Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,4,Mod(121,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.121");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.i (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: | \(12.3904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{295})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 295x^{2} + 87025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-8.58778 - 14.8745i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.151 |
Dual form | 210.4.i.i.121.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −2.58778 | − | 18.3386i | −0.139727 | − | 0.990190i | ||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 5.00000 | − | 8.66025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −3.91222 | + | 6.77616i | −0.107234 | + | 0.185735i | −0.914649 | − | 0.404249i | \(-0.867533\pi\) |
0.807415 | + | 0.589985i | \(0.200866\pi\) | |||||||
\(12\) | 6.00000 | + | 10.3923i | 0.144338 | + | 0.250000i | ||||
\(13\) | −32.8244 | −0.700297 | −0.350148 | − | 0.936694i | \(-0.613869\pi\) | ||||
−0.350148 | + | 0.936694i | \(0.613869\pi\) | |||||||
\(14\) | −29.1756 | + | 22.8207i | −0.556964 | + | 0.435650i | ||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 34.4389 | − | 59.6499i | 0.491333 | − | 0.851014i | −0.508617 | − | 0.860993i | \(-0.669843\pi\) |
0.999950 | + | 0.00997894i | \(0.00317645\pi\) | |||||||
\(18\) | −9.00000 | + | 15.5885i | −0.117851 | + | 0.204124i | ||||
\(19\) | −22.8511 | − | 39.5793i | −0.275916 | − | 0.477901i | 0.694450 | − | 0.719541i | \(-0.255648\pi\) |
−0.970366 | + | 0.241640i | \(0.922315\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | −51.5267 | − | 20.7846i | −0.535431 | − | 0.215980i | ||||
\(22\) | 15.6489 | 0.151652 | ||||||||
\(23\) | −108.790 | − | 188.430i | −0.986274 | − | 1.70828i | −0.636135 | − | 0.771578i | \(-0.719468\pi\) |
−0.350139 | − | 0.936698i | \(-0.613866\pi\) | |||||||
\(24\) | 12.0000 | − | 20.7846i | 0.102062 | − | 0.176777i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 32.8244 | + | 56.8536i | 0.247592 | + | 0.428843i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 68.7023 | + | 27.7128i | 0.463697 | + | 0.187044i | ||||
\(29\) | −126.527 | −0.810187 | −0.405093 | − | 0.914275i | \(-0.632761\pi\) | ||||
−0.405093 | + | 0.914275i | \(0.632761\pi\) | |||||||
\(30\) | −15.0000 | − | 25.9808i | −0.0912871 | − | 0.158114i | ||||
\(31\) | −84.5534 | + | 146.451i | −0.489879 | + | 0.848495i | −0.999932 | − | 0.0116480i | \(-0.996292\pi\) |
0.510054 | + | 0.860143i | \(0.329626\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 11.7367 | + | 20.3285i | 0.0619118 | + | 0.107234i | ||||
\(34\) | −137.756 | −0.694850 | ||||||||
\(35\) | 72.9389 | − | 57.0519i | 0.352255 | − | 0.275529i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 121.290 | + | 210.081i | 0.538918 | + | 0.933433i | 0.998963 | + | 0.0455374i | \(0.0145000\pi\) |
−0.460045 | + | 0.887896i | \(0.652167\pi\) | |||||||
\(38\) | −45.7023 | + | 79.1586i | −0.195102 | + | 0.337927i | ||||
\(39\) | −49.2367 | + | 85.2804i | −0.202158 | + | 0.350148i | ||||
\(40\) | 20.0000 | + | 34.6410i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −286.985 | −1.09316 | −0.546579 | − | 0.837408i | \(-0.684070\pi\) | ||||
−0.546579 | + | 0.837408i | \(0.684070\pi\) | |||||||
\(42\) | 15.5267 | + | 110.031i | 0.0570433 | + | 0.404243i | ||||
\(43\) | −54.2289 | −0.192322 | −0.0961609 | − | 0.995366i | \(-0.530656\pi\) | ||||
−0.0961609 | + | 0.995366i | \(0.530656\pi\) | |||||||
\(44\) | −15.6489 | − | 27.1046i | −0.0536172 | − | 0.0928677i | ||||
\(45\) | 22.5000 | − | 38.9711i | 0.0745356 | − | 0.129099i | ||||
\(46\) | −217.580 | + | 376.860i | −0.697401 | + | 1.20793i | ||||
\(47\) | −113.351 | − | 196.330i | −0.351786 | − | 0.609312i | 0.634776 | − | 0.772696i | \(-0.281092\pi\) |
−0.986563 | + | 0.163384i | \(0.947759\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | −329.607 | + | 94.9125i | −0.960953 | + | 0.276713i | ||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | −103.317 | − | 178.950i | −0.283671 | − | 0.491333i | ||||
\(52\) | 65.6489 | − | 113.707i | 0.175074 | − | 0.303237i | ||||
\(53\) | 26.8778 | − | 46.5538i | 0.0696595 | − | 0.120654i | −0.829092 | − | 0.559112i | \(-0.811142\pi\) |
0.898751 | + | 0.438459i | \(0.144475\pi\) | |||||||
\(54\) | 27.0000 | + | 46.7654i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −39.1222 | −0.0959133 | ||||||||
\(56\) | −20.7023 | − | 146.709i | −0.0494010 | − | 0.350085i | ||||
\(57\) | −137.107 | −0.318601 | ||||||||
\(58\) | 126.527 | + | 219.151i | 0.286444 | + | 0.496136i | ||||
\(59\) | 435.301 | − | 753.964i | 0.960532 | − | 1.66369i | 0.239365 | − | 0.970930i | \(-0.423061\pi\) |
0.721167 | − | 0.692761i | \(-0.243606\pi\) | |||||||
\(60\) | −30.0000 | + | 51.9615i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 232.351 | + | 402.444i | 0.487697 | + | 0.844716i | 0.999900 | − | 0.0141486i | \(-0.00450378\pi\) |
−0.512203 | + | 0.858864i | \(0.671170\pi\) | |||||||
\(62\) | 338.214 | 0.692793 | ||||||||
\(63\) | −131.290 | + | 102.693i | −0.262555 | + | 0.205367i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −82.0611 | − | 142.134i | −0.156591 | − | 0.271224i | ||||
\(66\) | 23.4733 | − | 40.6570i | 0.0437782 | − | 0.0758262i | ||||
\(67\) | 105.359 | − | 182.487i | 0.192114 | − | 0.332751i | −0.753837 | − | 0.657062i | \(-0.771799\pi\) |
0.945951 | + | 0.324311i | \(0.105132\pi\) | |||||||
\(68\) | 137.756 | + | 238.600i | 0.245667 | + | 0.425507i | ||||
\(69\) | −652.740 | −1.13885 | ||||||||
\(70\) | −171.756 | − | 69.2820i | −0.293268 | − | 0.118297i | ||||
\(71\) | 236.389 | 0.395130 | 0.197565 | − | 0.980290i | \(-0.436697\pi\) | ||||
0.197565 | + | 0.980290i | \(0.436697\pi\) | |||||||
\(72\) | −36.0000 | − | 62.3538i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 176.183 | − | 305.158i | 0.282475 | − | 0.489261i | −0.689519 | − | 0.724268i | \(-0.742178\pi\) |
0.971994 | + | 0.235007i | \(0.0755112\pi\) | |||||||
\(74\) | 242.580 | − | 420.161i | 0.381072 | − | 0.660037i | ||||
\(75\) | 37.5000 | + | 64.9519i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 182.809 | 0.275916 | ||||||||
\(77\) | 134.389 | + | 54.2093i | 0.198897 | + | 0.0802301i | ||||
\(78\) | 196.947 | 0.285895 | ||||||||
\(79\) | −391.362 | − | 677.860i | −0.557363 | − | 0.965382i | −0.997715 | − | 0.0675566i | \(-0.978480\pi\) |
0.440352 | − | 0.897825i | \(-0.354854\pi\) | |||||||
\(80\) | 40.0000 | − | 69.2820i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 286.985 | + | 497.072i | 0.386490 | + | 0.669420i | ||||
\(83\) | 956.709 | 1.26521 | 0.632605 | − | 0.774474i | \(-0.281986\pi\) | ||||
0.632605 | + | 0.774474i | \(0.281986\pi\) | |||||||
\(84\) | 175.053 | − | 136.924i | 0.227380 | − | 0.177853i | ||||
\(85\) | 344.389 | 0.439462 | ||||||||
\(86\) | 54.2289 | + | 93.9273i | 0.0679960 | + | 0.117773i | ||||
\(87\) | −189.790 | + | 328.726i | −0.233881 | + | 0.405093i | ||||
\(88\) | −31.2977 | + | 54.2093i | −0.0379131 | + | 0.0656674i | ||||
\(89\) | −93.0190 | − | 161.114i | −0.110786 | − | 0.191888i | 0.805301 | − | 0.592866i | \(-0.202004\pi\) |
−0.916088 | + | 0.400978i | \(0.868670\pi\) | |||||||
\(90\) | −90.0000 | −0.105409 | ||||||||
\(91\) | 84.9425 | + | 601.953i | 0.0978505 | + | 0.693427i | ||||
\(92\) | 870.320 | 0.986274 | ||||||||
\(93\) | 253.660 | + | 439.352i | 0.282832 | + | 0.489879i | ||||
\(94\) | −226.702 | + | 392.660i | −0.248751 | + | 0.430849i | ||||
\(95\) | 114.256 | − | 197.897i | 0.123393 | − | 0.213724i | ||||
\(96\) | 48.0000 | + | 83.1384i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 10.1068 | 0.0105792 | 0.00528962 | − | 0.999986i | \(-0.498316\pi\) | ||||
0.00528962 | + | 0.999986i | \(0.498316\pi\) | |||||||
\(98\) | 494.000 | + | 475.983i | 0.509199 | + | 0.490628i | ||||
\(99\) | 70.4199 | 0.0714896 | ||||||||
\(100\) | −50.0000 | − | 86.6025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 725.210 | − | 1256.10i | 0.714466 | − | 1.23749i | −0.248699 | − | 0.968581i | \(-0.580003\pi\) |
0.963165 | − | 0.268911i | \(-0.0866637\pi\) | |||||||
\(102\) | −206.633 | + | 357.900i | −0.200586 | + | 0.347425i | ||||
\(103\) | 322.695 | + | 558.923i | 0.308699 | + | 0.534683i | 0.978078 | − | 0.208238i | \(-0.0667730\pi\) |
−0.669379 | + | 0.742921i | \(0.733440\pi\) | |||||||
\(104\) | −262.595 | −0.247592 | ||||||||
\(105\) | −38.8167 | − | 275.079i | −0.0360774 | − | 0.255666i | ||||
\(106\) | −107.511 | −0.0985134 | ||||||||
\(107\) | 262.477 | + | 454.623i | 0.237146 | + | 0.410749i | 0.959894 | − | 0.280363i | \(-0.0904548\pi\) |
−0.722748 | + | 0.691111i | \(0.757121\pi\) | |||||||
\(108\) | 54.0000 | − | 93.5307i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 528.256 | − | 914.966i | 0.464199 | − | 0.804017i | −0.534966 | − | 0.844874i | \(-0.679676\pi\) |
0.999165 | + | 0.0408571i | \(0.0130088\pi\) | |||||||
\(110\) | 39.1222 | + | 67.7616i | 0.0339105 | + | 0.0587347i | ||||
\(111\) | 727.740 | 0.622289 | ||||||||
\(112\) | −233.405 | + | 182.566i | −0.196917 | + | 0.154026i | ||||
\(113\) | 252.809 | 0.210463 | 0.105231 | − | 0.994448i | \(-0.466442\pi\) | ||||
0.105231 | + | 0.994448i | \(0.466442\pi\) | |||||||
\(114\) | 137.107 | + | 237.476i | 0.112642 | + | 0.195102i | ||||
\(115\) | 543.950 | − | 942.149i | 0.441075 | − | 0.763964i | ||||
\(116\) | 253.053 | − | 438.301i | 0.202547 | − | 0.350821i | ||||
\(117\) | 147.710 | + | 255.841i | 0.116716 | + | 0.202158i | ||||
\(118\) | −1741.21 | −1.35840 | ||||||||
\(119\) | −1183.02 | − | 477.200i | −0.911318 | − | 0.367603i | ||||
\(120\) | 120.000 | 0.0912871 | ||||||||
\(121\) | 634.889 | + | 1099.66i | 0.477002 | + | 0.826191i | ||||
\(122\) | 464.702 | − | 804.888i | 0.344854 | − | 0.597304i | ||||
\(123\) | −430.477 | + | 745.608i | −0.315567 | + | 0.546579i | ||||
\(124\) | −338.214 | − | 585.803i | −0.244939 | − | 0.424247i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 309.160 | + | 124.708i | 0.218589 | + | 0.0881733i | ||||
\(127\) | 2419.14 | 1.69027 | 0.845135 | − | 0.534552i | \(-0.179520\pi\) | ||||
0.845135 | + | 0.534552i | \(0.179520\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −81.3434 | + | 140.891i | −0.0555185 | + | 0.0961609i | ||||
\(130\) | −164.122 | + | 284.268i | −0.110727 | + | 0.191784i | ||||
\(131\) | 825.282 | + | 1429.43i | 0.550422 | + | 0.953358i | 0.998244 | + | 0.0592359i | \(0.0188664\pi\) |
−0.447822 | + | 0.894123i | \(0.647800\pi\) | |||||||
\(132\) | −93.8932 | −0.0619118 | ||||||||
\(133\) | −666.695 | + | 521.480i | −0.434660 | + | 0.339985i | ||||
\(134\) | −421.435 | −0.271690 | ||||||||
\(135\) | −67.5000 | − | 116.913i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 275.511 | − | 477.200i | 0.173712 | − | 0.300879i | ||||
\(137\) | 885.950 | − | 1534.51i | 0.552495 | − | 0.956950i | −0.445599 | − | 0.895233i | \(-0.647009\pi\) |
0.998094 | − | 0.0617168i | \(-0.0196575\pi\) | |||||||
\(138\) | 652.740 | + | 1130.58i | 0.402644 | + | 0.697401i | ||||
\(139\) | −2360.54 | −1.44042 | −0.720211 | − | 0.693755i | \(-0.755955\pi\) | ||||
−0.720211 | + | 0.693755i | \(0.755955\pi\) | |||||||
\(140\) | 51.7556 | + | 366.772i | 0.0312439 | + | 0.221413i | ||||
\(141\) | −680.107 | −0.406208 | ||||||||
\(142\) | −236.389 | − | 409.438i | −0.139700 | − | 0.241967i | ||||
\(143\) | 128.416 | − | 222.424i | 0.0750959 | − | 0.130070i | ||||
\(144\) | −72.0000 | + | 124.708i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −316.317 | − | 547.877i | −0.181163 | − | 0.313784i | ||||
\(146\) | −704.733 | −0.399480 | ||||||||
\(147\) | −247.820 | + | 998.712i | −0.139047 | + | 0.560356i | ||||
\(148\) | −970.320 | −0.538918 | ||||||||
\(149\) | −587.587 | − | 1017.73i | −0.323067 | − | 0.559569i | 0.658052 | − | 0.752972i | \(-0.271381\pi\) |
−0.981119 | + | 0.193404i | \(0.938047\pi\) | |||||||
\(150\) | 75.0000 | − | 129.904i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | 1089.95 | − | 1887.84i | 0.587408 | − | 1.01742i | −0.407163 | − | 0.913356i | \(-0.633482\pi\) |
0.994571 | − | 0.104065i | \(-0.0331849\pi\) | |||||||
\(152\) | −182.809 | − | 316.635i | −0.0975511 | − | 0.168963i | ||||
\(153\) | −619.900 | −0.327555 | ||||||||
\(154\) | −40.4959 | − | 286.978i | −0.0211899 | − | 0.150165i | ||||
\(155\) | −845.534 | −0.438161 | ||||||||
\(156\) | −196.947 | − | 341.122i | −0.101079 | − | 0.175074i | ||||
\(157\) | −1352.34 | + | 2342.31i | −0.687440 | + | 1.19068i | 0.285223 | + | 0.958461i | \(0.407932\pi\) |
−0.972663 | + | 0.232220i | \(0.925401\pi\) | |||||||
\(158\) | −782.725 | + | 1355.72i | −0.394115 | + | 0.682628i | ||||
\(159\) | −80.6335 | − | 139.661i | −0.0402179 | − | 0.0696595i | ||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | −3174.01 | + | 2482.67i | −1.55371 | + | 1.21529i | ||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1300.43 | + | 2252.41i | 0.624891 | + | 1.08234i | 0.988562 | + | 0.150816i | \(0.0481901\pi\) |
−0.363670 | + | 0.931528i | \(0.618477\pi\) | |||||||
\(164\) | 573.969 | − | 994.144i | 0.273289 | − | 0.473351i | ||||
\(165\) | −58.6833 | + | 101.642i | −0.0276878 | + | 0.0479567i | ||||
\(166\) | −956.709 | − | 1657.07i | −0.447320 | − | 0.774780i | ||||
\(167\) | −3581.70 | −1.65964 | −0.829821 | − | 0.558029i | \(-0.811558\pi\) | ||||
−0.829821 | + | 0.558029i | \(0.811558\pi\) | |||||||
\(168\) | −412.214 | − | 166.277i | −0.189303 | − | 0.0763604i | ||||
\(169\) | −1119.56 | −0.509584 | ||||||||
\(170\) | −344.389 | − | 596.499i | −0.155373 | − | 0.269114i | ||||
\(171\) | −205.660 | + | 356.214i | −0.0919721 | + | 0.159300i | ||||
\(172\) | 108.458 | − | 187.855i | 0.0480804 | − | 0.0832778i | ||||
\(173\) | 1273.34 | + | 2205.48i | 0.559595 | + | 0.969247i | 0.997530 | + | 0.0702403i | \(0.0223766\pi\) |
−0.437935 | + | 0.899007i | \(0.644290\pi\) | |||||||
\(174\) | 759.160 | 0.330757 | ||||||||
\(175\) | 429.389 | + | 173.205i | 0.185479 | + | 0.0748176i | ||||
\(176\) | 125.191 | 0.0536172 | ||||||||
\(177\) | −1305.90 | − | 2261.89i | −0.554564 | − | 0.960532i | ||||
\(178\) | −186.038 | + | 322.227i | −0.0783378 | + | 0.135685i | ||||
\(179\) | 1967.11 | − | 3407.13i | 0.821388 | − | 1.42269i | −0.0832607 | − | 0.996528i | \(-0.526533\pi\) |
0.904649 | − | 0.426158i | \(-0.140133\pi\) | |||||||
\(180\) | 90.0000 | + | 155.885i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −2931.18 | −1.20372 | −0.601859 | − | 0.798602i | \(-0.705573\pi\) | ||||
−0.601859 | + | 0.798602i | \(0.705573\pi\) | |||||||
\(182\) | 957.671 | − | 749.078i | 0.390040 | − | 0.305084i | ||||
\(183\) | 1394.11 | 0.563144 | ||||||||
\(184\) | −870.320 | − | 1507.44i | −0.348700 | − | 0.603967i | ||||
\(185\) | −606.450 | + | 1050.40i | −0.241011 | + | 0.417444i | ||||
\(186\) | 507.320 | − | 878.705i | 0.199992 | − | 0.346396i | ||||
\(187\) | 269.465 | + | 466.727i | 0.105376 | + | 0.182516i | ||||
\(188\) | 906.809 | 0.351786 | ||||||||
\(189\) | 69.8701 | + | 495.142i | 0.0268905 | + | 0.190562i | ||||
\(190\) | −457.023 | −0.174505 | ||||||||
\(191\) | 1722.16 | + | 2982.87i | 0.652414 | + | 1.13001i | 0.982535 | + | 0.186076i | \(0.0595771\pi\) |
−0.330121 | + | 0.943939i | \(0.607090\pi\) | |||||||
\(192\) | 96.0000 | − | 166.277i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 912.443 | − | 1580.40i | 0.340306 | − | 0.589428i | −0.644183 | − | 0.764871i | \(-0.722803\pi\) |
0.984489 | + | 0.175444i | \(0.0561360\pi\) | |||||||
\(194\) | −10.1068 | − | 17.5054i | −0.00374033 | − | 0.00647844i | ||||
\(195\) | −492.367 | −0.180816 | ||||||||
\(196\) | 330.427 | − | 1331.62i | 0.120418 | − | 0.485283i | ||||
\(197\) | −1760.47 | −0.636690 | −0.318345 | − | 0.947975i | \(-0.603127\pi\) | ||||
−0.318345 | + | 0.947975i | \(0.603127\pi\) | |||||||
\(198\) | −70.4199 | − | 121.971i | −0.0252754 | − | 0.0437782i | ||||
\(199\) | −841.733 | + | 1457.92i | −0.299844 | + | 0.519344i | −0.976100 | − | 0.217322i | \(-0.930268\pi\) |
0.676256 | + | 0.736666i | \(0.263601\pi\) | |||||||
\(200\) | −100.000 | + | 173.205i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −316.077 | − | 547.461i | −0.110917 | − | 0.192114i | ||||
\(202\) | −2900.84 | −1.01041 | ||||||||
\(203\) | 327.423 | + | 2320.32i | 0.113205 | + | 0.802239i | ||||
\(204\) | 826.534 | 0.283671 | ||||||||
\(205\) | −717.461 | − | 1242.68i | −0.244437 | − | 0.423378i | ||||
\(206\) | 645.389 | − | 1117.85i | 0.218283 | − | 0.378078i | ||||
\(207\) | −979.110 | + | 1695.87i | −0.328758 | + | 0.569425i | ||||
\(208\) | 262.595 | + | 454.829i | 0.0875371 | + | 0.151619i | ||||
\(209\) | 357.594 | 0.118351 | ||||||||
\(210\) | −437.633 | + | 342.311i | −0.143808 | + | 0.112484i | ||||
\(211\) | 5897.72 | 1.92425 | 0.962124 | − | 0.272614i | \(-0.0878882\pi\) | ||||
0.962124 | + | 0.272614i | \(0.0878882\pi\) | |||||||
\(212\) | 107.511 | + | 186.215i | 0.0348297 | + | 0.0603269i | ||||
\(213\) | 354.584 | − | 614.157i | 0.114064 | − | 0.197565i | ||||
\(214\) | 524.954 | − | 909.247i | 0.167687 | − | 0.290443i | ||||
\(215\) | −135.572 | − | 234.818i | −0.0430045 | − | 0.0744859i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 2904.50 | + | 1171.61i | 0.908620 | + | 0.366515i | ||||
\(218\) | −2113.02 | −0.656477 | ||||||||
\(219\) | −528.550 | − | 915.475i | −0.163087 | − | 0.282475i | ||||
\(220\) | 78.2444 | − | 135.523i | 0.0239783 | − | 0.0415317i | ||||
\(221\) | −1130.44 | + | 1957.98i | −0.344079 | + | 0.595962i | ||||
\(222\) | −727.740 | − | 1260.48i | −0.220012 | − | 0.381072i | ||||
\(223\) | −78.3677 | −0.0235331 | −0.0117666 | − | 0.999931i | \(-0.503745\pi\) | ||||
−0.0117666 | + | 0.999931i | \(0.503745\pi\) | |||||||
\(224\) | 549.618 | + | 221.703i | 0.163942 | + | 0.0661300i | ||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −252.809 | − | 437.878i | −0.0744098 | − | 0.128881i | ||||
\(227\) | −387.714 | + | 671.541i | −0.113363 | + | 0.196351i | −0.917124 | − | 0.398601i | \(-0.869496\pi\) |
0.803761 | + | 0.594952i | \(0.202829\pi\) | |||||||
\(228\) | 274.214 | − | 474.952i | 0.0796502 | − | 0.137958i | ||||
\(229\) | −583.110 | − | 1009.98i | −0.168266 | − | 0.291446i | 0.769544 | − | 0.638594i | \(-0.220484\pi\) |
−0.937810 | + | 0.347148i | \(0.887150\pi\) | |||||||
\(230\) | −2175.80 | −0.623774 | ||||||||
\(231\) | 342.423 | − | 267.839i | 0.0975317 | − | 0.0762880i | ||||
\(232\) | −1012.21 | −0.286444 | ||||||||
\(233\) | −704.153 | − | 1219.63i | −0.197985 | − | 0.342921i | 0.749890 | − | 0.661563i | \(-0.230107\pi\) |
−0.947875 | + | 0.318642i | \(0.896773\pi\) | |||||||
\(234\) | 295.420 | − | 511.682i | 0.0825308 | − | 0.142948i | ||||
\(235\) | 566.756 | − | 981.650i | 0.157324 | − | 0.272493i | ||||
\(236\) | 1741.21 | + | 3015.86i | 0.480266 | + | 0.831845i | ||||
\(237\) | −2348.17 | −0.643588 | ||||||||
\(238\) | 356.482 | + | 2526.24i | 0.0970894 | + | 0.688033i | ||||
\(239\) | 4474.37 | 1.21097 | 0.605487 | − | 0.795855i | \(-0.292978\pi\) | ||||
0.605487 | + | 0.795855i | \(0.292978\pi\) | |||||||
\(240\) | −120.000 | − | 207.846i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | −1485.23 | + | 2572.49i | −0.396979 | + | 0.687588i | −0.993352 | − | 0.115120i | \(-0.963275\pi\) |
0.596372 | + | 0.802708i | \(0.296608\pi\) | |||||||
\(242\) | 1269.78 | − | 2199.32i | 0.337291 | − | 0.584205i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −1858.81 | −0.487697 | ||||||||
\(245\) | −1235.00 | − | 1189.96i | −0.322046 | − | 0.310301i | ||||
\(246\) | 1721.91 | 0.446280 | ||||||||
\(247\) | 750.075 | + | 1299.17i | 0.193223 | + | 0.334673i | ||||
\(248\) | −676.427 | + | 1171.61i | −0.173198 | + | 0.299988i | ||||
\(249\) | 1435.06 | − | 2485.60i | 0.365235 | − | 0.632605i | ||||
\(250\) | 125.000 | + | 216.506i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −4254.34 | −1.06985 | −0.534924 | − | 0.844900i | \(-0.679660\pi\) | ||||
−0.534924 | + | 0.844900i | \(0.679660\pi\) | |||||||
\(252\) | −93.1602 | − | 660.189i | −0.0232878 | − | 0.165032i | ||||
\(253\) | 1702.44 | 0.423050 | ||||||||
\(254\) | −2419.14 | − | 4190.08i | −0.597601 | − | 1.03508i | ||||
\(255\) | 516.584 | − | 894.749i | 0.126862 | − | 0.219731i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1326.58 | − | 2297.70i | −0.321982 | − | 0.557690i | 0.658915 | − | 0.752218i | \(-0.271016\pi\) |
−0.980897 | + | 0.194528i | \(0.937683\pi\) | |||||||
\(258\) | 325.374 | 0.0785150 | ||||||||
\(259\) | 3538.71 | − | 2767.93i | 0.848975 | − | 0.664057i | ||||
\(260\) | 656.489 | 0.156591 | ||||||||
\(261\) | 569.370 | + | 986.178i | 0.135031 | + | 0.233881i | ||||
\(262\) | 1650.56 | − | 2858.86i | 0.389207 | − | 0.674126i | ||||
\(263\) | 3298.82 | − | 5713.72i | 0.773436 | − | 1.33963i | −0.162233 | − | 0.986752i | \(-0.551870\pi\) |
0.935669 | − | 0.352878i | \(-0.114797\pi\) | |||||||
\(264\) | 93.8932 | + | 162.628i | 0.0218891 | + | 0.0379131i | ||||
\(265\) | 268.778 | 0.0623053 | ||||||||
\(266\) | 1569.92 | + | 633.269i | 0.361873 | + | 0.145971i | ||||
\(267\) | −558.114 | −0.127925 | ||||||||
\(268\) | 421.435 | + | 729.947i | 0.0960569 | + | 0.166376i | ||||
\(269\) | −2331.85 | + | 4038.88i | −0.528532 | + | 0.915445i | 0.470914 | + | 0.882179i | \(0.343924\pi\) |
−0.999447 | + | 0.0332659i | \(0.989409\pi\) | |||||||
\(270\) | −135.000 | + | 233.827i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −451.337 | − | 781.738i | −0.101169 | − | 0.175230i | 0.810998 | − | 0.585049i | \(-0.198925\pi\) |
−0.912166 | + | 0.409820i | \(0.865592\pi\) | |||||||
\(272\) | −1102.05 | −0.245667 | ||||||||
\(273\) | 1691.33 | + | 682.243i | 0.374961 | + | 0.151250i | ||||
\(274\) | −3543.80 | −0.781346 | ||||||||
\(275\) | −97.8054 | − | 169.404i | −0.0214469 | − | 0.0371471i | ||||
\(276\) | 1305.48 | − | 2261.16i | 0.284713 | − | 0.493137i | ||||
\(277\) | −322.588 | + | 558.738i | −0.0699726 | + | 0.121196i | −0.898889 | − | 0.438176i | \(-0.855625\pi\) |
0.828916 | + | 0.559373i | \(0.188958\pi\) | |||||||
\(278\) | 2360.54 | + | 4088.58i | 0.509266 | + | 0.882074i | ||||
\(279\) | 1521.96 | 0.326586 | ||||||||
\(280\) | 583.511 | − | 456.415i | 0.124541 | − | 0.0974143i | ||||
\(281\) | −4459.75 | −0.946785 | −0.473392 | − | 0.880852i | \(-0.656971\pi\) | ||||
−0.473392 | + | 0.880852i | \(0.656971\pi\) | |||||||
\(282\) | 680.107 | + | 1177.98i | 0.143616 | + | 0.248751i | ||||
\(283\) | 2755.61 | − | 4772.86i | 0.578813 | − | 1.00253i | −0.416803 | − | 0.908997i | \(-0.636850\pi\) |
0.995616 | − | 0.0935364i | \(-0.0298172\pi\) | |||||||
\(284\) | −472.778 | + | 818.876i | −0.0987825 | + | 0.171096i | ||||
\(285\) | −342.767 | − | 593.690i | −0.0712413 | − | 0.123393i | ||||
\(286\) | −513.665 | −0.106202 | ||||||||
\(287\) | 742.654 | + | 5262.89i | 0.152744 | + | 1.08243i | ||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 84.4229 | + | 146.225i | 0.0171836 | + | 0.0297628i | ||||
\(290\) | −632.633 | + | 1095.75i | −0.128102 | + | 0.221879i | ||||
\(291\) | 15.1602 | − | 26.2582i | 0.00305397 | − | 0.00528962i | ||||
\(292\) | 704.733 | + | 1220.63i | 0.141238 | + | 0.244631i | ||||
\(293\) | 2837.19 | 0.565701 | 0.282851 | − | 0.959164i | \(-0.408720\pi\) | ||||
0.282851 | + | 0.959164i | \(0.408720\pi\) | |||||||
\(294\) | 1977.64 | − | 569.475i | 0.392307 | − | 0.112968i | ||||
\(295\) | 4353.01 | 0.859126 | ||||||||
\(296\) | 970.320 | + | 1680.64i | 0.190536 | + | 0.330018i | ||||
\(297\) | 105.630 | − | 182.956i | 0.0206373 | − | 0.0357448i | ||||
\(298\) | −1175.17 | + | 2035.46i | −0.228443 | + | 0.395675i | ||||
\(299\) | 3570.97 | + | 6185.10i | 0.690684 | + | 1.19630i | ||||
\(300\) | −300.000 | −0.0577350 | ||||||||
\(301\) | 140.333 | + | 994.482i | 0.0268726 | + | 0.190435i | ||||
\(302\) | −4359.79 | −0.830720 | ||||||||
\(303\) | −2175.63 | − | 3768.30i | −0.412497 | − | 0.714466i | ||||
\(304\) | −365.618 | + | 633.269i | −0.0689791 | + | 0.119475i | ||||
\(305\) | −1161.76 | + | 2012.22i | −0.218105 | + | 0.377768i | ||||
\(306\) | 619.900 | + | 1073.70i | 0.115808 | + | 0.200586i | ||||
\(307\) | 7929.20 | 1.47408 | 0.737041 | − | 0.675848i | \(-0.236222\pi\) | ||||
0.737041 | + | 0.675848i | \(0.236222\pi\) | |||||||
\(308\) | −456.565 | + | 357.119i | −0.0844649 | + | 0.0660673i | ||||
\(309\) | 1936.17 | 0.356455 | ||||||||
\(310\) | 845.534 | + | 1464.51i | 0.154913 | + | 0.268318i | ||||
\(311\) | −4140.93 | + | 7172.29i | −0.755017 | + | 1.30773i | 0.190349 | + | 0.981717i | \(0.439038\pi\) |
−0.945366 | + | 0.326012i | \(0.894295\pi\) | |||||||
\(312\) | −393.893 | + | 682.243i | −0.0714738 | + | 0.123796i | ||||
\(313\) | −342.703 | − | 593.579i | −0.0618872 | − | 0.107192i | 0.833422 | − | 0.552638i | \(-0.186379\pi\) |
−0.895309 | + | 0.445446i | \(0.853045\pi\) | |||||||
\(314\) | 5409.34 | 0.972188 | ||||||||
\(315\) | −772.900 | − | 311.769i | −0.138248 | − | 0.0557657i | ||||
\(316\) | 3130.90 | 0.557363 | ||||||||
\(317\) | −2896.87 | − | 5017.53i | −0.513264 | − | 0.888999i | −0.999882 | − | 0.0153840i | \(-0.995103\pi\) |
0.486618 | − | 0.873615i | \(-0.338230\pi\) | |||||||
\(318\) | −161.267 | + | 279.323i | −0.0284384 | + | 0.0492567i | ||||
\(319\) | 495.000 | − | 857.365i | 0.0868799 | − | 0.150480i | ||||
\(320\) | 160.000 | + | 277.128i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 1574.86 | 0.273832 | ||||||||
\(322\) | 7474.12 | + | 3014.88i | 1.29353 | + | 0.521778i | ||||
\(323\) | −3147.87 | −0.542267 | ||||||||
\(324\) | −162.000 | − | 280.592i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 410.305 | − | 710.670i | 0.0700297 | − | 0.121295i | ||||
\(326\) | 2600.85 | − | 4504.81i | 0.441865 | − | 0.765333i | ||||
\(327\) | −1584.77 | − | 2744.90i | −0.268006 | − | 0.464199i | ||||
\(328\) | −2295.88 | −0.386490 | ||||||||
\(329\) | −3307.08 | + | 2586.76i | −0.554181 | + | 0.433473i | ||||
\(330\) | 234.733 | 0.0391565 | ||||||||
\(331\) | 780.150 | + | 1351.26i | 0.129550 | + | 0.224387i | 0.923502 | − | 0.383593i | \(-0.125314\pi\) |
−0.793953 | + | 0.607980i | \(0.791980\pi\) | |||||||
\(332\) | −1913.42 | + | 3314.14i | −0.316303 | + | 0.547852i | ||||
\(333\) | 1091.61 | − | 1890.72i | 0.179639 | − | 0.311144i | ||||
\(334\) | 3581.70 | + | 6203.69i | 0.586772 | + | 1.01632i | ||||
\(335\) | 1053.59 | 0.171832 | ||||||||
\(336\) | 124.214 | + | 880.252i | 0.0201679 | + | 0.142922i | ||||
\(337\) | 1543.88 | 0.249556 | 0.124778 | − | 0.992185i | \(-0.460178\pi\) | ||||
0.124778 | + | 0.992185i | \(0.460178\pi\) | |||||||
\(338\) | 1119.56 | + | 1939.13i | 0.180165 | + | 0.312055i | ||||
\(339\) | 379.214 | − | 656.817i | 0.0607553 | − | 0.105231i | ||||
\(340\) | −688.778 | + | 1193.00i | −0.109865 | + | 0.190292i | ||||
\(341\) | −661.583 | − | 1145.89i | −0.105064 | − | 0.181976i | ||||
\(342\) | 822.641 | 0.130068 | ||||||||
\(343\) | 2593.51 | + | 5798.91i | 0.408269 | + | 0.912862i | ||||
\(344\) | −433.832 | −0.0679960 | ||||||||
\(345\) | −1631.85 | − | 2826.45i | −0.254655 | − | 0.441075i | ||||
\(346\) | 2546.67 | − | 4410.96i | 0.395693 | − | 0.685361i | ||||
\(347\) | 239.604 | − | 415.006i | 0.0370680 | − | 0.0642037i | −0.846896 | − | 0.531758i | \(-0.821532\pi\) |
0.883964 | + | 0.467555i | \(0.154865\pi\) | |||||||
\(348\) | −759.160 | − | 1314.90i | −0.116940 | − | 0.202547i | ||||
\(349\) | −9446.15 | −1.44883 | −0.724414 | − | 0.689366i | \(-0.757889\pi\) | ||||
−0.724414 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(350\) | −129.389 | − | 916.929i | −0.0197604 | − | 0.140034i | ||||
\(351\) | 886.260 | 0.134772 | ||||||||
\(352\) | −125.191 | − | 216.837i | −0.0189565 | − | 0.0328337i | ||||
\(353\) | 3447.72 | − | 5971.62i | 0.519840 | − | 0.900390i | −0.479894 | − | 0.877327i | \(-0.659325\pi\) |
0.999734 | − | 0.0230630i | \(-0.00734183\pi\) | |||||||
\(354\) | −2611.81 | + | 4523.78i | −0.392136 | + | 0.679199i | ||||
\(355\) | 590.973 | + | 1023.59i | 0.0883537 | + | 0.153033i | ||||
\(356\) | 744.152 | 0.110786 | ||||||||
\(357\) | −3014.32 | + | 2357.76i | −0.446877 | + | 0.349541i | ||||
\(358\) | −7868.43 | −1.16162 | ||||||||
\(359\) | 1414.83 | + | 2450.55i | 0.207999 | + | 0.360265i | 0.951084 | − | 0.308932i | \(-0.0999715\pi\) |
−0.743085 | + | 0.669197i | \(0.766638\pi\) | |||||||
\(360\) | 180.000 | − | 311.769i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 2385.15 | − | 4131.20i | 0.347740 | − | 0.602304i | ||||
\(362\) | 2931.18 | + | 5076.96i | 0.425579 | + | 0.737124i | ||||
\(363\) | 3809.33 | 0.550794 | ||||||||
\(364\) | −2255.11 | − | 909.657i | −0.324725 | − | 0.130986i | ||||
\(365\) | 1761.83 | 0.252654 | ||||||||
\(366\) | −1394.11 | − | 2414.66i | −0.199101 | − | 0.344854i | ||||
\(367\) | 117.848 | − | 204.118i | 0.0167618 | − | 0.0290323i | −0.857523 | − | 0.514446i | \(-0.827998\pi\) |
0.874285 | + | 0.485414i | \(0.161331\pi\) | |||||||
\(368\) | −1740.64 | + | 3014.88i | −0.246568 | + | 0.427069i | ||||
\(369\) | 1291.43 | + | 2236.82i | 0.182193 | + | 0.315567i | ||||
\(370\) | 2425.80 | 0.340842 | ||||||||
\(371\) | −923.283 | − | 372.430i | −0.129203 | − | 0.0521175i | ||||
\(372\) | −2029.28 | −0.282832 | ||||||||
\(373\) | −5935.43 | − | 10280.5i | −0.823928 | − | 1.42708i | −0.902736 | − | 0.430195i | \(-0.858445\pi\) |
0.0788083 | − | 0.996890i | \(-0.474889\pi\) | |||||||
\(374\) | 538.930 | − | 933.454i | 0.0745118 | − | 0.129058i | ||||
\(375\) | −187.500 | + | 324.760i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −906.809 | − | 1570.64i | −0.124375 | − | 0.215424i | ||||
\(377\) | 4153.17 | 0.567371 | ||||||||
\(378\) | 787.740 | − | 616.160i | 0.107188 | − | 0.0838409i | ||||
\(379\) | 2277.70 | 0.308701 | 0.154351 | − | 0.988016i | \(-0.450671\pi\) | ||||
0.154351 | + | 0.988016i | \(0.450671\pi\) | |||||||
\(380\) | 457.023 | + | 791.586i | 0.0616967 | + | 0.106862i | ||||
\(381\) | 3628.72 | − | 6285.12i | 0.487939 | − | 0.845135i | ||||
\(382\) | 3444.32 | − | 5965.74i | 0.461327 | − | 0.799041i | ||||
\(383\) | −2029.07 | − | 3514.46i | −0.270707 | − | 0.468879i | 0.698336 | − | 0.715770i | \(-0.253924\pi\) |
−0.969043 | + | 0.246891i | \(0.920591\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 101.240 | + | 717.445i | 0.0134017 | + | 0.0949724i | ||||
\(386\) | −3649.77 | −0.481266 | ||||||||
\(387\) | 244.030 | + | 422.673i | 0.0320536 | + | 0.0555185i | ||||
\(388\) | −20.2135 | + | 35.0109i | −0.00264481 | + | 0.00458095i | ||||
\(389\) | 1701.16 | − | 2946.49i | 0.221728 | − | 0.384044i | −0.733605 | − | 0.679576i | \(-0.762164\pi\) |
0.955333 | + | 0.295532i | \(0.0954970\pi\) | |||||||
\(390\) | 492.367 | + | 852.804i | 0.0639281 | + | 0.110727i | ||||
\(391\) | −14986.4 | −1.93836 | ||||||||
\(392\) | −2636.85 | + | 759.300i | −0.339748 | + | 0.0978327i | ||||
\(393\) | 4951.69 | 0.635572 | ||||||||
\(394\) | 1760.47 | + | 3049.21i | 0.225104 | + | 0.389891i | ||||
\(395\) | 1956.81 | − | 3389.30i | 0.249261 | − | 0.431732i | ||||
\(396\) | −140.840 | + | 243.942i | −0.0178724 | + | 0.0309559i | ||||
\(397\) | −2600.77 | − | 4504.67i | −0.328788 | − | 0.569478i | 0.653483 | − | 0.756941i | \(-0.273307\pi\) |
−0.982272 | + | 0.187463i | \(0.939974\pi\) | |||||||
\(398\) | 3366.93 | 0.424043 | ||||||||
\(399\) | 354.802 | + | 2514.34i | 0.0445171 | + | 0.315475i | ||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 426.130 | + | 738.080i | 0.0530672 | + | 0.0919151i | 0.891339 | − | 0.453338i | \(-0.149767\pi\) |
−0.838272 | + | 0.545253i | \(0.816434\pi\) | |||||||
\(402\) | −632.153 | + | 1094.92i | −0.0784302 | + | 0.135845i | ||||
\(403\) | 2775.42 | − | 4807.16i | 0.343060 | − | 0.594198i | ||||
\(404\) | 2900.84 | + | 5024.40i | 0.357233 | + | 0.618746i | ||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 3691.49 | − | 2887.43i | 0.451245 | − | 0.352958i | ||||
\(407\) | −1898.05 | −0.231162 | ||||||||
\(408\) | −826.534 | − | 1431.60i | −0.100293 | − | 0.173712i | ||||
\(409\) | −7347.38 | + | 12726.0i | −0.888276 | + | 1.53854i | −0.0463634 | + | 0.998925i | \(0.514763\pi\) |
−0.841912 | + | 0.539614i | \(0.818570\pi\) | |||||||
\(410\) | −1434.92 | + | 2485.36i | −0.172843 | + | 0.299374i | ||||
\(411\) | −2657.85 | − | 4603.53i | −0.318983 | − | 0.552495i | ||||
\(412\) | −2581.56 | −0.308699 | ||||||||
\(413\) | −14953.1 | − | 6031.71i | −1.78158 | − | 0.718647i | ||||
\(414\) | 3916.44 | 0.464934 | ||||||||
\(415\) | 2391.77 | + | 4142.67i | 0.282910 | + | 0.490014i | ||||
\(416\) | 525.191 | − | 909.657i | 0.0618981 | − | 0.107211i | ||||
\(417\) | −3540.81 | + | 6132.87i | −0.415814 | + | 0.720211i | ||||
\(418\) | −357.594 | − | 619.372i | −0.0418433 | − | 0.0724748i | ||||
\(419\) | 283.053 | 0.0330025 | 0.0165013 | − | 0.999864i | \(-0.494747\pi\) | ||||
0.0165013 | + | 0.999864i | \(0.494747\pi\) | |||||||
\(420\) | 1030.53 | + | 415.692i | 0.119726 | + | 0.0482945i | ||||
\(421\) | −10854.3 | −1.25655 | −0.628274 | − | 0.777992i | \(-0.716238\pi\) | ||||
−0.628274 | + | 0.777992i | \(0.716238\pi\) | |||||||
\(422\) | −5897.72 | − | 10215.2i | −0.680324 | − | 1.17836i | ||||
\(423\) | −1020.16 | + | 1766.97i | −0.117262 | + | 0.203104i | ||||
\(424\) | 215.023 | − | 372.430i | 0.0246283 | − | 0.0426575i | ||||
\(425\) | 860.973 | + | 1491.25i | 0.0982666 | + | 0.170203i | ||||
\(426\) | −1418.33 | −0.161311 | ||||||||
\(427\) | 6778.98 | − | 5302.43i | 0.768285 | − | 0.600942i | ||||
\(428\) | −2099.82 | −0.237146 | ||||||||
\(429\) | −385.249 | − | 667.271i | −0.0433566 | − | 0.0750959i | ||||
\(430\) | −271.145 | + | 469.636i | −0.0304087 | + | 0.0526695i | ||||
\(431\) | 3652.17 | − | 6325.74i | 0.408164 | − | 0.706961i | −0.586520 | − | 0.809935i | \(-0.699502\pi\) |
0.994684 | + | 0.102974i | \(0.0328358\pi\) | |||||||
\(432\) | 216.000 | + | 374.123i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 2406.12 | 0.267046 | 0.133523 | − | 0.991046i | \(-0.457371\pi\) | ||||
0.133523 | + | 0.991046i | \(0.457371\pi\) | |||||||
\(434\) | −875.223 | − | 6202.35i | −0.0968019 | − | 0.685997i | ||||
\(435\) | −1897.90 | −0.209189 | ||||||||
\(436\) | 2113.02 | + | 3659.86i | 0.232100 | + | 0.402008i | ||||
\(437\) | −4971.95 | + | 8611.67i | −0.544258 | + | 0.942682i | ||||
\(438\) | −1057.10 | + | 1830.95i | −0.115320 | + | 0.199740i | ||||
\(439\) | −6550.07 | − | 11345.1i | −0.712114 | − | 1.23342i | −0.964062 | − | 0.265676i | \(-0.914405\pi\) |
0.251949 | − | 0.967741i | \(-0.418929\pi\) | |||||||
\(440\) | −312.977 | −0.0339105 | ||||||||
\(441\) | 2223.00 | + | 2141.92i | 0.240039 | + | 0.231284i | ||||
\(442\) | 4521.75 | 0.486601 | ||||||||
\(443\) | −4860.10 | − | 8417.94i | −0.521242 | − | 0.902818i | −0.999695 | − | 0.0247043i | \(-0.992136\pi\) |
0.478453 | − | 0.878113i | \(-0.341198\pi\) | |||||||
\(444\) | −1455.48 | + | 2520.97i | −0.155572 | + | 0.269459i | ||||
\(445\) | 465.095 | − | 805.568i | 0.0495452 | − | 0.0858148i | ||||
\(446\) | 78.3677 | + | 135.737i | 0.00832021 | + | 0.0144110i | ||||
\(447\) | −3525.52 | −0.373046 | ||||||||
\(448\) | −165.618 | − | 1173.67i | −0.0174659 | − | 0.123774i | ||||
\(449\) | 11339.0 | 1.19181 | 0.595905 | − | 0.803055i | \(-0.296794\pi\) | ||||
0.595905 | + | 0.803055i | \(0.296794\pi\) | |||||||
\(450\) | −225.000 | − | 389.711i | −0.0235702 | − | 0.0408248i | ||||
\(451\) | 1122.75 | − | 1944.65i | 0.117224 | − | 0.203038i | ||||
\(452\) | −505.618 | + | 875.756i | −0.0526156 | + | 0.0911330i | ||||
\(453\) | −3269.84 | − | 5663.53i | −0.339140 | − | 0.587408i | ||||
\(454\) | 1550.86 | 0.160320 | ||||||||
\(455\) | −2394.18 | + | 1872.70i | −0.246683 | + | 0.192952i | ||||
\(456\) | −1096.85 | −0.112642 | ||||||||
\(457\) | 2893.24 | + | 5011.23i | 0.296148 | + | 0.512944i | 0.975251 | − | 0.221099i | \(-0.0709643\pi\) |
−0.679103 | + | 0.734043i | \(0.737631\pi\) | |||||||
\(458\) | −1166.22 | + | 2019.95i | −0.118982 | + | 0.206083i | ||||
\(459\) | −929.851 | + | 1610.55i | −0.0945571 | + | 0.163778i | ||||
\(460\) | 2175.80 | + | 3768.60i | 0.220537 | + | 0.381982i | ||||
\(461\) | 9403.13 | 0.949995 | 0.474997 | − | 0.879987i | \(-0.342449\pi\) | ||||
0.474997 | + | 0.879987i | \(0.342449\pi\) | |||||||
\(462\) | −806.335 | − | 325.256i | −0.0811993 | − | 0.0327538i | ||||
\(463\) | −13355.7 | −1.34059 | −0.670295 | − | 0.742094i | \(-0.733833\pi\) | ||||
−0.670295 | + | 0.742094i | \(0.733833\pi\) | |||||||
\(464\) | 1012.21 | + | 1753.21i | 0.101273 | + | 0.175411i | ||||
\(465\) | −1268.30 | + | 2196.76i | −0.126486 | + | 0.219080i | ||||
\(466\) | −1408.31 | + | 2439.26i | −0.139997 | + | 0.242482i | ||||
\(467\) | −2867.44 | − | 4966.56i | −0.284132 | − | 0.492130i | 0.688267 | − | 0.725458i | \(-0.258372\pi\) |
−0.972398 | + | 0.233327i | \(0.925039\pi\) | |||||||
\(468\) | −1181.68 | −0.116716 | ||||||||
\(469\) | −3619.19 | − | 1459.89i | −0.356330 | − | 0.143735i | ||||
\(470\) | −2267.02 | −0.222489 | ||||||||
\(471\) | 4057.01 | + | 7026.94i | 0.396894 | + | 0.687440i | ||||
\(472\) | 3482.41 | − | 6031.71i | 0.339599 | − | 0.588203i | ||||
\(473\) | 212.155 | − | 367.464i | 0.0206235 | − | 0.0357210i | ||||
\(474\) | 2348.17 | + | 4067.16i | 0.227543 | + | 0.394115i | ||||
\(475\) | 1142.56 | 0.110366 | ||||||||
\(476\) | 4019.10 | − | 3143.69i | 0.387006 | − | 0.302711i | ||||
\(477\) | −483.801 | −0.0464397 | ||||||||
\(478\) | −4474.37 | − | 7749.83i | −0.428144 | − | 0.741567i | ||||
\(479\) | −7321.19 | + | 12680.7i | −0.698358 | + | 1.20959i | 0.270677 | + | 0.962670i | \(0.412752\pi\) |
−0.969035 | + | 0.246922i | \(0.920581\pi\) | |||||||
\(480\) | −240.000 | + | 415.692i | −0.0228218 | + | 0.0395285i | ||||
\(481\) | −3981.28 | − | 6895.77i | −0.377403 | − | 0.653680i | ||||
\(482\) | 5940.92 | 0.561413 | ||||||||
\(483\) | 1689.15 | + | 11970.3i | 0.159128 | + | 1.12768i | ||||
\(484\) | −5079.11 | −0.477002 | ||||||||
\(485\) | 25.2669 | + | 43.7636i | 0.00236559 | + | 0.00409732i | ||||
\(486\) | 243.000 | − | 420.888i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −2836.53 | + | 4913.01i | −0.263933 | + | 0.457145i | −0.967283 | − | 0.253698i | \(-0.918353\pi\) |
0.703351 | + | 0.710843i | \(0.251686\pi\) | |||||||
\(488\) | 1858.81 | + | 3219.55i | 0.172427 | + | 0.298652i | ||||
\(489\) | 7802.56 | 0.721563 | ||||||||
\(490\) | −826.068 | + | 3329.04i | −0.0761590 | + | 0.306920i | ||||
\(491\) | −7355.77 | −0.676092 | −0.338046 | − | 0.941130i | \(-0.609766\pi\) | ||||
−0.338046 | + | 0.941130i | \(0.609766\pi\) | |||||||
\(492\) | −1721.91 | − | 2982.43i | −0.157784 | − | 0.273289i | ||||
\(493\) | −4357.44 | + | 7547.31i | −0.398072 | + | 0.689480i | ||||
\(494\) | 1500.15 | − | 2598.34i | 0.136630 | − | 0.236649i | ||||
\(495\) | 176.050 | + | 304.927i | 0.0159856 | + | 0.0276878i | ||||
\(496\) | 2705.71 | 0.244939 | ||||||||
\(497\) | −611.723 | − | 4335.04i | −0.0552104 | − | 0.391254i | ||||
\(498\) | −5740.26 | −0.516520 | ||||||||
\(499\) | −10223.6 | − | 17707.8i | −0.917177 | − | 1.58860i | −0.803682 | − | 0.595058i | \(-0.797129\pi\) |
−0.113495 | − | 0.993539i | \(-0.536204\pi\) | |||||||
\(500\) | 250.000 | − | 433.013i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −5372.55 | + | 9305.53i | −0.479098 | + | 0.829821i | ||||
\(502\) | 4254.34 | + | 7368.74i | 0.378248 | + | 0.655145i | ||||
\(503\) | 11116.9 | 0.985448 | 0.492724 | − | 0.870186i | \(-0.336001\pi\) | ||||
0.492724 | + | 0.870186i | \(0.336001\pi\) | |||||||
\(504\) | −1050.32 | + | 821.547i | −0.0928274 | + | 0.0726083i | ||||
\(505\) | 7252.10 | 0.639038 | ||||||||
\(506\) | −1702.44 | − | 2948.71i | −0.149571 | − | 0.259064i | ||||
\(507\) | −1679.33 | + | 2908.69i | −0.147104 | + | 0.254792i | ||||
\(508\) | −4838.29 | + | 8380.16i | −0.422568 | + | 0.731909i | ||||
\(509\) | 7854.88 | + | 13605.1i | 0.684011 | + | 1.18474i | 0.973747 | + | 0.227635i | \(0.0730992\pi\) |
−0.289736 | + | 0.957107i | \(0.593567\pi\) | |||||||
\(510\) | −2066.33 | −0.179409 | ||||||||
\(511\) | −6052.09 | − | 2441.27i | −0.523931 | − | 0.211341i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 616.980 | + | 1068.64i | 0.0531001 | + | 0.0919721i | ||||
\(514\) | −2653.15 | + | 4595.39i | −0.227676 | + | 0.394346i | ||||
\(515\) | −1613.47 | + | 2794.62i | −0.138055 | + | 0.239118i | ||||
\(516\) | −325.374 | − | 563.564i | −0.0277593 | − | 0.0480804i | ||||
\(517\) | 1773.82 | 0.150894 | ||||||||
\(518\) | −8332.90 | − | 3361.29i | −0.706808 | − | 0.285109i | ||||
\(519\) | 7640.01 | 0.646165 | ||||||||
\(520\) | −656.489 | − | 1137.07i | −0.0553633 | − | 0.0958921i | ||||
\(521\) | 8097.17 | − | 14024.7i | 0.680889 | − | 1.17933i | −0.293821 | − | 0.955861i | \(-0.594927\pi\) |
0.974710 | − | 0.223474i | \(-0.0717398\pi\) | |||||||
\(522\) | 1138.74 | − | 1972.36i | 0.0954814 | − | 0.165379i | ||||
\(523\) | −8365.97 | − | 14490.3i | −0.699461 | − | 1.21150i | −0.968653 | − | 0.248416i | \(-0.920090\pi\) |
0.269192 | − | 0.963086i | \(-0.413243\pi\) | |||||||
\(524\) | −6602.26 | −0.550422 | ||||||||
\(525\) | 1094.08 | − | 855.778i | 0.0909519 | − | 0.0711414i | ||||
\(526\) | −13195.3 | −1.09380 | ||||||||
\(527\) | 5823.85 | + | 10087.2i | 0.481387 | + | 0.833787i | ||||
\(528\) | 187.786 | − | 325.256i | 0.0154779 | − | 0.0268086i | ||||
\(529\) | −17587.0 | + | 30461.7i | −1.44547 | + | 2.50363i | ||||
\(530\) | −268.778 | − | 465.538i | −0.0220283 | − | 0.0381541i | ||||
\(531\) | −7835.42 | −0.640355 | ||||||||
\(532\) | −473.070 | − | 3352.46i | −0.0385530 | − | 0.273210i | ||||
\(533\) | 9420.11 | 0.765535 | ||||||||
\(534\) | 558.114 | + | 966.682i | 0.0452284 | + | 0.0783378i | ||||
\(535\) | −1312.38 | + | 2273.12i | −0.106055 | + | 0.183692i | ||||
\(536\) | 842.871 | − | 1459.89i | 0.0679225 | − | 0.117645i | ||||
\(537\) | −5901.32 | − | 10221.4i | −0.474229 | − | 0.821388i | ||||
\(538\) | 9327.39 | 0.747458 | ||||||||
\(539\) | 646.351 | − | 2604.79i | 0.0516518 | − | 0.208156i | ||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | 12492.9 | + | 21638.3i | 0.992811 | + | 1.71960i | 0.600065 | + | 0.799951i | \(0.295141\pi\) |
0.392745 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(542\) | −902.674 | + | 1563.48i | −0.0715372 | + | 0.123906i | ||||
\(543\) | −4396.77 | + | 7615.44i | −0.347484 | + | 0.601859i | ||||
\(544\) | 1102.05 | + | 1908.80i | 0.0868562 | + | 0.150439i | ||||
\(545\) | 5282.56 | 0.415192 | ||||||||
\(546\) | −509.655 | − | 3611.72i | −0.0399473 | − | 0.283090i | ||||
\(547\) | 21010.7 | 1.64233 | 0.821164 | − | 0.570692i | \(-0.193325\pi\) | ||||
0.821164 | + | 0.570692i | \(0.193325\pi\) | |||||||
\(548\) | 3543.80 | + | 6138.04i | 0.276248 | + | 0.478475i | ||||
\(549\) | 2091.16 | − | 3622.00i | 0.162566 | − | 0.281572i | ||||
\(550\) | −195.611 | + | 338.808i | −0.0151652 | + | 0.0262669i | ||||
\(551\) | 2891.28 | + | 5007.84i | 0.223544 | + | 0.387189i | ||||
\(552\) | −5221.92 | −0.402644 | ||||||||
\(553\) | −11418.2 | + | 8931.18i | −0.878033 | + | 0.686786i | ||||
\(554\) | 1290.35 | 0.0989563 | ||||||||
\(555\) | 1819.35 | + | 3151.21i | 0.139148 | + | 0.241011i | ||||
\(556\) | 4721.08 | − | 8177.16i | 0.360105 | − | 0.623721i | ||||
\(557\) | 10437.2 | − | 18077.8i | 0.793964 | − | 1.37519i | −0.129530 | − | 0.991575i | \(-0.541347\pi\) |
0.923495 | − | 0.383611i | \(-0.125320\pi\) | |||||||
\(558\) | −1521.96 | − | 2636.11i | −0.115465 | − | 0.199992i | ||||
\(559\) | 1780.03 | 0.134682 | ||||||||
\(560\) | −1374.05 | − | 554.256i | −0.103686 | − | 0.0418243i | ||||
\(561\) | 1616.79 | 0.121677 | ||||||||
\(562\) | 4459.75 | + | 7724.52i | 0.334739 | + | 0.579785i | ||||
\(563\) | 10267.8 | − | 17784.4i | 0.768628 | − | 1.33130i | −0.169678 | − | 0.985499i | \(-0.554273\pi\) |
0.938307 | − | 0.345804i | \(-0.112394\pi\) | |||||||
\(564\) | 1360.21 | − | 2355.96i | 0.101552 | − | 0.175893i | ||||
\(565\) | 632.023 | + | 1094.70i | 0.0470609 | + | 0.0815118i | ||||
\(566\) | −11022.4 | −0.818565 | ||||||||
\(567\) | 1391.22 | + | 561.184i | 0.103044 | + | 0.0415653i | ||||
\(568\) | 1891.11 | 0.139700 | ||||||||
\(569\) | 9924.76 | + | 17190.2i | 0.731226 | + | 1.26652i | 0.956359 | + | 0.292193i | \(0.0943849\pi\) |
−0.225133 | + | 0.974328i | \(0.572282\pi\) | |||||||
\(570\) | −685.534 | + | 1187.38i | −0.0503752 | + | 0.0872524i | ||||
\(571\) | −690.132 | + | 1195.34i | −0.0505799 | + | 0.0876070i | −0.890207 | − | 0.455557i | \(-0.849440\pi\) |
0.839627 | + | 0.543164i | \(0.182774\pi\) | |||||||
\(572\) | 513.665 | + | 889.695i | 0.0375480 | + | 0.0650350i | ||||
\(573\) | 10333.0 | 0.753343 | ||||||||
\(574\) | 8372.94 | − | 6549.20i | 0.608850 | − | 0.476234i | ||||
\(575\) | 5439.50 | 0.394509 | ||||||||
\(576\) | −288.000 | − | 498.831i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 5872.85 | − | 10172.1i | 0.423726 | − | 0.733916i | −0.572574 | − | 0.819853i | \(-0.694055\pi\) |
0.996301 | + | 0.0859373i | \(0.0273885\pi\) | |||||||
\(578\) | 168.846 | − | 292.450i | 0.0121506 | − | 0.0210455i | ||||
\(579\) | −2737.33 | − | 4741.19i | −0.196476 | − | 0.340306i | ||||
\(580\) | 2530.53 | 0.181163 | ||||||||
\(581\) | −2475.76 | − | 17544.7i | −0.176784 | − | 1.25280i | ||||
\(582\) | −60.6406 | −0.00431896 | ||||||||
\(583\) | 210.304 | + | 364.257i | 0.0149398 | + | 0.0258765i | ||||
\(584\) | 1409.47 | − | 2441.27i | 0.0998701 | − | 0.172980i | ||||
\(585\) | −738.550 | + | 1279.21i | −0.0521971 | + | 0.0904079i | ||||
\(586\) | −2837.19 | − | 4914.16i | −0.200006 | − | 0.346420i | ||||
\(587\) | 10286.3 | 0.723272 | 0.361636 | − | 0.932319i | \(-0.382218\pi\) | ||||
0.361636 | + | 0.932319i | \(0.382218\pi\) | |||||||
\(588\) | −2964.00 | − | 2855.90i | −0.207880 | − | 0.200298i | ||||
\(589\) | 7728.56 | 0.540662 | ||||||||
\(590\) | −4353.01 | − | 7539.64i | −0.303747 | − | 0.526105i | ||||
\(591\) | −2640.70 | + | 4573.82i | −0.183797 | + | 0.318345i | ||||
\(592\) | 1940.64 | − | 3361.29i | 0.134729 | − | 0.233358i | ||||
\(593\) | −7919.78 | − | 13717.5i | −0.548443 | − | 0.949931i | −0.998382 | − | 0.0568712i | \(-0.981888\pi\) |
0.449939 | − | 0.893059i | \(-0.351446\pi\) | |||||||
\(594\) | −422.520 | −0.0291855 | ||||||||
\(595\) | −891.204 | − | 6315.61i | −0.0614047 | − | 0.435151i | ||||
\(596\) | 4700.70 | 0.323067 | ||||||||
\(597\) | 2525.20 | + | 4373.77i | 0.173115 | + | 0.299844i | ||||
\(598\) | 7141.94 | − | 12370.2i | 0.488388 | − | 0.845912i | ||||
\(599\) | 5260.42 | − | 9111.31i | 0.358823 | − | 0.621500i | −0.628942 | − | 0.777453i | \(-0.716512\pi\) |
0.987764 | + | 0.155953i | \(0.0498449\pi\) | |||||||
\(600\) | 300.000 | + | 519.615i | 0.0204124 | + | 0.0353553i | ||||
\(601\) | 7734.31 | 0.524941 | 0.262470 | − | 0.964940i | \(-0.415463\pi\) | ||||
0.262470 | + | 0.964940i | \(0.415463\pi\) | |||||||
\(602\) | 1582.16 | − | 1237.55i | 0.107116 | − | 0.0837850i | ||||
\(603\) | −1896.46 | −0.128076 | ||||||||
\(604\) | 4359.79 | + | 7551.37i | 0.293704 | + | 0.508710i | ||||
\(605\) | −3174.45 | + | 5498.30i | −0.213322 | + | 0.369484i | ||||
\(606\) | −4351.26 | + | 7536.60i | −0.291680 | + | 0.505204i | ||||
\(607\) | 945.663 | + | 1637.94i | 0.0632344 | + | 0.109525i | 0.895909 | − | 0.444237i | \(-0.146525\pi\) |
−0.832675 | + | 0.553762i | \(0.813192\pi\) | |||||||
\(608\) | 1462.47 | 0.0975511 | ||||||||
\(609\) | 6519.50 | + | 2629.81i | 0.433799 | + | 0.174984i | ||||
\(610\) | 4647.02 | 0.308447 | ||||||||
\(611\) | 3720.69 | + | 6444.42i | 0.246355 | + | 0.426699i | ||||
\(612\) | 1239.80 | − | 2147.40i | 0.0818888 | − | 0.141836i | ||||
\(613\) | −6791.21 | + | 11762.7i | −0.447462 | + | 0.775027i | −0.998220 | − | 0.0596380i | \(-0.981005\pi\) |
0.550758 | + | 0.834665i | \(0.314339\pi\) | |||||||
\(614\) | −7929.20 | − | 13733.8i | −0.521167 | − | 0.902688i | ||||
\(615\) | −4304.77 | −0.282252 | ||||||||
\(616\) | 1075.11 | + | 433.674i | 0.0703207 | + | 0.0283656i | ||||
\(617\) | −22334.6 | −1.45731 | −0.728653 | − | 0.684883i | \(-0.759853\pi\) | ||||
−0.728653 | + | 0.684883i | \(0.759853\pi\) | |||||||
\(618\) | −1936.17 | − | 3353.54i | −0.126026 | − | 0.218283i | ||||
\(619\) | −3503.23 | + | 6067.77i | −0.227474 | + | 0.393997i | −0.957059 | − | 0.289894i | \(-0.906380\pi\) |
0.729585 | + | 0.683891i | \(0.239713\pi\) | |||||||
\(620\) | 1691.07 | − | 2929.02i | 0.109540 | − | 0.189729i | ||||
\(621\) | 2937.33 | + | 5087.61i | 0.189808 | + | 0.328758i | ||||
\(622\) | 16563.7 | 1.06776 | ||||||||
\(623\) | −2713.88 | + | 2122.76i | −0.174525 | + | 0.136512i | ||||
\(624\) | 1575.57 | 0.101079 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −685.406 | + | 1187.16i | −0.0437609 | + | 0.0757961i | ||||
\(627\) | 536.392 | − | 929.057i | 0.0341649 | − | 0.0591754i | ||||
\(628\) | −5409.34 | − | 9369.26i | −0.343720 | − | 0.595341i | ||||
\(629\) | 16708.4 | 1.05915 | ||||||||
\(630\) | 232.900 | + | 1650.47i | 0.0147285 | + | 0.104375i | ||||
\(631\) | 11554.9 | 0.728993 | 0.364497 | − | 0.931205i | \(-0.381241\pi\) | ||||
0.364497 | + | 0.931205i | \(0.381241\pi\) | |||||||
\(632\) | −3130.90 | − | 5422.88i | −0.197058 | − | 0.341314i | ||||
\(633\) | 8846.59 | − | 15322.7i | 0.555482 | − | 0.962124i | ||||
\(634\) | −5793.75 | + | 10035.1i | −0.362932 | + | 0.628617i | ||||
\(635\) | 6047.86 | + | 10475.2i | 0.377956 | + | 0.654639i | ||||
\(636\) | 645.068 | 0.0402179 | ||||||||
\(637\) | 10819.2 | − | 3115.45i | 0.672952 | − | 0.193781i | ||||
\(638\) | −1980.00 | −0.122867 | ||||||||
\(639\) | −1063.75 | − | 1842.47i | −0.0658550 | − | 0.114064i | ||||
\(640\) | 320.000 | − | 554.256i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 12940.8 | − | 22414.0i | 0.797393 | − | 1.38113i | −0.123915 | − | 0.992293i | \(-0.539545\pi\) |
0.921308 | − | 0.388833i | \(-0.127122\pi\) | |||||||
\(642\) | −1574.86 | − | 2727.74i | −0.0968144 | − | 0.167687i | ||||
\(643\) | −10120.7 | −0.620716 | −0.310358 | − | 0.950620i | \(-0.600449\pi\) | ||||
−0.310358 | + | 0.950620i | \(0.600449\pi\) | |||||||
\(644\) | −2252.20 | − | 15960.4i | −0.137809 | − | 0.976598i | ||||
\(645\) | −813.434 | −0.0496573 | ||||||||
\(646\) | 3147.87 | + | 5452.27i | 0.191720 | + | 0.332069i | ||||
\(647\) | −8130.91 | + | 14083.2i | −0.494064 | + | 0.855743i | −0.999977 | − | 0.00684126i | \(-0.997822\pi\) |
0.505913 | + | 0.862585i | \(0.331156\pi\) | |||||||
\(648\) | −324.000 | + | 561.184i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 3405.99 | + | 5899.34i | 0.206004 | + | 0.356810i | ||||
\(650\) | −1641.22 | −0.0990369 | ||||||||
\(651\) | 7400.68 | − | 5788.71i | 0.445554 | − | 0.348506i | ||||
\(652\) | −10403.4 | −0.624891 | ||||||||
\(653\) | 7340.21 | + | 12713.6i | 0.439885 | + | 0.761903i | 0.997680 | − | 0.0680756i | \(-0.0216859\pi\) |
−0.557795 | + | 0.829979i | \(0.688353\pi\) | |||||||
\(654\) | −3169.53 | + | 5489.79i | −0.189509 | + | 0.328238i | ||||
\(655\) | −4126.41 | + | 7147.15i | −0.246156 | + | 0.426355i | ||||
\(656\) | 2295.88 | + | 3976.58i | 0.136645 | + | 0.236676i | ||||
\(657\) | −3171.30 | −0.188317 | ||||||||
\(658\) | 7787.48 | + | 3141.28i | 0.461379 | + | 0.186109i | ||||
\(659\) | 5940.61 | 0.351158 | 0.175579 | − | 0.984465i | \(-0.443820\pi\) | ||||
0.175579 | + | 0.984465i | \(0.443820\pi\) | |||||||
\(660\) | −234.733 | − | 406.570i | −0.0138439 | − | 0.0239783i | ||||
\(661\) | −13491.7 | + | 23368.3i | −0.793897 | + | 1.37507i | 0.129640 | + | 0.991561i | \(0.458618\pi\) |
−0.923537 | + | 0.383509i | \(0.874715\pi\) | |||||||
\(662\) | 1560.30 | − | 2702.52i | 0.0916054 | − | 0.158665i | ||||
\(663\) | 3391.31 | + | 5873.93i | 0.198654 | + | 0.344079i | ||||
\(664\) | 7653.68 | 0.447320 | ||||||||
\(665\) | −3924.81 | − | 1583.17i | −0.228869 | − | 0.0923200i | ||||
\(666\) | −4366.44 | −0.254048 | ||||||||
\(667\) | 13764.8 | + | 23841.4i | 0.799066 | + | 1.38402i | ||||
\(668\) | 7163.40 | − | 12407.4i | 0.414911 | − | 0.718646i | ||||
\(669\) | −117.551 | + | 203.605i | −0.00679343 | + | 0.0117666i | ||||
\(670\) | −1053.59 | − | 1824.87i | −0.0607517 | − | 0.105225i | ||||
\(671\) | −3636.03 | −0.209192 | ||||||||
\(672\) | 1400.43 | − | 1095.40i | 0.0803908 | − | 0.0628807i | ||||
\(673\) | 16002.0 | 0.916543 | 0.458272 | − | 0.888812i | \(-0.348469\pi\) | ||||
0.458272 | + | 0.888812i | \(0.348469\pi\) | |||||||
\(674\) | −1543.88 | − | 2674.07i | −0.0882314 | − | 0.152821i | ||||
\(675\) | 337.500 | − | 584.567i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 2239.11 | − | 3878.26i | 0.127396 | − | 0.220656i | ||||
\(677\) | −8877.67 | − | 15376.6i | −0.503983 | − | 0.872925i | −0.999989 | − | 0.00460562i | \(-0.998534\pi\) |
0.496006 | − | 0.868319i | \(-0.334799\pi\) | |||||||
\(678\) | −1516.85 | −0.0859210 | ||||||||
\(679\) | −26.1541 | − | 185.344i | −0.00147821 | − | 0.0104755i | ||||
\(680\) | 2755.11 | 0.155373 | ||||||||
\(681\) | 1163.14 | + | 2014.62i | 0.0654504 | + | 0.113363i | ||||
\(682\) | −1323.17 | + | 2291.79i | −0.0742912 | + | 0.128676i | ||||
\(683\) | −5310.74 | + | 9198.46i | −0.297525 | + | 0.515329i | −0.975569 | − | 0.219693i | \(-0.929495\pi\) |
0.678044 | + | 0.735021i | \(0.262828\pi\) | |||||||
\(684\) | −822.641 | − | 1424.86i | −0.0459860 | − | 0.0796502i | ||||
\(685\) | 8859.50 | 0.494167 | ||||||||
\(686\) | 7450.49 | − | 10291.0i | 0.414666 | − | 0.572758i | ||||
\(687\) | −3498.66 | −0.194297 | ||||||||
\(688\) | 433.832 | + | 751.418i | 0.0240402 | + | 0.0416389i | ||||
\(689\) | −882.249 | + | 1528.10i | −0.0487823 | + | 0.0844935i | ||||
\(690\) | −3263.70 | + | 5652.90i | −0.180068 | + | 0.311887i | ||||
\(691\) | −9992.87 | − | 17308.2i | −0.550140 | − | 0.952871i | −0.998264 | − | 0.0588992i | \(-0.981241\pi\) |
0.448124 | − | 0.893972i | \(-0.352092\pi\) | |||||||
\(692\) | −10186.7 | −0.559595 | ||||||||
\(693\) | −182.231 | − | 1291.40i | −0.00998903 | − | 0.0707883i | ||||
\(694\) | −958.415 | −0.0524221 | ||||||||
\(695\) | −5901.36 | − | 10221.4i | −0.322088 | − | 0.557873i | ||||
\(696\) | −1518.32 | + | 2629.81i | −0.0826893 | + | 0.143222i | ||||
\(697\) | −9883.44 | + | 17118.6i | −0.537105 | + | 0.930292i | ||||
\(698\) | 9446.15 | + | 16361.2i | 0.512238 | + | 0.887222i | ||||
\(699\) | −4224.92 | −0.228614 | ||||||||
\(700\) | −1458.78 | + | 1141.04i | −0.0787666 | + | 0.0616102i | ||||
\(701\) | 2403.01 | 0.129473 | 0.0647363 | − | 0.997902i | \(-0.479379\pi\) | ||||
0.0647363 | + | 0.997902i | \(0.479379\pi\) | |||||||
\(702\) | −886.260 | − | 1535.05i | −0.0476492 | − | 0.0825308i | ||||
\(703\) | 5543.23 | − | 9601.15i | 0.297392 | − | 0.515099i | ||||
\(704\) | −250.382 | + | 433.674i | −0.0134043 | + | 0.0232169i | ||||
\(705\) | −1700.27 | − | 2944.95i | −0.0908309 | − | 0.157324i | ||||
\(706\) | −13790.9 | −0.735165 | ||||||||
\(707\) | −24911.8 | − | 10048.8i | −1.32518 | − | 0.534546i | ||||
\(708\) | 10447.2 | 0.554564 | ||||||||
\(709\) | 122.017 | + | 211.339i | 0.00646323 | + | 0.0111946i | 0.869239 | − | 0.494392i | \(-0.164609\pi\) |
−0.862776 | + | 0.505587i | \(0.831276\pi\) | |||||||
\(710\) | 1181.95 | − | 2047.19i | 0.0624755 | − | 0.108211i | ||||
\(711\) | −3522.26 | + | 6100.74i | −0.185788 | + | 0.321794i | ||||
\(712\) | −744.152 | − | 1288.91i | −0.0391689 | − | 0.0678426i | ||||
\(713\) | 36794.3 | 1.93262 | ||||||||
\(714\) | 7098.09 | + | 2863.20i | 0.372044 | + | 0.150073i | ||||
\(715\) | 1284.16 | 0.0671678 | ||||||||
\(716\) | 7868.43 | + | 13628.5i | 0.410694 | + | 0.711343i | ||||
\(717\) | 6711.55 | − | 11624.7i | 0.349578 | − | 0.605487i | ||||
\(718\) | 2829.65 | − | 4901.10i | 0.147078 | − | 0.254746i | ||||
\(719\) | 5581.70 | + | 9667.78i | 0.289516 | + | 0.501457i | 0.973694 | − | 0.227858i | \(-0.0731722\pi\) |
−0.684178 | + | 0.729315i | \(0.739839\pi\) | |||||||
\(720\) | −720.000 | −0.0372678 | ||||||||
\(721\) | 9414.80 | − | 7364.13i | 0.486304 | − | 0.380381i | ||||
\(722\) | −9540.61 | −0.491779 | ||||||||
\(723\) | 4455.69 | + | 7717.48i | 0.229196 | + | 0.396979i | ||||
\(724\) | 5862.37 | − | 10153.9i | 0.300930 | − | 0.521226i | ||||
\(725\) | 1581.58 | − | 2739.38i | 0.0810187 | − | 0.140328i | ||||
\(726\) | −3809.33 | − | 6597.96i | −0.194735 | − | 0.337291i | ||||
\(727\) | −28908.7 | −1.47478 | −0.737389 | − | 0.675469i | \(-0.763941\pi\) | ||||
−0.737389 | + | 0.675469i | \(0.763941\pi\) | |||||||
\(728\) | 679.540 | + | 4815.63i | 0.0345954 | + | 0.245163i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1761.83 | − | 3051.58i | −0.0893265 | − | 0.154718i | ||||
\(731\) | −1867.59 | + | 3234.75i | −0.0944941 | + | 0.163669i | ||||
\(732\) | −2788.21 | + | 4829.33i | −0.140786 | + | 0.243848i | ||||
\(733\) | 5200.37 | + | 9007.31i | 0.262047 | + | 0.453878i | 0.966786 | − | 0.255589i | \(-0.0822692\pi\) |
−0.704739 | + | 0.709467i | \(0.748936\pi\) | |||||||
\(734\) | −471.390 | −0.0237048 | ||||||||
\(735\) | −4944.10 | + | 1423.69i | −0.248117 | + | 0.0714469i | ||||
\(736\) | 6962.56 | 0.348700 | ||||||||
\(737\) | 824.373 | + | 1427.86i | 0.0412024 | + | 0.0713647i | ||||
\(738\) | 2582.86 | − | 4473.65i | 0.128830 | − | 0.223140i | ||||
\(739\) | 9966.69 | − | 17262.8i | 0.496117 | − | 0.859300i | −0.503873 | − | 0.863778i | \(-0.668092\pi\) |
0.999990 | + | 0.00447759i | \(0.00142527\pi\) | |||||||
\(740\) | −2425.80 | − | 4201.61i | −0.120506 | − | 0.208722i | ||||
\(741\) | 4500.45 | 0.223115 | ||||||||
\(742\) | 278.216 | + | 1971.60i | 0.0137650 | + | 0.0975470i | ||||
\(743\) | −37573.6 | −1.85524 | −0.927619 | − | 0.373527i | \(-0.878148\pi\) | ||||
−0.927619 | + | 0.373527i | \(0.878148\pi\) | |||||||
\(744\) | 2029.28 | + | 3514.82i | 0.0999960 | + | 0.173198i | ||||
\(745\) | 2937.94 | − | 5088.65i | 0.144480 | − | 0.250247i | ||||
\(746\) | −11870.9 | + | 20560.9i | −0.582605 | + | 1.00910i | ||||
\(747\) | −4305.19 | − | 7456.81i | −0.210868 | − | 0.365235i | ||||
\(748\) | −2155.72 | −0.105376 | ||||||||
\(749\) | 7657.91 | − | 5989.92i | 0.373583 | − | 0.292212i | ||||
\(750\) | 750.000 | 0.0365148 | ||||||||
\(751\) | 2444.45 | + | 4233.91i | 0.118774 | + | 0.205723i | 0.919282 | − | 0.393599i | \(-0.128770\pi\) |
−0.800508 | + | 0.599322i | \(0.795437\pi\) | |||||||
\(752\) | −1813.62 | + | 3141.28i | −0.0879466 | + | 0.152328i | ||||
\(753\) | −6381.51 | + | 11053.1i | −0.308838 | + | 0.534924i | ||||
\(754\) | −4153.17 | − | 7193.50i | −0.200596 | − | 0.347443i | ||||
\(755\) | 10899.5 | 0.525394 | ||||||||
\(756\) | −1854.96 | − | 748.246i | −0.0892385 | − | 0.0359966i | ||||
\(757\) | −15222.3 | −0.730863 | −0.365431 | − | 0.930838i | \(-0.619078\pi\) | ||||
−0.365431 | + | 0.930838i | \(0.619078\pi\) | |||||||
\(758\) | −2277.70 | − | 3945.10i | −0.109142 | − | 0.189040i | ||||
\(759\) | 2553.66 | − | 4423.07i | 0.122124 | − | 0.211525i | ||||
\(760\) | 914.045 | − | 1583.17i | 0.0436262 | − | 0.0755628i | ||||
\(761\) | −2461.50 | − | 4263.44i | −0.117253 | − | 0.203087i | 0.801425 | − | 0.598095i | \(-0.204075\pi\) |
−0.918678 | + | 0.395007i | \(0.870742\pi\) | |||||||
\(762\) | −14514.9 | −0.690050 | ||||||||
\(763\) | −18146.2 | − | 7319.72i | −0.860990 | − | 0.347303i | ||||
\(764\) | −13777.3 | −0.652414 | ||||||||
\(765\) | −1549.75 | − | 2684.25i | −0.0732436 | − | 0.126862i | ||||
\(766\) | −4058.15 | + | 7028.92i | −0.191419 | + | 0.331547i | ||||
\(767\) | −14288.5 | + | 24748.4i | −0.672658 | + | 1.16508i | ||||
\(768\) | 384.000 | + | 665.108i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −17900.3 | −0.839402 | −0.419701 | − | 0.907663i | \(-0.637865\pi\) | ||||
−0.419701 | + | 0.907663i | \(0.637865\pi\) | |||||||
\(770\) | 1141.41 | − | 892.797i | 0.0534203 | − | 0.0417847i | ||||
\(771\) | −7959.45 | −0.371793 | ||||||||
\(772\) | 3649.77 | + | 6321.59i | 0.170153 | + | 0.294714i | ||||
\(773\) | −5179.63 | + | 8971.39i | −0.241007 | + | 0.417437i | −0.961001 | − | 0.276543i | \(-0.910811\pi\) |
0.719994 | + | 0.693980i | \(0.244144\pi\) | |||||||
\(774\) | 488.061 | − | 845.346i | 0.0226653 | − | 0.0392575i | ||||
\(775\) | −2113.83 | − | 3661.27i | −0.0979757 | − | 0.169699i | ||||
\(776\) | 80.8541 | 0.00374033 | ||||||||
\(777\) | −1883.23 | − | 13345.7i | −0.0869506 | − | 0.616184i | ||||
\(778\) | −6804.63 | −0.313570 | ||||||||
\(779\) | 6557.92 | + | 11358.7i | 0.301620 | + | 0.522421i | ||||
\(780\) | 984.733 | − | 1705.61i | 0.0452040 | − | 0.0782956i | ||||
\(781\) | −924.806 | + | 1601.81i | −0.0423715 | + | 0.0733896i | ||||
\(782\) | 14986.4 | + | 25957.3i | 0.685312 | + | 1.18700i | ||||
\(783\) | 3416.22 | 0.155921 | ||||||||
\(784\) | 3952.00 | + | 3807.87i | 0.180029 | + | 0.173463i | ||||
\(785\) | −13523.4 | −0.614865 | ||||||||
\(786\) | −4951.69 | − | 8576.59i | −0.224709 | − | 0.389207i | ||||
\(787\) | 392.771 | − | 680.299i | 0.0177901 | − | 0.0308133i | −0.856993 | − | 0.515328i | \(-0.827670\pi\) |
0.874783 | + | 0.484514i | \(0.161004\pi\) | |||||||
\(788\) | 3520.93 | − | 6098.43i | 0.159173 | − | 0.275695i | ||||
\(789\) | −9896.45 | − | 17141.2i | −0.446544 | − | 0.773436i | ||||
\(790\) | −7827.25 | −0.352508 | ||||||||
\(791\) | −654.215 | − | 4636.16i | −0.0294073 | − | 0.208398i | ||||
\(792\) | 563.359 | 0.0252754 | ||||||||
\(793\) | −7626.79 | − | 13210.0i | −0.341533 | − | 0.591552i | ||||
\(794\) | −5201.54 | + | 9009.34i | −0.232488 | + | 0.402682i | ||||
\(795\) | 403.167 | − | 698.306i | 0.0179860 | − | 0.0311527i | ||||
\(796\) | −3366.93 | − | 5831.70i | −0.149922 | − | 0.259672i | ||||
\(797\) | 2669.30 | 0.118634 | 0.0593170 | − | 0.998239i | \(-0.481108\pi\) | ||||
0.0593170 | + | 0.998239i | \(0.481108\pi\) | |||||||
\(798\) | 4000.17 | − | 3128.88i | 0.177449 | − | 0.138798i | ||||
\(799\) | −15614.8 | −0.691377 | ||||||||
\(800\) | −400.000 | − | 692.820i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −837.171 | + | 1450.02i | −0.0369288 | + | 0.0639626i | ||||
\(802\) | 852.261 | − | 1476.16i | 0.0375242 | − | 0.0649938i | ||||
\(803\) | 1378.53 | + | 2387.69i | 0.0605821 | + | 0.104931i | ||||
\(804\) | 2528.61 | 0.110917 | ||||||||
\(805\) | −18685.3 | − | 7537.19i | −0.818100 | − | 0.330002i | ||||
\(806\) | −11101.7 | −0.485161 | ||||||||
\(807\) | 6995.54 | + | 12116.6i | 0.305148 | + | 0.528532i | ||||
\(808\) | 5801.68 | − | 10048.8i | 0.252602 | − | 0.437519i | ||||
\(809\) | −4031.11 | + | 6982.08i | −0.175187 | + | 0.303433i | −0.940226 | − | 0.340551i | \(-0.889386\pi\) |
0.765039 | + | 0.643984i | \(0.222720\pi\) | |||||||
\(810\) | 405.000 | + | 701.481i | 0.0175682 | + | 0.0304290i | ||||
\(811\) | 2794.93 | 0.121015 | 0.0605075 | − | 0.998168i | \(-0.480728\pi\) | ||||
0.0605075 | + | 0.998168i | \(0.480728\pi\) | |||||||
\(812\) | −8692.67 | − | 3506.41i | −0.375681 | − | 0.151541i | ||||
\(813\) | −2708.02 | −0.116820 | ||||||||
\(814\) | 1898.05 | + | 3287.52i | 0.0817281 | + | 0.141557i | ||||
\(815\) | −6502.14 | + | 11262.0i | −0.279460 | + | 0.484039i | ||||
\(816\) | −1653.07 | + | 2863.20i | −0.0709178 | + | 0.122833i | ||||
\(817\) | 1239.19 | + | 2146.34i | 0.0530647 | + | 0.0919108i | ||||
\(818\) | 29389.5 | 1.25621 | ||||||||
\(819\) | 4309.52 | − | 3370.85i | 0.183867 | − | 0.143818i | ||||
\(820\) | 5739.69 | 0.244437 | ||||||||
\(821\) | 13501.7 | + | 23385.6i | 0.573948 | + | 0.994107i | 0.996155 | + | 0.0876074i | \(0.0279221\pi\) |
−0.422207 | + | 0.906499i | \(0.638745\pi\) | |||||||
\(822\) | −5315.70 | + | 9207.06i | −0.225555 | + | 0.390673i | ||||
\(823\) | −17321.0 | + | 30000.8i | −0.733623 | + | 1.27067i | 0.221702 | + | 0.975115i | \(0.428839\pi\) |
−0.955325 | + | 0.295558i | \(0.904494\pi\) | |||||||
\(824\) | 2581.56 | + | 4471.39i | 0.109142 | + | 0.189039i | ||||
\(825\) | −586.833 | −0.0247647 | ||||||||
\(826\) | 4505.86 | + | 31931.2i | 0.189805 | + | 1.34507i | ||||
\(827\) | −28417.3 | −1.19488 | −0.597441 | − | 0.801913i | \(-0.703816\pi\) | ||||
−0.597441 | + | 0.801913i | \(0.703816\pi\) | |||||||
\(828\) | −3916.44 | − | 6783.48i | −0.164379 | − | 0.284713i | ||||
\(829\) | 12726.2 | − | 22042.3i | 0.533169 | − | 0.923477i | −0.466080 | − | 0.884743i | \(-0.654334\pi\) |
0.999250 | − | 0.0387341i | \(-0.0123325\pi\) | |||||||
\(830\) | 4783.55 | − | 8285.35i | 0.200047 | − | 0.346492i | ||||
\(831\) | 967.763 | + | 1676.22i | 0.0403987 | + | 0.0699726i | ||||
\(832\) | −2100.76 | −0.0875371 | ||||||||
\(833\) | −5689.77 | + | 22929.7i | −0.236661 | + | 0.953742i | ||||
\(834\) | 14163.3 | 0.588050 | ||||||||
\(835\) | −8954.25 | − | 15509.2i | −0.371107 | − | 0.642777i | ||||
\(836\) | −715.189 | + | 1238.74i | −0.0295877 | + | 0.0512474i | ||||
\(837\) | 2282.94 | − | 3954.17i | 0.0942772 | − | 0.163293i | ||||
\(838\) | −283.053 | − | 490.263i | −0.0116682 | − | 0.0202098i | ||||
\(839\) | −41344.7 | −1.70128 | −0.850642 | − | 0.525745i | \(-0.823787\pi\) | ||||
−0.850642 | + | 0.525745i | \(0.823787\pi\) | |||||||
\(840\) | −310.534 | − | 2200.63i | −0.0127553 | − | 0.0903916i | ||||
\(841\) | −8380.00 | −0.343597 | ||||||||
\(842\) | 10854.3 | + | 18800.2i | 0.444257 | + | 0.769475i | ||||
\(843\) | −6689.63 | + | 11586.8i | −0.273313 | + | 0.473392i | ||||
\(844\) | −11795.4 | + | 20430.3i | −0.481062 | + | 0.833223i | ||||
\(845\) | −2798.89 | − | 4847.82i | −0.113946 | − | 0.197361i | ||||
\(846\) | 4080.64 | 0.165834 | ||||||||
\(847\) | 18523.2 | − | 14488.6i | 0.751436 | − | 0.587763i | ||||
\(848\) | −860.090 | −0.0348297 | ||||||||
\(849\) | −8266.83 | − | 14318.6i | −0.334178 | − | 0.578813i | ||||
\(850\) | 1721.95 | − | 2982.50i | 0.0694850 | − | 0.120352i | ||||
\(851\) | 26390.3 | − | 45709.3i | 1.06304 | − | 1.84124i | ||||
\(852\) | 1418.33 | + | 2456.63i | 0.0570321 | + | 0.0987825i | ||||
\(853\) | 30225.5 | 1.21325 | 0.606625 | − | 0.794988i | \(-0.292523\pi\) | ||||
0.606625 | + | 0.794988i | \(0.292523\pi\) | |||||||
\(854\) | −15963.0 | − | 6439.10i | −0.639630 | − | 0.258011i | ||||
\(855\) | −2056.60 | −0.0822623 | ||||||||
\(856\) | 2099.82 | + | 3636.99i | 0.0838437 | + | 0.145222i | ||||
\(857\) | −14201.0 | + | 24596.9i | −0.566042 | + | 0.980413i | 0.430910 | + | 0.902395i | \(0.358193\pi\) |
−0.996952 | + | 0.0780182i | \(0.975141\pi\) | |||||||
\(858\) | −770.498 | + | 1334.54i | −0.0306578 | + | 0.0531008i | ||||
\(859\) | −22954.7 | − | 39758.8i | −0.911764 | − | 1.57922i | −0.811571 | − | 0.584254i | \(-0.801387\pi\) |
−0.100194 | − | 0.994968i | \(-0.531946\pi\) | |||||||
\(860\) | 1084.58 | 0.0430045 | ||||||||
\(861\) | 14787.4 | + | 5964.86i | 0.585310 | + | 0.236100i | ||||
\(862\) | −14608.7 | −0.577231 | ||||||||
\(863\) | −10270.6 | − | 17789.2i | −0.405116 | − | 0.701682i | 0.589219 | − | 0.807974i | \(-0.299436\pi\) |
−0.994335 | + | 0.106291i | \(0.966102\pi\) | |||||||
\(864\) | 432.000 | − | 748.246i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −6366.68 | + | 11027.4i | −0.250258 | + | 0.433460i | ||||
\(866\) | −2406.12 | − | 4167.53i | −0.0944151 | − | 0.163532i | ||||
\(867\) | 506.538 | 0.0198419 | ||||||||
\(868\) | −9867.57 | + | 7718.29i | −0.385861 | + | 0.301815i | ||||
\(869\) | 6124.38 | 0.239074 | ||||||||
\(870\) | 1897.90 | + | 3287.26i | 0.0739596 | + | 0.128102i | ||||
\(871\) | −3458.34 | + | 5990.03i | −0.134537 | + | 0.233025i | ||||
\(872\) | 4226.05 | − | 7319.72i | 0.164119 | − | 0.284263i | ||||
\(873\) | −45.4805 | − | 78.7745i | −0.00176321 | − | 0.00305397i | ||||
\(874\) | 19887.8 | 0.769697 | ||||||||
\(875\) | 323.473 | + | 2292.32i | 0.0124976 | + | 0.0885653i | ||||
\(876\) | 4228.40 | 0.163087 | ||||||||
\(877\) | −22502.9 | − | 38976.2i | −0.866442 | − | 1.50072i | −0.865608 | − | 0.500722i | \(-0.833068\pi\) |
−0.000833382 | − | 1.00000i | \(-0.500265\pi\) | |||||||
\(878\) | −13100.1 | + | 22690.1i | −0.503540 | + | 0.872158i | ||||
\(879\) | 4255.79 | − | 7371.24i | 0.163304 | − | 0.282851i | ||||
\(880\) | 312.977 | + | 542.093i | 0.0119892 | + | 0.0207658i | ||||
\(881\) | −13039.0 | −0.498633 | −0.249316 | − | 0.968422i | \(-0.580206\pi\) | ||||
−0.249316 | + | 0.968422i | \(0.580206\pi\) | |||||||
\(882\) | 1486.92 | − | 5992.27i | 0.0567656 | − | 0.228765i | ||||
\(883\) | 50384.1 | 1.92023 | 0.960113 | − | 0.279611i | \(-0.0902055\pi\) | ||||
0.960113 | + | 0.279611i | \(0.0902055\pi\) | |||||||
\(884\) | −4521.75 | − | 7831.90i | −0.172040 | − | 0.297981i | ||||
\(885\) | 6529.52 | − | 11309.5i | 0.248008 | − | 0.429563i | ||||
\(886\) | −9720.19 | + | 16835.9i | −0.368574 | + | 0.638388i | ||||
\(887\) | 11947.1 | + | 20692.9i | 0.452247 | + | 0.783315i | 0.998525 | − | 0.0542887i | \(-0.0172891\pi\) |
−0.546278 | + | 0.837604i | \(0.683956\pi\) | |||||||
\(888\) | 5821.92 | 0.220012 | ||||||||
\(889\) | −6260.22 | − | 44363.7i | −0.236177 | − | 1.67369i | ||||
\(890\) | −1860.38 | −0.0700675 | ||||||||
\(891\) | −316.890 | − | 548.869i | −0.0119149 | − | 0.0206373i | ||||
\(892\) | 156.735 | − | 271.474i | 0.00588328 | − | 0.0101901i | ||||
\(893\) | −5180.40 | + | 8972.72i | −0.194127 | + | 0.336238i | ||||
\(894\) | 3525.52 | + | 6106.39i | 0.131892 | + | 0.228443i | ||||
\(895\) | 19671.1 | 0.734672 | ||||||||
\(896\) | −1867.24 | + | 1460.53i | −0.0696205 | + | 0.0544563i | ||||
\(897\) | 21425.8 | 0.797534 | ||||||||
\(898\) | −11339.0 | − | 19639.8i | −0.421368 | − | 0.729831i | ||||
\(899\) | 10698.3 | − | 18529.9i | 0.396893 | − | 0.687439i | ||||
\(900\) | −450.000 | + | 779.423i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −1851.29 | − | 3206.52i | −0.0684520 | − | 0.118562i | ||||
\(902\) | −4490.99 | −0.165780 | ||||||||
\(903\) | 2794.24 | + | 1127.13i | 0.102975 | + | 0.0415376i | ||||
\(904\) | 2022.47 | 0.0744098 | ||||||||
\(905\) | −7327.96 | − | 12692.4i | −0.269160 | − | 0.466198i | ||||
\(906\) | −6539.68 | + | 11327.1i | −0.239808 | + | 0.415360i | ||||
\(907\) | 24047.2 | − | 41650.9i | 0.880345 | − | 1.52480i | 0.0293865 | − | 0.999568i | \(-0.490645\pi\) |
0.850958 | − | 0.525233i | \(-0.176022\pi\) | |||||||
\(908\) | −1550.86 | − | 2686.16i | −0.0566817 | − | 0.0981756i | ||||
\(909\) | −13053.8 | −0.476311 | ||||||||
\(910\) | 5637.78 | + | 2274.14i | 0.205374 | + | 0.0828430i | ||||
\(911\) | −32936.0 | −1.19782 | −0.598912 | − | 0.800815i | \(-0.704400\pi\) | ||||
−0.598912 | + | 0.800815i | \(0.704400\pi\) | |||||||
\(912\) | 1096.85 | + | 1899.81i | 0.0398251 | + | 0.0689791i | ||||
\(913\) | −3742.86 | + | 6482.82i | −0.135674 | + | 0.234994i | ||||
\(914\) | 5786.47 | − | 10022.5i | 0.209409 | − | 0.362706i | ||||
\(915\) | 3485.27 | + | 6036.66i | 0.125923 | + | 0.218105i | ||||
\(916\) | 4664.88 | 0.168266 | ||||||||
\(917\) | 24078.1 | − | 18833.6i | 0.867097 | − | 0.678232i | ||||
\(918\) | 3719.40 | 0.133724 | ||||||||
\(919\) | −20987.8 | − | 36351.9i | −0.753344 | − | 1.30483i | −0.946194 | − | 0.323601i | \(-0.895106\pi\) |
0.192850 | − | 0.981228i | \(-0.438227\pi\) | |||||||
\(920\) | 4351.60 | − | 7537.19i | 0.155944 | − | 0.270102i | ||||
\(921\) | 11893.8 | − | 20600.7i | 0.425531 | − | 0.737041i | ||||
\(922\) | −9403.13 | − | 16286.7i | −0.335874 | − | 0.581751i | ||||
\(923\) | −7759.34 | −0.276708 | ||||||||
\(924\) | 242.975 | + | 1721.87i | 0.00865076 | + | 0.0613044i | ||||
\(925\) | −6064.50 | −0.215567 | ||||||||
\(926\) | 13355.7 | + | 23132.8i | 0.473970 | + | 0.820941i | ||||
\(927\) | 2904.25 | − | 5030.31i | 0.102900 | − | 0.178228i | ||||
\(928\) | 2024.43 | − | 3506.41i | 0.0716111 | − | 0.124034i | ||||
\(929\) | 6011.06 | + | 10411.5i | 0.212289 | + | 0.367696i | 0.952431 | − | 0.304756i | \(-0.0985748\pi\) |
−0.740141 | + | 0.672451i | \(0.765241\pi\) | |||||||
\(930\) | 5073.20 | 0.178878 | ||||||||
\(931\) | 11288.5 | + | 10876.8i | 0.397384 | + | 0.382891i | ||||
\(932\) | 5633.22 | 0.197985 | ||||||||
\(933\) | 12422.8 | + | 21516.9i | 0.435909 | + | 0.755017i | ||||
\(934\) | −5734.89 | + | 9933.12i | −0.200911 | + | 0.347989i | ||||
\(935\) | −1347.33 | + | 2333.64i | −0.0471254 | + | 0.0816236i | ||||
\(936\) | 1181.68 | + | 2046.73i | 0.0412654 | + | 0.0714738i | ||||
\(937\) | 46293.9 | 1.61404 | 0.807021 | − | 0.590523i | \(-0.201078\pi\) | ||||
0.807021 | + | 0.590523i | \(0.201078\pi\) | |||||||
\(938\) | 1090.58 | + | 7728.52i | 0.0379625 | + | 0.269025i | ||||
\(939\) | −2056.22 | −0.0714612 | ||||||||
\(940\) | 2267.02 | + | 3926.60i | 0.0786618 | + | 0.136246i | ||||
\(941\) | 4085.53 | − | 7076.35i | 0.141535 | − | 0.245146i | −0.786540 | − | 0.617540i | \(-0.788130\pi\) |
0.928075 | + | 0.372394i | \(0.121463\pi\) | |||||||
\(942\) | 8114.01 | − | 14053.9i | 0.280646 | − | 0.486094i | ||||
\(943\) | 31221.1 | + | 54076.5i | 1.07815 | + | 1.86741i | ||||
\(944\) | −13929.6 | −0.480266 | ||||||||
\(945\) | −1969.35 | + | 1540.40i | −0.0677915 | + | 0.0530256i | ||||
\(946\) | −848.622 | −0.0291660 | ||||||||
\(947\) | 11124.3 | + | 19267.8i | 0.381721 | + | 0.661161i | 0.991308 | − | 0.131558i | \(-0.0419981\pi\) |
−0.609587 | + | 0.792719i | \(0.708665\pi\) | |||||||
\(948\) | 4696.35 | − | 8134.31i | 0.160897 | − | 0.278682i | ||||
\(949\) | −5783.12 | + | 10016.7i | −0.197817 | + | 0.342628i | ||||
\(950\) | −1142.56 | − | 1978.97i | −0.0390204 | − | 0.0675854i | ||||
\(951\) | −17381.2 | −0.592666 | ||||||||
\(952\) | −9464.12 | − | 3817.60i | −0.322200 | − | 0.129967i | ||||
\(953\) | −29181.9 | −0.991915 | −0.495958 | − | 0.868347i | \(-0.665183\pi\) | ||||
−0.495958 | + | 0.868347i | \(0.665183\pi\) | |||||||
\(954\) | 483.801 | + | 837.968i | 0.0164189 | + | 0.0284384i | ||||
\(955\) | −8610.80 | + | 14914.3i | −0.291769 | + | 0.505358i | ||||
\(956\) | −8948.73 | + | 15499.7i | −0.302743 | + | 0.524367i | ||||
\(957\) | −1485.00 | − | 2572.10i | −0.0501601 | − | 0.0868799i | ||||
\(958\) | 29284.8 | 0.987628 | ||||||||
\(959\) | −30433.4 | − | 12276.1i | −1.02476 | − | 0.413363i | ||||
\(960\) | 960.000 | 0.0322749 | ||||||||
\(961\) | 596.950 | + | 1033.95i | 0.0200379 | + | 0.0347067i | ||||
\(962\) | −7962.55 | + | 13791.5i | −0.266864 | + | 0.462222i | ||||
\(963\) | 2362.29 | − | 4091.61i | 0.0790486 | − | 0.136916i | ||||
\(964\) | −5940.92 | − | 10290.0i | −0.198490 | − | 0.343794i | ||||
\(965\) | 9124.43 | 0.304379 | ||||||||
\(966\) | 19044.1 | − | 14896.0i | 0.634299 | − | 0.496140i | ||||
\(967\) | 25172.0 | 0.837100 | 0.418550 | − | 0.908194i | \(-0.362538\pi\) | ||||
0.418550 | + | 0.908194i | \(0.362538\pi\) | |||||||
\(968\) | 5079.11 | + | 8797.28i | 0.168646 | + | 0.292103i | ||||
\(969\) | −4721.81 | + | 8178.41i | −0.156539 | + | 0.271134i | ||||
\(970\) | 50.5338 | − | 87.5272i | 0.00167273 | − | 0.00289725i | ||||
\(971\) | 2133.20 | + | 3694.82i | 0.0705023 | + | 0.122114i | 0.899122 | − | 0.437699i | \(-0.144206\pi\) |
−0.828619 | + | 0.559813i | \(0.810873\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 6108.57 | + | 43289.0i | 0.201266 | + | 1.42629i | ||||
\(974\) | 11346.1 | 0.373257 | ||||||||
\(975\) | −1230.92 | − | 2132.01i | −0.0404317 | − | 0.0700297i | ||||
\(976\) | 3717.62 | − | 6439.10i | 0.121924 | − | 0.211179i | ||||
\(977\) | 11198.0 | − | 19395.4i | 0.366688 | − | 0.635122i | −0.622357 | − | 0.782733i | \(-0.713825\pi\) |
0.989046 | + | 0.147611i | \(0.0471583\pi\) | |||||||
\(978\) | −7802.56 | − | 13514.4i | −0.255111 | − | 0.441865i | ||||
\(979\) | 1455.64 | 0.0475205 | ||||||||
\(980\) | 6592.14 | − | 1898.25i | 0.214876 | − | 0.0618749i | ||||
\(981\) | −9508.60 | −0.309466 | ||||||||
\(982\) | 7355.77 | + | 12740.6i | 0.239035 | + | 0.414020i | ||||
\(983\) | −8843.45 | + | 15317.3i | −0.286940 | + | 0.496995i | −0.973078 | − | 0.230477i | \(-0.925971\pi\) |
0.686138 | + | 0.727472i | \(0.259305\pi\) | |||||||
\(984\) | −3443.82 | + | 5964.86i | −0.111570 | + | 0.193245i | ||||
\(985\) | −4401.16 | − | 7623.04i | −0.142368 | − | 0.246589i | ||||
\(986\) | 17429.8 | 0.562958 | ||||||||
\(987\) | 1759.97 | + | 12472.2i | 0.0567583 | + | 0.402223i | ||||
\(988\) | −6000.60 | −0.193223 | ||||||||
\(989\) | 5899.57 | + | 10218.4i | 0.189682 | + | 0.328539i | ||||
\(990\) | 352.100 | − | 609.854i | 0.0113035 | − | 0.0195782i | ||||
\(991\) | 20981.6 | − | 36341.2i | 0.672555 | − | 1.16490i | −0.304623 | − | 0.952473i | \(-0.598530\pi\) |
0.977177 | − | 0.212426i | \(-0.0681363\pi\) | |||||||
\(992\) | −2705.71 | − | 4686.42i | −0.0865991 | − | 0.149994i | ||||
\(993\) | 4680.90 | 0.149591 | ||||||||
\(994\) | −6896.79 | + | 5394.58i | −0.220073 | + | 0.172138i | ||||
\(995\) | −8417.33 | −0.268188 | ||||||||
\(996\) | 5740.26 | + | 9942.42i | 0.182617 | + | 0.316303i | ||||
\(997\) | 11603.2 | − | 20097.3i | 0.368582 | − | 0.638403i | −0.620762 | − | 0.783999i | \(-0.713177\pi\) |
0.989344 | + | 0.145596i | \(0.0465100\pi\) | |||||||
\(998\) | −20447.2 | + | 35415.6i | −0.648542 | + | 1.12331i | ||||
\(999\) | −3274.83 | − | 5672.17i | −0.103715 | − | 0.179639i |
(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 | 210.4.i.i.151.1 | yes | 4 | |
3.2 | odd | 2 | 630.4.k.m.361.1 | 4 | |||
7.2 | even | 3 | inner | 210.4.i.i.121.1 | ✓ | 4 | |
7.3 | odd | 6 | 1470.4.a.bs.1.1 | 2 | |||
7.4 | even | 3 | 1470.4.a.bn.1.1 | 2 | |||
21.2 | odd | 6 | 630.4.k.m.541.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.4.i.i.121.1 | ✓ | 4 | 7.2 | even | 3 | inner | |
210.4.i.i.151.1 | yes | 4 | 1.1 | even | 1 | trivial | |
630.4.k.m.361.1 | 4 | 3.2 | odd | 2 | |||
630.4.k.m.541.1 | 4 | 21.2 | odd | 6 | |||
1470.4.a.bn.1.1 | 2 | 7.4 | even | 3 | |||
1470.4.a.bs.1.1 | 2 | 7.3 | odd | 6 |