Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,4,Mod(271,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.271");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.7915471046\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.541 |
Dual form | 810.4.e.h.271.1 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 3.46410i | 0.107990 | − | 0.187044i | −0.806966 | − | 0.590598i | \(-0.798892\pi\) |
0.914956 | + | 0.403554i | \(0.132225\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −21.0000 | + | 36.3731i | −0.575613 | + | 0.996990i | 0.420362 | + | 0.907356i | \(0.361903\pi\) |
−0.995975 | + | 0.0896338i | \(0.971430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | − | 17.3205i | −0.213346 | − | 0.369527i | 0.739413 | − | 0.673252i | \(-0.235103\pi\) |
−0.952760 | + | 0.303725i | \(0.901770\pi\) | |||||||
\(14\) | 4.00000 | + | 6.92820i | 0.0763604 | + | 0.132260i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 93.0000 | 1.32681 | 0.663406 | − | 0.748259i | \(-0.269110\pi\) | ||||
0.663406 | + | 0.748259i | \(0.269110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 59.0000 | 0.712396 | 0.356198 | − | 0.934410i | \(-0.384073\pi\) | ||||
0.356198 | + | 0.934410i | \(0.384073\pi\) | |||||||
\(20\) | 10.0000 | − | 17.3205i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −42.0000 | − | 72.7461i | −0.407020 | − | 0.704979i | ||||
\(23\) | −4.50000 | − | 7.79423i | −0.0407963 | − | 0.0706613i | 0.844906 | − | 0.534914i | \(-0.179656\pi\) |
−0.885703 | + | 0.464253i | \(0.846323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 40.0000 | 0.301717 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.0000 | −0.107990 | ||||||||
\(29\) | −60.0000 | + | 103.923i | −0.384197 | + | 0.665449i | −0.991657 | − | 0.128901i | \(-0.958855\pi\) |
0.607460 | + | 0.794350i | \(0.292188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.5000 | − | 40.7032i | −0.136152 | − | 0.235823i | 0.789885 | − | 0.613255i | \(-0.210140\pi\) |
−0.926037 | + | 0.377433i | \(0.876807\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −93.0000 | + | 161.081i | −0.469099 | + | 0.812503i | ||||
\(35\) | 20.0000 | 0.0965891 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −262.000 | −1.16412 | −0.582061 | − | 0.813145i | \(-0.697754\pi\) | ||||
−0.582061 | + | 0.813145i | \(0.697754\pi\) | |||||||
\(38\) | −59.0000 | + | 102.191i | −0.251870 | + | 0.436252i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 20.0000 | + | 34.6410i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −63.0000 | − | 109.119i | −0.239974 | − | 0.415648i | 0.720732 | − | 0.693213i | \(-0.243806\pi\) |
−0.960707 | + | 0.277566i | \(0.910472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 89.0000 | − | 154.153i | 0.315637 | − | 0.546699i | −0.663936 | − | 0.747789i | \(-0.731115\pi\) |
0.979573 | + | 0.201091i | \(0.0644486\pi\) | |||||||
\(44\) | 168.000 | 0.575613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.0000 | 0.0576947 | ||||||||
\(47\) | −72.0000 | + | 124.708i | −0.223453 | + | 0.387032i | −0.955854 | − | 0.293842i | \(-0.905066\pi\) |
0.732401 | + | 0.680873i | \(0.238400\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 163.500 | + | 283.190i | 0.476676 | + | 0.825628i | ||||
\(50\) | −25.0000 | − | 43.3013i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −40.0000 | + | 69.2820i | −0.106673 | + | 0.184763i | ||||
\(53\) | 741.000 | 1.92046 | 0.960228 | − | 0.279217i | \(-0.0900748\pi\) | ||||
0.960228 | + | 0.279217i | \(0.0900748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −210.000 | −0.514844 | ||||||||
\(56\) | 16.0000 | − | 27.7128i | 0.0381802 | − | 0.0661300i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −120.000 | − | 207.846i | −0.271668 | − | 0.470544i | ||||
\(59\) | 222.000 | + | 384.515i | 0.489863 | + | 0.848468i | 0.999932 | − | 0.0116655i | \(-0.00371333\pi\) |
−0.510069 | + | 0.860134i | \(0.670380\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −110.500 | + | 191.392i | −0.231936 | + | 0.401724i | −0.958378 | − | 0.285503i | \(-0.907839\pi\) |
0.726442 | + | 0.687228i | \(0.241173\pi\) | |||||||
\(62\) | 94.0000 | 0.192549 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 50.0000 | − | 86.6025i | 0.0954113 | − | 0.165257i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 269.000 | + | 465.922i | 0.490501 | + | 0.849573i | 0.999940 | − | 0.0109338i | \(-0.00348039\pi\) |
−0.509439 | + | 0.860507i | \(0.670147\pi\) | |||||||
\(68\) | −186.000 | − | 322.161i | −0.331703 | − | 0.574527i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20.0000 | + | 34.6410i | −0.0341494 | + | 0.0591485i | ||||
\(71\) | 690.000 | 1.15335 | 0.576676 | − | 0.816973i | \(-0.304350\pi\) | ||||
0.576676 | + | 0.816973i | \(0.304350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1126.00 | −1.80532 | −0.902660 | − | 0.430355i | \(-0.858388\pi\) | ||||
−0.902660 | + | 0.430355i | \(0.858388\pi\) | |||||||
\(74\) | 262.000 | − | 453.797i | 0.411579 | − | 0.712877i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −118.000 | − | 204.382i | −0.178099 | − | 0.308477i | ||||
\(77\) | 84.0000 | + | 145.492i | 0.124321 | + | 0.215330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −332.500 | + | 575.907i | −0.473534 | + | 0.820185i | −0.999541 | − | 0.0302955i | \(-0.990355\pi\) |
0.526007 | + | 0.850480i | \(0.323689\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 252.000 | 0.339375 | ||||||||
\(83\) | −37.5000 | + | 64.9519i | −0.0495923 | + | 0.0858964i | −0.889756 | − | 0.456437i | \(-0.849126\pi\) |
0.840164 | + | 0.542333i | \(0.182459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 232.500 | + | 402.702i | 0.296684 | + | 0.513872i | ||||
\(86\) | 178.000 | + | 308.305i | 0.223189 | + | 0.386574i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −168.000 | + | 290.985i | −0.203510 | + | 0.352489i | ||||
\(89\) | −1086.00 | −1.29344 | −0.646718 | − | 0.762729i | \(-0.723859\pi\) | ||||
−0.646718 | + | 0.762729i | \(0.723859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −80.0000 | −0.0921569 | ||||||||
\(92\) | −18.0000 | + | 31.1769i | −0.0203981 | + | 0.0353306i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −144.000 | − | 249.415i | −0.158005 | − | 0.273673i | ||||
\(95\) | 147.500 | + | 255.477i | 0.159297 | + | 0.275910i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −772.000 | + | 1337.14i | −0.808090 | + | 1.39965i | 0.106095 | + | 0.994356i | \(0.466165\pi\) |
−0.914185 | + | 0.405297i | \(0.867168\pi\) | |||||||
\(98\) | −654.000 | −0.674122 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 66.0000 | − | 114.315i | 0.0650222 | − | 0.112622i | −0.831682 | − | 0.555253i | \(-0.812622\pi\) |
0.896704 | + | 0.442631i | \(0.145955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 446.000 | + | 772.495i | 0.426657 | + | 0.738992i | 0.996574 | − | 0.0827108i | \(-0.0263578\pi\) |
−0.569916 | + | 0.821703i | \(0.693024\pi\) | |||||||
\(104\) | −80.0000 | − | 138.564i | −0.0754293 | − | 0.130647i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −741.000 | + | 1283.45i | −0.678984 | + | 1.17603i | ||||
\(107\) | −1140.00 | −1.02998 | −0.514990 | − | 0.857196i | \(-0.672205\pi\) | ||||
−0.514990 | + | 0.857196i | \(0.672205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1735.00 | −1.52461 | −0.762307 | − | 0.647216i | \(-0.775933\pi\) | ||||
−0.762307 | + | 0.647216i | \(0.775933\pi\) | |||||||
\(110\) | 210.000 | − | 363.731i | 0.182025 | − | 0.315276i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 32.0000 | + | 55.4256i | 0.0269975 | + | 0.0467610i | ||||
\(113\) | 717.000 | + | 1241.88i | 0.596900 | + | 1.03386i | 0.993276 | + | 0.115773i | \(0.0369344\pi\) |
−0.396376 | + | 0.918088i | \(0.629732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.5000 | − | 38.9711i | 0.0182447 | − | 0.0316007i | ||||
\(116\) | 480.000 | 0.384197 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −888.000 | −0.692771 | ||||||||
\(119\) | 186.000 | − | 322.161i | 0.143282 | − | 0.248172i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −216.500 | − | 374.989i | −0.162660 | − | 0.281735i | ||||
\(122\) | −221.000 | − | 382.783i | −0.164003 | − | 0.284062i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −94.0000 | + | 162.813i | −0.0680762 | + | 0.117911i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 686.000 | 0.479312 | 0.239656 | − | 0.970858i | \(-0.422965\pi\) | ||||
0.239656 | + | 0.970858i | \(0.422965\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 100.000 | + | 173.205i | 0.0674660 | + | 0.116855i | ||||
\(131\) | 57.0000 | + | 98.7269i | 0.0380161 | + | 0.0658459i | 0.884407 | − | 0.466716i | \(-0.154563\pi\) |
−0.846391 | + | 0.532561i | \(0.821230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 118.000 | − | 204.382i | 0.0769316 | − | 0.133249i | ||||
\(134\) | −1076.00 | −0.693673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 744.000 | 0.469099 | ||||||||
\(137\) | −79.5000 | + | 137.698i | −0.0495777 | + | 0.0858711i | −0.889749 | − | 0.456450i | \(-0.849121\pi\) |
0.840172 | + | 0.542321i | \(0.182454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1138.00 | − | 1971.07i | −0.694417 | − | 1.20276i | −0.970377 | − | 0.241596i | \(-0.922329\pi\) |
0.275960 | − | 0.961169i | \(-0.411004\pi\) | |||||||
\(140\) | −40.0000 | − | 69.2820i | −0.0241473 | − | 0.0418243i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −690.000 | + | 1195.12i | −0.407771 | + | 0.706280i | ||||
\(143\) | 840.000 | 0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −600.000 | −0.343636 | ||||||||
\(146\) | 1126.00 | − | 1950.29i | 0.638277 | − | 1.10553i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 524.000 | + | 907.595i | 0.291031 | + | 0.504080i | ||||
\(149\) | 699.000 | + | 1210.70i | 0.384324 | + | 0.665669i | 0.991675 | − | 0.128765i | \(-0.0411011\pi\) |
−0.607351 | + | 0.794434i | \(0.707768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1312.00 | + | 2272.45i | −0.707080 | + | 1.22470i | 0.258856 | + | 0.965916i | \(0.416655\pi\) |
−0.965936 | + | 0.258782i | \(0.916679\pi\) | |||||||
\(152\) | 472.000 | 0.251870 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −336.000 | −0.175816 | ||||||||
\(155\) | 117.500 | − | 203.516i | 0.0608892 | − | 0.105463i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 197.000 | + | 341.214i | 0.100142 | + | 0.173451i | 0.911743 | − | 0.410761i | \(-0.134737\pi\) |
−0.811601 | + | 0.584212i | \(0.801404\pi\) | |||||||
\(158\) | −665.000 | − | 1151.81i | −0.334839 | − | 0.579958i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 80.0000 | − | 138.564i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −36.0000 | −0.0176223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3346.00 | −1.60785 | −0.803923 | − | 0.594733i | \(-0.797258\pi\) | ||||
−0.803923 | + | 0.594733i | \(0.797258\pi\) | |||||||
\(164\) | −252.000 | + | 436.477i | −0.119987 | + | 0.207824i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −75.0000 | − | 129.904i | −0.0350670 | − | 0.0607379i | ||||
\(167\) | 745.500 | + | 1291.24i | 0.345440 | + | 0.598320i | 0.985434 | − | 0.170060i | \(-0.0543963\pi\) |
−0.639993 | + | 0.768380i | \(0.721063\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 898.500 | − | 1556.25i | 0.408967 | − | 0.708351i | ||||
\(170\) | −930.000 | −0.419575 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −712.000 | −0.315637 | ||||||||
\(173\) | −1201.50 | + | 2081.06i | −0.528025 | + | 0.914566i | 0.471441 | + | 0.881898i | \(0.343734\pi\) |
−0.999466 | + | 0.0326688i | \(0.989599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.0000 | + | 86.6025i | 0.0215980 | + | 0.0374088i | ||||
\(176\) | −336.000 | − | 581.969i | −0.143903 | − | 0.249248i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1086.00 | − | 1881.01i | 0.457299 | − | 0.792064i | ||||
\(179\) | −2640.00 | −1.10236 | −0.551181 | − | 0.834386i | \(-0.685823\pi\) | ||||
−0.551181 | + | 0.834386i | \(0.685823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1073.00 | 0.440638 | 0.220319 | − | 0.975428i | \(-0.429290\pi\) | ||||
0.220319 | + | 0.975428i | \(0.429290\pi\) | |||||||
\(182\) | 80.0000 | − | 138.564i | 0.0325824 | − | 0.0564344i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −36.0000 | − | 62.3538i | −0.0144237 | − | 0.0249825i | ||||
\(185\) | −655.000 | − | 1134.49i | −0.260306 | − | 0.450863i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1953.00 | + | 3382.70i | −0.763730 | + | 1.32282i | ||||
\(188\) | 576.000 | 0.223453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −590.000 | −0.225279 | ||||||||
\(191\) | −735.000 | + | 1273.06i | −0.278444 | + | 0.482279i | −0.970998 | − | 0.239087i | \(-0.923152\pi\) |
0.692555 | + | 0.721366i | \(0.256485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2360.00 | + | 4087.64i | 0.880189 | + | 1.52453i | 0.851130 | + | 0.524955i | \(0.175918\pi\) |
0.0290591 | + | 0.999578i | \(0.490749\pi\) | |||||||
\(194\) | −1544.00 | − | 2674.29i | −0.571406 | − | 0.989704i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 654.000 | − | 1132.76i | 0.238338 | − | 0.412814i | ||||
\(197\) | −765.000 | −0.276670 | −0.138335 | − | 0.990385i | \(-0.544175\pi\) | ||||
−0.138335 | + | 0.990385i | \(0.544175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 668.000 | 0.237956 | 0.118978 | − | 0.992897i | \(-0.462038\pi\) | ||||
0.118978 | + | 0.992897i | \(0.462038\pi\) | |||||||
\(200\) | −100.000 | + | 173.205i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 132.000 | + | 228.631i | 0.0459777 | + | 0.0796356i | ||||
\(203\) | 240.000 | + | 415.692i | 0.0829788 | + | 0.143724i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 315.000 | − | 545.596i | 0.107320 | − | 0.185883i | ||||
\(206\) | −1784.00 | −0.603384 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 320.000 | 0.106673 | ||||||||
\(209\) | −1239.00 | + | 2146.01i | −0.410064 | + | 0.710252i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2300.50 | − | 3984.58i | −0.750583 | − | 1.30005i | −0.947541 | − | 0.319635i | \(-0.896440\pi\) |
0.196958 | − | 0.980412i | \(-0.436894\pi\) | |||||||
\(212\) | −1482.00 | − | 2566.90i | −0.480114 | − | 0.831582i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1140.00 | − | 1974.54i | 0.364153 | − | 0.630732i | ||||
\(215\) | 890.000 | 0.282314 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −188.000 | −0.0588123 | ||||||||
\(218\) | 1735.00 | − | 3005.11i | 0.539032 | − | 0.933631i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 420.000 | + | 727.461i | 0.128711 | + | 0.222934i | ||||
\(221\) | −930.000 | − | 1610.81i | −0.283070 | − | 0.490292i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1079.00 | − | 1868.88i | 0.324014 | − | 0.561209i | −0.657298 | − | 0.753631i | \(-0.728301\pi\) |
0.981312 | + | 0.192421i | \(0.0616341\pi\) | |||||||
\(224\) | −128.000 | −0.0381802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2868.00 | −0.844144 | ||||||||
\(227\) | −1561.50 | + | 2704.60i | −0.456566 | + | 0.790795i | −0.998777 | − | 0.0494474i | \(-0.984254\pi\) |
0.542211 | + | 0.840242i | \(0.317587\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1013.50 | − | 1755.43i | −0.292463 | − | 0.506560i | 0.681929 | − | 0.731419i | \(-0.261141\pi\) |
−0.974391 | + | 0.224858i | \(0.927808\pi\) | |||||||
\(230\) | 45.0000 | + | 77.9423i | 0.0129009 | + | 0.0223451i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −480.000 | + | 831.384i | −0.135834 | + | 0.235272i | ||||
\(233\) | −438.000 | −0.123152 | −0.0615758 | − | 0.998102i | \(-0.519613\pi\) | ||||
−0.0615758 | + | 0.998102i | \(0.519613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −720.000 | −0.199862 | ||||||||
\(236\) | 888.000 | − | 1538.06i | 0.244932 | − | 0.424234i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 372.000 | + | 644.323i | 0.101316 | + | 0.175484i | ||||
\(239\) | −3207.00 | − | 5554.69i | −0.867965 | − | 1.50336i | −0.864073 | − | 0.503367i | \(-0.832095\pi\) |
−0.00389189 | − | 0.999992i | \(-0.501239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1715.50 | + | 2971.33i | −0.458527 | + | 0.794193i | −0.998883 | − | 0.0472439i | \(-0.984956\pi\) |
0.540356 | + | 0.841436i | \(0.318290\pi\) | |||||||
\(242\) | 866.000 | 0.230035 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 884.000 | 0.231936 | ||||||||
\(245\) | −817.500 | + | 1415.95i | −0.213176 | + | 0.369232i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −590.000 | − | 1021.91i | −0.151987 | − | 0.263249i | ||||
\(248\) | −188.000 | − | 325.626i | −0.0481371 | − | 0.0833760i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 125.000 | − | 216.506i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 7308.00 | 1.83776 | 0.918878 | − | 0.394541i | \(-0.129096\pi\) | ||||
0.918878 | + | 0.394541i | \(0.129096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 378.000 | 0.0939314 | ||||||||
\(254\) | −686.000 | + | 1188.19i | −0.169462 | + | 0.293518i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1864.50 | + | 3229.41i | 0.452546 | + | 0.783833i | 0.998543 | − | 0.0539542i | \(-0.0171825\pi\) |
−0.545997 | + | 0.837787i | \(0.683849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −524.000 | + | 907.595i | −0.125713 | + | 0.217742i | ||||
\(260\) | −400.000 | −0.0954113 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −228.000 | −0.0537629 | ||||||||
\(263\) | 978.000 | − | 1693.95i | 0.229301 | − | 0.397160i | −0.728300 | − | 0.685258i | \(-0.759689\pi\) |
0.957601 | + | 0.288098i | \(0.0930228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1852.50 | + | 3208.62i | 0.429427 | + | 0.743789i | ||||
\(266\) | 236.000 | + | 408.764i | 0.0543988 | + | 0.0942215i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1076.00 | − | 1863.69i | 0.245251 | − | 0.424787i | ||||
\(269\) | 990.000 | 0.224392 | 0.112196 | − | 0.993686i | \(-0.464212\pi\) | ||||
0.112196 | + | 0.993686i | \(0.464212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8495.00 | 1.90419 | 0.952093 | − | 0.305808i | \(-0.0989266\pi\) | ||||
0.952093 | + | 0.305808i | \(0.0989266\pi\) | |||||||
\(272\) | −744.000 | + | 1288.65i | −0.165852 | + | 0.287263i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −159.000 | − | 275.396i | −0.0350567 | − | 0.0607200i | ||||
\(275\) | −525.000 | − | 909.327i | −0.115123 | − | 0.199398i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 683.000 | − | 1182.99i | 0.148150 | − | 0.256603i | −0.782394 | − | 0.622784i | \(-0.786002\pi\) |
0.930544 | + | 0.366181i | \(0.119335\pi\) | |||||||
\(278\) | 4552.00 | 0.982053 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 160.000 | 0.0341494 | ||||||||
\(281\) | −2760.00 | + | 4780.46i | −0.585935 | + | 1.01487i | 0.408823 | + | 0.912614i | \(0.365939\pi\) |
−0.994758 | + | 0.102256i | \(0.967394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2719.00 | − | 4709.45i | −0.571123 | − | 0.989214i | −0.996451 | − | 0.0841746i | \(-0.973175\pi\) |
0.425328 | − | 0.905039i | \(-0.360159\pi\) | |||||||
\(284\) | −1380.00 | − | 2390.23i | −0.288338 | − | 0.499416i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −840.000 | + | 1454.92i | −0.173672 | + | 0.300809i | ||||
\(287\) | −504.000 | −0.103659 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3736.00 | 0.760432 | ||||||||
\(290\) | 600.000 | − | 1039.23i | 0.121494 | − | 0.210434i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2252.00 | + | 3900.58i | 0.451330 | + | 0.781726i | ||||
\(293\) | 4126.50 | + | 7147.31i | 0.822774 | + | 1.42509i | 0.903609 | + | 0.428358i | \(0.140908\pi\) |
−0.0808352 | + | 0.996727i | \(0.525759\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1110.00 | + | 1922.58i | −0.219074 | + | 0.379447i | ||||
\(296\) | −2096.00 | −0.411579 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2796.00 | −0.543517 | ||||||||
\(299\) | −90.0000 | + | 155.885i | −0.0174075 | + | 0.0301506i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −356.000 | − | 616.610i | −0.0681711 | − | 0.118076i | ||||
\(302\) | −2624.00 | − | 4544.90i | −0.499981 | − | 0.865992i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −472.000 | + | 817.528i | −0.0890495 | + | 0.154238i | ||||
\(305\) | −1105.00 | −0.207450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9290.00 | 1.72706 | 0.863531 | − | 0.504295i | \(-0.168248\pi\) | ||||
0.863531 | + | 0.504295i | \(0.168248\pi\) | |||||||
\(308\) | 336.000 | − | 581.969i | 0.0621603 | − | 0.107665i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 235.000 | + | 407.032i | 0.0430552 | + | 0.0745737i | ||||
\(311\) | 4056.00 | + | 7025.20i | 0.739533 | + | 1.28091i | 0.952706 | + | 0.303894i | \(0.0982868\pi\) |
−0.213173 | + | 0.977014i | \(0.568380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3950.00 | − | 6841.60i | 0.713314 | − | 1.23550i | −0.250293 | − | 0.968170i | \(-0.580527\pi\) |
0.963606 | − | 0.267325i | \(-0.0861399\pi\) | |||||||
\(314\) | −788.000 | −0.141622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2660.00 | 0.473534 | ||||||||
\(317\) | 2209.50 | − | 3826.97i | 0.391476 | − | 0.678056i | −0.601168 | − | 0.799122i | \(-0.705298\pi\) |
0.992644 | + | 0.121066i | \(0.0386313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2520.00 | − | 4364.77i | −0.442298 | − | 0.766082i | ||||
\(320\) | 160.000 | + | 277.128i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 36.0000 | − | 62.3538i | 0.00623044 | − | 0.0107914i | ||||
\(323\) | 5487.00 | 0.945216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 500.000 | 0.0853385 | ||||||||
\(326\) | 3346.00 | − | 5795.44i | 0.568460 | − | 0.984601i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −504.000 | − | 872.954i | −0.0848437 | − | 0.146954i | ||||
\(329\) | 288.000 | + | 498.831i | 0.0482613 | + | 0.0835910i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4100.00 | − | 7101.41i | 0.680835 | − | 1.17924i | −0.293891 | − | 0.955839i | \(-0.594950\pi\) |
0.974726 | − | 0.223402i | \(-0.0717163\pi\) | |||||||
\(332\) | 300.000 | 0.0495923 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2982.00 | −0.488526 | ||||||||
\(335\) | −1345.00 | + | 2329.61i | −0.219359 | + | 0.379941i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4778.00 | + | 8275.74i | 0.772327 | + | 1.33771i | 0.936285 | + | 0.351242i | \(0.114241\pi\) |
−0.163957 | + | 0.986467i | \(0.552426\pi\) | |||||||
\(338\) | 1797.00 | + | 3112.50i | 0.289183 | + | 0.500880i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 930.000 | − | 1610.81i | 0.148342 | − | 0.256936i | ||||
\(341\) | 1974.00 | 0.313484 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2680.00 | 0.421885 | ||||||||
\(344\) | 712.000 | − | 1233.22i | 0.111594 | − | 0.193287i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2403.00 | − | 4162.12i | −0.373370 | − | 0.646696i | ||||
\(347\) | 5058.00 | + | 8760.71i | 0.782500 | + | 1.35533i | 0.930481 | + | 0.366340i | \(0.119389\pi\) |
−0.147980 | + | 0.988990i | \(0.547277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3375.50 | − | 5846.54i | 0.517726 | − | 0.896728i | −0.482062 | − | 0.876137i | \(-0.660112\pi\) |
0.999788 | − | 0.0205906i | \(-0.00655466\pi\) | |||||||
\(350\) | −200.000 | −0.0305441 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1344.00 | 0.203510 | ||||||||
\(353\) | 2031.00 | − | 3517.80i | 0.306230 | − | 0.530406i | −0.671304 | − | 0.741182i | \(-0.734266\pi\) |
0.977534 | + | 0.210776i | \(0.0675990\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1725.00 | + | 2987.79i | 0.257897 | + | 0.446691i | ||||
\(356\) | 2172.00 | + | 3762.01i | 0.323359 | + | 0.560074i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2640.00 | − | 4572.61i | 0.389744 | − | 0.675056i | ||||
\(359\) | −8778.00 | −1.29049 | −0.645244 | − | 0.763977i | \(-0.723244\pi\) | ||||
−0.645244 | + | 0.763977i | \(0.723244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3378.00 | −0.492492 | ||||||||
\(362\) | −1073.00 | + | 1858.49i | −0.155789 | + | 0.269835i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 160.000 | + | 277.128i | 0.0230392 | + | 0.0399051i | ||||
\(365\) | −2815.00 | − | 4875.72i | −0.403682 | − | 0.699197i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −478.000 | + | 827.920i | −0.0679875 | + | 0.117758i | −0.898015 | − | 0.439964i | \(-0.854991\pi\) |
0.830028 | + | 0.557722i | \(0.188324\pi\) | |||||||
\(368\) | 144.000 | 0.0203981 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2620.00 | 0.368128 | ||||||||
\(371\) | 1482.00 | − | 2566.90i | 0.207390 | − | 0.359210i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1150.00 | − | 1991.86i | −0.159637 | − | 0.276500i | 0.775101 | − | 0.631838i | \(-0.217699\pi\) |
−0.934738 | + | 0.355338i | \(0.884366\pi\) | |||||||
\(374\) | −3906.00 | − | 6765.39i | −0.540039 | − | 0.935374i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −576.000 | + | 997.661i | −0.0790025 | + | 0.136836i | ||||
\(377\) | 2400.00 | 0.327868 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 0.00393042 | 0.00196521 | − | 0.999998i | \(-0.499374\pi\) | ||||
0.00196521 | + | 0.999998i | \(0.499374\pi\) | |||||||
\(380\) | 590.000 | − | 1021.91i | 0.0796483 | − | 0.137955i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1470.00 | − | 2546.11i | −0.196889 | − | 0.341022i | ||||
\(383\) | 4063.50 | + | 7038.19i | 0.542128 | + | 0.938994i | 0.998782 | + | 0.0493491i | \(0.0157147\pi\) |
−0.456653 | + | 0.889645i | \(0.650952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −420.000 | + | 727.461i | −0.0555979 | + | 0.0962983i | ||||
\(386\) | −9440.00 | −1.24478 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6176.00 | 0.808090 | ||||||||
\(389\) | −3969.00 | + | 6874.51i | −0.517317 | + | 0.896019i | 0.482481 | + | 0.875907i | \(0.339736\pi\) |
−0.999798 | + | 0.0201127i | \(0.993598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −418.500 | − | 724.863i | −0.0541290 | − | 0.0937542i | ||||
\(392\) | 1308.00 | + | 2265.52i | 0.168531 | + | 0.291903i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 765.000 | − | 1325.02i | 0.0978176 | − | 0.169425i | ||||
\(395\) | −3325.00 | −0.423542 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 272.000 | 0.0343861 | 0.0171931 | − | 0.999852i | \(-0.494527\pi\) | ||||
0.0171931 | + | 0.999852i | \(0.494527\pi\) | |||||||
\(398\) | −668.000 | + | 1157.01i | −0.0841302 | + | 0.145718i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −200.000 | − | 346.410i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 2277.00 | + | 3943.88i | 0.283561 | + | 0.491142i | 0.972259 | − | 0.233906i | \(-0.0751508\pi\) |
−0.688698 | + | 0.725048i | \(0.741817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −470.000 | + | 814.064i | −0.0580952 | + | 0.100624i | ||||
\(404\) | −528.000 | −0.0650222 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −960.000 | −0.117350 | ||||||||
\(407\) | 5502.00 | − | 9529.74i | 0.670084 | − | 1.16062i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −500.500 | − | 866.891i | −0.0605089 | − | 0.104804i | 0.834184 | − | 0.551486i | \(-0.185939\pi\) |
−0.894693 | + | 0.446682i | \(0.852606\pi\) | |||||||
\(410\) | 630.000 | + | 1091.19i | 0.0758865 | + | 0.131439i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1784.00 | − | 3089.98i | 0.213329 | − | 0.369496i | ||||
\(413\) | 1776.00 | 0.211601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −375.000 | −0.0443567 | ||||||||
\(416\) | −320.000 | + | 554.256i | −0.0377146 | + | 0.0653237i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2478.00 | − | 4292.02i | −0.289959 | − | 0.502224i | ||||
\(419\) | −897.000 | − | 1553.65i | −0.104585 | − | 0.181147i | 0.808983 | − | 0.587832i | \(-0.200018\pi\) |
−0.913569 | + | 0.406684i | \(0.866685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8064.50 | − | 13968.1i | 0.933586 | − | 1.61702i | 0.156450 | − | 0.987686i | \(-0.449995\pi\) |
0.777136 | − | 0.629332i | \(-0.216672\pi\) | |||||||
\(422\) | 9202.00 | 1.06148 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5928.00 | 0.678984 | ||||||||
\(425\) | −1162.50 | + | 2013.51i | −0.132681 | + | 0.229811i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 442.000 | + | 765.566i | 0.0500934 | + | 0.0867643i | ||||
\(428\) | 2280.00 | + | 3949.08i | 0.257495 | + | 0.445995i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −890.000 | + | 1541.53i | −0.0998130 | + | 0.172881i | ||||
\(431\) | 13356.0 | 1.49266 | 0.746329 | − | 0.665577i | \(-0.231814\pi\) | ||||
0.746329 | + | 0.665577i | \(0.231814\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11500.0 | −1.27634 | −0.638169 | − | 0.769896i | \(-0.720308\pi\) | ||||
−0.638169 | + | 0.769896i | \(0.720308\pi\) | |||||||
\(434\) | 188.000 | − | 325.626i | 0.0207933 | − | 0.0360150i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3470.00 | + | 6010.22i | 0.381153 | + | 0.660177i | ||||
\(437\) | −265.500 | − | 459.859i | −0.0290631 | − | 0.0503388i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5574.50 | − | 9655.32i | 0.606051 | − | 1.04971i | −0.385833 | − | 0.922568i | \(-0.626086\pi\) |
0.991884 | − | 0.127143i | \(-0.0405806\pi\) | |||||||
\(440\) | −1680.00 | −0.182025 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3720.00 | 0.400322 | ||||||||
\(443\) | 1924.50 | − | 3333.33i | 0.206401 | − | 0.357497i | −0.744177 | − | 0.667982i | \(-0.767158\pi\) |
0.950578 | + | 0.310485i | \(0.100491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2715.00 | − | 4702.52i | −0.289221 | − | 0.500945i | ||||
\(446\) | 2158.00 | + | 3737.77i | 0.229113 | + | 0.396835i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 128.000 | − | 221.703i | 0.0134987 | − | 0.0233805i | ||||
\(449\) | −18048.0 | −1.89697 | −0.948483 | − | 0.316828i | \(-0.897382\pi\) | ||||
−0.948483 | + | 0.316828i | \(0.897382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5292.00 | 0.552529 | ||||||||
\(452\) | 2868.00 | − | 4967.52i | 0.298450 | − | 0.516930i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3123.00 | − | 5409.19i | −0.322841 | − | 0.559176i | ||||
\(455\) | −200.000 | − | 346.410i | −0.0206069 | − | 0.0356922i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2132.00 | − | 3692.73i | 0.218229 | − | 0.377984i | −0.736037 | − | 0.676941i | \(-0.763305\pi\) |
0.954267 | + | 0.298957i | \(0.0966386\pi\) | |||||||
\(458\) | 4054.00 | 0.413605 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −180.000 | −0.0182447 | ||||||||
\(461\) | −5121.00 | + | 8869.83i | −0.517373 | + | 0.896116i | 0.482424 | + | 0.875938i | \(0.339757\pi\) |
−0.999796 | + | 0.0201776i | \(0.993577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1651.00 | − | 2859.62i | −0.165720 | − | 0.287036i | 0.771191 | − | 0.636604i | \(-0.219662\pi\) |
−0.936911 | + | 0.349568i | \(0.886328\pi\) | |||||||
\(464\) | −960.000 | − | 1662.77i | −0.0960493 | − | 0.166362i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 438.000 | − | 758.638i | 0.0435407 | − | 0.0754147i | ||||
\(467\) | 1923.00 | 0.190548 | 0.0952739 | − | 0.995451i | \(-0.469627\pi\) | ||||
0.0952739 | + | 0.995451i | \(0.469627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2152.00 | 0.211877 | ||||||||
\(470\) | 720.000 | − | 1247.08i | 0.0706620 | − | 0.122390i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1776.00 | + | 3076.12i | 0.173193 | + | 0.299979i | ||||
\(473\) | 3738.00 | + | 6474.41i | 0.363369 | + | 0.629373i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −737.500 | + | 1277.39i | −0.0712396 | + | 0.123391i | ||||
\(476\) | −1488.00 | −0.143282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12828.0 | 1.22749 | ||||||||
\(479\) | 7623.00 | − | 13203.4i | 0.727148 | − | 1.25946i | −0.230936 | − | 0.972969i | \(-0.574179\pi\) |
0.958084 | − | 0.286488i | \(-0.0924878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2620.00 | + | 4537.97i | 0.248361 | + | 0.430174i | ||||
\(482\) | −3431.00 | − | 5942.67i | −0.324228 | − | 0.561579i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −866.000 | + | 1499.96i | −0.0813298 | + | 0.140867i | ||||
\(485\) | −7720.00 | −0.722778 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8206.00 | −0.763551 | −0.381776 | − | 0.924255i | \(-0.624687\pi\) | ||||
−0.381776 | + | 0.924255i | \(0.624687\pi\) | |||||||
\(488\) | −884.000 | + | 1531.13i | −0.0820016 | + | 0.142031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1635.00 | − | 2831.90i | −0.150738 | − | 0.261086i | ||||
\(491\) | −8403.00 | − | 14554.4i | −0.772346 | − | 1.33774i | −0.936274 | − | 0.351271i | \(-0.885750\pi\) |
0.163928 | − | 0.986472i | \(-0.447584\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5580.00 | + | 9664.84i | −0.509758 | + | 0.882926i | ||||
\(494\) | 2360.00 | 0.214942 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 752.000 | 0.0680762 | ||||||||
\(497\) | 1380.00 | − | 2390.23i | 0.124550 | − | 0.215727i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2712.50 | + | 4698.19i | 0.243343 | + | 0.421483i | 0.961664 | − | 0.274229i | \(-0.0884226\pi\) |
−0.718321 | + | 0.695711i | \(0.755089\pi\) | |||||||
\(500\) | 250.000 | + | 433.013i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7308.00 | + | 12657.8i | −0.649745 | + | 1.12539i | ||||
\(503\) | 19665.0 | 1.74318 | 0.871589 | − | 0.490236i | \(-0.163090\pi\) | ||||
0.871589 | + | 0.490236i | \(0.163090\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 660.000 | 0.0581577 | ||||||||
\(506\) | −378.000 | + | 654.715i | −0.0332098 | + | 0.0575210i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1372.00 | − | 2376.37i | −0.119828 | − | 0.207548i | ||||
\(509\) | −7362.00 | − | 12751.4i | −0.641090 | − | 1.11040i | −0.985190 | − | 0.171468i | \(-0.945149\pi\) |
0.344100 | − | 0.938933i | \(-0.388184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2252.00 | + | 3900.58i | −0.194956 | + | 0.337674i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7458.00 | −0.639997 | ||||||||
\(515\) | −2230.00 | + | 3862.47i | −0.190807 | + | 0.330487i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3024.00 | − | 5237.72i | −0.257244 | − | 0.445560i | ||||
\(518\) | −1048.00 | − | 1815.19i | −0.0888928 | − | 0.153967i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 400.000 | − | 692.820i | 0.0337330 | − | 0.0584273i | ||||
\(521\) | −2058.00 | −0.173057 | −0.0865284 | − | 0.996249i | \(-0.527577\pi\) | ||||
−0.0865284 | + | 0.996249i | \(0.527577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11912.0 | 0.995938 | 0.497969 | − | 0.867195i | \(-0.334079\pi\) | ||||
0.497969 | + | 0.867195i | \(0.334079\pi\) | |||||||
\(524\) | 228.000 | − | 394.908i | 0.0190081 | − | 0.0329229i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1956.00 | + | 3387.89i | 0.162140 | + | 0.280835i | ||||
\(527\) | −2185.50 | − | 3785.40i | −0.180649 | − | 0.312893i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6043.00 | − | 10466.8i | 0.496671 | − | 0.860260i | ||||
\(530\) | −7410.00 | −0.607302 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −944.000 | −0.0769316 | ||||||||
\(533\) | −1260.00 | + | 2182.38i | −0.102395 | + | 0.177354i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2850.00 | − | 4936.34i | −0.230311 | − | 0.398910i | ||||
\(536\) | 2152.00 | + | 3727.37i | 0.173418 | + | 0.300369i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −990.000 | + | 1714.73i | −0.0793344 | + | 0.137411i | ||||
\(539\) | −13734.0 | −1.09752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5170.00 | −0.410861 | −0.205430 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205430 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(542\) | −8495.00 | + | 14713.8i | −0.673232 | + | 1.16607i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1488.00 | − | 2577.29i | −0.117275 | − | 0.203126i | ||||
\(545\) | −4337.50 | − | 7512.77i | −0.340914 | − | 0.590480i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2093.00 | − | 3625.18i | 0.163602 | − | 0.283367i | −0.772556 | − | 0.634947i | \(-0.781022\pi\) |
0.936158 | + | 0.351580i | \(0.114355\pi\) | |||||||
\(548\) | 636.000 | 0.0495777 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2100.00 | 0.162808 | ||||||||
\(551\) | −3540.00 | + | 6131.46i | −0.273701 | + | 0.474063i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1330.00 | + | 2303.63i | 0.102274 | + | 0.177143i | ||||
\(554\) | 1366.00 | + | 2365.98i | 0.104758 | + | 0.181446i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4552.00 | + | 7884.30i | −0.347208 | + | 0.601382i | ||||
\(557\) | −13026.0 | −0.990896 | −0.495448 | − | 0.868637i | \(-0.664996\pi\) | ||||
−0.495448 | + | 0.868637i | \(0.664996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3560.00 | −0.269359 | ||||||||
\(560\) | −160.000 | + | 277.128i | −0.0120736 | + | 0.0209121i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5520.00 | − | 9560.92i | −0.414319 | − | 0.717621i | ||||
\(563\) | −5334.00 | − | 9238.76i | −0.399292 | − | 0.691594i | 0.594347 | − | 0.804209i | \(-0.297411\pi\) |
−0.993639 | + | 0.112615i | \(0.964077\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3585.00 | + | 6209.40i | −0.266942 | + | 0.462357i | ||||
\(566\) | 10876.0 | 0.807690 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5520.00 | 0.407771 | ||||||||
\(569\) | −7686.00 | + | 13312.5i | −0.566281 | + | 0.980827i | 0.430648 | + | 0.902520i | \(0.358285\pi\) |
−0.996929 | + | 0.0783076i | \(0.975048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7494.50 | + | 12980.9i | 0.549273 | + | 0.951369i | 0.998325 | + | 0.0578633i | \(0.0184287\pi\) |
−0.449051 | + | 0.893506i | \(0.648238\pi\) | |||||||
\(572\) | −1680.00 | − | 2909.85i | −0.122805 | − | 0.212704i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 504.000 | − | 872.954i | 0.0366490 | − | 0.0634780i | ||||
\(575\) | 225.000 | 0.0163185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1066.00 | −0.0769119 | −0.0384559 | − | 0.999260i | \(-0.512244\pi\) | ||||
−0.0384559 | + | 0.999260i | \(0.512244\pi\) | |||||||
\(578\) | −3736.00 | + | 6470.94i | −0.268853 | + | 0.465667i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1200.00 | + | 2078.46i | 0.0859091 | + | 0.148799i | ||||
\(581\) | 150.000 | + | 259.808i | 0.0107109 | + | 0.0185519i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15561.0 | + | 26952.4i | −1.10544 | + | 1.91468i | ||||
\(584\) | −9008.00 | −0.638277 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16506.0 | −1.16358 | ||||||||
\(587\) | −310.500 | + | 537.802i | −0.0218325 | + | 0.0378151i | −0.876735 | − | 0.480973i | \(-0.840283\pi\) |
0.854903 | + | 0.518788i | \(0.173617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1386.50 | − | 2401.49i | −0.0969945 | − | 0.167999i | ||||
\(590\) | −2220.00 | − | 3845.15i | −0.154908 | − | 0.268309i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2096.00 | − | 3630.38i | 0.145515 | − | 0.252040i | ||||
\(593\) | 20187.0 | 1.39794 | 0.698972 | − | 0.715149i | \(-0.253641\pi\) | ||||
0.698972 | + | 0.715149i | \(0.253641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1860.00 | 0.128156 | ||||||||
\(596\) | 2796.00 | − | 4842.81i | 0.192162 | − | 0.332835i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −180.000 | − | 311.769i | −0.0123089 | − | 0.0213197i | ||||
\(599\) | −9114.00 | − | 15785.9i | −0.621683 | − | 1.07679i | −0.989172 | − | 0.146758i | \(-0.953116\pi\) |
0.367490 | − | 0.930028i | \(-0.380217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5871.50 | − | 10169.7i | 0.398508 | − | 0.690237i | −0.595034 | − | 0.803701i | \(-0.702861\pi\) |
0.993542 | + | 0.113464i | \(0.0361947\pi\) | |||||||
\(602\) | 1424.00 | 0.0964085 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10496.0 | 0.707080 | ||||||||
\(605\) | 1082.50 | − | 1874.94i | 0.0727436 | − | 0.125996i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12209.0 | + | 21146.6i | 0.816389 | + | 1.41403i | 0.908326 | + | 0.418262i | \(0.137361\pi\) |
−0.0919375 | + | 0.995765i | \(0.529306\pi\) | |||||||
\(608\) | −944.000 | − | 1635.06i | −0.0629675 | − | 0.109063i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1105.00 | − | 1913.92i | 0.0733445 | − | 0.127036i | ||||
\(611\) | 2880.00 | 0.190691 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2672.00 | 0.176054 | 0.0880270 | − | 0.996118i | \(-0.471944\pi\) | ||||
0.0880270 | + | 0.996118i | \(0.471944\pi\) | |||||||
\(614\) | −9290.00 | + | 16090.8i | −0.610609 | + | 1.05761i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 672.000 | + | 1163.94i | 0.0439540 | + | 0.0761305i | ||||
\(617\) | −4300.50 | − | 7448.68i | −0.280602 | − | 0.486017i | 0.690931 | − | 0.722921i | \(-0.257201\pi\) |
−0.971533 | + | 0.236903i | \(0.923868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10654.0 | + | 18453.3i | −0.691794 | + | 1.19822i | 0.279456 | + | 0.960159i | \(0.409846\pi\) |
−0.971250 | + | 0.238064i | \(0.923487\pi\) | |||||||
\(620\) | −940.000 | −0.0608892 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16224.0 | −1.04586 | ||||||||
\(623\) | −2172.00 | + | 3762.01i | −0.139678 | + | 0.241929i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 7900.00 | + | 13683.2i | 0.504389 | + | 0.873627i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 788.000 | − | 1364.86i | 0.0500711 | − | 0.0867256i | ||||
\(629\) | −24366.0 | −1.54457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19015.0 | −1.19964 | −0.599822 | − | 0.800134i | \(-0.704762\pi\) | ||||
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(632\) | −2660.00 | + | 4607.26i | −0.167419 | + | 0.289979i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4419.00 | + | 7653.93i | 0.276815 | + | 0.479458i | ||||
\(635\) | 1715.00 | + | 2970.47i | 0.107177 | + | 0.185637i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3270.00 | − | 5663.81i | 0.203394 | − | 0.352289i | ||||
\(638\) | 10080.0 | 0.625503 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | −2208.00 | + | 3824.37i | −0.136054 | + | 0.235653i | −0.926000 | − | 0.377524i | \(-0.876775\pi\) |
0.789945 | + | 0.613177i | \(0.210109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3790.00 | − | 6564.47i | −0.232446 | − | 0.402609i | 0.726081 | − | 0.687609i | \(-0.241340\pi\) |
−0.958527 | + | 0.285000i | \(0.908006\pi\) | |||||||
\(644\) | 72.0000 | + | 124.708i | 0.00440559 | + | 0.00763070i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5487.00 | + | 9503.76i | −0.334184 | + | 0.578824i | ||||
\(647\) | 14901.0 | 0.905439 | 0.452719 | − | 0.891653i | \(-0.350454\pi\) | ||||
0.452719 | + | 0.891653i | \(0.350454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18648.0 | −1.12789 | ||||||||
\(650\) | −500.000 | + | 866.025i | −0.0301717 | + | 0.0522589i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6692.00 | + | 11590.9i | 0.401962 | + | 0.696218i | ||||
\(653\) | 6457.50 | + | 11184.7i | 0.386985 | + | 0.670278i | 0.992042 | − | 0.125904i | \(-0.0401830\pi\) |
−0.605057 | + | 0.796182i | \(0.706850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −285.000 | + | 493.634i | −0.0170013 | + | 0.0294472i | ||||
\(656\) | 2016.00 | 0.119987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1152.00 | −0.0682517 | ||||||||
\(659\) | 14064.0 | − | 24359.6i | 0.831344 | − | 1.43993i | −0.0656288 | − | 0.997844i | \(-0.520905\pi\) |
0.896973 | − | 0.442086i | \(-0.145761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4181.00 | + | 7241.70i | 0.246024 | + | 0.426127i | 0.962419 | − | 0.271569i | \(-0.0875424\pi\) |
−0.716395 | + | 0.697695i | \(0.754209\pi\) | |||||||
\(662\) | 8200.00 | + | 14202.8i | 0.481423 | + | 0.833849i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −300.000 | + | 519.615i | −0.0175335 | + | 0.0303689i | ||||
\(665\) | 1180.00 | 0.0688097 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1080.00 | 0.0626953 | ||||||||
\(668\) | 2982.00 | − | 5164.98i | 0.172720 | − | 0.299160i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2690.00 | − | 4659.22i | −0.155110 | − | 0.268659i | ||||
\(671\) | −4641.00 | − | 8038.45i | −0.267010 | − | 0.462475i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14854.0 | + | 25727.9i | −0.850787 | + | 1.47361i | 0.0297122 | + | 0.999558i | \(0.490541\pi\) |
−0.880499 | + | 0.474048i | \(0.842792\pi\) | |||||||
\(674\) | −19112.0 | −1.09224 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7188.00 | −0.408967 | ||||||||
\(677\) | 3381.00 | − | 5856.06i | 0.191939 | − | 0.332447i | −0.753954 | − | 0.656927i | \(-0.771856\pi\) |
0.945893 | + | 0.324480i | \(0.105189\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3088.00 | + | 5348.57i | 0.174531 | + | 0.302297i | ||||
\(680\) | 1860.00 | + | 3221.61i | 0.104894 | + | 0.181681i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1974.00 | + | 3419.07i | −0.110833 | + | 0.191969i | ||||
\(683\) | 19155.0 | 1.07313 | 0.536563 | − | 0.843860i | \(-0.319722\pi\) | ||||
0.536563 | + | 0.843860i | \(0.319722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −795.000 | −0.0443436 | ||||||||
\(686\) | −2680.00 | + | 4641.90i | −0.149159 | + | 0.258350i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1424.00 | + | 2466.44i | 0.0789091 | + | 0.136675i | ||||
\(689\) | −7410.00 | − | 12834.5i | −0.409722 | − | 0.709659i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11487.5 | − | 19896.9i | 0.632424 | − | 1.09539i | −0.354630 | − | 0.935007i | \(-0.615393\pi\) |
0.987055 | − | 0.160384i | \(-0.0512733\pi\) | |||||||
\(692\) | 9612.00 | 0.528025 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20232.0 | −1.10662 | ||||||||
\(695\) | 5690.00 | − | 9855.37i | 0.310553 | − | 0.537893i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5859.00 | − | 10148.1i | −0.318401 | − | 0.551487i | ||||
\(698\) | 6751.00 | + | 11693.1i | 0.366088 | + | 0.634082i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 200.000 | − | 346.410i | 0.0107990 | − | 0.0187044i | ||||
\(701\) | 6450.00 | 0.347522 | 0.173761 | − | 0.984788i | \(-0.444408\pi\) | ||||
0.173761 | + | 0.984788i | \(0.444408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15458.0 | −0.829317 | ||||||||
\(704\) | −1344.00 | + | 2327.88i | −0.0719516 | + | 0.124624i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4062.00 | + | 7035.59i | 0.216537 | + | 0.375054i | ||||
\(707\) | −264.000 | − | 457.261i | −0.0140435 | − | 0.0243240i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17269.0 | + | 29910.8i | −0.914740 | + | 1.58438i | −0.107459 | + | 0.994209i | \(0.534272\pi\) |
−0.807281 | + | 0.590167i | \(0.799062\pi\) | |||||||
\(710\) | −6900.00 | −0.364722 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8688.00 | −0.457299 | ||||||||
\(713\) | −211.500 | + | 366.329i | −0.0111090 | + | 0.0192414i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2100.00 | + | 3637.31i | 0.109840 | + | 0.190248i | ||||
\(716\) | 5280.00 | + | 9145.23i | 0.275591 | + | 0.477337i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8778.00 | − | 15203.9i | 0.456256 | − | 0.790259i | ||||
\(719\) | −27114.0 | −1.40637 | −0.703186 | − | 0.711006i | \(-0.748240\pi\) | ||||
−0.703186 | + | 0.711006i | \(0.748240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3568.00 | 0.184299 | ||||||||
\(722\) | 3378.00 | − | 5850.87i | 0.174122 | − | 0.301588i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2146.00 | − | 3716.98i | −0.110159 | − | 0.190802i | ||||
\(725\) | −1500.00 | − | 2598.08i | −0.0768395 | − | 0.133090i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −118.000 | + | 204.382i | −0.00601978 | + | 0.0104266i | −0.869020 | − | 0.494778i | \(-0.835249\pi\) |
0.863000 | + | 0.505204i | \(0.168583\pi\) | |||||||
\(728\) | −640.000 | −0.0325824 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11260.0 | 0.570892 | ||||||||
\(731\) | 8277.00 | − | 14336.2i | 0.418791 | − | 0.725367i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13564.0 | − | 23493.5i | −0.683489 | − | 1.18384i | −0.973909 | − | 0.226939i | \(-0.927128\pi\) |
0.290420 | − | 0.956899i | \(-0.406205\pi\) | |||||||
\(734\) | −956.000 | − | 1655.84i | −0.0480744 | − | 0.0832673i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −144.000 | + | 249.415i | −0.00721183 | + | 0.0124913i | ||||
\(737\) | −22596.0 | −1.12935 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5249.00 | 0.261282 | 0.130641 | − | 0.991430i | \(-0.458296\pi\) | ||||
0.130641 | + | 0.991430i | \(0.458296\pi\) | |||||||
\(740\) | −2620.00 | + | 4537.97i | −0.130153 | + | 0.225431i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2964.00 | + | 5133.80i | 0.146647 | + | 0.254000i | ||||
\(743\) | 6948.00 | + | 12034.3i | 0.343065 | + | 0.594206i | 0.985000 | − | 0.172553i | \(-0.0552015\pi\) |
−0.641935 | + | 0.766759i | \(0.721868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3495.00 | + | 6053.52i | −0.171875 | + | 0.297696i | ||||
\(746\) | 4600.00 | 0.225761 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15624.0 | 0.763730 | ||||||||
\(749\) | −2280.00 | + | 3949.08i | −0.111227 | + | 0.192652i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13832.5 | − | 23958.6i | −0.672111 | − | 1.16413i | −0.977304 | − | 0.211840i | \(-0.932055\pi\) |
0.305194 | − | 0.952290i | \(-0.401279\pi\) | |||||||
\(752\) | −1152.00 | − | 1995.32i | −0.0558632 | − | 0.0967579i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2400.00 | + | 4156.92i | −0.115919 | + | 0.200777i | ||||
\(755\) | −13120.0 | −0.632431 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8122.00 | −0.389959 | −0.194980 | − | 0.980807i | \(-0.562464\pi\) | ||||
−0.194980 | + | 0.980807i | \(0.562464\pi\) | |||||||
\(758\) | −29.0000 | + | 50.2295i | −0.00138961 | + | 0.00240688i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1180.00 | + | 2043.82i | 0.0563199 | + | 0.0975489i | ||||
\(761\) | 5292.00 | + | 9166.01i | 0.252083 | + | 0.436620i | 0.964099 | − | 0.265543i | \(-0.0855512\pi\) |
−0.712016 | + | 0.702163i | \(0.752218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3470.00 | + | 6010.22i | −0.164643 | + | 0.285170i | ||||
\(764\) | 5880.00 | 0.278444 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16254.0 | −0.766685 | ||||||||
\(767\) | 4440.00 | − | 7690.31i | 0.209021 | − | 0.362035i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9309.50 | + | 16124.5i | 0.436553 | + | 0.756132i | 0.997421 | − | 0.0717734i | \(-0.0228659\pi\) |
−0.560868 | + | 0.827905i | \(0.689533\pi\) | |||||||
\(770\) | −840.000 | − | 1454.92i | −0.0393136 | − | 0.0680932i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9440.00 | − | 16350.6i | 0.440095 | − | 0.762266i | ||||
\(773\) | −22251.0 | −1.03533 | −0.517667 | − | 0.855582i | \(-0.673199\pi\) | ||||
−0.517667 | + | 0.855582i | \(0.673199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1175.00 | 0.0544610 | ||||||||
\(776\) | −6176.00 | + | 10697.1i | −0.285703 | + | 0.494852i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7938.00 | − | 13749.0i | −0.365798 | − | 0.633581i | ||||
\(779\) | −3717.00 | − | 6438.03i | −0.170957 | − | 0.296106i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14490.0 | + | 25097.4i | −0.663883 | + | 1.14988i | ||||
\(782\) | 1674.00 | 0.0765500 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5232.00 | −0.238338 | ||||||||
\(785\) | −985.000 | + | 1706.07i | −0.0447849 | + | 0.0775697i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12427.0 | − | 21524.2i | −0.562865 | − | 0.974911i | −0.997245 | − | 0.0741809i | \(-0.976366\pi\) |
0.434380 | − | 0.900730i | \(-0.356968\pi\) | |||||||
\(788\) | 1530.00 | + | 2650.04i | 0.0691675 | + | 0.119802i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3325.00 | − | 5759.07i | 0.149745 | − | 0.259365i | ||||
\(791\) | 5736.00 | 0.257837 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4420.00 | 0.197930 | ||||||||
\(794\) | −272.000 | + | 471.118i | −0.0121573 | + | 0.0210571i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1336.00 | − | 2314.02i | −0.0594890 | − | 0.103038i | ||||
\(797\) | 1840.50 | + | 3187.84i | 0.0817991 | + | 0.141680i | 0.904023 | − | 0.427484i | \(-0.140600\pi\) |
−0.822224 | + | 0.569164i | \(0.807267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6696.00 | + | 11597.8i | −0.296480 | + | 0.513518i | ||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9108.00 | −0.401016 | ||||||||
\(803\) | 23646.0 | − | 40956.1i | 1.03916 | − | 1.79989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −90.0000 | − | 155.885i | −0.00394048 | − | 0.00682510i | ||||
\(806\) | −940.000 | − | 1628.13i | −0.0410795 | − | 0.0711518i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 528.000 | − | 914.523i | 0.0229888 | − | 0.0398178i | ||||
\(809\) | 5142.00 | 0.223465 | 0.111732 | − | 0.993738i | \(-0.464360\pi\) | ||||
0.111732 | + | 0.993738i | \(0.464360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18484.0 | −0.800322 | −0.400161 | − | 0.916445i | \(-0.631046\pi\) | ||||
−0.400161 | + | 0.916445i | \(0.631046\pi\) | |||||||
\(812\) | 960.000 | − | 1662.77i | 0.0414894 | − | 0.0718618i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11004.0 | + | 19059.5i | 0.473821 | + | 0.820681i | ||||
\(815\) | −8365.00 | − | 14488.6i | −0.359525 | − | 0.622716i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5251.00 | − | 9095.00i | 0.224858 | − | 0.389466i | ||||
\(818\) | 2002.00 | 0.0855725 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2520.00 | −0.107320 | ||||||||
\(821\) | 12507.0 | − | 21662.8i | 0.531665 | − | 0.920872i | −0.467651 | − | 0.883913i | \(-0.654900\pi\) |
0.999317 | − | 0.0369585i | \(-0.0117669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16073.0 | + | 27839.3i | 0.680765 | + | 1.17912i | 0.974748 | + | 0.223309i | \(0.0716858\pi\) |
−0.293983 | + | 0.955811i | \(0.594981\pi\) | |||||||
\(824\) | 3568.00 | + | 6179.96i | 0.150846 | + | 0.261273i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1776.00 | + | 3076.12i | −0.0748123 | + | 0.129579i | ||||
\(827\) | 10977.0 | 0.461557 | 0.230779 | − | 0.973006i | \(-0.425873\pi\) | ||||
0.230779 | + | 0.973006i | \(0.425873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36602.0 | 1.53346 | 0.766731 | − | 0.641969i | \(-0.221882\pi\) | ||||
0.766731 | + | 0.641969i | \(0.221882\pi\) | |||||||
\(830\) | 375.000 | − | 649.519i | 0.0156825 | − | 0.0271628i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −640.000 | − | 1108.51i | −0.0266683 | − | 0.0461908i | ||||
\(833\) | 15205.5 | + | 26336.7i | 0.632460 | + | 1.09545i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3727.50 | + | 6456.22i | −0.154486 | + | 0.267577i | ||||
\(836\) | 9912.00 | 0.410064 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3588.00 | 0.147906 | ||||||||
\(839\) | 5538.00 | − | 9592.10i | 0.227882 | − | 0.394703i | −0.729298 | − | 0.684196i | \(-0.760153\pi\) |
0.957180 | + | 0.289493i | \(0.0934866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4994.50 | + | 8650.73i | 0.204785 | + | 0.354698i | ||||
\(842\) | 16129.0 | + | 27936.2i | 0.660145 | + | 1.14340i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9202.00 | + | 15938.3i | −0.375291 | + | 0.650024i | ||||
\(845\) | 8985.00 | 0.365791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1732.00 | −0.0702624 | ||||||||
\(848\) | −5928.00 | + | 10267.6i | −0.240057 | + | 0.415791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2325.00 | − | 4027.02i | −0.0938198 | − | 0.162501i | ||||
\(851\) | 1179.00 | + | 2042.09i | 0.0474919 | + | 0.0822584i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18424.0 | + | 31911.3i | −0.739538 | + | 1.28092i | 0.213166 | + | 0.977016i | \(0.431623\pi\) |
−0.952704 | + | 0.303901i | \(0.901711\pi\) | |||||||
\(854\) | −1768.00 | −0.0708428 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9120.00 | −0.364153 | ||||||||
\(857\) | −13480.5 | + | 23348.9i | −0.537322 | + | 0.930669i | 0.461725 | + | 0.887023i | \(0.347231\pi\) |
−0.999047 | + | 0.0436461i | \(0.986103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 207.500 | + | 359.401i | 0.00824192 | + | 0.0142754i | 0.870117 | − | 0.492845i | \(-0.164043\pi\) |
−0.861875 | + | 0.507121i | \(0.830710\pi\) | |||||||
\(860\) | −1780.00 | − | 3083.05i | −0.0705785 | − | 0.122246i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13356.0 | + | 23133.3i | −0.527735 | + | 0.914063i | ||||
\(863\) | 45501.0 | 1.79475 | 0.897377 | − | 0.441265i | \(-0.145470\pi\) | ||||
0.897377 | + | 0.441265i | \(0.145470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12015.0 | −0.472280 | ||||||||
\(866\) | 11500.0 | − | 19918.6i | 0.451254 | − | 0.781595i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 376.000 | + | 651.251i | 0.0147031 | + | 0.0254665i | ||||
\(869\) | −13965.0 | − | 24188.1i | −0.545144 | − | 0.944217i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5380.00 | − | 9318.43i | 0.209293 | − | 0.362506i | ||||
\(872\) | −13880.0 | −0.539032 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1062.00 | 0.0411015 | ||||||||
\(875\) | −250.000 | + | 433.013i | −0.00965891 | + | 0.0167297i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17521.0 | − | 30347.3i | −0.674620 | − | 1.16848i | −0.976580 | − | 0.215156i | \(-0.930974\pi\) |
0.301959 | − | 0.953321i | \(-0.402359\pi\) | |||||||
\(878\) | 11149.0 | + | 19310.6i | 0.428543 | + | 0.742258i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1680.00 | − | 2909.85i | 0.0643554 | − | 0.111467i | ||||
\(881\) | −1080.00 | −0.0413009 | −0.0206505 | − | 0.999787i | \(-0.506574\pi\) | ||||
−0.0206505 | + | 0.999787i | \(0.506574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20164.0 | −0.768485 | −0.384243 | − | 0.923232i | \(-0.625537\pi\) | ||||
−0.384243 | + | 0.923232i | \(0.625537\pi\) | |||||||
\(884\) | −3720.00 | + | 6443.23i | −0.141535 | + | 0.245146i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3849.00 | + | 6666.66i | 0.145948 | + | 0.252789i | ||||
\(887\) | 10033.5 | + | 17378.5i | 0.379811 | + | 0.657851i | 0.991034 | − | 0.133607i | \(-0.0426558\pi\) |
−0.611224 | + | 0.791458i | \(0.709323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1372.00 | − | 2376.37i | 0.0517609 | − | 0.0896524i | ||||
\(890\) | 10860.0 | 0.409020 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8632.00 | −0.324014 | ||||||||
\(893\) | −4248.00 | + | 7357.75i | −0.159187 | + | 0.275720i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6600.00 | − | 11431.5i | −0.246496 | − | 0.426943i | ||||
\(896\) | 256.000 | + | 443.405i | 0.00954504 | + | 0.0165325i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18048.0 | − | 31260.1i | 0.670679 | − | 1.16165i | ||||
\(899\) | 5640.00 | 0.209238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68913.0 | 2.54809 | ||||||||
\(902\) | −5292.00 | + | 9166.01i | −0.195348 | + | 0.338353i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5736.00 | + | 9935.04i | 0.211036 | + | 0.365525i | ||||
\(905\) | 2682.50 | + | 4646.23i | 0.0985296 | + | 0.170658i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13262.0 | − | 22970.5i | 0.485510 | − | 0.840928i | −0.514351 | − | 0.857579i | \(-0.671967\pi\) |
0.999861 | + | 0.0166517i | \(0.00530064\pi\) | |||||||
\(908\) | 12492.0 | 0.456566 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 800.000 | 0.0291426 | ||||||||
\(911\) | 17784.0 | − | 30802.8i | 0.646773 | − | 1.12024i | −0.337116 | − | 0.941463i | \(-0.609451\pi\) |
0.983889 | − | 0.178781i | \(-0.0572152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1575.00 | − | 2727.98i | −0.0570919 | − | 0.0988860i | ||||
\(914\) | 4264.00 | + | 7385.46i | 0.154311 | + | 0.267275i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4054.00 | + | 7021.73i | −0.146231 | + | 0.253280i | ||||
\(917\) | 456.000 | 0.0164214 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23704.0 | −0.850841 | −0.425420 | − | 0.904996i | \(-0.639874\pi\) | ||||
−0.425420 | + | 0.904996i | \(0.639874\pi\) | |||||||
\(920\) | 180.000 | − | 311.769i | 0.00645046 | − | 0.0111725i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10242.0 | − | 17739.7i | −0.365838 | − | 0.633649i | ||||
\(923\) | −6900.00 | − | 11951.2i | −0.246063 | − | 0.426194i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3275.00 | − | 5672.47i | 0.116412 | − | 0.201632i | ||||
\(926\) | 6604.00 | 0.234364 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3840.00 | 0.135834 | ||||||||
\(929\) | −20295.0 | + | 35152.0i | −0.716746 | + | 1.24144i | 0.245536 | + | 0.969388i | \(0.421036\pi\) |
−0.962282 | + | 0.272054i | \(0.912297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9646.50 | + | 16708.2i | 0.339582 | + | 0.588174i | ||||
\(932\) | 876.000 | + | 1517.28i | 0.0307879 | + | 0.0533262i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1923.00 | + | 3330.73i | −0.0673688 | + | 0.116686i | ||||
\(935\) | −19530.0 | −0.683101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12964.0 | −0.451991 | −0.225995 | − | 0.974128i | \(-0.572563\pi\) | ||||
−0.225995 | + | 0.974128i | \(0.572563\pi\) | |||||||
\(938\) | −2152.00 | + | 3727.37i | −0.0749097 | + | 0.129747i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1440.00 | + | 2494.15i | 0.0499656 | + | 0.0865429i | ||||
\(941\) | 14961.0 | + | 25913.2i | 0.518294 | + | 0.897712i | 0.999774 | + | 0.0212545i | \(0.00676604\pi\) |
−0.481480 | + | 0.876457i | \(0.659901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −567.000 | + | 982.073i | −0.0195801 | + | 0.0339138i | ||||
\(944\) | −7104.00 | −0.244932 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14952.0 | −0.513881 | ||||||||
\(947\) | 2620.50 | − | 4538.84i | 0.0899206 | − | 0.155747i | −0.817557 | − | 0.575848i | \(-0.804672\pi\) |
0.907477 | + | 0.420101i | \(0.138005\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11260.0 | + | 19502.9i | 0.385158 | + | 0.667113i | ||||
\(950\) | −1475.00 | − | 2554.77i | −0.0503740 | − | 0.0872504i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1488.00 | − | 2577.29i | 0.0506579 | − | 0.0877421i | ||||
\(953\) | −26214.0 | −0.891033 | −0.445517 | − | 0.895274i | \(-0.646980\pi\) | ||||
−0.445517 | + | 0.895274i | \(0.646980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7350.00 | −0.249048 | ||||||||
\(956\) | −12828.0 | + | 22218.7i | −0.433982 | + | 0.751680i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15246.0 | + | 26406.8i | 0.514171 | + | 0.890570i | ||||
\(959\) | 318.000 | + | 550.792i | 0.0107078 | + | 0.0185464i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13791.0 | − | 23886.7i | 0.462925 | − | 0.801810i | ||||
\(962\) | −10480.0 | −0.351236 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13724.0 | 0.458527 | ||||||||
\(965\) | −11800.0 | + | 20438.2i | −0.393633 | + | 0.681792i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9139.00 | − | 15829.2i | −0.303920 | − | 0.526405i | 0.673100 | − | 0.739551i | \(-0.264962\pi\) |
−0.977020 | + | 0.213147i | \(0.931629\pi\) | |||||||
\(968\) | −1732.00 | − | 2999.91i | −0.0575089 | − | 0.0996083i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7720.00 | − | 13371.4i | 0.255540 | − | 0.442609i | ||||
\(971\) | 24942.0 | 0.824333 | 0.412166 | − | 0.911109i | \(-0.364772\pi\) | ||||
0.412166 | + | 0.911109i | \(0.364772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9104.00 | −0.299960 | ||||||||
\(974\) | 8206.00 | − | 14213.2i | 0.269956 | − | 0.467578i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1768.00 | − | 3062.27i | −0.0579839 | − | 0.100431i | ||||
\(977\) | −5613.00 | − | 9722.00i | −0.183803 | − | 0.318357i | 0.759369 | − | 0.650660i | \(-0.225508\pi\) |
−0.943173 | + | 0.332303i | \(0.892174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22806.0 | − | 39501.2i | 0.744518 | − | 1.28954i | ||||
\(980\) | 6540.00 | 0.213176 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33612.0 | 1.09226 | ||||||||
\(983\) | −11536.5 | + | 19981.8i | −0.374321 | + | 0.648342i | −0.990225 | − | 0.139478i | \(-0.955457\pi\) |
0.615904 | + | 0.787821i | \(0.288791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1912.50 | − | 3312.55i | −0.0618653 | − | 0.107154i | ||||
\(986\) | −11160.0 | − | 19329.7i | −0.360453 | − | 0.624323i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2360.00 | + | 4087.64i | −0.0759935 | + | 0.131625i | ||||
\(989\) | −1602.00 | −0.0515072 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22037.0 | 0.706386 | 0.353193 | − | 0.935551i | \(-0.385096\pi\) | ||||
0.353193 | + | 0.935551i | \(0.385096\pi\) | |||||||
\(992\) | −752.000 | + | 1302.50i | −0.0240686 | + | 0.0416880i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2760.00 | + | 4780.46i | 0.0880703 | + | 0.152542i | ||||
\(995\) | 1670.00 | + | 2892.52i | 0.0532086 | + | 0.0921600i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9541.00 | + | 16525.5i | −0.303076 | + | 0.524943i | −0.976831 | − | 0.214012i | \(-0.931347\pi\) |
0.673755 | + | 0.738955i | \(0.264680\pi\) | |||||||
\(998\) | −10850.0 | −0.344139 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 810.4.e.h.541.1 | 2 | ||
3.2 | odd | 2 | 810.4.e.q.541.1 | 2 | |||
9.2 | odd | 6 | 270.4.a.e.1.1 | ✓ | 1 | ||
9.4 | even | 3 | inner | 810.4.e.h.271.1 | 2 | ||
9.5 | odd | 6 | 810.4.e.q.271.1 | 2 | |||
9.7 | even | 3 | 270.4.a.i.1.1 | yes | 1 | ||
36.7 | odd | 6 | 2160.4.a.e.1.1 | 1 | |||
36.11 | even | 6 | 2160.4.a.o.1.1 | 1 | |||
45.2 | even | 12 | 1350.4.c.d.649.1 | 2 | |||
45.7 | odd | 12 | 1350.4.c.q.649.2 | 2 | |||
45.29 | odd | 6 | 1350.4.a.u.1.1 | 1 | |||
45.34 | even | 6 | 1350.4.a.g.1.1 | 1 | |||
45.38 | even | 12 | 1350.4.c.d.649.2 | 2 | |||
45.43 | odd | 12 | 1350.4.c.q.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.e.1.1 | ✓ | 1 | 9.2 | odd | 6 | ||
270.4.a.i.1.1 | yes | 1 | 9.7 | even | 3 | ||
810.4.e.h.271.1 | 2 | 9.4 | even | 3 | inner | ||
810.4.e.h.541.1 | 2 | 1.1 | even | 1 | trivial | ||
810.4.e.q.271.1 | 2 | 9.5 | odd | 6 | |||
810.4.e.q.541.1 | 2 | 3.2 | odd | 2 | |||
1350.4.a.g.1.1 | 1 | 45.34 | even | 6 | |||
1350.4.a.u.1.1 | 1 | 45.29 | odd | 6 | |||
1350.4.c.d.649.1 | 2 | 45.2 | even | 12 | |||
1350.4.c.d.649.2 | 2 | 45.38 | even | 12 | |||
1350.4.c.q.649.1 | 2 | 45.43 | odd | 12 | |||
1350.4.c.q.649.2 | 2 | 45.7 | odd | 12 | |||
2160.4.a.e.1.1 | 1 | 36.7 | odd | 6 | |||
2160.4.a.o.1.1 | 1 | 36.11 | even | 6 |