Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (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: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 30.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.30 |
Dual form | 49.6.c.b.18.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | − | 8.66025i | 0.883883 | − | 1.53093i | 0.0368954 | − | 0.999319i | \(-0.488253\pi\) |
0.846988 | − | 0.531612i | \(-0.178414\pi\) | |||||||
\(3\) | −7.00000 | − | 12.1244i | −0.449050 | − | 0.777778i | 0.549274 | − | 0.835642i | \(-0.314904\pi\) |
−0.998324 | + | 0.0578644i | \(0.981571\pi\) | |||||||
\(4\) | −34.0000 | − | 58.8897i | −1.06250 | − | 1.84030i | ||||
\(5\) | −28.0000 | + | 48.4974i | −0.500879 | + | 0.867548i | 0.499120 | + | 0.866533i | \(0.333657\pi\) |
−0.999999 | + | 0.00101554i | \(0.999677\pi\) | |||||||
\(6\) | −140.000 | −1.58763 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −360.000 | −1.98874 | ||||||||
\(9\) | 23.5000 | − | 40.7032i | 0.0967078 | − | 0.167503i | ||||
\(10\) | 280.000 | + | 484.974i | 0.885438 | + | 1.53362i | ||||
\(11\) | −116.000 | − | 200.918i | −0.289052 | − | 0.500653i | 0.684532 | − | 0.728983i | \(-0.260007\pi\) |
−0.973584 | + | 0.228330i | \(0.926673\pi\) | |||||||
\(12\) | −476.000 | + | 824.456i | −0.954232 | + | 1.65278i | ||||
\(13\) | 140.000 | 0.229757 | 0.114879 | − | 0.993380i | \(-0.463352\pi\) | ||||
0.114879 | + | 0.993380i | \(0.463352\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 784.000 | 0.899680 | ||||||||
\(16\) | −712.000 | + | 1233.22i | −0.695312 | + | 1.20432i | ||||
\(17\) | −861.000 | − | 1491.30i | −0.722572 | − | 1.25153i | −0.959966 | − | 0.280117i | \(-0.909627\pi\) |
0.237394 | − | 0.971413i | \(-0.423707\pi\) | |||||||
\(18\) | −235.000 | − | 407.032i | −0.170957 | − | 0.296106i | ||||
\(19\) | −49.0000 | + | 84.8705i | −0.0311395 | + | 0.0539353i | −0.881175 | − | 0.472790i | \(-0.843247\pi\) |
0.850036 | + | 0.526725i | \(0.176580\pi\) | |||||||
\(20\) | 3808.00 | 2.12874 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2320.00 | −1.02195 | ||||||||
\(23\) | −912.000 | + | 1579.63i | −0.359480 | + | 0.622638i | −0.987874 | − | 0.155257i | \(-0.950379\pi\) |
0.628394 | + | 0.777895i | \(0.283713\pi\) | |||||||
\(24\) | 2520.00 | + | 4364.77i | 0.893043 | + | 1.54680i | ||||
\(25\) | −5.50000 | − | 9.52628i | −0.00176000 | − | 0.00304841i | ||||
\(26\) | 700.000 | − | 1212.44i | 0.203079 | − | 0.351743i | ||||
\(27\) | −4060.00 | −1.07181 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3418.00 | 0.754705 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(30\) | 3920.00 | − | 6789.64i | 0.795212 | − | 1.37735i | ||||
\(31\) | −3822.00 | − | 6619.90i | −0.714310 | − | 1.23722i | −0.963225 | − | 0.268695i | \(-0.913408\pi\) |
0.248916 | − | 0.968525i | \(-0.419926\pi\) | |||||||
\(32\) | 1360.00 | + | 2355.59i | 0.234782 | + | 0.406654i | ||||
\(33\) | −1624.00 | + | 2812.85i | −0.259598 | + | 0.449637i | ||||
\(34\) | −17220.0 | −2.55468 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3196.00 | −0.411008 | ||||||||
\(37\) | 5199.00 | − | 9004.93i | 0.624332 | − | 1.08137i | −0.364338 | − | 0.931267i | \(-0.618705\pi\) |
0.988670 | − | 0.150108i | \(-0.0479620\pi\) | |||||||
\(38\) | 490.000 | + | 848.705i | 0.0550474 | + | 0.0953450i | ||||
\(39\) | −980.000 | − | 1697.41i | −0.103173 | − | 0.178700i | ||||
\(40\) | 10080.0 | − | 17459.1i | 0.996117 | − | 1.72533i | ||||
\(41\) | 17962.0 | 1.66876 | 0.834382 | − | 0.551186i | \(-0.185825\pi\) | ||||
0.834382 | + | 0.551186i | \(0.185825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10880.0 | 0.897342 | 0.448671 | − | 0.893697i | \(-0.351898\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351898\pi\) | |||||||
\(44\) | −7888.00 | + | 13662.4i | −0.614236 | + | 1.06389i | ||||
\(45\) | 1316.00 | + | 2279.38i | 0.0968779 | + | 0.167797i | ||||
\(46\) | 9120.00 | + | 15796.3i | 0.635478 | + | 1.10068i | ||||
\(47\) | 4662.00 | − | 8074.82i | 0.307842 | − | 0.533198i | −0.670048 | − | 0.742318i | \(-0.733727\pi\) |
0.977890 | + | 0.209120i | \(0.0670599\pi\) | |||||||
\(48\) | 19936.0 | 1.24892 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −110.000 | −0.00622254 | ||||||||
\(51\) | −12054.0 | + | 20878.1i | −0.648942 | + | 1.12400i | ||||
\(52\) | −4760.00 | − | 8244.56i | −0.244117 | − | 0.422824i | ||||
\(53\) | −1131.00 | − | 1958.95i | −0.0553061 | − | 0.0957930i | 0.837047 | − | 0.547131i | \(-0.184280\pi\) |
−0.892353 | + | 0.451338i | \(0.850947\pi\) | |||||||
\(54\) | −20300.0 | + | 35160.6i | −0.947353 | + | 1.64086i | ||||
\(55\) | 12992.0 | 0.579121 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1372.00 | 0.0559329 | ||||||||
\(58\) | 17090.0 | − | 29600.7i | 0.667071 | − | 1.15540i | ||||
\(59\) | −1365.00 | − | 2364.25i | −0.0510508 | − | 0.0884226i | 0.839371 | − | 0.543559i | \(-0.182924\pi\) |
−0.890422 | + | 0.455137i | \(0.849590\pi\) | |||||||
\(60\) | −26656.0 | − | 46169.5i | −0.955910 | − | 1.65568i | ||||
\(61\) | 12824.0 | − | 22211.8i | 0.441264 | − | 0.764292i | −0.556519 | − | 0.830835i | \(-0.687863\pi\) |
0.997784 | + | 0.0665424i | \(0.0211968\pi\) | |||||||
\(62\) | −76440.0 | −2.52547 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −18368.0 | −0.560547 | ||||||||
\(65\) | −3920.00 | + | 6789.64i | −0.115081 | + | 0.199326i | ||||
\(66\) | 16240.0 | + | 28128.5i | 0.458909 | + | 0.794853i | ||||
\(67\) | 24202.0 | + | 41919.1i | 0.658664 | + | 1.14084i | 0.980962 | + | 0.194202i | \(0.0622117\pi\) |
−0.322297 | + | 0.946639i | \(0.604455\pi\) | |||||||
\(68\) | −58548.0 | + | 101408.i | −1.53546 | + | 2.65950i | ||||
\(69\) | 25536.0 | 0.645699 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −58560.0 | −1.37865 | −0.689327 | − | 0.724450i | \(-0.742094\pi\) | ||||
−0.689327 | + | 0.724450i | \(0.742094\pi\) | |||||||
\(72\) | −8460.00 | + | 14653.1i | −0.192326 | + | 0.333119i | ||||
\(73\) | 34041.0 | + | 58960.7i | 0.747645 | + | 1.29496i | 0.948949 | + | 0.315430i | \(0.102149\pi\) |
−0.201304 | + | 0.979529i | \(0.564518\pi\) | |||||||
\(74\) | −51990.0 | − | 90049.3i | −1.10367 | − | 1.91162i | ||||
\(75\) | −77.0000 | + | 133.368i | −0.00158066 | + | 0.00273778i | ||||
\(76\) | 6664.00 | 0.132343 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −19600.0 | −0.364770 | ||||||||
\(79\) | −15892.0 | + | 27525.8i | −0.286491 | + | 0.496217i | −0.972970 | − | 0.230933i | \(-0.925822\pi\) |
0.686479 | + | 0.727150i | \(0.259155\pi\) | |||||||
\(80\) | −39872.0 | − | 69060.3i | −0.696535 | − | 1.20643i | ||||
\(81\) | 22709.5 | + | 39334.0i | 0.384587 | + | 0.666125i | ||||
\(82\) | 89810.0 | − | 155555.i | 1.47499 | − | 2.55476i | ||||
\(83\) | 20538.0 | 0.327237 | 0.163619 | − | 0.986524i | \(-0.447683\pi\) | ||||
0.163619 | + | 0.986524i | \(0.447683\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96432.0 | 1.44768 | ||||||||
\(86\) | 54400.0 | − | 94223.6i | 0.793145 | − | 1.37377i | ||||
\(87\) | −23926.0 | − | 41441.0i | −0.338900 | − | 0.586993i | ||||
\(88\) | 41760.0 | + | 72330.4i | 0.574849 | + | 0.995668i | ||||
\(89\) | −25291.0 | + | 43805.3i | −0.338447 | + | 0.586208i | −0.984141 | − | 0.177389i | \(-0.943235\pi\) |
0.645694 | + | 0.763597i | \(0.276568\pi\) | |||||||
\(90\) | 26320.0 | 0.342515 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 124032. | 1.52779 | ||||||||
\(93\) | −53508.0 | + | 92678.6i | −0.641522 | + | 1.11115i | ||||
\(94\) | −46620.0 | − | 80748.2i | −0.544193 | − | 0.942569i | ||||
\(95\) | −2744.00 | − | 4752.75i | −0.0311943 | − | 0.0540301i | ||||
\(96\) | 19040.0 | − | 32978.2i | 0.210857 | − | 0.365216i | ||||
\(97\) | 58506.0 | 0.631351 | 0.315676 | − | 0.948867i | \(-0.397769\pi\) | ||||
0.315676 | + | 0.948867i | \(0.397769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10904.0 | −0.111814 | ||||||||
\(100\) | −374.000 | + | 647.787i | −0.00374000 | + | 0.00647787i | ||||
\(101\) | 19348.0 | + | 33511.7i | 0.188726 | + | 0.326884i | 0.944826 | − | 0.327573i | \(-0.106231\pi\) |
−0.756099 | + | 0.654457i | \(0.772897\pi\) | |||||||
\(102\) | 120540. | + | 208781.i | 1.14718 | + | 1.98697i | ||||
\(103\) | 26530.0 | − | 45951.3i | 0.246402 | − | 0.426781i | −0.716123 | − | 0.697974i | \(-0.754085\pi\) |
0.962525 | + | 0.271193i | \(0.0874183\pi\) | |||||||
\(104\) | −50400.0 | −0.456927 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22620.0 | −0.195537 | ||||||||
\(107\) | 73162.0 | − | 126720.i | 0.617769 | − | 1.07001i | −0.372123 | − | 0.928183i | \(-0.621370\pi\) |
0.989892 | − | 0.141824i | \(-0.0452967\pi\) | |||||||
\(108\) | 138040. | + | 239092.i | 1.13880 | + | 1.97245i | ||||
\(109\) | −46449.0 | − | 80452.0i | −0.374464 | − | 0.648591i | 0.615783 | − | 0.787916i | \(-0.288840\pi\) |
−0.990247 | + | 0.139325i | \(0.955507\pi\) | |||||||
\(110\) | 64960.0 | − | 112514.i | 0.511875 | − | 0.886594i | ||||
\(111\) | −145572. | −1.12143 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −83354.0 | −0.614088 | −0.307044 | − | 0.951695i | \(-0.599340\pi\) | ||||
−0.307044 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(114\) | 6860.00 | − | 11881.9i | 0.0494381 | − | 0.0856293i | ||||
\(115\) | −51072.0 | − | 88459.3i | −0.360113 | − | 0.623733i | ||||
\(116\) | −116212. | − | 201285.i | −0.801874 | − | 1.38889i | ||||
\(117\) | 3290.00 | − | 5698.45i | 0.0222193 | − | 0.0384850i | ||||
\(118\) | −27300.0 | −0.180492 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −282240. | −1.78923 | ||||||||
\(121\) | 53613.5 | − | 92861.3i | 0.332898 | − | 0.576596i | ||||
\(122\) | −128240. | − | 222118.i | −0.780053 | − | 1.35109i | ||||
\(123\) | −125734. | − | 217778.i | −0.749359 | − | 1.29793i | ||||
\(124\) | −259896. | + | 450153.i | −1.51791 | + | 2.62909i | ||||
\(125\) | −174384. | −0.998232 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 60384.0 | 0.332210 | 0.166105 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166105 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(128\) | −135360. | + | 234450.i | −0.730240 | + | 1.26481i | ||||
\(129\) | −76160.0 | − | 131913.i | −0.402951 | − | 0.697932i | ||||
\(130\) | 39200.0 | + | 67896.4i | 0.203436 | + | 0.352361i | ||||
\(131\) | −30793.0 | + | 53335.0i | −0.156774 | + | 0.271540i | −0.933704 | − | 0.358047i | \(-0.883443\pi\) |
0.776930 | + | 0.629587i | \(0.216776\pi\) | |||||||
\(132\) | 220864. | 1.10329 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 484040. | 2.32873 | ||||||||
\(135\) | 113680. | − | 196900.i | 0.536846 | − | 0.929844i | ||||
\(136\) | 309960. | + | 536866.i | 1.43701 | + | 2.48897i | ||||
\(137\) | 102231. | + | 177069.i | 0.465352 | + | 0.806013i | 0.999217 | − | 0.0395567i | \(-0.0125946\pi\) |
−0.533866 | + | 0.845569i | \(0.679261\pi\) | |||||||
\(138\) | 127680. | − | 221148.i | 0.570723 | − | 0.988521i | ||||
\(139\) | 35406.0 | 0.155432 | 0.0777159 | − | 0.996976i | \(-0.475237\pi\) | ||||
0.0777159 | + | 0.996976i | \(0.475237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −130536. | −0.552946 | ||||||||
\(142\) | −292800. | + | 507144.i | −1.21857 | + | 2.11062i | ||||
\(143\) | −16240.0 | − | 28128.5i | −0.0664119 | − | 0.115029i | ||||
\(144\) | 33464.0 | + | 57961.3i | 0.134484 | + | 0.232934i | ||||
\(145\) | −95704.0 | + | 165764.i | −0.378016 | + | 0.654743i | ||||
\(146\) | 680820. | 2.64332 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −707064. | −2.65341 | ||||||||
\(149\) | 10113.0 | − | 17516.2i | 0.0373177 | − | 0.0646361i | −0.846763 | − | 0.531970i | \(-0.821452\pi\) |
0.884081 | + | 0.467334i | \(0.154785\pi\) | |||||||
\(150\) | 770.000 | + | 1333.68i | 0.00279423 | + | 0.00483975i | ||||
\(151\) | −35452.0 | − | 61404.7i | −0.126531 | − | 0.219159i | 0.795799 | − | 0.605561i | \(-0.207051\pi\) |
−0.922331 | + | 0.386402i | \(0.873718\pi\) | |||||||
\(152\) | 17640.0 | − | 30553.4i | 0.0619284 | − | 0.107263i | ||||
\(153\) | −80934.0 | −0.279513 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 428064. | 1.43113 | ||||||||
\(156\) | −66640.0 | + | 115424.i | −0.219242 | + | 0.379738i | ||||
\(157\) | 146762. | + | 254199.i | 0.475187 | + | 0.823048i | 0.999596 | − | 0.0284185i | \(-0.00904710\pi\) |
−0.524409 | + | 0.851466i | \(0.675714\pi\) | |||||||
\(158\) | 158920. | + | 275258.i | 0.506449 | + | 0.877196i | ||||
\(159\) | −15834.0 | + | 27425.3i | −0.0496704 | + | 0.0860317i | ||||
\(160\) | −152320. | −0.470389 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 454190. | 1.35972 | ||||||||
\(163\) | −6596.00 | + | 11424.6i | −0.0194452 | + | 0.0336800i | −0.875584 | − | 0.483065i | \(-0.839523\pi\) |
0.856139 | + | 0.516745i | \(0.172857\pi\) | |||||||
\(164\) | −610708. | − | 1.05778e6i | −1.77306 | − | 3.07103i | ||||
\(165\) | −90944.0 | − | 157520.i | −0.260054 | − | 0.450427i | ||||
\(166\) | 102690. | − | 177864.i | 0.289240 | − | 0.500978i | ||||
\(167\) | −493612. | −1.36960 | −0.684801 | − | 0.728730i | \(-0.740111\pi\) | ||||
−0.684801 | + | 0.728730i | \(0.740111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −351693. | −0.947212 | ||||||||
\(170\) | 482160. | − | 835126.i | 1.27958 | − | 2.21630i | ||||
\(171\) | 2303.00 | + | 3988.91i | 0.00602287 | + | 0.0104319i | ||||
\(172\) | −369920. | − | 640720.i | −0.953425 | − | 1.65138i | ||||
\(173\) | 120358. | − | 208466.i | 0.305745 | − | 0.529566i | −0.671682 | − | 0.740840i | \(-0.734428\pi\) |
0.977427 | + | 0.211274i | \(0.0677611\pi\) | |||||||
\(174\) | −478520. | −1.19819 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 330368. | 0.803926 | ||||||||
\(177\) | −19110.0 | + | 33099.5i | −0.0458488 | + | 0.0794124i | ||||
\(178\) | 252910. | + | 438053.i | 0.598296 | + | 1.03628i | ||||
\(179\) | −147466. | − | 255419.i | −0.344001 | − | 0.595827i | 0.641171 | − | 0.767398i | \(-0.278449\pi\) |
−0.985172 | + | 0.171571i | \(0.945116\pi\) | |||||||
\(180\) | 89488.0 | − | 154998.i | 0.205865 | − | 0.356569i | ||||
\(181\) | 336980. | 0.764553 | 0.382277 | − | 0.924048i | \(-0.375140\pi\) | ||||
0.382277 | + | 0.924048i | \(0.375140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −359072. | −0.792600 | ||||||||
\(184\) | 328320. | − | 568667.i | 0.714912 | − | 1.23826i | ||||
\(185\) | 291144. | + | 504276.i | 0.625430 | + | 1.08328i | ||||
\(186\) | 535080. | + | 926786.i | 1.13406 | + | 1.96425i | ||||
\(187\) | −199752. | + | 345981.i | −0.417722 | + | 0.723515i | ||||
\(188\) | −634032. | −1.30833 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −54880.0 | −0.110288 | ||||||||
\(191\) | −179132. | + | 310266.i | −0.355296 | + | 0.615390i | −0.987168 | − | 0.159682i | \(-0.948953\pi\) |
0.631873 | + | 0.775072i | \(0.282286\pi\) | |||||||
\(192\) | 128576. | + | 222700.i | 0.251714 | + | 0.435981i | ||||
\(193\) | 494777. | + | 856979.i | 0.956128 | + | 1.65606i | 0.731764 | + | 0.681558i | \(0.238697\pi\) |
0.224364 | + | 0.974505i | \(0.427970\pi\) | |||||||
\(194\) | 292530. | − | 506677.i | 0.558041 | − | 0.966555i | ||||
\(195\) | 109760. | 0.206708 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −990050. | −1.81757 | −0.908786 | − | 0.417263i | \(-0.862989\pi\) | ||||
−0.908786 | + | 0.417263i | \(0.862989\pi\) | |||||||
\(198\) | −54520.0 | + | 94431.4i | −0.0988309 | + | 0.171180i | ||||
\(199\) | −420378. | − | 728116.i | −0.752501 | − | 1.30337i | −0.946607 | − | 0.322390i | \(-0.895514\pi\) |
0.194106 | − | 0.980981i | \(-0.437820\pi\) | |||||||
\(200\) | 1980.00 | + | 3429.46i | 0.00350018 | + | 0.00606249i | ||||
\(201\) | 338828. | − | 586867.i | 0.591547 | − | 1.02459i | ||||
\(202\) | 386960. | 0.667249 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.63934e6 | 2.75800 | ||||||||
\(205\) | −502936. | + | 871111.i | −0.835849 | + | 1.44773i | ||||
\(206\) | −265300. | − | 459513.i | −0.435581 | − | 0.754449i | ||||
\(207\) | 42864.0 | + | 74242.6i | 0.0695291 | + | 0.120428i | ||||
\(208\) | −99680.0 | + | 172651.i | −0.159753 | + | 0.276701i | ||||
\(209\) | 22736.0 | 0.0360038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.15073e6 | 1.77938 | 0.889689 | − | 0.456568i | \(-0.150921\pi\) | ||||
0.889689 | + | 0.456568i | \(0.150921\pi\) | |||||||
\(212\) | −76908.0 | + | 133209.i | −0.117525 | + | 0.203560i | ||||
\(213\) | 409920. | + | 710002.i | 0.619085 | + | 1.07229i | ||||
\(214\) | −731620. | − | 1.26720e6i | −1.09207 | − | 1.89152i | ||||
\(215\) | −304640. | + | 527652.i | −0.449460 | + | 0.778487i | ||||
\(216\) | 1.46160e6 | 2.13154 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −928980. | −1.32393 | ||||||||
\(219\) | 476574. | − | 825450.i | 0.671460 | − | 1.16300i | ||||
\(220\) | −441728. | − | 765095.i | −0.615316 | − | 1.06576i | ||||
\(221\) | −120540. | − | 208781.i | −0.166016 | − | 0.287549i | ||||
\(222\) | −727860. | + | 1.26069e6i | −0.991209 | + | 1.71683i | ||||
\(223\) | 824264. | 1.10995 | 0.554976 | − | 0.831866i | \(-0.312727\pi\) | ||||
0.554976 | + | 0.831866i | \(0.312727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −517.000 | −0.000680823 | ||||||||
\(226\) | −416770. | + | 721867.i | −0.542782 | + | 0.940126i | ||||
\(227\) | 37191.0 | + | 64416.7i | 0.0479042 | + | 0.0829724i | 0.888983 | − | 0.457940i | \(-0.151412\pi\) |
−0.841079 | + | 0.540912i | \(0.818079\pi\) | |||||||
\(228\) | −46648.0 | − | 80796.7i | −0.0594287 | − | 0.102933i | ||||
\(229\) | 565978. | − | 980303.i | 0.713199 | − | 1.23530i | −0.250451 | − | 0.968129i | \(-0.580579\pi\) |
0.963650 | − | 0.267168i | \(-0.0860878\pi\) | |||||||
\(230\) | −1.02144e6 | −1.27319 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23048e6 | −1.50091 | ||||||||
\(233\) | 99363.0 | − | 172102.i | 0.119904 | − | 0.207680i | −0.799825 | − | 0.600233i | \(-0.795075\pi\) |
0.919730 | + | 0.392553i | \(0.128408\pi\) | |||||||
\(234\) | −32900.0 | − | 56984.5i | −0.0392786 | − | 0.0680326i | ||||
\(235\) | 261072. | + | 452190.i | 0.308383 | + | 0.534135i | ||||
\(236\) | −92820.0 | + | 160769.i | −0.108483 | + | 0.187898i | ||||
\(237\) | 444976. | 0.514595 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 482904. | 0.546847 | 0.273424 | − | 0.961894i | \(-0.411844\pi\) | ||||
0.273424 | + | 0.961894i | \(0.411844\pi\) | |||||||
\(240\) | −558208. | + | 966845.i | −0.625559 | + | 1.08350i | ||||
\(241\) | 402955. | + | 697939.i | 0.446904 | + | 0.774060i | 0.998183 | − | 0.0602611i | \(-0.0191933\pi\) |
−0.551279 | + | 0.834321i | \(0.685860\pi\) | |||||||
\(242\) | −536135. | − | 928613.i | −0.588485 | − | 1.01929i | ||||
\(243\) | −175357. | + | 303727.i | −0.190505 | + | 0.329965i | ||||
\(244\) | −1.74406e6 | −1.87537 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.51468e6 | −2.64938 | ||||||||
\(247\) | −6860.00 | + | 11881.9i | −0.00715454 | + | 0.0123920i | ||||
\(248\) | 1.37592e6 | + | 2.38316e6i | 1.42057 | + | 2.46051i | ||||
\(249\) | −143766. | − | 249010.i | −0.146946 | − | 0.254518i | ||||
\(250\) | −871920. | + | 1.51021e6i | −0.882321 | + | 1.52822i | ||||
\(251\) | −430738. | −0.431548 | −0.215774 | − | 0.976443i | \(-0.569227\pi\) | ||||
−0.215774 | + | 0.976443i | \(0.569227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 423168. | 0.415634 | ||||||||
\(254\) | 301920. | − | 522941.i | 0.293635 | − | 0.508590i | ||||
\(255\) | −675024. | − | 1.16918e6i | −0.650083 | − | 1.12598i | ||||
\(256\) | 1.05971e6 | + | 1.83548e6i | 1.01062 | + | 1.75045i | ||||
\(257\) | −588455. | + | 1.01923e6i | −0.555751 | + | 0.962589i | 0.442093 | + | 0.896969i | \(0.354236\pi\) |
−0.997845 | + | 0.0656204i | \(0.979097\pi\) | |||||||
\(258\) | −1.52320e6 | −1.42465 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 533120. | 0.489093 | ||||||||
\(261\) | 80323.0 | − | 139124.i | 0.0729858 | − | 0.126415i | ||||
\(262\) | 307930. | + | 533350.i | 0.277140 | + | 0.480020i | ||||
\(263\) | −645488. | − | 1.11802e6i | −0.575438 | − | 0.996688i | −0.995994 | − | 0.0894216i | \(-0.971498\pi\) |
0.420556 | − | 0.907267i | \(-0.361835\pi\) | |||||||
\(264\) | 584640. | − | 1.01263e6i | 0.516272 | − | 0.894210i | ||||
\(265\) | 126672. | 0.110807 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 708148. | 0.607919 | ||||||||
\(268\) | 1.64574e6 | − | 2.85050e6i | 1.39966 | − | 2.42429i | ||||
\(269\) | −638778. | − | 1.10640e6i | −0.538232 | − | 0.932245i | −0.998999 | − | 0.0447238i | \(-0.985759\pi\) |
0.460768 | − | 0.887521i | \(-0.347574\pi\) | |||||||
\(270\) | −1.13680e6 | − | 1.96900e6i | −0.949018 | − | 1.64375i | ||||
\(271\) | 825272. | − | 1.42941e6i | 0.682612 | − | 1.18232i | −0.291569 | − | 0.956550i | \(-0.594177\pi\) |
0.974181 | − | 0.225769i | \(-0.0724894\pi\) | |||||||
\(272\) | 2.45213e6 | 2.00965 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.04462e6 | 1.64527 | ||||||||
\(275\) | −1276.00 | + | 2210.10i | −0.00101746 | + | 0.00176230i | ||||
\(276\) | −868224. | − | 1.50381e6i | −0.686055 | − | 1.18828i | ||||
\(277\) | 532045. | + | 921529.i | 0.416628 | + | 0.721622i | 0.995598 | − | 0.0937276i | \(-0.0298783\pi\) |
−0.578969 | + | 0.815349i | \(0.696545\pi\) | |||||||
\(278\) | 177030. | − | 306625.i | 0.137384 | − | 0.237955i | ||||
\(279\) | −359268. | −0.276317 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22342.0 | −0.0168794 | −0.00843969 | − | 0.999964i | \(-0.502686\pi\) | ||||
−0.00843969 | + | 0.999964i | \(0.502686\pi\) | |||||||
\(282\) | −652680. | + | 1.13047e6i | −0.488740 | + | 0.846522i | ||||
\(283\) | −1.24787e6 | − | 2.16137e6i | −0.926196 | − | 1.60422i | −0.789626 | − | 0.613588i | \(-0.789726\pi\) |
−0.136570 | − | 0.990630i | \(-0.543608\pi\) | |||||||
\(284\) | 1.99104e6 | + | 3.44858e6i | 1.46482 | + | 2.53714i | ||||
\(285\) | −38416.0 | + | 66538.5i | −0.0280156 | + | 0.0485244i | ||||
\(286\) | −324800. | −0.234802 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 127840. | 0.0908208 | ||||||||
\(289\) | −772714. | + | 1.33838e6i | −0.544219 | + | 0.942615i | ||||
\(290\) | 957040. | + | 1.65764e6i | 0.668244 | + | 1.15743i | ||||
\(291\) | −409542. | − | 709348.i | −0.283508 | − | 0.491051i | ||||
\(292\) | 2.31479e6 | − | 4.00933e6i | 1.58874 | − | 2.75179i | ||||
\(293\) | 1.93178e6 | 1.31458 | 0.657291 | − | 0.753637i | \(-0.271702\pi\) | ||||
0.657291 | + | 0.753637i | \(0.271702\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 152880. | 0.102281 | ||||||||
\(296\) | −1.87164e6 | + | 3.24178e6i | −1.24163 | + | 2.15057i | ||||
\(297\) | 470960. | + | 815727.i | 0.309808 | + | 0.536604i | ||||
\(298\) | −101130. | − | 175162.i | −0.0659689 | − | 0.114262i | ||||
\(299\) | −127680. | + | 221148.i | −0.0825933 | + | 0.143056i | ||||
\(300\) | 10472.0 | 0.00671779 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −709040. | −0.447356 | ||||||||
\(303\) | 270872. | − | 469164.i | 0.169495 | − | 0.293574i | ||||
\(304\) | −69776.0 | − | 120856.i | −0.0433034 | − | 0.0750037i | ||||
\(305\) | 718144. | + | 1.24386e6i | 0.442040 | + | 0.765636i | ||||
\(306\) | −404670. | + | 700909.i | −0.247057 | + | 0.427916i | ||||
\(307\) | 459074. | 0.277995 | 0.138997 | − | 0.990293i | \(-0.455612\pi\) | ||||
0.138997 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −742840. | −0.442587 | ||||||||
\(310\) | 2.14032e6 | − | 3.70714e6i | 1.26495 | − | 2.19096i | ||||
\(311\) | 333564. | + | 577750.i | 0.195559 | + | 0.338718i | 0.947084 | − | 0.320987i | \(-0.104014\pi\) |
−0.751525 | + | 0.659705i | \(0.770681\pi\) | |||||||
\(312\) | 352800. | + | 611068.i | 0.205183 | + | 0.355388i | ||||
\(313\) | −55517.0 | + | 96158.3i | −0.0320306 | + | 0.0554786i | −0.881596 | − | 0.472004i | \(-0.843531\pi\) |
0.849566 | + | 0.527483i | \(0.176864\pi\) | |||||||
\(314\) | 2.93524e6 | 1.68004 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.16131e6 | 1.21759 | ||||||||
\(317\) | 34389.0 | − | 59563.5i | 0.0192208 | − | 0.0332914i | −0.856255 | − | 0.516553i | \(-0.827215\pi\) |
0.875476 | + | 0.483262i | \(0.160548\pi\) | |||||||
\(318\) | 158340. | + | 274253.i | 0.0878057 | + | 0.152084i | ||||
\(319\) | −396488. | − | 686737.i | −0.218149 | − | 0.377845i | ||||
\(320\) | 514304. | − | 890801.i | 0.280766 | − | 0.486301i | ||||
\(321\) | −2.04854e6 | −1.10964 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 168756. | 0.0900022 | ||||||||
\(324\) | 1.54425e6 | − | 2.67471e6i | 0.817248 | − | 1.41552i | ||||
\(325\) | −770.000 | − | 1333.68i | −0.000404373 | − | 0.000700395i | ||||
\(326\) | 65960.0 | + | 114246.i | 0.0343745 | + | 0.0595384i | ||||
\(327\) | −650286. | + | 1.12633e6i | −0.336306 | + | 0.582500i | ||||
\(328\) | −6.46632e6 | −3.31874 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.81888e6 | −0.919431 | ||||||||
\(331\) | 282224. | − | 488826.i | 0.141587 | − | 0.245236i | −0.786507 | − | 0.617581i | \(-0.788113\pi\) |
0.928094 | + | 0.372345i | \(0.121446\pi\) | |||||||
\(332\) | −698292. | − | 1.20948e6i | −0.347690 | − | 0.602216i | ||||
\(333\) | −244353. | − | 423232.i | −0.120756 | − | 0.209155i | ||||
\(334\) | −2.46806e6 | + | 4.27481e6i | −1.21057 | + | 2.09677i | ||||
\(335\) | −2.71062e6 | −1.31965 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.07729e6 | 0.996376 | 0.498188 | − | 0.867069i | \(-0.333999\pi\) | ||||
0.498188 | + | 0.867069i | \(0.333999\pi\) | |||||||
\(338\) | −1.75847e6 | + | 3.04575e6i | −0.837225 | + | 1.45012i | ||||
\(339\) | 583478. | + | 1.01061e6i | 0.275756 | + | 0.477624i | ||||
\(340\) | −3.27869e6 | − | 5.67885e6i | −1.53816 | − | 2.66418i | ||||
\(341\) | −886704. | + | 1.53582e6i | −0.412945 | + | 0.715243i | ||||
\(342\) | 46060.0 | 0.0212941 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.91680e6 | −1.78458 | ||||||||
\(345\) | −715008. | + | 1.23843e6i | −0.323417 | + | 0.560175i | ||||
\(346\) | −1.20358e6 | − | 2.08466e6i | −0.540486 | − | 0.936150i | ||||
\(347\) | 26624.0 | + | 46114.1i | 0.0118700 | + | 0.0205594i | 0.871899 | − | 0.489685i | \(-0.162888\pi\) |
−0.860029 | + | 0.510244i | \(0.829555\pi\) | |||||||
\(348\) | −1.62697e6 | + | 2.81799e6i | −0.720163 | + | 1.24736i | ||||
\(349\) | 2.27200e6 | 0.998494 | 0.499247 | − | 0.866460i | \(-0.333610\pi\) | ||||
0.499247 | + | 0.866460i | \(0.333610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −568400. | −0.246256 | ||||||||
\(352\) | 315520. | − | 546497.i | 0.135728 | − | 0.235088i | ||||
\(353\) | 2.00322e6 | + | 3.46969e6i | 0.855644 | + | 1.48202i | 0.876047 | + | 0.482227i | \(0.160172\pi\) |
−0.0204028 | + | 0.999792i | \(0.506495\pi\) | |||||||
\(354\) | 191100. | + | 330995.i | 0.0810499 | + | 0.140383i | ||||
\(355\) | 1.63968e6 | − | 2.84001e6i | 0.690539 | − | 1.19605i | ||||
\(356\) | 3.43958e6 | 1.43840 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.94932e6 | −1.21623 | ||||||||
\(359\) | −36892.0 | + | 63898.8i | −0.0151076 | + | 0.0261672i | −0.873480 | − | 0.486859i | \(-0.838142\pi\) |
0.858373 | + | 0.513027i | \(0.171476\pi\) | |||||||
\(360\) | −473760. | − | 820576.i | −0.192665 | − | 0.333705i | ||||
\(361\) | 1.23325e6 | + | 2.13605e6i | 0.498061 | + | 0.862666i | ||||
\(362\) | 1.68490e6 | − | 2.91833e6i | 0.675776 | − | 1.17048i | ||||
\(363\) | −1.50118e6 | −0.597951 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.81259e6 | −1.49792 | ||||||||
\(366\) | −1.79536e6 | + | 3.10965e6i | −0.700566 | + | 1.21342i | ||||
\(367\) | 702156. | + | 1.21617e6i | 0.272125 | + | 0.471334i | 0.969406 | − | 0.245464i | \(-0.0789402\pi\) |
−0.697281 | + | 0.716798i | \(0.745607\pi\) | |||||||
\(368\) | −1.29869e6 | − | 2.24939e6i | −0.499902 | − | 0.865856i | ||||
\(369\) | 422107. | − | 731111.i | 0.161383 | − | 0.279523i | ||||
\(370\) | 5.82288e6 | 2.21123 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.27709e6 | 2.72647 | ||||||||
\(373\) | 801617. | − | 1.38844e6i | 0.298329 | − | 0.516720i | −0.677425 | − | 0.735592i | \(-0.736904\pi\) |
0.975754 | + | 0.218872i | \(0.0702376\pi\) | |||||||
\(374\) | 1.99752e6 | + | 3.45981e6i | 0.738435 | + | 1.27901i | ||||
\(375\) | 1.22069e6 | + | 2.11429e6i | 0.448256 | + | 0.776403i | ||||
\(376\) | −1.67832e6 | + | 2.90694e6i | −0.612217 | + | 1.06039i | ||||
\(377\) | 478520. | 0.173399 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.77012e6 | −1.70581 | −0.852906 | − | 0.522064i | \(-0.825162\pi\) | ||||
−0.852906 | + | 0.522064i | \(0.825162\pi\) | |||||||
\(380\) | −186592. | + | 323187.i | −0.0662879 | + | 0.114814i | ||||
\(381\) | −422688. | − | 732117.i | −0.149179 | − | 0.258385i | ||||
\(382\) | 1.79132e6 | + | 3.10266e6i | 0.628080 | + | 1.08787i | ||||
\(383\) | −1.11539e6 | + | 1.93192e6i | −0.388536 | + | 0.672964i | −0.992253 | − | 0.124235i | \(-0.960352\pi\) |
0.603717 | + | 0.797199i | \(0.293686\pi\) | |||||||
\(384\) | 3.79008e6 | 1.31166 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.89554e6 | 3.38042 | ||||||||
\(387\) | 255680. | − | 442851.i | 0.0867799 | − | 0.150307i | ||||
\(388\) | −1.98920e6 | − | 3.44540e6i | −0.670811 | − | 1.16188i | ||||
\(389\) | −2.42012e6 | − | 4.19177e6i | −0.810892 | − | 1.40451i | −0.912240 | − | 0.409655i | \(-0.865649\pi\) |
0.101348 | − | 0.994851i | \(-0.467684\pi\) | |||||||
\(390\) | 548800. | − | 950549.i | 0.182706 | − | 0.316456i | ||||
\(391\) | 3.14093e6 | 1.03900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 862204. | 0.281597 | ||||||||
\(394\) | −4.95025e6 | + | 8.57408e6i | −1.60652 | + | 2.78258i | ||||
\(395\) | −889952. | − | 1.54144e6i | −0.286995 | − | 0.497089i | ||||
\(396\) | 370736. | + | 642134.i | 0.118803 | + | 0.205773i | ||||
\(397\) | 497910. | − | 862405.i | 0.158553 | − | 0.274622i | −0.775794 | − | 0.630986i | \(-0.782650\pi\) |
0.934347 | + | 0.356364i | \(0.115984\pi\) | |||||||
\(398\) | −8.40756e6 | −2.66049 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15664.0 | 0.00489500 | ||||||||
\(401\) | 1.65802e6 | − | 2.87178e6i | 0.514909 | − | 0.891848i | −0.484942 | − | 0.874546i | \(-0.661159\pi\) |
0.999850 | − | 0.0173014i | \(-0.00550748\pi\) | |||||||
\(402\) | −3.38828e6 | − | 5.86867e6i | −1.04572 | − | 1.81123i | ||||
\(403\) | −535080. | − | 926786.i | −0.164118 | − | 0.284261i | ||||
\(404\) | 1.31566e6 | − | 2.27880e6i | 0.401044 | − | 0.694628i | ||||
\(405\) | −2.54346e6 | −0.770527 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.41234e6 | −0.721858 | ||||||||
\(408\) | 4.33944e6 | − | 7.51613e6i | 1.29058 | − | 2.23534i | ||||
\(409\) | 1.53637e6 | + | 2.66107e6i | 0.454137 | + | 0.786588i | 0.998638 | − | 0.0521720i | \(-0.0166144\pi\) |
−0.544501 | + | 0.838760i | \(0.683281\pi\) | |||||||
\(410\) | 5.02936e6 | + | 8.71111e6i | 1.47759 | + | 2.55926i | ||||
\(411\) | 1.43123e6 | − | 2.47897e6i | 0.417932 | − | 0.723880i | ||||
\(412\) | −3.60808e6 | −1.04721 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 857280. | 0.245823 | ||||||||
\(415\) | −575064. | + | 996040.i | −0.163906 | + | 0.283894i | ||||
\(416\) | 190400. | + | 329782.i | 0.0539428 | + | 0.0934317i | ||||
\(417\) | −247842. | − | 429275.i | −0.0697967 | − | 0.120891i | ||||
\(418\) | 113680. | − | 196900.i | 0.0318232 | − | 0.0551193i | ||||
\(419\) | −2.81438e6 | −0.783154 | −0.391577 | − | 0.920145i | \(-0.628070\pi\) | ||||
−0.391577 | + | 0.920145i | \(0.628070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.05802e6 | 0.840883 | 0.420441 | − | 0.907320i | \(-0.361875\pi\) | ||||
0.420441 | + | 0.907320i | \(0.361875\pi\) | |||||||
\(422\) | 5.75366e6 | − | 9.96563e6i | 1.57276 | − | 2.72410i | ||||
\(423\) | −219114. | − | 379517.i | −0.0595414 | − | 0.103129i | ||||
\(424\) | 407160. | + | 705222.i | 0.109989 | + | 0.190507i | ||||
\(425\) | −9471.00 | + | 16404.3i | −0.00254345 | + | 0.00440539i | ||||
\(426\) | 8.19840e6 | 2.18880 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.95003e6 | −2.62552 | ||||||||
\(429\) | −227360. | + | 393799.i | −0.0596446 | + | 0.103307i | ||||
\(430\) | 3.04640e6 | + | 5.27652e6i | 0.794540 | + | 1.37618i | ||||
\(431\) | −968748. | − | 1.67792e6i | −0.251199 | − | 0.435089i | 0.712657 | − | 0.701512i | \(-0.247491\pi\) |
−0.963856 | + | 0.266423i | \(0.914158\pi\) | |||||||
\(432\) | 2.89072e6 | − | 5.00687e6i | 0.745241 | − | 1.29080i | ||||
\(433\) | −3.94790e6 | −1.01192 | −0.505961 | − | 0.862557i | \(-0.668862\pi\) | ||||
−0.505961 | + | 0.862557i | \(0.668862\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.67971e6 | 0.678993 | ||||||||
\(436\) | −3.15853e6 | + | 5.47074e6i | −0.795736 | + | 1.37826i | ||||
\(437\) | −89376.0 | − | 154804.i | −0.0223881 | − | 0.0387773i | ||||
\(438\) | −4.76574e6 | − | 8.25450e6i | −1.18698 | − | 2.05592i | ||||
\(439\) | −3.70885e6 | + | 6.42392e6i | −0.918498 | + | 1.59089i | −0.116800 | + | 0.993155i | \(0.537264\pi\) |
−0.801698 | + | 0.597730i | \(0.796070\pi\) | |||||||
\(440\) | −4.67712e6 | −1.15172 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.41080e6 | −0.586956 | ||||||||
\(443\) | −701346. | + | 1.21477e6i | −0.169794 | + | 0.294092i | −0.938347 | − | 0.345694i | \(-0.887644\pi\) |
0.768553 | + | 0.639786i | \(0.220977\pi\) | |||||||
\(444\) | 4.94945e6 | + | 8.57270e6i | 1.19151 | + | 2.06376i | ||||
\(445\) | −1.41630e6 | − | 2.45310e6i | −0.339042 | − | 0.587239i | ||||
\(446\) | 4.12132e6 | − | 7.13834e6i | 0.981068 | − | 1.69926i | ||||
\(447\) | −283164. | −0.0670300 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −590574. | −0.138248 | −0.0691239 | − | 0.997608i | \(-0.522020\pi\) | ||||
−0.0691239 | + | 0.997608i | \(0.522020\pi\) | |||||||
\(450\) | −2585.00 | + | 4477.35i | −0.000601768 | + | 0.00104229i | ||||
\(451\) | −2.08359e6 | − | 3.60889e6i | −0.482360 | − | 0.835472i | ||||
\(452\) | 2.83404e6 | + | 4.90869e6i | 0.652468 | + | 1.13011i | ||||
\(453\) | −496328. | + | 859665.i | −0.113638 | + | 0.196827i | ||||
\(454\) | 743820. | 0.169367 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −493920. | −0.111236 | ||||||||
\(457\) | 1.45242e6 | − | 2.51567e6i | 0.325313 | − | 0.563459i | −0.656262 | − | 0.754533i | \(-0.727864\pi\) |
0.981576 | + | 0.191073i | \(0.0611969\pi\) | |||||||
\(458\) | −5.65978e6 | − | 9.80303e6i | −1.26077 | − | 2.18372i | ||||
\(459\) | 3.49566e6 | + | 6.05466e6i | 0.774457 | + | 1.34140i | ||||
\(460\) | −3.47290e6 | + | 6.01523e6i | −0.765239 | + | 1.32543i | ||||
\(461\) | 922684. | 0.202209 | 0.101105 | − | 0.994876i | \(-0.467762\pi\) | ||||
0.101105 | + | 0.994876i | \(0.467762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.18235e6 | 1.55709 | 0.778546 | − | 0.627588i | \(-0.215958\pi\) | ||||
0.778546 | + | 0.627588i | \(0.215958\pi\) | |||||||
\(464\) | −2.43362e6 | + | 4.21515e6i | −0.524756 | + | 0.908903i | ||||
\(465\) | −2.99645e6 | − | 5.19000e6i | −0.642650 | − | 1.11310i | ||||
\(466\) | −993630. | − | 1.72102e6i | −0.211963 | − | 0.367131i | ||||
\(467\) | −306285. | + | 530501.i | −0.0649881 | + | 0.112563i | −0.896689 | − | 0.442662i | \(-0.854034\pi\) |
0.831701 | + | 0.555224i | \(0.187368\pi\) | |||||||
\(468\) | −447440. | −0.0944322 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.22144e6 | 1.09030 | ||||||||
\(471\) | 2.05467e6 | − | 3.55879e6i | 0.426766 | − | 0.739180i | ||||
\(472\) | 491400. | + | 851130.i | 0.101527 | + | 0.175849i | ||||
\(473\) | −1.26208e6 | − | 2.18599e6i | −0.259379 | − | 0.449257i | ||||
\(474\) | 2.22488e6 | − | 3.85361e6i | 0.454842 | − | 0.787810i | ||||
\(475\) | 1078.00 | 0.000219222 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −106314. | −0.0213941 | ||||||||
\(478\) | 2.41452e6 | − | 4.18207e6i | 0.483349 | − | 0.837185i | ||||
\(479\) | 1.30165e6 | + | 2.25452e6i | 0.259212 | + | 0.448969i | 0.966031 | − | 0.258426i | \(-0.0832038\pi\) |
−0.706819 | + | 0.707395i | \(0.749870\pi\) | |||||||
\(480\) | 1.06624e6 | + | 1.84678e6i | 0.211228 | + | 0.365858i | ||||
\(481\) | 727860. | − | 1.26069e6i | 0.143445 | − | 0.248454i | ||||
\(482\) | 8.05910e6 | 1.58004 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.29144e6 | −1.41482 | ||||||||
\(485\) | −1.63817e6 | + | 2.83739e6i | −0.316231 | + | 0.547728i | ||||
\(486\) | 1.75357e6 | + | 3.03727e6i | 0.336769 | + | 0.583301i | ||||
\(487\) | −2.73154e6 | − | 4.73117e6i | −0.521898 | − | 0.903954i | −0.999676 | − | 0.0254732i | \(-0.991891\pi\) |
0.477777 | − | 0.878481i | \(-0.341443\pi\) | |||||||
\(488\) | −4.61664e6 | + | 7.99626e6i | −0.877559 | + | 1.51998i | ||||
\(489\) | 184688. | 0.0349274 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.64090e6 | 0.307170 | 0.153585 | − | 0.988135i | \(-0.450918\pi\) | ||||
0.153585 | + | 0.988135i | \(0.450918\pi\) | |||||||
\(492\) | −8.54991e6 | + | 1.48089e7i | −1.59239 | + | 2.75810i | ||||
\(493\) | −2.94290e6 | − | 5.09725e6i | −0.545328 | − | 0.944536i | ||||
\(494\) | 68600.0 | + | 118819.i | 0.0126476 | + | 0.0219062i | ||||
\(495\) | 305312. | − | 528816.i | 0.0560055 | − | 0.0970044i | ||||
\(496\) | 1.08851e7 | 1.98667 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.87532e6 | −0.519533 | ||||||||
\(499\) | −1.49898e6 | + | 2.59631e6i | −0.269491 | + | 0.466773i | −0.968731 | − | 0.248115i | \(-0.920189\pi\) |
0.699239 | + | 0.714888i | \(0.253522\pi\) | |||||||
\(500\) | 5.92906e6 | + | 1.02694e7i | 1.06062 | + | 1.83705i | ||||
\(501\) | 3.45528e6 | + | 5.98473e6i | 0.615020 | + | 1.06525i | ||||
\(502\) | −2.15369e6 | + | 3.73030e6i | −0.381438 | + | 0.660670i | ||||
\(503\) | 6.89405e6 | 1.21494 | 0.607469 | − | 0.794343i | \(-0.292185\pi\) | ||||
0.607469 | + | 0.794343i | \(0.292185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.16698e6 | −0.378117 | ||||||||
\(506\) | 2.11584e6 | − | 3.66474e6i | 0.367372 | − | 0.636308i | ||||
\(507\) | 2.46185e6 | + | 4.26405e6i | 0.425346 | + | 0.736720i | ||||
\(508\) | −2.05306e6 | − | 3.55600e6i | −0.352973 | − | 0.611367i | ||||
\(509\) | 1.15238e6 | − | 1.99598e6i | 0.197152 | − | 0.341478i | −0.750452 | − | 0.660925i | \(-0.770164\pi\) |
0.947604 | + | 0.319447i | \(0.103497\pi\) | |||||||
\(510\) | −1.35005e7 | −2.29839 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.25312e7 | 2.11260 | ||||||||
\(513\) | 198940. | − | 344574.i | 0.0333756 | − | 0.0578082i | ||||
\(514\) | 5.88455e6 | + | 1.01923e7i | 0.982439 | + | 1.70163i | ||||
\(515\) | 1.48568e6 | + | 2.57327e6i | 0.246835 | + | 0.427531i | ||||
\(516\) | −5.17888e6 | + | 8.97008e6i | −0.856272 | + | 1.48311i | ||||
\(517\) | −2.16317e6 | −0.355929 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.37002e6 | −0.549180 | ||||||||
\(520\) | 1.41120e6 | − | 2.44427e6i | 0.228865 | − | 0.396407i | ||||
\(521\) | −6.04802e6 | − | 1.04755e7i | −0.976155 | − | 1.69075i | −0.676068 | − | 0.736839i | \(-0.736318\pi\) |
−0.300087 | − | 0.953912i | \(-0.597016\pi\) | |||||||
\(522\) | −803230. | − | 1.39124e6i | −0.129022 | − | 0.223473i | ||||
\(523\) | 2.74221e6 | − | 4.74966e6i | 0.438377 | − | 0.759290i | −0.559188 | − | 0.829041i | \(-0.688887\pi\) |
0.997564 | + | 0.0697505i | \(0.0222203\pi\) | |||||||
\(524\) | 4.18785e6 | 0.666289 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.29098e7 | −2.03448 | ||||||||
\(527\) | −6.58148e6 | + | 1.13995e7i | −1.03228 | + | 1.78796i | ||||
\(528\) | −2.31258e6 | − | 4.00550e6i | −0.361003 | − | 0.625276i | ||||
\(529\) | 1.55468e6 | + | 2.69279e6i | 0.241548 | + | 0.418373i | ||||
\(530\) | 633360. | − | 1.09701e6i | 0.0979402 | − | 0.169637i | ||||
\(531\) | −128310. | −0.0197480 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.51468e6 | 0.383411 | ||||||||
\(534\) | 3.54074e6 | − | 6.13274e6i | 0.537330 | − | 0.930682i | ||||
\(535\) | 4.09707e6 | + | 7.09634e6i | 0.618855 | + | 1.07189i | ||||
\(536\) | −8.71272e6 | − | 1.50909e7i | −1.30991 | − | 2.26883i | ||||
\(537\) | −2.06452e6 | + | 3.57586e6i | −0.308947 | + | 0.535112i | ||||
\(538\) | −1.27756e7 | −1.90294 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.54605e7 | −2.28160 | ||||||||
\(541\) | 3.35900e6 | − | 5.81795e6i | 0.493420 | − | 0.854628i | −0.506552 | − | 0.862210i | \(-0.669080\pi\) |
0.999971 | + | 0.00758172i | \(0.00241336\pi\) | |||||||
\(542\) | −8.25272e6 | − | 1.42941e7i | −1.20670 | − | 2.09006i | ||||
\(543\) | −2.35886e6 | − | 4.08567e6i | −0.343323 | − | 0.594652i | ||||
\(544\) | 2.34192e6 | − | 4.05632e6i | 0.339293 | − | 0.587673i | ||||
\(545\) | 5.20229e6 | 0.750245 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00235e6 | −0.714835 | −0.357418 | − | 0.933945i | \(-0.616343\pi\) | ||||
−0.357418 | + | 0.933945i | \(0.616343\pi\) | |||||||
\(548\) | 6.95171e6 | − | 1.20407e7i | 0.988872 | − | 1.71278i | ||||
\(549\) | −602728. | − | 1.04396e6i | −0.0853474 | − | 0.147826i | ||||
\(550\) | 12760.0 | + | 22101.0i | 0.00179864 | + | 0.00311533i | ||||
\(551\) | −167482. | + | 290087.i | −0.0235012 | + | 0.0407052i | ||||
\(552\) | −9.19296e6 | −1.28413 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.06409e7 | 1.47300 | ||||||||
\(555\) | 4.07602e6 | − | 7.05987e6i | 0.561699 | − | 0.972891i | ||||
\(556\) | −1.20380e6 | − | 2.08505e6i | −0.165146 | − | 0.286042i | ||||
\(557\) | −4.50980e6 | − | 7.81121e6i | −0.615913 | − | 1.06679i | −0.990224 | − | 0.139490i | \(-0.955454\pi\) |
0.374310 | − | 0.927304i | \(-0.377880\pi\) | |||||||
\(558\) | −1.79634e6 | + | 3.11135e6i | −0.244232 | + | 0.423023i | ||||
\(559\) | 1.52320e6 | 0.206171 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.59306e6 | 0.750312 | ||||||||
\(562\) | −111710. | + | 193487.i | −0.0149194 | + | 0.0258412i | ||||
\(563\) | 6.20255e6 | + | 1.07431e7i | 0.824707 | + | 1.42843i | 0.902143 | + | 0.431437i | \(0.141993\pi\) |
−0.0774366 | + | 0.996997i | \(0.524674\pi\) | |||||||
\(564\) | 4.43822e6 | + | 7.68723e6i | 0.587505 | + | 1.01759i | ||||
\(565\) | 2.33391e6 | − | 4.04245e6i | 0.307584 | − | 0.532751i | ||||
\(566\) | −2.49574e7 | −3.27460 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.10816e7 | 2.74178 | ||||||||
\(569\) | −3.24402e6 | + | 5.61881e6i | −0.420052 | + | 0.727551i | −0.995944 | − | 0.0899747i | \(-0.971321\pi\) |
0.575892 | + | 0.817526i | \(0.304655\pi\) | |||||||
\(570\) | 384160. | + | 665385.i | 0.0495251 | + | 0.0857799i | ||||
\(571\) | 5.11425e6 | + | 8.85814e6i | 0.656435 | + | 1.13698i | 0.981532 | + | 0.191298i | \(0.0612698\pi\) |
−0.325097 | + | 0.945681i | \(0.605397\pi\) | |||||||
\(572\) | −1.10432e6 | + | 1.91274e6i | −0.141125 | + | 0.244436i | ||||
\(573\) | 5.01570e6 | 0.638182 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20064.0 | 0.00253074 | ||||||||
\(576\) | −431648. | + | 747636.i | −0.0542093 | + | 0.0938932i | ||||
\(577\) | 1.32669e6 | + | 2.29789e6i | 0.165894 | + | 0.287336i | 0.936972 | − | 0.349404i | \(-0.113616\pi\) |
−0.771079 | + | 0.636740i | \(0.780283\pi\) | |||||||
\(578\) | 7.72714e6 | + | 1.33838e7i | 0.962053 | + | 1.66632i | ||||
\(579\) | 6.92688e6 | − | 1.19977e7i | 0.858699 | − | 1.48731i | ||||
\(580\) | 1.30157e7 | 1.60657 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.19084e6 | −1.00235 | ||||||||
\(583\) | −262392. | + | 454476.i | −0.0319727 | + | 0.0553783i | ||||
\(584\) | −1.22548e7 | − | 2.12259e7i | −1.48687 | − | 2.57533i | ||||
\(585\) | 184240. | + | 319113.i | 0.0222584 | + | 0.0385527i | ||||
\(586\) | 9.65888e6 | − | 1.67297e7i | 1.16194 | − | 2.01253i | ||||
\(587\) | 1.43044e7 | 1.71346 | 0.856729 | − | 0.515766i | \(-0.172493\pi\) | ||||
0.856729 | + | 0.515766i | \(0.172493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 749112. | 0.0889731 | ||||||||
\(590\) | 764400. | − | 1.32398e6i | 0.0904046 | − | 0.156585i | ||||
\(591\) | 6.93035e6 | + | 1.20037e7i | 0.816181 | + | 1.41367i | ||||
\(592\) | 7.40338e6 | + | 1.28230e7i | 0.868212 | + | 1.50379i | ||||
\(593\) | −5.01327e6 | + | 8.68323e6i | −0.585442 | + | 1.01402i | 0.409378 | + | 0.912365i | \(0.365746\pi\) |
−0.994820 | + | 0.101651i | \(0.967588\pi\) | |||||||
\(594\) | 9.41920e6 | 1.09534 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.37537e6 | −0.158600 | ||||||||
\(597\) | −5.88529e6 | + | 1.01936e7i | −0.675822 | + | 1.17056i | ||||
\(598\) | 1.27680e6 | + | 2.21148e6i | 0.146006 | + | 0.252889i | ||||
\(599\) | 3.76146e6 | + | 6.51504e6i | 0.428341 | + | 0.741908i | 0.996726 | − | 0.0808547i | \(-0.0257650\pi\) |
−0.568385 | + | 0.822763i | \(0.692432\pi\) | |||||||
\(600\) | 27720.0 | − | 48012.4i | 0.00314351 | − | 0.00544472i | ||||
\(601\) | −3.38625e6 | −0.382413 | −0.191207 | − | 0.981550i | \(-0.561240\pi\) | ||||
−0.191207 | + | 0.981550i | \(0.561240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.27499e6 | 0.254792 | ||||||||
\(604\) | −2.41074e6 | + | 4.17552e6i | −0.268879 | + | 0.465713i | ||||
\(605\) | 3.00236e6 | + | 5.20023e6i | 0.333483 | + | 0.577610i | ||||
\(606\) | −2.70872e6 | − | 4.69164e6i | −0.299628 | − | 0.518971i | ||||
\(607\) | −3.45430e6 | + | 5.98303e6i | −0.380530 | + | 0.659097i | −0.991138 | − | 0.132836i | \(-0.957592\pi\) |
0.610608 | + | 0.791933i | \(0.290925\pi\) | |||||||
\(608\) | −266560. | −0.0292439 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.43629e7 | 1.56285 | ||||||||
\(611\) | 652680. | − | 1.13047e6i | 0.0707290 | − | 0.122506i | ||||
\(612\) | 2.75176e6 | + | 4.76618e6i | 0.296983 | + | 0.514389i | ||||
\(613\) | 4.84448e6 | + | 8.39088e6i | 0.520710 | + | 0.901896i | 0.999710 | + | 0.0240812i | \(0.00766604\pi\) |
−0.479000 | + | 0.877815i | \(0.659001\pi\) | |||||||
\(614\) | 2.29537e6 | − | 3.97570e6i | 0.245715 | − | 0.425591i | ||||
\(615\) | 1.40822e7 | 1.50135 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.84742e6 | −0.829877 | −0.414939 | − | 0.909849i | \(-0.636197\pi\) | ||||
−0.414939 | + | 0.909849i | \(0.636197\pi\) | |||||||
\(618\) | −3.71420e6 | + | 6.43318e6i | −0.391196 | + | 0.677571i | ||||
\(619\) | −5.09860e6 | − | 8.83103e6i | −0.534840 | − | 0.926370i | −0.999171 | − | 0.0407086i | \(-0.987038\pi\) |
0.464331 | − | 0.885662i | \(-0.346295\pi\) | |||||||
\(620\) | −1.45542e7 | − | 2.52086e7i | −1.52058 | − | 2.63372i | ||||
\(621\) | 3.70272e6 | − | 6.41330e6i | 0.385294 | − | 0.667348i | ||||
\(622\) | 6.67128e6 | 0.691406 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.79104e6 | 0.286949 | ||||||||
\(625\) | 4.89994e6 | − | 8.48694e6i | 0.501754 | − | 0.869063i | ||||
\(626\) | 555170. | + | 961583.i | 0.0566226 | + | 0.0980733i | ||||
\(627\) | −159152. | − | 275659.i | −0.0161675 | − | 0.0280030i | ||||
\(628\) | 9.97982e6 | − | 1.72855e7i | 1.00977 | − | 1.74898i | ||||
\(629\) | −1.79054e7 | −1.80450 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.36258e6 | −0.836116 | −0.418058 | − | 0.908420i | \(-0.637289\pi\) | ||||
−0.418058 | + | 0.908420i | \(0.637289\pi\) | |||||||
\(632\) | 5.72112e6 | − | 9.90927e6i | 0.569755 | − | 0.986845i | ||||
\(633\) | −8.05512e6 | − | 1.39519e7i | −0.799030 | − | 1.38396i | ||||
\(634\) | −343890. | − | 595635.i | −0.0339779 | − | 0.0588514i | ||||
\(635\) | −1.69075e6 | + | 2.92847e6i | −0.166397 | + | 0.288208i | ||||
\(636\) | 2.15342e6 | 0.211099 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.92976e6 | −0.771273 | ||||||||
\(639\) | −1.37616e6 | + | 2.38358e6i | −0.133327 | + | 0.230928i | ||||
\(640\) | −7.58016e6 | − | 1.31292e7i | −0.731524 | − | 1.26704i | ||||
\(641\) | −551415. | − | 955079.i | −0.0530070 | − | 0.0918109i | 0.838304 | − | 0.545203i | \(-0.183547\pi\) |
−0.891311 | + | 0.453392i | \(0.850214\pi\) | |||||||
\(642\) | −1.02427e7 | + | 1.77408e7i | −0.980790 | + | 1.69878i | ||||
\(643\) | −1.71354e7 | −1.63443 | −0.817217 | − | 0.576330i | \(-0.804484\pi\) | ||||
−0.817217 | + | 0.576330i | \(0.804484\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.52992e6 | 0.807320 | ||||||||
\(646\) | 843780. | − | 1.46147e6i | 0.0795514 | − | 0.137787i | ||||
\(647\) | −27482.0 | − | 47600.2i | −0.00258100 | − | 0.00447042i | 0.864732 | − | 0.502234i | \(-0.167488\pi\) |
−0.867313 | + | 0.497763i | \(0.834155\pi\) | |||||||
\(648\) | −8.17542e6 | − | 1.41602e7i | −0.764843 | − | 1.32475i | ||||
\(649\) | −316680. | + | 548506.i | −0.0295127 | + | 0.0511175i | ||||
\(650\) | −15400.0 | −0.00142968 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 897056. | 0.0826420 | ||||||||
\(653\) | 242583. | − | 420166.i | 0.0222627 | − | 0.0385601i | −0.854679 | − | 0.519156i | \(-0.826246\pi\) |
0.876942 | + | 0.480596i | \(0.159580\pi\) | |||||||
\(654\) | 6.50286e6 | + | 1.12633e7i | 0.594511 | + | 1.02972i | ||||
\(655\) | −1.72441e6 | − | 2.98676e6i | −0.157050 | − | 0.272018i | ||||
\(656\) | −1.27889e7 | + | 2.21511e7i | −1.16031 | + | 2.00972i | ||||
\(657\) | 3.19985e6 | 0.289212 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.72136e6 | −0.244103 | −0.122051 | − | 0.992524i | \(-0.538947\pi\) | ||||
−0.122051 | + | 0.992524i | \(0.538947\pi\) | |||||||
\(660\) | −6.18419e6 | + | 1.07113e7i | −0.552616 | + | 0.957158i | ||||
\(661\) | −1.07262e6 | − | 1.85784e6i | −0.0954869 | − | 0.165388i | 0.814325 | − | 0.580409i | \(-0.197107\pi\) |
−0.909812 | + | 0.415021i | \(0.863774\pi\) | |||||||
\(662\) | −2.82224e6 | − | 4.88826e6i | −0.250293 | − | 0.433520i | ||||
\(663\) | −1.68756e6 | + | 2.92294e6i | −0.149099 | + | 0.258247i | ||||
\(664\) | −7.39368e6 | −0.650789 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.88706e6 | −0.426935 | ||||||||
\(667\) | −3.11722e6 | + | 5.39918e6i | −0.271302 | + | 0.469908i | ||||
\(668\) | 1.67828e7 | + | 2.90687e7i | 1.45520 | + | 2.52048i | ||||
\(669\) | −5.76985e6 | − | 9.99367e6i | −0.498424 | − | 0.863296i | ||||
\(670\) | −1.35531e7 | + | 2.34747e7i | −1.16641 | + | 2.02029i | ||||
\(671\) | −5.95034e6 | −0.510194 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.92796e6 | 0.249188 | 0.124594 | − | 0.992208i | \(-0.460237\pi\) | ||||
0.124594 | + | 0.992208i | \(0.460237\pi\) | |||||||
\(674\) | 1.03865e7 | − | 1.79899e7i | 0.880680 | − | 1.52538i | ||||
\(675\) | 22330.0 | + | 38676.7i | 0.00188638 | + | 0.00326731i | ||||
\(676\) | 1.19576e7 | + | 2.07111e7i | 1.00641 | + | 1.74316i | ||||
\(677\) | −6.74961e6 | + | 1.16907e7i | −0.565988 | + | 0.980319i | 0.430969 | + | 0.902367i | \(0.358172\pi\) |
−0.996957 | + | 0.0779529i | \(0.975162\pi\) | |||||||
\(678\) | 1.16696e7 | 0.974945 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.47155e7 | −2.87906 | ||||||||
\(681\) | 520674. | − | 901834.i | 0.0430227 | − | 0.0745176i | ||||
\(682\) | 8.86704e6 | + | 1.53582e7i | 0.729991 | + | 1.26438i | ||||
\(683\) | 2.71486e6 | + | 4.70228e6i | 0.222688 | + | 0.385706i | 0.955623 | − | 0.294592i | \(-0.0951837\pi\) |
−0.732936 | + | 0.680298i | \(0.761850\pi\) | |||||||
\(684\) | 156604. | − | 271246.i | 0.0127986 | − | 0.0221678i | ||||
\(685\) | −1.14499e7 | −0.932340 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.58474e7 | −1.28105 | ||||||||
\(688\) | −7.74656e6 | + | 1.34174e7i | −0.623933 | + | 1.08068i | ||||
\(689\) | −158340. | − | 274253.i | −0.0127070 | − | 0.0220091i | ||||
\(690\) | 7.15008e6 | + | 1.23843e7i | 0.571726 | + | 0.990259i | ||||
\(691\) | 1.04140e7 | − | 1.80376e7i | 0.829702 | − | 1.43709i | −0.0685703 | − | 0.997646i | \(-0.521844\pi\) |
0.898272 | − | 0.439440i | \(-0.144823\pi\) | |||||||
\(692\) | −1.63687e7 | −1.29942 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 532480. | 0.0419667 | ||||||||
\(695\) | −991368. | + | 1.71710e6i | −0.0778526 | + | 0.134845i | ||||
\(696\) | 8.61336e6 | + | 1.49188e7i | 0.673984 | + | 1.16737i | ||||
\(697\) | −1.54653e7 | − | 2.67867e7i | −1.20580 | − | 2.08851i | ||||
\(698\) | 1.13600e7 | − | 1.96761e7i | 0.882552 | − | 1.52863i | ||||
\(699\) | −2.78216e6 | −0.215372 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.35141e7 | 1.80731 | 0.903655 | − | 0.428261i | \(-0.140874\pi\) | ||||
0.903655 | + | 0.428261i | \(0.140874\pi\) | |||||||
\(702\) | −2.84200e6 | + | 4.92249e6i | −0.217661 | + | 0.377000i | ||||
\(703\) | 509502. | + | 882483.i | 0.0388828 | + | 0.0673470i | ||||
\(704\) | 2.13069e6 | + | 3.69046e6i | 0.162027 | + | 0.280640i | ||||
\(705\) | 3.65501e6 | − | 6.33066e6i | 0.276959 | − | 0.479707i | ||||
\(706\) | 4.00645e7 | 3.02516 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.59896e6 | 0.194857 | ||||||||
\(709\) | 9.78734e6 | − | 1.69522e7i | 0.731221 | − | 1.26651i | −0.225140 | − | 0.974326i | \(-0.572284\pi\) |
0.956361 | − | 0.292186i | \(-0.0943827\pi\) | |||||||
\(710\) | −1.63968e7 | − | 2.84001e7i | −1.22071 | − | 2.11434i | ||||
\(711\) | 746924. | + | 1.29371e6i | 0.0554118 | + | 0.0959761i | ||||
\(712\) | 9.10476e6 | − | 1.57699e7i | 0.673083 | − | 1.16581i | ||||
\(713\) | 1.39427e7 | 1.02712 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.81888e6 | 0.133057 | ||||||||
\(716\) | −1.00277e7 | + | 1.73685e7i | −0.731001 | + | 1.26613i | ||||
\(717\) | −3.38033e6 | − | 5.85490e6i | −0.245562 | − | 0.425326i | ||||
\(718\) | 368920. | + | 638988.i | 0.0267068 | + | 0.0462575i | ||||
\(719\) | −1.30576e7 | + | 2.26164e7i | −0.941978 | + | 1.63155i | −0.180287 | + | 0.983614i | \(0.557702\pi\) |
−0.761692 | + | 0.647940i | \(0.775631\pi\) | |||||||
\(720\) | −3.74797e6 | −0.269442 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.46650e7 | 1.76091 | ||||||||
\(723\) | 5.64137e6 | − | 9.77114e6i | 0.401364 | − | 0.695184i | ||||
\(724\) | −1.14573e7 | − | 1.98447e7i | −0.812338 | − | 1.40701i | ||||
\(725\) | −18799.0 | − | 32560.8i | −0.00132828 | − | 0.00230065i | ||||
\(726\) | −7.50589e6 | + | 1.30006e7i | −0.528519 | + | 0.915422i | ||||
\(727\) | −1.54126e7 | −1.08154 | −0.540768 | − | 0.841172i | \(-0.681866\pi\) | ||||
−0.540768 | + | 0.841172i | \(0.681866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59468e7 | 1.11136 | ||||||||
\(730\) | −1.90630e7 | + | 3.30180e7i | −1.32399 | + | 2.29321i | ||||
\(731\) | −9.36768e6 | − | 1.62253e7i | −0.648393 | − | 1.12305i | ||||
\(732\) | 1.22084e7 | + | 2.11457e7i | 0.842137 | + | 1.45862i | ||||
\(733\) | −8.49341e6 | + | 1.47110e7i | −0.583878 | + | 1.01131i | 0.411136 | + | 0.911574i | \(0.365132\pi\) |
−0.995014 | + | 0.0997324i | \(0.968201\pi\) | |||||||
\(734\) | 1.40431e7 | 0.962107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.96128e6 | −0.337597 | ||||||||
\(737\) | 5.61486e6 | − | 9.72523e6i | 0.380777 | − | 0.659525i | ||||
\(738\) | −4.22107e6 | − | 7.31111e6i | −0.285287 | − | 0.494131i | ||||
\(739\) | −1.00756e6 | − | 1.74514e6i | −0.0678669 | − | 0.117549i | 0.830095 | − | 0.557622i | \(-0.188286\pi\) |
−0.897962 | + | 0.440073i | \(0.854953\pi\) | |||||||
\(740\) | 1.97978e7 | − | 3.42908e7i | 1.32904 | − | 2.30196i | ||||
\(741\) | 192080. | 0.0128510 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.51381e7 | −1.00600 | −0.503001 | − | 0.864286i | \(-0.667771\pi\) | ||||
−0.503001 | + | 0.864286i | \(0.667771\pi\) | |||||||
\(744\) | 1.92629e7 | − | 3.33643e7i | 1.27582 | − | 2.20978i | ||||
\(745\) | 566328. | + | 980909.i | 0.0373833 | + | 0.0647497i | ||||
\(746\) | −8.01617e6 | − | 1.38844e7i | −0.527375 | − | 0.913441i | ||||
\(747\) | 482643. | − | 835962.i | 0.0316464 | − | 0.0548132i | ||||
\(748\) | 2.71663e7 | 1.77532 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.44138e7 | 1.58483 | ||||||||
\(751\) | −3.60700e6 | + | 6.24751e6i | −0.233371 | + | 0.404210i | −0.958798 | − | 0.284089i | \(-0.908309\pi\) |
0.725427 | + | 0.688299i | \(0.241642\pi\) | |||||||
\(752\) | 6.63869e6 | + | 1.14985e7i | 0.428093 | + | 0.741478i | ||||
\(753\) | 3.01517e6 | + | 5.22242e6i | 0.193787 | + | 0.335648i | ||||
\(754\) | 2.39260e6 | − | 4.14410e6i | 0.153265 | − | 0.265462i | ||||
\(755\) | 3.97062e6 | 0.253508 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.09697e7 | −0.695755 | −0.347877 | − | 0.937540i | \(-0.613097\pi\) | ||||
−0.347877 | + | 0.937540i | \(0.613097\pi\) | |||||||
\(758\) | −2.38506e7 | + | 4.13105e7i | −1.50774 | + | 2.61148i | ||||
\(759\) | −2.96218e6 | − | 5.13064e6i | −0.186641 | − | 0.323271i | ||||
\(760\) | 987840. | + | 1.71099e6i | 0.0620373 | + | 0.107452i | ||||
\(761\) | 9.62210e6 | − | 1.66660e7i | 0.602293 | − | 1.04320i | −0.390180 | − | 0.920739i | \(-0.627587\pi\) |
0.992473 | − | 0.122464i | \(-0.0390795\pi\) | |||||||
\(762\) | −8.45376e6 | −0.527427 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.43620e7 | 1.51001 | ||||||||
\(765\) | 2.26615e6 | − | 3.92509e6i | 0.140002 | − | 0.242491i | ||||
\(766\) | 1.11539e7 | + | 1.93192e7i | 0.686841 | + | 1.18964i | ||||
\(767\) | −191100. | − | 330995.i | −0.0117293 | − | 0.0203158i | ||||
\(768\) | 1.48360e7 | − | 2.56967e7i | 0.907638 | − | 1.57208i | ||||
\(769\) | −8.21185e6 | −0.500755 | −0.250378 | − | 0.968148i | \(-0.580555\pi\) | ||||
−0.250378 | + | 0.968148i | \(0.580555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.64767e7 | 0.998241 | ||||||||
\(772\) | 3.36448e7 | − | 5.82746e7i | 2.03177 | − | 3.51913i | ||||
\(773\) | 9.30933e6 | + | 1.61242e7i | 0.560363 | + | 0.970578i | 0.997465 | + | 0.0711653i | \(0.0226718\pi\) |
−0.437101 | + | 0.899412i | \(0.643995\pi\) | |||||||
\(774\) | −2.55680e6 | − | 4.42851e6i | −0.153407 | − | 0.265708i | ||||
\(775\) | −42042.0 | + | 72818.9i | −0.00251437 | + | 0.00435502i | ||||
\(776\) | −2.10622e7 | −1.25559 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.84024e7 | −2.86694 | ||||||||
\(779\) | −880138. | + | 1.52444e6i | −0.0519645 | + | 0.0900052i | ||||
\(780\) | −3.73184e6 | − | 6.46374e6i | −0.219627 | − | 0.380406i | ||||
\(781\) | 6.79296e6 | + | 1.17658e7i | 0.398503 | + | 0.690227i | ||||
\(782\) | 1.57046e7 | − | 2.72012e7i | 0.918356 | − | 1.59064i | ||||
\(783\) | −1.38771e7 | −0.808898 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.64373e7 | −0.952045 | ||||||||
\(786\) | 4.31102e6 | − | 7.46691e6i | 0.248899 | − | 0.431106i | ||||
\(787\) | 1.31250e7 | + | 2.27332e7i | 0.755377 | + | 1.30835i | 0.945187 | + | 0.326530i | \(0.105879\pi\) |
−0.189810 | + | 0.981821i | \(0.560787\pi\) | |||||||
\(788\) | 3.36617e7 | + | 5.83038e7i | 1.93117 | + | 3.34488i | ||||
\(789\) | −9.03683e6 | + | 1.56523e7i | −0.516801 | + | 0.895126i | ||||
\(790\) | −1.77990e7 | −1.01468 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.92544e6 | 0.222370 | ||||||||
\(793\) | 1.79536e6 | − | 3.10965e6i | 0.101384 | − | 0.175602i | ||||
\(794\) | −4.97910e6 | − | 8.62405e6i | −0.280285 | − | 0.485468i | ||||
\(795\) | −886704. | − | 1.53582e6i | −0.0497578 | − | 0.0861830i | ||||
\(796\) | −2.85857e7 | + | 4.95119e7i | −1.59907 | + | 2.76966i | ||||
\(797\) | 1.00373e7 | 0.559720 | 0.279860 | − | 0.960041i | \(-0.409712\pi\) | ||||
0.279860 | + | 0.960041i | \(0.409712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.60559e7 | −0.889751 | ||||||||
\(800\) | 14960.0 | − | 25911.5i | 0.000826431 | − | 0.00143142i | ||||
\(801\) | 1.18868e6 | + | 2.05885e6i | 0.0654610 | + | 0.113382i | ||||
\(802\) | −1.65802e7 | − | 2.87178e7i | −0.910238 | − | 1.57658i | ||||
\(803\) | 7.89751e6 | − | 1.36789e7i | 0.432217 | − | 0.748621i | ||||
\(804\) | −4.60806e7 | −2.51407 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.07016e7 | −0.580245 | ||||||||
\(807\) | −8.94289e6 | + | 1.54895e7i | −0.483386 | + | 0.837249i | ||||
\(808\) | −6.96528e6 | − | 1.20642e7i | −0.375327 | − | 0.650086i | ||||
\(809\) | −7.04420e6 | − | 1.22009e7i | −0.378408 | − | 0.655422i | 0.612423 | − | 0.790530i | \(-0.290195\pi\) |
−0.990831 | + | 0.135109i | \(0.956862\pi\) | |||||||
\(810\) | −1.27173e7 | + | 2.20270e7i | −0.681056 | + | 1.17962i | ||||
\(811\) | −1.81433e7 | −0.968646 | −0.484323 | − | 0.874889i | \(-0.660934\pi\) | ||||
−0.484323 | + | 0.874889i | \(0.660934\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.31076e7 | −1.22611 | ||||||||
\(814\) | −1.20617e7 | + | 2.08914e7i | −0.638038 | + | 1.10511i | ||||
\(815\) | −369376. | − | 639778.i | −0.0194794 | − | 0.0337392i | ||||
\(816\) | −1.71649e7 | − | 2.97305e7i | −0.902435 | − | 1.56306i | ||||
\(817\) | −533120. | + | 923391.i | −0.0279428 | + | 0.0483983i | ||||
\(818\) | 3.07273e7 | 1.60562 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.83993e7 | 3.55236 | ||||||||
\(821\) | 1.06835e7 | − | 1.85043e7i | 0.553164 | − | 0.958109i | −0.444880 | − | 0.895590i | \(-0.646754\pi\) |
0.998044 | − | 0.0625181i | \(-0.0199131\pi\) | |||||||
\(822\) | −1.43123e7 | − | 2.47897e7i | −0.738807 | − | 1.27965i | ||||
\(823\) | −8.90087e6 | − | 1.54168e7i | −0.458071 | − | 0.793402i | 0.540788 | − | 0.841159i | \(-0.318126\pi\) |
−0.998859 | + | 0.0477567i | \(0.984793\pi\) | |||||||
\(824\) | −9.55080e6 | + | 1.65425e7i | −0.490029 | + | 0.848755i | ||||
\(825\) | 35728.0 | 0.00182757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.62921e7 | 0.828350 | 0.414175 | − | 0.910197i | \(-0.364070\pi\) | ||||
0.414175 | + | 0.910197i | \(0.364070\pi\) | |||||||
\(828\) | 2.91475e6 | − | 5.04850e6i | 0.147749 | − | 0.255909i | ||||
\(829\) | −1.04250e6 | − | 1.80566e6i | −0.0526851 | − | 0.0912533i | 0.838480 | − | 0.544932i | \(-0.183445\pi\) |
−0.891165 | + | 0.453679i | \(0.850111\pi\) | |||||||
\(830\) | 5.75064e6 | + | 9.96040e6i | 0.289748 | + | 0.501859i | ||||
\(831\) | 7.44863e6 | − | 1.29014e7i | 0.374174 | − | 0.648089i | ||||
\(832\) | −2.57152e6 | −0.128790 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.95684e6 | −0.246769 | ||||||||
\(835\) | 1.38211e7 | − | 2.39389e7i | 0.686005 | − | 1.18820i | ||||
\(836\) | −773024. | − | 1.33892e6i | −0.0382540 | − | 0.0662579i | ||||
\(837\) | 1.55173e7 | + | 2.68768e7i | 0.765602 | + | 1.32606i | ||||
\(838\) | −1.40719e7 | + | 2.43732e7i | −0.692217 | + | 1.19896i | ||||
\(839\) | 2.27850e7 | 1.11749 | 0.558745 | − | 0.829340i | \(-0.311283\pi\) | ||||
0.558745 | + | 0.829340i | \(0.311283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.82842e6 | −0.430421 | ||||||||
\(842\) | 1.52901e7 | − | 2.64832e7i | 0.743242 | − | 1.28733i | ||||
\(843\) | 156394. | + | 270882.i | 0.00757968 | + | 0.0131284i | ||||
\(844\) | −3.91249e7 | − | 6.77663e7i | −1.89059 | − | 3.27460i | ||||
\(845\) | 9.84740e6 | − | 1.70562e7i | 0.474439 | − | 0.821752i | ||||
\(846\) | −4.38228e6 | −0.210511 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.22109e6 | 0.153820 | ||||||||
\(849\) | −1.74702e7 | + | 3.02592e7i | −0.831817 | + | 1.44075i | ||||
\(850\) | 94710.0 | + | 164043.i | 0.00449623 | + | 0.00778770i | ||||
\(851\) | 9.48298e6 | + | 1.64250e7i | 0.448870 | + | 0.777466i | ||||
\(852\) | 2.78746e7 | − | 4.82802e7i | 1.31556 | − | 2.27861i | ||||
\(853\) | 2.26975e7 | 1.06808 | 0.534042 | − | 0.845458i | \(-0.320672\pi\) | ||||
0.534042 | + | 0.845458i | \(0.320672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −257936. | −0.0120669 | ||||||||
\(856\) | −2.63383e7 | + | 4.56193e7i | −1.22858 | + | 2.12796i | ||||
\(857\) | 1.26450e7 | + | 2.19017e7i | 0.588120 | + | 1.01865i | 0.994479 | + | 0.104940i | \(0.0334650\pi\) |
−0.406359 | + | 0.913714i | \(0.633202\pi\) | |||||||
\(858\) | 2.27360e6 | + | 3.93799e6i | 0.105438 | + | 0.182623i | ||||
\(859\) | −5.19737e6 | + | 9.00210e6i | −0.240326 | + | 0.416257i | −0.960807 | − | 0.277218i | \(-0.910588\pi\) |
0.720481 | + | 0.693474i | \(0.243921\pi\) | |||||||
\(860\) | 4.14310e7 | 1.91020 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.93750e7 | −0.888122 | ||||||||
\(863\) | −2.16700e7 | + | 3.75335e7i | −0.990447 | + | 1.71551i | −0.375806 | + | 0.926698i | \(0.622634\pi\) |
−0.614642 | + | 0.788807i | \(0.710699\pi\) | |||||||
\(864\) | −5.52160e6 | − | 9.56369e6i | −0.251641 | − | 0.435854i | ||||
\(865\) | 6.74005e6 | + | 1.16741e7i | 0.306283 | + | 0.530498i | ||||
\(866\) | −1.97395e7 | + | 3.41898e7i | −0.894420 | + | 1.54918i | ||||
\(867\) | 2.16360e7 | 0.977527 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.37389e6 | 0.331243 | ||||||||
\(870\) | 1.33986e7 | − | 2.32070e7i | 0.600150 | − | 1.03949i | ||||
\(871\) | 3.38828e6 | + | 5.86867e6i | 0.151333 | + | 0.262117i | ||||
\(872\) | 1.67216e7 | + | 2.89627e7i | 0.744711 | + | 1.28988i | ||||
\(873\) | 1.37489e6 | − | 2.38138e6i | 0.0610566 | − | 0.105753i | ||||
\(874\) | −1.78752e6 | −0.0791539 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.48141e7 | −2.85370 | ||||||||
\(877\) | −1.85830e7 | + | 3.21866e7i | −0.815861 | + | 1.41311i | 0.0928475 | + | 0.995680i | \(0.470403\pi\) |
−0.908708 | + | 0.417432i | \(0.862930\pi\) | |||||||
\(878\) | 3.70885e7 | + | 6.42392e7i | 1.62369 | + | 2.81231i | ||||
\(879\) | −1.35224e7 | − | 2.34215e7i | −0.590313 | − | 1.02245i | ||||
\(880\) | −9.25030e6 | + | 1.60220e7i | −0.402670 | + | 0.697445i | ||||
\(881\) | −9.04785e6 | −0.392740 | −0.196370 | − | 0.980530i | \(-0.562915\pi\) | ||||
−0.196370 | + | 0.980530i | \(0.562915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.29679e7 | 1.42295 | 0.711474 | − | 0.702712i | \(-0.248028\pi\) | ||||
0.711474 | + | 0.702712i | \(0.248028\pi\) | |||||||
\(884\) | −8.19672e6 | + | 1.41971e7i | −0.352784 | + | 0.611041i | ||||
\(885\) | −1.07016e6 | − | 1.85357e6i | −0.0459294 | − | 0.0795520i | ||||
\(886\) | 7.01346e6 | + | 1.21477e7i | 0.300157 | + | 0.519887i | ||||
\(887\) | −8.05494e6 | + | 1.39516e7i | −0.343758 | + | 0.595407i | −0.985127 | − | 0.171826i | \(-0.945033\pi\) |
0.641369 | + | 0.767233i | \(0.278367\pi\) | |||||||
\(888\) | 5.24059e7 | 2.23022 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.83259e7 | −1.19870 | ||||||||
\(891\) | 5.26860e6 | − | 9.12549e6i | 0.222332 | − | 0.385090i | ||||
\(892\) | −2.80250e7 | − | 4.85407e7i | −1.17932 | − | 2.04265i | ||||
\(893\) | 456876. | + | 791332.i | 0.0191721 | + | 0.0332071i | ||||
\(894\) | −1.41582e6 | + | 2.45227e6i | −0.0592467 | + | 0.102618i | ||||
\(895\) | 1.65162e7 | 0.689211 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.57504e6 | 0.148354 | ||||||||
\(898\) | −2.95287e6 | + | 5.11452e6i | −0.122195 | + | 0.211648i | ||||
\(899\) | −1.30636e7 | − | 2.26268e7i | −0.539093 | − | 0.933736i | ||||
\(900\) | 17578.0 | + | 30446.0i | 0.000723374 | + | 0.00125292i | ||||
\(901\) | −1.94758e6 | + | 3.37331e6i | −0.0799252 | + | 0.138435i | ||||
\(902\) | −4.16718e7 | −1.70540 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00074e7 | 1.22126 | ||||||||
\(905\) | −9.43544e6 | + | 1.63427e7i | −0.382949 | + | 0.663287i | ||||
\(906\) | 4.96328e6 | + | 8.59665e6i | 0.200885 | + | 0.347944i | ||||
\(907\) | 2.23643e7 | + | 3.87361e7i | 0.902686 | + | 1.56350i | 0.823994 | + | 0.566599i | \(0.191741\pi\) |
0.0786925 | + | 0.996899i | \(0.474925\pi\) | |||||||
\(908\) | 2.52899e6 | − | 4.38034e6i | 0.101796 | − | 0.176316i | ||||
\(909\) | 1.81871e6 | 0.0730053 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.60518e6 | −0.263687 | −0.131844 | − | 0.991271i | \(-0.542090\pi\) | ||||
−0.131844 | + | 0.991271i | \(0.542090\pi\) | |||||||
\(912\) | −976864. | + | 1.69198e6i | −0.0388908 | + | 0.0673609i | ||||
\(913\) | −2.38241e6 | − | 4.12645e6i | −0.0945887 | − | 0.163832i | ||||
\(914\) | −1.45242e7 | − | 2.51567e7i | −0.575078 | − | 0.996065i | ||||
\(915\) | 1.00540e7 | − | 1.74141e7i | 0.396997 | − | 0.687618i | ||||
\(916\) | −7.69730e7 | −3.03110 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.99132e7 | 2.73812 | ||||||||
\(919\) | 1.54465e7 | − | 2.67541e7i | 0.603311 | − | 1.04496i | −0.389005 | − | 0.921236i | \(-0.627181\pi\) |
0.992316 | − | 0.123729i | \(-0.0394855\pi\) | |||||||
\(920\) | 1.83859e7 | + | 3.18453e7i | 0.716169 | + | 1.24044i | ||||
\(921\) | −3.21352e6 | − | 5.56598e6i | −0.124834 | − | 0.216218i | ||||
\(922\) | 4.61342e6 | − | 7.99068e6i | 0.178729 | − | 0.309568i | ||||
\(923\) | −8.19840e6 | −0.316756 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −114378. | −0.00439530 | ||||||||
\(926\) | 3.59118e7 | − | 6.22010e7i | 1.37629 | − | 2.38380i | ||||
\(927\) | −1.24691e6 | − | 2.15971e6i | −0.0476580 | − | 0.0825461i | ||||
\(928\) | 4.64848e6 | + | 8.05140e6i | 0.177191 | + | 0.306903i | ||||
\(929\) | −2.43608e6 | + | 4.21941e6i | −0.0926087 | + | 0.160403i | −0.908608 | − | 0.417650i | \(-0.862854\pi\) |
0.815999 | + | 0.578053i | \(0.196187\pi\) | |||||||
\(930\) | −5.99290e7 | −2.27211 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.35134e7 | −0.509593 | ||||||||
\(933\) | 4.66990e6 | − | 8.08850e6i | 0.175632 | − | 0.304203i | ||||
\(934\) | 3.06285e6 | + | 5.30501e6i | 0.114884 | + | 0.198984i | ||||
\(935\) | −1.11861e7 | − | 1.93749e7i | −0.418456 | − | 0.724788i | ||||
\(936\) | −1.18440e6 | + | 2.05144e6i | −0.0441885 | + | 0.0765366i | ||||
\(937\) | 3.25004e7 | 1.20932 | 0.604658 | − | 0.796485i | \(-0.293310\pi\) | ||||
0.604658 | + | 0.796485i | \(0.293310\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.55448e6 | 0.0575334 | ||||||||
\(940\) | 1.77529e7 | − | 3.07489e7i | 0.655314 | − | 1.13504i | ||||
\(941\) | −1.32020e6 | − | 2.28665e6i | −0.0486033 | − | 0.0841834i | 0.840700 | − | 0.541501i | \(-0.182144\pi\) |
−0.889304 | + | 0.457317i | \(0.848810\pi\) | |||||||
\(942\) | −2.05467e7 | − | 3.55879e7i | −0.754422 | − | 1.30670i | ||||
\(943\) | −1.63813e7 | + | 2.83733e7i | −0.599888 | + | 1.03904i | ||||
\(944\) | 3.88752e6 | 0.141985 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.52416e7 | −0.917042 | ||||||||
\(947\) | 2.04090e7 | − | 3.53494e7i | 0.739513 | − | 1.28087i | −0.213202 | − | 0.977008i | \(-0.568389\pi\) |
0.952715 | − | 0.303866i | \(-0.0982776\pi\) | |||||||
\(948\) | −1.51292e7 | − | 2.62045e7i | −0.546757 | − | 0.947012i | ||||
\(949\) | 4.76574e6 | + | 8.25450e6i | 0.171777 | + | 0.297526i | ||||
\(950\) | 5390.00 | − | 9335.75i | 0.000193767 | − | 0.000335614i | ||||
\(951\) | −962892. | −0.0345244 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.71983e6 | −0.239677 | −0.119838 | − | 0.992793i | \(-0.538238\pi\) | ||||
−0.119838 | + | 0.992793i | \(0.538238\pi\) | |||||||
\(954\) | −531570. | + | 920706.i | −0.0189099 | + | 0.0327529i | ||||
\(955\) | −1.00314e7 | − | 1.73749e7i | −0.355920 | − | 0.616472i | ||||
\(956\) | −1.64187e7 | − | 2.84381e7i | −0.581025 | − | 1.00637i | ||||
\(957\) | −5.55083e6 | + | 9.61432e6i | −0.195920 | + | 0.339343i | ||||
\(958\) | 2.60330e7 | 0.916454 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.44005e7 | −0.504313 | ||||||||
\(961\) | −1.49008e7 | + | 2.58089e7i | −0.520476 | + | 0.901491i | ||||
\(962\) | −7.27860e6 | − | 1.26069e7i | −0.253577 | − | 0.439209i | ||||
\(963\) | −3.43861e6 | − | 5.95585e6i | −0.119486 | − | 0.206956i | ||||
\(964\) | 2.74009e7 | − | 4.74598e7i | 0.949670 | − | 1.64488i | ||||
\(965\) | −5.54150e7 | −1.91562 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.78979e6 | −0.0959413 | −0.0479707 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479707 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(968\) | −1.93009e7 | + | 3.34301e7i | −0.662046 | + | 1.14670i | ||||
\(969\) | −1.18129e6 | − | 2.04606e6i | −0.0404155 | − | 0.0700017i | ||||
\(970\) | 1.63817e7 | + | 2.83739e7i | 0.559022 | + | 0.968255i | ||||
\(971\) | 1.66797e7 | − | 2.88901e7i | 0.567727 | − | 0.983333i | −0.429063 | − | 0.903275i | \(-0.641156\pi\) |
0.996790 | − | 0.0800582i | \(-0.0255106\pi\) | |||||||
\(972\) | 2.38486e7 | 0.809648 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.46309e7 | −1.84519 | ||||||||
\(975\) | −10780.0 | + | 18671.5i | −0.000363168 | + | 0.000629025i | ||||
\(976\) | 1.82614e7 | + | 3.16296e7i | 0.613633 | + | 1.06284i | ||||
\(977\) | 3.80016e6 | + | 6.58208e6i | 0.127370 | + | 0.220611i | 0.922657 | − | 0.385622i | \(-0.126013\pi\) |
−0.795287 | + | 0.606233i | \(0.792680\pi\) | |||||||
\(978\) | 923440. | − | 1.59944e6i | 0.0308718 | − | 0.0534715i | ||||
\(979\) | 1.17350e7 | 0.391316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.36621e6 | −0.144854 | ||||||||
\(982\) | 8.20450e6 | − | 1.42106e7i | 0.271502 | − | 0.470256i | ||||
\(983\) | −2.89880e6 | − | 5.02087e6i | −0.0956829 | − | 0.165728i | 0.814211 | − | 0.580570i | \(-0.197170\pi\) |
−0.909893 | + | 0.414842i | \(0.863837\pi\) | |||||||
\(984\) | 4.52642e7 | + | 7.84000e7i | 1.49028 | + | 2.58124i | ||||
\(985\) | 2.77214e7 | − | 4.80149e7i | 0.910384 | − | 1.57683i | ||||
\(986\) | −5.88580e7 | −1.92803 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 932960. | 0.0304068 | ||||||||
\(989\) | −9.92256e6 | + | 1.71864e7i | −0.322577 | + | 0.558719i | ||||
\(990\) | −3.05312e6 | − | 5.28816e6i | −0.0990047 | − | 0.171481i | ||||
\(991\) | −6.34125e6 | − | 1.09834e7i | −0.205112 | − | 0.355264i | 0.745057 | − | 0.667001i | \(-0.232422\pi\) |
−0.950168 | + | 0.311737i | \(0.899089\pi\) | |||||||
\(992\) | 1.03958e7 | − | 1.80061e7i | 0.335413 | − | 0.580953i | ||||
\(993\) | −7.90227e6 | −0.254319 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.70823e7 | 1.50765 | ||||||||
\(996\) | −9.77609e6 | + | 1.69327e7i | −0.312260 | + | 0.540851i | ||||
\(997\) | 7.22002e6 | + | 1.25054e7i | 0.230039 | + | 0.398439i | 0.957819 | − | 0.287371i | \(-0.0927814\pi\) |
−0.727781 | + | 0.685810i | \(0.759448\pi\) | |||||||
\(998\) | 1.49898e7 | + | 2.59631e7i | 0.476398 | + | 0.825146i | ||||
\(999\) | −2.11079e7 | + | 3.65600e7i | −0.669163 | + | 1.15902i |
(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 | 49.6.c.b.30.1 | 2 | ||
7.2 | even | 3 | 49.6.a.a.1.1 | 1 | |||
7.3 | odd | 6 | 49.6.c.c.18.1 | 2 | |||
7.4 | even | 3 | inner | 49.6.c.b.18.1 | 2 | ||
7.5 | odd | 6 | 7.6.a.a.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 49.6.c.c.30.1 | 2 | |||
21.2 | odd | 6 | 441.6.a.k.1.1 | 1 | |||
21.5 | even | 6 | 63.6.a.e.1.1 | 1 | |||
28.19 | even | 6 | 112.6.a.g.1.1 | 1 | |||
28.23 | odd | 6 | 784.6.a.c.1.1 | 1 | |||
35.12 | even | 12 | 175.6.b.a.99.1 | 2 | |||
35.19 | odd | 6 | 175.6.a.b.1.1 | 1 | |||
35.33 | even | 12 | 175.6.b.a.99.2 | 2 | |||
56.5 | odd | 6 | 448.6.a.m.1.1 | 1 | |||
56.19 | even | 6 | 448.6.a.c.1.1 | 1 | |||
77.54 | even | 6 | 847.6.a.b.1.1 | 1 | |||
84.47 | odd | 6 | 1008.6.a.y.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.a.1.1 | ✓ | 1 | 7.5 | odd | 6 | ||
49.6.a.a.1.1 | 1 | 7.2 | even | 3 | |||
49.6.c.b.18.1 | 2 | 7.4 | even | 3 | inner | ||
49.6.c.b.30.1 | 2 | 1.1 | even | 1 | trivial | ||
49.6.c.c.18.1 | 2 | 7.3 | odd | 6 | |||
49.6.c.c.30.1 | 2 | 7.6 | odd | 2 | |||
63.6.a.e.1.1 | 1 | 21.5 | even | 6 | |||
112.6.a.g.1.1 | 1 | 28.19 | even | 6 | |||
175.6.a.b.1.1 | 1 | 35.19 | odd | 6 | |||
175.6.b.a.99.1 | 2 | 35.12 | even | 12 | |||
175.6.b.a.99.2 | 2 | 35.33 | even | 12 | |||
441.6.a.k.1.1 | 1 | 21.2 | odd | 6 | |||
448.6.a.c.1.1 | 1 | 56.19 | even | 6 | |||
448.6.a.m.1.1 | 1 | 56.5 | odd | 6 | |||
784.6.a.c.1.1 | 1 | 28.23 | odd | 6 | |||
847.6.a.b.1.1 | 1 | 77.54 | even | 6 | |||
1008.6.a.y.1.1 | 1 | 84.47 | odd | 6 |