Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,6,Mod(21,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, 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("40.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.d (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: | \(6.41535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.14 | ||
Root | \(3.46430 + 1.99965i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 40.21 |
Dual form | 40.6.d.a.21.13 |
$q$-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 \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46465 | + | 5.46395i | 0.258917 | + | 0.965900i | ||||
\(3\) | − | 29.2080i | − | 1.87370i | −0.349736 | − | 0.936848i | \(-0.613729\pi\) | ||
0.349736 | − | 0.936848i | \(-0.386271\pi\) | |||||||
\(4\) | −27.7096 | + | 16.0056i | −0.865924 | + | 0.500175i | ||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 159.591 | − | 42.7797i | 1.80980 | − | 0.485132i | ||||
\(7\) | −168.173 | −1.29722 | −0.648608 | − | 0.761123i | \(-0.724648\pi\) | ||||
−0.648608 | + | 0.761123i | \(0.724648\pi\) | |||||||
\(8\) | −128.039 | − | 127.961i | −0.707322 | − | 0.706892i | ||||
\(9\) | −610.110 | −2.51074 | ||||||||
\(10\) | −136.599 | + | 36.6164i | −0.431963 | + | 0.115791i | ||||
\(11\) | − | 514.493i | − | 1.28203i | −0.767529 | − | 0.641014i | \(-0.778514\pi\) | ||
0.767529 | − | 0.641014i | \(-0.221486\pi\) | |||||||
\(12\) | 467.493 | + | 809.342i | 0.937177 | + | 1.62248i | ||||
\(13\) | 491.622i | 0.806813i | 0.915021 | + | 0.403406i | \(0.132174\pi\) | ||||
−0.915021 | + | 0.403406i | \(0.867826\pi\) | |||||||
\(14\) | −246.316 | − | 918.892i | −0.335871 | − | 1.25298i | ||||
\(15\) | 730.201 | 0.837943 | ||||||||
\(16\) | 511.641 | − | 887.017i | 0.499649 | − | 0.866228i | ||||
\(17\) | 183.094 | 0.153657 | 0.0768284 | − | 0.997044i | \(-0.475521\pi\) | ||||
0.0768284 | + | 0.997044i | \(0.475521\pi\) | |||||||
\(18\) | −893.600 | − | 3333.61i | −0.650073 | − | 2.42512i | ||||
\(19\) | − | 1250.96i | − | 0.794988i | −0.917605 | − | 0.397494i | \(-0.869880\pi\) | ||
0.917605 | − | 0.397494i | \(-0.130120\pi\) | |||||||
\(20\) | −400.140 | − | 692.739i | −0.223685 | − | 0.387253i | ||||
\(21\) | 4912.01i | 2.43059i | ||||||||
\(22\) | 2811.16 | − | 753.554i | 1.23831 | − | 0.331939i | ||||
\(23\) | −423.498 | −0.166929 | −0.0834646 | − | 0.996511i | \(-0.526599\pi\) | ||||
−0.0834646 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(24\) | −3737.49 | + | 3739.76i | −1.32450 | + | 1.32531i | ||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | −2686.20 | + | 720.056i | −0.779300 | + | 0.208897i | ||||
\(27\) | 10722.5i | 2.83067i | ||||||||
\(28\) | 4660.01 | − | 2691.72i | 1.12329 | − | 0.648835i | ||||
\(29\) | − | 3463.40i | − | 0.764729i | −0.924012 | − | 0.382364i | \(-0.875110\pi\) | ||
0.924012 | − | 0.382364i | \(-0.124890\pi\) | |||||||
\(30\) | 1069.49 | + | 3989.78i | 0.216957 | + | 0.809368i | ||||
\(31\) | 2343.92 | 0.438065 | 0.219032 | − | 0.975718i | \(-0.429710\pi\) | ||||
0.219032 | + | 0.975718i | \(0.429710\pi\) | |||||||
\(32\) | 5596.00 | + | 1496.41i | 0.966057 | + | 0.258330i | ||||
\(33\) | −15027.3 | −2.40213 | ||||||||
\(34\) | 268.170 | + | 1000.42i | 0.0397843 | + | 0.148417i | ||||
\(35\) | − | 4204.33i | − | 0.580132i | ||||||
\(36\) | 16905.9 | − | 9765.18i | 2.17411 | − | 1.25581i | ||||
\(37\) | − | 7388.25i | − | 0.887232i | −0.896217 | − | 0.443616i | \(-0.853695\pi\) | ||
0.896217 | − | 0.443616i | \(-0.146305\pi\) | |||||||
\(38\) | 6835.20 | − | 1832.23i | 0.767879 | − | 0.205836i | ||||
\(39\) | 14359.3 | 1.51172 | ||||||||
\(40\) | 3199.03 | − | 3200.97i | 0.316132 | − | 0.316324i | ||||
\(41\) | 4240.39 | 0.393954 | 0.196977 | − | 0.980408i | \(-0.436888\pi\) | ||||
0.196977 | + | 0.980408i | \(0.436888\pi\) | |||||||
\(42\) | −26839.0 | + | 7194.41i | −2.34770 | + | 0.629320i | ||||
\(43\) | 15159.4i | 1.25029i | 0.780510 | + | 0.625143i | \(0.214960\pi\) | ||||
−0.780510 | + | 0.625143i | \(0.785040\pi\) | |||||||
\(44\) | 8234.77 | + | 14256.4i | 0.641239 | + | 1.11014i | ||||
\(45\) | − | 15252.7i | − | 1.12284i | ||||||
\(46\) | −620.279 | − | 2313.98i | −0.0432208 | − | 0.161237i | ||||
\(47\) | −15357.8 | −1.01411 | −0.507055 | − | 0.861914i | \(-0.669266\pi\) | ||||
−0.507055 | + | 0.861914i | \(0.669266\pi\) | |||||||
\(48\) | −25908.0 | − | 14944.0i | −1.62305 | − | 0.936191i | ||||
\(49\) | 11475.3 | 0.682768 | ||||||||
\(50\) | −915.409 | − | 3414.97i | −0.0517834 | − | 0.193180i | ||||
\(51\) | − | 5347.82i | − | 0.287906i | ||||||
\(52\) | −7868.71 | − | 13622.6i | −0.403548 | − | 0.698639i | ||||
\(53\) | 11393.9i | 0.557162i | 0.960413 | + | 0.278581i | \(0.0898640\pi\) | ||||
−0.960413 | + | 0.278581i | \(0.910136\pi\) | |||||||
\(54\) | −58587.5 | + | 15704.8i | −2.73414 | + | 0.732907i | ||||
\(55\) | 12862.3 | 0.573340 | ||||||||
\(56\) | 21532.7 | + | 21519.7i | 0.917548 | + | 0.916991i | ||||
\(57\) | −36538.2 | −1.48957 | ||||||||
\(58\) | 18923.8 | − | 5072.68i | 0.738651 | − | 0.198001i | ||||
\(59\) | − | 11978.0i | − | 0.447974i | −0.974592 | − | 0.223987i | \(-0.928093\pi\) | ||
0.974592 | − | 0.223987i | \(-0.0719074\pi\) | |||||||
\(60\) | −20233.6 | + | 11687.3i | −0.725595 | + | 0.419118i | ||||
\(61\) | − | 41454.0i | − | 1.42640i | −0.700960 | − | 0.713200i | \(-0.747245\pi\) | ||
0.700960 | − | 0.713200i | \(-0.252755\pi\) | |||||||
\(62\) | 3433.03 | + | 12807.1i | 0.113422 | + | 0.423127i | ||||
\(63\) | 102604. | 3.25697 | ||||||||
\(64\) | 19.9046 | + | 32768.0i | 0.000607441 | + | 1.00000i | ||||
\(65\) | −12290.5 | −0.360818 | ||||||||
\(66\) | −22009.8 | − | 82108.6i | −0.621952 | − | 2.32022i | ||||
\(67\) | − | 66524.9i | − | 1.81049i | −0.424885 | − | 0.905247i | \(-0.639685\pi\) | ||
0.424885 | − | 0.905247i | \(-0.360315\pi\) | |||||||
\(68\) | −5073.46 | + | 2930.53i | −0.133055 | + | 0.0768553i | ||||
\(69\) | 12369.6i | 0.312775i | ||||||||
\(70\) | 22972.3 | − | 6157.90i | 0.560350 | − | 0.150206i | ||||
\(71\) | −26214.5 | −0.617157 | −0.308579 | − | 0.951199i | \(-0.599853\pi\) | ||||
−0.308579 | + | 0.951199i | \(0.599853\pi\) | |||||||
\(72\) | 78117.7 | + | 78070.3i | 1.77590 | + | 1.77482i | ||||
\(73\) | −86291.9 | −1.89523 | −0.947617 | − | 0.319409i | \(-0.896516\pi\) | ||||
−0.947617 | + | 0.319409i | \(0.896516\pi\) | |||||||
\(74\) | 40369.0 | − | 10821.2i | 0.856977 | − | 0.229719i | ||||
\(75\) | 18255.0i | 0.374739i | ||||||||
\(76\) | 20022.4 | + | 34663.7i | 0.397633 | + | 0.688399i | ||||
\(77\) | 86524.0i | 1.66307i | ||||||||
\(78\) | 21031.4 | + | 78458.6i | 0.391410 | + | 1.46017i | ||||
\(79\) | −19799.4 | −0.356931 | −0.178466 | − | 0.983946i | \(-0.557113\pi\) | ||||
−0.178466 | + | 0.983946i | \(0.557113\pi\) | |||||||
\(80\) | 22175.4 | + | 12791.0i | 0.387389 | + | 0.223450i | ||||
\(81\) | 164928. | 2.79307 | ||||||||
\(82\) | 6210.70 | + | 23169.3i | 0.102001 | + | 0.380520i | ||||
\(83\) | 8370.24i | 0.133365i | 0.997774 | + | 0.0666826i | \(0.0212415\pi\) | ||||
−0.997774 | + | 0.0666826i | \(0.978759\pi\) | |||||||
\(84\) | −78619.8 | − | 136110.i | −1.21572 | − | 2.10471i | ||||
\(85\) | 4577.35i | 0.0687174i | ||||||||
\(86\) | −82830.0 | + | 22203.2i | −1.20765 | + | 0.323720i | ||||
\(87\) | −101159. | −1.43287 | ||||||||
\(88\) | −65835.1 | + | 65875.1i | −0.906255 | + | 0.906806i | ||||
\(89\) | −3824.45 | −0.0511793 | −0.0255896 | − | 0.999673i | \(-0.508146\pi\) | ||||
−0.0255896 | + | 0.999673i | \(0.508146\pi\) | |||||||
\(90\) | 83340.2 | − | 22340.0i | 1.08455 | − | 0.290721i | ||||
\(91\) | − | 82677.7i | − | 1.04661i | ||||||
\(92\) | 11735.0 | − | 6778.35i | 0.144548 | − | 0.0834939i | ||||
\(93\) | − | 68461.3i | − | 0.820801i | ||||||
\(94\) | −22493.9 | − | 83914.4i | −0.262570 | − | 0.979528i | ||||
\(95\) | 31274.1 | 0.355529 | ||||||||
\(96\) | 43707.1 | − | 163448.i | 0.484032 | − | 1.81010i | ||||
\(97\) | 35158.5 | 0.379403 | 0.189702 | − | 0.981842i | \(-0.439248\pi\) | ||||
0.189702 | + | 0.981842i | \(0.439248\pi\) | |||||||
\(98\) | 16807.3 | + | 62700.4i | 0.176780 | + | 0.659486i | ||||
\(99\) | 313897.i | 3.21884i | ||||||||
\(100\) | 17318.5 | − | 10003.5i | 0.173185 | − | 0.100035i | ||||
\(101\) | 99536.3i | 0.970908i | 0.874262 | + | 0.485454i | \(0.161346\pi\) | ||||
−0.874262 | + | 0.485454i | \(0.838654\pi\) | |||||||
\(102\) | 29220.2 | − | 7832.71i | 0.278089 | − | 0.0745438i | ||||
\(103\) | 46921.2 | 0.435789 | 0.217895 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217895 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(104\) | 62908.5 | − | 62946.7i | 0.570329 | − | 0.570676i | ||||
\(105\) | −122800. | −1.08699 | ||||||||
\(106\) | −62255.5 | + | 16688.1i | −0.538162 | + | 0.144259i | ||||
\(107\) | 38381.3i | 0.324086i | 0.986784 | + | 0.162043i | \(0.0518083\pi\) | ||||
−0.986784 | + | 0.162043i | \(0.948192\pi\) | |||||||
\(108\) | −171621. | − | 297117.i | −1.41583 | − | 2.45114i | ||||
\(109\) | 14288.7i | 0.115193i | 0.998340 | + | 0.0575966i | \(0.0183437\pi\) | ||||
−0.998340 | + | 0.0575966i | \(0.981656\pi\) | |||||||
\(110\) | 18838.9 | + | 70279.1i | 0.148447 | + | 0.553789i | ||||
\(111\) | −215796. | −1.66240 | ||||||||
\(112\) | −86044.4 | + | 149173.i | −0.648153 | + | 1.12368i | ||||
\(113\) | 130552. | 0.961804 | 0.480902 | − | 0.876774i | \(-0.340309\pi\) | ||||
0.480902 | + | 0.876774i | \(0.340309\pi\) | |||||||
\(114\) | −53515.8 | − | 199643.i | −0.385674 | − | 1.43877i | ||||
\(115\) | − | 10587.5i | − | 0.0746530i | ||||||
\(116\) | 55433.8 | + | 95969.3i | 0.382498 | + | 0.662197i | ||||
\(117\) | − | 299943.i | − | 2.02570i | ||||||
\(118\) | 65447.1 | − | 17543.6i | 0.432698 | − | 0.115988i | ||||
\(119\) | −30791.5 | −0.199326 | ||||||||
\(120\) | −93494.1 | − | 93437.3i | −0.592695 | − | 0.592335i | ||||
\(121\) | −103652. | −0.643596 | ||||||||
\(122\) | 226503. | − | 60715.7i | 1.37776 | − | 0.369319i | ||||
\(123\) | − | 123853.i | − | 0.738151i | ||||||
\(124\) | −64949.0 | + | 37515.9i | −0.379331 | + | 0.219109i | ||||
\(125\) | − | 15625.0i | − | 0.0894427i | ||||||
\(126\) | 150280. | + | 560624.i | 0.843284 | + | 3.14591i | ||||
\(127\) | −327594. | −1.80230 | −0.901150 | − | 0.433508i | \(-0.857276\pi\) | ||||
−0.901150 | + | 0.433508i | \(0.857276\pi\) | |||||||
\(128\) | −179014. | + | 48102.6i | −0.965742 | + | 0.259504i | ||||
\(129\) | 442775. | 2.34266 | ||||||||
\(130\) | −18001.4 | − | 67155.0i | −0.0934218 | − | 0.348514i | ||||
\(131\) | − | 116999.i | − | 0.595669i | −0.954618 | − | 0.297834i | \(-0.903736\pi\) | ||
0.954618 | − | 0.297834i | \(-0.0962643\pi\) | |||||||
\(132\) | 416401. | − | 240522.i | 2.08006 | − | 1.20149i | ||||
\(133\) | 210379.i | 1.03127i | ||||||||
\(134\) | 363489. | − | 97436.0i | 1.74876 | − | 0.468768i | ||||
\(135\) | −268064. | −1.26591 | ||||||||
\(136\) | −23443.1 | − | 23428.9i | −0.108685 | − | 0.108619i | ||||
\(137\) | −74409.1 | −0.338707 | −0.169354 | − | 0.985555i | \(-0.554168\pi\) | ||||
−0.169354 | + | 0.985555i | \(0.554168\pi\) | |||||||
\(138\) | −67586.7 | + | 18117.1i | −0.302109 | + | 0.0809826i | ||||
\(139\) | − | 80434.5i | − | 0.353106i | −0.984291 | − | 0.176553i | \(-0.943505\pi\) | ||
0.984291 | − | 0.176553i | \(-0.0564947\pi\) | |||||||
\(140\) | 67292.9 | + | 116500.i | 0.290168 | + | 0.502351i | ||||
\(141\) | 448572.i | 1.90013i | ||||||||
\(142\) | −38395.2 | − | 143235.i | −0.159792 | − | 0.596112i | ||||
\(143\) | 252936. | 1.03436 | ||||||||
\(144\) | −312157. | + | 541178.i | −1.25449 | + | 2.17487i | ||||
\(145\) | 86585.0 | 0.341997 | ||||||||
\(146\) | −126388. | − | 471495.i | −0.490708 | − | 1.83061i | ||||
\(147\) | − | 335171.i | − | 1.27930i | ||||||
\(148\) | 118253. | + | 204725.i | 0.443771 | + | 0.768275i | ||||
\(149\) | 57917.4i | 0.213719i | 0.994274 | + | 0.106860i | \(0.0340795\pi\) | ||||
−0.994274 | + | 0.106860i | \(0.965920\pi\) | |||||||
\(150\) | −99744.6 | + | 26737.3i | −0.361961 | + | 0.0970263i | ||||
\(151\) | 450813. | 1.60899 | 0.804497 | − | 0.593957i | \(-0.202435\pi\) | ||||
0.804497 | + | 0.593957i | \(0.202435\pi\) | |||||||
\(152\) | −160075. | + | 160172.i | −0.561971 | + | 0.562312i | ||||
\(153\) | −111707. | −0.385792 | ||||||||
\(154\) | −472763. | + | 126728.i | −1.60636 | + | 0.430596i | ||||
\(155\) | 58598.0i | 0.195909i | ||||||||
\(156\) | −397890. | + | 229829.i | −1.30904 | + | 0.756126i | ||||
\(157\) | − | 72067.3i | − | 0.233340i | −0.993171 | − | 0.116670i | \(-0.962778\pi\) | ||
0.993171 | − | 0.116670i | \(-0.0372220\pi\) | |||||||
\(158\) | −28999.3 | − | 108183.i | −0.0924155 | − | 0.344760i | ||||
\(159\) | 332792. | 1.04395 | ||||||||
\(160\) | −37410.2 | + | 139900.i | −0.115529 | + | 0.432034i | ||||
\(161\) | 71221.2 | 0.216543 | ||||||||
\(162\) | 241563. | + | 901159.i | 0.723173 | + | 2.69783i | ||||
\(163\) | − | 471144.i | − | 1.38895i | −0.719519 | − | 0.694473i | \(-0.755638\pi\) | ||
0.719519 | − | 0.694473i | \(-0.244362\pi\) | |||||||
\(164\) | −117499. | + | 67870.0i | −0.341134 | + | 0.197046i | ||||
\(165\) | − | 375683.i | − | 1.07427i | ||||||
\(166\) | −45734.6 | + | 12259.5i | −0.128817 | + | 0.0345305i | ||||
\(167\) | 519164. | 1.44050 | 0.720250 | − | 0.693715i | \(-0.244027\pi\) | ||||
0.720250 | + | 0.693715i | \(0.244027\pi\) | |||||||
\(168\) | 628547. | − | 628929.i | 1.71816 | − | 1.71921i | ||||
\(169\) | 129601. | 0.349053 | ||||||||
\(170\) | −25010.4 | + | 6704.24i | −0.0663741 | + | 0.0177921i | ||||
\(171\) | 763225.i | 1.99601i | ||||||||
\(172\) | −242635. | − | 420059.i | −0.625363 | − | 1.08265i | ||||
\(173\) | 726898.i | 1.84654i | 0.384153 | + | 0.923269i | \(0.374494\pi\) | ||||
−0.384153 | + | 0.923269i | \(0.625506\pi\) | |||||||
\(174\) | −148163. | − | 552728.i | −0.370994 | − | 1.38401i | ||||
\(175\) | 105108. | 0.259443 | ||||||||
\(176\) | −456364. | − | 263236.i | −1.11053 | − | 0.640564i | ||||
\(177\) | −349853. | −0.839368 | ||||||||
\(178\) | −5601.50 | − | 20896.6i | −0.0132512 | − | 0.0494340i | ||||
\(179\) | − | 327278.i | − | 0.763457i | −0.924274 | − | 0.381729i | \(-0.875329\pi\) | ||
0.924274 | − | 0.381729i | \(-0.124671\pi\) | |||||||
\(180\) | 244129. | + | 422647.i | 0.561615 | + | 0.972291i | ||||
\(181\) | − | 651584.i | − | 1.47834i | −0.673519 | − | 0.739170i | \(-0.735218\pi\) | ||
0.673519 | − | 0.739170i | \(-0.264782\pi\) | |||||||
\(182\) | 451747. | − | 121094.i | 1.01092 | − | 0.270985i | ||||
\(183\) | −1.21079e6 | −2.67264 | ||||||||
\(184\) | 54224.3 | + | 54191.3i | 0.118073 | + | 0.118001i | ||||
\(185\) | 184706. | 0.396782 | ||||||||
\(186\) | 374069. | − | 100272.i | 0.792811 | − | 0.212519i | ||||
\(187\) | − | 94200.5i | − | 0.196992i | ||||||
\(188\) | 425558. | − | 245811.i | 0.878142 | − | 0.507232i | ||||
\(189\) | − | 1.80325e6i | − | 3.67198i | ||||||
\(190\) | 45805.7 | + | 170880.i | 0.0920526 | + | 0.343406i | ||||
\(191\) | −427987. | −0.848882 | −0.424441 | − | 0.905456i | \(-0.639529\pi\) | ||||
−0.424441 | + | 0.905456i | \(0.639529\pi\) | |||||||
\(192\) | 957089. | − | 581.375i | 1.87370 | − | 0.00113816i | ||||
\(193\) | 560696. | 1.08351 | 0.541757 | − | 0.840535i | \(-0.317759\pi\) | ||||
0.541757 | + | 0.840535i | \(0.317759\pi\) | |||||||
\(194\) | 51495.1 | + | 192104.i | 0.0982339 | + | 0.366465i | ||||
\(195\) | 358983.i | 0.676063i | ||||||||
\(196\) | −317975. | + | 183669.i | −0.591226 | + | 0.341504i | ||||
\(197\) | 268824.i | 0.493518i | 0.969077 | + | 0.246759i | \(0.0793656\pi\) | ||||
−0.969077 | + | 0.246759i | \(0.920634\pi\) | |||||||
\(198\) | −1.71512e6 | + | 459751.i | −3.10907 | + | 0.833411i | ||||
\(199\) | 512715. | 0.917789 | 0.458895 | − | 0.888491i | \(-0.348246\pi\) | ||||
0.458895 | + | 0.888491i | \(0.348246\pi\) | |||||||
\(200\) | 80024.3 | + | 79975.7i | 0.141464 | + | 0.141378i | ||||
\(201\) | −1.94306e6 | −3.39232 | ||||||||
\(202\) | −543862. | + | 145786.i | −0.937799 | + | 0.251384i | ||||
\(203\) | 582451.i | 0.992018i | ||||||||
\(204\) | 85595.1 | + | 148186.i | 0.144004 | + | 0.249305i | ||||
\(205\) | 106010.i | 0.176182i | ||||||||
\(206\) | 68723.4 | + | 256376.i | 0.112833 | + | 0.420929i | ||||
\(207\) | 258380. | 0.419116 | ||||||||
\(208\) | 436077. | + | 251534.i | 0.698884 | + | 0.403123i | ||||
\(209\) | −643612. | −1.01920 | ||||||||
\(210\) | −179860. | − | 670975.i | −0.281441 | − | 1.04993i | ||||
\(211\) | − | 661872.i | − | 1.02345i | −0.859148 | − | 0.511726i | \(-0.829006\pi\) | ||
0.859148 | − | 0.511726i | \(-0.170994\pi\) | |||||||
\(212\) | −182366. | − | 315719.i | −0.278679 | − | 0.482460i | ||||
\(213\) | 765674.i | 1.15637i | ||||||||
\(214\) | −209713. | + | 56215.3i | −0.313034 | + | 0.0839112i | ||||
\(215\) | −378984. | −0.559145 | ||||||||
\(216\) | 1.37207e6 | − | 1.37290e6i | 2.00098 | − | 2.00219i | ||||
\(217\) | −394185. | −0.568265 | ||||||||
\(218\) | −78072.9 | + | 20928.0i | −0.111265 | + | 0.0298255i | ||||
\(219\) | 2.52042e6i | 3.55109i | ||||||||
\(220\) | −356409. | + | 205869.i | −0.496469 | + | 0.286771i | ||||
\(221\) | 90013.0i | 0.123972i | ||||||||
\(222\) | −316067. | − | 1.17910e6i | −0.430424 | − | 1.60571i | ||||
\(223\) | 1.06479e6 | 1.43384 | 0.716922 | − | 0.697153i | \(-0.245550\pi\) | ||||
0.716922 | + | 0.697153i | \(0.245550\pi\) | |||||||
\(224\) | −941098. | − | 251656.i | −1.25318 | − | 0.335110i | ||||
\(225\) | 381318. | 0.502148 | ||||||||
\(226\) | 191213. | + | 713329.i | 0.249027 | + | 0.929006i | ||||
\(227\) | 619730.i | 0.798248i | 0.916897 | + | 0.399124i | \(0.130686\pi\) | ||||
−0.916897 | + | 0.399124i | \(0.869314\pi\) | |||||||
\(228\) | 1.01246e6 | − | 584816.i | 1.28985 | − | 0.745044i | ||||
\(229\) | 434907.i | 0.548035i | 0.961725 | + | 0.274017i | \(0.0883525\pi\) | ||||
−0.961725 | + | 0.274017i | \(0.911647\pi\) | |||||||
\(230\) | 57849.4 | − | 15507.0i | 0.0721073 | − | 0.0193289i | ||||
\(231\) | 2.52720e6 | 3.11608 | ||||||||
\(232\) | −443180. | + | 443450.i | −0.540581 | + | 0.540909i | ||||
\(233\) | 793810. | 0.957915 | 0.478957 | − | 0.877838i | \(-0.341015\pi\) | ||||
0.478957 | + | 0.877838i | \(0.341015\pi\) | |||||||
\(234\) | 1.63888e6 | − | 439313.i | 1.95662 | − | 0.524487i | ||||
\(235\) | − | 383945.i | − | 0.453523i | ||||||
\(236\) | 191715. | + | 331904.i | 0.224066 | + | 0.387912i | ||||
\(237\) | 578302.i | 0.668781i | ||||||||
\(238\) | −45099.0 | − | 168244.i | −0.0516089 | − | 0.192529i | ||||
\(239\) | −1.64777e6 | −1.86596 | −0.932978 | − | 0.359933i | \(-0.882800\pi\) | ||||
−0.932978 | + | 0.359933i | \(0.882800\pi\) | |||||||
\(240\) | 373601. | − | 647701.i | 0.418677 | − | 0.725849i | ||||
\(241\) | 592599. | 0.657231 | 0.328616 | − | 0.944464i | \(-0.393418\pi\) | ||||
0.328616 | + | 0.944464i | \(0.393418\pi\) | |||||||
\(242\) | −151814. | − | 566349.i | −0.166638 | − | 0.621649i | ||||
\(243\) | − | 2.21164e6i | − | 2.40270i | ||||||
\(244\) | 663496. | + | 1.14867e6i | 0.713450 | + | 1.23515i | ||||
\(245\) | 286882.i | 0.305343i | ||||||||
\(246\) | 676729. | − | 181402.i | 0.712979 | − | 0.191120i | ||||
\(247\) | 615001. | 0.641406 | ||||||||
\(248\) | −300113. | − | 299930.i | −0.309853 | − | 0.309665i | ||||
\(249\) | 244478. | 0.249886 | ||||||||
\(250\) | 85374.3 | − | 22885.2i | 0.0863927 | − | 0.0231582i | ||||
\(251\) | − | 1.64581e6i | − | 1.64890i | −0.565933 | − | 0.824451i | \(-0.691484\pi\) | ||
0.565933 | − | 0.824451i | \(-0.308516\pi\) | |||||||
\(252\) | −2.84312e6 | + | 1.64224e6i | −2.82029 | + | 1.62906i | ||||
\(253\) | 217887.i | 0.214008i | ||||||||
\(254\) | −479813. | − | 1.78996e6i | −0.466646 | − | 1.74084i | ||||
\(255\) | 133695. | 0.128756 | ||||||||
\(256\) | −525023. | − | 907669.i | −0.500701 | − | 0.865620i | ||||
\(257\) | −1.18756e6 | −1.12156 | −0.560779 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560779 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(258\) | 648513. | + | 2.41930e6i | 0.606554 | + | 2.26277i | ||||
\(259\) | 1.24251e6i | 1.15093i | ||||||||
\(260\) | 340566. | − | 196718.i | 0.312441 | − | 0.180472i | ||||
\(261\) | 2.11305e6i | 1.92003i | ||||||||
\(262\) | 639279. | − | 171364.i | 0.575356 | − | 0.154229i | ||||
\(263\) | −1.62916e6 | −1.45236 | −0.726180 | − | 0.687505i | \(-0.758706\pi\) | ||||
−0.726180 | + | 0.687505i | \(0.758706\pi\) | |||||||
\(264\) | 1.92408e6 | + | 1.92291e6i | 1.69908 | + | 1.69805i | ||||
\(265\) | −284846. | −0.249170 | ||||||||
\(266\) | −1.14950e6 | + | 308132.i | −0.996104 | + | 0.267013i | ||||
\(267\) | 111705.i | 0.0958944i | ||||||||
\(268\) | 1.06477e6 | + | 1.84338e6i | 0.905565 | + | 1.56775i | ||||
\(269\) | − | 895226.i | − | 0.754314i | −0.926149 | − | 0.377157i | \(-0.876902\pi\) | ||
0.926149 | − | 0.377157i | \(-0.123098\pi\) | |||||||
\(270\) | −392621. | − | 1.46469e6i | −0.327766 | − | 1.22274i | ||||
\(271\) | 16721.4 | 0.0138309 | 0.00691545 | − | 0.999976i | \(-0.497799\pi\) | ||||
0.00691545 | + | 0.999976i | \(0.497799\pi\) | |||||||
\(272\) | 93678.4 | − | 162408.i | 0.0767745 | − | 0.133102i | ||||
\(273\) | −2.41485e6 | −1.96103 | ||||||||
\(274\) | −108984. | − | 406568.i | −0.0876970 | − | 0.327157i | ||||
\(275\) | 321558.i | 0.256406i | ||||||||
\(276\) | −197982. | − | 342755.i | −0.156442 | − | 0.270839i | ||||
\(277\) | − | 573914.i | − | 0.449415i | −0.974426 | − | 0.224708i | \(-0.927857\pi\) | ||
0.974426 | − | 0.224708i | \(-0.0721427\pi\) | |||||||
\(278\) | 439490. | − | 117809.i | 0.341065 | − | 0.0914251i | ||||
\(279\) | −1.43005e6 | −1.09987 | ||||||||
\(280\) | −537991. | + | 538318.i | −0.410091 | + | 0.410340i | ||||
\(281\) | 1.95965e6 | 1.48052 | 0.740258 | − | 0.672322i | \(-0.234703\pi\) | ||||
0.740258 | + | 0.672322i | \(0.234703\pi\) | |||||||
\(282\) | −2.45097e6 | + | 657003.i | −1.83534 | + | 0.491976i | ||||
\(283\) | − | 2.04454e6i | − | 1.51751i | −0.651378 | − | 0.758753i | \(-0.725809\pi\) | ||
0.651378 | − | 0.758753i | \(-0.274191\pi\) | |||||||
\(284\) | 726393. | − | 419579.i | 0.534411 | − | 0.308687i | ||||
\(285\) | − | 913455.i | − | 0.666154i | ||||||
\(286\) | 370464. | + | 1.38203e6i | 0.267812 | + | 0.999085i | ||||
\(287\) | −713120. | −0.511044 | ||||||||
\(288\) | −3.41417e6 | − | 912972.i | −2.42552 | − | 0.648599i | ||||
\(289\) | −1.38633e6 | −0.976390 | ||||||||
\(290\) | 126817. | + | 473096.i | 0.0885488 | + | 0.330335i | ||||
\(291\) | − | 1.02691e6i | − | 0.710886i | ||||||
\(292\) | 2.39111e6 | − | 1.38115e6i | 1.64113 | − | 0.947949i | ||||
\(293\) | − | 2.25113e6i | − | 1.53190i | −0.642899 | − | 0.765951i | \(-0.722269\pi\) | ||
0.642899 | − | 0.765951i | \(-0.277731\pi\) | |||||||
\(294\) | 1.83136e6 | − | 490909.i | 1.23568 | − | 0.331232i | ||||
\(295\) | 299449. | 0.200340 | ||||||||
\(296\) | −945408. | + | 945983.i | −0.627177 | + | 0.627558i | ||||
\(297\) | 5.51667e6 | 3.62899 | ||||||||
\(298\) | −316458. | + | 84829.1i | −0.206431 | + | 0.0553355i | ||||
\(299\) | − | 208201.i | − | 0.134681i | ||||||
\(300\) | −292183. | − | 505839.i | −0.187435 | − | 0.324496i | ||||
\(301\) | − | 2.54940e6i | − | 1.62189i | ||||||
\(302\) | 660286. | + | 2.46322e6i | 0.416596 | + | 1.55413i | ||||
\(303\) | 2.90726e6 | 1.81919 | ||||||||
\(304\) | −1.10963e6 | − | 640044.i | −0.688641 | − | 0.397215i | ||||
\(305\) | 1.03635e6 | 0.637906 | ||||||||
\(306\) | −163613. | − | 610364.i | −0.0998881 | − | 0.372636i | ||||
\(307\) | 572436.i | 0.346642i | 0.984865 | + | 0.173321i | \(0.0554498\pi\) | ||||
−0.984865 | + | 0.173321i | \(0.944550\pi\) | |||||||
\(308\) | −1.38487e6 | − | 2.39754e6i | −0.831825 | − | 1.44009i | ||||
\(309\) | − | 1.37048e6i | − | 0.816537i | ||||||
\(310\) | −320177. | + | 85825.8i | −0.189228 | + | 0.0507240i | ||||
\(311\) | −2.86177e6 | −1.67778 | −0.838889 | − | 0.544303i | \(-0.816794\pi\) | ||||
−0.838889 | + | 0.544303i | \(0.816794\pi\) | |||||||
\(312\) | −1.83855e6 | − | 1.83743e6i | −1.06927 | − | 1.06862i | ||||
\(313\) | −345643. | −0.199419 | −0.0997095 | − | 0.995017i | \(-0.531791\pi\) | ||||
−0.0997095 | + | 0.995017i | \(0.531791\pi\) | |||||||
\(314\) | 393772. | − | 105554.i | 0.225383 | − | 0.0604156i | ||||
\(315\) | 2.56510e6i | 1.45656i | ||||||||
\(316\) | 548633. | − | 316902.i | 0.309075 | − | 0.178528i | ||||
\(317\) | 2.84370e6i | 1.58941i | 0.606995 | + | 0.794706i | \(0.292375\pi\) | ||||
−0.606995 | + | 0.794706i | \(0.707625\pi\) | |||||||
\(318\) | 487426. | + | 1.81836e6i | 0.270297 | + | 1.00835i | ||||
\(319\) | −1.78189e6 | −0.980404 | ||||||||
\(320\) | −819200. | + | 497.616i | −0.447214 | + | 0.000271656i | ||||
\(321\) | 1.12104e6 | 0.607238 | ||||||||
\(322\) | 104314. | + | 389149.i | 0.0560667 | + | 0.209159i | ||||
\(323\) | − | 229044.i | − | 0.122155i | ||||||
\(324\) | −4.57008e6 | + | 2.63977e6i | −2.41859 | + | 1.39702i | ||||
\(325\) | − | 307264.i | − | 0.161363i | ||||||
\(326\) | 2.57431e6 | − | 690064.i | 1.34158 | − | 0.359621i | ||||
\(327\) | 417345. | 0.215837 | ||||||||
\(328\) | −542934. | − | 542605.i | −0.278652 | − | 0.278483i | ||||
\(329\) | 2.58278e6 | 1.31552 | ||||||||
\(330\) | 2.05272e6 | − | 550246.i | 1.03763 | − | 0.278146i | ||||
\(331\) | 2.20630e6i | 1.10686i | 0.832895 | + | 0.553431i | \(0.186682\pi\) | ||||
−0.832895 | + | 0.553431i | \(0.813318\pi\) | |||||||
\(332\) | −133971. | − | 231936.i | −0.0667060 | − | 0.115484i | ||||
\(333\) | 4.50764e6i | 2.22761i | ||||||||
\(334\) | 760396. | + | 2.83669e6i | 0.372970 | + | 1.39138i | ||||
\(335\) | 1.66312e6 | 0.809678 | ||||||||
\(336\) | 4.35704e6 | + | 2.51319e6i | 2.10544 | + | 1.21444i | ||||
\(337\) | −210820. | −0.101120 | −0.0505599 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505599 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(338\) | 189821. | + | 708134.i | 0.0903758 | + | 0.337150i | ||||
\(339\) | − | 3.81316e6i | − | 1.80213i | ||||||
\(340\) | −73263.3 | − | 126836.i | −0.0343708 | − | 0.0595041i | ||||
\(341\) | − | 1.20593e6i | − | 0.561611i | ||||||
\(342\) | −4.17022e6 | + | 1.11786e6i | −1.92794 | + | 0.516800i | ||||
\(343\) | 896652. | 0.411518 | ||||||||
\(344\) | 1.93981e6 | − | 1.94099e6i | 0.883818 | − | 0.884355i | ||||
\(345\) | −309239. | −0.139877 | ||||||||
\(346\) | −3.97174e6 | + | 1.06466e6i | −1.78357 | + | 0.478100i | ||||
\(347\) | 2.39916e6i | 1.06963i | 0.844968 | + | 0.534817i | \(0.179619\pi\) | ||||
−0.844968 | + | 0.534817i | \(0.820381\pi\) | |||||||
\(348\) | 2.80307e6 | − | 1.61911e6i | 1.24076 | − | 0.716686i | ||||
\(349\) | − | 1.76207e6i | − | 0.774392i | −0.921997 | − | 0.387196i | \(-0.873444\pi\) | ||
0.921997 | − | 0.387196i | \(-0.126556\pi\) | |||||||
\(350\) | 153947. | + | 574307.i | 0.0671742 | + | 0.250596i | ||||
\(351\) | −5.27144e6 | −2.28382 | ||||||||
\(352\) | 769891. | − | 2.87910e6i | 0.331186 | − | 1.23851i | ||||
\(353\) | −2.11387e6 | −0.902904 | −0.451452 | − | 0.892296i | \(-0.649094\pi\) | ||||
−0.451452 | + | 0.892296i | \(0.649094\pi\) | |||||||
\(354\) | −512414. | − | 1.91158e6i | −0.217327 | − | 0.810745i | ||||
\(355\) | − | 655363.i | − | 0.276001i | ||||||
\(356\) | 105974. | − | 61212.7i | 0.0443174 | − | 0.0255986i | ||||
\(357\) | 899360.i | 0.373476i | ||||||||
\(358\) | 1.78823e6 | − | 479350.i | 0.737423 | − | 0.197672i | ||||
\(359\) | −25391.5 | −0.0103981 | −0.00519903 | − | 0.999986i | \(-0.501655\pi\) | ||||
−0.00519903 | + | 0.999986i | \(0.501655\pi\) | |||||||
\(360\) | −1.95176e6 | + | 1.95294e6i | −0.793724 | + | 0.794206i | ||||
\(361\) | 911190. | 0.367994 | ||||||||
\(362\) | 3.56023e6 | − | 954346.i | 1.42793 | − | 0.382767i | ||||
\(363\) | 3.02747e6i | 1.20590i | ||||||||
\(364\) | 1.32331e6 | + | 2.29096e6i | 0.523489 | + | 0.906285i | ||||
\(365\) | − | 2.15730e6i | − | 0.847574i | ||||||
\(366\) | −1.77339e6 | − | 6.61569e6i | −0.691992 | − | 2.58150i | ||||
\(367\) | 1.55872e6 | 0.604091 | 0.302046 | − | 0.953293i | \(-0.402330\pi\) | ||||
0.302046 | + | 0.953293i | \(0.402330\pi\) | |||||||
\(368\) | −216679. | + | 375650.i | −0.0834060 | + | 0.144599i | ||||
\(369\) | −2.58710e6 | −0.989116 | ||||||||
\(370\) | 270531. | + | 1.00923e6i | 0.102734 | + | 0.383252i | ||||
\(371\) | − | 1.91614e6i | − | 0.722759i | ||||||
\(372\) | 1.09576e6 | + | 1.89703e6i | 0.410544 | + | 0.710751i | ||||
\(373\) | 741743.i | 0.276046i | 0.990429 | + | 0.138023i | \(0.0440748\pi\) | ||||
−0.990429 | + | 0.138023i | \(0.955925\pi\) | |||||||
\(374\) | 514707. | − | 137971.i | 0.190275 | − | 0.0510046i | ||||
\(375\) | −456376. | −0.167589 | ||||||||
\(376\) | 1.96640e6 | + | 1.96520e6i | 0.717301 | + | 0.716866i | ||||
\(377\) | 1.70268e6 | 0.616993 | ||||||||
\(378\) | 9.85286e6 | − | 2.64113e6i | 3.54677 | − | 0.950738i | ||||
\(379\) | 2.61039e6i | 0.933487i | 0.884393 | + | 0.466743i | \(0.154573\pi\) | ||||
−0.884393 | + | 0.466743i | \(0.845427\pi\) | |||||||
\(380\) | −866591. | + | 500561.i | −0.307862 | + | 0.177827i | ||||
\(381\) | 9.56839e6i | 3.37696i | ||||||||
\(382\) | −626853. | − | 2.33850e6i | −0.219790 | − | 0.819935i | ||||
\(383\) | −3.05949e6 | −1.06574 | −0.532871 | − | 0.846197i | \(-0.678887\pi\) | ||||
−0.532871 | + | 0.846197i | \(0.678887\pi\) | |||||||
\(384\) | 1.40498e6 | + | 5.22864e6i | 0.486231 | + | 1.80951i | ||||
\(385\) | −2.16310e6 | −0.743746 | ||||||||
\(386\) | 821227. | + | 3.06362e6i | 0.280540 | + | 1.04657i | ||||
\(387\) | − | 9.24887e6i | − | 3.13914i | ||||||
\(388\) | −974227. | + | 562733.i | −0.328534 | + | 0.189768i | ||||
\(389\) | 498203.i | 0.166929i | 0.996511 | + | 0.0834646i | \(0.0265985\pi\) | ||||
−0.996511 | + | 0.0834646i | \(0.973401\pi\) | |||||||
\(390\) | −1.96146e6 | + | 525786.i | −0.653009 | + | 0.175044i | ||||
\(391\) | −77540.0 | −0.0256498 | ||||||||
\(392\) | −1.46928e6 | − | 1.46839e6i | −0.482937 | − | 0.482643i | ||||
\(393\) | −3.41732e6 | −1.11610 | ||||||||
\(394\) | −1.46884e6 | + | 393735.i | −0.476689 | + | 0.127780i | ||||
\(395\) | − | 494985.i | − | 0.159624i | ||||||
\(396\) | −5.02411e6 | − | 8.69795e6i | −1.60998 | − | 2.78727i | ||||
\(397\) | − | 3.95290e6i | − | 1.25875i | −0.777101 | − | 0.629376i | \(-0.783311\pi\) | ||
0.777101 | − | 0.629376i | \(-0.216689\pi\) | |||||||
\(398\) | 750950. | + | 2.80145e6i | 0.237631 | + | 0.886492i | ||||
\(399\) | 6.14475e6 | 1.93229 | ||||||||
\(400\) | −319776. | + | 554386.i | −0.0999299 | + | 0.173246i | ||||
\(401\) | −1.15248e6 | −0.357909 | −0.178955 | − | 0.983857i | \(-0.557272\pi\) | ||||
−0.178955 | + | 0.983857i | \(0.557272\pi\) | |||||||
\(402\) | −2.84591e6 | − | 1.06168e7i | −0.878328 | − | 3.27664i | ||||
\(403\) | 1.15232e6i | 0.353436i | ||||||||
\(404\) | −1.59314e6 | − | 2.75811e6i | −0.485624 | − | 0.840732i | ||||
\(405\) | 4.12320e6i | 1.24910i | ||||||||
\(406\) | −3.18249e6 | + | 853090.i | −0.958190 | + | 0.256850i | ||||
\(407\) | −3.80120e6 | −1.13746 | ||||||||
\(408\) | −684313. | + | 684728.i | −0.203519 | + | 0.203642i | ||||
\(409\) | 2.54459e6 | 0.752159 | 0.376079 | − | 0.926587i | \(-0.377272\pi\) | ||||
0.376079 | + | 0.926587i | \(0.377272\pi\) | |||||||
\(410\) | −579232. | + | 155268.i | −0.170174 | + | 0.0456164i | ||||
\(411\) | 2.17334e6i | 0.634635i | ||||||||
\(412\) | −1.30017e6 | + | 751003.i | −0.377360 | + | 0.217971i | ||||
\(413\) | 2.01438e6i | 0.581119i | ||||||||
\(414\) | 378438. | + | 1.41178e6i | 0.108516 | + | 0.404824i | ||||
\(415\) | −209256. | −0.0596427 | ||||||||
\(416\) | −735667. | + | 2.75111e6i | −0.208424 | + | 0.779427i | ||||
\(417\) | −2.34933e6 | −0.661614 | ||||||||
\(418\) | −942669. | − | 3.51666e6i | −0.263887 | − | 0.984442i | ||||
\(419\) | 62820.4i | 0.0174810i | 0.999962 | + | 0.00874049i | \(0.00278222\pi\) | ||||
−0.999962 | + | 0.00874049i | \(0.997218\pi\) | |||||||
\(420\) | 3.40275e6 | − | 1.96549e6i | 0.941253 | − | 0.543687i | ||||
\(421\) | − | 1.89940e6i | − | 0.522289i | −0.965300 | − | 0.261145i | \(-0.915900\pi\) | ||
0.965300 | − | 0.261145i | \(-0.0841000\pi\) | |||||||
\(422\) | 3.61644e6 | − | 969414.i | 0.988553 | − | 0.264989i | ||||
\(423\) | 9.36995e6 | 2.54616 | ||||||||
\(424\) | 1.45797e6 | − | 1.45886e6i | 0.393853 | − | 0.394092i | ||||
\(425\) | −114434. | −0.0307314 | ||||||||
\(426\) | −4.18361e6 | + | 1.12145e6i | −1.11693 | + | 0.299402i | ||||
\(427\) | 6.97145e6i | 1.85035i | ||||||||
\(428\) | −614316. | − | 1.06353e6i | −0.162100 | − | 0.280634i | ||||
\(429\) | − | 7.38776e6i | − | 1.93807i | ||||||
\(430\) | −555081. | − | 2.07075e6i | −0.144772 | − | 0.540078i | ||||
\(431\) | 5.91659e6 | 1.53419 | 0.767094 | − | 0.641535i | \(-0.221702\pi\) | ||||
0.767094 | + | 0.641535i | \(0.221702\pi\) | |||||||
\(432\) | 9.51109e6 | + | 5.48609e6i | 2.45200 | + | 1.41434i | ||||
\(433\) | −1.64308e6 | −0.421153 | −0.210577 | − | 0.977577i | \(-0.567534\pi\) | ||||
−0.210577 | + | 0.977577i | \(0.567534\pi\) | |||||||
\(434\) | −577345. | − | 2.15381e6i | −0.147133 | − | 0.548886i | ||||
\(435\) | − | 2.52898e6i | − | 0.640799i | ||||||
\(436\) | −228700. | − | 395934.i | −0.0576168 | − | 0.0997486i | ||||
\(437\) | 529781.i | 0.132707i | ||||||||
\(438\) | −1.37714e7 | + | 3.69154e6i | −3.43000 | + | 0.919438i | ||||
\(439\) | −4.34976e6 | −1.07722 | −0.538610 | − | 0.842555i | \(-0.681050\pi\) | ||||
−0.538610 | + | 0.842555i | \(0.681050\pi\) | |||||||
\(440\) | −1.64688e6 | − | 1.64588e6i | −0.405536 | − | 0.405290i | ||||
\(441\) | −7.00118e6 | −1.71425 | ||||||||
\(442\) | −491827. | + | 131838.i | −0.119745 | + | 0.0320985i | ||||
\(443\) | 2.27280e6i | 0.550239i | 0.961410 | + | 0.275119i | \(0.0887174\pi\) | ||||
−0.961410 | + | 0.275119i | \(0.911283\pi\) | |||||||
\(444\) | 5.97962e6 | − | 3.45395e6i | 1.43951 | − | 0.831493i | ||||
\(445\) | − | 95611.3i | − | 0.0228881i | ||||||
\(446\) | 1.55955e6 | + | 5.81796e6i | 0.371246 | + | 1.38495i | ||||
\(447\) | 1.69165e6 | 0.400445 | ||||||||
\(448\) | −3347.43 | − | 5.51070e6i | −0.000787982 | − | 1.29722i | ||||
\(449\) | 7.36304e6 | 1.72362 | 0.861809 | − | 0.507233i | \(-0.169331\pi\) | ||||
0.861809 | + | 0.507233i | \(0.169331\pi\) | |||||||
\(450\) | 558500. | + | 2.08351e6i | 0.130015 | + | 0.485024i | ||||
\(451\) | − | 2.18165e6i | − | 0.505060i | ||||||
\(452\) | −3.61753e6 | + | 2.08956e6i | −0.832849 | + | 0.481071i | ||||
\(453\) | − | 1.31674e7i | − | 3.01477i | ||||||
\(454\) | −3.38618e6 | + | 907690.i | −0.771027 | + | 0.206680i | ||||
\(455\) | 2.06694e6 | 0.468058 | ||||||||
\(456\) | 4.67831e6 | + | 4.67547e6i | 1.05360 | + | 1.05296i | ||||
\(457\) | −6.23984e6 | −1.39760 | −0.698800 | − | 0.715317i | \(-0.746282\pi\) | ||||
−0.698800 | + | 0.715317i | \(0.746282\pi\) | |||||||
\(458\) | −2.37631e6 | + | 636989.i | −0.529346 | + | 0.141895i | ||||
\(459\) | 1.96323e6i | 0.434951i | ||||||||
\(460\) | 169459. | + | 293374.i | 0.0373396 | + | 0.0646438i | ||||
\(461\) | − | 832291.i | − | 0.182399i | −0.995833 | − | 0.0911996i | \(-0.970930\pi\) | ||
0.995833 | − | 0.0911996i | \(-0.0290701\pi\) | |||||||
\(462\) | 3.70147e6 | + | 1.38085e7i | 0.806806 | + | 3.00982i | ||||
\(463\) | −3.61852e6 | −0.784474 | −0.392237 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392237 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(464\) | −3.07209e6 | − | 1.77202e6i | −0.662429 | − | 0.382096i | ||||
\(465\) | 1.71153e6 | 0.367073 | ||||||||
\(466\) | 1.16266e6 | + | 4.33734e6i | 0.248020 | + | 0.925249i | ||||
\(467\) | − | 286010.i | − | 0.0606861i | −0.999540 | − | 0.0303431i | \(-0.990340\pi\) | ||
0.999540 | − | 0.0303431i | \(-0.00965998\pi\) | |||||||
\(468\) | 4.80077e6 | + | 8.31130e6i | 1.01320 | + | 1.75410i | ||||
\(469\) | 1.11877e7i | 2.34860i | ||||||||
\(470\) | 2.09786e6 | − | 562347.i | 0.438058 | − | 0.117425i | ||||
\(471\) | −2.10494e6 | −0.437208 | ||||||||
\(472\) | −1.53271e6 | + | 1.53365e6i | −0.316670 | + | 0.316862i | ||||
\(473\) | 7.79938e6 | 1.60290 | ||||||||
\(474\) | −3.15981e6 | + | 847013.i | −0.645975 | + | 0.173159i | ||||
\(475\) | 781852.i | 0.158998i | ||||||||
\(476\) | 853220. | − | 492837.i | 0.172601 | − | 0.0996980i | ||||
\(477\) | − | 6.95150e6i | − | 1.39889i | ||||||
\(478\) | −2.41341e6 | − | 9.00333e6i | −0.483128 | − | 1.80233i | ||||
\(479\) | −2.28996e6 | −0.456026 | −0.228013 | − | 0.973658i | \(-0.573223\pi\) | ||||
−0.228013 | + | 0.973658i | \(0.573223\pi\) | |||||||
\(480\) | 4.08620e6 | + | 1.09268e6i | 0.809500 | + | 0.216466i | ||||
\(481\) | 3.63222e6 | 0.715830 | ||||||||
\(482\) | 867953. | + | 3.23793e6i | 0.170168 | + | 0.634820i | ||||
\(483\) | − | 2.08023e6i | − | 0.405736i | ||||||
\(484\) | 2.87215e6 | − | 1.65901e6i | 0.557306 | − | 0.321911i | ||||
\(485\) | 878962.i | 0.169674i | ||||||||
\(486\) | 1.20843e7 | − | 3.23930e6i | 2.32077 | − | 0.622100i | ||||
\(487\) | 6.55915e6 | 1.25321 | 0.626607 | − | 0.779335i | \(-0.284443\pi\) | ||||
0.626607 | + | 0.779335i | \(0.284443\pi\) | |||||||
\(488\) | −5.30450e6 | + | 5.30772e6i | −1.00831 | + | 1.00892i | ||||
\(489\) | −1.37612e7 | −2.60246 | ||||||||
\(490\) | −1.56751e6 | + | 420183.i | −0.294931 | + | 0.0790585i | ||||
\(491\) | 3.50573e6i | 0.656257i | 0.944633 | + | 0.328129i | \(0.106418\pi\) | ||||
−0.944633 | + | 0.328129i | \(0.893582\pi\) | |||||||
\(492\) | 1.98235e6 | + | 3.43192e6i | 0.369205 | + | 0.639183i | ||||
\(493\) | − | 634127.i | − | 0.117506i | ||||||
\(494\) | 900764. | + | 3.36034e6i | 0.166071 | + | 0.619534i | ||||
\(495\) | −7.84742e6 | −1.43951 | ||||||||
\(496\) | 1.19924e6 | − | 2.07910e6i | 0.218879 | − | 0.379464i | ||||
\(497\) | 4.40858e6 | 0.800586 | ||||||||
\(498\) | 358076. | + | 1.33582e6i | 0.0646997 | + | 0.241365i | ||||
\(499\) | 1.11789e6i | 0.200977i | 0.994938 | + | 0.100489i | \(0.0320406\pi\) | ||||
−0.994938 | + | 0.100489i | \(0.967959\pi\) | |||||||
\(500\) | 250088. | + | 432962.i | 0.0447370 | + | 0.0774506i | ||||
\(501\) | − | 1.51638e7i | − | 2.69906i | ||||||
\(502\) | 8.99262e6 | − | 2.41054e6i | 1.59267 | − | 0.426929i | ||||
\(503\) | −3.97264e6 | −0.700098 | −0.350049 | − | 0.936731i | \(-0.613835\pi\) | ||||
−0.350049 | + | 0.936731i | \(0.613835\pi\) | |||||||
\(504\) | −1.31373e7 | − | 1.31293e7i | −2.30372 | − | 2.30233i | ||||
\(505\) | −2.48841e6 | −0.434203 | ||||||||
\(506\) | −1.19052e6 | + | 319129.i | −0.206710 | + | 0.0554102i | ||||
\(507\) | − | 3.78539e6i | − | 0.654020i | ||||||
\(508\) | 9.07750e6 | − | 5.24335e6i | 1.56065 | − | 0.901466i | ||||
\(509\) | 5.19239e6i | 0.888327i | 0.895946 | + | 0.444164i | \(0.146499\pi\) | ||||
−0.895946 | + | 0.444164i | \(0.853501\pi\) | |||||||
\(510\) | 195818. | + | 730506.i | 0.0333370 | + | 0.124365i | ||||
\(511\) | 1.45120e7 | 2.45853 | ||||||||
\(512\) | 4.19048e6 | − | 4.19812e6i | 0.706462 | − | 0.707751i | ||||
\(513\) | 1.34135e7 | 2.25035 | ||||||||
\(514\) | −1.73936e6 | − | 6.48875e6i | −0.290390 | − | 1.08331i | ||||
\(515\) | 1.17303e6i | 0.194891i | ||||||||
\(516\) | −1.22691e7 | + | 7.08689e6i | −2.02856 | + | 1.17174i | ||||
\(517\) | 7.90148e6i | 1.30012i | ||||||||
\(518\) | −6.78900e6 | + | 1.81984e6i | −1.11168 | + | 0.297995i | ||||
\(519\) | 2.12313e7 | 3.45985 | ||||||||
\(520\) | 1.57367e6 | + | 1.57271e6i | 0.255214 | + | 0.255059i | ||||
\(521\) | 1.09827e6 | 0.177262 | 0.0886311 | − | 0.996065i | \(-0.471751\pi\) | ||||
0.0886311 | + | 0.996065i | \(0.471751\pi\) | |||||||
\(522\) | −1.15456e7 | + | 3.09489e6i | −1.85456 | + | 0.497129i | ||||
\(523\) | − | 8.67189e6i | − | 1.38631i | −0.720790 | − | 0.693154i | \(-0.756221\pi\) | ||
0.720790 | − | 0.693154i | \(-0.243779\pi\) | |||||||
\(524\) | 1.87264e6 | + | 3.24200e6i | 0.297939 | + | 0.515804i | ||||
\(525\) | − | 3.07001e6i | − | 0.486118i | ||||||
\(526\) | −2.38616e6 | − | 8.90165e6i | −0.376040 | − | 1.40283i | ||||
\(527\) | 429158. | 0.0673116 | ||||||||
\(528\) | −7.68859e6 | + | 1.33295e7i | −1.20022 | + | 2.08079i | ||||
\(529\) | −6.25699e6 | −0.972135 | ||||||||
\(530\) | −417202. | − | 1.55639e6i | −0.0645144 | − | 0.240673i | ||||
\(531\) | 7.30787e6i | 1.12475i | ||||||||
\(532\) | −3.36724e6 | − | 5.82950e6i | −0.515816 | − | 0.893002i | ||||
\(533\) | 2.08467e6i | 0.317847i | ||||||||
\(534\) | −610349. | + | 163609.i | −0.0926244 | + | 0.0248287i | ||||
\(535\) | −959532. | −0.144936 | ||||||||
\(536\) | −8.51260e6 | + | 8.51777e6i | −1.27982 | + | 1.28060i | ||||
\(537\) | −9.55916e6 | −1.43049 | ||||||||
\(538\) | 4.89148e6 | − | 1.31120e6i | 0.728592 | − | 0.195305i | ||||
\(539\) | − | 5.90395e6i | − | 0.875328i | ||||||
\(540\) | 7.42793e6 | − | 4.29052e6i | 1.09618 | − | 0.633178i | ||||
\(541\) | 746497.i | 0.109657i | 0.998496 | + | 0.0548283i | \(0.0174612\pi\) | ||||
−0.998496 | + | 0.0548283i | \(0.982539\pi\) | |||||||
\(542\) | 24491.1 | + | 91365.2i | 0.00358105 | + | 0.0133593i | ||||
\(543\) | −1.90315e7 | −2.76996 | ||||||||
\(544\) | 1.02459e6 | + | 273983.i | 0.148441 | + | 0.0396942i | ||||
\(545\) | −357218. | −0.0515160 | ||||||||
\(546\) | −3.53693e6 | − | 1.31946e7i | −0.507744 | − | 1.89416i | ||||
\(547\) | 2.52087e6i | 0.360231i | 0.983645 | + | 0.180116i | \(0.0576472\pi\) | ||||
−0.983645 | + | 0.180116i | \(0.942353\pi\) | |||||||
\(548\) | 2.06184e6 | − | 1.19096e6i | 0.293295 | − | 0.169413i | ||||
\(549\) | 2.52915e7i | 3.58132i | ||||||||
\(550\) | −1.75698e6 | + | 470971.i | −0.247662 | + | 0.0663877i | ||||
\(551\) | −4.33258e6 | −0.607950 | ||||||||
\(552\) | 1.58282e6 | − | 1.58378e6i | 0.221098 | − | 0.221232i | ||||
\(553\) | 3.32973e6 | 0.463017 | ||||||||
\(554\) | 3.13584e6 | − | 840586.i | 0.434090 | − | 0.116361i | ||||
\(555\) | − | 5.39490e6i | − | 0.743449i | ||||||
\(556\) | 1.28740e6 | + | 2.22880e6i | 0.176615 | + | 0.305763i | ||||
\(557\) | − | 186236.i | − | 0.0254347i | −0.999919 | − | 0.0127173i | \(-0.995952\pi\) | ||
0.999919 | − | 0.0127173i | \(-0.00404816\pi\) | |||||||
\(558\) | −2.09453e6 | − | 7.81371e6i | −0.284774 | − | 1.06236i | ||||
\(559\) | −7.45267e6 | −1.00875 | ||||||||
\(560\) | −3.72932e6 | − | 2.15111e6i | −0.502527 | − | 0.289863i | ||||
\(561\) | −2.75141e6 | −0.369104 | ||||||||
\(562\) | 2.87021e6 | + | 1.07075e7i | 0.383331 | + | 1.43003i | ||||
\(563\) | − | 358662.i | − | 0.0476886i | −0.999716 | − | 0.0238443i | \(-0.992409\pi\) | ||
0.999716 | − | 0.0238443i | \(-0.00759059\pi\) | |||||||
\(564\) | −7.17966e6 | − | 1.24297e7i | −0.950400 | − | 1.64537i | ||||
\(565\) | 3.26379e6i | 0.430132i | ||||||||
\(566\) | 1.11713e7 | − | 2.99455e6i | 1.46576 | − | 0.392908i | ||||
\(567\) | −2.77365e7 | −3.62321 | ||||||||
\(568\) | 3.35648e6 | + | 3.35444e6i | 0.436529 | + | 0.436263i | ||||
\(569\) | 1.08964e7 | 1.41093 | 0.705463 | − | 0.708747i | \(-0.250739\pi\) | ||||
0.705463 | + | 0.708747i | \(0.250739\pi\) | |||||||
\(570\) | 4.99107e6 | − | 1.33790e6i | 0.643438 | − | 0.172479i | ||||
\(571\) | − | 1.93042e6i | − | 0.247778i | −0.992296 | − | 0.123889i | \(-0.960463\pi\) | ||
0.992296 | − | 0.123889i | \(-0.0395366\pi\) | |||||||
\(572\) | −7.00874e6 | + | 4.04839e6i | −0.895674 | + | 0.517360i | ||||
\(573\) | 1.25007e7i | 1.59055i | ||||||||
\(574\) | −1.04447e6 | − | 3.89645e6i | −0.132318 | − | 0.493617i | ||||
\(575\) | 264687. | 0.0333858 | ||||||||
\(576\) | −12144.0 | − | 1.99921e7i | −0.00152513 | − | 2.51074i | ||||
\(577\) | −1.33310e7 | −1.66695 | −0.833477 | − | 0.552555i | \(-0.813653\pi\) | ||||
−0.833477 | + | 0.552555i | \(0.813653\pi\) | |||||||
\(578\) | −2.03050e6 | − | 7.57486e6i | −0.252804 | − | 0.943094i | ||||
\(579\) | − | 1.63768e7i | − | 2.03018i | ||||||
\(580\) | −2.39923e6 | + | 1.38585e6i | −0.296144 | + | 0.171059i | ||||
\(581\) | − | 1.40765e6i | − | 0.173003i | ||||||
\(582\) | 5.61099e6 | − | 1.50407e6i | 0.686645 | − | 0.184060i | ||||
\(583\) | 5.86206e6 | 0.714297 | ||||||||
\(584\) | 1.10487e7 | + | 1.10420e7i | 1.34054 | + | 1.33973i | ||||
\(585\) | 7.49858e6 | 0.905919 | ||||||||
\(586\) | 1.23001e7 | − | 3.29712e6i | 1.47966 | − | 0.396635i | ||||
\(587\) | − | 7.15350e6i | − | 0.856887i | −0.903569 | − | 0.428443i | \(-0.859062\pi\) | ||
0.903569 | − | 0.428443i | \(-0.140938\pi\) | |||||||
\(588\) | 5.36461e6 | + | 9.28743e6i | 0.639875 | + | 1.10778i | ||||
\(589\) | − | 2.93216e6i | − | 0.348256i | ||||||
\(590\) | 438590. | + | 1.63618e6i | 0.0518715 | + | 0.193509i | ||||
\(591\) | 7.85183e6 | 0.924703 | ||||||||
\(592\) | −6.55350e6 | − | 3.78013e6i | −0.768545 | − | 0.443305i | ||||
\(593\) | 1.46858e7 | 1.71499 | 0.857496 | − | 0.514490i | \(-0.172019\pi\) | ||||
0.857496 | + | 0.514490i | \(0.172019\pi\) | |||||||
\(594\) | 8.08002e6 | + | 3.01428e7i | 0.939608 | + | 3.50524i | ||||
\(595\) | − | 769788.i | − | 0.0891413i | ||||||
\(596\) | −927004. | − | 1.60487e6i | −0.106897 | − | 0.185065i | ||||
\(597\) | − | 1.49754e7i | − | 1.71966i | ||||||
\(598\) | 1.13760e6 | − | 304943.i | 0.130088 | − | 0.0348711i | ||||
\(599\) | −9.83597e6 | −1.12008 | −0.560042 | − | 0.828465i | \(-0.689215\pi\) | ||||
−0.560042 | + | 0.828465i | \(0.689215\pi\) | |||||||
\(600\) | 2.33593e6 | − | 2.33735e6i | 0.264900 | − | 0.265061i | ||||
\(601\) | 2.68643e6 | 0.303381 | 0.151691 | − | 0.988428i | \(-0.451528\pi\) | ||||
0.151691 | + | 0.988428i | \(0.451528\pi\) | |||||||
\(602\) | 1.39298e7 | − | 3.73399e6i | 1.56658 | − | 0.419935i | ||||
\(603\) | 4.05875e7i | 4.54568i | ||||||||
\(604\) | −1.24918e7 | + | 7.21554e6i | −1.39327 | + | 0.804779i | ||||
\(605\) | − | 2.59130e6i | − | 0.287825i | ||||||
\(606\) | 4.25813e6 | + | 1.58851e7i | 0.471018 | + | 1.75715i | ||||
\(607\) | 387079. | 0.0426411 | 0.0213205 | − | 0.999773i | \(-0.493213\pi\) | ||||
0.0213205 | + | 0.999773i | \(0.493213\pi\) | |||||||
\(608\) | 1.87195e6 | − | 7.00039e6i | 0.205369 | − | 0.768003i | ||||
\(609\) | 1.70123e7 | 1.85874 | ||||||||
\(610\) | 1.51789e6 | + | 5.66256e6i | 0.165165 | + | 0.616153i | ||||
\(611\) | − | 7.55024e6i | − | 0.818196i | ||||||
\(612\) | 3.09536e6 | − | 1.78795e6i | 0.334067 | − | 0.192964i | ||||
\(613\) | − | 1.37500e7i | − | 1.47792i | −0.673748 | − | 0.738962i | \(-0.735316\pi\) | ||
0.673748 | − | 0.738962i | \(-0.264684\pi\) | |||||||
\(614\) | −3.12777e6 | + | 838422.i | −0.334821 | + | 0.0897515i | ||||
\(615\) | 3.09633e6 | 0.330111 | ||||||||
\(616\) | 1.10717e7 | − | 1.10784e7i | 1.17561 | − | 1.17632i | ||||
\(617\) | −1.13239e7 | −1.19752 | −0.598758 | − | 0.800930i | \(-0.704339\pi\) | ||||
−0.598758 | + | 0.800930i | \(0.704339\pi\) | |||||||
\(618\) | 7.48823e6 | − | 2.00728e6i | 0.788693 | − | 0.211415i | ||||
\(619\) | 6.62505e6i | 0.694965i | 0.937687 | + | 0.347482i | \(0.112963\pi\) | ||||
−0.937687 | + | 0.347482i | \(0.887037\pi\) | |||||||
\(620\) | −937896. | − | 1.62372e6i | −0.0979886 | − | 0.169642i | ||||
\(621\) | − | 4.54098e6i | − | 0.472521i | ||||||
\(622\) | −4.19151e6 | − | 1.56366e7i | −0.434405 | − | 1.62057i | ||||
\(623\) | 643171. | 0.0663905 | ||||||||
\(624\) | 7.34681e6 | − | 1.27370e7i | 0.755331 | − | 1.30950i | ||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −506247. | − | 1.88857e6i | −0.0516329 | − | 0.192619i | ||||
\(627\) | 1.87986e7i | 1.90967i | ||||||||
\(628\) | 1.15348e6 | + | 1.99695e6i | 0.116711 | + | 0.202055i | ||||
\(629\) | − | 1.35274e6i | − | 0.136329i | ||||||
\(630\) | −1.40156e7 | + | 3.75699e6i | −1.40689 | + | 0.377128i | ||||
\(631\) | −1.12049e7 | −1.12030 | −0.560152 | − | 0.828390i | \(-0.689257\pi\) | ||||
−0.560152 | + | 0.828390i | \(0.689257\pi\) | |||||||
\(632\) | 2.53509e6 | + | 2.53355e6i | 0.252465 | + | 0.252312i | ||||
\(633\) | −1.93320e7 | −1.91764 | ||||||||
\(634\) | −1.55379e7 | + | 4.16505e6i | −1.53521 | + | 0.411525i | ||||
\(635\) | − | 8.18986e6i | − | 0.806013i | ||||||
\(636\) | −9.22153e6 | + | 5.32654e6i | −0.903983 | + | 0.522159i | ||||
\(637\) | 5.64150e6i | 0.550866i | ||||||||
\(638\) | −2.60986e6 | − | 9.73618e6i | −0.253843 | − | 0.946972i | ||||
\(639\) | 1.59937e7 | 1.54952 | ||||||||
\(640\) | −1.20256e6 | − | 4.47534e6i | −0.116053 | − | 0.431893i | ||||
\(641\) | −5.35866e6 | −0.515123 | −0.257562 | − | 0.966262i | \(-0.582919\pi\) | ||||
−0.257562 | + | 0.966262i | \(0.582919\pi\) | |||||||
\(642\) | 1.64194e6 | + | 6.12532e6i | 0.157224 | + | 0.586531i | ||||
\(643\) | 5.64079e6i | 0.538038i | 0.963135 | + | 0.269019i | \(0.0866994\pi\) | ||||
−0.963135 | + | 0.269019i | \(0.913301\pi\) | |||||||
\(644\) | −1.97351e6 | + | 1.13994e6i | −0.187510 | + | 0.108310i | ||||
\(645\) | 1.10694e7i | 1.04767i | ||||||||
\(646\) | 1.25148e6 | − | 335470.i | 0.117990 | − | 0.0316281i | ||||
\(647\) | 5.67405e6 | 0.532884 | 0.266442 | − | 0.963851i | \(-0.414152\pi\) | ||||
0.266442 | + | 0.963851i | \(0.414152\pi\) | |||||||
\(648\) | −2.11172e7 | − | 2.11044e7i | −1.97560 | − | 1.97440i | ||||
\(649\) | −6.16258e6 | −0.574316 | ||||||||
\(650\) | 1.67887e6 | − | 450035.i | 0.155860 | − | 0.0417795i | ||||
\(651\) | 1.15134e7i | 1.06476i | ||||||||
\(652\) | 7.54096e6 | + | 1.30552e7i | 0.694716 | + | 1.20272i | ||||
\(653\) | 1.50064e7i | 1.37719i | 0.725148 | + | 0.688593i | \(0.241771\pi\) | ||||
−0.725148 | + | 0.688593i | \(0.758229\pi\) | |||||||
\(654\) | 611267. | + | 2.28036e6i | 0.0558839 | + | 0.208477i | ||||
\(655\) | 2.92498e6 | 0.266391 | ||||||||
\(656\) | 2.16955e6 | − | 3.76130e6i | 0.196839 | − | 0.341254i | ||||
\(657\) | 5.26475e7 | 4.75844 | ||||||||
\(658\) | 3.78287e6 | + | 1.41122e7i | 0.340610 | + | 1.27066i | ||||
\(659\) | − | 7.48265e6i | − | 0.671184i | −0.942007 | − | 0.335592i | \(-0.891064\pi\) | ||
0.942007 | − | 0.335592i | \(-0.108936\pi\) | |||||||
\(660\) | 6.01304e6 | + | 1.04100e7i | 0.537321 | + | 0.930233i | ||||
\(661\) | 1.85142e7i | 1.64817i | 0.566467 | + | 0.824084i | \(0.308310\pi\) | ||||
−0.566467 | + | 0.824084i | \(0.691690\pi\) | |||||||
\(662\) | −1.20551e7 | + | 3.23146e6i | −1.06912 | + | 0.286585i | ||||
\(663\) | 2.62910e6 | 0.232286 | ||||||||
\(664\) | 1.07107e6 | − | 1.07172e6i | 0.0942748 | − | 0.0943321i | ||||
\(665\) | −5.25947e6 | −0.461198 | ||||||||
\(666\) | −2.46295e7 | + | 6.60214e6i | −2.15164 | + | 0.576765i | ||||
\(667\) | 1.46674e6i | 0.127656i | ||||||||
\(668\) | −1.43858e7 | + | 8.30953e6i | −1.24736 | + | 0.720502i | ||||
\(669\) | − | 3.11004e7i | − | 2.68659i | ||||||
\(670\) | 2.43590e6 | + | 9.08722e6i | 0.209639 | + | 0.782067i | ||||
\(671\) | −2.13278e7 | −1.82869 | ||||||||
\(672\) | −7.35038e6 | + | 2.74876e7i | −0.627894 | + | 2.34809i | ||||
\(673\) | −4.62662e6 | −0.393755 | −0.196878 | − | 0.980428i | \(-0.563080\pi\) | ||||
−0.196878 | + | 0.980428i | \(0.563080\pi\) | |||||||
\(674\) | −308778. | − | 1.15191e6i | −0.0261816 | − | 0.0976716i | ||||
\(675\) | − | 6.70159e6i | − | 0.566133i | ||||||
\(676\) | −3.59119e6 | + | 2.07434e6i | −0.302254 | + | 0.174588i | ||||
\(677\) | − | 1.21437e7i | − | 1.01831i | −0.860675 | − | 0.509155i | \(-0.829958\pi\) | ||
0.860675 | − | 0.509155i | \(-0.170042\pi\) | |||||||
\(678\) | 2.08349e7 | − | 5.58496e6i | 1.74068 | − | 0.466601i | ||||
\(679\) | −5.91272e6 | −0.492168 | ||||||||
\(680\) | 585723. | − | 586079.i | 0.0485758 | − | 0.0486053i | ||||
\(681\) | 1.81011e7 | 1.49567 | ||||||||
\(682\) | 6.58914e6 | − | 1.76627e6i | 0.542460 | − | 0.145411i | ||||
\(683\) | − | 9.19906e6i | − | 0.754557i | −0.926100 | − | 0.377278i | \(-0.876860\pi\) | ||
0.926100 | − | 0.377278i | \(-0.123140\pi\) | |||||||
\(684\) | −1.22159e7 | − | 2.11486e7i | −0.998354 | − | 1.72839i | ||||
\(685\) | − | 1.86023e6i | − | 0.151474i | ||||||
\(686\) | 1.31329e6 | + | 4.89927e6i | 0.106549 | + | 0.397485i | ||||
\(687\) | 1.27028e7 | 1.02685 | ||||||||
\(688\) | 1.34466e7 | + | 7.75615e6i | 1.08303 | + | 0.624705i | ||||
\(689\) | −5.60147e6 | −0.449525 | ||||||||
\(690\) | −452928. | − | 1.68967e6i | −0.0362165 | − | 0.135107i | ||||
\(691\) | − | 1.02344e7i | − | 0.815394i | −0.913117 | − | 0.407697i | \(-0.866332\pi\) | ||
0.913117 | − | 0.407697i | \(-0.133668\pi\) | |||||||
\(692\) | −1.16345e7 | − | 2.01420e7i | −0.923593 | − | 1.59896i | ||||
\(693\) | − | 5.27891e7i | − | 4.17553i | ||||||
\(694\) | −1.31089e7 | + | 3.51394e6i | −1.03316 | + | 0.276946i | ||||
\(695\) | 2.01086e6 | 0.157914 | ||||||||
\(696\) | 1.29523e7 | + | 1.29444e7i | 1.01350 | + | 1.01288i | ||||
\(697\) | 776389. | 0.0605338 | ||||||||
\(698\) | 9.62789e6 | − | 2.58083e6i | 0.747985 | − | 0.200503i | ||||
\(699\) | − | 2.31856e7i | − | 1.79484i | ||||||
\(700\) | −2.91251e6 | + | 1.68232e6i | −0.224658 | + | 0.129767i | ||||
\(701\) | 1.23863e6i | 0.0952023i | 0.998866 | + | 0.0476011i | \(0.0151576\pi\) | ||||
−0.998866 | + | 0.0476011i | \(0.984842\pi\) | |||||||
\(702\) | −7.72084e6 | − | 2.88029e7i | −0.591319 | − | 2.20594i | ||||
\(703\) | −9.24242e6 | −0.705339 | ||||||||
\(704\) | 1.68589e7 | − | 10240.8i | 1.28203 | − | 0.000778757i | ||||
\(705\) | −1.12143e7 | −0.849765 | ||||||||
\(706\) | −3.09609e6 | − | 1.15501e7i | −0.233777 | − | 0.872114i | ||||
\(707\) | − | 1.67394e7i | − | 1.25948i | ||||||
\(708\) | 9.69428e6 | − | 5.59961e6i | 0.726829 | − | 0.419831i | ||||
\(709\) | 2.52759e7i | 1.88839i | 0.329386 | + | 0.944195i | \(0.393158\pi\) | ||||
−0.329386 | + | 0.944195i | \(0.606842\pi\) | |||||||
\(710\) | 3.58087e6 | − | 959880.i | 0.266589 | − | 0.0714613i | ||||
\(711\) | 1.20798e7 | 0.896161 | ||||||||
\(712\) | 489678. | + | 489381.i | 0.0362002 | + | 0.0361782i | ||||
\(713\) | −992646. | −0.0731258 | ||||||||
\(714\) | −4.91406e6 | + | 1.31725e6i | −0.360741 | + | 0.0966993i | ||||
\(715\) | 6.32340e6i | 0.462578i | ||||||||
\(716\) | 5.23829e6 | + | 9.06874e6i | 0.381863 | + | 0.661096i | ||||
\(717\) | 4.81281e7i | 3.49624i | ||||||||
\(718\) | −37189.8 | − | 138738.i | −0.00269223 | − | 0.0100435i | ||||
\(719\) | −5.23203e6 | −0.377440 | −0.188720 | − | 0.982031i | \(-0.560434\pi\) | ||||
−0.188720 | + | 0.982031i | \(0.560434\pi\) | |||||||
\(720\) | −1.35294e7 | − | 7.80392e6i | −0.972632 | − | 0.561024i | ||||
\(721\) | −7.89090e6 | −0.565313 | ||||||||
\(722\) | 1.33458e6 | + | 4.97870e6i | 0.0952799 | + | 0.355445i | ||||
\(723\) | − | 1.73087e7i | − | 1.23145i | ||||||
\(724\) | 1.04290e7 | + | 1.80551e7i | 0.739429 | + | 1.28013i | ||||
\(725\) | 2.16462e6i | 0.152946i | ||||||||
\(726\) | −1.65419e7 | + | 4.43419e6i | −1.16478 | + | 0.312229i | ||||
\(727\) | 1.79530e7 | 1.25980 | 0.629899 | − | 0.776677i | \(-0.283096\pi\) | ||||
0.629899 | + | 0.776677i | \(0.283096\pi\) | |||||||
\(728\) | −1.05795e7 | + | 1.05860e7i | −0.739840 | + | 0.740290i | ||||
\(729\) | −2.45203e7 | −1.70886 | ||||||||
\(730\) | 1.17874e7 | − | 3.15970e6i | 0.818672 | − | 0.219451i | ||||
\(731\) | 2.77559e6i | 0.192115i | ||||||||
\(732\) | 3.35504e7 | − | 1.93794e7i | 2.31430 | − | 1.33679i | ||||
\(733\) | − | 2.06019e6i | − | 0.141627i | −0.997490 | − | 0.0708137i | \(-0.977440\pi\) | ||
0.997490 | − | 0.0708137i | \(-0.0225596\pi\) | |||||||
\(734\) | 2.28299e6 | + | 8.51677e6i | 0.156409 | + | 0.583492i | ||||
\(735\) | 8.37927e6 | 0.572121 | ||||||||
\(736\) | −2.36990e6 | − | 633726.i | −0.161263 | − | 0.0431228i | ||||
\(737\) | −3.42266e7 | −2.32111 | ||||||||
\(738\) | −3.78921e6 | − | 1.41358e7i | −0.256099 | − | 0.955387i | ||||
\(739\) | 1.47746e6i | 0.0995187i | 0.998761 | + | 0.0497594i | \(0.0158454\pi\) | ||||
−0.998761 | + | 0.0497594i | \(0.984155\pi\) | |||||||
\(740\) | −5.11813e6 | + | 2.95633e6i | −0.343583 | + | 0.198461i | ||||
\(741\) | − | 1.79630e7i | − | 1.20180i | ||||||
\(742\) | 1.04697e7 | − | 2.80649e6i | 0.698112 | − | 0.187134i | ||||
\(743\) | 2.46543e7 | 1.63840 | 0.819200 | − | 0.573508i | \(-0.194418\pi\) | ||||
0.819200 | + | 0.573508i | \(0.194418\pi\) | |||||||
\(744\) | −8.76038e6 | + | 8.76570e6i | −0.580217 | + | 0.580570i | ||||
\(745\) | −1.44794e6 | −0.0955782 | ||||||||
\(746\) | −4.05285e6 | + | 1.08640e6i | −0.266633 | + | 0.0714729i | ||||
\(747\) | − | 5.10676e6i | − | 0.334845i | ||||||
\(748\) | 1.50774e6 | + | 2.61026e6i | 0.0985307 | + | 0.170580i | ||||
\(749\) | − | 6.45471e6i | − | 0.420409i | ||||||
\(750\) | −668433. | − | 2.49362e6i | −0.0433915 | − | 0.161874i | ||||
\(751\) | −6.30342e6 | −0.407827 | −0.203914 | − | 0.978989i | \(-0.565366\pi\) | ||||
−0.203914 | + | 0.978989i | \(0.565366\pi\) | |||||||
\(752\) | −7.85768e6 | + | 1.36226e7i | −0.506699 | + | 0.878450i | ||||
\(753\) | −4.80708e7 | −3.08954 | ||||||||
\(754\) | 2.49384e6 | + | 9.30338e6i | 0.159750 | + | 0.595953i | ||||
\(755\) | 1.12703e7i | 0.719564i | ||||||||
\(756\) | 2.88621e7 | + | 4.99672e7i | 1.83664 | + | 3.17966i | ||||
\(757\) | − | 1.44827e7i | − | 0.918567i | −0.888290 | − | 0.459284i | \(-0.848106\pi\) | ||
0.888290 | − | 0.459284i | \(-0.151894\pi\) | |||||||
\(758\) | −1.42631e7 | + | 3.82333e6i | −0.901655 | + | 0.241695i | ||||
\(759\) | 6.36405e6 | 0.400986 | ||||||||
\(760\) | −4.00430e6 | − | 4.00187e6i | −0.251474 | − | 0.251321i | ||||
\(761\) | 9.50962e6 | 0.595253 | 0.297626 | − | 0.954682i | \(-0.403805\pi\) | ||||
0.297626 | + | 0.954682i | \(0.403805\pi\) | |||||||
\(762\) | −5.22812e7 | + | 1.40144e7i | −3.26181 | + | 0.874353i | ||||
\(763\) | − | 2.40298e6i | − | 0.149430i | ||||||
\(764\) | 1.18593e7 | − | 6.85020e6i | 0.735067 | − | 0.424590i | ||||
\(765\) | − | 2.79268e6i | − | 0.172531i | ||||||
\(766\) | −4.48109e6 | − | 1.67169e7i | −0.275938 | − | 1.02940i | ||||
\(767\) | 5.88863e6 | 0.361431 | ||||||||
\(768\) | −2.65112e7 | + | 1.53349e7i | −1.62191 | + | 0.938162i | ||||
\(769\) | 2.88208e6 | 0.175748 | 0.0878741 | − | 0.996132i | \(-0.471993\pi\) | ||||
0.0878741 | + | 0.996132i | \(0.471993\pi\) | |||||||
\(770\) | −3.16819e6 | − | 1.18191e7i | −0.192568 | − | 0.718384i | ||||
\(771\) | 3.46862e7i | 2.10146i | ||||||||
\(772\) | −1.55367e7 | + | 8.97429e6i | −0.938241 | + | 0.541947i | ||||
\(773\) | 1.83423e7i | 1.10409i | 0.833815 | + | 0.552044i | \(0.186152\pi\) | ||||
−0.833815 | + | 0.552044i | \(0.813848\pi\) | |||||||
\(774\) | 5.05354e7 | − | 1.35464e7i | 3.03210 | − | 0.812777i | ||||
\(775\) | −1.46495e6 | −0.0876130 | ||||||||
\(776\) | −4.50165e6 | − | 4.49892e6i | −0.268360 | − | 0.268197i | ||||
\(777\) | 3.62912e7 | 2.15650 | ||||||||
\(778\) | −2.72216e6 | + | 729695.i | −0.161237 | + | 0.0432208i | ||||
\(779\) | − | 5.30457e6i | − | 0.313189i | ||||||
\(780\) | −5.74574e6 | − | 9.94726e6i | −0.338150 | − | 0.585419i | ||||
\(781\) | 1.34872e7i | 0.791213i | ||||||||
\(782\) | −113569. | − | 423675.i | −0.00664117 | − | 0.0247751i | ||||
\(783\) | 3.71365e7 | 2.16469 | ||||||||
\(784\) | 5.87123e6 | − | 1.01788e7i | 0.341145 | − | 0.591433i | ||||
\(785\) | 1.80168e6 | 0.104353 | ||||||||
\(786\) | −5.00519e6 | − | 1.86721e7i | −0.288978 | − | 1.07804i | ||||
\(787\) | − | 1.35279e7i | − | 0.778564i | −0.921119 | − | 0.389282i | \(-0.872723\pi\) | ||
0.921119 | − | 0.389282i | \(-0.127277\pi\) | |||||||
\(788\) | −4.30270e6 | − | 7.44901e6i | −0.246846 | − | 0.427349i | ||||
\(789\) | 4.75846e7i | 2.72128i | ||||||||
\(790\) | 2.70458e6 | − | 724982.i | 0.154181 | − | 0.0413295i | ||||
\(791\) | −2.19553e7 | −1.24767 | ||||||||
\(792\) | 4.01666e7 | − | 4.01910e7i | 2.27537 | − | 2.27675i | ||||
\(793\) | 2.03797e7 | 1.15084 | ||||||||
\(794\) | 2.15985e7 | − | 5.78964e6i | 1.21583 | − | 0.325912i | ||||
\(795\) | 8.31981e6i | 0.466869i | ||||||||
\(796\) | −1.42071e7 | + | 8.20631e6i | −0.794736 | + | 0.459056i | ||||
\(797\) | − | 3.10994e7i | − | 1.73423i | −0.498109 | − | 0.867115i | \(-0.665972\pi\) | ||
0.498109 | − | 0.867115i | \(-0.334028\pi\) | |||||||
\(798\) | 8.99994e6 | + | 3.35746e7i | 0.500302 | + | 1.86640i | ||||
\(799\) | −2.81192e6 | −0.155825 | ||||||||
\(800\) | −3.49750e6 | − | 935255.i | −0.193211 | − | 0.0516660i | ||||
\(801\) | 2.33333e6 | 0.128498 | ||||||||
\(802\) | −1.68799e6 | − | 6.29710e6i | −0.0926687 | − | 0.345704i | ||||
\(803\) | 4.43965e7i | 2.42974i | ||||||||
\(804\) | 5.38414e7 | − | 3.10999e7i | 2.93749 | − | 1.69675i | ||||
\(805\) | 1.78053e6i | 0.0968410i | ||||||||
\(806\) | −6.29623e6 | + | 1.68775e6i | −0.341384 | + | 0.0915106i | ||||
\(807\) | −2.61478e7 | −1.41336 | ||||||||
\(808\) | 1.27368e7 | − | 1.27445e7i | 0.686327 | − | 0.686744i | ||||
\(809\) | 1.19594e6 | 0.0642449 | 0.0321225 | − | 0.999484i | \(-0.489773\pi\) | ||||
0.0321225 | + | 0.999484i | \(0.489773\pi\) | |||||||
\(810\) | −2.25290e7 | + | 6.03907e6i | −1.20650 | + | 0.323413i | ||||
\(811\) | − | 5.59211e6i | − | 0.298554i | −0.988795 | − | 0.149277i | \(-0.952305\pi\) | ||
0.988795 | − | 0.149277i | \(-0.0476947\pi\) | |||||||
\(812\) | −9.32249e6 | − | 1.61395e7i | −0.496183 | − | 0.859012i | ||||
\(813\) | − | 488400.i | − | 0.0259149i | ||||||
\(814\) | −5.56744e6 | − | 2.07696e7i | −0.294507 | − | 1.09867i | ||||
\(815\) | 1.17786e7 | 0.621155 | ||||||||
\(816\) | −4.74361e6 | − | 2.73616e6i | −0.249392 | − | 0.143852i | ||||
\(817\) | 1.89638e7 | 0.993963 | ||||||||
\(818\) | 3.72694e6 | + | 1.39035e7i | 0.194747 | + | 0.726510i | ||||
\(819\) | 5.04424e7i | 2.62776i | ||||||||
\(820\) | −1.69675e6 | − | 2.93748e6i | −0.0881217 | − | 0.152560i | ||||
\(821\) | − | 2.42817e7i | − | 1.25725i | −0.777708 | − | 0.628625i | \(-0.783618\pi\) | ||
0.777708 | − | 0.628625i | \(-0.216382\pi\) | |||||||
\(822\) | −1.18750e7 | + | 3.18320e6i | −0.612993 | + | 0.164318i | ||||
\(823\) | −1.21094e7 | −0.623193 | −0.311597 | − | 0.950214i | \(-0.600864\pi\) | ||||
−0.311597 | + | 0.950214i | \(0.600864\pi\) | |||||||
\(824\) | −6.00774e6 | − | 6.00410e6i | −0.308243 | − | 0.308056i | ||||
\(825\) | 9.39208e6 | 0.480426 | ||||||||
\(826\) | −1.10065e7 | + | 2.95037e6i | −0.561303 | + | 0.150462i | ||||
\(827\) | 2.18004e7i | 1.10841i | 0.832380 | + | 0.554205i | \(0.186977\pi\) | ||||
−0.832380 | + | 0.554205i | \(0.813023\pi\) | |||||||
\(828\) | −7.15961e6 | + | 4.13554e6i | −0.362922 | + | 0.209631i | ||||
\(829\) | − | 2.81218e7i | − | 1.42121i | −0.703593 | − | 0.710603i | \(-0.748422\pi\) | ||
0.703593 | − | 0.710603i | \(-0.251578\pi\) | |||||||
\(830\) | −306488. | − | 1.14336e6i | −0.0154425 | − | 0.0576089i | ||||
\(831\) | −1.67629e7 | −0.842067 | ||||||||
\(832\) | −1.61095e7 | + | 9785.55i | −0.806813 | + | 0.000490091i | ||||
\(833\) | 2.10106e6 | 0.104912 | ||||||||
\(834\) | −3.44096e6 | − | 1.28366e7i | −0.171303 | − | 0.639052i | ||||
\(835\) | 1.29791e7i | 0.644211i | ||||||||
\(836\) | 1.78342e7 | − | 1.03014e7i | 0.882547 | − | 0.509777i | ||||
\(837\) | 2.51328e7i | 1.24002i | ||||||||
\(838\) | −343248. | + | 92010.2i | −0.0168849 | + | 0.00452612i | ||||
\(839\) | 1.77035e6 | 0.0868270 | 0.0434135 | − | 0.999057i | \(-0.486177\pi\) | ||||
0.0434135 | + | 0.999057i | \(0.486177\pi\) | |||||||
\(840\) | 1.57232e7 | + | 1.57137e7i | 0.768853 | + | 0.768386i | ||||
\(841\) | 8.51602e6 | 0.415190 | ||||||||
\(842\) | 1.03782e7 | − | 2.78197e6i | 0.504479 | − | 0.135230i | ||||
\(843\) | − | 5.72376e7i | − | 2.77404i | ||||||
\(844\) | 1.05937e7 | + | 1.83402e7i | 0.511906 | + | 0.886233i | ||||
\(845\) | 3.24003e6i | 0.156101i | ||||||||
\(846\) | 1.37237e7 | + | 5.11970e7i | 0.659245 | + | 2.45934i | ||||
\(847\) | 1.74315e7 | 0.834883 | ||||||||
\(848\) | 1.01066e7 | + | 5.82956e6i | 0.482629 | + | 0.278385i | ||||
\(849\) | −5.97171e7 | −2.84335 | ||||||||
\(850\) | −167606. | − | 625261.i | −0.00795687 | − | 0.0296834i | ||||
\(851\) | 3.12891e6i | 0.148105i | ||||||||
\(852\) | −1.22551e7 | − | 2.12165e7i | −0.578385 | − | 1.00132i | ||||
\(853\) | − | 2.98606e7i | − | 1.40516i | −0.711604 | − | 0.702581i | \(-0.752031\pi\) | ||
0.711604 | − | 0.702581i | \(-0.247969\pi\) | |||||||
\(854\) | −3.80917e7 | + | 1.02108e7i | −1.78725 | + | 0.479087i | ||||
\(855\) | −1.90806e7 | −0.892641 | ||||||||
\(856\) | 4.91131e6 | − | 4.91429e6i | 0.229094 | − | 0.229233i | ||||
\(857\) | −1.59538e7 | −0.742012 | −0.371006 | − | 0.928630i | \(-0.620987\pi\) | ||||
−0.371006 | + | 0.928630i | \(0.620987\pi\) | |||||||
\(858\) | 4.03664e7 | − | 1.08205e7i | 1.87198 | − | 0.501799i | ||||
\(859\) | − | 2.68382e7i | − | 1.24099i | −0.784209 | − | 0.620497i | \(-0.786931\pi\) | ||
0.784209 | − | 0.620497i | \(-0.213069\pi\) | |||||||
\(860\) | 1.05015e7 | − | 6.06587e6i | 0.484177 | − | 0.279671i | ||||
\(861\) | 2.08288e7i | 0.957541i | ||||||||
\(862\) | 8.66576e6 | + | 3.23280e7i | 0.397227 | + | 1.48187i | ||||
\(863\) | 1.99512e7 | 0.911891 | 0.455946 | − | 0.890008i | \(-0.349301\pi\) | ||||
0.455946 | + | 0.890008i | \(0.349301\pi\) | |||||||
\(864\) | −1.60453e7 | + | 6.00034e7i | −0.731246 | + | 2.73458i | ||||
\(865\) | −1.81725e7 | −0.825797 | ||||||||
\(866\) | −2.40655e6 | − | 8.97773e6i | −0.109044 | − | 0.406792i | ||||
\(867\) | 4.04921e7i | 1.82946i | ||||||||
\(868\) | 1.09227e7 | − | 6.30917e6i | 0.492074 | − | 0.284232i | ||||
\(869\) | 1.01867e7i | 0.457596i | ||||||||
\(870\) | 1.38182e7 | − | 3.70408e6i | 0.618947 | − | 0.165914i | ||||
\(871\) | 3.27051e7 | 1.46073 | ||||||||
\(872\) | 1.82840e6 | − | 1.82951e6i | 0.0814292 | − | 0.0814787i | ||||
\(873\) | −2.14505e7 | −0.952582 | ||||||||
\(874\) | −2.89470e6 | + | 775946.i | −0.128181 | + | 0.0343600i | ||||
\(875\) | 2.62771e6i | 0.116026i | ||||||||
\(876\) | −4.03408e7 | − | 6.98397e7i | −1.77617 | − | 3.07498i | ||||
\(877\) | − | 2.73500e7i | − | 1.20077i | −0.799712 | − | 0.600384i | \(-0.795014\pi\) | ||
0.799712 | − | 0.600384i | \(-0.204986\pi\) | |||||||
\(878\) | −6.37090e6 | − | 2.37669e7i | −0.278910 | − | 1.04049i | ||||
\(879\) | −6.57510e7 | −2.87032 | ||||||||
\(880\) | 6.58089e6 | − | 1.14091e7i | 0.286469 | − | 0.496643i | ||||
\(881\) | −3.29524e7 | −1.43037 | −0.715184 | − | 0.698937i | \(-0.753657\pi\) | ||||
−0.715184 | + | 0.698937i | \(0.753657\pi\) | |||||||
\(882\) | −1.02543e7 | − | 3.82541e7i | −0.443849 | − | 1.65580i | ||||
\(883\) | 1.45135e7i | 0.626429i | 0.949682 | + | 0.313214i | \(0.101406\pi\) | ||||
−0.949682 | + | 0.313214i | \(0.898594\pi\) | |||||||
\(884\) | −1.44071e6 | − | 2.49422e6i | −0.0620079 | − | 0.107351i | ||||
\(885\) | − | 8.74633e6i | − | 0.375377i | ||||||
\(886\) | −1.24185e7 | + | 3.32886e6i | −0.531475 | + | 0.142466i | ||||
\(887\) | 2.89058e7 | 1.23360 | 0.616802 | − | 0.787118i | \(-0.288428\pi\) | ||||
0.616802 | + | 0.787118i | \(0.288428\pi\) | |||||||
\(888\) | 2.76303e7 | + | 2.76135e7i | 1.17585 | + | 1.17514i | ||||
\(889\) | 5.50926e7 | 2.33797 | ||||||||
\(890\) | 522415. | − | 140037.i | 0.0221076 | − | 0.00592610i | ||||
\(891\) | − | 8.48543e7i | − | 3.58079i | ||||||
\(892\) | −2.95049e7 | + | 1.70426e7i | −1.24160 | + | 0.717173i | ||||
\(893\) | 1.92121e7i | 0.806205i | ||||||||
\(894\) | 2.47769e6 | + | 9.24312e6i | 0.103682 | + | 0.386790i | ||||
\(895\) | 8.18196e6 | 0.341428 | ||||||||
\(896\) | 3.01053e7 | − | 8.08957e6i | 1.25278 | − | 0.336632i | ||||
\(897\) | −6.08114e6 | −0.252351 | ||||||||
\(898\) | 1.07843e7 | + | 4.02313e7i | 0.446274 | + | 1.66484i | ||||
\(899\) | − | 8.11793e6i | − | 0.335001i | ||||||
\(900\) | −1.05662e7 | + | 6.10323e6i | −0.434822 | + | 0.251162i | ||||
\(901\) | 2.08615e6i | 0.0856117i | ||||||||
\(902\) | 1.19204e7 | − | 3.19536e6i | 0.487838 | − | 0.130769i | ||||
\(903\) | −7.44630e7 | −3.03893 | ||||||||
\(904\) | −1.67157e7 | − | 1.67055e7i | −0.680305 | − | 0.679892i | ||||
\(905\) | 1.62896e7 | 0.661134 | ||||||||
\(906\) | 7.19459e7 | − | 1.92857e7i | 2.91196 | − | 0.780574i | ||||
\(907\) | 1.75219e7i | 0.707233i | 0.935390 | + | 0.353617i | \(0.115048\pi\) | ||||
−0.935390 | + | 0.353617i | \(0.884952\pi\) | |||||||
\(908\) | −9.91915e6 | − | 1.71724e7i | −0.399264 | − | 0.691222i | ||||
\(909\) | − | 6.07280e7i | − | 2.43770i | ||||||
\(910\) | 3.02736e6 | + | 1.12937e7i | 0.121188 | + | 0.452097i | ||||
\(911\) | −5.49598e6 | −0.219406 | −0.109703 | − | 0.993964i | \(-0.534990\pi\) | ||||
−0.109703 | + | 0.993964i | \(0.534990\pi\) | |||||||
\(912\) | −1.86944e7 | + | 3.24100e7i | −0.744261 | + | 1.29030i | ||||
\(913\) | 4.30643e6 | 0.170978 | ||||||||
\(914\) | −9.13922e6 | − | 3.40942e7i | −0.361862 | − | 1.34994i | ||||
\(915\) | − | 3.02697e7i | − | 1.19524i | ||||||
\(916\) | −6.96096e6 | − | 1.20511e7i | −0.274113 | − | 0.474556i | ||||
\(917\) | 1.96762e7i | 0.772711i | ||||||||
\(918\) | −1.07270e7 | + | 2.87546e6i | −0.420119 | + | 0.112616i | ||||
\(919\) | 1.89582e6 | 0.0740472 | 0.0370236 | − | 0.999314i | \(-0.488212\pi\) | ||||
0.0370236 | + | 0.999314i | \(0.488212\pi\) | |||||||
\(920\) | −1.35478e6 | + | 1.35561e6i | −0.0527716 | + | 0.0528037i | ||||
\(921\) | 1.67197e7 | 0.649502 | ||||||||
\(922\) | 4.54760e6 | − | 1.21902e6i | 0.176179 | − | 0.0472262i | ||||
\(923\) | − | 1.28876e7i | − | 0.497930i | ||||||
\(924\) | −7.00275e7 | + | 4.04493e7i | −2.69829 | + | 1.55859i | ||||
\(925\) | 4.61765e6i | 0.177446i | ||||||||
\(926\) | −5.29988e6 | − | 1.97714e7i | −0.203114 | − | 0.757723i | ||||
\(927\) | −2.86271e7 | −1.09415 | ||||||||
\(928\) | 5.18266e6 | − | 1.93812e7i | 0.197552 | − | 0.738771i | ||||
\(929\) | 3.44700e7 | 1.31040 | 0.655198 | − | 0.755457i | \(-0.272585\pi\) | ||||
0.655198 | + | 0.755457i | \(0.272585\pi\) | |||||||
\(930\) | 2.50680e6 | + | 9.35173e6i | 0.0950414 | + | 0.354556i | ||||
\(931\) | − | 1.43552e7i | − | 0.542793i | ||||||
\(932\) | −2.19961e7 | + | 1.27054e7i | −0.829481 | + | 0.479125i | ||||
\(933\) | 8.35868e7i | 3.14365i | ||||||||
\(934\) | 1.56275e6 | − | 418906.i | 0.0586167 | − | 0.0157127i | ||||
\(935\) | 2.35501e6 | 0.0880977 | ||||||||
\(936\) | −3.83811e7 | + | 3.84044e7i | −1.43195 | + | 1.43282i | ||||
\(937\) | 3.96544e7 | 1.47551 | 0.737756 | − | 0.675068i | \(-0.235886\pi\) | ||||
0.737756 | + | 0.675068i | \(0.235886\pi\) | |||||||
\(938\) | −6.11292e7 | + | 1.63861e7i | −2.26851 | + | 0.608093i | ||||
\(939\) | 1.00955e7i | 0.373651i | ||||||||
\(940\) | 6.14528e6 | + | 1.06390e7i | 0.226841 | + | 0.392717i | ||||
\(941\) | 1.88367e7i | 0.693474i | 0.937962 | + | 0.346737i | \(0.112710\pi\) | ||||
−0.937962 | + | 0.346737i | \(0.887290\pi\) | |||||||
\(942\) | −3.08302e6 | − | 1.15013e7i | −0.113201 | − | 0.422299i | ||||
\(943\) | −1.79580e6 | −0.0657625 | ||||||||
\(944\) | −1.06247e7 | − | 6.12842e6i | −0.388048 | − | 0.223830i | ||||
\(945\) | 4.50812e7 | 1.64216 | ||||||||
\(946\) | 1.14234e7 | + | 4.26154e7i | 0.415019 | + | 1.54824i | ||||
\(947\) | − | 4.04648e6i | − | 0.146623i | −0.997309 | − | 0.0733115i | \(-0.976643\pi\) | ||
0.997309 | − | 0.0733115i | \(-0.0233567\pi\) | |||||||
\(948\) | −9.25607e6 | − | 1.60245e7i | −0.334508 | − | 0.579113i | ||||
\(949\) | − | 4.24230e7i | − | 1.52910i | ||||||
\(950\) | −4.27200e6 | + | 1.14514e6i | −0.153576 | + | 0.0411672i | ||||
\(951\) | 8.30590e7 | 2.97807 | ||||||||
\(952\) | 3.94251e6 | + | 3.94012e6i | 0.140988 | + | 0.140902i | ||||
\(953\) | 4.74092e7 | 1.69095 | 0.845474 | − | 0.534016i | \(-0.179318\pi\) | ||||
0.845474 | + | 0.534016i | \(0.179318\pi\) | |||||||
\(954\) | 3.79827e7 | − | 1.01816e7i | 1.35118 | − | 0.362195i | ||||
\(955\) | − | 1.06997e7i | − | 0.379632i | ||||||
\(956\) | 4.56590e7 | − | 2.63735e7i | 1.61578 | − | 0.933305i | ||||
\(957\) | 5.20456e7i | 1.83698i | ||||||||
\(958\) | −3.35401e6 | − | 1.25123e7i | −0.118073 | − | 0.440476i | ||||
\(959\) | 1.25136e7 | 0.439376 | ||||||||
\(960\) | 14534.4 | + | 2.39272e7i | 0.000509001 | + | 0.837942i | ||||
\(961\) | −2.31352e7 | −0.808099 | ||||||||
\(962\) | 5.31995e6 | + | 1.98463e7i | 0.185340 | + | 0.691420i | ||||
\(963\) | − | 2.34168e7i | − | 0.813695i | ||||||
\(964\) | −1.64207e7 | + | 9.48491e6i | −0.569112 | + | 0.328731i | ||||
\(965\) | 1.40174e7i | 0.484562i | ||||||||
\(966\) | 1.13663e7 | − | 3.04682e6i | 0.391900 | − | 0.105052i | ||||
\(967\) | −1.05815e7 | −0.363898 | −0.181949 | − | 0.983308i | \(-0.558241\pi\) | ||||
−0.181949 | + | 0.983308i | \(0.558241\pi\) | |||||||
\(968\) | 1.32715e7 | + | 1.32634e7i | 0.455229 | + | 0.454953i | ||||
\(969\) | −6.68992e6 | −0.228882 | ||||||||
\(970\) | −4.80261e6 | + | 1.28738e6i | −0.163888 | + | 0.0439315i | ||||
\(971\) | 3.45206e7i | 1.17498i | 0.809232 | + | 0.587489i | \(0.199884\pi\) | ||||
−0.809232 | + | 0.587489i | \(0.800116\pi\) | |||||||
\(972\) | 3.53987e7 | + | 6.12837e7i | 1.20177 | + | 2.08056i | ||||
\(973\) | 1.35269e7i | 0.458055i | ||||||||
\(974\) | 9.60689e6 | + | 3.58389e7i | 0.324478 | + | 1.21048i | ||||
\(975\) | −8.97457e6 | −0.302344 | ||||||||
\(976\) | −3.67704e7 | − | 2.12095e7i | −1.23559 | − | 0.712700i | ||||
\(977\) | −1.80039e7 | −0.603433 | −0.301717 | − | 0.953398i | \(-0.597560\pi\) | ||||
−0.301717 | + | 0.953398i | \(0.597560\pi\) | |||||||
\(978\) | −2.01554e7 | − | 7.51906e7i | −0.673821 | − | 2.51372i | ||||
\(979\) | 1.96765e6i | 0.0656133i | ||||||||
\(980\) | −4.59172e6 | − | 7.94938e6i | −0.152725 | − | 0.264404i | ||||
\(981\) | − | 8.71768e6i | − | 0.289220i | ||||||
\(982\) | −1.91551e7 | + | 5.13468e6i | −0.633879 | + | 0.169916i | ||||
\(983\) | −2.71815e7 | −0.897200 | −0.448600 | − | 0.893733i | \(-0.648077\pi\) | ||||
−0.448600 | + | 0.893733i | \(0.648077\pi\) | |||||||
\(984\) | −1.58484e7 | + | 1.58580e7i | −0.521793 | + | 0.522110i | ||||
\(985\) | −6.72061e6 | −0.220708 | ||||||||
\(986\) | 3.46484e6 | − | 928778.i | 0.113499 | − | 0.0304242i | ||||
\(987\) | − | 7.54378e7i | − | 2.46488i | ||||||
\(988\) | −1.70414e7 | + | 9.84346e6i | −0.555409 | + | 0.320816i | ||||
\(989\) | − | 6.41996e6i | − | 0.208709i | ||||||
\(990\) | −1.14938e7 | − | 4.28780e7i | −0.372713 | − | 1.39042i | ||||
\(991\) | −2.26954e7 | −0.734097 | −0.367048 | − | 0.930202i | \(-0.619632\pi\) | ||||
−0.367048 | + | 0.930202i | \(0.619632\pi\) | |||||||
\(992\) | 1.31166e7 | + | 3.50746e6i | 0.423195 | + | 0.113165i | ||||
\(993\) | 6.44416e7 | 2.07393 | ||||||||
\(994\) | 6.45705e6 | + | 2.40883e7i | 0.207285 | + | 0.773286i | ||||
\(995\) | 1.28179e7i | 0.410448i | ||||||||
\(996\) | −6.77439e6 | + | 3.91302e6i | −0.216382 | + | 0.124987i | ||||
\(997\) | − | 2.28102e7i | − | 0.726762i | −0.931641 | − | 0.363381i | \(-0.881622\pi\) | ||
0.931641 | − | 0.363381i | \(-0.118378\pi\) | |||||||
\(998\) | −6.10809e6 | + | 1.63732e6i | −0.194124 | + | 0.0520364i | ||||
\(999\) | 7.92208e7 | 2.51146 |
(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 | 40.6.d.a.21.14 | yes | 20 | |
3.2 | odd | 2 | 360.6.k.b.181.7 | 20 | |||
4.3 | odd | 2 | 160.6.d.a.81.20 | 20 | |||
5.2 | odd | 4 | 200.6.f.b.149.4 | 20 | |||
5.3 | odd | 4 | 200.6.f.c.149.17 | 20 | |||
5.4 | even | 2 | 200.6.d.b.101.7 | 20 | |||
8.3 | odd | 2 | 160.6.d.a.81.1 | 20 | |||
8.5 | even | 2 | inner | 40.6.d.a.21.13 | ✓ | 20 | |
20.3 | even | 4 | 800.6.f.b.49.1 | 20 | |||
20.7 | even | 4 | 800.6.f.c.49.20 | 20 | |||
20.19 | odd | 2 | 800.6.d.c.401.1 | 20 | |||
24.5 | odd | 2 | 360.6.k.b.181.8 | 20 | |||
40.3 | even | 4 | 800.6.f.c.49.19 | 20 | |||
40.13 | odd | 4 | 200.6.f.b.149.3 | 20 | |||
40.19 | odd | 2 | 800.6.d.c.401.20 | 20 | |||
40.27 | even | 4 | 800.6.f.b.49.2 | 20 | |||
40.29 | even | 2 | 200.6.d.b.101.8 | 20 | |||
40.37 | odd | 4 | 200.6.f.c.149.18 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.d.a.21.13 | ✓ | 20 | 8.5 | even | 2 | inner | |
40.6.d.a.21.14 | yes | 20 | 1.1 | even | 1 | trivial | |
160.6.d.a.81.1 | 20 | 8.3 | odd | 2 | |||
160.6.d.a.81.20 | 20 | 4.3 | odd | 2 | |||
200.6.d.b.101.7 | 20 | 5.4 | even | 2 | |||
200.6.d.b.101.8 | 20 | 40.29 | even | 2 | |||
200.6.f.b.149.3 | 20 | 40.13 | odd | 4 | |||
200.6.f.b.149.4 | 20 | 5.2 | odd | 4 | |||
200.6.f.c.149.17 | 20 | 5.3 | odd | 4 | |||
200.6.f.c.149.18 | 20 | 40.37 | odd | 4 | |||
360.6.k.b.181.7 | 20 | 3.2 | odd | 2 | |||
360.6.k.b.181.8 | 20 | 24.5 | odd | 2 | |||
800.6.d.c.401.1 | 20 | 20.19 | odd | 2 | |||
800.6.d.c.401.20 | 20 | 40.19 | odd | 2 | |||
800.6.f.b.49.1 | 20 | 20.3 | even | 4 | |||
800.6.f.b.49.2 | 20 | 40.27 | even | 4 | |||
800.6.f.c.49.19 | 20 | 40.3 | even | 4 | |||
800.6.f.c.49.20 | 20 | 20.7 | even | 4 |