Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,7,Mod(5,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.5");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.d (of order \(4\), 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: | \(2.99070308706\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + 275595012 x^{4} - 541321656 x^{3} + 523196552 x^{2} + \cdots + 56070144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(9.50218 + 9.50218i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.5 |
Dual form | 13.7.d.a.8.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.50218 | + | 8.50218i | −1.06277 | + | 1.06277i | −0.0648795 | + | 0.997893i | \(0.520666\pi\) |
−0.997893 | + | 0.0648795i | \(0.979334\pi\) | |||||||
\(3\) | −17.1101 | −0.633708 | −0.316854 | − | 0.948474i | \(-0.602627\pi\) | ||||
−0.316854 | + | 0.948474i | \(0.602627\pi\) | |||||||
\(4\) | − | 80.5742i | − | 1.25897i | ||||||
\(5\) | 73.6481 | − | 73.6481i | 0.589185 | − | 0.589185i | −0.348226 | − | 0.937411i | \(-0.613216\pi\) |
0.937411 | + | 0.348226i | \(0.113216\pi\) | |||||||
\(6\) | 145.473 | − | 145.473i | 0.673488 | − | 0.673488i | ||||
\(7\) | −214.232 | − | 214.232i | −0.624583 | − | 0.624583i | 0.322117 | − | 0.946700i | \(-0.395606\pi\) |
−0.946700 | + | 0.322117i | \(0.895606\pi\) | |||||||
\(8\) | 140.917 | + | 140.917i | 0.275228 | + | 0.275228i | ||||
\(9\) | −436.244 | −0.598414 | ||||||||
\(10\) | 1252.34i | 1.25234i | ||||||||
\(11\) | 231.998 | + | 231.998i | 0.174304 | + | 0.174304i | 0.788867 | − | 0.614563i | \(-0.210668\pi\) |
−0.614563 | + | 0.788867i | \(0.710668\pi\) | |||||||
\(12\) | 1378.63i | 0.797820i | ||||||||
\(13\) | −2079.64 | − | 708.440i | −0.946584 | − | 0.322458i | ||||
\(14\) | 3642.88 | 1.32758 | ||||||||
\(15\) | −1260.13 | + | 1260.13i | −0.373371 | + | 0.373371i | ||||
\(16\) | 2760.55 | 0.673962 | ||||||||
\(17\) | − | 7527.26i | − | 1.53211i | −0.642774 | − | 0.766056i | \(-0.722217\pi\) | ||
0.642774 | − | 0.766056i | \(-0.277783\pi\) | |||||||
\(18\) | 3709.02 | − | 3709.02i | 0.635978 | − | 0.635978i | ||||
\(19\) | −8308.11 | + | 8308.11i | −1.21127 | + | 1.21127i | −0.240662 | + | 0.970609i | \(0.577364\pi\) |
−0.970609 | + | 0.240662i | \(0.922636\pi\) | |||||||
\(20\) | −5934.13 | − | 5934.13i | −0.741767 | − | 0.741767i | ||||
\(21\) | 3665.53 | + | 3665.53i | 0.395803 | + | 0.395803i | ||||
\(22\) | −3944.99 | −0.370491 | ||||||||
\(23\) | − | 2393.16i | − | 0.196693i | −0.995152 | − | 0.0983465i | \(-0.968645\pi\) | ||
0.995152 | − | 0.0983465i | \(-0.0313554\pi\) | |||||||
\(24\) | −2411.10 | − | 2411.10i | −0.174414 | − | 0.174414i | ||||
\(25\) | 4776.92i | 0.305723i | ||||||||
\(26\) | 23704.8 | − | 11658.2i | 1.34870 | − | 0.663304i | ||||
\(27\) | 19937.5 | 1.01293 | ||||||||
\(28\) | −17261.6 | + | 17261.6i | −0.786332 | + | 0.786332i | ||||
\(29\) | −923.972 | −0.0378848 | −0.0189424 | − | 0.999821i | \(-0.506030\pi\) | ||||
−0.0189424 | + | 0.999821i | \(0.506030\pi\) | |||||||
\(30\) | − | 21427.7i | − | 0.793617i | ||||||
\(31\) | −16413.9 | + | 16413.9i | −0.550968 | + | 0.550968i | −0.926720 | − | 0.375752i | \(-0.877384\pi\) |
0.375752 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(32\) | −32489.4 | + | 32489.4i | −0.991497 | + | 0.991497i | ||||
\(33\) | −3969.52 | − | 3969.52i | −0.110458 | − | 0.110458i | ||||
\(34\) | 63998.2 | + | 63998.2i | 1.62829 | + | 1.62829i | ||||
\(35\) | −31555.5 | −0.735989 | ||||||||
\(36\) | 35150.0i | 0.753386i | ||||||||
\(37\) | −36119.9 | − | 36119.9i | −0.713085 | − | 0.713085i | 0.254095 | − | 0.967179i | \(-0.418222\pi\) |
−0.967179 | + | 0.254095i | \(0.918222\pi\) | |||||||
\(38\) | − | 141274.i | − | 2.57461i | ||||||
\(39\) | 35583.0 | + | 12121.5i | 0.599858 | + | 0.204344i | ||||
\(40\) | 20756.5 | 0.324320 | ||||||||
\(41\) | 44410.3 | − | 44410.3i | 0.644366 | − | 0.644366i | −0.307260 | − | 0.951626i | \(-0.599412\pi\) |
0.951626 | + | 0.307260i | \(0.0994121\pi\) | |||||||
\(42\) | −62330.1 | −0.841298 | ||||||||
\(43\) | − | 97972.1i | − | 1.23225i | −0.787650 | − | 0.616123i | \(-0.788703\pi\) | ||
0.787650 | − | 0.616123i | \(-0.211297\pi\) | |||||||
\(44\) | 18693.1 | − | 18693.1i | 0.219444 | − | 0.219444i | ||||
\(45\) | −32128.5 | + | 32128.5i | −0.352576 | + | 0.352576i | ||||
\(46\) | 20347.1 | + | 20347.1i | 0.209040 | + | 0.209040i | ||||
\(47\) | 112049. | + | 112049.i | 1.07923 | + | 1.07923i | 0.996578 | + | 0.0826547i | \(0.0263398\pi\) |
0.0826547 | + | 0.996578i | \(0.473660\pi\) | |||||||
\(48\) | −47233.3 | −0.427095 | ||||||||
\(49\) | − | 25858.3i | − | 0.219792i | ||||||
\(50\) | −40614.2 | − | 40614.2i | −0.324914 | − | 0.324914i | ||||
\(51\) | 128792.i | 0.970912i | ||||||||
\(52\) | −57081.9 | + | 167566.i | −0.405965 | + | 1.19172i | ||||
\(53\) | −57734.9 | −0.387803 | −0.193901 | − | 0.981021i | \(-0.562114\pi\) | ||||
−0.193901 | + | 0.981021i | \(0.562114\pi\) | |||||||
\(54\) | −169512. | + | 169512.i | −1.07651 | + | 1.07651i | ||||
\(55\) | 34172.5 | 0.205394 | ||||||||
\(56\) | − | 60377.7i | − | 0.343805i | ||||||
\(57\) | 142153. | − | 142153.i | 0.767592 | − | 0.767592i | ||||
\(58\) | 7855.78 | − | 7855.78i | 0.0402629 | − | 0.0402629i | ||||
\(59\) | −57409.6 | − | 57409.6i | −0.279530 | − | 0.279530i | 0.553391 | − | 0.832921i | \(-0.313333\pi\) |
−0.832921 | + | 0.553391i | \(0.813333\pi\) | |||||||
\(60\) | 101534. | + | 101534.i | 0.470064 | + | 0.470064i | ||||
\(61\) | 413374. | 1.82118 | 0.910591 | − | 0.413309i | \(-0.135627\pi\) | ||||
0.910591 | + | 0.413309i | \(0.135627\pi\) | |||||||
\(62\) | − | 279108.i | − | 1.17111i | ||||||
\(63\) | 93457.4 | + | 93457.4i | 0.373759 | + | 0.373759i | ||||
\(64\) | − | 375786.i | − | 1.43351i | ||||||
\(65\) | −205337. | + | 100987.i | −0.747700 | + | 0.367725i | ||||
\(66\) | 67499.2 | 0.234783 | ||||||||
\(67\) | −265261. | + | 265261.i | −0.881960 | + | 0.881960i | −0.993734 | − | 0.111774i | \(-0.964347\pi\) |
0.111774 | + | 0.993734i | \(0.464347\pi\) | |||||||
\(68\) | −606503. | −1.92888 | ||||||||
\(69\) | 40947.3i | 0.124646i | ||||||||
\(70\) | 268291. | − | 268291.i | 0.782189 | − | 0.782189i | ||||
\(71\) | −28896.4 | + | 28896.4i | −0.0807364 | + | 0.0807364i | −0.746322 | − | 0.665585i | \(-0.768182\pi\) |
0.665585 | + | 0.746322i | \(0.268182\pi\) | |||||||
\(72\) | −61474.0 | − | 61474.0i | −0.164700 | − | 0.164700i | ||||
\(73\) | −395624. | − | 395624.i | −1.01698 | − | 1.01698i | −0.999853 | − | 0.0171315i | \(-0.994547\pi\) |
−0.0171315 | − | 0.999853i | \(-0.505453\pi\) | |||||||
\(74\) | 614195. | 1.51569 | ||||||||
\(75\) | − | 81733.7i | − | 0.193739i | ||||||
\(76\) | 669419. | + | 669419.i | 1.52496 | + | 1.52496i | ||||
\(77\) | − | 99403.0i | − | 0.217734i | ||||||
\(78\) | −405592. | + | 199474.i | −0.854684 | + | 0.420341i | ||||
\(79\) | −419351. | −0.850543 | −0.425271 | − | 0.905066i | \(-0.639821\pi\) | ||||
−0.425271 | + | 0.905066i | \(0.639821\pi\) | |||||||
\(80\) | 203309. | − | 203309.i | 0.397088 | − | 0.397088i | ||||
\(81\) | −23110.5 | −0.0434865 | ||||||||
\(82\) | 755169.i | 1.36963i | ||||||||
\(83\) | 59175.0 | − | 59175.0i | 0.103491 | − | 0.103491i | −0.653465 | − | 0.756957i | \(-0.726685\pi\) |
0.756957 | + | 0.653465i | \(0.226685\pi\) | |||||||
\(84\) | 295347. | − | 295347.i | 0.498305 | − | 0.498305i | ||||
\(85\) | −554369. | − | 554369.i | −0.902697 | − | 0.902697i | ||||
\(86\) | 832977. | + | 832977.i | 1.30960 | + | 1.30960i | ||||
\(87\) | 15809.3 | 0.0240079 | ||||||||
\(88\) | 65384.9i | 0.0959465i | ||||||||
\(89\) | −61088.3 | − | 61088.3i | −0.0866538 | − | 0.0866538i | 0.662451 | − | 0.749105i | \(-0.269516\pi\) |
−0.749105 | + | 0.662451i | \(0.769516\pi\) | |||||||
\(90\) | − | 546325.i | − | 0.749417i | ||||||
\(91\) | 293756. | + | 597297.i | 0.389818 | + | 0.792622i | ||||
\(92\) | −192827. | −0.247631 | ||||||||
\(93\) | 280844. | − | 280844.i | 0.349153 | − | 0.349153i | ||||
\(94\) | −1.90533e6 | −2.29396 | ||||||||
\(95\) | 1.22375e6i | 1.42732i | ||||||||
\(96\) | 555897. | − | 555897.i | 0.628319 | − | 0.628319i | ||||
\(97\) | −235474. | + | 235474.i | −0.258004 | + | 0.258004i | −0.824242 | − | 0.566238i | \(-0.808398\pi\) |
0.566238 | + | 0.824242i | \(0.308398\pi\) | |||||||
\(98\) | 219852. | + | 219852.i | 0.233589 | + | 0.233589i | ||||
\(99\) | −101208. | − | 101208.i | −0.104306 | − | 0.104306i | ||||
\(100\) | 384896. | 0.384896 | ||||||||
\(101\) | − | 1.08351e6i | − | 1.05165i | −0.850594 | − | 0.525823i | \(-0.823757\pi\) | ||
0.850594 | − | 0.525823i | \(-0.176243\pi\) | |||||||
\(102\) | −1.09502e6 | − | 1.09502e6i | −1.03186 | − | 1.03186i | ||||
\(103\) | 228949.i | 0.209521i | 0.994497 | + | 0.104760i | \(0.0334076\pi\) | ||||
−0.994497 | + | 0.104760i | \(0.966592\pi\) | |||||||
\(104\) | −193226. | − | 392887.i | −0.171777 | − | 0.349275i | ||||
\(105\) | 539919. | 0.466402 | ||||||||
\(106\) | 490873. | − | 490873.i | 0.412146 | − | 0.412146i | ||||
\(107\) | 1.77111e6 | 1.44575 | 0.722876 | − | 0.690978i | \(-0.242820\pi\) | ||||
0.722876 | + | 0.690978i | \(0.242820\pi\) | |||||||
\(108\) | − | 1.60644e6i | − | 1.27525i | ||||||
\(109\) | 539118. | − | 539118.i | 0.416298 | − | 0.416298i | −0.467627 | − | 0.883926i | \(-0.654891\pi\) |
0.883926 | + | 0.467627i | \(0.154891\pi\) | |||||||
\(110\) | −290541. | + | 290541.i | −0.218288 | + | 0.218288i | ||||
\(111\) | 618015. | + | 618015.i | 0.451887 | + | 0.451887i | ||||
\(112\) | −591398. | − | 591398.i | −0.420945 | − | 0.420945i | ||||
\(113\) | −1.11945e6 | −0.775832 | −0.387916 | − | 0.921695i | \(-0.626805\pi\) | ||||
−0.387916 | + | 0.921695i | \(0.626805\pi\) | |||||||
\(114\) | 2.41722e6i | 1.63155i | ||||||||
\(115\) | −176252. | − | 176252.i | −0.115889 | − | 0.115889i | ||||
\(116\) | 74448.3i | 0.0476959i | ||||||||
\(117\) | 907232. | + | 309052.i | 0.566449 | + | 0.192963i | ||||
\(118\) | 976214. | 0.594154 | ||||||||
\(119\) | −1.61258e6 | + | 1.61258e6i | −0.956931 | + | 0.956931i | ||||
\(120\) | −355146. | −0.205524 | ||||||||
\(121\) | − | 1.66391e6i | − | 0.939236i | ||||||
\(122\) | −3.51458e6 | + | 3.51458e6i | −1.93550 | + | 1.93550i | ||||
\(123\) | −759866. | + | 759866.i | −0.408340 | + | 0.408340i | ||||
\(124\) | 1.32254e6 | + | 1.32254e6i | 0.693653 | + | 0.693653i | ||||
\(125\) | 1.50256e6 | + | 1.50256e6i | 0.769312 | + | 0.769312i | ||||
\(126\) | −1.58918e6 | −0.794442 | ||||||||
\(127\) | − | 2.01939e6i | − | 0.985846i | −0.870073 | − | 0.492923i | \(-0.835928\pi\) | ||
0.870073 | − | 0.492923i | \(-0.164072\pi\) | |||||||
\(128\) | 1.11568e6 | + | 1.11568e6i | 0.531997 | + | 0.531997i | ||||
\(129\) | 1.67631e6i | 0.780884i | ||||||||
\(130\) | 887207. | − | 2.60442e6i | 0.403826 | − | 1.18544i | ||||
\(131\) | 589259. | 0.262115 | 0.131058 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131058 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | −319841. | + | 319841.i | −0.139063 | + | 0.139063i | ||||
\(133\) | 3.55972e6 | 1.51308 | ||||||||
\(134\) | − | 4.51059e6i | − | 1.87465i | ||||||
\(135\) | 1.46836e6 | − | 1.46836e6i | 0.596802 | − | 0.596802i | ||||
\(136\) | 1.06072e6 | − | 1.06072e6i | 0.421680 | − | 0.421680i | ||||
\(137\) | −2.66749e6 | − | 2.66749e6i | −1.03739 | − | 1.03739i | −0.999273 | − | 0.0381144i | \(-0.987865\pi\) |
−0.0381144 | − | 0.999273i | \(-0.512135\pi\) | |||||||
\(138\) | −348142. | − | 348142.i | −0.132470 | − | 0.132470i | ||||
\(139\) | −1.55840e6 | −0.580277 | −0.290139 | − | 0.956985i | \(-0.593701\pi\) | ||||
−0.290139 | + | 0.956985i | \(0.593701\pi\) | |||||||
\(140\) | 2.54256e6i | 0.926590i | ||||||||
\(141\) | −1.91718e6 | − | 1.91718e6i | −0.683919 | − | 0.683919i | ||||
\(142\) | − | 491366.i | − | 0.171609i | ||||||
\(143\) | −318117. | − | 646831.i | −0.108788 | − | 0.221199i | ||||
\(144\) | −1.20427e6 | −0.403309 | ||||||||
\(145\) | −68048.8 | + | 68048.8i | −0.0223211 | + | 0.0223211i | ||||
\(146\) | 6.72734e6 | 2.16165 | ||||||||
\(147\) | 442439.i | 0.139284i | ||||||||
\(148\) | −2.91033e6 | + | 2.91033e6i | −0.897753 | + | 0.897753i | ||||
\(149\) | −962956. | + | 962956.i | −0.291104 | + | 0.291104i | −0.837516 | − | 0.546413i | \(-0.815993\pi\) |
0.546413 | + | 0.837516i | \(0.315993\pi\) | |||||||
\(150\) | 694914. | + | 694914.i | 0.205901 | + | 0.205901i | ||||
\(151\) | −2.31936e6 | − | 2.31936e6i | −0.673655 | − | 0.673655i | 0.284902 | − | 0.958557i | \(-0.408039\pi\) |
−0.958557 | + | 0.284902i | \(0.908039\pi\) | |||||||
\(152\) | −2.34150e6 | −0.666751 | ||||||||
\(153\) | 3.28372e6i | 0.916837i | ||||||||
\(154\) | 845142. | + | 845142.i | 0.231402 | + | 0.231402i | ||||
\(155\) | 2.41770e6i | 0.649244i | ||||||||
\(156\) | 976679. | − | 2.86707e6i | 0.257263 | − | 0.755204i | ||||
\(157\) | −3.16541e6 | −0.817958 | −0.408979 | − | 0.912544i | \(-0.634115\pi\) | ||||
−0.408979 | + | 0.912544i | \(0.634115\pi\) | |||||||
\(158\) | 3.56540e6 | − | 3.56540e6i | 0.903934 | − | 0.903934i | ||||
\(159\) | 987851. | 0.245754 | ||||||||
\(160\) | 4.78556e6i | 1.16835i | ||||||||
\(161\) | −512692. | + | 512692.i | −0.122851 | + | 0.122851i | ||||
\(162\) | 196490. | − | 196490.i | 0.0462163 | − | 0.0462163i | ||||
\(163\) | 3.38001e6 | + | 3.38001e6i | 0.780467 | + | 0.780467i | 0.979910 | − | 0.199442i | \(-0.0639130\pi\) |
−0.199442 | + | 0.979910i | \(0.563913\pi\) | |||||||
\(164\) | −3.57833e6 | − | 3.57833e6i | −0.811238 | − | 0.811238i | ||||
\(165\) | −584695. | −0.130160 | ||||||||
\(166\) | 1.00623e6i | 0.219976i | ||||||||
\(167\) | −3.82024e6 | − | 3.82024e6i | −0.820241 | − | 0.820241i | 0.165902 | − | 0.986142i | \(-0.446947\pi\) |
−0.986142 | + | 0.165902i | \(0.946947\pi\) | |||||||
\(168\) | 1.03307e6i | 0.217872i | ||||||||
\(169\) | 3.82304e6 | + | 2.94661e6i | 0.792042 | + | 0.610467i | ||||
\(170\) | 9.42668e6 | 1.91872 | ||||||||
\(171\) | 3.62436e6 | − | 3.62436e6i | 0.724842 | − | 0.724842i | ||||
\(172\) | −7.89402e6 | −1.55136 | ||||||||
\(173\) | 7.45195e6i | 1.43923i | 0.694371 | + | 0.719617i | \(0.255683\pi\) | ||||
−0.694371 | + | 0.719617i | \(0.744317\pi\) | |||||||
\(174\) | −134413. | + | 134413.i | −0.0255149 | + | 0.0255149i | ||||
\(175\) | 1.02337e6 | − | 1.02337e6i | 0.190949 | − | 0.190949i | ||||
\(176\) | 640443. | + | 640443.i | 0.117474 | + | 0.117474i | ||||
\(177\) | 982285. | + | 982285.i | 0.177141 | + | 0.177141i | ||||
\(178\) | 1.03877e6 | 0.184187 | ||||||||
\(179\) | − | 9.93321e6i | − | 1.73193i | −0.500104 | − | 0.865966i | \(-0.666705\pi\) | ||
0.500104 | − | 0.865966i | \(-0.333295\pi\) | |||||||
\(180\) | 2.58873e6 | + | 2.58873e6i | 0.443884 | + | 0.443884i | ||||
\(181\) | 8.22334e6i | 1.38680i | 0.720555 | + | 0.693398i | \(0.243887\pi\) | ||||
−0.720555 | + | 0.693398i | \(0.756113\pi\) | |||||||
\(182\) | −7.57589e6 | − | 2.58076e6i | −1.25667 | − | 0.428088i | ||||
\(183\) | −7.07287e6 | −1.15410 | ||||||||
\(184\) | 337237. | − | 337237.i | 0.0541354 | − | 0.0541354i | ||||
\(185\) | −5.32032e6 | −0.840277 | ||||||||
\(186\) | 4.77557e6i | 0.742141i | ||||||||
\(187\) | 1.74631e6 | − | 1.74631e6i | 0.267053 | − | 0.267053i | ||||
\(188\) | 9.02827e6 | − | 9.02827e6i | 1.35872 | − | 1.35872i | ||||
\(189\) | −4.27124e6 | − | 4.27124e6i | −0.632657 | − | 0.632657i | ||||
\(190\) | −1.04046e7 | − | 1.04046e7i | −1.51692 | − | 1.51692i | ||||
\(191\) | −1.03422e6 | −0.148427 | −0.0742136 | − | 0.997242i | \(-0.523645\pi\) | ||||
−0.0742136 | + | 0.997242i | \(0.523645\pi\) | |||||||
\(192\) | 6.42974e6i | 0.908426i | ||||||||
\(193\) | 5.78870e6 | + | 5.78870e6i | 0.805210 | + | 0.805210i | 0.983905 | − | 0.178695i | \(-0.0571875\pi\) |
−0.178695 | + | 0.983905i | \(0.557187\pi\) | |||||||
\(194\) | − | 4.00408e6i | − | 0.548400i | ||||||
\(195\) | 3.51334e6 | − | 1.72789e6i | 0.473823 | − | 0.233031i | ||||
\(196\) | −2.08351e6 | −0.276712 | ||||||||
\(197\) | 3.82189e6 | − | 3.82189e6i | 0.499896 | − | 0.499896i | −0.411510 | − | 0.911405i | \(-0.634998\pi\) |
0.911405 | + | 0.411510i | \(0.134998\pi\) | |||||||
\(198\) | 1.72098e6 | 0.221707 | ||||||||
\(199\) | 893097.i | 0.113329i | 0.998393 | + | 0.0566643i | \(0.0180465\pi\) | ||||
−0.998393 | + | 0.0566643i | \(0.981954\pi\) | |||||||
\(200\) | −673147. | + | 673147.i | −0.0841434 | + | 0.0841434i | ||||
\(201\) | 4.53865e6 | − | 4.53865e6i | 0.558905 | − | 0.558905i | ||||
\(202\) | 9.21222e6 | + | 9.21222e6i | 1.11766 | + | 1.11766i | ||||
\(203\) | 197944. | + | 197944.i | 0.0236622 | + | 0.0236622i | ||||
\(204\) | 1.03773e7 | 1.22235 | ||||||||
\(205\) | − | 6.54147e6i | − | 0.759301i | ||||||
\(206\) | −1.94657e6 | − | 1.94657e6i | −0.222673 | − | 0.222673i | ||||
\(207\) | 1.04400e6i | 0.117704i | ||||||||
\(208\) | −5.74096e6 | − | 1.95568e6i | −0.637962 | − | 0.217324i | ||||
\(209\) | −3.85494e6 | −0.422258 | ||||||||
\(210\) | −4.59049e6 | + | 4.59049e6i | −0.495680 | + | 0.495680i | ||||
\(211\) | −92262.9 | −0.00982154 | −0.00491077 | − | 0.999988i | \(-0.501563\pi\) | ||||
−0.00491077 | + | 0.999988i | \(0.501563\pi\) | |||||||
\(212\) | 4.65194e6i | 0.488233i | ||||||||
\(213\) | 494422. | − | 494422.i | 0.0511633 | − | 0.0511633i | ||||
\(214\) | −1.50583e7 | + | 1.50583e7i | −1.53651 | + | 1.53651i | ||||
\(215\) | −7.21546e6 | − | 7.21546e6i | −0.726020 | − | 0.726020i | ||||
\(216\) | 2.80952e6 | + | 2.80952e6i | 0.278786 | + | 0.278786i | ||||
\(217\) | 7.03276e6 | 0.688251 | ||||||||
\(218\) | 9.16736e6i | 0.884861i | ||||||||
\(219\) | 6.76918e6 | + | 6.76918e6i | 0.644471 | + | 0.644471i | ||||
\(220\) | − | 2.75342e6i | − | 0.258586i | ||||||
\(221\) | −5.33261e6 | + | 1.56540e7i | −0.494041 | + | 1.45027i | ||||
\(222\) | −1.05090e7 | −0.960507 | ||||||||
\(223\) | −8.85625e6 | + | 8.85625e6i | −0.798611 | + | 0.798611i | −0.982876 | − | 0.184266i | \(-0.941009\pi\) |
0.184266 | + | 0.982876i | \(0.441009\pi\) | |||||||
\(224\) | 1.39205e7 | 1.23854 | ||||||||
\(225\) | − | 2.08390e6i | − | 0.182949i | ||||||
\(226\) | 9.51773e6 | − | 9.51773e6i | 0.824533 | − | 0.824533i | ||||
\(227\) | 7.90170e6 | − | 7.90170e6i | 0.675527 | − | 0.675527i | −0.283457 | − | 0.958985i | \(-0.591481\pi\) |
0.958985 | + | 0.283457i | \(0.0914815\pi\) | |||||||
\(228\) | −1.14538e7 | − | 1.14538e7i | −0.966377 | − | 0.966377i | ||||
\(229\) | 2.28875e6 | + | 2.28875e6i | 0.190587 | + | 0.190587i | 0.795950 | − | 0.605363i | \(-0.206972\pi\) |
−0.605363 | + | 0.795950i | \(0.706972\pi\) | |||||||
\(230\) | 2.99705e6 | 0.246326 | ||||||||
\(231\) | 1.70080e6i | 0.137980i | ||||||||
\(232\) | −130203. | − | 130203.i | −0.0104269 | − | 0.0104269i | ||||
\(233\) | − | 1.13768e7i | − | 0.899401i | −0.893179 | − | 0.449701i | \(-0.851531\pi\) | ||
0.893179 | − | 0.449701i | \(-0.148469\pi\) | |||||||
\(234\) | −1.03411e7 | + | 5.08583e6i | −0.807083 | + | 0.396931i | ||||
\(235\) | 1.65044e7 | 1.27173 | ||||||||
\(236\) | −4.62573e6 | + | 4.62573e6i | −0.351920 | + | 0.351920i | ||||
\(237\) | 7.17514e6 | 0.538996 | ||||||||
\(238\) | − | 2.74209e7i | − | 2.03400i | ||||||
\(239\) | −7.79723e6 | + | 7.79723e6i | −0.571145 | + | 0.571145i | −0.932448 | − | 0.361303i | \(-0.882332\pi\) |
0.361303 | + | 0.932448i | \(0.382332\pi\) | |||||||
\(240\) | −3.47864e6 | + | 3.47864e6i | −0.251638 | + | 0.251638i | ||||
\(241\) | 81950.5 | + | 81950.5i | 0.00585464 | + | 0.00585464i | 0.710028 | − | 0.704173i | \(-0.248682\pi\) |
−0.704173 | + | 0.710028i | \(0.748682\pi\) | |||||||
\(242\) | 1.41469e7 | + | 1.41469e7i | 0.998195 | + | 0.998195i | ||||
\(243\) | −1.41390e7 | −0.985370 | ||||||||
\(244\) | − | 3.33072e7i | − | 2.29282i | ||||||
\(245\) | −1.90442e6 | − | 1.90442e6i | −0.129498 | − | 0.129498i | ||||
\(246\) | − | 1.29210e7i | − | 0.867945i | ||||||
\(247\) | 2.31637e7 | − | 1.13921e7i | 1.53715 | − | 0.755986i | ||||
\(248\) | −4.62598e6 | −0.303284 | ||||||||
\(249\) | −1.01249e6 | + | 1.01249e6i | −0.0655833 | + | 0.0655833i | ||||
\(250\) | −2.55501e7 | −1.63521 | ||||||||
\(251\) | − | 9.96309e6i | − | 0.630047i | −0.949084 | − | 0.315023i | \(-0.897988\pi\) | ||
0.949084 | − | 0.315023i | \(-0.102012\pi\) | |||||||
\(252\) | 7.53025e6 | − | 7.53025e6i | 0.470552 | − | 0.470552i | ||||
\(253\) | 555210. | − | 555210.i | 0.0342844 | − | 0.0342844i | ||||
\(254\) | 1.71692e7 | + | 1.71692e7i | 1.04773 | + | 1.04773i | ||||
\(255\) | 9.48531e6 | + | 9.48531e6i | 0.572046 | + | 0.572046i | ||||
\(256\) | 5.07888e6 | 0.302725 | ||||||||
\(257\) | 1.76493e7i | 1.03975i | 0.854242 | + | 0.519875i | \(0.174022\pi\) | ||||
−0.854242 | + | 0.519875i | \(0.825978\pi\) | |||||||
\(258\) | −1.42523e7 | − | 1.42523e7i | −0.829902 | − | 0.829902i | ||||
\(259\) | 1.54761e7i | 0.890761i | ||||||||
\(260\) | 8.13691e6 | + | 1.65449e7i | 0.462956 | + | 0.941333i | ||||
\(261\) | 403077. | 0.0226708 | ||||||||
\(262\) | −5.00999e6 | + | 5.00999e6i | −0.278569 | + | 0.278569i | ||||
\(263\) | −2.69228e7 | −1.47997 | −0.739985 | − | 0.672624i | \(-0.765167\pi\) | ||||
−0.739985 | + | 0.672624i | \(0.765167\pi\) | |||||||
\(264\) | − | 1.11874e6i | − | 0.0608021i | ||||||
\(265\) | −4.25207e6 | + | 4.25207e6i | −0.228487 | + | 0.228487i | ||||
\(266\) | −3.02654e7 | + | 3.02654e7i | −1.60806 | + | 1.60806i | ||||
\(267\) | 1.04523e6 | + | 1.04523e6i | 0.0549132 | + | 0.0549132i | ||||
\(268\) | 2.13732e7 | + | 2.13732e7i | 1.11036 | + | 1.11036i | ||||
\(269\) | −2.28689e7 | −1.17487 | −0.587433 | − | 0.809273i | \(-0.699861\pi\) | ||||
−0.587433 | + | 0.809273i | \(0.699861\pi\) | |||||||
\(270\) | 2.49685e7i | 1.26853i | ||||||||
\(271\) | −1.13591e7 | − | 1.13591e7i | −0.570736 | − | 0.570736i | 0.361598 | − | 0.932334i | \(-0.382231\pi\) |
−0.932334 | + | 0.361598i | \(0.882231\pi\) | |||||||
\(272\) | − | 2.07794e7i | − | 1.03259i | ||||||
\(273\) | −5.02620e6 | − | 1.02198e7i | −0.247031 | − | 0.502291i | ||||
\(274\) | 4.53590e7 | 2.20501 | ||||||||
\(275\) | −1.10824e6 | + | 1.10824e6i | −0.0532887 | + | 0.0532887i | ||||
\(276\) | 3.29930e6 | 0.156926 | ||||||||
\(277\) | − | 1.30080e7i | − | 0.612028i | −0.952027 | − | 0.306014i | \(-0.901005\pi\) | ||
0.952027 | − | 0.306014i | \(-0.0989955\pi\) | |||||||
\(278\) | 1.32498e7 | − | 1.32498e7i | 0.616703 | − | 0.616703i | ||||
\(279\) | 7.16046e6 | − | 7.16046e6i | 0.329707 | − | 0.329707i | ||||
\(280\) | −4.44670e6 | − | 4.44670e6i | −0.202565 | − | 0.202565i | ||||
\(281\) | 2.37985e7 | + | 2.37985e7i | 1.07258 | + | 1.07258i | 0.997151 | + | 0.0754330i | \(0.0240339\pi\) |
0.0754330 | + | 0.997151i | \(0.475966\pi\) | |||||||
\(282\) | 3.26003e7 | 1.45370 | ||||||||
\(283\) | − | 1.24423e7i | − | 0.548959i | −0.961593 | − | 0.274480i | \(-0.911494\pi\) | ||
0.961593 | − | 0.274480i | \(-0.0885056\pi\) | |||||||
\(284\) | 2.32831e6 | + | 2.32831e6i | 0.101645 | + | 0.101645i | ||||
\(285\) | − | 2.09385e7i | − | 0.904507i | ||||||
\(286\) | 8.20417e6 | + | 2.79479e6i | 0.350701 | + | 0.119468i | ||||
\(287\) | −1.90282e7 | −0.804920 | ||||||||
\(288\) | 1.41733e7 | − | 1.41733e7i | 0.593325 | − | 0.593325i | ||||
\(289\) | −3.25221e7 | −1.34737 | ||||||||
\(290\) | − | 1.15713e6i | − | 0.0474446i | ||||||
\(291\) | 4.02898e6 | − | 4.02898e6i | 0.163499 | − | 0.163499i | ||||
\(292\) | −3.18771e7 | + | 3.18771e7i | −1.28035 | + | 1.28035i | ||||
\(293\) | −9.08257e6 | − | 9.08257e6i | −0.361082 | − | 0.361082i | 0.503129 | − | 0.864211i | \(-0.332182\pi\) |
−0.864211 | + | 0.503129i | \(0.832182\pi\) | |||||||
\(294\) | −3.76170e6 | − | 3.76170e6i | −0.148027 | − | 0.148027i | ||||
\(295\) | −8.45622e6 | −0.329390 | ||||||||
\(296\) | − | 1.01798e7i | − | 0.392521i | ||||||
\(297\) | 4.62546e6 | + | 4.62546e6i | 0.176557 | + | 0.176557i | ||||
\(298\) | − | 1.63745e7i | − | 0.618754i | ||||||
\(299\) | −1.69541e6 | + | 4.97693e6i | −0.0634252 | + | 0.186186i | ||||
\(300\) | −6.58562e6 | −0.243912 | ||||||||
\(301\) | −2.09888e7 | + | 2.09888e7i | −0.769639 | + | 0.769639i | ||||
\(302\) | 3.94392e7 | 1.43188 | ||||||||
\(303\) | 1.85390e7i | 0.666437i | ||||||||
\(304\) | −2.29349e7 | + | 2.29349e7i | −0.816351 | + | 0.816351i | ||||
\(305\) | 3.04442e7 | − | 3.04442e7i | 1.07301 | − | 1.07301i | ||||
\(306\) | −2.79188e7 | − | 2.79188e7i | −0.974389 | − | 0.974389i | ||||
\(307\) | −9.60324e6 | − | 9.60324e6i | −0.331897 | − | 0.331897i | 0.521410 | − | 0.853306i | \(-0.325406\pi\) |
−0.853306 | + | 0.521410i | \(0.825406\pi\) | |||||||
\(308\) | −8.00931e6 | −0.274121 | ||||||||
\(309\) | − | 3.91735e6i | − | 0.132775i | ||||||
\(310\) | −2.05558e7 | − | 2.05558e7i | −0.689999 | − | 0.689999i | ||||
\(311\) | 3.04628e7i | 1.01272i | 0.862323 | + | 0.506359i | \(0.169009\pi\) | ||||
−0.862323 | + | 0.506359i | \(0.830991\pi\) | |||||||
\(312\) | 3.30611e6 | + | 6.72235e6i | 0.108856 | + | 0.221339i | ||||
\(313\) | 2.06729e7 | 0.674170 | 0.337085 | − | 0.941474i | \(-0.390559\pi\) | ||||
0.337085 | + | 0.941474i | \(0.390559\pi\) | |||||||
\(314\) | 2.69129e7 | − | 2.69129e7i | 0.869303 | − | 0.869303i | ||||
\(315\) | 1.37659e7 | 0.440426 | ||||||||
\(316\) | 3.37888e7i | 1.07081i | ||||||||
\(317\) | 3.69040e7 | − | 3.69040e7i | 1.15850 | − | 1.15850i | 0.173701 | − | 0.984798i | \(-0.444427\pi\) |
0.984798 | − | 0.173701i | \(-0.0555727\pi\) | |||||||
\(318\) | −8.39889e6 | + | 8.39889e6i | −0.261180 | + | 0.261180i | ||||
\(319\) | −214360. | − | 214360.i | −0.00660347 | − | 0.00660347i | ||||
\(320\) | −2.76759e7 | − | 2.76759e7i | −0.844601 | − | 0.844601i | ||||
\(321\) | −3.03039e7 | −0.916184 | ||||||||
\(322\) | − | 8.71800e6i | − | 0.261126i | ||||||
\(323\) | 6.25373e7 | + | 6.25373e7i | 1.85580 | + | 1.85580i | ||||
\(324\) | 1.86211e6i | 0.0547483i | ||||||||
\(325\) | 3.38416e6 | − | 9.93430e6i | 0.0985827 | − | 0.289392i | ||||
\(326\) | −5.74749e7 | −1.65892 | ||||||||
\(327\) | −9.22438e6 | + | 9.22438e6i | −0.263812 | + | 0.263812i | ||||
\(328\) | 1.25163e7 | 0.354695 | ||||||||
\(329\) | − | 4.80090e7i | − | 1.34814i | ||||||
\(330\) | 4.97119e6 | − | 4.97119e6i | 0.138331 | − | 0.138331i | ||||
\(331\) | 1.82030e7 | − | 1.82030e7i | 0.501949 | − | 0.501949i | −0.410094 | − | 0.912043i | \(-0.634504\pi\) |
0.912043 | + | 0.410094i | \(0.134504\pi\) | |||||||
\(332\) | −4.76798e6 | − | 4.76798e6i | −0.130293 | − | 0.130293i | ||||
\(333\) | 1.57571e7 | + | 1.57571e7i | 0.426720 | + | 0.426720i | ||||
\(334\) | 6.49608e7 | 1.74346 | ||||||||
\(335\) | 3.90719e7i | 1.03927i | ||||||||
\(336\) | 1.01189e7 | + | 1.01189e7i | 0.266757 | + | 0.266757i | ||||
\(337\) | 2.14657e7i | 0.560860i | 0.959874 | + | 0.280430i | \(0.0904771\pi\) | ||||
−0.959874 | + | 0.280430i | \(0.909523\pi\) | |||||||
\(338\) | −5.75567e7 | + | 7.45156e6i | −1.49055 | + | 0.192973i | ||||
\(339\) | 1.91538e7 | 0.491651 | ||||||||
\(340\) | −4.46678e7 | + | 4.46678e7i | −1.13647 | + | 1.13647i | ||||
\(341\) | −7.61600e6 | −0.192072 | ||||||||
\(342\) | 6.16299e7i | 1.54068i | ||||||||
\(343\) | −3.07439e7 | + | 3.07439e7i | −0.761861 | + | 0.761861i | ||||
\(344\) | 1.38059e7 | − | 1.38059e7i | 0.339148 | − | 0.339148i | ||||
\(345\) | 3.01569e6 | + | 3.01569e6i | 0.0734395 | + | 0.0734395i | ||||
\(346\) | −6.33578e7 | − | 6.33578e7i | −1.52958 | − | 1.52958i | ||||
\(347\) | 5.37467e7 | 1.28636 | 0.643181 | − | 0.765714i | \(-0.277614\pi\) | ||||
0.643181 | + | 0.765714i | \(0.277614\pi\) | |||||||
\(348\) | − | 1.27382e6i | − | 0.0302253i | ||||||
\(349\) | 3.37710e7 | + | 3.37710e7i | 0.794452 | + | 0.794452i | 0.982214 | − | 0.187762i | \(-0.0601235\pi\) |
−0.187762 | + | 0.982214i | \(0.560123\pi\) | |||||||
\(350\) | 1.74017e7i | 0.405871i | ||||||||
\(351\) | −4.14628e7 | − | 1.41245e7i | −0.958821 | − | 0.326626i | ||||
\(352\) | −1.50750e7 | −0.345643 | ||||||||
\(353\) | 9.93725e6 | − | 9.93725e6i | 0.225914 | − | 0.225914i | −0.585070 | − | 0.810983i | \(-0.698933\pi\) |
0.810983 | + | 0.585070i | \(0.198933\pi\) | |||||||
\(354\) | −1.67031e7 | −0.376520 | ||||||||
\(355\) | 4.25634e6i | 0.0951373i | ||||||||
\(356\) | −4.92214e6 | + | 4.92214e6i | −0.109095 | + | 0.109095i | ||||
\(357\) | 2.75914e7 | − | 2.75914e7i | 0.606415 | − | 0.606415i | ||||
\(358\) | 8.44540e7 | + | 8.44540e7i | 1.84065 | + | 1.84065i | ||||
\(359\) | −3.97856e7 | − | 3.97856e7i | −0.859890 | − | 0.859890i | 0.131435 | − | 0.991325i | \(-0.458042\pi\) |
−0.991325 | + | 0.131435i | \(0.958042\pi\) | |||||||
\(360\) | −9.05488e6 | −0.194078 | ||||||||
\(361\) | − | 9.10034e7i | − | 1.93435i | ||||||
\(362\) | −6.99163e7 | − | 6.99163e7i | −1.47385 | − | 1.47385i | ||||
\(363\) | 2.84698e7i | 0.595202i | ||||||||
\(364\) | 4.81267e7 | − | 2.36691e7i | 0.997888 | − | 0.490770i | ||||
\(365\) | −5.82739e7 | −1.19838 | ||||||||
\(366\) | 6.01348e7 | − | 6.01348e7i | 1.22654 | − | 1.22654i | ||||
\(367\) | −2.88272e7 | −0.583183 | −0.291591 | − | 0.956543i | \(-0.594185\pi\) | ||||
−0.291591 | + | 0.956543i | \(0.594185\pi\) | |||||||
\(368\) | − | 6.60645e6i | − | 0.132564i | ||||||
\(369\) | −1.93737e7 | + | 1.93737e7i | −0.385597 | + | 0.385597i | ||||
\(370\) | 4.52343e7 | − | 4.52343e7i | 0.893023 | − | 0.893023i | ||||
\(371\) | 1.23687e7 | + | 1.23687e7i | 0.242215 | + | 0.242215i | ||||
\(372\) | −2.26287e7 | − | 2.26287e7i | −0.439574 | − | 0.439574i | ||||
\(373\) | −1.80799e7 | −0.348393 | −0.174196 | − | 0.984711i | \(-0.555733\pi\) | ||||
−0.174196 | + | 0.984711i | \(0.555733\pi\) | |||||||
\(374\) | 2.96950e7i | 0.567633i | ||||||||
\(375\) | −2.57090e7 | − | 2.57090e7i | −0.487519 | − | 0.487519i | ||||
\(376\) | 3.15792e7i | 0.594070i | ||||||||
\(377\) | 1.92153e6 | + | 654579.i | 0.0358611 | + | 0.0122162i | ||||
\(378\) | 7.26297e7 | 1.34474 | ||||||||
\(379\) | 3.50989e7 | − | 3.50989e7i | 0.644727 | − | 0.644727i | −0.306987 | − | 0.951714i | \(-0.599321\pi\) |
0.951714 | + | 0.306987i | \(0.0993208\pi\) | |||||||
\(380\) | 9.86028e7 | 1.79696 | ||||||||
\(381\) | 3.45520e7i | 0.624738i | ||||||||
\(382\) | 8.79314e6 | − | 8.79314e6i | 0.157744 | − | 0.157744i | ||||
\(383\) | 2.88898e7 | − | 2.88898e7i | 0.514219 | − | 0.514219i | −0.401597 | − | 0.915816i | \(-0.631545\pi\) |
0.915816 | + | 0.401597i | \(0.131545\pi\) | |||||||
\(384\) | −1.90894e7 | − | 1.90894e7i | −0.337131 | − | 0.337131i | ||||
\(385\) | −7.32084e6 | − | 7.32084e6i | −0.128286 | − | 0.128286i | ||||
\(386\) | −9.84331e7 | −1.71151 | ||||||||
\(387\) | 4.27397e7i | 0.737393i | ||||||||
\(388\) | 1.89731e7 | + | 1.89731e7i | 0.324820 | + | 0.324820i | ||||
\(389\) | − | 2.20087e7i | − | 0.373891i | −0.982370 | − | 0.186945i | \(-0.940141\pi\) | ||
0.982370 | − | 0.186945i | \(-0.0598587\pi\) | |||||||
\(390\) | −1.51802e7 | + | 4.45619e7i | −0.255908 | + | 0.751225i | ||||
\(391\) | −1.80140e7 | −0.301356 | ||||||||
\(392\) | 3.64387e6 | − | 3.64387e6i | 0.0604929 | − | 0.0604929i | ||||
\(393\) | −1.00823e7 | −0.166105 | ||||||||
\(394\) | 6.49888e7i | 1.06255i | ||||||||
\(395\) | −3.08844e7 | + | 3.08844e7i | −0.501127 | + | 0.501127i | ||||
\(396\) | −8.15474e6 | + | 8.15474e6i | −0.131318 | + | 0.131318i | ||||
\(397\) | −1.81293e7 | − | 1.81293e7i | −0.289740 | − | 0.289740i | 0.547237 | − | 0.836977i | \(-0.315679\pi\) |
−0.836977 | + | 0.547237i | \(0.815679\pi\) | |||||||
\(398\) | −7.59327e6 | − | 7.59327e6i | −0.120442 | − | 0.120442i | ||||
\(399\) | −6.09073e7 | −0.958850 | ||||||||
\(400\) | 1.31869e7i | 0.206046i | ||||||||
\(401\) | 1.55442e7 | + | 1.55442e7i | 0.241066 | + | 0.241066i | 0.817291 | − | 0.576225i | \(-0.195475\pi\) |
−0.576225 | + | 0.817291i | \(0.695475\pi\) | |||||||
\(402\) | 7.71768e7i | 1.18798i | ||||||||
\(403\) | 4.57633e7 | − | 2.25068e7i | 0.699202 | − | 0.343874i | ||||
\(404\) | −8.73032e7 | −1.32399 | ||||||||
\(405\) | −1.70205e6 | + | 1.70205e6i | −0.0256216 | + | 0.0256216i | ||||
\(406\) | −3.36592e6 | −0.0502951 | ||||||||
\(407\) | − | 1.67595e7i | − | 0.248587i | ||||||
\(408\) | −1.81490e7 | + | 1.81490e7i | −0.267222 | + | 0.267222i | ||||
\(409\) | −7.10021e7 | + | 7.10021e7i | −1.03777 | + | 1.03777i | −0.0385117 | + | 0.999258i | \(0.512262\pi\) |
−0.999258 | + | 0.0385117i | \(0.987738\pi\) | |||||||
\(410\) | 5.56168e7 | + | 5.56168e7i | 0.806964 | + | 0.806964i | ||||
\(411\) | 4.56411e7 | + | 4.56411e7i | 0.657401 | + | 0.657401i | ||||
\(412\) | 1.84474e7 | 0.263781 | ||||||||
\(413\) | 2.45979e7i | 0.349180i | ||||||||
\(414\) | −8.87630e6 | − | 8.87630e6i | −0.125092 | − | 0.125092i | ||||
\(415\) | − | 8.71626e6i | − | 0.121951i | ||||||
\(416\) | 9.05831e7 | − | 4.45496e7i | 1.25825 | − | 0.618819i | ||||
\(417\) | 2.66645e7 | 0.367726 | ||||||||
\(418\) | 3.27754e7 | − | 3.27754e7i | 0.448765 | − | 0.448765i | ||||
\(419\) | 8.55705e7 | 1.16327 | 0.581637 | − | 0.813448i | \(-0.302412\pi\) | ||||
0.581637 | + | 0.813448i | \(0.302412\pi\) | |||||||
\(420\) | − | 4.35035e7i | − | 0.587187i | ||||||
\(421\) | −2.05616e6 | + | 2.05616e6i | −0.0275557 | + | 0.0275557i | −0.720750 | − | 0.693195i | \(-0.756203\pi\) |
0.693195 | + | 0.720750i | \(0.256203\pi\) | |||||||
\(422\) | 784436. | − | 784436.i | 0.0104381 | − | 0.0104381i | ||||
\(423\) | −4.88808e7 | − | 4.88808e7i | −0.645828 | − | 0.645828i | ||||
\(424\) | −8.13581e6 | − | 8.13581e6i | −0.106734 | − | 0.106734i | ||||
\(425\) | 3.59571e7 | 0.468402 | ||||||||
\(426\) | 8.40732e6i | 0.108750i | ||||||||
\(427\) | −8.85578e7 | − | 8.85578e7i | −1.13748 | − | 1.13748i | ||||
\(428\) | − | 1.42706e8i | − | 1.82016i | ||||||
\(429\) | 5.44303e6 | + | 1.10674e7i | 0.0689396 | + | 0.140176i | ||||
\(430\) | 1.22694e8 | 1.54319 | ||||||||
\(431\) | −1.77261e7 | + | 1.77261e7i | −0.221402 | + | 0.221402i | −0.809089 | − | 0.587687i | \(-0.800039\pi\) |
0.587687 | + | 0.809089i | \(0.300039\pi\) | |||||||
\(432\) | 5.50384e7 | 0.682675 | ||||||||
\(433\) | 2.97891e7i | 0.366939i | 0.983025 | + | 0.183470i | \(0.0587329\pi\) | ||||
−0.983025 | + | 0.183470i | \(0.941267\pi\) | |||||||
\(434\) | −5.97938e7 | + | 5.97938e7i | −0.731454 | + | 0.731454i | ||||
\(435\) | 1.16432e6 | − | 1.16432e6i | 0.0141451 | − | 0.0141451i | ||||
\(436\) | −4.34390e7 | − | 4.34390e7i | −0.524108 | − | 0.524108i | ||||
\(437\) | 1.98827e7 | + | 1.98827e7i | 0.238249 | + | 0.238249i | ||||
\(438\) | −1.15106e8 | −1.36985 | ||||||||
\(439\) | 3.81149e7i | 0.450507i | 0.974300 | + | 0.225254i | \(0.0723210\pi\) | ||||
−0.974300 | + | 0.225254i | \(0.927679\pi\) | |||||||
\(440\) | 4.81547e6 | + | 4.81547e6i | 0.0565302 | + | 0.0565302i | ||||
\(441\) | 1.12805e7i | 0.131527i | ||||||||
\(442\) | −8.77546e7 | − | 1.78432e8i | −1.01626 | − | 2.06636i | ||||
\(443\) | −3.81620e6 | −0.0438955 | −0.0219478 | − | 0.999759i | \(-0.506987\pi\) | ||||
−0.0219478 | + | 0.999759i | \(0.506987\pi\) | |||||||
\(444\) | 4.97961e7 | − | 4.97961e7i | 0.568913 | − | 0.568913i | ||||
\(445\) | −8.99807e6 | −0.102110 | ||||||||
\(446\) | − | 1.50595e8i | − | 1.69748i | ||||||
\(447\) | 1.64763e7 | − | 1.64763e7i | 0.184475 | − | 0.184475i | ||||
\(448\) | −8.05053e7 | + | 8.05053e7i | −0.895345 | + | 0.895345i | ||||
\(449\) | 6.41269e6 | + | 6.41269e6i | 0.0708437 | + | 0.0708437i | 0.741641 | − | 0.670797i | \(-0.234048\pi\) |
−0.670797 | + | 0.741641i | \(0.734048\pi\) | |||||||
\(450\) | 1.77177e7 | + | 1.77177e7i | 0.194433 | + | 0.194433i | ||||
\(451\) | 2.06063e7 | 0.224631 | ||||||||
\(452\) | 9.01984e7i | 0.976750i | ||||||||
\(453\) | 3.96845e7 | + | 3.96845e7i | 0.426900 | + | 0.426900i | ||||
\(454\) | 1.34363e8i | 1.43586i | ||||||||
\(455\) | 6.56243e7 | + | 2.23552e7i | 0.696676 | + | 0.237326i | ||||
\(456\) | 4.00634e7 | 0.422525 | ||||||||
\(457\) | −9.92694e7 | + | 9.92694e7i | −1.04008 | + | 1.04008i | −0.0409178 | + | 0.999163i | \(0.513028\pi\) |
−0.999163 | + | 0.0409178i | \(0.986972\pi\) | |||||||
\(458\) | −3.89188e7 | −0.405101 | ||||||||
\(459\) | − | 1.50075e8i | − | 1.55192i | ||||||
\(460\) | −1.42014e7 | + | 1.42014e7i | −0.145900 | + | 0.145900i | ||||
\(461\) | −9.89943e6 | + | 9.89943e6i | −0.101043 | + | 0.101043i | −0.755821 | − | 0.654778i | \(-0.772762\pi\) |
0.654778 | + | 0.755821i | \(0.272762\pi\) | |||||||
\(462\) | −1.44605e7 | − | 1.44605e7i | −0.146641 | − | 0.146641i | ||||
\(463\) | −3.23972e7 | − | 3.23972e7i | −0.326411 | − | 0.326411i | 0.524809 | − | 0.851220i | \(-0.324137\pi\) |
−0.851220 | + | 0.524809i | \(0.824137\pi\) | |||||||
\(464\) | −2.55067e6 | −0.0255329 | ||||||||
\(465\) | − | 4.13672e7i | − | 0.411431i | ||||||
\(466\) | 9.67279e7 | + | 9.67279e7i | 0.955859 | + | 0.955859i | ||||
\(467\) | 4.30021e7i | 0.422220i | 0.977462 | + | 0.211110i | \(0.0677079\pi\) | ||||
−0.977462 | + | 0.211110i | \(0.932292\pi\) | |||||||
\(468\) | 2.49016e7 | − | 7.30995e7i | 0.242935 | − | 0.713143i | ||||
\(469\) | 1.13655e8 | 1.10171 | ||||||||
\(470\) | −1.40324e8 | + | 1.40324e8i | −1.35157 | + | 1.35157i | ||||
\(471\) | 5.41605e7 | 0.518346 | ||||||||
\(472\) | − | 1.61799e7i | − | 0.153869i | ||||||
\(473\) | 2.27294e7 | − | 2.27294e7i | 0.214785 | − | 0.214785i | ||||
\(474\) | −6.10043e7 | + | 6.10043e7i | −0.572830 | + | 0.572830i | ||||
\(475\) | −3.96872e7 | − | 3.96872e7i | −0.370313 | − | 0.370313i | ||||
\(476\) | 1.29932e8 | + | 1.29932e8i | 1.20475 | + | 1.20475i | ||||
\(477\) | 2.51865e7 | 0.232067 | ||||||||
\(478\) | − | 1.32587e8i | − | 1.21400i | ||||||
\(479\) | −7.79320e7 | − | 7.79320e7i | −0.709103 | − | 0.709103i | 0.257243 | − | 0.966347i | \(-0.417186\pi\) |
−0.966347 | + | 0.257243i | \(0.917186\pi\) | |||||||
\(480\) | − | 8.18815e7i | − | 0.740392i | ||||||
\(481\) | 4.95277e7 | + | 1.00705e8i | 0.445055 | + | 0.904934i | ||||
\(482\) | −1.39352e6 | −0.0124443 | ||||||||
\(483\) | 8.77222e6 | − | 8.77222e6i | 0.0778517 | − | 0.0778517i | ||||
\(484\) | −1.34069e8 | −1.18247 | ||||||||
\(485\) | 3.46843e7i | 0.304024i | ||||||||
\(486\) | 1.20212e8 | − | 1.20212e8i | 1.04722 | − | 1.04722i | ||||
\(487\) | 1.40906e6 | − | 1.40906e6i | 0.0121995 | − | 0.0121995i | −0.700981 | − | 0.713180i | \(-0.747254\pi\) |
0.713180 | + | 0.700981i | \(0.247254\pi\) | |||||||
\(488\) | 5.82512e7 | + | 5.82512e7i | 0.501240 | + | 0.501240i | ||||
\(489\) | −5.78323e7 | − | 5.78323e7i | −0.494589 | − | 0.494589i | ||||
\(490\) | 3.23834e7 | 0.275254 | ||||||||
\(491\) | − | 3.42671e7i | − | 0.289490i | −0.989469 | − | 0.144745i | \(-0.953764\pi\) | ||
0.989469 | − | 0.144745i | \(-0.0462362\pi\) | |||||||
\(492\) | 6.12256e7 | + | 6.12256e7i | 0.514088 | + | 0.514088i | ||||
\(493\) | 6.95498e6i | 0.0580437i | ||||||||
\(494\) | −1.00084e8 | + | 2.93800e8i | −0.830203 | + | 2.43709i | ||||
\(495\) | −1.49075e7 | −0.122911 | ||||||||
\(496\) | −4.53114e7 | + | 4.53114e7i | −0.371332 | + | 0.371332i | ||||
\(497\) | 1.23811e7 | 0.100853 | ||||||||
\(498\) | − | 1.72168e7i | − | 0.139400i | ||||||
\(499\) | 9.89459e7 | − | 9.89459e7i | 0.796336 | − | 0.796336i | −0.186180 | − | 0.982516i | \(-0.559611\pi\) |
0.982516 | + | 0.186180i | \(0.0596108\pi\) | |||||||
\(500\) | 1.21068e8 | − | 1.21068e8i | 0.968542 | − | 0.968542i | ||||
\(501\) | 6.53648e7 | + | 6.53648e7i | 0.519793 | + | 0.519793i | ||||
\(502\) | 8.47080e7 | + | 8.47080e7i | 0.669597 | + | 0.669597i | ||||
\(503\) | −7.51556e7 | −0.590551 | −0.295276 | − | 0.955412i | \(-0.595411\pi\) | ||||
−0.295276 | + | 0.955412i | \(0.595411\pi\) | |||||||
\(504\) | 2.63394e7i | 0.205738i | ||||||||
\(505\) | −7.97986e7 | − | 7.97986e7i | −0.619614 | − | 0.619614i | ||||
\(506\) | 9.44100e6i | 0.0728730i | ||||||||
\(507\) | −6.54126e7 | − | 5.04168e7i | −0.501923 | − | 0.386858i | ||||
\(508\) | −1.62711e8 | −1.24115 | ||||||||
\(509\) | 1.63158e8 | − | 1.63158e8i | 1.23724 | − | 1.23724i | 0.276117 | − | 0.961124i | \(-0.410952\pi\) |
0.961124 | − | 0.276117i | \(-0.0890477\pi\) | |||||||
\(510\) | −1.61292e8 | −1.21591 | ||||||||
\(511\) | 1.69511e8i | 1.27038i | ||||||||
\(512\) | −1.14585e8 | + | 1.14585e8i | −0.853725 | + | 0.853725i | ||||
\(513\) | −1.65643e8 | + | 1.65643e8i | −1.22693 | + | 1.22693i | ||||
\(514\) | −1.50058e8 | − | 1.50058e8i | −1.10502 | − | 1.10502i | ||||
\(515\) | 1.68617e7 | + | 1.68617e7i | 0.123447 | + | 0.123447i | ||||
\(516\) | 1.35068e8 | 0.983110 | ||||||||
\(517\) | 5.19905e7i | 0.376229i | ||||||||
\(518\) | −1.31580e8 | − | 1.31580e8i | −0.946676 | − | 0.946676i | ||||
\(519\) | − | 1.27504e8i | − | 0.912055i | ||||||
\(520\) | −4.31661e7 | − | 1.47047e7i | −0.306996 | − | 0.104579i | ||||
\(521\) | 6.71801e6 | 0.0475037 | 0.0237518 | − | 0.999718i | \(-0.492439\pi\) | ||||
0.0237518 | + | 0.999718i | \(0.492439\pi\) | |||||||
\(522\) | −3.42704e6 | + | 3.42704e6i | −0.0240939 | + | 0.0240939i | ||||
\(523\) | 1.17314e8 | 0.820060 | 0.410030 | − | 0.912072i | \(-0.365518\pi\) | ||||
0.410030 | + | 0.912072i | \(0.365518\pi\) | |||||||
\(524\) | − | 4.74791e7i | − | 0.329996i | ||||||
\(525\) | −1.75100e7 | + | 1.75100e7i | −0.121006 | + | 0.121006i | ||||
\(526\) | 2.28902e8 | − | 2.28902e8i | 1.57287 | − | 1.57287i | ||||
\(527\) | 1.23552e8 | + | 1.23552e8i | 0.844145 | + | 0.844145i | ||||
\(528\) | −1.09581e7 | − | 1.09581e7i | −0.0744444 | − | 0.0744444i | ||||
\(529\) | 1.42309e8 | 0.961312 | ||||||||
\(530\) | − | 7.23037e7i | − | 0.485660i | ||||||
\(531\) | 2.50446e7 | + | 2.50446e7i | 0.167275 | + | 0.167275i | ||||
\(532\) | − | 2.86822e8i | − | 1.90492i | ||||||
\(533\) | −1.23820e8 | + | 6.08957e7i | −0.817727 | + | 0.402165i | ||||
\(534\) | −1.77734e7 | −0.116721 | ||||||||
\(535\) | 1.30439e8 | − | 1.30439e8i | 0.851815 | − | 0.851815i | ||||
\(536\) | −7.47593e7 | −0.485480 | ||||||||
\(537\) | 1.69958e8i | 1.09754i | ||||||||
\(538\) | 1.94436e8 | − | 1.94436e8i | 1.24862 | − | 1.24862i | ||||
\(539\) | 5.99910e6 | − | 5.99910e6i | 0.0383107 | − | 0.0383107i | ||||
\(540\) | −1.18312e8 | − | 1.18312e8i | −0.751356 | − | 0.751356i | ||||
\(541\) | −2.04171e7 | − | 2.04171e7i | −0.128944 | − | 0.128944i | 0.639689 | − | 0.768634i | \(-0.279063\pi\) |
−0.768634 | + | 0.639689i | \(0.779063\pi\) | |||||||
\(542\) | 1.93154e8 | 1.21312 | ||||||||
\(543\) | − | 1.40702e8i | − | 0.878824i | ||||||
\(544\) | 2.44556e8 | + | 2.44556e8i | 1.51908 | + | 1.51908i | ||||
\(545\) | − | 7.94101e7i | − | 0.490553i | ||||||
\(546\) | 1.29624e8 | + | 4.41571e7i | 0.796359 | + | 0.271283i | ||||
\(547\) | −2.99984e8 | −1.83289 | −0.916444 | − | 0.400162i | \(-0.868954\pi\) | ||||
−0.916444 | + | 0.400162i | \(0.868954\pi\) | |||||||
\(548\) | −2.14931e8 | + | 2.14931e8i | −1.30604 | + | 1.30604i | ||||
\(549\) | −1.80332e8 | −1.08982 | ||||||||
\(550\) | − | 1.88449e7i | − | 0.113268i | ||||||
\(551\) | 7.67646e6 | − | 7.67646e6i | 0.0458887 | − | 0.0458887i | ||||
\(552\) | −5.77016e6 | + | 5.77016e6i | −0.0343060 | + | 0.0343060i | ||||
\(553\) | 8.98383e7 | + | 8.98383e7i | 0.531234 | + | 0.531234i | ||||
\(554\) | 1.10596e8 | + | 1.10596e8i | 0.650447 | + | 0.650447i | ||||
\(555\) | 9.10313e7 | 0.532490 | ||||||||
\(556\) | 1.25567e8i | 0.730552i | ||||||||
\(557\) | −4.42993e7 | − | 4.42993e7i | −0.256349 | − | 0.256349i | 0.567218 | − | 0.823567i | \(-0.308020\pi\) |
−0.823567 | + | 0.567218i | \(0.808020\pi\) | |||||||
\(558\) | 1.21759e8i | 0.700808i | ||||||||
\(559\) | −6.94073e7 | + | 2.03747e8i | −0.397347 | + | 1.16642i | ||||
\(560\) | −8.71107e7 | −0.496029 | ||||||||
\(561\) | −2.98796e7 | + | 2.98796e7i | −0.169234 | + | 0.169234i | ||||
\(562\) | −4.04679e8 | −2.27983 | ||||||||
\(563\) | 2.83040e8i | 1.58607i | 0.609176 | + | 0.793035i | \(0.291500\pi\) | ||||
−0.609176 | + | 0.793035i | \(0.708500\pi\) | |||||||
\(564\) | −1.54475e8 | + | 1.54475e8i | −0.861034 | + | 0.861034i | ||||
\(565\) | −8.24450e7 | + | 8.24450e7i | −0.457108 | + | 0.457108i | ||||
\(566\) | 1.05786e8 | + | 1.05786e8i | 0.583419 | + | 0.583419i | ||||
\(567\) | 4.95101e6 | + | 4.95101e6i | 0.0271609 | + | 0.0271609i | ||||
\(568\) | −8.14398e6 | −0.0444418 | ||||||||
\(569\) | − | 2.74227e8i | − | 1.48858i | −0.667854 | − | 0.744292i | \(-0.732787\pi\) | ||
0.667854 | − | 0.744292i | \(-0.267213\pi\) | |||||||
\(570\) | 1.78023e8 | + | 1.78023e8i | 0.961285 | + | 0.961285i | ||||
\(571\) | − | 5.50772e7i | − | 0.295845i | −0.988999 | − | 0.147922i | \(-0.952741\pi\) | ||
0.988999 | − | 0.147922i | \(-0.0472585\pi\) | |||||||
\(572\) | −5.21179e7 | + | 2.56321e7i | −0.278483 | + | 0.136960i | ||||
\(573\) | 1.76956e7 | 0.0940595 | ||||||||
\(574\) | 1.61781e8 | − | 1.61781e8i | 0.855447 | − | 0.855447i | ||||
\(575\) | 1.14320e7 | 0.0601336 | ||||||||
\(576\) | 1.63934e8i | 0.857832i | ||||||||
\(577\) | 8.09540e7 | − | 8.09540e7i | 0.421416 | − | 0.421416i | −0.464275 | − | 0.885691i | \(-0.653685\pi\) |
0.885691 | + | 0.464275i | \(0.153685\pi\) | |||||||
\(578\) | 2.76509e8 | − | 2.76509e8i | 1.43194 | − | 1.43194i | ||||
\(579\) | −9.90453e7 | − | 9.90453e7i | −0.510268 | − | 0.510268i | ||||
\(580\) | 5.48297e6 | + | 5.48297e6i | 0.0281017 | + | 0.0281017i | ||||
\(581\) | −2.53544e7 | −0.129278 | ||||||||
\(582\) | 6.85102e7i | 0.347525i | ||||||||
\(583\) | −1.33944e7 | − | 1.33944e7i | −0.0675955 | − | 0.0675955i | ||||
\(584\) | − | 1.11500e8i | − | 0.559805i | ||||||
\(585\) | 8.95770e7 | − | 4.40548e7i | 0.447434 | − | 0.220052i | ||||
\(586\) | 1.54443e8 | 0.767497 | ||||||||
\(587\) | −2.01036e8 | + | 2.01036e8i | −0.993938 | + | 0.993938i | −0.999982 | − | 0.00604390i | \(-0.998076\pi\) |
0.00604390 | + | 0.999982i | \(0.498076\pi\) | |||||||
\(588\) | 3.56492e7 | 0.175355 | ||||||||
\(589\) | − | 2.72737e8i | − | 1.33474i | ||||||
\(590\) | 7.18963e7 | − | 7.18963e7i | 0.350066 | − | 0.350066i | ||||
\(591\) | −6.53930e7 | + | 6.53930e7i | −0.316788 | + | 0.316788i | ||||
\(592\) | −9.97107e7 | − | 9.97107e7i | −0.480592 | − | 0.480592i | ||||
\(593\) | −1.05754e8 | − | 1.05754e8i | −0.507147 | − | 0.507147i | 0.406503 | − | 0.913650i | \(-0.366748\pi\) |
−0.913650 | + | 0.406503i | \(0.866748\pi\) | |||||||
\(594\) | −7.86530e7 | −0.375281 | ||||||||
\(595\) | 2.37527e8i | 1.12762i | ||||||||
\(596\) | 7.75894e7 | + | 7.75894e7i | 0.366491 | + | 0.366491i | ||||
\(597\) | − | 1.52810e7i | − | 0.0718172i | ||||||
\(598\) | −2.79001e7 | − | 5.67295e7i | −0.130467 | − | 0.265280i | ||||
\(599\) | 9.05205e7 | 0.421179 | 0.210589 | − | 0.977575i | \(-0.432462\pi\) | ||||
0.210589 | + | 0.977575i | \(0.432462\pi\) | |||||||
\(600\) | 1.15176e7 | − | 1.15176e7i | 0.0533224 | − | 0.0533224i | ||||
\(601\) | 2.05850e8 | 0.948262 | 0.474131 | − | 0.880454i | \(-0.342762\pi\) | ||||
0.474131 | + | 0.880454i | \(0.342762\pi\) | |||||||
\(602\) | − | 3.56900e8i | − | 1.63590i | ||||||
\(603\) | 1.15718e8 | − | 1.15718e8i | 0.527777 | − | 0.527777i | ||||
\(604\) | −1.86881e8 | + | 1.86881e8i | −0.848112 | + | 0.848112i | ||||
\(605\) | −1.22544e8 | − | 1.22544e8i | −0.553384 | − | 0.553384i | ||||
\(606\) | −1.57622e8 | − | 1.57622e8i | −0.708271 | − | 0.708271i | ||||
\(607\) | 1.14080e8 | 0.510085 | 0.255043 | − | 0.966930i | \(-0.417910\pi\) | ||||
0.255043 | + | 0.966930i | \(0.417910\pi\) | |||||||
\(608\) | − | 5.39850e8i | − | 2.40194i | ||||||
\(609\) | −3.38685e6 | − | 3.38685e6i | −0.0149949 | − | 0.0149949i | ||||
\(610\) | 5.17684e8i | 2.28074i | ||||||||
\(611\) | −1.53642e8 | − | 3.12403e8i | −0.673577 | − | 1.36959i | ||||
\(612\) | 2.64583e8 | 1.15427 | ||||||||
\(613\) | −1.12421e6 | + | 1.12421e6i | −0.00488052 | + | 0.00488052i | −0.709543 | − | 0.704662i | \(-0.751099\pi\) |
0.704662 | + | 0.709543i | \(0.251099\pi\) | |||||||
\(614\) | 1.63297e8 | 0.705461 | ||||||||
\(615\) | 1.11925e8i | 0.481175i | ||||||||
\(616\) | 1.40075e7 | − | 1.40075e7i | 0.0599266 | − | 0.0599266i | ||||
\(617\) | −1.05308e8 | + | 1.05308e8i | −0.448336 | + | 0.448336i | −0.894801 | − | 0.446465i | \(-0.852683\pi\) |
0.446465 | + | 0.894801i | \(0.352683\pi\) | |||||||
\(618\) | 3.33060e7 | + | 3.33060e7i | 0.141110 | + | 0.141110i | ||||
\(619\) | 3.88419e6 | + | 3.88419e6i | 0.0163768 | + | 0.0163768i | 0.715248 | − | 0.698871i | \(-0.246314\pi\) |
−0.698871 | + | 0.715248i | \(0.746314\pi\) | |||||||
\(620\) | 1.94804e8 | 0.817380 | ||||||||
\(621\) | − | 4.77136e7i | − | 0.199236i | ||||||
\(622\) | −2.59000e8 | − | 2.59000e8i | −1.07629 | − | 1.07629i | ||||
\(623\) | 2.61741e7i | 0.108245i | ||||||||
\(624\) | 9.82286e7 | + | 3.34620e7i | 0.404282 | + | 0.137720i | ||||
\(625\) | 1.46682e8 | 0.600811 | ||||||||
\(626\) | −1.75765e8 | + | 1.75765e8i | −0.716489 | + | 0.716489i | ||||
\(627\) | 6.59584e7 | 0.267589 | ||||||||
\(628\) | 2.55050e8i | 1.02979i | ||||||||
\(629\) | −2.71884e8 | + | 2.71884e8i | −1.09253 | + | 1.09253i | ||||
\(630\) | −1.17040e8 | + | 1.17040e8i | −0.468073 | + | 0.468073i | ||||
\(631\) | −2.27959e7 | − | 2.27959e7i | −0.0907336 | − | 0.0907336i | 0.660283 | − | 0.751017i | \(-0.270436\pi\) |
−0.751017 | + | 0.660283i | \(0.770436\pi\) | |||||||
\(632\) | −5.90935e7 | − | 5.90935e7i | −0.234093 | − | 0.234093i | ||||
\(633\) | 1.57863e6 | 0.00622399 | ||||||||
\(634\) | 6.27529e8i | 2.46244i | ||||||||
\(635\) | −1.48724e8 | − | 1.48724e8i | −0.580845 | − | 0.580845i | ||||
\(636\) | − | 7.95953e7i | − | 0.309397i | ||||||
\(637\) | −1.83191e7 | + | 5.37762e7i | −0.0708737 | + | 0.208052i | ||||
\(638\) | 3.64506e6 | 0.0140360 | ||||||||
\(639\) | 1.26059e7 | − | 1.26059e7i | 0.0483138 | − | 0.0483138i | ||||
\(640\) | 1.64335e8 | 0.626889 | ||||||||
\(641\) | − | 4.33034e8i | − | 1.64417i | −0.569363 | − | 0.822086i | \(-0.692810\pi\) | ||
0.569363 | − | 0.822086i | \(-0.307190\pi\) | |||||||
\(642\) | 2.57649e8 | − | 2.57649e8i | 0.973696 | − | 0.973696i | ||||
\(643\) | −1.52097e8 | + | 1.52097e8i | −0.572122 | + | 0.572122i | −0.932721 | − | 0.360599i | \(-0.882572\pi\) |
0.360599 | + | 0.932721i | \(0.382572\pi\) | |||||||
\(644\) | 4.13097e7 | + | 4.13097e7i | 0.154666 | + | 0.154666i | ||||
\(645\) | 1.23457e8 | + | 1.23457e8i | 0.460085 | + | 0.460085i | ||||
\(646\) | −1.06341e9 | −3.94459 | ||||||||
\(647\) | 3.36634e8i | 1.24293i | 0.783444 | + | 0.621463i | \(0.213461\pi\) | ||||
−0.783444 | + | 0.621463i | \(0.786539\pi\) | |||||||
\(648\) | −3.25666e6 | − | 3.25666e6i | −0.0119687 | − | 0.0119687i | ||||
\(649\) | − | 2.66379e7i | − | 0.0974464i | ||||||
\(650\) | 5.56904e7 | + | 1.13236e8i | 0.202787 | + | 0.412329i | ||||
\(651\) | −1.20331e8 | −0.436150 | ||||||||
\(652\) | 2.72341e8 | − | 2.72341e8i | 0.982586 | − | 0.982586i | ||||
\(653\) | 2.78026e8 | 0.998496 | 0.499248 | − | 0.866459i | \(-0.333610\pi\) | ||||
0.499248 | + | 0.866459i | \(0.333610\pi\) | |||||||
\(654\) | − | 1.56855e8i | − | 0.560744i | ||||||
\(655\) | 4.33978e7 | − | 4.33978e7i | 0.154434 | − | 0.154434i | ||||
\(656\) | 1.22597e8 | − | 1.22597e8i | 0.434278 | − | 0.434278i | ||||
\(657\) | 1.72589e8 | + | 1.72589e8i | 0.608578 | + | 0.608578i | ||||
\(658\) | 4.08182e8 | + | 4.08182e8i | 1.43277 | + | 1.43277i | ||||
\(659\) | 3.97164e8 | 1.38776 | 0.693878 | − | 0.720093i | \(-0.255901\pi\) | ||||
0.693878 | + | 0.720093i | \(0.255901\pi\) | |||||||
\(660\) | 4.71113e7i | 0.163868i | ||||||||
\(661\) | 1.57276e8 | + | 1.57276e8i | 0.544577 | + | 0.544577i | 0.924867 | − | 0.380290i | \(-0.124176\pi\) |
−0.380290 | + | 0.924867i | \(0.624176\pi\) | |||||||
\(662\) | 3.09531e8i | 1.06692i | ||||||||
\(663\) | 9.12416e7 | − | 2.67842e8i | 0.313078 | − | 0.919049i | ||||
\(664\) | 1.66775e7 | 0.0569674 | ||||||||
\(665\) | 2.62167e8 | − | 2.62167e8i | 0.891483 | − | 0.891483i | ||||
\(666\) | −2.67939e8 | −0.907012 | ||||||||
\(667\) | 2.21122e6i | 0.00745167i | ||||||||
\(668\) | −3.07813e8 | + | 3.07813e8i | −1.03266 | + | 1.03266i | ||||
\(669\) | 1.51531e8 | − | 1.51531e8i | 0.506086 | − | 0.506086i | ||||
\(670\) | −3.32196e8 | − | 3.32196e8i | −1.10451 | − | 1.10451i | ||||
\(671\) | 9.59021e7 | + | 9.59021e7i | 0.317439 | + | 0.317439i | ||||
\(672\) | −2.38182e8 | −0.784875 | ||||||||
\(673\) | 1.93344e8i | 0.634285i | 0.948378 | + | 0.317143i | \(0.102723\pi\) | ||||
−0.948378 | + | 0.317143i | \(0.897277\pi\) | |||||||
\(674\) | −1.82505e8 | − | 1.82505e8i | −0.596067 | − | 0.596067i | ||||
\(675\) | 9.52396e7i | 0.309675i | ||||||||
\(676\) | 2.37420e8 | − | 3.08038e8i | 0.768560 | − | 0.997158i | ||||
\(677\) | −4.36390e7 | −0.140640 | −0.0703201 | − | 0.997524i | \(-0.522402\pi\) | ||||
−0.0703201 | + | 0.997524i | \(0.522402\pi\) | |||||||
\(678\) | −1.62849e8 | + | 1.62849e8i | −0.522513 | + | 0.522513i | ||||
\(679\) | 1.00892e8 | 0.322290 | ||||||||
\(680\) | − | 1.56239e8i | − | 0.496894i | ||||||
\(681\) | −1.35199e8 | + | 1.35199e8i | −0.428087 | + | 0.428087i | ||||
\(682\) | 6.47526e7 | − | 6.47526e7i | 0.204129 | − | 0.204129i | ||||
\(683\) | 4.34212e8 | + | 4.34212e8i | 1.36282 | + | 1.36282i | 0.870299 | + | 0.492523i | \(0.163925\pi\) |
0.492523 | + | 0.870299i | \(0.336075\pi\) | |||||||
\(684\) | −2.92030e8 | − | 2.92030e8i | −0.912555 | − | 0.912555i | ||||
\(685\) | −3.92911e8 | −1.22243 | ||||||||
\(686\) | − | 5.22780e8i | − | 1.61937i | ||||||
\(687\) | −3.91609e7 | − | 3.91609e7i | −0.120776 | − | 0.120776i | ||||
\(688\) | − | 2.70457e8i | − | 0.830487i | ||||||
\(689\) | 1.20068e8 | + | 4.09017e7i | 0.367088 | + | 0.125050i | ||||
\(690\) | −5.12799e7 | −0.156099 | ||||||||
\(691\) | −4.86878e7 | + | 4.86878e7i | −0.147566 | + | 0.147566i | −0.777030 | − | 0.629464i | \(-0.783275\pi\) |
0.629464 | + | 0.777030i | \(0.283275\pi\) | |||||||
\(692\) | 6.00435e8 | 1.81196 | ||||||||
\(693\) | 4.33639e7i | 0.130295i | ||||||||
\(694\) | −4.56964e8 | + | 4.56964e8i | −1.36711 | + | 1.36711i | ||||
\(695\) | −1.14773e8 | + | 1.14773e8i | −0.341890 | + | 0.341890i | ||||
\(696\) | 2.22779e6 | + | 2.22779e6i | 0.00660764 | + | 0.00660764i | ||||
\(697\) | −3.34288e8 | − | 3.34288e8i | −0.987240 | − | 0.987240i | ||||
\(698\) | −5.74255e8 | −1.68864 | ||||||||
\(699\) | 1.94659e8i | 0.569958i | ||||||||
\(700\) | −8.24571e7 | − | 8.24571e7i | −0.240400 | − | 0.240400i | ||||
\(701\) | − | 2.55548e8i | − | 0.741853i | −0.928662 | − | 0.370926i | \(-0.879040\pi\) | ||
0.928662 | − | 0.370926i | \(-0.120960\pi\) | |||||||
\(702\) | 4.72613e8 | − | 2.32436e8i | 1.36614 | − | 0.671879i | ||||
\(703\) | 6.00176e8 | 1.72748 | ||||||||
\(704\) | 8.71817e7 | − | 8.71817e7i | 0.249866 | − | 0.249866i | ||||
\(705\) | −2.82393e8 | −0.805909 | ||||||||
\(706\) | 1.68977e8i | 0.480190i | ||||||||
\(707\) | −2.32123e8 | + | 2.32123e8i | −0.656841 | + | 0.656841i | ||||
\(708\) | 7.91468e7 | − | 7.91468e7i | 0.223015 | − | 0.223015i | ||||
\(709\) | −2.99236e8 | − | 2.99236e8i | −0.839604 | − | 0.839604i | 0.149202 | − | 0.988807i | \(-0.452329\pi\) |
−0.988807 | + | 0.149202i | \(0.952329\pi\) | |||||||
\(710\) | −3.61881e7 | − | 3.61881e7i | −0.101109 | − | 0.101109i | ||||
\(711\) | 1.82939e8 | 0.508977 | ||||||||
\(712\) | − | 1.72167e7i | − | 0.0476991i | ||||||
\(713\) | 3.92811e7 | + | 3.92811e7i | 0.108372 | + | 0.108372i | ||||
\(714\) | 4.69175e8i | 1.28896i | ||||||||
\(715\) | −7.10666e7 | − | 2.42091e7i | −0.194423 | − | 0.0662310i | ||||
\(716\) | −8.00360e8 | −2.18045 | ||||||||
\(717\) | 1.33412e8 | − | 1.33412e8i | 0.361939 | − | 0.361939i | ||||
\(718\) | 6.76530e8 | 1.82774 | ||||||||
\(719\) | − | 3.54786e8i | − | 0.954508i | −0.878766 | − | 0.477254i | \(-0.841632\pi\) | ||
0.878766 | − | 0.477254i | \(-0.158368\pi\) | |||||||
\(720\) | −8.86924e7 | + | 8.86924e7i | −0.237623 | + | 0.237623i | ||||
\(721\) | 4.90482e7 | − | 4.90482e7i | 0.130863 | − | 0.130863i | ||||
\(722\) | 7.73727e8 | + | 7.73727e8i | 2.05578 | + | 2.05578i | ||||
\(723\) | −1.40218e6 | − | 1.40218e6i | −0.00371013 | − | 0.00371013i | ||||
\(724\) | 6.62589e8 | 1.74594 | ||||||||
\(725\) | − | 4.41374e6i | − | 0.0115822i | ||||||
\(726\) | −2.42055e8 | − | 2.42055e8i | −0.632564 | − | 0.632564i | ||||
\(727\) | − | 6.94762e8i | − | 1.80814i | −0.427380 | − | 0.904072i | \(-0.640563\pi\) | ||
0.427380 | − | 0.904072i | \(-0.359437\pi\) | |||||||
\(728\) | −4.27739e7 | + | 1.25564e8i | −0.110863 | + | 0.325440i | ||||
\(729\) | 2.58767e8 | 0.667924 | ||||||||
\(730\) | 4.95456e8 | − | 4.95456e8i | 1.27361 | − | 1.27361i | ||||
\(731\) | −7.37462e8 | −1.88794 | ||||||||
\(732\) | 5.69891e8i | 1.45298i | ||||||||
\(733\) | 1.25593e8 | − | 1.25593e8i | 0.318898 | − | 0.318898i | −0.529446 | − | 0.848344i | \(-0.677600\pi\) |
0.848344 | + | 0.529446i | \(0.177600\pi\) | |||||||
\(734\) | 2.45094e8 | − | 2.45094e8i | 0.619791 | − | 0.619791i | ||||
\(735\) | 3.25848e7 | + | 3.25848e7i | 0.0820641 | + | 0.0820641i | ||||
\(736\) | 7.77524e7 | + | 7.77524e7i | 0.195020 | + | 0.195020i | ||||
\(737\) | −1.23080e8 | −0.307458 | ||||||||
\(738\) | − | 3.29438e8i | − | 0.819605i | ||||||
\(739\) | −1.66032e8 | − | 1.66032e8i | −0.411395 | − | 0.411395i | 0.470829 | − | 0.882224i | \(-0.343955\pi\) |
−0.882224 | + | 0.470829i | \(0.843955\pi\) | |||||||
\(740\) | 4.28680e8i | 1.05788i | ||||||||
\(741\) | −3.96334e8 | + | 1.94920e8i | −0.974106 | + | 0.479074i | ||||
\(742\) | −2.10321e8 | −0.514839 | ||||||||
\(743\) | −4.33230e8 | + | 4.33230e8i | −1.05621 | + | 1.05621i | −0.0578917 | + | 0.998323i | \(0.518438\pi\) |
−0.998323 | + | 0.0578917i | \(0.981562\pi\) | |||||||
\(744\) | 7.91511e7 | 0.192193 | ||||||||
\(745\) | 1.41840e8i | 0.343028i | ||||||||
\(746\) | 1.53718e8 | − | 1.53718e8i | 0.370262 | − | 0.370262i | ||||
\(747\) | −2.58148e7 | + | 2.58148e7i | −0.0619307 | + | 0.0619307i | ||||
\(748\) | −1.40708e8 | − | 1.40708e8i | −0.336212 | − | 0.336212i | ||||
\(749\) | −3.79428e8 | − | 3.79428e8i | −0.902992 | − | 0.902992i | ||||
\(750\) | 4.37165e8 | 1.03624 | ||||||||
\(751\) | 4.61949e8i | 1.09062i | 0.838234 | + | 0.545311i | \(0.183588\pi\) | ||||
−0.838234 | + | 0.545311i | \(0.816412\pi\) | |||||||
\(752\) | 3.09317e8 | + | 3.09317e8i | 0.727362 | + | 0.727362i | ||||
\(753\) | 1.70470e8i | 0.399266i | ||||||||
\(754\) | −2.19026e7 | + | 1.07719e7i | −0.0510953 | + | 0.0251291i | ||||
\(755\) | −3.41633e8 | −0.793814 | ||||||||
\(756\) | −3.44152e8 | + | 3.44152e8i | −0.796498 | + | 0.796498i | ||||
\(757\) | 3.67377e8 | 0.846885 | 0.423443 | − | 0.905923i | \(-0.360821\pi\) | ||||
0.423443 | + | 0.905923i | \(0.360821\pi\) | |||||||
\(758\) | 5.96834e8i | 1.37040i | ||||||||
\(759\) | −9.49972e6 | + | 9.49972e6i | −0.0217263 | + | 0.0217263i | ||||
\(760\) | −1.72447e8 | + | 1.72447e8i | −0.392839 | + | 0.392839i | ||||
\(761\) | 2.78595e8 | + | 2.78595e8i | 0.632150 | + | 0.632150i | 0.948607 | − | 0.316457i | \(-0.102493\pi\) |
−0.316457 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(762\) | −2.93767e8 | − | 2.93767e8i | −0.663955 | − | 0.663955i | ||||
\(763\) | −2.30993e8 | −0.520026 | ||||||||
\(764\) | 8.33315e7i | 0.186866i | ||||||||
\(765\) | 2.41840e8 | + | 2.41840e8i | 0.540186 | + | 0.540186i | ||||
\(766\) | 4.91253e8i | 1.09300i | ||||||||
\(767\) | 7.87204e7 | + | 1.60063e8i | 0.174462 | + | 0.354735i | ||||
\(768\) | −8.69002e7 | −0.191839 | ||||||||
\(769\) | 4.33883e7 | − | 4.33883e7i | 0.0954098 | − | 0.0954098i | −0.657791 | − | 0.753201i | \(-0.728509\pi\) |
0.753201 | + | 0.657791i | \(0.228509\pi\) | |||||||
\(770\) | 1.24486e8 | 0.272677 | ||||||||
\(771\) | − | 3.01982e8i | − | 0.658899i | ||||||
\(772\) | 4.66420e8 | − | 4.66420e8i | 1.01374 | − | 1.01374i | ||||
\(773\) | 1.03754e8 | − | 1.03754e8i | 0.224629 | − | 0.224629i | −0.585815 | − | 0.810444i | \(-0.699226\pi\) |
0.810444 | + | 0.585815i | \(0.199226\pi\) | |||||||
\(774\) | −3.63381e8 | − | 3.63381e8i | −0.783681 | − | 0.783681i | ||||
\(775\) | −7.84079e7 | − | 7.84079e7i | −0.168444 | − | 0.168444i | ||||
\(776\) | −6.63643e7 | −0.142020 | ||||||||
\(777\) | − | 2.64797e8i | − | 0.564482i | ||||||
\(778\) | 1.87122e8 | + | 1.87122e8i | 0.397361 | + | 0.397361i | ||||
\(779\) | 7.37932e8i | 1.56100i | ||||||||
\(780\) | −1.39224e8 | − | 2.83085e8i | −0.293379 | − | 0.596530i | ||||
\(781\) | −1.34079e7 | −0.0281453 | ||||||||
\(782\) | 1.53158e8 | − | 1.53158e8i | 0.320273 | − | 0.320273i | ||||
\(783\) | −1.84217e7 | −0.0383746 | ||||||||
\(784\) | − | 7.13832e7i | − | 0.148132i | ||||||
\(785\) | −2.33126e8 | + | 2.33126e8i | −0.481928 | + | 0.481928i | ||||
\(786\) | 8.57215e7 | − | 8.57215e7i | 0.176531 | − | 0.176531i | ||||
\(787\) | −5.52470e8 | − | 5.52470e8i | −1.13340 | − | 1.13340i | −0.989608 | − | 0.143795i | \(-0.954069\pi\) |
−0.143795 | − | 0.989608i | \(-0.545931\pi\) | |||||||
\(788\) | −3.07946e8 | − | 3.07946e8i | −0.629355 | − | 0.629355i | ||||
\(789\) | 4.60652e8 | 0.937868 | ||||||||
\(790\) | − | 5.25169e8i | − | 1.06517i | ||||||
\(791\) | 2.39821e8 | + | 2.39821e8i | 0.484571 | + | 0.484571i | ||||
\(792\) | − | 2.85238e7i | − | 0.0574158i | ||||||
\(793\) | −8.59670e8 | − | 2.92850e8i | −1.72390 | − | 0.587254i | ||||
\(794\) | 3.08277e8 | 0.615856 | ||||||||
\(795\) | 7.27533e7 | − | 7.27533e7i | 0.144794 | − | 0.144794i | ||||
\(796\) | 7.19605e7 | 0.142677 | ||||||||
\(797\) | − | 1.61019e7i | − | 0.0318054i | −0.999874 | − | 0.0159027i | \(-0.994938\pi\) | ||
0.999874 | − | 0.0159027i | \(-0.00506220\pi\) | |||||||
\(798\) | 5.17845e8 | − | 5.17845e8i | 1.01904 | − | 1.01904i | ||||
\(799\) | 8.43424e8 | − | 8.43424e8i | 1.65351 | − | 1.65351i | ||||
\(800\) | −1.55199e8 | − | 1.55199e8i | −0.303123 | − | 0.303123i | ||||
\(801\) | 2.66494e7 | + | 2.66494e7i | 0.0518549 | + | 0.0518549i | ||||
\(802\) | −2.64320e8 | −0.512397 | ||||||||
\(803\) | − | 1.83568e8i | − | 0.354529i | ||||||
\(804\) | −3.65698e8 | − | 3.65698e8i | −0.703646 | − | 0.703646i | ||||
\(805\) | 7.55176e7i | 0.144764i | ||||||||
\(806\) | −1.97731e8 | + | 5.80445e8i | −0.377633 | + | 1.10855i | ||||
\(807\) | 3.91290e8 | 0.744522 | ||||||||
\(808\) | 1.52685e8 | − | 1.52685e8i | 0.289442 | − | 0.289442i | ||||
\(809\) | −4.23919e8 | −0.800640 | −0.400320 | − | 0.916375i | \(-0.631101\pi\) | ||||
−0.400320 | + | 0.916375i | \(0.631101\pi\) | |||||||
\(810\) | − | 2.89422e7i | − | 0.0544599i | ||||||
\(811\) | 3.13841e8 | − | 3.13841e8i | 0.588365 | − | 0.588365i | −0.348823 | − | 0.937189i | \(-0.613419\pi\) |
0.937189 | + | 0.348823i | \(0.113419\pi\) | |||||||
\(812\) | 1.59492e7 | − | 1.59492e7i | 0.0297900 | − | 0.0297900i | ||||
\(813\) | 1.94355e8 | + | 1.94355e8i | 0.361680 | + | 0.361680i | ||||
\(814\) | 1.42492e8 | + | 1.42492e8i | 0.264191 | + | 0.264191i | ||||
\(815\) | 4.97862e8 | 0.919679 | ||||||||
\(816\) | 3.55538e8i | 0.654358i | ||||||||
\(817\) | 8.13963e8 | + | 8.13963e8i | 1.49258 | + | 1.49258i | ||||
\(818\) | − | 1.20734e9i | − | 2.20583i | ||||||
\(819\) | −1.28149e8 | − | 2.60567e8i | −0.233273 | − | 0.474316i | ||||
\(820\) | −5.27074e8 | −0.955938 | ||||||||
\(821\) | 3.18406e8 | − | 3.18406e8i | 0.575376 | − | 0.575376i | −0.358250 | − | 0.933626i | \(-0.616626\pi\) |
0.933626 | + | 0.358250i | \(0.116626\pi\) | |||||||
\(822\) | −7.76097e8 | −1.39734 | ||||||||
\(823\) | 5.96016e8i | 1.06920i | 0.845106 | + | 0.534599i | \(0.179537\pi\) | ||||
−0.845106 | + | 0.534599i | \(0.820463\pi\) | |||||||
\(824\) | −3.22627e7 | + | 3.22627e7i | −0.0576660 | + | 0.0576660i | ||||
\(825\) | 1.89621e7 | − | 1.89621e7i | 0.0337695 | − | 0.0337695i | ||||
\(826\) | −2.09136e8 | − | 2.09136e8i | −0.371098 | − | 0.371098i | ||||
\(827\) | 3.09467e8 | + | 3.09467e8i | 0.547140 | + | 0.547140i | 0.925612 | − | 0.378473i | \(-0.123551\pi\) |
−0.378473 | + | 0.925612i | \(0.623551\pi\) | |||||||
\(828\) | 8.41197e7 | 0.148186 | ||||||||
\(829\) | 6.94933e8i | 1.21977i | 0.792489 | + | 0.609887i | \(0.208785\pi\) | ||||
−0.792489 | + | 0.609887i | \(0.791215\pi\) | |||||||
\(830\) | 7.41072e7 | + | 7.41072e7i | 0.129606 | + | 0.129606i | ||||
\(831\) | 2.22569e8i | 0.387847i | ||||||||
\(832\) | −2.66221e8 | + | 7.81501e8i | −0.462246 | + | 1.35694i | ||||
\(833\) | −1.94643e8 | −0.336746 | ||||||||
\(834\) | −2.26706e8 | + | 2.26706e8i | −0.390809 | + | 0.390809i | ||||
\(835\) | −5.62707e8 | −0.966547 | ||||||||
\(836\) | 3.10608e8i | 0.531611i | ||||||||
\(837\) | −3.27251e8 | + | 3.27251e8i | −0.558091 | + | 0.558091i | ||||
\(838\) | −7.27536e8 | + | 7.27536e8i | −1.23630 | + | 1.23630i | ||||
\(839\) | 1.75155e6 | + | 1.75155e6i | 0.00296577 | + | 0.00296577i | 0.708588 | − | 0.705622i | \(-0.249332\pi\) |
−0.705622 | + | 0.708588i | \(0.749332\pi\) | |||||||
\(840\) | 7.60836e7 | + | 7.60836e7i | 0.128367 | + | 0.128367i | ||||
\(841\) | −5.93970e8 | −0.998565 | ||||||||
\(842\) | − | 3.49638e7i | − | 0.0585709i | ||||||
\(843\) | −4.07196e8 | − | 4.07196e8i | −0.679705 | − | 0.679705i | ||||
\(844\) | 7.43400e6i | 0.0123650i | ||||||||
\(845\) | 4.98571e8 | − | 6.45473e7i | 0.826337 | − | 0.106981i | ||||
\(846\) | 8.31186e8 | 1.37274 | ||||||||
\(847\) | −3.56464e8 | + | 3.56464e8i | −0.586631 | + | 0.586631i | ||||
\(848\) | −1.59380e8 | −0.261364 | ||||||||
\(849\) | 2.12889e8i | 0.347880i | ||||||||
\(850\) | −3.05714e8 | + | 3.05714e8i | −0.497804 | + | 0.497804i | ||||
\(851\) | −8.64408e7 | + | 8.64408e7i | −0.140259 | + | 0.140259i | ||||
\(852\) | −3.98376e7 | − | 3.98376e7i | −0.0644131 | − | 0.0644131i | ||||
\(853\) | 3.99606e8 | + | 3.99606e8i | 0.643850 | + | 0.643850i | 0.951500 | − | 0.307650i | \(-0.0995425\pi\) |
−0.307650 | + | 0.951500i | \(0.599543\pi\) | |||||||
\(854\) | 1.50587e9 | 2.41776 | ||||||||
\(855\) | − | 5.33854e8i | − | 0.854131i | ||||||
\(856\) | 2.49578e8 | + | 2.49578e8i | 0.397911 | + | 0.397911i | ||||
\(857\) | − | 9.84583e8i | − | 1.56426i | −0.623113 | − | 0.782132i | \(-0.714132\pi\) | ||
0.623113 | − | 0.782132i | \(-0.285868\pi\) | |||||||
\(858\) | −1.40374e8 | − | 4.78191e7i | −0.222242 | − | 0.0757076i | ||||
\(859\) | −4.66714e8 | −0.736328 | −0.368164 | − | 0.929761i | \(-0.620013\pi\) | ||||
−0.368164 | + | 0.929761i | \(0.620013\pi\) | |||||||
\(860\) | −5.81380e8 | + | 5.81380e8i | −0.914038 | + | 0.914038i | ||||
\(861\) | 3.25575e8 | 0.510084 | ||||||||
\(862\) | − | 3.01421e8i | − | 0.470600i | ||||||
\(863\) | 6.18379e8 | − | 6.18379e8i | 0.962104 | − | 0.962104i | −0.0372036 | − | 0.999308i | \(-0.511845\pi\) |
0.999308 | + | 0.0372036i | \(0.0118450\pi\) | |||||||
\(864\) | −6.47755e8 | + | 6.47755e8i | −1.00431 | + | 1.00431i | ||||
\(865\) | 5.48822e8 | + | 5.48822e8i | 0.847975 | + | 0.847975i | ||||
\(866\) | −2.53273e8 | − | 2.53273e8i | −0.389973 | − | 0.389973i | ||||
\(867\) | 5.56458e8 | 0.853837 | ||||||||
\(868\) | − | 5.66659e8i | − | 0.866488i | ||||||
\(869\) | −9.72887e7 | − | 9.72887e7i | −0.148253 | − | 0.148253i | ||||
\(870\) | 1.97986e7i | 0.0300660i | ||||||||
\(871\) | 7.39570e8 | − | 3.63727e8i | 1.11924 | − | 0.550454i | ||||
\(872\) | 1.51941e8 | 0.229154 | ||||||||
\(873\) | 1.02724e8 | − | 1.02724e8i | 0.154393 | − | 0.154393i | ||||
\(874\) | −3.38092e8 | −0.506408 | ||||||||
\(875\) | − | 6.43794e8i | − | 0.960998i | ||||||
\(876\) | 5.45421e8 | − | 5.45421e8i | 0.811371 | − | 0.811371i | ||||
\(877\) | −3.05312e8 | + | 3.05312e8i | −0.452632 | + | 0.452632i | −0.896227 | − | 0.443595i | \(-0.853703\pi\) |
0.443595 | + | 0.896227i | \(0.353703\pi\) | |||||||
\(878\) | −3.24060e8 | − | 3.24060e8i | −0.478787 | − | 0.478787i | ||||
\(879\) | 1.55404e8 | + | 1.55404e8i | 0.228821 | + | 0.228821i | ||||
\(880\) | 9.43349e7 | 0.138428 | ||||||||
\(881\) | − | 5.29881e6i | − | 0.00774908i | −0.999992 | − | 0.00387454i | \(-0.998767\pi\) | ||
0.999992 | − | 0.00387454i | \(-0.00123331\pi\) | |||||||
\(882\) | −9.59092e7 | − | 9.59092e7i | −0.139783 | − | 0.139783i | ||||
\(883\) | − | 7.31615e8i | − | 1.06268i | −0.847160 | − | 0.531338i | \(-0.821690\pi\) | ||
0.847160 | − | 0.531338i | \(-0.178310\pi\) | |||||||
\(884\) | 1.26131e9 | + | 4.29671e8i | 1.82585 | + | 0.621984i | ||||
\(885\) | 1.44687e8 | 0.208737 | ||||||||
\(886\) | 3.24460e7 | − | 3.24460e7i | 0.0466509 | − | 0.0466509i | ||||
\(887\) | −2.32665e8 | −0.333396 | −0.166698 | − | 0.986008i | \(-0.553311\pi\) | ||||
−0.166698 | + | 0.986008i | \(0.553311\pi\) | |||||||
\(888\) | 1.74177e8i | 0.248744i | ||||||||
\(889\) | −4.32618e8 | + | 4.32618e8i | −0.615742 | + | 0.615742i | ||||
\(890\) | 7.65032e7 | − | 7.65032e7i | 0.108520 | − | 0.108520i | ||||
\(891\) | −5.36161e6 | − | 5.36161e6i | −0.00757987 | − | 0.00757987i | ||||
\(892\) | 7.13585e8 | + | 7.13585e8i | 1.00543 | + | 1.00543i | ||||
\(893\) | −1.86183e9 | −2.61449 | ||||||||
\(894\) | 2.80169e8i | 0.392109i | ||||||||
\(895\) | −7.31562e8 | − | 7.31562e8i | −1.02043 | − | 1.02043i | ||||
\(896\) | − | 4.78028e8i | − | 0.664553i | ||||||
\(897\) | 2.90087e7 | − | 8.51559e7i | 0.0401931 | − | 0.117988i | ||||
\(898\) | −1.09044e8 | −0.150582 | ||||||||
\(899\) | 1.51660e7 | − | 1.51660e7i | 0.0208733 | − | 0.0208733i | ||||
\(900\) | −1.67909e8 | −0.230327 | ||||||||
\(901\) | 4.34586e8i | 0.594157i | ||||||||
\(902\) | −1.75198e8 | + | 1.75198e8i | −0.238732 | + | 0.238732i | ||||
\(903\) | 3.59120e8 | − | 3.59120e8i | 0.487727 | − | 0.487727i | ||||
\(904\) | −1.57748e8 | − | 1.57748e8i | −0.213530 | − | 0.213530i | ||||
\(905\) | 6.05633e8 | + | 6.05633e8i | 0.817079 | + | 0.817079i | ||||
\(906\) | −6.74810e8 | −0.907396 | ||||||||
\(907\) | − | 5.05806e8i | − | 0.677894i | −0.940805 | − | 0.338947i | \(-0.889929\pi\) | ||
0.940805 | − | 0.338947i | \(-0.110071\pi\) | |||||||
\(908\) | −6.36673e8 | − | 6.36673e8i | −0.850470 | − | 0.850470i | ||||
\(909\) | 4.72676e8i | 0.629320i | ||||||||
\(910\) | −7.48018e8 | + | 3.67882e8i | −0.992631 | + | 0.488185i | ||||
\(911\) | −1.00881e9 | −1.33431 | −0.667154 | − | 0.744920i | \(-0.732488\pi\) | ||||
−0.667154 | + | 0.744920i | \(0.732488\pi\) | |||||||
\(912\) | 3.92420e8 | − | 3.92420e8i | 0.517328 | − | 0.517328i | ||||
\(913\) | 2.74570e7 | 0.0360779 | ||||||||
\(914\) | − | 1.68801e9i | − | 2.21074i | ||||||
\(915\) | −5.20903e8 | + | 5.20903e8i | −0.679977 | + | 0.679977i | ||||
\(916\) | 1.84414e8 | − | 1.84414e8i | 0.239943 | − | 0.239943i | ||||
\(917\) | −1.26238e8 | − | 1.26238e8i | −0.163713 | − | 0.163713i | ||||
\(918\) | 1.27596e9 | + | 1.27596e9i | 1.64934 | + | 1.64934i | ||||
\(919\) | 1.36736e9 | 1.76172 | 0.880860 | − | 0.473378i | \(-0.156965\pi\) | ||||
0.880860 | + | 0.473378i | \(0.156965\pi\) | |||||||
\(920\) | − | 4.96737e7i | − | 0.0637915i | ||||||
\(921\) | 1.64313e8 | + | 1.64313e8i | 0.210326 | + | 0.210326i | ||||
\(922\) | − | 1.68334e8i | − | 0.214772i | ||||||
\(923\) | 8.05657e7 | − | 3.96229e7i | 0.102458 | − | 0.0503897i | ||||
\(924\) | 1.37040e8 | 0.173713 | ||||||||
\(925\) | 1.72542e8 | − | 1.72542e8i | 0.218006 | − | 0.218006i | ||||
\(926\) | 5.50894e8 | 0.693801 | ||||||||
\(927\) | − | 9.98777e7i | − | 0.125380i | ||||||
\(928\) | 3.00193e7 | − | 3.00193e7i | 0.0375626 | − | 0.0375626i | ||||
\(929\) | −7.69217e8 | + | 7.69217e8i | −0.959404 | + | 0.959404i | −0.999208 | − | 0.0398032i | \(-0.987327\pi\) |
0.0398032 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(930\) | 3.51711e8 | + | 3.51711e8i | 0.437258 | + | 0.437258i | ||||
\(931\) | 2.14834e8 | + | 2.14834e8i | 0.266228 | + | 0.266228i | ||||
\(932\) | −9.16679e8 | −1.13232 | ||||||||
\(933\) | − | 5.21222e8i | − | 0.641768i | ||||||
\(934\) | −3.65612e8 | − | 3.65612e8i | −0.448724 | − | 0.448724i | ||||
\(935\) | − | 2.57225e8i | − | 0.314687i | ||||||
\(936\) | 8.42935e7 | + | 1.71395e8i | 0.102794 | + | 0.209011i | ||||
\(937\) | 1.42415e9 | 1.73116 | 0.865581 | − | 0.500769i | \(-0.166949\pi\) | ||||
0.865581 | + | 0.500769i | \(0.166949\pi\) | |||||||
\(938\) | −9.66313e8 | + | 9.66313e8i | −1.17087 | + | 1.17087i | ||||
\(939\) | −3.53717e8 | −0.427227 | ||||||||
\(940\) | − | 1.32983e9i | − | 1.60108i | ||||||
\(941\) | 1.07583e9 | − | 1.07583e9i | 1.29115 | − | 1.29115i | 0.357072 | − | 0.934077i | \(-0.383775\pi\) |
0.934077 | − | 0.357072i | \(-0.116225\pi\) | |||||||
\(942\) | −4.60483e8 | + | 4.60483e8i | −0.550884 | + | 0.550884i | ||||
\(943\) | −1.06281e8 | − | 1.06281e8i | −0.126742 | − | 0.126742i | ||||
\(944\) | −1.58482e8 | − | 1.58482e8i | −0.188393 | − | 0.188393i | ||||
\(945\) | −6.29137e8 | −0.745504 | ||||||||
\(946\) | 3.86499e8i | 0.456536i | ||||||||
\(947\) | 3.72519e8 | + | 3.72519e8i | 0.438630 | + | 0.438630i | 0.891551 | − | 0.452921i | \(-0.149618\pi\) |
−0.452921 | + | 0.891551i | \(0.649618\pi\) | |||||||
\(948\) | − | 5.78131e8i | − | 0.678580i | ||||||
\(949\) | 5.42482e8 | + | 1.10303e9i | 0.634727 | + | 1.29060i | ||||
\(950\) | 6.74855e8 | 0.787118 | ||||||||
\(951\) | −6.31432e8 | + | 6.31432e8i | −0.734151 | + | 0.734151i | ||||
\(952\) | −4.54479e8 | −0.526748 | ||||||||
\(953\) | − | 6.36621e8i | − | 0.735534i | −0.929918 | − | 0.367767i | \(-0.880122\pi\) | ||
0.929918 | − | 0.367767i | \(-0.119878\pi\) | |||||||
\(954\) | −2.14140e8 | + | 2.14140e8i | −0.246634 | + | 0.246634i | ||||
\(955\) | −7.61684e7 | + | 7.61684e7i | −0.0874510 | + | 0.0874510i | ||||
\(956\) | 6.28255e8 | + | 6.28255e8i | 0.719056 | + | 0.719056i | ||||
\(957\) | 3.66773e6 | + | 3.66773e6i | 0.00418467 | + | 0.00418467i | ||||
\(958\) | 1.32518e9 | 1.50723 | ||||||||
\(959\) | 1.14292e9i | 1.29587i | ||||||||
\(960\) | 4.73538e8 | + | 4.73538e8i | 0.535231 | + | 0.535231i | ||||
\(961\) | 3.48672e8i | 0.392868i | ||||||||
\(962\) | −1.27731e9 | − | 4.35120e8i | −1.43473 | − | 0.488747i | ||||
\(963\) | −7.72635e8 | −0.865158 | ||||||||
\(964\) | 6.60309e6 | − | 6.60309e6i | 0.00737083 | − | 0.00737083i | ||||
\(965\) | 8.52653e8 | 0.948834 | ||||||||
\(966\) | 1.49166e8i | 0.165477i | ||||||||
\(967\) | −1.65872e8 | + | 1.65872e8i | −0.183440 | + | 0.183440i | −0.792853 | − | 0.609413i | \(-0.791405\pi\) |
0.609413 | + | 0.792853i | \(0.291405\pi\) | |||||||
\(968\) | 2.34473e8 | − | 2.34473e8i | 0.258504 | − | 0.258504i | ||||
\(969\) | −1.07002e9 | − | 1.07002e9i | −1.17604 | − | 1.17604i | ||||
\(970\) | −2.94893e8 | − | 2.94893e8i | −0.323109 | − | 0.323109i | ||||
\(971\) | −2.03038e8 | −0.221779 | −0.110889 | − | 0.993833i | \(-0.535370\pi\) | ||||
−0.110889 | + | 0.993833i | \(0.535370\pi\) | |||||||
\(972\) | 1.13924e9i | 1.24055i | ||||||||
\(973\) | 3.33860e8 | + | 3.33860e8i | 0.362431 | + | 0.362431i | ||||
\(974\) | 2.39602e7i | 0.0259306i | ||||||||
\(975\) | −5.79034e7 | + | 1.69977e8i | −0.0624727 | + | 0.183390i | ||||
\(976\) | 1.14114e9 | 1.22741 | ||||||||
\(977\) | 2.63431e8 | − | 2.63431e8i | 0.282477 | − | 0.282477i | −0.551619 | − | 0.834096i | \(-0.685990\pi\) |
0.834096 | + | 0.551619i | \(0.185990\pi\) | |||||||
\(978\) | 9.83402e8 | 1.05127 | ||||||||
\(979\) | − | 2.83448e7i | − | 0.0302082i | ||||||
\(980\) | −1.53447e8 | + | 1.53447e8i | −0.163035 | + | 0.163035i | ||||
\(981\) | −2.35187e8 | + | 2.35187e8i | −0.249119 | + | 0.249119i | ||||
\(982\) | 2.91346e8 | + | 2.91346e8i | 0.307662 | + | 0.307662i | ||||
\(983\) | 3.97286e8 | + | 3.97286e8i | 0.418256 | + | 0.418256i | 0.884602 | − | 0.466346i | \(-0.154430\pi\) |
−0.466346 | + | 0.884602i | \(0.654430\pi\) | |||||||
\(984\) | −2.14155e8 | −0.224773 | ||||||||
\(985\) | − | 5.62950e8i | − | 0.589062i | ||||||
\(986\) | −5.91325e7 | − | 5.91325e7i | −0.0616873 | − | 0.0616873i | ||||
\(987\) | 8.21440e8i | 0.854328i | ||||||||
\(988\) | −9.17910e8 | − | 1.86640e9i | −0.951764 | − | 1.93523i | ||||
\(989\) | −2.34463e8 | −0.242374 | ||||||||
\(990\) | 1.26747e8 | − | 1.26747e8i | 0.130626 | − | 0.130626i | ||||
\(991\) | 1.89931e8 | 0.195153 | 0.0975763 | − | 0.995228i | \(-0.468891\pi\) | ||||
0.0975763 | + | 0.995228i | \(0.468891\pi\) | |||||||
\(992\) | − | 1.06655e9i | − | 1.09257i | ||||||
\(993\) | −3.11456e8 | + | 3.11456e8i | −0.318089 | + | 0.318089i | ||||
\(994\) | −1.05266e8 | + | 1.05266e8i | −0.107184 | + | 0.107184i | ||||
\(995\) | 6.57749e7 | + | 6.57749e7i | 0.0667714 | + | 0.0667714i | ||||
\(996\) | 8.15807e7 | + | 8.15807e7i | 0.0825676 | + | 0.0825676i | ||||
\(997\) | −1.93733e9 | −1.95487 | −0.977433 | − | 0.211244i | \(-0.932249\pi\) | ||||
−0.977433 | + | 0.211244i | \(0.932249\pi\) | |||||||
\(998\) | 1.68251e9i | 1.69265i | ||||||||
\(999\) | −7.20139e8 | − | 7.20139e8i | −0.722303 | − | 0.722303i |
(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 | 13.7.d.a.5.1 | ✓ | 12 | |
3.2 | odd | 2 | 117.7.j.b.109.6 | 12 | |||
4.3 | odd | 2 | 208.7.t.c.161.4 | 12 | |||
13.8 | odd | 4 | inner | 13.7.d.a.8.1 | yes | 12 | |
39.8 | even | 4 | 117.7.j.b.73.6 | 12 | |||
52.47 | even | 4 | 208.7.t.c.177.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.7.d.a.5.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
13.7.d.a.8.1 | yes | 12 | 13.8 | odd | 4 | inner | |
117.7.j.b.73.6 | 12 | 39.8 | even | 4 | |||
117.7.j.b.109.6 | 12 | 3.2 | odd | 2 | |||
208.7.t.c.161.4 | 12 | 4.3 | odd | 2 | |||
208.7.t.c.177.4 | 12 | 52.47 | even | 4 |