Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(64,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.f (of order \(3\), degree \(2\), not 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: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + 599392 x^{8} - 1089732 x^{7} + 4808401 x^{6} - 7939134 x^{5} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{14} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(-2.47591 - 4.28840i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.64 |
Dual form | 189.4.f.b.127.1 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47591 | − | 4.28840i | −0.875365 | − | 1.51618i | −0.856373 | − | 0.516357i | \(-0.827288\pi\) |
−0.0189918 | − | 0.999820i | \(-0.506046\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.26023 | + | 14.3071i | −1.03253 | + | 1.78839i | ||||
\(5\) | 8.06998 | − | 13.9776i | 0.721801 | − | 1.25020i | −0.238476 | − | 0.971148i | \(-0.576648\pi\) |
0.960277 | − | 0.279048i | \(-0.0900187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50000 | + | 6.06218i | 0.188982 | + | 0.327327i | ||||
\(8\) | 42.1917 | 1.86463 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −79.9221 | −2.52736 | ||||||||
\(11\) | −15.3185 | − | 26.5325i | −0.419883 | − | 0.727259i | 0.576044 | − | 0.817419i | \(-0.304596\pi\) |
−0.995927 | + | 0.0901595i | \(0.971262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39.0059 | − | 67.5603i | 0.832177 | − | 1.44137i | −0.0641315 | − | 0.997941i | \(-0.520428\pi\) |
0.896308 | − | 0.443431i | \(-0.146239\pi\) | |||||||
\(14\) | 17.3313 | − | 30.0188i | 0.330857 | − | 0.573061i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −38.3809 | − | 66.4776i | −0.599701 | − | 1.03871i | ||||
\(17\) | −106.992 | −1.52643 | −0.763214 | − | 0.646146i | \(-0.776380\pi\) | ||||
−0.763214 | + | 0.646146i | \(0.776380\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −49.5081 | −0.597787 | −0.298893 | − | 0.954287i | \(-0.596617\pi\) | ||||
−0.298893 | + | 0.954287i | \(0.596617\pi\) | |||||||
\(20\) | 133.320 | + | 230.917i | 1.49056 | + | 2.58173i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −75.8546 | + | 131.384i | −0.735102 | + | 1.27323i | ||||
\(23\) | 19.5071 | − | 33.7873i | 0.176848 | − | 0.306310i | −0.763951 | − | 0.645274i | \(-0.776743\pi\) |
0.940799 | + | 0.338964i | \(0.110076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67.7492 | − | 117.345i | −0.541993 | − | 0.938760i | ||||
\(26\) | −386.300 | −2.91383 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −115.643 | −0.780518 | ||||||||
\(29\) | 2.87388 | + | 4.97771i | 0.0184023 | + | 0.0318737i | 0.875080 | − | 0.483978i | \(-0.160809\pi\) |
−0.856678 | + | 0.515852i | \(0.827475\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −92.2467 | + | 159.776i | −0.534451 | + | 0.925697i | 0.464738 | + | 0.885448i | \(0.346148\pi\) |
−0.999190 | + | 0.0402489i | \(0.987185\pi\) | |||||||
\(32\) | −21.2881 | + | 36.8720i | −0.117601 | + | 0.203691i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 264.901 | + | 458.822i | 1.33618 | + | 2.31434i | ||||
\(35\) | 112.980 | 0.545630 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 91.0901 | 0.404733 | 0.202366 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202366 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(38\) | 122.578 | + | 212.310i | 0.523282 | + | 0.906350i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 340.486 | − | 589.739i | 1.34589 | − | 2.33115i | ||||
\(41\) | −41.4346 | + | 71.7668i | −0.157829 | + | 0.273368i | −0.934086 | − | 0.357049i | \(-0.883783\pi\) |
0.776256 | + | 0.630417i | \(0.217116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45.6371 | + | 79.0458i | 0.161851 | + | 0.280334i | 0.935533 | − | 0.353241i | \(-0.114920\pi\) |
−0.773682 | + | 0.633575i | \(0.781587\pi\) | |||||||
\(44\) | 506.139 | 1.73417 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −193.191 | −0.619227 | ||||||||
\(47\) | 118.982 | + | 206.083i | 0.369262 | + | 0.639580i | 0.989450 | − | 0.144872i | \(-0.0462772\pi\) |
−0.620188 | + | 0.784453i | \(0.712944\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | + | 42.4352i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −335.481 | + | 581.070i | −0.948884 | + | 1.64352i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 644.396 | + | 1116.13i | 1.71849 | + | 2.97652i | ||||
\(53\) | −497.669 | −1.28981 | −0.644906 | − | 0.764262i | \(-0.723104\pi\) | ||||
−0.644906 | + | 0.764262i | \(0.723104\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −494.481 | −1.21229 | ||||||||
\(56\) | 147.671 | + | 255.773i | 0.352381 | + | 0.610342i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.2309 | − | 24.6487i | 0.0322174 | − | 0.0558022i | ||||
\(59\) | −2.10297 | + | 3.64245i | −0.00464039 | + | 0.00803740i | −0.868336 | − | 0.495976i | \(-0.834810\pi\) |
0.863696 | + | 0.504013i | \(0.168144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −313.196 | − | 542.471i | −0.657387 | − | 1.13863i | −0.981290 | − | 0.192537i | \(-0.938328\pi\) |
0.323903 | − | 0.946090i | \(-0.395005\pi\) | |||||||
\(62\) | 913.577 | 1.87136 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −403.264 | −0.787626 | ||||||||
\(65\) | −629.554 | − | 1090.42i | −1.20133 | − | 2.08077i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 339.310 | − | 587.702i | 0.618706 | − | 1.07163i | −0.371016 | − | 0.928627i | \(-0.620990\pi\) |
0.989722 | − | 0.143004i | \(-0.0456763\pi\) | |||||||
\(68\) | 883.775 | − | 1530.74i | 1.57608 | − | 2.72985i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −279.727 | − | 484.502i | −0.477626 | − | 0.827272i | ||||
\(71\) | −747.071 | −1.24875 | −0.624374 | − | 0.781126i | \(-0.714646\pi\) | ||||
−0.624374 | + | 0.781126i | \(0.714646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −23.2628 | −0.0372974 | −0.0186487 | − | 0.999826i | \(-0.505936\pi\) | ||||
−0.0186487 | + | 0.999826i | \(0.505936\pi\) | |||||||
\(74\) | −225.531 | − | 390.630i | −0.354289 | − | 0.613647i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 408.948 | − | 708.319i | 0.617232 | − | 1.06908i | ||||
\(77\) | 107.230 | − | 185.728i | 0.158701 | − | 0.274878i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −77.0203 | − | 133.403i | −0.109689 | − | 0.189987i | 0.805955 | − | 0.591977i | \(-0.201652\pi\) |
−0.915644 | + | 0.401989i | \(0.868319\pi\) | |||||||
\(80\) | −1238.93 | −1.73146 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 410.353 | 0.552633 | ||||||||
\(83\) | 141.098 | + | 244.389i | 0.186597 | + | 0.323195i | 0.944113 | − | 0.329621i | \(-0.106921\pi\) |
−0.757517 | + | 0.652816i | \(0.773588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −863.420 | + | 1495.49i | −1.10178 | + | 1.90833i | ||||
\(86\) | 225.986 | − | 391.420i | 0.283357 | − | 0.490790i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −646.315 | − | 1119.45i | −0.782925 | − | 1.35607i | ||||
\(89\) | −111.091 | −0.132311 | −0.0661554 | − | 0.997809i | \(-0.521073\pi\) | ||||
−0.0661554 | + | 0.997809i | \(0.521073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 546.083 | 0.629067 | ||||||||
\(92\) | 322.266 | + | 558.181i | 0.365202 | + | 0.632548i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 589.177 | − | 1020.48i | 0.646478 | − | 1.11973i | ||||
\(95\) | −399.530 | + | 692.006i | −0.431483 | + | 0.747350i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −555.045 | − | 961.367i | −0.580993 | − | 1.00631i | −0.995362 | − | 0.0962003i | \(-0.969331\pi\) |
0.414369 | − | 0.910109i | \(-0.364002\pi\) | |||||||
\(98\) | 242.639 | 0.250104 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2238.49 | 2.23849 | ||||||||
\(101\) | −699.163 | − | 1210.99i | −0.688805 | − | 1.19305i | −0.972225 | − | 0.234050i | \(-0.924802\pi\) |
0.283419 | − | 0.958996i | \(-0.408531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −723.877 | + | 1253.79i | −0.692483 | + | 1.19942i | 0.278539 | + | 0.960425i | \(0.410150\pi\) |
−0.971022 | + | 0.238991i | \(0.923183\pi\) | |||||||
\(104\) | 1645.73 | − | 2850.48i | 1.55170 | − | 2.68762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1232.18 | + | 2134.20i | 1.12906 | + | 1.95558i | ||||
\(107\) | 1063.28 | 0.960664 | 0.480332 | − | 0.877087i | \(-0.340516\pi\) | ||||
0.480332 | + | 0.877087i | \(0.340516\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1933.34 | 1.69890 | 0.849450 | − | 0.527669i | \(-0.176934\pi\) | ||||
0.849450 | + | 0.527669i | \(0.176934\pi\) | |||||||
\(110\) | 1224.29 | + | 2120.53i | 1.06120 | + | 1.83804i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 268.666 | − | 465.343i | 0.226666 | − | 0.392596i | ||||
\(113\) | 770.314 | − | 1334.22i | 0.641284 | − | 1.11074i | −0.343863 | − | 0.939020i | \(-0.611736\pi\) |
0.985146 | − | 0.171716i | \(-0.0549311\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −314.844 | − | 545.325i | −0.255298 | − | 0.442190i | ||||
\(116\) | −94.9556 | −0.0760035 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.8270 | 0.0162482 | ||||||||
\(119\) | −374.471 | − | 648.602i | −0.288468 | − | 0.499641i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 196.184 | − | 339.801i | 0.147396 | − | 0.255298i | ||||
\(122\) | −1550.89 | + | 2686.21i | −1.15091 | + | 1.99343i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1523.96 | − | 2639.57i | −1.10367 | − | 1.91162i | ||||
\(125\) | −169.442 | −0.121243 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1471.23 | 1.02796 | 0.513980 | − | 0.857802i | \(-0.328171\pi\) | ||||
0.513980 | + | 0.857802i | \(0.328171\pi\) | |||||||
\(128\) | 1168.75 | + | 2024.33i | 0.807061 | + | 1.39787i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3117.43 | + | 5399.56i | −2.10321 | + | 3.64286i | ||||
\(131\) | 339.376 | − | 587.816i | 0.226347 | − | 0.392044i | −0.730376 | − | 0.683045i | \(-0.760655\pi\) |
0.956723 | + | 0.291001i | \(0.0939884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −173.278 | − | 300.127i | −0.112971 | − | 0.195672i | ||||
\(134\) | −3360.40 | −2.16638 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4514.16 | −2.84622 | ||||||||
\(137\) | 909.980 | + | 1576.13i | 0.567480 | + | 0.982905i | 0.996814 | + | 0.0797591i | \(0.0254151\pi\) |
−0.429334 | + | 0.903146i | \(0.641252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1459.34 | − | 2527.65i | 0.890499 | − | 1.54239i | 0.0512202 | − | 0.998687i | \(-0.483689\pi\) |
0.839279 | − | 0.543702i | \(-0.182978\pi\) | |||||||
\(140\) | −933.238 | + | 1616.42i | −0.563379 | + | 0.975800i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1849.68 | + | 3203.74i | 1.09311 | + | 1.89332i | ||||
\(143\) | −2390.06 | −1.39767 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 92.7686 | 0.0531311 | ||||||||
\(146\) | 57.5966 | + | 99.7602i | 0.0326488 | + | 0.0565494i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −752.425 | + | 1303.24i | −0.417898 | + | 0.723821i | ||||
\(149\) | −492.243 | + | 852.590i | −0.270645 | + | 0.468771i | −0.969027 | − | 0.246954i | \(-0.920570\pi\) |
0.698382 | + | 0.715725i | \(0.253904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 64.9327 | + | 112.467i | 0.0349943 | + | 0.0606120i | 0.882992 | − | 0.469388i | \(-0.155525\pi\) |
−0.847998 | + | 0.530000i | \(0.822192\pi\) | |||||||
\(152\) | −2088.83 | −1.11465 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1061.96 | −0.555685 | ||||||||
\(155\) | 1488.86 | + | 2578.78i | 0.771535 | + | 1.33634i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 108.515 | − | 187.954i | 0.0551621 | − | 0.0955436i | −0.837126 | − | 0.547011i | \(-0.815766\pi\) |
0.892288 | + | 0.451467i | \(0.149099\pi\) | |||||||
\(158\) | −381.390 | + | 660.587i | −0.192036 | + | 0.332617i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 343.589 | + | 595.113i | 0.169769 | + | 0.294049i | ||||
\(161\) | 273.099 | 0.133685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 40.7178 | 0.0195660 | 0.00978302 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978302 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(164\) | −684.518 | − | 1185.62i | −0.325926 | − | 0.564521i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 698.691 | − | 1210.17i | 0.326680 | − | 0.565827i | ||||
\(167\) | 862.994 | − | 1494.75i | 0.399883 | − | 0.692618i | −0.593828 | − | 0.804592i | \(-0.702384\pi\) |
0.993711 | + | 0.111974i | \(0.0357174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1944.43 | − | 3367.84i | −0.885037 | − | 1.53293i | ||||
\(170\) | 8550.99 | 3.85783 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1507.89 | −0.668463 | ||||||||
\(173\) | −291.438 | − | 504.786i | −0.128079 | − | 0.221839i | 0.794853 | − | 0.606802i | \(-0.207548\pi\) |
−0.922932 | + | 0.384962i | \(0.874214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 474.244 | − | 821.415i | 0.204854 | − | 0.354818i | ||||
\(176\) | −1175.88 | + | 2036.68i | −0.503609 | + | 0.872276i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 275.052 | + | 476.404i | 0.115820 | + | 0.200607i | ||||
\(179\) | 3699.88 | 1.54493 | 0.772465 | − | 0.635058i | \(-0.219024\pi\) | ||||
0.772465 | + | 0.635058i | \(0.219024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2872.98 | 1.17982 | 0.589908 | − | 0.807470i | \(-0.299164\pi\) | ||||
0.589908 | + | 0.807470i | \(0.299164\pi\) | |||||||
\(182\) | −1352.05 | − | 2341.82i | −0.550663 | − | 0.953776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 823.037 | − | 1425.54i | 0.329756 | − | 0.571154i | ||||
\(185\) | 735.095 | − | 1273.22i | 0.292137 | − | 0.505995i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1638.96 | + | 2838.76i | 0.640922 | + | 1.11011i | ||||
\(188\) | −3931.27 | −1.52509 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3956.79 | 1.51082 | ||||||||
\(191\) | −136.646 | − | 236.678i | −0.0517663 | − | 0.0896619i | 0.838981 | − | 0.544161i | \(-0.183152\pi\) |
−0.890747 | + | 0.454499i | \(0.849818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −422.139 | + | 731.166i | −0.157442 | + | 0.272697i | −0.933945 | − | 0.357416i | \(-0.883658\pi\) |
0.776504 | + | 0.630113i | \(0.216991\pi\) | |||||||
\(194\) | −2748.48 | + | 4760.51i | −1.01716 | + | 1.76178i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −404.751 | − | 701.049i | −0.147504 | − | 0.255484i | ||||
\(197\) | −2506.77 | −0.906600 | −0.453300 | − | 0.891358i | \(-0.649753\pi\) | ||||
−0.453300 | + | 0.891358i | \(0.649753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3938.12 | −1.40284 | −0.701421 | − | 0.712747i | \(-0.747451\pi\) | ||||
−0.701421 | + | 0.712747i | \(0.747451\pi\) | |||||||
\(200\) | −2858.45 | − | 4950.98i | −1.01061 | − | 1.75044i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3462.13 | + | 5996.58i | −1.20591 | + | 2.08870i | ||||
\(203\) | −20.1172 | + | 34.8439i | −0.00695541 | + | 0.0120471i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 668.753 | + | 1158.31i | 0.227843 | + | 0.394635i | ||||
\(206\) | 7169.01 | 2.42470 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5988.32 | −1.99623 | ||||||||
\(209\) | 758.393 | + | 1313.57i | 0.251001 | + | 0.434746i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 33.4253 | − | 57.8944i | 0.0109057 | − | 0.0188892i | −0.860521 | − | 0.509415i | \(-0.829862\pi\) |
0.871427 | + | 0.490526i | \(0.163195\pi\) | |||||||
\(212\) | 4110.86 | − | 7120.21i | 1.33177 | − | 2.30669i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2632.58 | − | 4559.76i | −0.840931 | − | 1.45654i | ||||
\(215\) | 1473.16 | 0.467297 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1291.45 | −0.404007 | ||||||||
\(218\) | −4786.76 | − | 8290.92i | −1.48716 | − | 2.57583i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4084.53 | − | 7074.61i | 1.25172 | − | 2.16805i | ||||
\(221\) | −4173.31 | + | 7228.38i | −1.27026 | + | 2.20015i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1243.80 | − | 2154.33i | −0.373502 | − | 0.646925i | 0.616599 | − | 0.787277i | \(-0.288510\pi\) |
−0.990102 | + | 0.140352i | \(0.955177\pi\) | |||||||
\(224\) | −298.033 | −0.0888981 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7628.90 | −2.24543 | ||||||||
\(227\) | 1923.36 | + | 3331.36i | 0.562370 | + | 0.974054i | 0.997289 | + | 0.0735843i | \(0.0234438\pi\) |
−0.434919 | + | 0.900470i | \(0.643223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2005.94 | − | 3474.40i | 0.578849 | − | 1.00260i | −0.416762 | − | 0.909015i | \(-0.636835\pi\) |
0.995612 | − | 0.0935809i | \(-0.0298314\pi\) | |||||||
\(230\) | −1559.05 | + | 2700.35i | −0.446959 | + | 0.774155i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 121.254 | + | 210.018i | 0.0343134 | + | 0.0594325i | ||||
\(233\) | −5724.20 | −1.60946 | −0.804732 | − | 0.593639i | \(-0.797691\pi\) | ||||
−0.804732 | + | 0.593639i | \(0.797691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3840.73 | 1.06613 | ||||||||
\(236\) | −34.7420 | − | 60.1749i | −0.00958267 | − | 0.0165977i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1854.31 | + | 3211.76i | −0.505029 | + | 0.874737i | ||||
\(239\) | 3059.79 | − | 5299.71i | 0.828122 | − | 1.43435i | −0.0713879 | − | 0.997449i | \(-0.522743\pi\) |
0.899510 | − | 0.436901i | \(-0.143924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −246.401 | − | 426.780i | −0.0658594 | − | 0.114072i | 0.831216 | − | 0.555950i | \(-0.187646\pi\) |
−0.897075 | + | 0.441879i | \(0.854312\pi\) | |||||||
\(242\) | −1942.94 | −0.516102 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10348.3 | 2.71508 | ||||||||
\(245\) | 395.429 | + | 684.903i | 0.103114 | + | 0.178599i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1931.11 | + | 3344.78i | −0.497464 | + | 0.861633i | ||||
\(248\) | −3892.04 | + | 6741.22i | −0.996552 | + | 1.72608i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 419.523 | + | 726.636i | 0.106132 | + | 0.183826i | ||||
\(251\) | 1859.25 | 0.467548 | 0.233774 | − | 0.972291i | \(-0.424892\pi\) | ||||
0.233774 | + | 0.972291i | \(0.424892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1195.28 | −0.297022 | ||||||||
\(254\) | −3642.63 | − | 6309.23i | −0.899840 | − | 1.55857i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4174.37 | − | 7230.23i | 1.01913 | − | 1.76519i | ||||
\(257\) | 1885.96 | − | 3266.57i | 0.457753 | − | 0.792852i | −0.541088 | − | 0.840966i | \(-0.681988\pi\) |
0.998842 | + | 0.0481134i | \(0.0153209\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 318.815 | + | 552.204i | 0.0764873 | + | 0.132480i | ||||
\(260\) | 20801.0 | 4.96164 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3361.05 | −0.792544 | ||||||||
\(263\) | 20.3689 | + | 35.2800i | 0.00477568 | + | 0.00827171i | 0.868403 | − | 0.495858i | \(-0.165147\pi\) |
−0.863628 | + | 0.504130i | \(0.831813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4016.18 | + | 6956.22i | −0.930988 | + | 1.61252i | ||||
\(266\) | −858.043 | + | 1486.17i | −0.197782 | + | 0.342568i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5605.56 | + | 9709.11i | 1.27766 | + | 2.21298i | ||||
\(269\) | −1404.08 | −0.318247 | −0.159124 | − | 0.987259i | \(-0.550867\pi\) | ||||
−0.159124 | + | 0.987259i | \(0.550867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −222.681 | −0.0499148 | −0.0249574 | − | 0.999689i | \(-0.507945\pi\) | ||||
−0.0249574 | + | 0.999689i | \(0.507945\pi\) | |||||||
\(272\) | 4106.43 | + | 7112.55i | 0.915400 | + | 1.58552i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4506.05 | − | 7804.71i | 0.993505 | − | 1.72080i | ||||
\(275\) | −2075.64 | + | 3595.11i | −0.455148 | + | 0.788339i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2889.62 | + | 5004.98i | 0.626789 | + | 1.08563i | 0.988192 | + | 0.153221i | \(0.0489647\pi\) |
−0.361403 | + | 0.932410i | \(0.617702\pi\) | |||||||
\(278\) | −14452.7 | −3.11805 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4766.80 | 1.01740 | ||||||||
\(281\) | 1885.10 | + | 3265.09i | 0.400198 | + | 0.693162i | 0.993749 | − | 0.111633i | \(-0.0356082\pi\) |
−0.593552 | + | 0.804796i | \(0.702275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2402.06 | − | 4160.49i | 0.504549 | − | 0.873905i | −0.495437 | − | 0.868644i | \(-0.664992\pi\) |
0.999986 | − | 0.00526120i | \(-0.00167470\pi\) | |||||||
\(284\) | 6170.98 | − | 10688.4i | 1.28937 | − | 2.23325i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5917.56 | + | 10249.5i | 1.22347 | + | 2.11911i | ||||
\(287\) | −580.084 | −0.119308 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6534.21 | 1.32998 | ||||||||
\(290\) | −229.686 | − | 397.829i | −0.0465091 | − | 0.0805562i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 192.156 | − | 332.824i | 0.0385106 | − | 0.0667023i | ||||
\(293\) | 1493.45 | − | 2586.74i | 0.297777 | − | 0.515764i | −0.677850 | − | 0.735200i | \(-0.737088\pi\) |
0.975627 | + | 0.219436i | \(0.0704216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.9418 | + | 58.7890i | 0.00669888 | + | 0.0116028i | ||||
\(296\) | 3843.24 | 0.754676 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4874.99 | 0.947653 | ||||||||
\(299\) | −1521.78 | − | 2635.81i | −0.294338 | − | 0.509808i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −319.460 | + | 553.321i | −0.0611739 | + | 0.105956i | ||||
\(302\) | 321.534 | − | 556.914i | 0.0612657 | − | 0.106115i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1900.16 | + | 3291.18i | 0.358493 | + | 0.620928i | ||||
\(305\) | −10109.9 | −1.89801 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2881.52 | −0.535691 | −0.267845 | − | 0.963462i | \(-0.586312\pi\) | ||||
−0.267845 | + | 0.963462i | \(0.586312\pi\) | |||||||
\(308\) | 1771.49 | + | 3068.30i | 0.327726 | + | 0.567639i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7372.55 | − | 12769.6i | 1.35075 | − | 2.33957i | ||||
\(311\) | 3398.84 | − | 5886.96i | 0.619712 | − | 1.07337i | −0.369826 | − | 0.929101i | \(-0.620583\pi\) |
0.989538 | − | 0.144272i | \(-0.0460840\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −470.871 | − | 815.572i | −0.0850326 | − | 0.147281i | 0.820373 | − | 0.571829i | \(-0.193766\pi\) |
−0.905405 | + | 0.424549i | \(0.860433\pi\) | |||||||
\(314\) | −1074.69 | −0.193148 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2544.82 | 0.453029 | ||||||||
\(317\) | 1816.50 | + | 3146.27i | 0.321845 | + | 0.557452i | 0.980869 | − | 0.194670i | \(-0.0623636\pi\) |
−0.659024 | + | 0.752122i | \(0.729030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 88.0473 | − | 152.502i | 0.0154536 | − | 0.0267664i | ||||
\(320\) | −3254.34 | + | 5636.68i | −0.568509 | + | 0.984687i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −676.168 | − | 1171.16i | −0.117023 | − | 0.202690i | ||||
\(323\) | 5296.96 | 0.912478 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10570.5 | −1.80414 | ||||||||
\(326\) | −100.813 | − | 174.614i | −0.0171274 | − | 0.0296656i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1748.20 | + | 3027.96i | −0.294293 | + | 0.509730i | ||||
\(329\) | −832.874 | + | 1442.58i | −0.139568 | + | 0.241739i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1375.17 | − | 2381.86i | −0.228357 | − | 0.395525i | 0.728965 | − | 0.684551i | \(-0.240002\pi\) |
−0.957321 | + | 0.289026i | \(0.906669\pi\) | |||||||
\(332\) | −4662.01 | −0.770665 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8546.77 | −1.40017 | ||||||||
\(335\) | −5476.45 | − | 9485.49i | −0.893166 | − | 1.54701i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2916.14 | + | 5050.90i | −0.471372 | + | 0.816440i | −0.999464 | − | 0.0327474i | \(-0.989574\pi\) |
0.528092 | + | 0.849187i | \(0.322908\pi\) | |||||||
\(338\) | −9628.43 | + | 16676.9i | −1.54946 | + | 2.68374i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14264.1 | − | 24706.1i | −2.27523 | − | 3.94082i | ||||
\(341\) | 5652.34 | 0.897629 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 1925.51 | + | 3335.07i | 0.301792 | + | 0.522719i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1443.15 | + | 2499.61i | −0.224232 | + | 0.388380i | ||||
\(347\) | 1704.98 | − | 2953.11i | 0.263770 | − | 0.456863i | −0.703471 | − | 0.710724i | \(-0.748367\pi\) |
0.967241 | + | 0.253862i | \(0.0817008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2973.73 | − | 5150.66i | −0.456104 | − | 0.789996i | 0.542647 | − | 0.839961i | \(-0.317422\pi\) |
−0.998751 | + | 0.0499654i | \(0.984089\pi\) | |||||||
\(350\) | −4696.74 | −0.717289 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1304.41 | 0.197515 | ||||||||
\(353\) | −265.847 | − | 460.460i | −0.0400838 | − | 0.0694273i | 0.845287 | − | 0.534312i | \(-0.179429\pi\) |
−0.885371 | + | 0.464885i | \(0.846096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6028.85 | + | 10442.3i | −0.901347 | + | 1.56118i | ||||
\(356\) | 917.640 | − | 1589.40i | 0.136615 | − | 0.236624i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9160.57 | − | 15866.6i | −1.35238 | − | 2.34239i | ||||
\(359\) | 7555.95 | 1.11083 | 0.555415 | − | 0.831573i | \(-0.312559\pi\) | ||||
0.555415 | + | 0.831573i | \(0.312559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4407.94 | −0.642651 | ||||||||
\(362\) | −7113.22 | − | 12320.5i | −1.03277 | − | 1.78881i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4510.77 | + | 7812.88i | −0.649529 | + | 1.12502i | ||||
\(365\) | −187.730 | + | 325.159i | −0.0269213 | + | 0.0466290i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4851.61 | + | 8403.24i | 0.690060 | + | 1.19522i | 0.971818 | + | 0.235733i | \(0.0757492\pi\) |
−0.281758 | + | 0.959486i | \(0.590917\pi\) | |||||||
\(368\) | −2994.79 | −0.424224 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7280.11 | −1.02290 | ||||||||
\(371\) | −1741.84 | − | 3016.96i | −0.243752 | − | 0.422190i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.09728 | + | 12.2928i | −0.000985210 | + | 0.00170643i | −0.866518 | − | 0.499147i | \(-0.833647\pi\) |
0.865532 | + | 0.500853i | \(0.166980\pi\) | |||||||
\(374\) | 8115.81 | − | 14057.0i | 1.12208 | − | 1.94350i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5020.05 | + | 8694.98i | 0.688536 | + | 1.19258i | ||||
\(377\) | 448.393 | 0.0612558 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2618.92 | −0.354948 | −0.177474 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177474 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(380\) | −6600.41 | − | 11432.2i | −0.891037 | − | 1.54332i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −676.646 | + | 1171.98i | −0.0906288 | + | 0.156974i | ||||
\(383\) | −4344.62 | + | 7525.10i | −0.579633 | + | 1.00395i | 0.415888 | + | 0.909416i | \(0.363471\pi\) |
−0.995521 | + | 0.0945386i | \(0.969862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1730.69 | − | 2997.63i | −0.229101 | − | 0.396815i | ||||
\(386\) | 4180.71 | 0.551276 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18339.2 | 2.39957 | ||||||||
\(389\) | 5302.27 | + | 9183.80i | 0.691094 | + | 1.19701i | 0.971480 | + | 0.237123i | \(0.0762045\pi\) |
−0.280385 | + | 0.959888i | \(0.590462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2087.10 | + | 3614.96i | −0.269946 | + | 0.467560i | ||||
\(392\) | −1033.70 | + | 1790.41i | −0.133188 | + | 0.230688i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6206.53 | + | 10750.0i | 0.793606 | + | 1.37457i | ||||
\(395\) | −2486.21 | −0.316695 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2918.97 | 0.369015 | 0.184508 | − | 0.982831i | \(-0.440931\pi\) | ||||
0.184508 | + | 0.982831i | \(0.440931\pi\) | |||||||
\(398\) | 9750.41 | + | 16888.2i | 1.22800 | + | 2.12696i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5200.54 | + | 9007.60i | −0.650068 | + | 1.12595i | ||||
\(401\) | 2129.01 | − | 3687.56i | 0.265132 | − | 0.459222i | −0.702466 | − | 0.711717i | \(-0.747918\pi\) |
0.967598 | + | 0.252495i | \(0.0812512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7196.34 | + | 12464.4i | 0.889516 | + | 1.54069i | ||||
\(404\) | 23101.0 | 2.84484 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 199.233 | 0.0243541 | ||||||||
\(407\) | −1395.37 | − | 2416.85i | −0.169941 | − | 0.294346i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2308.33 | − | 3998.14i | 0.279070 | − | 0.483363i | −0.692084 | − | 0.721817i | \(-0.743307\pi\) |
0.971154 | + | 0.238454i | \(0.0766406\pi\) | |||||||
\(410\) | 3311.54 | − | 5735.75i | 0.398891 | − | 0.690899i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11958.8 | − | 20713.2i | −1.43002 | − | 2.47686i | ||||
\(413\) | −29.4416 | −0.00350781 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4554.63 | 0.538742 | ||||||||
\(416\) | 1660.72 | + | 2876.46i | 0.195730 | + | 0.339014i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3755.42 | − | 6504.58i | 0.439434 | − | 0.761122i | ||||
\(419\) | 997.567 | − | 1727.84i | 0.116311 | − | 0.201457i | −0.801992 | − | 0.597335i | \(-0.796226\pi\) |
0.918303 | + | 0.395878i | \(0.129560\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8281.75 | − | 14344.4i | −0.958736 | − | 1.66058i | −0.725577 | − | 0.688141i | \(-0.758427\pi\) |
−0.233160 | − | 0.972438i | \(-0.574907\pi\) | |||||||
\(422\) | −331.032 | −0.0381857 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20997.5 | −2.40502 | ||||||||
\(425\) | 7248.59 | + | 12554.9i | 0.827314 | + | 1.43295i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2192.37 | − | 3797.30i | 0.248469 | − | 0.430361i | ||||
\(428\) | −8782.92 | + | 15212.5i | −0.991912 | + | 1.71804i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3647.41 | − | 6317.50i | −0.409055 | − | 0.708505i | ||||
\(431\) | −1439.27 | −0.160852 | −0.0804258 | − | 0.996761i | \(-0.525628\pi\) | ||||
−0.0804258 | + | 0.996761i | \(0.525628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6467.98 | −0.717856 | −0.358928 | − | 0.933365i | \(-0.616858\pi\) | ||||
−0.358928 | + | 0.933365i | \(0.616858\pi\) | |||||||
\(434\) | 3197.52 | + | 5538.26i | 0.353654 | + | 0.612547i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15969.8 | + | 27660.5i | −1.75416 | + | 3.03830i | ||||
\(437\) | −965.760 | + | 1672.74i | −0.105717 | + | 0.183108i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6255.01 | + | 10834.0i | 0.680035 | + | 1.17785i | 0.974970 | + | 0.222337i | \(0.0713686\pi\) |
−0.294935 | + | 0.955517i | \(0.595298\pi\) | |||||||
\(440\) | −20863.0 | −2.26047 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 41330.9 | 4.44776 | ||||||||
\(443\) | 3510.58 | + | 6080.51i | 0.376507 | + | 0.652130i | 0.990551 | − | 0.137142i | \(-0.0437916\pi\) |
−0.614044 | + | 0.789272i | \(0.710458\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −896.506 | + | 1552.79i | −0.0955021 | + | 0.165415i | ||||
\(446\) | −6159.07 | + | 10667.8i | −0.653902 | + | 1.13259i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1411.43 | − | 2444.66i | −0.148847 | − | 0.257811i | ||||
\(449\) | −5184.19 | −0.544894 | −0.272447 | − | 0.962171i | \(-0.587833\pi\) | ||||
−0.272447 | + | 0.962171i | \(0.587833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2538.87 | 0.265079 | ||||||||
\(452\) | 12725.9 | + | 22042.0i | 1.32429 | + | 2.29373i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9524.13 | − | 16496.3i | 0.984559 | − | 1.70531i | ||||
\(455\) | 4406.88 | − | 7632.94i | 0.454061 | − | 0.786457i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1288.14 | − | 2231.12i | −0.131853 | − | 0.228375i | 0.792538 | − | 0.609822i | \(-0.208759\pi\) |
−0.924391 | + | 0.381447i | \(0.875426\pi\) | |||||||
\(458\) | −19866.1 | −2.02682 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10402.7 | 1.05441 | ||||||||
\(461\) | −8952.21 | − | 15505.7i | −0.904438 | − | 1.56653i | −0.821670 | − | 0.569963i | \(-0.806957\pi\) |
−0.0827674 | − | 0.996569i | \(-0.526376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5631.93 | + | 9754.79i | −0.565309 | + | 0.979144i | 0.431712 | + | 0.902012i | \(0.357910\pi\) |
−0.997021 | + | 0.0771323i | \(0.975424\pi\) | |||||||
\(464\) | 220.604 | − | 382.097i | 0.0220717 | − | 0.0382293i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14172.6 | + | 24547.6i | 1.40887 | + | 2.44023i | ||||
\(467\) | −9817.00 | −0.972755 | −0.486377 | − | 0.873749i | \(-0.661682\pi\) | ||||
−0.486377 | + | 0.873749i | \(0.661682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4750.34 | 0.467698 | ||||||||
\(470\) | −9509.29 | − | 16470.6i | −0.933257 | − | 1.61645i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −88.7278 | + | 153.681i | −0.00865260 | + | 0.0149867i | ||||
\(473\) | 1398.19 | − | 2421.73i | 0.135917 | − | 0.235415i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3354.13 | + | 5809.53i | 0.323996 | + | 0.561178i | ||||
\(476\) | 12372.9 | 1.19140 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30303.0 | −2.89964 | ||||||||
\(479\) | 3675.86 | + | 6366.78i | 0.350636 | + | 0.607319i | 0.986361 | − | 0.164597i | \(-0.0526322\pi\) |
−0.635725 | + | 0.771915i | \(0.719299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3553.05 | − | 6154.07i | 0.336809 | − | 0.583371i | ||||
\(482\) | −1220.13 | + | 2113.33i | −0.115302 | + | 0.199709i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3241.05 | + | 5613.67i | 0.304381 | + | 0.527204i | ||||
\(485\) | −17916.8 | −1.67745 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15312.1 | 1.42476 | 0.712378 | − | 0.701796i | \(-0.247618\pi\) | ||||
0.712378 | + | 0.701796i | \(0.247618\pi\) | |||||||
\(488\) | −13214.3 | − | 22887.8i | −1.22578 | − | 2.12312i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1958.09 | − | 3391.51i | 0.180526 | − | 0.312679i | ||||
\(491\) | −8989.47 | + | 15570.2i | −0.826251 | + | 1.43111i | 0.0747090 | + | 0.997205i | \(0.476197\pi\) |
−0.900960 | + | 0.433903i | \(0.857136\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −307.481 | − | 532.573i | −0.0280898 | − | 0.0486529i | ||||
\(494\) | 19125.0 | 1.74185 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14162.0 | 1.28204 | ||||||||
\(497\) | −2614.75 | − | 4528.88i | −0.235991 | − | 0.408748i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9407.52 | − | 16294.3i | 0.843965 | − | 1.46179i | −0.0425521 | − | 0.999094i | \(-0.513549\pi\) |
0.886517 | − | 0.462696i | \(-0.153118\pi\) | |||||||
\(500\) | 1399.63 | − | 2424.23i | 0.125187 | − | 0.216830i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4603.32 | − | 7973.19i | −0.409275 | − | 0.708886i | ||||
\(503\) | 6228.19 | 0.552090 | 0.276045 | − | 0.961145i | \(-0.410976\pi\) | ||||
0.276045 | + | 0.961145i | \(0.410976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22568.9 | −1.98872 | ||||||||
\(506\) | 2959.40 | + | 5125.84i | 0.260003 | + | 0.450339i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12152.7 | + | 21049.1i | −1.06140 | + | 1.83839i | ||||
\(509\) | −5901.69 | + | 10222.0i | −0.513925 | + | 0.890144i | 0.485944 | + | 0.873990i | \(0.338476\pi\) |
−0.999870 | + | 0.0161547i | \(0.994858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −81.4199 | − | 141.023i | −0.00704854 | − | 0.0122084i | ||||
\(512\) | −22641.4 | −1.95433 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18677.8 | −1.60281 | ||||||||
\(515\) | 11683.4 | + | 20236.2i | 0.999670 | + | 1.73148i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3645.26 | − | 6313.78i | 0.310094 | − | 0.537098i | ||||
\(518\) | 1578.71 | − | 2734.41i | 0.133909 | − | 0.231937i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −26562.0 | − | 46006.7i | −2.24004 | − | 3.87986i | ||||
\(521\) | 7277.82 | 0.611990 | 0.305995 | − | 0.952033i | \(-0.401011\pi\) | ||||
0.305995 | + | 0.952033i | \(0.401011\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18929.2 | 1.58263 | 0.791316 | − | 0.611408i | \(-0.209397\pi\) | ||||
0.791316 | + | 0.611408i | \(0.209397\pi\) | |||||||
\(524\) | 5606.64 | + | 9710.99i | 0.467419 | + | 0.809593i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 100.863 | − | 174.700i | 0.00836092 | − | 0.0144815i | ||||
\(527\) | 9869.62 | − | 17094.7i | 0.815802 | − | 1.41301i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5322.45 | + | 9218.75i | 0.437449 | + | 0.757685i | ||||
\(530\) | 39774.7 | 3.25982 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5725.28 | 0.466583 | ||||||||
\(533\) | 3232.39 | + | 5598.67i | 0.262684 | + | 0.454981i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8580.63 | − | 14862.1i | 0.693408 | − | 1.20102i | ||||
\(536\) | 14316.1 | − | 24796.2i | 1.15366 | − | 1.99819i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3476.38 | + | 6021.26i | 0.278582 | + | 0.482519i | ||||
\(539\) | 1501.22 | 0.119967 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3018.24 | 0.239860 | 0.119930 | − | 0.992782i | \(-0.461733\pi\) | ||||
0.119930 | + | 0.992782i | \(0.461733\pi\) | |||||||
\(542\) | 551.337 | + | 954.944i | 0.0436936 | + | 0.0756796i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2277.65 | − | 3945.00i | 0.179510 | − | 0.310920i | ||||
\(545\) | 15602.0 | − | 27023.5i | 1.22627 | − | 2.12396i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4726.68 | + | 8186.86i | 0.369467 | + | 0.639936i | 0.989482 | − | 0.144654i | \(-0.0462069\pi\) |
−0.620015 | + | 0.784590i | \(0.712874\pi\) | |||||||
\(548\) | −30066.6 | −2.34376 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20556.3 | 1.59368 | ||||||||
\(551\) | −142.280 | − | 246.437i | −0.0110006 | − | 0.0190537i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 539.142 | − | 933.821i | 0.0414587 | − | 0.0718085i | ||||
\(554\) | 14308.9 | − | 24783.7i | 1.09734 | − | 1.90065i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24108.9 | + | 41757.8i | 1.83893 | + | 3.18512i | ||||
\(557\) | −6175.74 | −0.469793 | −0.234896 | − | 0.972020i | \(-0.575475\pi\) | ||||
−0.234896 | + | 0.972020i | \(0.575475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7120.47 | 0.538755 | ||||||||
\(560\) | −4336.26 | − | 7510.62i | −0.327215 | − | 0.566753i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9334.65 | − | 16168.1i | 0.700638 | − | 1.21354i | ||||
\(563\) | 6329.56 | − | 10963.1i | 0.473817 | − | 0.820675i | −0.525734 | − | 0.850649i | \(-0.676209\pi\) |
0.999551 | + | 0.0299739i | \(0.00954242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12432.8 | − | 21534.3i | −0.925758 | − | 1.60346i | ||||
\(566\) | −23789.1 | −1.76666 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31520.2 | −2.32845 | ||||||||
\(569\) | 9605.51 | + | 16637.2i | 0.707704 | + | 1.22578i | 0.965707 | + | 0.259636i | \(0.0836024\pi\) |
−0.258002 | + | 0.966144i | \(0.583064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3780.12 | − | 6547.37i | 0.277046 | − | 0.479858i | −0.693603 | − | 0.720357i | \(-0.743978\pi\) |
0.970649 | + | 0.240499i | \(0.0773112\pi\) | |||||||
\(572\) | 19742.4 | − | 34194.9i | 1.44313 | − | 2.49958i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1436.23 | + | 2487.63i | 0.104438 | + | 0.180892i | ||||
\(575\) | −5286.36 | −0.383402 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14126.1 | −1.01920 | −0.509598 | − | 0.860413i | \(-0.670206\pi\) | ||||
−0.509598 | + | 0.860413i | \(0.670206\pi\) | |||||||
\(578\) | −16178.1 | − | 28021.3i | −1.16422 | − | 2.01649i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −766.290 | + | 1327.25i | −0.0548594 | + | 0.0950193i | ||||
\(581\) | −987.686 | + | 1710.72i | −0.0705269 | + | 0.122156i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7623.56 | + | 13204.4i | 0.541571 | + | 0.938028i | ||||
\(584\) | −981.497 | −0.0695456 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14790.6 | −1.04265 | ||||||||
\(587\) | 5811.15 | + | 10065.2i | 0.408606 | + | 0.707727i | 0.994734 | − | 0.102492i | \(-0.0326816\pi\) |
−0.586128 | + | 0.810219i | \(0.699348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4566.96 | − | 7910.21i | 0.319488 | − | 0.553369i | ||||
\(590\) | 168.074 | − | 291.112i | 0.0117279 | − | 0.0203134i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3496.11 | − | 6055.45i | −0.242719 | − | 0.420401i | ||||
\(593\) | 22182.5 | 1.53613 | 0.768064 | − | 0.640373i | \(-0.221220\pi\) | ||||
0.768064 | + | 0.640373i | \(0.221220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12087.9 | −0.832865 | ||||||||
\(596\) | −8132.07 | − | 14085.2i | −0.558897 | − | 0.968038i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7535.59 | + | 13052.0i | −0.515306 | + | 0.892537i | ||||
\(599\) | −11203.2 | + | 19404.5i | −0.764189 | + | 1.32361i | 0.176485 | + | 0.984303i | \(0.443527\pi\) |
−0.940674 | + | 0.339311i | \(0.889806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5627.94 | − | 9747.88i | −0.381977 | − | 0.661604i | 0.609367 | − | 0.792888i | \(-0.291423\pi\) |
−0.991345 | + | 0.131284i | \(0.958090\pi\) | |||||||
\(602\) | 3163.81 | 0.214198 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2145.43 | −0.144531 | ||||||||
\(605\) | −3166.41 | − | 5484.38i | −0.212781 | − | 0.368548i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6156.29 | − | 10663.0i | 0.411658 | − | 0.713012i | −0.583413 | − | 0.812175i | \(-0.698283\pi\) |
0.995071 | + | 0.0991632i | \(0.0316166\pi\) | |||||||
\(608\) | 1053.93 | − | 1825.47i | 0.0703004 | − | 0.121764i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25031.2 | + | 43355.4i | 1.66145 | + | 2.87772i | ||||
\(611\) | 18564.0 | 1.22916 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26835.4 | −1.76814 | −0.884070 | − | 0.467354i | \(-0.845207\pi\) | ||||
−0.884070 | + | 0.467354i | \(0.845207\pi\) | |||||||
\(614\) | 7134.37 | + | 12357.1i | 0.468925 | + | 0.812202i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4524.21 | − | 7836.16i | 0.295918 | − | 0.512545i | ||||
\(617\) | −10882.7 | + | 18849.4i | −0.710084 | + | 1.22990i | 0.254741 | + | 0.967009i | \(0.418010\pi\) |
−0.964825 | + | 0.262893i | \(0.915323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3557.64 | − | 6162.01i | −0.231007 | − | 0.400117i | 0.727097 | − | 0.686534i | \(-0.240869\pi\) |
−0.958105 | + | 0.286418i | \(0.907535\pi\) | |||||||
\(620\) | −49193.2 | −3.18653 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −33660.8 | −2.16990 | ||||||||
\(623\) | −388.820 | − | 673.456i | −0.0250044 | − | 0.0433089i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7101.25 | − | 12299.7i | 0.454480 | − | 0.787182i | ||||
\(626\) | −2331.67 | + | 4038.56i | −0.148869 | + | 0.257849i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1792.72 | + | 3105.08i | 0.113913 | + | 0.197303i | ||||
\(629\) | −9745.88 | −0.617796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11639.8 | −0.734345 | −0.367173 | − | 0.930153i | \(-0.619674\pi\) | ||||
−0.367173 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(632\) | −3249.61 | − | 5628.50i | −0.204530 | − | 0.354256i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8994.98 | − | 15579.8i | 0.563464 | − | 0.975948i | ||||
\(635\) | 11872.8 | − | 20564.3i | 0.741982 | − | 1.28515i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1911.29 | + | 3310.45i | 0.118882 | + | 0.205910i | ||||
\(638\) | −871.988 | −0.0541102 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37727.1 | 2.33015 | ||||||||
\(641\) | −12837.8 | − | 22235.7i | −0.791048 | − | 1.37014i | −0.925318 | − | 0.379191i | \(-0.876202\pi\) |
0.134270 | − | 0.990945i | \(-0.457131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8573.42 | − | 14849.6i | 0.525821 | − | 0.910748i | −0.473727 | − | 0.880672i | \(-0.657092\pi\) |
0.999548 | − | 0.0300764i | \(-0.00957506\pi\) | |||||||
\(644\) | −2255.86 | + | 3907.27i | −0.138033 | + | 0.239081i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13114.8 | − | 22715.4i | −0.798752 | − | 1.38348i | ||||
\(647\) | 13104.3 | 0.796263 | 0.398132 | − | 0.917328i | \(-0.369659\pi\) | ||||
0.398132 | + | 0.917328i | \(0.369659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 128.858 | 0.00779369 | ||||||||
\(650\) | 26171.5 | + | 45330.4i | 1.57928 | + | 2.73539i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −336.338 | + | 582.555i | −0.0202025 | + | 0.0349917i | ||||
\(653\) | −8373.04 | + | 14502.5i | −0.501780 | + | 0.869108i | 0.498218 | + | 0.867052i | \(0.333988\pi\) |
−0.999998 | + | 0.00205652i | \(0.999345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5477.51 | − | 9487.33i | −0.326754 | − | 0.565955i | ||||
\(656\) | 6361.18 | 0.378601 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8248.47 | 0.488691 | ||||||||
\(659\) | −12133.6 | − | 21015.9i | −0.717232 | − | 1.24228i | −0.962092 | − | 0.272724i | \(-0.912075\pi\) |
0.244860 | − | 0.969558i | \(-0.421258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7233.95 | + | 12529.6i | −0.425670 | + | 0.737282i | −0.996483 | − | 0.0837981i | \(-0.973295\pi\) |
0.570813 | + | 0.821080i | \(0.306628\pi\) | |||||||
\(662\) | −6809.57 | + | 11794.5i | −0.399791 | + | 0.692458i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5953.16 | + | 10311.2i | 0.347933 | + | 0.602638i | ||||
\(665\) | −5593.42 | −0.326170 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 224.244 | 0.0130176 | ||||||||
\(668\) | 14257.0 | + | 24693.9i | 0.825781 | + | 1.43029i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −27118.4 | + | 46970.4i | −1.56369 | + | 2.70839i | ||||
\(671\) | −9595.41 | + | 16619.7i | −0.552052 | + | 0.956181i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7479.13 | + | 12954.2i | 0.428379 | + | 0.741975i | 0.996729 | − | 0.0808120i | \(-0.0257513\pi\) |
−0.568350 | + | 0.822787i | \(0.692418\pi\) | |||||||
\(674\) | 28880.4 | 1.65049 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64245.6 | 3.65530 | ||||||||
\(677\) | −12861.9 | − | 22277.4i | −0.730165 | − | 1.26468i | −0.956812 | − | 0.290706i | \(-0.906110\pi\) |
0.226647 | − | 0.973977i | \(-0.427224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3885.32 | − | 6729.57i | 0.219595 | − | 0.380349i | ||||
\(680\) | −36429.2 | + | 63097.2i | −2.05440 | + | 3.55833i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13994.7 | − | 24239.5i | −0.785753 | − | 1.36096i | ||||
\(683\) | 2949.64 | 0.165248 | 0.0826242 | − | 0.996581i | \(-0.473670\pi\) | ||||
0.0826242 | + | 0.996581i | \(0.473670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29374.1 | 1.63843 | ||||||||
\(686\) | 849.236 | + | 1470.92i | 0.0472653 | + | 0.0818659i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3503.18 | − | 6067.69i | 0.194124 | − | 0.336233i | ||||
\(689\) | −19412.0 | + | 33622.6i | −1.07335 | + | 1.85910i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4059.96 | + | 7032.05i | 0.223514 | + | 0.387137i | 0.955873 | − | 0.293782i | \(-0.0949139\pi\) |
−0.732359 | + | 0.680919i | \(0.761581\pi\) | |||||||
\(692\) | 9629.38 | 0.528980 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16885.5 | −0.923579 | ||||||||
\(695\) | −23553.6 | − | 40796.1i | −1.28553 | − | 2.22660i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4433.16 | − | 7678.45i | 0.240915 | − | 0.417277i | ||||
\(698\) | −14725.4 | + | 25505.1i | −0.798515 | + | 1.38307i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7834.73 | + | 13570.1i | 0.423035 | + | 0.732719i | ||||
\(701\) | 15870.9 | 0.855115 | 0.427558 | − | 0.903988i | \(-0.359374\pi\) | ||||
0.427558 | + | 0.903988i | \(0.359374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4509.70 | −0.241944 | ||||||||
\(704\) | 6177.43 | + | 10699.6i | 0.330711 | + | 0.572808i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1316.42 | + | 2280.11i | −0.0701760 | + | 0.121548i | ||||
\(707\) | 4894.14 | − | 8476.90i | 0.260344 | − | 0.450929i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7436.79 | + | 12880.9i | 0.393928 | + | 0.682303i | 0.992964 | − | 0.118419i | \(-0.0377827\pi\) |
−0.599036 | + | 0.800722i | \(0.704449\pi\) | |||||||
\(710\) | 59707.5 | 3.15603 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4687.13 | −0.246710 | ||||||||
\(713\) | 3598.93 | + | 6233.53i | 0.189034 | + | 0.327416i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19287.7 | + | 33407.3i | −1.00884 | + | 1.74736i | ||||
\(716\) | −30561.9 | + | 52934.7i | −1.59518 | + | 2.76294i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18707.8 | − | 32402.9i | −0.972382 | − | 1.68421i | ||||
\(719\) | −31809.4 | −1.64992 | −0.824959 | − | 0.565192i | \(-0.808802\pi\) | ||||
−0.824959 | + | 0.565192i | \(0.808802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10134.3 | −0.523468 | ||||||||
\(722\) | 10913.7 | + | 18903.0i | 0.562554 | + | 0.974373i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23731.4 | + | 41104.1i | −1.21819 | + | 2.10997i | ||||
\(725\) | 389.406 | − | 674.471i | 0.0199478 | − | 0.0345506i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8385.91 | − | 14524.8i | −0.427808 | − | 0.740984i | 0.568870 | − | 0.822427i | \(-0.307381\pi\) |
−0.996678 | + | 0.0814427i | \(0.974047\pi\) | |||||||
\(728\) | 23040.2 | 1.17297 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1859.21 | 0.0942638 | ||||||||
\(731\) | −4882.79 | − | 8457.24i | −0.247054 | − | 0.427910i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15894.2 | − | 27529.5i | 0.800906 | − | 1.38721i | −0.118114 | − | 0.993000i | \(-0.537685\pi\) |
0.919020 | − | 0.394210i | \(-0.128982\pi\) | |||||||
\(734\) | 24024.3 | − | 41611.3i | 1.20811 | − | 2.09251i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 830.537 | + | 1438.53i | 0.0415951 | + | 0.0720448i | ||||
\(737\) | −20791.0 | −1.03914 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17098.2 | −0.851107 | −0.425553 | − | 0.904933i | \(-0.639921\pi\) | ||||
−0.425553 | + | 0.904933i | \(0.639921\pi\) | |||||||
\(740\) | 12144.1 | + | 21034.2i | 0.603279 | + | 1.04491i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8625.27 | + | 14939.4i | −0.426743 | + | 0.739141i | ||||
\(743\) | −308.950 | + | 535.118i | −0.0152548 | + | 0.0264220i | −0.873552 | − | 0.486731i | \(-0.838189\pi\) |
0.858297 | + | 0.513153i | \(0.171523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7944.78 | + | 13760.8i | 0.390704 | + | 0.676719i | ||||
\(746\) | 70.2888 | 0.00344967 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −54152.6 | −2.64708 | ||||||||
\(749\) | 3721.47 | + | 6445.78i | 0.181548 | + | 0.314451i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13234.5 | + | 22922.8i | −0.643053 | + | 1.11380i | 0.341694 | + | 0.939811i | \(0.388999\pi\) |
−0.984747 | + | 0.173990i | \(0.944334\pi\) | |||||||
\(752\) | 9133.26 | − | 15819.3i | 0.442893 | − | 0.767114i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1110.18 | − | 1922.89i | −0.0536212 | − | 0.0928746i | ||||
\(755\) | 2096.02 | 0.101036 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40262.5 | 1.93311 | 0.966557 | − | 0.256453i | \(-0.0825538\pi\) | ||||
0.966557 | + | 0.256453i | \(0.0825538\pi\) | |||||||
\(758\) | 6484.21 | + | 11231.0i | 0.310709 | + | 0.538163i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16856.8 | + | 29196.9i | −0.804555 | + | 1.39353i | ||||
\(761\) | 19445.6 | − | 33680.8i | 0.926286 | − | 1.60438i | 0.136807 | − | 0.990598i | \(-0.456316\pi\) |
0.789479 | − | 0.613777i | \(-0.210351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6766.68 | + | 11720.2i | 0.321062 | + | 0.556096i | ||||
\(764\) | 4514.91 | 0.213801 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43027.5 | 2.02956 | ||||||||
\(767\) | 164.057 | + | 284.154i | 0.00772326 | + | 0.0133771i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13910.2 | + | 24093.2i | −0.652296 | + | 1.12981i | 0.330268 | + | 0.943887i | \(0.392861\pi\) |
−0.982564 | + | 0.185923i | \(0.940473\pi\) | |||||||
\(770\) | −8570.03 | + | 14843.7i | −0.401094 | + | 0.694715i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6973.93 | − | 12079.2i | −0.325126 | − | 0.563135i | ||||
\(773\) | −25952.0 | −1.20754 | −0.603770 | − | 0.797159i | \(-0.706335\pi\) | ||||
−0.603770 | + | 0.797159i | \(0.706335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24998.5 | 1.15868 | ||||||||
\(776\) | −23418.3 | − | 40561.7i | −1.08333 | − | 1.87639i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26255.8 | − | 45476.5i | 1.20992 | − | 2.09564i | ||||
\(779\) | 2051.35 | − | 3553.04i | 0.0943482 | − | 0.163416i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11444.0 | + | 19821.7i | 0.524328 | + | 0.908163i | ||||
\(782\) | 20669.8 | 0.945206 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3761.32 | 0.171343 | ||||||||
\(785\) | −1751.43 | − | 3033.57i | −0.0796322 | − | 0.137927i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21058.2 | + | 36473.8i | −0.953802 | + | 1.65203i | −0.216715 | + | 0.976235i | \(0.569534\pi\) |
−0.737087 | + | 0.675798i | \(0.763799\pi\) | |||||||
\(788\) | 20706.5 | − | 35864.7i | 0.936090 | − | 1.62136i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6155.62 | + | 10661.8i | 0.277224 | + | 0.480166i | ||||
\(791\) | 10784.4 | 0.484765 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48866.0 | −2.18825 | ||||||||
\(794\) | −7227.10 | − | 12517.7i | −0.323023 | − | 0.559492i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32529.7 | − | 56343.2i | 1.44847 | − | 2.50883i | ||||
\(797\) | 6485.71 | − | 11233.6i | 0.288250 | − | 0.499264i | −0.685142 | − | 0.728410i | \(-0.740260\pi\) |
0.973392 | + | 0.229145i | \(0.0735931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12730.1 | − | 22049.1i | −0.563652 | − | 0.976274i | ||||
\(800\) | 5769.00 | 0.254956 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21085.0 | −0.928349 | ||||||||
\(803\) | 356.353 | + | 617.221i | 0.0156605 | + | 0.0271248i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2203.91 | − | 3817.28i | 0.0964937 | − | 0.167132i | ||||
\(806\) | 35634.9 | − | 61721.5i | 1.55730 | − | 2.69733i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −29498.9 | − | 51093.5i | −1.28436 | − | 2.22458i | ||||
\(809\) | 9053.03 | 0.393433 | 0.196717 | − | 0.980460i | \(-0.436972\pi\) | ||||
0.196717 | + | 0.980460i | \(0.436972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2374.82 | −0.102825 | −0.0514127 | − | 0.998677i | \(-0.516372\pi\) | ||||
−0.0514127 | + | 0.998677i | \(0.516372\pi\) | |||||||
\(812\) | −332.345 | − | 575.638i | −0.0143633 | − | 0.0248780i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6909.60 | + | 11967.8i | −0.297520 | + | 0.515320i | ||||
\(815\) | 328.592 | − | 569.138i | 0.0141228 | − | 0.0244614i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2259.41 | − | 3913.41i | −0.0967524 | − | 0.167580i | ||||
\(818\) | −22860.8 | −0.977152 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22096.2 | −0.941016 | ||||||||
\(821\) | 2574.93 | + | 4459.91i | 0.109459 | + | 0.189588i | 0.915551 | − | 0.402202i | \(-0.131755\pi\) |
−0.806092 | + | 0.591790i | \(0.798422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1437.48 | + | 2489.79i | −0.0608839 | + | 0.105454i | −0.894861 | − | 0.446345i | \(-0.852725\pi\) |
0.833977 | + | 0.551799i | \(0.186059\pi\) | |||||||
\(824\) | −30541.6 | + | 52899.6i | −1.29122 | + | 2.23646i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 72.8945 | + | 126.257i | 0.00307061 | + | 0.00531846i | ||||
\(827\) | −515.502 | −0.0216757 | −0.0108378 | − | 0.999941i | \(-0.503450\pi\) | ||||
−0.0108378 | + | 0.999941i | \(0.503450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14698.3 | −0.615793 | −0.307897 | − | 0.951420i | \(-0.599625\pi\) | ||||
−0.307897 | + | 0.951420i | \(0.599625\pi\) | |||||||
\(830\) | −11276.8 | − | 19532.1i | −0.471596 | − | 0.816829i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15729.7 | + | 27244.7i | −0.655444 | + | 1.13526i | ||||
\(833\) | 2621.30 | − | 4540.22i | 0.109031 | − | 0.188847i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13928.7 | − | 24125.2i | −0.577272 | − | 0.999864i | ||||
\(836\) | −25058.0 | −1.03666 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9879.53 | −0.407259 | ||||||||
\(839\) | −2205.55 | − | 3820.12i | −0.0907557 | − | 0.157194i | 0.817074 | − | 0.576533i | \(-0.195595\pi\) |
−0.907829 | + | 0.419340i | \(0.862262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12178.0 | − | 21092.9i | 0.499323 | − | 0.864852i | ||||
\(842\) | −41009.7 | + | 71030.9i | −1.67849 | + | 2.90723i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 552.201 | + | 956.441i | 0.0225208 | + | 0.0390072i | ||||
\(845\) | −62765.9 | −2.55528 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2746.58 | 0.111421 | ||||||||
\(848\) | 19100.9 | + | 33083.8i | 0.773501 | + | 1.33974i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 35893.7 | − | 62169.7i | 1.44840 | − | 2.50871i | ||||
\(851\) | 1776.90 | − | 3077.68i | 0.0715763 | − | 0.123974i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10950.2 | − | 18966.3i | −0.439540 | − | 0.761306i | 0.558114 | − | 0.829764i | \(-0.311525\pi\) |
−0.997654 | + | 0.0684586i | \(0.978192\pi\) | |||||||
\(854\) | −21712.4 | −0.870004 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44861.5 | 1.79128 | ||||||||
\(857\) | 11901.6 | + | 20614.1i | 0.474388 | + | 0.821664i | 0.999570 | − | 0.0293263i | \(-0.00933618\pi\) |
−0.525182 | + | 0.850990i | \(0.676003\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22244.1 | + | 38527.8i | −0.883536 | + | 1.53033i | −0.0361535 | + | 0.999346i | \(0.511511\pi\) |
−0.847382 | + | 0.530983i | \(0.821823\pi\) | |||||||
\(860\) | −12168.7 | + | 21076.7i | −0.482497 | + | 0.835710i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3563.49 | + | 6172.15i | 0.140804 | + | 0.243880i | ||||
\(863\) | 34544.3 | 1.36258 | 0.681288 | − | 0.732016i | \(-0.261420\pi\) | ||||
0.681288 | + | 0.732016i | \(0.261420\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9407.60 | −0.369790 | ||||||||
\(866\) | 16014.1 | + | 27737.3i | 0.628386 | + | 1.08840i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10667.7 | − | 18477.0i | 0.417149 | − | 0.722523i | ||||
\(869\) | −2359.68 | + | 4087.08i | −0.0921134 | + | 0.159545i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26470.2 | − | 45847.8i | −1.02975 | − | 1.78357i | ||||
\(872\) | 81570.8 | 3.16782 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9564.52 | 0.370166 | ||||||||
\(875\) | −593.048 | − | 1027.19i | −0.0229128 | − | 0.0396861i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16602.3 | + | 28756.0i | −0.639246 | + | 1.10721i | 0.346353 | + | 0.938104i | \(0.387420\pi\) |
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(878\) | 30973.6 | − | 53647.9i | 1.19056 | − | 2.06211i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18978.6 | + | 32871.9i | 0.727010 | + | 1.25922i | ||||
\(881\) | −23411.1 | −0.895278 | −0.447639 | − | 0.894214i | \(-0.647735\pi\) | ||||
−0.447639 | + | 0.894214i | \(0.647735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12881.8 | −0.490947 | −0.245473 | − | 0.969403i | \(-0.578943\pi\) | ||||
−0.245473 | + | 0.969403i | \(0.578943\pi\) | |||||||
\(884\) | −68944.9 | − | 119416.i | −2.62316 | − | 4.54344i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17383.7 | − | 30109.5i | 0.659163 | − | 1.14170i | ||||
\(887\) | 2811.78 | − | 4870.15i | 0.106438 | − | 0.184356i | −0.807887 | − | 0.589338i | \(-0.799389\pi\) |
0.914325 | + | 0.404982i | \(0.132722\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5149.31 | + | 8918.88i | 0.194266 | + | 0.336479i | ||||
\(890\) | 8878.66 | 0.334397 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41096.3 | 1.54261 | ||||||||
\(893\) | −5890.58 | − | 10202.8i | −0.220740 | − | 0.382333i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29858.0 | − | 51715.6i | 1.11513 | − | 1.93146i | ||||
\(896\) | −8181.25 | + | 14170.3i | −0.305041 | + | 0.528346i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12835.6 | + | 22231.9i | 0.476981 | + | 0.826155i | ||||
\(899\) | −1060.42 | −0.0393405 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53246.4 | 1.96881 | ||||||||
\(902\) | −6286.01 | − | 10887.7i | −0.232041 | − | 0.401907i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32500.8 | − | 56293.1i | 1.19575 | − | 2.07111i | ||||
\(905\) | 23184.9 | − | 40157.4i | 0.851592 | − | 1.47500i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18281.5 | − | 31664.5i | −0.669269 | − | 1.15921i | −0.978109 | − | 0.208093i | \(-0.933274\pi\) |
0.308840 | − | 0.951114i | \(-0.400059\pi\) | |||||||
\(908\) | −63549.6 | −2.32265 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −43644.1 | −1.58988 | ||||||||
\(911\) | 9963.46 | + | 17257.2i | 0.362354 | + | 0.627615i | 0.988348 | − | 0.152213i | \(-0.0486400\pi\) |
−0.625994 | + | 0.779828i | \(0.715307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4322.83 | − | 7487.37i | 0.156698 | − | 0.271408i | ||||
\(914\) | −6378.63 | + | 11048.1i | −0.230838 | + | 0.399824i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33139.1 | + | 57398.6i | 1.19536 | + | 2.07042i | ||||
\(917\) | 4751.26 | 0.171102 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48298.1 | 1.73363 | 0.866816 | − | 0.498628i | \(-0.166163\pi\) | ||||
0.866816 | + | 0.498628i | \(0.166163\pi\) | |||||||
\(920\) | −13283.8 | − | 23008.2i | −0.476036 | − | 0.824519i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −44329.6 | + | 76781.2i | −1.58343 | + | 2.74258i | ||||
\(923\) | −29140.2 | + | 50472.3i | −1.03918 | + | 1.79991i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6171.28 | − | 10689.0i | −0.219362 | − | 0.379947i | ||||
\(926\) | 55776.5 | 1.97941 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −244.718 | −0.00865652 | ||||||||
\(929\) | 7808.00 | + | 13523.9i | 0.275751 | + | 0.477614i | 0.970324 | − | 0.241808i | \(-0.0777403\pi\) |
−0.694574 | + | 0.719422i | \(0.744407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1212.95 | − | 2100.89i | 0.0426990 | − | 0.0739569i | ||||
\(932\) | 47283.2 | − | 81896.9i | 1.66182 | − | 2.87835i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24306.0 | + | 42099.2i | 0.851516 | + | 1.47487i | ||||
\(935\) | 52905.4 | 1.85047 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25030.1 | 0.872678 | 0.436339 | − | 0.899782i | \(-0.356275\pi\) | ||||
0.436339 | + | 0.899782i | \(0.356275\pi\) | |||||||
\(938\) | −11761.4 | − | 20371.3i | −0.409407 | − | 0.709113i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −31725.3 | + | 54949.8i | −1.10081 | + | 1.90667i | ||||
\(941\) | 8006.44 | − | 13867.6i | 0.277367 | − | 0.480414i | −0.693363 | − | 0.720589i | \(-0.743872\pi\) |
0.970730 | + | 0.240175i | \(0.0772049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1616.54 | + | 2799.92i | 0.0558236 | + | 0.0966894i | ||||
\(944\) | 322.855 | 0.0111314 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13847.1 | −0.475908 | ||||||||
\(947\) | −606.613 | − | 1050.69i | −0.0208155 | − | 0.0360535i | 0.855430 | − | 0.517918i | \(-0.173293\pi\) |
−0.876246 | + | 0.481865i | \(0.839960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −907.388 | + | 1571.64i | −0.0310380 | + | 0.0537594i | ||||
\(950\) | 16609.0 | − | 28767.7i | 0.567230 | − | 0.982471i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15799.5 | − | 27365.6i | −0.537885 | − | 0.931644i | ||||
\(953\) | 20143.9 | 0.684705 | 0.342352 | − | 0.939572i | \(-0.388776\pi\) | ||||
0.342352 | + | 0.939572i | \(0.388776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4410.92 | −0.149460 | ||||||||
\(956\) | 50549.1 | + | 87553.5i | 1.71012 | + | 2.96201i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18202.2 | − | 31527.1i | 0.613869 | − | 1.06325i | ||||
\(959\) | −6369.86 | + | 11032.9i | −0.214487 | + | 0.371503i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2123.40 | − | 3677.84i | −0.0712767 | − | 0.123455i | ||||
\(962\) | −35188.1 | −1.17932 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8141.32 | 0.272007 | ||||||||
\(965\) | 6813.31 | + | 11801.0i | 0.227283 | + | 0.393666i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13701.4 | + | 23731.5i | −0.455642 | + | 0.789196i | −0.998725 | − | 0.0504835i | \(-0.983924\pi\) |
0.543082 | + | 0.839679i | \(0.317257\pi\) | |||||||
\(968\) | 8277.34 | − | 14336.8i | 0.274839 | − | 0.476035i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 44360.4 | + | 76834.4i | 1.46838 | + | 2.54330i | ||||
\(971\) | 25837.8 | 0.853938 | 0.426969 | − | 0.904266i | \(-0.359581\pi\) | ||||
0.426969 | + | 0.904266i | \(0.359581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20430.7 | 0.673154 | ||||||||
\(974\) | −37911.2 | − | 65664.2i | −1.24718 | − | 2.16018i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24041.4 | + | 41641.0i | −0.788471 | + | 1.36567i | ||||
\(977\) | −11031.0 | + | 19106.2i | −0.361221 | + | 0.625653i | −0.988162 | − | 0.153414i | \(-0.950973\pi\) |
0.626941 | + | 0.779066i | \(0.284307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1701.76 | + | 2947.53i | 0.0555551 | + | 0.0962243i | ||||
\(980\) | −13065.3 | −0.425874 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 89028.3 | 2.89308 | ||||||||
\(983\) | −5900.89 | − | 10220.6i | −0.191464 | − | 0.331626i | 0.754271 | − | 0.656563i | \(-0.227990\pi\) |
−0.945736 | + | 0.324937i | \(0.894657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20229.6 | + | 35038.7i | −0.654385 | + | 1.13343i | ||||
\(986\) | −1522.59 | + | 2637.20i | −0.0491776 | + | 0.0851781i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31902.8 | − | 55257.3i | −1.02729 | − | 1.77932i | ||||
\(989\) | 3560.99 | 0.114492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46761.9 | −1.49893 | −0.749465 | − | 0.662044i | \(-0.769689\pi\) | ||||
−0.749465 | + | 0.662044i | \(0.769689\pi\) | |||||||
\(992\) | −3927.51 | − | 6802.65i | −0.125704 | − | 0.217726i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12947.8 | + | 22426.2i | −0.413157 | + | 0.715608i | ||||
\(995\) | −31780.5 | + | 55045.5i | −1.01257 | + | 1.75383i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19130.6 | + | 33135.1i | 0.607695 | + | 1.05256i | 0.991619 | + | 0.129194i | \(0.0412389\pi\) |
−0.383925 | + | 0.923364i | \(0.625428\pi\) | |||||||
\(998\) | −93168.6 | −2.95511 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.4.f.b.64.1 | 16 | ||
3.2 | odd | 2 | 63.4.f.b.22.8 | ✓ | 16 | ||
9.2 | odd | 6 | 63.4.f.b.43.8 | yes | 16 | ||
9.4 | even | 3 | 567.4.a.g.1.8 | 8 | |||
9.5 | odd | 6 | 567.4.a.i.1.1 | 8 | |||
9.7 | even | 3 | inner | 189.4.f.b.127.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.8 | ✓ | 16 | 3.2 | odd | 2 | ||
63.4.f.b.43.8 | yes | 16 | 9.2 | odd | 6 | ||
189.4.f.b.64.1 | 16 | 1.1 | even | 1 | trivial | ||
189.4.f.b.127.1 | 16 | 9.7 | even | 3 | inner | ||
567.4.a.g.1.8 | 8 | 9.4 | even | 3 | |||
567.4.a.i.1.1 | 8 | 9.5 | odd | 6 |