | − | 2.89489i | −0.230305 | − | 0.230305i | ||||
\(159\) | 0.250112 | + | 0.280180i | 0.0198352 | + | 0.0222197i | ||||
\(160\) | 2.58423i | 0.204301i | ||||||||
\(161\) | −9.61619 | − | 9.61619i | −0.757862 | − | 0.757862i | ||||
\(162\) | 4.77183 | + | 7.63084i | 0.374910 | + | 0.599535i | ||||
\(163\) | −2.81201 | − | 2.81201i | −0.220254 | − | 0.220254i | 0.588352 | − | 0.808605i | \(-0.299777\pi\) |
−0.808605 | + | 0.588352i | \(0.799777\pi\) | |||||||
\(164\) | 7.89729 | − | 7.89729i | 0.616675 | − | 0.616675i | ||||
\(165\) | −10.8937 | + | 9.72461i | −0.848071 | + | 0.757060i | ||||
\(166\) | − | 14.9558i | − | 1.16079i | ||||||
\(167\) | −0.959150 | + | 0.959150i | −0.0742212 | + | 0.0742212i | −0.743243 | − | 0.669022i | \(-0.766713\pi\) |
0.669022 | + | 0.743243i | \(0.266713\pi\) | |||||||
\(168\) | −4.80810 | + | 4.29211i | −0.370953 | + | 0.331144i | ||||
\(169\) | −7.67822 | + | 10.4902i | −0.590632 | + | 0.806941i | ||||
\(170\) | 3.48289i | 0.267125i | ||||||||
\(171\) | 9.46831 | + | 11.8992i | 0.724060 | + | 0.909955i | ||||
\(172\) | 9.10912 | 0.694564 | ||||||||
\(173\) | 17.4960 | 1.33020 | 0.665099 | − | 0.746755i | \(-0.268389\pi\) | ||||
0.665099 | + | 0.746755i | \(0.268389\pi\) | |||||||
\(174\) | 0.358338 | − | 6.31988i | 0.0271655 | − | 0.479109i | ||||
\(175\) | 4.41577 | − | 4.41577i | 0.333801 | − | 0.333801i | ||||
\(176\) | 2.30690 | − | 2.30690i | 0.173889 | − | 0.173889i | ||||
\(177\) | −0.506767 | + | 8.93766i | −0.0380909 | + | 0.671796i | ||||
\(178\) | −12.5249 | −0.938780 | ||||||||
\(179\) | −18.1015 | −1.35297 | −0.676484 | − | 0.736458i | \(-0.736497\pi\) | ||||
−0.676484 | + | 0.736458i | \(0.736497\pi\) | |||||||
\(180\) | 4.82717 | + | 6.06650i | 0.359796 | + | 0.452170i | ||||
\(181\) | 1.90600i | 0.141672i | 0.997488 | + | 0.0708361i | \(0.0225667\pi\) | ||||
−0.997488 | + | 0.0708361i | \(0.977433\pi\) | |||||||
\(182\) | −11.9650 | + | 6.06996i | −0.886908 | + | 0.449936i | ||||
\(183\) | 8.43090 | − | 7.52613i | 0.623230 | − | 0.556348i | ||||
\(184\) | 2.58423 | − | 2.58423i | 0.190512 | − | 0.190512i | ||||
\(185\) | 7.13753i | 0.524762i | ||||||||
\(186\) | −0.587994 | + | 0.524893i | −0.0431138 | + | 0.0384870i | ||||
\(187\) | 3.10912 | − | 3.10912i | 0.227361 | − | 0.227361i | ||||
\(188\) | 4.72222 | + | 4.72222i | 0.344403 | + | 0.344403i | ||||
\(189\) | −3.26967 | + | 19.0570i | −0.237833 | + | 1.38619i | ||||
\(190\) | 9.26245 | + | 9.26245i | 0.671969 | + | 0.671969i | ||||
\(191\) | 6.35014i | 0.459480i | 0.973252 | + | 0.229740i | \(0.0737876\pi\) | ||||
−0.973252 | + | 0.229740i | \(0.926212\pi\) | |||||||
\(192\) | −1.15345 | − | 1.29211i | −0.0832430 | − | 0.0932502i | ||||
\(193\) | −4.26245 | − | 4.26245i | −0.306818 | − | 0.306818i | 0.536856 | − | 0.843674i | \(-0.319612\pi\) |
−0.843674 | + | 0.536856i | \(0.819612\pi\) | |||||||
\(194\) | −0.238226 | −0.0171036 | ||||||||
\(195\) | 6.47492 | + | 14.7826i | 0.463679 | + | 1.05861i | ||||
\(196\) | −6.84667 | −0.489048 | ||||||||
\(197\) | −2.78647 | − | 2.78647i | −0.198528 | − | 0.198528i | 0.600841 | − | 0.799369i | \(-0.294833\pi\) |
−0.799369 | + | 0.600841i | \(0.794833\pi\) | |||||||
\(198\) | 1.10633 | − | 9.72461i | 0.0786235 | − | 0.691098i | ||||
\(199\) | 17.2927i | 1.22585i | 0.790142 | + | 0.612923i | \(0.210007\pi\) | ||||
−0.790142 | + | 0.612923i | \(0.789993\pi\) | |||||||
\(200\) | 1.18668 | + | 1.18668i | 0.0839111 | + | 0.0839111i | ||||
\(201\) | 0.313719 | − | 5.53295i | 0.0221280 | − | 0.390264i | ||||
\(202\) | 12.5249 | + | 12.5249i | 0.881248 | + | 0.881248i | ||||
\(203\) | 9.61619 | − | 9.61619i | 0.674924 | − | 0.674924i | ||||
\(204\) | −1.55456 | − | 1.74144i | −0.108841 | − | 0.121925i | ||||
\(205\) | − | 28.8618i | − | 2.01580i | ||||||
\(206\) | 5.59039 | − | 5.59039i | 0.389501 | − | 0.389501i | ||||
\(207\) | 1.23933 | − | 10.8937i | 0.0861393 | − | 0.757162i | ||||
\(208\) | −1.63122 | − | 3.21545i | −0.113105 | − | 0.222951i | ||||
\(209\) | − | 16.5369i | − | 1.14388i | ||||||
\(210\) | −0.942868 | + | 16.6290i | −0.0650641 | + | 1.14751i | ||||
\(211\) | 9.41577 | 0.648209 | 0.324104 | − | 0.946021i | \(-0.394937\pi\) | ||||
0.324104 | + | 0.946021i | \(0.394937\pi\) | |||||||
\(212\) | −0.216838 | −0.0148925 | ||||||||
\(213\) | 0.265146 | + | 0.0150338i | 0.0181675 | + | 0.00103010i | ||||
\(214\) | −3.26245 | + | 3.26245i | −0.223016 | + | 0.223016i | ||||
\(215\) | 16.6453 | − | 16.6453i | 1.13520 | − | 1.13520i | ||||
\(216\) | −5.12132 | − | 0.878680i | −0.348462 | − | 0.0597866i | ||||
\(217\) | −1.69334 | −0.114952 | ||||||||
\(218\) | −13.0326 | −0.882680 | ||||||||
\(219\) | −8.76544 | − | 0.497002i | −0.592314 | − | 0.0335843i | ||||
\(220\) | − | 8.43090i | − | 0.568411i | ||||||
\(221\) | −2.19848 | − | 4.33362i | −0.147886 | − | 0.291511i | ||||
\(222\) | −3.18578 | − | 3.56877i | −0.213816 | − | 0.239520i | ||||
\(223\) | −5.89367 | + | 5.89367i | −0.394669 | + | 0.394669i | −0.876348 | − | 0.481679i | \(-0.840027\pi\) |
0.481679 | + | 0.876348i | \(0.340027\pi\) | |||||||
\(224\) | − | 3.72111i | − | 0.248627i | ||||||
\(225\) | 5.00240 | + | 0.569103i | 0.333493 | + | 0.0379402i | ||||
\(226\) | 2.43090 | − | 2.43090i | 0.161701 | − | 0.161701i | ||||
\(227\) | −9.22759 | − | 9.22759i | −0.612457 | − | 0.612457i | 0.331129 | − | 0.943586i | \(-0.392571\pi\) |
−0.943586 | + | 0.331129i | \(0.892571\pi\) | |||||||
\(228\) | −8.76544 | − | 0.497002i | −0.580506 | − | 0.0329148i | ||||
\(229\) | 9.21545 | + | 9.21545i | 0.608974 | + | 0.608974i | 0.942678 | − | 0.333704i | \(-0.108299\pi\) |
−0.333704 | + | 0.942678i | \(0.608299\pi\) | |||||||
\(230\) | − | 9.44443i | − | 0.622747i | ||||||
\(231\) | 15.6862 | − | 14.0028i | 1.03207 | − | 0.921316i | ||||
\(232\) | 2.58423 | + | 2.58423i | 0.169663 | + | 0.169663i | ||||
\(233\) | −2.52374 | −0.165335 | −0.0826677 | − | 0.996577i | \(-0.526344\pi\) | ||||
−0.0826677 | + | 0.996577i | \(0.526344\pi\) | |||||||
\(234\) | −9.83557 | − | 4.50128i | −0.642971 | − | 0.294258i | ||||
\(235\) | 17.2580 | 1.12579 | ||||||||
\(236\) | −3.65465 | − | 3.65465i | −0.237897 | − | 0.237897i | ||||
\(237\) | 5.28990 | − | 4.72222i | 0.343616 | − | 0.306741i | ||||
\(238\) | − | 5.01512i | − | 0.325082i | ||||||
\(239\) | −7.20087 | − | 7.20087i | −0.465786 | − | 0.465786i | 0.434760 | − | 0.900546i | \(-0.356833\pi\) |
−0.900546 | + | 0.434760i | \(0.856833\pi\) | |||||||
\(240\) | −4.46883 | − | 0.253383i | −0.288462 | − | 0.0163558i | ||||
\(241\) | 20.4460 | + | 20.4460i | 1.31704 | + | 1.31704i | 0.916105 | + | 0.400939i | \(0.131316\pi\) |
0.400939 | + | 0.916105i | \(0.368684\pi\) | |||||||
\(242\) | 0.252043 | − | 0.252043i | 0.0162019 | − | 0.0162019i | ||||
\(243\) | −13.6637 | + | 7.50359i | −0.876525 | + | 0.481356i | ||||
\(244\) | 6.52489i | 0.417713i | ||||||||
\(245\) | −12.5111 | + | 12.5111i | −0.799304 | + | 0.799304i | ||||
\(246\) | 12.8822 | + | 14.4309i | 0.821342 | + | 0.920080i | ||||
\(247\) | −17.3716 | − | 5.67822i | −1.10533 | − | 0.361297i | ||||
\(248\) | − | 0.455064i | − | 0.0288966i | ||||||
\(249\) | 25.8626 | + | 1.46642i | 1.63898 | + | 0.0929303i | ||||
\(250\) | −8.58423 | −0.542914 | ||||||||
\(251\) | 18.4901 | 1.16708 | 0.583541 | − | 0.812083i | \(-0.301667\pi\) | ||||
0.583541 | + | 0.812083i | \(0.301667\pi\) | |||||||
\(252\) | −6.95080 | − | 8.73535i | −0.437859 | − | 0.550276i | ||||
\(253\) | −8.43090 | + | 8.43090i | −0.530046 | + | 0.530046i | ||||
\(254\) | 7.83082 | − | 7.83082i | 0.491349 | − | 0.491349i | ||||
\(255\) | −6.02286 | − | 0.341497i | −0.377166 | − | 0.0213854i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6696 | 0.852688 | 0.426344 | − | 0.904561i | \(-0.359801\pi\) | ||||
0.426344 | + | 0.904561i | \(0.359801\pi\) | |||||||
\(258\) | −0.893149 | + | 15.7522i | −0.0556050 | + | 0.980686i | ||||
\(259\) | − | 10.2776i | − | 0.638617i | ||||||
\(260\) | −8.85644 | − | 2.89489i | −0.549253 | − | 0.179534i | ||||
\(261\) | 10.8937 | + | 1.23933i | 0.674301 | + | 0.0767126i | ||||
\(262\) | 12.7997 | − | 12.7997i | 0.790767 | − | 0.790767i | ||||
\(263\) | − | 14.6186i | − | 0.901421i | −0.892670 | − | 0.450710i | \(-0.851171\pi\) | ||
0.892670 | − | 0.450710i | \(-0.148829\pi\) | |||||||
\(264\) | 3.76307 | + | 4.21545i | 0.231601 | + | 0.259443i | ||||
\(265\) | −0.396234 | + | 0.396234i | −0.0243405 | + | 0.0243405i | ||||
\(266\) | −13.3373 | − | 13.3373i | −0.817763 | − | 0.817763i | ||||
\(267\) | 1.22807 | − | 21.6590i | 0.0751564 | − | 1.32551i | ||||
\(268\) | 2.26245 | + | 2.26245i | 0.138201 | + | 0.138201i | ||||
\(269\) | 15.7946i | 0.963012i | 0.876443 | + | 0.481506i | \(0.159910\pi\) | ||||
−0.876443 | + | 0.481506i | \(0.840090\pi\) | |||||||
\(270\) | −10.9639 | + | 7.75268i | −0.667244 | + | 0.471813i | ||||
\(271\) | 16.2306 | + | 16.2306i | 0.985937 | + | 0.985937i | 0.999902 | − | 0.0139655i | \(-0.00444549\pi\) |
−0.0139655 | + | 0.999902i | \(0.504445\pi\) | |||||||
\(272\) | 1.34775 | 0.0817193 | ||||||||
\(273\) | −9.32345 | − | 21.2860i | −0.564281 | − | 1.28829i | ||||
\(274\) | −1.38111 | −0.0834360 | ||||||||
\(275\) | −3.87149 | − | 3.87149i | −0.233459 | − | 0.233459i | ||||
\(276\) | 4.21545 | + | 4.72222i | 0.253740 | + | 0.284244i | ||||
\(277\) | − | 26.1489i | − | 1.57114i | −0.618775 | − | 0.785568i | \(-0.712371\pi\) | ||
0.618775 | − | 0.785568i | \(-0.287629\pi\) | |||||||
\(278\) | 5.02691 | + | 5.02691i | 0.301494 | + | 0.301494i | ||||
\(279\) | −0.850031 | − | 1.06827i | −0.0508900 | − | 0.0639555i | ||||
\(280\) | −6.79967 | − | 6.79967i | −0.406358 | − | 0.406358i | ||||
\(281\) | −3.06665 | + | 3.06665i | −0.182941 | + | 0.182941i | −0.792636 | − | 0.609695i | \(-0.791292\pi\) |
0.609695 | + | 0.792636i | \(0.291292\pi\) | |||||||
\(282\) | −8.62901 | + | 7.70299i | −0.513850 | + | 0.458706i | ||||
\(283\) | 9.35644i | 0.556183i | 0.960555 | + | 0.278091i | \(0.0897018\pi\) | ||||
−0.960555 | + | 0.278091i | \(0.910298\pi\) | |||||||
\(284\) | −0.108419 | + | 0.108419i | −0.00643350 | + | 0.00643350i | ||||
\(285\) | −16.9255 | + | 15.1091i | −1.00258 | + | 0.894987i | ||||
\(286\) | 5.32178 | + | 10.4902i | 0.314683 | + | 0.620300i | ||||
\(287\) | 41.5591i | 2.45315i | ||||||||
\(288\) | 2.34751 | − | 1.86794i | 0.138328 | − | 0.110069i | ||||
\(289\) | −15.1836 | −0.893151 | ||||||||
\(290\) | 9.44443 | 0.554596 | ||||||||
\(291\) | 0.0233580 | − | 0.411957i | 0.00136927 | − | 0.0241493i | ||||
\(292\) | 3.58423 | − | 3.58423i | 0.209751 | − | 0.209751i | ||||
\(293\) | −3.00331 | + | 3.00331i | −0.175455 | + | 0.175455i | −0.789371 | − | 0.613916i | \(-0.789593\pi\) |
0.613916 | + | 0.789371i | \(0.289593\pi\) | |||||||
\(294\) | 0.671316 | − | 11.8398i | 0.0391520 | − | 0.690509i | ||||
\(295\) | −13.3564 | −0.777642 | ||||||||
\(296\) | 2.76196 | 0.160536 | ||||||||
\(297\) | 16.7080 | + | 2.86665i | 0.969498 | + | 0.166340i | ||||
\(298\) | − | 12.5249i | − | 0.725548i | ||||||
\(299\) | 5.96154 | + | 11.7513i | 0.344765 | + | 0.679597i | ||||
\(300\) | −2.16845 | + | 1.93574i | −0.125196 | + | 0.111760i | ||||
\(301\) | −23.9681 | + | 23.9681i | −1.38150 | + | 1.38150i | ||||
\(302\) | 16.6873i | 0.960244i | ||||||||
\(303\) | −22.8870 | + | 20.4309i | −1.31483 | + | 1.17372i | ||||
\(304\) | 3.58423 | − | 3.58423i | 0.205569 | − | 0.205569i | ||||
\(305\) | 11.9231 | + | 11.9231i | 0.682714 | + | 0.682714i | ||||
\(306\) | 3.16386 | − | 2.51751i | 0.180866 | − | 0.143916i | ||||
\(307\) | −3.24732 | − | 3.24732i | −0.185335 | − | 0.185335i | 0.608341 | − | 0.793676i | \(-0.291835\pi\) |
−0.793676 | + | 0.608341i | \(0.791835\pi\) | |||||||
\(308\) | 12.1399i | 0.691737i | ||||||||
\(309\) | 9.11917 | + | 10.2154i | 0.518772 | + | 0.581137i | ||||
\(310\) | −0.831549 | − | 0.831549i | −0.0472288 | − | 0.0472288i | ||||
\(311\) | −3.43781 | −0.194940 | −0.0974701 | − | 0.995238i | \(-0.531075\pi\) | ||||
−0.0974701 | + | 0.995238i | \(0.531075\pi\) | |||||||
\(312\) | 5.72033 | − | 2.50556i | 0.323850 | − | 0.141849i | ||||
\(313\) | 1.50977 | 0.0853373 | 0.0426686 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426686 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(314\) | 13.3373 | + | 13.3373i | 0.752668 | + | 0.752668i | ||||
\(315\) | −28.6637 | − | 3.26095i | −1.61502 | − | 0.183734i | ||||
\(316\) | 4.09400i | 0.230305i | ||||||||
\(317\) | −16.1657 | − | 16.1657i | −0.907958 | − | 0.907958i | 0.0881494 | − | 0.996107i | \(-0.471905\pi\) |
−0.996107 | + | 0.0881494i | \(0.971905\pi\) | |||||||
\(318\) | 0.0212610 | − | 0.374973i | 0.00119226 | − | 0.0210274i | ||||
\(319\) | −8.43090 | − | 8.43090i | −0.472040 | − | 0.472040i | ||||
\(320\) | 1.82732 | − | 1.82732i | 0.102150 | − | 0.102150i | ||||
\(321\) | −5.32178 | − | 5.96154i | −0.297033 | − | 0.332741i | ||||
\(322\) | 13.5993i | 0.757862i | ||||||||
\(323\) | 4.83063 | − | 4.83063i | 0.268784 | − | 0.268784i | ||||
\(324\) | 2.02162 | − | 8.77001i | 0.112312 | − | 0.487223i | ||||
\(325\) | −5.39623 | + | 2.73755i | −0.299329 | + | 0.151852i | ||||
\(326\) | 3.97678i | 0.220254i | ||||||||
\(327\) | 1.27785 | − | 22.5369i | 0.0706652 | − | 1.24630i | ||||
\(328\) | −11.1685 | −0.616675 | ||||||||
\(329\) | −24.8504 | −1.37005 | ||||||||
\(330\) | 14.5793 | + | 0.826650i | 0.802565 | + | 0.0455056i | ||||
\(331\) | 5.52489 | − | 5.52489i | 0.303676 | − | 0.303676i | −0.538774 | − | 0.842450i | \(-0.681112\pi\) |
0.842450 | + | 0.538774i | \(0.181112\pi\) | |||||||
\(332\) | −10.5753 | + | 10.5753i | −0.580397 | + | 0.580397i | ||||
\(333\) | 6.48374 | − | 5.15917i | 0.355307 | − | 0.282721i | ||||
\(334\) | 1.35644 | 0.0742212 | ||||||||
\(335\) | 8.26844 | 0.451753 | ||||||||
\(336\) | 6.43482 | + | 0.364855i | 0.351048 | + | 0.0199045i | ||||
\(337\) | − | 18.8271i | − | 1.02558i | −0.858514 | − | 0.512790i | \(-0.828612\pi\) | ||
0.858514 | − | 0.512790i | \(-0.171388\pi\) | |||||||
\(338\) | 12.8470 | − | 1.98839i | 0.698787 | − | 0.108154i | ||||
\(339\) | 3.96534 | + | 4.44204i | 0.215368 | + | 0.241258i | ||||
\(340\) | 2.46277 | − | 2.46277i | 0.133563 | − | 0.133563i | ||||
\(341\) | 1.48462i | 0.0803968i | ||||||||
\(342\) | 1.71890 | − | 15.1091i | 0.0929477 | − | 0.817008i | ||||
\(343\) | −0.403440 | + | 0.403440i | −0.0217837 | + | 0.0217837i | ||||
\(344\) | −6.44112 | − | 6.44112i | −0.347282 | − | 0.347282i | ||||
\(345\) | 16.3320 | + | 0.926027i | 0.879285 | + | 0.0498556i | ||||
\(346\) | −12.3716 | − | 12.3716i | −0.665099 | − | 0.665099i | ||||
\(347\) | − | 29.2823i | − | 1.57195i | −0.618256 | − | 0.785977i | \(-0.712160\pi\) | ||
0.618256 | − | 0.785977i | \(-0.287840\pi\) | |||||||
\(348\) | −4.72222 | + | 4.21545i | −0.253137 | + | 0.225972i | ||||
\(349\) | 4.87855 | + | 4.87855i | 0.261143 | + | 0.261143i | 0.825518 | − | 0.564376i | \(-0.190883\pi\) |
−0.564376 | + | 0.825518i | \(0.690883\pi\) | |||||||
\(350\) | −6.24485 | −0.333801 | ||||||||
\(351\) | 8.74832 | − | 16.5670i | 0.466951 | − | 0.884283i | ||||
\(352\) | −3.26245 | −0.173889 | ||||||||
\(353\) | 5.59039 | + | 5.59039i | 0.297546 | + | 0.297546i | 0.840052 | − | 0.542506i | \(-0.182524\pi\) |
−0.542506 | + | 0.840052i | \(0.682524\pi\) | |||||||
\(354\) | 6.67822 | − | 5.96154i | 0.354943 | − | 0.316853i | ||||
\(355\) | 0.396234i | 0.0210299i | ||||||||
\(356\) | 8.85644 | + | 8.85644i | 0.469390 | + | 0.469390i | ||||
\(357\) | 8.67252 | + | 0.491733i | 0.458998 | + | 0.0260253i | ||||
\(358\) | 12.7997 | + | 12.7997i | 0.676484 | + | 0.676484i | ||||
\(359\) | −12.8822 | + | 12.8822i | −0.679899 | + | 0.679899i | −0.959977 | − | 0.280079i | \(-0.909639\pi\) |
0.280079 | + | 0.959977i | \(0.409639\pi\) | |||||||
\(360\) | 0.876338 | − | 7.70299i | 0.0461871 | − | 0.405983i | ||||
\(361\) | − | 6.69334i | − | 0.352281i | ||||||
\(362\) | 1.34775 | − | 1.34775i | 0.0708361 | − | 0.0708361i | ||||
\(363\) | 0.411138 | + | 0.460564i | 0.0215791 | + | 0.0241733i | ||||
\(364\) | 12.7527 | + | 4.16845i | 0.668422 | + | 0.218486i | ||||
\(365\) | − | 13.0991i | − | 0.685637i | ||||||
\(366\) | −11.2833 | − | 0.639766i | −0.589789 | − | 0.0334411i | ||||
\(367\) | 7.56910 | 0.395104 | 0.197552 | − | 0.980292i | \(-0.436701\pi\) | ||||
0.197552 | + | 0.980292i | \(0.436701\pi\) | |||||||
\(368\) | −3.65465 | −0.190512 | ||||||||
\(369\) | −26.2181 | + | 20.8620i | −1.36486 | + | 1.08603i | ||||
\(370\) | 5.04700 | − | 5.04700i | 0.262381 | − | 0.262381i | ||||
\(371\) | 0.570551 | − | 0.570551i | 0.0296215 | − | 0.0296215i | ||||
\(372\) | 0.786930 | + | 0.0446190i | 0.0408004 | + | 0.00231339i | ||||
\(373\) | 15.8120 | 0.818715 | 0.409357 | − | 0.912374i | \(-0.365753\pi\) | ||||
0.409357 | + | 0.912374i | \(0.365753\pi\) | |||||||
\(374\) | −4.39696 | −0.227361 | ||||||||
\(375\) | 0.841683 | − | 14.8445i | 0.0434643 | − | 0.766565i | ||||
\(376\) | − | 6.67822i | − | 0.344403i | ||||||
\(377\) | −11.7513 | + | 5.96154i | −0.605224 | + | 0.307035i | ||||
\(378\) | 15.7873 | − | 11.1633i | 0.812013 | − | 0.574180i | ||||
\(379\) | 5.33690 | − | 5.33690i | 0.274138 | − | 0.274138i | −0.556625 | − | 0.830764i | \(-0.687904\pi\) |
0.830764 | + | 0.556625i | \(0.187904\pi\) | |||||||
\(380\) | − | 13.0991i | − | 0.671969i | ||||||
\(381\) | 12.7738 | + | 14.3094i | 0.654423 | + | 0.733095i | ||||
\(382\) | 4.49023 | − | 4.49023i | 0.229740 | − | 0.229740i | ||||
\(383\) | 10.8555 | + | 10.8555i | 0.554691 | + | 0.554691i | 0.927791 | − | 0.373100i | \(-0.121705\pi\) |
−0.373100 | + | 0.927791i | \(0.621705\pi\) | |||||||
\(384\) | −0.0980500 | + | 1.72927i | −0.00500359 | + | 0.0882466i | ||||
\(385\) | 22.1836 | + | 22.1836i | 1.13058 | + | 1.13058i | ||||
\(386\) | 6.02801i | 0.306818i | ||||||||
\(387\) | −27.1522 | − | 3.08900i | −1.38022 | − | 0.157023i | ||||
\(388\) | 0.168451 | + | 0.168451i | 0.00855180 | + | 0.00855180i | ||||
\(389\) | 4.61380 | 0.233929 | 0.116964 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116964 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(390\) | 5.87443 | − | 15.0314i | 0.297464 | − | 0.761142i | ||||
\(391\) | −4.92554 | −0.249096 | ||||||||
\(392\) | 4.84133 | + | 4.84133i | 0.244524 | + | 0.244524i | ||||
\(393\) | 20.8791 | + | 23.3891i | 1.05321 | + | 1.17983i | ||||
\(394\) | 3.94067i | 0.198528i | ||||||||
\(395\) | 7.48105 | + | 7.48105i | 0.376413 | + | 0.376413i | ||||
\(396\) | −7.65863 | + | 6.09404i | −0.384861 | + | 0.306237i | ||||
\(397\) | −12.5400 | − | 12.5400i | −0.629365 | − | 0.629365i | 0.318543 | − | 0.947908i | \(-0.396806\pi\) |
−0.947908 | + | 0.318543i | \(0.896806\pi\) | |||||||
\(398\) | 12.2278 | − | 12.2278i | 0.612923 | − | 0.612923i | ||||
\(399\) | 24.3716 | − | 21.7561i | 1.22010 | − | 1.08917i | ||||
\(400\) | − | 1.67822i | − | 0.0839111i | ||||||
\(401\) | 3.63720 | − | 3.63720i | 0.181633 | − | 0.181633i | −0.610434 | − | 0.792067i | \(-0.709005\pi\) |
0.792067 | + | 0.610434i | \(0.209005\pi\) | |||||||
\(402\) | −4.13422 | + | 3.69056i | −0.206196 | + | 0.184068i | ||||
\(403\) | 1.55956 | + | 0.509770i | 0.0776870 | + | 0.0253935i | ||||
\(404\) | − | 17.7129i | − | 0.881248i | ||||||
\(405\) | −12.3315 | − | 19.7198i | −0.612756 | − | 0.979885i | ||||
\(406\) | −13.5993 | −0.674924 | ||||||||
\(407\) | −9.01075 | −0.446646 | ||||||||
\(408\) | −0.132147 | + | 2.33063i | −0.00654224 | + | 0.115383i | ||||
\(409\) | 18.5993 | − | 18.5993i | 0.919679 | − | 0.919679i | −0.0773272 | − | 0.997006i | \(-0.524639\pi\) |
0.997006 | + | 0.0773272i | \(0.0246386\pi\) | |||||||
\(410\) | −20.4084 | + | 20.4084i | −1.00790 | + | 1.00790i | ||||
\(411\) | 0.135418 | − | 2.38832i | 0.00667968 | − | 0.117807i | ||||
\(412\) | −7.90600 | −0.389501 | ||||||||
\(413\) | 19.2324 | 0.946364 | ||||||||
\(414\) | −8.57933 | + | 6.82665i | −0.421651 | + | 0.335512i | ||||
\(415\) | 38.6491i | 1.89721i | ||||||||
\(416\) | −1.12022 | + | 3.42711i | −0.0549231 | + | 0.168028i | ||||
\(417\) | −9.18578 | + | 8.20001i | −0.449830 | + | 0.401556i | ||||
\(418\) | −11.6933 | + | 11.6933i | −0.571940 | + | 0.571940i | ||||
\(419\) | − | 0.353712i | − | 0.0172800i | −0.999963 | − | 0.00863998i | \(-0.997250\pi\) | ||
0.999963 | − | 0.00863998i | \(-0.00275023\pi\) | |||||||
\(420\) | 12.4252 | − | 11.0918i | 0.606288 | − | 0.541224i | ||||
\(421\) | −22.9088 | + | 22.9088i | −1.11651 | + | 1.11651i | −0.124256 | + | 0.992250i | \(0.539654\pi\) |
−0.992250 | + | 0.124256i | \(0.960346\pi\) | |||||||
\(422\) | −6.65796 | − | 6.65796i | −0.324104 | − | 0.324104i | ||||
\(423\) | −12.4745 | − | 15.6772i | −0.606531 | − | 0.762252i | ||||
\(424\) | 0.153328 | + | 0.153328i | 0.00744626 | + | 0.00744626i | ||||
\(425\) | − | 2.26182i | − | 0.109714i | ||||||
\(426\) | −0.176856 | − | 0.198117i | −0.00856870 | − | 0.00959880i | ||||
\(427\) | −17.1685 | − | 17.1685i | −0.830840 | − | 0.830840i | ||||
\(428\) | 4.61380 | 0.223016 | ||||||||
\(429\) | −18.6623 | + | 8.17424i | −0.901023 | + | 0.394656i | ||||
\(430\) | −23.5400 | −1.13520 | ||||||||
\(431\) | 5.89820 | + | 5.89820i | 0.284106 | + | 0.284106i | 0.834744 | − | 0.550638i | \(-0.185615\pi\) |
−0.550638 | + | 0.834744i | \(0.685615\pi\) | |||||||
\(432\) | 3.00000 | + | 4.24264i | 0.144338 | + | 0.204124i | ||||
\(433\) | − | 37.6093i | − | 1.80739i | −0.428177 | − | 0.903695i | \(-0.640844\pi\) | ||
0.428177 | − | 0.903695i | \(-0.359156\pi\) | |||||||
\(434\) | 1.19738 | + | 1.19738i | 0.0574758 | + | 0.0574758i | ||||
\(435\) | −0.926027 | + | 16.3320i | −0.0443996 | + | 0.783060i | ||||
\(436\) | 9.21545 | + | 9.21545i | 0.441340 | + | 0.441340i | ||||
\(437\) | −13.0991 | + | 13.0991i | −0.626614 | + | 0.626614i | ||||
\(438\) | 5.84667 | + | 6.54954i | 0.279365 | + | 0.312949i | ||||
\(439\) | − | 18.0000i | − | 0.859093i | −0.903045 | − | 0.429547i | \(-0.858673\pi\) | ||
0.903045 | − | 0.429547i | \(-0.141327\pi\) | |||||||
\(440\) | −5.96154 | + | 5.96154i | −0.284205 | + | 0.284205i | ||||
\(441\) | 20.4084 | + | 2.32178i | 0.971827 | + | 0.110561i | ||||
\(442\) | −1.50977 | + | 4.61889i | −0.0718124 | + | 0.219698i | ||||
\(443\) | − | 30.8018i | − | 1.46344i | −0.681608 | − | 0.731718i | \(-0.738719\pi\) | ||
0.681608 | − | 0.731718i | \(-0.261281\pi\) | |||||||
\(444\) | −0.270810 | + | 4.77619i | −0.0128521 | + | 0.226668i | ||||
\(445\) | 32.3671 | 1.53435 | ||||||||
\(446\) | 8.33491 | 0.394669 | ||||||||
\(447\) | 21.6590 | + | 1.22807i | 1.02443 | + | 0.0580855i | ||||
\(448\) | −2.63122 | + | 2.63122i | −0.124314 | + | 0.124314i | ||||
\(449\) | −19.2149 | + | 19.2149i | −0.906809 | + | 0.906809i | −0.996013 | − | 0.0892043i | \(-0.971568\pi\) |
0.0892043 | + | 0.996013i | \(0.471568\pi\) | |||||||
\(450\) | −3.13481 | − | 3.93964i | −0.147776 | − | 0.185717i | ||||
\(451\) | 36.4365 | 1.71573 | ||||||||
\(452\) | −3.43781 | −0.161701 | ||||||||
\(453\) | −28.8568 | − | 1.63619i | −1.35581 | − | 0.0768747i | ||||
\(454\) | 13.0498i | 0.612457i | ||||||||
\(455\) | 30.9204 | − | 15.6862i | 1.44957 | − | 0.735378i | ||||
\(456\) | 5.84667 | + | 6.54954i | 0.273796 | + | 0.306710i | ||||
\(457\) | 11.4656 | − | 11.4656i | 0.536336 | − | 0.536336i | −0.386115 | − | 0.922451i | \(-0.626183\pi\) |
0.922451 | + | 0.386115i | \(0.126183\pi\) | |||||||
\(458\) | − | 13.0326i | − | 0.608974i | ||||||
\(459\) | 4.04325 | + | 5.71801i | 0.188723 | + | 0.266894i | ||||
\(460\) | −6.67822 | + | 6.67822i | −0.311374 | + | 0.311374i | ||||
\(461\) | −2.60452 | − | 2.60452i | −0.121305 | − | 0.121305i | 0.643848 | − | 0.765153i | \(-0.277337\pi\) |
−0.765153 | + | 0.643848i | \(0.777337\pi\) | |||||||
\(462\) | −20.9933 | − | 1.19032i | −0.976695 | − | 0.0553787i | ||||
\(463\) | 8.20311 | + | 8.20311i | 0.381231 | + | 0.381231i | 0.871546 | − | 0.490315i | \(-0.163118\pi\) |
−0.490315 | + | 0.871546i | \(0.663118\pi\) | |||||||
\(464\) | − | 3.65465i | − | 0.169663i | ||||||
\(465\) | 1.51951 | − | 1.35644i | 0.0704655 | − | 0.0629035i | ||||
\(466\) | 1.78455 | + | 1.78455i | 0.0826677 | + | 0.0826677i | ||||
\(467\) | −22.7603 | −1.05322 | −0.526612 | − | 0.850106i | \(-0.676538\pi\) | ||||
−0.526612 | + | 0.850106i | \(0.676538\pi\) | |||||||
\(468\) | 3.77191 | + | 10.1377i | 0.174357 | + | 0.468615i | ||||
\(469\) | −11.9060 | −0.549768 | ||||||||
\(470\) | −12.2033 | − | 12.2033i | −0.562895 | − | 0.562895i | ||||
\(471\) | −24.3716 | + | 21.7561i | −1.12298 | + | 1.00247i | ||||
\(472\) | 5.16845i | 0.237897i | ||||||||
\(473\) | 21.0138 | + | 21.0138i | 0.966216 | + | 0.966216i | ||||
\(474\) | −7.07964 | − | 0.401416i | −0.325179 | − | 0.0184377i | ||||
\(475\) | −6.01512 | − | 6.01512i | −0.275993 | − | 0.275993i | ||||
\(476\) | −3.54623 | + | 3.54623i | −0.162541 | + | 0.162541i | ||||
\(477\) | 0.646346 | + | 0.0735322i | 0.0295942 | + | 0.00336681i | ||||
\(478\) | 10.1836i | 0.465786i | ||||||||
\(479\) | 17.3876 | − | 17.3876i | 0.794460 | − | 0.794460i | −0.187755 | − | 0.982216i | \(-0.560121\pi\) |
0.982216 | + | 0.187755i | \(0.0601212\pi\) | |||||||
\(480\) | 2.98077 | + | 3.33911i | 0.136053 | + | 0.152409i | ||||
\(481\) | −3.09400 | + | 9.46556i | −0.141074 | + | 0.431592i | ||||
\(482\) | − | 28.9150i | − | 1.31704i | ||||||
\(483\) | −23.5170 | − | 1.33342i | −1.07006 | − | 0.0606725i | ||||
\(484\) | −0.356442 | −0.0162019 | ||||||||
\(485\) | 0.615628 | 0.0279542 | ||||||||
\(486\) | 14.9675 | + | 4.35584i | 0.678941 | + | 0.197585i | ||||
\(487\) | −10.0151 | + | 10.0151i | −0.453829 | + | 0.453829i | −0.896623 | − | 0.442795i | \(-0.853987\pi\) |
0.442795 | + | 0.896623i | \(0.353987\pi\) | |||||||
\(488\) | 4.61380 | − | 4.61380i | 0.208857 | − | 0.208857i | ||||
\(489\) | −6.87694 | − | 0.389923i | −0.310986 | − | 0.0176329i | ||||
\(490\) | 17.6933 | 0.799304 | ||||||||
\(491\) | 0.822276 | 0.0371088 | 0.0185544 | − | 0.999828i | \(-0.494094\pi\) | ||||
0.0185544 | + | 0.999828i | \(0.494094\pi\) | |||||||
\(492\) | 1.09507 | − | 19.3133i | 0.0493694 | − | 0.870711i | ||||
\(493\) | − | 4.92554i | − | 0.221835i | ||||||
\(494\) | 8.26844 | + | 16.2987i | 0.372015 | + | 0.733311i | ||||
\(495\) | −2.85901 | + | 25.1306i | −0.128503 | + | 1.12954i | ||||
\(496\) | −0.321779 | + | 0.321779i | −0.0144483 | + | 0.0144483i | ||||
\(497\) | − | 0.570551i | − | 0.0255927i | ||||||
\(498\) | −17.2507 | − | 19.3246i | −0.773024 | − | 0.865955i | ||||
\(499\) | −4.32178 | + | 4.32178i | −0.193469 | + | 0.193469i | −0.797193 | − | 0.603724i | \(-0.793683\pi\) |
0.603724 | + | 0.797193i | \(0.293683\pi\) | |||||||
\(500\) | 6.06996 | + | 6.06996i | 0.271457 | + | 0.271457i | ||||
\(501\) | −0.132999 | + | 2.34566i | −0.00594197 | + | 0.104796i | ||||
\(502\) | −13.0745 | − | 13.0745i | −0.583541 | − | 0.583541i | ||||
\(503\) | 38.1212i | 1.69974i | 0.526991 | + | 0.849871i | \(0.323320\pi\) | ||||
−0.526991 | + | 0.849871i | \(0.676680\pi\) | |||||||
\(504\) | −1.26187 | + | 11.0918i | −0.0562081 | + | 0.494067i | ||||
\(505\) | −32.3671 | − | 32.3671i | −1.44032 | − | 1.44032i | ||||
\(506\) | 11.9231 | 0.530046 | ||||||||
\(507\) | 2.17882 | + | 22.4110i | 0.0967647 | + | 0.995307i | ||||
\(508\) | −11.0745 | −0.491349 | ||||||||
\(509\) | −20.7795 | − | 20.7795i | −0.921036 | − | 0.921036i | 0.0760664 | − | 0.997103i | \(-0.475764\pi\) |
−0.997103 | + | 0.0760664i | \(0.975764\pi\) | |||||||
\(510\) | 4.01733 | + | 4.50028i | 0.177890 | + | 0.199276i | ||||
\(511\) | 18.8618i | 0.834397i | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 25.9593 | + | 4.45390i | 1.14613 | + | 0.196645i | ||||
\(514\) | −9.66589 | − | 9.66589i | −0.426344 | − | 0.426344i | ||||
\(515\) | −14.4468 | + | 14.4468i | −0.636603 | + | 0.636603i | ||||
\(516\) | 11.7700 | − | 10.5069i | 0.518146 | − | 0.462541i | ||||
\(517\) | 21.7873i | 0.958206i | ||||||||
\(518\) | −7.26734 | + | 7.26734i | −0.319309 | + | 0.319309i | ||||
\(519\) | 22.6068 | − | 20.1808i | 0.992331 | − | 0.885838i | ||||
\(520\) | 4.21545 | + | 8.30944i | 0.184860 | + | 0.364393i | ||||
\(521\) | 0.171761i | 0.00752497i | 0.999993 | + | 0.00376248i | \(0.00119764\pi\) | ||||
−0.999993 | + | 0.00376248i | \(0.998802\pi\) | |||||||
\(522\) | −6.82665 | − | 8.57933i | −0.298794 | − | 0.375507i | ||||
\(523\) | 20.8618 | 0.912223 | 0.456111 | − | 0.889923i | \(-0.349242\pi\) | ||||
0.456111 | + | 0.889923i | \(0.349242\pi\) | |||||||
\(524\) | −18.1015 | −0.790767 | ||||||||
\(525\) | 0.612308 | − | 10.7990i | 0.0267233 | − | 0.471309i | ||||
\(526\) | −10.3369 | + | 10.3369i | −0.450710 | + | 0.450710i | ||||
\(527\) | −0.433677 | + | 0.433677i | −0.0188913 | + | 0.0188913i | ||||
\(528\) | 0.319883 | − | 5.64166i | 0.0139211 | − | 0.245522i | ||||
\(529\) | −9.64356 | −0.419285 | ||||||||
\(530\) | 0.560360 | 0.0243405 | ||||||||
\(531\) | 9.65434 | + | 12.1330i | 0.418963 | + | 0.526527i | ||||
\(532\) | 18.8618i | 0.817763i | ||||||||
\(533\) | 12.5111 | − | 38.2756i | 0.541915 | − | 1.65790i | ||||
\(534\) | −16.1836 | + | 14.4468i | −0.700332 | + | 0.625175i | ||||
\(535\) | 8.43090 | − | 8.43090i | 0.364499 | − | 0.364499i | ||||
\(536\) | − | 3.19958i | − | 0.138201i | ||||||
\(537\) | −23.3891 | + | 20.8791i | −1.00932 | + | 0.901001i | ||||
\(538\) | 11.1685 | − | 11.1685i | 0.481506 | − | 0.481506i | ||||
\(539\) | −15.7946 | − | 15.7946i | −0.680320 | − | 0.680320i | ||||
\(540\) | 13.2346 | + | 2.27071i | 0.569528 | + | 0.0977156i | ||||
\(541\) | −22.6021 | − | 22.6021i | −0.971742 | − | 0.971742i | 0.0278698 | − | 0.999612i | \(-0.491128\pi\) |
−0.999612 | + | 0.0278698i | \(0.991128\pi\) | |||||||
\(542\) | − | 22.9535i | − | 0.985937i | ||||||
\(543\) | 2.19848 | + | 2.46277i | 0.0943458 | + | 0.105688i | ||||
\(544\) | −0.953002 | − | 0.953002i | −0.0408596 | − | 0.0408596i | ||||
\(545\) | 33.6792 | 1.44266 | ||||||||
\(546\) | −8.45879 | + | 21.6441i | −0.362003 | + | 0.926284i | ||||
\(547\) | 33.7527 | 1.44316 | 0.721580 | − | 0.692331i | \(-0.243416\pi\) | ||||
0.721580 | + | 0.692331i | \(0.243416\pi\) | |||||||
\(548\) | 0.976593 | + | 0.976593i | 0.0417180 | + | 0.0417180i | ||||
\(549\) | 2.21266 | − | 19.4492i | 0.0944340 | − | 0.830073i | ||||
\(550\) | 5.47511i | 0.233459i | ||||||||
\(551\) | −13.0991 | − | 13.0991i | −0.558039 | − | 0.558039i | ||||
\(552\) | 0.358338 | − | 6.31988i | 0.0152519 | − | 0.268992i | ||||
\(553\) | −10.7722 | − | 10.7722i | −0.458081 | − | 0.458081i | ||||
\(554\) | −18.4901 | + | 18.4901i | −0.785568 | + | 0.785568i | ||||
\(555\) | 8.23278 | + | 9.22250i | 0.349462 | + | 0.391473i | ||||
\(556\) | − | 7.10912i | − | 0.301494i | ||||||
\(557\) | −7.40027 | + | 7.40027i | −0.313559 | + | 0.313559i | −0.846287 | − | 0.532727i | \(-0.821167\pi\) |
0.532727 | + | 0.846287i | \(0.321167\pi\) | |||||||
\(558\) | −0.154317 | + | 1.35644i | −0.00653276 | + | 0.0574228i | ||||
\(559\) | 29.2899 | − | 14.8590i | 1.23883 | − | 0.628469i | ||||
\(560\) | 9.61619i | 0.406358i | ||||||||
\(561\) | 0.431122 | − | 7.60354i | 0.0182020 | − | 0.321022i | ||||
\(562\) | 4.33690 | 0.182941 | ||||||||
\(563\) | −38.1111 | −1.60619 | −0.803095 | − | 0.595851i | \(-0.796815\pi\) | ||||
−0.803095 | + | 0.595851i | \(0.796815\pi\) | |||||||
\(564\) | 11.5485 | + | 0.654800i | 0.486278 | + | 0.0275720i | ||||
\(565\) | −6.28199 | + | 6.28199i | −0.264285 | + | 0.264285i | ||||
\(566\) | 6.61600 | − | 6.61600i | 0.278091 | − | 0.278091i | ||||
\(567\) | 17.7565 | + | 28.3952i | 0.745703 | + | 1.19249i | ||||
\(568\) | 0.153328 | 0.00643350 | ||||||||
\(569\) | 38.2930 | 1.60533 | 0.802663 | − | 0.596433i | \(-0.203416\pi\) | ||||
0.802663 | + | 0.596433i | \(0.203416\pi\) | |||||||
\(570\) | 22.6519 | + | 1.28436i | 0.948783 | + | 0.0537961i | ||||
\(571\) | 34.6145i | 1.44857i | 0.689500 | + | 0.724285i | \(0.257830\pi\) | ||||
−0.689500 | + | 0.724285i | \(0.742170\pi\) | |||||||
\(572\) | 3.65465 | − | 11.1808i | 0.152808 | − | 0.467492i | ||||
\(573\) | 7.32457 | + | 8.20510i | 0.305988 | + | 0.342773i | ||||
\(574\) | 29.3867 | − | 29.3867i | 1.22658 | − | 1.22658i | ||||
\(575\) | 6.13331i | 0.255777i | ||||||||
\(576\) | −2.98077 | − | 0.339111i | −0.124199 | − | 0.0141296i | ||||
\(577\) | 4.72243 | − | 4.72243i | 0.196597 | − | 0.196597i | −0.601942 | − | 0.798540i | \(-0.705606\pi\) |
0.798540 | + | 0.601942i | \(0.205606\pi\) | |||||||
\(578\) | 10.7364 | + | 10.7364i | 0.446576 | + | 0.446576i | ||||
\(579\) | −10.4241 | − | 0.591046i | −0.433210 | − | 0.0245631i | ||||
\(580\) | −6.67822 | − | 6.67822i | −0.277298 | − | 0.277298i | ||||
\(581\) | − | 55.6522i | − | 2.30884i | ||||||
\(582\) | −0.307814 | + | 0.274781i | −0.0127593 | + | 0.0113900i | ||||
\(583\) | −0.500224 | − | 0.500224i | −0.0207172 | − | 0.0207172i | ||||
\(584\) | −5.06886 | −0.209751 | ||||||||
\(585\) | 25.4173 | + | 11.6323i | 1.05088 | + | 0.480937i | ||||
\(586\) | 4.24732 | 0.175455 | ||||||||
\(587\) | 11.0090 | + | 11.0090i | 0.454391 | + | 0.454391i | 0.896809 | − | 0.442418i | \(-0.145879\pi\) |
−0.442418 | + | 0.896809i | \(0.645879\pi\) | |||||||
\(588\) | −8.84667 | + | 7.89729i | −0.364831 | + | 0.325679i | ||||
\(589\) | 2.30666i | 0.0950441i | ||||||||
\(590\) | 9.44443 | + | 9.44443i | 0.388821 | + | 0.388821i | ||||
\(591\) | −6.81449 | − | 0.386383i | −0.280311 | − | 0.0158937i | ||||
\(592\) | −1.95300 | − | 1.95300i | −0.0802679 | − | 0.0802679i | ||||
\(593\) | 8.06905 | − | 8.06905i | 0.331356 | − | 0.331356i | −0.521745 | − | 0.853101i | \(-0.674719\pi\) |
0.853101 | + | 0.521745i | \(0.174719\pi\) | |||||||
\(594\) | −9.78734 | − | 13.8414i | −0.401579 | − | 0.567919i | ||||
\(595\) | 12.9602i | 0.531317i | ||||||||
\(596\) | −8.85644 | + | 8.85644i | −0.362774 | + | 0.362774i | ||||
\(597\) | 19.9462 | + | 22.3441i | 0.816345 | + | 0.914483i | ||||
\(598\) | 4.09400 | − | 12.5249i | 0.167416 | − | 0.512181i | ||||
\(599\) | − | 22.0180i | − | 0.899633i | −0.893121 | − | 0.449816i | \(-0.851489\pi\) | ||
0.893121 | − | 0.449816i | \(-0.148511\pi\) | |||||||
\(600\) | 2.90210 | + | 0.164550i | 0.118478 | + | 0.00671771i | ||||
\(601\) | −38.2529 | −1.56037 | −0.780184 | − | 0.625550i | \(-0.784875\pi\) | ||||
−0.780184 | + | 0.625550i | \(0.784875\pi\) | |||||||
\(602\) | 33.8960 | 1.38150 | ||||||||
\(603\) | −5.97662 | − | 7.51106i | −0.243387 | − | 0.305874i | ||||
\(604\) | 11.7997 | − | 11.7997i | 0.480122 | − | 0.480122i | ||||
\(605\) | −0.651335 | + | 0.651335i | −0.0264805 | + | 0.0264805i | ||||
\(606\) | 30.6304 | + | 1.73675i | 1.24427 | + | 0.0705506i | ||||
\(607\) | 8.06933 | 0.327524 | 0.163762 | − | 0.986500i | \(-0.447637\pi\) | ||||
0.163762 | + | 0.986500i | \(0.447637\pi\) | |||||||
\(608\) | −5.06886 | −0.205569 | ||||||||
\(609\) | 1.33342 | − | 23.5170i | 0.0540328 | − | 0.952957i | ||||
\(610\) | − | 16.8618i | − | 0.682714i | ||||||
\(611\) | 22.8870 | + | 7.48105i | 0.925910 | + | 0.302651i | ||||
\(612\) | −4.01733 | − | 0.457036i | −0.162391 | − | 0.0184746i | ||||
\(613\) | −23.0896 | + | 23.0896i | −0.932579 | + | 0.932579i | −0.997867 | − | 0.0652872i | \(-0.979204\pi\) |
0.0652872 | + | 0.997867i | \(0.479204\pi\) | |||||||
\(614\) | 4.59241i | 0.185335i | ||||||||
\(615\) | −33.2906 | − | 37.2927i | −1.34241 | − | 1.50379i | ||||
\(616\) | 8.58423 | − | 8.58423i | 0.345868 | − | 0.345868i | ||||
\(617\) | −32.9195 | − | 32.9195i | −1.32529 | − | 1.32529i | −0.909430 | − | 0.415858i | \(-0.863481\pi\) |
−0.415858 | − | 0.909430i | \(-0.636519\pi\) | |||||||
\(618\) | 0.775184 | − | 13.6716i | 0.0311825 | − | 0.549954i | ||||
\(619\) | −25.3716 | − | 25.3716i | −1.01977 | − | 1.01977i | −0.999801 | − | 0.0199687i | \(-0.993643\pi\) |
−0.0199687 | − | 0.999801i | \(-0.506357\pi\) | |||||||
\(620\) | 1.17599i | 0.0472288i | ||||||||
\(621\) | −10.9639 | − | 15.5054i | −0.439968 | − | 0.622208i | ||||
\(622\) | 2.43090 | + | 2.43090i | 0.0974701 | + | 0.0974701i | ||||
\(623\) | −46.6065 | −1.86725 | ||||||||
\(624\) | −5.81658 | − | 2.27319i | −0.232850 | − | 0.0910004i | ||||
\(625\) | 30.5747 | 1.22299 | ||||||||
\(626\) | −1.06757 | − | 1.06757i | −0.0426686 | − | 0.0426686i | ||||
\(627\) | −19.0745 | − | 21.3675i | −0.761760 | − | 0.853337i | ||||
\(628\) | − | 18.8618i | − | 0.752668i | ||||||
\(629\) | −2.63216 | − | 2.63216i | −0.104951 | − | 0.104951i | ||||
\(630\) | 17.9624 | + | 22.5741i | 0.715641 | + | 0.899375i | ||||
\(631\) | −0.200326 | − | 0.200326i | −0.00797485 | − | 0.00797485i | 0.703108 | − | 0.711083i | \(-0.251795\pi\) |
−0.711083 | + | 0.703108i | \(0.751795\pi\) | |||||||
\(632\) | 2.89489 | − | 2.89489i | 0.115153 | − | 0.115153i | ||||
\(633\) | 12.1662 | − | 10.8606i | 0.483565 | − | 0.431671i | ||||
\(634\) | 22.8618i | 0.907958i | ||||||||
\(635\) | −20.2366 | + | 20.2366i | −0.803065 | + | 0.803065i | ||||
\(636\) | −0.280180 | + | 0.250112i | −0.0111099 | + | 0.00991759i | ||||
\(637\) | −22.0151 | + | 11.1685i | −0.872271 | + | 0.442510i | ||||
\(638\) | 11.9231i | 0.472040i | ||||||||
\(639\) | 0.359939 | − | 0.286407i | 0.0142390 | − | 0.0113301i | ||||
\(640\) | −2.58423 | −0.102150 | ||||||||
\(641\) | 34.2846 | 1.35416 | 0.677081 | − | 0.735908i | \(-0.263245\pi\) | ||||
0.677081 | + | 0.735908i | \(0.263245\pi\) | |||||||
\(642\) | −0.452383 | + | 7.97851i | −0.0178541 | + | 0.314887i | ||||
\(643\) | −10.7873 | + | 10.7873i | −0.425411 | + | 0.425411i | −0.887062 | − | 0.461651i | \(-0.847257\pi\) |
0.461651 | + | 0.887062i | \(0.347257\pi\) | |||||||
\(644\) | 9.61619 | − | 9.61619i | 0.378931 | − | 0.378931i | ||||
\(645\) | 2.30810 | − | 40.7071i | 0.0908813 | − | 1.60284i | ||||
\(646\) | −6.83155 | −0.268784 | ||||||||
\(647\) | −2.69550 | −0.105971 | −0.0529855 | − | 0.998595i | \(-0.516874\pi\) | ||||
−0.0529855 | + | 0.998595i | \(0.516874\pi\) | |||||||
\(648\) | −7.63084 | + | 4.77183i | −0.299768 | + | 0.187455i | ||||
\(649\) | − | 16.8618i | − | 0.661883i | ||||||
\(650\) | 5.75146 | + | 1.87997i | 0.225591 | + | 0.0737385i | ||||
\(651\) | −2.18799 | + | 1.95319i | −0.0857541 | + | 0.0765514i | ||||
\(652\) | 2.81201 | − | 2.81201i | 0.110127 | − | 0.110127i | ||||
\(653\) | 43.4774i | 1.70140i | 0.525651 | + | 0.850700i | \(0.323822\pi\) | ||||
−0.525651 | + | 0.850700i | \(0.676178\pi\) | |||||||
\(654\) | −16.8396 | + | 15.0325i | −0.658481 | + | 0.587815i | ||||
\(655\) | −33.0772 | + | 33.0772i | −1.29243 | + | 1.29243i | ||||
\(656\) | 7.89729 | + | 7.89729i | 0.308337 | + | 0.308337i | ||||
\(657\) | −11.8992 | + | 9.46831i | −0.464232 | + | 0.369394i | ||||
\(658\) | 17.5719 | + | 17.5719i | 0.685024 | + | 0.685024i | ||||
\(659\) | 39.2972i | 1.53080i | 0.643553 | + | 0.765401i | \(0.277460\pi\) | ||||
−0.643553 | + | 0.765401i | \(0.722540\pi\) | |||||||
\(660\) | −9.72461 | − | 10.8937i | −0.378530 | − | 0.424036i | ||||
\(661\) | 27.4958 | + | 27.4958i | 1.06946 | + | 1.06946i | 0.997400 | + | 0.0720628i | \(0.0229582\pi\) |
0.0720628 | + | 0.997400i | \(0.477042\pi\) | |||||||
\(662\) | −7.81338 | −0.303676 | ||||||||
\(663\) | −7.83929 | − | 3.06369i | −0.304453 | − | 0.118984i | ||||
\(664\) | 14.9558 | 0.580397 | ||||||||
\(665\) | 34.4666 | + | 34.4666i | 1.33656 | + | 1.33656i | ||||
\(666\) | −8.23278 | − | 0.936611i | −0.319014 | − | 0.0362929i | ||||
\(667\) | 13.3564i | 0.517164i | ||||||||
\(668\) | −0.959150 | − | 0.959150i | −0.0371106 | − | 0.0371106i | ||||
\(669\) | −0.817238 | + | 14.4133i | −0.0315962 | + | 0.557252i | ||||
\(670\) | −5.84667 | − | 5.84667i | −0.225877 | − | 0.225877i | ||||
\(671\) | −15.0523 | + | 15.0523i | −0.581086 | + | 0.581086i | ||||
\(672\) | −4.29211 | − | 4.80810i | −0.165572 | − | 0.185476i | ||||
\(673\) | − | 7.29153i | − | 0.281068i | −0.990076 | − | 0.140534i | \(-0.955118\pi\) | ||
0.990076 | − | 0.140534i | \(-0.0448819\pi\) | |||||||
\(674\) | −13.3128 | + | 13.3128i | −0.512790 | + | 0.512790i | ||||
\(675\) | 7.12009 | − | 5.03466i | 0.274052 | − | 0.193784i | ||||
\(676\) | −10.4902 | − | 7.67822i | −0.403470 | − | 0.295316i | ||||
\(677\) | 16.3200i | 0.627230i | 0.949550 | + | 0.313615i | \(0.101540\pi\) | ||||
−0.949550 | + | 0.313615i | \(0.898460\pi\) | |||||||
\(678\) | 0.337077 | − | 5.94491i | 0.0129454 | − | 0.228313i | ||||
\(679\) | −0.886464 | −0.0340194 | ||||||||
\(680\) | −3.48289 | −0.133563 | ||||||||
\(681\) | −22.5666 | − | 1.27953i | −0.864756 | − | 0.0490318i | ||||
\(682\) | 1.04979 | − | 1.04979i | 0.0401984 | − | 0.0401984i | ||||
\(683\) | −0.171761 | + | 0.171761i | −0.00657223 | + | 0.00657223i | −0.710385 | − | 0.703813i | \(-0.751479\pi\) |
0.703813 | + | 0.710385i | \(0.251479\pi\) | |||||||
\(684\) | −11.8992 | + | 9.46831i | −0.454978 | + | 0.362030i | ||||
\(685\) | 3.56910 | 0.136368 | ||||||||
\(686\) | 0.570551 | 0.0217837 | ||||||||
\(687\) | 22.5369 | + | 1.27785i | 0.859838 | + | 0.0487529i | ||||
\(688\) | 9.10912i | 0.347282i | ||||||||
\(689\) | −0.697233 | + | 0.353712i | −0.0265625 | + | 0.0134754i | ||||
\(690\) | −10.8937 | − | 12.2033i | −0.414715 | − | 0.464571i | ||||
\(691\) | 18.3218 | − | 18.3218i | 0.696993 | − | 0.696993i | −0.266768 | − | 0.963761i | \(-0.585956\pi\) |
0.963761 | + | 0.266768i | \(0.0859556\pi\) | |||||||
\(692\) | 17.4960i | 0.665099i | ||||||||
\(693\) | 4.11678 | − | 36.1864i | 0.156383 | − | 1.37461i | ||||
\(694\) | −20.7057 | + | 20.7057i | −0.785977 | + | 0.785977i | ||||
\(695\) | −12.9907 | − | 12.9907i | −0.492764 | − | 0.492764i | ||||
\(696\) | 6.31988 | + | 0.358338i | 0.239555 | + | 0.0135828i | ||||
\(697\) | 10.6436 | + | 10.6436i | 0.403153 | + | 0.403153i | ||||
\(698\) | − | 6.89931i | − | 0.261143i | ||||||
\(699\) | −3.26095 | + | 2.91100i | −0.123341 | + | 0.110104i | ||||
\(700\) | 4.41577 | + | 4.41577i | 0.166901 | + | 0.166901i | ||||
\(701\) | −33.7243 | −1.27375 | −0.636874 | − | 0.770968i | \(-0.719773\pi\) | ||||
−0.636874 | + | 0.770968i | \(0.719773\pi\) | |||||||
\(702\) | −17.9007 | + | 5.52867i | −0.675617 | + | 0.208666i | ||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 2.30690 | + | 2.30690i | 0.0869445 | + | 0.0869445i | ||||
\(705\) | 22.2993 | − | 19.9063i | 0.839841 | − | 0.749713i | ||||
\(706\) | − | 7.90600i | − | 0.297546i | ||||||
\(707\) | 46.6065 | + | 46.6065i | 1.75282 | + | 1.75282i | ||||
\(708\) | −8.93766 | − | 0.506767i | −0.335898 | − | 0.0190455i | ||||
\(709\) | −3.79689 | − | 3.79689i | −0.142595 | − | 0.142595i | 0.632206 | − | 0.774801i | \(-0.282150\pi\) |
−0.774801 | + | 0.632206i | \(0.782150\pi\) | |||||||
\(710\) | 0.280180 | − | 0.280180i | 0.0105150 | − | 0.0105150i | ||||
\(711\) | 1.38832 | − | 12.2033i | 0.0520660 | − | 0.457658i | ||||
\(712\) | − | 12.5249i | − | 0.469390i | ||||||
\(713\) | 1.17599 | − | 1.17599i | 0.0440411 | − | 0.0440411i | ||||
\(714\) | −5.78469 | − | 6.48010i | −0.216487 | − | 0.242512i | ||||
\(715\) | −13.7527 | − | 27.1091i | −0.514321 | − | 1.01382i | ||||
\(716\) | − | 18.1015i | − | 0.676484i | ||||||
\(717\) | −17.6102 | − | 0.998500i | −0.657664 | − | 0.0372897i | ||||
\(718\) | 18.2182 | 0.679899 | ||||||||
\(719\) | 30.6300 | 1.14231 | 0.571153 | − | 0.820844i | \(-0.306496\pi\) | ||||
0.571153 | + | 0.820844i | \(0.306496\pi\) | |||||||
\(720\) | −6.06650 | + | 4.82717i | −0.226085 | + | 0.179898i | ||||
\(721\) | 20.8025 | − | 20.8025i | 0.774724 | − | 0.774724i | ||||
\(722\) | −4.73291 | + | 4.73291i | −0.176141 | + | 0.176141i | ||||
\(723\) | 50.0020 | + | 2.83512i | 1.85959 | + | 0.105439i | ||||
\(724\) | −1.90600 | −0.0708361 | ||||||||
\(725\) | −6.13331 | −0.227785 | ||||||||
\(726\) | 0.0349492 | − | 0.616386i | 0.00129709 | − | 0.0228762i | ||||
\(727\) | − | 0.430897i | − | 0.0159811i | −0.999968 | − | 0.00799055i | \(-0.997457\pi\) | ||
0.999968 | − | 0.00799055i | \(-0.00254350\pi\) | |||||||
\(728\) | −6.06996 | − | 11.9650i | −0.224968 | − | 0.443454i | ||||
\(729\) | −9.00000 | + | 25.4558i | −0.333333 | + | 0.942809i | ||||
\(730\) | −9.26245 | + | 9.26245i | −0.342819 | + | 0.342819i | ||||
\(731\) | 12.2768i | 0.454074i | ||||||||
\(732\) | 7.52613 | + | 8.43090i | 0.278174 | + | 0.311615i | ||||
\(733\) | 8.50256 | − | 8.50256i | 0.314049 | − | 0.314049i | −0.532427 | − | 0.846476i | \(-0.678720\pi\) |
0.846476 | + | 0.532427i | \(0.178720\pi\) | |||||||
\(734\) | −5.35216 | − | 5.35216i | −0.197552 | − | 0.197552i | ||||
\(735\) | −1.73483 | + | 30.5966i | −0.0639903 | + | 1.12857i | ||||
\(736\) | 2.58423 | + | 2.58423i | 0.0952558 | + | 0.0952558i | ||||
\(737\) | 10.4385i | 0.384506i | ||||||||
\(738\) | 33.2906 | + | 3.78734i | 1.22544 | + | 0.139414i | ||||
\(739\) | 15.1836 | + | 15.1836i | 0.558537 | + | 0.558537i | 0.928891 | − | 0.370354i | \(-0.120764\pi\) |
−0.370354 | + | 0.928891i | \(0.620764\pi\) | |||||||
\(740\) | −7.13753 | −0.262381 | ||||||||
\(741\) | −28.9956 | + | 12.7003i | −1.06518 | + | 0.466558i | ||||
\(742\) | −0.806880 | −0.0296215 | ||||||||
\(743\) | −1.06757 | − | 1.06757i | −0.0391653 | − | 0.0391653i | 0.687253 | − | 0.726418i | \(-0.258816\pi\) |
−0.726418 | + | 0.687253i | \(0.758816\pi\) | |||||||
\(744\) | −0.524893 | − | 0.587994i | −0.0192435 | − | 0.0215569i | ||||
\(745\) | 32.3671i | 1.18584i | ||||||||
\(746\) | −11.1808 | − | 11.1808i | −0.409357 | − | 0.409357i | ||||
\(747\) | 35.1089 | − | 27.9365i | 1.28457 | − | 1.02214i | ||||
\(748\) | 3.10912 | + | 3.10912i | 0.113681 | + | 0.113681i | ||||
\(749\) | −12.1399 | + | 12.1399i | −0.443583 | + | 0.443583i | ||||
\(750\) | −11.0918 | + | 9.90147i | −0.405015 | + | 0.361550i | ||||
\(751\) | − | 1.88134i | − | 0.0686509i | −0.999411 | − | 0.0343255i | \(-0.989072\pi\) | ||
0.999411 | − | 0.0343255i | \(-0.0109283\pi\) | |||||||
\(752\) | −4.72222 | + | 4.72222i | −0.172201 | + | 0.172201i | ||||
\(753\) | 23.8913 | − | 21.3274i | 0.870646 | − | 0.777212i | ||||
\(754\) | 12.5249 | + | 4.09400i | 0.456130 | + | 0.149095i | ||||
\(755\) | − | 43.1236i | − | 1.56943i | ||||||
\(756\) | −19.0570 | − | 3.26967i | −0.693097 | − | 0.118917i | ||||
\(757\) | −28.6189 | −1.04017 | −0.520086 | − | 0.854114i | \(-0.674100\pi\) | ||||
−0.520086 | + | 0.854114i | \(0.674100\pi\) | |||||||
\(758\) | −7.54752 | −0.274138 | ||||||||
\(759\) | −1.16906 | + | 20.6183i | −0.0424342 | + | 0.748396i | ||||
\(760\) | −9.26245 | + | 9.26245i | −0.335984 | + | 0.335984i | ||||
\(761\) | −30.4408 | + | 30.4408i | −1.10348 | + | 1.10348i | −0.109490 | + | 0.993988i | \(0.534922\pi\) |
−0.993988 | + | 0.109490i | \(0.965078\pi\) | |||||||
\(762\) | 1.08585 | − | 19.1508i | 0.0393362 | − | 0.693759i | ||||
\(763\) | −48.4958 | −1.75567 | ||||||||
\(764\) | −6.35014 | −0.229740 | ||||||||
\(765\) | −8.17612 | + | 6.50581i | −0.295608 | + | 0.235218i | ||||
\(766\) | − | 15.3520i | − | 0.554691i | ||||||
\(767\) | −17.7129 | − | 5.78978i | −0.639575 | − | 0.209057i | ||||
\(768\) | 1.29211 | − | 1.15345i | 0.0466251 | − | 0.0416215i | ||||
\(769\) | 14.9956 | − | 14.9956i | 0.540755 | − | 0.540755i | −0.382996 | − | 0.923750i | \(-0.625108\pi\) |
0.923750 | + | 0.382996i | \(0.125108\pi\) | |||||||
\(770\) | − | 31.3723i | − | 1.13058i | ||||||
\(771\) | 17.6627 | − | 15.7672i | 0.636107 | − | 0.567843i | ||||
\(772\) | 4.26245 | − | 4.26245i | 0.153409 | − | 0.153409i | ||||
\(773\) | 6.25917 | + | 6.25917i | 0.225127 | + | 0.225127i | 0.810653 | − | 0.585527i | \(-0.199112\pi\) |
−0.585527 | + | 0.810653i | \(0.699112\pi\) | |||||||
\(774\) | 17.0153 | + | 21.3838i | 0.611601 | + | 0.768623i | ||||
\(775\) | 0.540016 | + | 0.540016i | 0.0193980 | + | 0.0193980i | ||||
\(776\) | − | 0.238226i | − | 0.00855180i | ||||||
\(777\) | −11.8547 | − | 13.2798i | −0.425283 | − | 0.476409i | ||||
\(778\) | −3.26245 | − | 3.26245i | −0.116964 | − | 0.116964i | ||||
\(779\) | 56.6113 | 2.02831 | ||||||||
\(780\) | −14.7826 | + | 6.47492i | −0.529303 | + | 0.231839i | ||||
\(781\) | −0.500224 | −0.0178994 | ||||||||
\(782\) | 3.48289 | + | 3.48289i | 0.124548 | + | 0.124548i | ||||
\(783\) | 15.5054 | − | 10.9639i | 0.554116 | − | 0.391819i | ||||
\(784\) | − | 6.84667i | − | 0.244524i | ||||||
\(785\) | −34.4666 | − | 34.4666i | −1.23017 | − | 1.23017i | ||||
\(786\) | 1.77485 | − | 31.3024i | 0.0633068 | − | 1.11652i | ||||
\(787\) | 7.15333 | + | 7.15333i | 0.254989 | + | 0.254989i | 0.823012 | − | 0.568024i | \(-0.192292\pi\) |
−0.568024 | + | 0.823012i | \(0.692292\pi\) | |||||||
\(788\) | 2.78647 | − | 2.78647i | 0.0992640 | − | 0.0992640i | ||||
\(789\) | −16.8618 | − | 18.8889i | −0.600296 | − | 0.672461i | ||||
\(790\) | − | 10.5798i | − | 0.376413i | ||||||
\(791\) | 9.04564 | − | 9.04564i | 0.321626 | − | 0.321626i | ||||
\(792\) | 9.72461 | + | 1.10633i | 0.345549 | + | 0.0393117i | ||||
\(793\) | 10.6436 | + | 20.9805i | 0.377964 | + | 0.745038i | ||||
\(794\) | 17.7343i | 0.629365i | ||||||||
\(795\) | −0.0549433 | + | 0.969015i | −0.00194864 | + | 0.0343674i | ||||
\(796\) | −17.2927 | −0.612923 | ||||||||
\(797\) | 28.0263 | 0.992742 | 0.496371 | − | 0.868110i | \(-0.334665\pi\) | ||||
0.496371 | + | 0.868110i | \(0.334665\pi\) | |||||||
\(798\) | −32.6172 | − | 1.84940i | −1.15464 | − | 0.0654680i | ||||
\(799\) | −6.36436 | + | 6.36436i | −0.225155 | + | 0.225155i | ||||
\(800\) | −1.18668 | + | 1.18668i | −0.0419555 | + | 0.0419555i | ||||
\(801\) | −23.3957 | − | 29.4023i | −0.826647 | − | 1.03888i | ||||
\(802\) | −5.14378 | −0.181633 | ||||||||
\(803\) | 16.5369 | 0.583574 | ||||||||
\(804\) | 5.53295 | + | 0.313719i | 0.195132 | + | 0.0110640i | ||||
\(805\) | − | 35.1438i | − | 1.23866i | ||||||
\(806\) | −0.742311 | − | 1.46324i | −0.0261468 | − | 0.0515403i | ||||
\(807\) | 18.2182 | + | 20.4084i | 0.641312 | + | 0.718409i | ||||
\(808\) | −12.5249 | + | 12.5249i | −0.440624 | + | 0.440624i | ||||
\(809\) | − | 35.1638i | − | 1.23629i | −0.786062 | − | 0.618147i | \(-0.787884\pi\) | ||
0.786062 | − | 0.618147i | \(-0.212116\pi\) | |||||||
\(810\) | −5.22433 | + | 22.6637i | −0.183564 | + | 0.796320i | ||||
\(811\) | 31.2529 | − | 31.2529i | 1.09744 | − | 1.09744i | 0.102728 | − | 0.994709i | \(-0.467243\pi\) |
0.994709 | − | 0.102728i | \(-0.0327572\pi\) | |||||||
\(812\) | 9.61619 | + | 9.61619i | 0.337462 | + | 0.337462i | ||||
\(813\) | 39.6929 | + | 2.25059i | 1.39209 | + | 0.0789317i | ||||
\(814\) | 6.37157 | + | 6.37157i | 0.223323 | + | 0.223323i | ||||
\(815\) | − | 10.2769i | − | 0.359984i | ||||||
\(816\) | 1.74144 | − | 1.55456i | 0.0609627 | − | 0.0544205i | ||||
\(817\) | 32.6491 | + | 32.6491i | 1.14225 | + | 1.14225i | ||||
\(818\) | −26.3035 | −0.919679 | ||||||||
\(819\) | −36.5993 | − | 16.7498i | −1.27888 | − | 0.585284i | ||||
\(820\) | 28.8618 | 1.00790 | ||||||||
\(821\) | 13.0081 | + | 13.0081i | 0.453986 | + | 0.453986i | 0.896675 | − | 0.442689i | \(-0.145976\pi\) |
−0.442689 | + | 0.896675i | \(0.645976\pi\) | |||||||
\(822\) | −1.78455 | + | 1.59304i | −0.0622434 | + | 0.0555637i | ||||
\(823\) | − | 19.5356i | − | 0.680968i | −0.940250 | − | 0.340484i | \(-0.889409\pi\) | ||
0.940250 | − | 0.340484i | \(-0.110591\pi\) | |||||||
\(824\) | 5.59039 | + | 5.59039i | 0.194750 | + | 0.194750i | ||||
\(825\) | −9.46796 | − | 0.536834i | −0.329632 | − | 0.0186902i | ||||
\(826\) | −13.5993 | − | 13.5993i | −0.473182 | − | 0.473182i | ||||
\(827\) | 18.6720 | − | 18.6720i | 0.649290 | − | 0.649290i | −0.303532 | − | 0.952821i | \(-0.598166\pi\) |
0.952821 | + | 0.303532i | \(0.0981658\pi\) | |||||||
\(828\) | 10.8937 | + | 1.23933i | 0.378581 | + | 0.0430697i | ||||
\(829\) | 2.85622i | 0.0992006i | 0.998769 | + | 0.0496003i | \(0.0157947\pi\) | ||||
−0.998769 | + | 0.0496003i | \(0.984205\pi\) | |||||||
\(830\) | 27.3291 | − | 27.3291i | 0.948606 | − | 0.948606i | ||||
\(831\) | −30.1614 | − | 33.7873i | −1.04629 | − | 1.17207i | ||||
\(832\) | 3.21545 | − | 1.63122i | 0.111476 | − | 0.0565525i | ||||
\(833\) | − | 9.22759i | − | 0.319717i | ||||||
\(834\) | 12.2936 | + | 0.697049i | 0.425693 | + | 0.0241368i | ||||
\(835\) | −3.50535 | −0.121308 | ||||||||
\(836\) | 16.5369 | 0.571940 | ||||||||
\(837\) | −2.33053 | − | 0.399856i | −0.0805549 | − | 0.0138210i | ||||
\(838\) | −0.250112 | + | 0.250112i | −0.00863998 | + | 0.00863998i | ||||
\(839\) | 35.2438 | − | 35.2438i | 1.21675 | − | 1.21675i | 0.247988 | − | 0.968763i | \(-0.420231\pi\) |
0.968763 | − | 0.247988i | \(-0.0797693\pi\) | |||||||
\(840\) | −16.6290 | − | 0.942868i | −0.573756 | − | 0.0325320i | ||||
\(841\) | 15.6436 | 0.539433 | ||||||||
\(842\) | 32.3979 | 1.11651 | ||||||||
\(843\) | −0.425233 | + | 7.49969i | −0.0146458 | + | 0.258303i | ||||
\(844\) | 9.41577i | 0.324104i | ||||||||
\(845\) | −33.1996 | + | 5.13845i | −1.14210 | + | 0.176768i | ||||
\(846\) | −2.26466 | + | 19.9063i | −0.0778605 | + | 0.684391i | ||||
\(847\) | 0.937879 | − | 0.937879i | 0.0322259 | − | 0.0322259i | ||||
\(848\) | − | 0.216838i | − | 0.00744626i | ||||||
\(849\) | 10.7922 | + | 12.0896i | 0.370387 | + | 0.414913i | ||||
\(850\) | −1.59935 | + | 1.59935i | −0.0548572 | + | 0.0548572i | ||||
\(851\) | 7.13753 | + | 7.13753i | 0.244671 | + | 0.244671i | ||||
\(852\) | −0.0150338 | + | 0.265146i | −0.000515050 | + | 0.00908375i | ||||
\(853\) | 31.6217 | + | 31.6217i | 1.08271 | + | 1.08271i | 0.996256 | + | 0.0864494i | \(0.0275521\pi\) |
0.0864494 | + | 0.996256i | \(0.472448\pi\) | |||||||
\(854\) | 24.2799i | 0.830840i | ||||||||
\(855\) | −4.44204 | + | 39.0454i | −0.151914 | + | 1.33532i | ||||
\(856\) | −3.26245 | − | 3.26245i | −0.111508 | − | 0.111508i | ||||
\(857\) | −21.9628 | −0.750234 | −0.375117 | − | 0.926978i | \(-0.622397\pi\) | ||||
−0.375117 | + | 0.926978i | \(0.622397\pi\) | |||||||
\(858\) | 18.9763 | + | 7.41616i | 0.647840 | + | 0.253183i | ||||
\(859\) | −37.2680 | −1.27157 | −0.635784 | − | 0.771867i | \(-0.719323\pi\) | ||||
−0.635784 | + | 0.771867i | \(0.719323\pi\) | |||||||
\(860\) | 16.6453 | + | 16.6453i | 0.567600 | + | 0.567600i | ||||
\(861\) | 47.9363 | + | 53.6990i | 1.63366 | + | 1.83006i | ||||
\(862\) | − | 8.34132i | − | 0.284106i | ||||||
\(863\) | −36.6549 | − | 36.6549i | −1.24775 | − | 1.24775i | −0.956713 | − | 0.291034i | \(-0.906001\pi\) |
−0.291034 | − | 0.956713i | \(-0.593999\pi\) | |||||||
\(864\) | 0.878680 | − | 5.12132i | 0.0298933 | − | 0.174231i | ||||
\(865\) | 31.9709 | + | 31.9709i | 1.08704 | + | 1.08704i | ||||
\(866\) | −26.5938 | + | 26.5938i | −0.903695 | + | 0.903695i | ||||
\(867\) | −19.6189 | + | 17.5135i | −0.666292 | + | 0.594789i | ||||
\(868\) | − | 1.69334i | − | 0.0574758i | ||||||
\(869\) | −9.44443 | + | 9.44443i | −0.320380 | + | 0.320380i | ||||
\(870\) | 12.2033 | − | 10.8937i | 0.413730 | − | 0.369330i | ||||
\(871\) | 10.9653 | + | 3.58423i | 0.371546 | + | 0.121447i | ||||
\(872\) | − | 13.0326i | − | 0.441340i | ||||||
\(873\) | −0.444990 | − | 0.559237i | −0.0150606 | − | 0.0189273i | ||||
\(874\) | 18.5249 | 0.626614 | ||||||||
\(875\) | −31.9429 | −1.07987 | ||||||||
\(876\) | 0.497002 | − | 8.76544i | 0.0167921 | − | 0.296157i | ||||
\(877\) | −9.24012 | + | 9.24012i | −0.312017 | + | 0.312017i | −0.845690 | − | 0.533674i | \(-0.820811\pi\) |
0.533674 | + | 0.845690i | \(0.320811\pi\) | |||||||
\(878\) | −12.7279 | + | 12.7279i | −0.429547 | + | 0.429547i | ||||
\(879\) | −0.416450 | + | 7.34478i | −0.0140465 | + | 0.247733i | ||||
\(880\) | 8.43090 | 0.284205 | ||||||||
\(881\) | −40.6450 | −1.36936 | −0.684682 | − | 0.728842i | \(-0.740059\pi\) | ||||
−0.684682 | + | 0.728842i | \(0.740059\pi\) | |||||||
\(882\) | −12.7892 | − | 16.0726i | −0.430633 | − | 0.541194i | ||||
\(883\) | − | 13.2580i | − | 0.446168i | −0.974799 | − | 0.223084i | \(-0.928388\pi\) | ||
0.974799 | − | 0.223084i | \(-0.0716125\pi\) | |||||||
\(884\) | 4.33362 | − | 2.19848i | 0.145755 | − | 0.0739428i | ||||
\(885\) | −17.2580 | + | 15.4060i | −0.580122 | + | 0.517866i | ||||
\(886\) | −21.7801 | + | 21.7801i | −0.731718 | + | 0.731718i | ||||
\(887\) | − | 17.2792i | − | 0.580179i | −0.957000 | − | 0.290089i | \(-0.906315\pi\) | ||
0.957000 | − | 0.290089i | \(-0.0936850\pi\) | |||||||
\(888\) | 3.56877 | − | 3.18578i | 0.119760 | − | 0.106908i | ||||
\(889\) | 29.1394 | − | 29.1394i | 0.977303 | − | 0.977303i | ||||
\(890\) | −22.8870 | − | 22.8870i | −0.767175 | − | 0.767175i | ||||
\(891\) | 24.8952 | − | 15.5678i | 0.834020 | − | 0.521542i | ||||
\(892\) | −5.89367 | − | 5.89367i | −0.197335 | − | 0.197335i | ||||
\(893\) | 33.8510i | 1.13278i | ||||||||
\(894\) | −14.4468 | − | 16.1836i | −0.483174 | − | 0.541260i | ||||
\(895\) | −33.0772 | − | 33.0772i | −1.10565 | − | 1.10565i | ||||
\(896\) | 3.72111 | 0.124314 | ||||||||
\(897\) | 21.2575 | + | 8.30770i | 0.709769 | + | 0.277386i | ||||
\(898\) | 27.1740 | 0.906809 | ||||||||
\(899\) | 1.17599 | + | 1.17599i | 0.0392214 | + | 0.0392214i | ||||
\(900\) | −0.569103 | + | 5.00240i | −0.0189701 | + | 0.166747i | ||||
\(901\) | − | 0.292244i | − | 0.00973605i | ||||||
\(902\) | −25.7645 | − | 25.7645i | −0.857863 | − | 0.857863i | ||||
\(903\) | −3.32351 | + | 58.6155i | −0.110599 | + | 1.95060i | ||||
\(904\) | 2.43090 | + | 2.43090i | 0.0808504 | + | 0.0808504i | ||||
\(905\) | −3.48289 | + | 3.48289i | −0.115775 | + | 0.115775i | ||||
\(906\) | 19.2479 | + | 21.5618i | 0.639469 | + | 0.716343i | ||||
\(907\) | − | 12.4656i | − | 0.413912i | −0.978350 | − | 0.206956i | \(-0.933644\pi\) | ||
0.978350 | − | 0.206956i | \(-0.0663557\pi\) | |||||||
\(908\) | 9.22759 | − | 9.22759i | 0.306228 | − | 0.306228i | ||||
\(909\) | −6.00662 | + | 52.7980i | −0.199227 | + | 1.75120i | ||||
\(910\) | −32.9558 | − | 10.7722i | −1.09247 | − | 0.357096i | ||||
\(911\) | 8.70212i | 0.288314i | 0.989555 | + | 0.144157i | \(0.0460470\pi\) | ||||
−0.989555 | + | 0.144157i | \(0.953953\pi\) | |||||||
\(912\) | 0.497002 | − | 8.76544i | 0.0164574 | − | 0.290253i | ||||
\(913\) | −48.7925 | −1.61480 | ||||||||
\(914\) | −16.2148 | −0.536336 | ||||||||
\(915\) | 29.1587 | + | 1.65330i | 0.963955 | + | 0.0546564i | ||||
\(916\) | −9.21545 | + | 9.21545i | −0.304487 | + | 0.304487i | ||||
\(917\) | 47.6290 | − | 47.6290i | 1.57285 | − | 1.57285i | ||||
\(918\) | 1.18424 | − | 6.90225i | 0.0390857 | − | 0.227808i | ||||
\(919\) | −50.9311 | −1.68006 | −0.840031 | − | 0.542538i | \(-0.817463\pi\) | ||||
−0.840031 | + | 0.542538i | \(0.817463\pi\) | |||||||
\(920\) | 9.44443 | 0.311374 | ||||||||
\(921\) | −7.94153 | − | 0.450286i | −0.261682 | − | 0.0148374i | ||||
\(922\) | 3.68335i | 0.121305i | ||||||||
\(923\) | −0.171761 | + | 0.525473i | −0.00565357 | + | 0.0172961i | ||||
\(924\) | 14.0028 | + | 15.6862i | 0.460658 | + | 0.516037i | ||||
\(925\) | −3.27757 | + | 3.27757i | −0.107766 | + | 0.107766i | ||||
\(926\) | − | 11.6010i | − | 0.381231i | ||||||
\(927\) | 23.5660 | + | 2.68101i | 0.774009 | + | 0.0880559i | ||||
\(928\) | −2.58423 | + | 2.58423i | −0.0848314 | + | 0.0848314i | ||||
\(929\) | 13.2534 | + | 13.2534i | 0.434830 | + | 0.434830i | 0.890268 | − | 0.455438i | \(-0.150517\pi\) |
−0.455438 | + | 0.890268i | \(0.650517\pi\) | |||||||
\(930\) | −2.03360 | − | 0.115306i | −0.0666845 | − | 0.00378102i | ||||
\(931\) | −24.5400 | − | 24.5400i | −0.804267 | − | 0.804267i | ||||
\(932\) | − | 2.52374i | − | 0.0826677i | ||||||
\(933\) | −4.44204 | + | 3.96534i | −0.145426 | + | 0.129819i | ||||
\(934\) | 16.0940 | + | 16.0940i | 0.526612 | + | 0.526612i | ||||
\(935\) | 11.3627 | 0.371601 | ||||||||
\(936\) | 4.50128 | − | 9.83557i | 0.147129 | − | 0.321486i | ||||
\(937\) | −46.8227 | −1.52963 | −0.764816 | − | 0.644249i | \(-0.777170\pi\) | ||||
−0.764816 | + | 0.644249i | \(0.777170\pi\) | |||||||
\(938\) | 8.41882 | + | 8.41882i | 0.274884 | + | 0.274884i | ||||
\(939\) | 1.95079 | − | 1.74144i | 0.0636617 | − | 0.0568298i | ||||
\(940\) | 17.2580i | 0.562895i | ||||||||
\(941\) | 29.2015 | + | 29.2015i | 0.951941 | + | 0.951941i | 0.998897 | − | 0.0469563i | \(-0.0149522\pi\) |
−0.0469563 | + | 0.998897i | \(0.514952\pi\) | |||||||
\(942\) | 32.6172 | + | 1.84940i | 1.06273 | + | 0.0602567i | ||||
\(943\) | −28.8618 | − | 28.8618i | −0.939869 | − | 0.939869i | ||||
\(944\) | 3.65465 | − | 3.65465i | 0.118949 | − | 0.118949i | ||||
\(945\) | −40.7980 | + | 28.8486i | −1.32716 | + | 0.938444i | ||||
\(946\) | − | 29.7180i | − | 0.966216i | ||||||
\(947\) | −15.7495 | + | 15.7495i | −0.511790 | + | 0.511790i | −0.915075 | − | 0.403285i | \(-0.867868\pi\) |
0.403285 | + | 0.915075i | \(0.367868\pi\) | |||||||
\(948\) | 4.72222 | + | 5.28990i | 0.153370 | + | 0.171808i | ||||
\(949\) | 5.67822 | − | 17.3716i | 0.184323 | − | 0.563905i | ||||
\(950\) | 8.50667i | 0.275993i | ||||||||
\(951\) | −39.5343 | − | 2.24160i | −1.28199 | − | 0.0726888i | ||||
\(952\) | 5.01512 | 0.162541 | ||||||||
\(953\) | −11.6612 | −0.377742 | −0.188871 | − | 0.982002i | \(-0.560483\pi\) | ||||
−0.188871 | + | 0.982002i | \(0.560483\pi\) | |||||||
\(954\) | −0.405041 | − | 0.509031i | −0.0131137 | − | 0.0164805i | ||||
\(955\) | −11.6038 | + | 11.6038i | −0.375489 | + | 0.375489i | ||||
\(956\) | 7.20087 | − | 7.20087i | 0.232893 | − | 0.232893i | ||||
\(957\) | −20.6183 | − | 1.16906i | −0.666494 | − | 0.0377903i | ||||
\(958\) | −24.5898 | −0.794460 | ||||||||
\(959\) | −5.13927 | −0.165956 | ||||||||
\(960\) | 0.253383 | − | 4.46883i | 0.00817791 | − | 0.144231i | ||||
\(961\) | 30.7929i | 0.993320i | ||||||||
\(962\) | 8.88095 | − | 4.50538i | 0.286333 | − | 0.145259i | ||||
\(963\) | −13.7527 | − | 1.56459i | −0.443174 | − | 0.0504181i | ||||
\(964\) | −20.4460 | + | 20.4460i | −0.658522 | + | 0.658522i | ||||
\(965\) | − | 15.5777i | − | 0.501465i | ||||||
\(966\) | 15.6862 | + | 17.5719i | 0.504694 | + | 0.565366i | ||||
\(967\) | 30.7857 | − | 30.7857i | 0.990002 | − | 0.990002i | −0.00994880 | − | 0.999951i | \(-0.503167\pi\) |
0.999951 | + | 0.00994880i | \(0.00316685\pi\) | |||||||
\(968\) | 0.252043 | + | 0.252043i | 0.00810096 | + | 0.00810096i | ||||
\(969\) | 0.669834 | − | 11.8136i | 0.0215182 | − | 0.379508i | ||||
\(970\) | −0.435315 | − | 0.435315i | −0.0139771 | − | 0.0139771i | ||||
\(971\) | − | 8.74884i | − | 0.280764i | −0.990097 | − | 0.140382i | \(-0.955167\pi\) | ||
0.990097 | − | 0.140382i | \(-0.0448330\pi\) | |||||||
\(972\) | −7.50359 | − | 13.6637i | −0.240678 | − | 0.438263i | ||||
\(973\) | 18.7057 | + | 18.7057i | 0.599677 | + | 0.599677i | ||||
\(974\) | 14.1635 | 0.453829 | ||||||||
\(975\) | −3.81491 | + | 9.76151i | −0.122175 | + | 0.312618i | ||||
\(976\) | −6.52489 | −0.208857 | ||||||||
\(977\) | 10.7297 | + | 10.7297i | 0.343272 | + | 0.343272i | 0.857596 | − | 0.514324i | \(-0.171957\pi\) |
−0.514324 | + | 0.857596i | \(0.671957\pi\) | |||||||
\(978\) | 4.58701 | + | 5.13845i | 0.146677 | + | 0.164309i | ||||
\(979\) | 40.8618i | 1.30595i | ||||||||
\(980\) | −12.5111 | − | 12.5111i | −0.399652 | − | 0.399652i | ||||
\(981\) | −24.3441 | − | 30.5942i | −0.777247 | − | 0.976798i | ||||
\(982\) | −0.581437 | − | 0.581437i | −0.0185544 | − | 0.0185544i | ||||
\(983\) | 12.8087 | − | 12.8087i | 0.408534 | − | 0.408534i | −0.472693 | − | 0.881227i | \(-0.656718\pi\) |
0.881227 | + | 0.472693i | \(0.156718\pi\) | |||||||
\(984\) | −14.4309 | + | 12.8822i | −0.460040 | + | 0.410671i | ||||
\(985\) | − | 10.1836i | − | 0.324476i | ||||||
\(986\) | −3.48289 | + | 3.48289i | −0.110918 | + | 0.110918i | ||||
\(987\) | −32.1095 | + | 28.6637i | −1.02206 | + | 0.912375i | ||||
\(988\) | 5.67822 | − | 17.3716i | 0.180648 | − | 0.552663i | ||||
\(989\) | − | 33.2906i | − | 1.05858i | ||||||
\(990\) | 19.7916 | − | 15.7484i | 0.629019 | − | 0.500517i | ||||
\(991\) | 45.2289 | 1.43674 | 0.718372 | − | 0.695659i | \(-0.244887\pi\) | ||||
0.718372 | + | 0.695659i | \(0.244887\pi\) | |||||||
\(992\) | 0.455064 | 0.0144483 | ||||||||
\(993\) | 0.766102 | − | 13.5115i | 0.0243115 | − | 0.428773i | ||||
\(994\) | −0.403440 | + | 0.403440i | −0.0127963 | + | 0.0127963i | ||||
\(995\) | −31.5993 | + | 31.5993i | −1.00177 | + | 1.00177i | ||||
\(996\) | −1.46642 | + | 25.8626i | −0.0464652 | + | 0.819489i | ||||
\(997\) | 49.4416 | 1.56583 | 0.782916 | − | 0.622128i | \(-0.213732\pi\) | ||||
0.782916 | + | 0.622128i | \(0.213732\pi\) | |||||||
\(998\) | 6.11192 | 0.193469 | ||||||||
\(999\) | 2.42688 | − | 14.1449i | 0.0767831 | − | 0.447525i |
(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 | 78.2.g.a.5.3 | ✓ | 12 | |
3.2 | odd | 2 | inner | 78.2.g.a.5.6 | yes | 12 | |
4.3 | odd | 2 | 624.2.bf.f.161.2 | 12 | |||
12.11 | even | 2 | 624.2.bf.f.161.1 | 12 | |||
13.5 | odd | 4 | 1014.2.g.b.437.3 | 12 | |||
13.8 | odd | 4 | inner | 78.2.g.a.47.6 | yes | 12 | |
13.12 | even | 2 | 1014.2.g.b.239.6 | 12 | |||
39.5 | even | 4 | 1014.2.g.b.437.6 | 12 | |||
39.8 | even | 4 | inner | 78.2.g.a.47.3 | yes | 12 | |
39.38 | odd | 2 | 1014.2.g.b.239.3 | 12 | |||
52.47 | even | 4 | 624.2.bf.f.593.2 | 12 | |||
156.47 | odd | 4 | 624.2.bf.f.593.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.g.a.5.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
78.2.g.a.5.6 | yes | 12 | 3.2 | odd | 2 | inner | |
78.2.g.a.47.3 | yes | 12 | 39.8 | even | 4 | inner | |
78.2.g.a.47.6 | yes | 12 | 13.8 | odd | 4 | inner | |
624.2.bf.f.161.1 | 12 | 12.11 | even | 2 | |||
624.2.bf.f.161.2 | 12 | 4.3 | odd | 2 | |||
624.2.bf.f.593.1 | 12 | 156.47 | odd | 4 | |||
624.2.bf.f.593.2 | 12 | 52.47 | even | 4 | |||
1014.2.g.b.239.3 | 12 | 39.38 | odd | 2 | |||
1014.2.g.b.239.6 | 12 | 13.12 | even | 2 | |||
1014.2.g.b.437.3 | 12 | 13.5 | odd | 4 | |||
1014.2.g.b.437.6 | 12 | 39.5 | even | 4 |