Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(11,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.e (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: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.14 | ||
Character | \(\chi\) | \(=\) | 60.11 |
Dual form | 60.4.e.a.11.13 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.235442 | + | 2.81861i | 0.0832413 | + | 0.996529i | ||||
\(3\) | 5.18580 | − | 0.327893i | 0.998007 | − | 0.0631030i | ||||
\(4\) | −7.88913 | + | 1.32724i | −0.986142 | + | 0.165905i | ||||
\(5\) | 5.00000i | 0.447214i | ||||||||
\(6\) | 2.14516 | + | 14.5395i | 0.145959 | + | 0.989291i | ||||
\(7\) | 26.3120i | 1.42072i | 0.703841 | + | 0.710358i | \(0.251467\pi\) | ||||
−0.703841 | + | 0.710358i | \(0.748533\pi\) | |||||||
\(8\) | −5.59840 | − | 21.9239i | −0.247417 | − | 0.968909i | ||||
\(9\) | 26.7850 | − | 3.40077i | 0.992036 | − | 0.125954i | ||||
\(10\) | −14.0931 | + | 1.17721i | −0.445662 | + | 0.0372266i | ||||
\(11\) | 41.8165 | 1.14620 | 0.573098 | − | 0.819487i | \(-0.305742\pi\) | ||||
0.573098 | + | 0.819487i | \(0.305742\pi\) | |||||||
\(12\) | −40.4763 | + | 9.46957i | −0.973707 | + | 0.227803i | ||||
\(13\) | −62.0996 | −1.32487 | −0.662436 | − | 0.749119i | \(-0.730477\pi\) | ||||
−0.662436 | + | 0.749119i | \(0.730477\pi\) | |||||||
\(14\) | −74.1633 | + | 6.19495i | −1.41578 | + | 0.118262i | ||||
\(15\) | 1.63946 | + | 25.9290i | 0.0282205 | + | 0.446322i | ||||
\(16\) | 60.4769 | − | 20.9415i | 0.944951 | − | 0.327211i | ||||
\(17\) | − | 57.4334i | − | 0.819391i | −0.912222 | − | 0.409696i | \(-0.865635\pi\) | ||
0.912222 | − | 0.409696i | \(-0.134365\pi\) | |||||||
\(18\) | 15.8917 | + | 74.6957i | 0.208096 | + | 0.978108i | ||||
\(19\) | − | 72.8787i | − | 0.879975i | −0.898004 | − | 0.439987i | \(-0.854983\pi\) | ||
0.898004 | − | 0.439987i | \(-0.145017\pi\) | |||||||
\(20\) | −6.63619 | − | 39.4457i | −0.0741949 | − | 0.441016i | ||||
\(21\) | 8.62751 | + | 136.449i | 0.0896513 | + | 1.41788i | ||||
\(22\) | 9.84535 | + | 117.864i | 0.0954108 | + | 1.14222i | ||||
\(23\) | 144.939 | 1.31399 | 0.656996 | − | 0.753894i | \(-0.271827\pi\) | ||||
0.656996 | + | 0.753894i | \(0.271827\pi\) | |||||||
\(24\) | −36.2208 | − | 111.857i | −0.308065 | − | 0.951365i | ||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | −14.6208 | − | 175.035i | −0.110284 | − | 1.32027i | ||||
\(27\) | 137.786 | − | 26.4183i | 0.982111 | − | 0.188304i | ||||
\(28\) | −34.9223 | − | 207.579i | −0.235703 | − | 1.40103i | ||||
\(29\) | − | 100.810i | − | 0.645513i | −0.946482 | − | 0.322757i | \(-0.895390\pi\) | ||
0.946482 | − | 0.322757i | \(-0.104610\pi\) | |||||||
\(30\) | −72.6977 | + | 10.7258i | −0.442424 | + | 0.0652750i | ||||
\(31\) | − | 130.044i | − | 0.753440i | −0.926327 | − | 0.376720i | \(-0.877052\pi\) | ||
0.926327 | − | 0.376720i | \(-0.122948\pi\) | |||||||
\(32\) | 73.2648 | + | 165.530i | 0.404734 | + | 0.914434i | ||||
\(33\) | 216.852 | − | 13.7113i | 1.14391 | − | 0.0723283i | ||||
\(34\) | 161.882 | − | 13.5222i | 0.816547 | − | 0.0682071i | ||||
\(35\) | −131.560 | −0.635363 | ||||||||
\(36\) | −206.797 | + | 62.3792i | −0.957392 | + | 0.288792i | ||||
\(37\) | 10.8369 | 0.0481505 | 0.0240752 | − | 0.999710i | \(-0.492336\pi\) | ||||
0.0240752 | + | 0.999710i | \(0.492336\pi\) | |||||||
\(38\) | 205.417 | − | 17.1587i | 0.876921 | − | 0.0732502i | ||||
\(39\) | −322.036 | + | 20.3620i | −1.32223 | + | 0.0836033i | ||||
\(40\) | 109.620 | − | 27.9920i | 0.433309 | − | 0.110648i | ||||
\(41\) | − | 17.9491i | − | 0.0683701i | −0.999416 | − | 0.0341851i | \(-0.989116\pi\) | ||
0.999416 | − | 0.0341851i | \(-0.0108836\pi\) | |||||||
\(42\) | −382.565 | + | 56.4433i | −1.40550 | + | 0.207367i | ||||
\(43\) | 366.646i | 1.30030i | 0.759805 | + | 0.650151i | \(0.225294\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774706\pi\) | |||||||
\(44\) | −329.896 | + | 55.5004i | −1.13031 | + | 0.190159i | ||||
\(45\) | 17.0038 | + | 133.925i | 0.0563285 | + | 0.443652i | ||||
\(46\) | 34.1247 | + | 408.526i | 0.109378 | + | 1.30943i | ||||
\(47\) | −257.954 | −0.800562 | −0.400281 | − | 0.916392i | \(-0.631088\pi\) | ||||
−0.400281 | + | 0.916392i | \(0.631088\pi\) | |||||||
\(48\) | 306.754 | − | 128.428i | 0.922420 | − | 0.386188i | ||||
\(49\) | −349.322 | −1.01843 | ||||||||
\(50\) | −5.88605 | − | 70.4653i | −0.0166483 | − | 0.199306i | ||||
\(51\) | −18.8320 | − | 297.838i | −0.0517060 | − | 0.817758i | ||||
\(52\) | 489.912 | − | 82.4209i | 1.30651 | − | 0.219802i | ||||
\(53\) | 147.704i | 0.382806i | 0.981512 | + | 0.191403i | \(0.0613038\pi\) | ||||
−0.981512 | + | 0.191403i | \(0.938696\pi\) | |||||||
\(54\) | 106.904 | + | 382.146i | 0.269402 | + | 0.963028i | ||||
\(55\) | 209.083i | 0.512594i | ||||||||
\(56\) | 576.862 | − | 147.305i | 1.37654 | − | 0.351509i | ||||
\(57\) | −23.8964 | − | 377.934i | −0.0555290 | − | 0.878221i | ||||
\(58\) | 284.143 | − | 23.7348i | 0.643273 | − | 0.0537333i | ||||
\(59\) | −442.815 | −0.977112 | −0.488556 | − | 0.872533i | \(-0.662476\pi\) | ||||
−0.488556 | + | 0.872533i | \(0.662476\pi\) | |||||||
\(60\) | −47.3479 | − | 202.381i | −0.101876 | − | 0.435455i | ||||
\(61\) | −279.593 | −0.586856 | −0.293428 | − | 0.955981i | \(-0.594796\pi\) | ||||
−0.293428 | + | 0.955981i | \(0.594796\pi\) | |||||||
\(62\) | 366.544 | − | 30.6178i | 0.750825 | − | 0.0627173i | ||||
\(63\) | 89.4811 | + | 704.766i | 0.178945 | + | 1.40940i | ||||
\(64\) | −449.316 | + | 245.478i | −0.877570 | + | 0.479448i | ||||
\(65\) | − | 310.498i | − | 0.592500i | ||||||
\(66\) | 89.7029 | + | 607.993i | 0.167298 | + | 1.13392i | ||||
\(67\) | − | 735.331i | − | 1.34082i | −0.741991 | − | 0.670410i | \(-0.766118\pi\) | ||
0.741991 | − | 0.670410i | \(-0.233882\pi\) | |||||||
\(68\) | 76.2278 | + | 453.100i | 0.135941 | + | 0.808036i | ||||
\(69\) | 751.623 | − | 47.5244i | 1.31137 | − | 0.0829168i | ||||
\(70\) | −30.9747 | − | 370.817i | −0.0528884 | − | 0.633158i | ||||
\(71\) | 299.317 | 0.500315 | 0.250157 | − | 0.968205i | \(-0.419518\pi\) | ||||
0.250157 | + | 0.968205i | \(0.419518\pi\) | |||||||
\(72\) | −224.511 | − | 568.193i | −0.367485 | − | 0.930030i | ||||
\(73\) | −740.346 | −1.18700 | −0.593500 | − | 0.804834i | \(-0.702254\pi\) | ||||
−0.593500 | + | 0.804834i | \(0.702254\pi\) | |||||||
\(74\) | 2.55145 | + | 30.5449i | 0.00400811 | + | 0.0479834i | ||||
\(75\) | −129.645 | + | 8.19732i | −0.199601 | + | 0.0126206i | ||||
\(76\) | 96.7274 | + | 574.950i | 0.145992 | + | 0.867780i | ||||
\(77\) | 1100.28i | 1.62842i | ||||||||
\(78\) | −133.213 | − | 902.899i | −0.193377 | − | 1.31068i | ||||
\(79\) | 209.278i | 0.298046i | 0.988834 | + | 0.149023i | \(0.0476128\pi\) | ||||
−0.988834 | + | 0.149023i | \(0.952387\pi\) | |||||||
\(80\) | 104.708 | + | 302.384i | 0.146333 | + | 0.422595i | ||||
\(81\) | 705.870 | − | 182.179i | 0.968271 | − | 0.249903i | ||||
\(82\) | 50.5915 | − | 4.22596i | 0.0681329 | − | 0.00569122i | ||||
\(83\) | −89.4750 | −0.118327 | −0.0591636 | − | 0.998248i | \(-0.518843\pi\) | ||||
−0.0591636 | + | 0.998248i | \(0.518843\pi\) | |||||||
\(84\) | −249.164 | − | 1065.01i | −0.323643 | − | 1.38336i | ||||
\(85\) | 287.167 | 0.366443 | ||||||||
\(86\) | −1033.43 | + | 86.3238i | −1.29579 | + | 0.108239i | ||||
\(87\) | −33.0547 | − | 522.778i | −0.0407338 | − | 0.644227i | ||||
\(88\) | −234.105 | − | 916.781i | −0.283588 | − | 1.11056i | ||||
\(89\) | 353.462i | 0.420976i | 0.977596 | + | 0.210488i | \(0.0675053\pi\) | ||||
−0.977596 | + | 0.210488i | \(0.932495\pi\) | |||||||
\(90\) | −373.479 | + | 79.4587i | −0.437423 | + | 0.0930632i | ||||
\(91\) | − | 1633.96i | − | 1.88226i | ||||||
\(92\) | −1143.44 | + | 192.368i | −1.29578 | + | 0.217998i | ||||
\(93\) | −42.6405 | − | 674.383i | −0.0475443 | − | 0.751938i | ||||
\(94\) | −60.7331 | − | 727.071i | −0.0666398 | − | 0.797784i | ||||
\(95\) | 364.393 | 0.393537 | ||||||||
\(96\) | 434.212 | + | 834.383i | 0.461631 | + | 0.887072i | ||||
\(97\) | 902.465 | 0.944654 | 0.472327 | − | 0.881424i | \(-0.343414\pi\) | ||||
0.472327 | + | 0.881424i | \(0.343414\pi\) | |||||||
\(98\) | −82.2450 | − | 984.602i | −0.0847755 | − | 1.01490i | ||||
\(99\) | 1120.05 | − | 142.208i | 1.13707 | − | 0.144368i | ||||
\(100\) | 197.228 | − | 33.1809i | 0.197228 | − | 0.0331809i | ||||
\(101\) | − | 1092.24i | − | 1.07606i | −0.842925 | − | 0.538031i | \(-0.819169\pi\) | ||
0.842925 | − | 0.538031i | \(-0.180831\pi\) | |||||||
\(102\) | 835.056 | − | 123.204i | 0.810616 | − | 0.119598i | ||||
\(103\) | 1871.41i | 1.79025i | 0.445813 | + | 0.895126i | \(0.352915\pi\) | ||||
−0.445813 | + | 0.895126i | \(0.647085\pi\) | |||||||
\(104\) | 347.658 | + | 1361.47i | 0.327795 | + | 1.28368i | ||||
\(105\) | −682.244 | + | 43.1376i | −0.634097 | + | 0.0400933i | ||||
\(106\) | −416.321 | + | 34.7758i | −0.381478 | + | 0.0318653i | ||||
\(107\) | 1142.20 | 1.03197 | 0.515985 | − | 0.856598i | \(-0.327426\pi\) | ||||
0.515985 | + | 0.856598i | \(0.327426\pi\) | |||||||
\(108\) | −1051.95 | + | 391.293i | −0.937260 | + | 0.348631i | ||||
\(109\) | −1091.23 | −0.958906 | −0.479453 | − | 0.877568i | \(-0.659165\pi\) | ||||
−0.479453 | + | 0.877568i | \(0.659165\pi\) | |||||||
\(110\) | −589.322 | + | 49.2268i | −0.510815 | + | 0.0426690i | ||||
\(111\) | 56.1977 | − | 3.55332i | 0.0480545 | − | 0.00303844i | ||||
\(112\) | 551.013 | + | 1591.27i | 0.464874 | + | 1.34251i | ||||
\(113\) | 1143.42i | 0.951893i | 0.879474 | + | 0.475947i | \(0.157894\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842106\pi\) | |||||||
\(114\) | 1059.62 | − | 156.336i | 0.870551 | − | 0.128441i | ||||
\(115\) | 724.694i | 0.587635i | ||||||||
\(116\) | 133.798 | + | 795.301i | 0.107094 | + | 0.636567i | ||||
\(117\) | −1663.34 | + | 211.186i | −1.31432 | + | 0.166873i | ||||
\(118\) | −104.257 | − | 1248.12i | −0.0813360 | − | 0.973720i | ||||
\(119\) | 1511.19 | 1.16412 | ||||||||
\(120\) | 559.286 | − | 181.104i | 0.425464 | − | 0.137771i | ||||
\(121\) | 417.620 | 0.313764 | ||||||||
\(122\) | −65.8279 | − | 788.064i | −0.0488506 | − | 0.584819i | ||||
\(123\) | −5.88537 | − | 93.0803i | −0.00431436 | − | 0.0682339i | ||||
\(124\) | 172.600 | + | 1025.94i | 0.124999 | + | 0.742998i | ||||
\(125\) | − | 125.000i | − | 0.0894427i | ||||||
\(126\) | −1965.39 | + | 418.144i | −1.38961 | + | 0.295645i | ||||
\(127\) | 1454.56i | 1.01631i | 0.861266 | + | 0.508155i | \(0.169672\pi\) | ||||
−0.861266 | + | 0.508155i | \(0.830328\pi\) | |||||||
\(128\) | −797.694 | − | 1208.65i | −0.550835 | − | 0.834614i | ||||
\(129\) | 120.220 | + | 1901.35i | 0.0820529 | + | 1.29771i | ||||
\(130\) | 875.173 | − | 73.1042i | 0.590444 | − | 0.0493205i | ||||
\(131\) | −748.305 | −0.499082 | −0.249541 | − | 0.968364i | \(-0.580280\pi\) | ||||
−0.249541 | + | 0.968364i | \(0.580280\pi\) | |||||||
\(132\) | −1692.58 | + | 395.984i | −1.11606 | + | 0.261106i | ||||
\(133\) | 1917.59 | 1.25019 | ||||||||
\(134\) | 2072.61 | − | 173.128i | 1.33617 | − | 0.111612i | ||||
\(135\) | 132.091 | + | 688.932i | 0.0842120 | + | 0.439213i | ||||
\(136\) | −1259.17 | + | 321.535i | −0.793916 | + | 0.202731i | ||||
\(137\) | − | 1259.05i | − | 0.785165i | −0.919717 | − | 0.392582i | \(-0.871582\pi\) | ||
0.919717 | − | 0.392582i | \(-0.128418\pi\) | |||||||
\(138\) | 310.916 | + | 2107.34i | 0.191789 | + | 1.29992i | ||||
\(139\) | − | 2071.90i | − | 1.26429i | −0.774849 | − | 0.632146i | \(-0.782174\pi\) | ||
0.774849 | − | 0.632146i | \(-0.217826\pi\) | |||||||
\(140\) | 1037.89 | − | 174.611i | 0.626558 | − | 0.105410i | ||||
\(141\) | −1337.70 | + | 84.5812i | −0.798967 | + | 0.0505179i | ||||
\(142\) | 70.4717 | + | 843.657i | 0.0416468 | + | 0.498578i | ||||
\(143\) | −2596.79 | −1.51856 | ||||||||
\(144\) | 1548.65 | − | 766.586i | 0.896212 | − | 0.443626i | ||||
\(145\) | 504.048 | 0.288682 | ||||||||
\(146\) | −174.308 | − | 2086.75i | −0.0988073 | − | 1.18288i | ||||
\(147\) | −1811.51 | + | 114.540i | −1.01640 | + | 0.0642660i | ||||
\(148\) | −85.4934 | + | 14.3831i | −0.0474832 | + | 0.00798839i | ||||
\(149\) | − | 3570.32i | − | 1.96303i | −0.191382 | − | 0.981516i | \(-0.561297\pi\) | ||
0.191382 | − | 0.981516i | \(-0.438703\pi\) | |||||||
\(150\) | −53.6289 | − | 363.489i | −0.0291919 | − | 0.197858i | ||||
\(151\) | 208.116i | 0.112161i | 0.998426 | + | 0.0560803i | \(0.0178603\pi\) | ||||
−0.998426 | + | 0.0560803i | \(0.982140\pi\) | |||||||
\(152\) | −1597.79 | + | 408.004i | −0.852616 | + | 0.217720i | ||||
\(153\) | −195.318 | − | 1538.35i | −0.103206 | − | 0.812866i | ||||
\(154\) | −3101.25 | + | 259.051i | −1.62277 | + | 0.135551i | ||||
\(155\) | 650.221 | 0.336948 | ||||||||
\(156\) | 2513.56 | − | 588.057i | 1.29004 | − | 0.301809i | ||||
\(157\) | 2057.73 | 1.04602 | 0.523010 | − | 0.852327i | \(-0.324809\pi\) | ||||
0.523010 | + | 0.852327i | \(0.324809\pi\) | |||||||
\(158\) | −589.873 | + | 49.2728i | −0.297011 | + | 0.0248097i | ||||
\(159\) | 48.4311 | + | 765.964i | 0.0241562 | + | 0.382043i | ||||
\(160\) | −827.651 | + | 366.324i | −0.408947 | + | 0.181003i | ||||
\(161\) | 3813.63i | 1.86681i | ||||||||
\(162\) | 679.683 | + | 1946.68i | 0.329635 | + | 0.944108i | ||||
\(163\) | − | 1088.30i | − | 0.522957i | −0.965209 | − | 0.261478i | \(-0.915790\pi\) | ||
0.965209 | − | 0.261478i | \(-0.0842100\pi\) | |||||||
\(164\) | 23.8227 | + | 141.603i | 0.0113429 | + | 0.0674226i | ||||
\(165\) | 68.5566 | + | 1084.26i | 0.0323462 | + | 0.511573i | ||||
\(166\) | −21.0662 | − | 252.195i | −0.00984971 | − | 0.117917i | ||||
\(167\) | −1395.62 | −0.646686 | −0.323343 | − | 0.946282i | \(-0.604807\pi\) | ||||
−0.323343 | + | 0.946282i | \(0.604807\pi\) | |||||||
\(168\) | 2943.19 | − | 953.043i | 1.35162 | − | 0.437672i | ||||
\(169\) | 1659.36 | 0.755283 | ||||||||
\(170\) | 67.6111 | + | 809.412i | 0.0305032 | + | 0.365171i | ||||
\(171\) | −247.844 | − | 1952.05i | −0.110837 | − | 0.872967i | ||||
\(172\) | −486.626 | − | 2892.52i | −0.215726 | − | 1.28228i | ||||
\(173\) | − | 158.379i | − | 0.0696030i | −0.999394 | − | 0.0348015i | \(-0.988920\pi\) | ||
0.999394 | − | 0.0348015i | \(-0.0110799\pi\) | |||||||
\(174\) | 1465.73 | − | 216.252i | 0.638600 | − | 0.0942187i | ||||
\(175\) | − | 657.800i | − | 0.284143i | ||||||
\(176\) | 2528.93 | − | 875.701i | 1.08310 | − | 0.375048i | ||||
\(177\) | −2296.35 | + | 145.196i | −0.975164 | + | 0.0616586i | ||||
\(178\) | −996.272 | + | 83.2197i | −0.419515 | + | 0.0350426i | ||||
\(179\) | −403.729 | −0.168582 | −0.0842909 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842909 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(180\) | −311.896 | − | 1033.98i | −0.129152 | − | 0.428159i | ||||
\(181\) | 218.428 | 0.0896996 | 0.0448498 | − | 0.998994i | \(-0.485719\pi\) | ||||
0.0448498 | + | 0.998994i | \(0.485719\pi\) | |||||||
\(182\) | 4605.51 | − | 384.704i | 1.87573 | − | 0.156682i | ||||
\(183\) | −1449.91 | + | 91.6765i | −0.585686 | + | 0.0370323i | ||||
\(184\) | −811.425 | − | 3177.63i | −0.325104 | − | 1.27314i | ||||
\(185\) | 54.1843i | 0.0215336i | ||||||||
\(186\) | 1890.78 | − | 278.965i | 0.745371 | − | 0.109972i | ||||
\(187\) | − | 2401.66i | − | 0.939182i | ||||||
\(188\) | 2035.03 | − | 342.366i | 0.789468 | − | 0.132817i | ||||
\(189\) | 695.118 | + | 3625.44i | 0.267526 | + | 1.39530i | ||||
\(190\) | 85.7935 | + | 1027.08i | 0.0327585 | + | 0.392171i | ||||
\(191\) | −1680.33 | −0.636566 | −0.318283 | − | 0.947996i | \(-0.603106\pi\) | ||||
−0.318283 | + | 0.947996i | \(0.603106\pi\) | |||||||
\(192\) | −2249.57 | + | 1420.32i | −0.845566 | + | 0.533870i | ||||
\(193\) | −4835.77 | −1.80356 | −0.901779 | − | 0.432198i | \(-0.857738\pi\) | ||||
−0.901779 | + | 0.432198i | \(0.857738\pi\) | |||||||
\(194\) | 212.478 | + | 2543.70i | 0.0786342 | + | 0.941375i | ||||
\(195\) | −101.810 | − | 1610.18i | −0.0373885 | − | 0.591319i | ||||
\(196\) | 2755.85 | − | 463.633i | 1.00432 | − | 0.168963i | ||||
\(197\) | − | 3000.08i | − | 1.08501i | −0.840053 | − | 0.542504i | \(-0.817476\pi\) | ||
0.840053 | − | 0.542504i | \(-0.182524\pi\) | |||||||
\(198\) | 664.537 | + | 3123.51i | 0.238518 | + | 1.12110i | ||||
\(199\) | 3482.66i | 1.24060i | 0.784365 | + | 0.620300i | \(0.212989\pi\) | ||||
−0.784365 | + | 0.620300i | \(0.787011\pi\) | |||||||
\(200\) | 139.960 | + | 548.098i | 0.0494833 | + | 0.193782i | ||||
\(201\) | −241.110 | − | 3813.28i | −0.0846098 | − | 1.33815i | ||||
\(202\) | 3078.61 | − | 257.160i | 1.07233 | − | 0.0895727i | ||||
\(203\) | 2652.50 | 0.917090 | ||||||||
\(204\) | 543.870 | + | 2324.69i | 0.186659 | + | 0.797847i | ||||
\(205\) | 89.7454 | 0.0305761 | ||||||||
\(206\) | −5274.79 | + | 440.609i | −1.78404 | + | 0.149023i | ||||
\(207\) | 3882.18 | − | 492.903i | 1.30353 | − | 0.165503i | ||||
\(208\) | −3755.59 | + | 1300.46i | −1.25194 | + | 0.433513i | ||||
\(209\) | − | 3047.53i | − | 1.00862i | ||||||
\(210\) | −282.217 | − | 1912.82i | −0.0927372 | − | 0.628559i | ||||
\(211\) | 4616.43i | 1.50620i | 0.657906 | + | 0.753100i | \(0.271442\pi\) | ||||
−0.657906 | + | 0.753100i | \(0.728558\pi\) | |||||||
\(212\) | −196.039 | − | 1165.26i | −0.0635094 | − | 0.377501i | ||||
\(213\) | 1552.20 | − | 98.1437i | 0.499318 | − | 0.0315713i | ||||
\(214\) | 268.922 | + | 3219.42i | 0.0859025 | + | 1.02839i | ||||
\(215\) | −1833.23 | −0.581513 | ||||||||
\(216\) | −1350.58 | − | 2872.92i | −0.425440 | − | 0.904987i | ||||
\(217\) | 3421.72 | 1.07042 | ||||||||
\(218\) | −256.921 | − | 3075.75i | −0.0798205 | − | 0.955578i | ||||
\(219\) | −3839.28 | + | 242.754i | −1.18463 | + | 0.0749032i | ||||
\(220\) | −277.502 | − | 1649.48i | −0.0850418 | − | 0.505491i | ||||
\(221\) | 3566.59i | 1.08559i | ||||||||
\(222\) | 23.2467 | + | 157.563i | 0.00702801 | + | 0.0476348i | ||||
\(223\) | − | 3869.17i | − | 1.16188i | −0.813947 | − | 0.580940i | \(-0.802685\pi\) | ||
0.813947 | − | 0.580940i | \(-0.197315\pi\) | |||||||
\(224\) | −4355.43 | + | 1927.74i | −1.29915 | + | 0.575012i | ||||
\(225\) | −669.624 | + | 85.0192i | −0.198407 | + | 0.0251909i | ||||
\(226\) | −3222.86 | + | 269.209i | −0.948589 | + | 0.0792368i | ||||
\(227\) | −345.177 | −0.100926 | −0.0504630 | − | 0.998726i | \(-0.516070\pi\) | ||||
−0.0504630 | + | 0.998726i | \(0.516070\pi\) | |||||||
\(228\) | 690.130 | + | 2949.86i | 0.200460 | + | 0.856838i | ||||
\(229\) | −3839.52 | −1.10796 | −0.553979 | − | 0.832530i | \(-0.686891\pi\) | ||||
−0.553979 | + | 0.832530i | \(0.686891\pi\) | |||||||
\(230\) | −2042.63 | + | 170.623i | −0.585596 | + | 0.0489155i | ||||
\(231\) | 360.772 | + | 5705.81i | 0.102758 | + | 1.62517i | ||||
\(232\) | −2210.14 | + | 564.373i | −0.625444 | + | 0.159711i | ||||
\(233\) | 4045.88i | 1.13757i | 0.822486 | + | 0.568786i | \(0.192587\pi\) | ||||
−0.822486 | + | 0.568786i | \(0.807413\pi\) | |||||||
\(234\) | −986.871 | − | 4638.57i | −0.275700 | − | 1.29587i | ||||
\(235\) | − | 1289.77i | − | 0.358022i | ||||||
\(236\) | 3493.43 | − | 587.721i | 0.963571 | − | 0.162107i | ||||
\(237\) | 68.6207 | + | 1085.27i | 0.0188076 | + | 0.297452i | ||||
\(238\) | 355.797 | + | 4259.45i | 0.0969029 | + | 1.16008i | ||||
\(239\) | 2154.87 | 0.583208 | 0.291604 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291604 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(240\) | 642.142 | + | 1533.77i | 0.172709 | + | 0.412519i | ||||
\(241\) | 2662.28 | 0.711587 | 0.355793 | − | 0.934565i | \(-0.384211\pi\) | ||||
0.355793 | + | 0.934565i | \(0.384211\pi\) | |||||||
\(242\) | 98.3252 | + | 1177.11i | 0.0261181 | + | 0.312675i | ||||
\(243\) | 3600.76 | − | 1176.19i | 0.950572 | − | 0.310505i | ||||
\(244\) | 2205.75 | − | 371.086i | 0.578723 | − | 0.0973622i | ||||
\(245\) | − | 1746.61i | − | 0.455456i | ||||||
\(246\) | 260.971 | − | 38.5036i | 0.0676379 | − | 0.00997926i | ||||
\(247\) | 4525.74i | 1.16585i | ||||||||
\(248\) | −2851.08 | + | 728.039i | −0.730015 | + | 0.186413i | ||||
\(249\) | −463.999 | + | 29.3382i | −0.118091 | + | 0.00746680i | ||||
\(250\) | 352.326 | − | 29.4302i | 0.0891323 | − | 0.00744532i | ||||
\(251\) | 5028.01 | 1.26440 | 0.632202 | − | 0.774804i | \(-0.282151\pi\) | ||||
0.632202 | + | 0.774804i | \(0.282151\pi\) | |||||||
\(252\) | −1641.32 | − | 5441.23i | −0.410292 | − | 1.36018i | ||||
\(253\) | 6060.83 | 1.50609 | ||||||||
\(254\) | −4099.84 | + | 342.464i | −1.01278 | + | 0.0845989i | ||||
\(255\) | 1489.19 | − | 94.1600i | 0.365713 | − | 0.0231236i | ||||
\(256\) | 3218.91 | − | 2532.95i | 0.785866 | − | 0.618397i | ||||
\(257\) | 6527.24i | 1.58427i | 0.610344 | + | 0.792136i | \(0.291031\pi\) | ||||
−0.610344 | + | 0.792136i | \(0.708969\pi\) | |||||||
\(258\) | −5330.86 | + | 786.512i | −1.28638 | + | 0.189791i | ||||
\(259\) | 285.139i | 0.0684081i | ||||||||
\(260\) | 412.105 | + | 2449.56i | 0.0982986 | + | 0.584289i | ||||
\(261\) | −342.830 | − | 2700.18i | −0.0813052 | − | 0.640372i | ||||
\(262\) | −176.182 | − | 2109.18i | −0.0415442 | − | 0.497350i | ||||
\(263\) | 5689.37 | 1.33392 | 0.666962 | − | 0.745092i | \(-0.267594\pi\) | ||||
0.666962 | + | 0.745092i | \(0.267594\pi\) | |||||||
\(264\) | −1514.63 | − | 4677.48i | −0.353102 | − | 1.09045i | ||||
\(265\) | −738.521 | −0.171196 | ||||||||
\(266\) | 451.480 | + | 5404.93i | 0.104068 | + | 1.24585i | ||||
\(267\) | 115.898 | + | 1832.98i | 0.0265649 | + | 0.420137i | ||||
\(268\) | 975.959 | + | 5801.13i | 0.222448 | + | 1.32224i | ||||
\(269\) | − | 1257.39i | − | 0.284998i | −0.989795 | − | 0.142499i | \(-0.954486\pi\) | ||
0.989795 | − | 0.142499i | \(-0.0455138\pi\) | |||||||
\(270\) | −1910.73 | + | 534.518i | −0.430679 | + | 0.120480i | ||||
\(271\) | − | 1301.08i | − | 0.291642i | −0.989311 | − | 0.145821i | \(-0.953418\pi\) | ||
0.989311 | − | 0.145821i | \(-0.0465824\pi\) | |||||||
\(272\) | −1202.74 | − | 3473.39i | −0.268114 | − | 0.774285i | ||||
\(273\) | −535.765 | − | 8473.41i | −0.118776 | − | 1.87851i | ||||
\(274\) | 3548.76 | − | 296.432i | 0.782440 | − | 0.0653581i | ||||
\(275\) | −1045.41 | −0.229239 | ||||||||
\(276\) | −5866.58 | + | 1372.51i | −1.27944 | + | 0.299331i | ||||
\(277\) | −8335.26 | −1.80800 | −0.904002 | − | 0.427528i | \(-0.859385\pi\) | ||||
−0.904002 | + | 0.427528i | \(0.859385\pi\) | |||||||
\(278\) | 5839.89 | − | 487.813i | 1.25990 | − | 0.105241i | ||||
\(279\) | −442.250 | − | 3483.23i | −0.0948990 | − | 0.747439i | ||||
\(280\) | 736.526 | + | 2884.31i | 0.157199 | + | 0.615609i | ||||
\(281\) | − | 2714.03i | − | 0.576177i | −0.957604 | − | 0.288088i | \(-0.906980\pi\) | ||
0.957604 | − | 0.288088i | \(-0.0930197\pi\) | |||||||
\(282\) | −553.351 | − | 3750.53i | −0.116850 | − | 0.791989i | ||||
\(283\) | − | 6298.67i | − | 1.32303i | −0.749933 | − | 0.661514i | \(-0.769914\pi\) | ||
0.749933 | − | 0.661514i | \(-0.230086\pi\) | |||||||
\(284\) | −2361.35 | + | 397.264i | −0.493381 | + | 0.0830046i | ||||
\(285\) | 1889.67 | − | 119.482i | 0.392752 | − | 0.0248333i | ||||
\(286\) | −611.392 | − | 7319.33i | −0.126407 | − | 1.51329i | ||||
\(287\) | 472.276 | 0.0971345 | ||||||||
\(288\) | 2525.33 | + | 4184.57i | 0.516688 | + | 0.856174i | ||||
\(289\) | 1614.40 | 0.328598 | ||||||||
\(290\) | 118.674 | + | 1420.72i | 0.0240303 | + | 0.287680i | ||||
\(291\) | 4680.00 | − | 295.911i | 0.942771 | − | 0.0596104i | ||||
\(292\) | 5840.69 | − | 982.616i | 1.17055 | − | 0.196929i | ||||
\(293\) | 8362.65i | 1.66741i | 0.552210 | + | 0.833705i | \(0.313785\pi\) | ||||
−0.552210 | + | 0.833705i | \(0.686215\pi\) | |||||||
\(294\) | −749.350 | − | 5078.98i | −0.148650 | − | 1.00752i | ||||
\(295\) | − | 2214.07i | − | 0.436978i | ||||||
\(296\) | −60.6690 | − | 237.586i | −0.0119132 | − | 0.0466534i | ||||
\(297\) | 5761.74 | − | 1104.72i | 1.12569 | − | 0.215833i | ||||
\(298\) | 10063.3 | − | 840.602i | 1.95622 | − | 0.163405i | ||||
\(299\) | −9000.64 | −1.74087 | ||||||||
\(300\) | 1011.91 | − | 236.739i | 0.194741 | − | 0.0455605i | ||||
\(301\) | −9647.19 | −1.84736 | ||||||||
\(302\) | −586.599 | + | 48.9993i | −0.111771 | + | 0.00933639i | ||||
\(303\) | −358.138 | − | 5664.15i | −0.0679026 | − | 1.07392i | ||||
\(304\) | −1526.19 | − | 4407.48i | −0.287938 | − | 0.831533i | ||||
\(305\) | − | 1397.96i | − | 0.262450i | ||||||
\(306\) | 4290.03 | − | 912.717i | 0.801453 | − | 0.170512i | ||||
\(307\) | 3054.26i | 0.567805i | 0.958853 | + | 0.283902i | \(0.0916292\pi\) | ||||
−0.958853 | + | 0.283902i | \(0.908371\pi\) | |||||||
\(308\) | −1460.33 | − | 8680.23i | −0.270162 | − | 1.60585i | ||||
\(309\) | 613.623 | + | 9704.78i | 0.112970 | + | 1.78668i | ||||
\(310\) | 153.089 | + | 1832.72i | 0.0280480 | + | 0.335779i | ||||
\(311\) | −3174.41 | −0.578792 | −0.289396 | − | 0.957210i | \(-0.593454\pi\) | ||||
−0.289396 | + | 0.957210i | \(0.593454\pi\) | |||||||
\(312\) | 2249.30 | + | 6946.29i | 0.408146 | + | 1.26044i | ||||
\(313\) | −1929.89 | −0.348510 | −0.174255 | − | 0.984701i | \(-0.555752\pi\) | ||||
−0.174255 | + | 0.984701i | \(0.555752\pi\) | |||||||
\(314\) | 484.477 | + | 5799.95i | 0.0870720 | + | 1.04239i | ||||
\(315\) | −3523.83 | + | 447.405i | −0.630303 | + | 0.0800268i | ||||
\(316\) | −277.761 | − | 1651.02i | −0.0494472 | − | 0.293915i | ||||
\(317\) | − | 2361.25i | − | 0.418362i | −0.977877 | − | 0.209181i | \(-0.932920\pi\) | ||
0.977877 | − | 0.209181i | \(-0.0670798\pi\) | |||||||
\(318\) | −2147.55 | + | 316.848i | −0.378707 | + | 0.0558741i | ||||
\(319\) | − | 4215.51i | − | 0.739884i | ||||||
\(320\) | −1227.39 | − | 2246.58i | −0.214416 | − | 0.392461i | ||||
\(321\) | 5923.23 | − | 374.520i | 1.02991 | − | 0.0651204i | ||||
\(322\) | −10749.1 | + | 897.888i | −1.86033 | + | 0.155396i | ||||
\(323\) | −4185.67 | −0.721043 | ||||||||
\(324\) | −5326.90 | + | 2374.09i | −0.913392 | + | 0.407080i | ||||
\(325\) | 1552.49 | 0.264974 | ||||||||
\(326\) | 3067.48 | − | 256.230i | 0.521142 | − | 0.0435316i | ||||
\(327\) | −5658.89 | + | 357.806i | −0.956995 | + | 0.0605098i | ||||
\(328\) | −393.514 | + | 100.486i | −0.0662445 | + | 0.0169159i | ||||
\(329\) | − | 6787.28i | − | 1.13737i | ||||||
\(330\) | −3039.96 | + | 448.514i | −0.507105 | + | 0.0748179i | ||||
\(331\) | 9926.27i | 1.64833i | 0.566350 | + | 0.824165i | \(0.308355\pi\) | ||||
−0.566350 | + | 0.824165i | \(0.691645\pi\) | |||||||
\(332\) | 705.881 | − | 118.755i | 0.116687 | − | 0.0196310i | ||||
\(333\) | 290.265 | − | 36.8536i | 0.0477670 | − | 0.00606477i | ||||
\(334\) | −328.588 | − | 3933.72i | −0.0538310 | − | 0.644442i | ||||
\(335\) | 3676.66 | 0.599633 | ||||||||
\(336\) | 3379.21 | + | 8071.32i | 0.548663 | + | 1.31050i | ||||
\(337\) | −7538.30 | −1.21851 | −0.609254 | − | 0.792975i | \(-0.708531\pi\) | ||||
−0.609254 | + | 0.792975i | \(0.708531\pi\) | |||||||
\(338\) | 390.682 | + | 4677.08i | 0.0628707 | + | 0.752662i | ||||
\(339\) | 374.919 | + | 5929.54i | 0.0600673 | + | 0.949996i | ||||
\(340\) | −2265.50 | + | 381.139i | −0.361365 | + | 0.0607946i | ||||
\(341\) | − | 5437.99i | − | 0.863589i | ||||||
\(342\) | 5443.73 | − | 1158.17i | 0.860711 | − | 0.183119i | ||||
\(343\) | − | 166.342i | − | 0.0261855i | ||||||
\(344\) | 8038.31 | − | 2052.63i | 1.25987 | − | 0.321716i | ||||
\(345\) | 237.622 | + | 3758.12i | 0.0370815 | + | 0.586464i | ||||
\(346\) | 446.408 | − | 37.2890i | 0.0693614 | − | 0.00579384i | ||||
\(347\) | 1157.23 | 0.179030 | 0.0895148 | − | 0.995985i | \(-0.471468\pi\) | ||||
0.0895148 | + | 0.995985i | \(0.471468\pi\) | |||||||
\(348\) | 954.624 | + | 4080.40i | 0.147050 | + | 0.628541i | ||||
\(349\) | 7043.61 | 1.08033 | 0.540166 | − | 0.841558i | \(-0.318361\pi\) | ||||
0.540166 | + | 0.841558i | \(0.318361\pi\) | |||||||
\(350\) | 1854.08 | − | 154.874i | 0.283157 | − | 0.0236524i | ||||
\(351\) | −8556.47 | + | 1640.56i | −1.30117 | + | 0.249478i | ||||
\(352\) | 3063.68 | + | 6921.90i | 0.463905 | + | 1.04812i | ||||
\(353\) | − | 421.398i | − | 0.0635376i | −0.999495 | − | 0.0317688i | \(-0.989886\pi\) | ||
0.999495 | − | 0.0317688i | \(-0.0101140\pi\) | |||||||
\(354\) | −949.907 | − | 6438.33i | −0.142619 | − | 0.966647i | ||||
\(355\) | 1496.58i | 0.223748i | ||||||||
\(356\) | −469.128 | − | 2788.51i | −0.0698420 | − | 0.415142i | ||||
\(357\) | 7836.72 | − | 495.508i | 1.16180 | − | 0.0734595i | ||||
\(358\) | −95.0547 | − | 1137.96i | −0.0140330 | − | 0.167997i | ||||
\(359\) | 4581.36 | 0.673523 | 0.336762 | − | 0.941590i | \(-0.390668\pi\) | ||||
0.336762 | + | 0.941590i | \(0.390668\pi\) | |||||||
\(360\) | 2840.96 | − | 1122.56i | 0.415922 | − | 0.164344i | ||||
\(361\) | 1547.70 | 0.225645 | ||||||||
\(362\) | 51.4271 | + | 615.664i | 0.00746671 | + | 0.0893883i | ||||
\(363\) | 2165.69 | − | 136.935i | 0.313139 | − | 0.0197994i | ||||
\(364\) | 2168.66 | + | 12890.6i | 0.312277 | + | 1.85618i | ||||
\(365\) | − | 3701.73i | − | 0.530842i | ||||||
\(366\) | −599.770 | − | 4065.15i | −0.0856571 | − | 0.580571i | ||||
\(367\) | − | 3683.56i | − | 0.523925i | −0.965078 | − | 0.261963i | \(-0.915630\pi\) | ||
0.965078 | − | 0.261963i | \(-0.0843697\pi\) | |||||||
\(368\) | 8765.45 | − | 3035.24i | 1.24166 | − | 0.429953i | ||||
\(369\) | −61.0407 | − | 480.766i | −0.00861152 | − | 0.0678256i | ||||
\(370\) | −152.724 | + | 12.7572i | −0.0214588 | + | 0.00179248i | ||||
\(371\) | −3886.39 | −0.543859 | ||||||||
\(372\) | 1231.46 | + | 5263.70i | 0.171635 | + | 0.733630i | ||||
\(373\) | −4542.08 | −0.630510 | −0.315255 | − | 0.949007i | \(-0.602090\pi\) | ||||
−0.315255 | + | 0.949007i | \(0.602090\pi\) | |||||||
\(374\) | 6769.36 | − | 565.452i | 0.935923 | − | 0.0781787i | ||||
\(375\) | −40.9866 | − | 648.225i | −0.00564410 | − | 0.0892645i | ||||
\(376\) | 1444.13 | + | 5655.36i | 0.198072 | + | 0.775672i | ||||
\(377\) | 6260.24i | 0.855222i | ||||||||
\(378\) | −10055.0 | + | 2812.85i | −1.36819 | + | 0.382744i | ||||
\(379\) | − | 63.4024i | − | 0.00859304i | −0.999991 | − | 0.00429652i | \(-0.998632\pi\) | ||
0.999991 | − | 0.00429652i | \(-0.00136763\pi\) | |||||||
\(380\) | −2874.75 | + | 483.637i | −0.388083 | + | 0.0652896i | ||||
\(381\) | 476.940 | + | 7543.05i | 0.0641322 | + | 1.01428i | ||||
\(382\) | −395.619 | − | 4736.18i | −0.0529885 | − | 0.634357i | ||||
\(383\) | −12158.8 | −1.62216 | −0.811078 | − | 0.584938i | \(-0.801119\pi\) | ||||
−0.811078 | + | 0.584938i | \(0.801119\pi\) | |||||||
\(384\) | −4532.98 | − | 6006.26i | −0.602403 | − | 0.798192i | ||||
\(385\) | −5501.38 | −0.728250 | ||||||||
\(386\) | −1138.54 | − | 13630.2i | −0.150130 | − | 1.79730i | ||||
\(387\) | 1246.88 | + | 9820.60i | 0.163779 | + | 1.28995i | ||||
\(388\) | −7119.66 | + | 1197.79i | −0.931562 | + | 0.156722i | ||||
\(389\) | − | 4854.49i | − | 0.632731i | −0.948637 | − | 0.316365i | \(-0.897537\pi\) | ||
0.948637 | − | 0.316365i | \(-0.102463\pi\) | |||||||
\(390\) | 4514.50 | − | 666.066i | 0.586155 | − | 0.0864809i | ||||
\(391\) | − | 8324.33i | − | 1.07667i | ||||||
\(392\) | 1955.64 | + | 7658.50i | 0.251977 | + | 0.986767i | ||||
\(393\) | −3880.56 | + | 245.364i | −0.498087 | + | 0.0314936i | ||||
\(394\) | 8456.05 | − | 706.344i | 1.08124 | − | 0.0903175i | ||||
\(395\) | −1046.39 | −0.133290 | ||||||||
\(396\) | −8647.51 | + | 2608.48i | −1.09736 | + | 0.331013i | ||||
\(397\) | 1031.79 | 0.130438 | 0.0652191 | − | 0.997871i | \(-0.479225\pi\) | ||||
0.0652191 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(398\) | −9816.27 | + | 819.965i | −1.23629 | + | 0.103269i | ||||
\(399\) | 9944.21 | − | 628.762i | 1.24770 | − | 0.0788909i | ||||
\(400\) | −1511.92 | + | 523.538i | −0.188990 | + | 0.0654422i | ||||
\(401\) | 10339.2i | 1.28757i | 0.765207 | + | 0.643784i | \(0.222636\pi\) | ||||
−0.765207 | + | 0.643784i | \(0.777364\pi\) | |||||||
\(402\) | 10691.4 | − | 1577.40i | 1.32646 | − | 0.195705i | ||||
\(403\) | 8075.69i | 0.998210i | ||||||||
\(404\) | 1449.67 | + | 8616.85i | 0.178524 | + | 1.06115i | ||||
\(405\) | 910.895 | + | 3529.35i | 0.111760 | + | 0.433024i | ||||
\(406\) | 624.510 | + | 7476.38i | 0.0763397 | + | 0.913907i | ||||
\(407\) | 453.159 | 0.0551899 | ||||||||
\(408\) | −6424.35 | + | 2080.29i | −0.779540 | + | 0.252425i | ||||
\(409\) | −9261.32 | −1.11966 | −0.559832 | − | 0.828606i | \(-0.689134\pi\) | ||||
−0.559832 | + | 0.828606i | \(0.689134\pi\) | |||||||
\(410\) | 21.1298 | + | 252.957i | 0.00254519 | + | 0.0304699i | ||||
\(411\) | −412.832 | − | 6529.16i | −0.0495462 | − | 0.783600i | ||||
\(412\) | −2483.81 | − | 14763.8i | −0.297011 | − | 1.76544i | ||||
\(413\) | − | 11651.3i | − | 1.38820i | ||||||
\(414\) | 2303.33 | + | 10826.3i | 0.273436 | + | 1.28523i | ||||
\(415\) | − | 447.375i | − | 0.0529175i | ||||||
\(416\) | −4549.71 | − | 10279.4i | −0.536221 | − | 1.21151i | ||||
\(417\) | −679.362 | − | 10744.5i | −0.0797806 | − | 1.26177i | ||||
\(418\) | 8589.81 | − | 717.517i | 1.00512 | − | 0.0839591i | ||||
\(419\) | 3057.12 | 0.356444 | 0.178222 | − | 0.983990i | \(-0.442966\pi\) | ||||
0.178222 | + | 0.983990i | \(0.442966\pi\) | |||||||
\(420\) | 5325.06 | − | 1245.82i | 0.618658 | − | 0.144737i | ||||
\(421\) | 9355.98 | 1.08309 | 0.541547 | − | 0.840670i | \(-0.317839\pi\) | ||||
0.541547 | + | 0.840670i | \(0.317839\pi\) | |||||||
\(422\) | −13011.9 | + | 1086.90i | −1.50097 | + | 0.125378i | ||||
\(423\) | −6909.29 | + | 877.241i | −0.794187 | + | 0.100834i | ||||
\(424\) | 3238.25 | − | 826.907i | 0.370905 | − | 0.0947126i | ||||
\(425\) | 1435.84i | 0.163878i | ||||||||
\(426\) | 642.081 | + | 4351.93i | 0.0730256 | + | 0.494957i | ||||
\(427\) | − | 7356.65i | − | 0.833755i | ||||||
\(428\) | −9010.98 | + | 1515.97i | −1.01767 | + | 0.171209i | ||||
\(429\) | −13466.4 | + | 851.467i | −1.51553 | + | 0.0958257i | ||||
\(430\) | −431.619 | − | 5167.16i | −0.0484058 | − | 0.579494i | ||||
\(431\) | 4915.07 | 0.549306 | 0.274653 | − | 0.961543i | \(-0.411437\pi\) | ||||
0.274653 | + | 0.961543i | \(0.411437\pi\) | |||||||
\(432\) | 7779.65 | − | 4483.15i | 0.866432 | − | 0.499296i | ||||
\(433\) | 13859.1 | 1.53816 | 0.769082 | − | 0.639150i | \(-0.220714\pi\) | ||||
0.769082 | + | 0.639150i | \(0.220714\pi\) | |||||||
\(434\) | 805.617 | + | 9644.51i | 0.0891034 | + | 1.06671i | ||||
\(435\) | 2613.89 | − | 165.274i | 0.288107 | − | 0.0182167i | ||||
\(436\) | 8608.85 | − | 1448.32i | 0.945617 | − | 0.159087i | ||||
\(437\) | − | 10563.0i | − | 1.15628i | ||||||
\(438\) | −1588.16 | − | 10764.3i | −0.173254 | − | 1.17429i | ||||
\(439\) | 7001.72i | 0.761216i | 0.924736 | + | 0.380608i | \(0.124285\pi\) | ||||
−0.924736 | + | 0.380608i | \(0.875715\pi\) | |||||||
\(440\) | 4583.91 | − | 1170.53i | 0.496657 | − | 0.126824i | ||||
\(441\) | −9356.58 | + | 1187.96i | −1.01032 | + | 0.128276i | ||||
\(442\) | −10052.8 | + | 839.725i | −1.08182 | + | 0.0903657i | ||||
\(443\) | 12384.9 | 1.32828 | 0.664138 | − | 0.747610i | \(-0.268799\pi\) | ||||
0.664138 | + | 0.747610i | \(0.268799\pi\) | |||||||
\(444\) | −438.635 | + | 102.620i | −0.0468845 | + | 0.0109688i | ||||
\(445\) | −1767.31 | −0.188266 | ||||||||
\(446\) | 10905.7 | − | 910.965i | 1.15785 | − | 0.0967163i | ||||
\(447\) | −1170.68 | − | 18514.9i | −0.123873 | − | 1.95912i | ||||
\(448\) | −6459.01 | − | 11822.4i | −0.681160 | − | 1.24678i | ||||
\(449\) | 10889.4i | 1.14455i | 0.820061 | + | 0.572277i | \(0.193940\pi\) | ||||
−0.820061 | + | 0.572277i | \(0.806060\pi\) | |||||||
\(450\) | −397.294 | − | 1867.39i | −0.0416191 | − | 0.195622i | ||||
\(451\) | − | 750.568i | − | 0.0783655i | ||||||
\(452\) | −1517.59 | − | 9020.59i | −0.157924 | − | 0.938701i | ||||
\(453\) | 68.2398 | + | 1079.25i | 0.00707767 | + | 0.111937i | ||||
\(454\) | −81.2691 | − | 972.919i | −0.00840120 | − | 0.100576i | ||||
\(455\) | 8169.82 | 0.841774 | ||||||||
\(456\) | −8152.01 | + | 2639.73i | −0.837178 | + | 0.271089i | ||||
\(457\) | 5583.72 | 0.571543 | 0.285772 | − | 0.958298i | \(-0.407750\pi\) | ||||
0.285772 | + | 0.958298i | \(0.407750\pi\) | |||||||
\(458\) | −903.983 | − | 10822.1i | −0.0922279 | − | 1.10411i | ||||
\(459\) | −1517.29 | − | 7913.54i | −0.154294 | − | 0.804733i | ||||
\(460\) | −961.841 | − | 5717.21i | −0.0974915 | − | 0.579492i | ||||
\(461\) | − | 3455.46i | − | 0.349103i | −0.984648 | − | 0.174552i | \(-0.944152\pi\) | ||
0.984648 | − | 0.174552i | \(-0.0558476\pi\) | |||||||
\(462\) | −15997.5 | + | 2360.26i | −1.61098 | + | 0.237683i | ||||
\(463\) | 1399.18i | 0.140444i | 0.997531 | + | 0.0702220i | \(0.0223708\pi\) | ||||
−0.997531 | + | 0.0702220i | \(0.977629\pi\) | |||||||
\(464\) | −2111.11 | − | 6096.65i | −0.211219 | − | 0.609978i | ||||
\(465\) | 3371.91 | − | 213.203i | 0.336277 | − | 0.0212624i | ||||
\(466\) | −11403.8 | + | 952.569i | −1.13362 | + | 0.0946929i | ||||
\(467\) | 3413.27 | 0.338217 | 0.169109 | − | 0.985597i | \(-0.445911\pi\) | ||||
0.169109 | + | 0.985597i | \(0.445911\pi\) | |||||||
\(468\) | 12842.0 | − | 3873.72i | 1.26842 | − | 0.382613i | ||||
\(469\) | 19348.0 | 1.90492 | ||||||||
\(470\) | 3635.36 | − | 303.666i | 0.356780 | − | 0.0298022i | ||||
\(471\) | 10671.0 | − | 674.716i | 1.04393 | − | 0.0660069i | ||||
\(472\) | 2479.05 | + | 9708.23i | 0.241754 | + | 0.946732i | ||||
\(473\) | 15331.9i | 1.49040i | ||||||||
\(474\) | −3042.80 | + | 448.933i | −0.294854 | + | 0.0435025i | ||||
\(475\) | 1821.97i | 0.175995i | ||||||||
\(476\) | −11922.0 | + | 2005.71i | −1.14799 | + | 0.193133i | ||||
\(477\) | 502.308 | + | 3956.25i | 0.0482161 | + | 0.379758i | ||||
\(478\) | 507.346 | + | 6073.73i | 0.0485470 | + | 0.581184i | ||||
\(479\) | 18073.4 | 1.72399 | 0.861996 | − | 0.506914i | \(-0.169214\pi\) | ||||
0.861996 | + | 0.506914i | \(0.169214\pi\) | |||||||
\(480\) | −4171.92 | + | 2171.06i | −0.396711 | + | 0.206448i | ||||
\(481\) | −672.964 | −0.0637932 | ||||||||
\(482\) | 626.812 | + | 7503.93i | 0.0592334 | + | 0.709117i | ||||
\(483\) | 1250.46 | + | 19776.7i | 0.117801 | + | 1.86309i | ||||
\(484\) | −3294.66 | + | 554.281i | −0.309416 | + | 0.0520549i | ||||
\(485\) | 4512.32i | 0.422462i | ||||||||
\(486\) | 4163.00 | + | 9872.22i | 0.388554 | + | 0.921426i | ||||
\(487\) | − | 5637.63i | − | 0.524570i | −0.964991 | − | 0.262285i | \(-0.915524\pi\) | ||
0.964991 | − | 0.262285i | \(-0.0844760\pi\) | |||||||
\(488\) | 1565.27 | + | 6129.77i | 0.145198 | + | 0.568610i | ||||
\(489\) | −356.844 | − | 5643.68i | −0.0330001 | − | 0.521914i | ||||
\(490\) | 4923.01 | − | 411.225i | 0.453876 | − | 0.0379128i | ||||
\(491\) | 153.464 | 0.0141054 | 0.00705269 | − | 0.999975i | \(-0.497755\pi\) | ||||
0.00705269 | + | 0.999975i | \(0.497755\pi\) | |||||||
\(492\) | 169.970 | + | 726.512i | 0.0155749 | + | 0.0665725i | ||||
\(493\) | −5789.84 | −0.528928 | ||||||||
\(494\) | −12756.3 | + | 1065.55i | −1.16181 | + | 0.0970471i | ||||
\(495\) | 711.041 | + | 5600.27i | 0.0645635 | + | 0.508512i | ||||
\(496\) | −2723.32 | − | 7864.67i | −0.246534 | − | 0.711964i | ||||
\(497\) | 7875.62i | 0.710805i | ||||||||
\(498\) | −191.938 | − | 1300.93i | −0.0172710 | − | 0.117060i | ||||
\(499\) | 12507.6i | 1.12208i | 0.827790 | + | 0.561038i | \(0.189598\pi\) | ||||
−0.827790 | + | 0.561038i | \(0.810402\pi\) | |||||||
\(500\) | 165.905 | + | 986.142i | 0.0148390 | + | 0.0882032i | ||||
\(501\) | −7237.42 | + | 457.615i | −0.645398 | + | 0.0408078i | ||||
\(502\) | 1183.80 | + | 14172.0i | 0.105251 | + | 1.26001i | ||||
\(503\) | −18132.9 | −1.60737 | −0.803683 | − | 0.595058i | \(-0.797129\pi\) | ||||
−0.803683 | + | 0.595058i | \(0.797129\pi\) | |||||||
\(504\) | 14950.3 | − | 5907.34i | 1.32131 | − | 0.522091i | ||||
\(505\) | 5461.21 | 0.481229 | ||||||||
\(506\) | 1426.97 | + | 17083.1i | 0.125369 | + | 1.50087i | ||||
\(507\) | 8605.09 | − | 544.091i | 0.753778 | − | 0.0476606i | ||||
\(508\) | −1930.55 | − | 11475.2i | −0.168611 | − | 1.00223i | ||||
\(509\) | − | 10913.0i | − | 0.950312i | −0.879902 | − | 0.475156i | \(-0.842392\pi\) | ||
0.879902 | − | 0.475156i | \(-0.157608\pi\) | |||||||
\(510\) | 616.018 | + | 4175.28i | 0.0534858 | + | 0.362518i | ||||
\(511\) | − | 19480.0i | − | 1.68639i | ||||||
\(512\) | 7897.28 | + | 8476.48i | 0.681667 | + | 0.731662i | ||||
\(513\) | −1925.33 | − | 10041.7i | −0.165703 | − | 0.864233i | ||||
\(514\) | −18397.7 | + | 1536.79i | −1.57877 | + | 0.131877i | ||||
\(515\) | −9357.07 | −0.800625 | ||||||||
\(516\) | −3471.98 | − | 14840.5i | −0.296212 | − | 1.26611i | ||||
\(517\) | −10786.7 | −0.917601 | ||||||||
\(518\) | −803.697 | + | 67.1338i | −0.0681707 | + | 0.00569438i | ||||
\(519\) | −51.9312 | − | 821.320i | −0.00439215 | − | 0.0694642i | ||||
\(520\) | −6807.33 | + | 1738.29i | −0.574079 | + | 0.146594i | ||||
\(521\) | − | 4652.88i | − | 0.391260i | −0.980678 | − | 0.195630i | \(-0.937325\pi\) | ||
0.980678 | − | 0.195630i | \(-0.0626751\pi\) | |||||||
\(522\) | 7530.05 | − | 1602.04i | 0.631382 | − | 0.134328i | ||||
\(523\) | 18369.3i | 1.53582i | 0.640556 | + | 0.767911i | \(0.278704\pi\) | ||||
−0.640556 | + | 0.767911i | \(0.721296\pi\) | |||||||
\(524\) | 5903.48 | − | 993.179i | 0.492166 | − | 0.0828001i | ||||
\(525\) | −215.688 | − | 3411.22i | −0.0179303 | − | 0.283577i | ||||
\(526\) | 1339.52 | + | 16036.1i | 0.111037 | + | 1.32929i | ||||
\(527\) | −7468.88 | −0.617362 | ||||||||
\(528\) | 12827.4 | − | 5370.43i | 1.05727 | − | 0.442647i | ||||
\(529\) | 8840.26 | 0.726577 | ||||||||
\(530\) | −173.879 | − | 2081.60i | −0.0142506 | − | 0.170602i | ||||
\(531\) | −11860.8 | + | 1505.91i | −0.969330 | + | 0.123072i | ||||
\(532\) | −15128.1 | + | 2545.09i | −1.23287 | + | 0.207413i | ||||
\(533\) | 1114.63i | 0.0905816i | ||||||||
\(534\) | −5139.17 | + | 758.231i | −0.416468 | + | 0.0614454i | ||||
\(535\) | 5711.01i | 0.461511i | ||||||||
\(536\) | −16121.3 | + | 4116.68i | −1.29913 | + | 0.331741i | ||||
\(537\) | −2093.66 | + | 132.380i | −0.168246 | + | 0.0106380i | ||||
\(538\) | 3544.10 | − | 296.042i | 0.284009 | − | 0.0237236i | ||||
\(539\) | −14607.4 | −1.16732 | ||||||||
\(540\) | −1956.46 | − | 5259.76i | −0.155913 | − | 0.419155i | ||||
\(541\) | 4665.50 | 0.370768 | 0.185384 | − | 0.982666i | \(-0.440647\pi\) | ||||
0.185384 | + | 0.982666i | \(0.440647\pi\) | |||||||
\(542\) | 3667.24 | − | 306.329i | 0.290630 | − | 0.0242766i | ||||
\(543\) | 1132.72 | − | 71.6209i | 0.0895208 | − | 0.00566031i | ||||
\(544\) | 9506.97 | − | 4207.85i | 0.749279 | − | 0.331636i | ||||
\(545\) | − | 5456.14i | − | 0.428836i | ||||||
\(546\) | 23757.1 | − | 3505.11i | 1.86211 | − | 0.274734i | ||||
\(547\) | 10501.6i | 0.820873i | 0.911889 | + | 0.410437i | \(0.134624\pi\) | ||||
−0.911889 | + | 0.410437i | \(0.865376\pi\) | |||||||
\(548\) | 1671.05 | + | 9932.78i | 0.130263 | + | 0.774284i | ||||
\(549\) | −7488.89 | + | 950.831i | −0.582182 | + | 0.0739171i | ||||
\(550\) | −246.134 | − | 2946.61i | −0.0190822 | − | 0.228444i | ||||
\(551\) | −7346.87 | −0.568035 | ||||||||
\(552\) | −5249.81 | − | 16212.5i | −0.404795 | − | 1.25009i | ||||
\(553\) | −5506.52 | −0.423438 | ||||||||
\(554\) | −1962.47 | − | 23493.9i | −0.150501 | − | 1.80173i | ||||
\(555\) | 17.7666 | + | 280.989i | 0.00135883 | + | 0.0214906i | ||||
\(556\) | 2749.91 | + | 16345.5i | 0.209752 | + | 1.24677i | ||||
\(557\) | 11169.6i | 0.849680i | 0.905268 | + | 0.424840i | \(0.139670\pi\) | ||||
−0.905268 | + | 0.424840i | \(0.860330\pi\) | |||||||
\(558\) | 9713.75 | − | 2066.63i | 0.736946 | − | 0.156787i | ||||
\(559\) | − | 22768.6i | − | 1.72273i | ||||||
\(560\) | −7956.34 | + | 2755.07i | −0.600387 | + | 0.207898i | ||||
\(561\) | −787.488 | − | 12454.5i | −0.0592652 | − | 0.937311i | ||||
\(562\) | 7649.81 | − | 638.997i | 0.574177 | − | 0.0479617i | ||||
\(563\) | 22377.8 | 1.67515 | 0.837576 | − | 0.546321i | \(-0.183972\pi\) | ||||
0.837576 | + | 0.546321i | \(0.183972\pi\) | |||||||
\(564\) | 10441.0 | − | 2442.71i | 0.779513 | − | 0.182370i | ||||
\(565\) | −5717.10 | −0.425699 | ||||||||
\(566\) | 17753.5 | − | 1482.97i | 1.31844 | − | 0.110131i | ||||
\(567\) | 4793.50 | + | 18572.8i | 0.355040 | + | 1.37564i | ||||
\(568\) | −1675.69 | − | 6562.19i | −0.123786 | − | 0.484760i | ||||
\(569\) | 21371.4i | 1.57458i | 0.616585 | + | 0.787288i | \(0.288516\pi\) | ||||
−0.616585 | + | 0.787288i | \(0.711484\pi\) | |||||||
\(570\) | 781.681 | + | 5298.11i | 0.0574403 | + | 0.389322i | ||||
\(571\) | − | 10994.1i | − | 0.805757i | −0.915254 | − | 0.402878i | \(-0.868010\pi\) | ||
0.915254 | − | 0.402878i | \(-0.131990\pi\) | |||||||
\(572\) | 20486.4 | − | 3446.55i | 1.49752 | − | 0.251936i | ||||
\(573\) | −8713.83 | + | 550.966i | −0.635297 | + | 0.0401692i | ||||
\(574\) | 111.194 | + | 1331.16i | 0.00808560 | + | 0.0967974i | ||||
\(575\) | −3623.47 | −0.262799 | ||||||||
\(576\) | −11200.1 | + | 8103.13i | −0.810192 | + | 0.586164i | ||||
\(577\) | 2014.98 | 0.145381 | 0.0726906 | − | 0.997355i | \(-0.476841\pi\) | ||||
0.0726906 | + | 0.997355i | \(0.476841\pi\) | |||||||
\(578\) | 380.098 | + | 4550.37i | 0.0273529 | + | 0.327458i | ||||
\(579\) | −25077.3 | + | 1585.61i | −1.79996 | + | 0.113810i | ||||
\(580\) | −3976.50 | + | 668.992i | −0.284682 | + | 0.0478937i | ||||
\(581\) | − | 2354.27i | − | 0.168109i | ||||||
\(582\) | 1935.93 | + | 13121.4i | 0.137881 | + | 0.934537i | ||||
\(583\) | 6176.47i | 0.438771i | ||||||||
\(584\) | 4144.75 | + | 16231.3i | 0.293683 | + | 1.15009i | ||||
\(585\) | −1055.93 | − | 8316.68i | −0.0746280 | − | 0.587782i | ||||
\(586\) | −23571.1 | + | 1968.92i | −1.66162 | + | 0.138797i | ||||
\(587\) | −17180.7 | −1.20804 | −0.604022 | − | 0.796968i | \(-0.706436\pi\) | ||||
−0.604022 | + | 0.796968i | \(0.706436\pi\) | |||||||
\(588\) | 14139.2 | − | 3307.93i | 0.991654 | − | 0.232001i | ||||
\(589\) | −9477.45 | −0.663008 | ||||||||
\(590\) | 6240.61 | − | 521.286i | 0.435461 | − | 0.0363746i | ||||
\(591\) | −983.703 | − | 15557.8i | −0.0684672 | − | 1.08285i | ||||
\(592\) | 655.379 | − | 226.940i | 0.0454999 | − | 0.0157554i | ||||
\(593\) | − | 6700.22i | − | 0.463988i | −0.972717 | − | 0.231994i | \(-0.925475\pi\) | ||
0.972717 | − | 0.231994i | \(-0.0745250\pi\) | |||||||
\(594\) | 4470.33 | + | 15980.0i | 0.308788 | + | 1.10382i | ||||
\(595\) | 7555.94i | 0.520611i | ||||||||
\(596\) | 4738.66 | + | 28166.7i | 0.325676 | + | 1.93583i | ||||
\(597\) | 1141.94 | + | 18060.4i | 0.0782856 | + | 1.23813i | ||||
\(598\) | −2119.13 | − | 25369.3i | −0.144912 | − | 1.73483i | ||||
\(599\) | −1618.60 | −0.110407 | −0.0552037 | − | 0.998475i | \(-0.517581\pi\) | ||||
−0.0552037 | + | 0.998475i | \(0.517581\pi\) | |||||||
\(600\) | 905.521 | + | 2796.43i | 0.0616129 | + | 0.190273i | ||||
\(601\) | 6101.93 | 0.414148 | 0.207074 | − | 0.978325i | \(-0.433606\pi\) | ||||
0.207074 | + | 0.978325i | \(0.433606\pi\) | |||||||
\(602\) | −2271.35 | − | 27191.7i | −0.153776 | − | 1.84095i | ||||
\(603\) | −2500.69 | − | 19695.8i | −0.168882 | − | 1.33014i | ||||
\(604\) | −276.220 | − | 1641.86i | −0.0186080 | − | 0.110606i | ||||
\(605\) | 2088.10i | 0.140320i | ||||||||
\(606\) | 15880.7 | − | 2343.03i | 1.06454 | − | 0.157061i | ||||
\(607\) | − | 3490.58i | − | 0.233407i | −0.993167 | − | 0.116704i | \(-0.962767\pi\) | ||
0.993167 | − | 0.116704i | \(-0.0372328\pi\) | |||||||
\(608\) | 12063.6 | − | 5339.44i | 0.804679 | − | 0.356156i | ||||
\(609\) | 13755.3 | − | 869.737i | 0.915262 | − | 0.0578711i | ||||
\(610\) | 3940.32 | − | 329.139i | 0.261539 | − | 0.0218467i | ||||
\(611\) | 16018.8 | 1.06064 | ||||||||
\(612\) | 3582.65 | + | 11877.0i | 0.236634 | + | 0.784478i | ||||
\(613\) | 14259.5 | 0.939535 | 0.469767 | − | 0.882790i | \(-0.344338\pi\) | ||||
0.469767 | + | 0.882790i | \(0.344338\pi\) | |||||||
\(614\) | −8608.78 | + | 719.102i | −0.565834 | + | 0.0472648i | ||||
\(615\) | 465.401 | − | 29.4269i | 0.0305151 | − | 0.00192944i | ||||
\(616\) | 24122.4 | − | 6159.79i | 1.57779 | − | 0.402897i | ||||
\(617\) | − | 24504.0i | − | 1.59886i | −0.600763 | − | 0.799428i | \(-0.705136\pi\) | ||
0.600763 | − | 0.799428i | \(-0.294864\pi\) | |||||||
\(618\) | −27209.5 | + | 4014.48i | −1.77108 | + | 0.261304i | ||||
\(619\) | − | 20921.7i | − | 1.35850i | −0.733906 | − | 0.679251i | \(-0.762305\pi\) | ||
0.733906 | − | 0.679251i | \(-0.237695\pi\) | |||||||
\(620\) | −5129.68 | + | 862.998i | −0.332279 | + | 0.0559013i | ||||
\(621\) | 19970.6 | − | 3829.04i | 1.29049 | − | 0.247430i | ||||
\(622\) | −747.389 | − | 8947.42i | −0.0481793 | − | 0.576783i | ||||
\(623\) | −9300.29 | −0.598087 | ||||||||
\(624\) | −19049.3 | + | 7975.35i | −1.22209 | + | 0.511650i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −454.376 | − | 5439.60i | −0.0290104 | − | 0.347301i | ||||
\(627\) | −999.263 | − | 15803.9i | −0.0636471 | − | 1.00661i | ||||
\(628\) | −16233.7 | + | 2731.10i | −1.03152 | + | 0.173540i | ||||
\(629\) | − | 622.398i | − | 0.0394541i | ||||||
\(630\) | −2090.72 | − | 9826.97i | −0.132216 | − | 0.621454i | ||||
\(631\) | 21088.4i | 1.33045i | 0.746642 | + | 0.665226i | \(0.231665\pi\) | ||||
−0.746642 | + | 0.665226i | \(0.768335\pi\) | |||||||
\(632\) | 4588.19 | − | 1171.62i | 0.288779 | − | 0.0737414i | ||||
\(633\) | 1513.69 | + | 23939.9i | 0.0950457 | + | 1.50320i | ||||
\(634\) | 6655.43 | − | 555.936i | 0.416910 | − | 0.0348250i | ||||
\(635\) | −7272.80 | −0.454508 | ||||||||
\(636\) | −1398.70 | − | 5978.51i | −0.0872043 | − | 0.372741i | ||||
\(637\) | 21692.7 | 1.34929 | ||||||||
\(638\) | 11881.9 | − | 992.507i | 0.737316 | − | 0.0615889i | ||||
\(639\) | 8017.19 | − | 1017.91i | 0.496330 | − | 0.0630168i | ||||
\(640\) | 6043.25 | − | 3988.47i | 0.373251 | − | 0.246341i | ||||
\(641\) | 1545.86i | 0.0952537i | 0.998865 | + | 0.0476269i | \(0.0151658\pi\) | ||||
−0.998865 | + | 0.0476269i | \(0.984834\pi\) | |||||||
\(642\) | 2450.20 | + | 16607.1i | 0.150626 | + | 1.02092i | ||||
\(643\) | 3919.16i | 0.240368i | 0.992752 | + | 0.120184i | \(0.0383484\pi\) | ||||
−0.992752 | + | 0.120184i | \(0.961652\pi\) | |||||||
\(644\) | −5061.60 | − | 30086.3i | −0.309712 | − | 1.84094i | ||||
\(645\) | −9506.76 | + | 601.102i | −0.580354 | + | 0.0366952i | ||||
\(646\) | −985.482 | − | 11797.8i | −0.0600206 | − | 0.718541i | ||||
\(647\) | 10568.6 | 0.642187 | 0.321094 | − | 0.947047i | \(-0.395950\pi\) | ||||
0.321094 | + | 0.947047i | \(0.395950\pi\) | |||||||
\(648\) | −7945.82 | − | 14455.5i | −0.481699 | − | 0.876337i | ||||
\(649\) | −18517.0 | −1.11996 | ||||||||
\(650\) | 365.521 | + | 4375.86i | 0.0220568 | + | 0.264055i | ||||
\(651\) | 17744.4 | − | 1121.96i | 1.06829 | − | 0.0675469i | ||||
\(652\) | 1444.43 | + | 8585.71i | 0.0867610 | + | 0.515709i | ||||
\(653\) | − | 17960.1i | − | 1.07631i | −0.842845 | − | 0.538156i | \(-0.819121\pi\) | ||
0.842845 | − | 0.538156i | \(-0.180879\pi\) | |||||||
\(654\) | −2340.85 | − | 15866.0i | −0.139961 | − | 0.948637i | ||||
\(655\) | − | 3741.53i | − | 0.223196i | ||||||
\(656\) | −375.881 | − | 1085.50i | −0.0223715 | − | 0.0646064i | ||||
\(657\) | −19830.2 | + | 2517.75i | −1.17755 | + | 0.149508i | ||||
\(658\) | 19130.7 | − | 1598.01i | 1.13342 | − | 0.0946762i | ||||
\(659\) | −30263.9 | −1.78894 | −0.894472 | − | 0.447124i | \(-0.852448\pi\) | ||||
−0.894472 | + | 0.447124i | \(0.852448\pi\) | |||||||
\(660\) | −1979.92 | − | 8462.88i | −0.116770 | − | 0.499117i | ||||
\(661\) | 732.138 | 0.0430815 | 0.0215408 | − | 0.999768i | \(-0.493143\pi\) | ||||
0.0215408 | + | 0.999768i | \(0.493143\pi\) | |||||||
\(662\) | −27978.3 | + | 2337.06i | −1.64261 | + | 0.137209i | ||||
\(663\) | 1169.46 | + | 18495.6i | 0.0685038 | + | 1.08342i | ||||
\(664\) | 500.917 | + | 1961.64i | 0.0292761 | + | 0.114648i | ||||
\(665\) | 9587.93i | 0.559103i | ||||||||
\(666\) | 172.217 | + | 809.467i | 0.0100199 | + | 0.0470964i | ||||
\(667\) | − | 14611.2i | − | 0.848199i | ||||||
\(668\) | 11010.3 | − | 1852.32i | 0.637724 | − | 0.107288i | ||||
\(669\) | −1268.67 | − | 20064.7i | −0.0733180 | − | 1.15956i | ||||
\(670\) | 865.638 | + | 10363.1i | 0.0499142 | + | 0.597552i | ||||
\(671\) | −11691.6 | −0.672652 | ||||||||
\(672\) | −21954.3 | + | 11425.0i | −1.26028 | + | 0.655847i | ||||
\(673\) | 1970.80 | 0.112881 | 0.0564404 | − | 0.998406i | \(-0.482025\pi\) | ||||
0.0564404 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(674\) | −1774.83 | − | 21247.5i | −0.101430 | − | 1.21428i | ||||
\(675\) | −3444.66 | + | 660.457i | −0.196422 | + | 0.0376608i | ||||
\(676\) | −13090.9 | + | 2202.36i | −0.744816 | + | 0.125305i | ||||
\(677\) | 12741.7i | 0.723341i | 0.932306 | + | 0.361671i | \(0.117793\pi\) | ||||
−0.932306 | + | 0.361671i | \(0.882207\pi\) | |||||||
\(678\) | −16624.8 | + | 2452.81i | −0.941699 | + | 0.138938i | ||||
\(679\) | 23745.7i | 1.34208i | ||||||||
\(680\) | −1607.68 | − | 6295.83i | −0.0906641 | − | 0.355050i | ||||
\(681\) | −1790.02 | + | 113.181i | −0.100725 | + | 0.00636873i | ||||
\(682\) | 15327.6 | − | 1280.33i | 0.860592 | − | 0.0718862i | ||||
\(683\) | 31694.1 | 1.77561 | 0.887805 | − | 0.460220i | \(-0.152230\pi\) | ||||
0.887805 | + | 0.460220i | \(0.152230\pi\) | |||||||
\(684\) | 4546.11 | + | 15071.1i | 0.254130 | + | 0.842481i | ||||
\(685\) | 6295.23 | 0.351136 | ||||||||
\(686\) | 468.853 | − | 39.1638i | 0.0260946 | − | 0.00217971i | ||||
\(687\) | −19911.0 | + | 1258.95i | −1.10575 | + | 0.0699155i | ||||
\(688\) | 7678.12 | + | 22173.6i | 0.425473 | + | 1.22872i | ||||
\(689\) | − | 9172.37i | − | 0.507169i | ||||||
\(690\) | −10536.7 | + | 1554.58i | −0.581342 | + | 0.0857709i | ||||
\(691\) | − | 7103.88i | − | 0.391092i | −0.980695 | − | 0.195546i | \(-0.937352\pi\) | ||
0.980695 | − | 0.195546i | \(-0.0626479\pi\) | |||||||
\(692\) | 210.206 | + | 1249.47i | 0.0115475 | + | 0.0686384i | ||||
\(693\) | 3741.79 | + | 29470.9i | 0.205106 | + | 1.61545i | ||||
\(694\) | 272.460 | + | 3261.78i | 0.0149026 | + | 0.178408i | ||||
\(695\) | 10359.5 | 0.565409 | ||||||||
\(696\) | −11276.3 | + | 3651.41i | −0.614119 | + | 0.198860i | ||||
\(697\) | −1030.88 | −0.0560219 | ||||||||
\(698\) | 1658.36 | + | 19853.2i | 0.0899282 | + | 1.07658i | ||||
\(699\) | 1326.61 | + | 20981.1i | 0.0717841 | + | 1.13530i | ||||
\(700\) | 873.057 | + | 5189.47i | 0.0471407 | + | 0.280205i | ||||
\(701\) | 6869.08i | 0.370102i | 0.982729 | + | 0.185051i | \(0.0592451\pi\) | ||||
−0.982729 | + | 0.185051i | \(0.940755\pi\) | |||||||
\(702\) | −6638.67 | − | 23731.1i | −0.356923 | − | 1.27589i | ||||
\(703\) | − | 789.776i | − | 0.0423712i | ||||||
\(704\) | −18788.8 | + | 10265.0i | −1.00587 | + | 0.549542i | ||||
\(705\) | −422.906 | − | 6688.48i | −0.0225923 | − | 0.357309i | ||||
\(706\) | 1187.76 | − | 99.2147i | 0.0633170 | − | 0.00528895i | ||||
\(707\) | 28739.1 | 1.52878 | ||||||||
\(708\) | 17923.5 | − | 4193.27i | 0.951421 | − | 0.222589i | ||||
\(709\) | −4579.11 | −0.242556 | −0.121278 | − | 0.992619i | \(-0.538699\pi\) | ||||
−0.121278 | + | 0.992619i | \(0.538699\pi\) | |||||||
\(710\) | −4218.29 | + | 352.358i | −0.222971 | + | 0.0186250i | ||||
\(711\) | 711.706 | + | 5605.50i | 0.0375401 | + | 0.295672i | ||||
\(712\) | 7749.27 | − | 1978.82i | 0.407888 | − | 0.104157i | ||||
\(713\) | − | 18848.5i | − | 0.990014i | ||||||
\(714\) | 3241.73 | + | 21972.0i | 0.169914 | + | 1.15165i | ||||
\(715\) | − | 12983.9i | − | 0.679121i | ||||||
\(716\) | 3185.07 | − | 535.845i | 0.166245 | − | 0.0279685i | ||||
\(717\) | 11174.7 | − | 706.565i | 0.582046 | − | 0.0368022i | ||||
\(718\) | 1078.64 | + | 12913.1i | 0.0560649 | + | 0.671186i | ||||
\(719\) | 13012.9 | 0.674967 | 0.337483 | − | 0.941332i | \(-0.390424\pi\) | ||||
0.337483 | + | 0.941332i | \(0.390424\pi\) | |||||||
\(720\) | 3832.93 | + | 7743.27i | 0.198396 | + | 0.400798i | ||||
\(721\) | −49240.7 | −2.54344 | ||||||||
\(722\) | 364.392 | + | 4362.35i | 0.0187829 | + | 0.224861i | ||||
\(723\) | 13806.0 | − | 872.941i | 0.710169 | − | 0.0449032i | ||||
\(724\) | −1723.21 | + | 289.906i | −0.0884565 | + | 0.0148816i | ||||
\(725\) | 2520.24i | 0.129103i | ||||||||
\(726\) | 895.860 | + | 6072.00i | 0.0457968 | + | 0.310404i | ||||
\(727\) | 8777.55i | 0.447787i | 0.974614 | + | 0.223894i | \(0.0718768\pi\) | ||||
−0.974614 | + | 0.223894i | \(0.928123\pi\) | |||||||
\(728\) | −35822.9 | + | 9147.59i | −1.82374 | + | 0.465703i | ||||
\(729\) | 18287.1 | − | 7280.16i | 0.929083 | − | 0.369870i | ||||
\(730\) | 10433.7 | − | 871.542i | 0.529000 | − | 0.0441880i | ||||
\(731\) | 21057.7 | 1.06546 | ||||||||
\(732\) | 11316.9 | − | 2647.63i | 0.571426 | − | 0.133687i | ||||
\(733\) | −36538.2 | −1.84116 | −0.920580 | − | 0.390554i | \(-0.872283\pi\) | ||||
−0.920580 | + | 0.390554i | \(0.872283\pi\) | |||||||
\(734\) | 10382.5 | − | 867.265i | 0.522107 | − | 0.0436122i | ||||
\(735\) | −572.700 | − | 9057.56i | −0.0287406 | − | 0.454549i | ||||
\(736\) | 10618.9 | + | 23991.8i | 0.531818 | + | 1.20156i | ||||
\(737\) | − | 30749.0i | − | 1.53684i | ||||||
\(738\) | 1340.72 | − | 285.242i | 0.0668734 | − | 0.0142275i | ||||
\(739\) | 11350.7i | 0.565008i | 0.959266 | + | 0.282504i | \(0.0911651\pi\) | ||||
−0.959266 | + | 0.282504i | \(0.908835\pi\) | |||||||
\(740\) | −71.9154 | − | 427.467i | −0.00357252 | − | 0.0212351i | ||||
\(741\) | 1483.96 | + | 23469.5i | 0.0735688 | + | 1.16353i | ||||
\(742\) | −915.020 | − | 10954.2i | −0.0452715 | − | 0.541971i | ||||
\(743\) | −9663.11 | −0.477127 | −0.238563 | − | 0.971127i | \(-0.576676\pi\) | ||||
−0.238563 | + | 0.971127i | \(0.576676\pi\) | |||||||
\(744\) | −14546.4 | + | 4710.31i | −0.716796 | + | 0.232108i | ||||
\(745\) | 17851.6 | 0.877894 | ||||||||
\(746\) | −1069.40 | − | 12802.4i | −0.0524844 | − | 0.628322i | ||||
\(747\) | −2396.59 | + | 304.284i | −0.117385 | + | 0.0149038i | ||||
\(748\) | 3187.58 | + | 18947.1i | 0.155815 | + | 0.926167i | ||||
\(749\) | 30053.6i | 1.46614i | ||||||||
\(750\) | 1817.44 | − | 268.144i | 0.0884848 | − | 0.0130550i | ||||
\(751\) | 15714.3i | 0.763548i | 0.924256 | + | 0.381774i | \(0.124687\pi\) | ||||
−0.924256 | + | 0.381774i | \(0.875313\pi\) | |||||||
\(752\) | −15600.2 | + | 5401.94i | −0.756492 | + | 0.261953i | ||||
\(753\) | 26074.2 | − | 1648.65i | 1.26188 | − | 0.0797876i | ||||
\(754\) | −17645.2 | + | 1473.92i | −0.852253 | + | 0.0711897i | ||||
\(755\) | −1040.58 | −0.0501598 | ||||||||
\(756\) | −10295.7 | − | 27679.0i | −0.495305 | − | 1.33158i | ||||
\(757\) | −21007.8 | −1.00864 | −0.504321 | − | 0.863516i | \(-0.668257\pi\) | ||||
−0.504321 | + | 0.863516i | \(0.668257\pi\) | |||||||
\(758\) | 178.707 | − | 14.9276i | 0.00856322 | − | 0.000715296i | ||||
\(759\) | 31430.3 | − | 1987.30i | 1.50309 | − | 0.0950389i | ||||
\(760\) | −2040.02 | − | 7988.93i | −0.0973675 | − | 0.381301i | ||||
\(761\) | 13202.6i | 0.628901i | 0.949274 | + | 0.314451i | \(0.101820\pi\) | ||||
−0.949274 | + | 0.314451i | \(0.898180\pi\) | |||||||
\(762\) | −21148.6 | + | 3120.26i | −1.00543 | + | 0.148340i | ||||
\(763\) | − | 28712.4i | − | 1.36233i | ||||||
\(764\) | 13256.3 | − | 2230.19i | 0.627744 | − | 0.105609i | ||||
\(765\) | 7691.76 | − | 976.589i | 0.363525 | − | 0.0461551i | ||||
\(766\) | −2862.69 | − | 34270.9i | −0.135030 | − | 1.61653i | ||||
\(767\) | 27498.6 | 1.29455 | ||||||||
\(768\) | 15862.1 | − | 14190.8i | 0.745277 | − | 0.666755i | ||||
\(769\) | −5051.50 | −0.236881 | −0.118441 | − | 0.992961i | \(-0.537790\pi\) | ||||
−0.118441 | + | 0.992961i | \(0.537790\pi\) | |||||||
\(770\) | −1295.26 | − | 15506.3i | −0.0606205 | − | 0.725723i | ||||
\(771\) | 2140.23 | + | 33848.9i | 0.0999723 | + | 1.58112i | ||||
\(772\) | 38150.1 | − | 6418.22i | 1.77856 | − | 0.299219i | ||||
\(773\) | − | 21369.0i | − | 0.994296i | −0.867666 | − | 0.497148i | \(-0.834381\pi\) | ||
0.867666 | − | 0.497148i | \(-0.165619\pi\) | |||||||
\(774\) | −27386.9 | + | 5826.64i | −1.27184 | + | 0.270587i | ||||
\(775\) | 3251.10i | 0.150688i | ||||||||
\(776\) | −5052.36 | − | 19785.6i | −0.233723 | − | 0.915284i | ||||
\(777\) | 93.4951 | + | 1478.68i | 0.00431676 | + | 0.0682718i | ||||
\(778\) | 13682.9 | − | 1142.95i | 0.630535 | − | 0.0526693i | ||||
\(779\) | −1308.11 | −0.0601640 | ||||||||
\(780\) | 2940.28 | + | 12567.8i | 0.134973 | + | 0.576922i | ||||
\(781\) | 12516.4 | 0.573458 | ||||||||
\(782\) | 23463.0 | − | 1959.90i | 1.07294 | − | 0.0896237i | ||||
\(783\) | −2663.22 | − | 13890.2i | −0.121553 | − | 0.633965i | ||||
\(784\) | −21125.9 | + | 7315.33i | −0.962368 | + | 0.333242i | ||||
\(785\) | 10288.7i | 0.467794i | ||||||||
\(786\) | −1605.23 | − | 10880.0i | −0.0728457 | − | 0.493737i | ||||
\(787\) | 14306.2i | 0.647981i | 0.946060 | + | 0.323991i | \(0.105025\pi\) | ||||
−0.946060 | + | 0.323991i | \(0.894975\pi\) | |||||||
\(788\) | 3981.82 | + | 23668.0i | 0.180008 | + | 1.06997i | ||||
\(789\) | 29503.9 | − | 1865.50i | 1.33126 | − | 0.0841745i | ||||
\(790\) | −246.364 | − | 2949.36i | −0.0110952 | − | 0.132827i | ||||
\(791\) | −30085.7 | −1.35237 | ||||||||
\(792\) | −9388.27 | − | 23759.8i | −0.421209 | − | 1.06600i | ||||
\(793\) | 17362.6 | 0.777508 | ||||||||
\(794\) | 242.926 | + | 2908.21i | 0.0108578 | + | 0.129985i | ||||
\(795\) | −3829.82 | + | 242.156i | −0.170855 | + | 0.0108030i | ||||
\(796\) | −4622.32 | − | 27475.2i | −0.205821 | − | 1.22341i | ||||
\(797\) | − | 12905.8i | − | 0.573587i | −0.957992 | − | 0.286793i | \(-0.907411\pi\) | ||
0.957992 | − | 0.286793i | \(-0.0925893\pi\) | |||||||
\(798\) | 4113.52 | + | 27880.8i | 0.182477 | + | 1.23680i | ||||
\(799\) | 14815.2i | 0.655974i | ||||||||
\(800\) | −1831.62 | − | 4138.26i | −0.0809469 | − | 0.182887i | ||||
\(801\) | 1202.04 | + | 9467.47i | 0.0530238 | + | 0.417624i | ||||
\(802\) | −29142.2 | + | 2434.28i | −1.28310 | + | 0.107179i | ||||
\(803\) | −30958.7 | −1.36053 | ||||||||
\(804\) | 6963.27 | + | 29763.4i | 0.305442 | + | 1.30557i | ||||
\(805\) | −19068.2 | −0.834862 | ||||||||
\(806\) | −22762.2 | + | 1901.36i | −0.994746 | + | 0.0830923i | ||||
\(807\) | −412.289 | − | 6520.57i | −0.0179842 | − | 0.284430i | ||||
\(808\) | −23946.2 | + | 6114.81i | −1.04261 | + | 0.266235i | ||||
\(809\) | 7580.76i | 0.329450i | 0.986340 | + | 0.164725i | \(0.0526737\pi\) | ||||
−0.986340 | + | 0.164725i | \(0.947326\pi\) | |||||||
\(810\) | −9733.39 | + | 3398.41i | −0.422218 | + | 0.147417i | ||||
\(811\) | − | 14898.1i | − | 0.645058i | −0.946560 | − | 0.322529i | \(-0.895467\pi\) | ||
0.946560 | − | 0.322529i | \(-0.104533\pi\) | |||||||
\(812\) | −20926.0 | + | 3520.50i | −0.904381 | + | 0.152150i | ||||
\(813\) | −426.615 | − | 6747.14i | −0.0184035 | − | 0.291061i | ||||
\(814\) | 106.693 | + | 1277.28i | 0.00459407 | + | 0.0549983i | ||||
\(815\) | 5441.48 | 0.233873 | ||||||||
\(816\) | −7376.08 | − | 17617.9i | −0.316439 | − | 0.755823i | ||||
\(817\) | 26720.7 | 1.14423 | ||||||||
\(818\) | −2180.50 | − | 26104.0i | −0.0932022 | − | 1.11578i | ||||
\(819\) | −5556.74 | − | 43765.7i | −0.237079 | − | 1.86727i | ||||
\(820\) | −708.014 | + | 119.113i | −0.0301523 | + | 0.00507271i | ||||
\(821\) | − | 23658.4i | − | 1.00570i | −0.864372 | − | 0.502852i | \(-0.832284\pi\) | ||
0.864372 | − | 0.502852i | \(-0.167716\pi\) | |||||||
\(822\) | 18306.0 | − | 2700.85i | 0.776756 | − | 0.114602i | ||||
\(823\) | − | 27699.9i | − | 1.17322i | −0.809870 | − | 0.586609i | \(-0.800462\pi\) | ||
0.809870 | − | 0.586609i | \(-0.199538\pi\) | |||||||
\(824\) | 41028.7 | − | 10476.9i | 1.73459 | − | 0.442938i | ||||
\(825\) | −5421.30 | + | 342.783i | −0.228782 | + | 0.0144657i | ||||
\(826\) | 32840.6 | − | 2743.22i | 1.38338 | − | 0.115555i | ||||
\(827\) | −34271.4 | −1.44103 | −0.720516 | − | 0.693438i | \(-0.756095\pi\) | ||||
−0.720516 | + | 0.693438i | \(0.756095\pi\) | |||||||
\(828\) | −29972.9 | + | 9041.16i | −1.25801 | + | 0.379471i | ||||
\(829\) | −18183.3 | −0.761799 | −0.380899 | − | 0.924617i | \(-0.624386\pi\) | ||||
−0.380899 | + | 0.924617i | \(0.624386\pi\) | |||||||
\(830\) | 1260.98 | − | 105.331i | 0.0527339 | − | 0.00440492i | ||||
\(831\) | −43225.0 | + | 2733.07i | −1.80440 | + | 0.114090i | ||||
\(832\) | 27902.3 | − | 15244.1i | 1.16267 | − | 0.635207i | ||||
\(833\) | 20062.7i | 0.834493i | ||||||||
\(834\) | 30124.5 | − | 4444.56i | 1.25075 | − | 0.184535i | ||||
\(835\) | − | 6978.12i | − | 0.289207i | ||||||
\(836\) | 4044.80 | + | 24042.4i | 0.167335 | + | 0.994645i | ||||
\(837\) | −3435.55 | − | 17918.3i | −0.141876 | − | 0.739961i | ||||
\(838\) | 719.773 | + | 8616.83i | 0.0296708 | + | 0.355207i | ||||
\(839\) | 25752.3 | 1.05967 | 0.529837 | − | 0.848099i | \(-0.322253\pi\) | ||||
0.529837 | + | 0.848099i | \(0.322253\pi\) | |||||||
\(840\) | 4765.22 | + | 14715.9i | 0.195733 | + | 0.604462i | ||||
\(841\) | 14226.4 | 0.583313 | ||||||||
\(842\) | 2202.79 | + | 26370.9i | 0.0901581 | + | 1.07934i | ||||
\(843\) | −889.912 | − | 14074.4i | −0.0363585 | − | 0.575029i | ||||
\(844\) | −6127.10 | − | 36419.6i | −0.249886 | − | 1.48533i | ||||
\(845\) | 8296.79i | 0.337773i | ||||||||
\(846\) | −4099.34 | − | 19268.0i | −0.166594 | − | 0.783037i | ||||
\(847\) | 10988.4i | 0.445769i | ||||||||
\(848\) | 3093.15 | + | 8932.69i | 0.125258 | + | 0.361733i | ||||
\(849\) | −2065.29 | − | 32663.6i | −0.0834870 | − | 1.32039i | ||||
\(850\) | −4047.06 | + | 338.056i | −0.163309 | + | 0.0136414i | ||||
\(851\) | 1570.68 | 0.0632694 | ||||||||
\(852\) | −12115.2 | + | 2834.40i | −0.487160 | + | 0.113973i | ||||
\(853\) | −32006.5 | −1.28474 | −0.642369 | − | 0.766395i | \(-0.722049\pi\) | ||||
−0.642369 | + | 0.766395i | \(0.722049\pi\) | |||||||
\(854\) | 20735.5 | − | 1732.06i | 0.830861 | − | 0.0694028i | ||||
\(855\) | 9760.27 | − | 1239.22i | 0.390403 | − | 0.0495677i | ||||
\(856\) | −6394.50 | − | 25041.5i | −0.255327 | − | 0.999885i | ||||
\(857\) | 46463.2i | 1.85199i | 0.377539 | + | 0.925994i | \(0.376770\pi\) | ||||
−0.377539 | + | 0.925994i | \(0.623230\pi\) | |||||||
\(858\) | −5570.51 | − | 37756.1i | −0.221648 | − | 1.50230i | ||||
\(859\) | − | 33474.7i | − | 1.32962i | −0.747013 | − | 0.664809i | \(-0.768513\pi\) | ||
0.747013 | − | 0.664809i | \(-0.231487\pi\) | |||||||
\(860\) | 14462.6 | − | 2433.13i | 0.573454 | − | 0.0964757i | ||||
\(861\) | 2449.13 | − | 154.856i | 0.0969409 | − | 0.00612947i | ||||
\(862\) | 1157.21 | + | 13853.7i | 0.0457249 | + | 0.547399i | ||||
\(863\) | −183.100 | −0.00722223 | −0.00361112 | − | 0.999993i | \(-0.501149\pi\) | ||||
−0.00361112 | + | 0.999993i | \(0.501149\pi\) | |||||||
\(864\) | 14467.9 | + | 20872.3i | 0.569686 | + | 0.821863i | ||||
\(865\) | 791.894 | 0.0311274 | ||||||||
\(866\) | 3263.01 | + | 39063.4i | 0.128039 | + | 1.53283i | ||||
\(867\) | 8371.96 | − | 529.351i | 0.327943 | − | 0.0207355i | ||||
\(868\) | −26994.4 | + | 4541.44i | −1.05559 | + | 0.177588i | ||||
\(869\) | 8751.27i | 0.341618i | ||||||||
\(870\) | 1081.26 | + | 7328.63i | 0.0421359 | + | 0.285591i | ||||
\(871\) | 45663.7i | 1.77641i | ||||||||
\(872\) | 6109.13 | + | 23924.0i | 0.237249 | + | 0.929093i | ||||
\(873\) | 24172.5 | − | 3069.07i | 0.937130 | − | 0.118983i | ||||
\(874\) | 29772.8 | − | 2486.96i | 1.15227 | − | 0.0962502i | ||||
\(875\) | 3289.00 | 0.127073 | ||||||||
\(876\) | 29966.4 | − | 7010.76i | 1.15579 | − | 0.270402i | ||||
\(877\) | 19800.4 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(878\) | −19735.1 | + | 1648.50i | −0.758574 | + | 0.0633646i | ||||
\(879\) | 2742.05 | + | 43367.0i | 0.105219 | + | 1.66409i | ||||
\(880\) | 4378.50 | + | 12644.7i | 0.167727 | + | 0.484377i | ||||
\(881\) | − | 16266.4i | − | 0.622053i | −0.950401 | − | 0.311026i | \(-0.899327\pi\) | ||
0.950401 | − | 0.311026i | \(-0.100673\pi\) | |||||||
\(882\) | −5551.34 | − | 26092.9i | −0.211931 | − | 0.996136i | ||||
\(883\) | − | 45218.6i | − | 1.72336i | −0.507453 | − | 0.861679i | \(-0.669413\pi\) | ||
0.507453 | − | 0.861679i | \(-0.330587\pi\) | |||||||
\(884\) | −4733.71 | − | 28137.3i | −0.180104 | − | 1.07054i | ||||
\(885\) | −725.979 | − | 11481.7i | −0.0275746 | − | 0.436107i | ||||
\(886\) | 2915.93 | + | 34908.3i | 0.110567 | + | 1.32367i | ||||
\(887\) | −48410.6 | −1.83255 | −0.916273 | − | 0.400553i | \(-0.868818\pi\) | ||||
−0.916273 | + | 0.400553i | \(0.868818\pi\) | |||||||
\(888\) | −392.520 | − | 1212.18i | −0.0148335 | − | 0.0458087i | ||||
\(889\) | −38272.4 | −1.44389 | ||||||||
\(890\) | −416.099 | − | 4981.36i | −0.0156715 | − | 0.187613i | ||||
\(891\) | 29517.0 | − | 7618.09i | 1.10983 | − | 0.286437i | ||||
\(892\) | 5135.31 | + | 30524.4i | 0.192761 | + | 1.14578i | ||||
\(893\) | 18799.3i | 0.704475i | ||||||||
\(894\) | 51910.8 | − | 7658.88i | 1.94201 | − | 0.286523i | ||||
\(895\) | − | 2018.65i | − | 0.0753920i | ||||||
\(896\) | 31802.0 | − | 20988.9i | 1.18575 | − | 0.782579i | ||||
\(897\) | −46675.5 | + | 2951.24i | −1.73740 | + | 0.109854i | ||||
\(898\) | −30693.1 | + | 2563.83i | −1.14058 | + | 0.0952741i | ||||
\(899\) | −13109.7 | −0.486355 | ||||||||
\(900\) | 5169.92 | − | 1559.48i | 0.191478 | − | 0.0577585i | ||||
\(901\) | 8483.16 | 0.313668 | ||||||||
\(902\) | 2115.56 | − | 176.715i | 0.0780936 | − | 0.00652325i | ||||
\(903\) | −50028.4 | + | 3163.24i | −1.84368 | + | 0.116574i | ||||
\(904\) | 25068.2 | − | 6401.32i | 0.922298 | − | 0.235514i | ||||
\(905\) | 1092.14i | 0.0401149i | ||||||||
\(906\) | −3025.91 | + | 446.442i | −0.110959 | + | 0.0163709i | ||||
\(907\) | 23267.3i | 0.851795i | 0.904771 | + | 0.425898i | \(0.140042\pi\) | ||||
−0.904771 | + | 0.425898i | \(0.859958\pi\) | |||||||
\(908\) | 2723.15 | − | 458.132i | 0.0995273 | − | 0.0167441i | ||||
\(909\) | −3714.46 | − | 29255.7i | −0.135535 | − | 1.06749i | ||||
\(910\) | 1923.52 | + | 23027.6i | 0.0700703 | + | 0.838853i | ||||
\(911\) | 3858.37 | 0.140322 | 0.0701610 | − | 0.997536i | \(-0.477649\pi\) | ||||
0.0701610 | + | 0.997536i | \(0.477649\pi\) | |||||||
\(912\) | −9359.69 | − | 22355.8i | −0.339836 | − | 0.811706i | ||||
\(913\) | −3741.53 | −0.135626 | ||||||||
\(914\) | 1314.64 | + | 15738.3i | 0.0475760 | + | 0.569560i | ||||
\(915\) | −458.382 | − | 7249.56i | −0.0165614 | − | 0.261927i | ||||
\(916\) | 30290.5 | − | 5095.95i | 1.09260 | − | 0.183816i | ||||
\(917\) | − | 19689.4i | − | 0.709053i | ||||||
\(918\) | 21948.0 | − | 6139.84i | 0.789096 | − | 0.220746i | ||||
\(919\) | 3155.27i | 0.113257i | 0.998395 | + | 0.0566284i | \(0.0180350\pi\) | ||||
−0.998395 | + | 0.0566284i | \(0.981965\pi\) | |||||||
\(920\) | 15888.1 | − | 4057.13i | 0.569365 | − | 0.145391i | ||||
\(921\) | 1001.47 | + | 15838.8i | 0.0358302 | + | 0.566673i | ||||
\(922\) | 9739.59 | − | 813.559i | 0.347892 | − | 0.0290598i | ||||
\(923\) | −18587.4 | −0.662852 | ||||||||
\(924\) | −10419.1 | − | 44535.1i | −0.370958 | − | 1.58560i | ||||
\(925\) | −270.921 | −0.00963010 | ||||||||
\(926\) | −3943.75 | + | 329.426i | −0.139957 | + | 0.0116907i | ||||
\(927\) | 6364.25 | + | 50125.8i | 0.225490 | + | 1.77599i | ||||
\(928\) | 16687.0 | − | 7385.79i | 0.590279 | − | 0.261261i | ||||
\(929\) | 47364.8i | 1.67275i | 0.548155 | + | 0.836377i | \(0.315330\pi\) | ||||
−0.548155 | + | 0.836377i | \(0.684670\pi\) | |||||||
\(930\) | 1394.82 | + | 9453.92i | 0.0491808 | + | 0.333340i | ||||
\(931\) | 25458.1i | 0.896194i | ||||||||
\(932\) | −5369.84 | − | 31918.5i | −0.188729 | − | 1.12181i | ||||
\(933\) | −16461.8 | + | 1040.87i | −0.577638 | + | 0.0365235i | ||||
\(934\) | 803.627 | + | 9620.69i | 0.0281536 | + | 0.337043i | ||||
\(935\) | 12008.3 | 0.420015 | ||||||||
\(936\) | 13942.0 | + | 35284.5i | 0.486870 | + | 1.23217i | ||||
\(937\) | 12573.9 | 0.438389 | 0.219194 | − | 0.975681i | \(-0.429657\pi\) | ||||
0.219194 | + | 0.975681i | \(0.429657\pi\) | |||||||
\(938\) | 4555.34 | + | 54534.6i | 0.158568 | + | 1.89831i | ||||
\(939\) | −10008.0 | + | 632.796i | −0.347816 | + | 0.0219920i | ||||
\(940\) | 1711.83 | + | 10175.2i | 0.0593976 | + | 0.353061i | ||||
\(941\) | − | 9368.78i | − | 0.324563i | −0.986745 | − | 0.162281i | \(-0.948115\pi\) | ||
0.986745 | − | 0.162281i | \(-0.0518852\pi\) | |||||||
\(942\) | 4414.16 | + | 29918.5i | 0.152676 | + | 1.03482i | ||||
\(943\) | − | 2601.52i | − | 0.0898379i | ||||||
\(944\) | −26780.1 | + | 9273.21i | −0.923323 | + | 0.319722i | ||||
\(945\) | −18127.2 | + | 3475.59i | −0.623997 | + | 0.119641i | ||||
\(946\) | −43214.5 | + | 3609.76i | −1.48523 | + | 0.124063i | ||||
\(947\) | 6725.68 | 0.230787 | 0.115393 | − | 0.993320i | \(-0.463187\pi\) | ||||
0.115393 | + | 0.993320i | \(0.463187\pi\) | |||||||
\(948\) | −1981.77 | − | 8470.78i | −0.0678955 | − | 0.290209i | ||||
\(949\) | 45975.2 | 1.57262 | ||||||||
\(950\) | −5135.42 | + | 428.967i | −0.175384 | + | 0.0146500i | ||||
\(951\) | −774.235 | − | 12244.9i | −0.0263999 | − | 0.417528i | ||||
\(952\) | −8460.24 | − | 33131.2i | −0.288023 | − | 1.12793i | ||||
\(953\) | − | 53834.3i | − | 1.82987i | −0.403602 | − | 0.914935i | \(-0.632242\pi\) | ||
0.403602 | − | 0.914935i | \(-0.367758\pi\) | |||||||
\(954\) | −11032.9 | + | 2347.28i | −0.374426 | + | 0.0796603i | ||||
\(955\) | − | 8401.63i | − | 0.284681i | ||||||
\(956\) | −17000.0 | + | 2860.02i | −0.575126 | + | 0.0967570i | ||||
\(957\) | −1382.23 | − | 21860.8i | −0.0466889 | − | 0.738410i | ||||
\(958\) | 4255.22 | + | 50941.8i | 0.143507 | + | 1.71801i | ||||
\(959\) | 33128.0 | 1.11550 | ||||||||
\(960\) | −7101.62 | − | 11247.9i | −0.238754 | − | 0.378149i | ||||
\(961\) | 12879.5 | 0.432329 | ||||||||
\(962\) | −158.444 | − | 1896.82i | −0.00531022 | − | 0.0635718i | ||||
\(963\) | 30593.8 | − | 3884.36i | 1.02375 | − | 0.129981i | ||||
\(964\) | −21003.1 | + | 3533.48i | −0.701725 | + | 0.118056i | ||||
\(965\) | − | 24178.9i | − | 0.806575i | ||||||
\(966\) | −55448.5 | + | 8180.83i | −1.84682 | + | 0.272478i | ||||
\(967\) | 5199.14i | 0.172899i | 0.996256 | + | 0.0864494i | \(0.0275521\pi\) | ||||
−0.996256 | + | 0.0864494i | \(0.972448\pi\) | |||||||
\(968\) | −2338.00 | − | 9155.86i | −0.0776304 | − | 0.304009i | ||||
\(969\) | −21706.0 | + | 1372.45i | −0.719606 | + | 0.0455000i | ||||
\(970\) | −12718.5 | + | 1062.39i | −0.420996 | + | 0.0351663i | ||||
\(971\) | −31817.8 | −1.05158 | −0.525788 | − | 0.850616i | \(-0.676230\pi\) | ||||
−0.525788 | + | 0.850616i | \(0.676230\pi\) | |||||||
\(972\) | −26845.8 | + | 14058.2i | −0.885884 | + | 0.463907i | ||||
\(973\) | 54516.0 | 1.79620 | ||||||||
\(974\) | 15890.3 | − | 1327.33i | 0.522749 | − | 0.0436658i | ||||
\(975\) | 8050.89 | − | 509.050i | 0.264446 | − | 0.0167207i | ||||
\(976\) | −16908.9 | + | 5855.10i | −0.554550 | + | 0.192026i | ||||
\(977\) | 49441.8i | 1.61902i | 0.587107 | + | 0.809510i | \(0.300267\pi\) | ||||
−0.587107 | + | 0.809510i | \(0.699733\pi\) | |||||||
\(978\) | 15823.3 | − | 2334.56i | 0.517356 | − | 0.0763304i | ||||
\(979\) | 14780.5i | 0.482521i | ||||||||
\(980\) | 2318.17 | + | 13779.2i | 0.0755624 | + | 0.449144i | ||||
\(981\) | −29228.5 | + | 3711.02i | −0.951269 | + | 0.120778i | ||||
\(982\) | 36.1319 | + | 432.556i | 0.00117415 | + | 0.0140564i | ||||
\(983\) | −6929.51 | −0.224839 | −0.112420 | − | 0.993661i | \(-0.535860\pi\) | ||||
−0.112420 | + | 0.993661i | \(0.535860\pi\) | |||||||
\(984\) | −2007.74 | + | 650.131i | −0.0650450 | + | 0.0210624i | ||||
\(985\) | 15000.4 | 0.485230 | ||||||||
\(986\) | −1363.17 | − | 16319.3i | −0.0440286 | − | 0.527092i | ||||
\(987\) | −2225.50 | − | 35197.5i | −0.0717715 | − | 1.13510i | ||||
\(988\) | −6006.73 | − | 35704.1i | −0.193421 | − | 1.14970i | ||||
\(989\) | 53141.2i | 1.70859i | ||||||||
\(990\) | −15617.6 | + | 3322.69i | −0.501373 | + | 0.106669i | ||||
\(991\) | 18340.4i | 0.587893i | 0.955822 | + | 0.293947i | \(0.0949688\pi\) | ||||
−0.955822 | + | 0.293947i | \(0.905031\pi\) | |||||||
\(992\) | 21526.3 | − | 9527.66i | 0.688971 | − | 0.304943i | ||||
\(993\) | 3254.75 | + | 51475.6i | 0.104015 | + | 1.64505i | ||||
\(994\) | −22198.3 | + | 1854.25i | −0.708338 | + | 0.0591683i | ||||
\(995\) | −17413.3 | −0.554813 | ||||||||
\(996\) | 3621.61 | − | 847.290i | 0.115216 | − | 0.0269552i | ||||
\(997\) | −11489.5 | −0.364970 | −0.182485 | − | 0.983209i | \(-0.558414\pi\) | ||||
−0.182485 | + | 0.983209i | \(0.558414\pi\) | |||||||
\(998\) | −35254.0 | + | 2944.80i | −1.11818 | + | 0.0934030i | ||||
\(999\) | 1493.17 | − | 286.291i | 0.0472891 | − | 0.00906692i |
(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 | 60.4.e.a.11.14 | yes | 24 | |
3.2 | odd | 2 | inner | 60.4.e.a.11.11 | ✓ | 24 | |
4.3 | odd | 2 | inner | 60.4.e.a.11.12 | yes | 24 | |
8.3 | odd | 2 | 960.4.h.d.191.23 | 24 | |||
8.5 | even | 2 | 960.4.h.d.191.2 | 24 | |||
12.11 | even | 2 | inner | 60.4.e.a.11.13 | yes | 24 | |
24.5 | odd | 2 | 960.4.h.d.191.24 | 24 | |||
24.11 | even | 2 | 960.4.h.d.191.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.e.a.11.11 | ✓ | 24 | 3.2 | odd | 2 | inner | |
60.4.e.a.11.12 | yes | 24 | 4.3 | odd | 2 | inner | |
60.4.e.a.11.13 | yes | 24 | 12.11 | even | 2 | inner | |
60.4.e.a.11.14 | yes | 24 | 1.1 | even | 1 | trivial | |
960.4.h.d.191.1 | 24 | 24.11 | even | 2 | |||
960.4.h.d.191.2 | 24 | 8.5 | even | 2 | |||
960.4.h.d.191.23 | 24 | 8.3 | odd | 2 | |||
960.4.h.d.191.24 | 24 | 24.5 | odd | 2 |