Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,7,Mod(10,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.10");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.59178475946\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 486x^{10} + 82401x^{8} + 6062364x^{6} + 204706260x^{4} + 2964086784x^{2} + 15081209856 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.9 | ||
Root | \(6.83773i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.10 |
Dual form | 33.7.c.a.10.4 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.83773i | 0.854717i | 0.904082 | + | 0.427358i | \(0.140556\pi\) | ||||
−0.904082 | + | 0.427358i | \(0.859444\pi\) | |||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | 17.2454 | 0.269460 | ||||||||
\(5\) | 167.968 | 1.34375 | 0.671874 | − | 0.740666i | \(-0.265490\pi\) | ||||
0.671874 | + | 0.740666i | \(0.265490\pi\) | |||||||
\(6\) | − | 106.590i | − | 0.493471i | ||||||
\(7\) | − | 106.676i | − | 0.311008i | −0.987835 | − | 0.155504i | \(-0.950300\pi\) | ||
0.987835 | − | 0.155504i | \(-0.0497002\pi\) | |||||||
\(8\) | 555.534i | 1.08503i | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 1148.52i | 1.14852i | ||||||||
\(11\) | −6.11220 | + | 1330.99i | −0.00459219 | + | 0.999989i | ||||
\(12\) | −268.829 | −0.155573 | ||||||||
\(13\) | 1477.21i | 0.672377i | 0.941795 | + | 0.336189i | \(0.109138\pi\) | ||||
−0.941795 | + | 0.336189i | \(0.890862\pi\) | |||||||
\(14\) | 729.420 | 0.265824 | ||||||||
\(15\) | −2618.37 | −0.775813 | ||||||||
\(16\) | −2694.89 | −0.657932 | ||||||||
\(17\) | − | 3756.53i | − | 0.764610i | −0.924036 | − | 0.382305i | \(-0.875130\pi\) | ||
0.924036 | − | 0.382305i | \(-0.124870\pi\) | |||||||
\(18\) | 1661.57i | 0.284906i | ||||||||
\(19\) | 7553.37i | 1.10124i | 0.834758 | + | 0.550618i | \(0.185608\pi\) | ||||
−0.834758 | + | 0.550618i | \(0.814392\pi\) | |||||||
\(20\) | 2896.68 | 0.362086 | ||||||||
\(21\) | 1662.91i | 0.179561i | ||||||||
\(22\) | −9100.93 | − | 41.7936i | −0.854708 | − | 0.00392502i | ||||
\(23\) | 19146.0 | 1.57360 | 0.786800 | − | 0.617208i | \(-0.211736\pi\) | ||||
0.786800 | + | 0.617208i | \(0.211736\pi\) | |||||||
\(24\) | − | 8659.92i | − | 0.626441i | ||||||
\(25\) | 12588.4 | 0.805656 | ||||||||
\(26\) | −10100.8 | −0.574692 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | − | 1839.67i | − | 0.0838041i | ||||||
\(29\) | − | 32413.5i | − | 1.32902i | −0.747279 | − | 0.664510i | \(-0.768640\pi\) | ||
0.747279 | − | 0.664510i | \(-0.231360\pi\) | |||||||
\(30\) | − | 17903.7i | − | 0.663100i | ||||||
\(31\) | −2788.96 | −0.0936175 | −0.0468088 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468088 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(32\) | 17127.3i | 0.522683i | ||||||||
\(33\) | 95.2798 | − | 20748.0i | 0.00265130 | − | 0.577344i | ||||
\(34\) | 25686.1 | 0.653524 | ||||||||
\(35\) | − | 17918.2i | − | 0.417916i | ||||||
\(36\) | 4190.64 | 0.0898199 | ||||||||
\(37\) | −47245.9 | −0.932736 | −0.466368 | − | 0.884591i | \(-0.654438\pi\) | ||||
−0.466368 | + | 0.884591i | \(0.654438\pi\) | |||||||
\(38\) | −51647.9 | −0.941244 | ||||||||
\(39\) | − | 23027.5i | − | 0.388197i | ||||||
\(40\) | 93312.2i | 1.45800i | ||||||||
\(41\) | − | 106739.i | − | 1.54871i | −0.632749 | − | 0.774357i | \(-0.718074\pi\) | ||
0.632749 | − | 0.774357i | \(-0.281926\pi\) | |||||||
\(42\) | −11370.5 | −0.153473 | ||||||||
\(43\) | 29591.3i | 0.372185i | 0.982532 | + | 0.186093i | \(0.0595825\pi\) | ||||
−0.982532 | + | 0.186093i | \(0.940418\pi\) | |||||||
\(44\) | −105.407 | + | 22953.4i | −0.00123741 | + | 0.269457i | ||||
\(45\) | 40816.3 | 0.447916 | ||||||||
\(46\) | 130915.i | 1.34498i | ||||||||
\(47\) | 9092.07 | 0.0875728 | 0.0437864 | − | 0.999041i | \(-0.486058\pi\) | ||||
0.0437864 | + | 0.999041i | \(0.486058\pi\) | |||||||
\(48\) | 42009.2 | 0.379857 | ||||||||
\(49\) | 106269. | 0.903274 | ||||||||
\(50\) | 86076.0i | 0.688608i | ||||||||
\(51\) | 58558.5i | 0.441448i | ||||||||
\(52\) | 25475.1i | 0.181178i | ||||||||
\(53\) | −154022. | −1.03456 | −0.517279 | − | 0.855817i | \(-0.673055\pi\) | ||||
−0.517279 | + | 0.855817i | \(0.673055\pi\) | |||||||
\(54\) | − | 25901.3i | − | 0.164490i | ||||||
\(55\) | −1026.66 | + | 223564.i | −0.00617074 | + | 1.34373i | ||||
\(56\) | 59262.1 | 0.337453 | ||||||||
\(57\) | − | 117745.i | − | 0.635798i | ||||||
\(58\) | 221635. | 1.13594 | ||||||||
\(59\) | 33867.9 | 0.164904 | 0.0824521 | − | 0.996595i | \(-0.473725\pi\) | ||||
0.0824521 | + | 0.996595i | \(0.473725\pi\) | |||||||
\(60\) | −45154.8 | −0.209050 | ||||||||
\(61\) | − | 388487.i | − | 1.71154i | −0.517358 | − | 0.855769i | \(-0.673085\pi\) | ||
0.517358 | − | 0.855769i | \(-0.326915\pi\) | |||||||
\(62\) | − | 19070.2i | − | 0.0800165i | ||||||
\(63\) | − | 25922.2i | − | 0.103669i | ||||||
\(64\) | −289585. | −1.10468 | ||||||||
\(65\) | 248125.i | 0.903505i | ||||||||
\(66\) | 141869. | + | 651.498i | 0.493466 | + | 0.00226611i | ||||
\(67\) | −447890. | −1.48918 | −0.744590 | − | 0.667522i | \(-0.767355\pi\) | ||||
−0.744590 | + | 0.667522i | \(0.767355\pi\) | |||||||
\(68\) | − | 64782.9i | − | 0.206031i | ||||||
\(69\) | −298456. | −0.908518 | ||||||||
\(70\) | 122520. | 0.357200 | ||||||||
\(71\) | 403082. | 1.12621 | 0.563104 | − | 0.826386i | \(-0.309607\pi\) | ||||
0.563104 | + | 0.826386i | \(0.309607\pi\) | |||||||
\(72\) | 134995.i | 0.361676i | ||||||||
\(73\) | − | 92785.3i | − | 0.238512i | −0.992864 | − | 0.119256i | \(-0.961949\pi\) | ||
0.992864 | − | 0.119256i | \(-0.0380510\pi\) | |||||||
\(74\) | − | 323055.i | − | 0.797225i | ||||||
\(75\) | −196233. | −0.465146 | ||||||||
\(76\) | 130261.i | 0.296738i | ||||||||
\(77\) | 141984. | + | 652.024i | 0.311005 | + | 0.00142821i | ||||
\(78\) | 157456. | 0.331799 | ||||||||
\(79\) | − | 689152.i | − | 1.39776i | −0.715237 | − | 0.698881i | \(-0.753681\pi\) | ||
0.715237 | − | 0.698881i | \(-0.246319\pi\) | |||||||
\(80\) | −452656. | −0.884094 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 729852. | 1.32371 | ||||||||
\(83\) | − | 583952.i | − | 1.02127i | −0.859796 | − | 0.510637i | \(-0.829409\pi\) | ||
0.859796 | − | 0.510637i | \(-0.170591\pi\) | |||||||
\(84\) | 28677.6i | 0.0483843i | ||||||||
\(85\) | − | 630978.i | − | 1.02744i | ||||||
\(86\) | −202338. | −0.318113 | ||||||||
\(87\) | 505276.i | 0.767310i | ||||||||
\(88\) | −739409. | − | 3395.54i | −1.08502 | − | 0.00498265i | ||||
\(89\) | 910609. | 1.29170 | 0.645850 | − | 0.763464i | \(-0.276503\pi\) | ||||
0.645850 | + | 0.763464i | \(0.276503\pi\) | |||||||
\(90\) | 279091.i | 0.382841i | ||||||||
\(91\) | 157583. | 0.209115 | ||||||||
\(92\) | 330181. | 0.424022 | ||||||||
\(93\) | 43475.6 | 0.0540501 | ||||||||
\(94\) | 62169.1i | 0.0748499i | ||||||||
\(95\) | 1.26873e6i | 1.47978i | ||||||||
\(96\) | − | 266988.i | − | 0.301771i | ||||||
\(97\) | 242113. | 0.265279 | 0.132639 | − | 0.991164i | \(-0.457655\pi\) | ||||
0.132639 | + | 0.991164i | \(0.457655\pi\) | |||||||
\(98\) | 726641.i | 0.772043i | ||||||||
\(99\) | −1485.27 | + | 323430.i | −0.00153073 | + | 0.333330i | ||||
\(100\) | 217092. | 0.217092 | ||||||||
\(101\) | 1.19786e6i | 1.16263i | 0.813677 | + | 0.581317i | \(0.197462\pi\) | ||||
−0.813677 | + | 0.581317i | \(0.802538\pi\) | |||||||
\(102\) | −400407. | −0.377313 | ||||||||
\(103\) | −1.12725e6 | −1.03159 | −0.515795 | − | 0.856712i | \(-0.672503\pi\) | ||||
−0.515795 | + | 0.856712i | \(0.672503\pi\) | |||||||
\(104\) | −820643. | −0.729548 | ||||||||
\(105\) | 279316.i | 0.241284i | ||||||||
\(106\) | − | 1.05316e6i | − | 0.884253i | ||||||
\(107\) | 443790.i | 0.362265i | 0.983459 | + | 0.181132i | \(0.0579763\pi\) | ||||
−0.983459 | + | 0.181132i | \(0.942024\pi\) | |||||||
\(108\) | −65325.5 | −0.0518575 | ||||||||
\(109\) | 125793.i | 0.0971350i | 0.998820 | + | 0.0485675i | \(0.0154656\pi\) | ||||
−0.998820 | + | 0.0485675i | \(0.984534\pi\) | |||||||
\(110\) | −1.52867e6 | − | 7020.00i | −1.14851 | − | 0.00527423i | ||||
\(111\) | 736490. | 0.538515 | ||||||||
\(112\) | 287479.i | 0.204622i | ||||||||
\(113\) | −1.63723e6 | −1.13468 | −0.567340 | − | 0.823484i | \(-0.692027\pi\) | ||||
−0.567340 | + | 0.823484i | \(0.692027\pi\) | |||||||
\(114\) | 805112. | 0.543427 | ||||||||
\(115\) | 3.21592e6 | 2.11452 | ||||||||
\(116\) | − | 558984.i | − | 0.358117i | ||||||
\(117\) | 358963.i | 0.224126i | ||||||||
\(118\) | 231579.i | 0.140946i | ||||||||
\(119\) | −400730. | −0.237800 | ||||||||
\(120\) | − | 1.45459e6i | − | 0.841779i | ||||||
\(121\) | −1.77149e6 | − | 16270.5i | −0.999958 | − | 0.00918428i | ||||
\(122\) | 2.65637e6 | 1.46288 | ||||||||
\(123\) | 1.66389e6i | 0.894150i | ||||||||
\(124\) | −48096.8 | −0.0252261 | ||||||||
\(125\) | −510056. | −0.261149 | ||||||||
\(126\) | 177249. | 0.0886079 | ||||||||
\(127\) | 1.18360e6i | 0.577823i | 0.957356 | + | 0.288912i | \(0.0932934\pi\) | ||||
−0.957356 | + | 0.288912i | \(0.906707\pi\) | |||||||
\(128\) | − | 883957.i | − | 0.421503i | ||||||
\(129\) | − | 461283.i | − | 0.214881i | ||||||
\(130\) | −1.69661e6 | −0.772241 | ||||||||
\(131\) | − | 3.01385e6i | − | 1.34063i | −0.742078 | − | 0.670314i | \(-0.766160\pi\) | ||
0.742078 | − | 0.670314i | \(-0.233840\pi\) | |||||||
\(132\) | 1643.14 | − | 357808.i | 0.000714419 | − | 0.155571i | ||||
\(133\) | 805762. | 0.342493 | ||||||||
\(134\) | − | 3.06255e6i | − | 1.27283i | ||||||
\(135\) | −636263. | −0.258604 | ||||||||
\(136\) | 2.08688e6 | 0.829623 | ||||||||
\(137\) | 3.74843e6 | 1.45777 | 0.728883 | − | 0.684638i | \(-0.240040\pi\) | ||||
0.728883 | + | 0.684638i | \(0.240040\pi\) | |||||||
\(138\) | − | 2.04077e6i | − | 0.776526i | ||||||
\(139\) | 386320.i | 0.143848i | 0.997410 | + | 0.0719239i | \(0.0229139\pi\) | ||||
−0.997410 | + | 0.0719239i | \(0.977086\pi\) | |||||||
\(140\) | − | 309006.i | − | 0.112612i | ||||||
\(141\) | −141731. | −0.0505602 | ||||||||
\(142\) | 2.75617e6i | 0.962588i | ||||||||
\(143\) | −1.96615e6 | − | 9029.02i | −0.672370 | − | 0.00308768i | ||||
\(144\) | −654858. | −0.219311 | ||||||||
\(145\) | − | 5.44444e6i | − | 1.78587i | ||||||
\(146\) | 634441. | 0.203860 | ||||||||
\(147\) | −1.65657e6 | −0.521505 | ||||||||
\(148\) | −814775. | −0.251335 | ||||||||
\(149\) | 3.12076e6i | 0.943411i | 0.881756 | + | 0.471706i | \(0.156362\pi\) | ||||
−0.881756 | + | 0.471706i | \(0.843638\pi\) | |||||||
\(150\) | − | 1.34179e6i | − | 0.397568i | ||||||
\(151\) | 5.18473e6i | 1.50590i | 0.658079 | + | 0.752949i | \(0.271369\pi\) | ||||
−0.658079 | + | 0.752949i | \(0.728631\pi\) | |||||||
\(152\) | −4.19616e6 | −1.19487 | ||||||||
\(153\) | − | 912836.i | − | 0.254870i | ||||||
\(154\) | −4458.37 | + | 970848.i | −0.00122071 | + | 0.265821i | ||||
\(155\) | −468457. | −0.125798 | ||||||||
\(156\) | − | 397118.i | − | 0.104603i | ||||||
\(157\) | −3.66366e6 | −0.946709 | −0.473354 | − | 0.880872i | \(-0.656957\pi\) | ||||
−0.473354 | + | 0.880872i | \(0.656957\pi\) | |||||||
\(158\) | 4.71223e6 | 1.19469 | ||||||||
\(159\) | 2.40096e6 | 0.597302 | ||||||||
\(160\) | 2.87684e6i | 0.702354i | ||||||||
\(161\) | − | 2.04241e6i | − | 0.489402i | ||||||
\(162\) | 403761.i | 0.0949685i | ||||||||
\(163\) | −7.42247e6 | −1.71390 | −0.856950 | − | 0.515400i | \(-0.827643\pi\) | ||||
−0.856950 | + | 0.515400i | \(0.827643\pi\) | |||||||
\(164\) | − | 1.84076e6i | − | 0.417316i | ||||||
\(165\) | 16004.0 | − | 3.48501e6i | 0.00356268 | − | 0.775805i | ||||
\(166\) | 3.99291e6 | 0.872901 | ||||||||
\(167\) | 7.02650e6i | 1.50865i | 0.656499 | + | 0.754327i | \(0.272037\pi\) | ||||
−0.656499 | + | 0.754327i | \(0.727963\pi\) | |||||||
\(168\) | −923804. | −0.194828 | ||||||||
\(169\) | 2.64465e6 | 0.547909 | ||||||||
\(170\) | 4.31446e6 | 0.878172 | ||||||||
\(171\) | 1.83547e6i | 0.367078i | ||||||||
\(172\) | 510315.i | 0.100289i | ||||||||
\(173\) | 55753.3i | 0.0107679i | 0.999986 | + | 0.00538396i | \(0.00171378\pi\) | ||||
−0.999986 | + | 0.00538396i | \(0.998286\pi\) | |||||||
\(174\) | −3.45494e6 | −0.655833 | ||||||||
\(175\) | − | 1.34288e6i | − | 0.250566i | ||||||
\(176\) | 16471.7 | − | 3.58686e6i | 0.00302135 | − | 0.657925i | ||||
\(177\) | −527948. | −0.0952075 | ||||||||
\(178\) | 6.22650e6i | 1.10404i | ||||||||
\(179\) | 4.97167e6 | 0.866848 | 0.433424 | − | 0.901190i | \(-0.357305\pi\) | ||||
0.433424 | + | 0.901190i | \(0.357305\pi\) | |||||||
\(180\) | 703894. | 0.120695 | ||||||||
\(181\) | 7.48474e6 | 1.26224 | 0.631118 | − | 0.775686i | \(-0.282596\pi\) | ||||
0.631118 | + | 0.775686i | \(0.282596\pi\) | |||||||
\(182\) | 1.07751e6i | 0.178734i | ||||||||
\(183\) | 6.05591e6i | 0.988157i | ||||||||
\(184\) | 1.06363e7i | 1.70740i | ||||||||
\(185\) | −7.93581e6 | −1.25336 | ||||||||
\(186\) | 297274.i | 0.0461975i | ||||||||
\(187\) | 4.99988e6 | + | 22960.7i | 0.764602 | + | 0.00351123i | ||||
\(188\) | 156796. | 0.0235973 | ||||||||
\(189\) | 404087.i | 0.0598535i | ||||||||
\(190\) | −8.67522e6 | −1.26479 | ||||||||
\(191\) | −2.65845e6 | −0.381529 | −0.190765 | − | 0.981636i | \(-0.561097\pi\) | ||||
−0.190765 | + | 0.981636i | \(0.561097\pi\) | |||||||
\(192\) | 4.51418e6 | 0.637786 | ||||||||
\(193\) | − | 5.47809e6i | − | 0.762004i | −0.924574 | − | 0.381002i | \(-0.875579\pi\) | ||
0.924574 | − | 0.381002i | \(-0.124421\pi\) | |||||||
\(194\) | 1.65550e6i | 0.226738i | ||||||||
\(195\) | − | 3.86789e6i | − | 0.521639i | ||||||
\(196\) | 1.83266e6 | 0.243396 | ||||||||
\(197\) | − | 8.06552e6i | − | 1.05495i | −0.849569 | − | 0.527477i | \(-0.823138\pi\) | ||
0.849569 | − | 0.527477i | \(-0.176862\pi\) | |||||||
\(198\) | −2.21153e6 | − | 10155.8i | −0.284903 | − | 0.00130834i | ||||
\(199\) | 6.47778e6 | 0.821990 | 0.410995 | − | 0.911638i | \(-0.365181\pi\) | ||||
0.410995 | + | 0.911638i | \(0.365181\pi\) | |||||||
\(200\) | 6.99328e6i | 0.874160i | ||||||||
\(201\) | 6.98192e6 | 0.859779 | ||||||||
\(202\) | −8.19066e6 | −0.993722 | ||||||||
\(203\) | −3.45773e6 | −0.413336 | ||||||||
\(204\) | 1.00986e6i | 0.118952i | ||||||||
\(205\) | − | 1.79288e7i | − | 2.08108i | ||||||
\(206\) | − | 7.70781e6i | − | 0.881717i | ||||||
\(207\) | 4.65248e6 | 0.524533 | ||||||||
\(208\) | − | 3.98092e6i | − | 0.442378i | ||||||
\(209\) | −1.00534e7 | − | 46167.7i | −1.10122 | − | 0.00505708i | ||||
\(210\) | −1.90989e6 | −0.206229 | ||||||||
\(211\) | − | 1.64166e7i | − | 1.74758i | −0.486307 | − | 0.873788i | \(-0.661656\pi\) | ||
0.486307 | − | 0.873788i | \(-0.338344\pi\) | |||||||
\(212\) | −2.65617e6 | −0.278771 | ||||||||
\(213\) | −6.28343e6 | −0.650216 | ||||||||
\(214\) | −3.03452e6 | −0.309634 | ||||||||
\(215\) | 4.97041e6i | 0.500123i | ||||||||
\(216\) | − | 2.10436e6i | − | 0.208814i | ||||||
\(217\) | 297514.i | 0.0291158i | ||||||||
\(218\) | −860137. | −0.0830229 | ||||||||
\(219\) | 1.44638e6i | 0.137705i | ||||||||
\(220\) | −17705.1 | + | 3.85545e6i | −0.00166276 | + | 0.362082i | ||||
\(221\) | 5.54919e6 | 0.514106 | ||||||||
\(222\) | 5.03592e6i | 0.460278i | ||||||||
\(223\) | −166842. | −0.0150449 | −0.00752247 | − | 0.999972i | \(-0.502394\pi\) | ||||
−0.00752247 | + | 0.999972i | \(0.502394\pi\) | |||||||
\(224\) | 1.82706e6 | 0.162559 | ||||||||
\(225\) | 3.05898e6 | 0.268552 | ||||||||
\(226\) | − | 1.11949e7i | − | 0.969829i | ||||||
\(227\) | 9.96667e6i | 0.852064i | 0.904708 | + | 0.426032i | \(0.140089\pi\) | ||||
−0.904708 | + | 0.426032i | \(0.859911\pi\) | |||||||
\(228\) | − | 2.03057e6i | − | 0.171322i | ||||||
\(229\) | −2.21008e6 | −0.184036 | −0.0920178 | − | 0.995757i | \(-0.529332\pi\) | ||||
−0.0920178 | + | 0.995757i | \(0.529332\pi\) | |||||||
\(230\) | 2.19896e7i | 1.80732i | ||||||||
\(231\) | −2.21331e6 | − | 10164.0i | −0.179559 | − | 0.000824576i | ||||
\(232\) | 1.80068e7 | 1.44202 | ||||||||
\(233\) | − | 1.26959e7i | − | 1.00368i | −0.864959 | − | 0.501842i | \(-0.832656\pi\) | ||
0.864959 | − | 0.501842i | \(-0.167344\pi\) | |||||||
\(234\) | −2.45449e6 | −0.191564 | ||||||||
\(235\) | 1.52718e6 | 0.117676 | ||||||||
\(236\) | 584066. | 0.0444350 | ||||||||
\(237\) | 1.07428e7i | 0.806999i | ||||||||
\(238\) | − | 2.74009e6i | − | 0.203251i | ||||||
\(239\) | 3.07580e6i | 0.225301i | 0.993635 | + | 0.112651i | \(0.0359341\pi\) | ||||
−0.993635 | + | 0.112651i | \(0.964066\pi\) | |||||||
\(240\) | 7.05621e6 | 0.510432 | ||||||||
\(241\) | − | 4.38898e6i | − | 0.313554i | −0.987634 | − | 0.156777i | \(-0.949890\pi\) | ||
0.987634 | − | 0.156777i | \(-0.0501104\pi\) | |||||||
\(242\) | 111253. | − | 1.21129e7i | 0.00784996 | − | 0.854681i | ||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | − | 6.69961e6i | − | 0.461190i | ||||||
\(245\) | 1.78499e7 | 1.21377 | ||||||||
\(246\) | −1.13773e7 | −0.764245 | ||||||||
\(247\) | −1.11579e7 | −0.740445 | ||||||||
\(248\) | − | 1.54936e6i | − | 0.101578i | ||||||
\(249\) | 9.10291e6i | 0.589633i | ||||||||
\(250\) | − | 3.48763e6i | − | 0.223208i | ||||||
\(251\) | 7.16804e6 | 0.453293 | 0.226647 | − | 0.973977i | \(-0.427224\pi\) | ||||
0.226647 | + | 0.973977i | \(0.427224\pi\) | |||||||
\(252\) | − | 447039.i | − | 0.0279347i | ||||||
\(253\) | −117024. | + | 2.54830e7i | −0.00722627 | + | 1.57358i | ||||
\(254\) | −8.09316e6 | −0.493875 | ||||||||
\(255\) | 9.83597e6i | 0.593194i | ||||||||
\(256\) | −1.24892e7 | −0.744412 | ||||||||
\(257\) | 1.70060e7 | 1.00185 | 0.500925 | − | 0.865491i | \(-0.332993\pi\) | ||||
0.500925 | + | 0.865491i | \(0.332993\pi\) | |||||||
\(258\) | 3.15413e6 | 0.183663 | ||||||||
\(259\) | 5.03999e6i | 0.290088i | ||||||||
\(260\) | 4.27902e6i | 0.243458i | ||||||||
\(261\) | − | 7.87648e6i | − | 0.443007i | ||||||
\(262\) | 2.06079e7 | 1.14586 | ||||||||
\(263\) | 2.06276e6i | 0.113392i | 0.998391 | + | 0.0566959i | \(0.0180565\pi\) | ||||
−0.998391 | + | 0.0566959i | \(0.981943\pi\) | |||||||
\(264\) | 1.15262e7 | + | 52931.2i | 0.626435 | + | 0.00287674i | ||||
\(265\) | −2.58708e7 | −1.39018 | ||||||||
\(266\) | 5.50958e6i | 0.292734i | ||||||||
\(267\) | −1.41950e7 | −0.745764 | ||||||||
\(268\) | −7.72405e6 | −0.401274 | ||||||||
\(269\) | −2.39222e7 | −1.22898 | −0.614490 | − | 0.788924i | \(-0.710638\pi\) | ||||
−0.614490 | + | 0.788924i | \(0.710638\pi\) | |||||||
\(270\) | − | 4.35060e6i | − | 0.221033i | ||||||
\(271\) | 1.41620e7i | 0.711569i | 0.934568 | + | 0.355785i | \(0.115786\pi\) | ||||
−0.934568 | + | 0.355785i | \(0.884214\pi\) | |||||||
\(272\) | 1.01234e7i | 0.503061i | ||||||||
\(273\) | −2.45647e6 | −0.120732 | ||||||||
\(274\) | 2.56308e7i | 1.24598i | ||||||||
\(275\) | −76942.7 | + | 1.67550e7i | −0.00369973 | + | 0.805648i | ||||
\(276\) | −5.14700e6 | −0.244809 | ||||||||
\(277\) | − | 8.93142e6i | − | 0.420224i | −0.977677 | − | 0.210112i | \(-0.932617\pi\) | ||
0.977677 | − | 0.210112i | \(-0.0673829\pi\) | |||||||
\(278\) | −2.64156e6 | −0.122949 | ||||||||
\(279\) | −677717. | −0.0312058 | ||||||||
\(280\) | 9.95415e6 | 0.453451 | ||||||||
\(281\) | − | 2.81484e7i | − | 1.26863i | −0.773075 | − | 0.634314i | \(-0.781283\pi\) | ||
0.773075 | − | 0.634314i | \(-0.218717\pi\) | |||||||
\(282\) | − | 969121.i | − | 0.0432146i | ||||||
\(283\) | − | 2.31052e6i | − | 0.101941i | −0.998700 | − | 0.0509707i | \(-0.983768\pi\) | ||
0.998700 | − | 0.0509707i | \(-0.0162315\pi\) | |||||||
\(284\) | 6.95131e6 | 0.303467 | ||||||||
\(285\) | − | 1.97775e7i | − | 0.854352i | ||||||
\(286\) | 61738.1 | − | 1.34440e7i | 0.00263909 | − | 0.574686i | ||||
\(287\) | −1.13865e7 | −0.481662 | ||||||||
\(288\) | 4.16193e6i | 0.174228i | ||||||||
\(289\) | 1.00261e7 | 0.415372 | ||||||||
\(290\) | 3.72276e7 | 1.52641 | ||||||||
\(291\) | −3.77416e6 | −0.153159 | ||||||||
\(292\) | − | 1.60012e6i | − | 0.0642694i | ||||||
\(293\) | 2.08718e7i | 0.829770i | 0.909874 | + | 0.414885i | \(0.136178\pi\) | ||||
−0.909874 | + | 0.414885i | \(0.863822\pi\) | |||||||
\(294\) | − | 1.13272e7i | − | 0.445739i | ||||||
\(295\) | 5.68873e6 | 0.221590 | ||||||||
\(296\) | − | 2.62467e7i | − | 1.01204i | ||||||
\(297\) | 23153.0 | − | 5.04177e6i | 0.000883767 | − | 0.192448i | ||||
\(298\) | −2.13389e7 | −0.806349 | ||||||||
\(299\) | 2.82827e7i | 1.05805i | ||||||||
\(300\) | −3.38413e6 | −0.125338 | ||||||||
\(301\) | 3.15668e6 | 0.115753 | ||||||||
\(302\) | −3.54518e7 | −1.28712 | ||||||||
\(303\) | − | 1.86728e7i | − | 0.671247i | ||||||
\(304\) | − | 2.03555e7i | − | 0.724538i | ||||||
\(305\) | − | 6.52535e7i | − | 2.29987i | ||||||
\(306\) | 6.24173e6 | 0.217841 | ||||||||
\(307\) | 4.82621e7i | 1.66798i | 0.551779 | + | 0.833991i | \(0.313949\pi\) | ||||
−0.551779 | + | 0.833991i | \(0.686051\pi\) | |||||||
\(308\) | 2.44857e6 | + | 11244.4i | 0.0838032 | + | 0.000384844i | ||||
\(309\) | 1.75720e7 | 0.595589 | ||||||||
\(310\) | − | 3.20318e6i | − | 0.107522i | ||||||
\(311\) | 3.66670e7 | 1.21897 | 0.609487 | − | 0.792796i | \(-0.291375\pi\) | ||||
0.609487 | + | 0.792796i | \(0.291375\pi\) | |||||||
\(312\) | 1.27926e7 | 0.421205 | ||||||||
\(313\) | 1.16945e7 | 0.381371 | 0.190685 | − | 0.981651i | \(-0.438929\pi\) | ||||
0.190685 | + | 0.981651i | \(0.438929\pi\) | |||||||
\(314\) | − | 2.50511e7i | − | 0.809168i | ||||||
\(315\) | − | 4.35411e6i | − | 0.139305i | ||||||
\(316\) | − | 1.18847e7i | − | 0.376641i | ||||||
\(317\) | −2.32210e7 | −0.728959 | −0.364480 | − | 0.931211i | \(-0.618753\pi\) | ||||
−0.364480 | + | 0.931211i | \(0.618753\pi\) | |||||||
\(318\) | 1.64171e7i | 0.510524i | ||||||||
\(319\) | 4.31419e7 | + | 198118.i | 1.32901 | + | 0.00610311i | ||||
\(320\) | −4.86411e7 | −1.48441 | ||||||||
\(321\) | − | 6.91800e6i | − | 0.209154i | ||||||
\(322\) | 1.39655e7 | 0.418300 | ||||||||
\(323\) | 2.83744e7 | 0.842015 | ||||||||
\(324\) | 1.01832e6 | 0.0299400 | ||||||||
\(325\) | 1.85957e7i | 0.541705i | ||||||||
\(326\) | − | 5.07528e7i | − | 1.46490i | ||||||
\(327\) | − | 1.96091e6i | − | 0.0560809i | ||||||
\(328\) | 5.92971e7 | 1.68040 | ||||||||
\(329\) | − | 969903.i | − | 0.0272358i | ||||||
\(330\) | 2.38296e7 | + | 109431.i | 0.663093 | + | 0.00304508i | ||||
\(331\) | −7.23306e7 | −1.99452 | −0.997259 | − | 0.0739895i | \(-0.976427\pi\) | ||||
−0.997259 | + | 0.0739895i | \(0.976427\pi\) | |||||||
\(332\) | − | 1.00705e7i | − | 0.275192i | ||||||
\(333\) | −1.14807e7 | −0.310912 | ||||||||
\(334\) | −4.80453e7 | −1.28947 | ||||||||
\(335\) | −7.52314e7 | −2.00108 | ||||||||
\(336\) | − | 4.48136e6i | − | 0.118139i | ||||||
\(337\) | 5.02800e7i | 1.31373i | 0.754009 | + | 0.656864i | \(0.228118\pi\) | ||||
−0.754009 | + | 0.656864i | \(0.771882\pi\) | |||||||
\(338\) | 1.80834e7i | 0.468307i | ||||||||
\(339\) | 2.55218e7 | 0.655108 | ||||||||
\(340\) | − | 1.08815e7i | − | 0.276854i | ||||||
\(341\) | 17046.7 | − | 3.71207e6i | 0.000429909 | − | 0.0936165i | ||||
\(342\) | −1.25504e7 | −0.313748 | ||||||||
\(343\) | − | 2.38867e7i | − | 0.591934i | ||||||
\(344\) | −1.64390e7 | −0.403831 | ||||||||
\(345\) | −5.01312e7 | −1.22082 | ||||||||
\(346\) | −381226. | −0.00920352 | ||||||||
\(347\) | 6.93649e7i | 1.66017i | 0.557640 | + | 0.830083i | \(0.311707\pi\) | ||||
−0.557640 | + | 0.830083i | \(0.688293\pi\) | |||||||
\(348\) | 8.71370e6i | 0.206759i | ||||||||
\(349\) | 7.37818e7i | 1.73569i | 0.496832 | + | 0.867847i | \(0.334497\pi\) | ||||
−0.496832 | + | 0.867847i | \(0.665503\pi\) | |||||||
\(350\) | 9.18222e6 | 0.214163 | ||||||||
\(351\) | − | 5.59567e6i | − | 0.129399i | ||||||
\(352\) | −2.27962e7 | − | 104685.i | −0.522677 | − | 0.00240026i | ||||
\(353\) | 8.56348e7 | 1.94682 | 0.973410 | − | 0.229068i | \(-0.0735678\pi\) | ||||
0.973410 | + | 0.229068i | \(0.0735678\pi\) | |||||||
\(354\) | − | 3.60997e6i | − | 0.0813755i | ||||||
\(355\) | 6.77050e7 | 1.51334 | ||||||||
\(356\) | 1.57038e7 | 0.348061 | ||||||||
\(357\) | 6.24677e6 | 0.137294 | ||||||||
\(358\) | 3.39949e7i | 0.740910i | ||||||||
\(359\) | 197244.i | 0.00426304i | 0.999998 | + | 0.00213152i | \(0.000678485\pi\) | ||||
−0.999998 | + | 0.00213152i | \(0.999322\pi\) | |||||||
\(360\) | 2.26749e7i | 0.486001i | ||||||||
\(361\) | −1.00075e7 | −0.212719 | ||||||||
\(362\) | 5.11786e7i | 1.07885i | ||||||||
\(363\) | 2.76147e7 | + | 253632.i | 0.577326 | + | 0.00530255i | ||||
\(364\) | 2.71758e6 | 0.0563480 | ||||||||
\(365\) | − | 1.55850e7i | − | 0.320500i | ||||||
\(366\) | −4.14087e7 | −0.844594 | ||||||||
\(367\) | −5.96138e7 | −1.20600 | −0.603002 | − | 0.797740i | \(-0.706029\pi\) | ||||
−0.603002 | + | 0.797740i | \(0.706029\pi\) | |||||||
\(368\) | −5.15963e7 | −1.03532 | ||||||||
\(369\) | − | 2.59375e7i | − | 0.516238i | ||||||
\(370\) | − | 5.42630e7i | − | 1.07127i | ||||||
\(371\) | 1.64304e7i | 0.321756i | ||||||||
\(372\) | 749754. | 0.0145643 | ||||||||
\(373\) | − | 5.14277e7i | − | 0.990992i | −0.868610 | − | 0.495496i | \(-0.834986\pi\) | ||
0.868610 | − | 0.495496i | \(-0.165014\pi\) | |||||||
\(374\) | −156999. | + | 3.41879e7i | −0.00300111 | + | 0.653518i | ||||
\(375\) | 7.95099e6 | 0.150774 | ||||||||
\(376\) | 5.05096e6i | 0.0950189i | ||||||||
\(377\) | 4.78816e7 | 0.893603 | ||||||||
\(378\) | −2.76304e6 | −0.0511578 | ||||||||
\(379\) | −1.17931e7 | −0.216627 | −0.108313 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108313 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(380\) | 2.18797e7i | 0.398741i | ||||||||
\(381\) | − | 1.84505e7i | − | 0.333606i | ||||||
\(382\) | − | 1.81777e7i | − | 0.326099i | ||||||
\(383\) | 5.28514e7 | 0.940719 | 0.470360 | − | 0.882475i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882475i | \(0.344124\pi\) | |||||||
\(384\) | 1.37795e7i | 0.243355i | ||||||||
\(385\) | 2.38488e7 | + | 109519.i | 0.417912 | + | 0.00191915i | ||||
\(386\) | 3.74577e7 | 0.651298 | ||||||||
\(387\) | 7.19069e6i | 0.124062i | ||||||||
\(388\) | 4.17533e6 | 0.0714819 | ||||||||
\(389\) | −1.48909e7 | −0.252972 | −0.126486 | − | 0.991968i | \(-0.540370\pi\) | ||||
−0.126486 | + | 0.991968i | \(0.540370\pi\) | |||||||
\(390\) | 2.64476e7 | 0.445853 | ||||||||
\(391\) | − | 7.19224e7i | − | 1.20319i | ||||||
\(392\) | 5.90362e7i | 0.980078i | ||||||||
\(393\) | 4.69813e7i | 0.774012i | ||||||||
\(394\) | 5.51499e7 | 0.901687 | ||||||||
\(395\) | − | 1.15756e8i | − | 1.87824i | ||||||
\(396\) | −25614.0 | + | 5.57768e6i | −0.000412470 | + | 0.0898189i | ||||
\(397\) | 3.05302e7 | 0.487930 | 0.243965 | − | 0.969784i | \(-0.421552\pi\) | ||||
0.243965 | + | 0.969784i | \(0.421552\pi\) | |||||||
\(398\) | 4.42933e7i | 0.702569i | ||||||||
\(399\) | −1.25606e7 | −0.197738 | ||||||||
\(400\) | −3.39243e7 | −0.530067 | ||||||||
\(401\) | −1.03890e8 | −1.61116 | −0.805581 | − | 0.592486i | \(-0.798147\pi\) | ||||
−0.805581 | + | 0.592486i | \(0.798147\pi\) | |||||||
\(402\) | 4.77405e7i | 0.734867i | ||||||||
\(403\) | − | 4.11989e6i | − | 0.0629463i | ||||||
\(404\) | 2.06576e7i | 0.313283i | ||||||||
\(405\) | 9.91837e6 | 0.149305 | ||||||||
\(406\) | − | 2.36431e7i | − | 0.353285i | ||||||
\(407\) | 288776. | − | 6.28836e7i | 0.00428330 | − | 0.932726i | ||||
\(408\) | −3.25312e7 | −0.478983 | ||||||||
\(409\) | 8.25556e7i | 1.20664i | 0.797500 | + | 0.603319i | \(0.206155\pi\) | ||||
−0.797500 | + | 0.603319i | \(0.793845\pi\) | |||||||
\(410\) | 1.22592e8 | 1.77873 | ||||||||
\(411\) | −5.84323e7 | −0.841642 | ||||||||
\(412\) | −1.94398e7 | −0.277972 | ||||||||
\(413\) | − | 3.61288e6i | − | 0.0512866i | ||||||
\(414\) | 3.18124e7i | 0.448327i | ||||||||
\(415\) | − | 9.80854e7i | − | 1.37234i | ||||||
\(416\) | −2.53006e7 | −0.351440 | ||||||||
\(417\) | − | 6.02214e6i | − | 0.0830506i | ||||||
\(418\) | 315683. | − | 6.87427e7i | 0.00432237 | − | 0.941234i | ||||
\(419\) | −6.47436e7 | −0.880146 | −0.440073 | − | 0.897962i | \(-0.645048\pi\) | ||||
−0.440073 | + | 0.897962i | \(0.645048\pi\) | |||||||
\(420\) | 4.81693e6i | 0.0650163i | ||||||||
\(421\) | −1.02270e8 | −1.37058 | −0.685288 | − | 0.728272i | \(-0.740324\pi\) | ||||
−0.685288 | + | 0.728272i | \(0.740324\pi\) | |||||||
\(422\) | 1.12252e8 | 1.49368 | ||||||||
\(423\) | 2.20937e6 | 0.0291909 | ||||||||
\(424\) | − | 8.55644e7i | − | 1.12252i | ||||||
\(425\) | − | 4.72886e7i | − | 0.616013i | ||||||
\(426\) | − | 4.29644e7i | − | 0.555750i | ||||||
\(427\) | −4.14421e7 | −0.532302 | ||||||||
\(428\) | 7.65334e6i | 0.0976157i | ||||||||
\(429\) | 3.06492e7 | + | 140749.i | 0.388193 | + | 0.00178267i | ||||
\(430\) | −3.39863e7 | −0.427463 | ||||||||
\(431\) | − | 1.48166e8i | − | 1.85062i | −0.379218 | − | 0.925308i | \(-0.623807\pi\) | ||
0.379218 | − | 0.925308i | \(-0.376193\pi\) | |||||||
\(432\) | 1.02082e7 | 0.126619 | ||||||||
\(433\) | −3.21907e7 | −0.396521 | −0.198260 | − | 0.980149i | \(-0.563529\pi\) | ||||
−0.198260 | + | 0.980149i | \(0.563529\pi\) | |||||||
\(434\) | −2.03432e6 | −0.0248858 | ||||||||
\(435\) | 8.48704e7i | 1.03107i | ||||||||
\(436\) | 2.16935e6i | 0.0261740i | ||||||||
\(437\) | 1.44617e8i | 1.73290i | ||||||||
\(438\) | −9.88996e6 | −0.117699 | ||||||||
\(439\) | − | 1.63606e8i | − | 1.93377i | −0.255209 | − | 0.966886i | \(-0.582144\pi\) | ||
0.255209 | − | 0.966886i | \(-0.417856\pi\) | |||||||
\(440\) | −1.24197e8 | − | 570343.i | −1.45799 | − | 0.00669543i | ||||
\(441\) | 2.58234e7 | 0.301091 | ||||||||
\(442\) | 3.79439e7i | 0.439415i | ||||||||
\(443\) | 3.88693e7 | 0.447091 | 0.223545 | − | 0.974694i | \(-0.428237\pi\) | ||||
0.223545 | + | 0.974694i | \(0.428237\pi\) | |||||||
\(444\) | 1.27011e7 | 0.145108 | ||||||||
\(445\) | 1.52954e8 | 1.73572 | ||||||||
\(446\) | − | 1.14082e6i | − | 0.0128592i | ||||||
\(447\) | − | 4.86478e7i | − | 0.544679i | ||||||
\(448\) | 3.08917e7i | 0.343564i | ||||||||
\(449\) | −1.44674e8 | −1.59828 | −0.799138 | − | 0.601148i | \(-0.794710\pi\) | ||||
−0.799138 | + | 0.601148i | \(0.794710\pi\) | |||||||
\(450\) | 2.09165e7i | 0.229536i | ||||||||
\(451\) | 1.42068e8 | + | 652410.i | 1.54870 | + | 0.00711198i | ||||
\(452\) | −2.82346e7 | −0.305750 | ||||||||
\(453\) | − | 8.08220e7i | − | 0.869431i | ||||||
\(454\) | −6.81494e7 | −0.728274 | ||||||||
\(455\) | 2.64689e7 | 0.280997 | ||||||||
\(456\) | 6.54116e7 | 0.689859 | ||||||||
\(457\) | 1.57900e8i | 1.65438i | 0.561924 | + | 0.827189i | \(0.310061\pi\) | ||||
−0.561924 | + | 0.827189i | \(0.689939\pi\) | |||||||
\(458\) | − | 1.51119e7i | − | 0.157298i | ||||||
\(459\) | 1.42297e7i | 0.147149i | ||||||||
\(460\) | 5.54599e7 | 0.569778 | ||||||||
\(461\) | 1.75494e8i | 1.79126i | 0.444800 | + | 0.895630i | \(0.353275\pi\) | ||||
−0.444800 | + | 0.895630i | \(0.646725\pi\) | |||||||
\(462\) | 69499.0 | − | 1.51340e7i | 0.000704779 | − | 0.153472i | ||||
\(463\) | 2.76136e7 | 0.278215 | 0.139108 | − | 0.990277i | \(-0.455577\pi\) | ||||
0.139108 | + | 0.990277i | \(0.455577\pi\) | |||||||
\(464\) | 8.73507e7i | 0.874405i | ||||||||
\(465\) | 7.30252e6 | 0.0726297 | ||||||||
\(466\) | 8.68115e7 | 0.857866 | ||||||||
\(467\) | −3.64285e7 | −0.357676 | −0.178838 | − | 0.983879i | \(-0.557234\pi\) | ||||
−0.178838 | + | 0.983879i | \(0.557234\pi\) | |||||||
\(468\) | 6.19046e6i | 0.0603928i | ||||||||
\(469\) | 4.77791e7i | 0.463147i | ||||||||
\(470\) | 1.04424e7i | 0.100579i | ||||||||
\(471\) | 5.71108e7 | 0.546583 | ||||||||
\(472\) | 1.88148e7i | 0.178926i | ||||||||
\(473\) | −3.93856e7 | − | 180868.i | −0.372181 | − | 0.00170914i | ||||
\(474\) | −7.34565e7 | −0.689755 | ||||||||
\(475\) | 9.50847e7i | 0.887217i | ||||||||
\(476\) | −6.91076e6 | −0.0640774 | ||||||||
\(477\) | −3.74273e7 | −0.344852 | ||||||||
\(478\) | −2.10315e7 | −0.192569 | ||||||||
\(479\) | − | 1.36993e7i | − | 0.124649i | −0.998056 | − | 0.0623247i | \(-0.980149\pi\) | ||
0.998056 | − | 0.0623247i | \(-0.0198514\pi\) | |||||||
\(480\) | − | 4.48455e7i | − | 0.405504i | ||||||
\(481\) | − | 6.97922e7i | − | 0.627151i | ||||||
\(482\) | 3.00107e7 | 0.268000 | ||||||||
\(483\) | 3.18381e7i | 0.282557i | ||||||||
\(484\) | −3.05500e7 | − | 280592.i | −0.269448 | − | 0.00247479i | ||||
\(485\) | 4.06673e7 | 0.356467 | ||||||||
\(486\) | − | 6.29402e6i | − | 0.0548301i | ||||||
\(487\) | −1.17206e8 | −1.01476 | −0.507381 | − | 0.861722i | \(-0.669386\pi\) | ||||
−0.507381 | + | 0.861722i | \(0.669386\pi\) | |||||||
\(488\) | 2.15818e8 | 1.85707 | ||||||||
\(489\) | 1.15705e8 | 0.989521 | ||||||||
\(490\) | 1.22053e8i | 1.03743i | ||||||||
\(491\) | − | 3.86176e7i | − | 0.326243i | −0.986606 | − | 0.163121i | \(-0.947844\pi\) | ||
0.986606 | − | 0.163121i | \(-0.0521562\pi\) | |||||||
\(492\) | 2.86945e7i | 0.240937i | ||||||||
\(493\) | −1.21762e8 | −1.01618 | ||||||||
\(494\) | − | 7.62950e7i | − | 0.632871i | ||||||
\(495\) | −249478. | + | 5.43259e7i | −0.00205691 | + | 0.447911i | ||||
\(496\) | 7.51594e6 | 0.0615940 | ||||||||
\(497\) | − | 4.29991e7i | − | 0.350260i | ||||||
\(498\) | −6.22432e7 | −0.503969 | ||||||||
\(499\) | 6.22876e7 | 0.501303 | 0.250651 | − | 0.968077i | \(-0.419355\pi\) | ||||
0.250651 | + | 0.968077i | \(0.419355\pi\) | |||||||
\(500\) | −8.79613e6 | −0.0703690 | ||||||||
\(501\) | − | 1.09532e8i | − | 0.871022i | ||||||
\(502\) | 4.90131e7i | 0.387437i | ||||||||
\(503\) | 3.35178e7i | 0.263373i | 0.991291 | + | 0.131687i | \(0.0420393\pi\) | ||||
−0.991291 | + | 0.131687i | \(0.957961\pi\) | |||||||
\(504\) | 1.44007e7 | 0.112484 | ||||||||
\(505\) | 2.01203e8i | 1.56229i | ||||||||
\(506\) | −1.74246e8 | − | 800180.i | −1.34497 | − | 0.00617641i | ||||
\(507\) | −4.12260e7 | −0.316335 | ||||||||
\(508\) | 2.04117e7i | 0.155700i | ||||||||
\(509\) | 9.00026e7 | 0.682499 | 0.341249 | − | 0.939973i | \(-0.389150\pi\) | ||||
0.341249 | + | 0.939973i | \(0.389150\pi\) | |||||||
\(510\) | −6.72557e7 | −0.507013 | ||||||||
\(511\) | −9.89794e6 | −0.0741792 | ||||||||
\(512\) | − | 1.41971e8i | − | 1.05776i | ||||||
\(513\) | − | 2.86121e7i | − | 0.211933i | ||||||
\(514\) | 1.16282e8i | 0.856298i | ||||||||
\(515\) | −1.89342e8 | −1.38620 | ||||||||
\(516\) | − | 7.95502e6i | − | 0.0579018i | ||||||
\(517\) | −55572.6 | + | 1.21014e7i | −0.000402151 | + | 0.0875718i | ||||
\(518\) | −3.44621e7 | −0.247943 | ||||||||
\(519\) | − | 869107.i | − | 0.00621686i | ||||||
\(520\) | −1.37842e8 | −0.980328 | ||||||||
\(521\) | 4.44753e7 | 0.314489 | 0.157245 | − | 0.987560i | \(-0.449739\pi\) | ||||
0.157245 | + | 0.987560i | \(0.449739\pi\) | |||||||
\(522\) | 5.38572e7 | 0.378645 | ||||||||
\(523\) | − | 1.45157e8i | − | 1.01469i | −0.861743 | − | 0.507345i | \(-0.830627\pi\) | ||
0.861743 | − | 0.507345i | \(-0.169373\pi\) | |||||||
\(524\) | − | 5.19751e7i | − | 0.361245i | ||||||
\(525\) | 2.09334e7i | 0.144664i | ||||||||
\(526\) | −1.41046e7 | −0.0969178 | ||||||||
\(527\) | 1.04768e7i | 0.0715809i | ||||||||
\(528\) | −256769. | + | 5.59136e7i | −0.00174438 | + | 0.379853i | ||||
\(529\) | 2.18533e8 | 1.47622 | ||||||||
\(530\) | − | 1.76898e8i | − | 1.18821i | ||||||
\(531\) | 8.22989e6 | 0.0549681 | ||||||||
\(532\) | 1.38957e7 | 0.0922880 | ||||||||
\(533\) | 1.57676e8 | 1.04132 | ||||||||
\(534\) | − | 9.70615e7i | − | 0.637417i | ||||||
\(535\) | 7.45427e7i | 0.486792i | ||||||||
\(536\) | − | 2.48819e8i | − | 1.61580i | ||||||
\(537\) | −7.75007e7 | −0.500475 | ||||||||
\(538\) | − | 1.63574e8i | − | 1.05043i | ||||||
\(539\) | −649539. | + | 1.41443e8i | −0.00414800 | + | 0.903264i | ||||
\(540\) | −1.09726e7 | −0.0696834 | ||||||||
\(541\) | 1.08867e8i | 0.687550i | 0.939052 | + | 0.343775i | \(0.111706\pi\) | ||||
−0.939052 | + | 0.343775i | \(0.888294\pi\) | |||||||
\(542\) | −9.68361e7 | −0.608190 | ||||||||
\(543\) | −1.16676e8 | −0.728753 | ||||||||
\(544\) | 6.43391e7 | 0.399648 | ||||||||
\(545\) | 2.11292e7i | 0.130525i | ||||||||
\(546\) | − | 1.67967e7i | − | 0.103192i | ||||||
\(547\) | − | 2.45302e8i | − | 1.49879i | −0.662125 | − | 0.749393i | \(-0.730345\pi\) | ||
0.662125 | − | 0.749393i | \(-0.269655\pi\) | |||||||
\(548\) | 6.46432e7 | 0.392809 | ||||||||
\(549\) | − | 9.44022e7i | − | 0.570513i | ||||||
\(550\) | −1.14566e8 | − | 526114.i | −0.688601 | − | 0.00316222i | ||||
\(551\) | 2.44831e8 | 1.46356 | ||||||||
\(552\) | − | 1.65803e8i | − | 0.985768i | ||||||
\(553\) | −7.35158e7 | −0.434716 | ||||||||
\(554\) | 6.10706e7 | 0.359173 | ||||||||
\(555\) | 1.23707e8 | 0.723629 | ||||||||
\(556\) | 6.66226e6i | 0.0387612i | ||||||||
\(557\) | − | 6.54683e6i | − | 0.0378849i | −0.999821 | − | 0.0189424i | \(-0.993970\pi\) | ||
0.999821 | − | 0.0189424i | \(-0.00602992\pi\) | |||||||
\(558\) | − | 4.63405e6i | − | 0.0266722i | ||||||
\(559\) | −4.37127e7 | −0.250249 | ||||||||
\(560\) | 4.82875e7i | 0.274960i | ||||||||
\(561\) | −7.79405e7 | − | 357921.i | −0.441443 | − | 0.00202721i | ||||
\(562\) | 1.92471e8 | 1.08432 | ||||||||
\(563\) | 1.49596e8i | 0.838291i | 0.907919 | + | 0.419145i | \(0.137670\pi\) | ||||
−0.907919 | + | 0.419145i | \(0.862330\pi\) | |||||||
\(564\) | −2.44422e6 | −0.0136239 | ||||||||
\(565\) | −2.75002e8 | −1.52472 | ||||||||
\(566\) | 1.57987e7 | 0.0871310 | ||||||||
\(567\) | − | 6.29910e6i | − | 0.0345565i | ||||||
\(568\) | 2.23926e8i | 1.22197i | ||||||||
\(569\) | − | 6.51412e7i | − | 0.353605i | −0.984246 | − | 0.176803i | \(-0.943425\pi\) | ||
0.984246 | − | 0.176803i | \(-0.0565754\pi\) | |||||||
\(570\) | 1.35233e8 | 0.730229 | ||||||||
\(571\) | 1.70982e8i | 0.918419i | 0.888328 | + | 0.459210i | \(0.151867\pi\) | ||||
−0.888328 | + | 0.459210i | \(0.848133\pi\) | |||||||
\(572\) | −3.39071e7 | − | 155709.i | −0.181177 | − | 0.000832006i | ||||
\(573\) | 4.14411e7 | 0.220276 | ||||||||
\(574\) | − | 7.78575e7i | − | 0.411685i | ||||||
\(575\) | 2.41017e8 | 1.26778 | ||||||||
\(576\) | −7.03691e7 | −0.368226 | ||||||||
\(577\) | 1.88869e8 | 0.983181 | 0.491590 | − | 0.870827i | \(-0.336416\pi\) | ||||
0.491590 | + | 0.870827i | \(0.336416\pi\) | |||||||
\(578\) | 6.85556e7i | 0.355025i | ||||||||
\(579\) | 8.53950e7i | 0.439943i | ||||||||
\(580\) | − | 9.38916e7i | − | 0.481219i | ||||||
\(581\) | −6.22935e7 | −0.317625 | ||||||||
\(582\) | − | 2.58067e7i | − | 0.130907i | ||||||
\(583\) | 941412. | − | 2.05001e8i | 0.00475088 | − | 1.03455i | ||||
\(584\) | 5.15454e7 | 0.258792 | ||||||||
\(585\) | 6.02944e7i | 0.301168i | ||||||||
\(586\) | −1.42716e8 | −0.709219 | ||||||||
\(587\) | 6.29602e7 | 0.311280 | 0.155640 | − | 0.987814i | \(-0.450256\pi\) | ||||
0.155640 | + | 0.987814i | \(0.450256\pi\) | |||||||
\(588\) | −2.85683e7 | −0.140525 | ||||||||
\(589\) | − | 2.10661e7i | − | 0.103095i | ||||||
\(590\) | 3.88980e7i | 0.189396i | ||||||||
\(591\) | 1.25729e8i | 0.609078i | ||||||||
\(592\) | 1.27322e8 | 0.613677 | ||||||||
\(593\) | − | 6.10792e7i | − | 0.292906i | −0.989218 | − | 0.146453i | \(-0.953214\pi\) | ||
0.989218 | − | 0.146453i | \(-0.0467858\pi\) | |||||||
\(594\) | 3.44743e7 | + | 158314.i | 0.164489 | + | 0.000755370i | ||||
\(595\) | −6.73100e7 | −0.319543 | ||||||||
\(596\) | 5.38187e7i | 0.254211i | ||||||||
\(597\) | −1.00979e8 | −0.474576 | ||||||||
\(598\) | −1.93390e8 | −0.904335 | ||||||||
\(599\) | −3.90561e8 | −1.81722 | −0.908612 | − | 0.417641i | \(-0.862857\pi\) | ||||
−0.908612 | + | 0.417641i | \(0.862857\pi\) | |||||||
\(600\) | − | 1.09014e8i | − | 0.504696i | ||||||
\(601\) | 1.87303e8i | 0.862824i | 0.902155 | + | 0.431412i | \(0.141984\pi\) | ||||
−0.902155 | + | 0.431412i | \(0.858016\pi\) | |||||||
\(602\) | 2.15845e7i | 0.0989357i | ||||||||
\(603\) | −1.08837e8 | −0.496393 | ||||||||
\(604\) | 8.94129e7i | 0.405779i | ||||||||
\(605\) | −2.97554e8 | − | 2.73293e6i | −1.34369 | − | 0.0123413i | ||||
\(606\) | 1.27680e8 | 0.573726 | ||||||||
\(607\) | − | 9.38323e7i | − | 0.419552i | −0.977749 | − | 0.209776i | \(-0.932726\pi\) | ||
0.977749 | − | 0.209776i | \(-0.0672735\pi\) | |||||||
\(608\) | −1.29369e8 | −0.575597 | ||||||||
\(609\) | 5.39007e7 | 0.238640 | ||||||||
\(610\) | 4.46186e8 | 1.96574 | ||||||||
\(611\) | 1.34309e7i | 0.0588819i | ||||||||
\(612\) | − | 1.57422e7i | − | 0.0686771i | ||||||
\(613\) | − | 3.63707e8i | − | 1.57896i | −0.613777 | − | 0.789479i | \(-0.710351\pi\) | ||
0.613777 | − | 0.789479i | \(-0.289649\pi\) | |||||||
\(614\) | −3.30003e8 | −1.42565 | ||||||||
\(615\) | 2.79482e8i | 1.20151i | ||||||||
\(616\) | −362222. | + | 7.88770e7i | −0.00154965 | + | 0.337449i | ||||
\(617\) | 1.21121e8 | 0.515659 | 0.257830 | − | 0.966190i | \(-0.416993\pi\) | ||||
0.257830 | + | 0.966190i | \(0.416993\pi\) | |||||||
\(618\) | 1.20153e8i | 0.509059i | ||||||||
\(619\) | 2.40580e8 | 1.01435 | 0.507174 | − | 0.861844i | \(-0.330690\pi\) | ||||
0.507174 | + | 0.861844i | \(0.330690\pi\) | |||||||
\(620\) | −8.07874e6 | −0.0338976 | ||||||||
\(621\) | −7.25249e7 | −0.302839 | ||||||||
\(622\) | 2.50719e8i | 1.04188i | ||||||||
\(623\) | − | 9.71399e7i | − | 0.401729i | ||||||
\(624\) | 6.20565e7i | 0.255407i | ||||||||
\(625\) | −2.82367e8 | −1.15657 | ||||||||
\(626\) | 7.99636e7i | 0.325964i | ||||||||
\(627\) | 1.56717e8 | + | 719684.i | 0.635792 | + | 0.00291971i | ||||
\(628\) | −6.31814e7 | −0.255100 | ||||||||
\(629\) | 1.77480e8i | 0.713179i | ||||||||
\(630\) | 2.97723e7 | 0.119067 | ||||||||
\(631\) | 4.09539e7 | 0.163007 | 0.0815036 | − | 0.996673i | \(-0.474028\pi\) | ||||
0.0815036 | + | 0.996673i | \(0.474028\pi\) | |||||||
\(632\) | 3.82847e8 | 1.51661 | ||||||||
\(633\) | 2.55910e8i | 1.00896i | ||||||||
\(634\) | − | 1.58779e8i | − | 0.623054i | ||||||
\(635\) | 1.98808e8i | 0.776448i | ||||||||
\(636\) | 4.14056e7 | 0.160949 | ||||||||
\(637\) | 1.56982e8i | 0.607341i | ||||||||
\(638\) | −1.35468e6 | + | 2.94993e8i | −0.00521643 | + | 1.13592i | ||||
\(639\) | 9.79489e7 | 0.375402 | ||||||||
\(640\) | − | 1.48477e8i | − | 0.566394i | ||||||
\(641\) | 1.34211e8 | 0.509582 | 0.254791 | − | 0.966996i | \(-0.417993\pi\) | ||||
0.254791 | + | 0.966996i | \(0.417993\pi\) | |||||||
\(642\) | 4.73034e7 | 0.178767 | ||||||||
\(643\) | −1.25960e8 | −0.473806 | −0.236903 | − | 0.971533i | \(-0.576132\pi\) | ||||
−0.236903 | + | 0.971533i | \(0.576132\pi\) | |||||||
\(644\) | − | 3.52223e7i | − | 0.131874i | ||||||
\(645\) | − | 7.74810e7i | − | 0.288746i | ||||||
\(646\) | 1.94017e8i | 0.719684i | ||||||||
\(647\) | −4.30179e8 | −1.58831 | −0.794157 | − | 0.607712i | \(-0.792087\pi\) | ||||
−0.794157 | + | 0.607712i | \(0.792087\pi\) | |||||||
\(648\) | 3.28038e7i | 0.120559i | ||||||||
\(649\) | −207007. | + | 4.50777e7i | −0.000757272 | + | 0.164903i | ||||
\(650\) | −1.27153e8 | −0.463004 | ||||||||
\(651\) | − | 4.63779e6i | − | 0.0168100i | ||||||
\(652\) | −1.28004e8 | −0.461827 | ||||||||
\(653\) | 1.35951e8 | 0.488250 | 0.244125 | − | 0.969744i | \(-0.421499\pi\) | ||||
0.244125 | + | 0.969744i | \(0.421499\pi\) | |||||||
\(654\) | 1.34082e7 | 0.0479333 | ||||||||
\(655\) | − | 5.06232e8i | − | 1.80146i | ||||||
\(656\) | 2.87649e8i | 1.01895i | ||||||||
\(657\) | − | 2.25468e7i | − | 0.0795041i | ||||||
\(658\) | 6.63194e6 | 0.0232789 | ||||||||
\(659\) | 1.68435e8i | 0.588542i | 0.955722 | + | 0.294271i | \(0.0950768\pi\) | ||||
−0.955722 | + | 0.294271i | \(0.904923\pi\) | |||||||
\(660\) | 275996. | − | 6.01005e7i | 0.000959998 | − | 0.209048i | ||||
\(661\) | 3.91844e7 | 0.135678 | 0.0678390 | − | 0.997696i | \(-0.478390\pi\) | ||||
0.0678390 | + | 0.997696i | \(0.478390\pi\) | |||||||
\(662\) | − | 4.94577e8i | − | 1.70475i | ||||||
\(663\) | −8.65033e7 | −0.296819 | ||||||||
\(664\) | 3.24405e8 | 1.10811 | ||||||||
\(665\) | 1.35343e8 | 0.460224 | ||||||||
\(666\) | − | 7.85023e7i | − | 0.265742i | ||||||
\(667\) | − | 6.20588e8i | − | 2.09135i | ||||||
\(668\) | 1.21175e8i | 0.406521i | ||||||||
\(669\) | 2.60081e6 | 0.00868620 | ||||||||
\(670\) | − | 5.14412e8i | − | 1.71036i | ||||||
\(671\) | 5.17070e8 | + | 2.37451e6i | 1.71152 | + | 0.00785970i | ||||
\(672\) | −2.84811e7 | −0.0938532 | ||||||||
\(673\) | 8.78526e7i | 0.288210i | 0.989562 | + | 0.144105i | \(0.0460304\pi\) | ||||
−0.989562 | + | 0.144105i | \(0.953970\pi\) | |||||||
\(674\) | −3.43801e8 | −1.12287 | ||||||||
\(675\) | −4.76847e7 | −0.155049 | ||||||||
\(676\) | 4.56081e7 | 0.147639 | ||||||||
\(677\) | − | 2.96010e8i | − | 0.953983i | −0.878908 | − | 0.476992i | \(-0.841727\pi\) | ||
0.878908 | − | 0.476992i | \(-0.158273\pi\) | |||||||
\(678\) | 1.74511e8i | 0.559931i | ||||||||
\(679\) | − | 2.58276e7i | − | 0.0825038i | ||||||
\(680\) | 3.50530e8 | 1.11480 | ||||||||
\(681\) | − | 1.55365e8i | − | 0.491940i | ||||||
\(682\) | 2.53821e7 | + | 116561.i | 0.0800156 | + | 0.000367451i | ||||
\(683\) | −1.53227e8 | −0.480920 | −0.240460 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240460 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(684\) | 3.16534e7i | 0.0989128i | ||||||||
\(685\) | 6.29618e8 | 1.95887 | ||||||||
\(686\) | 1.63331e8 | 0.505935 | ||||||||
\(687\) | 3.44518e7 | 0.106253 | ||||||||
\(688\) | − | 7.97454e7i | − | 0.244873i | ||||||
\(689\) | − | 2.27523e8i | − | 0.695613i | ||||||
\(690\) | − | 3.42784e8i | − | 1.04345i | ||||||
\(691\) | −1.45410e8 | −0.440716 | −0.220358 | − | 0.975419i | \(-0.570723\pi\) | ||||
−0.220358 | + | 0.975419i | \(0.570723\pi\) | |||||||
\(692\) | 961488.i | 0.00290152i | ||||||||
\(693\) | 3.45021e7 | + | 158442.i | 0.103668 | + | 0.000476069i | ||||
\(694\) | −4.74299e8 | −1.41897 | ||||||||
\(695\) | 6.48896e7i | 0.193295i | ||||||||
\(696\) | −2.80698e8 | −0.832553 | ||||||||
\(697\) | −4.00967e8 | −1.18416 | ||||||||
\(698\) | −5.04500e8 | −1.48353 | ||||||||
\(699\) | 1.97910e8i | 0.579478i | ||||||||
\(700\) | − | 2.31584e7i | − | 0.0675173i | ||||||
\(701\) | 1.72482e8i | 0.500714i | 0.968154 | + | 0.250357i | \(0.0805480\pi\) | ||||
−0.968154 | + | 0.250357i | \(0.919452\pi\) | |||||||
\(702\) | 3.82617e7 | 0.110600 | ||||||||
\(703\) | − | 3.56866e8i | − | 1.02716i | ||||||
\(704\) | 1.77000e6 | − | 3.85433e8i | 0.00507289 | − | 1.10467i | ||||
\(705\) | −2.38064e7 | −0.0679401 | ||||||||
\(706\) | 5.85548e8i | 1.66398i | ||||||||
\(707\) | 1.27783e8 | 0.361588 | ||||||||
\(708\) | −9.10468e6 | −0.0256546 | ||||||||
\(709\) | −6.64899e7 | −0.186559 | −0.0932797 | − | 0.995640i | \(-0.529735\pi\) | ||||
−0.0932797 | + | 0.995640i | \(0.529735\pi\) | |||||||
\(710\) | 4.62949e8i | 1.29347i | ||||||||
\(711\) | − | 1.67464e8i | − | 0.465921i | ||||||
\(712\) | 5.05875e8i | 1.40153i | ||||||||
\(713\) | −5.33974e7 | −0.147317 | ||||||||
\(714\) | 4.27137e7i | 0.117347i | ||||||||
\(715\) | −3.30251e8 | − | 1.51659e6i | −0.903495 | − | 0.00414907i | ||||
\(716\) | 8.57385e7 | 0.233581 | ||||||||
\(717\) | − | 4.79469e7i | − | 0.130078i | ||||||
\(718\) | −1.34870e6 | −0.00364369 | ||||||||
\(719\) | 1.69376e8 | 0.455687 | 0.227843 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227843 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(720\) | −1.09995e8 | −0.294698 | ||||||||
\(721\) | 1.20250e8i | 0.320833i | ||||||||
\(722\) | − | 6.84289e7i | − | 0.181814i | ||||||
\(723\) | 6.84175e7i | 0.181031i | ||||||||
\(724\) | 1.29077e8 | 0.340122 | ||||||||
\(725\) | − | 4.08033e8i | − | 1.07073i | ||||||
\(726\) | −1.73427e6 | + | 1.88822e8i | −0.00453217 | + | 0.493450i | ||||
\(727\) | −4.83665e7 | −0.125876 | −0.0629378 | − | 0.998017i | \(-0.520047\pi\) | ||||
−0.0629378 | + | 0.998017i | \(0.520047\pi\) | |||||||
\(728\) | 8.75427e7i | 0.226895i | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 1.06566e8 | 0.273937 | ||||||||
\(731\) | 1.11161e8 | 0.284576 | ||||||||
\(732\) | 1.04437e8i | 0.266268i | ||||||||
\(733\) | − | 2.29809e7i | − | 0.0583520i | −0.999574 | − | 0.0291760i | \(-0.990712\pi\) | ||
0.999574 | − | 0.0291760i | \(-0.00928833\pi\) | |||||||
\(734\) | − | 4.07623e8i | − | 1.03079i | ||||||
\(735\) | −2.78252e8 | −0.700771 | ||||||||
\(736\) | 3.27919e8i | 0.822494i | ||||||||
\(737\) | 2.73760e6 | − | 5.96136e8i | 0.00683860 | − | 1.48916i | ||||
\(738\) | 1.77354e8 | 0.441237 | ||||||||
\(739\) | − | 3.23451e8i | − | 0.801448i | −0.916199 | − | 0.400724i | \(-0.868759\pi\) | ||
0.916199 | − | 0.400724i | \(-0.131241\pi\) | |||||||
\(740\) | −1.36856e8 | −0.337730 | ||||||||
\(741\) | 1.73935e8 | 0.427496 | ||||||||
\(742\) | −1.12347e8 | −0.275010 | ||||||||
\(743\) | 8.01300e7i | 0.195357i | 0.995218 | + | 0.0976785i | \(0.0311417\pi\) | ||||
−0.995218 | + | 0.0976785i | \(0.968858\pi\) | |||||||
\(744\) | 2.41522e7i | 0.0586459i | ||||||||
\(745\) | 5.24188e8i | 1.26771i | ||||||||
\(746\) | 3.51649e8 | 0.847018 | ||||||||
\(747\) | − | 1.41900e8i | − | 0.340425i | ||||||
\(748\) | 8.62251e7 | + | 395966.i | 0.206029 | + | 0.000946135i | ||||
\(749\) | 4.73416e7 | 0.112667 | ||||||||
\(750\) | 5.43667e7i | 0.128869i | ||||||||
\(751\) | 3.04740e8 | 0.719464 | 0.359732 | − | 0.933056i | \(-0.382868\pi\) | ||||
0.359732 | + | 0.933056i | \(0.382868\pi\) | |||||||
\(752\) | −2.45021e7 | −0.0576169 | ||||||||
\(753\) | −1.11739e8 | −0.261709 | ||||||||
\(754\) | 3.27402e8i | 0.763777i | ||||||||
\(755\) | 8.70871e8i | 2.02355i | ||||||||
\(756\) | 6.96865e6i | 0.0161281i | ||||||||
\(757\) | 3.75853e8 | 0.866423 | 0.433211 | − | 0.901292i | \(-0.357380\pi\) | ||||
0.433211 | + | 0.901292i | \(0.357380\pi\) | |||||||
\(758\) | − | 8.06383e7i | − | 0.185154i | ||||||
\(759\) | 1.82423e6 | − | 3.97241e8i | 0.00417209 | − | 0.908509i | ||||
\(760\) | −7.04822e8 | −1.60560 | ||||||||
\(761\) | − | 8.34472e7i | − | 0.189347i | −0.995508 | − | 0.0946734i | \(-0.969819\pi\) | ||
0.995508 | − | 0.0946734i | \(-0.0301807\pi\) | |||||||
\(762\) | 1.26160e8 | 0.285139 | ||||||||
\(763\) | 1.34190e7 | 0.0302098 | ||||||||
\(764\) | −4.58460e7 | −0.102807 | ||||||||
\(765\) | − | 1.53328e8i | − | 0.342481i | ||||||
\(766\) | 3.61384e8i | 0.804049i | ||||||||
\(767\) | 5.00301e7i | 0.110878i | ||||||||
\(768\) | 1.94687e8 | 0.429786 | ||||||||
\(769\) | 2.86185e8i | 0.629316i | 0.949205 | + | 0.314658i | \(0.101890\pi\) | ||||
−0.949205 | + | 0.314658i | \(0.898110\pi\) | |||||||
\(770\) | −748864. | + | 1.63072e8i | −0.00164033 | + | 0.357196i | ||||
\(771\) | −2.65097e8 | −0.578418 | ||||||||
\(772\) | − | 9.44720e7i | − | 0.205329i | ||||||
\(773\) | 4.76538e7 | 0.103171 | 0.0515856 | − | 0.998669i | \(-0.483572\pi\) | ||||
0.0515856 | + | 0.998669i | \(0.483572\pi\) | |||||||
\(774\) | −4.91680e7 | −0.106038 | ||||||||
\(775\) | −3.51085e7 | −0.0754236 | ||||||||
\(776\) | 1.34502e8i | 0.287835i | ||||||||
\(777\) | − | 7.85657e7i | − | 0.167483i | ||||||
\(778\) | − | 1.01820e8i | − | 0.216220i | ||||||
\(779\) | 8.06238e8 | 1.70550 | ||||||||
\(780\) | − | 6.67033e7i | − | 0.140561i | ||||||
\(781\) | −2.46372e6 | + | 5.36496e8i | −0.00517176 | + | 1.12620i | ||||
\(782\) | 4.91786e8 | 1.02839 | ||||||||
\(783\) | 1.22782e8i | 0.255770i | ||||||||
\(784\) | −2.86384e8 | −0.594293 | ||||||||
\(785\) | −6.15379e8 | −1.27214 | ||||||||
\(786\) | −3.21246e8 | −0.661561 | ||||||||
\(787\) | 5.56740e8i | 1.14216i | 0.820893 | + | 0.571082i | \(0.193476\pi\) | ||||
−0.820893 | + | 0.571082i | \(0.806524\pi\) | |||||||
\(788\) | − | 1.39093e8i | − | 0.284268i | ||||||
\(789\) | − | 3.21552e7i | − | 0.0654667i | ||||||
\(790\) | 7.91506e8 | 1.60536 | ||||||||
\(791\) | 1.74652e8i | 0.352895i | ||||||||
\(792\) | −1.79676e8 | − | 825116.i | −0.361672 | − | 0.00166088i | ||||
\(793\) | 5.73877e8 | 1.15080 | ||||||||
\(794\) | 2.08757e8i | 0.417042i | ||||||||
\(795\) | 4.03286e8 | 0.802623 | ||||||||
\(796\) | 1.11712e8 | 0.221493 | ||||||||
\(797\) | −9.50514e8 | −1.87752 | −0.938758 | − | 0.344578i | \(-0.888022\pi\) | ||||
−0.938758 | + | 0.344578i | \(0.888022\pi\) | |||||||
\(798\) | − | 8.58859e7i | − | 0.169010i | ||||||
\(799\) | − | 3.41546e7i | − | 0.0669590i | ||||||
\(800\) | 2.15605e8i | 0.421103i | ||||||||
\(801\) | 2.21278e8 | 0.430567 | ||||||||
\(802\) | − | 7.10370e8i | − | 1.37709i | ||||||
\(803\) | 1.23496e8 | + | 567123.i | 0.238510 | + | 0.00109529i | ||||
\(804\) | 1.20406e8 | 0.231676 | ||||||||
\(805\) | − | 3.43061e8i | − | 0.657633i | ||||||
\(806\) | 2.81707e7 | 0.0538012 | ||||||||
\(807\) | 3.72911e8 | 0.709552 | ||||||||
\(808\) | −6.65454e8 | −1.26149 | ||||||||
\(809\) | 1.52651e8i | 0.288307i | 0.989555 | + | 0.144153i | \(0.0460459\pi\) | ||||
−0.989555 | + | 0.144153i | \(0.953954\pi\) | |||||||
\(810\) | 6.78191e7i | 0.127614i | ||||||||
\(811\) | 8.42898e8i | 1.58020i | 0.612977 | + | 0.790101i | \(0.289972\pi\) | ||||
−0.612977 | + | 0.790101i | \(0.710028\pi\) | |||||||
\(812\) | −5.96300e7 | −0.111377 | ||||||||
\(813\) | − | 2.20764e8i | − | 0.410825i | ||||||
\(814\) | 4.29981e8 | + | 1.97458e6i | 0.797217 | + | 0.00366101i | ||||
\(815\) | −1.24674e9 | −2.30305 | ||||||||
\(816\) | − | 1.57809e8i | − | 0.290442i | ||||||
\(817\) | −2.23514e8 | −0.409863 | ||||||||
\(818\) | −5.64493e8 | −1.03133 | ||||||||
\(819\) | 3.82926e7 | 0.0697049 | ||||||||
\(820\) | − | 3.09189e8i | − | 0.560767i | ||||||
\(821\) | − | 9.26534e8i | − | 1.67429i | −0.546978 | − | 0.837147i | \(-0.684222\pi\) | ||
0.546978 | − | 0.837147i | \(-0.315778\pi\) | |||||||
\(822\) | − | 3.99544e8i | − | 0.719365i | ||||||
\(823\) | 1.31419e8 | 0.235754 | 0.117877 | − | 0.993028i | \(-0.462391\pi\) | ||||
0.117877 | + | 0.993028i | \(0.462391\pi\) | |||||||
\(824\) | − | 6.26224e8i | − | 1.11930i | ||||||
\(825\) | 1.19942e6 | − | 2.61184e8i | 0.00213604 | − | 0.465141i | ||||
\(826\) | 2.47039e7 | 0.0438355 | ||||||||
\(827\) | 8.17101e8i | 1.44464i | 0.691560 | + | 0.722319i | \(0.256924\pi\) | ||||
−0.691560 | + | 0.722319i | \(0.743076\pi\) | |||||||
\(828\) | 8.02339e7 | 0.141341 | ||||||||
\(829\) | −4.96211e8 | −0.870969 | −0.435485 | − | 0.900196i | \(-0.643423\pi\) | ||||
−0.435485 | + | 0.900196i | \(0.643423\pi\) | |||||||
\(830\) | 6.70682e8 | 1.17296 | ||||||||
\(831\) | 1.39227e8i | 0.242617i | ||||||||
\(832\) | − | 4.27778e8i | − | 0.742760i | ||||||
\(833\) | − | 3.99203e8i | − | 0.690652i | ||||||
\(834\) | 4.11778e7 | 0.0709847 | ||||||||
\(835\) | 1.18023e9i | 2.02725i | ||||||||
\(836\) | −1.73376e8 | − | 796182.i | −0.296735 | − | 0.00136268i | ||||
\(837\) | 1.05646e7 | 0.0180167 | ||||||||
\(838\) | − | 4.42700e8i | − | 0.752276i | ||||||
\(839\) | −4.43438e8 | −0.750840 | −0.375420 | − | 0.926855i | \(-0.622502\pi\) | ||||
−0.375420 | + | 0.926855i | \(0.622502\pi\) | |||||||
\(840\) | −1.55170e8 | −0.261800 | ||||||||
\(841\) | −4.55810e8 | −0.766296 | ||||||||
\(842\) | − | 6.99297e8i | − | 1.17145i | ||||||
\(843\) | 4.38790e8i | 0.732443i | ||||||||
\(844\) | − | 2.83111e8i | − | 0.470901i | ||||||
\(845\) | 4.44218e8 | 0.736251 | ||||||||
\(846\) | 1.51071e7i | 0.0249500i | ||||||||
\(847\) | −1.73567e6 | + | 1.88975e8i | −0.00285639 | + | 0.310995i | ||||
\(848\) | 4.15072e8 | 0.680668 | ||||||||
\(849\) | 3.60175e7i | 0.0588559i | ||||||||
\(850\) | 3.23347e8 | 0.526516 | ||||||||
\(851\) | −9.04569e8 | −1.46775 | ||||||||
\(852\) | −1.08360e8 | −0.175207 | ||||||||
\(853\) | − | 7.61169e8i | − | 1.22641i | −0.789926 | − | 0.613203i | \(-0.789881\pi\) | ||
0.789926 | − | 0.613203i | \(-0.210119\pi\) | |||||||
\(854\) | − | 2.83370e8i | − | 0.454967i | ||||||
\(855\) | 3.08301e8i | 0.493261i | ||||||||
\(856\) | −2.46541e8 | −0.393068 | ||||||||
\(857\) | − | 5.58230e8i | − | 0.886892i | −0.896301 | − | 0.443446i | \(-0.853756\pi\) | ||
0.896301 | − | 0.443446i | \(-0.146244\pi\) | |||||||
\(858\) | −962401. | + | 2.09571e8i | −0.00152368 | + | 0.331795i | ||||
\(859\) | 3.18162e8 | 0.501960 | 0.250980 | − | 0.967992i | \(-0.419247\pi\) | ||||
0.250980 | + | 0.967992i | \(0.419247\pi\) | |||||||
\(860\) | 8.57167e7i | 0.134763i | ||||||||
\(861\) | 1.77497e8 | 0.278088 | ||||||||
\(862\) | 1.01312e9 | 1.58175 | ||||||||
\(863\) | 5.96968e8 | 0.928793 | 0.464396 | − | 0.885627i | \(-0.346271\pi\) | ||||
0.464396 | + | 0.885627i | \(0.346271\pi\) | |||||||
\(864\) | − | 6.48780e7i | − | 0.100590i | ||||||
\(865\) | 9.36478e6i | 0.0144694i | ||||||||
\(866\) | − | 2.20111e8i | − | 0.338913i | ||||||
\(867\) | −1.56291e8 | −0.239815 | ||||||||
\(868\) | 5.13076e6i | 0.00784553i | ||||||||
\(869\) | 9.17251e8 | + | 4.21223e6i | 1.39775 | + | 0.00641879i | ||||
\(870\) | −5.80321e8 | −0.881274 | ||||||||
\(871\) | − | 6.61629e8i | − | 1.00129i | ||||||
\(872\) | −6.98822e7 | −0.105394 | ||||||||
\(873\) | 5.88334e7 | 0.0884262 | ||||||||
\(874\) | −9.88851e8 | −1.48114 | ||||||||
\(875\) | 5.44106e7i | 0.0812194i | ||||||||
\(876\) | 2.49434e7i | 0.0371060i | ||||||||
\(877\) | 7.72686e7i | 0.114552i | 0.998358 | + | 0.0572762i | \(0.0182416\pi\) | ||||
−0.998358 | + | 0.0572762i | \(0.981758\pi\) | |||||||
\(878\) | 1.11869e9 | 1.65283 | ||||||||
\(879\) | − | 3.25360e8i | − | 0.479068i | ||||||
\(880\) | 2.76673e6 | − | 6.02479e8i | 0.00405993 | − | 0.884085i | ||||
\(881\) | −8.67528e8 | −1.26869 | −0.634345 | − | 0.773050i | \(-0.718730\pi\) | ||||
−0.634345 | + | 0.773050i | \(0.718730\pi\) | |||||||
\(882\) | 1.76574e8i | 0.257348i | ||||||||
\(883\) | −1.92633e8 | −0.279800 | −0.139900 | − | 0.990166i | \(-0.544678\pi\) | ||||
−0.139900 | + | 0.990166i | \(0.544678\pi\) | |||||||
\(884\) | 9.56981e7 | 0.138531 | ||||||||
\(885\) | −8.86786e7 | −0.127935 | ||||||||
\(886\) | 2.65778e8i | 0.382136i | ||||||||
\(887\) | − | 5.93411e8i | − | 0.850325i | −0.905117 | − | 0.425162i | \(-0.860217\pi\) | ||
0.905117 | − | 0.425162i | \(-0.139783\pi\) | |||||||
\(888\) | 4.09146e8i | 0.584304i | ||||||||
\(889\) | 1.26262e8 | 0.179708 | ||||||||
\(890\) | 1.04586e9i | 1.48355i | ||||||||
\(891\) | −360919. | + | 7.85934e7i | −0.000510243 | + | 0.111110i | ||||
\(892\) | −2.87726e6 | −0.00405400 | ||||||||
\(893\) | 6.86758e7i | 0.0964382i | ||||||||
\(894\) | 3.32641e8 | 0.465546 | ||||||||
\(895\) | 8.35083e8 | 1.16482 | ||||||||
\(896\) | −9.42968e7 | −0.131091 | ||||||||
\(897\) | − | 4.40884e8i | − | 0.610867i | ||||||
\(898\) | − | 9.89242e8i | − | 1.36607i | ||||||
\(899\) | 9.03999e7i | 0.124420i | ||||||||
\(900\) | 5.27533e7 | 0.0723639 | ||||||||
\(901\) | 5.78587e8i | 0.791032i | ||||||||
\(902\) | −4.46100e6 | + | 9.71423e8i | −0.00607873 | + | 1.32370i | ||||
\(903\) | −4.92077e7 | −0.0668298 | ||||||||
\(904\) | − | 9.09535e8i | − | 1.23116i | ||||||
\(905\) | 1.25720e9 | 1.69613 | ||||||||
\(906\) | 5.52639e8 | 0.743117 | ||||||||
\(907\) | −5.96148e8 | −0.798973 | −0.399486 | − | 0.916739i | \(-0.630812\pi\) | ||||
−0.399486 | + | 0.916739i | \(0.630812\pi\) | |||||||
\(908\) | 1.71879e8i | 0.229597i | ||||||||
\(909\) | 2.91081e8i | 0.387545i | ||||||||
\(910\) | 1.80987e8i | 0.240173i | ||||||||
\(911\) | −3.63584e8 | −0.480894 | −0.240447 | − | 0.970662i | \(-0.577294\pi\) | ||||
−0.240447 | + | 0.970662i | \(0.577294\pi\) | |||||||
\(912\) | 3.17311e8i | 0.418312i | ||||||||
\(913\) | 7.77231e8 | + | 3.56923e6i | 1.02126 | + | 0.00468989i | ||||
\(914\) | −1.07968e9 | −1.41402 | ||||||||
\(915\) | 1.01720e9i | 1.32783i | ||||||||
\(916\) | −3.81138e7 | −0.0495902 | ||||||||
\(917\) | −3.21505e8 | −0.416946 | ||||||||
\(918\) | −9.72989e7 | −0.125771 | ||||||||
\(919\) | 4.73761e8i | 0.610397i | 0.952289 | + | 0.305199i | \(0.0987228\pi\) | ||||
−0.952289 | + | 0.305199i | \(0.901277\pi\) | |||||||
\(920\) | 1.78655e9i | 2.29431i | ||||||||
\(921\) | − | 7.52332e8i | − | 0.963009i | ||||||
\(922\) | −1.19998e9 | −1.53102 | ||||||||
\(923\) | 5.95438e8i | 0.757236i | ||||||||
\(924\) | −3.81695e7 | − | 175283.i | −0.0483838 | − | 0.000222190i | ||||
\(925\) | −5.94749e8 | −0.751465 | ||||||||
\(926\) | 1.88815e8i | 0.237795i | ||||||||
\(927\) | −2.73921e8 | −0.343863 | ||||||||
\(928\) | 5.55154e8 | 0.694656 | ||||||||
\(929\) | 5.40376e8 | 0.673983 | 0.336992 | − | 0.941508i | \(-0.390591\pi\) | ||||
0.336992 | + | 0.941508i | \(0.390591\pi\) | |||||||
\(930\) | 4.99327e7i | 0.0620778i | ||||||||
\(931\) | 8.02691e8i | 0.994717i | ||||||||
\(932\) | − | 2.18947e8i | − | 0.270452i | ||||||
\(933\) | −5.71582e8 | −0.703775 | ||||||||
\(934\) | − | 2.49088e8i | − | 0.305712i | ||||||
\(935\) | 8.39823e8 | + | 3.85666e6i | 1.02743 | + | 0.00471821i | ||||
\(936\) | −1.99416e8 | −0.243183 | ||||||||
\(937\) | 3.23723e8i | 0.393509i | 0.980453 | + | 0.196755i | \(0.0630402\pi\) | ||||
−0.980453 | + | 0.196755i | \(0.936960\pi\) | |||||||
\(938\) | −3.26700e8 | −0.395860 | ||||||||
\(939\) | −1.82299e8 | −0.220184 | ||||||||
\(940\) | 2.63369e7 | 0.0317088 | ||||||||
\(941\) | 9.06630e8i | 1.08808i | 0.839059 | + | 0.544041i | \(0.183106\pi\) | ||||
−0.839059 | + | 0.544041i | \(0.816894\pi\) | |||||||
\(942\) | 3.90509e8i | 0.467173i | ||||||||
\(943\) | − | 2.04362e9i | − | 2.43706i | ||||||
\(944\) | −9.12702e7 | −0.108496 | ||||||||
\(945\) | 6.78739e7i | 0.0804280i | ||||||||
\(946\) | 1.23673e6 | − | 2.69309e8i | 0.00146083 | − | 0.318110i | ||||
\(947\) | 8.05666e8 | 0.948648 | 0.474324 | − | 0.880350i | \(-0.342692\pi\) | ||||
0.474324 | + | 0.880350i | \(0.342692\pi\) | |||||||
\(948\) | 1.85264e8i | 0.217454i | ||||||||
\(949\) | 1.37064e8 | 0.160370 | ||||||||
\(950\) | −6.50164e8 | −0.758319 | ||||||||
\(951\) | 3.61980e8 | 0.420865 | ||||||||
\(952\) | − | 2.22620e8i | − | 0.258019i | ||||||
\(953\) | 1.14404e9i | 1.32179i | 0.750477 | + | 0.660897i | \(0.229824\pi\) | ||||
−0.750477 | + | 0.660897i | \(0.770176\pi\) | |||||||
\(954\) | − | 2.55918e8i | − | 0.294751i | ||||||
\(955\) | −4.46535e8 | −0.512679 | ||||||||
\(956\) | 5.30434e7i | 0.0607096i | ||||||||
\(957\) | −6.72516e8 | − | 3.08835e6i | −0.767302 | − | 0.00352363i | ||||
\(958\) | 9.36718e7 | 0.106540 | ||||||||
\(959\) | − | 3.99867e8i | − | 0.453377i | ||||||
\(960\) | 7.58239e8 | 0.857023 | ||||||||
\(961\) | −8.79725e8 | −0.991236 | ||||||||
\(962\) | 4.77221e8 | 0.536036 | ||||||||
\(963\) | 1.07841e8i | 0.120755i | ||||||||
\(964\) | − | 7.56898e7i | − | 0.0844902i | ||||||
\(965\) | − | 9.20146e8i | − | 1.02394i | ||||||
\(966\) | −2.17700e8 | −0.241506 | ||||||||
\(967\) | − | 1.85371e8i | − | 0.205004i | −0.994733 | − | 0.102502i | \(-0.967315\pi\) | ||
0.994733 | − | 0.102502i | \(-0.0326848\pi\) | |||||||
\(968\) | 9.03883e6 | − | 9.84122e8i | 0.00996520 | − | 1.08498i | ||||
\(969\) | −4.42314e8 | −0.486138 | ||||||||
\(970\) | 2.78072e8i | 0.304679i | ||||||||
\(971\) | −1.08140e9 | −1.18121 | −0.590607 | − | 0.806959i | \(-0.701112\pi\) | ||||
−0.590607 | + | 0.806959i | \(0.701112\pi\) | |||||||
\(972\) | −1.58741e7 | −0.0172858 | ||||||||
\(973\) | 4.12110e7 | 0.0447378 | ||||||||
\(974\) | − | 8.01426e8i | − | 0.867335i | ||||||
\(975\) | − | 2.89879e8i | − | 0.312754i | ||||||
\(976\) | 1.04693e9i | 1.12608i | ||||||||
\(977\) | 6.32251e8 | 0.677963 | 0.338982 | − | 0.940793i | \(-0.389918\pi\) | ||||
0.338982 | + | 0.940793i | \(0.389918\pi\) | |||||||
\(978\) | 7.91158e8i | 0.845760i | ||||||||
\(979\) | −5.56583e6 | + | 1.21201e9i | −0.00593173 | + | 1.29169i | ||||
\(980\) | 3.07829e8 | 0.327062 | ||||||||
\(981\) | 3.05676e7i | 0.0323783i | ||||||||
\(982\) | 2.64057e8 | 0.278845 | ||||||||
\(983\) | −5.06500e8 | −0.533235 | −0.266618 | − | 0.963802i | \(-0.585906\pi\) | ||||
−0.266618 | + | 0.963802i | \(0.585906\pi\) | |||||||
\(984\) | −9.24351e8 | −0.970178 | ||||||||
\(985\) | − | 1.35475e9i | − | 1.41759i | ||||||
\(986\) | − | 8.32577e8i | − | 0.868547i | ||||||
\(987\) | 1.51193e7i | 0.0157246i | ||||||||
\(988\) | −1.92423e8 | −0.199520 | ||||||||
\(989\) | 5.66555e8i | 0.585671i | ||||||||
\(990\) | −3.71466e8 | − | 1.70586e6i | −0.382837 | − | 0.00175808i | ||||
\(991\) | 9.14651e8 | 0.939798 | 0.469899 | − | 0.882720i | \(-0.344290\pi\) | ||||
0.469899 | + | 0.882720i | \(0.344290\pi\) | |||||||
\(992\) | − | 4.77673e7i | − | 0.0489323i | ||||||
\(993\) | 1.12752e9 | 1.15154 | ||||||||
\(994\) | 2.94016e8 | 0.299373 | ||||||||
\(995\) | 1.08806e9 | 1.10455 | ||||||||
\(996\) | 1.56983e8i | 0.158882i | ||||||||
\(997\) | 5.92226e8i | 0.597588i | 0.954318 | + | 0.298794i | \(0.0965844\pi\) | ||||
−0.954318 | + | 0.298794i | \(0.903416\pi\) | |||||||
\(998\) | 4.25906e8i | 0.428472i | ||||||||
\(999\) | 1.78967e8 | 0.179505 |
(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 | 33.7.c.a.10.9 | yes | 12 | |
3.2 | odd | 2 | 99.7.c.d.10.4 | 12 | |||
4.3 | odd | 2 | 528.7.j.c.241.12 | 12 | |||
11.10 | odd | 2 | inner | 33.7.c.a.10.4 | ✓ | 12 | |
33.32 | even | 2 | 99.7.c.d.10.9 | 12 | |||
44.43 | even | 2 | 528.7.j.c.241.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.7.c.a.10.4 | ✓ | 12 | 11.10 | odd | 2 | inner | |
33.7.c.a.10.9 | yes | 12 | 1.1 | even | 1 | trivial | |
99.7.c.d.10.4 | 12 | 3.2 | odd | 2 | |||
99.7.c.d.10.9 | 12 | 33.32 | even | 2 | |||
528.7.j.c.241.11 | 12 | 44.43 | even | 2 | |||
528.7.j.c.241.12 | 12 | 4.3 | odd | 2 |