Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 84 x^{8} - 140 x^{7} + 6309 x^{6} - 5214 x^{5} + 67648 x^{4} + 164178 x^{3} + 511389 x^{2} + \cdots + 443556 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 63.4 | ||
Root | \(2.13869 - 3.70432i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.63 |
Dual form | 74.4.c.b.47.4 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.63869 | − | 2.83829i | 0.315366 | − | 0.546230i | −0.664149 | − | 0.747600i | \(-0.731206\pi\) |
0.979515 | + | 0.201370i | \(0.0645394\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −9.76482 | + | 16.9132i | −0.873392 | + | 1.51276i | −0.0149266 | + | 0.999889i | \(0.504751\pi\) |
−0.858466 | + | 0.512871i | \(0.828582\pi\) | |||||||
\(6\) | −6.55476 | −0.445995 | ||||||||
\(7\) | −7.16860 | + | 12.4164i | −0.387068 | + | 0.670421i | −0.992054 | − | 0.125815i | \(-0.959845\pi\) |
0.604986 | + | 0.796236i | \(0.293179\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 8.12939 | + | 14.0805i | 0.301089 | + | 0.521501i | ||||
\(10\) | 39.0593 | 1.23516 | ||||||||
\(11\) | −40.4367 | −1.10837 | −0.554187 | − | 0.832392i | \(-0.686971\pi\) | ||||
−0.554187 | + | 0.832392i | \(0.686971\pi\) | |||||||
\(12\) | 6.55476 | + | 11.3532i | 0.157683 | + | 0.273115i | ||||
\(13\) | 29.3756 | − | 50.8801i | 0.626718 | − | 1.08551i | −0.361488 | − | 0.932377i | \(-0.617731\pi\) |
0.988206 | − | 0.153131i | \(-0.0489355\pi\) | |||||||
\(14\) | 28.6744 | 0.547397 | ||||||||
\(15\) | 32.0030 | + | 55.4309i | 0.550876 | + | 0.954146i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 43.7292 | + | 75.7411i | 0.623875 | + | 1.08058i | 0.988757 | + | 0.149530i | \(0.0477760\pi\) |
−0.364882 | + | 0.931054i | \(0.618891\pi\) | |||||||
\(18\) | 16.2588 | − | 28.1610i | 0.212902 | − | 0.368757i | ||||
\(19\) | −55.4904 | + | 96.1122i | −0.670020 | + | 1.16051i | 0.307878 | + | 0.951426i | \(0.400381\pi\) |
−0.977898 | + | 0.209083i | \(0.932952\pi\) | |||||||
\(20\) | −39.0593 | − | 67.6527i | −0.436696 | − | 0.756380i | ||||
\(21\) | 23.4942 | + | 40.6932i | 0.244136 | + | 0.422856i | ||||
\(22\) | 40.4367 | + | 70.0384i | 0.391869 | + | 0.678738i | ||||
\(23\) | −124.640 | −1.12996 | −0.564982 | − | 0.825103i | \(-0.691117\pi\) | ||||
−0.564982 | + | 0.825103i | \(0.691117\pi\) | |||||||
\(24\) | 13.1095 | − | 22.7064i | 0.111499 | − | 0.193121i | ||||
\(25\) | −128.203 | − | 222.055i | −1.02563 | − | 1.77644i | ||||
\(26\) | −117.503 | −0.886313 | ||||||||
\(27\) | 141.775 | 1.01054 | ||||||||
\(28\) | −28.6744 | − | 49.6655i | −0.193534 | − | 0.335211i | ||||
\(29\) | 169.593 | 1.08595 | 0.542977 | − | 0.839747i | \(-0.317297\pi\) | ||||
0.542977 | + | 0.839747i | \(0.317297\pi\) | |||||||
\(30\) | 64.0061 | − | 110.862i | 0.389528 | − | 0.674683i | ||||
\(31\) | −121.827 | −0.705830 | −0.352915 | − | 0.935655i | \(-0.614810\pi\) | ||||
−0.352915 | + | 0.935655i | \(0.614810\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −66.2632 | + | 114.771i | −0.349544 | + | 0.605427i | ||||
\(34\) | 87.4583 | − | 151.482i | 0.441146 | − | 0.764088i | ||||
\(35\) | −140.000 | − | 242.487i | −0.676124 | − | 1.17108i | ||||
\(36\) | −65.0351 | −0.301089 | ||||||||
\(37\) | 24.0088 | − | 223.778i | 0.106676 | − | 0.994294i | ||||
\(38\) | 221.962 | 0.947551 | ||||||||
\(39\) | −96.2751 | − | 166.753i | −0.395291 | − | 0.684664i | ||||
\(40\) | −78.1186 | + | 135.305i | −0.308791 | + | 0.534841i | ||||
\(41\) | −120.562 | + | 208.819i | −0.459234 | + | 0.795416i | −0.998921 | − | 0.0464495i | \(-0.985209\pi\) |
0.539687 | + | 0.841866i | \(0.318543\pi\) | |||||||
\(42\) | 46.9884 | − | 81.3864i | 0.172630 | − | 0.299005i | ||||
\(43\) | 222.885 | 0.790457 | 0.395229 | − | 0.918583i | \(-0.370665\pi\) | ||||
0.395229 | + | 0.918583i | \(0.370665\pi\) | |||||||
\(44\) | 80.8734 | − | 140.077i | 0.277094 | − | 0.479940i | ||||
\(45\) | −317.528 | −1.05187 | ||||||||
\(46\) | 124.640 | + | 215.882i | 0.399503 | + | 0.691959i | ||||
\(47\) | −242.748 | −0.753371 | −0.376686 | − | 0.926341i | \(-0.622936\pi\) | ||||
−0.376686 | + | 0.926341i | \(0.622936\pi\) | |||||||
\(48\) | −52.4381 | −0.157683 | ||||||||
\(49\) | 68.7224 | + | 119.031i | 0.200357 | + | 0.347028i | ||||
\(50\) | −256.407 | + | 444.110i | −0.725228 | + | 1.25613i | ||||
\(51\) | 286.634 | 0.786996 | ||||||||
\(52\) | 117.503 | + | 203.520i | 0.313359 | + | 0.542754i | ||||
\(53\) | 255.140 | + | 441.915i | 0.661247 | + | 1.14531i | 0.980288 | + | 0.197573i | \(0.0633059\pi\) |
−0.319041 | + | 0.947741i | \(0.603361\pi\) | |||||||
\(54\) | −141.775 | − | 245.562i | −0.357281 | − | 0.618830i | ||||
\(55\) | 394.857 | − | 683.912i | 0.968045 | − | 1.67670i | ||||
\(56\) | −57.3488 | + | 99.3310i | −0.136849 | + | 0.237030i | ||||
\(57\) | 181.863 | + | 314.996i | 0.422603 | + | 0.731970i | ||||
\(58\) | −169.593 | − | 293.744i | −0.383943 | − | 0.665009i | ||||
\(59\) | 138.167 | + | 239.312i | 0.304878 | + | 0.528065i | 0.977234 | − | 0.212163i | \(-0.0680509\pi\) |
−0.672356 | + | 0.740228i | \(0.734718\pi\) | |||||||
\(60\) | −256.024 | −0.550876 | ||||||||
\(61\) | 185.389 | − | 321.103i | 0.389125 | − | 0.673984i | −0.603207 | − | 0.797584i | \(-0.706111\pi\) |
0.992332 | + | 0.123601i | \(0.0394442\pi\) | |||||||
\(62\) | 121.827 | + | 211.010i | 0.249549 | + | 0.432231i | ||||
\(63\) | −233.105 | −0.466167 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 573.696 | + | 993.670i | 1.09474 | + | 1.89615i | ||||
\(66\) | 265.053 | 0.494329 | ||||||||
\(67\) | 55.8336 | − | 96.7066i | 0.101808 | − | 0.176337i | −0.810621 | − | 0.585571i | \(-0.800871\pi\) |
0.912430 | + | 0.409233i | \(0.134204\pi\) | |||||||
\(68\) | −349.833 | −0.623875 | ||||||||
\(69\) | −204.246 | + | 353.764i | −0.356352 | + | 0.617220i | ||||
\(70\) | −280.000 | + | 484.975i | −0.478092 | + | 0.828080i | ||||
\(71\) | 304.129 | − | 526.767i | 0.508359 | − | 0.880504i | −0.491594 | − | 0.870825i | \(-0.663586\pi\) |
0.999953 | − | 0.00967951i | \(-0.00308113\pi\) | |||||||
\(72\) | 65.0351 | + | 112.644i | 0.106451 | + | 0.184378i | ||||
\(73\) | −64.7080 | −0.103747 | −0.0518733 | − | 0.998654i | \(-0.516519\pi\) | ||||
−0.0518733 | + | 0.998654i | \(0.516519\pi\) | |||||||
\(74\) | −411.604 | + | 182.193i | −0.646594 | + | 0.286210i | ||||
\(75\) | −840.343 | −1.29379 | ||||||||
\(76\) | −221.962 | − | 384.449i | −0.335010 | − | 0.580254i | ||||
\(77\) | 289.874 | − | 502.077i | 0.429016 | − | 0.743078i | ||||
\(78\) | −192.550 | + | 333.507i | −0.279513 | + | 0.484131i | ||||
\(79\) | 444.196 | − | 769.369i | 0.632606 | − | 1.09571i | −0.354411 | − | 0.935090i | \(-0.615318\pi\) |
0.987017 | − | 0.160616i | \(-0.0513482\pi\) | |||||||
\(80\) | 312.474 | 0.436696 | ||||||||
\(81\) | 12.8325 | − | 22.2265i | 0.0176029 | − | 0.0304890i | ||||
\(82\) | 482.247 | 0.649455 | ||||||||
\(83\) | 643.348 | + | 1114.31i | 0.850802 | + | 1.47363i | 0.880485 | + | 0.474073i | \(0.157217\pi\) |
−0.0296830 | + | 0.999559i | \(0.509450\pi\) | |||||||
\(84\) | −187.954 | −0.244136 | ||||||||
\(85\) | −1708.03 | −2.17955 | ||||||||
\(86\) | −222.885 | − | 386.048i | −0.279469 | − | 0.484054i | ||||
\(87\) | 277.911 | − | 481.356i | 0.342473 | − | 0.593181i | ||||
\(88\) | −323.493 | −0.391869 | ||||||||
\(89\) | −201.644 | − | 349.257i | −0.240160 | − | 0.415969i | 0.720600 | − | 0.693351i | \(-0.243866\pi\) |
−0.960760 | + | 0.277382i | \(0.910533\pi\) | |||||||
\(90\) | 317.528 | + | 549.975i | 0.371893 | + | 0.644138i | ||||
\(91\) | 421.164 | + | 729.478i | 0.485165 | + | 0.840330i | ||||
\(92\) | 249.279 | − | 431.765i | 0.282491 | − | 0.489289i | ||||
\(93\) | −199.636 | + | 345.780i | −0.222595 | + | 0.385546i | ||||
\(94\) | 242.748 | + | 420.452i | 0.266357 | + | 0.461344i | ||||
\(95\) | −1083.71 | − | 1877.04i | −1.17038 | − | 2.02716i | ||||
\(96\) | 52.4381 | + | 90.8254i | 0.0557494 | + | 0.0965607i | ||||
\(97\) | 1827.81 | 1.91326 | 0.956631 | − | 0.291303i | \(-0.0940886\pi\) | ||||
0.956631 | + | 0.291303i | \(0.0940886\pi\) | |||||||
\(98\) | 137.445 | − | 238.061i | 0.141674 | − | 0.245386i | ||||
\(99\) | −328.726 | − | 569.369i | −0.333719 | − | 0.578018i | ||||
\(100\) | 1025.63 | 1.02563 | ||||||||
\(101\) | −375.420 | −0.369858 | −0.184929 | − | 0.982752i | \(-0.559206\pi\) | ||||
−0.184929 | + | 0.982752i | \(0.559206\pi\) | |||||||
\(102\) | −286.634 | − | 496.465i | −0.278245 | − | 0.481935i | ||||
\(103\) | −396.336 | −0.379147 | −0.189573 | − | 0.981867i | \(-0.560711\pi\) | ||||
−0.189573 | + | 0.981867i | \(0.560711\pi\) | |||||||
\(104\) | 235.005 | − | 407.041i | 0.221578 | − | 0.383785i | ||||
\(105\) | −917.668 | −0.852907 | ||||||||
\(106\) | 510.279 | − | 883.829i | 0.467572 | − | 0.809859i | ||||
\(107\) | −740.214 | + | 1282.09i | −0.668778 | + | 1.15836i | 0.309469 | + | 0.950910i | \(0.399849\pi\) |
−0.978246 | + | 0.207447i | \(0.933484\pi\) | |||||||
\(108\) | −283.551 | + | 491.125i | −0.252636 | + | 0.437579i | ||||
\(109\) | 326.247 | + | 565.076i | 0.286686 | + | 0.496555i | 0.973017 | − | 0.230735i | \(-0.0741130\pi\) |
−0.686331 | + | 0.727290i | \(0.740780\pi\) | |||||||
\(110\) | −1579.43 | −1.36902 | ||||||||
\(111\) | −595.805 | − | 434.847i | −0.509471 | − | 0.371836i | ||||
\(112\) | 229.395 | 0.193534 | ||||||||
\(113\) | 417.178 | + | 722.574i | 0.347299 | + | 0.601540i | 0.985769 | − | 0.168107i | \(-0.0537655\pi\) |
−0.638469 | + | 0.769647i | \(0.720432\pi\) | |||||||
\(114\) | 363.726 | − | 629.993i | 0.298825 | − | 0.517581i | ||||
\(115\) | 1217.08 | − | 2108.05i | 0.986902 | − | 1.70936i | ||||
\(116\) | −339.187 | + | 587.488i | −0.271489 | + | 0.470232i | ||||
\(117\) | 955.224 | 0.754790 | ||||||||
\(118\) | 276.334 | − | 478.625i | 0.215582 | − | 0.373398i | ||||
\(119\) | −1253.91 | −0.965928 | ||||||||
\(120\) | 256.024 | + | 443.447i | 0.194764 | + | 0.337342i | ||||
\(121\) | 304.125 | 0.228493 | ||||||||
\(122\) | −741.555 | −0.550305 | ||||||||
\(123\) | 395.127 | + | 684.380i | 0.289654 | + | 0.501695i | ||||
\(124\) | 243.654 | − | 422.020i | 0.176458 | − | 0.305633i | ||||
\(125\) | 2566.33 | 1.83632 | ||||||||
\(126\) | 233.105 | + | 403.750i | 0.164815 | + | 0.285468i | ||||
\(127\) | 234.631 | + | 406.392i | 0.163938 | + | 0.283949i | 0.936278 | − | 0.351261i | \(-0.114247\pi\) |
−0.772340 | + | 0.635210i | \(0.780914\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 365.240 | − | 632.614i | 0.249283 | − | 0.431771i | ||||
\(130\) | 1147.39 | − | 1987.34i | 0.774099 | − | 1.34078i | ||||
\(131\) | −803.797 | − | 1392.22i | −0.536092 | − | 0.928539i | −0.999110 | − | 0.0421899i | \(-0.986567\pi\) |
0.463017 | − | 0.886349i | \(-0.346767\pi\) | |||||||
\(132\) | −265.053 | − | 459.085i | −0.174772 | − | 0.302714i | ||||
\(133\) | −795.577 | − | 1377.98i | −0.518687 | − | 0.898391i | ||||
\(134\) | −223.334 | −0.143979 | ||||||||
\(135\) | −1384.41 | + | 2397.87i | −0.882602 | + | 1.52871i | ||||
\(136\) | 349.833 | + | 605.929i | 0.220573 | + | 0.382044i | ||||
\(137\) | −2083.19 | −1.29911 | −0.649557 | − | 0.760313i | \(-0.725046\pi\) | ||||
−0.649557 | + | 0.760313i | \(0.725046\pi\) | |||||||
\(138\) | 816.984 | 0.503958 | ||||||||
\(139\) | −15.9174 | − | 27.5698i | −0.00971293 | − | 0.0168233i | 0.861128 | − | 0.508388i | \(-0.169758\pi\) |
−0.870841 | + | 0.491565i | \(0.836425\pi\) | |||||||
\(140\) | 1120.00 | 0.676124 | ||||||||
\(141\) | −397.789 | + | 688.990i | −0.237588 | + | 0.411514i | ||||
\(142\) | −1216.52 | −0.718929 | ||||||||
\(143\) | −1187.85 | + | 2057.42i | −0.694638 | + | 1.20315i | ||||
\(144\) | 130.070 | − | 225.288i | 0.0752721 | − | 0.130375i | ||||
\(145\) | −1656.05 | + | 2868.36i | −0.948464 | + | 1.64279i | ||||
\(146\) | 64.7080 | + | 112.077i | 0.0366799 | + | 0.0635315i | ||||
\(147\) | 450.459 | 0.252743 | ||||||||
\(148\) | 727.172 | + | 530.725i | 0.403873 | + | 0.294766i | ||||
\(149\) | −836.896 | −0.460142 | −0.230071 | − | 0.973174i | \(-0.573896\pi\) | ||||
−0.230071 | + | 0.973174i | \(0.573896\pi\) | |||||||
\(150\) | 840.343 | + | 1455.52i | 0.457425 | + | 0.792283i | ||||
\(151\) | −848.341 | + | 1469.37i | −0.457199 | + | 0.791892i | −0.998812 | − | 0.0487364i | \(-0.984481\pi\) |
0.541613 | + | 0.840628i | \(0.317814\pi\) | |||||||
\(152\) | −443.923 | + | 768.898i | −0.236888 | + | 0.410302i | ||||
\(153\) | −710.983 | + | 1231.46i | −0.375683 | + | 0.650703i | ||||
\(154\) | −1159.50 | −0.606720 | ||||||||
\(155\) | 1189.62 | − | 2060.48i | 0.616467 | − | 1.06775i | ||||
\(156\) | 770.201 | 0.395291 | ||||||||
\(157\) | 1406.86 | + | 2436.75i | 0.715157 | + | 1.23869i | 0.962899 | + | 0.269863i | \(0.0869783\pi\) |
−0.247741 | + | 0.968826i | \(0.579688\pi\) | |||||||
\(158\) | −1776.78 | −0.894641 | ||||||||
\(159\) | 1672.38 | 0.834140 | ||||||||
\(160\) | −312.474 | − | 541.221i | −0.154395 | − | 0.267421i | ||||
\(161\) | 893.492 | − | 1547.57i | 0.437373 | − | 0.757552i | ||||
\(162\) | −51.3299 | −0.0248942 | ||||||||
\(163\) | 1042.63 | + | 1805.89i | 0.501012 | + | 0.867779i | 0.999999 | + | 0.00116944i | \(0.000372245\pi\) |
−0.498987 | + | 0.866610i | \(0.666294\pi\) | |||||||
\(164\) | −482.247 | − | 835.277i | −0.229617 | − | 0.397708i | ||||
\(165\) | −1294.10 | − | 2241.44i | −0.610577 | − | 1.05755i | ||||
\(166\) | 1286.70 | − | 2228.62i | 0.601608 | − | 1.04202i | ||||
\(167\) | 911.200 | − | 1578.24i | 0.422220 | − | 0.731307i | −0.573936 | − | 0.818900i | \(-0.694584\pi\) |
0.996156 | + | 0.0875933i | \(0.0279176\pi\) | |||||||
\(168\) | 187.954 | + | 325.546i | 0.0863152 | + | 0.149502i | ||||
\(169\) | −627.355 | − | 1086.61i | −0.285551 | − | 0.494589i | ||||
\(170\) | 1708.03 | + | 2958.39i | 0.770588 | + | 1.33470i | ||||
\(171\) | −1804.41 | −0.806941 | ||||||||
\(172\) | −445.770 | + | 772.097i | −0.197614 | + | 0.342278i | ||||
\(173\) | 1202.26 | + | 2082.38i | 0.528360 | + | 0.915147i | 0.999453 | + | 0.0330633i | \(0.0105263\pi\) |
−0.471093 | + | 0.882084i | \(0.656140\pi\) | |||||||
\(174\) | −1111.64 | −0.484330 | ||||||||
\(175\) | 3676.16 | 1.58795 | ||||||||
\(176\) | 323.493 | + | 560.307i | 0.138547 | + | 0.239970i | ||||
\(177\) | 905.652 | 0.384593 | ||||||||
\(178\) | −403.288 | + | 698.515i | −0.169819 | + | 0.294134i | ||||
\(179\) | 1980.59 | 0.827019 | 0.413509 | − | 0.910500i | \(-0.364303\pi\) | ||||
0.413509 | + | 0.910500i | \(0.364303\pi\) | |||||||
\(180\) | 635.056 | − | 1099.95i | 0.262968 | − | 0.455475i | ||||
\(181\) | 584.421 | − | 1012.25i | 0.239998 | − | 0.415689i | −0.720715 | − | 0.693231i | \(-0.756187\pi\) |
0.960713 | + | 0.277542i | \(0.0895199\pi\) | |||||||
\(182\) | 842.328 | − | 1458.96i | 0.343063 | − | 0.594203i | ||||
\(183\) | −607.590 | − | 1052.38i | −0.245433 | − | 0.425103i | ||||
\(184\) | −997.118 | −0.399503 | ||||||||
\(185\) | 3550.35 | + | 2591.22i | 1.41096 | + | 1.02978i | ||||
\(186\) | 798.545 | 0.314797 | ||||||||
\(187\) | −1768.26 | − | 3062.72i | −0.691487 | − | 1.19769i | ||||
\(188\) | 485.496 | − | 840.904i | 0.188343 | − | 0.326219i | ||||
\(189\) | −1016.33 | + | 1760.34i | −0.391149 | + | 0.677491i | ||||
\(190\) | −2167.42 | + | 3754.08i | −0.827584 | + | 1.43342i | ||||
\(191\) | 1907.58 | 0.722659 | 0.361329 | − | 0.932438i | \(-0.382323\pi\) | ||||
0.361329 | + | 0.932438i | \(0.382323\pi\) | |||||||
\(192\) | 104.876 | − | 181.651i | 0.0394208 | − | 0.0682787i | ||||
\(193\) | −4944.00 | −1.84392 | −0.921960 | − | 0.387285i | \(-0.873413\pi\) | ||||
−0.921960 | + | 0.387285i | \(0.873413\pi\) | |||||||
\(194\) | −1827.81 | − | 3165.87i | −0.676440 | − | 1.17163i | ||||
\(195\) | 3760.44 | 1.38098 | ||||||||
\(196\) | −549.779 | −0.200357 | ||||||||
\(197\) | −1041.70 | − | 1804.27i | −0.376741 | − | 0.652534i | 0.613845 | − | 0.789426i | \(-0.289622\pi\) |
−0.990586 | + | 0.136892i | \(0.956289\pi\) | |||||||
\(198\) | −657.451 | + | 1138.74i | −0.235975 | + | 0.408720i | ||||
\(199\) | −699.778 | −0.249276 | −0.124638 | − | 0.992202i | \(-0.539777\pi\) | ||||
−0.124638 | + | 0.992202i | \(0.539777\pi\) | |||||||
\(200\) | −1025.63 | − | 1776.44i | −0.362614 | − | 0.628066i | ||||
\(201\) | −182.988 | − | 316.944i | −0.0642137 | − | 0.111221i | ||||
\(202\) | 375.420 | + | 650.247i | 0.130765 | + | 0.226491i | ||||
\(203\) | −1215.75 | + | 2105.73i | −0.420338 | + | 0.728047i | ||||
\(204\) | −573.268 | + | 992.930i | −0.196749 | + | 0.340779i | ||||
\(205\) | −2354.53 | − | 4078.16i | −0.802183 | − | 1.38942i | ||||
\(206\) | 396.336 | + | 686.474i | 0.134049 | + | 0.232179i | ||||
\(207\) | −1013.25 | − | 1754.99i | −0.340219 | − | 0.589277i | ||||
\(208\) | −940.020 | −0.313359 | ||||||||
\(209\) | 2243.85 | − | 3886.46i | 0.742633 | − | 1.28628i | ||||
\(210\) | 917.668 | + | 1589.45i | 0.301548 | + | 0.522296i | ||||
\(211\) | −1986.19 | −0.648032 | −0.324016 | − | 0.946052i | \(-0.605033\pi\) | ||||
−0.324016 | + | 0.946052i | \(0.605033\pi\) | |||||||
\(212\) | −2041.12 | −0.661247 | ||||||||
\(213\) | −996.747 | − | 1726.42i | −0.320638 | − | 0.555362i | ||||
\(214\) | 2960.86 | 0.945794 | ||||||||
\(215\) | −2176.43 | + | 3769.69i | −0.690379 | + | 1.19577i | ||||
\(216\) | 1134.20 | 0.357281 | ||||||||
\(217\) | 873.327 | − | 1512.65i | 0.273204 | − | 0.473204i | ||||
\(218\) | 652.494 | − | 1130.15i | 0.202718 | − | 0.351117i | ||||
\(219\) | −106.036 | + | 183.660i | −0.0327181 | + | 0.0566695i | ||||
\(220\) | 1579.43 | + | 2735.65i | 0.484023 | + | 0.838352i | ||||
\(221\) | 5138.29 | 1.56398 | ||||||||
\(222\) | −157.372 | + | 1466.81i | −0.0475771 | + | 0.443450i | ||||
\(223\) | −6485.56 | −1.94756 | −0.973778 | − | 0.227500i | \(-0.926945\pi\) | ||||
−0.973778 | + | 0.227500i | \(0.926945\pi\) | |||||||
\(224\) | −229.395 | − | 397.324i | −0.0684246 | − | 0.118515i | ||||
\(225\) | 2084.43 | − | 3610.34i | 0.617610 | − | 1.06973i | ||||
\(226\) | 834.356 | − | 1445.15i | 0.245578 | − | 0.425353i | ||||
\(227\) | 326.504 | − | 565.522i | 0.0954663 | − | 0.165353i | −0.814337 | − | 0.580393i | \(-0.802899\pi\) |
0.909803 | + | 0.415040i | \(0.136232\pi\) | |||||||
\(228\) | −1454.91 | −0.422603 | ||||||||
\(229\) | −915.324 | + | 1585.39i | −0.264132 | + | 0.457491i | −0.967336 | − | 0.253498i | \(-0.918419\pi\) |
0.703204 | + | 0.710989i | \(0.251752\pi\) | |||||||
\(230\) | −4868.34 | −1.39569 | ||||||||
\(231\) | −950.028 | − | 1645.50i | −0.270594 | − | 0.468683i | ||||
\(232\) | 1356.75 | 0.383943 | ||||||||
\(233\) | −1770.50 | −0.497809 | −0.248904 | − | 0.968528i | \(-0.580071\pi\) | ||||
−0.248904 | + | 0.968528i | \(0.580071\pi\) | |||||||
\(234\) | −955.224 | − | 1654.50i | −0.266859 | − | 0.462213i | ||||
\(235\) | 2370.39 | − | 4105.64i | 0.657988 | − | 1.13967i | ||||
\(236\) | −1105.34 | −0.304878 | ||||||||
\(237\) | −1455.80 | − | 2521.52i | −0.399005 | − | 0.691097i | ||||
\(238\) | 1253.91 | + | 2171.83i | 0.341507 | + | 0.591508i | ||||
\(239\) | −362.719 | − | 628.248i | −0.0981689 | − | 0.170034i | 0.812758 | − | 0.582602i | \(-0.197965\pi\) |
−0.910927 | + | 0.412568i | \(0.864632\pi\) | |||||||
\(240\) | 512.048 | − | 886.894i | 0.137719 | − | 0.238537i | ||||
\(241\) | 2196.19 | − | 3803.91i | 0.587008 | − | 1.01673i | −0.407614 | − | 0.913154i | \(-0.633639\pi\) |
0.994622 | − | 0.103573i | \(-0.0330276\pi\) | |||||||
\(242\) | −304.125 | − | 526.760i | −0.0807846 | − | 0.139923i | ||||
\(243\) | 1871.91 | + | 3242.25i | 0.494170 | + | 0.855927i | ||||
\(244\) | 741.555 | + | 1284.41i | 0.194562 | + | 0.336992i | ||||
\(245\) | −2684.25 | −0.699960 | ||||||||
\(246\) | 790.254 | − | 1368.76i | 0.204816 | − | 0.354752i | ||||
\(247\) | 3260.13 | + | 5646.72i | 0.839827 | + | 1.45462i | ||||
\(248\) | −974.614 | −0.249549 | ||||||||
\(249\) | 4216.99 | 1.07326 | ||||||||
\(250\) | −2566.33 | − | 4445.02i | −0.649236 | − | 1.12451i | ||||
\(251\) | 2148.42 | 0.540266 | 0.270133 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270133 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(252\) | 466.211 | − | 807.501i | 0.116542 | − | 0.201856i | ||||
\(253\) | 5040.02 | 1.25242 | ||||||||
\(254\) | 469.262 | − | 812.785i | 0.115922 | − | 0.200782i | ||||
\(255\) | −2798.93 | + | 4847.89i | −0.687356 | + | 1.19054i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −435.037 | − | 753.506i | −0.105591 | − | 0.182889i | 0.808389 | − | 0.588649i | \(-0.200340\pi\) |
−0.913979 | + | 0.405760i | \(0.867007\pi\) | |||||||
\(258\) | −1460.96 | −0.352540 | ||||||||
\(259\) | 2606.40 | + | 1902.28i | 0.625305 | + | 0.456377i | ||||
\(260\) | −4589.56 | −1.09474 | ||||||||
\(261\) | 1378.69 | + | 2387.96i | 0.326968 | + | 0.566326i | ||||
\(262\) | −1607.59 | + | 2784.44i | −0.379075 | + | 0.656576i | ||||
\(263\) | −1049.43 | + | 1817.66i | −0.246048 | + | 0.426167i | −0.962426 | − | 0.271545i | \(-0.912465\pi\) |
0.716378 | + | 0.697712i | \(0.245799\pi\) | |||||||
\(264\) | −530.105 | + | 918.169i | −0.123582 | + | 0.214051i | ||||
\(265\) | −9965.57 | −2.31011 | ||||||||
\(266\) | −1591.15 | + | 2755.96i | −0.366767 | + | 0.635259i | ||||
\(267\) | −1321.73 | −0.302953 | ||||||||
\(268\) | 223.334 | + | 386.826i | 0.0509041 | + | 0.0881686i | ||||
\(269\) | 5485.74 | 1.24339 | 0.621695 | − | 0.783260i | \(-0.286444\pi\) | ||||
0.621695 | + | 0.783260i | \(0.286444\pi\) | |||||||
\(270\) | 5537.65 | 1.24819 | ||||||||
\(271\) | 3048.66 | + | 5280.43i | 0.683369 | + | 1.18363i | 0.973946 | + | 0.226778i | \(0.0728192\pi\) |
−0.290578 | + | 0.956851i | \(0.593847\pi\) | |||||||
\(272\) | 699.667 | − | 1211.86i | 0.155969 | − | 0.270146i | ||||
\(273\) | 2760.63 | 0.612018 | ||||||||
\(274\) | 2083.19 | + | 3608.19i | 0.459306 | + | 0.795542i | ||||
\(275\) | 5184.12 | + | 8979.16i | 1.13678 | + | 1.96896i | ||||
\(276\) | −816.984 | − | 1415.06i | −0.178176 | − | 0.308610i | ||||
\(277\) | 229.957 | − | 398.297i | 0.0498800 | − | 0.0863948i | −0.840007 | − | 0.542575i | \(-0.817449\pi\) |
0.889887 | + | 0.456180i | \(0.150783\pi\) | |||||||
\(278\) | −31.8348 | + | 55.1395i | −0.00686808 | + | 0.0118959i | ||||
\(279\) | −990.377 | − | 1715.38i | −0.212517 | − | 0.368091i | ||||
\(280\) | −1120.00 | − | 1939.90i | −0.239046 | − | 0.414040i | ||||
\(281\) | −1367.74 | − | 2369.00i | −0.290365 | − | 0.502927i | 0.683531 | − | 0.729922i | \(-0.260443\pi\) |
−0.973896 | + | 0.226994i | \(0.927110\pi\) | |||||||
\(282\) | 1591.16 | 0.336000 | ||||||||
\(283\) | 806.341 | − | 1396.62i | 0.169371 | − | 0.293359i | −0.768828 | − | 0.639456i | \(-0.779160\pi\) |
0.938199 | + | 0.346097i | \(0.112493\pi\) | |||||||
\(284\) | 1216.52 | + | 2107.07i | 0.254180 | + | 0.440252i | ||||
\(285\) | −7103.45 | −1.47639 | ||||||||
\(286\) | 4751.41 | 0.982367 | ||||||||
\(287\) | −1728.52 | − | 2993.88i | −0.355509 | − | 0.615760i | ||||
\(288\) | −520.281 | −0.106451 | ||||||||
\(289\) | −1367.98 | + | 2369.41i | −0.278441 | + | 0.482273i | ||||
\(290\) | 6624.19 | 1.34133 | ||||||||
\(291\) | 2995.22 | − | 5187.87i | 0.603378 | − | 1.04508i | ||||
\(292\) | 129.416 | − | 224.155i | 0.0259366 | − | 0.0449236i | ||||
\(293\) | −71.6884 | + | 124.168i | −0.0142938 | + | 0.0247576i | −0.873084 | − | 0.487570i | \(-0.837883\pi\) |
0.858790 | + | 0.512328i | \(0.171217\pi\) | |||||||
\(294\) | −450.459 | − | 780.217i | −0.0893581 | − | 0.154773i | ||||
\(295\) | −5396.71 | −1.06511 | ||||||||
\(296\) | 192.071 | − | 1790.22i | 0.0377158 | − | 0.351536i | ||||
\(297\) | −5732.93 | −1.12006 | ||||||||
\(298\) | 836.896 | + | 1449.55i | 0.162685 | + | 0.281778i | ||||
\(299\) | −3661.37 | + | 6341.68i | −0.708169 | + | 1.22658i | ||||
\(300\) | 1680.69 | − | 2911.03i | 0.323448 | − | 0.560229i | ||||
\(301\) | −1597.77 | + | 2767.43i | −0.305961 | + | 0.529939i | ||||
\(302\) | 3393.36 | 0.646577 | ||||||||
\(303\) | −615.197 | + | 1065.55i | −0.116641 | + | 0.202028i | ||||
\(304\) | 1775.69 | 0.335010 | ||||||||
\(305\) | 3620.58 | + | 6271.02i | 0.679717 | + | 1.17730i | ||||
\(306\) | 2843.93 | 0.531296 | ||||||||
\(307\) | 9023.26 | 1.67747 | 0.838737 | − | 0.544537i | \(-0.183294\pi\) | ||||
0.838737 | + | 0.544537i | \(0.183294\pi\) | |||||||
\(308\) | 1159.50 | + | 2008.31i | 0.214508 | + | 0.371539i | ||||
\(309\) | −649.472 | + | 1124.92i | −0.119570 | + | 0.207101i | ||||
\(310\) | −4758.47 | −0.871815 | ||||||||
\(311\) | −3418.00 | − | 5920.14i | −0.623205 | − | 1.07942i | −0.988885 | − | 0.148682i | \(-0.952497\pi\) |
0.365680 | − | 0.930741i | \(-0.380837\pi\) | |||||||
\(312\) | −770.201 | − | 1334.03i | −0.139757 | − | 0.242065i | ||||
\(313\) | 3652.69 | + | 6326.64i | 0.659623 | + | 1.14250i | 0.980713 | + | 0.195452i | \(0.0626175\pi\) |
−0.321090 | + | 0.947049i | \(0.604049\pi\) | |||||||
\(314\) | 2813.72 | − | 4873.51i | 0.505693 | − | 0.875885i | ||||
\(315\) | 2276.23 | − | 3942.55i | 0.407147 | − | 0.705199i | ||||
\(316\) | 1776.78 | + | 3077.48i | 0.316303 | + | 0.547853i | ||||
\(317\) | −3370.39 | − | 5837.69i | −0.597161 | − | 1.03431i | −0.993238 | − | 0.116096i | \(-0.962962\pi\) |
0.396077 | − | 0.918217i | \(-0.370371\pi\) | |||||||
\(318\) | −1672.38 | − | 2896.64i | −0.294913 | − | 0.510804i | ||||
\(319\) | −6857.79 | −1.20364 | ||||||||
\(320\) | −624.949 | + | 1082.44i | −0.109174 | + | 0.189095i | ||||
\(321\) | 2425.96 | + | 4201.89i | 0.421819 | + | 0.730613i | ||||
\(322\) | −3573.97 | −0.618539 | ||||||||
\(323\) | −9706.20 | −1.67204 | ||||||||
\(324\) | 51.3299 | + | 88.9060i | 0.00880143 | + | 0.0152445i | ||||
\(325\) | −15064.2 | −2.57112 | ||||||||
\(326\) | 2085.26 | − | 3611.77i | 0.354269 | − | 0.613612i | ||||
\(327\) | 2138.47 | 0.361644 | ||||||||
\(328\) | −964.494 | + | 1670.55i | −0.162364 | + | 0.281222i | ||||
\(329\) | 1740.16 | − | 3014.05i | 0.291606 | − | 0.505076i | ||||
\(330\) | −2588.19 | + | 4482.88i | −0.431743 | + | 0.747801i | ||||
\(331\) | 157.812 | + | 273.339i | 0.0262059 | + | 0.0453900i | 0.878831 | − | 0.477133i | \(-0.158324\pi\) |
−0.852625 | + | 0.522523i | \(0.824991\pi\) | |||||||
\(332\) | −5146.78 | −0.850802 | ||||||||
\(333\) | 3346.09 | − | 1481.12i | 0.550644 | − | 0.243739i | ||||
\(334\) | −3644.80 | −0.597109 | ||||||||
\(335\) | 1090.41 | + | 1888.64i | 0.177837 | + | 0.308023i | ||||
\(336\) | 375.908 | − | 651.091i | 0.0610340 | − | 0.105714i | ||||
\(337\) | −1236.33 | + | 2141.39i | −0.199844 | + | 0.346140i | −0.948478 | − | 0.316844i | \(-0.897377\pi\) |
0.748634 | + | 0.662984i | \(0.230710\pi\) | |||||||
\(338\) | −1254.71 | + | 2173.22i | −0.201915 | + | 0.349727i | ||||
\(339\) | 2734.50 | 0.438106 | ||||||||
\(340\) | 3416.06 | − | 5916.79i | 0.544888 | − | 0.943773i | ||||
\(341\) | 4926.27 | 0.782324 | ||||||||
\(342\) | 1804.41 | + | 3125.34i | 0.285297 | + | 0.494149i | ||||
\(343\) | −6888.23 | −1.08434 | ||||||||
\(344\) | 1783.08 | 0.279469 | ||||||||
\(345\) | −3988.85 | − | 6908.89i | −0.622471 | − | 1.07815i | ||||
\(346\) | 2404.53 | − | 4164.76i | 0.373607 | − | 0.647107i | ||||
\(347\) | 11277.1 | 1.74463 | 0.872314 | − | 0.488946i | \(-0.162618\pi\) | ||||
0.872314 | + | 0.488946i | \(0.162618\pi\) | |||||||
\(348\) | 1111.64 | + | 1925.42i | 0.171237 | + | 0.296590i | ||||
\(349\) | −636.556 | − | 1102.55i | −0.0976334 | − | 0.169106i | 0.813071 | − | 0.582164i | \(-0.197794\pi\) |
−0.910705 | + | 0.413058i | \(0.864461\pi\) | |||||||
\(350\) | −3676.16 | − | 6367.29i | −0.561425 | − | 0.972417i | ||||
\(351\) | 4164.74 | − | 7213.55i | 0.633326 | − | 1.09695i | ||||
\(352\) | 646.987 | − | 1120.61i | 0.0979674 | − | 0.169684i | ||||
\(353\) | −1108.53 | − | 1920.03i | −0.167142 | − | 0.289499i | 0.770272 | − | 0.637716i | \(-0.220121\pi\) |
−0.937414 | + | 0.348217i | \(0.886787\pi\) | |||||||
\(354\) | −905.652 | − | 1568.64i | −0.135974 | − | 0.235514i | ||||
\(355\) | 5939.54 | + | 10287.6i | 0.887994 | + | 1.53805i | ||||
\(356\) | 1613.15 | 0.240160 | ||||||||
\(357\) | −2054.77 | + | 3558.96i | −0.304621 | + | 0.527619i | ||||
\(358\) | −1980.59 | − | 3430.48i | −0.292395 | − | 0.506443i | ||||
\(359\) | 11858.5 | 1.74336 | 0.871680 | − | 0.490076i | \(-0.163031\pi\) | ||||
0.871680 | + | 0.490076i | \(0.163031\pi\) | |||||||
\(360\) | −2540.23 | −0.371893 | ||||||||
\(361\) | −2728.88 | − | 4726.55i | −0.397853 | − | 0.689102i | ||||
\(362\) | −2337.68 | −0.339409 | ||||||||
\(363\) | 498.366 | − | 863.196i | 0.0720591 | − | 0.124810i | ||||
\(364\) | −3369.31 | −0.485165 | ||||||||
\(365\) | 631.862 | − | 1094.42i | 0.0906114 | − | 0.156944i | ||||
\(366\) | −1215.18 | + | 2104.75i | −0.173548 | + | 0.300593i | ||||
\(367\) | −744.563 | + | 1289.62i | −0.105901 | + | 0.183427i | −0.914106 | − | 0.405475i | \(-0.867106\pi\) |
0.808205 | + | 0.588902i | \(0.200439\pi\) | |||||||
\(368\) | 997.118 | + | 1727.06i | 0.141246 | + | 0.244644i | ||||
\(369\) | −3920.38 | −0.553080 | ||||||||
\(370\) | 937.767 | − | 8740.61i | 0.131763 | − | 1.22812i | ||||
\(371\) | −7315.97 | −1.02379 | ||||||||
\(372\) | −798.545 | − | 1383.12i | −0.111297 | − | 0.192773i | ||||
\(373\) | 4540.62 | − | 7864.59i | 0.630307 | − | 1.09172i | −0.357182 | − | 0.934035i | \(-0.616262\pi\) |
0.987489 | − | 0.157689i | \(-0.0504043\pi\) | |||||||
\(374\) | −3536.52 | + | 6125.44i | −0.488955 | + | 0.846895i | ||||
\(375\) | 4205.42 | − | 7284.00i | 0.579112 | − | 1.00305i | ||||
\(376\) | −1941.98 | −0.266357 | ||||||||
\(377\) | 4981.91 | − | 8628.92i | 0.680587 | − | 1.17881i | ||||
\(378\) | 4065.33 | 0.553169 | ||||||||
\(379\) | −6322.24 | − | 10950.4i | −0.856864 | − | 1.48413i | −0.874905 | − | 0.484295i | \(-0.839076\pi\) |
0.0180411 | − | 0.999837i | \(-0.494257\pi\) | |||||||
\(380\) | 8669.67 | 1.17038 | ||||||||
\(381\) | 1537.95 | 0.206802 | ||||||||
\(382\) | −1907.58 | − | 3304.03i | −0.255498 | − | 0.442536i | ||||
\(383\) | 5567.73 | − | 9643.59i | 0.742814 | − | 1.28659i | −0.208395 | − | 0.978045i | \(-0.566824\pi\) |
0.951209 | − | 0.308547i | \(-0.0998426\pi\) | |||||||
\(384\) | −419.505 | −0.0557494 | ||||||||
\(385\) | 5661.14 | + | 9805.39i | 0.749399 | + | 1.29800i | ||||
\(386\) | 4944.00 | + | 8563.25i | 0.651924 | + | 1.12917i | ||||
\(387\) | 1811.92 | + | 3138.34i | 0.237998 | + | 0.412224i | ||||
\(388\) | −3655.63 | + | 6331.73i | −0.478315 | + | 0.828467i | ||||
\(389\) | −6167.97 | + | 10683.2i | −0.803929 | + | 1.39245i | 0.113083 | + | 0.993586i | \(0.463927\pi\) |
−0.917012 | + | 0.398860i | \(0.869406\pi\) | |||||||
\(390\) | −3760.44 | − | 6513.27i | −0.488249 | − | 0.845672i | ||||
\(391\) | −5450.39 | − | 9440.35i | −0.704957 | − | 1.22102i | ||||
\(392\) | 549.779 | + | 952.245i | 0.0708368 | + | 0.122693i | ||||
\(393\) | −5268.70 | −0.676261 | ||||||||
\(394\) | −2083.40 | + | 3608.55i | −0.266396 | + | 0.461411i | ||||
\(395\) | 8674.98 | + | 15025.5i | 1.10503 | + | 1.91396i | ||||
\(396\) | 2629.80 | 0.333719 | ||||||||
\(397\) | 11963.0 | 1.51235 | 0.756176 | − | 0.654368i | \(-0.227065\pi\) | ||||
0.756176 | + | 0.654368i | \(0.227065\pi\) | |||||||
\(398\) | 699.778 | + | 1212.05i | 0.0881325 | + | 0.152650i | ||||
\(399\) | −5214.82 | −0.654304 | ||||||||
\(400\) | −2051.26 | + | 3552.88i | −0.256407 | + | 0.444110i | ||||
\(401\) | −9154.59 | −1.14005 | −0.570023 | − | 0.821629i | \(-0.693066\pi\) | ||||
−0.570023 | + | 0.821629i | \(0.693066\pi\) | |||||||
\(402\) | −365.976 | + | 633.888i | −0.0454060 | + | 0.0786455i | ||||
\(403\) | −3578.74 | + | 6198.56i | −0.442356 | + | 0.766184i | ||||
\(404\) | 750.840 | − | 1300.49i | 0.0924646 | − | 0.160153i | ||||
\(405\) | 250.614 | + | 434.076i | 0.0307484 | + | 0.0532578i | ||||
\(406\) | 4862.98 | 0.594448 | ||||||||
\(407\) | −970.837 | + | 9048.84i | −0.118237 | + | 1.10205i | ||||
\(408\) | 2293.07 | 0.278245 | ||||||||
\(409\) | 3939.82 | + | 6823.98i | 0.476312 | + | 0.824997i | 0.999632 | − | 0.0271393i | \(-0.00863978\pi\) |
−0.523319 | + | 0.852137i | \(0.675306\pi\) | |||||||
\(410\) | −4709.06 | + | 8156.33i | −0.567229 | + | 0.982469i | ||||
\(411\) | −3413.70 | + | 5912.70i | −0.409697 | + | 0.709615i | ||||
\(412\) | 792.672 | − | 1372.95i | 0.0947867 | − | 0.164175i | ||||
\(413\) | −3961.86 | −0.472035 | ||||||||
\(414\) | −2026.49 | + | 3509.98i | −0.240571 | + | 0.416682i | ||||
\(415\) | −25128.7 | −2.97234 | ||||||||
\(416\) | 940.020 | + | 1628.16i | 0.110789 | + | 0.191892i | ||||
\(417\) | −104.335 | −0.0122525 | ||||||||
\(418\) | −8975.39 | −1.05024 | ||||||||
\(419\) | −5922.24 | − | 10257.6i | −0.690502 | − | 1.19598i | −0.971674 | − | 0.236327i | \(-0.924056\pi\) |
0.281172 | − | 0.959657i | \(-0.409277\pi\) | |||||||
\(420\) | 1835.34 | − | 3178.89i | 0.213227 | − | 0.369319i | ||||
\(421\) | 8301.07 | 0.960972 | 0.480486 | − | 0.877002i | \(-0.340460\pi\) | ||||
0.480486 | + | 0.877002i | \(0.340460\pi\) | |||||||
\(422\) | 1986.19 | + | 3440.18i | 0.229114 | + | 0.396837i | ||||
\(423\) | −1973.39 | − | 3418.02i | −0.226831 | − | 0.392884i | ||||
\(424\) | 2041.12 | + | 3535.32i | 0.233786 | + | 0.404930i | ||||
\(425\) | 11212.5 | − | 19420.6i | 1.27973 | − | 2.21655i | ||||
\(426\) | −1993.49 | + | 3452.83i | −0.226726 | + | 0.392700i | ||||
\(427\) | 2657.96 | + | 4603.72i | 0.301235 | + | 0.521755i | ||||
\(428\) | −2960.86 | − | 5128.35i | −0.334389 | − | 0.579178i | ||||
\(429\) | 3893.04 | + | 6742.95i | 0.438130 | + | 0.758864i | ||||
\(430\) | 8705.73 | 0.976344 | ||||||||
\(431\) | 4475.64 | − | 7752.04i | 0.500195 | − | 0.866364i | −0.499805 | − | 0.866138i | \(-0.666595\pi\) |
1.00000 | 0.000225567i | \(-7.18003e-5\pi\) | ||||||||
\(432\) | −1134.20 | − | 1964.50i | −0.126318 | − | 0.218789i | ||||
\(433\) | 13402.0 | 1.48743 | 0.743717 | − | 0.668495i | \(-0.233061\pi\) | ||||
0.743717 | + | 0.668495i | \(0.233061\pi\) | |||||||
\(434\) | −3493.31 | −0.386369 | ||||||||
\(435\) | 5427.50 | + | 9400.70i | 0.598227 | + | 1.03616i | ||||
\(436\) | −2609.97 | −0.286686 | ||||||||
\(437\) | 6916.31 | − | 11979.4i | 0.757099 | − | 1.31133i | ||||
\(438\) | 424.145 | 0.0462704 | ||||||||
\(439\) | 1800.71 | − | 3118.92i | 0.195770 | − | 0.339084i | −0.751383 | − | 0.659867i | \(-0.770613\pi\) |
0.947153 | + | 0.320783i | \(0.103946\pi\) | |||||||
\(440\) | 3158.86 | − | 5471.30i | 0.342256 | − | 0.592804i | ||||
\(441\) | −1117.34 | + | 1935.29i | −0.120650 | + | 0.208972i | ||||
\(442\) | −5138.29 | − | 8899.77i | −0.552949 | − | 0.957735i | ||||
\(443\) | −8635.66 | −0.926168 | −0.463084 | − | 0.886314i | \(-0.653257\pi\) | ||||
−0.463084 | + | 0.886314i | \(0.653257\pi\) | |||||||
\(444\) | 2697.96 | − | 1194.23i | 0.288378 | − | 0.127648i | ||||
\(445\) | 7876.07 | 0.839014 | ||||||||
\(446\) | 6485.56 | + | 11233.3i | 0.688565 | + | 1.19263i | ||||
\(447\) | −1371.41 | + | 2375.36i | −0.145113 | + | 0.251344i | ||||
\(448\) | −458.790 | + | 794.648i | −0.0483835 | + | 0.0838027i | ||||
\(449\) | 1749.13 | − | 3029.57i | 0.183845 | − | 0.318429i | −0.759342 | − | 0.650692i | \(-0.774479\pi\) |
0.943187 | + | 0.332263i | \(0.107812\pi\) | |||||||
\(450\) | −8337.73 | −0.873432 | ||||||||
\(451\) | 4875.12 | − | 8443.95i | 0.509003 | − | 0.881619i | ||||
\(452\) | −3337.43 | −0.347299 | ||||||||
\(453\) | 2780.34 | + | 4815.68i | 0.288370 | + | 0.499471i | ||||
\(454\) | −1306.02 | −0.135010 | ||||||||
\(455\) | −16450.4 | −1.69496 | ||||||||
\(456\) | 1454.91 | + | 2519.97i | 0.149413 | + | 0.258790i | ||||
\(457\) | −2840.03 | + | 4919.07i | −0.290702 | + | 0.503511i | −0.973976 | − | 0.226651i | \(-0.927222\pi\) |
0.683274 | + | 0.730162i | \(0.260556\pi\) | |||||||
\(458\) | 3661.30 | 0.373540 | ||||||||
\(459\) | 6199.72 | + | 10738.2i | 0.630454 | + | 1.09198i | ||||
\(460\) | 4868.34 | + | 8432.21i | 0.493451 | + | 0.854682i | ||||
\(461\) | −1791.48 | − | 3102.94i | −0.180993 | − | 0.313489i | 0.761226 | − | 0.648487i | \(-0.224598\pi\) |
−0.942219 | + | 0.334998i | \(0.891264\pi\) | |||||||
\(462\) | −1900.06 | + | 3290.99i | −0.191339 | + | 0.331409i | ||||
\(463\) | −5659.51 | + | 9802.56i | −0.568077 | + | 0.983938i | 0.428679 | + | 0.903457i | \(0.358979\pi\) |
−0.996756 | + | 0.0804816i | \(0.974354\pi\) | |||||||
\(464\) | −1356.75 | − | 2349.95i | −0.135744 | − | 0.235116i | ||||
\(465\) | −3898.83 | − | 6752.96i | −0.388825 | − | 0.673465i | ||||
\(466\) | 1770.50 | + | 3066.60i | 0.176002 | + | 0.304844i | ||||
\(467\) | 9315.84 | 0.923095 | 0.461548 | − | 0.887115i | \(-0.347294\pi\) | ||||
0.461548 | + | 0.887115i | \(0.347294\pi\) | |||||||
\(468\) | −1910.45 | + | 3308.99i | −0.188698 | + | 0.326834i | ||||
\(469\) | 800.497 | + | 1386.50i | 0.0788135 | + | 0.136509i | ||||
\(470\) | −9481.57 | −0.930536 | ||||||||
\(471\) | 9221.63 | 0.902145 | ||||||||
\(472\) | 1105.34 | + | 1914.50i | 0.107791 | + | 0.186699i | ||||
\(473\) | −9012.73 | −0.876123 | ||||||||
\(474\) | −2911.60 | + | 5043.03i | −0.282139 | + | 0.488679i | ||||
\(475\) | 28456.3 | 2.74876 | ||||||||
\(476\) | 2507.81 | − | 4343.66i | 0.241482 | − | 0.418259i | ||||
\(477\) | −4148.26 | + | 7184.99i | −0.398188 | + | 0.689682i | ||||
\(478\) | −725.439 | + | 1256.50i | −0.0694159 | + | 0.120232i | ||||
\(479\) | 97.7274 | + | 169.269i | 0.00932208 | + | 0.0161463i | 0.870649 | − | 0.491905i | \(-0.163699\pi\) |
−0.861327 | + | 0.508051i | \(0.830366\pi\) | |||||||
\(480\) | −2048.19 | −0.194764 | ||||||||
\(481\) | −10680.6 | − | 7795.19i | −1.01246 | − | 0.738940i | ||||
\(482\) | −8784.75 | −0.830155 | ||||||||
\(483\) | −2928.31 | − | 5071.99i | −0.275865 | − | 0.477813i | ||||
\(484\) | −608.250 | + | 1053.52i | −0.0571234 | + | 0.0989406i | ||||
\(485\) | −17848.3 | + | 30914.1i | −1.67103 | + | 2.89431i | ||||
\(486\) | 3743.82 | − | 6484.49i | 0.349431 | − | 0.605232i | ||||
\(487\) | −4852.49 | −0.451514 | −0.225757 | − | 0.974184i | \(-0.572485\pi\) | ||||
−0.225757 | + | 0.974184i | \(0.572485\pi\) | |||||||
\(488\) | 1483.11 | − | 2568.82i | 0.137576 | − | 0.238289i | ||||
\(489\) | 6834.18 | 0.632009 | ||||||||
\(490\) | 2684.25 | + | 4649.25i | 0.247473 | + | 0.428636i | ||||
\(491\) | −18733.9 | −1.72190 | −0.860948 | − | 0.508693i | \(-0.830129\pi\) | ||||
−0.860948 | + | 0.508693i | \(0.830129\pi\) | |||||||
\(492\) | −3161.01 | −0.289654 | ||||||||
\(493\) | 7416.17 | + | 12845.2i | 0.677500 | + | 1.17346i | ||||
\(494\) | 6520.27 | − | 11293.4i | 0.593847 | − | 1.02857i | ||||
\(495\) | 12839.8 | 1.16587 | ||||||||
\(496\) | 974.614 | + | 1688.08i | 0.0882288 | + | 0.152817i | ||||
\(497\) | 4360.36 | + | 7552.37i | 0.393539 | + | 0.681630i | ||||
\(498\) | −4216.99 | − | 7304.04i | −0.379454 | − | 0.657233i | ||||
\(499\) | 2921.86 | − | 5060.82i | 0.262126 | − | 0.454015i | −0.704681 | − | 0.709524i | \(-0.748910\pi\) |
0.966807 | + | 0.255510i | \(0.0822432\pi\) | |||||||
\(500\) | −5132.66 | + | 8890.03i | −0.459079 | + | 0.795149i | ||||
\(501\) | −2986.35 | − | 5172.51i | −0.266308 | − | 0.461259i | ||||
\(502\) | −2148.42 | − | 3721.17i | −0.191013 | − | 0.330844i | ||||
\(503\) | −9419.11 | − | 16314.4i | −0.834945 | − | 1.44617i | −0.894075 | − | 0.447916i | \(-0.852166\pi\) |
0.0591307 | − | 0.998250i | \(-0.481167\pi\) | |||||||
\(504\) | −1864.84 | −0.164815 | ||||||||
\(505\) | 3665.91 | − | 6349.54i | 0.323031 | − | 0.559507i | ||||
\(506\) | −5040.02 | − | 8729.56i | −0.442799 | − | 0.766950i | ||||
\(507\) | −4112.16 | −0.360212 | ||||||||
\(508\) | −1877.05 | −0.163938 | ||||||||
\(509\) | 2361.49 | + | 4090.22i | 0.205641 | + | 0.356180i | 0.950337 | − | 0.311224i | \(-0.100739\pi\) |
−0.744696 | + | 0.667404i | \(0.767405\pi\) | |||||||
\(510\) | 11195.7 | 0.972069 | ||||||||
\(511\) | 463.865 | − | 803.439i | 0.0401569 | − | 0.0695539i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −7867.18 | + | 13626.4i | −0.677085 | + | 1.17275i | ||||
\(514\) | −870.074 | + | 1507.01i | −0.0746640 | + | 0.129322i | ||||
\(515\) | 3870.15 | − | 6703.29i | 0.331144 | − | 0.573558i | ||||
\(516\) | 1460.96 | + | 2530.45i | 0.124642 | + | 0.215886i | ||||
\(517\) | 9815.92 | 0.835017 | ||||||||
\(518\) | 688.438 | − | 6416.70i | 0.0583943 | − | 0.544273i | ||||
\(519\) | 7880.54 | 0.666508 | ||||||||
\(520\) | 4589.56 | + | 7949.36i | 0.387049 | + | 0.670389i | ||||
\(521\) | 5163.09 | − | 8942.74i | 0.434164 | − | 0.751993i | −0.563063 | − | 0.826414i | \(-0.690377\pi\) |
0.997227 | + | 0.0744204i | \(0.0237107\pi\) | |||||||
\(522\) | 2757.38 | − | 4775.92i | 0.231202 | − | 0.400453i | ||||
\(523\) | 2228.10 | − | 3859.18i | 0.186287 | − | 0.322658i | −0.757723 | − | 0.652577i | \(-0.773688\pi\) |
0.944009 | + | 0.329919i | \(0.107021\pi\) | |||||||
\(524\) | 6430.38 | 0.536092 | ||||||||
\(525\) | 6024.08 | − | 10434.0i | 0.500786 | − | 0.867386i | ||||
\(526\) | 4197.71 | 0.347964 | ||||||||
\(527\) | −5327.38 | − | 9227.30i | −0.440350 | − | 0.762708i | ||||
\(528\) | 2120.42 | 0.174772 | ||||||||
\(529\) | 3368.06 | 0.276820 | ||||||||
\(530\) | 9965.57 | + | 17260.9i | 0.816748 | + | 1.41465i | ||||
\(531\) | −2246.43 | + | 3890.93i | −0.183591 | + | 0.317989i | ||||
\(532\) | 6364.62 | 0.518687 | ||||||||
\(533\) | 7083.16 | + | 12268.4i | 0.575620 | + | 0.997004i | ||||
\(534\) | 1321.73 | + | 2289.30i | 0.107110 | + | 0.185520i | ||||
\(535\) | −14456.1 | − | 25038.7i | −1.16821 | − | 2.02340i | ||||
\(536\) | 446.668 | − | 773.652i | 0.0359947 | − | 0.0623446i | ||||
\(537\) | 3245.58 | − | 5621.50i | 0.260814 | − | 0.451742i | ||||
\(538\) | −5485.74 | − | 9501.59i | −0.439604 | − | 0.761417i | ||||
\(539\) | −2778.90 | − | 4813.20i | −0.222070 | − | 0.384637i | ||||
\(540\) | −5537.65 | − | 9591.49i | −0.441301 | − | 0.764355i | ||||
\(541\) | −16418.6 | −1.30479 | −0.652394 | − | 0.757880i | \(-0.726235\pi\) | ||||
−0.652394 | + | 0.757880i | \(0.726235\pi\) | |||||||
\(542\) | 6097.32 | − | 10560.9i | 0.483215 | − | 0.836952i | ||||
\(543\) | −1915.37 | − | 3317.52i | −0.151374 | − | 0.262188i | ||||
\(544\) | −2798.67 | −0.220573 | ||||||||
\(545\) | −12743.0 | −1.00156 | ||||||||
\(546\) | −2760.63 | − | 4781.55i | −0.216381 | − | 0.374783i | ||||
\(547\) | 4313.47 | 0.337168 | 0.168584 | − | 0.985687i | \(-0.446081\pi\) | ||||
0.168584 | + | 0.985687i | \(0.446081\pi\) | |||||||
\(548\) | 4166.37 | − | 7216.37i | 0.324779 | − | 0.562533i | ||||
\(549\) | 6028.39 | 0.468644 | ||||||||
\(550\) | 10368.2 | − | 17958.3i | 0.803825 | − | 1.39226i | ||||
\(551\) | −9410.80 | + | 16300.0i | −0.727611 | + | 1.26026i | ||||
\(552\) | −1633.97 | + | 2830.11i | −0.125990 | + | 0.218220i | ||||
\(553\) | 6368.52 | + | 11030.6i | 0.489723 | + | 0.848226i | ||||
\(554\) | −919.828 | −0.0705410 | ||||||||
\(555\) | 13172.6 | − | 5830.74i | 1.00747 | − | 0.445948i | ||||
\(556\) | 127.339 | 0.00971293 | ||||||||
\(557\) | −5045.77 | − | 8739.53i | −0.383835 | − | 0.664822i | 0.607772 | − | 0.794112i | \(-0.292064\pi\) |
−0.991607 | + | 0.129290i | \(0.958730\pi\) | |||||||
\(558\) | −1980.75 | + | 3430.77i | −0.150272 | + | 0.260280i | ||||
\(559\) | 6547.39 | − | 11340.4i | 0.495394 | − | 0.858047i | ||||
\(560\) | −2240.00 | + | 3879.80i | −0.169031 | + | 0.292770i | ||||
\(561\) | −11590.5 | −0.872286 | ||||||||
\(562\) | −2735.48 | + | 4738.00i | −0.205319 | + | 0.355623i | ||||
\(563\) | −4130.68 | −0.309214 | −0.154607 | − | 0.987976i | \(-0.549411\pi\) | ||||
−0.154607 | + | 0.987976i | \(0.549411\pi\) | |||||||
\(564\) | −1591.16 | − | 2755.96i | −0.118794 | − | 0.205757i | ||||
\(565\) | −16294.7 | −1.21331 | ||||||||
\(566\) | −3225.37 | −0.239527 | ||||||||
\(567\) | 183.982 | + | 318.666i | 0.0136270 | + | 0.0236027i | ||||
\(568\) | 2433.03 | − | 4214.14i | 0.179732 | − | 0.311305i | ||||
\(569\) | −19461.5 | −1.43386 | −0.716930 | − | 0.697145i | \(-0.754453\pi\) | ||||
−0.716930 | + | 0.697145i | \(0.754453\pi\) | |||||||
\(570\) | 7103.45 | + | 12303.5i | 0.521984 | + | 0.904102i | ||||
\(571\) | −6245.22 | − | 10817.0i | −0.457714 | − | 0.792783i | 0.541126 | − | 0.840941i | \(-0.317998\pi\) |
−0.998840 | + | 0.0481582i | \(0.984665\pi\) | |||||||
\(572\) | −4751.41 | − | 8229.69i | −0.347319 | − | 0.601574i | ||||
\(573\) | 3125.94 | − | 5414.28i | 0.227902 | − | 0.394738i | ||||
\(574\) | −3457.04 | + | 5987.76i | −0.251383 | + | 0.435408i | ||||
\(575\) | 15979.2 | + | 27676.9i | 1.15892 | + | 2.00731i | ||||
\(576\) | 520.281 | + | 901.153i | 0.0376361 | + | 0.0651876i | ||||
\(577\) | 13409.4 | + | 23225.7i | 0.967486 | + | 1.67573i | 0.702782 | + | 0.711405i | \(0.251941\pi\) |
0.264704 | + | 0.964330i | \(0.414726\pi\) | |||||||
\(578\) | 5471.91 | 0.393774 | ||||||||
\(579\) | −8101.68 | + | 14032.5i | −0.581510 | + | 1.00720i | ||||
\(580\) | −6624.19 | − | 11473.4i | −0.474232 | − | 0.821394i | ||||
\(581\) | −18447.6 | −1.31727 | ||||||||
\(582\) | −11980.9 | −0.853305 | ||||||||
\(583\) | −10317.0 | − | 17869.6i | −0.732909 | − | 1.26944i | ||||
\(584\) | −517.664 | −0.0366799 | ||||||||
\(585\) | −9327.59 | + | 16155.9i | −0.659228 | + | 1.14182i | ||||
\(586\) | 286.754 | 0.0202145 | ||||||||
\(587\) | 8343.21 | − | 14450.9i | 0.586646 | − | 1.01610i | −0.408022 | − | 0.912972i | \(-0.633781\pi\) |
0.994668 | − | 0.103128i | \(-0.0328852\pi\) | |||||||
\(588\) | −900.917 | + | 1560.43i | −0.0631857 | + | 0.109441i | ||||
\(589\) | 6760.22 | − | 11709.0i | 0.472920 | − | 0.819122i | ||||
\(590\) | 5396.71 | + | 9347.37i | 0.376574 | + | 0.652246i | ||||
\(591\) | −6828.08 | −0.475245 | ||||||||
\(592\) | −3292.83 | + | 1457.55i | −0.228605 | + | 0.101191i | ||||
\(593\) | 8424.55 | 0.583398 | 0.291699 | − | 0.956510i | \(-0.405780\pi\) | ||||
0.291699 | + | 0.956510i | \(0.405780\pi\) | |||||||
\(594\) | 5732.93 | + | 9929.72i | 0.396002 | + | 0.685895i | ||||
\(595\) | 12244.2 | − | 21207.5i | 0.843634 | − | 1.46122i | ||||
\(596\) | 1673.79 | − | 2899.09i | 0.115036 | − | 0.199247i | ||||
\(597\) | −1146.72 | + | 1986.18i | −0.0786133 | + | 0.136162i | ||||
\(598\) | 14645.5 | 1.00150 | ||||||||
\(599\) | −3201.65 | + | 5545.42i | −0.218391 | + | 0.378264i | −0.954316 | − | 0.298799i | \(-0.903414\pi\) |
0.735926 | + | 0.677062i | \(0.236747\pi\) | |||||||
\(600\) | −6722.74 | −0.457425 | ||||||||
\(601\) | 4467.65 | + | 7738.20i | 0.303227 | + | 0.525204i | 0.976865 | − | 0.213857i | \(-0.0686027\pi\) |
−0.673638 | + | 0.739061i | \(0.735269\pi\) | |||||||
\(602\) | 6391.10 | 0.432694 | ||||||||
\(603\) | 1815.57 | 0.122613 | ||||||||
\(604\) | −3393.36 | − | 5877.48i | −0.228599 | − | 0.395946i | ||||
\(605\) | −2969.72 | + | 5143.71i | −0.199564 | + | 0.345656i | ||||
\(606\) | 2460.79 | 0.164955 | ||||||||
\(607\) | 2781.58 | + | 4817.83i | 0.185998 | + | 0.322158i | 0.943912 | − | 0.330196i | \(-0.107115\pi\) |
−0.757914 | + | 0.652354i | \(0.773782\pi\) | |||||||
\(608\) | −1775.69 | − | 3075.59i | −0.118444 | − | 0.205151i | ||||
\(609\) | 3984.46 | + | 6901.29i | 0.265121 | + | 0.459203i | ||||
\(610\) | 7241.16 | − | 12542.0i | 0.480632 | − | 0.832480i | ||||
\(611\) | −7130.88 | + | 12351.0i | −0.472151 | + | 0.817790i | ||||
\(612\) | −2843.93 | − | 4925.83i | −0.187842 | − | 0.325351i | ||||
\(613\) | −8527.92 | − | 14770.8i | −0.561892 | − | 0.973225i | −0.997331 | − | 0.0730068i | \(-0.976741\pi\) |
0.435440 | − | 0.900218i | \(-0.356593\pi\) | |||||||
\(614\) | −9023.26 | − | 15628.7i | −0.593077 | − | 1.02724i | ||||
\(615\) | −15433.4 | −1.01192 | ||||||||
\(616\) | 2318.99 | − | 4016.62i | 0.151680 | − | 0.262718i | ||||
\(617\) | 14075.3 | + | 24379.1i | 0.918395 | + | 1.59071i | 0.801853 | + | 0.597521i | \(0.203847\pi\) |
0.116542 | + | 0.993186i | \(0.462819\pi\) | |||||||
\(618\) | 2597.89 | 0.169098 | ||||||||
\(619\) | 9297.70 | 0.603726 | 0.301863 | − | 0.953351i | \(-0.402392\pi\) | ||||
0.301863 | + | 0.953351i | \(0.402392\pi\) | |||||||
\(620\) | 4758.47 | + | 8241.91i | 0.308233 | + | 0.533876i | ||||
\(621\) | −17670.9 | −1.14188 | ||||||||
\(622\) | −6835.99 | + | 11840.3i | −0.440673 | + | 0.763267i | ||||
\(623\) | 5782.02 | 0.371832 | ||||||||
\(624\) | −1540.40 | + | 2668.05i | −0.0988228 | + | 0.171166i | ||||
\(625\) | −9034.33 | + | 15647.9i | −0.578197 | + | 1.00147i | ||||
\(626\) | 7305.38 | − | 12653.3i | 0.466424 | − | 0.807870i | ||||
\(627\) | −7353.94 | − | 12737.4i | −0.468402 | − | 0.811297i | ||||
\(628\) | −11254.9 | −0.715157 | ||||||||
\(629\) | 17999.1 | − | 7967.17i | 1.14097 | − | 0.505043i | ||||
\(630\) | −9104.93 | −0.575792 | ||||||||
\(631\) | 10438.0 | + | 18079.2i | 0.658527 | + | 1.14060i | 0.980997 | + | 0.194023i | \(0.0621536\pi\) |
−0.322470 | + | 0.946580i | \(0.604513\pi\) | |||||||
\(632\) | 3553.56 | − | 6154.95i | 0.223660 | − | 0.387391i | ||||
\(633\) | −3254.74 | + | 5637.38i | −0.204367 | + | 0.353975i | ||||
\(634\) | −6740.78 | + | 11675.4i | −0.422256 | + | 0.731370i | ||||
\(635\) | −9164.51 | −0.572728 | ||||||||
\(636\) | −3344.76 | + | 5793.29i | −0.208535 | + | 0.361193i | ||||
\(637\) | 8075.05 | 0.502269 | ||||||||
\(638\) | 6857.79 | + | 11878.0i | 0.425552 | + | 0.737078i | ||||
\(639\) | 9889.54 | 0.612245 | ||||||||
\(640\) | 2499.79 | 0.154395 | ||||||||
\(641\) | −4128.47 | − | 7150.72i | −0.254391 | − | 0.440619i | 0.710339 | − | 0.703860i | \(-0.248542\pi\) |
−0.964730 | + | 0.263241i | \(0.915208\pi\) | |||||||
\(642\) | 4851.93 | − | 8403.78i | 0.298271 | − | 0.516621i | ||||
\(643\) | 18513.8 | 1.13548 | 0.567740 | − | 0.823208i | \(-0.307818\pi\) | ||||
0.567740 | + | 0.823208i | \(0.307818\pi\) | |||||||
\(644\) | 3573.97 | + | 6190.30i | 0.218687 | + | 0.378776i | ||||
\(645\) | 7133.00 | + | 12354.7i | 0.435444 | + | 0.754212i | ||||
\(646\) | 9706.20 | + | 16811.6i | 0.591154 | + | 1.02391i | ||||
\(647\) | −6941.93 | + | 12023.8i | −0.421817 | + | 0.730609i | −0.996117 | − | 0.0880362i | \(-0.971941\pi\) |
0.574300 | + | 0.818645i | \(0.305274\pi\) | |||||||
\(648\) | 102.660 | − | 177.812i | 0.00622355 | − | 0.0107795i | ||||
\(649\) | −5587.02 | − | 9677.00i | −0.337919 | − | 0.585293i | ||||
\(650\) | 15064.2 | + | 26092.0i | 0.909027 | + | 1.57448i | ||||
\(651\) | −2862.23 | − | 4957.52i | −0.172319 | − | 0.298465i | ||||
\(652\) | −8341.03 | −0.501012 | ||||||||
\(653\) | 15016.1 | − | 26008.6i | 0.899885 | − | 1.55865i | 0.0722448 | − | 0.997387i | \(-0.476984\pi\) |
0.827640 | − | 0.561259i | \(-0.189683\pi\) | |||||||
\(654\) | −2138.47 | − | 3703.94i | −0.127861 | − | 0.221461i | ||||
\(655\) | 31395.7 | 1.87288 | ||||||||
\(656\) | 3857.98 | 0.229617 | ||||||||
\(657\) | −526.036 | − | 911.122i | −0.0312369 | − | 0.0541039i | ||||
\(658\) | −6960.65 | −0.412393 | ||||||||
\(659\) | −11871.7 | + | 20562.4i | −0.701755 | + | 1.21547i | 0.266096 | + | 0.963947i | \(0.414266\pi\) |
−0.967850 | + | 0.251528i | \(0.919067\pi\) | |||||||
\(660\) | 10352.8 | 0.610577 | ||||||||
\(661\) | −7496.15 | + | 12983.7i | −0.441099 | + | 0.764006i | −0.997771 | − | 0.0667260i | \(-0.978745\pi\) |
0.556672 | + | 0.830732i | \(0.312078\pi\) | |||||||
\(662\) | 315.625 | − | 546.679i | 0.0185304 | − | 0.0320956i | ||||
\(663\) | 8420.06 | − | 14584.0i | 0.493225 | − | 0.854290i | ||||
\(664\) | 5146.78 | + | 8914.49i | 0.300804 | + | 0.521008i | ||||
\(665\) | 31074.7 | 1.81207 | ||||||||
\(666\) | −5911.46 | − | 4314.47i | −0.343941 | − | 0.251024i | ||||
\(667\) | −21138.1 | −1.22709 | ||||||||
\(668\) | 3644.80 | + | 6312.98i | 0.211110 | + | 0.365653i | ||||
\(669\) | −10627.8 | + | 18407.9i | −0.614193 | + | 1.06381i | ||||
\(670\) | 2180.82 | − | 3777.29i | 0.125750 | − | 0.217805i | ||||
\(671\) | −7496.51 | + | 12984.3i | −0.431296 | + | 0.747026i | ||||
\(672\) | −1503.63 | −0.0863152 | ||||||||
\(673\) | 6961.84 | − | 12058.3i | 0.398751 | − | 0.690656i | −0.594821 | − | 0.803858i | \(-0.702777\pi\) |
0.993572 | + | 0.113202i | \(0.0361106\pi\) | |||||||
\(674\) | 4945.34 | 0.282622 | ||||||||
\(675\) | −18176.1 | − | 31481.9i | −1.03644 | − | 1.79517i | ||||
\(676\) | 5018.84 | 0.285551 | ||||||||
\(677\) | −15195.9 | −0.862666 | −0.431333 | − | 0.902193i | \(-0.641957\pi\) | ||||
−0.431333 | + | 0.902193i | \(0.641957\pi\) | |||||||
\(678\) | −2734.50 | − | 4736.30i | −0.154894 | − | 0.268284i | ||||
\(679\) | −13102.9 | + | 22694.8i | −0.740562 | + | 1.28269i | ||||
\(680\) | −13664.2 | −0.770588 | ||||||||
\(681\) | −1070.08 | − | 1853.43i | −0.0602137 | − | 0.104293i | ||||
\(682\) | −4926.27 | − | 8532.55i | −0.276593 | − | 0.479074i | ||||
\(683\) | 11281.3 | + | 19539.8i | 0.632016 | + | 1.09468i | 0.987139 | + | 0.159865i | \(0.0511057\pi\) |
−0.355123 | + | 0.934820i | \(0.615561\pi\) | |||||||
\(684\) | 3608.83 | − | 6250.67i | 0.201735 | − | 0.349416i | ||||
\(685\) | 20342.0 | − | 35233.3i | 1.13464 | − | 1.96525i | ||||
\(686\) | 6888.23 | + | 11930.8i | 0.383373 | + | 0.664022i | ||||
\(687\) | 2999.86 | + | 5195.92i | 0.166597 | + | 0.288554i | ||||
\(688\) | −1783.08 | − | 3088.39i | −0.0988072 | − | 0.171139i | ||||
\(689\) | 29979.5 | 1.65766 | ||||||||
\(690\) | −7977.70 | + | 13817.8i | −0.440153 | + | 0.762368i | ||||
\(691\) | 4942.77 | + | 8561.12i | 0.272115 | + | 0.471317i | 0.969403 | − | 0.245474i | \(-0.0789435\pi\) |
−0.697288 | + | 0.716791i | \(0.745610\pi\) | |||||||
\(692\) | −9618.10 | −0.528360 | ||||||||
\(693\) | 9426.01 | 0.516687 | ||||||||
\(694\) | −11277.1 | − | 19532.5i | −0.616819 | − | 1.06836i | ||||
\(695\) | 621.723 | 0.0339328 | ||||||||
\(696\) | 2223.29 | − | 3850.85i | 0.121083 | − | 0.209721i | ||||
\(697\) | −21088.3 | −1.14602 | ||||||||
\(698\) | −1273.11 | + | 2205.09i | −0.0690372 | + | 0.119576i | ||||
\(699\) | −2901.30 | + | 5025.21i | −0.156992 | + | 0.271918i | ||||
\(700\) | −7352.32 | + | 12734.6i | −0.396988 | + | 0.687603i | ||||
\(701\) | 10548.0 | + | 18269.7i | 0.568322 | + | 0.984363i | 0.996732 | + | 0.0807787i | \(0.0257407\pi\) |
−0.428410 | + | 0.903585i | \(0.640926\pi\) | |||||||
\(702\) | −16659.0 | −0.895659 | ||||||||
\(703\) | 20175.5 | + | 14725.1i | 1.08241 | + | 0.789995i | ||||
\(704\) | −2587.95 | −0.138547 | ||||||||
\(705\) | −7768.67 | − | 13455.7i | −0.415014 | − | 0.718826i | ||||
\(706\) | −2217.06 | + | 3840.06i | −0.118187 | + | 0.204706i | ||||
\(707\) | 2691.24 | − | 4661.36i | 0.143160 | − | 0.247961i | ||||
\(708\) | −1811.30 | + | 3137.27i | −0.0961483 | + | 0.166534i | ||||
\(709\) | −12083.4 | −0.640059 | −0.320029 | − | 0.947408i | \(-0.603693\pi\) | ||||
−0.320029 | + | 0.947408i | \(0.603693\pi\) | |||||||
\(710\) | 11879.1 | − | 20575.2i | 0.627907 | − | 1.08757i | ||||
\(711\) | 14444.2 | 0.761882 | ||||||||
\(712\) | −1613.15 | − | 2794.06i | −0.0849093 | − | 0.147067i | ||||
\(713\) | 15184.5 | 0.797563 | ||||||||
\(714\) | 8219.06 | 0.430799 | ||||||||
\(715\) | −23198.3 | − | 40180.7i | −1.21338 | − | 2.10164i | ||||
\(716\) | −3961.18 | + | 6860.97i | −0.206755 | + | 0.358110i | ||||
\(717\) | −2377.54 | −0.123837 | ||||||||
\(718\) | −11858.5 | − | 20539.5i | −0.616371 | − | 1.06759i | ||||
\(719\) | −12499.8 | − | 21650.4i | −0.648352 | − | 1.12298i | −0.983516 | − | 0.180819i | \(-0.942125\pi\) |
0.335164 | − | 0.942160i | \(-0.391208\pi\) | |||||||
\(720\) | 2540.23 | + | 4399.80i | 0.131484 | + | 0.227737i | ||||
\(721\) | 2841.17 | − | 4921.06i | 0.146756 | − | 0.254188i | ||||
\(722\) | −5457.75 | + | 9453.10i | −0.281325 | + | 0.487269i | ||||
\(723\) | −7197.74 | − | 12466.9i | −0.370245 | − | 0.641283i | ||||
\(724\) | 2337.68 | + | 4048.99i | 0.119999 | + | 0.207844i | ||||
\(725\) | −21742.4 | − | 37659.0i | −1.11379 | − | 1.92913i | ||||
\(726\) | −1993.47 | −0.101907 | ||||||||
\(727\) | −8380.51 | + | 14515.5i | −0.427532 | + | 0.740508i | −0.996653 | − | 0.0817460i | \(-0.973950\pi\) |
0.569121 | + | 0.822254i | \(0.307284\pi\) | |||||||
\(728\) | 3369.31 | + | 5835.82i | 0.171532 | + | 0.297102i | ||||
\(729\) | 12962.9 | 0.658583 | ||||||||
\(730\) | −2527.45 | −0.128144 | ||||||||
\(731\) | 9746.58 | + | 16881.6i | 0.493147 | + | 0.854155i | ||||
\(732\) | 4860.72 | 0.245433 | ||||||||
\(733\) | −943.797 | + | 1634.71i | −0.0475579 | + | 0.0823727i | −0.888824 | − | 0.458248i | \(-0.848477\pi\) |
0.841267 | + | 0.540621i | \(0.181811\pi\) | |||||||
\(734\) | 2978.25 | 0.149767 | ||||||||
\(735\) | −4398.65 | + | 7618.68i | −0.220744 | + | 0.382339i | ||||
\(736\) | 1994.24 | − | 3454.12i | 0.0998757 | − | 0.172990i | ||||
\(737\) | −2257.72 | + | 3910.49i | −0.112842 | + | 0.195448i | ||||
\(738\) | 3920.38 | + | 6790.29i | 0.195543 | + | 0.338691i | ||||
\(739\) | 19993.7 | 0.995236 | 0.497618 | − | 0.867396i | \(-0.334208\pi\) | ||||
0.497618 | + | 0.867396i | \(0.334208\pi\) | |||||||
\(740\) | −16076.9 | + | 7116.35i | −0.798649 | + | 0.353516i | ||||
\(741\) | 21369.4 | 1.05941 | ||||||||
\(742\) | 7315.97 | + | 12671.6i | 0.361965 | + | 0.626941i | ||||
\(743\) | −18059.9 | + | 31280.6i | −0.891726 | + | 1.54451i | −0.0539209 | + | 0.998545i | \(0.517172\pi\) |
−0.837805 | + | 0.545969i | \(0.816161\pi\) | |||||||
\(744\) | −1597.09 | + | 2766.24i | −0.0786992 | + | 0.136311i | ||||
\(745\) | 8172.14 | − | 14154.6i | 0.401885 | − | 0.696085i | ||||
\(746\) | −18162.5 | −0.891389 | ||||||||
\(747\) | −10460.1 | + | 18117.3i | −0.512334 | + | 0.887388i | ||||
\(748\) | 14146.1 | 0.691487 | ||||||||
\(749\) | −10612.6 | − | 18381.6i | −0.517725 | − | 0.896726i | ||||
\(750\) | −16821.7 | −0.818988 | ||||||||
\(751\) | 23374.7 | 1.13576 | 0.567879 | − | 0.823112i | \(-0.307764\pi\) | ||||
0.567879 | + | 0.823112i | \(0.307764\pi\) | |||||||
\(752\) | 1941.98 | + | 3363.62i | 0.0941714 | + | 0.163110i | ||||
\(753\) | 3520.59 | − | 6097.84i | 0.170382 | − | 0.295110i | ||||
\(754\) | −19927.6 | −0.962496 | ||||||||
\(755\) | −16567.8 | − | 28696.3i | −0.798628 | − | 1.38326i | ||||
\(756\) | −4065.33 | − | 7041.35i | −0.195575 | − | 0.338745i | ||||
\(757\) | 3087.94 | + | 5348.47i | 0.148260 | + | 0.256794i | 0.930585 | − | 0.366077i | \(-0.119299\pi\) |
−0.782324 | + | 0.622871i | \(0.785966\pi\) | |||||||
\(758\) | −12644.5 | + | 21900.9i | −0.605894 | + | 1.04944i | ||||
\(759\) | 8259.02 | − | 14305.1i | 0.394972 | − | 0.684111i | ||||
\(760\) | −8669.67 | − | 15016.3i | −0.413792 | − | 0.716709i | ||||
\(761\) | −11647.3 | − | 20173.8i | −0.554816 | − | 0.960970i | −0.997918 | − | 0.0644988i | \(-0.979455\pi\) |
0.443101 | − | 0.896472i | \(-0.353878\pi\) | |||||||
\(762\) | −1537.95 | − | 2663.80i | −0.0731155 | − | 0.126640i | ||||
\(763\) | −9354.93 | −0.443868 | ||||||||
\(764\) | −3815.16 | + | 6608.06i | −0.180665 | + | 0.312920i | ||||
\(765\) | −13885.2 | − | 24049.9i | −0.656238 | − | 1.13664i | ||||
\(766\) | −22270.9 | −1.05050 | ||||||||
\(767\) | 16235.0 | 0.764291 | ||||||||
\(768\) | 419.505 | + | 726.603i | 0.0197104 | + | 0.0341394i | ||||
\(769\) | −14698.7 | −0.689269 | −0.344635 | − | 0.938737i | \(-0.611997\pi\) | ||||
−0.344635 | + | 0.938737i | \(0.611997\pi\) | |||||||
\(770\) | 11322.3 | − | 19610.8i | 0.529905 | − | 0.917822i | ||||
\(771\) | −2851.56 | −0.133199 | ||||||||
\(772\) | 9887.99 | − | 17126.5i | 0.460980 | − | 0.798441i | ||||
\(773\) | 12907.4 | − | 22356.2i | 0.600576 | − | 1.04023i | −0.392158 | − | 0.919898i | \(-0.628271\pi\) |
0.992734 | − | 0.120330i | \(-0.0383954\pi\) | |||||||
\(774\) | 3623.84 | − | 6276.68i | 0.168290 | − | 0.291486i | ||||
\(775\) | 15618.6 | + | 27052.2i | 0.723919 | + | 1.25386i | ||||
\(776\) | 14622.5 | 0.676440 | ||||||||
\(777\) | 9670.31 | − | 4280.49i | 0.446487 | − | 0.197634i | ||||
\(778\) | 24671.9 | 1.13693 | ||||||||
\(779\) | −13380.1 | − | 23174.9i | −0.615392 | − | 1.06589i | ||||
\(780\) | −7520.87 | + | 13026.5i | −0.345244 | + | 0.597980i | ||||
\(781\) | −12298.0 | + | 21300.7i | −0.563452 | + | 0.975928i | ||||
\(782\) | −10900.8 | + | 18880.7i | −0.498480 | + | 0.863392i | ||||
\(783\) | 24044.2 | 1.09741 | ||||||||
\(784\) | 1099.56 | − | 1904.49i | 0.0500892 | − | 0.0867570i | ||||
\(785\) | −54951.0 | −2.49845 | ||||||||
\(786\) | 5268.70 | + | 9125.65i | 0.239094 | + | 0.414124i | ||||
\(787\) | 15468.0 | 0.700601 | 0.350301 | − | 0.936637i | \(-0.386079\pi\) | ||||
0.350301 | + | 0.936637i | \(0.386079\pi\) | |||||||
\(788\) | 8333.58 | 0.376741 | ||||||||
\(789\) | 3439.38 | + | 5957.17i | 0.155190 | + | 0.268797i | ||||
\(790\) | 17350.0 | − | 30051.0i | 0.781372 | − | 1.35338i | ||||
\(791\) | −11962.3 | −0.537714 | ||||||||
\(792\) | −2629.80 | − | 4554.95i | −0.117987 | − | 0.204360i | ||||
\(793\) | −10891.8 | − | 18865.2i | −0.487743 | − | 0.844795i | ||||
\(794\) | −11963.0 | − | 20720.5i | −0.534697 | − | 0.926123i | ||||
\(795\) | −16330.5 | + | 28285.2i | −0.728531 | + | 1.26185i | ||||
\(796\) | 1399.56 | − | 2424.10i | 0.0623191 | − | 0.107940i | ||||
\(797\) | 1742.17 | + | 3017.53i | 0.0774291 | + | 0.134111i | 0.902140 | − | 0.431443i | \(-0.141996\pi\) |
−0.824711 | + | 0.565554i | \(0.808662\pi\) | |||||||
\(798\) | 5214.82 | + | 9032.33i | 0.231332 | + | 0.400678i | ||||
\(799\) | −10615.2 | − | 18386.0i | −0.470010 | − | 0.814080i | ||||
\(800\) | 8205.02 | 0.362614 | ||||||||
\(801\) | 3278.48 | − | 5678.50i | 0.144619 | − | 0.250487i | ||||
\(802\) | 9154.59 | + | 15856.2i | 0.403067 | + | 0.698133i | ||||
\(803\) | 2616.58 | 0.114990 | ||||||||
\(804\) | 1463.90 | 0.0642137 | ||||||||
\(805\) | 17449.6 | + | 30223.6i | 0.763996 | + | 1.32328i | ||||
\(806\) | 14315.0 | 0.625586 | ||||||||
\(807\) | 8989.43 | − | 15570.2i | 0.392123 | − | 0.679176i | ||||
\(808\) | −3003.36 | −0.130765 | ||||||||
\(809\) | 9625.33 | − | 16671.6i | 0.418305 | − | 0.724525i | −0.577464 | − | 0.816416i | \(-0.695958\pi\) |
0.995769 | + | 0.0918908i | \(0.0292911\pi\) | |||||||
\(810\) | 501.228 | − | 868.152i | 0.0217424 | − | 0.0376589i | ||||
\(811\) | −4946.47 | + | 8567.54i | −0.214173 | + | 0.370958i | −0.953016 | − | 0.302919i | \(-0.902039\pi\) |
0.738844 | + | 0.673877i | \(0.235372\pi\) | |||||||
\(812\) | −4862.98 | − | 8422.94i | −0.210169 | − | 0.364024i | ||||
\(813\) | 19983.2 | 0.862045 | ||||||||
\(814\) | 16643.9 | − | 7367.30i | 0.716668 | − | 0.317228i | ||||
\(815\) | −40724.4 | −1.75032 | ||||||||
\(816\) | −2293.07 | − | 3971.72i | −0.0983745 | − | 0.170390i | ||||
\(817\) | −12368.0 | + | 21422.0i | −0.529622 | + | 0.917332i | ||||
\(818\) | 7879.65 | − | 13648.0i | 0.336804 | − | 0.583361i | ||||
\(819\) | −6847.62 | + | 11860.4i | −0.292155 | + | 0.506028i | ||||
\(820\) | 18836.2 | 0.802183 | ||||||||
\(821\) | 15029.5 | − | 26031.8i | 0.638894 | − | 1.10660i | −0.346781 | − | 0.937946i | \(-0.612725\pi\) |
0.985676 | − | 0.168652i | \(-0.0539413\pi\) | |||||||
\(822\) | 13654.8 | 0.579398 | ||||||||
\(823\) | 4654.26 | + | 8061.41i | 0.197129 | + | 0.341438i | 0.947596 | − | 0.319470i | \(-0.103505\pi\) |
−0.750467 | + | 0.660908i | \(0.770172\pi\) | |||||||
\(824\) | −3170.69 | −0.134049 | ||||||||
\(825\) | 33980.7 | 1.43401 | ||||||||
\(826\) | 3961.86 | + | 6862.14i | 0.166889 | + | 0.289061i | ||||
\(827\) | 7985.05 | − | 13830.5i | 0.335753 | − | 0.581541i | −0.647876 | − | 0.761745i | \(-0.724343\pi\) |
0.983629 | + | 0.180205i | \(0.0576760\pi\) | |||||||
\(828\) | 8105.96 | 0.340219 | ||||||||
\(829\) | −19184.4 | − | 33228.4i | −0.803742 | − | 1.39212i | −0.917137 | − | 0.398573i | \(-0.869506\pi\) |
0.113394 | − | 0.993550i | \(-0.463828\pi\) | |||||||
\(830\) | 25128.7 | + | 43524.2i | 1.05088 | + | 1.82018i | ||||
\(831\) | −753.656 | − | 1305.37i | −0.0314609 | − | 0.0544920i | ||||
\(832\) | 1880.04 | − | 3256.33i | 0.0783397 | − | 0.135688i | ||||
\(833\) | −6010.34 | + | 10410.2i | −0.249995 | + | 0.433004i | ||||
\(834\) | 104.335 | + | 180.713i | 0.00433192 | + | 0.00750310i | ||||
\(835\) | 17795.4 | + | 30822.6i | 0.737528 | + | 1.27744i | ||||
\(836\) | 8975.39 | + | 15545.8i | 0.371316 | + | 0.643139i | ||||
\(837\) | −17272.0 | −0.713273 | ||||||||
\(838\) | −11844.5 | + | 20515.2i | −0.488258 | + | 0.845688i | ||||
\(839\) | 4242.95 | + | 7349.01i | 0.174592 | + | 0.302403i | 0.940020 | − | 0.341119i | \(-0.110806\pi\) |
−0.765428 | + | 0.643522i | \(0.777473\pi\) | |||||||
\(840\) | −7341.34 | −0.301548 | ||||||||
\(841\) | 4372.88 | 0.179297 | ||||||||
\(842\) | −8301.07 | − | 14377.9i | −0.339755 | − | 0.588473i | ||||
\(843\) | −8965.22 | −0.366285 | ||||||||
\(844\) | 3972.37 | − | 6880.35i | 0.162008 | − | 0.280606i | ||||
\(845\) | 24504.0 | 0.997591 | ||||||||
\(846\) | −3946.79 | + | 6836.04i | −0.160394 | + | 0.277811i | ||||
\(847\) | −2180.15 | + | 3776.13i | −0.0884425 | + | 0.153187i | ||||
\(848\) | 4082.23 | − | 7070.63i | 0.165312 | − | 0.286328i | ||||
\(849\) | −2642.69 | − | 4577.27i | −0.106828 | − | 0.185031i | ||||
\(850\) | −44849.8 | −1.80981 | ||||||||
\(851\) | −2992.45 | + | 27891.6i | −0.120540 | + | 1.12352i | ||||
\(852\) | 7973.98 | 0.320638 | ||||||||
\(853\) | 8605.48 | + | 14905.1i | 0.345423 | + | 0.598291i | 0.985431 | − | 0.170078i | \(-0.0544020\pi\) |
−0.640007 | + | 0.768369i | \(0.721069\pi\) | |||||||
\(854\) | 5315.91 | − | 9207.43i | 0.213006 | − | 0.368937i | ||||
\(855\) | 17619.8 | − | 30518.3i | 0.704776 | − | 1.22071i | ||||
\(856\) | −5921.71 | + | 10256.7i | −0.236449 | + | 0.409541i | ||||
\(857\) | 23152.2 | 0.922828 | 0.461414 | − | 0.887185i | \(-0.347342\pi\) | ||||
0.461414 | + | 0.887185i | \(0.347342\pi\) | |||||||
\(858\) | 7786.09 | − | 13485.9i | 0.309805 | − | 0.536598i | ||||
\(859\) | 39889.3 | 1.58441 | 0.792203 | − | 0.610258i | \(-0.208934\pi\) | ||||
0.792203 | + | 0.610258i | \(0.208934\pi\) | |||||||
\(860\) | −8705.73 | − | 15078.8i | −0.345190 | − | 0.597886i | ||||
\(861\) | −11330.0 | −0.448462 | ||||||||
\(862\) | −17902.6 | −0.707383 | ||||||||
\(863\) | 1837.49 | + | 3182.63i | 0.0724785 | + | 0.125536i | 0.899987 | − | 0.435917i | \(-0.143576\pi\) |
−0.827508 | + | 0.561453i | \(0.810242\pi\) | |||||||
\(864\) | −2268.41 | + | 3929.00i | −0.0893204 | + | 0.154707i | ||||
\(865\) | −46959.5 | −1.84586 | ||||||||
\(866\) | −13402.0 | − | 23212.9i | −0.525887 | − | 0.910863i | ||||
\(867\) | 4483.38 | + | 7765.45i | 0.175621 | + | 0.304185i | ||||
\(868\) | 3493.31 | + | 6050.59i | 0.136602 | + | 0.236602i | ||||
\(869\) | −17961.8 | + | 31110.7i | −0.701165 | + | 1.21445i | ||||
\(870\) | 10855.0 | − | 18801.4i | 0.423010 | − | 0.732675i | ||||
\(871\) | −3280.29 | − | 5681.63i | −0.127610 | − | 0.221027i | ||||
\(872\) | 2609.97 | + | 4520.61i | 0.101359 | + | 0.175559i | ||||
\(873\) | 14859.0 | + | 25736.6i | 0.576061 | + | 0.997767i | ||||
\(874\) | −27665.3 | −1.07070 | ||||||||
\(875\) | −18397.0 | + | 31864.5i | −0.710780 | + | 1.23111i | ||||
\(876\) | −424.145 | − | 734.641i | −0.0163591 | − | 0.0283347i | ||||
\(877\) | 11582.9 | 0.445984 | 0.222992 | − | 0.974820i | \(-0.428418\pi\) | ||||
0.222992 | + | 0.974820i | \(0.428418\pi\) | |||||||
\(878\) | −7202.83 | −0.276861 | ||||||||
\(879\) | 234.950 | + | 406.945i | 0.00901555 | + | 0.0156154i | ||||
\(880\) | −12635.4 | −0.484023 | ||||||||
\(881\) | −20799.8 | + | 36026.3i | −0.795419 | + | 1.37771i | 0.127154 | + | 0.991883i | \(0.459416\pi\) |
−0.922573 | + | 0.385822i | \(0.873918\pi\) | |||||||
\(882\) | 4469.37 | 0.170625 | ||||||||
\(883\) | −1612.79 | + | 2793.43i | −0.0614662 | + | 0.106463i | −0.895121 | − | 0.445823i | \(-0.852911\pi\) |
0.833655 | + | 0.552286i | \(0.186244\pi\) | |||||||
\(884\) | −10276.6 | + | 17799.5i | −0.390994 | + | 0.677221i | ||||
\(885\) | −8843.53 | + | 15317.4i | −0.335901 | + | 0.581797i | ||||
\(886\) | 8635.66 | + | 14957.4i | 0.327450 | + | 0.567160i | ||||
\(887\) | 11869.6 | 0.449315 | 0.224657 | − | 0.974438i | \(-0.427874\pi\) | ||||
0.224657 | + | 0.974438i | \(0.427874\pi\) | |||||||
\(888\) | −4766.44 | − | 3478.77i | −0.180125 | − | 0.131464i | ||||
\(889\) | −6727.90 | −0.253820 | ||||||||
\(890\) | −7876.07 | − | 13641.7i | −0.296636 | − | 0.513789i | ||||
\(891\) | −518.903 | + | 898.766i | −0.0195106 | + | 0.0337933i | ||||
\(892\) | 12971.1 | − | 22466.6i | 0.486889 | − | 0.843317i | ||||
\(893\) | 13470.2 | − | 23331.1i | 0.504774 | − | 0.874294i | ||||
\(894\) | 5485.65 | 0.205221 | ||||||||
\(895\) | −19340.1 | + | 33498.1i | −0.722312 | + | 1.25108i | ||||
\(896\) | 1835.16 | 0.0684246 | ||||||||
\(897\) | 11999.7 | + | 20784.1i | 0.446665 | + | 0.773646i | ||||
\(898\) | −6996.50 | −0.259996 | ||||||||
\(899\) | −20661.0 | −0.766499 | ||||||||
\(900\) | 8337.73 | + | 14441.4i | 0.308805 | + | 0.534866i | ||||
\(901\) | −22314.1 | + | 38649.1i | −0.825072 | + | 1.42907i | ||||
\(902\) | −19500.5 | −0.719839 | ||||||||
\(903\) | 5236.51 | + | 9069.91i | 0.192979 | + | 0.334250i | ||||
\(904\) | 3337.43 | + | 5780.59i | 0.122789 | + | 0.212676i | ||||
\(905\) | 11413.5 | + | 19768.8i | 0.419225 | + | 0.726119i | ||||
\(906\) | 5560.67 | − | 9631.37i | 0.203908 | − | 0.353180i | ||||
\(907\) | −3787.34 | + | 6559.87i | −0.138651 | + | 0.240151i | −0.926986 | − | 0.375095i | \(-0.877610\pi\) |
0.788335 | + | 0.615246i | \(0.210943\pi\) | |||||||
\(908\) | 1306.02 | + | 2262.09i | 0.0477332 | + | 0.0826763i | ||||
\(909\) | −3051.94 | − | 5286.11i | −0.111360 | − | 0.192881i | ||||
\(910\) | 16450.4 | + | 28492.9i | 0.599258 | + | 1.03794i | ||||
\(911\) | 18746.2 | 0.681765 | 0.340883 | − | 0.940106i | \(-0.389274\pi\) | ||||
0.340883 | + | 0.940106i | \(0.389274\pi\) | |||||||
\(912\) | 2909.81 | − | 5039.94i | 0.105651 | − | 0.182992i | ||||
\(913\) | −26014.8 | − | 45059.0i | −0.943007 | − | 1.63334i | ||||
\(914\) | 11360.1 | 0.411115 | ||||||||
\(915\) | 23732.0 | 0.857439 | ||||||||
\(916\) | −3661.30 | − | 6341.55i | −0.132066 | − | 0.228745i | ||||
\(917\) | 23048.4 | 0.830017 | ||||||||
\(918\) | 12399.4 | − | 21476.5i | 0.445798 | − | 0.772145i | ||||
\(919\) | 5586.86 | 0.200537 | 0.100269 | − | 0.994960i | \(-0.468030\pi\) | ||||
0.100269 | + | 0.994960i | \(0.468030\pi\) | |||||||
\(920\) | 9736.68 | − | 16864.4i | 0.348923 | − | 0.604352i | ||||
\(921\) | 14786.3 | − | 25610.7i | 0.529018 | − | 0.916287i | ||||
\(922\) | −3582.96 | + | 6205.88i | −0.127981 | + | 0.221670i | ||||
\(923\) | −17868.0 | − | 30948.2i | −0.637196 | − | 1.10366i | ||||
\(924\) | 7600.23 | 0.270594 | ||||||||
\(925\) | −52769.0 | + | 23357.8i | −1.87571 | + | 0.830271i | ||||
\(926\) | 22638.0 | 0.803382 | ||||||||
\(927\) | −3221.97 | − | 5580.61i | −0.114157 | − | 0.197725i | ||||
\(928\) | −2713.49 | + | 4699.91i | −0.0959857 | + | 0.166252i | ||||
\(929\) | −7054.69 | + | 12219.1i | −0.249146 | + | 0.431534i | −0.963289 | − | 0.268466i | \(-0.913483\pi\) |
0.714143 | + | 0.700000i | \(0.246817\pi\) | |||||||
\(930\) | −7797.65 | + | 13505.9i | −0.274941 | + | 0.476212i | ||||
\(931\) | −15253.7 | −0.536972 | ||||||||
\(932\) | 3541.00 | − | 6133.20i | 0.124452 | − | 0.215558i | ||||
\(933\) | −22404.1 | −0.786151 | ||||||||
\(934\) | −9315.84 | − | 16135.5i | −0.326363 | − | 0.565278i | ||||
\(935\) | 69067.0 | 2.41576 | ||||||||
\(936\) | 7641.79 | 0.266859 | ||||||||
\(937\) | −6461.09 | − | 11190.9i | −0.225266 | − | 0.390173i | 0.731133 | − | 0.682235i | \(-0.238992\pi\) |
−0.956399 | + | 0.292062i | \(0.905659\pi\) | |||||||
\(938\) | 1600.99 | − | 2773.00i | 0.0557295 | − | 0.0965264i | ||||
\(939\) | 23942.5 | 0.832091 | ||||||||
\(940\) | 9481.57 | + | 16422.6i | 0.328994 | + | 0.569835i | ||||
\(941\) | −10770.7 | − | 18655.4i | −0.373129 | − | 0.646278i | 0.616916 | − | 0.787029i | \(-0.288382\pi\) |
−0.990045 | + | 0.140751i | \(0.955048\pi\) | |||||||
\(942\) | −9221.63 | − | 15972.3i | −0.318957 | − | 0.552449i | ||||
\(943\) | 15026.8 | − | 26027.2i | 0.518918 | − | 0.898792i | ||||
\(944\) | 2210.67 | − | 3829.00i | 0.0762196 | − | 0.132016i | ||||
\(945\) | −19848.6 | − | 34378.8i | −0.683254 | − | 1.18343i | ||||
\(946\) | 9012.73 | + | 15610.5i | 0.309756 | + | 0.536513i | ||||
\(947\) | 5494.60 | + | 9516.93i | 0.188543 | + | 0.326567i | 0.944765 | − | 0.327749i | \(-0.106290\pi\) |
−0.756221 | + | 0.654316i | \(0.772957\pi\) | |||||||
\(948\) | 11646.4 | 0.399005 | ||||||||
\(949\) | −1900.84 | + | 3292.35i | −0.0650198 | + | 0.112618i | ||||
\(950\) | −28456.3 | − | 49287.7i | −0.971835 | − | 1.68327i | ||||
\(951\) | −22092.1 | −0.753297 | ||||||||
\(952\) | −10031.3 | −0.341507 | ||||||||
\(953\) | 14247.3 | + | 24677.1i | 0.484278 | + | 0.838794i | 0.999837 | − | 0.0180601i | \(-0.00574901\pi\) |
−0.515559 | + | 0.856854i | \(0.672416\pi\) | |||||||
\(954\) | 16593.0 | 0.563123 | ||||||||
\(955\) | −18627.2 | + | 32263.3i | −0.631164 | + | 1.09321i | ||||
\(956\) | 2901.75 | 0.0981689 | ||||||||
\(957\) | −11237.8 | + | 19464.4i | −0.379588 | + | 0.657466i | ||||
\(958\) | 195.455 | − | 338.538i | 0.00659171 | − | 0.0114172i | ||||
\(959\) | 14933.5 | − | 25865.6i | 0.502846 | − | 0.870954i | ||||
\(960\) | 2048.19 | + | 3547.58i | 0.0688596 | + | 0.119268i | ||||
\(961\) | −14949.2 | −0.501804 | ||||||||
\(962\) | −2821.10 | + | 26294.5i | −0.0945486 | + | 0.881256i | ||||
\(963\) | −24070.0 | −0.805445 | ||||||||
\(964\) | 8784.75 | + | 15215.6i | 0.293504 | + | 0.508364i | ||||
\(965\) | 48277.2 | − | 83618.6i | 1.61047 | − | 2.78941i | ||||
\(966\) | −5856.63 | + | 10144.0i | −0.195066 | + | 0.337864i | ||||
\(967\) | 5715.49 | − | 9899.52i | 0.190070 | − | 0.329211i | −0.755203 | − | 0.655491i | \(-0.772462\pi\) |
0.945273 | + | 0.326280i | \(0.105795\pi\) | |||||||
\(968\) | 2433.00 | 0.0807846 | ||||||||
\(969\) | −15905.5 | + | 27549.1i | −0.527303 | + | 0.913316i | ||||
\(970\) | 71393.1 | 2.36319 | ||||||||
\(971\) | −12674.7 | − | 21953.3i | −0.418899 | − | 0.725555i | 0.576930 | − | 0.816794i | \(-0.304251\pi\) |
−0.995829 | + | 0.0912388i | \(0.970917\pi\) | |||||||
\(972\) | −14975.3 | −0.494170 | ||||||||
\(973\) | 456.422 | 0.0150383 | ||||||||
\(974\) | 4852.49 | + | 8404.75i | 0.159634 | + | 0.276495i | ||||
\(975\) | −24685.6 | + | 42756.7i | −0.810843 | + | 1.40442i | ||||
\(976\) | −5932.44 | −0.194562 | ||||||||
\(977\) | −8911.05 | − | 15434.4i | −0.291801 | − | 0.505415i | 0.682434 | − | 0.730947i | \(-0.260921\pi\) |
−0.974236 | + | 0.225532i | \(0.927588\pi\) | |||||||
\(978\) | −6834.18 | − | 11837.2i | −0.223449 | − | 0.387025i | ||||
\(979\) | 8153.81 | + | 14122.8i | 0.266187 | + | 0.461049i | ||||
\(980\) | 5368.49 | − | 9298.50i | 0.174990 | − | 0.303092i | ||||
\(981\) | −5304.38 | + | 9187.45i | −0.172636 | + | 0.299014i | ||||
\(982\) | 18733.9 | + | 32448.1i | 0.608782 | + | 1.05444i | ||||
\(983\) | 16682.4 | + | 28894.8i | 0.541289 | + | 0.937540i | 0.998830 | + | 0.0483514i | \(0.0153967\pi\) |
−0.457542 | + | 0.889188i | \(0.651270\pi\) | |||||||
\(984\) | 3161.01 | + | 5475.04i | 0.102408 | + | 0.177376i | ||||
\(985\) | 40688.0 | 1.31617 | ||||||||
\(986\) | 14832.3 | − | 25690.4i | 0.479065 | − | 0.829765i | ||||
\(987\) | −5703.18 | − | 9878.19i | −0.183925 | − | 0.318568i | ||||
\(988\) | −26081.1 | −0.839827 | ||||||||
\(989\) | −27780.3 | −0.893189 | ||||||||
\(990\) | −12839.8 | − | 22239.2i | −0.412197 | − | 0.713946i | ||||
\(991\) | 13204.3 | 0.423256 | 0.211628 | − | 0.977350i | \(-0.432123\pi\) | ||||
0.211628 | + | 0.977350i | \(0.432123\pi\) | |||||||
\(992\) | 1949.23 | − | 3376.16i | 0.0623872 | − | 0.108058i | ||||
\(993\) | 1034.42 | 0.0330578 | ||||||||
\(994\) | 8720.72 | − | 15104.7i | 0.278274 | − | 0.481985i | ||||
\(995\) | 6833.21 | − | 11835.5i | 0.217716 | − | 0.377095i | ||||
\(996\) | −8433.98 | + | 14608.1i | −0.268314 | + | 0.464734i | ||||
\(997\) | −21877.7 | − | 37893.3i | −0.694959 | − | 1.20370i | −0.970194 | − | 0.242328i | \(-0.922089\pi\) |
0.275235 | − | 0.961377i | \(-0.411244\pi\) | |||||||
\(998\) | −11687.5 | −0.370701 | ||||||||
\(999\) | 3403.86 | − | 31726.2i | 0.107801 | − | 1.00478i |
(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 | 74.4.c.b.63.4 | yes | 10 | |
3.2 | odd | 2 | 666.4.f.d.433.5 | 10 | |||
37.10 | even | 3 | inner | 74.4.c.b.47.4 | ✓ | 10 | |
111.47 | odd | 6 | 666.4.f.d.343.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.c.b.47.4 | ✓ | 10 | 37.10 | even | 3 | inner | |
74.4.c.b.63.4 | yes | 10 | 1.1 | even | 1 | trivial | |
666.4.f.d.343.5 | 10 | 111.47 | odd | 6 | |||
666.4.f.d.433.5 | 10 | 3.2 | odd | 2 |