Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.c (of order \(2\), degree \(1\), 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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.2 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.25 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 10.4306i | − | 1.84389i | −0.387326 | − | 0.921943i | \(-0.626601\pi\) | ||
0.387326 | − | 0.921943i | \(-0.373399\pi\) | |||||||
\(3\) | − | 9.00000i | − | 0.577350i | ||||||
\(4\) | −76.7973 | −2.39991 | ||||||||
\(5\) | −52.2792 | + | 19.7960i | −0.935199 | + | 0.354121i | ||||
\(6\) | −93.8753 | −1.06457 | ||||||||
\(7\) | 21.9028i | 0.168949i | 0.996426 | + | 0.0844744i | \(0.0269211\pi\) | ||||
−0.996426 | + | 0.0844744i | \(0.973079\pi\) | |||||||
\(8\) | 467.262i | 2.58128i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 206.484 | + | 545.303i | 0.652959 | + | 1.72440i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 691.175i | 1.38559i | ||||||||
\(13\) | − | 460.797i | − | 0.756225i | −0.925760 | − | 0.378113i | \(-0.876573\pi\) | ||
0.925760 | − | 0.378113i | \(-0.123427\pi\) | |||||||
\(14\) | 228.459 | 0.311522 | ||||||||
\(15\) | 178.164 | + | 470.513i | 0.204452 | + | 0.539938i | ||||
\(16\) | 2416.31 | 2.35967 | ||||||||
\(17\) | 2318.63i | 1.94585i | 0.231127 | + | 0.972924i | \(0.425759\pi\) | ||||
−0.231127 | + | 0.972924i | \(0.574241\pi\) | |||||||
\(18\) | 844.878i | 0.614629i | ||||||||
\(19\) | −800.141 | −0.508490 | −0.254245 | − | 0.967140i | \(-0.581827\pi\) | ||||
−0.254245 | + | 0.967140i | \(0.581827\pi\) | |||||||
\(20\) | 4014.90 | − | 1520.28i | 2.24440 | − | 0.849861i | ||||
\(21\) | 197.125 | 0.0975426 | ||||||||
\(22\) | − | 1262.10i | − | 0.555952i | ||||||
\(23\) | − | 4781.90i | − | 1.88487i | −0.334391 | − | 0.942434i | \(-0.608531\pi\) | ||
0.334391 | − | 0.942434i | \(-0.391469\pi\) | |||||||
\(24\) | 4205.36 | 1.49030 | ||||||||
\(25\) | 2341.24 | − | 2069.84i | 0.749196 | − | 0.662348i | ||||
\(26\) | −4806.39 | −1.39439 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | − | 1682.08i | − | 0.405462i | ||||||
\(29\) | −911.582 | −0.201280 | −0.100640 | − | 0.994923i | \(-0.532089\pi\) | ||||
−0.100640 | + | 0.994923i | \(0.532089\pi\) | |||||||
\(30\) | 4907.73 | − | 1858.35i | 0.995583 | − | 0.376986i | ||||
\(31\) | −944.328 | −0.176489 | −0.0882447 | − | 0.996099i | \(-0.528126\pi\) | ||||
−0.0882447 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(32\) | − | 10251.1i | − | 1.76969i | ||||||
\(33\) | − | 1089.00i | − | 0.174078i | ||||||
\(34\) | 24184.7 | 3.58792 | ||||||||
\(35\) | −433.588 | − | 1145.06i | −0.0598283 | − | 0.158001i | ||||
\(36\) | 6220.58 | 0.799971 | ||||||||
\(37\) | 12825.4i | 1.54017i | 0.637942 | + | 0.770084i | \(0.279786\pi\) | ||||
−0.637942 | + | 0.770084i | \(0.720214\pi\) | |||||||
\(38\) | 8345.95i | 0.937598i | ||||||||
\(39\) | −4147.17 | −0.436607 | ||||||||
\(40\) | −9249.91 | − | 24428.1i | −0.914087 | − | 2.41401i | ||||
\(41\) | 8712.22 | 0.809411 | 0.404706 | − | 0.914447i | \(-0.367374\pi\) | ||||
0.404706 | + | 0.914447i | \(0.367374\pi\) | |||||||
\(42\) | − | 2056.13i | − | 0.179857i | ||||||
\(43\) | 20504.8i | 1.69116i | 0.533852 | + | 0.845578i | \(0.320744\pi\) | ||||
−0.533852 | + | 0.845578i | \(0.679256\pi\) | |||||||
\(44\) | −9292.47 | −0.723601 | ||||||||
\(45\) | 4234.62 | − | 1603.47i | 0.311733 | − | 0.118040i | ||||
\(46\) | −49878.1 | −3.47548 | ||||||||
\(47\) | − | 9288.25i | − | 0.613323i | −0.951819 | − | 0.306662i | \(-0.900788\pi\) | ||
0.951819 | − | 0.306662i | \(-0.0992120\pi\) | |||||||
\(48\) | − | 21746.8i | − | 1.36236i | ||||||
\(49\) | 16327.3 | 0.971456 | ||||||||
\(50\) | −21589.6 | − | 24420.5i | −1.22129 | − | 1.38143i | ||||
\(51\) | 20867.7 | 1.12344 | ||||||||
\(52\) | 35388.0i | 1.81488i | ||||||||
\(53\) | − | 23263.1i | − | 1.13757i | −0.822486 | − | 0.568785i | \(-0.807414\pi\) | ||
0.822486 | − | 0.568785i | \(-0.192586\pi\) | |||||||
\(54\) | 7603.90 | 0.354856 | ||||||||
\(55\) | −6325.79 | + | 2395.31i | −0.281973 | + | 0.106772i | ||||
\(56\) | −10234.4 | −0.436104 | ||||||||
\(57\) | 7201.27i | 0.293577i | ||||||||
\(58\) | 9508.34i | 0.371137i | ||||||||
\(59\) | −20726.7 | −0.775177 | −0.387588 | − | 0.921833i | \(-0.626692\pi\) | ||||
−0.387588 | + | 0.921833i | \(0.626692\pi\) | |||||||
\(60\) | −13682.5 | − | 36134.1i | −0.490667 | − | 1.29580i | ||||
\(61\) | −6625.93 | −0.227993 | −0.113997 | − | 0.993481i | \(-0.536365\pi\) | ||||
−0.113997 | + | 0.993481i | \(0.536365\pi\) | |||||||
\(62\) | 9849.90i | 0.325426i | ||||||||
\(63\) | − | 1774.13i | − | 0.0563162i | ||||||
\(64\) | −29603.6 | −0.903429 | ||||||||
\(65\) | 9121.93 | + | 24090.1i | 0.267796 | + | 0.707222i | ||||
\(66\) | −11358.9 | −0.320979 | ||||||||
\(67\) | 57904.9i | 1.57590i | 0.615739 | + | 0.787950i | \(0.288857\pi\) | ||||
−0.615739 | + | 0.787950i | \(0.711143\pi\) | |||||||
\(68\) | − | 178064.i | − | 4.66987i | ||||||
\(69\) | −43037.1 | −1.08823 | ||||||||
\(70\) | −11943.7 | + | 4522.58i | −0.291335 | + | 0.110317i | ||||
\(71\) | 38362.5 | 0.903153 | 0.451577 | − | 0.892232i | \(-0.350862\pi\) | ||||
0.451577 | + | 0.892232i | \(0.350862\pi\) | |||||||
\(72\) | − | 37848.2i | − | 0.860427i | ||||||
\(73\) | − | 8431.57i | − | 0.185183i | −0.995704 | − | 0.0925916i | \(-0.970485\pi\) | ||
0.995704 | − | 0.0925916i | \(-0.0295151\pi\) | |||||||
\(74\) | 133777. | 2.83989 | ||||||||
\(75\) | −18628.5 | − | 21071.1i | −0.382407 | − | 0.432549i | ||||
\(76\) | 61448.7 | 1.22033 | ||||||||
\(77\) | 2650.24i | 0.0509400i | ||||||||
\(78\) | 43257.5i | 0.805053i | ||||||||
\(79\) | 1683.43 | 0.0303478 | 0.0151739 | − | 0.999885i | \(-0.495170\pi\) | ||||
0.0151739 | + | 0.999885i | \(0.495170\pi\) | |||||||
\(80\) | −126323. | + | 47833.2i | −2.20677 | + | 0.835611i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − | 90873.6i | − | 1.49246i | ||||||
\(83\) | − | 7798.26i | − | 0.124252i | −0.998068 | − | 0.0621259i | \(-0.980212\pi\) | ||
0.998068 | − | 0.0621259i | \(-0.0197880\pi\) | |||||||
\(84\) | −15138.7 | −0.234094 | ||||||||
\(85\) | −45899.5 | − | 121216.i | −0.689066 | − | 1.81976i | ||||
\(86\) | 213877. | 3.11830 | ||||||||
\(87\) | 8204.23i | 0.116209i | ||||||||
\(88\) | 56538.7i | 0.778286i | ||||||||
\(89\) | 83079.0 | 1.11177 | 0.555887 | − | 0.831258i | \(-0.312379\pi\) | ||||
0.555887 | + | 0.831258i | \(0.312379\pi\) | |||||||
\(90\) | −16725.2 | − | 44169.6i | −0.217653 | − | 0.574800i | ||||
\(91\) | 10092.8 | 0.127763 | ||||||||
\(92\) | 367237.i | 4.52352i | ||||||||
\(93\) | 8498.95i | 0.101896i | ||||||||
\(94\) | −96882.0 | −1.13090 | ||||||||
\(95\) | 41830.8 | − | 15839.6i | 0.475540 | − | 0.180067i | ||||
\(96\) | −92260.2 | −1.02173 | ||||||||
\(97\) | 14678.5i | 0.158399i | 0.996859 | + | 0.0791997i | \(0.0252365\pi\) | ||||
−0.996859 | + | 0.0791997i | \(0.974764\pi\) | |||||||
\(98\) | − | 170303.i | − | 1.79125i | ||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −179801. | + | 158958.i | −1.79801 | + | 1.58958i | ||||
\(101\) | −19178.1 | −0.187069 | −0.0935345 | − | 0.995616i | \(-0.529817\pi\) | ||||
−0.0935345 | + | 0.995616i | \(0.529817\pi\) | |||||||
\(102\) | − | 217662.i | − | 2.07149i | ||||||
\(103\) | 127841.i | 1.18735i | 0.804705 | + | 0.593675i | \(0.202323\pi\) | ||||
−0.804705 | + | 0.593675i | \(0.797677\pi\) | |||||||
\(104\) | 215313. | 1.95203 | ||||||||
\(105\) | −10305.6 | + | 3902.29i | −0.0912218 | + | 0.0345419i | ||||
\(106\) | −242648. | −2.09755 | ||||||||
\(107\) | 52736.6i | 0.445300i | 0.974898 | + | 0.222650i | \(0.0714707\pi\) | ||||
−0.974898 | + | 0.222650i | \(0.928529\pi\) | |||||||
\(108\) | − | 55985.2i | − | 0.461864i | ||||||
\(109\) | 233661. | 1.88374 | 0.941869 | − | 0.335979i | \(-0.109067\pi\) | ||||
0.941869 | + | 0.335979i | \(0.109067\pi\) | |||||||
\(110\) | 24984.5 | + | 65981.7i | 0.196875 | + | 0.519926i | ||||
\(111\) | 115429. | 0.889216 | ||||||||
\(112\) | 52923.9i | 0.398664i | ||||||||
\(113\) | 36635.5i | 0.269902i | 0.990852 | + | 0.134951i | \(0.0430876\pi\) | ||||
−0.990852 | + | 0.134951i | \(0.956912\pi\) | |||||||
\(114\) | 75113.5 | 0.541323 | ||||||||
\(115\) | 94662.5 | + | 249994.i | 0.667472 | + | 1.76273i | ||||
\(116\) | 70007.0 | 0.483055 | ||||||||
\(117\) | 37324.6i | 0.252075i | ||||||||
\(118\) | 216192.i | 1.42934i | ||||||||
\(119\) | −50784.5 | −0.328748 | ||||||||
\(120\) | −219853. | + | 83249.2i | −1.39373 | + | 0.527748i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 69112.4i | 0.420394i | ||||||||
\(123\) | − | 78410.0i | − | 0.467314i | ||||||
\(124\) | 72521.8 | 0.423559 | ||||||||
\(125\) | −81423.7 | + | 154557.i | −0.466096 | + | 0.884734i | ||||
\(126\) | −18505.2 | −0.103841 | ||||||||
\(127\) | 256889.i | 1.41330i | 0.707561 | + | 0.706652i | \(0.249795\pi\) | ||||
−0.707561 | + | 0.706652i | \(0.750205\pi\) | |||||||
\(128\) | − | 19253.6i | − | 0.103869i | ||||||
\(129\) | 184543. | 0.976390 | ||||||||
\(130\) | 251274. | − | 95147.1i | 1.30404 | − | 0.493784i | ||||
\(131\) | −109508. | −0.557531 | −0.278765 | − | 0.960359i | \(-0.589925\pi\) | ||||
−0.278765 | + | 0.960359i | \(0.589925\pi\) | |||||||
\(132\) | 83632.2i | 0.417771i | ||||||||
\(133\) | − | 17525.4i | − | 0.0859088i | ||||||
\(134\) | 603983. | 2.90578 | ||||||||
\(135\) | −14431.3 | − | 38111.6i | −0.0681507 | − | 0.179979i | ||||
\(136\) | −1.08341e6 | −5.02278 | ||||||||
\(137\) | 149903.i | 0.682355i | 0.939999 | + | 0.341177i | \(0.110826\pi\) | ||||
−0.939999 | + | 0.341177i | \(0.889174\pi\) | |||||||
\(138\) | 448903.i | 2.00657i | ||||||||
\(139\) | 113251. | 0.497168 | 0.248584 | − | 0.968610i | \(-0.420035\pi\) | ||||
0.248584 | + | 0.968610i | \(0.420035\pi\) | |||||||
\(140\) | 33298.4 | + | 87937.7i | 0.143583 | + | 0.379188i | ||||
\(141\) | −83594.3 | −0.354102 | ||||||||
\(142\) | − | 400144.i | − | 1.66531i | ||||||
\(143\) | − | 55756.4i | − | 0.228011i | ||||||
\(144\) | −195721. | −0.786558 | ||||||||
\(145\) | 47656.8 | − | 18045.7i | 0.188237 | − | 0.0712775i | ||||
\(146\) | −87946.3 | −0.341456 | ||||||||
\(147\) | − | 146945.i | − | 0.560871i | ||||||
\(148\) | − | 984959.i | − | 3.69627i | ||||||
\(149\) | 61807.9 | 0.228075 | 0.114038 | − | 0.993476i | \(-0.463622\pi\) | ||||
0.114038 | + | 0.993476i | \(0.463622\pi\) | |||||||
\(150\) | −219785. | + | 194307.i | −0.797570 | + | 0.705115i | ||||
\(151\) | −256778. | −0.916465 | −0.458233 | − | 0.888832i | \(-0.651517\pi\) | ||||
−0.458233 | + | 0.888832i | \(0.651517\pi\) | |||||||
\(152\) | − | 373876.i | − | 1.31256i | ||||||
\(153\) | − | 187809.i | − | 0.648616i | ||||||
\(154\) | 27643.6 | 0.0939275 | ||||||||
\(155\) | 49368.7 | − | 18693.9i | 0.165053 | − | 0.0624987i | ||||
\(156\) | 318492. | 1.04782 | ||||||||
\(157\) | − | 116054.i | − | 0.375761i | −0.982192 | − | 0.187880i | \(-0.939838\pi\) | ||
0.982192 | − | 0.187880i | \(-0.0601617\pi\) | |||||||
\(158\) | − | 17559.2i | − | 0.0559579i | ||||||
\(159\) | −209368. | −0.656776 | ||||||||
\(160\) | 202931. | + | 535921.i | 0.626685 | + | 1.65501i | ||||
\(161\) | 104737. | 0.318446 | ||||||||
\(162\) | − | 68435.1i | − | 0.204876i | ||||||
\(163\) | 322117.i | 0.949609i | 0.880091 | + | 0.474805i | \(0.157481\pi\) | ||||
−0.880091 | + | 0.474805i | \(0.842519\pi\) | |||||||
\(164\) | −669075. | −1.94252 | ||||||||
\(165\) | 21557.8 | + | 56932.1i | 0.0616446 | + | 0.162797i | ||||
\(166\) | −81340.5 | −0.229106 | ||||||||
\(167\) | − | 435361.i | − | 1.20797i | −0.796994 | − | 0.603987i | \(-0.793578\pi\) | ||
0.796994 | − | 0.603987i | \(-0.206422\pi\) | |||||||
\(168\) | 92109.2i | 0.251785i | ||||||||
\(169\) | 158959. | 0.428123 | ||||||||
\(170\) | −1.26436e6 | + | 478759.i | −3.35542 | + | 1.27056i | ||||
\(171\) | 64811.5 | 0.169497 | ||||||||
\(172\) | − | 1.57471e6i | − | 4.05863i | ||||||
\(173\) | 700319.i | 1.77902i | 0.456916 | + | 0.889510i | \(0.348954\pi\) | ||||
−0.456916 | + | 0.889510i | \(0.651046\pi\) | |||||||
\(174\) | 85575.0 | 0.214276 | ||||||||
\(175\) | 45335.3 | + | 51279.7i | 0.111903 | + | 0.126576i | ||||
\(176\) | 292373. | 0.711469 | ||||||||
\(177\) | 186541.i | 0.447548i | ||||||||
\(178\) | − | 866563.i | − | 2.04998i | ||||||
\(179\) | −228192. | −0.532314 | −0.266157 | − | 0.963930i | \(-0.585754\pi\) | ||||
−0.266157 | + | 0.963930i | \(0.585754\pi\) | |||||||
\(180\) | −325207. | + | 123142.i | −0.748133 | + | 0.283287i | ||||
\(181\) | 511598. | 1.16073 | 0.580366 | − | 0.814356i | \(-0.302909\pi\) | ||||
0.580366 | + | 0.814356i | \(0.302909\pi\) | |||||||
\(182\) | − | 105273.i | − | 0.235581i | ||||||
\(183\) | 59633.4i | 0.131632i | ||||||||
\(184\) | 2.23440e6 | 4.86538 | ||||||||
\(185\) | −253892. | − | 670505.i | −0.545406 | − | 1.44036i | ||||
\(186\) | 88649.1 | 0.187885 | ||||||||
\(187\) | 280554.i | 0.586695i | ||||||||
\(188\) | 713312.i | 1.47192i | ||||||||
\(189\) | −15967.2 | −0.0325142 | ||||||||
\(190\) | −165216. | − | 436320.i | −0.332023 | − | 0.876841i | ||||
\(191\) | −803150. | −1.59299 | −0.796496 | − | 0.604644i | \(-0.793315\pi\) | ||||
−0.796496 | + | 0.604644i | \(0.793315\pi\) | |||||||
\(192\) | 266432.i | 0.521595i | ||||||||
\(193\) | 578708.i | 1.11832i | 0.829059 | + | 0.559160i | \(0.188876\pi\) | ||||
−0.829059 | + | 0.559160i | \(0.811124\pi\) | |||||||
\(194\) | 153106. | 0.292070 | ||||||||
\(195\) | 216811. | − | 82097.4i | 0.408315 | − | 0.154612i | ||||
\(196\) | −1.25389e6 | −2.33141 | ||||||||
\(197\) | 278554.i | 0.511381i | 0.966759 | + | 0.255690i | \(0.0823027\pi\) | ||||
−0.966759 | + | 0.255690i | \(0.917697\pi\) | |||||||
\(198\) | 102230.i | 0.185317i | ||||||||
\(199\) | −843631. | −1.51015 | −0.755074 | − | 0.655639i | \(-0.772399\pi\) | ||||
−0.755074 | + | 0.655639i | \(0.772399\pi\) | |||||||
\(200\) | 967157. | + | 1.09397e6i | 1.70971 | + | 1.93389i | ||||
\(201\) | 521144. | 0.909846 | ||||||||
\(202\) | 200039.i | 0.344934i | ||||||||
\(203\) | − | 19966.2i | − | 0.0340060i | ||||||
\(204\) | −1.60258e6 | −2.69615 | ||||||||
\(205\) | −455468. | + | 172467.i | −0.756961 | + | 0.286630i | ||||
\(206\) | 1.33346e6 | 2.18934 | ||||||||
\(207\) | 387334.i | 0.628290i | ||||||||
\(208\) | − | 1.11343e6i | − | 1.78445i | ||||||
\(209\) | −96817.1 | −0.153316 | ||||||||
\(210\) | 40703.2 | + | 107493.i | 0.0636913 | + | 0.168203i | ||||
\(211\) | 48614.4 | 0.0751724 | 0.0375862 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375862 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(212\) | 1.78654e6i | 2.73007i | ||||||||
\(213\) | − | 345263.i | − | 0.521436i | ||||||
\(214\) | 550074. | 0.821082 | ||||||||
\(215\) | −405912. | − | 1.07197e6i | −0.598874 | − | 1.58157i | ||||
\(216\) | −340634. | −0.496768 | ||||||||
\(217\) | − | 20683.4i | − | 0.0298177i | ||||||
\(218\) | − | 2.43723e6i | − | 3.47340i | ||||||
\(219\) | −75884.1 | −0.106916 | ||||||||
\(220\) | 485803. | − | 183954.i | 0.676712 | − | 0.256243i | ||||
\(221\) | 1.06842e6 | 1.47150 | ||||||||
\(222\) | − | 1.20399e6i | − | 1.63961i | ||||||
\(223\) | − | 473625.i | − | 0.637782i | −0.947791 | − | 0.318891i | \(-0.896690\pi\) | ||
0.947791 | − | 0.318891i | \(-0.103310\pi\) | |||||||
\(224\) | 224529. | 0.298987 | ||||||||
\(225\) | −189640. | + | 167657.i | −0.249732 | + | 0.220783i | ||||
\(226\) | 382130. | 0.497668 | ||||||||
\(227\) | 767793.i | 0.988962i | 0.869188 | + | 0.494481i | \(0.164642\pi\) | ||||
−0.869188 | + | 0.494481i | \(0.835358\pi\) | |||||||
\(228\) | − | 553038.i | − | 0.704560i | ||||||
\(229\) | −580162. | −0.731073 | −0.365536 | − | 0.930797i | \(-0.619114\pi\) | ||||
−0.365536 | + | 0.930797i | \(0.619114\pi\) | |||||||
\(230\) | 2.60759e6 | − | 987386.i | 3.25027 | − | 1.23074i | ||||
\(231\) | 23852.2 | 0.0294102 | ||||||||
\(232\) | − | 425947.i | − | 0.519560i | ||||||
\(233\) | − | 298663.i | − | 0.360406i | −0.983629 | − | 0.180203i | \(-0.942325\pi\) | ||
0.983629 | − | 0.180203i | \(-0.0576754\pi\) | |||||||
\(234\) | 389317. | 0.464798 | ||||||||
\(235\) | 183870. | + | 485583.i | 0.217191 | + | 0.573580i | ||||
\(236\) | 1.59176e6 | 1.86036 | ||||||||
\(237\) | − | 15150.9i | − | 0.0175213i | ||||||
\(238\) | 529712.i | 0.606174i | ||||||||
\(239\) | −324060. | −0.366970 | −0.183485 | − | 0.983023i | \(-0.558738\pi\) | ||||
−0.183485 | + | 0.983023i | \(0.558738\pi\) | |||||||
\(240\) | 430499. | + | 1.13690e6i | 0.482440 | + | 1.27408i | ||||
\(241\) | −679917. | −0.754073 | −0.377036 | − | 0.926198i | \(-0.623057\pi\) | ||||
−0.377036 | + | 0.926198i | \(0.623057\pi\) | |||||||
\(242\) | − | 152714.i | − | 0.167626i | ||||||
\(243\) | − | 59049.0i | − | 0.0641500i | ||||||
\(244\) | 508853. | 0.547165 | ||||||||
\(245\) | −853577. | + | 323214.i | −0.908505 | + | 0.344013i | ||||
\(246\) | −817863. | −0.861673 | ||||||||
\(247\) | 368703.i | 0.384533i | ||||||||
\(248\) | − | 441249.i | − | 0.455569i | ||||||
\(249\) | −70184.4 | −0.0717368 | ||||||||
\(250\) | 1.61212e6 | + | 849297.i | 1.63135 | + | 0.859428i | ||||
\(251\) | 1.78432e6 | 1.78767 | 0.893836 | − | 0.448393i | \(-0.148004\pi\) | ||||
0.893836 | + | 0.448393i | \(0.148004\pi\) | |||||||
\(252\) | 136248.i | 0.135154i | ||||||||
\(253\) | − | 578610.i | − | 0.568309i | ||||||
\(254\) | 2.67950e6 | 2.60597 | ||||||||
\(255\) | −1.09094e6 | + | 413096.i | −1.05064 | + | 0.397832i | ||||
\(256\) | −1.14814e6 | −1.09495 | ||||||||
\(257\) | − | 891074.i | − | 0.841552i | −0.907165 | − | 0.420776i | \(-0.861758\pi\) | ||
0.907165 | − | 0.420776i | \(-0.138242\pi\) | |||||||
\(258\) | − | 1.92489e6i | − | 1.80035i | ||||||
\(259\) | −280913. | −0.260209 | ||||||||
\(260\) | −700539. | − | 1.85006e6i | −0.642686 | − | 1.69727i | ||||
\(261\) | 73838.1 | 0.0670933 | ||||||||
\(262\) | 1.14224e6i | 1.02802i | ||||||||
\(263\) | 1.27856e6i | 1.13980i | 0.821713 | + | 0.569902i | \(0.193019\pi\) | ||||
−0.821713 | + | 0.569902i | \(0.806981\pi\) | |||||||
\(264\) | 508848. | 0.449344 | ||||||||
\(265\) | 460516. | + | 1.21618e6i | 0.402838 | + | 1.06385i | ||||
\(266\) | −182800. | −0.158406 | ||||||||
\(267\) | − | 747711.i | − | 0.641883i | ||||||
\(268\) | − | 4.44694e6i | − | 3.78203i | ||||||
\(269\) | −454281. | −0.382775 | −0.191388 | − | 0.981515i | \(-0.561299\pi\) | ||||
−0.191388 | + | 0.981515i | \(0.561299\pi\) | |||||||
\(270\) | −397526. | + | 150527.i | −0.331861 | + | 0.125662i | ||||
\(271\) | −2.02780e6 | −1.67726 | −0.838632 | − | 0.544698i | \(-0.816644\pi\) | ||||
−0.838632 | + | 0.544698i | \(0.816644\pi\) | |||||||
\(272\) | 5.60252e6i | 4.59157i | ||||||||
\(273\) | − | 90834.8i | − | 0.0737642i | ||||||
\(274\) | 1.56358e6 | 1.25818 | ||||||||
\(275\) | 283290. | − | 250450.i | 0.225891 | − | 0.199705i | ||||
\(276\) | 3.30513e6 | 2.61166 | ||||||||
\(277\) | 1.27638e6i | 0.999496i | 0.866171 | + | 0.499748i | \(0.166574\pi\) | ||||
−0.866171 | + | 0.499748i | \(0.833426\pi\) | |||||||
\(278\) | − | 1.18127e6i | − | 0.916722i | ||||||
\(279\) | 76490.6 | 0.0588298 | ||||||||
\(280\) | 535044. | − | 202599.i | 0.407845 | − | 0.154434i | ||||
\(281\) | −1.02183e6 | −0.771994 | −0.385997 | − | 0.922500i | \(-0.626143\pi\) | ||||
−0.385997 | + | 0.922500i | \(0.626143\pi\) | |||||||
\(282\) | 871938.i | 0.652924i | ||||||||
\(283\) | 75339.2i | 0.0559184i | 0.999609 | + | 0.0279592i | \(0.00890085\pi\) | ||||
−0.999609 | + | 0.0279592i | \(0.991099\pi\) | |||||||
\(284\) | −2.94614e6 | −2.16749 | ||||||||
\(285\) | −142556. | − | 376477.i | −0.103962 | − | 0.274553i | ||||
\(286\) | −581573. | −0.420425 | ||||||||
\(287\) | 190822.i | 0.136749i | ||||||||
\(288\) | 830342.i | 0.589896i | ||||||||
\(289\) | −3.95618e6 | −2.78632 | ||||||||
\(290\) | −188227. | − | 497089.i | −0.131428 | − | 0.347087i | ||||
\(291\) | 132107. | 0.0914519 | ||||||||
\(292\) | 647522.i | 0.444424i | ||||||||
\(293\) | − | 661394.i | − | 0.450082i | −0.974349 | − | 0.225041i | \(-0.927748\pi\) | ||
0.974349 | − | 0.225041i | \(-0.0722516\pi\) | |||||||
\(294\) | −1.53273e6 | −1.03418 | ||||||||
\(295\) | 1.08358e6 | − | 410306.i | 0.724945 | − | 0.274507i | ||||
\(296\) | −5.99284e6 | −3.97561 | ||||||||
\(297\) | 88209.0i | 0.0580259i | ||||||||
\(298\) | − | 644693.i | − | 0.420545i | ||||||
\(299\) | −2.20349e6 | −1.42539 | ||||||||
\(300\) | 1.43062e6 | + | 1.61821e6i | 0.917744 | + | 1.03808i | ||||
\(301\) | −449112. | −0.285719 | ||||||||
\(302\) | 2.67835e6i | 1.68986i | ||||||||
\(303\) | 172603.i | 0.108004i | ||||||||
\(304\) | −1.93339e6 | −1.19987 | ||||||||
\(305\) | 346399. | − | 131167.i | 0.213219 | − | 0.0807373i | ||||
\(306\) | −1.95896e6 | −1.19597 | ||||||||
\(307\) | 962329.i | 0.582744i | 0.956610 | + | 0.291372i | \(0.0941117\pi\) | ||||
−0.956610 | + | 0.291372i | \(0.905888\pi\) | |||||||
\(308\) | − | 203531.i | − | 0.122252i | ||||||
\(309\) | 1.15057e6 | 0.685517 | ||||||||
\(310\) | −194988. | − | 514945.i | −0.115240 | − | 0.304338i | ||||
\(311\) | 645247. | 0.378290 | 0.189145 | − | 0.981949i | \(-0.439428\pi\) | ||||
0.189145 | + | 0.981949i | \(0.439428\pi\) | |||||||
\(312\) | − | 1.93782e6i | − | 1.12701i | ||||||
\(313\) | 3.21424e6i | 1.85446i | 0.374495 | + | 0.927229i | \(0.377816\pi\) | ||||
−0.374495 | + | 0.927229i | \(0.622184\pi\) | |||||||
\(314\) | −1.21051e6 | −0.692860 | ||||||||
\(315\) | 35120.6 | + | 92750.1i | 0.0199428 | + | 0.0526669i | ||||
\(316\) | −129283. | −0.0728321 | ||||||||
\(317\) | 1.59691e6i | 0.892552i | 0.894895 | + | 0.446276i | \(0.147250\pi\) | ||||
−0.894895 | + | 0.446276i | \(0.852750\pi\) | |||||||
\(318\) | 2.18383e6i | 1.21102i | ||||||||
\(319\) | −110301. | −0.0606882 | ||||||||
\(320\) | 1.54765e6 | − | 586031.i | 0.844886 | − | 0.319923i | ||||
\(321\) | 474629. | 0.257094 | ||||||||
\(322\) | − | 1.09247e6i | − | 0.587178i | ||||||
\(323\) | − | 1.85523e6i | − | 0.989445i | ||||||
\(324\) | −503867. | −0.266657 | ||||||||
\(325\) | −953775. | − | 1.07884e6i | −0.500885 | − | 0.566561i | ||||
\(326\) | 3.35987e6 | 1.75097 | ||||||||
\(327\) | − | 2.10295e6i | − | 1.08758i | ||||||
\(328\) | 4.07089e6i | 2.08932i | ||||||||
\(329\) | 203439. | 0.103620 | ||||||||
\(330\) | 593835. | − | 224861.i | 0.300180 | − | 0.113666i | ||||
\(331\) | 1.89235e6 | 0.949363 | 0.474682 | − | 0.880158i | \(-0.342563\pi\) | ||||
0.474682 | + | 0.880158i | \(0.342563\pi\) | |||||||
\(332\) | 598885.i | 0.298194i | ||||||||
\(333\) | − | 1.03886e6i | − | 0.513389i | ||||||
\(334\) | −4.54107e6 | −2.22737 | ||||||||
\(335\) | −1.14629e6 | − | 3.02723e6i | −0.558060 | − | 1.47378i | ||||
\(336\) | 476315. | 0.230169 | ||||||||
\(337\) | 1.58818e6i | 0.761772i | 0.924622 | + | 0.380886i | \(0.124381\pi\) | ||||
−0.924622 | + | 0.380886i | \(0.875619\pi\) | |||||||
\(338\) | − | 1.65804e6i | − | 0.789410i | ||||||
\(339\) | 329719. | 0.155828 | ||||||||
\(340\) | 3.52496e6 | + | 9.30906e6i | 1.65370 | + | 4.36726i | ||||
\(341\) | −114264. | −0.0532136 | ||||||||
\(342\) | − | 676022.i | − | 0.312533i | ||||||
\(343\) | 725734.i | 0.333075i | ||||||||
\(344\) | −9.58110e6 | −4.36535 | ||||||||
\(345\) | 2.24995e6 | − | 851962.i | 1.01771 | − | 0.385365i | ||||
\(346\) | 7.30474e6 | 3.28031 | ||||||||
\(347\) | − | 1.31246e6i | − | 0.585141i | −0.956244 | − | 0.292571i | \(-0.905489\pi\) | ||
0.956244 | − | 0.292571i | \(-0.0945107\pi\) | |||||||
\(348\) | − | 630063.i | − | 0.278892i | ||||||
\(349\) | 3.90078e6 | 1.71430 | 0.857151 | − | 0.515065i | \(-0.172232\pi\) | ||||
0.857151 | + | 0.515065i | \(0.172232\pi\) | |||||||
\(350\) | 534878. | − | 472874.i | 0.233391 | − | 0.206336i | ||||
\(351\) | 335921. | 0.145536 | ||||||||
\(352\) | − | 1.24039e6i | − | 0.533581i | ||||||
\(353\) | − | 3.32103e6i | − | 1.41852i | −0.704946 | − | 0.709261i | \(-0.749029\pi\) | ||
0.704946 | − | 0.709261i | \(-0.250971\pi\) | |||||||
\(354\) | 1.94573e6 | 0.825228 | ||||||||
\(355\) | −2.00556e6 | + | 759424.i | −0.844628 | + | 0.319826i | ||||
\(356\) | −6.38024e6 | −2.66816 | ||||||||
\(357\) | 457060.i | 0.189803i | ||||||||
\(358\) | 2.38018e6i | 0.981527i | ||||||||
\(359\) | −2.37759e6 | −0.973647 | −0.486823 | − | 0.873500i | \(-0.661845\pi\) | ||||
−0.486823 | + | 0.873500i | \(0.661845\pi\) | |||||||
\(360\) | 749243. | + | 1.97868e6i | 0.304696 | + | 0.804671i | ||||
\(361\) | −1.83587e6 | −0.741438 | ||||||||
\(362\) | − | 5.33627e6i | − | 2.14026i | ||||||
\(363\) | − | 131769.i | − | 0.0524864i | ||||||
\(364\) | −775096. | −0.306621 | ||||||||
\(365\) | 166911. | + | 440796.i | 0.0655773 | + | 0.173183i | ||||
\(366\) | 622011. | 0.242714 | ||||||||
\(367\) | − | 3.52479e6i | − | 1.36605i | −0.730393 | − | 0.683027i | \(-0.760663\pi\) | ||
0.730393 | − | 0.683027i | \(-0.239337\pi\) | |||||||
\(368\) | − | 1.15545e7i | − | 4.44768i | ||||||
\(369\) | −705690. | −0.269804 | ||||||||
\(370\) | −6.99376e6 | + | 2.64825e6i | −2.65587 | + | 1.00567i | ||||
\(371\) | 509528. | 0.192191 | ||||||||
\(372\) | − | 652696.i | − | 0.244542i | ||||||
\(373\) | 3.82557e6i | 1.42372i | 0.702322 | + | 0.711859i | \(0.252147\pi\) | ||||
−0.702322 | + | 0.711859i | \(0.747853\pi\) | |||||||
\(374\) | 2.92634e6 | 1.08180 | ||||||||
\(375\) | 1.39101e6 | + | 732813.i | 0.510801 | + | 0.269101i | ||||
\(376\) | 4.34005e6 | 1.58316 | ||||||||
\(377\) | 420054.i | 0.152213i | ||||||||
\(378\) | 166547.i | 0.0599525i | ||||||||
\(379\) | −3.70497e6 | −1.32491 | −0.662456 | − | 0.749101i | \(-0.730486\pi\) | ||||
−0.662456 | + | 0.749101i | \(0.730486\pi\) | |||||||
\(380\) | −3.21249e6 | + | 1.21644e6i | −1.14126 | + | 0.432146i | ||||
\(381\) | 2.31200e6 | 0.815972 | ||||||||
\(382\) | 8.37733e6i | 2.93729i | ||||||||
\(383\) | 789569.i | 0.275038i | 0.990499 | + | 0.137519i | \(0.0439129\pi\) | ||||
−0.990499 | + | 0.137519i | \(0.956087\pi\) | |||||||
\(384\) | −173283. | −0.0599691 | ||||||||
\(385\) | −52464.1 | − | 138553.i | −0.0180389 | − | 0.0476390i | ||||
\(386\) | 6.03627e6 | 2.06206 | ||||||||
\(387\) | − | 1.66089e6i | − | 0.563719i | ||||||
\(388\) | − | 1.12727e6i | − | 0.380145i | ||||||
\(389\) | 4.73042e6 | 1.58499 | 0.792494 | − | 0.609879i | \(-0.208782\pi\) | ||||
0.792494 | + | 0.609879i | \(0.208782\pi\) | |||||||
\(390\) | −856324. | − | 2.26147e6i | −0.285087 | − | 0.752886i | ||||
\(391\) | 1.10875e7 | 3.66767 | ||||||||
\(392\) | 7.62911e6i | 2.50760i | ||||||||
\(393\) | 985575.i | 0.321891i | ||||||||
\(394\) | 2.90549e6 | 0.942928 | ||||||||
\(395\) | −88008.4 | + | 33325.1i | −0.0283812 | + | 0.0107468i | ||||
\(396\) | 752690. | 0.241200 | ||||||||
\(397\) | − | 2.42880e6i | − | 0.773421i | −0.922201 | − | 0.386711i | \(-0.873611\pi\) | ||
0.922201 | − | 0.386711i | \(-0.126389\pi\) | |||||||
\(398\) | 8.79957e6i | 2.78454i | ||||||||
\(399\) | −157728. | −0.0495995 | ||||||||
\(400\) | 5.65715e6 | − | 5.00136e6i | 1.76786 | − | 1.56293i | ||||
\(401\) | 276251. | 0.0857914 | 0.0428957 | − | 0.999080i | \(-0.486342\pi\) | ||||
0.0428957 | + | 0.999080i | \(0.486342\pi\) | |||||||
\(402\) | − | 5.43585e6i | − | 1.67765i | ||||||
\(403\) | 435144.i | 0.133466i | ||||||||
\(404\) | 1.47282e6 | 0.448949 | ||||||||
\(405\) | −343004. | + | 129881.i | −0.103911 | + | 0.0393468i | ||||
\(406\) | −208259. | −0.0627032 | ||||||||
\(407\) | 1.55188e6i | 0.464378i | ||||||||
\(408\) | 9.75066e6i | 2.89990i | ||||||||
\(409\) | 563175. | 0.166470 | 0.0832349 | − | 0.996530i | \(-0.473475\pi\) | ||||
0.0832349 | + | 0.996530i | \(0.473475\pi\) | |||||||
\(410\) | 1.79893e6 | + | 4.75081e6i | 0.528513 | + | 1.39575i | ||||
\(411\) | 1.34913e6 | 0.393958 | ||||||||
\(412\) | − | 9.81787e6i | − | 2.84954i | ||||||
\(413\) | − | 453974.i | − | 0.130965i | ||||||
\(414\) | 4.04012e6 | 1.15849 | ||||||||
\(415\) | 154374. | + | 407687.i | 0.0440002 | + | 0.116200i | ||||
\(416\) | −4.72369e6 | −1.33828 | ||||||||
\(417\) | − | 1.01926e6i | − | 0.287040i | ||||||
\(418\) | 1.00986e6i | 0.282696i | ||||||||
\(419\) | −707010. | −0.196739 | −0.0983695 | − | 0.995150i | \(-0.531363\pi\) | ||||
−0.0983695 | + | 0.995150i | \(0.531363\pi\) | |||||||
\(420\) | 791439. | − | 299685.i | 0.218924 | − | 0.0828976i | ||||
\(421\) | 4.56766e6 | 1.25600 | 0.627999 | − | 0.778214i | \(-0.283874\pi\) | ||||
0.627999 | + | 0.778214i | \(0.283874\pi\) | |||||||
\(422\) | − | 507077.i | − | 0.138609i | ||||||
\(423\) | 752349.i | 0.204441i | ||||||||
\(424\) | 1.08700e7 | 2.93639 | ||||||||
\(425\) | 4.79918e6 | + | 5.42846e6i | 1.28883 | + | 1.45782i | ||||
\(426\) | −3.60130e6 | −0.961468 | ||||||||
\(427\) | − | 145127.i | − | 0.0385192i | ||||||
\(428\) | − | 4.05003e6i | − | 1.06868i | ||||||
\(429\) | −501808. | −0.131642 | ||||||||
\(430\) | −1.11813e7 | + | 4.23390e6i | −2.91623 | + | 1.10426i | ||||
\(431\) | 6.16454e6 | 1.59848 | 0.799241 | − | 0.601011i | \(-0.205235\pi\) | ||||
0.799241 | + | 0.601011i | \(0.205235\pi\) | |||||||
\(432\) | 1.76149e6i | 0.454120i | ||||||||
\(433\) | 2.94520e6i | 0.754910i | 0.926028 | + | 0.377455i | \(0.123201\pi\) | ||||
−0.926028 | + | 0.377455i | \(0.876799\pi\) | |||||||
\(434\) | −215741. | −0.0549804 | ||||||||
\(435\) | −162411. | − | 428911.i | −0.0411521 | − | 0.108679i | ||||
\(436\) | −1.79446e7 | −4.52081 | ||||||||
\(437\) | 3.82620e6i | 0.958438i | ||||||||
\(438\) | 791517.i | 0.197140i | ||||||||
\(439\) | 5.90123e6 | 1.46144 | 0.730720 | − | 0.682677i | \(-0.239184\pi\) | ||||
0.730720 | + | 0.682677i | \(0.239184\pi\) | |||||||
\(440\) | −1.11924e6 | − | 2.95580e6i | −0.275608 | − | 0.727853i | ||||
\(441\) | −1.32251e6 | −0.323819 | ||||||||
\(442\) | − | 1.11442e7i | − | 2.71328i | ||||||
\(443\) | − | 4.58354e6i | − | 1.10966i | −0.831963 | − | 0.554832i | \(-0.812783\pi\) | ||
0.831963 | − | 0.554832i | \(-0.187217\pi\) | |||||||
\(444\) | −8.86463e6 | −2.13404 | ||||||||
\(445\) | −4.34331e6 | + | 1.64463e6i | −1.03973 | + | 0.393703i | ||||
\(446\) | −4.94019e6 | −1.17600 | ||||||||
\(447\) | − | 556271.i | − | 0.131679i | ||||||
\(448\) | − | 648401.i | − | 0.152633i | ||||||
\(449\) | −6.61995e6 | −1.54967 | −0.774834 | − | 0.632164i | \(-0.782167\pi\) | ||||
−0.774834 | + | 0.632164i | \(0.782167\pi\) | |||||||
\(450\) | 1.74876e6 | + | 1.97806e6i | 0.407098 | + | 0.460477i | ||||
\(451\) | 1.05418e6 | 0.244047 | ||||||||
\(452\) | − | 2.81350e6i | − | 0.647741i | ||||||
\(453\) | 2.31101e6i | 0.529122i | ||||||||
\(454\) | 8.00854e6 | 1.82353 | ||||||||
\(455\) | −527642. | + | 199796.i | −0.119484 | + | 0.0452437i | ||||
\(456\) | −3.36488e6 | −0.757805 | ||||||||
\(457\) | − | 6.37429e6i | − | 1.42771i | −0.700292 | − | 0.713857i | \(-0.746947\pi\) | ||
0.700292 | − | 0.713857i | \(-0.253053\pi\) | |||||||
\(458\) | 6.05143e6i | 1.34801i | ||||||||
\(459\) | −1.69028e6 | −0.374478 | ||||||||
\(460\) | −7.26982e6 | − | 1.91989e7i | −1.60188 | − | 4.23040i | ||||
\(461\) | −5.36939e6 | −1.17672 | −0.588359 | − | 0.808600i | \(-0.700226\pi\) | ||||
−0.588359 | + | 0.808600i | \(0.700226\pi\) | |||||||
\(462\) | − | 248792.i | − | 0.0542290i | ||||||
\(463\) | − | 7.13889e6i | − | 1.54767i | −0.633387 | − | 0.773835i | \(-0.718336\pi\) | ||
0.633387 | − | 0.773835i | \(-0.281664\pi\) | |||||||
\(464\) | −2.20266e6 | −0.474955 | ||||||||
\(465\) | −168245. | − | 444319.i | −0.0360836 | − | 0.0952933i | ||||
\(466\) | −3.11523e6 | −0.664547 | ||||||||
\(467\) | − | 5.11617e6i | − | 1.08556i | −0.839876 | − | 0.542779i | \(-0.817372\pi\) | ||
0.839876 | − | 0.542779i | \(-0.182628\pi\) | |||||||
\(468\) | − | 2.86642e6i | − | 0.604959i | ||||||
\(469\) | −1.26828e6 | −0.266246 | ||||||||
\(470\) | 5.06492e6 | − | 1.91787e6i | 1.05762 | − | 0.400475i | ||||
\(471\) | −1.04449e6 | −0.216946 | ||||||||
\(472\) | − | 9.68481e6i | − | 2.00095i | ||||||
\(473\) | 2.48108e6i | 0.509903i | ||||||||
\(474\) | −158033. | −0.0323073 | ||||||||
\(475\) | −1.87332e6 | + | 1.65616e6i | −0.380959 | + | 0.336798i | ||||
\(476\) | 3.90011e6 | 0.788968 | ||||||||
\(477\) | 1.88431e6i | 0.379190i | ||||||||
\(478\) | 3.38013e6i | 0.676650i | ||||||||
\(479\) | 715144. | 0.142415 | 0.0712074 | − | 0.997462i | \(-0.477315\pi\) | ||||
0.0712074 | + | 0.997462i | \(0.477315\pi\) | |||||||
\(480\) | 4.82329e6 | − | 1.82638e6i | 0.955522 | − | 0.361816i | ||||
\(481\) | 5.90993e6 | 1.16471 | ||||||||
\(482\) | 7.09194e6i | 1.39042i | ||||||||
\(483\) | − | 942634.i | − | 0.183855i | ||||||
\(484\) | −1.12439e6 | −0.218174 | ||||||||
\(485\) | −290576. | − | 767383.i | −0.0560926 | − | 0.148135i | ||||
\(486\) | −615916. | −0.118285 | ||||||||
\(487\) | 9.41305e6i | 1.79849i | 0.437445 | + | 0.899245i | \(0.355883\pi\) | ||||
−0.437445 | + | 0.899245i | \(0.644117\pi\) | |||||||
\(488\) | − | 3.09605e6i | − | 0.588515i | ||||||
\(489\) | 2.89906e6 | 0.548257 | ||||||||
\(490\) | 3.37132e6 | + | 8.90332e6i | 0.634321 | + | 1.67518i | ||||
\(491\) | −2.03825e6 | −0.381551 | −0.190776 | − | 0.981634i | \(-0.561100\pi\) | ||||
−0.190776 | + | 0.981634i | \(0.561100\pi\) | |||||||
\(492\) | 6.02167e6i | 1.12151i | ||||||||
\(493\) | − | 2.11362e6i | − | 0.391660i | ||||||
\(494\) | 3.84579e6 | 0.709036 | ||||||||
\(495\) | 512389. | − | 194020.i | 0.0939911 | − | 0.0355905i | ||||
\(496\) | −2.28179e6 | −0.416458 | ||||||||
\(497\) | 840248.i | 0.152587i | ||||||||
\(498\) | 732065.i | 0.132274i | ||||||||
\(499\) | 2.29272e6 | 0.412192 | 0.206096 | − | 0.978532i | \(-0.433924\pi\) | ||||
0.206096 | + | 0.978532i | \(0.433924\pi\) | |||||||
\(500\) | 6.25311e6 | − | 1.18695e7i | 1.11859 | − | 2.12329i | ||||
\(501\) | −3.91825e6 | −0.697425 | ||||||||
\(502\) | − | 1.86115e7i | − | 3.29626i | ||||||
\(503\) | − | 6.36926e6i | − | 1.12246i | −0.827661 | − | 0.561228i | \(-0.810329\pi\) | ||
0.827661 | − | 0.561228i | \(-0.189671\pi\) | |||||||
\(504\) | 828983. | 0.145368 | ||||||||
\(505\) | 1.00262e6 | − | 379649.i | 0.174947 | − | 0.0662451i | ||||
\(506\) | −6.03525e6 | −1.04790 | ||||||||
\(507\) | − | 1.43063e6i | − | 0.247177i | ||||||
\(508\) | − | 1.97284e7i | − | 3.39181i | ||||||
\(509\) | 5.66660e6 | 0.969456 | 0.484728 | − | 0.874665i | \(-0.338919\pi\) | ||||
0.484728 | + | 0.874665i | \(0.338919\pi\) | |||||||
\(510\) | 4.30883e6 | + | 1.13792e7i | 0.733558 | + | 1.93725i | ||||
\(511\) | 184675. | 0.0312864 | ||||||||
\(512\) | 1.13597e7i | 1.91510i | ||||||||
\(513\) | − | 583303.i | − | 0.0978590i | ||||||
\(514\) | −9.29442e6 | −1.55172 | ||||||||
\(515\) | −2.53075e6 | − | 6.68345e6i | −0.420466 | − | 1.11041i | ||||
\(516\) | −1.41724e7 | −2.34325 | ||||||||
\(517\) | − | 1.12388e6i | − | 0.184924i | ||||||
\(518\) | 2.93009e6i | 0.479796i | ||||||||
\(519\) | 6.30287e6 | 1.02712 | ||||||||
\(520\) | −1.12564e7 | + | 4.26233e6i | −1.82554 | + | 0.691256i | ||||
\(521\) | 6.07157e6 | 0.979956 | 0.489978 | − | 0.871735i | \(-0.337005\pi\) | ||||
0.489978 | + | 0.871735i | \(0.337005\pi\) | |||||||
\(522\) | − | 770175.i | − | 0.123712i | ||||||
\(523\) | 2.50083e6i | 0.399789i | 0.979817 | + | 0.199894i | \(0.0640599\pi\) | ||||
−0.979817 | + | 0.199894i | \(0.935940\pi\) | |||||||
\(524\) | 8.40994e6 | 1.33803 | ||||||||
\(525\) | 461517. | − | 408018.i | 0.0730785 | − | 0.0646072i | ||||
\(526\) | 1.33361e7 | 2.10167 | ||||||||
\(527\) | − | 2.18954e6i | − | 0.343421i | ||||||
\(528\) | − | 2.63136e6i | − | 0.410767i | ||||||
\(529\) | −1.64302e7 | −2.55273 | ||||||||
\(530\) | 1.26855e7 | − | 4.80346e6i | 1.96163 | − | 0.742787i | ||||
\(531\) | 1.67886e6 | 0.258392 | ||||||||
\(532\) | 1.34590e6i | 0.206174i | ||||||||
\(533\) | − | 4.01457e6i | − | 0.612098i | ||||||
\(534\) | −7.79907e6 | −1.18356 | ||||||||
\(535\) | −1.04397e6 | − | 2.75703e6i | −0.157690 | − | 0.416444i | ||||
\(536\) | −2.70568e7 | −4.06784 | ||||||||
\(537\) | 2.05373e6i | 0.307332i | ||||||||
\(538\) | 4.73842e6i | 0.705794i | ||||||||
\(539\) | 1.97560e6 | 0.292905 | ||||||||
\(540\) | 1.10828e6 | + | 2.92686e6i | 0.163556 | + | 0.431935i | ||||
\(541\) | 2.70948e6 | 0.398009 | 0.199004 | − | 0.979999i | \(-0.436229\pi\) | ||||
0.199004 | + | 0.979999i | \(0.436229\pi\) | |||||||
\(542\) | 2.11511e7i | 3.09268i | ||||||||
\(543\) | − | 4.60438e6i | − | 0.670149i | ||||||
\(544\) | 2.37686e7 | 3.44354 | ||||||||
\(545\) | −1.22156e7 | + | 4.62556e6i | −1.76167 | + | 0.667072i | ||||
\(546\) | −947461. | −0.136013 | ||||||||
\(547\) | 9.99302e6i | 1.42800i | 0.700145 | + | 0.714000i | \(0.253119\pi\) | ||||
−0.700145 | + | 0.714000i | \(0.746881\pi\) | |||||||
\(548\) | − | 1.15122e7i | − | 1.63759i | ||||||
\(549\) | 536700. | 0.0759978 | ||||||||
\(550\) | −2.61235e6 | − | 2.95488e6i | −0.368234 | − | 0.416517i | ||||
\(551\) | 729394. | 0.102349 | ||||||||
\(552\) | − | 2.01096e7i | − | 2.80903i | ||||||
\(553\) | 36871.9i | 0.00512722i | ||||||||
\(554\) | 1.33134e7 | 1.84296 | ||||||||
\(555\) | −6.03454e6 | + | 2.28503e6i | −0.831595 | + | 0.314891i | ||||
\(556\) | −8.69734e6 | −1.19316 | ||||||||
\(557\) | − | 2.85519e6i | − | 0.389940i | −0.980809 | − | 0.194970i | \(-0.937539\pi\) | ||
0.980809 | − | 0.194970i | \(-0.0624609\pi\) | |||||||
\(558\) | − | 797842.i | − | 0.108475i | ||||||
\(559\) | 9.44854e6 | 1.27890 | ||||||||
\(560\) | −1.04768e6 | − | 2.76682e6i | −0.141175 | − | 0.372830i | ||||
\(561\) | 2.52499e6 | 0.338729 | ||||||||
\(562\) | 1.06583e7i | 1.42347i | ||||||||
\(563\) | 8.74359e6i | 1.16257i | 0.813700 | + | 0.581285i | \(0.197450\pi\) | ||||
−0.813700 | + | 0.581285i | \(0.802550\pi\) | |||||||
\(564\) | 6.41981e6 | 0.849815 | ||||||||
\(565\) | −725235. | − | 1.91527e6i | −0.0955779 | − | 0.252412i | ||||
\(566\) | 785832. | 0.103107 | ||||||||
\(567\) | 143704.i | 0.0187721i | ||||||||
\(568\) | 1.79254e7i | 2.33129i | ||||||||
\(569\) | −4.89251e6 | −0.633507 | −0.316753 | − | 0.948508i | \(-0.602593\pi\) | ||||
−0.316753 | + | 0.948508i | \(0.602593\pi\) | |||||||
\(570\) | −3.92688e6 | + | 1.48695e6i | −0.506245 | + | 0.191694i | ||||
\(571\) | 1.65650e6 | 0.212619 | 0.106310 | − | 0.994333i | \(-0.466097\pi\) | ||||
0.106310 | + | 0.994333i | \(0.466097\pi\) | |||||||
\(572\) | 4.28194e6i | 0.547206i | ||||||||
\(573\) | 7.22835e6i | 0.919714i | ||||||||
\(574\) | 1.99039e6 | 0.252150 | ||||||||
\(575\) | −9.89776e6 | − | 1.11956e7i | −1.24844 | − | 1.41214i | ||||
\(576\) | 2.39789e6 | 0.301143 | ||||||||
\(577\) | 1.33417e7i | 1.66829i | 0.551547 | + | 0.834144i | \(0.314038\pi\) | ||||
−0.551547 | + | 0.834144i | \(0.685962\pi\) | |||||||
\(578\) | 4.12653e7i | 5.13766i | ||||||||
\(579\) | 5.20837e6 | 0.645663 | ||||||||
\(580\) | −3.65991e6 | + | 1.38586e6i | −0.451753 | + | 0.171060i | ||||
\(581\) | 170804. | 0.0209922 | ||||||||
\(582\) | − | 1.37795e6i | − | 0.168627i | ||||||
\(583\) | − | 2.81484e6i | − | 0.342990i | ||||||
\(584\) | 3.93975e6 | 0.478010 | ||||||||
\(585\) | −738876. | − | 1.95130e6i | −0.0892652 | − | 0.235741i | ||||
\(586\) | −6.89874e6 | −0.829900 | ||||||||
\(587\) | 3.82733e6i | 0.458460i | 0.973372 | + | 0.229230i | \(0.0736207\pi\) | ||||
−0.973372 | + | 0.229230i | \(0.926379\pi\) | |||||||
\(588\) | 1.12850e7i | 1.34604i | ||||||||
\(589\) | 755596. | 0.0897432 | ||||||||
\(590\) | −4.27973e6 | − | 1.13024e7i | −0.506159 | − | 1.33672i | ||||
\(591\) | 2.50699e6 | 0.295246 | ||||||||
\(592\) | 3.09902e7i | 3.63430i | ||||||||
\(593\) | − | 3.31931e6i | − | 0.387625i | −0.981039 | − | 0.193812i | \(-0.937915\pi\) | ||
0.981039 | − | 0.193812i | \(-0.0620853\pi\) | |||||||
\(594\) | 920072. | 0.106993 | ||||||||
\(595\) | 2.65497e6 | − | 1.00533e6i | 0.307445 | − | 0.116417i | ||||
\(596\) | −4.74668e6 | −0.547362 | ||||||||
\(597\) | 7.59268e6i | 0.871885i | ||||||||
\(598\) | 2.29837e7i | 2.62825i | ||||||||
\(599\) | 7.82165e6 | 0.890699 | 0.445350 | − | 0.895357i | \(-0.353079\pi\) | ||||
0.445350 | + | 0.895357i | \(0.353079\pi\) | |||||||
\(600\) | 9.84574e6 | − | 8.70441e6i | 1.11653 | − | 0.987100i | ||||
\(601\) | 1.52108e7 | 1.71778 | 0.858889 | − | 0.512162i | \(-0.171155\pi\) | ||||
0.858889 | + | 0.512162i | \(0.171155\pi\) | |||||||
\(602\) | 4.68451e6i | 0.526833i | ||||||||
\(603\) | − | 4.69030e6i | − | 0.525300i | ||||||
\(604\) | 1.97199e7 | 2.19944 | ||||||||
\(605\) | −765420. | + | 289833.i | −0.0850181 | + | 0.0321928i | ||||
\(606\) | 1.80035e6 | 0.199148 | ||||||||
\(607\) | − | 1.34079e7i | − | 1.47703i | −0.674236 | − | 0.738516i | \(-0.735527\pi\) | ||
0.674236 | − | 0.738516i | \(-0.264473\pi\) | |||||||
\(608\) | 8.20235e6i | 0.899870i | ||||||||
\(609\) | −179696. | −0.0196334 | ||||||||
\(610\) | −1.36815e6 | − | 3.61314e6i | −0.148870 | − | 0.393152i | ||||
\(611\) | −4.28000e6 | −0.463811 | ||||||||
\(612\) | 1.44232e7i | 1.55662i | ||||||||
\(613\) | − | 1.15459e7i | − | 1.24102i | −0.784199 | − | 0.620509i | \(-0.786926\pi\) | ||
0.784199 | − | 0.620509i | \(-0.213074\pi\) | |||||||
\(614\) | 1.00377e7 | 1.07451 | ||||||||
\(615\) | 1.55220e6 | + | 4.09922e6i | 0.165486 | + | 0.437032i | ||||
\(616\) | −1.23836e6 | −0.131490 | ||||||||
\(617\) | − | 1.07188e7i | − | 1.13353i | −0.823881 | − | 0.566763i | \(-0.808195\pi\) | ||
0.823881 | − | 0.566763i | \(-0.191805\pi\) | |||||||
\(618\) | − | 1.20012e7i | − | 1.26401i | ||||||
\(619\) | −8.11579e6 | −0.851342 | −0.425671 | − | 0.904878i | \(-0.639962\pi\) | ||||
−0.425671 | + | 0.904878i | \(0.639962\pi\) | |||||||
\(620\) | −3.79138e6 | + | 1.43564e6i | −0.396113 | + | 0.149991i | ||||
\(621\) | 3.48601e6 | 0.362743 | ||||||||
\(622\) | − | 6.73031e6i | − | 0.697524i | ||||||
\(623\) | 1.81966e6i | 0.187833i | ||||||||
\(624\) | −1.00208e7 | −1.03025 | ||||||||
\(625\) | 1.19717e6 | − | 9.69197e6i | 0.122590 | − | 0.992457i | ||||
\(626\) | 3.35264e7 | 3.41941 | ||||||||
\(627\) | 871354.i | 0.0885168i | ||||||||
\(628\) | 8.91264e6i | 0.901793i | ||||||||
\(629\) | −2.97374e7 | −2.99693 | ||||||||
\(630\) | 967438. | − | 366329.i | 0.0971118 | − | 0.0367722i | ||||
\(631\) | 1.00476e7 | 1.00459 | 0.502295 | − | 0.864696i | \(-0.332489\pi\) | ||||
0.502295 | + | 0.864696i | \(0.332489\pi\) | |||||||
\(632\) | 786603.i | 0.0783362i | ||||||||
\(633\) | − | 437529.i | − | 0.0434008i | ||||||
\(634\) | 1.66568e7 | 1.64576 | ||||||||
\(635\) | −5.08537e6 | − | 1.34299e7i | −0.500481 | − | 1.32172i | ||||
\(636\) | 1.60789e7 | 1.57621 | ||||||||
\(637\) | − | 7.52356e6i | − | 0.734640i | ||||||
\(638\) | 1.15051e6i | 0.111902i | ||||||||
\(639\) | −3.10737e6 | −0.301051 | ||||||||
\(640\) | 381145. | + | 1.00657e6i | 0.0367824 | + | 0.0971387i | ||||
\(641\) | −1.25041e6 | −0.120200 | −0.0601002 | − | 0.998192i | \(-0.519142\pi\) | ||||
−0.0601002 | + | 0.998192i | \(0.519142\pi\) | |||||||
\(642\) | − | 4.95067e6i | − | 0.474052i | ||||||
\(643\) | − | 1.68108e7i | − | 1.60347i | −0.597681 | − | 0.801734i | \(-0.703911\pi\) | ||
0.597681 | − | 0.801734i | \(-0.296089\pi\) | |||||||
\(644\) | −8.04353e6 | −0.764244 | ||||||||
\(645\) | −9.64776e6 | + | 3.65321e6i | −0.913119 | + | 0.345760i | ||||
\(646\) | −1.93511e7 | −1.82442 | ||||||||
\(647\) | 1.96602e6i | 0.184640i | 0.995729 | + | 0.0923202i | \(0.0294283\pi\) | ||||
−0.995729 | + | 0.0923202i | \(0.970572\pi\) | |||||||
\(648\) | 3.06571e6i | 0.286809i | ||||||||
\(649\) | −2.50793e6 | −0.233725 | ||||||||
\(650\) | −1.12529e7 | + | 9.94844e6i | −1.04467 | + | 0.923574i | ||||
\(651\) | −186151. | −0.0172152 | ||||||||
\(652\) | − | 2.47377e7i | − | 2.27898i | ||||||
\(653\) | 2.26355e6i | 0.207734i | 0.994591 | + | 0.103867i | \(0.0331216\pi\) | ||||
−0.994591 | + | 0.103867i | \(0.966878\pi\) | |||||||
\(654\) | −2.19350e7 | −2.00537 | ||||||||
\(655\) | 5.72501e6 | − | 2.16782e6i | 0.521402 | − | 0.197434i | ||||
\(656\) | 2.10514e7 | 1.90995 | ||||||||
\(657\) | 682957.i | 0.0617277i | ||||||||
\(658\) | − | 2.12199e6i | − | 0.191064i | ||||||
\(659\) | 4.02181e6 | 0.360752 | 0.180376 | − | 0.983598i | \(-0.442269\pi\) | ||||
0.180376 | + | 0.983598i | \(0.442269\pi\) | |||||||
\(660\) | −1.65558e6 | − | 4.37223e6i | −0.147942 | − | 0.390700i | ||||
\(661\) | −1.60875e7 | −1.43214 | −0.716071 | − | 0.698027i | \(-0.754061\pi\) | ||||
−0.716071 | + | 0.698027i | \(0.754061\pi\) | |||||||
\(662\) | − | 1.97384e7i | − | 1.75052i | ||||||
\(663\) | − | 9.61575e6i | − | 0.849570i | ||||||
\(664\) | 3.64383e6 | 0.320729 | ||||||||
\(665\) | 346932. | + | 916212.i | 0.0304221 | + | 0.0803419i | ||||
\(666\) | −1.08359e7 | −0.946631 | ||||||||
\(667\) | 4.35909e6i | 0.379386i | ||||||||
\(668\) | 3.34345e7i | 2.89904i | ||||||||
\(669\) | −4.26262e6 | −0.368224 | ||||||||
\(670\) | −3.15758e7 | + | 1.19564e7i | −2.71748 | + | 1.02900i | ||||
\(671\) | −801738. | −0.0687426 | ||||||||
\(672\) | − | 2.02076e6i | − | 0.172620i | ||||||
\(673\) | − | 5.69741e6i | − | 0.484886i | −0.970166 | − | 0.242443i | \(-0.922051\pi\) | ||
0.970166 | − | 0.242443i | \(-0.0779487\pi\) | |||||||
\(674\) | 1.65657e7 | 1.40462 | ||||||||
\(675\) | 1.50891e6 | + | 1.70676e6i | 0.127469 | + | 0.144183i | ||||
\(676\) | −1.22076e7 | −1.02746 | ||||||||
\(677\) | − | 2.57893e6i | − | 0.216256i | −0.994137 | − | 0.108128i | \(-0.965514\pi\) | ||
0.994137 | − | 0.108128i | \(-0.0344856\pi\) | |||||||
\(678\) | − | 3.43917e6i | − | 0.287329i | ||||||
\(679\) | −321501. | −0.0267614 | ||||||||
\(680\) | 5.66397e7 | − | 2.14471e7i | 4.69730 | − | 1.77867i | ||||
\(681\) | 6.91014e6 | 0.570978 | ||||||||
\(682\) | 1.19184e6i | 0.0981197i | ||||||||
\(683\) | 1.28680e7i | 1.05550i | 0.849400 | + | 0.527750i | \(0.176964\pi\) | ||||
−0.849400 | + | 0.527750i | \(0.823036\pi\) | |||||||
\(684\) | −4.97734e6 | −0.406778 | ||||||||
\(685\) | −2.96749e6 | − | 7.83684e6i | −0.241636 | − | 0.638138i | ||||
\(686\) | 7.56983e6 | 0.614152 | ||||||||
\(687\) | 5.22146e6i | 0.422085i | ||||||||
\(688\) | 4.95458e7i | 3.99058i | ||||||||
\(689\) | −1.07196e7 | −0.860259 | ||||||||
\(690\) | −8.88647e6 | − | 2.34683e7i | −0.710570 | − | 1.87654i | ||||
\(691\) | −3.61306e6 | −0.287859 | −0.143930 | − | 0.989588i | \(-0.545974\pi\) | ||||
−0.143930 | + | 0.989588i | \(0.545974\pi\) | |||||||
\(692\) | − | 5.37826e7i | − | 4.26949i | ||||||
\(693\) | − | 214670.i | − | 0.0169800i | ||||||
\(694\) | −1.36897e7 | −1.07893 | ||||||||
\(695\) | −5.92066e6 | + | 2.24191e6i | −0.464952 | + | 0.176058i | ||||
\(696\) | −3.83353e6 | −0.299968 | ||||||||
\(697\) | 2.02004e7i | 1.57499i | ||||||||
\(698\) | − | 4.06874e7i | − | 3.16098i | ||||||
\(699\) | −2.68797e6 | −0.208080 | ||||||||
\(700\) | −3.48163e6 | − | 3.93814e6i | −0.268557 | − | 0.303771i | ||||
\(701\) | 1.60588e7 | 1.23429 | 0.617147 | − | 0.786848i | \(-0.288288\pi\) | ||||
0.617147 | + | 0.786848i | \(0.288288\pi\) | |||||||
\(702\) | − | 3.50386e6i | − | 0.268351i | ||||||
\(703\) | − | 1.02622e7i | − | 0.783161i | ||||||
\(704\) | −3.58203e6 | −0.272394 | ||||||||
\(705\) | 4.37025e6 | − | 1.65483e6i | 0.331156 | − | 0.125395i | ||||
\(706\) | −3.46403e7 | −2.61559 | ||||||||
\(707\) | − | 420054.i | − | 0.0316051i | ||||||
\(708\) | − | 1.43258e7i | − | 1.07408i | ||||||
\(709\) | 6.79151e6 | 0.507400 | 0.253700 | − | 0.967283i | \(-0.418352\pi\) | ||||
0.253700 | + | 0.967283i | \(0.418352\pi\) | |||||||
\(710\) | 7.92124e6 | + | 2.09192e7i | 0.589722 | + | 1.55740i | ||||
\(711\) | −136358. | −0.0101159 | ||||||||
\(712\) | 3.88197e7i | 2.86980i | ||||||||
\(713\) | 4.51568e6i | 0.332659i | ||||||||
\(714\) | 4.76741e6 | 0.349975 | ||||||||
\(715\) | 1.10375e6 | + | 2.91490e6i | 0.0807434 | + | 0.213235i | ||||
\(716\) | 1.75245e7 | 1.27751 | ||||||||
\(717\) | 2.91654e6i | 0.211870i | ||||||||
\(718\) | 2.47997e7i | 1.79529i | ||||||||
\(719\) | −9.17382e6 | −0.661802 | −0.330901 | − | 0.943666i | \(-0.607353\pi\) | ||||
−0.330901 | + | 0.943666i | \(0.607353\pi\) | |||||||
\(720\) | 1.02321e7 | − | 3.87449e6i | 0.735589 | − | 0.278537i | ||||
\(721\) | −2.80009e6 | −0.200601 | ||||||||
\(722\) | 1.91492e7i | 1.36713i | ||||||||
\(723\) | 6.11925e6i | 0.435364i | ||||||||
\(724\) | −3.92893e7 | −2.78566 | ||||||||
\(725\) | −2.13423e6 | + | 1.88683e6i | −0.150798 | + | 0.133317i | ||||
\(726\) | −1.37443e6 | −0.0967789 | ||||||||
\(727\) | − | 1.19986e7i | − | 0.841966i | −0.907069 | − | 0.420983i | \(-0.861685\pi\) | ||
0.907069 | − | 0.420983i | \(-0.138315\pi\) | |||||||
\(728\) | 4.71596e6i | 0.329793i | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 4.59776e6 | − | 1.74098e6i | 0.319330 | − | 0.120917i | ||||
\(731\) | −4.75429e7 | −3.29073 | ||||||||
\(732\) | − | 4.57968e6i | − | 0.315906i | ||||||
\(733\) | 3.87027e6i | 0.266061i | 0.991112 | + | 0.133031i | \(0.0424709\pi\) | ||||
−0.991112 | + | 0.133031i | \(0.957529\pi\) | |||||||
\(734\) | −3.67657e7 | −2.51885 | ||||||||
\(735\) | 2.90893e6 | + | 7.68219e6i | 0.198616 | + | 0.524526i | ||||
\(736\) | −4.90199e7 | −3.33563 | ||||||||
\(737\) | 7.00650e6i | 0.475152i | ||||||||
\(738\) | 7.36077e6i | 0.497487i | ||||||||
\(739\) | 1.26699e7 | 0.853416 | 0.426708 | − | 0.904390i | \(-0.359673\pi\) | ||||
0.426708 | + | 0.904390i | \(0.359673\pi\) | |||||||
\(740\) | 1.94982e7 | + | 5.14929e7i | 1.30893 | + | 3.45675i | ||||
\(741\) | 3.31832e6 | 0.222010 | ||||||||
\(742\) | − | 5.31468e6i | − | 0.354378i | ||||||
\(743\) | − | 1.07430e7i | − | 0.713929i | −0.934118 | − | 0.356965i | \(-0.883812\pi\) | ||
0.934118 | − | 0.356965i | \(-0.116188\pi\) | |||||||
\(744\) | −3.97124e6 | −0.263023 | ||||||||
\(745\) | −3.23127e6 | + | 1.22355e6i | −0.213296 | + | 0.0807664i | ||||
\(746\) | 3.99030e7 | 2.62517 | ||||||||
\(747\) | 631659.i | 0.0414173i | ||||||||
\(748\) | − | 2.15458e7i | − | 1.40802i | ||||||
\(749\) | −1.15508e6 | −0.0752329 | ||||||||
\(750\) | 7.64367e6 | − | 1.45091e7i | 0.496191 | − | 0.941859i | ||||
\(751\) | −1.60278e7 | −1.03699 | −0.518493 | − | 0.855082i | \(-0.673507\pi\) | ||||
−0.518493 | + | 0.855082i | \(0.673507\pi\) | |||||||
\(752\) | − | 2.24433e7i | − | 1.44724i | ||||||
\(753\) | − | 1.60589e7i | − | 1.03211i | ||||||
\(754\) | 4.38141e6 | 0.280663 | ||||||||
\(755\) | 1.34242e7 | − | 5.08318e6i | 0.857078 | − | 0.324540i | ||||
\(756\) | 1.22623e6 | 0.0780313 | ||||||||
\(757\) | 2.27246e7i | 1.44131i | 0.693294 | + | 0.720654i | \(0.256159\pi\) | ||||
−0.693294 | + | 0.720654i | \(0.743841\pi\) | |||||||
\(758\) | 3.86451e7i | 2.44299i | ||||||||
\(759\) | −5.20749e6 | −0.328114 | ||||||||
\(760\) | 7.40124e6 | + | 1.95459e7i | 0.464804 | + | 1.22750i | ||||
\(761\) | 1.62869e7 | 1.01948 | 0.509738 | − | 0.860330i | \(-0.329742\pi\) | ||||
0.509738 | + | 0.860330i | \(0.329742\pi\) | |||||||
\(762\) | − | 2.41155e7i | − | 1.50456i | ||||||
\(763\) | 5.11784e6i | 0.318255i | ||||||||
\(764\) | 6.16797e7 | 3.82304 | ||||||||
\(765\) | 3.71786e6 | + | 9.81850e6i | 0.229689 | + | 0.606585i | ||||
\(766\) | 8.23568e6 | 0.507139 | ||||||||
\(767\) | 9.55081e6i | 0.586208i | ||||||||
\(768\) | 1.03333e7i | 0.632171i | ||||||||
\(769\) | −8.82491e6 | −0.538139 | −0.269069 | − | 0.963121i | \(-0.586716\pi\) | ||||
−0.269069 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(770\) | −1.44519e6 | + | 547232.i | −0.0878409 | + | 0.0332617i | ||||
\(771\) | −8.01966e6 | −0.485870 | ||||||||
\(772\) | − | 4.44432e7i | − | 2.68387i | ||||||
\(773\) | 2.36592e7i | 1.42413i | 0.702111 | + | 0.712067i | \(0.252241\pi\) | ||||
−0.702111 | + | 0.712067i | \(0.747759\pi\) | |||||||
\(774\) | −1.73240e7 | −1.03943 | ||||||||
\(775\) | −2.21090e6 | + | 1.95461e6i | −0.132225 | + | 0.116897i | ||||
\(776\) | −6.85872e6 | −0.408873 | ||||||||
\(777\) | 2.52822e6i | 0.150232i | ||||||||
\(778\) | − | 4.93411e7i | − | 2.92254i | ||||||
\(779\) | −6.97101e6 | −0.411578 | ||||||||
\(780\) | −1.66505e7 | + | 6.30485e6i | −0.979920 | + | 0.371055i | ||||
\(781\) | 4.64187e6 | 0.272311 | ||||||||
\(782\) | − | 1.15649e8i | − | 6.76276i | ||||||
\(783\) | − | 664543.i | − | 0.0387363i | ||||||
\(784\) | 3.94517e7 | 2.29232 | ||||||||
\(785\) | 2.29740e6 | + | 6.06722e6i | 0.133065 | + | 0.351411i | ||||
\(786\) | 1.02801e7 | 0.593529 | ||||||||
\(787\) | − | 1.96332e7i | − | 1.12994i | −0.825112 | − | 0.564969i | \(-0.808888\pi\) | ||
0.825112 | − | 0.564969i | \(-0.191112\pi\) | |||||||
\(788\) | − | 2.13922e7i | − | 1.22727i | ||||||
\(789\) | 1.15070e7 | 0.658066 | ||||||||
\(790\) | 347601. | + | 917980.i | 0.0198159 | + | 0.0523318i | ||||
\(791\) | −802420. | −0.0455995 | ||||||||
\(792\) | − | 4.57963e6i | − | 0.259429i | ||||||
\(793\) | 3.05321e6i | 0.172414i | ||||||||
\(794\) | −2.53339e7 | −1.42610 | ||||||||
\(795\) | 1.09456e7 | − | 4.14464e6i | 0.614217 | − | 0.232578i | ||||
\(796\) | 6.47885e7 | 3.62423 | ||||||||
\(797\) | 2.52639e7i | 1.40882i | 0.709795 | + | 0.704408i | \(0.248788\pi\) | ||||
−0.709795 | + | 0.704408i | \(0.751212\pi\) | |||||||
\(798\) | 1.64520e6i | 0.0914557i | ||||||||
\(799\) | 2.15360e7 | 1.19343 | ||||||||
\(800\) | −2.12182e7 | − | 2.40003e7i | −1.17215 | − | 1.32584i | ||||
\(801\) | −6.72940e6 | −0.370591 | ||||||||
\(802\) | − | 2.88147e6i | − | 0.158189i | ||||||
\(803\) | − | 1.02022e6i | − | 0.0558348i | ||||||
\(804\) | −4.00225e7 | −2.18355 | ||||||||
\(805\) | −5.47558e6 | + | 2.07337e6i | −0.297811 | + | 0.112769i | ||||
\(806\) | 4.53880e6 | 0.246096 | ||||||||
\(807\) | 4.08853e6i | 0.220995i | ||||||||
\(808\) | − | 8.96119e6i | − | 0.482878i | ||||||
\(809\) | 1.60088e6 | 0.0859978 | 0.0429989 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429989 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(810\) | 1.35474e6 | + | 3.57774e6i | 0.0725510 | + | 0.191600i | ||||
\(811\) | −1.70463e7 | −0.910079 | −0.455040 | − | 0.890471i | \(-0.650375\pi\) | ||||
−0.455040 | + | 0.890471i | \(0.650375\pi\) | |||||||
\(812\) | 1.53335e6i | 0.0816115i | ||||||||
\(813\) | 1.82502e7i | 0.968369i | ||||||||
\(814\) | 1.61870e7 | 0.856260 | ||||||||
\(815\) | −6.37663e6 | − | 1.68400e7i | −0.336277 | − | 0.888074i | ||||
\(816\) | 5.04227e7 | 2.65094 | ||||||||
\(817\) | − | 1.64067e7i | − | 0.859937i | ||||||
\(818\) | − | 5.87425e6i | − | 0.306951i | ||||||
\(819\) | −817513. | −0.0425878 | ||||||||
\(820\) | 3.49787e7 | − | 1.32450e7i | 1.81664 | − | 0.687887i | ||||
\(821\) | 1.11036e7 | 0.574919 | 0.287459 | − | 0.957793i | \(-0.407189\pi\) | ||||
0.287459 | + | 0.957793i | \(0.407189\pi\) | |||||||
\(822\) | − | 1.40722e7i | − | 0.726413i | ||||||
\(823\) | 1.15634e7i | 0.595097i | 0.954707 | + | 0.297548i | \(0.0961690\pi\) | ||||
−0.954707 | + | 0.297548i | \(0.903831\pi\) | |||||||
\(824\) | −5.97355e7 | −3.06488 | ||||||||
\(825\) | −2.25405e6 | − | 2.54961e6i | −0.115300 | − | 0.130418i | ||||
\(826\) | −4.73522e6 | −0.241485 | ||||||||
\(827\) | 3.02353e7i | 1.53727i | 0.639686 | + | 0.768636i | \(0.279064\pi\) | ||||
−0.639686 | + | 0.768636i | \(0.720936\pi\) | |||||||
\(828\) | − | 2.97462e7i | − | 1.50784i | ||||||
\(829\) | 1.68978e7 | 0.853974 | 0.426987 | − | 0.904258i | \(-0.359575\pi\) | ||||
0.426987 | + | 0.904258i | \(0.359575\pi\) | |||||||
\(830\) | 4.25242e6 | − | 1.61022e6i | 0.214260 | − | 0.0811314i | ||||
\(831\) | 1.14874e7 | 0.577060 | ||||||||
\(832\) | 1.36412e7i | 0.683196i | ||||||||
\(833\) | 3.78569e7i | 1.89031i | ||||||||
\(834\) | −1.06314e7 | −0.529270 | ||||||||
\(835\) | 8.61839e6 | + | 2.27603e7i | 0.427770 | + | 1.12970i | ||||
\(836\) | 7.43529e6 | 0.367944 | ||||||||
\(837\) | − | 688415.i | − | 0.0339654i | ||||||
\(838\) | 7.37454e6i | 0.362764i | ||||||||
\(839\) | 6.03413e6 | 0.295944 | 0.147972 | − | 0.988992i | \(-0.452725\pi\) | ||||
0.147972 | + | 0.988992i | \(0.452725\pi\) | |||||||
\(840\) | −1.82339e6 | − | 4.81540e6i | −0.0891624 | − | 0.235469i | ||||
\(841\) | −1.96802e7 | −0.959486 | ||||||||
\(842\) | − | 4.76434e7i | − | 2.31592i | ||||||
\(843\) | 9.19650e6i | 0.445711i | ||||||||
\(844\) | −3.73345e6 | −0.180407 | ||||||||
\(845\) | −8.31026e6 | + | 3.14675e6i | −0.400380 | + | 0.151607i | ||||
\(846\) | 7.84744e6 | 0.376966 | ||||||||
\(847\) | 320679.i | 0.0153590i | ||||||||
\(848\) | − | 5.62108e7i | − | 2.68429i | ||||||
\(849\) | 678053. | 0.0322845 | ||||||||
\(850\) | 5.66221e7 | − | 5.00583e7i | 2.68806 | − | 2.37645i | ||||
\(851\) | 6.13300e7 | 2.90301 | ||||||||
\(852\) | 2.65152e7i | 1.25140i | ||||||||
\(853\) | − | 2.44547e7i | − | 1.15077i | −0.817882 | − | 0.575386i | \(-0.804852\pi\) | ||
0.817882 | − | 0.575386i | \(-0.195148\pi\) | |||||||
\(854\) | −1.51376e6 | −0.0710250 | ||||||||
\(855\) | −3.38829e6 | + | 1.28301e6i | −0.158513 | + | 0.0600224i | ||||
\(856\) | −2.46418e7 | −1.14945 | ||||||||
\(857\) | − | 9.19253e6i | − | 0.427546i | −0.976883 | − | 0.213773i | \(-0.931425\pi\) | ||
0.976883 | − | 0.213773i | \(-0.0685753\pi\) | |||||||
\(858\) | 5.23415e6i | 0.242733i | ||||||||
\(859\) | 1.84087e7 | 0.851219 | 0.425610 | − | 0.904907i | \(-0.360060\pi\) | ||||
0.425610 | + | 0.904907i | \(0.360060\pi\) | |||||||
\(860\) | 3.11729e7 | + | 8.23246e7i | 1.43725 | + | 3.79563i | ||||
\(861\) | 1.71740e6 | 0.0789521 | ||||||||
\(862\) | − | 6.42999e7i | − | 2.94742i | ||||||
\(863\) | − | 8.55693e6i | − | 0.391103i | −0.980693 | − | 0.195551i | \(-0.937350\pi\) | ||
0.980693 | − | 0.195551i | \(-0.0626497\pi\) | |||||||
\(864\) | 7.47308e6 | 0.340577 | ||||||||
\(865\) | −1.38635e7 | − | 3.66121e7i | −0.629989 | − | 1.66374i | ||||
\(866\) | 3.07202e7 | 1.39197 | ||||||||
\(867\) | 3.56056e7i | 1.60868i | ||||||||
\(868\) | 1.58843e6i | 0.0715598i | ||||||||
\(869\) | 203695. | 0.00915021 | ||||||||
\(870\) | −4.47380e6 | + | 1.69404e6i | −0.200391 | + | 0.0758798i | ||||
\(871\) | 2.66824e7 | 1.19174 | ||||||||
\(872\) | 1.09181e8i | 4.86246i | ||||||||
\(873\) | − | 1.18896e6i | − | 0.0527998i | ||||||
\(874\) | 3.99095e7 | 1.76725 | ||||||||
\(875\) | −3.38523e6 | − | 1.78341e6i | −0.149475 | − | 0.0787464i | ||||
\(876\) | 5.82769e6 | 0.256588 | ||||||||
\(877\) | 3.62307e7i | 1.59066i | 0.606177 | + | 0.795330i | \(0.292702\pi\) | ||||
−0.606177 | + | 0.795330i | \(0.707298\pi\) | |||||||
\(878\) | − | 6.15533e7i | − | 2.69473i | ||||||
\(879\) | −5.95255e6 | −0.259855 | ||||||||
\(880\) | −1.52850e7 | + | 5.78781e6i | −0.665365 | + | 0.251946i | ||||
\(881\) | −2.54635e7 | −1.10530 | −0.552649 | − | 0.833414i | \(-0.686383\pi\) | ||||
−0.552649 | + | 0.833414i | \(0.686383\pi\) | |||||||
\(882\) | 1.37945e7i | 0.597085i | ||||||||
\(883\) | 1.25573e6i | 0.0541995i | 0.999633 | + | 0.0270998i | \(0.00862718\pi\) | ||||
−0.999633 | + | 0.0270998i | \(0.991373\pi\) | |||||||
\(884\) | −8.20515e7 | −3.53147 | ||||||||
\(885\) | −3.69275e6 | − | 9.75220e6i | −0.158486 | − | 0.418547i | ||||
\(886\) | −4.78090e7 | −2.04609 | ||||||||
\(887\) | − | 2.38712e7i | − | 1.01874i | −0.860547 | − | 0.509371i | \(-0.829878\pi\) | ||
0.860547 | − | 0.509371i | \(-0.170122\pi\) | |||||||
\(888\) | 5.39356e7i | 2.29532i | ||||||||
\(889\) | −5.62659e6 | −0.238776 | ||||||||
\(890\) | 1.71545e7 | + | 4.53033e7i | 0.725943 | + | 1.91714i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 3.63731e7i | 1.53062i | ||||||||
\(893\) | 7.43192e6i | 0.311869i | ||||||||
\(894\) | −5.80224e6 | −0.242802 | ||||||||
\(895\) | 1.19297e7 | − | 4.51729e6i | 0.497820 | − | 0.188504i | ||||
\(896\) | 421709. | 0.0175486 | ||||||||
\(897\) | 1.98314e7i | 0.822947i | ||||||||
\(898\) | 6.90500e7i | 2.85741i | ||||||||
\(899\) | 860832. | 0.0355238 | ||||||||
\(900\) | 1.45639e7 | − | 1.28756e7i | 0.599336 | − | 0.529860i | ||||
\(901\) | 5.39385e7 | 2.21354 | ||||||||
\(902\) | − | 1.09957e7i | − | 0.449994i | ||||||
\(903\) | 4.04201e6i | 0.164960i | ||||||||
\(904\) | −1.71184e7 | −0.696692 | ||||||||
\(905\) | −2.67459e7 | + | 1.01276e7i | −1.08552 | + | 0.411040i | ||||
\(906\) | 2.41052e7 | 0.975640 | ||||||||
\(907\) | − | 1.51874e7i | − | 0.613007i | −0.951870 | − | 0.306504i | \(-0.900841\pi\) | ||
0.951870 | − | 0.306504i | \(-0.0991591\pi\) | |||||||
\(908\) | − | 5.89644e7i | − | 2.37342i | ||||||
\(909\) | 1.55342e6 | 0.0623563 | ||||||||
\(910\) | 2.08399e6 | + | 5.50361e6i | 0.0834242 | + | 0.220315i | ||||
\(911\) | 2.87742e6 | 0.114870 | 0.0574352 | − | 0.998349i | \(-0.481708\pi\) | ||||
0.0574352 | + | 0.998349i | \(0.481708\pi\) | |||||||
\(912\) | 1.74005e7i | 0.692746i | ||||||||
\(913\) | − | 943590.i | − | 0.0374633i | ||||||
\(914\) | −6.64876e7 | −2.63254 | ||||||||
\(915\) | −1.18050e6 | − | 3.11759e6i | −0.0466137 | − | 0.123102i | ||||
\(916\) | 4.45549e7 | 1.75451 | ||||||||
\(917\) | − | 2.39854e6i | − | 0.0941941i | ||||||
\(918\) | 1.76306e7i | 0.690495i | ||||||||
\(919\) | −3.83454e7 | −1.49770 | −0.748849 | − | 0.662741i | \(-0.769393\pi\) | ||||
−0.748849 | + | 0.662741i | \(0.769393\pi\) | |||||||
\(920\) | −1.16813e8 | + | 4.42322e7i | −4.55010 | + | 1.72293i | ||||
\(921\) | 8.66096e6 | 0.336447 | ||||||||
\(922\) | 5.60059e7i | 2.16973i | ||||||||
\(923\) | − | 1.76773e7i | − | 0.682987i | ||||||
\(924\) | −1.83178e6 | −0.0705820 | ||||||||
\(925\) | 2.65466e7 | + | 3.00274e7i | 1.02013 | + | 1.15389i | ||||
\(926\) | −7.44629e7 | −2.85373 | ||||||||
\(927\) | − | 1.03552e7i | − | 0.395783i | ||||||
\(928\) | 9.34474e6i | 0.356203i | ||||||||
\(929\) | −3.31484e7 | −1.26015 | −0.630077 | − | 0.776533i | \(-0.716977\pi\) | ||||
−0.630077 | + | 0.776533i | \(0.716977\pi\) | |||||||
\(930\) | −4.63451e6 | + | 1.75490e6i | −0.175710 | + | 0.0665341i | ||||
\(931\) | −1.30641e7 | −0.493976 | ||||||||
\(932\) | 2.29365e7i | 0.864943i | ||||||||
\(933\) | − | 5.80722e6i | − | 0.218406i | ||||||
\(934\) | −5.33647e7 | −2.00164 | ||||||||
\(935\) | −5.55384e6 | − | 1.46671e7i | −0.207761 | − | 0.548677i | ||||
\(936\) | −1.74403e7 | −0.650677 | ||||||||
\(937\) | 2.93312e7i | 1.09139i | 0.837984 | + | 0.545695i | \(0.183734\pi\) | ||||
−0.837984 | + | 0.545695i | \(0.816266\pi\) | |||||||
\(938\) | 1.32289e7i | 0.490928i | ||||||||
\(939\) | 2.89281e7 | 1.07067 | ||||||||
\(940\) | −1.41207e7 | − | 3.72914e7i | −0.521239 | − | 1.37654i | ||||
\(941\) | −9.43943e6 | −0.347513 | −0.173757 | − | 0.984789i | \(-0.555591\pi\) | ||||
−0.173757 | + | 0.984789i | \(0.555591\pi\) | |||||||
\(942\) | 1.08946e7i | 0.400023i | ||||||||
\(943\) | − | 4.16610e7i | − | 1.52563i | ||||||
\(944\) | −5.00821e7 | −1.82917 | ||||||||
\(945\) | 834751. | − | 316086.i | 0.0304073 | − | 0.0115140i | ||||
\(946\) | 2.58791e7 | 0.940202 | ||||||||
\(947\) | 2.37783e7i | 0.861601i | 0.902447 | + | 0.430801i | \(0.141769\pi\) | ||||
−0.902447 | + | 0.430801i | \(0.858231\pi\) | |||||||
\(948\) | 1.16355e6i | 0.0420496i | ||||||||
\(949\) | −3.88524e6 | −0.140040 | ||||||||
\(950\) | 1.72748e7 | + | 1.95399e7i | 0.621016 | + | 0.702445i | ||||
\(951\) | 1.43722e7 | 0.515315 | ||||||||
\(952\) | − | 2.37297e7i | − | 0.848592i | ||||||
\(953\) | 2.31442e7i | 0.825488i | 0.910847 | + | 0.412744i | \(0.135429\pi\) | ||||
−0.910847 | + | 0.412744i | \(0.864571\pi\) | |||||||
\(954\) | 1.96545e7 | 0.699183 | ||||||||
\(955\) | 4.19881e7 | − | 1.58991e7i | 1.48976 | − | 0.564112i | ||||
\(956\) | 2.48869e7 | 0.880696 | ||||||||
\(957\) | 992712.i | 0.0350383i | ||||||||
\(958\) | − | 7.45938e6i | − | 0.262597i | ||||||
\(959\) | −3.28331e6 | −0.115283 | ||||||||
\(960\) | −5.27428e6 | − | 1.39289e7i | −0.184708 | − | 0.487795i | ||||
\(961\) | −2.77374e7 | −0.968851 | ||||||||
\(962\) | − | 6.16440e7i | − | 2.14760i | ||||||
\(963\) | − | 4.27167e6i | − | 0.148433i | ||||||
\(964\) | 5.22158e7 | 1.80971 | ||||||||
\(965\) | −1.14561e7 | − | 3.02544e7i | −0.396021 | − | 1.04585i | ||||
\(966\) | −9.83223e6 | −0.339008 | ||||||||
\(967\) | 7.71333e6i | 0.265262i | 0.991165 | + | 0.132631i | \(0.0423426\pi\) | ||||
−0.991165 | + | 0.132631i | \(0.957657\pi\) | |||||||
\(968\) | 6.84118e6i | 0.234662i | ||||||||
\(969\) | −1.66971e7 | −0.571256 | ||||||||
\(970\) | −8.00426e6 | + | 3.03088e6i | −0.273144 | + | 0.103428i | ||||
\(971\) | −4.66559e7 | −1.58803 | −0.794014 | − | 0.607899i | \(-0.792012\pi\) | ||||
−0.794014 | + | 0.607899i | \(0.792012\pi\) | |||||||
\(972\) | 4.53480e6i | 0.153955i | ||||||||
\(973\) | 2.48051e6i | 0.0839960i | ||||||||
\(974\) | 9.81837e7 | 3.31621 | ||||||||
\(975\) | −9.70952e6 | + | 8.58398e6i | −0.327104 | + | 0.289186i | ||||
\(976\) | −1.60103e7 | −0.537990 | ||||||||
\(977\) | 1.28308e7i | 0.430050i | 0.976609 | + | 0.215025i | \(0.0689833\pi\) | ||||
−0.976609 | + | 0.215025i | \(0.931017\pi\) | |||||||
\(978\) | − | 3.02389e7i | − | 1.01092i | ||||||
\(979\) | 1.00526e7 | 0.335212 | ||||||||
\(980\) | 6.55524e7 | − | 2.48220e7i | 2.18034 | − | 0.825603i | ||||
\(981\) | −1.89266e7 | −0.627913 | ||||||||
\(982\) | 2.12601e7i | 0.703537i | ||||||||
\(983\) | − | 7.06277e6i | − | 0.233126i | −0.993183 | − | 0.116563i | \(-0.962812\pi\) | ||
0.993183 | − | 0.116563i | \(-0.0371878\pi\) | |||||||
\(984\) | 3.66380e7 | 1.20627 | ||||||||
\(985\) | −5.51426e6 | − | 1.45626e7i | −0.181091 | − | 0.478243i | ||||
\(986\) | −2.20463e7 | −0.722176 | ||||||||
\(987\) | − | 1.83095e6i | − | 0.0598251i | ||||||
\(988\) | − | 2.83154e7i | − | 0.922847i | ||||||
\(989\) | 9.80518e7 | 3.18761 | ||||||||
\(990\) | −2.02375e6 | − | 5.34452e6i | −0.0656249 | − | 0.173309i | ||||
\(991\) | 1.51956e7 | 0.491512 | 0.245756 | − | 0.969332i | \(-0.420964\pi\) | ||||
0.245756 | + | 0.969332i | \(0.420964\pi\) | |||||||
\(992\) | 9.68043e6i | 0.312331i | ||||||||
\(993\) | − | 1.70312e7i | − | 0.548115i | ||||||
\(994\) | 8.76428e6 | 0.281352 | ||||||||
\(995\) | 4.41044e7 | − | 1.67005e7i | 1.41229 | − | 0.534776i | ||||
\(996\) | 5.38997e6 | 0.172162 | ||||||||
\(997\) | 3.19469e7i | 1.01787i | 0.860806 | + | 0.508934i | \(0.169960\pi\) | ||||
−0.860806 | + | 0.508934i | \(0.830040\pi\) | |||||||
\(998\) | − | 2.39144e7i | − | 0.760035i | ||||||
\(999\) | −9.34975e6 | −0.296405 |
(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 | 165.6.c.b.34.2 | ✓ | 26 | |
5.2 | odd | 4 | 825.6.a.v.1.13 | 13 | |||
5.3 | odd | 4 | 825.6.a.y.1.1 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.25 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.2 | ✓ | 26 | 1.1 | even | 1 | trivial | |
165.6.c.b.34.25 | yes | 26 | 5.4 | even | 2 | inner | |
825.6.a.v.1.13 | 13 | 5.2 | odd | 4 | |||
825.6.a.y.1.1 | 13 | 5.3 | odd | 4 |