Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,6,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.8684026662\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1317 x^{14} - 2712 x^{13} + 1206654 x^{12} - 2683704 x^{11} + 572597881 x^{10} - 1472178324 x^{9} + 197936317446 x^{8} + \cdots + 683643854869056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(11.5099 + 19.9358i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.47 |
Dual form | 74.6.c.b.63.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | − | 3.46410i | 0.353553 | − | 0.612372i | ||||
\(3\) | −12.0099 | − | 20.8018i | −0.770436 | − | 1.33443i | −0.937324 | − | 0.348459i | \(-0.886705\pi\) |
0.166888 | − | 0.985976i | \(-0.446628\pi\) | |||||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | 51.5512 | + | 89.2893i | 0.922176 | + | 1.59726i | 0.796041 | + | 0.605243i | \(0.206924\pi\) |
0.126135 | + | 0.992013i | \(0.459743\pi\) | |||||||
\(6\) | −96.0793 | −1.08956 | ||||||||
\(7\) | 102.698 | + | 177.878i | 0.792168 | + | 1.37207i | 0.924622 | + | 0.380886i | \(0.124381\pi\) |
−0.132454 | + | 0.991189i | \(0.542286\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −166.976 | + | 289.211i | −0.687144 | + | 1.19017i | ||||
\(10\) | 412.410 | 1.30415 | ||||||||
\(11\) | −395.366 | −0.985185 | −0.492593 | − | 0.870260i | \(-0.663951\pi\) | ||||
−0.492593 | + | 0.870260i | \(0.663951\pi\) | |||||||
\(12\) | −192.159 | + | 332.828i | −0.385218 | + | 0.667217i | ||||
\(13\) | 368.381 | + | 638.054i | 0.604559 | + | 1.04713i | 0.992121 | + | 0.125283i | \(0.0399838\pi\) |
−0.387562 | + | 0.921843i | \(0.626683\pi\) | |||||||
\(14\) | 821.585 | 1.12029 | ||||||||
\(15\) | 1238.25 | − | 2144.71i | 1.42096 | − | 2.46117i | ||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | −47.1240 | + | 81.6211i | −0.0395475 | + | 0.0684984i | −0.885122 | − | 0.465360i | \(-0.845925\pi\) |
0.845574 | + | 0.533858i | \(0.179258\pi\) | |||||||
\(18\) | 667.904 | + | 1156.84i | 0.485884 | + | 0.841576i | ||||
\(19\) | −200.998 | − | 348.139i | −0.127734 | − | 0.221242i | 0.795064 | − | 0.606525i | \(-0.207437\pi\) |
−0.922798 | + | 0.385283i | \(0.874104\pi\) | |||||||
\(20\) | 824.819 | − | 1428.63i | 0.461088 | − | 0.798628i | ||||
\(21\) | 2466.79 | − | 4272.61i | 1.22063 | − | 2.11419i | ||||
\(22\) | −790.733 | + | 1369.59i | −0.348316 | + | 0.603300i | ||||
\(23\) | 3297.11 | 1.29961 | 0.649807 | − | 0.760100i | \(-0.274850\pi\) | ||||
0.649807 | + | 0.760100i | \(0.274850\pi\) | |||||||
\(24\) | 768.634 | + | 1331.31i | 0.272390 | + | 0.471794i | ||||
\(25\) | −3752.56 | + | 6499.62i | −1.20082 | + | 2.07988i | ||||
\(26\) | 2947.05 | 0.854975 | ||||||||
\(27\) | 2184.65 | 0.576731 | ||||||||
\(28\) | 1643.17 | − | 2846.05i | 0.396084 | − | 0.686037i | ||||
\(29\) | −3952.87 | −0.872805 | −0.436402 | − | 0.899752i | \(-0.643748\pi\) | ||||
−0.436402 | + | 0.899752i | \(0.643748\pi\) | |||||||
\(30\) | −4953.01 | − | 8578.86i | −1.00477 | − | 1.74031i | ||||
\(31\) | −4751.96 | −0.888114 | −0.444057 | − | 0.895999i | \(-0.646461\pi\) | ||||
−0.444057 | + | 0.895999i | \(0.646461\pi\) | |||||||
\(32\) | 512.000 | + | 886.810i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 4748.32 | + | 8224.32i | 0.759023 | + | 1.31467i | ||||
\(34\) | 188.496 | + | 326.484i | 0.0279643 | + | 0.0484357i | ||||
\(35\) | −10588.4 | + | 18339.7i | −1.46104 | + | 2.53059i | ||||
\(36\) | 5343.23 | 0.687144 | ||||||||
\(37\) | 8326.31 | + | 128.327i | 0.999881 | + | 0.0154104i | ||||
\(38\) | −1607.98 | −0.180644 | ||||||||
\(39\) | 8848.44 | − | 15325.9i | 0.931548 | − | 1.61349i | ||||
\(40\) | −3299.28 | − | 5714.52i | −0.326038 | − | 0.564715i | ||||
\(41\) | −1206.71 | − | 2090.08i | −0.112110 | − | 0.194179i | 0.804511 | − | 0.593938i | \(-0.202427\pi\) |
−0.916621 | + | 0.399758i | \(0.869094\pi\) | |||||||
\(42\) | −9867.16 | − | 17090.4i | −0.863116 | − | 1.49496i | ||||
\(43\) | 14421.7 | 1.18945 | 0.594725 | − | 0.803929i | \(-0.297261\pi\) | ||||
0.594725 | + | 0.803929i | \(0.297261\pi\) | |||||||
\(44\) | 3162.93 | + | 5478.36i | 0.246296 | + | 0.426598i | ||||
\(45\) | −34431.3 | −2.53467 | ||||||||
\(46\) | 6594.22 | − | 11421.5i | 0.459483 | − | 0.795847i | ||||
\(47\) | 18875.6 | 1.24639 | 0.623197 | − | 0.782065i | \(-0.285834\pi\) | ||||
0.623197 | + | 0.782065i | \(0.285834\pi\) | |||||||
\(48\) | 6149.08 | 0.385218 | ||||||||
\(49\) | −12690.3 | + | 21980.2i | −0.755060 | + | 1.30780i | ||||
\(50\) | 15010.2 | + | 25998.5i | 0.849106 | + | 1.47070i | ||||
\(51\) | 2263.82 | 0.121875 | ||||||||
\(52\) | 5894.09 | − | 10208.9i | 0.302279 | − | 0.523563i | ||||
\(53\) | −17285.8 | + | 29939.8i | −0.845276 | + | 1.46406i | 0.0401045 | + | 0.999195i | \(0.487231\pi\) |
−0.885381 | + | 0.464866i | \(0.846102\pi\) | |||||||
\(54\) | 4369.31 | − | 7567.87i | 0.203905 | − | 0.353174i | ||||
\(55\) | −20381.6 | − | 35302.0i | −0.908515 | − | 1.57359i | ||||
\(56\) | −6572.68 | − | 11384.2i | −0.280074 | − | 0.485102i | ||||
\(57\) | −4827.94 | + | 8362.24i | −0.196822 | + | 0.340906i | ||||
\(58\) | −7905.73 | + | 13693.1i | −0.308583 | + | 0.534482i | ||||
\(59\) | 18594.1 | − | 32205.9i | 0.695416 | − | 1.20450i | −0.274625 | − | 0.961551i | \(-0.588554\pi\) |
0.970040 | − | 0.242944i | \(-0.0781131\pi\) | |||||||
\(60\) | −39624.0 | −1.42096 | ||||||||
\(61\) | 242.034 | + | 419.215i | 0.00832821 | + | 0.0144249i | 0.870159 | − | 0.492770i | \(-0.164016\pi\) |
−0.861831 | + | 0.507195i | \(0.830682\pi\) | |||||||
\(62\) | −9503.92 | + | 16461.3i | −0.313996 | + | 0.543856i | ||||
\(63\) | −68592.5 | −2.17733 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −37980.9 | + | 65784.9i | −1.11502 | + | 1.93127i | ||||
\(66\) | 37986.5 | 1.07342 | ||||||||
\(67\) | −21219.9 | − | 36754.0i | −0.577507 | − | 1.00027i | −0.995764 | − | 0.0919423i | \(-0.970692\pi\) |
0.418258 | − | 0.908328i | \(-0.362641\pi\) | |||||||
\(68\) | 1507.97 | 0.0395475 | ||||||||
\(69\) | −39598.0 | − | 68585.8i | −1.00127 | − | 1.73425i | ||||
\(70\) | 42353.7 | + | 73358.7i | 1.03311 | + | 1.78940i | ||||
\(71\) | 9423.11 | + | 16321.3i | 0.221844 | + | 0.384246i | 0.955368 | − | 0.295418i | \(-0.0954590\pi\) |
−0.733524 | + | 0.679664i | \(0.762126\pi\) | |||||||
\(72\) | 10686.5 | − | 18509.5i | 0.242942 | − | 0.420788i | ||||
\(73\) | 18097.1 | 0.397468 | 0.198734 | − | 0.980053i | \(-0.436317\pi\) | ||||
0.198734 | + | 0.980053i | \(0.436317\pi\) | |||||||
\(74\) | 17097.2 | − | 28586.5i | 0.362948 | − | 0.606851i | ||||
\(75\) | 180271. | 3.70061 | ||||||||
\(76\) | −3215.97 | + | 5570.22i | −0.0638672 | + | 0.110621i | ||||
\(77\) | −40603.4 | − | 70327.1i | −0.780432 | − | 1.35175i | ||||
\(78\) | −35393.8 | − | 61303.8i | −0.658704 | − | 1.14091i | ||||
\(79\) | 2880.58 | + | 4989.31i | 0.0519292 | + | 0.0899441i | 0.890822 | − | 0.454353i | \(-0.150130\pi\) |
−0.838892 | + | 0.544297i | \(0.816796\pi\) | |||||||
\(80\) | −26394.2 | −0.461088 | ||||||||
\(81\) | 14337.7 | + | 24833.6i | 0.242810 | + | 0.420559i | ||||
\(82\) | −9653.66 | −0.158547 | ||||||||
\(83\) | −24374.9 | + | 42218.6i | −0.388372 | + | 0.672680i | −0.992231 | − | 0.124412i | \(-0.960296\pi\) |
0.603859 | + | 0.797091i | \(0.293629\pi\) | |||||||
\(84\) | −78937.3 | −1.22063 | ||||||||
\(85\) | −9717.19 | −0.145879 | ||||||||
\(86\) | 28843.5 | − | 49958.4i | 0.420534 | − | 0.728387i | ||||
\(87\) | 47473.6 | + | 82226.7i | 0.672441 | + | 1.16470i | ||||
\(88\) | 25303.4 | 0.348316 | ||||||||
\(89\) | 63249.4 | − | 109551.i | 0.846412 | − | 1.46603i | −0.0379777 | − | 0.999279i | \(-0.512092\pi\) |
0.884389 | − | 0.466750i | \(-0.154575\pi\) | |||||||
\(90\) | −68862.6 | + | 119273.i | −0.896142 | + | 1.55216i | ||||
\(91\) | −75664.0 | + | 131054.i | −0.957824 | + | 1.65900i | ||||
\(92\) | −26376.9 | − | 45686.1i | −0.324903 | − | 0.562749i | ||||
\(93\) | 57070.6 | + | 98849.2i | 0.684235 | + | 1.18513i | ||||
\(94\) | 37751.1 | − | 65386.9i | 0.440667 | − | 0.763257i | ||||
\(95\) | 20723.4 | − | 35894.0i | 0.235587 | − | 0.408049i | ||||
\(96\) | 12298.2 | − | 21301.0i | 0.136195 | − | 0.235897i | ||||
\(97\) | −93103.5 | −1.00470 | −0.502350 | − | 0.864664i | \(-0.667531\pi\) | ||||
−0.502350 | + | 0.864664i | \(0.667531\pi\) | |||||||
\(98\) | 50761.1 | + | 87920.9i | 0.533908 | + | 0.924755i | ||||
\(99\) | 66016.7 | − | 114344.i | 0.676965 | − | 1.17254i | ||||
\(100\) | 120082. | 1.20082 | ||||||||
\(101\) | 100789. | 0.983127 | 0.491564 | − | 0.870842i | \(-0.336426\pi\) | ||||
0.491564 | + | 0.870842i | \(0.336426\pi\) | |||||||
\(102\) | 4527.64 | − | 7842.10i | 0.0430895 | − | 0.0746332i | ||||
\(103\) | 12605.5 | 0.117076 | 0.0585380 | − | 0.998285i | \(-0.481356\pi\) | ||||
0.0585380 | + | 0.998285i | \(0.481356\pi\) | |||||||
\(104\) | −23576.4 | − | 40835.5i | −0.213744 | − | 0.370215i | ||||
\(105\) | 508664. | 4.50254 | ||||||||
\(106\) | 69143.0 | + | 119759.i | 0.597701 | + | 1.03525i | ||||
\(107\) | −65071.7 | − | 112708.i | −0.549456 | − | 0.951686i | −0.998312 | − | 0.0580815i | \(-0.981502\pi\) |
0.448856 | − | 0.893604i | \(-0.351832\pi\) | |||||||
\(108\) | −17477.2 | − | 30271.5i | −0.144183 | − | 0.249732i | ||||
\(109\) | −50187.2 | + | 86926.8i | −0.404601 | + | 0.700789i | −0.994275 | − | 0.106852i | \(-0.965923\pi\) |
0.589674 | + | 0.807641i | \(0.299256\pi\) | |||||||
\(110\) | −163053. | −1.28483 | ||||||||
\(111\) | −97328.9 | − | 174743.i | −0.749781 | − | 1.34615i | ||||
\(112\) | −52581.4 | −0.396084 | ||||||||
\(113\) | 70801.4 | − | 122632.i | 0.521610 | − | 0.903455i | −0.478074 | − | 0.878319i | \(-0.658665\pi\) |
0.999684 | − | 0.0251352i | \(-0.00800163\pi\) | |||||||
\(114\) | 19311.8 | + | 33448.9i | 0.139174 | + | 0.241057i | ||||
\(115\) | 169970. | + | 294397.i | 1.19847 | + | 2.07581i | ||||
\(116\) | 31622.9 | + | 54772.5i | 0.218201 | + | 0.377936i | ||||
\(117\) | −246043. | −1.66168 | ||||||||
\(118\) | −74376.3 | − | 128824.i | −0.491733 | − | 0.851707i | ||||
\(119\) | −19358.2 | −0.125313 | ||||||||
\(120\) | −79248.1 | + | 137262.i | −0.502384 | + | 0.870154i | ||||
\(121\) | −4736.43 | −0.0294095 | ||||||||
\(122\) | 1936.27 | 0.0117779 | ||||||||
\(123\) | −28984.9 | + | 50203.3i | −0.172746 | + | 0.299206i | ||||
\(124\) | 38015.7 | + | 65845.1i | 0.222028 | + | 0.384564i | ||||
\(125\) | −451600. | −2.58511 | ||||||||
\(126\) | −137185. | + | 237611.i | −0.769804 | + | 1.33334i | ||||
\(127\) | −19181.4 | + | 33223.1i | −0.105529 | + | 0.182781i | −0.913954 | − | 0.405818i | \(-0.866987\pi\) |
0.808425 | + | 0.588599i | \(0.200320\pi\) | |||||||
\(128\) | 8192.00 | − | 14189.0i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −173204. | − | 299998.i | −0.916396 | − | 1.58724i | ||||
\(130\) | 151924. | + | 263140.i | 0.788438 | + | 1.36561i | ||||
\(131\) | −60785.5 | + | 105284.i | −0.309472 | + | 0.536022i | −0.978247 | − | 0.207443i | \(-0.933486\pi\) |
0.668775 | + | 0.743465i | \(0.266819\pi\) | |||||||
\(132\) | 75973.1 | − | 131589.i | 0.379511 | − | 0.657333i | ||||
\(133\) | 41284.2 | − | 71506.4i | 0.202374 | − | 0.350522i | ||||
\(134\) | −169759. | −0.816718 | ||||||||
\(135\) | 112622. | + | 195066.i | 0.531848 | + | 0.921187i | ||||
\(136\) | 3015.93 | − | 5223.75i | 0.0139822 | − | 0.0242178i | ||||
\(137\) | 265094. | 1.20670 | 0.603348 | − | 0.797478i | \(-0.293833\pi\) | ||||
0.603348 | + | 0.797478i | \(0.293833\pi\) | |||||||
\(138\) | −316784. | −1.41601 | ||||||||
\(139\) | 23589.5 | − | 40858.2i | 0.103558 | − | 0.179367i | −0.809590 | − | 0.586995i | \(-0.800311\pi\) |
0.913148 | + | 0.407628i | \(0.133644\pi\) | |||||||
\(140\) | 338829. | 1.46104 | ||||||||
\(141\) | −226694. | − | 392645.i | −0.960267 | − | 1.66323i | ||||
\(142\) | 75384.9 | 0.313735 | ||||||||
\(143\) | −145645. | − | 252265.i | −0.595602 | − | 1.03161i | ||||
\(144\) | −42745.9 | − | 74038.0i | −0.171786 | − | 0.297542i | ||||
\(145\) | −203775. | − | 352949.i | −0.804880 | − | 1.39409i | ||||
\(146\) | 36194.2 | − | 62690.3i | 0.140526 | − | 0.243399i | ||||
\(147\) | 609637. | 2.32690 | ||||||||
\(148\) | −64832.4 | − | 116399.i | −0.243297 | − | 0.436814i | ||||
\(149\) | −419756. | −1.54893 | −0.774464 | − | 0.632618i | \(-0.781980\pi\) | ||||
−0.774464 | + | 0.632618i | \(0.781980\pi\) | |||||||
\(150\) | 360543. | − | 624479.i | 1.30836 | − | 2.26615i | ||||
\(151\) | 85369.2 | + | 147864.i | 0.304691 | + | 0.527740i | 0.977192 | − | 0.212356i | \(-0.0681136\pi\) |
−0.672502 | + | 0.740095i | \(0.734780\pi\) | |||||||
\(152\) | 12863.9 | + | 22280.9i | 0.0451609 | + | 0.0782210i | ||||
\(153\) | −15737.1 | − | 27257.5i | −0.0543497 | − | 0.0941365i | ||||
\(154\) | −324827. | −1.10370 | ||||||||
\(155\) | −244969. | − | 424299.i | −0.818997 | − | 1.41854i | ||||
\(156\) | −283150. | −0.931548 | ||||||||
\(157\) | 12609.3 | − | 21839.9i | 0.0408265 | − | 0.0707135i | −0.844890 | − | 0.534940i | \(-0.820334\pi\) |
0.885717 | + | 0.464226i | \(0.153668\pi\) | |||||||
\(158\) | 23044.6 | 0.0734390 | ||||||||
\(159\) | 830402. | 2.60493 | ||||||||
\(160\) | −52788.4 | + | 91432.3i | −0.163019 | + | 0.282358i | ||||
\(161\) | 338607. | + | 586485.i | 1.02951 | + | 1.78317i | ||||
\(162\) | 114701. | 0.343385 | ||||||||
\(163\) | −265396. | + | 459680.i | −0.782395 | + | 1.35515i | 0.148148 | + | 0.988965i | \(0.452669\pi\) |
−0.930543 | + | 0.366183i | \(0.880665\pi\) | |||||||
\(164\) | −19307.3 | + | 33441.3i | −0.0560548 | + | 0.0970897i | ||||
\(165\) | −489563. | + | 847948.i | −1.39991 | + | 2.42471i | ||||
\(166\) | 97499.6 | + | 168874.i | 0.274620 | + | 0.475656i | ||||
\(167\) | −101601. | − | 175978.i | −0.281907 | − | 0.488277i | 0.689948 | − | 0.723859i | \(-0.257634\pi\) |
−0.971854 | + | 0.235583i | \(0.924300\pi\) | |||||||
\(168\) | −157875. | + | 273447.i | −0.431558 | + | 0.747480i | ||||
\(169\) | −85762.1 | + | 148544.i | −0.230982 | + | 0.400073i | ||||
\(170\) | −19434.4 | + | 33661.3i | −0.0515761 | + | 0.0893324i | ||||
\(171\) | 134247. | 0.351088 | ||||||||
\(172\) | −115374. | − | 199833.i | −0.297363 | − | 0.515047i | ||||
\(173\) | 168746. | − | 292276.i | 0.428665 | − | 0.742469i | −0.568090 | − | 0.822966i | \(-0.692318\pi\) |
0.996755 | + | 0.0804975i | \(0.0256509\pi\) | |||||||
\(174\) | 379789. | 0.950975 | ||||||||
\(175\) | −1.54152e6 | −3.80500 | ||||||||
\(176\) | 50606.9 | − | 87653.7i | 0.123148 | − | 0.213299i | ||||
\(177\) | −893253. | −2.14309 | ||||||||
\(178\) | −252998. | − | 438205.i | −0.598504 | − | 1.03664i | ||||
\(179\) | 526576. | 1.22837 | 0.614184 | − | 0.789163i | \(-0.289485\pi\) | ||||
0.614184 | + | 0.789163i | \(0.289485\pi\) | |||||||
\(180\) | 275450. | + | 477094.i | 0.633668 | + | 1.09755i | ||||
\(181\) | −12263.7 | − | 21241.4i | −0.0278245 | − | 0.0481934i | 0.851778 | − | 0.523903i | \(-0.175525\pi\) |
−0.879602 | + | 0.475710i | \(0.842191\pi\) | |||||||
\(182\) | 302656. | + | 524215.i | 0.677284 | + | 1.17309i | ||||
\(183\) | 5813.62 | − | 10069.5i | 0.0128327 | − | 0.0222269i | ||||
\(184\) | −211015. | −0.459483 | ||||||||
\(185\) | 417773. | + | 750066.i | 0.897452 | + | 1.61128i | ||||
\(186\) | 456565. | 0.967654 | ||||||||
\(187\) | 18631.2 | − | 32270.2i | 0.0389617 | − | 0.0674836i | ||||
\(188\) | −151004. | − | 261547.i | −0.311598 | − | 0.539704i | ||||
\(189\) | 224360. | + | 388603.i | 0.456868 | + | 0.791318i | ||||
\(190\) | −82893.6 | − | 143576.i | −0.166585 | − | 0.288534i | ||||
\(191\) | −41380.7 | −0.0820757 | −0.0410379 | − | 0.999158i | \(-0.513066\pi\) | ||||
−0.0410379 | + | 0.999158i | \(0.513066\pi\) | |||||||
\(192\) | −49192.6 | − | 85204.1i | −0.0963045 | − | 0.166804i | ||||
\(193\) | 431522. | 0.833891 | 0.416946 | − | 0.908931i | \(-0.363101\pi\) | ||||
0.416946 | + | 0.908931i | \(0.363101\pi\) | |||||||
\(194\) | −186207. | + | 322520.i | −0.355215 | + | 0.615251i | ||||
\(195\) | 1.82459e6 | 3.43620 | ||||||||
\(196\) | 406089. | 0.755060 | ||||||||
\(197\) | 367477. | − | 636488.i | 0.674628 | − | 1.16849i | −0.301950 | − | 0.953324i | \(-0.597637\pi\) |
0.976578 | − | 0.215166i | \(-0.0690292\pi\) | |||||||
\(198\) | −264067. | − | 457377.i | −0.478686 | − | 0.829109i | ||||
\(199\) | −14916.3 | −0.0267011 | −0.0133506 | − | 0.999911i | \(-0.504250\pi\) | ||||
−0.0133506 | + | 0.999911i | \(0.504250\pi\) | |||||||
\(200\) | 240164. | − | 415975.i | 0.424553 | − | 0.735348i | ||||
\(201\) | −509699. | + | 882825.i | −0.889864 | + | 1.54129i | ||||
\(202\) | 201578. | − | 349143.i | 0.347588 | − | 0.602040i | ||||
\(203\) | −405952. | − | 703129.i | −0.691408 | − | 1.19755i | ||||
\(204\) | −18110.6 | − | 31368.4i | −0.0304689 | − | 0.0527736i | ||||
\(205\) | 124414. | − | 215492.i | 0.206769 | − | 0.358135i | ||||
\(206\) | 25211.1 | − | 43666.8i | 0.0413926 | − | 0.0716942i | ||||
\(207\) | −550539. | + | 953561.i | −0.893022 | + | 1.54676i | ||||
\(208\) | −188611. | −0.302279 | ||||||||
\(209\) | 79467.9 | + | 137642.i | 0.125842 | + | 0.217965i | ||||
\(210\) | 1.01733e6 | − | 1.76206e6i | 1.59189 | − | 2.75723i | ||||
\(211\) | 800984. | 1.23856 | 0.619281 | − | 0.785169i | \(-0.287424\pi\) | ||||
0.619281 | + | 0.785169i | \(0.287424\pi\) | |||||||
\(212\) | 553144. | 0.845276 | ||||||||
\(213\) | 226341. | − | 392035.i | 0.341834 | − | 0.592074i | ||||
\(214\) | −520574. | −0.777048 | ||||||||
\(215\) | 743458. | + | 1.28771e6i | 1.09688 | + | 1.89986i | ||||
\(216\) | −139818. | −0.203905 | ||||||||
\(217\) | −488017. | − | 845270.i | −0.703535 | − | 1.21856i | ||||
\(218\) | 200749. | + | 347707.i | 0.286096 | + | 0.495533i | ||||
\(219\) | −217345. | − | 376452.i | −0.306224 | − | 0.530395i | ||||
\(220\) | −326106. | + | 564832.i | −0.454257 | + | 0.786797i | ||||
\(221\) | −69438.2 | −0.0956352 | ||||||||
\(222\) | −799986. | − | 12329.6i | −1.08943 | − | 0.0167906i | ||||
\(223\) | 374778. | 0.504675 | 0.252338 | − | 0.967639i | \(-0.418801\pi\) | ||||
0.252338 | + | 0.967639i | \(0.418801\pi\) | |||||||
\(224\) | −105163. | + | 182147.i | −0.140037 | + | 0.242551i | ||||
\(225\) | −1.25317e6 | − | 2.17056e6i | −1.65027 | − | 2.85835i | ||||
\(226\) | −283206. | − | 490526.i | −0.368834 | − | 0.638839i | ||||
\(227\) | −679305. | − | 1.17659e6i | −0.874984 | − | 1.51552i | −0.856779 | − | 0.515683i | \(-0.827538\pi\) |
−0.0182048 | − | 0.999834i | \(-0.505795\pi\) | |||||||
\(228\) | 154494. | 0.196822 | ||||||||
\(229\) | 141201. | + | 244567.i | 0.177929 | + | 0.308183i | 0.941171 | − | 0.337930i | \(-0.109727\pi\) |
−0.763242 | + | 0.646113i | \(0.776393\pi\) | |||||||
\(230\) | 1.35976e6 | 1.69490 | ||||||||
\(231\) | −975286. | + | 1.68924e6i | −1.20255 | + | 2.08287i | ||||
\(232\) | 252983. | 0.308583 | ||||||||
\(233\) | 1.37724e6 | 1.66196 | 0.830979 | − | 0.556304i | \(-0.187781\pi\) | ||||
0.830979 | + | 0.556304i | \(0.187781\pi\) | |||||||
\(234\) | −492086. | + | 852318.i | −0.587491 | + | 1.01756i | ||||
\(235\) | 973058. | + | 1.68539e6i | 1.14939 | + | 1.99081i | ||||
\(236\) | −595010. | −0.695416 | ||||||||
\(237\) | 69191.0 | − | 119842.i | 0.0800163 | − | 0.138592i | ||||
\(238\) | −38716.3 | + | 67058.6i | −0.0443049 | + | 0.0767383i | ||||
\(239\) | 785113. | − | 1.35986e6i | 0.889073 | − | 1.53992i | 0.0481000 | − | 0.998843i | \(-0.484683\pi\) |
0.840973 | − | 0.541077i | \(-0.181983\pi\) | |||||||
\(240\) | 316992. | + | 549047.i | 0.355239 | + | 0.615292i | ||||
\(241\) | 335694. | + | 581439.i | 0.372307 | + | 0.644854i | 0.989920 | − | 0.141628i | \(-0.0452336\pi\) |
−0.617613 | + | 0.786482i | \(0.711900\pi\) | |||||||
\(242\) | −9472.87 | + | 16407.5i | −0.0103978 | + | 0.0180096i | ||||
\(243\) | 609824. | − | 1.05625e6i | 0.662504 | − | 1.14749i | ||||
\(244\) | 3872.54 | − | 6707.44i | 0.00416411 | − | 0.00721244i | ||||
\(245\) | −2.61680e6 | −2.78519 | ||||||||
\(246\) | 115940. | + | 200813.i | 0.122150 | + | 0.211570i | ||||
\(247\) | 148088. | − | 256495.i | 0.154446 | − | 0.267508i | ||||
\(248\) | 304125. | 0.313996 | ||||||||
\(249\) | 1.17096e6 | 1.19686 | ||||||||
\(250\) | −903200. | + | 1.56439e6i | −0.913974 | + | 1.58305i | ||||
\(251\) | −1.31724e6 | −1.31972 | −0.659859 | − | 0.751389i | \(-0.729384\pi\) | ||||
−0.659859 | + | 0.751389i | \(0.729384\pi\) | |||||||
\(252\) | 548740. | + | 950445.i | 0.544334 | + | 0.942813i | ||||
\(253\) | −1.30357e6 | −1.28036 | ||||||||
\(254\) | 76725.5 | + | 132892.i | 0.0746200 | + | 0.129246i | ||||
\(255\) | 116703. | + | 202135.i | 0.112391 | + | 0.194666i | ||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −441178. | + | 764143.i | −0.416659 | + | 0.721675i | −0.995601 | − | 0.0936938i | \(-0.970133\pi\) |
0.578942 | + | 0.815369i | \(0.303466\pi\) | |||||||
\(258\) | −1.38563e6 | −1.29598 | ||||||||
\(259\) | 832270. | + | 1.49425e6i | 0.770930 | + | 1.38412i | ||||
\(260\) | 1.21539e6 | 1.11502 | ||||||||
\(261\) | 660034. | − | 1.14321e6i | 0.599743 | − | 1.03879i | ||||
\(262\) | 243142. | + | 421134.i | 0.218830 | + | 0.379025i | ||||
\(263\) | −575323. | − | 996488.i | −0.512888 | − | 0.888347i | −0.999888 | − | 0.0149458i | \(-0.995242\pi\) |
0.487001 | − | 0.873402i | \(-0.338091\pi\) | |||||||
\(264\) | −303892. | − | 526357.i | −0.268355 | − | 0.464805i | ||||
\(265\) | −3.56441e6 | −3.11797 | ||||||||
\(266\) | −165137. | − | 286026.i | −0.143100 | − | 0.247857i | ||||
\(267\) | −3.03848e6 | −2.60843 | ||||||||
\(268\) | −339519. | + | 588064.i | −0.288753 | + | 0.500135i | ||||
\(269\) | −296005. | −0.249413 | −0.124706 | − | 0.992194i | \(-0.539799\pi\) | ||||
−0.124706 | + | 0.992194i | \(0.539799\pi\) | |||||||
\(270\) | 900973. | 0.752146 | ||||||||
\(271\) | −605333. | + | 1.04847e6i | −0.500693 | + | 0.867225i | 0.499307 | + | 0.866425i | \(0.333588\pi\) |
−1.00000 | 0.000800193i | \(0.999745\pi\) | ||||||||
\(272\) | −12063.7 | − | 20895.0i | −0.00988689 | − | 0.0171246i | ||||
\(273\) | 3.63487e6 | 2.95177 | ||||||||
\(274\) | 530188. | − | 918312.i | 0.426632 | − | 0.738948i | ||||
\(275\) | 1.48363e6 | − | 2.56973e6i | 1.18303 | − | 2.04906i | ||||
\(276\) | −633568. | + | 1.09737e6i | −0.500635 | + | 0.867125i | ||||
\(277\) | −47249.7 | − | 81838.9i | −0.0369998 | − | 0.0640856i | 0.846932 | − | 0.531700i | \(-0.178447\pi\) |
−0.883932 | + | 0.467615i | \(0.845113\pi\) | |||||||
\(278\) | −94358.0 | − | 163433.i | −0.0732263 | − | 0.126832i | ||||
\(279\) | 793463. | − | 1.37432e6i | 0.610262 | − | 1.05701i | ||||
\(280\) | 677659. | − | 1.17374e6i | 0.516554 | − | 0.894698i | ||||
\(281\) | 82232.5 | − | 142431.i | 0.0621266 | − | 0.107606i | −0.833289 | − | 0.552837i | \(-0.813545\pi\) |
0.895416 | + | 0.445231i | \(0.146878\pi\) | |||||||
\(282\) | −1.81355e6 | −1.35802 | ||||||||
\(283\) | 302440. | + | 523841.i | 0.224477 | + | 0.388806i | 0.956162 | − | 0.292837i | \(-0.0945992\pi\) |
−0.731685 | + | 0.681643i | \(0.761266\pi\) | |||||||
\(284\) | 150770. | − | 261141.i | 0.110922 | − | 0.192123i | ||||
\(285\) | −995544. | −0.726020 | ||||||||
\(286\) | −1.16516e6 | −0.842309 | ||||||||
\(287\) | 247853. | − | 429294.i | 0.177619 | − | 0.307645i | ||||
\(288\) | −341967. | −0.242942 | ||||||||
\(289\) | 705487. | + | 1.22194e6i | 0.496872 | + | 0.860608i | ||||
\(290\) | −1.63020e6 | −1.13827 | ||||||||
\(291\) | 1.11817e6 | + | 1.93672e6i | 0.774058 | + | 1.34071i | ||||
\(292\) | −144777. | − | 250761.i | −0.0993670 | − | 0.172109i | ||||
\(293\) | 329899. | + | 571401.i | 0.224498 | + | 0.388841i | 0.956169 | − | 0.292817i | \(-0.0945926\pi\) |
−0.731671 | + | 0.681658i | \(0.761259\pi\) | |||||||
\(294\) | 1.21927e6 | − | 2.11184e6i | 0.822684 | − | 1.42493i | ||||
\(295\) | 3.83419e6 | 2.56518 | ||||||||
\(296\) | −532884. | − | 8212.92i | −0.353511 | − | 0.00544839i | ||||
\(297\) | −863739. | −0.568187 | ||||||||
\(298\) | −839512. | + | 1.45408e6i | −0.547629 | + | 0.948521i | ||||
\(299\) | 1.21459e6 | + | 2.10374e6i | 0.785692 | + | 1.36086i | ||||
\(300\) | −1.44217e6 | − | 2.49791e6i | −0.925154 | − | 1.60241i | ||||
\(301\) | 1.48108e6 | + | 2.56531e6i | 0.942245 | + | 1.63202i | ||||
\(302\) | 682954. | 0.430898 | ||||||||
\(303\) | −1.21047e6 | − | 2.09659e6i | −0.757437 | − | 1.31192i | ||||
\(304\) | 102911. | 0.0638672 | ||||||||
\(305\) | −24954.3 | + | 43222.1i | −0.0153602 | + | 0.0266046i | ||||
\(306\) | −125897. | −0.0768621 | ||||||||
\(307\) | −1.85269e6 | −1.12191 | −0.560954 | − | 0.827847i | \(-0.689566\pi\) | ||||
−0.560954 | + | 0.827847i | \(0.689566\pi\) | |||||||
\(308\) | −649654. | + | 1.12523e6i | −0.390216 | + | 0.675874i | ||||
\(309\) | −151391. | − | 262218.i | −0.0901997 | − | 0.156230i | ||||
\(310\) | −1.95975e6 | −1.15824 | ||||||||
\(311\) | 695600. | − | 1.20482e6i | 0.407811 | − | 0.706349i | −0.586833 | − | 0.809708i | \(-0.699626\pi\) |
0.994644 | + | 0.103359i | \(0.0329589\pi\) | |||||||
\(312\) | −566300. | + | 980861.i | −0.329352 | + | 0.570454i | ||||
\(313\) | 343263. | − | 594548.i | 0.198046 | − | 0.343025i | −0.749849 | − | 0.661609i | \(-0.769874\pi\) |
0.947895 | + | 0.318584i | \(0.103207\pi\) | |||||||
\(314\) | −50437.2 | − | 87359.7i | −0.0288687 | − | 0.0500020i | ||||
\(315\) | −3.53603e6 | − | 6.12458e6i | −2.00789 | − | 3.47776i | ||||
\(316\) | 46089.2 | − | 79828.9i | 0.0259646 | − | 0.0449720i | ||||
\(317\) | 599318. | − | 1.03805e6i | 0.334973 | − | 0.580189i | −0.648507 | − | 0.761209i | \(-0.724606\pi\) |
0.983480 | + | 0.181019i | \(0.0579396\pi\) | |||||||
\(318\) | 1.66080e6 | − | 2.87660e6i | 0.920981 | − | 1.59519i | ||||
\(319\) | 1.56283e6 | 0.859875 | ||||||||
\(320\) | 211154. | + | 365729.i | 0.115272 | + | 0.199657i | ||||
\(321\) | −1.56301e6 | + | 2.70722e6i | −0.846642 | + | 1.46643i | ||||
\(322\) | 2.70886e6 | 1.45595 | ||||||||
\(323\) | 37887.3 | 0.0202063 | ||||||||
\(324\) | 229403. | − | 397337.i | 0.121405 | − | 0.210279i | ||||
\(325\) | −5.52947e6 | −2.90386 | ||||||||
\(326\) | 1.06159e6 | + | 1.83872e6i | 0.553237 | + | 0.958234i | ||||
\(327\) | 2.41098e6 | 1.24688 | ||||||||
\(328\) | 77229.3 | + | 133765.i | 0.0396367 | + | 0.0686528i | ||||
\(329\) | 1.93848e6 | + | 3.35755e6i | 0.987353 | + | 1.71015i | ||||
\(330\) | 1.95825e6 | + | 3.39179e6i | 0.989882 | + | 1.71453i | ||||
\(331\) | 300320. | − | 520169.i | 0.150666 | − | 0.260960i | −0.780807 | − | 0.624773i | \(-0.785192\pi\) |
0.931472 | + | 0.363812i | \(0.118525\pi\) | |||||||
\(332\) | 779997. | 0.388372 | ||||||||
\(333\) | −1.42741e6 | + | 2.38663e6i | −0.705404 | + | 1.17944i | ||||
\(334\) | −812805. | −0.398676 | ||||||||
\(335\) | 2.18783e6 | − | 3.78943e6i | 1.06513 | − | 1.84485i | ||||
\(336\) | 631498. | + | 1.09379e6i | 0.305157 | + | 0.528548i | ||||
\(337\) | 773295. | + | 1.33939e6i | 0.370912 | + | 0.642438i | 0.989706 | − | 0.143115i | \(-0.0457119\pi\) |
−0.618794 | + | 0.785553i | \(0.712379\pi\) | |||||||
\(338\) | 343048. | + | 594177.i | 0.163329 | + | 0.282894i | ||||
\(339\) | −3.40127e6 | −1.60747 | ||||||||
\(340\) | 77737.5 | + | 134645.i | 0.0364698 | + | 0.0631676i | ||||
\(341\) | 1.87876e6 | 0.874957 | ||||||||
\(342\) | 268495. | − | 465047.i | 0.124128 | − | 0.214997i | ||||
\(343\) | −1.76098e6 | −0.808200 | ||||||||
\(344\) | −922991. | −0.420534 | ||||||||
\(345\) | 4.08265e6 | − | 7.07136e6i | 1.84669 | − | 3.19857i | ||||
\(346\) | −674983. | − | 1.16910e6i | −0.303112 | − | 0.525005i | ||||
\(347\) | 908469. | 0.405029 | 0.202515 | − | 0.979279i | \(-0.435089\pi\) | ||||
0.202515 | + | 0.979279i | \(0.435089\pi\) | |||||||
\(348\) | 759577. | − | 1.31563e6i | 0.336220 | − | 0.582351i | ||||
\(349\) | 1.60641e6 | − | 2.78238e6i | 0.705981 | − | 1.22279i | −0.260355 | − | 0.965513i | \(-0.583840\pi\) |
0.966336 | − | 0.257282i | \(-0.0828269\pi\) | |||||||
\(350\) | −3.08304e6 | + | 5.33998e6i | −1.34527 | + | 2.33007i | ||||
\(351\) | 804784. | + | 1.39393e6i | 0.348668 | + | 0.603910i | ||||
\(352\) | −202428. | − | 350615.i | −0.0870789 | − | 0.150825i | ||||
\(353\) | −1.42231e6 | + | 2.46351e6i | −0.607515 | + | 1.05225i | 0.384134 | + | 0.923277i | \(0.374500\pi\) |
−0.991649 | + | 0.128969i | \(0.958833\pi\) | |||||||
\(354\) | −1.78651e6 | + | 3.09432e6i | −0.757698 | + | 1.31237i | ||||
\(355\) | −971545. | + | 1.68277e6i | −0.409159 | + | 0.708684i | ||||
\(356\) | −2.02398e6 | −0.846412 | ||||||||
\(357\) | 232490. | + | 402684.i | 0.0965458 | + | 0.167222i | ||||
\(358\) | 1.05315e6 | − | 1.82411e6i | 0.434294 | − | 0.752219i | ||||
\(359\) | −480380. | −0.196720 | −0.0983600 | − | 0.995151i | \(-0.531360\pi\) | ||||
−0.0983600 | + | 0.995151i | \(0.531360\pi\) | |||||||
\(360\) | 2.20360e6 | 0.896142 | ||||||||
\(361\) | 1.15725e6 | − | 2.00441e6i | 0.467368 | − | 0.809505i | ||||
\(362\) | −98110.0 | −0.0393497 | ||||||||
\(363\) | 56884.2 | + | 98526.3i | 0.0226582 | + | 0.0392451i | ||||
\(364\) | 2.42125e6 | 0.957824 | ||||||||
\(365\) | 932928. | + | 1.61588e6i | 0.366536 | + | 0.634858i | ||||
\(366\) | −23254.5 | − | 40277.9i | −0.00907410 | − | 0.0157168i | ||||
\(367\) | 1.72561e6 | + | 2.98885e6i | 0.668772 | + | 1.15835i | 0.978248 | + | 0.207440i | \(0.0665131\pi\) |
−0.309476 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(368\) | −422030. | + | 730978.i | −0.162452 | + | 0.281374i | ||||
\(369\) | 805965. | 0.308142 | ||||||||
\(370\) | 3.43385e6 | + | 52923.2i | 1.30400 | + | 0.0200975i | ||||
\(371\) | −7.10086e6 | −2.67840 | ||||||||
\(372\) | 913130. | − | 1.58159e6i | 0.342117 | − | 0.592565i | ||||
\(373\) | −1.36199e6 | − | 2.35904e6i | −0.506876 | − | 0.877936i | −0.999968 | − | 0.00795847i | \(-0.997467\pi\) |
0.493092 | − | 0.869977i | \(-0.335867\pi\) | |||||||
\(374\) | −74524.9 | − | 129081.i | −0.0275501 | − | 0.0477181i | ||||
\(375\) | 5.42368e6 | + | 9.39408e6i | 1.99166 | + | 3.44966i | ||||
\(376\) | −1.20804e6 | −0.440667 | ||||||||
\(377\) | −1.45616e6 | − | 2.52214e6i | −0.527662 | − | 0.913937i | ||||
\(378\) | 1.79488e6 | 0.646109 | ||||||||
\(379\) | 1.18806e6 | − | 2.05778e6i | 0.424855 | − | 0.735871i | −0.571552 | − | 0.820566i | \(-0.693658\pi\) |
0.996407 | + | 0.0846953i | \(0.0269917\pi\) | |||||||
\(380\) | −663148. | −0.235587 | ||||||||
\(381\) | 921467. | 0.325212 | ||||||||
\(382\) | −82761.5 | + | 143347.i | −0.0290182 | + | 0.0502609i | ||||
\(383\) | 1.89324e6 | + | 3.27918e6i | 0.659489 | + | 1.14227i | 0.980748 | + | 0.195277i | \(0.0625607\pi\) |
−0.321259 | + | 0.946991i | \(0.604106\pi\) | |||||||
\(384\) | −393541. | −0.136195 | ||||||||
\(385\) | 4.18631e6 | − | 7.25089e6i | 1.43939 | − | 2.49310i | ||||
\(386\) | 863044. | − | 1.49484e6i | 0.294825 | − | 0.510652i | ||||
\(387\) | −2.40809e6 | + | 4.17093e6i | −0.817324 | + | 1.41565i | ||||
\(388\) | 744828. | + | 1.29008e6i | 0.251175 | + | 0.435048i | ||||
\(389\) | −431721. | − | 747762.i | −0.144654 | − | 0.250547i | 0.784590 | − | 0.620015i | \(-0.212873\pi\) |
−0.929244 | + | 0.369468i | \(0.879540\pi\) | |||||||
\(390\) | 3.64918e6 | − | 6.32057e6i | 1.21488 | − | 2.10424i | ||||
\(391\) | −155373. | + | 269114.i | −0.0513965 | + | 0.0890214i | ||||
\(392\) | 812178. | − | 1.40673e6i | 0.266954 | − | 0.462378i | ||||
\(393\) | 2.92012e6 | 0.953715 | ||||||||
\(394\) | −1.46991e6 | − | 2.54595e6i | −0.477034 | − | 0.826247i | ||||
\(395\) | −296995. | + | 514410.i | −0.0957758 | + | 0.165889i | ||||
\(396\) | −2.11254e6 | −0.676965 | ||||||||
\(397\) | −535341. | −0.170472 | −0.0852362 | − | 0.996361i | \(-0.527164\pi\) | ||||
−0.0852362 | + | 0.996361i | \(0.527164\pi\) | |||||||
\(398\) | −29832.7 | + | 51671.7i | −0.00944027 | + | 0.0163510i | ||||
\(399\) | −1.98328e6 | −0.623666 | ||||||||
\(400\) | −960654. | − | 1.66390e6i | −0.300204 | − | 0.519969i | ||||
\(401\) | 4.66669e6 | 1.44927 | 0.724633 | − | 0.689135i | \(-0.242009\pi\) | ||||
0.724633 | + | 0.689135i | \(0.242009\pi\) | |||||||
\(402\) | 2.03880e6 | + | 3.53130e6i | 0.629229 | + | 1.08986i | ||||
\(403\) | −1.75053e6 | − | 3.03201e6i | −0.536917 | − | 0.929967i | ||||
\(404\) | −806312. | − | 1.39657e6i | −0.245782 | − | 0.425707i | ||||
\(405\) | −1.47825e6 | + | 2.56040e6i | −0.447827 | + | 0.775658i | ||||
\(406\) | −3.24761e6 | −0.977798 | ||||||||
\(407\) | −3.29194e6 | − | 50736.1i | −0.985069 | − | 0.0151821i | ||||
\(408\) | −144884. | −0.0430895 | ||||||||
\(409\) | −3.12109e6 | + | 5.40588e6i | −0.922566 | + | 1.59793i | −0.127136 | + | 0.991885i | \(0.540578\pi\) |
−0.795430 | + | 0.606046i | \(0.792755\pi\) | |||||||
\(410\) | −497658. | − | 861969.i | −0.146208 | − | 0.253240i | ||||
\(411\) | −3.18375e6 | − | 5.51442e6i | −0.929683 | − | 1.61026i | ||||
\(412\) | −100844. | − | 174667.i | −0.0292690 | − | 0.0506954i | ||||
\(413\) | 7.63830e6 | 2.20354 | ||||||||
\(414\) | 2.20216e6 | + | 3.81424e6i | 0.631462 | + | 1.09372i | ||||
\(415\) | −5.02622e6 | −1.43259 | ||||||||
\(416\) | −377222. | + | 653367.i | −0.106872 | + | 0.185108i | ||||
\(417\) | −1.13323e6 | −0.319138 | ||||||||
\(418\) | 635743. | 0.177968 | ||||||||
\(419\) | −106254. | + | 184038.i | −0.0295672 | + | 0.0512120i | −0.880430 | − | 0.474175i | \(-0.842746\pi\) |
0.850863 | + | 0.525387i | \(0.176080\pi\) | |||||||
\(420\) | −4.06931e6 | − | 7.04826e6i | −1.12564 | − | 1.94966i | ||||
\(421\) | −1.51283e6 | −0.415993 | −0.207996 | − | 0.978130i | \(-0.566694\pi\) | ||||
−0.207996 | + | 0.978130i | \(0.566694\pi\) | |||||||
\(422\) | 1.60197e6 | − | 2.77469e6i | 0.437898 | − | 0.758461i | ||||
\(423\) | −3.15177e6 | + | 5.45902e6i | −0.856452 | + | 1.48342i | ||||
\(424\) | 1.10629e6 | − | 1.91615e6i | 0.298850 | − | 0.517624i | ||||
\(425\) | −353671. | − | 612575.i | −0.0949788 | − | 0.164508i | ||||
\(426\) | −905366. | − | 1.56814e6i | −0.241713 | − | 0.418659i | ||||
\(427\) | −49712.9 | + | 86105.2i | −0.0131947 | + | 0.0228539i | ||||
\(428\) | −1.04115e6 | + | 1.80332e6i | −0.274728 | + | 0.475843i | ||||
\(429\) | −3.49838e6 | + | 6.05936e6i | −0.917747 | + | 1.58959i | ||||
\(430\) | 5.94766e6 | 1.55123 | ||||||||
\(431\) | −2.42496e6 | − | 4.20015e6i | −0.628798 | − | 1.08911i | −0.987793 | − | 0.155771i | \(-0.950214\pi\) |
0.358995 | − | 0.933340i | \(-0.383120\pi\) | |||||||
\(432\) | −279636. | + | 484343.i | −0.0720914 | + | 0.124866i | ||||
\(433\) | −1.39094e6 | −0.356523 | −0.178262 | − | 0.983983i | \(-0.557047\pi\) | ||||
−0.178262 | + | 0.983983i | \(0.557047\pi\) | |||||||
\(434\) | −3.90414e6 | −0.994949 | ||||||||
\(435\) | −4.89464e6 | + | 8.47777e6i | −1.24022 | + | 2.14812i | ||||
\(436\) | 1.60599e6 | 0.404601 | ||||||||
\(437\) | −662713. | − | 1.14785e6i | −0.166005 | − | 0.287530i | ||||
\(438\) | −1.73876e6 | −0.433066 | ||||||||
\(439\) | 514433. | + | 891024.i | 0.127399 | + | 0.220662i | 0.922668 | − | 0.385595i | \(-0.126004\pi\) |
−0.795269 | + | 0.606257i | \(0.792670\pi\) | |||||||
\(440\) | 1.30442e6 | + | 2.25933e6i | 0.321208 | + | 0.556349i | ||||
\(441\) | −4.23795e6 | − | 7.34034e6i | −1.03767 | − | 1.79730i | ||||
\(442\) | −138876. | + | 240541.i | −0.0338122 | + | 0.0585644i | ||||
\(443\) | −2.93007e6 | −0.709363 | −0.354682 | − | 0.934987i | \(-0.615411\pi\) | ||||
−0.354682 | + | 0.934987i | \(0.615411\pi\) | |||||||
\(444\) | −1.64268e6 | + | 2.74658e6i | −0.395454 | + | 0.661202i | ||||
\(445\) | 1.30423e7 | 3.12216 | ||||||||
\(446\) | 749556. | − | 1.29827e6i | 0.178430 | − | 0.309049i | ||||
\(447\) | 5.04123e6 | + | 8.73167e6i | 1.19335 | + | 2.06694i | ||||
\(448\) | 420651. | + | 728589.i | 0.0990210 | + | 0.171509i | ||||
\(449\) | 223128. | + | 386469.i | 0.0522322 | + | 0.0904688i | 0.890959 | − | 0.454083i | \(-0.150033\pi\) |
−0.838727 | + | 0.544552i | \(0.816700\pi\) | |||||||
\(450\) | −1.00254e7 | −2.33383 | ||||||||
\(451\) | 477092. | + | 826347.i | 0.110449 | + | 0.191303i | ||||
\(452\) | −2.26564e6 | −0.521610 | ||||||||
\(453\) | 2.05055e6 | − | 3.55166e6i | 0.469489 | − | 0.813180i | ||||
\(454\) | −5.43444e6 | −1.23741 | ||||||||
\(455\) | −1.56023e7 | −3.53313 | ||||||||
\(456\) | 308988. | − | 535183.i | 0.0695872 | − | 0.120529i | ||||
\(457\) | 2.33406e6 | + | 4.04272e6i | 0.522784 | + | 0.905488i | 0.999649 | + | 0.0265113i | \(0.00843979\pi\) |
−0.476865 | + | 0.878977i | \(0.658227\pi\) | |||||||
\(458\) | 1.12960e6 | 0.251630 | ||||||||
\(459\) | −102950. | + | 178314.i | −0.0228083 | + | 0.0395051i | ||||
\(460\) | 2.71952e6 | − | 4.71035e6i | 0.599236 | − | 1.03791i | ||||
\(461\) | 1.94278e6 | − | 3.36499e6i | 0.425766 | − | 0.737448i | −0.570726 | − | 0.821141i | \(-0.693338\pi\) |
0.996492 | + | 0.0836926i | \(0.0266714\pi\) | |||||||
\(462\) | 3.90114e6 | + | 6.75698e6i | 0.850329 | + | 1.47281i | ||||
\(463\) | −3.49742e6 | − | 6.05770e6i | −0.758219 | − | 1.31327i | −0.943758 | − | 0.330637i | \(-0.892736\pi\) |
0.185539 | − | 0.982637i | \(-0.440597\pi\) | |||||||
\(464\) | 505967. | − | 876360.i | 0.109101 | − | 0.188968i | ||||
\(465\) | −5.88412e6 | + | 1.01916e7i | −1.26197 | + | 2.18580i | ||||
\(466\) | 2.75448e6 | − | 4.77090e6i | 0.587591 | − | 1.01774i | ||||
\(467\) | 510592. | 0.108338 | 0.0541691 | − | 0.998532i | \(-0.482749\pi\) | ||||
0.0541691 | + | 0.998532i | \(0.482749\pi\) | |||||||
\(468\) | 1.96834e6 | + | 3.40927e6i | 0.415419 | + | 0.719527i | ||||
\(469\) | 4.35849e6 | − | 7.54913e6i | 0.914964 | − | 1.58476i | ||||
\(470\) | 7.78446e6 | 1.62549 | ||||||||
\(471\) | −605746. | −0.125817 | ||||||||
\(472\) | −1.19002e6 | + | 2.06118e6i | −0.245867 | + | 0.425853i | ||||
\(473\) | −5.70187e6 | −1.17183 | ||||||||
\(474\) | −276764. | − | 479369.i | −0.0565801 | − | 0.0979996i | ||||
\(475\) | 3.01703e6 | 0.613543 | ||||||||
\(476\) | 154865. | + | 268235.i | 0.0313283 | + | 0.0542622i | ||||
\(477\) | −5.77262e6 | − | 9.99846e6i | −1.16165 | − | 2.01204i | ||||
\(478\) | −3.14045e6 | − | 5.43942e6i | −0.628670 | − | 1.08889i | ||||
\(479\) | 3.44049e6 | − | 5.95910e6i | 0.685143 | − | 1.18670i | −0.288249 | − | 0.957555i | \(-0.593073\pi\) |
0.973392 | − | 0.229147i | \(-0.0735935\pi\) | |||||||
\(480\) | 2.53594e6 | 0.502384 | ||||||||
\(481\) | 2.98537e6 | + | 5.35991e6i | 0.588350 | + | 1.05632i | ||||
\(482\) | 2.68555e6 | 0.526521 | ||||||||
\(483\) | 8.13328e6 | − | 1.40873e7i | 1.58635 | − | 2.74763i | ||||
\(484\) | 37891.5 | + | 65630.0i | 0.00735238 | + | 0.0127347i | ||||
\(485\) | −4.79960e6 | − | 8.31315e6i | −0.926511 | − | 1.60476i | ||||
\(486\) | −2.43930e6 | − | 4.22498e6i | −0.468461 | − | 0.811399i | ||||
\(487\) | 2.84576e6 | 0.543722 | 0.271861 | − | 0.962337i | \(-0.412361\pi\) | ||||
0.271861 | + | 0.962337i | \(0.412361\pi\) | |||||||
\(488\) | −15490.2 | − | 26829.8i | −0.00294447 | − | 0.00509997i | ||||
\(489\) | 1.27496e7 | 2.41114 | ||||||||
\(490\) | −5.23360e6 | + | 9.06486e6i | −0.984714 | + | 1.70557i | ||||
\(491\) | −8.84738e6 | −1.65619 | −0.828097 | − | 0.560585i | \(-0.810576\pi\) | ||||
−0.828097 | + | 0.560585i | \(0.810576\pi\) | |||||||
\(492\) | 927517. | 0.172746 | ||||||||
\(493\) | 186275. | − | 322637.i | 0.0345173 | − | 0.0597857i | ||||
\(494\) | −592350. | − | 1.02598e6i | −0.109210 | − | 0.189157i | ||||
\(495\) | 1.36130e7 | 2.49712 | ||||||||
\(496\) | 608251. | − | 1.05352e6i | 0.111014 | − | 0.192282i | ||||
\(497\) | −1.93547e6 | + | 3.35233e6i | −0.351476 | + | 0.608774i | ||||
\(498\) | 2.34192e6 | − | 4.05633e6i | 0.423155 | − | 0.732926i | ||||
\(499\) | −591814. | − | 1.02505e6i | −0.106398 | − | 0.184287i | 0.807910 | − | 0.589305i | \(-0.200598\pi\) |
−0.914309 | + | 0.405018i | \(0.867265\pi\) | |||||||
\(500\) | 3.61280e6 | + | 6.25755e6i | 0.646277 | + | 1.11939i | ||||
\(501\) | −2.44043e6 | + | 4.22695e6i | −0.434382 | + | 0.752372i | ||||
\(502\) | −2.63448e6 | + | 4.56306e6i | −0.466591 | + | 0.808159i | ||||
\(503\) | −55908.5 | + | 96836.3i | −0.00985275 | + | 0.0170655i | −0.870910 | − | 0.491443i | \(-0.836470\pi\) |
0.861057 | + | 0.508508i | \(0.169803\pi\) | |||||||
\(504\) | 4.38992e6 | 0.769804 | ||||||||
\(505\) | 5.19580e6 | + | 8.99938e6i | 0.906616 | + | 1.57031i | ||||
\(506\) | −2.60713e6 | + | 4.51569e6i | −0.452676 | + | 0.784057i | ||||
\(507\) | 4.11998e6 | 0.711829 | ||||||||
\(508\) | 613804. | 0.105529 | ||||||||
\(509\) | −2.30496e6 | + | 3.99230e6i | −0.394338 | + | 0.683013i | −0.993016 | − | 0.117976i | \(-0.962359\pi\) |
0.598679 | + | 0.800989i | \(0.295693\pi\) | |||||||
\(510\) | 933621. | 0.158944 | ||||||||
\(511\) | 1.85854e6 | + | 3.21908e6i | 0.314861 | + | 0.545356i | ||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −439111. | − | 760563.i | −0.0736684 | − | 0.127597i | ||||
\(514\) | 1.76471e6 | + | 3.05657e6i | 0.294623 | + | 0.510301i | ||||
\(515\) | 649830. | + | 1.12554e6i | 0.107965 | + | 0.187000i | ||||
\(516\) | −2.77126e6 | + | 4.79997e6i | −0.458198 | + | 0.793622i | ||||
\(517\) | −7.46276e6 | −1.22793 | ||||||||
\(518\) | 6.84077e6 | + | 105431.i | 1.12016 | + | 0.0172642i | ||||
\(519\) | −8.10649e6 | −1.32103 | ||||||||
\(520\) | 2.43078e6 | − | 4.21023e6i | 0.394219 | − | 0.682807i | ||||
\(521\) | −3.44452e6 | − | 5.96608e6i | −0.555948 | − | 0.962930i | −0.997829 | − | 0.0658564i | \(-0.979022\pi\) |
0.441881 | − | 0.897074i | \(-0.354311\pi\) | |||||||
\(522\) | −2.64014e6 | − | 4.57285e6i | −0.424082 | − | 0.734532i | ||||
\(523\) | −5.58785e6 | − | 9.67844e6i | −0.893286 | − | 1.54722i | −0.835911 | − | 0.548865i | \(-0.815060\pi\) |
−0.0573752 | − | 0.998353i | \(-0.518273\pi\) | |||||||
\(524\) | 1.94514e6 | 0.309472 | ||||||||
\(525\) | 1.85135e7 | + | 3.20664e7i | 2.93151 | + | 5.07752i | ||||
\(526\) | −4.60258e6 | −0.725333 | ||||||||
\(527\) | 223931. | − | 387860.i | 0.0351227 | − | 0.0608343i | ||||
\(528\) | −2.43114e6 | −0.379511 | ||||||||
\(529\) | 4.43460e6 | 0.688994 | ||||||||
\(530\) | −7.12881e6 | + | 1.23475e7i | −1.10237 | + | 1.90936i | ||||
\(531\) | 6.20953e6 | + | 1.07552e7i | 0.955702 | + | 1.65532i | ||||
\(532\) | −1.32110e6 | −0.202374 | ||||||||
\(533\) | 889056. | − | 1.53989e6i | 0.135554 | − | 0.234786i | ||||
\(534\) | −6.07696e6 | + | 1.05256e7i | −0.922218 | + | 1.59733i | ||||
\(535\) | 6.70905e6 | − | 1.16204e7i | 1.01339 | − | 1.75524i | ||||
\(536\) | 1.35808e6 | + | 2.35226e6i | 0.204179 | + | 0.353649i | ||||
\(537\) | −6.32414e6 | − | 1.09537e7i | −0.946380 | − | 1.63918i | ||||
\(538\) | −592011. | + | 1.02539e6i | −0.0881808 | + | 0.152734i | ||||
\(539\) | 5.01731e6 | − | 8.69024e6i | 0.743874 | − | 1.28843i | ||||
\(540\) | 1.80195e6 | − | 3.12106e6i | 0.265924 | − | 0.460594i | ||||
\(541\) | −1.53349e6 | −0.225262 | −0.112631 | − | 0.993637i | \(-0.535928\pi\) | ||||
−0.112631 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(542\) | 2.42133e6 | + | 4.19387e6i | 0.354043 | + | 0.613221i | ||||
\(543\) | −294573. | + | 510216.i | −0.0428740 | + | 0.0742599i | ||||
\(544\) | −96509.9 | −0.0139822 | ||||||||
\(545\) | −1.03488e7 | −1.49245 | ||||||||
\(546\) | 7.26974e6 | − | 1.25916e7i | 1.04361 | − | 1.80758i | ||||
\(547\) | −1.21105e6 | −0.173059 | −0.0865296 | − | 0.996249i | \(-0.527578\pi\) | ||||
−0.0865296 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(548\) | −2.12075e6 | − | 3.67325e6i | −0.301674 | − | 0.522515i | ||||
\(549\) | −161656. | −0.0228907 | ||||||||
\(550\) | −5.93454e6 | − | 1.02789e7i | −0.836527 | − | 1.44891i | ||||
\(551\) | 794518. | + | 1.37615e6i | 0.111487 | + | 0.193101i | ||||
\(552\) | 2.53427e6 | + | 4.38949e6i | 0.354002 | + | 0.613150i | ||||
\(553\) | −591660. | + | 1.02478e6i | −0.0822733 | + | 0.142502i | ||||
\(554\) | −377998. | −0.0523257 | ||||||||
\(555\) | 1.05853e7 | − | 1.76987e7i | 1.45871 | − | 2.43898i | ||||
\(556\) | −754864. | −0.103558 | ||||||||
\(557\) | −3.47569e6 | + | 6.02008e6i | −0.474683 | + | 0.822175i | −0.999580 | − | 0.0289911i | \(-0.990771\pi\) |
0.524897 | + | 0.851166i | \(0.324104\pi\) | |||||||
\(558\) | −3.17385e6 | − | 5.49728e6i | −0.431521 | − | 0.747415i | ||||
\(559\) | 5.31269e6 | + | 9.20185e6i | 0.719093 | + | 1.24551i | ||||
\(560\) | −2.71064e6 | − | 4.69496e6i | −0.365259 | − | 0.632647i | ||||
\(561\) | −895038. | −0.120070 | ||||||||
\(562\) | −328930. | − | 569723.i | −0.0439301 | − | 0.0760892i | ||||
\(563\) | 9.86649e6 | 1.31187 | 0.655936 | − | 0.754816i | \(-0.272274\pi\) | ||||
0.655936 | + | 0.754816i | \(0.272274\pi\) | |||||||
\(564\) | −3.62710e6 | + | 6.28232e6i | −0.480133 | + | 0.831616i | ||||
\(565\) | 1.45996e7 | 1.92406 | ||||||||
\(566\) | 2.41952e6 | 0.317459 | ||||||||
\(567\) | −2.94490e6 | + | 5.10072e6i | −0.384692 | + | 0.666306i | ||||
\(568\) | −603079. | − | 1.04456e6i | −0.0784338 | − | 0.135851i | ||||
\(569\) | 9.95306e6 | 1.28877 | 0.644386 | − | 0.764701i | \(-0.277113\pi\) | ||||
0.644386 | + | 0.764701i | \(0.277113\pi\) | |||||||
\(570\) | −1.99109e6 | + | 3.44867e6i | −0.256687 | + | 0.444595i | ||||
\(571\) | 4.81461e6 | − | 8.33915e6i | 0.617975 | − | 1.07036i | −0.371880 | − | 0.928281i | \(-0.621287\pi\) |
0.989855 | − | 0.142083i | \(-0.0453801\pi\) | |||||||
\(572\) | −2.33033e6 | + | 4.03624e6i | −0.297801 | + | 0.515807i | ||||
\(573\) | 496979. | + | 860793.i | 0.0632341 | + | 0.109525i | ||||
\(574\) | −991412. | − | 1.71718e6i | −0.125596 | − | 0.217538i | ||||
\(575\) | −1.23726e7 | + | 2.14300e7i | −1.56060 | + | 2.70304i | ||||
\(576\) | −683934. | + | 1.18461e6i | −0.0858930 | + | 0.148771i | ||||
\(577\) | −3.02925e6 | + | 5.24682e6i | −0.378788 | + | 0.656080i | −0.990886 | − | 0.134702i | \(-0.956992\pi\) |
0.612098 | + | 0.790782i | \(0.290326\pi\) | |||||||
\(578\) | 5.64390e6 | 0.702683 | ||||||||
\(579\) | −5.18254e6 | − | 8.97642e6i | −0.642460 | − | 1.11277i | ||||
\(580\) | −3.26040e6 | + | 5.64718e6i | −0.402440 | + | 0.697046i | ||||
\(581\) | −1.00130e7 | −1.23062 | ||||||||
\(582\) | 8.94532e6 | 1.09468 | ||||||||
\(583\) | 6.83421e6 | − | 1.18372e7i | 0.832754 | − | 1.44237i | ||||
\(584\) | −1.15822e6 | −0.140526 | ||||||||
\(585\) | −1.26838e7 | − | 2.19690e7i | −1.53236 | − | 2.65412i | ||||
\(586\) | 2.63919e6 | 0.317487 | ||||||||
\(587\) | −3.55915e6 | − | 6.16463e6i | −0.426335 | − | 0.738434i | 0.570209 | − | 0.821500i | \(-0.306862\pi\) |
−0.996544 | + | 0.0830659i | \(0.973529\pi\) | |||||||
\(588\) | −4.87710e6 | − | 8.44738e6i | −0.581725 | − | 1.00758i | ||||
\(589\) | 955135. | + | 1.65434e6i | 0.113443 | + | 0.196488i | ||||
\(590\) | 7.66838e6 | − | 1.32820e7i | 0.906929 | − | 1.57085i | ||||
\(591\) | −1.76535e7 | −2.07903 | ||||||||
\(592\) | −1.09422e6 | + | 1.82954e6i | −0.128322 | + | 0.214554i | ||||
\(593\) | 9.42260e6 | 1.10036 | 0.550179 | − | 0.835047i | \(-0.314559\pi\) | ||||
0.550179 | + | 0.835047i | \(0.314559\pi\) | |||||||
\(594\) | −1.72748e6 | + | 2.99208e6i | −0.200884 | + | 0.347942i | ||||
\(595\) | −997937. | − | 1.72848e6i | −0.115561 | − | 0.200157i | ||||
\(596\) | 3.35805e6 | + | 5.81631e6i | 0.387232 | + | 0.670706i | ||||
\(597\) | 179144. | + | 310286.i | 0.0205715 | + | 0.0356309i | ||||
\(598\) | 9.71674e6 | 1.11114 | ||||||||
\(599\) | 619395. | + | 1.07282e6i | 0.0705343 | + | 0.122169i | 0.899136 | − | 0.437670i | \(-0.144196\pi\) |
−0.828601 | + | 0.559839i | \(0.810863\pi\) | |||||||
\(600\) | −1.15374e7 | −1.30836 | ||||||||
\(601\) | 3.04422e6 | − | 5.27275e6i | 0.343788 | − | 0.595458i | −0.641345 | − | 0.767253i | \(-0.721623\pi\) |
0.985133 | + | 0.171795i | \(0.0549566\pi\) | |||||||
\(602\) | 1.18487e7 | 1.33254 | ||||||||
\(603\) | 1.41729e7 | 1.58732 | ||||||||
\(604\) | 1.36591e6 | − | 2.36582e6i | 0.152345 | − | 0.263870i | ||||
\(605\) | −244169. | − | 422913.i | −0.0271208 | − | 0.0469746i | ||||
\(606\) | −9.68374e6 | −1.07118 | ||||||||
\(607\) | −2.18634e6 | + | 3.78685e6i | −0.240849 | + | 0.417163i | −0.960956 | − | 0.276699i | \(-0.910759\pi\) |
0.720107 | + | 0.693863i | \(0.244093\pi\) | |||||||
\(608\) | 205822. | − | 356494.i | 0.0225805 | − | 0.0391105i | ||||
\(609\) | −9.75089e6 | + | 1.68890e7i | −1.06537 | + | 1.84528i | ||||
\(610\) | 99817.2 | + | 172888.i | 0.0108613 | + | 0.0188123i | ||||
\(611\) | 6.95339e6 | + | 1.20436e7i | 0.753518 | + | 1.30513i | ||||
\(612\) | −251794. | + | 436121.i | −0.0271749 | + | 0.0470683i | ||||
\(613\) | −1.67511e6 | + | 2.90138e6i | −0.180050 | + | 0.311855i | −0.941897 | − | 0.335901i | \(-0.890959\pi\) |
0.761848 | + | 0.647756i | \(0.224293\pi\) | |||||||
\(614\) | −3.70538e6 | + | 6.41791e6i | −0.396654 | + | 0.687026i | ||||
\(615\) | −5.97683e6 | −0.637211 | ||||||||
\(616\) | 2.59862e6 | + | 4.50093e6i | 0.275924 | + | 0.477915i | ||||
\(617\) | −312937. | + | 542022.i | −0.0330936 | + | 0.0573198i | −0.882098 | − | 0.471066i | \(-0.843869\pi\) |
0.849004 | + | 0.528386i | \(0.177203\pi\) | |||||||
\(618\) | −1.21113e6 | −0.127562 | ||||||||
\(619\) | 4.23865e6 | 0.444632 | 0.222316 | − | 0.974975i | \(-0.428638\pi\) | ||||
0.222316 | + | 0.974975i | \(0.428638\pi\) | |||||||
\(620\) | −3.91951e6 | + | 6.78879e6i | −0.409499 | + | 0.709272i | ||||
\(621\) | 7.20305e6 | 0.749527 | ||||||||
\(622\) | −2.78240e6 | − | 4.81926e6i | −0.288366 | − | 0.499464i | ||||
\(623\) | 2.59824e7 | 2.68200 | ||||||||
\(624\) | 2.26520e6 | + | 3.92344e6i | 0.232887 | + | 0.403372i | ||||
\(625\) | −1.15538e7 | − | 2.00118e7i | −1.18311 | − | 2.04920i | ||||
\(626\) | −1.37305e6 | − | 2.37819e6i | −0.140040 | − | 0.242556i | ||||
\(627\) | 1.90880e6 | − | 3.30615e6i | 0.193907 | − | 0.335856i | ||||
\(628\) | −403497. | −0.0408265 | ||||||||
\(629\) | −402843. | + | 673556.i | −0.0405984 | + | 0.0678808i | ||||
\(630\) | −2.82882e7 | −2.83958 | ||||||||
\(631\) | −6.23079e6 | + | 1.07921e7i | −0.622974 | + | 1.07902i | 0.365955 | + | 0.930633i | \(0.380742\pi\) |
−0.988929 | + | 0.148390i | \(0.952591\pi\) | |||||||
\(632\) | −184357. | − | 319316.i | −0.0183598 | − | 0.0318000i | ||||
\(633\) | −9.61975e6 | − | 1.66619e7i | −0.954233 | − | 1.65278i | ||||
\(634\) | −2.39727e6 | − | 4.15220e6i | −0.236861 | − | 0.410256i | ||||
\(635\) | −3.95529e6 | −0.389264 | ||||||||
\(636\) | −6.64321e6 | − | 1.15064e7i | −0.651232 | − | 1.12797i | ||||
\(637\) | −1.86994e7 | −1.82591 | ||||||||
\(638\) | 3.12566e6 | − | 5.41380e6i | 0.304012 | − | 0.526564i | ||||
\(639\) | −6.29374e6 | −0.609756 | ||||||||
\(640\) | 1.68923e6 | 0.163019 | ||||||||
\(641\) | −3.42273e6 | + | 5.92833e6i | −0.329024 | + | 0.569885i | −0.982318 | − | 0.187218i | \(-0.940053\pi\) |
0.653295 | + | 0.757104i | \(0.273386\pi\) | |||||||
\(642\) | 6.25205e6 | + | 1.08289e7i | 0.598666 | + | 1.03692i | ||||
\(643\) | −5.22377e6 | −0.498261 | −0.249130 | − | 0.968470i | \(-0.580145\pi\) | ||||
−0.249130 | + | 0.968470i | \(0.580145\pi\) | |||||||
\(644\) | 5.41771e6 | − | 9.38375e6i | 0.514756 | − | 0.891583i | ||||
\(645\) | 1.78577e7 | − | 3.09305e7i | 1.69016 | − | 2.92744i | ||||
\(646\) | 75774.6 | − | 131245.i | 0.00714402 | − | 0.0123738i | ||||
\(647\) | 987639. | + | 1.71064e6i | 0.0927550 | + | 0.160656i | 0.908669 | − | 0.417516i | \(-0.137099\pi\) |
−0.815914 | + | 0.578173i | \(0.803766\pi\) | |||||||
\(648\) | −917611. | − | 1.58935e6i | −0.0858462 | − | 0.148690i | ||||
\(649\) | −7.35147e6 | + | 1.27331e7i | −0.685113 | + | 1.18665i | ||||
\(650\) | −1.10589e7 | + | 1.91547e7i | −1.02667 | + | 1.77824i | ||||
\(651\) | −1.17221e7 | + | 2.03032e7i | −1.08406 | + | 1.87764i | ||||
\(652\) | 8.49269e6 | 0.782395 | ||||||||
\(653\) | 1.11118e6 | + | 1.92462e6i | 0.101977 | + | 0.176629i | 0.912499 | − | 0.409079i | \(-0.134150\pi\) |
−0.810522 | + | 0.585708i | \(0.800817\pi\) | |||||||
\(654\) | 4.82195e6 | − | 8.35187e6i | 0.440838 | − | 0.763553i | ||||
\(655\) | −1.25343e7 | −1.14155 | ||||||||
\(656\) | 617834. | 0.0560548 | ||||||||
\(657\) | −3.02179e6 | + | 5.23389e6i | −0.273118 | + | 0.473054i | ||||
\(658\) | 1.55079e7 | 1.39633 | ||||||||
\(659\) | −1.61293e6 | − | 2.79368e6i | −0.144678 | − | 0.250589i | 0.784575 | − | 0.620034i | \(-0.212881\pi\) |
−0.929253 | + | 0.369445i | \(0.879548\pi\) | |||||||
\(660\) | 1.56660e7 | 1.39991 | ||||||||
\(661\) | 8.53576e6 | + | 1.47844e7i | 0.759869 | + | 1.31613i | 0.942917 | + | 0.333027i | \(0.108070\pi\) |
−0.183049 | + | 0.983104i | \(0.558597\pi\) | |||||||
\(662\) | −1.20128e6 | − | 2.08068e6i | −0.106537 | − | 0.184527i | ||||
\(663\) | 833947. | + | 1.44444e6i | 0.0736809 | + | 0.127619i | ||||
\(664\) | 1.55999e6 | − | 2.70199e6i | 0.137310 | − | 0.237828i | ||||
\(665\) | 8.51301e6 | 0.746498 | ||||||||
\(666\) | 5.41273e6 | + | 9.71796e6i | 0.472858 | + | 0.848964i | ||||
\(667\) | −1.30330e7 | −1.13431 | ||||||||
\(668\) | −1.62561e6 | + | 2.81564e6i | −0.140953 | + | 0.244138i | ||||
\(669\) | −4.50105e6 | − | 7.79605e6i | −0.388820 | − | 0.673456i | ||||
\(670\) | −8.75130e6 | − | 1.51577e7i | −0.753157 | − | 1.30451i | ||||
\(671\) | −95692.1 | − | 165744.i | −0.00820483 | − | 0.0142112i | ||||
\(672\) | 5.05199e6 | 0.431558 | ||||||||
\(673\) | 8.35440e6 | + | 1.44702e7i | 0.711013 | + | 1.23151i | 0.964477 | + | 0.264166i | \(0.0850965\pi\) |
−0.253465 | + | 0.967345i | \(0.581570\pi\) | |||||||
\(674\) | 6.18636e6 | 0.524549 | ||||||||
\(675\) | −8.19804e6 | + | 1.41994e7i | −0.692549 | + | 1.19953i | ||||
\(676\) | 2.74439e6 | 0.230982 | ||||||||
\(677\) | 1.14872e7 | 0.963257 | 0.481629 | − | 0.876375i | \(-0.340045\pi\) | ||||
0.481629 | + | 0.876375i | \(0.340045\pi\) | |||||||
\(678\) | −6.80255e6 | + | 1.17824e7i | −0.568326 | + | 0.984369i | ||||
\(679\) | −9.56155e6 | − | 1.65611e7i | −0.795892 | − | 1.37852i | ||||
\(680\) | 621900. | 0.0515761 | ||||||||
\(681\) | −1.63168e7 | + | 2.82615e7i | −1.34824 | + | 2.33522i | ||||
\(682\) | 3.75753e6 | − | 6.50823e6i | 0.309344 | − | 0.535799i | ||||
\(683\) | 3.25933e6 | − | 5.64532e6i | 0.267347 | − | 0.463059i | −0.700829 | − | 0.713330i | \(-0.747186\pi\) |
0.968176 | + | 0.250270i | \(0.0805195\pi\) | |||||||
\(684\) | −1.07398e6 | − | 1.86019e6i | −0.0877720 | − | 0.152026i | ||||
\(685\) | 1.36659e7 | + | 2.36700e7i | 1.11279 | + | 1.92740i | ||||
\(686\) | −3.52196e6 | + | 6.10021e6i | −0.285742 | + | 0.494919i | ||||
\(687\) | 3.39161e6 | − | 5.87445e6i | 0.274167 | − | 0.474871i | ||||
\(688\) | −1.84598e6 | + | 3.19734e6i | −0.148681 | + | 0.257524i | ||||
\(689\) | −2.54710e7 | −2.04408 | ||||||||
\(690\) | −1.63306e7 | − | 2.82854e7i | −1.30581 | − | 2.26173i | ||||
\(691\) | −1.03095e7 | + | 1.78566e7i | −0.821380 | + | 1.42267i | 0.0832746 | + | 0.996527i | \(0.473462\pi\) |
−0.904655 | + | 0.426145i | \(0.859871\pi\) | |||||||
\(692\) | −5.39986e6 | −0.428665 | ||||||||
\(693\) | 2.71192e7 | 2.14508 | ||||||||
\(694\) | 1.81694e6 | − | 3.14703e6i | 0.143199 | − | 0.248029i | ||||
\(695\) | 4.86427e6 | 0.381993 | ||||||||
\(696\) | −3.03831e6 | − | 5.26251e6i | −0.237744 | − | 0.411784i | ||||
\(697\) | 227459. | 0.0177346 | ||||||||
\(698\) | −6.42564e6 | − | 1.11295e7i | −0.499204 | − | 0.864647i | ||||
\(699\) | −1.65405e7 | − | 2.86491e7i | −1.28043 | − | 2.21777i | ||||
\(700\) | 1.23322e7 | + | 2.13599e7i | 0.951249 | + | 1.64761i | ||||
\(701\) | 7.37806e6 | − | 1.27792e7i | 0.567084 | − | 0.982218i | −0.429769 | − | 0.902939i | \(-0.641405\pi\) |
0.996852 | − | 0.0792787i | \(-0.0252617\pi\) | |||||||
\(702\) | 6.43828e6 | 0.493091 | ||||||||
\(703\) | −1.62890e6 | − | 2.92451e6i | −0.124310 | − | 0.223185i | ||||
\(704\) | −1.61942e6 | −0.123148 | ||||||||
\(705\) | 2.33727e7 | − | 4.04827e7i | 1.77107 | − | 3.06758i | ||||
\(706\) | 5.68923e6 | + | 9.85404e6i | 0.429578 | + | 0.744050i | ||||
\(707\) | 1.03508e7 | + | 1.79282e7i | 0.778802 | + | 1.34892i | ||||
\(708\) | 7.14602e6 | + | 1.23773e7i | 0.535774 | + | 0.927987i | ||||
\(709\) | −2.84672e6 | −0.212682 | −0.106341 | − | 0.994330i | \(-0.533913\pi\) | ||||
−0.106341 | + | 0.994330i | \(0.533913\pi\) | |||||||
\(710\) | 3.88618e6 | + | 6.73106e6i | 0.289319 | + | 0.501116i | ||||
\(711\) | −1.92395e6 | −0.142731 | ||||||||
\(712\) | −4.04796e6 | + | 7.01128e6i | −0.299252 | + | 0.518319i | ||||
\(713\) | −1.56677e7 | −1.15420 | ||||||||
\(714\) | 1.85992e6 | 0.136536 | ||||||||
\(715\) | 1.50164e7 | − | 2.60091e7i | 1.09850 | − | 1.90266i | ||||
\(716\) | −4.21261e6 | − | 7.29645e6i | −0.307092 | − | 0.531899i | ||||
\(717\) | −3.77166e7 | −2.73990 | ||||||||
\(718\) | −960760. | + | 1.66408e6i | −0.0695511 | + | 0.120466i | ||||
\(719\) | −6.14389e6 | + | 1.06415e7i | −0.443222 | + | 0.767683i | −0.997926 | − | 0.0643642i | \(-0.979498\pi\) |
0.554704 | + | 0.832048i | \(0.312831\pi\) | |||||||
\(720\) | 4.40720e6 | − | 7.63350e6i | 0.316834 | − | 0.548773i | ||||
\(721\) | 1.29456e6 | + | 2.24225e6i | 0.0927439 | + | 0.160637i | ||||
\(722\) | −4.62900e6 | − | 8.01766e6i | −0.330479 | − | 0.572406i | ||||
\(723\) | 8.06331e6 | − | 1.39661e7i | 0.573678 | − | 0.993639i | ||||
\(724\) | −196220. | + | 339863.i | −0.0139122 | + | 0.0240967i | ||||
\(725\) | 1.48333e7 | − | 2.56921e7i | 1.04808 | − | 1.81533i | ||||
\(726\) | 455073. | 0.0320435 | ||||||||
\(727\) | 1.07543e7 | + | 1.86270e7i | 0.754653 | + | 1.30710i | 0.945547 | + | 0.325486i | \(0.105528\pi\) |
−0.190894 | + | 0.981611i | \(0.561139\pi\) | |||||||
\(728\) | 4.84249e6 | − | 8.38745e6i | 0.338642 | − | 0.586545i | ||||
\(729\) | −2.23276e7 | −1.55605 | ||||||||
\(730\) | 7.46343e6 | 0.518360 | ||||||||
\(731\) | −679610. | + | 1.17712e6i | −0.0470399 | + | 0.0814754i | ||||
\(732\) | −186036. | −0.0128327 | ||||||||
\(733\) | 4.59209e6 | + | 7.95373e6i | 0.315682 | + | 0.546778i | 0.979582 | − | 0.201043i | \(-0.0644332\pi\) |
−0.663900 | + | 0.747821i | \(0.731100\pi\) | |||||||
\(734\) | 1.38049e7 | 0.945786 | ||||||||
\(735\) | 3.14275e7 | + | 5.44341e7i | 2.14581 | + | 3.71666i | ||||
\(736\) | 1.68812e6 | + | 2.92391e6i | 0.114871 | + | 0.198962i | ||||
\(737\) | 8.38965e6 | + | 1.45313e7i | 0.568951 | + | 0.985452i | ||||
\(738\) | 1.61193e6 | − | 2.79195e6i | 0.108945 | − | 0.188697i | ||||
\(739\) | −5.02845e6 | −0.338706 | −0.169353 | − | 0.985555i | \(-0.554168\pi\) | ||||
−0.169353 | + | 0.985555i | \(0.554168\pi\) | |||||||
\(740\) | 7.05104e6 | − | 1.17894e7i | 0.473340 | − | 0.791428i | ||||
\(741\) | −7.11408e6 | −0.475963 | ||||||||
\(742\) | −1.42017e7 | + | 2.45981e7i | −0.946958 | + | 1.64018i | ||||
\(743\) | −4.42667e6 | − | 7.66721e6i | −0.294174 | − | 0.509525i | 0.680618 | − | 0.732638i | \(-0.261711\pi\) |
−0.974792 | + | 0.223113i | \(0.928378\pi\) | |||||||
\(744\) | −3.65252e6 | − | 6.32635e6i | −0.241914 | − | 0.419007i | ||||
\(745\) | −2.16389e7 | − | 3.74797e7i | −1.42838 | − | 2.47404i | ||||
\(746\) | −1.08959e7 | −0.716831 | ||||||||
\(747\) | −8.14005e6 | − | 1.40990e7i | −0.533735 | − | 0.924456i | ||||
\(748\) | −596199. | −0.0389617 | ||||||||
\(749\) | 1.33655e7 | − | 2.31497e7i | 0.870523 | − | 1.50779i | ||||
\(750\) | 4.33894e7 | 2.81664 | ||||||||
\(751\) | 5.56144e6 | 0.359822 | 0.179911 | − | 0.983683i | \(-0.442419\pi\) | ||||
0.179911 | + | 0.983683i | \(0.442419\pi\) | |||||||
\(752\) | −2.41607e6 | + | 4.18476e6i | −0.155799 | + | 0.269852i | ||||
\(753\) | 1.58200e7 | + | 2.74010e7i | 1.01676 | + | 1.76108i | ||||
\(754\) | −1.16493e7 | −0.746226 | ||||||||
\(755\) | −8.80178e6 | + | 1.52451e7i | −0.561957 | + | 0.973338i | ||||
\(756\) | 3.58976e6 | − | 6.21764e6i | 0.228434 | − | 0.395659i | ||||
\(757\) | 1.14793e7 | − | 1.98827e7i | 0.728072 | − | 1.26106i | −0.229625 | − | 0.973279i | \(-0.573750\pi\) |
0.957697 | − | 0.287778i | \(-0.0929166\pi\) | |||||||
\(758\) | −4.75225e6 | − | 8.23113e6i | −0.300418 | − | 0.520339i | ||||
\(759\) | 1.56557e7 | + | 2.71165e7i | 0.986436 | + | 1.70856i | ||||
\(760\) | −1.32630e6 | + | 2.29721e6i | −0.0832927 | + | 0.144267i | ||||
\(761\) | −6.27405e6 | + | 1.08670e7i | −0.392723 | + | 0.680216i | −0.992808 | − | 0.119720i | \(-0.961800\pi\) |
0.600085 | + | 0.799937i | \(0.295134\pi\) | |||||||
\(762\) | 1.84293e6 | − | 3.19205e6i | 0.114980 | − | 0.199151i | ||||
\(763\) | −2.06165e7 | −1.28205 | ||||||||
\(764\) | 331046. | + | 573388.i | 0.0205189 | + | 0.0355398i | ||||
\(765\) | 1.62254e6 | − | 2.81032e6i | 0.100240 | − | 0.173621i | ||||
\(766\) | 1.51459e7 | 0.932659 | ||||||||
\(767\) | 2.73988e7 | 1.68168 | ||||||||
\(768\) | −787082. | + | 1.36327e6i | −0.0481523 | + | 0.0834022i | ||||
\(769\) | −1.96795e7 | −1.20004 | −0.600022 | − | 0.799984i | \(-0.704842\pi\) | ||||
−0.600022 | + | 0.799984i | \(0.704842\pi\) | |||||||
\(770\) | −1.67452e7 | − | 2.90036e7i | −1.01780 | − | 1.76289i | ||||
\(771\) | 2.11940e7 | 1.28404 | ||||||||
\(772\) | −3.45218e6 | − | 5.97934e6i | −0.208473 | − | 0.361086i | ||||
\(773\) | −5.16058e6 | − | 8.93839e6i | −0.310635 | − | 0.538035i | 0.667865 | − | 0.744282i | \(-0.267208\pi\) |
−0.978500 | + | 0.206247i | \(0.933875\pi\) | |||||||
\(774\) | 9.63234e6 | + | 1.66837e7i | 0.577936 | + | 1.00101i | ||||
\(775\) | 1.78320e7 | − | 3.08859e7i | 1.06646 | − | 1.84717i | ||||
\(776\) | 5.95863e6 | 0.355215 | ||||||||
\(777\) | 2.10876e7 | − | 3.52585e7i | 1.25307 | − | 2.09513i | ||||
\(778\) | −3.45377e6 | −0.204571 | ||||||||
\(779\) | −485092. | + | 840204.i | −0.0286405 | + | 0.0496068i | ||||
\(780\) | −1.45967e7 | − | 2.52823e7i | −0.859051 | − | 1.48792i | ||||
\(781\) | −3.72558e6 | − | 6.45290e6i | −0.218558 | − | 0.378553i | ||||
\(782\) | 621492. | + | 1.07646e6i | 0.0363428 | + | 0.0629476i | ||||
\(783\) | −8.63565e6 | −0.503374 | ||||||||
\(784\) | −3.24871e6 | − | 5.62694e6i | −0.188765 | − | 0.326950i | ||||
\(785\) | 2.60010e6 | 0.150597 | ||||||||
\(786\) | 5.84023e6 | − | 1.01156e7i | 0.337189 | − | 0.584029i | ||||
\(787\) | 2.79254e6 | 0.160717 | 0.0803587 | − | 0.996766i | \(-0.474393\pi\) | ||||
0.0803587 | + | 0.996766i | \(0.474393\pi\) | |||||||
\(788\) | −1.17593e7 | −0.674628 | ||||||||
\(789\) | −1.38192e7 | + | 2.39355e7i | −0.790294 | + | 1.36883i | ||||
\(790\) | 1.18798e6 | + | 2.05764e6i | 0.0677237 | + | 0.117301i | ||||
\(791\) | 2.90847e7 | 1.65281 | ||||||||
\(792\) | −4.22507e6 | + | 7.31804e6i | −0.239343 | + | 0.414554i | ||||
\(793\) | −178321. | + | 308862.i | −0.0100698 | + | 0.0174414i | ||||
\(794\) | −1.07068e6 | + | 1.85447e6i | −0.0602711 | + | 0.104393i | ||||
\(795\) | 4.28082e7 | + | 7.41460e7i | 2.40220 | + | 4.16073i | ||||
\(796\) | 119331. | + | 206687.i | 0.00667528 | + | 0.0115619i | ||||
\(797\) | 9.30020e6 | − | 1.61084e7i | 0.518616 | − | 0.898270i | −0.481150 | − | 0.876639i | \(-0.659781\pi\) |
0.999766 | − | 0.0216316i | \(-0.00688608\pi\) | |||||||
\(798\) | −3.96656e6 | + | 6.87028e6i | −0.220499 | + | 0.381916i | ||||
\(799\) | −889491. | + | 1.54064e6i | −0.0492918 | + | 0.0853759i | ||||
\(800\) | −7.68523e6 | −0.424553 | ||||||||
\(801\) | 2.11223e7 | + | 3.65849e7i | 1.16321 | + | 2.01475i | ||||
\(802\) | 9.33339e6 | − | 1.61659e7i | 0.512393 | − | 0.887491i | ||||
\(803\) | −7.15499e6 | −0.391580 | ||||||||
\(804\) | 1.63104e7 | 0.889864 | ||||||||
\(805\) | −3.49112e7 | + | 6.04680e7i | −1.89878 | + | 3.28879i | ||||
\(806\) | −1.40042e7 | −0.759315 | ||||||||
\(807\) | 3.55500e6 | + | 6.15744e6i | 0.192157 | + | 0.332825i | ||||
\(808\) | −6.45050e6 | −0.347588 | ||||||||
\(809\) | −1.56542e6 | − | 2.71140e6i | −0.0840932 | − | 0.145654i | 0.820911 | − | 0.571056i | \(-0.193466\pi\) |
−0.905004 | + | 0.425402i | \(0.860133\pi\) | |||||||
\(810\) | 5.91299e6 | + | 1.02416e7i | 0.316661 | + | 0.548473i | ||||
\(811\) | 2.14826e6 | + | 3.72089e6i | 0.114692 | + | 0.198653i | 0.917657 | − | 0.397374i | \(-0.130079\pi\) |
−0.802964 | + | 0.596027i | \(0.796745\pi\) | |||||||
\(812\) | −6.49523e6 | + | 1.12501e7i | −0.345704 | + | 0.598777i | ||||
\(813\) | 2.90800e7 | 1.54301 | ||||||||
\(814\) | −6.75964e6 | + | 1.13022e7i | −0.357571 | + | 0.597861i | ||||
\(815\) | −5.47260e7 | −2.88602 | ||||||||
\(816\) | −289769. | + | 501894.i | −0.0152344 | + | 0.0263868i | ||||
\(817\) | −2.89874e6 | − | 5.02077e6i | −0.151934 | − | 0.263157i | ||||
\(818\) | 1.24843e7 | + | 2.16235e7i | 0.652353 | + | 1.12991i | ||||
\(819\) | −2.52681e7 | − | 4.37657e7i | −1.31633 | − | 2.27994i | ||||
\(820\) | −3.98126e6 | −0.206769 | ||||||||
\(821\) | 1.20562e7 | + | 2.08819e7i | 0.624239 | + | 1.08121i | 0.988688 | + | 0.149990i | \(0.0479242\pi\) |
−0.364449 | + | 0.931224i | \(0.618743\pi\) | |||||||
\(822\) | −2.54700e7 | −1.31477 | ||||||||
\(823\) | −1.01013e7 | + | 1.74960e7i | −0.519849 | + | 0.900406i | 0.479884 | + | 0.877332i | \(0.340679\pi\) |
−0.999734 | + | 0.0230738i | \(0.992655\pi\) | |||||||
\(824\) | −806754. | −0.0413926 | ||||||||
\(825\) | −7.12733e7 | −3.64579 | ||||||||
\(826\) | 1.52766e7 | − | 2.64599e7i | 0.779070 | − | 1.34939i | ||||
\(827\) | 1.43337e6 | + | 2.48267e6i | 0.0728777 | + | 0.126228i | 0.900161 | − | 0.435557i | \(-0.143448\pi\) |
−0.827284 | + | 0.561784i | \(0.810115\pi\) | |||||||
\(828\) | 1.76172e7 | 0.893022 | ||||||||
\(829\) | 477710. | − | 827419.i | 0.0241423 | − | 0.0418157i | −0.853702 | − | 0.520762i | \(-0.825648\pi\) |
0.877844 | + | 0.478946i | \(0.158981\pi\) | |||||||
\(830\) | −1.00524e7 | + | 1.74113e7i | −0.506497 | + | 0.877278i | ||||
\(831\) | −1.13493e6 | + | 1.96576e6i | −0.0570120 | + | 0.0987477i | ||||
\(832\) | 1.50889e6 | + | 2.61347e6i | 0.0755698 | + | 0.130891i | ||||
\(833\) | −1.19603e6 | − | 2.07159e6i | −0.0597215 | − | 0.103441i | ||||
\(834\) | −2.26646e6 | + | 3.92563e6i | −0.112832 | + | 0.195431i | ||||
\(835\) | 1.04753e7 | − | 1.81437e7i | 0.519935 | − | 0.900554i | ||||
\(836\) | 1.27149e6 | − | 2.20228e6i | 0.0629210 | − | 0.108982i | ||||
\(837\) | −1.03814e7 | −0.512203 | ||||||||
\(838\) | 425017. | + | 736150.i | 0.0209072 | + | 0.0362123i | ||||
\(839\) | 1.85410e7 | − | 3.21140e7i | 0.909344 | − | 1.57503i | 0.0943674 | − | 0.995537i | \(-0.469917\pi\) |
0.814977 | − | 0.579493i | \(-0.196750\pi\) | |||||||
\(840\) | −3.25545e7 | −1.59189 | ||||||||
\(841\) | −4.88600e6 | −0.238212 | ||||||||
\(842\) | −3.02567e6 | + | 5.24061e6i | −0.147076 | + | 0.254743i | ||||
\(843\) | −3.95042e6 | −0.191458 | ||||||||
\(844\) | −6.40787e6 | − | 1.10988e7i | −0.309641 | − | 0.536313i | ||||
\(845\) | −1.76846e7 | −0.852026 | ||||||||
\(846\) | 1.26071e7 | + | 2.18361e7i | 0.605603 | + | 1.04894i | ||||
\(847\) | −486423. | − | 842509.i | −0.0232973 | − | 0.0403521i | ||||
\(848\) | −4.42515e6 | − | 7.66459e6i | −0.211319 | − | 0.366015i | ||||
\(849\) | 7.26455e6 | − | 1.25826e7i | 0.345891 | − | 0.599101i | ||||
\(850\) | −2.82936e6 | −0.134320 | ||||||||
\(851\) | 2.74528e7 | + | 423108.i | 1.29946 | + | 0.0200275i | ||||
\(852\) | −7.24293e6 | −0.341834 | ||||||||
\(853\) | −6.60414e6 | + | 1.14387e7i | −0.310773 | + | 0.538275i | −0.978530 | − | 0.206105i | \(-0.933921\pi\) |
0.667757 | + | 0.744380i | \(0.267255\pi\) | |||||||
\(854\) | 198851. | + | 344421.i | 0.00933005 | + | 0.0161601i | ||||
\(855\) | 6.92062e6 | + | 1.19869e7i | 0.323765 | + | 0.560777i | ||||
\(856\) | 4.16459e6 | + | 7.21328e6i | 0.194262 | + | 0.336472i | ||||
\(857\) | 2.61370e7 | 1.21564 | 0.607818 | − | 0.794076i | \(-0.292045\pi\) | ||||
0.607818 | + | 0.794076i | \(0.292045\pi\) | |||||||
\(858\) | 1.39935e7 | + | 2.42375e7i | 0.648945 | + | 1.12401i | ||||
\(859\) | −2.51655e7 | −1.16365 | −0.581825 | − | 0.813314i | \(-0.697661\pi\) | ||||
−0.581825 | + | 0.813314i | \(0.697661\pi\) | |||||||
\(860\) | 1.18953e7 | − | 2.06033e7i | 0.548442 | − | 0.949929i | ||||
\(861\) | −1.19068e7 | −0.547377 | ||||||||
\(862\) | −1.93997e7 | −0.889255 | ||||||||
\(863\) | −5.74881e6 | + | 9.95722e6i | −0.262755 | + | 0.455105i | −0.966973 | − | 0.254879i | \(-0.917964\pi\) |
0.704218 | + | 0.709984i | \(0.251298\pi\) | |||||||
\(864\) | 1.11854e6 | + | 1.93737e6i | 0.0509763 | + | 0.0882936i | ||||
\(865\) | 3.47962e7 | 1.58122 | ||||||||
\(866\) | −2.78188e6 | + | 4.81835e6i | −0.126050 | + | 0.218325i | ||||
\(867\) | 1.69457e7 | − | 2.93508e7i | 0.765616 | − | 1.32609i | ||||
\(868\) | −7.80827e6 | + | 1.35243e7i | −0.351767 | + | 0.609279i | ||||
\(869\) | −1.13888e6 | − | 1.97260e6i | −0.0511599 | − | 0.0886116i | ||||
\(870\) | 1.95786e7 | + | 3.39111e7i | 0.876966 | + | 1.51895i | ||||
\(871\) | 1.56340e7 | − | 2.70789e7i | 0.698273 | − | 1.20944i | ||||
\(872\) | 3.21198e6 | − | 5.56332e6i | 0.143048 | − | 0.247766i | ||||
\(873\) | 1.55461e7 | − | 2.69266e7i | 0.690375 | − | 1.19576i | ||||
\(874\) | −5.30170e6 | −0.234767 | ||||||||
\(875\) | −4.63784e7 | − | 8.03298e7i | −2.04784 | − | 3.54696i | ||||
\(876\) | −3.47752e6 | + | 6.02324e6i | −0.153112 | + | 0.265198i | ||||
\(877\) | −4.63660e6 | −0.203564 | −0.101782 | − | 0.994807i | \(-0.532454\pi\) | ||||
−0.101782 | + | 0.994807i | \(0.532454\pi\) | |||||||
\(878\) | 4.11546e6 | 0.180170 | ||||||||
\(879\) | 7.92411e6 | − | 1.37250e7i | 0.345922 | − | 0.599155i | ||||
\(880\) | 1.04354e7 | 0.454257 | ||||||||
\(881\) | 1.51867e7 | + | 2.63042e7i | 0.659210 | + | 1.14179i | 0.980820 | + | 0.194914i | \(0.0624426\pi\) |
−0.321610 | + | 0.946872i | \(0.604224\pi\) | |||||||
\(882\) | −3.39036e7 | −1.46749 | ||||||||
\(883\) | −497335. | − | 861410.i | −0.0214658 | − | 0.0371799i | 0.855093 | − | 0.518475i | \(-0.173500\pi\) |
−0.876559 | + | 0.481295i | \(0.840167\pi\) | |||||||
\(884\) | 555506. | + | 962164.i | 0.0239088 | + | 0.0414113i | ||||
\(885\) | −4.60483e7 | − | 7.97579e7i | −1.97631 | − | 3.42307i | ||||
\(886\) | −5.86014e6 | + | 1.01501e7i | −0.250798 | + | 0.434395i | ||||
\(887\) | −1.42289e7 | −0.607241 | −0.303621 | − | 0.952793i | \(-0.598196\pi\) | ||||
−0.303621 | + | 0.952793i | \(0.598196\pi\) | |||||||
\(888\) | 6.22905e6 | + | 1.11836e7i | 0.265088 | + | 0.475936i | ||||
\(889\) | −7.87956e6 | −0.334386 | ||||||||
\(890\) | 2.60847e7 | − | 4.51800e7i | 1.10385 | − | 1.91193i | ||||
\(891\) | −5.66863e6 | − | 9.81836e6i | −0.239213 | − | 0.414328i | ||||
\(892\) | −2.99822e6 | − | 5.19308e6i | −0.126169 | − | 0.218531i | ||||
\(893\) | −3.79395e6 | − | 6.57132e6i | −0.159207 | − | 0.275755i | ||||
\(894\) | 4.03299e7 | 1.68765 | ||||||||
\(895\) | 2.71456e7 | + | 4.70176e7i | 1.13277 | + | 1.96202i | ||||
\(896\) | 3.36521e6 | 0.140037 | ||||||||
\(897\) | 2.91743e7 | − | 5.05314e7i | 1.21065 | − | 2.09691i | ||||
\(898\) | 1.78502e6 | 0.0738675 | ||||||||
\(899\) | 1.87839e7 | 0.775150 | ||||||||
\(900\) | −2.00508e7 | + | 3.47290e7i | −0.825135 | + | 1.42918i | ||||
\(901\) | −1.62915e6 | − | 2.82177e6i | −0.0668572 | − | 0.115800i | ||||
\(902\) | 3.81673e6 | 0.156198 | ||||||||
\(903\) | 3.55754e7 | − | 6.16184e7i | 1.45188 | − | 2.51473i | ||||
\(904\) | −4.53129e6 | + | 7.84842e6i | −0.184417 | + | 0.319419i | ||||
\(905\) | 1.26442e6 | − | 2.19004e6i | 0.0513181 | − | 0.0888856i | ||||
\(906\) | −8.20222e6 | − | 1.42067e7i | −0.331979 | − | 0.575005i | ||||
\(907\) | −2.19475e7 | − | 3.80142e7i | −0.885863 | − | 1.53436i | −0.844721 | − | 0.535206i | \(-0.820234\pi\) |
−0.0411417 | − | 0.999153i | \(-0.513099\pi\) | |||||||
\(908\) | −1.08689e7 | + | 1.88255e7i | −0.437492 | + | 0.757759i | ||||
\(909\) | −1.68294e7 | + | 2.91493e7i | −0.675550 | + | 1.17009i | ||||
\(910\) | −3.12046e7 | + | 5.40479e7i | −1.24915 | + | 2.16359i | ||||
\(911\) | −2.73730e7 | −1.09276 | −0.546382 | − | 0.837536i | \(-0.683995\pi\) | ||||
−0.546382 | + | 0.837536i | \(0.683995\pi\) | |||||||
\(912\) | −1.23595e6 | − | 2.14073e6i | −0.0492056 | − | 0.0852266i | ||||
\(913\) | 9.63702e6 | − | 1.66918e7i | 0.382618 | − | 0.662714i | ||||
\(914\) | 1.86725e7 | 0.739328 | ||||||||
\(915\) | 1.19880e6 | 0.0473361 | ||||||||
\(916\) | 2.25921e6 | − | 3.91307e6i | 0.0889647 | − | 0.154091i | ||||
\(917\) | −2.49702e7 | −0.980616 | ||||||||
\(918\) | 411798. | + | 713256.i | 0.0161279 | + | 0.0279343i | ||||
\(919\) | 9.32028e6 | 0.364033 | 0.182016 | − | 0.983296i | \(-0.441738\pi\) | ||||
0.182016 | + | 0.983296i | \(0.441738\pi\) | |||||||
\(920\) | −1.08781e7 | − | 1.88414e7i | −0.423724 | − | 0.733911i | ||||
\(921\) | 2.22507e7 | + | 3.85393e7i | 0.864359 | + | 1.49711i | ||||
\(922\) | −7.77111e6 | − | 1.34600e7i | −0.301062 | − | 0.521455i | ||||
\(923\) | −6.94258e6 | + | 1.20249e7i | −0.268236 | + | 0.464598i | ||||
\(924\) | 3.12091e7 | 1.20255 | ||||||||
\(925\) | −3.20790e7 | + | 5.36363e7i | −1.23273 | + | 2.06113i | ||||
\(926\) | −2.79793e7 | −1.07228 | ||||||||
\(927\) | −2.10482e6 | + | 3.64566e6i | −0.0804482 | + | 0.139340i | ||||
\(928\) | −2.02387e6 | − | 3.50544e6i | −0.0771458 | − | 0.133620i | ||||
\(929\) | 2.35370e6 | + | 4.07673e6i | 0.0894770 | + | 0.154979i | 0.907290 | − | 0.420505i | \(-0.138147\pi\) |
−0.817813 | + | 0.575484i | \(0.804814\pi\) | |||||||
\(930\) | 2.35365e7 | + | 4.07664e7i | 0.892348 | + | 1.54559i | ||||
\(931\) | 1.02029e7 | 0.385788 | ||||||||
\(932\) | −1.10179e7 | − | 1.90836e7i | −0.415490 | − | 0.719649i | ||||
\(933\) | −3.34164e7 | −1.25677 | ||||||||
\(934\) | 1.02118e6 | − | 1.76874e6i | 0.0383033 | − | 0.0663433i | ||||
\(935\) | 3.84185e6 | 0.143718 | ||||||||
\(936\) | 1.57468e7 | 0.587491 | ||||||||
\(937\) | −1.88772e7 | + | 3.26963e7i | −0.702406 | + | 1.21660i | 0.265213 | + | 0.964190i | \(0.414558\pi\) |
−0.967619 | + | 0.252414i | \(0.918776\pi\) | |||||||
\(938\) | −1.74340e7 | − | 3.01965e7i | −0.646977 | − | 1.12060i | ||||
\(939\) | −1.64902e7 | −0.610327 | ||||||||
\(940\) | 1.55689e7 | − | 2.69662e7i | 0.574697 | − | 0.995405i | ||||
\(941\) | −1.38473e7 | + | 2.39842e7i | −0.509790 | + | 0.882982i | 0.490146 | + | 0.871641i | \(0.336944\pi\) |
−0.999936 | + | 0.0113418i | \(0.996390\pi\) | |||||||
\(942\) | −1.21149e6 | + | 2.09837e6i | −0.0444829 | + | 0.0770467i | ||||
\(943\) | −3.97865e6 | − | 6.89122e6i | −0.145699 | − | 0.252358i | ||||
\(944\) | 4.76008e6 | + | 8.24470e6i | 0.173854 | + | 0.301124i | ||||
\(945\) | −2.31320e7 | + | 4.00659e7i | −0.842625 | + | 1.45947i | ||||
\(946\) | −1.14037e7 | + | 1.97519e7i | −0.414304 | + | 0.717596i | ||||
\(947\) | −1.13434e7 | + | 1.96474e7i | −0.411026 | + | 0.711918i | −0.995002 | − | 0.0998530i | \(-0.968163\pi\) |
0.583976 | + | 0.811771i | \(0.301496\pi\) | |||||||
\(948\) | −2.21411e6 | −0.0800163 | ||||||||
\(949\) | 6.66663e6 | + | 1.15469e7i | 0.240293 | + | 0.416199i | ||||
\(950\) | 6.03405e6 | − | 1.04513e7i | 0.216920 | − | 0.375717i | ||||
\(951\) | −2.87910e7 | −1.03230 | ||||||||
\(952\) | 1.23892e6 | 0.0443049 | ||||||||
\(953\) | −2.26437e6 | + | 3.92200e6i | −0.0807635 | + | 0.139887i | −0.903578 | − | 0.428423i | \(-0.859069\pi\) |
0.822815 | + | 0.568310i | \(0.192403\pi\) | |||||||
\(954\) | −4.61809e7 | −1.64283 | ||||||||
\(955\) | −2.13323e6 | − | 3.69486e6i | −0.0756883 | − | 0.131096i | ||||
\(956\) | −2.51236e7 | −0.889073 | ||||||||
\(957\) | −1.87695e7 | − | 3.25097e7i | −0.662479 | − | 1.14745i | ||||
\(958\) | −1.37619e7 | − | 2.38364e7i | −0.484469 | − | 0.839125i | ||||
\(959\) | 2.72246e7 | + | 4.71544e7i | 0.955906 | + | 1.65568i | ||||
\(960\) | 5.07188e6 | − | 8.78475e6i | 0.177620 | − | 0.307646i | ||||
\(961\) | −6.04803e6 | −0.211254 | ||||||||
\(962\) | 2.45380e7 | + | 378185.i | 0.854874 | + | 0.0131755i | ||||
\(963\) | 4.34617e7 | 1.51022 | ||||||||
\(964\) | 5.37111e6 | − | 9.30303e6i | 0.186153 | − | 0.322427i | ||||
\(965\) | 2.22455e7 | + | 3.85303e7i | 0.768995 | + | 1.33194i | ||||
\(966\) | −3.25331e7 | − | 5.63490e7i | −1.12172 | − | 1.94287i | ||||
\(967\) | 8.87152e6 | + | 1.53659e7i | 0.305093 | + | 0.528436i | 0.977282 | − | 0.211943i | \(-0.0679792\pi\) |
−0.672189 | + | 0.740379i | \(0.734646\pi\) | |||||||
\(968\) | 303132. | 0.0103978 | ||||||||
\(969\) | −455023. | − | 788123.i | −0.0155677 | − | 0.0269640i | ||||
\(970\) | −3.83968e7 | −1.31028 | ||||||||
\(971\) | −8.98454e6 | + | 1.55617e7i | −0.305807 | + | 0.529674i | −0.977441 | − | 0.211210i | \(-0.932260\pi\) |
0.671633 | + | 0.740884i | \(0.265593\pi\) | |||||||
\(972\) | −1.95144e7 | −0.662504 | ||||||||
\(973\) | 9.69039e6 | 0.328140 | ||||||||
\(974\) | 5.69153e6 | − | 9.85802e6i | 0.192235 | − | 0.332960i | ||||
\(975\) | 6.64085e7 | + | 1.15023e8i | 2.23724 | + | 3.87501i | ||||
\(976\) | −123921. | −0.00416411 | ||||||||
\(977\) | 1.04737e7 | − | 1.81410e7i | 0.351046 | − | 0.608030i | −0.635387 | − | 0.772194i | \(-0.719159\pi\) |
0.986433 | + | 0.164164i | \(0.0524926\pi\) | |||||||
\(978\) | 2.54991e7 | − | 4.41657e7i | 0.852468 | − | 1.47652i | ||||
\(979\) | −2.50067e7 | + | 4.33129e7i | −0.833873 | + | 1.44431i | ||||
\(980\) | 2.09344e7 | + | 3.62594e7i | 0.696298 | + | 1.20602i | ||||
\(981\) | −1.67601e7 | − | 2.90294e7i | −0.556038 | − | 0.963087i | ||||
\(982\) | −1.76948e7 | + | 3.06482e7i | −0.585553 | + | 1.01421i | ||||
\(983\) | −2.72947e7 | + | 4.72759e7i | −0.900939 | + | 1.56047i | −0.0746606 | + | 0.997209i | \(0.523787\pi\) |
−0.826278 | + | 0.563262i | \(0.809546\pi\) | |||||||
\(984\) | 1.85503e6 | − | 3.21301e6i | 0.0610751 | − | 0.105785i | ||||
\(985\) | 7.57755e7 | 2.48850 | ||||||||
\(986\) | −745099. | − | 1.29055e6i | −0.0244074 | − | 0.0422749i | ||||
\(987\) | 4.65620e7 | − | 8.06478e7i | 1.52139 | − | 2.63512i | ||||
\(988\) | −4.73880e6 | −0.154446 | ||||||||
\(989\) | 4.75501e7 | 1.54583 | ||||||||
\(990\) | 2.72259e7 | − | 4.71567e7i | 0.882866 | − | 1.52917i | ||||
\(991\) | 5.06058e7 | 1.63688 | 0.818438 | − | 0.574594i | \(-0.194840\pi\) | ||||
0.818438 | + | 0.574594i | \(0.194840\pi\) | |||||||
\(992\) | −2.43300e6 | − | 4.21409e6i | −0.0784989 | − | 0.135964i | ||||
\(993\) | −1.44273e7 | −0.464313 | ||||||||
\(994\) | 7.74188e6 | + | 1.34093e7i | 0.248531 | + | 0.430468i | ||||
\(995\) | −768955. | − | 1.33187e6i | −0.0246231 | − | 0.0426485i | ||||
\(996\) | −9.36770e6 | − | 1.62253e7i | −0.299216 | − | 0.518257i | ||||
\(997\) | 8.99550e6 | − | 1.55807e7i | 0.286607 | − | 0.496418i | −0.686390 | − | 0.727233i | \(-0.740806\pi\) |
0.972998 | + | 0.230815i | \(0.0741392\pi\) | |||||||
\(998\) | −4.73451e6 | −0.150470 | ||||||||
\(999\) | 1.81901e7 | + | 280350.i | 0.576663 | + | 0.00888764i |
(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 | 74.6.c.b.47.2 | ✓ | 16 | |
37.26 | even | 3 | inner | 74.6.c.b.63.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.6.c.b.47.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
74.6.c.b.63.2 | yes | 16 | 37.26 | even | 3 | inner |