Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,5,Mod(8,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.96402929859\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 8.3 | ||
Root | \(0.625165i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.8 |
Dual form | 19.5.d.a.12.3 |
$q$-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 \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.541408 | − | 0.312582i | −0.135352 | − | 0.0781456i | 0.430795 | − | 0.902450i | \(-0.358233\pi\) |
−0.566147 | + | 0.824304i | \(0.691567\pi\) | |||||||
\(3\) | −8.70876 | − | 5.02800i | −0.967640 | − | 0.558667i | −0.0691240 | − | 0.997608i | \(-0.522020\pi\) |
−0.898516 | + | 0.438941i | \(0.855354\pi\) | |||||||
\(4\) | −7.80458 | − | 13.5179i | −0.487787 | − | 0.844871i | ||||
\(5\) | 4.61985 | − | 8.00181i | 0.184794 | − | 0.320072i | −0.758713 | − | 0.651425i | \(-0.774172\pi\) |
0.943507 | + | 0.331353i | \(0.107505\pi\) | |||||||
\(6\) | 3.14333 | + | 5.44441i | 0.0873147 | + | 0.151234i | ||||
\(7\) | 0.274467 | 0.00560136 | 0.00280068 | − | 0.999996i | \(-0.499109\pi\) | ||||
0.00280068 | + | 0.999996i | \(0.499109\pi\) | |||||||
\(8\) | 19.7609i | 0.308765i | ||||||||
\(9\) | 10.0617 | + | 17.4273i | 0.124218 | + | 0.215152i | ||||
\(10\) | −5.00245 | + | 2.88816i | −0.0500245 | + | 0.0288816i | ||||
\(11\) | 45.5269 | 0.376255 | 0.188128 | − | 0.982145i | \(-0.439758\pi\) | ||||
0.188128 | + | 0.982145i | \(0.439758\pi\) | |||||||
\(12\) | 156.966i | 1.09004i | ||||||||
\(13\) | 111.271 | − | 64.2421i | 0.658406 | − | 0.380131i | −0.133263 | − | 0.991081i | \(-0.542546\pi\) |
0.791669 | + | 0.610950i | \(0.209212\pi\) | |||||||
\(14\) | −0.148599 | − | 0.0857934i | −0.000758156 | − | 0.000437722i | ||||
\(15\) | −80.4663 | + | 46.4572i | −0.357628 | + | 0.206476i | ||||
\(16\) | −118.696 | + | 205.588i | −0.463658 | + | 0.803079i | ||||
\(17\) | 212.040 | − | 367.264i | 0.733702 | − | 1.27081i | −0.221589 | − | 0.975140i | \(-0.571124\pi\) |
0.955291 | − | 0.295669i | \(-0.0955425\pi\) | |||||||
\(18\) | − | 12.5804i | − | 0.0388284i | ||||||
\(19\) | −280.252 | − | 227.552i | −0.776322 | − | 0.630337i | ||||
\(20\) | −144.224 | −0.360560 | ||||||||
\(21\) | −2.39026 | − | 1.38002i | −0.00542010 | − | 0.00312930i | ||||
\(22\) | −24.6486 | − | 14.2309i | −0.0509269 | − | 0.0294027i | ||||
\(23\) | −286.876 | − | 496.884i | −0.542299 | − | 0.939289i | −0.998772 | − | 0.0495518i | \(-0.984221\pi\) |
0.456473 | − | 0.889737i | \(-0.349113\pi\) | |||||||
\(24\) | 99.3581 | − | 172.093i | 0.172497 | − | 0.298773i | ||||
\(25\) | 269.814 | + | 467.332i | 0.431702 | + | 0.747731i | ||||
\(26\) | −80.3238 | −0.118822 | ||||||||
\(27\) | 612.176i | 0.839748i | ||||||||
\(28\) | −2.14210 | − | 3.71022i | −0.00273227 | − | 0.00473243i | ||||
\(29\) | 763.678 | − | 440.909i | 0.908059 | − | 0.524268i | 0.0282529 | − | 0.999601i | \(-0.491006\pi\) |
0.879806 | + | 0.475333i | \(0.157672\pi\) | |||||||
\(30\) | 58.0868 | 0.0645409 | ||||||||
\(31\) | 1531.33i | 1.59348i | 0.604326 | + | 0.796738i | \(0.293443\pi\) | ||||
−0.604326 | + | 0.796738i | \(0.706557\pi\) | |||||||
\(32\) | 402.342 | − | 232.292i | 0.392912 | − | 0.226848i | ||||
\(33\) | −396.483 | − | 228.909i | −0.364079 | − | 0.210201i | ||||
\(34\) | −229.600 | + | 132.560i | −0.198616 | + | 0.114671i | ||||
\(35\) | 1.26799 | − | 2.19623i | 0.00103510 | − | 0.00179284i | ||||
\(36\) | 157.054 | − | 272.026i | 0.121184 | − | 0.209897i | ||||
\(37\) | − | 71.9344i | − | 0.0525452i | −0.999655 | − | 0.0262726i | \(-0.991636\pi\) | ||
0.999655 | − | 0.0262726i | \(-0.00836380\pi\) | |||||||
\(38\) | 80.6022 | + | 210.800i | 0.0558187 | + | 0.145984i | ||||
\(39\) | −1292.04 | −0.849467 | ||||||||
\(40\) | 158.123 | + | 91.2925i | 0.0988270 | + | 0.0570578i | ||||
\(41\) | 1112.58 | + | 642.350i | 0.661857 | + | 0.382123i | 0.792984 | − | 0.609242i | \(-0.208526\pi\) |
−0.131127 | + | 0.991366i | \(0.541860\pi\) | |||||||
\(42\) | 0.862740 | + | 1.49431i | 0.000489081 | + | 0.000847114i | ||||
\(43\) | 603.976 | − | 1046.12i | 0.326650 | − | 0.565775i | −0.655195 | − | 0.755460i | \(-0.727413\pi\) |
0.981845 | + | 0.189685i | \(0.0607468\pi\) | |||||||
\(44\) | −355.318 | − | 615.429i | −0.183532 | − | 0.317887i | ||||
\(45\) | 185.933 | 0.0918189 | ||||||||
\(46\) | 358.690i | 0.169513i | ||||||||
\(47\) | −1347.59 | − | 2334.09i | −0.610045 | − | 1.05663i | −0.991232 | − | 0.132131i | \(-0.957818\pi\) |
0.381187 | − | 0.924498i | \(-0.375515\pi\) | |||||||
\(48\) | 2067.40 | − | 1193.61i | 0.897308 | − | 0.518061i | ||||
\(49\) | −2400.92 | −0.999969 | ||||||||
\(50\) | − | 337.356i | − | 0.134943i | ||||||
\(51\) | −3693.21 | + | 2132.27i | −1.41992 | + | 0.819790i | ||||
\(52\) | −1736.84 | − | 1002.77i | −0.642323 | − | 0.370846i | ||||
\(53\) | 1834.78 | − | 1059.31i | 0.653177 | − | 0.377112i | −0.136495 | − | 0.990641i | \(-0.543584\pi\) |
0.789673 | + | 0.613529i | \(0.210250\pi\) | |||||||
\(54\) | 191.356 | − | 331.437i | 0.0656226 | − | 0.113662i | ||||
\(55\) | 210.327 | − | 364.297i | 0.0695296 | − | 0.120429i | ||||
\(56\) | 5.42372i | 0.00172950i | ||||||||
\(57\) | 1296.52 | + | 3390.80i | 0.399051 | + | 1.04364i | ||||
\(58\) | −551.282 | −0.163877 | ||||||||
\(59\) | 4850.33 | + | 2800.34i | 1.39337 | + | 0.804465i | 0.993687 | − | 0.112187i | \(-0.0357857\pi\) |
0.399686 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(60\) | 1256.01 | + | 725.158i | 0.348892 | + | 0.201433i | ||||
\(61\) | 1240.48 | + | 2148.57i | 0.333372 | + | 0.577417i | 0.983171 | − | 0.182689i | \(-0.0584803\pi\) |
−0.649799 | + | 0.760106i | \(0.725147\pi\) | |||||||
\(62\) | 478.666 | − | 829.075i | 0.124523 | − | 0.215680i | ||||
\(63\) | 2.76159 | + | 4.78322i | 0.000695790 | + | 0.00120514i | ||||
\(64\) | 3507.84 | 0.856407 | ||||||||
\(65\) | − | 1187.16i | − | 0.280983i | ||||||
\(66\) | 143.106 | + | 247.867i | 0.0328526 | + | 0.0569024i | ||||
\(67\) | −656.457 | + | 379.006i | −0.146237 | + | 0.0844298i | −0.571333 | − | 0.820718i | \(-0.693574\pi\) |
0.425096 | + | 0.905148i | \(0.360240\pi\) | |||||||
\(68\) | −6619.53 | −1.43156 | ||||||||
\(69\) | 5769.66i | 1.21186i | ||||||||
\(70\) | −1.37300 | + | 0.792705i | −0.000280205 | + | 0.000161776i | ||||
\(71\) | −5268.29 | − | 3041.65i | −1.04509 | − | 0.603381i | −0.123817 | − | 0.992305i | \(-0.539514\pi\) |
−0.921270 | + | 0.388924i | \(0.872847\pi\) | |||||||
\(72\) | −344.380 | + | 198.828i | −0.0664313 | + | 0.0383541i | ||||
\(73\) | 3512.83 | − | 6084.39i | 0.659191 | − | 1.14175i | −0.321635 | − | 0.946864i | \(-0.604232\pi\) |
0.980826 | − | 0.194888i | \(-0.0624343\pi\) | |||||||
\(74\) | −22.4854 | + | 38.9459i | −0.00410618 | + | 0.00711211i | ||||
\(75\) | − | 5426.51i | − | 0.964712i | ||||||
\(76\) | −888.778 | + | 5564.38i | −0.153874 | + | 0.963362i | ||||
\(77\) | 12.4956 | 0.00210754 | ||||||||
\(78\) | 699.521 | + | 403.869i | 0.114977 | + | 0.0663821i | ||||
\(79\) | −2796.99 | − | 1614.84i | −0.448164 | − | 0.258747i | 0.258891 | − | 0.965907i | \(-0.416643\pi\) |
−0.707054 | + | 0.707159i | \(0.749976\pi\) | |||||||
\(80\) | 1096.72 | + | 1899.57i | 0.171362 | + | 0.296808i | ||||
\(81\) | 3893.02 | − | 6742.91i | 0.593358 | − | 1.02773i | ||||
\(82\) | −401.574 | − | 695.547i | −0.0597225 | − | 0.103442i | ||||
\(83\) | 5586.78 | 0.810971 | 0.405485 | − | 0.914102i | \(-0.367103\pi\) | ||||
0.405485 | + | 0.914102i | \(0.367103\pi\) | |||||||
\(84\) | 43.0819i | 0.00610572i | ||||||||
\(85\) | −1959.18 | − | 3393.40i | −0.271167 | − | 0.469675i | ||||
\(86\) | −653.995 | + | 377.584i | −0.0884256 | + | 0.0510525i | ||||
\(87\) | −8867.58 | −1.17157 | ||||||||
\(88\) | 899.653i | 0.116174i | ||||||||
\(89\) | −4918.49 | + | 2839.69i | −0.620943 | + | 0.358502i | −0.777236 | − | 0.629209i | \(-0.783379\pi\) |
0.156293 | + | 0.987711i | \(0.450046\pi\) | |||||||
\(90\) | −100.666 | − | 58.1195i | −0.0124279 | − | 0.00717524i | ||||
\(91\) | 30.5401 | − | 17.6323i | 0.00368797 | − | 0.00212925i | ||||
\(92\) | −4477.90 | + | 7755.95i | −0.529052 | + | 0.916345i | ||||
\(93\) | 7699.53 | − | 13336.0i | 0.890222 | − | 1.54191i | ||||
\(94\) | 1684.93i | 0.190689i | ||||||||
\(95\) | −3115.55 | + | 1191.27i | −0.345213 | + | 0.131997i | ||||
\(96\) | −4671.87 | −0.506930 | ||||||||
\(97\) | 10277.2 | + | 5933.52i | 1.09227 | + | 0.630622i | 0.934180 | − | 0.356803i | \(-0.116133\pi\) |
0.158089 | + | 0.987425i | \(0.449467\pi\) | |||||||
\(98\) | 1299.88 | + | 750.487i | 0.135348 | + | 0.0781431i | ||||
\(99\) | 458.076 | + | 793.411i | 0.0467377 | + | 0.0809520i | ||||
\(100\) | 4211.57 | − | 7294.66i | 0.421157 | − | 0.729466i | ||||
\(101\) | 7781.01 | + | 13477.1i | 0.762769 | + | 1.32116i | 0.941418 | + | 0.337242i | \(0.109494\pi\) |
−0.178649 | + | 0.983913i | \(0.557173\pi\) | |||||||
\(102\) | 2666.05 | 0.256252 | ||||||||
\(103\) | 1961.40i | 0.184881i | 0.995718 | + | 0.0924403i | \(0.0294667\pi\) | ||||
−0.995718 | + | 0.0924403i | \(0.970533\pi\) | |||||||
\(104\) | 1269.48 | + | 2198.81i | 0.117371 | + | 0.203293i | ||||
\(105\) | −22.0853 | + | 12.7510i | −0.00200320 | + | 0.00115655i | ||||
\(106\) | −1324.48 | −0.117879 | ||||||||
\(107\) | 18401.5i | 1.60726i | 0.595128 | + | 0.803631i | \(0.297102\pi\) | ||||
−0.595128 | + | 0.803631i | \(0.702898\pi\) | |||||||
\(108\) | 8275.36 | − | 4777.78i | 0.709479 | − | 0.409618i | ||||
\(109\) | −6715.47 | − | 3877.18i | −0.565228 | − | 0.326334i | 0.190013 | − | 0.981782i | \(-0.439147\pi\) |
−0.755241 | + | 0.655447i | \(0.772480\pi\) | |||||||
\(110\) | −227.746 | + | 131.489i | −0.0188220 | + | 0.0108669i | ||||
\(111\) | −361.687 | + | 626.460i | −0.0293553 | + | 0.0508449i | ||||
\(112\) | −32.5782 | + | 56.4271i | −0.00259712 | + | 0.00449834i | ||||
\(113\) | − | 4465.17i | − | 0.349688i | −0.984596 | − | 0.174844i | \(-0.944058\pi\) | ||
0.984596 | − | 0.174844i | \(-0.0559421\pi\) | |||||||
\(114\) | 357.959 | − | 2241.08i | 0.0275438 | − | 0.172444i | ||||
\(115\) | −5301.29 | −0.400854 | ||||||||
\(116\) | −11920.4 | − | 6882.23i | −0.885878 | − | 0.511462i | ||||
\(117\) | 2239.14 | + | 1292.77i | 0.163572 | + | 0.0944383i | ||||
\(118\) | −1750.67 | − | 3032.26i | −0.125731 | − | 0.217772i | ||||
\(119\) | 58.1979 | − | 100.802i | 0.00410973 | − | 0.00711826i | ||||
\(120\) | −918.038 | − | 1590.09i | −0.0637526 | − | 0.110423i | ||||
\(121\) | −12568.3 | −0.858432 | ||||||||
\(122\) | − | 1551.00i | − | 0.104206i | ||||||
\(123\) | −6459.47 | − | 11188.1i | −0.426960 | − | 0.739516i | ||||
\(124\) | 20700.4 | − | 11951.4i | 1.34628 | − | 0.777276i | ||||
\(125\) | 10760.8 | 0.688691 | ||||||||
\(126\) | − | 3.45290i | − | 0.000217492i | ||||||
\(127\) | −355.004 | + | 204.962i | −0.0220103 | + | 0.0127076i | −0.510965 | − | 0.859602i | \(-0.670712\pi\) |
0.488954 | + | 0.872309i | \(0.337378\pi\) | |||||||
\(128\) | −8336.65 | − | 4813.17i | −0.508829 | − | 0.293772i | ||||
\(129\) | −10519.8 | + | 6073.59i | −0.632159 | + | 0.364977i | ||||
\(130\) | −371.084 | + | 642.736i | −0.0219576 | + | 0.0380317i | ||||
\(131\) | −1477.71 | + | 2559.46i | −0.0861084 | + | 0.149144i | −0.905863 | − | 0.423571i | \(-0.860776\pi\) |
0.819755 | + | 0.572715i | \(0.194110\pi\) | |||||||
\(132\) | 7146.17i | 0.410134i | ||||||||
\(133\) | −76.9199 | − | 62.4554i | −0.00434846 | − | 0.00353075i | ||||
\(134\) | 473.882 | 0.0263913 | ||||||||
\(135\) | 4898.52 | + | 2828.16i | 0.268780 | + | 0.155180i | ||||
\(136\) | 7257.48 | + | 4190.11i | 0.392381 | + | 0.226541i | ||||
\(137\) | −13132.3 | − | 22745.8i | −0.699679 | − | 1.21188i | −0.968578 | − | 0.248711i | \(-0.919993\pi\) |
0.268899 | − | 0.963168i | \(-0.413340\pi\) | |||||||
\(138\) | 1803.49 | − | 3123.74i | 0.0947014 | − | 0.164028i | ||||
\(139\) | −2168.28 | − | 3755.57i | −0.112224 | − | 0.194378i | 0.804443 | − | 0.594030i | \(-0.202464\pi\) |
−0.916667 | + | 0.399653i | \(0.869131\pi\) | |||||||
\(140\) | −39.5847 | −0.00201963 | ||||||||
\(141\) | 27102.7i | 1.36325i | ||||||||
\(142\) | 1901.53 | + | 3293.55i | 0.0943032 | + | 0.163338i | ||||
\(143\) | 5065.80 | − | 2924.74i | 0.247729 | − | 0.143026i | ||||
\(144\) | −4777.13 | −0.230379 | ||||||||
\(145\) | − | 8147.73i | − | 0.387526i | ||||||
\(146\) | −3803.75 | + | 2196.09i | −0.178446 | + | 0.103026i | ||||
\(147\) | 20909.1 | + | 12071.9i | 0.967610 | + | 0.558650i | ||||
\(148\) | −972.405 | + | 561.418i | −0.0443939 | + | 0.0256309i | ||||
\(149\) | −1635.85 | + | 2833.37i | −0.0736835 | + | 0.127623i | −0.900513 | − | 0.434829i | \(-0.856809\pi\) |
0.826830 | + | 0.562453i | \(0.190142\pi\) | |||||||
\(150\) | −1696.23 | + | 2937.96i | −0.0753880 | + | 0.130576i | ||||
\(151\) | − | 3278.86i | − | 0.143803i | −0.997412 | − | 0.0719016i | \(-0.977093\pi\) | ||
0.997412 | − | 0.0719016i | \(-0.0229068\pi\) | |||||||
\(152\) | 4496.63 | − | 5538.04i | 0.194626 | − | 0.239701i | ||||
\(153\) | 8533.90 | 0.364556 | ||||||||
\(154\) | −6.76523 | − | 3.90591i | −0.000285260 | − | 0.000164695i | ||||
\(155\) | 12253.4 | + | 7074.51i | 0.510027 | + | 0.294464i | ||||
\(156\) | 10083.8 | + | 17465.7i | 0.414359 | + | 0.717690i | ||||
\(157\) | −15632.5 | + | 27076.3i | −0.634204 | + | 1.09847i | 0.352479 | + | 0.935820i | \(0.385339\pi\) |
−0.986683 | + | 0.162654i | \(0.947995\pi\) | |||||||
\(158\) | 1009.54 | + | 1748.58i | 0.0404399 | + | 0.0700440i | ||||
\(159\) | −21304.8 | −0.842721 | ||||||||
\(160\) | − | 4292.62i | − | 0.167680i | ||||||
\(161\) | −78.7379 | − | 136.378i | −0.00303761 | − | 0.00526130i | ||||
\(162\) | −4215.43 | + | 2433.78i | −0.160624 | + | 0.0927366i | ||||
\(163\) | 32759.0 | 1.23298 | 0.616489 | − | 0.787363i | \(-0.288554\pi\) | ||||
0.616489 | + | 0.787363i | \(0.288554\pi\) | |||||||
\(164\) | − | 20053.1i | − | 0.745579i | ||||||
\(165\) | −3663.38 | + | 2115.05i | −0.134559 | + | 0.0776878i | ||||
\(166\) | −3024.73 | − | 1746.33i | −0.109767 | − | 0.0633738i | ||||
\(167\) | 22419.2 | − | 12943.7i | 0.803872 | − | 0.464116i | −0.0409511 | − | 0.999161i | \(-0.513039\pi\) |
0.844823 | + | 0.535045i | \(0.179705\pi\) | |||||||
\(168\) | 27.2705 | − | 47.2339i | 0.000966216 | − | 0.00167354i | ||||
\(169\) | −6026.39 | + | 10438.0i | −0.211001 | + | 0.365464i | ||||
\(170\) | 2449.62i | 0.0847621i | ||||||||
\(171\) | 1145.81 | − | 7173.59i | 0.0391851 | − | 0.245326i | ||||
\(172\) | −18855.1 | −0.637342 | ||||||||
\(173\) | −3010.79 | − | 1738.28i | −0.100598 | − | 0.0580802i | 0.448857 | − | 0.893604i | \(-0.351831\pi\) |
−0.549455 | + | 0.835523i | \(0.685165\pi\) | |||||||
\(174\) | 4800.98 | + | 2771.85i | 0.158574 | + | 0.0915527i | ||||
\(175\) | 74.0550 | + | 128.267i | 0.00241812 | + | 0.00418831i | ||||
\(176\) | −5403.88 | + | 9359.79i | −0.174454 | + | 0.302163i | ||||
\(177\) | −28160.3 | − | 48775.0i | −0.898856 | − | 1.55686i | ||||
\(178\) | 3550.55 | 0.112061 | ||||||||
\(179\) | − | 40116.5i | − | 1.25204i | −0.779809 | − | 0.626018i | \(-0.784684\pi\) | ||
0.779809 | − | 0.626018i | \(-0.215316\pi\) | |||||||
\(180\) | −1451.13 | − | 2513.44i | −0.0447880 | − | 0.0775752i | ||||
\(181\) | −43406.5 | + | 25060.8i | −1.32494 | + | 0.764957i | −0.984513 | − | 0.175313i | \(-0.943906\pi\) |
−0.340431 | + | 0.940269i | \(0.610573\pi\) | |||||||
\(182\) | −22.0462 | −0.000665566 | ||||||||
\(183\) | − | 24948.5i | − | 0.744975i | ||||||
\(184\) | 9818.89 | − | 5668.94i | 0.290019 | − | 0.167443i | ||||
\(185\) | −575.605 | − | 332.326i | −0.0168183 | − | 0.00971003i | ||||
\(186\) | −8337.18 | + | 4813.47i | −0.240987 | + | 0.139134i | ||||
\(187\) | 9653.51 | − | 16720.4i | 0.276059 | − | 0.478148i | ||||
\(188\) | −21034.7 | + | 36433.2i | −0.595143 | + | 1.03082i | ||||
\(189\) | 168.022i | 0.00470373i | ||||||||
\(190\) | 2059.15 | + | 328.901i | 0.0570402 | + | 0.00911083i | ||||
\(191\) | 65019.2 | 1.78227 | 0.891137 | − | 0.453734i | \(-0.149908\pi\) | ||||
0.891137 | + | 0.453734i | \(0.149908\pi\) | |||||||
\(192\) | −30549.0 | − | 17637.5i | −0.828694 | − | 0.478447i | ||||
\(193\) | −57399.9 | − | 33139.8i | −1.54098 | − | 0.889684i | −0.998777 | − | 0.0494353i | \(-0.984258\pi\) |
−0.542201 | − | 0.840249i | \(-0.682409\pi\) | |||||||
\(194\) | −3709.43 | − | 6424.91i | −0.0985606 | − | 0.170712i | ||||
\(195\) | −5969.02 | + | 10338.6i | −0.156976 | + | 0.271891i | ||||
\(196\) | 18738.2 | + | 32455.5i | 0.487771 | + | 0.844845i | ||||
\(197\) | 44015.7 | 1.13416 | 0.567081 | − | 0.823662i | \(-0.308073\pi\) | ||||
0.567081 | + | 0.823662i | \(0.308073\pi\) | |||||||
\(198\) | − | 572.746i | − | 0.0146094i | ||||||
\(199\) | 35353.3 | + | 61233.7i | 0.892738 | + | 1.54627i | 0.836580 | + | 0.547845i | \(0.184552\pi\) |
0.0561582 | + | 0.998422i | \(0.482115\pi\) | |||||||
\(200\) | −9234.91 | + | 5331.78i | −0.230873 | + | 0.133294i | ||||
\(201\) | 7622.57 | 0.188673 | ||||||||
\(202\) | − | 9728.82i | − | 0.238428i | ||||||
\(203\) | 209.604 | − | 121.015i | 0.00508637 | − | 0.00293661i | ||||
\(204\) | 57647.9 | + | 33283.0i | 1.38523 | + | 0.799765i | ||||
\(205\) | 10279.9 | − | 5935.11i | 0.244614 | − | 0.141228i | ||||
\(206\) | 613.098 | − | 1061.92i | 0.0144476 | − | 0.0250240i | ||||
\(207\) | 5772.90 | − | 9998.96i | 0.134727 | − | 0.233353i | ||||
\(208\) | 30501.3i | 0.705003i | ||||||||
\(209\) | −12759.0 | − | 10359.7i | −0.292095 | − | 0.237168i | ||||
\(210\) | 15.9429 | 0.000361517 | ||||||||
\(211\) | −15047.0 | − | 8687.41i | −0.337976 | − | 0.195131i | 0.321400 | − | 0.946943i | \(-0.395846\pi\) |
−0.659377 | + | 0.751813i | \(0.729180\pi\) | |||||||
\(212\) | −28639.3 | − | 16534.9i | −0.637222 | − | 0.367900i | ||||
\(213\) | 30586.8 | + | 52977.9i | 0.674179 | + | 1.16771i | ||||
\(214\) | 5752.00 | − | 9962.75i | 0.125600 | − | 0.217546i | ||||
\(215\) | −5580.55 | − | 9665.80i | −0.120726 | − | 0.209103i | ||||
\(216\) | −12097.2 | −0.259284 | ||||||||
\(217\) | 420.299i | 0.00892563i | ||||||||
\(218\) | 2423.88 | + | 4198.27i | 0.0510032 | + | 0.0883401i | ||||
\(219\) | −61184.7 | + | 35325.0i | −1.27572 | + | 0.736536i | ||||
\(220\) | −6566.06 | −0.135662 | ||||||||
\(221\) | − | 54487.6i | − | 1.11561i | ||||||
\(222\) | 391.640 | − | 226.114i | 0.00794660 | − | 0.00458797i | ||||
\(223\) | 21863.6 | + | 12622.9i | 0.439654 | + | 0.253835i | 0.703451 | − | 0.710744i | \(-0.251641\pi\) |
−0.263797 | + | 0.964578i | \(0.584975\pi\) | |||||||
\(224\) | 110.429 | − | 63.7565i | 0.00220084 | − | 0.00127066i | ||||
\(225\) | −5429.56 | + | 9404.27i | −0.107250 | + | 0.185763i | ||||
\(226\) | −1395.73 | + | 2417.48i | −0.0273266 | + | 0.0473310i | ||||
\(227\) | 916.210i | 0.0177805i | 0.999960 | + | 0.00889024i | \(0.00282989\pi\) | ||||
−0.999960 | + | 0.00889024i | \(0.997170\pi\) | |||||||
\(228\) | 35717.9 | − | 43990.0i | 0.687093 | − | 0.846223i | ||||
\(229\) | −4664.33 | −0.0889443 | −0.0444721 | − | 0.999011i | \(-0.514161\pi\) | ||||
−0.0444721 | + | 0.999011i | \(0.514161\pi\) | |||||||
\(230\) | 2870.16 | + | 1657.09i | 0.0542564 | + | 0.0313250i | ||||
\(231\) | −108.821 | − | 62.8280i | −0.00203934 | − | 0.00117741i | ||||
\(232\) | 8712.78 | + | 15091.0i | 0.161875 | + | 0.280376i | ||||
\(233\) | −33186.8 | + | 57481.2i | −0.611299 | + | 1.05880i | 0.379723 | + | 0.925100i | \(0.376019\pi\) |
−0.991022 | + | 0.133701i | \(0.957314\pi\) | |||||||
\(234\) | −808.191 | − | 1399.83i | −0.0147599 | − | 0.0255648i | ||||
\(235\) | −24902.6 | −0.450930 | ||||||||
\(236\) | − | 87422.0i | − | 1.56963i | ||||||
\(237\) | 16238.9 | + | 28126.6i | 0.289107 | + | 0.500749i | ||||
\(238\) | −63.0176 | + | 36.3833i | −0.00111252 | + | 0.000642314i | ||||
\(239\) | 32277.5 | 0.565073 | 0.282537 | − | 0.959257i | \(-0.408824\pi\) | ||||
0.282537 | + | 0.959257i | \(0.408824\pi\) | |||||||
\(240\) | − | 22057.2i | − | 0.382938i | ||||||
\(241\) | 71795.8 | − | 41451.3i | 1.23613 | − | 0.713681i | 0.267830 | − | 0.963466i | \(-0.413693\pi\) |
0.968301 | + | 0.249785i | \(0.0803600\pi\) | |||||||
\(242\) | 6804.59 | + | 3928.63i | 0.116191 | + | 0.0670827i | ||||
\(243\) | −24863.8 | + | 14355.1i | −0.421070 | + | 0.243105i | ||||
\(244\) | 19362.8 | − | 33537.3i | 0.325228 | − | 0.563312i | ||||
\(245\) | −11091.9 | + | 19211.7i | −0.184788 | + | 0.320062i | ||||
\(246\) | 8076.47i | 0.133460i | ||||||||
\(247\) | −45802.2 | − | 7315.83i | −0.750746 | − | 0.119914i | ||||
\(248\) | −30260.5 | −0.492009 | ||||||||
\(249\) | −48653.9 | − | 28090.3i | −0.784728 | − | 0.453063i | ||||
\(250\) | −5825.99 | − | 3363.64i | −0.0932158 | − | 0.0538182i | ||||
\(251\) | −32836.9 | − | 56875.1i | −0.521212 | − | 0.902766i | −0.999696 | − | 0.0246692i | \(-0.992147\pi\) |
0.478484 | − | 0.878096i | \(-0.341187\pi\) | |||||||
\(252\) | 43.1061 | − | 74.6620i | 0.000678794 | − | 0.00117571i | ||||
\(253\) | −13060.6 | − | 22621.6i | −0.204043 | − | 0.353412i | ||||
\(254\) | 256.270 | 0.00397219 | ||||||||
\(255\) | 39403.1i | 0.605969i | ||||||||
\(256\) | −25053.7 | − | 43394.3i | −0.382290 | − | 0.662145i | ||||
\(257\) | −7843.69 | + | 4528.55i | −0.118756 | + | 0.0685635i | −0.558201 | − | 0.829706i | \(-0.688508\pi\) |
0.439446 | + | 0.898269i | \(0.355175\pi\) | |||||||
\(258\) | 7593.99 | 0.114085 | ||||||||
\(259\) | − | 19.7436i | − | 0.000294325i | ||||||
\(260\) | −16047.9 | + | 9265.25i | −0.237395 | + | 0.137060i | ||||
\(261\) | 15367.7 | + | 8872.57i | 0.225595 | + | 0.130247i | ||||
\(262\) | 1600.08 | − | 923.809i | 0.0233099 | − | 0.0134580i | ||||
\(263\) | −46299.9 | + | 80193.7i | −0.669373 | + | 1.15939i | 0.308707 | + | 0.951157i | \(0.400104\pi\) |
−0.978080 | + | 0.208231i | \(0.933230\pi\) | |||||||
\(264\) | 4523.46 | − | 7834.87i | 0.0649027 | − | 0.112415i | ||||
\(265\) | − | 19575.4i | − | 0.278752i | ||||||
\(266\) | 22.1226 | + | 57.8576i | 0.000312661 | + | 0.000817707i | ||||
\(267\) | 57111.9 | 0.801132 | ||||||||
\(268\) | 10246.7 | + | 5915.96i | 0.142665 | + | 0.0823675i | ||||
\(269\) | 43611.5 | + | 25179.1i | 0.602693 | + | 0.347965i | 0.770100 | − | 0.637923i | \(-0.220206\pi\) |
−0.167407 | + | 0.985888i | \(0.553540\pi\) | |||||||
\(270\) | −1768.07 | − | 3062.38i | −0.0242533 | − | 0.0420080i | ||||
\(271\) | −3028.20 | + | 5245.00i | −0.0412331 | + | 0.0714179i | −0.885905 | − | 0.463866i | \(-0.846462\pi\) |
0.844672 | + | 0.535284i | \(0.179795\pi\) | |||||||
\(272\) | 50336.8 | + | 87185.8i | 0.680373 | + | 1.17844i | ||||
\(273\) | −354.622 | −0.00475817 | ||||||||
\(274\) | 16419.7i | 0.218707i | ||||||||
\(275\) | 12283.8 | + | 21276.1i | 0.162430 | + | 0.281337i | ||||
\(276\) | 77993.9 | − | 45029.8i | 1.02386 | − | 0.591128i | ||||
\(277\) | 94487.4 | 1.23144 | 0.615721 | − | 0.787964i | \(-0.288865\pi\) | ||||
0.615721 | + | 0.787964i | \(0.288865\pi\) | |||||||
\(278\) | 2711.06i | 0.0350792i | ||||||||
\(279\) | −26687.0 | + | 15407.7i | −0.342839 | + | 0.197938i | ||||
\(280\) | 43.3995 | + | 25.0567i | 0.000553566 | + | 0.000319601i | ||||
\(281\) | 25206.5 | − | 14553.0i | 0.319227 | − | 0.184306i | −0.331821 | − | 0.943342i | \(-0.607663\pi\) |
0.651048 | + | 0.759036i | \(0.274330\pi\) | |||||||
\(282\) | 8471.84 | − | 14673.6i | 0.106532 | − | 0.184518i | ||||
\(283\) | −34326.4 | + | 59455.1i | −0.428603 | + | 0.742363i | −0.996749 | − | 0.0805650i | \(-0.974328\pi\) |
0.568146 | + | 0.822928i | \(0.307661\pi\) | |||||||
\(284\) | 94955.1i | 1.17729i | ||||||||
\(285\) | 33122.3 | + | 5290.50i | 0.407784 | + | 0.0651339i | ||||
\(286\) | −3656.89 | −0.0447075 | ||||||||
\(287\) | 305.367 | + | 176.304i | 0.00370730 | + | 0.00214041i | ||||
\(288\) | 8096.46 | + | 4674.49i | 0.0976136 | + | 0.0563572i | ||||
\(289\) | −48161.3 | − | 83417.8i | −0.576637 | − | 0.998765i | ||||
\(290\) | −2546.84 | + | 4411.25i | −0.0302834 | + | 0.0524525i | ||||
\(291\) | −59667.5 | − | 103347.i | −0.704615 | − | 1.22043i | ||||
\(292\) | −109665. | −1.28618 | ||||||||
\(293\) | 155003.i | 1.80553i | 0.430132 | + | 0.902766i | \(0.358467\pi\) | ||||
−0.430132 | + | 0.902766i | \(0.641533\pi\) | |||||||
\(294\) | −7546.90 | − | 13071.6i | −0.0873120 | − | 0.151229i | ||||
\(295\) | 44815.6 | − | 25874.3i | 0.514974 | − | 0.297320i | ||||
\(296\) | 1421.49 | 0.0162241 | ||||||||
\(297\) | 27870.5i | 0.315960i | ||||||||
\(298\) | 1771.32 | − | 1022.67i | 0.0199464 | − | 0.0115161i | ||||
\(299\) | −63841.8 | − | 36859.1i | −0.714106 | − | 0.412289i | ||||
\(300\) | −73355.2 | + | 42351.6i | −0.815057 | + | 0.470574i | ||||
\(301\) | 165.771 | − | 287.124i | 0.00182969 | − | 0.00316911i | ||||
\(302\) | −1024.91 | + | 1775.20i | −0.0112376 | + | 0.0194641i | ||||
\(303\) | − | 156492.i | − | 1.70454i | ||||||
\(304\) | 80046.9 | − | 30607.0i | 0.866158 | − | 0.331187i | ||||
\(305\) | 22923.2 | 0.246420 | ||||||||
\(306\) | −4620.32 | − | 2667.54i | −0.0493434 | − | 0.0284885i | ||||
\(307\) | 86829.3 | + | 50130.9i | 0.921275 | + | 0.531899i | 0.884042 | − | 0.467408i | \(-0.154812\pi\) |
0.0372337 | + | 0.999307i | \(0.488145\pi\) | |||||||
\(308\) | −97.5230 | − | 168.915i | −0.00102803 | − | 0.00178060i | ||||
\(309\) | 9861.92 | − | 17081.3i | 0.103287 | − | 0.178898i | ||||
\(310\) | −4422.73 | − | 7660.39i | −0.0460222 | − | 0.0797127i | ||||
\(311\) | −43558.3 | −0.450350 | −0.225175 | − | 0.974318i | \(-0.572295\pi\) | ||||
−0.225175 | + | 0.974318i | \(0.572295\pi\) | |||||||
\(312\) | − | 25531.9i | − | 0.262285i | ||||||
\(313\) | −33606.5 | − | 58208.2i | −0.343032 | − | 0.594149i | 0.641962 | − | 0.766736i | \(-0.278121\pi\) |
−0.984994 | + | 0.172587i | \(0.944787\pi\) | |||||||
\(314\) | 16927.1 | − | 9772.88i | 0.171682 | − | 0.0991205i | ||||
\(315\) | 51.0325 | 0.000514311 | ||||||||
\(316\) | 50412.7i | 0.504854i | ||||||||
\(317\) | −20383.1 | + | 11768.2i | −0.202839 | + | 0.117109i | −0.597979 | − | 0.801512i | \(-0.704029\pi\) |
0.395140 | + | 0.918621i | \(0.370696\pi\) | |||||||
\(318\) | 11534.6 | + | 6659.51i | 0.114064 | + | 0.0658549i | ||||
\(319\) | 34767.8 | − | 20073.2i | 0.341662 | − | 0.197259i | ||||
\(320\) | 16205.7 | − | 28069.1i | 0.158259 | − | 0.274112i | ||||
\(321\) | 92523.1 | − | 160255.i | 0.897925 | − | 1.55525i | ||||
\(322\) | 98.4483i | 0.000949504i | ||||||||
\(323\) | −142996. | + | 54676.4i | −1.37063 | + | 0.524077i | ||||
\(324\) | −121534. | −1.15773 | ||||||||
\(325\) | 60044.8 | + | 34666.9i | 0.568471 | + | 0.328207i | ||||
\(326\) | −17736.0 | − | 10239.9i | −0.166886 | − | 0.0963518i | ||||
\(327\) | 38988.9 | + | 67530.8i | 0.364625 | + | 0.631548i | ||||
\(328\) | −12693.4 | + | 21985.7i | −0.117986 | + | 0.204358i | ||||
\(329\) | −369.868 | − | 640.631i | −0.00341708 | − | 0.00591856i | ||||
\(330\) | 2644.51 | 0.0242838 | ||||||||
\(331\) | − | 23677.2i | − | 0.216110i | −0.994145 | − | 0.108055i | \(-0.965538\pi\) | ||
0.994145 | − | 0.108055i | \(-0.0344622\pi\) | |||||||
\(332\) | −43602.5 | − | 75521.7i | −0.395581 | − | 0.685166i | ||||
\(333\) | 1253.62 | − | 723.780i | 0.0113052 | − | 0.00652707i | ||||
\(334\) | −16183.9 | −0.145074 | ||||||||
\(335\) | 7003.79i | 0.0624085i | ||||||||
\(336\) | 567.432 | − | 327.607i | 0.00502615 | − | 0.00290185i | ||||
\(337\) | −135878. | − | 78449.2i | −1.19644 | − | 0.690763i | −0.236677 | − | 0.971588i | \(-0.576058\pi\) |
−0.959759 | + | 0.280825i | \(0.909392\pi\) | |||||||
\(338\) | 6525.48 | − | 3767.49i | 0.0571188 | − | 0.0329776i | ||||
\(339\) | −22450.9 | + | 38886.1i | −0.195359 | + | 0.338372i | ||||
\(340\) | −30581.2 | + | 52968.2i | −0.264543 | + | 0.458203i | ||||
\(341\) | 69716.6i | 0.599553i | ||||||||
\(342\) | −2862.69 | + | 3525.68i | −0.0244750 | + | 0.0301433i | ||||
\(343\) | −1317.97 | −0.0112025 | ||||||||
\(344\) | 20672.3 | + | 11935.1i | 0.174691 | + | 0.100858i | ||||
\(345\) | 46167.7 | + | 26654.9i | 0.387882 | + | 0.223944i | ||||
\(346\) | 1086.71 | + | 1882.24i | 0.00907742 | + | 0.0157225i | ||||
\(347\) | 102854. | − | 178148.i | 0.854204 | − | 1.47953i | −0.0231772 | − | 0.999731i | \(-0.507378\pi\) |
0.877381 | − | 0.479794i | \(-0.159288\pi\) | |||||||
\(348\) | 69207.8 | + | 119871.i | 0.571474 | + | 0.989822i | ||||
\(349\) | 147121. | 1.20788 | 0.603939 | − | 0.797031i | \(-0.293597\pi\) | ||||
0.603939 | + | 0.797031i | \(0.293597\pi\) | |||||||
\(350\) | − | 92.5931i | − | 0.000755862i | ||||||
\(351\) | 39327.5 | + | 68117.3i | 0.319214 | + | 0.552895i | ||||
\(352\) | 18317.4 | − | 10575.5i | 0.147835 | − | 0.0853527i | ||||
\(353\) | −75142.1 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(354\) | 35209.6i | 0.280966i | ||||||||
\(355\) | −48677.3 | + | 28103.9i | −0.386251 | + | 0.223002i | ||||
\(356\) | 76773.5 | + | 44325.2i | 0.605775 | + | 0.349745i | ||||
\(357\) | −1013.66 | + | 585.238i | −0.00795348 | + | 0.00459194i | ||||
\(358\) | −12539.7 | + | 21719.4i | −0.0978410 | + | 0.169466i | ||||
\(359\) | 9387.33 | − | 16259.3i | 0.0728372 | − | 0.126158i | −0.827307 | − | 0.561751i | \(-0.810128\pi\) |
0.900144 | + | 0.435593i | \(0.143461\pi\) | |||||||
\(360\) | 3674.22i | 0.0283504i | ||||||||
\(361\) | 26761.5 | + | 127544.i | 0.205350 | + | 0.978688i | ||||
\(362\) | 31334.2 | 0.239112 | ||||||||
\(363\) | 109454. | + | 63193.5i | 0.830653 | + | 0.479578i | ||||
\(364\) | −476.705 | − | 275.226i | −0.00359789 | − | 0.00207724i | ||||
\(365\) | −32457.4 | − | 56217.9i | −0.243629 | − | 0.421977i | ||||
\(366\) | −7798.45 | + | 13507.3i | −0.0582165 | + | 0.100834i | ||||
\(367\) | 22404.8 | + | 38806.3i | 0.166345 | + | 0.288118i | 0.937132 | − | 0.348975i | \(-0.113470\pi\) |
−0.770787 | + | 0.637093i | \(0.780137\pi\) | |||||||
\(368\) | 136205. | 1.00576 | ||||||||
\(369\) | 25852.4i | 0.189867i | ||||||||
\(370\) | 207.758 | + | 359.848i | 0.00151759 | + | 0.00262855i | ||||
\(371\) | 503.585 | − | 290.745i | 0.00365868 | − | 0.00211234i | ||||
\(372\) | −240367. | −1.73695 | ||||||||
\(373\) | 163639.i | 1.17617i | 0.808799 | + | 0.588085i | \(0.200118\pi\) | ||||
−0.808799 | + | 0.588085i | \(0.799882\pi\) | |||||||
\(374\) | −10453.0 | + | 6035.03i | −0.0747304 | + | 0.0431456i | ||||
\(375\) | −93713.3 | − | 54105.4i | −0.666405 | − | 0.384749i | ||||
\(376\) | 46123.8 | − | 26629.6i | 0.326249 | − | 0.188360i | ||||
\(377\) | 56649.9 | − | 98120.6i | 0.398581 | − | 0.690363i | ||||
\(378\) | 52.5207 | − | 90.9685i | 0.000367576 | − | 0.000636660i | ||||
\(379\) | − | 132155.i | − | 0.920039i | −0.887909 | − | 0.460019i | \(-0.847842\pi\) | ||
0.887909 | − | 0.460019i | \(-0.152158\pi\) | |||||||
\(380\) | 40419.1 | + | 32818.4i | 0.279910 | + | 0.227274i | ||||
\(381\) | 4122.19 | 0.0283974 | ||||||||
\(382\) | −35201.9 | − | 20323.8i | −0.241235 | − | 0.139277i | ||||
\(383\) | −200322. | − | 115656.i | −1.36562 | − | 0.788442i | −0.375256 | − | 0.926921i | \(-0.622445\pi\) |
−0.990365 | + | 0.138479i | \(0.955779\pi\) | |||||||
\(384\) | 48401.2 | + | 83833.4i | 0.328242 | + | 0.568532i | ||||
\(385\) | 57.7278 | − | 99.9875i | 0.000389461 | − | 0.000674565i | ||||
\(386\) | 20717.9 | + | 35884.4i | 0.139050 | + | 0.240841i | ||||
\(387\) | 24308.0 | 0.162303 | ||||||||
\(388\) | − | 185235.i | − | 1.23043i | ||||||
\(389\) | −826.840 | − | 1432.13i | −0.00546414 | − | 0.00946418i | 0.863280 | − | 0.504725i | \(-0.168406\pi\) |
−0.868745 | + | 0.495260i | \(0.835073\pi\) | |||||||
\(390\) | 6463.36 | − | 3731.62i | 0.0424941 | − | 0.0245340i | ||||
\(391\) | −243317. | −1.59154 | ||||||||
\(392\) | − | 47444.5i | − | 0.308755i | ||||||
\(393\) | 25738.0 | − | 14859.8i | 0.166644 | − | 0.0962118i | ||||
\(394\) | −23830.5 | − | 13758.5i | −0.153511 | − | 0.0886297i | ||||
\(395\) | −25843.3 | + | 14920.6i | −0.165636 | + | 0.0956299i | ||||
\(396\) | 7150.19 | − | 12384.5i | 0.0455960 | − | 0.0789746i | ||||
\(397\) | 102128. | − | 176890.i | 0.647981 | − | 1.12234i | −0.335623 | − | 0.941996i | \(-0.608947\pi\) |
0.983604 | − | 0.180340i | \(-0.0577198\pi\) | |||||||
\(398\) | − | 44203.3i | − | 0.279054i | ||||||
\(399\) | 355.851 | + | 930.662i | 0.00223523 | + | 0.00584583i | ||||
\(400\) | −128104. | −0.800649 | ||||||||
\(401\) | 56182.7 | + | 32437.1i | 0.349393 | + | 0.201722i | 0.664418 | − | 0.747361i | \(-0.268680\pi\) |
−0.315025 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(402\) | −4126.92 | − | 2382.68i | −0.0255373 | − | 0.0147439i | ||||
\(403\) | 98375.9 | + | 170392.i | 0.605729 | + | 1.04915i | ||||
\(404\) | 121455. | − | 210366.i | 0.744137 | − | 1.28888i | ||||
\(405\) | −35970.3 | − | 62302.4i | −0.219298 | − | 0.379835i | ||||
\(406\) | −151.309 | −0.000917934 | ||||||||
\(407\) | − | 3274.95i | − | 0.0197704i | ||||||
\(408\) | −42135.7 | − | 72981.2i | −0.253122 | − | 0.438421i | ||||
\(409\) | −219413. | + | 126678.i | −1.31164 | + | 0.757276i | −0.982368 | − | 0.186958i | \(-0.940137\pi\) |
−0.329273 | + | 0.944235i | \(0.606804\pi\) | |||||||
\(410\) | −7420.84 | −0.0441454 | ||||||||
\(411\) | 264117.i | 1.56355i | ||||||||
\(412\) | 26514.1 | − | 15307.9i | 0.156200 | − | 0.0901823i | ||||
\(413\) | 1331.25 | + | 768.600i | 0.00780479 | + | 0.00450610i | ||||
\(414\) | −6251.00 | + | 3609.01i | −0.0364711 | + | 0.0210566i | ||||
\(415\) | 25810.0 | − | 44704.3i | 0.149862 | − | 0.259569i | ||||
\(416\) | 29845.9 | − | 51694.6i | 0.172464 | − | 0.298716i | ||||
\(417\) | 43608.5i | 0.250783i | ||||||||
\(418\) | 3669.57 | + | 9597.07i | 0.0210021 | + | 0.0549271i | ||||
\(419\) | −46712.5 | −0.266076 | −0.133038 | − | 0.991111i | \(-0.542473\pi\) | ||||
−0.133038 | + | 0.991111i | \(0.542473\pi\) | |||||||
\(420\) | 344.733 | + | 199.032i | 0.00195427 | + | 0.00112830i | ||||
\(421\) | 19528.3 | + | 11274.7i | 0.110179 | + | 0.0636121i | 0.554077 | − | 0.832465i | \(-0.313071\pi\) |
−0.443898 | + | 0.896078i | \(0.646405\pi\) | |||||||
\(422\) | 5431.06 | + | 9406.88i | 0.0304972 | + | 0.0528227i | ||||
\(423\) | 27118.0 | − | 46969.7i | 0.151557 | − | 0.262505i | ||||
\(424\) | 20932.9 | + | 36256.9i | 0.116439 | + | 0.201678i | ||||
\(425\) | 228845. | 1.26696 | ||||||||
\(426\) | − | 38243.6i | − | 0.210736i | ||||||
\(427\) | 340.469 | + | 589.710i | 0.00186733 | + | 0.00323432i | ||||
\(428\) | 248751. | − | 143616.i | 1.35793 | − | 0.784001i | ||||
\(429\) | −58822.5 | −0.319616 | ||||||||
\(430\) | 6977.53i | 0.0377368i | ||||||||
\(431\) | −215793. | + | 124588.i | −1.16167 | + | 0.670690i | −0.951704 | − | 0.307018i | \(-0.900669\pi\) |
−0.209966 | + | 0.977709i | \(0.567335\pi\) | |||||||
\(432\) | −125856. | − | 72663.2i | −0.674384 | − | 0.389356i | ||||
\(433\) | 38427.2 | − | 22186.0i | 0.204957 | − | 0.118332i | −0.394008 | − | 0.919107i | \(-0.628912\pi\) |
0.598966 | + | 0.800775i | \(0.295579\pi\) | |||||||
\(434\) | 131.378 | − | 227.553i | 0.000697498 | − | 0.00120810i | ||||
\(435\) | −40966.8 | + | 70956.7i | −0.216498 | + | 0.374986i | ||||
\(436\) | 121039.i | 0.636726i | ||||||||
\(437\) | −32669.1 | + | 204532.i | −0.171070 | + | 1.07102i | ||||
\(438\) | 44167.9 | 0.230228 | ||||||||
\(439\) | 211594. | + | 122164.i | 1.09793 | + | 0.633888i | 0.935676 | − | 0.352861i | \(-0.114791\pi\) |
0.162251 | + | 0.986749i | \(0.448125\pi\) | |||||||
\(440\) | 7198.85 | + | 4156.26i | 0.0371842 | + | 0.0214683i | ||||
\(441\) | −24157.3 | − | 41841.7i | −0.124214 | − | 0.215145i | ||||
\(442\) | −17031.9 | + | 29500.0i | −0.0871801 | + | 0.151000i | ||||
\(443\) | −29784.6 | − | 51588.5i | −0.151770 | − | 0.262873i | 0.780108 | − | 0.625644i | \(-0.215164\pi\) |
−0.931878 | + | 0.362772i | \(0.881831\pi\) | |||||||
\(444\) | 11291.3 | 0.0572765 | ||||||||
\(445\) | 52475.7i | 0.264996i | ||||||||
\(446\) | −7891.41 | − | 13668.3i | −0.0396721 | − | 0.0687141i | ||||
\(447\) | 28492.4 | − | 16450.1i | 0.142598 | − | 0.0823291i | ||||
\(448\) | 962.786 | 0.00479705 | ||||||||
\(449\) | − | 181264.i | − | 0.899122i | −0.893250 | − | 0.449561i | \(-0.851580\pi\) | ||
0.893250 | − | 0.449561i | \(-0.148420\pi\) | |||||||
\(450\) | 5879.22 | − | 3394.37i | 0.0290332 | − | 0.0167623i | ||||
\(451\) | 50652.4 | + | 29244.2i | 0.249027 | + | 0.143776i | ||||
\(452\) | −60359.9 | + | 34848.8i | −0.295441 | + | 0.170573i | ||||
\(453\) | −16486.1 | + | 28554.8i | −0.0803381 | + | 0.139150i | ||||
\(454\) | 286.391 | − | 496.044i | 0.00138947 | − | 0.00240662i | ||||
\(455\) | − | 325.835i | − | 0.00157389i | ||||||
\(456\) | −67005.4 | + | 25620.4i | −0.322241 | + | 0.123213i | ||||
\(457\) | −51325.5 | −0.245754 | −0.122877 | − | 0.992422i | \(-0.539212\pi\) | ||||
−0.122877 | + | 0.992422i | \(0.539212\pi\) | |||||||
\(458\) | 2525.31 | + | 1457.99i | 0.0120388 | + | 0.00695060i | ||||
\(459\) | 224830. | + | 129806.i | 1.06716 | + | 0.616125i | ||||
\(460\) | 41374.4 | + | 71662.6i | 0.195531 | + | 0.338670i | ||||
\(461\) | −66811.0 | + | 115720.i | −0.314373 | + | 0.544511i | −0.979304 | − | 0.202394i | \(-0.935128\pi\) |
0.664931 | + | 0.746905i | \(0.268461\pi\) | |||||||
\(462\) | 39.2778 | + | 68.0312i | 0.000184019 | + | 0.000318731i | ||||
\(463\) | −171665. | −0.800792 | −0.400396 | − | 0.916342i | \(-0.631127\pi\) | ||||
−0.400396 | + | 0.916342i | \(0.631127\pi\) | |||||||
\(464\) | 209338.i | 0.972324i | ||||||||
\(465\) | −71141.3 | − | 123220.i | −0.329015 | − | 0.569871i | ||||
\(466\) | 35935.2 | − | 20747.2i | 0.165481 | − | 0.0955406i | ||||
\(467\) | 143069. | 0.656012 | 0.328006 | − | 0.944676i | \(-0.393623\pi\) | ||||
0.328006 | + | 0.944676i | \(0.393623\pi\) | |||||||
\(468\) | − | 40358.0i | − | 0.184263i | ||||||
\(469\) | −180.176 | + | 104.024i | −0.000819125 | + | 0.000472922i | ||||
\(470\) | 13482.5 | + | 7784.12i | 0.0610343 | + | 0.0352382i | ||||
\(471\) | 272279. | − | 157201.i | 1.22736 | − | 0.708618i | ||||
\(472\) | −55337.4 | + | 95847.1i | −0.248390 | + | 0.430224i | ||||
\(473\) | 27497.1 | − | 47626.4i | 0.122904 | − | 0.212876i | ||||
\(474\) | − | 20303.9i | − | 0.0903699i | ||||||
\(475\) | 30726.1 | − | 192367.i | 0.136182 | − | 0.852598i | ||||
\(476\) | −1816.84 | −0.00801868 | ||||||||
\(477\) | 36921.8 | + | 21316.8i | 0.162273 | + | 0.0936883i | ||||
\(478\) | −17475.3 | − | 10089.4i | −0.0764838 | − | 0.0441580i | ||||
\(479\) | −202937. | − | 351498.i | −0.884485 | − | 1.53197i | −0.846302 | − | 0.532703i | \(-0.821176\pi\) |
−0.0381829 | − | 0.999271i | \(-0.512157\pi\) | |||||||
\(480\) | −21583.3 | + | 37383.4i | −0.0936775 | + | 0.162254i | ||||
\(481\) | −4621.22 | − | 8004.19i | −0.0199741 | − | 0.0345961i | ||||
\(482\) | −51827.8 | −0.223084 | ||||||||
\(483\) | 1583.58i | 0.00678806i | ||||||||
\(484\) | 98090.4 | + | 169898.i | 0.418732 | + | 0.725264i | ||||
\(485\) | 94957.7 | − | 54823.9i | 0.403689 | − | 0.233070i | ||||
\(486\) | 17948.6 | 0.0759903 | ||||||||
\(487\) | 252587.i | 1.06501i | 0.846428 | + | 0.532503i | \(0.178749\pi\) | ||||
−0.846428 | + | 0.532503i | \(0.821251\pi\) | |||||||
\(488\) | −42457.7 | + | 24513.0i | −0.178286 | + | 0.102933i | ||||
\(489\) | −285290. | − | 164712.i | −1.19308 | − | 0.688825i | ||||
\(490\) | 12010.5 | − | 6934.26i | 0.0500229 | − | 0.0288807i | ||||
\(491\) | 82201.6 | − | 142377.i | 0.340971 | − | 0.590579i | −0.643642 | − | 0.765326i | \(-0.722578\pi\) |
0.984613 | + | 0.174747i | \(0.0559109\pi\) | |||||||
\(492\) | −100827. | + | 174637.i | −0.416530 | + | 0.721452i | ||||
\(493\) | − | 373962.i | − | 1.53863i | ||||||
\(494\) | 22510.9 | + | 18277.8i | 0.0922443 | + | 0.0748980i | ||||
\(495\) | 8464.96 | 0.0345473 | ||||||||
\(496\) | −314823. | − | 181763.i | −1.27969 | − | 0.738827i | ||||
\(497\) | −1445.97 | − | 834.831i | −0.00585391 | − | 0.00337976i | ||||
\(498\) | 17561.1 | + | 30416.7i | 0.0708097 | + | 0.122646i | ||||
\(499\) | 32862.8 | − | 56920.1i | 0.131979 | − | 0.228594i | −0.792461 | − | 0.609923i | \(-0.791200\pi\) |
0.924439 | + | 0.381329i | \(0.124534\pi\) | |||||||
\(500\) | −83983.6 | − | 145464.i | −0.335934 | − | 0.581855i | ||||
\(501\) | −260325. | −1.03715 | ||||||||
\(502\) | 41056.9i | 0.162922i | ||||||||
\(503\) | −92338.3 | − | 159935.i | −0.364961 | − | 0.632130i | 0.623809 | − | 0.781577i | \(-0.285584\pi\) |
−0.988770 | + | 0.149446i | \(0.952251\pi\) | |||||||
\(504\) | −94.5208 | + | 54.5716i | −0.000372106 | + | 0.000214835i | ||||
\(505\) | 143788. | 0.563820 | ||||||||
\(506\) | 16330.0i | 0.0637801i | ||||||||
\(507\) | 104965. | − | 60601.5i | 0.408346 | − | 0.235758i | ||||
\(508\) | 5541.32 | + | 3199.28i | 0.0214726 | + | 0.0123972i | ||||
\(509\) | −395925. | + | 228587.i | −1.52819 | + | 0.882301i | −0.528752 | + | 0.848777i | \(0.677340\pi\) |
−0.999438 | + | 0.0335240i | \(0.989327\pi\) | |||||||
\(510\) | 12316.7 | − | 21333.2i | 0.0473538 | − | 0.0820192i | ||||
\(511\) | 964.154 | − | 1669.96i | 0.00369236 | − | 0.00639536i | ||||
\(512\) | 185347.i | 0.707042i | ||||||||
\(513\) | 139302. | − | 171564.i | 0.529324 | − | 0.651915i | ||||
\(514\) | 5662.18 | 0.0214318 | ||||||||
\(515\) | 15694.7 | + | 9061.36i | 0.0591752 | + | 0.0341648i | ||||
\(516\) | 164205. | + | 94803.7i | 0.616718 | + | 0.356062i | ||||
\(517\) | −61351.5 | − | 106264.i | −0.229532 | − | 0.397562i | ||||
\(518\) | −6.17150 | + | 10.6894i | −2.30002e−5 | + | 3.98375e-5i | ||||
\(519\) | 17480.2 | + | 30276.5i | 0.0648950 | + | 0.112401i | ||||
\(520\) | 23459.3 | 0.0867577 | ||||||||
\(521\) | 301070.i | 1.10916i | 0.832132 | + | 0.554578i | \(0.187120\pi\) | ||||
−0.832132 | + | 0.554578i | \(0.812880\pi\) | |||||||
\(522\) | −5546.81 | − | 9607.36i | −0.0203565 | − | 0.0352584i | ||||
\(523\) | 142864. | − | 82482.4i | 0.522298 | − | 0.301549i | −0.215576 | − | 0.976487i | \(-0.569163\pi\) |
0.737874 | + | 0.674938i | \(0.235830\pi\) | |||||||
\(524\) | 46131.5 | 0.168010 | ||||||||
\(525\) | − | 1489.39i | − | 0.00540370i | ||||||
\(526\) | 50134.3 | − | 28945.0i | 0.181202 | − | 0.104617i | ||||
\(527\) | 562402. | + | 324703.i | 2.02500 | + | 1.16914i | ||||
\(528\) | 94122.1 | − | 54341.4i | 0.337617 | − | 0.194923i | ||||
\(529\) | −24675.3 | + | 42738.9i | −0.0881762 | + | 0.152726i | ||||
\(530\) | −6118.91 | + | 10598.3i | −0.0217832 | + | 0.0377297i | ||||
\(531\) | 112704.i | 0.399716i | ||||||||
\(532\) | −243.940 | + | 1527.24i | −0.000861905 | + | 0.00539614i | ||||
\(533\) | 165064. | 0.581028 | ||||||||
\(534\) | −30920.9 | − | 17852.2i | −0.108435 | − | 0.0626050i | ||||
\(535\) | 147246. | + | 85012.3i | 0.514440 | + | 0.297012i | ||||
\(536\) | −7489.50 | − | 12972.2i | −0.0260689 | − | 0.0451527i | ||||
\(537\) | −201706. | + | 349365.i | −0.699471 | + | 1.21152i | ||||
\(538\) | −15741.1 | − | 27264.3i | −0.0543838 | − | 0.0941955i | ||||
\(539\) | −109307. | −0.376243 | ||||||||
\(540\) | − | 88290.5i | − | 0.302779i | ||||||
\(541\) | −23100.4 | − | 40011.0i | −0.0789268 | − | 0.136705i | 0.823860 | − | 0.566793i | \(-0.191816\pi\) |
−0.902787 | + | 0.430088i | \(0.858483\pi\) | |||||||
\(542\) | 3278.99 | − | 1893.13i | 0.0111620 | − | 0.00644438i | ||||
\(543\) | 504022. | 1.70943 | ||||||||
\(544\) | − | 197021.i | − | 0.665755i | ||||||
\(545\) | −62048.9 | + | 35823.9i | −0.208901 | + | 0.120609i | ||||
\(546\) | 191.995 | + | 110.848i | 0.000644028 | + | 0.000371830i | ||||
\(547\) | −75590.9 | + | 43642.4i | −0.252636 | + | 0.145859i | −0.620971 | − | 0.783834i | \(-0.713261\pi\) |
0.368335 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(548\) | −204984. | + | 355043.i | −0.682588 | + | 1.18228i | ||||
\(549\) | −24962.5 | + | 43236.3i | −0.0828216 | + | 0.143451i | ||||
\(550\) | − | 15358.8i | − | 0.0507728i | ||||||
\(551\) | −314352. | − | 50210.3i | −1.03541 | − | 0.165383i | ||||
\(552\) | −114014. | −0.374179 | ||||||||
\(553\) | −767.681 | − | 443.221i | −0.00251033 | − | 0.00144934i | ||||
\(554\) | −51156.3 | − | 29535.1i | −0.166678 | − | 0.0962318i | ||||
\(555\) | 3341.87 | + | 5788.29i | 0.0108494 | + | 0.0187916i | ||||
\(556\) | −33845.0 | + | 58621.3i | −0.109483 | + | 0.189630i | ||||
\(557\) | 95840.4 | + | 166000.i | 0.308914 | + | 0.535055i | 0.978125 | − | 0.208017i | \(-0.0667010\pi\) |
−0.669211 | + | 0.743073i | \(0.733368\pi\) | |||||||
\(558\) | 19264.7 | 0.0618720 | ||||||||
\(559\) | − | 155203.i | − | 0.496679i | ||||||
\(560\) | 301.013 | + | 521.369i | 0.000959862 | + | 0.00166253i | ||||
\(561\) | −168140. | + | 97075.8i | −0.534252 | + | 0.308450i | ||||
\(562\) | −18196.0 | −0.0576108 | ||||||||
\(563\) | − | 488949.i | − | 1.54258i | −0.636486 | − | 0.771288i | \(-0.719613\pi\) | ||
0.636486 | − | 0.771288i | \(-0.280387\pi\) | |||||||
\(564\) | 366373. | − | 211526.i | 1.15177 | − | 0.664974i | ||||
\(565\) | −35729.4 | − | 20628.4i | −0.111926 | − | 0.0646202i | ||||
\(566\) | 37169.2 | − | 21459.7i | 0.116025 | − | 0.0669869i | ||||
\(567\) | 1068.50 | − | 1850.70i | 0.00332361 | − | 0.00575666i | ||||
\(568\) | 60105.8 | − | 104106.i | 0.186303 | − | 0.322686i | ||||
\(569\) | 606639.i | 1.87372i | 0.349699 | + | 0.936862i | \(0.386284\pi\) | ||||
−0.349699 | + | 0.936862i | \(0.613716\pi\) | |||||||
\(570\) | −16278.9 | − | 13217.7i | −0.0501045 | − | 0.0406825i | ||||
\(571\) | 92670.7 | 0.284230 | 0.142115 | − | 0.989850i | \(-0.454610\pi\) | ||||
0.142115 | + | 0.989850i | \(0.454610\pi\) | |||||||
\(572\) | −79073.0 | − | 45652.8i | −0.241677 | − | 0.139533i | ||||
\(573\) | −566236. | − | 326917.i | −1.72460 | − | 0.995698i | ||||
\(574\) | −110.219 | − | 190.904i | −0.000334527 | − | 0.000579418i | ||||
\(575\) | 154806. | − | 268133.i | 0.468224 | − | 0.810987i | ||||
\(576\) | 35294.7 | + | 61132.3i | 0.106381 | + | 0.184258i | ||||
\(577\) | −117869. | −0.354037 | −0.177019 | − | 0.984208i | \(-0.556645\pi\) | ||||
−0.177019 | + | 0.984208i | \(0.556645\pi\) | |||||||
\(578\) | 60217.5i | 0.180247i | ||||||||
\(579\) | 333255. | + | 577214.i | 0.994075 | + | 1.72179i | ||||
\(580\) | −110141. | + | 63589.7i | −0.327410 | + | 0.189030i | ||||
\(581\) | 1533.38 | 0.00454254 | ||||||||
\(582\) | 74604.0i | 0.220250i | ||||||||
\(583\) | 83531.6 | − | 48227.0i | 0.245761 | − | 0.141890i | ||||
\(584\) | 120233. | + | 69416.7i | 0.352532 | + | 0.203535i | ||||
\(585\) | 20688.9 | − | 11944.8i | 0.0604542 | − | 0.0349032i | ||||
\(586\) | 48451.2 | − | 83920.0i | 0.141094 | − | 0.244383i | ||||
\(587\) | −35695.9 | + | 61827.1i | −0.103596 | + | 0.179433i | −0.913164 | − | 0.407593i | \(-0.866368\pi\) |
0.809568 | + | 0.587026i | \(0.199701\pi\) | |||||||
\(588\) | − | 376863.i | − | 1.09001i | ||||||
\(589\) | 348457. | − | 429158.i | 1.00443 | − | 1.23705i | ||||
\(590\) | −32351.4 | −0.0929370 | ||||||||
\(591\) | −383322. | − | 221311.i | −1.09746 | − | 0.633619i | ||||
\(592\) | 14788.9 | + | 8538.36i | 0.0421980 | + | 0.0243630i | ||||
\(593\) | 70754.5 | + | 122550.i | 0.201208 | + | 0.348502i | 0.948918 | − | 0.315523i | \(-0.102180\pi\) |
−0.747710 | + | 0.664025i | \(0.768847\pi\) | |||||||
\(594\) | 8711.82 | − | 15089.3i | 0.0246908 | − | 0.0427658i | ||||
\(595\) | −537.730 | − | 931.376i | −0.00151891 | − | 0.00263082i | ||||
\(596\) | 51068.4 | 0.143767 | ||||||||
\(597\) | − | 711026.i | − | 1.99497i | ||||||
\(598\) | 23043.0 | + | 39911.6i | 0.0644372 | + | 0.111608i | ||||
\(599\) | −462882. | + | 267245.i | −1.29008 | + | 0.744828i | −0.978668 | − | 0.205447i | \(-0.934135\pi\) |
−0.311412 | + | 0.950275i | \(0.600802\pi\) | |||||||
\(600\) | 107233. | 0.297869 | ||||||||
\(601\) | − | 126491.i | − | 0.350196i | −0.984551 | − | 0.175098i | \(-0.943976\pi\) | ||
0.984551 | − | 0.175098i | \(-0.0560243\pi\) | |||||||
\(602\) | −179.500 | + | 103.634i | −0.000495304 | + | 0.000285964i | ||||
\(603\) | −13210.1 | − | 7626.85i | −0.0363305 | − | 0.0209754i | ||||
\(604\) | −44323.4 | + | 25590.1i | −0.121495 | + | 0.0701453i | ||||
\(605\) | −58063.6 | + | 100569.i | −0.158633 | + | 0.274760i | ||||
\(606\) | −48916.6 | + | 84726.0i | −0.133202 | + | 0.230713i | ||||
\(607\) | − | 75673.3i | − | 0.205383i | −0.994713 | − | 0.102692i | \(-0.967255\pi\) | ||
0.994713 | − | 0.102692i | \(-0.0327455\pi\) | |||||||
\(608\) | −165616. | − | 26453.2i | −0.448017 | − | 0.0715601i | ||||
\(609\) | −2433.86 | −0.00656236 | ||||||||
\(610\) | −12410.8 | − | 7165.39i | −0.0333535 | − | 0.0192566i | ||||
\(611\) | −299894. | − | 173144.i | −0.803315 | − | 0.463794i | ||||
\(612\) | −66603.5 | − | 115361.i | −0.177826 | − | 0.308003i | ||||
\(613\) | −336906. | + | 583538.i | −0.896577 | + | 1.55292i | −0.0647358 | + | 0.997902i | \(0.520620\pi\) |
−0.831841 | + | 0.555014i | \(0.812713\pi\) | |||||||
\(614\) | −31340.1 | − | 54282.6i | −0.0831310 | − | 0.143987i | ||||
\(615\) | −119367. | −0.315598 | ||||||||
\(616\) | 246.925i | 0.000650734i | ||||||||
\(617\) | −75123.6 | − | 130118.i | −0.197336 | − | 0.341796i | 0.750328 | − | 0.661066i | \(-0.229896\pi\) |
−0.947664 | + | 0.319270i | \(0.896562\pi\) | |||||||
\(618\) | −10678.7 | + | 6165.32i | −0.0279602 | + | 0.0161428i | ||||
\(619\) | −98758.2 | −0.257746 | −0.128873 | − | 0.991661i | \(-0.541136\pi\) | ||||
−0.128873 | + | 0.991661i | \(0.541136\pi\) | |||||||
\(620\) | − | 220854.i | − | 0.574543i | ||||||
\(621\) | 304181. | − | 175619.i | 0.788766 | − | 0.455394i | ||||
\(622\) | 23582.8 | + | 13615.5i | 0.0609558 | + | 0.0351928i | ||||
\(623\) | −1349.96 | + | 779.401i | −0.00347813 | + | 0.00200810i | ||||
\(624\) | 153360. | − | 265628.i | 0.393862 | − | 0.682189i | ||||
\(625\) | −118921. | + | 205976.i | −0.304437 | + | 0.527300i | ||||
\(626\) | 42019.2i | 0.107226i | ||||||||
\(627\) | 59026.4 | + | 154373.i | 0.150145 | + | 0.392677i | ||||
\(628\) | 488021. | 1.23742 | ||||||||
\(629\) | −26418.9 | − | 15253.0i | −0.0667750 | − | 0.0385525i | ||||
\(630\) | −27.6294 | − | 15.9519i | −6.96131e−5 | − | 4.01911e-5i | ||||
\(631\) | 338314. | + | 585977.i | 0.849691 | + | 1.47171i | 0.881484 | + | 0.472214i | \(0.156545\pi\) |
−0.0317927 | + | 0.999494i | \(0.510122\pi\) | |||||||
\(632\) | 31910.8 | − | 55271.1i | 0.0798920 | − | 0.138377i | ||||
\(633\) | 87360.7 | + | 151313.i | 0.218026 | + | 0.377632i | ||||
\(634\) | 14714.1 | 0.0366063 | ||||||||
\(635\) | 3787.56i | 0.00939318i | ||||||||
\(636\) | 166275. | + | 287997.i | 0.411068 | + | 0.711990i | ||||
\(637\) | −267152. | + | 154241.i | −0.658386 | + | 0.380119i | ||||
\(638\) | −25098.1 | −0.0616595 | ||||||||
\(639\) | − | 122416.i | − | 0.299804i | ||||||
\(640\) | −77028.1 | + | 44472.2i | −0.188057 | + | 0.108575i | ||||
\(641\) | 615303. | + | 355245.i | 1.49752 | + | 0.864594i | 0.999996 | − | 0.00285662i | \(-0.000909293\pi\) |
0.497524 | + | 0.867450i | \(0.334243\pi\) | |||||||
\(642\) | −100186. | + | 57842.2i | −0.243072 | + | 0.140338i | ||||
\(643\) | 70190.5 | − | 121574.i | 0.169768 | − | 0.294047i | −0.768570 | − | 0.639766i | \(-0.779031\pi\) |
0.938338 | + | 0.345718i | \(0.112365\pi\) | |||||||
\(644\) | −1229.03 | + | 2128.75i | −0.00296341 | + | 0.00513278i | ||||
\(645\) | 112236.i | 0.269782i | ||||||||
\(646\) | 94510.2 | + | 15095.8i | 0.226472 | + | 0.0361735i | ||||
\(647\) | 439296. | 1.04942 | 0.524710 | − | 0.851281i | \(-0.324174\pi\) | ||||
0.524710 | + | 0.851281i | \(0.324174\pi\) | |||||||
\(648\) | 133246. | + | 76929.7i | 0.317325 | + | 0.183208i | ||||
\(649\) | 220820. | + | 127491.i | 0.524264 | + | 0.302684i | ||||
\(650\) | −21672.5 | − | 37537.9i | −0.0512958 | − | 0.0888470i | ||||
\(651\) | 2113.27 | − | 3660.28i | 0.00498646 | − | 0.00863680i | ||||
\(652\) | −255670. | − | 442834.i | −0.601430 | − | 1.04171i | ||||
\(653\) | 694597. | 1.62894 | 0.814472 | − | 0.580203i | \(-0.197027\pi\) | ||||
0.814472 | + | 0.580203i | \(0.197027\pi\) | |||||||
\(654\) | − | 48749.0i | − | 0.113975i | ||||||
\(655\) | 13653.5 | + | 23648.6i | 0.0318246 | + | 0.0551218i | ||||
\(656\) | −264119. | + | 152489.i | −0.613751 | + | 0.354349i | ||||
\(657\) | 141380. | 0.327534 | ||||||||
\(658\) | 462.457i | 0.00106812i | ||||||||
\(659\) | −544541. | + | 314391.i | −1.25389 | + | 0.723935i | −0.971880 | − | 0.235476i | \(-0.924335\pi\) |
−0.282012 | + | 0.959411i | \(0.591002\pi\) | |||||||
\(660\) | 57182.3 | + | 33014.2i | 0.131272 | + | 0.0757902i | ||||
\(661\) | −16257.2 | + | 9386.09i | −0.0372085 | + | 0.0214823i | −0.518489 | − | 0.855084i | \(-0.673505\pi\) |
0.481280 | + | 0.876567i | \(0.340172\pi\) | |||||||
\(662\) | −7401.07 | + | 12819.0i | −0.0168880 | + | 0.0292509i | ||||
\(663\) | −273964. | + | 474519.i | −0.623256 | + | 1.07951i | ||||
\(664\) | 110400.i | 0.250399i | ||||||||
\(665\) | −855.114 | + | 326.964i | −0.00193366 | + | 0.000739361i | ||||
\(666\) | −904.963 | −0.00204025 | ||||||||
\(667\) | −438162. | − | 252973.i | −0.984879 | − | 0.568620i | ||||
\(668\) | −349945. | − | 202041.i | −0.784236 | − | 0.452779i | ||||
\(669\) | −126936. | − | 219860.i | −0.283618 | − | 0.491241i | ||||
\(670\) | 2189.26 | − | 3791.91i | 0.00487694 | − | 0.00844712i | ||||
\(671\) | 56475.0 | + | 97817.5i | 0.125433 | + | 0.217256i | ||||
\(672\) | −1282.27 | −0.00283950 | ||||||||
\(673\) | 39754.5i | 0.0877721i | 0.999037 | + | 0.0438861i | \(0.0139739\pi\) | ||||
−0.999037 | + | 0.0438861i | \(0.986026\pi\) | |||||||
\(674\) | 49043.7 | + | 84946.2i | 0.107960 | + | 0.186992i | ||||
\(675\) | −286089. | + | 165174.i | −0.627905 | + | 0.362521i | ||||
\(676\) | 188134. | 0.411693 | ||||||||
\(677\) | − | 739937.i | − | 1.61442i | −0.590262 | − | 0.807212i | \(-0.700975\pi\) | ||
0.590262 | − | 0.807212i | \(-0.299025\pi\) | |||||||
\(678\) | 24310.2 | − | 14035.5i | 0.0528846 | − | 0.0305329i | ||||
\(679\) | 2820.74 | + | 1628.55i | 0.00611819 | + | 0.00353234i | ||||
\(680\) | 67056.8 | − | 38715.3i | 0.145019 | − | 0.0837268i | ||||
\(681\) | 4606.71 | − | 7979.05i | 0.00993337 | − | 0.0172051i | ||||
\(682\) | 21792.2 | − | 37745.2i | 0.0468524 | − | 0.0811508i | ||||
\(683\) | − | 244927.i | − | 0.525043i | −0.964926 | − | 0.262522i | \(-0.915446\pi\) | ||
0.964926 | − | 0.262522i | \(-0.0845541\pi\) | |||||||
\(684\) | −105915. | + | 40497.9i | −0.226383 | + | 0.0865606i | ||||
\(685\) | −242676. | −0.517185 | ||||||||
\(686\) | 713.559 | + | 411.974i | 0.00151629 | + | 0.000875429i | ||||
\(687\) | 40620.5 | + | 23452.3i | 0.0860660 | + | 0.0496903i | ||||
\(688\) | 143380. | + | 248341.i | 0.302908 | + | 0.524652i | ||||
\(689\) | 136104. | − | 235740.i | 0.286704 | − | 0.496586i | ||||
\(690\) | −16663.7 | − | 28862.4i | −0.0350005 | − | 0.0606226i | ||||
\(691\) | −607326. | −1.27194 | −0.635969 | − | 0.771715i | \(-0.719399\pi\) | ||||
−0.635969 | + | 0.771715i | \(0.719399\pi\) | |||||||
\(692\) | 54266.3i | 0.113323i | ||||||||
\(693\) | 125.727 | + | 217.765i | 0.000261795 | + | 0.000453442i | ||||
\(694\) | −111372. | + | 64300.6i | −0.231237 | + | 0.133505i | ||||
\(695\) | −40068.5 | −0.0829532 | ||||||||
\(696\) | − | 175232.i | − | 0.361738i | ||||||
\(697\) | 471823. | − | 272407.i | 0.971212 | − | 0.560729i | ||||
\(698\) | −79652.4 | − | 45987.3i | −0.163489 | − | 0.0943903i | ||||
\(699\) | 578032. | − | 333727.i | 1.18303 | − | 0.683025i | ||||
\(700\) | 1155.94 | − | 2002.14i | 0.00235905 | − | 0.00408600i | ||||
\(701\) | 88390.8 | − | 153097.i | 0.179875 | − | 0.311553i | −0.761963 | − | 0.647621i | \(-0.775764\pi\) |
0.941838 | + | 0.336068i | \(0.109097\pi\) | |||||||
\(702\) | − | 49172.3i | − | 0.0997807i | ||||||
\(703\) | −16368.8 | + | 20159.8i | −0.0331212 | + | 0.0407920i | ||||
\(704\) | 159701. | 0.322228 | ||||||||
\(705\) | 216871. | + | 125210.i | 0.436338 | + | 0.251920i | ||||
\(706\) | 40682.5 | + | 23488.1i | 0.0816204 | + | 0.0471236i | ||||
\(707\) | 2135.63 | + | 3699.02i | 0.00427255 | + | 0.00740027i | ||||
\(708\) | −439558. | + | 761337.i | −0.876900 | + | 1.51883i | ||||
\(709\) | −312672. | − | 541564.i | −0.622009 | − | 1.07735i | −0.989111 | − | 0.147171i | \(-0.952983\pi\) |
0.367102 | − | 0.930181i | \(-0.380350\pi\) | |||||||
\(710\) | 35139.1 | 0.0697066 | ||||||||
\(711\) | − | 64992.0i | − | 0.128564i | ||||||
\(712\) | −56115.0 | − | 97194.0i | −0.110693 | − | 0.191725i | ||||
\(713\) | 760893. | − | 439302.i | 1.49673 | − | 0.864140i | ||||
\(714\) | 731.741 | 0.00143536 | ||||||||
\(715\) | − | 54047.5i | − | 0.105721i | ||||||
\(716\) | −542292. | + | 313092.i | −1.05781 | + | 0.610726i | ||||
\(717\) | −281097. | − | 162292.i | −0.546787 | − | 0.315688i | ||||
\(718\) | −10164.8 | + | 5868.62i | −0.0197173 | + | 0.0113838i | ||||
\(719\) | 47265.5 | − | 81866.2i | 0.0914295 | − | 0.158360i | −0.816683 | − | 0.577086i | \(-0.804190\pi\) |
0.908113 | + | 0.418726i | \(0.137523\pi\) | |||||||
\(720\) | −22069.6 | + | 38225.7i | −0.0425726 | + | 0.0737379i | ||||
\(721\) | 538.339i | 0.00103558i | ||||||||
\(722\) | 25379.0 | − | 77418.4i | 0.0486856 | − | 0.148515i | ||||
\(723\) | −833669. | −1.59484 | ||||||||
\(724\) | 677539. | + | 391178.i | 1.29258 | + | 0.746271i | ||||
\(725\) | 412102. | + | 237927.i | 0.784023 | + | 0.452656i | ||||
\(726\) | −39506.3 | − | 68427.0i | −0.0749538 | − | 0.129824i | ||||
\(727\) | 4503.05 | − | 7799.52i | 0.00851997 | − | 0.0147570i | −0.861734 | − | 0.507360i | \(-0.830621\pi\) |
0.870254 | + | 0.492603i | \(0.163955\pi\) | |||||||
\(728\) | 348.431 | + | 603.501i | 0.000657437 | + | 0.00113871i | ||||
\(729\) | −341959. | −0.643456 | ||||||||
\(730\) | 40582.5i | 0.0761540i | ||||||||
\(731\) | −256134. | − | 443637.i | −0.479328 | − | 0.830220i | ||||
\(732\) | −337252. | + | 194712.i | −0.629408 | + | 0.363389i | ||||
\(733\) | −234971. | −0.437326 | −0.218663 | − | 0.975800i | \(-0.570170\pi\) | ||||
−0.218663 | + | 0.975800i | \(0.570170\pi\) | |||||||
\(734\) | − | 28013.4i | − | 0.0519965i | ||||||
\(735\) | 193193. | − | 111540.i | 0.357617 | − | 0.206470i | ||||
\(736\) | −230845. | − | 133278.i | −0.426152 | − | 0.246039i | ||||
\(737\) | −29886.4 | + | 17254.9i | −0.0550223 | + | 0.0317672i | ||||
\(738\) | 8081.01 | − | 13996.7i | 0.0148372 | − | 0.0256988i | ||||
\(739\) | −156095. | + | 270364.i | −0.285825 | + | 0.495063i | −0.972809 | − | 0.231609i | \(-0.925601\pi\) |
0.686984 | + | 0.726673i | \(0.258934\pi\) | |||||||
\(740\) | 10374.7i | 0.0189457i | ||||||||
\(741\) | 362097. | + | 294006.i | 0.659460 | + | 0.535450i | ||||
\(742\) | −363.527 | −0.000660281 | ||||||||
\(743\) | −424908. | − | 245321.i | −0.769693 | − | 0.444383i | 0.0630720 | − | 0.998009i | \(-0.479910\pi\) |
−0.832765 | + | 0.553626i | \(0.813244\pi\) | |||||||
\(744\) | 263531. | + | 152150.i | 0.476087 | + | 0.274869i | ||||
\(745\) | 15114.7 | + | 26179.5i | 0.0272325 | + | 0.0471681i | ||||
\(746\) | 51150.8 | − | 88595.7i | 0.0919125 | − | 0.159197i | ||||
\(747\) | 56212.3 | + | 97362.5i | 0.100737 | + | 0.174482i | ||||
\(748\) | −301367. | −0.538632 | ||||||||
\(749\) | 5050.61i | 0.00900286i | ||||||||
\(750\) | 33824.8 | + | 58586.2i | 0.0601329 | + | 0.104153i | ||||
\(751\) | 695752. | − | 401693.i | 1.23360 | − | 0.712220i | 0.265822 | − | 0.964022i | \(-0.414357\pi\) |
0.967779 | + | 0.251802i | \(0.0810233\pi\) | |||||||
\(752\) | 639816. | 1.13141 | ||||||||
\(753\) | 660416.i | 1.16474i | ||||||||
\(754\) | −61341.5 | + | 35415.5i | −0.107898 | + | 0.0622947i | ||||
\(755\) | −26236.8 | − | 15147.8i | −0.0460274 | − | 0.0265739i | ||||
\(756\) | 2271.31 | − | 1311.34i | 0.00397405 | − | 0.00229442i | ||||
\(757\) | 37763.2 | − | 65407.7i | 0.0658987 | − | 0.114140i | −0.831194 | − | 0.555983i | \(-0.812342\pi\) |
0.897092 | + | 0.441843i | \(0.145675\pi\) | |||||||
\(758\) | −41309.4 | + | 71550.0i | −0.0718970 | + | 0.124529i | ||||
\(759\) | 262674.i | 0.455968i | ||||||||
\(760\) | −23540.6 | − | 61566.1i | −0.0407559 | − | 0.106590i | ||||
\(761\) | 854120. | 1.47486 | 0.737428 | − | 0.675426i | \(-0.236040\pi\) | ||||
0.737428 | + | 0.675426i | \(0.236040\pi\) | |||||||
\(762\) | −2231.79 | − | 1288.52i | −0.00384365 | − | 0.00221913i | ||||
\(763\) | −1843.17 | − | 1064.16i | −0.00316604 | − | 0.00182792i | ||||
\(764\) | −507447. | − | 878925.i | −0.869369 | − | 1.50579i | ||||
\(765\) | 39425.3 | − | 68286.6i | 0.0673677 | − | 0.116684i | ||||
\(766\) | 72303.9 | + | 125234.i | 0.123226 | + | 0.213435i | ||||
\(767\) | 719600. | 1.22321 | ||||||||
\(768\) | 503881.i | 0.854291i | ||||||||
\(769\) | 268960. | + | 465853.i | 0.454816 | + | 0.787764i | 0.998678 | − | 0.0514105i | \(-0.0163717\pi\) |
−0.543862 | + | 0.839175i | \(0.683038\pi\) | |||||||
\(770\) | −62.5086 | + | 36.0894i | −0.000105429 | + | 6.08692e-5i | ||||
\(771\) | 91078.4 | 0.153217 | ||||||||
\(772\) | 1.03457e6i | 1.73590i | ||||||||
\(773\) | −374936. | + | 216469.i | −0.627477 | + | 0.362274i | −0.779774 | − | 0.626061i | \(-0.784666\pi\) |
0.152297 | + | 0.988335i | \(0.451333\pi\) | |||||||
\(774\) | −13160.6 | − | 7598.26i | −0.0219681 | − | 0.0126833i | ||||
\(775\) | −715639. | + | 413174.i | −1.19149 | + | 0.687907i | ||||
\(776\) | −117252. | + | 203086.i | −0.194714 | + | 0.337254i | ||||
\(777\) | −99.2709 | + | 171.942i | −0.000164430 | + | 0.000284800i | ||||
\(778\) | 1033.82i | 0.00170799i | ||||||||
\(779\) | −165636. | − | 433190.i | −0.272948 | − | 0.713844i | ||||
\(780\) | 186343. | 0.306284 | ||||||||
\(781\) | −239849. | − | 138477.i | −0.393219 | − | 0.227025i | ||||
\(782\) | 131734. | + | 76056.5i | 0.215419 | + | 0.124372i | ||||
\(783\) | 269914. | + | 467505.i | 0.440253 | + | 0.762541i | ||||
\(784\) | 284981. | − | 493602.i | 0.463643 | − | 0.803054i | ||||
\(785\) | 144439. | + | 250176.i | 0.234394 | + | 0.405982i | ||||
\(786\) | −18579.7 | −0.0300741 | ||||||||
\(787\) | 451093.i | 0.728311i | 0.931338 | + | 0.364155i | \(0.118642\pi\) | ||||
−0.931338 | + | 0.364155i | \(0.881358\pi\) | |||||||
\(788\) | −343524. | − | 595001.i | −0.553229 | − | 0.958220i | ||||
\(789\) | 806429. | − | 465592.i | 1.29542 | − | 0.747913i | ||||
\(790\) | 18655.7 | 0.0298922 | ||||||||
\(791\) | − | 1225.54i | − | 0.00195873i | ||||||
\(792\) | −15678.5 | + | 9052.01i | −0.0249951 | + | 0.0144309i | ||||
\(793\) | 276057. | + | 159382.i | 0.438988 | + | 0.253450i | ||||
\(794\) | −110586. | + | 63846.6i | −0.175411 | + | 0.101274i | ||||
\(795\) | −98425.0 | + | 170477.i | −0.155730 | + | 0.269732i | ||||
\(796\) | 551836. | − | 955808.i | 0.870931 | − | 1.50850i | ||||
\(797\) | 698630.i | 1.09984i | 0.835216 | + | 0.549921i | \(0.185342\pi\) | ||||
−0.835216 | + | 0.549921i | \(0.814658\pi\) | |||||||
\(798\) | 98.2479 | − | 615.101i | 0.000154283 | − | 0.000965919i | ||||
\(799\) | −1.14297e6 | −1.79036 | ||||||||
\(800\) | 217115. | + | 125351.i | 0.339242 | + | 0.195862i | ||||
\(801\) | −98976.4 | − | 57144.0i | −0.154265 | − | 0.0890648i | ||||
\(802\) | −20278.5 | − | 35123.4i | −0.0315274 | − | 0.0546070i | ||||
\(803\) | 159928. | − | 277003.i | 0.248024 | − | 0.429590i | ||||
\(804\) | −59491.0 | − | 103041.i | −0.0920320 | − | 0.159404i | ||||
\(805\) | −1455.03 | −0.00224533 | ||||||||
\(806\) | − | 123002.i | − | 0.189340i | ||||||
\(807\) | −253201. | − | 438557.i | −0.388793 | − | 0.673409i | ||||
\(808\) | −266320. | + | 153760.i | −0.407926 | + | 0.235516i | ||||
\(809\) | −1.25493e6 | −1.91744 | −0.958722 | − | 0.284345i | \(-0.908224\pi\) | ||||
−0.958722 | + | 0.284345i | \(0.908224\pi\) | |||||||
\(810\) | 44974.7i | 0.0685486i | ||||||||
\(811\) | 475389. | − | 274466.i | 0.722782 | − | 0.417298i | −0.0929939 | − | 0.995667i | \(-0.529644\pi\) |
0.815776 | + | 0.578368i | \(0.196310\pi\) | |||||||
\(812\) | −3271.75 | − | 1888.94i | −0.00496212 | − | 0.00286488i | ||||
\(813\) | 52743.8 | − | 30451.6i | 0.0797977 | − | 0.0460712i | ||||
\(814\) | −1023.69 | + | 1773.08i | −0.00154497 | + | 0.00267597i | ||||
\(815\) | 151342. | − | 262131.i | 0.227847 | − | 0.394642i | ||||
\(816\) | − | 1.01237e6i | − | 1.52041i | ||||||
\(817\) | −407311. | + | 155741.i | −0.610214 | + | 0.233323i | ||||
\(818\) | 158389. | 0.236711 | ||||||||
\(819\) | 614.568 | + | 354.821i | 0.000916225 | + | 0.000528983i | ||||
\(820\) | −160461. | − | 92642.2i | −0.238639 | − | 0.137778i | ||||
\(821\) | −488125. | − | 845457.i | −0.724177 | − | 1.25431i | −0.959312 | − | 0.282348i | \(-0.908887\pi\) |
0.235135 | − | 0.971963i | \(-0.424447\pi\) | |||||||
\(822\) | 82558.2 | − | 142995.i | 0.122185 | − | 0.211630i | ||||
\(823\) | 404279. | + | 700231.i | 0.596872 | + | 1.03381i | 0.993280 | + | 0.115738i | \(0.0369233\pi\) |
−0.396408 | + | 0.918074i | \(0.629743\pi\) | |||||||
\(824\) | −38759.1 | −0.0570846 | ||||||||
\(825\) | − | 247052.i | − | 0.362978i | ||||||
\(826\) | −480.502 | − | 832.253i | −0.000704263 | − | 0.00121982i | ||||
\(827\) | 737136. | − | 425586.i | 1.07780 | − | 0.622266i | 0.147495 | − | 0.989063i | \(-0.452879\pi\) |
0.930301 | + | 0.366797i | \(0.119546\pi\) | |||||||
\(828\) | −180220. | −0.262871 | ||||||||
\(829\) | 305115.i | 0.443970i | 0.975050 | + | 0.221985i | \(0.0712537\pi\) | ||||
−0.975050 | + | 0.221985i | \(0.928746\pi\) | |||||||
\(830\) | −27947.5 | + | 16135.5i | −0.0405684 | + | 0.0234222i | ||||
\(831\) | −822868. | − | 475083.i | −1.19159 | − | 0.687967i | ||||
\(832\) | 390320. | − | 225351.i | 0.563864 | − | 0.325547i | ||||
\(833\) | −509092. | + | 881773.i | −0.733679 | + | 1.27077i | ||||
\(834\) | 13631.2 | − | 23610.0i | 0.0195976 | − | 0.0339441i | ||||
\(835\) | − | 239192.i | − | 0.343063i | ||||||
\(836\) | −40463.3 | + | 253329.i | −0.0578960 | + | 0.362470i | ||||
\(837\) | −937444. | −1.33812 | ||||||||
\(838\) | 25290.6 | + | 14601.5i | 0.0360139 | + | 0.0207927i | ||||
\(839\) | 222988. | + | 128742.i | 0.316781 | + | 0.182893i | 0.649957 | − | 0.759971i | \(-0.274787\pi\) |
−0.333176 | + | 0.942865i | \(0.608120\pi\) | |||||||
\(840\) | −251.971 | − | 436.426i | −0.000357101 | − | 0.000618518i | ||||
\(841\) | 35161.8 | − | 60902.1i | 0.0497141 | − | 0.0861073i | ||||
\(842\) | −7048.53 | − | 12208.4i | −0.00994201 | − | 0.0172201i | ||||
\(843\) | −292690. | −0.411863 | ||||||||
\(844\) | 271207.i | 0.380728i | ||||||||
\(845\) | 55682.0 | + | 96444.1i | 0.0779833 | + | 0.135071i | ||||
\(846\) | −29363.8 | + | 16953.2i | −0.0410272 | + | 0.0236870i | ||||
\(847\) | −3449.58 | −0.00480839 | ||||||||
\(848\) | 502944.i | 0.699404i | ||||||||
\(849\) | 597881. | − | 345187.i | 0.829467 | − | 0.478893i | ||||
\(850\) | −123899. | − | 71533.0i | −0.171486 | − | 0.0990076i | ||||
\(851\) | −35743.1 | + | 20636.3i | −0.0493552 | + | 0.0284952i | ||||
\(852\) | 477435. | − | 826941.i | 0.657711 | − | 1.13919i | ||||
\(853\) | 349883. | − | 606015.i | 0.480866 | − | 0.832885i | −0.518893 | − | 0.854839i | \(-0.673656\pi\) |
0.999759 | + | 0.0219545i | \(0.00698891\pi\) | |||||||
\(854\) | − | 425.699i | − | 0.000583696i | ||||||
\(855\) | −52108.2 | − | 42309.4i | −0.0712810 | − | 0.0578769i | ||||
\(856\) | −363632. | −0.496266 | ||||||||
\(857\) | 402851. | + | 232586.i | 0.548508 | + | 0.316681i | 0.748520 | − | 0.663112i | \(-0.230765\pi\) |
−0.200012 | + | 0.979793i | \(0.564098\pi\) | |||||||
\(858\) | 31847.0 | + | 18386.9i | 0.0432607 | + | 0.0249766i | ||||
\(859\) | 359632. | + | 622900.i | 0.487384 | + | 0.844174i | 0.999895 | − | 0.0145066i | \(-0.00461777\pi\) |
−0.512511 | + | 0.858681i | \(0.671284\pi\) | |||||||
\(860\) | −87107.8 | + | 150875.i | −0.117777 | + | 0.203996i | ||||
\(861\) | −1772.91 | − | 3070.77i | −0.00239156 | − | 0.00414230i | ||||
\(862\) | 155776. | 0.209646 | ||||||||
\(863\) | 380009.i | 0.510237i | 0.966910 | + | 0.255118i | \(0.0821145\pi\) | ||||
−0.966910 | + | 0.255118i | \(0.917886\pi\) | |||||||
\(864\) | 142204. | + | 246304.i | 0.190495 | + | 0.329947i | ||||
\(865\) | −27818.8 | + | 16061.2i | −0.0371797 | + | 0.0214657i | ||||
\(866\) | −27739.8 | −0.0369885 | ||||||||
\(867\) | 968621.i | 1.28859i | ||||||||
\(868\) | 5681.57 | − | 3280.26i | 0.00754101 | − | 0.00435380i | ||||
\(869\) | −127338. | − | 73518.7i | −0.168624 | − | 0.0973550i | ||||
\(870\) | 44359.6 | − | 25611.0i | 0.0586069 | − | 0.0338367i | ||||
\(871\) | −48696.3 | + | 84344.4i | −0.0641888 | + | 0.111178i | ||||
\(872\) | 76616.7 | − | 132704.i | 0.100761 | − | 0.174522i | ||||
\(873\) | 238804.i | 0.313338i | ||||||||
\(874\) | 81620.4 | − | 100524.i | 0.106850 | − | 0.131597i | ||||
\(875\) | 2953.48 | 0.00385761 | ||||||||
\(876\) | 955043. | + | 551394.i | 1.24456 | + | 0.718545i | ||||
\(877\) | −7312.18 | − | 4221.69i | −0.00950710 | − | 0.00548892i | 0.495239 | − | 0.868757i | \(-0.335081\pi\) |
−0.504746 | + | 0.863268i | \(0.668414\pi\) | |||||||
\(878\) | −76372.4 | − | 132281.i | −0.0990711 | − | 0.171596i | ||||
\(879\) | 779357. | − | 1.34989e6i | 1.00869 | − | 1.74711i | ||||
\(880\) | 49930.2 | + | 86481.6i | 0.0644759 | + | 0.111676i | ||||
\(881\) | 631669. | 0.813838 | 0.406919 | − | 0.913464i | \(-0.366603\pi\) | ||||
0.406919 | + | 0.913464i | \(0.366603\pi\) | |||||||
\(882\) | 30204.6i | 0.0388272i | ||||||||
\(883\) | −31430.2 | − | 54438.8i | −0.0403113 | − | 0.0698211i | 0.845166 | − | 0.534504i | \(-0.179502\pi\) |
−0.885477 | + | 0.464683i | \(0.846168\pi\) | |||||||
\(884\) | −736560. | + | 425253.i | −0.942548 | + | 0.544180i | ||||
\(885\) | −520384. | −0.664412 | ||||||||
\(886\) | 37240.6i | 0.0474405i | ||||||||
\(887\) | −770362. | + | 444769.i | −0.979146 | + | 0.565310i | −0.902012 | − | 0.431711i | \(-0.857910\pi\) |
−0.0771338 | + | 0.997021i | \(0.524577\pi\) | |||||||
\(888\) | −12379.4 | − | 7147.26i | −0.0156991 | − | 0.00906388i | ||||
\(889\) | −97.4368 | + | 56.2551i | −0.000123288 | + | 7.11801e-5i | ||||
\(890\) | 16403.0 | − | 28410.8i | 0.0207082 | − | 0.0358677i | ||||
\(891\) | 177237. | − | 306984.i | 0.223254 | − | 0.386687i | ||||
\(892\) | − | 394067.i | − | 0.495268i | ||||||
\(893\) | −153462. | + | 960780.i | −0.192441 | + | 1.20482i | ||||
\(894\) | −20568.0 | −0.0257346 | ||||||||
\(895\) | −321004. | − | 185332.i | −0.400742 | − | 0.231368i | ||||
\(896\) | −2288.13 | − | 1321.05i | −0.00285013 | − | 0.00164553i | ||||
\(897\) | 370655. | + | 641994.i | 0.460665 | + | 0.797895i | ||||
\(898\) | −56659.9 | + | 98137.8i | −0.0702624 | + | 0.121698i | ||||
\(899\) | 675178. | + | 1.16944e6i | 0.835408 | + | 1.44697i | ||||
\(900\) | 169502. | 0.209261 | ||||||||
\(901\) | − | 898462.i | − | 1.10675i | ||||||
\(902\) | −18282.4 | − | 31666.1i | −0.0224709 | − | 0.0389207i | ||||
\(903\) | −2887.33 | + | 1667.00i | −0.00354095 | + | 0.00204437i | ||||
\(904\) | 88235.9 | 0.107971 | ||||||||
\(905\) | 463107.i | 0.565437i | ||||||||
\(906\) | 17851.4 | − | 10306.5i | 0.0217479 | − | 0.0125561i | ||||
\(907\) | −408359. | − | 235766.i | −0.496396 | − | 0.286594i | 0.230828 | − | 0.972995i | \(-0.425856\pi\) |
−0.727224 | + | 0.686400i | \(0.759190\pi\) | |||||||
\(908\) | 12385.3 | − | 7150.64i | 0.0150222 | − | 0.00867308i | ||||
\(909\) | −156580. | + | 271204.i | −0.189499 | + | 0.328223i | ||||
\(910\) | −101.850 | + | 176.410i | −0.000122993 | + | 0.000213029i | ||||
\(911\) | 227945.i | 0.274659i | 0.990525 | + | 0.137329i | \(0.0438518\pi\) | ||||
−0.990525 | + | 0.137329i | \(0.956148\pi\) | |||||||
\(912\) | −851001. | − | 135927.i | −1.02315 | − | 0.163424i | ||||
\(913\) | 254348. | 0.305132 | ||||||||
\(914\) | 27788.1 | + | 16043.4i | 0.0332633 | + | 0.0192046i | ||||
\(915\) | −199633. | − | 115258.i | −0.238446 | − | 0.137667i | ||||
\(916\) | 36403.1 | + | 63052.1i | 0.0433858 | + | 0.0751464i | ||||
\(917\) | −405.581 | + | 702.487i | −0.000482324 | + | 0.000835410i | ||||
\(918\) | −81150.0 | − | 140556.i | −0.0962949 | − | 0.166788i | ||||
\(919\) | 1.19281e6 | 1.41235 | 0.706173 | − | 0.708040i | \(-0.250420\pi\) | ||||
0.706173 | + | 0.708040i | \(0.250420\pi\) | |||||||
\(920\) | − | 104759.i | − | 0.123770i | ||||||
\(921\) | −504117. | − | 873156.i | −0.594309 | − | 1.02937i | ||||
\(922\) | 72344.0 | − | 41767.8i | 0.0851022 | − | 0.0491338i | ||||
\(923\) | −781607. | −0.917456 | ||||||||
\(924\) | 1961.39i | 0.00229731i | ||||||||
\(925\) | 33617.2 | − | 19408.9i | 0.0392897 | − | 0.0226839i | ||||
\(926\) | 92940.9 | + | 53659.4i | 0.108389 | + | 0.0625784i | ||||
\(927\) | −34181.9 | + | 19734.9i | −0.0397774 | + | 0.0229655i | ||||
\(928\) | 204840. | − | 354793.i | 0.237858 | − | 0.411983i | ||||
\(929\) | −146300. | + | 253398.i | −0.169516 | + | 0.293611i | −0.938250 | − | 0.345958i | \(-0.887554\pi\) |
0.768734 | + | 0.639569i | \(0.220887\pi\) | |||||||
\(930\) | 88950.0i | 0.102844i | ||||||||
\(931\) | 672864. | + | 546334.i | 0.776297 | + | 0.630317i | ||||
\(932\) | 1.03604e6 | 1.19273 | ||||||||
\(933\) | 379338. | + | 219011.i | 0.435776 | + | 0.251596i | ||||
\(934\) | −77458.8 | − | 44720.9i | −0.0887926 | − | 0.0512645i | ||||
\(935\) | −89195.5 | − | 154491.i | −0.102028 | − | 0.176718i | ||||
\(936\) | −25546.3 | + | 44247.4i | −0.0291592 | + | 0.0505052i | ||||
\(937\) | −580745. | − | 1.00588e6i | −0.661464 | − | 1.14569i | −0.980231 | − | 0.197857i | \(-0.936602\pi\) |
0.318767 | − | 0.947833i | \(-0.396731\pi\) | |||||||
\(938\) | 130.065 | 0.000147827 | ||||||||
\(939\) | 675895.i | 0.766564i | ||||||||
\(940\) | 194355. | + | 336632.i | 0.219958 | + | 0.380978i | ||||
\(941\) | 494228. | − | 285343.i | 0.558147 | − | 0.322246i | −0.194254 | − | 0.980951i | \(-0.562229\pi\) |
0.752401 | + | 0.658705i | \(0.228895\pi\) | |||||||
\(942\) | −196552. | −0.221501 | ||||||||
\(943\) | − | 737099.i | − | 0.828900i | ||||||
\(944\) | −1.15143e6 | + | 664781.i | −1.29210 | + | 0.745993i | ||||
\(945\) | 1344.48 | + | 776.236i | 0.00150553 | + | 0.000869221i | ||||
\(946\) | −29774.4 | + | 17190.2i | −0.0332706 | + | 0.0192088i | ||||
\(947\) | 443648. | − | 768420.i | 0.494696 | − | 0.856838i | −0.505285 | − | 0.862952i | \(-0.668613\pi\) |
0.999981 | + | 0.00611394i | \(0.00194614\pi\) | |||||||
\(948\) | 253475. | − | 439032.i | 0.282045 | − | 0.488517i | ||||
\(949\) | − | 902686.i | − | 1.00232i | ||||||
\(950\) | −76766.0 | + | 94544.8i | −0.0850593 | + | 0.104759i | ||||
\(951\) | 236682. | 0.261700 | ||||||||
\(952\) | 1991.94 | + | 1150.04i | 0.00219787 | + | 0.00126894i | ||||
\(953\) | −323576. | − | 186816.i | −0.356279 | − | 0.205698i | 0.311168 | − | 0.950355i | \(-0.399280\pi\) |
−0.667447 | + | 0.744657i | \(0.732613\pi\) | |||||||
\(954\) | −13326.5 | − | 23082.2i | −0.0146426 | − | 0.0253618i | ||||
\(955\) | 300378. | − | 520271.i | 0.329353 | − | 0.570457i | ||||
\(956\) | −251913. | − | 436326.i | −0.275635 | − | 0.477414i | ||||
\(957\) | −403713. | −0.440808 | ||||||||
\(958\) | 253738.i | 0.276474i | ||||||||
\(959\) | −3604.37 | − | 6242.96i | −0.00391915 | − | 0.00678818i | ||||
\(960\) | −282263. | + | 162965.i | −0.306275 | + | 0.176828i | ||||
\(961\) | −1.42145e6 | −1.53916 | ||||||||
\(962\) | 5778.05i | 0.00624354i | ||||||||
\(963\) | −320690. | + | 185150.i | −0.345806 | + | 0.199651i | ||||
\(964\) | −1.12067e6 | − | 647020.i | −1.20594 | − | 0.696248i | ||||
\(965\) | −530357. | + | 306202.i | −0.569527 | + | 0.328816i | ||||
\(966\) | 494.999 | − | 857.363i | 0.000530457 | − | 0.000918778i | ||||
\(967\) | −426457. | + | 738645.i | −0.456060 | + | 0.789919i | −0.998748 | − | 0.0500149i | \(-0.984073\pi\) |
0.542688 | + | 0.839934i | \(0.317406\pi\) | |||||||
\(968\) | − | 248361.i | − | 0.265053i | ||||||
\(969\) | 1.52023e6 | + | 242821.i | 1.61906 | + | 0.258606i | ||||
\(970\) | −68547.9 | −0.0728535 | ||||||||
\(971\) | −75186.2 | − | 43408.8i | −0.0797443 | − | 0.0460404i | 0.459598 | − | 0.888127i | \(-0.347994\pi\) |
−0.539342 | + | 0.842087i | \(0.681327\pi\) | |||||||
\(972\) | 388103. | + | 224071.i | 0.410785 | + | 0.237167i | ||||
\(973\) | −595.121 | − | 1030.78i | −0.000628607 | − | 0.00108878i | ||||
\(974\) | 78954.1 | − | 136752.i | 0.0832255 | − | 0.144151i | ||||
\(975\) | −348610. | − | 603811.i | −0.366717 | − | 0.635172i | ||||
\(976\) | −588960. | −0.618282 | ||||||||
\(977\) | − | 1.54915e6i | − | 1.62295i | −0.584387 | − | 0.811475i | \(-0.698665\pi\) | ||
0.584387 | − | 0.811475i | \(-0.301335\pi\) | |||||||
\(978\) | 102972. | + | 178353.i | 0.107657 | + | 0.186468i | ||||
\(979\) | −223923. | + | 129282.i | −0.233633 | + | 0.134888i | ||||
\(980\) | 346271. | 0.360548 | ||||||||
\(981\) | − | 156043.i | − | 0.162147i | ||||||
\(982\) | −89009.3 | + | 51389.6i | −0.0923023 | + | 0.0532908i | ||||
\(983\) | −420874. | − | 242992.i | −0.435557 | − | 0.251469i | 0.266154 | − | 0.963930i | \(-0.414247\pi\) |
−0.701711 | + | 0.712462i | \(0.747580\pi\) | |||||||
\(984\) | 221088. | − | 127645.i | 0.228336 | − | 0.131830i | ||||
\(985\) | 203346. | − | 352205.i | 0.209586 | − | 0.363014i | ||||
\(986\) | −116894. | + | 202466.i | −0.120237 | + | 0.208256i | ||||
\(987\) | 7438.80i | 0.00763604i | ||||||||
\(988\) | 258573. | + | 676249.i | 0.264892 | + | 0.692776i | ||||
\(989\) | −693065. | −0.708568 | ||||||||
\(990\) | −4583.00 | − | 2646.00i | −0.00467606 | − | 0.00269972i | ||||
\(991\) | 664833. | + | 383842.i | 0.676964 | + | 0.390845i | 0.798710 | − | 0.601716i | \(-0.205516\pi\) |
−0.121746 | + | 0.992561i | \(0.538849\pi\) | |||||||
\(992\) | 355716. | + | 616118.i | 0.361477 | + | 0.626096i | ||||
\(993\) | −119049. | + | 206199.i | −0.120733 | + | 0.209116i | ||||
\(994\) | 521.906 | + | 903.969i | 0.000528226 | + | 0.000914915i | ||||
\(995\) | 653307. | 0.659890 | ||||||||
\(996\) | 876934.i | 0.883991i | ||||||||
\(997\) | −165150. | − | 286047.i | −0.166145 | − | 0.287772i | 0.770916 | − | 0.636936i | \(-0.219799\pi\) |
−0.937061 | + | 0.349165i | \(0.886465\pi\) | |||||||
\(998\) | −35584.4 | + | 20544.7i | −0.0357272 | + | 0.0206271i | ||||
\(999\) | 44036.6 | 0.0441248 |
(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 | 19.5.d.a.8.3 | ✓ | 10 | |
3.2 | odd | 2 | 171.5.p.a.46.3 | 10 | |||
4.3 | odd | 2 | 304.5.r.a.65.5 | 10 | |||
19.12 | odd | 6 | inner | 19.5.d.a.12.3 | yes | 10 | |
57.50 | even | 6 | 171.5.p.a.145.3 | 10 | |||
76.31 | even | 6 | 304.5.r.a.145.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.5.d.a.8.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
19.5.d.a.12.3 | yes | 10 | 19.12 | odd | 6 | inner | |
171.5.p.a.46.3 | 10 | 3.2 | odd | 2 | |||
171.5.p.a.145.3 | 10 | 57.50 | even | 6 | |||
304.5.r.a.65.5 | 10 | 4.3 | odd | 2 | |||
304.5.r.a.145.5 | 10 | 76.31 | even | 6 |