Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(239,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(8.09683076496\) |
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: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 437.3 | ||
Root | \(1.72927 + 0.0980500i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.437 |
Dual form | 1014.2.g.b.239.3 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | −0.168498 | − | 0.985702i | \(-0.553892\pi\) |
0.985702 | + | 0.168498i | \(0.0538917\pi\) | |||||||
\(6\) | −0.0980500 | + | 1.72927i | −0.0400288 | + | 0.705973i | ||||
\(7\) | 2.63122 | − | 2.63122i | 0.994509 | − | 0.994509i | −0.00547608 | − | 0.999985i | \(-0.501743\pi\) |
0.999985 | + | 0.00547608i | \(0.00174310\pi\) | |||||||
\(8\) | 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 | 0.267893 | − | 0.963449i | \(-0.413673\pi\) |
−0.963449 | + | 0.267893i | \(0.913673\pi\) | |||||||
\(12\) | −1.15345 | − | 1.29211i | −0.332972 | − | 0.373001i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.72111i | 0.994509i | ||||||||
\(15\) | 0.253383 | − | 4.46883i | 0.0654233 | − | 1.15385i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.34775 | 0.326877 | 0.163439 | − | 0.986554i | \(-0.447741\pi\) | ||||
0.163439 | + | 0.986554i | \(0.447741\pi\) | |||||||
\(18\) | 1.86794 | + | 2.34751i | 0.440277 | + | 0.553314i | ||||
\(19\) | 3.58423 | + | 3.58423i | 0.822278 | + | 0.822278i | 0.986434 | − | 0.164157i | \(-0.0524902\pi\) |
−0.164157 | + | 0.986434i | \(0.552490\pi\) | |||||||
\(20\) | −1.82732 | − | 1.82732i | −0.408602 | − | 0.408602i | ||||
\(21\) | 0.364855 | − | 6.43482i | 0.0796179 | − | 1.40419i | ||||
\(22\) | 3.26245 | 0.695556 | ||||||||
\(23\) | −3.65465 | −0.762047 | −0.381023 | − | 0.924565i | \(-0.624428\pi\) | ||||
−0.381023 | + | 0.924565i | \(0.624428\pi\) | |||||||
\(24\) | 1.72927 | + | 0.0980500i | 0.352986 | + | 0.0200144i | ||||
\(25\) | − | 1.67822i | − | 0.335644i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −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 | \(-0.263012\pi\) |
−0.735413 | + | 0.677619i | \(0.763012\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −5.64166 | − | 0.319883i | −0.982087 | − | 0.0556845i | ||||
\(34\) | −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 | \(-0.822902\pi\) |
0.528107 | + | 0.849178i | \(0.322902\pi\) | |||||||
\(38\) | −5.06886 | −0.822278 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.58423 | 0.408602 | ||||||||
\(41\) | −7.89729 | + | 7.89729i | −1.23335 | + | 1.23335i | −0.270680 | + | 0.962670i | \(0.587248\pi\) |
−0.962670 | + | 0.270680i | \(0.912752\pi\) | |||||||
\(42\) | 4.29211 | + | 4.80810i | 0.662287 | + | 0.741905i | ||||
\(43\) | 9.10912i | 1.38913i | 0.719431 | + | 0.694564i | \(0.244403\pi\) | ||||
−0.719431 | + | 0.694564i | \(0.755597\pi\) | |||||||
\(44\) | −2.30690 | + | 2.30690i | −0.347778 | + | 0.347778i | ||||
\(45\) | −4.82717 | − | 6.06650i | −0.719592 | − | 0.904340i | ||||
\(46\) | 2.58423 | − | 2.58423i | 0.381023 | − | 0.381023i | ||||
\(47\) | 4.72222 | + | 4.72222i | 0.688806 | + | 0.688806i | 0.961968 | − | 0.273162i | \(-0.0880695\pi\) |
−0.273162 | + | 0.961968i | \(0.588070\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.216838i | 0.0297851i | 0.999889 | + | 0.0148925i | \(0.00474061\pi\) | ||||
−0.999889 | + | 0.0148925i | \(0.995259\pi\) | |||||||
\(54\) | 5.12132 | + | 0.878680i | 0.696923 | + | 0.119573i | ||||
\(55\) | −8.43090 | −1.13682 | ||||||||
\(56\) | 3.72111 | 0.497254 | ||||||||
\(57\) | 8.76544 | + | 0.497002i | 1.16101 | + | 0.0658295i | ||||
\(58\) | −2.58423 | − | 2.58423i | −0.339325 | − | 0.339325i | ||||
\(59\) | −3.65465 | − | 3.65465i | −0.475794 | − | 0.475794i | 0.427989 | − | 0.903784i | \(-0.359222\pi\) |
−0.903784 | + | 0.427989i | \(0.859222\pi\) | |||||||
\(60\) | −4.46883 | − | 0.253383i | −0.576924 | − | 0.0327117i | ||||
\(61\) | 6.52489 | 0.835427 | 0.417713 | − | 0.908579i | \(-0.362832\pi\) | ||||
0.417713 | + | 0.908579i | \(0.362832\pi\) | |||||||
\(62\) | 0.455064 | 0.0577932 | ||||||||
\(63\) | −6.95080 | − | 8.73535i | −0.875719 | − | 1.10055i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.21545 | − | 3.76307i | 0.518886 | − | 0.463201i | ||||
\(67\) | −2.26245 | − | 2.26245i | −0.276402 | − | 0.276402i | 0.555269 | − | 0.831671i | \(-0.312615\pi\) |
−0.831671 | + | 0.555269i | \(0.812615\pi\) | |||||||
\(68\) | − | 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 | −0.700644 | − | 0.713511i | \(-0.747104\pi\) |
0.713511 | + | 0.700644i | \(0.247104\pi\) | |||||||
\(72\) | 2.34751 | − | 1.86794i | 0.276657 | − | 0.220138i | ||||
\(73\) | 3.58423 | − | 3.58423i | 0.419502 | − | 0.419502i | −0.465530 | − | 0.885032i | \(-0.654136\pi\) |
0.885032 | + | 0.465530i | \(0.154136\pi\) | |||||||
\(74\) | − | 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 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | 0.176492 | − | 0.984302i | \(-0.443525\pi\) |
0.984302 | − | 0.176492i | \(-0.0564751\pi\) | |||||||
\(84\) | −6.43482 | − | 0.364855i | −0.702096 | − | 0.0398090i | ||||
\(85\) | 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 | 0.998231 | − | 0.0594508i | \(-0.0189349\pi\) |
−0.0594508 | + | 0.998231i | \(0.518935\pi\) | |||||||
\(90\) | 7.70299 | + | 0.876338i | 0.811966 | + | 0.0923742i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.65465i | 0.381023i | ||||||||
\(93\) | −0.786930 | − | 0.0446190i | −0.0816008 | − | 0.00462678i | ||||
\(94\) | −6.67822 | −0.688806 | ||||||||
\(95\) | 13.0991 | 1.34394 | ||||||||
\(96\) | 0.0980500 | − | 1.72927i | 0.0100072 | − | 0.176493i | ||||
\(97\) | −0.168451 | − | 0.168451i | −0.0171036 | − | 0.0171036i | 0.698503 | − | 0.715607i | \(-0.253850\pi\) |
−0.715607 | + | 0.698503i | \(0.753850\pi\) | |||||||
\(98\) | 4.84133 | + | 4.84133i | 0.489048 | + | 0.489048i | ||||
\(99\) | −7.65863 | + | 6.09404i | −0.769721 | + | 0.612475i | ||||
\(100\) | −1.67822 | −0.167822 | ||||||||
\(101\) | 17.7129 | 1.76250 | 0.881248 | − | 0.472653i | \(-0.156704\pi\) | ||||
0.881248 | + | 0.472653i | \(0.156704\pi\) | |||||||
\(102\) | −0.132147 | + | 2.33063i | −0.0130845 | + | 0.230766i | ||||
\(103\) | − | 7.90600i | − | 0.779002i | −0.921026 | − | 0.389501i | \(-0.872648\pi\) | ||
0.921026 | − | 0.389501i | \(-0.127352\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −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 | \(-0.464554\pi\) |
−0.993806 | + | 0.111126i | \(0.964554\pi\) | |||||||
\(110\) | 5.96154 | − | 5.96154i | 0.568411 | − | 0.568411i | ||||
\(111\) | −0.270810 | + | 4.77619i | −0.0257042 | + | 0.453336i | ||||
\(112\) | −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 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(123\) | −1.09507 | + | 19.3133i | −0.0987389 | + | 1.74142i | ||||
\(124\) | −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 | \(-0.836504\pi\) | ||
0.870962 | − | 0.491349i | \(-0.163496\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 10.5069 | + | 11.7700i | 0.925081 | + | 1.03629i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1015i | 1.58153i | 0.612118 | + | 0.790767i | \(0.290318\pi\) | ||||
−0.612118 | + | 0.790767i | \(0.709682\pi\) | |||||||
\(132\) | −0.319883 | + | 5.64166i | −0.0278422 | + | 0.491044i | ||||
\(133\) | 18.8618 | 1.63553 | ||||||||
\(134\) | 3.19958 | 0.276402 | ||||||||
\(135\) | −13.2346 | − | 2.27071i | −1.13906 | − | 0.195431i | ||||
\(136\) | 0.953002 | + | 0.953002i | 0.0817193 | + | 0.0817193i | ||||
\(137\) | 0.976593 | + | 0.976593i | 0.0834360 | + | 0.0834360i | 0.747593 | − | 0.664157i | \(-0.231209\pi\) |
−0.664157 | + | 0.747593i | \(0.731209\pi\) | |||||||
\(138\) | 0.358338 | − | 6.31988i | 0.0305038 | − | 0.537984i | ||||
\(139\) | −7.10912 | −0.602988 | −0.301494 | − | 0.953468i | \(-0.597485\pi\) | ||||
−0.301494 | + | 0.953468i | \(0.597485\pi\) | |||||||
\(140\) | −9.61619 | −0.812717 | ||||||||
\(141\) | 11.5485 | + | 0.654800i | 0.972557 | + | 0.0551441i | ||||
\(142\) | 0.153328i | 0.0128670i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −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 | −0.244182 | − | 0.969729i | \(-0.578519\pi\) |
0.969729 | + | 0.244182i | \(0.0785194\pi\) | |||||||
\(150\) | 2.90210 | + | 0.164550i | 0.236956 | + | 0.0134354i | ||||
\(151\) | 11.7997 | − | 11.7997i | 0.960244 | − | 0.960244i | −0.0389955 | − | 0.999239i | \(-0.512416\pi\) |
0.999239 | + | 0.0389955i | \(0.0124158\pi\) | |||||||
\(152\) | 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 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −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 | ||||
\(162\) | 7.63084 | − | 4.77183i | 0.599535 | − | 0.374910i | ||||
\(163\) | 2.81201 | − | 2.81201i | 0.220254 | − | 0.220254i | −0.588352 | − | 0.808605i | \(-0.700223\pi\) |
0.808605 | + | 0.588352i | \(0.200223\pi\) | |||||||
\(164\) | 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 | 0.669022 | − | 0.743243i | \(-0.266713\pi\) |
−0.743243 | + | 0.669022i | \(0.766713\pi\) | |||||||
\(168\) | 4.80810 | − | 4.29211i | 0.370953 | − | 0.331144i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.48289i | 0.267125i | ||||||||
\(171\) | 11.8992 | − | 9.46831i | 0.909955 | − | 0.724060i | ||||
\(172\) | 9.10912 | 0.694564 | ||||||||
\(173\) | −17.4960 | −1.33020 | −0.665099 | − | 0.746755i | \(-0.731611\pi\) | ||||
−0.665099 | + | 0.746755i | \(0.731611\pi\) | |||||||
\(174\) | −6.31988 | − | 0.358338i | −0.479109 | − | 0.0271655i | ||||
\(175\) | −4.41577 | − | 4.41577i | −0.333801 | − | 0.333801i | ||||
\(176\) | 2.30690 | + | 2.30690i | 0.173889 | + | 0.173889i | ||||
\(177\) | −8.93766 | − | 0.506767i | −0.671796 | − | 0.0380909i | ||||
\(178\) | −12.5249 | −0.938780 | ||||||||
\(179\) | 18.1015 | 1.35297 | 0.676484 | − | 0.736458i | \(-0.263503\pi\) | ||||
0.676484 | + | 0.736458i | \(0.263503\pi\) | |||||||
\(180\) | −6.06650 | + | 4.82717i | −0.452170 | + | 0.359796i | ||||
\(181\) | − | 1.90600i | − | 0.141672i | −0.997488 | − | 0.0708361i | \(-0.977433\pi\) | ||
0.997488 | − | 0.0708361i | \(-0.0225667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 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 | ||||
\(189\) | −19.0570 | − | 3.26967i | −1.38619 | − | 0.237833i | ||||
\(190\) | −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 | \(-0.680388\pi\) |
0.843674 | + | 0.536856i | \(0.180388\pi\) | |||||||
\(194\) | 0.238226 | 0.0171036 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.84667 | −0.489048 | ||||||||
\(197\) | −2.78647 | + | 2.78647i | −0.198528 | + | 0.198528i | −0.799369 | − | 0.600841i | \(-0.794833\pi\) |
0.600841 | + | 0.799369i | \(0.294833\pi\) | |||||||
\(198\) | 1.10633 | − | 9.72461i | 0.0786235 | − | 0.691098i | ||||
\(199\) | − | 17.2927i | − | 1.22585i | −0.790142 | − | 0.612923i | \(-0.789993\pi\) | ||
0.790142 | − | 0.612923i | \(-0.210007\pi\) | |||||||
\(200\) | 1.18668 | − | 1.18668i | 0.0839111 | − | 0.0839111i | ||||
\(201\) | −5.53295 | − | 0.313719i | −0.390264 | − | 0.0221280i | ||||
\(202\) | −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 | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.5369i | − | 1.14388i | ||||||
\(210\) | 16.6290 | + | 0.942868i | 1.14751 | + | 0.0650641i | ||||
\(211\) | 9.41577 | 0.648209 | 0.324104 | − | 0.946021i | \(-0.394937\pi\) | ||||
0.324104 | + | 0.946021i | \(0.394937\pi\) | |||||||
\(212\) | 0.216838 | 0.0148925 | ||||||||
\(213\) | 0.0150338 | − | 0.265146i | 0.00103010 | − | 0.0181675i | ||||
\(214\) | 3.26245 | + | 3.26245i | 0.223016 | + | 0.223016i | ||||
\(215\) | 16.6453 | + | 16.6453i | 1.13520 | + | 1.13520i | ||||
\(216\) | 0.878680 | − | 5.12132i | 0.0597866 | − | 0.348462i | ||||
\(217\) | −1.69334 | −0.114952 | ||||||||
\(218\) | 13.0326 | 0.882680 | ||||||||
\(219\) | 0.497002 | − | 8.76544i | 0.0335843 | − | 0.592314i | ||||
\(220\) | 8.43090i | 0.568411i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.18578 | − | 3.56877i | −0.213816 | − | 0.239520i | ||||
\(223\) | 5.89367 | + | 5.89367i | 0.394669 | + | 0.394669i | 0.876348 | − | 0.481679i | \(-0.159973\pi\) |
−0.481679 | + | 0.876348i | \(0.659973\pi\) | |||||||
\(224\) | − | 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 | −0.943586 | − | 0.331129i | \(-0.892571\pi\) |
0.331129 | + | 0.943586i | \(0.392571\pi\) | |||||||
\(228\) | 0.497002 | − | 8.76544i | 0.0329148 | − | 0.580506i | ||||
\(229\) | −9.21545 | + | 9.21545i | −0.608974 | + | 0.608974i | −0.942678 | − | 0.333704i | \(-0.891701\pi\) |
0.333704 | + | 0.942678i | \(0.391701\pi\) | |||||||
\(230\) | − | 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 | \(-0.473656\pi\) | ||||
0.0826677 | + | 0.996577i | \(0.473656\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 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 | −0.900546 | − | 0.434760i | \(-0.856833\pi\) |
0.434760 | + | 0.900546i | \(0.356833\pi\) | |||||||
\(240\) | −0.253383 | + | 4.46883i | −0.0163558 | + | 0.288462i | ||||
\(241\) | −20.4460 | + | 20.4460i | −1.31704 | + | 1.31704i | −0.400939 | + | 0.916105i | \(0.631316\pi\) |
−0.916105 | + | 0.400939i | \(0.868684\pi\) | |||||||
\(242\) | 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 | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 0.455064i | − | 0.0288966i | ||||||
\(249\) | 1.46642 | − | 25.8626i | 0.0929303 | − | 1.63898i | ||||
\(250\) | −8.58423 | −0.542914 | ||||||||
\(251\) | −18.4901 | −1.16708 | −0.583541 | − | 0.812083i | \(-0.698333\pi\) | ||||
−0.583541 | + | 0.812083i | \(0.698333\pi\) | |||||||
\(252\) | −8.73535 | + | 6.95080i | −0.550276 | + | 0.437859i | ||||
\(253\) | 8.43090 | + | 8.43090i | 0.530046 | + | 0.530046i | ||||
\(254\) | 7.83082 | + | 7.83082i | 0.491349 | + | 0.491349i | ||||
\(255\) | 0.341497 | − | 6.02286i | 0.0213854 | − | 0.377166i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.6696 | −0.852688 | −0.426344 | − | 0.904561i | \(-0.640199\pi\) | ||||
−0.426344 | + | 0.904561i | \(0.640199\pi\) | |||||||
\(258\) | −15.7522 | − | 0.893149i | −0.980686 | − | 0.0556050i | ||||
\(259\) | 10.2776i | 0.638617i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 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 | ||||
\(267\) | 21.6590 | + | 1.22807i | 1.32551 | + | 0.0751564i | ||||
\(268\) | −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 | \(-0.995555\pi\) |
0.0139655 | + | 0.999902i | \(0.495555\pi\) | |||||||
\(272\) | −1.34775 | −0.0817193 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −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 | \(0.287629\pi\) | ||||
−0.618775 | + | 0.785568i | \(0.712371\pi\) | |||||||
\(278\) | 5.02691 | − | 5.02691i | 0.301494 | − | 0.301494i | ||||
\(279\) | −1.06827 | + | 0.850031i | −0.0639555 | + | 0.0508900i | ||||
\(280\) | 6.79967 | − | 6.79967i | 0.406358 | − | 0.406358i | ||||
\(281\) | −3.06665 | − | 3.06665i | −0.182941 | − | 0.182941i | 0.609695 | − | 0.792636i | \(-0.291292\pi\) |
−0.792636 | + | 0.609695i | \(0.791292\pi\) | |||||||
\(282\) | −8.62901 | + | 7.70299i | −0.513850 | + | 0.458706i | ||||
\(283\) | − | 9.35644i | − | 0.556183i | −0.960555 | − | 0.278091i | \(-0.910298\pi\) | ||
0.960555 | − | 0.278091i | \(-0.0897018\pi\) | |||||||
\(284\) | −0.108419 | − | 0.108419i | −0.00643350 | − | 0.00643350i | ||||
\(285\) | 16.9255 | − | 15.1091i | 1.00258 | − | 0.894987i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 41.5591i | 2.45315i | ||||||||
\(288\) | −1.86794 | − | 2.34751i | −0.110069 | − | 0.138328i | ||||
\(289\) | −15.1836 | −0.893151 | ||||||||
\(290\) | −9.44443 | −0.554596 | ||||||||
\(291\) | −0.411957 | − | 0.0233580i | −0.0241493 | − | 0.00136927i | ||||
\(292\) | −3.58423 | − | 3.58423i | −0.209751 | − | 0.209751i | ||||
\(293\) | −3.00331 | − | 3.00331i | −0.175455 | − | 0.175455i | 0.613916 | − | 0.789371i | \(-0.289593\pi\) |
−0.789371 | + | 0.613916i | \(0.789593\pi\) | |||||||
\(294\) | 11.8398 | + | 0.671316i | 0.690509 | + | 0.0391520i | ||||
\(295\) | −13.3564 | −0.777642 | ||||||||
\(296\) | −2.76196 | −0.160536 | ||||||||
\(297\) | −2.86665 | + | 16.7080i | −0.166340 | + | 0.969498i | ||||
\(298\) | 12.5249i | 0.725548i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −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 | ||||
\(306\) | 2.51751 | + | 3.16386i | 0.143916 | + | 0.180866i | ||||
\(307\) | 3.24732 | − | 3.24732i | 0.185335 | − | 0.185335i | −0.608341 | − | 0.793676i | \(-0.708165\pi\) |
0.793676 | + | 0.608341i | \(0.208165\pi\) | |||||||
\(308\) | 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 | \(-0.468925\pi\) | ||||
0.0974701 | + | 0.995238i | \(0.468925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | −0.996107 | − | 0.0881494i | \(-0.971905\pi\) |
0.0881494 | + | 0.996107i | \(0.471905\pi\) | |||||||
\(318\) | −0.374973 | − | 0.0212610i | −0.0210274 | − | 0.00119226i | ||||
\(319\) | 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 | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.97678i | 0.220254i | ||||||||
\(327\) | −22.5369 | − | 1.27785i | −1.24630 | − | 0.0706652i | ||||
\(328\) | −11.1685 | −0.616675 | ||||||||
\(329\) | 24.8504 | 1.37005 | ||||||||
\(330\) | 0.826650 | − | 14.5793i | 0.0455056 | − | 0.802565i | ||||
\(331\) | −5.52489 | − | 5.52489i | −0.303676 | − | 0.303676i | 0.538774 | − | 0.842450i | \(-0.318888\pi\) |
−0.842450 | + | 0.538774i | \(0.818888\pi\) | |||||||
\(332\) | −10.5753 | − | 10.5753i | −0.580397 | − | 0.580397i | ||||
\(333\) | 5.15917 | + | 6.48374i | 0.282721 | + | 0.355307i | ||||
\(334\) | 1.35644 | 0.0742212 | ||||||||
\(335\) | −8.26844 | −0.451753 | ||||||||
\(336\) | −0.364855 | + | 6.43482i | −0.0199045 | + | 0.351048i | ||||
\(337\) | 18.8271i | 1.02558i | 0.858514 | + | 0.512790i | \(0.171388\pi\) | ||||
−0.858514 | + | 0.512790i | \(0.828612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 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 | ||||
\(345\) | −0.926027 | + | 16.3320i | −0.0498556 | + | 0.879285i | ||||
\(346\) | 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 | \(-0.809117\pi\) |
0.564376 | + | 0.825518i | \(0.309117\pi\) | |||||||
\(350\) | 6.24485 | 0.333801 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.26245 | −0.173889 | ||||||||
\(353\) | 5.59039 | − | 5.59039i | 0.297546 | − | 0.297546i | −0.542506 | − | 0.840052i | \(-0.682524\pi\) |
0.840052 | + | 0.542506i | \(0.182524\pi\) | |||||||
\(354\) | 6.67822 | − | 5.96154i | 0.354943 | − | 0.316853i | ||||
\(355\) | − | 0.396234i | − | 0.0210299i | ||||||
\(356\) | 8.85644 | − | 8.85644i | 0.469390 | − | 0.469390i | ||||
\(357\) | 0.491733 | − | 8.67252i | 0.0260253 | − | 0.458998i | ||||
\(358\) | −12.7997 | + | 12.7997i | −0.676484 | + | 0.676484i | ||||
\(359\) | −12.8822 | − | 12.8822i | −0.679899 | − | 0.679899i | 0.280079 | − | 0.959977i | \(-0.409639\pi\) |
−0.959977 | + | 0.280079i | \(0.909639\pi\) | |||||||
\(360\) | 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 | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13.0991i | − | 0.685637i | ||||||
\(366\) | −0.639766 | + | 11.2833i | −0.0334411 | + | 0.589789i | ||||
\(367\) | 7.56910 | 0.395104 | 0.197552 | − | 0.980292i | \(-0.436701\pi\) | ||||
0.197552 | + | 0.980292i | \(0.436701\pi\) | |||||||
\(368\) | 3.65465 | 0.190512 | ||||||||
\(369\) | 20.8620 | + | 26.2181i | 1.08603 | + | 1.36486i | ||||
\(370\) | −5.04700 | − | 5.04700i | −0.262381 | − | 0.262381i | ||||
\(371\) | 0.570551 | + | 0.570551i | 0.0296215 | + | 0.0296215i | ||||
\(372\) | −0.0446190 | + | 0.786930i | −0.00231339 | + | 0.0408004i | ||||
\(373\) | 15.8120 | 0.818715 | 0.409357 | − | 0.912374i | \(-0.365753\pi\) | ||||
0.409357 | + | 0.912374i | \(0.365753\pi\) | |||||||
\(374\) | 4.39696 | 0.227361 | ||||||||
\(375\) | 14.8445 | + | 0.841683i | 0.766565 | + | 0.0434643i | ||||
\(376\) | 6.67822i | 0.344403i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 15.7873 | − | 11.1633i | 0.812013 | − | 0.574180i | ||||
\(379\) | −5.33690 | − | 5.33690i | −0.274138 | − | 0.274138i | 0.556625 | − | 0.830764i | \(-0.312096\pi\) |
−0.830764 | + | 0.556625i | \(0.812096\pi\) | |||||||
\(380\) | − | 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 | −0.373100 | − | 0.927791i | \(-0.621705\pi\) |
0.927791 | + | 0.373100i | \(0.121705\pi\) | |||||||
\(384\) | −1.72927 | − | 0.0980500i | −0.0882466 | − | 0.00500359i | ||||
\(385\) | −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 | \(-0.537316\pi\) | ||||
−0.116964 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −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 | ||||
\(396\) | 6.09404 | + | 7.65863i | 0.306237 | + | 0.384861i | ||||
\(397\) | 12.5400 | − | 12.5400i | 0.629365 | − | 0.629365i | −0.318543 | − | 0.947908i | \(-0.603194\pi\) |
0.947908 | + | 0.318543i | \(0.103194\pi\) | |||||||
\(398\) | 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 | 0.792067 | − | 0.610434i | \(-0.209005\pi\) |
−0.610434 | + | 0.792067i | \(0.709005\pi\) | |||||||
\(402\) | 4.13422 | − | 3.69056i | 0.206196 | − | 0.184068i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 17.7129i | − | 0.881248i | ||||||
\(405\) | −19.7198 | + | 12.3315i | −0.979885 | + | 0.612756i | ||||
\(406\) | −13.5993 | −0.674924 | ||||||||
\(407\) | 9.01075 | 0.446646 | ||||||||
\(408\) | 2.33063 | + | 0.132147i | 0.115383 | + | 0.00654224i | ||||
\(409\) | −18.5993 | − | 18.5993i | −0.919679 | − | 0.919679i | 0.0773272 | − | 0.997006i | \(-0.475361\pi\) |
−0.997006 | + | 0.0773272i | \(0.975361\pi\) | |||||||
\(410\) | −20.4084 | − | 20.4084i | −1.00790 | − | 1.00790i | ||||
\(411\) | 2.38832 | + | 0.135418i | 0.117807 | + | 0.00667968i | ||||
\(412\) | −7.90600 | −0.389501 | ||||||||
\(413\) | −19.2324 | −0.946364 | ||||||||
\(414\) | −6.82665 | − | 8.57933i | −0.335512 | − | 0.421651i | ||||
\(415\) | − | 38.6491i | − | 1.89721i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −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 | 0.992250 | + | 0.124256i | \(0.0396544\pi\) |
0.124256 | + | 0.992250i | \(0.460346\pi\) | |||||||
\(422\) | −6.65796 | + | 6.65796i | −0.324104 | + | 0.324104i | ||||
\(423\) | 15.6772 | − | 12.4745i | 0.762252 | − | 0.606531i | ||||
\(424\) | −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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.5400 | −1.13520 | ||||||||
\(431\) | 5.89820 | − | 5.89820i | 0.284106 | − | 0.284106i | −0.550638 | − | 0.834744i | \(-0.685615\pi\) |
0.834744 | + | 0.550638i | \(0.185615\pi\) | |||||||
\(432\) | 3.00000 | + | 4.24264i | 0.144338 | + | 0.204124i | ||||
\(433\) | 37.6093i | 1.80739i | 0.428177 | + | 0.903695i | \(0.359156\pi\) | ||||
−0.428177 | + | 0.903695i | \(0.640844\pi\) | |||||||
\(434\) | 1.19738 | − | 1.19738i | 0.0574758 | − | 0.0574758i | ||||
\(435\) | 16.3320 | + | 0.926027i | 0.783060 | + | 0.0443996i | ||||
\(436\) | −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 | \(0.141327\pi\) | ||||
−0.903045 | + | 0.429547i | \(0.858673\pi\) | |||||||
\(440\) | −5.96154 | − | 5.96154i | −0.284205 | − | 0.284205i | ||||
\(441\) | −20.4084 | − | 2.32178i | −0.971827 | − | 0.110561i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 30.8018i | − | 1.46344i | −0.681608 | − | 0.731718i | \(-0.738719\pi\) | ||
0.681608 | − | 0.731718i | \(-0.261281\pi\) | |||||||
\(444\) | 4.77619 | + | 0.270810i | 0.226668 | + | 0.0128521i | ||||
\(445\) | 32.3671 | 1.53435 | ||||||||
\(446\) | −8.33491 | −0.394669 | ||||||||
\(447\) | 1.22807 | − | 21.6590i | 0.0580855 | − | 1.02443i | ||||
\(448\) | 2.63122 | + | 2.63122i | 0.124314 | + | 0.124314i | ||||
\(449\) | −19.2149 | − | 19.2149i | −0.906809 | − | 0.906809i | 0.0892043 | − | 0.996013i | \(-0.471568\pi\) |
−0.996013 | + | 0.0892043i | \(0.971568\pi\) | |||||||
\(450\) | 3.93964 | − | 3.13481i | 0.185717 | − | 0.147776i | ||||
\(451\) | 36.4365 | 1.71573 | ||||||||
\(452\) | 3.43781 | 0.161701 | ||||||||
\(453\) | 1.63619 | − | 28.8568i | 0.0768747 | − | 1.35581i | ||||
\(454\) | − | 13.0498i | − | 0.612457i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.84667 | + | 6.54954i | 0.273796 | + | 0.306710i | ||||
\(457\) | −11.4656 | − | 11.4656i | −0.536336 | − | 0.536336i | 0.386115 | − | 0.922451i | \(-0.373817\pi\) |
−0.922451 | + | 0.386115i | \(0.873817\pi\) | |||||||
\(458\) | − | 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 | −0.765153 | − | 0.643848i | \(-0.777337\pi\) |
0.643848 | + | 0.765153i | \(0.277337\pi\) | |||||||
\(462\) | 1.19032 | − | 20.9933i | 0.0553787 | − | 0.976695i | ||||
\(463\) | −8.20311 | + | 8.20311i | −0.381231 | + | 0.381231i | −0.871546 | − | 0.490315i | \(-0.836882\pi\) |
0.490315 | + | 0.871546i | \(0.336882\pi\) | |||||||
\(464\) | − | 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 | \(-0.323462\pi\) | ||||
0.526612 | + | 0.850106i | \(0.323462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −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 | ||||
\(474\) | −0.401416 | + | 7.07964i | −0.0184377 | + | 0.325179i | ||||
\(475\) | 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 | 0.982216 | − | 0.187755i | \(-0.0601212\pi\) |
−0.187755 | + | 0.982216i | \(0.560121\pi\) | |||||||
\(480\) | −2.98077 | − | 3.33911i | −0.136053 | − | 0.152409i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 28.9150i | − | 1.31704i | ||||||
\(483\) | −1.33342 | + | 23.5170i | −0.0606725 | + | 1.07006i | ||||
\(484\) | −0.356442 | −0.0162019 | ||||||||
\(485\) | −0.615628 | −0.0279542 | ||||||||
\(486\) | 4.35584 | − | 14.9675i | 0.197585 | − | 0.678941i | ||||
\(487\) | 10.0151 | + | 10.0151i | 0.453829 | + | 0.453829i | 0.896623 | − | 0.442795i | \(-0.146013\pi\) |
−0.442795 | + | 0.896623i | \(0.646013\pi\) | |||||||
\(488\) | 4.61380 | + | 4.61380i | 0.208857 | + | 0.208857i | ||||
\(489\) | 0.389923 | − | 6.87694i | 0.0176329 | − | 0.310986i | ||||
\(490\) | 17.6933 | 0.799304 | ||||||||
\(491\) | −0.822276 | −0.0371088 | −0.0185544 | − | 0.999828i | \(-0.505906\pi\) | ||||
−0.0185544 | + | 0.999828i | \(0.505906\pi\) | |||||||
\(492\) | 19.3133 | + | 1.09507i | 0.870711 | + | 0.0493694i | ||||
\(493\) | 4.92554i | 0.221835i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −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 | \(-0.206317\pi\) |
−0.603724 | + | 0.797193i | \(0.706317\pi\) | |||||||
\(500\) | 6.06996 | − | 6.06996i | 0.271457 | − | 0.271457i | ||||
\(501\) | −2.34566 | − | 0.132999i | −0.104796 | − | 0.00594197i | ||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.0745 | −0.491349 | ||||||||
\(509\) | −20.7795 | + | 20.7795i | −0.921036 | + | 0.921036i | −0.997103 | − | 0.0760664i | \(-0.975764\pi\) |
0.0760664 | + | 0.997103i | \(0.475764\pi\) | |||||||
\(510\) | 4.01733 | + | 4.50028i | 0.177890 | + | 0.199276i | ||||
\(511\) | − | 18.8618i | − | 0.834397i | ||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.45390 | − | 25.9593i | 0.196645 | − | 1.14613i | ||||
\(514\) | 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 | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.171761i | 0.00752497i | 0.999993 | + | 0.00376248i | \(0.00119764\pi\) | ||||
−0.999993 | + | 0.00376248i | \(0.998802\pi\) | |||||||
\(522\) | −8.57933 | + | 6.82665i | −0.375507 | + | 0.298794i | ||||
\(523\) | 20.8618 | 0.912223 | 0.456111 | − | 0.889923i | \(-0.349242\pi\) | ||||
0.456111 | + | 0.889923i | \(0.349242\pi\) | |||||||
\(524\) | 18.1015 | 0.790767 | ||||||||
\(525\) | −10.7990 | − | 0.612308i | −0.471309 | − | 0.0267233i | ||||
\(526\) | 10.3369 | + | 10.3369i | 0.450710 | + | 0.450710i | ||||
\(527\) | −0.433677 | − | 0.433677i | −0.0188913 | − | 0.0188913i | ||||
\(528\) | 5.64166 | + | 0.319883i | 0.245522 | + | 0.0139211i | ||||
\(529\) | −9.64356 | −0.419285 | ||||||||
\(530\) | −0.560360 | −0.0243405 | ||||||||
\(531\) | −12.1330 | + | 9.65434i | −0.526527 | + | 0.418963i | ||||
\(532\) | − | 18.8618i | − | 0.817763i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −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 | ||||
\(540\) | −2.27071 | + | 13.2346i | −0.0977156 | + | 0.569528i | ||||
\(541\) | 22.6021 | − | 22.6021i | 0.971742 | − | 0.971742i | −0.0278698 | − | 0.999612i | \(-0.508872\pi\) |
0.999612 | + | 0.0278698i | \(0.00887238\pi\) | |||||||
\(542\) | − | 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 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | ||||
\(552\) | −6.31988 | − | 0.358338i | −0.268992 | − | 0.0152519i | ||||
\(553\) | 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 | 0.532727 | − | 0.846287i | \(-0.321167\pi\) |
−0.846287 | + | 0.532727i | \(0.821167\pi\) | |||||||
\(558\) | 0.154317 | − | 1.35644i | 0.00653276 | − | 0.0574228i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9.61619i | 0.406358i | ||||||||
\(561\) | −7.60354 | − | 0.431122i | −0.321022 | − | 0.0182020i | ||||
\(562\) | 4.33690 | 0.182941 | ||||||||
\(563\) | 38.1111 | 1.60619 | 0.803095 | − | 0.595851i | \(-0.203185\pi\) | ||||
0.803095 | + | 0.595851i | \(0.203185\pi\) | |||||||
\(564\) | 0.654800 | − | 11.5485i | 0.0275720 | − | 0.486278i | ||||
\(565\) | 6.28199 | + | 6.28199i | 0.264285 | + | 0.264285i | ||||
\(566\) | 6.61600 | + | 6.61600i | 0.278091 | + | 0.278091i | ||||
\(567\) | −28.3952 | + | 17.7565i | −1.19249 | + | 0.745703i | ||||
\(568\) | 0.153328 | 0.00643350 | ||||||||
\(569\) | −38.2930 | −1.60533 | −0.802663 | − | 0.596433i | \(-0.796584\pi\) | ||||
−0.802663 | + | 0.596433i | \(0.796584\pi\) | |||||||
\(570\) | −1.28436 | + | 22.6519i | −0.0537961 | + | 0.948783i | ||||
\(571\) | − | 34.6145i | − | 1.44857i | −0.689500 | − | 0.724285i | \(-0.742170\pi\) | ||
0.689500 | − | 0.724285i | \(-0.257830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 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 | \(-0.294394\pi\) |
−0.798540 | + | 0.601942i | \(0.794394\pi\) | |||||||
\(578\) | 10.7364 | − | 10.7364i | 0.446576 | − | 0.446576i | ||||
\(579\) | 0.591046 | − | 10.4241i | 0.0245631 | − | 0.433210i | ||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.24732 | 0.175455 | ||||||||
\(587\) | 11.0090 | − | 11.0090i | 0.454391 | − | 0.454391i | −0.442418 | − | 0.896809i | \(-0.645879\pi\) |
0.896809 | + | 0.442418i | \(0.145879\pi\) | |||||||
\(588\) | −8.84667 | + | 7.89729i | −0.364831 | + | 0.325679i | ||||
\(589\) | − | 2.30666i | − | 0.0950441i | ||||||
\(590\) | 9.44443 | − | 9.44443i | 0.388821 | − | 0.388821i | ||||
\(591\) | −0.386383 | + | 6.81449i | −0.0158937 | + | 0.280311i | ||||
\(592\) | 1.95300 | − | 1.95300i | 0.0802679 | − | 0.0802679i | ||||
\(593\) | 8.06905 | + | 8.06905i | 0.331356 | + | 0.331356i | 0.853101 | − | 0.521745i | \(-0.174719\pi\) |
−0.521745 | + | 0.853101i | \(0.674719\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 22.0180i | − | 0.899633i | −0.893121 | − | 0.449816i | \(-0.851489\pi\) | ||
0.893121 | − | 0.449816i | \(-0.148511\pi\) | |||||||
\(600\) | 0.164550 | − | 2.90210i | 0.00671771 | − | 0.118478i | ||||
\(601\) | −38.2529 | −1.56037 | −0.780184 | − | 0.625550i | \(-0.784875\pi\) | ||||
−0.780184 | + | 0.625550i | \(0.784875\pi\) | |||||||
\(602\) | −33.8960 | −1.38150 | ||||||||
\(603\) | −7.51106 | + | 5.97662i | −0.305874 | + | 0.243387i | ||||
\(604\) | −11.7997 | − | 11.7997i | −0.480122 | − | 0.480122i | ||||
\(605\) | −0.651335 | − | 0.651335i | −0.0264805 | − | 0.0264805i | ||||
\(606\) | −1.73675 | + | 30.6304i | −0.0705506 | + | 1.24427i | ||||
\(607\) | 8.06933 | 0.327524 | 0.163762 | − | 0.986500i | \(-0.447637\pi\) | ||||
0.163762 | + | 0.986500i | \(0.447637\pi\) | |||||||
\(608\) | 5.06886 | 0.205569 | ||||||||
\(609\) | 23.5170 | + | 1.33342i | 0.952957 | + | 0.0540328i | ||||
\(610\) | 16.8618i | 0.682714i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.01733 | − | 0.457036i | −0.162391 | − | 0.0184746i | ||||
\(613\) | 23.0896 | + | 23.0896i | 0.932579 | + | 0.932579i | 0.997867 | − | 0.0652872i | \(-0.0207964\pi\) |
−0.0652872 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(614\) | 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 | −0.415858 | + | 0.909430i | \(0.636519\pi\) |
−0.909430 | + | 0.415858i | \(0.863481\pi\) | |||||||
\(618\) | 13.6716 | + | 0.775184i | 0.549954 | + | 0.0311825i | ||||
\(619\) | 25.3716 | − | 25.3716i | 1.01977 | − | 1.01977i | 0.0199687 | − | 0.999801i | \(-0.493643\pi\) |
0.999801 | − | 0.0199687i | \(-0.00635666\pi\) | |||||||
\(620\) | 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 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 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 | ||||
\(630\) | 22.5741 | − | 17.9624i | 0.899375 | − | 0.715641i | ||||
\(631\) | 0.200326 | − | 0.200326i | 0.00797485 | − | 0.00797485i | −0.703108 | − | 0.711083i | \(-0.748205\pi\) |
0.711083 | + | 0.703108i | \(0.248205\pi\) | |||||||
\(632\) | 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 | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.9231i | 0.472040i | ||||||||
\(639\) | −0.286407 | − | 0.359939i | −0.0113301 | − | 0.0142390i | ||||
\(640\) | −2.58423 | −0.102150 | ||||||||
\(641\) | −34.2846 | −1.35416 | −0.677081 | − | 0.735908i | \(-0.736755\pi\) | ||||
−0.677081 | + | 0.735908i | \(0.736755\pi\) | |||||||
\(642\) | 7.97851 | + | 0.452383i | 0.314887 | + | 0.0178541i | ||||
\(643\) | 10.7873 | + | 10.7873i | 0.425411 | + | 0.425411i | 0.887062 | − | 0.461651i | \(-0.152743\pi\) |
−0.461651 | + | 0.887062i | \(0.652743\pi\) | |||||||
\(644\) | 9.61619 | + | 9.61619i | 0.378931 | + | 0.378931i | ||||
\(645\) | 40.7071 | + | 2.30810i | 1.60284 | + | 0.0908813i | ||||
\(646\) | −6.83155 | −0.268784 | ||||||||
\(647\) | 2.69550 | 0.105971 | 0.0529855 | − | 0.998595i | \(-0.483126\pi\) | ||||
0.0529855 | + | 0.998595i | \(0.483126\pi\) | |||||||
\(648\) | −4.77183 | − | 7.63084i | −0.187455 | − | 0.299768i | ||||
\(649\) | 16.8618i | 0.661883i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −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 | ||||
\(657\) | −9.46831 | − | 11.8992i | −0.369394 | − | 0.464232i | ||||
\(658\) | −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 | −0.0720628 | + | 0.997400i | \(0.522958\pi\) |
−0.997400 | + | 0.0720628i | \(0.977042\pi\) | |||||||
\(662\) | 7.81338 | 0.303676 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 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 | ||||
\(669\) | 14.4133 | + | 0.817238i | 0.557252 | + | 0.0315962i | ||||
\(670\) | 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 | \(0.0448819\pi\) | ||||
−0.990076 | + | 0.140534i | \(0.955118\pi\) | |||||||
\(674\) | −13.3128 | − | 13.3128i | −0.512790 | − | 0.512790i | ||||
\(675\) | −7.12009 | + | 5.03466i | −0.274052 | + | 0.193784i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.3200i | 0.627230i | 0.949550 | + | 0.313615i | \(0.101540\pi\) | ||||
−0.949550 | + | 0.313615i | \(0.898460\pi\) | |||||||
\(678\) | −5.94491 | − | 0.337077i | −0.228313 | − | 0.0129454i | ||||
\(679\) | −0.886464 | −0.0340194 | ||||||||
\(680\) | 3.48289 | 0.133563 | ||||||||
\(681\) | −1.27953 | + | 22.5666i | −0.0490318 | + | 0.864756i | ||||
\(682\) | −1.04979 | − | 1.04979i | −0.0401984 | − | 0.0401984i | ||||
\(683\) | −0.171761 | − | 0.171761i | −0.00657223 | − | 0.00657223i | 0.703813 | − | 0.710385i | \(-0.251479\pi\) |
−0.710385 | + | 0.703813i | \(0.751479\pi\) | |||||||
\(684\) | −9.46831 | − | 11.8992i | −0.362030 | − | 0.454978i | ||||
\(685\) | 3.56910 | 0.136368 | ||||||||
\(686\) | −0.570551 | −0.0217837 | ||||||||
\(687\) | −1.27785 | + | 22.5369i | −0.0487529 | + | 0.859838i | ||||
\(688\) | − | 9.10912i | − | 0.347282i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −10.8937 | − | 12.2033i | −0.414715 | − | 0.464571i | ||||
\(691\) | −18.3218 | − | 18.3218i | −0.696993 | − | 0.696993i | 0.266768 | − | 0.963761i | \(-0.414044\pi\) |
−0.963761 | + | 0.266768i | \(0.914044\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | −0.358338 | + | 6.31988i | −0.0135828 | + | 0.239555i | ||||
\(697\) | −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 | \(-0.280227\pi\) | ||||
0.636874 | + | 0.770968i | \(0.280227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −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 | ||||
\(708\) | −0.506767 | + | 8.93766i | −0.0190455 | + | 0.335898i | ||||
\(709\) | 3.79689 | − | 3.79689i | 0.142595 | − | 0.142595i | −0.632206 | − | 0.774801i | \(-0.717850\pi\) |
0.774801 | + | 0.632206i | \(0.217850\pi\) | |||||||
\(710\) | 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 | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 18.1015i | − | 0.676484i | ||||||
\(717\) | −0.998500 | + | 17.6102i | −0.0372897 | + | 0.657664i | ||||
\(718\) | 18.2182 | 0.679899 | ||||||||
\(719\) | −30.6300 | −1.14231 | −0.571153 | − | 0.820844i | \(-0.693504\pi\) | ||||
−0.571153 | + | 0.820844i | \(0.693504\pi\) | |||||||
\(720\) | 4.82717 | + | 6.06650i | 0.179898 | + | 0.226085i | ||||
\(721\) | −20.8025 | − | 20.8025i | −0.774724 | − | 0.774724i | ||||
\(722\) | −4.73291 | − | 4.73291i | −0.176141 | − | 0.176141i | ||||
\(723\) | −2.83512 | + | 50.0020i | −0.105439 | + | 1.85959i | ||||
\(724\) | −1.90600 | −0.0708361 | ||||||||
\(725\) | 6.13331 | 0.227785 | ||||||||
\(726\) | 0.616386 | + | 0.0349492i | 0.0228762 | + | 0.00129709i | ||||
\(727\) | 0.430897i | 0.0159811i | 0.999968 | + | 0.00799055i | \(0.00254350\pi\) | ||||
−0.999968 | + | 0.00799055i | \(0.997457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −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 | \(-0.321280\pi\) |
−0.846476 | + | 0.532427i | \(0.821280\pi\) | |||||||
\(734\) | −5.35216 | + | 5.35216i | −0.197552 | + | 0.197552i | ||||
\(735\) | −30.5966 | − | 1.73483i | −1.12857 | − | 0.0639903i | ||||
\(736\) | −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 | \(-0.879236\pi\) |
0.370354 | + | 0.928891i | \(0.379236\pi\) | |||||||
\(740\) | 7.13753 | 0.262381 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.806880 | −0.0296215 | ||||||||
\(743\) | −1.06757 | + | 1.06757i | −0.0391653 | + | 0.0391653i | −0.726418 | − | 0.687253i | \(-0.758816\pi\) |
0.687253 | + | 0.726418i | \(0.258816\pi\) | |||||||
\(744\) | −0.524893 | − | 0.587994i | −0.0192435 | − | 0.0215569i | ||||
\(745\) | − | 32.3671i | − | 1.18584i | ||||||
\(746\) | −11.1808 | + | 11.1808i | −0.409357 | + | 0.409357i | ||||
\(747\) | −27.9365 | − | 35.1089i | −1.02214 | − | 1.28457i | ||||
\(748\) | −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 | \(0.0109283\pi\) | ||||
−0.999411 | + | 0.0343255i | \(0.989072\pi\) | |||||||
\(752\) | −4.72222 | − | 4.72222i | −0.172201 | − | 0.172201i | ||||
\(753\) | −23.8913 | + | 21.3274i | −0.870646 | + | 0.777212i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 43.1236i | − | 1.56943i | ||||||
\(756\) | −3.26967 | + | 19.0570i | −0.118917 | + | 0.693097i | ||||
\(757\) | −28.6189 | −1.04017 | −0.520086 | − | 0.854114i | \(-0.674100\pi\) | ||||
−0.520086 | + | 0.854114i | \(0.674100\pi\) | |||||||
\(758\) | 7.54752 | 0.274138 | ||||||||
\(759\) | 20.6183 | + | 1.16906i | 0.748396 | + | 0.0424342i | ||||
\(760\) | 9.26245 | + | 9.26245i | 0.335984 | + | 0.335984i | ||||
\(761\) | −30.4408 | − | 30.4408i | −1.10348 | − | 1.10348i | −0.993988 | − | 0.109490i | \(-0.965078\pi\) |
−0.109490 | − | 0.993988i | \(-0.534922\pi\) | |||||||
\(762\) | 19.1508 | + | 1.08585i | 0.693759 | + | 0.0393362i | ||||
\(763\) | −48.4958 | −1.75567 | ||||||||
\(764\) | 6.35014 | 0.229740 | ||||||||
\(765\) | −6.50581 | − | 8.17612i | −0.235218 | − | 0.295608i | ||||
\(766\) | 15.3520i | 0.554691i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.29211 | − | 1.15345i | 0.0466251 | − | 0.0416215i | ||||
\(769\) | −14.9956 | − | 14.9956i | −0.540755 | − | 0.540755i | 0.382996 | − | 0.923750i | \(-0.374892\pi\) |
−0.923750 | + | 0.382996i | \(0.874892\pi\) | |||||||
\(770\) | − | 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 | −0.585527 | − | 0.810653i | \(-0.699112\pi\) |
0.810653 | + | 0.585527i | \(0.199112\pi\) | |||||||
\(774\) | −21.3838 | + | 17.0153i | −0.768623 | + | 0.611601i | ||||
\(775\) | −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 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −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 | ||||
\(786\) | −31.3024 | − | 1.77485i | −1.11652 | − | 0.0633068i | ||||
\(787\) | −7.15333 | + | 7.15333i | −0.254989 | + | 0.254989i | −0.823012 | − | 0.568024i | \(-0.807708\pi\) |
0.568024 | + | 0.823012i | \(0.307708\pi\) | |||||||
\(788\) | 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 | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 17.7343i | 0.629365i | ||||||||
\(795\) | 0.969015 | + | 0.0549433i | 0.0343674 | + | 0.00194864i | ||||
\(796\) | −17.2927 | −0.612923 | ||||||||
\(797\) | −28.0263 | −0.992742 | −0.496371 | − | 0.868110i | \(-0.665335\pi\) | ||||
−0.496371 | + | 0.868110i | \(0.665335\pi\) | |||||||
\(798\) | −1.84940 | + | 32.6172i | −0.0654680 | + | 1.15464i | ||||
\(799\) | 6.36436 | + | 6.36436i | 0.225155 | + | 0.225155i | ||||
\(800\) | −1.18668 | − | 1.18668i | −0.0419555 | − | 0.0419555i | ||||
\(801\) | 29.4023 | − | 23.3957i | 1.03888 | − | 0.826647i | ||||
\(802\) | −5.14378 | −0.181633 | ||||||||
\(803\) | −16.5369 | −0.583574 | ||||||||
\(804\) | −0.313719 | + | 5.53295i | −0.0110640 | + | 0.195132i | ||||
\(805\) | 35.1438i | 1.23866i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 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 | −0.994709 | − | 0.102728i | \(-0.967243\pi\) |
−0.102728 | − | 0.994709i | \(-0.532757\pi\) | |||||||
\(812\) | 9.61619 | − | 9.61619i | 0.337462 | − | 0.337462i | ||||
\(813\) | −2.25059 | + | 39.6929i | −0.0789317 | + | 1.39209i | ||||
\(814\) | −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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.8618 | 1.00790 | ||||||||
\(821\) | 13.0081 | − | 13.0081i | 0.453986 | − | 0.453986i | −0.442689 | − | 0.896675i | \(-0.645976\pi\) |
0.896675 | + | 0.442689i | \(0.145976\pi\) | |||||||
\(822\) | −1.78455 | + | 1.59304i | −0.0622434 | + | 0.0555637i | ||||
\(823\) | 19.5356i | 0.680968i | 0.940250 | + | 0.340484i | \(0.110591\pi\) | ||||
−0.940250 | + | 0.340484i | \(0.889409\pi\) | |||||||
\(824\) | 5.59039 | − | 5.59039i | 0.194750 | − | 0.194750i | ||||
\(825\) | −0.536834 | + | 9.46796i | −0.0186902 | + | 0.329632i | ||||
\(826\) | 13.5993 | − | 13.5993i | 0.473182 | − | 0.473182i | ||||
\(827\) | 18.6720 | + | 18.6720i | 0.649290 | + | 0.649290i | 0.952821 | − | 0.303532i | \(-0.0981658\pi\) |
−0.303532 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(828\) | 10.8937 | + | 1.23933i | 0.378581 | + | 0.0430697i | ||||
\(829\) | − | 2.85622i | − | 0.0992006i | −0.998769 | − | 0.0496003i | \(-0.984205\pi\) | ||
0.998769 | − | 0.0496003i | \(-0.0157947\pi\) | |||||||
\(830\) | 27.3291 | + | 27.3291i | 0.948606 | + | 0.948606i | ||||
\(831\) | 30.1614 | + | 33.7873i | 1.04629 | + | 1.17207i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 9.22759i | − | 0.319717i | ||||||
\(834\) | 0.697049 | − | 12.2936i | 0.0241368 | − | 0.425693i | ||||
\(835\) | −3.50535 | −0.121308 | ||||||||
\(836\) | −16.5369 | −0.571940 | ||||||||
\(837\) | −0.399856 | + | 2.33053i | −0.0138210 | + | 0.0805549i | ||||
\(838\) | 0.250112 | + | 0.250112i | 0.00863998 | + | 0.00863998i | ||||
\(839\) | 35.2438 | + | 35.2438i | 1.21675 | + | 1.21675i | 0.968763 | + | 0.247988i | \(0.0797693\pi\) |
0.247988 | + | 0.968763i | \(0.420231\pi\) | |||||||
\(840\) | 0.942868 | − | 16.6290i | 0.0325320 | − | 0.573756i | ||||
\(841\) | 15.6436 | 0.539433 | ||||||||
\(842\) | −32.3979 | −1.11651 | ||||||||
\(843\) | −7.49969 | − | 0.425233i | −0.258303 | − | 0.0146458i | ||||
\(844\) | − | 9.41577i | − | 0.324104i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −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 | ||||
\(852\) | −0.265146 | − | 0.0150338i | −0.00908375 | − | 0.000515050i | ||||
\(853\) | −31.6217 | + | 31.6217i | −1.08271 | + | 1.08271i | −0.0864494 | + | 0.996256i | \(0.527552\pi\) |
−0.996256 | + | 0.0864494i | \(0.972448\pi\) | |||||||
\(854\) | 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 | \(-0.377603\pi\) | ||||
0.375117 | + | 0.926978i | \(0.377603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −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 | −0.291034 | + | 0.956713i | \(0.593999\pi\) |
−0.956713 | + | 0.291034i | \(0.906001\pi\) | |||||||
\(864\) | −5.12132 | − | 0.878680i | −0.174231 | − | 0.0298933i | ||||
\(865\) | −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 | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 13.0326i | − | 0.441340i | ||||||
\(873\) | −0.559237 | + | 0.444990i | −0.0189273 | + | 0.0150606i | ||||
\(874\) | 18.5249 | 0.626614 | ||||||||
\(875\) | 31.9429 | 1.07987 | ||||||||
\(876\) | −8.76544 | − | 0.497002i | −0.296157 | − | 0.0167921i | ||||
\(877\) | 9.24012 | + | 9.24012i | 0.312017 | + | 0.312017i | 0.845690 | − | 0.533674i | \(-0.179189\pi\) |
−0.533674 | + | 0.845690i | \(0.679189\pi\) | |||||||
\(878\) | −12.7279 | − | 12.7279i | −0.429547 | − | 0.429547i | ||||
\(879\) | −7.34478 | − | 0.416450i | −0.247733 | − | 0.0140465i | ||||
\(880\) | 8.43090 | 0.284205 | ||||||||
\(881\) | 40.6450 | 1.36936 | 0.684682 | − | 0.728842i | \(-0.259941\pi\) | ||||
0.684682 | + | 0.728842i | \(0.259941\pi\) | |||||||
\(882\) | 16.0726 | − | 12.7892i | 0.541194 | − | 0.430633i | ||||
\(883\) | 13.2580i | 0.446168i | 0.974799 | + | 0.223084i | \(0.0716125\pi\) | ||||
−0.974799 | + | 0.223084i | \(0.928388\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −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 | ||||
\(891\) | 15.5678 | + | 24.8952i | 0.521542 | + | 0.834020i | ||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||
\(903\) | 58.6155 | + | 3.32351i | 1.95060 | + | 0.110599i | ||||
\(904\) | −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 | \(0.0663557\pi\) | ||||
−0.978350 | + | 0.206956i | \(0.933644\pi\) | |||||||
\(908\) | 9.22759 | + | 9.22759i | 0.306228 | + | 0.306228i | ||||
\(909\) | 6.00662 | − | 52.7980i | 0.199227 | − | 1.75120i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.70212i | 0.288314i | 0.989555 | + | 0.144157i | \(0.0460470\pi\) | ||||
−0.989555 | + | 0.144157i | \(0.953953\pi\) | |||||||
\(912\) | −8.76544 | − | 0.497002i | −0.290253 | − | 0.0164574i | ||||
\(913\) | −48.7925 | −1.61480 | ||||||||
\(914\) | 16.2148 | 0.536336 | ||||||||
\(915\) | 1.65330 | − | 29.1587i | 0.0546564 | − | 0.963955i | ||||
\(916\) | 9.21545 | + | 9.21545i | 0.304487 | + | 0.304487i | ||||
\(917\) | 47.6290 | + | 47.6290i | 1.57285 | + | 1.57285i | ||||
\(918\) | 6.90225 | + | 1.18424i | 0.227808 | + | 0.0390857i | ||||
\(919\) | −50.9311 | −1.68006 | −0.840031 | − | 0.542538i | \(-0.817463\pi\) | ||||
−0.840031 | + | 0.542538i | \(0.817463\pi\) | |||||||
\(920\) | −9.44443 | −0.311374 | ||||||||
\(921\) | 0.450286 | − | 7.94153i | 0.0148374 | − | 0.261682i | ||||
\(922\) | − | 3.68335i | − | 0.121305i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 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 | −0.455438 | − | 0.890268i | \(-0.650517\pi\) |
0.890268 | + | 0.455438i | \(0.150517\pi\) | |||||||
\(930\) | 0.115306 | − | 2.03360i | 0.00378102 | − | 0.0666845i | ||||
\(931\) | 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 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −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 | −0.0469563 | − | 0.998897i | \(-0.514952\pi\) |
0.998897 | + | 0.0469563i | \(0.0149522\pi\) | |||||||
\(942\) | 1.84940 | − | 32.6172i | 0.0602567 | − | 1.06273i | ||||
\(943\) | 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 | 0.403285 | − | 0.915075i | \(-0.367868\pi\) |
−0.915075 | + | 0.403285i | \(0.867868\pi\) | |||||||
\(948\) | −4.72222 | − | 5.28990i | −0.153370 | − | 0.171808i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 8.50667i | 0.275993i | ||||||||
\(951\) | −2.24160 | + | 39.5343i | −0.0726888 | + | 1.28199i | ||||
\(952\) | 5.01512 | 0.162541 | ||||||||
\(953\) | 11.6612 | 0.377742 | 0.188871 | − | 0.982002i | \(-0.439517\pi\) | ||||
0.188871 | + | 0.982002i | \(0.439517\pi\) | |||||||
\(954\) | −0.509031 | + | 0.405041i | −0.0164805 | + | 0.0131137i | ||||
\(955\) | 11.6038 | + | 11.6038i | 0.375489 | + | 0.375489i | ||||
\(956\) | 7.20087 | + | 7.20087i | 0.232893 | + | 0.232893i | ||||
\(957\) | 1.16906 | − | 20.6183i | 0.0377903 | − | 0.666494i | ||||
\(958\) | −24.5898 | −0.794460 | ||||||||
\(959\) | 5.13927 | 0.165956 | ||||||||
\(960\) | 4.46883 | + | 0.253383i | 0.144231 | + | 0.00817791i | ||||
\(961\) | − | 30.7929i | − | 0.993320i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −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 | \(-0.496833\pi\) |
−0.999951 | + | 0.00994880i | \(0.996833\pi\) | |||||||
\(968\) | 0.252043 | − | 0.252043i | 0.00810096 | − | 0.00810096i | ||||
\(969\) | 11.8136 | + | 0.669834i | 0.379508 | + | 0.0215182i | ||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.52489 | −0.208857 | ||||||||
\(977\) | 10.7297 | − | 10.7297i | 0.343272 | − | 0.343272i | −0.514324 | − | 0.857596i | \(-0.671957\pi\) |
0.857596 | + | 0.514324i | \(0.171957\pi\) | |||||||
\(978\) | 4.58701 | + | 5.13845i | 0.146677 | + | 0.164309i | ||||
\(979\) | − | 40.8618i | − | 1.30595i | ||||||
\(980\) | −12.5111 | + | 12.5111i | −0.399652 | + | 0.399652i | ||||
\(981\) | −30.5942 | + | 24.3441i | −0.976798 | + | 0.777247i | ||||
\(982\) | 0.581437 | − | 0.581437i | 0.0185544 | − | 0.0185544i | ||||
\(983\) | 12.8087 | + | 12.8087i | 0.408534 | + | 0.408534i | 0.881227 | − | 0.472693i | \(-0.156718\pi\) |
−0.472693 | + | 0.881227i | \(0.656718\pi\) | |||||||
\(984\) | −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 | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 33.2906i | − | 1.05858i | ||||||
\(990\) | −15.7484 | − | 19.7916i | −0.500517 | − | 0.629019i | ||||
\(991\) | 45.2289 | 1.43674 | 0.718372 | − | 0.695659i | \(-0.244887\pi\) | ||||
0.718372 | + | 0.695659i | \(0.244887\pi\) | |||||||
\(992\) | −0.455064 | −0.0144483 | ||||||||
\(993\) | −13.5115 | − | 0.766102i | −0.428773 | − | 0.0243115i | ||||
\(994\) | 0.403440 | + | 0.403440i | 0.0127963 | + | 0.0127963i | ||||
\(995\) | −31.5993 | − | 31.5993i | −1.00177 | − | 1.00177i | ||||
\(996\) | −25.8626 | − | 1.46642i | −0.819489 | − | 0.0464652i | ||||
\(997\) | 49.4416 | 1.56583 | 0.782916 | − | 0.622128i | \(-0.213732\pi\) | ||||
0.782916 | + | 0.622128i | \(0.213732\pi\) | |||||||
\(998\) | −6.11192 | −0.193469 | ||||||||
\(999\) | 14.1449 | + | 2.42688i | 0.447525 | + | 0.0767831i |
(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 | 1014.2.g.b.437.3 | 12 | ||
3.2 | odd | 2 | inner | 1014.2.g.b.437.6 | 12 | ||
13.5 | odd | 4 | inner | 1014.2.g.b.239.6 | 12 | ||
13.8 | odd | 4 | 78.2.g.a.5.3 | ✓ | 12 | ||
13.12 | even | 2 | 78.2.g.a.47.6 | yes | 12 | ||
39.5 | even | 4 | inner | 1014.2.g.b.239.3 | 12 | ||
39.8 | even | 4 | 78.2.g.a.5.6 | yes | 12 | ||
39.38 | odd | 2 | 78.2.g.a.47.3 | yes | 12 | ||
52.47 | even | 4 | 624.2.bf.f.161.2 | 12 | |||
52.51 | odd | 2 | 624.2.bf.f.593.2 | 12 | |||
156.47 | odd | 4 | 624.2.bf.f.161.1 | 12 | |||
156.155 | even | 2 | 624.2.bf.f.593.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.g.a.5.3 | ✓ | 12 | 13.8 | odd | 4 | ||
78.2.g.a.5.6 | yes | 12 | 39.8 | even | 4 | ||
78.2.g.a.47.3 | yes | 12 | 39.38 | odd | 2 | ||
78.2.g.a.47.6 | yes | 12 | 13.12 | even | 2 | ||
624.2.bf.f.161.1 | 12 | 156.47 | odd | 4 | |||
624.2.bf.f.161.2 | 12 | 52.47 | even | 4 | |||
624.2.bf.f.593.1 | 12 | 156.155 | even | 2 | |||
624.2.bf.f.593.2 | 12 | 52.51 | odd | 2 | |||
1014.2.g.b.239.3 | 12 | 39.5 | even | 4 | inner | ||
1014.2.g.b.239.6 | 12 | 13.5 | odd | 4 | inner | ||
1014.2.g.b.437.3 | 12 | 1.1 | even | 1 | trivial | ||
1014.2.g.b.437.6 | 12 | 3.2 | odd | 2 | inner |