Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.o.271.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 0.633975i | 0.129410 | − | 0.224144i | −0.794038 | − | 0.607868i | \(-0.792025\pi\) |
0.923448 | + | 0.383724i | \(0.125358\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.73205 | + | 6.46410i | 0.466506 | + | 0.808013i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | − | 6.00000i | 0.187044 | − | 0.323970i | −0.757219 | − | 0.653161i | \(-0.773443\pi\) |
0.944263 | + | 0.329191i | \(0.106776\pi\) | |||||||
\(8\) | 11.3205 | 0.500301 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.66025 | −0.115747 | ||||||||
\(11\) | −18.7487 | + | 32.4737i | −0.513904 | + | 0.890109i | 0.485965 | + | 0.873978i | \(0.338468\pi\) |
−0.999870 | + | 0.0161306i | \(0.994865\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.4641 | + | 33.7128i | 0.415259 | + | 0.719250i | 0.995456 | − | 0.0952265i | \(-0.0303575\pi\) |
−0.580196 | + | 0.814477i | \(0.697024\pi\) | |||||||
\(14\) | −2.53590 | − | 4.39230i | −0.0484105 | − | 0.0838495i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −25.7128 | + | 44.5359i | −0.401763 | + | 0.695873i | ||||
\(17\) | −80.9948 | −1.15554 | −0.577769 | − | 0.816201i | \(-0.696076\pi\) | ||||
−0.577769 | + | 0.816201i | \(0.696076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 112.779 | 1.36176 | 0.680878 | − | 0.732396i | \(-0.261598\pi\) | ||||
0.680878 | + | 0.732396i | \(0.261598\pi\) | |||||||
\(20\) | 18.6603 | − | 32.3205i | 0.208628 | − | 0.361354i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.7250 | + | 23.7724i | 0.133008 | + | 0.230377i | ||||
\(23\) | −6.71281 | − | 11.6269i | −0.0608573 | − | 0.105408i | 0.833992 | − | 0.551777i | \(-0.186050\pi\) |
−0.894849 | + | 0.446369i | \(0.852717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 28.4974 | 0.214954 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 51.7128 | 0.349029 | ||||||||
\(29\) | 21.7154 | − | 37.6122i | 0.139050 | − | 0.240841i | −0.788087 | − | 0.615563i | \(-0.788928\pi\) |
0.927137 | + | 0.374722i | \(0.122262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 74.8923 | + | 129.717i | 0.433905 | + | 0.751546i | 0.997206 | − | 0.0747066i | \(-0.0238020\pi\) |
−0.563301 | + | 0.826252i | \(0.690469\pi\) | |||||||
\(32\) | 64.1051 | + | 111.033i | 0.354134 | + | 0.613378i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −29.6462 | + | 51.3487i | −0.149538 | + | 0.259007i | ||||
\(35\) | −34.6410 | −0.167297 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −218.344 | −0.970147 | −0.485074 | − | 0.874473i | \(-0.661207\pi\) | ||||
−0.485074 | + | 0.874473i | \(0.661207\pi\) | |||||||
\(38\) | 41.2801 | − | 71.4993i | 0.176224 | − | 0.305229i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −28.3013 | − | 49.0192i | −0.111871 | − | 0.193766i | ||||
\(41\) | 186.069 | + | 322.281i | 0.708759 | + | 1.22761i | 0.965318 | + | 0.261078i | \(0.0840781\pi\) |
−0.256558 | + | 0.966529i | \(0.582589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −230.100 | + | 398.545i | −0.816045 | + | 1.41343i | 0.0925309 | + | 0.995710i | \(0.470504\pi\) |
−0.908575 | + | 0.417721i | \(0.862829\pi\) | |||||||
\(44\) | −279.885 | −0.958959 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.82824 | −0.0315021 | ||||||||
\(47\) | 107.144 | − | 185.578i | 0.332521 | − | 0.575944i | −0.650484 | − | 0.759520i | \(-0.725434\pi\) |
0.983006 | + | 0.183576i | \(0.0587673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 147.500 | + | 255.477i | 0.430029 | + | 0.744832i | ||||
\(50\) | 9.15064 | + | 15.8494i | 0.0258819 | + | 0.0448288i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −145.282 | + | 251.636i | −0.387442 | + | 0.671070i | ||||
\(53\) | −445.205 | −1.15384 | −0.576921 | − | 0.816800i | \(-0.695746\pi\) | ||||
−0.576921 | + | 0.816800i | \(0.695746\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.487 | 0.459650 | ||||||||
\(56\) | 39.2154 | − | 67.9230i | 0.0935782 | − | 0.162082i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.8968 | − | 27.5340i | −0.0359888 | − | 0.0623344i | ||||
\(59\) | 200.749 | + | 347.707i | 0.442970 | + | 0.767247i | 0.997908 | − | 0.0646445i | \(-0.0205913\pi\) |
−0.554938 | + | 0.831892i | \(0.687258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.723122 | + | 1.25248i | −0.00151781 | + | 0.00262892i | −0.866783 | − | 0.498685i | \(-0.833816\pi\) |
0.865266 | + | 0.501314i | \(0.167150\pi\) | |||||||
\(62\) | 109.650 | 0.224606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −317.549 | −0.620212 | ||||||||
\(65\) | 97.3205 | − | 168.564i | 0.185710 | − | 0.321658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 408.033 | + | 706.734i | 0.744018 | + | 1.28868i | 0.950652 | + | 0.310259i | \(0.100416\pi\) |
−0.206634 | + | 0.978418i | \(0.566251\pi\) | |||||||
\(68\) | −302.277 | − | 523.559i | −0.539066 | − | 0.933689i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.6795 | + | 21.9615i | −0.0216498 | + | 0.0374986i | ||||
\(71\) | −147.518 | −0.246580 | −0.123290 | − | 0.992371i | \(-0.539345\pi\) | ||||
−0.123290 | + | 0.992371i | \(0.539345\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 432.651 | 0.693671 | 0.346836 | − | 0.937926i | \(-0.387256\pi\) | ||||
0.346836 | + | 0.937926i | \(0.387256\pi\) | |||||||
\(74\) | −79.9193 | + | 138.424i | −0.125546 | + | 0.217453i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 420.899 | + | 729.018i | 0.635268 | + | 1.10032i | ||||
\(77\) | 129.895 | + | 224.985i | 0.192245 | + | 0.332979i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −192.067 | + | 332.669i | −0.273534 | + | 0.473775i | −0.969764 | − | 0.244044i | \(-0.921526\pi\) |
0.696230 | + | 0.717819i | \(0.254859\pi\) | |||||||
\(80\) | 257.128 | 0.359347 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 272.424 | 0.366881 | ||||||||
\(83\) | 630.615 | − | 1092.26i | 0.833964 | − | 1.44447i | −0.0609071 | − | 0.998143i | \(-0.519399\pi\) |
0.894871 | − | 0.446325i | \(-0.147267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 202.487 | + | 350.718i | 0.258386 | + | 0.447538i | ||||
\(86\) | 168.445 | + | 291.755i | 0.211208 | + | 0.365823i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −212.245 | + | 367.619i | −0.257107 | + | 0.445322i | ||||
\(89\) | −513.000 | −0.610988 | −0.305494 | − | 0.952194i | \(-0.598822\pi\) | ||||
−0.305494 | + | 0.952194i | \(0.598822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 269.703 | 0.310687 | ||||||||
\(92\) | 50.1051 | − | 86.7846i | 0.0567806 | − | 0.0983470i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −78.4346 | − | 135.853i | −0.0860628 | − | 0.149065i | ||||
\(95\) | −281.949 | − | 488.349i | −0.304498 | − | 0.527406i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 548.051 | − | 949.252i | 0.573672 | − | 0.993629i | −0.422513 | − | 0.906357i | \(-0.638852\pi\) |
0.996185 | − | 0.0872717i | \(-0.0278148\pi\) | |||||||
\(98\) | 215.955 | 0.222599 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −186.603 | −0.186603 | ||||||||
\(101\) | −597.043 | + | 1034.11i | −0.588198 | + | 1.01879i | 0.406270 | + | 0.913753i | \(0.366829\pi\) |
−0.994468 | + | 0.105036i | \(0.966504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −90.7513 | − | 157.186i | −0.0868154 | − | 0.150369i | 0.819348 | − | 0.573297i | \(-0.194336\pi\) |
−0.906163 | + | 0.422928i | \(0.861002\pi\) | |||||||
\(104\) | 220.344 | + | 381.646i | 0.207754 | + | 0.359841i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −162.956 | + | 282.249i | −0.149318 | + | 0.258627i | ||||
\(107\) | 611.667 | 0.552636 | 0.276318 | − | 0.961066i | \(-0.410886\pi\) | ||||
0.276318 | + | 0.961066i | \(0.410886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 550.467 | 0.483717 | 0.241859 | − | 0.970312i | \(-0.422243\pi\) | ||||
0.241859 | + | 0.970312i | \(0.422243\pi\) | |||||||
\(110\) | 68.6250 | − | 118.862i | 0.0594831 | − | 0.103028i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 178.144 | + | 308.554i | 0.150295 | + | 0.260318i | ||||
\(113\) | 237.951 | + | 412.144i | 0.198094 | + | 0.343108i | 0.947910 | − | 0.318538i | \(-0.103192\pi\) |
−0.749817 | + | 0.661646i | \(0.769858\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −33.5641 | + | 58.1347i | −0.0272162 | + | 0.0471399i | ||||
\(116\) | 324.172 | 0.259471 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 293.917 | 0.229298 | ||||||||
\(119\) | −280.574 | + | 485.969i | −0.216136 | + | 0.374359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −37.5284 | − | 65.0010i | −0.0281956 | − | 0.0488362i | ||||
\(122\) | 0.529362 | + | 0.916883i | 0.000392838 | + | 0.000680415i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −559.004 | + | 968.223i | −0.404839 | + | 0.701202i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1645.91 | −1.15001 | −0.575003 | − | 0.818152i | \(-0.694999\pi\) | ||||
−0.575003 | + | 0.818152i | \(0.694999\pi\) | |||||||
\(128\) | −629.072 | + | 1089.58i | −0.434395 | + | 0.752395i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −71.2436 | − | 123.397i | −0.0480652 | − | 0.0832513i | ||||
\(131\) | −193.354 | − | 334.898i | −0.128957 | − | 0.223360i | 0.794316 | − | 0.607505i | \(-0.207830\pi\) |
−0.923273 | + | 0.384145i | \(0.874496\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 390.679 | − | 676.677i | 0.254708 | − | 0.441168i | ||||
\(134\) | 597.402 | 0.385132 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −916.903 | −0.578116 | ||||||||
\(137\) | 1486.61 | − | 2574.88i | 0.927078 | − | 1.60575i | 0.138893 | − | 0.990307i | \(-0.455646\pi\) |
0.788185 | − | 0.615439i | \(-0.211021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1173.68 | − | 2032.87i | −0.716187 | − | 1.24047i | −0.962500 | − | 0.271282i | \(-0.912552\pi\) |
0.246313 | − | 0.969190i | \(-0.420781\pi\) | |||||||
\(140\) | −129.282 | − | 223.923i | −0.0780452 | − | 0.135178i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −53.9954 | + | 93.5227i | −0.0319098 | + | 0.0552694i | ||||
\(143\) | −1459.71 | −0.853614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −217.154 | −0.124370 | ||||||||
\(146\) | 158.361 | − | 274.290i | 0.0897677 | − | 0.155482i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −814.869 | − | 1411.39i | −0.452580 | − | 0.783891i | ||||
\(149\) | −701.046 | − | 1214.25i | −0.385449 | − | 0.667618i | 0.606382 | − | 0.795173i | \(-0.292620\pi\) |
−0.991831 | + | 0.127556i | \(0.959287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1470.63 | − | 2547.21i | 0.792571 | − | 1.37277i | −0.131799 | − | 0.991276i | \(-0.542075\pi\) |
0.924370 | − | 0.381497i | \(-0.124591\pi\) | |||||||
\(152\) | 1276.72 | 0.681288 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 190.179 | 0.0995135 | ||||||||
\(155\) | 374.462 | − | 648.586i | 0.194048 | − | 0.336101i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1275.99 | − | 2210.08i | −0.648631 | − | 1.12346i | −0.983450 | − | 0.181179i | \(-0.942009\pi\) |
0.334819 | − | 0.942282i | \(-0.391325\pi\) | |||||||
\(158\) | 140.603 | + | 243.531i | 0.0707958 | + | 0.122622i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 320.526 | − | 555.167i | 0.158374 | − | 0.274311i | ||||
\(161\) | −93.0155 | −0.0455320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 351.559 | 0.168934 | 0.0844669 | − | 0.996426i | \(-0.473081\pi\) | ||||
0.0844669 | + | 0.996426i | \(0.473081\pi\) | |||||||
\(164\) | −1388.84 | + | 2405.54i | −0.661281 | + | 1.14537i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −461.642 | − | 799.588i | −0.215846 | − | 0.373856i | ||||
\(167\) | 10.4947 | + | 18.1773i | 0.00486288 | + | 0.00842276i | 0.868447 | − | 0.495783i | \(-0.165119\pi\) |
−0.863584 | + | 0.504205i | \(0.831785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 340.797 | − | 590.279i | 0.155119 | − | 0.268675i | ||||
\(170\) | 296.462 | 0.133750 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3434.98 | −1.52276 | ||||||||
\(173\) | −2262.30 | + | 3918.43i | −0.994219 | + | 1.72204i | −0.404121 | + | 0.914706i | \(0.632423\pi\) |
−0.590098 | + | 0.807332i | \(0.700911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 86.6025 | + | 150.000i | 0.0374088 | + | 0.0647939i | ||||
\(176\) | −964.164 | − | 1669.98i | −0.412935 | − | 0.715225i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −187.771 | + | 325.229i | −0.0790676 | + | 0.136949i | ||||
\(179\) | −3626.79 | −1.51441 | −0.757204 | − | 0.653179i | \(-0.773435\pi\) | ||||
−0.757204 | + | 0.653179i | \(0.773435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3551.41 | 1.45842 | 0.729210 | − | 0.684289i | \(-0.239888\pi\) | ||||
0.729210 | + | 0.684289i | \(0.239888\pi\) | |||||||
\(182\) | 98.7180 | − | 170.985i | 0.0402058 | − | 0.0696386i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −75.9925 | − | 131.623i | −0.0304469 | − | 0.0527357i | ||||
\(185\) | 545.859 | + | 945.455i | 0.216932 | + | 0.375736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1518.55 | − | 2630.20i | 0.593836 | − | 1.02855i | ||||
\(188\) | 1599.46 | 0.620493 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −412.801 | −0.157620 | ||||||||
\(191\) | −139.825 | + | 242.185i | −0.0529707 | + | 0.0917479i | −0.891295 | − | 0.453424i | \(-0.850202\pi\) |
0.838324 | + | 0.545172i | \(0.183536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −133.080 | − | 230.501i | −0.0496336 | − | 0.0859679i | 0.840141 | − | 0.542368i | \(-0.182472\pi\) |
−0.889775 | + | 0.456400i | \(0.849139\pi\) | |||||||
\(194\) | −401.201 | − | 694.901i | −0.148477 | − | 0.257170i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1100.95 | + | 1906.91i | −0.401223 | + | 0.694938i | ||||
\(197\) | 4731.12 | 1.71106 | 0.855528 | − | 0.517756i | \(-0.173232\pi\) | ||||
0.855528 | + | 0.517756i | \(0.173232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2879.69 | 1.02581 | 0.512904 | − | 0.858446i | \(-0.328570\pi\) | ||||
0.512904 | + | 0.858446i | \(0.328570\pi\) | |||||||
\(200\) | −141.506 | + | 245.096i | −0.0500301 | + | 0.0866546i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 437.066 | + | 757.021i | 0.152237 | + | 0.263682i | ||||
\(203\) | −150.449 | − | 260.585i | −0.0520169 | − | 0.0900959i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 930.346 | − | 1611.41i | 0.316967 | − | 0.549003i | ||||
\(206\) | −132.869 | −0.0449390 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2001.91 | −0.667343 | ||||||||
\(209\) | −2114.47 | + | 3662.37i | −0.699813 | + | 1.21211i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1364.10 | − | 2362.69i | −0.445065 | − | 0.770875i | 0.552992 | − | 0.833187i | \(-0.313486\pi\) |
−0.998057 | + | 0.0623117i | \(0.980153\pi\) | |||||||
\(212\) | −1661.53 | − | 2877.85i | −0.538275 | − | 0.932319i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 223.886 | − | 387.781i | 0.0715164 | − | 0.123870i | ||||
\(215\) | 2301.00 | 0.729892 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1037.74 | 0.324637 | ||||||||
\(218\) | 201.485 | − | 348.982i | 0.0625976 | − | 0.108422i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 699.711 | + | 1211.94i | 0.214430 | + | 0.371403i | ||||
\(221\) | −1576.49 | − | 2730.56i | −0.479848 | − | 0.831120i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1837.42 | − | 3182.51i | 0.551762 | − | 0.955680i | −0.446386 | − | 0.894841i | \(-0.647289\pi\) |
0.998148 | − | 0.0608392i | \(-0.0193777\pi\) | |||||||
\(224\) | 888.267 | 0.264954 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 348.385 | 0.102541 | ||||||||
\(227\) | 2886.96 | − | 5000.36i | 0.844115 | − | 1.46205i | −0.0422732 | − | 0.999106i | \(-0.513460\pi\) |
0.886388 | − | 0.462943i | \(-0.153207\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2409.14 | − | 4172.75i | −0.695198 | − | 1.20412i | −0.970114 | − | 0.242650i | \(-0.921983\pi\) |
0.274916 | − | 0.961468i | \(-0.411350\pi\) | |||||||
\(230\) | 24.5706 | + | 42.5575i | 0.00704408 | + | 0.0122007i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 245.829 | − | 425.789i | 0.0695667 | − | 0.120493i | ||||
\(233\) | −91.0828 | −0.0256096 | −0.0128048 | − | 0.999918i | \(-0.504076\pi\) | ||||
−0.0128048 | + | 0.999918i | \(0.504076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1071.44 | −0.297416 | ||||||||
\(236\) | −1498.41 | + | 2595.32i | −0.413297 | + | 0.715851i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 205.395 | + | 355.754i | 0.0559402 | + | 0.0968912i | ||||
\(239\) | 2743.42 | + | 4751.74i | 0.742498 | + | 1.28604i | 0.951354 | + | 0.308098i | \(0.0996926\pi\) |
−0.208856 | + | 0.977946i | \(0.566974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1508.60 | + | 2612.97i | −0.403225 | + | 0.698406i | −0.994113 | − | 0.108347i | \(-0.965444\pi\) |
0.590888 | + | 0.806754i | \(0.298778\pi\) | |||||||
\(242\) | −54.9453 | −0.0145951 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.7949 | −0.00283227 | ||||||||
\(245\) | 737.500 | − | 1277.39i | 0.192315 | − | 0.333099i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2195.15 | + | 3802.11i | 0.565482 | + | 0.979444i | ||||
\(248\) | 847.819 | + | 1468.47i | 0.217083 | + | 0.375999i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 45.7532 | − | 79.2468i | 0.0115747 | − | 0.0200480i | ||||
\(251\) | 2740.98 | 0.689280 | 0.344640 | − | 0.938735i | \(-0.388001\pi\) | ||||
0.344640 | + | 0.938735i | \(0.388001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 503.426 | 0.125099 | ||||||||
\(254\) | −602.444 | + | 1043.46i | −0.148822 | + | 0.257767i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −809.682 | − | 1402.41i | −0.197676 | − | 0.342385i | ||||
\(257\) | −1260.70 | − | 2183.60i | −0.305993 | − | 0.529996i | 0.671489 | − | 0.741015i | \(-0.265655\pi\) |
−0.977482 | + | 0.211019i | \(0.932322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −756.364 | + | 1310.06i | −0.181460 | + | 0.314298i | ||||
\(260\) | 1452.82 | 0.346539 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −283.089 | −0.0667531 | ||||||||
\(263\) | −2243.86 | + | 3886.48i | −0.526092 | + | 0.911219i | 0.473446 | + | 0.880823i | \(0.343010\pi\) |
−0.999538 | + | 0.0303955i | \(0.990323\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1113.01 | + | 1927.79i | 0.258007 | + | 0.446881i | ||||
\(266\) | −285.997 | − | 495.362i | −0.0659234 | − | 0.114183i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3045.60 | + | 5275.14i | −0.694178 | + | 1.20235i | ||||
\(269\) | −8531.47 | −1.93373 | −0.966864 | − | 0.255291i | \(-0.917829\pi\) | ||||
−0.966864 | + | 0.255291i | \(0.917829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −123.097 | −0.0275927 | −0.0137964 | − | 0.999905i | \(-0.504392\pi\) | ||||
−0.0137964 | + | 0.999905i | \(0.504392\pi\) | |||||||
\(272\) | 2082.61 | − | 3607.18i | 0.464252 | − | 0.804108i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1088.27 | − | 1884.95i | −0.239945 | − | 0.415598i | ||||
\(275\) | −468.718 | − | 811.843i | −0.102781 | − | 0.178022i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3278.79 | − | 5679.03i | 0.711204 | − | 1.23184i | −0.253201 | − | 0.967414i | \(-0.581484\pi\) |
0.964405 | − | 0.264428i | \(-0.0851831\pi\) | |||||||
\(278\) | −1718.38 | −0.370726 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −392.154 | −0.0836989 | ||||||||
\(281\) | 3542.02 | − | 6134.96i | 0.751954 | − | 1.30242i | −0.194920 | − | 0.980819i | \(-0.562445\pi\) |
0.946874 | − | 0.321604i | \(-0.104222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1036.47 | − | 1795.21i | −0.217709 | − | 0.377082i | 0.736399 | − | 0.676548i | \(-0.236525\pi\) |
−0.954107 | + | 0.299466i | \(0.903192\pi\) | |||||||
\(284\) | −550.545 | − | 953.572i | −0.115031 | − | 0.199240i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −534.290 | + | 925.417i | −0.110466 | + | 0.191332i | ||||
\(287\) | 2578.25 | 0.530276 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1647.16 | 0.335267 | ||||||||
\(290\) | −79.4838 | + | 137.670i | −0.0160947 | + | 0.0278768i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1614.68 | + | 2796.70i | 0.323602 | + | 0.560495i | ||||
\(293\) | 3564.20 | + | 6173.38i | 0.710658 | + | 1.23090i | 0.964610 | + | 0.263680i | \(0.0849362\pi\) |
−0.253952 | + | 0.967217i | \(0.581730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1003.74 | − | 1738.53i | 0.198102 | − | 0.343123i | ||||
\(296\) | −2471.76 | −0.485365 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1026.40 | −0.199523 | ||||||||
\(299\) | 261.318 | − | 452.616i | 0.0505431 | − | 0.0875433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1594.18 | + | 2761.20i | 0.305272 | + | 0.528747i | ||||
\(302\) | −1076.58 | − | 1864.68i | −0.205132 | − | 0.355300i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2899.88 | + | 5022.73i | −0.547103 | + | 0.947610i | ||||
\(305\) | 7.23122 | 0.00135757 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6334.70 | −1.17766 | −0.588828 | − | 0.808259i | \(-0.700410\pi\) | ||||
−0.588828 | + | 0.808259i | \(0.700410\pi\) | |||||||
\(308\) | −969.549 | + | 1679.31i | −0.179367 | + | 0.310673i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −274.125 | − | 474.798i | −0.0502234 | − | 0.0869894i | ||||
\(311\) | 3696.95 | + | 6403.30i | 0.674067 | + | 1.16752i | 0.976741 | + | 0.214423i | \(0.0687872\pi\) |
−0.302674 | + | 0.953094i | \(0.597879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 466.528 | − | 808.050i | 0.0842482 | − | 0.145922i | −0.820822 | − | 0.571184i | \(-0.806484\pi\) |
0.905071 | + | 0.425261i | \(0.139818\pi\) | |||||||
\(314\) | −1868.18 | −0.335756 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2867.21 | −0.510421 | ||||||||
\(317\) | 4367.34 | − | 7564.45i | 0.773799 | − | 1.34026i | −0.161669 | − | 0.986845i | \(-0.551688\pi\) |
0.935467 | − | 0.353413i | \(-0.114979\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 814.271 | + | 1410.36i | 0.142917 | + | 0.247539i | ||||
\(320\) | 793.872 | + | 1375.03i | 0.138684 | + | 0.240207i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −34.0460 | + | 58.9694i | −0.00589227 | + | 0.0102057i | ||||
\(323\) | −9134.55 | −1.57356 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −973.205 | −0.166104 | ||||||||
\(326\) | 128.679 | − | 222.879i | 0.0218617 | − | 0.0378655i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2106.40 | + | 3648.39i | 0.354593 | + | 0.614172i | ||||
\(329\) | −742.313 | − | 1285.72i | −0.124392 | − | 0.215454i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 645.266 | − | 1117.63i | 0.107151 | − | 0.185591i | −0.807464 | − | 0.589917i | \(-0.799160\pi\) |
0.914615 | + | 0.404326i | \(0.132494\pi\) | |||||||
\(332\) | 9413.95 | 1.55620 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.3652 | 0.00251721 | ||||||||
\(335\) | 2040.17 | − | 3533.67i | 0.332735 | − | 0.576314i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5000.66 | + | 8661.40i | 0.808318 | + | 1.40005i | 0.914028 | + | 0.405651i | \(0.132955\pi\) |
−0.105710 | + | 0.994397i | \(0.533711\pi\) | |||||||
\(338\) | −249.481 | − | 432.114i | −0.0401479 | − | 0.0695382i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1511.38 | + | 2617.79i | −0.241077 | + | 0.417558i | ||||
\(341\) | −5616.54 | −0.891943 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4420.19 | 0.695825 | ||||||||
\(344\) | −2604.85 | + | 4511.73i | −0.408267 | + | 0.707140i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1656.12 | + | 2868.49i | 0.257323 | + | 0.445696i | ||||
\(347\) | 3234.18 | + | 5601.77i | 0.500346 | + | 0.866625i | 1.00000 | 0.000399827i | \(0.000127269\pi\) | |
−0.499654 | + | 0.866225i | \(0.666539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5584.89 | + | 9673.32i | −0.856597 | + | 1.48367i | 0.0185577 | + | 0.999828i | \(0.494093\pi\) |
−0.875155 | + | 0.483842i | \(0.839241\pi\) | |||||||
\(350\) | 126.795 | 0.0193642 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4807.55 | −0.727964 | ||||||||
\(353\) | 908.387 | − | 1573.37i | 0.136965 | − | 0.237230i | −0.789382 | − | 0.613903i | \(-0.789599\pi\) |
0.926346 | + | 0.376673i | \(0.122932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 368.795 | + | 638.772i | 0.0551369 | + | 0.0955000i | ||||
\(356\) | −1914.54 | − | 3316.08i | −0.285030 | − | 0.493686i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1327.50 | + | 2299.29i | −0.195979 | + | 0.339445i | ||||
\(359\) | −918.073 | −0.134969 | −0.0674847 | − | 0.997720i | \(-0.521497\pi\) | ||||
−0.0674847 | + | 0.997720i | \(0.521497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5860.21 | 0.854382 | ||||||||
\(362\) | 1299.91 | − | 2251.50i | 0.188734 | − | 0.326896i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1006.54 | + | 1743.38i | 0.144937 | + | 0.251039i | ||||
\(365\) | −1081.63 | − | 1873.44i | −0.155110 | − | 0.268658i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3677.14 | + | 6368.99i | −0.523011 | + | 0.905881i | 0.476630 | + | 0.879104i | \(0.341858\pi\) |
−0.999641 | + | 0.0267777i | \(0.991475\pi\) | |||||||
\(368\) | 690.421 | 0.0978008 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 799.193 | 0.112292 | ||||||||
\(371\) | −1542.24 | + | 2671.23i | −0.215819 | + | 0.373810i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 301.303 | + | 521.873i | 0.0418255 | + | 0.0724438i | 0.886180 | − | 0.463341i | \(-0.153349\pi\) |
−0.844355 | + | 0.535784i | \(0.820016\pi\) | |||||||
\(374\) | −1111.66 | − | 1925.44i | −0.153696 | − | 0.266209i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1212.92 | − | 2100.84i | 0.166361 | − | 0.288145i | ||||
\(377\) | 1690.68 | 0.230967 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13319.0 | 1.80515 | 0.902575 | − | 0.430533i | \(-0.141674\pi\) | ||||
0.902575 | + | 0.430533i | \(0.141674\pi\) | |||||||
\(380\) | 2104.49 | − | 3645.09i | 0.284101 | − | 0.492077i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 102.359 | + | 177.291i | 0.0137098 | + | 0.0237461i | ||||
\(383\) | −4268.87 | − | 7393.91i | −0.569528 | − | 0.986452i | −0.996613 | − | 0.0822399i | \(-0.973793\pi\) |
0.427084 | − | 0.904212i | \(-0.359541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 649.474 | − | 1124.92i | 0.0859748 | − | 0.148913i | ||||
\(386\) | −194.842 | −0.0256922 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8181.42 | 1.07049 | ||||||||
\(389\) | −6319.99 | + | 10946.5i | −0.823744 | + | 1.42677i | 0.0791316 | + | 0.996864i | \(0.474785\pi\) |
−0.902875 | + | 0.429902i | \(0.858548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 543.703 | + | 941.722i | 0.0703229 | + | 0.121803i | ||||
\(392\) | 1669.77 | + | 2892.14i | 0.215144 | + | 0.372640i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1731.71 | − | 2999.41i | 0.221427 | − | 0.383523i | ||||
\(395\) | 1920.67 | 0.244656 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5473.94 | 0.692013 | 0.346006 | − | 0.938232i | \(-0.387538\pi\) | ||||
0.346006 | + | 0.938232i | \(0.387538\pi\) | |||||||
\(398\) | 1054.04 | − | 1825.65i | 0.132749 | − | 0.229929i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −642.820 | − | 1113.40i | −0.0803525 | − | 0.139175i | ||||
\(401\) | 6522.82 | + | 11297.9i | 0.812305 | + | 1.40695i | 0.911247 | + | 0.411860i | \(0.135121\pi\) |
−0.0989419 | + | 0.995093i | \(0.531546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2915.42 | + | 5049.66i | −0.360366 | + | 0.624172i | ||||
\(404\) | −8912.79 | −1.09759 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −220.272 | −0.0269259 | ||||||||
\(407\) | 4093.66 | − | 7090.43i | 0.498563 | − | 0.863537i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3591.36 | + | 6220.41i | 0.434184 | + | 0.752029i | 0.997229 | − | 0.0743978i | \(-0.0237035\pi\) |
−0.563045 | + | 0.826426i | \(0.690370\pi\) | |||||||
\(410\) | −681.061 | − | 1179.63i | −0.0820370 | − | 0.142092i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 677.377 | − | 1173.25i | 0.0809999 | − | 0.140296i | ||||
\(413\) | 2781.66 | 0.331420 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6306.15 | −0.745920 | ||||||||
\(416\) | −2495.50 | + | 4322.33i | −0.294115 | + | 0.509422i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1547.90 | + | 2681.04i | 0.181125 | + | 0.313718i | ||||
\(419\) | 4360.20 | + | 7552.09i | 0.508376 | + | 0.880534i | 0.999953 | + | 0.00969927i | \(0.00308742\pi\) |
−0.491577 | + | 0.870834i | \(0.663579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3276.51 | + | 5675.09i | −0.379305 | + | 0.656976i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791124i | \(0.290504\pi\) | |||||||
\(422\) | −1997.18 | −0.230383 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5039.95 | −0.577268 | ||||||||
\(425\) | 1012.44 | − | 1753.59i | 0.115554 | − | 0.200145i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00994 | + | 8.67747i | 0.000567794 | + | 0.000983448i | ||||
\(428\) | 2282.77 | + | 3953.88i | 0.257808 | + | 0.446537i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 842.224 | − | 1458.78i | 0.0944550 | − | 0.163601i | ||||
\(431\) | −5217.70 | −0.583127 | −0.291564 | − | 0.956551i | \(-0.594176\pi\) | ||||
−0.291564 | + | 0.956551i | \(0.594176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3377.56 | 0.374862 | 0.187431 | − | 0.982278i | \(-0.439984\pi\) | ||||
0.187431 | + | 0.982278i | \(0.439984\pi\) | |||||||
\(434\) | 379.839 | − | 657.900i | 0.0420111 | − | 0.0727654i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2054.37 | + | 3558.27i | 0.225657 | + | 0.390850i | ||||
\(437\) | −757.067 | − | 1311.28i | −0.0828729 | − | 0.143540i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1069.46 | + | 1852.36i | −0.116270 | + | 0.201386i | −0.918287 | − | 0.395916i | \(-0.870427\pi\) |
0.802017 | + | 0.597302i | \(0.203761\pi\) | |||||||
\(440\) | 2122.45 | 0.229963 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2308.14 | −0.248387 | ||||||||
\(443\) | 4256.31 | − | 7372.15i | 0.456486 | − | 0.790658i | −0.542286 | − | 0.840194i | \(-0.682441\pi\) |
0.998772 | + | 0.0495363i | \(0.0157744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1282.50 | + | 2221.36i | 0.136621 | + | 0.236634i | ||||
\(446\) | −1345.09 | − | 2329.76i | −0.142807 | − | 0.247348i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1100.02 | + | 1905.29i | −0.116007 | + | 0.200930i | ||||
\(449\) | 4542.67 | 0.477465 | 0.238733 | − | 0.971085i | \(-0.423268\pi\) | ||||
0.238733 | + | 0.971085i | \(0.423268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13954.2 | −1.45694 | ||||||||
\(452\) | −1776.09 | + | 3076.28i | −0.184824 | + | 0.320124i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2113.40 | − | 3660.51i | −0.218473 | − | 0.378406i | ||||
\(455\) | −674.256 | − | 1167.85i | −0.0694717 | − | 0.120329i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8971.10 | − | 15538.4i | 0.918272 | − | 1.59049i | 0.116232 | − | 0.993222i | \(-0.462918\pi\) |
0.802039 | − | 0.597271i | \(-0.203748\pi\) | |||||||
\(458\) | −3527.22 | −0.359861 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −501.051 | −0.0507862 | ||||||||
\(461\) | −2590.44 | + | 4486.78i | −0.261711 | + | 0.453297i | −0.966697 | − | 0.255924i | \(-0.917620\pi\) |
0.704985 | + | 0.709222i | \(0.250954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7096.44 | − | 12291.4i | −0.712310 | − | 1.23376i | −0.963988 | − | 0.265947i | \(-0.914315\pi\) |
0.251677 | − | 0.967811i | \(-0.419018\pi\) | |||||||
\(464\) | 1116.73 | + | 1934.23i | 0.111730 | + | 0.193522i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.3386 | + | 57.7442i | −0.00331413 | + | 0.00574023i | ||||
\(467\) | 11886.3 | 1.17780 | 0.588901 | − | 0.808205i | \(-0.299561\pi\) | ||||
0.588901 | + | 0.808205i | \(0.299561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5653.88 | 0.556656 | ||||||||
\(470\) | −392.173 | + | 679.263i | −0.0384885 | + | 0.0666640i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2272.58 | + | 3936.22i | 0.221618 | + | 0.383854i | ||||
\(473\) | −8628.16 | − | 14944.4i | −0.838738 | − | 1.45274i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1409.74 | + | 2441.75i | −0.136176 | + | 0.235863i | ||||
\(476\) | −4188.47 | −0.403316 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4016.65 | 0.384345 | ||||||||
\(479\) | −2159.73 | + | 3740.76i | −0.206014 | + | 0.356826i | −0.950455 | − | 0.310861i | \(-0.899382\pi\) |
0.744442 | + | 0.667688i | \(0.232716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4249.86 | − | 7360.97i | −0.402863 | − | 0.697779i | ||||
\(482\) | 1104.37 | + | 1912.82i | 0.104362 | + | 0.180761i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 280.115 | − | 485.174i | 0.0263069 | − | 0.0455648i | ||||
\(485\) | −5480.51 | −0.513108 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6436.94 | −0.598944 | −0.299472 | − | 0.954105i | \(-0.596810\pi\) | ||||
−0.299472 | + | 0.954105i | \(0.596810\pi\) | |||||||
\(488\) | −8.18611 | + | 14.1788i | −0.000759361 | + | 0.00131525i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −539.887 | − | 935.113i | −0.0497748 | − | 0.0862124i | ||||
\(491\) | −1448.87 | − | 2509.51i | −0.133170 | − | 0.230657i | 0.791727 | − | 0.610875i | \(-0.209182\pi\) |
−0.924897 | + | 0.380218i | \(0.875849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1758.83 | + | 3046.39i | −0.160677 | + | 0.278301i | ||||
\(494\) | 3213.92 | 0.292715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7702.77 | −0.697307 | ||||||||
\(497\) | −511.017 | + | 885.108i | −0.0461213 | + | 0.0798844i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7527.29 | − | 13037.6i | −0.675286 | − | 1.16963i | −0.976385 | − | 0.216037i | \(-0.930687\pi\) |
0.301099 | − | 0.953593i | \(-0.402646\pi\) | |||||||
\(500\) | 466.506 | + | 808.013i | 0.0417256 | + | 0.0722709i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1003.27 | − | 1737.71i | 0.0891994 | − | 0.154498i | ||||
\(503\) | −15582.5 | −1.38129 | −0.690646 | − | 0.723193i | \(-0.742674\pi\) | ||||
−0.690646 | + | 0.723193i | \(0.742674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5970.43 | 0.526101 | ||||||||
\(506\) | 184.267 | − | 319.160i | 0.0161891 | − | 0.0280403i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6142.61 | − | 10639.3i | −0.536485 | − | 0.929219i | ||||
\(509\) | 2035.51 | + | 3525.60i | 0.177254 | + | 0.307013i | 0.940939 | − | 0.338576i | \(-0.109945\pi\) |
−0.763685 | + | 0.645589i | \(0.776612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1498.75 | − | 2595.91i | 0.129747 | − | 0.224728i | ||||
\(512\) | −11250.6 | −0.971116 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1845.79 | −0.158394 | ||||||||
\(515\) | −453.756 | + | 785.929i | −0.0388250 | + | 0.0672469i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4017.61 | + | 6958.70i | 0.341768 | + | 0.591960i | ||||
\(518\) | 553.697 | + | 959.031i | 0.0469653 | + | 0.0813464i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1101.72 | − | 1908.23i | 0.0929106 | − | 0.160926i | ||||
\(521\) | 18597.9 | 1.56389 | 0.781947 | − | 0.623345i | \(-0.214227\pi\) | ||||
0.781947 | + | 0.623345i | \(0.214227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12073.5 | −1.00944 | −0.504722 | − | 0.863282i | \(-0.668405\pi\) | ||||
−0.504722 | + | 0.863282i | \(0.668405\pi\) | |||||||
\(524\) | 1443.21 | − | 2499.72i | 0.120319 | − | 0.208398i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1642.62 | + | 2845.10i | 0.136163 | + | 0.235841i | ||||
\(527\) | −6065.89 | − | 10506.4i | −0.501393 | − | 0.868439i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5993.38 | − | 10380.8i | 0.492593 | − | 0.853196i | ||||
\(530\) | 1629.56 | 0.133554 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5832.14 | 0.475292 | ||||||||
\(533\) | −7243.34 | + | 12545.8i | −0.588638 | + | 1.01955i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1529.17 | − | 2648.59i | −0.123573 | − | 0.214035i | ||||
\(536\) | 4619.14 | + | 8000.59i | 0.372233 | + | 0.644726i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3122.74 | + | 5408.74i | −0.250243 | + | 0.433433i | ||||
\(539\) | −11061.7 | −0.883976 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1802.04 | 0.143208 | 0.0716041 | − | 0.997433i | \(-0.477188\pi\) | ||||
0.0716041 | + | 0.997433i | \(0.477188\pi\) | |||||||
\(542\) | −45.0567 | + | 78.0405i | −0.00357076 | + | 0.00618474i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5192.18 | − | 8993.13i | −0.409215 | − | 0.708781i | ||||
\(545\) | −1376.17 | − | 2383.59i | −0.108162 | − | 0.187343i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3294.86 | + | 5706.87i | −0.257547 | + | 0.446084i | −0.965584 | − | 0.260091i | \(-0.916248\pi\) |
0.708037 | + | 0.706175i | \(0.249581\pi\) | |||||||
\(548\) | 22192.4 | 1.72995 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −686.250 | −0.0532033 | ||||||||
\(551\) | 2449.05 | − | 4241.88i | 0.189352 | − | 0.327968i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1330.68 | + | 2304.80i | 0.102326 | + | 0.177233i | ||||
\(554\) | −2400.24 | − | 4157.34i | −0.184073 | − | 0.318824i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8760.44 | − | 15173.5i | 0.668211 | − | 1.15738i | ||||
\(557\) | 21128.6 | 1.60727 | 0.803633 | − | 0.595125i | \(-0.202897\pi\) | ||||
0.803633 | + | 0.595125i | \(0.202897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17914.8 | −1.35548 | ||||||||
\(560\) | 890.718 | − | 1542.77i | 0.0672138 | − | 0.116418i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2592.94 | − | 4491.10i | −0.194620 | − | 0.337092i | ||||
\(563\) | 55.2137 | + | 95.6330i | 0.00413318 | + | 0.00715888i | 0.868085 | − | 0.496416i | \(-0.165351\pi\) |
−0.863951 | + | 0.503575i | \(0.832018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1189.76 | − | 2060.72i | 0.0885901 | − | 0.153443i | ||||
\(566\) | −1517.49 | −0.112694 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1669.98 | −0.123364 | ||||||||
\(569\) | 3465.04 | − | 6001.63i | 0.255294 | − | 0.442182i | −0.709682 | − | 0.704523i | \(-0.751161\pi\) |
0.964975 | + | 0.262341i | \(0.0844945\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10632.3 | − | 18415.7i | −0.779244 | − | 1.34969i | −0.932378 | − | 0.361484i | \(-0.882270\pi\) |
0.153134 | − | 0.988205i | \(-0.451063\pi\) | |||||||
\(572\) | −5447.70 | − | 9435.70i | −0.398217 | − | 0.689731i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 943.705 | − | 1634.55i | 0.0686228 | − | 0.118858i | ||||
\(575\) | 335.641 | 0.0243429 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2927.39 | 0.211211 | 0.105606 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105606 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(578\) | 602.904 | − | 1044.26i | 0.0433867 | − | 0.0751480i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −810.429 | − | 1403.70i | −0.0580194 | − | 0.100493i | ||||
\(581\) | −4369.03 | − | 7567.38i | −0.311976 | − | 0.540358i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8347.02 | − | 14457.5i | 0.592965 | − | 1.02704i | ||||
\(584\) | 4897.83 | 0.347044 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5218.35 | 0.367864 | ||||||||
\(587\) | −10875.2 | + | 18836.4i | −0.764683 | + | 1.32447i | 0.175732 | + | 0.984438i | \(0.443771\pi\) |
−0.940414 | + | 0.340031i | \(0.889562\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8446.31 | + | 14629.4i | 0.590873 | + | 1.02342i | ||||
\(590\) | −734.791 | − | 1272.70i | −0.0512727 | − | 0.0888069i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5614.23 | − | 9724.12i | 0.389769 | − | 0.675100i | ||||
\(593\) | 5635.88 | 0.390283 | 0.195142 | − | 0.980775i | \(-0.437483\pi\) | ||||
0.195142 | + | 0.980775i | \(0.437483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2805.74 | 0.193318 | ||||||||
\(596\) | 5232.68 | − | 9063.27i | 0.359629 | − | 0.622896i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −191.298 | − | 331.338i | −0.0130815 | − | 0.0226579i | ||||
\(599\) | −9162.20 | − | 15869.4i | −0.624970 | − | 1.08248i | −0.988547 | − | 0.150916i | \(-0.951778\pi\) |
0.363576 | − | 0.931564i | \(-0.381556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1251.95 | − | 2168.44i | 0.0849719 | − | 0.147176i | −0.820407 | − | 0.571779i | \(-0.806253\pi\) |
0.905379 | + | 0.424604i | \(0.139587\pi\) | |||||||
\(602\) | 2334.04 | 0.158021 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21953.9 | 1.47896 | ||||||||
\(605\) | −187.642 | + | 325.005i | −0.0126095 | + | 0.0218402i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8733.32 | − | 15126.6i | −0.583978 | − | 1.01148i | −0.995002 | − | 0.0998550i | \(-0.968162\pi\) |
0.411024 | − | 0.911624i | \(-0.365171\pi\) | |||||||
\(608\) | 7229.74 | + | 12522.3i | 0.482245 | + | 0.835272i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.64681 | − | 4.58441i | 0.000175682 | − | 0.000304291i | ||||
\(611\) | 8341.82 | 0.552330 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2244.45 | −0.147883 | −0.0739417 | − | 0.997263i | \(-0.523558\pi\) | ||||
−0.0739417 | + | 0.997263i | \(0.523558\pi\) | |||||||
\(614\) | −2318.66 | + | 4016.04i | −0.152400 | + | 0.263964i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1470.48 | + | 2546.94i | 0.0961805 | + | 0.166589i | ||||
\(617\) | 2904.92 | + | 5031.47i | 0.189542 | + | 0.328297i | 0.945098 | − | 0.326788i | \(-0.105966\pi\) |
−0.755555 | + | 0.655085i | \(0.772633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 771.742 | − | 1336.70i | 0.0501114 | − | 0.0867954i | −0.839882 | − | 0.542770i | \(-0.817376\pi\) |
0.889993 | + | 0.455974i | \(0.150709\pi\) | |||||||
\(620\) | 5590.04 | 0.362099 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5412.71 | 0.348922 | ||||||||
\(623\) | −1777.08 | + | 3078.00i | −0.114281 | + | 0.197941i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −341.522 | − | 591.533i | −0.0218050 | − | 0.0377675i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9524.11 | − | 16496.2i | 0.605181 | − | 1.04820i | ||||
\(629\) | 17684.7 | 1.12104 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7992.93 | 0.504269 | 0.252134 | − | 0.967692i | \(-0.418868\pi\) | ||||
0.252134 | + | 0.967692i | \(0.418868\pi\) | |||||||
\(632\) | −2174.29 | + | 3765.98i | −0.136849 | + | 0.237030i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3197.11 | − | 5537.56i | −0.200274 | − | 0.346884i | ||||
\(635\) | 4114.77 | + | 7126.99i | 0.257149 | + | 0.445395i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5741.91 | + | 9945.28i | −0.357147 | + | 0.618597i | ||||
\(638\) | 1192.18 | 0.0739791 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6290.72 | 0.388535 | ||||||||
\(641\) | −13064.9 | + | 22629.1i | −0.805044 | + | 1.39438i | 0.111217 | + | 0.993796i | \(0.464525\pi\) |
−0.916261 | + | 0.400581i | \(0.868808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14386.1 | + | 24917.4i | 0.882319 | + | 1.52822i | 0.848756 | + | 0.528784i | \(0.177352\pi\) |
0.0335621 | + | 0.999437i | \(0.489315\pi\) | |||||||
\(644\) | −347.138 | − | 601.261i | −0.0212409 | − | 0.0367904i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3343.48 | + | 5791.08i | −0.203634 | + | 0.352704i | ||||
\(647\) | −7156.38 | −0.434847 | −0.217424 | − | 0.976077i | \(-0.569765\pi\) | ||||
−0.217424 | + | 0.976077i | \(0.569765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15055.1 | −0.910578 | ||||||||
\(650\) | −356.218 | + | 616.987i | −0.0214954 | + | 0.0372311i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1312.04 | + | 2272.51i | 0.0788087 | + | 0.136501i | ||||
\(653\) | −7717.43 | − | 13367.0i | −0.462491 | − | 0.801057i | 0.536594 | − | 0.843841i | \(-0.319711\pi\) |
−0.999084 | + | 0.0427836i | \(0.986377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −966.768 | + | 1674.49i | −0.0576714 | + | 0.0998898i | ||||
\(656\) | −19137.5 | −1.13901 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1086.82 | −0.0643901 | ||||||||
\(659\) | 3231.32 | − | 5596.81i | 0.191008 | − | 0.330836i | −0.754577 | − | 0.656212i | \(-0.772158\pi\) |
0.945585 | + | 0.325376i | \(0.105491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −873.801 | − | 1513.47i | −0.0514174 | − | 0.0890576i | 0.839171 | − | 0.543867i | \(-0.183041\pi\) |
−0.890589 | + | 0.454810i | \(0.849707\pi\) | |||||||
\(662\) | −472.368 | − | 818.165i | −0.0277328 | − | 0.0480345i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7138.88 | − | 12364.9i | 0.417233 | − | 0.722668i | ||||
\(665\) | −3906.79 | −0.227818 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −583.085 | −0.0338488 | ||||||||
\(668\) | −78.3332 | + | 135.677i | −0.00453713 | + | 0.00785854i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1493.51 | − | 2586.83i | −0.0861181 | − | 0.149161i | ||||
\(671\) | −27.1152 | − | 46.9650i | −0.00156002 | − | 0.00270203i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2739.19 | − | 4744.42i | 0.156892 | − | 0.271744i | −0.776855 | − | 0.629680i | \(-0.783186\pi\) |
0.933746 | + | 0.357936i | \(0.116519\pi\) | |||||||
\(674\) | 7321.47 | 0.418416 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5087.49 | 0.289457 | ||||||||
\(677\) | 2009.27 | − | 3480.15i | 0.114066 | − | 0.197567i | −0.803340 | − | 0.595520i | \(-0.796946\pi\) |
0.917406 | + | 0.397953i | \(0.130279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3797.01 | − | 6576.61i | −0.214604 | − | 0.371704i | ||||
\(680\) | 2292.26 | + | 3970.31i | 0.129271 | + | 0.223903i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2055.80 | + | 3560.74i | −0.115426 | + | 0.199924i | ||||
\(683\) | 9894.95 | 0.554348 | 0.277174 | − | 0.960820i | \(-0.410602\pi\) | ||||
0.277174 | + | 0.960820i | \(0.410602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14866.1 | −0.829204 | ||||||||
\(686\) | 1617.90 | − | 2802.29i | 0.0900464 | − | 0.155965i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11833.0 | − | 20495.4i | −0.655713 | − | 1.13573i | ||||
\(689\) | −8665.52 | − | 15009.1i | −0.479144 | − | 0.829901i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10924.0 | + | 18920.9i | −0.601400 | + | 1.04166i | 0.391209 | + | 0.920302i | \(0.372057\pi\) |
−0.992609 | + | 0.121354i | \(0.961276\pi\) | |||||||
\(692\) | −33772.1 | −1.85524 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4735.18 | 0.258998 | ||||||||
\(695\) | −5868.38 | + | 10164.3i | −0.320289 | + | 0.554756i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15070.6 | − | 26103.1i | −0.818998 | − | 1.41855i | ||||
\(698\) | 4088.43 | + | 7081.36i | 0.221704 | + | 0.384002i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −646.410 | + | 1119.62i | −0.0349029 | + | 0.0604535i | ||||
\(701\) | 15506.5 | 0.835480 | 0.417740 | − | 0.908567i | \(-0.362822\pi\) | ||||
0.417740 | + | 0.908567i | \(0.362822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24624.7 | −1.32110 | ||||||||
\(704\) | 5953.63 | − | 10312.0i | 0.318730 | − | 0.552056i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −664.986 | − | 1151.79i | −0.0354491 | − | 0.0613996i | ||||
\(707\) | 4136.44 | + | 7164.52i | 0.220038 | + | 0.381117i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3199.85 | + | 5542.30i | −0.169496 | + | 0.293576i | −0.938243 | − | 0.345977i | \(-0.887547\pi\) |
0.768747 | + | 0.639553i | \(0.220881\pi\) | |||||||
\(710\) | 539.954 | 0.0285410 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5807.42 | −0.305677 | ||||||||
\(713\) | 1005.48 | − | 1741.54i | 0.0528126 | − | 0.0914741i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3649.27 | + | 6320.72i | 0.190874 | + | 0.330603i | ||||
\(716\) | −13535.4 | − | 23443.9i | −0.706481 | − | 1.22366i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −336.038 | + | 582.035i | −0.0174663 | + | 0.0302526i | ||||
\(719\) | 1771.66 | 0.0918941 | 0.0459470 | − | 0.998944i | \(-0.485369\pi\) | ||||
0.0459470 | + | 0.998944i | \(0.485369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1257.49 | −0.0649532 | ||||||||
\(722\) | 2144.98 | − | 3715.22i | 0.110565 | − | 0.191504i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13254.0 | + | 22956.7i | 0.680363 | + | 1.17842i | ||||
\(725\) | 542.885 | + | 940.304i | 0.0278100 | + | 0.0481683i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4787.53 | + | 8292.25i | −0.244236 | + | 0.423030i | −0.961917 | − | 0.273343i | \(-0.911871\pi\) |
0.717680 | + | 0.696373i | \(0.245204\pi\) | |||||||
\(728\) | 3053.17 | 0.155437 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1583.61 | −0.0802907 | ||||||||
\(731\) | 18636.9 | − | 32280.1i | 0.942970 | − | 1.63327i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9895.25 | + | 17139.1i | 0.498622 | + | 0.863638i | 0.999999 | − | 0.00159099i | \(-0.000506428\pi\) |
−0.501377 | + | 0.865229i | \(0.667173\pi\) | |||||||
\(734\) | 2691.85 | + | 4662.42i | 0.135365 | + | 0.234459i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 860.651 | − | 1490.69i | 0.0431033 | − | 0.0746571i | ||||
\(737\) | −30600.4 | −1.52942 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13106.5 | −0.652407 | −0.326203 | − | 0.945300i | \(-0.605769\pi\) | ||||
−0.326203 | + | 0.945300i | \(0.605769\pi\) | |||||||
\(740\) | −4074.35 | + | 7056.97i | −0.202400 | + | 0.350567i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1128.99 | + | 1955.48i | 0.0558581 | + | 0.0967491i | ||||
\(743\) | 8534.44 | + | 14782.1i | 0.421398 | + | 0.729882i | 0.996076 | − | 0.0884970i | \(-0.0282064\pi\) |
−0.574679 | + | 0.818379i | \(0.694873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3505.23 | + | 6071.24i | −0.172378 | + | 0.298568i | ||||
\(746\) | 441.139 | 0.0216505 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22669.2 | 1.10811 | ||||||||
\(749\) | 2118.88 | − | 3670.00i | 0.103367 | − | 0.179037i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2056.46 | − | 3561.90i | −0.0999220 | − | 0.173070i | 0.811730 | − | 0.584033i | \(-0.198526\pi\) |
−0.911652 | + | 0.410963i | \(0.865193\pi\) | |||||||
\(752\) | 5509.93 | + | 9543.47i | 0.267189 | + | 0.462785i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 618.833 | − | 1071.85i | 0.0298893 | − | 0.0517698i | ||||
\(755\) | −14706.3 | −0.708897 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17493.6 | 0.839915 | 0.419958 | − | 0.907544i | \(-0.362045\pi\) | ||||
0.419958 | + | 0.907544i | \(0.362045\pi\) | |||||||
\(758\) | 4875.10 | − | 8443.92i | 0.233604 | − | 0.404613i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3191.80 | − | 5528.36i | −0.152341 | − | 0.263862i | ||||
\(761\) | −2606.02 | − | 4513.76i | −0.124137 | − | 0.215011i | 0.797258 | − | 0.603638i | \(-0.206283\pi\) |
−0.921395 | + | 0.388627i | \(0.872949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1906.87 | − | 3302.80i | 0.0904763 | − | 0.156710i | ||||
\(764\) | −2087.34 | −0.0988447 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6250.07 | −0.294809 | ||||||||
\(767\) | −7814.79 | + | 13535.6i | −0.367895 | + | 0.637213i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11662.3 | + | 20199.7i | 0.546885 | + | 0.947232i | 0.998486 | + | 0.0550119i | \(0.0175197\pi\) |
−0.451601 | + | 0.892220i | \(0.649147\pi\) | |||||||
\(770\) | −475.448 | − | 823.501i | −0.0222519 | − | 0.0385414i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 993.321 | − | 1720.48i | 0.0463088 | − | 0.0802092i | ||||
\(773\) | −20455.0 | −0.951765 | −0.475883 | − | 0.879509i | \(-0.657871\pi\) | ||||
−0.475883 | + | 0.879509i | \(0.657871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3744.62 | −0.173562 | ||||||||
\(776\) | 6204.22 | − | 10746.0i | 0.287008 | − | 0.497113i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4626.56 | + | 8013.43i | 0.213201 | + | 0.369274i | ||||
\(779\) | 20984.8 | + | 36346.7i | 0.965158 | + | 1.67170i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2765.77 | − | 4790.46i | 0.126718 | − | 0.219483i | ||||
\(782\) | 796.037 | 0.0364018 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15170.6 | −0.691079 | ||||||||
\(785\) | −6379.95 | + | 11050.4i | −0.290077 | + | 0.502427i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4555.49 | − | 7890.33i | −0.206335 | − | 0.357382i | 0.744222 | − | 0.667932i | \(-0.232820\pi\) |
−0.950557 | + | 0.310549i | \(0.899487\pi\) | |||||||
\(788\) | 17656.8 | + | 30582.4i | 0.798219 | + | 1.38256i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 703.013 | − | 1217.65i | 0.0316608 | − | 0.0548382i | ||||
\(791\) | 3297.15 | 0.148209 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.2997 | −0.00252114 | ||||||||
\(794\) | 2003.60 | − | 3470.34i | 0.0895530 | − | 0.155110i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10747.2 | + | 18614.6i | 0.478546 | + | 0.828867i | ||||
\(797\) | −3962.54 | − | 6863.33i | −0.176111 | − | 0.305033i | 0.764434 | − | 0.644702i | \(-0.223018\pi\) |
−0.940545 | + | 0.339668i | \(0.889685\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8678.08 | + | 15030.9i | −0.384241 | + | 0.665524i | ||||
\(800\) | −3205.26 | −0.141654 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9550.08 | 0.420480 | ||||||||
\(803\) | −8111.65 | + | 14049.8i | −0.356481 | + | 0.617443i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 232.539 | + | 402.769i | 0.0101813 | + | 0.0176345i | ||||
\(806\) | 2134.24 | + | 3696.61i | 0.0932696 | + | 0.161548i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6758.84 | + | 11706.6i | −0.294276 | + | 0.509701i | ||||
\(809\) | 33705.8 | 1.46481 | 0.732406 | − | 0.680868i | \(-0.238397\pi\) | ||||
0.732406 | + | 0.680868i | \(0.238397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10424.5 | 0.451360 | 0.225680 | − | 0.974201i | \(-0.427540\pi\) | ||||
0.225680 | + | 0.974201i | \(0.427540\pi\) | |||||||
\(812\) | 1122.96 | − | 1945.03i | 0.0485324 | − | 0.0840606i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2996.77 | − | 5190.55i | −0.129038 | − | 0.223500i | ||||
\(815\) | −878.897 | − | 1522.29i | −0.0377748 | − | 0.0654278i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25950.5 | + | 44947.7i | −1.11125 | + | 1.92475i | ||||
\(818\) | 5258.11 | 0.224750 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13888.4 | 0.591468 | ||||||||
\(821\) | −4733.83 | + | 8199.23i | −0.201232 | + | 0.348545i | −0.948926 | − | 0.315499i | \(-0.897828\pi\) |
0.747693 | + | 0.664044i | \(0.231161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −580.274 | − | 1005.06i | −0.0245772 | − | 0.0425690i | 0.853475 | − | 0.521133i | \(-0.174491\pi\) |
−0.878052 | + | 0.478564i | \(0.841157\pi\) | |||||||
\(824\) | −1027.35 | − | 1779.42i | −0.0434338 | − | 0.0752296i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1018.16 | − | 1763.50i | 0.0428889 | − | 0.0742857i | ||||
\(827\) | −26499.9 | −1.11426 | −0.557128 | − | 0.830426i | \(-0.688097\pi\) | ||||
−0.557128 | + | 0.830426i | \(0.688097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 653.861 | 0.0273939 | 0.0136969 | − | 0.999906i | \(-0.495640\pi\) | ||||
0.0136969 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(830\) | −2308.21 | + | 3997.94i | −0.0965292 | + | 0.167193i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6180.80 | − | 10705.5i | −0.257549 | − | 0.446088i | ||||
\(833\) | −11946.7 | − | 20692.4i | −0.496915 | − | 0.860682i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.4733 | − | 90.8864i | 0.00217475 | − | 0.00376677i | ||||
\(836\) | −31565.2 | −1.30587 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6383.77 | 0.263155 | ||||||||
\(839\) | 20634.8 | − | 35740.6i | 0.849099 | − | 1.47068i | −0.0329145 | − | 0.999458i | \(-0.510479\pi\) |
0.882013 | − | 0.471224i | \(-0.156188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11251.4 | + | 19488.0i | 0.461330 | + | 0.799047i | ||||
\(842\) | 2398.57 | + | 4154.45i | 0.0981714 | + | 0.170038i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10181.8 | − | 17635.4i | 0.415251 | − | 0.719236i | ||||
\(845\) | −3407.97 | −0.138743 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −520.008 | −0.0210953 | ||||||||
\(848\) | 11447.5 | − | 19827.6i | 0.463571 | − | 0.802928i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −741.154 | − | 1283.72i | −0.0299075 | − | 0.0518013i | ||||
\(851\) | 1465.70 | + | 2538.67i | 0.0590406 | + | 0.102261i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2534.70 | + | 4390.22i | −0.101743 | + | 0.176223i | −0.912403 | − | 0.409294i | \(-0.865775\pi\) |
0.810660 | + | 0.585517i | \(0.199108\pi\) | |||||||
\(854\) | 7.33506 | 0.000293912 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6924.38 | 0.276484 | ||||||||
\(857\) | −21819.5 | + | 37792.4i | −0.869707 | + | 1.50638i | −0.00741160 | + | 0.999973i | \(0.502359\pi\) |
−0.862296 | + | 0.506405i | \(0.830974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6449.06 | + | 11170.1i | 0.256157 | + | 0.443678i | 0.965209 | − | 0.261479i | \(-0.0842101\pi\) |
−0.709052 | + | 0.705156i | \(0.750877\pi\) | |||||||
\(860\) | 8587.45 | + | 14873.9i | 0.340499 | + | 0.589762i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1909.81 | + | 3307.89i | −0.0754622 | + | 0.130704i | ||||
\(863\) | −8962.98 | −0.353538 | −0.176769 | − | 0.984252i | \(-0.556565\pi\) | ||||
−0.176769 | + | 0.984252i | \(0.556565\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22623.0 | 0.889256 | ||||||||
\(866\) | 1236.27 | − | 2141.29i | 0.0485107 | − | 0.0840230i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3872.89 | + | 6708.05i | 0.151445 | + | 0.262311i | ||||
\(869\) | −7202.00 | − | 12474.2i | −0.281141 | − | 0.486950i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15884.0 | + | 27511.9i | −0.617921 | + | 1.07027i | ||||
\(872\) | 6231.56 | 0.242004 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1108.42 | −0.0428982 | ||||||||
\(875\) | 433.013 | − | 750.000i | 0.0167297 | − | 0.0289767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18860.1 | + | 32666.6i | 0.726179 | + | 1.25778i | 0.958487 | + | 0.285136i | \(0.0920388\pi\) |
−0.232308 | + | 0.972642i | \(0.574628\pi\) | |||||||
\(878\) | 782.900 | + | 1356.02i | 0.0300929 | + | 0.0521225i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4820.82 | + | 8349.91i | −0.184670 | + | 0.319858i | ||||
\(881\) | 7961.44 | 0.304458 | 0.152229 | − | 0.988345i | \(-0.451355\pi\) | ||||
0.152229 | + | 0.988345i | \(0.451355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37426.4 | −1.42639 | −0.713193 | − | 0.700968i | \(-0.752752\pi\) | ||||
−0.713193 | + | 0.700968i | \(0.752752\pi\) | |||||||
\(884\) | 11767.1 | − | 20381.2i | 0.447704 | − | 0.775446i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3115.84 | − | 5396.79i | −0.118147 | − | 0.204637i | ||||
\(887\) | 13426.7 | + | 23255.6i | 0.508256 | + | 0.880325i | 0.999954 | + | 0.00955935i | \(0.00304288\pi\) |
−0.491699 | + | 0.870766i | \(0.663624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5701.59 | + | 9875.44i | −0.215101 | + | 0.372567i | ||||
\(890\) | 1877.71 | 0.0707202 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27429.4 | 1.02960 | ||||||||
\(893\) | 12083.6 | − | 20929.4i | 0.452813 | − | 0.784295i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9066.97 | + | 15704.5i | 0.338632 | + | 0.586527i | ||||
\(896\) | 4358.34 | + | 7548.86i | 0.162502 | + | 0.281462i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1662.73 | − | 2879.94i | 0.0617885 | − | 0.107021i | ||||
\(899\) | 6505.26 | 0.241338 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36059.3 | 1.33331 | ||||||||
\(902\) | −5107.60 | + | 8846.63i | −0.188542 | + | 0.326564i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2693.73 | + | 4665.67i | 0.0991063 | + | 0.171657i | ||||
\(905\) | −8878.52 | − | 15378.1i | −0.326113 | − | 0.564844i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13575.4 | + | 23513.4i | −0.496985 | + | 0.860803i | −0.999994 | − | 0.00347836i | \(-0.998893\pi\) |
0.503009 | + | 0.864281i | \(0.332226\pi\) | |||||||
\(908\) | 43097.1 | 1.57514 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −987.180 | −0.0359612 | ||||||||
\(911\) | 7650.25 | − | 13250.6i | 0.278226 | − | 0.481902i | −0.692718 | − | 0.721209i | \(-0.743587\pi\) |
0.970944 | + | 0.239307i | \(0.0769202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23646.4 | + | 40956.8i | 0.857156 | + | 1.48464i | ||||
\(914\) | −6567.30 | − | 11374.9i | −0.237666 | − | 0.411650i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17982.1 | − | 31145.8i | 0.648628 | − | 1.12346i | ||||
\(917\) | −2679.19 | −0.0964826 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26325.6 | −0.944943 | −0.472471 | − | 0.881346i | \(-0.656638\pi\) | ||||
−0.472471 | + | 0.881346i | \(0.656638\pi\) | |||||||
\(920\) | −379.962 | + | 658.114i | −0.0136163 | + | 0.0235841i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1896.34 | + | 3284.55i | 0.0677359 | + | 0.117322i | ||||
\(923\) | −2871.31 | − | 4973.25i | −0.102395 | − | 0.177353i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2729.29 | − | 4727.28i | 0.0970147 | − | 0.168034i | ||||
\(926\) | −10389.9 | −0.368719 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5568.27 | 0.196969 | ||||||||
\(929\) | 17753.5 | − | 30750.0i | 0.626991 | − | 1.08598i | −0.361162 | − | 0.932503i | \(-0.617620\pi\) |
0.988152 | − | 0.153477i | \(-0.0490469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16635.0 | + | 28812.6i | 0.585595 | + | 1.01428i | ||||
\(932\) | −339.926 | − | 588.769i | −0.0119470 | − | 0.0206929i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4350.70 | − | 7535.63i | 0.152419 | − | 0.263997i | ||||
\(935\) | −15185.5 | −0.531143 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35105.4 | 1.22395 | 0.611975 | − | 0.790877i | \(-0.290375\pi\) | ||||
0.611975 | + | 0.790877i | \(0.290375\pi\) | |||||||
\(938\) | 2069.46 | − | 3584.41i | 0.0720366 | − | 0.124771i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3998.65 | − | 6925.87i | −0.138746 | − | 0.240316i | ||||
\(941\) | 1787.23 | + | 3095.58i | 0.0619151 | + | 0.107240i | 0.895321 | − | 0.445421i | \(-0.146946\pi\) |
−0.833406 | + | 0.552661i | \(0.813613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2498.10 | − | 4326.83i | 0.0862664 | − | 0.149418i | ||||
\(944\) | −20647.3 | −0.711876 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12632.5 | −0.434163 | ||||||||
\(947\) | −16529.2 | + | 28629.5i | −0.567189 | + | 0.982400i | 0.429653 | + | 0.902994i | \(0.358636\pi\) |
−0.996842 | + | 0.0794061i | \(0.974698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8421.17 | + | 14585.9i | 0.288053 | + | 0.498923i | ||||
\(950\) | 1032.00 | + | 1787.48i | 0.0352449 | + | 0.0610459i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3176.24 | + | 5501.42i | −0.108133 | + | 0.187292i | ||||
\(953\) | 1355.24 | 0.0460656 | 0.0230328 | − | 0.999735i | \(-0.492668\pi\) | ||||
0.0230328 | + | 0.999735i | \(0.492668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1398.25 | 0.0473784 | ||||||||
\(956\) | −20477.2 | + | 35467.5i | −0.692760 | + | 1.19990i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1581.03 | + | 2738.43i | 0.0533203 | + | 0.0923534i | ||||
\(959\) | −10299.5 | − | 17839.3i | −0.346809 | − | 0.600690i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3677.79 | − | 6370.11i | 0.123453 | − | 0.213827i | ||||
\(962\) | −6222.23 | −0.208537 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22520.6 | −0.752428 | ||||||||
\(965\) | −665.399 | + | 1152.50i | −0.0221968 | + | 0.0384460i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28059.0 | − | 48599.6i | −0.933110 | − | 1.61619i | −0.777971 | − | 0.628301i | \(-0.783751\pi\) |
−0.155139 | − | 0.987893i | \(-0.549583\pi\) | |||||||
\(968\) | −424.840 | − | 735.844i | −0.0141063 | − | 0.0244328i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2006.01 | + | 3474.51i | −0.0664010 | + | 0.115010i | ||||
\(971\) | 32718.5 | 1.08135 | 0.540673 | − | 0.841233i | \(-0.318170\pi\) | ||||
0.540673 | + | 0.841233i | \(0.318170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16262.9 | −0.535834 | ||||||||
\(974\) | −2356.08 | + | 4080.86i | −0.0775090 | + | 0.134250i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.1870 | − | 64.4098i | −0.00121960 | − | 0.00211241i | ||||
\(977\) | 4425.44 | + | 7665.09i | 0.144915 | + | 0.251001i | 0.929341 | − | 0.369222i | \(-0.120376\pi\) |
−0.784426 | + | 0.620222i | \(0.787042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9618.09 | − | 16659.0i | 0.313989 | − | 0.543845i | ||||
\(980\) | 11009.5 | 0.358864 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2121.29 | −0.0689338 | ||||||||
\(983\) | 17054.0 | − | 29538.3i | 0.553343 | − | 0.958419i | −0.444687 | − | 0.895686i | \(-0.646685\pi\) |
0.998030 | − | 0.0627329i | \(-0.0199816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11827.8 | − | 20486.3i | −0.382604 | − | 0.662689i | ||||
\(986\) | 1287.56 | + | 2230.11i | 0.0415864 | + | 0.0720297i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16384.8 | + | 28379.4i | −0.527602 | + | 0.913834i | ||||
\(989\) | 6178.47 | 0.198649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52154.2 | −1.67178 | −0.835890 | − | 0.548897i | \(-0.815048\pi\) | ||||
−0.835890 | + | 0.548897i | \(0.815048\pi\) | |||||||
\(992\) | −9601.96 | + | 16631.1i | −0.307321 | + | 0.532296i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 374.091 | + | 647.944i | 0.0119371 | + | 0.0206756i | ||||
\(995\) | −7199.23 | − | 12469.4i | −0.229378 | − | 0.397294i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1055.55 | + | 1828.27i | −0.0335302 | + | 0.0580760i | −0.882304 | − | 0.470681i | \(-0.844008\pi\) |
0.848773 | + | 0.528757i | \(0.177342\pi\) | |||||||
\(998\) | −11020.7 | −0.349554 | ||||||||
\(999\) | 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 | 405.4.e.o.136.2 | 4 | ||
3.2 | odd | 2 | 405.4.e.p.136.1 | 4 | |||
9.2 | odd | 6 | 405.4.a.c.1.2 | ✓ | 2 | ||
9.4 | even | 3 | inner | 405.4.e.o.271.2 | 4 | ||
9.5 | odd | 6 | 405.4.e.p.271.1 | 4 | |||
9.7 | even | 3 | 405.4.a.f.1.1 | yes | 2 | ||
45.29 | odd | 6 | 2025.4.a.m.1.1 | 2 | |||
45.34 | even | 6 | 2025.4.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.c.1.2 | ✓ | 2 | 9.2 | odd | 6 | ||
405.4.a.f.1.1 | yes | 2 | 9.7 | even | 3 | ||
405.4.e.o.136.2 | 4 | 1.1 | even | 1 | trivial | ||
405.4.e.o.271.2 | 4 | 9.4 | even | 3 | inner | ||
405.4.e.p.136.1 | 4 | 3.2 | odd | 2 | |||
405.4.e.p.271.1 | 4 | 9.5 | odd | 6 | |||
2025.4.a.i.1.2 | 2 | 45.34 | even | 6 | |||
2025.4.a.m.1.1 | 2 | 45.29 | odd | 6 |