Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(26,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.t (of order \(6\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.9 | ||
Root | \(-0.983931 + 1.42544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.101 |
Dual form | 525.2.t.h.26.9 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.94891 | − | 1.12521i | 1.37809 | − | 0.795640i | 0.386160 | − | 0.922432i | \(-0.373801\pi\) |
0.991929 | + | 0.126791i | \(0.0404679\pi\) | |||||||
\(3\) | 0.983931 | − | 1.42544i | 0.568073 | − | 0.822978i | ||||
\(4\) | 1.53217 | − | 2.65380i | 0.766087 | − | 1.32690i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.313682 | − | 3.88518i | 0.128060 | − | 1.58612i | ||||
\(7\) | −1.42897 | − | 2.22667i | −0.540099 | − | 0.841602i | ||||
\(8\) | − | 2.39522i | − | 0.846839i | ||||||
\(9\) | −1.06376 | − | 2.80507i | −0.354587 | − | 0.935023i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64925 | + | 0.952197i | 0.497269 | + | 0.287098i | 0.727585 | − | 0.686018i | \(-0.240643\pi\) |
−0.230316 | + | 0.973116i | \(0.573976\pi\) | |||||||
\(12\) | −2.27529 | − | 4.79518i | −0.656819 | − | 1.38425i | ||||
\(13\) | 5.07948i | 1.40879i | 0.709806 | + | 0.704397i | \(0.248783\pi\) | ||||
−0.709806 | + | 0.704397i | \(0.751217\pi\) | |||||||
\(14\) | −5.29039 | − | 2.73170i | −1.41392 | − | 0.730078i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.369233 | + | 0.639530i | 0.0923082 | + | 0.159882i | ||||
\(17\) | −2.22839 | + | 3.85968i | −0.540463 | + | 0.936110i | 0.458414 | + | 0.888739i | \(0.348418\pi\) |
−0.998877 | + | 0.0473710i | \(0.984916\pi\) | |||||||
\(18\) | −5.22946 | − | 4.26988i | −1.23259 | − | 1.00642i | ||||
\(19\) | 3.85670 | − | 2.22667i | 0.884788 | − | 0.510833i | 0.0125541 | − | 0.999921i | \(-0.496004\pi\) |
0.872234 | + | 0.489088i | \(0.162670\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.57999 | − | 0.153979i | −0.999435 | − | 0.0336010i | ||||
\(22\) | 4.28567 | 0.913708 | ||||||||
\(23\) | −2.46489 | + | 1.42310i | −0.513965 | + | 0.296738i | −0.734462 | − | 0.678650i | \(-0.762565\pi\) |
0.220497 | + | 0.975388i | \(0.429232\pi\) | |||||||
\(24\) | −3.41425 | − | 2.35673i | −0.696930 | − | 0.481066i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.71546 | + | 9.89947i | 1.12089 | + | 1.94145i | ||||
\(27\) | −5.04513 | − | 1.24366i | −0.970935 | − | 0.239343i | ||||
\(28\) | −8.09857 | + | 0.380555i | −1.53049 | + | 0.0719181i | ||||
\(29\) | − | 8.82675i | − | 1.63909i | −0.573018 | − | 0.819543i | \(-0.694227\pi\) | ||
0.573018 | − | 0.819543i | \(-0.305773\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.81162 | + | 2.77799i | 0.864193 | + | 0.498942i | 0.865414 | − | 0.501057i | \(-0.167055\pi\) |
−0.00122124 | + | 0.999999i | \(0.500389\pi\) | |||||||
\(32\) | 5.58785 | + | 3.22615i | 0.987802 | + | 0.570308i | ||||
\(33\) | 2.98005 | − | 1.41402i | 0.518761 | − | 0.246149i | ||||
\(34\) | 10.0296i | 1.72006i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.07397 | − | 1.47484i | −1.51233 | − | 0.245807i | ||||
\(37\) | −2.32292 | − | 4.02342i | −0.381886 | − | 0.661446i | 0.609446 | − | 0.792828i | \(-0.291392\pi\) |
−0.991332 | + | 0.131382i | \(0.958059\pi\) | |||||||
\(38\) | 5.01092 | − | 8.67917i | 0.812878 | − | 1.40795i | ||||
\(39\) | 7.24050 | + | 4.99786i | 1.15941 | + | 0.800298i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.250819 | −0.0391713 | −0.0195857 | − | 0.999808i | \(-0.506235\pi\) | ||||
−0.0195857 | + | 0.999808i | \(0.506235\pi\) | |||||||
\(42\) | −9.09926 | + | 4.85334i | −1.40405 | + | 0.748886i | ||||
\(43\) | 9.23735 | 1.40868 | 0.704341 | − | 0.709862i | \(-0.251243\pi\) | ||||
0.704341 | + | 0.709862i | \(0.251243\pi\) | |||||||
\(44\) | 5.05389 | − | 2.91786i | 0.761902 | − | 0.439885i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.20257 | + | 5.54701i | −0.472193 | + | 0.817863i | ||||
\(47\) | −1.53816 | − | 2.66417i | −0.224364 | − | 0.388610i | 0.731765 | − | 0.681557i | \(-0.238697\pi\) |
−0.956128 | + | 0.292948i | \(0.905364\pi\) | |||||||
\(48\) | 1.27491 | + | 0.102934i | 0.184018 | + | 0.0148572i | ||||
\(49\) | −2.91610 | + | 6.36367i | −0.416586 | + | 0.909096i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.30916 | + | 6.97409i | 0.463376 | + | 0.976568i | ||||
\(52\) | 13.4799 | + | 7.78265i | 1.86933 | + | 1.07926i | ||||
\(53\) | −2.09711 | − | 1.21077i | −0.288060 | − | 0.166312i | 0.349007 | − | 0.937120i | \(-0.386519\pi\) |
−0.637067 | + | 0.770809i | \(0.719852\pi\) | |||||||
\(54\) | −11.2319 | + | 3.25301i | −1.52847 | + | 0.442679i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.33336 | + | 3.42269i | −0.712701 | + | 0.457377i | ||||
\(57\) | 0.620744 | − | 7.68839i | 0.0822196 | − | 1.01835i | ||||
\(58\) | −9.93190 | − | 17.2026i | −1.30412 | − | 2.25881i | ||||
\(59\) | −6.95983 | + | 12.0548i | −0.906093 | + | 1.56940i | −0.0866494 | + | 0.996239i | \(0.527616\pi\) |
−0.819443 | + | 0.573160i | \(0.805717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.51554 | + | 0.874995i | −0.194044 | + | 0.112032i | −0.593875 | − | 0.804558i | \(-0.702402\pi\) |
0.399830 | + | 0.916589i | \(0.369069\pi\) | |||||||
\(62\) | 12.5032 | 1.58791 | ||||||||
\(63\) | −4.72588 | + | 6.37700i | −0.595405 | + | 0.803426i | ||||
\(64\) | 13.0434 | 1.63042 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.21680 | − | 6.10897i | 0.519052 | − | 0.751962i | ||||
\(67\) | −4.14868 | + | 7.18573i | −0.506842 | + | 0.877876i | 0.493127 | + | 0.869958i | \(0.335854\pi\) |
−0.999969 | + | 0.00791862i | \(0.997479\pi\) | |||||||
\(68\) | 6.82855 | + | 11.8274i | 0.828084 | + | 1.43428i | ||||
\(69\) | −0.396729 | + | 4.91379i | −0.0477606 | + | 0.591551i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.68436i | − | 1.14932i | −0.818392 | − | 0.574661i | \(-0.805134\pi\) | ||
0.818392 | − | 0.574661i | \(-0.194866\pi\) | |||||||
\(72\) | −6.71876 | + | 2.54794i | −0.791814 | + | 0.300278i | ||||
\(73\) | −5.47076 | − | 3.15855i | −0.640304 | − | 0.369680i | 0.144427 | − | 0.989515i | \(-0.453866\pi\) |
−0.784732 | + | 0.619835i | \(0.787199\pi\) | |||||||
\(74\) | −9.05434 | − | 5.22752i | −1.05255 | − | 0.607687i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 13.6466i | − | 1.56537i | ||||||
\(77\) | −0.236503 | − | 5.03300i | −0.0269520 | − | 0.573564i | ||||
\(78\) | 19.7347 | + | 1.59334i | 2.23452 | + | 0.180410i | ||||
\(79\) | 1.59436 | + | 2.76150i | 0.179379 | + | 0.310694i | 0.941668 | − | 0.336543i | \(-0.109258\pi\) |
−0.762289 | + | 0.647237i | \(0.775924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.73682 | + | 5.96785i | −0.748536 | + | 0.663094i | ||||
\(82\) | −0.488824 | + | 0.282223i | −0.0539816 | + | 0.0311663i | ||||
\(83\) | −8.98988 | −0.986768 | −0.493384 | − | 0.869812i | \(-0.664240\pi\) | ||||
−0.493384 | + | 0.869812i | \(0.664240\pi\) | |||||||
\(84\) | −7.42597 | + | 11.9185i | −0.810240 | + | 1.30041i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.0028 | − | 10.3939i | 1.94129 | − | 1.12080i | ||||
\(87\) | −12.5820 | − | 8.68491i | −1.34893 | − | 0.931120i | ||||
\(88\) | 2.28072 | − | 3.95033i | 0.243126 | − | 0.421106i | ||||
\(89\) | 5.43599 | + | 9.41541i | 0.576213 | + | 0.998031i | 0.995909 | + | 0.0903658i | \(0.0288036\pi\) |
−0.419695 | + | 0.907665i | \(0.637863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.3103 | − | 7.25841i | 1.18564 | − | 0.760889i | ||||
\(92\) | 8.72178i | 0.909308i | ||||||||
\(93\) | 8.69416 | − | 4.12533i | 0.901543 | − | 0.427777i | ||||
\(94\) | −5.99548 | − | 3.46149i | −0.618387 | − | 0.357026i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.0967 | − | 4.79084i | 1.03049 | − | 0.488963i | ||||
\(97\) | 8.94486i | 0.908213i | 0.890947 | + | 0.454107i | \(0.150041\pi\) | ||||
−0.890947 | + | 0.454107i | \(0.849959\pi\) | |||||||
\(98\) | 1.47721 | + | 15.6835i | 0.149220 | + | 1.58427i | ||||
\(99\) | 0.916566 | − | 5.63918i | 0.0921184 | − | 0.566759i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.71346 | + | 8.16395i | −0.469007 | + | 0.812344i | −0.999372 | − | 0.0354254i | \(-0.988721\pi\) |
0.530365 | + | 0.847769i | \(0.322055\pi\) | |||||||
\(102\) | 14.2966 | + | 9.86840i | 1.41557 | + | 0.977117i | ||||
\(103\) | 5.45692 | − | 3.15056i | 0.537686 | − | 0.310433i | −0.206454 | − | 0.978456i | \(-0.566192\pi\) |
0.744141 | + | 0.668023i | \(0.232859\pi\) | |||||||
\(104\) | 12.1665 | 1.19302 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.44944 | −0.529297 | ||||||||
\(107\) | −14.3818 | + | 8.30336i | −1.39034 | + | 0.802716i | −0.993353 | − | 0.115107i | \(-0.963279\pi\) |
−0.396991 | + | 0.917822i | \(0.629946\pi\) | |||||||
\(108\) | −11.0305 | + | 11.4833i | −1.06141 | + | 1.10498i | ||||
\(109\) | 9.20177 | − | 15.9379i | 0.881370 | − | 1.52658i | 0.0315518 | − | 0.999502i | \(-0.489955\pi\) |
0.849818 | − | 0.527076i | \(-0.176712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.02073 | − | 0.647577i | −0.761294 | − | 0.0614653i | ||||
\(112\) | 0.896399 | − | 1.73603i | 0.0847018 | − | 0.164039i | ||||
\(113\) | 4.37678i | 0.411733i | 0.978580 | + | 0.205866i | \(0.0660012\pi\) | ||||
−0.978580 | + | 0.205866i | \(0.933999\pi\) | |||||||
\(114\) | −7.44124 | − | 15.6825i | −0.696936 | − | 1.46880i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −23.4245 | − | 13.5241i | −2.17491 | − | 1.25568i | ||||
\(117\) | 14.2483 | − | 5.40336i | 1.31726 | − | 0.499540i | ||||
\(118\) | 31.3250i | 2.88370i | ||||||||
\(119\) | 11.7785 | − | 0.553477i | 1.07973 | − | 0.0507372i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.68664 | − | 6.38545i | −0.335149 | − | 0.580495i | ||||
\(122\) | −1.96910 | + | 3.41058i | −0.178274 | + | 0.308779i | ||||
\(123\) | −0.246788 | + | 0.357528i | −0.0222522 | + | 0.0322372i | ||||
\(124\) | 14.7445 | − | 8.51273i | 1.32409 | − | 0.764466i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.03489 | + | 17.7458i | −0.181283 | + | 1.58092i | ||||
\(127\) | 12.7846 | 1.13445 | 0.567223 | − | 0.823564i | \(-0.308018\pi\) | ||||
0.567223 | + | 0.823564i | \(0.308018\pi\) | |||||||
\(128\) | 14.2447 | − | 8.22419i | 1.25907 | − | 0.726922i | ||||
\(129\) | 9.08891 | − | 13.1673i | 0.800234 | − | 1.15932i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59617 | − | 4.49669i | −0.226828 | − | 0.392878i | 0.730038 | − | 0.683406i | \(-0.239502\pi\) |
−0.956866 | + | 0.290528i | \(0.906169\pi\) | |||||||
\(132\) | 0.813434 | − | 10.0750i | 0.0708003 | − | 0.876916i | ||||
\(133\) | −10.4692 | − | 5.40576i | −0.907791 | − | 0.468739i | ||||
\(134\) | 18.6725i | 1.61306i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.24478 | + | 5.33748i | 0.792734 | + | 0.457685i | ||||
\(137\) | −11.6770 | − | 6.74170i | −0.997630 | − | 0.575982i | −0.0900838 | − | 0.995934i | \(-0.528713\pi\) |
−0.907546 | + | 0.419952i | \(0.862047\pi\) | |||||||
\(138\) | 4.75583 | + | 10.0229i | 0.404843 | + | 0.853210i | ||||
\(139\) | 2.02188i | 0.171493i | 0.996317 | + | 0.0857466i | \(0.0273276\pi\) | ||||
−0.996317 | + | 0.0857466i | \(0.972672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.31106 | − | 0.428804i | −0.447272 | − | 0.0361118i | ||||
\(142\) | −10.8969 | − | 18.8740i | −0.914447 | − | 1.58387i | ||||
\(143\) | −4.83667 | + | 8.37736i | −0.404463 | + | 0.700550i | ||||
\(144\) | 1.40115 | − | 1.71603i | 0.116762 | − | 0.143003i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.2161 | −1.17653 | ||||||||
\(147\) | 6.20179 | + | 10.4181i | 0.511515 | + | 0.859274i | ||||
\(148\) | −14.2365 | −1.17023 | ||||||||
\(149\) | 1.11049 | − | 0.641143i | 0.0909750 | − | 0.0525244i | −0.453822 | − | 0.891092i | \(-0.649940\pi\) |
0.544797 | + | 0.838568i | \(0.316607\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50501 | + | 6.07085i | −0.285233 | + | 0.494039i | −0.972666 | − | 0.232210i | \(-0.925404\pi\) |
0.687432 | + | 0.726248i | \(0.258738\pi\) | |||||||
\(152\) | −5.33336 | − | 9.23766i | −0.432593 | − | 0.749273i | ||||
\(153\) | 13.1971 | + | 2.14500i | 1.06693 | + | 0.173413i | ||||
\(154\) | −6.12408 | − | 9.54277i | −0.493493 | − | 0.768978i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 24.3570 | − | 11.5573i | 1.95012 | − | 0.925323i | ||||
\(157\) | −2.17668 | − | 1.25671i | −0.173718 | − | 0.100296i | 0.410620 | − | 0.911807i | \(-0.365312\pi\) |
−0.584338 | + | 0.811511i | \(0.698646\pi\) | |||||||
\(158\) | 6.21452 | + | 3.58795i | 0.494401 | + | 0.285442i | ||||
\(159\) | −3.78928 | + | 1.79799i | −0.300510 | + | 0.142590i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.69103 | + | 3.45492i | 0.527327 | + | 0.272286i | ||||
\(162\) | −6.41443 | + | 19.2111i | −0.503965 | + | 1.50937i | ||||
\(163\) | 1.73224 | + | 3.00033i | 0.135680 | + | 0.235004i | 0.925857 | − | 0.377874i | \(-0.123345\pi\) |
−0.790177 | + | 0.612879i | \(0.790011\pi\) | |||||||
\(164\) | −0.384298 | + | 0.665624i | −0.0300087 | + | 0.0519765i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.5205 | + | 10.1155i | −1.35985 | + | 0.785112i | ||||
\(167\) | −3.29851 | −0.255246 | −0.127623 | − | 0.991823i | \(-0.540735\pi\) | ||||
−0.127623 | + | 0.991823i | \(0.540735\pi\) | |||||||
\(168\) | −0.368814 | + | 10.9701i | −0.0284546 | + | 0.846360i | ||||
\(169\) | −12.8011 | −0.984703 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3486 | − | 8.44967i | −0.791375 | − | 0.646163i | ||||
\(172\) | 14.1532 | − | 24.5141i | 1.07917 | − | 1.86918i | ||||
\(173\) | −8.72018 | − | 15.1038i | −0.662983 | − | 1.14832i | −0.979828 | − | 0.199843i | \(-0.935957\pi\) |
0.316845 | − | 0.948477i | \(-0.397376\pi\) | |||||||
\(174\) | −34.2935 | − | 2.76879i | −2.59979 | − | 0.209901i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.40633i | 0.106006i | ||||||||
\(177\) | 10.3354 | + | 21.7819i | 0.776855 | + | 1.63723i | ||||
\(178\) | 21.1885 | + | 12.2332i | 1.58815 | + | 0.916917i | ||||
\(179\) | −19.5347 | − | 11.2784i | −1.46009 | − | 0.842985i | −0.461077 | − | 0.887360i | \(-0.652537\pi\) |
−0.999015 | + | 0.0443755i | \(0.985870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.48204i | − | 0.258818i | −0.991591 | − | 0.129409i | \(-0.958692\pi\) | ||
0.991591 | − | 0.129409i | \(-0.0413080\pi\) | |||||||
\(182\) | 13.8756 | − | 26.8725i | 1.02853 | − | 1.99192i | ||||
\(183\) | −0.243929 | + | 3.02124i | −0.0180317 | + | 0.223336i | ||||
\(184\) | 3.40865 | + | 5.90396i | 0.251289 | + | 0.435245i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.3023 | − | 17.8226i | 0.902050 | − | 1.30682i | ||||
\(187\) | −7.35035 | + | 4.24373i | −0.537511 | + | 0.310332i | ||||
\(188\) | −9.42692 | −0.687529 | ||||||||
\(189\) | 4.44009 | + | 13.0110i | 0.322969 | + | 0.946409i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.27801 | − | 4.77931i | 0.598976 | − | 0.345819i | −0.169663 | − | 0.985502i | \(-0.554268\pi\) |
0.768638 | + | 0.639683i | \(0.220935\pi\) | |||||||
\(192\) | 12.8338 | − | 18.5926i | 0.926198 | − | 1.34180i | ||||
\(193\) | 2.88510 | − | 4.99714i | 0.207674 | − | 0.359702i | −0.743307 | − | 0.668950i | \(-0.766744\pi\) |
0.950981 | + | 0.309248i | \(0.100077\pi\) | |||||||
\(194\) | 10.0648 | + | 17.4328i | 0.722611 | + | 1.25160i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.4200 | + | 17.4890i | 0.887140 | + | 1.24922i | ||||
\(197\) | − | 4.34500i | − | 0.309568i | −0.987948 | − | 0.154784i | \(-0.950532\pi\) | ||
0.987948 | − | 0.154784i | \(-0.0494682\pi\) | |||||||
\(198\) | −4.55893 | − | 12.0216i | −0.323989 | − | 0.854338i | ||||
\(199\) | 7.53338 | + | 4.34940i | 0.534027 | + | 0.308321i | 0.742655 | − | 0.669674i | \(-0.233566\pi\) |
−0.208628 | + | 0.977995i | \(0.566900\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.16081 | + | 12.9840i | 0.434550 | + | 0.915817i | ||||
\(202\) | 21.2144i | 1.49264i | ||||||||
\(203\) | −19.6542 | + | 12.6131i | −1.37946 | + | 0.885269i | ||||
\(204\) | 23.5781 | + | 1.90364i | 1.65080 | + | 0.133282i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.09004 | − | 12.2803i | 0.493987 | − | 0.855610i | ||||
\(207\) | 6.61396 | + | 5.40034i | 0.459702 | + | 0.375350i | ||||
\(208\) | −3.24848 | + | 1.87551i | −0.225242 | + | 0.130043i | ||||
\(209\) | 8.48091 | 0.586637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6975 | 0.736446 | 0.368223 | − | 0.929737i | \(-0.379966\pi\) | ||||
0.368223 | + | 0.929737i | \(0.379966\pi\) | |||||||
\(212\) | −6.42627 | + | 3.71021i | −0.441358 | + | 0.254818i | ||||
\(213\) | −13.8045 | − | 9.52873i | −0.945867 | − | 0.652898i | ||||
\(214\) | −18.6860 | + | 32.3650i | −1.27735 | + | 2.21243i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.97885 | + | 12.0842i | −0.202685 | + | 0.822225i | ||||
\(217\) | −0.689986 | − | 14.6835i | −0.0468393 | − | 0.996784i | ||||
\(218\) | − | 41.4155i | − | 2.80501i | ||||||
\(219\) | −9.88517 | + | 4.69046i | −0.667978 | + | 0.316952i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.6052 | − | 11.3190i | −1.31879 | − | 0.761402i | ||||
\(222\) | −16.3604 | + | 7.76290i | −1.09804 | + | 0.521012i | ||||
\(223\) | − | 16.9483i | − | 1.13494i | −0.823394 | − | 0.567471i | \(-0.807922\pi\) | ||
0.823394 | − | 0.567471i | \(-0.192078\pi\) | |||||||
\(224\) | −0.801297 | − | 17.0523i | −0.0535389 | − | 1.13936i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.92477 | + | 8.52996i | 0.327591 | + | 0.567404i | ||||
\(227\) | −1.21572 | + | 2.10568i | −0.0806899 | + | 0.139759i | −0.903546 | − | 0.428490i | \(-0.859046\pi\) |
0.822857 | + | 0.568249i | \(0.192379\pi\) | |||||||
\(228\) | −19.4524 | − | 13.4273i | −1.28827 | − | 0.889244i | ||||
\(229\) | 0.204081 | − | 0.117826i | 0.0134861 | − | 0.00778618i | −0.493242 | − | 0.869892i | \(-0.664188\pi\) |
0.506728 | + | 0.862106i | \(0.330855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.40695 | − | 4.61500i | −0.487341 | − | 0.303645i | ||||
\(232\) | −21.1420 | −1.38804 | ||||||||
\(233\) | 9.59675 | − | 5.54068i | 0.628704 | − | 0.362982i | −0.151546 | − | 0.988450i | \(-0.548425\pi\) |
0.780250 | + | 0.625468i | \(0.215092\pi\) | |||||||
\(234\) | 21.6888 | − | 26.5629i | 1.41784 | − | 1.73647i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.3273 | + | 36.9401i | 1.38829 | + | 2.40459i | ||||
\(237\) | 5.50510 | + | 0.444470i | 0.357594 | + | 0.0288714i | ||||
\(238\) | 22.3325 | − | 14.3319i | 1.44760 | − | 0.929001i | ||||
\(239\) | 9.67610i | 0.625895i | 0.949770 | + | 0.312948i | \(0.101316\pi\) | ||||
−0.949770 | + | 0.312948i | \(0.898684\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9240 | − | 8.03902i | −0.896923 | − | 0.517839i | −0.0207223 | − | 0.999785i | \(-0.506597\pi\) |
−0.876201 | + | 0.481947i | \(0.839930\pi\) | |||||||
\(242\) | −14.3699 | − | 8.29646i | −0.923731 | − | 0.533316i | ||||
\(243\) | 1.87825 | + | 15.4749i | 0.120490 | + | 0.992715i | ||||
\(244\) | 5.36258i | 0.343304i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0786773 | + | 0.974478i | −0.00501628 | + | 0.0621304i | ||||
\(247\) | 11.3103 | + | 19.5901i | 0.719659 | + | 1.24649i | ||||
\(248\) | 6.65390 | − | 11.5249i | 0.422523 | − | 0.731832i | ||||
\(249\) | −8.84542 | + | 12.8145i | −0.560556 | + | 0.812089i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.3809 | 0.907716 | 0.453858 | − | 0.891074i | \(-0.350047\pi\) | ||||
0.453858 | + | 0.891074i | \(0.350047\pi\) | |||||||
\(252\) | 9.68243 | + | 22.3122i | 0.609936 | + | 1.40554i | ||||
\(253\) | −5.42031 | −0.340772 | ||||||||
\(254\) | 24.9160 | − | 14.3852i | 1.56337 | − | 0.902611i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.46442 | − | 9.46465i | 0.341526 | − | 0.591541i | ||||
\(257\) | 2.37985 | + | 4.12202i | 0.148451 | + | 0.257125i | 0.930655 | − | 0.365898i | \(-0.119238\pi\) |
−0.782204 | + | 0.623022i | \(0.785905\pi\) | |||||||
\(258\) | 2.89759 | − | 35.8888i | 0.180396 | − | 2.23434i | ||||
\(259\) | −5.63944 | + | 10.9217i | −0.350417 | + | 0.678642i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.7596 | + | 9.38955i | −1.53258 | + | 0.581199i | ||||
\(262\) | −10.1194 | − | 5.84244i | −0.625179 | − | 0.360947i | ||||
\(263\) | 4.89251 | + | 2.82469i | 0.301685 | + | 0.174178i | 0.643200 | − | 0.765698i | \(-0.277607\pi\) |
−0.341514 | + | 0.939877i | \(0.610940\pi\) | |||||||
\(264\) | −3.38689 | − | 7.13788i | −0.208448 | − | 0.439306i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.4861 | + | 1.24459i | −1.62396 | + | 0.0763108i | ||||
\(267\) | 18.7697 | + | 1.51543i | 1.14869 | + | 0.0927427i | ||||
\(268\) | 12.7130 | + | 22.0196i | 0.776570 | + | 1.34506i | ||||
\(269\) | 0.356044 | − | 0.616686i | 0.0217084 | − | 0.0376000i | −0.854967 | − | 0.518682i | \(-0.826423\pi\) |
0.876676 | + | 0.481082i | \(0.159756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.80074 | − | 1.61701i | 0.170133 | − | 0.0982264i | −0.412516 | − | 0.910951i | \(-0.635350\pi\) |
0.582649 | + | 0.812724i | \(0.302016\pi\) | |||||||
\(272\) | −3.29117 | −0.199557 | ||||||||
\(273\) | 0.782133 | − | 23.2640i | 0.0473369 | − | 1.40800i | ||||
\(274\) | −30.3432 | −1.83310 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.4324 | + | 8.58162i | 0.748341 | + | 0.516553i | ||||
\(277\) | −11.4567 | + | 19.8435i | −0.688364 | + | 1.19228i | 0.284002 | + | 0.958824i | \(0.408338\pi\) |
−0.972367 | + | 0.233459i | \(0.924996\pi\) | |||||||
\(278\) | 2.27503 | + | 3.94046i | 0.136447 | + | 0.236333i | ||||
\(279\) | 2.67404 | − | 16.4521i | 0.160091 | − | 0.984959i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0342i | 0.717900i | 0.933357 | + | 0.358950i | \(0.116865\pi\) | ||||
−0.933357 | + | 0.358950i | \(0.883135\pi\) | |||||||
\(282\) | −10.8333 | + | 5.14034i | −0.645113 | + | 0.306102i | ||||
\(283\) | −15.5030 | − | 8.95065i | −0.921556 | − | 0.532061i | −0.0374249 | − | 0.999299i | \(-0.511916\pi\) |
−0.884131 | + | 0.467239i | \(0.845249\pi\) | |||||||
\(284\) | −25.7004 | − | 14.8381i | −1.52504 | − | 0.880481i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.7690i | 1.28723i | ||||||||
\(287\) | 0.358412 | + | 0.558491i | 0.0211564 | + | 0.0329667i | ||||
\(288\) | 3.10542 | − | 19.1062i | 0.182989 | − | 1.12584i | ||||
\(289\) | −1.43141 | − | 2.47928i | −0.0842008 | − | 0.145840i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7504 | + | 8.80112i | 0.747440 | + | 0.515931i | ||||
\(292\) | −16.7643 | + | 9.67889i | −0.981058 | + | 0.566414i | ||||
\(293\) | −8.87318 | −0.518377 | −0.259188 | − | 0.965827i | \(-0.583455\pi\) | ||||
−0.259188 | + | 0.965827i | \(0.583455\pi\) | |||||||
\(294\) | 23.8093 | + | 13.3258i | 1.38859 | + | 0.777174i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.63697 | + | 5.56391i | −0.560138 | + | 0.323396i | ||||
\(297\) | −7.13648 | − | 6.85507i | −0.414101 | − | 0.397772i | ||||
\(298\) | 1.44283 | − | 2.49906i | 0.0835811 | − | 0.144767i | ||||
\(299\) | −7.22863 | − | 12.5204i | −0.418043 | − | 0.724071i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.1999 | − | 20.5685i | −0.760828 | − | 1.18555i | ||||
\(302\) | 15.7754i | 0.907773i | ||||||||
\(303\) | 6.99951 | + | 14.7515i | 0.402111 | + | 0.847453i | ||||
\(304\) | 2.84804 | + | 1.64432i | 0.163346 | + | 0.0943081i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 28.1336 | − | 10.6691i | 1.60829 | − | 0.609910i | ||||
\(307\) | − | 8.99889i | − | 0.513594i | −0.966465 | − | 0.256797i | \(-0.917333\pi\) | ||
0.966465 | − | 0.256797i | \(-0.0826671\pi\) | |||||||
\(308\) | −13.7190 | − | 7.08380i | −0.781710 | − | 0.403637i | ||||
\(309\) | 0.878303 | − | 10.8784i | 0.0499649 | − | 0.618853i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.29851 | − | 5.71318i | 0.187041 | − | 0.323965i | −0.757221 | − | 0.653159i | \(-0.773444\pi\) |
0.944262 | + | 0.329194i | \(0.106777\pi\) | |||||||
\(312\) | 11.9710 | − | 17.3426i | 0.677723 | − | 0.981831i | ||||
\(313\) | 16.7007 | − | 9.64215i | 0.943979 | − | 0.545007i | 0.0527736 | − | 0.998607i | \(-0.483194\pi\) |
0.891205 | + | 0.453600i | \(0.149861\pi\) | |||||||
\(314\) | −5.65621 | −0.319198 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.77132 | 0.549680 | ||||||||
\(317\) | 16.6152 | − | 9.59278i | 0.933202 | − | 0.538784i | 0.0453790 | − | 0.998970i | \(-0.485550\pi\) |
0.887823 | + | 0.460186i | \(0.152217\pi\) | |||||||
\(318\) | −5.36187 | + | 7.76786i | −0.300679 | + | 0.435600i | ||||
\(319\) | 8.40481 | − | 14.5576i | 0.470579 | − | 0.815066i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.31479 | + | 28.6704i | −0.129199 | + | 1.60022i | ||||
\(322\) | 16.9277 | − | 0.795441i | 0.943345 | − | 0.0443282i | ||||
\(323\) | 19.8475i | 1.10435i | ||||||||
\(324\) | 5.51551 | + | 27.0220i | 0.306417 | + | 1.50122i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.75198 | + | 3.89826i | 0.373958 | + | 0.215905i | ||||
\(327\) | −13.6647 | − | 28.7984i | −0.755659 | − | 1.59256i | ||||
\(328\) | 0.600767i | 0.0331718i | ||||||||
\(329\) | −3.73425 | + | 7.23199i | −0.205876 | + | 0.398713i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.98753 | − | 10.3707i | −0.329104 | − | 0.570026i | 0.653230 | − | 0.757160i | \(-0.273413\pi\) |
−0.982334 | + | 0.187134i | \(0.940080\pi\) | |||||||
\(332\) | −13.7741 | + | 23.8574i | −0.755950 | + | 1.30934i | ||||
\(333\) | −8.81493 | + | 10.7959i | −0.483055 | + | 0.591612i | ||||
\(334\) | −6.42851 | + | 3.71150i | −0.351752 | + | 0.203084i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.59261 | − | 2.98589i | −0.0868839 | − | 0.162894i | ||||
\(337\) | −12.6992 | −0.691769 | −0.345885 | − | 0.938277i | \(-0.612421\pi\) | ||||
−0.345885 | + | 0.938277i | \(0.612421\pi\) | |||||||
\(338\) | −24.9483 | + | 14.4039i | −1.35701 | + | 0.783469i | ||||
\(339\) | 6.23884 | + | 4.30644i | 0.338847 | + | 0.233894i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.29039 | + | 9.16323i | 0.286491 | + | 0.496217i | ||||
\(342\) | −29.6761 | − | 4.82341i | −1.60470 | − | 0.260820i | ||||
\(343\) | 18.3368 | − | 2.60028i | 0.990095 | − | 0.140402i | ||||
\(344\) | − | 22.1255i | − | 1.19293i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.9897 | − | 19.6240i | −1.82730 | − | 1.05499i | ||||
\(347\) | 4.85815 | + | 2.80486i | 0.260799 | + | 0.150573i | 0.624699 | − | 0.780866i | \(-0.285222\pi\) |
−0.363900 | + | 0.931438i | \(0.618555\pi\) | |||||||
\(348\) | −42.3259 | + | 20.0834i | −2.26890 | + | 1.07658i | ||||
\(349\) | − | 33.8725i | − | 1.81315i | −0.422041 | − | 0.906577i | \(-0.638686\pi\) | ||
0.422041 | − | 0.906577i | \(-0.361314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.31717 | − | 25.6266i | 0.337186 | − | 1.36785i | ||||
\(352\) | 6.14386 | + | 10.6415i | 0.327469 | + | 0.567192i | ||||
\(353\) | 18.3706 | − | 31.8188i | 0.977767 | − | 1.69354i | 0.307281 | − | 0.951619i | \(-0.400581\pi\) |
0.670485 | − | 0.741923i | \(-0.266086\pi\) | |||||||
\(354\) | 44.6519 | + | 30.8216i | 2.37322 | + | 1.63815i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 33.3155 | 1.76572 | ||||||||
\(357\) | 10.8003 | − | 17.3342i | 0.571612 | − | 0.917421i | ||||
\(358\) | −50.7619 | −2.68285 | ||||||||
\(359\) | −21.1388 | + | 12.2045i | −1.11566 | + | 0.644127i | −0.940290 | − | 0.340375i | \(-0.889446\pi\) |
−0.175371 | + | 0.984502i | \(0.556113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.416104 | − | 0.720714i | 0.0219002 | − | 0.0379323i | ||||
\(362\) | −3.91801 | − | 6.78619i | −0.205926 | − | 0.356674i | ||||
\(363\) | −12.7295 | − | 1.02775i | −0.668124 | − | 0.0539429i | ||||
\(364\) | −1.93302 | − | 41.1365i | −0.101318 | − | 2.15614i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.92412 | + | 6.16260i | 0.152846 | + | 0.322124i | ||||
\(367\) | −17.8968 | − | 10.3327i | −0.934203 | − | 0.539362i | −0.0460646 | − | 0.998938i | \(-0.514668\pi\) |
−0.888138 | + | 0.459576i | \(0.848001\pi\) | |||||||
\(368\) | −1.82024 | − | 1.05091i | −0.0948864 | − | 0.0547827i | ||||
\(369\) | 0.266812 | + | 0.703565i | 0.0138897 | + | 0.0366261i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.300725 | + | 6.39971i | 0.0156129 | + | 0.332256i | ||||
\(372\) | 2.37316 | − | 29.3933i | 0.123042 | − | 1.52397i | ||||
\(373\) | 10.4361 | + | 18.0759i | 0.540363 | + | 0.935936i | 0.998883 | + | 0.0472520i | \(0.0150464\pi\) |
−0.458520 | + | 0.888684i | \(0.651620\pi\) | |||||||
\(374\) | −9.55013 | + | 16.5413i | −0.493825 | + | 0.855331i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.38128 | + | 3.68424i | −0.329090 | + | 0.190000i | ||||
\(377\) | 44.8353 | 2.30914 | ||||||||
\(378\) | 23.2934 | + | 20.3612i | 1.19808 | + | 1.04727i | ||||
\(379\) | −27.0384 | −1.38887 | −0.694435 | − | 0.719556i | \(-0.744345\pi\) | ||||
−0.694435 | + | 0.719556i | \(0.744345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5791 | − | 18.2236i | 0.644447 | − | 0.933624i | ||||
\(382\) | 10.7554 | − | 18.6289i | 0.550295 | − | 0.953138i | ||||
\(383\) | 3.16723 | + | 5.48580i | 0.161838 | + | 0.280311i | 0.935528 | − | 0.353253i | \(-0.114924\pi\) |
−0.773690 | + | 0.633564i | \(0.781591\pi\) | |||||||
\(384\) | 2.29272 | − | 28.3970i | 0.117000 | − | 1.44913i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.9853i | − | 0.660936i | ||||||
\(387\) | −9.82633 | − | 25.9114i | −0.499501 | − | 1.31715i | ||||
\(388\) | 23.7379 | + | 13.7051i | 1.20511 | + | 0.695770i | ||||
\(389\) | −10.7869 | − | 6.22784i | −0.546919 | − | 0.315764i | 0.200959 | − | 0.979600i | \(-0.435594\pi\) |
−0.747879 | + | 0.663836i | \(0.768927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.6849i | − | 0.641503i | ||||||
\(392\) | 15.2424 | + | 6.98471i | 0.769858 | + | 0.352781i | ||||
\(393\) | −8.96422 | − | 0.723752i | −0.452185 | − | 0.0365085i | ||||
\(394\) | −4.88902 | − | 8.46803i | −0.246305 | − | 0.426613i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −13.5609 | − | 11.0726i | −0.681463 | − | 0.556419i | ||||
\(397\) | 24.6611 | − | 14.2381i | 1.23771 | − | 0.714591i | 0.269082 | − | 0.963117i | \(-0.413280\pi\) |
0.968625 | + | 0.248527i | \(0.0799463\pi\) | |||||||
\(398\) | 19.5759 | 0.981250 | ||||||||
\(399\) | −18.0065 | + | 9.60426i | −0.901453 | + | 0.480815i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7515 | − | 7.36207i | 0.636779 | − | 0.367644i | −0.146594 | − | 0.989197i | \(-0.546831\pi\) |
0.783373 | + | 0.621552i | \(0.213498\pi\) | |||||||
\(402\) | 26.6165 | + | 18.3724i | 1.32751 | + | 0.916333i | ||||
\(403\) | −14.1108 | + | 24.4405i | −0.702907 | + | 1.21747i | ||||
\(404\) | 14.4437 | + | 25.0172i | 0.718600 | + | 1.24465i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.1120 | + | 46.6970i | −1.19666 | + | 2.31753i | ||||
\(407\) | − | 8.84751i | − | 0.438555i | ||||||
\(408\) | 16.7045 | − | 7.92618i | 0.826995 | − | 0.392404i | ||||
\(409\) | −0.810609 | − | 0.468005i | −0.0400820 | − | 0.0231414i | 0.479825 | − | 0.877364i | \(-0.340700\pi\) |
−0.519907 | + | 0.854223i | \(0.674033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.0992 | + | 10.0115i | −1.04075 | + | 0.493828i | ||||
\(412\) | − | 19.3088i | − | 0.951276i | ||||||
\(413\) | 36.7874 | − | 1.72865i | 1.81019 | − | 0.0850615i | ||||
\(414\) | 18.9665 | + | 3.08273i | 0.932154 | + | 0.151508i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.3872 | + | 28.3834i | −0.803446 | + | 1.39161i | ||||
\(417\) | 2.88206 | + | 1.98939i | 0.141135 | + | 0.0974206i | ||||
\(418\) | 16.5286 | − | 9.54277i | 0.808438 | − | 0.466752i | ||||
\(419\) | 30.1515 | 1.47299 | 0.736497 | − | 0.676440i | \(-0.236478\pi\) | ||||
0.736497 | + | 0.676440i | \(0.236478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.3685 | 1.77249 | 0.886245 | − | 0.463217i | \(-0.153305\pi\) | ||||
0.886245 | + | 0.463217i | \(0.153305\pi\) | |||||||
\(422\) | 20.8485 | − | 12.0369i | 1.01489 | − | 0.585946i | ||||
\(423\) | −5.83695 | + | 7.14869i | −0.283802 | + | 0.347581i | ||||
\(424\) | −2.90005 | + | 5.02304i | −0.140839 | + | 0.243940i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −37.6255 | − | 3.03780i | −1.82296 | − | 0.147182i | ||||
\(427\) | 4.11397 | + | 2.12426i | 0.199089 | + | 0.102800i | ||||
\(428\) | 50.8887i | 2.45980i | ||||||||
\(429\) | 7.18248 | + | 15.1371i | 0.346773 | + | 0.730827i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9349 | + | 6.89063i | 0.574885 | + | 0.331910i | 0.759098 | − | 0.650976i | \(-0.225640\pi\) |
−0.184213 | + | 0.982886i | \(0.558974\pi\) | |||||||
\(432\) | −1.06747 | − | 3.68571i | −0.0513584 | − | 0.177329i | ||||
\(433\) | 1.16840i | 0.0561499i | 0.999606 | + | 0.0280750i | \(0.00893771\pi\) | ||||
−0.999606 | + | 0.0280750i | \(0.991062\pi\) | |||||||
\(434\) | −17.8667 | − | 27.8406i | −0.857630 | − | 1.33639i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.1974 | − | 48.8394i | −1.35041 | − | 2.33898i | ||||
\(437\) | −6.33756 | + | 10.9770i | −0.303167 | + | 0.525100i | ||||
\(438\) | −13.9876 | + | 20.2641i | −0.668354 | + | 0.968258i | ||||
\(439\) | 2.50353 | − | 1.44541i | 0.119487 | − | 0.0689858i | −0.439065 | − | 0.898455i | \(-0.644690\pi\) |
0.558552 | + | 0.829469i | \(0.311357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.9526 | + | 1.41044i | 0.997742 | + | 0.0671640i | ||||
\(442\) | −50.9450 | −2.42321 | ||||||||
\(443\) | 14.2948 | − | 8.25313i | 0.679169 | − | 0.392118i | −0.120373 | − | 0.992729i | \(-0.538409\pi\) |
0.799542 | + | 0.600611i | \(0.205076\pi\) | |||||||
\(444\) | −14.0077 | + | 20.2932i | −0.664776 | + | 0.963075i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.0703 | − | 33.0307i | −0.903005 | − | 1.56405i | ||||
\(447\) | 0.178736 | − | 2.21378i | 0.00845392 | − | 0.104708i | ||||
\(448\) | −18.6386 | − | 29.0433i | −0.880589 | − | 1.37217i | ||||
\(449\) | − | 25.9824i | − | 1.22618i | −0.790012 | − | 0.613092i | \(-0.789925\pi\) | ||
0.790012 | − | 0.613092i | \(-0.210075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.413664 | − | 0.238829i | −0.0194787 | − | 0.0112460i | ||||
\(452\) | 11.6151 | + | 6.70598i | 0.546329 | + | 0.315423i | ||||
\(453\) | 5.20495 | + | 10.9695i | 0.244550 | + | 0.515391i | ||||
\(454\) | 5.47172i | 0.256801i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.4154 | − | 1.48682i | −0.862380 | − | 0.0696267i | ||||
\(457\) | −0.750953 | − | 1.30069i | −0.0351281 | − | 0.0608436i | 0.847927 | − | 0.530113i | \(-0.177851\pi\) |
−0.883055 | + | 0.469270i | \(0.844517\pi\) | |||||||
\(458\) | 0.265158 | − | 0.459266i | 0.0123900 | − | 0.0214601i | ||||
\(459\) | 16.0426 | − | 16.7012i | 0.748806 | − | 0.779545i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.40468 | 0.0654225 | 0.0327113 | − | 0.999465i | \(-0.489586\pi\) | ||||
0.0327113 | + | 0.999465i | \(0.489586\pi\) | |||||||
\(462\) | −19.6283 | − | 0.659903i | −0.913192 | − | 0.0307015i | ||||
\(463\) | −20.2056 | −0.939033 | −0.469516 | − | 0.882924i | \(-0.655572\pi\) | ||||
−0.469516 | + | 0.882924i | \(0.655572\pi\) | |||||||
\(464\) | 5.64497 | − | 3.25912i | 0.262061 | − | 0.151301i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.4688 | − | 21.5966i | 0.577607 | − | 1.00044i | ||||
\(467\) | 19.3296 | + | 33.4798i | 0.894467 | + | 1.54926i | 0.834463 | + | 0.551064i | \(0.185778\pi\) |
0.0600041 | + | 0.998198i | \(0.480889\pi\) | |||||||
\(468\) | 7.49143 | − | 46.0911i | 0.346291 | − | 2.13056i | ||||
\(469\) | 21.9286 | − | 1.03043i | 1.01257 | − | 0.0475809i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.93306 | + | 1.86621i | −0.181226 | + | 0.0859906i | ||||
\(472\) | 28.8739 | + | 16.6703i | 1.32903 | + | 0.767314i | ||||
\(473\) | 15.2347 | + | 8.79578i | 0.700494 | + | 0.404430i | ||||
\(474\) | 11.2291 | − | 5.32813i | 0.515768 | − | 0.244729i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 16.5779 | − | 32.1059i | 0.759848 | − | 1.47157i | ||||
\(477\) | −1.16546 | + | 7.17050i | −0.0533627 | + | 0.328315i | ||||
\(478\) | 10.8876 | + | 18.8579i | 0.497987 | + | 0.862539i | ||||
\(479\) | −15.3467 | + | 26.5813i | −0.701210 | + | 1.21453i | 0.266832 | + | 0.963743i | \(0.414023\pi\) |
−0.968042 | + | 0.250788i | \(0.919310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.4369 | − | 11.7992i | 0.931841 | − | 0.537999i | ||||
\(482\) | −36.1822 | −1.64805 | ||||||||
\(483\) | 11.5083 | − | 6.13826i | 0.523645 | − | 0.279301i | ||||
\(484\) | −22.5943 | −1.02701 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 21.0730 | + | 28.0458i | 0.955889 | + | 1.27218i | ||||
\(487\) | −14.8500 | + | 25.7209i | −0.672915 | + | 1.16552i | 0.304158 | + | 0.952622i | \(0.401625\pi\) |
−0.977074 | + | 0.212902i | \(0.931708\pi\) | |||||||
\(488\) | 2.09581 | + | 3.63004i | 0.0948727 | + | 0.164324i | ||||
\(489\) | 5.98120 | + | 0.482910i | 0.270479 | + | 0.0218379i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.13665i | 0.322073i | 0.986948 | + | 0.161036i | \(0.0514836\pi\) | ||||
−0.986948 | + | 0.161036i | \(0.948516\pi\) | |||||||
\(492\) | 0.570685 | + | 1.20272i | 0.0257285 | + | 0.0542229i | ||||
\(493\) | 34.0684 | + | 19.6694i | 1.53436 | + | 0.885866i | ||||
\(494\) | 44.0857 | + | 25.4529i | 1.98351 | + | 1.14518i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.10290i | 0.184226i | ||||||||
\(497\) | −21.5639 | + | 13.8386i | −0.967271 | + | 0.620747i | ||||
\(498\) | −2.81996 | + | 34.9273i | −0.126365 | + | 1.56513i | ||||
\(499\) | 6.67079 | + | 11.5541i | 0.298626 | + | 0.517235i | 0.975822 | − | 0.218568i | \(-0.0701385\pi\) |
−0.677196 | + | 0.735802i | \(0.736805\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.24550 | + | 4.70183i | −0.144998 | + | 0.210062i | ||||
\(502\) | 28.0272 | − | 16.1815i | 1.25091 | − | 0.722216i | ||||
\(503\) | −30.4353 | −1.35704 | −0.678522 | − | 0.734580i | \(-0.737379\pi\) | ||||
−0.678522 | + | 0.734580i | \(0.737379\pi\) | |||||||
\(504\) | 15.2743 | + | 11.3195i | 0.680372 | + | 0.504212i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.5637 | + | 6.09896i | −0.469614 | + | 0.271132i | ||||
\(507\) | −12.5954 | + | 18.2473i | −0.559383 | + | 0.810389i | ||||
\(508\) | 19.5882 | − | 33.9277i | 0.869084 | − | 1.50530i | ||||
\(509\) | −16.4870 | − | 28.5563i | −0.730774 | − | 1.26574i | −0.956553 | − | 0.291559i | \(-0.905826\pi\) |
0.225779 | − | 0.974179i | \(-0.427507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.784506 | + | 16.6950i | 0.0347045 | + | 0.738545i | ||||
\(512\) | 8.30237i | 0.366916i | ||||||||
\(513\) | −22.2268 | + | 6.43738i | −0.981336 | + | 0.284217i | ||||
\(514\) | 9.27624 | + | 5.35564i | 0.409157 | + | 0.236227i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.0176 | − | 44.2948i | −0.925249 | − | 1.94997i | ||||
\(517\) | − | 5.85853i | − | 0.257658i | ||||||
\(518\) | 1.29839 | + | 27.6310i | 0.0570480 | + | 1.21404i | ||||
\(519\) | −30.1096 | − | 2.43099i | −1.32167 | − | 0.106708i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.7254 | + | 22.0411i | −0.557511 | + | 0.965638i | 0.440192 | + | 0.897904i | \(0.354910\pi\) |
−0.997703 | + | 0.0677342i | \(0.978423\pi\) | |||||||
\(522\) | −37.6892 | + | 46.1591i | −1.64961 | + | 2.02033i | ||||
\(523\) | 20.9524 | − | 12.0969i | 0.916184 | − | 0.528959i | 0.0337685 | − | 0.999430i | \(-0.489249\pi\) |
0.882416 | + | 0.470470i | \(0.155916\pi\) | |||||||
\(524\) | −15.9111 | −0.695081 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.7134 | 0.554332 | ||||||||
\(527\) | −21.4443 | + | 12.3809i | −0.934129 | + | 0.539320i | ||||
\(528\) | 2.00464 | + | 1.38373i | 0.0872407 | + | 0.0602192i | ||||
\(529\) | −7.44955 | + | 12.9030i | −0.323893 | + | 0.561000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.2181 | + | 6.69940i | 1.78871 | + | 0.290729i | ||||
\(532\) | −30.3864 | + | 19.5005i | −1.31742 | + | 0.845454i | ||||
\(533\) | − | 1.27403i | − | 0.0551844i | ||||||
\(534\) | 38.2857 | − | 18.1664i | 1.65679 | − | 0.786136i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17.2114 | + | 9.93701i | 0.743419 | + | 0.429213i | ||||
\(537\) | −35.2974 | + | 16.7484i | −1.52320 | + | 0.722748i | ||||
\(538\) | − | 1.60249i | − | 0.0690882i | ||||||
\(539\) | −10.8689 | + | 7.71861i | −0.468155 | + | 0.332464i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8529 | + | 30.9222i | 0.767557 | + | 1.32945i | 0.938884 | + | 0.344233i | \(0.111861\pi\) |
−0.171328 | + | 0.985214i | \(0.554806\pi\) | |||||||
\(542\) | 3.63894 | − | 6.30282i | 0.156306 | − | 0.270729i | ||||
\(543\) | −4.96344 | − | 3.42609i | −0.213002 | − | 0.147027i | ||||
\(544\) | −24.9038 | + | 14.3782i | −1.06774 | + | 0.616460i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −24.6524 | − | 46.2195i | −1.05503 | − | 1.97801i | ||||
\(547\) | 14.1119 | 0.603380 | 0.301690 | − | 0.953406i | \(-0.402449\pi\) | ||||
0.301690 | + | 0.953406i | \(0.402449\pi\) | |||||||
\(548\) | −35.7823 | + | 20.6589i | −1.52854 | + | 0.882505i | ||||
\(549\) | 4.06659 | + | 3.32040i | 0.173558 | + | 0.141711i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.6542 | − | 34.0421i | −0.837299 | − | 1.45024i | ||||
\(552\) | 11.7696 | + | 0.950254i | 0.500948 | + | 0.0404455i | ||||
\(553\) | 3.87067 | − | 7.49620i | 0.164598 | − | 0.318771i | ||||
\(554\) | 51.5644i | 2.19076i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.36566 | + | 3.09787i | 0.227555 | + | 0.131379i | ||||
\(557\) | 27.2162 | + | 15.7133i | 1.15319 | + | 0.665792i | 0.949661 | − | 0.313278i | \(-0.101427\pi\) |
0.203524 | + | 0.979070i | \(0.434760\pi\) | |||||||
\(558\) | −13.3005 | − | 35.0725i | −0.563054 | − | 1.48474i | ||||
\(559\) | 46.9209i | 1.98454i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.18305 | + | 14.6530i | −0.0499486 | + | 0.618651i | ||||
\(562\) | 13.5409 | + | 23.4536i | 0.571190 | + | 0.989330i | ||||
\(563\) | −16.0333 | + | 27.7705i | −0.675723 | + | 1.17039i | 0.300535 | + | 0.953771i | \(0.402835\pi\) |
−0.976257 | + | 0.216615i | \(0.930498\pi\) | |||||||
\(564\) | −9.27544 | + | 13.4375i | −0.390566 | + | 0.565822i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −40.2853 | −1.69332 | ||||||||
\(567\) | 22.9151 | + | 6.47281i | 0.962345 | + | 0.271833i | ||||
\(568\) | −23.1962 | −0.973290 | ||||||||
\(569\) | 17.1344 | − | 9.89257i | 0.718313 | − | 0.414718i | −0.0958187 | − | 0.995399i | \(-0.530547\pi\) |
0.814131 | + | 0.580681i | \(0.197214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9459 | + | 22.4229i | −0.541768 | + | 0.938370i | 0.457035 | + | 0.889449i | \(0.348912\pi\) |
−0.998803 | + | 0.0489208i | \(0.984422\pi\) | |||||||
\(572\) | 14.8212 | + | 25.6711i | 0.619707 | + | 1.07336i | ||||
\(573\) | 1.33236 | − | 16.5023i | 0.0556602 | − | 0.689394i | ||||
\(574\) | 1.32693 | + | 0.685162i | 0.0553850 | + | 0.0285981i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.8750 | − | 36.5876i | −0.578127 | − | 1.52448i | ||||
\(577\) | −20.3323 | − | 11.7388i | −0.846443 | − | 0.488694i | 0.0130060 | − | 0.999915i | \(-0.495860\pi\) |
−0.859449 | + | 0.511221i | \(0.829193\pi\) | |||||||
\(578\) | −5.57940 | − | 3.22127i | −0.232073 | − | 0.133987i | ||||
\(579\) | −4.28439 | − | 9.02938i | −0.178053 | − | 0.375248i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8463 | + | 20.0175i | 0.532952 | + | 0.830465i | ||||
\(582\) | 34.7524 | + | 2.80584i | 1.44053 | + | 0.116306i | ||||
\(583\) | −2.30578 | − | 3.99372i | −0.0954955 | − | 0.165403i | ||||
\(584\) | −7.56542 | + | 13.1037i | −0.313059 | + | 0.542234i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.2930 | + | 9.98415i | −0.714369 | + | 0.412441i | ||||
\(587\) | 36.1962 | 1.49398 | 0.746988 | − | 0.664837i | \(-0.231499\pi\) | ||||
0.746988 | + | 0.664837i | \(0.231499\pi\) | |||||||
\(588\) | 37.1499 | − | 0.495928i | 1.53204 | − | 0.0204517i | ||||
\(589\) | 24.7427 | 1.01950 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.19354 | − | 4.27518i | −0.254768 | − | 0.175857i | ||||
\(592\) | 1.71540 | − | 2.97115i | 0.0705024 | − | 0.122114i | ||||
\(593\) | 7.50446 | + | 12.9981i | 0.308171 | + | 0.533768i | 0.977962 | − | 0.208781i | \(-0.0669497\pi\) |
−0.669791 | + | 0.742550i | \(0.733616\pi\) | |||||||
\(594\) | −21.6217 | − | 5.32994i | −0.887151 | − | 0.218690i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.92937i | − | 0.160953i | ||||||
\(597\) | 13.6121 | − | 6.45888i | 0.557108 | − | 0.264344i | ||||
\(598\) | −28.1760 | − | 16.2674i | −1.15220 | − | 0.665223i | ||||
\(599\) | 11.3793 | + | 6.56986i | 0.464947 | + | 0.268437i | 0.714122 | − | 0.700021i | \(-0.246826\pi\) |
−0.249175 | + | 0.968458i | \(0.580159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2898i | 0.705267i | 0.935762 | + | 0.352633i | \(0.114714\pi\) | ||||
−0.935762 | + | 0.352633i | \(0.885286\pi\) | |||||||
\(602\) | −48.8692 | − | 25.2337i | −1.99176 | − | 1.02845i | ||||
\(603\) | 24.5697 | + | 3.99344i | 1.00055 | + | 0.162625i | ||||
\(604\) | 10.7406 | + | 18.6032i | 0.437027 | + | 0.756954i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 30.2399 | + | 20.8735i | 1.22841 | + | 0.847930i | ||||
\(607\) | 0.391428 | − | 0.225991i | 0.0158876 | − | 0.00917270i | −0.492035 | − | 0.870575i | \(-0.663747\pi\) |
0.507923 | + | 0.861403i | \(0.330414\pi\) | |||||||
\(608\) | 28.7342 | 1.16533 | ||||||||
\(609\) | −1.35913 | + | 40.4264i | −0.0550749 | + | 1.63816i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5326 | − | 7.81306i | 0.547471 | − | 0.316083i | ||||
\(612\) | 25.9127 | − | 31.7361i | 1.04746 | − | 1.28286i | ||||
\(613\) | −0.774834 | + | 1.34205i | −0.0312953 | + | 0.0542050i | −0.881249 | − | 0.472653i | \(-0.843297\pi\) |
0.849954 | + | 0.526858i | \(0.176630\pi\) | |||||||
\(614\) | −10.1256 | − | 17.5380i | −0.408636 | − | 0.707778i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0552 | + | 0.566476i | −0.485716 | + | 0.0228240i | ||||
\(617\) | − | 42.6618i | − | 1.71750i | −0.512394 | − | 0.858751i | \(-0.671241\pi\) | ||
0.512394 | − | 0.858751i | \(-0.328759\pi\) | |||||||
\(618\) | −10.5287 | − | 22.1894i | −0.423528 | − | 0.892589i | ||||
\(619\) | 21.8956 | + | 12.6414i | 0.880058 | + | 0.508102i | 0.870677 | − | 0.491854i | \(-0.163681\pi\) |
0.00938032 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.2055 | − | 4.11425i | 0.570049 | − | 0.165099i | ||||
\(622\) | − | 14.8460i | − | 0.595270i | ||||||
\(623\) | 13.1971 | − | 25.5584i | 0.528732 | − | 1.02398i | ||||
\(624\) | −0.522850 | + | 6.47589i | −0.0209307 | + | 0.259243i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.6988 | − | 37.5834i | 0.867258 | − | 1.50214i | ||||
\(627\) | 8.34463 | − | 12.0890i | 0.333252 | − | 0.482790i | ||||
\(628\) | −6.67010 | + | 3.85098i | −0.266166 | + | 0.153671i | ||||
\(629\) | 20.7055 | 0.825581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.91791 | 0.195779 | 0.0978895 | − | 0.995197i | \(-0.468791\pi\) | ||||
0.0978895 | + | 0.995197i | \(0.468791\pi\) | |||||||
\(632\) | 6.61441 | − | 3.81883i | 0.263107 | − | 0.151905i | ||||
\(633\) | 10.5256 | − | 15.2487i | 0.418355 | − | 0.606079i | ||||
\(634\) | 21.5877 | − | 37.3910i | 0.857357 | − | 1.48499i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.03432 | + | 12.8109i | −0.0410135 | + | 0.507983i | ||||
\(637\) | −32.3242 | − | 14.8123i | −1.28073 | − | 0.586885i | ||||
\(638\) | − | 37.8285i | − | 1.49765i | ||||||
\(639\) | −27.1653 | + | 10.3018i | −1.07464 | + | 0.407535i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0323 | − | 6.36950i | −0.435750 | − | 0.251580i | 0.266043 | − | 0.963961i | \(-0.414284\pi\) |
−0.701793 | + | 0.712381i | \(0.747617\pi\) | |||||||
\(642\) | 27.7487 | + | 58.4807i | 1.09516 | + | 2.30805i | ||||
\(643\) | − | 2.51652i | − | 0.0992419i | −0.998768 | − | 0.0496210i | \(-0.984199\pi\) | ||
0.998768 | − | 0.0496210i | \(-0.0158013\pi\) | |||||||
\(644\) | 19.4205 | − | 12.4631i | 0.765275 | − | 0.491116i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.3325 | + | 38.6811i | 0.878662 | + | 1.52189i | ||||
\(647\) | 20.2058 | − | 34.9974i | 0.794371 | − | 1.37589i | −0.128866 | − | 0.991662i | \(-0.541134\pi\) |
0.923238 | − | 0.384230i | \(-0.125533\pi\) | |||||||
\(648\) | 14.2943 | + | 16.1362i | 0.561534 | + | 0.633889i | ||||
\(649\) | −22.9571 | + | 13.2543i | −0.901143 | + | 0.520275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.6094 | − | 13.4641i | −0.846940 | − | 0.527698i | ||||
\(652\) | 10.6164 | 0.415770 | ||||||||
\(653\) | 36.9723 | − | 21.3460i | 1.44684 | − | 0.835332i | 0.448546 | − | 0.893760i | \(-0.351942\pi\) |
0.998292 | + | 0.0584277i | \(0.0186087\pi\) | |||||||
\(654\) | −59.0354 | − | 40.7500i | −2.30847 | − | 1.59345i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.0926106 | − | 0.160406i | −0.00361584 | − | 0.00626281i | ||||
\(657\) | −3.04035 | + | 18.7058i | −0.118616 | + | 0.729783i | ||||
\(658\) | 0.859751 | + | 18.2963i | 0.0335166 | + | 0.713265i | ||||
\(659\) | − | 2.08754i | − | 0.0813192i | −0.999173 | − | 0.0406596i | \(-0.987054\pi\) | ||
0.999173 | − | 0.0406596i | \(-0.0129459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5058 | + | 11.8391i | 0.797585 | + | 0.460486i | 0.842626 | − | 0.538499i | \(-0.181009\pi\) |
−0.0450412 | + | 0.998985i | \(0.514342\pi\) | |||||||
\(662\) | −23.3384 | − | 13.4744i | −0.907071 | − | 0.523698i | ||||
\(663\) | −35.4248 | + | 16.8088i | −1.37578 | + | 0.652801i | ||||
\(664\) | 21.5328i | 0.835633i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.03191 | + | 30.9589i | −0.194983 | + | 1.19963i | ||||
\(667\) | 12.5614 | + | 21.7570i | 0.486379 | + | 0.842433i | ||||
\(668\) | −5.05389 | + | 8.75359i | −0.195541 | + | 0.338687i | ||||
\(669\) | −24.1588 | − | 16.6759i | −0.934032 | − | 0.644729i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.33267 | −0.128656 | ||||||||
\(672\) | −25.0955 | − | 15.6361i | −0.968081 | − | 0.603177i | ||||
\(673\) | 29.6317 | 1.14222 | 0.571108 | − | 0.820875i | \(-0.306514\pi\) | ||||
0.571108 | + | 0.820875i | \(0.306514\pi\) | |||||||
\(674\) | −24.7496 | + | 14.2892i | −0.953320 | + | 0.550400i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.6136 | + | 33.9717i | −0.754368 | + | 1.30660i | ||||
\(677\) | −17.0667 | − | 29.5604i | −0.655927 | − | 1.13610i | −0.981661 | − | 0.190637i | \(-0.938945\pi\) |
0.325734 | − | 0.945462i | \(-0.394389\pi\) | |||||||
\(678\) | 17.0046 | + | 1.37291i | 0.653057 | + | 0.0527265i | ||||
\(679\) | 19.9172 | − | 12.7819i | 0.764354 | − | 0.490525i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.80534 | + | 3.80478i | 0.0691809 | + | 0.145799i | ||||
\(682\) | 20.6210 | + | 11.9056i | 0.789620 | + | 0.455887i | ||||
\(683\) | 17.0344 | + | 9.83481i | 0.651803 | + | 0.376319i | 0.789147 | − | 0.614205i | \(-0.210523\pi\) |
−0.137344 | + | 0.990523i | \(0.543857\pi\) | |||||||
\(684\) | −38.2796 | + | 14.5167i | −1.46366 | + | 0.555060i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32.8110 | − | 25.7004i | 1.25273 | − | 0.981246i | ||||
\(687\) | 0.0328473 | − | 0.406838i | 0.00125320 | − | 0.0155219i | ||||
\(688\) | 3.41073 | + | 5.90756i | 0.130033 | + | 0.225224i | ||||
\(689\) | 6.15006 | − | 10.6522i | 0.234299 | − | 0.405817i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.800772 | + | 0.462326i | −0.0304628 | + | 0.0175877i | −0.515154 | − | 0.857098i | \(-0.672265\pi\) |
0.484691 | + | 0.874685i | \(0.338932\pi\) | |||||||
\(692\) | −53.4433 | −2.03161 | ||||||||
\(693\) | −13.8663 | + | 6.01732i | −0.526738 | + | 0.228579i | ||||
\(694\) | 12.6242 | 0.479206 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20.8023 | + | 30.1367i | −0.788508 | + | 1.14233i | ||||
\(697\) | 0.558922 | − | 0.968081i | 0.0211707 | − | 0.0366687i | ||||
\(698\) | −38.1135 | − | 66.0145i | −1.44262 | − | 2.49869i | ||||
\(699\) | 1.54462 | − | 19.1312i | 0.0584228 | − | 0.723610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.206478i | − | 0.00779858i | −0.999992 | − | 0.00389929i | \(-0.998759\pi\) | ||
0.999992 | − | 0.00389929i | \(-0.00124119\pi\) | |||||||
\(702\) | −16.5236 | − | 57.0522i | −0.623643 | − | 2.15330i | ||||
\(703\) | −17.9176 | − | 10.3447i | −0.675776 | − | 0.390160i | ||||
\(704\) | 21.5118 | + | 12.4199i | 0.810758 | + | 0.468091i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 82.6826i | − | 3.11180i | ||||||
\(707\) | 24.9138 | − | 1.17071i | 0.936980 | − | 0.0440291i | ||||
\(708\) | 73.6405 | + | 5.94558i | 2.76758 | + | 0.223449i | ||||
\(709\) | −20.5452 | − | 35.5852i | −0.771589 | − | 1.33643i | −0.936692 | − | 0.350156i | \(-0.886129\pi\) |
0.165102 | − | 0.986276i | \(-0.447205\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.05020 | − | 7.40986i | 0.226900 | − | 0.277891i | ||||
\(712\) | 22.5520 | − | 13.0204i | 0.845171 | − | 0.487960i | ||||
\(713\) | −15.8135 | −0.592220 | ||||||||
\(714\) | 1.54434 | − | 45.9353i | 0.0577956 | − | 1.71909i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −59.8611 | + | 34.5608i | −2.23712 | + | 1.29160i | ||||
\(717\) | 13.7927 | + | 9.52061i | 0.515098 | + | 0.355554i | ||||
\(718\) | −27.4651 | + | 47.5709i | −1.02499 | + | 1.77533i | ||||
\(719\) | 4.36496 | + | 7.56034i | 0.162786 | + | 0.281953i | 0.935867 | − | 0.352354i | \(-0.114619\pi\) |
−0.773081 | + | 0.634307i | \(0.781285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.8130 | − | 7.64871i | −0.551665 | − | 0.284853i | ||||
\(722\) | − | 1.87281i | − | 0.0696988i | ||||||
\(723\) | −25.1594 | + | 11.9380i | −0.935687 | + | 0.443978i | ||||
\(724\) | −9.24065 | − | 5.33509i | −0.343426 | − | 0.198277i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −25.9651 | + | 12.3203i | −0.963654 | + | 0.457248i | ||||
\(727\) | − | 26.6400i | − | 0.988024i | −0.869455 | − | 0.494012i | \(-0.835530\pi\) | ||
0.869455 | − | 0.494012i | \(-0.164470\pi\) | |||||||
\(728\) | −17.3855 | − | 27.0907i | −0.644350 | − | 1.00405i | ||||
\(729\) | 23.9066 | + | 12.5489i | 0.885430 | + | 0.464774i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.5844 | + | 35.6532i | −0.761341 | + | 1.31868i | ||||
\(732\) | 7.64404 | + | 5.27640i | 0.282532 | + | 0.195022i | ||||
\(733\) | −27.1888 | + | 15.6975i | −1.00424 | + | 0.579800i | −0.909501 | − | 0.415702i | \(-0.863536\pi\) |
−0.0947418 | + | 0.995502i | \(0.530203\pi\) | |||||||
\(734\) | −46.5056 | −1.71655 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.3646 | −0.676927 | ||||||||
\(737\) | −13.6845 | + | 7.90073i | −0.504074 | + | 0.291027i | ||||
\(738\) | 1.31165 | + | 1.07097i | 0.0482824 | + | 0.0394229i | ||||
\(739\) | −6.49377 | + | 11.2475i | −0.238877 | + | 0.413747i | −0.960392 | − | 0.278651i | \(-0.910113\pi\) |
0.721515 | + | 0.692399i | \(0.243446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.0530 | + | 3.15306i | 1.43465 | + | 0.115831i | ||||
\(742\) | 7.78708 | + | 12.1341i | 0.285873 | + | 0.445457i | ||||
\(743\) | − | 20.9456i | − | 0.768419i | −0.923246 | − | 0.384209i | \(-0.874474\pi\) | ||
0.923246 | − | 0.384209i | \(-0.125526\pi\) | |||||||
\(744\) | −9.88108 | − | 20.8244i | −0.362258 | − | 0.763461i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 40.6783 | + | 23.4856i | 1.48934 | + | 0.859869i | ||||
\(747\) | 9.56309 | + | 25.2172i | 0.349895 | + | 0.922651i | ||||
\(748\) | 26.0085i | 0.950966i | ||||||||
\(749\) | 39.0400 | + | 20.1583i | 1.42649 | + | 0.736570i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.17046 | − | 3.75935i | −0.0792014 | − | 0.137181i | 0.823704 | − | 0.567020i | \(-0.191904\pi\) |
−0.902906 | + | 0.429839i | \(0.858570\pi\) | |||||||
\(752\) | 1.13588 | − | 1.96740i | 0.0414212 | − | 0.0717437i | ||||
\(753\) | 14.1498 | − | 20.4992i | 0.515649 | − | 0.747031i | ||||
\(754\) | 87.3801 | − | 50.4489i | 3.18220 | − | 1.83724i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 41.3316 | + | 8.15195i | 1.50321 | + | 0.296484i | ||||
\(757\) | 0.401257 | 0.0145839 | 0.00729196 | − | 0.999973i | \(-0.497679\pi\) | ||||
0.00729196 | + | 0.999973i | \(0.497679\pi\) | |||||||
\(758\) | −52.6955 | + | 30.4238i | −1.91399 | + | 1.10504i | ||||
\(759\) | −5.33320 | + | 7.72632i | −0.193583 | + | 0.280448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.1371 | − | 36.6105i | −0.766219 | − | 1.32713i | −0.939600 | − | 0.342275i | \(-0.888803\pi\) |
0.173381 | − | 0.984855i | \(-0.444531\pi\) | |||||||
\(762\) | 4.01028 | − | 49.6703i | 0.145277 | − | 1.79937i | ||||
\(763\) | −48.6375 | + | 2.28550i | −1.76080 | + | 0.0827406i | ||||
\(764\) | − | 29.2909i | − | 1.05971i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.3453 | + | 7.12757i | 0.446054 | + | 0.257530i | ||||
\(767\) | −61.2320 | − | 35.3523i | −2.21096 | − | 1.27650i | ||||
\(768\) | −8.11469 | − | 17.1018i | −0.292814 | − | 0.617107i | ||||
\(769\) | − | 0.306962i | − | 0.0110693i | −0.999985 | − | 0.00553466i | \(-0.998238\pi\) | ||
0.999985 | − | 0.00553466i | \(-0.00176175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.21730 | + | 0.663448i | 0.295939 | + | 0.0238935i | ||||
\(772\) | −8.84096 | − | 15.3130i | −0.318193 | − | 0.551126i | ||||
\(773\) | −1.06021 | + | 1.83633i | −0.0381330 | + | 0.0660483i | −0.884462 | − | 0.466612i | \(-0.845474\pi\) |
0.846329 | + | 0.532661i | \(0.178808\pi\) | |||||||
\(774\) | −48.3063 | − | 39.4424i | −1.73633 | − | 1.41773i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 21.4249 | 0.769110 | ||||||||
\(777\) | 10.0194 | + | 18.7849i | 0.359445 | + | 0.673904i | ||||
\(778\) | −28.0304 | −1.00494 | ||||||||
\(779\) | −0.967334 | + | 0.558491i | −0.0346583 | + | 0.0200100i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.22142 | − | 15.9720i | 0.329968 | − | 0.571522i | ||||
\(782\) | −14.2731 | − | 24.7218i | −0.510406 | − | 0.884049i | ||||
\(783\) | −10.9775 | + | 44.5321i | −0.392304 | + | 1.59145i | ||||
\(784\) | −5.14648 | + | 0.484741i | −0.183803 | + | 0.0173122i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.2849 | + | 8.67606i | −0.652199 | + | 0.309465i | ||||
\(787\) | 17.7119 | + | 10.2260i | 0.631360 | + | 0.364516i | 0.781279 | − | 0.624183i | \(-0.214568\pi\) |
−0.149919 | + | 0.988698i | \(0.547901\pi\) | |||||||
\(788\) | −11.5308 | − | 6.65730i | −0.410767 | − | 0.237156i | ||||
\(789\) | 8.84032 | − | 4.19468i | 0.314724 | − | 0.149335i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.74563 | − | 6.25427i | 0.346515 | − | 0.222376i | ||||
\(792\) | −13.5071 | − | 2.19538i | −0.479954 | − | 0.0780094i | ||||
\(793\) | −4.44452 | − | 7.69814i | −0.157830 | − | 0.273369i | ||||
\(794\) | 32.0416 | − | 55.4977i | 1.13711 | − | 1.96954i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.0849 | − | 13.3281i | 0.818223 | − | 0.472401i | ||||
\(797\) | −21.2684 | −0.753365 | −0.376682 | − | 0.926342i | \(-0.622935\pi\) | ||||
−0.376682 | + | 0.926342i | \(0.622935\pi\) | |||||||
\(798\) | −24.2864 | + | 38.9789i | −0.859728 | + | 1.37984i | ||||
\(799\) | 13.7105 | 0.485042 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.6283 | − | 25.2641i | 0.728864 | − | 0.892662i | ||||
\(802\) | 16.5677 | − | 28.6961i | 0.585025 | − | 1.01329i | ||||
\(803\) | −6.01512 | − | 10.4185i | −0.212269 | − | 0.367661i | ||||
\(804\) | 43.8963 | + | 3.54410i | 1.54810 | + | 0.124991i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 63.5100i | 2.23704i | ||||||||
\(807\) | −0.528726 | − | 1.11429i | −0.0186121 | − | 0.0392250i | ||||
\(808\) | 19.5545 | + | 11.2898i | 0.687924 | + | 0.397173i | ||||
\(809\) | −19.3311 | − | 11.1608i | −0.679646 | − | 0.392394i | 0.120075 | − | 0.992765i | \(-0.461686\pi\) |
−0.799722 | + | 0.600371i | \(0.795020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.7633i | − | 1.39628i | −0.715962 | − | 0.698139i | \(-0.754012\pi\) | ||
0.715962 | − | 0.698139i | \(-0.245988\pi\) | |||||||
\(812\) | 3.35906 | + | 71.4840i | 0.117880 | + | 2.50860i | ||||
\(813\) | 0.450786 | − | 5.58332i | 0.0158097 | − | 0.195816i | ||||
\(814\) | −9.95527 | − | 17.2430i | −0.348932 | − | 0.604368i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.23829 | + | 4.69137i | −0.113363 | + | 0.164231i | ||||
\(817\) | 35.6257 | − | 20.5685i | 1.24639 | − | 0.719601i | ||||
\(818\) | −2.10641 | −0.0736488 | ||||||||
\(819\) | −32.3918 | − | 24.0050i | −1.13186 | − | 0.838803i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.1580 | + | 19.7211i | −1.19212 | + | 0.688272i | −0.958787 | − | 0.284125i | \(-0.908297\pi\) |
−0.233335 | + | 0.972397i | \(0.574964\pi\) | |||||||
\(822\) | −29.8556 | + | 43.2524i | −1.04133 | + | 1.50860i | ||||
\(823\) | 23.8993 | − | 41.3948i | 0.833077 | − | 1.44293i | −0.0625104 | − | 0.998044i | \(-0.519911\pi\) |
0.895587 | − | 0.444887i | \(-0.146756\pi\) | |||||||
\(824\) | −7.54628 | − | 13.0705i | −0.262887 | − | 0.455334i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 69.7503 | − | 44.7623i | 2.42692 | − | 1.55748i | ||||
\(827\) | 40.7367i | 1.41655i | 0.705935 | + | 0.708277i | \(0.250527\pi\) | ||||
−0.705935 | + | 0.708277i | \(0.749473\pi\) | |||||||
\(828\) | 24.4652 | − | 9.27789i | 0.850224 | − | 0.322429i | ||||
\(829\) | −18.8083 | − | 10.8590i | −0.653238 | − | 0.377147i | 0.136458 | − | 0.990646i | \(-0.456428\pi\) |
−0.789696 | + | 0.613499i | \(0.789762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.0132 | + | 35.8555i | 0.590182 | + | 1.24381i | ||||
\(832\) | 66.2536i | 2.29693i | ||||||||
\(833\) | −18.0635 | − | 25.4360i | −0.625864 | − | 0.881303i | ||||
\(834\) | 7.85536 | + | 0.634225i | 0.272009 | + | 0.0219614i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.9942 | − | 22.5067i | 0.449415 | − | 0.778410i | ||||
\(837\) | −20.8204 | − | 19.9994i | −0.719657 | − | 0.691279i | ||||
\(838\) | 58.7626 | − | 33.9266i | 2.02992 | − | 1.17197i | ||||
\(839\) | 9.40638 | 0.324744 | 0.162372 | − | 0.986730i | \(-0.448085\pi\) | ||||
0.162372 | + | 0.986730i | \(0.448085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −48.9115 | −1.68660 | ||||||||
\(842\) | 70.8790 | − | 40.9220i | 2.44265 | − | 1.41026i | ||||
\(843\) | 17.1540 | + | 11.8408i | 0.590816 | + | 0.407819i | ||||
\(844\) | 16.3904 | − | 28.3891i | 0.564182 | − | 0.977192i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.33197 | + | 20.4999i | −0.114555 | + | 0.704803i | ||||
\(847\) | −8.95019 | + | 17.3335i | −0.307532 | + | 0.595587i | ||||
\(848\) | − | 1.78822i | − | 0.0614077i | ||||||
\(849\) | −28.0125 | + | 13.2918i | −0.961385 | + | 0.456172i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4515 | + | 6.61152i | 0.392552 | + | 0.226640i | ||||
\(852\) | −46.4382 | + | 22.0347i | −1.59095 | + | 0.754896i | ||||
\(853\) | 28.2296i | 0.966562i | 0.875465 | + | 0.483281i | \(0.160555\pi\) | ||||
−0.875465 | + | 0.483281i | \(0.839445\pi\) | |||||||
\(854\) | 10.4080 | − | 0.489076i | 0.356154 | − | 0.0167358i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.8884 | + | 34.4477i | 0.679771 | + | 1.17740i | ||||
\(857\) | 8.37845 | − | 14.5119i | 0.286202 | − | 0.495717i | −0.686698 | − | 0.726943i | \(-0.740940\pi\) |
0.972900 | + | 0.231226i | \(0.0742737\pi\) | |||||||
\(858\) | 31.0304 | + | 21.4192i | 1.05936 | + | 0.731238i | ||||
\(859\) | 8.38608 | − | 4.84171i | 0.286129 | − | 0.165197i | −0.350066 | − | 0.936725i | \(-0.613841\pi\) |
0.636195 | + | 0.771528i | \(0.280507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.14875 | + | 0.0386209i | 0.0391492 | + | 0.00131620i | ||||
\(862\) | 31.0135 | 1.05632 | ||||||||
\(863\) | 19.0593 | − | 11.0039i | 0.648785 | − | 0.374576i | −0.139206 | − | 0.990263i | \(-0.544455\pi\) |
0.787990 | + | 0.615687i | \(0.211122\pi\) | |||||||
\(864\) | −24.1792 | − | 23.2257i | −0.822592 | − | 0.790155i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.31469 | + | 2.27712i | 0.0446751 | + | 0.0773796i | ||||
\(867\) | −4.94248 | − | 0.399046i | −0.167855 | − | 0.0135523i | ||||
\(868\) | −40.0244 | − | 20.6667i | −1.35852 | − | 0.701472i | ||||
\(869\) | 6.07256i | 0.205998i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.4998 | − | 21.0732i | −1.23675 | − | 0.714036i | ||||
\(872\) | −38.1749 | − | 22.0403i | −1.29276 | − | 0.746378i | ||||
\(873\) | 25.0910 | − | 9.51520i | 0.849200 | − | 0.322041i | ||||
\(874\) | 28.5242i | 0.964847i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.69825 | + | 33.4199i | −0.0911655 | + | 1.12915i | ||||
\(877\) | −10.5609 | − | 18.2921i | −0.356617 | − | 0.617679i | 0.630776 | − | 0.775965i | \(-0.282737\pi\) |
−0.987393 | + | 0.158286i | \(0.949403\pi\) | |||||||
\(878\) | 3.25277 | − | 5.63397i | 0.109776 | − | 0.190137i | ||||
\(879\) | −8.73059 | + | 12.6482i | −0.294475 | + | 0.426613i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.3021 | −1.49258 | −0.746288 | − | 0.665623i | \(-0.768166\pi\) | ||||
−0.746288 | + | 0.665623i | \(0.768166\pi\) | |||||||
\(882\) | 42.4218 | − | 20.8271i | 1.42842 | − | 0.701286i | ||||
\(883\) | −5.12282 | −0.172397 | −0.0861984 | − | 0.996278i | \(-0.527472\pi\) | ||||
−0.0861984 | + | 0.996278i | \(0.527472\pi\) | |||||||
\(884\) | −60.0771 | + | 34.6855i | −2.02061 | + | 1.16660i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.5729 | − | 32.1693i | 0.623970 | − | 1.08075i | ||||
\(887\) | −3.87397 | − | 6.70992i | −0.130075 | − | 0.225297i | 0.793630 | − | 0.608401i | \(-0.208189\pi\) |
−0.923705 | + | 0.383104i | \(0.874855\pi\) | |||||||
\(888\) | −1.55109 | + | 19.2114i | −0.0520512 | + | 0.644693i | ||||
\(889\) | −18.2687 | − | 28.4670i | −0.612713 | − | 0.954751i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.7933 | + | 3.42771i | −0.562597 | + | 0.114833i | ||||
\(892\) | −44.9774 | − | 25.9677i | −1.50596 | − | 0.869464i | ||||
\(893\) | −11.8645 | − | 6.84995i | −0.397029 | − | 0.229225i | ||||
\(894\) | −2.14262 | − | 4.51558i | −0.0716598 | − | 0.151024i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −38.6678 | − | 19.9661i | −1.29180 | − | 0.667022i | ||||
\(897\) | −24.9595 | − | 2.01518i | −0.833374 | − | 0.0672848i | ||||
\(898\) | −29.2355 | − | 50.6374i | −0.975601 | − | 1.68979i | ||||
\(899\) | 24.5206 | − | 42.4710i | 0.817809 | − | 1.41649i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.34634 | − | 5.39611i | 0.311372 | − | 0.179770i | ||||
\(902\) | −1.07493 | −0.0357912 | ||||||||
\(903\) | −42.3069 | − | 1.42236i | −1.40789 | − | 0.0473331i | ||||
\(904\) | 10.4833 | 0.348671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.4869 | + | 15.5219i | 0.747078 | + | 0.515681i | ||||
\(907\) | −12.2639 | + | 21.2416i | −0.407215 | + | 0.705316i | −0.994576 | − | 0.104008i | \(-0.966833\pi\) |
0.587362 | + | 0.809324i | \(0.300167\pi\) | |||||||
\(908\) | 3.72538 | + | 6.45254i | 0.123631 | + | 0.214135i | ||||
\(909\) | 27.9145 | + | 4.53708i | 0.925864 | + | 0.150486i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 43.8824i | − | 1.45389i | −0.686697 | − | 0.726944i | \(-0.740940\pi\) | ||
0.686697 | − | 0.726944i | \(-0.259060\pi\) | |||||||
\(912\) | 5.14615 | − | 2.44182i | 0.170406 | − | 0.0808567i | ||||
\(913\) | −14.8266 | − | 8.56014i | −0.490689 | − | 0.283299i | ||||
\(914\) | −2.92708 | − | 1.68995i | −0.0968193 | − | 0.0558986i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 0.722122i | − | 0.0238596i | ||||||
\(917\) | −6.30281 | + | 12.2064i | −0.208137 | + | 0.403092i | ||||
\(918\) | 12.4734 | − | 50.6004i | 0.411684 | − | 1.67006i | ||||
\(919\) | 7.85902 | + | 13.6122i | 0.259245 | + | 0.449026i | 0.966040 | − | 0.258393i | \(-0.0831929\pi\) |
−0.706795 | + | 0.707419i | \(0.749860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.8274 | − | 8.85428i | −0.422676 | − | 0.291758i | ||||
\(922\) | 2.73760 | − | 1.58056i | 0.0901581 | − | 0.0520528i | ||||
\(923\) | 49.1915 | 1.61916 | ||||||||
\(924\) | −23.5960 | + | 12.5856i | −0.776253 | + | 0.414036i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39.3789 | + | 22.7354i | −1.29407 | + | 0.747132i | ||||
\(927\) | −14.6424 | − | 11.9556i | −0.480919 | − | 0.392674i | ||||
\(928\) | 28.4764 | − | 49.3225i | 0.934783 | − | 1.61909i | ||||
\(929\) | 9.87128 | + | 17.0976i | 0.323866 | + | 0.560952i | 0.981282 | − | 0.192575i | \(-0.0616839\pi\) |
−0.657416 | + | 0.753528i | \(0.728351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.92324 | + | 31.0360i | 0.0958054 | + | 1.01716i | ||||
\(932\) | − | 33.9572i | − | 1.11230i | ||||||
\(933\) | −4.89830 | − | 10.3232i | −0.160363 | − | 0.337967i | ||||
\(934\) | 75.3434 | + | 43.4995i | 2.46531 | + | 1.42335i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.9422 | − | 34.1278i | −0.423030 | − | 1.11550i | ||||
\(937\) | 37.1538i | 1.21376i | 0.794793 | + | 0.606881i | \(0.207580\pi\) | ||||
−0.794793 | + | 0.606881i | \(0.792420\pi\) | |||||||
\(938\) | 41.5774 | − | 26.6824i | 1.35755 | − | 0.871210i | ||||
\(939\) | 2.68801 | − | 33.2930i | 0.0877199 | − | 1.08648i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.1049 | − | 27.8945i | 0.525005 | − | 0.909336i | −0.474571 | − | 0.880217i | \(-0.657397\pi\) |
0.999576 | − | 0.0291183i | \(-0.00926996\pi\) | |||||||
\(942\) | −5.56532 | + | 8.06259i | −0.181328 | + | 0.262693i | ||||
\(943\) | 0.618241 | − | 0.356942i | 0.0201327 | − | 0.0116236i | ||||
\(944\) | −10.2792 | −0.334559 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.5882 | 1.28712 | ||||||||
\(947\) | −24.5694 | + | 14.1852i | −0.798400 | + | 0.460956i | −0.842911 | − | 0.538053i | \(-0.819160\pi\) |
0.0445115 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(948\) | 9.61430 | − | 13.9284i | 0.312258 | − | 0.452375i | ||||
\(949\) | 16.0438 | − | 27.7886i | 0.520803 | − | 0.902057i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.67425 | − | 33.1226i | 0.0867185 | − | 1.07407i | ||||
\(952\) | −1.32570 | − | 28.2122i | −0.0429662 | − | 0.914361i | ||||
\(953\) | 28.4105i | 0.920305i | 0.887840 | + | 0.460153i | \(0.152205\pi\) | ||||
−0.887840 | + | 0.460153i | \(0.847795\pi\) | |||||||
\(954\) | 5.79691 | + | 15.2861i | 0.187682 | + | 0.494904i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.6785 | + | 14.8255i | 0.830501 | + | 0.479490i | ||||
\(957\) | −12.4812 | − | 26.3042i | −0.403459 | − | 0.850293i | ||||
\(958\) | 69.0729i | 2.23164i | ||||||||
\(959\) | 1.67447 | + | 35.6344i | 0.0540716 | + | 1.15069i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0655266 | − | 0.113495i | −0.00211376 | − | 0.00366114i | ||||
\(962\) | 26.5531 | − | 45.9913i | 0.856107 | − | 1.48282i | ||||
\(963\) | 38.5903 | + | 31.5092i | 1.24356 | + | 1.01537i | ||||
\(964\) | −42.6680 | + | 24.6344i | −1.37424 | + | 0.793419i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.5219 | − | 24.9121i | 0.499407 | − | 0.801535i | ||||
\(967\) | 42.3117 | 1.36065 | 0.680326 | − | 0.732909i | \(-0.261838\pi\) | ||||
0.680326 | + | 0.732909i | \(0.261838\pi\) | |||||||
\(968\) | −15.2946 | + | 8.83032i | −0.491586 | + | 0.283817i | ||||
\(969\) | 28.2914 | + | 19.5286i | 0.908852 | + | 0.627348i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7297 | + | 20.3164i | 0.376424 | + | 0.651985i | 0.990539 | − | 0.137231i | \(-0.0438203\pi\) |
−0.614115 | + | 0.789216i | \(0.710487\pi\) | |||||||
\(972\) | 43.9451 | + | 18.7257i | 1.40954 | + | 0.600628i | ||||
\(973\) | 4.50205 | − | 2.88919i | 0.144329 | − | 0.0926233i | ||||
\(974\) | 66.8370i | 2.14159i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.11917 | − | 0.646154i | −0.0358238 | − | 0.0206829i | ||||
\(977\) | 30.4577 | + | 17.5848i | 0.974429 | + | 0.562587i | 0.900584 | − | 0.434683i | \(-0.143139\pi\) |
0.0738456 | + | 0.997270i | \(0.476473\pi\) | |||||||
\(978\) | 12.2002 | − | 5.78893i | 0.390120 | − | 0.185110i | ||||
\(979\) | 20.7045i | 0.661720i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −54.4955 | − | 8.85745i | −1.73991 | − | 0.282796i | ||||
\(982\) | 8.03020 | + | 13.9087i | 0.256254 | + | 0.443845i | ||||
\(983\) | −20.8391 | + | 36.0944i | −0.664665 | + | 1.15123i | 0.314711 | + | 0.949187i | \(0.398092\pi\) |
−0.979376 | + | 0.202046i | \(0.935241\pi\) | |||||||
\(984\) | 0.856358 | + | 0.591113i | 0.0272997 | + | 0.0188440i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 88.5285 | 2.81932 | ||||||||
\(987\) | 6.63453 | + | 12.4387i | 0.211179 | + | 0.395929i | ||||
\(988\) | 69.3175 | 2.20528 | ||||||||
\(989\) | −22.7690 | + | 13.1457i | −0.724013 | + | 0.418009i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.1571 | + | 38.3773i | −0.703844 | + | 1.21909i | 0.263262 | + | 0.964724i | \(0.415201\pi\) |
−0.967107 | + | 0.254370i | \(0.918132\pi\) | |||||||
\(992\) | 17.9244 | + | 31.0460i | 0.569101 | + | 0.985711i | ||||
\(993\) | −20.6741 | − | 1.66919i | −0.656074 | − | 0.0529700i | ||||
\(994\) | −26.4548 | + | 51.2340i | −0.839094 | + | 1.62505i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 20.4546 | + | 43.1081i | 0.648127 | + | 1.36593i | ||||
\(997\) | 38.6961 | + | 22.3412i | 1.22552 | + | 0.707552i | 0.966089 | − | 0.258210i | \(-0.0831327\pi\) |
0.259428 | + | 0.965763i | \(0.416466\pi\) | |||||||
\(998\) | 26.0016 | + | 15.0120i | 0.823065 | + | 0.475197i | ||||
\(999\) | 6.71565 | + | 23.1876i | 0.212474 | + | 0.733622i |
(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 | 525.2.t.h.101.9 | yes | 20 | |
3.2 | odd | 2 | inner | 525.2.t.h.101.2 | yes | 20 | |
5.2 | odd | 4 | 525.2.q.g.374.18 | 40 | |||
5.3 | odd | 4 | 525.2.q.g.374.3 | 40 | |||
5.4 | even | 2 | 525.2.t.i.101.2 | yes | 20 | ||
7.5 | odd | 6 | inner | 525.2.t.h.26.2 | ✓ | 20 | |
15.2 | even | 4 | 525.2.q.g.374.4 | 40 | |||
15.8 | even | 4 | 525.2.q.g.374.17 | 40 | |||
15.14 | odd | 2 | 525.2.t.i.101.9 | yes | 20 | ||
21.5 | even | 6 | inner | 525.2.t.h.26.9 | yes | 20 | |
35.12 | even | 12 | 525.2.q.g.299.17 | 40 | |||
35.19 | odd | 6 | 525.2.t.i.26.9 | yes | 20 | ||
35.33 | even | 12 | 525.2.q.g.299.4 | 40 | |||
105.47 | odd | 12 | 525.2.q.g.299.3 | 40 | |||
105.68 | odd | 12 | 525.2.q.g.299.18 | 40 | |||
105.89 | even | 6 | 525.2.t.i.26.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.q.g.299.3 | 40 | 105.47 | odd | 12 | |||
525.2.q.g.299.4 | 40 | 35.33 | even | 12 | |||
525.2.q.g.299.17 | 40 | 35.12 | even | 12 | |||
525.2.q.g.299.18 | 40 | 105.68 | odd | 12 | |||
525.2.q.g.374.3 | 40 | 5.3 | odd | 4 | |||
525.2.q.g.374.4 | 40 | 15.2 | even | 4 | |||
525.2.q.g.374.17 | 40 | 15.8 | even | 4 | |||
525.2.q.g.374.18 | 40 | 5.2 | odd | 4 | |||
525.2.t.h.26.2 | ✓ | 20 | 7.5 | odd | 6 | inner | |
525.2.t.h.26.9 | yes | 20 | 21.5 | even | 6 | inner | |
525.2.t.h.101.2 | yes | 20 | 3.2 | odd | 2 | inner | |
525.2.t.h.101.9 | yes | 20 | 1.1 | even | 1 | trivial | |
525.2.t.i.26.2 | yes | 20 | 105.89 | even | 6 | ||
525.2.t.i.26.9 | yes | 20 | 35.19 | odd | 6 | ||
525.2.t.i.101.2 | yes | 20 | 5.4 | even | 2 | ||
525.2.t.i.101.9 | yes | 20 | 15.14 | odd | 2 |