Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(41,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.b (of order \(2\), degree \(1\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.8 | ||
Root | \(-0.948735i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.41 |
Dual form | 105.4.b.b.41.9 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.948735i | − | 0.335429i | −0.985836 | − | 0.167714i | \(-0.946361\pi\) | ||
0.985836 | − | 0.167714i | \(-0.0536386\pi\) | |||||||
\(3\) | −4.24029 | − | 3.00332i | −0.816044 | − | 0.577989i | ||||
\(4\) | 7.09990 | 0.887488 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −2.84936 | + | 4.02291i | −0.193874 | + | 0.273725i | ||||
\(7\) | 15.4514 | + | 10.2104i | 0.834299 | + | 0.551312i | ||||
\(8\) | − | 14.3258i | − | 0.633117i | ||||||
\(9\) | 8.96014 | + | 25.4699i | 0.331857 | + | 0.943330i | ||||
\(10\) | − | 4.74368i | − | 0.150008i | ||||||
\(11\) | − | 22.6742i | − | 0.621501i | −0.950491 | − | 0.310751i | \(-0.899420\pi\) | ||
0.950491 | − | 0.310751i | \(-0.100580\pi\) | |||||||
\(12\) | −30.1056 | − | 21.3233i | −0.724229 | − | 0.512958i | ||||
\(13\) | − | 64.3163i | − | 1.37216i | −0.727525 | − | 0.686082i | \(-0.759329\pi\) | ||
0.727525 | − | 0.686082i | \(-0.240671\pi\) | |||||||
\(14\) | 9.68701 | − | 14.6593i | 0.184926 | − | 0.279848i | ||||
\(15\) | −21.2015 | − | 15.0166i | −0.364946 | − | 0.258485i | ||||
\(16\) | 43.2078 | 0.675122 | ||||||||
\(17\) | 9.57247 | 0.136569 | 0.0682843 | − | 0.997666i | \(-0.478248\pi\) | ||||
0.0682843 | + | 0.997666i | \(0.478248\pi\) | |||||||
\(18\) | 24.1642 | − | 8.50080i | 0.316420 | − | 0.111314i | ||||
\(19\) | − | 13.8330i | − | 0.167027i | −0.996507 | − | 0.0835134i | \(-0.973386\pi\) | ||
0.996507 | − | 0.0835134i | \(-0.0266141\pi\) | |||||||
\(20\) | 35.4995 | 0.396897 | ||||||||
\(21\) | −34.8534 | − | 89.7009i | −0.362173 | − | 0.932111i | ||||
\(22\) | −21.5118 | −0.208469 | ||||||||
\(23\) | − | 134.579i | − | 1.22007i | −0.792373 | − | 0.610037i | \(-0.791155\pi\) | ||
0.792373 | − | 0.610037i | \(-0.208845\pi\) | |||||||
\(24\) | −43.0250 | + | 60.7456i | −0.365935 | + | 0.516652i | ||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −61.0191 | −0.460263 | ||||||||
\(27\) | 38.5007 | − | 134.910i | 0.274424 | − | 0.961609i | ||||
\(28\) | 109.704 | + | 72.4931i | 0.740430 | + | 0.489283i | ||||
\(29\) | 194.631i | 1.24628i | 0.782111 | + | 0.623140i | \(0.214143\pi\) | ||||
−0.782111 | + | 0.623140i | \(0.785857\pi\) | |||||||
\(30\) | −14.2468 | + | 20.1146i | −0.0867031 | + | 0.122413i | ||||
\(31\) | 207.276i | 1.20090i | 0.799664 | + | 0.600448i | \(0.205011\pi\) | ||||
−0.799664 | + | 0.600448i | \(0.794989\pi\) | |||||||
\(32\) | − | 155.599i | − | 0.859573i | ||||||
\(33\) | −68.0978 | + | 96.1450i | −0.359221 | + | 0.507173i | ||||
\(34\) | − | 9.08174i | − | 0.0458090i | ||||||
\(35\) | 77.2572 | + | 51.0522i | 0.373110 | + | 0.246554i | ||||
\(36\) | 63.6161 | + | 180.834i | 0.294519 | + | 0.837193i | ||||
\(37\) | −171.473 | −0.761891 | −0.380946 | − | 0.924597i | \(-0.624401\pi\) | ||||
−0.380946 | + | 0.924597i | \(0.624401\pi\) | |||||||
\(38\) | −13.1239 | −0.0560256 | ||||||||
\(39\) | −193.162 | + | 272.720i | −0.793096 | + | 1.11975i | ||||
\(40\) | − | 71.6291i | − | 0.283139i | ||||||
\(41\) | 214.915 | 0.818635 | 0.409318 | − | 0.912392i | \(-0.365767\pi\) | ||||
0.409318 | + | 0.912392i | \(0.365767\pi\) | |||||||
\(42\) | −85.1024 | + | 33.0666i | −0.312657 | + | 0.121483i | ||||
\(43\) | −322.180 | −1.14260 | −0.571302 | − | 0.820740i | \(-0.693562\pi\) | ||||
−0.571302 | + | 0.820740i | \(0.693562\pi\) | |||||||
\(44\) | − | 160.984i | − | 0.551575i | ||||||
\(45\) | 44.8007 | + | 127.350i | 0.148411 | + | 0.421870i | ||||
\(46\) | −127.680 | −0.409248 | ||||||||
\(47\) | 582.288 | 1.80714 | 0.903569 | − | 0.428443i | \(-0.140938\pi\) | ||||
0.903569 | + | 0.428443i | \(0.140938\pi\) | |||||||
\(48\) | −183.214 | − | 129.767i | −0.550930 | − | 0.390213i | ||||
\(49\) | 134.494 | + | 315.532i | 0.392110 | + | 0.919918i | ||||
\(50\) | − | 23.7184i | − | 0.0670857i | ||||||
\(51\) | −40.5901 | − | 28.7492i | −0.111446 | − | 0.0789351i | ||||
\(52\) | − | 456.639i | − | 1.21778i | ||||||
\(53\) | 534.126i | 1.38430i | 0.721754 | + | 0.692150i | \(0.243336\pi\) | ||||
−0.721754 | + | 0.692150i | \(0.756664\pi\) | |||||||
\(54\) | −127.994 | − | 36.5270i | −0.322551 | − | 0.0920498i | ||||
\(55\) | − | 113.371i | − | 0.277944i | ||||||
\(56\) | 146.273 | − | 221.354i | 0.349045 | − | 0.528209i | ||||
\(57\) | −41.5450 | + | 58.6560i | −0.0965397 | + | 0.136301i | ||||
\(58\) | 184.653 | 0.418038 | ||||||||
\(59\) | −324.893 | −0.716907 | −0.358454 | − | 0.933548i | \(-0.616696\pi\) | ||||
−0.358454 | + | 0.933548i | \(0.616696\pi\) | |||||||
\(60\) | −150.528 | − | 106.616i | −0.323885 | − | 0.229402i | ||||
\(61\) | − | 32.4225i | − | 0.0680538i | −0.999421 | − | 0.0340269i | \(-0.989167\pi\) | ||
0.999421 | − | 0.0340269i | \(-0.0108332\pi\) | |||||||
\(62\) | 196.650 | 0.402815 | ||||||||
\(63\) | −121.612 | + | 485.034i | −0.243201 | + | 0.969976i | ||||
\(64\) | 198.040 | 0.386797 | ||||||||
\(65\) | − | 321.581i | − | 0.613650i | ||||||
\(66\) | 91.2162 | + | 64.6067i | 0.170120 | + | 0.120493i | ||||
\(67\) | −781.863 | −1.42567 | −0.712834 | − | 0.701333i | \(-0.752589\pi\) | ||||
−0.712834 | + | 0.701333i | \(0.752589\pi\) | |||||||
\(68\) | 67.9636 | 0.121203 | ||||||||
\(69\) | −404.184 | + | 570.655i | −0.705190 | + | 0.995635i | ||||
\(70\) | 48.4350 | − | 73.2966i | 0.0827013 | − | 0.125152i | ||||
\(71\) | − | 357.938i | − | 0.598302i | −0.954206 | − | 0.299151i | \(-0.903297\pi\) | ||
0.954206 | − | 0.299151i | \(-0.0967034\pi\) | |||||||
\(72\) | 364.877 | − | 128.361i | 0.597238 | − | 0.210104i | ||||
\(73\) | 925.788i | 1.48432i | 0.670224 | + | 0.742159i | \(0.266198\pi\) | ||||
−0.670224 | + | 0.742159i | \(0.733802\pi\) | |||||||
\(74\) | 162.682i | 0.255560i | ||||||||
\(75\) | −106.007 | − | 75.0830i | −0.163209 | − | 0.115598i | ||||
\(76\) | − | 98.2130i | − | 0.148234i | ||||||
\(77\) | 231.513 | − | 350.348i | 0.342641 | − | 0.518518i | ||||
\(78\) | 258.739 | + | 183.260i | 0.375595 | + | 0.266027i | ||||
\(79\) | 827.285 | 1.17819 | 0.589094 | − | 0.808064i | \(-0.299485\pi\) | ||||
0.589094 | + | 0.808064i | \(0.299485\pi\) | |||||||
\(80\) | 216.039 | 0.301924 | ||||||||
\(81\) | −568.432 | + | 456.428i | −0.779742 | + | 0.626101i | ||||
\(82\) | − | 203.897i | − | 0.274594i | ||||||
\(83\) | −131.055 | −0.173315 | −0.0866575 | − | 0.996238i | \(-0.527619\pi\) | ||||
−0.0866575 | + | 0.996238i | \(0.527619\pi\) | |||||||
\(84\) | −247.455 | − | 636.867i | −0.321424 | − | 0.827237i | ||||
\(85\) | 47.8624 | 0.0610753 | ||||||||
\(86\) | 305.664i | 0.383262i | ||||||||
\(87\) | 584.540 | − | 825.293i | 0.720336 | − | 1.01702i | ||||
\(88\) | −324.826 | −0.393483 | ||||||||
\(89\) | −505.040 | −0.601508 | −0.300754 | − | 0.953702i | \(-0.597238\pi\) | ||||
−0.300754 | + | 0.953702i | \(0.597238\pi\) | |||||||
\(90\) | 120.821 | − | 42.5040i | 0.141507 | − | 0.0497813i | ||||
\(91\) | 656.698 | − | 993.779i | 0.756490 | − | 1.14479i | ||||
\(92\) | − | 955.499i | − | 1.08280i | ||||||
\(93\) | 622.515 | − | 878.909i | 0.694105 | − | 0.979985i | ||||
\(94\) | − | 552.437i | − | 0.606166i | ||||||
\(95\) | − | 69.1650i | − | 0.0746967i | ||||||
\(96\) | −467.314 | + | 659.786i | −0.496824 | + | 0.701449i | ||||
\(97\) | 86.3424i | 0.0903788i | 0.998978 | + | 0.0451894i | \(0.0143891\pi\) | ||||
−0.998978 | + | 0.0451894i | \(0.985611\pi\) | |||||||
\(98\) | 299.356 | − | 127.599i | 0.308567 | − | 0.131525i | ||||
\(99\) | 577.509 | − | 203.164i | 0.586281 | − | 0.206250i | ||||
\(100\) | 177.498 | 0.177498 | ||||||||
\(101\) | −895.757 | −0.882486 | −0.441243 | − | 0.897388i | \(-0.645462\pi\) | ||||
−0.441243 | + | 0.897388i | \(0.645462\pi\) | |||||||
\(102\) | −27.2754 | + | 38.5092i | −0.0264771 | + | 0.0373822i | ||||
\(103\) | − | 486.200i | − | 0.465114i | −0.972583 | − | 0.232557i | \(-0.925291\pi\) | ||
0.972583 | − | 0.232557i | \(-0.0747092\pi\) | |||||||
\(104\) | −921.383 | −0.868740 | ||||||||
\(105\) | −174.267 | − | 448.504i | −0.161969 | − | 0.416853i | ||||
\(106\) | 506.744 | 0.464334 | ||||||||
\(107\) | − | 728.790i | − | 0.658456i | −0.944250 | − | 0.329228i | \(-0.893212\pi\) | ||
0.944250 | − | 0.329228i | \(-0.106788\pi\) | |||||||
\(108\) | 273.351 | − | 957.847i | 0.243548 | − | 0.853416i | ||||
\(109\) | −1064.25 | −0.935197 | −0.467599 | − | 0.883941i | \(-0.654881\pi\) | ||||
−0.467599 | + | 0.883941i | \(0.654881\pi\) | |||||||
\(110\) | −107.559 | −0.0932303 | ||||||||
\(111\) | 727.095 | + | 514.988i | 0.621737 | + | 0.440365i | ||||
\(112\) | 667.623 | + | 441.171i | 0.563254 | + | 0.372203i | ||||
\(113\) | 1991.46i | 1.65788i | 0.559335 | + | 0.828941i | \(0.311056\pi\) | ||||
−0.559335 | + | 0.828941i | \(0.688944\pi\) | |||||||
\(114\) | 55.6490 | + | 39.4152i | 0.0457194 | + | 0.0323822i | ||||
\(115\) | − | 672.896i | − | 0.545634i | ||||||
\(116\) | 1381.86i | 1.10606i | ||||||||
\(117\) | 1638.13 | − | 576.283i | 1.29440 | − | 0.455362i | ||||
\(118\) | 308.238i | 0.240471i | ||||||||
\(119\) | 147.908 | + | 97.7392i | 0.113939 | + | 0.0752919i | ||||
\(120\) | −215.125 | + | 303.728i | −0.163651 | + | 0.231054i | ||||
\(121\) | 816.883 | 0.613736 | ||||||||
\(122\) | −30.7604 | −0.0228272 | ||||||||
\(123\) | −911.301 | − | 645.458i | −0.668043 | − | 0.473162i | ||||
\(124\) | 1471.64i | 1.06578i | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 460.168 | + | 115.378i | 0.325358 | + | 0.0815766i | ||||
\(127\) | −1019.14 | −0.712081 | −0.356041 | − | 0.934471i | \(-0.615874\pi\) | ||||
−0.356041 | + | 0.934471i | \(0.615874\pi\) | |||||||
\(128\) | − | 1432.68i | − | 0.989315i | ||||||
\(129\) | 1366.14 | + | 967.610i | 0.932416 | + | 0.660413i | ||||
\(130\) | −305.096 | −0.205836 | ||||||||
\(131\) | −2187.34 | −1.45885 | −0.729424 | − | 0.684062i | \(-0.760212\pi\) | ||||
−0.729424 | + | 0.684062i | \(0.760212\pi\) | |||||||
\(132\) | −483.487 | + | 682.620i | −0.318804 | + | 0.450110i | ||||
\(133\) | 141.241 | − | 213.740i | 0.0920839 | − | 0.139350i | ||||
\(134\) | 741.781i | 0.478210i | ||||||||
\(135\) | 192.503 | − | 674.550i | 0.122726 | − | 0.430044i | ||||
\(136\) | − | 137.133i | − | 0.0864639i | ||||||
\(137\) | 2492.50i | 1.55437i | 0.629274 | + | 0.777184i | \(0.283353\pi\) | ||||
−0.629274 | + | 0.777184i | \(0.716647\pi\) | |||||||
\(138\) | 541.401 | + | 383.464i | 0.333964 | + | 0.236541i | ||||
\(139\) | 1432.68i | 0.874234i | 0.899405 | + | 0.437117i | \(0.144000\pi\) | ||||
−0.899405 | + | 0.437117i | \(0.856000\pi\) | |||||||
\(140\) | 548.518 | + | 362.466i | 0.331130 | + | 0.218814i | ||||
\(141\) | −2469.07 | − | 1748.80i | −1.47470 | − | 1.04451i | ||||
\(142\) | −339.588 | −0.200688 | ||||||||
\(143\) | −1458.32 | −0.852802 | ||||||||
\(144\) | 387.148 | + | 1100.50i | 0.224044 | + | 0.636863i | ||||
\(145\) | 973.156i | 0.557353i | ||||||||
\(146\) | 878.327 | 0.497883 | ||||||||
\(147\) | 377.351 | − | 1741.88i | 0.211724 | − | 0.977330i | ||||
\(148\) | −1217.44 | −0.676169 | ||||||||
\(149\) | 1519.04i | 0.835198i | 0.908632 | + | 0.417599i | \(0.137128\pi\) | ||||
−0.908632 | + | 0.417599i | \(0.862872\pi\) | |||||||
\(150\) | −71.2339 | + | 100.573i | −0.0387748 | + | 0.0547449i | ||||
\(151\) | 83.5248 | 0.0450142 | 0.0225071 | − | 0.999747i | \(-0.492835\pi\) | ||||
0.0225071 | + | 0.999747i | \(0.492835\pi\) | |||||||
\(152\) | −198.169 | −0.105748 | ||||||||
\(153\) | 85.7707 | + | 243.810i | 0.0453212 | + | 0.128829i | ||||
\(154\) | −332.388 | − | 219.645i | −0.173926 | − | 0.114932i | ||||
\(155\) | 1036.38i | 0.537057i | ||||||||
\(156\) | −1371.43 | + | 1936.28i | −0.703863 | + | 0.993761i | ||||
\(157\) | 1716.82i | 0.872719i | 0.899772 | + | 0.436360i | \(0.143732\pi\) | ||||
−0.899772 | + | 0.436360i | \(0.856268\pi\) | |||||||
\(158\) | − | 784.875i | − | 0.395198i | ||||||
\(159\) | 1604.15 | − | 2264.85i | 0.800110 | − | 1.12965i | ||||
\(160\) | − | 777.996i | − | 0.384413i | ||||||
\(161\) | 1374.11 | − | 2079.44i | 0.672642 | − | 1.01791i | ||||
\(162\) | 433.029 | + | 539.291i | 0.210012 | + | 0.261548i | ||||
\(163\) | 2329.29 | 1.11929 | 0.559643 | − | 0.828734i | \(-0.310938\pi\) | ||||
0.559643 | + | 0.828734i | \(0.310938\pi\) | |||||||
\(164\) | 1525.87 | 0.726529 | ||||||||
\(165\) | −340.489 | + | 480.725i | −0.160649 | + | 0.226815i | ||||
\(166\) | 124.336i | 0.0581348i | ||||||||
\(167\) | −774.390 | −0.358827 | −0.179413 | − | 0.983774i | \(-0.557420\pi\) | ||||
−0.179413 | + | 0.983774i | \(0.557420\pi\) | |||||||
\(168\) | −1285.04 | + | 499.303i | −0.590136 | + | 0.229298i | ||||
\(169\) | −1939.58 | −0.882832 | ||||||||
\(170\) | − | 45.4087i | − | 0.0204864i | ||||||
\(171\) | 352.325 | − | 123.946i | 0.157561 | − | 0.0554290i | ||||
\(172\) | −2287.45 | −1.01405 | ||||||||
\(173\) | −1593.30 | −0.700212 | −0.350106 | − | 0.936710i | \(-0.613854\pi\) | ||||
−0.350106 | + | 0.936710i | \(0.613854\pi\) | |||||||
\(174\) | −782.984 | − | 554.573i | −0.341137 | − | 0.241621i | ||||
\(175\) | 386.286 | + | 255.261i | 0.166860 | + | 0.110262i | ||||
\(176\) | − | 979.701i | − | 0.419589i | ||||||
\(177\) | 1377.64 | + | 975.759i | 0.585028 | + | 0.414365i | ||||
\(178\) | 479.150i | 0.201763i | ||||||||
\(179\) | − | 1433.50i | − | 0.598576i | −0.954163 | − | 0.299288i | \(-0.903251\pi\) | ||
0.954163 | − | 0.299288i | \(-0.0967492\pi\) | |||||||
\(180\) | 318.080 | + | 904.169i | 0.131713 | + | 0.374404i | ||||
\(181\) | − | 4655.24i | − | 1.91172i | −0.293825 | − | 0.955859i | \(-0.594928\pi\) | ||
0.293825 | − | 0.955859i | \(-0.405072\pi\) | |||||||
\(182\) | −942.833 | − | 623.032i | −0.383997 | − | 0.253748i | ||||
\(183\) | −97.3752 | + | 137.481i | −0.0393343 | + | 0.0555349i | ||||
\(184\) | −1927.96 | −0.772450 | ||||||||
\(185\) | −857.365 | −0.340728 | ||||||||
\(186\) | −833.852 | − | 590.602i | −0.328715 | − | 0.232823i | ||||
\(187\) | − | 217.048i | − | 0.0848775i | ||||||
\(188\) | 4134.19 | 1.60381 | ||||||||
\(189\) | 1972.38 | − | 1691.44i | 0.759098 | − | 0.650976i | ||||
\(190\) | −65.6193 | −0.0250554 | ||||||||
\(191\) | 1104.23i | 0.418322i | 0.977881 | + | 0.209161i | \(0.0670732\pi\) | ||||
−0.977881 | + | 0.209161i | \(0.932927\pi\) | |||||||
\(192\) | −839.747 | − | 594.777i | −0.315643 | − | 0.223564i | ||||
\(193\) | 1575.84 | 0.587726 | 0.293863 | − | 0.955848i | \(-0.405059\pi\) | ||||
0.293863 | + | 0.955848i | \(0.405059\pi\) | |||||||
\(194\) | 81.9161 | 0.0303156 | ||||||||
\(195\) | −965.812 | + | 1363.60i | −0.354683 | + | 0.500766i | ||||
\(196\) | 954.892 | + | 2240.25i | 0.347993 | + | 0.816416i | ||||
\(197\) | − | 373.569i | − | 0.135105i | −0.997716 | − | 0.0675525i | \(-0.978481\pi\) | ||
0.997716 | − | 0.0675525i | \(-0.0215190\pi\) | |||||||
\(198\) | −192.748 | − | 547.903i | −0.0691820 | − | 0.196655i | ||||
\(199\) | 419.925i | 0.149586i | 0.997199 | + | 0.0747931i | \(0.0238296\pi\) | ||||
−0.997199 | + | 0.0747931i | \(0.976170\pi\) | |||||||
\(200\) | − | 358.145i | − | 0.126623i | ||||||
\(201\) | 3315.33 | + | 2348.18i | 1.16341 | + | 0.824021i | ||||
\(202\) | 849.836i | 0.296011i | ||||||||
\(203\) | −1987.27 | + | 3007.33i | −0.687089 | + | 1.03977i | ||||
\(204\) | −288.185 | − | 204.116i | −0.0989069 | − | 0.0700540i | ||||
\(205\) | 1074.57 | 0.366105 | ||||||||
\(206\) | −461.275 | −0.156013 | ||||||||
\(207\) | 3427.72 | − | 1205.85i | 1.15093 | − | 0.404890i | ||||
\(208\) | − | 2778.96i | − | 0.926378i | ||||||
\(209\) | −313.652 | −0.103807 | ||||||||
\(210\) | −425.512 | + | 165.333i | −0.139824 | + | 0.0543289i | ||||
\(211\) | 5139.58 | 1.67689 | 0.838443 | − | 0.544989i | \(-0.183466\pi\) | ||||
0.838443 | + | 0.544989i | \(0.183466\pi\) | |||||||
\(212\) | 3792.24i | 1.22855i | ||||||||
\(213\) | −1075.00 | + | 1517.76i | −0.345812 | + | 0.488241i | ||||
\(214\) | −691.429 | −0.220865 | ||||||||
\(215\) | −1610.90 | −0.510988 | ||||||||
\(216\) | −1932.69 | − | 551.553i | −0.608811 | − | 0.173743i | ||||
\(217\) | −2116.37 | + | 3202.71i | −0.662069 | + | 1.00191i | ||||
\(218\) | 1009.69i | 0.313692i | ||||||||
\(219\) | 2780.44 | − | 3925.61i | 0.857920 | − | 1.21127i | ||||
\(220\) | − | 804.921i | − | 0.246672i | ||||||
\(221\) | − | 615.666i | − | 0.187394i | ||||||
\(222\) | 488.587 | − | 689.821i | 0.147711 | − | 0.208548i | ||||
\(223\) | − | 2700.19i | − | 0.810843i | −0.914130 | − | 0.405422i | \(-0.867125\pi\) | ||
0.914130 | − | 0.405422i | \(-0.132875\pi\) | |||||||
\(224\) | 1588.74 | − | 2404.23i | 0.473893 | − | 0.717141i | ||||
\(225\) | 224.003 | + | 636.748i | 0.0663714 | + | 0.188666i | ||||
\(226\) | 1889.37 | 0.556101 | ||||||||
\(227\) | −2992.08 | −0.874852 | −0.437426 | − | 0.899254i | \(-0.644110\pi\) | ||||
−0.437426 | + | 0.899254i | \(0.644110\pi\) | |||||||
\(228\) | −294.965 | + | 416.452i | −0.0856778 | + | 0.120966i | ||||
\(229\) | − | 3637.31i | − | 1.04961i | −0.851224 | − | 0.524803i | \(-0.824139\pi\) | ||
0.851224 | − | 0.524803i | \(-0.175861\pi\) | |||||||
\(230\) | −638.400 | −0.183021 | ||||||||
\(231\) | −2033.89 | + | 790.271i | −0.579308 | + | 0.225091i | ||||
\(232\) | 2788.25 | 0.789041 | ||||||||
\(233\) | − | 6001.00i | − | 1.68729i | −0.536901 | − | 0.843645i | \(-0.680405\pi\) | ||
0.536901 | − | 0.843645i | \(-0.319595\pi\) | |||||||
\(234\) | −546.740 | − | 1554.15i | −0.152741 | − | 0.434180i | ||||
\(235\) | 2911.44 | 0.808176 | ||||||||
\(236\) | −2306.71 | −0.636246 | ||||||||
\(237\) | −3507.93 | − | 2484.60i | −0.961454 | − | 0.680980i | ||||
\(238\) | 92.7286 | − | 140.326i | 0.0252551 | − | 0.0382184i | ||||
\(239\) | − | 5173.92i | − | 1.40031i | −0.713992 | − | 0.700153i | \(-0.753115\pi\) | ||
0.713992 | − | 0.700153i | \(-0.246885\pi\) | |||||||
\(240\) | −916.068 | − | 648.834i | −0.246383 | − | 0.174509i | ||||
\(241\) | − | 729.389i | − | 0.194955i | −0.995238 | − | 0.0974773i | \(-0.968923\pi\) | ||
0.995238 | − | 0.0974773i | \(-0.0310774\pi\) | |||||||
\(242\) | − | 775.005i | − | 0.205865i | ||||||
\(243\) | 3781.11 | − | 228.203i | 0.998184 | − | 0.0602439i | ||||
\(244\) | − | 230.197i | − | 0.0603969i | ||||||
\(245\) | 672.469 | + | 1577.66i | 0.175357 | + | 0.411400i | ||||
\(246\) | −612.369 | + | 864.584i | −0.158712 | + | 0.224081i | ||||
\(247\) | −889.688 | −0.229188 | ||||||||
\(248\) | 2969.39 | 0.760308 | ||||||||
\(249\) | 555.711 | + | 393.600i | 0.141433 | + | 0.100174i | ||||
\(250\) | − | 118.592i | − | 0.0300016i | ||||||
\(251\) | 6404.70 | 1.61060 | 0.805301 | − | 0.592866i | \(-0.202004\pi\) | ||||
0.805301 | + | 0.592866i | \(0.202004\pi\) | |||||||
\(252\) | −863.433 | + | 3443.69i | −0.215838 | + | 0.860842i | ||||
\(253\) | −3051.47 | −0.758278 | ||||||||
\(254\) | 966.897i | 0.238852i | ||||||||
\(255\) | −202.950 | − | 143.746i | −0.0498402 | − | 0.0353009i | ||||
\(256\) | 225.084 | 0.0549521 | ||||||||
\(257\) | −4199.90 | −1.01939 | −0.509694 | − | 0.860356i | \(-0.670241\pi\) | ||||
−0.509694 | + | 0.860356i | \(0.670241\pi\) | |||||||
\(258\) | 918.006 | − | 1296.10i | 0.221521 | − | 0.312759i | ||||
\(259\) | −2649.50 | − | 1750.81i | −0.635645 | − | 0.420040i | ||||
\(260\) | − | 2283.20i | − | 0.544607i | ||||||
\(261\) | −4957.24 | + | 1743.92i | −1.17565 | + | 0.413586i | ||||
\(262\) | 2075.21i | 0.489339i | ||||||||
\(263\) | 1003.82i | 0.235353i | 0.993052 | + | 0.117677i | \(0.0375447\pi\) | ||||
−0.993052 | + | 0.117677i | \(0.962455\pi\) | |||||||
\(264\) | 1377.36 | + | 975.556i | 0.321100 | + | 0.227429i | ||||
\(265\) | 2670.63i | 0.619077i | ||||||||
\(266\) | −202.783 | − | 134.000i | −0.0467421 | − | 0.0308876i | ||||
\(267\) | 2141.52 | + | 1516.80i | 0.490857 | + | 0.347665i | ||||
\(268\) | −5551.15 | −1.26526 | ||||||||
\(269\) | 7904.46 | 1.79161 | 0.895805 | − | 0.444447i | \(-0.146600\pi\) | ||||
0.895805 | + | 0.444447i | \(0.146600\pi\) | |||||||
\(270\) | −639.969 | − | 182.635i | −0.144249 | − | 0.0411659i | ||||
\(271\) | − | 2525.75i | − | 0.566157i | −0.959097 | − | 0.283079i | \(-0.908644\pi\) | ||
0.959097 | − | 0.283079i | \(-0.0913557\pi\) | |||||||
\(272\) | 413.605 | 0.0922004 | ||||||||
\(273\) | −5769.22 | + | 2241.64i | −1.27901 | + | 0.496960i | ||||
\(274\) | 2364.72 | 0.521379 | ||||||||
\(275\) | − | 566.854i | − | 0.124300i | ||||||
\(276\) | −2869.67 | + | 4051.59i | −0.625847 | + | 0.883614i | ||||
\(277\) | 329.076 | 0.0713801 | 0.0356900 | − | 0.999363i | \(-0.488637\pi\) | ||||
0.0356900 | + | 0.999363i | \(0.488637\pi\) | |||||||
\(278\) | 1359.24 | 0.293243 | ||||||||
\(279\) | −5279.29 | + | 1857.22i | −1.13284 | + | 0.398526i | ||||
\(280\) | 731.364 | − | 1106.77i | 0.156098 | − | 0.236222i | ||||
\(281\) | 445.607i | 0.0946002i | 0.998881 | + | 0.0473001i | \(0.0150617\pi\) | ||||
−0.998881 | + | 0.0473001i | \(0.984938\pi\) | |||||||
\(282\) | −1659.15 | + | 2342.50i | −0.350357 | + | 0.494658i | ||||
\(283\) | 2885.26i | 0.606047i | 0.952983 | + | 0.303023i | \(0.0979960\pi\) | ||||
−0.952983 | + | 0.303023i | \(0.902004\pi\) | |||||||
\(284\) | − | 2541.32i | − | 0.530985i | ||||||
\(285\) | −207.725 | + | 293.280i | −0.0431739 | + | 0.0609558i | ||||
\(286\) | 1383.56i | 0.286054i | ||||||||
\(287\) | 3320.74 | + | 2194.37i | 0.682987 | + | 0.451324i | ||||
\(288\) | 3963.10 | − | 1394.19i | 0.810860 | − | 0.285255i | ||||
\(289\) | −4821.37 | −0.981349 | ||||||||
\(290\) | 923.267 | 0.186952 | ||||||||
\(291\) | 259.314 | − | 366.117i | 0.0522379 | − | 0.0737531i | ||||
\(292\) | 6573.00i | 1.31731i | ||||||||
\(293\) | 7104.19 | 1.41649 | 0.708245 | − | 0.705967i | \(-0.249487\pi\) | ||||
0.708245 | + | 0.705967i | \(0.249487\pi\) | |||||||
\(294\) | −1652.58 | − | 358.006i | −0.327824 | − | 0.0710181i | ||||
\(295\) | −1624.47 | −0.320611 | ||||||||
\(296\) | 2456.49i | 0.482366i | ||||||||
\(297\) | −3058.97 | − | 872.970i | −0.597641 | − | 0.170555i | ||||
\(298\) | 1441.17 | 0.280149 | ||||||||
\(299\) | −8655.63 | −1.67414 | ||||||||
\(300\) | −752.641 | − | 533.082i | −0.144846 | − | 0.102592i | ||||
\(301\) | −4978.14 | − | 3289.60i | −0.953274 | − | 0.629932i | ||||
\(302\) | − | 79.2429i | − | 0.0150991i | ||||||
\(303\) | 3798.27 | + | 2690.24i | 0.720148 | + | 0.510068i | ||||
\(304\) | − | 597.694i | − | 0.112763i | ||||||
\(305\) | − | 162.113i | − | 0.0304346i | ||||||
\(306\) | 231.311 | − | 81.3737i | 0.0432130 | − | 0.0152020i | ||||
\(307\) | 1618.65i | 0.300916i | 0.988616 | + | 0.150458i | \(0.0480748\pi\) | ||||
−0.988616 | + | 0.150458i | \(0.951925\pi\) | |||||||
\(308\) | 1643.72 | − | 2487.44i | 0.304090 | − | 0.460178i | ||||
\(309\) | −1460.22 | + | 2061.63i | −0.268831 | + | 0.379554i | ||||
\(310\) | 983.248 | 0.180144 | ||||||||
\(311\) | 2623.36 | 0.478318 | 0.239159 | − | 0.970980i | \(-0.423128\pi\) | ||||
0.239159 | + | 0.970980i | \(0.423128\pi\) | |||||||
\(312\) | 3906.93 | + | 2767.21i | 0.708931 | + | 0.502123i | ||||
\(313\) | 5619.16i | 1.01474i | 0.861728 | + | 0.507371i | \(0.169382\pi\) | ||||
−0.861728 | + | 0.507371i | \(0.830618\pi\) | |||||||
\(314\) | 1628.81 | 0.292735 | ||||||||
\(315\) | −608.060 | + | 2425.17i | −0.108763 | + | 0.433786i | ||||
\(316\) | 5873.64 | 1.04563 | ||||||||
\(317\) | 2281.14i | 0.404169i | 0.979368 | + | 0.202084i | \(0.0647715\pi\) | ||||
−0.979368 | + | 0.202084i | \(0.935228\pi\) | |||||||
\(318\) | −2148.74 | − | 1521.92i | −0.378917 | − | 0.268380i | ||||
\(319\) | 4413.10 | 0.774564 | ||||||||
\(320\) | 990.200 | 0.172981 | ||||||||
\(321\) | −2188.79 | + | 3090.28i | −0.380581 | + | 0.537329i | ||||
\(322\) | −1972.84 | − | 1303.67i | −0.341435 | − | 0.225623i | ||||
\(323\) | − | 132.416i | − | 0.0228106i | ||||||
\(324\) | −4035.81 | + | 3240.59i | −0.692011 | + | 0.555657i | ||||
\(325\) | − | 1607.91i | − | 0.274433i | ||||||
\(326\) | − | 2209.88i | − | 0.375441i | ||||||
\(327\) | 4512.72 | + | 3196.28i | 0.763162 | + | 0.540534i | ||||
\(328\) | − | 3078.83i | − | 0.518292i | ||||||
\(329\) | 8997.19 | + | 5945.42i | 1.50769 | + | 0.996297i | ||||
\(330\) | 456.081 | + | 323.034i | 0.0760801 | + | 0.0538861i | ||||
\(331\) | −270.671 | −0.0449468 | −0.0224734 | − | 0.999747i | \(-0.507154\pi\) | ||||
−0.0224734 | + | 0.999747i | \(0.507154\pi\) | |||||||
\(332\) | −930.477 | −0.153815 | ||||||||
\(333\) | −1536.42 | − | 4367.40i | −0.252839 | − | 0.718715i | ||||
\(334\) | 734.691i | 0.120361i | ||||||||
\(335\) | −3909.31 | −0.637578 | ||||||||
\(336\) | −1505.94 | − | 3875.78i | −0.244511 | − | 0.629289i | ||||
\(337\) | −4842.16 | −0.782698 | −0.391349 | − | 0.920242i | \(-0.627991\pi\) | ||||
−0.391349 | + | 0.920242i | \(0.627991\pi\) | |||||||
\(338\) | 1840.15i | 0.296127i | ||||||||
\(339\) | 5980.99 | − | 8444.37i | 0.958238 | − | 1.35291i | ||||
\(340\) | 339.818 | 0.0542036 | ||||||||
\(341\) | 4699.80 | 0.746359 | ||||||||
\(342\) | −117.592 | − | 334.264i | −0.0185925 | − | 0.0528506i | ||||
\(343\) | −1143.60 | + | 6248.66i | −0.180025 | + | 0.983662i | ||||
\(344\) | 4615.49i | 0.723403i | ||||||||
\(345\) | −2020.92 | + | 2853.28i | −0.315370 | + | 0.445261i | ||||
\(346\) | 1511.62i | 0.234871i | ||||||||
\(347\) | − | 9182.70i | − | 1.42061i | −0.703892 | − | 0.710307i | \(-0.748556\pi\) | ||
0.703892 | − | 0.710307i | \(-0.251444\pi\) | |||||||
\(348\) | 4150.17 | − | 5859.50i | 0.639289 | − | 0.902592i | ||||
\(349\) | 11353.5i | 1.74138i | 0.491832 | + | 0.870690i | \(0.336327\pi\) | ||||
−0.491832 | + | 0.870690i | \(0.663673\pi\) | |||||||
\(350\) | 242.175 | − | 366.483i | 0.0369852 | − | 0.0559696i | ||||
\(351\) | −8676.91 | − | 2476.22i | −1.31948 | − | 0.376555i | ||||
\(352\) | −3528.08 | −0.534226 | ||||||||
\(353\) | −12645.6 | −1.90669 | −0.953343 | − | 0.301890i | \(-0.902382\pi\) | ||||
−0.953343 | + | 0.301890i | \(0.902382\pi\) | |||||||
\(354\) | 925.737 | − | 1307.02i | 0.138990 | − | 0.196235i | ||||
\(355\) | − | 1789.69i | − | 0.267569i | ||||||
\(356\) | −3585.74 | −0.533831 | ||||||||
\(357\) | −333.633 | − | 858.659i | −0.0494614 | − | 0.127297i | ||||
\(358\) | −1360.02 | −0.200780 | ||||||||
\(359\) | − | 1779.92i | − | 0.261673i | −0.991404 | − | 0.130836i | \(-0.958234\pi\) | ||
0.991404 | − | 0.130836i | \(-0.0417663\pi\) | |||||||
\(360\) | 1824.38 | − | 641.806i | 0.267093 | − | 0.0939615i | ||||
\(361\) | 6667.65 | 0.972102 | ||||||||
\(362\) | −4416.59 | −0.641245 | ||||||||
\(363\) | −3463.82 | − | 2453.36i | −0.500836 | − | 0.354733i | ||||
\(364\) | 4662.49 | − | 7055.73i | 0.671376 | − | 1.01599i | ||||
\(365\) | 4628.94i | 0.663807i | ||||||||
\(366\) | 130.433 | + | 92.3833i | 0.0186280 | + | 0.0131939i | ||||
\(367\) | − | 11678.2i | − | 1.66102i | −0.557003 | − | 0.830510i | \(-0.688049\pi\) | ||
0.557003 | − | 0.830510i | \(-0.311951\pi\) | |||||||
\(368\) | − | 5814.87i | − | 0.823699i | ||||||
\(369\) | 1925.67 | + | 5473.86i | 0.271670 | + | 0.772243i | ||||
\(370\) | 813.412i | 0.114290i | ||||||||
\(371\) | −5453.66 | + | 8253.01i | −0.763181 | + | 1.15492i | ||||
\(372\) | 4419.79 | − | 6240.16i | 0.616010 | − | 0.869724i | ||||
\(373\) | −3272.51 | −0.454273 | −0.227137 | − | 0.973863i | \(-0.572936\pi\) | ||||
−0.227137 | + | 0.973863i | \(0.572936\pi\) | |||||||
\(374\) | −205.921 | −0.0284704 | ||||||||
\(375\) | −530.036 | − | 375.415i | −0.0729892 | − | 0.0516969i | ||||
\(376\) | − | 8341.75i | − | 1.14413i | ||||||
\(377\) | 12517.9 | 1.71010 | ||||||||
\(378\) | −1604.73 | − | 1871.27i | −0.218356 | − | 0.254623i | ||||
\(379\) | −617.624 | −0.0837077 | −0.0418538 | − | 0.999124i | \(-0.513326\pi\) | ||||
−0.0418538 | + | 0.999124i | \(0.513326\pi\) | |||||||
\(380\) | − | 491.065i | − | 0.0662924i | ||||||
\(381\) | 4321.46 | + | 3060.81i | 0.581090 | + | 0.411575i | ||||
\(382\) | 1047.62 | 0.140317 | ||||||||
\(383\) | −9244.28 | −1.23332 | −0.616659 | − | 0.787230i | \(-0.711514\pi\) | ||||
−0.616659 | + | 0.787230i | \(0.711514\pi\) | |||||||
\(384\) | −4302.80 | + | 6074.99i | −0.571814 | + | 0.807325i | ||||
\(385\) | 1157.57 | − | 1751.74i | 0.153234 | − | 0.231888i | ||||
\(386\) | − | 1495.05i | − | 0.197140i | ||||||
\(387\) | −2886.78 | − | 8205.89i | −0.379181 | − | 1.07785i | ||||
\(388\) | 613.022i | 0.0802100i | ||||||||
\(389\) | 1016.89i | 0.132541i | 0.997802 | + | 0.0662706i | \(0.0211101\pi\) | ||||
−0.997802 | + | 0.0662706i | \(0.978890\pi\) | |||||||
\(390\) | 1293.69 | + | 916.300i | 0.167971 | + | 0.118971i | ||||
\(391\) | − | 1288.26i | − | 0.166624i | ||||||
\(392\) | 4520.25 | − | 1926.73i | 0.582416 | − | 0.248252i | ||||
\(393\) | 9274.98 | + | 6569.29i | 1.19049 | + | 0.843199i | ||||
\(394\) | −354.418 | −0.0453181 | ||||||||
\(395\) | 4136.43 | 0.526902 | ||||||||
\(396\) | 4100.25 | − | 1442.44i | 0.520317 | − | 0.183044i | ||||
\(397\) | 4603.25i | 0.581941i | 0.956732 | + | 0.290971i | \(0.0939782\pi\) | ||||
−0.956732 | + | 0.290971i | \(0.906022\pi\) | |||||||
\(398\) | 398.397 | 0.0501755 | ||||||||
\(399\) | −1240.83 | + | 482.127i | −0.155688 | + | 0.0604926i | ||||
\(400\) | 1080.20 | 0.135024 | ||||||||
\(401\) | − | 6522.49i | − | 0.812263i | −0.913815 | − | 0.406132i | \(-0.866877\pi\) | ||
0.913815 | − | 0.406132i | \(-0.133123\pi\) | |||||||
\(402\) | 2227.81 | − | 3145.37i | 0.276400 | − | 0.390240i | ||||
\(403\) | 13331.2 | 1.64783 | ||||||||
\(404\) | −6359.78 | −0.783196 | ||||||||
\(405\) | −2842.16 | + | 2282.14i | −0.348711 | + | 0.280001i | ||||
\(406\) | 2853.16 | + | 1885.39i | 0.348768 | + | 0.230469i | ||||
\(407\) | 3888.00i | 0.473516i | ||||||||
\(408\) | −411.855 | + | 581.486i | −0.0499752 | + | 0.0705584i | ||||
\(409\) | − | 668.576i | − | 0.0808287i | −0.999183 | − | 0.0404143i | \(-0.987132\pi\) | ||
0.999183 | − | 0.0404143i | \(-0.0128678\pi\) | |||||||
\(410\) | − | 1019.49i | − | 0.122802i | ||||||
\(411\) | 7485.77 | − | 10568.9i | 0.898408 | − | 1.26843i | ||||
\(412\) | − | 3451.97i | − | 0.412783i | ||||||
\(413\) | −5020.07 | − | 3317.31i | −0.598115 | − | 0.395240i | ||||
\(414\) | −1144.03 | − | 3252.00i | −0.135812 | − | 0.386056i | ||||
\(415\) | −655.274 | −0.0775088 | ||||||||
\(416\) | −10007.6 | −1.17947 | ||||||||
\(417\) | 4302.80 | − | 6074.99i | 0.505298 | − | 0.713414i | ||||
\(418\) | 297.573i | 0.0348200i | ||||||||
\(419\) | −16682.5 | −1.94509 | −0.972544 | − | 0.232719i | \(-0.925238\pi\) | ||||
−0.972544 | + | 0.232719i | \(0.925238\pi\) | |||||||
\(420\) | −1237.28 | − | 3184.34i | −0.143745 | − | 0.369952i | ||||
\(421\) | −2711.43 | −0.313888 | −0.156944 | − | 0.987608i | \(-0.550164\pi\) | ||||
−0.156944 | + | 0.987608i | \(0.550164\pi\) | |||||||
\(422\) | − | 4876.10i | − | 0.562476i | ||||||
\(423\) | 5217.38 | + | 14830.8i | 0.599711 | + | 1.70473i | ||||
\(424\) | 7651.79 | 0.876424 | ||||||||
\(425\) | 239.312 | 0.0273137 | ||||||||
\(426\) | 1439.95 | + | 1019.89i | 0.163770 | + | 0.115995i | ||||
\(427\) | 331.048 | − | 500.975i | 0.0375189 | − | 0.0567772i | ||||
\(428\) | − | 5174.34i | − | 0.584372i | ||||||
\(429\) | 6183.69 | + | 4379.79i | 0.695924 | + | 0.492910i | ||||
\(430\) | 1528.32i | 0.171400i | ||||||||
\(431\) | − | 2719.42i | − | 0.303921i | −0.988387 | − | 0.151961i | \(-0.951441\pi\) | ||
0.988387 | − | 0.151961i | \(-0.0485587\pi\) | |||||||
\(432\) | 1663.53 | − | 5829.16i | 0.185270 | − | 0.649203i | ||||
\(433\) | − | 7084.08i | − | 0.786233i | −0.919489 | − | 0.393117i | \(-0.871397\pi\) | ||
0.919489 | − | 0.393117i | \(-0.128603\pi\) | |||||||
\(434\) | 3038.52 | + | 2007.88i | 0.336068 | + | 0.222077i | ||||
\(435\) | 2922.70 | − | 4126.46i | 0.322144 | − | 0.454825i | ||||
\(436\) | −7556.06 | −0.829976 | ||||||||
\(437\) | −1861.64 | −0.203785 | ||||||||
\(438\) | −3724.36 | − | 2637.90i | −0.406295 | − | 0.287771i | ||||
\(439\) | 7781.46i | 0.845989i | 0.906132 | + | 0.422994i | \(0.139021\pi\) | ||||
−0.906132 | + | 0.422994i | \(0.860979\pi\) | |||||||
\(440\) | −1624.13 | −0.175971 | ||||||||
\(441\) | −6831.49 | + | 6252.75i | −0.737662 | + | 0.675170i | ||||
\(442\) | −584.104 | −0.0628574 | ||||||||
\(443\) | 15917.2i | 1.70710i | 0.521008 | + | 0.853552i | \(0.325556\pi\) | ||||
−0.521008 | + | 0.853552i | \(0.674444\pi\) | |||||||
\(444\) | 5162.30 | + | 3656.36i | 0.551784 | + | 0.390818i | ||||
\(445\) | −2525.20 | −0.269002 | ||||||||
\(446\) | −2561.77 | −0.271980 | ||||||||
\(447\) | 4562.16 | − | 6441.16i | 0.482735 | − | 0.681558i | ||||
\(448\) | 3060.00 | + | 2022.08i | 0.322704 | + | 0.213246i | ||||
\(449\) | − | 362.637i | − | 0.0381156i | −0.999818 | − | 0.0190578i | \(-0.993933\pi\) | ||
0.999818 | − | 0.0190578i | \(-0.00606665\pi\) | |||||||
\(450\) | 604.105 | − | 212.520i | 0.0632840 | − | 0.0222629i | ||||
\(451\) | − | 4873.01i | − | 0.508783i | ||||||
\(452\) | 14139.2i | 1.47135i | ||||||||
\(453\) | −354.169 | − | 250.852i | −0.0367336 | − | 0.0260177i | ||||
\(454\) | 2838.69i | 0.293450i | ||||||||
\(455\) | 3283.49 | − | 4968.89i | 0.338313 | − | 0.511968i | ||||
\(456\) | 840.295 | + | 595.165i | 0.0862947 | + | 0.0611210i | ||||
\(457\) | 10948.8 | 1.12071 | 0.560355 | − | 0.828252i | \(-0.310665\pi\) | ||||
0.560355 | + | 0.828252i | \(0.310665\pi\) | |||||||
\(458\) | −3450.84 | −0.352068 | ||||||||
\(459\) | 368.547 | − | 1291.42i | 0.0374777 | − | 0.131325i | ||||
\(460\) | − | 4777.50i | − | 0.484243i | ||||||
\(461\) | 9669.50 | 0.976906 | 0.488453 | − | 0.872590i | \(-0.337561\pi\) | ||||
0.488453 | + | 0.872590i | \(0.337561\pi\) | |||||||
\(462\) | 749.758 | + | 1929.62i | 0.0755019 | + | 0.194317i | ||||
\(463\) | −2566.64 | −0.257628 | −0.128814 | − | 0.991669i | \(-0.541117\pi\) | ||||
−0.128814 | + | 0.991669i | \(0.541117\pi\) | |||||||
\(464\) | 8409.58i | 0.841390i | ||||||||
\(465\) | 3112.57 | − | 4394.54i | 0.310413 | − | 0.438263i | ||||
\(466\) | −5693.36 | −0.565966 | ||||||||
\(467\) | 7093.06 | 0.702843 | 0.351422 | − | 0.936217i | \(-0.385698\pi\) | ||||
0.351422 | + | 0.936217i | \(0.385698\pi\) | |||||||
\(468\) | 11630.6 | − | 4091.55i | 1.14877 | − | 0.404128i | ||||
\(469\) | −12080.9 | − | 7983.16i | −1.18943 | − | 0.785988i | ||||
\(470\) | − | 2762.19i | − | 0.271086i | ||||||
\(471\) | 5156.15 | − | 7279.80i | 0.504422 | − | 0.712178i | ||||
\(472\) | 4654.36i | 0.453886i | ||||||||
\(473\) | 7305.16i | 0.710130i | ||||||||
\(474\) | −2357.23 | + | 3328.10i | −0.228420 | + | 0.322499i | ||||
\(475\) | − | 345.825i | − | 0.0334054i | ||||||
\(476\) | 1050.14 | + | 693.938i | 0.101119 | + | 0.0668206i | ||||
\(477\) | −13604.1 | + | 4785.84i | −1.30585 | + | 0.459389i | ||||
\(478\) | −4908.69 | −0.469703 | ||||||||
\(479\) | −3853.70 | −0.367599 | −0.183800 | − | 0.982964i | \(-0.558840\pi\) | ||||
−0.183800 | + | 0.982964i | \(0.558840\pi\) | |||||||
\(480\) | −2336.57 | + | 3298.93i | −0.222186 | + | 0.313698i | ||||
\(481\) | 11028.5i | 1.04544i | ||||||||
\(482\) | −691.997 | −0.0653934 | ||||||||
\(483\) | −12071.9 | + | 4690.54i | −1.13724 | + | 0.441878i | ||||
\(484\) | 5799.79 | 0.544683 | ||||||||
\(485\) | 431.712i | 0.0404186i | ||||||||
\(486\) | −216.505 | − | 3587.28i | −0.0202075 | − | 0.334819i | ||||
\(487\) | −15436.4 | −1.43632 | −0.718162 | − | 0.695876i | \(-0.755016\pi\) | ||||
−0.718162 | + | 0.695876i | \(0.755016\pi\) | |||||||
\(488\) | −464.479 | −0.0430860 | ||||||||
\(489\) | −9876.85 | − | 6995.59i | −0.913387 | − | 0.646935i | ||||
\(490\) | 1496.78 | − | 637.995i | 0.137995 | − | 0.0588197i | ||||
\(491\) | 11840.5i | 1.08829i | 0.838990 | + | 0.544147i | \(0.183147\pi\) | ||||
−0.838990 | + | 0.544147i | \(0.816853\pi\) | |||||||
\(492\) | −6470.15 | − | 4582.69i | −0.592880 | − | 0.419926i | ||||
\(493\) | 1863.10i | 0.170203i | ||||||||
\(494\) | 844.078i | 0.0768762i | ||||||||
\(495\) | 2887.54 | − | 1015.82i | 0.262193 | − | 0.0922376i | ||||
\(496\) | 8955.92i | 0.810752i | ||||||||
\(497\) | 3654.71 | − | 5530.66i | 0.329851 | − | 0.499163i | ||||
\(498\) | 373.422 | − | 527.223i | 0.0336013 | − | 0.0474406i | ||||
\(499\) | 4648.67 | 0.417040 | 0.208520 | − | 0.978018i | \(-0.433135\pi\) | ||||
0.208520 | + | 0.978018i | \(0.433135\pi\) | |||||||
\(500\) | 887.488 | 0.0793793 | ||||||||
\(501\) | 3283.64 | + | 2325.74i | 0.292819 | + | 0.207398i | ||||
\(502\) | − | 6076.37i | − | 0.540242i | ||||||
\(503\) | 22018.7 | 1.95182 | 0.975910 | − | 0.218174i | \(-0.0700101\pi\) | ||||
0.975910 | + | 0.218174i | \(0.0700101\pi\) | |||||||
\(504\) | 6948.50 | + | 1742.19i | 0.614109 | + | 0.153975i | ||||
\(505\) | −4478.78 | −0.394660 | ||||||||
\(506\) | 2895.04i | 0.254348i | ||||||||
\(507\) | 8224.40 | + | 5825.19i | 0.720430 | + | 0.510268i | ||||
\(508\) | −7235.81 | −0.631963 | ||||||||
\(509\) | −7752.57 | −0.675101 | −0.337551 | − | 0.941307i | \(-0.609598\pi\) | ||||
−0.337551 | + | 0.941307i | \(0.609598\pi\) | |||||||
\(510\) | −136.377 | + | 192.546i | −0.0118409 | + | 0.0167178i | ||||
\(511\) | −9452.70 | + | 14304.7i | −0.818323 | + | 1.23837i | ||||
\(512\) | − | 11675.0i | − | 1.00775i | ||||||
\(513\) | −1866.21 | − | 532.580i | −0.160614 | − | 0.0458362i | ||||
\(514\) | 3984.60i | 0.341932i | ||||||||
\(515\) | − | 2431.00i | − | 0.208005i | ||||||
\(516\) | 9699.44 | + | 6869.93i | 0.827508 | + | 0.586109i | ||||
\(517\) | − | 13202.9i | − | 1.12314i | ||||||
\(518\) | −1661.06 | + | 2513.68i | −0.140893 | + | 0.213214i | ||||
\(519\) | 6756.08 | + | 4785.20i | 0.571404 | + | 0.404715i | ||||
\(520\) | −4606.91 | −0.388513 | ||||||||
\(521\) | −6080.85 | −0.511338 | −0.255669 | − | 0.966764i | \(-0.582296\pi\) | ||||
−0.255669 | + | 0.966764i | \(0.582296\pi\) | |||||||
\(522\) | 1654.52 | + | 4703.10i | 0.138729 | + | 0.394347i | ||||
\(523\) | − | 13407.4i | − | 1.12096i | −0.828167 | − | 0.560482i | \(-0.810616\pi\) | ||
0.828167 | − | 0.560482i | \(-0.189384\pi\) | |||||||
\(524\) | −15529.9 | −1.29471 | ||||||||
\(525\) | −871.334 | − | 2242.52i | −0.0724346 | − | 0.186422i | ||||
\(526\) | 952.356 | 0.0789443 | ||||||||
\(527\) | 1984.14i | 0.164005i | ||||||||
\(528\) | −2942.35 | + | 4154.22i | −0.242518 | + | 0.342404i | ||||
\(529\) | −5944.57 | −0.488581 | ||||||||
\(530\) | 2533.72 | 0.207656 | ||||||||
\(531\) | −2911.09 | − | 8275.00i | −0.237911 | − | 0.676280i | ||||
\(532\) | 1002.80 | − | 1517.53i | 0.0817233 | − | 0.123672i | ||||
\(533\) | − | 13822.5i | − | 1.12330i | ||||||
\(534\) | 1439.04 | − | 2031.73i | 0.116617 | − | 0.164647i | ||||
\(535\) | − | 3643.95i | − | 0.294471i | ||||||
\(536\) | 11200.8i | 0.902615i | ||||||||
\(537\) | −4305.27 | + | 6078.48i | −0.345971 | + | 0.488465i | ||||
\(538\) | − | 7499.24i | − | 0.600957i | ||||||
\(539\) | 7154.42 | − | 3049.53i | 0.571731 | − | 0.243697i | ||||
\(540\) | 1366.75 | − | 4789.24i | 0.108918 | − | 0.381659i | ||||
\(541\) | 20040.7 | 1.59264 | 0.796321 | − | 0.604875i | \(-0.206777\pi\) | ||||
0.796321 | + | 0.604875i | \(0.206777\pi\) | |||||||
\(542\) | −2396.27 | −0.189905 | ||||||||
\(543\) | −13981.2 | + | 19739.6i | −1.10495 | + | 1.56005i | ||||
\(544\) | − | 1489.47i | − | 0.117391i | ||||||
\(545\) | −5321.24 | −0.418233 | ||||||||
\(546\) | 2126.72 | + | 5473.47i | 0.166695 | + | 0.429016i | ||||
\(547\) | 3820.80 | 0.298657 | 0.149329 | − | 0.988788i | \(-0.452289\pi\) | ||||
0.149329 | + | 0.988788i | \(0.452289\pi\) | |||||||
\(548\) | 17696.5i | 1.37948i | ||||||||
\(549\) | 825.799 | − | 290.510i | 0.0641971 | − | 0.0225841i | ||||
\(550\) | −537.794 | −0.0416939 | ||||||||
\(551\) | 2692.33 | 0.208162 | ||||||||
\(552\) | 8175.10 | + | 5790.27i | 0.630354 | + | 0.446468i | ||||
\(553\) | 12782.7 | + | 8446.95i | 0.982961 | + | 0.649549i | ||||
\(554\) | − | 312.206i | − | 0.0239429i | ||||||
\(555\) | 3635.48 | + | 2574.94i | 0.278049 | + | 0.196937i | ||||
\(556\) | 10171.9i | 0.775872i | ||||||||
\(557\) | − | 14135.0i | − | 1.07526i | −0.843182 | − | 0.537629i | \(-0.819320\pi\) | ||
0.843182 | − | 0.537629i | \(-0.180680\pi\) | |||||||
\(558\) | 1762.01 | + | 5008.65i | 0.133677 | + | 0.379987i | ||||
\(559\) | 20721.4i | 1.56784i | ||||||||
\(560\) | 3338.11 | + | 2205.85i | 0.251895 | + | 0.166454i | ||||
\(561\) | −651.864 | + | 920.346i | −0.0490583 | + | 0.0692638i | ||||
\(562\) | 422.763 | 0.0317316 | ||||||||
\(563\) | −12949.4 | −0.969366 | −0.484683 | − | 0.874690i | \(-0.661065\pi\) | ||||
−0.484683 | + | 0.874690i | \(0.661065\pi\) | |||||||
\(564\) | −17530.2 | − | 12416.3i | −1.30878 | − | 0.926986i | ||||
\(565\) | 9957.30i | 0.741428i | ||||||||
\(566\) | 2737.35 | 0.203285 | ||||||||
\(567\) | −13443.4 | + | 1248.52i | −0.995715 | + | 0.0924745i | ||||
\(568\) | −5127.75 | −0.378795 | ||||||||
\(569\) | − | 18520.3i | − | 1.36452i | −0.731109 | − | 0.682260i | \(-0.760997\pi\) | ||
0.731109 | − | 0.682260i | \(-0.239003\pi\) | |||||||
\(570\) | 278.245 | + | 197.076i | 0.0204463 | + | 0.0144818i | ||||
\(571\) | −13858.2 | −1.01567 | −0.507835 | − | 0.861455i | \(-0.669554\pi\) | ||||
−0.507835 | + | 0.861455i | \(0.669554\pi\) | |||||||
\(572\) | −10353.9 | −0.756851 | ||||||||
\(573\) | 3316.36 | − | 4682.26i | 0.241785 | − | 0.341369i | ||||
\(574\) | 2081.88 | − | 3150.51i | 0.151387 | − | 0.229093i | ||||
\(575\) | − | 3364.48i | − | 0.244015i | ||||||
\(576\) | 1774.47 | + | 5044.06i | 0.128361 | + | 0.364877i | ||||
\(577\) | 10176.6i | 0.734245i | 0.930173 | + | 0.367122i | \(0.119657\pi\) | ||||
−0.930173 | + | 0.367122i | \(0.880343\pi\) | |||||||
\(578\) | 4574.20i | 0.329173i | ||||||||
\(579\) | −6682.00 | − | 4732.74i | −0.479610 | − | 0.339699i | ||||
\(580\) | 6909.31i | 0.494644i | ||||||||
\(581\) | −2024.99 | − | 1338.13i | −0.144597 | − | 0.0955506i | ||||
\(582\) | −347.348 | − | 246.020i | −0.0247389 | − | 0.0175221i | ||||
\(583\) | 12110.9 | 0.860344 | ||||||||
\(584\) | 13262.7 | 0.939748 | ||||||||
\(585\) | 8190.65 | − | 2881.41i | 0.578874 | − | 0.203644i | ||||
\(586\) | − | 6740.00i | − | 0.475131i | ||||||
\(587\) | 10161.5 | 0.714499 | 0.357249 | − | 0.934009i | \(-0.383715\pi\) | ||||
0.357249 | + | 0.934009i | \(0.383715\pi\) | |||||||
\(588\) | 2679.15 | − | 12367.1i | 0.187902 | − | 0.867368i | ||||
\(589\) | 2867.24 | 0.200582 | ||||||||
\(590\) | 1541.19i | 0.107542i | ||||||||
\(591\) | −1121.95 | + | 1584.04i | −0.0780892 | + | 0.110252i | ||||
\(592\) | −7408.97 | −0.514369 | ||||||||
\(593\) | 13035.7 | 0.902722 | 0.451361 | − | 0.892341i | \(-0.350939\pi\) | ||||
0.451361 | + | 0.892341i | \(0.350939\pi\) | |||||||
\(594\) | −828.218 | + | 2902.15i | −0.0572091 | + | 0.200466i | ||||
\(595\) | 739.542 | + | 488.696i | 0.0509551 | + | 0.0336716i | ||||
\(596\) | 10785.0i | 0.741228i | ||||||||
\(597\) | 1261.17 | − | 1780.60i | 0.0864592 | − | 0.122069i | ||||
\(598\) | 8211.91i | 0.561555i | ||||||||
\(599\) | 26428.7i | 1.80275i | 0.433039 | + | 0.901375i | \(0.357441\pi\) | ||||
−0.433039 | + | 0.901375i | \(0.642559\pi\) | |||||||
\(600\) | −1075.62 | + | 1518.64i | −0.0731870 | + | 0.103330i | ||||
\(601\) | − | 20188.0i | − | 1.37019i | −0.728452 | − | 0.685096i | \(-0.759760\pi\) | ||
0.728452 | − | 0.685096i | \(-0.240240\pi\) | |||||||
\(602\) | −3120.96 | + | 4722.94i | −0.211297 | + | 0.319755i | ||||
\(603\) | −7005.60 | − | 19914.0i | −0.473118 | − | 1.34487i | ||||
\(604\) | 593.017 | 0.0399496 | ||||||||
\(605\) | 4084.41 | 0.274471 | ||||||||
\(606\) | 2552.33 | − | 3603.55i | 0.171091 | − | 0.241558i | ||||
\(607\) | − | 20701.4i | − | 1.38426i | −0.721773 | − | 0.692130i | \(-0.756672\pi\) | ||
0.721773 | − | 0.692130i | \(-0.243328\pi\) | |||||||
\(608\) | −2152.41 | −0.143572 | ||||||||
\(609\) | 17458.6 | − | 6783.55i | 1.16167 | − | 0.451368i | ||||
\(610\) | −153.802 | −0.0102086 | ||||||||
\(611\) | − | 37450.6i | − | 2.47969i | ||||||
\(612\) | 608.963 | + | 1731.03i | 0.0402220 | + | 0.114334i | ||||
\(613\) | 10042.5 | 0.661686 | 0.330843 | − | 0.943686i | \(-0.392667\pi\) | ||||
0.330843 | + | 0.943686i | \(0.392667\pi\) | |||||||
\(614\) | 1535.67 | 0.100936 | ||||||||
\(615\) | −4556.51 | − | 3227.29i | −0.298758 | − | 0.211605i | ||||
\(616\) | −5019.02 | − | 3316.61i | −0.328283 | − | 0.216932i | ||||
\(617\) | 19935.4i | 1.30076i | 0.759609 | + | 0.650380i | \(0.225390\pi\) | ||||
−0.759609 | + | 0.650380i | \(0.774610\pi\) | |||||||
\(618\) | 1955.94 | + | 1385.36i | 0.127313 | + | 0.0901736i | ||||
\(619\) | − | 24406.2i | − | 1.58476i | −0.610027 | − | 0.792380i | \(-0.708842\pi\) | ||
0.610027 | − | 0.792380i | \(-0.291158\pi\) | |||||||
\(620\) | 7358.18i | 0.476632i | ||||||||
\(621\) | −18156.1 | − | 5181.39i | −1.17323 | − | 0.334818i | ||||
\(622\) | − | 2488.87i | − | 0.160442i | ||||||
\(623\) | −7803.60 | − | 5156.69i | −0.501837 | − | 0.331618i | ||||
\(624\) | −8346.12 | + | 11783.6i | −0.535436 | + | 0.755965i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 5331.10 | 0.340373 | ||||||||
\(627\) | 1329.98 | + | 941.997i | 0.0847115 | + | 0.0599996i | ||||
\(628\) | 12189.2i | 0.774528i | ||||||||
\(629\) | −1641.42 | −0.104050 | ||||||||
\(630\) | 2300.84 | + | 576.888i | 0.145504 | + | 0.0364822i | ||||
\(631\) | −321.373 | −0.0202752 | −0.0101376 | − | 0.999949i | \(-0.503227\pi\) | ||||
−0.0101376 | + | 0.999949i | \(0.503227\pi\) | |||||||
\(632\) | − | 11851.5i | − | 0.745931i | ||||||
\(633\) | −21793.3 | − | 15435.8i | −1.36841 | − | 0.969223i | ||||
\(634\) | 2164.20 | 0.135570 | ||||||||
\(635\) | −5095.71 | −0.318452 | ||||||||
\(636\) | 11389.3 | − | 16080.2i | 0.710088 | − | 1.00255i | ||||
\(637\) | 20293.8 | − | 8650.14i | 1.26228 | − | 0.538039i | ||||
\(638\) | − | 4186.86i | − | 0.259811i | ||||||
\(639\) | 9116.65 | − | 3207.17i | 0.564396 | − | 0.198551i | ||||
\(640\) | − | 7163.41i | − | 0.442435i | ||||||
\(641\) | − | 21926.6i | − | 1.35109i | −0.737318 | − | 0.675546i | \(-0.763908\pi\) | ||
0.737318 | − | 0.675546i | \(-0.236092\pi\) | |||||||
\(642\) | 2931.86 | + | 2076.58i | 0.180236 | + | 0.127658i | ||||
\(643\) | 2824.13i | 0.173208i | 0.996243 | + | 0.0866039i | \(0.0276015\pi\) | ||||
−0.996243 | + | 0.0866039i | \(0.972399\pi\) | |||||||
\(644\) | 9756.07 | − | 14763.8i | 0.596961 | − | 0.903380i | ||||
\(645\) | 6830.69 | + | 4838.05i | 0.416989 | + | 0.295346i | ||||
\(646\) | −125.628 | −0.00765133 | ||||||||
\(647\) | −2998.63 | −0.182208 | −0.0911039 | − | 0.995841i | \(-0.529040\pi\) | ||||
−0.0911039 | + | 0.995841i | \(0.529040\pi\) | |||||||
\(648\) | 6538.70 | + | 8143.25i | 0.396395 | + | 0.493668i | ||||
\(649\) | 7366.69i | 0.445559i | ||||||||
\(650\) | −1525.48 | −0.0920526 | ||||||||
\(651\) | 18592.8 | − | 7224.25i | 1.11937 | − | 0.434932i | ||||
\(652\) | 16537.7 | 0.993353 | ||||||||
\(653\) | − | 19590.2i | − | 1.17400i | −0.809585 | − | 0.587002i | \(-0.800308\pi\) | ||
0.809585 | − | 0.587002i | \(-0.199692\pi\) | |||||||
\(654\) | 3032.42 | − | 4281.38i | 0.181311 | − | 0.255987i | ||||
\(655\) | −10936.7 | −0.652417 | ||||||||
\(656\) | 9286.00 | 0.552679 | ||||||||
\(657\) | −23579.7 | + | 8295.18i | −1.40020 | + | 0.492581i | ||||
\(658\) | 5640.63 | − | 8535.95i | 0.334186 | − | 0.505723i | ||||
\(659\) | − | 4145.27i | − | 0.245033i | −0.992466 | − | 0.122517i | \(-0.960904\pi\) | ||
0.992466 | − | 0.122517i | \(-0.0390965\pi\) | |||||||
\(660\) | −2417.44 | + | 3413.10i | −0.142574 | + | 0.201295i | ||||
\(661\) | 106.053i | 0.00624055i | 0.999995 | + | 0.00312027i | \(0.000993215\pi\) | ||||
−0.999995 | + | 0.00312027i | \(0.999007\pi\) | |||||||
\(662\) | 256.795i | 0.0150765i | ||||||||
\(663\) | −1849.04 | + | 2610.60i | −0.108312 | + | 0.152922i | ||||
\(664\) | 1877.47i | 0.109729i | ||||||||
\(665\) | 706.206 | − | 1068.70i | 0.0411812 | − | 0.0623194i | ||||
\(666\) | −4143.51 | + | 1457.66i | −0.241077 | + | 0.0848094i | ||||
\(667\) | 26193.3 | 1.52055 | ||||||||
\(668\) | −5498.09 | −0.318454 | ||||||||
\(669\) | −8109.53 | + | 11449.6i | −0.468659 | + | 0.661684i | ||||
\(670\) | 3708.90i | 0.213862i | ||||||||
\(671\) | −735.153 | −0.0422955 | ||||||||
\(672\) | −13957.4 | + | 5423.16i | −0.801217 | + | 0.311314i | ||||
\(673\) | −2113.29 | −0.121042 | −0.0605209 | − | 0.998167i | \(-0.519276\pi\) | ||||
−0.0605209 | + | 0.998167i | \(0.519276\pi\) | |||||||
\(674\) | 4593.93i | 0.262539i | ||||||||
\(675\) | 962.517 | − | 3372.75i | 0.0548849 | − | 0.192322i | ||||
\(676\) | −13770.8 | −0.783503 | ||||||||
\(677\) | 4033.61 | 0.228987 | 0.114494 | − | 0.993424i | \(-0.463475\pi\) | ||||
0.114494 | + | 0.993424i | \(0.463475\pi\) | |||||||
\(678\) | −8011.47 | − | 5674.38i | −0.453803 | − | 0.321421i | ||||
\(679\) | −881.594 | + | 1334.11i | −0.0498269 | + | 0.0754029i | ||||
\(680\) | − | 685.667i | − | 0.0386678i | ||||||
\(681\) | 12687.3 | + | 8986.18i | 0.713918 | + | 0.505655i | ||||
\(682\) | − | 4458.87i | − | 0.250350i | ||||||
\(683\) | − | 649.189i | − | 0.0363697i | −0.999835 | − | 0.0181849i | \(-0.994211\pi\) | ||
0.999835 | − | 0.0181849i | \(-0.00578874\pi\) | |||||||
\(684\) | 2501.48 | − | 880.002i | 0.139834 | − | 0.0491926i | ||||
\(685\) | 12462.5i | 0.695134i | ||||||||
\(686\) | 5928.33 | + | 1084.97i | 0.329948 | + | 0.0603855i | ||||
\(687\) | −10924.0 | + | 15423.2i | −0.606661 | + | 0.856526i | ||||
\(688\) | −13920.7 | −0.771398 | ||||||||
\(689\) | 34353.0 | 1.89948 | ||||||||
\(690\) | 2707.00 | + | 1917.32i | 0.149353 | + | 0.105784i | ||||
\(691\) | 16178.2i | 0.890663i | 0.895366 | + | 0.445332i | \(0.146914\pi\) | ||||
−0.895366 | + | 0.445332i | \(0.853086\pi\) | |||||||
\(692\) | −11312.3 | −0.621430 | ||||||||
\(693\) | 10997.7 | + | 2757.45i | 0.602841 | + | 0.151150i | ||||
\(694\) | −8711.96 | −0.476515 | ||||||||
\(695\) | 7163.41i | 0.390969i | ||||||||
\(696\) | −11823.0 | − | 8374.00i | −0.643892 | − | 0.456057i | ||||
\(697\) | 2057.27 | 0.111800 | ||||||||
\(698\) | 10771.5 | 0.584109 | ||||||||
\(699\) | −18022.9 | + | 25446.0i | −0.975236 | + | 1.37690i | ||||
\(700\) | 2742.59 | + | 1812.33i | 0.148086 | + | 0.0978565i | ||||
\(701\) | 2026.49i | 0.109186i | 0.998509 | + | 0.0545932i | \(0.0173862\pi\) | ||||
−0.998509 | + | 0.0545932i | \(0.982614\pi\) | |||||||
\(702\) | −2349.28 | + | 8232.09i | −0.126307 | + | 0.442593i | ||||
\(703\) | 2371.99i | 0.127256i | ||||||||
\(704\) | − | 4490.39i | − | 0.240395i | ||||||
\(705\) | −12345.4 | − | 8743.99i | −0.659508 | − | 0.467117i | ||||
\(706\) | 11997.4i | 0.639557i | ||||||||
\(707\) | −13840.7 | − | 9146.07i | −0.736258 | − | 0.486525i | ||||
\(708\) | 9781.13 | + | 6927.79i | 0.519205 | + | 0.367743i | ||||
\(709\) | 821.533 | 0.0435167 | 0.0217583 | − | 0.999763i | \(-0.493074\pi\) | ||||
0.0217583 | + | 0.999763i | \(0.493074\pi\) | |||||||
\(710\) | −1697.94 | −0.0897502 | ||||||||
\(711\) | 7412.59 | + | 21070.9i | 0.390990 | + | 1.11142i | ||||
\(712\) | 7235.11i | 0.380825i | ||||||||
\(713\) | 27895.0 | 1.46518 | ||||||||
\(714\) | −814.640 | + | 316.529i | −0.0426991 | + | 0.0165908i | ||||
\(715\) | −7291.59 | −0.381384 | ||||||||
\(716\) | − | 10177.7i | − | 0.531229i | ||||||
\(717\) | −15539.0 | + | 21938.9i | −0.809362 | + | 1.14271i | ||||
\(718\) | −1688.67 | −0.0877725 | ||||||||
\(719\) | 20915.2 | 1.08485 | 0.542423 | − | 0.840106i | \(-0.317507\pi\) | ||||
0.542423 | + | 0.840106i | \(0.317507\pi\) | |||||||
\(720\) | 1935.74 | + | 5502.49i | 0.100195 | + | 0.284814i | ||||
\(721\) | 4964.32 | − | 7512.49i | 0.256423 | − | 0.388044i | ||||
\(722\) | − | 6325.83i | − | 0.326071i | ||||||
\(723\) | −2190.59 | + | 3092.82i | −0.112682 | + | 0.159092i | ||||
\(724\) | − | 33051.7i | − | 1.69663i | ||||||
\(725\) | 4865.78i | 0.249256i | ||||||||
\(726\) | −2327.59 | + | 3286.25i | −0.118988 | + | 0.167995i | ||||
\(727\) | 36038.5i | 1.83851i | 0.393666 | + | 0.919253i | \(0.371207\pi\) | ||||
−0.393666 | + | 0.919253i | \(0.628793\pi\) | |||||||
\(728\) | −14236.7 | − | 9407.72i | −0.724789 | − | 0.478947i | ||||
\(729\) | −16718.4 | − | 10388.2i | −0.849383 | − | 0.527778i | ||||
\(730\) | 4391.64 | 0.222660 | ||||||||
\(731\) | −3084.06 | −0.156044 | ||||||||
\(732\) | −691.354 | + | 976.101i | −0.0349087 | + | 0.0492865i | ||||
\(733\) | − | 21345.1i | − | 1.07558i | −0.843079 | − | 0.537790i | \(-0.819259\pi\) | ||
0.843079 | − | 0.537790i | \(-0.180741\pi\) | |||||||
\(734\) | −11079.5 | −0.557154 | ||||||||
\(735\) | 1886.75 | − | 8709.38i | 0.0946857 | − | 0.437075i | ||||
\(736\) | −20940.4 | −1.04874 | ||||||||
\(737\) | 17728.1i | 0.886055i | ||||||||
\(738\) | 5193.24 | − | 1826.95i | 0.259032 | − | 0.0911258i | ||||
\(739\) | −5664.66 | −0.281973 | −0.140986 | − | 0.990012i | \(-0.545027\pi\) | ||||
−0.140986 | + | 0.990012i | \(0.545027\pi\) | |||||||
\(740\) | −6087.20 | −0.302392 | ||||||||
\(741\) | 3772.53 | + | 2672.02i | 0.187028 | + | 0.132468i | ||||
\(742\) | 7829.93 | + | 5174.08i | 0.387393 | + | 0.255993i | ||||
\(743\) | 9650.55i | 0.476506i | 0.971203 | + | 0.238253i | \(0.0765748\pi\) | ||||
−0.971203 | + | 0.238253i | \(0.923425\pi\) | |||||||
\(744\) | −12591.1 | − | 8918.03i | −0.620445 | − | 0.439450i | ||||
\(745\) | 7595.19i | 0.373512i | ||||||||
\(746\) | 3104.74i | 0.152376i | ||||||||
\(747\) | −1174.27 | − | 3337.96i | −0.0575158 | − | 0.163493i | ||||
\(748\) | − | 1541.02i | − | 0.0753278i | ||||||
\(749\) | 7441.27 | − | 11260.9i | 0.363015 | − | 0.549349i | ||||
\(750\) | −356.169 | + | 502.864i | −0.0173406 | + | 0.0244827i | ||||
\(751\) | −25540.0 | −1.24097 | −0.620484 | − | 0.784219i | \(-0.713064\pi\) | ||||
−0.620484 | + | 0.784219i | \(0.713064\pi\) | |||||||
\(752\) | 25159.4 | 1.22004 | ||||||||
\(753\) | −27157.8 | − | 19235.4i | −1.31432 | − | 0.930911i | ||||
\(754\) | − | 11876.2i | − | 0.573616i | ||||||
\(755\) | 417.624 | 0.0201310 | ||||||||
\(756\) | 14003.7 | − | 12009.1i | 0.673690 | − | 0.577733i | ||||
\(757\) | −6554.94 | −0.314721 | −0.157360 | − | 0.987541i | \(-0.550298\pi\) | ||||
−0.157360 | + | 0.987541i | \(0.550298\pi\) | |||||||
\(758\) | 585.962i | 0.0280780i | ||||||||
\(759\) | 12939.1 | + | 9164.54i | 0.618788 | + | 0.438276i | ||||
\(760\) | −990.845 | −0.0472918 | ||||||||
\(761\) | −14488.6 | −0.690160 | −0.345080 | − | 0.938573i | \(-0.612148\pi\) | ||||
−0.345080 | + | 0.938573i | \(0.612148\pi\) | |||||||
\(762\) | 2903.90 | − | 4099.92i | 0.138054 | − | 0.194914i | ||||
\(763\) | −16444.2 | − | 10866.4i | −0.780234 | − | 0.515585i | ||||
\(764\) | 7839.94i | 0.371255i | ||||||||
\(765\) | 428.853 | + | 1219.05i | 0.0202683 | + | 0.0576142i | ||||
\(766\) | 8770.38i | 0.413690i | ||||||||
\(767\) | 20895.9i | 0.983714i | ||||||||
\(768\) | −954.421 | − | 675.999i | −0.0448434 | − | 0.0317617i | ||||
\(769\) | − | 17124.6i | − | 0.803031i | −0.915852 | − | 0.401515i | \(-0.868484\pi\) | ||
0.915852 | − | 0.401515i | \(-0.131516\pi\) | |||||||
\(770\) | −1661.94 | − | 1098.22i | −0.0777820 | − | 0.0513990i | ||||
\(771\) | 17808.8 | + | 12613.6i | 0.831866 | + | 0.589195i | ||||
\(772\) | 11188.3 | 0.521600 | ||||||||
\(773\) | 12317.6 | 0.573137 | 0.286569 | − | 0.958060i | \(-0.407485\pi\) | ||||
0.286569 | + | 0.958060i | \(0.407485\pi\) | |||||||
\(774\) | −7785.22 | + | 2738.79i | −0.361543 | + | 0.127188i | ||||
\(775\) | 5181.89i | 0.240179i | ||||||||
\(776\) | 1236.92 | 0.0572204 | ||||||||
\(777\) | 5976.41 | + | 15381.3i | 0.275936 | + | 0.710167i | ||||
\(778\) | 964.763 | 0.0444581 | ||||||||
\(779\) | − | 2972.92i | − | 0.136734i | ||||||
\(780\) | −6857.17 | + | 9681.42i | −0.314777 | + | 0.444423i | ||||
\(781\) | −8115.94 | −0.371845 | ||||||||
\(782\) | −1222.21 | −0.0558904 | ||||||||
\(783\) | 26257.7 | + | 7493.43i | 1.19843 | + | 0.342009i | ||||
\(784\) | 5811.18 | + | 13633.4i | 0.264722 | + | 0.621057i | ||||
\(785\) | 8584.09i | 0.390292i | ||||||||
\(786\) | 6232.52 | − | 8799.50i | 0.282833 | − | 0.399323i | ||||
\(787\) | 5526.55i | 0.250318i | 0.992137 | + | 0.125159i | \(0.0399441\pi\) | ||||
−0.992137 | + | 0.125159i | \(0.960056\pi\) | |||||||
\(788\) | − | 2652.30i | − | 0.119904i | ||||||
\(789\) | 3014.78 | − | 4256.47i | 0.136032 | − | 0.192059i | ||||
\(790\) | − | 3924.37i | − | 0.176738i | ||||||
\(791\) | −20333.7 | + | 30770.9i | −0.914011 | + | 1.38317i | ||||
\(792\) | −2910.48 | − | 8273.28i | −0.130580 | − | 0.371185i | ||||
\(793\) | −2085.30 | −0.0933809 | ||||||||
\(794\) | 4367.27 | 0.195200 | ||||||||
\(795\) | 8020.76 | − | 11324.2i | 0.357820 | − | 0.505195i | ||||
\(796\) | 2981.42i | 0.132756i | ||||||||
\(797\) | −32322.3 | −1.43653 | −0.718266 | − | 0.695769i | \(-0.755064\pi\) | ||||
−0.718266 | + | 0.695769i | \(0.755064\pi\) | |||||||
\(798\) | 457.411 | + | 1177.22i | 0.0202909 | + | 0.0522221i | ||||
\(799\) | 5573.94 | 0.246798 | ||||||||
\(800\) | − | 3889.98i | − | 0.171915i | ||||||
\(801\) | −4525.23 | − | 12863.3i | −0.199614 | − | 0.567420i | ||||
\(802\) | −6188.12 | −0.272456 | ||||||||
\(803\) | 20991.5 | 0.922506 | ||||||||
\(804\) | 23538.5 | + | 16671.9i | 1.03251 | + | 0.731308i | ||||
\(805\) | 6870.57 | − | 10397.2i | 0.300814 | − | 0.455222i | ||||
\(806\) | − | 12647.8i | − | 0.552728i | ||||||
\(807\) | −33517.2 | − | 23739.6i | −1.46203 | − | 1.03553i | ||||
\(808\) | 12832.4i | 0.558717i | ||||||||
\(809\) | − | 23348.8i | − | 1.01471i | −0.861737 | − | 0.507355i | \(-0.830623\pi\) | ||
0.861737 | − | 0.507355i | \(-0.169377\pi\) | |||||||
\(810\) | 2165.15 | + | 2696.46i | 0.0939203 | + | 0.116968i | ||||
\(811\) | − | 5514.22i | − | 0.238755i | −0.992849 | − | 0.119378i | \(-0.961910\pi\) | ||
0.992849 | − | 0.119378i | \(-0.0380899\pi\) | |||||||
\(812\) | −14109.4 | + | 21351.7i | −0.609783 | + | 0.922783i | ||||
\(813\) | −7585.65 | + | 10709.9i | −0.327233 | + | 0.462009i | ||||
\(814\) | 3688.69 | 0.158831 | ||||||||
\(815\) | 11646.4 | 0.500560 | ||||||||
\(816\) | −1753.81 | − | 1242.19i | −0.0752396 | − | 0.0532908i | ||||
\(817\) | 4456.72i | 0.190846i | ||||||||
\(818\) | −634.301 | −0.0271123 | ||||||||
\(819\) | 31195.5 | + | 7821.63i | 1.33097 | + | 0.333712i | ||||
\(820\) | 7629.37 | 0.324914 | ||||||||
\(821\) | 23388.8i | 0.994244i | 0.867681 | + | 0.497122i | \(0.165610\pi\) | ||||
−0.867681 | + | 0.497122i | \(0.834390\pi\) | |||||||
\(822\) | −10027.1 | − | 7102.01i | −0.425469 | − | 0.301352i | ||||
\(823\) | −25766.4 | −1.09132 | −0.545662 | − | 0.838005i | \(-0.683722\pi\) | ||||
−0.545662 | + | 0.838005i | \(0.683722\pi\) | |||||||
\(824\) | −6965.21 | −0.294472 | ||||||||
\(825\) | −1702.44 | + | 2403.63i | −0.0718442 | + | 0.101435i | ||||
\(826\) | −3147.25 | + | 4762.72i | −0.132575 | + | 0.200625i | ||||
\(827\) | − | 1204.96i | − | 0.0506657i | −0.999679 | − | 0.0253329i | \(-0.991935\pi\) | ||
0.999679 | − | 0.0253329i | \(-0.00806456\pi\) | |||||||
\(828\) | 24336.5 | − | 8561.40i | 1.02144 | − | 0.359335i | ||||
\(829\) | − | 14942.6i | − | 0.626027i | −0.949749 | − | 0.313013i | \(-0.898661\pi\) | ||
0.949749 | − | 0.313013i | \(-0.101339\pi\) | |||||||
\(830\) | 621.682i | 0.0259987i | ||||||||
\(831\) | −1395.38 | − | 988.321i | −0.0582493 | − | 0.0412569i | ||||
\(832\) | − | 12737.2i | − | 0.530748i | ||||||
\(833\) | 1287.44 | + | 3020.42i | 0.0535499 | + | 0.125632i | ||||
\(834\) | −5763.56 | − | 4082.22i | −0.239299 | − | 0.169491i | ||||
\(835\) | −3871.95 | −0.160472 | ||||||||
\(836\) | −2226.90 | −0.0921278 | ||||||||
\(837\) | 27963.5 | + | 7980.25i | 1.15479 | + | 0.329555i | ||||
\(838\) | 15827.2i | 0.652438i | ||||||||
\(839\) | −27243.7 | −1.12104 | −0.560522 | − | 0.828140i | \(-0.689399\pi\) | ||||
−0.560522 | + | 0.828140i | \(0.689399\pi\) | |||||||
\(840\) | −6425.19 | + | 2496.51i | −0.263917 | + | 0.102545i | ||||
\(841\) | −13492.3 | −0.553211 | ||||||||
\(842\) | 2572.43i | 0.105287i | ||||||||
\(843\) | 1338.30 | − | 1889.50i | 0.0546779 | − | 0.0771980i | ||||
\(844\) | 36490.5 | 1.48822 | ||||||||
\(845\) | −9697.91 | −0.394815 | ||||||||
\(846\) | 14070.5 | − | 4949.92i | 0.571814 | − | 0.201160i | ||||
\(847\) | 12622.0 | + | 8340.73i | 0.512039 | + | 0.338360i | ||||
\(848\) | 23078.4i | 0.934571i | ||||||||
\(849\) | 8665.37 | − | 12234.4i | 0.350288 | − | 0.494561i | ||||
\(850\) | − | 227.044i | − | 0.00916180i | ||||||
\(851\) | 23076.7i | 0.929564i | ||||||||
\(852\) | −7632.41 | + | 10776.0i | −0.306904 | + | 0.433308i | ||||
\(853\) | − | 36573.7i | − | 1.46807i | −0.679114 | − | 0.734033i | \(-0.737636\pi\) | ||
0.679114 | − | 0.734033i | \(-0.262364\pi\) | |||||||
\(854\) | −475.292 | − | 314.077i | −0.0190447 | − | 0.0125849i | ||||
\(855\) | 1761.63 | − | 619.728i | 0.0704636 | − | 0.0247886i | ||||
\(856\) | −10440.5 | −0.416880 | ||||||||
\(857\) | −17793.8 | −0.709245 | −0.354623 | − | 0.935010i | \(-0.615391\pi\) | ||||
−0.354623 | + | 0.935010i | \(0.615391\pi\) | |||||||
\(858\) | 4155.27 | − | 5866.69i | 0.165336 | − | 0.233433i | ||||
\(859\) | 18563.7i | 0.737353i | 0.929558 | + | 0.368676i | \(0.120189\pi\) | ||||
−0.929558 | + | 0.368676i | \(0.879811\pi\) | |||||||
\(860\) | −11437.2 | −0.453496 | ||||||||
\(861\) | −7490.50 | − | 19278.0i | −0.296487 | − | 0.763059i | ||||
\(862\) | −2580.01 | −0.101944 | ||||||||
\(863\) | 9471.58i | 0.373599i | 0.982398 | + | 0.186800i | \(0.0598115\pi\) | ||||
−0.982398 | + | 0.186800i | \(0.940188\pi\) | |||||||
\(864\) | −20991.9 | − | 5990.68i | −0.826572 | − | 0.235888i | ||||
\(865\) | −7966.52 | −0.313144 | ||||||||
\(866\) | −6720.92 | −0.263725 | ||||||||
\(867\) | 20444.0 | + | 14480.1i | 0.800824 | + | 0.567209i | ||||
\(868\) | −15026.1 | + | 22738.9i | −0.587578 | + | 0.889180i | ||||
\(869\) | − | 18758.0i | − | 0.732246i | ||||||
\(870\) | −3914.92 | − | 2772.87i | −0.152561 | − | 0.108056i | ||||
\(871\) | 50286.5i | 1.95625i | ||||||||
\(872\) | 15246.2i | 0.592090i | ||||||||
\(873\) | −2199.13 | + | 773.640i | −0.0852570 | + | 0.0299928i | ||||
\(874\) | 1766.20i | 0.0683554i | ||||||||
\(875\) | 1931.43 | + | 1276.31i | 0.0746220 | + | 0.0493108i | ||||
\(876\) | 19740.8 | − | 27871.4i | 0.761393 | − | 1.07499i | ||||
\(877\) | 19182.6 | 0.738596 | 0.369298 | − | 0.929311i | \(-0.379598\pi\) | ||||
0.369298 | + | 0.929311i | \(0.379598\pi\) | |||||||
\(878\) | 7382.55 | 0.283769 | ||||||||
\(879\) | −30123.8 | − | 21336.2i | −1.15592 | − | 0.818716i | ||||
\(880\) | − | 4898.50i | − | 0.187646i | ||||||
\(881\) | 26982.4 | 1.03185 | 0.515925 | − | 0.856634i | \(-0.327448\pi\) | ||||
0.515925 | + | 0.856634i | \(0.327448\pi\) | |||||||
\(882\) | 5932.21 | + | 6481.27i | 0.226471 | + | 0.247433i | ||||
\(883\) | 36699.9 | 1.39870 | 0.699349 | − | 0.714781i | \(-0.253473\pi\) | ||||
0.699349 | + | 0.714781i | \(0.253473\pi\) | |||||||
\(884\) | − | 4371.17i | − | 0.166310i | ||||||
\(885\) | 6888.21 | + | 4878.79i | 0.261633 | + | 0.185309i | ||||
\(886\) | 15101.2 | 0.572611 | ||||||||
\(887\) | 23512.3 | 0.890040 | 0.445020 | − | 0.895521i | \(-0.353197\pi\) | ||||
0.445020 | + | 0.895521i | \(0.353197\pi\) | |||||||
\(888\) | 7377.62 | − | 10416.2i | 0.278803 | − | 0.393632i | ||||
\(889\) | −15747.2 | − | 10405.9i | −0.594089 | − | 0.392579i | ||||
\(890\) | 2395.75i | 0.0902311i | ||||||||
\(891\) | 10349.1 | + | 12888.7i | 0.389123 | + | 0.484611i | ||||
\(892\) | − | 19171.1i | − | 0.719613i | ||||||
\(893\) | − | 8054.80i | − | 0.301840i | ||||||
\(894\) | −6110.96 | − | 4328.28i | −0.228614 | − | 0.161923i | ||||
\(895\) | − | 7167.52i | − | 0.267691i | ||||||
\(896\) | 14628.3 | − | 22137.0i | 0.545421 | − | 0.825385i | ||||
\(897\) | 36702.4 | + | 25995.6i | 1.36617 | + | 0.967636i | ||||
\(898\) | −344.047 | −0.0127851 | ||||||||
\(899\) | −40342.3 | −1.49665 | ||||||||
\(900\) | 1590.40 | + | 4520.84i | 0.0589038 | + | 0.167439i | ||||
\(901\) | 5112.91i | 0.189052i | ||||||||
\(902\) | −4623.20 | −0.170660 | ||||||||
\(903\) | 11229.1 | + | 28899.8i | 0.413820 | + | 1.06503i | ||||
\(904\) | 28529.3 | 1.04963 | ||||||||
\(905\) | − | 23276.2i | − | 0.854947i | ||||||
\(906\) | −237.992 | + | 336.013i | −0.00872709 | + | 0.0123215i | ||||
\(907\) | −11736.3 | −0.429655 | −0.214828 | − | 0.976652i | \(-0.568919\pi\) | ||||
−0.214828 | + | 0.976652i | \(0.568919\pi\) | |||||||
\(908\) | −21243.5 | −0.776420 | ||||||||
\(909\) | −8026.10 | − | 22814.8i | −0.292859 | − | 0.832476i | ||||
\(910\) | −4714.17 | − | 3115.16i | −0.171729 | − | 0.113480i | ||||
\(911\) | − | 8694.31i | − | 0.316197i | −0.987423 | − | 0.158098i | \(-0.949464\pi\) | ||
0.987423 | − | 0.158098i | \(-0.0505363\pi\) | |||||||
\(912\) | −1795.07 | + | 2534.40i | −0.0651761 | + | 0.0920200i | ||||
\(913\) | 2971.56i | 0.107716i | ||||||||
\(914\) | − | 10387.5i | − | 0.375918i | ||||||
\(915\) | −486.876 | + | 687.405i | −0.0175908 | + | 0.0248360i | ||||
\(916\) | − | 25824.5i | − | 0.931513i | ||||||
\(917\) | −33797.6 | − | 22333.7i | −1.21712 | − | 0.804281i | ||||
\(918\) | −1225.22 | − | 349.653i | −0.0440503 | − | 0.0125711i | ||||
\(919\) | −44592.6 | −1.60063 | −0.800313 | − | 0.599583i | \(-0.795333\pi\) | ||||
−0.800313 | + | 0.599583i | \(0.795333\pi\) | |||||||
\(920\) | −9639.78 | −0.345450 | ||||||||
\(921\) | 4861.32 | − | 6863.54i | 0.173926 | − | 0.245561i | ||||
\(922\) | − | 9173.80i | − | 0.327682i | ||||||
\(923\) | −23021.2 | −0.820968 | ||||||||
\(924\) | −14440.4 | + | 5610.84i | −0.514129 | + | 0.199765i | ||||
\(925\) | −4286.82 | −0.152378 | ||||||||
\(926\) | 2435.06i | 0.0864159i | ||||||||
\(927\) | 12383.5 | − | 4356.42i | 0.438756 | − | 0.154351i | ||||
\(928\) | 30284.5 | 1.07127 | ||||||||
\(929\) | 39730.9 | 1.40315 | 0.701576 | − | 0.712595i | \(-0.252480\pi\) | ||||
0.701576 | + | 0.712595i | \(0.252480\pi\) | |||||||
\(930\) | −4169.26 | − | 2953.01i | −0.147006 | − | 0.104121i | ||||
\(931\) | 4364.76 | − | 1860.45i | 0.153651 | − | 0.0654929i | ||||
\(932\) | − | 42606.5i | − | 1.49745i | ||||||
\(933\) | −11123.8 | − | 7878.78i | −0.390329 | − | 0.276463i | ||||
\(934\) | − | 6729.44i | − | 0.235754i | ||||||
\(935\) | − | 1085.24i | − | 0.0379584i | ||||||
\(936\) | −8255.72 | − | 23467.5i | −0.288298 | − | 0.819509i | ||||
\(937\) | − | 23843.3i | − | 0.831297i | −0.909525 | − | 0.415648i | \(-0.863555\pi\) | ||
0.909525 | − | 0.415648i | \(-0.136445\pi\) | |||||||
\(938\) | −7573.91 | + | 11461.6i | −0.263643 | + | 0.398970i | ||||
\(939\) | 16876.2 | − | 23826.9i | 0.586509 | − | 0.828074i | ||||
\(940\) | 20670.9 | 0.717247 | ||||||||
\(941\) | 2927.06 | 0.101402 | 0.0507011 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507011 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(942\) | −6906.61 | − | 4891.82i | −0.238885 | − | 0.169198i | ||||
\(943\) | − | 28923.1i | − | 0.998796i | ||||||
\(944\) | −14037.9 | −0.484000 | ||||||||
\(945\) | 9861.91 | − | 8457.22i | 0.339479 | − | 0.291125i | ||||
\(946\) | 6930.67 | 0.238198 | ||||||||
\(947\) | 11812.3i | 0.405330i | 0.979248 | + | 0.202665i | \(0.0649602\pi\) | ||||
−0.979248 | + | 0.202665i | \(0.935040\pi\) | |||||||
\(948\) | −24906.0 | − | 17640.4i | −0.853278 | − | 0.604361i | ||||
\(949\) | 59543.2 | 2.03673 | ||||||||
\(950\) | −328.097 | −0.0112051 | ||||||||
\(951\) | 6850.99 | − | 9672.69i | 0.233605 | − | 0.329820i | ||||
\(952\) | 1400.19 | − | 2118.91i | 0.0476686 | − | 0.0721368i | ||||
\(953\) | 2528.03i | 0.0859297i | 0.999077 | + | 0.0429648i | \(0.0136803\pi\) | ||||
−0.999077 | + | 0.0429648i | \(0.986320\pi\) | |||||||
\(954\) | 4540.50 | + | 12906.7i | 0.154092 | + | 0.438020i | ||||
\(955\) | 5521.16i | 0.187079i | ||||||||
\(956\) | − | 36734.4i | − | 1.24276i | ||||||
\(957\) | −18712.8 | − | 13253.9i | −0.632079 | − | 0.447690i | ||||
\(958\) | 3656.14i | 0.123303i | ||||||||
\(959\) | −25449.5 | + | 38512.7i | −0.856942 | + | 1.29681i | ||||
\(960\) | −4198.73 | − | 2973.89i | −0.141160 | − | 0.0999810i | ||||
\(961\) | −13172.2 | −0.442152 | ||||||||
\(962\) | 10463.1 | 0.350670 | ||||||||
\(963\) | 18562.2 | − | 6530.06i | 0.621141 | − | 0.218513i | ||||
\(964\) | − | 5178.59i | − | 0.173020i | ||||||
\(965\) | 7879.18 | 0.262839 | ||||||||
\(966\) | 4450.08 | + | 11453.0i | 0.148218 | + | 0.381464i | ||||
\(967\) | −6480.21 | −0.215501 | −0.107751 | − | 0.994178i | \(-0.534365\pi\) | ||||
−0.107751 | + | 0.994178i | \(0.534365\pi\) | |||||||
\(968\) | − | 11702.5i | − | 0.388567i | ||||||
\(969\) | −397.688 | + | 561.483i | −0.0131843 | + | 0.0186145i | ||||
\(970\) | 409.580 | 0.0135576 | ||||||||
\(971\) | −15246.9 | −0.503909 | −0.251955 | − | 0.967739i | \(-0.581073\pi\) | ||||
−0.251955 | + | 0.967739i | \(0.581073\pi\) | |||||||
\(972\) | 26845.5 | − | 1620.22i | 0.885876 | − | 0.0534657i | ||||
\(973\) | −14628.3 | + | 22137.0i | −0.481976 | + | 0.729373i | ||||
\(974\) | 14645.0i | 0.481784i | ||||||||
\(975\) | −4829.06 | + | 6817.99i | −0.158619 | + | 0.223949i | ||||
\(976\) | − | 1400.91i | − | 0.0459446i | ||||||
\(977\) | − | 11247.9i | − | 0.368324i | −0.982896 | − | 0.184162i | \(-0.941043\pi\) | ||
0.982896 | − | 0.184162i | \(-0.0589571\pi\) | |||||||
\(978\) | −6636.96 | + | 9370.51i | −0.217001 | + | 0.306376i | ||||
\(979\) | 11451.4i | 0.373838i | ||||||||
\(980\) | 4774.46 | + | 11201.2i | 0.155627 | + | 0.365112i | ||||
\(981\) | −9535.81 | − | 27106.3i | −0.310352 | − | 0.882199i | ||||
\(982\) | 11233.5 | 0.365045 | ||||||||
\(983\) | −30561.8 | −0.991629 | −0.495815 | − | 0.868428i | \(-0.665130\pi\) | ||||
−0.495815 | + | 0.868428i | \(0.665130\pi\) | |||||||
\(984\) | −9246.71 | + | 13055.1i | −0.299567 | + | 0.422950i | ||||
\(985\) | − | 1867.84i | − | 0.0604208i | ||||||
\(986\) | 1767.59 | 0.0570908 | ||||||||
\(987\) | −20294.7 | − | 52231.7i | −0.654496 | − | 1.68445i | ||||
\(988\) | −6316.69 | −0.203402 | ||||||||
\(989\) | 43358.7i | 1.39406i | ||||||||
\(990\) | −963.742 | − | 2739.51i | −0.0309391 | − | 0.0879469i | ||||
\(991\) | 13827.0 | 0.443218 | 0.221609 | − | 0.975136i | \(-0.428869\pi\) | ||||
0.221609 | + | 0.975136i | \(0.428869\pi\) | |||||||
\(992\) | 32251.9 | 1.03226 | ||||||||
\(993\) | 1147.72 | + | 812.910i | 0.0366786 | + | 0.0259788i | ||||
\(994\) | −5247.13 | − | 3467.35i | −0.167433 | − | 0.110641i | ||||
\(995\) | 2099.62i | 0.0668970i | ||||||||
\(996\) | 3945.49 | + | 2794.52i | 0.125520 | + | 0.0889034i | ||||
\(997\) | 33231.0i | 1.05560i | 0.849368 | + | 0.527801i | \(0.176983\pi\) | ||||
−0.849368 | + | 0.527801i | \(0.823017\pi\) | |||||||
\(998\) | − | 4410.36i | − | 0.139887i | ||||||
\(999\) | −6601.82 | + | 23133.4i | −0.209081 | + | 0.732641i |
(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 | 105.4.b.b.41.8 | yes | 16 | |
3.2 | odd | 2 | 105.4.b.a.41.9 | yes | 16 | ||
7.6 | odd | 2 | 105.4.b.a.41.8 | ✓ | 16 | ||
21.20 | even | 2 | inner | 105.4.b.b.41.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.b.a.41.8 | ✓ | 16 | 7.6 | odd | 2 | ||
105.4.b.a.41.9 | yes | 16 | 3.2 | odd | 2 | ||
105.4.b.b.41.8 | yes | 16 | 1.1 | even | 1 | trivial | |
105.4.b.b.41.9 | yes | 16 | 21.20 | even | 2 | inner |